commit b54ed3ab5b857fb848b352271d0198d982308a01 Author: Lonney Date: Fri Dec 20 13:27:36 2024 -0900 Initial commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..962c118 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +# Ignore files and directories generated by the operating system +.DS_Store +Thumbs.db \ No newline at end of file diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..604ecf0 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2024 antenna2 + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..6842cfa --- /dev/null +++ b/README.md @@ -0,0 +1,80 @@ +# Cebik W4RNL (SK) Website and Document Collection + +This is the version hosted at [www.antenna2.net/cebik](https://www.antenna2.net/cebik/) + +Updates include: + +- Pages updated to compliant HTML with CSS setting the styling. +- Books and model sets added (included with additional downloads with purchase of ON5AU's AAM book). +- Some missing/orphaned modeling, VHF, and wire antenna content found and added. +- For better readability, background image replaced with similar solid background color, preformatted text no longer bold and has a different background color set with borders. +- De-duplicated symposiums and magazine articles, linked original HTML pages the PDFs were created from. +- Broken internal links have been fixed, and where possible external broken links have been updated with copies stored by the Internet Archive. +- The online Moxon Rectangle calculator has been moved to the top of the page, and includes a 93 ohm option used in the Turnstile Moxon Rectangle Fixed-Position Satellite Antennas page. +- Otherwise the overall look and feel of the Cebik pages is maintained. + +## Update Process + +### Broken Links + +An application called Deep Trawl and a combination of find and grep queries were used to find broken links. Internal broken links corrected, external broken links point to [Internet Web Archive](https://www.archive.org/) copies, external links updated to use https where possible and open in a new tab (target="_blank"). + +### Moxon Javascript Calculator + +The [Online Moxon Calculator](https://www.antenna2.net/cebik/content/moxon/moxpage.html) relied on a second `` tag part way down the page to function. Code was updated (using ChatGPT) to remove this depdance, add the 93 ohm option and a calculate button. + +### HTML Syntax Issues + +A combination of custom Python scripts (written with help from ChatGPT) [https://github.com/lonney9/HTML-Scripts](https://github.com/lonney9/HTML-Scripts) and [HTML Tidy](https://www.html-tidy.org/) were used to tidy and update the HTML with styling set by one CSS file. As a result the pages load and render faster in standards compliant mode. + +1. HTML tag cleanup removes: + - HTML doctype line matching ``. + - Opening and closing font tags ` `. + - Alt attribute from `` tags (case-insensitive), these contained the img name and size (not useful). + - Bold tags ` ` from around the `
` tags. + - Hyphens `-` from infront of the words `wavelegth` and `degrees`. +2. HTML Tidy run with out CSS option, output encoding US-ACSII - this converts non standard characters to HTML entities. This tidies the HTML and corrects syntax errors, HTML tidy has bugs which dont handle every situation, a number of manual edits were made to the HTML to allow for this. +3. Add CSS link to each page, the relative path is calculated and used. +4. Image de-duplication, navigation and header image files were found throughout the directory structure. Image names were identified, script moved them into an /images folder, updated the paths with relative links, then instances of that image then deleted. + +This sequence of scripts were run dozens of times by making a copy of the source HTML, and checking the results, fixing small issues, and repating until no more issues were found. + +### File Structure + +The file structure was tidied, images relocated from content/ root, PVC page and images moved into their own directory, links pages and images moved into their down directory, books and downloads page updated, couple instances where it made sense to merge pages that was done. + +## To Do List + +- Magazines page: Find better/smaller file size PDF copies of "NEC and MININEC Guide to Further Information" (4.4 mb), and "NEC-4.1. +- Limitations of Importance to Hams" (22mb) - these are images. +- Edit PDF files to remove references to defunt cebik and antennex domains. +- Finish updating page titles and set meta keywords on the magazine column pages (around 250 pages), and add them into the Topic Index. +- Add linked navigation footer and index pages based on directory structure. +- Improve viewing on mobile devices. + +## Visitor Statistics + +[https://github.com/lonney9/Go-Access](https://github.com/lonney9/Go-Access). + +### Sitemap.xml + +Shell script used generate sitemap.xml + +### Robots.txt + +Disallows indexing PDF books and magazine articles that were not part of the original Cebik site. + +## Nested Repos www-live and cebik + +Useful if you want to serve the site over the local network. + +With Python installed run the following from with-in the web root level, e.g. www-live: + +```bash +python3 -m http.server 8000 +``` + +To replicate the same setup I use, clone www-live first, then cd into www-live and clone cebik. + +.gitignore in www-live handles not including the nested cebik repo. diff --git a/books/Antenna-Modeling-Notes-Models-Vol-1-4.zip b/books/Antenna-Modeling-Notes-Models-Vol-1-4.zip new file mode 100644 index 0000000..e4a0167 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Models-Vol-1-4.zip differ diff --git a/books/Antenna-Modeling-Notes-Vol-1.pdf b/books/Antenna-Modeling-Notes-Vol-1.pdf new file mode 100644 index 0000000..0b465a7 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-1.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-2.pdf b/books/Antenna-Modeling-Notes-Vol-2.pdf new file mode 100644 index 0000000..3603685 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-2.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-3.pdf b/books/Antenna-Modeling-Notes-Vol-3.pdf new file mode 100644 index 0000000..107641f Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-3.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-4.pdf b/books/Antenna-Modeling-Notes-Vol-4.pdf new file mode 100644 index 0000000..f172d68 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-4.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-5.pdf b/books/Antenna-Modeling-Notes-Vol-5.pdf new file mode 100644 index 0000000..8638c81 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-5.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-6.pdf b/books/Antenna-Modeling-Notes-Vol-6.pdf new file mode 100644 index 0000000..daf0751 Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-6.pdf differ diff --git a/books/Antenna-Modeling-Notes-Vol-7.pdf b/books/Antenna-Modeling-Notes-Vol-7.pdf new file mode 100644 index 0000000..ff7d82e Binary files /dev/null and b/books/Antenna-Modeling-Notes-Vol-7.pdf differ diff --git a/books/Antennas-Made-of-Wires-Models.zip b/books/Antennas-Made-of-Wires-Models.zip new file mode 100644 index 0000000..39d4913 Binary files /dev/null and b/books/Antennas-Made-of-Wires-Models.zip differ diff --git a/books/Antennas-Made-of-Wires-Vol-1.pdf b/books/Antennas-Made-of-Wires-Vol-1.pdf new file mode 100644 index 0000000..8bf73bd Binary files /dev/null and b/books/Antennas-Made-of-Wires-Vol-1.pdf differ diff --git a/books/Antennas-Made-of-Wires-Vol-2.pdf b/books/Antennas-Made-of-Wires-Vol-2.pdf new file mode 100644 index 0000000..8c4fb12 Binary files /dev/null and b/books/Antennas-Made-of-Wires-Vol-2.pdf differ diff --git a/books/Antennas-Made-of-Wires-Vol-3.pdf b/books/Antennas-Made-of-Wires-Vol-3.pdf new file mode 100644 index 0000000..82177de Binary files /dev/null and b/books/Antennas-Made-of-Wires-Vol-3.pdf differ diff --git a/books/Basic-Antenna-Modeling.pdf b/books/Basic-Antenna-Modeling.pdf new file mode 100644 index 0000000..a1bfcb9 --- /dev/null +++ b/books/Basic-Antenna-Modeling.pdf @@ -0,0 +1,17618 @@ +%PDF-1.6 % +2653 0 obj <> endobj 2954 0 obj <>stream + + + + + 2001-10-07T21:17Z + Microsoft Word 9.0 + 2007-10-20T09:52:34-05:00 + 2007-10-20T09:52:34-05:00 + + + application/pdf + + + L.B. 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+

Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters
+ Part 1: A Review of Design and Modeling Techniques

+
+
+

L. B. Cebik, W4RNL

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Suppose that you had a vertical array for 160 meters that produced a pattern like the azimuth pattern in Fig. 1. Notice that the elevation angle is 15 degrees, and that the peak front-to-back ratio is nearly 40 dB. What might it take to achieve such a pattern? In most instances, folks would speculate on phased monopoles. Now let's add the ability to remotely switch the direction of the array in 60 degree intervals throughout the entire circle. What might that ability require?

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Before our speculation carries us too far into BC-band fields of towers, let me give away the secret. The array is a single driven element about 1/2 wl tall with sloping parasitic guys (or pseudo-guys). It will be the subject of this design study (since my yard and budget are too small for implementation). However, even though based on modeling studies in NEC-4, the array avoids almost all of the modeling flaws that have made parasitic vertical arrays so contentious. In fact, as a prelude to looking at the new array, let's look first at some facts about modeling some well established arrays.

+

Buried Radial Systems

+

In most 160-meter literature, we find 2 sorts of radial system models, neither of which are accurate models of buried radial systems. By a buried radial system, I mean a set of radials anywhere from near the surface down to about 2' into the soil. In general, this covers most of the radial systems in use at 160-meter installations.

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The two most common systems used in models of buried radials are the near-ground elevated radial system and the no-radial system using a MININEC ground. Of the two, the latter is the most common, since it is the simplest to model. Of the two, the MININEC ground system creates the worse models, but both are completely inadequate as substitutes for modeling a buried radial system.

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Modeling a buried radial system requires a version of NEC higher than NEC-2. Obtaining NEC-4, for which there are commercial implementations, is an expensive proposition, and most individuals may find the investment beyond their means relative to the benefits. However, the differences in the models and their results yielded by NEC-4, relative to the weak substitutes currently used, dictates that any individual or institution that wishes to claim any degree of good correlation between models and reality for vertical arrays on 160 meters should have this software.

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+ +
+

I can illustrate the point with a short series of models. First consider simple 1/4 wl monopole over a field of buried radials whose numbers might vary from 4 to 128. We can model this situation fairly easily in NEC-4. Using Fig. 2 as a guide, we can see some of the requirements for such models. The vertical wire must have a junction at the surface (Z = 0) level. The source segment should be the same length as the immediately adjacent segments for maximum accuracy. These requirements set the minimum segment length in the model. One consequence of the minimum segment length is a limit on the diameter of the main element if we retain a safe 4-to-1 length-to-diameter ratio for the complex geometry of radial system models. For our example, let's use 0.001 wl or 0.164 m as the minimum length, which corresponds to a radial field buried about 6.5" deep. I shall use a 25-mm diameter main element and 2-mm diameter radials for the examples.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    Table 1.  Soil types used in the study
+
+      Soil Type               Conductivity            Permittivity
+                              Siemens/meter           dielectric constant
+      Very Poor               0.001                    5
+      Poor                    0.002                   13
+      Good (Average)          0.005                   13
+      Very Good               0.0303                  20
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I shall note in passing that my modeling studies show only interesting but faint numerical difference as we move the radial field from about 3" deep to about 25" deep--differences that would not add up to a tenth of a dB difference in performance for any given soil quality. As Table 1 indicates, we shall use in these notes the standard sample soil qualities of Very Poor through Very Good to check on differentials based on ground differences. That these labels indicate samples that are indeed fair and that the other aspects of these preliminary notes on modeling are accurate has been demonstrated in a series of articles for The National Contest Journal that appeared in 2001.

+

In order to control the size of models, one may use length-tapering of the elements, including both the main and radial wires. Fig. 2 shows the technique in sufficient detail for these notes. The main element is a constant 40-m throughout the monopole exercise, while the radial will be an exact 1/4 wl at 1.83 MHz, the test frequency throughout these notes. However, the key question concerns results.

+
+ +
+

Fig. 3 provides part of the answer. It summarizes the gain of a 40-m tall monopole over radial fields from 4 to 128 radials over the sample soils. Note that for most of the samples, the far-field gain peaks at about 64 radials. However, for Very Poor Soil, gain continues to rise, even at the 128-radial level, with well over a 3 dB differential when moving from 4 to 128 radials in the system. I should add here that most of standard categories of soil conductivity and permittivity are based on measurements made for AM BC service. Amateurs should not be surprised to find conductivity levels well under 1 mS/m, the lowest value in both the standard charts and the sample types used here. For example, a set of tests on some Maine soil at 7 MHz yielded a conductivity of about 0.2 mS/m, with an indirectly derived permittivity of 7, which happens to be the textbook value for shale. In short, one should not over-estimate the quality of one's soil, even if maps suggest pretty good stuff under foot. The gain line for Very Poor soil comes closest to reflecting experiential reports of signal improvements occasioned by adding radials to one's system.

+
+ +
+

The gain curves are reflected in NEC-4 reports of anticipated feedpoint values for monopoles, as shown in Fig. 4. The curves do not begin to converge until we have at least 32 radials under the monopole. At that point, construction variables would mask any ground-occasioned differences in measured values.

+

One of the reasons that so many modelers use the MININEC ground system in vertical modeling is that the NEC-2 alternative of placing a ground plane at about 0.001 wl above ground shows strong correlations to the results of using the no-radial MININEC ground. Unfortunately, the near-ground radial system has only very limited correlations to the buried-radial system we have glanced at so far. Hence, both systems are faulty as adequate models of a buried-radial system.

+
+ +
+

So that we do not encounter graphic grid lock in a morass of lines, let's simply compare sample buried radial systems results to those that would be yielded for the same antenna connected directly to a MININEC ground. This latter facility is available in EZNEC as an adjunct to the normal NEC-2 array of ground options. Fig. 5 shows the MININEC-ground curve in relationship to curves for 8, 32, and 128 buried radials, all in NEC-4, for various soil qualities. Although the MININEC curve traces adequately the curves for larger radial systems, it does not come close to reflecting the situation with a smaller radial field.

+
+ +
+

More telling is Fig. 6, a graph of the modeled source resistance values for the same set of models. A MININEC ground provides a single source impedance figure, taken over none of the same ground types, but over perfect ground. It comes close to tracking only the field of 128 radials, with serious deficiencies for any small radial field.

+

MININEC vs. Buried Radials for Parasitic-Guy Arrays

+

We might live with the differentials between large buried-radial systems and the MININEC no-radial system of modeling were it not for a weakness in the MININEC ground system that almost all modelers of 160-meter arrays routinely overlook. A guy-wire used as a parasitic element slopes and therefore has a horizontal as well as a vertical component to its far field. Virtually all versions of MININEC warn modelers that placing a horizontal antenna closer than about 0.2 wl to the ground results in increasing inaccuracies to the output reports. In general, the gain reports will be increasingly too high and the source impedance reports too low as we bring the wire closer to the ground. The restriction on the MININEC ground accuracy applies not only to driven elements, but as well to parasitic elements and not only to truly horizontal elements, but as well to sloping elements.

+
+ +
+

Let's illustrate the problem with a simple classic array, illustrated in Fig. 7. We shall test this array at 1.83 MHz over the MININEC ground and over a buried radial system. Since both elements are grounded, we shall use a set of intersecting radial systems, outlined in simplified form in Fig. 8. However, the actual modeled system uses 32 radials per intersecting system, with junctions where shortened radials meet. (Techniques for constructing buried models of intersecting radial systems are fully described in the NCJ series noted earlier.) Otherwise, the buried radial system is constructed just as for the single monopole.

+
+ +
+
+ +
+

If we compare MININEC-ground models over various soils to models over buried 32-radial systems (a region where the monopole models converge reasonably well), we find that the MININEC-ground model over-estimates gain by an average of a full dB, as shown in Fig. 9. Fig. 10 is even more dramatic, as it reveals the degree of over-estimation of the front-to-back ratio that occurs in the MININEC-ground model compared to the buried-radial model. Given that full-size unloaded horizontally oriented drive-reflector Yagis achieve only about 10 to 12 dB front-to-back ratio maximums, there should be little question as to which model type is the more believable. To see the overall differences between the two types of models, we may compare elevation patterns over good soil of the two models, as shown in Fig. 11.

+
+ +
+
+ +
+

To confirm that the results of the first example are not a simple aberration, let's try another standard guy-wire array using 3 elements, as shown in Fig. 12. The sloping guys function as a director and an inductively loaded reflector. For the buried-radial version of this model, we shall require a system of three 32-radial fields that intersect along two lines, as sketched in simplified form in Fig. 13.

+
+ +
+
+ +
+

With 2 sloping elements, the differences between the MININEC-ground model and the buried-radial model become further accentuated. Fig. 14 compares the gain values over different soil types for the two models. Even over Very Good soil, the MININEC-ground model over-estimates the array gain by a full dB, with that differential growing to nearly 5 dB over Very Poor ground. The front-to-back ratio comparison in Fig. 15 is equally impressive, with the MININEC-ground model over-reporting the ratio by an average of 10 dB.

+
+ +
+
+ +
+

In addition to these differences, the buried-radial ground model requires a different inductive loading value than needed by the MININEC-ground model: 22 vs. 33 Ohms inductive reactance. Interestingly, the use of a near-ground elevated radial system requires a load in the reflector that is quite close to the MININEC value, further illustrating that neither system adequately substitutes for a buried-radial model--if buried radials happen to be what we are modeling. Fig. 16 summarizes the differences in comparative elevation plots for the MININEC-ground and buried-radial models over Good soil.

+
+ +
+

It has been necessary to review the inadequacies of the MININEC-ground system of modeling vertical arrays, especially when the array uses sloping elements, for two major reasons. One reason is the prevalence of the use of such models and their general acceptance as substitutes for models of buried radial systems. The second reason, related to the first, is that the MININEC-ground models present an illusion that guyed monopole arrays come sufficiently close to outstanding performance, especially with respect to the front-to-back ratio, that we need not seriously consider further techniques of improvement.

+

Little could be further from the truth for sloping parasitic monopole arrays. In general, buried-radial system models suggest that both the gain and front-to-back ratio performance of most sloping parasitic element arrays leaves a vast region for improvement. The increments of gain and front-to-back ratio offered by such arrays are worthy, compared to a single monopole, and this level of improvement may be satisfactory for a large number of antenna installations. However, when we compare the performance to the azimuth pattern in Fig. 1, we can easily see that further improvement is possible.

+

1/2 Wavelength Phased 1-Tower Arrays

+

Before we look at a possible improvement upon a parasitic array, let's briefly review some of the potential for phased arrays using 1/2 wl radiators. Among the classics is the K8UR array (first presented in CQ for December, 1989) that consists of a central grounded tower that functions as a passive element in the system. Surrounding the tower are 4 dipoles, the upper halves of which are attached to non-conductive guy wires. Each wire is angled at 30 degrees relative to the vertical tower, conforming to standard guying practice. At the roughly centered feedpoints, the dipoles are folded back toward the tower, forming another 30 degree angle to it. The entire ensemble resembles the outline sketch in Fig. 17.

+
+ +
+

The reason for the double circles in each dipole is the use of a split feed for each element to ensure centering of the feedpoint. Single feeds on each wire in the segment nearest the center result in only about 1-Ohm differences of resistance and reactance, so simpler modeling is possible. However, when scaled for study in the context of 160 meters, the initial models were disappointing using any method of feed.

+

The K8UR system requires a phased feed system that some literature casually specified as -90 degrees on the forward element, +90 degrees on the rear element, and 0 degrees on the side elements, all at the same current amplitude. Unfortunately, models of this system produce mediocre performance, with front-to-back ratios that do not reach 10 dB over any soil quality.

+
+ +
+

The problem does not lie with the arrangement of the tower and the wires. In fact, excess concern with the spacing of the wires from the tower and the positioning of the fold-back points to yield a square that is 1/4 wl on a side has produced less than optimal performance from the array. Fig. 18 compares the elevation patterns of two models of the array. One uses the recommend fold-back point to form the square that is 1/4 wl per side and spaces the wires a minimum of 2.6 m from the central tower. The other model uses a fold-back point that is exactly halfway along the driven wires, while allowing the wires to be within 0.5 m of the central tower. The improvement in the reduction of very high angle radiation by using the mid-point fold-back is clearly evident in this comparison over good quality soil. It holds for every other soil type, with the mid-point version also showing about a degree lower take-off angle over each soil type.

+

In the mid-point model, a 72-m tower simulated by a 250-mm wire forms the central element. 80-m long 2-mm diameter wires form the phased dipoles. Obtaining at least an excellent front-to-back ratio--whatever the gain turns out to be--is simply a matter (for the modeler) of introducing the correct current magnitude and phase for the 4 fed dipoles. In the case of the K8UR array, as modeled here, the process is simplified because the side wires can be left at a magnitude of 1 and a phase angle of zero.

+

For the arrangement noted, over good soil, the forward wire required a current magnitude of 1.05 at a -130 degree angle, while to rear element required a magnitude of 1.06 at 136 degrees to achieve a balance between maximum gain and maximum front-to-back ratio. For good soil, the optimized version of the mid-point model shows a gain of 6.45 dBi at an elevation angle of 17 degrees with a front-to-back ratio of 45 dB and a horizontal beamwidth of 90 degrees. Table 2 provides additional performance potentials over various soils.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+     Table 2.  K8UR Array with Mid-Point Dipole Feed
+72-m high 250-mm diameter tower, 80-m long 2-mm diameter center-fed dipoles, no
+radials.
+
+Soil        Gain  TO    Fr-Bk B/W   Feed Current Relative Magnitude and Phase
+Quality     dBi   angle Ratio -3 dB       Dir               Ref         Sides
+Very Poor   3.9   21°   42.6  94°   1.05 @ -130°      1.07 @ 136°       1.0 @ 0°
+Poor        5.4   19°   44.9  92°   1.05 @ -130°      1.06 @ 136°       1.0 @ 0°
+Good        6.5   17°   45.0  90°   1.05 @ -130°      1.06 @ 136°       1.0 @ 0°
+Very Good   8.8   13°   44.0  88°   1.05 @ -130°      1.06 @ 136°       1.0 @ 0°
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table lists the required relative current magnitudes and phase angles for each active element for each soil type. This information is likely more useful than the resultant feedpoint impedances.

+
+ +
+

The K8UR system is capable of truly outstanding performance using a well-designed phasing system--one capable of handling the inevitable variations that occur from one installation to the next. Fig. 19 shows the potential performance over various soils in overlaid azimuth patterns, each taken at the TO angle for the soil type. The array is a bit sensitive. Changes in the side wire phase angle as little as 5 degrees reduced the front-to-back ratio to under 20 dB. Its only other limitation is in direction switching. When fully optimized, the -3 dB bandwidth of under 95 degrees leaves a slight weakness (up to -3 dB) along the bearings that mark the dividing points between available headings.

+

The K8UR array is an example of a phased array that avoids the use of separate towers for the individual active elements. For our purposes, the array forms a touchstone for simpler systems that require only a single driven element. We shall look at a couple of possibilities for parasitic arrays in Part 2.

+
+ +
+

Updated 1-1-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for December, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
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+ +

Go to Main Index

+

Topics: MF, Vertical


+ + diff --git a/content/160/160sb.html b/content/160/160sb.html new file mode 100644 index 0000000..ca1acac --- /dev/null +++ b/content/160/160sb.html @@ -0,0 +1,197 @@ + + + + + + Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters Part 2 + + + +
+

Pursuing the (Nearly) Perfect Parasitic Vertical Array for 160 Meters
+ Part 2: Some Parasitic Possibilities

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In Part 1 of this short series, we examined the modeling practices by which analysis of 160-meter vertical arrays are made and designs created. In addition, we took a brief look at phased arrays using a single central support, of which the K8UR system is one of the most outstanding.

+

In this part, we shall examine the possibilities of using a single driven element and using parasitic wires--guys--in order to create a vertical array. Whether or not practical, the possibilities are most interesting from a design perspective. Throughout, we shall observe the modeling cautions established in Part 1, with all modeling done over radial systems in NEC-4 unless clearly specified otherwise.

+

A 4-Guy Parasitic Array

+

It is possible to transform a version of the K8UR array into a parasitic array. However, the guys would extend in the normal fashion. Immediately lost would be the suppression of very high angle radiation from the antenna. In return, the builder would gain the simplicity of feeding a single element without concern for relative current magnitude and phase on the guys. The resulting array would have the appearance of the outline in Fig. 20.

+
+ +
+

The achieve maximum performance from the array, it is necessary to use a guy angle a bit less than the standard 30 degrees: about 27 degrees appears optimum. As well, as Table 3 shows, the director, the reflector, and the two side guys have different lengths. The table shows these values along with modeled performance data. The feedpoint impedance assumes base feeding of the 1/2 wl central tower, although shunt feeding and other systems are equally applicable to the array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+    Table 3.  A 4-Guy Parasitic Array
+Tower:  80-m high, 250-mm diameter, base 1 m above ground; guys: 25-mm diameter,
+spaced 0.6 m from tower with virtual anchor point at 78.7 m; no radials.
+
+Soil        Element Length-m        Gain  TO    Fr-Bk  B/W        Feed Z
+Quality     Dir   Ref   Sides       dBi   angle ratio  -3 dB      R +/- jX
+Very Poor   72.75 79.0  83.5        2.4   26°   29.3   154°       1590-4950
+Poor        71.25 79.0  84.0        3.9   22°   32.1   130°       1330-4750
+Good        70.5  79.0  84.0        5.0   20°   40.1   121°       1200-4700
+Very Good   68.25 79.0  83.5        7.2   15°   40.4   112°        910-4690
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

To illustrate the pattern types produced by the array, Fig. 21 provides the azimuth and elevation patterns over Good soil. Because it is common practice to place this type of array over a radial system, I modeled the system in 3 configurations for each soil type. The table shows the values for the model using no radials under the driven tower. Fig. 22 graphs the gain of this configuration, along with two radial systems, one at ground level (Z=0) and the other with the radials buried 0.001 wl (about 0.164 m or 6.5") below ground. The radial systems consisted of 32 wires, each 2 mm in diameter and 1/2 wl long (81.91 m).

+
+ +
+

The graph shows that maximum improvement occurs with buried radials over Very Poor soil, an improvement of about 1.2 dB relative to the radial-less system. However, the use of radials does increase the elevation angle of maximum radiation by 2 degrees for Very Poor soil--and by lesser amounts for better soils. The use of radials in models shows virtually no improvement over Very Good soil.

+

In principle, the 4-guy parasitic array gives the builder the advantage of a system that is relatively easy to feed--something like a set-and-forget array. However, constructing the array is somewhat finicky. Changing the reflector length by as little as 0.5 m drops the front-to-back ratio to the 20 dB region, and slight length variations in the side guys have similarly large effects upon performance. Only the director shows slow changes in performance with changes in length. Hence, for any given installation where the ground conditions are not fully known, the potential for mis-building the 4-guy array is great.

+

A second disadvantage associated with the 4-guy array lies in the area of switching directions. Changing directions with the array requires altering the parasitic guys so that for each one, three lengths are possible. The complexities of such switching are likely no less than trying to optimally phase a K8UR array. Consequently, it is a strong question mark as to whether this system could live up to the promise of a parasitic system to provide greater simplicity than a fully phased guy-dipole array.

+

The Basic 7-Element 1/2 Wavelength Parasitic-Guy Array

+

The following section of this report outlines a potential improvement on the 1/2 wl parasitic guy arrays that is based on an antenna developed for AM BC use. It achieves--at only a slight reduction of array gain--the desired simplicity of switching with full horizon coverage for a steerable array. As well, the array is forgiving of small construction errors--that is, changes in element length yield only small changes of performance for all elements.

+

The array employs a driven element that is roughly 1/2 wl long. Automatically, a 79.2-m main element places this array outside the structural capabilities of most 160-meter operators, but that is no hindrance to a study of the antenna. In the course of the discussion, a number of modeling issues will arise, such as modeling with and without a radial system. These questions will be addressed along the way.

+
+ +
+

First, however, we should look at the antenna under study, sketched in Fig. 23. It consists of a central driven element, fed at the base. There is virtually no difference in performance when the antenna base is raised and lowered between 1 m from the ground to about 3.5 m from the ground, so long as everything else in the design remains the same.

+

The guys are 6 in number, 3 acting as directors and 3 as reflectors. Experiments began with the standard 3-element guyed system and proceeded to a 4-element system, as 2 of three equally spaced guys became reflectors. The double reflector systems showed some improvement. Adding the third reflector guy in line with the director (for a 5-element array) again showed improvement. However, not until I added the two remaining directors to fill out the sloping parasitic system at 60 degree intervals did improvements reach their limit.

+

The headings of Table 4 and Table 5 provide dimensions for the radials for two radically different models. The first uses a large 250-mm diameter main element (roughly 10"), with 25-mm diameter (about 1") guys. The second employs a more modest 25-mm (1") main element, with 2-mm (between AWG #14 and AWG #12) guys. The differences between the performance levels of the two versions range from less than 0.1 dB over Very Good soil to about 0.2 dB over Very Poor soil for all cases modeled.

+

The change in main element and guy diameters does require a small shift in parasitic element lengths for optimal performance. The reflector length changes are minimal: 81.5 m for the fat main element, 82.0 m for the thin driver. The changes needed in the director lengths are more extensive: 67.9 m for the fat driver, 71.0 m for the thin main element. All three directors and all three reflectors may each have identical lengths.

+

The guys may turn out to be, for some installations, pseudo-guy wires. They begin in fairly close proximity to the main elements, spaced only far enough away for safety relative to the high voltages at the ends of both elements. Each parasitic guy begins about 0.6 m away from the main element, about 1.1 m down from the peak height of the main element. The dimensions are partial functions of performance optimization and partial functions of the angle of the guys relative to the main element. The designation "pseudo-guy" arises from the fact that an angle of 27 degrees relative to the driver turns out to be best for the parasitic guys. (The angles away from 27 degrees toward 24 degrees and toward 30 degrees result in a slow rate of performance degradation. Thus, concern over precision--for example, in a worry over catenary angle changes--would be misplaced.) Since the optimal angle is less than normally used for top guys in commercial installations, the parasitic guys may best be implemented as non-structural wires. Of course, to prevent unwanted interactions, the structural guys are presumed to be composed of non-conductive materials. Incidentally, given the element diameters involved, all elements are modeled as copper. Changes in materials make differences only in the 0.0X column of gain figures and less than 1 dB in the front-to-back figures.

+

Performance and Radials

+

Table 4 and Table 5 present the modeled performance figures for the two versions of the array. Note that there are three sets of figures for each antenna model. The first group models the antenna over various soils using no ground radial system. The second places a radial system exactly at ground level. Had the driven element been connected to this junction, NEC-4 would have yielded some unusable figures. However, with no source segment attached to the Z=0 junction, the calculations produce normal results. The third set of figures places a radial system 0.001 wl below ground, the same depth as used with earlier models. In the present array, each radial is 81.91 m long, that is, a half wavelength. Both the at-ground and buried radial systems consist of 32 radials each.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Table 4.  7-element parasitic array: Version A
+
+Driver = 79.2-m vertical, 250 mm diameter; 3 reflectors = sloping 25-mm guys,
+81.5 m; 3 directors = sloping 25-mm guys, 67.9 m; single 81.91-m (0.5 wavelength)
+radial system, 2 mm diameter, uniform segmentation: 21 segments per 1/2
+wavelength (where used); NEC-4.
+
+Soil Type         Gain  TO Angle    Front-to Back     Source Impedance
+                  dBi   degrees     Ratio dB          R +/- J X Ohms
+
+No Radials
+Very Poor         2.15  25          19.92             3256 + j 3760
+Poor              3.70  23          23.84             3329 + j 3806
+Good              4.78  20          28.12             3350 + j 3854
+Very Good         6.86  15          36.07             3410 + j 3893
+
+32 Radials, 1/2 wavelength long, at ground level
+Very Poor         2.64  26          22.38             3234 + j 3818
+Poor              4.03  23          26.41             3331 + j 3843
+Good              4.99  20          30.16             3362 + j 3878
+Very Good         6.90  15          36.41             3415 + j 3897
+
+32 Radials, 1/2 wavelength long, 0.001 wavelength below ground
+Very Poor         3.27  27          25.54             3316 + j 4000
+Poor              4.28  24          27.67             3364 + j 3937
+Good              5.08  20          31.29             3390 + j 3917
+Very Good         6.91  15          36.10             3420 + j 3905
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Table 5.  7-element parasitic array:  Version B
+
+Driver = 79.2-m vertical, 25 mm diameter; 3 reflectors = sloping 2-mm guys, 82
+m; 3 directors = sloping 2-mm guys, 71 m; single 81.91-m (0.5 wavelength) radial
+system, 2 mm diameter, uniform segmentation: 21 segments per 1/2 wavelength
+(where used); NEC-4.
+
+Soil Type         Gain  TO Angle    Front-to Back     Source Impedance
+                  dBi   degrees     Ratio dB          R +/- J X Ohms
+
+No Radials
+Very Poor         1.94  25          22.02             2701 + j 2431
+Poor              3.55  23          26.85             2698 + j 2325
+Good              4.66  20          31.97             2724 + j 2266
+Very Good         6.77  15          33.13             2706 + j 2185
+
+32 Radials, 1/2 wavelength long, at ground level
+Very Poor         2.48  26          25.44             2779 + j 2398
+Poor              3.90  23          30.75             2732 + j 2294
+Good              4.89  21          33.94             2735 + j 2238
+Very Good         6.81  15          33.31             2706 + j 2178
+
+32 Radials, 1/2 wavelength long, 0.001 wavelength below ground
+Very Poor         3.18  27          30.37             2844 + j 2214
+Poor              4.19  24          33.09             2770 + j 2203
+Good              5.00  21          35.41             2741 + j 2188
+Very Good         6.83  15          32.73             2707 + j 2168
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

All the of models used the same set of element lengths. There is little change if one extends the towers close to the ground (<1 m). As well, it is possible to develop specific reflector and director lengths, not only for each central driven element diameter, but as well for each soil type. However, the reflector will vary only about 1 m across the range of soils used in this study, while the director may vary as much as 4 m.

+

The 6-guy parasitic array does not reach the gain levels of the K8UR optimally phased system for any given soil type. The K8UR advantage in gain is a consistent 0.6 dB, largely because the beamwidth of the parasitic array is about 35 degrees wider between -3 dB points than the fully phased array. The beamwidth of the parasitic guy array varies between 128 and 129 degrees for all versions. As well, the 6-guy system does not cancel out the very high angle radiation as well as an optimally phased K8UR array.

+

Compared to the 4-guy system, the 6-guy array has slightly less gain (0.3 to 0.4 dB), but equal front-to-back potential. Unlike the 4-guy system, the parasitic element lengths are less critical, especially the directors. For instance, over very good ground, one model varied the length of the director by a total of 5 m with a net change of gain of 0.05 dB and a net change of front-to-back ratio of under 2 dB. The reflector lengths are somewhat more critical. However, the key is to keep all directors and all reflectors as close to the same length as feasible. Once this is achieved during construction, one gains the advantage of operational simplicity in the 6-guy array: once set, it requires no operational adjustments and few mechanical adjustments over the lifetime of the system.

+
+ +
+

In Fig. 24, we can see the modeled gain differences among the different modeled radial systems. As soil quality improves, the differentials in gain disappear. Even with Very Poor soil. there is a maximum differential of about 1.1 dB between the no-radial and the buried radial models for the fat-element version shown in the graph. The thin-element version shows a differential of 1.25 dB.

+
+ +
+

Fig. 25 shows differentials in front-to-back ratio, using the fat main element. Once again, the greatest differential occurs over Very Poor Soil and amounts to about 5 dB. As the soil quality improves, the differentials decrease. The thin element numbers can be easily garnered from Table 5.

+
+ +
+

In Fig. 26, we can compare the performance of the radial-less version of the antenna over various soils, using overlaid elevation patterns. Since the far-field performance is not just a function of what is occurring within the near-field region of the antenna, but depends also on the soil quality at a distance in the so-called Fresnel zone, we expect rising performance with improved soil quality. Anyone interested in a study of the antenna in more complex soil conditions can create an inner and outer soil quality differentiation using standard NEC capabilities.

+

A secondary factor involved with soil quality is the elevation angle of maximum radiation (Take-Off or TO angle). Here, the tables make a good guide to modeling report numbers. Although all three versions of each of the two models show a 15 degree TO angle over Very Good soil, we should also note the increasing TO angle as we move the radials from ground to below-ground level for Very Poor soil. The differences are not large, but they are consistent for both the fat and thin main element models.

+

As main elements go, both the fat and thin elements are short, relative to a resonant length. However, they are both approaching the region in which resistance and reactance approach their peaks. The thinner element is electrically shorter and thus shows lower resistance and reactance numbers at the source. Interestingly, bringing either main element within 1 m of ground suffices to carry the element beyond resonance so that it shows a capacitive reactance.

+
+ +
+

The small changes in antenna performance occasioned by the presence or absence of a radial system under that antenna are bound to arouse questions relative to experiential reports of much greater changes for real 1/2 wl vertical systems. The differential of experience and modeling does not represent a fault of the modeling software, but owes to a quite different factor. Because the model places the source directly on the element, it represents a simplified model of the actual antenna system. An actual antenna might look something like the system on the right of Fig. 27, where a network does more than simply transform impedance for the convenience of the feedline to the remote source. The network also completes the antenna system at ground. For maximum system efficiency (or minimal loss), the source ground point and the antenna base ground point must show zero potential differential. At best, we can only approximate this condition in real systems, and a large radial system is one way to achieve this goal.

+

The simplified model that uses a source placed on the element represents, then, the maximum that such a system can achieve. Any losses in portions of the system not modeled must be separately accounted for, or one must create an adequate model that will accurately show such losses. In the end, one must view even the model using an extensive buried-radial system as a simplified model of the full antenna system. Since each parasitic element--as well as the main element--is coupled to the ground (with or without radials), the results that might emerge from a fully adequate model would be affected in rather complex ways. Even over Very Good soil, where the presence of a radial system appears to have minimal consequences for radiation patterns, overall system effectiveness considerations for physical antennas still make the use of a considerable radial system advisable with 1/2 wl radiators and parasitic elements.

+

Some Further Possibilities and Concerns

+

On the assumption that implementing the array is feasible enough to entertain further development thoughts, there are a few cautions to observe. Foremost is lightning protection. The matching network should provide a full and heavy path from deep ground to the main element. For many purposes, such a path will yield relatively good protection for the unterminated parasitic elements in the array. However, if the location of the antenna is in any way sensitive, then added protections should be provided to the lower ends of the parasitic guys in the form of very high impedance RF but very low impedance charge paths to ground. At the very least, each parasitic element should be provided with a static discharge path. An array of this order is not a toy and should be treated with the same care as commercial BC installations.

+
+ +
+

Having registered due caution, we can turn to happier potentials of the array. One of the more interesting is the fact that with a switch and a half dozen remote relays, we can steer the direction of the array in 60 degree increments. Fig. 28 shows the simplicity of the switching arrangement: a 3-pole, 6-position rotary switch. The object is to convert a director into a reflector with the remote relay adding a length of guy to a director. (Of course, relays with wide terminal separation and high voltage contacts are necessary, and should not be operated with power applied to the antenna.)

+

Since opposing guys will always be of opposite types (reflector or director), the simple switch suffices to provide relay activation, so long as the contacts are properly staggered to direct the antenna according to operator wishes. The indicated clockwise change in direction can be altered to suit the user's needs. Missing from the figure is the return line from each relay coil.

+

For most purposes, the broadness of the array pattern will not yield great increases in signal strength for a single 60 degree change in heading. However, one may also think of the switching arrangement as a rear null direction switch. The switch position might easily become a method of increasing the signal-to-noise ratio by deep-nulling a bit of QRM. The directional capabilities of the system give the array a bit of an advantage over shorter phased systems which would require several towers to achieve the same directional capabilities.

+
+ +
+

As a second potential for the array, consider erecting two of them spaced about 1/2 wl apart. The array might well look like the outline sketch in Fig. 29. For both sub-arrays, the directors are all on one side of the line between the two elements, with all of the reflectors on the other side. If we feed the system in phase, we obtain some interesting improvements in both gain and directivity.

+
+ +
+

Fig. 30 shows the azimuth pattern of the 250-mm diameter version of the array over good soil at a TO angle of 21 degrees. In exchange for a decrease in the absolute 180 degrees front-to-back ratio, we obtain an entire rear area that is never worse than 18 dB down from the forward lobe. As well, the forward lobe now has a beamwidth of under 64 degrees.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+               Table 6.  Two 7-element parasitic arrays in phase
+
+For each array:  Driver = 79.2-m vertical, 250 mm diameter; 3 reflectors =
+sloping 25-mm guys, 81.5 m; 3 directors = sloping 25-mm guys, 67.9 m;  array
+spacing 81.95 m (1/2 wl); NEC-4.
+
+Soil Type   Gain  TO Angle    Front-to Back     Beamwidth   Source Impedance
+            dBi   degrees     Ratio dB          degrees     R +/- J X Ohms
+
+No Radials
+Very Poor   4.88  26          15.99             63          3837 + j 3726
+Poor        6.46  23          19.06             60          3914 + j 3726
+Good        7.58  21          21.54             58          3793 + j 3750
+Very Good   9.63  15          26.54             56          4062 + j 3733
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Table 6 shows the entire set of numbers reported for the large-diameter version of the array. The smaller diameter figures are similar. For every level of soil quality, the gain increases between 2.75 and 2.8 dB, with a worst-case beamwidth (Very Poor soil) of 63 degrees. As well, the front-to-back ratio reflects the performance around the entire rear section of the pattern.

+

The increase in performance has its price. The dual array is now a single direction affair--or at most, a reversible direction array, if there are two desired directions close to 180 degrees apart. Lost is the ability to swing the array in 60 degree increments at the twist of a switch.

+

Conclusion

+

The 7-element parasitic-guy array described here is just a design exercise, not intended for implementation in the amateur radio environment. However, it does demonstrate what may be possible in terms of achieving phased performance from a single parasitic array through the judicious placement and dimensioning of guys. In the process of developing the array, the exercise has also let us set into some perspective the fairly poor state of modeling of previous sloping-guy parasitic arrays and to show some directions that promise better modeling results.

+

One final note: the array design (for any frequency and variation of materials) is proprietary and described by permission for information purposes only. Commercial applications may not be undertaken without express permission or license, and a patent application may presently be pending. However unlikely such applications may be, this note is a necessary final word on our foray into developing a nearly perfect parasitic vertical array.

+
+ +
+

Updated 2-1-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for January, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: MF, Vertical


+ + diff --git a/content/160/160v.html b/content/160/160v.html new file mode 100644 index 0000000..5a4b3a7 --- /dev/null +++ b/content/160/160v.html @@ -0,0 +1,40 @@ + + + + + + Modeling 160-Meter Vertical Arrays Index + + + +
+

Modeling 160-Meter Vertical Arrays

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

Nowhere else on the amateur allocations are vertical antennas and arrays more widely used than on 160 meters. The advent of antenna modeling software has made the design and analysis of such arrays far easier than earlier pencil-and-paper and cut-and-try methods. In fact, the ease with which one can use modern software tools may also be the root of some problems that beset such array work. One difficulty is a lack of appreciation of what these tools have to offer and where they meet their limits. In some cases, the software offers us more than we know how to use wisely, because we are not fully aware of what the different options really mean. The ground quality options offered to us by modeling software is a case in point.

+

A second group of problems surrounds the availability of shortcuts, again, mostly in the area of ground concerns. NEC-2 offers us a highly accurate Sommerfeld-Norton ground calculating system, but this most commonly used form of NEC does not permit the modeling of buried radial systems. A work-around is the use of radials placed very close to the ground--within about 0.001 wavelength. A more tempting shortcut offered on some implementations of NEC-2 is the MININEC ground. With this system, we simply omit the radials and let the vertical monopole elements touch the ground. Very often we use these alternatives to a buried-radial system without knowing much about their accuracy relative to a more complete model. That lack of knowledge has led to numerous inadequate and possibly misleading models.

+

NEC-4 has the ability to handle buried wires and hence permits the complete modeling of a radial system. The models correlate quite well to reality and to standard calculations used by such engineering efforts in fields such as the AM broadcast industry. The question at hand is how well the short cut and substitute models measure up to full models of arrays using vertical antenna elements.

+

Let's be a bit more specific in what each part of the series will cover. In this first part, we shall examine some baseline data on 1/4 wavelength verticals using various types of modeled ground systems available to us within versions of NEC. In the second part, we shall seek a more comprehensive view and appreciation of the relative effects of soil conductivity and permittivity (relative dielectric constant) on the performance of our baseline antenna model. Since the project will simultaneously involve some problems associated with using the MININEC (no-radial) ground system and with the construction of models of radial systems, we shall tackle both problems in Part 3. The 4th episode will be devoted to a potpourri of models of some common vertically polarized antennas we typically use on 160 meters, as we seek some guidelines for the most adequate modeling possible. In the final installment, we shall look at the suggested use of inner and outer ground qualities to simulate a radial system.

+

This series of items, each which has appeared in The National Contest Journal in 2000-2001, will address these and related questions of significance to modeling 160-meter vertical arrays. Each episode in the 5-part collection will appear at this site after it has appeared in print. I hope the notes are useful to you.

+

1. Some Baseline Data (Nov/Dec, 2000, pp. 19-24)

+

2. Appreciating Conductivity and Permittivity (Mar/Apr, 2001, pp. 4-9)

+

3. Complex Radial Systems and Limitations of the MININEC (No-Radial) Ground (May/Jun, 2001, pp. 3-8)

+

4. A Potpourri of 160-Meter Vertical Antennas and Modeling Issues (Jul/Aug, 2001, pp. 4-9)

+

5. The Use of Multiple Ground Qualities in Lieu of Radials (Sep/Oct, 2001, pp. 4-9)

+
+ +
+

Updated 08-01-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: MF, Vertical


+ + diff --git a/content/160/160v1.html b/content/160/160v1.html new file mode 100644 index 0000000..3d786d6 --- /dev/null +++ b/content/160/160v1.html @@ -0,0 +1,447 @@ + + + + + + Modeling 160-Meter Vertical Arrays Part 1: Some Baseline Data + + + +
+

Modeling 160-Meter Vertical Arrays
+ Part 1: Some Baseline Data

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

For rather obvious reasons, 160 meters shows a higher percentage of vertical antennas and arrays relative to the total number of antennas in use than any other band. With the advent of NEC and MININEC, the tools that we use for designing and analyzing antennas for 160 have shifted from hand calculations to computer-aided design programs. However, the more I read, the less content I am that we have a full appreciation for what those modeling programs tell us. No where is the absence of understanding more evident than in the treatment of radial systems, whether they are attached to the antenna as part of its structure or simply lie beneath an independent antenna element.

+

There are two major ways that we might proceed in at least partially correcting this relative vacuum. One is mathematical and has recently been started by Rudy Severns, N6LF, in "Verticals, Ground Systems, and Some History, " QST (July, 2000), 38-44. An alternative route is to do some systematic modeling related to 160-meter vertical antennas and arrays. By capturing in a reasonably comprehensive way the span of results that antenna modeling systems present to us, we can gain some perspective and reasonable expectations of well-wrought antenna models.

+

This series will take the latter approach. In this first part, we shall examine some baseline data on 1/4 wavelength verticals using various types of modeled ground systems available to us within versions of NEC. In the second part, we shall seek a more comprehensive view and appreciation of the relative effects of soil conductivity and permittivity (relative dielectric constant) on the performance of our baseline antenna model. Since the project will simultaneously involve some problems associated with using the MININEC (no-radial) ground system and with the construction of models of radial systems, we shall tackle both problems in Part 3. The 4th episode will be devoted to a potpourri of models of some common vertically polarized antennas we typically use on 160 meters, as we seek some guidelines for the most adequate modeling possible. In the final installment, we shall look at the suggested use of inner and outer ground qualities to simulate a radial system.

+

There is some disputation afoot regarding the adequacy of models of just the sort that we shall examine relative to the performance of the physical antennas modeled. This series will not address that cluster of questions, since that larger topic necessarily involves the use of adequate testing methodology upon actual antennas as one side of the coin. Here, we shall be looking at what sorts of things different kinds of models tell us, and the number of variations on radial system modeling alone will more than fill our plate. However, a thorough understanding of what such models tell us is the other side of the coin under discussion, so I shall not be wholly blind to implications of the work done here.

+

Throughout these episodes, I shall be using both NEC-2 and NEC-4 in commercial implementations--EZNEC, GNEC, and NEC-Win Plus. These programs have input and output facilities that greatly ease the construction and interpretation of models, such as radial-makers, and the like. I shall indicate which level of NEC is used for every model explored. As well, the major output of this study is an array of data presented in tables and graphs. I shall limit text to an amount necessary to take a guided walk through the data, but it would require a book to extract every nuance from the information gathered. You may wish to study the data at length and draw further inferences from them.

+

The 1/4-Wavelength Vertical Monopole and Its Radial System

+
+ +
+
+ 1. The basic 1/4 wavelength monopole and variations among models used in this study. +
+

Any model of a 1/4 wavelength vertical monopole must necessarily include several elements, shown in Fig. 1. Of course, there is the vertical element itself. In all cases, I shall use a 40-m tall element that is 25 mm in diameter. (Because metrics are so common in 160-meter antenna work, all dimensions will be in metric form. 25 mm is just under 1" in diameter.) Wherever a radial system is used, it will consist of 2 mm diameter wire (about 0.0787" or between AWG #14 and AWG #12). Everything will be copper for simplicity and because changes of material in these models yield changes in results that have no affect on the trends in which we shall be most interested. The test frequency will be 1.83 MHz, and therefore 1/4 wavelength radials will be 40.96 m long.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Soil types used in the study.
+
+Soil Type         Conductivity            Permittivity
+                  Siemans/meter           dielectric constant
+Very Poor         0.001                    5
+Poor              0.002                   13
+Good (Average)    0.005                   13
+Very Good         0.0303                  20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Beneath the antenna will be the ground, as defined by a combination of conductivity and dielectric constant (permittivity). Table 1 lists the de facto standard range of values typically used as a fair sampling of the effects of soil quality on antenna performance. In the next part of our exploration, we shall look at the question of whether this short table represents a fair sampling or not. For the moment, we may content ourselves with these categories. Their origin lies in the table of found in The ARRL Antenna Book (p. 3-6), which is itself an adaptation of the table presented by Terman in Radio Engineer's Handbook (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862.

+

The four levels of soil quality--Very Poor, Poor, Good, and Very Good--have been a standard set of ground quality models since they were placed into early versions of ELNEC by Roy Lewallen, W7EL. Unfortunately, the "Good" category has obtained the alternate label "Average," which may be dubious, even if it is the general default used in most commercial implementations of NEC. Hence, we see more antennas modeled over "Average" ground than any other sort. The practice presents no hindrance to the understanding of models of horizontally polarized antennas, but it may create some limitations in our thinking about verticals for the MF and lower HF region.

+

We shall bypass some inherent limitations of all NEC models at MF and lower HF. NEC presumes a flat uncluttered terrain and a uniform soil constitution beneath the antenna. Neither condition may obtain in any given situation. Although we can model important ground clutter with wire grid assemblies, we cannot capture in a NEC model the stratified soil that may underlie a given antenna site. Since our work will be limited to comparisons among models, these limitations will not affect the results.

+

Now to the crux of the problem with modeling vertical arrays on 160 meters: we can use a considerable number of modeling techniques related to the radial system to make comparisons among antennas. Here is the short list of common radial system modeling techniques:

+
    +
  • 1. Buried radials: available only in versions of NEC above 2, which in practical terms of commercial implementations, requires NEC-4. Exigencies of modeling wires near the surface usually result in the use of length-tapered elements to yield finite model sizes.
    • +
  • 2. Elevated radials, within 0.001 wavelengths of ground to simulate buried radials. This is the standard NEC-2 method of handling of radial systems, although there are two major versions:
    • +
  • 2a. Uniform segmentation of all wires, which results in very large models for adequately segmented antennas with 30 or more radials.
    • +
  • 2b. Length-tapered elements, which yield smaller models, often able to be run on segment- limited implementations of NEC.
    • +
  • 3. Use of the MININEC ground (available with the NEC core in versions of EZNEC) without modeling the radial system itself.
    • +
+

To look at the ways in which these modeling systems converge and diverge, we can take a simple 1/4 wavelength monopole for 1.83 MHz and model it in each system using (where relevant) from 4 to 128 1/4 wavelength radials over each type of soil quality shown in Table 1. The number of radials will double in each step. This will give us a baseline of data for making some comparisons among the systems. Throughout, I shall list results in more numeric detail than might be significant for practical operation. Since we are interested in the numerical trends internal to modeling, the added precision of recorded results is wholly appropriate.

+

Elevated and Buried Radial System Results

+

The notion of elevated and buried radial systems, as used here, are limited to radial systems near the soil surface. (Placing a radial system on or under the soil is not possible in NEC-2 and placing the radial system at Z=0 in NEC-4 yields unusable results. Hence, our choices are limited.) For NEC-2 or NEC-4, we may follow a standard practice of placing the radial system at the minimum recommended height above ground. For the frequency in use, the 0.001 wavelength recommendation translates into a height of 0.164 m or about 6.5". By simple raising the entire system by this height from its initially modeled ground level, we may use standard uniform segmentation of the elements. However, because a radial system is a complex structure, use of the minimum segmentation levels (about 10 per half wavelength) will often not yield convergence of the model. The models used here employed 20 segments per quarter wavelength. Remember that this type of model is said to simulate buried radials.

+
+ +
+
+ 2. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an above-ground uniformly segmented model. +
+

Although NEC-2 recommends a limit of about 30 wires to a single junction, the limitation does not apply to NEC-4. Therefore, the uniform segmentation models over the various soil types proceeded to 128 radials. Whether NEC-4 can handle this number of wires at a junction for the models involved is indicated by the results. (Even in NEC-2, all of the models easily pass the average gain test, with the highest deviation from a perfect 1.000 appearing with only 4 radials: 1.0397. The 128-radial model produce an average gain test result of 1.0096. However, the average gain test is a necessary but not sufficient test of model adequacy and does not reveal every possible flaw in models.) Table 2 and Fig. 2 provide the data in different forms. For uniform segmentation, the smooth curves in Fig. 2 indicate that nothing erratic happens at the uppermost numbers of radials.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground;
+NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -2.15       27                44.51 + j 22.49
+Poor              -0.51       25                42.07 + j 27.30
+Good               0.51       22                42.84 + j 29.04
+Very Good          2.30       17                43.82 + j 25.37
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.61       27                38.90 + j  6.11
+Poor              -0.05       24                37.59 + j  9.71
+Good               0.96       22                38.52 + j 11.79
+Very Good          2.74       17                39.64 + j 12.17
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.42       27                36.80 + j  0.02
+Poor               0.08       25                36.29 + j  2.88
+Good               1.09       22                37.27 + j  4.45
+Very Good          2.90       16                38.14 + j  5.74
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.38       27                35.93 - j  2.20
+Poor               0.07       24                35.92 + j  0.55
+Good               1.09       22                36.96 + j  1.89
+Very Good          2.93       17                37.87 + j  3.15
+
+64-radials:  65 wires; 1300 segments
+Very Poor         -1.31       27                35.19 - j  2.92
+Poor               0.05       25                35.81 - j  0.21
+Good               1.02       22                37.09 + j  1.22
+Very Good          2.91       16                38.02 + j  2.57
+
+128-radials:  129 wires; 2580 segments
+Very Poor         -1.18       27                34.43 - j  2.57
+Poor               0.11       25                35.43 - j  0.26
+Good               0.98       22                37.07 + j  0.99
+Very Good          2.86       17                38.25 + j  2.52
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

However, the data reported by NEC-4 are interesting in their own right. The region of 16 to 32 radials is where the curves level off and modeling additional radials produces no further significant increases in the modeled far field gain, with the possible exception of the worst soil qualities. Moreover, the curves are nearly congruent, indicating that for each soil type, increasing the number of radials has a similar effect on gain. The impedance data in Table 2 indicates a similar set of trends for the source resistance. Indeed, from 32 radials upward, the source impedance changes virtually negligibly.

+

The model sizes listed in Table 2 provide ample incentive to use length tapering on the elements to reduce model size. 32 radials of uniform segmentation at the specified density of 20 per 1/4 wavelength overrun the 500-segment limitation of some programs. However, by using length tapering of each wire toward the junction, a 32-radial model requires only 397 segment. The standards of length tapering used in the model are based on two factors. First, the buried radial model will require wires as short as 0.001 wavelength (0.164 m). Hence, this figure became the lower length limit for tapering, with 0.04 wavelength selected as the upper limit. Standard length- segmenting features on programs like EZNEC begin with a wire of the shortest specified length and add wires of progressively doubled lengths until the maximum segment length is reached. The remaining element length is then segmented at a segment length that does not exceed the limit. Second, as shown in a detail of Fig. 1, the segments on either side of the source segment should be the same length as the source segment. For the above-ground radial system, this stricture required a separate source wire from 0.164 m to 0.328 m above ground, with the tapering of the element beginning above that point.

+
+ +
+
+ 3. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an above-ground tapered-length element model. +
+

The results from this set of models appear in Table 3 and Fig. 3. Impedance values in the table are slightly lower than for the uniformly segmented model simply because the source (which may be pictured as centered in its segment) is located closer to the radial junction. However, the range of values is quite similar, as we would expect from comparable models. The gain curves in Fig. 3 are almost clones of those in Fig. 2. Once more the region between 16 and 32 radials marks a practical peak beyond which values do not change significantly by any standard.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+above ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  31 wires; 61 segments
+Very Poor         -1.90       27                41.91 + j 18.38
+Poor              -0.33       25                40.27 + j 22.38
+Good               0.66       22                41.28 + j 23.89
+Very Good          2.45       17                42.26 + j 21.04
+
+8-radials:  55 wires; 109 segments
+Very Poor         -1.47       27                37.49 + j  3.69
+Poor               0.03       25                36.84 + j  6.82
+Good               1.01       22                37.99 + j  8.78
+Very Good          2.81       17                38.89 + j  9.56
+
+16-radials:  103 wires; 205 segments
+Very Poor         -1.34       27                35.91 - j  1.80
+Poor               0.09       25                36.08 + j  0.89
+Good               1.06       22                37.37 + j  2.61
+Very Good          2.92       16                37.91 + j  4.36
+
+32-radials:  199 wires; 397 segments
+Very Poor         -1.29       27                35.09 - j  3.55
+Poor               0.09       25                35.69 - j  1.05
+Good               1.04       22                37.24 + j  0.48
+Very Good          2.92       16                37.83 + j  2.46
+
+64-radials:  391 wires; 781 segments
+Very Poor         -1.23       27                34.36 - j  3.63
+Poor               0.10       25                35.24 - j  1.36
+Good               1.02       22                36.97 - j  0.10
+Very Good          2.91       16                37.91 + j  1.99
+
+128-radials:  775 wires; 1549 segments
+Very Poor         -1.12       27                33.81 - j  3.04
+Poor               0.17       25                34.80 - j  0.95
+Good               1.03       22                36.51 + j  0.04
+Very Good          2.87       16                37.97 + j  1.89
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

When we bury radials in a NEC-4 model, we should adhere to a number of required and advisable modeling practices. The radial junction is 0.164 m below ground. There must be a segment junction at the Z=0 point. As well the source should be above ground, and its adjacent segment lengths should be equal. These needs dictate that we once more use 0.001 wavelength as the shortest wire length in the tapered length elements, as shown in another detail of Fig. 1. We can place a wire of this length from the radial junction to the ground level and one more above it as the source junction. The length-tapering process then ensures that all of these conditions are met. The choice of the 25 mm diameter main element in all of these models easily meets recommended length-to-diameter ratio recommendations in all versions of NEC. The choice of burying the radials 0.001 wavelength deep was occasioned by the desire to make the models in this episode as structurally comparable as possible. In a future episode, we shall examine techniques for burying radial closer to the ground surface.

+
+ +
+
+ 4. Gain reports of the 1/4 wavelength monopole over various soil qualities for 4 to 128 radials for an below-ground tapered-length element model. +
+
+ +
+
+ 5. Source resistance reports from two models over Very Poor and Very Good soil: above-ground and below-ground radial systems. +
+

The results of this model appear in Table 4 and Fig. 4. Immediately apparent from the table is the much higher range and higher initial values of source impedance. Only over Very Good soil does the impedance of the 4-radial model approach that shown for the comparable above-ground radial system models. For lesser quality soils, impedances remain higher until we reach the 32- radial models. Fig. 5 compares tapered-length above- and below-ground radials systems in terms of the source resistance--limited to Very Poor and Very Good soils to avoid a graphic grid lock of lines. Although the Very Good soil below- and above-ground curves parallel each other, the Very Poor soil resistance lines dramatically show much wider differences. If we use the premise that the below-ground radial system better reflects the situation of most real installations, then the notion that the above-ground system is adequate for modeling radial systems is thrown into jeopardy.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 4.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -4.37       27                87.04 + j 25.31
+Poor              -2.49       25                72.45 + j 19.47
+Good              -0.71       23                60.96 + j 20.42
+Very Good          2.10       17                47.34 + j 14.52
+
+8-radials:  56 wires; 110 segments
+Very Poor         -3.11       28                65.90 + j 18.09
+Poor              -1.51       25                58.63 + j 15.18
+Good              -0.04       23                52.43 + j 15.94
+Very Good          2.60       17                44.34 + j 12.60
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.61       28                52.71 + j 12.43
+Poor              -0.16       25                49.71 + j 12.18
+Good               0.86       23                46.79 + j 12.83
+Very Good          2.79       16                42.20 + j 11.18
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.32       27                44.89 + j  7.54
+Poor               0.17       25                43.44 + j  9.55
+Good               1.12       22                42.67 + j 10.46
+Very Good          2.94       17                40.48 + j 10.03
+
+64-radials:  392 wires; 782 segments
+Very Poor         -1.19       27                40.68 + j  4.11
+Poor               0.32       25                39.43 + j  7.08
+Good               1.26       22                39.73 + j  8.50
+Very Good          3.05       17                39.06 + j  9.07
+
+128-radials:  776 wires; 1550 segments
+Very Poor         -1.12       28                38.60 + j  2.18
+Poor               0.17       25                37.32 + j  5.29
+Good               1.03       23                37.91 + j  6.99
+Very Good          2.87       17                37.94 + j  8.27
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The gain curves, read either from the table or the graph, also show a much wider span of values as we add radials. In general, not unexpectedly, the worse the soil quality, the greater the influence of adding more radials to the radial system. Indeed, the span of gain values and their progression, especially in the Very Poor soil category, tends to reflect better some operational reports than do the above-ground radial system models.

+

Some Miscellaneous Modeling Issues

In setting up the models for developing some baseline data, I restricted the main element diameter to 25 mm in order to easily meet the length-to-diameter requirements within the tapered length models. Table 5 tends to show why this move is needed and may serve as a caution about hasty modeling. The first portion of the table shows the results (from 4 to 32 radials) of increasing the element diameter to 0.164 m (a reasonable but approximate substitute for a standard Rohn tower section). With a length-to-diameter ratio of 1:1, the values--although usable for some purposes--show considerable wandering relative to the progressions in Fig. 3, the above-ground tapered length system with a 25 mm element. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 5.  Increasing the diameter of the vertical monopole to 0.164 m and to 0.25 m.
+
+A. 40-m vertical monopole, 164 mm (0.001 wavelength) diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter; tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -1.65       27                40.65 + j 17.92
+Poor              -0.14       25                39.82 + j 21.57
+Good               0.83       22                41.16 + j 23.06
+Very Good          2.64       17                42.11 + j 21.49
+
+8-radials:  56 wires; 110 segments
+Very Poor         -1.65       27                40.11 + j  7.46
+Poor              -0.18       24                39.81 + j 10.76
+Good               0.80       22                41.25 + j 12.80
+Very Good          2.62       17                42.24 + j 14.04
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.51       27                38.41 + j  2.69
+Poor              -0.10       24                38.77 + j  5.54
+Good               0.88       22                40.30 + j  7.32
+Very Good          2.74       17                41.00 + j  9.36
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.56       27                38.33 + j  1.12
+Poor              -0.18       25                39.15 + j  3.76
+Good               0.77       22                40.95 + j  5.31
+Very Good          2.66       17                41.76 + j  7.61
+
+B. 40-m vertical monopole, 250 mm (0.001 wavelength) diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter; tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -1.19       27                36.97 + j 17.53
+Poor               0.32       25                36.26 + j 20.92
+Good               1.29       23                37.53 + j 22.29
+Very Good          3.10       17                38.47 + j 20.82
+
+8-radials:  56 wires; 110 segments
+Very Poor         -1.26       28                37.07 + j  8.09
+Poor               0.21       24                36.84 + j 11.19
+Good               1.19       22                38.22 + j 13.05
+Very Good          3.01       17                39.21 + j 14.20
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.42       27                37.94 + j  3.78
+Poor               0.00       25                38.36 + j  6.58
+Good               0.98       22                39.91 + j  8.29
+Very Good          2.84       17                40.67 + j 10.35
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.52       27                38.33 + j  2.31
+Poor              -0.14       25                39.21 + j  4.93
+Good               0.82       22                41.05 + j  6.46
+Very Good          2.70       16                41.94 + j  8.77
+
+C.  40-m vertical monopole, 250 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground;
+NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -1.97       27                44.41 + j 24.37
+Poor              -0.39       24                42.67 + j 28.77
+Good               0.62       22                43.72 + j 30.49
+Very Good          2.43       17                44.73 + j 28.03
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.57       27                40.01 + j 10.70
+Poor              -0.04       25                39.17 + j 14.23
+Good               0.96       22                40.34 + j 16.30
+Very Good          2.76       16                41.41 + j 17.24
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.42       27                38.24 + j  5.37
+Poor               0.04       25                38.18 + j  8.34
+Good               1.04       22                39.46 + j 10.06
+Very Good          2.89       17                40.27 + j 11.87
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.36       27                37.20 + j  3.45
+Poor               0.04       24                37.72 + j  6.23
+Good               1.03       22                39.23 + j  7.75
+Very Good          2.90       17                40.09 + j  9.72
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Increasing the diameter further to .25 m (a bit less than 10") yields values that continuously decrease as we add radials, suggesting their unreliability. However, for above-ground radial system models, returning to the standard or uniform segmentation corrects the difficulty, since at 20 segments per 1/4 wavelength, the length-to-diameter relationships are well within limits.

+

The upshot of this exercise is that it may be very difficult to adequately model some monopole and radial systems where the monopole is very fat and the radials are buried very close to the ground surface. However, in Part 3, we shall show at least one way around this problem.

+
+ +
+
+ 6. NEC-2 and NEC-4 gain reports over Very Good soil for uniformly segmented and tapered- length element models. +
+
+ +
+
+ 7. NEC-2 and NEC-4 source resistance reports over Very Good soil for uniformly segmented and tapered-length element models. +
+

For those restricted to modeling in NEC-2, the natural question to ask is how well NEC-2 values correspond to those we have so far viewed from NEC-4. Only the figures from Tables 2 and 3 are relevant, since NEC-2 does not permit buried radials. Table 6 shows the results of running the Table 2 and Table 3 models in NEC-2, up to 32 radials to remain within the recommended junction limitations. The figures are well within usable agreement, although the NEC-2 gain numbers tend to run a bit higher and the resistance figures a bit lower than those yielded by NEC-4. Fig. 6 compares NEC-2 and NEC-4 standard and tapered-length values for gain, while Fig. 7 does the same for the source resistance--both over Very Good Soil. The high degree of parallelism among the curves suggests that NEC-2 is as usable as NEC-4 with respect to these types of modeled radial systems.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 6.  NEC-2 Values for Table 2 and Table 3 models (to 32 radials only).
+
+A.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm diameter,
+uniform segmentation: 20 segments per wire; radials 0.001 wavelength above ground; NEC-2.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  5 wires; 100 segments
+Very Poor         -2.09       27                43.91 + j 20.92
+Poor              -0.50       25                42.00 + j 25.72
+Good               0.53       23                42.60 + j 27.69
+Very Good          2.50       17                41.87 + j 26.15
+
+8-radials:  9 wires; 180 segments
+Very Poor         -1.56       27                38.48 + j  4.94
+Poor              -0.06       25                37.74 + j  8.53
+Good               0.95       23                38.58 + j 10.80
+Very Good          2.86       17                38.53 + j 12.81
+
+16-radials:  17 wires; 340 segments
+Very Poor         -1.37       27                36.36 - j  1.40
+Poor               0.05       25                36.56 + j  1.78
+Good               1.05       23                37.59 + j  3.69
+Very Good          2.98       17                37.49 + j  6.51
+
+32-radials:  33 wires; 660 segments
+Very Poor         -1.29       27                35.19 - j  3.20
+Poor               0.06       25                36.04 - j  0.51
+Good               1.04       23                37.38 + j  1.24
+Very Good          2.99       17                37.39 + j  4.25
+
+B.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm diameter,
+tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength above
+ground; NEC-2.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  31 wires; 61 segments
+Very Poor         -1.74       27                40.38 + j 16.41
+Poor              -0.22       25                39.26 + j 20.34
+Good               0.79       23                40.12 + j 22.01
+Very Good          2.73       17                39.71 + j 21.23
+
+8-radials:  55 wires; 109 segments
+Very Poor         -1.36       27                36.57 + j  3.14
+Poor               0.09       25                36.31 + j  6.29
+Good               1.08       23                37.34 + j  8.39
+Very Good          2.99       17                37.39 + j 10.58
+
+16-radials:  103 wires; 205 segments
+Very Poor         -1.23       27                35.06 - j  2.01
+Poor               0.15       25                35.56 + j  0.73
+Good               1.14       23                36.75 + j  2.60
+Very Good          3.07       17                36.69 + j  5.49
+
+32-radials:  199 wires; 397 segments
+Very Poor         -1.18       27                34.17 - j  3.63
+Poor               0.15       25                35.15 - j  1.13
+Good               1.12       23                36.57 + j  0.55
+Very Good          3.07       17                36.64 + j  3.52
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We have not so far looked at the use of the MININEC ground as a means of simplifying models of vertical antennas. In this system, we simply connect the base of the vertical to ground and omit the ground radials. Table 7 corrects this absence in quick order. Note that the source impedance of a model using the MININEC ground calculation system is invariant for the 25-mm and the 250-mm diameter models, since it is calculated by reference to perfect ground and not to the particular soil type specified for the other output figures.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 7.  MININEC Values:  40-m vertical monopole, direct connection to ground (no radials),
+fed at the lowest segment; NEC-4.
+
+A.  25 mm diameter
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+Perfect                                         37.08 + j  6.12
+Very Poor         -1.00       27
+Poor               0.31       25
+Good               1.41       23
+Very Good          3.16       17
+
+A.  250 mm diameter
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+Perfect                                         39.01 + j 12.67
+Very Poor         -0.99       27
+Poor               0.32       25
+Good               1.42       23
+Very Good          3.17       17
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

How we should characterize the gain reports of the MININEC ground simplification might be initially puzzling. However, there is one condition under which the three NEC-based ground systems converge--at 32 radials. For the examples used in this baseline exploration, the gain values for each soil types are very close indeed for the two above-ground systems and the buried system. Fig. 8 shows the convergence, with the MININEC no-radial values shown in the separate higher line. In general, MININEC ground system gain values tend to be overly optimistic relative to those yielded by ground systems using radials.

+
+ +
+
+ 8. 32-radial system gain reports over various soil types for all models, with MININEC-ground (no-radials) added. +
+

Although the MININEC no-radial modeling system might be a usable substitute for the above- ground radial systems, it is certainly no substitute for the NEC-4 buried radial system. Simplified MININEC-ground models are wholly insensitive to the variations in source resistance exhibited by the buried-radial system. Moreover, the buried-radial system itself varies from other NEC radial systems by showing performance increases beyond the 32-radial level. As we shall see in Part 3, there are some possible illicit uses of the MININEC no-radial system that can result in significant antenna analysis errors.

+

In general, then, the most sensitive method of modeling 1/4 wavelength monopoles is to use a buried radial system (assuming the actual or proposed antenna will place the radials either on or below ground). However, this technique is available only in NEC-4 among currently available commercial implementations of NEC. Second choice among those restricted to NEC-2 is to use 32-radial models, and to use length-tapering if there is a 500-segment limitation in the program. However, above-ground radial system models will not approach the sensitivity of more adequate methods, especially over Poor to Very Poor soils, if these models are substitutes for a buried radial system.

+

There are contexts in which one should not replace the most sensitive modeling methods with substitutes that are not fully consistent in output with the best techniques. Casual modeling for personal satisfaction is one matter, but serious work is quite another. For modeling which others might treat as authoritative for antenna design, analysis, or selection, only the most sensitive techniques will do, even if reaching this level involves upgrading software or being patient while very large (2500-segment) models run.

+

Although we have established a kind of baseline for 160-meter vertical antenna systems, we have only spot-checked the possible values of conductivity and permittivity that characterize the soils over which we model antennas. To appreciate the ways in which these two parameters affect the outcome of modeling efforts, we shall do a more thorough survey next time.

+
+ +
+

Updated 03-10-01. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Nov./Dec., 2000), pp. 19-25. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Return to Series Index

+

Go to Main Index

+

Topics: MF, Vertical


+ + diff --git a/content/160/160v2.html b/content/160/160v2.html new file mode 100644 index 0000000..50f5d56 --- /dev/null +++ b/content/160/160v2.html @@ -0,0 +1,453 @@ + + + + + + Modeling 160-Meter Vertical Arrays Part 2: Appreciating Conductivity and Permittivity + + + +
+

Modeling 160-Meter Vertical Arrays
+ Part 2: Appreciating Conductivity and Permittivity

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

In the first installment of this series, we established a data baseline relative to 160-meter 1/4 wavelength vertical antennas, exploring the types of modeled radial systems and the number of radials used in each system. We concluded that, as a model of the typical buried radial system, only a model of a buried system appears to be sufficiently sensitive to changes occasioned by differences in soil quality. Other alternatives have, at best, only limited correlations to the physically buried system.

+

Our exploration was limited by the use of four "standard" soil types, and we raised the question of whether these standards represented a fair sampling of conditions underlying a vertical antenna. This question is part of a larger one: how do the combined effects of soil conductivity and permittivity (relative dielectric constant) influence the performance of vertical antennas within the context of NEC modeling systems?

+

We might take a strictly mathematical approach to this question, since the ground effects are calculated (in the Sommerfeld-Norton ground system that is part of NEC) by standard engineering formulations. However, for many modelers, this approach fails to generate a set of reasonable expectations of antenna performance. Therefore, a second approach may be preferable: to take a standard antenna and ground radial system of varying numbers of radials and to model it using a wide span of combinations of conductivity and permittivity. We shall use this second approach in this episode, with the hope of eliciting some useful patterns of thought about ground effects on a vertical antenna system. Once more, the data tables will outweigh the text by a considerable margin.

+

Conductivity and Permittivity

Soil conductivity is measurable in units of Siemens (or "mhos") per meter (S/m), the inverse of resistivity in Ohms per meter. Of the two relevant ground quality properties, it is the more intuitive. Measurements are relatively frequency specific so that a general DC or low frequency RF measurement may not be exact for a proposed antenna system in the MF or lower HF region. The calculation systems in which conductivity plays a roles normally do not account for variations in the value by virtue of soil stratification, but instead presume an average value that characterizes a homogenous soil beneath the antenna. +

Permittivity or the relative dielectric constant is less well understood by many amateurs. The main use of the dielectric constant with which most of us are familiar pertains to capacitors: a capacitor can become more compact by using a dielectric with a high value. Soils exhibit the same property. Some values of the relative dielectric constant for materials relevant to antennas installation appear in Table 1, which is derives from John D. Kraus, Antennas, 2nd Ed. (1988), pp. 665 and 851.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Some permittivity (relative dielectric constant) values (from Kraus, Antennas, 2nd
+Ed.).
+
+Material                      Dielectric Constant
+Vacuum                        1.0
+Dry air                       1.0006
+Fresh snow                    1.5
+Clay Soil                     14
+Sandy Soil                    10
+Slate stone                   7
+Urban ground                  4
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Soil qualities are categorized by combinations of values for both conductivity and permittivity. In Table 2 is a listing of the soil types found in the table of found in The ARRL Antenna Book (p. 3-6), with the type descriptions truncated. The ARRL table is taken from Terman's Radio Engineer's Handbook (p. 709), which derives from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. Immediately apparent in the Table 2 listing is the fact that there are many more soil quality types than the standard four that we used in Part 1.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  Some soil types (from ARRL Antenna Book).
+
+Type                   Conductivity          Permittivity          Category
+Pastoral 1             0.0303                20                    Very Good
+Pastoral 2             0.01                  14
+Flat marshy            0.0075                12
+Pastoral 3             0.006                 13
+Pastoral 4             0.005                 13                    Average (Good)
+Rocky                  0.002                 12-14                 Poor
+Sandy                  0.002                 10
+City                   0.001                  5                    Very Poor
+Heavy Industrial       0.001                  3                    Extremely Poor
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

However, there is a pattern of mutual increases in both conductivity and permittivity, and the range of each is finite. (I have omitted both fresh and salt water as too special to warrant inclusion here.) Conductivity ranges from 0.001 S/m to a bit over 0.03 S/m, with a greater degree of differentiation among lower values. Permittivity values tend to be more linearly arranged, with a maximum value of 20. The minimum "vacuum" or free space value would be 1. With these patterns in mind, we stand a chance of acquiring an appreciation for the relative effects of each of the two variables on vertical antenna performance over the full span of possibilities within a finite project.

+

The span of conductivity values lends itself to a Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, and 34 mS/m. A linear progression of dielectric constants (1, 5, 9, 13, 17, 21) covers this range well. Within the matrix of these values are combinations either exactly or very close to values in the standard soil quality chart. However, if we look at all of the values in the matrix, we might acquire a perspective on the relative effects of each component. Finding where the standard values fit within the overall matrix of possible values is the goal of our exercise.

+
+ +
+
+ 1. Basic techniques to construct the buried radial system vertical monopole used in developing the data in Tables 3-1 through 3-8. +
+

All we need now is an antenna model to which we can apply these values. Let's use the 1/4- wavelength 40-m tall vertical, 25 mm in diameter, that we employed in Part 1. We shall use a radial system buried 0.001 wavelength deep in the various soils. The model dictates the use of NEC-4, and the details of the fine structure of the tapered-length elements appear in Fig. 1. The radials are 2 mm in diameter, and everything is copper.

+

The Results

The detailed results of the exercise in systematic modeling appear in Tables 3-1 through 3-8. Each table represents a different level of conductivity, with sub-tables for each level of dielectric constant in the progression. Each combination of conductivity and permittivity is carried through systems of 4, 8, 16, 32, and 64 radials to check the modeled effects of the radials system size. In the Gain and Source Resistance columns, I have identified the maximum and minimum values. The Source Reactance column identifies the minimum values of reactances for each radial system size as a measure of the nearest approach to resonance. +

Before walking through the tables themselves to observe some interesting detailed phenomena, we might well show some summary results. For every combination of conductivity and permittivity value, there is a range of gain values and a range of source resistance values as we increase the number of radials from 4 to 64. These figures are indicative of certain important trends in the tables.

+
+ +
+
+ 2. Maximum and average gain differentials for 4 to 64 radial systems and dielectric constant between 1 and 21 plotted against conductivities of 0.001 to 0.34 S/m. +
+

Fig. 2 is a graph of the maximum and the average differential of gain values for changes in the radials system for all values of permittivity for each of the conductivity levels. The importance of showing both sets of numbers together is this: the higher the difference between maximum and average gain values, the greater difference that the value of dielectric constant makes to antenna performance. In contrast, the lower the differential between maximum and average values, the less the importance of the dielectric constant to antenna performance.

+

Two aspects of the graph are of special note. First, as the conductivity value rises above about 0.005 S/m, the difference between the maximum and the average values becomes insignificant. For soils with a conductivity of about 0.008 S/m, the value of permittivity makes no significant difference to antenna performance. Below a conductivity value of about 0.005 S/m, permittivity can make a considerable difference in performance. Second, at the highest values of conductivity explored, the overall change in gain between 4 and 64 radials falls well under 1 dB, regardless of the permittivity value.

+
+ +
+
+ 3. Maximum and average gain differentials for 4 to 64 radial systems and conductivities of 0.001 to 0.34 S/m plotted against dielectric constants between 1 and 21. +
+

Fig. 3 illustrates the same point from the opposing perspective of permittivity. The graph plots gain differentials for the span of 4 to 64 radials for each level of conductivity against dielectric constant. This graph replicates the conclusion that wide changes in the dielectric constant make little difference to soils with conductivities above the 0.005 S/m level. However, the chart adds another conclusion to our list. Changes in the dielectric constant value in the region from 1 to 9 makes a far greater difference in performance than values above that level.

+
+ +
+
+ 4. Maximum and average source resistance differentials for 4 to 64 radial systems and dielectric constants between 1 and 21 plotted against conductivities of 0.001 to 0.34 S/m. +
+

Similar conclusions derive from examining the source resistance data in the same manner. Fig. 4 plots of maximum and average differentials of source resistance, with the lines beginning to merge at the 0.005 S/m level. Above that level of conductivity, differences in permittivity have little effect on the source resistance. To take the obverse perspective, Fig. 5 plots the source resistance as a function of the relative dielectric constant for each sampled level of conductivity. Except to repeat the initial conclusion, one might well ignore the lines for conductivity values above 0.005 S/m. The curves for lower values of conductivity show an interesting pattern of effects from changing values of permittivity. Differentials do not peak at the lowest combination of conductivity and permittivity. Instead, peaks occur at different levels of permittivity for each of the lower values of conductivity.

+
+ +
+
+ 5. Maximum and average source resistance differentials for 4 to 64 radial systems and conductivities of 0.001 to 0.34 S/m plotted against dielectric constants between 1 and 21. +
+

The upshot is that higher levels of conductivity show great regularity in gain and source resistance values as they vary while we increase the number of radials in the system. However, at lower levels of conductivity, permittivity plays a more variable role in setting maximum and minimum values of gain and gain differential, as well as source resistance and resistance differentials. To explore this a bit further, let's take a short walk through some of the tables.

+

A Short Look at the Tables

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-1 through 3-8.  160-meter vertical monopole: 40 m tall, 25 mm diameter; 40.96-m
+(0.25 wavelength) radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire; radials 0.001 wavelength below ground; NEC-4.  "TO Angle" = elevation angle of
+maximum radiation.  For each sub-table, a trailing "+" means the highest value in that
+category and a trailing "-" means the lowest value in that category, where category is the
+column parameter except for the values of source reactance, in which case the minimum
+values are shown for each level of radials.
+
+Table 3-1.  Conductivity = 0.001
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -4.76-        28                     86.13                 34.14
+ 8                     -3.62         28                     65.93                 21.77
+16                     -2.84         27                     53.89                 13.57
+32                     -2.37         28                     46.89                  7.88
+64                     -2.13         28                     42.93                  4.28
+Dielectric constant = 5
+ 4                     -4.37         27                     87.04+                25.31
+ 8                     -3.11         28                     65.90                 18.09
+16                     -2.18         28                     52.71                 12.43
+32                     -1.61         27                     44.89                  7.54-
+64                     -1.32         27                     40.68                  4.11-
+Dielectric constant = 9
+ 4                     -3.80         27                     83.72                 17.87
+ 8                     -3.56         27                     64.66                 14.62
+16                     -1.56         27                     51.87                 11.75
+32                     -0.88         27                     43.49                  8.12
+64                     -0.54         27                     38.93                  4.91
+Dielectric constant = 13
+ 4                     -3.28         27                     79.27                 14.23
+ 8                     -2.11         26                     62.60                 12.19
+16                     -1.13         26                     51.36                 10.94
+32                     -0.39         26                     43.13                  8.66
+64                      0.01         26                     38.30                  5.87
+Dielectric constant = 17
+ 4                     -2.91         25                     76.43                 12.50
+ 8                     -1.74         26                     60.59                 10.98
+16                     -0.79         26                     50.59                 10.24
+32                     -0.03         26                     42.92                  8.94
+64                      0.41         26                     38.00                  6.63
+Dielectric constant = 21
+ 4                     -2.59         25                     74.33                 10.32-
+ 8                     -1.45         26                     59.13                 10.24-
+16                     -0.52         25                     49.82                  9.83-
+32                      0.24         25                     42.80                  9.10
+64                      0.70+        25                     37.93-                 7.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-2.  Conductivity = 0.002
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -2.80-        25                     72.68                 29.22
+ 8                     -1.90         26                     59.18                 20.31
+16                     -1.26         25                     50.59                 14.44
+32                     -0.83         25                     44.92                 10.17
+64                     -0.58         26                     41.35                  7.11
+Dielectric constant = 5
+ 4                     -2.79         26                     73.51+                25.71
+ 8                     -1.85         25                     59.44                 18.46
+16                     -1.14         25                     50.44                 13.57
+32                     -0.65         26                     44.43                  9.77
+64                     -0.38         25                     40.68                  6.89
+Dielectric constant = 9
+ 4                     -2.68         25                     73.39                 22.33
+ 8                     -1.70         25                     59.27                 16.69
+16                     -0.95         25                     50.16                 12.80
+32                     -0.42         25                     43.95                  9.58
+64                     -0.11         25                     40.04                  6.88-
+Dielectric constant = 13
+ 4                     -2.49         25                     72.45                 19.47
+ 8                     -1.51         25                     58.63                 15.18
+16                     -0.74         25                     49.71                 12.18
+32                     -0.16         25                     43.44                  9.55
+64                      0.17         25                     39.43                  7.08
+Dielectric constant = 17
+ 4                     -2.29         25                     71.39                 17.11
+ 8                     -1.31         25                     58.05                 13.93
+16                     -0.54         25                     49.43                 11.63
+32                      0.06         25                     43.25                  9.50-
+64                      0.42         25                     39.15                  7.28
+Dielectric constant = 21
+ 4                     -2.06         25                     70.02                 15.30-
+ 8                     -1.11         25                     57.27                 12.98-
+16                     -0.34         25                     49.03                 11.21-
+32                      0.27         25                     43.03                  9.52
+64                      0.65+        25                     38.91-                 7.55
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-3.  Conductivity = 0.003
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -1.77         24                     66.44                 26.48
+ 8                     -1.01         23                     55.74                 19.15
+16                     -0.44         24                     48.79                 14.29
+32                     -0.04         24                     43.94                 10.72
+64                      0.19         23                     40.72                  8.04
+Dielectric constant = 5
+ 4                     -1.82-        24                     67.10                 24.55
+ 8                     -1.02         24                     56.00                 18.07
+16                     -0.42         24                     48.79                 13.73
+32                      0.01         24                     44.76                 10.46
+64                      0.27         24                     40.42                  7.91
+Dielectric constant = 9
+ 4                     -1.81         24                     67.37+                22.58
+ 8                     -0.98         24                     56.07                 16.98
+16                     -0.36         24                     48.73                 13.18
+32                      0.10         24                     43.56                 10.24
+64                      0.38         24                     40.11                  7.83-
+Dielectric constant = 13
+ 4                     -1.75         24                     67.30                 20.73
+ 8                     -0.91         24                     55.96                 15.98
+16                     -0.27         24                     48.59                 12.70
+32                      0.22         24                     43.36                 10.09
+64                      0.52         24                     39.82                  7.83-
+Dielectric constant = 17
+ 4                     -1.66         24                     66.96                 19.05
+ 8                     -0.82         24                     55.72                 15.07
+16                     -0.16         24                     48.41                 12.27
+32                      0.34         24                     43.17                  9.98
+64                      0.66         24                     39.57                  7.89
+Dielectric constant = 21
+ 4                     -1.55         23                     66.43                 17.58-
+ 8                     -0.71         24                     55.39                 14.28-
+16                     -0.05         24                     48.20                 11.90-
+32                      0.47         24                     43.00                  9.90
+64                      0.80+        23                     39.37-                 7.97
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-4.  Conductivity = 0.005
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                     -0.64         22                     60.19                 23.25
+ 8                     -0.01         22                     52.16                 17.60
+16                      0.45         22                     46.82                 13.77
+32                      0.80         22                     42.93                 10.93
+64                      1.03         23                     40.17                  8.73
+Dielectric constant = 5
+ 4                     -0.68         23                     60.59                 22.36
+ 8                     -0.04         22                     52.34                 17.09
+16                      0.44         22                     46.88                 13.49
+32                      0.80         22                     42.89                 10.80
+64                      1.04         22                     40.06                  8.67
+Dielectric constant = 9
+ 4                     -0.71-        22                     60.88                 21.43
+ 8                     -0.05         23                     52.47                 16.55
+16                      0.44         22                     46.90                 13.20
+32                      0.82         22                     42.84                 10.66
+64                      1.07         22                     39.94                  8.62
+Dielectric constant = 13
+ 4                     -0.71-        23                     60.96                 20.42
+ 8                     -0.04         23                     52.43                 15.94
+16                      0.47         23                     46.79                 12.83
+32                      0.86         22                     42.67                 10.46
+64                      1.12         22                     39.73                  8.50-
+Dielectric constant = 17
+ 4                     -0.71-        23                     61.15+                19.58
+ 8                     -0.04         22                     52.55                 15.50
+16                      0.48         22                     46.87                 12.64
+32                      0.89         23                     42.71                 10.42
+64                      1.16         22                     39.72                  8.56
+Dielectric constant = 21
+ 4                     -0.69         22                     61.14                 18.70-
+ 8                     -0.01         22                     52.52                 15.01-
+16                      0.52         23                     46.83                 12.38-
+32                      0.93         22                     42.65                 10.33-
+64                      1.22+        23                     39.62-                 8.56
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-5.  Conductivity = 0.008
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      0.26         21                     55.68                 20.58
+ 8                      0.77         21                     49.51                 16.19
+16                      1.15         20                     45.32                 13.14
+32                      1.45         21                     42.17                 10.84
+64                      1.66         21                     39.81                  9.01
+Dielectric constant = 5
+ 4                      0.22         21                     55.92                 20.14
+ 8                      0.74         20                     49.63                 15.93
+16                      1.14         21                     45.36                 12.99
+32                      1.44         20                     42.17                 10.76
+64                      1.66         21                     39.77                  8.98
+Dielectric constant = 9
+ 4                      0.19         20                     56.12                 19.67
+ 8                      0.73         21                     49.73                 15.65
+16                      1.13         21                     45.40                 12.83
+32                      1.44         21                     42.16                 10.68
+64                      1.66         20                     39.73                  8.95
+Dielectric constant = 13
+ 4                      0.17         21                     56.42                 19.20
+ 8                      0.71         21                     49.81                 15.37
+16                      1.12         21                     45.43                 12.67
+32                      1.44         21                     42.15                 10.60
+64                      1.67         21                     39.68                  8.92
+Dielectric constant = 17
+ 4                      0.16         21                     56.42                 18.73
+ 8                      0.70         20                     49.87                 15.10
+16                      1.12         21                     45.45                 12.52
+32                      1.45         21                     42.13                 10.53
+64                      1.68         20                     39.64                  8.90
+Dielectric constant = 21
+ 4                      0.15-        21                     56.52+                18.26-
+ 8                      0.70         21                     49.92                 14.82-
+16                      1.12         21                     45.46                 12.36-
+32                      1.46         21                     42.12                 10.45-
+64                      1.70+        21                     39.60-                 8.88-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-6.  Conductivity = 0.013
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      1.04         19                     51.99                 18.19
+ 8                      1.45         19                     47.28                 14.85
+16                      1.77         20                     44.02                 12.47
+32                      2.01         19                     41.51                 10.63
+64                      2.20+        19                     39.54                  9.15
+Dielectric constant = 5
+ 4                      1.02         19                     52.12                 17.96
+ 8                      1.44         19                     47.35                 14.71
+16                      1.75         19                     44.05                 12.38
+32                      2.01         19                     41.51                 10.58
+64                      2.20+        19                     39.52                  9.12
+Dielectric constant = 9
+ 4                      1.00         19                     52.24                 17.74
+ 8                      1.42         19                     47.42                 14.57
+16                      1.74         19                     44.08                 12.30
+32                      2.00         19                     41.52                 10.53
+64                      2.20+        20                     39.51                  9.11
+Dielectric constant = 13
+ 4                      0.98         19                     52.34                 17.51
+ 8                      1.41         19                     47.48                 14.43
+16                      1.73         19                     44.10                 12.21
+32                      2.00         20                     41.52                 10.49
+64                      2.19         19                     39.50                  9.08
+Dielectric constant = 17
+ 4                      0.97         20                     52.44                 17.27
+ 8                      1.40         19                     47.53                 14.29
+16                      1.73         20                     44.13                 12.13
+32                      1.99         19                     41.52                 10.44
+64                      2.19         19                     39.48                  9.06
+Dielectric constant = 21
+ 4                      0.95-        19                     52.53+                17.03-
+ 8                      1.39         19                     47.57                 14.14-
+16                      1.72         19                     44.15                 12.04-
+32                      1.99         19                     42.52                 10.39-
+64                      2.20+        20                     39.37-                 9.05-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-7.  Conductivity = 0.021
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      1.70         18                     49.04                 16.17
+ 8                      2.03         18                     45.45                 13.65
+16                      2.28         17                     42.91                 11.81
+32                      2.49         18                     40.90                 10.36
+64                      2.65+        17                     39.28                  9.16
+Dielectric constant = 5
+ 4                      1.69         18                     49.11                 16.05
+ 8                      2.02         18                     45.49                 13.58
+16                      2.28         18                     42.93                 11.76
+32                      2.48         17                     40.91                 10.33
+64                      2.65+        18                     39.27                  9.15
+Dielectric constant = 9
+ 4                      1.67         17                     49.18                 15.94
+ 8                      2.01         18                     45.53                 13.50
+16                      2.27         18                     42.95                 11.71
+32                      2.48         18                     40.92                 10.30
+64                      2.65+        18                     39.27                  9.13
+Dielectric constant = 13
+ 4                      1.66         18                     49.24                 15.82
+ 8                      2.00         18                     45.57                 13.42
+16                      2.26         18                     42.97                 11.67
+32                      2.47         18                     40.92                 10.27
+64                      2.64         18                     39.27                  9.12
+Dielectric constant = 17
+ 4                      1.65         18                     49.30                 15.71
+ 8                      1.99         18                     45.60                 13.36
+16                      2.25         18                     42.98                 11.63
+32                      2.47         18                     40.93                 10.25
+64                      2.64         18                     39.26-                 9.11
+Dielectric constant = 21
+ 4                      1.64-        18                     49.35+                15.60-
+ 8                      1.99         18                     45.63                 13.28-
+16                      2.25         18                     43.00                 11.58-
+32                      2.46         18                     40.93                 10.22-
+64                      2.64         18                     39.26-                 9.10-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3-8.  Conductivity = 0.034
+
+No. of                 Gain          TO Angle               Source R              Source jX
+Radials                dBi           degrees                Ohms                  Ohms
+Dielectric constant = 1
+ 4                      2.26         16                     46.62                 14.44
+ 8                      2.53         16                     43.87                 12.56
+16                      2.73         16                     41.91                 11.15
+32                      2.90         17                     40.32                 10.01
+64                      3.04+        17                     39.00                  9.07
+Dielectric constant = 5
+ 4                      2.26         17                     46.66                 14.39
+ 8                      2.52         16                     43.90                 12.52
+16                      2.73         17                     41.92                 11.13
+32                      2.89         16                     40.33                 10.00
+64                      3.04+        17                     39.00                  9.06
+Dielectric constant = 9
+ 4                      2.25         16                     46.69                 14.34
+ 8                      2.52         17                     43.92                 12.49
+16                      2.72         16                     41.93                 11.11
+32                      2.89         16                     40.33                  9.99
+64                      3.03         16                     39.00                  9.06
+Dielectric constant = 13
+ 4                      2.24         16                     46.72                 14.28
+ 8                      2.51         16                     43.94                 12.45
+16                      2.72         17                     41.94                 11.08
+32                      2.89         17                     40.34                  9.97
+64                      3.03         16                     39.00                  9.04
+Dielectric constant = 17
+ 4                      2.24         17                     46.76                 14.23
+ 8                      2.51         17                     43.96                 12.41
+16                      2.71         16                     41.95                 11.06
+32                      2.88         16                     40.34                  9.96
+64                      3.03         17                     39.00                  9.04
+Dielectric constant = 21
+ 4                      2.23-        17                     46.79+                14.16-
+ 8                      2.50         16                     43.98                 12.37-
+16                      2.71         17                     41.97                 11.03-
+32                      2.88         17                     40.35                  9.94-
+64                      3.02         16                     39.00-                 9.03-
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In Table 3-1, we have the lowest value of conductivity examined: 0.001 S/m. Lower values of conductivity have been measured for some antenna sites. However, this table includes the lowest value on the ARRL chart. In fact, the value 0.001 S/m with a dielectric constant of 5 is the Very Poor category. Interestingly, this combination yields the highest source resistance, even though the lowest gain occurs with a 0.001 S/m--1 combination. Although soils with very low conductivity and very high dielectric constant are improbable, the lowest values of reactance occur with the highest values of permittivity for radial systems between 4 and 16 radials. However, for larger radial systems, the lowest reactance values occur with a dielectric constant of 5. (Contrast this variability with Tables 3-5 through 3-8, where the lowest reactance values for all sizes of radial systems occurs with the highest values of permittivity.)

+

A change in conductivity from 0.001 S/m to 0.002 S/m makes a large difference on the modeled gain performance of the test antenna at lower levels of permittivity, as shown in Table 3-2. However, when we reach a permittivity of 9 (close to the standard of Poor soil), the differences from a conductivity of 0.001 S/m have shrunk considerably. Nevertheless, at this dielectric constant level, differentials between 4 and 64 radial systems level off in the 2.6 dB region--which is still sufficient reason to increase a radial system to the maximum feasible size.

+

In both Tables 3-2 and 3-3 (for conductivities of 0.002 and 0.003 S/m, respectively), we continue to find that the minimum gain values and that maximum source resistance values do not occur at the extremes of the chart. Indeed, minimum gain shows a progression toward a higher values of dielectric constant with increases in conductivity. Maximum source resistance shows the same trend, but does not wind up in the same dielectric constant box as minimum gain.

+

Table 3-4, for a conductivity of 0.005 S/m represents a broad middle set of grounds with charted dielectric constants in the 12-14 range. In the table, minimum gain covers a broad range of permittivity--9 to 17, with the peak source resistance appearing at a permittivity of 17. However, for any size radial system, the curves are beginning to broaden. With 64 radials, the modeled gain varies only by 0.19 dB over the entire range of dielectric constants. Nonetheless, considerable variation remains in both the gain and source resistance columns for small to large radial systems.

+

With Table 3-5, we enter the region of greatest regularity in phenomena, indicating the reduced influence of dielectric constant--or, what amounts to the same thing, the domination of conductivity as the major ground factor affecting antenna performance. Both gain and source resistance maximums and minimums occur with a dielectric constant of 21. Tables 3- 6 through 3-8 reflect similar trends. With Very Good soil, or its nearest tabular counterpart (0.034 S/m and 21), the difference between 4 and 64 radials models out at under a 0.8 dB difference in gain--at least for the particular model of a monopole and radial system used in this exercise.

+

Our quick stroll through the tables should be somewhat of a revelation, especially when set against the standard soil quality values displayed in Table 2. In most instances, for a given value of conductivity, the associated value of dielectric constant in the standard listing reflects one of the minimums or maximums, as relevant from the broader modeled Tables 3-1 through 3-8. At the lower values of conductivity, the dielectric constant not only plays a larger role in determining modeled antenna performance, but as well, that influence varies from one value to the next of conductivity. The standard listing in Table 2 tends to capture the maximum combined influence of both factors.

+

As a consequence, the use of the "short" list of four values (Very Poor, Poor, Good, and Very Good) tends to be a fair sampling of the soil quality properties as they influence modeled vertical antenna performance. The large stretch between the values associated with Good soil (0.005 S/m and 13) and those associated with Very Good soil (0.0303 S/m and 20) becomes quite reasonable in view of two factors. First, as conductivity increases greatly, the amount of change in antenna performance for any given size radial system between conductivity steps decreases significantly. Second, variations in the dielectric constant become relatively insignificant. Hence, the seemingly odd values associated with Very Good soil become as good as any other figures for conductivities above 0.02 S/m.

+

There are, of course, very good mathematical reasons for the patterns that we have observed. However, by presenting the calculations in combination with a standardized vertical antenna model, the consequences of those calculation become perhaps a bit more vivid--and perhaps even a bit more useful in establishing patterns of reasonable expectation for antenna models. Of course, the results given here apply to 160 meters and to a 1/4 wavelength monopole with a buried radial system. Rather than extrapolate the results too far from the situation modeled, one should develop a comparable systematic modeling study for such other antenna system structures and frequencies as may be of greatest interest.

+

We have so far limited ourselves to single radial systems and single element vertical arrays. In the next episode, we shall look at ways to develop models of more complex situations, along with some limitations of using the MININEC ground as a substitute for actually modeling radials.

+
+ +
+

Updated 03-10-01. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Mar./Apr., 2001), pp. 4-9. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

Return to Series Index

+

Go to Main Index

+

Topics: MF, Vertical


+ + diff --git a/content/160/160v3.html b/content/160/160v3.html new file mode 100644 index 0000000..fc6c4da --- /dev/null +++ b/content/160/160v3.html @@ -0,0 +1,257 @@ + + + + + + Modeling 160-Meter Vertical Arrays Part 3: Complex Radial Systems + + + +
+

Modeling 160-Meter Vertical Arrays
+ Part 3: Complex Radial Systems and
+ Limitations of the MININEC (No-Radial) Ground

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

In our examination of 160-meter vertical antenna modeling, we have noted that it is advisable to model full ground radial systems in lieu of using short-cut methods. As well, models of

+

buried radial systems appear to replicate best actual buried radial systems. We also examined the effects of soil conductivity and permittivity on model predictions, and established that--within limits--the now-traditional soil types that range from Very Poor to Very Good provide a reasonable sampling of modeled vertical antenna behavior.

+

These results strongly suggest that anyone who wishes seriously to model 160-meter vertical antennas or arrays should develop some modeling techniques that allow the efficient development of radial systems. In this episode, we shall look at a few of these techniques. In addition, we shall also examine some further reasons for using them.

+

Complex Radial System Construction

With simple radial systems consisting of a single set of radials--however many may be required--the "radial-maker" facilities within commercial implementations of NEC provide the most rapid construction. We simply specify the radial parameters and how many we need, and the automated software does the rest. The actual mathematics of radials is fairly simple, but becomes tedious when done with a calculator. With a specimen radial of a certain length, we can obtain the angle for each succeeding radial by dividing the total number need into 360 degrees. If we set the first radial along the X-axis, then the angle and a little sine and cosine work will net us the X and Y coordinates of each radial. We need only calculate for the first 90 degrees of the circle, since the remaining radials will have the same absolute numerical values, with only sign changes to place the new radial in the proper quadrant. +

Length-tapering the radial elements (and the vertical element as well) proves useful, especially for buried radial systems. In such cases, we need at least a 1-segment wire from the surface (Z=0) to the buried radials. Since the source will be placed as low as possible on the main element above ground and since it is most accurate to have the segments on either side of the source the same length as the source segment, the segments near the junction of the element and radials often require very short lengths. With uniform segmentation, the models become exceptionally large if the radial system is larger than about 16 radials. By tapering the segment lengths toward the junction area to the shortest necessary length, we can reduce the size of the model and speed run times.

+

The technique in its simplest form--with a single set of 1-segment wires handling the source and radial junction region, as shown in Part 1 of this series--limits the main element diameter that we may model accurately. Using a 0.001 wavelength minimum segment length, which is about 0.164 m or 6.5" at 1.83 MHz, element diameters may be limited to something below this figure. Although linear elements may use segment length-to-diameter ratios as low as 1:1, more complex geometries may dictate a larger ratio, sometimes as high as 4:1. For any given case, convergence testing and the average gain test are both applicable to evaluating the adequacy of a model.

+

For fatter main elements or for radials buried at a shallow depth, we may wish to resort to a different technique of modeling radials. See Fig. 1. In this sketch, we have shallow radials and a "fat" main element. Let's suppose that the diameter is about 0.125 m and that we wish to maintain a 4:1 length-to-diameter ratio for each segment. The shortest segment length we can use is 0.5 m. Suppose also that the radials are at some shallow depth under the surface, perhaps 0.05 m. This figure is only 0.0003 wavelength. Using the simple technique of buried radial construction would involve us in modeling conflicts.

+
+ +
+
+ Fig. 1. Modeling tapered-length elements and radials for shallow radial systems or for large-diameter elements. +
+

However, we may slope our radials from the main element to the surface and then to the buried level portion of the radial. If the base of the main element is 0.05 m above ground, then two 1-segment wires per radial will satisfy NEC-4 requirements for the radial start. We may then length-taper the remaining portion of each radial. As well, we can set the length of the source region of the main element as a 1-segment wire that is 0.5 m long. Then the main element may be length-tapered above that point. In both cases, a minimum segment length of 0.5 m will satisfy the need for equal segment lengths on each side of the source segment.

+
+ +
+
+ Fig. 2. Simplified sketch of the junction between two intersecting radial systems. +
+

If we become serious about modeling 160-meter verticals, then we shall be placing each 1/4 wavelength monopole element on a radial system. For many designs, we may end up with overlapping radial systems. Fig. 2 shows a 2-system example, simplified to 16 radials for clarity. Note that three of the radials overlap in this case. To prevent the calculating core from rejecting the model because wires intersect at "mid-segment" points, we can resort to several strategies. Displacing one radial system vertically is one possibility, although it leads to potential models that do not reflect the actual system design. Most overlapping radial systems end up with junctions of the radials that would otherwise overlap. The modeler should thus shorten the radials so that they form a junction along the line labels "radial junction line" in the sketch. The junction points may be connected with an actual modeled wire or left open, according the actual physical radial system being modeled.

+
+ +
+
+ Fig. 3. Simplified sketch of the junction between three intersecting radial systems. +
+

In some cases, we may have more than 2 intersecting radial systems. Fig. 3 shows three systems, more closely spaced than the pair in Fig. 2. The more closely spaced the main elements in an array, the more intersecting radials we shall encounter. Perhaps the most complex system of which I am aware is a 5 element array, with 4 radial systems forming a square around the central system.

+
+ +
+
+ Fig. 4. Calculating the revised coordinates for intersecting radials. +
+

Recalculating the coordinates of radial ends so that the radial intersections are correctly placed and segmented is a straight forward process. Fig. 4 can provide some guidance. Let the "main" radial system be centered at X=0 and Y=0. If we know the radial junction line coordinate for at least one axis, we can take the ratio of that coordinate relative to the coordinate of the full length radial. Since we are working with congruent triangles for each radial, the new coordinate in the other axis will be reduced by the same ratio. As well, in a uniformly segmented radial, the ratio will also determine the new level of segmentation for the shortened radial. The new coordinate and segmentation data will equally apply to the radial that intersects the one just calculated.

+

Although the work is a bit tedious, it is necessary to construct reasonably correct models of intersecting radial systems. For large systems, one might transfer the work to a utility program or a spreadsheet.

+

Why Not Simplify?

The detail work required to set up complex radial systems often leads modelers to accept short-cut methods that yield smaller, simpler models. The standard technique is to use a MININEC ground with no radials, with the attendant assumption that the results approximate those which one might obtain with a full radial system. I suspect that we had better test the assumption. +
+ +
+
+ Fig. 5. Using tilting 1/4 wavelength monopoles to test the limits of the MININEC no-radial ground system. +
+

Fig. 5 represents our initial test case. Let's set up a vertical over ground. We shall run the vertical over the standard 4 ground qualities (Very Poor, Poor, Good, and Very Good) using 3 systems. First is the MININEC ground with the vertical connected at its lower end directly to the surface--with no radials. The second system is a 32-radial array that is 0.001 wavelength above the ground. The third is a 32-radial array buried 0.001 wavelength below the surface. The choice of 32 radials stems from our observation in Part 1 that with this size radial system, we obtain the closest correlation among modeled results in NEC-4. Radials and the main element will be length- tapered for model economy. As always, the radial systems are set within the Sommerfeld-Norton ground calculation system.

+

Subsequently, we shall perform the same set of modeling runs with the main element tilted from vertical by 30 degrees, 45 degrees, and 60 degrees, as indicated in Fig. 5. If the simplified MININEC no-radial ground system is an adequate approximation of a 32-radial system, then the level of correlation that occurs with the main element exactly vertical should hold up for the tilt-tests.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25
+wavelength) radials, 2 mm diameter, tapered segmentation: 0.001
+to 0.04 wavelength per wire (where used); NEC-4.
+
+Soil Type      Gain           TO Angle       Source Impedance
+               dBi            degrees        R +/- J X Ohms
+
+A.  Antenna Vertical
+
+MININEC (no-radial) ground
+Very Poor      -1.00          27             37.08 + j  6.12*
+Poor            0.31          25             *MININEC Impedance
+Good            1.41          23             is over perfect
+Very Good       3.16          17             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -1.29          27             35.09 - j  3.55
+Poor            0.09          25             35.69 - j  1.05
+Good            1.04          22             37.24 + j  0.48
+Very Good       2.92          16             37.83 + j  2.46
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -1.61          27             44.89 + j  7.54
+Poor           -0.16          25             43.44 + j  9.55
+Good            0.86          22             42.67 + j 10.46
+Very Good       2.79          17             40.48 + j 10.03
+
+B.  Antenna Tilted 30 Degrees
+
+MININEC (no-radial) ground
+Very Poor       0.74          32             29.19 - j  0.42*
+Poor            1.37          29             *MININEC Impedance
+Good            1.97          25             is over perfect
+Very Good       3.13          18             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.23          31             26.46 - j  7.68
+Poor            0.79          27             26.64 - j  5.59
+Good            1.51          24             27.62 - j  4.19
+Very Good       3.10          18             27.95 - j  2.30
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -1.74          31             46.21 - j  1.30
+Poor           -0.26          28             40.20 + j  2.82
+Good            0.67          24             37.53 + j  5.67
+Very Good       2.48          18             33.65 + j  5.50
+
+C.  Antenna Tilted 45 Degrees
+
+MININEC (no-radial) ground
+Very Poor       1.77          36             20.36 - j 10.10*
+Poor            2.01          32             *MININEC Impedance
+Good            2.30          27             is over perfect
+Very Good       3.06          19             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.07          35             19.55 - j 14.31
+Poor            0.81          31             19.35 - j 12.65
+Good            1.45          26             19.77 - j 11.44
+Very Good       2.94          19             19.63 - j 10.39
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -2.05          35             39.46 - j  7.78
+Poor           -0.60          31             32.61 - j  3.80
+Good            0.32          26             29.35 - j  0.97
+Very Good       2.12          19             25.01 - j  1.96
+
+D.  Antenna Tilted 60 Degrees
+
+MININEC (no-radial) ground
+Very Poor       3.32          44             10.58 - j 25.59*
+Poor            3.05          37             *MININEC Impedance
+Good            2.93          31             is over perfect
+Very Good       3.07          21             ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor      -0.08          38             11.33 - j 24.68
+Poor            0.74          34             10.77 - j 23.70
+Good            1.34          28             10.78 - j 22.95
+Very Good       2.70          21             10.48 - j 22.34
+
+32 Radials, 0.001 wavelength below ground
+Very Poor      -2.99          42             31.17 - j 16.75
+Poor           -1.51          35             23.80 - j 13.34
+Good           -0.55          30             20.15 - j 10.89
+Very Good       1.26          21             15.69 - j 13.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The results of the runs appear in Table 1. In portion A, the results are the same as those presented in Part 1 of this series. Perhaps the only serious departure from a reasonably close correlation of results lies in the source impedance values for the buried radial system.

+
+ +
+
+ Fig. 6. Gain reports over various ground qualities for a monopole tilted 30 degrees from vertical. +
+

Fig. 6 summarizes the gain data from portion B of the table. The gain data divergence for Very Poor soil has grown from 0.61 dB for the vertical main element to 2.48 dB for the element with a 30° tilt, with lesser divergence as the soil quality improves. The MININEC ground shows a single impedance value, since it is calculated over perfect ground, while the above-ground radial system shows a tight set of values in the same region. However, the source impedance values for the buried-radial system show a wider spread and coincides with the spread of gain values.

+
+ +
+
+ Fig. 7. Gain reports over various ground qualities for a monopole tilted 45 degrees from vertical. +
+

The trends noted with respect to the 30-degree tilt model continue through the 45-degree and 60-degree models. Gain values data is summarized in Fig. 7 and Fig. 8 for these two cases. By the time we reach a 60-degree tilt, over Very Poor soil, the MININEC ground system shows a 3 dB advantage over the above-ground radial system, which in turn shows another 3 dB gain over the buried radial system.

+
+ +
+
+ Fig. 8. Gain reports over various ground qualities for a monopole tilted 60 degrees from vertical. +
+

The failure of the MININEC ground to track with the buried radial system stems from the known limitations of the MININEC ground calculation system. Any wire with a horizontal far-field component will display inaccurate results below about 0.2 wavelength from the surface. The error grows greater as we we place the wire closer to the surface. The inaccuracies show up not only in driven elements, but in any array in which one or more parasitic elements fall into the error-prone region of the MININEC ground system. Those inaccuracies affect elements with even the slightest tilt.

+

The "intermediate" level results obtained for the above- ground radial system are also suggestive. The departure of these results from the buried-radial system speak to the limitations of an above-ground radial system as an approximation of a buried radial system. Even in the case of the 32-radial system, the one showing the closest correlation between above-ground and buried radial systems for vertical elements, the divergence of results for tilted main elements suggest that the only good model of a buried-radial system is a buried-radial system model. Unfortunately, these results have economic consequences: since NEC-4 is the main vehicle for method-of-moments modeling of buried radial systems, serious modelers must obtain a license and then either develop their own interfaces or purchase one of the commercial implementations of the NEC-4 core. Outside the U.S., serious modelers may also encounter restrictions in licensure.

+

A 2-Element Parasitic Vertical Array

Lest the exercise using a tilted vertical be viewed as a Don Quixote sort of quest, let's look at an old standard sort of array using a single sloping parasitic element. We shall take a 25-mm diameter main element, 40 m long, as our driver. The choice of diameters permits us to use a simplified connection for the above-ground and buried radial systems. The parasitic reflector is a 2-mm diameter guy wire that meets the ground or the radial system and which terminates at the position specified in Fig. 9. +
+ +
+
+ Fig. 9. Outline of a 2-element parasitic vertical array using a sloping guy wire as the reflector. +
+

For our test runs, we shall use a MININEC ground with no radials, as is so often done in models of this and very closely similar arrays. We shall also run the model over above-ground and buried radial systems. The radial systems will be intersecting 32-radial arrays, with the line of intersection 13.5 m from each element. As always, we shall run the model over sample ground qualities ranging from Very Poor to Very Good.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  2-element parasitic array:  driver = 40-m vertical
+monopole, 25 mm diameter; reflector = sloping 2-mm guy, 40.5 m
+long; intersecting 32 40.96-m (0.25 wavelength) radial system, 2
+mm diameter, tapered segmentation: 0.001 to 0.04 wavelength per
+wire (where used); NEC-4.
+
+Soil Type      Gain           TO Angle  Front-to Back       Source Impedance
+               dBi            degrees   Ratio dB            R +/- J X Ohms
+
+MININEC (no-radial) ground
+Very Poor       2.00          30        11.36               40.19 + j 53.02*
+Poor            3.34          26        14.25               *MININEC Impedance
+Good            4.62          24        17.11               is over perfect
+Very Good       6.36          18        19.50
+ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor       0.96          30        11.45               65.61 + j 43.13
+Poor            2.23          27        11.56               65.99 + j 46.27
+Good            3.29          24        11.89               65.76 + j 47.90
+Very Good       5.13          17        12.86               59.82 + j 52.06
+
+32 Radials, 0.001 wavelength below ground
+Very Poor       0.97          29        10.79               61.71 + j 41.67
+Poor            2.36          27        10.80               58.24 + j 44.17
+Good            3.51          23        11.16               56.80 + j 46.49
+Very Good       5.50          18        11.36               52.90 + j 47.48
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+
+ Fig. 10. Gain reports for the 2-element array using MININEC and radial-system models. +
+

Table 2 summarizes the results of these runs. Fig. 10 summarizes the gain data. For this system, in which the parasitic element forms an angle of about 34 degrees to the plane of the driver, both radial system gain reports are consistent for all of the soil types. However, the MININEC ground system reports gains that are about 1 dB higher for all soil types.

+
+ +
+
+ Fig. 11. Front-to-back ratio reports for the 2-element array using MININEC and radial-system models. +
+

Fig. 11 reveals an even greater weakness of the MININEC no- radial system for this type of array. The front-to-back figures for the two radial systems do not perfectly coincide, but are reasonably close for operational purposes. In contrast, the MININEC no-radial system shows a nearly linear increase in the front-to-back ratio as we move from one soil quality to the next better soil quality. Over Good soil (conductivity = 0.005, dielectric constant = 13), there is a full 5 dB over-estimation of the front-to-back ratio relative to either radial system.

+
+ +
+
+ Fig. 12. Source resistance reports for the 2-element array using MININEC and radial-system models. +
+

Similar divergences between the MININEC no-radial system of modeling vertical arrays and the two radial systems show up in the figures calculated for the source impedance. The reactances do not vary significantly among the models. However, as shown in Fig. 12, the source resistance values do vary considerably. The MININEC no-radial system calculates a single value over perfect ground--a value that fails to come close to the values calculated by either radial system. Interestingly, the buried-radial system shows a steadier decline in source resistance as we change soil types than does the above-ground system--another suggestion that neither one is a fully adequate approximation of the other.

+
+ +
+
+ Fig. 13. Comparative elevation patterns for the 2-element array using the MININEC no-radial ground and using a 32-radial buried radial system. +
+

The different analyses of the array appear striking in elevation plots. Fig. 13 overlays the MININEC pattern and the buried-radial pattern for Good soil. The differences are self-explanatory.

+

For practical modeling of vertical arrays, then, the MININEC no-radial system has serious shortcomings in approximating models of radial systems. Its use in serious modeling work is likely unjustified, given the availability of NEC facilities for modeling radial systems of any necessary size. Likewise, above- ground radial systems fail to track adequately with buried-radial systems so that the use of one as an approximation for the other becomes suspect without the modeler laying out situation-specific ground work to justify their use. Since that groundwork would necessarily involve the use of buried radials, one might as well model buried radials with buried radials.

+

I am well aware that 2 examples do not alone make a general case, let alone a trend. so in the final episode of this series, we shall examine a potpourri of antennas and some further antenna modeling issues related to 160-meter verticals.

+
+ +
+

Updated 03-10-01. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (May/Jun., 2001), pp. 3-8. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 4

+

Return to Series Index

+

Go to Main Index

+

Topics: MF, Vertical


+ + diff --git a/content/160/160v4.html b/content/160/160v4.html new file mode 100644 index 0000000..51d8a39 --- /dev/null +++ b/content/160/160v4.html @@ -0,0 +1,300 @@ + + + + + + Modeling 160-Meter Vertical Arrays Part 4: A Potpourri of 160-Meter Vertical Antennas and Modeling Issues + + + +
+

Modeling 160-Meter Vertical Arrays
+ Part 4: A Potpourri of 160-Meter Vertical Antennas and Modeling Issues

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

So far, I have drawn some tentative conclusions about the inadequacies involved in using the MININEC no-radial system as a substitute for models employing radials, and of similar inadequacies of above-ground radial system models as substitutes for buried-radial system models. The converse of these negatively stated ideas is the following: For radial systems, (usually) only radial-system models will suffice, and for buried-radial systems, (usually) only buried radial-system models will suffice. As general propositions, these statements need further grounding. Although one might resort profitably to an examination of the mathematics of ground calculations, we shall stay with our present mode of demonstrating both the scope and the limits of these propositions by the use of demonstration models. In this way, we can also gain some appreciation of the likely properties of these antennas--or at least of these antenna models.

+

The Venerable Inverted-L

One of the most popular "beginners" antennas for 160 is the inverted-L. When the total length is approximately 1/4 wavelength, the inverted-L is simply a vertical monopole with the top bent over for structural convenience. The implementations of this antenna are as varied as the circumstances in which they are constructed. However, let's settle for test purposes on a 2-mm diameter wire that is 40 m long. +

Inverted-Ls vary in shape depending upon the vertical and horizontal territory and supports that are available to the builder. Some are quite tall, with only a small horizontal portion. Others are quite low, in the 10-m height range (about 33'), with the remainder spread horizontally. Therefore, let's test the three versions shown in Fig. 1 as a reasonably fair sampling of the diverse forms of the L. As usual in this series, we shall use the MININEC no-radial ground system, the 32-radial above-ground system and the 32-radial buried system as test vehicles. The radial systems will use tapered-length techniques as laid out in earlier installments of the series.

+
+ +
+
+ 1. Three versions of the inverted-L to be examined over various ground systems and soil qualities. +
+

Table 1 shows the results of modeling the inverted L in its three iterations. As we saw in Part 3 when working with tilted verticals, the MININEC no-radial system results diverge from the radial systems in an ever-more radical manner as we shorten the vertical portion and extend the horizontal portion of the antenna. The pattern of the antenna is stronger away from the horizontal wire by a small amount (1 to 2 dB) so that the patterns are not perfectly circular. The table shows the maximum gain figures.

+ 
Table 1.  Inverted-L, 40-m vertical total length, 2 mm diameter; 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire (where
+used); NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+A.  Vertical = 30 m; horizontal = 10 m
+
+MININEC (no-radial) ground
+Very Poor              -0.79         28                     31.64 - j 13.76*
+Poor                    0.38         27                     *MININEC Impedance
+Good                    1.40         24                     is over perfect
+Very Good               3.01         17                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -1.23         29                     31.18 - j 21.22
+Poor                    0.12         25                     30.91 - j 18.78
+Good                    1.09         23                     31.54 - j 17.62
+Very Good               2.80         17                     32.26 - j 16.85
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -1.12         29                     35.76 - j  7.66
+Poor                   -0.01         26                     36.34 - j  6.96
+Good                    0.86         23                     36.19 - j  7.09
+Very Good               2.60         17                     34.82 - j  8.00
+
+B.  Vertical = 20 m; horizontal = 20 m
+
+MININEC (no-radial) ground
+Very Poor               0.26         33                     20.32 - j 22.33*
+Poor                    1.01         30                     *MININEC Impedance
+Good                    1.73         25                     is over perfect
+Very Good               2.92         19                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -0.60         32                     21.04 - j 27.51
+Poor                    0.45         29                     20.64 - j 25.79
+Good                    1.22         26                     20.75 - j 24.94
+Very Good               2.61         19                     21.02 - j 24.87
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -0.61         33                     25.07 - j 14.62
+Poor                    0.17         29                     25.30 - j 14.33
+Good                    0.86         26                     24.80 - j 14.56
+Very Good               2.30         19                     23.38 - j 15.90
+
+ C.  Vertical = 10 m; horizontal = 30 m
+
+MININEC (no-radial) ground
+Very Poor               2.72         45                      7.73 - j 23.91*
+Poor                    2.54         39                     *MININEC Impedance
+Good                    2.59         33                     is over perfect
+Very Good               2.71         24                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor              -0.08         49                     10.22 - j 24.59
+Poor                   -0.43         41                      9.62 - j 24.11
+Good                    0.86         34                      9.23 - j 23.83
+Very Good               1.75         24                      8.78 - j 24.92
+
+32 Radials, 0.001 wavelength below ground
+Very Poor              -0.65         46                     14.57 - j 12.34
+Poor                   -0.37         39                     13.98 - j 12.95
+Good                    0.07         34                     12.86 - j 13.55
+Very Good               1.04         23                     11.09 - j 15.97
+

Fig. 2 shows the maximum gain values for the shortest of the inverted-Ls over various soil qualities for each of the three modeled ground systems. The nearly level gain--and its elevated value--for the MININEC no-radial system are once more unrealistic as approximations of the gain values for either radial system. Over poor soil, the difference between the MININEC ground result and the buried radials system result is nearly 3.5 dB.

+
+ +
+
+ 2. Gain reports for the shortest inverted-L using 3 different ground systems. +
+

Similar divergences show up in the source resistance values. For the tallest L, the differences among all three systems are minor. However, for the shortest version, the MININEC value becomes a poor indicator of what a buried-radial system model will show. Whatever the parameter, the different models of ground once more prove inadequate approximations of each other.

+

A 3-Element Parasitic Array Using Sloping Guys

Since the inverted-L requires only a single radial set, models are simple to construct. In contrast, a 3-element parasitic array of the sort shown in Fig. 3 is a far more tedious project. Again, the array is an adaptation of a fairly standard arrangement. The 40-m long driver is 25 mm in diameter. Each 2-mm diameter guy is 38.7 m long and slopes 54 degrees relative to the ground (or 36 degrees relative to the driver). In this array, a loading inductor serves to increase the electrical length of the reflector. Our interest in this particular array stems not only from the differences in reports from using different radial systems, but as well, differences that may emerge in the required value of the loading inductor to achieve maximum front-to-back ratio. +
+ +
+
+ 3. Outline of the 3-element parasitic array to be examined over various ground systems and soil qualities. +
+

Each element base is centered in a radial system for other than the MININEC no- radial test runs. Fig. 4 is a screen "grab" of the length-tapered intersecting 32-radial system used with the model for the test runs. There are 26 intersections. The initial model with uniform segmentation required 99 wires and 1559 segments. With length-tapering, the model has shrunk to 1015 segments, but needs 619 wires. The obvious question is whether the added work of setting up the model over a radial system is worth the effort.

+
+ +
+
+ 4. Sketch of 3 intersecting radial systems, 32 radials each, used with the 3- element parasitic array. +
+

The results appear in Table 2. The divergence in gain among the three ground systems is perfectly in parallel with results obtained for other arrays with sloping parasitic guys. Over Very Poor soil, the MININEC system shows over 4.5 dB of excess gain, although this shrinks to about 1.1 dB over Very Good soil. Interestingly, the above-ground radial system shows better gain than the buried system when over Very Poor soil, but less gain over Very Good soil.

+ 
Table 2.  3-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector and director = sloping 2-mm guy, 38.7 m long; intersecting 32 40.96-m (0.25
+wavelength) radial system, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire (where used); NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+MININEC (no-radial) ground: Load = 2.87 uH, Q = 300
+Very Poor               4.85         29             20.85                 15.11 + j 32.45*
+Poor                    5.73         26             23.53                 *MININEC
+Impedance
+Good                    6.75         23             24.92                 is over perfect
+Very Good               8.15         17             27.55                 ground.
+
+32 Radials, 0.001 wavelength above ground:  Load = 2.78 uH, Q = 300
+Very Poor               1.53         28             16.74                 16.95 + j 43.54
+Poor                    2.69         26             16.02                 15.77 + j 43.78
+Good                    3.71         22             15.45                 14.98 + j 43.57
+Very Good               6.14         16             18.20                 14.56 + j 40.27
+
+32 Radials, 0.001 wavelength below ground:  Load = 1.91 uH, Q = 300
+Very Poor               0.15         27             12.23                 14.46 + j 32.44
+Poor                    2.16         25             12.99                 11.93 + j 31.72
+Good                    4.06         22             13.62                 10.12 + j 31.10
+Very Good               6.98         16             15.36                  8.62 + j 27.93
+

The most dramatic differences occur in the front-to-back reports, as summarized in Fig. 5. Two facets of the front-to-back ratio are significant. First, the maximum obtainable ratios for the radial systems are mediocre (although operationally usable) compared to the reports of the MININEC no-radial system. The no-radial and the buried-radial systems show parallel curves, but the above-ground system curve does not join the parallel until the transition from Good to Very Good soil.

+
+ +
+
+ 5. Front-to-back ratio reports of the 3-element parasitic array over various grounds. +
+

It is impossible to ignore all comparisons to reality, and the front-to-back ratios of the 2-element (in Part 3) and the 3-element parasitic arrays are a case in point. The values reported by the radial system models for both cases are in line with typical 2- and 3-element horizontal parasitic beams. For the 3-element array, only the most highly optimized 3- element horizontal beams show the level of front-to-back ratio reported by the MININEC no- radial model. Yet, it would be difficult to assert that the vertical array uses dimensions that approach any degree of optimization, with the possible exception of refining the loading coil.

+

The loading inductor in the models is the second important area of divergence among the models. To obtain the highest values of front-to-back ratio, the loading inductors were assigned a Q of 300. In other words, the load uses a series value of resistance about 1/300 of the required inductive reactance and its associated inductance at the 1.83 MHz test frequency. The difference in required loading coil between the no-radial and the above- ground radial system represent about 1 Ohm of reactance: 33 Ohms for the MININEC ground model and 32 Ohms for the above-ground radial system. However, to obtain the best front-to-back ratio of which the model was capable with the buried radial system, the loading inductance had to be reduced to about 1.9 uH or 22 Ohms reactance.

+
+ +
+
+ 6. Elevation patterns of the 3-element parasitic array as modeled over a MININEC (no-radial) ground and over intersecting radial systems both above and below ground. +
+

Fig. 6 shows the elevation patterns for the three models over Good soil. The differences in the predicted patterns among the three ground systems are clearly evident. It is well to be reminded at this point that the data and patterns apply only to the modeled radial systems and that some variance will become apparent with changes in the model. For example, changing radial length and number will likely alter the reported data to some degree, in line with expectations that might emerge from our survey of system ranging from 4 to 128 radials in Part 1.

+

Where the MININEC Ground System Works

So far we have examined cases in which the results of using the MININEC no-radial system diverge in very significant ways from results obtained from using modeled radial systems. Not all models exhibit such large levels of deviation among models. For example, let's examine a pair of 1/4 wavelength monopoles, each 40 m long and 25 mm in diameter and positioned as shown in Fig. 7. We shall space them 84 m apart, which is just over 1/2 wavelength. The selected separation is intentional so that the 1/4 wavelength radials that we place under each monopole for certain tests do not overlap. Therefore, we end up with elementary though large models for the above-ground and buried radial systems--about 400 wires and 795 segments for length-tapered models. Of course, the MININEC no-radial model is simple by comparison. +
+ +
+
+ 7. Two 1/4 wavelength monopoles spaced 1/2 wavelength apart and fed in phase (with non-intersecting radial systems). +
+

We shall feed each monopole in phase with the other and examine the results, as we have for each test case so far. Table 3 lays out the numbers. Fig. 8 graphs the gain figures in order to show that there is little difference among the three modeling systems. In fact, for this particular antenna, the MININEC and the above-ground systems yield figures that are closer than those of the buried-radial system. Fig. 9 compares the MININEC no-radial azimuth pattern with the buried-radial model pattern to show that there would be little or no operationally significant difference in the numbers.

+ 
Table 3.  Two 40-m, 25-mm diameter monopoles, separated 84 m fed in phase; 40.96-m
+(0.25 wavelength) radials, 2 mm diameter, tapered segmentation: 0.001 to 0.04 wavelength
+per wire (where used); NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+MININEC (no-radial) ground
+Very Poor               2.96         27                     29.05 - j  7.60*
+Poor                    4.27         25                     *MININEC Impedance
+Good                    5.37         23                     is over perfect
+Very Good               7.11         16                     ground.
+
+32 Radials, 0.001 wavelength above ground
+Very Poor               2.95         27                     26.40 - j 22.70
+Poor                    4.27         25                     26.95 - j 11.40
+Good                    5.21         22                     28.00 - j 10.80
+Very Good               6.98         17                     28.90 - j 10.30
+
+32 Radials, 0.001 wavelength below ground
+Very Poor               2.36         27                     35.25 - j  2.93
+Poor                    3.84         25                     33.71 + j  1.78
+Good                    4.90         22                     32.80 - j  1.50
+Very Good               6.79         17                     31.32 - j  2.74
+

The one arena in Table 3 in which we find a difference that may be significant is the source impedance figures. Of course, the MININEC values show no variation, while the above-ground radial system figures show only small variations (with the exception of the reactance over Very Poor Soil). The values are for each of the two feedpoints of the 2- element array. As we have noted before, the buried radial system shows a wider range of variation with changes in soil quality and generally higher values than for each of the other ground systems. For this antenna, the variation carries over into the reactance column, where the array appears to be closer to resonance at 1.83 MHz than with either of the other ground modeling systems.

+
+ +
+
+ 8. Gain reports of the two 1/4 wavelength monopoles spaced 1/2 wavelength apart and fed in phase. +
+
+ +
+
+ 9. Azimuth patterns for the in-phase fed pair of monopoles over MININEC (no- radial) ground and over a buried radial system. +
+

Despite these differences, all three ground modeling systems would generally be adequate for analyzing the array in question. Where the elements are perfectly vertical, they do not encroach on the error-producing aspects of the MININEC ground. As well, the model lacks potential complications that might be introduced by the use of intersecting radial systems. As a result, we have a type of case in which the simplification of the ground system to a MININEC no-radial model yields reasonable results.

+

A 1/4-Wavelength Monopole Over 32 Radials Buried at 3 Depths

I have shown exemplary applications of overlapping radial systems, but have not yet shown an example that uses the technique of sloping the first two sections of each radial in order to model either a "fat" monopole or a shallow buried radial system. To rectify this gap, let's consider a monopole that is 250 mm in diameter. As always, we shall leave the top height at 40 m. In addition to working with the fat monopole, let's consider whether the depth of the buried radial system makes a difference to performance. With a 32-radial system, we shall use depths of 0.0005 wavelength (0.082 m or 3.23"), 0.001 wavelength (0.164 m or 6.46"), 0.002 wavelength (0.328 m or 12.91"), 0.003 wavelength (0.492 m or 19.37"), and 0.004 wavelength (0.656 m or 25.82"). +
+ +
+
+ 10. The model set-up for testing a vertical monopole over a 32-wire radial system buried at 5 depths. +
+

Fig. 10 shows the general modeling set-up for the areas of the antenna nearest the junction. Only the first of the 32 radials is shown, but the separate values for the x and the Z axes appear on the sketch. The objective was to keep the shortest wire or segment length at 1 m, which is 4 times the diameter of the monopole. As well, the length of segments adjacent to the source wire are equal to its length. The models consisted of 164 wires and 460 total segments and were run over the usual span of Very Poor to Very Good Soil.

+ 
Table 4.  Vertical monopole, top at 40 m, 250 mm diameter; 32 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered with interior wires slanted; depth 0.0005 wavelength to 0.004
+wavelength, NEC-4.
+
+Depth: 0.0005 wavelength, 0.082 m
+Very Poor              -1.31         28                     43.08 + j 13.11
+Poor                   -0.07         25                     44.68 + j 14.49
+Good                    0.86         22                     44.86 + j 14.64
+Very Good               2.72         17                     43.41 + j 14.34
+
+Depth: 0.001 wavelength, 0.164 m
+Very Poor              -1.30         27                     43.91 + j 13.33
+Poor                   -0.06         25                     44.71 + j 14.56
+Good                    0.87         23                     44.85 + j 14.63
+Very Good               2.72         17                     43.40 + j 14.26
+
+Depth: 0.002 wavelength, 0.328 m
+Very Poor              -1.21         27                     43.36 + j 13.66
+Poor                    0.01         25                     44.15 + j 14.68
+Good                    0.94         22                     44.24 + j 14.65
+Very Good               2.78         17                     42.79 + j 14.09
+
+Depth: 0.003 wavelength, 0.492 m
+Very Poor              -1.14         28                     43.06 + j 14.10
+Poor                    0.06         25                     43.94 + j 14.95
+Good                    0.99         22                     43.92 + j 14.88
+Very Good               2.82         17                     42.46 + j 14.07
+
+Depth: 0.004 wavelength, 0.656 m
+Very Poor              -1.09         28                     42.83 + j 14.73
+Poor                    0.11         25                     43.68 + j 15.54
+Good                    1.03         23                     43.71 + j 15.32
+Very Good               2.85         17                     42.25 + j 14.24
+

The results of the runs in Table 4 yield operationally insignificant but numerically interesting differences for any soil quality. As with the other models which we have surveyed, the results over very poor soil strongly suggest the need for more radials. See Part , which has some data for some systems up to 128 radials. For Very Good soil, 32 radials may suffice.

+
+ +
+
+ 11. Gain reports for a 1/4 wavelength vertical monopole over 32 radials buried at 5 depths. +
+

The gain figures represent the most interesting facet of the runs. As shown in the graph in Fig. 11, the radial systems at depths of 0.0005 and 0.001 wavelength are even numerically insignificantly different. The question raised by these two runs is whether the maximum 0.01 gain difference over any one soil represents a trend or a mere artifact of rounding. Deepening the radial system to 0.002 through 0.004 wavelength shows that there is indeed a trend. For the depths modeled, the deeper the radial system, the higher the gain.

+

What these runs do not establish is whether there is a maximum depth below which the performance of the monopole would decrease. The rate of gain increase itself decreases as we move from 0.003 to 0.004 wavelength, suggesting that there is indeed a limit. The differences are not artifacts of the changing radius of the portions of the slanting radials that are above ground. This fact was established by modeling the 25-mm monopole using a single vertical wire below ground to the radial junction. The results of model runs with the radials wholly buried and between 0.001 and 0.004 wavelength below ground appear in Table 5. For the thinner monopole, maximum numerical gain reports appear at different depths of the radial field for each soil type, as indicated by the "+" notations in the table. Although the results of these studies do not yield any particular construction recommendations, since the differences are very small, the trends have their own fascination.

+ 
Table 5.  Vertical monopole, top at 40 m, 25 mm diameter; 32 40.96-m (0.25 wavelength)
+radials, 2 mm diameter, tapered with single wire to junction; depth 0.001 wavelength to 0.004
+wavelength, NEC-4.
+
+Depth: 0.001 wavelength, 0.164 m
+Very Poor              -1.61         27                     44.89 + j  7.54
+Poor                   -0.16         25                     43.44 + j  9.55
+Good                    0.86         22                     42.67 + j 10.46
+Very Good               2.79+        17                     40.48 + j 10.03
+
+Depth: 0.002 wavelength, 0.328 m
+Very Poor              -1.29         27                     42.07 + j 12.38
+Poor                   -0.04+        25                     42.48 + j 13.30
+Good                    0.91+        22                     42.36 + j 13.32
+Very Good               2.75         16                     40.87 + j 12.49
+
+Depth: 0.003 wavelength, 0.492 m
+Very Poor              -1.25+        27                     41.98 + j 15.48
+Poor                   -0.04+        25                     42.75 + j 16.20
+Good                    0.89         22                     42.75 + j 16.01
+Very Good               2.70         17                     41.48 + j 14.89
+
+Depth: 0.004 wavelength, 0.656 m
+Very Poor              -1.25+        27                     42.28 + j 18.41
+Poor                   -0.06         25                     43.23 + j 19.00
+Good                    0.85         22                     43.27 + j 18.68
+Very Good               2.62         16                     42.24 + j 17.24
+

Other buried-radial questions abound and are ripe for detailed and systematic modeling. For example, we have examined only 1/4 wavelength radials: other radial lengths have been recommended for various reasons. Moreover, this set of runs was made for 1.83 MHz only. The runs do not tell us what the modeling reports would be for various depths on other amateur bands on which the use of vertical antennas and arrays is common. All of that we shall leave as unfinished business (or, as texts are fond of saying, as exercises for the reader).

+

There are a myriad of other modeling questions associated with verticals that we shall also have to leave unanswered. For example, there is evidence in preliminary models that the required length of phasing line required to establish a maximum rear null in 1/4- wavelength monopole spaced 1/4 wavelength apart will vary somewhat with the soil quality. How this variation itself varies with the size and depth of a radial field remains unanswered. To this question we might also add one about 1/2 wavelength near-ground verticals that are base fed. Preliminary models suggest that only minor changes in performance occur with various types of radial systems beneath the antenna, a result that is at odds with user experiential reports. However, what remains to be developed are models that adequately handle all of the aspects of the antenna system, including the usual source-matching system that places a network between the base of the antenna and the ground.

+

To these questions, we may add any number of others that involve the development of adequate models of various arrays. One final simplification technique remains to be treated: the use of inner and outer ground qualities to simulate a radial system. We shall examine that proposal in the final episode of this series.

+
+ +
+

Updated 07-25-01. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Jul/Aug, 2001), pp. 4-9. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 5

+

Return to Series Index

+

Go to Main Index

+

Topics: Inverted L, MF, Vertical


+ + diff --git a/content/160/160v5.html b/content/160/160v5.html new file mode 100644 index 0000000..3bd5547 --- /dev/null +++ b/content/160/160v5.html @@ -0,0 +1,281 @@ + + + + + + Modeling 160-Meter Vertical Arrays Part 5: The Use of Multiple Ground Qualities in Lieu of Radials + + + +
+

Modeling 160-Meter Vertical Arrays
+ Part 5: The Use of Multiple Ground Qualities in Lieu of Radials

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

The final technique for simplifying the modeling of radials caught me by surprise. It consists of using the facility in NEC that allows 2 ground qualities--a set radius for an inner set of values, and from that point onward, some other values. The reasoning goes that a set of radials in effect improves the ground quality. Therefore, setting the inner radius to the length of the radial system at a high conductivity value, with a lesser value from that point outward, would largely replicate the effect of a radial system without requiring the modeling of radials.

+

Since the practice has some currency in various quarters, it deserves an examination, even if we know in advance that the interaction of buried radial systems is quite different from a simple soil quality improvement. We need to see to what degree the modeling technique yields something useful, even by way of indicators of antenna performance. To this end, let's go back to the very beginning of our work in this series and take a further look at the classic 1/4 wavelength monopole.

+

The 1/4 Wavelength Monopole Over Various Modeled Ground Systems

We have come a long distance from our starting point of looking at 1/4 wavelength monopoles both over radials systems and directly connected to ground with no radials in the model. We have been using the categories of soil quality in Table 1 as our bench marks along the way, having established the relative fairness of the spread of values in Part 2. + 
Table 1.  Soil types used in the study
+
+Soil Type              Conductivity                 Permittivity
+                       Siemans/meter                dielectric constant
+Very Poor              0.001                         5
+Poor                   0.002                        13
+Good (Average)         0.005                        13
+Very Good              0.0303                       20
+ 
Table 2.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001 wavelength
+below ground; NEC-4.
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor              -4.37         27                     87.04 + j 25.31
+Poor                   -2.49         25                     72.45 + j 19.47
+Good                   -0.71         23                     60.96 + j 20.42
+Very Good               2.10         17                     47.34 + j 14.52
+
+8-radials:  56 wires; 110 segments
+Very Poor              -3.11         28                     65.90 + j 18.09
+Poor                   -1.51         25                     58.63 + j 15.18
+Good                   -0.04         23                     52.43 + j 15.94
+Very Good               2.60         17                     44.34 + j 12.60
+
+16-radials:  104 wires; 206 segments
+Very Poor              -1.61         28                     52.71 + j 12.43
+Poor                   -0.16         25                     49.71 + j 12.18
+Good                    0.86         23                     46.79 + j 12.83
+Very Good               2.79         16                     42.20 + j 11.18
+
+32-radials:  200 wires; 398 segments
+Very Poor              -1.32         27                     44.89 + j  7.54
+Poor                    0.17         25                     43.44 + j  9.55
+Good                    1.12         22                     42.67 + j 10.46
+Very Good               2.94         17                     40.48 + j 10.03
+
+64-radials:  392 wires; 782 segments
+Very Poor              -1.19         27                     40.68 + j  4.11
+Poor                    0.32         25                     39.43 + j  7.08
+Good                    1.26         22                     39.73 + j  8.50
+Very Good               3.05         17                     39.06 + j  9.07
+
+128-radials:  776 wires; 1550 segments
+Very Poor              -1.12         28                     38.60 + j  2.18
+Poor                    0.17         25                     37.32 + j  5.29
+Good                    1.03         23                     37.91 + j  6.99
+Very Good               2.87         17                     37.94 + j  8.27
+

Table 2 reviews the modeled values in NEC-4 of a 25-mm diameter monopole over various size radial systems and soil qualities, when the 2-mm diameter radials are buried 0.001 Wavelength below ground (about 6.5" at 1.83 MHz, our test frequency). To consolidate the numbers in a different way, Fig. 1 graphs the gain in dBi of the monopoles, with each line representing a different soil quality and the individual lines tracing the numbers of radials from 4 to 128. The largest differentials appear in the region from 4 to 16 radials and over the poorest soils. We should not neglect the actual numbers for the gain values.

+
+ +
+
+ 1. Gain values for a 1/4 Wavelength monopole over various size buried radial systems and different soil qualities. +
+

Fig. 2 provides comparable curves for the source resistance calculated by NEC-4 for each of the cases graphed for gain in Fig. 1. As we would expect, the highest values of source resistance and the greatest rates of change occur when the radials are few and the soil is less than of Good quality.

+
+ +
+
+ 2. Source resistance values for a 1/4 Wavelength monopole over various size buried radial systems and different soil qualities. +
+

We have also looked at the type of model that uses no radials, but connects the 1/4 Wavelength monopole directly to ground. In earlier examinations, we looked only at the use of the MININEC ground. In Table 3 are values for direct connection to both the MININEC and the Sommerfeld-Norton ground in NEC-4. (The values for a NEC-2 ground may differ, since there is a distinct difference in the treatment of wire approaching and touching ground in the two system. NEC-2 does not permit buried wires, although NEC-4 handles buried wires routinely so long as certain modeling conventions are met.) Fig. 3 graphs the pair of gain curves that result from one soil quality to the next. The NEC-4 S-N curve roughly tracks the values from the 4-radial portion of Table 2. However, the MININEC curve reaches values not achieved by even the 64- and 128-radial portions of Table 2.

+ 
Table 3.  Direct Connection Values:  40-m vertical monopole, 25 mm diameter, direct
+connection to ground (no radials), fed at the lowest segment; NEC-4.
+
+
+Soil Type              Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+A.  MININEC ground
+Perfect                                                     37.08 + j  6.12
+Very Poor              -1.00         27
+Poor                    0.31         25
+Good                    1.41         23
+Very Good               3.16         17
+
+B.  Sommerfeld-Norton ground
+Very Poor              -2.26         27                     49.32 + j  8.11
+Poor                   -0.89         25                     48.78 + j 10.52
+Good                    0.31         22                     47.65 + j 11.48
+Very Good               2.48         17                     43.36 + j 10.21
+
+ +
+
+ 3. Gain values for a 1/4 Wavelength monopole over MININEC and S-N grounds without modeled radials. +
+

The technique that we shall try to compare to these modeled results appears in Fig. 4. We set the monopole touching ground. Beneath the antenna and for a radius of 1/4 Wavelength (40.96 m), we set the soil quality to some higher value. In these tests, we shall use a conductivity of about 0.03 S/m, corresponding to Very Good soil. From that radius outward, we shall use Very Poor soil for the contrast.

+
+ +
+
+ 4. Sketch of a monopole over a dual ground-quality system as a substitute for radials. +
+

Theoretically, NEC calculates the source impedance and currents from the inner radius soil quality, and would do so even had we specified the dividing boundary radius as zero. The far field is calculated using the second or outer ground quality. For the sake of this test, I used EZNEC Pro, which permitted runs using either NEC-2 or NEC-4 and gave access to the MININEC ground as well as to the standard NEC grounds (the high accuracy Sommerfeld-Norton ground calculation system and the "fast" or reflection coefficient calculation system). The results appear in Table 4.

+ 
Table 4.  Direct Connection Values:  40-m vertical monopole, 25 mm diameter, direct
+connection to ground (no radials), fed at the lowest segment; dual ground:  inner to 40.96 m
+Very Good, outer Very Poor.
+
+Ground System          Gain          TO Angle               Source Impedance
+                       dBi           degrees                R +/- J X Ohms
+A.  MININEC Ground
+NEC-4                   3.16         27                     37.08 + j  6.12
+NEC-2                   1.89         29                     37.08 + j  6.12
+
+B.  "Fast" NEC Ground
+NEC-4                   2.12         29                     35.14 + j  5.37
+NEC-2                  -5.07         29                     179.5 - j 163.0
+
+C.  Sommmerfeld-Norton NEC Ground
+NEC-4                   1.21         29                     43.36 + j 10.21
+NEC-2                   0.04         29                     56.79 + j  9.58
The values shown for the NEC-2 ground calculation systems are in the table largely for reference. They are not considered usable by most modeling software experts. Tradition has used the MININEC ground as a basis for simplified modeling. However, the gain figures for both cores using a MININEC ground exceed the highest value of far-field gain found in Table 2 for all but Very Good Soil. Note that the far-field gain is supposed to be a function of the outer soil quality, which was set at Very Poor. As well, the dual ground quality system of modeling does nothing to correct the fact that MININEC ground forces the source impedance to be calculated over perfect ground. At best, the Sommerfeld-Norton ground using NEC-4 yields values of gain and source impedance similar to those for Good soil and 32 buried radials (from Table 2). However, there is a significant difference in the calculated take-off angle for the two models. +

With respect to the simple 1/4 Wavelength monopole, at least, there is nothing in the data calculations to suggest that a dual ground system in any way provides usable data as a substitute for a buried radial system of any size. Since the closest correlation appeared in a NEC-4 S-N run, which presumes that one has NEC-4 at hand, one might as well model the buried radials in the first place.

+

A 2-Element Sloping-Parasitic Vertical Array Test

To determine whether the results for a 1/4 Wavelength monopole, as interpreted, represent a case of excessive finickiness, I went back to a model first examined in Part 3 of this series: a 2-element vertical array in which the reflector is a sloping guy wire. The outline of the array appears in Fig. 5. Both the 25-mm diameter driven element and the 2-mm diameter reflector guy are connected to ground--or to a radial system. +
+ +
+
+ 5. Sketch of the 2-element sloping-reflector array used as a test model. +
+

Because we wish to discover if there is a usable correlation between a dual ground quality system and a buried radial system, I extended the analysis of the array over buried radials. The 1/4 Wavelength length radial systems for the individual elements intersect--how many times being dependent on the number of radials in each system. I used 4, 8, 16, and 32 radials per element, and the resulting radial systems are sketched in Fig. 6.

+
+ +
+
+ 6. Sketches of the 4 levels of intersecting buried radial systems surveyed with the 2-element sloping-reflector array. +
+

The results of the model runs appear in Table 5, which provides values for each of our soil qualities for each level of radial system. Fig. 7 provides curves for the gain values, where each line represents a different size radial system. The curves are unexceptional. We should note that the gain barely reaches 5.3 dBi with 32 radials per element over Very Good soil.

+ 
Table 5.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; intersecting 40.96-m (0.25 wavelength) radial
+system, 2 mm diameter, 0.001 wavelength below ground, uniform segmentation; NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+4 Radials per element
+Very Poor              -3.03         28              5.89                 102.8 + j 53.58
+Poor                   -1.17         26              6.14                 86.89 + j 44.75
+Good                    0.88         23              7.04                 75.31 + j 47.33
+Very Good               4.03         17              8.84                 62.11 + j 46.58
+
+8 Radials per element
+Very Poor              -1.20         29              7.58                 82.12 + j 50.16
+Poor                    0.29         26              7.96                 73.99 + j 45.63
+Good                    1.94         23              8.62                 68.17 + j 47.52
+Very Good               4.54         17              9.73                 59.75 + j 47.78
+
+16 Radials per element
+Very Poor               0.25         29              9.40                 67.75 + j 49.90
+Poor                    1.49         26              9.54                 65.74 + j 48.23
+Good                    2.77         23              9.96                 63.06 + j 48.75
+Very Good               4.95         18             10.54                 57.70 + j 48.95
+
+32 Radials per element
+Very Poor               1.18         29             10.43                 60.03 + j 48.96
+Poor                    2.34         27             10.61                 59.34 + j 49.10
+Good                    3.40         23             11.04                 58.66 + j 49.77
+Very Good               5.29         17             11.26                 55.72 + j 50.06
+
+ +
+
+ 7. Gain values for the 2-element sloping-reflector array over various size buried radial systems and different soil qualities. +
+

Fig. 8 graphs in a similar way the modeled front-to-back ratios achieved by the array variations. The 4-radial-per-element system benefits most from soil quality improvements. However, even over Very Good soil, the model does not achieve an 11.3 dB front-to-back ratio.

+
+ +
+
+ 8. Front-to-back ratio values for the 2-element sloping-reflector array over various size buried radial systems and different soil qualities. +
+

If we use a direct connection to ground and no radials, the calculated numbers derived from NEC diverge from those yielded by the buried radial systems. Table 6 gives the modeling results of placing the two elements alone over the range of available grounds, including the MININEC ground, the "fast" NEC ground, and the S-N ground. Once more, the latter two are for reference and the general advice not to use these grounds for such purposes remains applicable.

+
+ +
+
+ 9. Gain values for the 2-element sloping-reflector array over MININEC, "fast, and S-N grounds without modeled radials. +
+

Fig. 9 graphs the gain values for the three sets of NEC-4 runs. Interestingly, the reflection coefficient ground in NEC-4 correlates very well to the MININEC ground. The S-N ground, when used in NEC-4 provides values that coincide roughly with a 12-radial-per- element system, if one can interpolate fairly from the data in Table 5.

+
+ +
+
+ 10. Front-to-back ratio values for the 2-element sloping-reflector array over MININEC, "fast, and S-N grounds without modeled radials. +
+

The correspondence in gain figures between the MININEC ground and the "fast" ground in NEC-4 disappears if we move to the front-to-back column. See Fig. 10. Although the "fast" ground curve is roughly congruent with the MININEC curve, the "fast" ground values are 5 dB lower. The S-N ground curve is much shallower, but the values are high, even when compared to the front-to-back values for the 32-radial-per-element buried radial system model.

+ 
Table 6.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; direct connection to ground (no radials); NEC-4.
+
+Soil Type              Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+A.  MININEC ground
+Very Poor               2.00         30             11.36                 40.19 + j 53.02*
+Poor                    3.34         26             14.25                 *MININEC
+Impedance
+Good                    4.62         24             17.11                 is over perfect
+Very Good               6.36         18             19.50                 ground.
+
+B.  "Fast" NEC Ground
+Very Poor               2.27         28              6.37                 50.40 + j 29.73
+Poor                    3.50         26              8.63                 50.14 + j 36.48
+Good                    4.67         23             10.82                 51.25 + j 42.49
+Very Good               6.35         18             14.66                 46.64 + j 49.99
+
+C.  Sommmerfeld-Norton NEC Ground
+Very Poor              -0.63         29             10.31                 69.16 + j 38.46
+Poor                    0.85         26             10.78                 65.61 + j 42.24
+Good                    2.35         23             11.81                 62.44 + j 45.83
+Very Good               4.82         18             13.44                 53.33 + j 48.39
+
+Note:  Use of NEC-2 and the S-N ground will yield reports that differ considerably from the
+values produced by NEC-4.  The following listing is simply to display the differential:
+
+D.  Sommmerfeld-Norton NEC Ground--NEC-2
+Very Poor              -11.0         28              0.58                 342.3 - j 169.9
+Poor                   -7.06         26              1.46                 180.3 - j 77.60
+Good                   -3.60         23              3.55                 122.5 + j  4.20
+Very Good               2.94         18             10.16                 61.57 + j 38.79
+

Table 6 provides S-N ground data for NEC-2, the version used by most hams. Once more, there is a very large difference in the values reported from yielded by NEC-4 under identical modeling parameter conditions. The values would hardly be useful as anything but artifacts. However, the remaining numbers in Table 6 have equally misleading data values and should also be set aside if one is modeling a buried radial system attached to the array in question.

+

The final step in our test is whether using a dual soil-quality system fairs any better than the simple MININEC ground. To examine this question, I altered the model to include Very Good ground under the antenna and Very Poor ground at a distance. Since the model involves radial systems that intersect, with about 1/8 Wavelength between element bases, I chose a radius of 3/8 Wavelength for the inner ground quality (61.43 m at 1.83 MHz). The results of the modeling appear in Table 7.

+ 
Table 7.  2-element parasitic array:  driver = 40-m vertical monopole, 25 mm diameter;
+reflector = sloping 2-mm guy, 40.4 m long; direct connection to ground (no radials), fed at the
+lowest segment; dual ground:  inner to 61.43 m (3/8 Wavelength from array center line) Very Good,
+outer Very Poor.
+
+Ground System          Gain          TO Angle       Front-to Back         Source Impedance
+                       dBi           degrees        Ratio dB              R +/- J X Ohms
+
+A.  MININEC Ground
+NEC-4                   6.36         18             19.50                 40.19 + j 53.02
+NEC-2                   6.82         11             18.58                 40.21 + j 53.02
+
+B.  "Fast" NEC Ground
+NEC-4                   6.03         25             14.43                 46.64 + j 49.99
+NEC-2                         No usable values
+
+C.  Sommmerfeld-Norton NEC Ground
+NEC-4                   4.45         25             14.04                 53.33 + j 48.39
+NEC-2                   3.51         11              9.58                 61.57 + j 38.79
Using the normal MININEC ground for the exercise produced excessively high values of gain and front-to-back ratio relative to the buried-radial models--in both NEC-4 and NEC-2. As well, NEC-2 depressed the TO angle by 7 degrees relative to any other report. Although the "fast" and S-N numbers are provided, once more they are no more than reference reports. The end result, however, is that the dual-ground system provides no usable data or even indicators of data for the array in question. +

Conclusion

+

As expected, the dual-ground modeling technique can be as misleading as any other substitute for a direct and detailed model of a buried radial system. The calculations for the way in which radials intersect with a given soil quality when buried is quite different from the calculations for the soil alone. As a result, a radial system is not equivalent with respect to antenna performance to a simple improvement of the soil quality.

+

Thinking of a radial system as an improvement in soil quality may have some utility when the concern is the overall RF ground for a station and its antenna(s). However, that mode of thought can be highly misleading when it comes to calculations that yield potential antenna performance figures. We have looked in review at the results for the standard techniques of simplifying models by placing them without radials over a MININEC ground, and the result is simply that both systems of simplification are equally but separately misleading. The only type of modeling that seems adequate to a buried radial system is a buried radial model. Any suggested simplification would require that we first test the simplified model against a full model with all buried radials modeled. If a reliable correlation appears--and it might, as illustrated in Part 4--then we can use the simplification. However, once we have the full model, the rationale for simplifying seems largely to disappear.

+

As one step in the direction of developing more adequate models of vertical antennas and arrays for 160 meters (or any other band, for that matter), this series has tried to set forth some basics of the varied results that different kinds of models produce, as well as to give some perspective on the divergence in reports yielded by the range of ground qualities that we can model. If any theme emerges from these notes, it should be this: to the degree possible, let us model accurately and without shortcut every possible aspect of a 160-meter vertical antenna or array and begin from the ground up.

+
+ +
+

Updated 09-25-01. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Sep/Oct, 2001), pp. 4-9. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Series Index

+

Go to Main Index

+

Topics: MF, Vertical


+ + diff --git a/content/a10/ant1.html b/content/a10/ant1.html new file mode 100644 index 0000000..3baff7b --- /dev/null +++ b/content/a10/ant1.html @@ -0,0 +1,65 @@ + + + + + dB, dBi, and dBd + + + +
+

No. 1: dB, dBi, and dBd

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

A most convenient way to compare power is as a ratio between two powers. For this purpose, we have the decibel or dB. One dB = 10 log (P1/P2), where P1 and P2 are any two powers it is relevant to compare. A power ratio of 2 is 3 dB; a ratio of 4 is 6 dB; a ratio of 10 is 10 dB. These marker points will guide you to intermediate values. Your transceiver output is 100 watts. Your linear output is 800 watts. Hence, your power gain is 9 dB to the antenna.

+

Antennas measure their power gain in the favored direction in dB. Since gain requires 2 powers to make the ratio, where does the second power come from? It comes from a standard reference. For most theoretical studies, the most common reference is dBi, decibels over an isotropic radiator. An isotropic radiator is a geometric point in free space with no material losses that radiates equally well in all directions. My rotatable aluminum backyard dipole at 35 feet over soils with average losses has a gain of over 7.5 dBi.

+

A second standard is dBd, decibels over a dipole in free space made of lossless infinitely thin wire. This theoretic dipole has a gain of 2.15 dBi. Hence, my backyard real dipole has a gain of over 5.35 dBd.

+

For many, if not most of the decisions you will make about antennas, neither dBi nor dBd are the real references. Suppose you wish to buy a 3- element monoband Yagi for 10. What improvement can you really expect over your dipole? Now your own antenna--an aluminum tube (with losses) antenna at a certain height over soil (with certain losses)--becomes the standard. Unfortunately, manufacturers do not rate their antennas by testing them on your mast in your yard. How can you use your knowledge of dBi and dBd to estimate the improvement the prospective antenna will make?

+

One way is to make antenna comparisons theoretically and extrapolate to your yard. Table 1 shows the gain figures for 3 antennas: a pretty good 3-element Yagi, a pretty good 2-element Yagi, and a dipole, all in free space. The 2-element Yagi has a forward gain of about 4.3 dB over the dipole, while the 3-element Yagi adds another 1.8 dB, for a total of 6.1 dB over the dipole. In the favored direction and in front-to-back ratio for nulling out QRM, you can expect similar performance from equivalent antennas mounted at the same height over the same terrain.

+ 
Table 1:  Relative Antenna Gain using dBi and dBd and Antennas in Free
+Space
+Antenna        Gain           Gain over      Gain over
+               in dBi         dipole         2-element
+                                             Yagi
+Dipole          2.1           ----           ----
+2-element Yagi  6.4           4.3 dB         ----
+3-element Yagi  8.2           6.1 dB         1.8 dB
+
+Antenna        Gain           Gain over      Gain over
+               in dBd         dipole         2-element
+                                             Yagi
+Real Dipole     0.0           ----           ----
+2-element Yagi  4.3           4.3 dB         ----
+3-element Yagi  6.1           6.1 dB         1.8 dB
+
+

Do not expect much more improvement than this, even if a manufacturer cites much higher numbers. The beams in this example can be tweaked for a little more gain or a little more front-to-back ratio, but not much and not both at once. And the ability of the antenna to hold its gain and front-to-back ratio over the entire 10-meter band will suffer.

+

As you might expect, it does not matter whether you make the gain comparison starting with figures in dBi or figures in dBd. You will get the same result. The only requirement is that you use the same reference for all your comparison calculations.

+

Since we started with a dipole, the charts seem to prefer dBd. That is an illusion, since we might have as easily started with a quarter-wave vertical, a 2-element Yagi (as column 3 shows), or ZL-Special. Moreover, had we placed the models over real ground, the gain numbers would have been intrinsically higher, beginning with a dipole gain of over 7.5 dBi or 5.4 dBd, but the differences would have been very similar.

+

Fig. 1 shows the free space azimuth patterns for the three antennas. Their relative proportions are identical no matter whether they start with dBi or dBd.

+
+ +
+

The relative gain of the 2-element Yagi over the dipole is evident, as is the relative gain of the 3-element Yagi over the dipole and the 2-element Yagi. That is what is crucial to know.
+

+
+ +

+
+

Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
+
+
+ + diff --git a/content/a10/ant10.html b/content/a10/ant10.html new file mode 100644 index 0000000..cd2369f --- /dev/null +++ b/content/a10/ant10.html @@ -0,0 +1,59 @@ + + + + + Notes on 10-Meter Antenna Tuners + + + +
+

No. 10 Notes on 10-Meter Antenna Tuners

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

There are many excellent antenna tuners (ATUs) on the market that will match at 80 or 160 meters. On 10, the match may be more of an illusion than an effective reality with some designs. If you are a dyed-in-the- wool 10-meter operator and use an antenna system that calls for an antenna tuner, you may be better off building your own.

+

So what is wrong with the commercial tuners? (Remember, not all of them are wrong. Compare the points made here with the features you see when you think about buying one.) A number of things go wrong in designs aimed at covering 160-10 meters.

+

1. The basic design: Most ATUs use a T-network with series capacitors and a shunt inductor, as schematically shown in Figure 1.

+
+ +
Figure 1. Typical Series-C T circuit. +

This design is a high-pass filter and provides little, if any, suppression of harmonic energy. One can argue that we should not rely on the ATU to do the job our rig's output circuitry should be doing. That argument is sound, but if there is a design that will also provide some harmonic energy suppression, it may be preferable. Two designs fill the bill.

+
+ +
Figure 2. Typical PI network. +

Figure 2 shows a PI network with shunt capacitors and a series inductor. It is inherently a low-pass filter.

+
+ +
Figure 3. Typical Series-L T circuit. +

The circuit in Figure 3 is also a high-pass filter: it is a T-circuit with series inductors and a shunt capacitor.

+

The reasons for using a series-C T are cost and size. The components for it are smaller for a given power level, since we can fit a 20+ microH coil (rotary or tapped) alongside a pair of 250 pF variable capacitors in a compact case. By contrast, the inductors for the other circuits may require up to and over 30 microH, and the capacitor for the series-L T may need values up to 1000 pF. That is, if you want to tune 80 or 160.

+

If you only want 10 meters, then the values drop. A 5 microH inductor (or 2) and a 250 pF air variable (or 2) give all the range anyone should need for 10.

+

2. Tapped inductors: A tapped inductor may do the job you require, but for some antenna situations, you may not be able to find the 1:1 SWR point. That is not fatal if you can find a point under 2:1. However, a good rotary inductor (or 2 in the series-L T circuit) is superior, since there is no required setting that is unavailable to you. You can find some good near bargains in rotary inductors at hamfests. The same applies to capacitors.

+

3. High-value components: The higher the highest value of a capacitor or coil, the higher the lowest value. The large frames of high-value rotary inductors may limit the lowest value to well over 1 microH. Capacitors are even worse, because the high maximum value does not tell the whole story. Usually, capacitors follow the rule, but you also have to watch out for construction. I have an old military capacitor with a maximum value of 35 pF. Unfortunately, its lowest value is 17 pF. It is built within a set of frame plates that surround the stators and limit how low it can go. By contrast, a 100 pF old E. F. Johnson capacitor in one of my units has a minimum value of about 10 pF. Its supporting metal work consists of two small plates on either end of the unit. If you roll your own, look for the capacitor's minimum value as well as its maximum value.

+

4. Closed tight cases: On ten meters, some commercial ATUs achieve a match more with stray capacitance and inductance than with the higher Q variable components that are supposed to do the work. Steel cases that cut the inductive fields of coils and provide several pF of shunt capacitance to the other components complicate and usually hinder the basic work of the matching network. A spacious case, however much against the grain of today's stylistic fetish of ultacompactness, is a plus for an ATU.

+

5. Poor ground paths: Ideally, there should be one good ground point for the ATU network. With large components, this condition is often impossible to attain. However, grounding should be as direct and compact as possible--and as near to the ground lugs of the coax sockets as possible. It should not rely on the bite of a lock washer through a painted surface. A rivet used as a ground connector is a prelude to malfunction. There are no shortcuts to good, short, wide ground paths and good mechanical and electrical connections. They are not expensive, but they do take care.

+

This list of difficulties is not an indictment of all ATUs. Many units have taken the trouble to be the best they can be as 80 or 160 through 10 meter units. However, you can probably do better yourself. For 10 (or realistically, 10-20 meters), a PI or series-L T circuit is achievable with parts you can obtain from hamfests. A PI might use a 5 to 10 microH inductor with a pair of 250 pF air variable capacitors of good power rating. A series-L T circuit might use a pair of 5 or 10 microH rotary inductors and a couple of 250 or 300 pF variable capacitors, with a switch to bring them into play either one or both at a time. A surplus or home brew case with plenty of room helps ensure that strays are minimized, as do well-planned ground paths. Consider a plexiglass case for the ultimate in avoidance of strays.

+

Remember, multiband is not always the most efficient, even if it is the most compact. The bands that take the beating are the ones at the high and low ends of the multiband range. Ten meters, unfortunately, is one of those ends. Hence, if you use a 10-meter antenna system calling for an ATU, consider building yourself a customized unit with all the advantages and none of the difficulties.
+

+
+ +

+
+

Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
+
+
+ + diff --git a/content/a10/ant10a1.gif b/content/a10/ant10a1.gif new file mode 100644 index 0000000..0d8a191 Binary files /dev/null and b/content/a10/ant10a1.gif differ diff --git a/content/a10/ant10a2.gif b/content/a10/ant10a2.gif new file mode 100644 index 0000000..c072247 Binary files /dev/null and b/content/a10/ant10a2.gif differ diff --git a/content/a10/ant10a3.gif b/content/a10/ant10a3.gif new file mode 100644 index 0000000..bbe3f9a Binary files /dev/null and b/content/a10/ant10a3.gif differ diff --git a/content/a10/ant11.html b/content/a10/ant11.html new file mode 100644 index 0000000..b456a25 --- /dev/null +++ b/content/a10/ant11.html @@ -0,0 +1,68 @@ + + + + + Mobile Antennas for 10 Meters + + + +
+

No. 11 Mobile Antennas for 10 Meters

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

I was asked to do a column on mobiles. While I claim no serious expertise on mobile antennas, there are some ideas worth considering, some information worth getting, and some safety thoughts worth taking very seriously.

+
+

Mobile in motion

+
Inherently, a mobile-in-motion antenna system, consisting typically of a shortened, loaded vertical antenna, is a very lossy system. Most of your power goes nowhere. However, do not let that discourage you, since some truly amazing hamming has been done mobile. Let the problem be your challenge. How can you minimize the losses? +

The first step is to ensure that a mobile rig in your car will not do bad things to your car's computer and equally bad things to your car's warranty. ARRL has published some contacts with automakers and distributors where you can get some (but probably not all) of the answers.

+

The second step is to prepare your car for a mobile antenna system. This involves close attention to power cabling, ground cabling, and decoupling RF from the battery and other auto electrical components. Use coax that can handle the automobile's hot and cold and greasy and dirty environment. Avoid foam insulated coax cables, as well as those like RG-8 and RG-58 with older types of jackets. RG-213 generally meets the needs of the mobile environment. The very best book I know of on the subject of mobiling is Don Johnson's (W6AAQ) 40+5 Years of HF Mobiling, which is from World Radio. Please do not just slap a rig in the car, mount an antenna on the roof, trunk lip, or plastic bumper, and try operating. Read Don's advise and carefully prepare your vehicle for a mobile set-up.

+

The third step is choosing an antenna. According to various sources, the bugcatchers (either Texas or California style) and the DKs (antennas that follow Don Johnson's design) appear to do the most consistent job across the ham bands. However, for 10, you can consider the Hamstick types or even an old fashioned quarter-wave whip with no loading.

+

Mounting brackets come in every conceivable size and shape. Brackets used by truckers for CB antennas will attach the antenna almost anywhere on the vehicle. The big question is this: where?

+

Since the vehicle serves as a ground plane for most mobile antennas, the best place is in the middle of the roof, which is often a bad place physically. The antenna hits every overpass (until it breaks, of course), and you have to put a hole in your new $15,000 to $30,000 car, an act to which warranty servers may not take kindly, especially if you lease your car.

+

Since trunks are making a comeback after a decade of hatchbacks, the trunk lip is a possibility. However, do not rely on the set screws of the trunk lip mount for a ground to vehicle metal. Add a short, wide strap from the ground of the base to a good bolt in the car metal.

+

Increasingly, you can find a metal bumper only on trucks and vans. However secure, the antenna base, where the highest current resides and creates the most intense part of the radiation field, is very close to ground without much of a ground plane below it.

+

Trucks and vans are becoming more popular as wheels for mobiles, and folks seem less fearful about making holes in them. Side-mounting mobile antennas well up the van wall or cab side is considered an acceptable alternative to roof mounting, and it lowers the tip of the antenna by a foot or so. Bumpers are strong on many of these vehicles: consider a sturdy extension to the antenna base to raise the entire assembly.

+

Once everything is in place, including the rig, do not just hit the road chatting away. If you have not watched a weaving car with a cellular phone in the driver's hands, you have not been paying attention. While some ham-drivers can learn to drive and talk and twiddle knobs all at once, many others are high-speed unguided missiles. Unless you are certain that you are safe, let your passenger do the operating. I learned that the semi-hard way--from a close call rather than from an accident. It was inches from being the other way around.

+
+

Mobile not in motion

+
The safest way for the driver to operate mobile is to stop the vehicle and operate a while. Here, the driver can select a potentially good site to maximize radiation in useful directions, as well as operate safely. Parking lots, open fields, and hilltops are all likely operating points. +

Once you stop your car, you should instantly realize that your antenna options increase dramatically. You can take a modified mag mount CB antenna, resonated for 10, and slap it on top of the vehicle so you can monitor the band while you assemble and raise some kind of antenna less dependent on the car for its ground plane.

+

With careful planning, you can create a dipole or a 2-element beam that breaks down into sections that store within the trunk or a similar storage space. A little tool kit with pliers, screwdrivers, and nut drivers can have a permanent place in the trunk. Here are a few tips for such antennas:

+
    +
  • 1. Avoid sheet metal screws as element length connectors. Their holes will wear out just when the band opens to Asia. Use hose clamps with a nut driver (usually faster and more sure-footed than a screwdriver).
    • +
  • 2. Protect the elements and the center connectors when not in use. A cheap golf-club bag (are there any such things any more?) or something similar is a good protective carrier.
    • +
  • 3. Store any loose hardware in a bag with a seal inside a plastic box with a clasp. Finding all but one absolutely necessary screw is Murphy's favorite joke on you. Better yet, have no loose hardware--keep it attached to one or the other of the pieces separated for storage. Then, keep a few EXTRA pieces in that bag in a box.
    • +
  • 4. Keep the antenna sturdy enough to store well, but as light as possible for easy assembly and raising. Remember, the antenna does not have to withstand gale-force winds in this application. Smaller diameter, thinner wall tubing will do a good job and prevent back pain.
    • +
+

The mast can be as simple as 4 5' sections of TV mast. There are also a number of extendable aluminum poles, most never intended as masts, that will support a light antenna in very small breezes. The search for the perfect stationary-mobile mast is endless.

+

Guying the mast, even for a brief stop is a good safety measure. One workable system requires a little 3/16 or 1/4 inch rope and a single concrete block. The mast slips into one of the block's holes, which generally is enough to prevent the end from skidding. A side bracket attached both to the door frame (of a car and perhaps the side rail of a pickup) holds the mast a few feet up. The guy ropes go from near the top of the mast to the other side of the car and are tied to the fore and aft bumper frames with a slight tension that holds the mast in place, but still lets you turn it.

+

You can also make up a tubular bracket a few feet long and attach it firmly to a pickup's rear bumper. The mast slides into it and is self-supporting.

+

Most studies show that over flat land, low horizontal antennas do best at a 5/8 wavelength height, which is just about 20' on 10 meters. Although the take-off angle is high (above 20 degrees ordinarily), short skip operation is quite good, and dx is often only about 2 S-units down from elevations above 1 wavelength (35'). Even though the take-off angle decreases with each increment in antenna height, try to avoid heights between 3/4 and 7/8 wavelength, since ground reflections tend to cancel some of the radiation in the lowest lobe, which is the most useful lobe for skip. If the land is not flat, diffraction effects can wash out some of these phenomena.

+

However, a 20' mast is the most many hams can handle mechanically in the field. Those who can get above 30' up need to ensure both personal safety and the safety of passengers. Not to mention saving that big wheeled investment from damage by a $10 homebrew antenna.

+

Of course, nothing says you cannot use a well-installed regular mobile antenna. When the band is open, antenna efficiency only makes a difference in pileups (station pileups, not vehicle pileups).

+

This style of mobile operation is more leisurely than mobile on the fly. It is also safer for everyone.

+

Drive safely. The life you save may be mine.
+

+
+ +

+
+

Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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No. 12 Multiband vs. 10-Meter Dipoles

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L. B. Cebik, W4RNL

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If we had unlimited money and space, we could ask the following question sensibly: What is the best 10-meter antenna? The answer might be about 4 stacked long-boom, many-element Yagis from about 70' on up on a rotatable tower on a one-hill island surrounded by ocean. Even that answer might get an argument. However, for most of us, the simple question of what the best 10-meter antenna might be is an exercise in irrelevancy.

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A more sensible question is usually this one: which of two alternatives is the better antenna? Each alternative might fit our yard and bank account. However, no general answer is possible. Even if one antenna does outperform another, there are always a number of other factors that affect the final decision. Can I maintain this antenna? What will my neighbors say when they see it? Is it compatible with the rose garden?

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With those qualifications in mind, let's compare two antennas on performance alone just because people have asked a certain question: which is better: a multiband wire antenna like a G5RV or a center-fed Zepp on the one hand, or a dipole cut for 10 meters on the other hand? And let's presume you have the room and supports for both antennas to make this a real comparison.

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If you like to work all of the HF ham bands and are limited to a single antenna, then the multiband wire is certainly an antenna to consider. An "80-meter" 135' center-fed Zepp, a G5RV 102' dipole, and a "40-meter" 67' center-fed Zepp are all long doublets, center-fed with parallel transmission lines and differ only in length. All require an antenna tuner, although some antennas show a low impedance on some bands. The 135' Zepp obviously works better on 80, although the 102' center-fed antenna does quite well there, and all three antennas can show respectable performance from 40-10.

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In fact, some folks praise these longer antennas because they show some gain over a 10-meter dipole on 10-10's favorite band. Unfortunately, that kind of claim is like preferring $10 bills over $5 dollar bills. I'll take the $5s if you give me enough more of them than the $10s. The bill size is not relevant until you know how many of each are at stake.

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When comparing any of the longer multiband wires with a 10-meter dipole, the extra gain is not relevant until we answer the question of where it goes and, equally, where it does not go. A lot of variables go into the answer to the "where" question, but we can give a glimpse into the answer with Figures 1, 2, and 3. Each shows the azimuth pattern of 3 antennas (2 dipoles and one multiband antenna) modeled at a height of 35' (a typical amateur backyard installation) over real ground at a 14-degree angle of maximum radiation at 28.5 MHz.

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Think of these patterns as looking down on the antenna from overhead. The dipoles are the simple figure-8 double loops. For the loops reaching out to 0 and 180 degrees, the antenna runs up and down the page through the center of the diagram. For the loops reaching maximum at the top and bottom of the diagram, the antenna runs left and right across the page. Each multiband antenna also runs left and right across the page.

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Figure 1 shows the 135' Zepp. It has four lobes that exceed the dipole limit by a good bit. However, notice how narrow they are. Notice also the nulls in the pattern. with some careful planning and some good luck in where your yard trees go, you might align the antenna so that one or more of the lobes points right where you find the stations you like to work most. Then again, you might end up aligning the antenna so that nulls point at your second and third favorite spots.

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Figure 2 shows the dipoles with a G5RV. Again, there are higher-gain narrow lobes, but aimed more at the 45-degree point on the pattern. The shorter antenna creates fewer lobes. Again, you might use this information to hit one or more of your targets, and possibly miss a few desirable targets.

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Figure 3 shows the same data for the 67' Zepp, about the length of a 40-meter dipole. There are only 4 lobes for this shorter antenna, but, of course, 4 nulls as well.

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Each of these antennas has its place in some ham's yard, especially for working the lower HF bands (and each antenna will show a different pattern on each band). But is any really significantly better than a dipole on 10 meters? Gain is nice, but those nulls can drive you crazy.

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Well, the dipole also has nulls off each side, so it too is limited. However, with an overall length of between 16' and 16.5' (depending on the element diameter), it is not too difficult to put up a rotatable dipole. You can hand-rotate the antenna mast or use a TV rotator. Then the nulls disappear. More correctly, they go where you put them, as you broadside the antenna to the desired signal. Hence, you only have to rotate a dipole less than 180 degrees to get full 360-degree coverage.

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A stack of TV masting with a house clamp only roughly tight or guys in guy rings would permit you to hand turn the mast. You can attach a short level rod to the mast to make turning easier. Except in odd late afternoon shorter skip conditions, where signals seem to come from every direction, you will likely only have to change the antenna's orientation every few hours.

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Am I "pushing" the rotatable dipole? Not really. Part of my point is that gain is not everything, especially if it does not point anywhere useful. Part of my point is that pointing is more simply done on 10 meters than many people believe, especially if they only look at monster 20-meter beams. Part of my point is that a multiband wire antenna is a very useful antenna for working all the bands. And part of my point is that, with a little ingenuity, a 10-meter dipole can do a lot of useful work for us without being unduly noticeable or expensive. Even if you already have that long wire, you might also consider adding a rotatable dipole to the antenna "farm." Now, if it is simple enough, you might even take it apart, toss it in the truck or trunk, and go portable with it--and put it back up when you get home.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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No. 14 EDZs: Stacked and Unstacked

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L. B. Cebik, W4RNL

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After an article on EDZs (extended double Zepps) appeared in Communications Quarterly in Fall, 1995 (link), I received some mail and phone calls on a version of the antenna I had not covered. So I thought I would bring it to your attention. The EDZ is a good fixed wire antenna for those who do not wish to fool with towers and rotators, but do wish to work some DX when the band fully reopens. It helps to have high trees or other tall poles to support the ends, and you have to like ATUs (antenna tuning units or transmatches). Even if you do not like these things, read on--they can grow on you.

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The Basic EDZ

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The basic EDZ is a 1.25 wavelength wire antenna fed at the center. Unlike a dipole, precision wire cutting is not required. A 10-meter EDZ needs about 44 feet of copper wire. The feedpoint impedance will be about 130 ohms with about 680 ohms of capacitive reactance. I recommend you use 450-ohm parallel feedline to an ATU. Although you can match the EDZ to 50- ohm coax at the antenna feedpoint, you would lose the ability to use the antenna on other bands. For every band 20-meters and up, the antenna is longer than a dipole and thus shows a little gain above a dipole. +

At 10-meters, an EDZ up 40' in the air shows about 3.5 dB gain over a dipole. Of course, both antennas are bidirectional. The EDZ gets its gain by shrinking the side-to-side beamwidth of its two main lobes. The dipole has a half-power beamwidth of about 78° while the EDZ cuts that to about 30° with two small side lobes in each direction. See Figure 1

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Some folks view the sidelobes as QRM producers. If you agree, see the ARRL Antenna Compendium, Vol. 4 for an EDZ with capacitors in the elements to eliminate them. However, you may lose some performance of the antenna on other bands.

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Almost any wire antenna for 10 up in the air 40' has a take-off angle of 12° above the horizon. Take-off angle means the elevation of the lobe with the most power in it. The half-power points are ±6° around that angle, so there is plenty of power in the low angles needed for efficient DXing. But perhaps we can do a little better.

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Stacked EDZs

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Stacking any two antennas will do two important things for you: 1. It will increase the system gain a bit and 2. it will lower the take-off angle a bit. Both those advantages are DXer delights. So let's get crackin' and stackin'. The system I shall show you derives from an article in the November, 1968, CQ by John Schultz, W2EEY called "The Expanded Lazy-H Antenna." (My thanks to Henry Pollock, WB4HFL, for sending me a copy of the article.) +

A vertical spacing of 5/8ths of a wavelength is about the most efficient gain producer when stacking antennas. This applies to Yagis and other arrays as well as EDZs. At 10 meters, this means a spacing of about 22' or so. Again, this number is not critical ±a foot. Figure 2 shows the general scheme. Assuming you have the side supports, there are only a few questions to ask about stacked EDZs.

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1. What do I get for my trouble? First, you get 3 to 4 dB additional gain in both directions, depending upon which wire you set at the 40' level, where we placed our one-wire EDZ. If you can put the second wire at about 60' or so, you will get the higher gain, plus a lower take-off angle of 9°. That puts the bulk of your power in the 10-meter far-DX zone. Figure 3 also shows a secondary lobe at about 28° for shorter paths. If you place the lower wire at about 20' up, you will get the lower gain and a basic take-off angle of 14°. That is still worth while.

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2. How do I aim single and stacked EDZs? With care, since they are fixed. In much of the US, the NE-SW corridor gets you both Europe and VK- ZL-land. Or you can broadside N-S for South America and over-the-pole and back scatter. Or, you can broadside to Asia. Finally, if you have lots of trees or poles, you can build 3 EDZ stacks and switch among them (a nice wiry dream).

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3. How do I feed the beast? The easiest feed system is to run 450- ohm parallel feeders from each feedpoint to a common center. At that point, you will see something like 75 ohms resistive and about 460 ohms inductive impedance. This situation gives us a choice.

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a. If you wish to use the antenna on 10 meters only, you can insert on each side of the line junction a 24 pF capacitor. This is a series connection on each side, with the ends then connected to each side of a coax connector. The capacitors cancel out the inductive reactance, leaving only about the same mismatch you would get with a dipole--and that's manageable.

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b. If you wish to use the antenna on all bands from 20 meters on up, just connect more 450-ohm parallel feeder and bring it to the shack and ATU. On 20 you will get dipole gain or better, with more gain on the other bands between 20 and 10.

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4. What does it cost? Well, #14 wire runs about 7 to 12 cents a foot, depending on its nature, and 88' of wire is in the $8.00 range. Add some insulators and rope for supports. Then add the 450-ohm parallel feeder, which is cheaper than coax. Even if you have to erect some supports (4 sections of 10' TV mast per side, plus rope guys and tie-down ring-screws in the ground), you might run the bill to $75 to $100. That will barely buy the TV rotator, let along the tower and very light beam that goes with it.

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Note that, as in all antenna work, we must compromise. The stacked EDZ requires supports and fixes your general directions to two, but saves you many dollars, pounds, yen, francs, marks, or lire. The long Yagi with the same gain gives you freedom of direction, but empties your pockets and requires constant maintenance. (Remember, Murphy's law says that when the rotator goes bad, it is always stuck in a direction with no hams in sight.) So the EDZ and the stacked EDZ array are suitable only for some people. But perhaps you are one of them.
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Updated 4-23-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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No. 15 Coax: The Short Story

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L. B. Cebik, W4RNL

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One good way to think about antennas is as a system: the antenna system. The antenna system consists of all components that get power from the rig (or, on reception, to the rig) into the transducer (that is the antenna proper) that converts the electrical energy (the energy that shocks) into electro-magnetic radiation (the energy form that lets your signal bounce off the ionosphere to all that good DX). Some of those components are inside your rig: the filtering and impedance matching components that establish a 50-ohm impedance at the coax connector.

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The remainder of the components are external: the antenna proper, the transmission line, the transmatch or antenna tuning unit (2 names for the same item, and it may also be in your rig's case), and any matching components at the antenna terminals (such as a beta or gamma match for a Yagi). All of these have to be working well to ensure maximum efficiency of energy conversion into RF radiation.

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The weak link in the system is often the transmission line, and just because it is a simple, no-adjustment component. It does not start off as the weak link: it just gets that way because we ignore it. Most 10-10ers use coax to feed their antennas, so let's confine our discussion to coaxial cables as transmission lines.

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Some Coax Basics

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Everyone knows what coax looks like. There is a center wire, which may be solid or stranded. Surrounding the center wire is some insulating material: it may be a solid, translucent plastic or a white softer foam. Around the insulation is a layer of conductors: these may be a mesh or braid of copper, or in recent cables, the conductor may consist of a foil with a mesh around it. Over these layers is a coating--usually a black jacket on ham wires, but sometimes gray or even white for special purpose cables. +

For the moment, forget the outer cover. The center wire, the insulating material, and the wire mesh that determine the characteristics of the cable as a transmission line. We can be a little more precise by remembering that alternating currents at HF frequencies travel at the surface of the wires. Hence, we are concerned with the outer surface of the center wire and the inner surface of the wire mesh: these two surfaces determine what the characteristic impedance of the cable will be. Of course, most of us use 50-ohm cables. Since getting a 50-ohm impedance depends on the ratio of the diameter of the center wire and the circle made by the wire mesh, we can make many different sizes of 50-ohm coax.

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Here is a table of the most common 50-ohm coaxial cables we hams use:

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Cable #         Outer        50 MHz         Maximum      Velocity
+                Diameter*    Loss**         Voltage***   Factor****
+RG-174           0.1"        5.7 dB          1100         .66
+RG-58            0.195"      3.1 dB          1400         .66
+RG-58 Foam       0.195"      3.3 dB          1400         .79
+RG-8X Foam       0.242"      2.1 dB          2000         .75
+RG-213           0.405"      1.3 dB          3700         .66
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* Outer diameter includes insulating jacket.
+ ** Losses at 10 meters will be about 2/3rds this figure; losses are approximate and vary somewhat from one listing to another.
+ *** Maximum operating voltages (rms) also vary from one list to another.
+ **** Velocity factors on foam cables vary from one listing to another.

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What can we learn from the table? Actually, several things.

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1. The fatter the cable, the lower the losses in the cable. So, use the fattest cable you can afford and handle in your situation.

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2. The fatter the cable, the higher the power handling capability (as roughly indicated by the operating voltage). So if you use an amplifier, use RG-213 or better.

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3. The outer diameter of the cable determines what coax connectors to use. RG-213 requires regular PL-259 plugs. RG-8X, being the same size as RG-59 (a 70-ohm cable) requires UG-176 adapters. RG-58 requires a UG-175 adaptor. Do NOT forget the adapters for the smaller cables: they relieve stress on the wires for longer-lasting connections.

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4. The velocity factors tell us how long a cable wavelength is relative to that same wavelength in free space. The cables with solid insulation will be an electrical wavelength long at only 2/3rds the length of the wave in free space. Notice that the foam insulations have higher velocity factors than the solid insulation types. For all foam and for cables with new numbers, be sure to check the velocity factor just in case you have to make up a cable that is a specific fraction of a wavelength long.

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In addition to these basic cables, there are a number of new cables. Beldon and others make a very low-loss version of RG-213 under company stock numbers. It is for VHF or for very long (100' +) runs of coax. And it costs more. There are also marine cables with jackets that resist sun, salt water, acids in the air, and almost any other contaminant. They also cost more.

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What Cable to Use

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Determining the best cable for an application is a combination of cable characteristics and practical realities. While no absolute rules are possible, here are some scenarios and recommendations. +

1. Mobile or portable: Since power with likely be no more than 100 watts and cable runs will be under 35' in most cases, RG-58 should do the job.

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2. High power contesting: Use RG-213 or better cable to handle the power and the longer cable runs to permanent antennas. One of the low loss cables may be in order if you use very high towers or antenna supports.

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3. Moderate power, but over 65 years old: Consider RG-8X. It is lighter and easier to handle than RG-213, but has more power handling ability and lower loss than RG-58. (For every tens years of age over 40, also consider lowering your tower by 10' to a height you can climb.)

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4. Coast-line or industrial area installations: consider some of the marine cables with their extra protection.

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5. Buried cable installation: RG-213 (an improved version of the old RG-8) should work fine, but for minimum maintenance, consider one of the cables with greater resistance to chemical and abrasive wear.

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Check at hamfests: sometimes a dealer will run a special on one of the marine or low-loss cables, bringing the price down to nearly the same as RG-213. I tend to avoid preassembled cables, since the crimped connectors are not as well-connected to the cables as carefully assembled regular connectors. However, I do use them for quick tests and for portable work. After a while, I end up replacing the connectors with soldered versions.

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The UG series of connectors was made to be taken on and off with ease, and to some degree, they depend on the abrasive effects of connecting and disconnecting to keep the center pin and the threads clean. If you use them at the antenna terminals, be prepared to disassemble and clean the connectors at least once a year, even if you use plenty of coax sealant to weather protect the connection.

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Coax Problems

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There are two types of coax problems: mechanical and electrical. +

Mechanical problems and maintenance: Nothing lasts forever (except love). Inspect your coax and connectors at least once per year or whenever you have any signal strength problems. Clean the connections and reseal them, if outdoors. Wipe down the coax to remove dirt and chemical build- up. Try to install your coax as much in the shade as possible to reduce the rate of sun deterioration of the outer jacket. For buried installations, check for standing water around the cable and improve drainage if necessary. Be certain that you use plenty of support on vertical runs (for example, up the leg of a tower). Avoid long, unsupported horizontal runs: use a support rope to which the coax is taped at small intervals. Coax was not made even to support its own weight. Avoid tight corners: the fatter the coax, the larger the radius of a corner. (This also prevents deformation of the cable, which can change its electrical characteristics.)

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After five years of outdoor use, replace your coax. It may have some good life in it, but the odds are that your signal strength on both transmission and reception have dropped as the aging cable ate more of the signal power. If you want to use the old cable, cut away and discard a few feet from each end, along with any segments with visible jacket damage. Then use the remaining cable for those shorter noncritical indoor runs of a few feet each. Or remove the jacket and extract the braid as a grounding strap. But keep your outdoor coax fresh.

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Electrical problems and maintenance: Remember that the transmission line characteristics of the coax involved only the outer surface of the center wire and the inner surface of the wire mesh. The wire mesh also has an outer surface perfectly capable of conducting HF electrical energy. In fact, it can act just like an antenna in parallel with your "real" antenna. That phenomenon can ruin the performance of your system (unless it is designed into the system, as in some wire antenna schemes). Hence, you need something to isolate the outer surface of the coax from the antenna currents. Many beam manufacturers already provide a "balun" or "line isolator" to take care of that potential problem. If your system does not have one, consider purchasing a 1:1 current balun or W2DU-type choke balun to install between the antenna terminals and the coax run.

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I also take one other precaution. Instead of running one piece of coax from the antenna terminals to the rig, I use several. The first goes from the beam terminals (actually, the choke balun) to the mast, around the rotator with a large strain-relief loop, and down abut 8 feet along a tower leg. I have grounded my tower legs as best I can, and I have a plate on the leg with a bulkhead (double female) coax connector. The first length of coax ends here and the second begins. electrically, the tower and the outer coax braid surface are at the same potential. The second coax length goes to another plate installed where the coax enters my home. At this weather protected point, when weather threatens, I can move the coax from the house run to a plate with coax connectors and a long pipe into the soil. Keeping heavy charges outdoors is my goal, especially when I am on vacation. This measure protects my home. A third run goes from the home- entry plate to a plate at the edge of my operating table. Routinely, whenever I am not on the air, the coax, ground strap, computer connector, and AC cord to the station are all completely disconnected, so that the station is isolated from any electrical dangers. This measure protects my rig. Finally, short lengths from the plate to my antenna tuners and rigs complete the connections.

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Do I get some losses from having so many coax connectors? Probably a little. But so far, in 40+ years of operating, I have had no problem with static charge build-up on the antenna, power line surges, ground surges, or other weather- and thunderstorm-related problems.

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Coax makes a very effective transmission line, but its effectiveness depends on sensible selection, thoughtful installation, regular maintenance, and timely replacement. You might want to check out your transmission lines before the sunspots numbers take your mind off everything except operating.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
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+
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+ + diff --git a/content/a10/ant16.html b/content/a10/ant16.html new file mode 100644 index 0000000..592ad13 --- /dev/null +++ b/content/a10/ant16.html @@ -0,0 +1,49 @@ + + + + + Antenna Noise + + + +
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No. 16 Antenna Noise

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L. B. Cebik, W4RNL

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+ We often hear reference to "noise" in antenna work, but often we are not sure what kind of noise is being talked about. So let's talk about noise and antennas. "Noise" comes in a wide variety of styles, but here is one way to divide the group into usefully smaller chunks: +

1. Man-made noise: This category includes the usual machinery sparking, faulty signs, auto engine sparking, etc. As you can see from thinking about the sources, it largely derives from spark generation and hence produces useless RF over a wide frequency range. Most human-made noise is vertically polarized and of ground wave propagation. Hence, ground-mounted verticals are most susceptible to this category of noise. A horizontal antenna generally shows an immediate 3 dB reduction. Additionally, antenna elevation also helps reduce the noise level. Finally, a narrow-band antenna also reduces the total amount of noise energy in this category from reaching the receiver. A parallel feedline-ATU arrangement sometimes shows improvement over the same antenna fed with coax by filtration action, i.e., narrowing the bandwidth of the energy allowed to reach the receiver.

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One technique that has been the subject of recent articles is the use of a short vertical noise sensing antenna (long enough to pick up local noise but too short for effective reception of propagated signals), inverting its signal, and combining the result with the regular antenna signal. With proper adjustment, local human-made noise can be cancelled quite effectively, with only slight reductions in received signal strength. The benefit lies in the large improvement in signal-to-noise ratio, the truer mark of effective reception.

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Except for very near by sources, such as an arcing pole pig, Man-made noises create the most problems on the lower HF bands.

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2. Atmospherics: There are two sources of "atmospheric" noise and energy coupling to antennas:

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a. Sparks: Nature also generates wide-band sparks in the form of lightning. There are other atmospheric noise sources, but especially on the lower HF bands, QRN is largely propagated lightning signals. As with all spark energy, the energy decreases as the frequency increases, hence, the quieter high bands. There is little difference in the reception of propagated spark energy between vertical and horizontal energy, since the polarization is lost in the skip refraction. Narrow-banding the pre-receiver reception system can reduce the total energy from such signals that reaches the receiver front end.

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b. Charges: The more that air molecules strike each other, the more they lose electrons and become charged. The thinner the atmosphere, as at high altitudes, the longer molecules can stay charged before recombining with lost electrons. It is from phenomena such as these that we get the static charge build-up on antennas. For most home antenna systems, charge build- up was no real problem with tube grids, but a real problem with solid-state front ends. The longer the antenna wire, the windier the location, and the drier the air, the more likely that static charge can build to damaging proportions. At the very least, static charge collection on an antenna is an additional noise source and problem.

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For some antennas mounted very high, the energies involved could not be drained effectively before damage occurred to antenna elements. At the extreme, the development of the quad loop was to solve HCJB's end coupling problem with its Yagis: at the high altitude of Quito, Ecuador, the energy coupling was burning the ends off the antenna elements.

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Loop antennas have no ends: hence, for a portion of the incoming energy, there is a reduction in the amount of energy coupled to the antenna from wire-end capacitance. Where the high voltage region is distributed across a wire length, whether vertical or horizontal, capacitive coupling is minimized. For this reason, some operators find quads and other loop antennas quiter than Yagis and dipoles.

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Regardless of antenna type, static charge is simple to drain away. One technique is to have the antenna at DC ground. Some antenna designs are naturally at DC ground. Loops go from the coax center to coax braid, and if the braid is well grounded, the charge does not build up. Placing an RF choke across the antenna terminals or from the hot terminal to a ground line can continuously drain charge build-up. In some multi-band antenna systems, parallel feed lines can carelessly omit this protection, but a pair of RF chokes, one from each line to ground where the feedline enters the house, can protect equipment. However, remember that the impedance level at that point can be high, requiring a very high value of RF choke to ensure that significant signal energy does not go through the choke.

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3. Mixing products: Two signals, neither of which is on the frequency to which we are tuned, can be mixed and produce a third signal (or a bunch of signals) that may fall on a frequency we want to use. The cure for mixing products begins by locating where the mixing occurs. If the mixing occurs in the receiver, then filtration of the unwanted frequency (or frequency range) is the best solution. If the mixing occurs externally to anything one's receiving and antenna system can control, then there is no cure immediately at hand. However, such problems often involve violations of technical standards by one or both of the signal generators involved as the sources of the mix, and patient bureaucratic pressure can sometimes alleviate the problem. If the mixing occurs within one's antenna system, then there is usually something wrong with the system--bad connections, unwanted couplings, less than optimal tuning set-ups: all of these are correctable and should be part of one's routine periodic maintenance on the antenna system.

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These are not all the noise sources. Power company equipment problems, such as arcing pole pigs, require a simple procedure: locate the problem transformer, keep on reporting the situation until you get action, and hope there is a ham on the technical staff that handles such complaints. RFI from light dimmers and other home products that use AC waveform chopping to control a voltage level has been noted in many articles and requires that we locate the source and cure it individually. Likewise with noise from computer timing circuits.

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Finally, some folks are condemned to live in areas where noise is beyond control and even beyond the ability of the best noise blanker to handle. The solution, short of illegally de-powering these sources, is to save money and move to a quiet location--or to concentrate on portable operation. However, antenna choice, feed system choice, filtration, noise cancelers, and noise blankers can go a long way toward reducing currently unlivable noise to a mere constant irritation.
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Updated 11-3-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
+
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+ + diff --git a/content/a10/ant17.html b/content/a10/ant17.html new file mode 100644 index 0000000..0f40630 --- /dev/null +++ b/content/a10/ant17.html @@ -0,0 +1,52 @@ + + + + + Some Misconceptions About SWR + + + +
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No. 17 Some Misconceptions About SWR

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L. B. Cebik, W4RNL

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+ We have all read dozens of articles about SWR. So we all know that the Voltage Standing Wave Ratio is a complex function of the relationship between the feedpoint impedance of our antenna and the characteristic impedance of our transmission line. When the antenna feedpoint impedance is a pure resistance, the relationship is simple: SWR equals the larger of the two divided by the smaller of the two. If the antenna feedpoint exhibits reactance in addition to resistance, then the SWR is higher by a somewhat more complex calculation. +

We also all know that generally, the better the match between the load, the transmission line, and the source (our transmitter outputs), the more power is consumed by the load. Hence, it is generally wise to strive for a well- matched antenna-feedline-transmitter system. So we place an SWR meter in the line in, at, or near the transmitter and monitor the SWR at that point.

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Despite all this knowledge, I still encounter some interesting misunderstandings about SWR. Of course, they come from outside the 10-10 ranks, so everyone can claim, "Well, I knew better than that." Even so, it may be useful to review a few of them.

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1. "My SWR is low, so my transmitter is safe." In olden days when tube- type rigs had adjustable output circuits, folks worried about burning out tubes and other components "because" of SWR. Actually, the combination of resistance and reactance seen by the transmitter output circuit would sometimes permit only a small RF transferral. However, operators continued to load their finals to full DC plate input power. What is not RF in a final is heat, and that excess conversion of DC power to heat is what destroyed tubes and stuff around the tubes.

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Today's transistor rigs have feedback circuits that sample the reverse voltage at the output and automatically reduce drive to the finals in the event of a high SWR. Thus, it is pretty difficult to hurt a rig by connecting it to a high SWR output load. However, SWR is NOT the only thing that can hurt a rig. Overdrive, with or without SSB compression, is a source of major stresses on a rig's circuitry. However, the chief rig killer seems to be voltage surges coming from the antenna, the power line, or the ground. And that is a matter of safety that calls for measures outside the rig--like disconnecting the antenna, power cord, and system ground to totally isolate the rig when not in use.

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2. "My antenna system is fine, because the SWR is better today than when I put it up three years ago." The fact of a lower SWR over time is often true. However, the conclusion drawn is false. If the SWR is lower than it used to be, the chief reason is an increase in losses in the system. Losses represent that portion of energy converted to heat along the line and at the antenna terminals, energy that is no longer available as energy to radiate. As systems age, cables become "lossier," terminals become corroded, and a variety of other things contribute to the problem.

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Yes, a lowering of SWR can indicate problems, not improvements. It is not impossible, but it is exceedingly rare for an antenna system to change its feedpoint impedance to match the transmission line. It is so rare that the lowering of SWR with time should always be taken as a sign that it is time for antenna system maintenance. Clean, deoxidize, tighten, and seal, as appropriate. If things do not improve, replace the outdoor coax with new stock (but save the old stuff for noncritical uses if it has any life left in it).

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3. "My antenna is operating very well because my SWR is a perfect 1:1 match." Unfortunately, my dummy load gives a nearly perfect 1:1 match, and I cannot hear anyone when it is in the line. SWR is one measure of impedance match, but it is not an indicator of the quality of antenna performance as an antenna. Antennas convert radio frequency energy--a form of AC voltage and current--into electro-magnetic radiation (and also the reverse for reception); and they also manage to focus that radiation in various patterns. How well an antenna does this job is only indirectly connected with the impedance match to the transmission line carrying the energy to be converted and directed.

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The practical consequences of this fact are pretty basic. First, before committing to an antenna, try to determine what kind of operating you want to do and select an antenna that will enhance that operation--within the limits of what you can handle in terms of finances, maintenance, and home site restrictions. Second, maintain your antenna regularly--even more regularly than most folks change automobile oil. Preventive maintenance will keep your antenna operating to its maximum ability. Third, if you build your own antenna for a long-term installation, use sensible quality materials. Stainless steel hardware is a must. Tubing and wire made for antennas or equally strong and conductive are necessary. Applying No-Ox or similar antioxidation conductive materials at connections of dissimilar metals is always a good idea.

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4. "My antenna has a feedpoint impedance of 100 ohms. Surely 50-ohm coax will give me lower losses than the more highly mismatched 450-ohm parallel feedline." This misconceptions stems from the belief that SWR is a direct measure of the ability of an antenna to "absorb" energy and convert it into radiation. SWR is only part of the story.

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Every transmission line displays two kinds of losses: first is a basic loss based on two significant factors: the ability of the wires to handle RF currents and the leakage between wires through the insulation. Because any coax we can afford compromises cost vs. effectiveness, all common coaxial cables have a higher basic loss per 100 feet than parallel feedline, whether 300-ohm or 450-ohm. In fact, for the HF bands, most parallel feedline has a minuscule loss compared to coax.

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The second loss source is a result of SWR--or rather the mismatch that SWR indicates. Since peak voltages climb, leakage increases. Since peak currents climb, heat conversion losses are higher. In effect, SWR puts a multiplier on the transmission line's basic loss. Since coax begins with significant basic losses, additional losses due to SWR are that much more significant. Parallel transmission lines begin with almost insignificant losses, and the same or higher multipliers usually mean that losses are still insignificant. Under some common conditions, a parallel transmission line with a 10:1 SWR may have lower power losses than a coax cable with a 3:1 SWR. Parallel transmission line is almost always the best bet for multiband wire antennas that require an antenna tuner.

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But remember that even at 3:1 SWR on the lower bands, like 80 meters, coax losses will still be too low to worry about. If your 75 meter dipole shows an SWR at the low end of 80 within the limits of your rig's built-in antenna tuner to handle and you would like to work a little CW, go for it.

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5. "My meter shows the reflected power to be 25 watts. I'm worried about losing that power at the antenna and what it must be doing to my rig." Most folks who see these kinds of readings have never looked seriously at their forward power under the same conditions. Suppose you set your rig to exactly 100 watts output. Your reflect power reads 25 watts on a decent meter. Your forward power will read at least 125 watts--perhaps a couple of watts more to account for the cable losses just described (and your rig will be putting out about 102 watts). The difference is 100 watts. Where is it--and where did the extra forward power come from?

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The reflected power simply returns to the forward direction and adds to the rig's power along the line. No need to worry about the rig, since it is not affected by the reflected power (except as the reverse voltage may activate a power reduction circuit). The antenna is receiving and converting 100 watts of power (less only the very small amount changed to heat due to cable losses). A receiving station cannot tell the difference in signal strength between an exactly matched dipole and one running a 10:1 SWR to a parallel feedline and ATU system. The received signal strengths will be the same, assuming the antennas occupied the same transmitting positions with the same propagation conditions. Both antennas converted just about 100 watts of RF energy into radiation. It may take about a dozen cycles for the high SWR system to build to full power and an equal number to return to zero, but when you have millions of cycles per second to use, those few make no difference to the signal intelligence.

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I hope these notes help all those "other" folks approach SWR and antennas a little more intelligently. WorldRadio's Kurt N. Sterba occasionally runs into SWR msconceptions, and I assure you that his treatment is far more entertaining than mine--except to the sources of those misconceptions, who are technical writers who ought to know better. He is a good incentive for writers to keep things right and sensible. The best extended treatment of SWR and for SWR misconceptions is still Walt Maxwell's book, Reflections. Unfortunately, it appears to be out of print. You may want to petition ARRL to reprint it. Hopefully your library has a copy. Mine is too dog- eared to be borrowed. Anything right in these notes belongs to Walt. Anything wrong is likely to be noted by Kurt.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
+
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+ + diff --git a/content/a10/ant18-3yagi1.gif b/content/a10/ant18-3yagi1.gif new file mode 100644 index 0000000..13cc4d3 Binary files /dev/null and b/content/a10/ant18-3yagi1.gif differ diff --git a/content/a10/ant18-3yagi2.gif b/content/a10/ant18-3yagi2.gif new file mode 100644 index 0000000..846f218 Binary files /dev/null and b/content/a10/ant18-3yagi2.gif differ diff --git a/content/a10/ant18.html b/content/a10/ant18.html new file mode 100644 index 0000000..ce8709b --- /dev/null +++ b/content/a10/ant18.html @@ -0,0 +1,53 @@ + + + + + The Simplest 3-Element Yagi? + + + +
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No. 18: The Simplest 3-Element Yagi?

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L. B. Cebik, W4RNL

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+ In a past episode, I described one of the simplest 2-element Yagis I have encountered. For those who would like a little more gain and a better front-to-back ratio, I want to describe a simple 3-element Yagi. Like the other beam, this one comes from Bill Orr, W6SAI, from his column in Ham Radio for May, 1990. +

This beam has two essential items for the casual home builder. First, the antenna has a 50-ohm feedpoint impedance with a wide SWR bandwidth. In fact, the SWR stays below 1.4:1 up and beyond 29 MHz when the antenna is modeled for 28.5 MHz. Second, the characteristics (gain, front-to-back ratio) are almost constant for the entire first MHz of 10 meters. The gain ranges from 12.3 to 12.5 dBi, while the front-to-back ratio remains better than 18 dB across the band. Figure 1 is an azimuth plot of the antenna taken every quarter MHz from 28 to 29 MHz at a 35' height. The differences from one line to another are too small to make any difference at all.

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For these benefits, there is a price to pay: lower gain. From a 3-element Yagi on a 12' boom, one can squeeze out another dB of forward gain and improve the front-to-back ratio by a couple more dB. However, these beams have two disadvantages for the home builder. First, they have a narrower bandwidth where these properties show up. Beyond certain frequency limits, the pattern begins to deteriorate. Second, the feedpoint impedance tends to be very much lower--in the 20-25 ohm range. The lower feedpoint impedance requires a matching network. Although adjusting matching networks can become routine, the process can take the pleasure out building one's first beam that works.

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Let's go ahead and build one of these wide-band specials. First, we need some dimensions. Figure 2 supplies the data.

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For 10-meters and simple installations, hardware store tubing is convenient and accessible. 1" aluminum tubing comes in 8' sections at most hardware depots. You will need 6 pieces, plus a shorter length of 7/8" tubing. You will also need a boom 12' long. One trick I have used is to take two pieces of 6' long 1.5" diameter aluminum tubing and lay them end to end. Now take two lengths of 1 3/8" tubing (or 1.25" if the larger tube is not available). Cut one smaller tube size length in half. Slide 3' of the 6' length of the smaller tubing inside one end of the larger tubing and fasten with stainless steel sheet metal screws. Slide the other piece of large tubing over the exposed 3' of smaller tubing, and fasten. Now slide the 3' lengths of the smaller tubing inside each end of the 12' boom, and fasten (but in such a way as not to interfere with the element mounting to come). We now have a 12' boom adequate for this simple beam.

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Now make up 3/8" plywood plates about 6" wide and 3' long. coat them well against the weather. You can taper the pieces outward from the center to save a few ounces of weight. Find stainless steel U-bolts that go around the boom and around the elements. Let the plates go below the boom, and the element go below the plates.

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Notice that two of the elements require aluminum pieces that are longer than the twin 8' sections of tubing we bought. Likewise, from the director, we shall cut off short section of tubing. Save them. For the reflector, set the tubes to the required extension. Take a 3' length of the 7/8" diameter tube and slide it inside one of the 1" diameter elements and fasten with sheet metal screws. Now slide either or both pieces of remnant director tubes over the 7/8" tube and position them so that they fit under the inner U-bolts. Again, fasten them to the 7/8" tube with screws. Now slide on the other 8' reflector section and fasten. The short segments of exposed 7/8" tubing will make no significant difference to antenna performance. (If you are a perfectionist, you can purchase one extra section of 1" tubing to make the reflector 1" in diameter for its entire length.)

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Since the director only requires trimming to specification and mounting with a pair of U bolts on each side of the plate, the last item of concern is the driven element. Mount the element leaving a 6" space at the center. Slide 18" sections of 7/8" into each 1" tube and bring the ends close together. (The perfectionists can cover the exposed 7/8" tubing with short lengths of 1" tubing for a uniform driven element.) Fasten loosely and begin thinking about a boom-to-mast mounting and a coax connection. A small plate with a coax connector and the shortest possible leads to the antenna elements takes care of the connection. I like to use a 1:1 choke balun of W2DU design (ferrite over a length of coax), and this can be taped to the boom.

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Mount the antenna about 10' off the ground pointing straight up. Adjust the driven element for resonance. Now get the beam up about 35' and begin waiting for sunspots.

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This beam has only one more element than our 2-element special, but it is twice as large and twice as ungainly with its 12' boom. However, its performance improvement over the 2- element Yagi will show up instantly--or as soon as there are some folks to work. You will notice the effects of the added gain and front-to-back ratio on your local net. The bill will come to about $75 or so, which is not bad, if you have priced commercial beams lately.

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There are beams with higher performance figures, but none any simpler to build than this wide-band special.
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Updated 2-21-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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+ + diff --git a/content/a10/ant19-1.gif b/content/a10/ant19-1.gif new file mode 100644 index 0000000..9ef7ab1 Binary files /dev/null and b/content/a10/ant19-1.gif differ diff --git a/content/a10/ant19-2.gif b/content/a10/ant19-2.gif new file mode 100644 index 0000000..0c98662 Binary files /dev/null and b/content/a10/ant19-2.gif differ diff --git a/content/a10/ant19-3.gif b/content/a10/ant19-3.gif new file mode 100644 index 0000000..8c2b9f1 Binary files /dev/null and b/content/a10/ant19-3.gif differ diff --git a/content/a10/ant19.html b/content/a10/ant19.html new file mode 100644 index 0000000..2786f61 --- /dev/null +++ b/content/a10/ant19.html @@ -0,0 +1,56 @@ + + + + + A 3-element 10-Meter Beam on an 8' Boom + + + +
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No. 19: A 3-element 10-Meter Beam on an 8' Boom

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L. B. Cebik, W4RNL

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+ As the sunspots return, the search for an inexpensive beam antenna continues. We have looked in past columns at 2-element Yagis and a wide-band 50-Ohm feed 3-element Yagi on a 12' boom. We can shrink the boom length down to 8' if we are willing to accept almost a half dB more gain, a good front-to-back ratio, and a matching network at the feedpoint to transform an impedance of around 25 ohms. +

The design is adapted for hardware store aluminum tubing from a design by Brian Beezley (K6STI) in the YA collection that comes with the ARRL Antenna Book. The original design called for smaller tubing that is often hard to find. The revision calls for 7/8" and 3/4" diameter tubing, which may be found at outlets like Lowes or Home Depot.

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Figure 1 shows the dimensions of the antenna. The inner 8' of tubing for each element is 7/8" diameter, with the remaining length consisting of 3/4" diameter stock. Three 8' lengths of 7/8" tubing and six 6' lengths of 3/4" tubing are all you need. You can fasten the tubing lengths with sheet metal screws, stainless steel hose clamps (with stainless steel screws), or "pop" rivets. Do not waste weight by using too much overlap in the tubing sections: 2-4" will do nicely. The reflector and the director are continuous elements, but the driven element is split in the middle for the matching system. I use small well- varnished (spar varnish) plywood plates to hold the elements to the boom--you can see the details in almost any of the other Yagi columns.

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My favorite 2-element boom--Schedule 40 PVC--gets a bit heavy by the time the boom reaches 8' long. So you might want to use 1.25" or larger diameter aluminum. A light-weight section of TV masting (the kind so light that I would never recommend that it be used as a mast) would also work if you are sure that it will stand the weather and not rust out in the first season.

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The key to the antenna is the matching system. My favorite for small antennas is the beta match, but a gamma or Tee match would do as well. The driven element length is set for a beta match, with a resistance of about 25 ohms and a reactance between 20 and 25 ohms. The reactance is the virtual series reactance needed by an L-circuit to transform the 50-Ohm coax cable impedance down to the 25-Ohm resistive antenna impedance.

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However, an L-circuit also needs an inductive reactance across the line, as shown in Figure 2. The inductive reactance can be a coil, as shown in the lower view. For 28.5 MHz and the 2:1 transformation needed here, the coil needs to be about 0.28 µH. A coil about 0.5" in diameter and wound with #12 copper house wire will have 6 turns spread over about 3/4" of length with half-inch leads to meet this need.

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The inductive reactance can also be a shorted transmission line stub or "hairpin." The hairpin can have many dimensions, depending on the wire thickness and the spacing. With a spacing (S) of 2" between wires, a hairpin of 1/8" wire will be about 7.7" long (L), while a similarly spaced hairpin of #12 wire will be about 6.8" long.

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In real life, not everything is exact, and the hairpin or coil may need adjusting to achieve a 1:1 SWR at the target frequency (28.5 MHz in this case). You can adjust the length and/or spacing of the hairpin. Likewise, you can squeeze or spread the coil turns. If neither trick works, adjust the length of the driven element and try again.

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How well does the antenna work? Across the first MHz of 10 meters, the gain ranges from about 7.3 dBi to 7.7 dBi (free space gain. In comparative terms, this is about halfway between the gain of the wide-band 50-Ohm beam and a highly optimized 3-element beam with a boom length of about 12' or so. The gain is high enough to compete favorably with most 3-element tri-banders on 10 meters. Figure 3 shows the pattern at 3 point across the band.

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The front-to-back ratio is about 18 dB at the band edges, but for most of the span between it is well over 20 dB, peaking above 27 dB near center band. Not too bad for an 8' boom.

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The entire beam will weight between 8 and 10 pounds, including the boom, depending on the materials used. An old TV rotator will turn it, and a guyed push-up mast or roof-top "tower" will put it at a good height. Remember that the fairly high front-to-back ratio is not only a QRM killer, but also a closed back door. In a local net or similar operations, you may also want to have a simple vertical or dipole around to tell when there are signals off the rear waiting for you to turn the beam in their direction.
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Updated 10-2-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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+ + diff --git a/content/a10/ant1a1.gif b/content/a10/ant1a1.gif new file mode 100644 index 0000000..45ff220 Binary files /dev/null and b/content/a10/ant1a1.gif differ diff --git a/content/a10/ant2.html b/content/a10/ant2.html new file mode 100644 index 0000000..86882ff --- /dev/null +++ b/content/a10/ant2.html @@ -0,0 +1,49 @@ + + + + + Invisible and Hidden Antennas + + + +
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No. 2: Invisible and Hidden Antennas

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L. B. Cebik, W4RNL

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If you live in an apartment, condo, or development with antenna restrictions, you may need to hide or disguise your antenna. Here are some ideas to get you started. First, some general principles, then some basic antenna types.

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Principles: The principles are few: 1. Safety: keep the antenna as far away from people as possible for their safety. 2. Propagation: put the antenna as high and in the clear as possible for maximum efficiency within the limits of needing to keep it out of sight. 3. Antenna tuner: with few exceptions, the hidden or invisible antenna will become a random length end-fed wire. Any of the T-matches (for example, MFJ's tuners) will do a good job matching the antenna to your rig. 4. Expectations: do not expect the performance of a long Yagi. Instead, expect to make a lot of great contacts.

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Antenna Types: The basic hidden antenna types are four: 1. disguised verticals, 2. thin wires, 3. attic antennas, and 4. loading existing metal. There are dozens of variations on each theme. But, forget loading the bedsprings.

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1. Disguised verticals: You can encase almost any type of vertical antenna in PVC, and call the outdoor structure a flag pole. For working dx from a development with restrictive covenants, this route is often useful, especially if you use a multiband vertical. Construction varies with the circumstances.

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2. Thin wires: Wire as small as #28 enamel makes a good antenna for 100- watt transceiver use. It is often invisible enough to leave running from a second-story apartment window to a tree. Or, you can put it on a reel and wind it out and in as necessary. Alternatively, you can string it in the attic, turning corners wherever necessary. I have used it with success taped to the edges of a second story ceiling. How much wire? How much have you got? Just do not end up with tight coils; try for maximum length in each direction used.

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Thin wire antennas, indoors or out, are random length wires fed at the end and need a transmatch. If possible, locate the transmatch where the wire leaves the building. Otherwise, try a piece of RG-213 from the tuner to the antenna wire. Ignore the coax losses. Try a sleeve balun (such as those sold by Radio Works) where the coax leaves the building. Ground the coax shield where the antenna begins and the tuner and every piece of equipment in the shack well--very well! The object is to do everything possible to keep the RF outside or away from the rig. Some combination of sleeve balun, ferrite cores, and the like will likely solve any RF-in-the- shack problems. Keep experimenting. And be willing to spend a few dollars on wide braid to use as grounding strap; it works well, as does a good, long ground rod (replaced every few years).

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3. Attic antennas: Way up and away from everything is best, but attics are not usually as bad as you might think. The frame and roof shingles do not absorb too much RF, and the braces can help support an antenna. In the attic, you can usually find room for dipoles for many bands, even if you have to bend the ends down or to the side. Mount the dipole as high in the structure as you can, and away from any metal duct work, metallic duct insulation, or house and phone wiring. Feed an attic dipole just as you would an outdoor antenna (coax and 1:1 choke balun). Trim it to resonance or minimum SWR.

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The attic may also hold a 2- or 3-element Yagi fixed on your favorite target. You can adjust element lengths for thinner wire elements and do away with the boom. If you use tubing, getting it into the attic may be a problem if the opening is small. First, build and test the antenna, then cut it into pieces that will fit the opening, developing couplings to reconstruct it on site. (Back before cable, I put a 12'-long TV log periodic in the attic just that way: I used wire on a wood frame, cut the wood into entry size pieces, and used linking pieces to reassemble the frame before restringing the wire. Great reception from Atlanta about 70 miles away.)

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4. Loading existing structures: Perhaps the most obvious aluminum structure to load is the gutter and down spout. Treat the system like a thin wire antenna and use a tuner, driving a ground rod near the feed point. Be sure to securely bond the joints, since painted aluminum joints with pop rivets make a shaky electrical system. Expect changes in pattern and antenna tuner settings with water, snow, or leaves in the gutter.

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You can also load patio umbrellas, existing aluminum flag poles, and other metal structures. You can shunt feed a grounded flag pole. Avoid iron and steel structures if an alternative is possible, since their losses are fairly high, but use them in a pinch. Even the frame of a sliding patio door will radiate and receive.

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Anticipated results: Compared to a high and free outdoor antenna, these substitutes will likely disappoint you for local area point-to-point work on 10 meters. However, do not sell them short with skip. Their low height will give high take-off angles, but still produce very solid contacts, even in 10-10 contests. The idea is NOT to try to compete with the 1.5 kW linears feeding 7-element quads at 105' altitudes. Instead, find modes of operation to which the antenna is better suited: rag chewing, nets, and even informal contesting. Most of these hidden or invisible antennas will usually outperform loops and other tiny antennas (but they will also work in making contacts).

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If your situation calls for these measures, develop an attitude: be on the lookout for better places (higher and bigger) for the next design. Most of these antennas are cheap, but do not skimp on quality coax, connectors, ground rods, baluns, and filtration. Use the same high quality components you would put into an outdoor tower and beam. Part of your attitude adjustment should be forgetting ultimate antenna efficiency, except when comparing two of your own models to see which one to keep.

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Last, be careful and considerate: keep RF out of the power lines and phone lines. It is often easier to try a different kind of hidden antenna than to filter or revise parts of the phone wiring.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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+ + diff --git a/content/a10/ant20.pdf b/content/a10/ant20.pdf new file mode 100644 index 0000000..322c085 Binary files /dev/null and b/content/a10/ant20.pdf differ diff --git a/content/a10/ant21-1.gif b/content/a10/ant21-1.gif new file mode 100644 index 0000000..8d1ddd5 Binary files /dev/null and b/content/a10/ant21-1.gif differ diff --git a/content/a10/ant21-2.gif b/content/a10/ant21-2.gif new file mode 100644 index 0000000..83e3e70 Binary files /dev/null and b/content/a10/ant21-2.gif differ diff --git a/content/a10/ant21-3.gif b/content/a10/ant21-3.gif new file mode 100644 index 0000000..fd7f1e4 Binary files /dev/null and b/content/a10/ant21-3.gif differ diff --git a/content/a10/ant21.html b/content/a10/ant21.html new file mode 100644 index 0000000..4b979c5 --- /dev/null +++ b/content/a10/ant21.html @@ -0,0 +1,68 @@ + + + + + A Simple 2-Element 10-Meter Quad + + + +
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No. 21: A Simple 2-Element 10-Meter Quad

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L. B. Cebik, W4RNL

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+ Quads are popular with many folks, and sometimes for good reasons. So let's see what a dedicated 10-meter 2-element quad might look like after some work in the home shop. We shall use only materials available locally: wire, PVC, and some hardware. +

Why a Quad? Quads beams consist of 2 1 wavelength (approximately) loops, ordinarily arranged so that one is the driven element and the other is the reflector. Since the elements are double the size of the half wavelength elements in a 2- element Yagi, we expect more gain-and we get it. In fact, a 2- element quad has almost as much gain as the 8'-boom Yagi or the wide-band Yagi we discussed in recent columns. However, the 2-element quad does not have as much gain as a fully optimized long-boom 3-element Yagi. Also, the front-to-back ratio of a quad fluctuates around the 20 dB figure, more like a 3-element Yagi than a 2-element Yagi.

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Physically, a quad beam--when compared to a Yagi--trades volume for horizontal area. Horizontally, even the 8'-boom Yagi requires a rectangle about 8' long by 16.5' wide. A quad of similar performance has a footprint only 5' long by 9.5' wide, or about 1/3 the area. However, the Yagi is flat, while the quad occupies a 450 cubic foot volume. (That just means that it is as high as it is wide.)

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If you decide that you want a quad for most of the HF bands, I recommend that you obtain one of the commercial models. These fairly complex structures are engineered for maximum strength and durability. However, if you need only a 10-meter model (and later want to tuck 6-meter or 2-meter quads within the same framework), then you can build one yourself with simple tools and materials.

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The Quad Beam Structure. As shown in Figure 1, a good 10- meter quad can be built from two wire loops. If the wire you use is #14 bare copper (stranded or solid), the driven element loop is 105.3" per side or 421.2" overall. The reflector loop is placed 60" behind the driven element and is 110.3" per side or 441.2" overall. If you decrease the wire size of a loop antenna, the total length becomes smaller as well (and not longer, as with a linear wire antenna element). For #18 bare copper wire, the dimensions per side drop to 105" and 110" respectively--not a big drop. but a noticeable one.

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These dimensions are for bare wire. Insulated wire has a 2-5% velocity factor, depending on the type and thickness of the insulation. It will require different dimensions that I have not modeled and tested.

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If we could just starch the wires and toss them in the air, the quad would be a very simple antenna. However, we need a supporting structure, shown by the dotted boom and arms in Figure 1. The support structure should be nonconductive, although a metal boom usually does not affect antenna tuning. For 10-meters, the arms can be strong fiberglass, quality bamboo (with lighter wire elements), or thin-wall PVC.

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The sketch shows what one might do with an all-PVC structure. The boom can be about 4-5' 1" or 1.25" nominal Schedule 40 PVC. (1" nominal PVC is closer to 1.25" in diameter, while 1.25" nominal PVC is closer to 1.5" in diameter.) The arms can be thinner-wall SDR-135 PVC, 0.5" diameter nominal. Each of the 4 arms per element should be just about 6.5' long, but lets add another half foot to each.

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Since PVC comes in standard 10' lengths, we shall need 8 pieces of the half-inch diameter stock, along with 4 end-to-end couplers (plus a 5' piece of fatter Schedule 40 for the boom). You can either drill the ends of the arms for the wires or use half-inch Tee fittings--although the smoother fittings add weight to the assembly.

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Assuming a 5' boom, use a 1 1/8" drill-mounted hole cutter to cut two pair of aligned holes in each end of the boom. The outer pair at each end should be about 6-9" in from the end, and the inner set another 1.5" further in. The hole-pairs should be at right angles to each other at each end, and the hole sets at each end should be very closely aligned with each other.

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Now we can make the wire supports. First, place an end-to-end coupler in each hole and run a stainless steel nut and bolt through the boom and coupler to fasten the assembly. Using PVC cement, add 7' lengths of the half-inch thin-wall PVC to each coupler end. Add Tees to the ends, or drill out and deburr generous holes for the wire about 1/2" in from each arm end.

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Use a length of cord marked the same length as the wire that will replace it--with some excess. Run the cord through the holes and stress the arms outward toward the boom end until the cord matches the element size. Tie it off. If you use fresh nylon cord, you can leave it in place even after you add the wire--it will not hurt anything. Since cord stretches, you may experience some flex reversals, but after a few of these, you will learn how to keep the arms flexed in the correct direction.

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Now add the wires. Make the reflector loop solid by twisting the ends of the wire together and soldering. The driven element requires a small insulated plate and a coax connector.

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Assuming you have or can build a boom-to-mast mounting plate and have the U-bolts to mount the structure, you are almost ready to go. But let's not hurry.

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Performance. The 2-element quad we have just built was designed for best front-to-back ratio from about 28.25 through 28.75 MHz. Below 28.25 MHz, the front-to-back ratio decreases rapidly to a little over 10 dB. Above the target frequency range, the front-to-back ratio decreases more slowly so that the 10 dB figure is not reached until about 29.4 MHz.

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Forward gain of this antenna is maximum at the low end of the band and decreases about 0.1 dB per 100 kHz. Gain is best in the first half MHz of 10 meters, rivaling the gain of the 8'-boom Yagi. It remains as good as any 2-element Yagi all the way to the top end of 10 meters.

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Since I am not trying to sell you anything, notice that I have told a story about what happens to the gain and front-to-back ratio rather than citing peak figures for each. Figure 2 shows the azimuth pattern at the elevation angle of maximum radiation when the antenna is modeled at 1 wavelength up (about 35' high).

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Figure 2 shows not only the variation in front-to-back ratio and the rear pattern, but also the gradual reduction in gain with increasing frequency.

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Feeding the antenna. The feedpoint impedance of the antenna alone varies from about 70 to 150 ohms across 10 meters. since we anticipate feeding the antenna with standard 50-ohm coaxial cable, we need to add one more component: a matching system.

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The simplest and most effective matching system for this antenna is a 1/4 wavelength section of 75-ohm coaxial cable, such as RG-11 (for higher power) or RG-59 (for lower power levels). Both cables have a velocity factor of 0.66, which means that a full wavelength of cable is 0.66 of the wavelength in free space. Let's use 28.5 MHz as our design frequency. A wavelength at this frequency is just about 34.5' long. A quarter wavelength is a little over 8.6' or 103.5" long. The quarter-wave matching section is 0.66 of this or 68.3" long.

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A perfect quarter wavelength will transform an impedance higher than 75 ohms to a lower impedance, which is just what we need. In fact, when fed with a 50-ohm cable to the shack, the quarter-wave section shows under 2:1 SWR all across the 10- meter band. Figure 3 shows anticipated SWR curve.

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Do not operate this antenna without the quarter-wave 75-ohm matching section or an equivalent matching circuit.

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If a 2-element quad meets your space and operating needs, this one will do the job about as well as it can be done. Feel free to alter the support structure using materials with which you are comfortable in your shop. (For me, PVC is tinker toys for adults.) A TV rotator will easily turn this light antenna. For best results, be sure the bottom wire is at least 20' up, and a tower or mast height of 35' is a good minimum target height for excellent DXing.
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Updated 10-2-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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+ + diff --git a/content/a10/ant22.html b/content/a10/ant22.html new file mode 100644 index 0000000..32d1181 --- /dev/null +++ b/content/a10/ant22.html @@ -0,0 +1,60 @@ + + + + + The Handy Quarter-Wave Matching Section + + + +
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No. 22: The Handy Quarter-Wave Matching Section

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L. B. Cebik, W4RNL

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In the quad project we looked at last time, we specified the use of a 1/4 wavelength matching section of 70- to 75-ohm coax between the antenna feedpoint and the 50-ohm coax run to the shack. Let's find out why we needed it and how the matching section does its work. These types of matching sections are handy and easy to make, so you may find them useful in future antenna projects.

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The Raw vs. the Matched Antenna: Let's start by comparing the feedpoint impedance of our quad both with and without the matching section. The figures are based on a quad beam that is self-resonant just below 28.25 MHz. The 1/4 wavelength section of 75-ohm, 0.66 velocity factor coax was cut for 28.5 MHz and turned out to be 68.3" long. All SWR figures are relative to 50 ohms.

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Frequency   Without matching section    With matching section
+in MHz           Feed Z       SWR           Feed Z       SWR
+            (R+/-jX Ohms)              (R+/-jX Ohms)
+28.00        70.6 - j29.2     1.81      66.9 + j27.1     1.73
+28.25        96.8 + j 3.4     1.94      58.1 - j 2.7     1.17
+28.50       125.1 + j25.9     2.63      43.1 - j 9.1     1.28
+28.75       150.1 + j39.4     3.23      34.9 - j 8.5     1.51
+29.00       168.6 + j47.7     3.67      30.7 - j 7.1     1.68
+29.25       180.8 + j54.8     3.97      28.2 - j 6.0     1.81
+29.50       188.2 + j63.1     4.22      26.6 - j 5.4     1.91
+29.75       192.6 + j73.6     4.45      25.1 - j 5.2     2.02
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Without the matching section, the SWR figures for the quad are high enough that the automatic shut down feature of most current solid state rigs would reduce rig output to almost nothing. With the matching section, the SWR figures within 10 meters permit normal operation.

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As the unmatched impedances go up, the matched impedances go down. This gives us a clue to how the matching section operates. Every length of coax of any characteristic impedance (Zo) is an impedance transformer. For odd lengths, the transformation is complex. However, when a length of coax is exactly 1/4 wavelength long at a given frequency, the transformation is simple, especially if the impedance to be transformed is wholly resistive. We can use a calculator to handle this equation:

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+ Zmatched = Zo2 / Zantenna +
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This little formula is only approximate in the real world. for example, with the quad, there is a reactive part of the antenna feedpoint impedance in every line of the table. Moreover, the matching section is only an exact 1/4 wavelength at 28.5 MHz and nowhere else. However, if the reactances are not too high and the frequency span is not to great, the simple equation makes a good approximation. As we look at the table, for a single ham band and for reactance values less than half the resistive values, the simple equation works well enough for antenna building.

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Remember that for purely resistive impedances, a 2:1 50-ohm SWR accommodates an impedance range of 25 to 100 ohms. This resistive range shrinks when we combine reactances with resistance. However, note the 4:1 range of impedance that these SWR limits can handle. (Also remember that the 2:1 ratio is somewhat arbitrary as a set of limits. It's chief effect is noted by automated power reduction circuits in transceivers. Apart from this, there would be little difference in radiated power between, say, SWRs of 1.8 and 2.5.)

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With a 1/4 wavelength 75-ohm matching section, again in purely resistive terms, we can take antenna feedpoint impedances between just above 56 ohms up to 225 ohms and transform them to values that fit the 50-ohm 2:1 SWR limits--again, a 4:1 range. Notice that our quad does not reach 225 ohms when the matched SWR exceeds 2:1, but notice also that there is considerable reactance that accompanies the resistive value at 29.75 MHz.

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Likewise, at 28 MHz, we would expect the antenna impedance of 70.6 ohms to yield about an 80-ohm figure instead of the 66.9-ohm figure that actually emerges. However, not only do we have reactance at the antenna feedpoint, but as well the matching section is shorter than 1/4 wavelength at this frequency. Hence, the impedance does not undergo a full quarter wavelength transformation. (Likewise, above 28.5 MHz, the impedance undergoes more than a 1/4 wavelength transformation.)

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These are the finer points of using a 1/4 wavelength matching section that affect the matching range by just a little bit and throw the actual impedances somewhat off the calculated results from the simple formula. But the simple formula works well enough for most ham antennas. To be on the safe side, if you have a range of antenna feedpoint impedances from about 80 to 200 ohms, then a 1/4 wavelength section of 75-ohm coax will transform them to values appropriate to a 50-ohm feedline and transceiver system.

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Other Applications: 50-ohm and 75-ohm coax cables are the ones most easily obtained by hams, even though other values are available from manufacturers. However, this fact does not limit us to matching only values above 50-ohms to our 50-ohm system. If you cut 2 lengths of 75-ohm cable to 1/4 wavelength and connect them in parallel (center conductor to center conductor and braid to braid at both ends), you have a 37.5- ohm cable. If we plug this value into the simple equation, we find that we can match impedances values below 50-ohms up to values within the 2:1 50-ohm SWR limits. This is useful for Yagis and other antennas that often have feedpoint impedances in the 20-35 ohm range. The double line can be a bit bulky, but that is about its only significant disadvantage over other matching methods.

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Consider another situation: At certain wire antenna heights below 1/2 wavelength, the feedpoint impedance of a dipole is not 70 ohms, but more like 80-95 ohms. The 75-ohm matching section would transform these values to a 70-60 ohm range. However, we can broaden the range over which these values apply by first running a section of 50-ohm cable that is 1/2 wavelength long or a multiple of 1/2 wavelength (allowing, of course, for the cables velocity factor). Cut the 50-ohm cable for a frequency at the band center, such as 7.15 MHz for a 40-meter dipole. Since the cable is short at the low end of the band, the impedance will be higher than at the antenna at the same frequency. Equally, since the cable is long at the high end of the band, the impedance will also be higher than at the antenna terminals. The result will be band edge values closer to 100-120 ohms.

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Now, if we plug in our 1/4 wavelength 75-ohm matching section, we have lower SWR values across the band than we would have by placing the 75-ohm matching section at the antenna terminals. In fact, such a system can, with some dipole heights on 80 meters, cover more than 4/5 of the band with under 2:1 SWR.

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75-ohm quarter wavelength matching sections (and derivatives) make up a quite flexible array of methods for adapting 50-ohm transmission line to antennas that do not present 50-ohms at their feedpoint terminals. However, they do have some major limitations. Because a length of coax is 1/4 wavelength long at only one frequency, this technique is for monoband antennas only. If you have a multiband antenna, you will have to use some other method of matching your 50-ohm coax/transceiver system to the antenna.

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Likewise, the transformations become far more complex the higher the reactance at the antenna feedpoint. Hence, the quarter wavelength matching system is also only for low- reactance matching situations, such as the one shown in the table for the quad. If you have higher reactances, you may need a different matching system.

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But where the 1/4 wavelength matching section is suited to the task, it is simple, inexpensive, low-loss, and effective. Those are pretty good credentials.

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Updated 1-24-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

+ + diff --git a/content/a10/ant23.html b/content/a10/ant23.html new file mode 100644 index 0000000..ae309cb --- /dev/null +++ b/content/a10/ant23.html @@ -0,0 +1,52 @@ + + + + + Some Notes on Antenna Safety + + + +
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No. 23: Some Notes on Antenna Safety

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L. B. Cebik, W4RNL

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What would you like to protect from harm? Yourself? Your family? Your home? Your station? Your neighbors and their property? I guess that is enough to start a column on safety. Obviously, we can never finish it, but perhaps a few ideas might help you fill some gaps in the safety net around all you wish to protect and preserve.

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Static Build-Up: As the wind and weather pass over the antenna elements, a charge builds up. On long wire antennas, it can generate enough of a charge to draw a visible spark across a gap to ground. On smaller antennas it can create unnecessary static. The best way to avoid problems here is to be sure that the antenna is at DC ground. Some antennas are designed with a DC ground; others are not. For low impedance antennas (less than 150 Ohms feedpoint impedance) fed with coax, the simplest way to insure a DC ground is to place an RF choke across the antenna terminals. This gives you a DC ground path but leaves the antenna RF-hot. At 10-meters, a 100 micro-H RF choke provides about 1800 ohms of reactive isolation, but a low resistance to charge build-up. Just be sure your coax braid is grounded somewhere along the line so that the charge has somewhere to go other than to your equipment.

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Parallel feedline systems, such as all-band doublets require a different treatment, since the impedances they may see can range up to 5000 ohms and more. Here we can use high value resistors where the feedline enters the house. Run a 1 Mohm resistor from each line to a ground rod where the line meets the shack. It is also useful to add a knife switch or other disconnector (with the alternate contacts directly grounded) to remove the connection to the equipment when the antenna is not in use.

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Station Grounding: Everyone is familiar with the need for a common ground bus for all station equipment with as short a lead as possible to a ground rod outdoors. If you have a tower, it should also be ground rodded. All ground rods (including the house ground at the electrical service entry) should be connected together by the largest copper wire you can obtain. Some folks use copper flashing cut into long strips. These days, braid is not recommended because its very large surface area open to weather deteriorates it quickly. Use solid mechanical connections, not solder (which melts in the presence of lightning like a teenager in the presence of a rock star: instantly).

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If ground rods are widely separated, add ground rods in a row from end to end, spaced about the length of each ground rod apart. This is not over-kill--just the opposite. It is over-safe by holding the resistance between everything in your house and shack at the absolute minimum. Even a slight resistance may give a lightning surge an alternative path to ground through your "stuff."

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Towers and Coax: Some studies have shown that the bulk of lightning current travels in the shield of the coax. A considerable voltage difference can exist between a tower leg and the coax braid if the first connection between the two is at the bottom of the tower. You may want to consider breaking your coax near the top of the tower, having one section to the antenna with the flex loop to accommodate rotation and another section down the leg of the tower. Securely fasten a plat to a tower leg and use a double female connector with chassis nuts (often called a bulkhead connector) to join the two coax lengths. This gives you a connection between the coax braid and the tower leg. This is not the only ground you should use, but an extra one.

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Total Disconnection: During violent electrical storms, surges can enter the station equipment from several sources: the antenna lines, the AC power lines, and ground. When dealing with surges, do not think in terms of complete electrical paths. A surge can charge components, cases, and chassis, and create high voltages across components that are designed for low voltages. Hence, during violent storms, do a complete disconnect.

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Outdoors, disconnect all antenna feed lines and reconnect them to a ground rod in the station ground system. Indoors, disconnect antenna feedlines from the station equipment. Unplug all equipment--or that power strip you use as a master switch. Most power switches are single pole, so one must unplug in order to break the neutral and ground line paths along which surges can travel. Also disconnect the station equipment from the master ground lead to the outdoor ground rod system. If you do some careful planning, you can make all these moves in under a minute. Just be sure that all connections are accessible and require no tools to connection and disconnection.

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While it may be true that a direct strike is rare, most damage occurs from nearby strikes that place heavy voltage surges on power lines, antennas, and the ground. You can do a lot to keep them outdoors, where they belong.

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Towers: Towers, whether free standing or on the roof top, require some special thought. Too few hams actually study tower installation before putting up the first one. Here are some things to think about:

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1. What are the requirements for the tower base, including the concrete, rebar, excavation, etc.? Never under-support a tower at its base.

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2. What, if any, are the guying requirements? If a tower is a guyed model, install the guying system to at least the manufacturer's standards. Be certain that guys are correctly and adequately anchored--and that they do not present a hazard to those who use your yard. If the tower can use a building support, be sure the building is up to the job. Most roof-line facia boards on a house are not.

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3. Where does the tower go? Place it where it cannot hurt neighboring property (or people) if the tower and antenna fall under the worst conditions imaginable. Also try to place it where it will not hurt your own home and family if it falls.

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4. Where do the feedlines go? Be sure that feedlines do not create either an electrical or a physical hazard for family members or visitors.

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5. What are the codes? The more urban your setting, the more you may be subject to codes and ordinances that require permits, special requirements (for example, conduit for control voltages over a certain value), inspections, and, in some cases, licensed installers. Do not under any conditions bypass these requirements. Investigate in advance to know what you have to do and what it will add to the cost of the installation.

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6. What about intruders? Towers are in some places classified as attractive dangers, which is what they might be to a neighborhood child with an urge to climb. Hollering is a deterrent, but not protection. Consider fencing in or cladding the lower tower sections so that the tower cannot be climbed.

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7. Are any of the tower conveniences dangerous? Crank-up and tilt-over towers are convenient, but usually rely on cables, pulleys, and gearing to go up, come down, and stay in position. Analyze the stresses on these auxiliary parts to ensure that they can safely handle the loads. Develop a maintenance schedule for inspecting and for replacing cables before their lifetime is ended. If they die on the job, disaster often results.

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RF Safety: RF hazards come in two varieties. One is radiation. Current FCC regulations provide standards for safe amounts. Use the worksheets and analyze your station, even if you think you may be exempt by virtue of power levels and spacings. Be sure.

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A second hazard comes from direct contact with antenna elements carrying RF currents. Ground mounted verticals and inverted Vee ends provide the greatest hazards, since both children and adults can come into contact with them--either directly or with some implement having a long metal handle.

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Isolate ground-mounted verticals with fencing or other barriers which are effective especially in preventing children from touching a potentially active antenna. A vertical in or adjacent to a children's play area may mean station silence during periods when children are present: if contact is not a danger, radiation may be.

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Elevate and insulate horizontal antenna ends above the level where anyone can touch them with a metal rod. Never underestimate the ingenuity of a child with a small mean streak or a large curiosity.

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Insurance: Carry all you can afford that may be relevant to hazards that antennas may present. However, never let the existence of insurance be a substitute for the best possible practice in the installation and maintenance of antennas and their supports. The lives you preserve may include your own and those of your loved ones.

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This is not a complete look at all the facets of antenna safety. We have not even reminded you to keep your antennas and supports well away from power lines. But perhaps we have said enough to prompt you to do a periodic inspection of your own safety measures--and perhaps some reading into the handbooks and other literature. The three key words are these: protect, divert, and prevent. They are three ways of saying that you care enough to do the very best.

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Updated 3-2-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 24: Three Ways to Skin a Quad Loop

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L. B. Cebik, W4RNL

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A single quad loop makes a compact and effective bi-directional array for 10 meters. It has somewhat more gain than a dipole, and most users note that it is quiet, that is, not as susceptible to local noise as an open-ended dipole. With some sort of supporting system, the loop is a good choice for many ham back yards.

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A quad loop does its work with the antenna in the vertical plane, like a giant fly swatter. Maximum radiation is off the two broad surfaces and is minimum off the edges.

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Now comes the hard part: deciding what kind of loop to use. There are at least three versions, each with advantages and disadvantages. Let's look at them in order of complexity.

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The Standard Square Loop

The first sketch (Fig. 1) shows a standard quad loop made from #12 AWG copper wire. (If you use a different size wire, you may have to change the dimensions just a bit for resonance.) This antenna is a proven performer, with about 3.3 dBi free space gain, which translates into about 8.3 dBi gain at 1 wavelength above ground for the bottom wire (about 35'). The elevation angle of maximum radiation is about 19 degrees, which provides access to low-angle incoming DX signals. +
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The feedpoint impedance is about 125 Ohms at the 28.5 MHz design resonance frequency. A quarter wavelength section of 75-Ohm coax (about 5.7' of standard RG-59 with a velocity factor of 0.66) will provide a very low-loss match for the 50-Ohm coax to the shack and provide less than 2:1 SWR over all of the first MHz of 10 meters, plus a little. With this set-up, the antenna has the broadest operating bandwidth of all of the loops we shall examine.

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The old standard way of making a quad loop is to use criss- cross spreaders of bamboo, fiberglass, or--more recently--PVC. However, there are no rules that forbid you from stretching the quad loop from its corners to trees or other vertical supports. You can also use tubular horizontal members and wires vertical sides, although you may have to adjust the dimensions--most likely to enlarge them a bit.

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The Elongated Loop

In July, 1996, K6STI wrote in QST of an old idea: by elongating the quad loop we can achieve a little more gain and, at the same time, bring the feedpoint impedance close to 50 Ohms for a convenient match with our standard 50-Ohm coaxial cables. +
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Fig. 2 shows the dimensions of a #12 AWG copper wire loop meeting these goals. The feedpoint impedance is almost exactly 50 Ohms at 28.5 MHz. However, the 2:1 SWR operating bandwidth is only about 800 kHz, somewhat narrower than the standard loop with a matching section attached.

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The gain of the loop with the bottom wire at about 35' is 8.9 dBi (4.2 dBi in free space), and the taller assembly lowers the take- off angle to 17 degrees. Both the gain and the lower angle of maximum radiation contribute a little extra to our DXing efforts.

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Most likely, you would want to build a fixed version of this kind of loop by supporting the wire from its corners by ropes running to adjacent supports. As an alternative, you can build a rotatable version by using tubular horizontals and wire vertical sides (again, with dimensional adjustments that owe to the fat horizontal elements) attached to (but insulated from) a center mast. With a height about 3' taller than the normal quad loop, support requires a bit more work than the standard loop. Yet, if the top of this loop and the top of the standard loop are level with each other, this elongated loop loses some of its advantages in gain and lowered take-off angle.

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The Hentenna

The Hentenna is an invention of Japanese hams (and "hen" means "what is it?"--or so I am told). It consists of the full wavelength upper loop with a secondary lower loop that allows a close match to 50-Ohm coaxial cable. See Fig. 3. +
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The gain of this antenna, if the bottom wire is at the same level as the other two loops (1 wavelength or 35'), is about 9.8 dB (5.0 dBi in free space), with a take-off angle of 15 degrees, making it a good DX antenna among loops. However, its performance depends very much on the added height of the upper wire, which is nearly 19' from the bottom. The antenna is 60% as wide but more than twice as tall as the standard square loop. If we lower the top wire to parallel it with the top wires of the other two loop designs, the hentenna turns out to be only a little better than they are.

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The operating 2:1 SWR bandwidth is the narrowest of the three loops, about 600 kHz or a little over half of the first MHz on 10 meters with the design frequency of 28.5 MHz used here. Like the other loops, construction can be all wire, with the corners attached by thin (UV-resistant) rope to supports. Or, you can once more use larger diameter upper and lower horizontal members with wires sides and a wire feedpoint element for a rotatable antenna.

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Pattern Comparison

To give you a better idea of what to expect from each antenna, here are two elevation patterns, each of which contains patterns for all three loops. +
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Fig. 4 compares the antennas using a common bottom horizontal wire height of 20'. This arrangement places the elongated loop top wire above that of the square loop, and the hentenna top wire above both the others. The advantage in gain and lowered angle of radiation for the larger kloops is clear.

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Fig. 5 reverses the procedure and places the top wires of all 3 antennas at 40' up. For many installations, top height is more absolute than bottom height. In this configuration, all three antennas have comparable TO angles, with only small gain advantages as the loops grow larger.

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Whichever loop you choose, assuming that a loop fits your operating needs, give your best ingenuity to construction. If at all possible, figure out how to make the antenna free standing so that you can rotate it by hand (if not by a TV rotator). You will need to turn at most less than a half turn, since the antenna is bidirectional. All of the loops have very deep side nulls on a plane with the wires, and just these nulls alone can get rid of more than half the QRM that might get in the way of your QSOs.

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Loops are also handy in contests, where you really do want to hear what is happening in most directions. You never know in advance from where your next contact will come. If you build the loop to be collapsible, you can set it up for Field Day and other hilltopping exercises.

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The basic quad loop is a versatile antenna that lends itself to many construction techniques. If you want a little more performance than a dipole can give and you think it is fun to have a fly swatter waving in the breeze above your QTH, then one of these three designs may be the next antenna to build.

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Updated 7-20-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 25: The 10-Meter L-Antenna

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L. B. Cebik, W4RNL

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A large number of 10-10ers are just getting started. They are unsure of whether to go with a vertically polarized antenna or a horizontally polarized antenna. They have heard that cross polarization reduces signal strength by some amount from 3 dB on upward. They do not yet know what the prevalent polarization is in the local area. They do not want to put a lot of money into their first antenna, but they would like to enjoy 10 meters for both skip and local contacts. They may also have some severe space restrictions. What's a person to do?

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There is a simple and cheap solution. But first, a little background. For skip paths, polarization makes no difference almost all of the time. The ionosphere skews polarization. Highly elevated beams have an advantage, but simple antennas perform well on 10 meters, whether vertical or horizontal.

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Polarization makes the greatest difference with local area contacts, where line of sight is the general rule. Some of the gang run verticals, some horizontals. How to get started before one discovers which types of operating are the most fun is the tough question.

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Why not make a simple L antenna out of hardware store supplies. Suppose you have a typical rooftop abut 25' up, and a chimney or similar solid mounting point. Less than 10' of aluminum tubing and less than 10' of copper or aluminum wire, along with some mounting hardware to keep the parts solidly mounted but insulated, will produce a nice compromise antenna.

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The vertical section consists of 2 pieces of tubing in the 3/4" diameter neighborhood. The tubing is self-supporting once you fix the base area solidly. The horizontal portion is wire, perhaps running along the roof ridge, elevated at least a few inches and more if you can manage it. Dimensions are not too critical. You can adjust the wire horizontal part by pruning the far end. And you can adjust the vertical part by sliding one section of tubing inside the other before clamping.

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Adjusting the antenna for minimum SWR will do just fine. The modeled feedpoint impedance is about 40-45 ohms, so it makes a good match for RG-58, RG-8, RG-8X, or RG-213 coax. I highly recommend a choke balun, such as the W2DU ferrite- over-coax designs, at the feedpoint to minimize RF on the outer braid of the feedline.

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What do you get for your $15 investment? A pretty good local antenna with both vertical and horizontal polarization. The patterns above assume the antenna is mounted atop the typical 25'-high rooftop crest. As the patterns show, the vertical part produces a vertically polarized signal (and receives the same) that is almost as strong (or sensitive) as a pure vertical. The horizontal wire produces a horizontally polarized signal (and receives the same) about half as good as a full size dipole. The result is a low-angle total pattern shaped like a kidney bean that will handle signals, whatever their polarization.

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By using light tubing for the horizontal piece, with perhaps a collapsible AM radio whip as the end section, you can make up a dandy portable or hill-topper antenna. A few nesting sections of PVC along with antenna pieces that also nest when not in use will make an antenna that takes almost no room in the car trunk. 5-10 minutes work, and you are on the air from your local scenic mountain or picnic area.

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To get a better idea of the antenna's operation, think of it as an inverted Vee that has been rotated until one leg points straight up and the other is parallel to the ground. Unlike the Vee, this antenna is a good candidate for a rooftop or an attic.

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In fact, if you must have an attic antenna, there is nothing wrong with using a Vee, either right-side-up or inverted, for getting a little polarization diversity to catch all the locals. Use 45-degree angles to maximize both types of polarization in the best compromise. If the L will not fit your attic vertically, then perhaps a Vee will fit the space.

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For outdoor use, the L is likely a better mechanical choice, since you need only one solid mount and a secondary mount to keep the horizontal wire horizontal. The antenna has a minimal profile, and you can even put a PVC tube over the vertical tubing and fly a flag from it.

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As with all elevated metal structures, be sure you have fat wire to a ground rod to bleed off charges built up by the weather. A 100 mH RF choke across the feedpoint terminals would not hurt either. Always build antennas with safety in mind.

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So, if you are undecided about vertical vs. horizontal polarization, if you do not want to put a lot of money into an antenna while finding out which you prefer, or if you just need a good, cheap local antenna for 10 (that will also do quite well with skip), then the L may be right for you. When you finally invest in your long term antenna, you may want to keep the L in place as a back-up or for emergencies.

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Updated 10-20-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 26: When Should I Use a Vertical on 10?

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L. B. Cebik, W4RNL

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Most of the antenna we have discussed in this column have been horizontally polarized. There are some good reasons for this fact. First, 10-meter horizontal antennas are fairly compact, with a half wavelength being about 16-17' long. Second, the shortness of a wavelength on 10 meters (35') generally simplifies the process of supporting a horizontal 10-meter antenna at a good height (at least 1/2 wavelength, with over 1 wavelength preferred for best performance). Third, even 3-element 10-meter Yagis are fairly light-weight, for easy support, even in field or hilltop operations.

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Nevertheless, there are some good reasons for using a vertically polarized antenna on 10. Although the gain of such antennas may not usually compete with a well-installed horizontal antenna of the same size, this factor is rarely a problem when the band is open. So let's look at the question of when to use a vertical.

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1. Mobile in Motion: The standard these days for mobile-in-motion operation is the short, center-loaded, magnetic mount vertical set on the car roof. Although the least efficient of almost any antenna used on 10, these antennas acquit themselves well. Full size 1/4 wavelength whips have gone out of vogue, especially with the increased use of plastics in autos. When auto bodies themselves become universally plastic or fiberglass, we may have to rethink the center-loaded mag-mount vertical for mobile operation.

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2. Lunch-Time Operation: With small rigs, short antennas, and an open band around noon, 10-meter lunchers are more numerous than we imagine. Since the lunch hour (or half-hour) is all too brief, operators want a system that wastes no time in set-up and take-down. The vertical--again, usually a mag-mount antenna in the parking lot--fills the bill.

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3. Local Convention: In some towns and cities, most of the locals may use vertical antennas. Sometimes, this represents a lot of mobile work; sometimes it represents former citizen's band operators who have joined the amateur ranks and cut down their old antennas to resonate on the higher frequencies. Since local work is mostly point-to-point, as in VHF operation, cross- polarized antennas result in major losses in signal strength. So if the local group is mostly vertical, then it will pay you to have a vertical at home (as well as on the car) to join the fun full strength.

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Since the path through the ionosphere generally skews signal polarization, distant stations will not suffer from being cross polarized relative to your antenna.

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4. Lack of Space: Many hams live in homes without large yard. So space for antennas must compete for space with play equipment, patio furniture, and flower gardens. A vertical may be the only antenna type the home owner can erect.

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The question here is not whether to use a vertical, but what kind of vertical to use. There are a number of multi-band verticals now on the market that will open many of the ham bands. They come in two major types.

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If the roof top is the mounting area of choice, then one of the 1/4 wavelength trap verticals may be best. The heaviest part of the antenna is mounted near the roof top or chimney mounting system for maximum support. The necessary radials, installed according to the antenna makers instructions, can run along the roof top. If the antenna is at the end of the house, radials in the open direction can be run to trees or fence post, well out of reach of children or adults.

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Where space is too restricted for an elevated radial system, one of the half wavelength verticals may be more fitting. Some demand an elevated mounting point and may rest well on top of a fence post, short flag pole, or even a mast attached to a deck post. Other models call for ground mounting and can be placed in the most clear usable place in the yard with buried coax.

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In all such installations, safety to children, family members, visitors, and neighbors is a top requirement. These antennas are rarely large enough to cause damage to neighboring property if they fall. Of course, they should be well clear of any utility lines crossing the yard. Finally, they should be isolated so that no one can get an RF burn by touching the antenna while in use. For some models, we achieve this last safety measure by elevating the antenna above reach, even by fence-climbers. Ground-mounted models require some extra thought. Setting up a flower bed and small fence around the antenna can keep most folks away. Sheathing the lower portion of the antenna in large-diameter black plastic down-spout drainage pipe for about 8' up is quite effective in preventing children from touching the antenna and has been found not to adversely affect performance. The protective sheathe can be attractively painted (with non-metallic paint) to call attention away from the antenna. Whatever the safety measures we take, we should also insure that they meet FCC requirements regarding RF exposure to other people.

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Even hams with room for a host of horizontally polarized antennas may wish to consider installing one of these multiband verticals. They make good (even if not great) low-band antennas, provide back-up service in case the main beams collapse in high winds or ice, and allow the operator to match the polarization of locals using mobile whips or other vertical antennas. so even if you can afford the highest, the biggest, and the best, one of these simpler antennas makes good sense as part of the antenna farm.

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5. Home Brewers: Some of us like to build antennas. Some of us have to build antennas to save the cost of commercial versions. Whatever the reason, a vertical dipole for mounting at least 20 to 25 feet up at the center on a non-conducting mast is a good starter project. I suggest a vertical dipole, since it saves a lot of grief over where to run the radials for a quarter- wavelength ground-plane model. The vertical dipole also takes less space than a horizontal dipole and requires no turning for maximum signal.

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You can construct a vertical dipole from hardware store materials: aluminum rod or tubing (a little over 8'), PVC, and wood are the main ingredients. Figure 1 shows in bare outline a vertical dipole I once used to capture Worked All Continents in about an hour at the height of a long-ago sunspot cycle. The 4x4 fencepost was the main support, with underground bracing from bagged concrete. The side rail 10' 2x4s supported a good quality 2x4 mast, with the 4" side running between the rails. Two long galvanized bolts braced the mast. Removing the lower bolt permitted tilt-over operation.

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The antenna itself began with an 8' length of aluminum tubing for the top extension. The lower part of the antenna consisted of insulated #12 house wire, purposely cut long. I tuned the antenna to frequency by trimming the lower wire for minimum SWR. Many local hams seemed initially horrified by the idea of a dipole made from unequal diameter elements and trimming only one end. They thought that terrible things would happen to performance, since the antenna was obviously as unbalanced as its builder.

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Actually, virtually nothing happens except for a bit of building and adjusting convenience. Half wavelength antennas lose nothing in performance by being fed slightly (or even radically) off-center. The feedpoint impedance does not begin to change noticeably until the feedpoint is well off center. The only precaution was for safety: the dipole end is a high-voltage point on the antenna, so it had to be inaccessible to human touch when in operation.

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There you have it: some good reasons for using vertical antennas on 10 meters, whether they are commercial multi-band antennas or home brew specials. There are other reasons of a specialized nature that we could add. For example, if you live by the seaside, expect an exceptional increase in performance over the same antenna placed on a rocky hillside in the Smoky Mountains. Verticals have proven to be more than good enough in some island contesting locations. Some operators even prefer the wider beamwidth of a vertically oriented Yagi to one that is horizontal. Whatever the reasons, vertical have and will always have an important place in 10-meter operation, even if we never mention FM and repeaters at all (which I just did).

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Updated 1-12-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

+ + diff --git a/content/a10/ant27-1.gif b/content/a10/ant27-1.gif new file mode 100644 index 0000000..6ec4cd5 Binary files /dev/null and b/content/a10/ant27-1.gif differ diff --git a/content/a10/ant27-2.gif b/content/a10/ant27-2.gif new file mode 100644 index 0000000..5806828 Binary files /dev/null and b/content/a10/ant27-2.gif differ diff --git a/content/a10/ant27.html b/content/a10/ant27.html new file mode 100644 index 0000000..a4e1c92 --- /dev/null +++ b/content/a10/ant27.html @@ -0,0 +1,45 @@ + + + + + A Compact Aluminum Moxon Rectangle + + + +
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No. 27: A Compact Aluminum Moxon Rectangle

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L. B. Cebik, W4RNL

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I often receive inquiries from folks who cannot quite support the width of a 10-meter Yagi (either 2 or 3 elements) because obstructions give them less than the 16.5' needed. Is there an antenna with decent performance that will fit in a space about 12-13' wide? If it can be home built to save money and require no fancy tuning or matching system, so much the better.

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In fact, there is an antenna that fits this category almost perfectly. Imagine an antenna with the gain of a 2-element Yagi (6 dBi), the front-to-back ratio of a 3-element Yagi (>20 dB from 28.3 to 28.5 MHz), and an SWR of below 2:1 from one end of 10 to the other. In fact, imagine that the antenna has better than 15 dB front-to-back ratio all the way down to 28 MHz and still has about 12 dB front-to-back ratio at 29.7 MHz. (All figures are free space modeling estimates.) Imagine also that the antenna can be directly connected to 50-ohm coax with no matching system whatsoever (even though I always recommend a 1:1 choke balun). Imagine also that you can make it yourself from hardware store materials, that it will weigh about 10-15 pounds including the boom, and that you can make it in your garage with no special tools. Imagine also that when it is done, you will still have change from a $50 bill.

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The antenna is the Moxon rectangle. Past versions that I built using wire elements required lots of PVC to support them. However, if we translate the antenna into hardware store aluminum tubing, we can build a 1-boom version. Now peak at the sketch of the pieces in Fig. 1. Some 7/8" and 3/4" diameter aluminum tubing form the main elements, with 3/4" tubing for the side elements. The corners can use radius-bent tubing or be squared by making some corner supports from L-stock. The combination of 7/8" and 3/4" aluminum tubing lets you telescope the ends into the center for a precise fit or a center frequency adjustment.

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Since the end spacing and alignment is critical to make the antenna give its full performance, you can slide a piece of CPVC or similar lightweight, durable tubing either inside the ends or over the ends and lock them in place with sheet metal screws. The rigid spacer is also a good idea to limit the twisting force placed on the curved or right-angle corners. Sheet metal screws also connect the 3/4" and 7/8" tubing together. Be sure that all hardware screws are stainless steel.

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For element-to-boom plates, you can use any durable material. Spar varnished 3/8" plywood or 1/4" LE plastic make good plates. About 3" by 9" (or longer) plates give ample room to U-bolt the elements to the plate and have room for U-bolts that go over the mast. As with all good antenna structure, let the elements hang under the boom. What boom? Well, almost anything, from 1-1/4" nominal diameter PVC to a good grade of aluminum tubing (thicker-wall than the usual 0.55" hardware store variety) to a 5' length of spar varnished 1.25" diameter closet rod. Make up a boom-to-mast plate similar to the boom-to-element plates, only a bit more square, and you are in business.

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The dimensions of the antenna in the drawing are too fussy, being direct translations of the computer model used to generate the antenna. Just try to keep the dimensions within about 1/4" of the drawing, and no one will be able to tell any difference in performance. Squaring the corners or missing the dimensions by a half inch will shift the performance centers by about 100 kHz at most. In most cases, you will not be aware of any difference at all.

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Note that the antenna is just about 12.5' wide and under 5' front-to-back, for a turning radius of about 6'8" or so. Strapped up on the side of the house, the antenna is unlikely to overhang the neighbor's yard line. The antenna is light enough for hand rotating, but an old TV rotator might come in handy. Because of the antenna's characteristics, you may not need to rotate it much.

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The pattern figure shows the optimal front-to-back ratio in azimuth patterns 20' and 35' antenna heights. Note the very broad forward lobe that is almost a cardioid, giving reception and transmission as wide as your peripheral vision. Behind you is silence--or at least a large dose of silencing. Les Moxon, G6XN, uses a wire version of the antenna with both elements remotely tuned: that way he works the world just by electrically reversing front and rear elements with a fixed mounting. If you want to learn more about the Moxon rectangle, find the Spring, 1995, issue of Communications Quarterly, and look at pages 55-70 (link).

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It is unlikely that anyone will ever produce this beam commercially, since it is a monobander without the super gain that avid DXers and contesters crave. You can only get that kind of performance from many Yagi elements. However, you can build your own compact antenna with a pretty good chance of success on the first try. It will beat a fixed wire dipole or a vertical hands down. So if you need a compact 10-meter beam for your compact home site, then you might roll your own version of the aluminum Moxon rectangle.

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For further details on the construction of this antenna, see The ARRL Antenna Compendium, Vol. 6, pp. 10-13.

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See the Moxon Rectangles and Online Calculator page for more information.

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Updated 3-12-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 28: Beta Coils and Hairpins

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L. B. Cebik, W4RNL

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In a number of columns, I have mentioned the beta match. Let's take a brief look at what it is and what it does.

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The beta match appears to be simply a small coil or hairpin placed across the terminals of an antenna, most often a Yagi. Some folks mistake the coil for an RF choke, while others mistake the hairpin for a short circuit.

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Actually, the beta coil or hairpin is one part of an impedance matching circuit, where the remaining elements are invisible, if you do not know what to look for. Many Yagi antennas have feedpoint impedances in the 20 to 35 Ohm range, somewhat low for feeding directly with coaxial cable. We need to raise the impedance to 50 Ohms--and that is what the beta match system does.

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The coil is not the only element in the circuit. There is also a capacitor--or, more correctly, some capacitive reactance. We get that part of the circuit from the antenna element itself.

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Fig. 28-1 shows how we move from a resonant driven element to a beta match. Let the resonant antenna impedance be low, say about 25 Ohms. If we shorten the element, the resistance does not change significantly, but the antenna becomes capacitively reactive, as the middle part of the figure shows.

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If we shorten the element by the right amount, we get the right capacitive reactance in series with the antenna resistance to go together with an inductance across the coil to make an L-circuit. An L-circuit is one of the fundamental impedance transformation circuits, and in this case, -Xa and XL together change the 25- Ohm antenna resistance to 50 Ohms.

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We can calculate the needed values if we know the antenna feedpoint resistance (Ra). (We know the coax has a characteristic impedance (Ro) of 50 Ohms.) First we calculate a value called "delta" by some and "working Q" by others. Delta = the square root of [(Ro/Ra)-1]. Now we can easily calculate the necessary values of capacitive reactance in the antenna (- Xa) and of inductive reactance to place across the terminals (XL). Xa = Delta times Ra. XL = Ro / Delta.

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Since these values are given as reactances, you need to convert the inductive reactance into a component value. The capacitive reactance will be developed by simply shortening the antenna element until the beta match gives us 50 Ohms.

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For reference, here is a small table of values we commonly encounter with beta matches with 50-Ohm coax for various values of antenna feedpoint resistance (Ra):

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Ra               33       25       17
+Delta            0.7      1.0      1.4
+Xa               23.6     25.0     23.6
+XL               70.7     50       35.4
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Notice that the capacitive reactance reaches a peak when delta = 1, while the inductive reactance gets smaller as the feedpoint resistance gets smaller.

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We have not yet converted these inductive reactances (XL) into a component value, because there are two distinct ways to achieve the required reactance across the coil. Fig. 28-2 below shows them both:

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The beta inductor is simply a coil with the value of inductance that provides the inductive reactance at the operating frequency. If you divide the required inductive reactance by the product of the operating frequency (in Hz) and twice pi, you get the right inductance.

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The hair pin version of the beta inductor is actually a small shorted stub of parallel transmission line. Rather than go through the calculation procedure, I shall simply once more recommend that you obtain a recent copy of HAMCALC, a suite of handy ham calculation programs in GW Basic. Among the selections on the disk is an excellent program that will calculate the dimensions of a hairpin for the match. It was written by Thomas Cefalo, Jr., WA1SPI. The program will also tell you the equivalent inductance in case you want to wind a coil. Other programs in HAMCALC will help you wind an accurate coil.

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Many antenna builders use the experimental technique of adjusting the driven element for a beta match. After calculating the beta coil or hair pin, they install it and then adjust the element length for a low SWR. Antenna modelers tend to determine the required element length in advance from their software and save some time fumbling for the right element length.

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Either way, the beta match results in a very low loss match. For inductor Qs over 100 (easy to obtain, but some maintenance is required to maintain the Q), losses will be well under 1%--and even less for the hairpin.

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If you like to build antennas, you should become familiar with the beta match. Some folks actually avoid the beta match because it is "too simple to really work." However, it does work, and very well indeed for antennas with moderately low feedpoint impedances. Since there are easy-to-use utility programs for calculating everything you need, there is no need to avoid either the beta match or antennas that require one.

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Updated 7-1-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

+ + diff --git a/content/a10/ant29.html b/content/a10/ant29.html new file mode 100644 index 0000000..4206d86 --- /dev/null +++ b/content/a10/ant29.html @@ -0,0 +1,69 @@ + + + + + Some Larger 10-Meter Yagi Designs + + + +
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No. 29: Some Larger 10-Meter Yagi Designs

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L. B. Cebik, W4RNL

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Occasionally, I am asked to recommend some larger Yagi designs that one might build for 10 meters. I can do little better than recommend the designs by Dean Straw, N6BV, that appear in the K6STI, Brian Beezley, program, YA, which has been distributed with The ARRL Antenna Book. In past columns, we have noted other designs originating from YA/YO. We have also featured various 2-element and 3-element Yagis of interest.

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The present designs use 4, 5, and 6 elements. Each has been optimized for stable gain, front-to-back ratio, and impedance across the first MHz of the band. I have cross-checked each of them on other antenna modeling programs to confirm the numbers, and all appear to be very promising designs for the home builder.

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The gain of a Yagi depends more on the boom length than on the raw number of elements. Therefore, each design will use a longer boom in conjunction with the increasing number of elements to achieve its objectives. Merely adding more elements within the same existing boom length will rarely produce any significant additional gain.

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The element listings use a combination of 5/8" (0.625") and 1/2" (0.5") diameter tubing. Only one side of the antenna, relative to the boom, is listed, with the other side being a mirror image. Both the outer segment length and the total half-element length is listed for convenience. The smaller diameter element sections should be at least 3" longer than the lengths listed for insertion into the larger diameter element sections. All dimensions will be in inches. The decimals in the tables correspond the 1/8" increments of length.

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The element assemblies are considered medium duty for maximum winds just over 90 miles per hour. For structural details of large Yagi construction, consult one or more of the many handbooks on antenna building. These beams are not casual projects, since they represent a considerable outlay for materials and result in large structures. Their weight may require a larger rotator and other improvements to your tower. Even the smallest of them should not be mounted on something so light as a telescoping mast.

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4-Element, 14' Boom Yagi
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+Distance from      Length of    Length of     Total (1/2)
+Reflector          0.625"       0.500"        Element Length
+  0.000            36.000       70.000        106.000
+ 36.000            36.000       63.875         99.875
+ 72.000            36.000       62.250         98.250
+162.000            36.000       53.125         89.125
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The mid-band free-space gain of this antenna is about 8.4 dBi, with an excellent (greater than 20 dB) front-to-back ratio.

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5-Element, 20' Boom Yagi
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+Distance from      Length of    Length of     Total (1/2)
+Reflector          0.625"       0.500"        Element Length
+  0.000            36.000       71.375        107.375
+ 36.000            36.000       63.375         99.375
+ 72.000            36.000       62.750         98.750
+140.000            36.000       61.500         97.500
+234.000            36.000       56.375         92.375
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The mid-band free-space gain of this antenna is about 9.7 dBi, with an excellent (greater than 20 dB) front-to-back ratio.

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6-Element, 36' Boom Yagi
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+Distance from      Length of    Length of     Total (1/2)
+Reflector          0.625"       0.500"        Element Length
+  0.000            36.000       70.875        106.875
+ 37.000            36.000       62.875         98.875
+ 80.000            36.000       62.375         98.375
+178.000            36.000       60.125         96.125
+305.000            36.000       59.250         95.250
+426.000            36.000       55.250         91.250
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The mid-band free-space gain of this antenna is about 11.6 dBi, with an excellent (greater than 20 dB) front-to-back ratio.

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All of these antennas have feedpoint impedances that are designed for a beta or similar matching system. The resistive part of the impedance is in the low-20s, with a comparable amount of capacitive reactance. You may lengthen the driven elements to resonance without adversely affecting antenna performance. A resonant driven element of about 25 Ohms can be matched to a 50-Ohm coaxial cable with a quarter wavelength section of 35-Ohm coaxial cable. Such cable can be purchased for about $3.00 per foot. You may also fabricate a satisfactory line using parallel lengths of 75-Ohm cable with the braids and the center conductors each soldered together at each end.

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The smallest of these monoband 10-meter beams will generally outperform the 10-meter section of all but the very largest tri- banders. The longest of the beams is a serious DX-hunting machine. To obtain the maximum performance from any of these beams, place them at least 1 wavelength above ground and preferably closer to 2 wavelengths.

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Installing large beams at considerable heights above ground is not a casual process. First, there may be zoning and other legal restrictions or permissions to consider. Second, proper tower installation may cost many times more than the materials in the beam. Safety for yourself, your family, your property, and your neighbor's property are of paramount importance. So too is durability of the performance of the whole system, including the tower, coax, rotator, guys, grounding system, and the antenna.

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Before moving to large beams and complex tower installations, learn all that you can about every aspect of the task. If you have any doubts, consult professional tower installers for answers and for help. Do not violate or ignore applicable laws and ordinances. Do not settle for any installation that does not measure up to good engineering standards. And, for heaven's sake, do not rely on luck to keep your antenna in the air and lightning in someone else's yard.

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As you can see, a big antenna--even for 10 meters--is only the beginning and not the end of a much larger enterprise. If you have all the other pieces in place, then one of the N6BV designs may be the answer to the antenna part of the puzzle. Other designs, some with feedpoint impedances in the 35 to 50 Ohm range are also available from various ham magazines. Collect lots of designs and ideas before you start cutting aluminum. The more design articles you read, the more you will learn about the art of building big beams.

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Updated 10-1-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 3: Where Does the Gain Come From?

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L. B. Cebik, W4RNL

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Earlier, we looked at 3 antennas modeled in free space: a dipole, a 2- element Yagi, and a 3-element Yagi. All were made from aluminum tubing and all were monoband antennas with no traps or other lossy components. The patterns we showed made it clear that the 3-element Yagi had the most gain and the highest front-to-back ratio. But that does not make it very clear from where the gain comes, given a constant transmitter output.

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Fig. 1 repeats the azimuth patterns to refresh our memory. An azimuth pattern is like standing over the antenna and seeing its radiation. For free space patterns, we use 0ø elevation, since the pattern is strongest straight on.

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The azimuth pattern does not give a whole picture of where the power is going. It does show that the beams project more power in the forward direction than the dipole, while "robbing" power from the rear. In reception terms, signals from straight ahead are strongest and weaker to the rear. However, they are weakest off the sides of the antennas.

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To accurately see the power pattern of an antenna, we must also look at it from the side in an elevation pattern. An elevation pattern is like standing beside the antenna and looking through the aluminum tubes, while seeing the radiation. Fig. 2 gives an elevation pattern in free space for the same 3 antennas (3-element, 2-element, and dipole). Notice the displacement of the beam antenna patterns to the right, which corresponds to the forward lobe of the beam antenna azimuth patterns.

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Only an astronaut can have a pattern radiating below the antenna site. Antenna gain over real ground also makes use of radiation reflected from the ground. Fig. 3 shows elevation patterns for the three antennas over real ground at 35' feet, about 1 wavelength above ground. The azimuth patterns would resemble those of Fig. 1, but they would not be taken at horizon level. Instead, they would use the angle of maximum power, sometimes called the take-off angle. The elevation patterns display this angle clearly and show that horizontal antennas above a real ground have a number of higher angle lobes as well as the main lobe. The complex pattern results from adding and subtracting reflected radiation from the above- ground pattern, depending on its relative phase.

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Comparing Fig. 2 to Fig. 3 can lead to a misunderstanding, since the apparent radiation pattern is the same size; that is, the radiation just reaches the outer ring. However, that way of styling our drawings is just a convenience for making comparisons within each drawing. In actuality, the power in the lowest lobe of Fig. 3 for each type of antenna is much greater than the power in just the horizontal direction of Fig. 2. Expressed another way, all of the power represented by the spheres or near- spheres in Fig. 2 is flattened, thus putting greater power into the lobes that extend horizontally. The total power in the lobes is a result of adding reflections to the main or incident power going that way. The net result is gain over free space and gain of one antenna over another. And since the gain can be both calculated and controlled by good antenna design, we can--within limits--achieve a good bit more success than early radio pioneers in making and maintaining radio communications.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
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No. 30: The V-Yagi

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L. B. Cebik, W4RNL

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In May, 1998, QST, NW3Z and WA3FET published an interesting 3-element beam for 40 meters, using one tubular element and two wire elements. The result was a light weight (for that band) beam with excellent SWR and F-B characteristics. It superficially resembled an old design by Dick bird, G4ZU, but had been optimized for performance resembling that of a Moxon rectangle: great F-B ratio, wide pattern forward, and direct coax feed. However, with an extra element, it had more gain. Why not adapt the design to 10 meter?

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As Fig. 1 shows, the adapted antenna for 10 meters has decent gain and good front-to-back ratio across the first MHz of the band. The patterns are taken with the antenna modeled at 35' (1wl) up.

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The SWR curve strongly suggests that direct coax feed is certainly in order. As always, I recommend a choke balun at the feedpoint.

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Now that we have seen what the antenna can do, all we need to know is what the antenna looks like and how hard it might be to build. Like all Yagis, it will have significant side-to-side and front-to-back dimension. However, unlike the usual Yagis, only one of the elements will be made from aluminum tubing, while the other two will made from #14 AWG copper wire.

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As the sketch shows, the driven element is the longest part of the antenna. Overall, it is 197" long, with a insulated mounting plate to permit direct connection of the feedline to the element. The inner parts of the element are 48" lengths of 1" diameter hardware store aluminum, while the outer ends are made from 7/8" diameter tubing from the same source.

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The dashed lines crossing the driven element are booms to support the wire elements. They can be made from fiberglass or aluminum, with the center boom stronger, since it is about 12' long. The end support booms can be lighter, but need to support the wire ends. If the end booms are made from aluminum, they should be insulated from the driven element and set farther outward, so that the wire elements can terminate at an insulator. Simple UV resistant rope (3/16" diameter) connects the wire and end-support boom to the driven element ends, which helps prevent the wires from loading the end supports too much.

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The wires are each 94.4" long from the center boom to the end (at an insulator or at the support boom). At the ends, they should be between 30 and 31 inches from the driver. Since both wires are the same length, we need to load one of then to electrically lengthen it to become a reflector. A shorted transmission line stub about 65.55ø long will do the job, although you may want to adjust the exact length when tuning up the antenna. The length in degrees translates into 50.125" of RG- 58/RG-8 (velocity factor 0.66) line. You can use standard stub equations to calculate the length of 300-Ohm or 450-Ohm line as a substitute.

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The V-Yagi will not give all of the gain that a 12' boom is capable of giving if the elements were linear and fatter. In fact, this antenna is about 1 dB shy of maximum gain for the boom length. On the plus side of the ledger, the antenna is quite light, study, and has a smaller turn radius, since the corners are shortened by the slope of the director and reflector wires. A TV rotator should turn the beam with ease. However, you may not have to turn this beam as often as you might have to turn a standard Yagi, since the beam width is quite a bit wider.

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The V-wire for 10 meters is not for everyone, not even for every addict of home brew antennas. However, I have learned over the years that different folks have different needs, different skills, and access to different materials. So I never try to prejudge what mechanical designs are acceptable and which are not. That would limit folks to only my own level of construction ability. Instead, I pass along ideas for designs, and let those who can make good use of them have at it. Others can pass up this design, hoping for a more suitable one in the next column.

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Over the past 7 years or so, we have looked at a lot of antenna idea. And yet, we have only scratched the surface.

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Updated 12-1-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 31: A Triangular Vertical Array

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L. B. Cebik, W4RNL

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Most beams we have discussed have been horizontal. I have not wanted to neglect fans of vertical antennas, but good designs that are not just horizontal antennas flipped 90 degrees are not easy to find.

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In some areas, the local gang use vertical whips and mobile antennas. Skip contacts do not care what polarization your antenna uses, since the ionosphere skews the polarization of the original signal. So the question is whether we can find a decent vertical antenna that will serve both local and distant needs.

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Well. . .how about a set of 3 vertical dipoles that require no rotator and only a simple weather sealed box with some relays inside. With a flip of a switch, you can cover the entire horizon in three broad lobes with little if any gap in coverage. The gain will not rival a long-boom Yagi, but the antenna array will give some gain and very decent a front-to-back ratio, with a direct coax feedline connection.

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Let's start with three vertical dipoles, each 15.6' long made of 3/4" hardware store aluminum tubing. See Fig. 1. We shall set these up in an equilateral triangle 8.6' on a side (1/4 wavelength). If we run a mast up the middle of the array, we can use PVC or other means of supporting the vertical at just about their center points, leaving the feedpoint separation free for connections. The arms for such a system would have to be just about 5' long from the center mast.

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Next, we shall cut 4.97' (yes, 5.0' is OK) lengths of RG-8 foam or RG-58 foam coax. We must use the foam type to get the right velocity factor (0.78) so that the lengths are electrically correct. Each line goes from one feedpoint to a central waterproof junction box. The coax from the shack and a 12-volt DC line also enter the junction box.

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The schematic diagram in Fig. 2 shows the hook-up for 3 DPDT 12-volt relays in the box. (The switch is shown in the box, but it will be in the shack.) As we change positions on the switch, we activate one relay, moving the connectors so that the center of the coax from one antenna goes to the RF cable and the shield goes to the shack coax shield. The inactive relays let the coax from the other two antennas simply be shorted out.

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The shorted lengths of coax are stubs that electrically lengthen the other two antenna elements so that they work better as reflectors. Now we have 2 reflectors and one driven element in a vertical array.

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The elevation pattern created by this system and shown in Fig. 3 gives us a low angle pattern, good for both local and dx contacts. The front-to-back ratio varies between 12.5 and 15 dB across the first MHz of 10 meters. The gain is very usable, but not world beating. However, remember that we saved the cost of a rotator with this array, and we can work the vertical locals with ease.

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In addition to all having gain and appreciable front-to- back ratio, we can cover the entire horizon just be changing the switch position. The switch simply converts one element from a reflector into a driven element, changing the overall heading of the array. The beamwidth of a vertical antenna is very large--well over 120 degrees between -3 dB points. Hence, three headings are enough to cover the world.

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The composite azimuth patterns in Fig. 4 give you a good idea of how large the beam width is and how good the overall coverage is. If you construct the basic support system well enough, you will have an antenna with no moving parts other than the relays in the box. Servicing a relay at the top of the tower is easier than servicing a rotator. +

The array can be fed directly with coaxial cable, as the SWR curve in Fig. 5 shows.

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All of the figures shown are modeled with the antenna at 35' at its center. The higher, the better, but the antenna will still work quite well with its lowest point at least 20' off the ground.

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Verticals acquit themselves very well on 10 meters, and this vertical array will add some directional gain and some QRM nulling. Relative to a beam, the cost will be low, and the maintenance should be easy. Possibly, it is time to think vertical.

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Updated 05-01-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 32: What the Heck is a Stub?

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L. B. Cebik, W4RNL

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Some of the antennas we have looked at in these columns have used transmission line stubs. I often receive this question: "Just what is a stub and what does it do?" So let's look at stubs. To keep things simple at the beginning, we shall confine ourselves to stubs shorter than a quarter wavelength.

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The Basic Principle

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A shown in Figure 1, a stub is a length of transmission line. When the line is shorted at the far end, it acts as an inductive reactance and can actually replace a coil. When the far end is open, the stub acts as a capacitive reactance and can replace a capacitor. Stubs would be too large to use in HF circuits, but they are convenient in antenna applications, where space is usually no problem. They can handle high voltages and currents, often with greater ease and cost-effectiveness than lumped components.

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The amount of inductive or capacitive reactance is proportional to the length of the stub. However, the relationship is not linear. Let's look at how we calculate the reactance of a shorted stub to see why.

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where XL is the inductive reactance in Ohms, ZO is the characteristic impedance of the transmission line used for the stub, and Ld is the length of the line in electrical degrees. since we are using lines shorter than 1/4 wavelength, Ld will be between 0 and 90 degrees.

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For the same value of reactance, the higher the ZO of the transmission line, the shorter the line length. Hence, parallel transmission line is often used for inductive stubs to save space. Since the tangent of angles above 45° grows larger very fast, we usually restrict ourselves to modest value of inductive reactance so that we can prune the line length precisely without overshooting the mark.

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Shorted stubs for inductive reactance are more common than open stubs for capacitive reactance. The reason is easy to see from the formula.

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where XC is the capacitive reactance in Ohms and the other terms have the same meaning as in the earlier equation. Smaller values of capacitive reactance (the most common need) require longer transmission line stubs. While some applications call for open stubs, shorted stubs for inductive reactance are far more common.

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Application #1

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Figure 2 shows one common use of shorted (inductively reactive) stubs: to load an antenna element to make it electrically longer than its physical length. We know that a Yagi reflector is longer than the driven element, but in the figure, they are the same physical length. The load value of XL is 85 Ohms to make the reflector work like an element somewhat longer than the physical length would permit. Now we can place a coil in the load position. At 28.5 MHz, a coil of 0.47 microH would do the job, but its resistive losses might be of concern. Short stub losses are nearly negligible, so let's use a stub instead.

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At the given frequency of 28.5 MHz, a shorted stub might be made from either RG-58 (50 Ohms, 0.66 VF coaxial cable) or parallel transmission line (for example, 450-Ohms, VF 0.95). The first step is to take the ratio of XL and ZO. For 50-Ohm cable, this is 1.7, and for 450-Ohm line, it is 0.19. The second step is to figure the length in degrees. The "arctan" (backing out the degrees when you know the tangent of an angle) of 1.7 is 59.5°, while the arctan for the 450-Ohm line is 10.7°.

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Now let's figure the real line lengths needed. First, we know that a wavelength at 28.5 MHz is abut 34.5' long for a full 360°. 59.5° means a 5.71' length. 10.7° is 1.025' long at the same frequency.

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However, remember that the actual transmission lines had VF (velocity factor) values. The coax value means that its length needs to be 0.66 times the calculated amount, or 3.77' (45.22"). The parallel line had a VF of 0.95 and thus needs to be about 0.97' (11.7") long. Personally, I would use, if possible, the 450-Ohm line, since it is shorter, lighter, and easier to handle. But that is not the right decision for every situation.

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Application #2

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Some antennas use a beta match system, which requires an inductive reactance across the antenna terminals so that an antenna with a low impedance can match a 50-Ohm coax system, as sketched in Figure 3. Although coils are quite effective, most commercial beta matches use a "hairpin." The hairpin is nothing more than a U-shaped piece of wire, which is itself nothing more than a shorted parallel transmission line.

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Using standard equations for L-networks we can calculate the inductive reactance we need to place across the coil. If the antenna has an impedance of 25 Ohms, then the required reactance is 50 Ohms. We can make a hairpin from our 450-Ohm transmission line, using the same procedure. 50/450 = 0.11. The arctan of this number is 6.34°. This number of electrical degrees amounts to 0.61' (7.29") at 28.5 MHz. If the VF is 0.95, then the final length is 0.58' (6.93").

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For both applications, we would start with lines a little long and prune them to exact length. We can do this by having an adjustable set of contacts at the terminals or we can trim the shorted end and resolder the shorting bar.

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The math in this exercise is mostly to acquaint you with the general properties of stubs--which call for shorter lengths and which call for longer. Those inclined to do so can calculate a bunch of 10-meter stubs to see what the lengths look like for various values of XL and XC and different types of transmission line. Then when you encounter stubs in articles, presence and general dimensions will be familiar to you.

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The antenna array we discussed in the last column used stubs in the reflectors. I'll bet the next column also has a stub.

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Updated 07-01-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 33: The Cheapest 2-Element Beam?

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L. B. Cebik, W4RNL

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"Can I build a small directional antenna for less than $20?" That was the challenge presented to me. The answer is yes. However, remember that this is a project designed for the dollar sign, so the gain and directivity will be modest. Here is what we need:

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  • 32' #14 copper wire (Radio Shack and elsewhere)
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The antenna is a 2-element wire parasitic beam with the ends tapered back toward each other. The elements are the same physical length, but the reflector is stub loaded to increase its electrical length. (See the last column for information on stubs.) Gain is about half an S-unit over a dipole, and the front-to-back ratio is about 2 S-unit. Feed is a direct coax match, and coverage is about 900 kHz of 10 meters.

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Figure 1 shows both the wire and support frame dimensions. The 2x2 determines the side-to-side dimensions, while the cross piece determines the maximum front-to-back dimension. The end cross pieces keep the wire ends 9" apart.

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Use a good marine (spar) varnish (or modern poly equivalent) on all wood. Expect to re-varnish the wood annually. Be sure the 2x2 does not sag a lot. The cross pieces can be PVC or 1x2. If wood, give it the same spar varnish treatment.

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Details of coax connector mounting, wire termination, and mast support are subject to many variations, so I shall bypass them here. Check with any handbook for many different ways to achieve the same goals. Likewise, mast details are omitted here.

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The figure shows the stub dangling, but you can tape it to the center cross piece. Not shown is the 1:1 choke balun at the antenna feedpoint that I use on all antennas to reduce RF on the outside of the coax to the shack.

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Figure 2 shows the azimuth pattern with the antenna at 20' over average ground. 20' is the height of two sections of TV masting, which makes an adequate support system for hand rotating the beam. Whatever system you use to elevate the antenna (which I shall assume is as inexpensive as the antenna itself), be certain that the mast is well guyed or bracketed for safety.

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The antenna pattern is not a paragon of gain or rear nulling, but it does have some nice features. The forward beamwidth is wide enough so that a single twist of the mast will cover all of Europe or all of the VK-ZL area--or from each of these places, a single setting will cover all of the USA and Canada. The rear has only one lobe, so that there are no antenna positions susceptible to QRM from some quartering rear direction.

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Figure 3 is the modeled SWR plot across the first MHz of 10 meters. The antenna was designed for 28.35 MHz to provide a low SWR for the most popular segment (28.3 to 28.5 MHz). You can shift the SWR curve downward by increasing the length of both wires equally about 2" or so--or shorten them by the same amount to move a bit up the band. However, keep the wire end separation at the prescribed 9" with the end cross pieces.

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The antenna is related to the standard Yagi, although the elements are not exactly parallel. The element end coupling also relates the design to the Moxon rectangle, but the sloping wires prevent us from achieving the high front-to-back ratio of that design while still having any forward gain worth using.

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So while the performance is modest, the price is attractive. The sdloping wire array is a fun antenna to play with, since the cost is so low. However, the most important aspect of the design is that in an emergency--perhaps after some natural disaster has knocked down all of the regular antennas--this design can be fabricated from scraps from the rubble. You can make the electrical elements from house wiring that is no longer functional and lash together a frame with bailing wire.

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If you have no inclination to play with the design at this time, you may wish to file this column away in your notebook labeled "In the event of emergency or disaster. . .."

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Updated 10-01-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 34: The Turnstile Antenna on 10

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L. B. Cebik, W4RNL

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Net control stations often ask for an omni-directional horizontally polarized antenna. One of the simplest antennas to meet this need is the turnstile. The basic outline appears in Fig. 1.

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Essentially, the turnstile consists of two dipoles at 90 degree angles to each other. One dipole is connected to the main feedline, in this case a 50-Ohm line (since the two dipoles together will give a 36-Ohm feedpoint impedance). Between the feedpoint of Dipole 1 and Dipole 2, we run a 90-degree or 1/4 wavelength section of 72-Ohm coax to effect the required phase shift between the two dipoles. It is this phase shift that gives the turnstile its nearly omni-directional pattern.

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For 1/2" to 5/8" tubing--or a combination of the two--the dipoles can each be 16.5' long--8' 3" on each side of center. This size will make them resonant at about 28.5 MHz. The dipoles must not touch each other. You can accomplish this by mounting them on opposite sides of a square plywood board or by keeping the feedpoint separations large enough so that nothing touches.

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Connect the main feedline across one dipole. Then connect the phasing line from the feedline connection points to the other dipole connection points. If you use a balun, connect it only to the main feedline. Let the phasing line droop. You can tape it together for control. But it is best to keep it spaced from any metal antenna mast you use to support the antenna.

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The phasing line length will depend on the velocity factor of the line you use. 72-Ohm coax comes with either solid or foam insulation. The solid insulation usually gives the line a 0.66 velocity factor, while foam lines have a velocity factor of about 0.78.

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Use the velocity factor as a multiplier on the basic 1/4 wavelength to determine the physical length of the line. 1/4 wavelength is about 8.63' at 28.5 MHz. A 0.66 VF line will be about 5.69' long, while a 0.78 VF line will be about 6.73' long. As with any antenna, be sure to weatherproof all connections to prevent rain from entering the coax line.

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Since the turnstile impedance is about 36 Ohms, a 50-Ohm feedline will show an SWR of between 1.3:1 and 1.4:1. Do not try to tune the antenna for a 1:1 SWR, since that will require shortening the elements below individual dipole resonance. The resultant pattern will no longer be omni-directional. On the other hand, once you have built the antenna close to the dimensions suggested here for both the elements and the phase line, it will be very broad-banded, covering all of 10-meters.

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What kind of performance can we expect from a turnstile. Fig. 2 gives us an answer.

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The pattern is a blunted circle with only a 1 dB decrease from maximum gain along two of the flattened edges. This is as close to a perfect circle as you will come with a horizontally polarized antenna of this efficiency. The maximum gain is about 5 dBi when the antenna is 1 wavelength (about 35') above ground. At this height, the antenna has 2 elevation lobes, one at 14 degrees for long hauls and the other at 48 degrees for short skip and e-layer reflections. The local point-to-point abilities of this antenna are quite good.

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As always with horizontal antennas, the higher, the better--up to about 1.75 wavelengths or so--especially for local contacts. The turnstile gain is lower than the maximum gain of a dipole along, but remember that a single dipole has only two main lobes working at one time. The turnstile has 4 overlapping lobes. Since the power for any operation is constant, it must distribute itself over more territory--and hence will not be quite as strong as when we can limit its coverage to two lobes. (The uni- directional beam gets its gain from concentrating almost all of the power in one lobe.)

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The turnstile can be a useful antenna for net control stations. It may also be useful for folks who want a dipole, but do not wish to turn it with every new incoming signal. You can orient the antenna along any axis, so you have some options in fitting it into the space you have.

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However, the turnstile has limitations. For its area, gain is not high. In the same footprint, you can create a small 3-element beam with much higher gain and directivity. Also beware of the temptation of folding the ends around to reduce the space required by the crossed dipoles. The omni-directional pattern will become a bi-directional, weak set of dipole lobes. Finally, the turnstile is a monoband antenna, due to the requirement for the 90-degree phasing line. If you want a turnstile for another band, you will have to design the entire antenna--both dipoles and the phasing line--for the new design frequency.

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So the turnstile is a special-purpose antenna. If it has the pattern you need, use it. If you need a different pattern, then try one of the other antennas in this series.

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Updated 12-01-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 35: A 10-Meter, 6-Element OWA Yagi

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L. B. Cebik, W4RNL

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There is a very interesting 20-meter Yagi design called the Optimized Wideband Antenna, or OWA. Although only one of several designs within this genre, developed by Nathan Miller, NW3Z and Jim Breakall, WA3FET, the 20-meter version is one of the most adaptable. It employs 6-elements in the space that many other designs use 5. Fig. 1 shows the general proportions of the antenna.

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The 20-meter antenna has several features that deserve special note. Director 1 is perhaps the most significant, since it represents the added element to previously standard 5-element designs. By the use of this parasitic element, the driver can be more closely spaced to the reflector and still show a feedpoint impedance very close to 50 Ohms resistive. Moreover, the antenna shows wideband VSWR characteristics, with values less than a 1.3:1 from 14.0 through 14.35 MHz.

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Not only is the feedpoint impedance quite stable, so too are the other main operating characteristics, including both gain and the front-to-back ratio. The antenna shows better than 10 dBi forward gain in free space models across the entire 20 meter band, with more than a 20 dB front-to-back ratio across the same span. Many 5-element designs show much larger variations in all three of the main Yagi parameters: gain, front-to-back ratio, and feedpoint impedance.

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The remaining elements of the OWA are also interesting. Directors 2 and 3 are either the same length or the forward director is slightly longer than the rearward member of the pair. Director 4 and the reflector are available for making small changes in the upper and lower frequency limits of the design to spread the operating characteristics across the desired bandwidth. The 20-meter band is about 2.5% of its center frequency. The OWA is capable if significantly greater operating bandwidths with little loss in any of its main characteristics.

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The reason for making extensive note of the OWA design is that it scales quite easily (but not without some readjustment) to create very usable Yagis for 10 meters. Although only a few hams have the wherewithal to construct a 48' boom Yagi for 20 meters, 24'-boom Yagis for 10 are more common--and more manageable. The resultant beam shows a free space gain above 10 dBi across the band, a front-to-back ratio always in excess of 20 dB, and very low 50-Ohm SWR values for direct coax feed systems.

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Scaling the initial OWA to 10 meters involved converting the 20-meter design into its equivalent uniform diameter element equivalent, scaling this antenna, and then creating a set of tapered diameter elements suitable for 10 meters, adjusting their lengths to be equivalent to the substitute model. The table lists the overall element length, the spacing from the reflector, and the exposed tubing lengths of each size tubing used on one side of the element. (Be sure to double the length of the largest size tubing and to have extra inches on the remaining sections for the tubes to nest.) All dimensions are in inches.

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Element   Overall    Spacing        0.5"           0.375"         0.25"
+          Length     from Refl.     Inner          Middle         Outer
+Reflector 216.8      ------         35.75          35.75          36.9
+Driver    209.2       44.68         35.75          35.75          33.1
+Dir 1     199.36      69.26         35.75          35.75          28.18
+Dir 2     193.23     132.40         35.75          35.75          25.12
+Dir 3     193.24     192.83         35.75          35.75          25.12
+Dir 4     186.05     282.96         35.75          35.75          21.53
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The antenna was scaled and reset to cover the span from 28 to 29 MHz. Some adjustment of the reflector and 4th director was required to achieve the added bandwidth. The first MHz of 10 meters represent a 3.5% operating bandwidth, about 40% greater than demanded of the 20-meter antenna. The following table shows representative modeled figures for 5 points across the band. All figures are based on free space models using NEC-4.1 with Leeson corrections invoked for greatest accuracy.

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Parameter      28.0      28.25     28.5      28.75     29.0
+Gain dBi       10.00     10.10     10.19     10.26     10.27
+F-B dB         20.29     26.57     30.22     24.47     21.34
+Feed Z:
+      R        38.4      41.9      44.4      44.6      36.5
+      jX       +5.0      -1.1      +1.3      +0.5      -2.6
+50-Ohm SWR      1.33      1.20      1.13      1.12      1.38
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The greater bandwidth demanded of the 10-meter design shows most clearly in the rise in SWR and decrease in feedpoint impedance at the low and high ends of the bandpass. Nonetheless, the design meets all of the objectives. The gain changes only by about a quarter dB across the band. With further tweaking, the feedpoint impedance might be brought upward toward 50 Ohms a bit, but the reactance figures are extremely low for an antenna covering a full MHz of 10 meters. All of this suggests that the OWA design concept is capable of significant expansion beyond its original implementation.

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The antenna pattern itself is a model of good behavior, with no undesirable side or rear lobes. Note in Fig. 2 the change in the shape of the rearward lobe across the band, which is a normal progression for well-behaved antennas of this type.

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Just for the drama, Fig. 3 shows the 50-Ohm SWR sweep, taken at 0.1 MHz intervals across the band. There are no impedance spikes anywhere in the bandpass of the antenna.

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As a high-performance 10-meter antenna covering all of the first MHz of the band, the 24' 6-element OWA is a worthy monoband competitor with other designs for the band.

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For those who prefer somewhat beefier construction, here are the dimensions of the NW3Z model on a 24' boom using 0.75" diameter inner tubing, 0.625" diameter middle tubing, and 0.5" diameter tip sections. Note that the element lengths and spacing are slightly different than the slim-element version above. When adapting Yagi designs, do not simply take the dimensions you find in an article and use whatever materials you have. Differences in element diameter and where the steps in the diameter occur will make a difference in the required element lengths and spacings. A hasty near-copy may not perform to full specifications.

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Element   Overall    Spacing        0.75"          0.625"         0.50"
+          Length     from Refl.     Inner          Middle         Outer
+Reflector 215.04     ------         24.00          18.00          65.52
+Driver    207.18      43.86         24.00          18.00          61.59
+Dir 1     195.80      69.18         24.00          18.00          55.90
+Dir 2     191.76     131.30         24.00          18.00          53.88
+Dir 3     192.34     192.70         24.00          18.00          54.17
+Dir 4     183.14     282.00         24.00          18.00          49.57
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All credit for the OWA design belongs to its originators. Further details can be found at the following website: http://www.contesting.com/nw3z/. This exercise has only shown that one of the implementations of the basic design can be advantageously adapted to other bands. None of the models presses any limit of the NEC and, therefore, they are quite reliable, both as analyses of the antennas and as guides to construction. Of course, using still another element diameter taper schedule than the ones shown will require resetting the element lengths to accommodate the materials used.

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In addition to being rather good Yagis of their size, the OWA designs may also serve as a standard against which to measure other designs that present themselves. Even if you never build one of these designs, the data provided here may be useful for comparative purposes.

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Updated 4-01-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 36: 4- and 5-Element OWA Yagis

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L. B. Cebik, W4RNL

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The OWA (Optimized Wide-band Antenna) design for Yagis means different things to different designers. For some, it means simply a low SWR across a passband (like 28-29 MHz), regardless of the impedance. To others, it means a low 50-Ohm SWR across the passband. Since many 10-meter users are more comfortable with a direct coax feed (with a choke balun for protection from common-mode currents down the line), let's take the latter approach.

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Last time, we looked at a 6-element 24' OWA using fairly thin elements. This time, let's look at some shorter designs using elements with larger diameters. In fact, in this episode and the next, we shall look at a total of 4 OWA design ranging from 13' to 36' long, all with the same element structure.

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Fig. 1 shows the element structure that all of the beam designs will use. The 4' center section is 3/5" tubing, with a short 1.5' (plus 3" for overlap) section of 5/8" tubing following. The "tips" are 1/2" tubing. All this can be obtained from sources that advertise in QST or CQ. In the element length tables, be sure to add 3" to the 1/2" tubing for overlap.

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For higher wind loads, you can let the 5/8" tubing go all the way through the 3/4" element. For lesser winds, the 3" overlap will do well.

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Of course, the driven element must be open at the center for the feedline connection. You can use a fiberglass tube or rod across the gap to keep the element aligned and to strengthen it.

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A 4-Element OWA

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OWA design requires one additional element to achieve the 50-Ohm feedpoint impedance compared to beams with feedpoint impedances in the 25-Ohm range. Shorter OWAs must also be a bit longer than their 3-element low-Z counterparts for the same performance. While a 3-element Yagi with about 8 dBi free space gain needs a 12' boom, our OWA will need a 13.5' boom. +
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Fig. 2 provides the outline of the 4-element version, with the spacing between elements shown. The following table lists the element spacing from the reflector, the tip length, and the total element length from tip-to-tip for reference, all in feet.

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Element            Space from          Tip Length          Total
+                   Reflector           Length              Length
+Reflector          0                   5.34'               17.68'
+Driver              5.12'              5.10'               17.20'
+Director 1          6.87'              4.57'               16.14'
+Director 2         13.00'              4.10'               15.20'
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The elements are designed to be insulated from the boom. If you change materials or element structures, an entire redesign will be needed. Do not be casual in your construction of Yagi designs you find in handbooks. They simply will not perform up to the original design if you alter the element diameters or the tapering schedule.

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The 4-element OWA provides an average gain of over 8 dBi (free-space). The front-to-back ratio is above 20 dB across the 28-29 MHz span. The 50-Ohm SWR is exceptionally low. Hence, the beam is a fit candidate for reproduction in the home workshop.

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A 5-Element OWA

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If we add about 6' to the boom and one more element (respacing all of the others), we can add about 1 dB to the overall gain of the OWA Yagi. A 19' boom will hold the elements, which use the same construction as the 4-element version. +
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Fig. 3 gives us the outline of the 5-element OWA, as well as the inter-element spacing. The following table provides the structural details.

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Element            Space from          Tip Length          Total
+                   Reflector           Length              Length
+Reflector          0                   5.52'               18.04'
+Driver              5.30'              5.16'               17.32'
+Director 1          6.70'              4.70'               16.40'
+Director 2         11.10'              4.65'               15.30'
+Director 3         18.70'              4.13'               15.26'
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For the extra element and boom length, we get a gain that ranges from 9.1 to 9.4 dBi (free space) across the 28-29 MHz span. The front-to-back ratio is close to or above 20 dB over that same frequency range. The SWR is quite smooth across this range.

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Once more, the design is for elements insulated from the boom. There are many systems for mounting elements to the boom. I tend to prefer 6" by 12" plates of polycarbonate (a generic name for the material sold as Lexan), which has good sun (UV) resistance, good RF properties, and is very strong. 1/4" thick material works well at 10 meters. It is much more durable and maintenance-free than plywood (which needs periodic varnishing) or more common acrylics (which become brittle after a season or two in the weather). I also use stainless steel hardware throughout, including U-bolts with saddles for the elements and the boom. Other systems also work well, but this one satisfies my experimental needs, meaning that antennas are always being reconstructed into new configurations.

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For reference, Fig. 4 shows the SWR curves for the two antennas from 28 to 29 MHz. These are for direct connection, using only a 1:1 choke or balun to move from the balanced feed element to the unbalanced coax cable. You can purchase a balun, make your own choke from coiled coax, or obtain a choke that uses ferrite beads.

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Be sure to weather seal all connections. For coax connectors, a wrapping of 3-M #33 electrical tape starts the job, followed by one of the black butylate sealants. Some folks like to cover the butylate with one more #33 tape coating. Do not stint on weather protecting connections, since water leakage into the feedline can ruin the performance of an otherwise great antenna system.

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In a future column, we shall go over some of the good practices to follow in building your own antenna. However, we must first finish our designs for 3/4-5/8-1/2" elements. Next time, we shall look at 6 and 7 element versions of the OWA, both with a flat 50-Ohm Feedpoint impedance, and with an extra dB or so every time we add an elements.

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Updated 7-01-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 37: 6- and 7-Element OWA Yagis

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L. B. Cebik, W4RNL

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Last time, we looked at some Yagi designs for fairly short-boom OWAs with direct 50-Ohm feedpoint impedances across the 28 to 29 MHz span. The 4-and 5-element designs provided about 8 dBi free-space gain and 9.2 dBi gain, respectively, which is quite good for monoband Yagis with their boom lengths.

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This time, we want to look at some longer versions of the OWA with more gain, but still keep the 50-Ohm feedpoint impedance. We shall look at 6- and 7-element Yagis on 24 and 36 foot booms.

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Fig. 1 reviews the element structure that we are using in this set of designs, a combination of 3/4, 5/8, and 1/2 inch diameter aluminum tubing. One reason that we shall review the 6-element OWA, when we already did an entire column on that antenna, is the new, larger tubing sizes. As a result of changing both the tubing sizes and the taper schedule (the places along the element length where we change tubing size), the element lengths will also change. However, the end result will be very similar performance between the two versions of the antenna.

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A 6-Element OWA

The original 6-element OWA is a very good antenna. So too is the new version. The only difference is in the tubing, which may be a matter of what an individual builder likes to use or has access to in his or her local area. Let's see how the new version turns out. +
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Fig. 2 gives us the outline of the 6-element OWA, as well as the inter-element spacing. The following table provides the structural details.

+ 
Element            Space from          Tip Length          Total
+                   Reflector           Length              Length
+Reflector          0                   5.46'               17.92'
+Driver              3.66'              5.13'               17.26'
+Director 1          5.77'              4.66'               16.32'
+Director 2         10.94'              4.49'               15.98'
+Director 3         16.06'              4.51'               16.02'
+Director 4         23.50'              4.13'               15.26'
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The free-space gain of this 6-element OWA varies from 10.1 to 10.2 dBi across the band, with a front-to-back ratio that never falls below 21 dB. Only at the upper limit of the frequency spread does the SWR get above 1.25:1 with a direct 50-Ohm feed system (including the recommended 1:1 choke/balun to suppress common mode currents).

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A 7-Element OWA

Adding one more element increases the boom length from 24' to 36' or so. Whether the added length is worth the effort depends on how important another dB of gain is to the operator. +
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Fig. 3 gives us the outline of the 7-element OWA, as well as the inter-element spacing. The following table provides the structural details.

+ 
Element            Space from          Tip Length          Total
+                   Reflector           Length              Length
+Reflector          0                   5.47'               17.94'
+Driver              3.66'              5.17'               17.34'
+Director 1          5.76'              4.64'               16.28'
+Director 2         10.89'              4.50'               16.00'
+Director 3         17.50'              4.51'               16.02'
+Director 4         26.40'              4.47'               15.94'
+Director 5         36.00'              4.11'               15.22'
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The gain ranges from 11.2 to 11.6 dB across the first MHz of 10 meters, with a peak near mid-band. The front-to-back ratio is a solid 20 dB. Although the SWR curve reaches 1.6:1 at 29 MHz, it is very tame across the remainder of the band. In fact, Fig. 4 gives us a sampling of both antenna SWR curves.

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Remember that these designs are specific to the tubing sizes and transition points from one size to the next. Any deviations from the prescribed tubing schedule would require refiguring the designs.

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As with all OWA designs, we must have 1 extra element for the given boom length and gain in order to secure the relatively smooth 50-Ohm SWR curve across the band. The element marked as Director 1 in all of the designs does not so much contribute to the antenna gain as it functions with the reflector to establish the antenna bandwidth and feedpoint impedance.

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How big do you want to go? I have seen an 8-element OWA design for 10 meters with something over 12 dB gain. But it was 48' long. The design can be found at the NW3Z web site via your search engine (search for "NW3Z"). As well, these designs might be tweaked for even better performance with an optimizing program. The versions shown here were hand-developed. If you prefer a direct 50-Ohm feedpoint impedance in a good Yagi antenna, then the OWA designs are the way to go.

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Updated 10-10-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 38: Notes on Home-Brewing 10-Meter Yagis

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L. B. Cebik, W4RNL

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Over the last several columns, we have examined the electrical designs of a number of Yagis ranging from 3 to 7 elements. Along the way, we have noted some construction pointers and preferences. However, let's pause a bit to see if we can pull some of those ideas together in one place--here.

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1. Element and Boom Stock: For casual and portable operations, where an antenna is not going to be in the wind for long periods of time, hardware depot aluminum tubing is usually satisfactory for elements. It comes--at least in my part of the country--in limited sizes, beginning at about 3/4" diameter. So designs using this span of tubing can rely on local purchase.

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6063-T832 and 6061-T6 are the more commonly used aluminum tubing for Yagi elements. Commercial houses can use thin wall versions of this tubing for lighter elements, since they have the machinery to resize the ends for perfect lap joints. However, 0.55" to 0.58" wall thicknesses are the ones used by most hams--and these are the versions carried by vendors like Texas Towers and others. Usually, for shipping ease, the tubing comes in 6' lengths, so designs need to take this into account. If you need to put two lengths together at the center of an element to get, for example, 12' of 5/8" tubing, use a short piece (about 1') of 1/2 inch tubing inside the inner ends of both 6' pieces to form a good electrical joint and stiffen the element on its mounting. For split driven elements, use a piece of fiberglass rod.

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For short boom, such as for a 2-element Yagi, 1 1/4" PVC works well, but longer than 5' or so, the material sags and is heavy. Aluminum tubing makes a good boom. For modest beams up to 12 to 14 feet long, you can nest 1.125 and 1.25 inch tubing to make a very durable boom. If you have only 6' lengths, you can stagger the sections, making sure that they meet tightly at their ends.

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2. Boom-to-Element Mounting: Commercial antennas often use special assemblies to join elements to the boom. Plates are bent and curved as necessary by equipment to which the average home builder has no access. However, if you like to build antennas, consider accumulating old broken beams from hams in your local area, even offering a few dollars to remove the "junk" from their yards. You will acquire a lot of unusable bent tubing and a number of quite unharmed boom-to-element plates (and also some boom-to-mast plates). Most of the junction assemblies will be reusable, even if you have to replace the original hardware with stainless steel nut and bolts from the local hardware depot. For 10-meter beams, if you have to build your own boom-to- element assemblies, it is best to design for elements that are insulated from the boom. (Directly connected elements and insulated elements usually require slightly different lengths to do the same job, so do not convert one type of assembly to the other without some redesign work.) Fig. 1 shows a method that I prefer--meaning that it is certainly not the only method available.

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Having used a lot of materials for the insulating plate, I have gone to polycarbonate, the generic name for Lexan. The material is UV resistant, has excellent RF properties, is exceptionally strong, and can be cut and drilled with woodworking tools. 6 by 12 inch plates of 1/4" material handle any 10-meter elements. Trimming the corners to save a little weight is feasible. Two U-bolts hold the boom and either 2 or 4 U-bolts hold the elements. The inner U-bolts are needed only if you have a split fed elements with no alignment rod running from end-to-end of the plate inside the aluminum.

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You can replicate the plate using good outdoor plywood in 1/4 or 3/8 inch thicknesses. However, plywood requires special attention both in the beginning and every year. Initially, seal the edges with a good exterior-grade fill. Then apply several coats of good spar varnish. I normally have done this to the wood before drilling U-bolt holes and then revarnished the word, getting varnish into the holes. An annual sanding and recoating is necessary, just as it would be for a wooden boat.

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Use stainless steel U-bolts, preferably with saddles. The saddles help prevent the U-bolts from collapsing the tubing when you tighten everything down. These will likely be a mail-order item. Drill the holes in the plate with precision to exactly fit the U-bolts with minimum amounts of free play (but no stress on the plate). This practice will keep your elements aligned as the wind tries to push them around.

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Note also that the elements are mounted beneath the plates, with the boom on top. This arrangement let's gravity help keep the elements level.

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There is a simpler method of mounting insulated elements. It involves a single U-bolt per elements that goes around the boom and through the element. It is best to use a curved plate that matches the element curve as a keeper. Between the U-bolt and the boom is a short section of split gray electrical PVC that acts as an insulator. (The gray PVC used for electrical conduit has the greatest UV resistance and hence will last longer in the sun before going brittle.) The tubing used in this system should be fairly large and should have an interior piece of tubing for reinforcement. Otherwise, the element will break off right at the U-bolt. This system requires even more careful machine work for good alignment and does weaken the element. So use the scheme, outlined in Fig. 2, with caution.

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3. Boom-to-Mast Plates: For very light antennas, you can use a non-metallic plate for the boom-to-mast junction. Again, plywood--with the proper treatment--can also do the job. However, I prefer metal plates either 1/4 or 3/8 inch thick, depending on the weight of the antenna and the diameters of both the boom and the mast. Predrilled plates are available from mail order sources, as is stock that lets you drill your own custom pattern of holes. The object of using a metal plate is to ensure a good electrical bond between the boom and the mast (and downward) so that the entire assembly (except for the elements) is a ground potential for bleeding charges off the antenna support system.

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For the larger U-bolts in this assembly, you can use saddle- types or you might wish to use muffler-type clamps. These U-bolt assemblies have a saddle with edges that some folks believe grips the boom and the mast better. However, if you do use these auto store components, be certain that all of the pieces are stainless steel. It will take a pair of U-bolts for the mast and another pair for the boom.

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You have a choice of shapes for the plate: a square (or rectangle) of a diamond. In principle, the diamond conserves the most weight and material. However, be certain that there is enough material beyond the U-bolt holes in a diamond plate to ensure that the material will not break under stress. Fig. 3 will reveal the areas of potential weakness.

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Alternatively, you might use for this assembly one of those commercially made fixtures with its complex bends and shapings to provide a maximum grip between the boom and the mast. Also, be sure the mount this fixture at the center of weight of the antenna boom.

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4. A Note About Stainless Steel Hardware: For antenna work, use stainless steel hardware everywhere. Make no exceptions. Although once hard to find, stainless steel nuts, bolts, U-bolts, and other fixtures are easy to locate at hardware depots. Do not use aluminum hardware, as it is very weak. All other hardware will create a bi-metallic junction that will corrode one or both of the pieces joined. Stainless steel has proven to be the most successful hardware for antenna jobs ranging from joining element sections of tubing to boom-to-mast plate mountings.

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The construction methods that we have noted will run the cost of a home brew Yagi only to about twice the cost of using junk-box components. However, the final cost will still be less than 1/3 the cost of a commercially made antenna--and it will last as long or longer than the commercial assembly. Even if the Yagi is home brew, if it is worth making, it is worth making well. Nothing is more frustrating than breaking a beam in the wind during a world-wide band opening.

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Updated 10-10-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 39: Frequently Asked Questions

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L. B. Cebik, W4RNL

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In our column for the last issue, we covered some fundamentals of the material side of beam construction. That exercise brought to mind a number of more general questions that folks have posed from time to time about antennas. So, let's try to give some succinct answer to these questions.

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1. With a wire antenna, does insulation make a difference in performance?

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This question is actually two questions in one. First, once we get the antenna set correctly, insulation makes no difference in how well the antenna performs. The gain will be virtually the same, whether the wire is bare or covered with any of the standard insulating materials.

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Second, insulation will make a difference in how long a wire must be to be resonant. If a bare wire is resonant on 10 meters (actually some specific frequency on 10 meters) at a length of 200", then an insulated wire will be resonant at the same frequency at a length from about 190" to about 198". Insulation creates a velocity factor (VF) so that the required physical length is always shorter than the required electrical length. If we set the VF of bare wire to 1.0, then the VF of insulated wire will be from 0.95 to 0.99.

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The nature of the insulation and its thickness determine the VF of insulated wire. The higher the dielectric constant of the material and the thicker the insulation, the lower the VF value. Unfortunately, there is no handy chart that you can consult when you buy insulated wire to tell you what the precise VF is. For dipoles, you simply prune to resonance.

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If you are thinking about a wire beam, where the elements are not resonant on the design frequency, then the best policy is to use the exact wire specified in the article or handbook from which you draw the design. There are techniques for handling insulated wire in these cases, but they generally require efforts or instruments that the average backyard antenna builder does not have.

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2. Does the feedpoint gap make a difference in the antenna element length?

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If a design that you are copying calls for an element length of 200", then this length remains constant, regardless of how large you make the feedpoint gap--within reason, of course. The gap can range (at 10 meters) from 1/4" to a couple of inches without disturbing the overall length of the antenna element. The leads from the feedline to the inner edges of the gap make up the missing element section.

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Remember that the feedline is in series with the antenna element. The feedline itself begins where the line is at its proper form to create currents of equal magnitude and opposite phase. When you turn the wires of a parallel feedline at right angles to the line to make the antenna connection, those wires are part of the antenna. When you separate the coax braid and center conductor to make the same kind of connection, those leads are parts of the antenna element. Even if not identical in diameter to the antenna element itself, the length is short enough at HF not to make any difference in the way the element performs.

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3. I have a multi-band doublet (or loop, etc.) that I use for all or most of the HF region. Can I connect a 4:1 balun at the antenna terminals and use coax to the antenna tuner in the shack?

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The answer to this question is yes, but there are better ways to handle the situation. The impedance presented by the antenna varies from one band to the next, ranging from very high to very low. If your coax run is long--perhaps 100' or so, your losses will climb according to the SWR on the line and the frequency. Higher frequencies and SWRs multiply natural coax losses.

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Let's look at alternatives to this system. The most efficient system is to run parallel transmission line from the antenna to the antenna tuner. Parallel transmission line naturally has much lower loss than coaxial cables (except for the very low-loss hard lines used at UHF and microwave frequencies). Hence, the multiplier that comes with high SWR values on the line tends to increase the loss by only a very little. Hence, in most cases, the losses in a high SWR parallel line system will be less than the losses in a perfectly matched 10-meter coax system.

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The installation rules for parallel line--whether it is 300-Ohm TV line, windowed vinyl 450-Ohm line, or open wire 600-Ohm line--differ from the rules that apply to coax. Keep the line free and clear of everything by several times the width of the line. Conductive materials--even wet wooden posts or trees--can disrupt the balance in the line and reduce its effective operation as a transmission line.

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4. If I run parallel into the house/shack, I get RF pick-up by the X (where X may equal the telephone, the TV, the rig, etc.). How can I have my parallel line and no interference?

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The losses of coax increase with line length. Hence, a short piece of coax--something less than about 20' at 10 meters--will not create significant losses. Even at a 10:1 SWR, 20' of RG-213 will have less than a 1 dB loss. Now lets assume that we can place the antenna tuner within 20' of where the coax would pass though the wall/window/etc. to reach the outside world.

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We can install our parallel line from the antenna to this same wall/window--keeping it free and clear of unbalancing forces in the outdoor run. At the entry point, we can install a 1:1 bead balun. From the coax end of the balun, we run our short length of coax to the antenna tuner.

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a. I specified a 1:1 balun, not a 4:1 balun. Sometimes the 4:1 balun will do the job--sometimes it will not. Since the antenna shows a different impedance on every band, it is rarely matched to the feedline headed toward the shack. At every point along the line, the impedance is transformed to a new value--and some of these values will be very low. Further transforming the impedance to a still lower value by a 4:1 ratio is likely to yield such a low impedance that the tuner may not be able to handle it. Hence, a 1:1 balun is the better choice.

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b. I tend to prefer bead baluns for this transition, although other 1:1 balun types may work. Bead baluns--originated by Walt Maxwell, W2DU--are compact and inexpensive (from such sources as the Wireman in South Carolina). No balun will be lossless in this application, but the losses will be modest at moderate power levels.

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c. At the coax end of the balun, run a short, heavy ground lead from the coax braid to a good ground rod. This measure helps prevent significant levels of RF from being on the outside of the coax braid and thus helps reduce coupling into conductors inside the shack.

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This system is not perfect, but it is effective for using an all-band antenna with parallel feedline while suppressing unwanted RF coupling to systems other than the amateur radio equipment.

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5. I have followed all of the recommendations and my all-band antenna will still not load up properly on 1 or more bands. What should I do?

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Let's assume that your system is flawless--good connections, not opens or shorts, etc. In this case, the most likely cause of a failure of the antenna to load is the length of transmission line.

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Earlier, I noted that when the antenna feedpoint impedance does not match the impedance of the feedline, the impedance is continually changing along the line. It is possible to calculate the impedance at the shack end of the line, but only if we know the impedance at the antenna feedpoint. In most cases, we do not know the impedance at the shack end of the line.

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The impedance may be a complex combination of a resistive value and a reactive value. Your antenna tuner has limits to the maximum and minimum resistive value that it will accept and transform. The reactive part of the impedance is the more likely culprit, since most tuner designs will compensate for only limited reactance. Depending on tuner design, the compensation range will be better for one type of reactance (capacitive or inductive) than for the other type. In most cases of a failure to provide a good match to the 50-Ohm requirement of the rig, the culprit an impedance at the tuner terminals that is outside the matching range of the tuner.

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Wait--do not throw away the tuner. Instead, change the length of the line to obtain a different combination of resistance and reactance at the tuner terminals. You can splice in a section (4 to 10 feet) of parallel line, either permanently or with knife switches. Just keep these added sections from folding over each other or coiling up. In other words, they should be free and clear like the rest of the line.

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Sometimes, you can find a single length of line that allows you to tune all bands with your multi-band wire antenna. In that case, you can make the connections permanent. In other cases, you can find two line lengths that between them allow you to handle all bands. A simple knife-switching system makes quick work of changing the connections.

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6. I have the ground line at the shack entry point. Is my system safe from lightning?

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Not especially. The safest system for an amateur station that does not need to operate during a thunderstorm is one that disconnects the antenna line from the shack lead and reconnects it directly to a ground rod. Then any charges that accumulate on the antenna go to ground and not to the equipment.

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In addition, set up your station so that you can do a complete disconnect in preparation for a thunderstorm. Disconnect--pulling the plug is best--the AC lines. Also disconnect the equipment from the outside ground line. Now the equipment is disconnected from every source of electrical surge.

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Sensitive solid state devices do not care if the supply line has a high surge or whether the ground side of the device has a high surge. In either case, the voltage across them is destructively high. Hence, isolating the equipment from both the supply voltage and the grounding lines is necessary to prevent surge damage. Surge protectors help, but when the storm is near, nothing succeeds like isolation.

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You can design your station to make all of these disconnects easy--easy enough to apply whenever you shut down after an operating session. The only step that requires a trip outdoors is changing the antenna lead from shack lead-in to ground rod. If you disconnect the antenna routinely along with the other indoor disconnects, you can save the trip outdoors for an impending storm and still be relatively safe. Of course, if you travel out-of-town, set up the station as if you will have a thunderstorm every day that you are gone.

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7. I have a beam on a tower. The base of the tower is strapped to ground rods. My coax from the antenna enters the shack, and I can change it from the rig to a second connector that goes to a ground rod outdoors. Am I safe?

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Maybe--maybe not. Experts suggests that most of the current in a lightning strike is in the coax braid. This current is very high, capable of destructively melting the insulation and arcing to other conductors. It is best if this current never enters the house at all. Hence, having an outdoor grounding system so that the coax never gets indoors during a thunderstorm is best.

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There is a second move that you can make. Since your have well-grounded the tower, and since the bulk of destructive lightning-induced current is in the braid, consider this measure. Near the top of the tower, clamp a small plate to a tower leg. On the plate, install a coax bulkhead connector--a double female connector with mounting hardware. Now run the antenna lead from the antenna to the connector and a second length of coax from the connector to the outdoor disconnect near ground level. The coax braid is now at the same potential as the tower leg and connected to the ground system serving the tower. You can add a second plate and connector at the tower base for added safety.

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If you maintain this system so that the connectors make excellent contact with the plates and the plates make excellent contact with the tower legs, you shunt currents on the outside of the braid to ground. However, this measure does not remove the need to disconnect the coax from the shack lead-in before it enters the shack. It just adds to the overall protection.

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There are more questions on my FAQ list. But these are enough for one column.

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Updated 10-10-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 4: Antennas and Low Sun Spot Counts

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L. B. Cebik, W4RNL

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As much as we hate to admit it, 10 meter conditions have been rotten. Instead of sunrise to sunset contacts across the ponds east to west, we hear only some weak north-south dx and a few weaker U.S. stations (from the U.S. perspective, of course). Occasionally during the day, the band will open a little for east-west skip. So, what kind of antenna is best for these conditions?

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The answer depends on another big question: what kind of operating do you want to do? Let's look at three main answers: a. I want to work my local chapter and friends. b. I want to work those super weak signals, c. I'll take whatever I can get whenever I can get it. Each answer suggests some different antennas.

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Local: Local chapters of 10-10 and other area communications are still wide open on 10 meters. That is because they are primarily point-to-point. (Note: we habitually call this ground wave, but usually it is not. Ground waves (or "surface" waves, as some call them) peter out on 10 very quickly. Just as on VHF, our elevated antennas look directly at each other: that is point-to-point.) Since most established hams have horizontal antennas, a vertical can be a disadvantage unless everyone is very close. Up to half the signal gets lost due to cross polarization.

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The basic local antenna is still the dipole. If possible, make it rotatable, even if by hand, and as high as you can get it. Aluminum rod or tubing about 16' long, fed with coax at the center on a single mast works quite well.

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If you live on the fringe of your local group, consider a simple 2-element beam, either fixed to point at the group or rotatable. The commercial HF5B is a typical compact multi-band design with a wide forward lobe (to catch everybody in the group) and modest front-to-back ratio. Since there is little trouble from QRM, the modest F-B ratio actually lets you hear someone off the back of the beam better than a station with a large beam designed to suppress virtually everything off the backside.

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You can build a 2-element Yagi from supply store parts. If you are into building antennas, you might want to consider other designs for the fun of it. The Moxon rectangle, a wire beam, has about the broadest forward lobe and excellent rear suppression, but a little less gain. The X-beam is a bit tricky to set up, but is quite compact (a square under 10' on a side). Linear loaded Yagis can cut the element length from 16 to 12 feet. And the ZL-special can be built from 300-ohm parallel line (TV ribbon) on a light frame or suspended at its ends and fed with coax. If any readers are interested in these designs, I'll present some details in future columns. Meanwhile, look at any of the antenna books to gather some basic ideas.

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Weak Signal Work: Much of the weak signal work done on 10 during sun spot lows is via backscatter, that is, by bouncing signals off the edge of the ionized layer, as weak as it is. That same layer, weakly hovering over the tropics, is responsible for the north-south skip that appears while the east-west path is too weak to support communications. So many 10-10ers point their beams south (or, if in the southern hemisphere, north) and listen carefully.

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For the best results on backscatter and very weak skip, an antenna with the maximum forward gain is best. Again, the front-to-back ratio is unimportant, since there is no QRM. (However, few hams want the antenna just for sun spot lows, so they do pay attention to front-to-back ratio.) A long Yagi is perhaps best among the aluminum antennas. If designs are optimized, the gain depends on the boom length, so the longer the better (if you can support it).

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Some wire antennas are capable of excellent gain, even if bidirectional. The extended double Zepp is over twice as long as a dipole, but narrows the beam width and has gain over the dipole. Dipoles (that is, antennas fed in the center) of a full wavelength can be set about a quarter wavelength apart and fed 180 degrees out of phase for additional gain. So too can EDZ dipoles (1.25 wavelengths long). These antennas usually (but not always) require parallel feeders and an antenna tuner. But the materials are cheap. Run the wires east to west for north and south lobes. For sun spot low backscatter and transequatorial skip, a fixed wire beam is not a bad choice. Again, if there is any reader interest, I'll provide more details in future columns.

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Anything I Can Get: For general operation, use what you have and be patient. First, learn the band's habits. When do the openings occur? In what directions? How long do they last? Then plan your operating accordingly. Second, be sure your receiver is quiet so you can hear what there is. Early synthesized rigs are noisier internally than the preceding generation of crystal-mixing rigs. Direct-digital synthesis in today's rigs still leaves some noise on 10. That's why Ten-Tec offers both synthesized and crystal-mixing rigs and why some hams hang onto their old Drakes, TS-520s, and so on. The antenna is part of a system, not a solution to everything.

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Third, plan your antenna for long term use, not just for the present lull in apparent activity. If you have room for antennas and like to build, have fun with experimental designs. But also plan the main system for the day when the sun spots return. (And, although we 10-10ers hate to admit it, that planning may involve operation on other bands, too.)

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Finally, use your antenna! Very often a band is only as dead as the operators sitting around complaining about it. Listen to 10 on contest weekends to discover its true potential. Contesters (inadvertently) QRM each other on a supposedly dead band. Vertical or horizontal, your antenna will do you no good if everyone thinks the band is dead without checking. Find net frequencies, especially the daily 10-10 nets, and listen. If you cannot hear the NCS, request a relay check-in to find out if anyone is in the right place to hear you. Try some "CQs" near frequencies that used to be active. Make your presence known. . .of course, within the boundaries of good operating practice. 10 meters is more open than you think.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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No. 40: More Frequently Asked Questions

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L. B. Cebik, W4RNL

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The frequently asked questions that we shall examine in this session related to beam antennas, most of which are varieties of Yagis. On ten meters, we find a variety of beam construction methods and a variety of matching systems. So our questions tend to relate to these two topics.

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1. Which is better: elements that attach directly to the boom or elements that are insulated from the boom?

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Like many frequently asked questions, this one contains an ambiguity, since the question does not refine the idea of being better into some specific set of concerns.

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a. With respect to performance, when the element lengths are suitably adjusted, there is no difference in gain, front-to-back ratio, pattern shape, or feedpoint impedance between a beam with elements directly connected to the metal tube forming the boom and a beam with the elements insulated from the boom.

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However, the element lengths required for a given set of performance figures will not be the same for the two methods of construction. Elements that are fully insulated and spaced by a non-conductive plate away from the boom will be the shortest. Elements attached to metal plates that are U-bolted to the boom tend to be the longest, since the plate acts as a short, fat portion of the element.

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These rules of thumb apply to elements that otherwise have the same lengths of tubing forming the element's decreasing diameter away from the element center. As we saw in a recent column, these "tapered-diameter-schedule" elements tend to be longer already than elements having a constant diameter. In both cases, the degree of length change from an ideal insulated uniform-diameter element is a complex affair to calculate, and Yagi design software is the best way to redesign one system of construction to another.

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For any beam with more than 2 elements, trying to field adjust the elements to the required lengths often leads to frustrating exercises in sliding tubing and to relatively poor results. The final suggestion, then, is that the backyard builder should use the exact techniques specified in a design being copied unless the builder has considerable experience in redesigning Yagis.

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b. The Yagi with element connected directly to the boom has a slight advantage in terms of noise and discharge of static build-up on the elements. The boom is connected to the mast and the mast to a grounded tower. Therefore, when the elements are connected to the boom, static charges bleed off the elements as the wind and other weather phenomena create them.

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Insulated elements can build considerable static charges over time. We can discharge them by connecting a high-value resistor (about 5,000 Ohms or more) or an RF choke (100 microHenries or so) between the element center and the boom.

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2. What does it mean to say that a certain Yagi design uses "direct feed?"

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Although many Yagi designs in current use have feedpoint impedance running from 20 to 30 Ohms, it is possible to design a high performance Yagi that shows a feedpoint impedance of 50 Ohms. In this case, we do not need a matching network, since the feedpoint impedance is the same as the characteristic impedance of the most common coaxial cables.

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However, we do have some constraints when using a direct feed driven element, as shown in Fig. 1. Regardless of the construction methods used for the other elements, the driven element must be insulated from the boom. The driven element must be split at the center to create a gap similar to what we find in a common wire dipole. The size of the gap is not critical at 10 meters and might range from 1/4" to 1".

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We connect the inner conductor of the coax to one side of the element, and the braid to the other side. Hence: direct feed.

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Since the coax is an unbalanced line and the Yagi driver is balanced, we can encounter radiation currents on the outside of the braid. To suppress these currents and maintain a good pattern with no radiation from the feedline, a 1:1 balun is a useful device to insert between the element terminals and the coax line. Bead-type balun chokes are the lightest and work well in this application. We can often use coils of the coax feedline to perform the choking function. Recommended coil sizes appear in The ARRL Antenna Book.

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Some Yagi designs using direct 50-Ohm feed have broader operating bandwidths than Yagis with lower feedpoint impedances. As well, the feedpoint losses are often less. Every connection represents a small loss, since the connection of one part to another will not have precisely zero Ohm resistance. When we lower the feedpoint impedance of the antenna, these resistive losses will be a higher percentage of the total impedance (the sum of the natural radiation resistance and the loss resistance) than when the radiation resistance is higher. As well, direct-feed systems usually have fewer connections than low impedance systems with matching networks.

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3. Which is best as a matching system for a Yagi: a gamma, a Tee, or a beta match?

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Once more we have an ambiguous question, the simplest answer to which is this: it all depends. . . The first consideration is whether a matching system is needed. If the Yagi has a feedpoint impedance well below 50 Ohms--say in the 20-30 Ohm range, then you will need a matching system. There are many fine Yagi designs with feedpoint impedances in this range, so understanding a little more about matching systems is wise.

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a. If you are determined to use a direct connection between the driven element and the boom, then you will need to use either a gamma or a Tee match. (There is also a more complex form of the gamma called the Omega match, but we can bypass it in these brief notes.)

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The most commonly used matching network for home-built Yagis is the gamma. As Fig. 2 shows, it consists of a line in parallel with part of the element and connected to the element. We add a series capacitor between the coax center conductor and the gamma line. By adjusting the line diameter, spacing from the element, length, and the capacitor value, we can arrive at a good match.

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The number of element playing a role in the gamma match system makes hand calculation of the dimensions very tedious. There are computer programs that can put you in the ball park and ease the adjustment. The first step is to reduce the length of the driven element to make is capacitively reactive, which often allows us to omit the capacitor.

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As a starting point, make the gama rod or line about 1/3 to 1/2 the diameter of the driven element itself. Then the line can be about 0.04 to 0.05 wavelength long and spaced (center-to-center) about 0.007 wavelength from the element. The capacitor should be about 7 pF per meter (about 70 pF at 10 meters) for a resonant driven element with an impedance of about 25 Ohms.

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If you use the capacitor, alternatively adjust the length of the gamma rod to the shorting bar to the main element and the capacitor until you obtain the best match. Replace the variable capacitor with a fixed capacitor. If you omit the capacitor, adjust the length of the gamma rod to the shorting bar and the length of the element until you get a perfect match.

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b. The gamma match can produce some distortion in the beam pattern, since it is an unbalanced system. The distortion has shown up more at VHF and UHF than at HF, but 10 meters is just on the cusp of the VHF region. Therefore, some beam builders prefer to us a Tee match. As Fig. 3 shows, the Tee looks like a double gamma and still permits a direct connection between the element and the boom.

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Tee match calculations are not just simple adjustments of gamma calculations. One Yagi optimizing program (YO by K6STI) has a Tee-match calculating module, and it allows you to either use the series capacitors or to omit them--although the Tee rods will be different for each case.

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Some builders use the Tee match not only to obtain a good match but also to raise the feedpoint impedance to 200 Ohms. Then they place a 4:1 balun at the feedpoint to arrive at the coax 50-Ohm impedance.

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As a balanced matching system, the Tee match avoids potential pattern distortions. However, it is the most complex of our matching systems and requires considerable patience to adjust.

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c. The simplest balanced matching system is the beta match. We have taken a long look at the beta match in past episodes of this column. Essentially, we shall form an L-network to transform a low antenna impedance to the higher coax cable impedance.

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The L-network requires a series capacitor on the low impedance or antenna side. We form this by shortening the element from its resonant length, thereby making it capacitively reactive. Then we add a shunt or parallel inductive reactance across the terminals--effectively on the coax side of the network.

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As shown in Fig. 4, we can use either of two ways to obtain the required shunt inductive reactance. One method is to make a length of parallel transmission line with a short at the far end. A shorted transmission line less than 1/4 wavelength provides inductive reactance. The amount depends on the wire spacing and diameter, as well as the line length. This is the so-called "hairpin" matching device.

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The other method uses a coil--wound to provide the inductance that has the required inductive reactance. Either method will do the job. The coil has slightly higher losses than the shorted transmission line hairpin, but provides a slightly wider operating bandwidth. The short at the end of the hairpin can float or you may ground it to the boom--there should be no difference in performance either way.

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L-network calculations abound. One convenient program for calculating a beta match while evaluating your antenna design is YW, a program accompanying The ARRL Antenna Book.

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The beta match does require that the driven element be insulated from the boom and have a center gap for the connections.

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3. What is the best way to make adjustments to my Yagi and its matching system?

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Only a few hardy folks who love working at heights enjoy adjusting a Yagi at the top of a tower. To make the initial adjustments on a Yagi, we can work closer to the ground, using a step ladder at most.

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Mount the Yagi pointing straight up. The reflector should be about 5' to 10' off the ground at 10 meters for best results on the widest variety of designs. You can jury-rig an assembly to support the beam while you do your work. Just be sure to move yourself and your ladder well out of the way when making measurements to test your adjustment work. Indeed, the test site should be as much in the open as your situation permits.

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Adjustments made by this system should hold if the antenna is a half wavelength or higher in its final position. The higher the front-to-back ratio of the beam, the better the system will work, since a high front-to-back ratio minimizes interactions with the ground. This adjustment system does not give 100% assurance that you will not have to make further adjustments when you get the beam mounted at its operating height, but it should handle 90% or more of the cases and the work.

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Hopefully, these brief answers to frequently asked questions will get you started toward better antenna building. As I have noted on several occasions, if you plan to roll your own antennas-- whatever the type--or if you simply want to understand antennas better, make sure that you have a copy of The ARRL Antenna Book on your shelf--or better, on your work bench opened to a relevant section.

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Updated 10-10-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 41: A 10-Meter J-Pole

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L. B. Cebik, W4RNL

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Many 10-10 operators live in restricted spaces calling for a vertical antenna. Sometimes, the roof-top is not accessible for a simple monopole with radials. However, the alternatives may also be unattractive for the situation. A vertical dipole calls for an elevated feedpoint with the feedline carried away at right angles to avoid RF pick-up on the outside of the line.

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So the question that emerges is this one: is there a 10-meter vertical that will cover all of the band that I can feed from the bottom without using any radials?

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The answer is "Yes: the J-pole." Ideally, a J-pole is a vertical dipole set above a quarter wavelength matching section composed of the same materials as the antenna. The end of a dipole shows a very high impedance, unsuited for coax feedline. However, a quarter wavelength of parallel feedline can transform a very high impedance into a very low one. With the right juggling of dipole length and matching section length, we can obtain a broad 50-Ohm feedpoint impedance.

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The J-pole has another advantage: the main radiation from the antenna begins where the dipole portion is above the two-legged matching section. The main current is about half-way up the free and clear dipole section. The effect is the same as placing a ground-plane monopole at a 1/2 wavelength height in terms of added signal strength.

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The J-pole's disadvantage--especially on 10 meters--is that it is a considerable structure. The version we shall examine is 20' tall. However, it does not have much side-to-side dimension. Like all vertical antennas, we should install it as far away from houses, trees, and shrubbery as our home site makes feasible. How high we should place the base of the antenna is a question that we shall look at before we are done.

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I have designed an interesting variation on the usual J-pole that uses common aluminum tubing that one can obtain either from a hardware depot or from one of the usual sources of antenna tubing stock (such as Texas Towers, among others). The bottom sections are 1: diameter stock, with the dipole consisting of 7/8" and 3/4" stock nested. Fig. 1 shows the basic details. The first thing that you will notice is that the antenna has several features unlike some of the VHF J-poles that are so common. The usual J-pole design has a shorting bar at the base and we then probe up the twin legs until we find the 50-Ohm matching point. This version has dimensions that place the 50-Ohm feedpoint at the very base of the antenna. Hence, the strap in the figure should be non-conductive (plastic, etc.), with a coax connector and fat leads to each leg. Remember that the feedline is in series with the connections. We also need to place a 1:1 choke balun at the feedpoint to suppress any RF on the outside of the coax.

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This design results in upper dimensions quite different from the usual J-pole. The legs are considerable longer than 1/4 wavelength--about 10" longer. At the same time, the upper section is shorter than 1/2 wavelength, nearly 90" shorter. Why?

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Essentially, the dipole leg extends well down into the double-leg region of the antenna. This does not block or cancel radiation, since the high current region is still well above the matching portion of the structure. Many J-pole enthusiasts believe that the structure should be as perfectly a 1/2 wavelength antenna + 1/4 wavelength section as possible. However, the currents in the matching section can never be equal in magnitude and opposite in phase, since one end of the matching section is open-ended and the other is continuous with the radiating portion of the antenna. Hence, such perfection is an illusion. The object is to arrive at a set of dimensions that will radiate effectively and provide a match for our feedline.

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The J-pole pattern is omni-directional, with only a very small offset created by the double-leg matching section. Fig. 2 shows a typical azimuth pattern, along with the very small offset in the direction of the open-end leg of the matching section. The offset cannot be detected in operation.

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Now we can see if raising the base of the antenna makes any difference to performance.

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Fig. 3 gives us the answer. With the antenna close to ground, we obtain a single-lobe elevation pattern about 1 dB (hardly detectable) weaker than more elevated base positions. The antenna will be about 20' tall overall, and most installations would opt for this height as the simplest mechanically.

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The middle pattern raises the base of the antenna 5' off the ground, for an overall height of 25' for the tip. We obtain close to maximum gain in the lowest lobe, along with some radiation at higher levels. Some folks prefer this height because it gives better short-skip performance without changing the DX performance.

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The bottom pattern raises the antenna base to 10' off the ground, for a total structure height of 30'--almost the same as a 1/4 wavelength ground-plane monopole for 40 meters. At this height, we do not gain more than a dab of gain at the lowest level, but we do acquire even stronger high-angle radiation.

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As we raise the antenna, we also acquire the need for sturdier base materials for installation. At the lowest level a buried 4x4 or PVC pipe section can support the antenna. The longer the support above ground, the longer the portion in the ground, if we wish a stable structure. Hence, most folks place the base fairly close to ground.

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The other structural cautions involve stabilizing the structure itself. First, note the spacers in Fig. 1. Any plastic material that will stand up to the sun will do to keep the matching section legs correctly spaced at 5" center-to-center. Second, the tapering diameter upper potions of the antenna will sway in the wind. Adding light rope (1/8" to 3/16" diameter) guys will limit the sway and the extend the life of the tubing.

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The mounting system that you devise for the antenna will detune it from its ideal conditions. However, the design has some adjustability in it. First, the long matching-section legs are composed of two pieces of tubing, with a linking tubing piece inside. Hence, we can lengthen the legs (or shorten them if we make the 1" sections total just a little less than 116"). As well, the upper sections of tubing are each shorter than the usual 6" store lengths. Hence, we have the ability to lengthen or shorten the overall height of the antenna.

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Tuning up the antenna is a matter of juggling the matching section leg lengths and the overall length of the antenna. Increasing the leg lengths while keeping the overall height constant raise both the resistance and the reactance at the feedpoint. Raising the total antenna height while keeping the matching legs constant raises reactance but lowers the resistance. Hence, by juggling the leg length and the total height, we can create an SWR curve that is less than 2:1 across the entire 10-meter band from 28.0 to 29.7 MHz. All-stainless-steel hose clamps with slots in the upper ends of the tubing make a good way to adjust and them tighten down the final assembly.

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These notes have only pointed at the mechanical features of a J-pole installation. Before buying any tubing for one, be sure to plan carefully the entire mounting system. If you use metal devices to attach the antenna to the mounting post or pole, expect to spend a bit of time retuning the antenna for full band coverage. Do not use a metal pole for mounting. Instead, use a ground lead from the coax side of the RF choke balun at the feedpoint and connect it to an 8' ground rod.

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If you use tubing diameters other than those listed, also expect to spend considerable time tuning up your version of the J-pole. As we raise the operating frequency, changes in element diameter of even 1/8" become larger influences on the resonant frequency of an antenna. At 10 meters, we cannot use the dimensions listed in an article unless we also use the same materials.

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Avoid the cheap aluminum electrical conduit for antenna elements, whether vertical or horizontal. It is both heavy and soft. The end result is often a bent element or a broken mounting system. The lighter and harder aluminum tubing used by commercial antenna makers is still the best material for the home antenna builder.

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The J-pole is not a magic antenna, but it is a useful addition to the array of verticals at our disposal. Expect it to perform like any other vertical dipole at the same top height. But if you need a vertical and want to feed it at the base, the J-pole may be a good candidate for the job.

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Updated 10-10-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 42: A Hilltopper Portable Dipole

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L. B. Cebik, W4RNL

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A rotatable dipole is a very useful antenna for portable or hilltop operations. Unlike a vertical that should have a ground plane, the dipole is horizontal and needs none. Of course, we do have to think about a support mast. It may consist of 3-4 5' sections of TV mast or even a painter's pole--each with at least 3 guy ropes and tent stakes to stabilize the system.

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But what about the antenna? We can make a dipole from wire, tubing, end-to-end whips, and a bunch of other materials. The featured system for this episode is made from tubing. We can easily obtain 3 6' lengths of aluminum tubing from sources like Texas Towers at very reasonable prices. We shall need 6' of 5/8" diameter, 6' of 1/2" diameter, and 6' of 3/8" diameter tubing. T6063-832 is the most usual tubing to use because each size nests well inside the next larger size.

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A good portable antenna should require an absolute minimum number of tools for assembly in the field. How about 1 wrench to tighten the center plate to the mast. We shall need no other tools to assemble and disassemble our antenna.

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Fig. 1 shows the basic tubing layout on each side of the center plate. We cut the 6' tubes in half. Then we carefully smooth the cuts so that the 3' sections will slide easily inside each other. The two larger tubes need a 33" exposure, with 3" inside the next tube. The smallest tube needs only a 30" exposure, and you can either cut off 3" or have 6" of tubing inside the next size. With 5" on the center plate (discussed a bit further on), we shall have 101" each side of center or 202" overall--a good size for the lower MHz of 10 meters.

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When not in use, slide the tubes for each side of the dipole inside each other. You will end up with an easily stored 3' long set of element pieces. As well, you will always have the correct sections in place, just in case the holes for comparable pieces on each side are not perfectly aligned for complete interchangeability.

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Our fastener will be the hitch-pin clip--also known as the hairpin cotter pin and some other names. For clarity, Fig. 2 shows the shape of the clip.

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We drill holes through each pair of tubes at the center of the tubing junctions all the way through. Clean the drilled holes. The hole size depends on the clip material diameter. Choose clips designed to fasten tubes of the diameters that you are using. When we assemble the antenna in the field, we simply align the holes and press a hitch-pin clip through them. The sections are secure.

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The electrical contact from one tube to the next depends on the tubes themselves. Hence, it makes sense to be sure that the tubing ends are clean inside and out before each field use. Do Not use the hitch-pin clip system for a permanent home antenna, since the tubes may accumulate dirt that may interrupt electrical contact. But for short term field use, this system work very well indeed.

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To avoid losing clips in the grass or gravel of the field site, you can tie a bright ribbon to each one. For storage, you can clip all of the clips to a designated master clip.

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Now all that we need is a center section so that we can assembly the elements and connect a length of coaxial cable. Fig. 3 shows the system that I am using.

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I had some polycarbonate (tradename: Lexan) plate 1/4" thick in the shop. However, you can use plywood or acrylic for the center plate. A 4" by 4" square will do the job. At the top and bottom of the plate, drill holes for U-bolts that are sized to the mast diameter that you will use.

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Note that the elements cross the plate just above the centerline in order to leave room for a coax connector. I used a short section of 1" by 1" L-stock, 1/16" thick for my connector. The connector is the version that mounts in a chassis hole. It is useful to cut the 5/8" connector hole and screw holes before cutting the stock to its final inch and a quarter length, and a bench vise helps hold things in place during this work. The plate is a bit wide than it needs to be for the connector so that the screw holes will miss the mast behind the plate. In fact, I placed the heads of the screws on the mast side of the plate so that the nuts would not interfere with the mast.

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Note that a short lead runs from the connector center pin and the ground lug to each side of the element. The element center pieces consist of scraps of 3/4" tubing lying around in the shop--cut-offs from old projects. In each 5" piece of 3/4" aluminum tubing, we need two sets of through holes. One set holds the tube to the place near the plate edge. The other set--at right angles to the first set--is at the inner end of each tube. The hardware holds solder lugs for the connector leads.

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We need one more piece of material for our assembly. 1/2" nominal CPVC just fits inside of 3/4" aluminum tubing. a 4" piece runs through the inner ends of each of the plate tubes. The CPVC keeps the tubes perfectly aligned and maintains the gap between them. A gap of about 1/2" between the ends of the 3/4" tubes works well, but 3/8" to 1" gaps are fine.

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Since we used about 2" of each 5" tube on the plate with the CPVC inside, we have 3" of tubing extending off each side of the plate. This is the necessary 3" overlap for the 5/8" section of element tubing. Of course, we use hitch-pin clips to secure the element section to the center plate tubes. When complete, we should never have to touch the nuts and bolts on the center plate in the field. (Check their tightness before taking the antenna to the field.) We simple hitch-pin the entire dipole together for use, connect a coax cable, and operate. Of course, fastening the plate to a mast and raising the mast will help our signals immensely.

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My YL (Jean, N4TZP) stitched up an old but sturdy bath towel into a carry bag with a draw-string. So the dipole pieces are protected from dirt and bumps, but are always ready for use. In the bag, I have a dedicated wrench sized to the U-bolts ready for action. The 4" by 10" center plate assembly and the 2 3' long element assemblies make a compact package to carry. I have a bright ribbon on the center of the wrench, matching the ribbons on the hitch-pin clips. Incidentally, I store the mass of hitch-pin clips in one of the holes on the 3/4" center plate tubes. My goal is always to make everything ready to use and difficult to lose.

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A little over 10 years ago, just before I started this series of antenna columns, I wrote an article for 10-10 News about a rotatable portable dipole using some materials adapted from the ground plane radials of an old CB antenna. I think that I like the present field antenna a little bit better. It stores in a smaller space and the materials are easily obtained. As well, the total cost is in the cheap range. While the shop work requires some care, the field work is as simple as I know how to make it.

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The antenna is also adaptable for use on upper floor apartment balconies. In fact, if your balcony is at least 20' above ground, you can use a horizontal mast and hand turn the antenna from horizontal to vertical polarization. It works well either way. The antenna is also usable in emergency situations, whether the emergency is a matter of community communications when other circuits are down or simply a matter of the main station beam failing just as the band opens.

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Updated 04-15-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 43: A Small 10-Meter Very-Wide-Band Yagi

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L. B. Cebik, W4RNL

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Some 10-meter fans like to work not only the low end of the band for the CW, digital, and SSB activity, but also the upper end of the band, for a few rounds of nostalgic AM action. In this episode, we shall look at a 4-element Yagi that covers all of 10 meters with a 50-Ohm (direct feed) SWR under 2:1 and with at least 7 dBi of free-space gain (about the same as a narrow-band 3-element Yagi with the same boom length). The front-to-back ratio will dip below 20 dB only at the band edges. All of this will fit on a boom just over 8' long.

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While we are at it, we shall look at some very sound assembly techniques for beam construction. This Yagi requires careful construction, and so we might as well use the best materials and techniques for putting it together. Even if you do not like the design, the construction methods are suitable to almost any 10-meter Yagi you might prefer.

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The Basic Design

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The Yagi consists of 4 elements, one of which is the 50-Ohm driver. Hence, we do not need a matching network, although a common-mode current suppressing choke--such as a 1:1 ferrite bead "balun" is always a good precaution at the feedpoint. There is a standard reflector, plus 2 directors. One of the directors is spaced close enough to the driver to count as a "slaved driver" to extend the performance of the antenna over the upper end of the band. Fig. 1 shows the general outlines of the antenna.

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The boom length, including ends to support the element mounting plates, should be about 9' long. You c an make one from 6' long pieces of 1.25" and 1.125" aluminum by using a 6' and 3' section of each type, but placing the junctions at opposite ends of the boom. The elements consist of lengths of 5/8" aluminum at the center with 1/2" aluminum tips. Obtain 6063-T832 high-grade aluminum tubes (by mail order, if necessary). Do not substitute elements of other diameters in this project, since the element interactions are very specific to the performance. All inner sections extend 54" from the element centers or the boom-line. The tip lengths will change from one element to the next in accord with the following table. Be sure to add 2 to 3 inches to the tip to fit inside the inner sections.

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+Element Lengths and Spacing:  4-Element Wide-Band 10-Meter Yagi
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+Element         Tip-to-Tip Length     Outer Tip Length     Space from         Space from Preceding
+                Inches                Inches               Reflector Inches   Element  Inches
+Reflector       215.5                 53.75                ----               ----
+Driver          207.2                 49.6                 37.5               37.5
+Director 1      191.8                 41.9                 45                  7.5
+Director 2      182.6                 37.3                 96                 51
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Construction

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Fig. 2 shows the construction of high-quality junctions of the elements to the boom (B). Item A is a nonconductive plate (polycarbonate), about 9" by 6" by 1/4". Do not use metal plates, since the dimensions shown are based on well-insulated and isolated elements, relative to the boom. The boom attaches to the plate with U-bolts equipped with saddles to reduce tube compression. The U-bolts and all other hardware, including washers and lock washers should be stainless steel. The elements are secured to the plate with similar U-bolts (F), sized to the element diameter.

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The driver assembly requires a gap--which is part of the overall element length, not an addition to it. Use a 1/2" diameter tube or fiberglass rod the length of the plate (E) to align the driver halves (D). Run #8 nut-bolt-washer-solder-lug combinations one each side of the driver (G) for connections. (See below for the coax connector). The parasitic elements use a simpler mount. Use 1/2" tubing the length of the plate as a junction between the parasitic element halves (H), with sheet metal screws (J) to complete the assembly.

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Fig. 3 shows one good way to add a female coax connector to the driver plate, using one set of the U-bolt nuts to hold it in place. Use a short section of aluminum L-stock, 1" by 1" by 1/16" thick (J). Cut a 5/8" hole in one side of the stick for a standard 1-hole connector (K). Use the shortest leads feasible from the connector to the element solder lugs (G). Coat all exposed soldered connections and the rear of the coax connector with a plastic insulating material, like PlastiDip. Be sure that the connector and its plate are on the mast side of the driver element for the shortest, most direct coax run.

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Performance

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How well does the antenna perform across 10 meters. The following table gives free-space figures across the band. Add about 5.5 dB to the gain for a height of about 1 wavelength.

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+Modeled Performance of the 4-Element Wide-Band 10-Meter Yagi
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+Freq.           Gain            F-B Ratio       Impedance               50-Ohm
+MHz             dBi             dB              R +/- jX Ohms           SWR
+28.0            7.04            19.2            49.4 - j 8.2            1.18
+28.25           7.02            22.0            49.7 - j 7.7            1.17
+28.5            7.04            25.4            48.7 - j 5.6            1.13
+28.75           7.10            30.7            47.4 - j 2.3            1.07
+29.0            7.19            32.8            46.6 + j 2.0            1.09
+29.25           7.31            25.9            47.1 + j 6.5            1.16
+29.5            7.44            21.0            49.2 + j 9.5            1.21
+29.7            7.55            18.0            51.7 + j 8.4            1.18
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For a Yagi covering a 7% bandwidth, the gain is remarkably smooth, climbing gradually in the upper part of the band. The front-to-back ratio dips below 20 dB only at the band edges, but is still very good. The key to the SWR performance is the spacing and sizing of the driver and the first director. Fig. 4 provides a graph of the 50-Ohm SWR across the entire 10-meter band. With proper construction, the 50-Ohm SWR should not rise above about 1.25:1 anywhere in the band.

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Since the antenna has a 50-Ohm feedpoint impedance, you do not need any kind of matching network. Direct coax feed is preferred. However, you may wish to install a ferrite bead choke of W2DU design (available from many sources, such as the Wireman of South Carolina) in order to attenuate common mode currents on your main feedline. Sources of other components include such places as Texas Towers for the aluminum tubing and DX Engineering for the stainless steel saddle U-bolts. All of these--and other suppliers--advertise in QST. These supply notes are not an endorsement of any particular provider, but only represent sources that I have successfully used.

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Even if you do not need a very-wide-band Yagi, the construction methods shown here are sound for almost any Yagi design. If you are copying a magazine design, look carefully at how the elements are mounted to the boom. If the elements are separated electrically, your version should also do so; and likewise for a design that specifies electrical contact with the boom. These specifications are not interchangeable, since boom contact requires a redesign of element lengths to compensate for the contact. This design uses insulated element mountings.

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If you ever thought that all Yagi designs were standardized, you now know differently. This little beam is an example of how Yagis can be designed to do specific jobs, and each job carries with it its own requirements for element length and spacing. You can explore past columns, as well as the An-Ten-Ten-nas book, for examples of other designs and the ways in which the design specifications affect the element lengths and spacing.

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Updated 04-15-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 44: A Large 10-Meter Very-Wide-Band Yagi

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L. B. Cebik, W4RNL

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In the last episode, we examined a 4-element very-wide-band Yagi on an 8'+ boom. The antenna covered all of 10 meters from 28.0 to 29.7 MHz with reasonable gain (7.0 dBi free-space or about 12.5 dBi over ground), good front-to-back ratio (20 dB), and a direct-feed 50-Ohm SWR of less than 1.25:1 across the band. We also discovered that we could build such a beam using high-grade materials, if we were willing to use mail order and similar sources of supply.

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This month, we shall explore a Yagi with similar coverage. The design is based on an original by Dean Straw, N6BV, of ARRL. The difference between Dean's Yagi and my smaller design last time is that his beam uses a 26' boom and has 6 elements. For the increase in boom length, we obtain an additional 3 dB of gain (10 dBi in free space or 15.5 dBi over ground), with all other operating specifications being the same as the smaller unit. The front-to-back ratio is about 20 dB across the band, and the 50-Ohm SWR does not rise above 1.25:1. If you like long-boom Yagis, you may take a shine to this one.

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Fig. 1 shows the general proportions of the antenna. Once more, we see that the first director is quite close to the driver, although not as close as in the short boom Yagi that we presented last time. However, this time, let's look at the performance characteristics before we examine the construction.

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Performance

The very-wide-band 6-element Yagis has very clean patterns that vary only slightly as we move across the band. It is quite natural for the rear lobes to change shape across a wide operating passband, while the forward lobe tends to hold its shape from one band edge to the other, +
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Fig. 2 shows representative azimuth patterns for the antenna at the band edges and at mid-band. The overall area within the rear lobe does not change much across the band, although the perimeter does change shape. The forward lobe is relative constant, with the emergence of very slight bulges at the upper end of the band. If we could have extended the operating range any further, we would find that these bulges would develop into small secondary forward lobes. If we had added more elements for higher gain, the secondary forward lobes would have become a permanent feature of all the patterns, as they are in most VHF Yagi design of 8 or more elements.

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+Modeled Performance of the 6-Element Wide-Band 10-Meter Yagi
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+Freq.      Gain         F-B Ratio    Impedance            50-Ohm
+MHz        dBi          dB           R +/- jX Ohms        SWR
+28.0       9.63         20.2         44.5 - j10.1         1.25
+28.25      9.72         21.8         50.1 - j 5,8         1.12
+28.5       9.83         22.9         52.9 - j 2.0         1.07
+28.75      9.98         21.8         55.2 + j 1.3         1.11
+29.0      10.09         20.9         56.7 + j 3.8         1.16
+29.25     10.22         20.1         56.7 + j 5.0         1.17
+29.5      10.32         19.8         53.7 + j 5.8         1.14
+29.7      10.37         20.2         48.3 + j 7.7         1.18
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The table of performance values from the design model shows how smooth the performance is across the band. The gain varies by only 0.75 dB in that entire span, an amount that would be completely undetectable operationally. The front-to-back ratio varies by only 3 dB, again, an amount that we would be hard pressed to detect, even in cross-town checks with a friend.

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The antenna uses a direct feed and is a good match for 50-Ohm coaxial cable. As usual, I recommend the use of a means of attenuating common-mode currents on the cable, that is, a ferrite bead choke balun of the W2DU type that is readily available from numerous sources. Unlike 1:1 current balun transformers that are bulky, the ferrite bead balun is relatively thin and liner. Hence, you can tape it to the boom and it projects hardly more than the coaxial cable itself. Fig. 3 shows the 50-Ohm SWR curves across the band. Notice that the values tend to undulate in minor ways, a feature of the driver-first-director combination.

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Construction

Except for requiring a very long boom, the 6-element very-wide-band Yagi uses the same construction as the 4-element version that we have already examined in detail. The elements consist of inner section of 5/8" diameter aluminum, with 1/2" tubing used for the tips. Use 6063-T832 tubing, which is available from suppliers. The design calls for elements that are well insulated from the boom, so the sketches in the last column are completely adaptable to this antenna, right down to the way of mounting a coaxial cable connector to the overall driver assembly. +

The inner 5/8"-diameter tubing sections extend 54" each side of centerline. Some builders may be concerned about the wind loading capability of such long inner sections. If you wish to strengthen them a good bit, the simply extend the inner tubes about a foot or so beyond the limits of the 9-12-inch long mounting plates. For the parasitic elements, these inner tubes will be 1/2" diameter aluminum. For the driver, the inner piece will be a non-conductive tube or a fiberglass rod, either with a 1/2" diameter.

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The following table provides element length and spacing dimensions. Be sure to add 2 to 3 inches to the lengths of the tips for the required overlap. An overlap under 2" is likely to be insecure, while one longer than about 3" simply adds unnecessary weight to the beam.

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+Element Lengths and Spacing:  6-Element Wide-Band 10-Meter Yagi
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+Element         Tip-to-Tip Length      Outer Tip Length      Space from             Space from Preceding
+                Inches                 Inches                Reflector Inches       Element Inches
+Reflector       214.6                  53.5                  ----                   ----
+Driver          201.6                  46.6                  50.9                   50.9
+Director 1      186.6                  39.3                  72.8                   21.9
+Director 2      184.0                  38.0                  136.2                  63.4
+Director 3      184.8                  38.4                  216.8                  80.6
+Director 4      174.0                  33.0                  312.0                  95.2
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Fig. 4 shows three generally accepted ways of joining two sections of elements. The easiest way is to use sheet metal screws. Most builders use two per junction, although they are divided on where to place them. Some builders place them in a line, while others place one on each side of the tube so that the points face each other. The second method uses a hole all the way through both tubes. Some builders are now using aircraft (not hobbyist) rivets, while others use a nut-bolt assembly with lock washers on each side. The third method cuts slots in the larger tube and uses stainless steel hose clamps to lock the sections together. With all hardware, be certain that all parts of it are stainless steel. Some auto hose clamps use stainless straps but plated ( rustable) screws.

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Like the smaller antenna, the design uses very specific element section diameters. Even changing the relative lengths of the inner and outer element sections can change performance noticeably. Trying to change the overall element diameters to use larger or smaller tubing will throw off the design even more. A Yagi depends for its performance on the mutual coupling between adjacent elements, and changes in element diameter alter that coupling. Unfortunately, too few books and articles point out this limitation of Yagi design, and too many beginning beam builders try to substitute handy materials--usually with very frustrating results. If you do not have the means of performing the re-design work, try to replicate any design that you like as exactly as possible.

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The 26' long 6-element very-wide-band Yagi is a sample of what can be done with Yagis. You may wish to compare its dimensions with designs that aim only to cover the first MHz of the band. The differences in element lengths, spacing, and overall boom length may be instructive.

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Updated 07-21-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 45: What Should I Expect from a Yagi?

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L. B. Cebik, W4RNL

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With commercial antenna makers spreading all manner of numbers around, it is difficult for the antenna buyer--or even the prospective antenna builder--to know exactly what to expect from a Yagi or similar beam. So let's take some time to survey the field and give some estimates based on many years of designing and analyzing Yagis. But first, a little terminology.

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I shall specify the gain of the Yagi designs in terms of free-space values that are average across the first MHz of 10 meters. The gain numbers will be in dBi, that is, dB over an isotropic source. Gain values in dBd, that is, gain over a dipole, are 2.15 dB lower than those given in dBi. Gain over ground varies according to antenna height, but at a height of 1 wavelength above average ground the gain values (whether in dBi or dBd, will be about 5.5-dB higher than the free-space value to account for both ground reflections and ground losses. By using free-space values throughout, you can get a comparative idea of the advantages of one design over another. So if one design has a gain advantage of 3.2 dB over another in free-space, then it will have the same advantage if we specify the values in dBd or specify the values over ground--or both. However, remember not to mix fruit: we are talking only of Yagi and similar designs based on horizontal half wavelength elements.

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Unfortunately, some advertising does not give you a clear picture of the conditions for the gain specification, so that you do not know if they are citing inferior gains over ground or superior gains in free-space. Some makers only express the gain in dB, so that you do not know what the reference standard is. There is also the problem of stating only the peak value so that you have no idea of the gain across the operating passband of the antenna. Then there are antenna makers who are completely honest, even if that honesty seems to make their products inferior to those of makers who rely on one or another form of vagueness, ambiguity, or downright unsupportable claims.

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Monoband Parasitic Arrays

Let's begin our survey with monoband Yagis for 10 meters. +
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Notes:

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  • 1. Ref-Dr means a reflector-driver design. Driver-Director designs are feasible, but have very narrow bandwidths.
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  • 2. Short-Med-Long-boom: boom length classification is relative to the number of elements in the Yagi and is based on building norms.
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  • 3. OWA means optimized wideband antenna design, based on initial work by WA3FET and NW3Z.
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  • 4. Very wide-band means the antenna will cover all of 10 meters.
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  • 5. Bandwidth is based on the 2:1 SWR curve after matching (if needed) with a gamma, beta, or Tee network.
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  • 6. Feedpoint Z is the resistive feedpoint impedance with the driver brought to resonance, and may be +/-5 Ohms from the listed value. For Yagis with more than 2 elements, making the driver impedance slightly capacitively or inductively reactive to suit a matching network does not affect performance.
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  • 7. Add about 5.5 dB to the free-space gain for the gain when placed about 1 wavelength (35' on 10 meters) above average ground. For a given mounting height above ground, regardless of the Yagi type, the elevation angle of radiation will be the same.
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Let's notice some trends. First, the gain does not always go up with the number of elements, but it does go up with the boom length. The only exception to this trend is when we design a very wide-bandwidth beam, such as starred entries on the list. Then we may require a longer boom to achieve the bandwidth and the 50-Ohm impedance.

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Second, adding an extra element on a given boom length does not usually increase gain. However, it does allow us to set the feedpoint impedance and to achieve greater control over the operating characteristics. For example, most of the Yagis with 3 or more elements show an upward gain trend across the band. However, the OWA design can center the gain curve and the front-to-back curve together so as to have more even performance across the band. As well, the OWA design allows a direct 50-Ohm feedpoint impedance and no need for a matching network.

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You can generalize on these rough expectations on other bands in a very simple manner. Find the ratio of the band names, for example, 20 meters divided by 10 meters equals 2. Then multiply the boom length of the 10-meter beam of your choice by that ratio. For example, a 20-meter equivalent of larger a long-boom 24' 5-element Yagi design, will have about 10.2 dBi gain if the boom is 48' long. These ratios are significant not only in the evaluation of monoband Yagis for other bands, but as well when we try to develop some reasonable expectations of more complex designs.

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The performance figures do not take into account non-electrical factors in a given beam's design. Commercial and home-built monoband designs may range from flimsy to greatly overweight, relative to the wind and ice loads at a desired operating location. The durability of both hardware and plastic fittings is an important question for both buyers and builders to address. As we look at booms that exceed about 24', we must also consider the needs for preventing excessive boom sag and stress.

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Remember that all of these Yagi designs are monoband antennas. Hence, the designers were able to optimize performance. Next, we shall see what happens when we cannot fully optimize performance.

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What Should I Expect of a Tri-Band Yagi?

The world of tri-band Yagi design is full of compromises. Depending on the design approach taken, the compromises may take many different forms, ranging from reduced gain on one of the bands to reduced bandwidth on another. Virtually all of the compromises result in reduced performance relative to a monoband Yagi for a given band. The design approaches are many and varied, as sampled by the diverse designs shown in Fig. 1. One design uses 10 elements on a shorter boom, with three of the elements serving as individual drivers for the three bands. The other design uses a reflector with a set of traps dividing 20 and 15 meters, and the forward-most director has a set of traps (shown as squares on the outline sketch) dividing 10 and 15 meters. The driver has 2 sets of traps and handles all 3 bands. These are only two of the many types of designs on today's market. +
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The question that faces us is how we can develop reasonable expectations from a tri-band design. One approach is to pose some basic questions.

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1. How long is the boom for each band, counting from the rear-most element to the forward-most element for that band?

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2. How many elements are active on each band?

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3. Are any elements in a given band loaded? This question can be tricky. For example, a 10-meter trap will not load the element on 10 meters, but it will form an inductive load on 15 or 20 meters. An element shortened by loading has slightly less gain potential than a full size element.

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4. Do any of the elements--especially directors--perform special functions that do not contribute significantly to gain? You may have difficulty determining the answer to this question, since non-gain element functions are difficult to determine without further analysis.

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Now let's apply the questions to our two subject antennas. The 10-element tri-bander at left, marked A, has a 3 element Yagi on 20 meters that occupies most of the boom. The 20-meter section of a tri-bander--if the elements are not loaded--tends to come closest to full size performance. If the boom length for the 3 elements approaches 16', then it will yield about 7 dBi of gain--about the same as the 10-meter monoband Yagi on an 8' boom. There are also 3 15-meter elements on a proportionately shorter boom. However, note that the forward director is behind the 20-meter director. This situation often reduces gain somewhat relative to placing it ahead of the 20-meter director. Hence, we can expect less than 7 dBi gain on this band.

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On 10 meters, there are 4 elements, and the boom length for them is similar to that of a 4-element short-boom monoband Yagi. However, note that the two directors bracket the 15-meter and 20-meter directors. Some of the function of the first 10-meter director is to "capture" the 10-meter energy to prevent the 20-meter element from controlling it. Hence, its function is not identical to that of the first director in a monoband beam. The result is a slight reduction in our gain expectations from the 10-meter elements--perhaps a half-dB reduction to the 8-dB region.

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In almost all tri-band designs, achieving a 20-dB front-to-back ratio is rare, with that value being a peak value. Values from 14 to 18 dB are more typical as averages.

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Now let's turn our questions to the design marked B in Fig. 1. It uses 6 physical elements, but some of them--as indicated by the squares--serve multiple duty. As we examine the design band by band, we need to count the elements that are active, even if only part of the element is active.

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The three longest elements--the two at each end and the driver with multiple sets of traps--form a 3-element Yagi for 20 meters on a boom that is longer than the one in our first design. The longer boom suggests higher gain, but the traps, especially in the driver, suggest some gain reduction at least due to element shortening. The net result is a gain value of about 7 dBi (free-space), since the boom length is still less than that of a long-boom 3-element monoband design.

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On 15 meters, we also have 3 elements. The reflector is the inner portion of the longest elements. Next comes driver, which terminates at the outer driver traps but passes through the inner traps. The director is the element behind the forward-most trapped element. The overall boom length is proportionately longer than for the first array and longer than for 20 meters. However, since the driver is still trapped for 10-meter use, the gain will not reach peak long-boom 15-meter levels, and once more falls in the 7 dB range.

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On 10 meters, we have 4 elements: the independent reflector, the inner portion of the driver, an independent director, and the inner portion of the forward element. Although as a monoband Yagi, these elements might form a good 4-element beam with a fairly long boom, the interactions with the other elements--especially those for 20 meters--will reduce the gain to about 8 dBi average. However, those same interactions have two other effects. First, they tend to make performance show sharp changes across the 10-meter passband. Second, they tend to reduce the operation bandwidth to about 800 kHz.

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The two tri-band designs turn out to be very comparable to each other, with the trapped design in B having a slight advantage in gain on 15 meters. However, gain is not everything. The placement of elements in a tri-bander must be a compromise between adequate gain over a sufficient bandwidth and the front-to-back ratio that can be achieved. Most current designs sacrifice some front-to-back ratio for gain, so realistic values tend to range from 14 to 18 dB. The exact value may vary from one band to the next. Our cursory analysis does not give us good clues to front-to-back performance.

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The estimates of performance for the trapped design presume very well designed low-loss traps, and my presumption is correct for some makers--but perhaps not for all. As well, traps tend to suffer environmental effects more severely than simple elements. They use a combination of materials, some of which may age faster than others in the seasonal cycles. Most have weep holes to drain accumulated humidity. The weep holes are also entries for bug nests and atmospheric particulates, either of which can cause eventual harm or lower performance. Since access to the insides of most commercial traps is difficult, routine maintenance and inspection become difficult. However, routine periodic maintenance is a key to the continued performance of any antenna, whether a monoband Yagi or a multi-band array.

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These notes are not designed to give definitive analyses of any particular monoband or tri-band array. Instead, they aim to give you a starting point in evaluating antennas that you might contemplate buying or building. In ads, thinking about commercial offerings, consider what the maker does not tell you. Then ask. If you do not get straight answers, factor that event into your evaluations along with the data that you do receive.

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Updated 10-01-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 46: The Persistent Vee-Beam Myth

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L. B. Cebik, W4RNL

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In a jigsaw puzzle, many pieces have similar shapes. You can force some pieces into the wrong places and end up with a messy and meaningless picture. The same rule applies to antenna work. Back in the 70s and 80s, backyard antenna builders created some interesting antennas and then made all sorts of miraculous claims for them. Since I receive numerous questions from folks reading old issues of ham magazines, a good number of them have focused on these miracle beams. One of the most persistent is the so-called Vee-beam.

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Right at the start, we have the seeds for a misunderstanding. There is a very legitimate use of the term Vee-beam that indicates an array with good directivity and high gain. However, this traditional beam uses wire elements many wavelengths long. The Vee-beams of the more recent vintage are Yagi size, that is, with elements about ½ wavelength from end to end. However, it appears that the Vee-beam builders wanted to claim long-wire results for their short element antennas. So claims arose that a 2-element Vee-beam would give performance equal to or better than a 3-element Yagi with straight elements. (I still see such claims on the Internet.)

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A second claim is that bending the elements forward will save space. If a standard Yagi is 16 to 17 feet wide, the Vee'd form will only be about 12 feet wide. So we have a seemingly compact antenna.

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Let's evaluate these claims by making a series of comparisons among 3 2-element beams. All of the antennas will use 5/8" diameter elements for our modeling exercise. There is nothing in any of the designs that will even remotely approach the limits of antenna modeling software, so results will be reliable.

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1. A standard Yagi: For the Yagi, I have selected a wide-band version having a natural feedpoint impedance in the vicinity of 50 Ohms. Hence, you do not need a matching network, such as a beta or gamma match. The reflector is 17.3' long, while the driver is 15.84' long. The elements are 5.5' apart. You can use closer spacing, but the lengths will change and the feedpoint impedance will go down. At 4.3' for the spacing, you will get 32 to 35 Ohms for the feedpoint impedance and need a matching network for your 50-Ohm coax cable feedline. The reduced spacing will give numerically detectable improvements in performance in modeling software, but not enough to be detectable in operation.

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2. A Moxon Rectangle: The Moxon is a compact 2-element beam that uses standard Yagi parasitic coupling plus element end coupling. Its gain is almost as good as the Yagi gain. However, the front-to-back ratio is exceptionally better. At 28 and 29 MHz, you can have about 18 dB of front-to-back ratio, compared to the 10-11-dB figure for a Yagi. More to the point is the size. The Moxon is only 12.5' side-to-side and 4.6' front-to-back. Like the wide-band Yagi, it has a natural 50-Ohm feedpoint impedance for direct connection to your coax cable.

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Both the wide-band Yagi and the Moxon rectangle should use a means of "common-mode current" suppression at the feedpoint. For this purpose, you may use a bulky 1:1 balun. However, a simpler bead-type choke, as designed by W2DU and available from numerous vendors, is just as effective. Its advantage is a diameter not much larger than coax cable. Hence, you can tape it to the boom and not add significant weight to the antenna.

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Structurally, the Yagi is larger overall. However, the Moxon requires a bit of extra fabrication effort. It needs 4 corners to the elements. So the space saving comes at a price, but one which many folks can pay without strain.

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3. The third antenna is a 10-meter Vee-beam. Each element has a "quadrant" form, that is, a 90-degree overall bend. The open ends point in the desired signal direction on the premise that we shall get added gain from them. The bending results in an overall beam width of about 12.4'. Unfortunately, the forward bending increases the front-to-back dimension to about 11.4'. So now we have a nearly square array. Fig. 1 shows the relative sizes of our 3 beams.

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The next question for our comparison concerns how well the three antennas perform. We can break that question into 2 parts.

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a. What kind of pattern do I get from each antenna?

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b. What kind of operating bandwidth do I get from each antenna?

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The pattern question is relatively easy to answer, if we break it down into parts. The Yagi provides the most gain--about 0.2 dB more than the Moxon and about 0.7 dB more than the Vee-beam.

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The Moxon rectangle has the best front-to-back performance, as noted earlier. The Yagi comes next, with a modest 11 dB front-to-back ratio. Which value is better for your operation depends on your needs. For nets, I prefer the Yagi, since I can hear--although more weakly--stations from the rear. For contests, I prefer the Moxon that quells rearward QRM very effectively. The Vee-beam is slightly poorer than the Yagi in the front-to-back performance.

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See Fig. 2 for overlaid patterns for the 3 antennas to confirm these notes.

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The patterns reveal something else about what happens when you Vee and element horizontally. The front-to-side ratio goes way down, since each half element radiates some energy to the side.

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We have noted that the Yagi and the Moxon have 50-Ohm feedpoint impedances. That number applies to the design frequency (28.35 MHz for all three antennas). But what about the band edges. For this performance specification, let's look at the SWR curves in Fig. 3.

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The wide-band Yagi 50-Ohm SWR curve may start higher than the other two, but only because the antenna provides coverage of the entire 10-meter band from 28.0 to 29.7 MHz. You can lengthen the driver slightly to bring the minimum SWR value down in frequency.

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In contrast, the Moxon rectangle provides a 50-Ohm SWR of 1.5:1 or less for the first full MHz of 10 meters. The rate of increase above the minimum point is slower than below the minimum point, so coverage extends to about 29.2 MHz or so before the SWR value reaches 2:1.

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The Vee-beam shows an entirely different pattern. First, whenever you change a straight element into a Vee, no matter where the Vee ends point, you lower the single element impedance. Hence, a simple inverted-Vee has an impedance closer to 50 Ohms than to the straight dipole 70-Ohm value. Second, whenever you add a second element, such as a parasitic reflector, you further lower the feedpoint impedance. Straight element Yagis produce 30-50-Ohm impedances, compared to a dipole's 70 Ohms. Since a Vee'd dipole is already at a lower feedpoint impedance, adding a reflector lowers the impedance even further. Hence, the Vee-beam has a resonant driver impedance of only 25 Ohms. This value is not fatal, since we can always add a matching network to raise the impedance.

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However, notice the overall SWR curve for the Vee-beam. Not only did we lower the impedance, but as well, we narrowed the 2:1 operating bandwidth. We have about 800 kHz of operating room, compared to the other beams. Although this value is adequate for most lower-end 10-meter activities, it does require that you tune the Vee-beam with great care and precision.

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So the bottom line is that we do not get anything special from the Vee-beam configuration that we cannot get from simpler, smaller, or wider-band arrangements. My preference is always to keep these antenna notes on the positive side. However, the Vee-beam myth has persisted for so long that I felt compelled to provide some legitimate comparisons. May the Vee-Yagi rest in peace beside Vee'd LPDAs and other members of the family. There are better ways to meet your 10-meter small beam needs.

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Updated 01-16-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 47: What is a Balun, and Do I Need One?

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L. B. Cebik, W4RNL

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The term BALUN is one of the most vaguely used words in antenna work. It has different levels of specificity, but writers are not always clear on what level they mean. So let's start at the beginning and see if we can straighten out the term. Once we are clear on what we are talking about, we shall be in a better position to decide if we need one. Finally, if we do need one, we can decide on what kind we can use for a given application.

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1. What is balun? The term balun is a contrived word composed of "balanced" and "unbalanced." In its most generic use, it indicates any device that helps us effect a transition from a balanced transmission line or circuit on one side and an unbalanced transmission line or circuit on the other side. In some of the basic materials that we studied in preparation to get our licenses, we encountered baluns, but without that name attached. Consider a standard link-coupled RF circuit composed of two coils. One side if hot at one end, but the other end is grounded. The other side is hot on both sides. It may or may not have a center ground. This circuit, whether tuned with capacitors for one frequency or left untuned for wide-band use, is a type of balun. However, the actual term grew up in relatively recent antenna work.

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When the term balun arose, it was in connection with transmission-line transformers. Transmission-line transformers are specially constructed transformers composed of multiple winding where adjacent turns have a very specific spacing. The spacing forms a transmission line with a characteristic impedance. Therefore, some folks always mean a transmission line transformer when they use the term balun, while others may mean only any device that effects a transition between balanced and unbalanced circuits.

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Transmission-line transformers come in many forms. One division is between linear and toroidal baluns, that is making use of transformer coils wound in a straight line or in the form of a circle. The second division is between air-wound transformers and those making use of a core that is normally composed of a ferrite material. So we find air-wound linear transformers, ferrite-core linear transformers, and ferrite-core toroidal transformers. Air-wound toroids are not normally used.

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We also find other divisions to think about. For example, there is the matter of the impedance ratio. The most common impedance ratios are 1:1, which uses a trifilar winding, and 4:1, which can use a bifilar winding. 4:1 baluns normally have their high impedance side correspond to the balanced side of the device. Most baluns in the 1:1 to the 4:1 range use a low Zo for the transformer winding. For a 1:1 balun intended for use with 50-Ohm system, the impedance is as low as we can get two round wires to go (about 80 Ohms). A 4:1 balun for transforming 200 Ohms to 50 Ohms might use the geometric mean between the two target values (100 Ohms). Other impedance ratios are certainly possible. As well, there are ununs, that is, unbalanced to unbalanced transformers that designers use in conjunctions with baluns to effect odd impedance transformations.

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There are also design types, such as the Guanella, but the most common distinction is the voltage vs. the current balun. For virtually all amateur antenna system applications, a current balun type is preferred. One of the guiding principles of balun design is that the device should be wide band, covering most of all of the HF region or perhaps a special design for VHF from 6 meters through at least 2 meters.

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We now have at least two devices that will effect the transition: a relatively standard link-coupled pair of RF coils and a transmission-line transformer. There are other devices. Some applications call for convention wide-band transformers, often wound on iron or ferrite toroidal cores. Other applications may call for a simple choke, a device that sets up a high inductive reactance to attenuate the flow of current where we do not want it to go. One way to make a choke that is suitable for a 10-meter antenna application is to make a coil of coax. Another way is to place a series of ferrite beads over a length of 50-Ohm coaxial cable.

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2. Where Should I Use a Balun? The most common application for a balun is at the terminals of a balanced antenna feedpoint that we are feeding with unbalance coaxial cable. See Fig. 1.

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The outer braid of the coax provides an alternative path for antenna currents at the terminals. The current on the braid goes under the name "common-mode current." Common-mode currents do nothing useful for communications. Whether or not they create a problem depends on many variables, but it is always wise to place a choke at the antenna terminals. Since the antenna (including any attached matching network) and the coax are both 50-Ohm devices, we can use any of the 1:1 balun devices available.

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Note the special reference to a tower leg and the earth ground that it implies. If feasible, it is advisable to form a connection between the coax braid of the transmission-line side of the choke and a tower leg. I am assuming that you have your tower--if you use one--well grounded. Such a connection is protection from a number of potential problems, and giving the remnant common-mode currents a path to the earth is one of them. Charge build-up on the antenna now also has a relatively easy path to the earth.

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If the coax between the antenna and the shack is long, and if the run turns enough corners, then you may still have common-mode currents in the shack due to signal coupling directly to the coax braid. If you have such a problem, it may show up as a difference between SWR reading on the rig's meter and on an external meter in the line. Or you may get a tingle or a bite from sharp corners of the transceiver case while transmitting. At its worst, it may show up on telephone lines, and it may even lock your VOX or keying circuit on some bands.

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One avenue to a cure that is highly effective (but, like all things in amateur stations, not universally perfect) is to install a second choke at the shack entry, as shown in Fig. 2. This 1:1 choke is not doing anything but attenuating currents on the outside of the coax line (where all transmission-line currents are on the inside, between the center conductor and the inside face of the braid). Note once more the reference to an earth ground. You may wish to place the second choke on the outside wall, close to the ground, so that you can have the shortest possible distance for the lead to the ground rod.

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The third major application for 1:1 baluns or choke may not involve any activity by the user. There is a new generation of balanced network tuners on the market, a partial replacement for link-coupled tuners of years gone by. The better of these tuners include on the input side a 1:1 balun. The tuner is for balanced parallel transmission lines at the output. The tuner changes the output terminal impedance to 50 Ohms, but the line is still balanced, so a 1:1 balun on the input side effects the change from balanced to unbalanced or single-ended lines to the transceiver. See Fig. 3.

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All of these applications call for a 1:1 balun, that is, a balun that does not effect any kind of impedance transformation. We only need to effect the balanced-to-unbalanced transformation while choking out any extraneous currents that may want to exist on the outside of the coax braid.

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3. What Kind of Balun Should I Use? Theoretically, you may use any type of 1:1 balun or choke available. In principle, any of the major types will do the jobs just described. Here are some options.

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a. Coiled coax: The coiled coax choke can be useful at the antenna terminals. For 10 meters, you may coil about 4-6 feet of RG-8/213 or RG-58 (for lower power) into 6 to 8 turns. Do not scramble wind the turns. Instead, wind them in a coil form and tape the turns together. You may use a short piece of 4 to 6 inch PVC as a form, although some folks have used empty plastic soda bottles as a form. (Protect any form from UV, since the sun will make the form go brittle in under a year without protection.) Coax coils are quite effective on single bands, but less effective for multi-band use.

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b. Commercial 1:1 current baluns: These devices come on many forms, usually potted inside permanently cemented PVC. Some have coax connectors at both ends, while others have wire leads on one side. A few are designed for wire-antenna center insulator/balun use, and may even have a top hanger eyebolt for inverted-Vee installations. Some current baluns are air wound, while others use either ferrite rods or ferrite toroids.

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Most of these units are bulky. Their best application is usually at the shack entry point, where weight and size do not make a major difference. Some have a built-in ground strap for easy connection to an earth-ground system. Balanced network antenna tuner makers use bare baluns inside the tuner case. (If you are thinking about buying one of the new balanced tuners, be certain to find out whether the tuner includes the balun, because it is essential to proper operation.

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c. Ferrite bead chokes: Walt Maxwell, W2DU, first devised these chokes in the 1980s, and they are highly effective. For HF use, the builder places about 50 Type 77 or type 73 ferrite beads over a length of coax. Type FB77-1024 beads fit over RG8/213 and similar larger diameter coax. Type FB73-2401 beads fit over RG58 for lower power applications. Walt's original design used the smaller beads of a length of RG-142, which appears similar to RG-58 but uses a Teflon dielectric and silver-coated wire to handle higher amateur powers. Of course, you must protect the assembly from the weather with a coating of some durable sort.

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I tend to prefer the ferrite bead chokes at the antenna terminals, especially with beams. They weigh less than most current baluns and coax coils, and they are less bulky. You can usually tape them to the antenna boom. I have used them for about a quarter century with good success in both shack entry and antenna terminal applications.

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So far, we have dealt with only 1:1 baluns and chokes. For coax systems, these are the ones that we need to effect balanced-to-unbalanced transitions (or vice versa) and to attenuate common mode currents that may exist on the outside of our coax braid.

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Due to the history of antenna tuners in the last 3 decades, the most talked-about balun is the 4:1 variety. In fact, when many hams think "balun," they almost automatically think "4:1 balun." We find them in almost all single-ended (unbalanced) network tuners as a way to simulate a balanced tuner output. So it looks like our work with baluns is only half done. The odds are 4:1 that next time we shall look in more detail at applications--both good and bad--for the ubiquitous 4:1 balun.

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Updated 05-1-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 48: The Ubiquitous 4:1 Balun

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L. B. Cebik, W4RNL

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In our last episode, we introduced the idea of a balun. We noted that in its most generic use, the term "balun" refers to any device that enables us to make a transition from a balanced circuit to an unbalanced circuit--or vice versa. The most common application of the term occurs in antenna and feedline work.

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More specifically, many uses of the term "balun" wish to indicate the use of a transmission-line transformer, a specialized wide-band transformer whose turns have a characteristic impedance, that is, whose turns are formed with transmission line sections. We noted that such impedance transformers come in many forms, ranging from linear air-wound versions to the more common toroidal form using a ferrite core (or cores, for high power transformers.

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Balun transformers can have a large range of impedance transformations, running at the low end from 1:1 up to as much as 9:1. Perhaps the individual who has written the most on the basic balun transformer and done the most in developing versions that one can build is Jerry Sevick, W2FMI. He has several books on the subject.

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In our last episode, we looked at the all-50-Ohm (or, more generally, the all coax) system. We discovered that the balun transformer is only one of the devices that we can use to effect a transition from a balanced to an unbalanced system. Besides the transmission line transformer, we could use a ferrite bead choke or even a specially would coil of coax to attenuate common-mode currents virtually anywhere along the line, depending on our needs.

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In this episode, let's look at the balun transformer itself. Its purpose is to transform impedances over a wide range of frequencies--for example, the entire HF range from 3 to 30 MHz. It just happens also to attenuate common mode currents as well.

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Fig. 1 shows the ideal situation for a transmission-line transformer as a balun--on the left. We buy or build a balun transformer with the desired impedance transformation relative to our 50-Ohm main feedline cable. Actually, most baluns are able to handle impedances over a range, so the 50-Ohm side can vary somewhat. If our balanced impedance is 200 Ohms, then a 4:1 balun will change that to 50 Ohms on the unbalanced side. In fact, I know of at least one contest operator who designs his beams to produce a 200-Ohm impedance in a Tee-match and then uses a 4:1 balun at the feedpoint for his 50-Ohm cable.

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However, we are not restricted to a 4:1 balun. In fact, the balanced side need not have a higher impedance than the input side. There are 4:1 baluns that will transform a 12.5-Ohm balanced impedance to a 50-Ohm unbalanced impedance. We cannot simply turn the common 4:1 balun around, since it is doing two jobs at once: transforming the impedance and effecting a balanced-to-unbalanced transition.

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We noted that the greatest efficiency occurs when the characteristic impedance of the balun winding is the geometric means between the high and low impedances. Sometimes, the transformation that we need is very high, for example, 16:1 in some cases (with terminated folded dipole all-band antennas, for example). In these instances, we may start with a 4:1 balun. Then we can add a 4:1 unun, that is, a transmission-line transformer designed for unbalanced input and output sides. The right side of Fig. 1 shows this option. If we must match 800 Ohms to 50 Ohms and go from a balanced side to an unbalanced side, then the dual transformer option is sometimes best.

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When used properly, transmission-line transformer baluns can be over 99% efficient. However, they do have their limits. For one, they tend to become lossy when the impedance on the antenna side has considerable reactance. Sevick recommends that all matching to remove reactance be done on the antenna side of any balun transformer. It is also possible to over-power baluns so that they begin to heat before the cores reach saturation. Whatever signal energy turns into heat is energy no longer available for radiation and communication.

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Now let's look at Fig. 2, the most common application of the ubiquitous 4:1 transmission-line transformer balun. The sketch shows in simplified form the typical unbalanced (or single-ended) network tuner. The coils and capacitors in a real tuner would be variable or switched, and the unit might even have a built-in SWR meter. However, we can see, just by looking at the ground symbols, that the main purpose of the tuner is to match unbalanced antenna impedances as they occur at the output coax connector to 50 Ohms at the other coax connector.

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However, the chief use for most antenna tuners is to handle multi-band wire antennas using parallel feedlines for low losses in the presence of a very wide range of antenna-terminal impedance values. Most multi-band antennas will not only show both high and low impedances, but as well, the impedances will have both resistive and reactive components, both of which may be high. The impedance at the balanced terminals of our tuner will be a function of 3 variables: the antenna terminal impedance, the characteristic impedance of our feedline, and the length of the line itself. When the antenna impedance is not an exact match for the feedline impedance, the value of impedance will undergo continuous transformation along the line every half wavelength at the operating frequency.

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To handle these impedances, tuner makers install a 4:1 balun. Depending on the tuner maker, these units may range from poor to excellent in quality. But they are still 4:1 baluns. Even at their highest efficiency, they transform the impedance at the terminals down to a value that is 25% of the tuner terminal value.

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However, because the impedance undergoes continuous transformation along the way, it may already have a low impedance at the tuner terminals. If it is already 20 Ohms (a value that has occurred in many instances), then a completely efficient 4:1 balun will transform it to 5 Ohms. Most tuners will be able to transform the 5 Ohms up to 50 Ohms, but they will not do so efficiently. Considerable power will be lost, not in the balun, but in the tuner. Since the tuner components are large, you may not be able to detect the heat, but the losses will be there.

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So far, we have assumed that the balun is completely efficient. However, as we have noted, the impedance at the tuner terminals may consist of both resistance and reactance. Many balun designs become lossy in the presence of high values of reactance.

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The end result is a system that is lossy by design. The 4:1 balun has been added to the single-ended tuner as an afterthought, a convenient way of claiming that the tuner will handle both balanced and unbalanced antenna side loads. However, we must always ask how well it will handle such loads, and the answer is not always pleasing.

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If you do use a multi-band antenna with parallel feedlines for operation on the "other" HF bands, there are better ways to handle the matching requirements. There are still a few link-coupled antenna tuners left over from ancient times, such as the Johnson Matchboxes produced from the 50s through the early 70s. European operators can still find a few good Annecke link-coupled tuners.

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More recently, several makers have introduced balanced network tuners. These tuners, shown in outline form in the last episode, do their matching work while still in the balanced configuration. At the transceiver side of the unit, where the impedance is now 50 Ohms or very close to it, some builders install a 1:1 current balun to transition from the balanced impedance to an unbalanced line, namely, the coax from your tuner to the rig. (I have recently seen a low cost balanced tuner circuit that does not indicate the presence of a balun. In this case, you will have to add one.)

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Balanced network tuners are not without limits. They have their widest matching range--that is, their ability to handle high impedances with relatively high reactive components) at the lowest frequencies. The matching range tends to narrow as the frequency goes up. At the high end of the spectrum, the required values of inductance and capacitance for high impedances tend to be below the minimum values that the components can achieve.

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Now let's suppose that you already have a single-ended network tuner. Let's also suppose that you want to spend your money on other things than a new balanced network tuner. Is there a way to press the unbalanced tuner into service and to get reasonably good (even if not perfect) performance from it? The answer is affirmative, and Fig. 3 shows how.

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First, we shall forget about the 4:1 balun inside the tuner and use the unbalanced coax connector antenna-side output. We shall obtain a short length of coax, just enough to reach from the tuner to the entry point for the feedline to our multi-band antenna. If we obtain the very lowest loss coax we lay our hands on, so much the better, and if we can keep the coax run as far under 20' as possible, so much the better to keep losses minimized. At the entry point, either indoors or outdoors, we shall install a 1:1 choke. For this application, I tend to prefer ferrite bead type chokes, since the antenna side terminals may have considerable reactance. Note that on the coax side of the choke, we run a s hort lead to a ground rod from the coax braid. The lead should be as short as feasible and the rod as long as possible. Finally, we connect our parallel feedline to the antenna side of our 1:1 choke.

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In this configuration, we use our single-end tuner in the mode for which the design is most apt. We do not transform any low impedances down any further. The system will have losses. The high SWR on the coax run becomes lossier the higher we go in frequency and the longer we make the run. Hence, keeping the run very short and using very low loss coax are essential. The choke will also suffer some losses, depending on the SWR value we see there. However, the system has proven more effective in many instances than using the 4:1 balun inside the tuner. As well, because the parallel line is wholly outdoors, the system has freed many ham shacks of troublesome RF indoors. The system is not perfect, but is has proven over the last 20 years to be reasonably effective.

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Updated 07-23-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 49: The Basic 10-Meter Monopole

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L. B. Cebik, W4RNL

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Over the last 12 years of this column, we have pretty much overlooked one of the most basic of all 10-meter antennas: the ¼ wavelength monopole with a ground plane. The antenna is simple to build, fairly compact, and performs reasonably well, so we had better fill in this gap.

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We shall not start with a ground-mounted antenna, simply because the losses are too high. However, when we elevate the monopole, we make a discovery. If we set the ground-plane radials at right angles to the monopole, the feedpoint impedance drops into the 20-25-Ohm range. Instead of adding a matching system for our 50-Ohm coaxial cable, we shall take a different tack. We shall let the radials bend downward at a 45-degree angle. This measure does two good things. First, it raises the feedpoint impedance to the 50-Ohm ballpark. Second, the radials, to the degree that they are partially vertical, add to the overall radiation from the antenna.

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Fig. 1 shows the outlines of a same monopole with drooping radials. The vertical section is about 8'-1" long if we use ¾" outside diameter tubing for the element. Of course, you can combine two sizes of tubing that nest together so that you can adjust the length for the lowest SWR at whatever frequency you prefer. The model used here is centered on 28.4 MHz. However, the operating bandwidth will generally cover all of 10 meters.

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The radials are 8' long when you use quarter-inch diameter rods. If you use thinner materials make them slightly longer, and if you use fatter tubes, then make them slightly shorter. Remember that you can make final adjustments to the main vertical element. The monopole uses 4 radials in a symmetrical pattern. Adding further radials to an elevated monopole will not improve performance, but it will add unnecessary weight.

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I shall not give any detailed construction advice, since there are as many ways to build a monopole with radials as there are builders. Use available materials and your own skills to work out the assembly. Check various handbooks and magazine articles for construction methods that match up with your preferences. Just be certain that the radials have a common connection and that the feedline connector has its center pin going to the vertical section, with its shell going to the radials.

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The next question is what I might mean by "elevating" the monopole. The answer to that question can be any base height from 10' on upward. We normally define the base of the antenna as the junction between the vertical element and the radials. Fig. 2 provides some selected elevation patterns at 10' intervals. Examine these patterns together with the table that follows them. Together, they will give you some idea of what to expect from the monopole a various heights you might use.

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Between a base height of 10' and 20', the lowest lobe is dominant. In fact, at 10' up, it is the only lobe. However, by the time that we reach 20', the upper lobe is just as strong. It is at an angle that is good for very little but noise and possibly some sporadic E-skip.

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From 25' up to 35' up, the lowest lobe is not the strongest lobe. The next higher lobe (as shown by the 30' pattern in Fig. 2) dominates. Nevertheless, as we continue to raise the antenna height, the gain in the lowest lobe continues to climb. Also notice that each new height shows the emergence or the rapid development of a new lobe. With vertical antennas, these lobes tend to merge so that we can only detect individual lobes by their peak values. (In contrast, a horizontal antenna would show very distinct lobes with very deep nulls between them.)

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By the time we move the antenna base to a height of 40', the lower lobe once more dominates the elevation pattern. The upper lobes have significant but not overriding strength. The progression of lobe development is not an accident. It is a function of the way in which the direct radiation from the antenna mixes with radiation reflected from the ground. When the antenna base is between about 5/8 wavelength up and 1 wavelength up, the combined direct and reflected radiation favors higher angles. Above 1 wavelength up, the combination of direct and reflected radiation again favors the lower angles.

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To a degree, you can translate these general pattern tendencies to almost any vertical antenna, including vertically oriented dipoles and Yagis. The key element in the translation is the height equivalence: the base height for the monopole is approximately equal to the center of the dipole and the boom of the Yagi.

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The general trend of the gain and TO angles (where the TO or Take off angle is the elevation angle of maximum radiation) suggests that the higher you mount the monopole, the better the performance. Since the feedpoint impedance shows remarkable stability, you may generally adjust the antenna for best SWR at a fairly low height and then finish the installation with no further adjustments.

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Not everyone has a handy tower to use for a highly elevated mount. The antenna is light enough to accept a chimney mount intended for an outdoor TV antenna (assuming in this age of cable that we remember such things). Mounting the antenna on top of your living space does call for some practical considerations.

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First, it is likely that the radials may droop so that the roof comes between pairs of them. If the attic space is clear of significant metal, the roof will not usually detune the antenna. However, if the attic rafters have metal-faced insulation, it may have an affect. In such cases, you may wish to extend the mounting pole high enough to clear the roofline.

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Second, the vertical element may gather static charges. Fig. 3 shows a cure for this potential problem.

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Across the coax connector--or, what amounts to the same thing, between the vertical element and the junction of the radials--connect an RF choke. A value of 10 uH is usually sufficient, and 100 UH will work as well. At 10 meters, the choke blocks RF energy, so you will not be shorting out the antenna relative to operation. However, the choke does provide a DC path to discharge static energy in the vertical element as it builds. So all of the parts of the antenna will be at the same potential.

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As an adjunct to this measure, where the coax would enter the house, connect a ground lead to the braid and the other end to a ground rod. Make this a stout lead and rod, since the monopole becomes a lightning rod. Remember that lightning rods tends to bring the ground potential to the rooftop, making it a less likely target for lightning than other nearby objects--such as trees--that can store and hold a charge that is more opposite to the cloud bottom charge. As a result, the other objects become more attractive than your antenna to cloud discharges. (However, if your antenna is the only tall object within a large area, then all bets are off and you need a strong discharge path for any strikes.) It is always wise when a storm approaches to disconnect your coax out of doors and reconnect the antenna lead to the earth-ground system.

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The monopole with drooping radials can be an effective vertical antenna. The principles of installation that apply to it also apply to any of the commercial trap verticals that you might use for multi-band operation.

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Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 5: What Difference Does Height Make?

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L. B. Cebik, W4RNL

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The general rule for antennas that we always hear is "The higher, the better." Is this true? Generally speaking, and for 10 meters, the answer is "Yes" in terms of antenna performance. (The answer may be "No" in terms of tower, rotator, antenna, and cable maintenance.) Why?

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"Why" always takes more time and space to answer, but the general principle is this: the higher the antenna, the lower the take-off angle. We can get a hold of the idea of "take-off angle" by looking at Fig. 1. It shows one antenna, a three element Yagi, at heights of 22, 35, and 52 feet. These correspond to heights of 5/8 wavelength, 1 wavelength, and 1 1/2 wavelength respectively. If you extrapolate these ideas to other bands, remember that the principles apply in terms of height in wavelengths or fractions thereof.

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We are interested in the lowest forward lobe to the right, the direction in which the beam is pointed. That is the main lobe, where the power is greatest (or the receiving gain is greatest). The angle of maximum radiation or gain is the take-off angle. At 22 feet, the angle for this antenna is 21 degrees; for 35 feet the angle is 14 degrees, and for 52 feet the angle is 9 degrees.

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Fig. 1: Elevation plot for a beam at 22', 35', and 52' +

There is a second principle to consider. Most of the time, the longer the path to a distant station, the lower the angle at which the signal bounces between the antenna and the ionospheric (skip) layer. On 10 meters, many dx stations require an angle under 10 degrees, especially during marginal conditions.

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The test antenna at all three heights has some power radiated under the 10 degree angle, but obviously that power increases at this angle as we raise the antenna height. When the band is wide open, that is, when skip is very strong, the differences may make no difference in the ability to make long distance contacts. The differences begin to show up under marginal conditions or in competitive situations, such as contests and dx pile-ups. Many dxers favor heights above 100 feet, especially for their 20 meter antennas (that is, about 1 1/2 wavelengths at 20, 3 wavelengths at 10).

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These principles are not absolutes. Skip conditions have many variables that can alter situations. Moreover, in some applications, we may want power in the high angle lobes. State-wide 75-meter SSB coverage conveniently calls for low antennas with high skip angles, and few of us can get a 75-meter dipole very high in terms of a wavelength. On 10, the secondary lobes of the beams are useful for using shorter skip paths.

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Take-off angles do not vary much among horizontal antenna types. At very low heights (about 1/2 wavelength), 3-element Yagis and quads have a couple of degrees advantage over dipoles and 2-element Yagis, but the difference in take-off angles washes out at 1 wavelength antenna heights. Hence, a dipole at 100' might outperform a 4-element Yagi at 25' for some dx paths.

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Height, especially at levels below 2 wavelengths, can make some subtle differences in performance as well. The gain, front-to-back ratio, and feedpoint impedance of an antenna are not constant as we raise it. Rather, for dipoles and Yagis, gain peaks at about 5/8 wavelength and again at 1 1/4 wavelength, 10 meter heights of about 22 and 44 feet. Gain dips at 7/8 wavelength, about 30 feet up. In some antenna designs, the dip may be almost a full dB below the maximum gain at favorable heights. Of course, if you have a multiband antenna, one band's maxima may be another band's minima, so some sort of compromise is in order. These subtler differences in antenna performance also complicate antenna comparisons.

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Front-to-back ratios in 2-element beams show a variable pattern of change, but director designs peak just where reflector designs dip and vice versa. Curves are smoother for 3-element Yagis. The ups and downs in gain and front-to-back ratio that parasitic beams show demonstrate the complex interactions not only directly among the elements, but also with ground reflected power that plays such an important role in real antennas. The exact phase difference between the radiated power and the ground reflected power adds or subtracts from the antenna's total in both calculable and measurable ways. How the ground reflections add or subtract varies from one kind of antenna to another.

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Antennas composed of 2 elements about 1/4 wavelength apart and fed 180- degrees out of phase show a bidirectional pattern with very significant gain over a dipole. They also display an immunity to some of the effects of height, general showing a smooth curve of gain increase with height. Another feature of these antennas is that they have a strong vertical null, that is, negligible radiation straight up. Hence, the interactions of ground reflected power with the antenna are largely confined to increasing the strength of the main lobes.

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These subtler interactions, of course, do not negate the first principle of antennas. Get the thing as high as you can legally, safely, and economically maintain. Then start operating.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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No. 50: Notes on Horizontal Antenna Height

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L. B. Cebik, W4RNL

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In the last issue, we looked at the simple ¼ wavelength vertical monopole. In the course of our examination, we paid close attention to the effects of height on the pattern of the antenna. We discovered that if we chose a height too great, we could send our signals into space rather than into the skip layers that give us long-distance 10-meter communications. Although we have touched upon the subject in the past, we should give equally close attention to the height of horizontal antennas.

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One advantage that all single layer horizontal antennas share is that their behavior is very regular as we change heights. By a "single-layer" antenna, I mean a single dipole, a single Yagi, etc. The situation does change a bit when we stack horizontal antennas. But most of us are limited to single layer antennas, and that is our proper starting point.

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As we raise the height of a horizontal antenna, 2 things happen. First, the lowest elevation lobe gets lower and lower. That is an advantage, because on 10 meters, most of the DX skip occurs at angles from about 5° to 10° or so above the horizon. The second phenomenon is that when we raise the antenna, more and more elevation lobes develop. Fig. 1 shows the situation of a dipole at 0.5 wavelength intervals up through a 2 wavelength height.

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For each half wavelength step, we find a new lobe. These lobes do not simply pop up, but develop. They first appear as a bulge straight up and then gradually split as we increase the height until they take their place in the set of lobes--with a new top bulge. Since we only have 90° of angular room for the lobes, every new lobe results in a lower angle for existing lobes, and each of them gets a bit thinner.

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Note that each elevation plot is labeled in terms of the height measured as a fraction of a wavelength. A wavelength at 10 meters is about 35', at 15 meters 44', and at 20 meters 70'. So if you use a tri-bander at 70', then your 20-meter lobes will look like the 1 wavelength picture, on 15 like the 1.5 wavelength picture, and on 10 meters like the 2 wavelength picture. In fact, we should run the same plotting exercise with a 3-element Yagi just for comparison. See Fig. 2.

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Note that in the forward direction, we find the same number of lobes at each height as for a dipole. At the lowest height, the Yagi main lobe is slightly lower than for the dipole as a function of the Yagi's added forward gain. But that advantage quickly fades as we raise the antenna higher. In addition, the rearward lobes of a Yagi tend to show some erratic properties, but so long as the front-to-back ratio is high--as it is in this design--the oddities create no problems. A 2 element Yagi, with lesser front-to-back ratio will show stronger rearward lobes with more standard differences in strength. The 3-element Yagi shown in the plot has a gain advantage over the dipole about 5.8 dB, although that advantage varies with height--assuming one of each type of antenna at the same height for comparison.

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How high should I place my antenna? For maximum DX, place it as high as is feasible. I have heard arguments to the effect that a half wavelength is the optimal height, because we have only a single forward elevation lobe. Unfortunately, that argument fails to account for two facts. As we raise the antenna, the gain of the lowest lobe increases. The 2 wavelength dipole is about a half-dB stronger than the ½ wavelength dipole. The 2 wavelength Yagi is about 1.5-dB stronger than the ½ wavelength version. The second fact returns us to the primary skip angles on 10 meters, which are very low for the longest DX (most of the time). With a height of 1.5-2 wavelength, the Yagi main lobe angles fall well into the prime skip angles. Those same angles receive about half of the available power when the Yagi is only 0.5 wavelength up. If a half wavelength is all you can manage, you will still do well, especially in strong sunspot periods. But greater height will bring even better results.

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These principles apply to what I have called the single-bay or single-layer horizontal antenna. The class of antennas includes single dipoles, Yagis, and flattop horizontal phased arrays, such as the ZL-Special or the 8JK. We can modify the lobe elevation structure by using horizontal antennas that are stacked vertically and phase fed. Many such arrays are possible, but here we can bring back an old favorite of mine just to illustrate how the elevation lobes change with stacking. The array is the expanded lazy-H. As shown at the top of Fig. 3, we run two extended double Zepp center-fed wires, each 44' or about 1.25 wavelength long. We place them one above the other, using a 5/8 wavelength spacing or 22'. Using parallel feeders, we run lines from each wire to a mid-point between them. At this junction, we run a parallel feeder back to the shack to a balanced antenna tuner. The antenna is usable on 40-10 meters with bi-directional narrow-beam high-gain patterns. The exact gain is a function of the overall antenna height, but with the base at 44' (about 1.25 wavelength) and the top is at 66', the gain is somewhat over 15 dBi--greater than the gain of the 3-element Yagi.

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The lower portion of Fig. 3 answers 2 questions at the same time. 1. Where does all the gain come from? 2. Where did all the Yagi and dipole upper angle lobes go to? (These questions will also give some work to the preposition police.) When we place horizontal antennas at a vertical spacing of 1/2 wavelength, most of the upward energy cancels out and re-appears at lower angles. In the present configuration, the spacing is about 5/8 wavelength, which does not cancel all of the vertical energy, but does yield the highest gain in the lowest lobe. Note that compared to the dipole and the Yagi, even the extended lazy-H second elevation lobe is small, releasing more energy for use in the lowest lobe.

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The actual mechanics of lobe formation is a matter of complex interactions of direct radiation and reflections from the ground at a distance from the antenna. My brief description above has a few terms that will not withstand mathematical treatment. However, we have a basic fact: an antenna will radiate all of the energy fed to it. If it does not go up at high angles, then it must go elsewhere. Since the linear nature of horizontal elements prevents the radiation going to the sides (in a well-designed array), then the energy must go into the main lobe or lobes. As a general rule, the higher the gain of an array, the narrower also that the beamwidth becomes. So if you plan to use a wire extended lazy-H, aim it well so that your gain goes in useful directions.

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However, our main theme this time is not beamwidth in the horizontal plane, but the elevation lobes that form the pattern of any horizontal antenna. The higher the horizontal antenna, the lower will be the lowest and strongest lobe. Hence, DXers try for the highest antenna position feasible. The higher we place the horizontal antenna, the more elevation lobes that form. Stacking antennas by the right spacing can increase gain in the lowest lobes and reduce relatively useless very high angle radiation.

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Finally, note that I always qualify my recommendation for height with the words "as feasible." There are questions of cost, maintenance, regulations, and simple family comfort that form part of our decision on how high to place an antenna. Higher is better, but only if you can handle it. My tower is only 35' tall, but my hill is nearly 100' above surrounding terrain. Mother nature has saved me a bundle of money and worry.

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Updated 01-05-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 51: The Tri-Moxon Switched Vertical Array

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L. B. Cebik, W4RNL

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Site and budget restrictions often rule out a rotatable Yagi as out 10-meter antenna. However, the basic dipole is bi-directional, denying us the full horizon. A simple vertical often lacks some of the gain we want. Suppose that we could come up with a vertical array with gain and front-to-back ratio and cover the entire horizon with a switch instead of a rotator. If we set three individual small antennas vertically, we can cover the horizon. If we select the right antennas, we can use a single support post about 35' tall and set the antenna in the form of a Y, switching to the unit that covers the relevant 1/3 of the field. Also, selecting the right antenna will let us make a Y that is less than 10' in radius.

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The right antenna is a vertically oriented wire Moxon rectangle. Using AWG #14 wire, we can string 3 of them in Y-formation, keeping each one 4' from the post. That distance will reduce interaction to acceptable levels. Each rectangle will cover 28-29 MHz with less than 1.7:1 SWR using 50-Ohm coax as the feedline. Fig. 1 shows the general outline of the system from the top and the side. We shall look at supporting the antenna before we finish.

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The right-most part of the sketch shows the general outline of each of the 3 Moxon rectangles. We have examined this array in past columns. As well, the design of Moxon rectangles has been reduced to a set of true equations that will reliably yield the dimensions of the antenna for any reasonable element diameter (using wire or aluminum tubing) for any design frequency from 3 to over 300 MHz. See my web site (..) for more detailed information on the antenna and links to downloading small design programs.

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SP is the 48" spacing of the reflector from the post, and the 3 antennas are at 120° angles to each other. The dimensions are the same for all 3 rectangles. They will work for AWG #12 wire as well as AWG #14.

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Dimension    Feet    Inches
+   A         12.63   151.5
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+   D         2.36    28.3
+   E         4.61    55.3
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Each vertical rectangle covers about 125° of the horizon. So by switching from one to the next, we can cover the full horizon with only minimal decreases in gain at the overlap points. See Fig. 2 for overlaid azimuth patterns.

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The front-to-back ratio is about 13 dB, in the range of a 2-element Yagi. The gain at the 11° elevation angle of maximum gain is about 6.6 dBi. The system has been designed for a top height of about 34-35', which places the lowest point of each rectangle just above 22'. The height selected is not accidental. At this height, each rectangle produces a broad vertical pattern suitable for both short- and long-range paths, with peaks at 11° and at 34°. Fig. 3 shows a typical elevation pattern.

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Any triple array of beams will interact. The advantage of using the tri-Moxon design is that the interaction is minimal due to the high front-to-back ratio of each rectangle. However, since they are not purely back-to-back, but at angles, we can only minimize the interaction. The Moxon allows a reduction in the needed spacing from each other relative to other antennas that we might similarly arrange--for example, three 2-element Yagis. The spacing shown allows an adequate front-to-back ratio and a smooth 50-Ohm SWR curve. Fig. 4 shows the SWR curve for a coaxial cable feed system. Wide spacing would further reduce interactions, but would take up more backyard space and complicate the support system.

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Fig. 1 carries the suggestion of supporting the entire set of 2 wire Moxon rectangles from a central support post. Fig. 5 shows one way to achieve this goal.

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First, all support elements must be non-conductive. A dead tree or a telephone pole that extends 35' above ground makes good central support posts. The sketch shows 1 of 3 rectangles supported by top and bottom horizontal "limbs." The limbs can be PVC or similar material capable of self-support for about 8-9 feet away from the central post. You can drill through the central post, and vertically displace each rectangle by a few inches so that the support "limbs" do not meet in the middle of the post. Set the top and bottom horizontal supports a little above and a little below the ends of the rectangle.

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Use synthetic twine or thin rope to keep the rectangle under tension between the horizontal supports. This technique keeps the wires from resting on the PVC or other material, which might change a dimension along the rectangle ends. As well, loops allow room for small adjustments to the rectangle dimensions to arrive at the most perfect passband. Although the sketch shows vertical corner supports, placing them at an angle will hold the corners taut. With a piece of twine filling the gap, you can hold the rectangle in perfect shape, even if PVC or similar limbs sag a bit along their length.

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Feed each Moxon rectangle with a 50-Ohm cable. You have two main choices for feeding the array. First, you can bring coax lines from each one all the way to the shack and switch them indoors. Second, you can obtain a remote coax switch and place it on the support post as shown in Fig. 5. Modeling shows that you get slightly better performance if the unused rectangles show an open circuit. So if the lines from the feedpoints to the remote switch are either 1/4 wavelength or 3/4 wavelength, the unused ones should be shorted at the switch end to yield an open circuit at the actual feedpoint. If the lines are 1/2 wavelength long to the switch box, the switch ends should be open to show the same condition at the feedpoint. However, the difference between the 2 conditions does not create enough difference to be called critical. If the lines go all the way to the shack, use the simplest switching feasible.

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The Tri-Moxon vertical array is not an answer to all situations. But it is a workable system using light wire individual antennas set to cover the entire horizon with gain, a reasonable front-to-back ratio, a good range of elevation angles, and direct 50-Ohm feed. It requires only 1 central support and standard construction techniques for the rest of the support structure. As well, it saves the cost of a tower and rotator. Hence, the array is worth adding to our collection of 10-meter antenna ideas.

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See the Moxon Rectangles and Online Calculator page for more information.

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Updated 04-18-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 52: Gain vs. Beamwidth

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L. B. Cebik, W4RNL

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Antenna ads are long on gain numbers, but woefully short on other important data. One of the major absences is a beamwidth specification. Omitting this information has led some wire antenna makers to advertise their wares as having on some bands more gain than a 2-element Yagi. They do not say in what direction the gain occurs relative to the fixed-position wire antenna and they do not say for how much of the horizon the gain number holds true.

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If you use a rotatable Yagi or similar array, beamwidth has only secondary importance. For the size beams that are practical on 10 meters, the beamwidth will vary from about 65° for short-boom arrays to about 50° for long-boom Yagis. What these number tell us mostly is that super-precise aiming is not too important, since the gain variation from mis-aiming will not be detectable within about +/-10° of the target bearing. However, if we have a fixed-position antenna that is horizontal, then beamwidth takes on added significance.

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Fig. 1 shows a typical azimuth pattern for a 2-element Moxon rectangle only to show what we mean by beamwidth. The vertical centerline on the plot shows the direction of maximum gain. At some angle on either side of this line, the gain level will be 3-dB lower than maximum gain. These two points are called "half-power points." The angle between the half-power points defines the antenna's beamwidth.

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If we cannot rotate or switch our antenna to place the main beam where we wish it to be, then beamwidth becomes an important consideration in selecting an antenna for 10 meters. In general, we want to be able to communicate over more of the horizon than we want to leave unattended (because no one lives in those directions). To ensure that we cover the complete horizon, many operators with limited space use vertical antennas and accept the reduced gain as the cost of coverage.

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There are too many different antennas to explore beamwidth factors in this short column. So let's take the extreme cases. One of those cases concerns 80- and 40-meter wires, about which manufacturer advertising tends to make misleading statements. The product is usually a 135' (or thereabouts) wire which is resonant on 80 meters and usable on all bands--a very old antenna indeed. The antenna in principle can be fed at the center, at one end, or at a position between, called off-center-feed.

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Fig. 2 shows what happens when we take any of these three feed systems and run the antenna on 10 meters. The maximum 10-meter gain runs between 10.5 and 12.3 dBi, depending on the feed system. However, as the half-power lines on the strongest lobes show, the gain applies only to selected lobes at a wide angle from broadside to the wire--which runs left to right across each pattern. The beamwidth for any of the feed systems is only about 20° wide. In many parts of the US, a 20° beamwidth will not cover all of Europe, assuming that you set up the antenna in exactly the right way. If we factor in wire sway during brisk breezes, we may find that signals vary widely in strength without any changes in the propagation.

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There are a number of fixed wire antenna designs that offer considerably more gain and a predictable direction for it. Many operators with budget constraints feel drawn to such antennas because they are cheap, fixed, and relatively easy to build. For example, we need not use aluminum tubing for Yagi elements. With proper design, we can have a high-gain 10-meter Yagi made from wire. Suppose we could have nearly 15-dBi forward gain with a high front-to-back ratio with an antenna that uses very little more wire than the 80-meter doublet.

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Fig. 3 shows the outlines of a 7-element wire Yagi with the desired gain. Note that the side and rear lobes have very low strength, giving us excellent forward performance. However, the beamwidth is only 47°. This antenna is for special purposes, for example, if we desire to communicate regularly in only one direction. There are numerous operators who maintain regular schedules with family members or colleagues. Others specialize in contacts with only one part of the world. For such folks, this type of antenna may be ideal. However, for the general operator, the antenna gives up over 85% of the horizon.

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I recently saw on the Internet some hype for a 10-meter Sterba curtain. The antenna was promoted as having very high gain and also as having multi-band capability. Unfortunately, on all bands other than the one for which the antenna is designed, the patterns, elevation angles, and gain are mediocre. The Sterba curtain arose in the early days of short-wave broadcasting as a bi-directional array with high gain on a selected frequency. In commercial and government circles, the array has fallen out of use in favor of arrays that show a single directional pattern and some frequency nimbleness (such as the LPDA). An alternative is the electrically steerable array.

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However, suppose we build the complex array composed of phased sections and end half-sections for only 10 meters. The question is what we may have if we successfully construct a Sterba curtain. The answer is two main lobes broadside to the wires. Each lobe shows a maximum gain of over 15 dBi. However, the beamwidth shrinks to 26°. The general arrangement of the antenna appears in Fig. 4. Invisible in the outline sketch is the fact that each vertical length of wire (except the end wires) is actually a phasing line consisting of two wires with a constant but relatively close spacing, that is, a transmission line. The pattern shows the main lobes and the narrow beamwidth. If you happen to live directly between two stations with which you wish to communicate regularly, a Sterba curtain might be useful. However, the cost is 85% of the horizon.

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Perhaps the king of all directional wire arrays by reputation is the rhombic. Fig. 5 shows the outline and the pattern. Each leg of the rhomboid is multiple wavelengths long, and the designer carefully calculates an angle between legs to yield maximum gain. Called a "traveling wave" antenna, the point furthest from the feedpoint has a terminating resistor, ordinarily about 600-800 O and capable of dissipating at least half the power supplied to the antenna.

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The rhombic's pattern shows very high gain, almost 18.5 dBi in this design case. For the SW broadcaster or special communicator of the 1930s, the antenna allowed a very narrow beamwidth for point-to-point fixes. In fact, the beamwidth is under 11°. If I had the space and desired to communicate with a single city (or perhaps the city and its suburbs), the rhombic might be the antenna of choice. However, for the general operator who wishes access to the entire world, the rhombic is one of the poorest choices possible. The only way to use a rhombic for horizon-wide communications is to mount it in an ocean on a rotatable island.

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These notes are designed to alert you to the temptations of gain at the expense of other important specifications that affect our operations. If you cannot install a rotatable antenna due to rotator/tower costs or deed restrictions, then perhaps a vertical or vertical array may be in order. Alternatively, you might be able to manage a TV mast to 20' or more above ground and mount a self-supporting dipole at the top. Then, you may hand rotate the dipole to be broadside to the desired communications path. With its 80° beamwidth for each of the two lobes, you would not have to move the antenna direction very often during the day, and you might lower it out of sight when not in use. (Hang some flags, pennants, or mock laundry from the element to disguise the antenna's true function.) The idea is to swap gain for a wide beamwidth to gain access to more of the horizon and hence more communications targets. Beamwidth does make a difference.

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Updated 07-31-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 53: A Short-Boom Wide-Band 3-Element Yagi

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L. B. Cebik, W4RNL

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In the course of these episodes, we have examined a fairly large number of Yagi designs. They include short beams with only 2 elements up to long beams with 8 elements. Some have used matching networks to raise their low feedpoint impedances to 50 Ohms, while others used a direct 50-Ohm feedpoint connection. A few designs just barely managed to show SWR values of under 2:1 across the first MHz of 10 meters, while other have been wide-band designs. So why should I add another Yagi to the collection?

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The simple answer is that the design in this episode is a bit different. A normal wide-band 2-element reflector-driver Yagi is about 5.5' long. A wide-band 3-element Yagi with a direct 50-O feedpoint is close to 11.5' long. There is considerable difference in the performance. The 3-element Yagi provides about 7.1 dBi free-space gain (add about 5.5 dBi when 1 wavelength above ground) and manages about 20-21-dB front-to-back ratio across the band. In contrast, the 2-element beam manages about 6.0-dBi gain across the band with only 10-12 dB front-to-back ratio. Now suppose that we could find a way to achieve about 6.7 dBi gain with about 16-17 dB front-to-back ratio and still keep the beam only 5.5' long. That beam would be worth at least a second look.

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Fig. 1 shows 3 overlaid patterns for the beam to cover the low, middle, and top parts of the usual 1 MHz region of 10 meters. The patterns show very little gain change (about 0.7 dB), and the front-to-back ratio holds up very well until we reach the very top of the band. The antenna uses a direct 50-Ohm feedpoint connection, and the lower part of Fig. 1 shows the SWR curve. Ideally, the SWR does not reach 1.4:1 anywhere within the 1 MHz of 10. In fact, we might redesign the antenna slightly and cover the entire 10-meter band with under 2:1 50-Ohm SWR.

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The performance improvement over a standard 2-element wide-band Yagi with the same boom length comes at a price: an extra element and a phase-line. The array that we are exploring has 2 driver elements spaced 25" apart with a single director 39" forward of the first driver. The total length is 64" plus a few inches at the boom ends. A 6' boom would serve very well. Let's take the structure in small steps.

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1. The Elements: We can build beams to be light or to withstand heavy winds. To give you a choice, I shall give 2 sets of dimensions. One set uses heavier elements for wind loads up to about 90-100 mph. The lighter version might be rated to the 60-70-mph level. Fig. 2 shows the way in which we construct the two types of elements using common aluminum tubing with 1/16" walls.

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The following table of dimensions applies only to these two element-diameter taper schedules. If you change the material diameters or the interior lengths of wider tubing, the beam may not perform as advertised. Remember to add about 2-3 inches to the lengths of the smaller tubes to provide a secure overlap.

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+3-Element Wide-Band Short-Boom Yagi with Phased Drivers: Dimensions
+Heavy-Duty Version using 0.75"/0.625"/0.6" elements
+Element             Total Length        Tip (0.5") Length       Spacing from Rear Element
+Rear Driver         205"                60.5"                   -----
+Forward Driver      193"                54.5"                   25"
+Director            190"                53"                     64"
+Medium-Duty Version using 0.625"/0.5"/0.375" elements
+Element             Total Length        Tip (0.5") Length       Spacing from Rear Element
+Rear Driver         206"                35"                     -----
+Forward Driver      194"                28"                     25"
+Director            191"                26.5"                   64"
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Both versions provide essentially identical performance across the band. The free-space gain varies from 6.4 dBi at 28 up to 7.1 dBi at 29 MHz. (Yagis with directors show a rising gain with frequency increases, while 2-element Yagis with only a reflector show a decreasing gain with rising frequency.) The front-to-back ratio peaks at almost 18 dB at mid-band. Its lowest value is about 14.5 dB at 29 MHz.

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2. The Overall Design: The general layout of the beam appears in Fig. 3. The top portion shows the relative position of the elements. In this design, I have started with a simple narrow-band driver-director array (and all 2-element driver-director Yagis have a very narrow beamwidth). I then changed the driver system to a pair of phased drivers in order to broaden the antenna's operating bandwidth. By the judicious selection of element spacing, element length, and the phase-line characteristic impedance, I ended up with a beam that spread the relatively good driver-director performance across the entire 1st MHz of 10 meters.

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The lower part of Fig. 3 shows the general layout of the interconnection of the 2 driver elements. The phase-line consists of a parallel transmission line with a 250-Ohm characteristic impedance. The line requires 1 (and only 1) half twist between the 2 drivers in order to provide the correct phasing for broadband service on 10. The coax connector--that is, the feedpoint for the main transmission line--goes on the forward driver. This position is convenient, since the position is fairly close to the mast.

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3. Making Your Own Phase-Line: Since you need only 25" of phase-line (plus a bit of extra for connections to the elements), you likely should make your own. The following table lists the center-to-center spacing for 250-Ohm lines using some common bare copper wires, listed by AWG size.

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+250-Ohm Transmission Line Dimensions
+AWG Wire Size          Wire Diameter          Center--to-Center Spacing
+#14                      0.0641"                   0.262"
+#12                      0.0808"                   0.330"
+#10                      0.1019"                   0.416"
+#12                      0.1285"                   0.525"
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You will need spacers about every 3" to maintain the wire spacing accurately. The best way to make spacers is to drill the wire holes in a long strip of plastic (such as polycarbonate or similar). Then cut the spacers to size after you complete the drilling. Do not make the holes too large; you want a tight fit. If you do not de-burr the holes, the spacer will tend to stay in place through all kinds of weather.

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You may already be tempted to substitute 300-Ohm TV twinlead for the specified homemade line. I do not recommend the substitution. Even high quality 300-Ohm line has a velocity factor of about 0.8. Using a taut line will make the TV phase-line about 25% longer electrically than the value needed to create the right conditions for the drivers to operate well. Two elements with a phase line use a fairly critical combination of element dimensions and spacing--along with a fairly critical phase-line characteristic impedance and electrical length--to get the job done. The job involves dividing the current at the feedpoint so that each driver element receives the correct current magnitude and phase angle for maximum gain from the pair (in the presence of the director element).

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4. General Assembly: There are many ways to construct Yagis. In this design, all of the dimensions apply to elements that are well insulated and isolated from a conductive boom. If you use a 6' section of aluminum tubing as a boom, you will need polycarbonate or similar non-conductive plates for the boom-to-element junctions. I prefer to use stainless steel U-bolts with saddles to grip the boom and the elements without crushing them. Saddled U-bolts with solid or cast saddles are available by mail. I prefer them to the typical muffler-style fixture with a U-shaped saddle that contacts the tubing in 2 lines.

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The director will be a continuous element, with no break in the center. So double the length of the largest tubing in Fig. 2 to arrive at the center-section length. Both drivers require a small gap (1/4" is fine) for connections. I tend to prefer fiberglass rod inside the largest tube and extending to the ends of the plate. This system has 2 advantages. First, it places an extra support under the element U-bolts and also aligns the whole element with only 2 element U-bolts near the outer edges of the plate. Second, the rod allows good support for #6 or #8 stainless-steel hardware for making the connections to the phase-line and to the coax connector leads. Fig. 4 shows the general scheme without the U-bolts.

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The side view shows the element below the boom for best stability. As well, the boom helps to keep ice and snow off the phase lines. The bottom view shows the phase-line and coax connection points. Keep the phase line taut. The sharp twist in reality will become a gradual twist along the line length. Using ¼" thick insulation plates and saddle U-bolts will provide enough spacing from the phase-line to minimize interaction with the boom.

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The coax connector can sit on a small metallic plate attached to the forward edge of the forward-driver plate. Just be sure that the screws you use to secure the coax connector plate do not contact the boom. Of course, all hardware should be stainless steel, which you can obtain from most home centers these days. For other construction ideas and methods, you can check any number of antenna books, along with past episodes in the series.

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The short-boom wide-band 3-element Yagi with phased drivers is one more design in the arsenal of directive beams for the 10-meter operator. If you have followed these columns for the 13 years in which I have been producing them, your design notebooks should have a large collection of potential designs for the new sunspot cycle.

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Updated 09-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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Return to Amateur Radio Page

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No. 54: An Orientation to Reasonable Yagi Expectations

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L. B. Cebik, W4RNL

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Sometimes, purchasing a Yagi can be as daunting a task as building one. The advertisements use a bewildering array of incompatible terms and specifications that often result in more confusion than information. In this episode, I shall introduce some of the most important ideas to consider when purchasing a Yagi (or similar) directive array. I cannot single-handedly change the ways of advertisers, but I can alert you to a few things to examine carefully along the way.

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1. The Physical Fundamentals: Even before you look at the specification sheets from various antenna makers, you should think about the physical requirements of a good, solid antenna installation. Fig. 1 shows some, but not all, or them.

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The upper part of the graphic shows the bare outlines of a strong installation, included a tower (with guys omitted), a rotator, feedline, rotator cable, anchorage, and ground rods. All of these items must make a coherent package so that the system will withstand the stresses placed on it by the antenna at the top. If you are aging as fast as I am, or if you live in an area with a regular threat of very severe weather, then you should consider the added expense of a system that let's you lower the tower or the antenna in a storm or when periodic maintenance is due.

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The antenna itself presents a number of physical concerns. We find 3 main construction philosophies in the world of Yagis. Some makers, like Force 12, use the willow theory of construction to produce light but flexible antennas. The American standard theory underlies most U.S. Yagis and uses fairly standard components, such as aluminum tubing with 1/16" walls. Most European-made Yagis subscribe to the oak theory, using aluminum with much thicker walls. In the end, their antennas tend to be 1.5 to 2 times heavier than U.S. beams with the same number of elements and wind-survival rating.

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Beams present the wind with a certain area. Rotators usually carry two important ratings: the maximum antenna weight and the wind area. We need to match the latter figure with the antenna, since it is a measure of the maximum rotating stress that a rotator will withstand. Antenna themselves have a wind survival rating--usually in miles per hour. If you expect winds higher than the antenna rating, then be able to lower the antenna in a windstorm or check with the maker for the same antenna built to a higher wind survival rating.

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The lower part of Fig. 1 suggests a few construction details to examine. How do the elements connect to the boom (and how does the boom connect to the mast)? Is all hardware stainless steel? Do clamps and U-bolts hold the elements and the boom without deforming them? Are all non-conductive (plastic) materials UV-protected for long life (or will a fixture become brittle and break in a few years)?

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HF elements normally use a collection of tapered diameter tubing sections. The graphic shows 3 general ways in which makers secure the sections together. All three methods have proven track records if the hardware is non-rusting and strong. If a connection requires a special tool, be certain that the maker supplies the tool.

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There are a few matters that the sketches cannot show. Be sure that the antenna fits inside your property. Find the distance from the mast to the tip of the longest element: that is the antenna turning radius. Be sure that it is well inside your property line with enough to spare to satisfy your insurance agent. If you antenna and tower fall, will they land completely on your property? Also be sure to adhere to any applicable laws, regulations, or covenants governing antennas in your area.

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2. The Electrical Properties: The radiation properties of Yagis are designed to confuse you to the point of buying into whatever a given maker tells you. Consider the forward gain number. Some makers use a free-space value in dBi, based on computer modeling of the antenna. This figure avoids the variations in gain that occur over ground. Some makers cite values at a certain height in feet or meters above ground. Of course, this figure changes height as measured in wavelengths as you change the operating band. Still other use a figure based on the antenna 1 wavelength above ground. This value changes in feet or meters depending on the operating frequency.

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Still other makers give gain figures in dBd, where the gain in dBd is 2.15 dB lower than the gain in dBi. When you combine these practices with the variations that I just cited, the gain values for seemingly similar Yagi designs can look very different. There is no solution to this morass except to perform calculations galore until you work through the specifications and come out with compatible figures for each candidate in your selection process.

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To give you some guidance, I have compiled some (but not all) of the 10-meter Yagi models in my collection from 2 to 8 elements. Table 1 gives the free-space specifications at 28.5 MHz for each design. The gain is not dependent on the number of elements alone, but also on the total boom length. Therefore, a short-boom (8') 3-element Yagi may shows a little over 7 dBi free-space gain, while a long-boom (12') version with the same number of elements may have about 8 dBi gain. However, once we reach the long-boom size for any given number of elements, we may see one of two phenomena. First, the operating bandwidth of the antenna may be narrower. Many 10-meter antennas are rated only between 28 and 28.8 MHz, while versions with one more element in the same general boom length may be rated for the entire 1st MHz of the band. Second, we may find a lower feedpoint impedance. With good matching systems, impedances in the 20-25-Ohm range are fine, but below that level, losses begin to increase.

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Except for the 2-element reflector-driver Yagis, most commercial monoband Yagis manage to achieve at least 20-dB front-to-back ratio over most of the band. Do not let peak values, such as the nearly 37 dB value of one 5-element model, fool you. Very high values like these only occur at a specific frequency, and there are usually quartering rear sidelobes with a more normal value close to 20 dB.

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Table 2 shows the performance of the same beams 1 wavelength above ground, about 35' at 10 meters. Compare the gain values to those for the free-space models. As the beam gets longer and has more forward gain, the amount of increase provided by the ground reflections with a moderate height gets smaller. As well, the TO angle, that is, the elevation angle of maximum radiation gets a bit lower. As you raise the antenna height, these differences tend to diminish until they virtually disappear.

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The final recommendation that I would make is to insist on seeing either the antenna patterns (such as in Fig. 2) or the gain, front-to-back, and impedance curves across the entire 10-meter band. In the figure, both antennas have about the same boom length. However, the 5-element antenna shows a relatively mediocre front-to-back ratio in the upper part of the band. If we had room for the graphs, we would also find that the 5-element antenna changes gain by about 1 dB across the band, while the 6-element design changes gain by only 0.2 dB. In terms of even performance across the band, the slightly higher element population of the 6-element design is superior, even though its peak gain does not match the value achieved by the 5-element beam at 29 MHz. You cannot reach your own conclusions about the antenna performance without the data for the antenna across the band. Do not be fooled by citations of peak values. As far as I am concerned, if a maker will not reveal all of the information about the performance of his antenna, he has lost me as a customer.

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These all-too-brief notes provide the starting point for what you should consider when deciding on which commercially made monoband Yagi to purchase. Once you start learning about what to consider, you will think of equally important points to ponder and questions to ask. Note that I specified monoband Yagis. If you want to consider multi-band Yagis, you will enter a very different ballpark.

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Updated 01-01-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 55: What to Expect from Multi-Band Yagis

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L. B. Cebik, W4RNL

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In the last episode, we examined some of the physical and electrical factors that go into setting up a Yagi. For that exercise, we reviewed a large sampling of monoband beam designs for 10 meters. Our goal was to set up some reasonable expectations of Yagi antennas considering both the boom length and the element population. We discovered a number of factors that might influence our decision about which beam to purchase. The factors included the weight, the wind-survival rating, the gain and other pattern features, and the operating bandwidth of the antenna.

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However, many 10-meter operators wish occasionally to use other bands. Hence, they are more interested in a multi-band Yagi, specifically, a beam covering 20, 15, and 10 meters. The effort to develop high-performance multi-band Yagis is many decades old. It has made very great strides since the advent of computer-aided antenna design. Nevertheless, the market today is filled with both modern and older designs. Fig. 1 compares in outline both types of tri-band Yagis.

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At the top is a more modern design. It uses 7 elements total, but each individual element has primary utility on only 1 of the 3 bands. The element lengths are clues to the band of primary use. This particular beam uses a master-slave driver assembly, as indicated by the 2 elements very close to the long (20-meter) driver with the circle indicating the feedpoint connection. The lower tri-band beam is a hybrid. It uses some dedicated elements (without square boxes). Other elements serve more than one band, as indicated by the square boxes that mark the location of traps. Advertising hype tends to either oversell the losses of traps or to remain silent on their losses, depending on which kind of tri-band Yagi we are trying to sell. Therefore, let's pay a little closer attention to tri-band Yagi design to see if we can develop some reasonable expectations of these antennas.

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1. The Earliest Tri-Band Yagis: Fig. 2 shows in outline form the general configuration of tri-band Yagis in the 1970s. These relatively early beams emerged from simple experimentation until the maker decided that the design was good enough to sell. The outline shows us two major factors to consider.

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First, we find only 3 elements. From our exploration of monoband beams, we might conclude (validly) that the boom length and the element spacing are optimal on only 1 of the 3 bands--at most. Therefore, on the other bands, performance is likely to be lower than on the most optimal band. In many designs, the goal on the non-optimal bands was first to produce an acceptable feedpoint impedance for the coax feedline and second to develop at least a fair front-to-back ratio. Users who graduated from dipoles and doublets to the beam often mistook the reduction of rearward QRM for forward gain--and they still do today. Both factors are important, but they are not the same.

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Second, we find traps in each element. Each trap (or equivalent device) terminates a higher-band length. On lower bands, it functions as a loading reactance. On 10 meters, the beam has no loading within the lengths for that band. However, the spacing is likely too wide for optimum 3-element 10-meter performance. On 15, the 10-meter traps load and shorten each element relative to its full trap-less length, but the spacing is likely closer to optimal. On 20, we have 2 loads per element side in each element. So the 20-meter elements are well below full size. In addition, the spacing is likely too short for full performance. Hence, in these designs, 20-meter performance tended to suffer most. (Incidentally, some tri-band designs appeared to have only one trap canister on each side of each element. However, each canister contained two traps, and the outer surface of the trap enclosure served as the intervening element section.)

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Traps are not the only way to terminate an element at some specified frequency. Fig. 3 shows the schematic of a trap and its equivalent linear-loading substitute. Ordinarily, we tune a trap to a frequency at or just below the lowest frequency on the band that it terminates. So we might use 27.8 MHz as the resonant frequency of a trap for 10 meters. Now consider the linear load. It is a section of shorted transmission line that the designer has folded back toward the center of the element. Ideally, at about 27.8 MHz, the line would be electrically ¼ wavelength long, forming a very high impedance, just like an ideal trap. Like the trap, at lower frequencies, the linear load was an inductive reactance that allowed us to shorten the overall length of the element on the lower frequency. The earliest linear-loaded element designers claimed that they had no losses and hence formed ideal ways to terminate or shorten an element. Unfortunately, those claims have not proven to be correct. The fold-back construction is one reason for less than perfect performance. The 2 lines interact with the apparent main element, so the linear-loading section rarely shows perfect transmission-line currents that are equal in magnitude and opposite in phase.

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The Q of a standard trap ranges up to about 250--a good value but not a perfect value. Each pair of traps in an element--when they function as loading devices on lower frequencies--tends to reduce the element's gain by about 0.5 dB. We cannot eliminate the loss with an ideal trap--such as a perfect linear load--because part of the gain loss comes from the shortening of the element. Hence, even ideal traps, of which there are none, would create some gain loss. (Unfortunately, many trap-haters attribute all of the gain loss to power dissipation, which is not true.) In our aboriginal tri-band design, 15 meters would show losses associated with a pair of traps in each element. On 20 meters, the losses would amount to the sum of 2 sets of traps in each element and the double shortening of the overall element length.

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There is no easy way to estimate accurately the gain of the early 3-element designs. You might use the monoband performance table in the last episode and compare the boom length and associated gain. But remember that on 10 meters, the boom length might be too long for 3 elements. Then you can come up with an estimated gain on that band. Next, for each trap that is active as an element-shortening load on one side of each element, subtract 0.5 dB. On 15 meters, we shall subtract about 1.5 dB. On 20, we might subtract as much as 3 dB from the potential gain. Since 20 meters is already short in boom length, we would wind up with very little forward gain (perhaps 2 to 2.5 dB) over a dipole at the same height. However, the front-to-back ratio might be useful to us.

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You can perform the same exercise on the hybrid beam shown in Fig. 1. However, only count the most active elements on each band. On 10 meters, we have 4 elements. To estimate the baseline potential gain, use the actual distance between the 10-meter reflector and the forward-most element. Since no trap loads the element, gain should be close to an optimal value for the boomlength. On 15 meters, the boomlength is between the rear-most element and the next-to-forward-most element. We find 1 trap on each side of 2 elements, the driver and the reflector. So we might reduce the potential gain by about 1 dB relative to what the boom length and 3 elements suggests for a monoband beam. (Remember to adjust the boomlength for the frequency change.) On 20 meters, we find 4 traps on each side of center for the full array. So we would subtract about 2 dB from the potential gain of a monoband 3-element beam with the same boomlength.

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These estimates are very rough and ready, but they prove out in all too many cases. Advertisers tend to make claims that cite the peak gain of the array on its best band for gain and let the buyer assume that they apply to all bands. So if you count traps and estimate the boom length on each band, your revised likely gain figure will in most cases be close to correct.

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2. Modern Tr-Band Yagis: Modern designs, like the upper sample in Fig. 1, do not use traps. Hence, we do not need to make adjustments for them. Each element serves a single frequency band. These designs have more elements and more aluminum tubing to bend or break in bad weather. However, their performance tends to be closer to monoband beams, if we know how to estimate it. Fig. 4 enlarges the small graphic of Fig. 1 and identifies each element. Note that the boomlength is different for each band of operation. We have a 2-element driver-reflector Yagi for 20 meters and another separate one for 15 meters. The 10-meter beam consists of a driver plus 2 directors.

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Since the element spacing on 20 and on 15 is close to optimal for these bands, we can expect fairly standard 2-element Yagi performance on these bands. Although we do not have a 10-meter reflector, we can expect 3-element short-boom performance on that band, or close to it.

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Element interactions will moderate these numbers to some degree. On larger modern tri-band Yagis, some 10-meter elements may be very close to 20-meter elements. They prevent the 20-meter elements from shifting the passband lower and hence add very little to the 10-meter gain. Element interaction also tends to reduce the front-to-back ratio relative to what we expect from 3-element or larger Yagis. Anticipate a front-to-back ratio of 12 to 17 dB from 3 or more elements on a band, rather than the standard monoband minimum value of 20 dB.

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All multi-band Yagis are compromises. We pay for the convenience of having 1 beam for 3 bands by obtaining lesser performance on many bands compared to monoband Yagis with relevantly similar boom lengths. If we know how to adjust our performance expectations, we shall end up neither overly disappointed nor overly enthused.

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In our exploration of tri-band Yagis, we have largely bypassed all of the physical considerations that go into a Yagi installation. Be sure to fully inform yourself about all of the important data so that your installation will be effective, secure, and safe.

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Updated 04-01-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 56: Some Ideas for Quad Loops in the Field

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L. B. Cebik, W4RNL

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As the sunspots slowly return to improve 10-meter propagation, some operators begin to think of picnics, accompanied by a rig and a portable antenna. In episode 42, we examined a simple 10-meter dipole that consisted of nesting 3' sections of aluminum tubing. With about 20' of mast, the antenna is capable of very good performance, and one can hand-turn it to broadside the desired station. We can do similar things with a simple quad loop with about half the side-to-side spread. As a bonus, we acquire just a little more gain, but not enough normally to make the difference between a go and a no-go contact.

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In this episode, we shall look at several configurations of the quad loop, some of which may be more useful to individuals, depending on local materials and construction preferences. Fig. 1 shows square and rectangular quad loops. The top pair use all-wire elements. I have selected AWG #16 as a compromise size that is quite strong but lighter than house wiring. If you change the wire size, you will have to refigure the loop sizes or experimentally find the length of wire that gives a resonant feedpoint at 28.4 MHz (our design frequency). In general (and unlike the case of dipoles), closed loops require longer wire circumferences as the wire gets fatter and smaller circumferences as the wire gets thinner.

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The lower pair use a hybrid construction method, with horizontals consisting of ¾" aluminum. You may use tubing, but L-stock is easier to manage for field assembly and disassembly. The side wires are AWG #16. All wires in these antennas are designed to be bare. If you use insulated wire, shorten the wires by 2% to 5%. Thicker insulation calls for the greater amount of shortening.

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Let's start with the all-wire quad loops. A standard square loop, fed at the center of the bottom wire, will have a resonant feedpoint impedance of about 125 Ohms. To create the simplest match to a 50-Ohm feedline, insert a ¼ wavelength section of 70-75-Ohm coax. The electrical length will be just under 104". However, you must multiply this length by the velocity factor of the line that you use. Most solid dielectric lines have a velocity factor of 0.67, resulting in a 70" length. Most foam dielectric lines have a velocity factor of about 0.8, resulting in a matching section length of 83". Both the square and the rectangular loops will cover from 28.0 to about 28.7 MHz with under 2:1 SWR. Since the total feedline length will be short compared to the amount used in a home station installation, you can extend the operating span by using an internal or external antenna tuner--with no significant losses.

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One reason some loop users prefer the rectangular shape is that it provides a direct 50-Ohm impedance and therefore requires no matching section. As well, if we place the bottom horizontal wire of both antennas at the same height--for example, 10' above ground in the field--we obtain slightly more gain and a slightly lower elevation angle due to the higher top wire. See Fig. 2. In most cases, the variables that field operations inevitably involve will wash out the small differences in the performance numbers. So the main reason for using the rectangular shape is to achieve a direct feed that requires no matching section. However, the resulting tall loop can be somewhat ungainly in the breeze.

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Let's consider how to construct both types of all-wire quad loops for field use, using Fig. 3 as a rough guide. We can start with a support mast. Unlike the dipole mast that had to reach the ultimate height of the antenna element, the quad loop mast only goes to the level between wires plus a little margin. PVC sections in 5' lengths (or whatever length fits the trunk or truck-bed) make a good mast, especially when the ends have threaded couplings cemented in place. Be sure to use some rope and long spikes (tent pegs or garden timber spikes) to set up a guying system. At the top of the uppermost section, we can install a plate with 4 stubs to receive the X-braces or support arms. If we use pressure insert fasteners for the outer pinning devices, we can fold the assembly to reduce its width during transport. The anchor plate can be almost anything from plywood to plastic.

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The support arms should be light, flexible, and strong. CPVC is useful and available at home centers. Fiberglass is perhaps better, but it may require mail order to obtain it. Assemble the entire support structure to string the wire initially. Be sure the wire is equally taut on all four sides of the loop, but not so taut that it stresses the support arms. Stress will likely result in a warping of the frame to one side or the other--and the warp may change in a stiff breeze. For permanent installations, I would normally suggest slip tubes at the corners, but for this antenna, I recommend that you fix the corner in place. Use non-conductive cable ties or similar, and add some epoxy after you are satisfied with the structure. The wire will help prevent the arms from sagging. For the square quad loop, the arms should be a minimum of 77.5" from the plate center to the tip. The rectangular loop requires arms that are minimally 82" long. You will have to solder in a coax connector at the center of the bottom wire, and you may wish to use a small plastic plate as a mounting.

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Using the lower quad configurations involves having thick horizontal element sections and wire vertical sections. ¾" L-stock makes a good horizontal element section. Note in Fig. 1 that the combination of thick and thin materials raises the impedance of a truly square loop to a very inconvenient value. A 150-Ohm impedance is somewhat low for a 4:1 balun, but too high for a 75-Ohm matching section. Therefore, if you prefer this configuration, try a slightly rectangular shape, as shown in Fig. 1, to obtain 125 Ohms. Then you can use a 75-Ohm matching line to good effect.

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Fig. 4 shows why some field operators prefer the thicker horizontal element sections. If we carry the mast up to the top element, we no longer need the 4 X-brace support arms. The horizontal L-stock supports the side wires with ease. Since the loop is over 9' tall, the central mast above the lowest element section should be in 2 sections. To each section, we can attach a small plywood or plastic plate to pin down the L-stock. I recommend that you use nuts and bolts near the centerline, but removable fasteners (such as hitch pin clips) near the outer edge. When not in use, you can fold the bottom elements up and the top elements down for easy transport. Be sure to add a bridge wire at the top to connect the two side of the horizontal element. At the bottom, add a coax connector and mounting plate and fasten it to the element support plate.

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For either type of quad, you can likely work out the wire and support structure in a way that allows you to store and transport that part of the system as a unit. The more items in the structure that you can fold, bend, and wrap-around for storage, the more quickly you can assemble and disassemble the unit in the field. As well, you create a smaller unit for transport.

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These notes do not aim to give you complete construction details of a portable or field quad loop. Instead, they simply provide some ideas and then rely on your own ingenuity for making a complete unit. Over the years, I have built and used several 10-meter quad loops. My personal favorite is the modest rectangle that uses ¾" L-stock and side wires. My versions allowed me to loosen the L-stock and fold the element sections next to the half-mast section. Without removing the side wires, I laid the two half-mast sections side by side and then used the side wires to wrap the entire antenna into a loosely secure bundle. The stored antenna was a little over 4' long (not including the mast sections and the guys below the part shown in Fig. 4). The only loose part was the bridge wire across the middle of the upper element, and I kept one end attached to one side of that element. In one version, I mounted the coax connector directly to one of the lower pieces of L-stock, with a bridge wire to the other section.

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The number of construction variations that are possible is as endless as the materials that we can find at a home center. In fact, the variations on field quad loops are almost as great as the pleasure of operating 10 meters from a hilltop or open field (on a sunny day with warm temperatures, a fine picnic lunch, and someone special with whom to share the fun).

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Updated 07-15-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 57: A Different Kind of 10-Meter Attic Antenna

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L. B. Cebik, W4RNL

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Due to restrictive covenants, many 10-meter operators must use attic antennas or devise other ways to hide the antenna. Older ranch-style homes used to be long and narrow. Hence, many attic antennas are dipoles oriented along the length of the attic. A 10-meter dipole is about 200" long. The operator had to orient the dipole according to the attic space, which might or might not place the wire broadside to the best target communications areas.

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The last decade or so has revised home architecture so that the long attic is gone. In its place is a collection of smaller attic spaces, often with more vertical than horizontal room. For these spaces, we need a new kind of attic 10-meter antenna--one that will largely free us from orientation worries and still perform well in the confined space. It must still keep its distance from all metal wiring, ductwork, and foil sheathing. Enter the Cuthbert Cube.

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A few years ago, Dave Cuthbert, WX7G, used some basic antenna folding ideas that had appeared in antenneX, an on-line antenna experimentation journal, and developed a 2-meter antenna as a desktop improvement on the usual FM rubber ducky. The design evolved from bending, folding, but not mutilating the 1 wavelength quad loop with a side feedpoint for vertical polarization. However, we can easily tip over the Cuthbert Cube (which is not quite truly cubical) and obtain horizontally polarize patterns, just like a bottom-fed quad loop. Fig. 1 shows the 2 orientations.

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The equivalent of 2-meter desktop height is probably 10' at the antenna bottom for the left part of the sketch, the vertically oriented cube. If we take patterns at that height, we obtain the elevation and azimuth plots on Fig. 2. The gain is modest on 10 meters: less than 1 dBi at an elevation angle of 17°. However, the pattern is nearly circular for the small volume occupied by the antenna.

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More relevant to 10-meter CW and SSB use is the horizontal orientation. If we assume that the modern attic allows a 20' height above ground for the bottom wires, then we obtain the patterns in Fig. 3. The elevation angle is about 21°, which is lower than for a dipole at the same height. Because we have a loop and the vertical wires carry some current, there is some vertically polarized radiation. So the azimuth pattern is not a traditional dipole figure-8, but instead a broad oval. The maximum gain lies along a line through the feedpoint and the gap between the rear vertical wires and is between 6.7 and 6.8 dBi, less than 1 dB lower than a dipole at the same height. However, the radiation to the sides is only about 5 dB below maximum, enough to hear signals in those directions when the propagation is good.

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The 10-meter version of the Cuthbert Cube is about 5'-3" on the feedpoint line. The vertical and the front-back dimensions are identical: 3'-7". Hence, some version of the antenna should not only fit within a small attic, but we should also be able to orient it for maximum gain in desired directions.

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The antenna is a closed loop and hence does not change its impedance much as we change height. The resistive part of the impedance is 50 Ohms at the design frequency. However, this antenna has a peculiarity: The inductively reactive part of the impedance increases as we reduce the element size. Hence, for element diameters from about 5/8" downward, we need to add a series capacitor in line with the feedpoint. A 75-pF to 100-pF variable from a hamfest sale will work fine. However, if we use 1" elements, then we no longer need the series capacitor, since the inductive reactance is no longer present at the design frequency. As well, we increase the passband covered with under 2:1 SWR to include all of the first MHz of 10 meters. Wire versions cover about 600 kHz of the band. Fig. 4 shows the 50-Ohm SWR curve for a Cuthbert Cube with 1" elements.

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Building the Cuthbert Cube requires a set of dimensions. The following table shows 2 sets: one for 28.4 MHz and intended for wire versions of the antenna. The second set shows dimensions for a design frequency of 28.6 MHz and is intended for the 1" version. Fig. 5 provides a guide to which dimension goes where. Dimension E is the gap or open space between the vertical wires in the antenna. The dimensions are equally applicable to the antenna when used vertically.

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+Dimensions for the Cuthbert Cube: All dimensions in inches
+28.4-MHz Design Frequency       28.6-MHz Design Frequency
+Dimension      Length           Dimension         Length
+A               63                 A               62.5
+B               43                 B               42.75
+C               43                 C               42.75
+D               16.75              D               16.5
+E               29.5               E               29.5
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A wire version will require some form of support structure. In a dry attic, wood and PVC--or some combination--are good candidates. You will likely need corner supports and a way to prevent the wires from pulling the ends of the supports toward each other. It is also likely that you will need two more supports for the vertical wires. Since these wires have low current, you can run the wires next to the support posts, rods, tubes, or dowels. You will also need a short support for a plate to hold the coax connector and the series capacitor. Fig. 6 shows a simple schematic representation of the feedpoint with a single variable capacitor. Once you know the required capacitance to produce the lowest SWR at the design frequency, you can replace the variable capacitor by a fixed capacitor of the right value. However, be sure that it can handle the power of your transmitting equipment. 500-volt capacitors are usually adequate for most standard transceivers.

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The 1" element version of the antenna does not require a series capacitor. In fact, it does not even require tubing. You can substitute 1" per side L-stock, which is available at many home centers. The stock usually comes in 1/16" and 1/8" thicknesses. The thickness will make no significant electrical difference, but the weight ratio is 2:1. However, heavier stock is somewhat more rigid. The stock easily let's you create nut-and-bolt corners. As well, you can mount a coax connector directly onto the element at the feedpoint and run a bridge wire from the connector pin to the continuation of the element on the other side of the small (1/4") gap. You can choose whether the connector points horizontally or downward, depending on the likely coax run in your attic and walls. Use any handy plastic strip to join the parts of the element on each side of the gap to sustain a physically rigid element.

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One advantage of this form of construction is that you can build everything in the shop and then break the antenna into pieces that you can get into the attic. A screwdriver and a nut-driver may be all the tools you need for in-place final assembly. As with all attic antenna, you want to raise it off the ceiling joists. You can hang it from the rafters or devise a wood or PVC set of elevating supports. The specific construction of your attic and how you want to orient the antenna will make your installation a custom effort.

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A stronger alternative construction method is to use copper pipe with a 1" outside diameter. (Piping sizes are "nominal," that is, listed by the minimum inside diameter, not the outside diameter. You will have to check the actual outside diameter of the pipe you select.) You can torch-solder or sweat the corners with 90° junctions. Only the feedpoint requires special attention to create a gap for the coax connector while retaining a rigid element. I do not recommend torch flames in the attic. So use this method of construction only for outdoor service or if your attic let's you fit the finished antenna through the entry.

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The horizontal Cuthbert Cube may not fit everyone's needs--or even everyone's attic. But for some 10-meter operators, it might make the difference between being on the air or not.

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Updated 10-15-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to An-Ten-Ten-nas Page

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No. 58: The Revere Theory of Vacation Antennas

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L. B. Cebik, W4RNL

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The theory is simple: Horizontal if by land and vertical if by sea, (And I on the opposite shore shall be). Of course, neither Paul Revere nor Henry Wadsworth Longfellow is responsible for the name of the theory. But the name is a catchy way of introducing you to why many contest and vacation operators on beaches or on boats use vertical antennas, while at home, they use horizontal antennas.

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For 10 meters, vertical antennas are simpler to use on vacation. A central element and some radial wires (if we are using a ¼ wavelength monopole) are usually easier to pack than a pair of support masts to hold up a dipole. The dipole is somewhat directional, so a tubular version on a single support mast resolves the turning question, if only by hand. However, that system can be ungainly on some boats. Actually, the choice of a vertical antenna for contests and vacations near or on the ocean depends less on mechanical simplicity than it does on performance.

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To see why verticals have once more become popular on or near salt water, let's perform a little exercise. Since I cannot afford a Caribbean vacation at the moment, we shall have to use modeling software. We shall look at four antennas, all simple ones, as shown in Fig. 1. The first is a center-fed vertical dipole with its bottom end 1' above ground. The second is a ground-mounted vertical monopole. The third antenna is simply the monopole raised ¼ wavelength above ground with 4 elevated radials. Finally comes the horizontal dipole that is ½ wavelength above ground.

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For each antenna, we shall select 4 ground environments. One must be salt water. The other three involve different levels of land-locked ground quality. The standard names are Very Good, Average, and Very Poor Ground. With 4 antennas and 4 ground quality levels, we have 16 tests to run.

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1. The Vertical Dipole. Like all good vertical antennas (but not necessarily arrays of verticals), the vertical dipole has an omni-directional azimuth pattern. So we can confine ourselves to the elevation pattern properties. The vertical dipole uses a 1" diameter with its bottom tip only 1' above ground level. We normally bring the feed horizontally from the center point or run coax inside the element to ground level. In either case, we add a common mode current choke at the point where the coax emerges from the antenna. The following table lists the maximum gain and the elevation angle for the four types of ground.

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+Vertical Dipole 1' above Ground
+Ground Quality        Salt Water        Very Good        Average        Very Poor
+Gain dBi              5.64              0.69             0.55           0.15
+Elevation Angle       8°                17°              18°            21°
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The largest change occurs between salt water and dry land. Fig. 2 compares elevation patterns for salt water and average soil. I omitted the other soil types, since they are relatively so close together that they would make a single fat line. The advantage of the salt-water ground is very clear in terms of both gain and a low elevation angle for good DX work.

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2. Ground-Mounted Vertical Monopole with Buried Radials. A vertical monopole at ground level is ¼ wavelength long and requires a field of radials. On salt water, the metal cladding of the keel or hull would normally substitute for the radial system, but on land, we need at least 32 buried radials for effectiveness. The table is based on a 32-radial field.

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+Vertical ¼-Wavelength Monopole with a Radial Field at Ground Level
+Ground Quality        Salt Water        Very Good        Average        Very Poor
+Gain dBi              4.27              -0.56            -0.31          -1.69
+Elevation Angle       11°               24°              27°            29°
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The shorter monopole is less effective than the vertical dipole, with higher elevation angles to accompany the lower gain. Fig. 3 again contrasts just the salt-water pattern with the pattern over average soil. The overall height of the lobes, regardless of soil quality, is immediately apparent. Ground-mounted vertical monopoles find almost no land use on 10 meters, although they are common on ships and buoys.

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3. Elevated Vertical Monopole with 4 Radials. The vertical monopole works best on 10 meters when we elevated it. The test case uses a height of ¼ wavelength between ground and the base of the system. Above about 0.5 wavelength, the higher angle lobes tend to dominate, which is not good for DX communications. Once we place the antenna about 2 wavelength above ground, the lowest lobe again becomes the strongest, but this height is normally not practical for a boat or the beach.

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+Vertical ¼-Wavelength Monopole with a 4-Radial Field ¼ Wavelength above Ground Level
+Ground Quality        Salt Water        Very Good        Average        Very Poor
+Gain dBi              6.31              0.82             1.15           1.24
+Elevation Angle       7°                14°              16°            19°
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The salt-water gain improves by about 2 dB with the 8.7' elevation of the antenna. The top portion of Fig. 4 compares salt water to average ground for consistency with the preceding figures. The gain over dry land also improves, but presents a seeming anomaly. The gain actually decreases as the soil quality improves. However, as the table and the bottom of Fig. 4 show, the elevation angle becomes (desirably) lower with improving ground quality. The operationally significant matter is the elevation angle rather than the small gain difference across the span of test grounds. Part of the reason for the seeming gain anomaly is the fact that as we improve the soil, the upper or second elevation lobe becomes more pronounced, although it is not problematical at the test height. The higher that we raise the base of this antenna system, the stronger that the second lobe will grow until it becomes the dominant lobe.

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4. Horizontal ½-Wavelength Dipole ½ Wavelength above Ground. For each of our test vertical antennas, the gain over salt water has been about 5 dB stronger than the gain over the best of the dry-land ground qualities. By comparison, the differential among the dry-land grounds has been small. A half wavelength horizontal dipole that is a half wavelength above ground has been an old stand-by of vacationers and casual contesters for many decades. The table shows why land operators tend to prefer it to a vertical, while beach and boat operators lean toward vertical antennas.

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+Horizontal ½-Wavelength Dipole ½-Wavelength above Ground Level
+Ground Quality        Salt Water        Very Good        Average        Very Poor
+Gain dBi              8.36              7.73             7.24           6.48
+Elevation Angle       29°               28°              28°            27°
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We find less than 2-dB gain differential between salt water and very poor soil, compared to the 5-dB differential for the vertical antennas. Fig. 5 provides both elevation and azimuth patterns for salt water and the worst soil quality. The dry-land elevation pattern shows where part of the missing 2 dB of energy goes: upward. The dry-land elevation beamwidths are wide enough to encompass the lower elevation angles for the vertical dipole and the elevated monopole, and they are about the same as for the ground-mounted vertical. For dry-land, then, the dipole provides considerably more gain than the vertical antenna and becomes the preferred antenna, even if we have to turn it broadside to our targets.

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The dipole, however, offers the beach and boat operator with very little gain advantage. The elevation angle increase tends to detract from DX signal strength more than the small gain increase helps it. Therefore, the best antenna for beach and boat operation--among simple antennas in these tests--is likely one of the verticals.

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The modeling tests have used a uniform ground medium in all directions from the antenna. The ground reflection region extends for several wavelengths away from the antenna. On a boat, the ocean is everywhere. However, on a beach, we usually have only 180° to 270° of salt-water horizon, depending on whether we can find a point of beach-land for our antenna. Selecting a place on an island with ocean between you and the main communications targets is good planning.

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However, coastal operations have benefited from verticals near the water's edge. Do not think about propagation as a single thin line between you and your target. RF refracts over a broad region. So a coastal path may actually consist of radio waves that go out over the water and return back to land at shallow angles relative to the straight-line bearing between the 2 points.

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The next time you operate from a vacation island or boat, do not discount the simple vertical antenna as a highly effective way to make a lot of contacts (propagation permitting). However, over dry land, a horizontal dipole even as low as ½ wavelength above ground may give you the stronger signal.

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Updated 01-15-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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No. 6 The Simplest 2-Element Yagi?

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L. B. Cebik, W4RNL

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Building a beam is not as difficult as it may seem. Of course, a many- element, multi-band Yagi is an advanced exercise in design and construction. However, a 2-element Yagi for 10 meters is entirely manageable for the novice builder. Parts are available from almost any large home supply warehouse. About $50 for all new materials will produce a very usable beam. Mast and rotator, of course, are extra, but a TV rotator and well-guyed mast will easily support a 10-meter 2-element Yagi.

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Fig. 1 shows the general outline of one of two forms of a 2-element Yagi. Some designs use a driven element and a director. The design in Fig. 1 uses a driven element and a reflector. The circle across the Y-axis line (the direction of forward gain) indicates the feedpoint.

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Fig. 1. General outline of a 2-element Yagi. +

In the December, 1990, issue of CQ, Bill Orr, W6SAI, presented "A Compact 2-Element Yagi for 10 Meters" (pp. 83-84). His design used a combination of 1" and 7/8" diameter aluminum tubing, along with a gamma match for the 30-ohm feedpoint impedance. His beam was remarkably well-behaved. The gain varied from 6.86 dBi down to 6.08 dBi from 28 to 29 MHz, while the front-to-back ratio varied from a low of 9.09 dB to a peak of 11.29 dB. The beam was 17.5' at its widest with the elements separated 4.25'. Fig. 2 shows the beam's pattern at the design center frequency (28.5 MHz). It offers neither the highest gain nor the highest front-to-back ratio obtainable with two elements, but it gives consistent performance over a wide bandwidth.

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It is possible to simplify Orr's construction, using either 1" or 0.75" diameter tubing available from hardware outlets. Moreover, by separating the elements 6', the feedpoint impedance increases to 50 ohms, allowing direct feed (with a 1:1 balun).

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Fig. 2 Azimuth pattern in free space of a wide-band 2-element Yagi. +

In fact, with 6' element separation and the dimensions shown below, SWR is less than 1.5:1 across the first MHz of 10 meters. We do lose some gain and front-to-back ratio, but less than 0.5 dB in each case, and the front- to-back ratio is more consistent across the band, never dropping below 10 dB.

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The dimensions for the elements are as follows:

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1" diameter aluminum tubing, 6' element separation:
+  Driven element:  15.9' (±7.95')  Reflector:  17.52' (±8.76')
+0.75" diameter aluminum tubing, 6' element separation:
+  Driven element:  15.98' (±7.99')  Reflector:  17.5' (±8.75')
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The driven element must be split at the center and fed like a standard dipole. To accommodate this, I mounted both elements on scrap plywood plates 3/8" thick, about 24" long and about 6" wide. Varnish or (better) fiberglass epoxy the plywood for weather protection. A pair of #10 stainless steel nuts and bolts (with both flat and lock washers) mount each half element to the plate. The bolts at the center make a good attachment point for a balun or for a coax connector to mate with another on a balun. Small U-bolts can be used for the outer fasteners.

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The reflector is longer than a pair of 8' aluminum tubes. I used a 1.5' long piece of tubing as the center for my 1" diameter version of the reflector. Inside was a 3' section of 7/8" diameter tubing that supported the 8' lengths of reflector tubing. The #10 hardware at the center goes through the center 1" tube, while the outer #10 hardware goes through (or around, if U-bolts) the 8' extensions. All the #10 hardware goes through the 7/8" tube. Additional sheet metal screws (also stainless steel) clamp the extension tubes to the inner tube at its ends, cutting down on vibration.

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For a boom, I used a 6.5' section of Schedule 40 PVC, 1.25" nominal diameter. A pair of 1.5" U-bolts holds each plate to the boom. Thick PVC tubing works well up to about this length, but much longer might produce too much sag. The plates go under the boom, and the elements are below the plates. Connections to the center of the driven element go to an extra set of lock washers and nuts on the element mounting hardware. The balun and coax are then taped to the boom and mast.

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There are very few cautions to give for this beam. Check dimensions. Be sure all metal-to-metal contact is very good. Use stainless steel hardware to avoid rust or using protective spray sealers that work their way between contact points. (However, use flexible coax sealer over any screw-type coax connection.) As with any beam, check both mechanical and electrical connections every few months and after any severe storms.

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Although the beam will perform well from a 20' mast, a 35' mast (or higher, of course) is even better. Expect some gain, almost 2 S-units of front-to- back ratio, and excellent rejection of signals off the side. This beam will not open 10 meters during the sunspot null, but it may let you work some of the weak backscatter signals on the band. In addition, it is useful in nets, since you can still hear locals off the rear while aimed at weaker signals. For versatility, the 2-element Yagi will certainly beat a fixed wire dipole hands down.
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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No. 7 The Poor Old ZL Special

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L. B. Cebik, W4RNL

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Because the ZL Special is such a mechanically simple and cheap antenna, it has spent its nearly half century of life misunderstood. Rightly understood, it has a place in the 10-10 inventory of antennas. It will not cure the blues on a rainy day or make DX in the absence of sunspots, but it may make a very useful attic or field antenna.

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ZL3MH (later ZL2OQ and recently a silent key) brought the antenna to ham attention in 1949, giving credit to W5LHI and W0GZR for basic information on the design. G2BCX, who has developed variations on the design from the earliest days to the present, dubbed it the "ZL Special," and the name stuck.

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The basic idea is deceptively simple: take a driven element and a slightly longer reflector and space them between a tenth and an eighth wavelength apart. Next, connect the elements with an eighth wavelength of transmission line (adjusted for velocity factor of the line) with a half twist, and feed the former driven element with ladder line to an antenna tuner. The result is a 135° phased array. In the early 1950s when hams had difficulties building Yagis at home, the antenna seemed to outperform 3-element Yagis and give almost miraculous front-to-back ratios. The claims are almost embarrassing today.

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First, the ZL Special, in any form, will have the gain of a 2-element Yagi at best. In fact, most decent designs show about 6.1 dBi forward gain in free space, about the same as the broadband Yagi described in the last column and about 4 dB better than a similar sized and placed dipole.

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Second, the front-to-back ratio can range from great to mediocre depending upon design care, luck, and Murphy. Figure 1 shows two patterns of the version we shall physically describe below. They are taken over real medium earth at a height of 20' (for reasons we shall also note below). Casual building can achieve the broader pattern, while extensive design and experimental work might approach the "perfect" pattern.

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The perfect pattern might not be more especially useful than the casual pattern, since it is so pinched. Any rear QRM just off center line will not feel the effects of the high front-to-back ratio, since it will fall within the off-center lobes. The casual pattern is only slightly worse than the lobes of the perfect pattern. Looking at the entire rear sector of an azimuth pattern is sometimes called analyzing the "front-to- rear" ratio.

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The casual pattern is still useful for certain kinds of applications. It provides a better than 15 dB front-to-rear ratio across the entire backside. If the mechanical features of the antenna fit your building needs, then it may pay to try a ZL Special.

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Most of ZL3MH's designs used unequal elements. A few years back, W7EL published a Field Day Special version of the antenna using equal length elements. Hence, I tend to call unequal element versions ZL Specials and equal element versions FD Specials. W7EL's antenna is made (like some predecessors) from 300-ohm good quality TV feedline. The general configuration appears in Fig. 2., scaled for 10-meter use.

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The elements are folded dipoles 16'2" long. The 300-ohm phasing section is 4'3¼" long with a half twist between the front and rear elements. The phase line here is designed to be the same length as the distance between elements, thus producing a taut assembly.

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You can feed the antenna in two basic ways. One way is to place capacitors in series with each feedpoint to compensate for some remaining inductive reactance at the feedpoint. Then a 1:1 choke balun links the feedpoint to regular coaxial cable. If finding the right amount of capacity to place at the feedpoint is a bit too much trouble, then feed the antenna with more 300-ohm ribbon brought to an antenna tuner. The feedpoint compensation will have no bearing on the basic properties of the antenna.

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Heavy plastic squares with stress-relief slots and small machine screws as tie-point anchors should make easy work of the mechanical connections, front and rear. You can tape the antenna to bamboo and simulate a Yagi, but that is probably not the best use of the antenna. Better applications are as an attic antenna or an antenna strung between trees on Field Day and similar operations. A spacer bar at each end of the antenna and some rope ties will hold the antenna in place. These applications prompted the 20' height patterns, since they rarely permit very high antennas.

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W7EL also noted a convenience: he attached half wavelength sections of twin lead dangling from both the front and rear junctions. One just dangles (without touching the ground) while the other is connected either to the antenna tuner or the coax feedline. Swapping leads reverses the direction of the array. The dangling open-end half wavelength line acts like a very high impedance, which affects antenna performance very little, if at all. Adjust these lines for the velocity factor of the ribbon cable, about .8 for most common 300-ohm twinlead.

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Sounds simple, doesn't it? Mechanically, it is simple, but electronically, things get a little more complex. Some call the ZL Special a 135° phased array because they think of the rear element as 180° minus the 45° twisted phase line out of phase with the front element. This is true with respect to impedance values found at each element. However, it is current magnitude and phase which determine the performance of the array, and the target ballpark for that current is 315° (which is also -45°) out of phase with the front element. The half twist of the phase line is equivalent to twisting the element itself 180° with respect to the front element, with an added 45° phase line between them.

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Now let's make it a little more complicated: for any 2-element horizontal antenna, there is an optimum current magnitude and phase angle for the center of the rear element to give the maximum front-to-back ratio. If the elements are about an eighth wavelength apart, the current magnitude is near the value on the front element and the current phase angle is nearly -45° relative to the front element. But, the antenna element lengths are also part of the overall geometry, and so the exact values for maximum front-to-back ratio are rarely these ideals. If you radically alter the geometry, like bending the elements toward each other at the ends, the natural values (or parasitic values, if you like to think in Yagi terms) change considerably from those found with straight elements at the same spacing.

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Finding the exact dimensions for a perfectly phased ZL Special can be daunting and unrewarding, especially since the values also change with the antenna height above ground. (The "perfect" pattern in Fig. 1 required a modeled rear element current of 1.01 times the current on the forward element and a phase angle of -40.8° and those values differ from the free space model values.) ZL1LE has developed a "lumped constant" matching network that permits him to tune his antenna to the deepest rear nulls as he feeds both junction points with half wavelength feedlines.

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However, there is a big difference between a usable antenna and a perfect antenna. Most ZL Special designs will show little loss in gain and at least 15 dB front-to-back ratio up to 5% above or below the optimal current level and up to 8 or 10 degrees off optimal phasing. Hence, even casual ZL Special designs get the job done, even if they are not perfect. That is why most antenna analysts (who are usually perfectionists) tend to hate the ZL Special, while many a poverty-level or teenage ham has learned to love the antenna.

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Like the hams of the 50s, I prefer to use an antenna tuner with the ZL Special because I do not have to recompensate the feedpoint every time I move the antenna. And tuning one up to acceptable performance is a matter of adjusting the length of the phasing line, usually making it longer and a bit more saggy than most of the magazine designs show. Twin lead is cheap enough to experiment with almost endlessly--or at least until the sunspots return.

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If your needs fit the mechanics of this antenna, try one. If you love it, you will love it even more for the savings. If you hate it, at least you won't be out much money, and the twinlead is reusable.

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For additional information about the ZL Special see Modeling and Understanding Small Beams Part 5: The ZL Special.


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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
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No. 8 Raiding the Hardware Store

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L. B. Cebik, W4RNL

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Home-made antennas have no warranties. We build them, modify them, fix them, and then use the pieces for another project. We move them from the roof to a mast, and from there to the attic. We fold, bend, staple, and mutilate them with great regularity. We do not have to think like manufacturers when we look for materials for small, experimental antennas. The hardware store will do just fine for 10-meter antennas (except for stock items like coax, ladder line, baluns, connectors, and #14 stranded copper wire).

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Think hardware store if you build any of the following: attic antennas, portable or field antennas, experimental or short-term antennas, hidden antennas, "hurry-up-and-get-it-in-the-air-because-the-contest-is- about-to-start" antennas. By hardware store, I mean anything from the traditional shop to the giant home improvement depots.

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The rule of thumb is this: if it is copper or aluminum, then it may be an antenna element; and if it is plastic--especially PVC or its offshoots--then it may be an insulator.

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Here are a few examples to get your creative juices flowing.

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1. Why tubing? Manufacturers use tubing for at least two good reasons. First, it is relatively strong among available antenna element materials. Secondly, it slips the wind better than most other economically feasible shapes. However, without a good shop, working with tubing is inconvenient. Lining up holes for connectors is a bear if we only have hand tools. We often crush it with both regular bolts and U-bolts. So, for experimental and field antennas, why not use something else.

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Angle aluminum is available in a wide variety of sizes. We can choose 1/16 or 1/8" thickness in half-inch or three-quarter-inch widths. I prefer the 1/16" thickness for its lightness and the 3/4" width because I can mount a coax connector right on the element (after grinding off two of the corners).

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Some years ago, I put together a collapsible square quad loop made from a combination of angle aluminum for the horizontal members and wire for the vertical. Construction and field assembly were a breeze because all the nuts and bolts went through flat surfaces. Any difference between the radiation of a tube and a complex angled surface was washed out in practice.

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Hardware stores also have flat aluminum bar and often you can find aluminum rods. The bar would flap too much as an antenna element, but it makes good connector straps in short lengths. If you can thread aluminum rod, you can link pieces, as I did some time back with a collapsible dipole.

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While you are thinking about alternatives to tubing and #14 wire, consider both 300-ohm twinlead and 450-ohm ladder line. You do not have to make folded dipoles out of them. Instead, just connect the wires together at the ends of an element to simulate a fatter wire for a slightly greater bandwidth than you can usually achieve with a single wire. For attic and field antennas, the slight weight difference may be offset by the wider QSY possibilities.

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The usual steel mast and steel or aluminum tower is a marvel of engineering, and most handbooks show metal plates using metal hardware to mount a metal mast to a metal boom to metal elements. The operative ideas are durability and lightning protection. For many indoor, experimental, and field operations, these ideas are secondary, at best.

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Schedule 40 PVC makes a good partial substitute for steel masting in short lengths. It works easily with hand tools. I have experienced no RF difficulties with it at 10 meters. I have used 1/2" to 1 1/2" diameters for various element support, mast, and boom exercises. The 2-element Yagi in a past episode used a PVC boom under 6' long, well within the sag limits of the tube.

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Schedule 40 PVC gives "nominal" or minimum diameters: the actual inside diameters are greater. 1.25" PVC has closer to a 1 3/8" inside diameter and a 1 11/16" outside diameter. 1" nominal will nest inside 1 1/4" nominal, but not tightly. However, most other sizes will not nest well or at all.

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Consider the following portable dipole. The elements on each side of center are 3/4" and 5/8" aluminum tubes that slide into each other for carrying. The center insulator is a 2' to 2.5' piece of 5/8" dowel--a foot or so of antenna element over each end of the dowel. The dowel slides into a hole through the near top of a 2' piece of 1" nominal PVC. The PVC slides over the end of a section of TV masting. 5' sections of the mast put the antenna as high as safe and feasible, with rope guying. The dipole is turnable by hand over 90° for nulling QRM into the element ends. Wherever the tubing fit is too loose, some electrical tape on the inner tube tightens the grip without gluing the assembly together. It all breaks down into a collection of tubes no longer than 5' maximum. Nest what you can; then lash the bundle together with the guy ropes for transport. It is possible to drill a hole and fasten a coax connector to the PVC top mast section, or you can make up a little plate for it from some scrap aluminum.

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For wire antenna element spacers, portable quad element supports, and similar light duty functions, try some of the lighter-weight tubing available. Half and three-quarter inch CPVC tubing is available, as is Schedule 315. For both 90° and 45° corners, as well as for section couplings, there are fittings that glue together so permanently that I have never had one fail yet.

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3. Flat and angled insulators: Sturdy plastic insulating plates are easy to fashion from thick freezer containers. They are temperature impervious for normal use lifetimes. The sides are either straight up or slightly angled, making good mounting lips. A hacksaw cuts these 4" square containers into handy sizes, and a 5/8" hole saw for wood cuts a perfect coax connector hole. The uses are limitless, but the first use that comes to mind is as a center insulator for either straight wire or folded dipoles.

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However, do not overlook round and "squared" plastic bottles for special uses. The semi-rectangular bottles used for some liquids have rounded 90° corners. Cut a pair of round holes (to match a boom, a mast, or an antenna element), one on each surface of a corner section. Squeeze the corner together and slip it over the mast, boom, or tube. Let go, and the corner grips well enough to withstand small loads and winds up to 45 mph. You can use this scheme to space feedline from a boom or mast or to suspend linear loading elements beneath a main element.

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4. Wood and the "auto" section: For most experimental, indoor, and field antennas, metal mast-to-boom and boom-to-element plates are not necessary (unless you just happen to have a stock of 3/16 to 1/4" thick aluminum). 3/8" or 1/2" plywood will do as well.

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Put away the varnish, because it will not last long in the weather. Instead, look in the auto supply part of any of the X-mart stores for a can of auto body work fiberglass resin liquid. Spread it liberally over the plywood piece (already cut and drilled). Give special care to the edges, where plywood is very porous. Once dry, recheck the hole sizes for easy hardware passage and redrill as needed. If your wood plate is lumpy, sand the surface flat, but not down to wood again. If you slip up, retouch the area. Now your plate is sealed against weather much more perfectly than any varnish I have found.

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The one exception is epoxy paint made to seal concrete and similar benches, tables, etc. It does much the same work about as well, but is not always readily available.

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Note that I do not use the fiberglass cloth in this process. It is unnecessary for this application.

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5. Hardware: For antenna work, use stainless steel hardware (nuts, bolts, washers, hose clamps, etc.) wherever possible. Stock sizes are now readily available in the depot-type stores, and there are in many medium to large cities specialty suppliers of stainless steel hardware. If it is rustable, do not use it for an electrical connection out of doors. Beware, for example, of those little wire-end rings: most turn to rust in a few months.

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For hardware that does only mechanical, but not electrical work, clear sprays can extend their useful lifetimes. Of course, such coatings take the hardware out of the secure grounding system. So if you need a ground lead from your antenna boom to the rod in the earth, run a separate flat braid. Do not rely on coated or rustable hardware for this job.

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This is just the start. If you like to play with experimental antennas, especially for 10 meters, just wander around a hardware depot. Buy a few fittings that look promising and cheap just to stare at in your leisure. I am sure you will find a use for some of them in your next project. Remember: antennas do not have to look like commercial versions to do the job you need them to do. They just have to be electrically and mechanically sound enough as antennas and convenient enough relative to your situation.

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Now where was I? Ah, yes. This elbow joint just fit over the end of the tube for my bedspring helical J-pole antenna. . ..
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Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to An-Ten-Ten-nas Page
+ Return to Amateur Radio Page
+
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+ + diff --git a/content/a10/ant9.html b/content/a10/ant9.html new file mode 100644 index 0000000..a98b74b --- /dev/null +++ b/content/a10/ant9.html @@ -0,0 +1,56 @@ + + + + + Fans and Bow Ties + + + +
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No. 9 Fans and Bow Ties

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L. B. Cebik, W4RNL

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Can you use a simple antenna that has an SWR of less than 1.5:1 all the way from 28.0 MHz up to 29.7 MHz? Then you need something stylish in the way of a fan or a bow tie.

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Fanning the ends of a dipole or spreading them into a bow about the middle of each side of the element is an old trick for increasing the SWR bandwidth of a dipole. The fatter the element, the broader the bandwidth of the antenna without any significant loss of performance. Ten-meter fans have been around a long time, but folks have almost forgotten them. Let's restore the memory. Remember that there is a good bit of activity at the upper end of 10, what with satellites, repeaters, HF packet and the like. An antenna that will let you work both the repeaters and the CW end of the band is worth remembering.

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Figure 1. A fan dipole for 10 meters. +

Figure 1 captures the essence and the dimensions of a fan dipole for 10 meters. It is a resonant dipole for 10 with a feedpoint impedance of just about 50 ohms resistive at resonance (about 28.75 MHz). A fan can be built with or without the center bar across the middle. However, if the middle bar is removed, the resonant point actually goes down in frequency to about 28.25 MHz with the dimensions given. So some shortening of the structure is in order.

+

The bandwidth of the antenna increases almost linearly as the vertical dimension is increased. Four feet is a good compromise between performance and ease of building the antenna. At this size, the gain is about the same as a wire or tube dipole having a narrower bandwidth. With the right construction, the antenna will slip the wind easily and be a very long-lasting antenna. It may even look odd enough to fool your neighbors into thinking it is not a ham antenna.

+

Building the fan begins with a centerplate: plywood with a coating of the epoxy used for fiberglass repairs works fine. Make the horizontal element 0.75" diameter aluminum from the hardware store. While you are there, pick up an 8' section of aluminum rod or tubing about 0.375" (3/8") diameter and cut it in two. These are the end verticals. You can drill a 3/8" hole in the end of the tube or use some other clamping system. I just slid the rod into the hole and locked its position with two tiny hose clamps, one above and one below the tube. A pair of bolts, with nuts on either side of the tube wall, press on the rod for electrical contact. Be sure to use lockwashers on the bolts for a good bite into the aluminum tube.

+

#14 stranded wire runs from the rod ends to the center of the dipole. Another set of hose clamps locks the wire in place at each end. Mount the plate on a mast, turn it by motor or hand, and the job is complete.

+

Be sure to use stainless steel hose clamps and hardware. A little conductive "butter" helps preserve contacts, especially where the metals are dissimilar.

+
+ +
Figure 2. A 10-meter bow tie antenna. +

An alternative to the fan dipole is the bow tie. Instead of spreading the antenna at the ends, we spread it in the middle of each half of the dipole. For the same bandwidth, we must have a longer antenna, spread a bit wider at maximum. However, the ends come back to the center tube, which makes construction a bit simpler for some folks. The same principles apply. However, notice that no vertical element is showing in the diagram. Use something nonconductive for this spreader. A length of Schedule 315 PVC (thinner wall) may do the job. The wire tension will keep the tubing from bowing, and a simple set of brackets will hold it to the center tube.

+

The SWR bandwidth of the bow tie is just as good as it is with the fan. If you think you can hear the difference made by 1/10th of a dB gain, then computer models say the bow tie is that much better than the fan. (Before you get caught up in the idea, forget trying to hear a 0.1 dB difference in anything; you cannot do it.) So the difference comes down to this: which antenna is easier for you to build.

+

Fans and bow ties used to be built from bent tubing, getting rid of the center horizontal tube. Personally, I do not recommend this construction. Even if you are an expert tubing bender and do not weaken the tubing by crimping it, the wind will transform your fan or bow tie into a crumpled scarf in very little time. Some modification of the suggested construction method, adapted to what you have in your shop, makes the strongest assembly.

+

Fans and bow ties, especially fans, lend themselves to 2-element beams quite readily. Ask the folks at Butternut, where they make a multi-band beam from 2 fans slightly larger than the dipole described above. They call it a "Butterfly" beam, so if you make a beam from two bow ties, you can call it a dragonfly beam.

+

Actually, a monoband beam for ten is not too difficult to build. With the basic fan dipole as a guide, you will have to lengthen the back element by about 5% or load it with a coil at the center. The driven element will be long, just about long enough to add the right inductive reactance for creating a beta match with a capacitor across the feedpoint terminals. You can experiment with a variable capacitor and then replace it with a fixed capacitor of the right value. About an eighth wavelength of spacing (about 4.3') will give the same performance as a "full size" 2-element Yagi, such as the "simplest" Yagi described in an earlier column.

+

While 10 is so marginal for everyday activity, I suppose I will not break any taboos by mentioning the fact that you can apply the same fan principle to wire antennas for the lower bands. With all the variables that go into wire antennas for 80, 40, and 30 meters, it likely makes no great difference if you connect the ends of the fan together or leave them separate. If you add a fan wire to an existing antenna, be prepared to shorten the antenna, since the spread wire will act like a thickening agent. Some hams have strung wires cut for the low end of the 80-meter CW band, the Novice portion of the band, and for 75 meters, all with one feed. However, 80 is so wide a band (as a percentage of the frequency), that these wires tend to act like 3 independent antennas with a common feed. So you can expect to see ups and downs in the SWR pattern rather than one single low point.

+

The fan and the bow tie are distant relatives to the cage antenna, a series of wires spaced apart along their entire length by special nonconductive spacers. The original theory was that the radiation from each added up, but actually, the only benefit was getting the equivalent of a fat wire from thin ones. You do not have to go that complex route to get a wide-band dipole for 10. The fan and the bow tie will do the job, and they are much easier to rotate the 90 degrees it takes to put a maximum face on the station you want to work.
+

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+ +

+
+

Updated 3-17-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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An-Ten-Ten-nas

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+
+

L. B. Cebik, W4RNL, 41159

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+ +
+

In each issue of the 10-10 News, I try to clarify a significant cluster of ideas used in antenna work. My object is to help members make the best decisions about the antennas they buy or build without imposing my own prejudices on them. The more we understand, the better our choices will be.

+ +

Highlighted entries are on line. I convert series entries to on-line documents as they appear in the 10-10 News.

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The first 30 columns are now available in print form from 10-10 International via the Data Manager. See the 10-10 web site for address information.

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+ +

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Updated 01-15-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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1. Converging Toward Excellence

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+

L. B. Cebik, W4RNL

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+ +

+ Whether you are using one of the versions of MININEC or one of the versions of NEC-2, a temptation will overcome you somewhere along the way in your antenna modeling career. You will ignore the convergence test. And in some cases, you may regret it, especially when your copper or aluminum antenna turns out to be well off the mark set by the model. +

So let's take a patient look at convergence testing. Our aim will be not just to be able to do it, but as well to understand why we should always do it.

+

Both NEC and MININEC calculate antenna properties based on the division of the antenna elements into a collection of short wires. Within the program limits, the shorter, the better. However, both NEC and MININEC make use of complex calculation matrices that take time to fill and resolve. The more segments we have, the longer the run time.

+

Because we are impatient, a bad habit has set in among many program users: to divide the antenna elements into as few segments as possible, again within certain generalizations in the instruction manuals. For MININEC, the recommended minimum number of segments per half wavelength is 10, while for NEC-2 it is 9 or 11. (When center feeding an antenna element, use an even number of segments for MININEC and an odd number of segments for NEC.)

+

What we often forget is that neither program is absolutely stable, and the best we can hope for is relative stability. What stability refers to is the fact that if we change the number of segments per half wavelength, without changing the overall dimensions, the program will produce different output data. What we strive for is a number of segments per half wavelength that--as we change the segmentation--produces output data differentials that are too small to be operationally significant. Of course, what counts as being operationally significant depends on the modeling goals for a given project.

+

We can illustrate the instability of the program by making some runs with an ordinary 20-meter dipole, as shown in Figure 1. (In all figures, the heavy black "dot" represents the source or feedpoint. It is shown as a dot rather than as a break in the wire to indicate that the wire is continuous and the source is inserted in series with the wire.) The only factor we shall change from model run to model run is the number of segments into which we divide this half wavelength of wire.

+
+ +
+

For NEC-2, we can make a table of the results:

+ 
Segments       Gain in dBi    Source Impedance (R+/-jX)
+11                  7.97           67.51 - j0.22
+15                  7.98           67.50 + j0.34
+21                  7.98           67.52 + j0.24
+25                  7.99           67.53 + j0.32
+31                  7.99           67.54 + j0.42
+35                  7.99           67.55 + j0.46
+41                  7.99           67.56 + j0.53
+45                  7.99           67.56 + j0.56
+

This example is the source of the fatal temptation to always use the minimum number of segments. It is operationally stable at the lowest level of segmentation for any purpose I can think of, since I have no instruments capable of trimming an antenna to the variations shown in the numbers.

+

However, the table does illustrate that the numbers in fact do change with the level of segmentation. As the first 4 lines of the source impedance entries show, the numbers may drift in either direction until some large number of segments are used.

+

A similar situation exists with MININEC. The segmentation varies from the NEC table to accommodate the source location.

+ 
Segments       Gain in dBi    Source Impedance (R+/-jX)
+10                  7.83           67.51 - j6.78
+16                  7.85           68.19 - j7.71
+20                  7.85           68.40 - j7.57
+26                  7.86           68.59 - j7.22
+30                  7.86           68.67 - j7.01
+36                  7.86           68.76 - j6.70
+40                  7.86           68.81 - j6.50
+46                  7.86           68.87 - j6.26
+

The intrinsically higher level of reactance is a function of MININEC's growing error in resonant length as the frequency climbs. Some programs correct for this error; others do not.

+

Nevertheless, we find a similar drift in values with increasing segmentation. However, for operational purposes, the numbers give us confidence that a dipole constructed from these dimensions would work perfectly well with only such trimming as our yard clutter and local terrain might make necessary.

+

One common way in which we often fail to observe even the minimum recommended segmentation is when we increase the frequency of operation of an antenna without altering the number of segments. Figure 2 shows the same antenna, but now operated at 28.0 MHz.

+
+ +
+

The results for NEC-2 are the following:

+ 
Total Segments   Gain in dBi  Source Impedance (R+/-jX)
+11                  9.58           3813 + j1438
+23                  9.61           4306 - j 376
+33                  9.62           4120 - j 945
+45                  9.62           3928 - j1266
+55                  9.62           3810 - j1415
+67                  9.62           3705 - j1529
+

Although the gain stabilizes as soon as we use at least 11 segments per half wavelength, the source impedance continues to move around considerably. since we would likely feed this antenna via a parallel transmission line and antenna tuner, we might easily overlook the variance.

+

However, the antenna as presently used can be viewed as two end-fed half- wavelength dipoles physically coupled. End feeding near resonance yields large changes in source impedance with very small changes in physical dimensions. Hence, changes in segmentation yield possibly significant differences in source impedance.

+

MININEC shows a similar set of figures:

+ 
Total Segments   Gain in dBi  Source Impedance (R+/-jX)
+10                  9.55           3401 - j1646
+22                  9.56           3537 - j1519
+32                  9.56           3485 - j1568
+44                  9.56           3431 - j1616
+54                  9.56           3399 - j1643
+66                  9.56           3366 - j1669
+

Interestingly, the source impedance figures for MININEC appear to be more stable than those for NEC-2. It should be remembered that all MININEC source impedance figures are calculated based on perfect ground, whatever the ground used to determine the far field figures. (Medium earth is used throughout these examples.) NEC-2 calculates source impedance based on the Sommerfeld-Norton ground conditions specified for the antenna.

+

In determining whether a satisfactory level of convergence has been achieved, the program user must determine how much variance is necessary to make it significant. The following driver-director 10-meter Yagi, shown in Figure 3 at a height of 1/2 wavelength, might be instructive here.

+
+ +
+

NEC-2 tabulates the results as follows:

+ 
Segments/Element  Gain in dBi Front-to-Back in dB Source Impedance (R+/-jX)
+11                  10.84          14.11               21.11 - j23.57
+15                  10.88          14.34               20.66 - j22.64
+21                  10.91          14.55               20.30 - j21.87
+25                  10.92          14.64               20.15 - j21.54
+31                  10.93          14.73               19.99 - j21.19
+35                  10.94          14.78               19.91 - j21.01
+41                  10.94          14.84               19.81 - j20.78
+45                  10.95          14.87               19.75 - j20.66
+

It might appear that, although the gain and the source impedance are fairly stable, especially in models using at least 21 segments per element, the front-to-back ratio continues to change at higher rate. However, from an operational standpoint, changes of a dB in this ratio are not especially detectable, and hence, the model might well be said to converge at about 21 segments per element--or less, if the needs are less critical.

+

Moreover, since we would likely use a matching system, such as the beta match or a series feedline section, between the feedpoint and the main 50- ohm coaxial feedline, the variations in the source impedance are unlikely to fall beyond normal adjustment limits. Hence, the home constructor might well judge the model to be well converged at the lowest level of segmentation. In terms of comparative design analysis, we might hold out for segmentation of at least 20 segments per element.

+

The corresponding MININEC model was run at the same frequency. Hence, its performance figures will be less impressive, since they reach a peak at a different frequency. However, for our purposes, the table shows a similar level of stability as the NEC-2 table above.

+ 
Segments/Element  Gain in dBi Front-to-Back in dB Source Impedance (R+/-jX)
+10                  10.49          10.71               21.91 - j29.20
+14                  10.53          10.90               21.72 - j28.79
+20                  10.56          11.18               21.29 - j27.75
+24                  10.61          11.34               21.01 - j27.11
+30                  10.64          11.47               20.81 - j26.40
+34                  10.65          11.57               20.63 - j25.79
+40                  10.68          11.71               20.37 - j25.27
+44                  10.68          11.75               20.31 - j24.94
+

Although stable enough for most purposes at the lowest level of segmentation, the figures are highly stable once we use more than 20 segments per elements.

+

Symmetrical structures, even of some complexity tend to show a higher level of stability than non-symmetrical structures, even of similar types. To illustrate the point, let's compare a pair of triangular designs, vertically oriented. The first is a right-angle delta for 7.15 MHz, shown in Figure 4.

+
+ +
+

Despite its angularity, the antenna is quite stable once the segments are shorter than the maximum recommended length. The segmentation column shows the number of segments in each angular leg, and then the horizontal leg.

+ 
Segments       Gain in dBi    Source Impedance (R+/-jX)
+6/6/8               1.73           63.83 + j1.49
+12/12/17            1.90           60.95 - j0.29
+18/18/25            1.89           60.99 - j0.77
+24/24/34            1.89           61.03 - j1.03
+30/30/42            1.89           61.06 - j1.18
+

The lowest level of segmentation results in segments longer than the maximum recommended length. Beyond that level, the model shows excellent stability over many levels of segmentation, despite the fact that the source is moving slightly each time, since it is specified as a percentage of the left leg.

+

One might be tempted to also model this antenna via MININEC. However, to do so would be to violate the limits of reliability with respect to the height of the antenna above ground. In general, as an antenna is brought closer to ground than about 0.2 wavelength, the gain increases inaccurately. For example, a fully length-tapered version of this antenna shows a MININEC source impedance of 64.5 - j23.6 ohms, somewhat off the NEC-2 mark, but not drastically. However, the antenna also shows a wholly unrealistic gain of 3.63 dBi.

+

For comparison, let's look at model of another triangle, one developed by W6RCA and shown in Figure 5.

+
+ +
+

Relative to the plane of the antenna facing us, the antenna is not symmetrical on either side of a line one might draw at to bisect the source. Although the angularity of the antenna might lead us to believe that its model will behave similarly to the right-angle delta, the NEC-2 table tells a different story when using a split-current source feed. (This feature is available on programs such as EZNEC. The model shows much less instability when using a split-voltage feed.) The segmentation column refers to the number of segments in the vertical leg, the horizontal leg, and the diagonal leg, respectively.

+ 
Segments       Gain in dBi    Source Impedance (R+/-jX)
+4/8/9               4.33           62.05 - j10.08
+7/12/14             2.87           47.99 - j 5.77
+9/16/19             2.45           44.10 - j 2.08
+11/21/23            2.32           42.65 - j 0.26
+13/25/28            2.24           41.83 + j 1.95
+16/29/33            2.21           41.37 + j 3.73
+18/33/37            2.19           41.19 + j 4.53
+

As with the right-angle delta model, the initial segmentation yields segment lengths longer than the maximum recommended values, and this fact is reflected in the unrealistically high gain and source impedance. By the point of maximum segmentation in the exercise, the model has stabilized to an operationally useful point--sufficiently so that the dimensions promise to make a good starting point for building such an antenna. However, the rate of change from one level of segmentation to the next is still significantly higher than it is for symmetrical antennas such as the dipoles, the Yagi, or the right-angle delta.

+

Inadequate segmentation on the split current-fed model does not just affect the gain and source impedance numbers. In fact, the entire far field pattern changes when comparing minimal segmentation models with adequately segmented models. Figure 6 compares the elevation pattern perpendicular to the face of the triangle for the 21-segment model and the same pattern produced by the 88-segment model. The latter is typical of the patterns of the group of more nearly converged models. The difference is not merely a matter of gain, but as well the correct portrayal of higher-angle radiation from the antenna. (Again, the model does not show the dramatic change in pattern shape when split-voltage-fed.)

+
+ +
+

Unlike the right-angle delta, the W6RCA triangle can be modeled via MININEC, since the bottom is about 0.22 wavelengths above ground. Even though MININEC advises against modeling with small numbers of segments when an antenna geometry contains right or acute angles, the exercise may be instructive. Again, for this example, the model is split-current fed.

+ 
Segments       Gain in dBi    Source Impedance (R+/-jX)
+4/8/9               3.43           64.17 - j210.2
+7/12/14             3.28           50.00 - j125.6
+9/16/19             3.32           45.72 - j 89.5
+11/21/23            3.37           42.66 - j 68.4
+13/25/28            3.38           42.02 - j 54.2
+16/29/33            3.39           41.68 - j 43.3
+18/33/37            3.39           41.68 - j 36.8
+

Although the model comes to show reasonable stability, its reported gain is well above that of the NEC-2 model, largely because it is near the border of reliability. This fact is significant, since many MININEC users think of the 0.2 wavelength height limit as a kind of breaking point. It is not.

+

Instead, it is a region where gain reports on different types of antennas become unreliable at different actual heights above ground.

+

The large swing of reactance in the source impedance is due to the fact that MININEC models in effect cut off sharp interior corners. The longer the length of individual segments meeting at an acute angle, the more wire is effectively trimmed in the computation of impedance and current interactions. As the segments grow shorter, the antenna gradually approaches its physical full size. A fully length-tapered version of the antenna model showed a gain of 3.38 dBi (still unreliably high), and a source impedance of 40.32 + j5.20 ohms, not far off the NEC-2 model.

+

The lessons taught by the W6RCA triangle are numerous and useful. First, it is unsafe in terms of model reliability to use the minimum number of segments per half wavelength recommended for wires in the model by the program. These program recommendations are based upon linear elements and apply at most to symmetrical antenna geometries.

+

Second, it is also unsafe to assume that some arbitrary larger number of segments per half wavelength will automatically yield a reliable model. The W6RCA triangle remained less stable with 44 segments per half- wavelength than many of the other models with under half that number.

+

The designer must make a series of convergence tests and reach a decision concerning the adequacy of stability in the model based on standards brought to the modeling exercise from a knowledge of the goals of the overall project. In some cases, stability adequate to one task may not suffice for another.

+

Third, inadequate convergence holds the potential for producing a model that misrepresents antenna performance in every way: gain, front-to-back ratio (if applicable), source impedance, and field pattern shape and strength. Although convergence alone cannot guarantee the adequacy of a model, it is one necessary condition to that goal.

+

Antenna modeling can be a very significant short-cut in the design and building of antennas. However, we can achieve the savings only if we do not take short-cuts with the modeling process itself. Convergence testing is one of those steps we should never omit, lest the minutes we save at the computer testing our models end up costing us hours of frustrating time spent trying to adjust an antenna that is based upon an inadequate model.

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Go to Main Index

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+

10. Tapering to Perfection

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+
+

L. B. Cebik, W4RNL

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+
+ +

+ Everyone who models HF (and low VHF) beams is faced with dealing with elements that do not have a constant diameter. We refer to such elements as tapered-diameter (or tapered radius) elements, in contrast to elements with a uniform diameter, that is, elements that are untapered. The latter have somehow picked up in some literature the self-contradictory name of mono-tapered elements. +
+ +
+

Figure 1 exaggerates--but only to a degree--the amount of stepping involved in most elements composed of several diameters of aluminum tubing. Normally, the maximum diameter shift from one section to another is about 0.25". However, some designers use a short, fat center wire in the element to simulate the effects of element-to-boom mounting plates and hardware. In these cases, the diameter shift may amount to as much as 2".

+

Native NEC-2 cannot handle tapered-diameter elements. It simply yields inaccurate results--ordinarily by over-reporting the gain and under-reporting the source impedance of the element. Consequently, in some implementations of NEC-2, correction factors have been installed to yield more accurate results.

+

Let's begin by comparing some simple cases of uncorrected and corrected NEC-2 reports for some simple tapered-diameter elements set up as dipoles in the 14 MHz range. The following table repeats an exercise we first encountered in installment 3 of this series. The entries in the table beneath each numbered label represent, first, the distance from the elements center at which a diameter shift occurs and, second, the diameter(s) of the element between shift points. The "Cor." entries give the length from center and the diameter of the substitute element used by NEC-2 to provide corrected results.

+ 
  Length(s) in inches         Free Space Gain          Source Impedance
+  Diameter(s) in inches         in dBi                 (R +/- jX Ohms)
+1.  Uniform element (no corrective needed)
+     -201.25...0                     2.12              71.8 - j 0.6
+            1.0
+2.  One step, far out
+     -204...-150...0       No Cor.   2.14              73.0 + j 4.4
+         .75    1.0
+     -201.45...0           Cor.      2.12              72.0 + j 0.4
+           0.966
+3.  One step, near center
+     -204...-50...0        No Cor.   2.22              72.4 + j 5.2
+         .75   1.0
+     -201.661...0          Cor.      2.13              71.8 - j 0.5
+           0.792
+4.  Two steps, modest taper
+-205.75...-100...-20...0   No Cor.   2.32              72.5 + j10.6
+       .75    1.0   1.25
+-201.49...0                Cor.      2.13              71.9 + j 0.1
+     0.889
+5.  Two steps, more extreme taper
+-208.5...-100...-20...0    No Cor.   2.82              67.6 + j17.1
+      .75    1.0   2.5
+-201.63...0                Cor.      2.13              72.1 + j 0.9
+     0.895
+

Notice especially the trends. Without correction, the closer the diameter step to the element center (and the source), the higher the reported gain and the lower the reported source impedance. The more numerous the steps and the greater the step sizes, the higher the reported gain and the lower the reported source impedance. By entry number 5, the figures have grown incredible. In contrast, the corrected elements yield figures that are all quite reasonable for a resonant 14 MHz dipole.

+

The simple lesson from this exercise is always to use the stepped-diameter correction feature when modeling stepped-diameter elements. However, there are numerous limitations to the tapered-diameter element correction scheme, as well as some cautions to be observed in using it. So let's spend a little time understanding the feature and learning to use it wisely. In addition, let's also pick up the habit of making sure that it is in effect when we want it to be.

+

A Bit of Background

Wherever the tapered-diameter correction feature is implemented, it creates a substitute element for the tapered one. The substitute element has a uniform diameter and a length that yield essentially the same self-impedance as the tapered diameter element. Thus, the substitute can be expected to behave--either by itself or in an array of elements--in the same way as the tapered element. +

The first method of calculating substitute elements was developed (to the best of my knowledge) by Jim Lawson, W2PV, in chapter 7 of his classic Yagi Antenna Design. Brian Beezley, K6STI, created improve algorithms for use in his NEC-Wires program. A quite different system was developed and explained by Dave Leeson, W6QHS, in chapter 8 of his equally classic Physical Design of Yagi Antennas. EZNEC, by W7EL, implements the Leeson correctives, as does NECWin Plus.

+

The Leeson correctives were calibrated against the MN (K6STI) version of MININEC. Indeed, MININEC is considered to be the standard of comparison for all tests of tapered-diameter calculations. It exhibits no problems with tapering schedules of all sorts. (A "tapering schedule" is simply where along an element the diameter changes and by how much.) We shall a bit farther on do some comparing of MININEC with both corrected and uncorrected NEC-2 outputs.

+

The basic principle of the substitute element is to derive an element with a uniform diameter and the same self-impedance as the original tapered- diameter element. The calculation method is accurate at and near element resonance, where the current distribution along the element is nearly sinusoidal (that is, nearly a sine wave in shape). This condition sets a number of limitations for the use of the corrective.

+

Some Practical Boundaries for Substitute Elements

In practical terms, the limitations are straightforward if we remember the what the calculation method requires. +

1. The tapered-diameter element must be within about 15% of resonance for the substitute element to be an accurate replacement. The near-resonance requirement applies to the physical length of the antenna without regard to loads, transmission lines, and sources that may be present. EZNEC, for example, cuts off the availability of the correction factor if the element does not meet this standard.

+

In antennas with many elements, only those meeting this (and other) constraints will have substitute elements calculated. Consequently, a tri-band beam might have the elements for one band (as determined by the frequency selection) substituted, but not those for other bands. This places a requirement for caution in using the results of such a model. For example, on some tri-band beams, the forward 20-meter director can affect performance on 10-meter, especially in limiting the upper frequency performance on that band. Depending upon beam design, the 20 meter director may carry significant current on 10 meters and be somewhat long as a full wavelength element on the upper band. However, it would not ordinarily have an uniform-diameter substitute calculated for it when the antenna is modeled at 10 meters.

+

2. If the tapered-diameter element is open at both ends (a dipole), it must be symmetrical about a center point along (but not necessarily on) one of the axes of the coordinate system. This requirement demands that the steps in a dipole's taper occur at equal distances from the center point of the element and in equal diameter steps for each corresponding step. EZNEC, for example, flags non-symmetries. In modeling, perhaps the chief reason for the absence of symmetry is transposing numbers when entering them in the wires table.

+

3. Loads, transmission lines, and sources are permitted only at the center point. Only one of each is permitted if the midpoint of the symmetrical element has no wire junction. Where the center is at a wire junction, split sources and loads may be used on segment immediately adjacent to the center-point junction. A load at a distance from the center--whether a resistance/reactance load, a resistance/inductance/capacitance load, or a shorted or open length of transmission line--would create an abrupt non-sinusoidal change in current magnitude along the element length, thus violating one of the conditions of accuracy. Center loads, transmission lines, and sources do not ordinarily disturb the current magnitude curve, although they may limit its highest value. Once more, EZNEC identifies misplaced loads, sources, and transmission lines.

+

Note that a serious loading coil used to shorten an element severely would ordinarily be used with an element already too short to pass the length test. Hence, such antennas could not access the corrective process.

+

For monopoles, connection to ground is essential for the substitution system to work. In these cases, the antenna element must be within length boundaries with respect to 1/4 wl resonance, and all source, load, and transmission line attachments must be to the segment immediately adjacent to the ground.

+

4. The taper-diameter element must be truly linear--that is, all wires making up the tapered-diameter element must be collinear. Ends must be open or, at most, one end may be grounded. Therefore, tapered diameter sections of elements that make up a complex geometry disable the corrective system. As a result, tapered-diameter elements used in Moxon rectangles, quad loops, capacity-hat dipoles/monopoles, and similar antennas cannot be directly modeled in NEC-2.

+
+ +
+

Figure 2 summaries the rules by calling attention to what goes beyond normal boundaries. The upshot is that the corrective system is quite limited in its applications. However, the design of HF Yagi beams and other arrays with linear tapered-diameter elements is such a widespread application of NEC-2 that the corrective system is considered essential to most users.

+

Some Practical Examples and a Subtle Limitation

Let us look at some examples of the tapered-diameter correction factor in operation to further our familiarity with it and to gain some sense of what counts as reasonable expectations of it. We shall look at some wire tables drawn from the EZNEC implementation of NEC-2. Then we shall examine 5 sets of output reports: 1. the results of a MININEC version of the model in AO; 2. the results of uncorrected EZNEC NEC-2; 3. the results of corrected EZNEC NEC-2; 4. the results of creating a single-wire uniform element of the same length, diameter and total number of segments as the substitute group of wires in the corrected NEC-2 report; and 5. the results of (uncorrected) NEC-4. The AO models will have their center sections decreased by one segment to properly place the source at the junction of segments and at the element center. NEC-4 models hypothetically should need no correction. The models are all of the driven elements of large Yagi antennas, so their independent source impedances may not be quite resonant. +

1. A 14.175 MHz driven element of W6NGZ design:

+
+ +
+ 
W6NGZ     Frequency = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+
+1       -205.95, 79.800,  0.000  W2E1 -156.00, 79.800,  0.000 6.25E-01   4
+2  W1E2 -156.00, 79.800,  0.000  W3E1 -120.00, 79.800,  0.000 7.50E-01   3
+3  W2E2 -120.00, 79.800,  0.000  W4E1 -72.000, 79.800,  0.000 8.75E-01   4
+4  W3E2 -72.000, 79.800,  0.000  W5E1  72.000, 79.800,  0.000 1.00E+00  13
+5  W4E2  72.000, 79.800,  0.000  W6E1 120.000, 79.800,  0.000 8.75E-01   4
+6  W5E2 120.000, 79.800,  0.000  W7E1 156.000, 79.800,  0.000 7.50E-01   3
+7  W6E2 156.000, 79.800,  0.000       205.950, 79.800,  0.000 6.25E-01   4
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           7     4 / 50.00   (  4 / 50.00)      1.000       0.000       I
+Ground type is Free Space
+

This antenna is symmetrical in the X-axis. Leaving the Y coordinate at its original spacing from the reflector is no problem for implementing the correction factor. The AO model uses 12 segments in the long center element. Note that the center element occupies about 35% of the total element length. Here are the reports.

+ 
Report Source       Gain dBi       Source Z (R+/-jX)
+AO                  2.13           77.0 + j 11.6
+NEC-2 (No Cor.)     2.21           77.3 + j 23.6
+NEC-2 (Cor.)        2.14           74.7 + j 11.9
+NEC-2 (1-Wire)      2.14           74.7 + j 11.9
+NEC-4               2.17           76.1 + j 12.9
+

This 35-segment model shows only a slight displacement from the MININEC standard. The key difference is in the reactance report, which seriously displaces resonance in uncorrected NEC-2, while the corrected NEC-2 report coincides with the AO report. The 1-wire substitute element agrees exactly with the subdivided group that composes the substitute model of the element: both show a source resistance that is about 2.3 Ohms lower than the AO report. Finally, note that the NEC-4 report, while closer by far to the corrected NEC-2 and AO reports than to the uncorrected NEC-2 report, is still a bit high in gain and also in the reported source reactance.

+

2. A 14.175 MHz driven element of WB0DGF design:

+
+ +
+ 
WB0DGF    Frequency = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1       -170.00,-209.50,  0.000  W2E1 -170.00,-156.50,  0.000 4.38E-01   7
+2  W1E2 -170.00,-156.50,  0.000  W3E1 -170.00,-132.50,  0.000 6.25E-01   3
+3  W2E2 -170.00,-132.50,  0.000  W4E1 -170.00,-82.000,  0.000 8.75E-01   6
+4  W3E2 -170.00,-82.000,  0.000  W5E1 -170.00,-36.000,  0.000 1.12E+00   6
+5  W4E2 -170.00,-36.000,  0.000  W6E1 -170.00,-10.000,  0.000 1.25E+00   3
+6  W5E2 -170.00,-10.000,  0.000  W7E1 -170.00, 10.000,  0.000 1.25E+00   3
+7  W6E2 -170.00, 10.000,  0.000  W8E1 -170.00, 36.000,  0.000 1.25E+00   3
+8  W7E2 -170.00, 36.000,  0.000  W9E1 -170.00, 82.000,  0.000 1.12E+00   6
+9  W8E2 -170.00, 82.000,  0.000 W10E1 -170.00,132.500,  0.000 8.75E-01   6
+10 W9E2 -170.00,132.500,  0.000 W11E1 -170.00,156.500,  0.000 6.25E-01   3
+11W10E2 -170.00,156.500,  0.000       -170.00,209.500,  0.000 4.38E-01   7
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           2     6 / 50.00   (  6 / 50.00)      0.707       0.000       V
+Ground type is Free Space
+

Two features of this element design (symmetrical in the Y-axis) are notable for our purposes. First, the center section (composed of three wires of 1.25" diameter) is half the length of the W6NGZ design, so that the first diameter step occurs closer to the source. Second, the diameter steps cover a greater range than the W6NGZ design, now ranging from 1.25" down to 0.4375" (in contrast to the W6NGZ range from 1.0" to 0.625"). Now let's look at the reports.

+ 
Report Source       Gain dBi       Source Z (R+/-jX)
+AO                  2.13           76.2 + j  0.8
+NEC-2 (No Cor.)     2.33           78.3 + j 30.9
+NEC-2 (Cor.)        2.13           72.4 + j  1.7
+NEC-2 (1-Wire)      2.13           72.4 + j  1.7
+NEC-4               2.21           75.8 + j  6.8
+

The gain and source reactance reports of AO and corrected NEC-2 are aligned, while the source resistance differs by about 3.8 Ohms, slightly more than the difference reported in the W6NGZ design. Note the high gain and inductive reactance difference for uncorrected NEC-2. Finally, note that NEC-4--for this more highly tapered-diameter model--shows a gain value that is no longer trustworthy.

+

3. A 14.175 MHz driven element of K6STI design:

+
+ +
+ 
K6STI     Frequency = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1       -203.50, 72.000,  0.000  W2E1 -138.00, 72.000,  0.000 5.00E-01   8
+2  W1E2 -138.00, 72.000,  0.000  W3E1 -96.000, 72.000,  0.000 6.25E-01   6
+3  W2E2 -96.000, 72.000,  0.000  W4E1 -48.000, 72.000,  0.000 7.50E-01   6
+4  W3E2 -48.000, 72.000,  0.000  W5E1  -4.000, 72.000,  0.000 8.75E-01   5
+5  W4E2  -4.000, 72.000,  0.000  W6E1   4.000, 72.000,  0.000 3.42E+00   1
+6  W5E2   4.000, 72.000,  0.000  W7E1  48.000, 72.000,  0.000 8.75E-01   5
+7  W6E2  48.000, 72.000,  0.000  W8E1  96.000, 72.000,  0.000 7.50E-01   6
+8  W7E2  96.000, 72.000,  0.000  W9E1 138.000, 72.000,  0.000 6.25E-01   6
+9  W8E2 138.000, 72.000,  0.000       203.500, 72.000,  0.000 5.00E-01   8
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+Ground type is Free Space
+

This design uses a short, wide-diameter center section to simulate the effects of element-to-boom hardware. Apart from this short center section, the subdivision of the element is intermediate between the W6NGZ and WB0DGF designs.

+ 
Report Source       Gain dBi       Source Z (R+/-jX)
+AO                  2.12           72.7 - j 13.1
+NEC-2 (No Cor.)     4.66           42.1 + j  5.1
+NEC-2 (Cor.)        2.16           68.9 - j 11.4
+NEC-2 (1-Wire)      2.12           69.6 - j 11.5
+NEC-4               3.06           59.1 - j  6.2
+

This 51-segment element makes every effort to equalize segment lengths from wire to wire within the group, letting the 8" center length determine the segment lengths in the other wires. Even so, the element presses the correction factor limits, showing some difference in gain between the corrected NEC-2 result and the 1-wire substitute element. The effect of a fat short center segment is clearly apparent in the uncorrected NEC-2 result, with its very high gain and very low source impedance report. Note that with this type of segmentation, uncorrected NEC-4 yields quite untrustworthy results.

+

Despite the fact that even close attention to segmentation density yields corrected NEC-2 results that press the limits of the system, I encounter many carelessly segmented tapered-diameter elements. Perhaps the modelers believe that any old arrangement of segments adding up to more than 10 per half wavelength will do the job. However, the segments adjoining the source segment must be very close in length to the source segment itself. Moreover, it is always good practice to equalize segments lengths in any element. Let's see what happens if we carelessly segment the K6STI element.

+

3. A 14.175 MHz driven element of K6STI design (carelessly segmented):

+
+ +
+ 
K6STI     Frequency = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1       -203.50, 72.000,  0.000  W2E1 -138.00, 72.000,  0.000 5.00E-01   4
+2  W1E2 -138.00, 72.000,  0.000  W3E1 -96.000, 72.000,  0.000 6.25E-01   3
+3  W2E2 -96.000, 72.000,  0.000  W4E1 -48.000, 72.000,  0.000 7.50E-01   3
+4  W3E2 -48.000, 72.000,  0.000  W5E1  -4.000, 72.000,  0.000 8.75E-01   2
+5  W4E2  -4.000, 72.000,  0.000  W6E1   4.000, 72.000,  0.000 3.42E+00   1
+6  W5E2   4.000, 72.000,  0.000  W7E1  48.000, 72.000,  0.000 8.75E-01   2
+7  W6E2  48.000, 72.000,  0.000  W8E1  96.000, 72.000,  0.000 7.50E-01   3
+8  W7E2  96.000, 72.000,  0.000  W9E1 138.000, 72.000,  0.000 6.25E-01   3
+9  W8E2 138.000, 72.000,  0.000       203.500, 72.000,  0.000 5.00E-01   4
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+Ground type is Free Space
+

The element is obviously the same as the one just run, but the segmentation has been cut to 25 segments total.

+ 
Report Source       Gain dBi       Source Z (R+/-jX)
+AO                  2.12           72.7 - j 13.1
+NEC-2 (No Cor.)     5.04           38.2 + j  2.5
+NEC-2 (Cor.)        2.68           61.1 - j 10.8
+NEC-2 (1-Wire)      2.12           69.5 - j 12.0
+NEC-4               3.93           48.2 - j  5.8
+

The AO numbers have not changed, but the only NEC report that shows sensible values is the 1-wire substitute. Both sets of figures are consistent with those for the carefully segmented version of the element. Both the raw NEC-2 and NEC-4 values are sufficiently off the mark to be completely unusable.

+

Of great importance is the fact that the corrected NEC-2 figures for this modeled element are also beyond the limits of reliability by a considerable margin. In previous models, we watched the margin of error in corrected NEC-2 reports grow, even in well-segmented elements. In this model, the corrected NEC-2 model and the 1-wire substitute have the same diameter, length, and total number of segment. The only difference between them is the length of segments, especially around the source point: the NEC-2 corrected model has very unequal segment lengths, while the segment length of the 1-wire substitute is uniform throughout the element. This demonstration shows that careful attention to segmentation of tapered-diameter elements is vital to deriving reliable results from the correction system.

+

Some Practical Conclusions

This episode has been light on the graphics and heavy on the tables, but for a purpose. The tables show the data that can help us improve our modeling techniques when employing the tapered-diameter correction factor implemented in various versions of NEC-2. +

The first step is to carefully model the tapered-diameter element so that it meets the basic criteria for implementing the correction system.

+

The second step is to check to ensure that the correction has been implemented. It is easy--despite programmers' best efforts--to overlook some error in the model set-up that may have prevented the automated correction system from working.

+

Third, even models that pass the basic tests require careful attention to segmentation to ensure that segments are as equal as the structure will permit.

+

Remember that errors tend to be cumulative so that unrealistically high gain reports on individual elements usually result in very significant over-estimates in the gain of an array within which the tapered-diameter elements are used. While such over-estimates may be momentarily pleasing to the designer's ego, they can be most assuredly embarrassing if caught by someone else.

+

Finally, even if you have access to NEC-4, do not assume that it is accurate in all cases. While NEC-4 improves on the performance of NEC-2 with respect to tapered-diameter elements, it has limitations which suggest that the correction system should also be used with it in all but the simplest tapered-diameter models.

+

The tapered-diameter element correction system is a valuable feature in any version of NEC-2 that implements it. However, it deserves to be used with both caution and care.
+

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+

Go to Main Index

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100. The Dipole and the Coax

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The most usual way to feed a resonant dipole uses a simple coaxial cable. Most basic handbooks and texts recommend that the system builder insert a common-mode choke at the feedpoint--between the dipole feedpoint terminals and the coaxial cable. Readily available forms of common-mode choke include a transmission line transformer with a 1:1 impedance ratio and a ferrite-bead collection following the designs proposed initially by Walt Maxwell (W2DU). In either case, the device establishes a compatibility between the balanced feedpoint of the dipole and the seemingly single-ended construction of the coaxial cable.

+
+ +
+

Fig. 1 presents one traditional way to portray the situation at the dipole feedpoint. Its general purpose is to show why the insertion of a balun is important as a precautionary measure in dipole construction. By extension, the situation applies to any split element fed by coaxial cable. The dipole is merely the most fundamental case.

+

At any given instant, the currents between the coaxial cable center conductor and the inner side of the shield or braid are equal and opposite. However, according to the graphic, once the cable terminates at the dipole feedpoint, the current has multiple paths of travel. The diagram suggests that the center conductor has only a single path: the left leg of the dipole within the figure. However, the current from the braid has 2 paths: the right leg of the dipole in the figure and the outer side of the coaxial cable braid. The function of the choke is then to attenuate so far as possible the current that would appear on the coaxial cable braid outer side. It performs this function largely by introducing a large inductive impedance to such currents. The function is similar to that of an RF choke within an amplifier circuit. However, the arrangement must have a form that does not disturb the currents between the center conductor and the inner side of the cable braid.

+
+ +
+

As suggested by Fig. 2, we then have 2 sets of currents to consider. The left portion not only portrays the current as directional, but also indicates the field between the center conductor and the inner side of the braid, so that we have at any point of measurement currents of equal magnitude but opposite polarity or phase angle. These are transmission-line currents in the conventional sense. If we replace the resonant antenna with a resistor of vanishingly small dimension (but still capable of converting the RF energy into heat without self-destruction), we should measure only transmission line currents at any measurement point. If we place a complex load of similarly small lumped components at the cable end, we shall obtain the same results, although the lack of a match between the cable characteristic impedance and the load will alter the pattern of current values along the line.

+

On the right in Fig. 2, we have the common-mode currents that appear on the surface side of the coaxial cable braid. Common-mode currents in theory may derive from either conductor, but always appear on the coaxial cable outer side due to skin effect. Therefore, in theory, the current on the braid outside side is the sum of currents other than transmission line currents on the entire coaxial cable structure. Since the transmission-line currents are equal in magnitude but opposite in phase angle, they cancel. The common mode currents are the remainder, whatever their source. Because common mode currents appear on the braid outer side, they are capable of radiation, just as the current on the antenna legs proper. Because those currents may appear all along the coaxial cable length, they may also be found at the transmitting equipment, where the cases form an irregular extension of the coaxial cable outer side. (Note: many writers would simply refer to the coaxial cable braid outer surface. However, at any frequency, there is always some depth to the current-conducting portion of the braid. Hence, I have used the term "outer side" instead. The depth of penetration, of course, is a function of frequency.)

+

The feedpoint of a dipole element represents a small gap in the antenna. Between the terminals of the gap, the feedline provides a series source of energy for the antenna, thus completing the path between those terminals. This very basic fact is important, because it drives the conventional method of trying to model the effects of common mode currents within both NEC and MININEC antenna modeling software. Neither software core is capable of physically modeling conventional coaxial cables. The transmission line function within NEC creates lossless non-radiating mathematical models of lines and hence cannot capture common mode radiation. Therefore, the method used to show common mode radiation is to place a third leg into the dipole. Its feedpoint end connects as closely as possible to one side of the feedpoint segment or pulse, depending upon the software used.

+

In these notes, we shall not question the appropriateness of the model as a means for effectively modeling common-mode currents on a coaxial cable feedline. That discussion belongs to another context. Within the prescribed modeling effort, there are a number of modeling issues that deserve review.

+

Modeling the "Coax" Wire With a Dipole

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Therefore, let's begin with a simple dipole that is resonant at 29.97925 MHz, where 1 wavelength = 10 meters. If we use 1-mm diameter wire and make the dipole 0.485 wavelength (4.85 meters), the antenna will show a free-space resonant impedance in both NEC and MININEC. The MININEC model will use 30 segments so that the center feedpoint falls on a pulse. The corresponding NEC model uses 31 segments so that its center feedpoint falls at the center of a segment. Both models show a free-space gain of 2.14 dBi. The reported MININEC source impedance is 71.84 - j0.56 Ohms, while the reported NEC-4 source impedance is 71.99 - j0.43 Ohms. The two values are close enough to qualify the models as the same for the purposes of the exercise to follow. The MININEC software used here is Antenna Model, while the NEC-4 software is EZNEC Pro/4.

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We shall try to model the coaxial cable using a 6.35-mm (1/4") diameter wire connected as close to the model source as possible. The conductor size corresponds roughly to the outer diameter of the braid in such cables as RG-58 and RG-8X. For the exercise, we shall use a third-wire length of 0.25 wavelength (2.5 meters). For the purposes of the exercise, the wire will run from its connection point straight downward, relative to a horizontal dipole. In modeling terms, we construct the dipole proper in the X-Y plane, with the third wire representing the coaxial cable modeled along the Z axis. Fig. 3 shows--for the MININEC model--the difference between the simple dipole and the dipole plus its "coax" wire. The outline of the NEC model would be similar.

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The diagram does list the ends of each wire. That aspect of the figure will change as we move from one model to another. Fig. 4 shows why, at least in part.

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The MININEC model places a source on a pulse, which occurs at the junction of two segments or wires. Since a junction of segments or wires contains an ambiguity relative to which of the segments has the pulse, the convention is to place the pulse on the higher-number segment (using an absolute segment count). Hence, the source pulse appears in the MINNEC model in the middle of Fig. 4 on the second or right-leg wire of the dipole. In order to calculate current correctly, we must bring both wire 1 (the left dipole leg) and wire 3 (the coax wire) together so that both wires have end 2 at the junction of wire 2, end 1.

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The model that we have just described brings the coax wire as close to the source as is possible. Presumably, this procedure adheres most closely to reality, as earlier described. The alternative modeling procedure in the lower part of Fig. 4 creates a 2-segment center wire for the dipole itself. The coax wire connects to one side of the center wire. We shall use this model only briefly to make a comparison near the end of these notes.

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In a NEC model, we cannot connect a coax wire directly to the source point. As the upper part of Fig. 4 shows, the source occupies a segment, and by convention, we mark this fact by placing the source indicator in the center of the segment. At best, we must connect the coax wire to the segment or the wire junction occurring at one or the other end of the source segment. Since every segment has a definite length, the coax wire junction will be offset from the true center of the dipole. Part of the exercise will be to explore the effects of that offset. In this case, the source appears on the last segment of wire 1, which extends past the dipole center so that the source segment is centered within the overall dipole length.

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NEC is sensitive to having the source segment be equal in length to the adjacent segments. The closer we can come to meeting this condition, the more accurate will be the reported source impedance. Hence, for both MININEC and NEC models, the goal was to use segment lengths as close to equal as feasible within the overall 30/31 segment structure of the 4.85-meter dipole.

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Some MININEC Results

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The MININEC model, as suggested by Fig. 4, uses 3 wires. The 1-mm diameter dipole wires are equal in length, and each has 15 segments. The length of the individual segments is 161.667 mm. The 6.35-mm-diameter coax wire is 2.5 m long and also uses 15 segments. Hence, the individual segments are 166.667 mm long, about 5 mm longer than those in the dipole.

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The following table summarizes the reported characteristics of both the dipole alone (reference to "dpl1" on graphics) and the dipole with its coax wire added (reference to "dpl4" on graphics). AGT refers to the average gain test value.

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+MININEC Models:  Standard Dipole vs. Dipole Plus Coax Wire: Free Space
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+Model          Maximum Free-Space   Source Impedance     AGT
+               Gain dBi             R+/-jX Ohms
+Dipole         2.14                 71.84 - j 0.56       0.9999
+Dipole Plus    2.04                 45.68 - j12.85       0.9994
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The currents on each side of the source segment of the standard dipole are, of course, exactly equal for the symmetrical element. However, for the dipole + coax wire model, we find the following values. W1e2 means wire 1, end 2, etc. W2e1 is the source pulse for the antenna.

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+Relative Current Levels at the Dipole + Coax Wire Feedpoint: MININEC
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+            Current Components            Current Magnitude/Phase Angle
+Wire/End    Ireal          Iimag          Imag             Iphase
+W2e1 (SO)   1.00000E+00    0.00000E+00    1.00000E+00       0.000
+W1e2        3.01968E-01   -3.47609E-01    4.60453E-01     -49.019
+W3e2        6.98032E-01    3.47609E-01    7.79795E-01      26.473
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The real and imaginary components of the non-source wire ends add up to equal the current value of the source-wire end. The model, then, carries with it the presumption that the current on one side of the source pulse divides between the two existing wires on the other side. The wires are all lossless in the models. The higher current on the coax wire is a function of its greater diameter, its greater length, and the non-linearity of its direction relative to the dipole. MININEC does not have the NEC limitation relative to junction of wires having different diameters, as indicated by the AGT score of the dipole + coax wire model. Hence, the model's reported values require no correctives.

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Fig. 5 presents the 3-D patterns in free space for both the simple dipole and the dipole + coax wire models. The simple dipole "donut" pattern is useful for reference in gauging the differences that are part of the dipole + coax wire pattern. To what degree the pattern bulges appear in the pattern of the antenna over a real ground requires that we revise the model. So I moved the dipole to place it 1 wavelength (10 meters) above average ground (conductivity 0.005 S/m; relative permittivity 13). The open end of the coax wire is now 7.5 m above ground. The following table summarizes the performance data for the simple dipole vs the dipole + coax wire.

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+MININEC Models:  Standard Dipole vs. Dipole Plus Coax Wire: 1 WL Above Average Ground
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+Model          Maximum    TO Angle     Source Impedance
+               Gain dBi   degrees      R+/-jX Ohms
+Dipole         7.65       14           70.29 - j 5.62
+Dipole Plus    6.68       14           45.11 - j14.75
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Fig. 6 presents azimuth and elevation patterns for both antennas. In order to gather a feel for the maximum gain reduction associated with the dipole + coax wire model, focus on the pattern places marked "Note." In the azimuth pattern, note the shallower nulls off the dipole ends, with the side toward the coax wire being shallower than the opposite side of the pattern. As well, in the elevation pattern, note the shallower null between elevation lobes. Energy that creates these shallower nulls is not available in the main bi-directional lobes that determine the maximum gain of the antenna.

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Some NEC Results

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As shown at the top of Fig. 4, the NEC model must have a slightly different structure relative to the MININEC model. The standard dipole uses 31 segments, each 156.452 mm long. The source is on segment 16 at the exact center of the dipole. When we add a coax wire, it must be at a junction of wires or segments. For simplicity within EZNEC, I cut the dipole wire into two pieces. Wire 1 is 2.503226 m long and has 16 segments. The source is on the last segment of this wire. Wire 2 is 2.346774 m long and has 15 segments. As a result of this division, the segment length remains unchanged and is the same on both wires. The coax wire, wire 3, begins at the junction of wires 2 and 3 and runs downward for 2.5 m. It uses 16 segments, each of which is 156.25 mm long, very close to the length of the segments in the dipole wires.

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The dipole + coax wire model contains two problematical features. First, the junction of the coax wire and the dipole wire is displaced from the exact dipole center by half the length of a model segment. Second, the coax wire, with a diameter of 6.35 mm, differs from the 1-mm diameter of the dipole wires, creating an angular junction of wires with dissimilar diameters. NEC has a known limitation in such cases, and the error is greater in NEC-2 than NEC-4. The following table summarizes the free-space performance reports of the 2 cores for both the simple dipole and the dipole + coax wire models. There is no significant difference between NEC-2 and NEC-4 with respect to the simple dipole.

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+NEC Models:  Standard Dipole vs. Dipole Plus Coax Wire: Free Space
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+Model          Maximum Free-Space   Source Impedance     AGT       AGT-dB     Corrected
+               Gain dBi             R+/-jX Ohms                               Gain dBi
+Dipole         2.14                 71.99 - j 0.43       1.000      +/-0.0    2.14
+Dipole Plus
+  NEC-4        1.72                 44.95 + j16.99       0.958      -0.19     1.91
+  NEC-2        1.66                 45.70 + j17.33       0.943      -0.25     1.91
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The source resistance of the models is close to the value for the corresponding MININEC value. However, the reactive component of the source impedance is about 30 Ohms distant from the MININEC value. Therefore, I created the alternative MININEC model shown in Fig. 4. In this model, the junction of the coax wire is 1 pulse/segment away from the source. All of the segments in the dipole portion of the model have the same length. Placing the junction another half-segment-length away from the source has interesting consequences. First, the free space gain of the model is 1.92 dBi, virtually the same as the corrected gain values for the NEC-2 and NEC-4 models. Second, the source impedance report is 45.99 + j32.94 Ohms. The resistive component has not changed by much, but the reactive component is considerably more inductive than the NEC reports. The junction position of the coax wire with the dipole wire, relative to the source, appears to make a consistent and systematic difference to the reported reactance at the source.

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The current reports for the NEC model also differ from those emerging from MININEC. NEC currents refer to specific segments, with the segment center taken as the virtual read-out position. The source segment current by assignment was 1 A RMS (the convention used within EZNEC software). Since the NEC core uses peak values, the NEC output report shows a corresponding value of 1.4142E0 as the peak value. The comparison of values must use the segment current on each side of the source segment. Hence, the perfect addition that we experienced with the MININEC model is not likely to appear. The question is to what degree we find the current division holding to the MININEC model standard. The following table tells us some of the story. The source is located on wire 1, segment 16. Wire 1, segment 15 is the adjacent segment on the dipole side without the coax wire. Wire 2, segment 1 is the first segment of the remainder of the dipole that meets with wire 3, segment 1, the first segment of the coax wire. The values are for NEC-4

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+Relative Current Levels at the Dipole + Coax Wire Feedpoint: NEC-4
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+               Current Components            Current Magnitude/Phase Angle
+Wire/Segment   Ireal          Iimag          Imag             Iphase
+W1s16 (SO)     1.4142E+00    -3.4217E-16     1.4142E+00        0.000
+W1s15          1.4047E+00    -7.9009E-03     1.4047E+00       -0.322
+W2s1           3.0643E-01    -3.9072E-02     3.0891E-01       -7.226
+W3s1           1.1108E+00     3.0984E-02     1.1112E+00        1.598
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The sum of the coax-side real current components is 1.4172E+00, which is only slightly higher than the real current on W1S15. The sum of the imaginary components is -8.088E-03, very close to the imaginary component on W1S15. Within the limits of the model adequacy, as indicated by the less-than-perfect AGT score, the currents add up correctly to indicate a current division on the coax-wire side of the dipole. However, relative to the MININEC model, we find two anomalies. First, the ratio of coax wire current to dipole wire current in the NEC-4 model is about 3.62:1, whereas in the MININEC model, the ratio is about 2.31:1. This difference is likely due to a combination of the position of the wire junction relative to the source position and the error introduced by the junction of wires with differing diameters.

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The second anomaly between the cores is less easily explained. The MININEC model showed widely divergent phase angles between the currents on the dipole and coax wires: -49 degrees and +26.5 degrees, respectively. The NEC-4 model shows only a small divergence of the same current phase angles: -7.2 and +1.6 degrees, respectively. It is likely that the lack of coincidence between the wire junction and the source forms the ultimate reason for the small difference in phase angles within the NEC-4 models. The lack of coincidence of the phase angles would require careful measurement of an actual antenna situation in order to decisively tell us which modeling core provides the more realistic report.

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Over real ground, using the same conditions as in the MININEC model, we obtain similar results, as shown by the following table. The dipole + coax wire model uses NEC-4 data.

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+NEC Models:  Standard Dipole vs. Dipole Plus Coax Wire: 1 WL Above Average Ground
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+Model          Maximum    TO Angle     Source Impedance
+               Gain dBi   degrees      R+/-jX Ohms
+Dipole         7.64       14           70.68 - j 5.64
+Dipole Plus    6.08       14           45.28 + j14.69
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Fig. 7 provides comparative simple dipole and dipole + coax wire azimuth and elevation patterns. The simple dipole patterns--as well as the tabular data--are virtually identical to those for the corresponding MININEC model. The gain data for the NEC model of the dipole + coax wire is 0.6-dB lower than in the MININEC model, a value that exceeds the free-space AGT correction factor. However, the pattern elements that reduce maximum gain relative to the simple dipole are evident in the figure. Of course, due to the position of the source relative to the wire junction, the azimuth pattern shows a reversal between the deeper and shallower nulls off the dipole ends. The patterns also show the relative strengths of the vertical and horizontal components of the total far field.

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Some Tentative Conclusions

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The test models use an artificial situation to allow some detailed comparisons between MININEC and NEC models of a dipole + coax wire. The MININEC version of the model, using the highly corrected Antenna Model implementation of the core, still requires careful construction in order to effectively model the coax wire as an alternative path for currents right at the feedpoint of the dipole. NEC has several limitations that prevent such exacting models, including the source placement within a segment rather than at its junction and the weakness of its ability to handle angular junctions of wires having dissimilar diameters.

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The results show both areas of correspondence and divergence. The resistive component of the source impedance shows a good correlation between models, although the reactive component is apparently sensitive to the position of the wire junction relative to the source. Gain and pattern values are comparable, if we allow for the imperfect AGT scores of the NEC models. Perhaps the greatest divergence appears in the reported current phase angles on the joining coax and dipole wires, along with the reported ratio of currents in each wire.

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The exercise has aimed to compare NEC and MININEC models attempting to capture the coax braid as an alternative path for antenna currents. As such, it sets up an artificial and simplified situation. Any complete model of the situation must include all of the factors shown in Fig. 8. Indeed, the list of factors is incomplete, but suggests that modeling the coax wire is not a simple task. Any results that presumes an open-ended wire termination will be suspect with respect to reality. Even a high-impedance choke or balun added to a line at the end of a 1/4 wavelength coax run will not necessarily terminate the common-mode currents, since the antenna element impedance is also very high at that point. Nothing short of a complete model will do for modeling an actual situation.

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Throughout, I have referred to the currents on the outer side of the coax braid as common mode currents. It is not wholly clear that the usage is correct, if we conceive of such currents as an alternative path for the current on the inner side of the braid at the junction with the antenna feedpoint. However, since common-mode currents will appear only on the outer side of coax braid, they are in some respects indistinguishable from what we might otherwise call "alternate-path" currents.

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Whether the alternate-route portrayal of these currents is complete in itself may rest on the measured feedpoint impedance of the dipole with the coax attached. (For a related set of experiments measuring dipole element and coax braid currents, see Roy Lewallen, W7EL, "Baluns: What They Do and How They Do It," The ARRL Antenna Compendium, Vol. 1, pp. 157-164.) In the test situation, we find a very large difference in the resistive components between the simple dipole and the dipole + coax wire models, regardless of the modeling software used. Confirmation of the simple alternate path scenario is as simple as measuring the impedance in the coaxial cable at the termination of the 0.25 wavelength line (without introducing any paths to ground or other disruptive conditions) and then back calculating to the actual feedpoint impedance at the dipole feedpoint.

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The situation does demonstrate that modeling is not an end in itself. In many situations, the results of modeling require experimental confirmation, if only to show that a model either is or is not a model of the situation under analysis. Unlike the present model set--with the definite difference between the source resistance of a simple dipole and of the dipole + coax--not all proposed models present clear cut cases for deciding whether or not the model captures a given electrical situation.

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Go to Main Index

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101. Modeling the Un-Modelable

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L. B. Cebik, W4RNL

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An alternative title for this episode might be "The Intimate Connection Between Modeling and Measuring--Both Before and After Modeling." With appropriate measurements before modeling, we can sometimes model structures that are technically outside the range of what NEC models best: bare round wires. We cannot model everything successfully, but by making some pre-modeling calibration measurements, we can model a good bit more than we might initially think. Let's see if we can approach the subject in a roughly systematic manner.

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NEC Limitations

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NEC (both -2 and -4) employs algorithms that presume thin round wires. When we model antenna structures that make use only of round wires, we tend to assume that the program is accurate. Often, we assume too much, forgetting that NEC has limitations. Tapered diameter elements plague NEC-2, and extreme tapers can lead to some errors even in NEC-4. Angular junctions of dissimilar diameter wires also lead to errors, and the Leeson corrections that apply to linear tapered diameter elements will not work. As well, the correctives will not work with mid-element loads or transmission lines that disrupt the current stepping from one segment to the next. Some angular junctions of wires with dissimilar diameters can also create a few problems. For example, a fat monopole with a set of thin radials at right angles to the main element tends to model accurately. However, sloping the radials tends to create errors.

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For these common cases, we have tests internal to NEC for evaluating and sometimes correcting errors created by at least mild cases of surpassing the round-wire limitations. The Average Gain Test, described in at least 2 past episodes, provides a model-adequacy figure of merit. For a lossless version of the model in free space, a value of 1.00 is ideal (2.00 if tested using a perfect ground). Anything less than 1.00 or greater than 1.00 indicates a level of inadequacy. The greater the departure from the ideal value, the less adequate the model. For some purposes, we can convert the Average Gain Test value into a correction for the reported gain value and for the reported feedpoint resistance value. For structures that include anything more than linear elements, the Average Gain Test is required. However, the Average Gain Test is a necessary and not a sufficient condition of model adequacy.

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NEC also comes with considerable advise on obtaining accurate results. For a given linear element, all segments should be the same length. This good-modeling practice is especially important in the region of the source. The source segment should be the same length as the adjacent segments. If wires are closely spaced, the segment junctions should align as closely as feasible for highest accuracy. The segment length should be several times the wire radius. As we create ever-narrower angles, we run risks of adjacent wire surface penetrations that may adversely affect accuracy. This quick scan of some of the normal round-wire modeling guidelines is just a reminder of the total list of good modeling practices.

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Even following all of the guidelines, we can still run into situations that defy the precision we tend to assume for models of dipoles and simple Yagis. Consider a right triangle with three sides having different lengths. Now feed the antenna at the most acute angle. Even with perfect proportions--that is, with identical segment lengths throughout--the model may not converge. The chief indicator of the fact that something is amiss is the fact that if we alternatively provide the model with a standard voltage source and then an indirect current source, we may obtain different feedpoint impedance values. This model prevents the source segment--or even the source-segment pair--from obtaining equal current levels in the segments immediately adjacent to each end of the source segment or segments.

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This brief review of some--but by no means all--NEC limitations is not designed to cast aspersions on either of the most-used NEC cores. Rather, the catalog does no more than record that NEC has something in common with all software that makes highly complex calculations: the software has limits and ways to determine in large measure how close to those limits a given model might be.

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Types of Models

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Over the years, I have developed some general categories of modeling efforts to flag what models may be good for. The borders between categories are judgment calls that perhaps only experience can certify. Nevertheless, they may be useful to illustrate the levels at which modeling may be useful.

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1. Design Models: the "design-model" category is reserved for antenna models with an existing track record of construction and testing to the model specification. The correlation between model and physical reality is sufficient to build directly from the dimensions specified in the model. Such models, of course, have passed all internal adequacy tests. In addition, they carry with them a set of physical correlation instructions or limitation notations. For example, a model may specify that it is for a non-conductive or well insulated/isolated support boom.

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The design category has very high standards, but is not at all unusual. From some Moxon rectangle and monoband quad designs that have been modeled by equation, many implementations have successfully emerged without the need for more than routine initial set-up procedures. The model of a 50-Ohm Moxon rectangle with uniform-diameter elements can be set up for design by entering only the element diameter and frequency. See Fig. 1. Numerous Yagi designs guide commercial production in several countries. Going beyond the limits of NEC, hybrid programs are yielding wireless antenna designs of all sorts.

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The design category also includes the other side of the modeling coin--analysis. Recently, I examined data on an interesting small antenna and was able to replicate the design and the test results. Some matters, difficult to measure in the test set-up, move from presumption to confirmed analysis status by virtue of the reliable model produced. One need not begin with a model: instead, modeling often serves as a supplementary analytical tool, not to mention as an educational tool when rightly used.

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2. General Guidance Models: models provide general guidance when they are reliable as models, but not necessarily models of an antenna that either exists or will be built exactly as modeled. The models meet all rigorous standards of adequacy, but do not have a direct correlation to any particular existing or anticipated set of construction processes.

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General guidance models require further design effort to move to the design-model category. The model would have to take into account significant appurtenances that may affect RF performance in the physical implementation. These added factors may range anywhere from a simple change of materials to lumpy brackets and other hardware within the mutual coupling range of the elements.

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Nonetheless, since the models are known to be reliable, they often serve as the basis for systematic modeling studies. Since one may create a sequence of models more efficiently than a sequence of test antennas, the relationship between the model and a test situation is normally not a 1:1 affair. Instead, models may identify key test points to confirm or disconfirm modeling trends that emerge from the study. As well--and as more than a mere incidental--general guidance models often save prototype and test efforts from any unproductive byways. As well, they often turn up unexplored directions in antenna work and provide a first-order quantification of information that has hitherto been only anecdotal. Such was the case, judging by the feedback, from some notes I produced on the loss "knee" frequency and the patterns of a typical terminated wide-band "folded dipole." See Fig. 2 for a sample pattern.

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3. Proof-of-Principle Models: This special category of model may be difficult to place properly with an example or two. Consider the gamma match (or the Tee match) used extensively in Yagi design and elsewhere. Ordinary procedures for building such a match employ gamma match tubing or rod that is much smaller in diameter than the elements to which it is attached. NEC does not handle well very closely spaced wires of different diameters and lengths, even when one carefully aligns the segment junctions. As well, there will be angular junctions of wires having dissimilar diameters. To model a gamma match and remain within the boundaries of what NEC does well, one must use gamma rod, connecting rod, and element diameters that are equal. The proportions required for this model do not correspond to normal Yagi construction, but do fall well within gamma match calculations. See Fig. 3 for a rough outline of the differences. Hence, one may not be able to model a given gamma match in NEC, but one can model a gamma match to prove the principle of the matching system as a physical construct and to examine certain properties, such as the currents along the gamma rod. (For a better correlation between models and physical implementations of gamma-matched antenna elements, a well-calibrated version of MININEC is often superior.)

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Consider next a solid-sheet fan dipole that might be used at UHF frequencies. The antenna may be too small for effective wire-grid construction, and even a wire-grid may prove problematical in terms of reflecting accurately the current distribution on a fan. One may approximate such a fan as a wire outline, as suggested in Fig. 4. The outline fan may not have the full frequency range of the solid-surface fan, but it will exhibit a good part of the broadband effects. Hence, in comparisons with other types of elements that might be used in an array, it can provide a proof of principle of those effects in a complex array, but is not quite satisfactory for full general guidance or design-level work.

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Proof-of-principle models do not have relaxed standards as models. Indeed, to serve as a proof of a principle, they need to be fully adequate as models within the software system being used. As well, the modeler must have enough knowledge of the system being modeled in principle to be able to specify both the correlations to and departures from reality, plus enough understanding of the principles themselves to be able to show that the model falls within the limits of those principles. Proof-of-principle modeling is not simply a matter of approximating an antenna system or getting into a ballpark estimate of what is happening. There must be a reasonably well-understood relationship between the models and physical antennas to be able to confirm that both fall under the same principles of operation. Theoretically, every proof-of- principle model should be susceptible to physical replication and testing, even if no one actually conducts the test.

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4. Suggestive Models: Sometimes it is not possible to construct a model that rigorously meets all internal standards of adequacy, but it may come close. In such borderline cases, the model may give every indication that over some part of the of the reported output data, there are reliable trends, even if the specific numerical data for any single item fail to meet reliability standards. Such models--when accompanied by a carefully wrought justification and set of limitations--may be used as suggestive of directions for further study.

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I recently approximated a Brown-Woodward bent fan dipole within a corner reflector array. The AGT value for the construct was too far from perfect for high confidence in it as a model of the actual driver. However, the relationship between the planes of the modeled version and of the corner reflector surface yielded some interesting impedance curves, especially when compared to standard fan and linear dipoles. See Fig. 5 for a sample of these curves. At most, these curves are suggestive of how the driver manages to widen the bandwidth of the corner array, but they are not adequate yet as proof-of-principle models.

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Categorizing modeling results requires a level of judgment that comes from long experience and solid familiarity with the foundations, procedures, and limitations of antenna modeling within a given software system. The process also requires solid familiarity with antenna theory and practice, as well as construction and testing techniques and practices.

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Physical Post-Modeling Testing

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I have briefly and incompletely reviewed some of NEC's limitations for two reasons. First, for a large number of modeling enterprises that fall well within the well-known limits of the core, we approach the exercise without thought to the limits. As a result, we tend to assume that the results are accurate to the realities of a physical implementation of an antenna design. That assumption is, of course, a dangerous temptation if we carry it outside the region of well-verified results. Second, even when we do not make assumptions about the correctness of NEC reports relative to corresponding physical antenna structures, most modelers reserve testing and measurement activities to post-modeling exercises. That is, they create a modeled design and then build a prototype to match the model and test its performance.

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Post-modeling physical testing is extremely important, and I have no intent to reduce that importance in these notes. However, we do tend to encounter two distinct groups of individuals whenever the measured results for a physical antenna do not agree closely with the reported results for the model. One group tends to almost automatically presume that there is something wrong with either the model or the software. The other group tends to presume that there is something wrong with the physical prototype.

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In principle, either possibility may be correct, but never as a presumption. In most cases, those who conduct the physical construction and testing of an antenna are not the same individuals who do the modeling. In sundry consulting activities, I have discovered that one of the chief causes of disparity between test measurements and modeling results is a failure of communication. When communications are clear, concise, and complete, virtually all dissimilarities between test measurements and model reports tend to dissolve.

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Dissolution of disparities tends to come in two forms. The first is a refinement of both the testing and the modeling structures and environments so that one can say that the modeled antenna is a very close analog of the physical antenna--and vice versa. The second form of removing conflicts between a model and a physical antenna is a comprehensive understanding of differences between the two. A physical Yagi may connect the elements to a conductive boom, with resultant changes in the required element lengths relative to a model. A model may involve geometric structures that require reference to and correction by the Average Gain Test value for gain and source resistance values. In many cases, apparent differences between a model and a physical antenna may disappear under appropriate calculation to adjust for those differences.

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The logic of this situation makes measurement a post-modeling activity, regardless of the temporal order of the modeling and the field testing. Equally, we might call the situation one of post-construction testing against a model. Consider Table 1.

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The table provides parallel columns of values for the length of a dipole resonant at 146 MHz. One column lists the measured value of the length of round elements trimmed to resonance. The other column lists the length of modeled dipoles trimmed to resonance within the software. It makes no difference which activity comes first in time. We simply cannot make a comparison until we have both columns filled in.

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Pre-Modeling Physical Testing

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There are a number of situations that NEC cannot directly model, many of which involve the proximity of the conductor with a non-conductive material. Of course, NEC-4 is able to model wires having an insulated sheath. Fig. 6 illustrates the dimensions involved and shows the parameters involved, as listed on a GNEC assistance screen. NEC-2 lacks this facility, but there is a work-around that is applicable in many situations. See episodes 50 and 83 for further details of modeling insulated wires with NEC.

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The questions of NEC's ability to model a structure emerge from situations other than the simple insulated wire. Fig. 7 shows some typical cases that have often occasioned e-mail questions.

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The situation that invites the most inquiries involves the left-most sketch, where a relatively thin and flat conductor is bonded to a non-conductive substrate. In fact, NEC has no direct means of dealing with this "PC-board" style of structure, although the use of such materials is common in the UHF region. First, the conductor is not round, and there is no standard list correlating flat strip surface areas to the surface areas of round conductors, at least not in any reliable way. Second, the substrate represents an insulator having a thickness, a relative permittivity, and a conductivity, but bonded to only one side of the conductor. Hence, we can assume that some sort of electrical lengthening occurs, but we cannot say in advance what the velocity factor will be. When we combine the two problems, we usually end up in a quandary about effectively modeling subject antennas without investing in very expensive hybrid software.

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The problem set may increase for many antenna designs adapted to printed circuit board materials. For example, a Yagi or a log-periodic dipole array may etch the elements on a single plane so that the adjacent elements expose their thin edges to each other. In addition, the substrate may fill part of the region between the elements, at least on one side of the plane of the element strips. Consequently, the substrate material plays a role not only in determining the electrical length of the elements, but as well in their mutual coupling.

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The situation of the center sketch in Fig. 7 often occasions questions, but is in fact quite simple. A number of antenna builders--mostly to use local materials--apply conductive tapes around non-conductive round structures and thereby form antenna elements. The sketch shows one typical case in which the tape completely circles the support and forms a closed cylinder. In this case, we may treat the element as a wire having the outer diameter of the tape surface. Of course, this assumes that the tape forms a fully complete and closed circle around the central support. The result is not dissimilar to the copper-clad steel wire known as copperweld. That steel has some conductivity and the central support for the tape has little or none matters not at all, since the RF currents will be near the surface in both cases.

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The right-most portion of Fig. 7 changes matters considerably. We still have a central support and an overlay of conductive tape. However, the conductive surface does not form a complete circle around the center material. If the circle is almost closed, then the element may act as if it were closed. However, if the gap is wide enough, then the semi-circle of tape may act more like the left-most figure. To the best of my knowledge, there are no handy guidelines for converting various forms of the right-most figure into equivalent round-wire values for modeling.

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There are methods for creating a conversion table between the structures on the left and right in Fig. 7 and round-wires values that we may model. They involve preliminary test antennas to determine the round wire-equivalent values for a given physical structure. One technique is simplicity in itself: create a dipole at the frequency of interest for the material and then find its corresponding round-wire equivalent diameter for resonance at the same element length.

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Fig. 8 shows a variety of shapes of alternative materials used for antennas in the amateur 2-meter band. Most of the materials come from hardware outlets. Builders use some of them because they are locally available. In some cases, builders find stock with flat surfaces easier to work. A few materials, such as measuring tape or rabbit ears, may have special features useful in transporting the antenna or using it in rough terrain.

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Prior to modeling, we may calibrate any of these materials to a selected round-wire diameter by using the dipole-resonance technique. Table 2 lists some results of measurements made locally at 146 MHz with some typical materials. Each material lists the resonant length and the round wire diameter with the most similar length from Table 1.

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The sample tables are for 146 MHz. It is not known how far from the listed frequency that the equivalencies would apply. For example, stock that is 1/16" thick is about 7.7e-4 wavelength at 146 MHz but only about 7.4e-5 wavelength at 14 MHz. Whether that change in relative thickness brings the 1/16" stock down to measuring tape thickness requires a re-run of the tests for the frequency of interest.

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Although the pre-modeling test runs are useful for independent elements, the tests have additional limitations besides their potential frequency restrictions. For arrays in which mutual coupling between elements is critical, very flat and wide stock may show some differences depending upon whether the elements are edge-to-edge or flat-to-flat. As well, without specific pre-modeling tests, one cannot know the effects of a continuous substrate on the mutual coupling between elements. However, with proper equipment, such tests are possible and may lead to round-wire, open-space equivalents.

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Desite the limitations, the exercise does demonstrate that all is not lost with respect to modeling if we use materials other than the round wires upon which NEC's algorithms are based. One question is whether all of that work is worth the effort. In most cases, of course, pre-testing or calibration of materials will be confined to only a few selected candidates. As well, once a material has found its round-wire equivalent diameter, then we may construct relatively diverse and complex arrays within the models and reserve prototype testing until we are satisfied with the modeling results. Hence, when we view the design of an antenna as a full-scale activity set, the modeling saves enough time to make the pre-testing phase well worth the effort involved.

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Conclusion

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We began with the idea that there is an intimate connection between modeling and measurement that extends from pre-modeling calibrations through post-modeling prototype testing. Modeling does not exist in a vacuum, since its results are either a physical antenna or an understanding of the performance of a physical antenna. These columns have tended to focus on modeling's internal working. However, we should never lose sight of the fact that modeling has an integral place within a larger set of activities that may involve measurement both before and after the modeling itself. As well, with appropriate pre-modeling calibration measurements, we may effectively model many (but not all) materials that would otherwise violate the NEC round-wire premises. Without those pre-modeling measurements, trying to model such materials would amount to mere speculation.

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102. True Azimuth Models
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L. B. Cebik, W4RNL

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After a short time in modeling with NEC, the core conventions become almost second nature. You model the antenna geometry using Cartesian conventions for each wire-end coordinate set. The core data produces phi and theta patterns. A phi pattern counts degrees counterclockwise. A theta pattern counts angles from the zenith downward toward the horizon. The pattern conventions are just the opposite of everyday and field engineering conventions. The latter use azimuth angles, generally counted from 0 at North clockwise. Elevation angles count from the horizon upward toward the zenith. The 2 systems appear in Fig. 1. Phi and theta angles are inside the circles, while azimuth and elevation angles are outside.

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Software implementations of NEC use various means of presenting polar plots. Virtually all commercial implementations of NEC do an easy conversion of theta plots into elevation plots. They simply subtract the theta angle from 90 to obtain an elevation angle. Azimuth patterns are a bit more difficult to handle. For example, EZNEC simply uses the phi conventions, but calls its plots "azimuth." There is a compass plot that we shall work with in a subsequent episode.

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Simple Rotational Models in NEC-Win Plus

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NSI products (NEC-Win Plus, NEC-Win Pro, and GNEC) handle the polar-plot situation in a different manner. They offer the user the option of pairing phi and theta plots or of selecting azimuth and elevation plots. Elevation plots convert theta plots by the usual method. Phi and azimuth plots use the outer-ring angle markings appropriate to each pattern, as shown in Fig. 2.

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By placing 0 degrees at the top of the plot, NSI polar plots can use the very same data, angle-by-angle, for both plots. Whether the plot on the right is a true azimuth pattern depends in part on the symmetry of the pattern. For antennas that produce symmetrical patterns, we cannot tell a true azimuth model from one that is casually modeled in the Cartesian coordinate system.

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There are some modeling tasks that require not just patterns that bear azimuth labels, but as well, true azimuth models. The NSI VOACAP output depends on using compass or azimuth bearings. Broadcast antennas make FCC submissions using azimuth concepts both to describe the antenna and to provide sample patterns. These submissions may include MW BC towers and antennas, or they may involve one or more antennas on a tower--and each such antenna may point in a different direction on the compass. No less complex are some of the fields of antennas used by government, military, and even advanced amateur installations. Hence, it may pay to learn how easy it is to create true azimuth models to make use of the polar plot labels to yield true azimuth patterns. We shall move from that point to creating true azimuth models.

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The process begins by attending to the correlation within NEC of the Cartesian coordinate system to the phi angles (and as a direct consequence, to azimuth angles). Consider Fig. 3.

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The circle on the right is identical to its right-side counterpart in Fig. 1. The circle on the left provides the connection between the coordinates used to set up the model and the polar plots. Zero degrees always corresponds to values extended along the +X axis of the coordinate system. If we select a phi pattern, then the pattern angles count counterclockwise toward 90 degrees phi or toward the +Y axis. The values proceed around through 180 and 270 degrees phi before return home to zero degrees.

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However, if we wish a true azimuth pattern, then we must proceed clockwise in the polar plot, with zero degrees representing North. Moving in a clockwise position toward East or 90 degrees azimuth, we end up at values extended along the -Y axis. From that point, we proceed to South or the -X axis, and further to West or the +Y axis. Finally, we return home to North and zero degrees once more.

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The trick to obtaining a true azimuth model is to set up the geometry adhering to the directions that will eventually yield a true azimuth pattern for the result. For antennas that have symmetrical patterns, such as the pair shown in Fig. 2, the process is simple: extend the boom or direction of radiation from the -X toward the +X direction. That will align the model and pattern toward North, with identical pattern features on both side of the North-South line. Fig. 4 shows a NEC-Win Plus version of a model designed precisely in accord with this instruction. In fact, it is the basis for the patterns in Fig. 2.

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The values in the X1 and X2 columns show that the antenna structure proceeds from a reflector at X=0 toward a director at X=186 (inches, in the case of this 14-MHz Yagi). The elements are linear and extend equally toward +Y and toward -Y. The result is a true azimuth model, and so the azimuth pattern is also true.

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Suppose that we need the antenna pointed Northeast, that is, at 45 degrees azimuth or compass bearing. The procedure is simple and may use more than one means. Programs like NEC-Win Pro and GNEC give access to the GM command. By specifying a 45-degree rotation around the Z-axis, we can effect the change of heading, so long as we remember to rotate clockwise. Since GM rotation would follow the phi conventions, we would specify the rotation angle as -45 degrees.

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NEC-Win Plus (which is also an "insert" within both Pro and GNEC) uses a different method. There is a main screen rotation control labeled with a circular arrow. To use this control, we first block the entire antenna geometry, that is, the entire set of wire entries on the main screen. Then, we click on the rotation button to open a screen that is similar to the help screen in Pro and GNEC for the GM command. One option is to rotate the blocked wires around the Z-axis by a specified amount. For the antenna to point Northeast, we select a rotation angle of +45 degrees. Note: the NEC-Win Plus rotation control around the Z-axis operates in accord with azimuth conventions, not in accord with phi conventions..

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Fig. 5 shows the resulting true azimuth pattern for the rotated beam. By comparing the original and new patterns, we can easily see the success of our maneuver. The result is not only a correct or true azimuth pattern for the antenna, one that includes the correct angular labels. As well, we have a true azimuth model. Fig. 6 shows the wire coordinates of the resulting beam.

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Although inspection may initially make the numbers seem to be a jumble of coordinate values, you may do a little mental math on the center wires for each complete element (wires 4, 19, and 18) to see that the beam's boom extends along a line that is 45 degrees from either axis and that the elements extend at right angles to the boom. On one side of the boom, the end-1 coordinates extend toward +X and +Y, and on the other side, the end-2 coordinates extend toward -X and -Y. Remember that these are directions and hence relative. End-1 coordinates are simply more positive and less negative than end-2 coordinates.

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Suppose that we had 2 identical beams in a stack, one above the other. In such a case, we might wish to see the outcome of rotating one or both beams until there is some desired angular separation in the boom directions. Normally, a stack of Yagis will have each antenna mounted so that the center of mass equalizes the boom-forward and boom-rearward moments. The mounting center will be very close to, but usually not precisely at the center of the boom, as measured from the rear-most element to the forward-most element. For most purposes. we may model the mast position as the boom center.

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To reposition each antenna with a boom-center at coordinates 0,0, we can use one of several procedures. The most straightforward would be to subtract one-half of the boom length (0.5*186 or 93 inches) from each X dimension while the boom is still aligned North and South. A second alternative is the use the NEC-Win Plus translation control and effect a block movement of the same amount on all wires in the model. A third way to the same goal is to use the GM command (if available) to effect a translation along the X-axis by the same amount. If we wish to move the antenna along the boom-line and to rotate it 45 degrees by using the GM command, we must use 2 separate GM commands. The GM command rotates before it translates, but our goal is to translate before we rotate. Hence, we cannot combine the two movements into a single command.

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To create a stack of 2 Yagis from our original model (Fig. 4), we shall illustrate the process by block copying the first antenna and pasting the result below the first 21 wire lines. To effect a vertical separation (arbitrarily 800" for the example), we set the Z-value for 21 wires to that number--or we may use the translation facility to make that move. Next, as shown by the left side of Fig. 7, we shall block all of the wires and move or translate both antennas -93 inches so that each is centered on its boom along the X-axis. The final step, shown on the right in Fig. 7, is to rotate one of the antennas. We block the wire lines for the antenna or 21-wire set of choice and enter the rotation as 45 degrees, remembering that in NEC-Win Plus, the rotation control system operates clockwise.

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The result of the work appears on the right side of Fig. 8. Note that the boom center is close to but not on the coordinate system center (0,0). Had we gotten the order of operations reversed and rotated before translating, we might have stacked the antennas as shown on the left in Fig. 8. The result might not have produced serious errors in this case, but in other cases it might yield very wrong results.

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True Azimuth Models in NEC-Win Plus

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Not all efforts to create a true azimuth model and plot combination are quite so simple as rotating an antenna having a symmetrical pattern. The are many modeling problems in which we begin the process with one or another form of azimuth data describing the geometry of the antennas. We shall explore a couple of simpler cases in order to maintain clarity on the principles involved. Suppose that we had a set of 3 monopoles that are 1/4 wavelength at 1 MHz. Since a wavelength at 1 MHz is 300 m, the monopoles are each 75-m long. Although a real-world exercise might include a buried radial system for each monopole, we shall use a perfect ground for our exercise. As well, the individual antennas have an arbitrary diameter of 0.1 m and use a conductivity appropriate to steel. Also for simplicity, we shall feed the individual antennas in phase.

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In many situations, one monopole may serve as a key against which we determine the positions of the others. We might receive a data list such as the following.

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+Tower         Distance      Azimuth Bearing
+Number        Meters        Degrees
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+  1           ---           ---
+  2           150           060
+  3           300           060
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We shall read this data by using tower 1 as the key, with the subsequent distances and bearings referenced to it. Without much difficulty, we recognize that this system forms a set of 3 monopoles fed in phase, with each monopole spaced by 1/2 wavelength from an adjacent monopole.

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NEC, and most commercial NEC input system, do not allow inputs using distances and headings derived from azimuth or compass data. We still need to translate this data into X and Y coordinates that create a true azimuth model. (Of course, we also need to handle the Z-coordinates, but they will each be 0 at end 1 and 75 at end 2 with meters as the unit of measure.) 60 degrees lies in the first azimuth quadrant. Hence, the towers will form a line between North and East, that is, between the +X and the -Y axes.

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We define the extension along the +X axis by the cosine of 60 degrees (0.5) and the extension along the -Y axis by the sine of 60 degrees (0.866). These two simple trig operations allow us to translate the original table so as to yield corresponding coordinates for each data entry.

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+Tower         Distance      Azimuth Bearing    +X coordinate    -Y coordinate
+Number        Meters        Degrees
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+  1           ---           ---                0               0
+  2           150           060                75              -129.9
+  3           300           060                150             -259.8
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Fig. 9 visually portrays the layout in terms of both the original and the derived data. The figure uses the distance between the towers rather than the cumulative distance from the origin. On the right is an azimuth pattern that confirms the accuracy of our set-up work. +
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Since the pattern is symmetrical across the line formed by the towers, strict adherence to the conventions of correspondence between azimuth headings and coordinates may seem excessively finicky. However, many FCC and other filings require a pattern that accurately reflects the gain (and often the field strength) in all map directions. Hence. a precision model is more than a desire; it is a necessity. Fig. 10 provides a screen view of the resulting model.

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An alternative form of initial data would use each succeeding monopole as a reference for the next. Let's examine such a case, again keeping the background elements simple. We shall retain the steel 0.1-m diameter monopoles and feed them in phase, although they will not form a straight line in this case. In fact, the initial data might take the form of the following table.

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+Tower         Reference         Distance      Azimuth Bearing
+Number        Tower             Meters        Degrees
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+  1           ---               ---           ---
+  2           1                 150           060
+  3           2                 150           030
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We can proceed in a cumulative manner, as in the first problem. However, that route would require us to calculate the end position in terms of a distance and angle from the origin. For the present case, that task is simple, but many other cases might involve solutions to irregular triangles. For now, it is easier to solve the two positions successively. For the second case, we shall initially assume a start at the origin and then simply add the +X and -Y values to the new +X and -Y values to arrive at the final coordinates. To keep the math simple, I selected the 30-degree azimuth heading for the 3rd monopole since the values of sine and cosine are simply flipped relative to the values for the 60-degree heading. The final data table prior to creating the model itself resembles the following one. Remember that the X values are positive and the Y values are negative.

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+Tower         Reference           Distance      Azimuth Bearing    +X coordinate    -Y coordinate
+Number        Tower               Meters        Degrees
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+  1           ---                 ---           ---                0                0
+  2           1                   150           060                75               -129.9
+  3           2                   150           030                204.9            -204.9
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As Fig. 11 shows, we have a bent line of monopoles, each a half wavelength from an adjacent monopole. The line formed from monopole 1 to monopole 3 has an azimuth bearing of 045 degrees. When fed in phase, the array produces the pattern shown to the right (over a perfect ground). Note that, relative to the line of towers if overlaid on the polar plot, the pattern is no longer symmetrical. We might easily contrive any number of non-symmtrical patterns by altering the feedpoint current magnitude and phase angle for each monopole. Fig. 12 provides the NEC-Win Plus model that produces this pattern and arrangement of monopoles.

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It is not necessary to use the first monopole as the key. In fact, in any array, we may set any point as the coordinate center and calculate from that point. For example, consider a system of 6 towers with a virtual center in a 2-by-3 arrangement. If we have the field dimensions and the bearing along the rectangle formed by the monopoles, we can easily calculate the azimuth bearing and distance to each monopole from the field center. With that data, simple sine and cosine operations will yield the required coordinates to produce a true azimuth model.

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Alternatively, we might have a field of rotatable directional beams. We would use the same techniques to locate the coordinates of the center of each beam antenna in the field relative to the point selected as the coordinate center. Since NEC-Win and NEC rotational commands use one of the coordinate axes as the center of rotation, we might have to use a multi-step process to place each antenna in its correct position pointing along the correct bearing. Create the antenna --centered along its boom--at the coordinate center and rotate it to the correct heading. Then move (translate) the antenna to the final position of the boom center at its field location.

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In any complex modeling exercise, it pays to pre-plan each maneuver and set up an order of operations--on paper. Although the exercises just suggested only count as moderately complex, it is still easy to lose track of what move occurs next in the progression. Hence, developing a detailed checklist that includes not just the order of operations, but also the quantities involved in each move, can go a long way toward making the process second nature, smooth, and (most important of all) accurate.

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The key to the effort lies in understanding the relationship between the polar plot in its azimuth form and the Cartesian coordinates that result in a true azimuth model. +X is always North or zero degrees azimuth. Clockwise, East or 90 degrees azimuth corresponds to the -Y direction on the coordinate system.

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Note also that these directions apply to the NSI implementations of NEC. They only apply to other software if that software follows the same conventions for translating a phi pattern into an azimuth pattern. One limitation in some software is to place zero degrees phi on the far right, allowing 90 degrees phi to occur at the top of the polar plot. This system is at odds with standard azimuth conventions in which zero degrees or North is always at the top of a plot. Such systems do not permit us to use the same set of rules for forming a true azimuth model.

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One of the implementations of NEC using the alternative polar-plot set up is EZNEC. Still, the program does have a compass plot facility. In the next episode, we shall explore how to create true azimuth models within the program.

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103. True Azimuth Models
+ EZNEC Software

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L. B. Cebik, W4RNL

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In the first of our 2 episodes on creating true azimuth patterns, we explored NSI software to see how to develop both true azimuth patterns and the models that yield those patterns. Because the NEC-Win polar plot places zero degrees at the top of the plot, the apparent difference between a phi plot (the inherent NEC plot from the radiation pattern tables) and an azimuth or compass plot is simple. The phi plot counts degrees in a counterclockwise direct, while a compass plot counts degrees in a clockwise direction.

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The creation of true azimuth models, however, requires something more from us as modelers. North equates with the +X-axis in the Cartesian coordinate system. Hence, East or 90 degrees azimuth corresponds to the -Y axis. For irregular sets of positions in the X-Y plane, we need to do some careful planning to obtain a model whose geometry produces a correct azimuth plot. Each step in the process is simple enough, even when we receive initial data in the form of distances and bearings. However, we can easily develop a model of moderate complexity and lose track of what comes next. Hence, I recommend a detailed pencil-and-paper procedure for setting up such models.

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Nevertheless, in NSI software, we can in a straightforward way create true azimuth or compass-oriented models that are useful for VOACAP, BC, and large antenna field analyses. In fact, we may do the same using EZNEC software. However, the procedures will not be identical, simply because the polar plot display conventions in EZNEC differ from those used by NSI software. Once we master the conventions applicable to EZNEC, we shall discover that every step possible in one software package is available in the other. They will simply differ in accord with convention differences. One result is that a true azimuth model created for one software set will not be readable as a true azimuth pattern by the other without significant revision of the model geometry.

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Simple Rotational Models in EZNEC

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EZNEC (Version 4) comes in 3 sizes: standard, plus, and pro. The last version is available with either the NEC-2 or NEC-4 core. However, all required functions to create true azimuth models are available on even the most basic version of the program.

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The process of creating true azimuth models begins with an understanding of the EZNEC azimuth plot. In its raw form, without the supplemental data shown, the plot is somewhat opaque, as suggested by Fig. 1. The plot shows the pattern of the same 3-element Yagi used to start the NSI notes, with the boom aligned along the X-axis. Thus, we discover the first difference between NSI software and corresponding EZNEC software. EZNEC places the standard plot zero-degree position on the far right. This procedure allows a pattern that coincides roughly with the normal way of presenting the Cartesian X and Y axes on a flat surface: The X-axis receives a horizontal line and the Y-axis receives a vertical line. In the plot shown, +Y corresponds to the top position of the plot circle.

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Because the plot does not show the degrees on the outer ring of the plot circle, the nature of the plot may not be immediately apparent. There is a data set attached to each plot to record various headings of interest in plot analsis. However, in this plot transfer, the only way to obtain degree markings is to add them with a paint program. Although EZNEC refers to the plot as an azimuth plot, it is actually a phi plot and counts degrees counterclockwise. (The EZNEC elevation plots do count degrees from the horizon upward.) For a myriad of antennas with symmetrical patterns on each side of the virtual boom line, the difference does not make a difference relative to understanding the antenna's operation.

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Among its options, EZNEC does offer a "Compass" plot. The compass plot counts degrees clockwise, with zero degrees positioned at the top of the plot circle. Note that there is a 90-degree difference between the zero-points of the standard plot and the compass plot. If we wish to create a model of an antenna pointed North, we must adopt a new set of convention. Fig. 2 shows the relationship of the plot conventions to the Cartesian geometry conventions.

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Since North corresponds to the Cartesian Y-axis, to point an antenna North requires that we form the model with the boom pointed toward +Y. The revised model will then have its elements extended (for a symmetrical model with linear elements) along the -Y to +Y axis, with East corresponding to the +X direction. If we revise our 3-element Yagi model accordingly, we can obtain both a standard and a compass pattern, as shown in Fig. 3.

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Note that there is no difference between the graphical portions of each plot. The differences appear in the data beneath the plot. The standard plot shows the cursor and the maximum gain heading to be 90 degrees, which we would expect of the phi pattern for a plot oriented 90 degrees counterclockwise to the plot in Fig. 1. In contrast, the compass plot shows the cursor and maximum gain at zero degrees, corresponding to the model's boom pointing North along the +Y axis.

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Fig. 4 provides us with the wire table for the model. If you compare it with the wire table from NEC-Win Plus in the preceding episode, you will find that all X-column Values are now in the Y column and vice versa.

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Let's rotate the antenna 45 degrees toward the Northeast (compass bearing 045 degrees) to parallel the same operation in the last episode. To set up the antenna for rotation, we should first move the wires by 93" so that the rotation point (coordinates 0,0) is at the center of the boom. EZNEC has move and rotate functions comparable to those in NSI software. They appear as options within the wire table array of possible modifications. Just like using the GM command, we must move the wires first and then rotate them. Fig. 5 shows the relevant maneuvers in terms of the assistance screens that appear. To center the antenna along its boom for a compass pattern, we move the wires -93" along the Y-axis or boom line. Then we rotate the antenna 45 degrees clockwise around the Z-axis to move the boom direction from North to Northeast.

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For reference, Fig. 6 shows a composite wire table after each maneuver. The table shows only the end-1 values, with the post-move set on the left and the post-rotation set on the right. If we had wished to place the antenna after rotation at some other position within a field of antennas, we would next perform another move operation, setting the distance along each axis into the appropriate X and Y boxes of the move screen. In EZNEC, it is possible to rotate a wire set around the center of a wire, but this operation would not preserve the centering of the antenna on its overall boomlength from reflector to director. In most cases, making adjustments to a model's position yields an accurate result if taken step-by-step in accord with a plan first noted on paper.

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Having set up the Yagi in true azimuth fashion, we obtain a compass plot that is accurate as a true azimuth plot. Fig. 7 shows the plot, its data, and the outline view of the antenna as its is aligned in the X-Y plane. The plot has its maximum gain at a 045-degree azimuth bearing, although to be certain, we must consult the data below the actual plot. The antenna outline confirms that the plot accurately portrays the antenna performance, given its alignment. It also confirms that we have moved and rotated the antenna correctly in accord with the compass-plot conventions that apply to EZNEC. The view also let's us know that the virtual boom center is offset by a small amount from the center or driver element. The feedpoint circle and the axis center circle do not coincide.

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Since we have turned the antenna after moving it, let's create a stack of 2 Yagis. We shall want the 2 antennas in the stack to point in different directions, perhaps one headed Northeast and the other North. EZNEC provides a variety of ways to create the stack. One way to proceed is to copy the existing wires to create a new set. The next step is to use either the height function or the move function to create a spacing between the 2 sets of wires. For this small exercise, I have selected 800" as the arbitrary separation. We may then rotate the new wires 45 degrees counterclockwise to point them North along the boom. If we wish to test other angles of separation between the antennas in the stack or other separation distances, we can use the move and rotate functions appropriately.

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Since we already have a beam pointing North, we can also import the file description from that model. For identical antennas in a stack, this procedure might be more cumbersome, since we would need to separate the antennas and ensure that each rotated on its boom center. However, there are many exercises in which we may have different antennas in the modeled stack. In that case, importing the added antenna model may prove to be the most practical maneuver.

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The operations to create stacks are available also in NSI software. The spreadsheet main face of NEC-Win Plus allows block copying of the first Yagi into a second version. The translation (move) function then allows us to set the separation. To create a stack of different antennas, we may block copy a set of wires and appended sources and loads from one model file to another. In advanced software that makes the full NEC command set available, we can accomplish the copy and move functions with the GM command.

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The results of our EZNEC stacking operations appear in Fig. 8. Although the wire table is too long to reproduce, the plot, the data, and the antenna model outline should suffice to establish that we have a successful true azimuth model and plot of the stack. I set the radiation pattern increment to 0.5 degrees so that the heading for maximum gain would read correctly (rather than showing the nearest integer value). Since the model is in free space, the maximum gain occurs rather exactly between the headings of the identical beams. Placing the stack over ground might amend the heading of maximum gain due to slightly different ground effects on the two antennas in the stack.

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The are many good reasons for studying the patterns of a stack with the individual beams pointing in different directions--assuming that this condition is among the planned modes of operation. Forward gain of the composite pattern is only 1 of several interesting facets of the stack. You may also wish to compare the beamwidth for a single antenna (66 degrees) with the beamwidth for the stack (77 degrees). Note also the change in the rearward lobes. Then mentally overlay two sets of individual-antenna rear lobes at 45 degrees to each other. Although the two antennas have some interaction with each other, the overlay process goes a long way toward showing the revised shape of the rearward radiation pattern in the stack.

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True Azimuth Models in EZNEC

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To complete our tour of setting up true azimuth models in EZNEC software, we must also tackle the types of situations that we examined for NSI software. There are many modeling problems in which we begin the process with one or another form of azimuth data describing the geometry of the antennas. We shall explore a couple of simpler cases in order to maintain clarity on the principles involved. Suppose that we had a set of 3 monopoles that are 1/4 wavelength at 1 MHz. Since a wavelength at 1 MHz is 300 m, the monopoles are each 75-m long. Although a real-world exercise might include a buried radial system for each monopole, we shall use a perfect ground for our exercise. As well, the individual antennas have an arbitrary diameter of 0.1 m (100 mm) and use a relatively low conductivity. Also for simplicity, we shall feed the individual antennas in phase.

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As we did with the NSI exercises, we may begin with data provides in the form of bearings and distances, perhaps against a map or site plat.

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+Tower         Distance      Azimuth Bearing
+Number        Meters        Degrees
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+  1           ---           ---
+  2           150           060
+  3           300           060
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The system once more consists of the monopole in a line, with 1/2 wavelength spacing between the individual antennas. For the exercise, we shall feed each monopole at its base in phase with the other two monopoles. Because the heading is 060 degrees, the line extends from Southwest to Northeast. If we let the first monopole be the key and place it at coordinates 0,0, then the remaining monopoles will fall somewhere between North and East. Once more, we can make use of the sine and cosine functions of 60 degrees to form multipliers for the distances and derive the proper coordinates. Because the second and third monopoles fall in the first quadrant, both X and Y will be positive.

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Since the Y-axis is North or zero degrees and the X-axis is 90 degrees, the X coordinate will be the sine of the angle times the distance or 0.866 * 150 = 129.9 m. The Y coordinate will be the sine of the angle times the distance or 0.5 * 150 = 75 m. The monopoles form a single line, so the second coordinate set can simply use the cumulative distance for X = 259.8 m and Y = 150 m. The completed table is below.

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+Tower         Distance      Azimuth Bearing    X coordinate     Y coordinate
+Number        Meters        Degrees
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+  1           ---           ---                0                0
+  2           150           060                129.9            75
+  3           300           060                259.8            150
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Fig. 9 provides a visual presentation of the monopole layout against the Y and X axes that form the South-to-North lines and the West-to-East line. The annotated antenna view has been turned so that the axes assume their proper positions relative to an azimuth map. The compass plot confirms that the main lobes of the radiation pattern are broadside to the line of monopoles, with maximum gain at 135 and 315 degrees azimuth.

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Fig. 10 shows the wire table for the model to confirm the use of the cordinates in the tables. As noted in the preceding episode, there are many applications in which precision azimuth pattern are required. Hence, the small bit of pre-modeling calculation that it takes to set up the true azimuth model is minuscule compared to having a pattern rejected by a licensing agency.

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The second exercise involves 3 towers that do not form a single line. Instead, the third tower moves off from the second at a different angle. We shall retain the in-phase feeding system over perfect ground to preserve the model's simplicity, since our goal is to get a handle on how to organize the coordinates within EZNEC to obtain a true azimuth model.

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+Tower         Reference         Distance      Azimuth Bearing
+Number        Tower             Meters        Degrees
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+  1           ---               ---           ---
+  2           1                 150           060
+  3           2                 150           030
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We may easily calculate the coordinates for the second monopole using the techniques employed for the first monopole system. Next, we can assume that the second monopole is at the coordinate center and calculate its coordinates. To the values for X and Y, we simple add the values for each coordinate derived for the position of monopole 2. The result of the small trig exercise appears in the following completed table.

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+Tower         Reference         Distance      Azimuth Bearing    X coordinate     Y coordinate
+Number        Tower             Meters        Degrees
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+  1           ---               ---           ---                0                0
+  2           1                 150           060                129.9            75
+  3           2                 150           030                204.9            204.9
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The results appear more graphically in Fig. 11, where the annotated antenna outline shows the final positions along with the original data and the calculated coordinates. The compass plot is identical to the one produced using NEC-Win Plus and the pattern is broadside to the virtual line from the first to the last of the monopoles. The lack of perfect symmetry on each side of that lines reveals the effects of the irregular line formed by the 3 antennas.

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As a confirmation of the model's use of the calculated coordinates, Fig. 12 shows the model's wire table.

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Producing true azimuth patterns in EZNEC turns out to be as straightforward as it did using NSI software. Once we located North (the +Y axis) and East (the +X axis), the remain steps became a matter of calculating coordinates from any data that might be supplied in terms of distance and azimuth bearing. Of course, we can always begin with coordinate data, so long as we remember to place the antenna or its parts against a paper version of the X-Y system with North set along the correct axis line. Figuring the antenna coordinates then becomes a matter of arranging the coordinates. If an antenna has an area as defined in the X-Y plane, then it may be easiest to arrange the antenna along one or another azis and then to move and/or rotate the antenna to the desired orientation.

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EZNEC and NEC-Win Plus both use proprietary file formats, neither of which is the standard ASCII NEC-input file format. However, NEC-Win Plus will save files in the standard format, and EZNEC Pro will do so as well. Hence, my own work often involves moving from one piece of software to the other by way of an intervening NEC model file. There is a relationship between the systems needed to produce true azimuth models in each type of software. When moving from NEC-Win Plus to EZNEC, rotate the antenna or antenna field 90 degrees counterclockwise in EZNEC. When moving from EZNEC to NEC-Win Plus (or other NSI software), rotate the antenna or antenna field 90 degrees clockwise in the NSI program. The results will yield true a azimuth model if the initial model was truly an azimuth model within its software.

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Producing true azimuth models is certainly not necessary for a large part of the modeling enterprise. However, for applications demanding true azimuth models and patterns, the two bodies of software that we have sampled provide guides to almost any other software implementing NEC. The software must have an azimuth pattern that counts degrees clockwise. With that available, the rest of the task has only 2 steps. The first is to determine how the azimuth pattern relates to the software's standard phi pattern. The second is to calculate the necessary coordinates for the antenna to produce a true azimuth model and a true azimuth pattern.

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Go to Main Index

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104. PS: I Change

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L. B. Cebik, W4RNL

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Suppose that we create a model of a ground-plane monopole with 4 radials. Let's use 7.15 MHz as the test frequency. The monopole will be 10.071 m long and 0.0125 m in radius. The radials will be 11.57 m long and 0.002 m in radius. We shall equip the model with a GM line so that we can readily change the height of the antenna assembly over ground, using the radials as the base height.

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+CM monopole 7.15 MHz 25-mm dia.
+CM over ave gnd
+CM 90-deg radials
+CE
+GW 1 11 0 0 0 0 0 10.071 .0125
+GW 2 11 11.57 0 0 0 0 0 .002
+GM 1 3 0 0 90 0 0 0 2 1 2 11
+GM 0 0 0 0 0 0 0 83.858
+GE -1 -1 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 1 0 1 0
+FR 0 1 0 0 7.15 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
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The model might begin as high as 2 wavelengths over ground (using the constants for average ground in this case). However, we shall be interested in lower heights, down to and including placing the radials below ground. We shall have to change the model design just slightly to accommodate NEC-4 guidelines that require a wire or segment junction at Z=0. One easy way to achieve this is to run the monopole down to the ground. Then let the innermost segment of each radial slope from Z=0 down to the radial level. The remaining radials segments form a flat plane. The radials are 0.001 wavelength below ground, about 0.042 m or 1.65".

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+CM monopole 7.15 MHz 25-mm dia.
+CM buried radials .001 wl
+CM 90-deg radials
+CE
+GW 1 11 0 0 0 0 0 10.071 .0125
+GW 2 1 1.05 0 -.042 0 0 0 .002
+GW 2 10 11.57 0 -.042 1.05 0 -.042 .002
+GM 1 3 0 0 90 0 0 0 2 1 2 11
+GE -1 -1 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 1 0 1 0
+FR 0 1 0 0 7.15 1
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+EN
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If we plot the data for models as they approach and then penetrate ground, we obtain an interesting set of discontinuities. All data use the usual units of measure.

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+4-Radial 90-Degree Ground-Plane Monopole From 2-WL Up to Below Ground: Performance with Various Ground Types
+Free-Space Reference Performance        Monopole: Len 10.071 m, Radius 0.0125 m         Freq.: 7.15 MHz
+Rad-L m     Rad-R m     Gain dBi     Bmwidth     Resist     React
+11.57       0.002       1.35         102         21.34      0.06
+Ground Type             Average: C 0.005, P 13
+Height wl     Height m     Gain dBi     TO Angle     Resist     React
+0.1           4.193        0.24         70           24.35      -4.84
+0.05          2.096        0.10         67           28.64      -3.48
+0.025         1.048       -0.04         65           31.75       0.22
+0.01          0.419       -0.22         64           34.64       7.85
+0.005         0.210       -0.38         64           36.52      16.53
+0.001         0.042       -1.37         64           47.26      52.34
+-0.001       -0.042       -2.37         64           64.75       7.98
+-0.005       -0.21-       -2.49         64           66.25      10.30
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Note that as we enter the ground, the gain drops rapidly. More significantly, the feedpoint impedance changes considerably. If we add more radials, the transition will be less extreme, but the 4-radial model makes a useful tool, if for no other reason than to arouse a bit of curiosity.

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Fig. 1 shows the relative current magnitude along the vertical monopole and along 2 of the 4 radials forming the ground plane. The model showing the current distribution is in free space, but any model having all of its wires above ground would show the same set of characteristics. I have set the maximum monopole current on the 4th segment of the radial as a marker. Note that the maximum radial current is just above the first monopole segment, indicating that we have very close to equal currents on the radials and on the monopole. Of course, each radial carries 1/4 of the total current below the feedpoint.

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Both current curves have very similar shapes. However, current magnitude does not tell us the complete story. The following list shows both the relative current magnitude and the current phase angle based on a source current of 1.0 at 0°. If we count upward on the monopole to the 5th entry, we find a magnitude of 0.81245. The corresponding entry for the radial, counting downward, is 0.21420, very close to the 1/4 wavelength monopole value. As well, note the similarity of current-phase value at the monopole top and the radial end. Remember that the radial has a much smaller radius than the monopole.

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+Monopole                       Radial
+Magnitude (A.)  Phase (Deg.)   Magnitude (A.)  Phase (Deg.)
+.09260          -2.93          .25147          -0.08
+.24609          -2.71          .24966          -0.27
+.38339          -2.49          .24298          -0.43
+.50941          -2.26          .23114          -0.56
+.62371          -2.01          .21420          -0.67
+.72512          -1.75          .19237          -0.78
+.81245          -1.47          .16600          -0.89
+.88456          -1.17          .13553          -0.99
+.94034          -0.82          .10146          -1.09
+.97902          -0.42          .06417          -1.19
+1.0000           0.00          .02318          -1.29
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If we lower the antenna so that the radials are below ground, we shall have to modify the model slightly. The monopole will just touch the ground. The radial wires will have 2 sections. The innermost segment will slope from ground level at the monopole base down to 0.001 wavelength below ground (about 0.042 m or 1.65"). The remaining segments will extend to 11.57 m to produce the same total length as the radials in the above-ground model. Fig 2 shows the model and the relative current magnitudes, followed by a tabular listing of magnitudes and phase angles.

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+Monopole                       Radial
+Magnitude (A.)  Phase (Deg.)   Magnitude (A.)  Phase (Deg.)
+.09286          -6.00          .24242          -7.83
+.24693          -5.66          .21041          -28.95
+.38486          -5.30          .17479          -51.49
+.51154          -4.90          .14094          -73.58
+.62647          -4.47          .11038          -95.00
+.72839          -3.99          .08337          -115.4
+.81606          -3.44          .05966          -134.6
+.88806          -2.81          .03914          -152.5
+.94333          -2.06          .02223          -170.1
+.98087          -1.10          .00972          170.08
+1.0000           0.00          .00222          139.95
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Since the models differ very slightly in construction due to the need to develop subsurface radials, the monopole current magnitudes are very close, but not identical, to the values for the preceding model. However, we do find a difference in the current phase angle range. For identical source values (1.0 A. at 0°), the preceding model tip current phase angle was only -2.93°, whereas the model with buried radials has a tip-segment phase angle of -6.0°. The above-ground model is a free-space version of the antenna with a source impedance of 21.35 + j0.07 Ohms. The model with buried radials uses average ground (C 0.005 S/m, P 13) and reports a source impedance of 64.69 - j 7.84 Ohms.

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The differences between the radial currents for the above-ground and the buried radial models are far more dramatic. Visually, the radial curve differs by rapidly decreasing in current magnitude as we move from the hub outward. The table confirms the curve. At the 5th entry upward, the monopole shows a value of 0.81606, while the corresponding radial entry shows a value of 0.11038, only half the magnitude for that position on the above-ground radial. The current phase changes along the buried radial are far more radical than those along the above-ground radial. One NEC convention is to maintain all phase reports in the 0°-180° range. The outer-most value is equivalent to a value of -220.05°, about 214° out of phase with the tip of the monopole. Note that these values are not true tip values, but the values at a position roughly comparable to the center of the relevant wire segments in the models.

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The comparison makes clear that the common above-ground portions of the two antennas yield essentially the same current distribution. However, the parts that move from above ground to below ground change their current distribution. Most modelers seem to be wholly unaware of this phenomenon. So it bears some exploration. Let's begin by reviewing some fundamentals about NEC's treatment of ground.

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For any given ground quality, we measure (or find in some table) values for conductivity (sigma) and relative permittivity (epsilon-r). Relative permittivity rests on the permittivity in free space (epsilon-0). Essentially, the program combines the listed values for conductivity and permittivity into a complex relative permittivity (epsilon-g):

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The term f is the frequency in Hz. As f changes, so too does the value of epsilon-g. Therefore, the effects of ground on buried-radial ground-plane antenna performance vary with conductivity, permittivity, and frequency.

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NEC also calculates another value called ks, the wave number in the sinusoidal current expansion in NEC. This value applies to any wire within a medium other than free-space (or a vacuum). Hence, it applies to all insulated wires and to any wires below ground level (assuming that a real ground is operative in the model). The value of ks modifies the length of a wave for the calculation of current along a wire. Hence,

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The current-propagation wave number has the effect of lengthen every applicable segment with respect to current calculations. The exact amount of lengthening depends upon the frequency and ground constants that the modeler selects.

+

We can easily determine the effect of the wave number on segment length by employing the PS command in NEC-4. The command requires only the command letters, with no following numerical entries. In fact, we can perform segment-length adjustment calculations without further model execution by following the PS command with EN, as in the following sample model. The model contains all of the GW, GN, FR, and EX elements to form a complete model, except that it lacks an output request other than the PS command. Hence, calculations stop after the PS command has done its work.

+ 
+GW 1 11 0 0 0 0 0 10.067 .0125
+GW 2 10 10.4823 0 -.04193 .953 0 -.04193 .002
+GW 2 1 .953 0 -.04193 0 0 0 .002
+GM 1 3 0 0 90 0 0 0 2 1 2 11
+GE -1 -1 0
+GN 2 0 0 0 13 .005
+EX 0 1 1 0 1 0
+FR 0 1 0 0 7.15 1
+PS
+EN
+
+

Although the report in the NEC output file shows the value of ks, we may confine our attention to the effects on segment lengths. I ran models of 160-m and 40-m ground-plane monopoles with 4 buried radials through the PS command, using 3 diverse ground-quality values, those for very good (C 0.0303 S/m, P 20), for average (C 0.005 S/m, P 13), and for very poor (C 0.001 S/m, P 5) soil. I also ran the same model in free space to illustrate how much wire values change as we bury the radials. Note that in the following lists, all values are normalized to fractions of a wavelength. As well, I converted the entries from engineering to decimal notation. In both cases, the monopole physical segment length is 0.02183 wavelength with a physical radius of 0.000298 wavelength.

+ 
+Radial Segment Length and Radius
+Frequency        Soil Quality           Segment Length          Segment Radius
+1.85 MHz         None                   0.02273 WL              0.0000477 WL
+                 Very Good              0.3904                  0.0008194
+                 Average                0.1612                  0.0003383
+                 Very Poor              0.0713                  0.0001577
+7.15 MHz         None                   0.02273 WL              0.0000477 WL
+                 Very Good              0.2017                  0.0004233
+                 Average                0.09664                 0.0002028
+                 Very Poor              0.05376                 0.0001128
+
+

To extract a simple example from the listing, the 7.15-MHz average-ground segment length is about 4.3 times the physical length, that is, the length in free-space when normalized to a fraction of a wavelength. With respect to current expansion, the radial point corresponding to the 5th monopole entry in the earlier model (Fig. 4-2) actually lies just inside the second segment, where we find a current magnitude of about 0.21. However, notice that the radius increases to the same degree, resulting in what appears to be a more rapid change of current phase angle. Since the current does not go to zero until we reach the radial tip, most of the table entries for the buried radial show very low values compared to the free-space model.

+

The NEC-4 manual recommends that we use lambda-s as the basis for calculating segment lengths for any wire within a medium other than free space, where free space includes any region above a real ground. Examining the PS command report shows that the calculated segment length for current expansion along a buried radial no longer agrees with the segment length for the monopole that is above ground. The segment-length difference appears at one end of the source segment, suggesting a possible error source in the model. The AGT cannot show this potential error, since the test uses free space as its venue. So the next question is what degree of error we might expect from not adjusting the segment length in accord with the value of lambda-s.

+

To obtain a sense of what error might be possible, I used the 40-m monopole and ran it in two forms, using very good, average, and very poor soil. The first run used the standard segmentation of the sloping-radial construction with a total of 11 segments per radial. The following lines sample the model over average ground.

+ 
+GW 1 11 0 0 0 0 0 10.067 .0125
+GW 2 10 10.4823 0 -.04193 .953 0 -.04193 .002
+GW 2 1 .953 0 -.04193 0 0 0 .002
+GM 1 3 0 0 90 0 0 0 2 1 2 11
+GE -1 -1 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 1 0 1 0
+FR 0 1 0 0 7.15 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
+
+

Next, I adjusted the number of segments in the radial entries (GW2) so that the calculated segment length for current expansion would more evenly match the monopole segment length. Again, here is a sample over average ground. Note the use of the PS command to allow confirmation of the segmentation.

+ 
+GW 1 11 0 0 0 0 0 10.067 .0125
+GW 2 40 10.4823 0 -.04193 .953 0 -.04193 .002
+GW 2 4 .953 0 -.04193 0 0 0 .002
+GM 1 3 0 0 90 0 0 0 2 1 2 44
+GE -1 -1 0
+GN 2 0 0 0 13 .005
+EX 0 1 1 0 1 0
+FR 0 1 0 0 7.15 1
+PS
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
+
+

For the adjusted models, the outlines in Fig. 3 show the distribution of segments between the sloping and the straight portion of the radials. The monopole, of course, remains unchanged. The look of the model outline represents the physical dimensions and not the electrical length of segments as calculated by NEC for use in the current expansion.

+
+ +
+

From the total of 6 models, I obtained the following results. The entries showing 11 segments per radial represent the unaltered models. The alternate model segment numbers represent values that yield calculated segment lengths about equal to those in the monopole.

+ 
+7.15-MHz Ground-Plane Monopole with 4 Buried Radials
+Soil Quality        Segments/Radial        Gain dBi         Source Impedance
+Very Poor           11                     -4.24            88.94 + 29.22 O
+                    26                     -4.13            86.63 + j26.22
+Average             11                     -2.36            64.60 + j7.29 O
+                    46                     -2.35            64.44 + j4.28
+Very Good           11                     0.46             50.91 + j8.19
+                    98                     0.24             53.53 + j5.75
+
+

None of the possible error differences are either fatal or unambiguous. For example, the amount of difference is greatest for the antenna over very good soil, but so too is the increase in the radial wire radius. The calculated radius is greater than the monopole radius. In some instances, using the calculated values of segment length and radius as a basis for adjustment may lead to an impossible conflict among NEC guidelines. For precision work, the problem would require considerable thought before finalizing a model. However, for general guidance in determining trends and rough properties, using unaltered models with 11 segments per radial will largely suffice. Remember that NEC ground systems have other limitations. For example, they presume a homogenous ground from horizon to horizon and from the surface downward. In many cases, the actual ground will be stratified, and the exact values of conductivity may not be measurable to the depth of RF penetration.

+

Within the context of NEC models using buried radials, the exercise does provide a foundation for understanding the different current distributions that we find in those radials, relative to above-ground models.

+

A Note on IS and PS

+

Because the IS or insulated sheath command also places a non-free-space medium around a specified wire, NEC-4 will adjust the segment lengths and radii for implementing the current expansion. Out of curiosity, you may invoke the PS command in trial models to see what happens. Let's begin with a simple dipole for 7.15 MHz using a 0.001-m radius wire.

+ 
+CM 7.15-MHz dipole in free space
+CM Radius 0.001 m
+CE
+GW 1 21 0 -10.2 0 0 10.2 0 .001
+GE
+FR 0 1 0 0 7.15 1
+EX 0 1 11 0 1 0
+PS
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

With a length of 20.4 m, the dipole is resonant, showing a source impedance of 70.11 - j0.08 Ohms. The free-space gain of this lossless wire is 2.14 dBi.

+

Next, let's add an IS command to place an insulating sheath around the wire. We shall use a high-quality plastic with a relative permittivity of 3 and a conductivity of 1E-10. The insulation will be 2-mm thick, resulting in a sheath radius of 0.003 m (around the 0.001-m radius wire). An insulation thickness that equals the wire diameter might fall into the relatively heavy insulation category, although thicker insulations certainly exist.

+ 
+CM 7.15-MHz dipole in free space
+CM Radius 0.001 m
+CM insulated
+CE
+GW 1 21 0 -9.726 0 0 9.726 0 .001
+GE
+IS 0 1 1 21 3 1e-10 .003
+FR 0 1 0 0 7.15 1
+EX 0 1 11 0 1 0
+PS
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

To obtain resonance we must shorten the antenna to 95.4% of its bare-wire form. The source impedance reports 66.34 - 0.04 Ohms and a free-space gain of 2.11 dBi.

+

Note that both models implement the PS command, since it takes so little run time and report space. However, only the report for the insulated wire model is relevant to satisfy our curiosity. If we explore the PS portion of the report, we encounter some entries in normalized form, that is, expressed as fractions of a wavelength. These values are for the adjusted segment length and adjusted wire radius. We must calculate the normalized physical dimensions by dividing the physical segment length and radius by 41.92902 m, a wavelength at 7.15 MHz. Now we can compare the results within the limits expressed by the report entries.

+ 
+Insulated 7.15-MHz Dipole
+                                              Segment Length     Segment Radius
+Normalized Physical Dimensions                2.209E-2           2.385E-5
+Adjusted Dimensions for Current Expansion     2.209E-2           2.385E-5
+
+

Within reporting limits, there is no difference in the values, although the effects of the insulation show up in the performance reports. However, the extent of the medium change is so small, that for all practical purposes, the modeler can ignore any segment length changes and use the same segmentation as he or she used for a bare wire model.

+

If the modeler specifies an upper medium (UM), usable only with the RCA ground system, the situation would be similar to specifying a ground, but apply to the region formerly treated as a vacuum or free-space. Under those conditions, application of the PS command in order to evaluate overall model segmentation is certainly in order.

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Go to Main Index

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+

105. Models, Symmetry, and Loads: A Couple of Reminders

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+

L. B. Cebik, W4RNL

+

+
+ +

+
+

While diagnosing an ailing model, I encountered a couple of areas in which a bit of clarification might be useful to other modelers. Since the points that we shall cover may be second nature to some modelers and temptations to error for others, let's just call these notes reminders.

+

The Destruction of Symmetry

+

The NEC manuals provide a list of conditions that "automatically reset the symmetry condition." The first item on the list--which is all that we need for this exercise--reads this way: "Addition of a wire or patch (GW, GH, CW, SP, etc.) will destroy all symmetry." The conditions apply equally to the GX and the GR symmetry commands.

+

The most common interpretation that newer modelers seem to apply to the statement is that the core will fail to produce the symmetric structure specified in either the GX or GR command. This interpretation is incorrect. Rather, the core produces the desired structure, but does not use the shorter form of calculation to arrive at the matrix values. Instead, the model is reset for the entire structure to a non-symmetry mode of calculation.

+

Consider the following models, all of which have the properties shown in Fig. 1.

+
+ +
+

The most direct form for this model would create all 5 wires in separate GW commands, using the following lines.

+ 
+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th passive vertical dipole at a distance
+CM Full version
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GW 3 11 0 .25 -.245 0 .25 .245 .001
+GW 4 11 0 .75 -.245 0 .75 .245 .001
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

The relevant performance data for the model is a maximum gain of 6.04 dBi, with a 36-degree beamwidth in the main or maximum-gain lobe. The reported source impedance is 49.383 -j21.986 Ohms. Both of the variations on this model will yield the same results to the last decimal place. The free-space azimuth pattern has the shape shown in Fig. 2. Note that the main lobe (by a tiny fraction of a dB) is away from the 5th vertical dipole.

+
+ +
+

An alternative to listing GW 3 and GW 4 is to use the GX commands to replicate the first 2 wires symmetrically across the Y-axis. This alternate form would take this appearance.

+ 
+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th passive vertical dipole at a distance
+CM GX, symmetry defeated
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GX 1 010
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

Since a GW entry (GW 5) follows the GX command, the common misconception is that wires 3 and 4 will not appear. Instead, the correct interpretation is that the GX command produces the required 2 wires, but does not invoke symmetry in its calculations. The following extract from the NEC output report gives us the telltale line.

+ 
+ TOTAL SEGMENTS USED=   55     NO. SEG. IN A SYMMETRIC CELL=   55     SYMMETRY FLAG=  0
+
+

If symmetry had been invoked, the number of segments in the symmetric cell would have been 22, the number of segments in the first 2 wire entries. As well, the symmetry flag would equal 1 rather than zero. The total number of segments in the model is 55, indicating that the core has created the requisite new wires or tags. The performance reports and the segment and current tables also show the existence of the created wires, but without the symmetry calculation shortcuts. In fact, the run times for this test model and for the first one were identical.

+

On some occasions, it may be necessary to successfully invoke symmetry due to model size or other factors. That route is irrelevant to the present array, but the model may be useful in its simplicity for illustrating one way to go about the process. The technique involves the use of a Numerical Green's File (NGF). We have examined NGFs in past episodes, but always in the context of saving the file for use with multiple new models that call up the results. We need not use separate NGF formation and use files. Instead, we can create and use the NGF results within the same model or .NEC file. We only need to use the NX or next structure command between the saving of the NGF and the call-up of its contents. Note that NEC-2 requires that the first command following NX must be a comment (CM or CE). However, NEC-4 permits a geometry command to directly follow the NX command. We may use the following model as a guide.

+ 
+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th passive vertical dipole at a distance
+CM GX, symmetry via NGF
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GX 1 010
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+WG test3.ngf
+NX
+CE
+GF test3.ngf
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

The first half of the model, prior to the NX command, creates the first 2 vertical dipoles and requests their replication via symmetry across the Y-axis. As in all NGF operations, we include ground, loading, and frequency information for the affected wires within this file. The WG command saves the results. The program used for these exercises allows the user to specify any file name and extension for the data storage. However, raw NEC-2 has limitations of the NGF filename, and different implementations of NEC-2 may use different specifications for this entry. Finally, note that we do not use the EN command before the NX command, because EN would terminate calculations.

+

Following the NX command, I have inserted a CE line so that the model will run on NEC-2 or NEC-4. The GW entry established the 5th dipole, while the EX lines provides the two sources. The results of this model are identical to those of the preceding tests, although we want to examine one special line-set of the NEC output report.

+ 
+   TOTAL SEGMENTS USED=   44     NO. SEG. IN A SYMMETRIC CELL=   22     SYMMETRY FLAG=  1
+ STRUCTURE HAS 1 PLANES OF SYMMETRY
+
+

In the first set of core calculations, the GX command creates 22 new segments, for a total of 44. The symmetry cell has the initial 22 segments and the flag is set to 1, indicating that symmetry is invoked for 1 plane. Because the model is so small and contains both parts of the process, the run time is no different than for the first 2 tests. However, for this demonstration, run time was not in question. For very large models, it may well become a key reason for using this technique. Our goal was to show how we can invoke symmetry and complete our modeling all within the same .NEC file.

+

If we wish to consider matters of file size and run times, we can turn to a different sort of model and simultaneously illustrate the same points for the GR or rotational symmetry command.

+
+ +
+

Fig. 3 shows the general properties of the models that we shall construct for this exercise. At the usual test frequency (299.2975 MHz, where 1 wavelength = 1 meter), we shall place 64 1/4 wavelength radials 0.05 m below ground. At the center, we shall construct a single monopole wire that meets the radials below ground and extends 0.25 wavelength above ground. By assigning 11 segments to the monopole wire, the junction of the second and third segments will intersect Z = 0, the ground level. The following model illustrates the simple set-up, using the GM command to replicate the radials 63 times beyond the original GW 1 specifications.

+ 
+CM 64 buried radials with monopole
+CM GM
+CE
+GW 1 11 0 0 -.05 .25 0 -.05 .001
+GM 1 63 0 0 5.625 0 0 0
+GW 65 11 0 0 -.05 0 0 .25 .001
+GE -1 -1 0
+FR 0 1 0 0 299.7925 1
+EX 0 65 3 0 1 0
+GN 2 0 0 0 5 .001
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

The model yields a maximum gain of -0.42 dBi at a TO angle of 59 degrees (theta). Fig. 4 shows the elevation/theta pattern for the model. The model made no attempt to achieve resonance, but used instead easily remembered dimension values. Hence, the reported source impedance is 46.125 - j730.025 Ohms. All versions of the model report identical results.

+
+ +
+

To shorten run times and further simply model formation, many modelers replace the GM command with a GR command. The GR command allows rotational symmetry and calculates the angle between each radials, so the modeler does not have to remember that a 64-radial system has a 5.625-degree angular separation between radial wires. The replacement model appears in the following lines.

+ 
+CM 64 buried radials with monopole
+CM GR
+CE
+GW 1 11 0 0 -.05 .25 0 -.05 .001
+GR 1 64
+GW 65 11 0 0 -.05 0 0 .25 .001
+GE -1 -1 0
+FR 0 1 0 0 299.7925 1
+EX 0 65 3 0 1 0
+GN 2 0 0 0 5 .001
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

Note that the GR entry is followed by the monopole GW entry. We could not place the monopole ahead of the GR command. That move would have resulted in the creation of 64 monopoles in the same position. By placing the monopole wire after the GR command, we obtain only one monopole, we create only a single monopole, but we defeat the invocation of symmetry. However, we do not defeat the creation of the radials themselves. The critical line from the NEC output report for the model confirms these notes.

+ 
+   TOTAL SEGMENTS USED=  715     NO. SEG. IN A SYMMETRIC CELL=  715     SYMMETRY FLAG=  0
+
+

The entire model--all 715 segments--form one symmetric cell, and the symmetry flag = 0; hence, the radials exist in the model, but it does not use symmetry in the calculations. The run time for this version of the model is identical to the run time required by the version using the GM command.

+

To invoke symmetry, we may employ the model style used for the final version of the vertical dipole array. We may create and run the radials alone and save the results in an NGF file. Within the same model, we may use the NX command to begin a second run that calls up the stored results and applies them to the enlarged model that now contains the monopole. The final model in this series appears in the following lines.

+ 
+CM 64 buried radials with monopole
+CM GR + NGF
+CE
+GW 1 11 0 0 -.05 .25 0 -.05 .001
+GR 1 64
+GE -1 -1 0
+FR 0 1 0 0 299.7925 1
+GN 2 0 0 0 5 .001
+WG radials.ngf
+NX
+GF radials.ngf
+GW 65 11 0 0 -.05 0 0 .25 .001
+GE -1 -1 0
+EX 0 65 3 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

If you run this model on NEC-2, insert at least a CE command prior to the GF entry that follows NX. The key NEC output report lines tell us that the first portion of the multi-run model has invoked symmetry.

+ 
+   TOTAL SEGMENTS USED=  704     NO. SEG. IN A SYMMETRIC CELL=   11     SYMMETRY FLAG= -1
+ STRUCTURE HAS  64 FOLD ROTATIONAL SYMMETRY
+
+

To create the NGF data, the first run uses only the total number of segments in the radials. The remaining 11 segments in the monopole do not appear until the second run. The symmetric cell shows only the number of segment in the initial radial, and the symmetry flag = -1, indicating rotational symmetry.

+

The total file begins to show the run-time advantage of using the GR command. The total run time for this latest version of the model is about 1/3 the time for the other two versions. Neither time is truly long for the current generation of PCs. However, the savings are indicative of what may accrue for larger models.

+

To illustrate that point, I enlarged the radial system to 120 1/4 wavelength radials. To replicate a common BC industry practice, I also inserted a set of 120 shorter radials between the longer radials. The total system-- or at least a portion of it--appears in Fig. 5.

+
+ +
+

Only the short radials appear fully, with all segments shown to give an idea of the model construction. However, the model-file appearance does not change much compared to the 64-radial models that we just viewed. Indeed, the only difference is a second GW line (which uses the same tag number as the first wire).

+ 
+CM 240 buried radials with monopole
+CM GR + NGF
+CE
+GW 1 11 0 0 -.05 .25 0 -.05 .0001
+GW 1 2 0 0 -.05 .04546 .0012 -.05 .0001
+GR 1 120
+GE -1 -1 0
+FR 0 1 0 0 299.7925 1
+GN 2 0 0 0 5 .001
+WG radials.ngf
+NX
+GF radials.ngf
+GW 65 11 0 0 -.05 0 0 .25 .0001
+GE -1 -1 0
+EX 0 65 3 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

The symmetry-cell size and the flag setting both tell us that the model invoked symmetry. Even so, the increased model size required about 21 times longer to run than the 64-radial model using the same technique. As we increase the number of segments, run times increase exponentially. Without symmetry, we would need to add a further multiplier to the run time.

+ 
+   TOTAL SEGMENTS USED= 1560     NO. SEG. IN A SYMMETRIC CELL=   13     SYMMETRY FLAG= -1
+ STRUCTURE HAS 120 FOLD ROTATIONAL SYMMETRY
+
+

The model style shown has one drawback. We are likely to forget that the file called radials.ngf remains in the directory (or folder) where we store models. Using symmetry, the file is not very large, only 314 KB. But it does take up space. Directory cleaning is an important adjunct function for almost all modeling. (Some implementations of NEC do not save any files except the model file unless the modeler makes a specific request to save something else.) Indeed, if we had created the radial system using the GM command and stored the results for possible future use, the .NGF file might have reached 10 MB of storage space, depending upon the number of segments in each radial. So the GR function has a second benefit besides run time: it produces smaller NGF files.

+

A Loaded Reminder

+

In the NEC manual, there is a chart of control commands that collects them into 3 groups. The following list is from the NEC-4 manual

+
+

Group I: FR, GN, IS, JN, LD, UM, VC

+

Group II: EX, NT, TL

+

Group III: CP, EN, GD, LE, LH, NE, NH, NX, PL, PQ, PS, PT, RP, WG, XQ

+
+

The 3 groups correspond roughly to the 3 steps of solution generation. First comes the interaction matrix: calculation and factoring in preparation for solving for currents. The next step is to solve for currents with a given excitation. Finally comes the calculation of near and/or far fields. The first step depends only upon geometry commands and control commands in Group I. The current solutions depend upon commands in both Group I and II. Following a Group II entry by a Group I entry may result in a repetition of the current solution, since the Group I entry would result in a change of the conditions necessary for that solution. The re-calculation would depend upon the placement in the control command sequence of commands that execute, such as XQ and RP.

+

In the course of examining our first 3 test cases, involving the collection of vertical dipoles, the importance became apparent of arranging to the extent possible all control commands in the sequence of the groups. Fig. 6 shows the set up for this modified version of the dipole array in free space. The loads will all by LD4 types with zero reactance and resistance values as shown in the diagram (in Ohms).

+
+ +
+

The first of the models uses a straightforward separate specification for each vertical dipole. It follows the simple geometry entries with the Group I entries of FR and LD, with all 3 LDs placed sequentially. Next come the 2 Group II EX commands. A pattern request completes the model.

+ 
+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th passive vertical dipole at a distance
+CM Full version-LD4s all before EX
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GW 3 11 0 .25 -.245 0 .25 .245 .001
+GW 4 11 0 .75 -.245 0 .75 .245 .001
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+LD 4 1 6 6 1e6 0
+LD 4 4 6 6 1e6 0
+LD 4 5 6 6 100 0
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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The model reports a maximum gain of 4.73 dBi with a 54-degree beamwidth. The reported source impedance is 61.157 - j12.362 Ohms. Fig. 7 shows the phi/azimuth pattern for the model.

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Now let's revise the model to reflect a tendency among some modelers. Suppose that we had only specified the 1-MOhm loads for GW 1 and GW4, followed by the 2 EX commands. Then we went back to add a load of 100 Ohms resistance to the 5th dipole. We might inattentively insert the new LD4 command just before the request for pattern (RP) command. The following lines show the basic model file.

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+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th inert vertical dipole at a distance
+CM Full version-LD4 on GW5 separated from other LD4s by EX
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GW 3 11 0 .25 -.245 0 .25 .245 .001
+GW 4 11 0 .75 -.245 0 .75 .245 .001
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+LD 4 1 6 6 1e6 0
+LD 4 4 6 6 1e6 0
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+LD 4 5 6 6 100 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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Interestingly, the model shows a maximum gain of 6.74 dBi with a beamwidth of 36 degrees. Fig. 8 shows the phi/azimuth pattern. The model reports a source impedance of 58.156 - j14.714 Ohms.

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The revised pattern alone is enough to show that something has gone astray in at least one of the 2 models. Just what went amiss becomes clear from the following revised model. It simply removes the high-resistance loads on GW1 and GW4 from the model.

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+CM Test model: 4 vertical dipoles, inner 2 fed
+CM 5th inert vertical dipole at a distance
+CM Full version-LD4 on GW5 only
+CE
+GW 1 11 0 -.75 -.245 0 -.75 .245 .001
+GW 2 11 0 -.25 -.245 0 -.25 .245 .001
+GW 3 11 0 .25 -.245 0 .25 .245 .001
+GW 4 11 0 .75 -.245 0 .75 .245 .001
+GW 5 11 .5 0 -.245 .5 0 .245 .001
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+EX 0 2 6 0 1 0
+EX 0 3 6 0 1 0
+LD 4 5 6 6 100 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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The new model with no loads on the outer passive vertical dipoles returns the identical results that we obtained from the version with the load on the 5th dipole following the EX commands and separated from the other LD4 loads. Fig. 8 is the correct phi/azimuth pattern for this model. In the earlier model, separating the load entries by the EX commands resulted in a re-calculation that in effect omitted the earlier loads. If we want to include the loads on the outer dipoles in the model results, we have to use a modeling format similar to the first model in the final sequence of tests.

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The lesson of these models is that it pays to group commands first by group level and second by type. The payback involves more important factors than mere run time. It also pays in terms of the accuracy of the output data.

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Conclusion

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Occasionally, we encounter interesting models that require diagnosis, and in the process, we either learn something new about the operation of NEC or we are reminded of some fine points about model construction that we might have let slip over months and years of modeling. This month's reminders are examples of that process. In fact, I might not have thought to mention either of the main ideas without the presence of a set of models to diagnose. While not every modeler might need these reminders, I thought I would pass them along while a. they were on my mind and b. I had a reasonable set of simple models by which to illustrate them.

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Go to Main Index

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106. Refining Our Notions of Azimuth Patterns

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L. B. Cebik, W4RNL

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Many of these columns evolve from e-mail correspondence that I receive relative to antenna modeling. Sometimes, I receive over a short period of time multiple notes on a single subject. At other times, I receive seemingly diverse inquiries that turn out to have a common thread. The latter situation provides the basis for these notes in pursuit of a better understanding of so-called azimuth patterns.

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The generic term in NEC for patterns taken along or parallel to the X-Y plane is a phi pattern. Starting with the X-axis, we count counterclockwise in degrees around the circle created by any phi pattern. When we speak of azimuth, we are resorting to the language of seamen, airmen, surveyors, and field engineers. That language presumes that there is a ground level at zero degrees elevation. (We shall, like NEC, presume a flat earth.) We count degrees from the North in a clockwise compass rose. In free-space, NEC may still have its phi pattern, since free space has a Cartesian X-Y plane. However, the idea of azimuth becomes problematical, because we lack a ground. So we often speak in terms of E-plane and H-plane patterns, but these patterns designations depend on how we have oriented the antenna, assuming a relative linear polarization. Software makers--for simplicity--tend to label all X-Y plane patterns as azimuth patterns. However, in many cases, the pattern produced is really a phi pattern that counts counterclockwise.

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As daunting as the mere labeling of phi/azimuth patterns can be, the problem is small compared to others that may occur is we are not careful. In these notes, we shall deal with only 2. One is the continuing subterranean discussion about the use of log vs. linear polar plots. The other involves azimuth patterns over ground when the pattern's elevation angle is more than a few degrees above the horizon.

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Log vs. Linear Polar Plots

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Although 3-dimensional plotting capabilities come with much modeling software, the most telling data usually derives from 2 dimensional patterns. We have already described the phi/azimuth pattern. Corresponding to it, but with a vertical dimension, is the theta/elevation plot. Most often, we set the phi/azimuth angle for a theta/elevation plot by reference either to the centerline of an antenna array or with respect to the direction of the strongest forward lobe. We can use other angles as the need arises. Theta/elevation patterns seem to present no major problems to newer antenna modelers. Even the translation between theta and elevation conventions is simple. An elevation angle is 90 - a theta angle (degrees) and vice versa. Perhaps the only difficulty involves setting up an elevation pattern's range of angles to be sure that we obtain a full circle in free space.

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Over ground, the phi/azimuth pattern causes the most discussion. The discussion tends to extend itself into free space because the plots with and without a ground beneath have such similar shapes. The discussion hinges around whether we ought to be using a logarithmic or a linear scale for the rings in the pattern. Some modelers, especially radio amateurs, may have never seen a linear plot, since most publications in the field use one or another form of log plot. Many developmental and field engineers are most experienced with linear plots, sometimes because the regulatory submissions that they make set requirements of plots--and they are almost always on linear scales.

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Over the years, the discussion has acquired some spurious reasoning. For example, a few linear plot proponents claim that we receive unrealistic plots using a log scale, since power gains are already in decibels, a log concept. More interesting is the claim that a log scale makes the main forward lobe of an antenna more dominant, giving a more favorable impression of the antenna performance than it deserves. Since most proponents of a log scale prefer it by habituation, there have been few replies, although log plots tend to dominate the presentations in most publications.

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So our question is simple: what difference does it make whether I use a linear or a log scale when making a polar plot? We can settle some of the issues by pursuing a simple exercise. Let's set up a model in free space and plot its phi/azimuth/E-plane pattern. My model is the following simple NEC listing.

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+CM 12-element Yagi, 223.5 MHz
+CE
+GW 1 19 0. .3225463 0. 0. -.3225463 0. .003175
+GW 2 19 .2628857 .3125082 0. .2628857 -.3125082 0. .003175
+GW 3 19 .3613731 .2856135 0. .3613731 -.2856135 0. .003175
+GW 4 19 .5981218 .2833407 0. .5981218 -.2833407 0. .003175
+GW 5 19 .8807049 .2799316 0. .8807049 -.2799316 0. .003175
+GW 6 19 1.209123 .2767118 0. 1.209123 -.2767118 0. .003175
+GW 7 19 1.577314 .2738708 0. 1.577314 -.2738708 0. .003175
+GW 8 19 1.971453 .2712192 0. 1.971453 -.2712192 0. .003175
+GW 9 19 2.385479 .2691358 0. 2.385479 -.2691358 0. .003175
+GW 10 19 2.819392 .2672419 0. 2.819392 -.2672419 0. .003175
+GW 11 19 3.272813 .2655372 0. 3.272813 -.2655372 0. .003175
+GW 12 19 3.745931 .2640221 0. 3.745931 -.2640221 0. .003175
+GE 0 0 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0 1 0 0 223.5 1
+GN -1
+EX 0 2 10 0  1.00000  0.00000
+RP 0 1 361 1000 90 0. 1.00000 1.00000 0.
+EN
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The dimensions of the 12-element Yagi are in meters. The LD5 entry casts the antenna in aluminum. The operating frequency is in the middle of the U.S. 220-MHz band. As shown in the outline sketch in Fig. 1, the second element is the driver, fed at its center.

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The antenna design rests on the work of DL6WU, Guenter Hoch. I am less interested at the moment in the overall performance of the antenna than in the fact that DL6WU designs tend to have significant forward sidelobes that are down from the main forward lobe by between 15 and 18 dB. That will give our polar phi/azimuth/E-plane plot a certain look. In fact, the look will not change if we uses a log scale and move from one software package to another, assuming that we normalize the plot, that is, set the plotting software so that the outer ring and the maximum forward lobe just meet. Therefore, GNEC and EZNEC Pro/4 patterns will appear identical. A plot produced by an ARRL publication may initially look different, but will be essentially the same. ARRL likes to place lines in 3 or 6 dB intervals, while most software uses 10 dB as a major circle in the plot. In short, the plot will look like the one at the upper left of Fig. 2.

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Perhaps the most significant reason for using a log-based polar plot of phi/azimuth/E-plane patterns is the fact that for any antenna, if we do not change the antenna placement or environment, the plot will be the same no matter which software we use for the plotting. We cannot make the same claim for linear polar plots.

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The plots shown comes from NSI software for a reason. EZNEC allows only one form of linear plot, but NSI software let's the user specify the inner limits and the ring increment for linear plots. As we change the inner limit and the increment, our polar plots may change their shape. Precisely here lies one of the problems with linear plotting of antenna patterns. If we do not have an external standard to direct our plotting, we can make the antenna look as sorry or as distinguished as we please. There are numerous applications in which we find external standards and some in which we find corporate standards that rest on long experience. In either case, we may directly compare plots and conduct fair evaluations.

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In the absence of such standards, the field is wide open. For example, the upper right pattern of Fig. 2 uses an inner limit of -100 dB with a 20-dB increment in the plotting circles. Using these scale factors, we can tell almost nothing about the antenna except perhaps that its front-to-back ratio is about 20 dB. The middle pair of linear scales use -50 and -40 dB inner limits. At this level, some of the antenna pattern details become much clearer. In fact, the -40-dB version of the plot is essentially the linear scale provided by EZNEC software. Where the scale rings have good labeling, we would have no trouble gleaning essentially the same information from both linear patterns. In fact, newer modelers may wish to track both patterns against the log pattern at the upper left in order to gain a more intuitive grasp of the differences between where on the plot various pattern levels occur.

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Just as the upper right pattern seems to obscure important data by virtue of its bulbous shape, the two patterns at the bottom of Fig. 2 may obscure important data by using an inner limit and increment level that are too small. In both cases--one somewhat more extreme than the other--the plot tends to enhance the pattern and to give it a purity that simply does not exist. I have seen plots of this order used in older articles, most recently in a review of professional literature on rhombic antennas. The plots could give the impression to the unwary reader that a rhombic antenna has no sidelobes worth mentioning, when in fact, the antenna sprays sidelobes everywhere, with the strongest ones only 8 to 12 dB below the strength of the main lobe.

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The linear pattern has plenty of uses and is not inherently simply a means to yield false impressions of an antenna. Field strength readings in volts/meter lend themselves to linear plotting. However, even in this enterprise, one needs a set of plotting standards to facilitate comparisons among plots. The one sure way to make such plots yield misimpressions is to allow scaling decisions to be idiosyncratic. The log plot of power gains obviates the danger by using a relatively constant scale, with only ring values as a plotting option. Having the scale prescribed and in unison with patterns produced by others is a good assurance to less experienced modelers that their results will in fact be comparable with other work. (This positive fact does not eliminate the many other ways in which one can mess up a model or the polar plot that we take of it. One common problem for azimuth plots over ground is the switching of the values for ground conductivity and relative permittivity. I have also seen plots that have intentionally used high values of conductivity and permittivity solely to enhance an antenna pattern. However, the connecting thread of these notes is not the ways in which we can give false impressions of an antenna's performance.) In the end, the use of plots--whether based on log or linear scales--requires good sense and standards if we are to derive from them all of the information available. If a linear plot is necessary for a power gain or other antenna property pattern, then in all cases the plotter needs to annotate the plot so that the user knows exactly how to interpret the data it encases. As well, the text should provide a rationale for the selected inner limit or a reference to an external standard, if it is applicable to the plot.

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Azimuth Plots Over Ground

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Phi/azimuth patterns taken over ground hold another potential problem--a lack of reader appreciation of what such patterns really are. Even those who make such plots using standard plotting techniques (for example, the usual log plot) may not fully appreciate what the data from the patterns may be telling us. The most common far-field plots shown on phi/azimuth patterns use relatively shallow elevation angles--somewhere between 1 and 25 degrees. At higher angles, we very often have an interest only in the general pattern shape and the maximum gain, so a lack of full understanding of the terms of an azimuth pattern holds no especial dangers. However, when we begin to look at the fuller data attached to such patterns, we often encounter hurdles for which we are not prepared.

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Once more, lets use a specific example. In this case, I shall select a very long-boom Yagi for 432 MHz. The antenna design specifically aims for high performance in as many categories as possible. The gain level is normal for the boom length. The good front-to-back values are overshadowed by the very high level of sidelobe attenuation. In addition, the antenna provides a direct 50-Ohm match and a passband wide enough to cover the entire 70-cm amateur band. Fig. 3 provides the free-space patterns and data, as well as a scale outline of the array. In this case, the patterns are log scale and from EZNEC Pro/4.

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One application for an antenna of this size is earth-moon-earth (EME) communications, using the moon as a passive and low-efficiency reflector. EME service requires that we be able to control the azimuth and elevation angles of the antenna. Therefore, one interest we may have in the antenna is its performance at various elevation angles. The antenna requires a minimum boom-center height of about 7.5 wavelengths to keep the reflector at least 1 wavelength above ground when pointed straight upward. I sampled the antenna performance at elevation angles from zero degrees through 90 degrees in 15-degree increments. The results appear in the series of elevation and azimuth plots shown in Fig. 4. The following table (Table 1) shows the values that correlate with the patterns.

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If we first examine only the elevation plots, we can observe an interesting pattern. As we elevate the antenna above an angle where the free-space vertical beamwidth interacts with the surface of the ground, the vertical beamwidth stabilizes at or very near to the free-space vertical beamwidth. We essentially achieve that situation by an elevation angle of 30 degrees.

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If we next examine the azimuth patterns, we find an oddity (at least, at first sight). The horizontal beamwidth increases steadily until we pass the 75-degree elevation level. Indeed, the azimuth pattern forward and rearward elements appears to broaden with each increase in elevation angle. However, the patterns for an elevation angle of 90 degrees return essentially to free-space values, with the exception that there are no longer any rearward lobes. Of course, we have changed the procedure at a 90-degree elevation angle and substituted H-plane and E-plane elevation patterns for the expected elevation and azimuth patterns. Below 90 degrees elevation, we do not have this option. Our task is to understand why the horizontal beamwidth and other aspects of the azimuth pattern broaden with an increasing elevation angle.

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The answer lies in simple but often overlooked aspects of the conical geometry that is a function of taking phi/azimuth patterns over ground. In every case, we use an elevation angle that is greater than zero. (Over perfect ground, we may take a phi/azimuth pattern at zero degrees elevation, but over real ground, the results are either a negligible set of power gain values or a message informing us that we have requested an illicit phi/azimuth pattern. If we need far-field values very near to ground level, we may specify a very small elevation angle, such as 0.1 degree and also set a finite distance for the pattern's field strength readings.)

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The result of our phi/azimuth pattern request is a pattern that involves something other than a flat circle. Instead, the field strength and power gain values occur on the surface of a cone. Many directional antenna patterns do not show the same elevation angle for the strongest forward lobe as for the strongest rearward lobe. When we examine the 180-degree front-to-back ratio calculated from pattern data by NEC software implementations, we discover that the ratio rests on the strength of the rearward lobe at the same elevation angle that we set for the forward lobe. At very low angles, the polar plot pattern does not show any significant distortion that results from the transfer of the conical surface data to a flat circular or polar plot. However, as we increase the angle, foreshortening distortions occur. Fig. 5 shows a sample of the situation, although the sketch is itself imperfect.

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The conical section on the left shows an elevation angle of 60 degrees (or a theta angle of 30 degrees). Let us suppose that we have sliced the cone vertically at page or screen level so that we see only half of the cone's surface. The visible section shows us the forward lobe of a hypothetical beam. The angle marked at the top of the sketch shows the beamwidth of the visible lobe. However, even this angle is slightly off the mark, since it transfers a curved surface that slopes away (or toward) the page or screen directly onto the flat page or screen. Nevertheless, the angle is close enough to the actual value to demonstrate what happens when we create a phi/azimuth pattern from this information.

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On the right is a polar plot of the pattern. The circles represent rings around the cone. For simplicity, the polar plot uses a linear set of ring scales so that the distance between rings is the same for both the conical section and for the polar plot. When we plot the points of contact between the rings and the pattern width onto the polar plot, we obtain the pattern in the flat polar plot. The plot produced by any graphic addition to NEC uses the data in its radiation pattern report, and this data results in the plot shown, assuming that we have specified the phi/azimuth pattern situation shown on the left.

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The conical section assumes that the half-power points of the pattern happen to coincide with the intersection of the pattern line with the next-to-outermost ring. Each point will shows a gain value that is 3 dB lower than the maximum power gain for the antenna. Those points will yield the same gain values when transferred to the flat polar plot. If we create the angle included between those points on the polar plot, we obtain an angle that is a bit over twice as wide as the angle included by the corresponding points on the surface of the cone. In fact, the proper relationship for the 60-degree elevation angle is 2:1, but remember that the representation of the cone surface is distorted by its representation on a flat surface.

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For most cases where the antenna is considerably above ground, we may determine (or approximate) the actual horizontal beamwidth from the reported value that results from the foreshortening effect of transferring a conical section to a flat circle.

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BWa = BWr * cos(elevation) or BWa = BWr * sin(theta)

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BWa is the actual horizontal beamwidth, BWr is the NEC report of the beamwidth, and the indicated angles are the elevation or theta angle at which we take the phi/azimuth pattern. For example, at an elevation angle of 45.4 degrees (the take-off angle that results from pointing the antenna at an angle of 45 degrees upward), we have a reported horizontal beamwidth of 27.8 degrees. The cosine of 45.4 degrees is 0.702. Multiplied times the reported horizontal beamwidth, we obtain 19.5 degrees actual beamwidth, a value that falls between the listed free-space value and the E-plane value that occurs with an elevation angle of 90 degrees.

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To confirm that the horizontal beamwidth has not actually undergone any significant change as we elevate the antenna, let's examine a few 3-dimensional patterns. Fig. 6 shows the subject antenna's patterns at aiming angles of 60, 75, and 90 degrees relative to ground. The pattern resolution is only 5 degrees, so considerable detail is missing from the graphics. The alternative would be to use a very small pattern increment and end up with patterns that appear only as black blobs.

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Despite te missing detail, we can observe that the main lobe of the beam retains its essential shape throughout the changes in elevation angle.

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Conclusion

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These notes represent an attempt to improve our understanding of oft-overlooked aspects of phi/azimuth patterns. The first exercise explored the differences between logarithmic and linear plots. The log plot emerged essentially to lend to phi/azimuth patterns a uniformity that had been lacking in commonly used linear plots. Since we may select the inner limit and the increment for a linear polar plot, these patterns may vary widely for applications that are not subject to external standards. Any user-developed linear polar plot of power gain values should plainly show the inner limit used. As well, the text should explain the rationale for the inner limit selection, even if the explanation is no more than a reference to an external or corporate standard.

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Phi/azimuth patterns over ground represent patterns taken on a conical surface. At small elevation angles, polar plots do not severely distort the conical section by transferring the data to a flat circle. However, as we increase the elevation angle for the phi/azimuth plot, the transfer does introduce appreciable foreshortening or broadening of the actual pattern. One result is a misreport of the horizontal beamwidth of an antenna, although we may use a simple calculation to produce a reasonable approximation of the correct value.

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These are but two of many aspects of NEC modeling results that we tend to overlook in the process of trying to produce usable data from a carefully constructed model geometry. However, even the best model is subject to misinterpretation of the output data unless we are very careful in how we present it and how we read the presentation.

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107. Scaling Models

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L. B. Cebik, W4RNL

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Scaing antennas from one frequency to another is common practice. In general, we wish to capture certain performance characteristics that we find at one frequency and transfer them to another. The most straightforward way to achieve this goal is to scale the antenna that has the desired characteristics.

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We often need or desire to scale antenna models from one frequency to another. The techniques of model scaling are identical to those of direct antenna scaling, although the way in which we go about the task may differ with the implementation of NEC or MININEC that we are using. Many implementations of modeling cores have a pre-core-run facility for either full or partial model scaling. As well, we may use one of the commands within the full NEC command set to arrive at the same result--a sort of unadvertised special.

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Basic Scaling

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To scale a model from one frequency to another requires us to change the element length, the element spacing, and the element diameter (or radius) everywhere in a model or antenna. Let's call the general idea of something to change when scaling the "dimension." We shall have an old or starting set of dimensions and a new or final set of dimensions. The amount of change depends on the old frequency or wavelength and the new frequency or wavelength. The basic formula is simple:

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+new wavelength       old frequency       new dimension
+--------------   =   -------------   =   -------------
+old wavelength       new frequency       old dimension
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Note that the dimension changes are directly proportional to the ratio of ratio of wavelengths and inversely proportional to the ratio of frequencies. Since we generally work with frequency in most initial thinking, we simply take the ratio of the old to the new frequency and multiply every old dimension by the value. The easy way to check on whether we are using the correct ratio is to remember that elements get shorter and thinner as we scale up in frequency and longer and fatter as we scale down in frequency.

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Some implementations of NEC and MININEC allow you to enter the wire diameter as an AWG value. In many instances, we forget to scale the wire diameter along with the element length and spacing. The cure is to remember to look at the wire gauge or diameter before declaring that the scaling is complete. In some cases, very thin wire antenna elements will show only small performance changes if we forget to change the wire size and if we are only scaling over a limited frequency range--for example, converting a 14-MHz antenna design to 18 MHz. However, the fatter the element or the greater the scaling ratio, the more significant it becomes to make certain that we scale the element diameter or radius along with the other dimensions.

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In NEC and MININEC, precise scaling will yield identical performance at both the old and the new frequencies only if certain model conditions exist. First, the antenna material should be "perfect" or "lossless." Even high conductivity materials such as copper show different working values of conductivity as we change frequency. The skin effect changes slowly as we change frequency--enough to show up in results that only make a relatively small frequency change during scaling. Second, the antenna environment should be free space or a perfect ground. Ground effects from any lossy ground change with frequency, again enough to show up in models that we scale over a relatively small range if the antenna is within a few wavelengths of the earth's surface.

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In most cases, it is useful to remove material losses and a lossy ground from an antenna model prior to scaling. Then proceed with the scaling calculations and test the model using the new values--remembering to a. change the test frequency for the revised model and b. save the model under a revised file name. Once you are satisfied that the scaling operation is correct, you can add in the material loss factor (LD5) and the lossy or real ground constants (GN).

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Sample Program Scaling Facilities

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Many implementations of NEC and MININEC contain facilities to assist in the scaling process. Let's sample a full scaling facility and a partial scaling facility. For a subject antenna, we shall begin in all cases with a 2-element Yagi designed for 28.5 MHz. To further focus on the scaling activity, I have placed it in free space and used lossless elements. So our only project will be to scale the antenna to 14.25 MHz. The ratio of the old frequency to the new frequency is 2:1 to keep the arithmetic obvious.

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We also have the option of manually calculating the new dimensions and manually entering them into the wire or GW entries. However, in some programs, such as EZNEC, we need not go through this process. Consider the 2 screens in Fig. 1 taken from the initial 10-meter antenna model. The upper screen shows the wire entries with all dimensions in meters. The lower screen shows our design frequency.

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EZNEC implements scaling through the frequency selection screen. Note the box marked "Rescale." Let's revise the frequency to 14.25 MHz and also click on the rescale box. The result will be the set of wire entries shown in Fig. 2. The user made none of the changes in the wire tables. Rather, the program made the necessary changes after the user entered the new frequency and checked the rescale box.

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Element length values appear in the Y-columns, with the spacing values in the X-columns. The program uses wire diameter as the entry dimension, and it has its own column. A quick comparison of Fig. 1 and Fig. 2 shows that EZNEC's scaling facility has doubled the element length, the element spacing, and the element diameter for the entire model geometry. The version of EZNEC on which I ran these models used NEC-4. For both models--the 10-meter and the 20-meter versions--the free-space gain reported as 6.28 dBi, with a 180-degree front-to-back ratio of 11.25 dB. In both cases, the feedpoint or source impedance was 32.59 - j0.30 Ohms.

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Not all programs that provide scaling facilities scale everything. Consider the same model in its NEC-Win Plus form, as shown by the upper portion of Fig. 3. The 10-meter antenna has the same dimensions as the EZNEC model. Because NEC-Win Plus uses NEC-2, we expect very small changes in the output report values. The free-space gain is 6.28 with a front-to-back value of 11.25. The source impedance is 32.58 - j0.55 Ohms. The differences from the NEC-4 report are wholly insignificant.

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The lower portion of the figure shows the scaling screen that the user accesses by clicking on a special button near the top of the NEC-Win Plus screen. The screen contains a wealth of information on the scaling maneuver, showing both initial and final values before the user locks the changes into place. To use this screen effectively, I blocked the full wire lines for the model from the left to the right extremes. The blocking encompassed everything, including segmentation, coordinates, wire diameter, and wire material.

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The scaling operation requires the user to enter the scaling factor, in this instance, 2.0. As well, the user must remember to change the model frequency before running the revised model. After making these changes and locking in the re-scaling, I ran the model. It returned a gain of 6.18 dBi, a front-to-back ratio of 11.72, and a source impedance of 33.57 - j70.01 Ohms. Something has gone astray, and in this case, it was carrying over operational expectations from one program to another.

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Fig. 4 shows us what went wrong by not reading the instructions appropriate to this implementation of NEC-2. The NEC-Win Plus scaling facility changes only the element lengths. However, as the X-column shows, it does not automatically change the spacing. As well, the diameter column shows that the program does not automate the diameter scaling. Hence, the model that gave us the aberrant results is not a true scaling of the original antenna. If we double both the element spacing and wire diameter, the corrected 20-meter scaling of the 10-meter Yagi produces the same output reports.

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Different implementations of NEC and MININEC will handle re-scaling a model in ways that range from a totally manual operation to complete automation. Since scaling is such a simple arithmetic operation, it usually makes little difference how we make the required changes. The key is to make all of them.

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The NEC GS Command The GS command in the NEC set is so easy to use that most instruction sets tend to overlook it. Even the NEC manuals give it only brief treatment. The command structure has only 3 entries, two integers and one floating decimal.

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+CMD      I1      I1      F1 (FSCALE)
+GS        0       0      0.3048
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The command's common use is to convert the units of measure in preceding geometry commands (such as GW) into meters, if they are not already in meters. The command must appear after all of the geometry commands that use an alternative unit of measure and before the GE or geometry section end command. NSI software provides a help screen for entering the scaling values, as shown in Fig. 5.

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For manual entry of the conversion unit, the integer entries are zero. Some manuals say they are not used. However, some core versions have automated conversion entries. If I1 = 1, then the conversion is from feet to meters (0.3048). If I1 = 2, then the conversion is from inches to meters. In these cases, I2 and F1 might not appear, or I2 might be zero. However, if both I1 and I1 are zero, then F1 must have a conversion factor value. The user can insert any appropriate value. For example, if the geometry entries are in millimeters, then the value of F1 is 0.001.

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+CM 2el Yagi 7.9/8.67/4.25 fs
+CE
+GW 1 21 0. 8.67 0. 0. -8.67 0. .04167
+GW 2 21 4.25 7.9 0. 4.25 -7.9 0. .04167
+GS 0 0 0.304800
+GE 0
+FR 0 1 0 0 28.5 0
+GN -1
+EX 0 2 11 0  1.00000  0.00000
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
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The sample model is essentially the same 2-element 10-meter Yagi, but with the 2 elements entered in feet. Hence, the conversion factor in the GS line is 0.3048. Since the dimensions are rounded, we shall find a very slight variance in the output reports, but at levels that are wholly insignificant. For example, the reported source impedance for the Yagi is 32.54 - j0.36 Ohms using the NEC-4 core.

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Suppose that we enter our coordinates and wire radius in meters. Since we do not need to convert the units to meters, we might overlook the GS card. The top portion of Fig. 6 shows the 10-meter Yagi entered in meters. However, the GS card is still useful to us in scaling the antenna to 14.25 MHz from its original frequency, 28.5 MHz. Note the "custom" conversion factor shown in Fig. 5. The lower portion of Fig. 6 shows the revised and scaled Yagi model with the GS card used to do the scaling--along with the required revision of the FR entry.

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To confirm the correct functioning of the GS command, we may examine a 1-line extract from the NEC output report's "Segmentation Data" section that lists the coordinates of all segments in the model. The first line for one end of the GW1 command appears for both the pre-scaled and the post-scaled models. The Y-coordinate, the segments lengths, and the wire radius entries show the scaling accomplished by the GS command. Both models in NEC-4 report a gain of 6.28 dBi, a front-to-back ratio of 11.25 dB, and a source impedance of 32.58 - j0.33 Ohms.

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+28.5-MHz Yagi Model
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.00000   2.51714   0.00000   0.25171    0.00000 -90.00000   0.01270     0    1    2      1
+14.25-MHz Yagi Model
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.00000   5.03429   0.00000   0.50343    0.00000 -90.00000   0.02540     0    1    2      1
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Other GS Potentials

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The GS command scaling potential is not limited to simple one-shot frequency conversions. The following practice is one sample of what we may do with the command in a more systematic way. We shall initially enter all geometry commands in meters. We shall also change the subject antenna to a 6-element Yagi. However, our basic design will use a frequency of 299.7925 MHz. At this frequency, 1 meter = 1 wavelength. Our basic model might resemble the following lines.

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+CM 6-el 300 Yagi
+CE
+GW 1 21 0. .251 0. 0. -.251 0. .001
+GW 2 21 .1251 .2484 0. .1251 -.2484 0. .001
+GW 3 21 .1705 .2312 0. .1705 -.2312 0. .001
+GW 4 21 .321 .225 0. .321 -.225 0. .001
+GW 5 21 .4617 .225 0. .4617 -.225 0. .001
+GW 6 21 .6713 .2167 0. .6713 -.2167 0. .001
+GE 0
+FR 0 11 0 0 295 1
+GN -1
+EX 0 2 11 0  1.00000  0.00000
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
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We may scale this Yagi to any frequency whatever using the GS command and one easy calculator step. The required GS custom conversion entry adheres to a simple equation where CF is the conversion factor.

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+CF = 299.7925 / new frequency
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Suppose that we wish to scale the Yagi to 15 MHz. The value of CF is 19.986167 (or any usable rounding of that value). The revised model would have the following appearance.

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+CM 6-el 300 Yagi
+CM Scaled to 15 MHz via GS
+CE
+GW 1 21 0. .251 0. 0. -.251 0. .001
+GW 2 21 .1251 .2484 0. .1251 -.2484 0. .001
+GW 3 21 .1705 .2312 0. .1705 -.2312 0. .001
+GW 4 21 .321 .225 0. .321 -.225 0. .001
+GW 5 21 .4617 .225 0. .4617 -.225 0. .001
+GW 6 21 .6713 .2167 0. .6713 -.2167 0. .001
+GS 0 0 19.986167
+GE 0
+FR 0 1 0 0 15 1
+GN -1
+EX 0 2 11 0  1.00000  0.00000
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
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Both models return a free-space gain of 10.28 dBi, a 180-degree front-to-back ratio of 31.12 dB, and a source impedance of 58.77 + j10.09 Ohms at 299.7925 MHz and at 15 MHz. The purpose of using the 6-element Yagi lies in the original model's frequency sweep specification. For a center frequency of about 300 MHz, the usable operating passband is about 10 MHz. Within that passband, the design has a free-space gain of at least 10.1 dBi, a 180-degree front-to-back ratio of 19.5 dB or higher, and a 50-Ohm SWR of under 1.3:1. When we apply the scaling conversion factor, we must also apply it to the operating passband. Hence, at 15 MHz, the equivalent passband is only about 0.5 MHz wide.

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The scaling technique is perfectly general and may be useful in a variety of modeling activities. However, it also has limitations. Perhaps the most notable limit is the wire radius, which is just under 20 mm at 15 MHz. Unless we are very judicious in constructing our master models, we may still have to optimize them at other frequencies for changes in wire radius, as well as for tapered element diameter schedules in HF antennas. However, any method of scaling an antenna design will result in these same supplementary tasks.

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One tendency among modelers is to freeze the potential for the GS command into an unbreakable habit. For example, some modelers believe that the GS command must precede the GE command and follow all other geometry commands. However, the command is more flexible than this over-simplified view. The GS command must simply follow the set of geometry commands that use a unit of measure other than meters. The following artificial sample mixes measures. GW1, the reflector, has its units in feet, while GW2, the driver, uses meters. We may as an exercise retain the mixed measures by inserting the GS card immediately after GW1 to convert its dimensions to meters. The following GW2 entry is unaffected by the action of the GS command.

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+CM 2el Yagi 7.9/8.67/4.25 fs
+CE
+GW 1 21 0. 8.67 0. 0. -8.67 0. .04167
+GS 0 0 0.304800
+GW 2 21 1.295 2.408 0. 1.295 -2.408 0. .0127
+GE 0
+FR 0 1 0 0 28.5 0
+GN -1
+EX 0 2 11 0  1.00000  0.00000
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
+
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The technique just described has very limited application. Using a uniform set of coordinate measures throughout the geometry section of a model is always good practice. Nevertheless, the technique does illustrate that the GS command is a bit more flexible than we might have previously thought.

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A more common situation might be to develop an initial model in a preferred set of units that are not meters. Then we might wish to scale the antenna. Although we shall use our simple 2-element Yagi as an illustration, the time factor required for manual revision of all geometry entries will increase very sharply for highly complex models. However, we might ease the task by using multiple GS cards. Consider the 28.5-MHz Yagi with its dimensions in feet. Next, we wish to scale the antenna to 14.25 MHz. The resulting model might have the following appearance.

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+CM 2el Yagi 7.9/8.67/4.25 fs
+CM Scaled to 14.25 MHz via GS
+CE
+GW 1 21 0. 8.67 0. 0. -8.67 0. .04167
+GW 2 21 4.25 7.9 0. 4.25 -7.9 0. .04167
+GS 0 0 0.304800
+GS 0 0 2
+GE 0
+FR 0 1 0 0 14.25 0
+GN -1
+EX 0 2 11 0  1.00000  0.00000
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
+
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The example shows that we may use strings of GS entries to accomplish different tasks. We might also have combined the two conversion factors externally. However, Murphy's Law tells us that in 3 months, we will no longer be able to remember what the GS value of 0.6096 means. Sometimes, separate entries (each with an appropriate side notation) are more useful. The small time it takes to enter 2 GS commands can save much head-scratching time later on.

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Conclusion

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Frequency scaling of antenna designs has a wide range of uses. They encompass practical design work as well as systematic explorations of antenna properties at various frequencies. As noted early on, scaling best occurs using a free-space or perfect-ground environment, with other model variables introduced after verification of successful scaling.

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The methods available to us for scaling designs also cover a considerable territory. We may manually calculate and enter scaled geometry values. We may use the facilities provided by the interface programming of the particular NEC or MININEC implementation that we are using. If we have access to the complete NEC command set, then we may achieve the same ends via the GS or geometry scaling command. The command is useful for more activities than just converting units of measure to meters. To confirm correct command use or to record the resulting coordinate and radius values, we must consult the NEC output report, using the segmentation-data section as our primary resource. I do not anticipate widespread use of the GS command for frequency scaling exercises in NEC. Nevertheless, it is useful to be aware of the command's potential and versatility.

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108. Dipoles: Variety and Modeling Hazards
+ Linear, V, and Folded Dipoles in NEC

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L. B. Cebik, W4RNL

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A dipole is in basic texts any antenna that exhibits a single current maximum to minimum transition from the center feedpoint to the wire end, and conversely, transitions from minimum to maximum voltage as we move from the center to the outer end of the wire. Basic antenna theory rests to some degree on the performance or the behavior of very short dipoles. In practical antenna circles, the term "dipole" is generally shorthand for a specific subset of these antenna. A practical dipole is a center-fed, resonant or near resonant 1/2 wavelength antenna usually using linear (wire or tubing) construction. When the antenna grows too long, we no longer have the current and voltage transitions that define the dipole, and so the antenna becomes a doublet--a center-fed wire with otherwise relatively undefined characteristics.

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In these notes for relative newcomers to antenna modeling, I shall use the practical-dipole definition. Practical dipoles include the idea of resonance, that is, a center feedpoint impedance that is entirely resistive (or nearly so), with no (or very little) remnant reactance. These antennas are very practical for many applications. At this point, we begin to encounter physical variations on the usual linear dipole construction. The key parameter shifts from the pattern of current an voltage along the wire to resonance, and we use resonance to determine that an antenna is an electrical half wavelength long and hence a dipole. Under this revised view of a practical dipole, we encounter many configurations, all of which count as dipoles if we use resonance and an electrical half wavelength as the key determining factors. Fig. 1 shows a number of these configurations, but by no means all of them.

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The standard linear dipole and its impedance-transforming partner, the folded dipole, are most familiar to virtually all antenna users. The fan dipole is actually 2 dipoles for separate frequencies with a common feedpoint. The V dipole occurs most commonly as an inverted V, although we may set the V angle at any value. At 90 degrees, with the legs parallel to the ground, we obtain a quadrant antenna. We may also form Ls and inverted-Ls with corner feedpoints as variations on the Vee. The zigzag dipole is simply any set of relative small departures from a truly linear arrangement, usually done to fit a dipole within a restricted space. The hatted dipole uses symmetrical structures at each end of the main element to obtain resonance with a shorter overall length than a full-length dipole requires. The bent or inverted-U form achieves element shortening with single extensions. However, these extensions radiate with vertical polarization, whereas the hat structures usually have self-canceling fields. The final example of a shortened dipole uses fold-back structures. The sketch shows only one of many possible forms, sometimes called the lazy N.

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These notes are not designed to evaluate the relative merits of the various configurations. Instead, we want to examine the modeling challenges that some of them might present. Some of the practical dipoles can easily result in unreliable models if we do not attend to software limitations, especially of NEC. So we shall examine the dipoles using both NEC-2 and NEC-4. One of our tools will be the Average Gain Test (AGT), which assesses the reliability of a model by sampling a lossless model in free space (or over perfect ground, which is not relevant here) over a full sphere of points and comparing the average gain to an isotropic source. Hence, an AGT value of 1.000 is excellent, but values above and below that value indicate potential degrees of unreliability. For source impedances close to resonance, we can derive corrected values by multiplying the AGT value times the reported source resistance. We can also convert the AGT value to a value in decibels. If the derived AGT-dB value is positive, we subtract it from the reported gain to obtain a correct gain value. (This note applies at any vector from the antenna, not just to maximum gain.) If the derived AGT-dB value is negative, we add its absolute value to the reported gain, since it tells us by how much (approximately) the gain report is low. We must always remember that the AGT is a necessary but not a sufficient condition of model adequacy. A good AGT score does not guarantee model adequacy.

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This first portion of our journey will deal only with modeling some of the dipoles in NEC (both -2 and -4). In the next episode, we shall compare our results with modeling the same antennas in at least two versions of MININEC. Once we have the basic terms and limits of each program under our belts, we can take up the remaining versions of the dipole using both general types of antenna modeling programs.

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The Standard Linear Dipole

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We may begin with the linear dipole. For our tests, we shall use a frequency of 28 MHz, with a 1" diameter lossless element. The only challenge is not skimping on the segments. Although the minimum segmentation per wavelength is 10, the recommended minimum is 20. Of course, in NEC, we use an odd number of segments to obtain a center source position. However, we need not always strive for the minimum recommended number of segments. The test model uses 41 segments. Our only opposing danger would be to use so many segments that we press the segment-length to wire-diameter (or radius) ratio. 41 segments with a 1" diameter comes nowhere close to such pressure. Fig. 2 shows the 3-dimensions free-space pattern and overlays the typical E-plane (azimuth) figure-8 pattern with which we are familiar. The listed gain figure sometimes surprises newer modelers who hear that a lossless dipole in free space has a gain of 2.15 dBi. That value applies to dipoles using vanishingly thin elements, which would be significantly longer than our 1" element. Shortening a linear dipole, even if only enough to restore resonance due to using a fat element, results in a gradual gain reduction.

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The impedance figure is from NEC-4. NEC-2 yields 71.95 + j 0.17 Ohms. Both values are from the EZNEC cores through version 4.0.20. Different implementations of NEC-2 and NEC-4 may use different Fortran compilers and result in values that differ even from these. In fact, different CPUs in various computer types can also result in variations, although all will be harmlessly small. Both NEC-2 and NEC-4 agree on the AGT score: 1.000, which requires no corrective on the gain or source resistance report.

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The total antenna length for our sample model is 199.4", although it will be more convenient for us to speak in half-lengths: +/-99.7". For many of our "deviant" dipoles, the half-length will be a useful catalog number. Although the antenna is an electrical half wavelength, as indicated by the resonant source impedance, the physical wire is only 0.473 wavelength.

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The V Dipole

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V dipoles occur using almost any included angle between the wires. Let's restrict ourselves to a single angle of 90 degrees between wires. That is equivalent to bending each leg 45 degrees from the linear configuration. In terms of modeling, the action will necessarily result in a model with at least 2 wires. MININEC models will place the source on the junction of the two wires at the apex. However, uncorrected MININEC 3.13 will provide two kinds of errors if we are not careful. First, there is a frequency offset that increases with rising frequency. Second, MININEC creates errors in current calculations at sharp angular wire junctions. We can largely overcome the second error condition by using a very large number of segments, since the amount of error varies with the segment lengths. However, many later implementations of MININEC 3.13 provide corrections for both error sources within the code and yield very reliable results. However, unless you possess more than one version of MININEC 3.13, you may not be able to assess the level of correction available within the program you use. I have provided some performance comparisons over a number of MININEC potential trouble spots in a past column.

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NEC users face a slightly different challenge. Since the apex of the V will be a junction of 2 wires and since NEC sources lie within segments, we must figure out where to place the source. Fig. 3 shows 3 of our options. The black squares are segment junctions, while the red dots are potential source locations. For all of our tests here, we shall stay at 28 MHz and retain the 1" diameter lossless element.

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The top version of the V model uses a simple procedure of placing the source on one of the segments adjacent to the apex of the V. The justification lies in the fact that at high current regions of most antennas, the current changes very slowly as we move away from the precise antenna center. Hence, the potential error is very small, especially since these models use the same total number of segments as the linear dipole (actually 42). The bottom model uses a split or dual source, with a source placed on each side of the apex. EZNEC will internally total the sum of the two source impedance values, but manual addition is simple enough. Otherwise, the model is identical to the top offset-source model.

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The middle model uses a different technique. It creates a level wire at the center. The wire uses 3 segments so that the segments adjacent to the center source segment are of equal length with the source segment. That model design maneuver tends to yield maximum accuracy in the current calculations. Each wire extends +/- 7.5" from the center point. The sloping legs each have 19 segments, for a total of 41 segments in the model, and the leg segment lengths are close to the length of the segments in the source wire.

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Fig. 4 shows two relevant facts about the models. The wire layouts have superimposed current magnitude curves that verify the current distribution as appropriate to a dipole as defined earlier. The E-plane patterns broadside to the plane of the V structures are virtually identical. To a casual viewer, the models might seem indistinguishable. However, the following table shows that there are indeed a few important distinctions among them.

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+Comparison of V-Dipole Models in NEC-2 and NEC-4
+All models use 1" diameter lossless elements in free space.
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+Source     Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+Method              Inches          dBi      R +/- j X Ohms                          Gain dBi
+Offset     NEC-2    +/-103.3        1.52     44.75 + j0.02        0.949   -0.23      1.75
+           NEC-4    +/-103.3        1.50     45.00 - j0.22        0.943   -0.25      1.75
+Split      NEC-2    +/-103.3        1.52     44.75 + j0.22        0.949   -0.23      1.75
+           NEC-4    +/-103.3        1.50     45.01 + j0.02        0.943   -0.25      1.75
+3-Wire     NEC-2    +/-102.3        1.72     41.31 + j0.25        1.004    0.02      1.70
+           NEC-4    +/-102.3        1.73     41.26 + j0.00        1.005    0.02      1.71
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+Note: Wire Length is the total half-element length from the apex to the tip in offset and split-source versions and from the source point to the wire tips in the 3-wire version.
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Between the offset-source and the split-source models we find only tiny differences. For each core, the difference falls mostly in a 0.2 consistent differential in the source reactance. We might assign the gain difference between NEC-2 and NEC-4 versions to differences in the core. This assignment would be correct, but not merely due to random compiler or CPU operations. If we move to the AGT and AGT-dB columns, we find values that are far less than perfect. The differences in the AGT values relative to the 2 cores are small but significant. If the initial gain report seemed low, it was. A corrected gain report brings the value more within expectations for a full-size antenna, even if we allow for some broadside gain loss to compensate for the shallower side nulls in the E-plane patterns.

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The less than perfect AGT values result from the use of relatively fat elements. Each segment is about 5" long, and the wire diameter is 1". At the apex of the V, the wire segments that join inter-penetrate a considerable, but not fatal distance relative to any use to which one might apply the model. If we had used thin wires, the small wire diameter would have resulted in much less penetration toward the junction segment centers, and the AGT values would have been closer to ideal values. Obviously, I have constructed the sample model to reveal the effect, rather than hiding it by the use of thin wires.

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The 3-wire version of the model achieves a set of AGT values much closer to ideal Whether the very small difference in correct gain values is a function of the core or of the slightly different structure is indeterminate from the available data, but we do note that the total amount of element from the source point to the element tip differs by an inch from the 2-wire models. As well, we may note that the 3-wire models result in lower source resistance values. However, you may wish to compare the values after multiply each reported resistance by the basic AGT value.

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Even if we discount this sequence of models as unlikely candidates for implementation, they do reveal the importance of making constant reference to the AGT values of a model. Had we used the raw reports from the 2-wire models as a comparator to the linear dipole, we would have drawn very wrong conclusions about the degree of gain deficit. As well, we should not be too hasty in discounting the models, since the design, turned 90 degrees so that all elements parallel the ground surface, forms a common structure of some antennas with forward-sweep elements.

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Folded Dipoles

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Folded dipoles are actually hybrid constructions. They are indeed dipoles, but the folded structure adds an extra set of currents. These transmission-line currents are a function of the folded dipole's impedance transformation relative to a linear dipole. The upper left portion of Fig. 5 shows the result of combining the 2 sets of currents. The transmission line currents are relatively constant in magnitude. Hence, the radiation currents overlay them. The resulting curve rises above and falls below the average current magnitude, but does not go to zero at the ends of the wires, as we would find for a linear dipole.

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Once we separate the two currents, the radiation currents are virtually identical to those that we find in a linear dipole. Hence, the radiation pattern on the upper right is indistinguishable from the patterns of standard dipole. The resonant folded dipole will be shorter than a line dipole, since the effective diameter of the two parallel wires, each the same diameter as the single wire in a linear dipole, is considerable greater. The 28-MHz model of a folded dipole with 1" diameter elements is 4.5" shorter at resonance than the linear dipole that we reviewed earlier. The modeled folded dipole uses a wires separation of 2" center-to-center, with 41 segments in each long element section.

+

With both elements having an equal diameter, the resonant impedance is between 281 and 282 Ohms, or about 4 times the impedance of a single element dipole (70 Ohms). However, the exact ratio of impedance transformation is only 4:1 if both elements have the same diameter. The lower half of Fig. 5 shows the key elements in calculating the transformation ratio, R. The equation involves the spacing (s) between elements and the relative diameters of the two element sections, where d1 is the section with the feedpoint and d2 is the section parallel to the driven section. Note that s, d1, and d2 must use the same units of measure for the equation to produce usable results. If both elements have the same diameter, then the ratio of logs reduces to 1, and the ratio turns out to be 4. If the driven section is smaller, then the ratio is greater than 4:1. If the undriven section is smaller, then the ratio is less than 4:1 but always greater than 1:1.

+

We may reduce the undriven section to any diameter. Let's use 0.1". The equation yields 1.89:1 as the transformation ratio. If we assume a linear dipole impedance of 70 Ohms, then the folded dipole with a larger driven section and a smaller undriven section should show an impedance close to 132.5 Ohms. Slight variations will occur because the equation does not take the end connecting wires into account. We shall use the same segmentation level (41 segments per section) that we used on the folded dipole with equal-diameter sections. Since the transformation involves only the transmission-line currents, the gain and pattern of the folded dipole with unequal-diameter elements should be the same (within close tolerances) as the corresponding results from the equal-diameter folded dipole. The following table summarizes the results for both kinds of folded dipole using both NEC-2 and NEC-4.

+ 
+Comparison of Folded-Dipole Models in NEC-2 and NEC-4: Equal and Unequal Diameter Elements
+All models use 1" diameter lossless driven elements in free space.  Second elements are 1"
+or 0.1" diameter lossless wires.
+
+Diameters     Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+Driven/Other           Inches          dBi      R +/- j X Ohms                          Gain dBi
+1"/1"         NEC-2    +/-97.45        2.13     281.6 - j0.54        1.000    0.00      2.13
+              NEC-4    +/-97.45        2.13     281.5 - j0.96        1.000    0.00      2.13
+1"/0.1"       NEC-2    +/-99.2         4.34     230.2 - j10.59       1.662    2.21      2.13
+              NEC-4    +/-99.2         2.96     164.5 + j0.60        1.209    0.82      2.14
+              Calculated Impedance              132.5
+Note: Wire Length is the total half-element length from the center to the tip.
+
+

The equal-diameter version of the folded dipole shows good results from both NEC-2 and NEC-4, since both cores produce an AGT of 1.000. The gain values are identical, and the reported impedance values are almost identical. However, the reported values for the folded dipole with unequal diameter sections fall way off the mark. NEC-2 is considerably worse than NEC-4 with respect to anticipated values of gain and impedance. In fact, both NEC-2 and NEC-4 become error prone with angular junctions of wires having dissimilar diameters. NEC-4 improves upon the performance of NEC-2 in this regard, but falls seriously into error as the change of diameter increases. In this model, the ratio is 10:1, so that even NEC-4 yields an unacceptable AGT value. Note that the AGT-dB values bring the gain report close to the anticipated value. However, at a certain level, the AGT value itself becomes useless in correcting the reported source resistance. MININEC does not share the NEC limitation relating to changes in element diameter at wire junctions. Hence, it is generally able to handle models like the folded dipole with unequal-diameter element sections with no problems. If the version of MININEC 3.13 has had other limitations corrected, then it should yield quite accurate results for our test case.

+

Both models that we have just examined used 41 segments on each long wire. The results are a set of well-aligned segment junctions in the closely spaced parallel wires. Although providing each wire with the same number of segments seems quite natural, we sometimes encounter cases of somewhat careless segmentation. Fig. 6 shows the center portions of equal-diameter folded dipoles that differ only in the assignment of segments per wire. (All end connection wires use 1 segment.) In one case, we have 61 segments on the driven wire and 31 on the other wire. The second case reverses the assignment. At the bottom, the figure shows the segmentation of the preferred model.

+
+ +
+

The upper two models clearly do not show a pattern of well-aligned segment junction. The following table shows the results of the misalignment, with all other factors being the same for all three models.

+ 
+Comparison of Folded-Dipole Models in NEC-2 and NEC-4: Careless vs. Careful Segmentation
+All models use 1" diameter lossless elements in free space.
+
+Segments      Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+Driven/Other           Inches          dBi      R +/- j X Ohms                          Gain dBi
+61/31         NEC-2    +/-97.45        1.88     342.5 + j2.31        0.946   -0.24      2.12
+              NEC-4    +/-97.45        1.71     329.1 - j2.33        0.909   -0.41      2.12
+31/61         NEC-2    +/-97.45        1.84     263.6 + j2.23        0.937   -0.28      2.13
+              NEC-4    +/-97.45        2.00     273.1 + j1.26        0.971   -0.13      2.12
+41/41         NEC-2    +/-97.45        2.13     281.6 - j0.54        1.000    0.00      2.13
+              NEC-4    +/-97.45        2.13     281.5 - j0.96        1.000    0.00      2.13
+
+Note: Wire Length is the total half-element length from the center to the tip.
+
+

Fig. 6 provides the NEC-4 reported data for each model. The degree to which the unevenly segmented models depart from correct values depends on both the core used (NEC-2 or NEC-4) and the ratio of segments in the 2 wires, where the ratio shows the misalignment. Admittedly, the sample models provide cases of extreme misalignment. However, even small misalignments can draw the results away from the ideal AGT values attained by the model with well aligned segments. Alignment becomes ever more critical as we close the spacing between wires. Once more, it pays dividends to check the AGT values for any model. Checking those values becomes even more important when we need or wish to compare the reports of one model with another, whether we are using similar or dissimilar geometries.

+

Conclusion to Part 1

+

We have not gone very far in our exploration of resonant half wavelength dipoles, and already we have seen some modeling snares. Some of those traps are modeling practices that we can easily avoid. Others involve limits to the NEC cores that we cannot avoid except by deferring the model construction. Folded dipoles with unequal elements form one of those NEC limitations and require the use of antenna modeling software that lacks the particular limitation involved. MININEC is one of those usable cores.

+

In addition to running into potential pitfalls, we have also run out of room in this column. Therefore, we shall have resume our journey in the next episode. We shall discover whether or not MININEC can handle those odd folded dipoles--and more.

+
+ +

+

Go to Main Index

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+

109. Dipoles: Variety and Modeling Hazards
+ Linear, V, and Folded Dipoles in MININEC

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the last episode, we explored modeling dipoles in NEC (-2 and -4). Along the way, we discovered (or re-discovered) some NEC limitations. Although we noted the use of MININEC along the way, we did not pause long enough to see clearly the degree to which MININEC (3.13) is subject to the same limitations, is subject too more severe limitations, or is able to overcome the noted limitations in NEC. Since many newer modelers (and a good number of quite experienced modelers) use MININEC, we should re-trace our steps, highlighting the alternative modeling program along the way.

+

Our focus is on the many forms of the dipole, understood in practical rather than textbook terms. For our purposes, a dipole is a center-fed resonant or near resonant antenna that is about 1/2 wavelength electrically. In fact, resonance defines what an electrical half wavelength is, since the forms in which we encounter dipoles are many. Among the types listed at the beginning of the last episode are the standard or linear dipole, the V or quadrant, the folded dipole, the fan dipole (usually a dual-band pair of dipoles with a common feedpoint), the bent or inverted-U, the hatted dipole, and the dipole with element fold-backs. In the course of looking at just the standard, V, and folded dipoles, we encountered enough potential modeling hazards to give us pause. We shall continue the NEC journey in the next episode, but for now, let's examine our initial dipoles with MININEC.

+

NEC calculating cores tend to show only small variations among them. Most result from developments at the LLNL source. Since NEC-2 is public domain, we find most variants in commands within its iterations. NEC-4 has undergone fewer post-release developments and shows much greater uniformity. In fact, there are only two commercial implementations of NEC-4. Public domain MININEC (version 3.13) has undergone far greater modification from a larger number of programmers. Originally written in Basic, the program is almost always found in one of the Windows languages these days. As well, raw MININEC had a considerable number of limitations that recent programming has overcome. However, not all programmers have attended to all limitations. For example, the MININEC ground calculation system has two major problems. First, when using a lossy ground, MININEC calculates the source impedance as if over perfect ground. Second, for any antenna with a horizontal component to the total far field pattern, the MININEC ground calculations become ever more inaccurate relative to antenna gain and impedance as the antenna drops below about 0.2 wavelength. Because MININEC uses a simplified reflection coefficient, little is possible to correct it. However, a few programs have successfully grafted the NEC Sommerfeld-Norton ground calculation system onto MININEC.

+

Less obvious but equally significant are certain errors that infect some MININEC calculations. First, MININEC begins to show an offset relative to both NEC-2 and NEC-4 calculations. Some, but not all, implementations of MININEC have introduced corrections for this offset. Second, MININEC uses a system of current "pulses," which are at segment junctions (in contrast to NEC's current placement at segment center regions). Hence, without correction or the use of a very large number of segments, MININEC models of angular antenna geometries can show significant error. In fact, the more acute the angle, the larger the error. Raw MININEC also shows some error for very close spaced wires, and this difficulty has undergone correction in many MININEC implementations. Finally, MININEC lacks the extensive command structure that we find in NEC. Hence, it is limited in the manipulations that we can perform on both the geometry and on the output. For example, it does not permit the use of elliptical plane waves and segment current analysis useful in receiving and radar reflection analysis. As well, we find no near-field analysis, inter-segment coupling analysis, transmission lines, or networks. To overcome these voids, a number of programmers have introduced adjunct programs to allow the modeler to perform calculations involving some of these elements while using the implementation of MININEC. Given that virtually no two implementations of MININEC resolve the same set of limitations in the same way, the program has well earned the distinction between "raw" and "cooked" versions. There is, of course, a revised "Expert MININEC" set of programs, but these proprietary efforts do not use the same algorithms as MININEC 3.13.

+

Since we cannot hope to treat every version of MININEC and still attend to the variety of dipoles and their limitations for modelers, I have chosen 2 from my small stock: Antenna Model (the most corrected version of MININEC commercially available) and MMANA (one of the least-revised versions with the virtue of being free). Because MININEC cores undergo such regular modification, it is significant to give the versions involved: V1.77 for MMANA and 2.0.0.595 for Antenna model. At the same time, I shall adhere to the basic structure of all antennas that we examined in the preceding episode. The test frequency is 28.0 MHz. The antenna elements--unless re-specified for a special test--will be 1" in diameter and be lossless. The environment will be free space.

+

For most NEC models, I used 41 segment per half wavelength. The fairly large number ensures convergence within NEC. The odd number of segments in a linear element places a centered source directly at the element center, since NEC places sources on segments and not on segment junctions. In MININEC, current pulses and therefore sources occur at segment junctions. Hence, to precisely center a source requires an even number of segments on the element. We shall normally use 40 segment.

+

With these preliminaries, we are ready to examine the baseline antenna for all other work, the linear or standard dipole.

+

The Standard Linear Dipole

+

The linear or standard dipole is the root antenna for all of these exercises. As in NEC, a MININEC model must adhere to certain limits on the ratio of the wire diameter or radius to the length of a segment. However, there appears to be no full agreement on the absolute limiting ratio. Antenna Model (AM) provides warnings if the segment falls below 1.25 the wire diameter. However, the program also provides an Average Gain Test (AGT) value as a second check on the model. AGT is not a standard MININEC feature, but an added provision of the AM programmers.

+
+ +
+

Fig. 1 shows the model geometry of the MININEC dipole. The markers indicate segment junctions. The NEC models used 41 segments, so the basic MININEC model will use 40 segments. The feedpoint appears on pulse 20, a fact that is informative: a pulse does not occur on the segment-1/end-1 point of the antenna. For initial comparisons, I used the same element length that yielded resonant antennas in NEC: 199.4" or 5.065 m. (My version of MMANA counts in meters.) The following table compares the results of NEC-2, NEC-4, AM, and MMANA models of the dipole at 28 MHz.

+ 
+Comparison of Linear Dipole Models in NEC-2, NEC-4 and MININEC
+All models use 1" diameter lossless driven elements in free space.  AGT data not
+available in MMANA.
+
+Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+         Inches          dBi      R +/- j X Ohms                          Gain dBi
+NEC
+NEC-2    +/-99.7         2.14     71.94 + j0.12        1.000    0.00      2.14
+NEC-4    +/-99.7         2.14     71.95 + j0.17        1.000    0.00      2.14
+MININEC
+A-M      +/-99.7         2.13     71.79 - j0.54        1.000    0.00      2.13
+MMANA    +/-99.7         2.12     70.48 - j5.46
+
+Note: Wire Length is the total half-element length from the center to the tip.
+
+

Between the 2 NEC cores and AM, there is no difference. However, MMANA, a relatively uncorrected version of MININEC 3.13, reports a source impedance that indicates a slightly short length for the dipole. MMANA reports a resonant length of about 200.4" (5.10 m) with an impedance of 71.14 + j0.40 Ohms. The length differential is a bit over 0.5%: not a fatal difference, but an indicator of an offset that continues to grow more important with rising frequency.

+

The AGT is only one test of model adequacy. Equally important--especially in MININEC--is the convergence test. Basically, the convergence test provides information on the level of segmentation necessary for a given model's geometry. At some level of segmentation, successive increases in the number of segments per wire should not yield any significant changes in the reported gain or source impedance. There is no fixed level of adequate convergence, since the required level is normally a function of the use to which one puts a modeling task. However, there are some models that never converge, and convergence is a necessary condition of model adequacy. As well, some models arrive at good convergence with a low number of segments, while others require a higher segment density.

+

As a second mode of comparison, I altered the segment count in both the AM and MMANA dipoles, beginning with 10 and doubling that number in successive steps. The last step yields segment lengths that trigger the AM warning about the ratio of wire diameter to segment length. In all cases, the dipole remained at its initial 199.4" length. The following table compares results.

+ 
+A Comparison of Convergence Tests for a Linear Dipole in 2 Versions of MININEC
+AGT data not available for MMANA.
+
+Program     No. of        Gain     Source Impedance     Change in      AGT
+            Segments      dBi      R +/- j X Ohms       Resistance
+AM           10           2.10     70.08 - j1.31        ---            0.9981
+             20           2.12     71.34 - j0.96        1.26           0.9991
+             40           2.13     71.79 - j0.54        0.45           0.9996
+             80           2.13     71.92 - j0.53        0.13           0.9998
+            160           2.13     72.06 - j0.36        0.14           0.9999
+MMANA        10           2.10     67.95 - j9.73        ---
+             20           2.12     69.55 - j7.33        1.60
+             40           2.12     70.47 - j5.46        0.92
+             80           2.13     71.02 - j4.03        0.55
+            160           2.13     71.16 - j4.21        0.14
+
+

For many purposes, both models might be considered to be adequately converged at the lowest segment density. However, it is clear that AM shows a higher level of convergence at lower levels of segmentation than does MMANA. We may note in passing that AM reports a more nearly ideal AGT value with increasing segmentation, although all 3 of the reported values round to 1.000. In the end, the point of the exercise is a. to stress the importance of running convergence tests, even on models using a simple geometry, and b. to note that different implementations of MININEC may shows differentials in the rate of convergence.

+
+ +
+

Fig. 2 provides both 3-dimensional and E-plane patterns for the dipole. Although these plots come from AM, the E-plane pattern does not differ in MMANA. Note that the side nulls are exceptionally deep for the linear dipole, yielding a nearly indefinitely large front-to-side ratio. Do not expect such deep nulls if you place the model over ground. At very low heights, the E-plane pattern will be at best an oval. At height of about 1 wavelength or more, the pattern will resemble a peanut.

+

The V Dipole

+

The V dipole includes in principle any electrical half wavelength, near-resonant antenna with legs that do not form a 180-degree angle. Although Vs come in many angles and orientations, the test models use a 90-degree angle (also called a quadrant antenna when both legs are parallel to the ground).

+

In NEC, the construction of a V dipole model required attention to the placement of the source. The actual feedpoint of a physical V antenna will be at the apex of the angle formed by the 2 wires. In NEC, we might use an offset source on the first segment of one of the wires meeting at the apex. Alternatively, we might use a split source, which yields two offset sources. We sum the impedance reported by both. The third alternative is to use a short level 3-segment wire and to place the source on the center segment. The angled wires then connect to the ends of the level wire. Although any of the three methods may be adequate for general purpose modeling, only the 3-wire model produced near-ideal AGT values. Again, the antenna used relatively fat (1" or 25.4 mm) elements to reveal any latent limitations that thin wire models might not detect.

+
+ +
+

In MININEC, modeling V dipoles is simpler, as shown in Fig. 3. Since the source appears at a pulse or a junction of 2 segments, we may place it directly at the apex of the V. The test models used 20 segments in each of the two wires. The following table compares the results for the NEC (-2 and -4) 3-wire model with the results for the AM and MMANA models. The AM model has priority in terms of setting the leg lengths. The MMANA model uses the AM dimensions to determine to what degree its reports may be at variance with the AM model reports.

+ 
+Comparison of V-Dipole Models in NEC-2, NEC-4, and MININEC
+All models use 1" diameter lossless elements in free space.
+
+Program    Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+                    Inches          dBi      R +/- j X Ohms                          Gain dBi
+3-Wire     NEC-2    +/-102.3        1.72     41.31 + j0.25        1.004    0.02      1.70
+           NEC-4    +/-102.3        1.73     41.26 + j0.00        1.005    0.02      1.71
+AM         MININEC  +/-104.65       1.76     44.32 - j0.68        1.002    0.01      1.75
+MMANA      MININEC  +/-104.65       1.75     43.54 + j2.67
+
+Note: Wire Length is the total half-element length from the apex to the tip in MININEC models
+and from the source point to the wire tips in the 3-wire NEC version.
+
+

We cannot draw any immediate conclusions from the difference in wire length from the antenna center to the tip because the MININEC and NEC models have slightly different geometries. However, the MININEC model achieves an excellent AGT rating in AM with the single centered source and only 2 leg wires.

+

The MMANA V-dipole model seems to be more coincident with the AM model than was the MMANA linear dipole model. However, MININEC has two potential error sources at work. One is the frequency offset. The other is the corner effect. If both are uncorrected, then they may in some cases be additive and in other cases be partially canceling. These error sources do not self-identify. However, we may again perform a convergence test on the two MININEC models of the V in order to compare changes in the performance. In the following table, the segment entry indicates the total number of segments. Half appear in each leg of the V.

+ 
+A Comparison of Convergence Tests for a V Dipole in 2 Versions of MININEC
+AGT data not available for MMANA.
+
+Program     No. of        Gain     Source Impedance     Change in      AGT
+            Segments      dBi      R +/- j X Ohms       Resistance
+AM           10           1.79     42.59 - j47.98       ---            1.0081
+             20           1.77     43.80 - j15.69       1.21           1.0046
+             40           1.76     44.32 - j0.68        0.52           1.0025
+             80           1.76     44.55 + j6.03        0.23           1.0013
+            160           1.76     44.65 + j8.09        0.10           1.0009
+MMANA        10           1.76     41.56 - j23.24       ---
+             20           1.75     42.82 - j5.82        1.26
+             40           1.75     43.54 + j2.67        0.72
+             80           1.75     43.99 + j6.64        0.45
+            160           1.75     44.14 + j7.56        0.15
+
+

Although the models show only small overall convergence test changes, the AM model is slightly more converged at lower segmentation levels than the MMANA model. AGT data are not available for the MMANA model. However, the AM models shows improving AGT values as the segmentation level increases, just as did the linear dipole model in AM. We may also note that the MMANA spread of reactance values is smaller than for AM. In this instance, the addition of segments to the model wires reduces the effect of the corner error tendency. Since most available versions of MININEC no longer have the very restricted total segment allowance that bothered DOS versions of the program, the use of many segments is no longer a hindrance to model construction or calculation speed, and accuracy improves in most cases. Although we must keep in mind that the MMANA model may be a product of two error tendencies that appear to partially cancel with the particular geometry of the present antenna, there is no reason not to use either MININEC model as the basis for building a V antenna (at least in free space).

+
+ +
+

The models used for the V dipole extend their legs in the -Z direction (downward, in earth terms). Hence, they radiate side-to-side as well as broadside. Both the 3-dimensional and E-plane patterns in Fig. 4 show the reduced depth of the side nulls. Since the patterns are normalized to the maximum gain of the antenna, we must consult the data tables to find the loss in maximum gain relative to a linear dipole that makes up the energy that fills in the side nulls.

+

Folded Dipoles

+

Both NEC-2 and NEC-4 handled the standard folded dipole well. The standard folded dipole employs driven and undriven long element sections that use wires having the same wire diameter. However, if we attempt to transform the feedpoint impedance by ratios other than 4:1, NEC models begin to fail. The degree of failure depended on the ratio of the two wire diameters, because NEC becomes error prone with angular junctions of wires with dissimilar diameters.

+

Modeling folded dipoles (and related structures, such as T matches and gamma matches) is an arena in which MININEC is superior to NEC. MININEC generally lacks any tendency toward error when we change the element diameters either along a linear section or at corners. To set up a MININEC folded dipooe, we use an even number of segments in the long element sections, since on one of those sections, we shall center a source. Fig. 5 shows the general layout, along with the impedance transformation equation for reference.

+
+ +
+

In the standard or 4:1-ratio folded dipole, all 4 wires will use 1" diameter lossless material, and the wires will be 2" apart. The alternative folded dipole uses 0.1" diameter elements for all wires except the 1" wire with the source segment. The MININEC long wires will use 40 segments, with 1-segment end wires. As we calculated in the last episode, the folded dipole should show a source impedance close to 132.5 Ohms. Let's run the MININEC models in both AM and MMANA and compare the results with those obtained from NEC-2 and NEC-4.

+ 
+Comparison of Folded-Dipole Models in NEC-2, NEC-4, and MININEC: Equal and Unequal Diameter Elements
+All models use 1" diameter lossless driven elements in free space.  Second elements are 1"
+or 0.1" diameter lossless wires.
+
+Diameters     Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+Driven/Other           Inches          dBi      R +/- j X Ohms                          Gain dBi
+1"/1"         NEC-2    +/-97.45        2.13     281.6 - j0.54        1.000    0.00      2.13
+              NEC-4    +/-97.45        2.13     281.5 - j0.96        1.000    0.00      2.13
+              AM       +/-97.70        2.13     281.9 + j0.35        1.000    0.00      2.13
+              MMANA    +/-97.70        2.11     278.6 + j37.92
+1"/0.1"       NEC-2    +/-99.2         4.34     230.2 - j10.59       1.662    2.21      2.13
+              NEC-4    +/-99.2         2.96     164.5 + j0.60        1.209    0.82      2.14
+              AM       +/-99.5         2.17     137.5 + j2.96        1.008    0.04      2.13
+              MMANA    +/-99.5         2.17     133.3 + j4.89
+              Calculated Impedance              132.5 (if a linear dipole = 70 Ohms)
+Note: Wire Length is the total half-element length from the center to the tip.
+
+

The data are very interesting and in more ways than establishing that both versions of MININEC are superior to NEC in handling folded dipoles with unequal elements. Note that when we use unequal element sizes (1" and 0.1" or 25.4 mm and 2.54 mm), the two versions of MININEC produce results that are very similar to each other, differing by no more that the linear dipoles differed. In contrast, the folded dipole with equal-diameter elements shows resonance in AM but has a considerable reactive component in MMANA. One possible source of the reactive component is the fact that uncorrected MININEC has a sensitivity to very closely spaced wires. With a pair of 1" diameter elements, the surfaces of the wires are 1" apart. When we use the unequal elements, the separation increases to 1.55".

+

In any model, it is always good practice to align to the degree feasible the segment junctions in parallel wires, especially when they are closely spaced. In NEC, we saw significant differences in the reported results when we radically misaligned the segments, using combinations of 31 segments in one wire and 61 segments in the other for the standard equal-diameter folded dipole. MININEC shows considerably less sensitivity to misaligned segments than either NEC-2 or NEC-4. To demonstrate the lesser sensitivity, I assigned 30 segments to one wire and 60 to the other for both AM and MMANA models. The following table shows the results, along with the NEC data for reference.

+ 
+Comparison of Folded-Dipole Models in NEC-2 and NEC-4: Careless vs. Careful Segmentation
+All models use 1" diameter lossless elements in free space.
+
+Segments      Core     Wire Length     Gain     Source Impedance     AGT     AGT-dB     Corrected
+Driven/Other           Inches          dBi      R +/- j X Ohms                          Gain dBi
+61/31         NEC-2    +/-97.45        1.88     342.5 + j2.31        0.946   -0.24      2.12
+31/61                  +/-97.45        1.84     263.6 + j2.23        0.937   -0.28      2.13
+41/41                  +/-97.45        2.13     281.6 - j0.54        1.000    0.00      2.13
+61/31         NEC-4    +/-97.45        1.71     329.1 - j2.33        0.909   -0.41      2.12
+31/61                  +/-97.45        2.00     273.1 + j1.26        0.971   -0.13      2.12
+41/41                  +/-97.45        2.13     281.5 - j0.96        1.000    0.00      2.13
+60/30         AM       +/-97.70        2.13     285.8 - j1.77        1.002    0.01      2.12
+30/60                  +/-97.70        2.12     278.0 + j1.17        0.999   -0.01      2.13
+40/40                  +/-97.70        2.13     281.9 + j0.35        1.000    0.00      2.13
+60/30         MMANA    +/-97.70        2.12     282.3 + j38.95
+30/60                  +/-97.70        2.10     274.5 + j39.19
+40/40                  +/-97.70        2.11     278.6 + j37.92
+
+Note: Wire Length is the total half-element length from the center to the tip.
+
+

The AM model shows only very small differences among its reported results, with gain deviations of no more than 0.01 dB relative to the well-aligned case. Although AGT correctives are not available for MMANA, its range of values are nearly as tightly clustered as the AM values. Since one example cannot certify the relative lack of sensitivity for all model geometries, good segment alignment remains good modeling practice, whatever core you may be using.

+
+ +
+

Fig. 6 shows 3-dimensional and E-plane patterns in free space for the equal-diameter folded dipole, as modeled in AM. The MMANA E-plane pattern would be identical, as would be the patterns for the unequal-diameter versions of the antenna. Note that the side nulls are almost but not quite as deep as the side nulls for the simple linear dipole. Do not forget that even the short end-connection wires do radiate, even if only a little.

+

Conclusion to Part 2

+

We have caught up to the NEC dipoles with our MININEC models. By framing the MININEC models in an episode of their own, we have been able to see a bit of the difference between corrected and uncorrected versions of MININEC, although in the HF region, the differences are small. Some of the differences become very significant at VHF and UHF frequencies, such as the frequency offset. As well, we have been able to see some modeling applications for which MININEC is superior to NEC, especially for geometries similar to the unequal-diameter folded dipole. Those applications are more numerous than one might initially believe. For that reason, I keep versions of both NEC and MININEC at hand, using the most accurate tool for any given job. Of course, we have also seen that for a number of cases, it makes no differences whether we use NEC or MININEC.

+

Still, we have fallen behind in our journey through the variety of dipoles. We have yet to work with inverted Us and hatted dipoles. Farther down the trail, the zigzag and fold-back versions await us. And at the end of this trip--but certainly not the end of all dipole varieties--stands the fan dipole for multi-band use. From this point forward, we shall be able to deal with our dipole types using NEC and MININEC together. From the standpoint of identifying modeling pitfalls and work-arounds, the sojourn should prove interesting.

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+

Go to Main Index

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+

11. A Ground Is Just a Ground--Unless It Is a Model of a Ground

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Recent months have brought me a series of questions relating to the use of a ground selection beneath a model. In addition, a few models that I have checked have shown a variety of ground selection errors. So it seems fit that we become a little better grounded in grounding. +

Ground Types in NEC-2 and MININEC

NEC-2 offers the modeler several different choices of grounds beneath the antenna, including no-ground (free space). Each has its own set of best applications for both speeding preliminary work and for final analysis of greatest accuracy. Let's familiarize ourselves with the types of ground, their typical entry in a .NEC file, and what they mean. +

1. Free Space: the term "free space" indicates that absence of any surface beneath the antenna. Therefore, the antenna radiates in all directions without reflections (other than those that are a function of the modeled antenna structure itself). Choice of free space or "no-ground" is often the best for comparison of antennas of similar types. Moreover, it usually provides the most rapid calculation speeds and yields the highest accuracy output data.

+

The absence of ground may appear in a .NEC file as simply no ground entry, that is, no GN card. It may also appear as the following:

+
+ 
GN  -1
+
+

2. Perfectly Conducting Ground: This option places beneath the antenna a perfectly conducting surface with perfect reflection properties--at a distance specified by the entries in the Z-axis column of the wire geometry cards. Although a wire may contact a perfect ground, horizontal wires should be above ground by a factor of at least the following:

+
+ +
+

where "h" is the wire height and "a" is the wire radius. In addition, h should be several times greater than "a" for valid results.

+

Since a perfect ground creates an image antenna identical to the original, it requires twice as long to fill the interaction matrix as a free space model. However, it is still faster than the use of either of the ground condition approximation systems. Thus, it has some interesting developmental applications. Selection of a perfect ground results in the following GN card entry:

+
+ 
GN  1
+
+

3. Finite Ground: Reflection Coefficient Approximation: Sometimes called the "fast" or "real" ground, this system employs an image model modified by Fresnel plane-wave reflection coefficient approximations for near fields. This system loses accuracy as an antenna is brought within several tenths of a wavelength toward the ground or lower and is most apt to relatively compact antenna structures. Nonetheless, it yields quite reasonable results, especially for preliminary developmental work, and is much faster than the more accurate Sommerfeld-Norton method.

+

Every finite ground requires at least the specification of values for the conductivity (in S/m) and the dielectric constant (permittivity) of the ground. A table of typical values for various types of soil appears further on in this colum. In general, vertical antennas close to the ground are more sensitive to changes in soil type than are horizontal antennas at their typical heights well above the ground surface. A typical GN card for a "fast" ground using "average" soil would appear as follows:

+
+ 
GN  0  0  0  0  13  .005
+
+

4. Finite Ground: Sommerfeld-Norton Method: The more accurate but slower (by a factor of 4) Sommerfeld-Norton (S-N, or SOMNEC) ground method uses exact solutions for fields in the presence of the specified ground and is accurate very close to ground. In fact, you may place wires as close to an S-N ground as to a perfect ground. For the highest accuracy of results for an antenna model above ground, the S-N method is the ground of choice. Except for the entry immediately following the card identification, a simple S-N ground entry looks identical to a reflection coefficient approximation ground entry card. For example,

+
+ 
GN  2  0  0  0  13  .005
+
+

As with all ground surfaces, the S-N ground extends indefinitely to the horizon. The S-N ground method also has provision for a second medium that extends a specified radius within ground specified in the card just shown. For our initial sampling of ground applications, we shall confine ourselves to simple grounds, that is to grounds whose properties extend from the antenna to infinity.

+
+ +
+

Selecting a ground type within NEC-2 takes different forms depending upon the way in which the program implements the process. The illustration above shows the pull-down box used in NEC-Win.

+

MININEC offers fewer ground type selections. Equivalent to the ones in NEC-2 are free space and perfect ground. The "real" ground system in MININEC is comparable (although not identical) to the "fast" ground system in NEC-2. It becomes less accurate for horizontal wires at heights greater than the accuracy limit for the NEC-2 "fast" ground system, and is generally considered inaccurate below 0.2 wavelengths of antenna height. (Note: these height limitations apply to horizontal or sloped wires with significant horizontally polarized radiation. Vertical antennas will require separate treatment.) In addition, the MININEC implementation of "real" ground applies only to far field calculations. MININEC calculates source impedance data using perfect ground, even when a "real" ground is selected. This feature can lead to source impedance errors for low horizontal wire antennas, such as those commonly used in the lower HF bands.

+
+ +
+

Selecting a MININEC ground type follows the same procedure as for NEC-2, with fewer selections. The illustration from NEC4WIN provides a sample.

+

EZNEC, which is an implementation of NEC-2, offers the use of the MININEC ground system in addition to the standard NEC-2 selections. This system is intended for use with certain types of models of vertical antennas, a topic we shall reserve for another column.

+

Ground Quality Description

The illustrations show a second facet of ground selection when the choice is "real," "fast," or "S-N": the selection of ground quality. There are two factors involved in filling in this choice: conductivity and dielectric constant (permittivity). Conductivity is measured in Siemens per meter and must always be entered as a decimal for anything other than salt water. One can measure soil conductivity, but the use of local or nationwide maps and tables is usually more convenient. The dielectric constant is normally beyond the means of most amateurs to measure and should be derived from a listing. It is virtually always an integer. +

NEC and MININEC create from the two numbers a composite used in creating values to correctly derive the reflections that contribute to the far field. Be certain to correctly locate the entry position for each value in the set. Reversing the values can create some interesting but erroneous modeling results. I once encountered a Beverage antenna with an apparent gain of 17 dBi until the ground quality figures were correctly placed.

+

The following soil descriptions are commonly used in antenna modeling. Always substitute more precise values wherever known. The table represents an adaptation of values found in The ARRL Antenna Book (p. 3-6), which are themselves an adaptation of the table presented by Terman in Radio Engineer's Handbook (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. Terman's value for the conductivity of the worst soil listed is an order of magnitude lower than the value shown here.

+ 
Soil Description                   Conductivity   Permittivity   Relative
+                                   in S/m         (Dielectric    Quality
+                                                   Constant)
+
+Fresh water                        0.001          80
+
+Salt water                         5.0            81
+
+Pastoral, low hills, rich
+soil, typical from Dallas,
+TX, to Lincoln, NE                 0.0303         20             Very Good
+
+Pastoral, low hills, rich
+soil, typical of OH and IL         0.01           14             Good
+
+Flat country, marshy, densely
+wooded, typical of LA near
+the Mississippi River              0.0075         12
+
+Pastoral, medium hills, and
+forestation, typical of MD,
+PA, NY (exclusive of mountains
+and coastline)                     0.006          13
+
+Pastoral, medium hills, and
+forestation, heavy clay soils,
+typical of central VA              0.005          13             Average
+
+Rocky soil, steep hills,
+typically mountainous              0.002          12-14          Poor
+
+Sandy, dry, flat, coastal          0.002          10
+
+Cities, industrial areas           0.001          5              Very Poor
+
+Cities, heavy industrial areas,                                  Extremely
+high buildings                     0.001          3               Poor
+

One of the preset values pairs offered by EZNEC is called "good" but uses the values for average soil from the table above.

+

Some Ground Modeling Limitations

In general, the best compact source of information on the effects of ground on antenna performance is Chapter 3 of recent editions of The ARRL Antenna Book. The information there will help you understand some of the limitations of modeled grounds. +

First, modeled grounds consist of flat, uncluttered surfaces. Unless you specifically model ground clutter into the overall antenna model, its effects will not appear in the reported antenna performance figures and graphics.

+

Second, because modeled ground is flat from the antenna to the horizon (or stepped at a uniform radius or in a regular square), the modeling program does not take into account terrain variations that may be very important to a given antenna situation. Both K6STI and N6BV have developed experimental software to help translate modeled results into reasonable expectations for variable terrain.

+

Third, the ground beneath an antenna model is uniform to an indefinitely large depth. Although this model of ground is sufficient for the upper HF region and above, at the lower HF region and below, it may not accurately portray the ground conditions for an antenna. The ground beneath an antenna is normally stratified and changes quality with depth. Lower frequency signals can penetrate the earth to considerable depths and thus be variably affected by the changing soil quality. At best, for modeling purposes, one can develop only an average single pair of quality figures for complex soils.

+

In addition to these limitations, we have noted that some ground modeling systems have accuracy limitations for horizontal antennas. However, we might best view these from a modeled example.

+

Horizontal Antennas Over Various Grounds

The following tables compare the values reported for a horizontal dipole over the various ground systems for NEC-2 and MININEC. For this test, I used EZNEC Pro in the NEC-2 mode for the NEC test, and ELNEC for the MININEC test. For each test I used a #14 copper wire dipole resonated initially in free space. In NEC-2, the length was 16.70', and the antenna yielded 2.08 dBi gain with a source impedance of 72.6 - 0.9 Ohms. In MININEC, the length was 16.75', which yields a gain of 2.14 dBi and a source impedance of 71.6 - 0.5 Ohms. All tests over ground used average ground (conductivity = 0.005 S/m; dielectric constant = 13). Gain is in dBi, Take-off angle is in degrees, and source impedance is in the form R +/- jX Ohms. +

In the tables, "N-Perfect" is NEC-2, perfect ground. "N-S-N" is the NEC Sommerfeld-Norton high accuracy ground system, generally considered to be the present standard of accuracy. "N-Fast" refers to the simplified ground system available in NEC. "N-MIN" points to a feature available only in EZNEC, which is the implementation of the MININEC ground system within NEC-2. "M-Perfect" in the gain table means perfect ground in MININEC, while "M-Real" refers to the real ground system in MININEC. In the source impedance table, "MININEC" covers both, since the source impedance is always calculated with reference to perfect ground in that system.

+ 
Gain and Elevation Angle of Maximum Radiation (Take-Off Angle) (xx/yy)
+
+Height (wl/ft) N-Perfect N-S-N     N-Fast    N-Min     M-Perfect M-Real
+1.0/34.5'      8.16/14*  7.59/14   7.58/14   7.58/14   8.17/14*  7.60/14
+0.9/31.1'      7.58/16   7.16/16   7.16/16   6.94/16   7.59/16   6.94/16
+0.8/27.6'      7.65/18*  7.09/17   7.10/17   6.93/17   7.66/18*  6.94/17
+0.7/24.2'      8.46/21   7.44/20   7.47/20   7.65/20   8.48/21   7.67/20
+0.6/20.7'      9.10/25   7.73/23   7.72/23   8.17/23   9.11/25   8.18/23
+0.5/17.3'      8.36/30   7.25/28   7.20/28   7.26/28   8.35/30   7.25/28
+0.4/13.8'      7.13/38   6.23/35   6.21/35   5.79/35   7.14/39   5.81/35
+0.3/10.4'      6.91/54   5.70/49   5.66/49   5.21/49   6.92/56   5.22/49
+0.2/ 6.9'      8.05/90   5.80/90   5.82/90   6.09/90   8.07/90   6.10/90
+0.1/ 3.5'      8.66/90   3.55/90   4.21/90   7.45/90   8.67/90   7.48/90
+

*At the indicated heights, both NEC and MININEC register the second lobe above ground to be the take-off angle (49 degrees and 70 degrees, respectively for the two heights in order). However, there is no significant difference in strength between the two lobes over perfect ground, and the lower one is shown here for tabular consistency.

+
+ +
+

The maximum gain figures are charted in the figure above to save a bit of time in tracking the tables. (Detailed tracking is well advised to become familiar with the minor differences in expectations for reported figures.). The variations in gain with antenna height are in general quite natural. They can be tracked against changes in the elevation patterns for the antenna at each height. When we move from the most general level to specifics plotted in the graph, however, certain changes take on significance in terms of modeling accuracy.

+

The most significant portion of the graph is to the far right. Contrast the rise in reported gain from using the MININEC ground (either in MININEC itself or within the EZNEC version of NEC-2) with the gain decreases reported by the two NEC ground systems. Note also that the NEC "fast" ground reports a higher gain than the Sommerfeld-Norton system. Even though the MININEC ground reports parallel the reports over perfect ground, they are quite untrustworthy over real ground at these low heights.

+

There are a few less evident anomalies between ground systems. MININEC and NEC perfect ground lines are in excellent accord, as are the S-N and "fast" ground reports above 0.3 wl antenna height. However, NEC shows less variation in gain reports over the more reliable span of the graph than does the MININEC ground, whichever system uses it.

+ 
Source Impedance (R +/- jX Ohms)
+Height (wl/ft)    N-Perfect  N-S-N      N-Fast     N-Min       MININEC
+1.0/34.5'         71.0-10.0  71.1-6.0   71.3-6.0   71.0-10.0   70.7-9.8
+0.9/31.1'         81.4-6.0   77.3-4.4   77.4-4.2   81.4-6.0    81.1-5.7
+0.8/27.6'         81.1+6.8   78.0+2.9   77.8+3.2   81.1+6.8    80.9+6.9
+0.7/24.2'         67.6+11.2  70.7+6.4   70.3+6.2   67.6+11.2   67.3+11.5
+0.6/20.7'         57.6-2.0   63.9-0.3   64.0-0.9   57.6-2.0    57.3-1.5
+0.5/17.3'         67.4-17.8  68.1-10.1  69.0-10.3  67.4-17.8   67.2-17.4
+0.4/13.8'         89.8-14.0  81.6-8.8   81.9-9.0   89.8-14.0   89.2-13.9
+0.3/10.4'         96.8+12.7  86.0+5.4   86.7+5.8   96.8+12.7   96.5+13.0
+0.2/ 6.9'         68.6+36.8  72.1+17.8  71.9+20.1  68.6+36.8   68.8+37.1
+0.1/ 3.5'         23.0+20.9  55.7+9.3   48.1+13.7  23.0+20.9   22.4+21.0
+

The gain inaccuracies at low heights reported by the NEC "fast" ground and the MININEC standard ground are accompanied by inaccuracies in reported source (feedpoint) impedance. Like the gain figures, MININEC figures are more extremely in error than those of the NEC "fast" ground, but both are untrustworthy.

+

Although I tend to distrust both the MININEC and NEC "fast" ground system below 0.25 wl horizontal antenna height, standard recommendation set a limit of about 0.2 wl. For reference, here is a chart of heights (in feet and meters) corresponding to 0.2 wl for selected frequencies in the amateur bands from 160 to 6 meters.

+ 
Frequency             0.2 wl            Frequency          0.2 wl
+in MHz            Feet       Meters     in MHz         Feet       Meters
+ 1.875            104.9      32.0       18.1           10.9       3.31
+ 3.5               56.2      17.1       21.1            9.32      2.84
+ 4.0               49.2      15.0       24.9            7.90      2.41
+ 7.1               27.7       8.45      28.1            7.00      2.13
+10.1               19.5       5.94      29.5            6.67      2.03
+14.1               14.0       4.25      52.0            3.78      1.15
+

Getting Used to Pattern Differences Over Different Grounds

In the early stages of antenna modeling, it pays to explore systematically the available ranges of program parameters using simple antennas, such as the sample dipole we used to demonstrate the similarities and differences in gain and source impedance reports at various antenna heights. In some cases, you will want to examine tabular data; in other cases, graphical patterns will best illustrate differences. +
+ +
+

The first major difference with which to familiarize yourself is the patterns differences between using perfect ground and using any of the real grounds. The figure shows a sample for a dipole 1 wl up between modeling it over perfect ground and over real ground. The most striking feature, of course, is the higher gain over perfect ground. As well, note the depth of the nulls in the pattern over perfect ground and the shallower nulls over real ground. Straight up, the antenna over real ground has significant radiation, in contrast to the antenna over perfect ground. Note also that the two lobes over perfect ground are very close to equal strength, whereas over real ground, the second lobe is significantly reduced in strength.

+

A second set of differences appear if we model a horizontal antenna over various qualities of ground. Although some routinely assert that the ground quality makes virtually no difference for a horizontal antenna, this statement is only relatively true at antenna heights approaching and above 1 wl. At lower heights the ground can begin to make a notable numerical difference. Whether that numerical difference makes a significant operational difference requires to modeler to examine the antenna within its intended framework of use.

+

Suppose we place our 10-meter dipole at heights of 1 wl and 1/2 wl above ground. Then let us systematically change the ground quality through a few standard variations, as defined earlier in this column. Gain figures are in dBi, while the Take-off angle is in degrees.

+ 
Ground            1 wl Height                1/2 wl Height
+Quality           Gain/TO Angle              Gain/TO Angle
+Perfect           8.16/14                    8.34/30
+Very Good         7.83/14                    7.67/28
+Average           7.58/14                    7.18/28
+Poor              7.56/14                    7.13/28
+Very Poor         7.16/14                    6.43/27
+VG to VP gain
+  difference      0.67 dB                    1.24 dB
+
+ +
+

Increasing the antenna height by double almost halves the gain differential between very good and very poor soils. At low heights, as shown in the elevation patterns in the figure, typical of horizontal antennas for the lower HF bands, soil quality can make a difference in the potential performance of a horizontal antenna. Above 1 wl for the antenna height, the difference becomes ever less significant.

+

More to Come

We have looked at the general nature of modeled ground systems, as well as at some of the differences among ground qualities. Still, our look has been limited: we have only used horizontal antennas to draw out some basic distinctions. Everything appears to be quite systematic. Placing horizontal elements close to ground begins to exceed the accuracy limitations of some of the ground modeling systems. Ground quality seems to affect gain--and to a lesser extent, take-off angle--in a regular fashion, with poorer grounds reducing gain more than better grounds. +

However, there is another entire class of antennas with which we must contend: the vertically polarized antennas. We should not expect from this unruly antenna group the well-behaved figures we obtained for horizontally polarized antennas. Making sense of modeling verticals at, near, and well above ground will be our task next month.
+

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+

110. Dipoles: Variety and Modeling Hazards
+ Tapered-Diameter, Bent, and Hatted Dipoles

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

We have so far examined dipoles that are straight and uniform in diameter, as well as those that are center-bent to form a V. We also tackled folded dipoles. Our goal is not to give a lesson in dipoles, but to demonstrate modeling techniques and limitations that may even affect such a simple antenna. Throughout the first 2 parts of the sequence of episodes, we have treated dipoles as center-fed near-resonant half wavelength antennas, setting aside the textbook "short" dipole concept as outside our needs.

+

We devoted an entire episode to modeling dipoles in NEC and a second session covered modeling those same dipoles in MININEC. As we proceed through the remaining collection of dipoles, we shall handle both programs together, since we no longer need to provide any introductory orientation to them. However, we shall continue to group the programs, covering NEC-4 and NEC-2 together and likewise collecting the Antenna Model (AM) and MMANA versions of MININEC 3.13--as very refined and relatively raw forms of the basic core.

+

Tapered-Diameter Dipoles

+

When we looked at linear or standard dipoles, we gave them a uniform diameter throughout the element. However, in the HF region, we commonly encounter tubular dipoles (and similar elements in more complex arrays) that use a tapered-diameter (or a stepped-diameter) element. In general, a tapered-diameter element is one that--counting from the center or feedpoint--uses gradually smaller diameter portions of the element. We shall presume that the taper is symmetrical relative to the element center.

+

Fig. 1 shows the general set-up for a series of test models that we shall examine. For simplicity, we shall use only 2 different diameters in creating the dipoles, a fatter inner section, where inner means closer to the feedpoint, and a thinner outer section that extends to the element tip. Hence, the outer or larger diameter applies to the inner element section, and the inner or smaller diameter applies to the outer element section. For 2 of our tests, the inner 1" section of the dipole will be +/-50" (total 100"), while the last 2 tests will change that length, using +/-25" (total 50") in one case and +/-75" (total 150") in the other. In all cases, I shall vary the segment assignment so that the total number of segments in the NEC models is 41 and in the MININEC models is 40.

+
+ +
+

For reference, the original uniform-diameter 1" dipoles are +/-99.7" (total 199.4") at the 28.0 MHz test frequency, using lossless wires in free space. One feature that we cannot fail to notice about the tapered-diameter elements is that every one of them is longer. The increased length is a function of the fact that the effective diameter of the total element is well under 1", requiring a longer element. We shall examine what counts as the effective diameter shortly. However, let's first tell a short story about NEC.

+

NEC-2 used current algorithms that created an inherent problem using tapered-diameter elements. In brief, NEC-2 could not yield reliable results for elements using tapered-diameter linear elements. NEC-4 revised the current algorithms to overcome the limitation. In fact, NEC-4 considerably improves the performance of the system for tapered-diameter elements, but it is not perfect. How imperfect it might be depends on several different factors. NEC-4 tends to be more perfect when the step between diameters is relatively small. Hence, we have the first case that uses a diameter step from 1.0" down to 0.875". If we use a larger step, say, from 1" to 0.5" as in the second case, then NEC-4 is less perfect. The perfection of NEC-4 results also rests on where along the dipole that the step occurs. In general, the higher the current in the region where the step occurs, the more imperfect the result will be. Hence, we have cases 3 and 4 that use the 1"-0.5" combination, but with different lengths of 1" tubing.

+

NEC-2 shows the same general pattern as NEC-4, but more extremely so. The first two sections of the following table create resonant directly modeled NEC-4 dipoles and then re-runs each of them with NEC-2. For the NEC-2 and NEC-4 directly modeled dipoles, the performance of the uniform-diameter dipole appears as a point of reference. In all cases, NEC-2 shows significant deviation from NEC-4. The higher the ratio of the two diameters, the greater the deviation. As well, the shorter the inner-fatter dipole section, the greater the deviation. Note that the NEC-2 AGT value is always higher than the NEC-4 value (except for the uniform-diameter reference dipole). In NEC-4, case 3 (with the short inner dipole section), we find an AGT value that deviates more than a little from the ideal. However, the NEC-2 value for the same case is much higher yet. Our justified conclusion is that raw NEC-2 is unreliable with tapered-diameter linear elements. While NEC-4 is superior, it has limitations.

+ 
+NEC Performance with Various Tapered-Diameter Elements
+
+Model    Method    Outer/Inner    Inner/Outer  Segment    Gain    Source Impedance    AGT    AGTdB
+                   Diameters      Length       Order      dBi     R +/- jX Ohms
+NEC-4
+1-1      Direct    1              99.7         41         2.14    71.94 + j0.12       1.000  0.00
+2-1                1/0.875        50/50.6      10-21-10   2.15    72.37 + j0.06       1.002  0.01
+2-2                1/0.5          50/54.5      10-21-10   2.20    74.10 - j0.12       1.010  0.04
+2-3                1/0.5          25/77.9      15-11-15   2.26    73.52 - j0.04       1.023  0.10
+2-4                1/0.5          75/28.3       5-31-5    2.16    72.85 - j0.01       1.003  0.01
+NEC-2
+1-1      Direct    1              99.7         41         2.14    71.95 + j0.17       1.000  0.00
+2-1                1/0.875        50/50.6      10-21-10   2.17    72.80 + j4.30       1.007  0.03
+2-2                1/0.5          50/54.5      10-21-10   2.30    76.10 + j19.43      1.033  0.14
+2-3                1/0.5          25/77.9      15-11-15   2.47    71.49 + j13.12      1.074  0.31
+2-4                1/0.5          75/28.3       5-31-5    2.20    76.15 + j15.71      1.009  0.04
+Leeson corrections (Apply to NEC-2 and to NEC-4 Models)
+2-1      Leeson    1/0.875        50/50.6      10-21-10   2.13    71.72 - j0.68       1.000  0.00
+2-2    Substitute  1/0.5          50/54.5      10-21-10   2.13    70.28 - j6.40       1.000  0.00
+2-3     Elements   1/0.5          25/77.9      15-11-15   2.13    70.58 - j5.51       1.000  0.00
+2-4                1/0.5          75/28.3       5-31-5    2.13    71.56 - j1.27       1.000  0.00
+Leeson Revised for Resonance
+2-1      Leeson    1/0.875        50/50.6      10-21-10   2.13    71.72 - j0.68       1.000  0.00
+2-2    Substitute  1/0.5          50/54.8      10-21-10   2.14    71.93 + j0.17       1.000  0.00
+2-3     Elements   1/0.5          25/78.45     15-11-15   2.14    71.90 + j0.02       1.000  0.00
+2-4                1/0.5          75/28.45      5-31-5    2.14    71.87 + j0.11       1.000  0.00
+
+Notes:  Outer and inner diameters in inches.  Inner and outer lengths are for each half of the
+element, with dimensions in inches.  Segmentation order is for the full elements for the left
+outer section, the middle section, and the right outer section.  All element wires are lossless, and
+the environment is free space.
+
+

The standard method of providing more accurate results for linear tapered-diameter elements in both NEC-2 and NEC-4 is to use substitute uniform-diameter elements having the same impedance at the test frequency as the tapered-diameter elements. The equations used were developed by David Leeson, based on original work by Schelkunoff. (See Chapter 8 of Physical Design of Yagi Antennas.) When using the Leeson corrections, the program does not calculate with the originally modeled elements. Instead, it uses substitute elements having the calculated equivalent uniform diameter and length. Fig. 2 shows case 3 in final form. The equivalent uniform diameter is about 0.56", just a little fatter than the smaller of the two materials used in the dipole with the short inner section. Note also that the tip length limit is shorter than the tapered element in the upper section. The modeler does not vary the uniform-diameter substitute element. Instead, he changes the dimensions of the physical tapered-diameter element parts to achieve the desired goal--in this case, resonance.

+
+ +
+

The tapered- or stepped-diameter element corrections do have restrictions. There must be at least two wires in the group. At least two of the wires must have different diameters. All wires in the group must be collinear (in a straight line). All wires must be connected to each other. Both ends of the group must be open, or one end open and one connected to ground (a case that we shall not examine in these dipole notes). The group must be nearly resonant (within about 15% of half-wave resonance if both ends are open). Only one source is permitted in the group, and it must be at the center if the ends are open. If the ends are open and the center of the group is a wire or segment junction, the source must be a split source. The rules for loads are the same as for sources, except that two equal loads must be used wherever a split source would be used. A single transmission line can be connected to the group. If the ends of the group are open, the center of the group must be a segment center--not a segment or wire junction--and the transmission line can be connected only to this segment.

+

The third section of the table shows the corrections applied to the physical dimensions generated in the original NEC-4 models. With only a small diameter step, the model called 2-1 shows very similar results in NEC-4 with or without the corrections. Likewise, the model called 2-4--which uses a long inner section and a shorter tip--also displays similar impedance values for the uncorrected NEC-4 and the corrected versions. (Note that the table shows corrections using NEC-4 only. Corrected NEC-2 values are too close to the corrected NEC-4 values to require repetition. In fact, the 2 cores yield corrected values that are about as close together as the NEC-2 and NEC-4 values for model 1-1, the uniform-diameter dipole.)

+

The difficult cases are the second and third, both of which use a large diameter change between the two dipole sections, along with a shorter inner section. Although the gain report is not a problem, the source impedance is off the mark relative to establishing resonant lengths. Therefore, the final part of the table revises the physical tip length to yield corrected elements that are resonant. Comparing the outer-section lengths between the third and fourth parts of the table will give you an idea of what sort of adjustment these cases require--about 3/4" per dipole leg or about 1.5" overall.

+

One fair question that we might pose about the corrections is the method used to substantiate the essential correctness and adequacy of the equations. Part of the confirmation process involved comparing the corrected results with MININEC dipoles that we may directly model (without any correction) using the same stepped-diameter structure. Since MININEC uses current pulses located at segment junctions, it does not undergo the same errors with stepped-diameter elements experienced by NEC.

+

As a demonstration of MININEC's ability to handle tapered-diameter elements without need for correction. I took the final corrected structure lengths and created models in AM. The top portion of the following table shows the results. Only case 2-4 shows a significant deviation between the corrected NEC models and the MININEC model. However, for each case in which the source reactance report exceed +/-j1 Ohm, I revised the AM model to bring it within our working definition of resonance. In one case (model 2-3), I needed no revision. In two other cases, the tip-length revision was 0.2" or less.

+ 
+MININEC Performance with Various Tapered-Diameter Elements
+
+Model     Outer/Inner    Inner/Outer  Segment    Gain    Source Impedance    AGT    AGTdB
+          Diameters      Length       Order      dBi     R +/- jX Ohms
+AM
+1-1       1              99.7         40         2.13    71.79 - j0.54       1.000  0.00
+2-1       1/0.875        50/50.6      10-20-10   2.13    72.12 - j2.14       1.000  0.00
+2-1A      1/0.875        50/50.8      10-20-10   2.13    72.62 - j0.33       1.000  0.00
+2-2       1/0.5          50/54.8      10-20-10   2.16    75.30 - j1.38       1.000  0.00
+2-2A      1/0.5          50/54.9      10-20-10   2.16    75.56 - j0.51       1.000  0.00
+2-3       1/0.5          25/78.45     15-10-15   2.15    75.97 - j0.47       1.000  0.00
+2-4       1/0.5          75/28.45      5-30-5    2.14    72.09 - j4.33       1.000  0.00
+2-4A      1/0.5          75/29.0       5-30-5    2.17    73.35 - j0.06       1.000  0.00
+MMANA
+1-1       1              99.7         40         2.12    70.47 - j5.48
+2-1A      1/0.875        50/50.8      10-20-10   2.13    71.29 - j5.27
+2-2A      1/0.5          50/54.9      10-20-10   2.15    74.20 - j5.59
+2-3       1/0.5          25/78.45     15-10-15   2.15    74.76 - j5.22
+2-4A      1/0.5          75/29.0       5-30-5    2.14    71.97 - j5.20
+
+Notes:  Outer and inner diameters in inches.  Inner and outer lengths are for each half of the
+element, with dimensions in inches.  Segmentation order is for the full elements for the left
+outer section, the middle section, and the right outer section.  All element wires are lossless, and
+the environment is free space.  All models are direct.
+
+

I re-created the revised MININEC models using MMANA. The lower part of the table shows the MMANA results. Note that there is a consistent -j5-Ohm reactance on all of the sources, the same value that applies to the MMANA version of the uniform-diameter dipole. In the last episode, we attributed this reactance--relative to resonance in the AM models--to an uncorrected frequency offset in raw MININEC 3.13. In all other respects, the results are consistent with those of AM.

+

Inverted-U Dipoles

+

The NEC element taper corrections apply only to straight or collinear elements. However, not all dipoles are straight. In fact, one very old design--with many contemporary applications--is the inverted U, a dipole using a straight or horizontal section with the outer parts of the element pointed vertically downward (or, in free space, in the -Z direction). Although the bent section may have the same diameter as the horizontal section, when we use a tubular inner or horizontal element, the verticals often use either smaller tubing or wire. Therefore, to see the effects of changing vertical leg sizes, I set up the variations shown in Fig. 3.

+
+ +
+

The first option uses a horizontal length of +/-70" (total 140"), with the vertical legs long enough to achieve resonance. The second option shortens the horizontal dimension to +/-50" (total 100"), again with vertical legs long enough to resonate the dipole. For each option, I used 1", 0.5", and 0.1" diameter vertical end wires.

+

In the first table, we find the results for NEC-4 and NEC-2. Since the element corrections do not work with angular junctions in the elements, we only find the results for direct modeling. I resonated each models in NEC-4 and then re-ran it in NEC-2 to see the amount or variance created by the older core's lesser ability to handle junctions of wire with different diameters.

+ 
+NEC Performance with Various Inverted-U Dipoles
+
+Core     Horizontal     Vertical     Vertical       Gain    Source Impedance    AGT      AGTdB
+         Length         Diameter     Length/End     dBi     R +/- jX Ohms
+
+NEC-4    +/-70          1"           34.0           1.96    58.19 - j0.52       1.002     0.01
+NEC-2                                               1.96    58.35 + j0.43       1.002     0.01
+NEC-4    +/-70          0.5"         37.8           1.95    58.28 - j0.30       1.002     0.01
+NEC-2                                               1.94    60.91 + j16.55      1.001     0.01
+NEC-4    +/-70          0.1"         45.4           1.91    58.53 + j0.43       1.002     0.01
+NEC-2                                               1.90    65.69 + j45.32      1.002     0.01
+
+NEC-4    +/-50          1"           55.3           1.60    38.97 + j0.19       1.004     0.02
+NEC-2                                               1.60    39.06 + j1.16       1.004     0.02
+NEC-4    +/-50          0.5"         59.1           1.57    39.11 - j0.62       1.005     0.02
+NEC-2                                               1.56    40.48 + j17.46      1.006     0.03
+NEC-4    +/-50          0.1"         66.5           1.49    39.64 + j0.11       1.007     0.03
+NEC-2                                               1.49    43.32 + j48.20      1.015     0.06
+
+Notes:  All horizontal sections use 1" diameter wire.  Vertical legs use 1", 0.5", or 0.1" wire.
+All element wires are lossless, and the environment is free space.  All dimensions in inches.
+
+

In both the long and short horizontal options, NEC-2 handles the 1" vertical end wires quite well, and the variance from NEC-4 values is minimal. The NEC-4 and NEC-2 AGT values are the same, and the source impedances vary by only about j1-Ohm reactance. However, as we reduce the diameter of the vertical end wires and create a higher ratio between the diameters of the horizontal and vertical wires, the variance increases dramatically. The variance level is almost independent of the horizontal length.

+

When we turn to MININEC, we once more find that we may use the program directly without concern for the difference in the element diameter. However, this statement presumes that we are using a version of MININEC with the angular problem and the frequency offset corrected. In the present case, the use of 40 segments in the half wavelength dipole overall is sufficient to overcome the corner problem by minimizing the corner shortening effect.

+

The following table presents the MININEC results, starting with models in AM that use the NEC-4 resonant dimensions. In every case, we find that MININEC produces slightly different results, even when both the horizontal and the vertical element sections have the same diameter. Therefore, the table includes revised AM models to bring the MININEC models to resonance. As we decrease the diameter of of the vertical wires, the NEC-4 dimensions work less and less well. In addition, shortening the horizontal section of the inverted U produces an increase in the amount by which the AM MININEC results deviate from the NEC-4 results. Since even NEC-4 has difficulty with wire junctions with different diameter wires, the MININEC results are the more reliable.

+

Before we complete our examination of the data in the new table, compare the AGT values for the MININEC models in AM with the values for the NEC-4 models. The AGT values for the NEC models appear to be very good or better for all models. However, the MININEC results suggest otherwise. The Average Gain Test is a necessary but not a sufficient condition of model adequacy. In this case, the AGT fails to reveal the inadequacies of the NEC-4 models when the horizontal and the vertical wires have very different diameters.

+ 
+MININEC Performance with Various Inverted-U Dipoles
+
+Core     Horizontal     Vertical     Vertical       Gain    Source Impedance    AGT
+         Length         Diameter     Length/End     dBi     R +/- jX Ohms
+
+AM       +/-70          1"           34.0           1.95    58.42 - j1.78       0.9989
+AM-Revised                           34.2           1.95    58.67 - j0.23       0.9989
+MMANA                                34.2           1.95    57.59 - j5.19
+AM       +/-70          0.5"         37.8           1.93    57.16 - j9.70       0.9989
+AM-Revised                           39.1           1.93    58.72 - j0.20       0.9989
+MMANA                                39.1           1.93    57.61 - j5.41
+AM       +/-70          0.1"         45.4           1.91    55.18 - j18.90      0.9989
+AM-Revised                           48.1           1.89    58.87 - j0.50       0.9989
+MMANA                                48.1           1.89    57.56 - j6.93
+
+AM       +/-50          1"           55.3           1.58    39.10 - j3.04       0.9989
+AM-Revised                           55.6           1.58    39.32 - j0.64       0.9989
+MMANA                                55.6           1.58    38.64 - j5.46
+AM       +/-50          0.5"         59.1           1.56    38.42 - j13.82      0.9989
+AM-Revised                           60.8           1.53    39.74 + j0.10       0.9989
+MMANA                                60.8           1.53    39.04 - j4.92
+AM       +/-50          0.1"         66.5           1.48    37.90 - j26.17      0.9989
+AM-Revised                           69.5           1.41    40.51 + j0.53       0.9989
+MMANA                                69.5           1.42    39.70 - j5.71
+
+Notes:  All horizontal sections use 1" diameter wire.  Vertical legs use 1", 0.5", or 0.1" wire.
+All element wires are lossless, and the environment is free space.  All dimensions in inches.
+
+

The MMANA models all use the same dimensions as the revised AM models. As a result, they all show the same trend in the capacitive reactance at the feedpoint. As well, within about +/-j1 Ohms, the values are consistent with those for the linear dipoles using both uniform and tapered-diameter elements.

+

The gain differences between the inverted Us with longer and shorter horizontal sections seem numerically noticeable. However, operationally, the maximum gain difference is not as great as it might seem. Fig. 4 compares the patterns for the two types of inverted Us in a free-space environment. The overlaid patterns show only a very small difference in maximum gain.

+
+ +
+

Where the two types of inverted Us differ most noticeably from an operational perspective is in the depth of the side nulls. As the horizontal section grows shorter and the vertical legs become longer, we obtain more radiation off the dipole "ends," that is, in line with the horizontal wire. With a horizontal section that is about 70% of the overall dipole length, the side nulls are almost 20 dB weaker than the maximum broadside lobes. In contrast, as we shorten the horizontal section to about 50% of the total length and extend the vertical legs to compensate, the side nulls are down by under 10 dB (or about 1.5 S-units) relative to maximum gain. You may wish to compare these patterns to the patterns for the V dipole with its legs forming a 90-degree angle, that is, with each leg dropped 45 degrees from the presumed horizontal line of a linear dipole.

+

Hatted Dipoles

+

One type of shortened dipole tends to show less variance than the inverted-U: the hatted dipole. The inverted U uses a simple extension of the main wire, but in a different direction. All parts of the wire contribute to the antenna's radiation pattern. However, the hatted dipole uses a shortened main element along with symmetrical structures at each end to bring the entire structure to resonance. Fig. 5 shows the outline of one type of hatted dipole. In this case, the end structures consist of 4 equal-length and equal-diameter spokes. We might also have used shorter spokes with a perimeter connecting the tips. We may increase the number of spokes for either assembly. Each increase in the number of spokes results in a decrease in spoke length (assuming that we make no changes in the horizontal element). Ultimately, we might use a circular solid surface as the end piece.

+
+ +
+

One key to the hatted dipole is the fact that each spoke provides a current distribution path for the antenna. The current in each spoke at the junction with the horizontal element is I*1/n, where n is the number of spoke and I is the current magnitude in the main element at the junction. The lower portion of Fig. 5 displays the current division graphically, but shows only 2 of the 4 spokes at each end of the dipole. The other key to the hat is its symmetrical structure. Since each spoke has the same current magnitude as every other spoke, the fields created tend to cancel out. Hence, the hatted dipole exhibits virtually no far-field radiation from the hat. The result is that, among all methods of loading dipoles in order to achieve resonance with a shorter length, the hatted dipole exhibits the highest gain and the highest resonant source resistance for any given horizontal section length.

+

Because the hat radiation is self-canceling, hatted dipoles tend to show considerably less variation between NEC-2 and NEC-4 models, and between NEC and MININEC models, than the inverted U and similar shortened dipoles with asymmetrical extensions of the horizontal element. To test this tendency, I created NEC and MININEC models of the hatted dipole with a horizontal length of +/-70" (total 140") for the 1" diameter material. The 4 spokes at each end use 0.1" diameter wires. Due to the shorter length of each spoke, they use 4 segments each so that their segment lengths are about the same as their segment lengths in the horizontal portion of the element. The following table summarizes the results of the tests.

+ 
+NEC and MININEC Performance with Hatted Dipoles
+
+Core             Spoke      Gain    Source Impedance    AGT        AGTdB
+                 Length     dBi     R +/- jX Ohms
+
+NEC-4            18.8       2.02    58.17 - j0.12       1.001       0.00
+NEC-2            18.8       2.02    59.59 + j8.81       1.000       0.00
+AM               18.8       2.01    56.78 - j11.26      0.999       0.00
+MMANA            18.8       2.01    55.72 - j16.33
+AM-Revised       19.6       2.01    58.48 - j0.37       0.9988     -0.01
+MMANA-Revised    19.6       2.07    57.37 - j5.62
+
+Notes:  All horizontal sections use 1" diameter wire and are +/-70".  Hat spokes use 0.1" wire.
+Each end hat uses 4 spokes (with other designs possible).  All element wires are lossless, and
+the environment is free space.  All dimensions in inches.
+
+

The NEC-4 initial models called for 18.8" spokes to arrive at resonance. Note the nearly ideal values of AGT, despite the difference between the NEC-4 and NEC-2 source impedance values. The MININEC models showed some deviation from the NEC-4 models, so I created a revised resonant version of the AM MININEC model using 19.6" spokes. In both the original and the revised MININEC models, the MMANA version shows a -j5-Ohm offset in source impedance from the AM models, a value that has been consistent for all of the models reviewed in this episode.

+

Perhaps the most notable aspect of the NEC-MININEC comparison is the reduction in the differences between NEC-4 and MININEC for the hatted dipole. With a 70% horizontal 1" element, the MININEC model of the inverted-U showed an 18-Ohm differential in reactance. The hatted dipole, using the same horizontal element and the same diameter (0.1") end wires, shows a difference of only 10 Ohms reactance. Since MININEC does not react adversely to junctions of wires with different diameters, we might then conclude that NEC is less sensitive to such changes when we create symmetrical structures at the main element ends.

+

I noted that the hatted dipole is the most successful among all shortened dipoles in retaining the characteristics of a full-size linear sipole. We can confirm part of that claim in the reported gain values for the hatted dipole. Despite shortening the main element by about 30%, we lose only about 0.13-dB of gain. Fig. 6 tells something of the rest of the story by showing 3-dimensional and E-plane patterns.

+
+ +
+

Unlike the V dipole and the inverted U, the hatted dipole pattern shows deep side nulls that are very comparable to the side nulls of a full-size linear dipole in the same free-space environment. The depth of these side nulls is also confirmation that the hat structures on the ends of the dipole have virtually no far-field radiation. (If they had even small but noticeable radiation, the side nulls would have been much shallower.) Despite the improved performance of the hatted dipole, we rarely find them in use. Offsetting the improvements is the fact that placing hats at the outer ends of a dipole creates weight and wind resistance at a position that we least want it to appear.

+

Conclusion

+

In our survey of tapered-diameter, bent, and hatted dipoles, well-corrected MININEC has proven to provide the most reliable results. In many cases, the differences between NEC and MININEC are too small to matter. Even some numerically noticeable differences wash out in the variables of construction methods that we do not model in detail. Modeling is rarely a substitute for field testing and adjustment. Instead, modeling simply puts us much closer to the final adjustment values.

+

MININEC's superiority with some forms of dipole structures is not a sufficient reason to throw out NEC and buy new software. At the start of this sequence of episodes, I noted a number of features that even well-corrected versions of MININEC lack. As well, NEC has some performance advantages over MININEC in with some geometries. To explore these matters, we shall require one more leg on our journey. Next time, we shall explore zigzag, fold-back, and fan dipoles.

+
+ +

+

Go to Main Index

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+

111. Dipoles: Variety and Modeling Hazards
+ Zigzag, Fold-Back, and Fan Dipoles

+
+
+

L. B. Cebik, W4RNL

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We have been examining the behavior of NEC and MININEC calculations for various kinds of dipoles, where the dipole is a center-fed near-resonant 1/2 wavelength antenna. In this final episode of the sequence, we shall be paying close attention to angles. All of the antennas that we shall discuss will use 1" diameter lossless wire at all points, and the environment will once more be free space at 28 MHz. By holding down the number of variables, we can once more focus on how each antenna modeling package treats the antenna's geometry.

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So far, we have looked at linear, V'd, and folded dipoles, as well as at dipoles with tapered-diameter, bent, and hatted elements. In our final collection, we find zigzag, fold-back, and fan dipoles. The last sample is not a simple dipole, but actually a combination of dipoles for separate frequencies that share the same feedpoint.

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Zigzag Dipoles

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Zigzag dipoles are most common in the lower HF region. Very often, antenna builders have too little space for a full-size dipole. One way to squeeze the antenna into the available space is to create as symmetrically as possible a zigzag shape. Our sample zigzag shape will depart from the norm a bit. Most zigzag dipoles have a relative constant height above ground and change direction in the X-Y plane. Our samples will zigzag vertically. As well, we conventionally measure a zigzag dipole by drawing a virtual line from one tip to the other through the feedpoint. In this exercise, we shall hold the central part of the element at a constant value of Z--comparable to a constant height above ground--and run the zigzag ends in the Z-axis.

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In fact, we shall look at two designs of the zigzag dipole. One version, shown on the left in Fig. 1, uses a 90-degree angle at the zigzag points. The other version, on the right, bends the zigzag farther so that the end wires form a 45-degree angle with the inner section of the dipole. In both cases, the center section will occupy about 50% of the dipole length (if it had been a linear dipole, that is, +/-50" (total 100"). The end sections will use whatever length we need to approach resonance at the source.

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As Fig. 2 shows, both versions of the zigzag antenna qualify as dipoles by effecting a single transition between maximum and minimum current on each side of the centered source. As in past models, the center section of the model will use 21 segment in NEC and 20 segments in MININEC. The number of segments used in the end wires will depend on their length, but each segment will be approximately the same length as the segments in the center section.

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In past exercises, I have started with a NEC-4 model and then tried to see by how much the NEC-2 results deviated from the reports of the NEC-4 model. I then transferred those dimensions to a MININEC model in AM. Often, I created a revised AM model at resonance in order to compare the results with the version of MININEC in MMANA. The latter versions has few, if any, corrections, while the AM version is highly corrected. In this exercise, we can abbreviate the procedure somewhat. I shall still begin with a NEC-4 model, if only because that starting point is consistent with past starting points. However, the amount of deviation among the cores will be too small to call for the creation of additional models. One contributing factor to this situation is the fact that for our angular models, all wires have the same diameter. The following table shows the results for both the 90-degree and the 45-degree zigzag dipoles.

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+Zigzag Dipoles in NEC and MININEC
+All elements 1" diameter and lossless in free space.
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+90-Degree Zigzag: Central Length: +/- 50", End Length: 56"
+Segmentation: NEC: 12-21-12, MININEC 12-20-12
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+Program     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+            dBi      R +/- jX Ohms                            dBi
+NEC-4       2.03     45.27 + j0.86        1.005      0.02     2.01
+NEC-2       2.03     45.33 + j1.19        1.004      0.02     2.01
+AM          2.01     45.29 - j2.15        0.9986    -0.01     2.02
+MMANA       2.00     44.50 - j6.71
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+45-Degree Zigzag: Central Length: +/- 50", End Length: 67.85"
+Segmentation: NEC: 14-21-14, MININEC 14-20-14
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+Program     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+            dBi      R +/- jX Ohms                            dBi
+NEC-4       2.00     18.49 + j0.06        1.010      0.04     1.96
+NEC-2       1.99     18.57 + j1.17        1.008      0.03     1.96
+AM          1.94     18.79 - j2.27        0.9989     0.00     1.94
+MMANA       1.94     18.50 - j6.30
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The 90-degree zigzag dipoles form a tight cluster of results. Only the MMANA source impedance shows more than a +/-j2-Ohm reactance shift, and it is about -j4.5 Ohms relative to the AM model--close to the amount that we have come to expect in dipoles from the uncorrected frequency offset at 28 MHz. The NEC cores actually show slightly less ideal values of AGT than the AM MININEC value. Although the MMANA core does not return an AGT value, we would expect it to approximate the AM value, since the frequency offset would not affect the AGT computation. As well, the use of a high number of segments is sufficient to minimize any further offset from corner foreshortening.

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The 1" diameter elements, although well within NEC segment-length to diameter (or radius) limits, is fat enough to create a degree of inter-penetration at the junctions of the 45-degree zigzag dipole. Hence, both the NEC-4 and the NEC-2 departures from the ideal (1.000) are about double the departures with 90-degree corners. In contrast, the AM version of MININEC is highly corrected for raw-MININEC corner aberrations. Hence, it yields an AGT value very close to ideal. The MMANA data is interesting because the source reactance is only about j4 Ohms off the AM value. In earlier episodes we noted the possibility that the frequency offset and the corner error potential might work in opposite directions. The difference in source reactance between AM and MMANA was between j5 and j5.5 Ohms for a linear dipole. The 90-degree zigzag reduced that value to about j4.5 Ohms, and the more acute angle of the 45-degree zigzag reduces the difference still further. We have at least partial confirmation of our earlier hypothesis.

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Fig. 2 provides E-plane patterns for the two zigzag dipole models. Due to our method of model construction, the modeling cores define the E-plane as aligned with the center section of the antenna, even though the wire extensions take off in opposite directions. Note the relatively low side-null values for these two antennas. The 90-degree version has side nulls that are down about 10 dB, while the 45-degree model sidelobes are down only about 5 dB, giving the pattern an oval appearance.

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In fact, the radiation fields from the zigzag dipoles broadside to the plane of the wires are not linear. The terms E-plane and H-plane generally apply to antennas with linear polarization, such that the E-plane is aligned with the polarization, and the H-plane is at right angles to the polarization. Because so much of the element resides in the extensions that are angular to the center section, a considerable portion of the radiation is in a plane other than the plane of the center section. The net result is elliptical polarization with the major axis at an angle to the center section of the antenna. The left two 3-dimensional plots in Fig. 3 show to what degree the zigzag dipole tilt the radiation field. The key indicator is the location of the true side nulls. Those nulls are both quite deep. The Y-axis line shows how angularly far from the true nulls that we find the E-plane patterns in Fig. 2.

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Fold-Back Dipoles

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The pattern on the far right in Fig. 3 represents a dipole with a different name, although it may initially seem like just another zigzag dipole with a tighter angle between the center section and the tip wires. First, we likely noticed from the tabular data that as we increased the zigzag angle, the end wires grew longer. As well, the source impedance dropped from a highly usable value with the 90-degree version to an impractically low value with the 45-degree version. To avoid having end wires that are longer than the entire center section and to restore--at least partially--the resistive component of the source impedance, we normally use a longer center section when we apply relatively extreme angles to the end wires. The longer center section combines with the fact that the end wires are more in line with the center section to produce a field that is almost oriented like the field for a linear dipole. Note that the Y-axis line almost (but not quite) coincides with the deepest part of the side null in the right-most 3-dimensional patter in Fig. 3.

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The resulting antenna uses a center section that is about 70% the length of a linear dipole, that is, about +/-70" (total 140"). Although the antenna is in the same family as the zigzag dipoles, it usually bears the name "fold-back" dipole. The name arises from the origins of the antenna, in which the builder could not fit elements into a given space and therefore folded them back at some convenient angle not too far from the orientation of the center section. The angle for the sample is 20 degrees, which requires end wires that are about 59.2" each for resonance with all-1" element construction. If you reverse the antenna image, you will find another name for the antenna--the lazy N. We occasionally find the antenna used vertically with an off-center feedpoint at one end of the center section as a convenience. However, for consistency with our other models, I have left the antenna horizontal and center-fed. Fig. 4 at the top shows the antenna outline, along with the relative current magnitude distribution along its total length.

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As suggested by the lower portion of Fig. 4, we have multiple ways to effect element fold-back. I once developed a B antenna (which one may also view as a sigma from the reverse side). For this exercise, I have modeled another fold-back antenna, again using the +/-70" center section of 1" lossless wire. The fold-backs are squared and parallel to the center wire section at a 2" distance. Note that the end sections for this antenna are longer than 1/2 the center section. One effect is to require that we place the end wires on opposite sides of the central wire, although this position has been optional with the earlier examples. Perhaps more significantly, note the relative current magnitude curve in Fig. 4. The feedpoint or source position does not mark the current peak. Rather, we have twin peaks that are somewhat separated from the source position. You might rightly ask whether this antenna qualifies as a true dipole under the definition that we imposed at the beginning. However, the only way to bring this antenna to resonance is to allow the deviant current curve. As well, the curve emerges as a natural evolution of such curves as we start with a linear dipole and gradually shorten the end section and add fold-back end wires. There are no discontinuities in the evolution of the current distribution. Therefore, we shall keep the model and save any disputation over the application of names for another day.

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With the longer center section, we expect to find that NEC-4 and NEC-2 will yield better AGT values than they did for the 45-degree zigzag dipole with its shorter center section. The following table confirms our expectation. In fact, the 2 NEC cores and the AM version of MININEC yield a very tight grouping of values across the span of data columns. Only the MMANA source data are out of line, with the MMANA MININEC core showing a large difference from the AM MININEC core. In terms of source reactance, we see a difference of j14.8 Ohms. To account for this larger deviation, we may note that the corner error in uncorrected MININEC increases as we move toward more acute angles. At 20 degrees, even the relatively high segmentation of the model in not sufficient to overcome this problem in MMANA.

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+Fold-Back Dipoles in NEC and MININEC
+All elements 1" diameter and lossless in free space.
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+20-Degree Angled Fold-Back: Central Length: +/- 70", End Length: 59.2"
+Segmentation: NEC: 13-31-13, MININEC 13-30-13
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+Program     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+            dBi      R +/- jX Ohms                            dBi
+NEC-4       1.94     29.95 - j0.09        1.003      0.01     1.93
+NEC-2       1.93     30.33 + j3.49        1.001      0.00     1.93
+AM          1.92     30.90 + j2.98        0.9986    -0.01     1.93
+MMANA       1.91     29.84 - j11.82
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+Parallel Fold-Back: Central Length: +/- 70", Spacing 2", End Length: 78.2"
+Segmentation: NEC: 17-31-17, MININEC 17-30-17
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+Program     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+            dBi      R +/- jX Ohms                            dBi
+NEC-4       1.59     15.33 - j0.13        0.921     -0.36     1.95
+NEC-2       1.61     15.28 + j2.27        0.926     -0.34     1.95
+AM          1.94     15.24 + j8.67        0.9983    -0.01     1.95
+MMANA       1.94     15.10 - j1.54
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The squared and parallel fold-back of the alternative model reveals a different problem in uncorrected MININEC. AM corrects for the error potential in very close wires. With a 2" center-to-center separation between the middle section and the fold-back sections of the antenna, the wire surfaces are only 1" apart. Under these conditions, the uncorrected version of MININEC in MMANA (at least in the version used for these exercises) shows a j10.2-Ohm difference in reactance relative to the AM model. The reactance shown in the source data for the AM model is a function of having begun with the NEC-4 modeled dimensions.

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Both NEC-4 and NEC-2 show deficiencies in modeling the parallel fold-back geometry. Although the dimensions are likely off the mark (at least relative to the AM model indications), the most dramatic evidence lies in the AGT values for both NEC cores. The gain report is more than 1/3-dB off its proper value. The corrected value tallies very well with the AM gain value. In fact, NEC makes the fold-back dipole look far worse than it really is in terms of dipole performance. The most likely source of the error that yields the AGT values reveals is the proximity of the wires. We did not encounter such an error when we examined folded dipoles that used the same spacing, wire diameter, and segmentation level. However, the folded dipole used wires that had the same length, end to end. The fold-back dipoles use wires with different lengths, even though the segmentation produces segment junctions that are as well aligned as the required lengths permit. The situation is simply one of the documented weaknesses within NEC. In this case, note that the level of the problem is virtually the same for both NEC-2 and NEC-4.

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Fig. 5 provides E-plane patterns for both versions of the fold-back dipole. The angled fold-back model shows deeper side nulls than either of the zigzag dipoles, but as we saw in Fig. 3, the conventional E-plane does not quite coincide with the angle of the deepest nulls. The parallel fold-back model shows very deep nulls that are limited only by the need for end connecting wires between the center and the fold-back wires.

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The fold-back dipoles show a pattern similar to the one that we encountered with zigzag dipoles. As we change construction in ways that require longer end wires, the source resistance decreases. Although the value for the 20-degree fold-back model falls within the usable range, the source resistance for the parallel fold-back model in impractically low. Such antenna performance features do not affect modeling adequacy and accuracy, but they may heavily influence the designs for antennas that we actually plan to build.

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Fan Dipoles

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The last of our exercise dipoles as actually two dipoles in one. A common technique used in both amateur and commercial dipole construction is tying together dipoles for more than one frequency by using separate dipole legs, but with a common feedpoint. Let's simulate this situation with combined dipoles for 28 MHz and for 14 MHz. The structure, for simplicity, will use 1" lossless wire throughout. The dipoles will have about a 30-degree angle between the wires for each frequency. Our question is not whether such a structure makes good building sense. Rather, we want to examine the best way to model such an antenna in order to provide reliable data reports.

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Fig. 6 shows a common way to model such antennas in both NEC and in MININEC. In NEC, we must place a source on a segment. With all wires joining at the center, we must choose which wire will receive the source. The source must be on either a 14-MHz wire or on a 28-MHz wire, but it cannot be on both. MININEC may give its users a false impression, since we normally say that pulses used for sources fall at segment junctions. Hence, it would appear that placing the source at one of the pulses at the junction of the wires would solve our problems. Conventional representations of the source position under these conditions will show it at the center of the junction. My representation in Fig. 6 shows the source to be slightly offset and distinctly on either a 14-MHz wire or on a 28-MHz wire. The following table of source impedance values for the various options for the various cores confirms the situation.

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+Unreliable Fan Dipoles for 14 and 28 MHz in NEC and MININEC
+All elements 1" diameter and lossless in free space.
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+Program     Source     28-MHz Source Z     14-MHz Source Z
+            Element    R +/- jX Ohms       R +/- jX Ohms
+NEC-4
+            28 MHz     33.02 + j26.58      32.53 - j323.2
+            14 MHz     792.6 + j927.6      72.84 - j17.52
+AM          28 MHz     30.14 + j21.23       9.72 - j261.9
+            14 MHz     416.9 + j375.4      68.48 - j21.05
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The NEC and the MININEC values both show that if we place the source on a 28-MHz wire, then the 28-MHz source impedance value is reasonable. (I did not bother to resonate the model, although that fact has nothing to do with the source impedance pattern.) With the source on the 28-MHz wire, both types of cores show very aberrant values for the source impedance on 14 MHz. Without changing antenna dimensions, if we move the source to a 14-MHz, wires, then we obtain reasonable values of source impedance for 14 MHz. However, the 28-MHz source impedance values become wholly unusable. The small exercise shows that we must come up with an alternative procedure for modeling fan dipoles.

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Fig. 7 shows a pair of alternative schemes. Let's first concentrate on the upper portion of the figure. We may create a source wire that is 3 segment long in NEC and 2 segments long in MININEC. In each case, the source position is exactly centered in this wire. As well, the wire has identical segment lengths on each side of the source and prior to any current division that will take place due to the use of dual dipoles. The dipole legs connect to the ends of the central source wire. The following tables shows the results for NEC-4, NEC-2, AM, and MMANA.

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+Fan Dipoles for 14 and 28 MHz in NEC and MININEC
+All elements 1" diameter and lossless in free space.  30-degree angle between wires.
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+Program    Frequency     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+           MHz           dBi      R +/- jX Ohms                            dBi
+NEC-4:  3-Segment Source Wire
+           28            0.93     37.52 + j0.55        1.096      0.40     0.53
+           14            2.53     55.27 + j0.32        1.110      0.45     2.08
+NEC-2:  3-Segment Source Wire
+           28            1.24     35.10 + j3.87        1.185      0.74     0.50
+           14            2.85     51.33 + j1.53        1.196      0.78     2.07
+AM (MININEC):  2-Segment Source Wire
+           28            0.53     40.39 - j6.07        0.9951    -0.02     0.55
+           14            2.07     61.18 - j3.00        0.9994     0.00     2.07
+MMANA (MININEC):  2-Segment Source Wire
+           28            1.45     36.72 - j17.76
+           14            2.08     60.47 - j5.32
+Note:  For 3-Segment Source-Wire models, the 14-MHz element is +/-199.3".  The
+28-MHz element is +/-106.7".  Lengths include 1/2 the source wire.
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With the same dimensions for each model, and using the NEC-4 model as our starting point, we find very reasonable results for the dipoles on both bands using a common feedpoint. The tabular data strongly suggest that in this case, AM would have been the proper starting point. It yields nearly ideal AGT values, while the NEC cores depart significantly from the ideal. The problematical AGT values would not occur had we used thin wire, which might be typical of a fam dipole installation. However, our goal is not to overlook potential problems, but to locate and identify them.

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The less-than-ideal NEC AGT values are functions of the angle between the dipole legs at the points of junction with the source wire. One indication of this fact is the higher or less ideal AGT value produced by NEC-2 relative to NEC-4. NEC-4 improves on the ability of the core to handle smaller angles. (Note that the smallest angle that either core can handle depends upon a number of variables. In this case, the large wire diameter and the fact that the wires to not form a field whose radiation is self-canceling result in the difficulty.)

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The lower portion of Fig. 7 shows a very usable work-around that is applicable to both NEC-2 and NEC-4, but is not possible within MININEC. The starting point for this version of the fan dipole is the use of wholly separate wires for the two dipoles. The source wires parallel each other at a minimum spacing. In this example, I used 2" center-to-center, although a slightly wider spacing would have been superior.

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The key to having a single feedpoint is the placement of the source on one of the two source wires. Which wire makes no difference. Between the middle segment of each wire, we create a transmission line via the TL command. The line's characteristic impedance is inconsequential within broad limits. Given the approximate impedances from the first type of model, I used 50 Ohms. The key to achieving a true parallel connection is the length of the transmission line. Since NEC transmission lines are mathematical only, their length is not the spacing between the connection points unless we specify that value. Instead, the TL command allows us to make the line length any value whatsoever. Since in a near-zero-length line, the impedance will not transform by any detectable amount, we may use 1E-10 m as the length. In some implementations of NEC, a value this short may not be allowed; simply use the shortest line length that is allowed.

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The resulting model is a more reliable NEC representation of the fan dipole. The dimensions may change relative to the common-wire source. In the following table, the 14-MHz legs are each 1.4" longer and the 28-MHz legs are each 2" shorter than in the previous model.

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+Fan Dipoles for 14 and 28 MHz in NEC
+All elements 1" diameter and lossless in freee space.  30-degree angle between wires.
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+Program    Frequency     Gain     Source Impedance     AGT       AGTdB     Corrected Gain
+           MHz           dBi      R +/- jX Ohms                            dBi
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+NEC-4:  Transmission-Line Parallel Source
+           28            0.66     48.36 - j0.35        0.998     -0.01     0.67
+           14            2.08     64.07 - j0.34        0.999      0.00     2.08
+NEC-2:  Transmission-Line Parallel Source
+           28            0.65     48.96 + j0.25        0.992     -0.03     0.68
+           14            2.05     64.47 - j0.32        0.993     -0.03     2.08
+Note:  For 3-Segment Source-Wire models, the 14-MHz element is +/-200.7".  The
+28-MHz element is +/-104.7".  Lengths include 1/2 the source wire.
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NEC-4 registers slightly superior AGT values, likely due to its small improvement in handling the closely spaced center wires relative to NEC-2. These wires, of course, are in the physical region of peak current. A small increase in the center-wire spacing would have yielded virtually ideal AGT scores. Noting all of this, a fan dipole constructed to approximate the model would still require considerable field adjustment of the leg lengths to account for construction variables. Fan dipoles are considerably more finicky or sensitive to minor changes than are almost any of the other models that we have examined, with the parallel fold-back model as a potential exception.

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Throughout the progression of models, we have recorded values for the 14-MHz tests that are consistent with any full-size dipole. The slight V in the legs lowers the gain and source resistance by very small amounts that fall below the level of being operationally significant. However, the 28-MHz source resistance is considerably lower, and the 28MHz maximum gain is both very low and more variable among the models. Fig. 8 shows part of the reason for the difference in performance. The upper sketch shows the current distribution at 14 MHz along all of the fan-dipole wires. The current magnitude on the 28-MHz dipole legs is very low and barely noticeable. However, when we operate the fan at 28 MHz, the relative current magnitude along the 14-MHz legs is appreciably higher. The consequence is that the 14-MHz elements exert partial control over the 28-MHz pattern. Most notable is an increase in the vertical component of the total field, which increases radiation to the sides of the array. At 14 MHz, the radiation had been almost totally broadside to the array.

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The result of this complication is that the 14-MHz far field produces an almost ideal dipole pattern. The left side of Fig. 9 shows 3-dimensional and E-plane plots at 14 MHz. With side nulls that are 20-dB down from maximum broadside gain, the pattern resembles the pattern for a V dipole, which is indeed what the antenna is at that frequency. The vertical component, which is at right angles to the main lobes, is very small, as shown by the small inner lobes of the pattern. Hence, the horizontal component and the total field form pattern lines that overlap for most of the E-plane circumference.

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At 28 MHz, the pattern has a much squarer appearance, as shown in the 3-dimensional and E-plane patterns to the right in Fig. 9. The side nulls are only about 8 dB below the maximum broadside gain, which does not occur on a perfect tangent to the antenna plane, but is offset slightly. The vertical component emerges from the combined radiation of the 14-MHz and the 28-MHz legs and rivals the horizontal component in strength--at least within about 8 dB. The total pattern, which is a combination of the 2 component patterns, takes on a much squarer shape. As well, it is sensitive to small changes in antenna shape--and in how the modeling software handles the calculations as one or more aspects of the antenna geometry press the limits of the modeling core. MMANA, for example, shows a higher maximum gain that is a function of calculating a larger vertical component. Hence, maximum gain occurs at a bearing well removed from the broadside tangent. In contrast, NEC and the AM version of MININEC calculate somewhat lower vertical components, and the maximum gain occurs only a bit off the broadside tangent line.

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Fan dipole users and builders tend to presume that the antenna operates "just like" a single dipole at each of the operating frequencies. Some combinations in fact approximate such performance. However, the sample that we have used illustrates a common case in which the performance of at least one of the two dipoles is unlike the performance of a standard or linear dipole. The examples have exacerbated the problems both in the antenna design and in the modeling of the design by using fat 1" diameter wires. Thin-wire versions of the fan dipole may well display the phenomena to a much lower degree.

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Conclusion

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We have not by any means exhausted the possibilities for variations on the 1/2 wavelength near-resonant dipole. However, it is likely that these notes have exhausted you. Except for the standard or linear dipole with a uniform diameter, the examples in the series of episodes have aimed to reveal various modeling pitfalls within a fairly unified context that has featured one of the most common antennas used in communications work at all frequencies. My goal has been to exhibit the pitfalls in a concrete setting rather than simply listing pitfalls and producing divergent examples to display the potential problems.

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Along the way, we have seen that the problems do not occur equally in all modeling cores. Each core has strengths and weaknesses when we press its limitations. Internally, MININEC exhibits the widest range of performance variability, since different implementations correct different numbers and types of raw MININEC difficulties. MMANA represents a virtually uncorrected core and AM represents a highly corrected and supplemented core. Versions of NEC-2 and of NEC-4 tend to yield very similar results to other versions of NEC-2 and NEC-4. However, the differences between the two NEC cores and the limitations that are common to both become the most significant features to observe when one is searching out modeling pitfalls.

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Any summary judgment about the relative merit of a highly corrected MININEC and either version of NEC would be wholly out of place. We have examined the cores only as they model various forms of the dipole. We have not examined how each core handles spot loads. Nor have we examined the vast array of geometry and control commands within NEC that are not a part of MININEC. Not only is our database woefully shy of the level needed for a summary judgment, but as well, such a judgment might prove more harmful than useful. The goal is to use each core where it is most reliable, effective, and efficient in generating and reporting on a desired model. In that regard, dipoles only begin the modeling work; they do not end it.

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Nevertheless, I find it interesting to count the ways that we can get into trouble modeling simple dipoles if we are not careful and alert, and if we do not use all of the facilities of a program to detect problems as well as to produce modeling reports.

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112. Wires Meeting Ground: 2 Cases

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L. B. Cebik, W4RNL

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For various good reasons, programmers who implement either NEC-2 or NEC-4 provide warnings about vertical wires that meet the ground (Z=0) and end at that point. For example, EZNEC Pro warns that "If you connect a wire to ground when using the High Accuracy [Sommerfeld-Norton or S-N] real ground type, the program makes the connection with an unpredictable series resistance." EZNEC no longer makes the less-accurate reflection-coefficient approximation (RCA) ground calculation system available. It was designed for faster results in an era of much slower computer speeds. Today, there is no significant difference in model run times when using either ground calculation system, so EZNEC has omitted RCA. The system is widely available on other implementations of NEC-2 and NEC-4 (such as NEC-Win Pro, GNEC, 4NEC2, and NEC2GO). However, EZNEC does provide access to the MININEC ground calculation system from its implementations of NEC-2 and NEC-4. (4NEC2 also provides the MININEC ground system within a NEC package.) Nevertheless, for all general modeling purposes, the modeler should use the more accurate S-N ground calculation system. (Antenna Model, a version of MININEC, now includes the S-N ground system in its program.)

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We have in past episodes explored the differences among the available ground calculation systems, listing the limits and the limitations of each one. In this episode, we shall focus on a slightly different way of looking at ground calculation systems by examining two different types of antennas that will test various ways of handling vertical wires that just reach the ground (Z = 0). The first case will extract data reports using a fairly standard test of wire-to-ground terminations. We shall look at differences among reports for a 1/4 wavelength monopole using the various ground systems when the monopole just reaches the ground and has no radials. We shall compare those reports with NEC-4 reports for the same monopole above ground, but with a buried radial system of 32 15' radials. We may call this the "normal" test situation for uncovering the problems that emerge when we fail to provide a proper termination for a wire that just touches the ground.

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Then we shall look at a different type of antenna: a 10 wavelength terminated long wire. On common configuration for such antennas is to bring the ends of the wires vertically back to the ground. We place the source on one end and the terminating resistor on the other end, in both cases, right at ground level. (This is not the only possible configuration for a terminated long wire, but it is perhaps the most common configuration. Unlike some alternatives, it provides a very large operating bandwidth--several octaves--but with a changing pattern, since the antenna changes its length as we change the operating frequency.) We shall look at 4 different ways to model this antenna configuration, in each case placing the antenna's horizontal run 1 wavelength above ground.

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As we shall discover, the matter of wires touching the ground with the S-N ground system (and others) are not quite so cut and dried as the simple modeling test might indicate.

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The "Normal" Test Situation

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Assessing the behavior of a vertical wire that just touches ground, with no other termination, when using the various ground systems in NEC-2 and NEC-4 usually involves setting up a 1/4 wavelength vertical monopole. So long as all models in the test sequence use the same monopole, frequency, and ground quality (wherever relevant), the selection of these parameters makes no significant difference to the test. Therefore, I shall begin with an aluminum monopole that is 33.25' tall with a 2" diameter. It will use 66 segments so that each segment is 0.5' long. This provision is not important for the tests that use the monopole alone. However, we shall also need a "properly" terminated monopole for comparison. For that set of runs, I shall extend the monopole 0.5' below ground and connect 32 aluminum radials, each 0.25" in diameter. Each radial will be 15' long. The length is short, but not so short as to invalidate the test comparisons. For adequate current distribution in a lossy medium, the radials are just about long enough, while allowing a very compact model. The ground quality--wherever relevant--will be average, that is, with a conductivity of 0.005 S/m and a relative permittivity of 13. Fig. 1 shows the outlines of the two models required for the test sequence.

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The model with buried radials requires NEC-4 because the radial wires are below ground. It also requires the S-N ground system for the same reason. However, the simpler model sets up a more complex situation. We shall run the model in both NEC-2 and NEC-4 for all tests. Every implementation of both cores provides access to a perfect ground, that is, one using the simple image-reflection calculation system built into NEC. Likewise, every implementation of both cores allows access to the S-N ground system. However, we must turn to programs like NEC-Win Pro and GNEC, if we wish to see the results of using the NEC reflection coefficient approximation system (RCA). To access the MININEC ground from within wither NEC-2 or NEC-4, we must use EZNEC or 4NEC2. If we make all of the relevant model runs, we wind up with a table similar to Table 1.

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Let's read the table from the bottom up. Both implementations of NEC-4 (EZNEC and GNEC) return virtually identical results for the monopole with buried radials. The tiny numerical variations between the reports are largely functions of using different compilers for the cores. Indeed, different CPUs may show further variations, depending upon their architecture. We should note that the gain and impedance values will also change as we alter both the number and the length of the radials beneath the monopole. Therefore, our reference buried-radial monopole array is simply one of many possible references that we might use.

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The upper part of the table uses a single model with no permitted variation in its geometry (if we are to keep it consistent with the buried-radial antenna). Only the ground system changes among the model runs. Except for the use of a perfect lossless ground, we find one constant among all of the models: a take-off (TO) angle of 26 degrees. In fact, a single elevation plot, shown in Fig. 2 is applicable to all of the models using a lossy ground.

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Regardless of the core or the program, the results over perfect ground coincide as completely as we could expect from separate compilations of the NEC-2 and NEC-4 cores. EZNEC gives us access to the MININEC ground, and the NEC-2 and NEC-4 results also coincide. As well, the feedpoint impedance values remind us that the MININEC ground always returns the impedance for perfect ground, not for the lossy average ground on which the far-field report is based.

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In NEC-2, the two programs (EZNEC and NECWin Pro) provide identical results for the S-N ground. Since only NECWin Pro (of the two programs) provides an RCA output in NEC-2, we can only note its values that appear to be even more divergent from reality than the S-N unusable results.

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In NEC-4, we find an additional divergence both among cores and among programs. The EZNEC and the GNEC results for the S-N ground do not agree. The RCA result for GNEC differs from the S-N value for the same program by almost the same gain difference as in the NEC-Win Pro S-N and RCA reports, but this is not in itself a suggestion that the GNEC/NECWin Pro results are superior to those of the EZNEC cores.

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In fact, we have no way to estimate--short of setting up a physical experiment--which set of reported values may be the more nearly correct for a monopole with no radials placed in contact with average soil. Internal consistency of results would be only one measure of reasonableness. As well, it would constitute a necessary but not a sufficient condition of reliability of the reports. However, we do not have internal consistency. In addition, we cannot use the reports for the antenna that uses 32 15' radials, because--at best--these results apply to only one of many possible arrangements. Other radial lengths and other numbers of radials would each yield different results for both the far-field gain and the feedpoint impedance.

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Buried-radial monopole systems that we model by using the S-N ground in NEC-4 do have a very reasonable track record of reliability relative to physical antennas--within the bounds of construction variables and the potential in any area for stratified soil. For example, the results coincide very well with the experimental results published in the classic Brown-Lewis-Epstein work on the 1930s. Since we do not have a similar record for the monopole without radials, the entire set of results over lossy ground using either the RCA or the S-N ground fall into the category of being simply unreliable. (We have examined the shortcomings of the MININEC ground system in other episodes.)

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Our sample model only illustrates the problem of trying to model a monopole without providing it with a radial system. Nevertheless, it shows why program manuals tend to recommend against simply bringing a vertical wire to ground and using no other termination for it.

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The Terminated Long Wire

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A single wire that is many wavelengths long, fed at one end and terminated by a correct impedance at the other end, creates a directional beam. It is one of the earliest directional antennas used in HF point-to-point communications. With the use of a proper termination, the antenna is capable of wideband operation over frequency spans of more than 4:1. However, the beamwidth and the sidelobes tend to vary as the antenna changes its length when measured in wavelengths as a function of the operating frequency.

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The terminated long wire has a number of possible configurations, but we are interested only in the most common of these ways of setting up the antenna. Let's consider a long wire that horizontally is 10 wavelengths. We shall set the antenna 1 wavelength above average soil. The most common way to feed the antenna is to bring a wire to ground and to place the source or feedpoint at the junction of the wire with the ground. Essentially, the ground forms the second terminal of the feedpoint. At the far end of the long wire, we shall also bring a wire from the end of the horizontal section down to ground. The ideal termination would be a complex impedance, the reactive part of which would vary with the operating frequency. However, for wideband use, we normally use a non-inductive resistor. Like the feedpoint, we place the resistor at the junction of the vertical wire and the ground. Ostensibly, the ground provides a return so that effectively the resistor and the feedpoint have a common terminal.

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Ideally, we can find a load impedance that will provide the proper conditions for achieving full traveling-wave status for the terminated long wire. The calculation is based on treating the wire as a transmission line, and the load impedance must equal the characteristic impedance of the line. Balanis (Antenna Theory: Analysis and Design, p. 495) provides the following equation to approximate the proper value of the termination.

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RL is the value of the impedance load in Ohms, h is the height of the wire, and d is the wire diameter, when both are in the same units. Note that the impedance of the line and hence the approximate load value is independent of frequency and dependent only upon a set of physical measurements that use the same units of measurement. The approximate recommended value of RL is 776 Ohms. For many installations, terminating resistors tend to range between 600 and 800 Ohms. The wire diameter is 4.745e-6 wavelength (or 0.16" wire at 3.5 MHz).

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Equally important to the model is the configuration that we employ for simulating the termination of the antenna ends at the ground. Essentially, we have 4 options (A though D) as sketched in Fig. 3.

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Option A brings the vertical elements of the antenna down to ground. The source or feedpoint is the first segment above ground of the left wire, while the terminating load appears on the last segment above ground at the far end of the antenna. Fig. 4 shows the general layout, along with elevation and azimuth patterns for the test model.

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In the EZNEC Pro/4 implementation of NEC, we have at least 4 ways to model the structure: over perfect ground, with a Sommerfeld-Norton (S-N) average ground using NEC-4, with an S-N average ground using NEC-2, and with a MININEC ground. Use of a perfect ground provides a reference baseline for checking the sensibleness of other models. However, neither NEC-2 nor NEC-4 recommends simply bringing a source wire to ground, since at a minimum, the source impedance is likely to be off the mark. The MININEC ground does not provide accurate impedance reports for the ground quality selected, since it is restricted to using the impedance report for perfect ground.

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Despite the limitations, we can tabulate the results. As a test case, I used a 10 wavelength terminated antenna alternately using termination resistors of 600, 800, and 1000 Ohms. For each option, Table 2 lists the maximum gain, the reported 180-degree front-to-back ratio, the elevation angle of maximum radiation, the beamwidth, the source impedance, and the 600-Ohm SWR at the test frequency.

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Using the sequence over perfect ground as a background reference, the NEC-2 results for the S-N average ground and the MININEC average ground data appear to coincide fairly well. However, the NEC-4 runs for the S-N average ground appear to yield somewhat high gain values with more than anticipated inductive reactance in the source impedance. The gain values for NEC-4 and the S-N ground are only about 2.5-dB lower than the values over perfect ground.

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Option B represents an adaptation of a NEC-2 technique for modeling vertical antennas with ground-plane radials. The return line between the load resistor and the source is 0.001 wavelength above ground, several times the diameter of the wire. See Fig. 5 for the layout and the associated elevation and azimuth patterns.

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In principle, the model violates no constraints, but as Table 3 for both NEC-2 and NEC-4 shows, it yields a poor model of the terminated long-wire antenna.

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Although NEC-2 and NEC-4 show a very close coincidence of data, the low gain, low front-to-back ratio, and high feedpoint impedance reports combine to suggest that this model is highly inadequate. The antenna amounts to a corner-fed terminated loop in which the low wire is an active part of the antenna rather than just a return line. However, the beamwidth and elevation-angle reports are consistent with the other models.

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NEC-4 does allow the use of a subterranean return wire, shown in Option C in Fig. 6. To test this option, I placed a return wire 0.01 wavelength below ground level, connecting it to the above ground vertical wires with short segments. Both the source and the load for the antenna remain above ground. The layout and patterns appear together in Fig. 6.

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Since this option is available only in NEC-4, the test-results in Table 4 are quite brief.

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The results are modest, but coincide roughly with the NEC-2 results in Option A. The front-to-back reports are consistent with those for perfect ground. The difficulties with the model include the model size, since the return wire requires as many segments as its above-ground counterpart in Option B. As well, the return wire may actually yield slightly low gain reports by carrying more current than the ground itself. A real installation would not likely use a buried ground wire.

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Therefore, I tried Option D, which replaces the below ground structure of option C with 2 simple ground rods. See Fig. 7 for the layout details and the patterns.

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Each rod is a 1-segment wire about 0.05 wavelength, which is the length of the segments in the vertical wires above ground. Therefore, the source has equal length segments on each side of the feedpoint segment. 0.05 wavelength is about 4.3 meters or 14'. This length may be longer than the average ground rod, but substituting shorter segments did not change the reports by any significant amount. The results of the test appear in Table 5.

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Except for the predicted very slight increase in maximum gain, all of the values correspond very well with those of the buried-return-wire model (option C), but with a 45% reduction in model size. For users of NEC-4, it is likely that this style of model is about as adequate as we may get for a terminated long-wire directional antenna. In fact, for users of NEC-2, the basic model (option A) coincides well enough for general guidance. In physical reality, there will be structural variables that will inevitably limit the precision attainable by any model. For example, the models presume a flat wire horizontal to the ground, which is not likely to appear with copper wire and real supports. Even if all supports provide the same height, catenary effects will vary the actual wire height above ground along the antenna pathway.

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The net result of these preliminary tests suggest that option D is a very usable model capable of giving good guidance on the performance of the common-configuration single terminated long-wire antenna. We may largely dispense with the creation of complex radial systems under each end of the antenna, systems that would not likely be part of an amateur long-wire installation.

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Almost incidentally, we may note two facts about these test long-wire antennas. First, we should expect some slight inductive reactance, since the wires are physically 10 wavelengths long. Hence, they are slightly long electrically, Second, the use of vertical wires at the ends of the main horizontal section modifies the performance relative to a configuration that uses only a horizontal wire. Fig. 8 compares the current distribution along two terminated long wires with equal-length horizontal sections. Since in long-wire technology, there is no perfect traveling-wave antenna, both versions show a standing wave superimposed on a certain constant traveling-wave current level. For the present context, the current distribution curves for the vertical sections of the lower sketch are most important. They limit both the gain and the front-to-back values for the antenna.

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In addition, the vertical wires also modify the transmission-line analogy that resulted in the choice of the terminating resistor. Virtually all of the tables show that as we increase values of the terminating resistor, the feedpoint impedance grows, but at a slower rate. Apart from the small inductive reactance, the feedpoint impedance would more closely match the terminating resistor value when both values are somewhat lower.

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Conclusion

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With a simple monopole and no radials, the NEC-2 model showed results that seemed most to diverge from our expectations of a physical antenna. The NEC-4 results appeared--however ultimately unreliable--to be considerably closer to reality--as indicated by the reference model using radials.

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In contrast, options C and D of the long-wire model with at least some buried elements provide a reference against which to measure the models without ground penetration. In this case, The NEC-2 model of option A more closely approximated the reference values on options C and D than did the corresponding option-A version using NEC-4. Although we cannot expect high precision (but only general planning guidance) from any of the models, the exercise does illustrate that we cannot draw singular universal conclusions. When wires just touch the ground, a model is suspect in the reliability of its reports. However, the level of reliability and the reasons for any given measure of distrust may vary with the type of antenna that we are modeling.

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113. When Simple Geometries Become Complex
+ A Rhombic Case Study

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L. B. Cebik, W4RNL

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The terminated rhombic beam holds the position of king among all long-wire arrays. It is an extension of basic long-wire technology, a small piece of which we sampled in the preceding episode. Initially developed by Edmond Bruce in the early 1930s, the antenna served point-to-point communications needs well into the 1960s. During the 4-decade heyday of the rhombic, amateurs dreamed of having one of these high-gain, narrow-beamwidth, broad-band antennas--and of the acreage necessary to hold it. One humorist reported that his ideal antenna would be a very large rhombic located on a rotatable island in the Caribbean.

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These notes are not aimed at evaluating the relative merits of the terminated rhombic. Instead, the goal is to address some questions that may arise in the course of modeling rhombic antennas of various types. Perhaps the simplest rhombic model appears in Fig. 1. The legs are 4 wavelengths each, which results in the specified dimensions. I selected the angle (alpha) between the centerline and each leg to yield the maximum gain for this model, which happens to be at a 3.5-MHz test frequency. The lossless model wires are 0.16" in diameter.

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The patterns below the model outline show the reported elevation and azimuth plots for the modest rhombic. One main reason for the commercial use of the rhombic was the very narrow beamwidth as well as the high gain. However, the relatively strong sidelobes remained a concern for rhombic designers into the 1960s. The last major rhombic development was the dual offset rhombic design of Edmund Laport.

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The following abbreviated list of references will provide more information on rhombics for those intrigued by long-wire technology. For a systematic treatment from a modeling perspective, see Long-Wire Notes, available from antenneX.

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Bruce E., "Developments in Short-Wave Directive Antennas," Proceedings of the IRE, August, 1931, Volume 19, Number 8: the introduction of the terminated inverted V and diamond (rhombic) antennas.

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Bruce E., Beck A.C., and Lowry L.R., "Horizontal Rhombic Antennas," Proceedings of the IRE, January, 1935, Volume 23, Number 1: the classic treatment of rhombic design, repeated in many text books.

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Graham, R. C, "Long-Wire Directive Antennas," QST, May, 1937: an excellent summary of long-wire technology to the date of publication.

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Harper, A. E., Rhombic Antenna Design (1941): a fundamental text on rhombics, based on engineering experience, with tables and nomographs as design aids.

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Johnson, R. C. (Ed.), Antenna Engineering Handbook, 3rd. Ed., Chapter 11, "Long-Wire Antennas" by Laport.

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Laport E. A., and Veldhuis, A. C., "Improved Antennas of the Rhombic Class," RCA Review, March, 1960, Volume XXI, Number 1: the introduction of the off-set dual rhombic.

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Multi-Modeling Potentials

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The model that produced the sample plots in Fig. 1 provides general guidance, but not refined analysis suitable for use as a final pre-building design. Besides lacking the environmental inputs relevant to a prospective building site, there are some fundamental modeling issues that preclude the use of this model as a precision replication of some particular rhombic or other long-wire array. First, the model uses one of several possible input configurations possible in NEC. Each configuration has its own strengths and weaknesses relative the NEC calculations. Second, the model uses a somewhat minimal segmentation density at 20 segments per wavelength.

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Fig. 2 shows the pointed-end configuration used for the sample model. L is the leg length and is the square root of the sum of the squares of dimensions A and B. One advantage of this model is that it replicates angle alpha accurately. However, it does require the use of split sources and loads. An alternative configuration that we shall have to use shortly is on the right. The model places a single source and a single load on short end wires that create a blunt-end rhombic. The dashed line shows the virtual leg that has length L. However, the actual leg length is L' + C. As well, the wire labeled L' has a shallower angle relative to the junction with C than given by alpha. If we make dimensions A and B the same as for the configuration on the left, then we have slightly distorted the rhombic shape. The degree of distortion is a function of 2 factors: the length of C and the leg length L. If C is very short and L is very long, then the distortion will be small relative to the pointed-end model.

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Fig. 3 illustrates the source and load treatments that accompany the two general configurations. Assume that all segments or distances between dots on the sketch have the same length. The pointed-end model places source excitation on the left-most segments of each of the two wires forming the feedpoint end of the rhombic. These sources are in series, and the net impedance of the source is the simple sum of the resistive and reactive components of each source. If we increase the segmentation density of the model, then the sources move closer to the actual tip of the rhombic. A similar condition applies to the series loads placed on the right-most segments of each wire approaching the termination end of the rhombic. The net resistive load is the sum of the two resistances, but if we increase segmentation density, the loads move closer to the actual tip of the rhombic.

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The lower sections of the sketch show alternative methods of placing sources and loads at the furthest extremes of the rhombic. The method on the left uses a single segment wire for the source and another for the load. If we carefully size the 1-segment wires so that their length just about equals the length of each segment, NEC should yield accurate results, although it is preferable to have equal-length segments in a line on each side of the source segment. The lower right sketch shows a 3-segment wire at each end of the rhombic that achieves this goal. However, even with careful sizing of the wire length to equalize segment lengths throughout the model, the 3-segment wires increase the distortion of the rhombic shape relative to either the pointed-end or the 1-segment blunt-end versions.

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The amount of distortion in the rhombic shape is not large, even with a 3-segment wire at each end. Table 1 provides information on the dimensions of a test rhombic using 4 wavelength legs and an alpha angle of 24.5°, the angle needed to optimize for maximum gain in the original pointed-end model. The table shows the dimensions for all three versions, including the changing value of C as the segments in the main legs (L') grow shorter with increasing segmentation density. The worst case of distortion occurs with a segmentation density of 20 segments per wavelength while using a pair of 3-segment end wires. For 20 segments per wavelength, the end wires have individual lengths of 0.14 wavelength (or C = 0.07 wavelength). The distortion amounts to adding about 4% to each leg wire overall, although the angular portion of the wire is under 4 wavelengths. Nonetheless, the combination of configuration, source, and load changes can affect the modeling outputs.

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Table 2 provides the results of running all models under identical environmental conditions by placing each rhombic 1 wavelength over average ground at the test frequency. We need to scan the table in several different ways. First, if we compare the 3 models regardless of segmentation, we note that the terminating resistor increases value as we add the blunt end wires and increase their length. The terminating resistor was set with a segmentation of 20 segments per wavelength and remains unchanged as we increase the segmentation density for each model. The SWR reference impedance is also the resistance of the termination. For each model, as we increase the segmentation density, the feedpoint reactance grows more capacitive, and the feedpoint resistance decreases. The change in reactance is more radical than the decrease in resistance. However, reducing the terminating resistance in each model for a better match with the feedpoint impedance for a given segmentation density will also reduce the magnitude of the reactance.

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Second, we can scan each model's table for other trends occasioned by increasing the number of segments per wire. The most dramatic case is the 180° front-to-back ratio, which is also a measure of the relative size of the lobe projecting directly rearward along the rhombic centerline. In all cases, it decreases as we increase the segmentation density, leveling off in the 24-25-dB region for all three models with 80 segments per wavelength. The beamwidth is stable for all models. So too is the front-to-sidelobe ratio, although the 3-segment end-wire model shows the greatest internal variation with changes in segmentation density.

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With respect to the reported forward gain, the pointed-end and 1-segment blunt-end models show the closest coincidence in two respects. First, the gain levels closely match at all levels of segmentation, as do most of the other data related to radiation patterns. Second, both models show a slowly decreasing gain value as the segmentation density increases. In contrast, the blunt-end model using 3 segments in each cross wire shows an initially higher gain value, and that value continues to increase with the segmentation density.

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The relatively close values that we find in Table 2 with respect to the performance of the pointed-end and blunt-end arrays, when each uses an optimized terminating resistor, can hide some differences. To show one of the differences, I varied the value of the terminating resistor across a wide set of values. The data in Table 3 selects 3 values that surround the final value and suffices to reveal the critical differences in model performance.

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The data columns related to the radiation patterns reveal a consistent set of curves. The gain shows almost no change, with a slight numerical increase as the value of the terminating resistor increases. The front-to-side ratio also increases with the value of the terminating resistor. The front-to-back ratio peaks at mid-range, a characteristic of rhombics as the terminating resistor approaches its optimal value. In these respects, the two models are fully consistent. Since the terminating resistor values are not too far apart, even the feedpoint resistance values are not distant from each other.

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The key difference between the progression of values lies in the reactance column. The pointed-end model shows a reactance that becomes more inductive as the value of the terminating resistor increases. In contrast, the blunt-end model, even though it uses only 1 segment on the short end wire, shows a reactance that becomes more capacitive as the value of the terminating resistor increases. Older literature from the 1940s suggests that the rhombic builder should use a set of perhaps 3 to 4 resistors in series rather than a single terminating resistor. The goal is to reduce the capacitance across the total termination by creating several capacitors in series. If the models reflect reality (a major presumption in the absence of a physical test rhombic), then the reactance columns might be natural. The pointed-end model already uses 2 resistors in series, and they extend from a position on one side wire to a position on the other. In contrast, the one-segment blunt-end model uses a single resistive load on a very short wire.

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With respect to physical reality, much of the variation among models falls below the level of practical measurement in HF arrays, and almost all lies outside operational concerns. However, internal to a series of interrelated modeling tasks, the data in Table 2 and in Table 3 are important. Some models cannot use the pointed-end geometry and so must use some form of the blunt-end model. The data at hand strongly suggests that if we wish to compare the results of the new models with past models, the 1-segment end-wire blunt model yields results that are most consistent with the pointed-end models. Since our goal is to detect and appreciate general trends in rhombic performance, consistency is a virtue, if not an absolute necessity.

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Multi-Wire Rhombics

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Many references on rhombic design recommend the use of multiple side wires to improve performance. The wires come together at each end of the rhombic to form a single source and a single terminating resistor. However, at the midline from which we measure the tilt angle or phi, the wires are vertically separated by a space that runs from a few feet at lower frequencies to a few inches in the upper HF range. Some literature warns about ensuring that the center wire of the set--the one that is level with respect to ground--is not shorter than the outer wires. However, the warning is misplaced, since the actual length difference is a small part of 1%. The key caution to use in creating a multi-wire rhombic is to ensure that all wires place equal tension on the connecting points. Although some 5-wire rhombics have existed, the most common configuration uses 3 wires.

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The multi-wire rhombic has enjoyed many claims of advantages over the single wire rhombic. Some have reported quieter operation, suggesting that the 3-wire array has weaker sidelobes. As well, the 3-wire array shows more forward gain than its 1-wire counterpart with the same leg length. In some places, we find claims that the 3-wire array shows a better SWR curve over an extended frequency span due to interaction among the wires that compensates for reactance. It also provides a better match for a 600-Ohm terminating resistor and common 600-Ohm transmission line. To evaluate the foundation of some of these claims, we must figure out how to model a 3-wire rhombic in a relatively reliable manner.

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Fig. 4 shows two alternative methods of modeling the 3-wire rhombic. The top view would be the same for both models. It only indicates that we must use a blunt-end technique for the model. Given the discussion of blunt-end vs. pointed-end models in the previous section, we shall use a 1-segment end wire to form the blunt ends.

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When we turn to end treatments in the lower portion of the figure, we can see more clearly our options. The simplest option (A) uses a single end wire at the source and load ends of the rhombic. The three side wires come together at each end of these wires. The source and the load are effectively centered within each end wire. The configuration presents two challenges to NEC as a calculating instrument. First, the three side wires approach the junction at very shallow angles, allowing for significant inter-penetration in the segments that form the junction. Second, NEC prefers a single segment on each side of a source segment prior to any division of the current.

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The alternative to the single end wire is the use of separate end wires for each side wire (B). We may place these wires very close together so long as we allow spaces that are several times the wire radius. We may model the separate end wires using a spacing of 0.001 wavelength to achieve a simulation of a single wire. At the load end of the array, we may use separate terminating resistors on each line. The value for a 3-wire rhombic is simply 3 times the desired equivalent single terminating resistor, since the loads are in parallel. Since the loads do not have a physical dimension, they do not affect the wire spacing.

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The source wires call for slightly different treatment, although we might use 3 sources and calculate their parallel value. A simpler procedure is to create a transmission line between each outer wire and the center wire. Since lines have no physical dimensions due to the wire geometry, we can assign them any desired length. Because we wish to simulate a parallel connection, we can assign a length of 1e-10 m or similar. The line's characteristic impedance can be virtually any value, since almost nothing happens over a near-zero line length. Using an impedance of about 600 Ohms will satisfy the situation. Of course, we place a single source on the center end wire, since transmission lines are in parallel with any source on the same segment.

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One way to evaluate the alternative modeling techniques is to track what happens if we vary the value of the terminating resistor. As a test case, we can create 3-wire rhombics with 4 wavelength legs. Table 4 provides the comparison. Since the two types of models call for different optimized terminating resistors, the resistor ranges differ. As well, they differ from the ranges used in Table 3, which compared pointed-end and blunt-end models of 1-wire rhombics with 4 wavelength legs. The data in that earlier table will also be important to the evaluation of 3-wire models. The 3-wire models use 1-segment end wires, so the 1-segment blunt-end model of the single wire rhombic is the appropriate comparator. All models will be 1 wavelength above average ground and use 0.16" diameter lossless wire.

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The use of a single end wire with 3 side wires joining at very small angles yields rather optimistic gain estimates compared to the 3-end-wire version of the model. In addition, the reactance undergoes virtually no change as we vary the value of the terminating resistor by 400 Ohms. Both of these data columns are at odds with the results for a 1-wire blunt-end rhombic model. In contrast, the 3-wire model that uses 3 end wires shows a more modest gain. As well, the pattern of capacitive reactance parallels the pattern shown in Table 3 for the blunt-end 1-wire rhombic. Finally, the triple end-wire model shows an optimized terminating resistor value of about 600 Ohms, a value that corresponds well with actual practice.

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A second relevant test of the modeling options is to compare them by varying the spacing between side wires at the midline point. As a sample, I ran the models for both options at 3 spacing increments: 0.0125 wavelength (narrow), 0.025 wavelength (medium), and 0.05 wavelength (wide). Wide spacing is 4 times narrow spacing. The total distance at the midline between the top and bottom wires is twice the spacing increment. The end-wire spacing for the triple end-wire model does not change. The results of these tests appear in Table 5.

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The weakness of the model using single end wires shows up in the table. The key datum is the feedpoint resistance, especially as we compare it with the corresponding datum for the triple end-wire model. As we increasing the wire spacing for the triple end-wire model, the reactance undergoes some change, but the resistance remains essentially constant. In contrast, the single end wire model shows only a small change of reactance, but a large change of resistance. As we increase the angle of the side wires as they approach their junction at the end wires, the resistive component moves closer to the 600-Ohm value of the triple end-wire model. The resistance change suggests that widening the angle at the junction reduces any calculation aberrations produced by wire inter-penetration.

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Option B, the triple end-wire model provides results that are thus superior to those of option A in at least 2 ways. First, they are consistent with the results for the blunt-end 1-wire rhombic model. Second, the results are internally consistent relative to widening the midline spacing between wires. Although the reported gain is lower for the triple end-wire model, it nevertheless shows an increase with respect to increasing wire spacing. Moreover, it shows a useful gain over a 1-wire rhombic. For wide 3-wire rhombic midline spacing, the gain improvement can be up to about 1.6 dB, as shown in Fig. 5. The gain advantage is slightly less for narrower midline wire spacing.

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Note that the 3-wire rhombic not only magnifies the main forward lobe. As well, it enlarges virtually every other lobes in the radiation pattern proportionally, and without changing either the angle or the general shape of each lobe. Especially interesting in the pattern are the two innermost forward sidelobes. From the shapes, we can tell that they are in fact pairs of overlapping lobes. Both the 1-wire and the 3-wire models use an alpha angle of 24.5° to maximize gain. The lobe structure might change slightly with other values of alpha. For example, if we widen the angle further, the combined innermost sidelobes on each side of the present main lobe will eventually become stronger than the central lobe, resulting in a 3-lobe forward pattern.

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To assure ourselves that we have fairly represented the advantages of the 3-wire rhombic over its 1-wire counterpart, we can perform one further test. We can increase the segmentation density of the triple end wire model and compare the progression with the one that we examined in the case of the blunt-end 1-wire rhombic. The comparison appears in Table 6. For both antennas, the steps use 20, 40, and 80 segments per wavelength, and the length of the end wire is reduced to maintain length parity with the adjacent segments of the side wires.

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The 1-wire and 3-wire rhombics show quite precise parallels in the progression of values in each data column, indicating that the models are appropriate comparators. The only small divergence occurs in the reactance data, as the 1-wire rhombic model has a 133-Ohm total range, while the 3-wire model varies by only 84 Ohms. In both cases, the capacitive reactance increases as the end-wires become shorter. (However, even at the shortest length with the highest segmentation density, the modeled end wires are long compared to typical physical structures until we reach the high end of the upper HF range.)

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The claims for 3-wire rhombics with which we began this section of notes find only partial confirmation in the models used to evaluate them. Using 3 wires does raise forward gain by an average of 1.5 dB for a 4 wavelength leg rhombic. The exact gain advantage depends on the wire spacing at the midline. As well, the optimum value for the terminating resistor drops from a value between 800 and 900 Ohms down to 600 Ohms. In both cases, the models reflect both calculations and practical experience with rhombics. However, reports of quieter operation--presumably meaning freedom from what Bruce called "static" in 1931--do not find confirmation in any property of the models. For a given leg length and value of alpha, the 3-wire rhombics produce patterns that are congruent in almost every detail with those produced by 1-wire rhombics. If 3-wire rhombics are in fact quieter than their 1-wire counterparts, the reasons must lie outside the realm of properties that NEC models can reveal.

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Among the claims associated with 3-wire rhombics is a flatter SWR curve over an extended frequency range. Over the intervening decades since the appearance of the original literature on rhombic design, accounts have undergone truncation, especially after the heyday of rhombics had passed into the history of radio communications. My suspicion is that the claim of a flatter extended-frequency SWR applies only to the use of 600-Ohm transmission lines, likely occasioned by early difficulties in constructing mechanically stable wider lines with a higher characteristic impedance. If we match the line impedance to the terminating resistor, then extended-frequency SWR curves show no significant differences. For example, Fig. 6 provides SWR curves for the 1-wire blunt-end model and for the narrow-spaced 3-wire rhombic, with each using the terminating resistor as the SWR reference impedance.

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The curves use a 0.1-MHz increment, which is sufficient to pick up at least some of the peak values that might occur. However, the peak SWR is 1.2:1 or less for both antennas, suggesting that there is no significant difference between them. The slightly higher values in the 3-wire curve result from the fact that the similar reactive components in both antennas represent a higher percentage of the resistive component in the more complex array. In the end, reactance compensation during final design and construction, when combined with the selection of the correct feedline impedance, will do more for the flatness of the SWR curve than the presence of 3 wires.

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(In fact, one account of single-wire rhombics suggested in one paragraph the use of 600-Ohm transmission line to the feedpoint and in another suggested that the terminating load might be placed conveniently near ground level by the use of another transmission line. If the termination line had a characteristic impedance of 800 Ohms, then line length would make no difference to performance, since it would match the presumed impedance of the terminating load and the antenna when viewed as a transmission line over ground. The account reflected common practice at the time of writing, and common practice is often the source of unnoticed inconsistencies.)

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In the end, a 3-wire rhombic appears to have no calculable properties other than those associated with the simulation of a very large diameter wire through the use of multiple conductors. Cage antenna elements and multiple-conductor dipole and quad loop elements are fairly common practices to increase the effective diameter of an element without resorting to excessively heavy single large elements. The rhombic 3-conductor side wires function in much the same way, although their tapered arrangement makes the determination of a single effective diameter a somewhat uncertain calculation. The use of multiple side wires is optional unless one requires either the small gain advantage or the use of 600-Ohm lines and an equal value of terminating resistor.

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Our small side-trip into 3-wire rhombics has had two goals. The first was to find an effective technique for modeling the antenna, a technique that would produce results that are fully consistent with both good NEC modeling practices and reports emerging from relevant 1-wire rhombic models. "Option B," the triple end-wire model accomplished this goal. The second goal was to understand within the limits of what models can tell us whether a 3-wire rhombic might have advantages over a 1-wire version of the same rhombic. Although we focused on a single mid-size rhombic (with 4 wavelength legs) designed to optimize gain, the results are suggestive for the entire range of possible rhombic sizes.

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Conclusion

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Our case study has illustrated one way in which an antenna with a relatively simple initial geometry can grow into a fairly complex model. The goal in all of the modeling exercises was to produce models that met as closely as possible all of the limits inherent in NEC (in this case, NEC-4). Key to the decisions as to which of alternative models best met these requirements were two factors. One was the internal consistency of results as tested by examining short progressions of variations in model designs and segmentation. The other factor was the reasonableness of the outcomes when compared to actual field practices in the construction of commercial rhombics.

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One may well ask why we should be so finicky with the selection of a model geometry. At various places, I have noted that the models are suited only for developing general trends in rhombic performance and not for specific guidance in building a rhombic. Let's look at the trends in these brief notes and extrapolate them to a larger project, perhaps one involving a systematic exploration of rhombics of many leg sizes ranging from perhaps 2 to 11 wavelengths. The trends include not just the common concerns for forward gain and front-to-back ratio. They encompass as well trends in the value of the terminating impedance, the feedpoint resistance and reactance (at both the design frequency and over a usable passband), and the nature of the forward sidelobes. Geometrically, rhombic concerns do not cease with the selection of the leg length, but also include the angles of the wires and the effects of those angles on the resultant radiation pattern.

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Fig. 5 overlaid patterns for single-wire and 3-wire rhombics in a direct comparison of radiation patterns. If we are to make such comparisons with any assurance that the comparison is valid, then the model on which each pattern is based must be consistent to the highest feasible level with the other model. Otherwise, we would have good reason to distrust the comparison--and the data that led up to it. One way to avoid rational distrust of model comparisons is to spend the required time to validate the models with respect to each other. These exercises have shown an example of the process.

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In some cases, modelers appear to be content if they can achieve a model of the antenna they may be studying. In other cases--like this one--it is important to find the model for the geometry involved.

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114. Modeling Folded Monopoles

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L. B. Cebik, W4RNL

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The folded monopole is an interesting variation on the standard linear monopole. Essentially, the folded monopole is one-half of a folded dipole. As such it retains two important properties. First, the act of folding results in an increase in the feedpoint resistance relative to the linear or open-ended monopole. The exact ratio of impedance transformation depends on the relative diameters of the fed and the "other" wire. The transformation ratio answers to the same equation that we have often seen for the folded dipole. Although the ratio of wire diameters provides the key variable in the equation, the spacing between the wires plays a significant role in two ways. The terms of the ratio itself are each ratios of diameter to spacing. For reference, the following equation appears in many texts, where R is the ratio of impedance compared to the open-ended linear antenna, s is the center-to-center spacing of the wires, and d1 and d2 are the 2 diameters, with d1 representing the fed wire.

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As well, the wires must be close enough to each other to ensure that the pair forms a transmission line and not a simple wide-spaced half loop. The fact that the folded monopole is itself a transmission line comprises the second major property of the folded monopole.

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If the folded monopole is shorter than a self-resonant length, that is, is shorter than an electrical quarter wavelength, then the transmission-line aspect of folded monopole behavior is a shorted transmission line. Alternatively expressed, the line is an inductive reactance up to about 50 degrees electrical length, depending upon the diameters and spacing of the wires in the folded monopole. The characteristic impedance of the line is mostly a function of the folded monopole physical properties. For a two-wire monopole, the key elements that set the characteristic impedance are the center-to-center element spacing and the diameter of the elements. For a given construction (that is, for a given element diameter, spacing, and total height), the characteristic impedance does not change with frequency (if we ignore the effects of a real or lossy ground for the moment). The inductive reactance becomes a function of the folded monopole height measured in terms of a wavelength. The inductive reactance is then a tangent function of the electrical length translated into degrees or radians. We then may calculate the equivalent inductance by using the standard relationship among reactance, inductance, and frequency. However, the source impedance of the folded monopole, being a function of both radiation and transmission-line characteristics, will not be the same as the inductive reactance of a shorted transmission having the same length.

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Many antenna designers for the MF and lower HF ranges prefer the folded monopole to the linear monopole, especially when the overall height must be shorter than a resonant length. Since the transmission-line aspect of the antenna's behavior always yields an inductive reactance for such lengths, tuning networks may use inherently high-Q capacitors exclusively and avoid low-Q inductors. The effort to design such antennas leads to modeling attempts in NEC or MININEC. The seemingly simple antenna should yield equally simple models. Unfortunately, all too often the simple models prove to be quite inadequate. In these notes, I want to review a number of places in which the modeling may go astray.

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For uniformity through the exercise, I shall use some constants. The modeling frequency will be 3.5 MHz. The lossless wire will be 0.1" in diameter, although we shall also use a 1" wire under certain specified conditions. To simplify ground radial aspects of the model--which might create some ungainly models--and to avoid the variable of the ground losses, I shall place the model on perfect ground. This ground type will satisfactorily reveal most of the modeling dangers that we may encounter. I shall also use two different programs and cores. One core is NEC-4, which performs better than NEC-2, but still not perfectly. I shall contrast the NEC-4 results with MININEC outputs from Antenna Model, perhaps the most corrected version of MININEC 3.13 available.

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Fig. 1 shows the initial evolution of the models that we shall examine in detail. The linear resonant monopole will become the standard against which we may compare the other models. Next, we shall turn to the two-wire or "hairpin" folded monopole. Finally, we shall examine a simple 5-wire cage folded monopole. In all cases, we shall designate a prime or fed wire. In the case of the cage, we shall use the center wire to simplify feeding. We shall later briefly note how to feed the outer wires in parallel. For reasons that we shall explain as we move along, the linear monopole uses more segments for essentially the same height as the outlines of the folded monopoles. The brief reason is that folded monopole models using the higher segment density would not show the space between wires very well.

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Both linear and folded monopoles show about the same gain and the same pattern shape, as revealed in Fig. 2. There is one very minor exception to this statement. A two-wire folded monopole will show a very slight difference between the gain broadside to the pair of wires than in line with the wires. Gain on the fed side will always be numerically but not operationally higher than gain in the direction of the unfed wire. The exact differential varies with the wire spacing, but generally is less than 0.1 dB for all practical spacing and wire-diameter values.

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Let's model the linear monopole over perfect ground in both NEC-4 and MININEC as a baseline data set for future reference. Table 1 shows the results of supplying the models with 69 segments, with the feedpoint or source on the lowest segment.

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The table shows that both cores provide the same output reports, just as we might expect for this modest frequency and well-segmented model. Each segment is about 1' long. Both models show an ideal or nearly ideal Average Gain Test (AGT) score. Antenna Model actually provides the raw calculated number, which over perfect ground is twice the value shown. I have adjusted the number to coincide with the EZNEC or free-space value. My reason is simple. 10 times the common log of the free-space AGT score provides the adjustment factor necessary to correct the gain report when the AGT score is not ideal. The AGT dBi entry provides the calculated correction factor, which is 0.0 for this simple model.

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We are now ready to create a model of a two-wire folded monopole. Fig. 3 will provide some guidance.

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Good modeling practice dictates that we adhere to certain guidelines when constructing the wires of a model. In NEC, keeping the segment length more than twice the diameter or 4 times the wire radius ensures the most accurate current calculations. We can reduce that ratio in NEC-2 by invoking the EK command, and NEC-4 generally is accurate with a 2:1 segment-length-to-diameter ratio. Antenna Model recommends that the segment length be at least 1.25 times the wire diameter for best accuracy with its modified MININEC core. The use of 1' segment lengths with 0.1" diameter wire ensures that we shall not have problems in this department.

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Second, adjacent segments should have similar lengths, especially in NEC and especially in high-current regions of the antenna assembly. The two-wire portion of the figure shows a spacing (and 1-segment end wire) that is 1' long, matching the segment length of the long wires. The resulting folded monopole will have 139 segments, not very high for today's fast computers. Some programs, like EZNEC, provide for a length-tapering feature to reduce the segment count while keeping the segment length at one or both ends of the wire at a selected minimum length (in this case 1'). The NEC GC command achieves the same goal but uses a different length-tapering algorithm. We may bypass these steps by creating a 139-segment model both in EZNEC and in Antenna Model. The results appear in Table 2.

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Once more, the output reports from the two programs are almost identical. Both programs can handle the folded monopole composed of a single wire diameter throughout with all of the other modeling guidelines in order. The height of the resonant folded monopole is shorter than the height of the linear monopole because, with respect to its radiation behavior, the double wire acts like a single fatter wire. The gain entry shows a sample of the in-line gain differential, while the main part of that entry shows the broadside value.

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The resistive component of the source impedance is 143.5 Ohms. The fact that the wires have the same diameter with a constant spacing between them yields the familiar 4:1 impedance transformation ratio. 4 times 36 Ohms (for the linear monopole) is 144 Ohms. So far, all is simple and well.

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Let's now create a cage-type folded monopole with the center wire fed, using the right side of Fig. 3 as a guide. The outer wires that return to ground use the same segmentation as the single return wire of the model that we have just reviewed. The end wires are each 1' long to preserve the identity of segment lengths throughout the model. Since we shall be reducing the overall antenna height, the total segment count for the model is 319. Table 3 shows the results.

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The models show several interesting facts about modeling cage-type folded monopoles. Starting with the impedance, we notice a very great increase in the resistive component. (The reactive component did not go to zero using height increments of 0.1', so the table shows the lowest value attained.) The cage monopole is essentially a form of coaxial transmission line structure. Ideally, the wire diameter values used to calculate the impedance transformation would use the center wire value and the effective diameter of the ring of cage wires. For these cases, the transformation equation will not work. If we feed the center wire, then 2S/d2 is 1 and its log is zero, leading to a calculational error or to an indefinitely large value for the ratio, depending on whether you are using a computer or a scratch pad. Likewise, if we feed the outer wires in parallel, then 2S/d1 becomes 1 and its log is zero. This partial result leads to a ratio of 1.0 for all cases. However, we cannot be certain that the value of d2 is in fact 2' for this example, since the structure has more open area than closed area, and the cage wires are thin. The reported values from the model are sufficiently high to establish that we have a thin fed wire and a very fat "other" or return wire, just the conditions that yield a very large transformation value by standard calculations.

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The other significant fact to note is the AGT of the NEC-4 output report. 0.988 is not an ideal value and requires a correction of 0.05 dB to the gain report. As the table suggests, when the calculated adjustment factor is negative, we increase the raw report by the absolute value of the adjustment factor. Had the calculated adjustment factor been positive, we would have subtracted it from the raw gain report. The MININEC AGT score shows no need for adjustment, and the raw gain report report is very close to the adjusted NEC-4 number.

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NEC-4 appears to drift somewhat off an ideal AGT value due to the proximity of 4 wires to the fed wire, as well as the current division at the top of the model. A single return-wire did not produce this consequence. NEC-2 is even further distant from an ideal AGT score, yielding a value of 0.928 for the same model. Hence, its gain report would be 0.32-dB low. Some scales of model adequacy as measured by the AGT score use limits of 1.05 and 0.95 as marking the ends of truly reliable models. I tend in most of my work to use even tighter limits. The NEC-2 AGT value lies well outside even fairly loose limiting values.

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Although the Average Gain Test is a necessary, but not a sufficient, condition of model adequacy, it is an important test for all models. Modelers should routinely apply the test, since it may minimally require correction of the gain reports. If one is conducting systematic modeling exercises designed to show performance trends, then the AGT is essential lest one misread the trends.

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If we are searching for general properties of a particular type of antenna, we may alter the model to overcome some of the limitations that we might encounter initially. Fig. 1 showed two-wire and five-wire folded monopoles that used fewer segments per unit of antenna height. However, each return wire used a wider spacing from the center fed wire. Let's explore this avenue of modeling to see what emerges. First, we may increase the spacing from the center wire to 3' and still have an effective folded monopole at 3.5 MHz. The end wires will use a single segment. To keep all segments roughly the same length, we shall reduce the total number of segments in the 2-wire monopole to 22. The overall height will be 66.3', in keeping with the increase in the "fat wire" effect of placing the wires 3' apart. Table 4 shows the results from the new model using each program.

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Increasing the spacing yields a two-wire NEC-4 model that is almost identical in performance to the more narrowly spaced two-wire model. The AGT is ideal and the impedance a virtually the same at 4 times the linear monopole value (within less than 1 Ohm). Interestingly, the MININEC results in Antenna Model show a nearly ideal AGT value and a very close impedance coincidence to the NEC-4 model. The gain remain on target (using the value boradside to the plane of the 2 wires).

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We have enough data to let us try a five-wire model in each system using the wider spacing and the reduced overall segmentation. The five-wire model will be shorter than the two-wire model, so the vertical wires will use 21 segments each. Table 5 provides the output reports.

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Both models provide excellent AGT values. As well, the difference between the gain values has decreased to merely 0.03 dB. However, we see a considerable difference in the reported impedance values. It is likely that some, if not all, of the difference stems from the fact that with a high impedance, very small differences between models will result in outsized changes of some calculated results. We normally think of such changes as modifications that we might make to the geometric structure. However, in this case, the difference is most likely a product of the difference in the calculation methods.

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Most folded monopole systems consist of one fat element (often a tower structure) and one or more thin wires. Without changing anything else, we may explore what happens when we increase the diameter of the fed wire to 1", that is, increase the diameter by a factor of 10. 1" is well below the effective diameter of most towers, but the differential with the return wire should be enough to reveal any calculation difficulties that might be a core function. If we apply the fed-wire diameter increase to the two-wire folded monopole, we obtain the results in Table 6. Note that we did not change the overall antenna height relative to the previous two-wire model.

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The MININEC version of the model shows one advantage of its system: it is less sensitive than NEC to junctions of wires having dissimilar diameters, whether those junctions are linear or angular. The AGT value is very close to the ideal and requires no gain report change. Both the gain and the impedance reports are closer to the calculated value than is the NEC report, although the difference is small.

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NEC-4 shows an AGT score that is off the mark by a noticeable amount. Hence, the raw gain report is about 0.12-dB too high, but after correction, it returns to the expected value. (NEC-2 under the same conditions produced an AGT score of 1.137, a wholly unreliable score for a model. The correction factor requires a raw gain reduction of 0.56 dB. The result might be in the ballpark for expectations, but we likely could not trust the impedance reports.) NEC-4's raw impedance report is fairly close to the MININEC report. However, trying to adjust it with the AGT multiplier carries it further from the MININEC value. In effect, we are now modeling in a region where NEC (-2 and -4) does not produce the most accurate results due to the junctions of wires with different diameters.

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The impedance reports are less than 4 times the impedance of the (36-Ohm) linear monopole because the fed wire is considerable larger in diameter than the return wire. As the fed wire increases in diameter for a constant-diameter return wire, the transformation ratio will continue to decrease, but it can never descend below a 1:1 ratio. A folded monopole (or a folded dipole) cannot be an impedance down-converter.

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When we apply the same fed-wire diameter increase to the five-wire model, we obtain interesting results. Once more, we retain the same overall antenna height that we used in the previous five-wire model with its uniform wire diameter. Table 7 shows the model reports.

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The NEC-4 model shows near resonance almost accidentally. However, the most important aspect of the report is the further departure from an ideal AGT score and the requirement for a sizable correction factor to the raw gain report. (NEC-2 produced an AGT score of 1.177 for the same model, indicating a required correction of 0.71 dB to the raw gain report.) In contrast, the MININEC model--as provided by Antenna Model--remains close to ideal in its AGT score. The raw gain report is also very close to the NEC-4 corrected value and well-suited to the shorter overall height of the model, relative to the 68.4' linear monopole. (Hence, the slightly higher two-wire gain reports remain an anomaly in the overall model progression.)

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Simple models of folded monopoles tend to ignore the remaining structure of a tower or mast that has been converted to folded monopole use. We may easily test whether or not we are well or poorly advised to ignore such upper-end lengths of structure beyond the limits of the folded-monopole proper. For these initial tests, we may add an extension to the 1" fed or center wire of both folded monopoles that we have just tested without an extension. Let's add 10' of 1" diameter wire to the top of the structure and use about 5 segments. Because the extension is a low-current region of the antenna, the exact segmentation will make only small differences to the source impedance report and almost none to the gain and AGT reports. The height of the antenna up to the extension is the same as in the previous two-wire and five-wire folded monopoles. See Fig. 4. Our goal is to see if the mast extension makes a difference, and if there is a difference, we expect it to appear most prominently in the source impedance report.

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If we run both models using EZNEC/4 and Antenna Model, we obtain the results in Table 8. In this case, we may pass over the AGT issues and focus on the source impedance. Compared to the values shown in Table 6, the new values clearly show that the extension raises the resistive component of the impedance and adds a very significant inductive reactance to the overall impedance.

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The five-wire version of the folded monopole shows the same general pattern of impedance. Compare Table 9 to Table 7. The inductive reactance has grown significantly--faster than in the two-wire model.

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Although feeding the center wire/fat wire of the various folded monopole models has served well to reveal some features of modeling, it does not reflect what AM BC and amateur applications may encounter in practice. Normally, we would feed the thinner wire, while leaving the central tower or fat wire grounded. The two-wire monopole requires only a small adjustment to correct this situation, but the five-wire models will need a different strategy. Fig. 5 shows our options.

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The two-wire model only requires that we move the source from the fat wire to the thin wire. We shall use the same model whose results appear in Table 6: a 66.3' folded monopole. This time we shall place the source on the lowest point of the 0.1" thin wire and leave the 1" fat wire as a return to perfect ground. The results of this model revision appear in Table 10.

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We do not lose the deficiencies of NEC by moving the source point. The AGT value shows that we need to adjust the gain report by 0.19 dB to obtain the expected value of about 5.15 dBi. However, note that the AGT value is now less than an ideal 1.0 rather than being greater than 1.0. The Antenna Model version of the revised model shows an admirable AGT value and gain value. Finally, note the increase in the source resistance that results from using a thin fed wire and a fat return wire (relative to the reverse situation shown in Table 6). Once more, the MININEC core reports an impedance that is closer to the calculated value.

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The five-wire monopole presents us with a different challenge. We might be tempted to end all 4 outer thin wires above ground by a foot and then connect all of them around the center wire. A short wire to ground from one corner would become the source wire. This procedure might seem to reflect the actual physical structure of a folded cage-type monopole, but it creates a number of modeling error sources. The segment lengths in the model are 3' long, so the series of connecting wires and the source wire introduces aberrant segment lengths. As well, the source segment and the adjacent segments would not have equal lengths, a desirable situation especially in NEC for the most accurate calculations. Moreover, the segment junctions of the outer wires would no longer parallel the segment junctions of the center wire, an undesirable condition in NEC for highest accuracy. Finally, the current division among the outer wires would not be equal, resulting in possible pattern and impedance errors

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A more secure method to retain whatever accuracy the model has would be to use 4 sources, one on each outer thin wire. This technique is equally applicable to NEC and to MININEC. To arrive at a net single-source impedance value, we need only divide one of the source impedance reports by 4, taking the resistive and the reactive components separately. If we use the model whose result appear in Table 7 as our starting point, we need only replace the single source on the center 1" wire with 4 sources, one on each of the outer thin wires. We shall leave the modeled antenna height at 61.3'. The results of our efforts appear in the top portion of Table 11.

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Because we are now feeding the outer conductor, the effective diameter of which is greater than 1", the net impedance is considerably lower than the value found in Table 7, the model the feeds the inner and effectively thinner conductor of this concentric model. However, do not be fooled by the deceptively attractive resistive value. An actual tower situation will place a much larger diameter center conductor into the model. As a useful but imperfect guide, BC engineers conventionally use the following diameters as 1-wire substitutes for antenna towers. For a triangular tower, use a wire with a radius of 0.37 times the face dimension. For a rectangular tower, use a wire with a radius that is 0.56 times the face dimension. You can adjust the spacing of the wires from the central tower and their diameter (and even their number) to arrive at a desired impedance, since the value (over perfect ground) will not go below 36 Ohms in an adequate model.

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The parallel-source method of feeding the cage folded monopole is convenient for initial modeling, but it will not suit models to which we wish to add matching components or loads. We may use in NEC an alternative technique that arrives at the same source impedance value, but uses only a single source. The right portion of Fig. 5 shows the essential elements of the technique. We terminate a transmission line at each of the former source segments. The other set of terminations appear on a single segment wire that is a considerable geometric distance from the antenna. The distance is sufficient to prevent the wire from interacting significantly with the main antenna wires. In the present case, the wire happens to be about 140' from the antenna. As well the wire is very short (0.3' in this case) and may be very thin, although I retained the 0.1" diameter used with other wires. The 4 transmission lines that terminate on this new wire are in parallel with each other and in parallel with a source that we place on the wire. The physical position of the new wire only prevents wire interactions, but does not itself determine the length of the transmission lines. We may set these lines to the shortest length feasible. I used 1E-10 feet in EZNEC, but you may use simply the shortest length allowed by your particular core. Because the line is not a physical line and plays no role in the matrix calculations, line routing is unimportant. As well, because the line is so short, its characteristic impedance is unimportant. I used 200 Ohms, which roughly corresponds to the impedance of the individual former source segments. The transmission-line technique places all 4 outer-wire segments in parallel. The single source on the remote wire records the parallel source value. The lower portion of Table 11 shows that we obtain the same source impedance that we derived from the parallel source technique.

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The alternative transmission-line feeding system has an important advantage. We may extend the remote wire structure and incorporate loading/matching impedances. The method appears in Chapter 14 of Intermediate Antenna Modeling (available from NSI or from antenneX), and so I shall not repeat it here. Essentially, we use a matrix of very short and thin wires to replicate the structure of a network, adding components to the series and/or parallel legs as needed to make up the actual network. (NEC2GO has a built-in method for creating source point networks.)

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However, the method also carries a caution. NEC-4 shows a usable but less than ideal AGT score. As we have seen, NEC-2 AGT values are much worse when we have junctions of wires with different diameters. The networks that we add can only be as accurate as the initial source impedance values prior to adding the new components, and NEC-2 source impedance values may be inaccurate.

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A folded monopole also tends to imply a buried radial system in the MF and lower HF regions of the spectrum. We have not looked at the effects of adding such a system or how best to model such a system. However, experience has taught that none of the alternative modeling systems that we might use will adequately substitute for a NEC-4 set of below-ground radials. (There are copious notes on this situation with respect to standard monopoles in Ground-Plane Notes, available in PDF book format on the Books Page.) The folded monopole requires careful treatment as we approach ground level to ensure that we do not violate good modeling procedures while developing a common ground point for all necessary wires.

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Those who build and install wire cages for AM BC antennas tend to call them "skirts," although the general informal name is often associated with an alternative use for the cage. Between the cage base and ground, installers may place tunning elements and thus detune the tower relative to a given frequency. The technique has application to cellular and other UHF antenna towers that fall within the quite large near-field radius of an existing AM BC antenna, where unwanted interactions might distort the certified pattern for the AM antenna system. It may also apply to the antennas of different stations whose antennas lie within the near-field of each other. In most cases, skirt assemblies have standard sizes (at least with respect to outside diameter). Installers have developed a considerable number of techniques for bringing the overall tuned filtering frequency to the desired point. If you model a commercial assembly, note the presence of periodic spacers and shorting rings. These assemblies serve both mechanical and electrical purposes. Hence, the shorting ring belongs in the model.

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Some engineers who employ cages on towers to convert the monopole into the alternative transmitting assembly also prefer the term "skirt," since the assembly (as noted above) does not answer to standard equations for folded dipoles/monopoles. See, for example, the NAB 1997 paper by Rackley, Cox, Moser, and King ("An Efficiency Comparison: AM/Medium-Wave Series-Fed vs. Skirt-Fed Radiators"). Other engineers retain the term "folded monopole" or use the expression "folded isopole." Whatever the preferred label, the cage-style folded monopole retains its incomplete shielding by the cage and hence leaves an impedance that one may best approximate by appropriate models, subject to field testing and adjustment.

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For those interested in ferreting out the effects of a relatively open but surrounding skirt, modeling may provide more data than just the anticipated feedpoint impedance. With respect to 2-wire folded or hairpin monopoles, Kuecken's method of separating transmission line from radiation currents (see pp. 224 ff of his Antennas and Transmission Lines) has proven effective for the analysis of both folded monopole and folded dipole models that use 2 wires. NEC and MININEC both provide a record of relative current levels along the wires of a caged or skirted antenna, and investigators might well use the data to develop the relative roles of transmission-line and radiation currents with these antennas.

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As incomplete as this treatment may be, it still provides some guidance on the initial modeling of both two-wire and cage-type folded monopoles. With due attention to AGT values and correctives, as well as to the reasonableness of reported output values from the calculating core in use, we may successfully model folded monopoles using either NEC or MININEC. However, as always, hasty or careless modeling leads to relatively useless results. The rule of GIGO strictly applies to antenna modeling.

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Go to Main Index

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115. Single, Bifilar, and Quadrifilar Helices

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L. B. Cebik, W4RNL

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Every so often, someone asks me if I have a sample file for a bifilar or a quadrifilar helix. Such helices are subject to numerous variations in mounting, connections, and feeding. Hence, rather than simply show a sample file, it may be useful to examine at least two ways in which we can create these antenna structures. In the following notes, we shall look at a version in which every segment appears as a separate wire and at a version that uses some of the "summary" or "global" geometry structure commands available in NEC-2 and NEC-4.

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All helices within these notes will use a single set of specifications. The helix turns will have a radius of 1 meter. The turns will be separated by 1 meter, and we shall use 3 turns, for a total helix length of 3 meters. Throughout, there will be 20 segments per turn to simulate within reasonable boundaries a continuously nearly circular structure. The wire diameter will be 1 mm (0.001 m), which gives us a wire radius of 0.5 mm (0.0005 m). The importance of giving both the diameter and the radius will become apparent as we proceed through the methods that we shall explore.

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A Review of Single-Helix Models using GH

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In episodes 62 and 63 of this series, we explored in some depth the use of the GH command to form a helix. In those episodes, we noted that the GH command was a later addition to NEC-2 and may differ according to the version you might be using. To form a single helix having the requisite specifications in the version of the command used by NEC-Win Pro, we can employ the help screen shown in Fig. 1.

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Several items are worth reviewing. The NEC-2 GH command requests a user specification of the spacing between turns and the total helix length, from which it calculates the number of turns. The helix uses a single wire radius throughout. The basic helix begins at Z=0 and progresses upward, with the first radius point along the X-axis. The basic helix orientation is right-handed. To create a left-handed helix, we would make the total length entry negative. The resulting model, carried only as far as the GE line plus a frequency entry, looks like the following lines.

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+CM Single helix-nec-2
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+GH 1 60 1 3 1 1 1 1 .0005
+GE
+FR 0 1 0 0 299.7925 1
+EN
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In NEC-4, the GH command changes its form, and the help screen in GNEC for our current structure appears in Fig. 2.

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In NEC-4, we specify the number of turns (with fractional turns possible) and the total length of the helix; the command then calculates the space required for each turn. NEC-2 had offered us separate radii for the X- and the Y-axes, but NEC-4 employs a uniform radius. In part, this change results from the desire to give the user a choice between log and Archimedes spirals. Our simple structure uses the uniformly spaced Archimedes spiral. Like the NEC-2 helix, the NEC-4 version begins at Z=0 with the first radius point along the X-axis. However, to form a left-hand helix in NEC-4 requires that we use a negative numbers for the number of turns. The resulting NEC-4 model of the basic single helix appears in the following lines.

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+CM Single helix-nec-4
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+GH 1 60 3 3 1 1 .0005 .0005 1
+GE
+FR 0 1 0 0 299.7925 1
+EN
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In both cases, we entered the total number of turns in the helix, allowing the command to distribute them among the individual turns. Fig. 3 shows the conventionalized outline of the helix that we created with the 2 versions of the GH command. The sketch includes segment markers to allow counting. More significantly, the sketch provides the reason why I chose the specifications for the sample model: they provide a very open structure so that we can hope to see the details of more complex helical arrangements.

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A few reminders may be in order here. Foremost is one that even some experienced modelers forget. Even though the model structure shown in the sample model files has no excitation or output request, we can still run the model and obtain an output report. The first lines of this report appear in Table 1.

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The output report is very useful for checking the correctness of our geometry entries. The lines replicate the instructions that we thought we gave the command (and sometimes, we do transpose numbers, mis-strike a key, etc.). As well, the NEC-4 GH command yields the total wire length in the helix, a useful piece of data for someone planning to build what he or she models.

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The GH command is not the only way to form a single helix. For example, EZNEC provides a helix-formation facility that will produce a segment-by-segment models. Its version of the single helix in our example will have 60 wires.

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If we wish to alter the position of either of our two sample models, we may employ the GM command. However, since this exercise will never get around to adding a source or an output request to the structural entries, we can leave the basic position alone. Besides, we shall have another use for the GM command. While we can employ as many GM commands as we need--so long as we use them in the correct order--minimizing other uses of them will make our fundamental use clearer.

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A Bifilar Helix

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There are several ways to form a bifilar helix. We shall give primary attention to two techniques. The first uses a program that creates geometry structures called NEC-Win Synth. Among the program's preset shapes is a bifilar helix. All that we need to do is to enter the critical data about the helix, namely our specifications from the beginning of these notes. Fig. 4 shows the specification screen.

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The data are the same that we used to generate a single helix. Although the program offers the option of using the wire diameter or the wire radius, it happens to be set in the diameter mode. That fact explains why I gave both values in the beginning. Since the helix values are by now quite familiar, we can see what our creation looks like in Fig. 5.

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The screen is part of the Synth program, which places the origin of the axes at the base of the created structure. Note that like the single helix, one of our double-helix starting points is along the X-axis. The program produces a wire-by-wire model in its own format, but you may save the structure file in the standard .NEC format for use in either NEC-2 or NEC-4. The model is incomplete as it emerges from Synth. It contains only the geometry structure and a frequency specification. You must add all other desired elements from within NEC-2 or NEC-4. The geometry section alone will contain 120 GW entries, as suggested by the following partial replication of the model.

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+CM Bifilar helix from NEC-Win Synth 1.0
+CE
+GW 1 1 1.00000 0.00000 0.00000 0.95106 0.30902 0.05000 0.00050
+GW 2 1 0.95106 0.30902 0.05000 0.80902 0.58779 0.10000 0.00050
+GW 3 1 0.80902 0.58779 0.10000 0.58779 0.80902 0.15000 0.00050
+GW 4 1 0.58779 0.80902 0.15000 0.30902 0.95106 0.20000 0.00050
+GW 5 1 0.30902 0.95106 0.20000 0.00000 1.00000 0.25000 0.00050
+GW 6 1 0.00000 1.00000 0.25000 -0.30902 0.95106 0.30000 0.00050
+GW 7 1 -0.30902 0.95106 0.30000 -0.58779 0.80902 0.35000 0.00050
+GW 8 1 -0.58779 0.80902 0.35000 -0.80902 0.58779 0.40000 0.00050
+GW 9 1 -0.80902 0.58779 0.40000 -0.95106 0.30902 0.45000 0.00050
+GW 10 1 -0.95106 0.30902 0.45000 -1.00000 0.00000 0.50000 0.00050
+GW 11 1 -1.00000 0.00000 0.50000 -0.95106 -0.30902 0.55000 0.00050
+GW 12 1 -0.95106 -0.30902 0.55000 -0.80902 -0.58779 0.60000 0.00050
+GW 13 1 -0.80902 -0.58779 0.60000 -0.58779 -0.80902 0.65000 0.00050
+GW 14 1 -0.58779 -0.80902 0.65000 -0.30902 -0.95106 0.70000 0.00050
+GW 15 1 -0.30902 -0.95106 0.70000 0.00000 -1.00000 0.75000 0.00050
+GW 16 1 0.00000 -1.00000 0.75000 0.30902 -0.95106 0.80000 0.00050
+GW 17 1 0.30902 -0.95106 0.80000 0.58779 -0.80902 0.85000 0.00050
+GW 18 1 0.58779 -0.80902 0.85000 0.80902 -0.58779 0.90000 0.00050
+GW 19 1 0.80902 -0.58779 0.90000 0.95106 -0.30902 0.95000 0.00050
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+GW 110 1 0.95106 -0.30902 2.45000 1.00000 0.00000 2.50000 0.00050
+GW 111 1 1.00000 0.00000 2.50000 0.95106 0.30902 2.55000 0.00050
+GW 112 1 0.95106 0.30902 2.55000 0.80902 0.58778 2.60000 0.00050
+GW 113 1 0.80902 0.58778 2.60000 0.58779 0.80902 2.65000 0.00050
+GW 114 1 0.58779 0.80902 2.65000 0.30902 0.95106 2.70000 0.00050
+GW 115 1 0.30902 0.95106 2.70000 0.00000 1.00000 2.75000 0.00050
+GW 116 1 0.00000 1.00000 2.75000 -0.30902 0.95106 2.80000 0.00050
+GW 117 1 -0.30902 0.95106 2.80000 -0.58778 0.80902 2.85000 0.00050
+GW 118 1 -0.58778 0.80902 2.85000 -0.80902 0.58779 2.90000 0.00050
+GW 119 1 -0.80902 0.58779 2.90000 -0.95106 0.30902 2.95000 0.00050
+GW 120 1 -0.95106 0.30902 2.95000 -1.00000 0.00000 3.00000 0.00050
+GS 0 0 1.000000
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

You may arrive at a virtually identical model in EZNEC with only a few steps. The first would be to create a single helix to the desired specifications. The program will produce a 60-wire structure in the Wires table. Next, you may copy the wires just produced and then rotate them 180 degrees in either a clockwise or counterclockwise around the Z axis. There are also functions for moving and rotating all 120-waires of the structure so that it ends up where and how you want it in the model.

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An alternative procedure that uses up much less model-file space uses the commands within NEC. Essentially, if we begin with the NEC-2 helix shown earlier, we need only use the GM command to rotate the helix by 180 degrees while replicating it once. The NEC-2 GM help screen appears in Fig. 6.

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The total NEC-2 model (so far) is somewhat shorter than the Synth or EZNEC models.

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+CM Bifilar helix-nec-2
+CE
+GH 1 60 1 3 1 1 1 1 .0005
+GM 1 1 0 0 180 0 0 0
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

The GM portion of the process when using NEC-4 looks almost exactly like the NEC-2 version, as suggested by the GM help screen for that core in Fig. 7.

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For our present needs, which only require us to replicate the entire original structure--with the half-twist--the screens of NEC-2 and NEC-4 are alike. However, had we wished to manipulate partial structures, NEC-2 would have allowed us to specify only complete tags. NEC-4 allows specification of start and stop tag and segment numbers. The difference lies in what does not appear in the lower left corner of each help screen. Had we used the start-stop option, the following NEC-4 model would not have a GM line that looks so much like the corresponding NEC-2 line.

+ 
+CM Bifilar helix-nec-4
+CE
+GH 1 60 3 3 1 1 .0005 .0005 1
+GM 1 1 0 0 180 0 0 0
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

The results of using GM on the initial GH line in either NEC-2 or NEC-4 produces a bifilar helix with the appearance of Fig. 8.

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Although I have tipped the axes in a slightly different manner than I did in Fig. 5, the GH-GM combination produces a bifilar helix with the same structure and orientation as the one that emerged from NEC-Win Synth. Since I have omitted the segment markers, the verification that all is well requires that we run the partial model and check the data in the NEC output file. Table 2 gives us the opening lines.

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The bottom line of this section of the report tells us that we have a 120-segment structure, just as planned, while the antenna sketch from the program tells us that we have opposing helices. The output report goes on to provide data on each segment within the 2-tag model, allowing us to correlate the two helices point by point. However, the NEC output report lists the coordinates at the center of each segment. In the programs used here, you would have to look at the antenna view facilities to identify the coordinates at each end of each segment, just in case you later wished to connect another wire to the structure, even at the top or the bottom.

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Note that none of the techniques that we have examined joins any of the helix ends. If you wish to create a connection, you will have to add a wire having the correct end coordinates.

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A Quadrifilar Helix

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We can easily create a quadrifilar helical structure using either of the techniques shown so far. The quadrifilar helix consists of 4 identical single helices separated by 90 degrees. In NEC-Win Synth, the process is as simple as selecting the correct pre-set shape from the list and then entering the vital specifications. Fig. 9 shows the specifications screen for the quadrifilar helix.

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Compare the data entries for Fig. 9 with those for Fig. 4. Nothing has changed except the output. As shown in Fig. 10, the structure now has 4 helices as requested. Like the bifilar structure, the top is open, so you will have to add crossing (usually non-touching) wires to close the upper end.

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Since we now have 4 inter-laced helices, the spacing between adjacent turns has shrunk accordingly. However, the individual helices are all identical to the original single helix with which we began.

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The Synth version (or an EZNEC version) of the quadrifilar helix with the initial specifications will have 240 wire entries, even before adding any connecting wires. The following lines sample the beginning and the ending of the geometry section of the model.

+ 
+CM Quadrifilar helix from NEC-Win Synth 1.0
+CE
+GW 1 1 1.00000 0.00000 0.00000 0.95106 0.30902 0.05000 0.00050
+GW 2 1 0.95106 0.30902 0.05000 0.80902 0.58779 0.10000 0.00050
+GW 3 1 0.80902 0.58779 0.10000 0.58779 0.80902 0.15000 0.00050
+GW 4 1 0.58779 0.80902 0.15000 0.30902 0.95106 0.20000 0.00050
+GW 5 1 0.30902 0.95106 0.20000 0.00000 1.00000 0.25000 0.00050
+GW 6 1 0.00000 1.00000 0.25000 -0.30902 0.95106 0.30000 0.00050
+GW 7 1 -0.30902 0.95106 0.30000 -0.58779 0.80902 0.35000 0.00050
+GW 8 1 -0.58779 0.80902 0.35000 -0.80902 0.58779 0.40000 0.00050
+GW 9 1 -0.80902 0.58779 0.40000 -0.95106 0.30902 0.45000 0.00050
+GW 10 1 -0.95106 0.30902 0.45000 -1.00000 0.00000 0.50000 0.00050
+GW 11 1 -1.00000 0.00000 0.50000 -0.95106 -0.30902 0.55000 0.00050
+GW 12 1 -0.95106 -0.30902 0.55000 -0.80902 -0.58779 0.60000 0.00050
+GW 13 1 -0.80902 -0.58779 0.60000 -0.58779 -0.80902 0.65000 0.00050
+GW 14 1 -0.58779 -0.80902 0.65000 -0.30902 -0.95106 0.70000 0.00050
+GW 15 1 -0.30902 -0.95106 0.70000 0.00000 -1.00000 0.75000 0.00050
+GW 16 1 0.00000 -1.00000 0.75000 0.30902 -0.95106 0.80000 0.00050
+GW 17 1 0.30902 -0.95106 0.80000 0.58779 -0.80902 0.85000 0.00050
+GW 18 1 0.58779 -0.80902 0.85000 0.80902 -0.58779 0.90000 0.00050
+GW 19 1 0.80902 -0.58779 0.90000 0.95106 -0.30902 0.95000 0.00050
+---
+GW 229 1 0.58779 0.80902 2.40000 0.30902 0.95106 2.45000 0.00050
+GW 230 1 0.30902 0.95106 2.45000 0.00000 1.00000 2.50000 0.00050
+GW 231 1 0.00000 1.00000 2.50000 -0.30902 0.95106 2.55000 0.00050
+GW 232 1 -0.30902 0.95106 2.55000 -0.58778 0.80902 2.60000 0.00050
+GW 233 1 -0.58778 0.80902 2.60000 -0.80902 0.58779 2.65000 0.00050
+GW 234 1 -0.80902 0.58779 2.65000 -0.95106 0.30902 2.70000 0.00050
+GW 235 1 -0.95106 0.30902 2.70000 -1.00000 0.00000 2.75000 0.00050
+GW 236 1 -1.00000 0.00000 2.75000 -0.95106 -0.30902 2.80000 0.00050
+GW 237 1 -0.95106 -0.30902 2.80000 -0.80902 -0.58778 2.85000 0.00050
+GW 238 1 -0.80902 -0.58778 2.85000 -0.58779 -0.80902 2.90000 0.00050
+GW 239 1 -0.58779 -0.80902 2.90000 -0.30902 -0.95106 2.95000 0.00050
+GW 240 1 -0.30902 -0.95106 2.95000 0.00000 -1.00000 3.00000 0.00050
+GS 0 0 1.000000
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

To create a quadrifilar helix using the NEC command set only requires that we add one more line to our bifilar model. It is another GM line. Since the GM lines are so similar between NEC-2 and NEC-4 in this application, a single sample will suffice for both cores. Fig. 11 shows the required replication and manipulation.

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The new GM command operates on the entire existing structure, which includes tags 1 and 2. We increment the tag numbers by 2 so that the new helices will bear the numbers 3 and 4. We replicate the entire structure once and give the new helices a 90-degree rotation. Now we have the quadrifilar helix, as shown in the following model lines. The lines show the NEC-4 version, which differs from the NEC-2 version only in the GH entry.

+ 
+CM Quadrifilar helix-nec-4
+CE
+GH 1 60 3 3 1 1 .0005 .0005 1
+GM 1 1 0 0 180 0 0 0
+GM 2 1 0 0 90 0 0 0
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

We could have created the same structure with only one GM line, as shown in the following variant model. The GM line creates 3 replicas of the original helix spaced at 90-degree intervals around the Z-axis.

+ 
+CM Quadrifilar helix-nec-4
+CE
+GH 1 60 3 3 1 1 .0005 .0005 1
+GM 1 3 0 0 90 0 0 0
+GE
+FR 0 1 0 0 299.7925 1
+EN
+
+

In either case, we can again use the NEC output file as one verification that our work is correct. Table 3 shows the initial lines of the output file for the double-GM version of the model.

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Regardless of whether we use 1 or 2 GM lines to produce the quadrifilar helix, the result will have the appearance of Fig. 12. You may compare this helix to the quadrifilar helix in Fig. 10 and to the other helical structures shown earlier.

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The basic bifilar and quadrifilar structures are straightforward to produce, using either segment-by-segment techniques that yield many wires or using the GH and GM commands for a compact model file.

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Which Model Should I Use?

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In terms of producing a compact helix model file, nothing exceeds the GH-GM method of fashioning a bifilar or a quadrifilar helical assembly. However, the diminutive file size (which has no bearing on the comparative speed of the core run or on the size of the output file) comes at a cost. Except for the initial junction of the helices with the X-Y plane, the coordinate values for all junctions are unknown and require supplemental aids to discover. As noted, the antenna view function of NEC-Win Pro, GNEC and some other programs allow one to find any segment and learn its end-1 and end-2 coordinates.

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In contrast, the seemingly very large geometry structure portions of files produced by NEC-Win Synth, EZNEC, and possibly other programs that create segment-by-segment helix models have the advantage of being quite transparent. By inspection, one can find any desired junction between segments/wires and use that junction for any other desired wire connection. Most evidently, this facility applies to the free ends at the top of the multiple helix, where cross connections are common. However, the ease of finding connections also applies when bridging lower sections of a helix for a feed system.

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Since each wire of a multiple helix is independent in the segment-by-segment construct, connections to ground often become simpler. Many initial experiments with multiple helices employ a perfect ground as an initial surface. However, advanced models may employ wire grids having either simple or complex geometries. The grid may offer connection junctions that do not align precisely with the lowest segments of the helices. In most cases, with a segment-by-segment model, one can simply alter the lowest coordinates to coincide with a wire ground junction without unduly distorting the overall shape of the bifilar or quadrifilar structure.

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In the end, the decisions as to which type of bifilar or quadrifilar model to adopt rests with the uses to which one puts the basic structure and the role it plays in the total model. Because the roles and uses are so numerous and varied, these notes have confined themselves to a single topic: forming the multiple helix with assurance that it is correct. The samples provided in this episode may serve as a guide to the production of multiple helices less amenable to graphical clarity and more adept at fulfilling useful communication functions.

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Go to Main Index

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116. Insulation Revisited

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L. B. Cebik, W4RNL

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In episode 50, we examined some of the basic factors in using the NEC-4 IS or Insulated Sheath command. 33 episodes later (in 83), we looked at a very partial workaround for implementing insulated sheaths in NEC-2 without rewriting the program to import the IS command. Another 33 episodes have gone by, and so we may revisit the IS command.

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In our initial look at the command, we made an assumption, namely, that for virtually all cases of insulated antenna wires, the conductivity of the insulation would be less than 1E5 S/m. The assumption rested on general expectations of common modern wire insulation materials, but had no solid foundation in calculations. Indeed, unless one has a considerable reference library, finding the conductivity of wire insulation turns out to be much more difficult than finding its relative permittivity. In the original episode, the graphs and charts used a constant conductivity of 1E-10 S/m to simplify charting the properties of insulation and arriving at reasonable graphs of insulated-wire antennas, including their velocity factor relative to a bare wire antenna.

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We should re-visit insulated wires to see if the assumptions in our original episode stand the test of calculation. In fact, differences between the way various programs implement the potential for insulating wires forces the issue upon us.

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Some Basics of Insulated Sheaths

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NEC-4's IS command assumes that the insulation extends from the surface of the wire to a user-designated outer limit, with no space between the wire and the insulation. Hence, the command is limited to common wire fabrication and does not extend to uses where we might suspend a bare wire within a tubular shell. The command itself is almost deceptively simple.

+ 
+IS     I1     ITAG     ITAGF     ITAGT     EPSR     SIG       RADI     Mnemonics
+       I1     I2       I3        I4        F1       F2        F3       Entry Labels
+IS     0      1        0         0         3.       2.50E-4   .002     Sample Entry
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As with all NEC entries, we have a series of integer (I1-I4) and a series of floating decimal (F1-F3) entries. I1 merely signals that new data will appear. (A -1 would cancel previous IS data.) I2 specifies the affected tag. I3 and I4 specify the first and last segments to which the data will apply. A pair of zeroes indicates that the data applies to all segments. We have only 3 floating decimal entries. The first is the relative permittivity of the insulation. The second specifies the conductivity of the insulation. The last entry provides the radius of the outer limit of the insulation, where the inner limit is automatically the radius of the wire beneath the insulation. F3 must use a number higher than the radius specified in the GW line referenced by the Tag number in entry I2. In the sample command, the data applies to all segments of Tag 1. The relative permittivity is 3.0, with a conductivity of 2.5E-4 S/m. The sheath radius is 2 mm, which is valid for the wire of Tag 1, which has a 1-mm radius. In more common terms, the wire diameter is 2 mm, the sheath thickness is 1 mm, and the total insulated wire diameter is 4 mm. Essentially, the IS command sets up a second medium for a limited space around the wire, and the conductivity and relative permittivity values that we insert employ the same parameters we apply to ground media.

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Some implementations of NEC use the IS command exclusively, while others--such as EZNEC--employ an entry system that differs in detail but not in calculation from the IS command. The differences involve shifting from one way of thinking about insulation to another, so let's compare the two entry systems. GNEC, as one example of an implementation using the IS command, provides a help screen that reflects the structure of the command. In contrast, EZNEC attaches insulation to the wire-entry screen. Fig. 1 shows the two entry screens along with some sketchy guidance to the dimensional differences between the two. Both help screens show the same parameters and values.

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The relative permittivity entries for the two insulations are the same, and the pencil-and-paper transformation of thickness to sheath radius is trivial (for this example, where the wire radius is 1 mm). The key is in the entries that are not the same in the two systems. The IS command requires a value of conductivity, and hitherto, we have simply assumed a very low value. The EZNEC entry requires a value called the "loss tangent," and only some modelers know where to find that. Probably, only a few know how to go from one to the other and back again. Let's see how to perform the required calculation.

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Relative permittivity (epsilonr) is, of course a form of short hand for the value of permittivity (epsilon).

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Epsilon0is the value of permittivity in a vacuum, namely 8.854E-12 F/m. Since the value is a constant, many computerized calculation system omit this term from user view, and NEC is one of those systems. So the relative permittivity of any material of concern is simply the comparative permittivity relative to a vacuum. Hence, we need only tabulate fairly simple numbers, ranging from 1 upward. We can often find lists of relative permittivity values in handbooks.

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A few handbooks, such as Reference Data for Engineers, Table 9, pp. 4-20 to 4-23, will also list another value, the dissipation factor. The following entries sample the list, which covers 4 pages of materials and values.

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+Sample "Characteristics of Insulating Materials"
+
+Material          Relative Permittivity               Dissipation Factor
+                  10E3 Hz     10E6 Hz     10E8 Hz     10E3 Hz     10E6 Hz     10E8 Hz
+Polycarbonate     3.02        2.96        -----       0.0021      0.010       ------
+Polyethylene      2.26        2.26        2.26       <0.0002     <0.0002      0.0002
+Teflon (PTFE)     2.1         2.1         2.1        <0.0005     <0.0003     <0.0002
+PVC (100%)        3.10        2.88        2.85        0.0185      0.0160      0.0081
+
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The values may vary somewhat over the range of frequencies, but normally quite slowly. For 30 MHz, taking the mean values between 10E6 Hz and 10E8 Hz (1 and 100 MHz) will normally be as close to correct in the HF range as the data itself will allow.

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The dissipation factor of an insulating material is the ratio of energy dissipated to energy stored in a dielectric. The value derived is the tangent of the loss angle (a function of the two factors having a 90-degree phase difference). In alternative terms and thanks to Roy Lewallen for the way of expressing it, the loss tangent is the ratio of the imaginary to real parts of the complex permittivity, which in turn is a function of the real permittivity (dielectric constant), frequency, and conductivity. Immediately, we should see that the conductivity will vary with both the relative permittivity and the frequency for any loss tangent value. In fact, we may convert a listed loss tangent value to a value of conductivity in a straightforward equation:

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C is the conductivity in S/m, epsilon0 is the permittivity of a vacuum, epsilonr is the relative permittivity of the insulating material at hand, F is the frequency in Hz, and lt is the listed loss tangent or dissipation factor. You may sometimes find a listing for a power factor: for values less than 0.1, you may treat the power factor, the dissipation factor, and the loss tangent as the same. In fact, all reasonable loss tangent values will by considerably less than 0.1.

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The conversion equation includes several constants: 2, PI, and epsilon0. If you wish to create a small spreadsheet to calculate back and forth between conductivity and loss tangent, you may combine the constants:

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This simplification reduces the conversion process to a shorter equation:

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Let's create a 30-MHz dipole using the values shown in Fig. 1 for the relative permittivity and for the EZNEC loss tangent. The result of conversion yields the conductivity value shown in the GNEC IS screen. This value of conductivity is very much less than the value assumed in episode 50 (1E-10 S/m). So our next concern is whether there are any practical consequences of the higher conductivity values calculated by converting from the loss tangent to conductivity at the frequency of operation. My scan of the plastic material in my reference shows very low values of loss tangent (0.0002 is perhaps the most common value). Nonetheless, we should see what emerges from a systematic scan of values.

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The Results from Using a Constant Conductivity and a Loss Tangent

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In episode 50, we ran through some exercises exploring various insulation thicknesses (0.5 mm, 1.0 mm, and 2.0 mm) around a 2-mm diameter bare copper wire dipole resonated at 30 MHz. In all cases, we used a constant value for conductivity. The constant rested on an initial exercise using some thick insulation with a constant value of relative permittivity and a variable conductivity. The initial results showed the changes in the antenna's feedpoint resistance and reactance without changing its length. The length originated from resonating the wire when bare. Fig. 2 shows the results of that initial exercise, using free-space models.

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The assigned relative permittivity is fairly high for plastics (although PVC may be as high as 3.5), and the insulation thickness is as great as the wire diameter. Even under these conditions, the feedpoint resistance remains stable until the conductivity increases above 1E-4 S/m. The reactance remains stable until we pass 1E-3 S/m. The calculated conductivity value in the sample in Fig. 1 appears to be on the resistance borderline but below the threshold for reactance variation. Hence, a preliminary estimate would suggest that we might find a few Ohms of feedpoint resistance variation, but the resonant length of the insulated dipole should not differ significantly from the modeled length using the very low conductance value of episode 50.

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Table 1 provides the values derived under the conditions of episode 50. They provide us with a touchstone for some further work and with a reference for some original results.

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This table (and others to come) require some background. In all cases, I varied the relative permittivity in increments of 0.25 between values of 1.0 and 3.0. The Res FQ entry shows the resonant frequency of the antenna at its original length under varying insulation conditions. The bare wire length was 4.832 m. However, for convenience, the following line marked DP Length uses the half-length of the dipole (based on modeling from -Y to +Y through the coordinate system origin). The DP length entry is for 30 MHz and produces resonance (within less than +/-j0.5 Ohms reactance). By comparison with the bare-wire length, we can arrive at a Wire VF or velocity factor for the specific insulation condition. The bottom line in each series lists the 30-MHz resonant feedpoint resistance (Zres) of the shortened antenna.

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Fig. 3 shows the change of resonant feedpoint resistance under the insulation conditions listed in Table 1. Fig. 4 shows the velocity factor of the insulated and resonated dipoles relative to a bare-wire dipole using the same basic starting wire diameter. Note that the curves are congruent between the two graphs, indicaing the orderliness of the progressions. See episode 50 for other graphed results from the exercise.

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Remember that the initial exercise used a constant conductivity (1E-10 S/m). Let's return to that exercise, but this time allow the conductivity to be variable, based on a selected loss tangent value. I have chosen a value of 0.0005, since this value is close to but somewhat higher than the most common value listed for plastic insulating materials. Table 2 records the results of going through the same set of exercises, but this time calculating the value of conductivity for each case. As the table shows, conductivity rises with each increase in relative permittivity.

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Although the values of conductivity change relative to the single value used for Table 1, none of the other values change. (There is a very slight change in the Zres or resonant impedance line that we shall address in more detail shortly.) The values are virtually identical between tables. In the period between generating these table (several years), versions of the software have changed, as have the computers and CPUs. As well, the basic compilers for the Fortran code have also changed. Each of these changes can result in a change in the final decimal digit for any entry. Hence, between the two tables, we may for all practical modeling purposes say that no change occurs, despite the differences in the values of conductivity.

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This result is consistent with the exercise shown in Fig. 2, even though the figure uses a thick insulation with a relative permittivity that is high for the range of plastics commonly used for wire insulation. The impedance values recorded in that table remain almost constant until the conductivity is significantly higher than the values that appear in Table 2. If the loss tangent is among the common values, then at 30 MHz, the presumption of a very low conductivity value does not harm the accuracy of the resulting models. In addition, the velocity factor graph (Fig. 4) remains usable as a general guide to dipole length shortening as a function of wire insulation of common sorts.

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Even though a loss tangent of 0.0005 may be common, there are instances in which the value may be higher. In fact, EZNEC provides a loss-tangent value of 0.05 for PVC. This value is 2 orders of magnitude higher than the value used for Table 2. Therefore, we likely should perform at least one more exercise. Let's retain our 2-mm diameter copper wire dipole at 30 MHz. As well, let's select the middle case from Table 2, the situation in which we use 1-mm thick insulation. However, let's change the basis of comparison. Let's explore loss-tangent values of 0.0005, 0.005, and 0.05 in order to see what changes may occur in the data that we accumulate in these free-space models. For each model at each level of relative permittivity, we arrive at a new value of conductivity, as shown in Table 3.

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Perhaps the first noticeable trait of the tabulated values is that a 10-fold increase in the loss tangent produces an exactly equivalent increase in the value of conductivity. Hence, the highest value of conductivity is about 2.5E-4 S/m. Nevertheless, almost nothing else changes. The self-resonant frequencies for the 4.832-m wire when insulated are the same, regardless of the conductivity. These frequencies would be determined largely by the feedpoint reactance, which does not change significantly until the conductivity reaches about 1E-3 S/m. Likewise, the required half-element length for resonance at 30 MHz does not change over the range of loss-tangent values scanned in the table. As a consequence, the insulated-wire velocity-factor graph (Fig. 4) remains usable for the entire set of loss-tangent values covered by the exercise.

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One factor does change: the feedpoint resistance at the 30-MHz resonant wire length. In fact, it shows a systematic rise as we increase the value of loss tangent, as shown in Fig. 5.

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The amount of change is systematic but still quite small between loss-tangent values of 0.0005 and 0.005. This value range corresponds at 30 MHz to a range center of 1.6E-6 S/m and 1.6E-5 S/m. Both of these midpoint conductivity values fall well below the expected resistance upward swing vs. conductivity. The loss-tangent value of 0.05 produces a more noticeable change that averages about 1.5 Ohms relative to the 2 lower curves. The associated mid-point conductivity is about 1.6E-4 S/m. Reference to Fig. 2 shows that the resistance curve has entered its area of noticeable climb in this region.

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The higher feedpoint resistance value is largely a function of the decreasing resistivity of the insulation under the specified conditions. Indeed, the mid-point value of resistivity is close to 6000 Ohms/m, a value that gives the insulation semi-conductor status. Small amounts of current may flow and equally may be dissipated as heat. With lower values of conductivity, the insulation is largely RF transparent. Dissipation appears to reach a peak at a conductivity of about 1E-2 S/m (100 Ohms/m). Once the insulation is more conductive, it becomes a part of the radiating wire itself, and the overall feedpoint resistance begins to decline.

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Conclusion

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I have conducted these exercises at 30 MHz, the upper limit of the HF range. We find most uses of insulated antenna elements at HF. Since the value of conductivity will rise and fall with the frequency, the 30-MHz case represents a worst-case analysis. However, it is wise to remember that insulation of the proportions used in these exercises will increase the insulation conductivity by a factor of 10 if we increase the frequency to 300 MHz.

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I sometimes receive questions about the effects of enamel (or its current replacement coating) on wire. In general, the enamel coating is too thin for its effect to appear when comparing it to bare wire of the same diameter. I have also received questions about anodized aluminum elements, and the same general answer applies. Forcing the emergence of aluminum oxide for a few molecules of depth into the aluminum has little effect on the element's performance compared to a bare element that has received a fresh polishing. However, both situations require special care with respect to ensuring good electrical contact at junctions.

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Most plastic coating used to insulate wires have a relative permittivity between 2 and 3, with loss tangents in the HF region of less than 0.001. The exercises have shown that in this range, nothing critical changes with respect to the value of loss tangent or a calculated conductivity value. Hence, one might safely use a generalized loss tangent of about 0.0005 or some very low value of conductivity (depending upon the software) and still wind up with a model that is accurate enough to serve as a basis for antenna building. In the HF region, construction and environmental variables will generally override any slight differences one might see in modeling tables.

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Go to Main Index

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117. Modeling and the Logic of Question Resolution

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L. B. Cebik, W4RNL

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Many beginning modelers quickly grow adept at arranging wires into the antenna geometry needed to create successful models. However, unless they are used to multi-step problem solving, these same modelers fail to realize that NEC and MININEC are useful for more than just stringing together wires into antenna forms and then requesting the usual output data. Modeling software is capable of resolving questions, although sometimes, the questions require multiple stages of modeling on the road to relatively final answers. Therefore, it might be useful to look at the logic of problem resolution as it applies to antenna modeling.

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Because this episode is for the newer modeler, let's look at a fairly straightforward question as a vehicle to demonstrate multi-step modeling. During the past two decades, some antenna builders have proposed an alternative structure for the common folded dipole antenna, especially when we construct the antenna from common forms of insulated transmission lines. Fig. 1 shows both the standard construction method and the "pinned" alternative.

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The pre-modeling-era reasoning behind the pinned version of the antenna runs something like the following: the insulated (vinyl-covered) transmission line has a velocity factor. For highest efficiency or radiation effectiveness, the transmission line portion of the folded dipole requires a termination at the length determined by multiplying the line's velocity factor as a transmission line times 1/2 wavelength. Those favoring shorting the line or placing pins through the line from one conductor to the other claimed noticeable performance improvements, while other folded dipole builders found no detectable difference. Although the issue has largely disappeared from sight in recent years, perhaps it may serve as an example of how we may use a few antenna models to resolve it. Modeling is, after all, less strenuous than erecting folded dipoles and working out all that would go into range measurements sensitive enough to detect any differences in performance--or to record reliably an absence of difference.

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Step 1: Setting Up the Test Situation

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The first step is to set up a workable modeling experimental situation. For this step, we shall want to model a bare-wire folded dipole to ensure that the most basic parts of the work are usable throughout the exercise. We shall also need to have this bare-wire folded-dipole model on hand for comparisons with the versions yet to emerge.

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a. We need to set up the basic modeling environment to yield fair comparisons among our models. For the present question, free-space is quite adequate. Any ground influences would apply equally to all versions of the folded dipole. Hence, we might as well eliminate ground effects entirely.

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b. We need to choose a reasonable wire size. AWG #18 copper wire is a fair choice in this case because parallel transmission lines often use the 0.0404"-diameter material beneath the vinyl. As well, the wire will ensure a high segment-length-to-wire-diameter ratio once we establish the remainder of the basic antenna specifications.

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c. We need to set a test frequency. I have selected 28.5 MHz. (Outside the realm of typical amateur radio installations, one might as easily have rounded this number to 30 MHz.) A folded dipole for this frequency will be about 200" long. However, since we eventually will be using a simulation of insulated transmission line, the wire separation will have to be fairly small. I selected 1" to ensure that the thin wires are not too close together for high accuracy. This decision sets the length of the segments on the end wires. Ideally, the segments in any model should all have the same length. For the anticipated antenna length, we would require close to 200 segments along each long wire in the folded dipole. At a total of about 400 segments, the model is large enough to be reliable but small enough for rapid runs on the current generation of computers. Fig. 2 shows the dimensions of the final model.

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Within the specified limits, the folded dipole produced the following free-space results:

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+Length: 198"     Gain: 2.10 dBi     Beamwidth: 78.2 deg.     Impedance: 289.1 + j2.8 Ohms
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The model for this antenna used EZNEC software in this case, although any version of NEC or MININEC would do equally well. The model wires appear in Fig. 3.

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This initial step is not an end in itself. Moreover, we should not merely accept and record the data. Instead we should spend a moment understanding it. A single-wire dipole when resonant will have a feedpoint impedance in free space that is between 70 and 72 Ohms. The folded dipole uses equal-diameter wires throughout, giving it a step-up ratio of 4:1 relative to the single-wire dipole impedance. If we subtract a tiny bit of the impedance as due to the losses in having twice the length of copper wire, then the reported impedance easily falls wholly within the standard range. If we doubt this fact, we can easily back up one step and model a resonant dipole made from AWG #18 copper wire.

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We might also expect a single wire resonant dipole made from AWG #18 wire to have a gain between 2.12 and 2.14 dBi. The folded dipole shows a tiny reduction--obviously too small to be operationally significant. The reduction is a natural consequence of the fact that a resonant folded dipole will be slightly shorter than a resonant single-wire dipole. As we shorten an antenna element, regardless of the feedpoint impedance, the gain will slowly decrease--again, insignificantly so, but noticeably from a numerical perspective.

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Now that we have a bare-wire folded dipole, we can begin the process of modeling a folded dipole from insulated parallel transmission line in which the wires are also 1" apart.

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Step 2: Simulating Insulated Transmission Line

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The bare-wire transmission line that forms the equally bare-wire folded dipole has the same form, that is, a 1" separation between two AWG #18 copper wires. Using common equations or a utility program, we discover that the line has an impedance of about 468 Ohms. However, this fact is only loosely applicable to our project.

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More significantly, we shall set up a half wavelength section of this line, modeling in the form of Fig. 4. A true half wavelength at 28.5 MHz is about 207.1". However, the copper losses shorten the line to 206.2" to obtain a test source impedance with virtually no reactance.

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Note that we have used a load impedance of 1000 Ohms resistive. The aim is to adjust the line length until we obtain a resistive impedance at the source end of the line. The length that we used yielded 992.1 + j0.7 Ohms. The difference in the resistive component goes to wire losses.

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The importance of the initial transmission-line test is to develop an insulated transmission line with a velocity factor (VF) that is more distant from 1.0. We may be arbitrary here, but still within the realm of possibility. Let's select a VF of 0.80. Now the task is to create insulated wires that will yield a nearly resonant source impedance with a line length that is 0.8 times the original length. 165" will be close enough for the shortened line length. Within EZNEC, we would select a permittivity of 2.505, with an insulation thickness of 0.185". We may leave the loss tangent at zero, since for all practical purposes--as shown in the preceding episode of this series--the resulting wire conductivity will not play a significant role in the results.

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Fig. 5 compares the wire tables for the two transmission lines. (We might have left the end wires bare, but the results would not significantly change.) With the specified insulation and the given line length, the source impedance is 989.8 + j0.1 Ohms. One reason for the slight difference between the bare-wire and the insulated-wire impedances is the fact that insulation between the wires does have a small but definite affect on the characteristic impedance of the line.

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The EZNEC method of implementing wire insulation is a substitute for the NEC-4 IS command. Numerous other NEC packages have implemented wire insulation in a variety of ways. Essentially, we need to know only a few pieces on information, as indicated in Fig. 6.

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EZNEC requests the thickness of the insulation. The thickness creates a radius for the outer surface once we adjust that value for the radius (or diameter) of the copper wire at the center. The IS command itself requires the entry of the insulated sheath outer radius, which cannot be smaller than the radius of the center wire. Both raw NEC-4 and EZNEC require a value for the relative permittivity (dielectric constant) of the insulating material. The IS command also requires a value of conductivity for the insulating material. An entry of 1e-10 will do for most excellent insulators. However, if we were using a specific insulating material, we likely would not find a conductivity value in reference books. Instead, we would find a value for the loss tangent, which--as shown last time--translates into a conductivity value. The following lines show just the wires and the IS commands of the EZNEC model saved in NEC format.

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+CM transmission line: covered
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+GW 1,199,0.,0.,0.,0.,4.191,0.,5.119E-4
+GW 2,1,0.,4.191,0.,0.,4.191,.0254,5.119E-4
+GW 3,199,0.,4.191,.0254,0.,0.,.0254,5.119E-4
+GW 4,1,0.,0.,0.,0.,0.,.0254,5.119E-4
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+GE 0
+IS 0, 1 ,0,0,2.505,0.,5.2109E-3
+IS 0, 2 ,0,0,2.505,0.,5.2109E-3
+IS 0, 3 ,0,0,2.505,0.,5.2109E-3
+IS 0, 4 ,0,0,2.505,0.,5.2109E-3
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+EN
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The IS lines specify the wire to which we apply the insulation. The following two zeroes indicate that we apply it to the entire wire, even though we might have selected only some of the segments. The next value is the relative permittivity, followed by the conductivity (which is zero, due to our selection of the zero loss tangent in the EZNEC model). The final value is the outer radius of the insulation in meters. In this translation from the EZNEC file, the wire radii also appear in meters. We might have used some other unit of measure for the wires in the geometry section and converted them to meters with the GS card. However, all ensuing control commands that involve a physical dimension, including the IS command, must use meters as the unit of physical measure.

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This entire exercise has aimed at producing an insulated transmission line with a velocity factor of 0.80. The shape of the insulation does not resemble the "dumb-bell" shape typically shown by cross sections of vinyl-coated lines. For this project, that difference is not a matter of concern. We only need and have achieved a transmission line with the required velocity factor. Since the two parallel wires are the same diameter, the step-up ratio will still be 4.

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Step 3: An Unpinned Insulated Folded Dipole

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The next step is to create a model of a folded dipole that uses the insulated transmission-line wire that we just produced. We may begin with the bare wire and use the insulation values that went into the transmission line. However, we shall not change the length of the folded dipole initially. With the insulation in place, we obtain the following free-space performance values.

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+Length: 198"     Gain: 2.10 dBi     Beamwidth: 78.2 deg.     Impedance: 419.8 + j271.5 Ohms
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The folded dipole is too long. Therefore, we may gradually reduce its length until we obtain a resonant feedpoint. When we stop, the free-space performance and length are as follows:

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+Length: 185.5"   Gain: 2.06 dBi     Beamwidth: 79.4 deg.     Impedance: 262.5 + j0.3 Ohms
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The very slight gain reduction is solely a function of having shortened the antenna. The shorter antenna also yields a slightly lower feedpoint impedance at resonance, relative to the bare-wire version. Here we may repeat the bare-wire folded-dipole data as a reference for the very small changes.

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+Length: 198"     Gain: 2.10 dBi     Beamwidth: 78.2 deg.     Impedance: 289.1 + j2.8 Ohms
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The insulated but unpinned folded dipole is shorter than the bare-wire version, but not by 20%. Rather, that ratio of the bare-to-insulated wire lengths is 0.937, which gives us the velocity factor of the insulated wire in antenna service (in contrast to its value in transmission-line service). We have long known that wire insulation has a velocity factor in antenna service, even for single-wire elements. The value depends on the insulation thickness and the relative permittivity of the insulation. Insulated antenna-wire velocity factors tend to range from about 0.92 to 0.98. When we apply insulation to a folded dipole we obtain the same result.

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Step 4: A Pinned Insulated Folded Dipole

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The final step in our exploration of the idea of pinning a folded dipole at the length indicated by the transmission-line velocity factor is to create the pinned version of the antenna model. We have already learned that 80% of a half wavelength at 28.5 MHz is just about 165". Therefore, we shall create two interior cross wires that are 82.5" from the antenna center. To implement these cross wires, we shall have to add 6 new wires to the overall model. Fig. 7 compares the two insulated folded dipole models.

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Whereas the unpinned folded dipole required a length of 185.5" for resonance, the pinned version is slightly shorter: 184.8". With this length adjustment, the pinned insulated folded dipole provides the following free-space performance numbers.

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+Length: 184.8"   Gain: 2.05 dBi     Beamwidth: 79.6 deg.     Impedance: 258.0 + j2.8 Ohms
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The initial model for the pinned folded dipole used the unpinned length but showed a j17.4-Ohm reactance at the feedpoint. We obtained the resonant length by shortening the outer ends in small increments until satisfied with the result. Had we moved the pins (interior cross wires), we might have made very large changes in position without significantly changing the feedpoint impedance by any significant amount. Feedpoint resonance is largely a function of the longest dimension of the folded dipole, not the pin position.

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The further shortening of the antenna reduces the gain by a tiny amount and equally reduces the resistive component of the feedpoint impedance. The bare-wire folded dipole showed 289 Ohms, while the unpinned insulated version showed 262.5 Ohms. The pinned folded dipole is down to 258 Ohms. All three values are equally usable, but the trend is worth noting.

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In operation, we would find not detectable difference among the 3 folded dipoles. Fig. 8 shows the patterns, which display no visible differences in pattern shape or half-power beamwidth values.

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Conclusion of the Problem

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We began with an open question: when using insulated transmission line to create a folded dipole, does pinning or shorting the antenna at the places indicated by the transmission-line's velocity factor change the folded dipole's performance? While the use of insulated transmission line for the antenna does exhibit an antenna velocity factor, pinning in accord with the transmission-line velocity factor does not change the antenna performance in any detectable way (other than the very tiny numerical differences shown by the models).

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It is likely that the idea of pinning a folded dipole arose when some radio amateurs realized that a folded dipole exhibited both transmission-line and radiation currents along its overall length. However, the existence of transmission line currents does not mean that the antenna requires transmission line treatment. If we were to separate the currents, following Kuecken's method developed for analysis of folded monopoles, we would discover that the transmission-line current remains constant along the wire and is 90 degrees out of phase with the radiation current. See "Unfolding the Story of the Folded Dipole" for further information on this aspect of folded dipoles. See Kuecken's Antennas and Transmission lines, page 225, for his analysis of the current along a folded monopole or dipole. (To perform the analysis, we would have to revise the order and direction of some wires in the model, but not change the overall geometry. The required addition and subtraction of values on each wire require that we account for the phase angle as well as the magnitude of the current.)

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In the end, the idea of pinning a folded dipole according to the transmission-line velocity factor rests on a misunderstanding of what occurs along the wires of the antenna. If we pin the folded dipole, we shorten the folded portion of the antenna. However, the wires extending outward form an extension that lengthens the antenna. The extensions are roughly equivalent to a single fat wire created by two thinner wires in parallel, with a common termination. There are numerous applications for using short folded dipoles or monopoles with short or long extensions. The gamma and T matches are cases in point, but well outside the scope of these notes.

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Conclusion to the Episode

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The exercise in analyzing the pinned insulated folded dipole was, of course, a pretext and a sample in this episode. Our efforts were designed to show the newer modeler that antenna modeling software has more applications than just the adjustment of wire geometries to analyze or perfect an antenna design. Sometimes, we can use the software to resolve sundry claims made about various types of antennas.

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However, the resolution of open questions (which unfortunately turn into exercises in disputation all too often) may not be a one-step process. There are some questions that we can answer just by modifying antenna geometry. For example, we can find the patterns of maximum gain and resonant feedpoint impedance for simple dipoles (and for other types of antennas) simply by adjusting the height of the antenna above ground and then readjusting the length until the antenna is resonant. The present case does not fall into this simple category.

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Our problem required us to pass through several steps in order to reach a resolution. The steps involved two different kinds of models, even though they were related to each other. More complex questions may involve more complex collections of models. The key is to develop an orderly process of steps required to set up as many bases as are necessary to combine into the final resolution. The logic of problem solution is a pre-requisite to advanced modeling exercises--even with entry-level modeling software.

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Some problems do not allow us to set up separate bases that we then combine in essentially a parallel combination. Occasionally, we may have to invoke long series of reiterations as we change the values of multiple variables. However, that kind of process is for some future episode in this series.

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Go to Main Index

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118. Modeling Odd Structures: the Gamma Match
+ Part 1. Gamma Modeling Basics

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L. B. Cebik, W4RNL

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Newer modelers often carry into the enterprise a number of presumptions about antenna structures or geometries. One of them is that small appurtenances on an antenna generally make no difference and thus we may ignore them, thus simplifying the model. In many cases, the presumption works, but sometimes it does not.

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The presumption toward simplification combines with an urge that the newer modeler should try to overcome. The urge is to create a single model for a given antenna. After all, we have only one subject antenna, and a single model should correspond to it. Along that road the modeler will eventually discover that he or she is blocking a host of information that might be acquired about the antenna's performance.

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In this episode, we shall explore what we can learn both by overcoming the presumption underlying simplification of models and by setting aside the urge to encapsulate everything in a single model. Our example will be the gamma-match assembly used by so many Yagi beams. However, the general ideas surrounding our exploration will have applications elsewhere. It may seem at times that we are discussing gamma matches, but our real subject matter is careful modeling.

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Why the Gamma Match Is So Hard to Model

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Let's suppose that a particular Yagi design uses a gamma match. We often encounter such assemblies when the manufacturer chooses to connect the antenna elements directly to the conductive boom. Fig. 1 shows one such assembly.

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The assembly has several features that automatically make it difficult to model. First, the connector plate and the shorting bar are not round wires. Second, the series capacitor takes the form of concentric tubes with a dielectric lining between them. Third, the gamma rod may extend beyond the shorting bar, although that extension is minimal in the photo. Fourth, the gamma rod is very often not the same diameter as the element. Fig. 2 summarizes in outline form the differences between the physical gamma match assembly and the model that we are likely to make.

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If we choose to model the gamma match, we are likely to add the minimal number of wires needed to do the job. As well, we are likely to place the series capacitor at the feedpoint to simplify the compensation for the usual inductive reactance at the feedpoint.

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These two measures assume that we are inclined to model the gamma match at all. Some modelers shrug off the match as being "simply a match," akin to beta and series matching systems, and they model the antenna without the match in place. Of course, beta matches and series matching systems add transmission lines or lumped components at the feedpoint and do not change the fundamental driven-element geometry. In contrast, the gamma match adds wires in the feedpoint region and thereby changes the geometry of the element. Short of extensive field-testing, we cannot know in the absence of an adequate model whether the driven element changes result in any pattern changes for the beam relative to the patterns without the match. Therefore, let's assume that modeling a gamma match is a worthy task, even if it creates a more complex model.

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We can only model a gamma match if the modeling software is capable of handling the task. NEC (both -2 and -4) faces some major challenges in this regard. If the gamma rod is not the same diameter as the main element, then we shall have from 2 to 4 angular junctions of wires with dissimilar diameters, depending on the diameter that we assign to the gamma connector plate and the shorting bar. In addition, NEC shows limitations when we bring into close proximity parallel wires of different diameters, even if we carefully align the segment junctions. In garden-variety cases, NEC will show average gain test (AGT) scores in the region 0.9 when 1.000 is the ideal. Hence, we may expect gain errors greater than 0.4 dB and impedance errors about 10% off the mark. For these reasons, many NEC modelers give up altogether trying to model gamma matches.

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Raw MININEC 3.13 has equal or greater difficulties. First, the core shows considerable error at corners unless we use a very high number of segments. Second, the uncorrected core has difficulties with closely spaced wires. Third, the core exhibits a frequency drift that leads to various degrees of inaccuracy as we raise the modeling frequency higher. One problem that MININEC does not have is handling junctions of wires with dissimilar diameters. However, if we compare the gamma structure to the listed problems, we might also disqualify MININEC as an appropriate modeling core. Seemingly we are left with nothing to use--at least within an economic price range.

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However, the development of MININEC has seen numerous correctives that largely overcome the flaws in the raw core. Perhaps the most refined version is part of the Antenna Model package, with correctives for corners, frequency, and closely spaced wires. In addition, Antenna Model has added the AGT test to the user-accessible outputs for running model assessments. Therefore, if we are willing to take the time to model a gamma match assembly, we may be able to learn something.

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Basic Modeling Requirements

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Let's begin with a 2-element 28-MHz beam for which we might use a gamma match. We shall specify the use of 0.5"-diameter elements. The driver will be 190.7" long, while the reflector will be 211.9" long. The spacing will be about 0.12 wavelength or 50.58". Without a gamma match, Antenna Model reports the feedpoint impedance as 29.84-j25.73 Ohms. The AGT score is 0.9997, which is exceedingly close to ideal.

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One limitation that is inherent to both NEC and MININEC is that neither core will reveal boom effects in the event that we wish to connect the element directly to the boom. However, that fact does not prevent us from using a gamma match; it only means that the results will not precisely reflect a real situation.

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We provided a modeling report, but omitted one critical fact: the level or density of segmentation. For the pre-gamma model, the level makes no difference, and we might use any value from about 10 segments per element upward. However, the segmentation density will make a considerable difference when we create the gamma model. Therefore, we use 100 segments per element for both the pre-gamma and the gamma model. Fig. 3 helps us explain why.

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At 28 MHz, each segment will be about 2" long. With the 0.5"-diameter elements, this segment length allows a 4:1 segment-length-to-diameter ratio, well above the limits for either NEC or MININEC. Next we shall construct a gamma match, as shown on the driver element in the outline. The main-element-to-gamma-rod spacing is 4" center-to-center. Note that we need to place the feedpoint or source at the connecting wire center, that is, on a pulse or segment junction. A 2-segment wire gives us the source position that we need and also allows for segments that are roughly equal in length with the segments on the other parts of the overall driver assembly.

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Note that the driver element itself now consists of 3 wires. The non-gamma side has 50 segments. We divide the gamma side into two parts such that the gamma section has N segments, and the remainder has 50-N segments. N is based on the length that we eventually assign to the gamma rod. Given the driver length, the final gamma rod requires 9.7 segments. Since we can only assign segments in integers, we give both the short main element section and the gamma rod 10 segments each, with the remainder of the main element receiving 40 segments. Fig. 4 provides a look at the Antenna Model Wire table that describes the geometry that we have just created.

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Several additional facts present themselves in the table. Foremost is the fact that our model uses a 0.375" diameter gamma rod. However, the 2-segment connecting wires use that same diameter as the main element. Although this initial strategy reflects the relatively "beefy" structure that we saw in Fig. 1, it does leave us with a future question about the affect of connecting wire diameter on gamma performance. In addition, the model has no gamma rod extension beyond the limit of the far-end connecting wire. Hence, we acquire a second question for future exploration. The wire table itself does not show the position of the source, which is at the center of the connecting wire at the element center. The series capacitor in the form of a load is also missing from this table. As a starting point, we place it at the same pulse as the source.

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With a gamma rod that is 18.47" long and a series capacitance of 38.32 pF, we obtain a gamma-match feedpoint impedance of 50.04+j0.07 Ohms. You may use any set of limits that you desire in setting the gamma assembly. Since I do a good bit of systematic modeling, I used very tight tolerances: 0.1 Ohm for either resistance or reactance relative to the 50-Ohm target value. The AGT score for this model is 1.0005, once more very close to ideal.

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With so many open questions, we cannot claim that this model is yet a good building guide. However, it does provide us with an internally consistent and adequate model of a gamma match for an element that is electrically independent of any supporting boom. Thus, we have a starting point for further exploration.

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The NEC Question

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We may construct the same model of a gamma-matched beam using NEC. I shall use NEC-4 (single-precision), as provided in the EZNEC Pro/4 package for the exercise. Fig. 5 shows the EZNEC wire table for ready comparison with the corresponding Antenna Model table in Fig. 4.

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For most linear elements with a center feedpoint we must use an odd number of segments in at least the driven element. However, the gamma match element is not on the main element, but on the connecting wire. Hence, we can replicate the MININEC segmentation--with one exception. Centered NEC sources require an odd number of segments. Therefore, I increased the segments in the connecting wires to 3. Having shorter segments in the connecting wires is the better option, since it allows the source to have a segment on either side of the source segment that is the same length as the source segment. NEC tends to be most accurate under this condition.

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If we use the same 18.47" gamma rod that we used in the earlier model, but change the series capacitor to 37.15 pF, we obtain a feedpoint impedance of 55.30-j0.06 Ohms. The NEC result is 5 Ohms off the target 50-Ohm value. If we check the AGT score for the model, NEC-4 returns a value of 0.902, a considerable distance from the ideal value. We would expect the forward gain of the antenna to be about 6.25 dBi, but the NEC report is a gain value of 5.80 dBi. NEC appears to be considerably off the mark with such numbers.

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In order to obtain a 50-Ohm feedpoint impedance within the prescribed limits for this exercise, we must change the modeled gamma rod length and the value of series capacitance. If we reduce the gamma rod length to 17.56" and use a 39.36-pF capacitance value, we can obtain 50.07-j0.01 Ohms. However, the trustworthiness of this report is cast in doubt by the 0.904 AGT score for the revised model. As well, we can find some further fluctuations that are interesting. For example, changing the ratio of gamma segments to remainder segments between 9-41 and 10-40 yields a 0.3" change in the required gamma-rod length--not much but noticeable. As well, single-precision and double-precision versions of NEC-4 yield slightly different values, a very unusual situation in more adequate (higher-AGT-score) models.

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All is not necessarily lost in terms of using NEC as a preliminary guide to gamma matching. The AGT scores can help us provide some correctives to the data. For example, we may translate a basic AGT score into a value in dB by taking 10 times the log of the AGT score. For the 0.902 value, we obtain -.45 dB. If we add this value to the gain report (5.80 dBi), we obtain the pre-gamma-match beam gain of 6.25 dBi, which coincides with the Antenna Model reports for both the pre-gamma and the gamma models.

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For a normal feedpoint that is close to resonant, we may generally correct the reported feedpoint impedance by multiply the basic AGT value times the report of the resistive component. 55.30 * 0.902 = 49.88 Ohms, very close to our target value. Therefore, we can employ the following strategy to model a gamma match. First, develop an approximate model using the required wire diameters. Actually, the only approximation will be the gamma-rod length. Obtain an AGT score. Divide the target impedance (in these examples, 50 Ohms) by the AGT to obtain a new target value. Redesign the gamma assembly to obtain the revised target impedance.

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Alternatively, you may design the gamma match for 50 Ohms. Divide the modeled gamma rod length by the square root of the AGT to obtain the actual value. The revised model had an AGT score of 0.904 and produced a 50-Ohm impedance with a gamma-rod length of 17.56". Applying this technique yields a revised gamma-rod length of 18.49", very close to the value produced by the Antenna Model version of the assembly.

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Both techniques are approximate and may vary as we change the precise ratio of gamma-rod segments to remainder segments. As well, the series capacitance will likely hold only within about +/-1pF. Nevertheless, they may prove useful if one only has a NEC program with which to work.

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Some Additional Questions and Additional Modeling

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For any gamma-matched beam, whatever the size, learning to construct such structures can be useful in more ways than just trying to model the gamma assembly itself. For example, the modeling technique is useful in seeing whether the assembly yields a significant distortion to the normal beam pattern. The gamma matches constructed for the sample models extend forward of the main element by the 4" spacing value that we selected. We may ask whether the gamma assembly in any way disturbs the pattern that we might obtain from the antenna without the gamma match in place.

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By means that may vary with the specific software that we use, we can compare the patterns of a pre-gamma and a gamma-matched model (understanding that the comparison will not account for any boom effects). For the sample models that we have used so far, Fig. 6 provides two sorts of comparison. For this exercise, I selected the EZNEC models precisely because the gamma-model shows a reduced gain. As a consequence, the forward lobes of the two beam patterns are fairly distinct. (A moderately poor AGT score ordinarily does not disrupt a radiation pattern shape.)

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The overlaid patterns show the degree to which the gamma assembly tilts the radiation pattern in the X-Y plane (ordinarily the azimuth plane). The amount is detectable, but minuscule, far below the level that we could notice in operation and likely below the level that we could measure. The smaller patterns to the right compare the degree to which the gamma match assembly might disturb the side nulls. For a match-less beam, the nulls exceed NEC's ability to record them in a finite number of digits. However, the side nulls in the gamma model have a limited depth--perhaps -40 dB relative to forward gain of the array. Although numerically detectable, the difference between -40-dB nulls and indefinitely large nulls is completely insignificant.

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On the basis of a single 2-element Yagi design that does not show boom effects, we cannot reach the conclusion that gamma matches do not distort beam patterns. The point of the example is not the conclusion, but the use of modeling to reach a preliminary conclusion on a case-by-case basis relative to an antenna design under analysis.

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In addition to examining the question of pattern distortion, we can also and easily perform some systematic modeling to answer "what-if" questions. Perhaps the first question is what happens when we change the diameter of the gamma rod. We may keep all of the model parameters as we began, using the same pre-gamma model. We shall also retain the connecting wires at the 0.5" main-element diameter and revise only the diameter of the gamma rod. In fact, for simplicity in this exercise, we shall keep the same ratio of segments on the gamma side: 10 segments for the gamma length and 40 for the remainder of the half elements. For each new gamma rod diameter, we shall record the gamma rod length and the series capacitance required to bring the feedpoint impedance to 50 Ohms within the tolerances that we previously used. The results will resemble those in Table 1.

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Those who are familiar with some of the algebraic methods of calculating gamma matches may be surprised by the very small change in the length of the gamma rod as we vary the rod diameter over a 5:1 range. The difference is a mere 0.25". The change in the required capacitance is larger (about 7 pF), but still small.

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The exact numbers in the table are less important than what they can tell us about the probable behavior of a gamma match. The models suggest that a gamma match is not especially sensitive to changes in the gamma rod diameter. We may easily perform a similar systematic investigation beginning with any main element diameter and any value for the spacing between the gamma rod and the main element. Therefore, we need not treat the results of this test as generally true. Instead, we can perform the requisite test for ourselves using the materials and test frequency for virtually any beam.

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Unfinished Business

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In the course of our exploration of the basic modeling techniques needed for the gamma match as an example of an "odd structure," we did not strive to develop a gamma match that we can build. Instead, we strove to assemble a model that we can rely upon, at least internally to the modeling enterprise. Unfortunately, all forms of gamma-match calculation have undergone only spot checks. Hence, we cannot determine which of the numerous systems of gamma design is the most accurate to physical reality. Nevertheless, we can examine the trends suggested by the models in anticipation of actual building experiences.

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We did encountered a number of questions left unanswered by our initial attempts to formulate and analyze gamma-match models. For example, we may wish to know the consequences of varying the spacing between the main element and the gamma rod. We may wish to understand the effects of leaving a gamma rod extension beyond the shorting bar. Do variations in the connecting-wire diameters have significant effects on the gamma-rod length or the series capacitance? Finally, what are the consequences of moving the series capacitor position from its ideal modeling position?

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Therefore, we may usefully spend another episode on this topic. Our goal will not be to come up with definitive answers. Instead, we shall examine the nature of the models that can provide those answers, at least within the limits of the modeling enterprise.

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Go to Main Index

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119. Modeling Odd Structures: the Gamma Match
+ Part 2. Gamma Assembly Variables

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L. B. Cebik, W4RNL

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In the preceding episode, we began an exploration of modeling "odd" structures that we find within the geometry of some antennas, using the gamma match as a good example. The gamma match has both basic and additional properties that are worth modeling in order to discover what effect a number of structural variables may have on the performance of the antenna. Because the gamma match assembly is primarily an impedance transformer, we have been less interested in such antenna performance properties as forward gain and front-to-back ratio than we have in the structure necessary to arrive at a desired feedpoint impedance.

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We began with a "pre-gamma" model to arrive at the antenna source impedance prior to adding the gamma-match structure. Our basic subject model used a test frequency of 28 MHz with 0.5" elements in a 2-element driver-reflector Yagi configuration. The driver was 190.7" long, while the reflector was 211.9" long. The spacing was about 0.12 wavelength or 50.58". Without a gamma match, Antenna Model reports the feedpoint impedance as 29.84-j25.73 Ohms. The AGT score for the basic or pre-gamma model was 0.9997, where the ideal value is 1.0000.

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Our decision to use Antenna Model software, a highly corrected version of MININEC 3.13, rested on its ability to handle--so far as tests internal to modeling can tell--accurate models of elements within a gamma-match assembly. NEC is subject to systematic errors that make its use difficult and potentially questionable. Less corrected versions of MININEC may yield equally erroneous results. Although Antenna Model may produce the most trustworthy models within the collection of extant wire antenna simulation programs, we must remember that our exercises lack one important step: the calibration of the simulation results with physical antennas. However, our goal in tracking these exercises has not been to yield a building guide. Rather, we have been concerned to explore what counts as good modeling practice for structures as "odd" as the gamma-match assembly.

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Our initial gamma-match model employed a basic structure consisting of several new wires and some modifications to the main driver element. As shown in the upper portion of Fig. 1, the main element now has 3 sections. We selected 100 segments as the total of the segments on all three element sections, with 50 assigned to the non-gamma side of the element. The ratio of segments on the gamma side, divided between the gamma assembly section and the remainder of the element, rests on equalizing to the degree possible the lengths of segments along the element. We assigned 2 segments to the source wire and to the shorting bar wire both to equalize segment lengths throughout the model and to place the source at the center of its wire. The latter consideration rests on the need to place MININEC sources (and loads) on a pulse or segment junction. Our initial spacing between the main element and the gamma bar was 4", yielding 2" segments that roughly correspond to the length of segments in the main element.

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The goal of the modeling was to produce a model that gave us a 50-Ohm feedpoint impedance, the value that corresponds to general amateur practice for the use of main feedlines. For the exercise, we arbitrarily set a close tolerance limit of 0.1 Ohm in the resistive and the reactive components. For many purposes, this limit is too fine, although it is useful for some systematic modeling exercises. We also began with a gamma-rod diameter of 0.375", although we left the end wires at the same 0.5"-diameter as the main wire. With a gamma rod that is 18.47" long and a series capacitance of 38.32 pF, we obtained a gamma-match feedpoint impedance of 50.04+j0.07 Ohms.

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The lower portion of Fig. 1 shows us a number of ways in which an actual gamma match may differ from the idealized model that we have been using. The variations fall into two general categories that we might call simple and complex variations. Simple variations involve selected modifications of single changes to one of the initial dimensions of the ideal gamma-match model. For example, before we closed the preceding episode, we explored the effects of changing the diameter of only the gamma rod, Wire 5 on the basic model wire table. Fig. 2 replicates that table from Antenna Model so that we may identify both the change that we have so far made and changes yet to come.

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The starred entry shows the entry with which we were concerned in our first foray into systematic modeling with the gamma-match assembly. As we changed the gamma rod diameter from 0.125" to 0.625" in 0.125" increments, we adjusted the gamma-rod length to arrive at a 50-Ohm impedance. This process involved changes to the wire-table entry wherever the initial wire-table shows 18.47. Because the source and the series capacitance load are on the same pulse, we could independently arrive at the desired source resistance and then modify the load capacitance value to remove any remnant reactance. Table 1 shows the results of our efforts.

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During our model modifications, we kept a close eye on the amount by which the gamma rod length changed in order to assure ourselves that the segment lengths on the main element remained stable. In this case, the total length change from the thinnest to the thickest gamma rod was about 0.25", so we could maintain the 10:40 segment division on the gamma side of the element. Of course, the gamma rod and the gamma section of the main element will have the same number of segments, and the two values on the gamma side of the element will add up to 50.

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The initial exercise left us with a number of unanswered questions that we might pose to the model, based on normal gamma construction methods and on the lower portion of Fig. 1.. For example, we may wish to know the consequences of varying the spacing between the main element and the gamma rod. We may wish to understand the effects of leaving a gamma rod extension beyond the shorting bar. Do variations in the connecting-wire diameters have significant effects on the gamma-rod length or the series capacitance? Finally, what are the consequences of moving the series capacitor position from its ideal modeling position? Some of these questions involve equally simple modifications to our initial gamma match model, while others may involve more complex modifications.

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The Gamma Spacing Question and Its Models

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The systematic testing of various gamma-rod diameters is only one of many such tests that we may perform to obtain a general idea of the properties of a gamma-match assembly. We may perform a similar test of gamma-rod-to-main-element spacing. Our basic model used a 4" center-to-center spacing between the rod and the element. We might wish to know something about what happens with narrower and wider spacing values.

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As a sample, we might specify alternative spacing values--perhaps 2" and 6"--in order to bracket our initial design. We shall retain the 0.5" main element and the original 0.375" rod diameters. Fig. 3 shows preliminary outlines of the three modeling situations and alerts us to some modeling cautions.

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The first caution concerns the change in the segment length for the connecting wires. A 2" spacing value will reduce the segment length to 1", while the 6" spacing value will increase the segment length to 3". Because we wish to keep the source centered in its connecting wire, we have no practical way to obtain exact 2" segment lengths. Therefore, we shall have to pay closer attention to the AGT scores for each model to assure ourselves that the results are reasonably reliable. The initial model with a 4" spacing value achieved a score of 1.0005, very close to ideal. We shall be interested in the scores for the alternative spacing values.

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The second caution concerns the segment length within the gamma rod. Casual modelers likely would simply try the new spacing and then adjust the gamma rod length (and the series capacitance), forgetting to be certain that the segment lengths throughout the entire driver element are as equal as feasible. However, we have already noted that unequal segment lengths among the sections of the driver may result in deviant source impedance reports. Hence, we shall reset the relative segmentation between the gamma section and the remainder in order to achieve the most ideal AGT score possible by obtaining the most equal segment lengths feasible.

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If we attend to these cautions, then we might obtain results such as those in Table 2.

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The table suggests a number of modeled gamma-assembly properties. First, despite the changes that we made in the relative segmentation, the models for the alternative spacing values are farther from the ideal score than the original model. Nevertheless, the probable accuracy of our 50-Ohm source impedance is within 1%. Therefore, the general trends shown by the length and capacitance numbers are reasonably reliable. Second, the gamma-rod length grows shorter as we increase rod spacing. Although not precise, the trend suggests that length changes linearly as the ratio of one spacing value to the next. Third, the required series capacitance decreases with increased spacing, although the amount is small and likely within the adjustment range of any type of capacitor used for this function.

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Note that these trends apply so far only to the particular initial feedpoint impedance of the pre-gamma model. For a truly systematic exploration of gamma behavior, we might wish to construct alternative models using a variety of pre-gamma feedpoint impedances. These impedances should not only include several resistance values, but as well a number of reactance values. From such a systematic survey, we might glean a wider view of gamma assembly trends and develop some rational expectations of gamma-assembly behavior at interpolated values for gamma spacing and rod diameter.

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Other Model Variations

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Let's return to our basic gamma model with the 0.5" and 0.375" diameter assembly elements. Fig. 2 showed us two conditions that might or might not have a significant impact on the assembly final dimensions. One factor is the extension of the gamma rod beyond the shorting bar. The second is the diameter that we assign to the two connecting wires to simulate the plates and bars that we might use to connect the gamma rod to the main element at each end. To ensure that we do not confuse potential effects, we should treat each case separately.

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Let's first add extensions to the gamma rod to simulate what might happen if the shorting bar does not come close to the end of the rod that we construct. The rod extensions will use the same 0.375" diameter as the main section of the rod. The extension lengths will consist of a new wire that we add to the model. The wire joins the junction of the shorting bar and the main section of the rod and runs parallel to the main element. Fig. 4 shows the outline of the construct, and points to a caution that we should observe.

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We have striven to equalize to the degree possible the lengths of all segments in the model. The average segment length is close to 2". Therefore, we should add gamma rod extensions in 2" increments, using 1 segment per each 2" of extension. Within these restrictions, we might usefully test 2", 4", and 6" extensions.

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For this test, we might bypass the earlier procedure of carefully adjusting the rod length and the series capacitance until we see if such a tedious procedure is necessary. Instead, let's retain the 18.47" rod length and the 38.32-pF series capacitance. What we shall observe is the effect of the extensions on the reported feedpoint impedance. The results appear in Table 3.

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We had set 0.1-Ohm limits on the initial search for the proper gamma rod and series capacitance for a 50-Ohm match. With no extensions, the source impedance values fall within the limits. As we add successively longer extensions, the reactance does not change in any way that drives it outside the initial limits. Hence, for any reasonable rod extension, the existence of that extension is not likely to require a series capacitor adjustment. The extensions do have a small affect on the source resistance. However, a full 6" extension displaces the match impedance by only about 1.6 Ohms. This change is likely to be well within the field adjustment variables. Hence, it appears not to be a significant factor. For the initial pre-gamma beam, at least, one might cut off the extension or to leave it according to non-electronic reasons.

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We should perform an additional test after returning the model to its initial gamma configuration. Let's explore what happens if we vary the 4" connecting wire diameters. We initially set them at 0.5", the same diameter as the main element. We might see what happens with connecting wires ranging from 0.125" to 1.0" in 0.125" increments. To simplify the exercise, we shall change both connecting wires at the same time.

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Because we shall be creating some radical differences in the wire diameters at gamma-assembly junctions, we shall pay close attention to the AGT scores to ensure that we do not exceed program limits. Because we might have to adjust both the gamma length and the series capacitance to obtain source impedance values within our limits, we can expect this exercise to be somewhat tedious. However, this feature of systematic modeling is unavoidable. The results of our survey appear in Table 4.

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Note that this and all other tables try to include all of the information about the starting points. After several exercises in systematic modeling, scratch pads notes and incomplete table data can obscure the initial model to which the new table's information may apply. Not every modeling caution applies to something that we enter into the software program--some apply to our record keeping procedures.

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The table shows that for the initial model, changing the size of the connecting wires by an 8:1 ratio creates only a quarter-inch change in the required gamma length. The required series capacitance changes by only about 3 pF. Some sources suggest that the connecting wire effects are much greater. However, for the present initial gamma model, we do not find significant effects from connecting wires ranging from very thin to very thick, relative to the element and rod diameters. The consistency of the AGT scores suggests that nothing in the modeling itself artificially washes out the anticipated effects. Hence, we now have a real question that we might pose to reality: are the supposed effects as great as some sources assume?

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Series Capacitor Placement

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The final part of our survey of gamma properties concerns the placement of the gamma capacitor. Fig. 1 shows a concentric capacitor installed on the gamma line. The capacitance is distributed along the section of line in which the two tubes overlap (with a dielectric between them). Hence, we have two difficulties at first sight. One is the changing diameter of the gamma rod. However, as we saw in one of our earlier surveys, the likely increment of diameter change is unlikely to create any significant difference in performance.

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The second potential problem concerns the capacitor position. At best, a model can only approximate the distributed capacitance. The version of MININEC in the Antenna Model implementation further limits the potential position of a gamma capacitor to the end of a wire or at its center--assuming that we have an even number of segments on the wire. Fig. 5 shows the relevant positions. The numbered dots represent not only available positions, but also the most popular positions for series capacitors in actual gamma-match construction.

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Position 1, which we seldom find in practice, is the ideal position on the same pulse as the source. All of our previous models have used this capacitor position. Builders tend to favor position 2 when using a standard variable capacitor (which they sometimes replace after adjustment with a fixed capacitor having the closest value). Position 3 approximates the position of a concentric tubular capacitor. Although not precise, it is useful for tracking the trends in gamma dimensions as we move the capacitor from one position to the next.

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Table 5 tracks the effects of the change of capacitor position, using the ideal position as the starting point. The required capacitance goes down as we move the capacitor away from the source, but not by enough to exceed construction variables in most cases. The major change lies in the required gamma rod length to achieve a 50-Ohm resonant feedpoint. The simple 2" move to the corner (position 2) requires an additional half-inch of gamma rod. Moving the capacitor to midway along the gamma rod calls for a further 1.5" increase in rod length. The 2" total exceeds 10% of the originally modeled gamma rod length--a significant amount.

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One further aspect of moving the series capacitor position does not show up in tabular results, but does appear as we work with the model trying to obtain the correct gamma rod length and the correct capacitor value. When the capacitor is on the same pulse as the source, the resistive and reactive components of the source impedance are independent. We adjust the rod length for an acceptable resistive component. Then we adjust the capacitor value for an acceptable reactive component. However, when we move the capacitor away from the ideal position, we discover that the rod length and the capacitor value interact in the model. Changing the value of the capacitor at position 3 alters both the reactance and the resistance at the source. In many cases, the resistance may not change enough to require a change in rod length, but occasionally, we may need to adjust both components until we find the correct values to yield the desired feedpoint impedance. Indeed, under these conditions, model adjustment reflects what we encounter when making field adjustments on a gamma match.

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Conclusion

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Although we may now conclude this exercise, we are far from concluding the modeling explorations that may go into understanding and designing a gamma match for a given antenna. Our model used a sample antenna that showed a moderate resistance and a considerable reactance at the source relative to the final gamma-match impedance. The trends that we observed apply to this situation. We have not explored other beam feedpoint impedance values, both resonant and non-resonant. We should not presume in advance of modeling that all trends applicable to our subject antenna would hold true of all antenna designs. Even if the trends are generally applicable, the rates of change may vary with the initial feedpoint values prior to adding the gamma assembly. Hence, other initial impedance values may show different levels of sensitivity to small changes than we found within the example.

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For each test, we also froze all but one dimension in order to explore systematically a single variable. In many cases, you may need to perform multiple explorations in order to determine for a given test frequency, initial impedance, and main element diameter the most promising gamma rod diameter, capacitor position, and rod length. One additional situation that we have not examined at all is modeling for boom effects. One technique often used to simulate boom effects is to install at the element center a short wire having a large diameter. Such a wire often creates a large difference in diameter within the main element in the gamma area, thus changing the surface-to-surface spacing between the main element and the gamma rod along the rod's length. As well, the short fat wire that compensates for the NEC and MININEC inability to handle transverse boom currents may also make it more difficult to maintain element length equality along the main element. Indeed, the diameter values often used for such exercises may exceed the segment-length limits that we imposed on our models to obtain adequate segmentation of the connecting wires and proper source placement. In all such cases, we need to keep a close eye on the AGT scores to assure ourselves of a reasonably adequate model.

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In fact, this episode and the preceding one have not aimed to provide a complete analysis of the gamma match--not even for the beam design used as our focal sample. Rather, the two-part series has tried to show many--but not all--of the modeling challenges that may go into modeling the gamma match as an example of an odd structure relative to normal or simple antenna construction. We varied our efforts along the way as we took into account as many of the physical aspects of the structure that may form variables in the overall element geometry. In the process, we showed a few ways in which we might evaluate whether the structure was relatively sensitive or relatively insensitive to changes in each variable. Even for the single beam example that we selected as a starting point, there is considerably more--and sometimes tedious--work ahead before we complete the portrait of the assembly. Systematic modeling is not a synonym for tedium, but the latter is at least the second cousin of the former.

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The fundamental principles involved in modeling odd structures are themselves simple. We need to take into account every physical aspect possible for the structure. We need to devise models that permit systematic variation of each significant aspect of the physical structure while remaining within the limits of the software to yield reliable models. Finally, we need to be as systematic as possible both in obtaining model reports and in recording them so that we produce reliable data--if not to the last numeric place, at least in terms of trends that will likely appear in the physical antenna.

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Go to Main Index

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12. Verticals At and Over Ground: Sensible Expectations

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L. B. Cebik, W4RNL

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+ Last month, we looked at the ground systems available in both MININEC and NEC and at the typical behavior of horizontal antennas over the selected ground system. Horizontal antennas exhibited some interesting general properties. The source impedance of the antenna varied considerably up and down, relative to the free space modeled source resistance of the same antenna, from close to ground to heights approaching or exceeding 1 wl. However, gain and the emergence of vertical lobes in the antenna pattern proceeded in a very regular manner. Soil quality beneath the antenna played a very small role in the reported performance of either MININEC or NEC models. +

The modeled performance of vertical antennas at or above ground system available in MININEC and NEC shows almost diametrically opposed characteristics. For example, the source impedance will vary by only a small amount, and above about 0.3 wl at the bottom of the antenna, hardly any variation at all. In contrast, the antenna gain and its vertical pattern lobes will vary widely and not altogether according to simplistic expectations as we place a vertical antenna at various heights over soils of differing quality.

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Apart from any problems associated with the possible accuracy or inaccuracy of models of vertical antennas above ground, the modeler needs to become acclimated to the range of variations that are typical for vertical antennas. This episode is designed to begin that process, with the hope that modelers will carry on with self-generated series of models of antennas and soil types most relevant to their primary activities.

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A Short Review of Ground and Ground System Basics

Although we shall give some attention to perfect ground, primary focus will be upon the real ground systems available in modeling programs. In MININEC, there is only one real ground system. In NEC, we have a choice between the so-called "fast" system and the more accurate but slower Sommerfeld-Norton (S-N) system. For most purposes, the S-N system is preferable, especially as computer speeds overcome differences in ground condition calculation systems. +

As we did last month, we shall employ the ground or soil quality categories commonly used. A relevant portion of the chart we used last month is reproduced for more immediate reference.

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Soil Description                   Conductivity   Permittivity   Relative
+                                   in S/m         (Dielectric    Quality
+                                                   Constant)
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+Salt water                         5.0            81
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+Pastoral, low hills, rich
+soil, typical from Dallas,
+TX, to Lincoln, NE                 0.0303         20             Very Good
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+Pastoral, medium hills, and
+forestation, heavy clay soils,
+typical of central VA              0.005          13             Average
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+Rocky soil, steep hills,
+typically mountainous              0.002          12-14          Poor
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+Sandy, dry, flat, coastal          0.002          10
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+Cities, industrial areas           0.001          5              Very Poor
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Except for the salt water entry, only the categories we shall use in our sample models are shown here. In calculating ground effects, modeling programs create from the values inserted for the conductivity and the dielectric constant a composite value. Remember that all MININEC and NEC ground calculations assume level terrain without obstructions other than those modeled. Additionally, they presuppose a homogenous soil beneath an antenna and to the horizon, rather than the sort of stratified soil layers we commonly encounter in practice. The effects of soil stratification are more pronounced at lower frequencies, where RF tends to penetrate more deeply into the ground, than at upper HF frequencies and above.

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The Simple No-Ground-Plane 1/4 wl Vertical

One typical model employed by nearly all modelers at one or another time in their work is the 1/4 wl vertical antenna terminated at the ground, as shown in Fig. 1. The test antenna is 1" diameter aluminum. No ground plane is used in the model. The source for a MININEC model can be placed at the junction of the wire end and the ground. For a NEC model, the source must be placed on the first segment relative to the ground end of the antenna. +
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When such antennas are place over perfect ground, the program creates an image antenna for calculations. Whether in MININEC or NEC, the results are virtually indistinguishable.

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Program        Gain      Source Impedance
+               dBi       R +/- jX Ohms
+MININEC        5.14      35.86 - j 0.75
+NEC            5.14      36.01 _ j 0.14
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The very slight difference in source impedance stems from two sources. First, the source on the MININEC model is at the end of the wire, while in the NEC model, it is inboard, on the first of the 20 segments in this 7.15 MHz model. Second, the required length for resonance (as arbitrarily set to a source reactance limit of +/- 1 Ohm) is 397" in MININEC and 396" in NEC.

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When we place these antennas over real grounds of the types available, we obtain far more disparate results. The following table is an illustration. VG is very good, Ave is average, P is poor, and VP is very poor, as defined in the table of ground quality types shown earlier and using the corresponding values of conductivity and dielectric constant in the models.

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System         Soil      Gain      TO Angle       Source Impedance
+               Quality   dBi       degrees        R +/- jX Ohms
+MININEC        VG         1.93     21             35.85 - j 0.75
+Real           Ave       -0.05     26             35.85 - j 0.75
+               P         -0.29     27             35.85 - j 0.75
+               VP        -1.77     29             35.85 - j 0.75
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+NEC            VG         2.45     21             31.98 - j 0.95
+Fast           Ave        0.97     26             28.61 + j 0.43
+               P          0.82     27             28.11 + j 1.73
+               VP        -0.18     28             25.14 + j 2.20
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+NEC            VG         0.88     21             45.85 + j 5.41
+S-N            Ave       -1.23     26             47.13 + j 3.65
+               P         -1.37     27             46.12 + j 4.09
+               VP        -2.37     29             41.23 + j 2.13
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Although the elevation angles of maximum radiation (TO angles) show excellent coincidence as we move from system to system, little else does. So let's graph some of the results and see what they might tell us.

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Fig. 2 graphs the reported gain of the antenna over the different soils. The intervals among soil types is not regular, and therefore, the lines should be read solely as connectors to keep the families of values well sorted. Each system shows comparable gain differences as we move from soil type to soil type. However, the reported values are distinctly different for any given soil type.

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In Fig. 3, we can view the reported source impedance values for the three systems. The MININEC line is flat because all MININEC source impedance values are calculated from perfect ground. Hence, they do not register any differences occasioned by changes in soil quality. In contrast, the NEC systems provide source impedance values quite distinct from the MININEC value: the "fast" system reporting consistently lower values and the S-N system reporting consistency higher values. However, the NEC progressions are not consistent with each other with respect either to value or to the progression of values from one soil type to the next.

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In general, connecting an antenna model to a NEC fast ground is considered the least accurate of all possibilities. The reported gain values are unrealistically high and the source impedance values unrealistically low for connection to a lossy medium like the earth. In contrast, the values for the S-N ground system yield lower gains and higher source impedance reports, giving them an air of realism.

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However, the sense of realism may have limited value, since virtually no real 1/4 wl antenna is directly connected to ground without a ground plane. Even were we to try to design such an antenna, at lower HF frequencies, there would be numerous variables of soil penetration and stratification to make the modeling results of dubious reliability. Moreover, I know of no definitive test results that would form a bench mark for assessing the reported values of either gain or source impedance.

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In most instances, modeling wires directly connected to ground is performed with a perfect ground and is used as a short-cut to modeling symmetrical antennas in free space. Alternatively, some preliminary modeling of phased and parasitic vertical antenna systems is done over perfect ground. Although the results are not especially accurate with respect to actual maximum gain, other factors--such as pattern shape and relative improvement--have proven useful.

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So why have we spent so much space and time on modeling the 1/4 wl antenna touching various grounds? The purpose has been to alert you to what you can expect to see should you attempt such models, whatever the goal and rationale.

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A More Realistic 1/2 wl Vertical Dipole Above Ground

We can develop more sophisticated expectations of what to expect by way of reports from models of vertical antennas by exploring the modeled behavior of a 1/2 wl vertical dipole at various heights above ground and over differing soil types. Fig. 4 sets the parameters of the exercise. +
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Because we wish to maximize accuracy and to watch the variations of source impedance with changes in height, we shall confine ourselves to NEC and the S-N ground system. We shall employ a 7.15 MHz 1" diameter aluminum dipole 792" long with 41 segments and fed at the center. For ease of tracking, we shall record the height of the antenna bottom limit as 0.2 through 1.0 wl up. For reference, the following table records actual bottom and top heights of the antenna.

+ 
Height         Bottom         Top
+in wl          Height "       Height "
+0.2             330           1122
+0.4             660           1452
+0.6             990           1782
+0.8            1320           2112
+1.0            1650           2442
+

Since our exercise is aimed at eliciting some of the features of modeling programs and not at replicating an actual antenna, it matters little that constructing an antenna meeting the above height conditions is not feasible for most builders. If we run this antenna through the various heights and over the soils we have previously defined, we get a fascinating table of results.

+ 
Soil      Height         Gain      TO Angle       Source Impedance
+Type      in wl          dBi       degrees        R +/- j X Ohms
+VG        0.2            1.75      11             67.97 - j 4.01
+          0.4            3.02      42             72.54 + j 1.55
+          0.6            4.60      33             72.33 - j 1.79
+          0.8            5.25      27             71.26 - j 0.14
+          1.0            5.37      22             72.48 - j 0.59
+
+Ave       0.2            0.32      14             68.46 - j 2.93
+          0.4            1.84      41             72.59 + j 1.01
+          0.6            3.14      32             72.13 - j 1.55
+          0.8            3.52      26             71.45 - j 0.20
+          1.0            3.44      22             72.35 - j 0.64
+
+P         0.2            1.09      14             68.88 - j 2.80
+          0.4            1.29      42             72.46 + j 0.86
+          0.6            2.58      33             72.15 - j 1.44
+          0.8            2.91      27             71.49 - j 0.26
+          1.0            3.21       9             72.30 - j 0.62
+
+VP        0.2            1.04      17             69.37 - j 1.91
+          0.4            2.03      15             72.49 + j 0.41
+          0.6            3.08      13             71.99 - j 1.24
+          0.8            3.87      11             71.65 - j 0.31
+          1.0            4.43      10             72.19 - j 0.65
+

The significance of the values may not be immediately apparent in tabular form, so let us take them by categories in more graphical form.

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Fig. 5 graphs the gain values report by NEC over S-N ground for the antenna through its height variations, using separate lines for each soil type. Note that, although certain general progressions are clear with respect to maximum gain, there are great irregularities in the graph as well. Especially notable is the apparent good performance of the antenna over very poor soil when compared to the performance of all but the antenna over very good soil. Indeed, below the level of very good soil, the reported gain of the antenna shows a different "leading soil" as we change antenna heights.

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This phenomena is not restricted to the particular antenna type used in the example. Similar results accrue to most vertically polarized antennas that do not require a ground plane. For example, side-fed delta loops, rectangles, half squares, and bobtail curtains all display the sort of variability with respect to maximum gain shown in the graph for the 1/2 wl vertical dipole.

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Part of the reason for the gain differentials and irregularities stems from the variability of the elevation angle of maximum radiation, which Fig. 6 demonstrates. Only the antenna over very poor soil exhibits a consistently low TO angle. Note that the antenna, when over poor soil, returns to a low TO angle at the maximum test height at which the bottom of the antenna is 1.0 wl up.

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To a degree, graphical results can be misleading and must be supplemented by comparing elevation patterns in order to see and settle many questions about the performance of the antenna over different qualities of soil. Let's begin with the height at which the antennas show a consistently low TO angle: 0.2 wl.

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In Fig 7, the elevation patterns for all 4 soil types are overlaid, with some indicators of which pattern is which. Of immediate importance is the fact that only over very good soil does the antenna pattern show a very marked null between the lower and upper vertical lobes of the pattern. In general, the poorer the soil, the shallower the null between the lobes.

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With only this much of a clue, we are in a better position to understand the high-low TO angle question. According to the table and the graphs, when the antenna is at a bottom height of 1 wl, it reports a TO angle of 22 degrees over average soil and 9 degrees over poor soil. What the elevation pattern in Fig. 8 shows us is that there is actually little to distinguish the two patterns. Over poor soil, the lower part of the combined (almost null-less) two lower lobes is less than 1 dB stronger than the upper part. In contrast, over average soil, the upper part of the combined 2 lower lobes is about 1 dB stronger than the lower part. The emergent third lobe at an angle of nearly 50 degrees is very similar for both antenna models.

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Soils ranging from poor (cond. = 0.002, d.c. = 13) to good (cond. = 0.01, d.c. = 14) can be viewed as middle range soils. They tend to exhibit in models a combined wave front that consists of the two lowest lobes with only an indistinct null between them.

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Fig. 9 shows the same antenna at the same height, but over very good and over very poor soil. Over very good soil, the lowest lobe is nearly missing, with only the second and third lobes prominent. In contrast, over very poor soil, the upper lobes become indistinctly differentiated, and the lowest lobe is most prominent. Even though the maximum gain of the antenna over very poor soil is not quite as strong as the maximum gain of the antenna over very good soil, the 7 dB advantage at the lowest angles (in the region of 10 degrees elevation) may be more useful to certain communications needs.

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In all of this, we have not mentioned the source impedance of the antenna under any of its conditions of height and soil. Fig. 10 tells us why.

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The graph shows that for any given height, the difference in source resistance is insignificant. The total variation in source resistance for all antenna models under all conditions is under 5 Ohms. Likewise, the total variation in source reactance is about 7-8 Ohms for all cases. With 1/2 wl vertical antennas at various heights, the source impedance will be no clue to the type of soil beneath the antenna. More likely candidates as good clues, if the models are at all accurate, will be the antenna's gain and its elevation angle of maximum radiation.

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How Accurate Are the Models?

To some degree, there is disagreement about the accuracy of models of the type used in our example relative to real antennas set up under the prescribed conditions. However, disagreement turns to agreement the higher the antenna is placed above ground. Hence, we may consider all but the lowest antenna placements as reflecting real performance. +

However, we must once again note the restrictions of even the S-N ground system in its assumptions of level terrain and homogenous soil. At lower VLF through lower HF, soil penetration is great and the nature of the complex stratification that often occurs may alter the performance of a real antenna relative to a given model. With vertical antennas, such as the one used in these examples, if translated into a real structure, modeling for a variety of conditions becomes one route to anticipating the possibilities and to analyzing the actual performance results. Indeed, the goal of modeling is sometimes not so much to exactly replicate a given antenna as it is to anticipate possibilities so that we know what they mean and can take appropriate actions, if the situation calls for any.

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A Quick Note on Salt Water

The table at the beginning of this column retained the conductivity and dielectric constant for salt water. The conductivity value is at least two orders of magnitude higher than even very good soil, and the dielectric constant is 4 times that of very good soil. For most purposes, these values are practical limits to the ability of the S-N ground system to yield accurate results. +

When the far field has primarily a salt water reflective ground, the performance of vertical dipoles such as the one in our example is significantly enhanced with respect both to gain and to TO angle. WWVH uses (as of 1999) vertical dipoles with the Pacific Ocean as their reflective ground. Boats and ships often use simple vertical antennas, some fairly short for their frequency of operation.

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Fig. 11 gives us an illustration of the modeled performance of our vertical dipole over perfect ground and over salt water, with the bottom only 5" above the surface. In contrast to our land models, the salt-water dipole loses little: its reported gain is less than 1 dB less than over perfect ground, and the elevation angle of maximum radiation is 7 degrees. The pattern for the short dipole also shown in the figure is about 2.5 dB down from the full-size dipole over perfect ground, and its TO angle is 9 degrees. This performance report comes from an antenna only 14' long, in contrast to the 66' dipole that is resonant at the 7.15 MHz test frequency. The base height of only 5" is a somewhat extreme case, but demonstrates the potential effect of salt water as a reflective ground for vertical antennas.

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Using salt water as the ground for our final examples is just a way of suggesting that these notes have only scratched the surface of the ways in which the selection of a ground system and a soil type may interact with vertical antennas to yield reports whose features form quite different regularities, compared to those we anticipate for horizontal antennas. Familiarizing yourself with the possibilities and potentials can go far toward allowing you to correctly interpret the modeling reports you get. When you do not have a pressing modeling project to perform, you might consider taking a variety of vertically polarized antennas and making systematic runs over many soil types. The results will be both illuminating and useful when a serious vertical antenna project comes along.
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120. Back on the Ground

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L. B. Cebik, W4RNL

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Our modeling notes have been looking up for many episodes. Perhaps it is time to look down for a change. In column 11, we looked at the basics of using the ground-entry commands, mostly as implemented in entry-level software. However, the goal was to create some realistic expectations of the models that we make when the ground is involved. In episode 34, we looked at the GN and GD commands to see both the opportunities and the limitations of giving a NEC model a second medium. One limitation of the second medium was the need to place it either at the same level or below the inner ground medium. A second limitation was the restriction to specifying either a perfect circle (relative to the coordinate system origin) or a straight line at some distance along the X-axis and extending indefinitely parallel to the +/-Y-axis for the boundary between ground media. Hence, NEC cannot directly replicate most rooftop or mountainside antenna locations.

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NEC offers us 4 basic ground selection options. Of course, there is free space, which eliminates the ground altogether from field calculations. Next, we may select a perfect ground, which engineers like to call by one or two abbreviations (to prove to one another that they have read the text and know how to talk "engineer-eze"). The NEC method of handling a perfect ground is to use image calculations that are almost as fast as free-space calculations. We may also select between two "real" ground calculation systems. The Reflection Coefficient Approximation (RCA or "fast") system uses a simplified set of calculations that we once widely used to speed NEC calculations on slow computers. The alternate selection is the Sommerfeld-Norton (SN) or "high accuracy" system that evaluates integrals developed and modified by the individuals after whom the method is named. The process is slower, and in the earlier days of NEC, modelers often saved the results for re-use to conserve computation time. The modern generation of desktop and laptop computers is fast enough to make the RCA method unnecessary, and one NEC implementation had dropped it as an option. Another implementation has by-passed the search for a usable SN result file and now calculates the SN ground anew for each model run. Users cannot tell the difference in run time.

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The RCA ground calculation system or method has a second cause of relative demise. Below about 0.2 wavelength, the results are no longer reliable. For horizontal wires, the RCA system shares this problem with the ground calculation system in MININEC, but shows variance curves (relative to SN calculations) that differ from the MININEC ground. The RCA method does have a provision that allows an approximation for a system of buried radials without having to model the radials, but it is not especially accurate. Likewise, the MININEC ground allows a vertical monopole to reach ground without introducing errors (by always presenting the source impedance over perfect ground), but it also shows significant deviations from models that create buried radials (in NEC-4) using the SN method for ground calculations. In "olden times" when computers worked at the speed of ox-carts, even a modest radial field might require the completion of a few chores or a lunch break during the core run. However, the current "interstate" speeds of computers allow very rapid calculation of large radial fields for multiple monopoles using the SN calculation methods that yield the highest accuracy available to modelers.

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What is NEC Doing When It Calculates Ground Influences?

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Whenever we invoke a non-free-space environment, NEC establishes a ground in the X-Y plane at Z=0. The program employs a flat earth, in contrast to the shallow curve of the real earth's surface. The ground surface at Z=0 is not an absolute limit on all NEC calculation functions. For example, if we invoke a second ground medium, we may place it below (but not above) Z=0 by specifying an increment in meters below the inner medium. A sample GN command with a circular boundary might look like the following entry (without the extra spaces used to separate entries).

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+GN    2     0           0  0        13    .005        81    5           10.7        10.7
+Card  Gnd   Nr of       Zeros       D.C.  Cond.       D.C.  Cond.       Boundary    Neg.
+Type  Type  Radials                 [Inner Med.]      [Outer Med.]      Radius      Outer
+                                                                                    Height
+
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This card specifies two media, an inner and an outer, with the inner medium having average soil values and the outer one having salt water values. The boundary radius tells us how far (in meters) from the coordinate system origin that the outer medium begins. Note that boundaries are always specified in terms of distance from the 0, 0, 0 point of the coordinate system, not necessarily from the antenna. Since we can alter the coordinates of the antenna's elements, we can place it anywhere in the inner medium region.

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The final number (again in meters, even if user interface entry is in other units) represents the distance by which the outer medium surface is below the inner medium surface. A commercial program might call for a negative number as an input to remind the user that the outer medium can never be higher than the inner medium. However, the NEC card requires that this value of lower ground be entered in the command as a positive distance downward. 10.7 meters is about 1 wavelength at the 28 MHz test frequency for the model we are using.

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We may also specify the second medium using the GD command in order to free the GN command for alternative uses. For further details on entering GN and GD commands, see episode 34 of this series. The setting of a second medium affects only the calculations for the radiated field. It does not affect the calculation of near fields or currents, even if the antenna geometry extends into the outer medium. As well, the second medium specification has no effect on the ground-wave calculations, which require an infinite flat ground and the primary ground parameters (conductivity and relative permittivity).

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The second facet of calculations that involve the region below Z=0, even when an SN ground has been specified, involves buried wires. A wire that penetrates the surface must have at least a segment junction at Z=0. NEC-4 will calculate the currents in buried wires, with suitable modifications of the segment lengths for these calculations based upon the medium specified for the primary ground parameters. Therefore, in the NEC output report, expect to see a difference in the segment information between the initial geometry portion of the report and the current calculation section.

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Many modelers observe a difference in the take-off (TO) angle (or theta/elevation angle of maximum field strength) when changing the ground parameters. The explanation for this phenomenon is straightforward, if we examine Fig. 1.

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If we take any antenna, its radiation will initially consist of direct rays in all elevation directions from the structure. Rays that intercept the earth's flat surface will divide into two components. One component will be a portion of the energy reflected upward. The second portion will be energy dissipated within the earth's surface. The figure only points to the division of energy and not to the complex manner in which energy penetrates the surface before being reflected (or refracted) upward.

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The elevation or theta angle of maximum field strength results from the combination of direct and reflected rays, taking due note of their strength and their relative phases. However, differing ground parameters yield not only differing level of energy loss, but as well, differing depths of penetration, resulting in differences in the reflected rays that parallel the direct rays in phase. The result is a different TO angle.

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Within the range of normal values for conductivity and permittivity, lower values of either or both terms normally results in higher TO angle. However, it is possible to specify values of conductivity and permittivity so low that the earth beneath the antenna becomes nearly RF transparent. Let's consider three (for the moment) arbitrary soil qualities called "average," "very poor," and "terrible." If we model a 40-meter 1/4 wavelength monopole with 16 radials buried about 0.1 m below ground, the three soil qualities listed produce the results shown in Table A. The TO Angle column lists the theta angle followed by the elevation angle.

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+Table A.  NEC-4 modeling reports for a 40-meter monopole and 16 buried radials with three soil qualities
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+Quality Name   Conductivity    Permittivity    Maximum Gain    TO Angle
+               S/m                             dBi             degrees
+Average        0.005           13              -0.73           63/27
+Very Poor      0.001           5               -1.31           60/30
+"Terrible"     0.0001          1.2             -0.49           63/27
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The hypothetical soil labeled "terrible" uses a conductivity value that appears within the original charts from which we draw the more usual soil types. However, the permittivity is approaching the absolute limit of 1 (relative to free space) and is a value not found for any existing soil. Nevertheless, as we enter these values into NEC, we obtain a slight rise in gain and a drop in the TO angle toward the horizon. Both values run counter to anticipated curves for a soil that is approaching the status of a reasonably good insulator. Fig. 2 overlays the modeled elevation patterns of the antenna under the three soil conditions.

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We enter values of conductivity and permittivity, but for many modelers, these values are strictly conventions. We tend to encounter conductivity in the arena of antenna materials. The basic term, sigma, describes conventional current due to electron motion. Tabular values of permittivity, epsilon, are actually the relative permittivity, epsilonr, which is the dielectric constant that we associate with materials used between capacitor plate. At root, the term represents displacement current. Relative permittivity derives from the absolute permittivity (epsilon) divided by the permittivity of free space (epsilon0), or

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Since absolute permittivity is also in pF/m, relative permittivity has no units. +

We enter separate values for conductivity and permittivity because we can measure each independently and because one may vary while the other remains constant. See "Practical RF Soil Testing" by Eric von Valtier, K8LV, in QEX for July/August, 2006, pp. 46-49, for a good summary of basic soil terms and concepts, as well as a technique for measurement.

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For use in SN calculations, NEC employs one of two formulations of complex permittivity (epsilong), according to how the modeler enters the value of sigma. If the entry is positive, as is normally the case, then

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Omega is the familiar 2 Pi f function. If the user enters sigma as a negative number, then +
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without regard for frequency. Since most users derive values from tables, the normal form is usually the form of choice. +

Expanding Our Appreciation of Soils

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The most common table of soil values from which modelers draw values is actually very old. Table 1 represents an adaptation of values found in The ARRL Antenna Book, 20th Edition (p. 3-13), which are themselves an adaptation of the table presented by Terman in Radio Engineer's Handbook (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. Terman's value for the conductivity of the worst soil listed is an order of magnitude lower than the value shown here. Sharp eyes will immediately spot the categories of average and very poor soil, although there is no such thing as "terrible" soil in the listing. The list shown is from Intermediate Antenna Modeling: A Hands-On Tutorial which can be found on the Books Page. I have put this table and the next one in the form of graphics so that--if you do not have some other convenient reference--you may download and print these tables on 1 or 2 sheets.

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In the absence of a need for a soil quality applicable to a particular location, most modelers opt to place antennas above average soil. Alternatively, they may select a range of soils over which to run a model, ranging from very good down to very poor. The ARRL Antenna Book does allow the modeler to regionalize--but not to localize--soil conductivity through the U. S. map that it presents in Fig. 19 on page 3-14 of the 20th edition. True localization would require measurements, such as those described by K8LV.

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Between 1939 and the present day, numerous measurements of soil conditions have occurred--where soil also covers various waters and ices. In addition to the standard soil qualities of the early list, NSI software also offers users options appearing in Table 2, a second listing from the tutorial book. The list comes from many sources.

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The lists in the two tables differ somewhat in the extremes of non-water values. The traditional list shows a maximum conductivity (in very good soil) that is about 3 times higher than the highest land conductivity in the newer list. The highest values of relative permittivity also differ (20 vs. 30), but above about 20, higher permittivity values tend to show no significant performance increases. Note that the entry a "City industrial area" uses the same conductivity value as our contrived terrible soil, lower than the lowest conductivity in the traditional list by a factor of 10. Both lists show a minimum permittivity value of 3, which is considerably higher than the arbitrary value assigned to terrible soil.

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Perhaps the greatest contribution of the expanded table is the detailed listing of water and ice values. However, for any critical modeling, the modeler himself remains responsible for the figures entered. In all cases, any account that makes use of the model should not only present the values of conductivity and permittivity used with the model, but should also provide a good reason for using them. I have seen a few cases in which antennas have claimed some advantage over other designs, where the advantage rested mostly on an unproclaimed use of better soil conditions.

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In any writing that makes use of antenna models over soil, there are two errors to avoid. One is suddenly to change the soil quality while still making non-soil-related comparisons. The second is inadvertently to reverse the conductivity and permittivity entries for an intended level of soil quality. Table B shows what happens to our 40-meter monopole with 16 buried radials over average ground with correct and with reversed entries.

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+Table B.  NEC-4 modeling reports for a 40-meter monopole and 16 buried radials over average ground
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+Entry          Conductivity    Permittivity    Maximum Gain    TO Angle
+               S/m                             dBi             degrees
+Correct        0.005           13              -0.73           63/27
+Reversed       13              0.005            4.79           82/08
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However implausible the error sounds, it is far more common than most people wish to believe, according to models that I have reviewed over the years. (I withhold the modeler names to protect the embarrassed.)

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Fig 3 shows the radical difference in patterns. Note that a 40-meter monopole over perfect ground would show a maximum gain of about 5.2 dBi, with maximum gain along the horizon. The unreal value of conductivity (2.5 times the value of salt water) tends to override the very low value of permittivity. The value that we plugged in is in fact lower than the minimum relative value (1), but the program dutifully calculated a set of results.

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Conclusion

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These notes will supplement previous episodes concerning NEC's ground entry system for real ground values of conductivity and permittivity. However, the potpourri of ideas by no means counts as completing the story of ground as it applies to antennas. Researchers continue to search for calculation methods even more accurate than the SN system, which has proven quite trustworthy for a large class of cases. As well, experimenters continue to refine methods of measuring both conductivity and permittivity to allow more antenna users to obtain truly local information. (Of course, we must use an extended sense of what is truly local, since we are interested not only in the ground immediately beneath an antenna, but as well for a considerable number of wavelengths away in the region in which ground reflections occur in the formation of the far field.)

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We have not mentioned MININEC extensively in these notes, since the standard MININEC ground calculation system uses a truncated method that is generally inaccurate for antennas having any horizontal component that is less than 0.2 wavelength above ground. However, one implementation of MININEC, Antenna Model, has grafted the SN calculation system onto the MININEC core, with very good results down to virtually the same limits that the system has with NEC. However, the MININEC core does not permit buried wires. Hence, monopoles with radial systems must lie totally above ground.

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Those who wish to look more deeply into the SN ground calculation methods may consult the NEC-2 and NEC-4 manuals. The lists of references in those volumes will lead to seminal books and papers at least through the appearance of the programs.

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121. Radiation Patterns and Propagation

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L. B. Cebik, W4RNL

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A number of statements that we might correctly make about the far-field radiation patterns produced by NEC tend to strike a dull chord among newer modelers--if my e-mail over the years has been any kind of indicator. Many of these statements seem to run counter to experience or reports of experience in one or more ways. Most of the answers to the quandaries lie in the realm of distinguishing antenna phenomena as NEC models than from what happens to HF signals as they propagate via the ionosphere toward and from a communications target. Therefore, I shall devote this episode to seeing the differences that are crucial to understanding NEC's reports and communications reports without conflict.

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In the process of developing these notes, we shall encounter a number of highly simplified sketches--along with the usual collection of NEC-based graphics. The sketches are not designed to capture all of the nuances of propagation, but only to focus on certain features. However, ionospheric propagation is a very complex phenomenon (or collection of phenomena). Hence, for every detail that I include, I shall omit dozens of others that occur simultaneously.

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Are antennas truly reciprocal?

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Our first question seems to arise because when we communicate, we often find that reciprocity over a communications path seems not to apply as often as it does apply. We call stations that do not hear us, and we receive reports from third parties that another station is calling us although we cannot hear him. Even when we do manage to communicate in the HF range, the signal strengths may differ at each end of the line. As a result of these situations, one may naturally ask whether antennas are reciprocal.

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Note that we are addressing this question in very broad terms. Many a theoretical debate arises from time to time as to whether antennas are "really" capable of being reciprocal. However, we shall not in these notes engage the question at such a theoretical level.

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The entry-level software used by most modelers gives no clue to a proper answer to the question. Most entry-level software restricts the user to only one of the excitation possibilities, the direct voltage source (EX0) (or an indirect current source). For example, we might encounter a 6-element Yagi modeled in free space. The following lines define the model in ASCII format.

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+CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0 1 0 0 146. 0
+GN -1
+EX 0 2 11 0 1 0.
+RP 0 1 361 1500 90. 0. 1.00000 1.00000 0.
+EN
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The EX command line specifies that we apply a voltage source to the center segment of wire 2. In most entry-level programs, we then request a radiation pattern (RP0). Since the antenna is in free space, we request an azimuth pattern, which is technically an E-plane pattern. The result appears in Fig. 1. Note that the wire entries place the element spacing values in the Y columns, while the elements extend in the +X and -X directions. The conventions of the software used here (NSI's GNEC) place 0 degrees at the top of the polar plot. The pattern is a phi pattern (where a true azimuth pattern would increase the degree values clockwise). Hence, the main lobe of the antenna points to the left at 90 degrees phi. +
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The side panel in the figure provides the analytical data to accompany the normalized plot on a logarithmic scale. One reason that I selected this antenna was its free-space gain value of just over 10 dBi. For data-gathering purposes, the XNDA specification in the RP0 command is 1500. When N=5, the radiation pattern portion of the NEC output file produces an additional table. It lists for each value of phi and theta the antenna gain normalized to the peak gain of the antenna. The bearing of peak gain will read 0 dB, and all other gain values will be negative, indicating how much below the peak gain they are, as recording in dB. However, even a pattern like this one does not show why the antenna is or is not reciprocal, or even what reciprocity might mean.

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An antenna is reciprocal if its receiving pattern and its transmitting pattern are the same. We ordinarily record the transmitting pattern in dBi, or dB relative to an isotropic source. Normalized, the gain appears relative to a peak value of 0 dB. The counterpart to transmitting gain would be receiving sensitivity. More advanced versions of NEC offer a number of options for deriving receiving patterns. They involve the EX1 command for linear antennas, that is, providing the antenna with external excitation in the form of linear plane waves. We systematically rotate the excitation around the antenna in a series of steps. Then we invoke the PT command to record the relative current at a selected point--our former feedpoint. Fig. 2 shows in simplified form with only 8 positions for the EX1 command how the development of receiving patterns differs from the development of transmit patterns.

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A typical model might have the following appearance. Note that NEC has a limitation in how large a receiving matrix may be. Therefore, the data generation has two parts, one from -90 to +90 degrees, the other from 90 to 270 degrees. Fig. 1 tells us why we selected the division of the work. Since we shall request normalized data, each section of data must contain a peak gain/current point, which occurs at 90 degrees phi. The program then normalizes the data against this value. The PT3 command allows us to capture only the normalized current in dB at a selected segment, in this case, the same segment that we formerly used as the transmit source or feedpoint.

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+CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+PT 3 2 11 11
+EX 1 1 181 0 90 0 90 0 1 0 0
+XQ
+PT 3 2 11 11
+EX 1 1 181 0 -90 180 90 0 1 0 0
+XQ
+EN
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The data for both the transmitting pattern and the receiving pattern can be transferred to a spreadsheet for graphing. For both sets of data, we have 361 data points (from 0 to 360 degrees phi). Table 1 provides a glimpse of the data from 0 to 120 degrees for the 6-element Yagi in free space at 146 MHz. Three data points call for attention: 0, 180, and 360 degrees. Each of these points represents a free-space side null. Values for these nulls have two properties that are problematical for graphing. First, they may have very large negative values. Graphing such values may result is severe compression of the upper part of the graph. Second, the values are subject to large variations with very small differences in the rounded values of numbers that go into their development. For the sake of graphing, I have set these numbers to an artificially high value of -100 dB.

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If we conjoined the two graphs--one for the transmitting pattern and one for the receiving pattern--we obtain a result like Fig. 3.

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Computer-generated graphs "write" the curve for one color and then overwrite it with the second color line. The result for our test case is the nearly complete disappearance of the red line beneath the green. A few red "dots" appear as verification that the line is present. However, as both the graph and the table suggest, the normalized pattern graphs are as identical as one might find in any data generation system. In short, within the limits of our ability to calculate and present the results, the patterns for transmitting gain and for receiving sensitivity are the same. From the perspective of NEC, the antenna performance is reciprocal with respect to transmitting and receiving.

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For further information on the use of the EX command in conjunction with the PT command to develop receiving patterns and information, see episode 88 of this series.

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Why do we continue to claim that a horizontal antenna performs better as we increase height? When we increase the height of an antenna from 1/2 wavelength to 1 wavelength, we find a high-angle lobe that simply wastes power.

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The question arises from looking at independent normalized elevation patterns for the same antenna at different heights. Fig. 4 captures the situation, so let's us see what might mislead a novice pattern reader.

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If we examine the patterns without reference to the numerical data and without some important external data, we might easily reach the same conclusion that prompted the question. The elevation plot for the Yagi at a height of 1/2 wavelength seems to contain more energy, and the forward pattern forms a continuous whole. Hence, more energy seems to be concentrated at lower elevation angles. In contrast, the pattern for a height of 1 wavelength contains two lobes with a very deep null between them. The upper lobe has a center angle of about 45 degrees, well above the elevation angles at which we find skip except under the most unusual conditions. The lower lobe has a narrower vertical beamwidth than we find in the forward lobe for the pattern at a height of 1/2 wavelength. In the abstract, then, the pattern for a height of 1 wavelength appears to be distinctly inferior.

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To determine if appearances are true or deceiving, we can do one of two things--or both. We can refer to the numerical data. Or, we may overlay the pattern so that their relative strengths become apparent. Fig. 5 provides the overlaid patterns (using EZNEC software) along with some supplementary data that NEC does not and cannot calculate.

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The portion of the figure that NEC does calculate shows the relative proportions of the two patterns. If we assume that the azimuth patterns for the two heights are similar to each other (and we may always check by looking at those patterns), the energy within the cross-sections of the elevation patterns is about the same. However, most of the energy in the pattern for the lower height is directed at higher angles relative to the lower of the two lobes that form the pattern for the upper height. Below about 15 degrees elevation, the higher antenna shows a significantly stronger radiation pattern (and by virtue of our earlier discussion, a more sensitive receiving pattern).

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At this point, we must combine the data from NEC with information derived from other sources. For example, extensive studies by Dean Straw, N6BV, have shown that most long-distance (DX) HF signals arrive at very low levels, as suggested in the additions to the patterns at the far right of Fig. 5. (The N6BV information is included with recent editions of The ARRL Antenna Book.) Despite the seeming waste of energy in the elevation region around 45 degrees, the higher antenna's lower lobe better intercepts the propagation angles at which much, if not most, long-distance HF energy arrives and departs. Indeed, the prime angles might even favor raising the horizontal antenna further.

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We have reached a certain "interface." NEC calculations produce patterns based on a set of constant conditions in the far-field region of the antenna, that is, from several wavelengths beyond the limits of the antenna outward. However, it says nothing about what occurs to either radiated or incoming energy that is a function of variables within the far field region. Moreover, NEC says nothing about nearer influences unless we expressly model them.

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Why can I sometimes hear a station but not be heard by them--and vice versa--at both HF and VHF frequencies?

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At HF, the vast majority of signals that we receive (and our return transmitted signals) undergo ionospheric refraction so long as the ionosphere is sufficiently ionized to allow refraction. This simple statement involves us in the very complex field of propagation. On an average day--depending on the time of day, the month of the year, and the strength of the sun's ionizing UV radiation--we find many ionized layers. Many monthly columns exist in journals that go into various details about the actions of these layers under the many combinations of influences. We shall not try to replicate those studies here. Indeed, if you wish to predict ionospheric conditions to assist your own operation, you may find considerable benefit in obtaining one of the programs that use VOACAP or similar calculation engines to develop profiles of the most probable propagation conditions for paths that you specify.

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Here, we can concentrate on the daytime F2 layer, which has perhaps the greatest influence on the path of long-distance HF signals. Fig. 6 provides a partial answer to our question of why HF signals have different strengths in each direction. They simple take slightly different elevation paths over the distance between two stations. It is possible for the two stations to have equal strengths, to have unequal strengths, or for one to be on target while the other is wholly off target.

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What the figure does not show is one of the reasons for the condition shown. The position of the sun relative to the path determines the strength of ionization all along the path. The strength of ionization influences the angle of refraction and how far through the ionized layer that energy travels before departing downward. (The strength of ionization also determines how much energy passes through the ionosphere to be lost into outer space and at what angles relative to the two stations and to the intermediate ground-reflection region. The ground reflection region near the center of the figure may also show differences in losses depending on whether the region is over dry land or salt water.)

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On a "normal" morning in the U.S., one might expect to hear first stations from eastern Europe. As the morning moves onward (or as the European afternoon moves onward), the strongest stations appear to come from western European areas. Very often, however, the western European stations could hear my U.S. signals earlier in the day (from various inland locations, such as Tennessee or Nebraska), but would call in vain for a reply. Their transmitted skip was landing somewhere other than at my location. However, as the sun moved, those signal began intercepting my antenna, while the more eastern stations in Europe faded.

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All of these phenomena occur beyond the limits of what NEC calculates as the antenna pattern. At best, we can arrange our models to produce patterns that are most likely to transmit and intercept signals at the most favored angles--or to understand why the limitations of our feasible installation will fall short of the ideal elevation angles. However, NEC will not take propagation effects into account.

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Even at VHF and UHF, there are a myriad of influences that NEC usually does not take into account. Some of these factors we may model and some fall outside of feasible modeling. For example, the antenna support structure may affect performance, and we may (often with some difficulty) model this structure. At a slightly larger distance from the antenna, but still close by, we find a myriad of objects that we often refer to as "clutter." The ground clutter may include power line, poles, trees, buildings, and other items too varied to list. If we view these objects as significant, we may always try to model them. However, the level of conductivity and the actual structure of the most conductive parts may not be visible.

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Modeling objects at a distance is standard engineering practice in some enterprises. For example, the potential of cell towers for distorting AM BC radiation patterns requires careful analysis within which modeling both the broadcast tower and the somewhat distant cell-phone tower plays a significant role.

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VHF and UHF line-of-sight communications often encounters terrain and building effects at further distances than we might use for counting ground clutter. Edge diffraction that "bends" radio waves into otherwise dark areas by a wall-like or knife-edge object may not appear in both directions for an intended communications path. In fact, diffraction may also affect the elevation patterns of HF antennas. For further information on these optically-related wave phenomena, see Chapters 3 and 23 of the most recent edition of The ARRL Antenna Book. One passage in Chapter 3 refers to the analysis of these phenomena as a limitation of NEC's flat-ground mode of analysis. The point being made is that NEC does not model everything. In some cases, we may incorporate some distant objects within the model, but often a wire grid stand-in--with the wires assigned a general conductivity that reflects the materials of the object--fails to act like the real object within the radiation pattern field. When it comes to propagation, there is no practical way to model its effects within NEC.

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When I communicate with stations along a coastline, I often acquire stronger signals with my antenna pointed somewhat off shore than when I align it with the station's geographic location? Is the NEC radiation pattern in error?

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Although this question seems unrelated to the ones that we have been addressing, it is actually a variation of the earlier questions. Once more, the effect is not a part of what NEC can calculate, but is instead a function of propagation phenomena. One term that we have used is the idea of a "ray," a representation of radiated energy as a straight line. In the ionosphere, we find that the ray is refracted in some kind of arc--if the angle is not too severe and the ionization is not either too weak or too strong--so that it re-emerges on a downward slope toward a communications target. The simplified portrait of rays appears in the upper portion of Fig. 7.

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The lower portion of the figure is also an oversimplification, but may be good enough to get across a general idea of some importance. Rays are not like bullets, although we often portray them that way. When the energy reaches the ionosphere, it disperses. Some is lost. Some is absorbed. Some proceeds along one of several directions that would support refraction for re-entry downward. Any single component may undergo many dispersions, usually continuously along the path through the ionosphere. The result is a downward "spray" of energy. The actual signal that we receive is the statistical sum of all of the effects. If that sum is strong enough at the reception site, then we have at least half the conditions needed for successful communications. (For a broadcast station, this one-way analysis may be all that we need, since the only goal is reception.)

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Dispersion effects are not only elevation phenomena. They also occur laterally, as suggested by Fig. 8. Once more, I have over-simplified the sketch so as not to lose the lines in a uniform gray mass. The actual dispersion effects are relatively continuous, rather then being stepped as shown in the sketch. Once more, what emerges as the downward energy will be--with respect to the target location--a statistical sum of all of the effects at work.

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Note that from a lateral perspective, the received signal may come from directions that have diverse azimuth bearings from the target location. Now let us suppose that at least some of the energy had to use two "hops" to reach the target. Reflections from dry ground tend to be lossier than reflections from salt water. Hence, we may find, at least on some occasions, that an off-shore antenna direction may produce stronger signals (in one or both directions) than a straight-line or great-circle bearing. The NEC radiation pattern would be correct in indicating the direction of the strongest signal. However, propagation effects would place the direction of the signal at a bearing that might not coincide with the actual target station location. Indeed, I am not aware that current propagation software takes this effect into account. Like NEC itself, propagation software has its calculating limitations.

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Conclusion

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These simple notes are no substitute for a proper study of the propagation of radio waves in any frequency region of interest. Rather, the notes have been designed to show in a somewhat rudimentary way what the NEC radiation patterns can and cannot tell us. With a flat ground and an ideal medium above ground, they give an accurate portrayal of both transmitting and receiving patterns for the class of antennas that we may model on the software.

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However, those patterns cannot tell us anything about phenomena that modify the patterns once energy leaves the antenna on transmission or before it arrives at the antenna on reception. We have distinguished two general categories of modification. One set includes objects that we might attempt to include within the model, whatever the difficulty we may have in arriving at adequate models of those structures. The other set of modifying phenomena we have no hope of capturing with NEC, namely, all of the possible influences of propagation. Our survey of propagation effects is both over-simplified and incomplete. We only examined a few facets of propagation that have a relationship to questions often raised by newer modelers as they try to connect NEC radiation patterns with communications experience. Understanding propagation may be more complex than understanding antenna modeling. Hence, these notes are not suitable for conversion into sound bites that may easily mislead you when you take them out of context. Rather, the notes form a suggestion for the study of a set of phenomena that play the major role in what goes on between antennas.

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The bottom line is that NEC radiation patterns give us useful information about a subject antenna. However, there is much in the use of that antenna that NEC cannot (and was never designed to) tell us.

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Go to Main Index

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122. Reciprocity: Home on the Range

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L. B. Cebik, W4RNL

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The ARRL Antenna Book (20th Ed., p. 2-1) contains a beginner's discursive explanation of reciprocity. "In the same fashion that a loudspeaker can act as a microphone, a radio antenna also follows the principle of reciprocity. In other words, an antenna can transmit as well as receive signals." This brief extract follows an explanation of an antenna as a "special transducer" capable of converting RF current into propagating electromagnetic waves and converting intercepted waves into electrical current. The context is the very beginning of a chapter called "Antenna Fundamentals." Hence, we should not expect mathematical sophistication.

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More mathematically inclined readers may wish to consult various college-level antenna texts. I keep a small number on my shelf as references, for example, Stutzman and Thiele, Antenna Theory and Design (2nd Ed., pp. 404-409), and Balanis, Antenna Theory: Analysis and Design (2nd Ed., pp. 127-132). I have listed the most relevant pages of each text for a reason. Balanis discusses reciprocity early in the text's development, but Stutzman and Thiele defer the treatment until late in the text. We shall have occasion to note the Stutzman and Thiele placement later. Both treatments share a common kernel, the development of antenna reciprocity from the Lorentz reciprocity theorem, which itself derives from Maxwell's equations. (Those comfortable with calculus may wish to compare the Stutzman and Thiele equation 9-36 with Balanis' equation 3-66.)

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A better-known text among amateur radio operators is Kraus, Antennas (2nd Ed., pp. 410-413). One interesting aspect of the Kraus treatment is that he uses a different starting point for his development of reciprocity. He begins with the Rayleigh-Helmholtz reciprocity theorem as generalized in the 1920s by J. R. Carson. (Rayleigh's initial context of sound is not unrelated to the ARRL basic analogy between antennas and loudspeakers.) Without ado, Kraus expresses the theorem in the following terms: "If an emf is applied to the terminals of an antenna A and the current measured at the terminals of another antenna B, then an equal current (in both amplitude and phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B." (p.411) Fig. 1 provides a graphic representation of the terms of the theorem.

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Kraus goes on to note some of the limiting conditions in which the theorem applies. Of course, the frequency of the applied emf (or voltage) must by the same, and the media must be "linear, passive and also isotropic." For our purposes in evaluating whether NEC honors reciprocity, the following note is critical: "An important consequence of this theorem is the fact that under these conditions the transmitting and receiving patterns of an antenna are the same."

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Kraus' statement gave us something that we could test and demonstrate within NEC, as we did in episodes 88 and 121 of this series. By using plane wave excitation (EX1) and checking the current magnitude at the wire segment that would serve as the source in a transmitted pattern, we were able to develop a receiving pattern. When we normalize both the transmit and the receive patterns, they formed a virtually perfect overlay. However, the demonstration required us to use portions of the NEC command set that are not generally available in entry-level software, such as basic EZNEC and NEC-Win Plus. These programs generally require us to use a voltage source (or an indirect current source) and they yield transmit patterns, that is, far-field data.

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The question for this episode is whether we can achieve the same goal of demonstrating reciprocity within NEC using only the tools generally available in entry-level software. With a little ingenuity, we can arrive at comparable results. In the process, we may also come to appreciate better the terms of reciprocity within NEC calculations.

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Home on the Range with Dipoles in Free Space

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We may model the Carson version of the reciprocity theorem simply by using two antennas and separating them by a considerable distance. Our basic models will use a number of simplifying conditions to prevent potential confusions introduced by intervening variables. For example, we shall use lossless or perfect wire in the models. Our first examples will use a free-space environment so that ground reflections and losses do not play a role in the development of data. Because the frequency is convenient for later purposes, we shall set the test antennas at 146 MHz, although any frequency will do as well. The initial two test antennas will be resonant (technically, near-resonant) dipoles. Each dipole is 38.3" long with a 0.1875" diameter. So long as the distance between the dipoles places them in the far field of each other, it would be adequate. Arbitrarily, I selected a distance of 1 mile (5280', 63360", 1609.344 m, 783.7366 wavelengths). Distance will affect the numbers that we gather, but not the principles involved. Fig. 2 shows the general outline of the modeling set-up.

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The following model in ASCII format shows the basic set-up. The dimensions are in meters.

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+CM dpl-dpl 1 mile fs
+CE
+GW 1,21,0.,-.48641,0.,0.,.48641,0.,.0023813
+GW 2,21,1609.344,-.48641,0.,1609.344,.48641,0.,.0023813
+GE 0
+FR 0,1,0,0,146.
+GN -1
+EX 0,1,11,0,200,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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For reference only, Fig. 3 shows the dipole pattern. The analysis panel provides the transmit performance data with one exception. The source impedance is 71.941 + j0.515 Ohms. Both antennas shown in Fig. 2 will be identical dipoles. As the pattern suggests, the NEC runs occurred on NSI software, specifically GNEC and NEC-4. However, for this and all following steps, any version of NEC will do.

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The transmit pattern is only background information for our real goal, the reading of the reported current on the center segment of the un-excited dipole. In terms of the model shown, we shall be interested in GW 2, segment 11. The NEC output report provides a table of current values for each segment within a model (unless the user selects a specific command to suppress printing them). We shall be using data for which most NEC implementations do not provide graphing capabilities, so we may expect to use alternative means to present the information.

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Special Note about EZNEC: NEC makes use of input and output voltage and current peak values. EZNEC uses RMS values for input and output voltages and currents. If we assign a specific numeric voltage value to an EZNEC source, we shall receive a certain numeric value for any segment current in its current table. These numeric values will coincide with those that NEC produces in other software if we remember that EZNEC up-converts to peak value at the start of the core run and then down-converts back to RMS in its output files.

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We are now prepared to look at some interesting cases involving reciprocity.

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Assessing the Receiving Pattern Shape

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In our initial notes on reciprocity, we noted that Stutzman and Thiele defer their account until late in the text, specifically in a chapter devoted to antenna testing and measurement. If reciprocity is correct, then we may test an antenna on a proper range using any of the 4 systems shown in Fig. 4. The top two versions of the test are complex and inconvenient. However, a version of the system at the upper left is commonly used with fixed broadcast towers by taking periodic field-strength readings at ground level and specified distances from the installation. The lower two versions of the test are more common for range tests used by manufacturers.

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We may evaluate the pattern of the dipoles in the model shown earlier by rotating either the excited or the un-excited antenna in useful increments. In fact, we may do both in succession and compare results. We might use 10-degree increments and confine the range of rotation to 90 degrees, since we expect two orders of symmetry in the pattern. A range would likely rotate one of the antennas through a complete cycle and perhaps trace the pattern continuously rather than using our stepped procedure.

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Since the two antennas are 1 mile apart in the model, I have arbitrarily raised the excitation voltage to 200 V pk, or a power level of 278 watts. (We shall shortly examine the question of the source voltage.) For pattern evaluation, we need not concern ourselves with the fact that the receiving antenna does not have a load that represents the feedpoint impedance. Instead, we shall concern ourselves with accurately rotating each antenna (in turn) in 10-degree increments and recording the magnitude and phase of the current on the center segment of the receiving antenna. Table 1 records the results of our rotational tests. NEC, of course, reports using engineering notation to maximize the number of significant digits in the smallest possible printing space. Indeed, an 8-unit printing space for any report value is standard in NEC tables.

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As the table shows, it does not matter whether we rotate the transmitting dipole or the receiving dipole, since we obtain identical results in both cases. (The deep null at 90 degrees is the only place where we find a minuscule difference in the calculated phase angle of the current.) The values appear plausible as reflections of the transmit pattern for the dipole. Since appearances may sometimes deceive, we should likely see if we can confirm the actual pattern shape. The pattern in Fig. 3 is a normalized pattern given in decibels. It has a convenient checkpoint in the pattern analysis information: at 40 degrees, the pattern should show a deficit of 3.13 dB relative to maximum gain.

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At this point, we may introduce the only significant external calculation that we need to make throughout these proceedings. We may convert ratios of current into gain values in dB by reference to the following common equation"

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If we let the current at 0 degrees be I1 and the current at 40 degrees be I2, we obtain a gain differential of 3.1297 dB. Since the half-power points coincide between the transmit radiation pattern and the receive patterns using either method of rotation, we can satisfy ourselves that the dipole patterns are the same in both modes of use. If we still have doubts, we may trace the normalized gain of the transmit radiation pattern at 10-degree increments and perform the same calculation at every one of them.

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Transmit Voltage and Receive Current

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Newer modelers are very often relatively new students to antennas. Therefore, it may be useful to employ the double-dipole range model in a second way. Let's allow the two dipoles to face each other, that is, be broadside to broadside. In this test or demonstration, we shall be paying close attention to the terms in which Carson expresses reciprocity: "If an emf is applied to the terminals of an antenna A and the current measured at the terminals of another antenna B, then an equal current (in both amplitude and phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B."

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A common misunderstanding of antennas is that the current at the receiving antenna will be proportional to the power applied to the transmit antenna, assuming that we have an unchanging set of antennas in an equally unchanging environment. However, as noted in the reciprocity theorem, the received current, as sampled at the erstwhile feedpoint of the receiving antenna, will be proportional to the feedpoint voltage at the transmitting antenna. Therefore, according to the theorem (and, of course, a good bit of other basic antenna theory), if we halve the transmitting antenna voltage, we should also halve the receiving current.

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We may measure (or model) the current in two ways. One way is to continue to use no load at the feedpoint segment of the receiving dipole. The other method is to use a matched load on the feedpoint segment. From our transmitting model, we know that the feedpoint impedance is 72.941 + j0.515 Ohms. We may introduce this load to the receiving dipole model by adding one line to the model itself. The LD 4 complex load command provides all that we need.

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+CM dpl-dpl 1 mile fs with receiving antenna load
+CE
+GW 1,21,0.,-.48641,0.,0.,.48641,0.,.0023813
+GW 2,21,1609.344,-.48641,0.,1609.344,.48641,0.,.0023813
+GE 0
+LD 4,2,11,11,71.941,.515
+FR 0,1,0,0,146.
+GN -1
+EX 0,1,11,0,200,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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Let's use source (EX 0) peak voltages of 200, 100, and 50 volts to see what we obtain at the receiving antenna under both conditions. The NEC output file provides the current values as two sets: one pair of values providing real and imaginary numbers, the other pair of values listing the magnitude and phase angle. Table 2 shows what the model reports.

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In my table transcriptions, I have also recorded the NEC report of the antenna input power. For each halving of the source voltage, the resulting power is 1/4 the previous value. In contrast, the receiving current progressions are exactly in step with the applied transmitting voltage. Halving the voltage value produces half the peak current in each of the report columns. Of course, in the model set-up, proportional changes of the real and imaginary components of the current result in the same phase angle throughout.

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In a number of e-mails that I have received regarding test-range models, the writer will inquire whether the receive antenna requires a load. The two sections of the table suggest one sort of answer. Installing a perfect load on the receiving antenna, that is, a load the matches the impedance of the antenna at that segment, results in current values that are exactly 1/2 the values recorded without the load. In this case, we obtained the load value by examining a transmitting version of the model and noting the source impedance. In some cases, one may wish to use a standard load, regardless of the feedpoint impedance. 50 Ohms is a common value. Unless the antenna happens to have a feedpoint impedance of 50 Ohms, expect a different set of current values.

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Home on the Range with Monopoles over Perfect Ground

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We may replicate the model set-up using monopoles over perfect ground instead of dipoles in free space. Since perfect ground pattern calculations use standard image techniques, we do not create any intervening variables to disturb the basic NEC processes. In fact, we may set up a resonant monopole using the same materials (19.15" of 3/16" diameter lossless wire) that we used for the dipoles. The following lines record a reference monopole in .NEC format.

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+CM monopole perfect ground
+CE
+GW 1,21,0.,0.,0.,0.,0.,.48641,.0023813
+GE 1
+FR 0,1,0,0,146.
+GN 1
+EX 0 1 1 0 200.00000  0.00000
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
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Fig. 5 shows the standard theta radiation pattern, while the side-bar provides most of the reference data that we may need. We may bypass an analysis of the received pattern shape by noting its near identity to one-half of a free-space dipole pattern. If you compare Fig. 5 to Fig. 3, you will find that the half power point is 40 degrees away from the angle of maximum gain in both cases. The reported impedance for the monopole is 36.146 + j0.833 Ohms. The value is very close to but not exactly half the dipole value. The dipole feedpoint occurs at the exact center of the antenna. The corresponding point on the monopole would be where the wire intersects ground level (Z=0). Since that position is not available, the monopole's feedpoint is on the closest segment (of the 21 segments on the wire) to ground, which places it very slightly off the virtual center point.

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Transmit Voltage and Receive Current

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Although we have introduced a perfect ground and shrunk the antennas into monopoles, we may otherwise use the same basic "range" model used for the dipoles. Fig. 6 outlines its basic dimensions. Since a monopole's phi pattern will be circular, we may ignore the pattern analysis step that we used with the dipole and turn directly to an examination of transmitted voltages and received currents.

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The test uses the same procedures invoked earlier. We shall begin with no load on the receive monopole feedpoint and later add a matched load of 36.146 + j0.833 Ohms. Within each data set, we shall begin with a source voltage of 200 volts peak and reduce it to 100 and then to 50 volts. Table 3 supplies the data from the NEC output report current tables.

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Based upon our dipole tests, the monopole data meets our emerging expectations. Halving the transmit antenna source voltage halves the receive antenna's feedpoint current. Because we are using only a finite number of decimal places in the calculation steps, we notice a very tiny numerical difference between corresponding steps in the I-imaginary column, just enough to change the phase angle by 0.001 degree.

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Dipole vs. Monopole Gain

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If we refer to the standard radiation patterns, we note that the monopole maximum gain is 3 dB greater than the maximum gain of the dipole in free space due to the addition of ground reflections as simulated by image calculation techniques. We may fairly ask if we can find the same gain in the receiving current data.

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The answer is affirmative if we do not leap directly into comparing the two receiving antennas in terms of the reported currents converted into dB values. Each current report occurs with reference to a particular feedpoint impedance. Therefore, we should first convert corresponding dipole and monopole current readings into power levels and then use the power version of the gain equation. Let's use the current magnitude values for a 200-volt source and a matched load in each case. The quick hand-calculator steps would have the following appearance.

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+P1 = I^2 R = (9.1530e-4)^2 * 36.146 = 3.0282e-5
+P2 = I^2 R = (4.6095e-4)^2 * 71.941 = 1.5286e-5
+Gain = 10 log(P1/P2) = 10 log(1.9811) = 2.969 dB
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The monopole over perfect ground (ignoring the slight difference in the current phase angles) has a 3-dB gain over the free-space dipole.

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More Complex Patterns

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In the preceding episode of this series, we compared the transmit and receive patterns of a 6-element Yagi using a standard transmit format (EX 0 and RP 0 commands) followed by a normalized receive pattern created by using an EX 1 and a PT 3 command. The final step in our range-test exercise will be to see whether we can replicate the results using transmit and receive patterns that substitute for the plane-wave excitation.

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The first step is to re-create the 6-element Yagi used in the preceding episode.

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+CM 6-el 2M Yagi
+CE
+GW 1,21,-.6885686,.514604,0.,-.6885686,-.514604,0.,.0023813
+GW 2,21,-.4312666,.5075174,0.,-.4312666,-.5075174,0.,.0023813
+GW 3,21,-.3247898,.4746752,0.,-.3247898,-.4746752,0.,.0023813
+GW 4,21,-.0300482,.461137,0.,-.0300482,-.461137,0.,.0023813
+GW 5,21,.2583942,.461137,0.,.2583942,-.461137,0.,.0023813
+GW 6,21,.6885684,.443992,0.,.6885684,-.443992,0.,.0023813
+GE 0
+FR 0,1,0,0,146.
+GN -1
+EX 0,2,11,0,1,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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Fig. 7 shows the Yagi pattern using the normal EX 0 and RP 0 combination of commands. The gain is 10.29 dBi. The Yagi provides us with more than one check point for verifying that the receive pattern is the same as the transmit pattern without resorting to developing an external polar plot. The 180-degree front-to-back ratio is 35.98 dB. Not shown in the analysis is the worst-case front-to-back ratio (which may also be called the front-to-sidelobe ratio). The reported value is 24.28 dB. Finally, we have the half-power or 3-dB point at 27 degrees from the main forward lobe heading. For reference, the feedpoint or source impedance is 50.00 + j9.53 Ohms.

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Assessing the Receiving Pattern Shape

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To evaluate the receiving pattern shape, we shall create a free-space range set-up identical to the one that we used for the dipole. The Yagi and the other range antenna (a dipole) will be 1 mile apart. We shall rotate the Yagi by adding a convenient GM command to the .NEC-format input or model file. However, entry-level software provides external convenient rotating means. The following model is one of two that we shall use.

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+CM 6-el 2M Yagi and dipole
+CE
+GW 1,21,-.6885686,.514604,0.,-.6885686,-.514604,0.,.0023813
+GW 2,21,-.4312666,.5075174,0.,-.4312666,-.5075174,0.,.0023813
+GW 3,21,-.3247898,.4746752,0.,-.3247898,-.4746752,0.,.0023813
+GW 4,21,-.0300482,.461137,0.,-.0300482,-.461137,0.,.0023813
+GW 5,21,.2583942,.461137,0.,.2583942,-.461137,0.,.0023813
+GW 6,21,.6885684,.443992,0.,.6885684,-.443992,0.,.0023813
+GM 0 0 0 0 00 0 0 0 1 1 6 21
+GW 7,21,1609.344,-.48641,0.,1609.344,.48641,0.,.0023813
+GE 0
+FR 0,1,0,0,146.
+LD 4 7 11 11 71.941 0.515
+GN -1
+EX 0 2 11 0 200.00000  0.00000
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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The dipole is GW 7. The GM line above it rotates the Yagi by changing the 00 entry to a number of degrees. We shall use 10-degree increments. However, since the Yagi pattern is symmetrical along only 1 axis, we shall work from 0 to 180 degrees. As we did in the case of the dipole, we shall use a 200 volt (peak) source voltage.

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The EX 0 command shows that the source is on wire 2 of the Yagi. Note that the LD 4 command places a matched load on the dipole, where we derive the load value from the source impedance of the dipole in a transmit set-up (71.94 + j0.52 Ohms). We read the current from the segment specified by the load. The alternative situation is to place the source on the dipole (wire 7, segment 11), and move the load to the Yagi (wire 2, segment 11). When we move the load, we also change its value to the Yagi matched value of 50.00 + j9.53 Ohms.

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Table 4 records the data from the two runs. In both cases, we rotate the Yagi. However, the left data columns record the current on the dipole feedpoint when the Yagi transmits. The right data columns record the current at the Yagi feedpoint when the dipole transmits. Fig. 8 shows the general scheme of what the pattern assessment demonstrates.

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The first notable fact about the demonstration data is the virtual identity of the received current values using the same source excitation voltage, regardless of which antenna transmits and which receives. We may also note that the current at 180 degrees is slightly higher than the current at 170 degrees, which corresponds to a slight rearward increase in transmit gain at 180 degrees for the Yagi when modeled alone.

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However, to confirm that the pattern in the receive mode on the range test coincides with the standard transmit pattern of Fig. 7, we need further check points. We may apply the same sort of gain calculations that we used with the dipole, but more points of reference on the pattern. For example, we may compare the maximum current at zero degrees with the current at 180 degrees to see if the value coincides with the front-to-back ratio. As well, we may perform the same calculation with respect to the front-to-sidelobe (or worst-case front-to-back ratio). In this case, the heading of the standard value is 126 degrees, so we may use the closest recorded heading, 130 degrees. Finally, as we did for the dipole, we may bracket the half-power points using the values at 20 and 30 degrees for the 27-degree heading of the half-power point. Moreover, we may use either set of currents--or both for the sake of demonstration. Table 5 shows the results of the calculations.

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The result show that the range set-up not only confirms that NEC honors reciprocity, but as well, that range testing is in principle a reliable way to determine that shape and relative strength of an antenna pattern. Of course, range testing was in use long before NEC was born, but we have nearly a generation of antenna modelers who may never have seen an antenna test range in operation. Hence, the NEC demonstration provides a means for a modeler to teach himself or herself what range testing involves--minus certain intervening variables, of course.

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Yagi Forward Gain

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All that we lack to complete the data--at least as far as this simplified demonstration goes--is the forward gain of the Yagi. We have already compared the gain of a dipole in free space to a monopole over ground. We may apply the same procedures to comparing a free-space dipole to a Yagi when both are in free space. Fig. 9 shows the model set-ups.

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We already have the necessary data for both the dipole and the Yagi when both test set-ups use the same excitation voltage. Since the antennas have different impedances, we cannot simply compare current data. However, by using the current and impedance information together, we can obtain appropriate power values and then use the dB-conversion equation to obtain the gain of the Yagi over the dipole. The following calculation uses data for a 200-volt source.

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+P1 = I^2 R = (1.3928e-3)^2 * 50.003 = 9.7000e-5
+P2 = I^2 R = (4.6163e-4)^2 * 71.941 = 1.5331e-5
+Gain = 10 log(P1/P2) = 10 log(6.3272) = 8.012 dB
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These calculations are slightly simplified in view of the relatively small phase angles involved. However, the Yagi shows a gain of about 8.0 dBd(r), that is, 8.0 dB over a dipole under identical range conditions.

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Conclusion

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These small and simple demonstrations illustrate several facets of modeling of which the beginning modeler may not be aware. First, they show that one may model reciprocity without requiring plane-wave excitation and receive patterns. The methods used here make use only of the facilities available on the most basic entry-level software.

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Second, if we approach antennas--as so many amateur radio operators do--without a thorough grounding in antenna basics, we may use NEC software to teach ourselves various fundamental principles. In this instance, we have explored the terms of the reciprocity theorem at a practical level. (College texts can provide additional grounding at a level that is even more fundamental.)

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Third, we may also look at modeling as an analog to range testing when we correctly set up a model. Moreover, we may expand the range-testing set-up to examine the effects of structures on antenna patterns, correlating the currents in such an intervening structure to the modifications it may make in a radiation pattern without the structure.

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Our little exercise that began in seeming pursuit of reciprocity has had much to teach us about antennas and antenna modeling that extends far beyond reciprocity itself.

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123. Radiating and Transmission-Line Currents

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L. B. Cebik, W4RNL

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In episode 100 of this series, we examined the modeling work-around often used to test a coaxial-cable-fed antenna for common mode currents. However, we seem to have no comparable work-around for detecting common-mode currents when we use parallel transmission lines. In fact, the help screens that accompany EZNEC record the following statement: "I don't know of any way to accurately model common-mode effects on a two-wire transmission line (that is, how to model a radiating two-wire line). If it's necessary to do this, the line will have to be modeled as two parallel wires."

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Interestingly, if we model a resonant dipole and a resonant folded dipole at the same frequency, we may examine the current tables and discover that the current magnitudes and phase angles that we encounter seem to have very little in common. We can perform the same test with a folded monopole and a single-wire monopole. The results will be the same. Both of the single-wire antennas will show a near-cosine-wave decrease in current magnitude as we move from the feedpoint to the wire end, and the phase angle will change by only a few degrees. The folded versions show current values very different from the single-wire models.

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Fig. 1 shows the physical arrangement of both the parallel transmission line and the folded dipole. It also raises the question of what these two structures have in common, besides the parallel wires, of course. The answer is quite straightforward. The currents that we record in models are actually composites of two types of currents. Because we have closely spaced wires that form transmission lines in both cases, we should expect to find transmission-line currents (IT. At any selected pair of point directly opposite each other along the line-pair, we should find current magnitudes that are equal, but with phase components that are 180 degrees opposite.

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If the current values that we record in our model (assuming a reasonably well constructed model) do not meet this condition, then we also have radiation currents (IR). Radiation currents have the same phase angle on both wires. When we encounter them on the antenna structure proper, such as along a folded dipole, we find the currents that are effective in making the wire structure an antenna. When we encounter them on a parallel transmission line, we usually (but not always) groan, since we generally do not wish our feedlines to radiate. As well, such currents, unless remediated, can created a number of problems at the equipment end of the feedline. Under these conditions, we tend to call radiation currents by a different name: common-mode currents. However, we are still talking about radiation currents.

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The radiation currents that we find on parallel transmission lines are the same as the currents that we sometimes find on the outer surface of the outer conductor in a coaxial cable. However, skin effect gives transmission-line and radiation currents separate paths in a coaxial cable. This condition also changes the methods of remediation or control of those currents, since we may introduce methods of attenuating the common-mode currents without affecting the transmission-line currents. When we have a parallel transmission line, we have difficulty sorting out the two types of currents, let alone attenuating one type without affecting the other type. Antenna models that create parallel transmission lines using wires will record only the composite current values.

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Externally Calculating Radiation and Transmission-Line Currents

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As much as we might wish our NEC and MININEC software to perform all antenna and feedline calculations for us, there are many useful calculations that we must perform externally to the core computations. Some are so widely used that those who implement NEC and MININEC often include them in their packages. Typical examples are the SWR calculations on which we rely. Some packages also include the calculation of the left-hand and right-hand components of circular polarization. Both of these calculations are further derivations from the output results of the core and not performed by the core itself.

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No package (to my knowledge) includes the calculation of transmission-line and radiation (common-mode) currents as a post-core facility. Therefore, if we wish to separate the two current components of parallel wires--whether as part of the antenna or as part of a modeled transmission line--we shall have to set up a spreadsheet or similar calculating convenience. The technique that we shall use derives from the account of "The Hairpin Monopole" in Kuecken's classic Antennas and Transmission Lines, pp. 224 ff. We shall have to modify the procedure to coincide with the way in which we set up the parallel wires in a model.

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Fig. 2 shows the two possibilities. On the left we have the procedure that I have arbitrarily called parallel segmentation. In this case, we start each of the parallel wires at some coordinate and move both wires in steps, either down-up or left-right. The alternative modeling convention, on the right in the figure, we can call serial segmentation. In this case, we tend to create wires "around the horn," so that end 2 of each wire in the model coincides with end 1 of the succeeding wire.

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If we model a simple structure, say a folded monopole over perfect ground, we may view the relative current magnitudes, as shown in Fig. 3. Viewing current magnitude alone will yield no differences in the portrait under each of the modeling alternatives. The only significant difference between the current tables for the alternative modeling conventions would appear in column that lists the current phase angle.

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To determine which of the following procedures that we should use, we must rely on the list of wires in the model. Fig. 4 shows the alternative wire tables that we obtain by each method, using our simple folded monopole over perfect ground. The tables come from EZNEC software.

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In the following notes, I shall present the requirements for setting up a calculation aid in rather more detail than required by engineers. However, many newer models, including radio amateurs, are keenly interested in radiation and common-mode currents. Hence, a little extra guidance is in order.

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The Calculations for Parallel Segmentation

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When we use a parallel-segmentation structure for parallel wires within an antenna element or a modeled transmission line, we begin with the basic relationship of the currents on the two wires (A and B) at any facing point along the parallel line.

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With the lines segmented in parallel, the current on line A is the sum of the radiation and the transmission-line currents. The current on line B is the difference of the two currents, with the transmission-line current subtracted from the radiation current. (When we use series segmentation, these basic conditions will change, as will everything past this starting point.) Using this starting point, we can derive simple equations for IR and IT.

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These equations are deceptively simple, since they do not take into account that the currents we encounter on each wire at facing points have a magnitude and a phase angle. Many current tables made available to the software user will provide only the current magnitude and phase. The NEC and MININEC output tables provide the current information in this form and as a pair of real and imaginary components. We shall need the components in further steps. If the available current table does not provide them, we can easily derive the values.

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Suppose that we have a current magnitude of 1.0 at 30 degrees. Then the real component will be 0.866 and the imaginary component will be 0.5. (We shall assume that the units of measure derive from whatever source your software provides.)

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We are looking for the magnitude and phase angle of the radiation current and of the transmission current. Once we have found the components of the original values on wires A and B, we can combine them and derive a current magnitude.

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Since IR involves the addition of components, we add the real and then the imaginary component values and then obtain the magnitude by taking the square root of the sum of the squares, finally dividing by 2 to obtain the final value. Obtaining IT involves taking differences, so the equation appears in the following form.

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If we wish to know the phase angle of the currents that we just calculated, we use the following equations.

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Many spreadsheets only perform trig calculations using radians. Therefore, when obtaining the real and imaginary components of the initial current magnitude and phase, you may have to convert the phase into radians before taking a sine or cosine value. Likewise, the final two equations may return their results in radians, and you may have to convert into degrees (unless you habitually work with radians).

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Before we examine what we obtain for our efforts in setting up a calculation aid, let's set out the calculations for the alternative modeling convention.

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The Calculations for Series Segmentation

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When we model parallel wires serially, our first caution will be to count segments carefully so that we specify exactly facing segments for Wire A and Wire B at any calculation point. If the segments do not exactly align, the calculations will be worthless.

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When we model parallel wires in a serial fashion, the basic terms of the current on the two wires change. The change results from the changes in the phase angle of the currents on one of the two wires.

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Under these conditions, the derived values for IT and IR will also change. Note that which current sums the wire currents and which current takes their difference have reversed relative to parallel segmentation.

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Once we have gone this far, the remainder of the calculation-aid set-up is similar to the procedures for parallel segmentation. Obtaining real and imaginary components for the current magnitudes and phase angles in Wires A and B is identical. In the calculation of IR and IT, we simply reverse the equations shown. The same cautions about spreadsheet conventions apply to serial segmentation.

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A Few Worked Examples

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We may look at a few examples of the analysis in action both to test one model set-up against the other and to see if the results make good sense.

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The Folded Monopole

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In Fig. 3 and Fig. 4, we saw the outlines of a folded monopole for 3.5 MHz. The model uses perfect ground for simplicity--a real ground would have required a radial system. Our interest in the model lies in the currents along the two wires. From the relative current magnitude graph, we can see that the current level does not go to zero at the tip of the antenna, a phenomenon that we would expect of a single-wire monopole.

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Table 1 provides the results of a spreadsheet calculating aid. The two parts of the table show the results for both parallel and series segmentation conventions. In both cases, the reported current values at 10-segment intervals along Wire 1 of the pair (ignoring the short end wire) are the same. In the column labeled Wire 2, we find virtually identical reports of current magnitude. However, the phase angles of these currents are very different, in fact, 180 degrees different. The phase angle difference forces the change in the basic conditions and progression of calculations.

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When we use the correct progression of calculations for the model set-up, we obtain virtually identical values for both the radiation and the transmission line currents. We may note in passing that the transmission-line current phase angles are about 90 degrees out of phase with the radiation currents. However, the phase values may change from + to - and back again depending upon the exact relationship between the currents on facing positions on the monopole. Folded dipole transmission-line currents will exhibit similar shifts.

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The folded monopole was resonant at the length shown in the wire table. In the radiation current magnitude columns, we note a very low value that is consistent with the fact that the sampling point is not precisely at the tip of the antenna, but inboard by virtually 6". To see if the radiation currents coincided with those we might expect from a single-wire monopole, I constructed two single-wire monopoles. One used the same length as the folded monopole and increased the diameter (to 2.7") to achieve resonance. The second used the same wire diameter as each wire in the folded monopole and increased the length to achieve resonance. Table 2 shows the radiating currents of all three models. Of course, for the single-wire monopoles, the radiating current level is the NEC report of the current on the prescribed segment.

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The current magnitudes show a very close correspondence among the three vertical antennas. From the mid-point toward the element end, the folded monopole current phase falls between the values for the two single-wire models. Below that level, the phase angle of the folded monopole is shifted slightly more positive by the fact that at the first segment, the currents on the two wires are not precisely equal. Nevertheless, the sorting of radiation from transmission-line currents produces a radiation-current pattern that would be virtually indistinguishable from the current pattern for a comparable single-wire monopole.

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A Center-Fed 1/2-Wavelength Antenna with a 1/2-Wavelength Parallel Feedline

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The folded monopole example tends to confirm the adequacy of the analysis that sorts radiation from transmission-line currents for the case of a folded antenna element. However, it does not speak to the question of parallel feedline radiation. We may legitimately wonder if the same analysis is adequate to this task.

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To test this question, we may begin with a center-fed half wavelength antenna constructed from AWG #12 copper wire. Rather than place the feedpoint on the center segment, we may also construct from the same wire a parallel feedline. For this and following examples, the test frequency is 28.5 MHz to minimize the model size. The feedline for the first sample model in this series is just long enough (209.1") to achieve resonance (77.7 - J0.1 Ohms). The feedline proceeds away from this free-space antenna at right angles, as shown in Fig. 5.

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The current magnitude curves show that the current peaks on the feedline are at least as high as the peak current on the antenna element. However, we learned early in our experience with practical antennas that the set-up for the model minimizes radiation currents. Hence, we would anticipate that the calculations will place virtually all of this current in the transmission-line current columns.

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Table 3 shows spot checks of the currents along each wire using both parallel and series model set-ups. The wire-2 values have the same magnitude for both set-ups, but the current phase values differ by 180 degrees. Because the radiation currents are so low, we find variability between the values produced by the two set-ups. However, the highest current value is less than 1% of the feedpoint current (1.0), rendering the calculated differences insignificant at a practical level. As we anticipated, we find much higher values in the transmission-line current column, and the two set-ups show a close fit in phase angle values.

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The bottom line of this initial exercise is that a center-fed wire antenna with a parallel transmission line at right angles to the antenna element wire exhibits virtually no radiation current. Were it not for the role this model plays as a comparator for succeeding examples, the exercise would be superfluous.

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An Off-Center-Fed 1/2-Wavelength Antenna with a 1/2-Wavelength Parallel Feedline

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If we move the wire's feedpoint away from center, the two wires of the transmission line will show a differential in current magnitude not only at the junction with the antenna wire, but also long the entire length of the feedline. The sample model moves the feedpoint 30" toward one end of the wire and adjusts the segmentation of the antenna element wires accordingly. However, I left the length of the feedline at 209.1", a length of antenna and feedline that yields a somewhat non-resonant feedpoint impedance (113.7 - j20.0 Ohms). Fig. 6 shows the general layout of the antenna as well as the relative current magnitude values along both the antenna and the feedline.

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From just the looks of this situation, we would expect that the radiation current levels on the transmission line will not be as insignificant as in the case of the center-fed antenna. Table 4 shows the results obtained for the OCF antenna feedline using both model set-ups and the same checkpoints along the feedline that we used in the preceding example.

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Wire 2 of the data from the NEC report shows the same close coincidence of magnitude values and the same 180-degree shift in phase angle for the two model set-ups that we have seen in all of the models so far explored. The transmission-line currents are not very distant in value from those we found on the centered feedline. The key change occurs in the radiation current column. Because the values are no longer trivially small, we find a very close coincidence of values between the two model set-ups. As we expected, the radiation current magnitudes values are much higher, amounting at their peak to about 27% of the peak current value at the center of the antenna element.

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In practical terms, we might be hard-pressed to detect a difference in the radiation pattern between the center-fed and the OCF antennas at any moderate height (perhaps less than 1 wavelength but greater than 1/2 wavelength) above ground. Peak radiation current occurs about halfway up the feedline toward the antenna element and is considerably weaker than the antenna current peak value. Nevertheless, the radiation currents do exist and would be measurable.

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An End-Fed 1/2-Wavelength Antenna with a 1/2-Wavelength Parallel Feedline

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Let's move the transmission line to the end of the 1/2 wavelength wire element. Our next model in fact leaves one segment on one side of the line to reflect the usual bits of wire that terminate the open side of an end-fed antenna. The remainder of the element connects to the other side of the transmission line. The line length is unchanged at 209.1". The outline and current magnitudes appear in Fig. 7.

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One of the lines appears to have a higher current peak than the other, although the graphic does not show us the current phase. Hence, we cannot know from the sketch whether the peaks or their differential mean anything yet for radiation currents. The peak current in the transmission line does seem to exceed the peak current on the antenna wire. That phenomenon results from the very high source impedance of the model: 2410 - j4020 Ohms. To obtain a look at the radiation and transmission-line components of the currents shown in Fig. 7, we must subject the NEC current reports to the sorting process. Table 5 provides the data for both forms of model set-up.

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The division of current between radiation and transmission-line components (with a 1/2 wavelength transmission line) may seem surprising. The transmission-line component rises to a very high level (given the source current of 1.0). In fact, the transmission line current peak (from the sample) is over 5 times the value of the peak radiation current level. In turn, the radiation current peak on the transmission line is only about half the value of the peak current that appears along the antenna element. The relative values of peak current between the transmission line and the antenna have steadily risen as we moved the transmission-line position from the antenna wire center toward the end. However, within the scope of the basic antenna parameters used to create the models, the feedline radiation has not challenged the dominant role of the antenna wire in setting the radiation pattern for the system. Moreover, had we used only the unsorted or composite current reports for the end-fed antenna, we might well have reached an unwarranted conclusion about feedline radiation.

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A Center-Fed 1/2-Wavelength Antenna with a Tilted 1/2-Wavelength Parallel Feedline

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All of the examples using the 209.1" feedline position the feedline at 90 degrees to the axis of the antenna wire. As a result, they show essentially the radiation current levels on the feedline as they result from the natural balance or imbalance of currents at the junction of the feedline with the antenna wire. Common practice is to extend the feedline at right angles to the antenna element for the greatest distance possible to avoid currents that might be induced in the feedline by coupling to the antenna fields.

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The analysis that separates the radiation from the transmission-line currents is also applicable to examining the situation in which we bring the feedline away at an angle other than 90 degrees. For a sample, let's begin with a center-fed wire. Then we may bring the feedline from the junction to a point directly under one leg of the antenna element. In fact, I terminated the feedline at the point directly under one end of the center-fed wire. The vertical distance between the wire and the source end of the feedline is about 184.5", resulting in a total line length that is almost exactly the same as for the original center-fed model--a little over 209". The result was a feedpoint impedance not very different from the original model: 73.1 + j0.4 Ohms for the tilted line model and 77.7 - J0.1 Ohms for the original model. Fig., 8 shows the basic outline of the tilted-feedline model.

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The sketch can mislead by virtue of the perspective, which I selected to show the current magnitude curves. The total antenna wire length is the same (within a few inches) of the transmission-line length. The feedline is about 28 degrees off vertical. The tilt is not radical, but clearly noticeable. Our next question is whether the tilt makes a difference in the radiation currents on the feedline. Table 6 compares the currents for the original center-fed wire and the new version with a tilted feedline. Both tables use the series segmentation set-up.

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We find very little difference between the two models in the transmission-line current columns. In the radiation current magnitude column, we find a significant difference. Radiation currents have increased by nearly a ten-fold average. The intrinsic current level is certainly not sufficient to alter that antenna radiation pattern. However, if we call the radiation current by their other name, common-mode currents, we may or may not have a cause for concern. At the equipment end of the feedline, the level of RF current necessary to create interference with sensitive solid-state circuitry is not very high at all. It is not at all clear from the sample model that we have surpassed the required threshold, which will vary with the power actually applied to the antenna-and-feedline system. The sample does nevertheless confirm that feedline routing can play a role in the level of radiation current on the feedline.

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Conclusion

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These brief notes have tried to show that an analysis of radiation or common-mode currents is possible for parallel two-wire transmission lines and that such an analysis as potential utility. The analysis makes use of current data from NEC models, but processes the data externally to NEC. NEC and MININEC are not ends in themselves, but a source of data that has extended utility once we know how to use the data.

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The sample models are simplified, since the goal was to show the technique of analysis, not to produce definitive results. To analyze an actual situation, the models would undergo many changes that only begin with replicating the actual antenna and feedline. The model would route the feedline exactly as it occurs, and would add a real ground to the model.

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Not everything that we may learn from NEC and MININEC models appears in the NEC output report data. The data may be a resource for numerous rounds of further analysis. We have only examined one such effort here.

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124. Modeling (with) Parabolic Reflectors

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L. B. Cebik, W4RNL

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Modeling with non-uniformly shaped wire-grid structures carries a considerable collection of cautions and warnings. Newer modelers are likely to overlook many of them while focusing on the complexities of the structure itself. Therefore, it may be useful to review some of the potentials and the limitations of models that include them. We shall focus on the parabolic reflector as one of the most popular wire-grid structures, paralleling the popularity of physical implementations in many aspect of UHF communications. However, virtually all of the notes along the way will apply equally to other not-uniform shapes.

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We employ uniform wire-grid structures when we create the rectangular shapes that form planar and corner reflectors. In these structures, the individual wires or wire segments are almost equal in length in both directions. Therefore, we may size the wire easily to form a good simulation of a solid surface. As we shall see, parabolic reflectors do not admit of such easy calculations.

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A parabola, of course, is a graphical solution to a certain type of quadratic equation. The antenna structures that we commonly call parabolas are paraboloids with uniform dimensions, as suggested by the 2 views in Fig. 1. The center of the dish is the vertex. The distance from the vertex to a point that is in line with the lip of the dish is the depth (d). The distance across the widest pair of points on the lip of the dish is the diameter (D). The parabolic reflector also has a focal point, and we can calculate the distance from this point to the vertex by a common equation.

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The focal length will equal the depth of the parabolic reflector under the condition that the depth is 1/4 the diameter. Most antenna handbooks will provide further information on parabolic reflectors. Our main concern is modeling the device.

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Most applications allow us to create the dish model by using a shape-synthesizing program of some sort. For this exercise, we shall use NSI's NEC-Win Synth. To create a parabola, we need only specify the depth, the radius, the wire diameter, and the desired segmentation. The program allows us to specify the coordinates for the 2 radii (that is, X-Y, Y-Z, etc.) and also allows us to use separate values for the pair. We shall use a circular outline for simplicity.

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The native output of NEC-Win Synth is a special file format that is directly compatible with NSI's NEC-Win Plus program that uses a spreadsheet format for its files. However, we can also save the file that we generated in .NEC format for direct importation to any NEC implementation. However, like other synthesis programs, we must use caution. The product is not a complete model file, but only the geometry of a model, along with the frequency specified.

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+CM Generated by NEC-Win Synth 1.0
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+GW 1 1 0.31623 0.00000 0.05000 0.30075 0.09772 0.05000 0.00500
+GW 2 1 0.30075 0.09772 0.05000 0.25583 0.18587 0.05000 0.00500
+GW 3 1 0.25583 0.18587 0.05000 0.18587 0.25583 0.05000 0.00500
+GW 4 1 0.18587 0.25583 0.05000 0.09772 0.30075 0.05000 0.00500
+GW 5 1 0.09772 0.30075 0.05000 0.00000 0.31623 0.05000 0.00500
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+GW 396 1 0.00000 -0.94868 0.45000 0.00000 -1.00000 0.50000 0.00500
+GW 397 1 0.29316 -0.90225 0.45000 0.30902 -0.95106 0.50000 0.00500
+GW 398 1 0.55762 -0.76750 0.45000 0.58779 -0.80902 0.50000 0.00500
+GW 399 1 0.76750 -0.55762 0.45000 0.80902 -0.58779 0.50000 0.00500
+GW 400 1 0.90225 -0.29316 0.45000 0.95106 -0.30902 0.50000 0.00500
+GS 0 0 1.000000
+FR 0 1 0 0 299.800000 1
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To complete the model, we must add a driver--if we are not exciting one of the wires in the assembly. We must also specify the excitation, add any material or other loading that we need, and request some for of output. Therefore, the lower portion of the incomplete sample shown requires some variation of the following set of lines. The request for far-field patterns is only one of numerous outputs that we might request.

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+GW 396 1 0.00000 -0.94868 0.45000 0.00000 -1.00000 0.50000 0.00500
+GW 397 1 0.29316 -0.90225 0.45000 0.30902 -0.95106 0.50000 0.00500
+GW 398 1 0.55762 -0.76750 0.45000 0.58779 -0.80902 0.50000 0.00500
+GW 399 1 0.76750 -0.55762 0.45000 0.80902 -0.58779 0.50000 0.00500
+GW 400 1 0.90225 -0.29316 0.45000 0.95106 -0.30902 0.50000 0.00500
+GW 501 11 0 -.24 .5 0 .24 .5 .005    !driver
+GS 0 0 1.000000
+GE
+FR 0 1 0 0 299.800000 1
+EX 0 501 6 0 1 0
+RP 0 361 1 1000 -90 90 1.00000 1.00000
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+EN
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If we were to run the incomplete model, all that we would obtain for our trouble is an output report that provides a set of segments and their connections. However, even this much information can be useful to us, since we may use the information to evaluation why the parabolic reflector is a non-uniform wire-grid structure. In lieu of the data lines, we may examine more closely the graphic portrait of the reflector, as shown in Fig. 2.

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The wire-grid assembly uses straight wires to approximate curved surfaces. It consists of several radials connected at semi-regular points by circles of wires. Normally, in a synthetic structure, each wire has 1 segment. The dish shown is 2 wavelengths in diameter and 0.5 wavelengths deep. Note that virtually no junction of wires at a right angle involves wires of equal length. The wires forming the circle increase their length systematically as we move from the vertex to the lip of the dish. The wires forming radials use equal length segments except at the innermost section. An ideal radial would have one more circle to achieve equal length segments throughout. However, the wires for the missing innermost circle would become exceptionally short.

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Missing from the line graphic is any indication of the wire diameter used in the parabolic structure. The selection of wire diameter interacts with the selection of the number of radials at the vertex, where all radials join. The model shown uses 20 radials as a minimum value to form a close approximation of a circle. Adjacent wires at the vertex form a small angle. As we increase the number of radials or as we increase the diameter of the wire, press the NEC limits for the inter-penetration of wires at the vertex. However, if we make the wires too thin, we run the risk of creating a leaky reflector, that is, one that does not approximate a solid surface.

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To examine the consequences, let's provide our 2 wavelength-diameter dish with a dipole placed at the focal point. Since the depth is 1/4 of the diameter, the focal point is 0.5 wavelength from the vertex, that is, even with the lip of the dish. We shall begin with a reflector-wire diameter of 0.01 wavelength and increase it up to 0.08 wavelength. Table 1 shows the results of these trials.

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This simple experiment has several dimensions. First, as we examine the maximum gain column, we notice a steady rise in gain solely by virtue of the increase in wire diameter. The gain appears to peak at the last entry. However, we should also note the average gain test (AGT) column, which shows a value that departs slowly but surely away from the ideal value of 1.0 for the free-space lossless model. We may convert the AGT value to decibels and correct the reported gain. The corrected gain shows a maximum value with 0.07 wavelength diameter wire. In addition, the 0.08 wavelength version of the model contains numerous warnings about wire inter-penetration.

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Given the curve of peak gain values, wire diameters between 0.05 wavelength and 0.07 wavelength are likely equally usable in most applications as the closest approximations of a solid surface parabolic dish. The technique shown here or a reasonable variation is the only way to discover how close to a solid surface that we may approximate with the non-uniform structure of the assembly.

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Second, we may also test the assembly by examining the far-field patterns produced by the parabola and its driver. Fig. 3 shows patterns for our basic dipole driver and the dish using thin wires and thick wires. The thin-wire version of the dish yields results that are far from those of a solid-surface dish. The fat-wire version is closer to the mark.

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Third, numerous modelers are surprised by the fact that even a solid surface--or our closest approximation of it--yields a set of rearward lobes, however, small that may be. Most texts focus on how rays intercept the dish surface and reflect in the forward direction. However, a parabolic dish shares some significant properties with rectangular reflectors. There are both semi-shadow and shadowed areas. As well, we encounter diffraction at the dish lip. Hence, every parabolic dish will have rearward far-field lobes. Advanced techniques of feeding the dish concentrate on minimizing these lobes while illuminating the dish to maximum advantage.

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Finally, we should note the gain values for the dipole driver. A number of texts provide an equation to calculate the gain of a dish relative to its diameter at the frequency of use.

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The equation has a fudge factor, k, the efficiency factor, given as 0.00 through 1.00. Most sample calculation use values between 0.5 and 0.55. However, the highest gain value in our table only emerges if we reduce the value of k to about 0.4. Most initial gain calculations presume an isotopic source of excitation. If we exchange the single dipole for a pair of turnstiled dipoles, the gain values do not change, but the source comes closer to be isotropic in free space. So we are left with a quandary: is the efficiency presumption behind the gain calculations off the mark, or is the model deficient enough to account for the difference between reported gain and pre-calculated gain? One of the limitations of modeling parabolic dishes in the absence of appropriate range or chamber tests is that we lack any means of forming an answer to the question.

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One interesting facet of modeling parabolic reflectors is the optimal placement of the driver assembly relative to the focal point of the parabola. Our initial test showed very little variation in position relative to reflector wire thickness. However, we did not survey the gain behavior of the total antenna as we changed the position of the driver. A small survey may be useful in terms of showing what to expect from modeled parabolic assemblies. Therefore, let's use our 2 wavelength diameter dish with a depth of 0.5 wavelength and a focal length of 0.5 wavelength. For comparison, we may create a 3 wavelength diameter dish that also uses a depth of 0.5 wavelength. The equation with which we began or simplified view of parabolas tells us that the focal length is 1.125 wavelengths. In both cases, we shall use a turnstiled-dipole driver for simplicity. (Remember that these notes do not focus on parabolic reflector technology, but upon modeling the reflector. Therefore. we may justifiably use simplified driver assemblies.)

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The smaller dish uses 0.07 wavelength wire in the reflector assembly. Table 2 provides us with some basic data on the modeled performance as we move the driver from 0.3 wavelengths to 1.1 wavelengths away from the vertex. The peak gain occurs at a distance (within the limits of the sampling) of 0.5 wavelengths. Maximum gain does not occur at the same distance as maximum front-to-back ratio. The reported beamwidth at the maximum gain distance coincides closely with the estimating equation, which sets the beamwidth as equal to 70 times a wavelength divided by the dish diameter (or 35 degrees, in this case). However, note the fluctuation in beamwidth as we move the driver position.

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Fig. 5 overlays 3 patterns for the smaller dish and its turnstiled dipole driver at the driver position for maximum gain. The three traces are almost indistinguishable. The smaller dish appears to show a coincidence with basic calculations in every way, except perhaps for the gain deficit. (We may note in passing that we find a secondary gain peak with the driver at 1.0 wavelength away from the vertex, but this peak is considerably lower than the main peak.)

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Let's turn to the larger dish that is 1.5 times the diameter of the smaller one. The diameter is 6 times the largest dimension of the driver. The depth remains at 0.5 wavelength. The focal point by calculation is 1.125 wavelengths from the vertex. For this dish, a wire of 0.06 wavelength diameter proved to be the largest usable value. If we move the turnstiled dipole driver from a closer point to a further point from the vertex, we obtain the data in Table 3.

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The optimal distance for maximum gain is not the focal point, but a different point considerably closer to the vertex. At a distance of 0.75 wavelength, we obtain maximum gain with a beamwidth about 3 degrees wider than the calculated value. A secondary gain peak occurs at a distance of 1.375 wavelengths and is only about 0.3-dB lower than the near-position gain. The beamwidth at the farther position is closer to the calculated value.

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The modeling result produces gain peaks that depart from standard rudimentary theory (but not perhaps from more advanced calculations). As well, the secondary peak is now a contender for use. Fig. 6 compares the patterns for the two position--again using an overlay of 3 patterns for each driver position. The two driver positions yield very distinct low-angle lobe structures. What we cannot specify solely on the basis of the models is whether the pictures are accurate to the behavior of a solid-surface dish on a test range.

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The gain values produced by the larger dish are also deficient compared to standardized calculations. Once more, a value of about 0.4 for k, the efficiency factor, would align the model report with the standard calculation of peak gain. One limitation of the system is that fully half of the radiation of the driver is away from the reflector. Therefore, we might wish to explore in perhaps the most crude manner what happens if we focus more energy on the reflector.

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Fig. 6 shows our final experiment. It replaces the simply driver with crossed or turnstiled Yagi elements forming a circularly polarized 3-element beam. The performance is modest, with about 7.5-dBi free-space forward gain and 11-dB front-to-back ratio. The array reflector elements are just over 0.5 wavelength long, and the boom length is exactly 0.5 wavelength. We shall direct the Yagi toward the reflector and try to find a mounting position that maximizes the gain. Table 4 summarizes the results for the 3 wavelength diameter dish. The listed distances are to the reflector, with the director 0.5 wavelength closer to the vertex.

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Once more we find a pair of distances at which the array gain peaks: 1.0 wavelength and 1.4 wavelength. (Subtract 0.25 wavelength for the distance to the center of the Yagi and 0.5 wavelength for the distance to the director.) Unlike the dipole driver, the Yagi gain values are very comparable. (Corrected for the AGT values, the are almost identical.) As well, we find nothing to choose in the beamwidth and front-to-back values. The comparative patterns for the two positions appear in Fig. 8 and show may major reasons in the sidelobe structure for selecting one position over the other.

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The gain values recorded by the Yagi driver with the 3 wavelength dish are above the pre-calculated gain values for dishes, largely as a result of the improved focus of energy from the driver onto the parabolic surface. Indeed, for some purposes, a modeler may wish to examine the current distribution on the modeled dish wires under various circumstance. Solely as an example of how we might find differences, I set the range of currents from 1.5e-3 down to 3.0e-4 to provide a range of color variation on the dish wires. Using the 2 positions of maximum gain, I obtained the graphical representations in Fig. 9.

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The two current magnitude plots show very different patterns of current distribution. (The closer position shows some red lines at the center; these are from the Yagi elements.) The farther driver position appears to illuminate the radials to a considerable degree, in contrast to the closer position situation. Whether this factor has a bearing on the reliability of the wire-grid reflector as a model for a solid-surface reflector remains unknown if we remain completely at the level of modeling.

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Conclusion

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These notes have not attempted to answer any questions about parabolic reflectors as physical antenna structures. Instead, we have been focusing on the parabola as an example of a non-uniform wire-grid modeling structure. We initially concentrated on the ways in which such structures press the limits of NEC guidelines. We found limits beyond which we could not go, especially in terms of the number of radials that we might use vs. the wire diameter that we might assign to the reflector. However, since the reflector is wholly passive--or at most parasitic--pushing the limits does not yield unusable AGT values.

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We also looked at some rudimentary models of parabolic arrays. Our goal was to develop some preliminary expectations of such models with a wire-grid parabolic reflector. We found ways in which the models fail to coincide with fundamental calculations associated with reflectors of this order. However, modeling alone does not provide corrections either to itself or to the basic equations. (I have for the most part resisted the temptation to suggest first-order possible explanations for some phenomena. For example, the driver assemblies are all within coupling range of the reflector, and it is uncertain whether the results deviate from a solid surface due to coupling to individual wires within the wire grid.)

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The net result--applicable to any non-uniform wire-grid structure--is that we can only use such structures with caution and with attention to all of the tests that we might apply to the model. The models are eminently useful so long as our expectations are suitably modest.

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125. When to Worry and When Not to Worry: a Case Study

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L. B. Cebik, W4RNL

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Everyone who models conscientiously using either NEC or MININEC worries over the results. Essentially, we find two general categories of worry. First is the basic adequacy of a model. Within NEC--and assuming adherence to the guidelines--the chief measure of model adequacy is the average gain test (AGT), which we have discussed extensively in past columns. Ideally, a free-space lossless model should show an AGT of 1.000 (2.00 for models using a perfect ground). There are no absolute rules for when an AGT score other than 1.000 renders a model inadequate. However, the more comparative and systematic a modeling exercise is, the closer to 1.000 that we require the AGT values to validate comparisons among models.

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The AGT rests upon performing a full spherical far-field scan for a model in free space (a hemisphere over perfect ground). Using sufficient and equally spaced (angularly, of course) increments for the sample, the average far-field gain should equal the reference gain so that the ratio is 1.000. As we examine more complex geometries, we should reduce the increment between each sampled point on the sphere to obtain the most accurate average value. (Automated AGT scans offered by some implementations of NEC often use 5-degree increments, which is normally adequate for linear elements in various arrays. However, changing the increment to a lower value is a good check to ascertain the best value to use in a given exercise.)

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We may often obtain corrected values for raw NEC gain reports by converting the reported AGT value into dB. The conversion consists of taking the log of the reported AGT value and multiplying by 10. A reporter AGT score of 1.010 converts to 0.04 dB. Since the AGT score is greater than 1, we subtract the converted value from the reported gain. Hence a raw gain report of 5.00 dBi becomes 4.96 dBi. Reported AGT values below 1.000 result in increases to the raw far-field gain report. An AGT report of 0.960 becomes -0.18 dB. Had the gain report been 5.00 dBi, the corrected gain value would be 5.18 dBi.

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We may also correct the resistive component of the reported source impedance using the AGT directly. The correction works best when the impedance is close to resonant, that is, has a relatively low reactive component. (Results with high reactive components appear to be mixed, with some results appearing to coincide with range test results and some appearing to diverge considerably.) To correct the impedance value, simply multiply the AGT score times the resistive component. Assume a reported value of 150 Ohms. An AGT score of 1.01 would convert this value to 151.5 Ohms. An AGT value of 0.960 would correct the reported resistance to 144 Ohms. How significant these corrects are depends upon the terms of the modeling exercise. If I were building an antenna with a target feedpoint impedance of 150 Ohms, I might expect construction variables to outweigh the range of variation within the example. However, for a sequence of modeled antenna geometry variations, I might wish to use corrected source impedance values in order to obtain a reasonable sequence of values associated with the variations, especially if each variation produces a different AGT value.

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The notion of construction variables leads us to the second major category of worry. The basic concern is how well a model conforms to a reasonable physical implementation of a modeled antenna. As we move ever higher in frequency, the bumps and the short leads that we usually do not model take on increased importance, since they grow as a function of a wavelength at higher frequencies. We might usefully make a catalog of compensatory measures that we sometimes take to overcome anticipated construction variations. However, we shall save that level of concern for some future column. Assuming that we would use general care in constructing a physical implementation of a modeled antenna, we shall restrict our concerns to general expectations for relative gain among relevantly comparable antennas and for their feedpoint impedances.

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Modeling yields numbers derived from calculations within the particular modeling core that we might use. Many implementations of NEC include graphical representations of those numbers, but the basic NEC output is a large collection of numbers. When we find differences between two sets of numbers, we tend to worry. However, only in some cases is the worry justified. To distinguish between justified worries and unjustified worries, let's look at a case study.

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Closed 1-Wavelength Loop Elements

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A closed 1-wavel;ength loop element with a single feedpoint provides major bi-directional far-field lobes broadside to the plane of the loop. There are two significant properties for us to note initially. First, the 1 wavelength loop provides directional gain over a simple half wavelength resonant dipole. In fact, we may usefully analyze the 1 wavelength loop as constituting two dipoles fed in phase with an average distance apart of about 1/4 wavelength. Second, whereas a physical dipole will by shorter than 1/2 wavelength at resonance, a full wavelength loop circumference will be greater than 1 wavelength at resonance. Part of the lengthening results from the mutual coupling between the two dipole elements presumed to be in the loop: resonance requires that we lengthen each of them by a small amount.

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Amateur antenna builders continually look for so-called "cutting formulas," those seemingly magical simplifications that supposedly give the right answer for element length using only a single constant and the design frequency. Unfortunately, the world of antennas is more complex than cutting formulas imagine. Even in free space, the required length for a dipole or a closed loop--at resonance--will vary with the wire diameter and to a much lesser degree on the material loss of the antenna wire or tubing. For our exercise, all antennas will be in free space and use 0.002-m (2-mm) lossless or perfect wire. Horizontally polarized antennas are also prone to variations in the required length for a resonant impedance as a function of the antenna height above ground, especially below 1 wavelength.

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The exercise that led to these notes emerged from a variety of claims that one hears about various closed loop configurations. One claim is that a perfectly circular loop has a significantly higher gain than a conventions square-sided loop (arranged to form either a square or a diamond). Presumably, the circle is a figure with an indefinitely high number of sides, compared to the 4 sides of the conventional HF quad loop. However, that account is at odds with claims made for a triangular or delta closed loop with equal side lengths, namely, that it is just as good as the 4-sided loop, again with equal side lengths. So I decided to example some models (free-space using 0.002-m diameter lossless wire) involving the configurations shown in Fig. 1. The test frequency is 300 MHz.

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The dipole, of course, provides a reference against which to measure the increased gain offered by each closed-loop configuration. The sequence of models included both square and diamond-shaped 4-sided loops. To place the feedpoint at conventional positions required a mid-side position for the square loop and a position at the lower point for the diamond-shaped version. The two delta or triangular loops are both equilateral triangles and differ only in the feedpoint position. Since the model is in free space, moving the mid-side position to the top wire makes no difference in performance relative to inverting the entire structure. The loops have from 33 to 44 segments total, so the circular loop uses 45 wires to complete the simulation of a true circle. In some implementations of NEC, one may use the GA (arc) command to create the circle. The software used here--EZNEC-Pro/4--creates circles using separate wires. However, the results are identical to circles created with the GA command.

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The sequence of seemingly comparable models yields the data shown in Table 1. With respect to the AGT values, we may note that the dipole and the circular loop achieve virtually perfect values, while the two angular loops fed at mid-side positions have identical very good values. Both require only a 0.02-dB decrease in the reported gain value.

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The point-fed angular loops, however, tell a different story. The AGT values diverge more widely from the ideal value as the angle between the sides decreases. As indicated in Fig. 1, both point-fed models use a "split-source" feed, that is, a pair of sources on segments adjacent to the point. The reported source impedance value is the sum of these series sources. Removing one of the sources does not change the result (or the AGT value) significantly.

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The table provides corrected maximum far-field gain values based on the raw report and the AGT score. We may note in more than a passing way that the corrected gain value for each point-fed model coincides very closely with the corresponding value for a mid-side source position. (In fact, the gain values form a progression from low to high as we move from the most angular structure--the delta or triangle--to the least angular--the circle.)

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The table does not list corrected source resistance values. Only the values for the point-fed positions would change noticeably. The corrected source resistance for the point-fed square-diamond becomes 131.6 Ohms, only 1 Ohm different from the mid-side fed square. Likewise, the adjusted point-fed delta source resistance becomes 126.0 Ohms, about 5 Ohms away from the mid-side source value.

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A MININEC Trial

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We may note two facts about the NEC models. First, NEC models place a source within a segment. Hence, we cannot obtain a perfect point-fed source location. For many purposes, the split-source work-around to this small limitation proves to be very satisfactory. However, in this particular exercise, the split-source technique does not provide models that are sufficiently adequate to let us make the comparisons required by the exercise goals, at least, not without correcting the reported gain and source resistance values. Second, the AGT departs more widely from the ideal value as we sharpen the angle between wires at the point feedpoint. The wire angles themselves--in these NEC-4 models--do not create a problem, since the mid-side feedpoints yield very good AGT values. Only when we place the feedpoint at the angular junction of two wires do we encounter the difficulty.

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MININEC (3.13) does not suffer one of the problems that we have just noted. We may place a source directly on a diamond or delta point, since MININEC places sources (as well as loads) on pulses, that is, on the junction between segments. However, uncorrected MININEC 3.13 suffers other difficulties, especially with angular junctions. Antenna Model is a highly corrected version of MININEC that has to a very large measure overcome the limitations of raw MININEC. It has several other features as well, including the ability to provide an AGT value and the ability to import NEC models. The latter feature is useful in ensuring that the models used in MININEC trials are as precise to their NEC-4 originals as is feasible. The result is a set of models with the outlines shown in Fig. 2.

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Since MININEC requires a pulse or segment junction for the mid-side fed models, Antenna Model automatically increases the segment count on the affected wire by 1 to obtain an even number of segments. To assure equal segments on equal-length wires, I increased the count on the other wires of the square and the mid-side fed delta to coincide with the count on the source wire. Otherwise, the models are identical to their NEC originals.

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Table 2 lists the results of the trials. The reference dipole and the circular loop provided excellent AGT values and showed resonance within the project limit of +/-j1.0 Ohm reactance. However, all other models required some dimensional alteration to bring them to resonance within the same limits. The table shows the initial impedance reports as well as the circumference of the corrected models. (Of course, the side lengths are the circumference divided by 4 for the square models and divided by 3 for the deltas.) All of the models display excellent AGT values. The gain values for each type of loop coincide relative to mid-side and point feeding, and the progression is virtually the same as we found in the NEC models, with increasing gain as we move from the triangle toward the circle. In a general way, our worries over the deviant AGT values provided by the NEC models were well founded.

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However, one worry was not as significant as it might seem at first sight. The angular models showed a departure from resonance of at least j10 Ohms, occasioning the work of revising the dimensions to bring the model back to resonance. If we bring a mere numerical sense of resonance to the project, the departure may seem large. However, we should also note that the feedpoint resistance ranges from about 120 to 150 Ohms. Therefore j10 Ohms departure is far less troublesome in any respect than the same reactance with a feedpoint resistance of 50 Ohms.

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To see how much of a worry the departure from resonance might be, I calculated the change of dimension between the imported NEC models and the corrected versions. The results appear in Table 3. The table lists the ratio of corrected to uncorrected circumference, the amount of change as a percentage, and the SWR of the original model relative to the reported feedpoint resistance.

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All but one of the models show less than a 1% required dimensional change. For these models, it would be inappropriate to worry about the differences relative to an eventual physical implementation of the loop structures. Construction variables would likely wash out the difference between the original and the adjusted dimensions. In practice, we likely could not distinguish between construction and modeling variations. As the title of this column suggests, some modeling differences are worth the worry; others are not.

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The one case in which we needed to change dimensions by more than 1% involves the point-fed delta loop. The 2.4% increase in the circumference to restore resonance in the MININEC model leaves us with a small worry that is more prominent in this program than in NEC. From Table 2, we find a corrected feedpoint impedance that is very much higher than expected. Indeed, the value is higher than the source impedance of the circular loop. The model from which we derived the feedpoint impedance uses only 16 segments per side. To MININEC models we may apply the convergence test, raising the number of segments per wire until the values for gain and impedance stabilize. For the point-fed delta, gain is not a problem, but the source impedance may be. Therefore, I increased the segmentation to 44 segments per side in small increments. At this level, the Antenna Model AGT value became 0.999, with a gain that was still 3.05 dBi. However, the resonant source impedance dropped to 132.6 - j 0.3 Ohms. Arriving at resonance at the converged value required a reduction in the delta circumference to 1.122 wavelengths. This circumference is very close to the original NEC-model value. At the same level of segmentation, the delta using a mid-side feedpoint showed no change in either the far-field gain of the source impedance. However, the circumference at resonance decreased to 1.109 wavelengths, virtually the same as required by the original NEC model.

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A Final Test

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The MININEC divergence between source impedance values using a point-fed source position and a mid-side source position remains somewhat worrisome when we compare those values to values derived from NEC models and corrected with reference to the AGT values. The worries may be minuscule in the context of developing a model that prepares us to construct a physical implementation of the antenna. However, from the perspective of systematic modeling for comparative purposes, the worries grow in both size and number.

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Instead of a single concern, we now have two, one general to modeling, the other specific to the present exercise. First, the MININEC AGT scores are universally exceptionally good, despite shortcomings that we found in some of the models. Whereas NEC AGT values are valuable up to an indefinable limit in providing corrected values to the reported gain and impedance, they are less valuable in MININEC. Instead, the convergence test provides perhaps the most critical test for MININEC model adequacy.

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Second, the point-fed model source impedance values do not show reasonable agreement between the NEC and the MININEC models, although all other models show good coincidence. Moreover, the MININEC models suggest that the impedance of a point-fed model (both diamond and delta) will be higher than the value exhibited by mid-side fed models. In contrast, NEC models suggest that the source impedance for mid-side and point feeding will be quite similar.

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In order to provide some resolution to this question, I compared three NEC models of the delta using a point source location. The first is our original models using split source, but with the segmentation density increase to 33 segments per wire. The second model blunted the feedpoint by inserting a 1-segment "bridge" wire to replace the sharp point. The segment length is identical to the segment length used in the long wires. The third model increased the length of the bridge wire to accommodate 3 segments so that the segments adjacent to the source segment are in the same plane as the source segment and have the same length. Fig. 3 shows the point end of the deltas under all three conditions.

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The results from all three models appear in Table 4. The data show a progressive increase in the AGT value toward the ideal, with the final model only slightly imperfect. The nature of the AGT values strongly suggests that the angle of the wires that approach the source segment plays a strong role in yielding less than adequate models. Only when we isolate the source segment from the angled wires do we arrive at a model that passes NEC AGT muster.

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The bridge wire technique has two interesting consequences relative to the reported and corrected output data. First, the gain report is higher than for the original mid-side fed delta. It is likely that the length of the 3-segment bridge wire that is parallel to the far side of the delta may account for the small increase in reported gain--an amount that is numerically signicant in this comparative exercise but not in operational terms. The second result is the corrected source impedance value, which is identical to the value yielded by the mid-side fed model of the delta. This result suggests that ideal models would show very comparable source values for resonant 1 wavelength closed loops of the same shape, regardless of whether the loop uses a mid-side or point source location.

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Conclusion

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Systematic modeling exercises raise numerous concerns along the way. The present exercise sought to compare 1 wavelength closed loops to examine a number of conflicting claims about their performance. Our interest in the exercise has less to do with the conclusions that we might reach about such loop structures than about the worries raised by the modeling effort. Some worries proved to be relatively insignificant. Other gave us pause and required us to employ all relevant model adequacy tests and even work-arounds to resolve. In the process, we also considered different contexts, some of which made the worries important and other of which reduce them to mere footnotes on the modeling effort.

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Knowing when to worry, how much to worry, and what to do about the worry are all parts of mastering the art and craft of antenna modeling.

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126. "Ideal" Polar Plots

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L. B. Cebik, W4RNL

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NEC outputs are strictly tabular. Most NEC users obtain a commercially available package that includes--as a matter of course--a polar plot facility for graphing the radiation pattern of an antenna model. Very often, we lose track of the fact that the software writer as a service to users adds these modules in order to make the results of a simulation more (visually) accessible to the modeler. Especially if we have used only one package, we face the temptation of thinking that the graphing facility is an integral part of the NEC calculation core.

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As post-calculation facilities, polar plot facilities come in many flavors. Commercial packages tend to develop modules to serve the widest range of users equally. However, numerous firms have developed their own modules for special purposes, for example, satisfying FCC requirements for antenna patterns. Many polar plot facilities offer a wide range of plotting alternatives. Some offer a choice between linear or log scaling of the plot. Many also offer a selection of what data to graph, including the total gain, component gain (either major-minor axis or vertical-horizontal), and possibly the phi and theta voltage components of the far field. A few offer left-hand and right-hand circularly polarized patterns. One package even offers azimuth patterns for ground-wave calculations.

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Polar plots are generally available for either azimuth/phi or elevation/theta patterns, as dictated by the selections available for calculation within NEC. These pattern choices use conventions inherent to the NEC coordinate system. An azimuth or phi pattern within NEC software generally is a pattern in the X-Y plane, with a user-selected angle relative to that plane (elevation) or to the zenith (theta). An elevation or theta pattern calculates values with the Z-axis as the basis and on a plane that the user selects by specifying a phi or azimuth angle, where zero degrees coincides with the X-axis in the model geometry. Free-space elevation/theta patterns may use a full 360 degrees plot, but models employing a ground are restricted to the hemisphere above ground.

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Within the polar plots, software writers try to provide a variety of critical information needed by most modelers. Therefore, patterns usually show a line from the pattern center along the heading of maximum gain. Where possible, the plot will also indicate with lines the limits of the half-power or 3-dB beamwidth. Some plotting facilities also show by a line the strongest lobe other than the maximum gain lobe. Finally, the plot may show one or another form of front-to-back ratio, usually in an inset to the plot and listed in tabular format. Indeed, in most cases, the key data registered by the bearing lines appears in the inset table.

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As excellent as are the polar plot facilities offered by various implementations of NEC, they are not quite ideal from the perspective of a heavy user. These notes enumerate some of the shortcomings of polar plot facilities and some of the features that I would like to have available. These features would be part of what I would like to think of as an ideal polar plot facility. I shall list them without regard to their programming feasibility. Inevitably, we shall encounter situations that will tell us why I am unlikely ever to see a polar plot facility that provides them. Even if I specify that they do not all need to appear at the same time, there are limitations arising from the nature of the antennas that we model that make many of the features impractical, if not impossible, to supply.

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Some "Back-and-Forth" Desires

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Many patterns (phi or theta) display multiple lobes in a context in which we can easily identify a forward and a rearward direction. Modules that identify both the strongest lobe and the next strongest lobe suffer a limitation. In some patterns, the second strongest lobe may be a secondary forward lobe, while in others, the second strongest lobe may be the strongest rearward lobe. Fig. 1 provides a sample of each type of pattern.

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Several difficulties arise from the fact that Sample A and Sample B identify different lobes as the second strongest, that is, as the major sidelobe. The accompanying data inset may identify the sidelobe, its bearing, and its strength (and relative strength to the main forward lobe). However, only Sample B gives us information on the main forward sidelobe; Sample A gives data for the main rearward lobe. Now suppose that we perform a frequency sweep for the subject antenna. In the course of the sweep, both patterns may appear, although at different frequencies. The sweep (for example, in EZNEC) will often record the data for the sidelobe strength. Unfortunately, such data is not usable as a record of the main forward sidelobe strength, since some of the values belong to a different lobe.

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If we focus only upon directional antennas of the type whose patterns appear in Fig. 1, we may arrive at a nearly ideal request for addition information on the plot. Fig. 2 summarizes in a series of color-coded lines a more satisfactory user situation. In viewing the figure, also imagine an enlarged inset with tabular data for all of the lines.

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First the plot should identify forward and rearward quadrants. This task is relatively easy for antennas with deep nulls that are 90 degrees off the main forward gain direction. As usual, the plot identified the main forward heading with a line, and also shows the 3-dB beamwidth limits. In addition to this information, the plot also identifies each of the remaining forward lobes. Immediately, we encounter a challenge, since there is no single standard for distinguishing a true lobe from a bulge in the pattern. We might apply a 3-dB rule, that is, to identify a lobe as such when there is a 3 dB difference between the lobe peak gain and both adjacent null regions (regions with lower gain values). This rule would give each lobe its own half-power points. Anything less than 3-dB would be a bulge, a common feature of many long Yagis used above their design frequencies.

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The more usual technique in identifying a lobe is simply to register when a pattern, following the progression of sampled plotting angles, shows an increase in gain relative to the values at both the preceding angle and the following angle. This method relieves the plotting facility of the need to determine if the lobe meets a 3-dB measure. The technique does not eliminate mere bulges, as illustrated in Fig. 3. The patterns are for the same Yagi, but with an operating frequency change of 100 kHz.

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Since the patterns are both symmetrical, the locating dot does not obscure the fact that each pattern shows an apparent projection at the dot location. In the left pattern, the dot at a phi angle of 63 degrees shows a higher gain than we obtain at 62 and 64 degrees. The progression, in dBi/degrees, is -9.68/62, -9.67/63, -9.70/64. A change of 0.01 dB suffices to mark a lobe, as the plot line indicates. 100 kHz higher, we find the following progression of values: -8.35/60, -8.40/61, -8.48/62, -8.58/63, -8.72/64. The progression shows a steady decrease in gain, but the rate of decrease changes through the sampled range. The changing rate of gain decrease is enough to yield a pattern bulge. (In some cases, but not this one, we may convert a bulge into a lobe by using a smaller increment between samples, such as 0.1 degrees.) Although we may consider bulges to be incipient lobes, their location will likely always be a viewer task.

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To the rear, we find in Fig. 2 a 180 degrees line that simply continues the line from the point of maximum gain. The line is marginally useful in distinguishing arrays with symmetrical patterns from those with non-symmetrical patterns (such as parasitic beams based on a corner-fed half square). More significant is the identification of each rearward lobe--with associated data shown on the tabular inset.

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Bringing Up the Rear

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Once we move to the rear quadrants of a directional antenna, the data becomes more complex, since we are very often interested in some kind of front-to-back ratio. Since it is the easiest to calculate, most polar plot facilities provide the 180-degree front-to-back ratio value. The 180° front-to-back ratio is the main lobe forward gain (or the maximum antenna gain) minus the gain of the lobe (however big or small) that is 180° away from the heading of the maximum forward gain. If the main forward lobe is split or does not align with the graph heading, the 180° front-to-back ratio is 180° away from the direction of maximum pattern strength. Hence, the value may not be for a direction directly to the rear of the antenna structure. Since a Yagi is usually symmetrical, the maximum gain will normally be directly forward, and the 180° front-to-back ratio will indicate the relative strength to the direct rear. Note that if we use a normalized scale, we can read the front-to-back ratio directly from the plot--between 25 and 30 dB relative to the maximum gain of the antenna in the leftmost pattern. The left portion of Fig. 4 shows a part of a Yagi pattern in which the 180-degree lobe is the strongest rearward lobe.

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In Fig. 4, the center pattern shows a 180-degree gain of very tiny proportions. Hence, the 180° front-to-back ratio is very large (over 40 dB compared to a "mere" 27 dB for the leftmost pattern). Yet, we find rearward lobes that have considerable strength. The line through one of those lobes indicates the direction of maximum strength. It is only about 22 dB weaker than the maximum gain. Some sources call this the worst-case front-to-back ratio, and its value is the maximum forward gain minus the highest value of gain in either rearward quadrant. For this antenna, the 180° front-to-back ratio does not give a true picture of the QRM levels from the rear, so some folks prefer to use this figure as a better indicator. The worst-case front-to-back ratio provides the most conservative value for rearward suppression of QRM. The rightmost graphic in Fig. 4 shows that the 180° and the worst-case front-to-back values do not require separate lobes, even thought the values differ.

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We are not done with front-to-back ratios. Each sketch in Fig. 4 contains an arc going from 90° on one side of the line of maximum gain around the rear to the other point that is 90° from the maximum gain line. Suppose that we add up all of the gain values at the headings that pass through the arc. Next take their average value. Subtract the average gain value to the rear from the maximum forward gain and you arrive at what some call the front-to-rear ratio. Others call this the averaged front-to-back ratio. A 5°-interval between rearward readings is often sufficient for this sampling. The rationale behind using the front-to-rear ratio is that it provides an averaged total picture of the rearward QRM suppression.

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Although I am not aware of any software that provides an average front-to-rear ratio, at least one maker (NSI) provides a user selection between the 180-degree and the worst-case values. The worst-case value is detected by using the main forward lobe bearing and creating sampling limits 90 degrees to the rear of that bearing. Within the rearward quadrants, the program then identifies the strongest lobe and uses its gain in the front-to-back calculation. The process sounds simple enough (at least arithmetically) until we encounter cases like the ones illustrated in Fig. 5.

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The azimuth pattern shown applies to a Moxon rectangle, which does not place its side nulls at the 90-degree mark relative to the heading of maximum gain. Rather, its nulls occur closer to 110 degrees off the main heading. Hence, the preset limit line for determining the worst-case front-to-back ratio uses a portion of the forward lobe as a legitimate direction for the worst-case front-to-back ratio calculation.

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The same consideration--that is, the location of the deep side nulls--applies equally to the calculation of the average front-to-rear gain value. If one were to implement this additional front-to-back calculation, one might use the preset limits that gave the odd heading for the worst-case rearward lobe or one might use some sort of comparative scheme to detect the deep side nulls and then to use the reduced scanning region to determine the average front-to-rear ratio.

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Although the challenges of determining "proper" values of the worst-case and the average front-to-back ratios are significant, they are not insurmountable. However, not all azimuth patterns have detectable side nulls that occur--either at all or anywhere close to the side of the beam pattern. Fig. 6 shows two cases--very typical for vertically oriented arrays--in which perhaps only the 180-degree front-to-back ratio makes good sense. On the left, we have a common cardioidal pattern with only one null directly opposite the main forward lobe direction. A worst-case direction would have to choose between the 180-degree direction or involve the main lobe. An averaged front-to-back ratio would have little, if any, meaning in this case.

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The right-side pattern has a rearward lobe, but it is problematical. Once more, the idea of a worst-case front-to-back ratio becomes co-terminal with the 180-degree front-to-back ratio. In theory, we can take an averaged front-to-rear reading using only the rearward lobe. However, the angles included in the calculation are so few as to make the calculation less than useful.

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Which Way Did He Go?

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Our hope for an ideal polar plot facility that includes on screen all of the information that we might wish to see--whether all at once or serially--has significant limitations in the rearward mode for directional antennas. Very likely, programming various scans and detection systems is less of a problem than having the system know when certain criteria are relevant and when they are not. Antenna models do not advertise themselves as having certain characteristics calling for the application of certain variations on standard measures. Rather, the patterns emerge from the data. At present, post-pattern interpretation remains a user operation.

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Of course, many antenna patterns are not directional in the sense of having strict forward and rearward headings and a single forward lobe. A primary example is the simple dipole, which has an E-plane bi-directional pattern. The left pattern in Fig. 7 shows the difficulty facing a polar plot facility.

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The plot identifies one of the dipole lobes as the main lobe and relegates the other to the status of a rear, side, or secondary lobe. Ordinarily, the software decides on the main lobe by selecting the first lobe exhibiting maximum gain that it encounters in sampling the gain values starting at zero degrees. Zero degrees conventionally aligns with the X-axis in the coordinate system of the model geometry. Hence, for a dipole with the element ends aligned parallel to the -Y/+Y axis, the main lobe will be at zero degrees. Had the element been aligned parallel to the -X/+X axis, the main lobe would be at 90 degrees, counting in the phi or counterclockwise manner. (Special note: many polar plot systems also sample adjacent angles for a span that extends until the gain value changes; the system then centers the indicator line within the range of angles showing the maximum gain value. The NEC output report records gain values in dB using 2 decimal places. Hence, for broad lobes like those of the dipole or for small angular increments such as 0.1 degree, there may well be a considerable set of angles having the same gain value. Similar techniques may be applied to any of the headings identified in terms of gain, such as rear and side lobes.)

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In fact, the identification of the first-encountered lobe as the main lobe and the other dipole lobe as non-main is arbitrary and a function of the polar plot system design. Electrically, both lobes are equal. However, it remains a user task to examine the plot and the data included with it to establish that the pattern is equally bi-directional. Certain cases, such as very closely spaced wires of which only one has a source, may exhibit bi-directional patterns broadside to the wire pair but show a very tiny (and normally operationally insignificant) differential in gain in the plane of the wires. For cases of true bi-directionality, the availability of a clear graphic representation of the pattern and confirming data tends to make the arbitrary designation of one lobe as the main lobe harmless.

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The right side of Fig. 7 present the same situation in a different context. Although the pattern is directional when looking at the plot from left to right, we find a symmetry when viewing the pattern vertically. (The pattern is for a single end-fed unterminated long-wire antenna, with the source at a position corresponding to the left side of the pattern.) Since this particular facility counts counterclockwise, the main lobe is at the first maximum-gain angle greater than zero. The sampling technique does not encounter the second and equal lobe until it is approaching 360 degrees in its sequential scan. Therefore, the lobe with the lower angular value receives the main lobe designation, with its equal mirror lobe receiving secondary status. Once, more, the user must use a careful review of the plot and associated data to confirm that the two lobes are equal.

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We may complicate the task facing a polar plot facility even further by increasing the number of main-lobe equivalents. The pattern shown in Fig. 8 is for a center-fed doublet that is many wavelengths long. The model extends the wire parallel to the -X/+X axis, so that the broadside direction is up and down relative to the page or screen. In this case, the program identifies the main lobe as the first lobe of maximum gain that it encounters counting counterclockwise from zero. The secondary lobe is the next lobe of maximum gain that it encounters as the angle of sampling increases. This lobe becomes the side lobe. However, two other lobes in the pattern have maximum gain values but receive no markers. In this case, the user who restricts himself to the graphics and data within the polar plot facility can only presume that the remaining main-lobe equivalents are in fact the symmetrical matches of the lobes bearing designations. Confirming true symmetry in the model requires attention to the detailed radiation pattern data in the NEC output report or to any convenient truncated version provided by the software. For simple models, such as those used to illustrate these notes, a presumption of symmetry may be justified. However, for more complex geometries, the presumption may hide subtle differences.

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By now, it should be clear that the desired identifications of all relevant lobes on a plot is likely impractical. This conclusion applies not only to the differentiation of all forward and rearward lobes for a directional antenna, but as well to antennas such as shown in Fig. 7 and Fig. 8. Indeed, a plot with lines indicating each lobe would clutter the graphical presentation and obscure the pattern shape. At the same time, scanning the tabular data is often cumbersome, since a full azimuth/phi scan with 1-degree increments will have 360 entries. If we use an increment of 0.1-degree, the number of entries increases tenfold.

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However, there is a technique that might be used to create a compact table that shows only the headings of lobes and nulls within the overall pattern. No system is likely to be perfect in the sense of recording where lobes should be but are mere bulges. For example, a vertical antenna place well above ground will show a depression of both gain and null-depth values in elevation/theta patterns at the pseudo-Brewster angle. Nevertheless, a suitably programmed sampling and comparison routine could identify all of the lobes and nulls in a pattern using a simple comparison with values at adjacent sampled angles. When placed in tabular form, the table might look something like Table 1, which records the lobes and nulls for the pattern in Fig. 8.

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One might embellish the table with whatever other data one might wish to have. Pattern component information is readily available from the NEC output report. The table itself calculates the ratio between the pattern's maximum gain and the lobe or null value. Note that NEC uses a limiting value of -99.99 dB for values lower than that number. Hence, the calculations for the ratio also use 99.99 as a placeholder. One version of MININEC provides lobe data within its polar plot screen, so the technique is not beyond possibility. However, for extremely complex plots, like those we might obtain from an unterminated rhombic with extremely long legs, the table may require considerable size. Hence, an independent table might be a better program facility.

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The existence of such a table can be quite useful. By examining the table and the polar plot together, the user may decide which lobes count as forward and rearward lobes for a non-standard directional antenna plot. As well, the short table allows quick identification of all equivalent main lobes and their headings. Moreover, the comparative null depth values in a many-lobed pattern can be very instructive. (Unfortunately, the information in Table 1 does not result from software, but only from an eyeball scan of the full radiation pattern data in the NEC output file. However, the exercise may have converted my eyes into a different kind of software.)

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Conclusion

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In my exploration of the "perfect" polar radiation pattern plot, I have purposely exceeded the boundaries of what we should expect such plots to show us, especially in the face of the great variety of possible antenna patterns that might emerge from models. The pretext has provided an opportunity for us to refine that ways in which we look at such plots to derive from them--and the accompanying tabular data--the most data. At the same time, the exercise has alerted us to limitations inherent in converting tabular data into a graphic form.

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We may overcome some of the limitations by creating external tables. For example, we might export the radiation pattern portion of the NEC output data to a spreadsheet which then automatically calculates the lobe and null information contained in Table 1. As well, we might use that data to create a rectangular graph of the lobes and nulls for easier identification. (NSI implementations of NEC provide such a facility. Fig. 9 provides a sample rectangular version of the polar plot in Fig. 8.) Nevertheless, tabular data remains the most precise method for identifying and quantifying the many lobes and nulls in a radiation pattern, as well as obtaining an accurate measure of their relative values and the rates of change.

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127. A Potpourri of Modeler Miscellanea

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L. B. Cebik, W4RNL

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In the course of modeling, analyzing models, looking at modeling software, and sundry activities, I run across bits of information that might be useful to other modelers. Normally, I wait until I have a sufficient collection of information of a particular theme and then incorporate my scraps of information into the broader column. However, some useful items seem never to have a thematic home. So they sit forlornly on note-pad sheets, pieced by the old-fashioned spindle file that I use. Some scraps of paper have multiple holes, because I use the notes myself. Eventually, the paper begins to yellow and grow crisp around the edges. That is my warning to either use the data or lose it in a fit of housekeeping.

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The notes in this column are my attempt to pass along some items that I have found useful. Perhaps the one common thread is that all of the small entries share is an involvement with numbers. None of these matters is particularly new. Instead, each matter represents something useful that we do not happen to find in common handbooks, especially those directed toward radio amateurs. A few are matters that we forget with age and distance from school. And some are items that we all too easily overlook on the first go-around and never return for a second look.

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1. Pseudo-Brewster Angles

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Chapter 3 of The ARRL Antenna Book contains an excellent introduction to the effects of ground upon antennas of various sorts. An interesting section of the treatment concerns the pseudo-Brewster angle (PBA) as applied to the radiation patterns of vertically polarized antennas (pp. 3-15 through 3-15 of the 20th edition). The PBA rests upon adapting optical concepts to the reflection of radio waves by the ground as a lossy medium. Let's assume that the radio source is a point that shines equally in all directions. It shines both downward and upward. Therefore, radio waves (or rays) at various angles above ground will sometimes add and sometimes subtract from each other, creating the lobes and nulls that become familiar in elevation patterns we draw from antenna modeling software. Unfortunately, the current chapter does not illustrate the PBA with any such patterns, so many folks just pass over the material without realizing its implications. Therefore, let's approach the PBA from the other direction.

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Fig. 1 shows the elevation patterns of a single vertical antenna (a J-pole), but over 3 different levels of ground quality. Very good ground has a standard definition of a conductivity of 0.0303 S/m ad a relative permittivity (dielectric constant) of 20. The values for average ground are 0.005 S/m and 13; while for very poor ground, the values are 0.001 S/m and 5. The red lines in the figure indicate an elevation region in which the lobes diminish in strength and the nulls diminish in depth. The result is a gain level that is close to the free-space gain of the antenna. This is the PBA, the angle at which the incident and reflected rays neither add nor subtract from each other.

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The next notable feature of Fig. 1 is that the angle changes as we change the ground quality. The better the ground quality, the lower the elevation of the PBA. The effect occurs at all frequencies, although it has a major impact on lower HF antenna installations. As well, the effect results largely from waves already in the far field, so adding radials to a monopole to improve ground quality has minimal consequence for the PBA. The figure uses antennas a many wavelengths above ground so that the effect shows clearly in the elevation pattern that consists of many lobes and nulls.

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The Antenna Book account provides a very precise and equally forbidding set of equations for calculating the PBA. They involve calculating the complex relative permittivity of the soil with the required frequency adjustments and then using this calculation in a long equation. In many instances, we only need to know the general vicinity of the PBA for the soil quality that we estimate beneath our feet. Over dry land, the soil conductivity plays only a small role in determining the PBA. Therefore, we may use the relative permittivity alone to calculate an estimated PBA that is good within perhaps +/-2 degrees of elevation over poorer soils and within perhaps +/-1 degree for better soils, all from the mid-HF region upward. One shortcut equation follows:

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Since we are only estimating the PBA, you might use either the arcsin or the arctan of the expression in parentheses, where epsilon is the symbol for relative permittivity. For very good soil, we obtain an angle of about 12.5-13 degrees. Average soil gives a value between 15.5 and 16 degrees. Very poor soil yields 24 to 26 degrees. You may compare these values to the angles of the lines in Fig. 1.

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The precise value of the PBA rests on several factors, such as the source being a true point, knowing with quite good accuracy the soil conductivity and permittivity at depths to which radio waves penetrate, and the frequency of operation. The crude estimate, which does not depart too far from the calculated values in the Antenna Book (Chapter 3, Table 3), bypasses most of these factors. Hence, its use is limited, mostly to partially explaining the depression region we find in elevation angles of all vertically polarized antennas and to setting an expectation that finds the depression region in these radiation patterns normal rather than odd. If your operating frequency is quite low or you are over salt water, use the entire equation in the Antenna Book.

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One final note: the PBA is not dependent upon antenna height. As shown in Fig. 2, antennas a different heights show just about the same PBA or depression region of the elevation pattern. However, the patterns that we encounter for lower vertical antenna heights become ambiguous. Very often, we cannot tell if the depression is a PBA effect or a simple shallow null between lower-angle lobes. As we raise the antenna--in this case to a height of 5 wavelengths--the picture grows clearer. Without PBA, the null between the lower two lobes in the upper portion of the figure would be deeper. Still, since we are never without PBA when using a vertical antenna, we cannot achieve the deeper null between lobes, at least not over dry land.

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For modelers, the introduction of the crude PBA calculation should take the mystery out of elevation patterns for vertical antennas, especially those well above ground. Those who have only modeled a few such antennas may wonder whether the depression region is a software problem or a problem with their particular model. Actually, it is neither. Rather it is part of the normal propagation of far-field radiation. (Horizontal antennas do not share this effect, at least not in the same way or to the degree shown by vertical antennas.)

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2. The Velocity Factor of Coaxial Cables

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Most introductory texts for amateur radio operators present the concept of a coaxial transmission line or coaxial cable in an abbreviated and incomplete manner. Fig. 3 outlines the essential dimensions of the cable necessary for calculating the characteristic impedance (Zo) of the line. The dimension D is the diameter of the inner surface of the shell or braid, also generally called the outer conductor. Dimension d is the outer diameter of the center or inner conductor. Due to skin effect at HF and above, current do not penetrate deeply into either conductor. Therefore, the outer surface of the braid or shell does not plat a role in the transmission-line function of the cable. However, it may play a role in radiation or common-mode currents.

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Between the inner and outer conductors of a coaxial transmission line, there is a space that cable makers fill with an insulating or dielectric material. The material may range from dry air to an inert gas to a foam material to a solid plastic material. The dielectric plays a role in the determination of the cable's Zo according to the relative dielectric constant or permittivity (epsilon) of the material. Therefore, the complete equation for calculating the Zo of a coaxial cable requires that we include the factor:

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In most lower-level treatments, we do not find epsilon. Rather, the treatments assume the improbable case of using dry air as the dielectric. Dry air has a relative permittivity of about 1.0, and so the term drops out. In fact, most of the cables used by radio amateurs (and professionals) use a dielectric other than air.

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The missing term then creates a mystery. Independently, we are told that all transmission lines have a velocity factor (VF) such that the cables electrical length is always longer than its physical length. The ratio of physical length to electrical length defines the VF value. Hence, a cable with a VF of 0.67 is electrically 1 wavelength long when the cable is physically about 2/3 wavelength long. We may acquire a sense of the source of the velocity factor's source by noting differences in the dielectric material used on cables with the same designation but using different dielectric materials.

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The unknown might go away if we began with the more complete equation for calculation a cables Zo. Then we could set up the relationship between epsilon and VF:

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This version of the relationship requires that we know the dielectric constant for the material used between cable conductors. In fact, cable specification tables are more likely simply to name the dielectric material and to list a velocity factor value. Therefore, we may turn the simple equation around.

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Using this equation, we may easily derive the dielectric constant for the cable material. For example, one common dielectric material used in cables is called FPE or foamed polyethylene. A typical cable VF using this dielectric is 0.78. Our handy equation yields a permittivity of about 1.6. Foamed polyethylene is a mixture of solid polyethylene and trapped dry air. Therefore, our exploration of the dielectric material must end here.

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Cables with solid dielectrics are historically older and use a solid polyethylene material. A typical VF value is 0.66. By our equation, the resulting permittivity value is about 2.3. A table in Kraus' Antennas shows the value as 2.2, very close to our calculation. (In fact, a value of 2.2 yields a VF of 0.67, another value found in some tables for older coaxial cables.)

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What we learn from this primitive little exercise is that the Zo and the VF of a cable are intimately related and not simply independent facts about cables. Of course, we also need to learn that cable specification tables list nominal or typical values for a line's VF. If the length of a line is critical to a given application, such as the construction of a matching section, then the builder must determine the VF of the line to be used. The precise VF of a line varies from one manufactured batch to the next. For example, some foam lines listed as having a VF of 0.78 actually turned to have a VF in the 0.70 to 0.72 range under tests in the high HF range.

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3. Modeling a Transformer Using NT

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In episodes 95 and 96 of this series, I examined the NEC NT or network command and introduced some rudimentary applications. Since writing those notes, I have acquired another application, but not a sufficient number of others to form an entire episode. So I shall note it in this collection.

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The NT or network command is less familiar to entry-level modelers, although its special application, the TL or transmission-line facility is very familiar. In NEC, a network is a 2-port y-parameter admittance network, as suggested by Fig. 4. The network has two ports, designated externally as end 1 and end 2. These ends simply attach to two different segments within the same model. For most applications, these segments require different wires, although the command allows the ends to be different segments on the same wire.

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Internally, we must enter values for three shunt or parallel admittance values: y11, y12, and y22. See the earlier episodes for more details on the meaning of these entries. Here we wish to focus on a special application: the creation of a rudimentary impedance transformer. To create the transformer, we must know the end-1 impedance (Z1) and the end-2 impedance (Z2). As well, we must decide upon a value for the Q of the end-1 side of the transformer. In our simplification, we may ignore the imaginary components (susceptances) of each entry and simply calculate values for the real components or conductances. We must also take two simple calculation steps before creating input values for the NT command. First, we calculate the ratio of the end-1 impedance to the end-2 impedance (Zr), an easy task. Second, we calculate the transformer turns ratio (Tr), which is simply the square root of the impedance ratio. Under these conditions, we can easily calculate the required real values for the NT command.

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To see how this works, let's examine a real model before and after installation of the transformer. Suppose that we have a resonant folded dipole, such as shown in the upper part of Fig. 5.. It .NEC-format model might look like the following lines.

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+CM fd #18 cu 1" 28.5
+CE
+GW 1,199,-2.513,0.,0.,2.513,0.,0.,5.119E-4
+GW 2,1,2.513,0.,0.,2.513,0.,.0254,5.119E-4
+GW 3,199,-2.513,0.,.0254,2.513,0.,.0254,5.119E-4
+GW 4,1,-2.513,0.,0.,-2.513,0.,.0254,5.119E-4
+GE 0
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+LD 5,3,0,0,5.7471E+7,1.
+LD 5,4,0,0,5.7471E+7,1.
+FR 0,1,0,0,28.5
+GN -1
+EX 0,1,100,0,1,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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If we run this model, we obtain a source impedance of 288.7 + j0.7 Ohms. Now let's suppose that we wish to install a transformer that yields a perfect match to 50 Ohms. The impedance ratio (Zr) is 5.774, while the turns ratio (Tr) is 2.403. Selection of Q is arbitrary with the user, but should reflect a reasonable component value. Let's use 500 as the value. Under these conditions, the value of Y11-real is 1.7319; the value of Y12-real is -4.1616; and the value of Y22-real is 10.0.

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Now we may rebuild the model to incorporate the NT-transformer. We begin by adding a new wire at some arbitrary distance from the antenna wires. The new wire is short and thin and serves as the segment for end 2 of the NT. As well, we move the antenna source (EX) to this wire to show the transformed source impedance. The NT command places end-1 on the former source segment at the center of wire (or tag) 1 in the model at segment 100. The revised model has the following appearance.

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+CM NT transformer
+CE
+GW 1,199,-2.513,0.,0.,2.513,0.,0.,5.119E-4
+GW 2,1,2.513,0.,0.,2.513,0.,.0254,5.119E-4
+GW 3,199,-2.513,0.,.0254,2.513,0.,.0254,5.119E-4
+GW 4,1,-2.513,0.,0.,-2.513,0.,.0254,5.119E-4
+GW 5,1,-.03048,0.,.9144,.03048,0.,.9144,5.119E-4
+GE 0
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+LD 5,3,0,0,5.7471E+7,1.
+LD 5,4,0,0,5.7471E+7,1.
+LD 5,5,0,0,5.7471E+7,1.
+FR 0,1,0,0,28.5
+GN -1
+EX 0,5,1,0,1,0.
+NT 1,100,5,1,1.731902,0.,-4.161612,0.,10.,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
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In the model, note GW5, the new wire and the placement for the EX command. The NT command shows its connections and the parallel admittance values in order. The zeroes following each numerical value entry represent the imaginary values that we skipped for this simplified transformer. If we run this model, we obtain a source impedance of 50.1 + j0.1 Ohms, just what we wanted.

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In using the NT command as a transformer, newer modelers should be cautious. First, be certain that you do not invert either the value of Zr or of Tr. Suppose that We had a case of up-transformation, say, from 50 to 200 Ohms. Zr is 0.25 and Tr is 0.5, working from end-1 to end-1 of the network. The temptation will be to think of the transformer as having a 4:1 Zr and a 2:1 Tr, when the situation requires just the obverse. Second, the use only of conductance components in the network provides an illusion of frequency-independence for the transformer. Hence, we might press it into service as a modeled substitute for a 4:1 balun, many of which are rated for 3.5-30-MHz use. However, over a wide frequency range, we may encounter at least two major variations from our simplified model. The first variation involves the Q of the device components, which may change over a wide frequency range. Remember that we only selected a plausible value, not an actual value. The second variation lies in the device we are modeling. Not all real transmission-line transformers handle highly reactive loads (or antenna element impedances) in the same way as our basic model of a transformer. I have directed these cautions to the newer modeler on the assumption that experienced modelers will automatically be duly cautious.

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4. The Center of a Triangle

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Our next bit of information arises out of numerous models that I have examined and e-mail questions. Suppose that we wish to model a geometric shape with the coordinate origin (X=Y=Z=0) at the center. The process is simple for squares and larger polygons. For example, if we have a horizontal square loop, we may take 1/2 the length of a side and use the number as the X and Y values (with suitable + and - designations) as the four corners of the loop. It is now centered on the coordinate system origin.

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However, if we wish to set up an equilateral triangle with the same result, troubles begin. Most of the difficulties stem either from sleeping in trig class or from too many passing years since that lesson. Most of the models that come my way use eyeball measures for the corner positions. If it sort of looks equilateral, then it is close enough for the model.

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The equilateral triangle is actually a model of simplicity if we remember that the sine of 30 degrees is 0.5 and the cosine of 30 degrees is 0.866. Each corner angle of the triangle will be 60 degrees, and we shall be interested in bisecting each angle into 30-degree angles to obtain a center triangle. Fig. 6 shows the general layout and the essential relationships among the parts.

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Bisecting each corner angle produces three lines. Where they cross is the center of the triangle. The process creates 6 right triangles, with each composed of an a-, a b-, and a c-line. Because any long line (a + b) is the side adjacent to the hypotenuse (S) of the figure, its length of 0.866 times S. Every b-line is 1/2 a, or every a-line is twice b. Since the junction of every a-line with the extending b-line is the center of the triangle, the distance from the center to a corner (that is, a) must be 2/3 of a + b. 2/3 of 0.866 S is .577 S. If we set up the triangle so that one corner is parallel to a coordinate axis (arbitrarily X), and if the center is at the system origin, then one corner of the triangle will be at 0.577 S in that direction. The remaining corners will be at -0.289 S along the X-axis. The Y coordinates will be + and - half the value of S. You may check your work by using Pythagoras' theorem in which the square of the hypotenuse (c) of a right triangle is the sum of the squares of the other two sides (a and b).

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Suppose that I needed an equilateral triangle that is 45' per side. The point along the +X-axis will be +25.97 (with a Y coordinate of zero, of course). The remaining corners will have coordinates of -13.01, -22.50 and -13.01, +22.50. If I apply the theorem to these "back" corner coordinates, I should come out with the value of the X-axis coordinate. Allowing for rounding, a result of 25.98 is close enough to ensure excellent symmetry and a circumference that is on target with the project. (Your hand calculator may give you further precision by adding decimal places to the process, but you will have to decide how many places you enter into your model.)

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There is, of course, nothing startling or new in all of this. The entire function of this note is to remind the forgetful (like me) that we can set an equilateral triangle with good precision. We can then use program rotation facilities to align the triangle however we need it. If the triangle is vertical, we can construct it in free space around the origin and raise it to height before adding a ground command.

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5. Rho's Phase Angle

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Thirty years ago, radio amateurs knew only one member of a famous trio: SWR (aka VSWR). Like the Ames Brothers other than Ed, the remaining members languished in obscurity. Today, we know all of the names: SWR, reflection coefficient, and return loss. We also know that the three facets of transmission-line behavior are intimately interrelated. That interrelationship has come at a cost.

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We ordinarily (in handbooks at least) begin with the reflection coefficient. The standard, slightly simplified equation has the following appearance, where Ro is the characteristic impedance of the feedline, and Rin and Xin are the resistive and reactive components of the antenna at the transmission line connecting point. |Rho| is the magnitude of the reflection coefficient.

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The simplification in the equation consists of omitting the reactive component of the transmission-line Zo. The reactance for virtually all transmission lines is very small, and users often do not have access to the value without using manufacturer data sheets. Since the reactance is so small, we may omit it without incurring any significant error in the results.

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Next, we often define VSWR based on the value of |rho|.

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Of course, we may calculate the VSWR directly from the Zo of the transmission line and the resistive and reactive components of the antenna feedpoint impedance. We simply substitute the |rho| equation right side for each occurrence of |rho| in the VSWR equation. Because the reflection coefficient fits more readily into other post-measurement calculations a bit more readily that the VSWR, more and more laboratory instruments using software-based calculations provide their results in terms of |rho| rather than SWR. However, if we use the correct Y-axis scale for each, the curves will be identical.

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The final member of the trio is return loss, RL.

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We normally measure RL in dB. Since the reflection coefficient will be less than 1, its log will return a negative number. Older texts handle RL as a negative number, but modern instrumentation has multiplied the result by -1 (hence the - sign in the equation) to yield p[ositive results. We multiply by 20 because the terms are for voltage and we wish a result in dB.

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Since we can derive any member of the trio from the basic terms (Zo, Rin, Xin), the three members of the group are mathematical manipulations, each developed to serve a useful purpose, but nevertheless indicating a set of relationships among the basic terms. If we go only this far, we lose sight of why many texts consider reflection coefficient to be the most fundamental of the three.

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Reflection coefficient |rho| not only has a magnitude, but a phase angle as well. Many texts aimed at radio amateurs omit the derivation of the reflection coefficient phase angle. (If the coefficient did not have a phase angle, we would not need to designate clearly that the calculated value is a magnitude by the use of |rho|.) To fill the blank, you may calculate the phase angle of |rho| by the following equation:

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From the magnitude and phase angle of |rho| you may derive the real and imaginary components just as you would for any other phasor quantity.

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I note this equation to complete the picture, not because you will have any major use for it. However, you may see the reflection coefficient used instead or or in addition to a value for VSWR, and the value of rho may include both a magnitude and a phase angle. For example, the latest implementation of EZNEC has a frequency sweep facility that lists all three members of the trio. Fig. 7 samples the sweep graph for a 5-element Yagi design in all three modes. Note that the graph does not change, but the scale of the Y-axis does. (Some instruments may reverse the vertical order of return-loss scale markings.) The graphing line will only change with changes in the value of Rin, Xin, or Zo.

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Conclusion

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Perhaps the only unifying theme within these notes is that all of them have generated questions from folks at various levels along the road to mastering the art and craft of modeling. Almost all of the answers that I have tried to give have also generated a similar response: "Of course! I should have thought of that!" In addition, I can now remove the papers from my spindle file and clear it for another batch of miscellaneous items that may be useful to one or another modeler.

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128. When Not to Use NEC for Antenna Modeling

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L. B. Cebik, W4RNL

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The following notes compile a number of replies that I have given to various theme-related e-mail inquiries on using NEC at or beyond the limits of its capabilities. In a number of cases, I have suggested that NEC (either -2 or -4) may not be the software of choice for various modeling enterprises. In other cases, I have suggested that the user must employ experimental calibration techniques prior to using NEC models, especially when the goal is to design a working antenna, even of ordinary types. Understanding what NEC can and cannot do is critical to making best use of the software. Let's examine a few interesting cases at or beyond the limits of NEC.

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Non-Round Elements

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One of the most common inquiries in home antenna construction is whether one might substitute non-round wires for round wires that most handbooks suggest for antenna elements. Of course, there are practical reasons for using round antenna elements. For the most part, round elements slip the wind better than most of the alternatives, especially when the elements have a significant radius. As well, many materials accumulate snow and ice faster and thicker than round elements. However, elements with flat surface appeal to home antenna builders for numerous reasons. First, the materials are readily available from various local sources. Second, they have flat surfaces that many less-experienced builders find easier to handle and drill than round elements.

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Rather than trying to adjudicate the pros and cons of element materials with flat surfaces, let's confine ourselves to the question of trying to use NEC to design or to refine the design of a typical antenna, perhaps a modest Yagi. Fundamentally, NEC begins with a thin-kernel model of all wires in the antenna geometry. The thin-kernel model presumes a bare round wire in free-space or its equivalent, that is, a vacuum or dry air. As the NEC-2 manual explains, "In the thin-wire kernel, the current on the surface of a segment is reduced to a filament of current on the segment axis. In the extended thin-wire kernel, a current uniformly distributed around the segment is assumed. The field of this current is approximated by the first two terms in a series expansion of the exact field in power of aa [where a is the wire radius]. The first term in the series, which is independent of a, is identical to the thin-wire kernel, while the second term extends the accuracy for larger values of a. Higher order approximations are not used because they would require excessive computation time."

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"In either of these approximations, only currents in the axial direction on a segment are considered, and there is no allowance for variation of the currents around the wire circumference. The acceptability of these approximations depends on both the value of a/wavelength and the tendency of the excitation to produce circumferential current or current variation. Unless (2*pi*a)/wavelength is much less than 1, the validity of these approximations should be considered." One potential arena in which the validity of these approximations may be tested is the modeling of a boom connected directly to the parasitic elements of a Yagi antenna. In practice, the connection or the very close proximity of a boom to the parasitic elements alters the required length of the elements to preserve array performance. However, in NEC-2 and NEC-4--when modeled within the other limitations of the software--the boom has no effect upon the parasitic elements.

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The NEC-2 manual goes on. "The accuracy of the numerical solution for the dominant axial current is also dependent on [the ratio of segment length to radius or Ls/R]. Small values of [Ls/R] may result in extraneous oscillation in the computed current near free wire ends, voltage sources, or lumped loads. Use of the extended thin-wire kernel will extend the limit on [Ls/R] to smaller values than are permissible with the normal thin-wire kernel." In general, Ls/R must be greater than 8 for errors under 1% for the normal thin-wire kernel. This amounts to a segment length-to-wire-diameter ratio of 4:1, for programs that input wire thickness as a diameter. The manual notes that "reasonable solutions" have been obtained for the normal thin-wire kernel for Ls/R values down to about 2, with equally "reasonable solutions" for the extended thin-wire kernel for Ls/R values down to about 0.5.

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In NEC-4, according to its manual, "the thin-wire approximation is now implemented with the current treated as a filament on the wire surface and the boundary condition enforced on the wire axis. With the boundary condition enforced on the wire axes, the openings at wire ends should be closed with end caps. This is particularly important when the ratio of segment length to radius is on the order of 2 or less. Wire ends are closed with flat caps in NEC-4, with the current and charge density assumed continuous from the wire onto the cap." NEC-4 also includes optional caps for use with voltage sources with equally low values of Ls/R. "This approximate treatment was found to be about as effective as the extended thin-wire kernel included as an option in [NEC-2 and] NEC-3. The extended thin-wire kernel option (EK card) has been dropped from NEC-4."

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I have repeated these extracts from earlier episodes in the series because every user needs periodically to review the fundamental premises underlying the software. These premises reveal to a large extent the limitations of the software. The thin-wire kernel model of the currents along an antenna element wire provides us with one of those limitations. We cannot automatically transfer the results of a model to a physical implementation that uses non-round elements.

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For many substitute elements, we may use NEC models effectively if we carry out for the frequency and material that we propose to use a series of simple experiments. I had occasion to perform such a calibration exercise in connection with the design and implementation of several alternative versions of a 3-element Yagi for 146 MHz. The procedure that I used may be instructive. However, for a specific project, the required effort will be considerably shorter than I needed for a survey that involved numerous materials.

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The first step involved constructing a series of round element dipoles for the test frequency. In this step, I was interested in learning to what degree physical antennas using the proposed construction methods might vary from models that included none of the hardware and other appertenances that are required parts of the proposed antenna. Table 1 summaries the results for a range of round 6063-T832 aluminum elements from 1/8" to 3/4" in diameter.

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The table itself does not comment on the accuracy of NEC software because it does not show the details of the models, such as the segment density. As well, it does not show the instrument calibration and accuracy. What the table does do is to provide me with a set of expectations relative to correlating other materials to round elements and from there to models.

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The nature of the project involved a number of potential element materials with alternative cross-sections. Fig. 1 shows the varieties that I subjected to tests. One might easily expand the shapes to include square tubing and U-channel aluminum stock. This particulkar collection happened to coincide with the project's overall goals.

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For each material, I created a dipole and brought it to resonance at 146 MHz by the simple expedient of successively shaving the dipole outer ends in small increments, using a disk sander for the final fine tuning. (Sanding, of course, does not apply to the collapsible whips.) Table 2 summarizes the results and shows the conclusions that I reached regarding the correlation of the material at the test frequency to the nearest commonly available U.S. round element size.

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One result that I found somewhat surprising was the close correlation between any of the flat or L shaped materials and round elements when I compared the element width measurement to the tubing diameter. So long as the stock has a significant thickness--1/16" at the test frequency--the width of the stock correlated to the round element with the same value for its diameter. However, for very thin materials, such as the measuring tapes, the simple correlations did not apply. However, the tests did not use techniques that allowed me to separate any effects due to using a very thin element and effects from the ferrous materials used in measuring tapes.

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The correlations allowed me to design and build working 3-element Yagis using any of the materials. In fact, I built one version that used a combination of materials as a demonstration. I can find no performance difference between it and its round-element counterpart. The use of calibration methods does allow the antenna builder to employ NEC in developing an antenna design, so long as one uses due caution. The calibration procedure used here applies to materials at the test frequency plus or minus about 20%. Beyond those limits, I would strongly urge a new set of calibration experiments. For example, if one wished to design a beam for the U.S. 223-MHz band or for the FM band, then one should use calibration experiments designed expressly for those frequencies.

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The Medium Surrounding a Wire

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NEC-4 added the IS or insulated sheath command to the collection of control commands available to the user. A number of implementations of NEC-2 have added codes that either replicate or simulate this command. The command allows the user to specify a wire in the geometry and to encase specified segments in a material having a user-selected set of values that include the material's relative permittivity, conductivity, and outer radius. Thickness is simply the sheath radius minus the wire radius. Numerous inquiries over the years have wondered how far one might extend the sheath to form essentially a special medium for the wire inside. Since the calculations that modify the fields calculated for the wire occur late in the sequence of NEC processes, it is likely that there is a practical limit about how thick one may make an insulated sheath, although I have seen no data on the precise limits.

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Of course, modelers can use the command creatively. One such example is the development of a hollow thermoplastic tube near a radiating wire. To create the tube, the modeler added a wire to the geometry and assigned to it the conductivity of air. The wire diameter corresponded to the inner diameter of the tube. The modeler then added an IS command using the values appropriate to the plastic involved. He gave the sheath a radius corresponding to the tube's outer diameter.

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The limitation of this technique is that one must need a round surface for the structure. However, most modelers are interested in flat non-conductive materials to which we may bond antenna wires. These substrates come in many forms. The next inquiry wondered if one might use the NEC-4 UM command to replicate the substrate. Unfortunately, the UM command has some limitations that largely preclude its use in this manner. Fig. 2 shows the situation modeled by employing the UM command.

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Most substrates have a finite dimension and thickness. The UM command uses a set of constants for the ground and another set for the upper medium. Except for the ground surface at Z=0, each medium is without limit. One may, of course, specify a second medium for the ground, but the depth of each medium will be without limit. Hence, we cannot limit a substrate to its actual thickness using the ground. The antenna environment is the upper medium, which also extends without limit in all directions in the hemisphere above ground. In addition, the UM command is usable only with the reflection coefficient approximation (RCA) ground calculation system, which has limitations of accuracy as the antenna is brought toward the ground surface.

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In general, neither the IS nor the UM command provides a means of approximating the situation of antenna elements bonded to a substrate.

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Substrates and Strip Elements

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A very wide range of antenna applications make use of modified printed circuit board techniques. The essential features of such antennas include the use of relatively wide strip elements having negligible thickness and the use of a substrate to which we bond the elements. The substrate has a certain set of dimensions, along with relevant values of conductivity and relative permittivity. Fig. 3 shows some of the techniques commonly used to form such antennas. The edge views show element ends as an artificially thick line, although the actual strips are very thin.

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The most common type of antenna-substrate combination etches elements on one side of the substrate, as shown at the upper left. However, we may use both sides of the board, as shown at the upper right, to create such antenna types as an LPDA. At the bottom are two variants of the theme, sandwiching the elements between two boards or fully encapsulating the antenna within a molded substrate. These latter forms provide the antenna with maximum protection from environmental or user damage.

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Trying to model these antennas in NEC presents the analyst with numerous problems. First, the strips are very wide compared to the thickness. As our initial experiments using measuring tape showed, when the thickness becomes almost negligible, the material does not perform like a round wire of any predictable diameter. The only way to form any kind of usable correlation is to perform a series of calibration experiments in advance of any modeling.

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The existence of the substrate in contact with the strips on one or both sides and the liited size of the substrate in all dimensions presents additional problems. Although one might reach a workable round-wire free-space approximation of the antenna plus substrate, the effort might require the pre-existence of the finished physical antenna before one could claim any utility to the modeled approximation. For simple antennas, such as dipoles, the problem may not seem difficult. However, for parasitic arrays, the substrate may modify the mutual coupling between elements as well as the performance of each element. Hence, the simple calibration procedure that we successfully used for element materials in free space may not be as successful in the presence of a substrate.

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Many of the techniques that we have just described also involve UHF and higher portions of the spectrum. At these frequencies, the width of the strip elements and even their round-wire correlates may press the limits of the segment-length to radius (Ls/R) recommendations for accuracy in NEC.

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Under these conditions, NEC may not be the software of choice for trying to model the antennas--at least not in detail. There are available hybrid programs, virtually all proprietary, that can handle the modeling situation more directly. In fact, many allow the direct input of CAD drawings, with appropriate translations for antenna calculations. These input potentials allow the user to handle the strip elements directly. In addition, they allow the inclusion of substrates having specific dimensions and properties. Some are also capable of handling an interesting circuit board possibility: the physical inclusion of both antenna and transmission-line strips, as suggested by Fig. 4.

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The sketch shows side-by-side phase line strips feeding the two dipoles from a centered location. (In some software, one may include circuitry beyond the limits of the antenna system.) The reality of the physical structure might use transmission-line strips on opposite sides of the board, where strip width and displacement, combined with the dielectric constant of the substrate, together permit a designer-selected characteristic impedance.

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Many packages employ FDTD techniques in calculating antenna properties within the complex structural situation described here. Although data is the critical calculation output, many such packages have labored long to present the outputs in very attractive graphical forms.

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For modeling enterprises of the sort described here--and others even more complex--hybrid packages are likely the software of choice. In general, these enterprises are not suited to individual efforts, because the investment required is very considerable. NEC users are accustomed to using relatively low-cost software. There are entry-level packages ranging from freeware to commercial implementations with full support at under $100 for NEC-2. NEC-4 requires a license, which is inexpensive for the individual serious user, and commercial NEC-4 packages run well under $1000. Hence, the practicing consulting engineer can easily afford the best of NEC.

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Full-featured hybrid packages may require $50,000 or more, in addition to the cost of sales commissions and seminars to ease the very steep learning curve required to use the packages effectively. The hybrid packages tend to be corporate investments, with costs recovered from the mass sale of systems that emerge from their use. Because these packages do much more than just allow one to design and analyze antennas, it is impossible to apportion costs to a single function. Nevertheless, the packages tend to fall well outside the range that most individuals can invest.

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I have not been more definite about the specific capabilities of hybrid packages because they also and easily fall outside my ability to afford. A web search or a recent issue of a journal for professional RF engineers will provide contact with the vendors of such packages. Over the last decade, the number of vendors has shrunk due to purchases and mergers. In the process, the capabilities of individual packages have increased for the same reason.

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Conclusion

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In these notes, we have examined three situations. The first involved the use of non-round shapes for which we can find for a given frequency range equivalent NEC wire sizes to provide accurate models of the physical antennas that use the odd materials. However, as we contemplate the combination of conductive and non-conductive materials in proximity, we may try to use some of the special commands available, especially in NEC-4. This second situation brought us to an understanding of some of the limitations of commands such as IS and UM. In general, these commands are unsatisfactory for use with strip elements bonded to substrates, a common construction technique for a wide variety of antennas used in the UHF and higher portions of the spectrum. This third situation brought us to the general conclusion that the round-wire, axial-current, free-space environment at the heart of NEC may not be the most apt vehicle for the design or analysis of the subject antennas. As versatile and flexible as NEC may be, it is not a universal software modeling system for all possible antennas.

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For round-wire antennas, NEC remains the software modeling system in widest use. It is generally very cost effective, especially for amateurs, consulting engineers, and others dealing with the design or analysis of one-of-a-kind antennas or antennas that fit its special capabilities. Indeed, the relatively low cost, even of NEC-4 plus a license, has led to the development of numerous work-arounds for some of its limits. For example, many Yagi designers who use a direct connection or extremely close proximity between antenna elements and a supporting conductive boom introduce short, fat center element sections to account for the boom effects that NEC cannot directly calculate. In these notes, we have seen the relative ease of calibrating materials with an odd cross-section to NEC's round wires. Other episodes in this series have shown additional work-arounds for situations that press NEC's limitations.

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Nevertheless, in the field of antenna modeling, NEC cannot do everything.

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129. Some Rudiments of Receiving Pattern Modeling

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L. B. Cebik, W4RNL

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In episode 88 of this series, we examined the use of two commands that are essential to developing antenna receiving data: EX (1 through 3) and PT (1 through 3). Nevertheless, I continue to receive inquiries on the basic methods of developing receiving data from both new modelers and radio amateurs. The requests contain various questions, of which the following three may be a summary.

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1. How do I obtain receiving data?

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2. What does the data tell me?

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3. Of what use is the data?

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Therefore, we might wish to begin again. We shall re-examine the commands, but reduce the scope of their possibilities to a limited subset. Then we can apply the commands to a few examples that will illustrate the process of developing useful information. The samples will be very rudimentary and hence have little new to show us. However, we are more interested in the basic methods of generating the information. We shall discover that we may often have to resort to supplementary external calculations (easily done with a spreadsheet) to make full and meaningful use of the information that we collect.

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Getting Started: EX 1 and PT 1

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To develop receiving patterns and data, we must have access to some control commands that many entry level implementations of NEC omit. (Even if our package has the commands, the odds are that we have not used them.) Most modelers use only the EX 0 excitation command to set the source voltage (or, indirectly, the current) on a selected segment of a modeled antenna geometry. The left side of Fig. 1 shows the situation with which we are most familiar.

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To obtain receiving data, we must use different options available for the EX command, namely, EX 1, EX 2, or EX 3:

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EX 1: incident plane wave, linear polarization

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EX 2: incident plane wave, right hand (thumb along the incident vector) elliptic polarization

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EX 3: incident plane wave, left hand (thumb along the incident vector) elliptic polarization

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In these notes, we shall bypass the elliptical polarization options and work solely with linear polarization, EX 1. Regardless of which of these incident plane wave excitation modes that we select, note from the figure that the excitation is external to the antenna geometry. However, the figure has an inevitable flaw. By giving the excitation a position external to the antenna, the sketch invites the temptation to think of the excitation as a point having different angular directions to various parts of the antenna wire. A more accurate picture, but one that I do not know how to draw, is to place the source at an indefinitely large distance from the antenna wire so that the illumination is uniform over the entire antenna geometry.

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We must set up the EX command to position the source relative to the antenna. The entry-line structure for them has a number of interesting properties that differ from the line structure of a simple voltage source. (Reminder: although you may use both an EX 0 voltage source and a plane wave source in the same model, the last source type will determine the format of the output report and the function of any RP command.)

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+Com  I1   I2     I3     I4   F1        F2        F3         F4    F5   F6    F7
+ID   Type # Thta # Phi  Not  Th angle  Ph angle  Eta        Theta Phi  Axis  El. field
+          angles angles used to vector to vector pol. angle step  step ratio V/m
+EX   1    1      8      0    90        0         90         0     45   0     0
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The sample entry is for a linear plane wave. Hence, F6 is 0 by non-relevance. F7 also has a 0, but that value indicates a default value of 1 V/m. In some problems designed to ferret out coupling potentials among wires, you may use a specific value that closely approximates the value from the source signal at the structure being examined in model form. NEC-2 lacks the F7 field and hence always uses 1 V/m. As we shall see, this limitation is not a significant problem.

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Most of the remaining entries define incident plane waves as a calculation loop within NEC (with some properties resembling the loop operation of frequency sweeps using the FR command). In the sample, for the sake of clarity, there is only one theta angle: 90 degrees. This angle is parallel to the plane of antenna elements that extend parallel to the X-Y plane and is equal to an elevation of 0 degrees. The sample specifies 8 phi-angle (azimuth-angle) steps at 45-degree increments, thus providing samples evenly spaced in the element plane.

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The F3 entry, called Eta, under linear polarization is easy to memorize. With a value of 0, the polarization is in the +/-Z direction--vertically polarized for antennas over ground. If F3 is 90, the polarization is in the X-Y plane--horizontally polarized for antennas over ground. We shall place our antenna in free space with the wire extended in the X-Y plane and then use horizontal polarization for simplicity, but there is no restriction against checking results when cross-polarized or with the polarization set to intermediate angles. When using EX 2 or EX 3, elliptical polarization, the entry changes its meaning and defines the major ellipse axis. (Remember that true circular polarization is simply a special case of elliptical polarization having equal axes.)

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Having set up the excitation, we must then enter commands that will give us useful data. We might use an RP 0 command to request a pattern, but this information will be of use only to those interested in radar and similar work. The pattern that we obtain will be for scattering data, the reflection of radio wave off of the object. However, we shall set up an antenna and will be more interested in the energy that we receive from the uniform 1 V/m illumination. NEC calculates for each segment in the geometry the peak current. This is highly useful information. To obtain it we must use the PT control command. Like the EX command, it has several options.

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PT -2: All current printed. This also occurs if PT is omitted altogether.

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PT -1: Suppress printing of all wire-segment currents.

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PT 0: Current printed for specified segments only.

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PT 1: Currents printed in a format designed for a receiving pattern.

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PT 2: Currents printed in a format designed for a receiving pattern, plus a normalized value for the last segment's current.

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PT 3: Only the normalized current is printed.

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The current tables that we obtain when using a modeled antenna with a voltage source result from not entering a PT command at all, which results in the PT -2 option by default. For receiving data, we need to look at the PT options from plus 1 through plus 3. In fact, we shall only use PT 1 in this episode, leaving the other options as (pardon the expression) an exercise for the reader. The PT entry is very simple.

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+Com  I1    I2     I3       I4
+ID   Type  Tag #  1st Seg  Last Seg
+PT   1     1      8        8
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The command only requires that we specify the tag (wire) number in which we are interested, along with the range of segments on that tag. Although we might in many instances be interested in the current magnitude and phase on many segments in a model, the sample reduces the range to a single segment.

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Let's combine these lines into a different set of concluding lines for our initial model.

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+PT 1 1 8 8
+EX 1 1 37 0 90 0 90 1 10 0 1
+XQ
+EN
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The EX 1 command specified 37 different readings separated by 10 degrees each on the phi circle, with all of them having a theta angle of 90 degrees. Eta is also 90 degrees, indication that if the antenna element is parallel to the X-Y plane, the excitation source will be polarized in plane with the element. Note that the PT command is not like RP, that is, it is not self-executing. Therefore, we must add the XQ command in order to force the program to calculate the currents.

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Orientation to a Specific Model

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Fig, 1 showed a model of a dipole. Let's confine ourselves to this familiar antenna and create a pair of models in a single model file (using the handy NX command) to illustrate the differences between a transmitting and a receiving situation.

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+CM dipole 300 MHz EX0/RP0
+CE
+GW 1 15 0 -.2373 0 0 .2373 0 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 0 1 8 0 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+NX
+CM dipole 300 MHz EX1/PT1 no load
+CE
+GW 1 15 0 -.2373 0 0 .2373 0 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 1 1 37 0 90 0 90 1 10 0 1
+PT 1 1 8 8
+XQ
+EN
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The geometry section of both models are identical, as is the FR command. The upper model uses an EX 0 source command to provide transmitting data that we can obtain from the tabular outputs or from a handy graphical representation of the radiation pattern. As we might expect, NEC calculates free-space gain as 2.13 dBi, with a source impedance of 71.72 - j0.16 Ohms. (The source impedance is often more important for receiving data gathering than the transmitting gain, which equally applies to reception by virtue of reciprocity.)

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At most, we might find a rectangular graph for the data gathered by the PT 1 command in the lower model. We can recognize that the specified tag and segment for the data is the very same segment that we used in the upper model as the source segment. Let's look at a few lines from the tabular data produced by the lower receiving model.

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+- - - RECEIVING PATTERN PARAMETERS - - -
+      ETA=  90.00 DEGREES
+      TYPE -LINEAR
+      AXIAL RATIO= 0.000
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+THETA      PHI          -  CURRENT  -         SEG
+(DEG)     (DEG)       MAGNITUDE    PHASE      NO.
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+90.00      0.00     4.3935E-03     -3.08        8
+90.00     10.00     4.2975E-03     -3.07        8
+90.00     20.00     4.0208E-03     -3.03        8
+90.00     30.00     3.5949E-03     -2.98        8
+90.00     40.00     3.0627E-03     -2.91        8
+90.00     50.00     2.4681E-03     -2.83        8
+90.00     60.00     1.8475E-03     -2.75        8
+90.00     70.00     1.2244E-03     -2.69        8
+90.00     80.00     6.0886E-04     -2.65        8
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As we move the plane-wave excitation source position, we can see that the current magnitude (in peak Amps) changes, as does the phase angle, on the segment of the antenna that formerly held the EX 0 voltage source. The question that arises next is how this data is meaningful to us. It is meaningful, but perhaps not just yet.

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Loading the Former Source Segment

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The source segment on a transmitting antenna becomes the load segment on the same antenna when receiving. However, if we think of the load as the receiver terminals, we normally are less interested in the current at the terminals than we are in the voltage. As well, a receiver presents the antenna feed segment with a load. We shall ignore for this simple exercise the role of the transmission line in setting the load at the feedpoint segment and assume a direct connection. Hence, to acquire meaning full data in an extended sense from the model, we normally would place a load on the feedpoint segment, as suggested in Fig. 2.

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The question that emerges is what load we should use. Let's explore a bit by placing resistive loads from 10 through 150 Ohms on the feedpoint segment (Tag 1, Segment 8). A simple LD 4 command will do the job. Then we can set up a model to progressively record the current that appears on the segment with each load value.

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+CM dipole 300 MHz EX1/PT1 loads
+CE
+GW 1 15 0 -.2373 0 0 .2373 0 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 10 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 20 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 30 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
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The partial model file shows the simple technique used to accumulate data on the performance of the antenna relative to feedpoint current using various resistive loads. (The file contains for reference a model version that uses no loading as a check on the model's formation.) We can place the results into a table on a spreadsheet, which will allow us to perform some supplementary calculations. See Table 1.

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The first data line below the resistive load values provides us with the data reported by NEC. Since we normally use RMS values of voltage and current for various purposes, the next line performs the required conversion. The following lines provide the power and the voltage for each load.

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The importance of placing a load on the feedpoint segment lies in the fact that it allows us to perform the last two calculations. P = I^2R, and E = IR = SQRT(PR). Without the load value, we have no way to determine these values. The pattern of values simply confirms what basic texts teach about energy. As we raise the value of the load resistor, the voltage at the receiver/feedpoint terminals increases. Fig. 3 graphs the rise in voltage with the increase in the selected load resistor.

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The graph also includes the calculated power at the feedpoint terminals. Note the peak in the power level at approximately 70 Ohms load resistance. We obtain maximum power transfer when the load matches the source impedance. The transmit version of the antenna yielded a source impedance of about 72 Ohms, and the 70-Ohm load resistor comes closest to matching that value. (Numerous modelers arbitrarily place 50-Ohm loads across the antenna terminals without first checking the antenna's source impedance. In some cases, there are good reasons for doing so, although in other cases, the load is a matter of habit. If the impedance of the antenna and the load are distant from each other and a transmission-line intervenes, then the load resistor may not accurately reflect the conditions at the receiver terminals.)

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The Effects of Eta

+

So far, we have only sampled the sorts of information that we likely knew about antennas under receiving conditions. Plane-wave excitation also permits us to sample some facets of performance that we have largely taken on faith. For example, we learn that cross polarization of linearly polarized antennas seriously degrades received signal strength. Our rudimentary experiments let us sample the effect in greater detail. The models that we are using are somewhat idealistic, since they use lossless wire in free space. However, as a start, they will give us a baseline against which to compare the results of antennas that we may place over ground.

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The only variable in this new exercise is the value of Eta as we hold other values constant. Fig. 4 shows the general situation. Let's retain the dipole set up parallel to the X-Y plane. Although the sketch shows a bit of displacement so as not to muddy the figure, the plane wave source is at 0 degree phi. If Eta = 90 degrees, it will be in-plane with the dipole. If Eta = 0 degrees, it will be cross polarized relative to the receiving dipole. As indicated by the sketch, we may select any angle in between.

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In order the give sense to the data, we must use a single value for the load resistor. For the runs that we shall make, 70 Ohms seems appropriate. We may set up a model following the same procedures used in the initial exercise.

+ 
+CM dipole 300 MHz EX1/PT1 70-Ohm load, variable Eta
+CE
+GW 1 15 0 -.2373 0 0 .2373 0 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 70 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 90 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 70 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 80 1 1 0 1
+PT 1 1 8 8
+XQ
+LD 4 1 8 8 70 0
+FR 0 1 0 0 299.7925 1
+EX 1 1 1 0 90 0 70 1 1 0 1
+PT 1 1 8 8
+XQ
+
+

In the new model shown partially above, the LD4 command is the same in each case. However, the F3 position of the EX 1 line changes in 10-degree steps from an in-plane condition toward a cross-polarized condition. Once more, we may tabulate the results and calculate the effects on the receiver terminal voltage, as shown in Table 2.

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The gradual decrease in the terminal voltage comes as no surprise in the progression of Eta values. The rate of decrease becomes apparent if we graph the voltage, as shown in Fig. 5.

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The graphs show the increasing rate of voltage decrease at the receiver terminals as we get farther away from an in-plane condition. In free space, the full cross-polarized condition results in zero volts. Over ground, we would not likely see the absolute zero shown by the free-space model. Ground reflections alone are sufficient to leave a remnant voltage (and segment current), although in models, the level is usually below the level of anything usable. In the real world, with many objects to reflect, refract, and diffract radio waves, we may find usable, if difficult signal levels.

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Varying the Excitation Position

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One of the most useful features of plane-wave excitation is the ease with which we may change the angle of the incident wave. By the proper selection of a range of theta and phi angles, we may not only change the angle of the incident wave, but we may survey a large collection of angles. Fig. 6 suggests the scope of the possibilities.

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I have drawn the circles as ovals for clarity. We may choose a starting value for theta and then select an increment and the number of theta steps. We may do the same for phi. How large we make the resulting table depends on both good sense and how large a table we are prepared to read. For the dipole, it would make no sense to sample more than a single theta angle, since we would obtain the same free-space results with every sequence of phi angles. Since we only need samples, we may use phi angles in 10-degree increments between 0 and 90 degrees. Beyond that point, we would replicate values. The model that we need--using a 70-Ohm feedpoint segment resistor--is very simple.

+ 
+CM dipole 300 MHz EX1/PT1 70-Ohm load, variable phi
+CE
+GW 1 15 0 -.2373 0 0 .2373 0 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 1 1 10 0 90 0 90 1 10 0 1
+LD 4 1 8 8 70 0
+PT 1 1 8 8
+XQ
+EN
+
+

The results are once more amenable to tabulation, as shown in Table 3. The final data entry is technically incorrect. The actual reported value is 8E-15, but it would have shown up as zero if entered in that form.

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We may also graph the calculated voltage values, along the way noticing differences between these voltages and those appearing in the data and graph for the Eta experiment. Fig. 7 gives us the visual reference.

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Although we shall not work these values in this exercise, you may wish to compare them with other data that you collect from models. For example, compare the voltage values as we move the incident-wave angle and compare the results with the gain values in the original transmitting antenna, especially as the transmitting antenna gain passes the -3-dB marks that define the bandwidth. The transmitting plot reports a beamwidth of 80 degrees or 40 degrees each side of phi = 0. At the 40-degree marks in Table 3, we find that the calculated power is just about half the value shown for 0 degrees phi. Of course, the current and voltage each show values that are about 0.7 of the values for 0 degrees phi.

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Conclusion

+

Our goal has not been to uncover anything new about dipoles. Instead, these notes have aimed at familiarizing you with the modeling moves necessary to let receiving data perform useful, even if mundane work. Varying the load resistor, the value of Eta, and the angle of the incident wave relative to the antenna are three variations that we may use individually or in concert to analyze the receiving behavior of simple or complex antenna geometries.

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Although we have used the NEC-2 given excitation value of 1 V/m, in NEC-4, we may select virtually any field strength value we might need for a given project. However, since we supplemented the reported data with rudimentary calculations of other values that we might need or want, we may as easily add a line adjusting the reported current values for adjusted excitation field strength values. The reported current will be directly proportional to the excitation voltage, from which other values will calculate as easily.

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Since our goal has been to display the main manipulations that we may require, we have also bypassed results that we might obtain using elliptically polarized plane-waves. For NEC, an axial ratio of 1.0 indicates a circularly polarized wave, while 0.0 yields linear polarization. By a judicious selection of the ratio of minor to major axis ratio and of the value of Eta, we can obtain virtually any desired degree of ellipticalness.

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Receive data can provide even newer modelers with important data on antenna performance, so long as the implementing software allows access to the EX 1 through EX 3 and the PT 1 through PT 3 commands. Supplementing NEC reports with additional calculations can extend the utility of the information.

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+ + diff --git a/content/amod/amod13.html b/content/amod/amod13.html new file mode 100644 index 0000000..8d8f230 --- /dev/null +++ b/content/amod/amod13.html @@ -0,0 +1,132 @@ + + + + + Some Center Loading Basics + + + +
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13. Notes on Reactive Antenna Loads and Their NEC Models:
+ A. Some Center Loading Basics

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+
+

L. B. Cebik, W4RNL

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+

Although the basics of changing the electrical length of an antenna wire by adding a reactive load to it are seemingly well-known, the precise relationship between real loads provided to real antennas and modeled loads provided to modeled antennas is not so certain as one might think. Therefore, this series of notes will try to look at some of the ins and outs of the matter--all without pretending either to authority or completeness. It will be enough if we can get a better handhold on the subject.

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For antennas up to (but not including) 1/2 wl long, the source impedance is capacitive. To bring the antenna to resonance, we electrically lengthen it by adding an inductive reactance. We can add the reactance at the element center, or we may split the load into two equal parts and place them farther out on the element. The require inductive reactance needed to bring an element to resonance increases the farther out along the element we place the reactances.

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Since every method of implementing an inductive reactance has some resistive loss, the reactive device has a Q, a ratio of inductive reactance to resistance. The higher the Q, the lower are the losses. The most common two means of providing an antenna in the HF region with an inductive reactance are the air-wound solenoid inductor and the shorted transmission line stub less than 1/4 wl long. Both are physical entities having both basic and functional loss mechanisms. For example, solenoid wire for any given RF frequency has an AC resistance that is a function of skin effect. In addition, the interaction of the individual turns of the coil may yield other losses. Whatever the source of the loss, the solenoids Q or figure of merit expresses them all within the resistive denominator of the ratio.

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Modeling Resistance-Reactance Loads

+

NEC (either -2 or -4) provides several means of modeling inductively reactive loads. The most common type is the following:

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Type 4: Complex loads consisting of a resistance and a reactance. This is the native type of load for NEC. All loads are eventually translated into values of resistance and reactance. However, this type of load remains constant. That is to say, for the frequency sweep specified in the simple model in the figure, the values of resistance and of reactance remain the same for each frequency checked.

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Type 4 loads are therefore not useful for frequency sweeps, since real solenoid components do not have the same reactance on every frequency. Reactance changes with frequency in relationship to a solenoid inductance. For most purposes in antenna work, the inductance and the resistance of the coil are treated as constants in simple inductive reactance loading problems.

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Type 4 loads, however, are especially useful for initial design work. For example, if one has a short center-fed antenna, the reactive component of the source impedance will specify the absolute value of center reactive load necessary to eliminate it. The type of reactance introduced will, of course, be the opposite of the reactive component of the source impedance. since antenna wires shorter than 1/2 wl show a capacitive reactance at the source, a center reactive load must be inductive.

+

Type 4 loads are also very useful for setting up or exploring the effects of the load Q on antenna performance. The results will apply only at the frequency for which the values hold good. However, one can easily obtain a family of value curves for comparing various antenna parameters.

+

Let's set up a test dipole to see the type 4 load at work.

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The test dipole is exactly 1/4 wl long at 7.15 MHz, which makes it far short of resonant. We shall introduce a reactive load at the center, in the same position as the source or feedpoint. In NEC models, the source and the load are in series when the modeler specified the same position or segment for both the source and the load. The effect is comparable to splitting the center-loading solenoid at the center to insert the source (normally a transmission line for operational amateur radio stations).

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The test model antenna uses lossless or perfect wire so that the only losses that appear will be from the load or loads we add. It uses 91 segments for reasons that will appear in later episodes. If this little test is replicated, be sure to use the same number of segments as in the example to obtain the same results. Antenna resonance in the modeling exercise is defined as a source impedance of less than +/-1.0 Ohm, and in most cases, the reactance will be less than +/-0.1 Ohm. Since there will be a slight drift in the source impedance as the segmentation of a given wire is changed, even for well-converged models, replication of results requires detailed replication of all of the model parameters.

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We may determine the required load for the antenna simply by reading the source impedance before inserting a load. We shall use two diameters of wires for this example: #8 and #12 AWG (with diameters of 0.1285" and 0.0808", respectively). To cancel out the capacitive reactance, the #8 antenna requires a center inductive reactance of 833.3 Ohms, while the #12 wire antenna of identical length requires 889.4 Ohms. For any value of Q, the resistance is simply the reactance divided by the selected Q value. Thus, we can select a range of Q-values to check. In this case, let us check a perfect inductively reactive load (R = 0), along with finite Q-values of 1000, 750, 500, 250, and 100. For the two antennas--which differ only in wire diameter--we get two families of values, which the following graph artificially connects with an identifying line just to keep the two antennas differentiated from each other.

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First, let's remember that the two antennas required two different reactive load values solely as a function of the source impedance. Both antennas use lossless wire, so the source impedance difference is a function of wire diameter. Now, if we look at the left-most line, where Q is infinite because the load resistance is zero, the antenna gain is the same for both wires. The fact that the value (1.85 dBi) is less than the traditional values for a resonant dipole (2.14-2.15 dBi) results from the length of the wire. It is much shorter than a resonant dipole. The wire shows the same gain without a load in place. Part of the gain of an antenna is a direct function of its length. In fact, you wish to obtain more gain from a dipole, make it longer--up to about 1.25 wl long. You may not like the resulting source impedance, but the antenna will have more gain simply by being longer--until it reaches a length where the pattern begins to degenerate into multiple lobes.

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Second, the divisions from left to right following no special pattern. Hence, the actual curve of the values is not apparent. The drop in gain from a perfect load to one with a high Q-value of 1000 is noticeable. The region between a Q of 1000 and a Q of 500 strongly suggests that the curve of gain does not track arithmetically. Indeed, the curve is much straighter if each selected Q-value is of a constant ratio with the immediately preceding value throughout the chart.

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Third, the two families of values track each other, with lower gain values for the #12 wire antenna. If we remember that the necessary inductive reactance for the #12 wire antenna was higher than for the #8 antenna, then it follows that for any given Q, the resistance will also be higher. The higher the resistance of a center load, the lower the gain.

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The type 4 load from which we derived the modeled data is a mathematical entity only. Whereas the wire is modeled as a physical entity, the load is only a mathematical modification of the results. Hence, any physical properties that the load may have will not play a role in its modeled performance. The length and diameter of the loading mechanism are never modeled in Type 4 loads, even if in reality they may play some kind of role in the performance of the antenna.

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Modeling Series Resistance-Inductance-Capacitance Loads

+

Equally mathematical are loads of the following type:

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Type 0: Loads consisting of the following is series: resistance, inductance, and capacitance. Missing elements are entered as values of zero (which the program automatically interprets as a missing value, not a zero value). to specify an inductor of 6 uH with a series resistance of 2 Ohms, one enters this: 2, 6E-6, 0. The final zero indicates that there is no capacitor.

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+

The LD line in the input file shows the load type and values for resistance and inductance, again with a missing capacitor. Another load type (Type 1) is available for parallel combinations of resistance, inductance, and capacitance. We shall not need it for this particular set of notes.

+

The advantage of using R-L-C loads is that NEC translates them into appropriate values of reactance for each frequency checked in a file request. Hence, with R-L-C loads, one may run a frequency sweep and have the correct reactance at each frequency is the sweep.

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However, there is an accompanying limitation. The value of R remains constant. Therefore, the Q of the reactive device changes slightly with each frequency checked, since the ratio of reactance to resistance changes across the range of the frequency sweep. For limited-range frequency sweeps, such as across one of the HF amateur bands, the possible error is too small to be significant.

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Of course, one needs to be able to translate reactance to inductance (or, in other cases, capacitance) and back again to set the proper values. If one begins with a value of inductance, one must find the value of reactance for the frequency in question in order to use a value of Q to set the resistance or to find the value of Q from an assigned or measured value of resistance. The standard relationship of reactance to inductance, where inductive reactance is 2 PI times frequency times inductance in basic units, is an essential utility tool for using R-L-C loads.

+

A set of frequency sweeps between 7.0 and 7.3 MHz in 0.05 MHz steps for the #8 perfect wire dipole, center-loaded at the design frequency of 7.15 MHz for resonance with an inductance of 18.549 uH will yield a family of SWR curves. For each curve, the source impedance against which the antenna impedance is compared is the resistive impedance of the antenna at resonance on the design frequency. Hence, each curve shows a 1:1 VSWR at design center.

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The graph shows a family of such curves for a perfect inductor (zero Ohms resistance) and for inductors with Qs of 1000, 750, 500, 250, and 100. The requisite values of series resistance for the inductor are 0.8333, 1.1111, 1.6666, 3.3332, and 8.333 Ohms from 1000 down to 100. Once more, as we suspected from the gain curves earlier, the results of altering Q are more geometric than arithmetic, varying more linearly as Q forms a constant ratio from one value to the next.

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Apparent in the graph is the fact that as we lower the Q of the loading coil, the operating bandwidth--set by any arbitrary selection of a VSWR ratio--become wider in terms of frequency. Often, we simply summarize the effect by saying that the increased losses broaden the operating bandwidth, as if the summary were an explanation. It is not.

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In fact, what occurs, as modeled, is interesting in itself--and somewhat obvious if we stop to think about it. Consider the following two tables of values of source impedance for the #8 and the #12 dipoles, each center- loaded. The #12 wire antenna requires a 19.798 uH inductor with suitable adjustments in the values of the series resistor for the Q-values indicated earlier.

+ 
#8 Wire Dipole           Source Impedance (R +/- jX Ohms)
+Freq.     Q=Inf.         1000           750            500              250            100
+7.00      12.58-46.28    13.41-46.29    13.69-46.28    14.24-46.29      15.91-46.29    20.91-46.29
+7.05      12.78-30.76    13.61-30.76    13.89-30.76    14.45-30.76      16.11-30.76    21.11-30.76
+7.10      12.98-15.30    13.82-15.30    14.09-15.30    14.65-15.30      16.32-15.30    21.32-15.30
+7.15      13.19-0.02     14.02-0.02     14.30-0.02     14.86-0.02       16.52-0.02     21.52-0.02
+7.20      13.40+15.26    14.23+15.26    14.51+15.26    15.06+15.26      16.73+15.26    21.73+15.25
+7.25      13.61+30.25    14.44+30.25    14.72+30.25    15.27+30.25      16.94+30.25    21.94+30.25
+7.30      13.82+45.29    14.65+45.29    14.93+45.29    15.49+45.30      17.15+45.29    22.15+45.30
+Delta R    1.24          1.24           1.24           1.25             1.24           1.24
+Delta X   91.57          91.58          91.57          91.59            91.57          91.59
+
+#12 Wire Dipole          Source Impedance (R +/- jX Ohms)
+Freq.     Q=Inf.         1000           750            500              250            100
+7.00      12.61-49.30    13.50-49.29    13.79-49.29    14.39-49.29      16.16-49.29    21.51-49.30
+7.05      12.81-32.78    13.70-32.78    13.99-32.78    14.59-32.78      16.37-32.78    21.70-32.78
+7.10      13.01-16.29    13.90-16.30    14.20-16.30    14.79-16.29      16.57-16.29    21.91-16.29
+7.15      13.22-0.00     14.11-0.00     14.40-0.00     15.00-0.00       16.78-0.01     22.11-0.00
+7.20      13.43+16.31    14.32+16.31    14.61+16.31    15.21+16.31      16.98+16.31    22.32+16.31
+7.25      13.64+32.29    14.53+32.29    14.82+32.29    15.42+32.28      17.19+32.28    22.53+32.28
+7.30      13.85+48.35    14.74+48.34    15.04+48.34    15.63+48.34      17.41+48.34    22.74+48.35
+Delta R    1.24          1.24           1.25           1.24             1.25           1.24
+Delta X   97.65          97.63          97.63          97.63            97.63          97.65
+

The limits of accuracy are set by the last digit in each number, plus or minus 1, as a function of the sum of rounding conventions within the program. Within those limits, which vary only the value in the hundredths column, for each antenna, the range of variation of both resistance and reactance is invariant, regardless of the value of Q. Since Q is a function of changing R, the values for source reactance do not change at all. The values of source resistance is simply the values at infinite Q plus the series resistance of the inductive load.

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In other words, the presence of a center load of finite Q does not alter the VSWR operating bandwidth curve by changing the source impedance other than adding the load resistance to the natural source resistance of the antenna without any load at all.

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What the addition of the load series resistance does is to change the ratio of resistance to reactance at any of the frequencies swept, essentially raising the ratio of resistance to reactance. For the test antennas, the amount of change ranges from a fraction of an Ohm to under 10 Ohms. However, in each case, the result is a change in the impedance phase angle toward the resistive and away from the reactive.

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The basic SWR equation shows the importance of this simple adjustment in terms of a lowering of the SWR at any frequency within the sweep range, when the value of Zo is the same as the value of Rin at the design center frequency. With values of Xin constant, higher values for Rin and Zo will together lower the VSWR relative to a design center frequency value of 1:1.

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Transmission Line Stub Loads

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Before we turn away from the modeling of center loads with the mathematical models available in NEC, let's look at the alternative method of creating an inductively reactive load: the transmission line stub. These stubs present us with an immediate modeling problem. Modeled transmission lines appear in parallel with sources. So we must move them. Moreover, a single stub would be very long (over 20' long for a 600-Ohm line). Common practice is to split the stub into two equal parts, installing one on either side of the line at the main element feed point. Our simple modeling counterpart would be to place TL entries in NEC on each of the adjoining segments to the source segment.

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(Note: Use of transmission-line loads implemented with TL entries is NOT recommended wherever the currents on the two transmission lines are unequal. On some occasions we may not know in advance that the currents are unequal. For this exercise, we are purposely violating the recommendation in order to study the consequences of trying to model load lines using TL entries.)

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However, we cannot simply use the value of the center-loading reactance and split it into two pieces. If the reactance is split and moved away from the source point, the sum of the pieces will be greater than the value of the exactly centered single reactance. The center loading reactance required for the #8 perfect wire dipole that is exactly 1/4 wl long overall in free space was 833.3 Ohms. Two reactances placed about 9" apart center- to-center, one on either side of the source, require 426.3 Ohms each (or 852.6 Ohms total)

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With a type 4 reactive load, we can move in two loading directions. One of them is a Type 0 series R-L-C load, which requires an inductance at 7.15 MHz of 9.4892E-6 H on each side of the source. The other direction is a pair of transmission line stubs each side of center. Since the models of the stubs are mathematical only and a form of a NEC network, they will not show any interaction, loss, or other factors other than reactance.

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The reactance of a shorted stub is equal to the characteristic impedance of the transmission line times the tangent of the electrical length of the stub in degrees or radians. Since we know that the stubs will each show 426.3 Ohms reactance, we can work backwards through the relationship to obtain the electrical length for a variety of common lines. Then we can obtain the physical length, since we know that a wavelength at the design frequency is 137.5624' long. For this exercise, we shall look at several common transmission lines with characteristic impedances of 50, 75, 300, 450, and 600 Ohms. We shall let the velocity factor be 1.00, since many of the lines offer options and variability. We have cut off the characteristic impedance at an upper limit of 600 Ohms, since with #8 wire, even 700-Ohm line requires over 22" of spacing without significantly altering the 600-Ohm values across the band.

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Let's first determine the VSWR for a pair of perfect solenoid coils and then for lines of 300, 450, and 600 Ohms across the 40 meter band. Each lossless coil will have a 9.4892 microH inductance. The line lengths required by each of the lines (including the ungraphed 50 and 75 Ohm lines) will be as follows:

+ 
Line Zo             50        75        300       450       600
+L (degrees)         83.31     80.02     54.86     43.45     35.39
+L (feet)            31.83     30.58     20.96     16.60     13.52
+
+

We create on the segments on each side of the source a TL or transmission line entry. Depending on the program we use, we might have to create a distant wire to terminate the stub or the program might do this for us and simply let us specify that we desire a short at end 2. Do not enter the length in electrical degrees, or a frequency sweep will not be accurate. That same electrical length, with a different physical length, will appear at each frequency checked by the sweep. Instead, enter the design center physical length of the stub, along with the characteristic impedance of the line. We shall explain in a moment why the 50 and 75 Ohm lines are not included in the graph below

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With all practical characteristic impedance lines, the SWR bandwidth is significantly narrower for a transmission line stub load than for a coil of indefinitely high Q. Note that the SWR bandwidth decreases as the characteristic impedance of the line decreases. The low impedance lines were omitted because their end values of SWR exceeded 100 and would have obscured the detail of the graph.

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The reason for the narrower bandwidth is not Q as ordinarily understood in terms of resistive losses within the reactive loading device. Neither loading means has any resistive losses in the models. Rather, the stubs have reduced bandwidth because the value of reactance is a tangential function of their electrical length as the frequency changes, which yields a curve quite unlike the curve of solenoid coil reactance vs. frequency. The difference shows up vividly in these examples, since the required reactance is so high. For small-value line-vs-coil applications, such as the values associated with beta matches, the curves across a ham band will not be significantly different if the stub uses a high characteristic impedance.

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To reinforce the differences between single-layer solenoids and transmission lines stubs as sources of reactance in antenna loading, let's look at tables of values for the perfect coil and the bank of transmission lines used.

+ 
             Source Impedance (R +/- jX Ohms)  (Values rounded)
+Frequency      Coil                          Line Zo
+MHz                      50         75         300        450        600
+7.00      13.1-47.3      13.0-207   13.0-154   13.1-64.8  13.1-56.3  13.1-52.7
+7.05      13.3-31.5      13.2-147   13.3-107   13.3-43.3  13.3-37.5  13.3-35.0
+7.10      13.5-15.6      13.5-78.5  13.5-55.9  13.5-21.7  13.5-18.7  13.5-17.5
+7.15      13.8-0.0       13.8-0.2   13.8-0.1   13.8+0.0   13.9-0.0   13.8+0.0
+7.20      14.0+15.7      14.0+91.5  14.0+61.2  14.0+22.0  14.0+18.8  14.0+17.6
+7.25      14.2+31.1      14.3+201   14.3+122   14.2+43.9  14.2+37.4  14.2+33.9
+7.30      14.4+46.6      14.7+334   14.6+205   14.5+66.1  14.5+56.2  14.4+52.3
+

The table shows several features of using transmission line stubs as loading elements at or near the center of the antenna element. First, the range of reactance variation is higher in all cases than for the perfect inductor. Second, although the phenomenon is smaller by far, the range of source resistance values is also greater for transmission line stubs than for perfect (and, by reference to earlier data, for finite-Q) inductors.

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Since all of the loading devices used here have no resistive losses, their Qs as determined by the usual ratio of reactance to resistance are identical. However, their operating bandwidths are not at all equal due to the manner in which the reactance changes with frequency for the two types of reactive loads. Although there are ways around the problem for special cases, there is no direct way to introduce losses into the transmission line model used by NEC. Hence, one cannot by this means explore the effects of accounting for losses in the stubs.

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Despite this shortcoming, TL models of transmission lines stubs do reveal some properties of their use as reactive loads. The fundamental differences in behavior relative to inductors across a band of frequencies should be clear. Second, for single frequency use, stubs are equivalent in all ways to inductors. Finally, we may note in passing that inductively reactive stub loads have an alternative name: linear loads. That name has, unfortunately, led to a number of persistent misunderstandings about their basic nature. We shall have to return to that name later.

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However, lest a small matter go unnoticed, let me set it out in relief. In splitting and moving the loading reactance only about 9" each side of the source, we found an increase in the required value of loading reactance. At the same time, the 7.15 MHz resonant source impedance for the antenna increase in the perfect reactance models from 13.19 Ohms to 13.76 Ohms. Although two cases alone do not constitute a trend, I shall bet that one is afoot. And with this, we have a prelude to looking at inductively reactive loads installed at a distance from the centered source of our very short dipole.

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Go to Main Index

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130. Models vs. Prototypes: Why Field Adjustment Will Always be Necessary

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L. B. Cebik, W4RNL

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Within the limits of their guidelines, NEC and MININEC produce highly accurate models of round-wire antennas when the environment is a vacuum or dry air. Over the years, I have designed some antennas such that the models when translated into a physical reality required no post-assembly adjustment to operate in accord with the specifications predicted by the model. Although most of the antennas were for the HF range, some had design frequencies well into the VHF and UHF region. Not all of them used simple geometries, such as uniform-diameter linear elements. For example, many used stepped-diameter elements and a few (Moxon rectangles and quads, especially) used non-linear elements. Even some designs using phase lines, such as LPDAs or dual-driver Yagis, have tightly fit predicted operating curves immediately upon assembly. My experiences are not unique.

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However, lest we begin to believe that there may be a "green-thumb" equivalent in antenna design work, my accumulated experience yields the conclusion that field adjustment of antenna prototypes is needed more often than not. Rarely are the adjustments gross. Rather, they fall into the range of fine-tuning. How finely we demand the tuning to be is always a matter of judgment. My first 10-meter stepped-diameter Moxon rectangle showed its SWR minimum 25 kHz below the model's prediction, well under 0.1% of the design frequency. Nevertheless, I dutifully shortened the elements enough to bring the array into alignment with the design model.

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There are a number of reasons why field adjustment is always a necessary step in the transition from a design model to a working antenna. Some of the reasons relate to modeling, and other to antenna construction. It may be useful to catalog a few of the situations that are almost guaranteed to require adjustment. The exercise will alert us to the relationship between cautions that we accumulate in the design process and the need always to be prepared to make field adjustments.

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1. Pressing NEC Limits and the AGT

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One of the most common reasons for a model requiring from moderate to extreme levels of field adjustment in the prototype stage is using a model that presses one or more of the limitations of NEC. Many of the limitations have received treatment in past episodes, although others remain less formally listed. In many cases, the limits are not absolute. Instead, as the modeler approaches the limit, the numbers gradually become less accurate.

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One of the most reliable general tests that a model is pressing limits, especially those for which NEC and its implementations issue no warnings, is the Average Gain Test (AGT). Too many modelers--both amateur and professional--fail to give the test due heed. Even though the AGT test is a necessary condition of model adequacy, it is not a sufficient condition, and there are configurations that achieve nearly ideal scores but still show aberrations. Despite this limitation, the AGT score is a relatively good guide that there is a potential need for prototype field adjustment.

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As a sample, we may resort to a very common case: the stepped diameter HF element. Fig. 1 shows a highly sectioned center-fed dipole element for 14.175 MHz. The element contains 51 segments total so that all segments are approximately the same length. Fig. 2 shows the element structure in an EZNEC Wires table, along with the usual method of handling such elements, the Leeson substitute element formulation.

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The total element length is set to provide a resonant feedpoint impedance when modeled in the substitute-element mode. The following table shows the results of modeling the element in that mode, plus modeling it with both NEC-2 and NEC-4 in uncorrected modes.

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+Modeled Results for a Stepped-Diameter Element at 14.175 MHz
+Total Length   Version   Feedpoint Z (Ohms)   FS Gain     AGT     AGT-dB
+411.5"         Leeson    71.16 + j 0.11       2.18 dBi    1.010   0.04
+               NEC-4     61.25 + j 3.05       3.07        1.235   0.92
+               NEC-2     43.54 + j11.51       4.68        1.786   2.52
+410"           NEC-4     60.50 - j 0.05       3.07        1.235   0.92
+408"           NEC-2     41.04 + j 0.74       4.66        1.784   2.51
+398.68 x 0.6743"         71.89 - j 0.07       2.14        1.000   0.00
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The NEC-2 results are the least accurate and also show the least ideal AGT score. Had we tried to model the element without the Leeson corrections, we would have ended up with a 408" element length and expectations of a 40-Ohm resonant feedpoint impedance, as shown lower down in the table. NEC-4 produces better results as a consequence of the current-calculation algorithm revision. However, it shows a significantly non-ideal AGT score, excessive gain, and an impedance about 10 Ohms lower than shown by the Leeson model. Had we used NEC-4 without correction and aimed the model for a resonant impedance, we would have ended up with a 410" element, but our impedance expectations would still be 10 Ohms low.

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Perhaps surprising to some folks is that fact that the Leeson-corrected substitute element is not perfect as shown in the lower portion of Fig. 2. The element has a special feature used by many modelers to simulate elements that connect directly to a conductive boom. The center section is short and very fat. The step from the center section diameter to the actual element diameter is large. In addition, the center section length allows only a single segment. Therefore, the segments adjacent to the source segment have lengths that differ from the center section. The combination of ingredients is enough to yield a slightly non-ideal AGT value and a slightly high gain report. If we replace the sectioned Leeson element with a single wire having the same overall length and the Leeson-specified diameter with the same total number of segments, we obtain the results in the bottom line. The AGT score is ideal and the gain report is correct for the free-space environment. Fortunately, the impedance does not change enough to suggest that we might have a problem using a Leeson-corrected model.

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The results of the test suggest several conclusions regarding the need for prototype field adjustment. Had we modeled the element using uncorrected NEC-2, the resulting dimension would need serious field revision to reach resonance at the design frequency. Had we used uncorrected NEC-4, we still would need significant field adjustment. Modeling the complexly structured elements using the Leeson substitute element (which yields identical results in both NEC-2 and NEC-4) would likely require the least adjustment, or perhaps none at all, depending on the designer's level of fussiness.

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There are innumerable other ways to press NEC limitations. The AGT test will catch most of them. The greater the degree to which the AGT score is not ideal (above and below 1.000 in free space), the greater will be the degree of likely field adjustment involved in the prototype.

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Unmodeled Wire Structures

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To the degree that a model fails to include all geometric features within its structure, the model's reported performance will be off the mark and require field adjustment in any physical prototype. This generalization has greater or lesser application, depending upon what we omit from a model. For example, with a Yagi, if the elements are well insulated and isolated from any conductive boom, omitting the boom from the model will do not harm. If the elements physically connect to the boom, modeling it will not produce more accurate results, since NEC does not calculate transverse currents. This case falls within the preceding category of modeling within NEC limitations and guidelines. However, there are a myriad of different kinds of cases in which we habitually model elements and then construct them in a different manner, where that manner results in a structure that differs by at least a small amount from the model.

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Perhaps one of the classic cases revolves around modeling quad loops. Fig. 3 shows four general ways in which builders physically connect the loop elements to the support arms of HF wire-loop quad antennas and arrays. In three of the four cases, we have conductive materials in proximity to each of 4 presumed corners for a square or diamond-shaped quad. Only the version with an RF-transparent support arm and an equally RF-transparent connector will reflect the structure that we normally model. Two of the remaining modes of construction employ conductive rings either in contact with or very closely coupled to the main loop. Each of these rings represents a closed 1-turn inductor that to one or another degree will detune the main loop relative to its modeled performance without the rings.

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To demonstrate the degree of detuning that is possible, consider a model of a square quad loop that is resonant when modeled without accounting for the ring connectors. The subject model is for 28.5 MHz and uses AWG #14 wire for the element. Fig. 4 shows the general outline of the quad loop, along with two variations.

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The top-right partial outline shows one corner of the basic loop as normally modeled. The lower sketch shows the same corner with a 1" square loop attached, simulating the ring connector often used in physical quads. Since the quad loop is about 109.5" per side exclusive of the loops, the small additions seem insignificant, even when we multiply the one shown by four. The following table tells another story.

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+A Quad Loop With and Without Corner Attachment Loops
+Version    Impedance (Ohms)    Max. Gain (dBi)    AGT     AGT-dB
+Without    125.4 - j 0.5       3.30               1.002   0.01
+With       128.1 + j24.5       3.29               1.001   0.01
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The sample will not exactly correspond to the loops and construction methods in any particular case, but it does show the degree to which the model may depart from reality in that reality contains loops the size of the ones included in the revised model. For every case of omitting details from models, the prototype will require adjustment to center the performance curves where the design model intended them to be. The problem becomes more acute with parasitic elements. One may use either a detailed or a shortcut procedure. The shortcut simply applies the percentage of change to the driver loop length to each of the parasitic elements. For greater precision, one would need to determine the resonant frequency of each parasitic element in the model and then adjust each corresponding physical element to self-resonance at the same frequency.

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As we increase the operating frequency, "lumps" and "gobs" that make no difference in the HF range may begin to make considerable difference in the UHF range. An element wire made from common materials becomes a significant percentage of a wavelength at UHF. Hence, some common practices related to fastening loops to cable connectors may take on some detuning significance. We often create closed wire loops by overlapping, twisting, and then soldering wire ends, a generally invisible practice at HF. However, doubling the wire diameter, even for a small part of a UHF loop can detune it from its uniform diameter in the model. As well, closing a loop at a current maximum or a current minimum point can also make a difference.

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Because we are wedded mentally to the arrangement of antenna features in horizontal beams, we often forget to make appropriate adjustments when rotating such beams for use with vertically polarized signals. A horizontal beam requires no attention to the mast, since the support is at right angles to the elements and the plane of the radiation pattern. Hence, we typically model horizontal beams without modeling the mast. When we turn the beam to orient it vertically, we cannot be so careless. Fig. 5 shows a vertically oriented beam with no boom modeled, along with two types of cases in which we model the support mast. One of the cases extended the conductive boom to a point 2" above the Yagi's boom at 240" (20') above average ground. The other case limits the conductive portion of the support mast to 180" (15') above ground, with a presumably RF-transparent mast section above that point.

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The test frequency for the antenna is 52 MHz, which makes the two mast lengths close to even multiples of a half wavelength. The following table catalogs the modeled results for the three cases.

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+A Vertical 6-Meter Phase-Fed Yagi with Different Mast Situations
+Version    Impedance (Ohms)     50-Ohm SWR    Max. Gain (dBi)    To Angle (Deg.)
+No Boom    43.6 + j 7.9         1.24          7.42                9
+242" Boom  26.2 + j17.9         2.23          6.31               27
+180" Boom  41.3 + j 5.8         1.26          7.24                9
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Carelessly using a full-length conductive mast results not only in a detuning of the closely space driver, but also distorts the pattern to raise the elevation angle of greatest field strength to an unusably high level. Shortening the conductive portion of the mast returns to the beam to nearly full "no-mast" performance. Still, a builder might wish to do further modeling to ascertain just how long the conductive portion of the support mast can be and not affect performance at all.

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Under certain circumstances, the close proximity of a mast can affect even a horizontal beam. Fig. 6 shows a 2-band Yagis with a common feedpoint. On the left is the typical mast-less model. The outline suggests that we are using a direct connection between the drivers for the two bands, a short section of exposed parallel transmission line.

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On the right is an added dot representing the likely placement of the support mast in order to support the beam near its center of mass. The position is beside the transmission line connecting the two drivers. The combination of the mast and the plate-hardware combination used to join the mast and the boom may have a significant affect on the driver connection line, even if the metal mass leaves the elements themselves unaffected. For example, it may alter the effective characteristic impedance of the line, resulting in altered driver impedances on one or both bands. To forecast the potential effects of a closely spaced mast assembly, we may wish to model a short thick wire in the vicinity (but unconnected to the antenna elements) to see what may happen with a prototype. The exercise may also allow us to pre-plan for the adjustments that we may make to the prototype by indicating trends in effects and which modifications restore performance. It is easier to go through the head-scratching process in front of a computer than at the top of the prototype's support structure.

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The are innumerable instances in which a model will be at variance with the prototype without any way of compensating within the model. The sketches in Fig. 7 shows the modeled and the actual situation that we often encounter with elements that necessarily change direction and yet have a significant element diameter. For example, we might encounter this situation in a Moxon rectangle in which the elements are relatively fat for the operating frequency and yet are metallically continuous. The physical antenna will require a bend on a radius that accommodates the element's diameter without weakening the structure. The bend radius "cuts" the corner, requiring an adjustment to both the left-right and the front-back dimensions to maintain the total element length. By using enough segments in the model's elements, we can often model an angular corner. However, we must ensure that we do not adversely affect the AGT score in the process so that we may correctly correlate the results of the corner simulation to the original model and to the physical prototype.

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Although we have looked at a number of cases in which our models omit certain details of the physical prototype, we have not exhausted the list of possibilities. Nevertheless, perhaps this abbreviated catalog will suffice to alert modelers to the potentials for variation between the model and the physical.

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Inductive Loading

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All forms of R-L-C loading in NEC models present limitations, some of which can affect the model-to-prototype correlation. These types of loads, whether set up as series or parallel circuits, have no geometric dimension and therefore play no role in the initial matrix calculations. Instead, the program applies the load's equivalent resistance and reactance (real and imaginary components of the load impedance) to the assigned segment after initial calculations. The result is a modification of the current on the loaded and other segments, with further consequences for the calculation of overall antenna fields.

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Inductive loads are susceptible to a growing inherent error as we move the inductance further from the high-current region of the antenna. In this connection, we might study the behavior of the current magnitude as we move loading inductances away from the center of a dipole, as shown in Fig. 8.

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The top current distribution curve applies to an unloaded short dipole that shows a source impedance of 29.45 - j402.6 Ohms. To bring the dipole to resonance, we may add an inductive load on the center segment, which is also the source segment. The reactance of the load is j402 Ohms. The equivalent inductance at 28.4 MHz is 2.25 uH. If we omit a series resistance and assume an indefinitely large value for the inductor's Q, we obtain a gain of 1.88 dBi in free space (for either the loaded or the unloaded dipole). The center-loaded dipole reports a source impedance of 29.45 - j0.56 Ohms. Assuming a Q of 300 requires that we add a resistance of 1.34 Ohms, and the gain drops to 1.69 dBi. The resistive center load component adds to the unloaded resistive component, so the source impedance becomes 30.79 - j0.56 Ohms.

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Center inductive loads are most accurate in NEC (equivalent to base-loading in a ground-mounted monopole) because the current at each end of the loaded segment is equal. This condition assures that the inductance reflects most closely a physical, that is, a virtually pure inductor. As we move the load outward from center, the situation changes, as shown in the lowest outline in Fig. 8. Assigning the two loading inductors positions that are midway from the source segment to the element tip, each inductive load requires a reactance of j402 Ohms to effect resonance. This value is equivalent to installing two 2.25-uH coils, one on each side of the center segment. With these inductors installed (without regard to inductor Q), the model reports a source impedance of 46.68 - j0.13 Ohms. If we add a series resistance to each inductance to equate with a Q of 300, we obtain a source impedance report of 48.69 - j0.23 Ohms. The gain with an infinite Q is 1.91 dBi and with a Q of 300 it is 1.73 dBi. (Note that there is no significant gain advantage to mid-element loading over center loading in dipoles.)

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The current distribution curve for the mid-element loading example points to a significant facet of load behavior if we assume the use of solenoid inductors. The current at each end of the inductor is different. To the degree that the current levels differ, the wire within the inductor serves a second purpose in addition to creating an inductive reactance. The wire also serves as part of the length of the antenna, even if so oriented that it cannot contribute significantly to the antennas radiation. The wire in the uncentered inductor(s) will have an affect on the length of dipole necessary to achieve resonance. However, since the inductors in the model have no wire (in the sense that the segmented wires of the element do have wire), the model cannot show the contribution of the physical inductor wire to the antenna's length. As a result, a physical element that is highly loaded away from the high-current region of the antenna will not have the same length as modeled. The net consequence is a requirement for field adjusting the physical prototype.

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Allied to the inherent inaccuracy (not severe but noticeable) of inductive loads away from the elements high-current region is a modeler oversight often encountered in models of trap elements. Consider an element designed for the amateur 12- and 17-meter bands, specifically 24.94 MHz and 18.118 MHz. A correctly modeled trap dipole would show source impedance values in the 71- to 73-Ohm range for each band using traps with a coil Q of 300. However, many modelers fail to achieve such results. We may understand why if we examine the trap situation shown in Fig. 9.

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With respect to components, a trap consists of a parallel combination of an inductance and a capacitance. NEC offers only series and parallel load configurations, as shown at the center of the figure. The parallel combination is the most apt, but does not capture the equivalent circuit of a trap, such as shown at the right. Therefore, we must convert the series R-L leg of equivalent circuit into a parallel combination of resistance and inductance to obtain the required components for a parallel circuit.

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Now we may add a further complication. We normally design traps for frequencies either at or just below the lower end of the band for which they operate as traps. The design frequency for the trap in the same antenna is 24.5 MHz. At the antenna's design frequency of 24.94 MHz, the trap serves as a slightly off-resonance parallel tuned circuit that presents a high impedance, thus terminating the antenna at the trap. At the lower frequency, many modelers simply presume that the capacitor disappears and that the remaining element loading is solely a function of the inductor value. Unfortunately, this assumption is incorrect. The loading reactance in each off-frequency trap (at 18.118 MHz) is a function of both components in a non-resonant parallel circuit. We cannot even preserve the parallel resistance that we used to set up the trap at the original frequency, since its value will also change. A model that uses only the value of the inductor (and its series resistance) to load the element for the lower band will be nearly 2' longer at resonance than one that re-calculates the net impedance of the entire trap.

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Now we may add in the previously noted difficulty with inductive loads inserted well away from the antenna's high-current region. Although we may not need to make a significant adjustment to the inner length of the element on 12 meters, we can expect to require a fairly sizable adjustment to the overall length of the element when operating on 17 meters, even if we correctly calculate the loading of the trap on the lower band.

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Conclusion

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Catalogs must end somewhere, and this point is probably as good as any. Our fundamental theme has been the fact that there are many circumstances that will dictate a need for field adjustment to a physical prototype of any antenna designed via NEC software. Some of those circumstances involve pressing NEC limitations, whether those limitations relate to guidelines for adequate model geometry or to software techniques for loading and other non-geometric program functions. Other circumstances involve limitations on how precisely we may reflect reality within a model, with some limitations relating to the software and others to the habits and conventions we bring to the modeling process.

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There are a large number of antennas that we can accurately model so that the model's specifications translate virtually exactly into a physical antenna that performs in according with model predictions. However, the number of cases that inherently call for field adjustment of the physical prototype is even larger. When converting a design model into a physical antenna, we should always be prepared to make such adjustments. If we use the software wisely, we can often know in advance the kinds of adjustment maneuvers that are most likely to bring the antenna into alignment with our design specifications.

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AM BC Modeling with NEC
+ 1. Basic Considerations

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L. B. Cebik, W4RNL

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Over the past few years, the National Association of Broadcasters (NAB) has been studying the possibility of using antenna modeling software for some of its submission to the Federal Communication Commission (FCC). The details of these discussions properly belong to the broadcasters, the consulting engineers, and the representatives of the Commission. These notes do not in any way constitute a commentary on the overall merits of the proposals. +

Instead, these notes have a much smaller mission. The program used by many consulting broadcast engineers is a proprietary version of MININEC. To the date of writing--likely long ago in terms of the time of publication--the use of NEC cores (either -2 or -4) has not received full attention. One seeming drawback to the use of NEC has been the absence of a ground calculating system equivalent to the MININEC ground calculating system. The latter system allows effective modeling--within limits--for ground-mounted monopoles without the need for modeling a full set of buried radials. A second limitation perceived to surround NEC is the absence of RMS inputs and outputs. A third note often made is that NEC typically calculates azimuth angles in terms of phi- or counter-clockwise-conventions rather than in terms of the compass rose azimuth headings that correspond to typical maps used in FCC submissions. The list goes on, but is perhaps not very convincing, since most of the items require relatively simple pre-core and post-core calculations.

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These notes will address some of the fundamental modeling steps needed to obtain from NEC (either -2 or -4) essentially the same outputs that might be obtained with any other modeling program. My object lies only in the steps required to obtain the outputs and their correlation with appropriate MININEC outputs. Where correlations are required, I shall use Antenna Model, a highly corrected version of MININEC 3.13--indeed so much corrected that its results are comparable to NEC-4 results well into the UHF region. However, like all forms of MININEC, Antenna Model has no limitations with respect to junctions of wires have different diameters. For such instances, NEC has well-proven work-arounds.

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These notes will use standard ASCII input files for NEC. GNEC by NSI is handy in this regard, since it makes both the NEC-2 and NEC-4 cores available to explore differences (things have changed since writing this. Be aware that NSI software is incompatible with Windows OSes beyond Win2K and may run/have issues with XP and not known to run on Vista at all - no upgrades in sight at this time). As well, the program makes use of peak values of voltage and current and so will alert us to when we need to make certain external calculations. Some implementations of NEC, such as EZNEC, already employ RMS values of voltage and current as user inputs and as tabular outputs. Such implementations save the routine calculation steps. However, by using the more rudimentary I/O facilities, we may better understand what the core does and what we must do in conjunction with the NEC cores.

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Setting Up the Most Basic Model

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The models used in preparing these notes all use 1 MHz as the working frequency. As well, the material used will be lossless or perfect wire. Initially, we shall use perfect ground, although we shall examine other options along the way to master their use. The models will also use only single monopoles to make clear the NEC-modeling steps that we must take.

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The first step is to model a monopole with a uniform diameter or radius over perfect ground. Consulting engineers have recommended that we may substitute for the typical triangular and square towers found in the industry a single wire with certain dimensions. We shall begin with a triangular tower having a face width of 2' (24").

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+Recommended Substitute Single-Wire Dimensions for Multi-Face Towers
+Tower Type      Diameter                  Radius
+Triangular      D = 0.74 * Face Width     R = 0.37 * Face Width
+Square          D = 1.12 * Face Width     R = 0.56 * Face Width
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+Note:  D and R are in the same units as the Face Width
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Perhaps the simplest model that we might construct in NEC has the following input file.

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+CM resonant monopole, perfect ground
+CE
+GW 1 41 0 0 234 0 0 0 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.0
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 1 361 1000 90 0 1 1
+EN
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The model requests a simple far-field radiation pattern (RP0) that is an azimuth pattern at zero degrees elevation (90 degrees theta), which is allowable with a perfect ground. The first wire entry (GW1) lists the wire, specified in terms of feet. The last entry in the GW line is the radius, which meets the recommended calculation. The 234' vertical dimension is just long enough to achieve resonance with perfect ground at the design frequency.

+

The model has an additional feature. It employs the standard NEC method of implementing a current source at the lowest of the 41 segments in the monopole, the one that makes contact with ground. The technique requires a remote substitute source wire, specified in GNEC as tag 30901 to keep it invisible in the antenna viewing system. In fact, if the user constructs the current source within NEC-Win Plus, the wire will remain invisible to the user, as it does in the EZNEC implementation of current sources. The wire's remoteness and small size prevent the substitute source wire from having any impact whatsoever on the current and radiation calculations for the monopole itself. The method also requires the setting of a network (NT command) between the remote wire and the monopole base segment. Since the NT "connection" has no physical or geometric dimension in the model, the remote wire is wholly acceptable. The NT command creates a 90-degree phase shift in the applied voltage and results in a current of the same magnitude appearing at the monopole base segment. For the first model, the source command (EX) specifies the remote wire as the source location and advances the phase of the applied voltage by 90 degrees. Hence, the last 2 entries in the EX line are the reverse of what we would find in a standard voltage-source situation. The real voltage is 0.0 and the imaginary voltage is 1.0. In standard versions of NEC, these are peak values.

+

Our first concern is the reported source impedance of the monopole. The following GNEC tabular output gives us the NEC-4 report.

+ 
+Input Impedance and VSWR
+
+Frequency      Tag  Seg. Real(Z)   Imag(Z)   Mag(Z)    Phase(Z)
+-----------------------------------------------------------------
+1.000000        1    41  36.020    0.307     36.021    0.488
+
+

If we construct the identical 234', 1.48' diameter, 41-segment perfect-ground model in MININEC, we shall find one major difference. The source location will be exactly at the junction of the lowest segment and ground. MININEC places sources and loads at pulses, which occur at segment junctions or on the last segment of a modeled wire. In contrast, NEC places sources, loads, transmission lines, and networks on a segment, conveniently but somewhat misleadingly said to be at the center of the segment. The MININEC current pulse extends from the center of a segment to the center of the adjacent segment. The NEC current extends from one segment junction to the next. (However, for the purpose of wire intersection, we may usually take the current to be most sensitive to impinging influences within the center third of a segment. Hence, intersecting wires should have radii that avoid penetration into this region.)

+

Despite the differences in the source position, the MININEC model yields a source impedance of 35.96 - 0.10 Ohms. The difference between this value and the NEC-4 value is less than the differences we are likely to see within one program moved between computers with different CPU architectures. One reason for the close correlation between source impedance values is the use of adequate segmentation in the NEC model. For a NEC model to most closely approximate the impedance at the junction with ground, the segments should be as numerous as the wire radius allows. The segments in the NEC model are about 5.7' long, which yields a segment-length-to-radius ratio of about 7.7:1.

+

The second concern is the current magnitude and phase on the monopole's lowest segment--its feedpoint. In the listed model, this is segment 41. NEC reports the following conditions.

+ 
+FREQUENCY     SEG.  TAG    COORD. OF SEG. CENTER     SEG.             - - - CURRENT (AMPS) - - -
+  (MHz)       NO.   NO.     X        Y        Z      LENGTH      REAL         IMAG.        MAG.        PHASE
+
+1.000000        41    1   0.0000   0.0000   0.0029  0.00580    1.0000E+00  -7.5894E-19   1.0000E+00    0.000
+
+

In conjunction with the current value, we also need to examine the power budget.

+ 
+ - - - POWER BUDGET - - -
+
+INPUT POWER    = 1.8010E+01 WATTS
+RADIATED POWER = 1.8010E+01 WATTS
+WIRE LOSS      = 0.0000E+00 WATTS
+EFFICIENCY     = 100.00 PERCENT
+
+

With a current magnitude of 1.0 (phase angle 0.0 degrees), the power supplied to the antenna (with 100% efficiency in this simplified case) is 18.01 Watts. However, most modelers would be interested in the current with some prescribed power level at the antenna source. Let's suppose that the power level is 1000 Watts. The ratio between the desired power level and the reported power level is 55.52. To adjust the source current, we need to take the square root of this ratio, or 7.45. The new value for the source current is simply the initial value times this value, an easy calculation, since the initial value was 1.0. Therefore, we may modify the starting model to arrive at the next one.

+ 
+CM resonant monopole, perfect ground
+CM adjusted source current for 1000 watts power
+CE
+GW 1 41 0 0 234 0 0 0 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 7.4515
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 1 361 1000 90 0 1 1
+EN
+
+

The only change occurs in the EX line, where we replace the imaginary current value for this current-source model. The power budget reflects the change.

+ 
+- - - POWER BUDGET - - -
+
+INPUT POWER    = 1.0000E+03 WATTS
+RADIATED POWER = 1.0000E+03 WATTS
+WIRE LOSS      = 0.0000E+00 WATTS
+EFFICIENCY     = 100.00 PERCENT
+
+

The power level is now 1000 watts, and the corresponding current on segment 41 appears in the current table.

+ 
+FREQUENCY     SEG.  TAG    COORD. OF SEG. CENTER     SEG.             - - - CURRENT (AMPS) - - -
+  (MHz)       NO.   NO.     X        Y        Z      LENGTH      REAL         IMAG.        MAG.        PHASE
+
+1.000000        41    1   0.0000   0.0000   0.0029  0.00580    7.4515E+00  -3.4694E-18   7.4515E+00    0.000
+
+

The reported current is 7.4515 Amps, as we would expect, except that this is a peak value for the current. To arrive at an RMS value, we must divide the reported value by the square root of 2 (or multiply by 0.7071). We thus obtain an RMS feedpoint-segment current of 5.269 Amps. From the current and the source impedance, we can easily calculate the source voltage at 189.8 Volts (RMS) at 0.48 degrees phase angle. (EZNEC allows a user-selected power level among its options and provides both input and output values in RMS, thus saving the need for these hand calculations, even though the arithmetic is very simple.)

+

Field Strength

+

Using NEC for single-monopole analysis normally does not require much attention to the circular azimuth pattern or even the double-hump elevation pattern. Interest in those patterns becomes more intense with the use of multiple towers with phased feed systems. That exercise lies in our future, but at the moment, we shall remain with our single tower at 234' and a design frequency of 1 MHz.

+

The central interest becomes the electrical field-strength initially over perfect ground. To obtain the field strength output, we need add only 1 line to our model (retaining the adjustment to the EX line that set the power level). The revised model below has a familiar look.

+ 
+CM resonant monopole, perfect ground
+CM field-strength
+CE
+GW 1 41 0 0 234 0 0 0 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 7.4515
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 1 361 1000 90 0 1 1
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

I have left the RP0 line in the model to allow comparison with the less-used RP1 output line. For a single frequency, both lines will yield outputs with only one FR line. However, if using a frequency sweep, repeat the FR line before the second radiation pattern request or the second RP line will show an output only for the highest frequency in the sweep loop.

+

The RP1 request changes some of the meanings of entries relative to the more regularly used RP0 command. The last entry specifies a distance in meters from the coordinate system in the X-Y plane and presumably from the antenna. The number in the last entry is 1 mile, expressed, as all control command distances and dimensions must be specified, in meters. The theta (or elevation) angle changes meaning and becomes the height of the observation, again in meters. We may get a better sense of the entries by viewing the GNEC help screen for RP1 commands in Fig. 1.

+
+ +
+

The command entries allow us to specify a start and a stop height, along with the number of steps. The program will perform the division to arrive at the value for the increment between steps. For the basic sample, I have set the height at 0 meters above Z=0, which is the value used automatically by MININEC post-core calculations of field-strength. Unlike a MININEC calculation, NEC calculates both surface and space waves to wind up with a field-strength calculation, although the two will be coincident over perfect ground. Note finally the simplification of the ground-wave request to a single azimuth bearing. We might select periodic azimuth positions for a phased array with directional properties, where the positions correspond to bearings on which we would take physical measurements.

+ 
+                        - - - RADIATED FIELDS NEAR GROUND - - -
+
+   - - - LOCATION - - -          - - E(THETA) - -        - - E(PHI) - -        - - E(RADIAL) - -
+  RHO      PHI         Z            MAG      PHASE         MAG      PHASE         MAG      PHASE
+METERS   DEGREES    METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES
+
+1609.34     0.00       0.00     2.7520E-01   134.12    4.6094E-22  -108.70    0.0000E+00     0.00
+
+

The field strength calculations are part of the final section of the NEC output report. From the entries for E(theta) and E(phi), we can recognize the vertical component of the field by its much higher value--as we would expect from a vertical monopole. In fact, as values drop below E-9 to E-10, the numerical value becomes unreliable. For example, had we used an azimuth specification of 0 to 360 degrees, the E(phi) values for zero and for 360 degrees might have differed, except for one property: both would be too small to be significant.

+

The E(theta) value is the field strength, but like all NEC output reports for voltage or current, the value is in peak Volts/meter. Applying the 0.7071 correction, we obtain 0.1956 V/m or (more commonly) 195.6 mV/m.

+

Suppose that we wish to obtain an approximation of the field strength over a soil quality other than perfect. For this task, we must revise the ground parameters in the model. Since we do not wish to model the buried radials, we must invoke the reflection coefficient approximation (RCA) system for ground calculations. The steps that we would take vary between NEC-2 and NEC-4. Let's begin with the NEC-4 procedure.

+ 
+CM resonant monopole, RCA ave ground
+CM NEC-4 procedures
+CE
+GW 1 41 0 0 234 0 0 0 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 0 120 0 0 13.0000 0.0050 75 .0025
+EX 0 30901 1 0 0.0 7.4507
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 1 361 1000 90 0 1 1
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

In NEC-4, we alter the type of ground that we wish and enter further data into the command. Fig. 2 can help us sort out the line entries.

+
+ +
+

The upper portion of the help screen shows us the selection of the ground calculating system and the ground quality (average: conductivity = 0.005 S/m, permittivity = 13). The lower portion of the screen shows a special feature available with the RCA system, namely, the ability to specify the number of radials, their length, and the wire radius (the latter two in meters). A standard AM BC radial field uses 120 radials about 1/4 wavelength long. I have arbitrarily selected a wire radius of 2.5-mm (about 0.2" diameter) for each radial. The RCA calculating system is not as accurate as the Sommerfeld-Norton (SN) system with a set of buried radials, but the model size and run time is much smaller with the RCA specification.

+

With the RCA ground system and no radial system specification, the feedpoint impedance of the monopole will differ from the value with a perfect ground. As we add radials, the source impedance levels off at the same value that we obtain for a perfect ground, as the extract from the model output file shows.

+ 
+Input Impedance and VSWR
+
+Frequency      Tag  Seg. Real(Z)   Imag(Z)   Mag(Z)    Phase(Z)
+------------------------------------------------------------------
+1.000000        1    41  36.020    0.307     36.021    0.488
+
+

The RCA radial system affects only the region beneath the antenna, but not the region beyond. Since our field-strength distance is 1 mile from the antenna, we obtain a different value than we obtained over perfect ground.

+ 
+                        - - - RADIATED FIELDS NEAR GROUND - - -
+
+   - - - LOCATION - - -          - - E(THETA) - -        - - E(PHI) - -        - - E(RADIAL) - -
+  RHO      PHI         Z            MAG      PHASE         MAG      PHASE         MAG      PHASE
+METERS   DEGREES    METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES
+
+1609.34     0.00       0.00     2.3839E-01    91.89    6.8932E-20   -28.12    2.4734E-02   -47.39
+
+

Once again, the E(theta) reading is in peak V/m. After translation, we arrive at 168.5 mV/m at a phase angle of 91.89 degrees.

+

In NEC-2, we must revise the set-up procedure to obtain a field-strength report. The GN command has the same appearance as it did in the NEC-4 model. So too does the RP1 line. However, the RP0 command has suddenly turned into an RP4 command, as shown in the NEC-2 model below.

+ 
+CM resonant monopole, RCA ave ground
+CM NEC-2 model file
+CE
+GW 1 41 0 0 234 0 0 0 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 0 120 0 0 13.0000 0.0050 75 .0025
+EX 0 30901 1 0 0.0 7.4507
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 4 181 1 0000 -90 90 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

NEC-2 sorted among the various output options by assigning each one a different integer. The use of a radial field without a second medium happens to be option 4. Moreover, NEC-2 does not accept theta angles of 90 degrees (elevation angles of 0 degrees) over any real ground. Therefore, for utility, I changes the pattern request to a theta (elevation) pattern, as shown in Fig. 3. The help screen determines the RP option number from its entries and automatically translates the line into an RP4 request.

+
+ +
+

We could have reverted to (or added) an elevation (theta) pattern request anywhere along this progression. At this stage, the elevation patterns is useful as a reminder that the far-field is negligible at an elevation angle of zero degrees, as shown in Fig. 4. Note the decrease in far-field gain from the perfect-ground value of about 5.2 dBi.

+
+ +
+

The NEC-2 field-strength table is very close to being identical to the NEC-4 version.

+ 
+                        - - - RADIATED FIELDS NEAR GROUND - - -
+
+   - - - LOCATION - - -          - - E(THETA) - -        - - E(PHI) - -        - - E(RADIAL) - -
+  RHO      PHI         Z            MAG      PHASE         MAG      PHASE         MAG      PHASE
+METERS   DEGREES    METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES
+
+1609.34     0.00       0.00     2.3753E-01    91.89    6.1979E-20   -78.41    2.4653E-02   -46.89
+
+

Translated to RMS terms, the E(theta) field strength is 167.9 mV/m at 91.89 degrees. The phase angle is the same, but the estimated field strength is about a half-milliVolt less. Part of the reason for the different derives from the NEC-2 source impedance report:

+ 
+Input Impedance and VSWR
+
+Frequency      Tag  Seg. Real(Z)   Imag(Z)   Mag(Z)    Phase(Z)
+-----------------------------------------------------------------
+1.000000        1    41  36.028    0.339     36.029    0.538
+
+

Of course, the differences between the NEC-2 and NEC-4 outputs are less than significant and possibly even less than insignificant.

+

Conclusion--So Far

+

Thus far, we have employed the standard recommended single-wire substitutions for a multi-face tower to arrive at some of the most used data in modeling AM BC towers. For clarity, we have used a resonant length for the tower model, which does not correspond to what the FCC considers to be a 90-degree tower. The simple monopole set up has allowed us to use both a perfect ground and an RCA ground with a radial screen to produce the data from the model. To this point, NEC has shown the ability to calculate as well as MININEC.

+

Still, we have just begun the journey into tower modeling. Suppose, for instance, that we wish to model the tower as a three-legged affair. The question for modelers who wish to be as economical as possible with their segments is whether we really need all that angular and cross bracing. NEC has both some promises and some pitfalls. In addition, we might ask whether the correlation between NEC and MININEC holds up for towers of other heights with significant reactance at the source segment. One might receive the impression that we are not close to the end of our journey.

+

Go to Main Index

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+

AM BC Modeling with NEC
+ 2. Quandaries: How Many Legs? How Good is Good?

+
+
+

L. B. Cebik, W4RNL

+
In the preceding episode, we moved step-by-step through the process needed in NEC to obtain most of the basic information required for simple monopoles in AM BC service. For simplicity, we used the NAB-recommended substitute for the complex interlaced pieces of a physical tower: a single wire with a diameter that was 0.72 times the face width of a presumed triangular tower 2' across. The simplification was justified in that episode because we wanted to feature the steps in the process, not the geometry of the monopole tower. +

In this set of notes, we shall consider in more detail the structure of towers, at least in the abstract. Most currently available new towers use a triangular structure, although many 4-sided towers still exist. We shall retain the presumed 24" spacing between vertical legs, even though 18" may be more common in practice. Our goal remains the illustration of modeling situations and techniques rather than a replication of actual engineering efforts.

+

In fact, for reference, we shall use one of the last of our models, a 234' tower composed of a single lossless wire that is 17.76" in diameter as a substitute for a 2' tower face. As the model listing shows, we have placed the antenna over perfect ground and requested both an elevation pattern and a ground wave reading for field strength at a design frequency of 1.0 MHz. The model uses a current source and includes the remote wire and network to achieve this goal. The source current in peak Amps is set for a power level of 1 kilowatt. The only difference between this model and those in the preceding episode is that the new one grows from the ground upward. It uses 41 segments to assure that the source is as close as feasible to the actual ground level. In this and subsequent models, I shall use NEC-4, although applying NEC-2 to the models should produce reasonably consistent results.

+ 
+CM resonant monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 234 0.74
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.4515
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

The following table summarizes the essential information in which we are interested in these notes. F-S indicates the field strength, and I have left the value in the NEC-report form of showing peak milliVolt/meter.

+ 
+Resonant Single-Wire Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+36.02 + j0.31     7.4515          5.15         1.999   0.00     275.2 mV/m @ -45.9 deg
+
+

The source impedance provides a means of correlating our standard model against what we obtain from succeeding models. The required current will reflect the same comparison from a different perspective. The combination of the gain and Average Gain Test (AGT) score, shown in both basic and dB form) will give us a measure of the model's adequacy as a model. (Note that for a monopole over perfect ground, an ideal AGT value is 2.000. Some programs such as EZNEC pre-convert this value to 1.000 so that results coincide with free-space applications of the AGT test.) The field strength reading provides an additional check on how severely a model may deviate from the standard form in terms of data that may be critical for some applications.

+

My reason for a somewhat elaborate set-up emerges from a collection of models that I have seen over the years. Many NEC modelers wish to model multi-legged towers as multi-legged geometry structures within the model. There are two general questions that such models pose. Are they necessary? Are they adequate? However, perhaps the most fundamental question is how we should source or feed multi-leg models.

+

Feeding 3-Legged Towers

+

We shall begin with the simplest possible multi-leg model: three 2"-diameter legs 2' apart center-to-center. The tower height remains 234' for this and all succeeding models. The model omits all crosspieces. Hence, it requires attention to the feedpoint.

+

As the model shows, we use 3 separate source segments, one per leg on the lowest segment of that leg. We adjust the current so that the total power fed to the model--summing all three legs--is 1 kW. The source impedance requires a post-run calculation that essentially takes any one of the source impedance values and divides it by 3 to obtain the net source impedance. The technique is equivalent to a centered physical feedpoint with negligible distance between that point and each leg. It also presumes that the legs in operation have equal current levels at any height, a situation relatively assured by the actual cross pieces on a tower.

+

One significant reason for using the 3-source technique is to avoid a large collection of very short wires in the base region of the model. The shortest length that a NEC segment should be for accuracy in the reported data is 0.001 wavelength. At 1 MHz, that length is 11.803". Even though shorter segments may still meet segment-length-to-diameter ratio guidelines, their presence jeopardizes the trustworthiness of some results. The 3-source method (which would become a 4-source method for a square tower) avoids both the problem of very short segments and a companion problem of adjacent segments in the model having very different lengths.

+ 
+CM resonant 3-leg monopole, perfect ground
+CM 3 sources
+CE
+GW 1 41 1.1547 0 0 1.1547 0 234 0.085
+GW 2 41 -0.5774 1 0 -0.5774 1 234 0.085
+GW 3 41 -0.5774 -1 0 -0.5774 -1 234 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.4928
+EX 0 30902 1 0 0.0 2.4928
+EX 0 30903 1 0 0.0 2.4928
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

The three tower legs in the model are set in a triangular pattern so that the center of the 3 legs is at X=0 and Y=0 in the coordinate system. Fig. 1 shows the handy relationships that make such arrangements routine.

+
+ +
+

Of course, to feed the 3 legs with separate current sources, we require 3 separate remote wires and networks. The following data provide the results of our modeling exercise. The impedance value shown is the calculated value derived from the 3 reported values.

+ 
+Resonant 3-Leg, 3-Source Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+35.76 - j0.76     2.4928/leg      5.15         1.999   0.00     275.2 mV/m @ -45.8 deg
+
+

The impedance is within a quarter-Ohm of the single-wire standard model, and all other data are virtually identical.

+

If a modeler wishes to obtain a composite or net source impedance without the need for a post-run calculation, there is a straightforward technique to obtain it. Let's use the very same 3 tower legs. However, instead of placing current sources on the lowest segment of the legs, we shall add a remote wire that is far enough away not to interact with the basic structure. The one-segment wire will be short and thin and will act as the source segment plus a terminal point for transmission lines running to each of the 3 legs, more specifically, to the segments formerly used as the source points. The physically modeled distance between the new wire and the tower legs does not determine the electrical distance between the points. The TL control command allows the user to specify that distance. If we select a very short distance, such a 0.001', the impedance cannot undergo any significant transformation. In effect, we have created a short circuit between each leg and the new wire. Since TL constructs are not part of the model geometry, they do not enter the calculations for the output data except for the source information.

+ 
+CM resonant 3-leg monopole, perfect ground
+CM 1 source segment, 3 TLs
+CE
+GW 1 41 1.1547 0 0 1.1547 0 234 0.085
+GW 2 41 -0.5774 1 0 -0.5774 1 234 0.085
+GW 3 41 -0.5774 -1 0 -0.5774 -1 234 0.085
+GW 4 1 5000 0 0.1 5000 0 1.1 0.005
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 7.4783
+NT 30901 1 4 1 0 0 0 1 0 0
+TL 1 1 4 1 50 .0001 0 0 0 0  ! User Defined VF = 1
+TL 2 1 4 1 50 .0001 0 0 0 0  ! User Defined VF = 1
+TL 3 1 4 1 50 .0001 0 0 0 0  ! User Defined VF = 1
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1 1
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

One difficulty with using the remote source wire is that visualization becomes difficult. Fig. 2 shows that we will not be able to visually inspect the tower legs, even at the maximum limits of viewer magnification.

+
+ +
+

Nevertheless, as shown in the data table, we are able to draw the desired information from the NEC output report and from program selections from that table. The current value is for the source segment and not for each leg. The current at each former source point on the tower legs is 2.4928 Apk, and the phase shift is only -0.007 degrees due to the use of the transmission-line connections.

+ 
+Resonant 3-Leg, 1-Source Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+35.76 - j0.76     7.4780          5.15         1.999   0.00     275.1 mV/m @ -45.8 deg
+
+

Since the legs are identical except for their position, we need not model all three. Instead, we may simplify the modeling by replicating 1 leg. Since we took the initial trouble to place the legs so that the coordinate center falls at the center of the triangle formed by the legs, we may simple replicate and rotate the first leg by 120 degrees. In the model, I have returned to the 3-source system to allow a visualization of the result.

+ 
+CM resonant 3-leg monopole, perfect ground
+CM 3 sources
+CM GM for legs 2 and 3
+CE
+GW 1 41 1.1547 0 0 1.1547 0 234 0.085
+GM 1 2 0 0 120 0 0 0
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.4928
+EX 0 30902 1 0 0.0 2.4928
+EX 0 30903 1 0 0.0 2.4928
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+
+ +
+

Since the GM command also increments the tag number by 1 for each added replication of the original wire, nothing else in the model requires change. In fact, the data for the model is identical to the data for the original 3-leg, 3-source model. Although the application of the GM command is fairly trivial in this application, it will play a more significant role in subsequent models. Our models, whose primary use has been to illustrate methods of feeding multi-leg towers, have used a highly simplified structure. Many modelers wish to show all of the towers pieces. Even when we keep the segment length above the NEC minimum, we may easily have 2000 or more segments. Modeling those segments as individual GW entries can result in some very large model files.

+

Modeling Tower Bits and Pieces

+

So far, we have looked at towers composed only of 3 legs and found them to yield results that are consistent with those produced by the NAB-recommended substitute single-wire tower model. However, many modelers wish to include all or some of the typical horizontal and sloping members that compose actual towers. Therefore, we should look in a progressive succession at constructing such models--and see what consequences emerge.

+

The first example is simple. We shall subdivide the 234' tower into 3 equal 58.5' sections. In addition to the vertical legs, we shall add a horizontal cross element at the top of each section, as shown in the partial model view in Fig. 4. For ease of viewing, we shall retain the 3-source method of feeding the tower, although the TL method of combining the sources into a single source always remains available.

+
+ +
+

Our first version of the model uses only wires (GW commands) to construct the tower.

+ 
+CM resonant 3-leg monopole  perfect ground
+CM 3 sources
+CM 4 sections with cross braces
+CE
+GW 1 10 1.1547 0 0 1.1547 0 58.5 0.085
+GW 2 10 -0.5774 1 0 -0.5774 1 58.5 0.085
+GW 3 10 -0.5774 -1 0 -0.5774 -1 58.5 0.085
+GW 4 1 1.1547 0 58.5 -0.5774 1 58.5 0.085
+GW 5 1 -0.5774 1 58.5 -0.5774 -1 58.5 0.085
+GW 6 1 -0.5774 -1 58.5 1.1547 0 58.5 0.085
+GW 7 10 1.1547 0 58.5 1.1547 0 117 0.085
+GW 8 10 -0.5774 1 58.5 -0.5774 1 117 0.085
+GW 9 10 -0.5774 -1 58.5 -0.5774 -1 117 0.085
+GW 10 1 1.1547 0 117 -0.5774 1 117 0.085
+GW 11 1 -0.5774 1 117 -0.5774 -1 117 0.085
+GW 12 1 -0.5774 -1 117 1.1547 0 117 0.085
+GW 13 10 1.1547 0 117 1.1547 0 175.5 0.085
+GW 14 10 -0.5774 1 117 -0.5774 1 175.5 0.085
+GW 15 10 -0.5774 -1 117 -0.5774 -1 175.5 0.085
+GW 16 1 1.1547 0 175.5 -0.5774 1 175.5 0.085
+GW 17 1 -0.5774 1 175.5 -0.5774 -1 175.5 0.085
+GW 18 1 -0.5774 -1 175.5 1.1547 0 175.5 0.085
+GW 19 10 1.1547 0 175.5 1.1547 0 234 0.085
+GW 20 10 -0.5774 1 175.5 -0.5774 1 234 0.085
+GW 21 10 -0.5774 -1 175.5 -0.5774 -1 234 0.085
+GW 22 1 1.1547 0 234 -0.5774 1 234 0.085
+GW 23 1 -0.5774 1 234 -0.5774 -1 234 0.085
+GW 24 1 -0.5774 -1 234 1.1547 0 234 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.479
+EX 0 30902 1 0 0.0 2.479
+EX 0 30903 1 0 0.0 2.479
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Even with only 4 sections, the model file size has grown considerably. Since each of the 4 sections is identical, we can shorten the file by using the GM command after completing the lowest section with GW commands. We simply replicate the section three more times, translating each new section 58.5' higher (+Z) than the preceding one.

+ 
+CM resonant 3-leg monopole  perfect ground
+CM 3 sources
+CM 4 sections with cross braces
+CE Section 1 = GW, Sections 2-4 = GM
+CE
+GW 1 10 1.1547 0 0 1.1547 0 58.5 0.085
+GW 2 10 -0.5774 1 0 -0.5774 1 58.5 0.085
+GW 3 10 -0.5774 -1 0 -0.5774 -1 58.5 0.085
+GW 4 1 1.1547 0 58.5 -0.5774 1 58.5 0.085
+GW 5 1 -0.5774 1 58.5 -0.5774 -1 58.5 0.085
+GW 6 1 -0.5774 -1 58.5 1.1547 0 58.5 0.085
+GM 6 3 0 0 0 0 0 58.5
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.479
+EX 0 30902 1 0 0.0 2.479
+EX 0 30903 1 0 0.0 2.479
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Both model files yield identical data output reports, summarized in the following table.

+ 
+Resonant 3-Leg, 3-Source 4-Section (with Simple Cross Pieces) Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+36.16 + j1.09     2.479/leg       5.15         1.999   0.00     275.2 mV/m @ -45.8 deg
+
+

The impedance of the 4-section model is about as much higher than the single-wire version as the 3-leg versions without cross pieces were lower. Resistive values all fall within a 1-Ohm range, while reactive values have a 2-Ohm range. Otherwise, the data are identical. The reason for the lack of difference is the exceptionally low current carried by the cross members. The current magnitude is at least 6 orders of magnitude lower than the current in the vertical legs, making the cross members superfluous in this arrangement.

+

Towers usually also contain sloping elements. When modeling such arrangements, the lowest section should omit the sloping wires. The current division below the source at Z=0 will lead to unusable values of impedance and other calculation inaccuracies.

+

As a first trial of adding sloping tower pieces, we shall retain the simple 4-section structure, with only horizontal cross pieces in the lowest section. Then we shall add sloping wires to the second section and replicate it twice more to reach the 234' top height. The model will prove instructive in several ways.

+ 
+CM resonant 3-leg monopole  perfect ground
+CM 3 sources
+CM 4 sections with cross braces
+CE
+GW 1 10 1.1547 0 0 1.1547 0 58.5 0.085
+GW 2 10 -0.5774 1 0 -0.5774 1 58.5 0.085
+GW 3 10 -0.5774 -1 0 -0.5774 -1 58.5 0.085
+GW 4 1 1.1547 0 58.5 -0.5774 1 58.5 0.085
+GW 5 1 -0.5774 1 58.5 -0.5774 -1 58.5 0.085
+GW 6 1 -0.5774 -1 58.5 1.1547 0 58.5 0.085
+GW 7 10 1.1547 0 58.5 1.1547 0 117 0.085
+GW 8 10 -0.5774 1 58.5 -0.5774 1 117 0.085
+GW 9 10 -0.5774 -1 58.5 -0.5774 -1 117 0.085
+GW 10 1 1.1547 0 117 -0.5774 1 117 0.085
+GW 11 1 -0.5774 1 117 -0.5774 -1 117 0.085
+GW 12 1 -0.5774 -1 117 1.1547 0 117 0.085
+GW 13 10 1.1547 0 58.5 -0.5774 1 117 0.085
+GW 14 10 -0.5774 1 58.5 -0.5774 -1 117 0.085
+GW 15 10 -0.5774 -1 58.5 1.1547 0 117 0.085
+GM 1 2 0 0 0 0 0 58.5 7 1 15 10
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.488
+EX 0 30902 1 0 0.0 2.488
+EX 0 30903 1 0 0.0 2.488
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+
+ +
+

The ease of replicating upper sections that are identical to lower sections is clear from the GM command line entry. Fig. 5 shows the lowest section and the beginning of the second section, with its added sloping wires. The right side of the figure shows a transition between upper sections in more detail. Initially, to avoid NEC's well-known accuracy slippage when we have angular junctions of wires with different diameters, I have modeled everything with 2" diameter (0.085' radius) wires.

+ 
+Resonant 3-Leg, 3-Source 4-Section (with Sloping and Horizontal Cross Pieces) Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+35.90 + j7.77     2.047/leg       5.25         2.047   +0.10    278.5 mV/m @ -45.8 deg
+
+

The data departs noticeably from the data from preceding models. The reactive component of the source impedance has increased, as has the gain value and the field-strength report (still in peak mV/m for easy comparison with other data tables). The key variance in the data is the AGT score. Although a value of 2.047 seems only a small deviation from the ideal value of 2.000, it results in a 0.1-dB error in the gain report. It is not possible from the data stream to know whether the impedance report is reliable in comparison to the reports for the other models. The last statement, of course, rests on a presumption that the difference is sufficient to make a difference to a modeling task. For tasks in which the difference makes no differences, there would be no reason to resort to the more complex model.

+

One key reason for the variance in AGT scores is the very shallow angle of the sloping wires at the intersection with the vertical model wires. The two wires inter-penetrate in the region of current sensitivity in the joining segments, although not enough to trigger NEC-4 warnings. To counter this problem, we need to better reflect reality and to use smaller tower sections.

+
+ +
+

Fig. 6 shows the outline of the lowest section without any sloping wires, along with the next section--prior to the use of the GM command to add 115 more 2' section to arrive at the 234' total tower height. Each 2' section, also 2' wide, uses 2 segments per wires to remain within the NEC minimum segment length. As well, all wires are 0.17' in diameter, consistent with preceding models of multi-leg towers in this exercise set. The total model has the following lines.

+ 
+CM resonant 3-leg monopole  perfect ground
+CM 3 sources
+CM 117 sections with cross braces (diameter = to legs)
+CE
+GW 1 2 1.1547 0 0 1.1547 0 2 0.085
+GW 2 2 -0.5774 1 0 -0.5774 1 2 0.085
+GW 3 2 -0.5774 -1 0 -0.5774 -1 2 0.085
+GW 4 2 1.1547 0 2 -0.5774 1 2 0.085
+GW 5 2 -0.5774 1 2 -0.5774 -1 2 0.085
+GW 6 2 -0.5774 -1 2 1.1547 0 2 0.085
+GW 7 2 1.1547 0 2 1.1547 0 4 0.085
+GW 8 2 -0.5774 1 2 -0.5774 1 4 0.085
+GW 9 2 -0.5774 -1 2 -0.5774 -1 4 0.085
+GW 10 2 1.1547 0 4 -0.5774 1 4 0.085
+GW 11 2 -0.5774 1 4 -0.5774 -1 4 0.085
+GW 12 2 -0.5774 -1 4 1.1547 0 4 0.085
+GW 13 2 1.1547 0 2 -0.5774 1 4 0.085
+GW 14 2 -0.5774 1 2 -0.5774 -1 4 0.085
+GW 15 2 -0.5774 -1 2 1.1547 0 4 0.085
+GM 9 115 0 0 0 0 0 2 7 1 15 2
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.472
+EX 0 30902 1 0 0.0 2.472
+EX 0 30903 1 0 0.0 2.472
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

The model takes all reasonable precautions to arrive at a balance between reflecting a realistic physical structure and meeting modeling guidelines. The following table shows the data that emerges from the 1053-wire, 2103-segment model.

+ 
+Resonant 3-Leg, 3-Source 117-Section (with Sloping and Horizontal Cross Pieces) Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+36.36 + j5.94     2.472/leg       5.21         2.028   +0.06    277.2 mV/m @ -46.5 deg
+
+

The AGT score, while more ideal than the preceding model, still departs from a perfect 2.000 value. The result is a gain value that is too high, and a corresponding field-strength value. The degree by which the model departs from the ideal is noticeable. Whether it is significant to a modeling task is a user-decision, largely created by the standards brought to the exercise. Again, if the differences are too small to make a difference to the enterprise, using the complex model loses its rationale.

+

To complete our sequence of hypothetical models, let's revise the complex model by showing one further modeler urge. The sloping and horizontal members of a tower generally are smaller in diameter than the legs. Although it is a technical violation of recommended NEC practice to have angular junctions of wires with dissimilar diameters, we shall reduce the diameter values of these linking pieces to 1" (0.0425' radius). The visual appearance of the model does not change, but the changes are noticeable in the model file.

+ 
+CM resonant 3-leg monopole  perfect ground
+CM 3 sources
+CM 117 sections with cross braces (1/2-diameter of legs)
+CE
+GW 1 2 1.1547 0 0 1.1547 0 2 0.085
+GW 2 2 -0.5774 1 0 -0.5774 1 2 0.085
+GW 3 2 -0.5774 -1 0 -0.5774 -1 2 0.085
+GW 4 2 1.1547 0 2 -0.5774 1 2 0.0425
+GW 5 2 -0.5774 1 2 -0.5774 -1 2 0.0425
+GW 6 2 -0.5774 -1 2 1.1547 0 2 0.0425
+GW 7 2 1.1547 0 2 1.1547 0 4 0.085
+GW 8 2 -0.5774 1 2 -0.5774 1 4 0.085
+GW 9 2 -0.5774 -1 2 -0.5774 -1 4 0.085
+GW 10 2 1.1547 0 4 -0.5774 1 4 0.0425
+GW 11 2 -0.5774 1 4 -0.5774 -1 4 0.0425
+GW 12 2 -0.5774 -1 4 1.1547 0 4 0.0425
+GW 13 2 1.1547 0 2 -0.5774 1 4 0.0425
+GW 14 2 -0.5774 1 2 -0.5774 -1 4 0.0425
+GW 15 2 -0.5774 -1 2 1.1547 0 4 0.0425
+GM 9 115 0 0 0 0 0 2 7 1 15 2
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 2.4733
+EX 0 30902 1 0 0.0 2.4733
+EX 0 30903 1 0 0.0 2.4733
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+ 
+Resonant 3-Leg, 3-Source 117-Section (with Sloping and Horizontal Cross Pieces) Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+36.33 + j6.02     2.4733/leg       5.21        2.029   +0.06    277.3 mV/m @ -46.5 deg
+
+

As the table shows, the numerical degradation of the model due to the changes is minuscule. In large measure, this small change is a function of the fact that vertical legs carry about 3 times the current of the sloping sections. Hence, they remain the dominant factors within the model, with the cross members having only a relatively small supporting role. Once more, if the numerical differences between the models are not significant to a modeling task, we lose any reason for constructing excessively complex tower models.

+

Conclusion

+

Our set of exercise models has shown that we may construct straightforward multi-leg tower models in lieu of using the NAB-recommended substitute single-wire tower model. For models using a uniform diameter or face-width for the total height, the simple 3-leg models, even with periodic horizontal crosspieces, show a very good correlation to the single-wire model. The feeding or sourcing method is easy to implement, whether we employ separate sources for each tower leg or develop a composite source using near-zero-length transmission lines.

+

When we increased the complexity of the tower models to include both horizontal and sloping cross members, we encountered some interesting results that raise questions that one cannot answer from a perspective wholly within modeling. The complex models depart somewhat from ideal AGT scores. Although the scores are in many contexts perfectly acceptable, in the present comparative context, they show variations in the data reports. The AGT value allows only a correction of the raw gain report. However, variations in the impedance value, especially relative to the reactive component, are not directly correctable.

+

The quandary left behind by these results is whether to use the data from the complex model or to use the data from one of the simpler models with a virtually ideal AGT score. (The AGT scores may or may not be as good when using NEC-2.) The quandary only becomes one if the report differences are sufficiently large to make a difference to the larger task within which the model plays a role. If the differences are not significant, then we have no reason to resort to excessively complex models of towers.

+

The correlations among impedance and other data values among the models is overall very tight. One may legitimately raise the question of whether the tight grouping of values is at least a partial function of the use of resonant tower sizes--234' at 1 MHz. A 90-degree tower for FCC is taller--about 273'. Many towers used in the AM BC service are considerable shorter. Before closing the book on tower modeling in NEC (with special reference to NEC-4), we should do a small survey of what happens when we have tower lengths with a considerable reactive component in their source impedance.

+

Go to Main Index

+ + diff --git a/content/amod/amod133-1.gif b/content/amod/amod133-1.gif new file mode 100644 index 0000000..a6d55ff Binary files /dev/null and b/content/amod/amod133-1.gif differ diff --git a/content/amod/amod133-2.gif b/content/amod/amod133-2.gif new file mode 100644 index 0000000..35c7a51 Binary files /dev/null and b/content/amod/amod133-2.gif differ diff --git a/content/amod/amod133-3.gif b/content/amod/amod133-3.gif new file mode 100644 index 0000000..7bfd1b0 Binary files /dev/null and b/content/amod/amod133-3.gif differ diff --git a/content/amod/amod133-4.gif b/content/amod/amod133-4.gif new file mode 100644 index 0000000..20547cf Binary files /dev/null and b/content/amod/amod133-4.gif differ diff --git a/content/amod/amod133.html b/content/amod/amod133.html new file mode 100644 index 0000000..adba14a --- /dev/null +++ b/content/amod/amod133.html @@ -0,0 +1,270 @@ + + + + + AM BC Modeling with NEC + + + +
+

AM BC Modeling with NEC
+ 3. The Long and the Short of It

+
+
+

L. B. Cebik, W4RNL

+
Our examination of the use of NEC in modeling towers intended for AM BC service rests on the foundation that the desired ground for such structures is a perfectly reflecting surface. All field-strength measurements are predicated on this ground, used for various theoretical reasons of considerable historical interest. So far, we have examined the steps required to obtain from the NEC modeling core the same results obtained from selected MININEC programs. In addition, we have looked for differences that may exist between models that use the NEC-recommended single-wire substitute towers and those using to one or another degree relatively completely detailed tower structures. +

For a certain class of towers, the substitutes and the more detailed geometries showed either a remarkably good correlation or deviations that we could not ascribe to a single cause due to slight deviations from the ideal Average Gain Test (AGT) score. The class of towers included only resonant or near resonant towers, considering the 1-MHz design frequency and the use of lossless conductors. Whether the close correlations hold for other tower lengths remains indeterminate, at least within this sequence of notes.

+

In this portion of our trek through the maze of towers, we shall explore the consequences of modeling towers having considerable, but not radical amounts of, reactance. We shall begin by going long, using a standard FCC length of 273' for a so-called 90-degree tower. Then we shall try a short tower, only 201' high. Both towers show source reactance values well above 50 Ohms, but much less than 100 Ohms. The heights are arbitrary with respect to the degree to which each departs from resonance. However, both heights are divisible by 3, setting the length of the sections into which we shall subdivide them for one type of model.

+
+ +
+

In each case, we shall look at three model types, as shown in Fig. 1. One will use the single-wire substitute model using NAB recommended diameter adjustment factors. In fact, all of the towers in this episode will presume a face width of 18" or 1.5'. The required radius is 0.37 times the face width or 0.555'. The second type of tower will use three legs only, with separate sources for each leg to simplify both the model and its viewing within software facilities (in this case, GNEC). As in past episodes, the leg diameter will be 2", that is, a radius of 0.085'. The third type of tower will show both horizontal and sloping members, except for the lowest section, which will include only horizontal members at the top of the section. Like the legs, the horizontal and sloping members will use 2"-diameter wires. Each vertical tower section will be 3' high, and we may use the GM command to replicate the necessary upper sections beyond the second one, which is the first to use a complete structure.

+

The three tower types will provide a sufficient basis for comparing the results with those we obtained in the preceding notes for similar tower structures.

+

A 273' 18"-Face Tower

+

At 1 MHz, a 90-degree tower is 273' high. This tower is nearly 40' taller than the resonant 24"-face tower that we used as our sample earlier. We expect to derive at least two easily predictable results. First, the source impedance will be inductively reactive. Second, the tower gain and field-strength values will be a bit higher than the 5.15-dBi and 275 mV/m values that we obtained at a nearly resonant length.

+

The single-wire model requires no change in segmentation, since the length increase does not significantly increase the length of each of the 41 segments. With a current source, the following lines show the model file.

+ 
+CM 90-degree monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 273 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 5.761
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

The excitation line indirectly shows the current level necessary to provide a 1-kW power level at the new tower height and source impedance. A simple table shows the critical values, at least relative to these simplified exercises.

+ 
+273' Single-Wire Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+60.27 + j84.91    5.761           5.30         1.999   0.00     280.0 mV/m @ -47.7 deg
+
+

The impedance magnitude is double the value of the resonant tower, resulting in a significantly lower current (7.45 A for the resonant tower). The gain is up about 0.15 dB, while the field-strength is about 5 mV/m higher. As a reminder, the model requests the ground wave, including both surface and sky wave components at ground (Z=0) level. Fig. 2 outlines the pattern and the relevant vector. The distance is 1 mile. In practice, of course, the modeler can select any height and distance (in meters) as the observation point.

+
+ +
+

One alternative to using the substitute single-wire tower is to model 3 independent legs, each with its own source. The method of combining sources by using a distant short, thin wire and 3 transmission-lines of near-zero length is always available for this and the next model. However, we shall use the separate-source method, since it allows us to view tower model details more easily in the software (GNEC) facilities. In fact, Fig. 3 shows the lower part of the alternative model, with one tower leg hidden.

+
+ +
+

Except for tripling the number of wires, sources, and networks, the model is not much more complex than the single-wire model. Since the face dimension of the triangular tower is smaller than for the models in the preceding episode, the X and Y coordinates have changed to place the coordinate center at the mid-tower position.

+ 
+CM 90-deg 3-leg monopole, perfect ground
+CM 3 sources
+CE
+GW 1 41 0.866 0 0 0.866 0 273 0.085
+GW 2 41 -0.433 .75 0 -0.433 .75 273 0.085
+GW 3 41 -0.433 -.75 0 -0.433 -.75 273 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.9217
+EX 0 30902 1 0 0.0 1.9217
+EX 0 30903 1 0 0.0 1.9217
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

In the earlier models, 3 independent legs yielded data values that closely correlated to the single-wire values. As the data table shows, the situation does not change much when we lengthen the tower to 273'.

+ 
+273' 3-Leg Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+60.17 + j83.97    1.9217/leg      5.30         1.999   0.00     280.0 mV/m @ -47.8 deg
+
+

The resistive component of the impedance is within 0.1-Ohm of the single-wire model, while the reactance report differs by just under 1 Ohm. Multiplying the current-per-leg by 3 gives us 5.765 Apk at 1 kW, an increase of 4 mA. In short, the data for the two models does not diverge significantly.

+

The full-structure simulation in the preceding episode used 2' vertical tower sections. For the present models, 3' sections are arithmetically more convenient. Each vertical and sloping member uses 3 segments, while the horizontal cross members use 2 segments. This procedure equalizes segments length to the degree possible within the model without unnecessarily multiplying the segment count. Fig. 4 shows the basic structure, using only the lower section and the second section of the much taller tower.

+
+ +
+

The leg and other element diameters and X-Y coordinates are the same as in the model with 3 independent legs. To complete the full 273' of the tower, we must use the GM command to replicate the second section 89 more times. Including the remote source wires, the model contains 819 wires and 2178 segments.

+ 
+CM 90-deg 3-leg monopole  perfect ground
+CM 3 sources
+CM 117 sections with cross braces
+CE
+GW 1 3 0.866 0 0 0.866 0 3 0.085
+GW 2 3 -0.433 .75 0 -0.433 .75 3 0.085
+GW 3 3 -0.433 -.75 0 -0.433 -.75 3 0.085
+GW 4 2 0.866 0 3 -0.433 .75 3 0.085
+GW 5 2 -0.433 .75 3 -0.433 -.75 3 0.085
+GW 6 2 -0.433 -.75 3 0.866 0 3 0.085
+GW 7 3 0.866 0 3 0.866 0 6 0.085
+GW 8 3 -0.433 .75 3 -0.433 .75 6 0.085
+GW 9 3 -0.433 -.75 3 -0.433 -.75 6 0.085
+GW 10 2 0.866 0 6 -0.433 .75 6 0.085
+GW 11 2 -0.433 .75 6 -0.433 -.75 6 0.085
+GW 12 2 -0.433 -.75 6 0.866 0 6 0.085
+GW 13 3 0.866 0 3 -0.433 .75 6 0.085
+GW 14 3 -0.433 .75 3 -0.433 -.75 6 0.085
+GW 15 3 -0.433 -.75 3 0.866 0 6 0.085
+GM 9 89 0 0 0 0 0 3 7 1 15 3
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.8857
+EX 0 30902 1 0 0.0 1.8857
+EX 0 30903 1 0 0.0 1.8857
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Like the resonant tower in the earlier exercises, the data for the full-structure model at 273' shows numerically noticeable differences relative to the simpler models.

+ 
+273' Full-Structure Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+62.49 + j86.20    1.8857/leg      5.40         2.043   0.09     283.2 mV/m @ -48.8 deg
+
+

The reported gain is about 0.1-dB high relative to the models with nearly ideal AGT scores. The field-strength report is also high. The AGT-dB value provides a means to correcting the gain report. It answers to a simple conversion equation: AGT-dB = 10 log(10)(AGT/2). (Note: when using the AGT test in free space, do not use the /2 portion of the equation.) A positive AGT-dB value shows by how much the gain report in dBi is high. The more nearly correct gain is simple the reported gain minus the AGT-dB value. To arrive at a more nearly correct field-strength value divide the reported value by SQRT (AGT/2) (again, omitting the /2 portion for AGT values taken in free space). The calculated correct value for the peak field-strength is 280.2 mV/m. This value is within 0.2 mV/m of the values shown for the simpler models.

+

The impedance components of the full-structure model are within about 2 Ohms of the values shown in the simpler models. For reference, a MININEC model of the substitute single-wire model showed a gain of 5.29 dBi, with a source impedance of 62.29 + 85.96 Ohms. All of the values within this collection of models are tightly grouped. Whether the differences reach the level of being significant is driven by the specifications brought to the modeling enterprise.

+

A 201' 18"-Face Tower

+

In most respects, modeling the tower that is shorter than resonant will be identical in procedure to modeling either a resonant or a long tower. For visual details, refer to the figures already shown in the first part of this exercise and in preceding exercises. Our interest will lie almost wholly with the models themselves and with the data that they report.

+

A 201' tower with an 18" triangular face width requires only one change when using the single-wire substitute with the NAB recommended radius (0.555'). Only the Z-coordinate for the upper end changes. The use of 41 segments in no way presses any NEC limits or recommendation. Therefore, we obtain a model like the following one.

+ 
+CM 201' monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 201 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 9.3772
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

For this model using perfect wire and perfect ground, we obtain the following data as a starting point in our comparisons.

+ 
+201' Single-Wire Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+22.75 - j70.37    9.3722          5.04         1.999   0.00     271.8 mV/m @ -44.4 deg
+
+

Although the precise numbers might not be predictable, their general range certainly meets expectations. The resistive component of the impedance is only about 2/3 of the resonant value and about 1/3 of the value for the long tower. The reactive component is capacitive and significant. The lower impedance requires a higher current (given in peak Amps) at the source for a constant power level of 1 kW. The AGT score is close enough to ideal that it does not require any correction of the gain value, which is lower than the value for a resonant tower due to the lesser height of our present tower. Since the gain is lower, the field-strength reading (given in peak mV/m) is also lower than for either resonant or the long tower. (Multiply the field strength by 0.7071 to obtain the RMS value.)

+

The single-wire model corresponds to the left hand sketch in Fig. 1. Our interest from a modeling perspective is the correlation of the data collection with alternative models, such as the center sketch of a 3-leg tower, where each leg is independent and we use 3 sources to feed the assembly. As we have done in previous switches from the single-wire to 3-leg towers, we shall use 2"-diameter legs (0.085' radius) and retain the 41 segments for each leg. The triangle for the tower is 18" (1.5') on a side, and the model will position the legs so that the coordinate center falls at the midpoint of the triangle of legs.

+ 
+CM 201' 3-leg monopole, perfect ground
+CM 3 sources
+CE
+GW 1 41 0.866 0 0 0.866 0 201 0.085
+GW 2 41 -0.433 .75 0 -0.433 .75 201 0.085
+GW 3 41 -0.433 -.75 0 -0.433 -.75 201 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 3.1298
+EX 0 30902 1 0 0.0 3.1298
+EX 0 30903 1 0 0.0 3.1298
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Once we are satisfied with the model structure, we may turn to the data.

+ 
+201' 3-Leg Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+22.69 - j70.20    3.1298/leg      5.04         1.999   0.00     271.8 mV/m @ -44.4 deg
+
+

The gain, field-strength, and AGT data are all identical to the values derived from the single-wire model. The total current is the sum for 3 legs or 9.389 Apk. The impedance reports for the two models are well within a quarter-Ohm of each other. Obviously, the single-wire and the 3-leg model (using independent legs) correlate extremely well no matter what standard we apply to them.

+

The most complex full-structure model uses the same basic sections as we used for the long tower: 3' sections using 3 segments for each vertical and sloping member and 2 segments for the horizontal members. All wires use a 2" diameter. The lowest section omits the sloping members to avoid unwanted current divisions at the point where the source segments meet the ground. We replicate the full 9-wire second section (as viewed in Fig. 4) the number of times necessary to reach the final tower height. 201' as a sample tower height is convenient, since it divides nicely into 3' sections. Beyond the second section, we require 65 replications at 3' intervals using the GM command on just the wires of the second section.

+ 
+CM 201' 3-leg monopole  perfect ground
+CM 3 sources
+CM 67 sections with cross braces
+CE
+GW 1 3 0.866 0 0 0.866 0 3 0.085
+GW 2 3 -0.433 .75 0 -0.433 .75 3 0.085
+GW 3 3 -0.433 -.75 0 -0.433 -.75 3 0.085
+GW 4 2 0.866 0 3 -0.433 .75 3 0.085
+GW 5 2 -0.433 .75 3 -0.433 -.75 3 0.085
+GW 6 2 -0.433 -.75 3 0.866 0 3 0.085
+GW 7 3 0.866 0 3 0.866 0 6 0.085
+GW 8 3 -0.433 .75 3 -0.433 .75 6 0.085
+GW 9 3 -0.433 -.75 3 -0.433 -.75 6 0.085
+GW 10 2 0.866 0 6 -0.433 .75 6 0.085
+GW 11 2 -0.433 .75 6 -0.433 -.75 6 0.085
+GW 12 2 -0.433 -.75 6 0.866 0 6 0.085
+GW 13 3 0.866 0 3 -0.433 .75 6 0.085
+GW 14 3 -0.433 .75 3 -0.433 -.75 6 0.085
+GW 15 3 -0.433 -.75 3 0.866 0 6 0.085
+GM 9 65 0 0 0 0 0 3 7 1 15 3
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 3.1729
+EX 0 30902 1 0 0.0 3.1729
+EX 0 30903 1 0 0.0 3.1729
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

From this model, we obtain an interesting data collection.

+ 
+201' Full-Structure Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+22.07 - j62.14    3.1729/leg      5.14         2.043   0.09     274.8 mV/m @ -44.7 deg
+
+

The AGT score--in both forms--for this model is the same as for the full-structure version of the long tower. Hence, we find a gain figure that is too great compared to the other models. If we subtract the AGT-dB value from the reported gain, the value falls into line with the other model reports. The field-strength is also too large. However, if we divide it by the square root of half the basic AGT value, we obtain 271.9 mV/m (pk), a value that again is in line with the reports from models with more nearly ideal AGT values.

+

The source impedance report is perhaps the most interesting item in the collection. The resistive component is within about a half-Ohm of the other reports. However, the reactive component is about 8 Ohms lower. The amount of variance from the other models is not correctable by usual techniques--at least not to a degree that brings the value into alignment with the values derived from the other two short-tower models. Whether the source impedance variations represent anything significant remains a judgment that requires reference to the overall task within which we do modeling of this order. If the variation is significant, the models do not tell us clearly which values to use, since the model with the deviant figures also has a slightly non-ideal AGT value. If the difference is not significant, then we need not--except perhaps for curiosity--use a full structure model with its increased wire (603) and segment (1602) counts.

+

Conclusion

+

Our collection of models does show some interesting trends. Using the AGT and AGT-dB values, we may correct the gain and field-strength reports of the full-structure models to coincide very tightly with the reports from the simpler models. Only the trends in the source impedance variations remain for exploration. To explore these trends, I revised the models in the last episode to reflect the structure used in the present models. The key difference is the use of an 18" triangle face width, down from the 24" value used earlier. As well, the full-structure model uses 3' sections, as described earlier in these notes. The 234' near-resonant height also divides nicely by 3. However, the thinner tower structure--at least in the simpler models, is about 0.5' shy of being a resonant length. We need not show the models involved, since we have already described the types of change required to move from one model to another of a different height. However, the data tables may prove instructive.

+ 
+Near Resonant (234') 18" Face Monopole Models: Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+Single-Wire Model
+35.65 - j 1.29    7.4897          5.14         1.999   0.00     275.1 mV/m @ -45.6 deg
+3-Leg Model
+35.57 - j 1.61    2.4993/leg      5.14         1.999   0.00     275.1 mV/m @ -45.6 deg
+Full-Structure Model
+35.47 + j 2.74    2.5029/leg      5.24         2.043   0.09     278.2 mV/m @ -46.2 deg
+
+

Within the range for the short through the long tower (201' to 273' at 1 MHz), the full-structure models show a rising deviation in the resistive impedance component from the simpler model values as we increase the tower height. The short full-structure tower is about 0.5-Ohm low. At resonance, the full-structure value is very close to equal, and at the greatest height in the collection, the resistive component is about 2 Ohms high. Three data points do not make a curve, but they may indicate a trend.

+

The reactive component of the source impedance of the full-structure models shows a seemingly more random set of fluctuations. The value for the tallest tower is only about 1 Ohm more inductive than the value reported by the simpler models. At a resonant height, the value is about 4 Ohms inductive compared to the counterpart models, while the shortest tower reports a reactance that is about 8 Ohms more capacitive than the other models.

+

As we have noted, it is not clear from the models themselves whether the trends and fluctuations are functions of the AGT deviation from the ideal or from the full structure itself. At each section start, we have a division of the current between the sloping and the vertical members of the section, although the vertical leg shows anywhere from 2 to nearly 4 times the current magnitude that we find on the corresponding sloping member.

+

For some applications, the variations may be meaningful. In such cases, and within the limits of NEC recommendations for proper structuring of the model geometry, one may wish to employ models that come closer to the actual physical structure of a tower under study. The key geometry factors include the minimum segment length relative to the design frequency, the segment-length-to-radius ratio, and the angle of intersection between joining members of the structure. In all such cases, the modeler must carefully check the AGT score to ensure that the model remains within whatever limits one sets for maximum departure from an ideal score. Although software makers provide some general guidance, the standards of acceptable deviation remain in the end a modeler responsibility based on the required degree of precision brought to the task. In all cases, where the AGT score indicates less than ideal values, the modeler should adjust the gain and the field-strength values accordingly.

+

In other applications, the variations among models may not be significant. In such cases, one may productively use the simpler models and bypass the tedious work of trying to capture every detail of structure that holds the tower legs together.

+

Go to Main Index

+ + diff --git a/content/amod/amod134-1.gif b/content/amod/amod134-1.gif new file mode 100644 index 0000000..8cb0810 Binary files /dev/null and b/content/amod/amod134-1.gif differ diff --git a/content/amod/amod134-2.gif b/content/amod/amod134-2.gif new file mode 100644 index 0000000..c06292e Binary files /dev/null and b/content/amod/amod134-2.gif differ diff --git a/content/amod/amod134-3.gif b/content/amod/amod134-3.gif new file mode 100644 index 0000000..af47f4b Binary files /dev/null and b/content/amod/amod134-3.gif differ diff --git a/content/amod/amod134.html b/content/amod/amod134.html new file mode 100644 index 0000000..2bb3743 --- /dev/null +++ b/content/amod/amod134.html @@ -0,0 +1,259 @@ + + + + + AM BC Modeling with NEC + + + +
+

AM BC Modeling with NEC
+ 4. Square, Sloping, and Tapered

+
+
+

L. B. Cebik, W4RNL

+
All of the samples that we have explored in our journey through modeling AM BC towers over perfect ground have used triangular towers with a uniform face-width along the total length. These towers have served well in examining the correlations among the chief types of models: the NEC-recommended substitute single-wire version, the alternative of using 3 independent legs, and the full-structure models. +

Although the triangular tower with a uniform face-width may be the most common sort of structure used, there are a number of other structures that we occasionally find. The notes in this episode work with a few of the non-standard tower shapes.

+

The Square Tower

+

The most notable alternative to a triangular tower is a square tower. We shall initially work with squares having a uniform face-width in order to correlate the results with past triangular towers that we have examined. Therefore, we shall use a face width of 18" (1.5') and a height of 234' at 1 MHz. As always we shall use lossless conductors and a perfect ground. As well, each model will use a current source, with its associated modeling requirement of an extra distant thin and short wire along with a network (NT) entry.

+

The simplest model consists of a single vertical wire with a single source. The NAB-recommend value for the wire radius is 0.56 times the face-width. For the 18" face of a square towers, the substitute wire requires a radius of 0.84' (10.08"). Except for the change of the radius, the single-wire 234' model, with 41 segments for the modeled wire, looks very much like the corresponding single-wire substitute model for a triangular tower.

+ 
+CM near-resonant monopole, perfect ground, square (0.56)
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 234 0.84
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.4329
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

For the moment, we shall by-pass the data that we may collect from this model of a square tower to move directly to the second way to handle the model. We may also model the tower as 4 independent legs, each 234' tall with 41 segments. As in past models, we shall use 2"-diameter legs (radius = 0.085'). In this tower arrangement, the legs form a square around the center of the coordinate system. Therefore, each leg has X- and Y-coordinates of 0.75', with numerical signs indicating the quadrant of each leg. Relative to triangular towers, we require one more source (with its added wire and network) and the divisor for the net source impedance will be 4 instead of 3. If we wish to employ a common source, then we simply add a 4th transmission line to the collection that we used for triangular towers. However, we may continue to use the separate source model and perform the simple external calculation. Although the model appears to be more complex than its triangular counterpart, it actually has only 4 more lines, each of which is a near copy of its neighbor.

+ 
+CM near-resonant monopole, perfect ground, square, straight
+CM 4 sources, independent legs
+CE
+GW 1 41 .75 .75 0 .75 .75 234 0.085
+GW 2 41 -.75 .75 0 -.75 .75 234 0.085
+GW 3 41 -.75 -.75 0 -.75 -.75 234 0.085
+GW 4 41 .75 -.75 0 .75 -.75 234 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GW 30904 1 9904.0000 9904.0000 9904.0000 9904.0001 9904.0001 9904.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.8643
+EX 0 30902 1 0 0.0 1.8643
+EX 0 30903 1 0 0.0 1.8643
+EX 0 30904 1 0 0.0 1.8643
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+NT 30904 1 4 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Once more we shall by-pass the data and move directly to the third type of model, one using a simulated full structure. Because we may divide 234' by 3' to obtain in integer for the total number of required sections (78), we can use 3' section for the model. The lowest section will use only a horizontal member at its upper limit, omitting the sloping sections. As we discovered with triangular towers, the use of sloping members in the lowest section results in a current division at the ground-contact end of the source segment, seriously distorting the model results. We introduce sloping model wires in the second section, as shown in Fig. 1. The view shows only the lowest two sections to reveal the segmentation scheme, which is the same as used for the full-structure triangular tower model in the preceding episode.

+
+ +
+

To complete the tower, we need only one further geometry command. The GM entry replicates the second section 76 more times to arrive at the total height required. The final model is a bit larger than its triangular counterpart, with 708 wires and 2488 segments. Lest the model size seem forbidding, the model required a 62-second total run time on a moderately old 1.8 GHz machine.

+ 
CM near-resonant monopole, perfect ground, square, straight
+CM 4 sources, full structure
+CE
+GW 1 3 .75 .75 0 .75 .75 3 0.085
+GW 2 3 -.75 .75 0 -.75 .75 3 0.085
+GW 3 3 -.75 -.75 0 -.75 -.75 3 0.085
+GW 4 3 .75 -.75 0 .75 -.75 3 0.085
+GW 5 2 .75 .75 3 -.75 .75 3 .085
+GW 6 2 -.75 .75 3 -.75 -.75 3 .085
+GW 7 2 -.75 -.75 3 .75 -.75 3 .085
+GW 8 2 .75 -.75 3 .75 .75 3 .085
+GW 9 3 .75 .75 3 .75 .75 6 0.085
+GW 10 3 -.75 .75 3 -.75 .75 6 0.085
+GW 11 3 -.75 -.75 3 -.75 -.75 6 0.085
+GW 12 3 .75 -.75 3 .75 -.75 6 0.085
+GW 13 2 .75 .75 6 -.75 .75 6 .085
+GW 14 2 -.75 .75 6 -.75 -.75 6 .085
+GW 15 2 -.75 -.75 6 .75 -.75 6 .085
+GW 16 2 .75 -.75 6 .75 .75 6 .085
+GW 17 3 .75 .75 3 -.75 .75 6 .085
+GW 18 3 -.75 .75 3 -.75 -.75 6 .085
+GW 19 3 -.75 -.75 3 .75 -.75 6 .085
+GW 20 3 .75 -.75 3 .75 .75 6 .085
+GM 9 76 0 0 0 0 0 3 9 1 20 3
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GW 30904 1 9904.0000 9904.0000 9904.0000 9904.0001 9904.0001 9904.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.8623
+EX 0 30902 1 0 0.0 1.8623
+EX 0 30903 1 0 0.0 1.8623
+EX 0 30904 1 0 0.0 1.8623
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+NT 30904 1 4 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

I have reserved the data collections to present them together, not only with each other, but with the data for the three models of 234' 18" face-width triangular towers from the preceding episode. The total data collection for the near-resonant tower models will prove instructive.

+ 
+Near Resonant (234') 18" Face Monopole Models: Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+
+Triangular
+Single-Wire Model
+35.65 - j 1.29    7.4897          5.14         1.999   0.00     275.1 mV/m @ -45.6 deg
+3-Leg Model
+35.57 - j 1.61    2.4993/leg      5.14         1.999   0.00     275.1 mV/m @ -45.6 deg
+Full-Structure Model
+35.47 + j 2.74    2.5029/leg      5.24         2.043   0.09     278.2 mV/m @ -46.2 deg
+
+Square
+Single-Wire Model
+36.20 + j 1.01    7.4329          5.15         1.999   0.00     275.2 mV/m @ -46.0 deg
+4-Leg Model
+35.97 + j 0.08    1.8643/leg      5.15         1.999   0.00     275.2 mV/m @ -45.9 deg
+Full-Structure Model
+36.04 + j 3.85    1.8623/leg      5.22         2.034   0.07     277.6 mV/m @ -46.6 deg
+
+

Within the data for square towers, we find a very small variation in the resistive component of the three models, about 0.25 Ohm. The reactance varies more widely among models, but less than 3 Ohms overall. Among the triangular models, we found slightly less variation in the resistive component and slightly more variation in the reactance. However, with both types of models, the full-structured version showed a less-then-ideal AGT value that required correction of the gain report and the field-strength report. If we correct the square-model field strength raw data by dividing the report by the square root of half the basic AGT score, we obtain a reading of 275.3 mV(pk)/m, which brings into accord with the raw reports of the simpler models. Applying the AGT-dB value to correct the raw gain reports also brings it into line with the other gain values.

+

Between the triangular and the square models, we find very little difference in the values. The seemingly fatter square tower shows a source impedance that is about 0.5-Ohm higher resistively and about 1-Ohm more inductive with respect to reactance. For many applications, the difference would not make a difference. Effectively, for the same face width, the square tower is 1.5 times fatter than the triangular model, but a 50% change in diameter does not change modeling results by a great amount.

+

A Sloping Square

+

One very common form for a square tower is a sloping structure that is broader at the base than at the top. To sample this configuration from a modeling perspective, we might consider a 234' tower consisting of 4 legs. The face width at the base might be 48" (4') and at the top 24" (2'). Fig. 2 illustrates one face of such a sloping structure, but not to scale. The rate of change of face width is only 0.05"/foot of height. However, that small rate will be sufficient to show us what to expect from such structures.

+
+ +
+

If we accept the correlation among the three model versions that we have so far examined, then we may develop a relatively simple model for the sloping tower. Perhaps the easiest model consists of 4 independent legs, using our standard 2" diameter (0.085' radius). Each leg slopes inward by the requisite amount to arrive at the desired top face width. Except for the X- and Y-coordinates, the model closely resembles the 4-leg version of the square tower with a uniform face width.

+ 
+CM near-resonant monopole, perfect ground, square, sloping legs
+CM 4 sources
+CE
+GW 1 41 2 2 0 1 1 234 0.085
+GW 2 41 -2 2 0 -1 1 234 0.085
+GW 3 41 -2 -2 0 -1 -1 234 0.085
+GW 4 41 2 -2 0 1 -1 234 0.085
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GW 30903 1 9903.0000 9903.0000 9903.0000 9903.0001 9903.0001 9903.0001 .00001
+GW 30904 1 9904.0000 9904.0000 9904.0000 9904.0001 9904.0001 9904.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.9062
+EX 0 30902 1 0 0.0 1.9062
+EX 0 30903 1 0 0.0 1.9062
+EX 0 30904 1 0 0.0 1.9062
+NT 30901 1 1 1 0 0 0 1 0 0
+NT 30902 1 2 1 0 0 0 1 0 0
+NT 30903 1 3 1 0 0 0 1 0 0
+NT 30904 1 4 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Because the tower is so much fatter than its uniform-face-width counterpart, we might expect the data to show some inductive reactance at a height of 234', which was very close to resonant with the 18" uniform face width. The data collection tells a somewhat different story.

+ 
+234' 4-Leg Sloping Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+34.41 - j 8.81    1.9062/leg      5.14         1.999   0.00     275.0 mV/m @ -46.5 deg
+
+

In fact, the tower "plays short." That is to say, due to the tapering of the effective diameter of the tower along its length from the source outward to ward the element end, the tower requires a larger value for its height to achieve resonance than a comparable uniform-diameter (or uniform-face-width) tower. The tower simply reflects one of the fundamental properties of elements that taper downward in diameter moving away from the feedpoint. (If it were practical to invert the tower so that it exhibited an increase in effective diameter as we moved away from the source at perfect ground level, it would show the properties of one-half of a biconical element and "play long." Of course, what we cannot do in reality, we often can do as a modeling exercise and thereby naturalize our expectations of element behavior.) For our very gently sloping tower to achieve resonance within j+/-1 Ohm of remnant reactance, we need to increase the height by about 5' or about 2%.

+

More radically sloped square towers, which might be more typical in actual installations, would show somewhat different results. The typical base face width will in practical installations generally increase faster than the rate of slope. These two tendencies tend to counteract each other, with the wider footprint shrinking the required height for resonance and the rate of slope increasing the required height. For anyone anticipating modeling a real physical square sloping tower, running a series of models for familiarization may be a useful exercise. The nearly ideal AGT score gives the 4-sloping-leg model as much validity as its uniform-face-width counterpart.

+

Tapered or Stepped-Diameter Triangular Towers

+

Although uncommon in the AM BC industry, we do find many triangular towers that employ the rough equivalent of the square tower's sloping legs. Technically, we should refer to such models as stepped-diameter structures, although it is common practice also to refer to them as tapered-diameter elements. (That is why I specifically referred to the square tower as having a sloping face width, since the width decreased continuously rather than in steps.) Fig. 3 shows a simplified but representative situation.

+
+ +
+

We may use the not-to-scale sketch to create some interesting models. However, trying to set up a full-structure model will usually end up in frustration. The steps between sections are normally sudden and very short, resulting in a need for wire segments that fall below the recommended NEC minimum length of 0.001 wavelength (or 11.803" at 1 MHz). If we find the NAB-recommended single-wire equivalent of tower faces acceptable, we can create a simplified model.

+

Let's begin with our 234' total height and break it into 4 equal 58.5' sections, each with its own face width. The base will be 24" wide and the top 12" wide, with equal face width steps between. Hence, we might end up with the following chart.

+ 
+Stepped-Diameter Triangular Tower Section Face Widths and Equivalent Diameters
+
+Section     Face-Width     Equiv. Diameter     Radius in Feet
+Base        24"            17.76"              0.74'
+2           20             14.80               0.6167
+3           16             11.84               0.4934
+Top         12              8.88               0.37
+
+

We can easily create a single-wire tower using 4 modeling wires having the desired properties.

+ 
+CM near-resonant monopole, perfect ground, stepped triangle
+CM NAB substitute single-wire monopole
+CE
+GW 1 10 0 0 0 0 0 58.5 .74
+GW 2 10 0 0 58.5 0 0 117 .6167
+GW 3 10 0 0 117 0 0 175.5 .4934
+GW 4 10 0 0 175.5 0 0 234 .37
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.7772
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Next, let's run the model, first using NEC-2 and then using NEC-4. We obtain the following data collection.

+ 
+234' Stepped-Diameter Triangular Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+NEC-2
+33.52 - j 7.85    7.7245          5.26         2.058   0.12     279.0 mV/m @ -45.6 deg
+NEC-4
+33.07 - j15.21    7.7777          5.18         2.020   0.04     276.2 mV/m @ -45.6 deg
+
+

With the number and size of the diameter steps, neither core yields a very precise results. As we would expect, the NEC-2 results shows a much poorer AGT score than the NEC-4 run, but both are off the mark where we wish to have relatively high precision.

+

The most common way to achieve precision in cases like this one is to use substitute elements with a uniform diameter. The most precise method available to calculate the length of these elements derives from the work of David Leeson (see chapter 8 of his Physical Design of Yagi Antennas). Leeson adapts the work of Schelkunoff to the calculation of the length and diameter of a uniform-diameter element equivalent to a stepped-diameter element. The equivalence equation is useful for unloaded elements within about 15% of resonance. If we do not wish to perform the calculations manually, we can turn to programs such as NEC-Win Plus or EZNEC that contain the facility within their input interface programming. Note that the substitute element will have a different length as well as diameter relative to the original. For the present sample, the required radius is 0.5593', while the element length is 226.292'. However, the resulting model is very simple.

+ 
+CM near-resonant monopole, perfect ground, leeson
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 226.292 .5593
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.4329
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

The substitute element provides us with the following data collection.

+ 
+Substitute Stepped-Diameter Triangular Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+32.15 - j17.47    7.8876          5.12         1.999   0.00     274.3 mV/m @ -45.3 deg
+
+

As we might expect from the tower height using the substitute element, the stepped-diameter tower is short of resonance. The NEC-2 data might have given the impression that its values were closer to the anticipated resonant impedance. However, it turns out that the NEC-2 run produced values further from accurate data, and both uncorrected models tended to produce reactance values that were too inductive. (A MININEC (Antenna Model) model using the dimensions for the original versions with a changing diameter yielded a gain of 5.13 dBi with a source impedance of 32.63 - j18.85 Ohms.)

+

Conclusion

+

In this episode, we examined some of the variations that we might well encountered in modeling monopole towers over perfect ground for various AM BC enterprises. As always, the samples were hypothetical, but illustrative of the principles involved in modeling tower structures. We saw that uniform-face-width square towers have simplified forms that are as reliable as the simplified forms used for triangular towers. As well, the full-structure versions of those models, even when adhering as strictly as possible to all NEC guidelines, still resulted in a slight deviation from an ideal AGT score--just enough to show report values that required correction.

+

The sloping-leg and stepped-face-width models, although uncommon in most practice, gave us an opportunity to select the best modeling technique for a given task. In the case of square towers with sloping legs, using independent tower legs for the model proved not merely to simplify the model, but also to avoid the modeling flaws that would easily result from trying to construct a full-structure model. The stepped-face-width triangular model using the NEC-recommended single-wire model allowed us to calculate a uniform-diameter substitute element for which NEC produces more reliable data.

+

We have traveled a considerable distance from our first procedural steps in using NEC to model AM BC towers under standard conditions. However, we still have steps to take.

+

Go to Main Index

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+

AM BC Modeling with NEC
+ 5. Multiple Tower Arrays

+
+
+

L. B. Cebik, W4RNL

+
In our journey through the netherworld of AM BC towers modeled over perfect ground, we have examined the techniques needed with NEC cores (especially NEC-4) for obtaining the type of results that modelers obtain from specialized MININEC programs. Among the items that we have explored are the correlations among models using the NAB-recommended substitute single wire tower models, independent 3- and 4-leg tower models, and full-structure models. We noted along the way steps necessary to ensure that we supply a model with a set power (in all the samples, 1 kW) and the output command necessary to obtain field-strength readings (RP1). We noted that NEC itself uses peak values of voltage and current. Hence, field-strength readings and supplied current specifications require adjustment by the usual 0.7071 multiplier to convert them into RMS values. We also looked at various cases in which one or another model version appeared to be preferable for various reasons. For example, we turned to the 4 independent leg model to handle square towers that slope from bottom to top. However, for working with stepped-diameter towers, the single-wire substitute model provides the most advantageous model. +

All of our samples in the 4 preceding episodes used a single tower centered on the coordinate system center (X=0, Y=0). Typical of those one-tower models was the near resonant 234' tower at 1 MHz, with an 18" face of a triangular tower. The model that we used earlier looked almost like the one that we shall show here.

+ 
+CM near-resonant monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 234 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.4897
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+RP 1 1 1 0000 0 0 1.00000 1.00000 3218.688
+EN
+
+

The only difference between past models and this one is that the new version adds a second RP1 command at a distance of 2 miles to the original that uses a distance of 1 mile. Both commands use ground level as the observation height for the command. The basic data collection is in the following lines.

+ 
+Near Resonant (234') 18" Face Triangular Single-Wire Monopole Model Data
+
+Impedance (Ohms)  Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile            F-S @ 2 miles
+35.65 - j 1.29    7.4897          5.14         1.999   0.00     275.1 mV/m @ -45.6 deg  137.5 mV/m @ -178.1 deg
+
+

If the only field-strength value in which we have any interest is the magnitude (in peak mv/m as shown or adjusted to RMS), then we need not add the second RP1 request. For perfect ground, field-strength magnitude values decrease linearly with distance from the antenna. However, if we have any interest in the phase angle, the second request is necessary to obtain the additional figures.

+

In this episode, the tower that we have just modeled will play a significant role, but not solo. In this episode, we shall look at some very basic cases that employ two towers with considerations of the current magnitude and phase angle at each source--remembering that we are using the standard method in NEC to provide current sources. The task will sometimes involve more than simply adding a second tower to the GW portion of the list.

+

Two Towers Fed In-Phase for a Broadside Pattern

+

Suppose that we need a pattern like the one shown in Fig. 1 to fulfill broadcast needs and restrictions. The simplest way to obtain it is with two towers, in this case, using broadside array techniques. In the present sample, we shall use only simple arrays to illustrate the modeling aspects. Actual arrays may be considerably more complex, and the resultant patterns may be equally complex. The pattern is laid out according to the compass-rose azimuth conventions favored by some agencies and many field engineers.

+
+ +
+

The desired coverage calls for a moderate increase in gain along the N-S axis with lesser gain in the E-W directions. One way to obtain such coverage is to arrange two towers about 1/4 wavelength apart in the E-W plane (+Y and -Y) and to feed them in phase. Initially, this feed requirement will use two sources, each supplied with the same current magnitude and phase angle, with the magnitude determined by our standard 1-kW power level. We shall use our single-wire substitute for a 234' tower in each case. A wavelength at 1 MHz is 983.571 feet, so the separation between towers is 245.893'.

+ 
+CM 2 near-resonant monopoles, perfect ground
+CM NAB substitute single-wire monopole
+CM in-phase feeding--1/-wl spacing
+CE
+GW 1 41 0 122.946 0 0 122.946 234 0.555
+GW 2 41 0 -122.946 0 0 -122.946 234 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 4.3339
+EX 0 30902 1 0 0.0 4.3339
+NT 30901 1 1 1 0 0 0 1 0 0 0
+NT 30902 1 2 1 0 0 0 1 0 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 37 0000 0 0 1.00000 10.00000 1609.344
+EN
+
+

The simple data collection, as we can see from the following lines, does not tell the full story, as it did for the single tower models. The collection also omits the 2-mile field-strength report.

+ 
+Two-Tower Broadside Array 18" Face Triangular Single-Wire Monopole Model Data
+
+Impedance (Ohms)    Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+53.24 - j17.40 x2   4.3339/tower    6.23 max.    1.999   0.00     311.5 mV/m @ -47.2 deg
+
+

The impedance reports are for each tower, as is the current magnitude. The gain and the field-strength values are maximum values, taken in the northern direction (0 degrees, which corresponds to the +X direction on the geometry coordinate system). However, we shall be interested in both the gain and the field strength in various directions around the pattern. Because the field strength is likely to be the more important figure, we may wish to examine a table of figures taken at suitable intervals. The following sample from the model traces 1/4 of the pattern (because it is symmetrical) at 10-degree intervals.

+ 
+**** Electric Field: Phi Pattern ****
+Z=0, Freq=1, File=fcc51.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+  Phi      Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+   0.00   3.1157E-001    -47.23   5.3620E-022   -108.51
+  10.00   3.0868E-001    -47.23   4.3494E-022    105.73
+  20.00   3.0040E-001    -47.23   3.2047E-022   -167.59
+  30.00   2.8786E-001    -47.23   1.9626E-022    137.96
+  40.00   2.7271E-001    -47.23   6.6090E-023    -66.91
+  50.00   2.5687E-001    -47.23   6.6090E-023    113.09
+  60.00   2.4224E-001    -47.23   1.9626E-022    -42.04
+  70.00   2.3051E-001    -47.23   3.2047E-022     12.41
+  80.00   2.2293E-001    -47.23   4.3494E-022    -74.27
+  90.00   2.2032E-001    -47.23   5.3620E-022     71.49
+
+

The E(theta) columns represent the vertical component of the field-strength calculations. The horizontal component (E(phi) is too small to be significant. To better visualize the changes in field strength as we move around the overall pattern, we may also graph the values, as shown in Fig. 2.

+
+ +
+

The combination of data allows significant evaluation of the likely performance of the 2-tower broadside array. Of course, the sample selects a spacing between towers that yields less than the full broadside bi-directional gain of such towers. Wider spacing will yield more gain in the N-S direction with less gain in the E-W direction. As a certain point as we increase spacing, the oval pattern will gradually evolve into a figure-8.

+

Our interest does not lie in what we can do with towers so much as it lies in what we can include in and show by appropriate modeling. For example, we may wish to include in the model a composite feed system so that we have only a single source. The normal form of feeding the system would be to bring transmission lines from each tower to a central point so that each line is equal in length (and characteristic impedance) to the other. We may set up such lines by selecting the junction point and placing a short, thin wire to serve as the source as well as the junction between lines. Let's arbitrarily set up two 600-Ohm transmission lines, one from each tower. The terminal points for the lines and the source will be a position exactly centered between the towers (Y=0) and 245' (1/4 wavelength) away from the towers. The general outline of the model will have the appearance of the set-up in Fig. 3.

+
+ +
+

To model this situation, without altering the tower positions or other attributes, we need a model that resembles the following lines.

+ 
CM 2 near-resonant monopoles  perfect ground
+CM NAB substitute single-wire monopole
+CM in-phase common feeding--1/4-wl spacing
+CE
+GW 1 41 0 122.946 0 0 122.946 234 0.555
+GW 2 41 0 -122.946 0 0 -122.946 234 0.555
+GW 3 1 -245 0 1 -245 0 2 0.0001
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.5138
+NT 30901 1 3 1 0 0 0 1 0 0
+TL 1 1 3 1 600 0 ! User Defined VF
+TL 2 1 3 1 600 0 ! User Defined VF
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1 1
+RP 0 1 361 1000 90 0 1 1
+RP 1 1 37 0000 0 0 1.00000 10.00000 1609.344
+EN
+
+

Form this model we may obtain the usual data collection.

+ 
+Two-Tower Broadside Array, Common Source, 18" Face Triangular Single-Wire Monopole Model Data
+
+Impedance (Ohms)    Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+872.8 - j1457.8     1.5138          6.23 max.    1.999   0.00     311.5 mV/m @ -47.2 deg
+
+

Only the impedance and the required current for 1kW differ from the dual-source model. To confirm the high source impedance, we may independently calculate the current transformation down each 600-Ohm line, with a length of 274.12' based on the separate source impedance values of 53.24 - j17.40 Ohms. The result will be separate impedances of about 1754 - j2920 Ohms, which combine in parallel to 877 - j1460 Ohms, very close to the modeled values, considering the rapid change in value for each small increment of length.

+

If the impedance is inconvenience due to the 100.3-degree lines required, we may always change the position of the junction. The shortest lines occur when we place the junction in line with the towers at Y=0, as suggested by Fig. 4. The lines have shrunk to 45 degrees.

+
+ +
+

The only change to the model is in the placement of GW3, as the following partial model file shows.

+ 
+GW 1 41 0 122.946 0 0 122.946 234 0.555
+GW 2 41 0 -122.946 0 0 -122.946 234 0.555
+GW 3 1 0 0 1 0 0 2 0.0001
+
+

We do not required changes in the TL command entries because we have used zeros (after the characteristic impedance entry of 600) to specify that the line length is the actual distance between the terminal points as defined by the wire entries.

+ 
+TL 1 1 3 1 600 0 ! User Defined VF
+TL 2 1 3 1 600 0 ! User Defined VF
+
+

In the data collection, we find that the only resultant differences occur in the entries for the composite source impedance and the required peak current level needed at this impedance to achieve a 1-kW power level.

+ 
+Two-Tower Broadside Array, Common Source, 18" Face Triangular Single-Wire Monopole Model Data
+
+Impedance (Ohms)    Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+49.96 + j 278.9     6.3272          6.23 max.    1.999   0.00     311.5 mV/m @ -47.2 deg
+
+

NEC employs lossless transmission lines for its calculations. At 1 MHz for virtually any line less than 1/2 wavelength long, the values for lossless line calculations will not differ significantly from calculations including line losses. The model set-ups also presume a velocity factor of 1.0. If the velocity factor of a line departs significantly from that value, one may always insert the electrical line length in place of our use of zero to force the program to use the actual distance between terminal points on the line.

+

Not all arrays require patterns with maximum field-strength values going north and south. Suppose that we require that the pattern have its gain maximum point aligned along an axis defined by compass heading of 60 and 240 degrees. In general, there are two major ways to achieve this goal. One is to set up each tower so that the broadside direction is automatically along the desired axis. The other method, shown here, is to set up the model in the simple manner shown earlier and then to turn the entire array around the Z-axis by the required 60 degrees. Note in the following model lines, that to turn the axis clockwise--as the present situation requires, we specify -60 degrees in the GM line. (+60 degrees turns the pattern counterclockwise.)

+ 
+CM 2 near-resonant monopoles  perfect ground
+CM NAB substitute single-wire monopole
+CM in-phase common feeding--1.4-wl spacing
+CM rotated for 60/240-deg AZ axis
+CE
+GW 1 41 0 122.946 0 0 122.946 234 0.555
+GW 2 41 0 -122.946 0 0 -122.946 234 0.555
+GW 3 1 -245 0 1 -245 0 2 0.0001
+GM 0 0 0 0 -60 0 0 0
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 1
+EX 0 30901 1 0 0.0 1.5138
+NT 30901 1 3 1 0 0 0 1 0 0
+TL 1 1 3 1 600 0 ! User Defined VF
+TL 2 1 3 1 600 0 ! User Defined VF
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1 1
+RP 0 1 361 1000 90 0 1 1
+RP 1 1 37 0000 0 0 1.00000 10.00000 1609.344
+EN
+
The model shown uses the long transmission lines. However, that fact only allows the GM rotation to show with clarity in Fig. 5. +
+ +
+

We need not show the data collection, since it has not changed. What has changed is the field-strength table. The magnitudes will be the same as the earlier sample shown, but the headings on which they occur will differ. Remember that for tabular information, NEC uses the phi or counterclockwise convention. Therefore, the 60-degree compass-rose azimuth bearing coincides with the phi 300-degree bearing in the following table.

+ 
+**** Electric Field: Phi Pattern ****
+Z=0, Freq=1, File=fcc53.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+  Phi      Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+   0.00   2.4224E-001    162.75   9.3641E-023   -108.70
+  10.00   2.3051E-001    162.75   7.5958E-023    105.52
+  20.00   2.2294E-001    162.75   5.5967E-023   -167.82
+  30.00   2.2032E-001    162.75   3.4275E-023    137.71
+  40.00   2.2294E-001    162.75   1.1542E-023    -67.17
+  50.00   2.3051E-001    162.75   1.1542E-023    112.83
+  60.00   2.4224E-001    162.75   3.4275E-023    -42.29
+  70.00   2.5687E-001    162.75   5.5967E-023     12.18
+  80.00   2.7271E-001    162.75   7.5958E-023    -74.48
+  90.00   2.8786E-001    162.75   9.3641E-023     71.30
+ 100.00   3.0041E-001    162.75   1.0848E-022    106.98
+ 110.00   3.0869E-001    162.75   1.2002E-022     53.35
+ 120.00   3.1158E-001    162.75   1.2792E-022    -66.10
+ 130.00   3.0869E-001    162.75   1.3192E-022    134.16
+ 140.00   3.0041E-001    162.75   1.3192E-022    -39.16
+ 150.00   2.8786E-001    162.75   1.2792E-022    161.09
+ 160.00   2.7271E-001    162.75   1.2002E-022     41.65
+ 170.00   2.5687E-001    162.75   1.0848E-022    -11.99
+ 180.00   2.4224E-001    162.75   9.3641E-023     23.69
+ 190.00   2.3051E-001    162.75   7.5958E-023    169.48
+ 200.00   2.2294E-001    162.75   5.5967E-023     82.82
+ 210.00   2.2032E-001    162.75   3.4275E-023    137.29
+ 220.00   2.2294E-001    162.75   1.1542E-023    -17.83
+ 230.00   2.3051E-001    162.75   1.1542E-023    162.17
+ 240.00   2.4224E-001    162.75   3.4275E-023    -42.71
+ 250.00   2.5687E-001    162.75   5.5967E-023    -97.18
+ 260.00   2.7271E-001    162.75   7.5958E-023    -10.52
+ 270.00   2.8786E-001    162.75   9.3641E-023   -156.31
+ 280.00   3.0041E-001    162.75   1.0848E-022    168.01
+ 290.00   3.0869E-001    162.75   1.2002E-022   -138.35
+ 300.00   3.1158E-001    162.75   1.2792E-022    -18.91
+ 310.00   3.0869E-001    162.75   1.3192E-022    140.84
+ 320.00   3.0041E-001    162.75   1.3192E-022    -45.84
+ 330.00   2.8786E-001    162.75   1.2792E-022    113.90
+ 340.00   2.7271E-001    162.75   1.2002E-022   -126.65
+ 350.00   2.5687E-001    162.75   1.0848E-022    -73.02
+ 360.00   2.4224E-001    162.75   9.3641E-023   -108.70
+
+

Fig. 6 re-confirms the successful rotation by showing the far-field pattern for the revised model. The lines on either side of the main axis lines indicate the half-power beamwidth, suggesting that the gain is about 3 dB weaker at right angles to the main axis. You may correlate this to the ratio of the relevant field-strength reports by the usual equation in which PdB = 20 log(10)(E1/E2).

+
+ +
+

The notes so far have dealt with the simple case in which the sources for each broadside element are identical with respect to current magnitude and phase angle. Not all arrays of towers have such an easy requirement.

+

An Endfire Array of Two Towers

+

For directional patterns, that is, patterns with a dominant lobe in only one direction, array designers generally use end-fire techniques so that the pattern is in line with the towers rather than broadside to them. We shall employ only a very basic two-tower array to note the key modeling points of interest. However, some installations have used up to 4 towers to obtain specific pattern shapes. As well, in some instances, designs have combined broadside with end-fire techniques for truly large arrays. Since there are texts devoted to the design of such arrays, we may focus on translating endfire arrays into models over perfect ground. We shall retain our 234' tower with the single-wire equivalent of an 18" face on a triangular structure. As was clear in the broadside array, mutual coupling between towers in relatively close proximity alters the source impedance so that each tower in the array is no longer self-resonant. (Compare the source impedance values for the initial 2-source broadside model with the source impedance of the reference single-tower model at the beginning of these notes.) Our present exercise will require even closer attention to the impedances reported for each tower.

+
+ +
+

Our sample will use two towers separated by 1/4 wavelength. To set the main-lobe direction at north (0 degrees azimuth), we align the towers along the X-axis. To ensure that we place the array center at the coordinate center, each tower is 1/8 wavelength from X=0. The resulting geometry is simply our broadside array turned 90 degrees. In fact, if we were to feed the two sources in phase, we would obtain the earlier broadside pattern with the stronger field-strength reading east and west.

+ 
+CM 2 near-resonant monopoles, perfect ground
+CM NAB substitute single-wire monopole
+CM end-fire two-tower array
+CM 90-degree feeding--1/4wl spacing
+CE
+GW 1 41 122.946 0 0 122.946 0 234 0.555
+GW 2 41 -122.946 0 0 -122.946 0 234 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 5.3579 0
+EX 0 30902 1 0 0.0 5.3579
+NT 30901 1 1 1 0 0 0 1 0 0 0
+NT 30902 1 2 1 0 0 0 1 0 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 37 0000 0 0 1.00000 10.00000 1609.344
+EN
+
+

In the model, GW 1 is the forward tower, that is, the tower in the direction of the main lobe, with GW 2 to the rear. Basic array theory tells us that we shall obtain a highly directional pattern if we feed the towers so that the rear tower has the same current magnitude as the forward tower. However, the phase angle of the rear tower current should be +90-degree relative to the forward tower (or the forward tower phase angle should be -90 degrees relative to the rearward tower). Some software allows the modeler to enter the desired values directly into the input interface screens. However, we shall do it the "old-fashioned" way by manipulating the currents on the remote EX entries for our current-fed array.

+

The problem at hand is simplified by the use of equal current magnitudes. However, the EX entry in NEC lists the excitation voltage in terms of real and imaginary components of the voltage that we shall transform into a current via the NT entries. Fig. 8 shows the help screens (a composite of 2 screens, one for each source) to assist us in sorting out the entries. The screens list both the components and the magnitude and phase angle, and we may set up the line by placing the values in either format. As the screen shows, the forward tower (1) is 90 degrees behind the rearward tower (2) with respect to the phase angle. Compare these entries to the EX commands in the model.

+
+ +
+

Now let's perform one more comparison: the EX entries with the currents that appear on the source segments of the two towers. We may glean this information from the NEC output file.

+ 
+**** Segment Current versus Frequency ****
+
+FREQUENCY     SEG.  TAG    COORD. OF SEG. CENTER     SEG.             - - - CURRENT (AMPS) - - -
+  (MHz)       NO.   NO.     X        Y        Z      LENGTH      REAL         IMAG.        MAG.        PHASE
+1.000000         1    1   0.1250   0.0000   0.0029  0.00580   -9.6451E-16  -4.3339E+00   4.3339E+00  -90.000
+1.000000        42    2  -0.1250   0.0000   0.0029  0.00580    4.3339E+00  -1.4008E-16   4.3339E+00    0.000
+
+

Although we entered the source voltages with phase angles of 0 and 90 degrees for towers 1 and 2, respectively, the currents on the sources have phase angles of -90 and 0 degrees, respectively. We now understand two things. First, the voltage entries for the EX line have preserved their phase difference in the conversion to current values on the source segments. Second, the NT command responsible for the conversion shifts the entered phase angle by -90 degrees relative to the final current reports on the affected segments. If we forget this second fact, it shows up quite rapidly, since the pattern for entering the phase angles backwards will also be backwards.

+
+ +
+

Fig. 9 shows the resulting far-field patterns that merges from the model that we have constructed. If we truly needed to reduce the rearward radiation further, we may juggle both the magnitude and the phase angle of the EX entries until satisfied. However, once we have established the desired pattern, we would need to re-adjust the current magnitudes with respect to the total power supplied to the array as indicated by the power budget portion of the NEC output report, using the technique shown in the first of these episodes. The values shown are for our pre-set power level of 1 kW.

+

The methods for obtaining a main-lobe direction other than north are the same as for the broadside array. We may perform pre-modeling calculations so as to place the towers in the correct positions to yield a pattern with the desired heading, or we may construct the tower using the X-axis as the main line and then rotate the tower wires using the GM command. Let's rotate the array so that the main lobe has a heading of 315 degrees on the compass-rose azimuth scale. We need to inform the GM command to rotate the structure +45 degrees to effect the counterclockwise rotation, as shown in the following model.

+ 
+CM 2 near-resonant monopoles, perfect ground
+CM NAB substitute single-wire monopole
+CM end-fire two-tower array
+CM 90-degree feeding--1/4wl spacing
+CM 315-deg AZ heading via GM
+CE
+GW 1 41 122.946 0 0 122.946 0 234 0.555
+GW 2 41 -122.946 0 0 -122.946 0 234 0.555
+GM 0 0 0 0 45 0 0 0
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GW 30902 1 9902.0000 9902.0000 9902.0000 9902.0001 9902.0001 9902.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 5.3579 0
+EX 0 30902 1 0 0.0 5.3579
+NT 30901 1 1 1 0 0 0 1 0 0 0
+NT 30902 1 2 1 0 0 0 1 0 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 37 0000 0 0 1.00000 10.00000 1609.344
+EN
+
+

Fig. 10 shows the resulting pattern.

+
+ +
+

The data collection for both of our sample endfire arrays is the same.

+ 
+Two-Tower Endfire Array, Source at 90-Degree Phasing, 18" Face Triangular Single-Wire Monopole Model Data
+
+Tower  Impedance (Ohms)    Current (Apk)   Gain (dBi)   AGT     AGT-dB   F-S @ 1 mile
+1      50.74 + j16.91      5.3579 @ -90    8.25 max.    1.999   0.00     393.5 mV/m @ -90.7 deg
+2      18.93 - j19.90      5.3579 @ 0 deg
+
+

Obtaining the desired phase shift and power division with a single ultimate source is subject to many techniques that we shall leave to external calculations. However, it is possible to construct a fairly complex model with a combination of TL and NT entries to incorporate the desired technique into the model. However, for most purposes, obtaining the individual source impedance values and the source-segment current magnitudes and ratios allow these calculations to proceed most efficiently externally to the model.

+

The data collection shows the maximum values for gain and field-strength (the latter still in peak form and needing conversion to RMS). Since most installations will need values in many directions to correlate with field measurements, the modeler should attend to the RP1 tabular output. The sample that follows shows the values for the rotated example. Once more, remember that NEC output reports employ the phi or counterclockwise convention for listing azimuth angles. Therefore, the value applicable to a compass-rose heading of 315 degrees occurs between the phi entries for 40 and 50 degrees.

+ 
+**** Electric Field: Phi Pattern ****
+Z=0, Freq=1, File=fcc55.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+  Phi      Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+   0.00   3.8121E-001    -90.93   4.6724E-022   -153.51
+  10.00   3.8834E-001    -90.77   3.7881E-022     60.73
+  20.00   3.9181E-001    -90.66   2.7900E-022    147.41
+  30.00   3.9313E-001    -90.58   1.7082E-022     92.96
+  40.00   3.9347E-001    -90.54   5.7515E-023   -111.91
+  50.00   3.9347E-001    -90.54   5.7515E-023     68.09
+  60.00   3.9313E-001    -90.58   1.7082E-022    -87.04
+  70.00   3.9181E-001    -90.66   2.7900E-022    -32.59
+  80.00   3.8834E-001    -90.77   3.7881E-022   -119.27
+  90.00   3.8121E-001    -90.93   4.6724E-022     26.49
+ 100.00   3.6887E-001    -91.12   5.4160E-022     62.13
+ 110.00   3.5005E-001    -91.35   5.9964E-022      8.46
+ 120.00   3.2409E-001    -91.64   6.3956E-022   -111.03
+ 130.00   2.9115E-001    -92.01   6.6011E-022     89.18
+ 140.00   2.5232E-001    -92.49   6.6063E-022    -84.18
+ 150.00   2.0949E-001    -93.14   6.4106E-022    116.03
+ 160.00   1.6509E-001    -94.10   6.0193E-022     -3.46
+ 170.00   1.2182E-001    -95.61   5.4442E-022    -57.13
+ 180.00   8.2234E-002    -98.30   4.7023E-022    -21.49
+ 190.00   4.8653E-002   -103.96   3.8163E-022    124.27
+ 200.00   2.3437E-002   -119.59   2.8130E-022     37.59
+ 210.00   1.1594E-002   -170.26   1.7232E-022     92.04
+ 220.00   1.3540E-002    146.90   5.8035E-023    -63.09
+ 230.00   1.3540E-002    146.90   5.8035E-023    116.91
+ 240.00   1.1594E-002   -170.26   1.7232E-022    -87.96
+ 250.00   2.3437E-002   -119.59   2.8130E-022   -142.41
+ 260.00   4.8653E-002   -103.96   3.8163E-022    -55.73
+ 270.00   8.2234E-002    -98.30   4.7023E-022    158.51
+ 280.00   1.2182E-001    -95.61   5.4442E-022    122.87
+ 290.00   1.6509E-001    -94.10   6.0193E-022    176.54
+ 300.00   2.0949E-001    -93.14   6.4106E-022    -63.97
+ 310.00   2.5232E-001    -92.49   6.6063E-022     95.82
+ 320.00   2.9115E-001    -92.01   6.6011E-022    -90.82
+ 330.00   3.2409E-001    -91.64   6.3956E-022     68.97
+ 340.00   3.5005E-001    -91.35   5.9964E-022   -171.54
+ 350.00   3.6887E-001    -91.12   5.4160E-022   -117.87
+ 360.00   3.8121E-001    -90.93   4.6724E-022   -153.51
+
+

Conclusion

+

The notes in this episode have focused on the modeling convention, methods, and cautions applicable to multi-tower installations. I have used very simple arrays in order to set the modeling aspects of the situation in bold relief. Far more complex arrays are possible--and with them come far more complex models.

+

Some implementations of NEC are set up to ease the process of modeling arrays. For example, EZNEC provides RMS input and output values of voltages and currents. As well, the use of current sources is completely hidden, allowing the user simply to set in place the desired source values for current magnitude and phase. Our use of a more generic form of NEC has had the goal of showing some of what may go on "behind the scenes" in such interfaces.

+

A five-episode run of notes on a single topic--however broad--might seem to answer most of the beginning level questions one might have about tower modeling. Unfortunately, there is at least one major category of question left over at the interface between AM BC tower modeling and tower modeling in general.

+

Go to Main Index

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+

AM BC Modeling with NEC
+ 6. Grounds

+
+
+

L. B. Cebik, W4RNL

+
We have essentially completed our journey through modeling broadcast towers with respect to the basic dimensions of modeling them. In many of the later episodes, we used NAB-recommended single-wire substitutes for full tower structures to maintain the clarity of the modeling suggestions in question. Of course, one may choose to model a full structure or a multi-leg alternative to the single-wire monopole. These notes only represent the barest of starts along the AM BC tower modeling task using NEC. +

Nevertheless, as we look back over our work, we may harbor questions based on one facet of the modeling work: the use of a perfect ground for all models. Actual AM BC antennas use extensive radial fields, normally with each of 120 radials about 1/4 wavelength long at the assigned frequency. (Many actual fields include intervening shorter radials, but we shall not work with them here.) The radials are buried within the earth's surface in soils of highly variable quality as we move from one site to another. Hence, some folks may question the ability of a perfect ground to replicate accurately the conditions. In one sense, the questions are otiose, since standard practice is to refer such towers to perfect ground. However, there remain for some a few nagging questions about correlating site measured values of feedpoint current magnitude and phase and field-strength measures as well to modeled values using perfect ground.

+

NEC-4 allows us to explore this questions to a limited degree. Like NEC-2, it uses the Sommerfeld-Norton (SN) ground calculating system, which many refer to as the "high accuracy" ground compared to the reflection coefficient approximation (RCA) system. To use the SN ground calculation system accurately requires that we create a buried radial field of actual wires (GW entries), a task only available in NEC-4. As we saw in an early episode, we may assign a radial field to the RCA ground calculating system, but that system does not create actual wires. Instead, it adjusts the ground losses in the ground calculations. If we add enough radials to the specification, the RCA ground calculating system will return source impedance values that are identical to those we obtain with a perfect ground. An open questions here is what values of source impedance we might obtain with true buried radials. Allied to this question is whether we can expect differences in either the far-field gain or the field-strength between models using the RCA system and models using the SN system with buried radials.

+

Ground and Buried Radial Models

+

All NEC modeling systems share some common traits. First, we specify ground quality in terms of two basic properties: conductivity (in S/m) and relative permittivity (no unit). From these entries, NEC calculates a complex permittivity value used in ground calculations. Conductivity values--as measured or taken from tables--generally range from 0.001 S/m up to about 0.05 S/m for land locations. One accepted value for salt water's conductivity is 5.0 S/m. Permittivity usually tracks conductivity in the sense that soils with high conductivity tend to have high values of permittivity. The range of permittivity values ranges roughly from 3 to 25 for land locations. Water locations may show values as high as 80. The direct parallel between conductivity and permittivity increases is not universal, and there are odd locations with respect to the general progression.

+

For our sampling purposes, we may resort to 3 values taken from very old (1939) tables.

+ 
+Sample Ground Qualities
+Label        Conductivity (S/m)     Permittivity
+Very Good     0.0303                 20
+Average       0.005                  13
+Very Poor     0.001                   5
+
+

For many kinds of modeling studies, very good soil yields data results about as distant from those emerging from average soil as very poor soil data depart from average soil values, although the directions are opposite.

+

NEC, however, regardless of the ground calculating system selected (except for perfect ground) has a limitation suggested by Fig. 1. The ground medium is homogenous and unlimited below the Z=0 level. As we increase the operating frequency of an antenna or as we make use of horizontal antennas, this feature becomes insignificant. However, using a relatively low frequency (1 MHz in all examples) and vertical monopoles, the NEC ground medium is subject to some degree of error based on two facts. First, real soils tend to be stratified, as suggested on the right in Fig. 1. Second, the lower the operating frequency, the deeper will be the penetration of RF energy into the ground. With a radial system, the penetration in the immediate vicinity of the antenna is limited, presumably controlled by the extensive radial field. However, in the region beyond the radial field, outside the control of antenna site builders, stratified soil may have an affect on the far field of an antenna that even SN models cannot fully calculate.

+
+ +
+

Within this limitation, we may still look at models using buried radials for the general purpose of comparing them with other kind of models. For this enterprise, we shall use 120 radials, each about 1/4 wavelength long at 1 MHz (245'), as shown in Fig. 2. We shall use a wire diameter of about 0.1", roughly corresponding to AWG #10 wire. Since our dimensions are in feet, we shall round the radius to 0.004'.

+
+ +
+

If we assign each radial 10 segments, we shall end up with 1200 segments in the radial field alone. (The 10-segment per radial assignment is not critical in this application, since the radials will be symmetrically arranged around the monopole that extends through the surface to make contact with the ultimate junction. As well, as we change the soil quality and hence the complex permittivity generated by NEC, the program will change the length of each segment in the current calculations based upon calculated affects of a medium that is not a vacuum or dry air.) We shall also wish to use the same set of 3 radial fields, each with a different soil quality, one more than one antenna. Under these conditions, we may wish to simplify the modeling by using Numerical Greens Files. For 1200 segments a Green's file may be exceedingly large. However, if we confine ourselves to entering only the radials in the Green's file models, we may shorten both calculating time and file size by the use of rotational symmetry. The GR command permits us to specify a single radial and to replicate it rotationally as many times as necessary while invoking symmetry. The resulting file for a 120-radial field in average soil appears in the following lines.

+ 
+CM 120 radials, average ground
+CE
+GW 1 10 0 0 -1.5 245 0 -1.5 .004
+GR 1 120
+GS 1 0 0
+GE -1 -1 0
+FR 0 1 0 0 1 1
+GN 2 0 0 0 13 .005
+LD 5 0 0 0 5.8E7 1
+WG ave120r5.wgf
+
The WG command writes the results of initial calculations to a file. Different implementations of NEC may allow only some file-name extensions. The model itself must contain the features shown in the sample. The GW entry lists one radial although the geometry to be replicated may be more complex. The GR command produces a total of 120 versions of the radial with equal angular spacing between them. The GR command will always produce the wires and segments specified. However, the model run will not invoke symmetry if the GR command is followed by a succeeding geometry command, such as another wire (GW). The GS command uses NEC-4 shorthand for converting feet to meters, while the GE command is set up for buried wires. +

In addition to the geometry elements, the Green's file model must also contain the overall specifications for the frequency and the ground quality. In these files, we must specify a single frequency. With respect to ground (GN), the only difference between this model and its counterparts for very good and very poor soils are the values for conductivity and relative permittivity. I have added an LD 5 command to construct the radials from copper wire. Any LD command within the model will apply only to the wires in the structure shown. It will not apply to wires that we later add to complete the modeling task. Finally, the WG command adds the file name for storing the results that we shall later call upon. The file name must begin with an alphabetic character, and a number at the start of the file name will generally produce an error message.

+

We shall produce three files, one for each type of ground. Each requires about 6 second to run and produces a file that is less than 600KB long. Unlike the NEC output file, the Green's file is not itself meaningfully readable by a user. Notable in these files is the depth of the buried radials: 1.5'. We shall discuss this aspect of the modeling as we complete our buried radial system monopole modeling work.

+

Completing the Model

+

The monopole that we use for these calculations is simplest and most reliable if a single-wire is brought to ground and then extended to meet the junction of the radials. To achieve this goal, we need to write a simple new model that first calls up the Green's file and then adds further model refinements, such as a source (EX) and output requests (RP). The following lines sample the model for a near resonant NAB-recommended single-wire monopole substituting for a triangular tower with an 18" (1.5') face.

+ 
+CM near-resonant monopole, perfect ground
+CM NAB substitute single-wire monopole
+CM buried 120 radials
+CE
+GF 0 ave120r5.wgf
+GW 301 41 0 0 0 0 0 234 0.555
+GW 302 1 0 0 -1.5 0 0 0 .555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE -1 0 0
+EX 0 30901 1 0 0.0 7.3971
+NT 30901 1 301 1 0 0 0 1 0 0
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Following the comment lines, the first geometry command (GF) calls the Green's file. Then we add our monopole, at least the portion that is above ground. NEC-4 requires that an element that passes through Z=0 must do so at either a wire junction or a segment junction. In most cases, we may best avoid errors later on by making Z=0 a position for a wire junction. Therefore, we place a second wire that runs from the junction with the radials to the ground end of the monopole. We assign the wires arbitrarily large tag numbers, large enough to assure us that the tag numbers of the radials do not overrun the monopole tag numbers. (NEC will not normally mind the overlap, but reading the NEC output file becomes much more difficult.)

+

Although in reality, we might make such connections with one or more wires that are considerably thinner than the tower legs or the single-wire substitute for the tower, NEC shows various degrees of inaccuracy when joining wires of different diameters. Therefore, the wire radius for the extension should be the same as for the aboveground portion of the assembly.

+
+ +
+

How long we should make this wire and therefore how deeply the model should bury the wires presents us with a bit of a problem. As shown in Fig. 3, the new model view shows only the new wires of the extended monopole. Since we cannot bring the wires together and replicate the dual medium in the AGT test, it cannot help us to determine the model adequacy. However, if we recall some basic NEC guidelines, we can perform a substitute test. The radius of the monopole and its extension is 0.555'. As the segment length (here the extension-wire length) approaches a ratio of 2:1 or less, the results of NEC calculations become less certain. The goal then becomes arriving at a balance between the ideal segment length (equal to the segments in the upper part of the monopole) and the shortest segment length that will not yield readily detectable drifts in the output reports.

+

To test the situation, I created radial fields at depths of 1' and 1.5'. Next I created a series of 234' monopole, beginning with a radius of 0.5" (0.04') and gradually increasing the radius to 4.5" (0.375'). With the radials at 1' below ground, the trend in the progression of impedance reports reversed direction in the final step between 0.375' and 0.555'. However, by increasing the depth of the radials (and the monopole extension) to 1.5', I obtained a normal progression of impedance values. Since the effects of different radial depths with the thinnest monopoles in the series were minimal, I chose the 1.5' radial depth for this exercise.

+

The model that calls the Green's file contains a set of control commands that do not replicate those of the Green's file model. Hence, we find no ground or frequency specification. Had we added an LD command for the monopole, it would appear in this file and apply only to the wires shown in this model. It would not apply to the wires in the Green's file. Of course, our completion model contains source information, including the added wire and network to invoke a current source and the adjustment to the current level to effect a power of 1 kW. Finally, we find output requests for an elevation/theta pattern and for a field-strength report at 1 mile at ground level.

+

We are now ready to look at the results of our models and compare them to models over perfect ground and over the RCA ground.

+

Near-Resonant and Long Monopoles over Various Grounds

+

The model format for all of the near-resonant monopoles over buried radials is identical except for the file name of the Green's file. The root or reference model over perfect ground uses the same monopole, but a different and simpler format.

+ 
+CM near-resonant monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 234 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 7.4897
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
+

Over the RCA ground, the NEC-4 model looks very much like the model over perfect ground, except for the entries in the GN command line. (Note: a NEC-2 model--as described in an earlier episode--will require an RP4 entry for the far-field pattern.) The entry not only specifies the ground quality, but as well the radial system (expressed in meters). Hence, we have 120 radials with a wire radius of 0.00127 m (which is the metric equivalent to the 0.1" diameter wires used with the SN system) and 75 meters (246') long each. We may use fatter radials in the RCA model since we do not construct them of individual wires and therefore need not be concerned about wire interpenetrations at angular junctions.

+ 
+CM resonant monopole, RCA ave ground
+CM NEC-4 procedures
+CE
+GW 1 41 0 0 234 0 0 0 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1
+GN 0 120 0 0 13.0000 0.0050 75 .00127
+EX 0 30901 1 0 0.0 7.4897
+NT 30901 1 1 41 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+EN
+
We may tabulate the results of the modeling as follows. + 
+Model Reports for a Near Resonant (234') 1-MHz Monopole with Varying Ground Situations
+System    Ground Quality  Impedance Ohms)   Current A(pk)   Max. Gain (dBi) TO Angle (Deg)  F-S @ 1 mile
+Perfect   Perfect         35.65 - j 1.29    7.4897          5.14            0               275.1 mV/m @ -45.6 deg
+SN        Very Good       37.29 + j 2.30    7.3235          3.37            16              263.3        -64.1
+          Average         36.55 + j 2.10    7.3971          2.00            21              234.8        -85.8
+          Very Poor       33.09 + j 1.82    7.7742          0.16            26              153.6        -121.3
+RCA       Very Good       35.65 - j 1.29    7.4897          3.89            15              268.8        115.5
+          Average         35.65 - j 1.29    7.4897          3.22            21              238.4        92.2
+          Very Poor       35.65 - j 1.29    7.4897          2.62            27              150.1        52.8
+
+

The table is revelatory in several respects. Over the SN ground, the impedance of the antenna system decreases as the soil quality decreases. For some people, this result is counter-intuitive, especially if we over-stress the idea that ground losses increase with a decrease in soil quality. To a large but incomplete degree, the size of the radial system overcomes this fact. However, the radials do not counteract all ground effects. As we lower the conductivity toward zero and decrease the relative permittivity toward 1, the ground increasingly acts like free space. In free space, a monopole with ground radials having the same dimensions as the system in the models will show lower feedpoint impedance values than we obtain over perfect ground using the image assumption that underlies the calculations. Even over very poor ground, the lower impedance appears. Of course, the radial system does not counteract the RF losses in the region beyond the radials that is responsible for the bulk of the reflected energy that combines with the incident energy.

+
+ +
+

Fig. 4 overlays the elevation patterns for the three ground qualities for each of the ground calculating systems. We may correlate the patterns to the maximum gain values in the table. The RCA system overestimates the maximum far-field gain with increasing calculational optimism as the ground quality decreases. Moreover, the figure shows that the RCA ground calculating system result in stronger high-angle radiation (in the 60-degree elevation angle region) than the SN system. In fact, the patterns for the 3 ground qualities in the RCA system are identical for elevation angles of 40 degrees or more. The SN system shows weaker radiation at every angle (except perhaps at 90 degrees elevation) as we decrease the ground quality.

+

For most AM BC applications, we are less interested in the higher angle radiation, except perhaps when calculating the consequences for skip in periods of darkness. More interesting are the field-strength reports. Here we find only small differences (3 to 5 mV/m) as we move from one ground system to the other.

+

To confirm that the results of the initial modeling sequence are not anomalous, I repeated the exercise using the 273' or 90-degree monopole. Since all of the models are identical to those already shown, the model over perfect ground may serve as a stand-in for the entire collection. The only differences will appear in the GW line specifying the monopole and in the EX line specifying the current necessary for a 1-kW power level. These models should show sufficient off-resonance qualities to detect anomalies, if present.

+ 
+CM 273' monopole, perfect ground
+CM NAB substitute single-wire monopole
+CE
+GW 1 41 0 0 0 0 0 273 0.555
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 .3048
+GE 1 0 0
+GN 1
+EX 0 30901 1 0 0.0 5.7606
+NT 30901 1 1 1 0 0 0 1 0 0
+FR 0 1 0 0 1 1
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+RP 1 1 1 0000 0 0 1.00000 1.00000 1609.344
+RP 1 1 1 0000 0 0 1.00000 1.00000 3218.688
+EN
+
+

The result can be tabulated in parallel to those shown for the shorter monopole.

+ 
+Model Reports for a 273' 1-MHz Monopole with Varying Ground Situations
+System    Ground Quality  Impedance Ohms)   Current A(pk)   Max. Gain (dBi) TO Angle (Deg)  F-S @ 1 mile
+Perfect   Perfect         60.27 + j84.91    5.7606          5.30            0               280.0 mV/m @ -47.7 deg
+SN        Very Good       62.30 + j88.31    5.6657          3.49            15              268.7        -66.2
+          Average         60.98 + j87.85    5.7268          2.04            20              239.1        -87.8
+          Very Poor       55.10 + j87.63    6.0246          0.13            25              156.2        -122.8
+RCA       Very Good       60.27 + j84.91    5.7606          3.89            16              272.8        113.4
+          Average         60.27 + j84.91    5.7606          3.01            22              241.2        90.4
+          Very Poor       60.27 + j84.91    5.7606          2.22            28              151.3        52.0
+
+
+ +
+

Fig. 5 shows no aberrations relative to the patterns in Fig. 4. However, the table has some oddities relative to the maximum far field strength of the signals as modeled over the different ground calculating systems. The SN ground gives the taller monopole slightly more gain over very good ground than its 234' counterpart. However, the gain increase grows smaller over decreasing ground quality so that the gain over very poor ground is a tiny amount less for the 273' tower. We find a similar trend, but with quite different numbers, over the RCA ground. With very good soil, the two monopoles report the same far-field gain. For all lesser quality soils, the taller tower actually reports a smaller value for maximum gain. Whatever the values for maximum far-field gain, the field-strength reports for any level of soil quality show a much smaller difference between systems--about 2-5 mV/m. However, in both tables, we find very different phase-angle reports between the two systems, with the SN reports more in accord with the value for perfect ground.

+

The source impedance reports replicate the results for the near-resonant monopole very closely. With 120 radials, the RCA system returns the same impedance as the model over perfect ground. The SN system shows a resistive component that decreases as the ground quality decreases. By the time we reach very poor ground, the source resistance is lower than the value reported for perfect ground.

+

The consistency of the source impedance reports between the two tables for system using monopoles of different length only confirms that the reports are true to the system of modeling employed.

+

Conclusion

+

With this episode, we can bring the series of notes on modeling AM BC monopoles to a close. Our focus has been on the modeling that goes into such systems, not on theory and practice within the design and engineering of AM BC towers. Hence, all of the models are very much simplified to allow us to see certain aspects of the process more clearly.

+

Even in this final section, it is not possible to suggest that one or another modeling system is superior. Such a conclusion is only possible if we bring to such a discussion the task-specific specifications in which modeling plays a role, but not the only role.

+

Nevertheless, the various episodes have shown that we may derive from NEC models the entire data set that AM BC modelers have traditionally derived from MININEC software--and some other things as well.

+

Go to Main Index

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+

NEC Implementations
+ Cores, Limitations, and Work-Arounds

+
+
+

L. B. Cebik, W4RNL

+
+ On this series of columns, we have examined the NEC-2 and NEC-4 programs, with some attention to MININEC, in order to master to some degree the geometry and control commands and to assure that our models are as adequate to various modeling tasks as we can make them. We have not used various programs to recommend the particular implementations of NEC, but only to illustrate how we may reach or approximate (in some cases) a point where the core will calculate usable results. However, we have not undertaken in any systematic way an account of some of the differences among implementations of the cores. We shall turn our attention to this subject from time to time. Our goal is not to review programs. Nor is it to make recommendations. Instead, the aim is to note the various ways by which we may achieve the same goals in modeling using different means. +

When working with implementations of NEC and MININEC, all notes carry a time-stamp. They are--assuming that I make no major blunders along the way--limited to program capabilities at the time of writing, which is always well in advance of publication. Therefore, if I assign a task method or a limitation to a program, the program may have changed by the time you read these notes. Hence, you have the final responsibility of investigating implementations of NEC or MININEC to determine current techniques and limitations before committing to one of them.

+

1. Core Concerns

+

Our first step is to note that both available versions of NEC (-2 and -4) and all versions of MININEC begin by assuming that the antenna is composed of thin round wires. Both use the Method of Moments to calculate the mutual impedance among the segments in a wire and in all of the wires that make up the antenna's geometry. From that point, the programs calculate the current in each segment relative to an assigned source, and from there the programs go on to calculate a wide variety of useful antenna performance data. The most commonly used data is the far-field radiation pattern, although some NEC entry-level programs also allow calculation of near-field, ground wave, and other data, depending upon the implementation.

+

NEC-2 is in the public domain. Therefore, programmers may modify the core as necessary to create a unified software package. For example, EZNEC, when using the NEC-2 core, does not transfer data to the core using the standard input file, illustrated in Fig. 1. In contrast, NEC-Win Plus creates a special input file in the standard format so that the core remains a separable module.

+
+ +
+

Licensing agreements with LLNL/UCal, which holds proprietary rights on NEC-4, require programmers to use the core as given or only with authorized correctives that emerge from time to time. There are, at present, only two programming sources for NEC-4 programs: EZNEC (Pro/4) and Nittany-Scientific (GNEC). Both create standard ASCII format input files for core runs. Since the use of NEC-4 requires a separate license from LLNL/UCal--in addition to any costs associated with commercial implementations--the licensee may use the supplied core with any other I/O system available and compatible. For example, both Multi-NEC and 4NEC2 permit (with greater or lesser difficulty) access to any NEC core using their input and output facilities. A good number of NEC-4 licensees have developed their own interface systems, either because it is a challenge or because there may be special individual or company needs.

+

NEC-4 from the 1990s is an advance over NEC-2. The 1980s core had some significant limitations, many centered on the current algorithm used. Two of those limitations prompted extensive further developments. NEC-2 could not handle buried wires, that is, wires placed with Z less than zero when using a real ground. As well, NEC-2 introduced significant errors in the performance calculations associated with antenna elements using a diameter taper schedule. The most common taper schedule is the gradual reduction in the wire (or tubing) diameter from the center of a dipole-type element to its tips. However, the limitation also applies to biconical elements constructed in the same manner. NEC-4 uses a more complex current algorithm that overcomes much--but not all--of the tapered element difficulty. It also permits the placement of wires below the surface of a ground medium, but with geometry rules for handling wires that pass through the surface.

+

The most accurate way to handle element taper schedules amounts to a program add-on by those who develop modeling software. The method involves the use of the Leeson correctives, which create uniform-diameter substitute elements equivalent to the tapered-diameter element. Programs perform calculations using the substitute elements, which have proven to be highly accurate for HF antenna design work when rightly used. One common modeler flaw involves allowing the segments in the substitute sections to have radically different lengths, especially in the high-current regions of the element. As well, the Leeson corrections are only applicable to linear elements without loads (except at the very center) within about +/-15% of self-resonance. (The substitute elements are also applicable to tapered diameter monopoles fed at the base with loads only at the base.) Fig. 2 illustrates a tapered element wire table and the substitute uniform-diameter element.

+
+ +
+

Both NEC-2 and NEC-4 originated as Fortran code for use on mainframe computers. As PCs developed faster speeds and much larger memory capacities, compiled Fortran that would run in the DOS/Windows environments became common and is at the heart of almost all present implementations of NEC. However, in the 1980s, those developments were yet to come. Rockway and Logan developed an alternative modeling program with reduced features that would run on mini-computers: MININEC. The current public domain version is 3.13, although without extensive modification, the program has many inadequacies when taken above the mid-HF region or into complex antenna geometries. The early MININEC resulted in a number of commercial DOS implementations, most notably EZNEC by W7EL and AO (MN) by K6STI. Although both programmers introduced some correctives to overcome MININEC limitations, the emergence of NEC-2 supplanted those efforts. Rockway and Logan re-developed the fundamental MININEC algorithms and have marketed various levels of Expert MININEC. Teri Software has extensively modified the calculation routines to produce perhaps the most accurate version of MININEC, and in the process added features only available previously in NEC, for example, the high accuracy Sommerfeld-Norton ground calculation system. There are freeware versions of MININEC available, such as MMANA. However attractive interface and auxiliary function provisions may make the program, the basic core accuracy remains the key to acceptability. For work that is to have widespread acceptance, only Antenna Model (AM) has overcome MININEC limitations so that, in regions where NEC-4 has known accuracy, benchmark models have matched the performance of the current standard in round-wire antenna modeling.

+

Both NEC-4 and AM's MININEC have limitations, and the use of the "other" core may be necessary for reasonable results. For example, MININEC cannot handle buried wires. Hence, for good results with buried radial fields of various sizes, NEC-4 remains necessary. On the other hand, NEC-4 tends to go astray with angular junctions of wires having different diameters, a common occurrence in many antennas using a folded geometry. MININEC does not suffer this limitation and may be necessary for these types of problems.

+

Unfortunately, I do not know of an implementation of the modeling cores that allows one to shift from one type of core (NEC or MININEC) to the other within the same program. One exception exists, although it is an Excel application: Multi-NEC by AC6LA. We might classify Multi-NEC as a spreadsheet shell containing both input and output facilities, but without a core of its own (other than a public-domain NEC-2 core). Rather, it will access certain cores that it recognizes and (for commercial implementations) for which it has prior agreements. Currently, Multi-NEC can access stand-alone NEC cores as well as the cores within NEC-Win/GNEC (Nittany-Scientific), EZNEC, 4NEC2, and Antenna Model. For crosschecking the results of a model in NEC and MININEC, Multi-NEC may be the easiest route.

+

2. File Keeping and Swapping

+

The alternative to using Multi-NEC to move among cores is to swap files from one program to another. This is not always as easy a process as it may seem on the surface, since many implementations of NEC and MININEC use unique formats or proprietary file coding to meet the needs of the individual implementation.

+

1. Formats: The model file may be stored as an ASCII file or in a proprietary format created by the programmer. In general, the use of an ASCII file becomes evident if you can open the file using Notepad. The file shown in Fig. 1 is perhaps the most rudimentary and universal type of file, and the file name would normally be followed by the extension .NEC. For reasons that will become clear as we go along, it is readable as given by almost any of the programs that we have mentioned.

+

EZNEC, NEC-Win Plus, and Antenna Model use non-ASCII file formats. There are many reasons for using such formats. For example, NEC-Win Plus uses a spreadsheet format that is capable of including equations in spreadsheet form. However, the program can also import and save files in .NEC format (of the most basic form). That does not mean, however, that the program can handle any .NEC model, since it recognizes only the commands that it uses in normal operation.

+

Not all ASCII-readable model files are readable by other programs as model input files. For example, as suggested by the sample in Fig. 3, NEC2GO files are in ASCII format, but under the extension .ANT. The format of the file derives from but is not limited to the MININEC program MN (part of AO) by K6STI, and the later NEC-Wires program. The format allows the modeler to include in the model file a collection of symbolic definitions and equations, which then enter the wire lines as symbols rather than numbers.

+
+ +
+

Compatibility: NEC2GO illustrates another limitation in swapping files. In its FAQ, the programmer notes that this version of NEC-2 is a flexible program for certain modeling purposes, but it does not offer full support of all NEC-2 input and output possibilities.

+
+

Nec2Go does not have provision for the following NEC2 Geometry/Control statements: GA - Wire Arc
+ GF - Read Greens Function file
+ GH - Helix/Spiral specification
+ GR - Generate Cylinder
+ GX - Reflection in coordinate planes
+ SP - Surface Patch
+ SM - Multiple Surface Patch
+ CP - Maximum Coupling calculation
+ NE/NH - Near Fields
+ PQ - Print control for charge on wires
+ WG - Write Greens Function

+
+

Other entry-level programs are similarly but not identically limited. For example, both EZNEC and NEC-Win Plus construct all model geometries using only the GW command (with an implicit GE command separating the geometry from the control commands that follow). To replicate the functions of some NEC commands, programs use different techniques. EZNEC employs a collection of structural facilities to develop various shapes. In contrast, NEC-Win Plus offers a spreadsheet with full variable and equation facilities by which one can create similar structures. In NEC2GO, the symbols and equations become part of the ASCII model file, while NEC-Win Plus uses a non-ASCII file format. When saving a file in .NEC form, NEC-Win Plus strips the file of the variables and equations and uses only the current set of numerical values derived from those variables and equations.

+

The control commands are equally limited in many entry-level programs. Virtually all entry-level NEC-2 programs allow access only to the standard voltage source in NEC. Programmers have developed a means of using a remote source wire and a network command--invisible to the user--to provide a virtual current source. (In contrast, MININEC, as in Antenna Model, employs a true current source.) In either type of system, the user does not have access to options for plane-wave excitation and some of the current-printing facilities that are useful in connection with this command. In contrast, full versions of NEC programs allow access to the entire command structure that the core can accept. In many cases, the use of these commands requires the modeler to understand the command entry requirements. One typical error that can infect even the work of an experienced modeler is to construct a wire geometry in a unit of measure other than meters and then forget that all control commands calling for dimensions must have them only in terms of meters.

+

The output calculations are similarly limited in entry-level programs to the RP0 or far-field radiation patterns. In some cases, there is also no provision for the modeler to vary XNDA. However, such programs may have special functions to provide an Average Gain Test--which involves several set-up steps to be accurate. One of those steps is a change in the so-called "normal" XNDA setting. Programs may overcome some of the limitations by post-core-run calculations. One feature that is growing in popularity is the calculation of left-hand and right-hand circular polarization components.

+

Only some entry-level programs allow access to the near-field commands, and then usually only in tabular form. Although the development of polar 2-D and 3-D plots has reached a high level, developing graphical displays for near-field calculation results has so far defied most NEC programs.

+

Not all model files that end with the extension .NEC and that are ASCII-readable are fully compatible with each other. For example, the 4NEC2 file shown in Fig. 4 derives from a set of algorithms from which one may develop models of a 3-element Yagi having certain properties over a very wide range of frequencies and element diameters. The original model used the spreadsheet function within NEC-Win Plus and has subsequently been transferred to an independent spreadsheet. Arie Voors, the developer of 4NEC2 has converted the required calculations to the file format that applies to his program, resulting in a model file with much more space devoted to the calculations than to the actual model structure.

+
+ +
+

In 4NEC2, symbolic expressions have a special code: SY. Otherwise, the progression of the NEC file follows the usual form for a .NEC file. Compare this file with the one in Fig. 3. Although both files do similar work, they are not fully compatible with each other.

+

NEC-4: Compatibility of files does not solely concern the storage format. It also involves cores. For example, NEC-4 has introduced new commands relative to NEC-2. For example, IS and UM do not exist in NEC-2. It has also eliminated others, such as EK. More easily overlooked in attempts to swap files is the fact that numerous NEC-4 commands differ in whole or part from their NEC-2 counterparts. The inter-relationships among the RP (radiation pattern), GE (geometry end), and the ground commands differ for the two programs. The GH (helix formation) command is wholly different between the two cores. As well, a few commands have added new floating decimal entries into which the NEC-4 user can place significant values. Therefore, not all NEC-2 .NEC files will run correctly with a NEC-4 core, and NEC-4 files may run incorrectly or not at all with NEC-2. There are enough perfectly compatible files relative to the two cores that it is easy to overlook the critical differences.

+

File Swapping: Setting aside the cautions that we have covered, the most-used way to move files from one program to another is by using the basic numerical entry .NEC file as the medium. Advanced versions of EZNEC can input and output files in .NEC format. In general, it informs the user when a command is not translatable, and as development time passes, fewer commands become unacceptable. NEC-Win Plus has always had the ability to input and output files in .NEC format, although always within the boundaries of its entry-level command structure. It will abort conversions that involve unrecognized commands. NEC2GO has added .NEC file compatibility.

+

Even the MININEC program Antenna Model will now read and convert .NEC files to its format. The process is not just a matter of file-format conversion, but also involves modifying the file to fit the MININEC requirements. Whereas NEC places all sources and loads within segments of wires, MININEC places sources and loads on pulses, which are located at the junction of wire segments. AM will move sources and loads to the nearest pulse. Since a centered feedpoint or source is such a common antenna feature, AM will also add a segment to the source wire to ensure that the NEC-centered source is also a MININEC-centered source position.

+

One of the most flexible vehicles for file-format swapping is Multi-NEC. Because this spreadsheet shell works so closely with the cores of existing programs, it also has the ability to accept files and to save files in a variety of formats. Besides the native Excel spreadsheet format (.WEG), the program handles files in EZNEC (.EZ), Antenna Model (.DEF), and standard (.NEC) formats. Within the limitations of recognized commands and numerical formats, one may use Multi-NEC as a means of transferring antenna geometries based on the wires (GW) commands from almost any program to almost any other--at least among the group that we have been considering. (Of course, Multi-NEC has numerous other features that recommend it, but those are for future episodes.)

+

Conclusion

+

Our initial entry into looking at divergent implementations of NEC and MININEC has focused primarily on differences among programs and cores. Nothing here represents a review of the implementations and even less a grading or ranking of the various programs available for round-wire antenna modeling. The focus on differences has aimed to alert the modeler who may move among programs to potential pitfalls and frustrations in order to avoid them to the degree possible. Various implementations have relatively exclusive features and auxiliary functions that we may wish to use from time to time. Understanding how the program facilities differ can ease the process--and even tell us whether we can do what we want to do.

+

In the end, the modeler must take final responsibility for the compatibility of his models with the program he wishes to apply to them. Knowing the differences among the cores and what is available and excluded by various implementations can change that task from guesswork into informed decision-making.

+

Also see the Antenna Modeling Programs page for more information.

+

Go to Main Index

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+

Types of Substitute Models

+
+
+

L. B. Cebik, W4RNL

+

+ We cannot model every possible antenna structure in NEC. Some structures are best suited for other types of software, for example, strip elements with a substrate on one side that has a definite dielectric constant. In fact, strip elements in free space may alone prove problematical unless we first perform some external equivalency tests to determine what size round wire best approximates the performance of a strip element. Very often, creating a series of simple dipoles at a design frequency will suffice, although there may be more critical situations in which we find a difference in the mutual coupling between strips relative to round wires. +

In some cases, the limitations of NEC-2 and NEC-4 may limit our modeling abilities. NEC-2 provides various degrees of error in the output report for linear elements with stepped diameters. NEC-4 largely, but not completely, corrects this error. For small diameter changes between steps, NEC-4 is highly accurate, but becomes less accurate as the diameter steps grow larger, especially in high-current regions of a structure. Both cores tend to show errors with changes in wire diameter at angular junctions. Many software packages have modules to create substitute elements using the Leeson corrections to form uniform-diameter elements out of stepped-diameter elements. However, an angular junction will normally prevent the functioning of these modules or facilities. In addition, NEC cannot directly model coaxial wire structures. Hence, we cannot capture the physical aspects of an antenna element composed of coaxially arranged wires.

+

We have not listed all of the limitations of the NEC cores, but we have enough to give us sufficient reason to develop substitute models where NEC may not directly go. In a broad way, we may divide the types of substitute models into three groups.

+
+

Type 1. Substituting one geometry for another

+

Type 2. Substituting the electrical equivalent for the original structure where we may check our work with the original structure

+

Type 3. Substituting the electrical equivalent for the original structure where we may not check our work by modeling the full structure

+
+

Each type of substitute has different consequences for our trust in the models and different cautions for creating the substitute model. Therefore, let's examine a sample of each type to see what we might learn.

+

Substituting on Geometry for Another

+

Perhaps the most common form of geometry substitution consists of replacing a highly complex multi-legged tower with a uniform-diameter round wire with the same height. As earlier episodes in the series established, the BC industry has developed some very reliable guidelines for the substitution. Extensive cross checks between the substitutes and full models of multi-legged towers have yielded the following equivalencies.

+ 
+Recommended Substitute Single-Wire Dimensions for Multi-Face Towers
+Tower Type      Diameter                  Radius
+Triangular      D = 0.74 * Face Width     R = 0.37 * Face Width
+Square          D = 1.12 * Face Width     R = 0.56 * Face Width
+
+Note:  D and R are in the same units as the Face Width
+
+

Modelers also face another problem--especially when using NEC-2--even for round tower sections when the tower steps the diameters of the sections. Let's consider a 60' tall tower over perfect ground (for simplicity of modeling) at 3.5 MHz. The tower consists of 6 10' sections, each 1/2" smaller in diameter than the next lower one. Let's use 3.5" for the base section diameter and taper it to 1" for the top section. The total tower is still short to achieve resonance at 3.5 MHz, so we shall add two short section of 1" diameter material to form a T at the tower top. We shall select lengths of tubing that just bring the tower to resonance over the prescribed ground. We shall place the source on the lowest segment of the lowest tower section.

+

We cannot simply invoke the Leeson corrections for the tower in this case, since the presence of the T-top will normally block the calculations, since the corrections only apply to linear section under certain conditions. Therefore, we shall have to proceed in steps, as indicated in Fig. 1.

+
+ +
+

First, we remove the T-top tubes from the tower. Now we may perform the Leeson correction calculations on the tower sections alone. Once we have derived the correct length and diameter of a uniform-diameter element that is equivalent to the original tower, we can replace the T-top and proceed to the final output reports that we might need. Fig. 2 shows the process as it might proceed using EZNEC's version of the correctives.

+
+ +
+

Some less-practiced modelers might object to the lower section of the wire table, since it includes angular junctions between very different wire diameters. Therefore, let's tabulate the results and see what we obtain. Raw Gain indicates the direct NEC output report. AGT is the average gain test score, and converts to the gain adjustment value in the AGT-dB column. The adjusted gain appears in Adj Gain. The Feed Z column reports the source impedance.

+ 
+Results of substituting one geometry for another:  sample 60' tower with a T-top
+
+Model              Raw Gain dBi   AGT     AGT-dB     Adj Gain dBi     Feed Z (R +/- jX Ohms)
+NEC-2 Original     5.41           1.062   0.26       5.15             35.8 + 14.4
+NEC-2 Substitute   5.10           1.000   0.00       5.10             32.7 - j9.1
+Substitute with
+  7.7' T elements  5.11           1.000   0.00       5.11             34.2 + j0.9
+NEC-4 Original     5.22           1.018   0.08       5.14             35.4 - j0.3
+
+

The sample problem shows several things, not the least of which is that nothing critical is at stake except perhaps for the correct array gain value. We easily bring this into line by adjusting it with the AGT score. As well, the model shows that the symmetrically placed T-top elements at 90 degrees to the tower do not create serious errors. Unlike a single bend, as we might find in an inverted-L configuration, symmetrical elements (from two to many) result in virtually complete field cancellations from these low-current additions and do not adversely affect the AGT score or the general reliability of the results.

+

The original model, as shown by the last line of the table, emerged from a NEC-4 exercise using no correctives. This model is the origin of the 6.8' T elements. However, even NEC-4 shows a small but not insignificant departure from the ideal AGT score, enough to require an adjustment to its gain report. Therefore, it also has a degree of unreliability that--while smaller than for the uncorrected NEC-2 model--casts some doubt on the accuracy of the 6.8' length for the T-top elements. Increasing their length to 7.7' each brings the corrected model to resonance. In fact, the only difference between the 2 cores with respect to the substitute model is a minuscule difference in the report source impedance. NEC-4 reports 34.0 - j0.3 Ohms.

+

The sample also informs us that geometric substitutions are not perfect solutions if we plan to build the modeled structure. Assuming that we could simulate perfect ground and construct the tower as originally specified, the exercise would alert us to allow for considerable adjustment range in the lengths of the T-top elements if our goal happened to be to bring the antenna to resonance at 3.5 MHz. Of course, we may increase the level of modeling complexity by adding an appropriate real ground and bury some radials (in NEC-4) according to the number we plan to place at the tower base. Nevertheless, in all of its simplicity and final indefiniteness, the sample illustrates one of the typical processes of using a substitute geometry to arrive at a more adequate, if not quite perfect, model of the tapered tower and T-top situation.

+

Substituting the Electrical Equivalent for the Original Structure Where We May Check Our Work with the Original Structure

+

We may sometimes simplify the modeling process by replacing complex wire structures with simplified electronic equivalents. The process is especially applicable if we can first establish the equivalence between the substitution technique and an all-wire structure. Once confirmed, we may apply the technique with confidence in situations where we might not be able to accurately produce an all-wire model.

+

One such situation is the placements of 1/4 wavelength phasing stubs composed of parallel transmission line between successive 1/2 wavelength sections in a collinear array. The use of stubs keeps all sections of the array in phase. Because the stubs occur at high-impedance points along the wire, where voltage and current are changing very rapidly, the use of the NEC TL facility is not recommended. Therefore, modelers normally create all-wire models of the collinear array, as suggested by the top sketch in Fig. 3. We shall explain the lower half shortly.

+
+ +
+

The accuracy of such models often is restricted to cases in which the phase-line wires and the main element wires have the same diameter. For example, suppose that we wished the 2 wavelength array to use AWG #12 wire. We might construct the phase lines from the same wire, perhaps using a spacing of 6". Such an arrangements for a 15-meter (21.225-MHz) antenna might be quite practical. However, if we were to apply the same principles to a vertical array for the VHF or UHF range, it is more likely that the main vertical element and the phasing line would have very different diameters.

+

Vadim Demidov recently sent me a note outlining an alternative procedure that does not require the very high segmentation often required of all-wire (sometimes called "brute-force") models. As Vadim explained his reasoning, "After splitting TEM and common-mode phenomena in the stub I suggested considering it as an ideal auto-transformer with its midpoint "grounded" by means of a quarter wavelength wire. In this type of model, a stub is represented by its common-mode equivalent, which is a single wire (without need for too fine segmentation), while the phasing transformer is made by a short transmission line linking two segments joining it." The result is the model in the lower sketch in Fig. 4, where the EZNEC designator "T" marks the location of the ideal transformer, and the vertical wire is the common-mode element.

+

To confirm the exercise, I converted the collinear 21.225-MHz array into a Demidov model. Fig. 4 shows what is involved. However, understand that this is a proof-of-principle exercise. Therefore, both models use the same level of segmentation on all wires in order to minimize modeling differences. My goal was to discover to what degree we can trust the Demidov electrical substitute as an accurate representation of the all-wire model of presumed accuracy.

+
+ +
+

The upper section of the model shows the original all wire structure, with the 6" spacing between the wires of the phasing lines. The lines are each 132" long. The middle section shows the simplified wire table of the Demidov substitute. The junctions between the main element wire and the common-mode wires appear at points exactly half way between the feedpoint and the wire outer ends. The bottom section of the figure shows the two ideal transformers. Each uses as close to an infinitesimal length as one's modeling program will permit. Anything from 1e-5 wavelength and shorter will do. The idea is to use a length of transmission line that is so short that no significant impedance transformation can occur along its length. The 300-Ohm characteristic impedance is largely arbitrary, as values between 50 and 600 Ohms work as well.

+ 
+Comparative results using NEC-4, single precision, on all-wire and a Demidov models of a 2-wavlength 21,225-MHz collinear array
+
+Model                   Gain dBi    Beamwidth    Feed X (R +/- jX Ohms)   AGT
+All-wire (AWG #12)      11.97       26.2 deg     2189 + j29               1.001
+Demidov substitute      12.05       26.2 deg     2133 - j57               1.001
+
+

The differences between the results are insignificant, especially in view of the fact that the critical junctions and the source position occur at very high impedance positions on the model. In fact, the models shown in Fig. 4 contain an illusion. The length of the common-mode stub in the sample is just about 3" longer than the parallel line stubs in the original model. The illusion is that the common-mode stub accounts for the original stub length plus 1/2 the spacing between stubs. In fact, if we change cores and run the same substitute model in each, variously using single and double precision versions of each core, we obtain different values for the source impedance. They are all very high resistively and fall on the very steep curve that marks the ordinary reversal of reactance. Hence, the differences do not make a difference. In a real construction situation, a builder would need to adjust the length of the stub for best performance, taking into account the velocity factor of the actual phase line used. A quarter wavelength at 21.225 MHz is 139", the length of the Demidov common-mode line shown. However, with real wires having a small copper loss plus any dielectric shortening required, the physical length in most cases will be shorter, as it is in the original model.

+

The exercise does show an example of a substitute modeling technique that can be verified against an all-wire model. Once confirmed, we may use the technique in other comparable situations, even those where a direct comparison may not be feasible due to the large size of the all-wire model or the inability to handle velocity factors easily.

+

Substituting the Electrical Equivalent for the Original Structure Where We May Not Check Our Work by Modeling the Full Structure

+

There are some types of antennas that we cannot directly model within NEC (or MININEC). By directly model, I mean to replicate the physical structure within the confines of the NEC wire facilities. One type of structure that we cannot effectively model physically is a coaxial element, where the physical antenna may use a coaxial cable as part or all of the structure. In some cases, especially with fairly simple structures, we may be able to construct reasonable replicas using a series of wires surrounding a central wire. However, in most cases, we must resort to various techniques to ensure that the surrounding wires form a single relevantly continuous conductor around the central wire.

+

One antenna type that has recently seen renewed popularity is the coaxial collinear array, especially in vertical form for VHF and UHF use. The antenna has a very long history, but came into prominence in the 1950s as a potential VHF mobile array and also in radar uses due to the potential for developing a very narrow bi-directional beamwidth in a horizontal orientation. In the 21st century, the amateur search for an ideal omni-directional vertical array with very high gain for line-of-sight paths has brought on a surge of interest. With the interest has come an urge to model the antenna.

+
+ +
+

Fig. 5, on the left, shows the outline of the form most amateur envision using. A shorted stub 1/4 wavelength top section completes the array. At the base, the lowest section consists of a 1/4 wavelength section with 4 radials to form the feed portion. Between the top and bottom section, we may place any number of 1/2 wavelength sections, 1 through n. Although the sketch shows only 2, the number is limited only by the physical space available to hang the somewhat floppy coaxial array.

+

The sections of the array consist of length of coaxial-cable transmission line. Hence, each section, whether 1/2 wavelength or 1/4 wavelength is electrically only that long. The physical length is shorter, since we multiply each electrical length by the velocity factor of the line used. At each junction, we reverse the connections of the lines so that we end up with the equivalent of a 1/4 wavelength phasing stub without the need to install one. The required phase reversal (that actually produces a phase continuation) results from the line connection reversals at each junction.

+

On the right of Fig. 5 we find a modeling work-around that has been proposed to capture the antenna's performance. We separate the TEM or transmission line currents from the radiating currents by using two separate sets of connections between sections. The physically modeled wire that is solid in the sketch does the radiating. The dotted line represents transmission-line section connected from one end to the other end of each section wire. Note that in this idealized model, the top and bottom sections are bare wire without transmission lines. As well, the feedpoint comes between sections rather than at the base of the antenna. Hence, the model will not simulate directly the conception of a coaxial collinear antenna sketched on the left. But it may give us some idea of what happens if we successfully manage to phase successive 1/2 wavelength sections of wire (with the length adjusted for the line velocity factor of the proposed cable).

+
+ +
+

Fig. 6 shows the wire and transmission-line tables from an EZNEC version of the antenna. For convenience, the original modeler has used a separate 1-segment wire between sections on which to make the connections for both the source and the transmission lines. However, the total length of each section consisting of a longer wire and the connecting section is 0.41-wavelement, the result of multiply 1/2 by the line velocity factor of 0.82. The antenna begins 0.5 wavelength above a perfect ground in the ideal model.

+

The model provides us with two important outputs. As shown in Fig. 7, the current distribution is in phase and quite even along the length of the antenna. Hence, the array attenuates high angle radiation very well, as shown in the elevation pattern to the right. (Over average ground, the gain drops to 10.35 dBi, nearly 4-dB lower than over perfect ground. The elevation angle is about 4 degrees, equivalent to a single dipole at a height of over 3 wavelengths, but with a gain advantage to the coaxial collinear array.)

+
+ +
+

Unlike the horizontal phased array that we previously discussed, we cannot compare the idealized coaxial collinear model with a physical version of the same antenna. Therefore, we must approach the substitute model with all due caution. For example, the reported impedance at the source is 269 + j54 Ohms. However, the model is exceptionally sensitive to changes in the velocity factor. Decreasing the value by only 0.01 drops the reported impedance to just above 100 Ohms, with a sizable remnant reactance. Variations in the velocity factor of cables between lots may vary by several percent. What the model cannot tell us is whether the physical implementation of the antenna will be equally sensitive to variations in the line velocity factor. Moreover, the model does not reveal what effect a revised lower section might have, should one wish to replicate the more use practical of using a base section that is 1/4 wavelength long with a set of radials. We may model such an arrangement, but casual modeling in this direction shows reduced gain, stronger high-angle lobes, and a departure from the smooth current magnitude curves of the ideal model. I shall not show any models taken in this direction because they leave us with the same difficulties in correlating the model with a real antenna.

+

It is possible in the abstract to create models that seemingly are the electrical equivalents of physical structures that fall outside the boundaries of direct capture in a wire structure. Many of these models may prove useful in seeing some basic properties of antenna types. However, they remain limited in their reliability as models--despite nearly perfect AGT scores--due to the fact that we have no way to compare the models with physically accurate versions. In most cases, we also lack detailed information on performance from rated test ranges. In the present case, just such information would be necessary to determine if the sensitivity to small changes in the cable velocity factor is a physical feature of the coaxial collinear antenna or an artifact of the idealized model.

+

Conclusion

+

We have examined several different types of substitute models ranging from simple geometry substitutions to replacing physical structures with their electrical equivalents. The goal is not to discourage the use of substitute models. Rather, the aim has been to alert modelers to the level of caution necessary to bring to the models. Especially in cases where we cannot model the antenna as a physical set of wires, we should exert the highest levels of caution.

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Go to Main Index

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+

Antenna Matching with EZNEC Version 5
+ Part 1. Transformers and Shunt Loads

+
+
+

L. B. Cebik, W4RNL

+
+ One of the most popular implementations of NEC, EZNEC, introduced in May, 2007, a new version (5) with a number of facilities that may be new to NEC users. The features include the ability to place loads in parallel to wire segments, the creation of ideal transformers, and the implementation of L-networks that use values of inductance and capacitance (or resistance and reactance). From the last item, we can create more complex networks by joining L-networks in series. A number of other implementations have facilities for calculating some of these items, but normally as adjuncts to the program. In EZNEC, the facilities are part of the input interface and therefore enter the core calculations. Moreover, the facilities are frequency nimble. For example, entering a shunt capacitor or inductor across the source wire of a model will produce correct results over a wide frequency span as an integral part of the model. In contrast, resistance-reactance loads or of Y-parameter networks insert constant values that apply only to a given frequency. As a consequence of pre-calculations in the interface, EZNEC output facilities, such as the total model sweep or the more limited SWR sweep will provide (within limits) accurate data for each frequency within the sweep. +

Newer modelers may be unaccustomed to using such facilities. Therefore, in this episode and the next, we shall look at some examples of modeling with these facilities. This session will examine ideal transformers and shunt component loads. The next will look at the use of L-networks in 2-element configurations and in combination to produce 3-element networks.

+

A Simple Short Loaded Dipole and an Ideal Transformer

+

The process of using simple series-connected loads--the norm for the NEC cores--is familiar to virtually all modelers. Suppose that we begin with a center-fed dipole that is only 1/4 wavelength (and composed of AWG #12 copper wire for this sample). The feedpoint impedance will produce a free-space impedance of about 15 - j840 Ohms at a test frequency of 14.175 MHz. One way to bring the antenna to resonance is to insert a center-loading inductor. For this and ensuing examples, we shall assume a realistic Q of 200 for inductors. An inductor in series with the source, that is, a center-loading coil) will need about 9.44 uH. Fig. 1 shows the outline of the simple antenna, along with wire and load tables for the model. Because we wish the model to provide accurate performance reports across the entire amateur 20-meter band, we have used an RLC network rather than a frequency-specific R-X network.

+
+ +
+

The 2.8-Ohm series resistance in the center-loading coil reduces antenna gain (without changing the basic shape of the free-space pattern). Of course, the shorter wire length (relative to a full 1/2 wavelength dipole) also contributes to showing a gain of 0.88 dBi rather than the 2+ dBi value that we expect of dipoles. However, as shown in Table 1, the antenna is now self-resonant within about +/-j1 Ohm. For reference, the table shows the 15-Ohm SWR values at the lower and upper ends of the operating passband, along with the power efficiency of the antenna, taking into account both the material loss of the copper wire (very small) and the losses in the center inductor (sizable).

+
+ +
+

The remaining operational difficulty with the antenna is the very low impedance. One way to bring the impedance closer to the standard coaxial cable and amateur equipment value of 50 Ohms is to insert a transformer of some sort between the existing feedpoint (ostensibly at the center of a split loading coil) and the feedline. In practice, we might wind a conventional transformer (with either an air or a powdered iron core) or a transmission-line transformer. We can simulate an ideal transformer within the program by entering the line shown in Fig. 2.

+
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The view of the antenna shows two squares at the feedpoint. One represents the normal series inductive load. The second, with an X at its center, represents the ideal transformer that appears in parallel with the source (with the load inductor in series with both the source and the transformer port). The second port of the transformer would normally go to a remote wire to serve as the new source wire. Ordinarily, we construct such wires at very large distances from the main antenna geometry, and we make them very short and thin. The goal is to avoid interactions with the main antenna element (or elements) that might change the performance reports. In version 5 of EZNEC, the program can create these remote wires as virtual wires that need not show up in either the wire table or the view of the antenna. Instead, the view indicates the existence of the virtual wire, but does not shrink the size of the antenna element in an effort to show both the source wire and the main element.

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Note that the specification of the transformer requires that we attend to both the port connections and the values. For highest accuracy, the relative impedance values should be close to the desired values (and not be simply arbitrary values that yield the same ratio of impedances). For the sample, I have used the approximate raw element impedance (15 Ohms) at Port 1, which connects to the element wire segment that used to be the source. Port 2 lists the desired impedance value and connects to the virtual wire to which the model has also assigned the source. In the sample, I have used the desired values, even though the impedance ratio is 1 to 3.33. In practice, one might have used 60 Ohms for Port 2 in order to simulate a 1:4 transmission-line transformer.

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One reason for referring to the transformer input and output terminals as ports is that the program creates for the core a network (or its equivalent) that follows the general rules described in episode 127 of this series. The program therefore follows Y-parameter port designations, even though the input values are impedance values rather than admittance values. It does not matter which port serves as the source and which as the load so long as the modeler associates the correct impedance value with the correct connection to the model's geometry.

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We can see the ideality of the transformer in Fig. 3, a dual SWR sweep of the model before and after the addition of the transformer. One line is the 50-Ohm SWR at the source with the transformer in place; the other line is the 15-Ohm SWR before the addition of the transformer. One of the lines is invisible, because the other lines overlays it with graphical perfection. Similar data appears in the SWR values at the band edges in Table 1. The line tracking of the sweeps provides evidence that the transformer is (within limits) frequency nimble and yields correct results for what is essentially a lossless component. As constituted at present, there is no practical way to introduce losses into the transformer facility. Its existence in the model yields only a 0.1% change in the model's reported power efficiency.

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Matching a Resonant 3-Element Yagi

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Let's change examples and review a broader spectrum of matching possibilities. As shown in Fig. 4, we shall now use a 3-element Yagi for 28.5 MHz, with the elements consisting of 1/2"-diameter aluminum. The antenna is full size and the driver is set to resonance, about 25.7 Ohms. Once more, the environment is free space, and the E-plane pattern shows the generally high performance potential of the design.

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With the listed feedpoint impedance of the parasitic array, we generally have two major avenues of conveniently matching the source to a 50-Ohm feedline. One method is to create a 37-Ohm 1/4 wavelength section of transmission line from the present source segment to a remote model wire that becomes the new source segment. Although 35-Ohm coaxial cables do exist, the more common amateur practice is to place two length of 70-75-Ohm line in parallel to create the desired line. A second method is to employ a 1:2 impedance transformer between old source segment and the new one. Fig. 5 outlines the options in schematic form.

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We may implement either matching system within the modeling facilities of EZNEC, V5, using in one case the transmission-line facility and in the other case the ideal transformer facility. In both cases, the source segment moves to the new virtual wire that is part of each model. Fig. 6 shows a close-up view of the driver element to record the designations for the transformer (X) and the transmission line (T) in the views of the antenna.

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The transformer version of the model follows the exact pattern that we selected for the dipole, with changes in segment numbers and impedance values to reflect the new situation. The transmission-line entry may seem a bit odd to those who are only used to working with the lossless lines of NEC itself. The program has instituted a method of accounting for approximate transmission-line losses by allowing the user to enter a loss value and a frequency. Such values are readily available from charts, such as the one on page 24-19 of The ARRL Antenna Book. The values in the sample entry are for a version of RG-59, a 70-Ohm cable that most amateur might use in a parallel arrangement to effect the 1/4 wavelength line. The listed physical length divided by the listed velocity factor would yield an electrical quarter wavelength.

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Table 2 shows the reported results of our variations in the methods of matching the 25-Ohm element impedance to a coaxial feedline. The table begins with data for the model with no matching systems. The second section uses three versions of the 1/4 wavelength matching section composed of transmission line. If we do not assign losses to the transmission line, the gain and front-to-back values remain the same as in the pre-matched model. The following two entries note the loss values that we may glean from tables for RG-11 (a half-inch cable) and RG-59 (a thinner cable). Note that the matching line losses do make a difference to the reported gain value (without altering the front-to-back value). However, losses are below the level of being operationally detectable, and the SWR limiting values have not changed by any amount that we could detect in normal testing. Since the 1/4 wavelength transformer is also part of the linear run of feedline cable, the net loss is simply the difference between the matching section loss and an equivalent length of main feedline cable.

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The bottom of the table shows the results from inserting an ideal transformer into the model. As both the gain and the efficiency values show, the ideal transformer leaves the basic values virtually unchanged. A real transformer of conventional design might introduce perhaps 2-3% losses. Such losses would bring the efficiency down to the level of the 1/4 wavelength transmission-line transformation system, with gain values that are likely to reflect those values. However, our goal is not to weigh the merits of specific implementations of a matching system. Rather, the goal has been to show the modeling facilities involved in both methods of matching.

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Matching a Non-Resonant 3-Element Yagi

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To advance our progression through the matching options offered as frequency-nimble facilities in EZNEC, V5, let's make a small alteration in the 3-element 28.5-MHz Yagi composed on 1/2"-diameter aluminum elements. Element spacing will be unchanged, as will the lengths of the director and reflector. However, we shall shorten the driver so that it shows an impedance of about 24 - j24 Ohms. Fig. 7 shows the general outline of the array, along with the free-space E-plane pattern. These graphics would not reveal the model changes. Hence, the figure also includes the wire table for comparison with the table in Fig. 4. The total driver length change is just about 0.4' or 4.75". The change makes virtually no difference to the beam's performance with respect to gain or the front-to-back ratio.

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The driver impedance conditions ripen the array for matching to a 50-Ohm cable via a beta or hairpin matching system. A beta match is simply an L-network in which the series load-side reactance is contained in the element impedance. Since the element series reactance is capacitive, the source-side shunt reactance must be inductive. We connect the shunt component directly across the feedpoint terminals, essentially in parallel with the source. In practice, we usually find one of three types of shunt components to create the required reactance. Fig. 8 shows the general options for our beam.

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Essentially, two of the three options boil down to one: a shorted transmission-line stub. The stub length depends on the required reactance, about j48 Ohms in the present case. It also depends upon the characteristic impedance (Zo) of the transmission line used to create the reactance: the higher the value of Zo, the shorter the line to achieve the reactance.

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The transmission-line facility of NEC is ideal for implementing a shunt inductive reactance across the feedpoint, since transmission-lines (as special forms of networks) appear in parallel with sources. EZNEC has long used a remote, invisible wire to effect transmission line opens and shorts, so the modeler need not create a special terminating wire for such lines. The latest version of the program adds the ability to calculate the losses of such lines when used as stubs (or in any other application). Fig. 9 shows two different stubs. One uses a 600-Ohm line, which would normally employ parallel transmission line--often homemade. From such lines, the label "hairpin" match emerged. The sample version uses the 10-MHz loss factor for 600-Ohm ladder line to estimate losses that the stub might introduce into the model.

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As an alternative to the 600-Ohm hairpin stub, we might also employ a length of common 50-Ohm cable to create the shorted stub. The impedance is less than 1/10 the impedance of the hairpin line, but the length is a little under 10 times longer. The difference appears because the reactance of a shorted stub is not a linear function of length, but a tangent function of the line length in electrical degrees (or radians). Despite the differences of appearance, both versions of the beta stub perform the same function with equal success.

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The third option is a shunt inductor, which by some convoluted logic received a bygone label of "hairpin inductor." Our problem with the shunt inductor (where an inductance of about 0.27 uH provides the required j48 Ohms at 28.5 MHz) lies in trying to create a model that includes it. In the past, we have needed to develop a physical structure composed of very short wires around an equally short source segment. Then we could add the inductive load to one of the wires in the box as a standard series connected load. To create a structure that provides the least effect on beam performance, we then had to use very short segments throughout the model, resulting in a sizable model (in terms of segment count) for a fairly simple beam. Fig. 10 shows such a model that uses 2" segments, which is approaching the limit for wires having a radius of 0.25". Indeed, the outline does not show entire elements due to space restrictions. However, the wire table shows the degree to which the initial model has grown. Despite its limitations, the work-around has been useful.

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The latest version of EZNEC puts the work-around out to pasture by allowing the user to create any of the standard loads (plus the EZNEC trap load) and to then place them either in series with or in parallel to sources or transmission lines on the same segment. Fig. 11 shows the simple 1-line Load entry that uses an inductor with a Q of 200. The load configuration (that is, the relationship of the load R-L-C or R-X elements) is a series arrangement, as is appropriate to the resistance and inductance in a coil. However, rather than the default series connection with the wire segment, the entry specifies a parallel connection. The antenna viewing feature differentiates load boxes by using squares for series-connected loads and diamonds for shunt or parallel-connected loads, as indicated in the upper right corner of the graphic.

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The first question is whether the arrangement works. Table 3 provides the results for the series of models illustrated in these notes, beginning with the pre-match model of the antenna. The pre-match SWR values emerge from a sweep that used a series inductor to allow the resistive portion of the feedpoint impedance to serve as the SWR reference.

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The second portion of the table shows the results of using models of shorted transmission-line stubs as the beta shunt component. For both hairpin and coaxial components, the table lists no-loss versions of the line as well as versions with loss factors derived from various tables. In principle, RG-58 results in a numerically noticeable loss that is greater than any other beta shunt. However, the total gain reduction is about 0.15-dB relative to a lossless situation, a level that one would be hard-pressed to measure under the best of circumstances.

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The final part of the table begins with the reported values from the all-wire bridge construction, which happen to extend so that its broadside is in the plane of the elements. The gain value seems to be numerically high, and it is. The AGT for the model is 1.011, indicating an overestimate of gain of about 0.05 dB. The remaining 0.4-dB is a function of the bridge wires themselves. Of course, once we add in the inductor losses from having a finite Q (200), the gain value comes down and disguises the result.

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We obtain a clearer picture of the effects of inductor losses by using the parallel connected inductive load. With no losses, the gain returns to the value shown by the pre-match version of the mode. Adding in the loss reduces the gain by only 0.02 dB, a reduction that is less than the better of the two coaxial cable shorted stubs. Once upon a time, some amateur texts claimed a wider operating bandwidth for beta inductors over hairpins due to the inductor's lower Q and higher losses. The small exercise shows that the losses, even with a Q as low as 200, rival those of the 600-Ohm hairpin. The difference in band-edge SWR values is largely a function of the different rates of reactance change for transmission-line stubs and inductors across a span of frequencies.

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We might briefly glimpse at part of the means by which EZNEC, V5, achieves frequency-nimble parallel-connected loads. The interface calculates a Y-parameter network at each frequency before supplying the data to the core for its run at each frequency within a sweep. EZNEC Pro/4 allows us to save .NEC format model files for each frequency. The models are identical except for the NT command that is unique to each frequency. Table 4 shows the NT lines for the parallel inductor in the sample model. After the two port location entry pairs, we find the Y-parameter equivalents of the inductive load for the specified frequency. The EZNEC interface calculates these values and supplies them to the core in the form applicable to its implementation of the NEC-2 and NEC-4 cores. (Data transfer to the core for its run may differ between core types.) The table suffices to show that by moving the calculation to the input interface portion of the program, it can achieve frequency-nimble and accurate results within the limits of each type of facility that it offers.

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To Be Continued

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We have examined only some of the facilities offered by the new version of EZNEC. The program also offers at all levels access to L-networks, from which we can construct networks with from 2 to N components. We shall see how to model a few of the options in our next episode.

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Go to Main Index

+ + diff --git a/content/amod/amod14.html b/content/amod/amod14.html new file mode 100644 index 0000000..fcb8fc1 --- /dev/null +++ b/content/amod/amod14.html @@ -0,0 +1,145 @@ + + + + + Some Mid-Element Loading Basics + + + +
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14. Notes on Reactive Antenna Loads and Their NEC Models:
+ B. Some Mid-Element Loading Basics

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L. B. Cebik, W4RNL

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In the first installment of these notes, we looked almost solely at short, center-loaded dipoles. Our test dipole is exactly 1/4 wl long (34.39') at 7.15 MHz and uses perfect or lossless wire of various sizes between AWG #8 and AWG #12. For reasons that will become apparent in still later episodes, the test model has 91 segments, each about 4.53" long. For Type 4 (complex R +/- jX) loads or for Type 0 (series R-L-C) loads, we placed the load on the center segment (#46).

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The one exception to this procedure arose when we substituted shorted transmission line stubs for the series R-L-C load, using the TL function of NEC. Since transmission lines appear in parallel with loads, we were forced to split the load and move the stubs to the segments immediately adjacent to the center segment (Segments #45 and #47). Two phenomena appeared:

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1. Even with such a small spacing between loads, the source impedance of the dipole increased by a measurable amount. Using the #8 AWG wire model, the resonant source resistance climbed from 13.2 Ohms to 13.8 Ohms.

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2. Likewise, the required reactance for loading the wire to resonance also increased. For the #8 wire model, the required reactance each side of center climbed from 416.65 Ohms to 426.3 Ohms just by moving the loads to a spacing of about 9" apart.

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These two phenomena form part of a set of trends with which all designers of loaded elements must be familiar. We shall look at them initially by using the same load-creation facilities of NEC that we used in looking at centered loads. Before we are finished with these basics, however, we shall formulate some questions about the reliability of models to tell us the entire story using only the "regular" means of load creation: Type 4, Type 0, and transmission line (TL) shorted stubs.

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Load Position Trends

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In theory, it is possible to split a center inductively reactive load and to place the halves symmetrically anywhere along the wire of our short dipole. As we move the load halves outward, we must increase the value of reactance of each half in order to bring the dipole to resonance. The following exercise is designed to generate an appreciation of how much reactance must be pressed into service for the purpose of re-resonating the dipole as we push the loads further outward.

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Let us take the #8 model and place the loads successively 10% further outward from center. In terms of total antenna length, this amounts to placing the load at the 45%-55% positions, the 40%-60% positions, etc. For a 91-segment dipole, we can only approximate these positions, but the results are certainly close enough to reveal the trends involved. The exercise can use simple R +/- jX loads. At each position, we increase the value of inductive reactance to bring the dipole to within +/- 1 Ohm reactance of resonance at 7.15 MHz.

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Initially, we can let the Q of the load be indefinitely high (or infinite, meaning resistively lossless) by setting the value of the load resistance to zero. We obtain the following table of results.

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Position  Position       Reactance in   Source Impedance    Free Space
+Approx %  Actual %       Ohms per Side  R +/- jX Ohms       Gain dBi
+ 5/95      4.95/95.05    3948           37.7 + j 0.3        1.91
+10/90     10.44/89.56    1939           34.4 - j 0.5        1.90
+15/85     14.84/85.16    1369           32.0 + j 0.4        1.89
+20/80     20/33/79.67     996           28.9 + j 0.8        1.88
+25/75     24.73/75.27     817           26.5 + j 0.8        1.87
+30/70     30.22/69.78     668           23.6 - j 0.6        1.87
+35/65     44.62/65.38     586           21.3 + j 0.7        1.86
+40/60     40.11/59.89     510           18.4 - j 0.5        1.86
+45/55     44.51/55.49     465           16.2 + j 0.7        1.86
+50/50     50/50           416.65        13.2 - j 0.0        1.85
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The most significant trend to note is the steady rise in the required reactance to bring the dipole to resonance as the load is moved progressively outward from center. The following graph shows the trend with some clarity.

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The source resistance and gain figures are predicated on the unlikely event of obtaining a perfect (lossless) inductively reactive load. A more realistic value would be a Q of about 300. This requires that for each load, we divide the reactance by 300 to obtain a series resistance for the total load. If we insert the required values of resistance into our R +/- jX loads, we obtain the following values at 7.15 MHz with our #8 lossless wire model. (Reactance values do not change and are not shown below.)

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Position  Series R  Source Impedance    Free Space     Inductance
+Approx %  Ohms      R +/- jX Ohms       Gain dBi       uH
+ 5/95     13.16     57.4 - j 0.9        0.08           87.9
+10/90      6.46     44.7 - j 0.9        0.77           43.2
+15/85      4.56     39.6 + j 0.2        0.96           30.5
+20/80      3.32     34.9 + j 0.6        1.07           22.2
+25/75      2.72     31.6 + j 0.7        1.11           18.2
+30/70      2.23     27.9 - j 0.7        1.13           14.9
+35/65      1.95     25.2 + j 0.6        1.13           13.0
+40/60      1.70     21.9 - j 0.5        1.12           11.4
+45/55      1.55     19.6 + j 0.7        1.02           10.4
+50/50      1.39     16.0 - j 0.2        1.02            9.3
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The inductance that yields the required reactance is shown in the right- most column for convenience, and we shall return to it in a moment. First, however, let us look at the values from left to right. The series resistance values can be compared to the reactance values in the preceding table to confirm a Q of 300. The other values may benefit from a bit of graphing.

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The source resistance increases approximately, but not exactly, as the loss resistance increases for each pair of loads. The small differential between the reported source resistance and the sum of the source resistance with an infinite Q and the total of resistive losses results from placing the loads ever farther from the center or source point of the dipole. Nonetheless, the trend is abundantly clear.

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The graph that compares the free space gain of the dipole without load losses and with losses of a Q=300 load is perhaps more interesting. The lossless loads show a wholly insignificant variation of gain, regardless of load position. However, with a Q=300 load, the gain of the dipole shows a rise of 0.1 dB when the loads are place 20% to 60% of the total element length each side of center outward from the center--relative to the gain with the load centered. Beyond the 60% mark (20/80%, in terms of total dipole length), the gain decreases severely and rapidly as a result of the equal rapid increase in resistive loss that goes along with the steep rise in required loading reactance.

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The 0.1 dB gain differential between center and mid-element loading is of questionable operational benefit. In a horizontal dipole, the use of mid-element loading in preference to center-loading is for other reasons, most often the higher source resistance of the dipole with mid-element loading. There remains a persistent myth that mid-element loading shows significantly higher gain than center loading. This myth derives from short mobile antenna experience using loaded monopoles. Field strength differences resulting from the environment within which such antennas work and from the very short lengths they use have become unwarrantedly generalized to cover all antennas making use of inductively reactive loads.

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A second source of the myth is an uncritical examination of current magnitude curves along loaded elements. The graph above displays the current magnitude for the R-L-C center-loaded element, the TL near-center-loaded element, and the mid-element R-L-C loaded element. Seemingly, the current magnitude (relative to a source value of 1.0) indicates a stronger far field based on the assumption that the field is roughly proportional to the current. However, that assumption needs considerable modification with loaded elements.

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One modification is occasioned by the current phase change along the element. For the mid-element loaded model, the rate of phase change along the element is much higher than for either center-loaded model. Moreover, the current magnitude curve is not a direct measure of the undissipated power in the element.

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Using the strictly mathematical models of loads of all sorts, we may replace the Type 4 loads with either series R-L-C loads or with transmission lines (TL networks). (Note: as in the preceding episode in this series, we are purposely violating the injunction against using TL loads where current magnitude on the two lines is unequal in order to study the effects of trying to model with them.) The right-most column of the table shows the equivalent inductance values for the reactance loads used in this exercise. Although the weight and gain drop associated with such large inductance values is reason enough not to place loading inductors at the far ends of antenna elements, there is another reason as well. In at least the most extreme case (87.9 uH), for any practical single-layer solenoid coil-winding technique, we would not reach the required inductance before the antenna had passed resonance and had begun to show an inductive reactance at the source. We shall return to this point in a later episode.

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Alternative Means of Placing Loads

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Although certainly precise enough to show the important trends associated with mid-element placement of loads, the technique of choosing segments on which to place loads was only approximate. Except at the very center of the dipole, the loads were a bit off their desired marks.

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We could so segment the dipole that the loads would appear (as centered on their segments) in the desired places--but only for this exercise. If we chose other percentage values for load placement, further revisions of segmentation would be required. There is an alternative.

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Consider the following problem (which, for the moment is academic only): suppose we wish to find the places along the dipole element where each of two mid-element loads are identical in required reactance to a single center load. For our 1/4 wl #8 perfect wire dipole, the required reactance of a center load is 833.3 Ohms to achieve resonance at 7.15 MHz. The question then is where along the wire to place two 833.3-Ohm loads also to achieve resonance.

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The model has 91 segments. If we place the loads on segments 23 and 69, the source impedance reports as 27.11 + j 31.7 Ohms, which indicates the loads are too far inboard. If we place the loads one segment further outward--on segments 22 and 70--the source impedance reports as 26.34 - j 39.04 Ohms, which indicates that the loads are too far outboard. Within the limits of the model, neither placement satisfies the requirement of achieving resonance within +/-1 Ohm.

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These unsatisfactory situations are indicated in parts A. and B of the figure above. The figure also indicates an alternative modeling method that permits precise load location without sacrificing model accuracy. The model in C. is a 5-wire model, all composed of the same type of wire. Two outer sections and a center section are long wires having many segments. Two special wires have 3 segments each, with the load placed on the center segment.

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The use of 3 segments on the load wires serves to ensure that the segments immediately adjacent to the load segment are equal in length to the load segment. The center wire and the outer wires are segmented so that each segment length is as close as possible--within the limits of the total segmentation of the antenna--to the length of the load wire segments.

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The .NEC model above shows the dimensions of the final model in terms of the wire geometry for the dipole with Type 4 reactive loads. For the #8 wire model, a center wire 199" long (+/- 99.5") used 45 segments, each 4.42" long. The outer wires are each 94.24" long and use 20 segments, each 4.71" long. The 3-segment load wires are 13.6" long, with segments 4.53" long. The total number of segments for the antenna remains 91.

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The loads are centered 106.3" each side of the source. With this configuration, the reported source impedance is 26.78 + 0.53 Ohms, well within the limits set for resonance. The figures are for a pure reactance, with no series resistance.

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The technique used here is subject to many variations, including resegmentation to achieve even closer segment length equality along the antenna. Even more precise placement is possible to achieve resonance within narrower limits (for example, +/- 0.1 Ohm). However, for the purposes of this demonstration, the techniques used are sufficiently precise for both placement and resonance.

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Center vs. Mid-Element Loading

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Having placed the 833.3-Ohm load correctly at mid-element positions, it useful to take a preliminary look at the performance curves that result from applying the equivalent Type 0 (series R-L-C) load at both center and mid-element positions. The inductive equivalent of 833.3 Ohms at 7.15 MHz is 1.8549E-5 H. We can look at the curves both for infinite Q and for some representative Q, say, 300. The series resistance required for a Q of 300 at the design frequency is 2.778 Ohms.

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Once more, we shall use our #8 lossless wire 34.39' dipole.

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#8 Wire Dipole           Source Impedance (R +/- jX Ohms)
+Freq.     Center Load    Center load    Mid-El. Load   Mid-El. Load
+MHz       Q=inf.         Q=300          Q=inf.         Q=300
+7.00      12.58-46.28    15.35-46.29    24.33-82.17    29.07-82.25
+7.05      12.78-30.76    15.56-30.76    25.11-55.15    29.98-55.23
+7.10      12.98-15.30    15.76-15.31    25.93-27.54    30.94-27.64
+7.15      13.19-0.02     15.97-0.02     26.78+0.53     31.93+0.40
+7.20      13.40+15.26    16.18+15.26    27.67+29.19    32.98+29.08
+7.25      13.61+30.25    16.39+30.25    28.60+58.35    34.07+58.54
+7.30      13.82+45.29    16.60+45.29    29.58+87.98    35.21+87.84
+Delta R    1.24          1.25           5.25           6.14
+Delta X   91.57          91.58          170.15         170.09
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Mid-element loading results in a larger swing of both source resistance and source reactance across the span of frequencies swept in this exercise. The result for resistance is larger not only in terms of Ohms, but also when taking the swing as a percentage of the design center frequency value. The result for reactance, however, is the opposite: as a percentage of the design center frequency resistance, the reactance swing is smaller for the mid-element load case than for the center loading case. Moreover, for the mid-element loads, there is not the virtual identity of swings for either resistance or reactance that holds over the frequency span swept by the models with center loads.

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The smaller change of reactance relative to the resonant source resistance also suggests that the SWR curves for the mid-element loading cases might be broader than for their center-load counterparts. Of course, SWR is plotted relative to the design center frequency resistance value, where the antenna is resonant within the prescribed limits for this exercise.

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The graph confirms our suspicions. The upper two curves are for the test runs at an indefinitely high Q, while the lower curves are for the value Q=300. In both pairs, the curve for the mid-element loaded dipole is broader than its center-load counterpart. Two cautions attend these curves. First, the effect of wire losses are not accounted within the overall curve, since we are using perfect wire in order to isolate, as best we can within the model, the phenomena that may ascribed directly to the load itself. Second, the conditions of modeling must be remembered: the model is a free space model that, of course, does not take any ground effects into account. The modeled loads assign both the series resistance and reactance and do not take into account any further effects that might accompany a real single-layer solenoid inductor placed in center or mid-element loading service. Although specified in a Type 0 load in terms of a series combination of resistance and reactance, the loads are strictly mathematical entities whose physical properties are not calculated in the overall antenna evaluation.

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The antenna free space gain for the various cases corresponds well to the curves earlier presented. The infinite-Q antenna shows a gain of 1.85 dBi for the center-loaded case and 1.87 dBi when mid-element loaded. When each loading inductor is set at a Q of 300, the gains are 1.02 dBi and 1.11 dBi, respectively. Again, these gain figures do not include any wire loss associated with the main element.

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While we are exploring these modeling curves, we might as well compare transmission line loading when placed at the same mid-element point with the case developed in Part 1. In that instance, we placed a split load in the segments immediately adjacent to the source segment, because placement exactly on the source segment would not have yielded valid series load results. Even that small move of the load position required that we use two 426.3-Ohm loads, rather than a pair of 416.65-Ohm loads (833.3/2). The resultant 600-Ohm (velocity factor = 1.0) transmission line stubs were each 13.52' long. To replace the mid-element 833.3-Ohm loads with transmission line stubs with the same characteristic impedance requires lengths of 20.73' each. Once more, remember that transmission lines used in NEC models are lossless and mathematical. Within those constraints, the results are as follows:

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#8 Wire   Source Impedance (R +/- jX Ohms)
+Freq.     Near-Center    Mid-Element
+MHz       Placement      Placement
+7.00      13.09-52.66    23.84-110.0
+7.05      13.31-35.04    24.76-74.67
+7.10      13.53-17.46    25.74-37.85
+7.15      13.76-0.03     26.78+0.42
+7.20      13.98+17.57    27.90+40.47
+7.25      14.21+34.88    29.09+82.25
+7.30      14.44+52.30    30.38+126.0
+Delta R    1.35          6.54
+Delta X   104.96         236.0
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The mid-element transmission line load source impedance value verifies that the transmission line stub is the correct replacement for the reactance load of 833.3 Ohms. However, even with a 600-Ohm transmission line, the variance of reactance across the band is very large. As we have noted, with transmission lines of lower impedance, the variance will be larger still.

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Comparing the SWR curves (relative to an SWR of 1:1 at resonance) for the near-center and the mid-element transmission line loads shows an interesting result that is opposite to results from using series R-L-C loads. The mid-element loading stub system yields a narrower SWR curve than the near-center loading system. This consequence follows from the much high values of reactance required of the stub. Since the reactance of the stub is a tangent function of the electrical length of the stub, stubs over 45 degrees long change their reactance values rapidly. The required stub length in this case is 54.2 degrees.

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Concerns About Modeled Loads

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Commonly, series R-L-C loads are considered to be adequate models of single-layer solenoid inductor performance in a loaded dipole or similar element. Despite their strictly mathematical nature, that is, the fact that their physical structure does not play a role in the calculation of predicted antenna performance, the resulting antenna performance figures are considered accurate enough for most practical design and analysis purposes. The key loss factor in a solenoid inductor is the series resistive loss, and other losses and factors that might cause variations from the predicted outcomes are considered too small to be of significance. Consequently, only in the most critical cases are solenoid loading coils physically modeled--and usually only where such coils are very simple. An example of such a case is the solenoid in the middle of many automobile UHF antennas for cellular telephone service.

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Transmission line loads, on the other hand, are widely distrusted as models of linear loads used in HF antennas. Most obviously, they do not permit the accurate introduction of resistive losses in the transmission line. Nor do they permit, except as an external calculation, the introduction of the line's velocity factor. (Some programs permit velocity factor information to be introduced into the interface between the user and the core calculation, subsequently converting it to the values needed by the core's network calculations.)

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Most antenna's employing linear loads use load wire having a diameter different from that of the main element. Although MININEC can directly handle these types of models, the required model often presses the segmentation limit of the program. (Some recent MININEC developments, such as NEC4WIN, have broken the 256-segment barrier, and one version permits virtually unlimited numbers of segments, but at the cost of slow calculation speeds.) MININEC has additional requirements in order to reduce errors at sharp corners, NEC (in either version 2 or version 4) is inaccurate when faced with angular junctions of wires having dissimilar diameters. Consequently, physically modeling existent antennas with linear loads is not normally attempted.

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However, it is possible to physically model linear loads using a uniform wire diameter throughout the model. While the technique does not yield an accurate model of a particular antenna, it does produce quite accurate results that can reveal some interesting properties of linear loads. The technique may also permit some preliminary sorting of different functions performed by a linear load and the conditions under which it performs them. Physically modeling some linear load configurations will therefore be our next task.

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Antenna Matching with EZNEC Version 5
+ Part 2. L-Networks

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L. B. Cebik, W4RNL

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The overall goal of this pair of episodes is to show how, fundamentally, to model with some of the new frequency-nimble facilities in EZNEC Version 5. In Part 1, we examined such functions as ideal transformers, parallel or shunt-connected loads, and transmission-line losses. In this session, we shall look at the use of the L-Network facility in creating networks from common components rather than from Y-parameters of complex structures. We shall begin with a single L-network to create a 2-element or 2-component network. Then we shall proceed to creating 3-compnent networks, such as Ts and Pis, by connecting together more than one L-Network in the program. +

Like parallel or shunt-connected loads, EZNEC L-Networks are frequency-nimble and use the same basic technique that was applied to parallel-connected loads. NEC contains an NT command for creating Y-parameter networks. Like R +/- jX loads, Y-parameter networks are frequency specific, and the user must change the command for each new frequency. Hence, a single set of NT values normally will not provide accurate results across a broad frequency sweep. EZNEC calculates a new NT command or its equivalent for each L-Network at each new frequency in a sweep. Therefore, for a given set of values for inductance and capacitance, the core has the correct data to provide accurate results at each frequency in a sweep.

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Our sample networks will apply to matching a self-resonant Yagi to a 50-Ohm coaxial feedline. The root problem is only one of many possible applications for L-networks. However, by focusing in on a single exercise, we can master the steps required to use the L-network facility effectively. Once you take this step, you can easily proceed on your own to other applications.

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2-Element/Component L-Networks

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Let's begin with the self-resonant 28.5-MHz 3-element Yagi using 1.2"-diameter aluminum elements, the same one that we used for part of the preceding episode. Fig. 1 shows the outline and the free-space E-plane pattern of the antenna, along with the wire table needed to create the model. All of the matching sections that we shall explore will be designed to convert the 27.5-Ohm feedpoint impedance to 50 Ohms.

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One way to effect the impedance conversion is to place an L-network between the antenna terminals and the feedline. L-networks are 2-component networks consisting of one series component and one shunt or parallel component. Let's call the cable impedance the source impedance, and the antenna terminal impedance will be the load impedance. If the source impedance is higher than the load impedance--as it is in our case--then the series component goes on the load side of the network, with the shunt component on the source side. If the load impedance is higher than the source impedance, then the shunt component goes on the load side with the series component on the source side. The L-network serves as the foundation for many more complex networks, which we can treat as collections of L-networks.

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Since our goal is to model with EZNEC L-Networks, we shall not cover the calculation of L-network components for given impedance transformation situations. Instead, we shall rely on one of many utility programs and spreadsheets to arrive at the required values for the series and the shunt components. Fig. 2 shows the values of capacitance and inductance needed for two forms of the L-network that will convert our terminal or load impedance to the 50-Ohm source or cable impedance.

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Although the two forms use very different components, both circuits have some things in common. First, the reactive series component is the opposite types from the reactive shunt component. (There are special cases of load impedances that may call for components of the same type, but they involve load or antenna terminal impedances with high reactance. Our loads are almost purely resistive.) Second, the absolute value of the series and the shunt reactances are the same. In both cases, the series reactance is 26 Ohms (with a sign appropriate to the type of reactance) and the shunt reactance is 51.5 Ohms (again with a sign appropriate to the type of reactance).

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To implement a model of the L-network in EZNEC, V5, we must get used to the conventions used by the program. Fig. 3 provides some guidance. A network consists of two ports. Port 1 always goes with the series branch or component. Port 2 always goes with the shunt branch or component. Labeling the ends of the network as Port 1 and Port 2 is simply a way to differentiate them. Depending on the application, either port may be the source and either may be the load. Our sample case shall call for Port 1 to connect to the antenna terminals, that is, to the source segment of the driver-element wire. Port 2 will use a virtual wire (described in the preceding episode), which will become the new source segment for the model. Other applications may reverse the ports for converting low source impedances to high load impedances.

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The sketch also shows us our options in assigning component values to the branches of an L-network. For a single-frequency application, we may use R+/-jX loads. For applications that may need to cover a range of frequencies, we can use several different forms of R-L-C configurations. The most common will be the series configuration. It will apply to our sample, since the most complex entry that we shall make is to have both resistance and inductance in series. As in Part 1, we shall assign a Q of 200 to all inductors. When we choose not to have one of the R-L-C components as part of the branch, we shall enter a zero. In this case, zero is not the component value, but instead is a NEC convention for indicating a missing element in a load. The EZNEC tables will use the word "short" to indicate the missing component.

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In addition to series R-L-C loads, we may also use a parallel configuration. EZNEC also makes available a trap configuration consisting of a series resistance and inductance that together are in parallel with a capacitance. Whichever configuration we select for an application, both branches of the L-network must use the same type of configuration. However, other loads that might be present in the antenna assembly can use any of the possible configurations and do not need to match the configuration used in the L-network.

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We can orient ourselves to the process of modeling an L-network by starting with a frequency-specific R +/- jX load in each branch of the L-network. Fig. 4 shows the model with the designation for the network (the L in the box) plus a designation that shows we are using a virtual wire, namely, V1 as the source wire. The first table shows the source entry that applies to both models. The two L-Network tables show the two versions of the network.

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Because the actual source impedance has several decimal places, as do the calculated components, the rounded numbers in the tables do not return identical source impedance values. The first version reports an impedance of 50.5 - j0.0 Ohms, while the second reports 53.6 - j0.0 Ohms. In practice, the difference does not make a difference, since every model will depart slightly from physical reality that includes small variations from the model.

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If we wish to employ series R-L-C branches in the L-network--the more normal case--the L-Network table becomes more complex. Fig. 5 shows the tables for the two varieties of L-networks pictured in Fig. 1. The first version provides a series inductor with a Q of 200 and a shunt branch holding the capacitor. (In a series R-L-C load, you may ignore the Frequency entry. It applies to trap-type loads. Traps are very often designed to be self-resonant at the bottom or just below the bottom of an operating passband.)

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The second version of the L-network uses a series capacitor with a shunt inductor--again with a Q of 200. Both versions connect Port 1 to the load wire, in this case, segment 11 of wire 2, the Yagi driver. Port 2 for both networks goes to wire V1, the remote short virtual wire, which also serves as the source segment.

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Table 1 lists the results of the modeling with each L-network. Each version lists a variant of the model that omits the series resistance in the inductor branch, this providing a lossless model, except for the aluminum element material, of course. These entries also supply the performance data (excluding the feedpoint impedance) for the basic or pre-match model.

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With a normal or lossy coil, both version of the L-network result in the same gain value and the same efficiency. Version 1 shows an impedance about as much below 50 Ohms as the impedance of version 2 is above 50 Ohms. The variance results from rounding the values, beginning with the original source impedance applied to the external L-network calculator.

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The modeler can be as creative as he or she wishes in the development of models that use a single L-network. For example, one might model a multi-band center-fed doublet, perhaps about 125' long overall. From the center segment of the doublet, one may insert a transmission line of choice, including the loss factor, and set its length to approximate the length of a practical line. Initially, one can place the source on the virtual wire that terminates the transmission line. From a record of source impedance values for the various bands, one can derive from an external L-network calculator the type of network and the component values needed to transform the impedance to 50 Ohms. (The type of network refers to whether the shunt or the series branch connects to the load.) Then one may go back and insert the prescribed L-network for each band into a separate model to confirm the results. If the modeler is dissatisfied with the results, perhaps due to the need for extreme component values in one or the other leg of the network, one might try different doublet lengths, different transmission-line characteristic impedances (with adjustments to the velocity factor and the loss factor), and even different line lengths. Since the line length is not a part of the overall antenna geometry, the procedure cannot account for disruptive influences on the line that a casual physical installation might encounter. Nevertheless, the exercise can give the modeler with an L-network tuner a good idea--well in advance of purchasing materials--what approximate setting an L-network tuner may need--not to mention the best line to use for a given installation.

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3-Element/Component Networks

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We can connect the individual ports of an L-Network in EZNEC to any wire, real or virtual. Therefore, we might place two (or more) L-Networks back-to-back to form a 3-component network, such as a PI or a T. Although rarely used at the terminals of an antenna, they are often the network forms used in antenna tuners. For our samples, we can dispense with the transmission line and connect our new networks directly to the terminals of our self-resonant 3-element Yagi. For the impedance of the driver (about 27.6 Ohms) and the cable or source impedance (50 Ohms), we might use any of the networks shown in Fig. 6. Indeed, there is a remaining option, the high-pass PI, but I have never seen it used in this type of application.

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Creating such networks will require that we use 2 L-Networks. In each case, the center component is shared by both networks, so we shall have to connect together either a pair of Port 1s or a pair of Port 2s, as shown in Fig. 7. For a PI network, the Port 1s go together (on a suitable virtual wire) so that we have two series branches connected in series. A T network requires that we bond the two Port 2s together on a wire. The result is two shunt branches connected in parallel. We also need to keep track of the ultimate ends of the system. For convenience, I shall adopt the convention of treating the first L-Network as connected to the load, that is, the antenna terminals (or, in the model, the proper driver segment). A new virtual wire, V2, which also receives the model source, terminates the far end of the second L-Network. Some convention of this sort is necessary to ensure model-to-model consistency and to thereby minimize the chances for misconnection errors.

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Let's begin by forming the low-pass PI network. Fig. 8 shows the model. but lists only one network and one virtual wire. On the right, we have the network to compare with the L-Network table that follows. In the table, we can readily identify the shunt capacitors at the extreme ends of the assembly.

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The series branches divide the inductor. In this case, the inductance and its series resistance for a Q of 200 form two equal parts. Since inductances and resistances simply add when in series, the sum of the resistive and the inductive values represent the total that forms the PI network. It is not necessary to divide the values in half. Other partitions will result in accurate results. However, for greatest accuracy, the smaller of the two parts should be above about 1% of the total. If you place all of the inductance in one L-Network and simply set the other network's series branch to zero, you will end up with a missing component, and the results may not be accurate. For reasons that will become clear as we proceed, the division in half is a convenient convention to adopt.

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Let's next form a low-pass T network from 2 L-Networks. Fig. 9 shows the ultimate network and the formation tables within EZNEC. The series components are clear. The two shunt capacitors each carry half the value of the total capacitance required by the T-network, since capacitances in parallel simply add. (Note: these exercises have presumed perfect capacitors with an indefinitely high Q. However, you may find occasion to assign a series-equivalent resistor to a capacitance to simulate a Q.) Once more, other splits in the total capacitance will work equally well so long as the lower value is at least 1% of the total. Do not place the entire capacitance within one L-network and treat the other shunt value as zero or a short.

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Our final sample uses a high-pass T network. As shown in Fig. 10, this situation produces two capacitors as the series elements. The inductance falls into the shunt branches of the 2 L-Networks. Here, equal parts for each shunt simplifies the arithmetic to an easy mental exercise. If we assign to each shunt branch twice the inductance and twice the resistance relative to the externally calculated total, the parallel combination will be correct. There are other combinations that will do the job, but they might require a calculator.

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The question that follows from these formation drills is whether results are accurate. The schematics reflect (with rounding) the network values derived from an external program, which we shall presume to be correct. Ideally, the source impedance for each model should by 50 Ohms. The data in Table 2 provides the reports from running the NEC models. Each entry in the table provides reports for perfect or lossless inductors and for inductors with a Q of 200.

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The low-pass PI network is interesting because it exhibits the lowest efficiency of the group with an inductor Q of 200. The high-pass and low-pass T networks are about equal with respect to efficiency. However, as the gain values suggest, none of the matching network types yields performance reductions that one could notice in operation. As well, the efficiencies of the 3-component networks is only 1% to 2% lower than the values associated with 2-component L-networks.

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A more direct measure of the EZNEC L-Network system is the source impedance reports. Using components calculated externally, the network systems produce the results expected within very close tolerances. Like the parallel-connected components examined in the preceding episode, the L-networks convert--at each frequency within a sweep range--into Y-parameter networks or their equivalents. Hence, the L-network system used in EZNEC provides accurate results across a significant span of frequencies.

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Nothing prevents us from using sequential L-Networks rather than back-to-back configurations. Although we would gain nothing from the process in many circumstances, let's create the situation to establish that they work. In the preceding episode, we examined a 1/4 wavelength shortened dipole for 14.175 MHz composed of AWG #12 copper wire. It used a 9.44-uH center-loading coil to bring it to resonance with an impedance of about 15.4 Ohms. Normally, we might use a single L-network with a series inductor on the load or antenna side of 0.26 uH, with a shunt capacitor on the source side of 337 pF. This arrangement would yield a source impedance of 49.7 - j0.3 Ohms.

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For our sequential system, let's install two L-networks arranged as shown in Fig. 11. The first network will convert the 15.5-Ohm load impedance to 27 Ohms. The second will convert the 27-Ohm impedance to 50 Ohms. The tables show the basic dipole, although I have omitted the inductive load. The network tables show the series and shunt branch values necessary to effect the 2-stage impedance transformation. As always, the inductors have a Q of 200.

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The 2-stage L-network system produces a source impedance on wire V2 of 49.8 - j0.2 Ohms. The dipole gain is 0.84, indicating a small network loss. The efficiency is 79.3%, considering the effects of both the network and the loading coil. A single-stage L-network shows an efficiency of 79.4%. Even though the 2-stage L-network system shows no advantage over a single-stage network--and indeed requires unnecessary component complexity--it does illustrate well enough the accuracy of EZNEC L-networks in the sequential mode. The SWR graph is identical to the one shown for the dipole in Part 1 of this episode pair.

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Conclusion

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The goal of these episodes has been to show the steps needed to model effectively using new facilities within the latest version of EZNEC. These facilities include transmission-line losses, parallel-connected loads, ideal transformers, and L-networks. As applicable, each facility shares the frequency-nimble properties of R-L-C loads in NEC. The program achieves this ability by recalculating an NT command or its equivalent for each frequency step within a defined sweep. Hence, the new facilities are highly useful in evaluating potential antenna performance across a band of frequencies.

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Although the examples have focused on antenna impedance matching, this application is but one of many possible uses to which we might put the facilities. For example, L-networks--and more complex networks that we might construct from them--are useful not only for impedance transformation, but as well for phase-shifting a signal. Learning the required modeling steps and developing personal conventions that make them consistent from one model to the next is crucial to error-free and confident modeling with the new facilities in this program.

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Circular R-X Graphs

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L. B. Cebik, W4RNL

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The NEC calculation cores produce only a tabular output. Any graphical outputs that we may wish represent post-core-run manipulations of the output data. Most of the work involves finding and parsing the data into a form that a graphing module may use to present the information in a more useful visual manner. Various implementations of NEC provide some of these graphs, namely, the ones most often required or desired by antenna modelers. +

Graphs that accompany an implementation of NEC generally come in two forms: polar and rectangular. Polar graphs generally apply to the radiation pattern outputs, since the data values appear in terms of angles and magnitudes. In past episodes, we have examined some of the considerations that go into the forms and plot ring arrangements for such graphs. It is also possible to present these graphs in rectangular form, using the X-axis of the graph for the angular information and the Y-axis for the magnitude. Rectangular graphs are also very useful to present other information, such as the current magnitude and/or phase angle along one or more wires in the model or the resistance, reactance, and SWR information over a specified frequency range.

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Some graphical outputs from NEC implementations involve post-core-run calculations. The most common calculation is the SWR relative to a user-selected (or a default) resistive impedance. In addition, some implementations have created polar plots of the left-hand and the right-hand circular components of radiations patterns using calculations based on the radiation pattern data. We have also examined some of these calculations in past episodes.

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There is one type of graph that is both very useful and very absent from implementations of NEC. In fact, the only NEC-related program that makes the graph available--to the best of my knowledge at the time of writing--is AC6LA's Multi-NEC. This Excel application does not use a core, but taps into the cores of a number of popular programs for the core run itself. However, Multi-NEC does provide a large collection of facilities unavailable in most NEC implementations.

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The graph to which I am referring is the X-Y graph. It is available in many graphing and in most spreadsheet programs. Instead of plotting the magnitude of Y against a progression of set values for the X-axis, the graph plots both X and Y as points on a field. The graphing facility normally calculates the field area needed to contain the points and then creates X- and Y-axes to accommodate the values. Some graphing programs allow the user to modify the axes limits and subdivisions. In addition, most X-Y graphing facilities add a line connecting the successive data points in the series.

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X-Y graphs have numerous uses. With respect to antennas, one of the most useful versions is a plot of resistance and reactance across a large frequency span. There is much that we can glean from a close examination of X-Y graphs of R +/-jX. So let's probe a bit further. Once we catch on to how we can create our own X-Y graphs of NEC output data and look at a few comparative situations, we may transform such graphs from mere interesting oddities into genuinely useful data presentations that we are likely to use often in the future.

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The Exercise

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To see what we might learn from X-Y graphs, we shall need a few antennas. Fig. 1 shows the four that we shall use. The first three are linear dipoles, but with very different length-to-diameter ratios (1000:1, 100:1, and 20:1). The last of the sequence is a biconical dipole composed of 4 wires simulating the element cones. To simplify graphing, I have resonated all four antennas at 300 MHz as 1/2 wavelength elements. We shall be interested in the impedance behavior of each antenna over an 8:1 frequency range (3 octaves).

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To obtain the requisite data, we need to conduct frequency sweeps across the prescribed range. I have selected a 30-MHz increment to yield 71 sweep steps as defined for the FR command, beginning at 300 MHz. We have enough steps to produce some interesting graphs, but not so many as to tax our patience while the core generates the necessary data. Some programs have tabular facilities to collect the impedance data from each run for each frequency into a single table. The partial table in Fig. 2 samples the information as presented by software. The entire table would be unnecessarily long, since we may view it more compactly for each of our subject antennas in graphical form.

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We shall be interested in the Z(real) and Z(imag) columns, since we wish to plot R and X. However, we might have as easily selected Z(mag) and Z(phase)--or any other pair of data items--for our work. R and X simply give us some focus to develop a sense of what we might eventually learn from the graphing exercise.

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Unless we are using Multi-NEC, we shall have to create graphs for ourselves externally to the NEC implementation. The first step is to perform whatever re-shaping we might need to do to enable us to import the data from the table into a spreadsheet. Many spreadsheets create separate columns only when the separator between data values in a table is of a certain sort. TAB is perhaps the most universal separator for easy spreadsheet entry. If we save the data table and open it in a word processing program, then we can find and replace a uniform series of spaces with a TAB code. From that point, we can copy and paste the revised table into a spreadsheet.

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The rest of the job is simply creating a graphic using the X-Y format, along with axis labels, titles, and any marker notations that we might find useful. For example, the X- and Y-axes of our graph will note only the range of values for R and X. They will not locate specific frequencies. Therefore, we may wish to add a few marker notations to facilitate comparing graphs.

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The 1000:1 L/d Dipole

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The very thin-wire dipole provides a useful starting point. At 300 MHz, its length is 0.4810 wavelength (or meters), with a diameter of 0.000481 wavelength (or meters). Both dimensions translate directly into meters at this frequency. Let's begin with a very conventional graph of the feedpoint or source resistance, reactance, and 72-Ohm SWR values. Fig. 3 provides the data as developed via EZPlots, another AC6LA program for analyzing frequency sweeps taken with EZNEC.

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The chart seems clear enough, despite the three data curves. Between the points of minimum SWR, which also generally mark the low values of R, we can see the peaking of the values of X as we increase frequency. As we increase the frequency, we can also see that the peak values of SWR systematically decrease, along with the peak values of R and X. The SWR peaks seem to correspond roughly to frequencies at which the antenna element is an integral multiple of 1 wavelength--but not exactly.

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If we take an X-Y graph of the resistance and the reactance, we obtain a chart with the appearance of Fig. 4. I have purposely shrunk the width of the chart so that the X- and the Y-divisions are about equal in space, even if not in numerical values. Since most such charts that appear in texts have a relatively square form, producing nearly circular patterns of data values, this shape gives the sample an air of familiarity. Unfortunately, my spreadsheet does not have a spline function to round the curves, and we do not have enough data points to yield a good round outer curve to the spiral.

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The spiral itself captures some of the essential features of the linear graph and sets them into fairly bold relief. As we increase the operating frequency, the resistance at the low-impedance resonances increases with each passage. In addition, with each increase in frequency, the peak values of resistance and reactance decline. The data points for resistance and reactance are the same ones that appeared in Fig. 3. However, the presentation in Fig. 4 allows us to see some of the interesting relationships more clearly.

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Note that I have added a few frequency markers. One points to the beginning of the curve at 300 MHz. The others mark the frequencies at which we might have expected the antenna to show a resonance as the reactance makes its sudden transition from a very high inductive value to a very high capacitive value. However, due to end effect and other factors, these frequencies to not mark resonant points on the curve.

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Rather than probe this single graph for various further details, let's turn to a second dipole. Some of the utility of X-Y graphs lies in comparing one with another--so long as the antennas involved are indeed comparable.

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The 100:1 L/d Dipole

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A fit comparator for the dipole with a length-to-diameter ratio of 1000:1 is another dipole with a 100:1 ratio. At 300 MHz, the length is 0.4676 wavelength (or meters) with a diameter of 0.004676 wavelength (or meters). Like the first antenna, it will be resonant at 300 MHz as a 1/2 wavelength dipole. The question that we may pose to our resistance vs. reactance X-Y graphs is how the two antennas behave similarly and differently between 300 and 2400 MHz.

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Fig. 5 shows the conventional graph of resistance, reactance, and 72-Ohm SWR for the fatter dipole, using a frequency-based X-axis. In many respects, the curves for the two dipoles are very similar in shape. However, if we compare the values on the left and the right Y-axes, we shall see that the peak values are far lower in every category.

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The left part of Fig. 6 shows the X-Y graph of resistance vs. reactance for the 100:1 dipole. The spiral resembles the one in Fig. 4, but with a few exceptions. For example, the peak values are rather vividly lower. The version of the graph on the right uses the same axis range as Fig. 4, and the smaller range of values in the new antenna's spiral becomes very clear.

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In addition, note the positions of the frequency markers on the graphs in Fig. 4 and Fig. 6. The fatter version of the antenna places the markers further along the spiral than does the thinner dipole. In addition, we may note that in both of the resistance vs. reactance graphs, we see a more extreme value of capacitive reactance than of inductive reactance.

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These are by no means new discoveries about dipoles of varying length-to-diameter ratios. Basic college texts will contain a number of equations by which to calculate the impedance behavior. The function of the X-Y graph is to present the data in a manner that naturalizes it so that it becomes part of our expectations of dipole behavior.

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The 20:1 L/d Dipole

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Two instances do not themselves establish a trend. Therefore, let's add one more dipole to our collection, this time with a length-to-diameter ratio of 20:1. The length at 300 MHz is 0.45 wavelength (or meters), with a diameter of 0.0225 wavelength (or meters). This dipole is about as fat as we dare let the model go while still expecting reliable data. Fig. 7 provides the resistance, reactance, and SWR data in the conventional format.

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Once more, the curves have their by-now familiar shapes, but the peak values have declined even further. Above about 1200 MHz, the resistance begins to flatten so that a value of about 100 Ohms becomes the median value. Indeed, a center-fed element with a 20:1 length-to-diameter ratio becomes a candidate for being a broadband antenna, were it not for the fluctuations in the reactance. For example, the antenna exhibits a 400-Ohm SWR of under 2:1 from about 400 through 575 MHz.

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The X-Y graph in Fig. 8 provides the spiral perspective on the fattest of our dipoles. The smaller range of both resistance and reactance values removes much of the distortion from the actual smooth curves of the transition between values. In fact, the 20:1 dipole shows total ranges of both resistance and reactance that are about 1/3 of the range shown by the 100:1 element and well under 20% of the ranges displayed in the spiral for the 1000:1 center-fed antenna. Nonetheless, all three spirals share the common trait of shrinking ranges of both resistance and reactance with rising frequencies. If we keep the 3:1 range difference in mind between the fatter two dipoles, we can also see that the frequency markers are farther along the spirals for the thicker of the two, continuing the potential trend that we saw when comparing the first two antennas in our exercise.

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We also raised the question as to whether the apparent domination of the spirals by capacitive rather than inductive reactance was a real phenomenon or an artifact of the increment selected for creating the curves. In fact, the phenomenon is real. From 400 to 600 MHz, the capacitive reactance peaks at about -j250 Ohms. However, the inductive reactance never quite reaches j100 Ohms. One might leave the explanation for this condition--reflected to lesser degrees in the thinner dipoles--as "an exercise for the reader," but we should not forget the capacitance between the element halves at the feedpoint gap created in the model and in real antennas. Most cage elements (assuming periodic rings around the wire collection to ensure even current distribution) bring the wires forming the fat dipole together in a sloping point, a structure that reduces the capacitance. Some wide-band elements may create a biconical structure for up to half the length of each side of the center feedpoint.

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And that last note brings us to the final element of our collection.

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The Biconical Dipole

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As a contrast to the uniform-diameter dipoles with which we have been working in order to develop an appreciation of resistance vs. reactance X-Y graphs, we may examine a sample biconical dipole having the structure shown in Fig. 1. We shall use 4 wires to simulate the cone, brining the ends of each wire together at the center of each end. The nominal slope of reach cone is 10 degrees relative to the dipole's centerline. The value is nominal, since the feedpoint region consists of a short 3-segment wire, with the middle segment serving as the source segment. Hence, there is about a 0.2-degree difference between the angle of each wire relative to where it joins the source wire and the virtual angle taken from the exact center to the outer tip of the cone wires. The differential is not sufficient to invalidate the very general outline of impedance behavior for the biconical antenna between 300 and 2400 MHz.

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Each of wires has a diameter at 300 MHz of 0.002 wavelength (meters). The overall length is 0.3522 wavelength (meters). The maximum distance across the extreme end of the element is 0.061 wavelength (meters). Whether we can call this dimension the diameter of the cone at its widest opening depends upon the degree to which 4 wires simulates a solid-surface cone, a consideration requiring a different context and discussion from the present topic. As well, because the biconical element changes its diameter along its length, we cannot readily assign to it a length-to-diameter ratio. However, see Kraus, Antennas, 2nd Ed., Section 9-11 for a discussion of and equations for calculating the impedance of thin cylinder and biconical elements. Imperfect as the simulated biconical structure may be, it does provide a good indication of biconical properties. Note, for example, the overall length, resonant at 300 MHz (with an impedance of 52 Ohms), in comparison to the lengths of the uniform-diameter dipoles, the shortest of which is 0.45 wavelength (meters)

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The conventional graph of resistance, reactance, and (52-Ohm) SWR in Fig. 9 displays much of what we expect in any dipole. The undulations of all three properties recorded in the graph resemble those of the 20:1 L/d dipole, although the biconical element shows slightly higher peak values in the first SWR cycle. For example, the fat dipole shows a peak resistance of about 400 Ohms, while the biconical antenna has a peak resistance of about 600 Ohms.

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Perhaps the most notable difference between the uniform-diameter dipoles and the biconical element becomes evident when we count SWR cycles. All of the cylindrical dipoles show an average of about 3-1/4 SWR cycles between 300 and 2400 MHz. In the same span, the biconical antenna exhibits about half a cycle less. Although we see a progressive broadening of the bandwidth as we increase the diameter of the dipoles, the biconical simulation outstrips the dipole progression by a significant margin.

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The X-Y graph of resistance and reactance in Fig. 10 reveals some additional properties that may, under certain circumstances, be useful to know. Unlike the uniform-diameter dipoles, the biconical antenna shows nearly equal inductive and capacitive reactance peaks in the first cycle of the spiral. However, as we raise the operating frequency, capacitive reactance begins to dominate each cycle. An average reactance line drawn across the face of the graph would fall in the vicinity of the -j50-Ohm marker. We must moderate this average by noting that the dominance of the capacitive reactance in the source impedance appears to become stronger with each successive cycle. In contrast, the uniform-diameter models seem to present a near symmetry of reactance in each cycle once we establish an average value line on the graph. To what degree modeling limitations may enter the values for the higher frequencies would become a necessary consideration for an actual antenna that might be under analysis.

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One of the important external additions to the graph is annotating the curves with frequency markers at critical points. In the case of the biconical dipole, these notes allow us to see clearly to what degree the antenna geometry has spread the undulations of resistance and reactance across a wider range than we found for the cylindrical dipoles.

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Conclusion

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Our excursion into the sample dipoles has not tried to establish anything new about these fundamental antennas. The exercise examples have simply served as a convenient way to illustrate the benefits of adding to what modeling programs provide by creating an external graphing functions. In this case, we have extracted the source information from NEC core runs over a wide frequency sweep to produce X-Y graphs of resistance and reactance. The result is a spiral graph of the values that served to reveal some properties more clearly than standard linear graphs. Although we have used an external spreadsheet to produce the sample graphs, Multi-NEC provides this facility as part of its spreadsheet shell for using a variety of NEC cores. Fig. 11 shows a resistance-reactance plot for a sample antenna in the Multi-NEC application.

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Although the resistance-reactance X-Y graph is the most common form in antenna work, other pairs of values may prove relevant for X-Y graphing in many contexts. Even at a fundamental level, the R-X plot has significant use. For example, amateurs often install single-wire antennas design to serve all frequencies from about 3.5 MHz through 30 MHz. A series of X-Y plots of resistance and reactance can assist the average ham in finding a wire length at the proposed height and ground conditions that best avoids radically high and radically low antenna impedance values in each amateur band so as to minimize losses in the selected parallel transmission-line to the station's antenna tuner. Since some current programs allow the entry of transmission lines with their listed velocity factors and loss factors, one might model the entire system using various trial element lengths to arrive at the best combinations that is usable within the antenna construction site.

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In short, additional post-core and post-program manipulation of data can serve useful purposes, and the X-Y graph is only one of them.

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Go to Main Index

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VOACAP Type 13 Files

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L. B. Cebik, W4RNL

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Between antenna modeling via NEC or MININEC and ionospheric propagation prediction software, we find a nexus that goes under a deceptively simple title: the type-13 file. In these notes, we shall look at three questions. What is a type-13 file? Why is it important for at least some modelers to develop such files? How can we make a type-13 file within NEC that is compatible with the most common propagation programs? Our account will be very general relative to the first two questions, since our focus will be on the modeling aspects of the Type 13 file. +

What is a type-13 file?

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Like modeling cores, such as NEC and MININEC, propagation software has one or two primary calculation cores with embellished implementing software. The older core is IONCAP, although the most commonly used package is VOACAP. In 1985, the Voice of America (VOA) adopted the Ionospheric Communications Analysis and Prediction Program (IONCAP) as the approved engineering model to be used for broadcast relay station design and antenna specification. As the program was modified for these purposes, the name was changed to the Voice of America Coverage Analysis Program (VOACAP) to distinguish it from the official National Telecommunications and Information Administration (NTIA) IONCAP program. The Fortran code for VOACAP is readily available, allowing a number of implementations, such as ACE-HF, available from antenneX (Note: This product was dropped by antenneX).

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Although developed for shortwave broadcast interests, the VOACAP program is equally useful for predictions of ionospheric propagation conditions governing long-range two-way communications in the HF range. Hence, we find the program widely used in government, military, commercial, and amateur installations designed for such communications. Within these installations, there are almost innumerable different antennas in use, too many for any program to contain as samples. Within VOACAP, we define an antenna not solely by its geometry, but as well by its height above ground (including ground mounted monopoles with various types of radial systems) and the quality of ground beneath the antenna at a specific frequency. In fact, VOACAP is not interested specifically in the antenna geometry, but in the far-field radiation pattern produced by the antenna at the selected frequency. Geometry (including electrical features that affect the far-field), height, frequency, and ground quality together determine the far-field pattern for a station interested in propagation predictions.

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To make the most accurate predictions of propagation potentials for a given station, VOACAP requires a frequency-specific radiation pattern file for any subject antenna. The file must meet certain standards. It must provide a 360-degree azimuth pattern in 1-degree increments. The azimuth pattern must proceed in compass-rose order, that is clockwise from the starting point--ordinarily North or 0 degrees. For each azimuth increment, the file must list the signal gain in dBi for each elevation angle from the horizon to the zenith in 91 entries. The result will be an ASCII file that is over 250 kB long. Moreover, virtually all implementations of VOACAP require the older file-name entry of no more than 8 characters, with a file extension of no more than 3 characters. In most cases, the extension will be .13.

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The file has several other requirements, illustrated by the partial file in Fig. 1. The figure shows only the first 3 azimuth headings of the 360 required by the file, but the remaining entry groups follow the same pattern as those shown. The filename is TF50280C.13, indicating a terminated folded dipole antenna that is 50 m long over average ground. The file is one of a large series of type-13 files for this antenna, one for every MHz of the anticipated operating range. Since terminated folded dipoles come in a considerable variety of lengths (and other details), the file name should use a code that allows ready identification of the antenna, the frequency, and the ground quality (where C indicates average ground with a conductivity of 0.002 S/m and a permittivity of 13 on the scale used in this particular coding system).

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For any group, the initial entry is -99.99 dBi, indicating an elevation angle of 0 degrees. The final entry in each group is the same, since every 90-degree elevation or zenith angle records the same far-field direction and hence the same gain. Note the internal grouping limits and the spacing required to have a file that is readable within VOACAP.

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Equally important are the initial entries. The first entry is a limited space for recording antenna details. The next 4 entries are standard except for the frequency entry, which should indicate the frequency for this particular file. Note again the spacing of the entries from the left edge to ensure that VOACAP can read the data correctly.

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Although this antenna creates a series of files at 1-MHz intervals (from 2 through 30 MHz), a developer of type-13 files should use the specific operating frequencies of operation. In general, a single frequency within each amateur or similarly narrow band will suffice for accurate propagation forecasts. Consult the applicable directions within specific implementations of VOACAP for recommendations on how to correlate type-13 files with the actual use of the propagation prediction software.

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Why is it important for at least some modelers to develop type-13 files?

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Accurate propagation forecasting depends upon using a reasonably accurate far-field projection of the actual antenna used at the site that is interested in such forecasts. The term "reasonably accurate" is subject to all manner of external considerations. For some very generalized applications, one of the sample models usually included in the VOACAP package may be sufficient. However, the variety of antennas available and in use precludes replication of all of them at all heights and over all types of ground. Hence, a customized collection of type-13 files may be necessary.

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Ideally, one should develop a model of the entire antenna installation so as to show all potential interactions among the antennas and relevant non-antenna objects. This extensive modeling is practical under two conditions. First, all antennas should be fixed (that is, not rotatable). Second, the modeling program must have a very large maximum segment count in order to include all antennas and relevant objects. In most cases, practical models will include only the subject antenna.

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However, subject antennas should be modeled accurately. A generalized label, such as "3-element Yagi," may not be specific enough for critical applications. Fig. 2 shows the azimuth patterns in free space of 2 3-element Yagis at the same frequency. The difference between the two is the boom length (and its consequences for element placement and length). The result is a full dB difference in forward gain.

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Under some conditions, the use of a single frequency within an amateur band may not suffice. Some antennas show relatively equal gain across and amateur band, while others may show considerable differences between the low end (CW and digital) and the high end (SSB). Compare the gain curves for the two Yagis of similar boom length in Fig. 3. The gain values are identical at mid-band. However, the 6-element version varies only slightly from one band edge to the other. In contrast, the 5-element version varies in gain by nearly a full dB from one band edge to the other. For maximum accuracy, if needed, one might wish to create separate type-13 files for the 5-element Yagi, one for the lower end of the band and one for the upper end.

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One questionable presumption used by many amateur operators is to treat tri-band Yagis of similar boom lengths as having similar characteristics. Fig. 4 shows the azimuth patterns of two different designs at 100' above average ground. The figure lists the modeled maximum gain values for each design at the TO angle (10, 7, and 5 degrees for 20, 15, and 10 meters, respectively). Although both designs use 24' booms, the band-to-band performance is quite different. The differences include not only the maximum gain on each band, but also the rearward lobe performance.

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The illustrations make a case for developing type-13 files for the specific antenna in use at an amateur station at the height and over the ground that applies to the site. The modeled performance may differ considerably from the values used in antenna specification sheets. These considerations also apply to non-amateur antenna installations. Commercial and governmental installations often assume that vendor specifications sheets are precise or that calculations by internal engineering staff are transferable without checking to propagation programs. In most cases, a better procedure would be to model each antenna, using the actual values for height and ground conditions, with a single modeling core. For non-amateur use, NEC-4 may be the most generally usable package, since it allows the modeling of buried ground radials for any monopoles at the site. We cannot assume that propagation predictions are "accurate enough" using program samples until or unless we compare the results with those obtained from more precisely modeled versions of the site antennas. Of course, once we have more precisely modeled antenna far fields, we need not make the comparison, since the resulting type-13 files will take precedence.

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How can we make a type-13 file within NEC that is compatible with the most common propagation programs?

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1. The first step in developing a VOACAP type-13 file is to orient the antenna properly. Using ACE-HF as an example of a VOACAP propagation forecasting and analysis program, we may heed the following guidelines.

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1. The software assumes that all antenna patterns (or mathematical antenna models) have their main beam energy pointed at zero degrees azimuth (north).

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2. For a rotatable beam, like a Yagi or log-periodic, the user simply sets an azimuth angle after choosing the directional antenna model. The angle is on a spinner that can be set from 1 to 360 degrees. This action points the antenna toward a distant target along a great circle line, just as a real operator would point the antenna at his station.

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3. To simplify the setting, there is a "Point At" control, which when checked, automatically points the antenna toward the distant station along a predetermined path. There are independent controls to do this with antennas at both ends of a circuit.

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4. For the case where a station uses a directional antenna but leaves it at a fixed setting, then the user sets the azimuth to his preferred direction and does not use the "Point At" control. This means that stations not on his predetermined great circle path will receive radiation off the side of the antenna's main beam, and will be so simulated.

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5. For fixed directional antennas, like a horizontal rhombic or a sloping V, the user must know the physical direction in which his antenna's main beam is facing. He then merely sets the azimuth control to that fixed angle and avoids the "Point At" control.

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6. For fixed high-gain directional antennas like the curtain dipole arrays used in International Broadcasting, the azimuth-angle control may be used to simulate the use of phased feeds to create slew angles. In that case, the slew angles are usually expressed with respect to the main beam's nominal angle, so they must be added (or subtracted) from that nominal angle. (It is, of course, an approximation to "slew" such models by varying the azimuth setting in this manner. For more accuracy, use separate models for each slew angle, since patterns for each slew angle may vary slightly from the broadside pattern.)

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The obvious consequence of these guidelines is that initial type-13 files should point North to 0 degrees azimuth if the antenna is directional. For bi-directional arrays, such as a lazy-H or a W8JK flattop, one of the two main lobes, which are symmetrical on each side of the antenna-wire plane, should point North. There are a number of nearly symmetrical arrays, such as unterminated long wires, Vees, or rhombics having several wavelengths of wire per side. In these cases, the end with the higher gain, normally away from the feedpoint, should face north. Vertical arrays with more than one (omni-directional) element should also be set into type-13 files with the main-beam lobe facing north, with one possible exception. A number of broadcast arrays undergo development using compass-rose azimuth bearings and directions--often figured from one of the elements. Hence, they already have fixed geometric characteristics that correspond to world map standard. One might create a type-13 model directly from the developmental (and licensing) model, with the understanding that the subject antenna should make use of no azimuth-changing controls available within the VOACAP program. There are a number of vertical arrays with switchable main lobes, such as the 4-square and similar phased arrays. The modeler faces some alternatives in this type of case. One is to create a single model with the main lobe pointed North and then to use program controls to point the lobe in one of the four main directions corresponding to the switching arrangement. A second alternative is to create 4 separate immovable models, one for each of the main lobe directs referenced to a compass rose.

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The final class of cases does not readily admit to any primary direction. A center-fed doublet and a terminated folded dipole represent one subclass of this group. In this kind of case, one may create a single model and set the antenna wire lengthwise along one of the compass axes. Then, one would use the azimuth-changing control to orient the wire to reflect its position on the actual site. This procedure would be necessary if one uses a pre-set collection of files, such as the set of terminated folded dipoles included with the ACE-HF package. Alternatively, one may create a fixed antenna model with the wire length having the actual compass directions used at the site. This model would require that the propagation software user make no changes to the azimuth. A second subclass emerges when we use off-center feeding. When such a wire antenna is 1/2 wavelength long, its pattern is virtually identical to the pattern of a center-fed antenna of the same length. However, as the operating frequency increases, the patterns of an off-center-fed antenna depart from the center-fed pattern, but are not identical to the patterns of an end-fed unterminated wire (the so-called end-fed Zepp). Since the patterns at many operating frequencies will be asymmetrical, the modeler and the propagation software user must be very careful that the final orientation of the antenna corresponds to the physical layout. Otherwise, the stronger lobes of the model may not reflect the stronger lobes of the real antenna.

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If an antenna site has multiple antennas of different types, such as some that are rotatable, some that are fixed, and some that are switched, all propagation software users should be alerted to the rules that apply to each antenna at each frequency within the collection of type-13 files for which propagation analysis may be relevant.

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2. The second step is to coordinate the compass-rose bearing for the antenna, even if simply pointed North to 0 degrees compass azimuth, to the modeling software to be used. NEC operates by using phi angles that count counterclockwise from a 0-degree point that corresponds to the X-axis of the wire layout in the model. (NEC also uses the theta convention, but the simple conversion to elevation angles is normally an automated feature in NEC implementations.) To create a type-13 file correctly--taking into account any asymmetries in the pattern--the software must be able to convert to a compass-rose or clockwise azimuth pattern.

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The required conversion may occur in one of two general ways. Programs like NEC-Win Plus employ a polar plot graphic that places the X-axis in a vertical position and labels the top point as zero degrees. Hence, for a directional antenna such as a Yagi, the modeler simply lays out the elements that are broadside to the main directional lobe along the +/-Y-axis. When creating a type-13 file, the program "merely" interrogates the NEC output data for the radiation pattern in reverse order.

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EZNEC allows the creation of type-13 files at its Plus and Pro levels (beginning with Version 5.0 of the program). However, EZNEC creates polar plots using a different convention, with the X-axis aligned horizontally in the plot, so 0 degrees is to the right. This convention places 90 degrees, which corresponds to the +Y-axis, at the top. The program offers within the polar plot function a compass-rose alternative with 0 degrees at the top, but the direction still corresponds to the +Y-axis. Therefore, to use this option and to create a pattern with the main lobe pointing North, the modeler must set the Yagi elements along the +/-X-axis. Fig. 5 contrasts the two conventions by showing the same antenna oriented each way and the resulting polar plot using the compass-rose pattern option. There is a shortcut relative to type-13 files and we shall discuss this mode of model creation as we proceed in step 3.

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3. Creating an EZNEC VOACAP type 13 file is the final step in the process. EZNEC's latest version provides perhaps the easiest means of creating type-13 files that are compatible with virtually all versions of IONCAP and VOACAP. The process begins by setting the antenna at the desired height above a real ground that best approximates conditions at the antenna site. The sample antenna will be a 3-element Yagi at 100' above average ground.

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As indicated by the starred items in Fig. 6, the next requirement is to select a 3-D pattern and to set the increment to 1-degree, as required by the VOACAP file. The resulting plot, shown as an inset on the EZNEC main screen, is not usable in determining lobe structures. A more normal step for that work would be a 5-degree increment. However, our goal is not to analyze the lobe structure, but instead to produce the type-13 file. The plot is clear enough to reveal that the model has its main lobe directed along the Y-axis for direct use with the compass-rose set-up.

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After the calculation is finished, there are three places where you can initiate the file writing action. If you chose the 3-D plot option, open the File menu in the 3D Plot Window, and select Write IONCAP/VOACAP File. If you chose the far-field table option, you can click the Write IONCAP/VOACAP File button at the lower left of the formatting dialog box which opens when the calculation is complete, or you can choose a format and use the option to write the IONCAP/VOACAP file in the File menu of the tabular data display. We have chosen the Plot rather than the Table option to verify that we have everything in the model correctly oriented. Therefore, we shall open the File option within the 3-D Plot window.

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The program will offer an option to "Write IONCAP/VOACAP File." Had we chosen to create a table rather than a plot, we would have received the same option. When we select this option, the program offers a default directory for storing such files, although the user may select a different directory. Use the earlier notes to give the file a distinctive name, perhaps identifying the operating frequency and the antenna type, with possibly a ground code, if relevant. EZNEC will add the extension .13. The program will write the file, virtually instantly on most modern computers. Fig. 7 shows the first 3 degrees of azimuth for our sample model with the main lobe oriented toward North as defined by the +Y-axis, corresponding to the EZNEC convention for compass-rose patterns. The antenna description line is seriously deficient for use in any serious context.

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The same process can be used with the pattern that we obtained when we oriented the main lobe along the X-axis. We assign a ground, select a 3-D pattern with an increment of 1-degree and obtain the 3-D pattern shown in Fig. 8. Again, the pattern itself has only one main use: to keep us informed about where the main lobe lies.

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When we select the option to write the type-13 file and choose a directory and filename, EZNEC will flash a new screen that only appears when the main lobe bearing does not coincide with the compass-rose North bearing. Fig. 9 shows this screen, which gives us the option of letting the plot value of 0 degrees be North or of setting the main lobe's maximum gain bearing to be North. Since we are dealing with a rotatable beam, we select the pattern maximum as the file's 0-degree bearing.

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If we had set in place an antenna having a fixed position and had already used coordinates that correspond with the real antenna, we likely would have received the same set of options. However, we would have chosen to let the plot North be the file's 0-degree bearing. Likewise, we might have set up a fixed antenna for multi-band use with the prospect of rotating it to its fixed position within the propagation program. For such an antenna, we might have files at many frequencies, reflecting a wide range of use. The patterns for each frequency would differ. In such a case, each frequency's type-13 file would again opt to let North = 0 degrees. Using the option of allowing the pattern maximum to be north applies only to rotatable and other directional antennas whose azimuth we may set within the propagation program.

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Fig. 10 shows the first three azimuth entries for the Yagi's pattern maximum = 0 degrees selection. Compare this partial file to the corresponding entries in Fig. 7. The values are identical, since the antenna has not changed other than turning 90 degrees. (In fact, I created the earlier compass rose version of the Yagi by rotating the present version by 90 degrees. The type-13 file creation function performed the same action, but at a different stage, namely, by operating on the NEC output radiation pattern data.)

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Conclusion

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The Yagi samples with which we have experimented are, of course, simplistic, since their main function was to show a procedure and process, not to produce a type-13 file for an actual antenna. That fact is clear from the incomplete file descriptions in the first line of each type-13 file. A more complete model would have used the stepped diameter structure for the actual antenna structure. As well, it might have included relevant surrounding objects, including inert antennas for other frequencies that we might have stacked above or below the subject antenna. In all cases, a serious type-13 file would have used the antenna's actual height above ground and would have included the most accurate ground specification one might be able to derive from local sources or measurements. (Ground quality precision is less important for horizontal antennas than for vertical antennas.) The degree of model complexity will always be a user judgment.

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Nevertheless, the addition of VOACAP type-13 file capabilities to NEC software provides a means for both amateurs and professionals to make better use of propagation software in the pursuit of more reliable communications.

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Go to Main Index

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Modeling Radiating Surfaces

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L. B. Cebik, W4RNL

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The notes in this exercise derive from my attempts to determine if it is possible to model with reasonable accuracy the results obtain by an experimental exercise conducted in 1952 by two RCA researchers, George H. Brown and O. M. Woodward, Jr. Among their numerous contributions to the development of VHF and UHF antennas, including the emergent television antenna industry, was an experimental characterization of conical and triangular antennas. (See "Experimentally Determined Radiation Characteristics of Conical and Triangular Antennas," RCA Review, Dec., 1952, pp, 425-452.) The work eventuated in the widespread use of solid-surface fan dipoles in TV antennas, especially for the new UHF channels from about 480 to 920 MHz. It even resulted in the bent bow-tie dipole used in corner-reflector TV antennas. I had some limited success in capturing in NEC models some, but by no means all, of the capabilities of the corner reflector with a bent bow-tie in Planar and Corner Reflectors. +

Brown and Woodward wanted to experimentally characterize the properties of bi-conical dipoles and fan dipoles, antennas that had undergone extensive theoretic analysis, but with what Brown and Woodward saw as "simplifying assumptions and approximations in order to satisfy the required boundary conditions and to reduce the mathematical difficulties." (p.425) As shown in simplified form in Fig. 1, they reduced the dipoles to UHF solid-surface monopoles with a very large highly conductive ground-plane surface to simulate a perfect ground (PEC).

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The practical interest in these antenna types does not involve their 1/2 wavelength impedance. Instead, it involves the impedance and radiation properties of these antenna shapes as they approach and surpass a 1 wavelength electrical length at a given operating frequency. A linear dipole shows a very high impedance at 1 wavelength, with regular repetitions of the impedance peak at integral multiples of that length. However, the biconical shape shows a regular decrease in the peak impedance as the angle formed by opposite sides of the cone gradually increases. At very large angles--about 60 degrees apex angle--the reactance swing associated with a linear dipole decreases to a level that is manageable for wide-band antenna service. In addition, the difference between the impedance at odd multiples of 1/2 wavelength and integral multiples of 1 wavelength also decreases. As a result, the biconical shape--with a sufficiently large apex angle--results in the potential for an antenna with a 300-Ohm SWR of less than 2:1 over a very broad frequency range. For reasons of pattern shape that we shall see along the way, VHF and UHF use of the phenomenon is limited to about a 2:1 frequency range. This characteristic is eminently convenient for TV antennas that typically use a 300-Ohm feedpoint impedance.

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Since the biconical dipole is somewhat complex as a manufactured item, Brown and Woodward also explored the easier-to-make flat triangular dipole, again with a solid surface. For equivalent apex angles, it showed similar characteristics, but not quite as flat a bandwidth impedance as the biconical antenna. However, the result was good enough to allow Brown and Woodward to report on a successful flat, solid, fan dipole using a 60-degree apex angle to cover 480 to 920 MHz with a 300-Ohm SWR level of less than 2:1.

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The Modeling Interest

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A number of questions arise from the Brown and Woodward work for the antenna modeler. First, one may ask whether it is possible to replicate in models the core of the Brown and Woodward experimental effort. Given the use of solid surface cones and triangles in the original experiments, this question does not have as easy an answer as we might like to give. NEC employs round wires to model the geometry of radiating elements. Its surface-patch facilities were intended to simplify the construction of surround bodies and objects--such as the hulls of ships--that might affect the antenna's radiation characteristics. Their function was not intended to serve as radiating elements with direct voltage sources. Hence, the NEC surface patches use considerably simplified equations to speed core runs. If we are to simulate the Brown and Woodward antennas, we must use round wires to form the surfaces.

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The second question that we shall explore is whether we may extrapolate the VHF/UHF results using solid-surface antenna elements down to the HF range. Wide-band center-fed elements have proven to be highly desirable over the decades since the Brown and Woodward paper, for example in curtain arrays for both SW broadcasting and over-the-horizon HF radar systems. However, the ability to extrapolate the experimental results will depend upon our ability to translate solid surface structures into structures using individual wire elements components. Hence, from the perspective of modeling, the first question is the key to the second. Although we may easily model wire-based extended-range elements at HF, relating their properties via models to the Brown and Woodward experiments requires that we be able to successfully (within reasonable limits) model the solid surfaces with round wires.

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The Biconical Dipole

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One advantage of modeling in NEC is that we may proceed directly to the biconical dipole and not pass through the monopole stage. Modelers have long known that we may model a solid-surface biconical dipole with reasonable success by using a collection of longitudinal wires, so long as we use enough of them. Fig. 2 shows the outline of a bi-conical dipole with a 40-degree apex angle. Each cone uses 12 wires. Experience has shown that there is very little difference in the output of models using 12, 25, and 45 wires per cone. To achieve a usable average gain test score (AGT), the more wires that we use, the thinner must be each wire, since all cone wires meet at a junction. As we increase the number of wires, the angle between wires at the junction becomes narrower, increasing the length along the first segment of each wire in which we have surface interpenetration for a given wire size. As we add more wires, the interpenetration increases unless with use thinner wires. In addition, the length and segmentation of the center or source wire connecting the two cones may require custom treatment to achieve the AGT score nearest to the ideal.

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The simulated biconical dipole in the figure is 16.8" long, with an end diameter of 5.2". The wire diameter is 0.002". The intended useful frequency range for the antenna is from 480 MHz to at least 920 MHz, to coincide with the Brown and Woodward TV fan dipole. To achieve this range, the 1/2 wavelength self-resonant frequency of the antenna is about 231 MHz in this free-space model. However, we are not interested in the first self-resonant point. Rather, we are interested in the antenna's behavior as it approaches and passes 1 wavelength.

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The biconical dipole meets the Brown and Woodward requirements for a UHF TV dipole. Those requirements include having a bi-directional pattern and a 300-Ohm SWR that is less than 2:1 across the passband. Table 1 shows the key antenna characteristics and the AGT value (with adjusted gain values) at the passband ends and at the approximate geometric mean frequency.

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+Table 1.  Biconical dipole performance
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+Frequency     Source Impedance     300-Ohm     Raw Gain     AGT     AGT-dB     Adj. Gain
+MHz           R +/- jX Ohms        SWR         dBi                             dBi
+480           346 + j187           1.80        2.59         1.012   0.05       2.54
+665           345 - j 58           1.26        3.32         1.012   0.05       3.27
+920           167 + j 33           1.83        3.30         1.012   0.05       3.25
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With respect to the desired SWR values, the tabular entries seem to describe a curve. The bottom half of Fig. 3 confirms the impression. The top half of the figure extends the SWR curve to 1500 MHz to establish the general pattern of biconical behavior. As we increase the electrical length of the antenna by increasing the operating frequency, the resistive and reactive components--as indicated indirectly by the SWR values--continue to decrease the difference between the values at odd multiples of a half wavelength and integral multiples of a full wavelength. In short, the higher the frequency of operation or the longer the antenna length for the 40-degree apex angle biconical antenna, the flatter the SWR curve grows.

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Our interest in this behavior is not to establish it. That has long been done via theoretical analysis and physical experimentation. Our interest lies in seeing whether the 12-wire biconical model can effectively and reasonably capture that behavior. The model does that job. There are variations on the model that will affect its dimensions, but with no great change in the results. For example, we may connect the outer ends of the cone wires to form a circle. Essentially, the end wires add length to each individual wire, a length that is roughly but not exactly half the distance between the wire tips. Hence, for the same performance curve, we would have to reduce the physical length of the cone. As well, adding or subtracting wires from the assembly will slightly change the required length for the same performance curve, although each such change should be accompanied by a change in the wire diameter within the limits of NEC's ability to handle angled junctions of wires at the center.

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Applications for the biconical antenna in TV antennas that might make use of a planar or a corner reflector rarely make use of the extended impedance stability of the antenna shape. All such arrays depend upon using a fed element with a bi-directional pattern. Fig. 4 shows sample free-space E-plane patterns for the biconical dipole within the passband of intended use with one extra pattern a bit beyond the upper limit.

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A linear dipole would show multiple lobes with stronger angular lobes than broadside lobes by the point at which the antenna is about 1.5 wavelengths long. The biconical dipole extends the range of bi-directional patterns to nearly the 2 wavelength point, although the 920-MHz pattern shows significant but non-fatal sidelobe development. By 1150 MHz, the pattern has become completely useless for a directional beam with a planar or corner reflector. (We shall be interested in comparing these patterns with a corresponding set for a flat-face fan dipole.)

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For some applications, the change in pattern is less important. For example, scaled by a factor of 100, the antenna would provide a very wide-band antenna for general purposes. The lowest frequency would by about 4.8 MHz, with an undetermined upper limit for a 300-Ohm feedpoint impedance that would not require a tunable matching network. A single transformation of 300 Ohms to 50 Ohms (by way of a balun) would satisfy the impedance requirements for most common transceiving equipment.

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The limitation for this antenna is that it would require a length of 140' with end diameters of 43.3'. As well, it likely would require considerable mounting height to overcome the effects of ground proximity on the feedpoint impedance across the operating span. The scaled wire size would be 0.2", equivalent to AWG #4 wire. However, one might easily use thinner wire by increasing the number of wires in each cone. With an additional scaling factor of 2, the antenna would cover 80 through 10 meters. If we increase the added scaling factor to 2.7, we might add 160 meters, but the chances of having a support system that would handle 115' diameter ends at a sufficient height to avoid deleterious ground effects on the source impedance would dwindle to the day-dream level.

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Our notes on modeling a biconical dipole have not sought to establish a number-by-number correlation to the Brown and Woodward experiments using a mono-conical element with a perfectly conducting ground-plane surface. Rather, our goal has been only to establish that we can simulate a biconical dipole with NEC's round wires. The successful result is not surprising, since there are many examples of physical antennas that employ the same technique. In fact, there are HF discones, a first cousin to the biconical dipole and a more immediate kin to the Brown and Woodward test antennas, that employ wire structures for successful operation.

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A Model of a Solid-Surface Fan (Triangular) Dipole

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Brown and Woodward also reported on their experiments with a triangular monopole using the same large highly conductive ground plane surface. The antenna was equivalent to one-half of a fan dipole. However, as suggested by Fig. 5, their element used a solid sheet rather than a simple outline of a fan. To see something of the performance difference, Table 2 provides performance figures for an outline fan dipole that is 14" from one end to the other and 7.8" tall at the ends. The apex angle is 60 degrees so that the element half, exclusive of the short center source wire, forms an equilateral triangle. This shape is very close to the UHF fan dipole created by Brown and Woodward for use from 480 to 920 MHz.

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+Table 2.  Fan outline dipole performance
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+Frequency     Source Impedance     300-Ohm     Raw Gain     AGT     AGT-dB     Adj. Gain
+MHz           R +/- jX Ohms        SWR         dBi                             dBi
+480           718 + j190           2.59        3.32         1.010   0.04       3.28
+665            93 - j276           6.13        6.42         1.018   0.08       6.34
+920           337 - j212           1.95        0.37         1.012   0.05       0.32 (multiple lobes)
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In effect, the fan outline operates more like a linear dipole than a biconical dipole. With a half wavelength resonance at 250 MHz, the 4-lobe structure at 920 MHz is an approach to an electrical 2 wavelength equivalent. To obtain performance that more closely approaches the Brown and Woodward results, we must fill the outline to simulate a solid surface. The right side of Fig. 5 shows the pattern used in the test model. One triangle results from an exercise using NEC-Win Synth and saved as a .NEC file. The 60-degree triangle was then re-opened in EZNEC Pro/4 v.5 as an incomplete model. EZNEC prefers to create models by using a single wire between junctions, but does accept without an error report a set of wires where wire crossings occur at segment junctions. I moved the triangle to one correct position for a dipole half and then replicated the structure and rotated it by 180 degrees to form the other dipole half. A short connecting wire between triangle apex points for the source completed the model.

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To simulate a solid surface requires that we use a sufficient wire diameter. Selecting the diameter is a compromise between true electrical solidity at all operating frequencies and an acceptable AGT score. A 0.1" diameter wire yielded AGT values that averaged about 1.06, not quite ideal but usable on the premise that we are seeking the operating trends and not construction guidance from the model. Table 3 provides the reported data from the model at the three sample frequencies. The half wavelength self-resonant frequency for the model is 252 MHz.

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+Table 3.  Wire-grid fan dipole performance
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+Frequency     Source Impedance     300-Ohm     Raw Gain     AGT     AGT-dB     Adj. Gain
+MHz           R +/- jX Ohms        SWR         dBi                             dBi
+480           278 + j194           1.94        2.91         1.057   0.24       2.67
+665           392 - j 56           1.37        3.89         1.059   0.25       3.64
+920           171 - j 61           1.86        5.42         1.067   0.28       5.14
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The SWR values are much closer to the biconical of Table 1 than they are to the fan outline values of Table 2. In fact, the SWR curve at the bottom of Fig. 6 is very close to the curve obtain by the Brown and Woodward fan dipole (Fig. 42 on p. 452 of the referenced article). The upper portion of the SWR charts shows the extended SWR curve to 1500 MHz. It almost replicates the smoothness of the corresponding biconical curve but shows a slight compression of values relative to frequency, suggesting that the wire-grid simulation of the flat fan dipole does not achieve the broad-banding effect to the same degree as the biconical element.

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The gain data for the wire-grid simulation of the fan does not quite match the performance reported by the Brown and Woodward experimental solid-surface fan. If we subtract the gain of a linear dipole (about 2 dB) from the values on the Brown and Woodward curve, the gain curves correspond. However, the pattern shapes reported by Brown and Woodward do not coincide with the curves in Fig. 7. The Brown and Woodward pattern for 920 MHz shows no sidelobe development, although the wire-grid fan pattern for the same frequency shows moderate sidelobe strength. By increasing the wire diameter of the wire-grid simulation of the solid surface, it is possible to reduce the sidelobe development in the 920-MHz pattern, but the model becomes wholly unreliable before the sidelobes diminish completely. Hence, the model fails to capture the pattern shapes reported by Brown and Woodward for the upper end of the operating spectrum.

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Although outside the operating passband of the antenna, the additional pattern for 1150 MHz allows some initial comparison with the performance of the biconical dipole at the same frequency. With respect to gain and pattern formation, the flat 60-degree fan shows a broader bandwidth than the 40-degree biconical antenna. The 1150-MHz pattern still shows the broadside lobes that are characteristic of a linear dipole just slightly longer than 1.5 wavelengths. In contrast, the biconical pattern at the same frequency displayed a pattern closer to a 2 wavelength linear dipole. The difference is largely due to the difference in the self-resonant half wavelength frequencies needed to obtain the desired SWR curves in the defined operating passband.

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The wire-grid fan dipole does manage to capture most of the data reported by Brown and Woodward for their UHD TV dipole, even if imperfectly. It also shows its relationship to the biconical shaped element and to the fan outline element. However, there are alternative structures used historically to simulate a solid flat fan shape. We now have enough modeling data that we are positioned to evaluate them as potential methods of capturing the Brown and Woodward solid-surface fan dipole.

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The Multi-Wire Fan Dipole Model

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One popular way sometimes used in the HF range to simulate a solid surface in a fan dipole is the use of a series of wires in each fan triangle, with each wire extending from the apex to the opposite side. Fig. 8 shows such a structure using 5 wires. In all dimensions, the fan dipole is identical to the wire-grid simulation of a solid surface. It is 14" from end to end and 7.8" high at the outer ends, with a 60-degree apex angle. The wire diameter for this model is also 0.1". The question for modeling is whether this model, much simpler to form, is an adequate simulation of the solid surface antenna upon which Brown and Woodward developed their data.

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If we were concerned about the half wavelength self-resonant performance of the antenna, the simplified model might serve. The self-resonant frequency is 260 MHz, which is not far from the 252-MHz self-resonant frequency of the wire-grid version. In both versions, the highest current occurs relatively close to the apex of each triangle, where the wire density in the multi-wire version is highest. However, the stable impedance performance of the solid-surface fan antenna depends upon using the antenna at a length that approaches and passes 1 wavelength. Current maximums occur at positions well away from the center source wire. In the multi-wire version of the fan dipole, the wire density diminishes steadily as we move away from the center source wire. Table 4 shows some of the consequences of the decreasing wire density toward the fan ends.

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+Table 4.  Multi-wire fan dipole performance
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+Frequency     Source Impedance     300-Ohm     Raw Gain     AGT     AGT-dB     Adj. Gain
+MHz           R +/- jX Ohms        SWR         dBi                             dBi
+480           285 + j188           1.87        2.79         1.027   0.12       2.67
+665           382 - j 76           1.39        3.86         1.048   0.20       3.66
+920           149 - j 58           2.10        5.68         1.077   0.32       5.36
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The results are both promising and disappointing. In some respects, the impedance data appears to be comparable to the data in Table 3 for the wire-grid model. However, the resistive component of the multi-wire model's impedance has a wider range of variation across the operating passband than we find in the wire-grid model's data. The consequences for the 300-Ohm SWR curve, in the lower half of Fig. 9, are a reduction in the 2:1 SWR bandwidth. The extended SWR curve at the top of the same figure shows essentially the same general pattern that we found in the wire-grid curve (Fig. 6), but with a much wider variation in value.

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With respect to gain and pattern shape, the multi-wire model using relatively fat (0.1" diameter) wires shows less variation from the wire-grid model than the SWR curves. The adjusted gain values are similar for the two models. As revealed by Fig. 10 (when compared to Fig. 7), the pattern shapes are very nearly twins, even at 1150 MHz. For some purposes, the simpler multi-wire model may be a suitable substitute for the more complex wire-grid model. However, the multi-wire version alone does not disclose its shortcomings with respect to capturing the solid-surface SWR curve.

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The 60-degree fan dipole might form a wide-band antenna in the HF range with suitable scaling. Roughly speaking, scaling the dimensions by a factor of 100 would yield an antenna theoretically covering 4.8 thought 9.2 MHz--and beyond, if the pattern shape is not a matter of concern. The resulting antenna would be a bit under 117' long with an end spread of 65'. However, the limiting factor in the scaling is the requirement to multiply the wire diameter by 100 to maintain the wire density. 10" diameter conductors generally fall outside the realm of feasibility for most (but by no means all) installations.

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The temptation is to use common wire sizes. The original UHF model wire is 0.1", corresponding closely to AWG #10 wire. If we retain this practical wire size, the multi-wire model loses its ability to capture the properties of a solid surface. In the UHF model, the wire size would scale to 0.001". Table 5 provides the kind of data that we obtain for such a model (and for an HF antenna using 0.1" wire).

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+Table 5.  Multi-thin-wire fan dipole performance
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+Frequency     Source Impedance     300-Ohm     Raw Gain     AGT     AGT-dB     Adj. Gain
+MHz           R +/- jX Ohms        SWR         dBi                             dBi
+480           289 + j391           3.48        2.50         0.965   -0.15      2.65
+665           864 - j 29           2.89        3.71         0.967   -0.15      3.86
+920           155 - j102           2.23        6.01         0.975   -0.11      6.12
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The impedance information from the thin-wire version of the 60-degree fan dipole shows very large excursions of both resistance and reactance. The 300-Ohm SWR curve for the operating range in Fig. 11 shows only one sudden dip below the 2:1 level, behavior that we might normally associate with a linear dipole/doublet at the self-resonant 3/2 wavelength mark. The frequency of the SWR minimum is 710 MHz in the model.

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The association of the thin-wire model with the behavior of a linear doublet also shows up in the sample free-space E-plane patterns, shown in Fig. 12. The 920-MHz pattern is especially interesting for the crisp sidelobes, similar to those we might find in the pattern for a 1.25 wavelength center-fed wire. All of the broadband patterns for both the biconical element and the fat-wire fans show far less of a null between the sidelobes and the main bi-directional lobes. The crispness of the lobe structure in the thin-wire model carries over into the pattern for 1150 MHz. Compare the null depth values to those in Fig. 10 for the fat-multi-wire version of the same antenna.

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In models and in physical antennas using multiple wires to simulate the performance of a solid surface, wire diameter and wire density both make a difference to the performance. As a fan element decreases the wire diameter without increasing the number of wires, the antenna gradually creases to perform like a solid surface. It becomes a version of a linear wire antenna with a somewhat wider bandwidth at the 1/2 wavelength resonant frequency region. However, using the necessary wire diameter and increasing the wire density are strategies that have undesirable consequences in physical antennas.

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Conclusion

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This exercise has explored the modeling of solid surface antennas, so easily fabricated for UHF frequencies, through the use of various round-wire modeling techniques. The Brown and Woodward experimental data from 1952 provided a standard against which we could measure to some degree the success of the modeling techniques. Biconical properties, with a few reservations, prove amenable to using a multiple-wire simulation, a method reflected in the construction of practical biconical antennas.

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The flat solid-surface fan elements explored by Brown and Woodward required that we use some form of wire-grid structure to simulate the surface adequately. Even fat-wire models composed of multiple linear elements showed some departure from the performance curves in the original experiments. As we discovered in the final exercise, the use of wires that are too thin degraded the performance from its desired levels completely with respect to broadband coverage.

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Even the wire-grid model failed to capture every nuance of solid-surface performance. Nevertheless, it proved productive to capturing most of the data experimentally derived by Brown and Woodward. Within the range of what the model successfully simulated and in what ways it fell short lie some lessons for effective modeling.

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Go to Main Index

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Receiving Directivity

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L. B. Cebik, W4RNL

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A number of years ago, a Ham suggested a somewhat different way of looking at the directivity, one especially applicable to receiving antennas, and--more specifically--receiving antennas designed for the lower HF and upper MF portions of the spectrum. In these regions, amateurs (and others) often use separate receiving antennas, many with very low gain. The goal is not forward gain, but an acceptable signal-to-noise ratio. Many receiving concepts, dating back to the original Beverage antenna, place antennas relatively low to the ground to reduce noise levels. In the process, they sacrifice one of the seemingly holy grails of antenna work, gain. However, these antennas, including the K9AY, the EWE, and others, provide very low-level signals, but even lower noise levels. Since modern receivers tend to have surplus gain, whether inherently or with pre-amplification, the resulting received signal improves its strength over the noise, with resulting improvements in readability. +

Despite their low gain, many of the low-band receiving antennas exhibit strikingly good directivity. Conventionally, we might think that one of the available versions of a front-to-back ratio might suffice to characterize the directivity adequately. However, if we review the various front-to-back ideas, we may soon learn why they may not be suitable to the special needs of low-band receiving antennas.

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Conventional Front-to-Back Ratios

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The language of upper HF directional antennas has grown very conventionalized over the decades. It rests on a 2-dimensional graphic portrayal of the far-field pattern of a directional beam, such as a Yagi-Uda array. Fig. 1 provides some of the key elements in the usual pattern description that we find in much literature. We find variations in some of the terms and in the style of the graphics used to present the pattern, but the terms shown in the sketch are very usual ones.

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One key to our discussion is the clear directivity of the pattern that allows us to distinguish forward and rearward lobes that represent gain maximums in the various directions. The pattern appears in normalized form, that is, with the maximum antenna gain just reaching the outer ring of the background scale. Other presentations either with a different level of gain for the outer ring or with a different scale for inner rings are possible and often useful. The key property of the pattern and its parts is the fact that it is a 2-dimensional portrayal. In free-space, the pattern represents the E-plane of the antenna, in this case a 3-element Yagi array. Over ground, the pattern would use a constant elevation angle. We normally select either the take-off angle, that is, the elevation angle of maximum gain, or some other elevation angle of special interest, such as the elevation angle dictated by a propagation forecast for strongest signals into or out of a target communications area.

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The 2-dimensional nature of the pattern has yielded the concept of the front-to-back ratio as a measure of directivity. First, not everyone uses the basic term in the same way. So we shall find some refinements in the terminology. Second, not everyone who uses the refined terminology uses it in the same way. Table 1 and Fig. 2 will be our guides, but only for part of the journey. Both the table and the graphic present information on the rearward performance of 3 sample antennas. Numbers and pictures do not always determine how people use words. Our first step will be to present some initial definitions (with modifications to come). These definitions will coincide with the labels in Table 1. The 180° front-to-back ratio is the main lobe forward gain (or the maximum antenna gain) minus the gain of the lobe (however big or small) that is 180° away from the heading of the maximum forward gain. This value of front-to-back ratio is most commonly used in general antenna literature and is the one shown in most NEC antenna software. If the main forward lobe is split or does not align with the graph heading, the 180° front-to-back ratio is 180° away from the direction of maximum pattern strength. Hence, the value may not be for a heading directly to the rear of the antenna structure. Since a Yagi is usually symmetrical, the maximum gain will normally be directly forward, and the 180° front-to-back ratio will indicate the relative strength to the direct rear. Note that if we use a normalized scale, we can read the front-to-back ratio directly from the plot--between 25 and 30 dB relative to the maximum gain of the antenna in the leftmost pattern.

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In Fig. 2, the leftmost pattern comes from Fig. 1. The strongest rearward lobe is 180° from the main lobe. However, the center pattern shows a 180-degree gain of very tiny proportions. Hence, the 180° front-to-back ratio is very large (over 40 dB compared to a "mere" 27 dB for the leftmost pattern). Yet, we find rearward lobes that have considerable strength. The line through one of those lobes indicates the direction of maximum strength. It is only about 22 dB weaker than the maximum gain. Some sources call this the worst-case front-to-back ratio, and its value is the maximum forward gain minus the highest value of gain in either rearward quadrant. For this antenna, the 180° front-to-back ratio does not give a true picture of the QRM levels from the rear, so some folks prefer to use this figure as a better indicator. The worst-case front-to-back ratio provides the most conservative value for rearward suppression of QRM. The rightmost graphic in Fig. 2 shows that the 180° and the worst-case front-to-back values do not require separate lobes, even thought the values differ. (We may debate elsewhere whether the 8-element Yagi main rearward radiation is a single main lobe or a junction of 3 overlapping lobes.) When we find the two ratios related to the same rearward lobe, we usually do not find much difference in their value.

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We are not done with front-to-back ratios. Each sketch in Fig. 2 contains an arc going from 90° on one side of the line of maximum gain around the rear to the other point that is 90° from the maximum gain line. Suppose that we add up all of the gain values at the headings that pass through the arc. Next take their average value. Subtract the average gain value to the rear from the maximum forward gain and you arrive at what some call the front-to-rear ratio. Others call this the averaged front-to-back ratio. Table 1 performs this task at 5° intervals, which is sufficient for this sampling. If you compare the front-to-rear ratio with the other front-to-back ratios, you can see why an antenna maker might use it. The value is higher than all of the other values (with the exception of the 180° front-to-back ratio for the 3-element short-boom Yagi). The rationale behind using the front-to-rear ratio is that it provides an averaged total picture of the rearward QRM suppression.

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The 2-dimensional scheme works reasonably well in characterizing the directivity of antennas used from the middle of the HF region through the UHF portion of the radio spectrum. In most cases, we are concerned with the rearward quadrants at angles equal or close to the elevation angle that we select for the forward lobe. However, even within this region, the scheme has limitations, especially the versions of the front-to-back ratio intended to overcome limitations of the 180° version. Fig. 3 offers just two samples.

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The conventions of front-to-back ratios arose largely with the Yagi array in mind. One feature of these antennas is that in the E-plane, the array exhibits a very deep null 90° away from the main forward direction. Therefore, the use of a 90° convention to set the limits between forward and rearward lobes seemed quite natural. The far-field pattern on the left in Fig. 3 is for a Moxon rectangle in a horizontal orientation. The deep side nulls do not occur at 90° from the main forward bearing, but somewhere between 110° and 120° from that bearing. An automated system for determining the worst-case front-to-back ratio, such as found in NSI software, would identify the worst-case rearward lobe bearing at 91° from the main forward heading. Whether or not this bearing deserves such an identification falls outside of our discussion, but the quandary is clear.

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The right side of Fig. 3 shows a pattern that is typical of many phased vertical arrays. In one sense, there are no rearward lobes, but only a single deep null 180° opposite the direction of maximum gain. From the pattern alone, it is not clear whether any of the font-to-back ratio conventions except the 180° version has appropriate application to such patterns.

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Re-Thinking Directivity

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In the lower HF and the MF portions of the spectrum, noise is a much more important and fundamental factor for receiving antennas than it is at higher frequencies. Noise may come from any direction, ranging from ground-wave paths to very high-angle propagation routes. As well, many more of the antenna used at lower frequencies have cardioidal and similar patterns such as the one on the right in Fig. 3. Together, these facts showed some of the shortcomings of the conventional front-to-back ratio ideas as a measure of receiving antenna directivity. Over the years, two efforts emerged to overcome these failings of the 2-dimensional system.

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DMF: The first of these systems of finding a replacement for the front-to-back ratio emerged from the work of John Devoldere, ON4UN, whose book, Low-Band DXing has acquired just fame. John calls his concept the Directivity Merit Figure (DMF). ON4UN calculates the average gain in the entire back azimuth half of the antenna, from 90° to 270° (where the bearing of maximum forward gain is presumed to be 0°), and over the entire elevation range from 2.5° to 87.5°. Doing all of this at 5° increments means that he considers 666 gain values. The average rearward gain now is the average of 666 values. Fig. 4 shows the rearward areas evaluated as elevation and azimuth slices of a 3-dimensional pattern (for a phased 2-element vertical array). He then defines a figure of merit for the directivity (front response to back half-hemisphere) as being the difference between the forward gain at an optimum wave angle (for example, 20°) and the average rearward gain. (See Chapter 7 of the most recent edition, section 1.8, page 7-8.)

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The process requires a separate utility program, since John compensates for the changing equivalent physical distance between angular points on the azimuth rings for different elevation angles. The elevation angles extend from 2.5° to 87.5° because NEC does not calculate a far field at 0°, that is, at ground-wave level using the RP0 command for real lossy, ground. (NEC does allow RP1 ground-wave analysis as a separate command, although this command may not be available on entry-level implementations of NEC.)

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DMF has the advantage of allowing a comparison of any bearing with a specific azimuth and elevation setting against the full rear half-hemisphere of the pattern. Hence, it takes into account the sensitivity of the pattern to noises from virtually all angles, as well as the various vertical as well as horizontal lobes and nulls in the rearward pattern. However, the advantage may also be a disadvantage insofar as noise may come from any direction. Hence, DMF provides a rough directivity figure that extends the concept of the averaged front-to-rear idea, but it does not directly provide an indicator of the overall directivity of an antenna with respect to sorting noise from signals in the desired direction.

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RDF: Several years ago, one Ham suggested an alternative analysis with several simplifying steps for antenna modelers and some inherent advantages over the DMF measure. This Ham's Receiving Directivity Factor (RDF) compares forward gain at a desired direction and elevation angle to average gain over the entire hemisphere. RDF includes all areas around and above the antenna, considering noise to be evenly distributed and aligned with the element polarization. (See Chapter 7 of the most recent edition of Low-Band DXing, section 1.9, page 7-9.)

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The RDF measure rests in part on the same calculations used to determine the value for the Average Gain Test (AGT). To obtain the average gain test value for a given antenna, the modeler removes all resistive loads, including the material conductivity of the model wires. The one sets up an RP0 command with an even spread of both azimuth and elevation (phi and theta) points. For most purposes, a 5° increment will suffice, but some complex patterns may require a small increment. In free space, the request will include a complete sphere, while over perfect ground, the request will create a hemisphere of sampling points. Fig. 5 shows the difference in the 3-dimensional pattern produced, in one case a phased 2-element vertical array and in the other a simple vertical dipole.

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To obtain the average gain, the RP0 XNDA entry should be either 1001 or 1002. The former prints the radiation pattern values plus the average gain data, while the latter prints only the average gain information. The following line is the NEC output report of the average power value for a simple monopole over perfect ground.

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AVERAGE POWER GAIN= 1.99891E+00       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
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A free-space pattern would have shown a value of 4 * PI steradians, and the value--assuming a very good model, would have been very close to 1.00000E+00. However, over perfect ground, the solid angle value is 2 * PI steradians, and the value of the very good model is close to 2.00000E+00. To remove any ambiguity, programs like EZNEC perform the necessary division to arrive at an AGT score over perfect ground that is consistent with the free-space value, in this case, 0.99945E+00.

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All AGT values are convertible to gain correction values in dB. 10 times the log of the AGT score (relative to 1.00000) yields the correction factor, which the modeler should subtract from the raw gain reported by NEC. In the sample case, no correction is necessary because the value is so close to the ideal. In fact, there is no universal standard of how close the AGT value should be to 1.00000 to be truly adequate. The allowable range of variation depends upon the specific modeling task. However, as we progress toward a hopefully reliable RDF measure, the initial AGT should be as close to 1.00000 as the modeler can make it. The AGT value is a measure of model adequacy and stands as a necessary but not a sufficient condition of true model adequacy.

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When we place an antenna over real lossy ground, we may still request the average gain via the RP0 XNDA values of 1001 or 1002. However, the value that we obtain will be significantly lower than the AGT value used to evaluate model adequacy. Consider a vertical monopole with 4 radials only a few feet above average ground (conductivity 0.005 S/m, permittivity 13). A sample model that includes material losses under these conditions returns the following report.

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AVERAGE POWER GAIN= 5.72269E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
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The average power gain for this example over ground is 1/2 the value shown or 2.86135E-01 relative to a standardized gain of 1.00000E00. One useful interpretation of this value is as a measure of radiation efficiency (in contrast to the power efficiency value provided by the NEC power budget section of the output report). Essentially, the antenna is almost 29% efficient relative to radiation in the far field. Like the AGT value, the average gain report is convertible to a gain value in dB by the same calculation used earlier. In this case, the calculation returns -5.43 dB.

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To calculate the RDF, we need one more modeled value: the gain at the elevation angle and azimuth angle selected by the user. The selected heading for the gain value need not necessarily be the elevation and azimuth angle of maximum gain, although we may often find it convenient for a general evaluation to use these values. The antenna model that produced the listed average power gain happens to show an omni-directional pattern with maximum gain at an elevation angle of 19°. The gain is 0.72 dBi. The difference between the overall average gain and gain at the desired direction and elevation angle is the RDF. Hence, the RDF for this antenna is 6.15 dB.

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Although we may easily calculate the RDF for an antenna in EZNEC as a 2 step process, some implementations of NEC, such as 4NEC2, have automated the process of obtaining an average gain value and then obtaining the gain at the desired azimuth and elevation angle in order to calculate the RDF.

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Unless used wisely, the RDF can mislead us, just as can any of the other measures of directivity that compare forward gain vs. rearward or overall gain. Fig. 6 provides the elevation pattern and the 3-dimensional pattern of an omni-directional vertical monopole for 3.6 MHz. At the TO angle, the gain is 0.1 dBi, while the average gain is 0.310 or -5.08 dB. Therefore, the RDF is 5.18 dB. As ON4UN points out in his book, omni-directionality in an antenna does not necessarily result in a low or non-existent RDF (or DMF), since the pattern shows relatively low gain at high elevation angles, all of which go into the calculation of average gain.

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If we create a simple pair of phased monopoles, we can obtain the pair of patterns shown in Fig. 7. These patterns show an average gain close to that of the single monopole (0.314 or -5.03 dB). This result is natural since the array elements use the same height, radial system, and material as the single monopole. However, phasing gives the array a gain of 3.37 dBi at the TO angle. The resulting RDF is 8.40 dB. The difference between the two antennas is 3.22 dB, roughly corresponding to the difference in their maximum gain (3.27 dB).

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The close relationship between the gain differential and the RDF differential occurs with these two antennas due to the similarities in the type of antenna and their elevation pattern properties. Had we selected very disparate antenna types for the examples, the two differentials might not have correlated well.

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In addition, when noise abatement is a key issue, the RDF measure will not always tell a complete story. As our Ham reports, for best noise attenuation, a narrow half-power beamwidth may be as important as a very high front-to-rear ratio. Moreover, the factor does not itself account for the bandwidth of an antenna. Many noise sources are very broad band. Receiving antennas vary in their bandwidth in terms of signal strength across a span of frequencies corresponding to the input bandwidth of a receiver. In some application, using a narrow bandwidth antenna may yield a better signal-to-noise ratio. These are factors that fall outside the single-frequency requirement for obtaining an RDF calculation.

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Nevertheless, the RDF is an adjunct function to NEC that some implementations of the modeling software may offer. Where not offered, we can easily calculate the value. It adds to list of useful measures that we may derive, even from entry-level versions of antenna modeling software.

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Serial Feedline Connections

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L. B. Cebik, W4RNL

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Modeling a set of feedlines that join at a parallel connection is simple and straightforward within NEC, even if the lines join at the source segment. When transmission lines that use the NEC TL facility join on the same segment, they are automatically in parallel with each other. Moreover, they are in parallel with any source that is also placed on the same segment. +

There are a few significant antenna system designs that may sometimes call for a serial connection of feedlines, as well as a further serial connection to a source. Radio amateurs especially do not think about this possibility when designing antenna systems, since the parallel connection is so ingrained into their thinking. Therefore, let's examine a few cases in which a serial connection of multiple feedlines is a plausible way to proceed and then develop some easy methods of modeling the situation within NEC.

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Junctions of 2 Identical Feedlines

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There are a number of simple 2-element phased arrays that have been available to designers for about 3/4 of a century. The designs are straightforward and reliable. Interestingly, in the past, we have used a parallel connection of the identical feedlines from each element to a center point that is also the main feedpoint for the array. Fig. 1 shows one such array, the venerable W8JK.

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The W8JK is a flattop or endfire array with its bi-directional main lobes off the end of the plane formed by the two wires. There are many version of the W8JK, with various element lengths and element spacing values. In general, the longer that we make the elements, the higher will be the gain of the array--up to an element length of about 1.25 wavelengths. As well, the closer that we space the elements, the higher will be the array gain, with the penalty that the impedance at the junction of the two phasing feedlines tends to decrease as the spacing decreases.

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Properly phasing the two elements means feeding one element 180 degrees out of phase with the other element. If we use identical lengths of identical feedlines for the phasing lines, then giving one and only one of the lines a half twist will effect the desired phasing.

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Most implementations of the W8JK array employ one of the common parallel feedlines. For our sample, we shall employ 600-Ohm open ladder line, since it has lower losses than 450-Ohm window line or 300-Ohm tubular transmitting line. The latter two have vinyl casings that provide structural integrity for the line, but those casings increase losses relative to the ladder line that uses only periodic spacers to maintain the distance between the two wires forming the feedline. Note that the 300-Ohm line specified is a version designed for transmitting applications. The typical TV twinlead, especially the cheaper varieties, may have much higher losses and, indeed, may not have a 300-Ohm characteristic impedance.

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In our example, let's also use the same 600-Ohm line as the main feedline. For many phased array installations, the length of feedline from the antenna system feedpoint junction to the equipment can be very long. Let's specify 100', although real installations may be much longer.

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One of the dangerous sound-bite ideas that pervades amateur radio practice is that the losses in a parallel feedline are so low that its length and the SWR mismatch between the line's characteristic impedance and the antenna terminal impedance do not matter. The line will provide a high-efficiency power transfer from the equipment to the antenna system (or vice versa on receive) regardless of the line length or the mismatch. Unfortunately, this sound bite is only correct up to a point. Like any feedline, even the 600-Ohm open ladder line has a baseline matched loss value per unit of length. A mismatch creates additional loss such that the SWR acts as a multiplier on the matched loss value. The higher the SWR value, based on the mismatch between the line characteristic impedance and the antenna terminal impedance, the greater will be the losses on the line. Table 1 provides some approximate values of loss in 600-Ohm open ladder line for 100' of the line at two frequencies--14.175 and 28.5 MHz in the sample--to show the rising losses as the SWR increases.

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The values are approximate because we can find slightly different values in different tables of matched loss values, as well as slightly different values for the characteristic impedance of the line. In addition, we would discover different loss values depending on whether the mismatch is due to very high or very low antenna terminal impedance values. However, the values shown are useful as approximations. You may explore AC6LA's TLD program or N6BV's TLW program for more refined figures for different line lengths, different antenna terminal impedance values, and different lines. The numbers in the chart derive from using purely resistive impedances.

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The baseline losses of 450-Ohm and 300-Ohm lines are considerably higher, relative to the 600-Ohm line shown. Hence, with very high SWR values, the overall loss for 100' of line will be proportionally higher. An SWR value of 32:1 is unusual, to say the least, if we think of impedances above 600 Ohms. A resistive impedance of 19,200 Ohms will yield the value. However, the much more commonly encountered value of 18.75 Ohms will also yield the same SWR value. The calculation of SWR from the antenna terminal impedance and the line characteristic impedance falls outside the scope of these notes, but the reactive component of the impedance is not a small factor in the calculation. Hence, in practical situations, SWR values above 10:1 are very common and values above 20:1 are not unusual.

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Now let's add a further premise to our exercise: we wish to minimize so far as possible losses along the main 600-Ohm feedline from the antenna system terminals to the equipment. The next question is what this might mean for our W8JK monoband flattop. Let's construct one in model form using 1 wavelength elements spaced 1/2 wavelength apart at 21.225 MHz. Further, let's place the model 1 wavelength above average ground. Initially, let's use two phase lines, each with its own source. We can give one of the phase lines a half twist by specifying that it is reversed or we can leave both lines normal and set one of the sources at a 180-degree phase angle. If we exercise either option, we obtain a pair of source impedance values that read close to 84 + j88 Ohms.

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If we construct the W8JK using the standard parallel connection of the feedlines, then the impedance at the system terminals at the source applied to the wire forming the junction of phase lines becomes about 42 + j44 Ohms. Of course, we might add series capacitance to the line and employ a 50-Ohm coaxial cable as the main feedline, but that exercise belongs to a different discussion. We are committed to using 600-Ohm ladder line as our main feedline. However, as shown in Table 2, the 600-Ohm SWR is above 14:1.

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One much neglected method of reducing the SWR on the main feedline is to use a series connection at the main junction of phasing and feedlines. Fig. 2 shows the difference in the connection in schematic form. The "+" and "-" signs are simply reference points to keep the connections correct. Since most installations would use some sort of fixture--perhaps a simple plate that provides terminals and strain relief for the lines--one method is no harder to implement than the other.

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The last line in Table 2 shows what we gain from using a serial connection. The 600-Ohm SWR is under 4:1. The voltage and current excursions along the main feedline will be much lower than with the parallel connection. A concomitant result is that the range of potential impedance values that the antenna tuner might encounter will be smaller than with the parallel connection. Let's assume that this condition is desirable and so we opt for the serial connection.

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Modeling the serial connection requires us to rethink the requirements. A parallel connection only needed one very short, very thin wire at the junction of the TL-based transmission lines, and this same wire served as the source wire segment as well. However, we need a different scheme for the serial connection. Fig. 3 shows a usable method for two-line serial junctions with a source.

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The triangle consists of three very short and very thin wires. In the HF region, I typically use AWG #20 wire (0.032" diameter). The segment lengths are between 0.0015 and 0.002 wavelengths long, to keep the segment length within NEC limits. The very small triangle can go between the elements without harm. However, you can also specify a considerable distance away from the main radiating elements, since the transmission-lines, using the TL facility, have lengths specified by the command and not by the geometric distance between the elements and the junction assembly.

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In all cases, the modeler should check the average gain test (AGT) for the array plus the serial assembly to ensure an adequate value for accuracy. The gain of the array should not change more than about 0.01 dB between the parallel and the serial models--or between either one and the model using separate sources, assuming that there is no difference in the specified transmission lines for the model set. In the figure, one dashed line is the "normal" line to one element, while the other dashed line is the "reversed" line to the second element. The source assembly is not totally invisible to the model, since the impedance values among the three models in the set will not show mathematical perfection to the last decimal place. Nonetheless, the models are good indicators of the anticipated performance, and construction variables will in most cases outweigh the slight differences in the calculated impedance values.

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Serial feeding is not a solution to all conditions associated with W8JK feedline junction values. Let's briefly consider a flattop array consisting of two 44' elements with a 22' spacing between them. The element length is about 1.25 wavelengths at 10 meters. As we reduce the operating frequency, the elements grow shorter when measured in wavelengths, but so too does the element spacing. As a consequence, the array provides relatively consistent gain performance from 10 meters down to 30 meters. Table 3 shows the free-space performance modeled for such an array using AWG #12 copper wire. As in the initial model, the phase lines are 600-Ohm open ladder line, as is the presumed main feedline.

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As the elements grow shorter while we reduce the operating frequency, the beamwidth grows wider. However, the maximum bi-directional gain remains relatively constant, varying by only 0.6 dB from one end of the operating spectrum to the other. The remaining columns show the feedpoint junction impedance with both parallel and serial feed systems, along with the 600-Ohm SWR as an indicator of probable losses along the main feedline. From 20 through 10 meters, the parallel feed system shows a maximum SWR value of nearly 15:1 at 15 meters, but the other values are lower, with the best values at 10 and 20 meters. However, the SWR value at 30 meters is above 40:1, a condition that promises possibly significant loss and very wide swings of voltage, current, and impedance along the main feedline. In contrast, the series feed system reduces the 30-meter SWR value almost by half, but ends up with higher SWR values on 10 and 20 meters. If we exclude a remote switching system at the main feedline junction with the phasing lines, the potential user is faced with a decision on which feeding system to use based upon which bands are more important to the station's operating goals.

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A second type of array suitable for potential serial feeding is the lazy-H, a broadside array consisting of two elements that are vertically arranged and that provide a bi-directional broadside pattern. Fig. 4 provides a sketch of a monoband version of the antenna using 1 wavelength elements and a spacing of 1/2 wavelength between the elements. For our sample, the midpoint between the elements, where the phasing lines join, is 1 wavelength above average ground. The difference between the lazy-H and the W8JK--a difference that is crucial to operation--lies in the phasing system. The vertically aligned lazy-H elements are fed in phase.

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Although different in their exact values, the impedance values at the lazy-H feedline junction are similar to those of the W8JK. Table 4 lists the impedance values for separately sourced phase lines, for a parallel combination, and for a serial combination. The performance of the array is almost incidental to our purpose in using it, but the lazy-H does show about 1.5-dB higher gain than the same wires and spacing applied to the W8JK, largely as a function of a reduction in the strength of the higher-angle elevation lobes. The TO angle is a degree lower than provided by the W8JK because the effective height of the lazy-H is a small distance above the center point between elements.

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Since the lazy-H individual source impedance values are lower than the corresponding W8JK values, the parallel feedpoint system results in a higher 600-Ohm SWR value. The serial feed system creates an SWR values that promises lower losses and narrower impedance excursions along the main feedline, which may result in an easier tuning task, depending upon the exact line length. The serial system for modeling can use the same triangle of short, thin wires used for the W8JK--either centered or at a large distance from the main radiating elements. The only modeling difference related to the phase lines is that both must be either "normal" or "reversed." Nevertheless, the physical implementation of a serial feedline system will have a quite different appearance, as suggested by the schematic outline in Fig. 5.

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Unlike the W8JK, the lazy-H radiation properties are not constant as we reduce the operating frequency. Shorter elements and reduced element spacing both reduce gain in the lazy-H, since we are feeding the elements in phase. Consider a pair of 44' lazy-H elements spaced 22' apart vertically in free space. The elements are about 1.25 wavelengths long on 10 meters, with a spacing of about 5/8 wavelength. These conditions optimize gain on 10 meters. On all lower bands, the shorter elements and decreased spacing--as a function of a wavelength--decrease gain. As well, they increase the beamwidth at a faster rate than we saw in the comparable data for the W8JK. Table 5 shows the data for all bands from 10 down to 30 meters using series and parallel feed systems.

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The gain of the lazy-H at 30 meters is marginal in the sense of being less than one dB higher than for a single-wire dipole. However, the array is usable if we can obtain satisfactory feedpoint junction impedance values. With a parallel connection, we find numerous bands with 600-Ohm SWR values above 10:1. Using a series connection, all but one of the bands shows a 600-Ohm SWR value of less than 10:1. However, the single band with a higher value is 10 meters, where the SWR value is very much higher and the losses for any given SWR value are the highest among all of the bands. Like the W8JK, the decision whether to use a parallel or a series connection does not make itself.

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We have used very specific examples of both the W8JK and the lazy-H array in providing examples of the required modeling for effective evaluation. One may change the transmission line, the phase line, and even the length of the phase lines in search of a better combination using either serial or parallel feeding. With a central feedpoint between the elements, the only requirement (besides the W8JK half twist) is that both phase line be identical, including length. However, there is in principle no restriction on the length of the phasing lines. Therefore, one may search for lengths that provide the lowest SWR values relative to the desired main feedline for the bands of highest interest. All of this, of course, rests on the initial premise that one of our goals is to reduce main line losses to a minimum and, almost incidentally, to provide the antenna tuner with the least extreme resistance or reactance conditions at the terminals.

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A Three-Line Serial Feeding Example

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Serial feeding is also possible with more than two lines that meet at a junction. Consider a triangle of three dipoles for 2 meters. Fig. 6 shows some of the details of a prototype modeled and built for an article in QST. The elements are 1/2" diameter aluminum on a PVC structure for support. The arm length, the element length, and the spacing between dipole tips are all selected to provide a horizontally polarized omni-directional pattern. The design case used the band center as the design frequency, because the pattern does not change within the confines of 2 meters and the SWR remains low at the final junction with the 50-Ohm main feedline.

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The design is predicated on the fact that a triangle of dipoles, properly spaced, yields the desired omni-directional pattern within perhaps 0.3 dB total variation. As detailed in other documents, the principles of operation differ from the 1961 Big Wheel arrangement. The older antenna creates a circular element with three high impedance feedpoints. Parallel lines from the feedpoints effect in the 1/4 wavelength distance to the hub an impedance transformation to a low value. At that point, the originators connected them in parallel. The design is highly finicky, since the exact characteristic impedance of the lines and their length determine the hub impedance values.

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The revised design actually uses less space than the wheel and can also be configured circularly. We shall omit that version since the question of parallel vs. serial feeding is identical for both straight and circular triangles of dipoles. The key difference between the original wheel and the present design is that the triangle uses independent dipoles. In the arrangement shown, each exhibits a feedpoint impedance very close to 50 Ohms. Therefore, we may run 50-Ohm cables from each dipole to the hub and replicate very closely the impedance at the dipole feedpoints.

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Standard treatment of the cables at the hub would be to connect them in parallel, as suggested on the left in Fig. 7. The net impedance would be from 15 to 17 Ohms, with some remnant reactance. However, any small reactance at such low impedance values will have a considerable impact upon any matching system that we might try to implement. In contrast, a small reactance in series with a higher impedance will have less impact. Therefore, we selected a series connection system, shown in the right, ensuring that the 50-Ohm lines to each dipole were identical. In the triangular configuration, regardless of the feed system, the builder must ensure the same dipole orientation to obtain the circular pattern. The modeling technique is identical to the one applied to the triangles, except that in this case, we form a square of very short, very thin wires, either at the hub of the triangle or at a considerable distance from the radiating elements.

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The net impedance at the hub is about 150 Ohms, usually with a bit of reactance. However, the reactance is rarely more than 10% to 15% of the resistance value. Therefore, one may use a 1/4 wavelength section of cable from the series junction to the main feedline. In this case, RG-62 93-Ohm line proved nearly ideal, with the length adjusted to center the SWR curve in the 2-meter band. Fig. 8 shows the modeled (and the tested) results of the exercise.

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The triangular antenna system appears only to establish that there is no practical limit to the number of identical feedlines that one may set into a serial configuration. However, when working under these simplifications, identity of line length and element structure are essential to ensure equal current at the feedpoints of the elements. Where an array requires unequal current magnitude and phase angle at each feedpoint, the modeler needs to do considerable advanced calculation, since series connections rest on voltage division.

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Conclusion

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Our goal has been to note the considerations that apply to modeling a series line assembly. Since the idea of such a method of feeding antennas is usually foreign to radio amateurs, we have provided some concrete examples that contrast parallel and series feeding methods. When an application calls for series feeding, there are ways to accomplish the modeling task for pre- and post-construction design evaluation. In most cases, adding a triangle or a square to the model will do the job.

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Go to Main Index

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Unequal Serial Feedline Connections

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L. B. Cebik, W4RNL

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In the preceding episode, we examined the modeling of series feedline connections at the source of a model. We looked at a few examples of arrays that used both 2-line and 3-line combinations to familiarize ourselves with both the modeling techniques that we need and with the differences between parallel and series connections of feedlines.

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The arrays that we examined had something in common, regardless of the connection. Each individual transmission-line termination had the same impedance. Therefore, we were able to use a simplified set of calculations, outlined in Fig. 1. For a parallel connection of individual termination impedances at each feedline, the net impedance was 1/N (Z), where N is the number of lines connected and Z is the impedance of the individual connection. Because we used a series representation of the impedance (R +/- jX Ohms), we could arrive at the net impedance by handling the resistance and reactance values individually.

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The series connection presented us with no more difficult an arithmetic task than the parallel connection. For three identical impedance values in series, the net impedance is the sum of the individual impedances, that is, N (Z). With the impedance values shown as R +/- jX Ohms, we could simply multiply R and X by the number (N) of lines being joined in serial fashion.

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The two forms in Fig. 1 contain a reminder that series and parallel connections doe have a difference. A parallel connection of feedlines, relative to the source, shows a constant voltage across each line but divides the total source current equally among the individual lines. In contrast, a series connection of feedlines shows the same current at each line, but there is a voltage drop across each line equal to the source voltage divided by the number of equal loads presented by the lines at the junction. These notes, of course, assume a lossless situation, which is consistent with the lossless lines created by the TL facility within NEC. We also assume, in accord with NEC, that the losses associated with the structure and loading of the elements within the array are equal and therefore do not disturb the basic calculations that rest on the impedance values that appear at the source-end of each transmission line.

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With respect to modeling parallel and series connections, we do encounter a difference, as suggested by Fig. 2. On the left is the very simple scheme required within NEC for modeling a parallel set of transmission lines in conjunction with a source. We need a single 1-segment very short, very thin wire--normally at a remote location relative to the radiating elements of the model--in order to join the lines and the source in parallel. The wire can be as short as about 0.001 wavelength. 1-mm (about AWG #20) is a good diameter, and if the program allows it, the wire can be lossless. Some programs, such as EZNEC, allow the specification of a virtual wire that automatically meets these criteria and does not appear in the graphic view is the antenna.

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Creating a series connection among the transmission lines and the source requires a more complex structure, as suggested by the remaining two outlines in Fig. 2. For each transmission line and for the source, we require a separate very thin, very short wire. These wires connect in series forming a complete circuit. Hence, two lines plus a source requires a triangle, while 3 lines plus a source requires a square. The construct creates the required series connection among the element. However, the structure has a finite dimension that forms a loop. The consequences are twofold. First, we need to check the average gain test (AGT) score to determine that the construct has not significantly changed the AGT value relative to the value obtained from a parallel connection. With very thin and very short wires in the construction, the AGT value at HF will normally change by no more than 0.001, an acceptable value under virtually all circumstances. Second, the loop formed by the construct will often add inductive reactance to the net impedance as related to the simple sum of the individual impedance values without the construct. The amount is normally small and should not be surprising. However, it may require noting relative to any physical implementation of the model under development.

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The models that we have so far examined presented equal loads to the junction of lines with the source. At the end of the preceding episode, I indicated that there are many situations in which the lines will not present equal loads. A question arises about how, under these circumstances, we may move from a parallel to a series connection. The modeling technique will remain the same. We shall switch from a single-wire junction to a more complex series construct of wires. However, to understand what is occurring, we may need to look at modeling practices and at the analysis of behavior of voltage and current under parallel and series connections. In this episode, we shall examine a single example using both types of connections. Our goal is to understand how we can model both ways to obtain a reasonably full analysis and understanding of how and why the two arrays differ.

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A 2-Element Horizontal Phased Array with Parallel Phaseline Connections with the Source

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Let's consider a 2-element phased array for 28.5 MHz. The design that we shall use emerges from an old design that I once developed to convert a driver-reflector Yagi of good performance of its type to better performance as a phased array, all without altering the elements. The driver and reflector used relatively thin stepped diameter elements so that the whole antenna broke into parts that stored within a PVC boom. The inner section consisted of 0.25" diameter rod, and the total length of the inner sections was 108" (54" each side of the centerline). The outer sections consisted of 0.1875" (3/16") diameter rod. The total length of the driver was 198" (45" per section), while the total length of the reflector was 211.2" (51.6" per section). I spaced the element 57.6" apart. As a Yagi, the array yielded a free-space gain of 6.24 dBi with a front-to-back ratio of 10.88 dB. The design frequency feedpoint impedance was about 40 + j8 Ohms, which provided a 50-Ohm SWR of less than 2:1 from 28 to 29 MHz.

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Out of curiosity, I developed a phasing harness for the Yagi that improved performance, as shown in Fig. 3. Using phasing techniques, the gain increased slightly, but the front-to-back ratio jumped by 10 dB. The Yagi configuration is limited to using only the geometry of the antenna elements to obtain its results. Adding a phase lines allows a broader control of the current magnitude and phase angle values on the individual elements to increase at least some of the performance values.

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As the outline shows, the phasing system consists of two lines, one from each element, to a main feedline junction. Essentially, we may analyze all 2-element phased arrays on this model, even thought some--like the well-known ZL-Special--used a zero length line from the forward element to the feedline junction. In this design, the forward phasing line consists of 6" of 50-Ohm, 0.78 VF cable, while the rearward line uses the same cable, but with a 64" length. The electrical lengths of these cables, of course, are the physical lengths divided by the velocity factor (VF).

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We may develop a fuller understanding of the phased array in the present (and, by extension, any other) design by using two models of the antenna and doing some external calculations. Fig. 4 shows the outlines of the two models. The upper model establishes the relative current magnitude and phase angle on the two elements required to produce the required performance (as listed in Fig. 3). Normally, we assign a current magnitude of 1.0 and a phase angle of zero on the forward element and then find the current magnitude and phase angle required for the rear element. The arrangement of lines used to establish phasing conditions must meet these requirements to obtain the listed performance. (At this point, we shall not concern ourselves with the resulting impedance at the junction of the phase lines in the lower portion of Fig. 4, although we shall eventually work with that detail.) Our fundamental question is the conditions that must exist at the junction of the two phase lines to obtain correct element phasing when we use the standard parallel connection of the lines and the source. In this and many other cases, the rearward line (TL2) has a half twist to effect a 180-degree phase shift relative to the junction or to the element phasing that would obtain with a normal line.

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Every transmission line (including those in phase-line service) transforms the impedance at the load end to another value at the source end. If the line happens to match the load, the impedance is constant along the line, but any difference between the line characteristic impedance (Zo) and the load impedance (Zl) results in a different impedance values at the source end except for lines that are exactly a multiple of 1/2 wavelength electrically. What amateurs often forget is that the current and voltage also undergo transformation along the line, and they are more critical to the phased array's performance than the impedance. Voltage and current undergo only one transformation per 360 degrees of electrical change.

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The required conditions for proper performance of a phased array include establishing the desired relative current magnitude levels and the required phase angle difference at the two elements. The junction end of the line also has conditions. A parallel connection divides the source current between the two lines. Each line's share of the current must result in the desired ratio of current magnitude and the desired difference in phase angle at the element ends of the line. In addition, the transformations along the line must result in identical voltage magnitudes and phase angles at the junction of the two lines with the source. Very often, we can obtain these conditions, but the combination of parallel voltage and current magnitudes and phase angles results in an unusable or at least a highly undesirable feedpoint impedance. Therefore, with available lines, the designer's options are limited. For example, a combination calling for a total physical length that is less than the spacing between elements would be unusable. As well, we cannot simply change the spacing, since a phased array is a combination of parasitic and directly fed energy at each element. Therefore, for the required performance, changing the element spacing would require a different ratio of current magnitude and an altered phase angle difference to arrive at the specified performance.

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To illustrate the required conditions, we can use the standard equations for impedance, voltage, and current transformation down a transmission line from load to source, that is, the junction end of each line. We shall let Zo be the characteristic impedance of the line at the design frequency, while Zl is the load impedance and Zs is the source end impedance. The script "l" is the electrical length of the line in either degrees or radians, according to the calculator's preferred measurement method.

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To calculate the voltage at the source end of the line, where El is the load voltage and Es is the source voltage, we can use a comparable standard equation.

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The current calculation, where Il is the load current and Is is the source current, also uses a standard equation.

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All of these equations are the versions for lossless lines, the type that appear in the NEC TL system. Therefore, any external calculations based on these equations should yield results that closely coincide with the NEC reports, especially if we are using NEC data for the input values. The calculations require separating and recombining the real and imaginary portions of the equations, a task well-suited to a spreadsheet or a utility program. TLD and TLW are suitable programs, although they include loss factors. However, the short length of the lines should make any differences inconsequential.

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The result of applying these equations to the situation of a modeled phased array allows us to examine how the arrays do their work. Table 1 provides relevant calculation results for the parallel junction version of our phased array. Note that the input voltage and current for the rearward line have been phase shifted by 180 degrees to account for the half-twist in that line.

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The boldface entry for the calculated voltage values at the junction of lines shows the identity (within a very close approximation) of voltage, with the current being split between the two lines. The net impedance is simply the parallel combination of the two impedance values. The calculation shows a very close coincidence with the reported feedpoint impedance from the NEC model. This should come as no surprise, since NEC makes calculations very similar to these in the course of a core run for the model with phase lines as TL command functions.

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The resulting impedance may seem troublesome, since it is neither resonant nor convenient to common matching systems. Had the impedance been close to resonance at about 25 Ohms, we might have applied a common equation to construct a 1/4 wavelength matching section. A 35.5-Ohm line (composed of RG-83 or of two parallel sections of 70-Ohm line) would have yielded a 50-Ohm final impedance value.

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Most amateurs forget that the special formula for exact 1/4 wavelength sections is only a single point along a spectrum of slowly changing impedance values. Therefore, we can create sections that are longer or shorter than 1/4 wavelength to approximate the exact match. A quarter wavelength at the design frequency is about 103" with a physical length that is the electrical length value times the lines velocity factor. In this case, we need a much shorter length of line. For a VF of 0.66, 34" will do, while for a VF of 0.78, 40" will provide a resonant feedpoint impedance of about 58 Ohms.

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The array, then, is quite usable, although I am not here recommending its use. Rather, the phased array with its parallel connections of feedlines and the feedpoint serves as a good example of its type.

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A 2-Element Horizontal Phased Array with Series Phaseline Connections with the Source

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For every parallel solution to a design challenge, there should also be a series solution. Therefore, let's use the same set of elements and see if we can develop a series phaseline and feedpoint connection. My purpose is not to claim that one or the other array is superior, but only to show what a series set of connections will entail. The final design for the revised array appears in outline form in Fig. 5, along with a free-space E-plane pattern. The gain and front-to-back data on the graphic show the near identity of performance between the new array and its parallel cousin.

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The basic outline shows that the feedpoint is not located in the same position as in the case of the parallel junction. The earlier system used 70" of total 50-Ohm, VF 0.78 line divided into a 6" forward section and a 64" rearward section (with its half twist). The new system uses a total of 79" of the same line, with a 25" forward section and a 54" rearward length (again, with a half twist). The new phasing lines are not identical in any way to the old ones, nor are they a mirror image of the old system. Series connections answer to a different set of conditions relative to parallel connections.

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Fig. 6 shows the two steps through which we shall proceed in hopes of obtaining a better understanding of the series connections. The lower portion of the graphic shows the feedpoint junction area. I could have avoided the double crossing of wires in the schematic representation, but the cross in TL2 is a reminder that the rear line receives a half twist. The junction area of the diagram shows the required connections to obtain a set of series junctions among the lines and the source.

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The key to analyzing the series situation is the understanding the each line creates a voltage drop across its transformed version of the element load. Therefore, the current through each of the source ends of the lines is the same. The actual element currents may differ in magnitude and phase angle, but the lines must be of the right length for the characteristic impedance so that the current magnitudes and phase angles at the junction are the same. We may go through the same set of calculations that we used for the parallel connection array to check our work and establish the correct condition at the feedpoint. Table 2 provides the results of those external calculations. Once more, the initial rear element voltage and current phase angles have been adjusted for the half-twist and its 180-degree alteration of the phase angle between the source and load ends of TL2.

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The boldface entry is for the current, which shows a very close coincidence of values. The net impedance at the feedpoint is simply the sum of the individual impedance values. The resistive component shows a tight alignment with the value reported by the NEC model. The model shows a higher reactance than we obtain from the calculations. However, the calculations do not include the triangular loop that creates the series connections. If we remodel the array for a separate source for each phase line, we obtain from NEC impedance values of 64.3 + j55.6 and 84.3 + j7.1 Ohms, for a net series impedance of 148.6 + j62.7 Ohms, very close to the calculated value. Although the connection triangular loop may seem small, it is significant.

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Neither of the two versions of the phased array is directly suited to the use of a 50-Ohm main feedline. We raised the impedance of the parallel connected version by the use of a section of 35-Ohm cable, usually constructed from two parallel sections of 70-Ohm cable. Even though the matching section cable impedance is not the geometric mean between the array impedance and the main line impedance, we found a length that provided a satisfactory 50-Ohm SWR. Similarly, we may use a 93-Ohm cable (such as RG-62 with a VF of 0.84) to serve as a matching section for the series connected version of the array. The array impedance is not perfect for use with a 1/4 wavelength of this cable, but a slightly longer cable (108" physically, 128.5" electrically) provides a satisfactory design-frequency resonant impedance (40.9 Ohms).

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In fact, both versions of the array, with the proper matching section, provide complete coverage of the first MHz of 10 meters with well under a 2:1 SWR value. Since both arrays also provide essentially the same performance in all vital categories, performance cannot be the deciding factor in selecting which version to use. Of course, these notes are not necessarily recommending either version for actual use.

+

Careful exploration of both series and parallel connected models can uncover other differences that might impact a selection. Both forms of the array undergo a considerable range of front-to-back values across the defined 1-MHz passband. However, the parallel-connected version shows a much higher change of gain from one end of the passband to the other: 0.88 dB. In contrast, the series connected version varies by only 0.17 dB across the same spread. Despite the gain stability advantage of the series connected version, the parallel-connected form may be simpler to construct. The phaseline system may use available coaxial cable connectors to effect all junctions, both with the elements and at the main junction of the phase lines.

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Conclusion

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The goal of these notes has been to show the modeling techniques necessary to replicate in NEC a series connection of feedlines and a source in cases more complex than those shown in the preceding episode. We selected a 2-element phased array that required two phase lines constructed using the TL facility. Since the two elements required different terminal current magnitude and phase angle values to obtain the desire performance, the parallel and the series pairs of phase lines proved to be quite different. The differences stemmed in large part from the fact that parallel connections divide current, while series connections divide voltage. Although NEC provides output data that is both reliable and useful in both cases, we resorted to external calculations to show that both systems established the conditions appropriate to each type.

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The external analysis was largely post-facto, that is, applied after finding the correct phase line values, including the characteristic impedance and the length. In this case, the element geometry was given, but any number of other geometries is possible. Since the process depends upon setting realistic performance goals in terms of the gain and the front-to-back ratio for any given geometry, I am not aware of any system for automatically calculating such phase lines. A systematic search among available line Zo values and length combinations within NEC remains one of the fastest routes to a reasonable design.

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Go to Main Index

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Warnings and Errors: What Does NEC Do and What Should You Do?

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L. B. Cebik, W4RNL

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Newer modelers often encounter situations in which a model aborts a core calculation run and simply returns an error notation. Some implementations of NEC, such as EZNEC, try to prevent the core run by pre-detecting the modeling error (or bad modeling practice), locating it, and labeling it to provide the modeler with a guide as to what should be changed. Other implementations of NEC, such as GNEC, provide pre-run checks within the antenna view system, but the modeler need not examine this facility before ordering the core to perform its calculations. Still other implementations provide no other error identifications other than what may appear in the NEC output report. +

In fact, when a run aborts, the first place that a modeler should look is in the NEC output file. Unfortunately, newer modelers fail to realize that NEC produces an output report even for an aborted run, and it identifies errors and warning that fall within its stock of checks. NEC-2 makes only a few checks and reports on very few errors. Some implementations of NEC have expanded the checklist. Therefore, any existing facilities that a program makes available should become a regular part of the modeler's pre-run routine. NEC-4's checking system is far more elaborate, but as we shall see, it is by no means complete, and some warning and error conditions may require considerable hunting to find.

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These notes will examine a few kinds of error and warning conditions. The goals interlace, since we sometimes presume that some NEC limits are the same throughout. So in the process of providing a few samples error and warning cases, we can also distinguish among a few ways in which NEC applies different limiting standards to models.

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Note that we shall push NEC of its limits on purpose. Therefore, the existence of a full output report on a model does not necessarily mean that the model follows good modeling practices. Reliable NEC output reports generally require us to stay well within the program's limits.

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Case 1: Crossed wires meeting at other than a segment or wire junction: Our first case is a clear violation of NEC rules. In the model below, the two wires cross and join in the middle of the center segment of each wire. Fig. 1 shows the view of the situation.

+ 
+CM crossing wires
+CE
+GW 1 9 0 0 0 0 0 .25 .001
+GW 2 9 -.125 0 .125 .125 0 .125 .001
+GE 0 0 0
+FR 0 1 0 0 299.7925 1
+EX 0 1 1 00 1 0
+EN
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NEC-2 will run this model without comment. However, NEC-4 may abort the run, depending on the setting of the GE command. Even if the model runs in accord with the user's instructions, the output report will return the error message in Fig. 2. The three lines are essentially encapsulated in the first line, but the segment-check feature aims for completeness.

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The second entry in the GE command dictates whether NEC-4 aborts the run in the presence of errors along or in the presence of either errors and/or warnings. Fig. 3 shows the GNEC set-up screen with explanations for the options to run or to abort in the center section. I have added the numbers that will appear in the command line for each user selection. NEC-2 does not have anything corresponding to the NEC-4 GE options.

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Regardless of which option you choose, referring to the output file is necessary to understand what error or warning is at work and hence what may be at fault with a model. Errors and warning applicable to the geometry (wire) structure of the model appear at the very beginning of the output report, immediately after the core's interpretation of the geometry commands through the GE command.

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There is a distinction between error and warning messages. "When segment testing is requested. . ., error messages are printed [in the output report] for illegal segment intersections and warning messages are printed for violations of the thin-wire approximation. An illegal intersection is indicated when the minimum separation of the segments at a point other than at the segment ends is less than 10-3 times the length of the shorter of the two segments. A violation of the thin-wire approximation is indicated when the minimum separation of non-connected segments is less than the sum of their radii. A warning message is also printed if the center of a segment is within the volume of another segment." (p. 27, NEC-4 Manual) This latter warning sets up a limit to the angle at which two wires may met based upon both the radius and the segment lengths in each wire. These are not the totality of warnings that may appear in a NEC-4 output report.

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Case 2: The interpenetration of parallel wires: When two wires are separated by less than the sum of their radii, we generically refer to them as interpenetrating. In other words, even though their axes are separate, their surfaces are not. The following model samples this condition with parallel wires. The sum of the radii is 0.012 m, but their axes are separated by only 0.01 m. Fig. 4 shows the outline of the situation and the set of warnings generated by NEC.

+ 
CM interpenetrating wires
CE
GW 1 9 0 0 0 0 0 .25 .006
GW 2 9 .01 0 0 .01 0 .25 .006
GE 0 0 0
FR 0 1 0 0 299.7925 1
EX 0 1 1 00 1 0
EN
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The outline of the parallel wires shows two distinct wires and does not reveal the interpenetration. Most (but not necessarily all) graphic representations of models use simple lines connecting the wire end coordinates. They normally do not show the wire thickness. Therefore, the outline may not show an error or a warning condition.

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Note that these are warnings and not an error. Therefore, it is possible to set up the GE command to allow this model to run, while still trapping errors with an abort of the run. However, the results of the run will not be reliable. Indeed, merely increasing the separation of the wires to eliminate the warning list may not be enough separation to yield a reliable model. For close spacing that does not result in interpenetration of wires, the average gain (AGT) test is still the most important first-order test of model reliability.

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Cases 3a and 3b: Angularly approaching wires: If two wires approach each other at an angle, it is possible to incur warnings of interpenetration at the narrow end of the angle. The following model, in which the wires meet at the "top", is such a case. Fig. 5 on the left shows the outline with a distinct junction of the wires at one end.

+ 
CM interpenetrating wires
CE
GW 1 9 0 0 0 0 0 .25 .006
GW 2 9 .013 0 0 0 0 .25 .006
GE 0 0 0
FR 0 1 0 0 299.7925 1
EX 0 1 1 00 1 0
RP 0 181 1 1000 -90 90 1.00000 1.00000
EN
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Because the wires are not parallel, the warning message differs from the previous case. The top four segments of each wire interpenetrate to the degree where the center of the listed wire is within the volume, that is, inside the radius, of the noted segment of the adjacent wire. This condition normally results in errors in the current calculations for the affected wire segments. (Also note that the error messages use the absolute segment number rather than the tag number and the relative segment number.)

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We may modify the case just slightly so that the wires do not join at the ends. We need modify only 1 of the 2 GW entries.

+ 
GW 1 9 0 0 0 0 0 .25 .006
GW 2 9 .013 0 0 .007 0 .25 .006
+

The revision results in the outline at the right of Fig. 5. The close center-to-center (C-C) spacing of the wires at the top indicates, by reference to the wire radii, that we certainly have wire segment interpenetration for at least two or three segments. However, because the wires are not parallel and do not meet at the end, NEC-4 shows no warnings. Wherever wires come into close proximity, the AGT test is a necessary step in model evaluation. Despite the seeming simplicity of the revised model, its AGT score is 0.937, meaning a gain error that approaches -0.3-dB. In most instances, model revision to improve the AGT score would be advisable.

+

If the implementation of NEC applies additional checks to the model, the situation might well be detected and reported. For example, some implementations take wire radius into consideration for all geometry situations. Such a system would report the interpenetration and either prevent a core calculation run or advise a model revision.

+

Case 4: Crossing interpenetrating wires: Although NEC-4 will not detect the situation of case 3b, it will detect wires that cross without touching at mid-segment while in a condition of surface interpenetration. The following model, with wires at right angles to each other, illustrates the condition.

+ 
CM interpenetrating wires
CE
GW 1 9 0 0 0 0 0 .25 .006
GW 2 9 -.125 .01 .125 .125 .01 .125 .006
GE 0 0 0
FR 0 1 0 0 299.7925 1
EX 0 1 1 00 1 0
EN
+

The wire axes are separated by 0.010 m while the radii are both 0.006. Hence there is a 0.002-m interpenetration at the crossing point, that is, relative to the center segments of both wires. Fig. 6 shows the outline and the warning. The warning message is specific to this type of modeling situation. As usual, the outline uses a single wire along the axis of each wire and therefore does not itself reveal the interpenetration.

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All of the errors and warnings that we have so far illustrated show themselves in the form of messages that occur immediately following the core's interpretation of the geometry entries. Although we have been using very simple cases with only GW entries, it is possible to incur "hidden" errors or warnings by the use of some of the other geometry commands. CW, GM, GX, GR, and GA all create wire segments that may or may not be in the clear relative to other wires in the geometry structure. Therefore, reference to the output report is essential to ensure that the overall structure meets the NEC guideline limits.

+

Case 5: Interpenetration insulated sheaths: Not all warnings and errors involve the geometry commands. Errors and warnings that concern control commands do not occur in the geometry section of the output report. Rather, they occur in the report section directly relevant to the command interpretation. As a result, we may easily overlook them and miss an unintended modification to the model.

+

The following model sets up two crossing wires that are--with respect to the GW commands--separated enough to pass all tests. The wire radii are 0.001-m, while the separation is 0.01-m. However, the subsequent IS commands set up two sheaths, each with a radius of 0.006-m. Therefore, the sheaths interpenetrate at the crossing point between wires.

+ 
CM interpenetrating wires-IS
CE
GW 1 9 0 0 0 0 0 .25 .001
GW 2 9 -.125 .01 .125 .125 .01 .125 .001
GE 0 0 0
IS 0 1 1 9 1 1e-10 .006
IS 0 1 1 9 1 1e-10 .006
FR 0 1 0 0 299.7925 1
EX 0 1 1 00 1 0
RP 0 181 1 1000 -90 90 1.00000 1.00000
EN
+

The 0.002-m interpenetration of insulating material may seem innocuous. However, as shown in Fig. 7, the warning advises otherwise. The interpenetration of sheaths results in one of the sheath commands being ignored, which modifies the model relative to the modeler's original intent to have two insulated wires.

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The warning appears only in the section of the output report devoted to the IS command. Unless an implementation of NEC uses an error checking system sufficiently extensive to report such problems before a core run, a careful reading of the output report may be the only way of catching the difficulty.

+

Case 6: Horizontal wires close to but above ground: The NEC-2 manual is quite explicit about the limits of a wire's height (z-coordinates) when the wire is not vertical. As shown in Fig. 8, the NEC-2 Manual, Section 3. Modeling Structures Over Ground, specifies that for a wire of radius a and height h to the wire axis, (h2 + a2)1/2 > (about) 10-6 wavelength. It also notes that h should be several times the radius for the thin-wire approximation to be valid.

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In the user guide for the GE command, the manual also states, "If the height of a horizontal wire is less than 10-3 times the segment length, I1 equal to 1 will connect the end of every segment in the wire to ground. I1 should then be -1 to avoid this disaster." I1 is the first digit of the GE command (where a zero means free space or no ground at all). A 1 means that there is a ground plane and that the currents on segments touching the ground in the X-Y plane are interpolated to their images below the ground and the charge at the wire base is zero. In contrast, -1 results in no current expansion modification so that the current on wires touching ground go to zero at ground or Z=0.

+

The situation sounds straightforward until we pose the question of when a horizontal wire is close enough to ground to incur the difference between setting GE at 1 or at -1. The options are the surface of the wire, as defined by its Z-coordinate plus the radius of the wire, or the axis of the wire, that is, its Z-coordinate alone. The warnings that emerge from the various cases of interpenetration might strongly suggest the first option to some, although the manual is not explicit on the matter.

+

Therefore, I set up a test model consisting of 36 horizontal radials with a simple monopole, as shown in Fig. 9. The wire radius is 0.001 m. The segment length for a radial is 0.025 m, while the segment length for the monopole is 0.0239 m. (At the test frequency, 1 m = 1 wavelength.)

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The basic model appears below. The initial height is 0.003 m above ground. This places the horizontal radial wires along their axes at 3 times the wire radius, a rough meeting of the injunction that the value of h be several times the value of a. The height also easily meets the minimum value of h and a taken together.

+ 
CM GR Radials for Monopole
CE
GW 1 10 0 0 .003 .25 0 .003 .001
GR 1 36
GW 37 10 0 0 .003 0 0 .243 .001
GE 1 2 0
GN 2 0 0 0 13.0000 0.0050
FR 0 1 0 0 299.7925 1
EX 0 37 1 00 1 0
RP 0 181 1 1000 -90 90 1.00000 1.00000
EN
+

I then gradually lowered the height of the entire assembly in small steps. Among the more important steps is a height of 0.0011 m. This height would be the last allowable height if NEC faulted the model when the horizontal wire surfaces touched ground. A height of 0.001 m would place the radial wire surfaces in contact with ground. The next height, 0.0009 m would count as a definite penetration of the wire surface into ground. A height of 0.00002 m would place the horizontal wire axes just below the limit of being greater than 1/1000 of the segment length above ground.

+

The question becomes at what height the model shows a fault with GE = 1 and with GE = -1. I ran the sequence of models in both NEC-2 and NEC-4 to see what kinds of error conditions might appear with each core. The results appear in Table 1.

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All heights from 0.003 m down to 0.0002 m produce no error reports in either NEC-2 or NEC-4 with GE set to 1. Moreover, the sequence of gain, theta-angle, and impedance values are quite sensible. In fact, both cores, although they return very slightly different numbers, show the same trends in all three categories. The progressions of both source resistance and source reactance are parallel throughout the progression. These results do not mean that pressing the base of the monopole and the radials downward represents good modeling practice, since the height no longer meets the height-to-wire-radius recommendation. It merely records the fact that nothing disastrous occurs.

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With GE = 1, the lowest two entries record the fact that the cores of both NEC-2 and NEC-4 abort the run and show an error (not a warning) message, as indicated in the table. Since I have only a limited number of NEC-2 cores, it is not clear whether the error report using that core originally came with the core or whether the implementation (NSI) added the message. The NEC-4 core message apparently is inherent to the core as issued.

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With GE = -1, both cores allow the full run with no error reported. When the wire axis is as close as 0.00002 m from the ground, both cores record sensible additions to the progression of values for higher values of Z. However, at Z=0, only the NEC-2 core records a seemingly sensible result, while the NEC-4 core result is not an extension of the progression of values in the table.

+

In both settings for the GE command, the models fall well below guidelines for good modeling practice and do not represent values for h that anyone should recommend for virtually any wire radius. Nevertheless, they allow one kind of answer to our inquiry into whether NEC uses the surface or the axis of the wire in determining when an error has occurred with GE = 1. The answer is that it uses the wire axis. Those who create implementations of either NEC-2 or NEC-4, of course, are free to alter this limit by applying run-abort messages or other flags to indicate when some part of a model lies outside the limits of recommended modeling practices. EZNEC, for example, applies the implicit Z-coordinate of the lowest point on a wire's surface to determine when the wire is too close to ground.

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Vertical and sloping wires, of course, can legitimately reach ground or have a terminating Z-coordinate of zero. Both types of wires are useful in NEC-2 with a perfect ground. For a sloping wire, NEC ignores the wire's surface penetration below ground. Likewise, when penetrating below ground in NEC-4, the wire must reach Z=0 at a segment junction or end, which includes a wire end. A new segment takes up the below-ground portion of the wire in either case. Again, NEC ignores the angular penetration of the segment either above or below ground.

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Conclusion: We have examined a number of error and warning conditions that can arise in NEC, especially NEC-4, with reference to messages and actions taken by the cores themselves. We have had several goals. The first has been to show the conditions under which NEC will return an error or warning message. Most, but not all, such messages are built into NEC-4 alone, which has an internal segment-checking system. For the most part, NEC-2 lacks the system and may let such models run.

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When NEC aborts a run--or even when it does not--we need to know where to find the error. The NEC output report is the locus of such reports. Reports relating to the basic geometry of the wire structure occur at the very beginning of the report. However, examining every section of the report is useful, since it may catch warning relating to control commands that can modify a model relative to one's initial intentions. The IS-command case well illustrated the need for close scrutiny of the report. That was our second goal.

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The final aim was to clarify some of the error and warning reports and when they occur and do not occur. The wire penetration of sloping but unjoined wires was a case in point that showed the limitations of the segment-checking system. The monopole + radial model in Case 6 allowed us to determine the basis for NEC error reports for horizontal wires that are too close to ground.

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Nothing in these notes is a license for any violation of good modeling practice. Applying the average gain test remains the first line of defense against inadequate models, but it only establishes the necessary, not the sufficient conditions of model adequacy. In the end, the final test is a correlation of the model with reliable measurements of physical implementations of the antenna modeled.

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Go to Main Index

+ + diff --git a/content/amod/amod15.html b/content/amod/amod15.html new file mode 100644 index 0000000..35b5660 --- /dev/null +++ b/content/amod/amod15.html @@ -0,0 +1,162 @@ + + + + + Some Linear Loading Basics + + + +
+

15. Notes on Reactive Antenna Loads and Their NEC Models:
+ C. Some Linear Loading Basics

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+

L. B. Cebik, W4RNL

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Linear loads do not model accurately using the TL facility of NEC. There are two major factors (and a number of minor ones) that contribute to the inaccuracy. First, the currents on the wires of the linear load are rarely, if ever, exactly equal in magnitude and opposite in phase. Consequently, the linear load does not as a pure transmission line. Second, most applications of linear loading snug the parallel load wires close to and parallel to the main radiating element. This placement creates complex interactions between the linear load wires and the antenna wire. often to the point that the contributions of each wire to the total far field and to the total element length cannot easily be distinguished.

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Nevertheless, NEC is able to physically model linear loads with a good level of accuracy, where "good" might be provisionally defined as providing reasonable guidance for building or providing reasonable calculations for analysis. Good accuracy, however, is subject to certain restrictions. For example, for best accuracy, the wires comprising the antenna element and the wires comprising the linear load must be the same diameter to avoid both closely spaced wires of differing diameters and wires of different diameters meeting at an angular junction. In both cases, NEC results can be quite inaccurate. One consequence of this restriction is that NEC cannot directly model most of the existing commercial antennas employing linear loading, since these antennas generally use element and load wires of radically different diameters.

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MININEC is subject to neither of these restrictions. With due attention to the need for very short segment lengths at angular junctions and to the overall segment limitation of many versions of MININEC, the program is capable of directly modeling virtually any linear loaded element. MININEC was the program of choice in my 10-meter study of linear loaded dipoles and Yagis in "Modeling and Understanding Small Beams: Part 4: Linear-Loaded Yagis." Communications Quarterly, (Summer, 1996), pages 85-106. These antennas used 0.75" aluminum elements and #12 copper wire linear loads, and MININEC provided excellent building guidance. Despite the different materials used, no construction correctives could be directly attributed to the program limitation of specifying a single material for the entire modeled structure. For conservative predicted results, the higher loss material (aluminum) was used throughout the modeling.

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Nonetheless, NEC (either -2 or -4) can model linear loaded elements where all wires are of the same diameter. This much capability is sufficient to reveal a number of linear load properties that are fundamental to this loading technique. Consequently, we may for this exercise employ some of the models already developed for other parts of this series and simply add to them various linear load configurations. Central to the work in this episode will be the 34.39' (412.68") short dipole that we have loaded in several ways. We shall principally use the #8 wire version. Throughout, we shall retain the use of 91 segments for the overall antenna main element, with an average segment length of about 4.53". This segment length will determine several other parameters in the course of physically modeling transmission lines or linear loads.

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In previous exercises, we have used perfect or zero-loss wire for the dipole element. So long as we could specify load losses in Type 0 or Type 4 loads (series R-L-C and series R-X loads, respectively), we could isolate losses directly attributable to the load. In this exercise, we shall physically model linear loads as wires in the antenna structure. In order to leave the "main" element perfect and register the material losses of the load wires, we shall have to use either NEC-Win Pro or GNEC (NEC-2 and NEC- 4 programs from Nittany Scientific), as these are the only commercial versions of NEC commonly available that permit specification of different materials for each wire in the antenna.

+

Also see the Antenna Modeling Programs page for more information.

+

Physically Modeling Transmission Lines

+

Modeled transmission lines must be parallel wire assemblies, since there is no practical way to model coaxial cables. (It is possible to simulate the cable braid with several wires of the same diameter as the center wires, but the cost in wire segment total makes the technique impractical here.) However, since a parallel wire line with significant spacing between wires represents the most common form of linear loading, this restriction will impose no problems.

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The linear loads we shall use will have a spacing of 4.53" center-to-center between wires. The diameter of a #8 AWG wire is about 0.1285". We can calculate the anticipated characteristic impedance of the resulting parallel line from this standard equation:

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+ +
+

where Zo is the characteristic impedance in Ohms, S is the center-to-center spacing of the wires, and d is the wire diameter, with both S and d in the same units. For the #8 line, the Zo is 510.1 Ohms.

+

The standard equation presumes an indefinitely long line without connection wires to either a source or load. Moreover, it is invariant for any wire type and thus does not account for variations in the materials one might use for an open line. (In addition, it does not account for spacers, insulation, and other line variables that are not a part of this exercise.) In fact, wires physically arranged as parallel transmission lines do not model with precisely the same characteristic impedance as those yielded by the standard equation.

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We can model transmission lines to determine their characteristic impedance using the figure above as guidance. The "top" and "bottom" wires are single segments, each 4.53" long. The parallel wires will be an odd multiple of a quarter wavelength for the frequency tested. In our case, the frequency is 7.15 MHz, and we shall check the line using lengths of 1/4, 3/4, and 5/4 wl.

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By adjusting the line to a length that yields resonance at the source for a given load, we can find the characteristic impedance of the line from the standard equation,

+
+ +
+

where Zo is the characteristic impedance of the line, ZL is the load impedance, and ZS is the source impedance. If we use a purely resistive load and bring the line length to resonance (defined as usual as less than +/- 1 Ohm reactance), the calculation is simplified. Let us initially specify a load of 5,000 Ohms resistance with a zero-loss (perfect) #8 wire line and see what we get.

+ 
Test Length    Resonant     ZS           Zo       Segs/Length    Delta L"
+ in WL         Length "  R +/- jX       Ohms
+1/4             409.9    59.2 - j 0.1   544.1      91 / 4.50"    2.75"
+3/4            1236.6    59.3 - j 0.0   544.6     271 / 4.56"    1.45"
+5/4            2063.0    59.5 + j 0.0   545.3     451 / 4.57"    0.40"
+

The "Delta L" figure is the departure of the resonant length from a perfect odd multiple of a quarter wavelength. The model has two wires at top and bottom which contribute to the overall line length and become error sources with respect to having a perfect parallel transmission line. However, the error they introduce decreases as the test line length increases.

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The selection of 5000 Ohms as the resistive load for this construction was arbitrary. For any given test length for the line, selection of a different load value will give slightly different results. Let's look at a 3/4 wl (1236.6") line and examine the characteristic impedance yielded by various load values.

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ZL                ZS                Zo
+Ohms           R +/- jX            Ohms
+    50         5920.0 - j 40       544.1
+   100         2961.0 - j 10       544.2
+   250         1185.0 - j 2.0      544.3
+ 1,000          296.3 - j 0.0      544.3
+ 2,500          118.6 - j 0.0      544.5
+ 5,000           59.3 - j 0.0      544.6
+10,000           29.7 - j 0.1      544.6
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With perfect wire, the range of variation in this second test of the characteristic impedance derived from the test model is not especially significant, with a maximum variance of about 0.5 Ohm for the range tested. The key variance in this exercise is between the modeled-derived Zo and the value calculated by the standard equation: about 33 Ohms--or a 6% variance, with the modeled impedance higher than the calculated value.

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If we specify the #8 wire to be copper (Resistivity = 1.72E-08), we end up with slightly different tables relative to those for perfect wire:

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Test Length    Resonant     ZS           Zo       Segs/Length    Delta L"
+ in WL         Length "  R +/- jX       Ohms
+1/4             409.7    60.1 + j 0.1   548.1      91 / 4.50"    2.98"
+3/4            1235.6    61.7 - j 0.0   555.4     271 / 4.56"    2.44"
+5/4            2061.0    63.4 - j 0.1   563.1     451 / 4.57"    2.40"
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The range of variation in derived Zo for the different test lengths, using the arbitrary 5000-Ohm load, is almost 15 Ohms. This represents a range of change of around 3%, which is well within the range of variation in real lines, especially those with insulation and a consequential velocity factor. However, the question remains as to whether the test yields accurate results. The second test provides the clue we need.

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ZL                ZS                Zo
+Ohms           R +/- jX            Ohms
+    50         5669.0 - j 80       532.4
+   100         2901.0 - j 22       538.6
+   250         1179.0 - j 5.3      542.9
+ 1,000          298.5 - j 0.5      546.3
+ 2,500          121.0 - j 0.1      550.0
+ 5,000           61.7 - j 0.0      555.4
+10,000           32.0 - j 0.0      565.9
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Note: when using low values of load impedance, it may not be possible to remove all of the reactance to the arbitrary standard of resonance that we have been using (+/- 1 Ohm reactance). However, if the reactance value is less than about 2% of the resistive value and slight line length changes to achieve resonance do not change the resistive value significantly, then the resulting resistive value will be usable.

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The test using different load values shows a wide range of values both above and below the values yielded by the perfect wire test. Since the approximate value of the characteristic impedance is also approximately the geometric mean between the adjacent load values (250 and 1000 Ohms), we can zero in on the actual line impedance by using that mean as a new load. If the first try does not yield a source impedance equal to the load we chose, we can adjust the load slightly until the results are equal within about 0.1 Ohms (to allow for rounding conventions in the software).

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Using this method, the final value for the perfect wire Zo is a little over 544.3 Ohms, while the final value for the copper wire is a little over 544.8 Ohms: very close indeed. In fact, we have extended the number of significant digits with respect to the characteristic impedance of the line too far for practical purposes in order to ensure clarity of the mathematical progressions. A value of 544 or 545 Ohms would suffice for all practical enterprises. This conclusion means that running the characteristic impedance modeling test with perfect wire with any reasonable load would have produced an acceptable result with a single test run.

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Modeling Transmission-Line Loads

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We have lingered over the transmission line modeling test not only to show that transmission line characteristic impedance may differ in modeling software from values derived from standard equations, but as well to ensure that when modeling transmission line loads, we do not draw the wrong conclusions from the results we encounter. In order to get a handle on drawing the right conclusions, the next step is to model some transmission line loads using our #8 parallel transmission line. Because the principles do not change whether or not we account for wire losses and because the models are for demonstration purposes and do not represent structures anyone would actually build, we may use perfect wire transmission lines for these tests.

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The models we shall construct use the basic 34.39' #8 perfect wire dipole. We shall insert transmission line loads at the segments adjacent to the feedpoint or source segment in the center and later at the points in the lines calling for 833.3-Ohm mid-element loads. From previous episodes of this exercise, we determined that loads placed immediately adjacent to the source for the 91-segment model required a reactance of 426.3 Ohms. We also used the 5-wire model to arrive at the positions of loads requiring 833.3 Ohms (the value of a single center load for this antenna).

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For our model, we may place the transmission lines parallel to each other or at 180 degrees apart. I have chosen the latter type of model to minimize interactions between the transmission lines, especially in the close-spaced model. Whichever model we choose, there will be a significant radiation component at right angles to the radiation from the main element.

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Let us take the Zo of the transmission line as 544 Ohms. Using the equations shown in earlier episodes, the 426.3-Ohm load requires a transmission line length of 174.6" while the 833.3-Ohm load is 260.7" long. Modeling these lines via the TL facility, in which the lines are mathematically but not physically modeled, would require these calculated values.

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Physically modeling the lines tells a quite different story, one that reveals why using the TL facility of NEC yields inaccurate results. To achieve resonance with the closely-spaced transmission line loads required a length of 155.3" for each line, almost 20" shorter than called for by the equation. The mid-element model required loads that were 157" long, more than 100" shorter than called for by the standard equations. (For alternate models using lines that parallel each other, the values were 151.2" and 156.5" respectively.) Each loading transmission line replaced one segment of the main element and the spacing was set at 4.53" between transmission line wires.

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A transmission line acts as a pure transmission line if and only if the currents everywhere along the line are equal in magnitude and opposite in phase on the two wires. An examination of the current tables produced by the NEC core reveals the degree to which this condition is not met by physical lines used as loads. In constructing models to perform this test, it is essential that the segments on each wire align perfectly.

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The current phase differential along the transmission line wires does not exceed 0.4 degrees in either case, so current magnitude comparisons are sufficiently accurate for the level of analysis required here.

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The graph shows the current magnitude differential between the transmission line wires for both cases tested. Current differential is greatest where the transmission line joins the main element. It does not reach zero at the far end of the line. The level of current differentials is far less along the closely-spaced or "center" load lines than along the mid-element load lines. Note, however, that there is nothing like a linear relationship between the degree of current magnitude differential and the degree of shortening of the lines.

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The current differential is an indicator of--but not a measure of--the fact that the lines have significant radiation. As radiating lines, they contribute linearly to the length of the antenna. To the degree that the wires in the load contribute to the linear length of the antenna wire, less reactive loading is required, and the lines required will be shorter than called for in standard equations. The higher the current magnitude differential, the greater the contribution to the antennas linear length and the higher the level of load shortening relative to equation-derived values. By mid-element, the contribution to the wires to the antennas linear length is so great that the load lines may be over a third shorter than their calculated value.

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In designing this overall exercise, I specifically chose a very short dipole (about 1/2 normal length) in order to set the effects we have noted in bold relief. Antennas only mildly shortened will show lesser current differentials in each of the models, and the degree of load shortening will be correspondingly less. Nonetheless, I know of no way of eliminating the fact that transmission line loads act as both reactive loads and as part of the linear antenna length--short of eliminating transmission lines as loads.

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The placement of the loads in this drill is far from optimal for maximum performance for the antenna. The gain of the close-spaced or center load model is 1.67 dBi, while the gain of the mid-element model is 1.88 dBi. The latter value is comparable to the values for zero-loss center and mid- element R-L-C loads (1.85 and 1.87 dBi, respectively), but there is considerable cross-polarized radiation that reduces the normal side nulls of a free space dipole model.

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Before we leave these informative but impractical models, we should briefly examine the SWR curves (relative to the source impedance at resonance for each model). The close-spaced or center loaded model shows a curve consistent with those we examined earlier in connection with transmission line loads generated with the TL facility. The mid-element line, in contrast, shows a very shallow curve, indicating a much wider operating bandwidth. This curve is in stark contrast to curves associated with TL- generated loads.

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The source of the broader SWR curve for the mid-element transmission line load lies mostly in the fact that the load lines act to a much higher degree as part of the linear or radiating length of the antenna. Consequently, the SWR curve approaches that of a standard full-size dipole. The major difference is that the shortened dipole has a resonant impedance of about 20 Ohms. (The resonant impedance of the close-spaced model is under 10 Ohms. The impedance of a perfect center-loaded dipole in this series of models is about 13 Ohms, while a perfect mid-element loaded version shows a resonant impedance of about 27 Ohms.)

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Linear Loads

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The transmission line loads that we have just explored place the load lines at right angles to the main element in order to minimize interactions. Conventional linear loads tend to place the loading lines parallel to and close by the main element.

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The sketch shows three typical linear load line assemblies. Actual antennas tend to fall into one of the three categories, although details may vary. The triangular load at the top feeds the center junction point of the linear load shorted lines, which then attach to the main element. Although we cannot accurately model actual structures in this exercise, the main element of most antennas of this type will be much larger in diameter than the load lines. For many purposes, the load lines may be placed in a plane with the main element, as shown in the middle sketch. Once more, the main or upper element will be larger in diameter than the load lines.

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A third popular assembly is shown at the bottom as a mid-element linear load. In this case, a "main" or larger diameter element is the feedpoint. The apparent load lines begin at mid-element and return toward the center, terminating and returning to the completion of the main element. Ordinarily, the apparent load lines are placed symmetrically about the main element, forming a triangle or a single plane. Why the sketch refers to this schema as a "pseudo-mid-element linear load" will become apparent as we proceed.

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The models for the tests were carefully constructed to achieve several goals. The segments throughout are all close to 4.53" long, and the spacing between lines is exactly that figure. Hence, the triangular models form equilateral triangles so that the influence of the main element is as equal upon both load lines as possible. The center separation between load ends (shorting segments) is also 4.53" or one segment's length. This procedure permitted alignment of all segments both between the load wires and on the main segment as well. All of the models are #8 AWG wire.

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In this sequence of test, however, we shall look both at load lines that use perfect wire and lines that use other materials. The figure below shows an in-plane model in which only the load lines (wires 2 through 8) are copper. In this way, we may isolate the losses due to the load from the losses due to the main element wire, which remains a perfect or zero- loss wire like the ones used in earlier R-X and R-L-C load models.

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The table below presents the load line lengths, measured from the source point for each of the three types of loads modeled. The "triangular mid- element" load line is measured from the source point both to the start and to the finish of the line outward. For the center triangular and in-plane models, line lengths for perfect, copper, and aluminum load lines are recorded, while the mid-element line is recorded only for the perfect wire version.

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Antenna             Load Material       Load-Line Length (")
+Triangular Center   Perfect             175.2"
+                    Copper              174.5"
+                    Aluminum            174.35"
+In-Plane Center     Perfect             188.0"
+                    Copper              187.3"
+                    Aluminum            187.15"
+Mid-Element         Perfect             176.43" (outer)
+                                        171.90" (inner)
+

The decrement in length for the loads with the use of materials having a reduced conductivity is identical for both the triangular and the in-plane models. The load length for the in-plane model is longer than for the triangular or the mid-element model. However, the mid-element model load structure is virtually identical in length to the equally triangular center loaded model. Note that the triangular model load lengths correspond very closely to lengths for a split center load reactance when calculated from standard equations using the 544-Ohm Zo of the load line. For the required 416.7-Ohm load, the required load line calculates to 171.7" or within 2% of the actual modeled line lengths.

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Although the triangular models are physically set to minimize unequal influence from the main element, the current differential on the load wires is not zero. The graph shows the two values of current differential to be almost precisely the same for the zero-loss wire models, with closely corresponding phase differences as well. With the exception of a 4.53" change of wire alignment, the two models are the same model in every operational respect. In the mid-element model, the so-called fed main element is actually one leg of the loading line, and the apparent second leg of the loading line corresponds to the main element in the triangular center-loaded model.

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In contrast, the current differential between the load wires of the in- plane model is much higher. The higher differential is due to the differential interaction between the main element and the individual wires which are at different distances from the main element.

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A further insight into the difference between the triangular and the in- plane models can be gather from examining the currents on the main element outward from center. Note once more the close coincidence between the triangular models. In contrast, the current magnitudes along the outbound wire for the in-plane model are lower everywhere. Part of this reduction is due to the increased length of the in-plane linear load, which results in an electrical shift in the position of the beginning of the main element at the antenna's center.

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As might be expected, the current distribution on the in-plane model results in a lower gain than for either triangular model. With perfect wire, both triangular models report an anticipated gain of 1.86 dBi, while the in-plane model gain is 1.79 dBi--not a big reduction, but noticeable. With copper loads, the triangular model gain is 1.35 dBi, while the in- plane gain is 1.30. An aluminum (6061-T6) loading wire set yields a gain of 1.11 dBi for the triangular models and 1.06 dBi for the in-plana model. The values for aluminum wire load lines (with perfect wire main elements) correspond closely to the values for center and mid-element load dipoles using R-L-C loads with a Q of 300 (1.02 and 1.11 dBi, respectively).

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Equally revealing about the behavior of linear loads are SWR curves for the three models, each predicated on the source impedance at resonance at the design center frequency of 7.15 MHz. The resonant source impedances are 12.0, 12.1, and 12.2 Ohms for the triangular center, in-plane center, and triangular mid-element models. The coincidence of the mid-element linear load model source impedance with the center loaded models and not with the mid-element transmission line load model examined earlier is further confirmation that the mid-element model is simply a minor variation of the triangular center loaded model. The SWR curves confirm this further by overlaying each other, while the in-plane curve is slightly broader, as one might expect of a very slightly lossier structure. The mid-element linear load model no where approaches the broadness of the mid-element transmission line load we explored earlier.

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The SWR curves for the triangular model for the three load line materials show the expected broadening of the curve with the use of materials with a lower conductivity. Similar results accrue to the in-plane model.

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Conclusion

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The linear load is essentially a shorted transmission line stub placed in line with the main element of the antenna it loads. As an antenna load, the stub cannot act as a pure transmission line; the current can never be equal in magnitude and exactly opposite in phase on the two wires making up the load line, since the current magnitude and phase on the antenna element into which it is inserted is not the same at any two points along a path from the antenna center outward. However, the condition is most closely approximated when loads are as exactly at center as possible and symmetrically placed about the main element to equalize its influence on each load wire.

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Since linear loads are transmission lines and answer in part to the equations for calculating length from required loading reactance-- especially when placed at the center of the antenna structure--their operating bandwidth curves, as reflected in the SWR curves shown, are narrower than for corresponding R-L-C loads.

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The graph above plots curves for center and mid-element loads using perfect loads and loads with a Q of 300. Additionally, the graph records the SWR curves for the triangular linear load model using perfect and copper wire. note that the curve for the copper wire linear load is sharper than any of the R-L-C loads except the center load with infinite Q. The broadest lines in the curve are for R-L-C curves with a Q of 300.

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Because the operating bandwidth of a linear load rests in large part on transmission line stub behavior and not on solenoid inductor behavior, losses cannot be directly correlated with operating bandwidth. Within each type of load, increases in bandwidth might point to increasing losses in the loads. However, cross-load type correlations are far less certain.

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To the degree that the currents on the linear load transmission line stubs are unequal, the wires also contribute to the linear length of the antenna. If placed at right angles to the main element wire, the radiation appears as a cross polarized field relative to the radiation from the main element. Moreover, the larger the current magnitude differential between load line wires, the more the wires act as linear contributions to the overall antenna length and the shorter the required stub.

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As with any complex electrical structure inserted into an antenna and modeled physically, the modeling calculations cannot directly account for all phenomena. For example, some theory exists to suggest that transmission line wires have greater losses for a given wire size and frequency of RF current than that same wires in an electrical circuit, due to the effects of the intense field between the wires. However, these effects turn out to be small, even for the long linear loads used in the very short modeled dipole. MININEC tests and other marginally valid tests within NEC suggests additional total field antenna gain losses between 0.1 and 0.2 dB. These losses, if present, have no noticeable effect on the operating bandwidth of the linear-loaded antenna models.

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While the bulk of the transmission-line view of linear loads has been previously established, presenting it here is useful if--for no other reason--than because it raises an interesting question. Just as linear loads have unequal current magnitudes at their junction with the main antenna element as a function of the current distribution along an antenna element, it would appear that solenoid inductors used as loads would share the same behavior. If this turns out to be the case, then the mathematical specification of loads within NEC would be equally incomplete, despite the high trust antenna designers and analyzers place in R-L-C loads of Type 0 and Type 1.

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It may be worth one more episode just to test the hypothesis and confirm (or disconfirm) the trust we place in Type 0 and Type 1 R-L-C loads.

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Go to Main Index

+ + diff --git a/content/amod/amod16.html b/content/amod/amod16.html new file mode 100644 index 0000000..8d5f665 --- /dev/null +++ b/content/amod/amod16.html @@ -0,0 +1,111 @@ + + + + + Some Solenoid Loading Basics + + + +
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16. Notes on Reactive Antenna Loads and Their NEC Models:
+ D. Some Solenoid Loading Basics

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L. B. Cebik, W4RNL

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The final question in our inquiry is whether Type 0, 1, or 4 mathematical loads (each within their application limitations) fully or adequately specify inductively reactive loads used in a shortened antenna. Answering this question via antenna construction would seem natural, were it not for our customary building practices and presumptions. When we install a loading coil and it proves too large relative to the wire length, we simply shorten the wire to match the coil. Then we fail to interrogate the situation further to discover why the coil was too large. Most of the time, we assume that we miscalculated or that the usual coil equations are not sufficiently accurate to yield a coil that requires no subsequent wire pruning.

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As a consequence, few modelers have explored the behavior of helically wound single layer solenoid inductors in their models--simply because winding a coil is too laborious a task relative to using the loading facilities built into NEC. We have presumed that the loads--especially Type 0 series R-L-C loads--adequate specify the loads we need.

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Yet nagging suspicions remain about such loads. The current differential that is present at each end of the load suggests that--like their linear load counterparts--these loads do not act like pure inductances, but may also function as simple current bearing wires. Models of helical dipole elements show very usable gain, which parallels the experience of those who have constructed such antennas. I guess we shall not know whether mathematical models of loads accurately reflect the operation of single layer solenoid inductances unless we actually wind some model coils and replace the Type 0 loads with them.

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Winding a Helix and Making a Model

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The basic model for the half-size (1/4 wl) 7.15 MHz dipole uses #8 (0.125" diameter) zero-loss wire that is 412.68" (34.39') long and divided into 91 segments. Each segment is about 4.53" long. For least error, the segments within the helix will be as close to this value as helix construction permits.

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The required center loading reactance for the antenna is 833.3 Ohms or 18.549 uH. We may let the coil be 3 segments long or 13.6" overall. Using the standard Wheeler equations (either the common 1928 version or the 1982 version), a circular single layer solenoid inductor of this length will require 10 turns and an 11.852" diameter.

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The most reasonable approximation of a circular solenoid is an octagonal structure. Fig. 1 shows the resultant structure and the basic relationships that determine the coordinates of the points around each loop. For this exercise, let's adopt the convention of extending the turns along the X-axis and using the Y-axis and the Z-axis for the radial points of each loop. Under this convention, the point references in the lower part of the drawing refer to Y and Z coordinates. Beginning, perhaps, with half the diameter as the value of R (5.926"), we might place the first entry at 0, 5.296, 0 (assuming a free space modeling environment). Intermediate points between the horizontal and the vertical will require values of 0.707 R (3.744"). (Note: rounding to one less decimal place will make no significant difference in the long run.)

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Each point progresses along the X-axis by the total length (13.6") divided by the number of turns (10) divided by the number of points in each turn (8), for a value of 0.17" in this case. Hence, the second point of the turn will be located at 0.17, 3.744, 3.744. We can then proceed to complete the first turn. Then, using whatever copy function may be present, we add progressively more turns, increasing the value for the X- coordinate by 1.36 with each turn.

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The resulting solenoid will be about 2.5% short in overall wire length used compared to a truly circular solenoid, suggesting a slightly lower inductance than provided by the Wheeler calculation. Since the wire is small compared to the turns spacing, a slight additional variance may also be encountered. Of greater significance for the model, each wire in the helix is about 4.56" long, a close match to the length of the segments in the remaining portions of the dipole wires.

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Once the coil is complete, it should be saved as a file, since we may use it later. For the initial test of center-loaded short dipole, we may replace the center 3 segments of the basic wire with the helix. The best coordinates for the coil may be -6.8 to + 6.8 on the X-axis to obtain a useful symmetry in the now enlarged geometry sheet--useful for visual error trapping. The formerly single wire is now two wires extending to + and to - 206.343" respectively, and each with 44 segments.

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Part of the extended exercise in looking at NEC loads, both mathematical and physical, has involved sorting out the losses attributable to the load from those which may be associated with the linear wire portion of the antenna. For this purpose, we shall need to make the linear wire lossless and the coil wire of a suitable material, namely, copper. At present, only GNEC (Nittany-Scientific) permits a wire-by-wire material selection. Fig. 2 shows a partial .NEC file from GNEC, with the dimensions in meters.

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The portion of the model shown shows the last few turns of the helix, wire by wire. The last wire (82) is the linear dipole wire in the +X direction. Skipping down to the Type 5 load lines (material loading), we see that wire 1 (and also 82) is skipped, being lossless, while the conductivity value for copper appears for each wire in the helix.

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Finally, because the turns of the helix have an equal number of wires per turn, a split feed is used at the wires forming the very center of the inductor.

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The Center-Loaded Half-Length Dipole

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The model just constructed in a free space environment yielded an inductive reactance of over 86 Ohms, indicating not that our octagonal coil was slightly small, but rather that it was considerably too large. Achieving resonance required a significantly smaller helix. In order to preserve the length of the coil that was equal to 3 segments of the linear wire, the coil was reduced in diameter. With a diameter of 11.12" the loaded antenna achieved resonance (as defined in this study as less than +/- 1 Ohm source reactance). Wheeler calculations for a circular coil of this diameter, length, and number of turns yielded an inductance value of about 16.6 uH, roughly 10% less than the value called for by the mathematical load systems provided in NEC. The length of the coil wires reduces to about 4.25" each, which is unlikely to induce any significant error in the model.

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The following table provides some basis for making comparisons between the physically modeled load and the Type 0 loads used in earlier parts of this exercise. In all cases, the linear portion of the antenna is composed of lossless wire.

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Load                Free Space          Source Impedance
+                    Gain dBi            R +/- jX Ohms
+Lossless Type 0     1.85                13.19 - j 0.02
+Q=300 Type 0        1.02                15.97 - j 0.01
+Copper Helix        1.35                10.61 + j 0.64
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The higher gain provided by the physically modeled center load should not be surprising, considering that the helix contains wire that radiates. See Fig. 3.

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The small but definite vertically polarized radiation field results from radiation from the portions of the helix that are vertically oriented. This field alone would not suffice to provide the added gain over the Q=300 center loaded model, but the entire 13.6" length of the inductor would. More precisely, that portion of the overall inductor wire beyond the 13.6" it replaces in the overall antenna length would suffice to provide additional gain.

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The actual Q of the inductor cannot be ascertained with accuracy. Some calculations estimate the Q at over 400, but only under the conditions that the wires be closer to half the spacing between turns. The modeled helix uses much smaller diameter wire, resulting in a decrease in Q, perhaps to the 200-300 range at best.

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Despite the lower Q estimate, the source impedance of the physically modeled helical loaded dipole is lower than even the Type 0 model at zero load loss. As Fig. 4 shows, the SWR curve is slightly steeper than even the R-L-C lossless load model--and a lossless helix yields a steeper curve yet.

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The actions of the physically modeled helix load are in part a function of the current magnitude and phase profile along the coil. Fig. 5 shows the two curves from the center point outward toward the end.

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The current magnitude differential between the source and the coil end is approximately 20% of the maximum value. Since the inductance of a helix is in theory predicated upon equal current magnitudes at both ends of the coil, the differential currents dictate that in part the indictor does not act solely as an inductor. The physical model of the center load provides indications that the helix also radiates in the manner of any length of wire included within the total length of the dipole--in terms of gain over the Type 0 load, the vertical radiation field, and the reduction in the required inductance to effect loading to resonance.

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There are potential error sources within the model. First, the octagonal inductor with less then optimal wire diameter relative to turns-spacing casts some doubt on the precision of the calculations relating inductance to turns, diameter, and length. However, most of these factors suggest that the octagonal coil's inductance would be low, when in fact, the model showed it to be very much higher than required for resonance.

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Second, the helix design, although apt to the modeling task, is very large and open compared to coils one might ordinarily apply as center loads in a shortened dipole. However, as an error source, the helix configuration would be a matter of degree and not of fundamental principle of operation. What the dimensionless load of a Type 0 load does not show is the relatively large early drop of current magnitude along the total length of the dipole. Fig. 5 shows the more dramatic drop occasioned by the physically modeled coil. Although different coil configurations may alter the amount of drop somewhat, the current magnitude curve is unlikely to resemble that for the Type 0 load.

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The plausibility of the physical model might be put to still another test. The original short dipole model was designed to permit one to place load values equal to the center load value at specific mid-element points. If the center load helix as modified to achieve resonance acts like a Type 0 load, then placing the same coils at the specified points should also result in resonance.

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The Mid-Element-Loaded Half-Length Dipole

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The original model was modified into a 5-wire model having the same operational characteristics as the original. The inserted 3-segment wires were placed at points between 99.5" and 113.1" from the center so that the Type 0 load was positioned 106.3" from the center. At these positions either side of center, a load of 833.3 Ohms (18.549 uH) resonated the antenna. The value of these two loads was the same as the value of the single center loading reactance.

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As shown in Fig. 7, the helix developed for the center load may directly replace the inserted 3-segment wires in the 5-wire model. By copying the original helix and changing the values for all of the X coordinates by the same amount, each coil may be placed in the correct position. The connection points to the coils are very slightly displaced relative to the axis line, but not by an amount to show up in a movement of the antennas resonant frequency. The 11.12" diameter (R = 5.56") helix was copied and transferred to these points and the model run.

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The result was a source impedance of about 29 + j 229 Ohms, indicating that the inductor size (16.6 uH) was much too large for resonance. This result was consistent with but considerably larger than expected. To create helices that allowed the overall antenna to achieve resonance required a reduction in the coil diameter to 10.2" (R = 5.10"). By Wheeler calculations, the inductance was reduced to about 14.3 uH for a truly circular coil. The wire length from coil point to coil point diminished to 3.90" compared to linear wire segment lengths of 4.53" each.

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The amount of reduction in coil size was about 14% relative to the final center loading coil and almost 23% relative to the inductance required by a Type 0 load. This reduction is consistent with several factors involved in inductive loading, including the fact that the further out along an element one places the inductor, the less it acts as an inductor and the more it acts as a compact form of wire length to increase the overall wire length to resonance. By the outer ends of a shortened dipole, helices and others forms of element extension cannot be viewed as inductances almost at all.

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The current magnitude and phase profile within the helix may be of some surprise to some. Along the mid-element loading helix, after size adjustment to resonance, the current does not show a steady progression lower in magnitude. Instead, there is a current peak about a fourth of the way outward from the inboard end of the coil. From that point onward, the current magnitude descends rapidly. The phase transition, although not linear, generally follows the progression along the entire antenna element.

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Compared to the center loading coil, the current magnitude excursion within the inductor is about 34% of the maximum value, and the end to end difference is about 30% of maximum current magnitude. This compares to the 20% differential from center to end for the center-loading coil. The greater differential of current magnitude along the mid-element inductor wire is another indicator that it is functioning to a greater extent than the center loading coil as part of the element length and hence requires less inductance and inductive reactance to effect loading to resonance.

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Like the physically modeled center load, the physically modeled mid-element load shows a much larger drop in current at its outer end than does a corresponding Type 0 load. The dramatic decrease in current immediately outside the loading helix appears vividly in Fig. 9, with the Type 0 load curve shown for comparison.

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Despite the close correspondence of current up to the load position and the dramatically lower current beyond that point for the physically modeled helix, the model shows a significantly higher gain than either the corresponding Type 0 load model or even the physically modeled center load. The following table summarizes the gain situation for various models.

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Antenna                            Free Space          Gain Relative to a
+                                   Gain dBi            Full Length Dipole
+Full-Length                          2.14                   ---
+Half-Length Lossless Wire            1.85                   -0.29 dB
+Type 0 Center Load, Q=300            1.02                   -1.12 dB
+Helical Center Load, Copper          1.35                   -0.79 dB
+Type 0 Mid-Element loads, Q=300      1.11                   -1.03 dB
+Helical mid-Element Loads, copper    1.71                   -0.43 dB
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The gain figures strongly suggest that the current within the turns of the helix is not going wholly to waste within a tightly coupled inductive field. That part of the current not devoted to the field, as indicated by the current differential at the coil ends and among the turns is contributing to the total field of the antenna.

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The use of Type 0 loads to characterize both center and mid-element loading strongly suggests that there is little difference between the gain potential of two antennas of equal length loaded in each manner. However, physically modeled loading helices tell a quite different story. Not only do both types of loaded antennas potentially perform better than mathematically inserted loads would indicate, but as well the empirical experience giving the nod in gain to mid-element loading gains some support from the physically modeled loading coils.

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Although the physically modeled center loaded antenna showed a steeper SWR curve than its Type 0 counterpart, the mid-element loaded antennas show a good correspondence between mathematical and physical loads. In fact, as shown in Fig. 10, the mid-element physical helices correspond nicely to mathematical loads with a Q of 300. This curve corresponds reasonably well with estimates for the Q of the coil at or just below 300, based upon reductions from the calculated Q of over 400 that presumed an ideal wire diameter to spacing ratio. The resonant source impedance of about 24.6 Ohms is a bit lower than the Type 0 model at Q=300, where the source impedance was about 31.9 Ohms.

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It should be noted for accuracy and completeness that the actual resonant frequency for the model using physically modeled mid-element coils with a 10.2" diameter was 7.16 MHz, and that the curves for this antenna actually run from 7.01 to 7.31 MHz. This 10 kHz displacement did not seem great enough to warrant reconstruction of the coils through the iterations necessary to move the resonant frequency. The estimated diameter would have been something of the order of 10.205" +/- 0.002" for resonance at 7.15".

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Potential Errors and Conclusions

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The potential error sources for the mid-element load model remain the same as for the center loading coil. The octagonal helices may in fact show a lower inductance than the values calculated by the Wheeler equations. Moreover, the widely spaced open helix may prove a better radiator than some more tightly wound loading coils. Unique to the modified mid-element loading coils is the shortening of the wires and a somewhat greater differential to the lengths of the segments in the linear wire portions of the antenna.

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Some of these possible error sources work in the wrong direction relative to the results, for example, the reduced inductance of octagonal helices relative to truly circular ones. The sum of the remaining error sources appears to be far short of what would be required to account for the radical reduction in required inductance for the loading coils. Indeed, the most telling part of the demonstration is the further reduction in coil size required in moving the center-loading inductor out to the position where the same value should have served as a mid-element loading inductor. Although absolute values of the inductors involved may be off the mark by some small amount, the trends are in all probability accurate reflections of anticipated antenna performance.

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As a consequence of these data and considerations, the bottom line seems inevitable: Type 0 (and by extension, Type 1 and Type 4) loads do not fully characterize the performance of inductively reactive loads in the form of single layer solenoids. For many purposes, that characterization may be adequate to a design task. For example, where design criteria permit adjustment of the antenna outer section length, designing to the Type 0 load value may cause not harm.

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However, using mathematical loads alone can give a potentially misleading impression of the gain of the loaded antenna. The gain for physically modeled loads is considerably higher than the gain for mathematical loads. Where multi-element arrays--such as Yagis--may employ center or mid-element loads in all elements, Type 0 load models may seriously underestimate the overall array gain.

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This exercise, along with the previous portions of this study, should be viewed as only a beginning to the investigations into modeling loaded shortened antennas. Further work might yield additional insights into the behavior of linear loads examined in the last episode. Likewise, for helical inductive loads, much remains to be done with respect to the use of more compact forms of inductance. Even using these models, additional data can be gathered for the use of linear wires with non-zero losses and for the use of other helix materials, such as aluminum.

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Nonetheless, if the present demonstration holds up as reasonably valid, then the suspicion raised at the outset has been established. In several important respects, the mathematical loading features provided within NEC do not fully characterize the action of these loads when physically modeled. Nevertheless, modeling actual loading inductors that form junctions with elements of radically different diameter from the coil wire and modeling small-diameter coils without violating adjacent segment length restrictions may prove to set major challenges for the amateur and the professional modeler. This study was carefully designed to use models that stayed well within all NEC restrictions. Most real antennas that use inductive reactance to electrically lengthen a physically short element will press those restrictions or result in quite large models.

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In other words, what we can establish in principle in a straightforward manner might prove to be an exceptional modeling challenge when real antennas and their parts are involved. Loads are not quite as simple as casual modeling might lead us to believe.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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17. Notes on Reactive Antenna Loads and Their NEC Models:
+ E. Some Unfinished Business on Modeling Loads

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L. B. Cebik, W4RNL

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In the first four sections of this series on inductively reactive loads used to electrically lengthen physically shortened antennas, we uncovered some interesting disparities between the standard mathematical models of loads and loads which are physically modeled. If the demonstration models are valid, then the following summary points are true in principle.

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1. Because the current magnitude and phase in a transmission line used to load a short antenna do not show a true transmission line relationship in a physical antenna, the use of the TL facility in NEC is not a reliable model of the real line and should be confirmed with a physically modeled transmission line load.

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2. Linear loads are a variety of transmission line stub load, but their behavior should be physically modeled for greatest reliability, especially when folded back from a mid-point along the so-called main element. Within the length of the linear load, which wire comprises the "main" element is ambiguous, since the radiation from that portion of the antenna is a function of the closely coupled fields from the element and the load wires in the stub.

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3. To a lesser but still significant degree, physical models of single layer solenoids, when modeled as helices, depart from the Type 0, 1, and 4 NEC mathematical models of them when placed as loads along an antenna element. In general, such loads show composite properties as inductances and as added wire length, the latter of which properties contributes to the radiation field of the antenna. The effect increases as the inductors are moved outward from the center of a dipole, with less inductance being required for the load than for a center loading coil. Even a center loading coil requires less inductance in physical models than called for by the NEC mathematical load.

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Although the exercises have demonstrated the effects, they fall far short of establishing a set of universal principles, mostly due to the limitations of NEC. Some of the potential error sources in NEC-4.1 have been reviewed in "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), pages 3-16.

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Throughout the exercises, NEC-4.1 was used in the EZNEC Pro and the Nittany-Scientific GNEC implementations. In all models, unless otherwise specified, the linear wire was modeled as lossless in order to sort out losses and performance curves due to the load from those attributable to the linear wire. Hence, all gain figures in previous exercises will be higher than with any real antenna using copper or aluminum elements. All models were constructed in free space.

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The model short dipole for 7.15 MHz was 1/2 full size at 34.39' (412.7") long and used #8 AWG (0.1285" diameter) wire. All physically modeled load structures used the same wire in order to avoid possible errors resulting from angular junctions of wires having dissimilar diameters. The original antenna was assigned 91 segments, each about 4.53" long. The selection of segment length served a number of purposes. First, it set the spacing of linear load wires from each other at a reasonable distance for accurate modeling. Second, it permitted the construction of octagonal single layer solenoid inductors that were exactly 3 segments long and whose wire lengths for each portion of each turn were close in length to the adjacent segments of the linear wire.

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The original model was revised for mid-element loading exercises into a 5- wire model. 3-segment wires were placed on each side of the center wire so that the center segment of the insert was positioned exactly where a mid- element load was equal in size (reactance and inductance) to a corresponding center load such that either system brought the antenna to resonance with no change in the overall length of the dipole. The overall segmentation was not changed, so that segment length among models remained close to equal. A 3-segment long (13.6") physical inductor model replaced the center 3 segments of the model for center loading and replaced the two inserts for mid-element loading tests.

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Subject to continuing review, it is believed that these models fall well within the limitations of NEC-4.1's ability to provide accurate results. It should be unnecessary to add that the relationship of the NEC-4.1 modeling system to real antennas is not like the relationship of a child's plastic toy to a real automobile. Rather, NEC-4.1 (and other versions of NEC and MININEC) are complex mathematical systems based upon both fundamental antenna theory and fundamental mathematical principles for calculating the various performance parameters of many types antennas. Those who dismiss antenna modeling in general largely reveal only a general lack appreciation of the role of mathematics in both antenna theory and antenna practice.

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Those who develop, implement, and work with any version of NEC are also conscious of its limitations. All version of NEC have been extensively tested against experimental results for many fundamental antenna types. However, it is possible to create antenna geometries that exceed the limitations of the calculation system. In such cases, NEC yields results that do not tally with either theory or practice. Since no program developer or development team can fully predict all of the antenna geometries (or environmental circumstances) that users will model, they can only enumerate some of the program limitations. Users will discover other limitations in the course of their work, and these limitations set the challenges for further development.

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This note is about some of the limitations that apply to the extension of the models used in this exercise set to various real antenna designs.

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Linear Load Limitations

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The difficulty of extending the models used for linear loads in these notes to real antennas can best be illustrated by taking up a few concrete examples of extant antennas.

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Fig. 1 shows a sketch that outlines the basic design features of one commercially manufactured antenna element using a linear load. To this point, I have been unable to construct a model of this element that falls within NEC limitations.

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The element uses a series of tubes of decreasing diameter as one moves from the center point outward. The NEC-2 limitation with tapered diameter elements is largely, but not completely, overcome in the NEC-4.1 algorithms. Modeling this element in NEC-2 with Leeson corrections (or, more properly, conversion of the element into its equivalent uniform diameter equivalent) is not possible, since the linear load junctions would block correction implementation (and the implementation of the correction would be inaccurate, since the element is not continuous).

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In this particular design, the linear load wires are very thin compared to the center element, and they are very closely spaced to the center element. All versions of NEC yield erroneous results when wires of different diameter are closely spaced. Moreover, there is a right-angle junction of wires of different diameter, another case in which NEC yields erroneous results.

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A second design of commercial origin appears in Fig. 2. In this case, the previously noted limitation involving angular junctions of wires having dissimilar diameters also applies to this design, since the load wires are very much thinner than the center element tubing. The tubing also uses a diameter tapering schedule, adding a definite limitation to modeling with NEC-2 and a minor limitation for NEC-4.1.

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The wires of the load are not parallel to each other. This feature would make the correlation of the load to transmission line stubs more complex, although for general purposes, the averaged characteristic impedance of the line might be used with fair accuracy. However, to the degree that physical models of parallel transmission lines yield results at variance form standard calculations, determining the characteristic impedance of the physically modeled line will prove more difficult.

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A third feature of this design is the placement of the long shorting bar near the center of the element. Physical models of shorted transmission line stubs take into account the current magnitude and phase of the shorting bar. In this instance of a long bar, the bar itself becomes an integral part of the line, one having a rapidly decreasing spacing between opposing segments. The design also may place the shorting bar at a distance from the element center point than used in the exercise models. Hence, the correlation drawn in the exercise between mid-element loads folded back to the center and loads properly called center linear loads may be less certain for this case.

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We can illustrate the difficulties of modeling a real linear load in NEC by looking once more, in Fig. 3, at the model of the in-plane center linear load, discussed in part 3. In that model, using #8 wire uniformly throughout the model, several facets of real antenna construction were simplified. The spacing between the three wires was set at 4.53" center-to-center. This spacing produced identical surface-to-surface spacings that were 0.1285" less than the center-to-center spacing.

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If we increase the "main" element to a 1" diameter, center-to-center spacings no longer correlate to surface-to-surface spacings, changing the relationship among the elements. In addition, we encounter the potential problem in NEC of closely spaced wires with different diameters.

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Fortunately, this model just barely fits within the MININEC segmentation limit and can be evaluation on that system. MININEC does not show a limitation with respect to closely spaced wires with different diameters. However, MININEC models tend to clip corners with angular connections, and we should expect (without invoking length tapering) some required change in the length of the loading wires if we hold the overall length constant.

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The following table shows the results of modeling the in-plane antenna in both NEC-4.1 and in MININEC. Load line lengths (from center to short) are given to indicate the require modifications to achieve a value close to resonance (in this demonstration, loosely defined as under +/- 5 Ohms). In addition, values are shown for models using lossless, copper, and aluminum wire throughout.

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                         MININEC                       NEC-4.1
+Main                Free Space     Feed Z         Free Space     Feed Z
+Element             Gain dBi       R+/-jX         Gain dBi       R+/-jX
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+#8 AWG                   (Load = 194.5")               (Load = 188")
+  Lossless wire     1.85           11.9-j1.2      1.79           12.1-j0.0
+  Copper            1.30           13.5-j1.2      1.25           13.7+j1.5
+  Aluminum          1.04           14.3-j1.2      0.99           14.5+j2.4
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+1"                       (Load = 158")                 (Load = 165.3")
+  Lossless wire     1.85           11.9+j4.5      1.25           13.7-j0.5
+  Copper            1.39           13.2+j4.5      0.83           15.1+j0.9
+  Aluminum          1.17           13.9+j4.5      0.62           15.9+j1.6
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In the table, gain figures are shown to 2 decimal places in order to show numerical trends that would have been erased by excessive rounding. (For operational purposes, figures to a single decimal place would suffice for many comparative cases, and the decimals might be dropped from certain generalized discussions. However, those who believe that showing gain to multiple decimal places should be dropped in all cases simply lack an appreciation for all of the purposes for which the antenna modeling programs can be put to effective use. Each degree of precision in reportage has its proper context. My own preference would be to see modeling reports overly precisely reported and then to do my own rounding than to see such figures pre-filtered.)

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The gain and impedance figures for the #8 model show excellent correlation between the modeling systems, with a maximum gain variance of 0.05 dB and a maximum resistive variance of 0.2 Ohms. If we look at the MININEC column and read downward, then the reported performance of the 1" main element version of the modeled antenna shows very sensible results. The lossless version of the model shows minuscule differences from the #8 version (actually none in the truncated decimals used here). The copper and aluminum versions of the 1" version show increases in gain over the #8 version as the material becomes more lossy. This is a function of the increased surface area of the larger element, and a similar trend shows up in full size dipoles. Likewise, the feedpoint impedance of the 1" antenna decreases more rapidly from the #8 version as the material loss increases, again for the same reason of lower overall losses. Once more, this trend also shows itself in unloaded antennas.

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Regardless of the absolute accuracy of the MININEC figures, the trends in numbers are not only intuitively sensible, they correlate with the behavior of models of unloaded antennas. In contrast, the NEC-4.1 figures for the 1" diameter main element model report decreases in gain and increases in feedpoint impedance for each material assignment. These numbers indicate either that the wire spacing for the element sizes involved and the frequency of test (7.15 MHz) has crossed the threshold at which NEC-4.1 no longer delivers accurate results or that the angular junction of the #8 wire with the 1" wire is yielding less than accurate results--or both. It is common in either error mode for NEC to report a gain that is too high/low while reporting an source impedance that is too low/high.

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Allowing for corner junction errors, MININEC remains the program of choice for modeling complex geometries that involve junctions of wires having dissimilar diameters and/or closely spaced wires of differing diameters. Recent developments in MININEC to break the segment limit, such as in NEC4WIN, will go far to make more complex MININEC models possible. However, not until the other MININEC limits are overcome--namely, raising the speed of matrix execution and grafting on the Sommerfeld-Norton ground calculation system--will the program be fully competent for all purposes.

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Solenoid Coil Limitations

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In the physical models of single-layer solenoid inductances used as loads, the constraints imposed on the exercise dictated the use of helices with a relatively large diameter (11.85") and a long length (13.6"). The wire size (0.1285") was relatively thin compared to the turns spacing (1.36"), which yielded a coil Q somewhat less than the theoretical maximum for the overall configuration.

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Fig. 4 shows some of the key parameters of coil construction that play a role in physical determination of coil inductance. Length, diameter and turns spacing are parts of the classic 1928 Wheeler approximation for single-layer solenoids (as found in ARRL Handbooks since almost time immemorial):

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where L is the inductance in uHenries, d is the diameter, l is the length, and n is the number of turns, and where d and l are in the same units. The number of turns can be determined from the length and turns spacing (or vice versa). For coils used at upper HF and higher, the lead length becomes a significant factor in the coil's inductance. In antenna modeling, the lead length is generally absorbed by the linear element length.

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In Fig. 5, we find some variations on the coils used in the physical models. If we let A represent the coil configuration used, we might obtains the same inductance (and reactance) using a coil like that in B, which uses the same spacing, but a smaller diameter and more turns. C spreads the turns over a longer length, while D uses a shorter length, closer spacing, and a larger diameter, perhaps to effect the highest Q configuration that might be practical. E employs fatter wire to achieve a high Q by optimizing the wire-diameter-to-turn-spacing ratio. Each of the preceding variants on the original coil was based on theoretical factors. However, in practical antenna design, one might also accept a somewhat lower Q in order to achieve a design that slipped wind by virtue of its small diameter, as suggested in F.

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Each coil configuration is likely to affect antenna performance slightly, due to different radiation field additions that depend on diameter and turn spacing. Some of the variants are more easily modeled than others. With proper attention to segment lengths, coils that use the same size wire as the main or linear element can be modeled with fair ease. However, length tapering of the linear element as it approaches the helix may be necessary for coils with small diameters. Where coils use wire diameters that differ from that of the main element, NEC (in any version) will exhibit a tendency toward erroneous results.

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The consequence is that modeling solenoids as physical loading elements in an antenna may not in all cases be practical, although the task itself may become design-specific, especially in view of all of the variations possible. Thus, it may be some time before there is a more general profile of the affects of coil design on the performance of shortened antenna elements that use them. However, whatever differential there is between a physical coil and a mathematical load will apply equally to both NEC and MININEC, since both use essentially the same mathematical loading schemes, allowing for the fact that NEC places the load on a segment and MININEC places a load on a pulse or junction of segments.

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It is perhaps a curiosity (since multiple types of coils have not been checked) that the loading coil used as the center load in part 4 of this series--and also used as the mid-element load--can be trebled to yield a 30-turn helical dipole only 40.8" long by less than 12" diameter. The resonant frequency of this experimental design was 7.105 MHz, only slightly lower than the standard design frequency used throughout the demonstration. If the exercise has any utility at all, it lies in the confirming the soundness of the advice to model solenoids using the material that will actually form the coil.

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Material            Free Space          Feedpoint Impedance
+                    Gain dBi            R +/- jX Ohms
+Lossless wire        1.76               0.3 + j 0.5
+Copper              -5.46               1.3 + j 1.6
+Aluminum            -6.99               1.9 + j 2.2
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The impracticality of the design, as indicated by the source impedance, is less important than a comparison of the anticipated gain of the antenna from the lossless wire to normal materials. Lossless wire makes the antenna look like a promising performer, while the gain figures for real materials tell the true story. There is no magic in this system. Indeed, it packs over 93' of wire into the helix, more than required for a standard 40-meter dipole. Yet, at 7-9 dB below the performance of a full size dipole, signals would be down by only about 1.5 S-units. Such performance would be usable under certain kinds of operating conditions, although the losses associated with feeding the antenna might attenuate signals even more than the basic design itself.

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Obviously, those interested in helical antennas will always benefit from making them as long and open as possible. An adequate model of a helical monopole or dipole will always take the form of a physical model.

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One final note on solenoids seems necessary, based on Fig. 6 above. A common practice, especially in commercial antenna manufacture is placing a solenoid within a shield, and the shield may be connected (or not) to either of the linear wires extending from it. At present, I am unaware of any technique of modeling this situation which has been correlated to experimental results. One can surround the solenoid with a series of wires or even a wire grid--with one end connected to an antenna wire if desired. To what degree antenna fields arising from the solenoid will interact with the shield and what the consequences for the overall antenna field will be remains an area yet to be fully explored. It, too, is likely to remain a project-specific task for antenna designers. If we add in the variables of coil construction that might be present within the shielding structure, the task is no small one. Note that the term "shield" is here used by convention. To whatever degree that casing plays a role in radiation field production, it shielding effects may be only mechanical. Its electrical role may turn out to be either simple or complex.

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Conclusion

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These notes are intended to provide a reasonably fair view of the limitations of the modeling studies undertaken in the first 4 parts of this series. They provide some cautions against taking the results of the work as numerically general principles, which they are not. They also caution against hasty modeling that might unwittingly cross the boundaries of NEC capabilities. Finally, they also outline a host of work that might be done to extend the study and to make its conclusions both more general and more precise.

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Some of the further work can be done with some modeling ingenuity. Other parts of the work might be undertaken in alternative programs, such as MININEC. However, there may be a residue of the effort that may have to await the next generation of modeling cores.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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18. Why Tri-Banders Are Hard to Model

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L. B. Cebik, W4RNL

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One of the most popular amateur radio antennas is the tri-band Yagi. It also happens to be one of the hardest antennas to model adequately, whether one is using NEC or MININEC. As a result, there are few, if any, reliable models available to the amateur modeler. The models that do exist tend to be done in one of the implementations of MININEC, unless they use a log-cell driver system. However, most of these models are proprietary. Moreover, many of them are used to guide final antenna design, but they do not represent exact models of the final design.

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It may be useful to understand some of the limitations of trying to model tri-band Yagis. The account--which is very general and not tied to the specific circumstances surrounding any particular commercial antenna--may give some insight into why tri-bander models are hard to come by. In addition, it may give the owner of one of these antennas some cautionary notes lest he or she give undue trust to a hasty home-generated model of the station beam. Modeling tri-band Yagis requires the greatest of care.

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Fig. 1 presents a sketch of a hypothetical tri-band Yagi. Its sole purpose is to register some of the features we shall look at in more detail. First, notice that the elements come in different lengths, each consisting of several different diameters of aluminum tubing. Second, notice that this tri-bander has traps, which are not universal in such antennas. Wherever they do occur, they present modeling problems of several sorts. Third, notice that some of the elements having different lengths are closely spaced. Finally, notice that this particular beam uses a driver system called the log-cell driver.

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Each of these features presents either NEC or MININEC with some problems. Not all of the problems are insurmountable, but some may require the use of substitute models, while others simply demand that there be a slight difference between the modeled structure and the physical structure. Still others may leave a few unanswered questions about the precision of the model relative to the real antenna.

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1. Tapered-Diameter Elements

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Most tri-band Yagis use tapered diameter elements composed of successive sections of aluminum tubing having a decreasing diameter from center to end. These element types present no special problem to MININEC. With NEC-2, the results of directly modeling such an element will be quite erroneous. NEC-4 makes an improvement upon NEC-2 for directly modeling tapered diameter elements, but tends to fall short of some requirements for precision. It grows increasingly inaccurate when the diameter step grows larger. This last condition is often encountered when modelers simulate boom-to-element mounting plates with large diameter, short-length segments.

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For a mono-band beam, these limitations can be overcome by careful segmentation of the wires making up an element and through the use of correction factors built into some of the commercial implementations of NEC-2. Variant correction schemes have been developed by Brian Beezley and by David Leeson. These schemes substitute a uniform diameter element of the correct length to give the same electrical performance as the tapered diameter element, thus eliminating the situation that creates errors in NEC-2 outputs.

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In a tri-band beam, we introduce a new problem: tapered diameter elements of different lengths, as shown in Fig. 2. MININEC would take this change in stride, since it requires no correction factor for tapered diameter elements. However, NEC-2--even with corrected elements--has a problem. The equations for a corrected element are only accurate within a reasonable margin from 1/2 wavelength resonance--about +/-15%. Commercial implementations of NEC-2 ordinarily provide corrected elements only if the element passes this length vs. frequency test. Elements cut for frequencies other than the band in question will ordinarily not undergo correction for their tapered diameter.

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How much error may be introduced into the model by virtue of having uncorrected tapered diameter elements may vary from model to model. My own modeling suggests that 10-meter elements play little role in the 20-meter performance of a tri-bander and have low current levels. Varying their length has in most cases (but not in all cases) little or no effect on any significant 20-meter parameter. Hence, there is little error from having uncorrected 10-meter elements in the model.

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The opposite case--the influence of 20-meter elements on 10-meter operation--is quite different. Although the level of influence varies from element to element in various designs, 20-meter directors often carry considerable current on 10-meters and may play a large role in 10-meter performance. In some designs, changes in the length of a 20-meter director can alter the gain vs. frequency curve for 10-meters. Thus, an uncorrected 20-meter element may become an error source when a tri-bander is modeled on 10 meters.

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2. Traps

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Some tri-band Yagi designs make use of trapped elements. Although many tri-bander designs have eliminated traps from the driven element, they remain in some reflectors and directors. Fig. 3 introduces us to some aspects of the difficulties of modeling trapped elements in Yagi designs.

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The upper sketch shows a typical trap in schematic form as inserted into an element. Normally, the trap is configured in the model as a parallel R-L-C "load," which both NEC and MININEC allow.

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In NEC-2, the only permissible loads for symmetrical elements are those positioned at the center of the element. The implementation of the tapered diameter correction requires that the curve of current magnitude along the element be continuous, and a load that is not at the center of the element creates a current magnitude discontinuity. Hence, most implementations test for loads outside the center-most segment, and the existence of such a load will defeat use of the correction.

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Although the placement of traps along an element is not a concern with MININEC, it is a potential source of error with NEC-2 models. The element remains uncorrected at any test frequency.

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The trap itself may call for careful treatment, since the parallel R-L-C mathematical model of the load, shown on the right in the lower sketch in Fig. 3, is a substitute for the circuit shown at the left. For most purposes, the resistance that limits the Q of the trap circuit can be viewed as a series resistance with the inductance (or inductive reactance) of the coil. Setting a value for the resistance in the modeled trap load requires a conversion of the series inductive arm into its parallel equivalent.

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Such conversions are straightforward calculations when a parallel resonant circuit is operated at its resonant frequency. However, traps are rarely operated in a truly resonant model. A trap tends to be resonant at a frequency just below the band edge for which it is a trap, giving a net capacitive reactance to the parallel circuit. At lower frequencies, the reactance is inductive, but not simply the inductance of the coil. There are standard handbook equations for calculating the reactance of any parallel tuned circuit off resonance.

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The net effect of the change of reactance off the resonant frequency of the trap is to alter the required value of the parallel resistance in the modeled trap with every change in frequency of test. Utility programs exist to ease the calculation of these values (for example, in the HAMCALC suite of utility programs). This requirement is in no way fatal to any tri-bander model (where traps are used in the design), but it does require care on the modeler's part lest the trapped element show greater or lesser losses than exist on the physical element itself. Later versions of EZNEC provide a user interface for automatically performing the calculations by entering the more common trap values, including the series coil resistance.

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Series and parallel modeled loads using the LD facilities of either NEC or MININEC are mathematical models, and as such, they do not perfectly model the physical elements they represent. Inductors do not show perfectly equal currents along their length when physically modeled, suggesting that they perform radiating as well as loading functions. The radiating function becomes more pronounced as a coil is moved further from the element's center. When coils are small enough in length and in diameter, the radiating function may approach negligible proportions, but is never zero.

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In Fig. 3, there is a "Shield (?)" notation. A trap (or a loading coil) may be placed inside a metal shell, and the shell may be connected to the inner portion of the element, to the outer portion of the element, or to nothing. To this time, I have not seen any reports on the effects of shielding--however connected--on the overall element performance. The presence or absence of a trap shield may or may not constitute a further potential error source for a trapped element.

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3. Close-Spaced Elements

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Fig. 4 shows a situation that is becoming more common in tri-bander designs: two elements of different lengths in close proximity. These elements may occur in designs which use open-sleeve coupling, where the "slave" 15- and 10-meter drivers are closely spaced to the fed or "master" 20-meter element. The exact spacing and element lengths determine the impedance seen at the feedpoint for each of the bands of operation.

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A second situation in which we can find similarly close-spaced elements of different lengths is in the director set. The 20-meter directors may function as part of the 10-meter director set, showing a single current magnitude curve which peaks at the center of the element. However, the 20-meter directors may not be the correct lengths to provide a 10-meter gain curve where the designer desires it. Placing a 10-meter director of the correct length on the driver side of the 20-meter element can permit the designer to better control the 10-meter performance curves. This new element may be as close as 4-8 inches from the old 20-meter element.

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Although MININEC has no trouble with this situation, NEC-2 does. Two elements of significantly different lengths that are closely spaced can introduce errors into the NEC-2 output reports. The effect is subject to a considerable number of variables, including frequency, diameter of the elements, elements lengths, and spacing. The close the spacing, the greater the effect on the model. The full particulars of this limitation, which affects both NEC-2 and NEC-4, were given in "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), pp. 3-16.

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Whether or not a given spacing poses a possible problem can be determined by the gain averaging test. Although the test results have been available in NEC, the test is just now appearing in new versions of commercial implementations of NEC. New versions of EZNEC (for Windows) and NEC-Win Plus will appear later this year or early in Y2K, and both will make the test available. One may test an entire complex antenna. However, where a specific question arises--as in the case of a pair of elements like the ones we have described--we may perform the test on just the element pair by placing a source at the center of the longer element.

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For the present case, the test would be performed in free space, with the resistive component of any loads disabled, including the resistivity of the antenna materials. For any antenna in these conditions, the average gain--or ratio of radiated power to power provided--will be 1, taking into account radiation in all possible directions. Ordinarily a fair sampling of directions, as indicated by taking gain readings every so many degrees over the sphere implicit in free space models, will provide a clear indication of how close the average gain of the model comes to 1. Values that deviate too far from 1 make the reliability of the model suspect. (Note: there is no absolute level at which a given model becomes untrustworthy. For some purposes, values above 0.8 and below 1.2 may indicate a usable model, while other modeling tasks may require values within about 0.05 of the ideal 1.0.)

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The gain averaging test is a necessary but not a sufficient condition of model adequacy. For example, the gain averaging test may not indicate all of the possible error sources we have described for tri-band Yagis.

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4. Log-Cell Drivers

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A typical log-cell driver set is roughly shown in Fig. 5.

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The log-cell consists of a driver set for the tri-band Yagi so that the set has a single point of connection with the antenna feedline. A true log-cell driver set has crossing lines of connection among the elements. Another driver-set type may use uncrossed connections and has been loosely dubbed "closed-sleeve" coupling. In this latter case, both direct connections and open-sleeve coupling (which depends on element spacing and length for a given source impedance on each band) may be at work.

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Modeling both log-cells and closed-sleeve drivers requires the construction of transmission lines from the source to each driver in the set. NEC-2 has fewer problems in creating such a model, since the transmission line is at the element center where currents are balanced. Since the TL facility of NEC-2 is purely mathematical, connection reversal presents no model construction difficulties over and above those of a closed-sleeve driver set. Indeed, the only difficulty for NEC lies in possible accuracy problems that might arise if the elements of different length are spaced too closely, as described earlier.

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Modeling the element-connecting transmission line in NEC-2 as a physical set of wires may be more difficult. The connecting wires are normally of a smaller diameter than the elements. Among its limitations, NEC has difficulties with junctions of wires having dissimilar diameters. (This limitation is also detailed in the QEX article referenced earlier.) Consequently, for most purposes (including the modeling of full LPDA antennas), use of the TL facility is recommended. (However, the technique described below as a work-around for MININEC can also be applied to NEC models.)

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These same driver sets can also create problems for MININEC, which has no TL facility. Therefore, one can only physically model transmission lines as wires. The log-cell is particular difficult, since the wires must maintain a constant distance between them to effect a transmission line.

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Apart from the line spacing, MININEC suffers another difficulty: at sharp angles, the core will "clip" corners and shorten elements unless the segment lengths at the angular junction are very short. Length-tapering routines are provided in some implementations of MININEC to provide short elements at the junction but segments of increasing length away from the junction. These routines are designed to use the least number of segments that can adequately model the element and still hold the total model within the 256 segment limit of the core in DOS versions. (Windows versions of MININEC 3.13 program have broken this limitation.)

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The log-cell and the closed-sleeve driver sets have a considerable number of right-angle junctions, and the potential for overrunning model size limitations is very good. The development of a MININEC model that can handle such driver-set complexities requires considerable ingenuity.

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When physically modeling crossing transmission lines, you can avoid extra line bends by using the set-up shown in Fig. 6. Set up two transmission lines as 4 wires (for a 3-driver set). The wires maintain a constant distance from each other, as determined by transmission line construction calculations (available in HAMCALC). Each element is offset from the centerline to intersect the correct wire junction of the transmission line. Alternate offsets as you move from one element to the next. The displacement of the element wires is less likely to create significant modeling errors than trying to maintain a constant distance between undulating wires of a transmission line that tries to bend its way to the connections.

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This is only one sample of the variety of modeling techniques that may be required to overcome complexities of design when they run up against limitations of the modeling software.

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Conclusion

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These notes are titled "Why Tri-Banders Are Hard to Model," not "Why Tri-Banders Are Impossible to Model." Certainly there are models that are sufficient guides to construction and that permit commercial designers to make final prototype adjustments in field tests. Whether these models suffice to confirm performance claims is an issue beyond the scope of these notes. However, to the extent that models require the use of substitute elements or leave open questions about the adequacy of the model to the physical antenna, they may be accounted by some to be less than fully acceptable. Nonetheless, these models will have served a very useful purpose in guiding the development of an antenna. The exactitude we demand of a model is a function of a well-defined set of task goals. (On the other hand, a sloppily defined task does not justify acceptance of a sloppy model or its over-optimistic performance predictions.)

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In terms of modeling one's own tri-bander, these notes may serve as a reminder of the caution one must use in building the model. There are limiting boundaries for both MININEC and NEC that one may cross without noticing them. Use great care in trying to model a tri-band Yagi--the job is harder than you may initially think.

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Go to Main Index

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19. What Can We Learn From Tables?

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L. B. Cebik, W4RNL

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Every commercial implementation of either NEC or MININEC tries to anticipate the needs of its users. Therefore, each tries to provide crucial data in the most usable form. Polar plots, SWR sweeps, etc. appear in graphical form, with supplementary numerical data. Some data is available in tabular form, often modified to make it more readable. Thus, a typical NEC output value of 2.1356E-03 will be rounded to 0.0021.

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Behind every form of data made available to the user lies a basic NEC core output table--or, more correctly, a collection of tables. Once you have generally mastered the readily available information, it is time to look at the core output in order to gather new data, refine data already in hand, and even to get a new slant on existing data.

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So let's look at a typical NEC core output file for a simple antenna: the 10-meter center-loaded dipole shown in Fig. 1.

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The antenna consist of a single modeled wire with 41 segments (each about 2.75" long for the overall 112" antenna length). The antenna wire is copper, with its characteristic loss factor. The center-loading coil is specified as a resistance and reactance (1 Ohm and 644 Ohms), which is equivalent to a 3.6 uH coil with a Q of about 600. Since we are using only one frequency for this model, the impedance load and the R-L-C load are equivalent. We shall set the antenna in free space, with no transmission lines, networks, or other complexities. This much of a model will already introduce us to an episode's worth of information from the NEC core output.

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Let's take up the core output a bit at a time. In many cases, the old "green sheet" output width of the data will be too wide for our screen, so I shall omit some columns of less interest to us here. (In other contexts, they may hold great interest.) Note that NEC operates only in meters, and converts everything to that measure. For simplicity, I have preconverted the data from our 112" antenna. Also note that NEC uses a radius, although conventional input systems let you input wire diameters or AWG wire sizes.

+ 
                  - - - STRUCTURE SPECIFICATION - - -
+
+                     COORDINATES MUST BE INPUT IN
+                     METERS OR BE SCALED TO METERS
+                    BEFORE STRUCTURE INPUT IS ENDED
+
+  WIRE
+  NO.      X1       Y1      Z1        X2       Y2       Z2     RADIUS  SEG.
+     1  0.00000  0.00000  0.00000   2.84480  0.00000  0.00000  0.00103   41
+      STRUCTURE SCALED BY FACTOR   1.00000
+TOTAL SEGMENTS USED= 41  NO. SEG. IN A SYMMETRIC CELL= 41  SYMMETRY FLAG= 0
+         - MULTIPLE WIRE JUNCTIONS -
+ JUNCTION    SEGMENTS  (- FOR END 1, + FOR END 2)
+  NONE
+

This portion of the file essentially replicates your wire entry for the antenna element(s). It is a good crosscheck against what you thought you entered. However, NEC goes further and sorts out every wire segment and its connections. Only the first 5 segments are shown below--with some columns omitted.

+ 
                 - - - - SEGMENTATION DATA - - - -
+
+                        COORDINATES IN METERS
+         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.   WIRE    CONNECTION DATA  TAG
+  NO.       X         Y         Z     LENGTH   RADIUS     I-   I    I+  NO.
+   1   0.03469   0.00000   0.00000   0.06939   0.00103    0    1    2    1
+   2   0.10408   0.00000   0.00000   0.06939   0.00103    1    2    3    1
+   3   0.17346   0.00000   0.00000   0.06939   0.00103    2    3    4    1
+   4   0.24285   0.00000   0.00000   0.06939   0.00103    3    4    5    1
+   5   0.31223   0.00000   0.00000   0.06939   0.00103    4    5    6    1
+

Note that each segment is located by the coordinates of its center, which is the focal point of NEC calculations. (MININEC focuses upon pulses, which are located at segment junctions or ends.) The connection data can be important in checking to ensure that complex wire structures that you devise are connected where you want them and not connected where you wish the wires to be separated.

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Many implementations of NEC have error checking routines. However, they cannot read the modeler's intentions. If you transpose numbers in a coordinate (for example, 42 instead of 24), the error checker will not catch the error unless it results in a standard error, such as wires that connect within a segment. Reviewing the coordinates of the segments and their connections is a good supplemental error check routine.

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INPUT LINE   1  EX   0    1   21    0  1.00000E+00  0.00000E+00
+                      0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
+INPUT LINE   2  LD   4    1   21   21  1.00000E+00  6.44000E+02
+                      0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
+INPUT LINE   3  LD   5    1    1   41  5.80010E+07  0.00000E+00
+                      0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
+INPUT LINE   4  FR   0    1    0    0  2.85000E+01  0.00000E+00
+                      0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
+INPUT LINE   5  RP   0    1  361 1000  9.00000E+01  0.00000E+00
+                      1.00000E+00  1.00000E+00  0.00000E+00  0.00000E+00
+

Each of the "Input Line" Entries is actually a single report line (split here to ensure that it fits the screen). These lines register the control cards. In this model, we have the source information (wire and segment of placement and the magnitude and phase of the source voltage); the center loading coil load (Type 4 impedance load showing wire and segment of placement and the resistance and reactance); the wire conductivity (showing the wire of placement and the segment range, as well as the conductivity of copper); the frequency request (a single frequency: 28.5 MHz); and the pattern request (an azimuth pattern of 360 degrees at zero degrees elevation, which NEC expresses as a 90-degree theta angle).

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These entries are once more useful as cross checks on what you intended to put into your model. To read values, you must grow accustomed to engineering notation (for example, 5.80010E+07) and to the positions of information along each line.

+ 
                 - - - - - - FREQUENCY - - - - - -
+                     FREQUENCY= 2.8500E+01 MHZ
+                   WAVELENGTH= 1.0519E+01 METERS
+

NEC reads the frequency in MHz and provides its equivalent in wave length. If you multiply the two figures, you will find that NEC uses 2.997915E+06 m/s as the speed of electromagnetic radiation.

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Since our antenna is in free space, we can skip over the "Antenna Environment" entry to the loading lines.

+ 
             - - - STRUCTURE IMPEDANCE LOADING - - -
+
+LOCATION                  IMPEDANCE (OHMS)      CONDUCTIVITY           TYPE
+ITAG FROM THRU            REAL      IMAGINARY   MHOS/METER
+
+ 1   21   21           1.0000E+00   6.4400E+02              FIXED IMPEDANCE
+ 1    1   41                                    5.8001E+07             WIRE
+NOTE: SOME OF THE ABOVE SEGMENTS HAVE BEEN LOADED TWICE - IMPEDANCES ADDED
+

These lines have unused columns omitted (those used for R-L-C loads). NEC uses the mathematical terminology of "real" and "imaginary" in place of the electrical terms "resistive" and "reactive" to characterize not only impedance, but as well every other quantity which may also have a phase angle. Note also that segment 21 (the element center segment) has both the impedance load and the wire conductivity load. Since conductivity is a measure per unit length, one cannot simply arithmetically add resistances to obtain the value used by NEC on that segment. The "Tag" and ITag" notations refer to the wire number.

+ 
              - - - ANTENNA INPUT PARAMETERS - - -
+
+TAG   SEG.      VOLTAGE (VOLTS)           CURRENT (AMPS)
+NO.   NO.      REAL        IMAG.         REAL        IMAG.
+ 1    21   1.00000E+00 0.00000E+00   5.80233E-02 1.91669E-03
+                IMPEDANCE (OHMS)          ADMITTANCE (MHOS)        POWER
+                REAL        IMAG.         REAL        IMAG.       (WATTS)
+           1.72157E+01-5.68686E-01   5.80233E-02 1.91669E-03   2.90117E-02
+

The "Antenna Input Parameters" report is actually a single line entry. Because of its length, I have split it to ensure a screen fit.

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NEC calculates the mutual impedances of all segments in a total antenna structure. With these figures, plus the source values (1 volt at 0 degrees phase angle in our example), the source or feedpoint collection of values can be calculated from Ohms Law and its derivative power equation. Admittance, of course, is simply the reciprocal of impedance. Had we set the voltage at a value other than 1.0, the other values (except the impedance and the admittance) would have changed accordingly.

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Some implementations permit the use of current sources by a network from a distant true voltage source to the user-designated source segment. Other implementations scale these figures so as to allow the user to specify a constant power value.

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Among the most important information provided by the NEC core output file is the current data. What follows is the table for 1/2 of the antenna we are using as our example. The other half of this symmetrical single element would show the same values in reverse order.

+ 
                - - - CURRENTS AND LOCATION - - -
+            LENGTHS NORMALIZED BY WAVELENGTH (OR 2.*PI/CABS(K))
+
+SEG. TAG   SEG. CENTER     SEG.          - - - CURRENT (AMPS) - - -
+NO. NO.   X      Y    Z  LENGTH    REAL       IMAG.        MAG.       PHASE
+ 1  1   0.0033  0.0  0.0 0.00660  2.1353E-03 3.4527E-05   2.1356E-03  0.926
+ 2  1   0.0099  0.0  0.0 0.00660  5.6942E-03 9.6119E-05   5.6950E-03  0.967
+ 3  1   0.0165  0.0  0.0 0.00660  8.9690E-03 1.5790E-04   8.9704E-03  1.009
+ 4  1   0.0231  0.0  0.0 0.00660  1.2127E-02 2.2233E-04   1.2129E-02  1.050
+ 5  1   0.0297  0.0  0.0 0.00660  1.5203E-02 2.8992E-04   1.5205E-02  1.093
+ 6  1   0.0363  0.0  0.0 0.00660  1.8213E-02 3.6086E-04   1.8216E-02  1.135
+ 7  1   0.0429  0.0  0.0 0.00660  2.1165E-02 4.3528E-04   2.1169E-02  1.178
+ 8  1   0.0495  0.0  0.0 0.00660  2.4062E-02 5.1323E-04   2.4068E-02  1.222
+ 9  1   0.0561  0.0  0.0 0.00660  2.6908E-02 5.9476E-04   2.6915E-02  1.266
+10  1   0.0627  0.0  0.0 0.00660  2.9703E-02 6.7991E-04   2.9711E-02  1.311
+11  1   0.0693  0.0  0.0 0.00660  3.2448E-02 7.6871E-04   3.2457E-02  1.357
+12  1   0.0759  0.0  0.0 0.00660  3.5144E-02 8.6124E-04   3.5154E-02  1.404
+13  1   0.0825  0.0  0.0 0.00660  3.7791E-02 9.5760E-04   3.7803E-02  1.452
+14  1   0.0890  0.0  0.0 0.00660  4.0392E-02 1.0579E-03   4.0406E-02  1.500
+15  1   0.0956  0.0  0.0 0.00660  4.2951E-02 1.1625E-03   4.2966E-02  1.550
+16  1   0.1022  0.0  0.0 0.00660  4.5472E-02 1.2717E-03   4.5490E-02  1.602
+17  1   0.1088  0.0  0.0 0.00660  4.7967E-02 1.3861E-03   4.7987E-02  1.655
+18  1   0.1154  0.0  0.0 0.00660  5.0456E-02 1.5070E-03   5.0478E-02  1.711
+19  1   0.1220  0.0  0.0 0.00660  5.2978E-02 1.6367E-03   5.3003E-02  1.769
+20  1   0.1286  0.0  0.0 0.00660  5.5668E-02 1.7830E-03   5.5697E-02  1.834
+21  1   0.1352  0.0  0.0 0.00660  5.8023E-02 1.9167E-03   5.8055E-02  1.892
+

I have truncated the 0.00000 entries for the Y and Z coordinates to make the table fit the space available. Note that the coordinate positions for the current placements are the segment centers. For this single element antenna, you can simply compare the current placement coordinates with the coordinates given in the segmentation data section of the report.

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Current values are based on the source voltage and the impedance, accounting for losses within a given segment. NEC reports these currents in two ways: as real and imaginary components and as a current magnitude and phase angle. For our center-loaded dipole, the curve of the current magnitude and phase are shown in Fig. 2.

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The current magnitude is shown on the left Y-axis, while the current phase value is shown on the right Y-axis. Note that neither curve is linear. Many users find that the current values are more meaningful when normalized to a source current of 1.0 with a phase angle of zero degrees.

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Fig. 3 re-plots the data using a current source as just specified. Now it is clear how the current levels at various points along the antenna wire compare with the source current. As well, with the phase angle referenced to zero, the amount of phase shift along the element is also clearer. (The nearly 1-degree phase shift is far more interesting than it is significant to antenna performance.)

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Different implementations of NEC provide differing ways of plotting the current data. Curves may be overlaid on outline drawings of the antenna elements--or they may be shown in color transitions rather than as curves. Some programs contain rectangular plot capabilities for plotting current. Virtually all programs make the current location and level data available as an immediate program output, thus saving the user the time of searching it out in the large NEC output file.

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Detailed current data can be instructive about antenna performance. Our single loaded element is far too simple to hold any surprises. However, I was surprised when examining a model of a tri-band beam to discover, first, that a 20-meter director had a very significant current magnitude on it (compared to the other directors) when the operating frequency was within the 10-meter band. The second surprise came from examining the current magnitude along the element. Although about 1 wl long at the 10-meter operating frequency, the 20-meter element showed a single current maximum at its center with ever-decreasing levels outward from the center. The 20-meter element was very actively involved in the formation of the pattern from the Yagi on 10 meters. In fact, its length--set for 20-meter performance--provided a limit on the operating bandwidth on 10 meters, pushing the performance curves closer to one end of the band than the other. For this particular model, changing the length of the 20- meter director could enhance performance across the first MHz of 10 meters, but at the expense of performance on 20 meters.

+ 
                   - - - POWER BUDGET - - -
+
+                INPUT POWER   = 2.9012E-02 WATTS
+                RADIATED POWER= 2.6950E-02 WATTS
+                WIRE LOSS     = 2.0613E-03 WATTS
+                EFFICIENCY    =  92.90 PERCENT
+

The "Power Budget" report in the NEC output file can be very instructive when considering an antenna by itself and when comparing more than one competing design. For our center-loaded dipole, the efficiency (the ratio of radiated power to input power X 100) is considerably less than that of an unloaded full-length dipole. The wire loss is the sum of all resistive losses in the antenna, the major portion of which occurs in the loading coil.

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Some programs make the power budget immediately available. Others provide alternative useful data, such as losses in loads of Type 0, 1, and 4. In many instances, it is important not just to know the overall losses in an antenna, but as well to identify the sources of these losses.

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                      - - - RADIATION PATTERNS - - -
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+- - ANGLES - -  - POWER GAINS -       - - E(THETA) - -      - - E(PHI) - -
+THETA   PHI   VERT.   HOR.    TOTAL    MAGNITUDE  PHASE   MAGNITUDE   PHASE
+DEGS   DEGS    DB      DB      DB       VOLTS      DEGS     VOLTS      DEGS
+90.00  0.00 -157.31 -999.99 -157.31  1.79796E-08 -39.79  0.00000E+00   0.00
+90.00  1.00 -157.31  -34.18  -34.18  1.79772E-08 -39.80  2.57884E-02 140.20
+90.00  2.00 -157.31  -28.16  -28.16  1.79700E-08 -39.82  5.15721E-02 140.18
+90.00  3.00 -157.32  -24.64  -24.64  1.79581E-08 -39.86  7.73462E-02 140.14
+90.00  4.00 -157.33  -22.14  -22.14  1.79415E-08 -39.91  1.03106E-01 140.09
+90.00  5.00 -157.34  -20.20  -20.20  1.79200E-08 -39.98  1.28847E-01 140.02
+90.00  6.00 -157.35  -18.62  -18.62  1.78938E-08 -40.06  1.54563E-01 139.94
+90.00  7.00 -157.37  -17.29  -17.29  1.78629E-08 -40.16  1.80251E-01 139.84
+90.00  8.00 -157.38  -16.13  -16.13  1.78271E-08 -40.27  2.05905E-01 139.73
+90.00  9.00 -157.40  -15.11  -15.11  1.77866E-08 -40.39  2.31520E-01 139.61
+90.00 10.00 -157.42  -14.20  -14.20  1.77413E-08 -40.53  2.57091E-01 139.47
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The only radiation pattern requested for our center-loaded dipole is an azimuth pattern at an elevation angle of zero degrees. Only the first 10 degrees of the report are shown here. When the entire data series is plotted, the pattern has the appearance of Fig. 4.

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Because graphical plotting involves the use of lines having some thickness on a finite overall graph size, some angles are difficult to resolve visually. Consequently, the radiation table report--often made separately available by implementations of NEC--is a useful source of data. The portion of the 360-degree report shown here includes the first 10 degrees, beginning with a direction that is at the side null of the dipole pattern. The depth of a free-space dipole null is indicated by the total field power gain. By comparison with the value at the next degree of pattern resolution, one can see to what extent this deep null is a point value and what sorts of values are more realistic to expect of an antenna that does not quite stand still in a small breeze.

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Very often, you can make important data more graphically accessible via rectangular graphs. Some software packages have internal rectangular graphing capabilities. However, in all cases, you can transport the data to a spreadsheet, where even more powerful graphing capabilities are normally available. In the present case, we can easily graph the radiation pattern on a rectangular chart to show the deep nulls, as in the top half of Fig. 5.

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What we gain in the ability to see the fine detail of the side nulls, we lose in terms of possibly misinterpreting the higher gain portions of the antenna pattern. The flat tops of the gain peaks in the upper graph do not permit resolution of important gain changes as we change the azimuth heading. However, by changing the Y-axis scale, we can enhance the presentation of these changes, as shown in the lower half of Fig. 5.

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In the end, translating tabular data into graphical form requires great care in order to present data accurately and without leaving misleading impressions. In all cases, be prepared to refer to the tabulated data in the NEC output report to resolve questions left by any graphic presentation.

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To make effective use of the radiation pattern report, it is important to understand the conventions used by NEC. The conventional elevation angle counts from the horizon upward, while the theta angle used by NEC counts from the zenith downward. Hence, a zero-degree elevation angle is a 90- degree theta angle. In addition, phi angles count in a counterclockwise direction, while azimuth angles use compass headings clockwise around the circle. (For most symmetrical antennas, the azimuth-phi distinction makes little or no difference, and I have seen software that simply uses the phi-angle as is while calling it an azimuth angle.)

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The report provides power gains in dBi (isotropic) for both vertically and horizontally polarized radiation, as well as the power gain for the total field. Ordinarily, all three fields are available graphically as well as tabularly.

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NEC also provides theta (vertical) and phi (horizontal) values of the electrical field of an antenna, in terms of voltage magnitude and phase (in volts per meter). Since no range is specified in the most typical pattern specifications (like the one we have been using in our example), the voltage values shown are the voltage as the range approaches infinity. I have shown them to illustrate some of the further data available for special purposes, and even further available columns of polarization information has been omitted.

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Had we chosen a different example, the resulting NEC output file would have looked somewhat different, but mostly by way of additions. Over real ground (fast or Sommerfeld-Norton), there would be a ground calculation entry of considerable interest. Additional sources and loads would have enlarged the entries for these items. Requests for alternative outputs--available in some implementations of NEC--would have produced substitutes for or additions to the pattern report we used in the sample.

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For complex antenna structures and requests for further output data, a NEC output file can grow to very significant proportions--proportions that defy printing except in cases where preservation of the data is vital. For example, a frequency sweep of free-space azimuth patterns for an antenna on 10 meters from 28 to 29 MHz at 0.1 MHz intervals would have yielded 11 pattern reports, each with 360 lines for a 1-degree resolution setting. In some implementations, it is also possible to make multiple pattern requests, which for the example might consist of an elevation pattern. The number of pattern reports in the frequency sweep would double. Now suppose we had chosen as our model antenna a 5-element quad beam, each element of which consisted of 4 wires with about 11 segments per side. The 880 segments would each appear in the segmentation data portion of the report.

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For reasons such as these, implementations of NEC rarely make all of the data in the NEC output file available, although some make the file itself available for consultation. Instead, they extract the most crucial information from the file and present it in separate tables, often in formats that make reading easier. The most common change is to convert the engineering notation to plain decimal notation, with a limit set to the number of digits shown.

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At the same time, implementations of NEC will often provide additional information that can be calculated from the NEC output file. The most prominent example is SWR data, which is normally referenced to 50 Ohms and to user-selected values. In some software, load loss figures are also available. These are only samples of many possible pre-NEC and post-NEC calculations that can enhance the basic core functions for the user.

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As you develop your modeling skills, you will discover that reference to the basic NEC output file becomes a normal part of the modeling routine. Familiarizing yourself with the types of data available and the ways in which the data is formatted can enhance the utility of the output file in your work. This note has at most pointed the way to the file, but has not yet penetrated significantly into what is available there. Penetration comes with the well-defined tasks that you will develop as you continue to model antennas.

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Go to Main Index

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2. Under the Limits: MININEC

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L. B. Cebik, W4RNL

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All antenna modeling software works within a set of limits. Exceeding the limits may yield a model, but one that is usually unreliable in terms of translating it into reality. Hence, we need to be thoroughly familiar with the limits of the software we use.

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Since most of us use a commercial implementation of one of the basic public domain calculation cores (MININEC or NEC-2), we must divide our attention between core considerations and program considerations. There are limitations of the MININEC calculation core itself which are initially common to all program implementations. However, some programs use proprietary correctives to overcome some limitations, and these will vary from one program to another. Hence, we shall have to make reference to differences among programs, but without necessarily recommending or dis-recommending any particular program.

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The three main commercial implementations of public domain MININEC (3.13) software in Windows format are the following:

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  • 1. Antenna Model -- http://www.antennamodel.com/
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  • 2. NEC4WIN -- http://www.orionmicro.com
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  • 3. MMANA -- http://www.qsl.net/mmhamsoft/
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(This list does not include the DOS programs AO/MN and ELNEC.)

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MININEC Limitations: Segmentation

Like NEC, MININEC analyzes an antenna by first analyzing the interaction among the individual straight segments that make up the elements. Segments are subdivisions of straight wires that compose the antenna structure, as shown in Figure 1. A dipole may have a single wire subdivided into many segments. A 2-element quad may be composed of many wires, only some of which may have more than one segment. +
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The recommended minimum number of segments per half wavelength is 10, although fewer can occasionally be used. The fewer the number of segments per half wavelength, the less reliable the results. Even 10 segments per wavelength may be too few to pass convergence tests described in the last episode. The shortest segment length recommended is 0.0001 wavelength.

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Although you can make a wire about as thin as you can imagine, your wires should not exceed a diameter of 0.02 wavelengths.

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The following chart provides some guidance into the long and short of segment length, as well as into maximum wire diameter.

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Frequency      Segment Length in "      Shortest Segment    Largest Wire
+               for 10 seg/0.5 wl        Length in "         Diameter in "
+1.8                 327.9                    0.6657              133.1
+3.5                 168.6                    0.3372               67.4
+7.0                  84.3                    0.1686               33.7
+10.1                 58.4                    0.1169               23.4
+14.0                 42.2                    0.0843               16.9
+18.068               32.7                    0.0653               13.1
+21.0                 28.1                    0.0562               11.2
+24.89                23.7                    0.0474                9.5
+28.0                 21.1                    0.0422                8.4
+50.0                 11.8                    0.0236                4.7
+144.0                 4.1                    0.0082                1.6
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The length limitations do not operate in isolation. First, the length should never be less than about 1.25 the wire diameter, and a greater ratio of length to diameter is preferable. Second, the ratio of lengths of adjoining segments should be less than 2:1.

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The preceding recommendations represent program limitations. In practice, these limits should be avoided by the greatest possible distance. We can accomplish this by adhering to some positive rules of thumb. First, insofar as feasible with linear elements, make the segment lengths equal, even where the element may be composed of wires of different diameter. Second, use at least twice the minimum recommended segmentation for any antenna more complex than a simple half wavelength dipole. (We shall soon discover an important situation in which to depart from these rules.) Figure 2 illustrates these rules of thumb in action for a two-element Yagi.

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Adherence to these rules of thumb has proven less critical in MININEC than in NEC and less critical where wires are widely spaced than when closely spaced. Nonetheless, they are reasonably good habits to get into, except where specifically counter-indicated, as in the case of segment length tapering, to be discussed in a moment. In all cases, increase segmentation as indicated by appropriate convergence testing.

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MININEC calculations are based upon placing a current pulse at the intersection of two segments (with wire end pulses added to non-continuous elements). The placement of the pulse (which differs from the manner in which NEC performs its calculations) also dictates the placement of antenna sources: they must be at pulses. Hence, a center-fed linear element should have an even number of segments so that there is a pulse segment junction) at the element center on which to place the source. Similar rules apply to the placement of loads: even if off center, they can only be placed at junctions of wire segments. Exact placement of sources and loads which are not at wire centers or ends requires that there be enough segments to position them very close to their physical counterparts. Figure 3 illustrates the situation.

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As Figure 3 shows, when source or load position is critical, you can always subdivide an element into wires of different length and place the source or load at the junction of the wires. Some programs limit the position of the source (and loads) to wire ends or centers; hence, the use of separate wires within a single antenna element may be necessary in order to place a source (or load) exactly where the antenna dimensions require it. This technique is especially applicable to antennas such as the off-center fed half wavelength wire, sometimes called the Windom.

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The MININEC system of pulse placement puts limitations on the construction of models involving angular geometries, such as the quad loop. The ends of pulses are roughly at the middle of segments. The effect resembles shortening the antenna by ignoring some of the wire at the corner. Hence, as suggested by Figure 4, with only close to the minimum recommended segmentation per half wavelength, a MININEC model quad loop will have to be made larger than in reality to achieve resonance at a desired frequency.

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There are two ways to overcome this limitation. One is to increase the number of segments, making each one very short. This technique results in a minimal shortening effect and can yield accurate quad models. A second technique is called segment length tapering. AO provides an automatic tapering option, while ELNEC provides an option for constructing an alternative model with either preset or user-controlled maximum and minimum segment lengths. In both cases, segments approaching critical angles become very short and gradually increase in length. The technique yields maximum accuracy with a minimum number of segments per wire.

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MININEC was created for the PC when the maximum memory available was 640 KB. Memory is the key limitation in the maximum number of segments available for a model. At one time, a maximum of about 128 pulses was standard. However, existing programs have increased this limit by various means. ELNEC uses a special program adjunct to increase the limit to about 256 pulses. AO has altered the code with machine-level routines so that the number of pulses is limited only by memory. NEC4WIN uses coding within the Windows 95 protocols to remove the limit from the number of available pulses.

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Despite these advances, when compared to NEC-2 programs, MININEC models have size restrictions that limit some types of modeling. Very large and complex geometries may call for considerable ingenuity. Even then, their accuracy may be suspect in some cases.

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Nevertheless, we shall see, when we discuss some of the limitations of NEC- 2, that MININEC does model some situations with a good deal more reliability than its FORTRAN counterpart.

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Grounds

Another general area in which MININEC shows significant limitations is in its options for grounding and the accuracy of models near ground. MININEC has, in addition to a free space option, a ground system that permits the definition of two ground condition sets. These ground condition specifications affect only the far field pattern of the antenna model. Source impedance and current data is developed as if the antenna were positioned over perfect ground. For many types of antennas, the differences between source impedance figures taken over perfect ground and those taken over less than perfect ground will not be operationally significant. The following table shows figures for a dipole modeled at 3.5 MHz 1 wavelength high in MININEC and also in NEC-2 with high accuracy Sommerfeld-Norton grounds ranging from perfect to very poor. The antenna was first resonated within +/- 1 ohm reactance over perfect ground and held at that length for the development of the other figures. MININEC dipoles have 20 segments; NEC dipoles have 21 segments. + 
                         MININEC                  NEC-2 (N-S Ground)
+Antenna   Cond. (S/m)    138.0' #12 copper        137.6' #12 copper
+Ground    & Die. Con.    Gain      Source Z       Gain      Source Z
+                         dBi       R +/- jX       dBi       R +/- jX
+Perfect                  8.12      73.1 + j0.38   8.12      73.2 - j0.42
+Very Good 0.0303/20      7.99      73.1 + j0.38   8.05      72.5 + j0.77
+Good      0.005/13       7.80      73.1 + j0.38   7.87      72.2 + j2.42
+Poor      0.002/13       7.64      73.1 + j0.38   7.69      72.6 + j3.30
+Very Poor 0.001/5        7.42      73.1 + j0.38   7.49      72.3 + j4.75
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This high dipole shows no major operational problem in using the MININEC figures in lieu of the NEC-2 figures. However, the NEC source figures do show a small but possibly significant reactance. To main resonance, the antenna calls for a change in length amounting to about 0.1' per ohm reactance. In other types of antennas at other heights, the difference might be greater and of higher significance.

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MININEC has a second inherent limitation respecting ground. Wires placed roughly parallel to the ground will yield both inaccurate current (and therefore gain) data and also source data when they are below about 0.2 wavelengths. (More accurate data close to the ground would have required a larger code at a time when PCs had severe memory limitations.) The following table compares MININEC and NEC-2 data for a 3.5 MHz dipole (resonated in free space) at heights from 0.05 to 0.30 wavelengths above medium or "average" earth (conductivity = 0.005 Siemens/meter; dielectric constant = 13).

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                         MININEC                  NEC-2 (S-N Ground)
+Antenna                  137.2' #12 copper        136.9' #12 copper
+Height                   Gain      Source Z       Gain      Source Z
+ W/L      Feet           dBi       R +/- jX       dBi       R +/- jX
+0.05      14.05          9.4        7.4 - j 4.9   1.2       48.9 + j15.4
+0.10      28.10          8.4       23.3 + j20.5   5.1       49.8 + j21.1
+0.15      42.15          7.7       45.9 + j35.1   6.4       62.5 + j26.9
+0.20      56.20          7.0       62.3 + j37.0   6.5       77.0 + j25.3
+0.25      70.26          6.2       87.7 + j28.3   6.2       87.8 + j17.3
+0.30      84.31          5.9       97.4 + j13.5   6.1       92.3 + j 6.1
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The low altitude gains calculated by MININEC are, of course, unrealistically high, whereas the ones calculated by NEC-2 are more reliable, in light of ground losses. Figures do not begin to coincide between the two programs until the dipole reaches about 0.25 wavelengths in height. Notice that figures for the dipole are not wholly reliable in MININEC at heights of 50 feet, a common amateur backyard dipole height for 80 meters. Similarly positioned 80-meter wire arrays of greater complexity will show equal or greater errors. The upshot is this: if models of antennas around or below the MININEC height limit are needed, then MININEC is not the program of choice for such models.

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The limitation just described also makes MININEC unreliable in the evaluation of ground planes for many lower HF verticals, since the ground plane normally consists of wires under, at, or just above the surface of ground and parallel to it. NEC-2 is more accurate using the Sommerfeld- Norton ground and placing wires at their height above the surface. Underground radials can be modeled at very small heights above the surface for reasonably accurate results. (NEC-4 has the ability to model wires underground.)

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Miscellaneous Limitations

There are a number of other less problematical limitations within MININEC. Some commercial implementations of MININEC have added corrective measures; others have not, most likely in the belief that the amount of error introduced is within the boundaries of normal antenna building practice. +

Frequency: As the frequency at which models are set increases, MININEC shows a gradual offset in the direction of showing an antenna to be shorter than its real-world counterpart would be. AO introduces a corrective for this offset to bring the results in line with NEC-2. To illustrate the phenomenon, the following results were obtained for a 3-element Yagi of uniform 0.5" aluminum elements at 28.5 MHz in free space:

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Program        Gain      Front-to-Back       Source Impedance
+               dBi            dB               R+/- jX Ohms
+NEC-4          8.11         27.15               25.7 - j0.8
+NEC-2          8.11         27.13               25.7 - j0.8
+AO (MIN)       8.09         26.89               25.7 - j0.3
+ELNEC (MIN)    8.04         27.21               26.5 - j6.0
+ELNEC at 28.65 MHz                              25.7 - j0.6
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The uncorrected MININEC model is resonant at a frequency about 150 kHz above the resonance shown by the other models or about 0.5% higher in frequency at 10 meters. Similar results are shown by AO when the frequency corrective is switched off. The actual amount of error is a function of both antenna element diameter and frequency and thus may become more significant in the upper HF and VHF region of the spectrum.

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Parallel Wires: Closely space wires, such as in a folded dipole can give erroneous outputs in MININEC unless carefully segment-length tapered toward the junctions with the short end-connecting wires. ELNEC has introduced a parallel wire correction feature that permits the use of low numbers of segments per half wavelength without length tapering with quite reasonable output results. The following table illustrates a simple folded dipole (partially shown in Figure 5) of #18 copper wire with 1" wire spacing and 16.6' total length at 28.5 MHz in free space.

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+ 
          Without correction            With correction
+No. seg./      Gain      Source Z       Gain      Source Z
+0.5 wl         dBi       R +/- jX       dBi       R +/- jX
+ 22            1.60      11.6 - j106    2.09      287 + j 8.5
+ 32            1.46      11.4 - j 85    2.10      288 + j 2.0
+ 42            1.21      11.0 - j 84    2.10      288 + j 3.1
+Full taper                              2.09      285 + j31.9
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AO results for tapered and uncorrected untapered folded dipoles are similar. The closely spaced parallel wire correction where wires join can be overcome either by a corrective or by segment length tapering. However, where the wires do not join, the modeler must use care in validating the modeled results in the absence of a parallel wire corrective.

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On the Positive Side

There are some aspects of modeling where MININEC shows significantly greater accuracy than NEC-2. We shall explore the NEC-2 limitations more extensively next time, but here we can simply list a few MININEC superiorities. +

Folded dipoles of dissimilar diameter wires: NEC in all its forms produces rather unreliable models of folded dipoles with dissimilar wires. The 4:1 source impedance ratio for a folded dipole occurs only when both wires are the same size. When the wires differ in diameter, the source impedance is a complex function of the wires diameter ratios and their spacing. Details of the calculation appear in The ARRL Antenna Book. Detailed models in MININEC show very reasonable approximations of the calculated results.

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Elements with tapered wire diameters: Yagi elements may start at the center with 1" or larger diameter tubing and decrease the diameter as you work your way out toward the end. MININEC handles these transitions in stride. In contrast, NEC-2 requires a special type of corrective, usually based on the Leeson correctives, which substitutes an equivalent single diameter element for the one you actually place in the model.

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Closely spaced wires: When wires are very closely spaced--say less than 10" or so at 20 meters (with frequency, wire diameter, and other variables thrown in), NEC results become unreliable, generally showing higher than realistic gain, but no change in the antenna pattern shape. In contrast, MININEC produces realistic results down to very close wire spacings. (However, never let two antenna wire surfaces overlap.)

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Changing diameters at angular corners: Again, NEC does not handle this situation well, producing unreliable models. Extensive modeling of the folded X-Beam, which normally uses tubular angled arms and wire tails, suggests that MININEC--when using segment length tapering at the angular corners--produces more reliable models. Likewise, tests with quad loops with tubular horizontal sections and wire vertical sections also suggests that MININEC models are more accurate than NEC models.

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This sampling of areas where MININEC produces more reliable models than NEC-2 suggests that for the foreseeable future, MININEC will maintain a significant place in antenna modeling. Indeed, over a broad middle ground that does not approach the limitations of either program, both will produce quite reliable models--sufficiently reliable to be guides of antenna construction. Our discussion of MININEC limitations is not aimed at lessening confidence in the program or its commercial implementations. Rather, it is designed to help us ensure model reliability by keeping our models away from the limits and well within arena where MININEC best does its work.

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For further information on MININEC limitations, the classic reference is Roy Lewallen, W7EL, "MININEC: The Other Side of the Sword," QST (February, 1991), 18-22.
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Go to Main Index

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20. The Average Gain Test

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L. B. Cebik, W4RNL

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We have noted in a past column (#1 of this series) the convergence test for model adequacy. In that test, we increase the number of segments per wavelength until the output reports no longer vary from one level of segmentation to the next by a significant amount. For some antenna, such as dipoles, converge may occur with as few as 10-15 segments per wavelength, while other antenna structures may require many times that figure. There are some antenna models that never converge. Convergence is considered a necessary but not a sufficient condition of model adequacy. A model may have its results converge and still be a poor model for reasons that convergence testing cannot reveal.

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In addition to the convergence test, there is another important test of model adequacy: the Average Gain test. Like convergence testing, it is a necessary but not a sufficient condition of model adequacy. Although the raw data necessary for performing the test has always been in the NEC output file, only recently has it found its way into commercial implementations of NEC. I anticipate that it will be available in upcoming releases of NEC-Win Plus and EZNEC for Windows.

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Essentially, we only need two numbers to perform the test: the input power and radiated power. For a lossless antenna, the input power and the average radiated power should be equal. Whatever the gain in one or more favored directions, it will be offset by nulls in other directions. Over the entire sphere of free space, the total amount of radiated power can never exceed the power supplied to the antenna. Hence, the ratio of average radiated power to supplied power should be 1. If the ratio differs by more than a small amount from 1, then the model may be considered suspect.

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The conditions under which an adequate model will show an Average Power Gain (GAVE) of 1 also establish the conditions for performing the Average Gain test. The model is set in free space. (We shall look at setting the model over perfect ground in a moment.) The wire material must be perfect or lossless. All "real" or resistive parts of loads, networks, and transmission lines must also be set to zero (which may require in a parallel R-L-C load a very high value for the parallel resistance).

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For test purposes, the model is run by taking a regular sample of the radiation pattern every few degrees, and the results are averaged. (Note: for these tests, the sample is taken as a power and not as a power ratio, although one can be easily converted to the other.) The result is a statistically fair reading of the average radiated power. To calculate the average power gain, we simply apply the following simple equation:

+
+ +
+

where GAVE is the average power gain, PRAD is the radiated power as averaged, and PIN is the input power as calculated from source information.

+

What about k? For a free space model, k = 1. However, if the test lossless model is placed over perfect ground, then k = 2.

+

The results will not vary by much if the only loss in the antenna is wire loss for high conductivity materials of reasonably large diameters. However, for the most reliable figure of merit, the test is best run on a wholly lossless version of the model being tested.

+

The average gain figure that results from the test may be higher or lower than 1.0. One proposed gradation of model merit uses the following dividing points:

+ 
GAVE Value Range                   Significance
+0.95 - 1.05                   Model is considered to have passed the test
+                              and is likely to be highly accurate.
+0.90 - 0.95 and 1.05 - 1.10   Model is quite usable for most purposes.
+0.80 - 0.90 and 1.10 - 1.20   Model may be useful, but adequacy can be
+                              improved.
+<0.80 and >1.20               Model is subject to question and should be
+                              refined.
+

The user may develop more strict limits for the adequacy of a model based on the specific tasks within which the model plays a role.

+

Most models that deviate in the test from an average gain of 1 show an inverse correlation between errors in gain and in the resistive component of the source impedance. As the gain climbs, the source impedance decreases, and vice versa. For limited purposes, the average gain value derived from the test can be used to correct both figures, using the following equations:

+
+ +
+

and

+
+ +
+

Obviously, an average gain value that is greater than 1 will increase the input resistance and decrease the gain. Values less than 1 will do the opposite. In no case should such corrections be applied and used unless the model has first been established as a good model relative to tests other than the Average Gain test. As we shall see, the Average Gain test can identify some questionable models, but certainly not all of them.

+

Some Test Cases

+

To familiarize ourselves with the average gain test and its utility, let's look at a few test cases. All of them were tested for average gain using the NEC-Win Plus implementation of the test, which rewrites a given model to establish the necessary lossless conditions. All of the models were run in free space.

+

1. A folded dipole with elements having different diameters. Fig. 1 shows the folded dipole we shall test, using the model shown in the lower portion of the drawing.

+
+ +
+

The test model uses a #12 wire for the source with a 1" wire as the continuous element. With the ratio of wire diameters given, the source impedance should be transformed by a factor of over 7 relative to a standard dipole, or something around 530 Ohms. (Standard equations for calculating the impedance transformation of a folded dipole--taking into account both wire diameters and the spacing between wires--can be found in the ARRL Antenna Book.) The free space antenna gain should be that of a standard folded dipole, in the 2.1 to 2.2 dBi range. NEC-2 returns a gain of 0.97 and a source impedance of under 400 Ohms for a model that is resonant and which reports the approximately correct values when modeled carefully in MININEC. (MININEC returns a free space gain of 2.2 dBi and a feedpoint impedance of about 530 Ohms for this test case.)

+

The Average Gain test yields a value of 0.75, indicating a highly untrustworthy NEC model. Note, however, that in this case, NEC returns values for gain and for impedance that are both less than one might reasonably anticipate from models of other folded dipoles and from calculations of the impedance transformation for the wire diameter ratios and wire spacing. Nonetheless, as a figure of merit, the Average Gain test correctly characterizes the model.

+

2. Close spaced elements of unequal length. The basic set-up for this condition appears in Fig. 2.

+
+ +
+

A resonant 1" diameter 14 MHz dipole is placed close to an unfed wire, also 1" diameter, approximately resonant on 21 MHz. NEC reports the 14 MHz free space gain and feedpoint impedance of this configuration in the following pattern:

+ 
Spacing in inches        Gain in dBi         Feedpoint Z (R +/- jX Ohms)
+     12                       2.2                 75 - j 0.3
+      4                       2.4                 74 + j 2.8
+      2                       3.3                 61 - j 0.1
+

Passing all three versions of the model through the Gain Averaging test yields the following set of values:

+ 
Spacing in inches        Average Gain
+     12                       1.0003
+      4                       1.0628
+      2                       1.2942
+

With a spacing of 12", the model completely passes the test. The gain figure, which is very slightly high for a resonant dipole, is the maximum gain in the direction of the secondary element, and the configuration shows a front-to-back ratio of nearly 0.1 dB. Hence, everything is quite normal and usable.

+

The figure for the 4" spacing version suggests that the model is quite usable for most purposes. Here is a case where a user should feel free to reach a more strict requirement if the modeling task requires quite high precision--as do many studies that systematically track performance predictions from NEC. The model with 2" spacing is clearly unusable for anything except accounts such as this one that point out its dangerously over-estimated gain and underestimated feedpoint impedance. In this example, the use of the Average Gain to correct the numbers yields quite good results.

+

3. A 2-element 7.1 MHz Yagi with highly tapered element diameters. The basic outline of the subject Yagi appears in Fig. 3.

+
+ +
+

From the center of each element outward, the prescribed element taper schedule is as follows (with all dimensions in inches):

+ 
Element Diameter         Section Length
+     4.7                       12
+     2.25                     108
+     2.0                      120
+     1.0                       66
+     0.75                      69
+     0.5                      to tip
+

The very large diameter center section simulates the effect of an element-to-boom mounting plate.

+

Without the Leeson corrections, NEC-2 returns for this 2-element Yagi a free space gain of about 6.2 dBi and a front-to-back ratio just above 8 dB. The feedpoint impedance is just about 43 Ohms. The Average Gain test returns a value of 1.25, indicating a model of highly dubious adequacy. By way of contrast, the model with substitute uniform diameter elements produced via the Leeson equations yields a gain of 5.8 dBi with a front-to-back ratio of about 10.6 dB. The feedpoint impedance is about 41 - j36 Ohms. Although the resistive component of this impedance appears to defy the correction function of the Average Gain test, it does not. Since the driver is highly reactive, it must be lengthened to achieve resonance, and this action will increase the resistive component of the impedance well above the level of the uncorrected source impedance. Likewise, shortening the uncorrected model's driver to yield about the same capacitive reactance as the corrected model will also lower the value of the resistive component of that impedance.

+

Some Other Test Cases

+

Although the three test cases we just ran generally confirm the utility of the Average Gain test, that test does not reveal every inadequate model. A few illustrations may be useful.

+

4. A quad loop with "fat" horizontal wires and "thin" vertical wires. Let's construct a 10-meter quad loop like the one shown in the lower half of Fig. 4.

+
+ +
+

Quad loops constructed entirely of 1" "fat wires" or of #12 "thin wires" both have bi-directional maximum free space gain values close to 3.3 dBi, with resonant feedpoint impedances between 125 and 130 Ohms. Suppose we construct a composite quad consisting of horizontal fat wires and vertical thin wires. NEC-2 reports the gain as about 3.6 dBi and the feedpoint impedance as 170 + j122 Ohms. By way of contrast, a MININEC model shows a feedpoint impedance closer to 135 Ohms, which is more in line with the mono-taper versions of the quad loop.

+

Interestingly, the Average Gain test produces a value of 0.9915, indicating a highly reliable model--at least so far as that test can indicate.

+

However, the quad with corner junctions of dissimilar diameter wires is an odd NEC model to be sure. Although its reported gain remains stable, the source impedance varies widely according to the number of segments per side. Some modelers believe that the most accurate results come not from the highest segmentation density, but from the lowest. Whatever the final verdict on the model, it is a case of a dubious model that the Average Gain test cannot catch.

+

5. A corner-fed non-symmetrical 40-meter triangle. Suppose we construct a right-angle triangle of #12 AWG wire and feed it at the lower corner, as shown in Fig. 5.

+
+ +
+

Even at low segmentation densities, the Average Gain test returns values such as 0.96, indicating a highly reliable model. However, this model requires many segments for results to convergence, due largely to the lack of symmetry in current magnitude adjacent to the feedpoint. Unfortunately, the Average Gain test can give no clue as to what this model requires for reliable results.

+

6. A folded-X beam for 28.5 MHz. Let's construct a folded-X beam using 1" wire for the X-portion and #18 wire for the "tails," as suggested in Fig. 6.

+
+ +
+

The folded X-beam is a highly unstable model in NEC-2. It will not converge at any level of segmentation density tried. The highly angular junctions of wires having very disparate diameters is the most likely source of the convergence failure. NEC-2 cannot provide any guidance for the dimensions of this antenna that will yield resonance and desired levels of gain and front-to-back characteristics. MININEC will provide the necessary guidance so long as the modeler gives due care to the sharp corners by using segment-length tapering techniques.

+

However, the Average Gain test certifies the folded X-beam model as reliable with a value of 0.9641.

+

The failure of the Average Gain test to reveal the defects of these last three examples is not a flaw of the test. Instead, these cases simply illustrate that passing the test is a necessary but not a sufficient condition of model adequacy. Adequate models will pass the test, but bad models will not always fail it.

+

Conclusion

+

The Average Gain test is a valuable addition to the collection of tests for evaluating the structural adequacy of our models. When combined with the convergence test, most models that go bad structurally can be detected. However, since each is a necessary but not sufficient condition of adequacy, there is no guarantee that some few models will pass both tests and still prove to be inadequate as models.

+

Notice that I qualified the idea of adequacy by referring to "structural" adequacy, that is, the basic geometry of the antenna. There are additional inadequacies that can result from using networks, transmission lines, and loads in less than optimal ways. Because any resistive component of these mathematical additions to the model will be eliminated for the purpose of running the Average Gain test, that test may not show flaws resulting from networks, transmission lines, and loads.

+

In the end, there may be no single test or battery of tests that will automatically detect all inadequate models. To the best of my knowledge, there has been no systematic attempt to identify and isolate the specific properties of antenna models which are likely to fail either the convergence test or the Average Gain test (or both). The small sample in this note is hardly even a beginning in that direction. In the end, knowing from experience when values are climbing or falling outside the boundaries of good sense and basic antenna theory is likely the last line of defense against an inadequate model. Nonetheless, the Average Gain test is a very useful addition to our repertoire of evaluative tools in modeling.

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Go to Main Index

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+

21. The NEC TL Facility

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

We have mentioned the use of the NEC TL facility along the way, but perhaps a concentrated dose of TL might get us better oriented to using mathematical transmission lines in NEC. Note that this facility is not available in public domain versions of MININEC.

+

First of all, let's look at the rules for when it is apt to use transmissions lines and what their limitations may be. The TL input for NEC (-2, -3, -4) is a special form of network input, designed specifically to enable modelers to place transmission lines into a model. Since we are dealing with a network, we must have two wires on which to place the ends of the line we create.

+

For applications where the line connects two antenna elements, the requirement for 2 wires poses no problem, as shown in Fig.1, part B. However, when we wish to connect a transmission line to a source to see the effects of line length on the impedance or when we wish to use transmission line stubs as reactances, then we must create the second wire, as shown in Fig. 1, Part A.

+
+ +
+

For the types of cases just noted, the second wire should be positioned and sized so that it plays no significant role in the far field of the antenna itself. This requirement forces the wire to be at some considerable distance from the antenna--the farther the better. Moreover, the wire should be thin and short--a single segment wire just meeting the lower limits of radius and length works fine. The wire should itself be lossless, if that option is available.

+

The position of the terminating wire makes no difference to the length of the transmission line in the mathematical model. The user will always specify the length of the transmission line, and this value will supersede the distance created by the modeled placement of the terminating wire.

+

The user will specify the segments of wires which represent the terminal points of the transmission line. As well, the user will specify the length and the characteristic impedance of the line. The basic length is the electrical length, assuming a velocity factor of 1.0. Some programs allow the user to specify the physical length and the velocity factor: the program then uses those numbers to calculate the electrical length for actual NEC calculations.

+

Since the line created by the TL entry is mathematical only, the line itself plays no role in the generation of the antenna's far field. This feature may be a modeling convenience in many cases, but in some other cases, it may represent a limitation on the model. If the transmission line plays a role in the antenna pattern, as is the case in many off- center-fed wire antennas, a physical model of the transmission may be preferable to use of the TL facility.

+
+ +
+

Sources and loads on the same segment appear in series with each other. TL entries are different. They appear in parallel with sources and loads that are placed on the same segment, as shown in Fig. 2. This factor must be kept in mind when trying to add a TL transmission line to a source segment that is already loaded. This feature is both a limitation and an opportunity--as we shall see further on.

+

Since TL transmission lines are mathematical, they show no losses. If you wish to know the losses involved in a transmission line application, you must hand calculate them or use other software, such TL by N6BV. These calculations may also reveal slight differences in the 2:1 SWR bandwidth of some models relative to the lossless line in the model.

+

The TL line will be accurate only if applied under balanced conditions, that is, where the current on each side of the line is the same. This restriction dictates that TL lines be used at such places as the center segment of a linear horizontal element. Applying a TL line off center will yield inaccurate results. Theoretically, one might apply a TL transmission line as a phasing section between two collinear dipoles. However, the current and voltage at the junction point are changing so rapidly that equalized currents are rarely feasible. For such applications, modeling a physical parallel transmission line is advisable.

+

How to Implement TL Transmission Lines

+

Depending upon the level of user help in a given implementation of NEC, the user may have to do little calculation--or a lot. EZNEC, for example, allows you to specify the two ends of the line--and offers preset options if you wish a shorted or open stub. These option eliminate the task of specifying a new wire in the model that represents the TL termination, since the program automatically generates the distant wire. For a shorted stub, the program specifies a very low resistance value as a load on the far wire--perhaps 1E-10 Ohms. For an open stub, the program loads the wire with a very high value of resistance, perhaps 1E10 Ohms.

+

With raw NEC and some programs, you must introduce the stub-terminating wires as added wires in the model description. Some programs require that you give them tag or wire numbers over a certain value so that they will not appear in views of the antenna.

+

You must then specify the characteristic impedance of the transmission line being mathematically simulated. EZNEC permits the entry of a velocity factor, and it also has a catalog of common transmission lines with their associated velocity factor values. Other software will require that you enter the electrical length of the line as well as the characteristic impedance. If this requirement applies to your software, you may simply divide the physical length by the velocity factor to determine the electrical length. Use care: even though you may have entered the antenna geometry in inches or feet, some programs will require that TL lengths be entered in meters, thus requiring one more conversion before finalizing the entry.

+
+ +
+

Fig. 3 shows a data entry box where no short-cuts are available. Here, standard NEC language is used. The "Tag" numbers are the wire numbers in the wire description portion of the model description, while the segment numbers are referenced to the segments themselves and not to percentages of the way along a wire. Hence, you must be careful to identify the correct segment number for exact placement of the TL. If you change the segmentation of the wire, you must return to this box and change the segment number for the TL on that wire if you wish it to be placed at a certain position, for example, at the wire center.

+

The line characteristic impedance is given as 50 Ohms, with an electrical length of 10.6 meters. This might represent 34.78' of line, if you did your original calculations in feet. If the velocity factor of the line is 0.66, then the physical length of the line would be only 22.95'. Be sure to keep records on paper of all calculations that lead up to NEC entries so that you can check your work later for errors.

+

The standard NEC entry for networks is in terms of admittance rather than impedance. Therefore, had we been building a shorted or open stub, we would need an entry here. A shorted stub would have virtually no resistance. In terms of admittance, we would insert a very high value, perhaps 1E10 mhos (now called Siemens). An open stub would require a very high resistance and require a very low value of admittance, perhaps 1E-10 in the real column. For stubs, you may ignore the "imaginary" column, which would take values of susceptance, the inverse of reactance.

+

A Few Real Examples

+

To gain a better handhold on the use of TL transmission lines, let's look at a few examples involving real design questions. For this exercise, we shall use a few sketches and some model descriptions taken from EZNEC.

+

1. A 3-Element 15-Meter Yagi With a Quarter Wavelength Matching Section:

+
+ +
+

Fig. 4 shows the outline of a 3-element 15-meter Yagi of good performance (8+ dBi free-space gain and 26 dB front-to-back ratio at 21.2 MHz). The elements have been sized so that the antenna is resonant at the design frequency. The feedpoint impedance is 24.8 + j 0.4 Ohms, too low for a match to the standard 50-Ohm coaxial cable.

+

However, we can insert a 35-Ohm quarter wavelength matching section to effect the match. To do so, we must add a 4th wire that is very short and of small diameter. Then, we add a quarter wavelength section of feedline according to the entry rules of the software we happen to be using. The line would be 11.6' or 3.54 m long electrically. If the velocity factor is taken into account, the line would be 7.655' long physically.

+

Below is the model description of the final arrangement:

+ 
3 el Yagi 3/4" el               Frequency = 21.2  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1        -11.554,  0.000,  0.000        11.554,  0.000,  0.000 7.50E-01  21
+2        -11.032,  6.991,  0.000        11.032,  6.991,  0.000 7.50E-01  21
+3        -10.381, 15.074,  0.000        10.381, 15.074,  0.000 7.50E-01  21
+4         -0.100,  6.991, -5.000         0.100,  6.991, -5.000    # 14    1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1     4 / 50.00   (  4 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1  Wire #/% From End 1  Length       Z0   Vel Rev/
+      Actual  (Specified)  Actual  (Specified)              Ohms Fact Norm
+
+1     2/50.0  (  2/50.0)    4/50.0  (  4/50.0)    7.655 ft   35.0  0.66  N
+
+Ground type is Free Space
+

The feedpoint impedance at the design frequency with the line in place is 49.4 - j 0.8 Ohms. Remember that TL entries are lossless, so there may be a small loss in the section that must be independently calculated.

+

Most interesting is the placement of the tiny wire (#4) used to terminate the transmission line and also to serve as the model source. I purposely placed it close to the antenna and vertically in line with the driven element. You should move this wire around in order to get some feel for how close or distant such added wires must be to have no significant effect on the antenna performance. In this case, the wire can be quite close without changing any of the performance figures. However, a distant wire placement is always in order.

+

2. A 4-Element 10-Meter Yagi With a Beta Match (Shorted Stub):

+
+ +
+

In Fig. 5, we have the outline of a 4-element Yagi. At 28.5 MHz, the design frequency, the antenna shows a free-space gain of 8.6 dBi with a 22 dB front-to-back ratio. The natural feedpoint impedance of the antenna is 25.8 - j 28.8 Ohms, a good candidate for a beta match. The simplest form of the standard beta match used to compensate for capacitive reactance is a hair pin or shorted stub having the correct inductive reactance according to standard L-circuit calculations. We can simulate the hair pin by creating a shorted stub of a reasonable characteristic impedance at the source junction.

+

For the model in this exercise, I used a 5" stub of 450-Ohm line with a velocity factor of 1.0. The EZNEC model description looks like this:

+ 
4 el 13' boom                         Frequency = 28.5  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -103.73,  0.000,  0.000       103.731,  0.000,  0.000 5.00E-01  21
+2        -97.942, 35.811,  0.000        97.942, 35.811,  0.000 5.00E-01  21
+3        -97.226, 65.653,  0.000        97.226, 65.653,  0.000 5.00E-01  21
+4        -91.078,152.195,  0.000        91.078,152.195,  0.000 5.00E-01  21
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1   Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)             Ohms Fact Norm
+
+1    2/50.0  (  2/50.0)  Short ckt (Short ck)    5.000 in   450.0  1.00
+
+Ground type is Free Space
+

In some software, you would need to create the distant wire for the shorted end of the TL stub and give it a very high admittance value. You may even have to convert the 5" length to its equivalent in meters.

+

With the stub specified, the feedpoint impedance is 43.4 + j25.2 Ohms, something less than a perfect match at the design frequency of 28.5 MHz. However, the stub length was not chosen for a perfect match at one frequency. Rather, the length was experimentally determined based on the goal of obtaining the widest 2:1 SWR operating bandwidth between 28 and 29 MHz. You should experiment with stub lengths (and characteristic impedances) to see the effects on SWR, both at the design frequency and across a desired band segment. Other values might easily improve on the operating bandwidth. You may also change the length of the driver to change the amount of capacitive reactance for which the beta match must compensate. The results may make full coverage from 28 to 29 MHz either easier or more difficult.

+

At a specific design frequency with the correct value of capacitive reactance to accompany the resistive portion of the feedpoint impedance, a beta match can be exceptionally efficient. However, as one moves away from the ideal conditions, small losses may accrue as the match must not only effect an impedance change, but must also compensate for non-ideal reactance values.

+

3. A 3-Element 10-Meter Phased Array With Director and a Beta Match (Open Stub):

+
+ +
+

Fig. 6 presents two uses of TL transmission lines in one example. There is a reversed phasing lines between the rear 2 elements of the array. In addition, there is a beta match to compensate for the natural 15.5 + j23.0 Ohms of the feedpoint impedance. Because the feedpoint reactance is inductive, an open stub will be required, calculated according to standard L-circuit techniques.

+ 
3-el ZL Sp 10m exp.                      Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1         -7.526,  7.876,  0.000         7.526,  7.876,  0.000 6.56E-01  41
+2         -8.313,  0.000,  0.000         8.313,  0.000,  0.000 6.56E-01  41
+3         -8.401, -4.375,  0.000         8.401, -4.375,  0.000 6.56E-01  41
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          21     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)    5.776 ft    50.0  0.66  R
+2    2/50.0  (  2/50.0)  Open ckt  (Open ckt)    3.201 ft    50.0  0.66
+
+Ground type is Free Space
+

The potential performance of this modeled antenna shows (at 28.5 MHz) a free-space gain of about 8.5 dBi and a front-to-back ratio of about 25 dB.

+

The phasing line in the model is evident, since it runs between wires 2 and 3 of the antenna structure. Note that the phase line has been reversed to achieve the correct current magnitude and phasing on the rearmost element. (For this example, we need not consider whether the use of 50-Ohm transmission line with a 0.66 velocity factor is feasible for a practical antenna.)

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The open circuit stub forming the beta match is about 3.2' of the same material. The wire for the termination, invisible in EZNEC, is distant from the array and supplied with a very low value for admittance to effect the open circuit condition.

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The final array shows a feedpoint impedance at 28.5 MHz of 46.1 + j12.9 Ohms. Once more, the stub length was not chosen for the lowest SWR at the design frequency. Instead, the length provides the widest possible 2:1 SWR operating band width for the array. You should experiment with other lengths and transmission line types to see the effect that these changes have on the SWR operating bandwidth.

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These examples should be sufficient to get you started on the road to effectively using the TL facility within NEC. Remember the requirements for balance and the fact that TL transmission lines are in parallel with sources and loads. Next time, we shall look at a few occasions where the physical construction of transmission lines may provide superior modeling results to the use of TL lines.

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22. Modeling Physical Transmission Lines

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L. B. Cebik, W4RNL

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Modeling transmission lines between the source and the antenna can take two forms. We can physically model parallel transmission lines. And, as we saw in the last column, we can model them as TL inputs.

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Physical Models of Parallel Transmission Lines

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Consider a simple antenna fed at the center, as sketched in Fig. 1. The source is in series with the antenna wire. Any transmission line we use to feed the antenna thus forms a series circuit with the antenna wire. At the base of the transmission line, the actual source is now in series with the two wires making up the line.

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These simple facts determine the basic rules for modeling a parallel transmission line as a parallel set of wires. First, we break the single antenna wire element into two segments, with the centermost ends spaced the same distance apart as the spacing of the wires in the transmission line.

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In the figure are a set of arrows indicating ends 1 and 2 of each wire, using a left-to-right convention for this example. Note that we keep the series of wires continuous so that End 2 of Wire 1 connects to End 1 of Wire 2. The model progresses continuously from one end to the other. This is crucial to ensure that the transmission line has equal and opposite currents at every point. (For many placements of transmission lines, the "equal and opposite currents" situation will not fully materialize in reality. However, we should always model the transmission line in the manner shown.)

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The source wire may simply be a one-segment wire from one side of the transmission line to the other. This wire will only be as long as the spacing between transmission line wires, and its segment length sets some specifications for the transmission line segmentation.

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Segments that meet at angular junctions should be about the same length and in any event within about a 2:1 length ratio. Closely spaced transmission lines require much shorter segments due to the close spacing of their wires. The similar junction at the top of the assembly, where transmission lines wires and antenna wires meet, dictates short antenna wire segment lengths. Even for simple antennas, the entire assembly can quickly grow past the overall segment limit (usually about 500) for modestly priced commercial NEC packages.

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One possible solution is to taper the segments lengths along the transmission line, especially at the end closest to the source. EZNEC provides for element length tapering. However, the shortest segment length selected should not be the standard value (0.0025 wavelength), but should match the element spacing. However, NEC-2 recommends that no segment be shorter than 0.001 wavelength long, which the spacing of a 300-ohm line will violate at many HF frequencies. Errors for lines in the 450-ohm to 600-ohm range run about 5 ohms difference from full segmentation (at the test frequency of 14.15 MHz), but length-tapered transmission line models may save from 30 to 130 segments per 1/4 wavelength of each side of the transmission line.

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Physical transmission lines are usually calculated according to one of two equations:

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where Zo is the characteristic impedance of the resulting air-insulated parallel feedline, S is the center-to-center wire spacing, and d is the wire diameter in the same units as S. The first form is handiest for calculators, while the second form is somewhat more accurate for closely spaced lines.

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Program suites such as HAMCALC have modules for calculating the Zo from the wire size and spacing of air-insulated lines--or for calculating any third factor from the other two. Note that these equations do not account for insulation other than air, and the velocity factor is either 1.0 or very close to it. Therefore, any models of physical transmission lines should be based on a velocity factor of 1.0 and the results later readjusted for the actual velocity factor of the line used. Likewise, any losses due to the dielectric must also be accounted for after modeling.

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Interestingly, an extensive series of models using NEC-4 reveals that transmission lines between 300 and 600 ohms show a higher impedance than that calculated for them with the equations. Fig. 2 shows the test modeling arrangement. Instead of an antenna structure at the top of the transmission line, the lines were bridged with a resistive load.

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The following table shows the results of using the arrangement with a carefully adjusted 1/4 wavelength line of #14 AWG copper wire at 14.15 MHz (210"). Theoretically, the source impedance should be the same as the load resistance only when both are equal to the line impedance, according to the standard 1/4 wavelength line equation:

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where Zo is the characteristic impedance of the line, Rl is the load resistance, and Zs is the reported source impedance, all in Ohms.

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First, there is a small and uneliminable reactance at the source from the test model. Second, the wires are very close together, approaching the limits of NEC-4 to handle, even when segments are carefully paralleled. In all cases, the modeled impedance is higher than the calculated impedance by from 5% to 7%.

+ 
Line Zo        Wire      Spacing   Modeled Zo     New Wire
+Calculated     Dia.      (inches)  in Ohms        Size for Zo
+600            0.064"    4.78"     635            0.086"
+450            0.064"    1.37"     483            0.084"
+300            0.064"    0.39"     316            0.075"
+

All results used segments lengths equal to the wire spacing. As the segment lengths were lengthened, the 600-ohm line was least affected, but the 300-ohm and 450-ohm lines changed values for each new segment length tried--without a definitive pattern. As the segment lengths increased, the far field from the test model increased from nearly -40 dBi to values in the low 30s. Increasing the wire size brought the line impedance close to the calculated value. Equally, one might widen the spacing.

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NEC-2 results with the same models correlated well with NEC-4 results with segment lengths greater than 0.005 wavelength. With shorter segments, the two programs apparently respond somewhat differently to closely spaced wires. Tapered-length transmission line models correlated well between the two programs, especially in the 450-ohm to 600-ohm Zo range.

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For many applications, the exact line impedance may be unimportant. However, when physically modeling lines where their impedance does make a difference, running a test model to determine the line Zo is recommended. Physical models of transmission lines are at best somewhat cumbersome. However, they are important to any application where the lines may experience unequal currents and therefore radiate. Typical of such applications is the off-center-fed wire antenna. Comparing the far fields (including both vertical and horizontal components) of the antenna alone and the antenna with its parallel feedline will provide an estimate of such things as the field shape modification occasioned by the feedline, any change of elevation angle of maximum radiation, and any far-field gain changes. An examination of the currents along the transmission line may also be useful in determining the degree of unbalance occasioned by the off-center feed point. Similar exercises may prove useful with other antenna types.

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Within their limitations, physically modeled parallel transmission lines can provide useful information, even if in some cases exactitude is sacrificed. To date, I have found no useful technique to model physically a coaxial cable such that the cable model fits within the segmentation limitations of versions of NEC aimed at radio amateurs.

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Some Applications for Physically Modeled Transmission Lines

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1. The Behavior of Off-Center-Fed Antennas

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In Fig. 3, we see three on many possible configurations of an off-center- fed 1/2 wl wire antenna (modeled with #12 copper wire at 7.15 MHz for this example at a height of 100' above average ground). We can model this antenna without a transmission line or with any length of line we might choose.

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For the example, I have used 1/4 wl and 1/2 wl transmission lines, each composed of #12 copper wire spaced 4.78" apart. The characteristic impedance of the line is approximately 600 Ohms. The segment lengths throughout the model adhere to this length, so that the model with a 1/2 wl line is sizable. Its description appears below as a sample: dimensions are in inches.

+ 
40 dipole 7.15 MHz                         Frequency = 7.15  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -244.00,  0.000,1200.00  W2E1  -2.390,  0.000,1200.00    # 12   51
+2   W1E2  -2.390,  0.000,1200.00  W3E1  -2.390,  0.000,374.620    # 12  172
+3   W2E2  -2.390,  0.000,374.620  W4E1   2.390,  0.000,374.620    # 12    1
+4   W3E2   2.390,  0.000,374.620  W5E1   2.390,  0.000,1200.00    # 12  172
+5   W4E2   2.390,  0.000,1200.00       557.000,  0.000,1200.00    # 12  117
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1     3 / 50.00   (  3 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+              --------------- MEDIA ---------------
+Medium        Conductivity(S/m)   Dielectric Const.    Ht(in)   R Coord(in)
+
+1                 5.000E-03            13.00           0 (def)     0 (def)
+

I purposely chose the line lengths to illustrate that physically modeling transmission lines can reveal antenna system behavior changes that would not show up without the line. Here is a brief table of results.

+ 
Antenna             Gain      TO Angle       Feedpoint Z
+                    dBi       degrees        R +/- jX Ohms
+No line             7.46      19             107 + j 0
+1/4 wl line         2.78      17              95 + j23
+1/2 wl line         5.77      18             156 - j61
+
+ +
+

Fig. 4 shows the differences in the azimuth patterns for the three versions of the antenna, each taken at the elevation angle of maximum radiation. The change in feedpoint impedance is partially a function of the mismatch between the transmission line and the characteristic impedance of the line. However, it is also a partial function of the imbalance of current along the line.

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Fig. 5 shows the current magnitudes along both the antenna and the transmission line for the version with a 1/2 wl line. Feedline radiation is not solely a result of current magnitude on the line. Instead, it stems from the difference of current magnitudes and the amount by which they fail to be 180 degrees out of phase. Consequently, it pays to examine the current tables for antennas such as this one in order to uncover the degree of imbalance on the line.

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As an exercise, you might well try other line lengths, especially those that are not an easy fraction of a wavelength.

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2. A Collinear EDZ Array With Phasing Lines

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In Fig. 6, we have a collinear extended-double-Zepp (EDZ) for 21.225 MHz. It is made 129' of #12 copper wire and is 46' above average earth--about 1 wl up. For the moment, we may ignore the current magnitude lines on the graph except to note the multiple occurrences of the typical EDZ current distribution.

+

Fig. 6 shows the construction of physical models of the phasing lines, composed here of 7' lengths of #12 wire spaced 6" between wires. These shorted stubs have a characteristic impedance of about 650 to 700 Ohms. The description file below shows the antenna geometry fully.

+ 
Collinear EDZs                           Frequency = 21.225  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1        -64.500,  0.000, 46.000  W2E1 -36.250,  0.000, 46.000    # 12   33
+2   W1E2 -36.250,  0.000, 46.000  W3E1 -36.250,  0.000, 39.000    # 12    5
+3   W2E2 -36.250,  0.000, 39.000  W4E1 -35.750,  0.000, 39.000    # 12    1
+4   W3E2 -35.750,  0.000, 39.000  W5E1 -35.750,  0.000, 46.000    # 12    5
+5   W4E2 -35.750,  0.000, 46.000  W6E1  35.750,  0.000, 46.000    # 12   61
+6   W5E2  35.750,  0.000, 46.000  W7E1  35.750,  0.000, 39.000    # 12    5
+7   W6E2  35.750,  0.000, 39.000  W8E1  36.250,  0.000, 39.000    # 12    1
+8   W7E2  36.250,  0.000, 39.000  W9E1  36.250,  0.000, 46.000    # 12    5
+9   W8E2  36.250,  0.000, 46.000        64.500,  0.000, 46.000    # 12   33
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          31     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+              --------------- MEDIA ---------------
+Medium        Conductivity(S/m)   Dielectric Const.    Ht(ft)   R Coord(ft)
+
+1                 5.000E-03            13.00           0 (def)     0 (def)
+

The potential performance of this antenna at an elevation angle of 14 degrees is a gain of 13.5 dBi with a beamwidth between -3 dB point of about 16 degrees. The feedpoint impedance is about 250 - j735 Ohms. Fig. 7 shows the azimuth pattern for the antenna model.

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As important as this pattern is the current table. Below is a portion of that table showing the segments just before and after the phasing lines, and the lines themselves. Only one side of the antenna is shown, since the other side has identical current magnitude and phase values.

+ 
Collinear EDZs                         Frequency = 21.225 MHz.
+
+         --------------- CURRENT DATA ---------------
+
+Wire No. 1:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 31                 .53941          -7.26
+ 32                 .66831          -3.83
+ 33      W2E1       .79846          -1.52
+
+Wire No. 2:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W1E2       .97776           0.57
+ 2                  1.1851           2.37
+ 3                  1.3554           3.70
+ 4                  1.4793           4.79
+ 5       W3E1       1.5519           5.81
+
+Wire No. 3:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W2E2       1.5713           6.55
+
+Wire No. 4:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W3E2       1.568            7.25
+ 2                  1.5154           8.19
+ 3                  1.4087           9.19
+ 4                  1.2527          10.36
+ 5       W5E1       1.0567          11.91
+
+Wire No. 5:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W4E2       .8601           13.91
+ 2                  .68562          16.47
+ 3                  .50825          20.48
+

In the table, wires 2, 3, and 4 compose the phasing line. We might be drawn to the fact that the current magnitudes on the facing wires (2 and 4) are very close to equal. Hence, we might erroneously conclude that a TL entry might well have substituted for the physically modeled phasing line. However, note the relative current phase between the lines--neither in or out of phase with each other. In fact, substituting TL entries for these physically modeled lines would have yielded an excess gain figure and a quite different feedpoint impedance.

+

Phasing lines between collinear sections of an antenna are almost always best modeled physically.

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3. A Linear-Loaded Dipole

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+

In Fig. 8, we find a linear loaded #12 copper wire short dipole for 28.5 MHz. The total length of the dipole is under 135", about 65% of a full size dipole.

+

Loading is accomplished with linear loads, which resemble shorted transmission line stubs. In fact, when linear load wires are arranged symmetrically relative to the main dipole wire (for example, in a triangle), transmission line calculations for loading work quite well in figuring the required length for the load lines each side of the center feedpoint. If we omit the linear load, we would find a high value of capacitive reactance at the source point. An equivalent inductive reactance would compensate for the capacitive reactance. We can calculate shorted stubs, each having half the required full value, and they would come very close to lengths required when building an actual linear loaded dipole.

+

However, the arrangement of lines in this model is linear, with each line a different distance from the main element. The model description tells the story succinctly.

+ 
linear-loaded short dipole               Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -67.300,  0.000,  0.000  W2E1  -1.200,  0.000,  0.000    # 12   34
+2   W1E2  -1.200,  0.000,  0.000  W3E1  -1.200,  0.000,  3.000    # 12    2
+3   W2E2  -1.200,  0.000,  3.000  W4E1 -28.200,  0.000,  3.000    # 12   13
+4   W3E2 -28.200,  0.000,  3.000  W5E1 -28.200,  0.000,  6.000    # 12    2
+5   W4E2 -28.200,  0.000,  6.000  W6E1  28.200,  0.000,  6.000    # 12   27
+6   W5E2  28.200,  0.000,  6.000  W7E1  28.200,  0.000,  3.000    # 12    2
+7   W6E2  28.200,  0.000,  3.000  W8E1   1.200,  0.000,  3.000    # 12   13
+8   W7E2   1.200,  0.000,  3.000  W9E1   1.200,  0.000,  0.000    # 12    2
+9   W8E2   1.200,  0.000,  0.000        67.300,  0.000,  0.000    # 12   34
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          14     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+

The linear load lines are spaced 3" apart and 3" from the main element. It makes no difference in free space that the load lines are above the element rather than below it. The free-space gain for the dipole is 1.7 dBi with a feedpoint impedance of 21 - j0 Ohms. Fig. 9 shows the expected dipole pattern.

+
+ +
+

More significant for model construction is the current table, a portion of which appears below.

+ 
linear-loaded short dipole              Frequency = 28.5 MHz.
+
+         --------------- CURRENT DATA ---------------
+
+Wire No. 1:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 21                 .57137          -1.50
+ 22                 .5929           -1.46
+ 23                 .61385          -1.42
+ 24                 .63428          -1.38
+ 25                 .6542           -1.34
+ 26                 .67366          -1.30
+ 27                 .69266          -1.25
+ 28                 .71122          -1.21
+ 29                 .72946          -1.16
+ 30                 .74741          -1.11
+ 31                 .76522          -1.06
+ 32                 .7831           -1.01
+ 33                 .8014           -0.95
+ 34      W2E1       .82098          -0.88
+
+Wire No. 2:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W1E2       .84048          -0.81
+ 2       W3E1       .85779          -0.75
+
+Wire No. 3:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W2E2       .87723          -0.68
+ 2                  .89596          -0.62
+ 3                  .91193          -0.58
+ 4                  .926            -0.54
+ 5                  .93844          -0.51
+ 6                  .94961          -0.49
+ 7                  .9595           -0.46
+ 8                  .96827          -0.45
+ 9                  .97598          -0.43
+ 10                 .98255          -0.41
+ 11                 .98806          -0.40
+ 12                 .99266          -0.39
+ 13      W4E1       .99633          -0.38
+
+Wire No. 4:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W3E2       .99895          -0.37
+ 2       W5E1       1.0021          -0.37
+
+Wire No. 5:
+Segment  Conn      Magnitude (A.)  Phase (Deg.)
+ 1       W4E2       1.0066          -0.36
+ 2                  1.0109          -0.35
+ 3                  1.0141          -0.34
+ 4                  1.0162          -0.33
+ 5                  1.0174          -0.31
+ 6                  1.0176          -0.29
+ 7                  1.017           -0.27
+ 8                  1.0155          -0.25
+ 9                  1.0134          -0.22
+ 10                 1.0105          -0.19
+ 11                 1.0073          -0.15
+ 12                 1.004           -0.11
+ 13                 1.0012          -0.06
+ 14                 .99999           0.00
+

Wires 1, 3, and 5 are the parallel sections of wire forming one side of the dipole. These are the wires on which to compare the current magnitudes and phases relative to each other. The current inequalities tell us that the shorted stub is not acting as a pure transmission line. Radiation is not solely a function of the main wire, but of the net current magnitude and phase of the three closely spaced wires composing the linear load and the main element. The current magnitude line in Fig. 8 gives a more graphical view of the rate of change of current along each of the relevant wires.

+

These examples are samples of when physically modeling transmission lines will provide a more accurate model than using the TL facility. Wherever the current at the terminals of the line is not equal, the line will contribute to the far field radiation pattern--either adding to or subtracting from the overall pattern. Under those conditions, physically modeling the transmission line will always be more accurate than using the TL facility in NEC.

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Go to Main Index

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23. Modeling LPDAs

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L. B. Cebik, W4RNL

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Log-Periodic Dipole Arrays are becoming more popular for amateur use and have become a mainstay of governmental and commercial broadcast and communications systems. When well engineered, they eliminate the necessity of re-matching a main coaxial cable feedline to the antenna over a wide frequency range. The frequency range may vary with the application. There are log-cell Yagis for monoband amateur use, LPDA arrays with a 1.0 to 1.5 octave range for the upper HF ham bands, and also arrays with over a 3-4 octave range for other services.

+

The design of LPDAs is covered well in the literature--at least with respect to long-standing design principles. There are some proprietary algorithms that vary from the standard, but most amateur radio LPDAs are still designed using the basic relationships shown in Fig. 1.

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+ +
+

The antenna array consists of a series of dipoles whose self-resonant frequencies and lengths are set up in a periodic fashion and whose spacing is equally periodic. The elements are interconnected with a transmission line that reverses connections at each new dipole element, with the feedpoint normally at the junction with the shortest dipole of the array. We shall not dwell on the design parameters, since they appear in Johnson and Jasik as well as in the ARRL Antenna Book. Our concern will be limited to modeling LPDAs.

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Essentially, we have two choices. We can attempt to model physically all aspects of the antenna array, as shown on the left in Fig. 2. Unfortunately, for NEC, this strategy quickly meets with some of the geometry limitations within the program. These limitations are functions of the calculation core and not of any particular implementation of NEC.

+

Since the elements are rarely of the same diameter as the transmission line wires, we encounter NEC's difficulties with angular junctions of dissimilar diameter wires. Results will rarely be accurate. Of course, every physical implementation of an LPDA has to deal with the crossing transmission line wires. The simplest scheme that works well appears in the left edge view. Let the inter-element transmission line (or phase line for short) be set up vertically. Then the left and right sides of each dipole can intersect alternate upper and lower wires of the phase line. The misalignment of up to a few inches of the two sides of the dipole will create no significant errors in the resulting antenna pattern or performance figures. However, the angular junction problem can only be overcome for a few designs using a constant diameter for all portions of the antenna.

+

MININEC (3.13) does not have the same angular junction limitation that troubles NEC, but MININEC does have limitations of its own. Sharp angular junctions require the use of high levels of segmentation or the use of length tapering to ensure that each junction is met with very short segment lengths. The short segment lengths minimize errors created by MININEC's tendency to "cut off" corners. The end result of overcoming the inherent MININEC limitation is a model that will overrun the maximum segment limitation of most versions of the program. Those programs that have extended the number of available segments will run very slowly with very high numbers of wires and segments in the model.

+

The most promising way to model an LPDA is to follow the lead of the right hand sketch in Fig. 2, which applies only to NEC (-2 or -4) models. Set up each dipole in its proper position. Use an odd number of segments on each dipole wire. (This note applies to the center wire of elements that have a tapered element diameter schedule, which in turn only applies to programs having corrections for NEC's difficulties with tapered diameter elements.)

+

From one dipole to the next, run a TL transmission line of the desired characteristic impedance. Reverse the connection of each transmission line installed. Place the source on the center of the shortest dipole. Many LPDA designs employ a shorted transmission line stub at the center of the longest element, and this can also be put in place in the model using the TL facility.

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The following model description, adapted from a test file in EZNEC, illustrates the model construction principles.

+ 
17-10m Log Per - ARRL Ant Book          Frequency = 28  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-163.46,  0.000         0.000,163.460,  0.000 1.25E+00  41
+2         39.230,-130.76,  0.000        39.230,130.760,  0.000 1.00E+00  33
+3         70.620,-104.62,  0.000        70.620,104.620,  0.000 7.50E-01  25
+4         95.720,-83.690,  0.000        95.720, 83.690,  0.000 6.25E-01  21
+5        115.810,-66.950,  0.000       115.810, 66.950,  0.000 5.00E-01  17
+
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           9     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length    Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)             Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  490.1  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  490.1  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  490.1  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  490.1  1.00  R
+5    1/50.0  (  1/50.0)  Short ckt (Short ck)    6.000 in   490.1  1.00
+
+Ground type is Free Space
+

Although this is a good illustration of the modeling technique, the model does not show exceptional performance.

+

Use of the TL facility avoids most of the difficulties of physically modeling the LPDA. However, the use of TL phasing lines has some limitations of its own. Theoretically, the phase line does not enter into the antenna's radiation on any frequency. However, physical placement of the stub can sometimes alter the antenna's performance on certain frequencies. As mathematical entities created by a network placed at a large distance from the antenna model proper, the TL phase line cannot show the potential effects of placement.

+

In addition, there are construction variables connected with the assembly of real LPDAs, and some of these cannot be captured by the suggested NEC modeling technique. For example, K4EWG presented a 20-10 meter LPDA in Vol. 3 of the ARRL Antenna Compendium. He used a number of interesting construction techniques, sketched in Fig. 3.

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+ +
+

His phase line consisted of two tubes having different diameters. Ordinarily, the impedance of the line created by the two should be calculable from the diameter of the smaller tube, but the physical effects of the arrangement would be missing from the suggested modeling technique. In addition, he used muffler clamps to connect the lower element set to the larger boom. Most significant are the overlapping element ends--8" each side of center line. Overlapping the ends of dipole elements does affect antenna impedance in ways that the simplified model cannot fully capture.

+

For the most part, none of these construction techniques--and others that might be comparable--affects the antenna pattern with respect to gain, shape, or front-to-back ratio. When trying to model an LPDA using construction methods that have physical significance, it is important to establish before finalizing a model that these physical factors do not have distorting affects relative to the propose final model. You can do this by modeling individual elements with all physical aspect taken into account and comparing the results with simplified single elements.

+

Where constructed elements of the sort illustrated have their main effect is on the performance of the phase line. Its net effective impedance may not match the design impedance that we calculate from standard equations and simple round wires. The most straightforward way to deal with phase line variables is to survey the antenna performances at each check point using a variety of phase-line characteristic impedances from about 75-80 Ohms at the lower end of the spectrum to about 200-250 Ohms at the upper end.

+

The resulting chart of performance figures should include at least gain (initially done as free-space gain in dBi), front-to-back ratio, and source impedance. You may encounter phase-line characteristic impedance values that are more favorable to a smooth VSWR curve than other characteristic impedance values. You may also encounter interesting anomalies. For example, at one frequency within the antenna design range, gain may increase with the characteristic impedance, while at another frequency, the gain may increase inversely with increases in the characteristic impedance.

+

In short, do not expect a smooth set of performance figures that vary only slightly with variations in the phase-line characteristic impedance or frequency. Indeed, do not expect all resulting radiation patterns to closely resemble those obtained from Yagis. There is an old over-simplification that suggests that at any frequency, relative to the dipole that is closest to resonance, the elements affecting the overall antenna performance at that frequency are those immediately adjacent to the near-resonant dipole. Actually, at least two elements either side of the near-resonant dipole carry significant current and thus have major consequences for the resulting antenna radiation pattern. Since all of the elements carry at least some current, antenna patterns can vary significantly from the smoothly rounded norm that we have come to expect from Yagis.

+
+ +
+

Fig. 4 shows one mild example, drawn from a model of a 3-30 MHz LPDA at 30 MHz. The array is 100' long and has 26 elements. Clearly apparent are the incipient lobes created by harmonic operation of elements distant from resonance at 30 MHz. Two extra notes are needed here. First, this is not the only type of pattern one might encounter. Diamond-shaped forward lobes are common. So, too, are split forward lobes with peaks separated from the center line by up to 20 degrees or so. Moreover, more than one of these effects may occur at once. Fortunately, most of the pattern aberrations do not occur on common single octave (for example, 20-10 meter) LPDAs of standard design.

+

Second, the characteristic impedance of the phase line has a bearing on the occurrence of these less-controlled azimuth pattern shapes. In general, the higher the impedance of the phase line, the smoother the outline of the azimuth pattern. However, the rear lobes may show some incipient lobes in the form of a slightly squared shape.

+

The gain reported by NEC is very likely to be less than the gain reported by designers who use some of the classic techniques associated with basic LPDA design instructions. The gain of an LPDA is a function of the value of Tau, one of the constants selected by the designer. Only values of Tau in the vicinity of 0.95 are capable of very high gain values, and only when these values are associated with very long boom lengths determined by an optimal value of the spacing constant, Sigma.

+

To see how this works, let us take a sample LPDA using 7 elements for 14 to 30 MHz and having a Tau of just over 0.85. We shall place these elements on three different booms of 20, 30, and 40 feet, respectively. These boom correspond to values of Sigma of 0.07, 0.10, and 0.14. The last value is closing in the optimum value one might calculate for Sigma (about 0.16). Although there are many ways of calculating potential gain in advance, Roger Cox, WB0DGF, reports in his program, LPCAD, that the gain values associated with the Tau of 0.85 should range from about 5.5 dBi to about 7.5 dBi. (Values are interpolated from his table.) We should expect the lower values to be associated with the shortest version of the antenna and the highest values to be connected to the longest version.

+

Here is a table of NEC-4 modeled results for the antenna. Gain is free-space gain in dBi, while front-to-back is the 180-degree ratio in dB. The shortest antenna uses a 75-Ohm phase line, while the longer models use 100-Ohm phase lines. All use a shorted stub from the longest element, and the stub is set to optimize performance and the feedpoint impedance.

+ 
          Gain/Front-Back Ratios of 7-Element LPDAs for 14-30 MHz
+Boom Length         20'                 30'                 40'
+  Frequency
+     14         5.1 /  8.2          5.7 /  9.7          6.2 / 10.4
+     18.12      5.8 /  9.8          7.3 / 13.1          7.2 / 22.6
+     21         6.2 / 14.0          6.7 / 21.5          7.3 / 22.4
+     24.95      6.3 / 16.8          6.6 / 17.2          7.5 / 27.9
+     28         6.2 / 16.9          6.2 / 17.2          6.2 / 17.7
+

This table demonstrates several properties you are likely to see in LPDA designs of modest proportions. First, the longer the boom (up to the limits of optimal Sigma), the higher the gain for the same number of elements. Second, for any given design, some gain or front-to-back figures may well occur that are higher or lower than we would expect from smoothing the curve of results. For example, the 30' version gain at 18.12 MHz if higher than expected from the other values, and the feedpoint impedance turns out to be lower than expected at that frequency. Here is a case that might be "normalized" by adjustment of the length of the shorted stub--if that operation does not disturb performance on another frequency.

+

Third, performance at the upper and lower limits of the design range tends to fall off unless the LPDA is designed to have wider frequency limits surrounding the frequencies actually used. There appears to be a balance one might draw between too high an element density and too low a density. Higher densities tend to increase low frequency performance, but can actually detract from higher frequency performance when carried too far. Likewise, too low an element density can yield lower gain and front-to-back performance at the frequency limits of the design.

+

The present design does not correspond exactly with any published design, although it is related to several. It uses constant diameter elements--all 1" in diameter. Some designs may benefit from staggering the element diameters by increasing the values by the inverse of Tau, counting from the shortest element to the longest.

+

The table of values represents no judgment about the three variants of one design other than this: the values are typical of NEC reports and largely coincident with expectations raised by WB0DGF's suggested table. However, they are significantly lower than values we often see reported for LPDA designs in amateur literature. Therefore, each modeler who anticipates more than casual modeling of LPDA designs should model many designs and develop appropriate expectations for himself or herself.

+

We are often led to believe that LPDA antennas exhibit relatively smooth VSWR curves across the range of their design. If you model LPDAs, develop other expectations, as illustrated by Fig. 5.

+
+ +
+

The SWR sweep in the graph is a function of NEC-4 calculations. Note that the SWR is well below 2:1 relative to a 50-Ohm standard for each of the amateur bands. While it modestly climbs above 2:1 at 17 and 17.5 MHz, it shows very major peaks in the 18.5 to 20 MHz range and again in the 29 to 29.5 MHz range. One of the functions of the shorted stub is to control the placement of the peaks so that the SWR is acceptable at the anticipated operating frequencies. Careful selection of the dipole lengths--as determined by the selection of the value for Tau--also contributes to lower SWR values at the desired frequencies.

+

As we lengthen the boom for the same set of elements, the SWR peaks decrease and the SWR becomes more manageable without critical adjustment to the value of Tau and the shorted stub. However, the curve will never be absolutely smooth. Moreover, the SWR value may never settle at a certain value, even when referenced to the most optimal impedance standard. What can happen with some designs is that the resistive component of the feedpoint impedance deviates most from the standard when the reactance is the lowest. Conversely, when the resistance is closest to the standard, the reactance reaches peak capacitive or inductive values. However, in some designs, the mean resistive component may shift as you move to different parts of the array's frequency range.

+

I have sampled some of the phenomena you may encounter when modeling LPDAs in order to remove some of the surprises that might shock a relatively inexperienced modeler out of further work with this kind of antenna design. Not all of the phenomena listed occur with every design--indeed, some designs will be very tame and well-controlled. However, the more phenomena with which you are acquainted, the less likely it will be that you will be discouraged from making optimizing adjustments to a model.

+

Nonetheless, even when you have achieved the best possible NEC model of an LPDA, expect to make field adjustments to compensate for construction factors that cannot be included in the model. NEC can be highly accurate in predicting the performance of a design, but it cannot adjust the shorted stub or decide for you whether or not to use a broad-band matching device between the antenna feedpoint and the coax.

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Go to Main Index

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24. The Power and the Source

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+

L. B. Cebik, W4RNL

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+
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+

A continuing source of confusion among newer modelers is the data that NEC produces concerning power and the source conditions. Few modelers realize that they have both limitations and opportunities in these parts of modeling. So let's look a little closer at both arenas.

+

Power

+

NEC provides a "power budget" report as part of its standard report. Although this report is accessible to users, few ever look at it in detail. A typical power budget appears in Fig. 1.

+
+ +
+

Without supplementary data, the numbers may be of little use. The model involved in this report is a folded dipole for 28.5 MHz. The actual power budget consists of 5 entries.

+

The input power is that supplied to the antenna at the source (or sources). It is a direct function of two factors: the source specified by the modeler and the source impedance calculated by the program. Let's assume that we opted for a 1 volt, 0-degree source--the most commonly used with NEC. NEC itself uses peak volts and reports output voltages and current in peak values. Programs like NEC-Win Plus use these values directly. Programs like EZNEC accept only r.m.s. values as inputs and report r.m.s. values as outputs. Adjustments needed to work with the core are made internally within the program.

+

NEC calculated for the segment on which the source happens to be placed an impedance of 398.8 + j23.5 Ohms, or 399.5 Ohms at a phase angle of 3.375 degrees. NEC calculated a peak current of 0.0025 A at a phase angle of 3.375 degrees. This is a simple application of Ohms law, dividing the specified voltage by the impedance of the source segment.

+

Now let the power, P, equal the traditional I2R. If we take only the current, which is 0.0025031 A (to be overly precise), square it, and multiply by the real or resistive part of the source impedance (398.815 Ohms), we get a power report of 0.0024988 watts, which is double the power reported in Fig. 1. However, Fig. 1 reports the NEC core peak value for current. The r.m.s value of current is 0.707 times the peak value. In other terms, the power (always an r.m.s. value) is half the value calculated from the peak current value. The result is 0.0012494 watts, just the value that Fig. 1 reports in engineering notation.

+

Notice that the radiated power has the same value. The structure losses, here reported as zero, are a function of the material we specify for the wires of the model. This model evidently specified perfect conductors and no load with resistive components. There are also no network losses, meaning that the model has no networks with resistive components.

+

When the Radiated Power equals the Input Power, the efficiency is 100%. NEC always calculates efficiency as a ratio of radiated power to input power (times 100, of course). The efficiency will include only those losses internal to the antenna model structure, including material losses, load losses, and network losses. Not included are any external factors that affect the antenna's environment. Let's illustrate using the simple ground-plane vertical for 7.05 MHz in Fig. 2. We shall initially use no loads and specify perfect conductors for all 5 wires. Also, we shall use the Sommerfeld-Norton ground system and average soil.

+
+ +
+

Here is the basic description for this small model

+ 
1/4 wl w/GP: 7.05 MHz                        Frequency = 7.05  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : m )  Conn.--- End 2 (x,y,z : m )  Dia(mm) Segs
+
+1          0.000,  0.000, 10.135  W2E1   0.000,  0.000,  0.000 5.00E+01  10
+2   W3E1   0.000,  0.000,  0.000        11.796,  0.000,  0.000 6.35E+00  10
+3   W4E1   0.000,  0.000,  0.000         0.000, 11.796,  0.000 6.35E+00  10
+4   W5E1   0.000,  0.000,  0.000       -11.796,  0.000,  0.000 6.35E+00  10
+5   W1E2   0.000,  0.000,  0.000         0.000,-11.796,  0.000 6.35E+00  10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     1 / 95.00   (  1 /100.00)     56.984       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+              --------------- MEDIA ---------------
+
+Medium        Conductivity(S/m)   Dielectric Const.    Ht(m )   R Coord(m )
+
+1                 5.000E-03            13.00           0 (def)     0 (def)
+

Using NEC-4, let's places the ground plane directly on the ground, that is at Z=0. (We cannot do this with NEC-2, which demands that the base of the antenna be elevated slightly above ground.) The resulting elevation pattern for the antenna appears in Fig. 3.

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+ +
+

Now let's place the antenna at a height of 42.5 m (1 wl) above ground, changing nothing in the model except the values for the Z-coordinates. The result is an elevation pattern like that in Fig. 4.

+
+ +
+

Despite the differences between the two patterns, both antennas show an efficiency of 100%, that is, a 1:1 ratio between the input power and the radiated power.

+

In fact, we can look at the power budgets for three conditions: 1. the perfect (lossless) wire model with no loads, 2. the same model with aluminum wires, and 3. a shortened aluminum wire version with a loading coil of 200 Ohms reactance and 1 Ohm resistance (Q= 200). The power budgets look like this:

+ 
Height         Input Power    Radiated Power      Wire Loss      Efficiency
+  m                 W              W                   W              %
+No wire or load losses
+ 0             9.9992E+00     9.9992E+00          0.0000E+00     100
+42.5           1.5162E+02     1.5162E+02          0.0000E+00     100
+Aluminum wire, no load
+ 0             9.9979E+00     9.9952E+00          2.7137E-03      99.97
+42.5           1.5079E+02     1.4993E+02          8.5922E-01      99.43
+Aluminum wire, load (1+j200 Ohms)
+ 0             1.2004E+01     1.1927E+01          7.7168E-02      99.36
+42.5           2.8589E+02     2.5892E+02          2.6971E+01      90.57
+

No entry for network loss will appear unless we introduce a network to the antenna system. However, we read in the chart differences of efficiency. Some are easy to interpret. For each height, we see a reduced efficiency as we add losses to the system--first the wire material, then the loading coil. However, we also see a difference in efficiency between ground and elevated mounting of the antenna. The efficiency goes down as the height goes up, although the maximum gain goes up with height.

+

The efficiency differences for each case result from the fact that we are dealing with I2R losses. The ground-mounted model shows an impedance over ten times that of the version 1 wl up. There is also a similar difference in current, with the elevated model showing the higher value. When each of the two currents is squared, a fixed resistance shows a greater loss in dissipated power. Nonetheless, the difference made by material losses is small in terms of far field radiation (<0.02 dB). The shorter, loaded version of the antenna shows about 2.2 dB lower strength in the ground mounted version and about 0.4 dB lower strength in the elevated model.

+

The maximum gain difference between the two sets of models--well over 10 dB--is, with respect to NEC, a function of the interaction of the antenna's radiation with its environment. NEC does not take the environmental factors into account when calculating efficiency. Analyses of the relative effectiveness of two antenna models must be done externally, normally beginning with the relative gain values, pattern shape, and similar factors.

+

What NEC does do when it has a constant 1 volt, 0-degree phase angle source is to account for the effects of the environment in the impedance of the source segment. The perfect-wire elevated vertical shows an input impedance of 21.4 - j0.6 Ohms, while the version planted on the ground has a source impedance of 191.1 - j159.8 Ohms. The result is different values of current on the source segment: 0.0467 A vs. 0.0040 A. (Since the values for the current vertical model are taken from EZNEC, they are r.m.s. values.) The result is a large difference in input power: 0.0467 W for the elevated vertical vs. 0.0031 W for the ground-mounted version. In each case, the antennas radiate all of the input power and have efficiencies of 100%.

+

Note the fact that the power for the elevated vertical has a numerical value which is the same as the numerical value of the current. Since the impedance is well over 99% resistive, the value of I2R and I2Z are virtually identical. However, for the ground mounted vertical, the impedance is highly reactive. Only the resistive or real portion of the impedance enters into the power calculation, and 0.00402 times 191.1 yields the value for the input (and the radiated) power.

+

The Convenience of 1 Amp

+

When using a voltage source in NEC, the current values that emerge along each wire tend to have inconvenient values. It is difficult to sense the slope of a curve, even though graphical representations of the relative current are helpful visual aids to this process. What can we do to obtain more convenient numerical values?

+

If all segment currents are referenced to a source current value of 1.0, the user can much more readily see the relationships among values at various segments along the wires making up the antenna. One easy way to do this is to specify a current source and give it a value of 1.0 at phase angle zero. However, a current source in NEC is created by a remote network normally invisible to the program user. Under certain conditions, a current source may not be as reliable as a voltage source. One case in which this is true is where the currents on wire segments adjacent to the source segment are not equal to each other. This phenomenon can occur where the feedpoint occurs at the corner of an element and the two sides are not of equal length or form a non-symmetrical structure relative to the source.

+

There is way to provide a source current of 1.0 A at a phase angle of 0 degrees and to stay within the a voltage source mode. This technique applies to single source antenna models. First, assign the model a normal voltage source value of 1.0 V at 0 degrees phase angle. Run the model and note the current magnitude and phase. Let us say that we get a report of 0.024 at -16.12 degrees.

+

Now take the inverse of the current magnitude, in this case 41.67 and enter it as a new voltage source value. For the source phase angle, use the negative of the current phase angle. In this case, we began with a negative phase angle, so we would enter a positive 16.12 degrees. At the specified frequency for the model, the current will now read 1.0 A at 0 degrees phase angle.

+
+ +
+

Fig. 5 can let us quickly demonstrate the utility of using 1 Amp as a source reference. Consider the current profile along the dipole segments. The following table will show only one half of the model, since the other half is a mirror image. You may decide which set of numbers provides the intuitively clearer portrait of the antenna's current levels.

+ 
Source                   Segment Number and Current Report
+ Type          1 (End)   2         3         4         5         6 (Center)
+1 Volt         .00237    .00645    .00984    .01241    .01403    .01458
+1 Amp          .0126     .4425     .6746     .8514     .9622     1.000
+

This technique is useful only at the design center frequency for the antenna model. Since the impedance will change as we alter the frequency of interest, so too will the required voltage source values to achieve a 1 A current. However, for single frequency investigations of current along antenna elements, the technique is a quick and easy way to view all current magnitudes in relationship to a source value of 1 and current phase angles in relationship to a source value of 0 degrees.

+

Power Specification

+

For some applications, it is useful to provide an antenna source with a set power level. Some programs, such as EZNEC provide this option. The program simply takes the core output and recalculates relevant values in terms of the power its sets based on what NEC reports using a standard source input set of values.

+

For programs that do not have this provision, we can do the job ourselves. Let's work through an example, using our ground-mounted 7.05 MHz vertical. If we provide the model with a voltage source of 1.0 at 0 degrees phase angle, it returns the following source data.

+
    +
  • Voltage: 1.0 V at 0.0 degrees
    • +
  • Current: 0.004014 A at 39.90 degrees
    • +
  • Impedance: 191.1 - j 159.8 Ohms
    • +
  • Power: 0.003079 Watts
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This is all the data we need to set a power level. Since these are EZNEC reports, the values are r.m.s. Our goal is to find the voltage magnitude needed for some specific power level. Let's set 10 watts as the required level.

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First, we need to find the impedance magnitude, which is

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where Z, R, and X have their usual meanings. For the example, the impedance is 249.11 Ohms.

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The value of voltage to use at the source is simply

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where P is 10, the power we selected, and Z is the impedance magnitude we just calculated. Theta is the phase angle, which for the example is simply 39.90 degrees. Since the collection of values is highly interrelated, there are other ways to arrive at the same numbers, but this one will certainly work. For the example, the desired voltage to supply the source with 10 watts is 56.98 Vr.m.s.

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If program needs demand a peak voltage value, we may simply multiply the r.m.s. value by 1.414 to arrive at 80.57 Vpk. Since the input voltage derivation uses values of power and impedance, the resulting calculation will always yield an r.m.s. voltage value which requires conversion for programs needing the peak value.

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There are numerous applications for which the specification of a specific power level is either necessary or desirable. One of the most important is the analysis of ground wave values. The RP1 output of NEC yields the total ground wave radiation. The user specifies--in the most usual type of case--a distance from the antenna and a height above ground for the reading. (This assumes that the antenna is centered at a location where the X and Y axis values are both zero.) NEC will report calculated values of radiation in volts per meter (which might be reported as mV/m in the user output report).

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The ground wave output is very useful in estimating the results of making changes in the antenna, changes that in each case might change the source impedance. With changes in source impedance and a simply voltage source, the input power to the antenna may be different for each modification. Recalculating the source voltage to give a uniform power input for each version of the antenna will make the ground wave output reports comparable. A similar utility to using a constant power input to the antenna applies when trying to compare different antennas at the same position.

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Fig. 6 illustrates a second instance where a constant power level can make instantly sensible current values that might otherwise seem initially confusing. The antenna is an open-double rectangle, fed either on the end vertical or on the center vertical. The array produces vertically polarized energy in the main, and is useful in the MF through lower HF region.

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If we provide the end-wire source with 1 A, using a current source, then feeding the end element produce a current on the end vertical center-point of 1.0 A and at the midpoint of the center vertical of 1.84 A. If we move the source to the center-wire, the current readings are 0.54 on the end wire and 1.0 on the center wire. The ratios are the same, but the values differ. Of course, an ideal double-rectangle with no losses and no ground effects would show vertical element current ratios of 1:2:1 from end to end. So too would any three equal length verticals spaced in a line at 1/2 wl intervals.

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The current value differences result from the change of source impedance when we move the source position. The ratio of impedances (28.4 - j11.0 to 8.6 - j3.0 Ohms) between end and center feeding is roughly the square of the ratio of currents. However, if we select a constant power--say, 10 watts--we get the following numeric current values. End feed: end wire = 0.59; center wire 1.09. Center feed: end wire 0.58; center wire 1.08. Had we used lossless wire, the numeric values would have been even closer. Nonetheless, the use of a constant power level relieves use from having to make further calculations to correlate current values on the elements of the open-double rectangle.

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These samples only begin to demonstrate the advantages of being able to transform source voltage, current, impedance, and power numbers from their initial input and report values into other values of more instant utility. Becoming more familiar with the power and source values used and reported by NEC can make the program (and its commercial implementations) more productive for even the casual user.

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Go to Main Index

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25. Bringing Up the Rear: Front-to-Back Ratios

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L. B. Cebik, W4RNL

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When we work with models of directional arrays, such as Yagi-Uda beams, we take great interest in the front-to-back ratio reported by either NEC or MININEC software. However, I am not certain we always fully appreciate the data provided to us by our models. Let's look at Fig. 1 as an illustration.

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Fig. 1 is the free-space azimuth pattern of a short-boom 3-element Yagi. Both EZNEC and NEC-Win software report the gain at 28.4 MHz as 7.09 dBi. However, EZNEC reports a front-to-back ratio of 32.56 dB, while NEC-Win reports that the front-to-back ratio is 21.63 dB.

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Is one of the software packages deeply in error? Not a bit. Each is simply reporting the front-to-back ratio according to a different but valid definition. Actually, there are three working notions of front-to-back ratio generally current in antenna work. Let's begin with the two that are relevant here.

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180-Degree front-to-back ratio: This ratio is simply the difference in gain between the maximum forward gain bearing and another bearing 180 degrees opposite.

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Worst-case front-to-back ratio: This ratio uses the maximum gain anywhere in the rear quadrants as the basis for establishing the ratio relative to the maximum forward gain. In most instance, the side points, as defined by the 90-degree angle from the maximum forward gain heading, determine where the rear quadrants begin.

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If we compare the azimuth pattern in Fig. 1 with the two definitions, we begin to suspect that EZNEC is reporting the 180-degree ratio, while NEC- Win is reporting the worst-case ratio. However, we need not guess; we can find out easily enough from the far-field radiation tables, a portion of which we can view here.

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Azimuth Pattern   Elevation angle = 0 deg
+Deg    V dB      H dB      Tot dB       Deg    V dB      H dB      Tot dB
+ 90    -99.99      7.09      7.09       180    -99.99    -99.99    -99.99
+ 95    -99.99      7.03      7.03       185    -99.99    -24.24    -24.24
+100    -99.99      6.83      6.83       190    -99.99    -19.24    -19.24
+105    -99.99      6.50      6.50       195    -99.99    -16.80    -16.80
+110    -99.99      6.03      6.03       200    -99.99    -15.47    -15.47
+115    -99.99      5.42      5.42       205    -99.99    -14.78    -14.78
+120    -99.99      4.67      4.67       210    -99.99    -14.54    -14.54
+125    -99.99      3.78      3.78       215    -99.99    -14.65    -14.65
+130    -99.99      2.73      2.73       220    -99.99    -15.05    -15.05
+135    -99.99      1.52      1.52       225    -99.99    -15.70    -15.70
+140    -99.99      0.12      0.12       230    -99.99    -16.59    -16.59
+145    -99.99     -1.49     -1.49       235    -99.99    -17.69    -17.69
+150    -99.99     -3.34     -3.34       240    -99.99    -18.97    -18.97
+155    -99.99     -5.50     -5.50       245    -99.99    -20.40    -20.40
+160    -99.99     -8.08     -8.08       250    -99.99    -21.88    -21.88
+165    -99.99    -11.28    -11.28       255    -99.99    -23.28    -23.28
+170    -99.99    -15.57    -15.57       260    -99.99    -24.44    -24.44
+175    -99.99    -22.41    -22.41       265    -99.99    -25.21    -25.21
+                                        270    -99.99    -25.47    -25.47
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For the antenna orientation in the model, 90 degrees represents the peak forward gain heading and shows a gain of 7.09 dBi. Directly opposite, at an angle of 270 degrees, we read a gain of -25.47 dBi. The 180-degree front-to-back ratio is the forward gain minus the gain directly opposite:

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+ 7.09 - (-25.47) = 32.56 dB +
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The rear quadrants begin at an angle of 180 degrees, 90 degrees the the rear of the maximum forward gain heading. At an angle of 210 degrees, we find the peak gain in the rear quadrants: -14.54 dBi. The worst case front-to-back ratio is the highest forward gain minus the highest gain in the rear quadrants:

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+ 7.09 - (-14.54) = 21.63 dB +
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Of course, the tables can always be used to find any set of gain relationships we may desire to know. The gain tables form a too-little used portion of the data available from NEC or MININEC models.

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For the present case, one might wish to ask which of the two front-to-back figures is "right," "more accurate," or "more important." Actually, both figures are equally right and accurate, since both calculate with equal precision from the data. Importance is a judgment to be gleaned from the concerns we bring to the investigation. If we are concerned about rear quadrant QRM in general, then the worst-case figure may be a more useful indicator of the likely levels we might experience when using this antenna. If we are seeking the best figure we can obtain relative to the immediate rearward direction, then the 180-degree figure may be more useful.

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In some cases, the difference may not make much of a difference. Fig. 2 shows the free-space azimuth pattern for a very long 1-octave LPDA. For most practical purposes, any measure would suffice, since the radiation to the rear does not exceed -40 dB in any rearward direction. Nevertheless, the pattern does reveal another facility of NEC and MININEC programs that we use too little--the ability to expand the plotting scale to investigate small pattern features.

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Fig. 3 sets the outer limit of the plot at -20 dB. This move automatically expands the rear quadrant lobes to much more visible proportions. Here, we can clearly see that no lobe to the rear exceeds the one which is 180- degrees opposite to the forward lobe. However, the gain value may seem odd: about -15.5 dB from the outer ring value. If we add this value to the outer ring value of -20 dB, we find the 180-degree lobe to have a gain of -35.5 dB. If we then use the 11.5 dBi gain of the forward lobe as our reference, we obtain a 180-degree front-to-back ratio of 47.0 dB. Since the 180-degree rear lobe is the strongest within the rear quadrants, this value is also the worst-case front-to-back ratio.

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The very high front-to-back ratio exhibited by the long LPDA may be very significant to commercial applications. Indeed, the long LPDA has in many arenas supplanted other wire arrays, and the high potential front-to-back ratio is one important reason (along with the absence of side lobes). Most amateur radio antenna applications tend to settle for a minimum front-to- back ratio of 20 dB, with anything more being a bonus. Hence, the 180- degree and the worst-case ratios might equally satisfy amateur antenna users. (Still, we know which of the two figures an advertiser is more likely to use.) Nonetheless, we might adjudicate the differential we often find between the two numbers by appealing to a third front-back notion.

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Front-to-rear ratio: To overcome misleading aspects of both 180-degree and worst-case front-to-back ratios, some engineers have adopted the front-to- rear ratio. This ratio is based on averaging the power gain of the antenna over the rear quadrant and using the resulting figure as the basis for a ratio with the forward gain. There is no general standard on exactly how many data points to use or where to locate them.

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Let's do a simple calculation relative to the antenna in Fig. 1 and its far-field table: since our antenna pattern is symmetrical on each side of the center line from front-to-rear, let's just add up the gain values at 5- degree intervals from the side point to the rear point and then obtain their average by dividing the total by the number of data point. There are statistically more sophisticated ways to obtain an average value, but this simple exercise can be easily checked by consulting the table above.

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Skipping the -99.99 side inset value, we obtain a total of -344.40 for the 18 points from 185 degrees through 270 degrees. The average gain for the quadrant is -19.13 dBi. Since the forward gain is 7.09 dBi, the front-to- rear ratio is

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+ 7.09 - (-19.13) = 26.22 dB +
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The front-to-rear ratio becomes a reasonable evaluation of overall rearward performance as we compare it a. to the smooth rearward lobes of the antenna pattern in Fig. 1 and b. to the 180-degree and the worst-case values, which are higher and lower, respectively, to the front-to-rear ratio we just roughly calculated. In this case, using any one of the three ratios would not seriously mislead a potential user of the antenna.

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There are cases, however, in which no single figure will adequately evaluate an antenna's rearward performance. Fig. 4 is the free-space azimuth pattern of a folded X-beam. Below is a partial set of gain values.

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Azimuth Pattern   Elevation angle = 0 deg
+Deg    V dB      H dB      Tot dB       Deg    V dB      H dB      Tot dB
+ 90    -99.99      7.34      7.34       185    -99.99     -8.64     -8.64
+ 95    -99.99      7.28      7.28       190    -99.99     -7.10     -7.10
+100    -99.99      7.11      7.11       195    -99.99     -6.17     -6.17
+105    -99.99      6.82      6.82       200    -99.99     -5.67     -5.67
+110    -99.99      6.41      6.41       205    -99.99     -5.52     -5.52
+115    -99.99      5.86      5.86       210    -99.99     -5.68     -5.68
+120    -99.99      5.18      5.18       215    -99.99     -6.12     -6.12
+125    -99.99      4.34      4.34       220    -99.99     -6.84     -6.84
+130    -99.99      3.33      3.33       225    -99.99     -7.86     -7.86
+135    -99.99      2.11      2.11       230    -99.99     -9.18     -9.18
+140    -99.99      0.65      0.65       235    -99.99    -10.86    -10.86
+145    -99.99     -1.14     -1.14       240    -99.99    -12.93    -12.93
+150    -99.99     -3.35     -3.35       245    -99.99    -15.46    -15.46
+155    -99.99     -6.21     -6.21       250    -99.99    -18.41    -18.41
+160    -99.99    -10.20    -10.20       255    -99.99    -21.47    -21.47
+165    -99.99    -16.67    -16.67       260    -99.99    -23.64    -23.64
+170    -99.99    -23.93    -23.93       265    -99.99    -24.26    -24.26
+175    -99.99    -15.57    -15.57       270    -99.99    -24.26    -24.26
+180    -99.99    -11.14    -11.14
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Using the 90 and 270 degree points, we obtain a 180-degree front-to-back ratio of 31.60 dB. Using the 90-degree point and the 205-degree point, where rearward gain is highest, we obtain a worst-case front-to-back ratio of 12.86 dB. For the third figure we shall again average the values between 185 degrees and 270 degrees (even though the minimum gain bearing is 170 degrees rather than 180 degrees) and divide by the 18 points to get a -12.23 dBi average rearward gain. The resulting front-to-rear ratio is 19.57 dB.

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The very high disparity among the three values makes it dubious whether one of those values would fully inform a potential antenna user. The very high 180-degree front-to-back value is very misleading unless QRM from quartering rear directions is judged in advanced to be an insignificant consideration. Even the front-to-rear ratio overrates the antenna's rearward performance by at least a receiving S-unit (6 dB) relative to the gain of the antenna at the 205-degree bearing and its counterpart to the other side. Nonetheless, using only the worst-case value can under- estimate antenna performance overall.

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In the end, obtaining all three figures and applying them in conjunction with careful observation of the azimuth pattern may be the only means of arriving at a satisfactory evaluation of the design. Of course, this evaluation only makes sense in the context of a set of performance objectives and needs.

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Simple techniques of calculating front-to-rear ratios, such as the one we have used to illustrate the principle, suffer limitations. One such limitation is illustrated in Fig. 5.

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The free-space azimuth pattern of the Moxon rectangle seems innocent enough until we try to calculate a front-to-rear ratio. Here is the table for our task.

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Azimuth Pattern   Elevation angle = 0 deg
+Deg    V dB      H dB      Tot dB       Deg    V dB      H dB      Tot dB
+ 90    -99.99      5.79      5.79       180    -99.99    -13.37    -13.37
+ 95    -99.99      5.74      5.74       185    -99.99    -16.95    -16.95
+100    -99.99      5.60      5.60       190    -99.99    -21.96    -21.96
+105    -99.99      5.35      5.35       195    -99.99    -31.20    -31.20
+110    -99.99      5.01      5.01       200    -99.99    -36.45    -36.45
+115    -99.99      4.57      4.57       205    -99.99    -26.38    -26.38
+120    -99.99      4.03      4.03       210    -99.99    -22.85    -22.85
+125    -99.99      3.38      3.38       215    -99.99    -21.12    -21.12
+130    -99.99      2.63      2.63       220    -99.99    -20.33    -20.33
+135    -99.99      1.78      1.78       225    -99.99    -20.15    -20.15
+140    -99.99      0.80      0.80       230    -99.99    -20.43    -20.43
+145    -99.99     -0.29     -0.29       235    -99.99    -21.10    -21.10
+150    -99.99     -1.52     -1.52       240    -99.99    -22.10    -22.10
+155    -99.99     -2.89     -2.89       245    -99.99    -23.34    -23.34
+160    -99.99     -4.44     -4.44       250    -99.99    -24.73    -24.73
+165    -99.99     -6.20     -6.20       255    -99.99    -26.07    -26.07
+170    -99.99     -8.21     -8.21       260    -99.99    -27.15    -27.15
+175    -99.99    -10.55    -10.55       265    -99.99    -27.82    -27.82
+                                        270    -99.99    -28.04    -28.04
+

The 180-degree front-to-back ratio is 33.83 dB. If we use our standard simple front-to-rear calculation for headings from 185 degrees through 270 degrees, we obtain a value of 30.13 dB. However, this value includes points within the main lobe as well as the deep side null--which occurs at 200 degrees. In some easy cases, the higher main lobe values may offset the side null, but in other cases, the inclusion of these value may skew the overall performance. If we use only those values from 205 degrees onward, the average rear gain becomes -23.69 dBi for a front-to-rear ratio of 29.48 dB. Although the differences from the simple calculation is not great in this case, the inclusion of main lobe and side null values reduces the degree of trust we can place in the first result. The fact that the revised front-to-rear ratio is different from the simple result should suffice to illustrate the care that must be used in developing such front- to-rear values.

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So far, we have worked with symmetrical azimuth patterns and could therefore use only one of the rear quadrants to calculate a front-to-rear ratio. Consider Fig. 6

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The azimuth pattern for the half-square 2-element parasitic array has a feedpoint that is necessarily offset from center. Hence, as the vertical and horizontal components of the overall pattern show, there is good reason for the total azimuth pattern to be slightly non-symmetrical. The forward lobe is scarcely affected, but the rear pattern shows great unevenness.

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Had we calculated the front-to-rear ratio by our simple method, the result would be too high or too low, depending on from which side of the center- line we draw our data. Obviously, an operational method of developing front-to-rear ratios should include both halves of the rear radiation pattern. Very likely, the operational method should also include a much finer resolution (perhaps to 1 degree) to obtain many more data points than we have used in our illustrations.

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So far, all of our sample cases have used free-space azimuth patterns. We have a dangerous tendency to assume that, when we take azimuth patterns at some antenna height over ground, the maximum rear gain occurs at the same elevation angle as the maximum forward gain. Therefore, the resulting front-to-back ratio becomes a safe estimate for the antenna's performance for signals from the rear of the antenna.

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Fig. 7 illustrates our presumptions in action. I purposely chose a quad model with significant rearward radiation to make the rear lobe clear in the elevation pattern. In this case, and in a large number of other cases involving horizontally polarized antennas, the rear lobe angle of maximum radiation is the same as the forward lobe angle of maximum radiation: about 13 degrees above the horizon for this illustration.

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However, it is never safe to assume that this phenomenon is universal. For example, see Fig. 8.

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The elevation pattern for this phased array of vertical elements shows a forward elevation angle of maximum radiation of 16 degrees. The corresponding rear elevation angle of maximum radiation is two degrees lower, at 14 degrees above the horizon. Although the difference may not make a very significant operational difference with this array. it does illustrate the need to locate such angles when evaluating the front-to-back or front-to-rear performance of an antenna placed over real ground. In this case, the elevation pattern supplements simple azimuth patterns. Of course, we can always turn to the far field tables for both elevation and azimuth patterns to complete our data needs.

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Many antenna modelers approach the software with limiting assumptions. Perhaps the most common are oversimplifications of the idea of a front-to- back ratio. In this set of exercises, I hope we have gone some distance in showing this basic idea to be somewhat more complex than some of us suspected. But more importantly, I hope the exercises have shown some of the resources within NEC and MININEC with which we can do a full analysis and evaluation of an antenna's rearward performance.

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26. The Scales of Equivalence

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L. B. Cebik, W4RNL

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Frequency scaling antennas consists of adjusting the dimensions of an antenna with a frequency F1 to some other frequency F2. The process is very straightforward in some kinds of cases, and somewhat circuitous in others. Let's examine a case of each type so that we can become aware of when simple scaling may fail us and the sorts of maneuvers we can perform to get the job done anyway.

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Simple Scaling

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The basic parameters of frequency scaling in its simplest for appear in Fig. 1.

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Scaling involves not only element length adjustments, but also element diameter adjustments of the same magnitude. The adjustments we must make are simply the inverse of the ratio of the two frequencies. If the initial frequency is 28.35 MHz and the target frequency is 14.175 MHz, then the ratio is 0.5. All element lengths, spacings, and diameters must therefore be multiplied by the inverse of the ratio--in this case by 2--to arrive at the final antenna dimensions.

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Let's examine the wire chart for a simple 2-element Yagi cut for 28.35 MHz.

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2-el Al Yagi:  28.35 MHz                Frequency = 28.35  MHz.
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+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -95.250, 52.000,  0.000        95.250, 52.000,  0.000 1.00E+00  21
+2        -105.75,  0.000,  0.000       105.750,  0.000,  0.000 1.00E+00  21
+

The element end coordinates are specified in the "X" columns; the element spacing is in the "Y" column; and the diameter is to the right.

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The modeled performance of this antenna is as follows.

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Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+28.0             6.29                11.32             31.18 - j 12.12
+28.35            6.03                11.00             36.46 - j  0.13
+28.7             5.80                10.35             41.55 + j 11.29
+

If we frequency scale this antenna to 14.175 MHz, all of the dimensions are multiplied by 2 to arrive at the following wire table.

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2-el Al Yagi: 14.175 MHz                   Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -190.50,104.000,  0.000       190.500,104.000,  0.000 2.00E+00  21
+2        -211.50,  0.000,  0.000       211.500,  0.000,  0.000 2.00E+00  21
+

Because every dimension is exactly scaled, we expect the resultant antenna to perform along its new frequency range exactly as the initial model performed within its own range. We shall not be disappointed by the modeled antenna performance figures.

+ 
Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+14.0             6.29                11.32             31.15 - j 12.12
+14.175           6.03                11.00             36.44 - j  0.14
+14.35            5.81                10.37             41.52 + j 11.29
+

I have reported values to more decimal places than would be operationally significant in order to show the degree to which scaling can be precise. Unfortunately, not every case of scaling lends itself to such easy arithmetical treatment.

+

A More Difficult Scaling Task

+

Let's next tackle a slightly more interesting scaling task. Our task will be to scale a 20-meter Yagi with complex stepped diameter elements into a 10-meter Yagi with a simpler element scheme, as in Fig. 2.

+
+ +
+

The frequency ratio will be 2:1. As we shall discover, that fact does not come close to resolving the scaling challenge.

+

Suppose we begin with a 4-element 20-meter Yagi having the following wire structure.

+ 
4-element 20M Yagi                         Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -217.50,  0.000,  0.000  W2E1 -154.00,  0.000,  0.000 5.00E-01   7
+2   W1E2 -154.00,  0.000,  0.000  W3E1 -134.00,  0.000,  0.000 6.25E-01   2
+3   W2E2 -134.00,  0.000,  0.000  W4E1 -92.000,  0.000,  0.000 7.50E-01   4
+4   W3E2 -92.000,  0.000,  0.000  W5E1 -72.000,  0.000,  0.000 8.75E-01   2
+5   W4E2 -72.000,  0.000,  0.000  W6E1 -48.000,  0.000,  0.000 1.00E+00   2
+6   W5E2 -48.000,  0.000,  0.000  W7E1  48.000,  0.000,  0.000 1.25E+00   9
+7   W6E2  48.000,  0.000,  0.000  W8E1  72.000,  0.000,  0.000 1.00E+00   2
+8   W7E2  72.000,  0.000,  0.000  W9E1  92.000,  0.000,  0.000 8.75E-01   2
+9   W8E2  92.000,  0.000,  0.000 W10E1 134.000,  0.000,  0.000 7.50E-01   4
+10  W9E2 134.000,  0.000,  0.000 W11E1 154.000,  0.000,  0.000 6.25E-01   2
+11 W10E2 154.000,  0.000,  0.000       217.500,  0.000,  0.000 5.00E-01   7
+12       -211.00, 72.000,  0.000 W13E1 -154.00, 72.000,  0.000 5.00E-01   5
+. . .
+22 W21E2 154.000, 72.000,  0.000       211.000, 72.000,  0.000 5.00E-01   5
+23       -203.55,141.000,  0.000 W24E1 -154.00,141.000,  0.000 5.00E-01   5
+. . .
+33 W32E2 154.000,141.000,  0.000       203.550,141.000,  0.000 5.00E-01   5
+34       -190.56,306.000,  0.000 W35E1 -154.00,306.000,  0.000 5.00E-01   4
+. . .
+44 W43E2 154.000,306.000,  0.000       190.560,306.000,  0.000 5.00E-01   4
+

For elements 2, 3, and 4, I have omitted the interior wires of the model, since they are identical to those in the first element. The design is adapted from a version created by N6BV. I have adjusted the dimensions so that the antenna properties are spread out across the 20-meter amateur band rather than being focused in the lower 200 kHz. Hence, the design-center frequency is 14.175 MHz for this model. As well, I have adjusted the driver length for resonance and adjusted the spacing so that the resonance impedance is close to 25 Ohms so that the design can be fed with a 1/4 wl section of 35-Ohm cable from the main 50-Ohm feedline. All in all, this is a nice little design that would fit a 26' boom.

+

Tabularly, the performance of this example follows this pattern.

+ 
Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+14.0             8.42                21.28             23.54 - j  6.99
+14.175           8.53                22.80             26.26 - j  0.73
+14.35            8.62                20.31             21.26 + j  4.89
+

More graphically, the overlaid free-space azimuth patterns for this antenna appear in Fig. 3.

+
+ +
+

Now let's scale the antenna directly, replacing every wire length, spacing, and diameter in the model with its half-size replacement for a design frequency of 28.35 MHz. The performance table is as follows.

+ 
Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+28.0             8.40                21.28             23.57 - j  6.97
+28.35            8.51                22.76             26.27 - j  0.71
+28.7             8.61                20.28             21.26 + j  4.95
+

The tabulated values tell us that Fig. 3 makes as good a representation of the azimuth patterns for the scaled antenna as for the original. Hence, we can go directly to the wire table for the directly scaled 10-meter antenna.

+ 
4-element 10M Yagi-scaled                  Frequency = 28.35  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -108.75,  0.000,  0.000  W2E1 -77.000,  0.000,  0.000 2.50E-01   7
+2   W1E2 -77.000,  0.000,  0.000  W3E1 -67.000,  0.000,  0.000 3.13E-01   2
+3   W2E2 -67.000,  0.000,  0.000  W4E1 -46.000,  0.000,  0.000 3.75E-01   4
+4   W3E2 -46.000,  0.000,  0.000  W5E1 -36.000,  0.000,  0.000 4.38E-01   2
+5   W4E2 -36.000,  0.000,  0.000  W6E1 -24.000,  0.000,  0.000 5.00E-01   2
+6   W5E2 -24.000,  0.000,  0.000  W7E1  24.000,  0.000,  0.000 6.25E-01   9
+7   W6E2  24.000,  0.000,  0.000  W8E1  36.000,  0.000,  0.000 5.00E-01   2
+8   W7E2  36.000,  0.000,  0.000  W9E1  46.000,  0.000,  0.000 4.38E-01   2
+9   W8E2  46.000,  0.000,  0.000 W10E1  67.000,  0.000,  0.000 3.75E-01   4
+10  W9E2  67.000,  0.000,  0.000 W11E1  77.000,  0.000,  0.000 3.13E-01   2
+11 W10E2  77.000,  0.000,  0.000       108.750,  0.000,  0.000 2.50E-01   7
+12       -105.50, 36.000,  0.000 W13E1 -77.000, 36.000,  0.000 2.50E-01   5
+. . .
+22 W21E2  77.000, 36.000,  0.000       105.500, 36.000,  0.000 2.50E-01   5
+23       -101.77, 70.500,  0.000 W24E1 -77.000, 70.500,  0.000 2.50E-01   5
+. . .
+33 W32E2  77.000, 70.500,  0.000       101.775, 70.500,  0.000 2.50E-01   5
+34       -95.280,153.000,  0.000 W35E1 -77.000,153.000,  0.000 2.50E-01   4
+. . .
+44 W43E2  77.000,153.000,  0.000        95.280,153.000,  0.000 2.50E-01   4
+

Once more I have omitted the interior structure of elements except for the reflector, since all 4 elements are the same in this respect. The problem posed by the scaled antenna is self-revealing from the truncated data: the stepped-diameter tubing schedule would require the use of thin-wall tubing of sizes that are not available. In short, we are unlikely to want to build the directly scaled model.

+

Suppose that we wish simply to use for each element an interior length of 0.5" diameter tubing and an outer tip of 0.375" diameter tubing. The temptation would be to use our scaled outer dimensions for each element and simply change the remainder of the wire schedule. The final result might look like this.

+ 
4-element 10M Yagi                        Frequency = 28.35  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -108.75,  0.000,  0.000  W2E1 -48.000,  0.000,  0.000 3.75E-01   6
+2   W1E2 -48.000,  0.000,  0.000  W3E1  48.000,  0.000,  0.000 5.00E-01   9
+3   W2E2  48.000,  0.000,  0.000       108.750,  0.000,  0.000 3.75E-01   6
+4        -105.50, 36.000,  0.000  W5E1 -48.000, 36.000,  0.000 3.75E-01   6
+5   W4E2 -48.000, 36.000,  0.000  W6E1  48.000, 36.000,  0.000 5.00E-01   9
+6   W5E2  48.000, 36.000,  0.000       105.500, 36.000,  0.000 3.75E-01   6
+7        -101.77, 70.500,  0.000  W8E1 -48.000, 70.500,  0.000 3.75E-01   5
+8   W7E2 -48.000, 70.500,  0.000  W9E1  48.000, 70.500,  0.000 5.00E-01   9
+9   W8E2  48.000, 70.500,  0.000       101.775, 70.500,  0.000 3.75E-01   5
+10       -95.280,153.000,  0.000 W11E1 -48.000,153.000,  0.000 3.75E-01   5
+11 W10E2 -48.000,153.000,  0.000 W12E1  48.000,153.000,  0.000 5.00E-01   9
+12 W11E2  48.000,153.000,  0.000        95.280,153.000,  0.000 3.75E-01   5
+

If we check this model, we would obtain a performance table similar to the following one.

+ 
Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+28.0             8.54                19.90             20.24 + j  6.85
+28.35            8.45                18.23             10.00 + j 20.49
+28.7             6.91                 8.32              3.56 + j 41.45
+

Graphically, the azimuth patterns would be those in Fig. 4.

+
+ +
+

Something has gone wrong with our scaling efforts. The elements are all too long. Unfortunately, many a home constructor of beams has been caught in this trap. Scaling an antenna's dimensions and then changing the stepped-diameter element schedule is a sure way to offset the performance curve of an antenna.

+

The Correction

+

The accuracy of NEC-2 (and to a lesser degree, NEC-4) depends upon the introduction of correction factors that substitute for stepped-diameter elements a uniform diameter element of the same impedance. Most NEC-2 software equipped with such correction factors use either the Leeson equations (EZNEC and NEC-Win Plus) or the Beezley equations (NEC-Wires). Let's compare the substitute uniform-element lengths and diameters of the elements for a. the impractical but exactly scaled 10-meter Yagi and b. the simplified but errant Yagi.

+ 
Element             Directly Scaled               Simplified
+               Length         Diameter       Length         Diameter
+Reflector      104.094"       0.396"         106.985"       0.434"
+Driver         100.990"       0.403"         103.765"       0.437"
+Dir. 1          97.448"       0.410"         100.078"       0.440"
+Dir. 2          91.317"       0.424"          93.663"       0.446"
+

The excess length of the Yagi with a simplified element structure is clearly apparent. However, there is no simple and sure means of shortening the uniform element lengths to the lengths used in the directly scaled version--at least not in extant implementations of NEC-2. However, there is a sure procedure to bring us very close indeed to the desired goal.

+

Every element in a Yagi has a self-resonant frequency. Using the directly scaled 10-meter beam as our guide (since we know its performance potential), let's find the self-resonant frequency for each element, using a reactance of under 1 Ohm to define resonance. Then, we shall adjust the length of the corresponding element in the simplified version of the antenna so that its self-resonant frequency is the same as in the directly scaled version. As a check on our work, we shall record the resultant substitute uniform-diameter element. The final result looks like this.

+ 
Element        Freq.     New Length          Subs. Length   Subs. Diameter
+Reflector      27.12     105.8"              104.062"       0.436"
+Driver         27.96     102.6"              100.894"       0.439"
+Dir. 1         28.94      99.1"               97.434"       0.442"
+Dir. 2         30.86      92.9"               91.317"       0.449"
+

If we compare the substitute uniform-diameter elements in our revised model, we shall see how close they are to the substitute uniform-diameter elements for the directly scaled model in both length and diameter. Given that similarity, we shall not require any spacing adjustments in our newly revised model with its simplified element structure. The final wire table looks like this.

+ 
4-element 10M Yagi-scale adj.              Frequency = 28.35  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -105.80,  0.000,  0.000  W2E1 -48.000,  0.000,  0.000 3.75E-01   6
+2   W1E2 -48.000,  0.000,  0.000  W3E1  48.000,  0.000,  0.000 5.00E-01   9
+3   W2E2  48.000,  0.000,  0.000       105.800,  0.000,  0.000 3.75E-01   6
+4        -102.60, 36.000,  0.000  W5E1 -48.000, 36.000,  0.000 3.75E-01   6
+5   W4E2 -48.000, 36.000,  0.000  W6E1  48.000, 36.000,  0.000 5.00E-01   9
+6   W5E2  48.000, 36.000,  0.000       102.600, 36.000,  0.000 3.75E-01   6
+7        -99.100, 70.500,  0.000  W8E1 -48.000, 70.500,  0.000 3.75E-01   5
+8   W7E2 -48.000, 70.500,  0.000  W9E1  48.000, 70.500,  0.000 5.00E-01   9
+9   W8E2  48.000, 70.500,  0.000        99.100, 70.500,  0.000 3.75E-01   5
+10       -92.900,153.000,  0.000 W11E1 -48.000,153.000,  0.000 3.75E-01   5
+11 W10E2 -48.000,153.000,  0.000 W12E1  48.000,153.000,  0.000 5.00E-01   9
+12 W11E2  48.000,153.000,  0.000        92.900,153.000,  0.000 3.75E-01   5
+

The proof of the method lies in performance, which NEC-2 reports in the following table.

+ 
Freq.          Free-Space          Front-to Back        Feedpoint Z
+ MHz            Gain dBi             Ratio dB          R +/- jX Ohms
+28.0             8.41                21.84             23.20 - j  7.59
+28.35            8.52                22.83             26.04 - j  1.37
+28.7             8.61                20.39             20.39 + j  3.99
+

In terms of azimuth patterns, Fig. 5 provides the same data more dramatically.

+
+ +
+

Conclusion

+

Frequency scaling begins as a simple process. However, the more complex the antenna structure, the more complex the process can become. I have used the example of changing the stepped-diameter structure of the elements for several reasons. First, in many instances, practical antenna construction demands element structures that differ from those of a directly scaled model. Second, many antenna constructors fall into the snare of simply changing element structure without first analyzing the potential consequences.

+

Third, the techniques required for restoring the poorly-scaled antenna model to a much more usable state are typical of techniques that may be required in many other situations. For the general process of modeling, it is this last reason which is the most important. The exercise is not a cure-all for all difficulties in the process of scaling antennas. However, it should alert you to what may make a scaling task go astray and what sorts of techniques may bring the model back into the fold.

+
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+

Go to Main Index

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+

27. Modeling By Equation
+ A. A Beginning

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Most beginning modelers acquire the habit of simply placing physical wire dimensions into the structure grid of NEC and MININEC input systems. The wire geometry may be systematic or random, initially, but that is a problem we looked at in an early installment in this series. In this episode, I should like to start an exploration of another way to model antennas: by the use of variables and equations.

+

In MININEC programs, AO permitted the use of variables and equations. Of presently available NEC-2 programs, perhaps NECWin Plus offers the most versatile system of modeling in this way. For example, the input file for AO does not itself show the physical values resulting from the use of variables and equations. However, the spreadsheet input screen of NECWin Plus allows the user to see, in alternative views of the structure spreadsheet, a. the numbers and equations used to set the values of variables, b. the values that result from those equations, c. the assignment of variables to the X, Y, and Z coordinates of the model structure, and d. the physical values of the X, Y, and Z coordinates that result from the preceding steps. So for this exercise, I shall make use of NECWin Plus to demonstrate a few (but by no means all) of the steps involved in modeling by variables--along with a couple of the advantages that accrue to the modeler. (In future episodes, we shall look at more complex structures and more complex ways of formulating variables.)

+
+ +
+

Fig. 1 represents our sample antenna--a simple quad loop. For simplicity, we shall begin with a free space model for 300 MHz, composed of #20 AWG (0.032" diameter) copper wire. A square quad loop consists of 4 equal sides. A simplistic approach to modeling by variables might simple let some variable A equal the physical length of a side and proceed from there.

+

Dimensions as Variables

+

However, when modeling by variables, it pays to do a preliminary inspection of the geometry of the antenna to see if one might obtain a more sophisticated and ultimately more useful selection of variables and values. Fig. 1 shows that a square quad loop can be framed against a center point so that we can take advantage of the Cartesian reference system. The example takes the 2-dimensional square and assigns the horizontal dimension to the X axis and the vertical dimension to the Z axis. Initially, Y will always equal zero.

+

In a free-space model, we can keep the structure centered by using values of A as +/-X and +/-Z values. This will come in handy later when we move the antenna over real ground. For initial purposes, A becomes about 1/8 wavelength long to form the approximately 1 wl total loop circumference. For the present, we shall not be concerned with whether the loop should be exactly 1 wl long, since that is something we shall discover from out modeling. Unless otherwise specified, the dimensional units for our exercise will be inches.

+
+ +
+

The first step is to define a variable as 1/8 wl long. Fig. 2 shows the NECWin Plus equations page, with A defined as W/8. (I shall by-pass the program specific instruction set by which we accomplish this, but it follows standard spreadsheet procedures.) Note that two other variables are already assigned permanent values: F for the initial frequency (and in this case the only frequency) of test, and W for the wavelength. Note that the wavelength entry has a reference to model parameters. The parameter of relevance here is the conversion factor for changing the modeling units (inches in this instance) into the NEC core requirement of meters. The result is the wavelength in the unit of choice.

+

The lower half of Fig. 2 shows the value of A in inches that results from establishing the equation that defines A. At the top of Fig. 2, is a button labeled Fn. When highlighted, we see the equations. When dark, we see the values that the equations yield. In this model, we have let A = W/8, whatever the value of W might be. You may also note the header information that establishes this as a free-space ("No Ground") model at 300 MHz. At 300 MHz, A has a value of 4.91797. . ." because a wavelength is 39.34383. . ." long.

+

We might have defined the value of A in terms of frequency, but that would have required that we confine the units of measure to a single system, or that we define conversion variables. Defining A in terms of the wavelength will give us some versatility later on.

+

The next question is how to set up a structure that makes use of the variable A to set antenna dimensions.

+
+ +
+

If we go from the equations page to the wires page, as we have in Fig. 3, we can set up the antenna structure using the variable A. Note the highlighted Fn button--we shall "un-highlight" it in a moment. We construct the quad in the normal manner, but we use values of "=-A" and "=A" instead of the normal numerical values we might otherwise use. Note that the structure parallels the set-up shown in Fig. 1, using the X and Z axes as the dimensional columns, leaving Y at zero. Many modelers prefer to use Y and Z, leaving X at zero, which achieves the same goal, but with the antenna aligned 90 degrees relative to the convention selected for the example. The antenna is constructed sequentially, beginning with the lower horizontal wire, then the right vertical, then the top horizontal, and finally the left vertical. Connections are sequential in order to facilitate an examination of the segment currents, should that become relevant to a task.

+

The remaining wire data to the right of the chart is constant for now. The source segment is the center segment of the lower horizontal wire. The conductivity entry of "copper" represents a specific numerical value built into a program table. You may discover that different programs (for proper reasons within the context of each program) may use very slightly different values for the conductivity of any material, mostly varying in the number of decimal places to which the value is carried.

+

Now, just how big is our antenna?

+
+ +
+

By flipping to the unhighlighted Fn version of the wires page (Fig. 4), we can view the values (in inches, our chosen unit of measure) for the variables in each position of the antenna structure. Perhaps the most difficult facet of this page to which we must grow accustomed is the number of digits in each value. We must remember that NEC programs are essentially calculating machines and do not choose the number of significant digits for us. We must do that according to the task at hand. For building this loop, we might round the figure for A into 4.92, and then translate that into 4 15/16" for measuring wire. Some other tasks involved in finding the trends in values might relevantly preserve additional decimal places. For now, we can simply accept the calculated value of A and focus on making sure that we have constructed the loop correctly by checking appropriate End 1s and End 2s of each wire.

+

We characterized this model as a trial. So let's run the model and see what we get. See Fig. 5.

+
+ +
+

Fig. 5 places all of the data we need at this point on the free-space azimuth pattern--even though the data comes from different places in the program. For this exercise, the most essential figure to note is the source impedance: 109 - j144 Ohms. Our loop is much too small to be a resonant quad loop for 300 MHz.

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Had we entered our coordinate values in terms of individual numbers, we would now be faced with revising each coordinate value by the amount we think might move the quad loop toward resonance. To suggest that this is a time consuming procedure is to make a very serious understatement. We would have to revise 16 values however many times it takes to find a value that allows the loop to be resonant with an Ohm or two. I have found that many modelers enlarge the concept of resonance to encompass many Ohms of reactance, not because the task does not require close tolerances, but because they simply tire of adjusting coordinate values on the wires page. Some programs have shortcuts that permit adjusting junctions and wire groups together, but there are still multiple steps involved--and each becomes an invitation to drop, double strike, or transpose a number along the way.

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With our model-by-variable system in place, we shall change the loop dimensions by changing only one number. For this we return to the equations page and look back at Fig. 2. Where we had entered the value for A as W/8, we shall enter a new value. To make the loop larger, we should choose a smaller value than 8 as the denominator. To keep the story brief, let's replace 8 with 7.43.

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Had we exercised a preference for multipliers rather than divisors, we might have started with a value of a of W*.125. Given that choice of equation formulation, to make the loop larger, we need a larger constant. The result would have been W*.1346 or thereabouts.

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The change we just made will make no difference to the version of the wires page that shows the assignment of variables to the coordinates of the structure. So we shall by-pass that version of the wires page and go directly to Fig. 6, the version of the wires page that shows the actual dimensions that result from the revised value for A.

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The value for A is now (at 300 MHz) about 5.3, a full 7% larger than the value with which we made our trial start. Each side of the quad is now about 10.6" long. The question is whether we have achieved resonance. So let's run the model once more.

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Fig. 7 shows the free-space azimuth pattern of the antenna, with the critical data added at the top. The loop achieves a resonant impedance of 129 Ohms, indicating that our initial task is complete. At this point, we should take a moment to appreciate the time we have saved in creeping up on the resonant dimensions of this simple loop. A little time spent with an initial analysis of the antenna geometry resulted in a much larger amount of time saved in the optimizing process.

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Wire Diameter as a Variable

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There is a limitation on the exercise we have just run. In order to focus on the aspects of dimensional modeling by the use of variables, we let the wire diameter become a constant. In virtually all programs, selecting a wire size from a chart--that is specifying the wire size in AWG values--creates a constant. For some purposes, it is better to make the wire size a variable.

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Therefore, let's return to Fig. 2 and add a new variable B to our list. We might simply list the value of B as 0.032 or so to represent the diameter of #20 AWG wire. However, let's go to the trouble of making the wire size a function of a wavelength. If we let B = W/1227.68 (or W*.008145), we shall have captured the diameter of #20 wire at 300 MHz. Wire size tables are readily available in many basic radio and electronics handbooks. Keeping a table handy at the computer is never a bad idea. We must now go back to the "variables" version of the wires page and replace all of the wire diameter entries with "=B" to put the variable into effect. The end result on the dimensions version of the wires page will look like Fig. 8.

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I shall not guarantee that the wire diameter shown is accurate for #20 AWG past the first 4 decimal places in inches, since paper tables end at that position. However, the wire size that is twice that diameter is listed at 0.0641, indicating the next digit in the #20 sequence is just below a 5. Some computer tables go much further--to 6 or more significant figures. Procedurally, one can seek out a value of the divisor (or multiplier) that yields a usable wire diameter value. Or, one can simply divide the wire size of #20 AWG by a wavelength. The actual wavelength is available on the equations page by clicking the Fn button. (For 300 MHz, the length is 39.34383202", according to the spreadsheet. If we divide .0320473 by this number, we arrive at about the same number for the divisor: 1227.68 or so. Once more, the calculating machine provides more digits than would be useful to most operational tasks. 6 significant digits is far beyond relevance to any imaginable task.)

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What we gain by making the making the wire diameter a function of a wavelength is a good bit more than the little trouble it took to create the variable and to put it into place on the wires page. Here are just two examples.

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1. Units conversion: Programs vary in the manner in which they handle the conversion of units. When changing units in some programs, it may be possible to specify whether we convert all of the numerical values or whether we keep the numerical values and only change the units they represent. In other programs, a change of units only changes the conversion factor for getting everything into meters for the NEC run. In such programs, any changes in numbers will be a task for the modeler.

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Design by variables and equations can change all of that. Since we defined all of our physical dimensions as functions of a wavelength, changing the units of measure will automatically change all of the physical values. If we remember from Fig. 2, the value for W, a wavelength, included adjustment into the currently selected units of measure by taking into account the adjustment factor for the eventual conversion into meters. Hence, the numerical value of W changes with each change we make in the units of measure. And if we change the value of W, then the values of A and B (the variables in our example) also change to the correct values for the selected unit of measure.

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As an experiment, let us change from inches to millimeters. The units of measure are listed in NECWin Plus at the right and above the geometry table. To see what happens with our change to millimeters, see Fig. 9.

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The numerical difference in all of the values on the dimensions version of the wires page are instantly evident. Since the physical lengths and diameters have not changed, running the program from this version of the page would make no difference in the output. Fig. 7 would still tell the same performance story. The NEC core input procedures would reconvert everything into meters for further processing.

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2. Frequency scaling: Complete frequency scaling requires that we multiply every dimension of an antenna by the ratio of the old frequency to the new frequency. Hence, if we go lower in frequency, we obtain larger dimensions, and vice versa. There may be a very slight adjustment to be made for differences in skin effect, but if we scale the wire diameter as well as the wire lengths, we come as close to perfection as is possible.

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If we fail to scale the wire diameter, we will find that the antenna at the new frequency may not perform as it did at the old frequency. The greater the frequency jump, the greater the difference in performance, if we simply let the wire size be a constant. For perfect scaling, we must make the wire diameter--like the wire lengths--a function of a wavelength.

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Fig. 10 shows the dimensions version of the wires page of our quad loop. The only change made was to change (at the upper left corner) the frequency. We moved from 300 MHz to 144 MHz. On the equations page, since F changed, so to did W, the length of a wave, and so on through every variable defined in terms of W. The result is the series of numerical values shown in Fig. 10.

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It is not necessary to show an azimuth pattern for this new antenna, since it is identical to that in Fig. 7. The reported source impedance is 129 - j0.4 Ohms.

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The wire diameter calls for comment. Our new diameter is 0.067", which does not coincide exactly with any AWG value. However, it is close enough to #14 AWG (0.0641") that using this size would likely turn up no measurable differences in loop dimensions--given the variables of physical construction.

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The exercise does suggest that there is a limit to physically scaling antennas. When the wire diameter reaches unreasonably thin or thick values, it is time to redesign the antenna. If we scale our 300 MHz loop of #20 wire to 28 MHz, it calls for 0.343" diameter copper wire. This diameter is an unreasonably heavy wire for a quad loop (unless one simulates it with a double strand of thinner wire, spaced to achieve the same resonance with the same loop length). Nevertheless, the model shows a resonant loop with a source impedance of 128 - j0.8 Ohms: a good model without any hope of direct implementation.

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Is There More?

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The exercise we have just run is only the beginning of modeling by the use of variables and equations. We took the process beyond the first step of merely assigning numerical values to our variables. By letting each variable be a function of a wavelength, we accumulated some advantages in addition to saving time in optimizing the antenna structure for a desired set of operating parameters. We gained the ability to switch units of measure and operating frequencies with a simple choice in each case.

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The type of modeling we have done--using wavelength as the key to our variables--can be simulated in other programs. For example, EZNEC allows direct conversion on its wires page from dimensional units to either other dimensional units or to wavelengths--with the wire diameter an additional option for this latter conversion. Much of what we have so far done can thus be accomplished in either popular NEC program.

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There are instances where simpler schemes for assigning variables may be preferable, but they would not have been as interesting. In the other direction, there are two directions in which we should look before leaving the subject of modeling by variables. One is how we might deal with more complex antenna structures, for example, those involving numerous elements. The second direction involves more complex equations by which we might specify the dimensions of an antenna element. This latter task is restricted to programs that contain a complete equations-and-variables facility. We shall also want to take a longer look at the importance of conventions in making the task of modeling by variables and equations as efficient as possible.

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28. Modeling By Equation
+ B. Bigger and Better Things

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L. B. Cebik, W4RNL

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In the last episode, we took a look at modeling antennas through the use of variables and equations. Our antenna was a simple square quad loop. The technique we chose, from the many possible ones, was to define variables for element length and wire diameter in terms of fractions of a wavelength. For initial simplicity, we kept everything in free space.

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In this installment, we shall move on to a moderately complex antenna--a 3-element quad. After we model it in free space, we shall move it over ground to see what that move might require by way of revisions to our variables and equations. Before we embark on this journey, let me throw in a few reminders about the importance of adopting conventions in your modeling.

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The Many Faces of Conventions

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Effective and efficient antenna modeling requires more than a random approach. The more systematic we become, the fewer things we have to decide in each modeling task. Not only do we save time, but as well, we are less likely to commit errors in the construction of our models.

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The rules of the modeling programs set some boundary limits to the ways in which we can proceed. Within those limits, we have a good bit of flexibility. Sometimes, we need to make use of that flexibility and model some special structure in an unusual but correct way. Most of the time, however, we are more likely to speed success in our modeling efforts if we develop some good procedures and stick with them until the special case comes along. I tend to call these procedures conventions. There are several types.

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1. Structural procedures: Creating a model, wire by wire, is best done by developing certain habits. For example, with linear elements, we can model from left to right or from right to left for each element. Either way permits us to track the currents along the element and easily read other portions of the NEC data output in ways that modeling from the center outward only confuses. However, our linear progressions should always move in the same direction from model to model.

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Loop elements, such as the one shown in Fig. 1, offer us additional opportunities to create conventions in our modeling. Since a loop is a continuous element composed of at least 4 wires, we shall normally encounter fewer confusions and errors if we model the circumference in a regular progression. The sketch shows a counterclockwise progression. Clockwise progressions are also good, but we should adopt one or the other for all of our loops.

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Fig. 1 also shows the loop symmetrically placed around a center point. For initial free-space modeling, one should let the center point be 0,0, so that each dimension of the antenna involves A or -A for each coordinate point. The advantage of this procedure becomes evident as soon as we wish to place a second loop behind or ahead of the first, but to use a different set of dimensions at the same time. The 0,0 center point ensures that each loop is aligned with the next one.

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A third facet of structural conventions involves the choice of coordinate axes for various antenna dimensions. The Z-axis handles vertical dimensions automatically. Some early programs for slower computers used the X axis as the axis of symmetry, forcing the modeler to set elements as +Y and -Y dimensions. Those rules are largely defunct, and the modeler can place side-to-side dimensions across either the X or the Y axis. The unused X- or Y-axis normally becomes the front-to-back axis, if the antenna has more than one element.

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The example in Fig. 1 uses the X-axis as the crossing point for the side-to-side dimensions of the loop. Hence, the wires that cross this axis will have +X and -X values. If we add further loops to form a beam, they will be spread along the Y axis. My preference for this arrangement is personal: it places the most changed dimension--element length--in the left column of most wire geometry sheets for easy visual identification. However, using the Y-axis for side-to-side dimensions and the X axis for front-to-back dimensions is equally apt, and tends to align the forward lobe of most azimuth patterns with the zero-degree mark on plots. The goal is to pick one system (according to your modeling goals overall) and to stick with it so long as it serves well.

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Fig. 2 shows a representative set of front-to-back conventions. In this sketch, all elements count their dimensions from the rear of the multi-element array, in this case, the reflector. It is set to zero. Each element will have a distance value that is positive, represented by the variables D and E in the sketch. The advantage of this scheme is that the total front-to-back dimension is always readily available to the modeler. The disadvantage is that distances from the second to the third element must be calculated.

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An alternative procedure is to set the driver at 0 along the selected front-to-back axis. Then, the reflector will have a negative value and the director (or directors) will have a positive value. A third scheme occasionally used is to set the array in equal distances forward and behind the zero point. However, this system can only be put in place after the final front-to-back dimension is known.

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For our work in this episode, we shall use the conventions shown in the sketches. I note this fact so that you can read the antenna structures directly from the screen captured graphics. If you model the subject antenna, give some thought to translating the model into the structural conventions you typically use. If you return to the model at a later date, you will be more likely to read the model correctly.

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2. Equation conventions: When constructing values for the variables out of which you will build the antenna model, give some preliminary thought to the ways in which you will develop the variables. Of course, the simplest system is to simply assign variables a numerical value. This system permits multiple dimensional changes with the change of a single value on the equations page. However, it is limited insofar as it does not permit full scaling of the antenna structure.

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Let's look at a different sort of example.

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Fig. 3 shows the equation set for a 3-element quad beam consisting of a reflector, driver, and director. The page actually reveals a great deal of information about how the modeling is being conducted.

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The equations all relate the antenna dimensions to a wavelength. One might choose to relate them to frequency. Although this latter scheme allows frequency scaling, it does not provide automatic numerical value changes with changes of units. Relating the numeric values to a wavelength provides both facilities.

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The equations also arrive at the final values by dividing the length of a wave by a certain number. Alternatively, one might have multiplied a wavelength by the reciprocal of the divisor, if that scheme is more efficient for a given modeler.

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There are also some conventions at work that logically group the values in the total set. A, B, and C are the variables controlling the reflector, driver, and director wire lengths, respectively. Note that each element has an independent equation related back to W, a wavelength. It is also possible to develop one variable, for instance, the driver, and then to key the reflector and director dimensions as functions of the driver.

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Since the reflector will be set to zero along the Y axis, D controls the reflector to driver spacing and E controls the reflector to director spacing. Even within the scheme used to assign values, one might have reorganized these variables. However, consistency from one model to the next reduces confusion and errors.

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The wire diameter is assigned to H, with G reserved. Since the initial model will be in free space, no height equation is necessary. However, to keep the dimensional variables well grouped ahead of the wire diameter, G is reserved for later use, while the wire diameter moves to H. Later, when we move the model over ground, G will have a value. More importantly, you will be able more easily to correlate the components of the free-space model to those of the model over ground.

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The end result is the use of A, B., and C for dimensions to be placed in the X column, D and E for dimensions to be placed in the Y column, and G for dimensions that go in the Z column. (Since the quad had a vertical dimension to begin with, using A in the Z column is, of course, inevitable.) Wire diameter comes last.

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No magic attaches to this particular system. It serves to illustrate one of many possible orderly schemes that permit easy reading by both the modeler and others. Nonetheless, in the process of suggesting that each modeler develop conventions that best facilitate modeling, I have also managed to explain the ones used in this exercise.

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Onward to the 3-Element Quad

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Fig. 1 and Fig. 2 together show the outline of a typical 3-element parasitic quad beam consisting of reflector, driver, and director elements. Fig. 3 listed the design equations for the antenna. How these dimensions translate into values appears in Fig. 4, the equations page set to show numerical values. As we did with the simple quad loop, we have used 300 MHz and free space as the background for the antenna. You may recognize the wire diameter as equivalent to #20 AWG. Also notable is the fact that adding to the number of elements in an array tends to multiply the number of variables required to fully describe the antenna.

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Two items are notable about the page shown in Fig. 4. First, the variable G has been left blank, with the wire diameter registered as variable H. As we noted, G will be used later to set a height value for checking the model over ground. Second, the variable E shows the total length of the antenna array from back-to-front. There would be no harm in defining further variables to provide instant calculation of the spacing from the driver to the director. By defining I (for example) as E - D, we would obtain that value, even though we do not plan to use the variable I in the set-up of the antenna geometry. In addition, should we desire the information, we might set other variables as ratios of the reflector to the driver length or the director to the driver length. Not every equation we define has to be used in the antenna geometry itself.

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Fig. 5 shows the actual geometry of the 3-element quad, described in terms of the variables we have just defined. The Y columns have been assigned the back-to-front dimension. Recording the variables for these distances has the additional benefit of allowing us easily to identify which element is which.

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The X and Z columns record the variables associated with each of the elements in terms of the half-lengths of each side of the quad. Note that each element follows identically the same pattern of development around the perimeter of the loop. Consistency of geometric layout is an aid to error detection as well as to later interpreting NEC output data.

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The final step in preparing to run our model consists of looking at the actual dimensions on the wires page (Fig. 6). In that process, we also note that the antenna is of copper wire and that the source segment is placed on the lower horizontal wire of the second (driver) element. Although this exercise has by-passed the placement of the source, that process is, of course, crucial to developing a successful model. It now time to run the model.

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The data we gather from the NEC core output is gathered together in Fig. 7. The free-space gain of this quad is about 9.5 dBi, a very respectable value for a monoband 3-element quad design. The gain is about 1.4 dB better than a 3-element Yagi having the same boom length and configured for a similar front-to-back value in excess of 20 dB. Given the smaller diameter of the wires in the quad relative to what would be typical for a Yagi at the same frequency, the modeled quad achieves as much as possible of the theoretical gain of quads over Yagis.

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The front-to-back figure should be referenced to the azimuth pattern. Although the pattern does not show trace lines that would identify the bearing for the front-to-back ratio, the value shown is clearly related to the strongest rearward lobes. In fact, the program used (NECWin Plus) routinely provides the worst-case front-to-back ratio. The more common 180-degree front-to-back ratio can be extrapolated from the pattern itself and approaches 25 dB. More exacting figures can be derived by comparing the forward gain (heading 270 in the example) with the rearward gain (heading 90 in the example).

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Above Ground

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To place the antenna above a desired ground requires two steps. The first is to define a ground. Fig. 8 shows the selection of the Sommerfeld-Norton ground, using the values for average ground (conductivity = 0.005 S/m; dielectric constant or relative permittivity = 13.0). Since the antenna is configured for horizontal polarization, the actual ground values chosen will not have a very significant effect upon antenna performance at heights greater than 1 wl above ground.

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Fig. 8 also shows how we plan to establish the antenna at a certain height above the ground we have just defined. The variable we earlier reserved is now assigned the value of 2*W, indicating a height of 2 wl. However, this entry does not say how we shall implement the height. Let us assume that the 2 wl height represents the height of the center of the quad structure. This is a common practice--and a good reason for centering each of the elements of the quad array on the same axis line.

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On the equations page, we could have used variable G to define several further variables. We might let I = G-A to cover the lower reflector element and J = G+A to handle the upper reflector element. We would need 4 more variables to cover all of the quad elements. However, there is a simpler method, shown in Fig. 9, the wires page using the variable entries version.

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When entering the antenna geometry as a set of variables, we are not limited to single letter assignments. We can enter more complex equations involving those variables. The equations can involve complex functions, but in the present case, we only need simple addition and subtraction involving the variable for the antenna height and the loop dimension variable. Lower wires will be below the value of G and upper wires will be above the value of G. Note that values in the X and Y columns are unaffected: everything we need to modify in order to place the antenna above ground occurs in the Z axis column.

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Fig. 10 shows the results of our new variable and our revised symbolic structure in the dimensions version of the wires page. The center of the antenna is about 6.5' above ground, with the upper and lower horizontal wires less than 6" distant from the center position. Of course, at this point (or any other point in the model development process), we could have selected other dimensional units. Many readers outside the U.S. will prefer millimeters for the dimensional unit for an antenna at 300 MHz.

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The final element to note before running the antenna model is the revision made to the azimuth pattern request. Only free-space NEC models should request an elevation angle of zero degrees. In this case, the elevation angle will be 7 degrees, the angle of maximum radiation or take-off angle.

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Fig. 7 captures the shape of the azimuth pattern of the antenna placed 2 wl above average ground. Only the detailed information requires revision. The array shows a gain of 15.1 dBi, with a worst-case front-to-back ratio of 20.7 dB. The feedpoint impedance is 29 - j0.0 Ohms.

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Since the model uses #20 wire at 300 MHz, it can be reasonably scaled to other VHF and UHF frequencies commonly used in amateur radio. Scaling to 2 meters will permit the use of #14 wire. However, scaling down to 6 meters will require something close to #4 wire to preserve the exact balance of factors in the design. Changing to a more common wire size--#12 or #14 AWG--will require adjustment of at least the variable for the driver wire length. You may also wish to experiment with the values for the reflector and director to see if changes in their dimensions result in better or worse overall antenna performance. From that point, you may wish to do some further scaling and adjusting to optimize the array for HF performance (on any band from 20 through 10 meters). In the process, you will certainly note the greater ease that variables and equations lend to the process of manually optimizing an antenna relative to having to change each dimension entry individually. If you like the results of your scaling and adjusting work, be sure to save the results under different file names for each version you wish to preserve.

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Same Song, Different Key

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Rather than detail the potential for scaling the quad (which is only an example in this context, but a pretty good example), let's take the same antenna and look at it in another way. Fig. 11 provides the first step.

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In this view of the antenna, we shall treat the driver as the central element and place it at the zero point on the Y axis. The reflector will use a negative value to record its position behind the driver, while the director will be placed ahead of the driver with a positive value.

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At the same time, we shall let the driver be the central element in another sense. We shall define the length dimensions for the reflector and the director in terms of the driver length. To keep our focus upon these elements of designing by variables and equations, let's place the antenna back into free space.

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Fig. 12 shows the results of our work, at least with respect to defining the basic variables we shall use. Note that the values for A and C are defined in terms of B. The order of definition does not make a difference: the spreadsheet form will find B and use it to determine the numerical value of A (as well as C). In this exercise, I have also changed from the use of denominators to the use of multipliers to set the values.

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In addition, the spacing is now defined in the terms set forth in Fig. 11. If we wish to know the total array length, we can always define an extra variable as the sum of D and E.

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The changes we have made to the equations page will require some revisions to the variable entries version of the wires page. See Fig. 13. Actually, only the variables assigned to the Y columns require change from the earlier example. The reflector is at -D, while the director is at +E. Using negative values for variables on this page allows us to simplify the equations page by letting most, if not all, of our basic equations be expressed in positive values.

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Flipping to the dimension entry version of the wires page shows that the resulting antenna is virtually identical to the earlier version. Compare Fig. 14 to Fig. 6. The numerical values for the two models are the same through 3 decimal places--which is at least one more than any practical application would call for when the dimensions are in inches. Consequently, we can expect the performance reports from the NEC core to be virtually identical for the two models.

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We have not explored all of the permutations and combinations of ways in which we can construct models using variables and equations. The procedure with which you become most comfortable may not coincide with either of the variants we have explored. However, developing a consistent procedure--except where a specific task may dictate otherwise--will go a long way toward naturalizing the process of modeling in this way. The larger the model, the more crucial it is to adhere to conventions that yield the quickest error detection, the clearest readout of your work, and the greatest ease in modifying the model en route to the perfect antenna.

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Once you have developed a sense of the conventions of modeling that work best for you, the door is open to the use of more complex equations. The ones we have explored have been of the simplest kind. Let's take one more look at the process of modeling with variables and equations next time--with an eye toward what we can do with slightly more complex equations.

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29. Modeling By Equation
+ C. Formulas and Blocks

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L. B. Cebik, W4RNL

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We have been looking at some of the elements of modeling via the use of variables and equations in slow motion for the benefit of newer modelers who have never modeled in this manner before. Our progress into new territory will be equally patient, since there are better and worse ways of getting to various ends--and we want always to choose the better way. Since we are working with the variable and equation provisions of a specific program--in this case, NECWin Plus--it is inevitable that certain aspects of the work will be program-specific. The more detail we understand about the processes, the easier it will be to adapt the procedures to other programs having the same capability.

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This is the third episode of this sequence (but perhaps not the last word that will ever be said in this series about modeling by equation). We shall look at the rudiments of other mathematical techniques used to define variables--leaning especially on a little trigonometry as applied to spreadsheet formulations. In addition, we shall also explore ways to cut long repetitive model-creation tasks down to simple work. Finally, we shall look at when and how to freeze a design that we initially create for frequency-scaling purposes.

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A Little Trig

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Many antenna designs are amenable to trig-treatment. Theoretically, most antenna designs can be handled with trig, since we can transform almost any geometry into a collection of angles and triangles. For example, a linear element can be viewed as two lines with a 180-degree angle. This way of thinking, of course, gets into the extremes of the unnecessary, although there are always a few folks who live by the motto, "Stop! Look! There must be a harder way!"

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More realistically, loop antennas--especially triangles or "deltas"--are most apt for trig-treatment. So let's pick one and see what we might do with it.

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Fig. 1 shows a typical equilateral delta, much used on the lower HF bands. The antenna consists of 3 sides of equal length (z). Since the angles of every triangle add up to 180 degrees, each corner angle is 60 degrees. Now we can appeal to basic trig functions to determine the values of +/-y and x so that we can model the antenna within 2 of the 3 Cartesian dimensions that form the basis of model construction in NEC. Note that we have cut the equilateral triangle in half along a vertical line to get two equal right triangles. This conversion makes the calculation of dimensions much easier.

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The two most important trig functions to absorb are sine and cosine (abbreviated "sin" and "cos"). The sine of an angle in a right triangle (or sin X in the sketch) is simply the length of the side opposite to the angle (x) divided by the hypotenuse (z). The cosine of that same angle, or cos X, is the side adjacent to the angle (y as equaling half the length of the base) divided by the hypotenuse. Now, if we know the angle and the hypotenuse, we can derive the length and hence the coordinates of the remaining sides. Of course, we also need to know some values for sines and cosines.

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Many modelers keep a few handy trig values in their head for rough calculations. The sine of 30 degrees is 0.5, which is also the cosine of 60 degrees. The sine of 60 degrees is about 0.866, which is also the cosine of 30 degrees. With an angle of 45 degrees, the sine and the cosine are equal: 0.707. These familiar numbers are handy and deserve commission to memory. However, if we model using variables and equations, we only need the numbers to check up on our work--an error detection system.

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Since a delta loop has a circumference of about 1 wl, we know that each side is about 1/3 wl long. We also know that the equations for half the base and the overall height shown in Fig. 1 are simple transformations of the basic trig relationships. Now, we can let the spreadsheet equations system of the program help us create a perfectly general delta loop.

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Fig. 2 shows the equations page for an equilateral delta loop. And nothing seems to correlate with what we have just said. The length of the hypotenuse (A) is not shown as W/3, but as W/2.84. The loop is larger than a wl in circumference, as it was with the quad loops we looked at earlier. Actually, the denominator of the equation for A was derived by resonating the final model--which used #12 AWG copper wire in free space--to a source impedance of 117 - j0.4 Ohms at 7 MHz. (We can by-pass absolute generality of design with the wire size specified in terms of a wavelength for this exercise. However, that option is always open to the modeler.)

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The second deviance from our initial discussion are the equations for B and C, the height and half-base length equations. This deviance results from the fact that spreadsheet math is a derivative of Basic, a programming language that does all its angles in radians rather than degrees. To use radians effectively requires that we remember just one fact: a circle has 2*PI radians or 360 degrees. Hence, to convert an angle from degrees to radians, we simply divide 2*PI by the result of 360/angle, where "angle" is the angle with which we are concerned. Since our equilateral triangle uses an angle of 60 degrees, 360/60 = 6. PI is about 3.1416, so 2*PI is about 6.2832. Hence, our angle in radians is 6.2832/6. We shall let the spreadsheet finish the calculation, but we know the angle is a little over 1 radian.

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Remember: if you forget to make the conversion into radians, your results will not make any sense at all. As well, you may do some of the conversion calculations on the scratch pad facility available on the equations page of NECWin Plus.

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We can construct our equilateral delta by using the variables we have just defined, as shown in Fig. 3. The baseline of the delta lies along the X axis (at Z = 0) from -C to +C, with the source centered. The two angled wires go to or from these end points to a common height, B. This is the easiest part of the process.

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Flipping from the variables version of the wires page to the dimensions version in Fig. 4, we find the final results of our modeling. Note that this will not necessarily be the first set of values you see if you begin the process by setting A = W/3 and then refine the denominator by checking for resonance. However, at 7 MHz and using #12 AWG copper wire in free space, this is where you will end up.

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Sometimes, trig can simplify our equations more than we might initially expect. Consider the right-angle delta, an alternative version of the delta we just explored. We shall retain the same wire size and material, and we shall keep the antenna in free space. Our interest will be in the angles, shown in Fig. 5.

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First, let's think about the perimeter of the right-angle delta. If we start with a wavelength, it is divided into three legs, but only 2 of them are equal: z. However, we know that a right triangle has two 45-degree angles and a 90-degree angle. The length y is the cosine of angle X times Z. Since the sin of 45 degrees is 0.707, y is .707*z, and the total length of the base is 1.414*z. (We can also use the old right-angle theorem from plane geometry: The square root of the sum of the squares of the two sides of the entire right triangle is the length of the entire base, which is the hypotenuse. The base is still 1.414*z.) So in terms of z, the total perimeter is 3.414*z. In terms of a wavelength, the length of z will be W/3.414 as a starting value.

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One of the conveniences of a right triangle is that the sine and the cosine of 45 degrees are both 0.707. Hence, we can define our right-angle delta with only two equations, one to define z in terms of a wavelength and one to define both the lengths x and y. Let's now turn to the equations page of our spreadsheet.

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In Fig. 6, we find the final equations for the right-angle delta. Values for the X and Z axes appear in the equation for variable B. This follows the same pattern we used earlier in converting from degrees to radians. We recognize the value of 2*PI. The denominator of 8 derives from dividing 360 degrees by 45 degrees.

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The final value for A comes from adjusting our initial denominator of 3.414 until the antenna achieved resonance with a source impedance of 196 + j0.6 Ohms. Once more, for a loop, the final size to give 1-wl resonance will be physically longer than 1 wl.

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The simplification of our set-up also shows up in the variables version of the wires page, Fig. 7.

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For a right triangle, we only need to set the baseline ends at -B and +B, and the height will be +B. For both deltas, we set the baseline at zero on the Z-axis. Should we wish to center the model vertically, using +/-Z values that are the same, we shall have to wait until we know the final physical dimensions, or we shall have to create a further equation for this purpose to the short list on the equations page. For example, we might have defined C as 1/2 the value of B and then specified Z coordinate of the baseline as -C and the peak as +C. Once we start down the road of modeling by equation, we can get as sophisticated as we desire. The key questions are these: Do we need the added fanciness? Will the resulting model be easy to read in the future? For this example, a baseline of zero on the Z axis will do just fine. If we develop a special need later on, we can adjust the equations. For example, a particular project might set a maximum height. In that case, we can revise the equations to work downward from that height.

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The final dimensions for the resonant right-angle delta appear in Fig. 8. As always, round off the excess precision to the level appropriate to the task at hand.

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Something Bigger: A Helical Dipole

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We have lingered over the basics of using trig functions in a spreadsheet model-by-equations system to prepare ourselves for larger tasks. The larger task I have chosen as an exercise is the creation of a helical dipole for 10 meters. What I wish to achieve is a helical dipole that is under 10' from end to end for a frequency of 28.5 MHz, using #12 wire. Since I might run into difficulties with the limits of NEC if I wind the helix too tightly, I shall specify a radius of 4".

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NEC must create a helix from straight wires. In fact, NEC has an input card that will automate the creation of a helix, but that card is normally not available on entry-level commercial versions of the program. No matter: manually creating a helix will give us some understanding of what goes on when we implement that card in an advanced NEC program.

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Fig. 9 shows us an outline of the helical dipole. Almost any representation of a helix made from straight wires will give some visual distortion of what is actually happening to the wire, and Fig. 9 is no exception. However, we can see the straight wire sections of each turn of the helix. Each one forms part of the circumference and also proceeds part way down the line from one end to the other. Since each wire is the same length, the increment of movement along the total length will also be the same for each successive wire.

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For the example, the total number of wires turned out to be an even number. Hence, I specified a split feed, using the last segment of one wire (28) and the first segment of the next wire (29). We shall look at the consequences of placing the source in this manner later on. First, we need to figure out how to make up the turns of the helix.

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Fig. 10 shows the cross section of one complete turn of the helix. Since the length of the entire assembly will lie along the X-axis, the turns will be defined for the Y- and Z- axes. The circle shows the true helical shape. For this exercise, I have chosen to use a hexagon as the substitute. An octagon would have been more true to the circle, but the hexagon is more interesting for our purposes. Obviously, when translating the final model into a physical antenna, we would likely discover that a true circular radius a bit under 6" will best capture the model.

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A hexagon can be subdivided into a collection of equilateral triangles. If we let the radius lie along the Y axis, the first set of X, Y, Z coordinates will be 0, 4, 0, indicating no progress along the length of the antenna, and a peak of +4" on the Y axis.

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The angle between successive point of the hexagon is 60 degrees. Therefore, we can use the same subdivisions of each triangle that we used with the equilateral delta. The value of Y for the second point will be half the base, or 2". The height of the triangle will be the sine of 60 degrees (0.866) times the radius, which becomes the hypotenuse of the triangle. The result is 3.46 for the Z-axis. The value of X increases by 2", which is half the radius.

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Continuing counterclockwise, the values for X increase regularly. However, the values for Y and Z are simple repetitions of the values already derived, with some sign changes depending on which side of the axis the value falls. Consequently, we can define our helical dipole with very few equations.

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Fig. 11 shows the equations page for the final helical dipole. The values used in the equations are fussy beyond belief--simply because I wished the subsequent wires page to have simple numbers. The radius is defined in terms of a wavelength at 28.5 MHz. The extended decimal value is simply what was necessary to get a radius of 4.0000000". Likewise, the value of 2*PI is carried out to many significant figures so that the equation shown on the working line (B5) would yield exactly 2.000000". You may truncate these values to practical sizes--if you are willing to live with longer decimals on the wires page.

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The equations page also involves a small fudge, intentionally placed there to illustrate a point. The denominator for variables B and C is 12. The number is the result of dividing 360 by 30. However, since the sine of 30 degrees = the cosine of 60 degrees, and vice versa, we simply assign the cosine of 30 to the Z axis and the sine of 30 to the Y axis to arrive at correct values. Familiarizing yourself with a little trig is very handy in antenna design. However, not in every case can you get away with doing something backwards.

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The variables we have just defined complete one turn of the helix. The next question is how we create the total structure of the entire dipole.

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Fig. 12 partially reveals a wires page, showing the variables through wire 29 of the 56 total wires in the model. There are just enough lines to show the source assignments. The wires table has some features we have not shown to this point.

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Let's begin with the easy part. Note that the Y and Z columns repeat themselves periodically, in fact, every 6 lines. To create the first 6 lines in each column, we manually enter the variables. Then we copy that block of 6 lines in the column and paste them to the next six lines. We can continue to paste until we reach line 54, the last line divisible by 6. The final step is to copy only the first two lines and past them to lines 55 and 56.

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Of equal ease is the specification of the wire diameter and material conductivity, since each can be selected in a single block operation encompassing all 56 lines of the model.

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We have covered every part of the model except the progression of the helix along the X axis. Here we use another spreadsheet facility. We enter the values of X on line 1. Then we set an equation on line 2 for the X-entries that, in each case, references the first line box and the increment defined by variable D. The values for X1 occur in column B, so the first formula become =B1+D. Likewise, for X2, in the E column, we get =E1+D. The spread sheet knows to read "D" as a variable from the equations page and to read "B1" and "E1" as the values within the boxes with those names.

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So much for the hard work. Spreadsheets have a special function that works this way. Let's place the heavily outlined box on line 2 and the column with the X1 values, which is B. We can now type CTL-C for "copy." The value goes to what Windows calls the "clipboard." Now, with the mouse, block the entire column from B3 (the next line) down to B56, the end of the model. Next, type CTL-V, which pastes the value on the clipboard to the boxes in the block. However, remember that this is a spreadsheet, and the special function is at work. Each new box value created will have the same form as the original formula: it will use the preceding B line and add D to it for the box at hand. Hence, the progression of values increases regularly from line 1 to line 56. We do the same for the X2 column, which is column E on the spreadsheet.

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Had we wished to keep the precise value within box B2, we would have had to signal that with a special sign. On this spreadsheet, surrounding B1 with $s (dollar signs) fore and aft would have done the job. Other spreadsheets may use other symbols.

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In the end, the laborious task of manually entering even the simple variables for the model is reduced to about a 5 minute job. As well, we have reduced the potential for entry errors of all sorts. If an error appears, we know to look back to the equations page or to the equations we entered on the variables version of the wires page. Hence, error correction also becomes a short-order task.

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Fig. 13 replicates the portion of the wires page shown in Fig. 12, but with the dimensions rather than the variables. My fussiness with the equations makes this page easy to read as an example. The increment of progression along the X-axis is clear, and we can extrapolate that the total number of wires is 56, with a total antenna length of 112". This value is under the 10' limit set out as a requirement for the antenna. As well, the regular cycles of the turns in the helix are also clear, as they repeat themselves every 6 wires.

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If we run the model at 28.5 MHz, we will obtain two values of impedance, each of which is about 12.68 + j2.69 Ohms. The impedance of the antenna for a single feed is simply the sum of the resistances and reactances: 25.5 + j5.4 Ohms, which is close to resonance. Although incidental to this exercise, the free-space gain of the helical dipole is 1.74 dBi, about 0.4 dB below a full length linear dipole for the same frequency. Helical dipoles are certainly usable, but even as open a helix as this one shows losses in dipole use. Had we tightened the increment or shrunk the diameter, we would have seen even lower gain.

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Nonetheless, the helical dipole has allowed us to create an extensive structure using the equations and variables provisions of a spreadsheet entries page for our model geometry. Other types of equations are certainly possible for other geometries, but the trig relationships we used allowed us to draw out some of the features of spreadsheet use. As well, the long repetitive structure of the helix gave us the occasion to use some of the time-saving features that spreadsheets offer.

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However, before we close the book on modeling by equations and variables, we have one more question to pose. When is maximum generality too much generality?

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Confining Our Models

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Suppose we wished to do a frequency sweep for the range from 28 to 29 MHz of the helical dipole we just designed for 28.5 MHz. Models designed by equations and variables are linked to the "Start" frequency (in the upper left corner of any of the screen captures shown) in NECWin Plus. Remember that we defined the variable A in terms of a wavelength and then defined the other variables in terms of the value of A. If we change the start frequency from the design frequency of 28.5 MHz down to 28 MHz, the dimensions of the antenna will change.

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To preserve the dimensions of the design we just created, we must "freeze" it. This task involves only one change in the equations page, and the change appears in Fig. 14.

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Note that we have changed the value of A from a wavelength-dependent value to a constant. The value of 4 (inches) derives from the dimensions on the wires page that proved successful when we ran the model. Now, all of the other variables depend on the set value of A and are independent of the frequency. At this point, we can set the frequency sweep with a start frequency of 28 MHz, an end frequency of 29 MHz, and any desired interval for the sweep check frequencies.

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Incidental to this exercise, but relevant to the modeling task at hand, is the fact that the Zo against which SWR will be calculated has been set to the design frequency source resistance for each of the sources. The resulting SWR curve will track a composite curve set to the value we might have used had we specified only a single source for the antenna. The helix, relative to the source resistance at or near resonance, shows a 2:1 SWR curve that is about 700 kHz wide, slightly reduced from the curve we might obtain from a full-length linear dipole of #12 AWG copper wire.

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If our interest in this particular design goes beyond the modeling session, we should save the revised model under a new file name.

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The upshot of this final move is to note that there are limitations to designing models by equations and variables for maximum generality. For every task, there is an appropriate level of generality somewhere between the maximum and, at the other extreme, specifying each dimension as simply a number on the wires page. It is not possible to specify in advance of knowing the task parameters what the proper level of generality should be. However, with some practice in both "normal" modeling with numbers and modeling with equations and variables, the modeler gains a sense of the level of generality that works best in each circumstance.

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In these three episodes, we have certainly only begun the process of modeling by equations and variables. Next month, we shall close the series by looking at a pair of examples that show a. there is always more than one way to formulate a model via equations, and b. the scratch pad facility can come in handy at times.

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Go to Main Index

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3. Within the Lines: NEC-2

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L. B. Cebik, W4RNL

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+ Last month, we looked at some of the limitations of MININEC and how to model effectively within those limits. This month, we shall give NEC-2 equal time. Virtually all of the limits we shall look at occur on all commercial implementations of NEC-2. +

The chief sources of commercial implementations of NEC-2 are the following:

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NEC-Win programs are for Windows 95, while NEC-Wires and EZNEC are DOS-based programs.

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The basic reference for NEC-2 is J. Burke, A. J. Pogio, "Numerical Electromagnetic Code (NEC) Method of Moments, a User Oriented Code," Vol. 2 (Part III: User's Guide), Tech. Doc. 116, Naval Systems Center, San Diego, 1982. For those desiring to create their own input and output systems, NEC-2 is public domain and available in FORTRAN and compiled versions. Ray Anderson, WB6TPU, maintains a site for downloading basic NEC-2 materials: URL: http://www.si-list.org/swindex.html (broken link not found in web.archive.org)

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Segmentation Limitations

Although the segmentation limitations of NEC-2 are similar to those of MININEC, they differ just enough so that the transition from one program to the other sometimes creates unanticipated difficulties. First, NEC places the equivalent of a MININEC pulse in the center (or distributed throughout) a wire segment. Hence, in NEC, you should think in terms of segmenting antenna lengths, especially those holding sources and loads, in odd numbers. Although many references speak of segmenting a center-fed half wavelength dipole into at least 10 segments, 9 or 11 are the proper numbers, as shown in Figure 1. +
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Segment length should be under 0.1 wavelength long, with 0.05 wavelength preferred (about 10-11 segments per half wavelength). Segments shorter than 0.001 wavelength should also be avoided. For reference, the following table provides a ham band list of the maximum and minimum recommended segments lengths.

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Frequency      Segment Length in inches    Shortest Segment
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+1.8                 327.9                    6.657
+3.5                 168.6                    3.372
+7.0                  84.3                    1.686
+10.1                 58.4                    1.169
+14.0                 42.2                    0.843
+18.068               32.7                    0.653
+21.0                 28.1                    0.562
+24.89                23.7                    0.474
+28.0                 21.1                    0.422
+50.0                 11.8                    0.236
+144.0                 4.1                    0.082
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Thin-wire segments are preferred: as with MININEC, the wire circumference divided by the wavelength should be much less than 1 for accurate results. Moreover, the ratio of segment length to diameter should be greater than 4 for errors less than 1%. If the model demands a smaller ratio, it should be approached cautiously by shortening segment lengths gradually with an eye toward results taking off on a tangent.

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Maintaining a larger segment length to diameter ratio at corners is also necessary to keep the center of one segment from falling within the radius of the other segment. Again, approaching this limit produces nothing sudden, so that it can be pressed, but cautiously.

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Unlike MININEC, angled antenna elements do not require special treatment other than the warning about very short segment-length-to-wire-diameter ratios. NEC-2 will model equally segmented wires in a quad quite handily.

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However, prevent wires from physically touching or coming in very close proximity when crossing. There is no hard and fast rule on where the proximity limits occurs, but separation by several wire diameters is recommended.

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Another NEC-2 limitation is the inability to model small loops, less the about 0.1 wavelength in circumference.

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NEC-2 documentation specifically recommends that closely space parallel wires be arranged so that the segments are carefully matched, as shown in Figure 2. As noted in the last episode, this practice is a good one to follow with all models.

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Junction Limitations

There are two junction limitations of note. The first limits the number of wires joined at a signal junction to 30. This limitation is especially applicable to models involving base-fed vertical antennas with radial systems modeled above ground. Extending the ground radial system to larger numbers with a direct connection to the vertical segment holding the source should be approached with caution by examining the sensibleness of the outputs as the limit is approached. A further note on elevated ground radial systems appears later in the discussion of grounds. +

The second junction limitation concerns feeding multiple antennas at a common source point. This problems differs from feeding a single bent element (such as inverted Vee) at the apex. In this case, the modeler can often use a split feed, feeding with separate sources the segments on each side of the wire junction. If the segments are short, the resulting sum of the two impedances will yield an accurate overall source impedance for the antenna. Some programs provide for a split voltage or current feed and report the source conditions (voltage, current, and impedance) as a single set of values.

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When multiple antenna elements join at a single point, it is no longer possible to employ a split feed effectively. The simplest case is the spread dipole for two bands with a single feedpoint, as shown in Figure 3.

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The simple work-around is also shown in Figure 3: adding a small common section of wire for the source and joining the diverging elements to the ends of this wire. Recommendations for these segments include a minimum length of 0.02 wavelength and 3 segments. Equally important, the adjoining segments of the diverging wires should be about the same length as those in the center section.

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Diameter Limitations

The key "diameter" limitation is much better known by most NEC-2 users: the stepped wire-diameter limitation. NEC-2 produces inaccurate results when an antenna element is composed of wires of differing diameters, as is commonly the case with HF Yagis using several sizes of aluminum tubing. The basic situation is shown in Figure 4. +
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If an element is constructed on each side of center by, say, only 2 wires of different diameters and the junction of these wires is past the mid-point on each side, modeled results will be more accurate than with elements having multiple diameter steps closer to the center. Large steps in diameter also increase the accuracy problem.

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Most commercial implementations of NEC-2 have incorporated a technique to overcome this problem effectively. Using equations developed by Dr. David Leeson, the programs calculate the antenna properties with substitute elements having a constant diameter. The resulting models have proven quite reliable. However, you must use caution in constructing the model to ensure that the stepped diameter element is continuous or collinear, with no bends or intervening geometric oddities along the way. For example, adding a mid-element capacity hat structure will disable the correction feature in some programs. Likewise, the source must be at the center of an element with open ends (such as a dipole), and loads must be symmetrically placed. Transmission lines are sometimes disallowed. Moreover, the element may be required to be within a certain percentage of resonance, which may complicate attempts to model in NEC-2 multi-band HF Yagis with stepped-diameter elements throughout.

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Let's take a closer look at the effects of using and not using the substitute elements in place of the stepped diameter elements. The following table shows several aluminum dipole elements for 14 MHz, ranging from a uniform 1" wire to a highly stepped set of wires. Lengths and diameters are from the end to center, with the other side symmetrical to the given side. Except for the uniform element, NEC-2 outputs are shown for both the substitute and the uncorrected elements.

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+Length(s) from center in inches     Free Space Gain    Source Impedance
+  Diameter(s) in inches                 in dBi         (R +/- jX Ohms)
+1.  Uniform element (no corrective needed)
+     -201.25...0                         2.12            71.8 - j 0.6
+            1.0
+2.  One step, far out
+     -204...-150...0       No Cor.       2.14            73.0 + j 4.4
+        0.75    1.0
+     -201.45...0           Cor.          2.12            72.0 + j 0.4
+          0.966
+3.  One step, near center
+     -204...-50...0        No Cor.       2.22            72.4 + j 5.2
+        0.75   1.0
+     -201.661...0          Cor.          2.13            71.8 - j 0.5
+           0.792
+4.  Two steps, modest taper
+-205.75...-100...-20...0   No Cor.       2.32            72.5 + j10.6
+      0.75    1.0  1.25
+-201.49...0                Cor.          2.13            71.9 + j 0.1
+     0.889
+5.  Two steps, more extreme taper
+-208.5...-100...-20...0    No Cor.       2.82            67.6 + j17.1
+     0.75    1.0   2.5
+-201.63...0                Cor.          2.13            72.1 + j 0.9
+     0.895
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The corrected substitute models ("Cor.") are those generated by the program as replacement elements for the original model, which reflects the intended tapered diameter structure. With only moderate levels of diameter stepping, uncorrected NEC-2 reports of gain rapidly become unreliably large, while source impedances improperly show the elements to be too long relative to resonance.

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Corner Dissimilar Wire-Diameter Limitations

Although linear stepped-diameter elements are correctable, non-linear elements with changes of diameter are not. In many instances, NEC-2 will produce unusable results. Two such cases are the quad loop and the folded dipole, each with wires of unequal diameter. +
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Consider the single quad loops in Figure 5. If we construct such a loop for 28.5 MHz of #14 wire, then about 9.13' of wire per side (1041/f) will yield a loop with a free space gain of about 3.24 dBi and a source impedance of 126-127 Ohms resistive. This is true whether we model the antenna as a fully length-tapered MININEC item or as a NEC-2 wire antenna with reasonable segmentation. If we make the element 1" in diameter, then 9.5' per side (1083/f) in both programs yields a gain of about 3.4 dBi with a resonant source impedance close to 132 Ohms.

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However, if we change the construction so that the horizontal portions are "fat" while keeping the vertical portions of "thin" wire, the results are far different. The following table shows how.

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Antenna Dimensions                 Free Space Gain     Source Impedance
+                                        dBi            (R+/-jX Ohms)
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+1.  0.5" dia hor/#12 vert:  10.15' per side
+     MININEC tapered                    3.61           136.7 - j 2.3
+     NEC-2                              3.57           175.4 + j140
+2.  1.0" dia hor/#14 vert:  10.7' per side
+     MININEC tapered                    3.80           141.6 - j 5.7
+3.  1.0" dia hor/#14 vert:  9.68' per side
+     NEC-2                              3.46           138.4 - j 0.5
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The first antenna uses the same model in both programs. Compared to the materials of antennas 2 and 3, this model has a less extreme difference in wire diameters between the horizontal and vertical portions. Although the gain figures produced are close, the source impedance are radically different, as NEC-2 suggests a far smaller loop size for resonance.

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Antennas 2. and 3. use a larger difference between the horizontal and vertical wire diameters. The two models use the same horizontal to vertical wire diameter ratios, and each is each brought close to resonance. Although the source impedances are now comparable between MININEC and NEC- 2, the loop sizes for resonance are very far apart.

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Divergent results of this order require empirical verification before either modeling system can be trusted for dissimilar diameter materials meeting at the corners of an antenna element. So I modeled a 50-Ohm fat-horizontal, thin-vertical wire loop for 146 MHz. The 0.75" diameter horizontal bars were 16" long. For resonance, NEC-2 called for 29.15" #14 (0.064" diameter) vertical wires, while NEC-4 called for 32.2" wires. Uncorrected MININEC resonated the loop with 33.7" vertical wires. The test antenna resonated with 33.75" vertical wires. The real antenna result can be up to about +/- 3/8" in error due to possible variances from the model created by screw heads and short leads to the antenna coax fitting. However, the dimensions are sufficiently accurate to demonstrate the greater reliability of MININEC results and the problems of modeling corner junctions of dissimilar diameter wires in NEC-4 and NEC-2.

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An interesting deviation from this pattern occurs when right-angle junctions of dissimilar diameter wires involve symmetrical arrangements of one size of the wires. These models include vertical antennas with elevated ground radial systems, dipoles or verticals with "capacity hats," and similar structures. In these cases, the apparent cancellation of radiation from the elements of the symmetrical portion of the structure yields accurate gain and source impedance reports. A series of experimental models, verified by measurements with antennas built from the models, showed an agreement between NEC-2 and MININEC models within 1 to 2 percent for the radial length in capacity hats on 10-meter dipoles and 2-element Yagis.

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Folded Dipole Limitations

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Folded dipoles using dissimilar diameter wires add another dimension to the NEC-2 limitations. Consider two folded dipoles, as shown in Figure 6. One consists of 2 parallel wires 0.5" in diameter spaced 0.25' apart and 16.1' long for 28.5 MHz. The other consists of one 0.5" diameter wire and one #12 (0.808" diameter) wire, also 0.25' apart and 16.2' long for 28.5 MHz. The results of modeling these antennas in both MININEC and NEC-2 are as follows:

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Antenna Dimensions                 Free Space Gain     Source Impedance
+                                        dBi            (R+/-jX Ohms)
+
+1.  2 x 0.5" dia; 16.1' long
+     MININEC                            2.22           285.7 + j 0.9
+     NEC-2                              2.22           285.9 + j 4.1
+2.  0.5" dia and #12; 16.2' long
+     MININEC                            2.21           530.5 + j 1.5
+     NEC-2                              0.69           375.2 + j25.8
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Both systems model the standard folded dipole with very reasonable accuracy. The second, non-standard, folded dipole with dissimilar wire diameters is another matter. Standard textbook equations for calculating the impedance of folded dipoles with dissimilar diameters yield a projected ratio for the source impedance of the folded dipole relative to a single-wire dipole of nearly 7.5:1, or between 530 and 535 Ohms. While the MININEC model falls in the ball park (considering that the formula does not account for antenna shortening or end connections between the two wires), the NEC- 2 model is clearly unusable.

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The end result of exploring these limitations is this: wherever NEC-2 is to be used with wire junctions or closely spaced wires of dissimilar diameters, extreme caution must be used to independently check the reliability of the reported performance specifications.

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Sommerfeld-Norton Ground

Unlike MININEC, NEC-2 has provision for a highly accurate ground effect calculation system variously called Sommerfeld-Norton, SOMNEC, and other names. Although NEC-2 also has a "fast" ground calculation algorithm (6-8 times faster in solutions than the S-N system), it is far more limited and less accurate than the S-N system. Hence, wherever calculation of ground effects is critical to antenna design, only the more accurate system should be used. This applies to such modeling tasks as low dipoles (under 0.2 wavelengths up), elevated ground planes, and Beverage antennas. +

The contrast between the results of the MININEC ground system and the S-N system are sufficiently vivid with low dipoles, that I shall repeat a table presented in the last episode. The following table compares NEC-2 (S-N) and MININEC data for a 3.5 MHz dipole (resonated in free space) at heights from 0.05 to 0.30 wavelengths above medium or "average" earth (conductivity = 0.005 Siemans/meter; dielectric constant = 13).

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                         MININEC                  NEC-2 (S-N Ground)
+Antenna                  137.2' #12 copper        136.9' #12 copper
+Height                   Gain      Source Z       Gain      Source Z
+ W/L      Feet           dBi       R +/- jX       dBi       R +/- jX
+0.05      14.05          9.4        7.4 - j 4.9   1.2       48.9 + j15.4
+0.10      28.10          8.4       23.3 + j20.5   5.1       49.8 + j21.1
+0.15      42.15          7.7       45.9 + j35.1   6.4       62.5 + j26.9
+0.20      56.20          7.0       62.3 + j37.0   6.5       77.0 + j25.3
+0.25      70.26          6.2       87.7 + j28.3   6.2       87.8 + j17.3
+0.30      84.31          5.9       97.4 + j13.5   6.1       92.3 + j 6.1
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Despite the clearly more reliable figures produce in NEC-2, the use of the S-N is not without some limitations. For example, NEC-2 is sometimes used to simulate surface ground radial systems with vertical antennas by placing the radial wires very close to the ground. One recommendation sets the minimum height at 0.0001 wavelength, with segment-length tapering techniques applied between that height up to 0.001 wavelength. For frequencies below the 80-meter ham band, some ground-wave measurements suggest that elevated radial models yield overly optimistic gain figures. Consequently, the limits of the S-N ground system should be approached cautiously.

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Another NEC-2 Potential: Transmission Lines

In addition to providing a more accurate ground modeling system than MININEC, NEC-2 also offers the modeler another unique provision: the introduction of transmission lines into the antenna structure. Transmission lines can be used to connect antenna elements, as in phased arrays or log periodics. They can also be shown as feedlines to an antenna by the addition of a very short, remote wire to provide the line with a terminating point and for placement of the antenna source. Transmission lines can also be shorted or left open by various techniques and thus used as inductively or capacitively reactive stubs. +

The transmission line models used in NEC-2 are mathematical, in contrast to the wire elements, which can be classified as "physical." Wire elements enter into the matrix calculations and contribute to far-field and other antenna performance specifications. However, transmission lines do not enter into far-field calculations. For example, providing a dipole with a transmission line will not yield results that show any radiation from the line.

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In addition, transmission lines in NEC-2 are lossless. Therefore, models using them will not reflect losses incurred in phasing lines, load lines, and similar applications. Determination of those losses must be done by separate calculations. Feedline losses, for example, can be calculated by such programs as N6BV's TLA, which is readily available.

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As with the sampling of MININEC limitations, our purpose in surveying some of NEC-2's limitations is not to cast doubt on the utility of the program as a highly competent antenna modeling software core. Quite the opposite: by being alert to the program's limitations, we can avoid producing and relying upon models that cross the limit lines. Staying within the lines is one key to productive and satisfying antenna modeling.

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Although NEC-4 is beyond the scope of this series, due to its sparse use in amateur circles, an account of some NEC-4 limitations appears in the May- June, 1998, issue of QEX.

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Go to Main Index

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30. Modeling By Equation
+ D. Scratch Pads and Coordinates

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L. B. Cebik, W4RNL

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In this small series of columns devoted to modeling by equation, we have looked at the very basics and then moved on to topics that may help us refine our techniques. The object has been to make maximum use of the facilities offered to us by any program containing a model-by-equation option, even though we have had to confine ourselves to a single program in order to sensibly link the various moves we have made.

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So far, we have explored the need to develop modeling conventions, even within the use of equations to define variables, so that the task of modeling remains orderly and unconfused. We have also examined a few more complex models in order to reach decisions about what part of the work best appears on the equations pages of the spreadsheet and what of the work best appears on the wire pages.

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In our exploration of modeling by equations, the examples we have so far used have all focused on the geometry of the antenna as either a function of wavelength or as a function of a physical structure. There are further options that lead us to use some other facilities within a modeling-by-equation system. In this column, we shall focus on two diverse examples that are especially suited to exploit these facilities. As in previous notes, we shall use the equations spreadsheet within NEC-Win Plus for our examples. But in this episode, we shall examine the utility of having a "scratch pad" at our disposal within the equations pages.

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A scratch pad is simply an area on the spread sheet in which we may store data and equations. The data and equations will be those which are necessary in the process of deriving the values for the variables that will appear on the wire coordinate page. However, the data and equations in question do not directly define these variables. In simple models, we may not need the scratch pad, but as models become more complex--either in structure or in the mathematics used to define the structure--reserving variables for use on the wires page and placing supplementary data and calculations on the scratch pad can be very useful. (There is a technique within our sample program for getting around the limited number of allowed variable, but it will not be needed for our sample models.)

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Another Look at the Quad Loop

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Let's return to the quad loop with which we began, as shown in Fig. 1.

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We have thought of the quad loop in terms of letting the values of A be constants or simple functions of wavelength. However, we can also look at the dimensions as a function of wire diameter. If we give the wire diameter as a fraction of a wavelength, then the resonant circumference for any frequency, also in wavelengths, can be approximated by the following equation:

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QLwl is the circumference/perimeter of the quad loop in wavelengths and dwl is the wire diameter as a fraction of a wavelength. The log is to the base 10. (The spreadsheet in NEC-Win Plus knows the difference between LOG, also known as the "common" logarithm, and LN, known as the "natural" logarithm. In contrast, GW Basic, still a useful programming language for simple utility programs, knows only natural logs, and the user must program in a conversion factor to derive common logs.). A restriction upon this approximation equation is that it applies with under 2% error for wire sizes from 10-5 to 10-2 wavelengths in diameter. Although the equation appears to be quite adequate for wires that are thinner than the lower defined limit, using the equation on fatter wires will rapidly yield inaccurate results. Most physically constructed quad loops will wires falling within the equation limits.

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Since the equations page already provides the wavelength in the selected units (W), implementing the required equations becomes very straightforward. The first step is to set a variable to the wire size. (Wire size here refers to wire diameter. Although NEC calculates using the wire radius, most NEC programs permit the user to input a wire diameter, since that value is normally better known. Conversion to the radius becomes an internal function of the user-to-core interface programming.) Since the wire size ultimately must be in the same units as we use for the wire-end coordinates, here is a handy conversion chart for common AWG wire sizes, given in inches, feet, and mm.

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AWG Size          Dia. Inches             Dia. Feet                        Dia. mm
+18                .0403                   .00336                        1.0236
+16                .0508                   .00423                        1.2903
+14                .0641                   .00534                        1.6281
+12                .0808                   .00673                        2.0523
+10                .1019                   .00849                        2.5883
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We can enter the desired wire size directly, or we might use up a bit of scratch pad or equation variable space by entering the diameter in a common unit (such as inches) and then converting it to the value in the desired units (in this example, feet). Suppose we enter .0641 as our wire diameter and let it equal A. Then B might equal this value divided by 12 to obtain a value in feet, the chosen unit of measure for the model. Finally C might equal B divided by W (the wavelength). I have taken this route only because we have plenty of pre-defined variables at our disposal for this small problem.

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We can now let D be the perimeter/circumference as defined in Equation 1 above, where dwl takes the value of variable C, as we have just derived it. In this example, we have used #12 AWG wire with a diameter of 0.0808" as the wire size. Note that in the upper portion of Fig. 2, the entry for the variable D follows Equation 1 exactly, although the notations differ.

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However, for developmental purposes we may wish to follow a different procedure in setting up the equation for D. In the lower portion of Fig. 2, we can see that the equation for D refers to D2, D3, and D4. These are values entered into column D, in the "scratch pad" area of the equations page. The entries in column E identify the values placed in column D. The equation for the variable D uses the active values in rows 2-4 of column D at the designated places.

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An advantage of using the scratch pad is that the modeler can make adjustments to the numerical values in the equation for variable D without having to rewrite the equation. In fact, adjustments were made in the development of the algorithm in question. The initial value in D2 was 1.0416 and the value in D4 was 0.0131. Further adjustments, including varying the exponent, to bring the curve further into alignment with NEC calculations for resonant quad loops would be a routine matter.

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We can convert the value of variable D (initially calculated in wavelengths) to a value in the selected units of measure by letting E equal D times W, the length of a wave in those units of measure. Fig. 3 shows the numerical values that result for a frequency of 28.5 MHz.

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The only additional step we need to take is to set up the coordinates. We have some choices here, one of which is to pre-convert the total perimeter length into +/- values for the 4 wires in the single square loop. So we can let G equal E divided by 8. (Note that, in the NEC-Win Plus spreadsheet used for our examples, F and W are preset variables for frequency and wavelength, respectively. Hence, our own list of variables will jump from E to G.) Fig. 4 shows the wires page that corresponds to the prescribed variables we have just described.

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From this set of variables entered on the wires page, we get the numerical values shown in Fig. 5.

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Even on the wires page, we have options. The definition of variable G was unnecessary, although for many purposes it is convenient. We might have done our division by 8 on the wires page itself, thus saving the use of one variable. In the present simple case, we have plenty of variables to use, but in more complex cases. we might wish to use the least number possible to ensure that all entries needing a variable have one. Fig. 6 shows our revised wires page variable entries, along with the dimension entries to verify that we achieve the same results as we obtained with our previous procedure.

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Learning to use all of the facilities at our disposal in the most efficient and effective manner takes some time, and this simple example only scratches the surface of the scratch pad.

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The Moxon Rectangle

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The Moxon Rectangle is a 2-element parasitic array with the ends of the elements folded to point toward each other. The mutual coupling of the elements and the coupling between the tips of the tails yields a nearly cardioidal pattern with a very high front-to-back ratio. Fig. 7 shows the general outline of the Moxon Rectangle, with identifications for all of the key dimensions.

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The critical dimension is the gap between the tips of the tails (dimension C). The other dimensions then determine the resonant frequency of the array (close to 50 Ohms) and the frequency of maximum front-to-back ratio. I once optimized a series of models using #14 copper wire for all of the HF bands from 40 meters to 10 meters. Barbara Craig, KC8KJA, performed a series of regressions on this data to develop a sequence of equations defining Moxon Rectangle dimensions for #14 bare copper wire, with results that are usable even at 2 meters.

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The following GW Basic utility program provides a listing of the equations that resulted from the regression analysis. Lines 40-80 supply the mathematics, using the design frequency that the user enters in line 20 and the constants defined in line 30.

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10  PRINT "Program to calculate the dimensions of"
+12  PRINT "a #14 AWG Bare Wire Moxon Rectangle"
+14  PRINT "Analysis by Barbara Craig, KC8KJA"
+16  PRINT "Output dimensions in Feet (See Fig. 7)
+20  INPUT "Enter frequency in MHz:";F
+30  A0=6.19653:B0=1.00058:A1=6.126836:B1=.99437:A2=6.19966:B2=1.00033:GA=.72
+40  A=GA*((EXP(A2)/F)^(1/B2))
+50  B=.5*((EXP(A1)/F)^(1/B1))-(.5*A)
+60  D=((1-GA)/2)*((EXP(A2)/F)^(1/B2))
+70  E=((EXP(A0))/F)^(1/B0)-A
+80  C=E-(B+D)
+90  PRINT "A = ";A
+100 PRINT "B = ";B
+110 PRINT "C = ";C
+120 PRINT "D = ";D
+130 PRINT "E = ";E
+140 END
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Fig. 8 shows one way in which we can enter the equations into the equations page of NEC-Win Plus. The spreadsheet mathematical forms here follow the Basic forms exactly. As the representative equation (for variable A, which corresponds to dimension A in Fig. 7) shows, we can enter the set of constants that emerged from the exercise in regressions directly into the equations. On the scratch pad, we have entered solely for reference the values of gamma and of alpha0-2 and beta0-2. However, the variable equations themselves contain all of the requisite information for dimension calculation. Variables A-E correspond to the dimensions in Fig. 7. (Although Basic requires rigorous serial calculation, which places the derivation of variable and dimension C last, the spreadsheet permits the user to list the variables in almost any desired order.)

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The equations apply only to antennas using #14 bare copper wire. The actual relationships among the dimensions is somewhat complex, since a fatter wire will require a wider gap. The resultant increase in dimension E will change the feedpoint impedance, as will the fatter wire itself. Elongating the array will restore the near-50-Ohm feedpoint impedance, but there will be adjustments to the overall length of both the driver and reflector elements to place the maximum front-to-back ratio at the design frequency. Hence, the relationships among the element dimensions will shift as we move to #10 wire or to aluminum tubing in the 0.5" to 1" range.

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With the prospect that regression analysis would produce differing constants for other wire diameters, a more useful way of entering the equations appears in Fig. 9. Here, the values in column D represent active values that we draw into the variable equations by means of column and row references. The sample equation for dimension A illustrates the method and may be compared directly with the sample equation in Fig. 8. D2, D7, and D8 replace the constants in the earlier version of the equation. Column E now holds reference data to identify each of the values in column D.

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Let us suppose that we have a new set of values for gamma and for A0-2 and B0-2 for some new wire size. We need not create an entirely new model. One option would be to replace the values in column D with the new values and to save the model under a new name. Another option would be to place the new values in column F and then to use further spreadsheet capabilities to let the equations page select the appropriate column of values, depending upon the wire size, which we might enter as a variable. Such possibilities go beyond the scope of these introductory exercises. However, if modeling by equation becomes a routine task, then exploring the full limits of the spreadsheet's language becomes an important part of the learning curve.

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Fig. 10 shows the set of values that emerge from either method of entering the equations. Variable G is useful for this and other sample models, because it gives us the option of setting the design frequency either to the current frequency of the model or to some specific frequency. The latter type of frequency assignment is useful when we wish to run a frequency sweep with the design frequency at neither end of the frequency range that we sweep.

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Fig. 11 displays the two forms of the wires page for this example. Note that it is necessary to decide several matters regarding the axes for the model. In this case, the X-axis uses +/- A values, requiring us to use half of the value of A. The Y-axis provides the front-to-back dimensions, with the reflector set a Y=0. All other values are positive. Only the tip of the driver tail requires a "complex" formulation, and dimension C is not referenced at all on the wires page (despite its importance to the antenna design). You may wish to reference the side-to-side dimensions to the Y-axis and the front-to-back dimensions to the X-axis. To capture a vertically oriented Moxon, the side-to-side dimensions would be referenced to the Z-axis, with the front-to-back dimensions referenced either to X or Y. To place the antenna at some specific height above ground would require the use of one more variable for the antenna height. In this case, the wires page variable entries would become a mixed function of the new height variable and the variable A, using techniques noted in previous episodes.

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Conclusion

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Together, the quad and Moxon examples illustrate one of the many uses of the scratch pad facility. Not only is it a place to enter reference data, it also serves as an active data pad that the variable equations can routinely reference. The scratch pad data need not be just a series of constants, but may also consist of equations. Indeed, any equation that is not used on the wires page may best be placed on the scratch pad. In addition, we may also use the scratch pad area for identifying notes and labels to ensure that the data we place there today can be interpreted months later. As an exercise to ensure mastery of these matters, you may wish to go through all of the examples in these 4 episodes, transferring to the scratch pad all data and equations that are not directly needed to specify a variable used on the wires pages.

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We could carry on this series of columns on modeling by equation almost indefinitely. However, I hope the selection of examples used in this and the preceding columns provides enough background and ideas to permit you to develop your own best methods of using this versatile adjunct to creating effective models. Although these notes have focused exclusively on elements that we may model through the use of equations, we must also remember that none of the requirements and limitations of NEC are set aside in the process. Segmentation, source placement, load placement and type, convergence testing, and GAT testing all remain important concerns to the modeler, no matter how simple or complex the equations of the model.

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31. A Case Study: a 90' Wire

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L. B. Cebik, W4RNL

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I assisted another amateur radio operator in analyzing his antenna, since it had largely evaded modeling. The purpose of the exercise was to provide some general information on the modeled performance of the antenna across the MF-HF amateur frequency spectrum for a typical amateur radio wire antenna fed by an antenna tuner. The purpose was not to be overly precise, and indeed, the input data and modeling conditions would have precluded precision. However, even carefully constrained modeling of a general nature can be useful. The following exploration is a case in point.

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The basic antenna is shown in Fig. 1. The radiator is about 90' long and runs from near the ground at the left (shed) to a maximum height of 25' about 50' from the shed and then down to a height of about 15' at the far right tree. It is fed at the base of the wire at the junction with the buried radial wires. The antenna may be variously classified as an end-fed random wire or as the type of antenna to which it most closely corresponds at each frequency of operation.

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The sketch supplied was incomplete. Therefore, I made a few assumptions that will not materially affect the modeled outcomes. First, I assumed that true north was straight up the page of the sketch. If north has a different bearing, one will have to adjust the azimuth headings in this report accordingly. I had to use a compass to approximate the angles of the wire.

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Second, the owner did not specify the wire size. I assumed #12 AWG copper wire. For the number of approximations required by this exercise, a small change in wire size will produce no radical changes in the patterns or impedances reports.

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Third, the owner did not specify the conductivity and dielectric constant of the soil in his area. Maps suggest that the conductivity is about 0.002 Siemens per meter, which corresponds to the class of soil listed as "poor." The corresponding dielectric constant is about 13. However, it may in fact be lower than this level, depending upon subsoil structure. For example, the dielectric constant of shale is about 7. Nonetheless, given other approximations, the difference will not alter projected performance by much.

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Before looking at the model of this antenna, let me note something about what this report can and cannot tell. What the NEC-2 models of the antenna provides is a general portrait of anticipated performance characteristics with the assumption of a level homogenous soil beneath the antenna. There are limitations to the data that emerges.

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1. NEC-2 cannot account for variations in the patterns created by the immediate terrain. The subject terrain is likely to be quite hilly, but not mountainous. An immediate hill may yield a stronger signal in the direction from the hill through the antenna, but this cannot be assured without the application of supplementary software into which topographical features can be placed. However, an awareness of one's immediate topography can assist one in accounting for differences in the model and actual operation.

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2. NEC-2 cannot place radials on or beneath the ground, as they are at the subject site. However, placing radials very close to the ground provides a very reasonable approximation of in-ground radial performance, with errors well within the limitations of other approximations made in this report.

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3. The antenna owner has chosen EZNEC as his modeling vehicle. Two factors limit the ability of this program to model both natural and constructed structures beyond the antenna wires. First, EZNEC permits only 500 segments, which limits the available segments for such structures. Second, the program allows only a single wire loss (or conductivity) value for all wires. Secondary structures in the vicinity of the antenna may require many different conductivity values for their approximating wire-grid structures. However, since no data on secondary structures was provided, modeling must do without them. The effects of such structures must remain an estimate used in conjunction with this report.

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The Model

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The EZNEC model for NEC-2 analysis of the antenna requires 8 wires, as shown in the side and top views of Fig. 2.

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The following model description has been annotated for correlation with Fig. 2.

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Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
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+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
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+Radiator wires
+1   W3E1   0.000,  0.000,  0.200  W2E1  45.500, 21.000, 25.000    # 12   50
+2   W1E2  45.500, 21.000, 25.000        82.607,  7.500, 15.000    # 12   40
+Radials
+3   W4E1   0.000,  0.000,  0.200        30.000,  0.000,  0.200    # 12   30
+4   W5E1   0.000,  0.000,  0.200        10.607, 10.607,  0.200    # 12   15
+5   W6E1   0.000,  0.000,  0.200         0.000, 90.000,  0.200    # 12   90
+6   W7E1   0.000,  0.000,  0.200         0.000,-60.000,  0.200    # 12   60
+7   W1E1   0.000,  0.000,  0.200  W8E1 -10.000,  0.000,  0.200    # 12   10
+8   W7E2 -10.000,  0.000,  0.200       -10.000,-50.000,  0.200    # 12   50
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+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
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+1           1     1 /  1.00   (  1 /  0.00)      1.000       0.000       V
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+Ground type is Real, high-accuracy analysis
+Conductivity = .002 S/m    Diel. Const. = 13
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+              --------------- MEDIA ---------------
+Medium       Conductivity(S/m)   Dielectric Const.    Ht(ft)   R Coord(ft)
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+1                2.000E-03            13.00           0 (def)     0 (def)
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The direction of each radial is an estimate based upon the original sketch. The two 60' radials have been arranged so that one is straight, while the other moves west for 10' and then south for the remaining 50'. This is as close to accurate as the sketch would permit.

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In NEC modeling, longer wires are subdivided into segments to permit the accurate calculation of mutual impedances, currents, and other output data. The segmentation of wires that NEC-2 recommends is approximately 9-11 segments per half wavelength (with a minimum of about 5 per half wavelength) at the shortest wavelength used. At 28.5 MHz, a wavelength is about 34.5' long, and the radiator is about 2.6 wavelengths long. Since the wire (#12) is thin, additional segmentation density is allowable and was used in the model to assure convergence, given the non-standard geometry of the assembly. A uniform segment length of 1' was used throughout the model. The result is a model using 345 segments.

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The antenna source or feedpoint is the lowest segment of the radiator wire nearest the junction of the radials. This approximates the actual feed system, which employs an automated tuning system.

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What the Model Suggests

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Given the numerous approximations required to model the antenna, the modeling output data must be taken as suggestive and indicative, but not precise. The following table provides a summary of the data for 160 through 10 meters (with 80-75 sampled at 3.6 and 3.9 MHz). The TO angle is the elevation angle of maximum radiation. It is a function of taking an elevation pattern in the azimuth heading of strongest radiation. The maximum gain in dBi is the gain at this elevation angle and azimuth angle. There are three exceptions. On 80 and 40 meters, the TO angle exceeds all but NVIS use, and so an alternative angle of 50 degrees was also used to sample gain. Comparing the TO angle gain value with the arbitrary lower angle value gives some idea of the rate of gain decrease as the signal angle departs from the TO angle.

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There are a pair of azimuth headings. The first corresponds to the heading provided by EZNEC, which actually counts azimuth in "phi" angle terms, that is counterclockwise. The second heading presumes that the compass heading of North is straight up the page, in accord with the original sketch. Therefore, the heading is a compass bearing resulting from that assumption. Finally, the table provides a report of estimated feedpoint impedance. given the assumptions of the model, the actual values of resistance and reactance may easily vary by 20% from the listed figures.

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Frequency      TO        Max. Gain EZNEC     Compass   Feedpoint Z
+  MHz          angle       dBi     azimuth   azimuth   (R +/- jX Ohms)
+  1.8          38        -6.7      169       281         25 - j 330
+  3.6          61        -3.0      215       235        180 + j 510
+               (50)      (-3.1)
+  3.9          63        -2.6      213       237        310 + j 760
+               (50)      (-2.8)
+  7.1          79        3.5       266       184         60 - j 180
+               (50)      (2.8)
+ 10.1          53        3.0        48        42       2300 - j 790
+ 14.1          44        3.1       314       136        245 + j 390
+ 18.1          45        3.2        91         1        135 + j  70
+ 21.1          40        4.5       343       107        470 - j 660
+ 24.9          35        5.0       343       107        660 + j 590
+ 28.5          32        4.0       346       104        220 + j 110
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The table contains some interesting data patterns. First, only on 30 meters does the antenna system offer a feedpoint impedance that may challenge the capabilities (or efficiency) of an automatic tuner. Second, except on the lowest bands, the antenna offers a reasonably constant gain. However, tables do not tell the entire story and should be read in conjunction with relevant azimuth and elevation patterns for the antenna. The following patterns and commentary employ an azimuth pattern taken at the TO angle except for the three cases listed as exceptions in the table. The elevation patterns are taken at the azimuth heading of maximum gain, which may require the user to orient himself to see properly what those patterns show.

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1.8 MHz: Fig. 3 supplies the patterns for this frequency. The solid line represents the total pattern. The dotted line represents the horizontal component, and the dashed line represents the vertical component. At 160 meters, note that the vertical component dominates the total pattern. Maximum radiation is in the direction opposite the length of the wire, that is, toward the west, using the conventions set forth earlier. A gain figure of -6.7 dBi seems low, but only about 2 S-units below the value that might emerge from a dipole that was set at least 1/2 wavelength above the ground. Because lower frequency RF penetrates the ground more deeply, and the ground is often stratified, the effects of the modeled ground may vary from those of real ground.

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3.6 MHz: In Fig. 4 we find azimuth and elevation patterns for 80 meters. The strengthening of the horizontal component broadside to the wire (but weakly along the length of the wire) tends to circularize the overall pattern. There is much high-angle radiation, but note in the elevation pattern the slow rate of decrease with the lowering of the elevation angle. Hence, performance at lower angles is likely to be consistent with higher angle performance.

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3.9 MHz: The similarity of the patterns in Fig. 5 to those in Fig. 4 suggests that only small changes in performance occur across the span from 80 to 75 meters. There is actually a slight gain decrease, which results from the fact that the antenna is in a transition from dominance by the vertical component to dominance by the horizontal component. However, the wire is very low for a horizontal wire at this frequency, resulting in a higher TO angle.

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7.1 MHz: On 40 meters, as shown in Fig. 6, the antenna begins to perform somewhat like an end-fed 1/2 wavelength wire, and the length is actually less than 3/4 wavelength. The proximity to the earth yields a high TO angle, but the increasingly dominant horizontal component yields a pattern roughly broadside to the bent wire radiator, favoring North-South paths (given the initial conventions of the study). The near 3/4 wavelength of the radiator yields a feedpoint impedance against the ground plane that has an expected low resistive component.

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10.1 MHz: On 30 meters (Fig. 7), the radiator is nearly 1/2 wavelength long, and like end-fed half wavelength antennas in general shows a high impedance. The pattern is a curious mix of horizontal and vertical component elements, with the horizontal component becoming increasingly dominant. However, both the wire slant and bend combine to give the antenna a NE-SW orientation. Drawing a line across the azimuth pattern on this axis will yield the elevation pattern.

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14.1 MHz: Fig. 8 is the beginning of two phenomena of note. One is the final domination of the horizontal component of the total pattern. The other is the development of multiple lobes. Since the antenna is now about 1.5 wavelengths long, additional lobe structures are to be expected. However, the slope and bend of the antenna yield fewer deep nulls than a pure horizontal doublet. Fewer deep nulls also tend to be accompanied by less strong major lobes. Hence, the pattern is nearly omni-directional, but at a modest gain level.

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18.1 MHz: The lobe structure becomes more apparent in Fig. 9 for the 17-meter band. This band also shows a danger in reading only tabular data. The strongest lobe is nearly due north. However, that lobe a fairly narrow. Almost as strong is the very broad lobe to the southeast, which is likely to yield more impressive coverage in actual operation. (This note, of course, does not take into consideration the potential effects of terrain and surrounding structures.)

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21.1 MHz: The 15-meter patterns in Fig. 10 reveal the continued evolution of lobe and null structures as the antenna becomes longer as a function of the wavelength in use. The low height of the antenna, relative to the dominance of the horizontal component, yields a fairly high TO angle. However, as the elevation pattern shows, the rate of gain decrease with a lower angles is slow, and there remains usable gain to quite low elevation angles.

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24.9 MHz: Once more the patterns in Fig. 11 show further development of lobes and nulls. However, overall, the patterns for 15 and 12 meters are very reasonably coincident. This fact permits one to anticipate strong and weak paths from one band to the next. As the frequency continues to increase, the antenna shows a distinct east-west orientation of major lobes.

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28.5 MHz: The 10-meter patterns in Fig. 12 are simply more complexly wrinkled versions of those for 15 and 12 meters. The east-west orientation--along the length of the radiator--dominates, but without many deep nulls away from the main lobes.

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Of What Use Is the Analysis?

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The modeled analysis of the antenna provides a generalized picture of how the antenna is likely to perform, once the data is adjusted for terrain and other interfering factors. It also shows the evolution of the antenna's patterns with increasing frequency. The end result is something like this: the antenna provides modest gain and performance potential within the matching abilities of an automated tuner on virtually all of the amateur bands from 160 through 10 meters--with only the impedance on 30 meters being potentially problematical.

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The model is also useful when placed in conjunction with other models of possible system alterations or improvements. For example, suppose one were to erect a wooden vertical support at the shed, perhaps 30' tall. Would such a structure yield a better or worse antenna? One option would be to run the initial length of the wire up the support and then over to the trees. However, one might limit the total length to 90' or one might uses about 120' of wire in the radiator. Determining which of these options, if either one, offers better performance than the current radiator would be indicated (but not guaranteed) by modeling the options.

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Another potential change in the system would be the addition of either more or longer radials--or both. Just how much, if any, improvement one might garner from an improved radial field can be loosely estimated from modeling various possibilities in this are.

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Besides measuring alterations to the present antenna system, one might also use the analysis of the current antenna as a baseline for considering other antenna types. In large measure (but not absolutely), comparisons among antenna types and configurations equally affected by local terrain and ground clutter will remain valid.

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Nonetheless, in using the numbers and patterns that have emerged from the analysis, one must be mindful of the limitations outlined early in the report. Not only are terrain and secondary structures not accounted for, but as well, there are a number of approximations that went into the model. Consequently, the model is best used for the trends it shows and not for the absolute values of the output numbers. However, even in a more modest role, the analysis is both useful in itself and potentially useful when contemplating system alterations.

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Go to Main Index

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32. A Case Study: Rotating a Beam

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L. B. Cebik, W4RNL

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Another request for assistance yielded a case with some interesting possibilities for modeling by equation. It involves a common situation: two stacked beams. The problem arose when the individual noted that one of the beams would be fixed in position. The other would rotate. What would be the effect, if any, on the patterns when the beams were not in alignment? To answer this question, he was faced with the prospect of remodeling the rotating beam every time he wished to check another angle of divergence between the two.

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There is a solution to this problem, and its form depends on the software in use. The solution can be applied to a spreadsheet or other calculating program, with the new rotating beam coordinates used to create a new model. If the software has a "modeling by equation" facility, the solution can be plugged into the software and the process of remodeling automated.

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The following notes will step through the problem--very likely in too much detail for some and too little detail for others. However, it will indicate what a modeler can do to rotate one antenna relative to another.

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Step 1: Simplify the design details.

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Well designed horizontal arrays for the HF spectrum use tapered element schedules for each wire. Although the solution to be shown can be applied to every element step, that process introduces needless tedium into the process. So the first step is to simplify the beam design so that it uses uniform diameter wires for each element.

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NEC-2 programs, such as NECWin Plus and EZNEC for Windows provide Leeson corrections for calculating the properties of arrays with linear elements having symmetrical stepped diameter structures. The correction produces equivalent elements having a uniform diameter. Since these substitute elements form the basis of calculation, the user should access the dimensions of these elements and use them for the project ahead.

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Step 2: Center the beam on the boom.

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Once we have a beam with uniform diameter elements, we should them place the beam mounting position at coordinates 0,0. There are numerous conventions used by modelers to develop antennas. Some place the reflector either at Y=0 or at X=0, so that all distances along the boom a cumulatively positive. Other modelers use a plus-minus system, so that the extreme elements are at the same distance from zero--whether or not the mid-point along the boom is the mounting point.

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Fig. 1 shows a model transformed from the first convention to the second. The second convention is closer to the desired goal of having 0,0 represent the mounting position. In the absence of a precise location of the true mounting point, the second convention can be used without introducing significant error into the resulting modeling tests.

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Fig. 1 also shows the dimensions of the beam we shall use as our running example. It is a 3-element 20-meter Yagi with 1" diameter elements. One of the merits of the model is the none of the elements will fall at 0,0 in our transformation of position.

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Step 3: Rethink the coordinates of the element ends.

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We normally think of a beam as a set of linear elements with end coordinates. For the moment, we need think only of the end coordinates and ignore the wire between them. What we shall develop is a method of accurately producing end coordinates for any angular position of the beam. Then, by placing those coordinates in the correct places in the modeling wires table, a correctly dimensioned beam will result--pointed just where we desire.

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Fig. 2 holds the key to rethinking the coordinates. From the mounting position (0,0,), let each coordinate set (6 of them in this case) be a function of a (dotted) line of length L with an angle A relative to the initial boom axis. Note that we are using angles from 0 to 360 degrees. More accurately, we shall be using angles from 0 to 2PI radians, since most spreadsheets know angles only in terms of radians. However, we can always convert an angular measure in degrees to one in radians (or back again) by the conversion equation

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where PI is carried to as many decimal places as you can stand.

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Step 4: Calculate L1-Ln and A1-An

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We may calculate the length of each radial (L1 through Ln) and angle (A1 through An) from the existing coordinates of our model that is centered on the mounting point. The necessary equations are basic trig:

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where Xn and Yn are the coordinates for any of the point, An is the angle relative to the axis of reference, and Ln is the length of the radial from the mounting point (0,0). For the beam we are using as our example, we derive the following table for the 6 points. Since you may be using a hand calculator, use whatever shortcuts you know that are allowed by trig to place the angles in the proper quadrant.

+ 
Coordinate Identification     Ln (")    An (degrees)   An (radians)
+Director End 1  (1)           230.2      54.0          0.943
+Director End 2  (6)           230.2     306.0          5.340
+Driver End 1    (2)           198.2      92.8          1.620
+Driver End 2    (5)           198.2     267.2          4.663
+Reflector End 1 (3)           247.6     123.1          2.149
+Reflector End 2 (4)           247.6     236.9          4.134
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For a given beam design, the lengths in the Ln column will remain constant.

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Step 5: Calculate coordinates for a new angle.

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To rotate the beam--in a clockwise fashion--we need only add to each angle the number of degrees (or radians) of rotation and then recalculate the coordinates. From the length of the radial and the angle, we may calculate the coordinates with equally basic trig equations:

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where A' is the new angle resulting from the rotation.

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Let's rotate our beam by 20 degrees and look at the new coordinates for the elements. 20 degrees is 0.349 radians. So we may simply increase the angles in the table above by this amount.

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Coordinate Identification     An (radians)        Xn        Yn
+Director End 1  (1)           1.292                221.3      63.4
+Director End 2  (6)           5.689               -128.8     190.8
+Driver End 1    (2)           1.970                182.7    - 76.9
+Driver End 2    (5)           5.012               -189.4      58.5
+Reflector End 1 (3)           2.499                148.4    -198.1
+Reflector End 2 (4)           4.483               -241.1    - 56.4
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If we rotate the beam another 70 degrees, we shall end up with a total 90- degree or 1.571-radian rotation. In this case, our dimensions will become those in the following table.

+ 
Coordinate Identification     An (radians)        Xn        Yn
+Director End 1  (1)           2.514                135.2    -186.3
+Director End 2  (6)           6.911                135.2     186.3
+Driver End 1    (2)           3.191               -  9.8    -198.0
+Driver End 2    (5)           6.235               -  9.8     198.0
+Reflector End 1 (3)           3.720               -135.2    -207.4
+Reflector End 2 (4)           5.706               -135.2    -207.4
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In other words, the antenna has it original dimensions, with the X and Y axes transposed.

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Fig. 3 shows a top view of the three antennas: the original, with 20- degrees rotation, and with 90 degrees rotation to verify that the results indeed rotate around a common mounting point.

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Step 6: Automate the model.

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Although we can use the basic trig equations and our reformulation of the model coordinates to create new models for any orientation about the mounting point, systematic modeling of a rotating beam can be much simplified. However, the requirement is a software package with a "model- by-equation" facility, such as NEC-Win Plus. We may simply plug our design data and equations into the equations and wires pages of the built-in spread sheet.

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Fig. 4 illustrates the initial stage of the project. Column D becomes a reference column for the design's radial lengths and the angles from 0 to 360 degrees, but given in radians, the calculating basis for spread sheets. Column E identifies each of the D-entries in terms of the designations in the figures we have used so far. Column F contains 2 entries: a converter for changing entries in degrees to radians and a place (F3) to enter the rotation of the Yagi from its initial setting. Since most of us are accustomed to thinking in terms of degrees, the entry is in those terms.

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Column B provides values for the pre-assigned variables A-J. A-G simply add the design angles to the additional rotation angle. H-J repeat the radial lengths as a matter of convenience.

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The page shows an entry of 20 degrees as the rotation of the basic 3- element Yagi. The Equations Values page, in Fig. 5, shows the calculated values for each of the adjusted angles, in column B. You can compare these values to those in one of the tables shown earlier.

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We did not calculate the coordinates on the equations page, since we may do that on the Wires page through equations (Fig. 6). All X values will involve a sine, while all Y values require a cosine. H, I, and J are the appropriate radial lengths used to determine the values of the coordinates. +
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The values yielded by the equations--both those on the equations page and those on the wires page--appear in Fig. 7. Since we are working with a free space model, Z is zero. However, for a real problem involving stacked beams--one of which is fixed, Z would take a positive value. In fact, one may add further lines to this model to create the fixed beam using numerical values throughout--since it is a constant. Then, simply by placing a new value in degrees in F3 on the equations page, one can rotate the movable beam to find the pattern consequences of this form of stacking.

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Fig. 8 shows the pattern of the rotating beam when moved 20 degrees from its initial orientation. The pattern values (gain and front-to-back ratio) plus the impedance data make a quick check on whether we have formulated our equations correctly.

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Putting the rotating beam to use involves simply assigning a set of ground conditions and adding the fixed beam. Fig. 9 shows the wires page for a sample situation. An identical beam to the rotating one has been added in lines 4-6. It has been left inert, on the premise that the upper rotating beam will be active alone when it is not aligned with the lower beam. Of course, the modeler is certainly free to change this premise, as well as the 50 and 90 foot heights assigned to the beams.

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In fact, it may be well for a modeler to investigate what happens within a site-specific model when the fixed beam driver is either closed or open at the feed point. The condition in the model is closed when no source is assigned to the driver wire. To open the driver, insert a very high resistive load (1E10) at the normal feed position on the wire.

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For our simple sample, the inert lower driver is closed. Fig. 10 combines azimuth patterns for the active upper antenna when in line with the lower antenna and when 20 degrees off clockwise. Nothing radical happens in this case. The gain differential is insignificant, as is the front-to-back ratio. However, as the figure reveals, there is some small distortion of the rear pattern as the antenna departs from the in-line condition. The source impedance shows a 2-Ohm change in reactance for this situation relative to the impedance of the upper antenna in isolation.

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There is no requirement that the two beams in the stack be identical. In fact, one can combine beams of many sorts simply by cutting and pasting entry lines. However, it is wise to ensure that the various beams in the stack use segments of roughly equal lengths to ensure that there are enough segments per half wavelength at the highest frequency tested.

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Although deriving and entering the equations needed to create a rotating beam takes three times as long as entering a single model, the net time saved will be considerable. If we take readings every 10 degrees, for example, the equations can save us about 80% of the time required to introduce individual models for each step of the way. The more complex the individual antenna models, the more time saved by the use of equations.

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Sometimes it is worth the effort to develop some models by equation.

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Go to Main Index

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33. A Clean Sweep

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L. B. Cebik, W4RNL

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It would not by uncommon to find an antenna advertisement of the following sort: 2-element antenna--peak gain 6.8 dBi free space, peak front-to-back ratio >32 dB, SWR >1.1:1 at design frequency. Such notices are common and have carried over into casual modeling practices. We design an antenna for a single frequency, even if we intend to use across a span of frequencies, for example, one of the amateur bands. So perhaps a short exercise in the utility of performing frequency sweeps might not be out of place.

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NEC cores (both -2 and -4) are set up for frequency sweeping, although the core set-up and common commercial program set-ups will look different. The basic FR (frequency) input line or "card" looks something like this:

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   FR         0         5         0     0     24.90     0.05
+     Type of Stepping  No. of FQs            Start FQ  Increment
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The Type of Stepping can be zero for normal linear stepping. If the entry is a "1", then the stepping is multiplicative. The next entry lists the number of frequency steps in the sweep. Either a 1 or a 0 in the entry gives a single frequency output. Following two inactive "zero" entries, we come to the sweep start frequency in MHz. The final entry is the increment between steps.

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In the example, the model would have produced output data for 24.90, 24.95, 25.00, 25.05, and 25.10 MHz.

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The most commonly used NEC-2 programs, NEC-Win Plus (NW+) and EZNEC for Windows (EZW) use the same variant input system for performing a frequency sweep.

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Fig. 1 shows the NW+ upper left corner frequency entry portion of the main screen. Instead of inputting a start frequency, the number of steps, and the increments, we put in start and stop frequencies as well as the increment. If the increment or "Step Size" creates a frequency value higher than the "end" frequency, the nearest lower frequency in the sequence is the upper limit for the sweep. The program translates the user input into the data needed for the FR card.

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EZW's window is more complex, but the frequency selection process is identical to that of NW+, as shown in the left portion of Fig. 2. (The remainder of the frequency sweep box represents a difference in software design philosophies of the two packages. NW+ produces output data for every frequency of a sweep from 1 to n steps. The user can then print or save the data he may need. EZW normally operates in a single frequency mode, with a frequency sweep called up as a special function. Hence, sweep output data is selected by the user and placed into special files. Both systems work equally well in yielding sweep data.)

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Frequency sweeps yield data at regular frequency intervals. Very often, it is useful to transfer this data to a spreadsheet with graphing capabilities, since the data of interest can exceed the internal graphing capabilities of NEC programs. I routinely transfer the entire data set to a spreadsheet such as EXCEL, Quattro Pro, or Lotus. (The graphs in this column are from Quattro Pro, although almost all spreadsheets have quite adequate graphing capabilities.)

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Sweeps and "Mini-Sweeps"

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Usual practice tends to call for the use of frequency increments that end in zero or five. For most of the wider HF amateur bands, the start frequency is usually an integer, which makes the practice seem natural.

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Consider a 40-meter 3-element quad array. We might generate a frequency sweep to determine the antenna's potential across the band from 7.0 to 7.3 MHz in 0.05 MHz increments. If we combine gain and front-to-back curves, the results might look something like Fig. 3.

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There is useful data in this graph. Note the smooth gain curve. The absence of corner squaring suggests that it is an adequate representation of the gain across the band, ranging from 7.5 dBi free space gain at the low end of the band to a little over 8.0 dBi at the upper band edge, with a peak at mid-band. Curve smoothness suggests that interpolated values will be close to those we might find in a model output file for any intermediate frequency along the way.

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The front-to-back curve presents an interpretive problem. Many quad designs, but certainly not all of them, show a very sharp and narrow-band front-to-back peak. The graphed values for 7.1 and 7.15 MHz suggest that there might be a peak somewhere between them. The only way to know for certain is to run a "mini-sweep" between 7.1 and 7.15 MHz, perhaps in 0.005 MHz increments.

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Fig. 4 shows the results of such a sweep in graphical form. The gain values show steps, since the output data was limited to 2 decimal places and the overall change across the new set of frequency limits is very small. The potential front-to-back value peak turned out to be only a small rise in value, approaching 16.8 dB at 7.13 MHz. Other designs have shown equally narrow peaks well over 20 dB. The mini-sweep was the only way to ascertain the nature of this design's front-to-back behavior at its peak.

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In general, whenever the data leaves potentially significant operating parameters ambiguous or vague, performing supplementary frequency sweeps over narrower frequency ranges is the easiest means of clarification. The ambiguities may not occur solely between graphed points of a sweep. Sometimes initial sweep data will raise questions regarding performance at the edges of the passband, calling for supplemental sweeps--or sometimes, simply for wider sweeps than are indicated by the intended limits of operation.

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Fig. 5 shows the 50-Ohm VSWR sweep of the subject quad model. I insert it here for two reasons. First, it completes the data set most commonly developed by a frequency sweep. However, on occasion, the modeler may find it useful to record (and graph) both the resistive and reactive components of the source impedance. The rates of change of resistance and reactance are often good indicators of the potential of a design for wide-band operation or for the addition of compensatory components to achieve a given source impedance. For example, in some lower HF wire antennas, the resistive component changes very little, while the reactance changes rapidly and almost linearly with frequency. By making such an antenna inductively reactive throughout its range, one may add a series variable capacitor to compensate for the inductive reactance of the antenna, thus achieving a relatively constant resistive impedance that matches a feedline of choice. Second, the SWR sweep in the present case is unambiguous in its indication of the narrow-band operation of the modeled antenna.

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Comparing Antennas via Sweeps

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Frequency sweeps are often very useful in comparing "competing" antenna designs for a given purpose. To illustrate the technique, I shall use a model of a hexbeam and a model of a Moxon rectangle. Neither model is a representation of a commercial antenna. Thus, no conclusions about the inherent potential or limitations of any such design can be drawn from the illustration. Both antenna types are generally interesting because they are compact and employ semi-closed geometries involving coupling between element ends as well as between parallel portions of the elements. The hexbeam looks like two "W" elements with the open ends facing each other. The rectangle is--well, rectangular. Both are 2-element arrays employing a driver and a reflector.

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Performing a frequency sweep of two antennas requires that we take account of normal sweep matters. We should use the same start and stop frequencies, as well as the same frequency increment throughout. Moreover, we should use enough frequency steps to obtain a relatively unambiguous picture of the antenna performance across the passband of interest. Let's use the range of 14.0 to 14.35 MHz as our passband, with an increment of 0.035 MHz. This increment provides 10 steps--or 11 total checkpoints--of operation.

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In addition, the modeler should note any other relevant factors that may affect the interpretation of the comparative output. For example, the hexbeam model in question has a design frequency of 14.10 MHz, while the Moxon was designed for a 14.15 MHz design center. The hexbeam is normally constructed from wire, so #12 AWG wire composes the elements. In contrast, a 20-meter Moxon can be easily fabricated from aluminum tubing, so its model employs 1" diameter elements.

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Fig. 6 shows the comparative free-space gain curves for the two models. Although the hexbeam has a higher gain at the low end of the passband, the rate of decrease in gain is much higher than that of the Moxon. Hence, the Moxon shows a 1 dB gain advantage at the upper end of the band.

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Notice the flattening of the curve of the hexbeam as it reaches the lowest frequency of the sweep. One might raise a question of whether the hexbeam reaches peak gain close to or far from the low end of the band. Hence, supplementary sweeps might be useful over the range from 13.5 to 14 MHz to answer this question.

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In Fig. 7 we find the 180-degree front-to-back curves for the two antennas over the prescribed range of frequencies. Both antennas exhibit the sharp front-to-back peak that marks semi-closed geometries (among others). Whether the absolute peak is higher than the graphed peaks makes less differences to the comparison of designs than the front-to-back ratio as one approaches the passband edges. A difference of 10 dB makes more difference here than at a frequency where the differential is between 30 and 40 dB.

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The 50-Ohm SWR curves for the two models under comparison appears in Fig. 8. Here we can most clearly see the attempt to design one antenna for 14.1 MHz and the other for 14.15 MHz. Although one design shows much steeper curves than the other, both exhibit the properties of closed and semi-closed geometries wherein the curves are noticeably steeper below the design frequency than above it. As well, the fact that one model uses thin (#12 AWG) wire and the other employs 1" tubing also is evidenced in the differences between the curves.

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The exercise has so far been geared toward a comparison of two designs, as if one had only a choice between the two. Of course, one may enter into the graphs as many designs as one likes, taking into account other properties of the antennas that do not show up in performance figures. For example, the total area (or volume) of an antenna may play a role in determining whether a design is a candidate at all. Additionally, one may place variants of the two designs into the picture in order to optimize each. None of these decisions will make any sense without first having a set of design specifications in hand to define what better and worse may mean.

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The one major exception to the need for a set of design criteria has also shown up in our small foray into comparative frequency sweeping. In the process of looking at the differences between the models, we also noted a number of family resemblances borne by all members of the close and semi-closed group of 2-element antennas. For some modelers, these characteristics may be common expectations; for others, they may amount to discoveries about the class of antennas involved. Modeling is not solely for design and analysis--it can also be for learning about antennas.

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Antennas on Different Bands

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Suppose we frequency scale the Moxon rectangle from 20 to 10 meters. We shall approximately halve the element lengths. As well, for proper scaling, we shall halve the element diameter down to 0.5". Now let's define 10-meter coverage as extending from 28 to 29 MHz. Let's use a design center frequency on 10 of 28.5 MHz.

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In recording a comparative frequency scan, we should do two things. First, we shall set up the 10-meter scan in the same number of steps as the 20-meter scan. The 10-step, 11-checkpoint scan is convenient on 10 meters where the increment become 0.1 MHz.

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Second, when we graph the results, we should use some sort of common scale. In this case, the checkpoints are each 10% of the total frequency span. Therefore, a percentage scale becomes very useful.

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Fig. 9 shows the gain curves for the two antennas. Initially, we might think that the two scales should overlap or at least closely parallel each other. However, the size of the passbands differs, not only in total width, but as well as a percentage of the center frequency. The 20-meter amateur band is about 2.47% of its center frequency, while the first MHz of the 10-meter band is 3.51% of the center frequency--a 42% difference. Consequently, over the defined passbands, the gain on 10 meters will show a larger total variation than on 20 meters. In fact, designs that are adequate for 20-meter coverage may require significant alteration is they are scaled and adjusted to cover 28-29 MHz.

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The front-to-back sweeps for the 20-meter and 10-meter Moxons appear in Fig. 10. These curves tell us a great deal about both the performance of the antenna in question and about the design parameters for each model. For example, the 20-meter version used a design frequency of 14.15 MHz, about 42% up from the lower end of the band. Setting the design frequency lower than mid-band takes into account the fact that for this design, the curves are steeper below the design frequency than above it. Displacing the design frequency permits the designer to achieve roughly equal front-to-back ratios at each band edge. In contrast, the 10-meter design was set for 28.5 MHz for 28-29 MHz coverage. As a result, the low-end front-to-back ratio is somewhat lower than the high-end value.

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As well, we can clearly see the consequence of operating the antenna over a frequency range that is a larger percentage of the design frequency, as it is on 10 meters. The average band-edge deficit in front-to-back ratio on the wider band is about 3 dB. Whether this amount is operationally significant is a design-evaluation decision that would require a set of project goals against which to measure the modeled values.

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In Fig. 11, we have the 50-Ohm SWR curves for the two antennas. Once more the relative displacement of the design frequency on the lower band shows up as a much more "centered" SWR curve than the one for the upper band. On 10 meters, the use of the exact passband center as the design frequency results in higher SWR values at the low end of the band. (Remember that the antenna used as an example here is designed for a direct connection to a 50-Ohm feedline, so adjustment of the curve via a matching network is not part of the project.) Besides the offset of the two SWR curves, we can see further evidence of the consequences of using the design over a frequency span that is a higher percentage of the design frequency.

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Linear vs. Multiplicative Steps

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We have looked at only some of the applications of frequency sweeps. Since a frequency sweep yields a NEC core run that produces all of the output data, we also have access to these data, ordinarily in tabular form. Among the most significant data that we might examine are the current magnitudes and phases, perhaps on the parasitic elements of a Yagi. These values may go a long way toward explaining the behavior of an array across an intended operational passband. Additionally, the change of source resistance and reactance across a passband is also valuable information to extract from a frequency sweep. Such data are useful in comparing two designs as well as in designing feedpoint matching systems.

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Most of the work we wish to do with frequency sweeps can be done using linear frequency steps. Therefore, basic NEC-2 programs may limit the user to this option. However, the basic NEC core input system permits another type of sweep. Let's re-examine the frequency input card once more.

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   FR         1         13        0     0     14.00     1.00206
+     Type of Stepping  No. of FQs            Start FQ  Increment
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We have modified the FR entry relative to the entries used throughout the exercise so far by changing the "Type of Stepping" value from 0 to 1. A zero indicates linear stepping, but a 1 activates multiplicative stepping. The start frequency is 14.0 MHz in the example. We can calculate the increment via the following equation

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where M.F. is the multiplying factor, N is the number of frequency steps, fHI is the highest frequency of the sweep, and fLO is the lowest frequency (the "start" frequency). In the example, the 12th root of the ratio of 14.35 to 14 is about 1.0020598.

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For most common purposes, we mentally extrapolate from linear sweeps those performance factors that are functions of a percentage of design frequency rather than strict linear frequency functions. However, on some occasions, it may be useful to view NEC output data more directly in these terms. In such cases--assuming one's program permits the use of multiplicative frequency sweeps--the use of this alternative input may prove beneficial.

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In this small foray into sweeping frequencies with antenna modeling programs, we have certainly not covered all of the potential uses. However, I hope that there is enough here to either get you started on the road toward making good use of the facility.

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Go to Main Index

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34. The Second Ground Medium

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L. B. Cebik, W4RNL

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Way back in the 11th column of this series, I discussed the use of the various types of ground available in both NEC and MININEC. What we by-passed at that time was the fact the these calculating cores permit the use of two ground media. Perhaps it is time to fill in that gap--at least partially. In this episode, we shall look at the use of using 2 ground media to define the ground beneath and away from the antenna.

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In order to keep the discussion focused on using more than one ground medium, I shall restrict the discussion to Sommerfeld-Norton (S-N) high accuracy grounds found in NEC. Multiple media can be defined for both MININEC and NEC real grounds of all sorts, and it is even possible to place a NEC perfect ground beneath the immediate vicinity of the antenna. However, for the sake of focus, I shall stay with the one ground type and concentrate on the 2 ground media possible within NEC..

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To define a single S-N ground, we simply follow the program directions for selecting the ground type and then plug in the values of conductivity (in Siemens per meter) and relative dielectric constant (or permittivity) that define a single medium. This medium pervades and defines the entire ground surface from coordinates 0, 0, 0 to the limits of the antenna's far field. In raw NEC terms, a typical card or entry would look like the following line (spaced out for identification of the entries):

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      GN    2     0           0  0        13    .005
+      Card  Gnd   Nr of       Zeros       D.C.  Cond.
+      Type  Type  Radials
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The "GN" card identifies both the ground type and medium. A type 2 ground is the Sommerfeld-Norton type. We set the number of NEC radials at zero (mandatory for a S-N ground). The following two columns are always zeros. The last two columns specify the relative dielectric constant and the conductivity: the values shown are those for what is commonly taken to be average ground. Note that the GN card accepts the values defining the medium in the reverse order of entry relative to the input system of most commercial implementations, which specify the entry of conductivity first. The ground definition is called in the NEC manual "an infinite ground plane," since it extends in every direction indefinitely. There are further columns, but if they are empty--as in this example--the program presumes that they have zero values. In many places around the NEC core, a zero value is interpreted as an absent value that then plays no role in the calculations or that triggers certain ways of handling the user input.

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As a refresher on the general classification of ground values used in most common sources, I shall repeat a table appearing in the earlier column on grounds. Always substitute more precise values wherever known. The table represents an adaptation of values found in The ARRL Antenna Book (p. 3-6), which are themselves an adaptation of the table presented by Terman in Radio Engineer's Handbook (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. Terman's value for the conductivity of the worst soil listed is an order of magnitude lower than the value shown here.

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Soil Description                    Conductivity      Permittivity      Relative
+                                    in S/m            (Dielectric       Quality
+                                                       Constant)
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+Fresh water                         0.001             80
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+Salt water                          5.0               81
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+Pastoral, low hills, rich
+soil, typical from Dallas,
+TX, to Lincoln, NE                  0.0303            20                Very Good
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+Pastoral, low hills, rich
+soil, typical of OH and IL          0.01              14                Good
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+Flat country, marshy, densely
+wooded, typical of LA near
+the Mississippi River               0.0075            12
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+Pastoral, medium hills, and
+forestation, typical of MD,
+PA, NY (exclusive of mountains
+and coastline)                      0.006             13
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+Pastoral, medium hills, and
+forestation, heavy clay soils,
+typical of central VA               0.005             13                Average
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+Rocky soil, steep hills,
+typically mountainous               0.002             12-14             Poor
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+Sandy, dry, flat, coastal           0.002             10
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+Cities, industrial areas            0.001             5                 Very Poor
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+Cities, heavy industrial areas,                                         Extremely
+high buildings                      0.001             3                  Poor
+

As a reminder, the ground beneath a NEC model is homogenous, whatever the degree of ground penetration by a signal. Real ground may be stratified within the region of ground penetration, especially from the lower HF to the VLF portions of the radio spectrum. Penetration more significantly affects the propagation of signals from vertically polarized antennas than from horizontally polarized ones, but both types are affected to some degree. Any errors created by the difference between modeled homogenous ground and real stratified ground, however, tend to be greater for vertical antennas.

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Fig. 1 shows a 10-meter dipole at a height of 1 wavelength above ground. With a single ground medium, we obtain an elevation pattern like the one shown in Fig. 2. Everything in the pattern--including the gain, the elevation angle of the lowest lobe, and the number of lobes--should be familiar to even relatively new modelers.

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So far, we have a modeling situation of no great interest or significance. However, there are numerous circumstances in which we may wish to simulate multiple ground media. As one hypothetical case, let's assume that the dipole we just examined is about 1 wavelength from the ocean.

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Let us restrict ourselves for the moment to using a circle to define the limits of the inner medium. There are other possibilities, but mastering them one at a time will be the order of the day. If we happen to be interested in the radiation toward an inland location, we can use the single medium model. If we are interested in the radiation out to sea and beyond, we can use the next model to emerge.

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When we use more than one medium, NEC calculates the current distribution and source impedance of the antenna based on the inner medium. The combined media play a role in the far field calculations. To specify a second medium, our GN card might look like the following entry:

+ 
      GN    2     0           0  0        13    .005        81    5           10.7
+      Card  Gnd   Nr of       Zeros       D.C.  Cond.       D.C.  Cond.       Boundary
+      Type  Type  Radials                 [Inner Med.]      [Outer Med.]      Radius
+

This card specifies two media, an inner and outer, with the inner medium having average soil values and the outer one having salt water values. The boundary radius tells us how far (in meters) from the coordinate system origin that the outer medium begins. Note that boundaries are always specified in terms of distance from the 0, 0, 0 point of the coordinate system, not necessarily from the antenna. Since we can alter the coordinates of the antenna elements, we can place it anywhere in the inner medium region.

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To obtain a far field NEC-2 plot that takes account of the outer medium, we have to make a change in the requested plot or RP card. The normal mode has a value of 0 in the first integer slot of the RP card. For a radial boundary between 2 ground media, we change this number to 3. There are other values, but for 2 media with a radial boundary--the limits of this column--the 3 will cover all our work. (If we leave the value at 0, the far field will be calculated in NEC-2 using only the inner medium, as if it extended indefinitely. Wherever a commercial program does not ask for a user change to the radiation pattern set-up, it is made automatically when the user specifies a second medium.)

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Fig. 3 provides an elevation plot for the antenna in its new environment. Note the increase in gain for the lobe at 14 degrees. Note also the nearly "knife-edge" change in gain value within the second lobe. Reality would not likely in this kind of case provide such a sharp change in gain. However, the boundary between modeled ground media is a sharp change and shows up as such in the calculations. The lower values of signal strength at higher angles result from reflection from within the inner medium (at least in part). The approximate 45-degree elevation changeover point for the 1 wavelength boundary radius is no accident.

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In this example, both ground media are at the same level, namely Z=0. However, we can go a step further in defining media by placing the outer level at a lower height by a defined amount. Let's assume that our salt water is a full wavelength below the ground beneath the antenna itself, which is above the ground by a wavelength. Then our GN card takes on this appearance:

+ 
GN    2     0           0  0        13    .005        81    5           10.7        10.7
+Card  Gnd   Nr of       Zeros       D.C.  Cond.       D.C.  Cond.       Boundary    Neg.
+Type  Type  Radials                 [Inner Med.]      [Outer Med.]      Radius      Outer
+                                                                                    Height
+

The new number (again in meters, even if user interface entry is in other units) represents the distance by which the outer medium surface is below the inner medium surface. A commercial program might call for a negative number as an input to remind the user that the outer medium can never be higher than the inner medium. However, the NEC card requires that this value of lower ground be entered on the card as a positive distance downward. 10.7 meters is about 1 wavelength at the 28 MHz test frequency for the model we are using.

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Fig. 4 presents the modeled elevation pattern for our old dipole in its revised environment. Note that the lowest lobe has dropped to 7 degrees, since the antenna is now about 2 wavelength above the medium most affecting far field patterns at elevation angles below 45 degrees. At that angle, the inner medium exerts the dominant effect. The model once more shows the knife-edge effect presented by the models sharp boundary--something unlikely in reality. However, the lower lobes are likely to be reasonably accurate with respect to a real situation.

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Let's change the scenario to explore some other modeling results that you may expect from NEC calculations with multiple media. The first move is the change our dipole into a vertical dipole for 30 MHz and to set its lowest point about 3' above ground. Fig. 5 shows the general scheme.

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Initially, let's set the antenna over a single ground medium defined as "very poor" (Cond. 0.001 S/m; D.C. 5).

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Fig. 6 presents the elevation pattern of the antenna over its very poor soil. Note the very modest gain figure for the antenna under these conditions.

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Next, let's make a change. Let's place a modest ground screen or ionizing salts in the ground in an effort to improve its quality. Let's estimate that the result is ground that qualifies as very good (Cond. 0.0303 S/m; D.C. 20). We shall leave the overall playing field level, but make the radial boundary 1/4 wavelength from the point beneath the antenna. Outside the boundary, the ground values remain at the very poor level.

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Now, a warning. What follows is what the NEC model reports and no more. No claim about reality is made for the purposes of this note.

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Fig. 7 shows the elevation pattern of the antenna with the revised soil conditions. The antenna shows a tad less gain and a slight increase in the elevation angle of maximum radiation. The ground improvement did not extend to the major portion of the fresnel or reflection zone of the antenna and hence does not show an improvement in radiation at low levels. This result is typical of modeling outputs for vertical antennas that do not use a set of radials as both a ground plane and antenna element completion, such as the group of 1 wavelength loops fed as vertically polarized antennas. As a useful exercise to acquaint yourself with multiple ground media, you may wish to change the inner medium values across a range of values, including but not exceeding those for salt water. There are some reports that values higher than those for salt water may yield inaccurate modeling results.

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For our next example, let's increase the frequency of our vertical dipole to 300 MHz to simulate another common situation: the placement of an antenna over a building top. To simplify matters, we can work in meters, since the nearly resonant vertical dipole is a bit shorter than 0.5 meters. Initially, we shall place the base of the antenna 5 meters above a single ground medium consisting of very good ground (Cond. 0.0303; D.C. 20).

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Fig. 8 shows the elevation pattern for this model. Note the gain of nearly 6.5 dBi at an elevation angle of 2.5 degrees. (In working with antenna more than a very few wavelengths above the ground, you will often obtain greater accuracy by reducing the pattern steps from 1 degree to about 0.1 degree, especially for elevation patterns.) These values are typical for VHF vertical dipoles.

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Now, let us make the case interesting. Let us assume that the antenna is 5 meters above a modestly tall building, perhaps 5 meters high. We shall assume--in order to preserve our simplified RP value of 3--that the building is circular and has a diameter of 10 meters, with the antenna mounted in the exact center. Beyond the building, the soil is very poor (Cond. 0.001; D.C. 5). Fig. 9 illustrates that situation.

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The GN card for this antenna looks something like the following lines:

+ 
GN    2     0           0  0        20    .0303       5     .001        5           5
+Card  Gnd   Nr of       Zeros       D.C.  Cond.       D.C.  Cond.       Boundary    Neg.
+Type  Type  Radials                 [Inner Med.]      [Outer Med.]      Radius      Outer
+                                                                                    Height
+
+ +
+

Fig. 10 provides the modeled elevation pattern for our VHF antenna atop the building. The "cliff" (as it is called in NEC manuals) results in a 1.2 dB gain for the antenna, with nearly half the elevation angle for the main lobe. As well, the increased radius (as a function of a wavelength) results in a lower angle for the transition between dominance by the inner and by the outer media--about 25 degrees.

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As an exercise, to increase further your familiarity with modeling results using 2 media, you might place antennas of various sizes (or resonant frequencies)--both horizontal and vertical--over this building and compare the results with their counterparts using a single medium. For some HF antennas, do not be surprised to get knife-edge effects the cut a lobe into a stronger and weaker part.

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Once more, reality may or may not exhibit the sharp change in pattern lobes. Remember that the roof top was considered a homogenous ground material having enough metal in it to simulate very good soil. Real buildings may range from very poor to even better than very good, depending on their composition and the frequency of the antennas involved. I chose the very good rating for the example with the assumption of there being a good bit of metal in the upper structure under the roof. In reality, both the amount and the arrangement of the metal may play a significant role is determining how good a ground medium a given roof top makes.

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Let's perform an additional experiment. Remember that the coordinates for a ground medium be 0, 0, 0, the coordinate system origin. However, there is no restriction on where we place our antenna. Therefore, let's return to the 30 MHz vertical dipole and place it about 1 meter (3') above the inner medium, which simulates a circular roof top. Next, let's place it 0.1 m from the building edge by changing the X or Y coordinate by 4.9 m.

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Fig. 11 shows the results of our move in an elevation pattern for the antenna. The shift in antenna position results in a pattern displacement over the edge of the building. At the same time, we see the emergence of higher-angle energy in the direction over the building edge. Although the displacement is--for most purposes--hardly fatal to the new antenna placement, the practice of modeling the antenna position as exactly as possible over or on the inner medium shows its merits. However, beware of placing the antenna beyond the inner medium. Because NEC will calculate the impedances and current distribution based on the inner medium, the results may not be accurate.

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We can specify the boundary between media as either a radius or a linear boundary. In NEC-2, the difference appears in the RP card, where the mode is specified as 2 rather than 3. The linear boundary occurs parallel to the Y axis as a value for X. To see the difference, let's look at two azimuth patterns of our 30 MHz vertical dipole. First, we shall examine a circular or radial cliff. With the antenna near the edge of the building--at 0.1 meter from the building edge, which is point X on Fig. 12--the alteration produced by the antenna position is a slight offset in the circular azimuth pattern.

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When the "cliff" is linear, it extends indefinitely and creates a larger change in the far field azimuth pattern. Fig. 13 illustrates the pattern from our 5-meter tall building with the antenna 0.1 meter from the edge. As an exercise, one might wish to run a selection of models in which the only difference is the type of boundary between the inner and outer ground media.

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We have restricted ourselves to S-N ground using two media with a radial boundary between them. These are not the only possibilities that NEC offers. For example, if we change to the NEC fast or reflection coefficient ground system, we can create a set of radials beneath the antenna. We can also add our second medium by the use of a GD (Ground Description) card instead of expanding the content of the GN card. For example, if the 2-media GN card were to look like this:

+ 
+GN    2     0           0  0        20    .0303       5     .001        5           5
+Card  Gnd   Nr of       Zeros       D.C.  Cond.       D.C.  Cond.       Boundary    Neg.
+Type  Type  Radials                 [Inner Med.]      [Outer Med.]      Radius      Outer
+                                                                                    Height
+

Then the corresponding pair of (NEC-2) GN and GD cards would have this appearance:

+ 
+GN    2     0           0  0        20    .0303
+Card  Gnd   Nr of       Zeros       D.C.  Cond.
+Type  Type  Radials                 [Inner Med.]
+
+GD       0  0  0  0      5       .001      5           5
+Card    (  Zeros   )     D.C.    Cond.     Boundary    Neg.
+Type                     [Outer Med.]      Radius      Outer Height
+

(Note: in NEC-4, the first GD integer position--a zero in NEC-2--uses a 1 for a linear boundary, a 2 for a circular boundary, and a 0 for no second medium. This system replaces the options found in the RP card for NEC-2. A NEC-4 card for the current outer medium would begin GD 2 0 0 0. . ., with the remainder as shown.)

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Whether one uses a single GN card or a GN-GD pair, the calculations would provide the same output. Commercial implementations of NEC tend to favor the use of the GD card for the second medium. Not all low-end programs allow the full spectrum of ground potentials. Multiple ground media may require advancement to a professional version of some programs.

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Although we have not surveyed all of the ground type and descriptions available in NEC, perhaps this much of a start may be useful. It pays to be well-grounded in NEC's multi-media potentials.

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Go to Main Index

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35. Notes on Using AZ-EL Plots Effectively

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L. B. Cebik, W4RNL

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The most common use for azimuth (AZ) and elevation (EL) plots might be summed up in the following example:

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Suppose that we have a 3-element Yagi designed for 28.5 MHz composed of 1/2" diameter elements placed at a height of 35' above average ground. The following table describes the model of this antenna.

+ 
3 el Yagi 1/2" al elements                   6/12/00     8:55:55 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 28.5 MHz.
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.          End 1     Coord. (ft)              End 2     Coord. (ft)     Dia (in)  Segs
+     Conn.      X       Y       Z       Conn.      X       Y       Z
+1            -8.595,      0,     35              8.595,      0,     35       0.5    21
+2            -8.207,    5.2,     35              8.207,    5.2,     35       0.5    21
+3            -7.722, 11.212,     35              7.722, 11.212,     35       0.5    21
+
+Total Segments:  63
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       2        50.00      50.00    11       1           0         V
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The 3-element Yagi would look, in outline, like Fig. 1.

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Most of us have grown accustomed--perhaps too much so--to examining the AZ-EL plots for only a small amount of information: maximum gain, front-to-back ratio, and elevation angle of maximum radiation. Since we know that the maximum forward gain of the antenna is (literally) straight forward, we can begin with an elevation plot by setting the azimuth angle for it along the axis we chose as the front-back direction. In this case, let's assume that the element stretch from end-to-end along the X-axis, which makes the Y-axis the standard beam direction. So we shall set the AZ heading to 90 degrees. The resulting EL pattern looks like Fig. 2.

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From Fig. 2, we pick up the maximum gain figure (13.35 dBi) and the take-off (TO) angle (elevation angle of maximum radiation): 14 degrees. The next step is to call for an AZ plot, setting the elevation angle to 14 degrees. The result looks like Fig. 3.

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An examination of Fig. 3 yields a confirmation of the maximum gain as well as the front- to-back ratio: 25.05 dB in 180-degree F-B terms.

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Very often, we neglect much of the information that is also included on these plots. For example, the horizontal beamwidth to the -3 dB or half-power points is 63.4 degrees. This data gives us some idea of the coverage of the antenna without having to change beam heading. It should also inform us of why it is a fairly futile exercise to try to orient a beam such that the reference heading of our rotator is correct to under 1 degree.

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The EL plot informs us that the vertical beamwidth to the -3 dB points is 14.4 degrees. Although the horizontal beamwidth was composed of symmetrical pattern portions left and right of the centerline, we should never assume that the same is true of a vertical beamwidth value. In this instance, the symmetry around the centerline is not severely distorted. The upper -3 dB point is 6.6 degrees above the TO angle and 7.8 degrees below the TO angle. Our coverage to the half-power points ranges from 6.6 to 21 degrees, covering most of the skip angles we are likely to encounter on 10 meters.

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Also notable in the elevation pattern is the secondary lobe at a higher angle. The plot informs us that its angle of maximum radiation is 45 degrees and that it is more than 3 dB weaker than the main lobe.

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How we use this information to evaluate the potential performance of the antenna involves a number of factors that go beyond what the model tells us. First, we have to determine the weight to give each element of the information relative to the purpose for which we might install this antenna. Second, we must factor in information that may alter the reliability of the modeled numbers relative to the actual site situation of the antenna itself. For example, terrain variations may require special treatment outside the realm of NEC modeling to determine more precise expectations of the antenna when pointed in various directions.

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Having said this much about AZ and EL plots, we tend to stop our investigation. In doing so, we often deny ourselves useful data that might be supplied by a few supplementary plots. Here are a couple of examples--using the same initial model--of what we might learn.

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Case 1--an alternative direction: Suppose that we have the 3-element Yagi set on a certain heading, perhaps the primary direction for communications. Now further suppose that there is a secondary heading about 20 degrees to the right of the primary bearing--with the new heading indicating a station or set of stations with which we wish to communicate.

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One solution to this situation is to move the beam heading by 20 degrees. However, one might wonder whether this solution is necessary. The ultimate answer to the question might well involve the type of operation involved. Casual contact leaves the operator plenty of time to change the antenna direction. However, there are contest and similar operational contexts in which every movement that can be classified as unnecessary is eliminated as part of the operational strategy. Hence, for some contexts, the decision to move or not to move the antenna heading may acquire some significance.

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One important piece of data that might enter into the decision process is how much signal strength we might lose by not moving the antenna. Alternatively, we can ask how much signal strength we would have in the secondary direction if we leave the heading in the primary direction. The answer is as simple as requesting a new elevation plot using a heading that is in the secondary direction.

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For such plots, it is useful to set the outer ring of the plot at the maximum gain obtained from our initial elevation plot--in this instance, 13.35 dBi. The resulting elevation plot will then show graphically as well as numerically the difference in signal strength. Fig. 4 shows the new plot.

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From the EL plot, we can discover that the gain in the secondary direction is 12.17 dBi, down 1.18 dB from the primary direction. Although we might have estimated these values from the initial azimuth plot, the ability to request alternative EL plots for any AZ bearing can provide a table of values that can contribute either to operational planning or to an evaluation of the potential antenna performance.

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Case 2--an alternative elevation angle: The TO angle or elevation angle of maximum radiation is not the only elevation angle that is important. An adjunct to many types of operation are programs and other sources that predict propagation. The predictions may also include estimated skip angles for different frequencies. These predictions in the short term may open the question of just how effective our subject antenna might be at its present height. Over a longer term, we might question whether or not it would be useful to change the antenna height to obtain better results.

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Suppose, then, that we are interested in a skip angle of 10 degrees--4 degrees lower than the TO angle that we initially obtained from our general analysis of the 3-element 10-meter Yagi. We can simply set the elevation angle for an AZ plot to the 10-degree mark. Once more, it is useful to set the outer ring of the AZ plot to the maximum gain level from our initial analysis--13.35 dBi. Then, the new AZ plot will graphically as well as numerically show the difference in signal strength. The result appears in Fig. 5.

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From Fig. 5, we learn that the forward gain at a 10-degree angle is 12.67 dBi, about 0.68 dB less than at the TO angle. We may also note in passing that the front-to-back ratio changes by only an insignificant amount. Just how we factor this information into the overall operational and construction planning will depend on all of the additional factors we have so far noted. Since we can request AZ plots for any elevation angle, we can develop detailed information across a spectrum of possible skip angles. Of course, all such data must be adjusted for any terrain affecting signal propagation to the antenna and its site.

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These two cases are only the beginning of the kind of information that we can gather if it is useful to us. For example, if we propose to raise the height of the antenna--anywhere from the present height of 35' to an upward limit of 200'--we may wish to develop detailed data about beamwidths and angles. The higher we raise the antenna in terms of wavelengths above ground, the more elevation lobes we shall encounter. Even though the lowest lobe is usually the main lobe of interest, we must also note that each lobe will have a narrower beamwidth as we increase the antenna height. This factor should be added into the data mix we obtain relative to potential skip angle we may encounter in operation. If the antenna surpasses certain heights (in terms of wavelengths above ground), we may discover that the null between the two lowest lobes potentially deprives us of possible communications paths on some occasions.

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For some of the necessary planning data, tables of values may suffice. In other instances, overlaying elevation plots can provide a graphic portrayal of both advantages and disadvantages.

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The cases we have been examining were based upon simple variations upon an initial determination of the antenna's maximum gain and the elevation angle at which it occurs. For many types of antennas whose general properties at a given frequency are well established, this procedure works well and leads us quickly to the desired supplementary information. However, not all antenna properties are well known in advance for some frequencies of operation.

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As a case in point, consider the antenna in Fig. 6. It is a 40-meter off-center-fed antenna, with the transmission line set at approximately the 300-Ohm position on 7.15 MHz. The antenna is of #14 wire and models a transmission line of about 410 Ohms, that is, 1" wire separation. The line is 35' long, with the antenna positioned 70' above average ground.

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The question we might pose is what the maximum gain might be for the antenna and at what TO angle, if we operate the antenna on 28.5 MHz. For our exercise, we shall present the antenna along the X-axis so that in the plots to follow, it would appear as a line from left to right across the center of the azimuth plots.

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We shall quickly discover that the antenna pattern is neither broadside to the wire nor off the wire ends at the frequency of operation. In order to answer our questions, we shall have to develop a procedure that allows us to "creep up" on the values for maximum gain and TO angle.

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In many instances, experience with similar antennas may let us start the process fairly close to the final values. However, for illustrative purposes, let's choose an arbitrary beginning point. We shall take an azimuth pattern at 14 degrees elevation and see where it leads. The pattern appears in Fig. 7.

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From the azimuth pattern we obtain 2 critical pieces of data. For reference, we shall record the gain (a low value of -0.83 dBi). As well, we shall record the azimuth angle of maximum radiation: 177 degrees.

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The next step is to request an elevation pattern at the azimuth angle of 177 degrees. From this elevation pattern, we obtain a new elevation angle of maximum radiation, 141 degrees. So we request an AZ pattern, using the new EL angle value. We continue the process until the AZ and EL patterns provide the same gain value and until the EL and AZ angle coincide on the respective plots. For this exercise, the following table summarizes the steps that led to final values.

+ 
Preset            Preset      Current           Max. Gain         Angle of
+Angle Type        Angle       Pattern Type      dBi               Max. Gain
+  EL                14          AZ              - 0.83             177
+  AZ               177          EL                6.20             141 (39)
+  EL                39          AZ                6.60              19
+  AZ                19          EL                7.11              22
+  EL                22          AZ                9.02              34
+  AZ                34          EL                9.76               7
+  EL                 7          AZ                9.90              37
+  AZ                37          EL                9.90               7
+

Note first that the last two steps in the table replicate the maximum gain. As well, each plot uses the other's angle of maximum radiation as the preset angle. This is generally the sign that one has arrived at the correct gain and angle values. There are some patterns so complex that it may be necessary to sample other regions of the overall plot fields, but these tend to be rare. Ordinarily, the number and placement of lobes will be a guide to suggesting further exploration.

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Fig. 8 provides a second factor to note. The AZ pattern clearly shows a null in the final pattern just where the initial pattern shows a lobe maximum. In the exploration of complex structures, it is never wise to assume that an AZ pattern retains a particular shape as we change the elevation angle. Although the antenna we used in the exercise seemed to be simple in structure, it was actually fairly complex. The horizontal portion consisted of a 2 wavelength collinear element. Since the parallel feedline does not have equal currents at its terminals, the line is unbalanced and makes a net contribution to the overall radiation pattern. The result is a complex radiation pattern whose elevation plots change with every change of azimuth bearing.

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Part of the pattern complexity appears in Fig. 9. We should note that the AZ heading for this plot is 37 degrees, that is, an angle that is neither along the plane of the wire nor broadside to it. In any data presentation, it is usually useful to mention this fact, since viewers tend to make erroneous assumptions about the azimuth bearings of elevation plots unless the correct bearing is called to their attention. It is for this very reason that I have moved the data from outside the plot region directly into the plot area.

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In addition, we may note that the special elevation angle that was counted on a 0-180 degree scale. When counted above the horizon, the angle of 141 degrees translated to 39 degrees. Some programs restrict elevation angles to the range of 0 through 90 degrees. Had we used the 141-degree angle, the maximum gain heading would have appeared on the opposite side of the plot. That position might well have led to wrong conclusions about the actual direction of maximum radiation.

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One technique for sorting out the various lobes, nulls, and oddities (if any) of the overall radiation pattern of a given antenna is to use a 3-D plot. 3-dimensional plots are commonly found in commercial implementations of NEC (and MININEC). They generally use a larger step size between azimuth and elevation pattern readings than might be used in 2-dimensional AZ and EL in order to speed the execution of the plot. However, they can be valuable adjuncts to the detailed information provided by standard AZ and EL plots.

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Fig. 10 provides an oblique view of the OCF that we have been exploring. Although the wider step size changes smooth curves into sharp angles, we can clearly see the exceptionally complex structure of the lobes and nulls at most elevation and azimuth angles. The pattern is oriented to place the strongest lobes, as revealed by the AZ and EL plots in Fig. 8 and Fig. 9, in the foreground.. (Hence, the axis letters appear as mirror images.)

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Fig. 11 presents a 3-D view of the patterns as viewed down the antenna wire from its end. This view is useful to establish that there are no broadside patterns stronger than the one we identified as the lobe of maximum gain. As well, we can see that there are no significant lobes below the angle of maximum radiation.

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Fig. 12 presents a 3-D view of the pattern with the wire running directly from left to right. This view gives us a sense of the strength of the pattern off each of the antenna ends, with the long side of the antenna obviously yielding the strongest pattern. The view also confirms that there are no lobes at upper levels stronger than the one identified as the lobe of maximum radiation.

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Some programs enable the user to specify a 2-D pattern from within the context of the 3-D pattern. To use this provision, one simply specifies graphically the "slice" desired for the 2-D view. In many cases, using both 3-D and 2-D patterns in conjunction can resolve more quickly the problem we set for ourselves of identifying the lobe of maximum radiation strength.

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With some antennas--for example, VHF antennas a large heights above ground, the multiplicity of elevation lobes may elude 3-D analysis and yield a false picture of the radiation pattern structure. A pattern, whether 2-D or 3-D, simply connects the dots between readings. 5 degrees is barely sufficient for lobe identification at the frequency and height of the present antenna. For 2-D patterns, 1 degree steps between readings generally suffices for most HF antennas at any reasonable height and for VHF antennas at lower heights. Above about 5 wl in height, the use of a 0.1-degree step is advisable in 2-D plots in order to ensure that you capture all elevation lobes.

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The cases we have examined in no way exhaust the potentials for AZ-EL plots to provide the modeler with useful information. However, they hopefully provide a start toward making new and productive use of this facility for those whose work has not yet gone beyond the "standard" sorts of patterns with which we began.

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Go to Main Index

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36. Getting a Grip on AZ/EL and Phi/Theta

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L. B. Cebik, W4RNL

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Among the unappreciated subtleties of NEC (in any version from -2 to -4) is the fact that the radiation pattern outputs make use of different conventions from those we ordinarily apply to antennas in both amateur and field engineering work. We tend to think of the horizontal dimensions for an antenna pattern in azimuth terms, which correspond to the headings on a standard compass. For elevation, we count from the ground upward.

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However, the NEC core does its work with radiation patterns using the conventions of phi and theta angles. Folks using "raw" NEC must either adopt the phi/theta angle counting scheme or be ready to make conversions into azimuth/elevation (AZ/EL) on a scratch pad. Those using commercial implementations of NEC have access to pre-conversions that show up as AZ/EL headings in the graphical and tabular outputs of NEC programs. In some programs, users may have a choice of graphical labels for some plots.

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However, not everything may be as it seems, that is, as pure elevation and azimuth plots. Therefore, perhaps it may be useful to start at the beginning and carry ourselves into the conventions used by at least a couple of commercial programs. In this way, we can become prepared for almost anything.

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In the course of our discussion, we shall uncover some implementation schemes that use the term "azimuth" but which are not quite pure azimuth structures. Our purpose in noting these departures is not to be critical. Very often, there are good programming reasons for the variants. We need to understand what is before us and how to interpret it well, and that will be our primary goal in looking at the structures of pattern plots.

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Elevation and Theta

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The simple beginning in our effort to get a handle upon both theta angles and elevation angles is to differentiate the two systems. The rule of thumb goes something like this: theta angles count downward from the zenith heading (directly overhead along the Z axis on the coordinate system). Elevation angle count from the horizon upward. Hence, for starters, we can think of a horizon as 90 degrees theta or zero degree elevation. Likewise, directly above the antenna is zero degrees theta and 90 degrees elevation.

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This simple convention works well for some purposes. For example, when we specify the elevation angle in a commercial version of NEC, we enter a value between 0 and 90. Likewise, if we specify a theta angle, we normally specify a value between 90 and 0. This practice is necessary when requesting an azimuth pattern for an antenna over real ground.

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However, this step is only the beginning of our understanding of how NEC counts. Examine Fig. 1.

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The circle in Fig. 1 represent a free-space 360-degree set of bearing that is possible for an antenna in free space. For antennas above ground, we use only the upper half of the circle. To understand how the NEC calculating core performs its radiation pattern duties, let's look on the inside of the circle. By convention, the direction to the right is the primary heading for theta (and for elevation) angles, and its theta value is +90. As we move up the circle, the angle decreases to 0. Moving back down the circle to the left, we find -90 as the value. This scheme is convenient, since for antennas above the horizon line, we have values between 0 and 90 in both directions.

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The situation becomes somewhat more complex if we extend the circle to the full 360 degrees for a free space pattern. By the time we return to our starting point, the inner circle reads -270. In many ways, this is a perfectly sensible scheme, since we can simply specify +90 degrees as the finish point for any theta pattern, whether over ground or in free space. The starting point then becomes 90 degrees minus 180 degrees for patterns over ground or 90 degrees minus 360 degrees for patterns in free space. (Remember that for NEC-2 patterns over ground, direct horizontal values (+90 and -90 degrees theta) are illicit.)

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If we turn our attention to the labels outside the circle, we encounter the conventions applicable to elevation patterns. Over ground, we have two choices, in the main. We can count upward from the right from 0 to 90 degrees overhead and back down to 0 at the left horizon point. Alternatively, we can count from 0 to 180 degrees moving from the far right to the far left. This latter scheme is useful when we wish to deal with a free- space pattern, since we can continue the count to the low point value of 270 and than back to 360 or 0 degrees.

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Notice that on a circle, theta values increase in a clockwise direction, while elevation values increase in a counterclockwise direction--if we adopt the convention of placing the prime direction or orientation to the right on the graph.

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One of the commercial implementations of NEC that I use, EZNEC, uses elevation angles instead of theta angles, since elevation is the standard used by most practical antenna folks. The program's graphical output for elevation patterns of all types uses a single set of labels, shown in the free-space pattern for a 3-element Yagi in Fig. 2.

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The EZNEC scheme exactly follows the conventions shown in the general scheme in Fig. 1. Incidentally, version 2 of EZNEC is used for this exercise, since the patterns show the labels at all times. Version 3.0 is now available for Windows, but uses the same scheme. However, the graphical angles are not labeled.

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The other NEC program that I use is NEC-Win Plus. It offers the user a choice of theta or elevation angles for the plots. Moreover, the user can also select from 4 different sets of labels for elevation/theta plots (with the designations arranged from left to tight on the actual graphic):

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  • 1. -90/0/90 (theta)
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  • 2. 180/90/0 (elevation)
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  • 3. 0/90/180
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  • 4. 0/90/0
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The first two selections replicate the standard theta and the elevation scheme also used by EZNEC. The third option is useful for reversed patterns. The fourth provides elevation angles in simple numbers for both directions away from the zenith. Fig. 3 provides a sample of a free-space pattern using the 0/90/0 scheme. Notice that area below the hypothetical horizon uses negative values, with the lowest point using a -90 degree value.

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Differences in the conventions used--either as provided by the software writer or as selected by the user--begin to show up in elevation patterns for antennas above ground. Let's set our 3-element Yagi about 1 wavelength above ground. In the EZNEC scheme, the new elevation pattern looks like Fig. 4.

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The 0-90-180 degree counting scheme (from right to left) requires that the user do some mental or pencil arithmetic to determine the elevation angle of the lowest rear lobe in the figure--which happens to be 13 degrees--the same as the main forward elevation angle. Not all antennas yield such symmetry.

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The NEC-Win Plus pattern (Fig. 5), using the 0/90/0 degree elevation scheme obviates the need for the simple arithmetic, although accurate location of the rear lobe angle would require that I alter the graphic by choosing 1. thinner lines for the plot and 2. a full screen plot that would be too large for easy replication in the format used in these columns. Both programs offer a wide selection of color and line widths to suit user preferences and specific applications of the graphics.

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In general, the differences between implementations of elevation pattern heading conventions is too slight to make a difference in how we use the programs. In all cases, we can easily arrive at the elevation angle we need to use in the overall antenna analyses we perform.

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Azimuth and Phi

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Theoretically, the differences between azimuth and phi angle systems are less complicated than those for elevation and theta. With azimuth and phi patterns, we always count a full 360 degrees around a circle, as shown in Fig. 6. We simply count in different directions. However, the use of the upper point of the circle as the stating or zero point is arbitrary.

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The inner part of the circle shows the phi counting scheme (used by the NEC core), which moves counter-clockwise around the circle. The outer labels show the standard azimuth scheme, which counts clockwise around the circle. The two schemes coincide at zero and 180 degrees.

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Some small difficulties of user orientation arise when implementations of NEC develop the azimuth pattern graphics for their programs. Then we begin to see some variations on the standard azimuth scheme. Most of the variations result from the fact that converting a phi pattern requires--for complete conversion to azimuth conventions--a full conversion of the data table that NEC produces. A simple re-labeling of the headings will not suffice to do a complete job. Hence, we find some shortcuts.

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Fig. 7 shows the azimuth pattern of our 3-element Yagi at a height of 1 wavelength above ground. By setting the elevation angle to the "take-off" angle or the angle of maximum radiation (13 degrees in this case), we obtain an azimuth pattern. Note that EZNEC (Version 2) sets the zero point to the right. In this manner, the background graphical setting, consisting of dots and heading numbers, is the same for both azimuth and elevation patterns. However, 90 degrees is not clockwise to the left of the zero point, but counter-clockwise to the right of the zero point. Hence, EZNEC's patterns are actually phi patterns.

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In the latest (Windows) version of EZNEC, the label-less pattern grid avoids the problem of orienting oneself to either phi or azimuth conventions. The user has a choice between counting counter-clockwise from zero (the phi convention) or using compass bearing (the azimuth convention), but this choice shows up only in data entries.

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In Fig. 8, we see the NEC-Win Plus azimuth pattern for the same antenna under the same conditions. NEC-Win Plus sets the zero point at the top of the graph and labels everything in standard azimuth terms. So far, it appears that orientation in the azimuth scheme presents no problem at all.

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The question of orientation toward the graphical pattern outputs does not become readily apparent until we decide to construct models in alternative ways to those most often used. For example, all of the models of the 3-element Yagi we have so far examined extend their linear elements along or parallel to the Y-axis. The forward portions of the antenna (or the front end of the boom) has a positive value on the X-axis, while the rear has a negative X-value.

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Now let's reverse the procedure. We shall model the same antenna with the linear elements extended left and right along or parallel to the X-axis. The front of the array will have a positive Y value, and the rear will have a negative Y-value. If we run this model, it will show exactly the same gain, front-to-back ratio, source impedance, and element currents as the first model. So the only remaining question is how it will appear in the azimuth pattern graphics.

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Fig. 9 shows the EZNEC version of the azimuth pattern. The forward lobe points toward 90 degrees, the heading of the Y-axis for positive values. However, contrary to azimuth conventions, the graphical heading is counterclockwise relative to the zero point. In short, we have a phi pattern.

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In Fig. 10, we have the NEC-Win Plus azimuth pattern. In this case, standard azimuth counting is employed in a clockwise direction. However, to place the pattern without converting the NEC table, the forward heading of the pattern now points to 270 degrees, the opposite direction of the positive forward Y-values (which would normally go to 90 degrees on a standard azimuth pattern).

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My point in setting these items into print is not either to review the two software implementations of NEC or to be critical. Rather, the aim is to orient the user so the he or she understands how to read the data that appears on these patterns. Initially, the difference of each from standard azimuth patterns are negligible because the antennas for our test produce symmetrical patterns along their centerlines. Hence, left and right make no difference at all.

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Not all antennas yield symmetrical patterns, and in some cases, left and right can make anywhere from a small to a large difference.

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To illustrate, let's use an antenna with only a small non-symmetry. It is a parasitic beam for 2-meters at a height of about 30' and modeled with the elements in the +/-X axis and the forward direction as a positive value of Y. Fig. 11 is the azimuth pattern in EZNEC, with the forward direction at 90 degrees. However, notice the rear quadrants, where the pattern becomes obviously larger on one side than on the other. The pattern in this case shows the larger lump at about 215 degrees, about 125 degrees from the forward direction. The actual point in the rear where the signal strength is greatest is on the more diminutive rear lobe, about 125 degrees in the other direction from the forward lobe centerline. Note that we have to determine each differential by arithmetic. As well, the increasing values of the heading as we moved left would be what we might expect had we been using a phi pattern rather than an azimuth pattern. +
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In Fig. 12, we see the NEC-Win Plus equivalent pattern. The bearing differentials are the same, but this time measured from a forward heading of 270 degrees--180 degrees in reverse of our expectations from having set the forward heading in the positive direction along the Y axis. However, the increasing values to the right of the forward lobe is consistent with the standard azimuth conventions.

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In each case, the exigencies of software development have created slight differences in the manner in which azimuth patterns are portrayed. For a symmetrical pattern, the differences make little or no difference and one can make few errors by virtue of the non- standard presentations. However, with non-symmetrical patterns, errors are possible. Although not likely to be significant in the case we are using as an illustration, the errors might well be important in other instances. Many off-center-fed multiband antennas, for example, show a pattern that is very sharply stronger to one side of center than to the other. There are arrays that are directional by virtue of the element phasing relationships rather than by virtue of geometry. In all such cases, the critical question is this: which side is which?

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The answer is fairly straightforward: ignore the heading numbers and place yourself as an ideal observer at the center of the pattern. Face in the direction that represents forward in the coordinate system within which you created the antenna structure. Non-symmetries will now be correctly identified in terms of left and right relative to your position. If you place a zero or north in the direction you are facing, then east will be to your right and west to your left. The pattern will be correct in either program for this way of looking at things.

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Fig 13 is a graphic representation of the way to ensure that you are correctly oriented toward non-symmetrical azimuth patterns, whatever their outer markings. Imagine yourself at the center of the antenna and the pattern. The antenna we are using here is a 2- element half-square--hence, the vertical elements at the ends of the horizontal phase lines. Since the horizontal members are parallel to the X-axis, the forward direction is in a positive direction in the Y axis. Notice that the feedpoint is on the side of the antenna showing the larger lobe.

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We have noted that the latest version of EZNEC has an option to use compass bearings instead of counting counter-clockwise from the X-axis. The latter system is the one used in earlier versions of the program and shown in the illustrations so far. The new option is more than a way to count clockwise in the azimuth manner. It changes, for some modeling exercises, the way we should model to have the antenna pattern register as facing north or to zero degrees.

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Fig. 14 illustrates an azimuth pattern in the new mode. As with the other patterns for the half-square beam, the horizontal portions of the elements are parallel to the X-axis, with the forward direction defined as a positive value of Y. The height requires a 3- degree elevation angle to record maximum radiation on the azimuth pattern. Because the antenna presents a slightly non-symmetrical pattern, the main lobe is offset 3 degrees from zero.

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Note that to place the forward direction ar zero degrees on the pattern, one must model the antenna with the element extending parallel to the X-axis. This is the opposite convention from the one used in other implementations of either phi or azimuth patterns, where the elements must parallel the Y-axis to get a forward reading of zero degrees.

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Although the pattern bears no heading labels, it does read correctly with respect to azimuth headings. Notice the line in the rear right quadrant, indicating the strongest side-lobe. The line, from the data series below the graphic, shows a bearing of 124 degrees, which is a correct number in azimuth terms relative to the zero heading directly up the page.

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The purpose in surveying all of these options and variants of elevation/theta and azimuth/phi labels on graphics is to make you aware of the differences. By becoming aware of them, they will not take you by surprise when you develop and then interrogate a pattern. You will know in advance the conventions themselves and the particular ways in which they are implemented by at least some software. You should be able to adapt these notes to cover any other piece of modeling software that you may be using.

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Since in all cases, the patterns are correct and correctly oriented to an ideal observer, the labels are simply ways to keep track of various facets of the pattern. Should absolutely correct azimuth labels be essential to some form of presentation, you can always run a screen grab of a pattern and then process it through a painting program. You need only change the labels to a set that is most suited to the presentation task.

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Go to Main Index

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37. Verticals: Using the MININEC Ground

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L. B. Cebik, W4RNL

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Many vertical antennas and arrays require extensive ground radial systems. A model of the radial system very often requires many times the number of segments as the antenna wires themselves. Many modelers resort to the use of MININEC or a MININEC ground system attached to a version of NEC-2 (for example, EZNEC) to avoid modeling the radials system. The run times are shorter, for starters. Additionally, some popular programs in the low- end range do not have a sufficient number of segments available to fully model a radial system and the antenna atop it.

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For reasons that are not altogether clear, the MININEC ground system with a 1/4 wavelength monopole directly connected to ground has achieved a reputation for accuracy that is denied to NEC using the same modeling scheme and the Sommerfeld-Norton ground calculation system. If the intrinsic gain figures are not themselves useful, so the reasoning goes, the comparative figures for a baseline monopole and a more complex array will be useable using a consistent MININEC ground.

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One disturbing tendency that has appeared in more than one volume containing otherwise impeccable technical information has been to combine or compare without caution the results of modeling using the simplified MININEC grounding system and modeling over Sommerfeld-Norton ground, with or without radials. In addition, a second disturbing tendency has emerged: to treat any predominantly vertical array as if it were purely vertical, even if some of the elements (driven or parasitic) slope.

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The MININEC ground system becomes inaccurate for some wire antennas when some or all of the height of wires in the array is below about 0.2 wavelengths. The Sommerfeld-Norton ground calculation scheme, a part of the basic NEC core, can be accurate to within about 0.001 wavelength of the ground, so long as the wire surface does not go below that level. Some research indicates that a closer approach is possible. NEC-2 calls for a limit of about 30 wires for any one junction, although with relatively thin wires, that limitation can be pressed without inaccuracies arising. Therefore, a 32-radial system is well within NEC-2 capabilities. Some low-end NEC programs (such as EZNEC and NEC-Win Plus) have facilities for automated radial system construction. With these abilities, it is surprising that few modelers actually model the radial systems, but opt instead to use a MININEC ground with a monopole directly connected to ground.

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Therefore, it would appear to be useful if we return to basics and find out what the modeling results would be for various situations involving vertical antennas and arrays using a number of different ground systems for the modeling task. In the following exercises, all of which at conducted at 7.15 MHz, I shall use a 2" diameter copper main element. All radials (where used) and guy wires employed as parasitic elements will be 0.25" in diameter and also copper. I shall use a segment length of close to 1'/segment to assure convergence of the models. Since I shall be looking at antenna over various ground qualities, the following table summarizes the categories and their related conductivity and permittivity.

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Ground Quality          Conductivity            Permittivity
+  Label                    S/m                  (relative dielectric constant)
+Very Poor               0.001                     5
+Poor                    0.002                    13
+Good (Average)          0.005                    13
+Very Good               0.0303                   20
+Salt Water              5.0                      81
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With this data to ensure uniform treatment of each example, we can proceed. Most of the modeling data presented in these exercises will be in tabular form. One note of caution: the exercises will be wholly in the realm of comparing one type of model with another. No claims are made for the accuracy of the data with respect to test range measurements.

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1. The 1/4 Wavelength Monopole

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Fig. 1 illustrates the two forms of our first exercise. I begin with a 1/4 wavelength monopole directly connected to ground. The antenna is 32.9' long and uses 33 segments. The antenna model is tested using the categories of ground quality shown in the table above.

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In the first model test table, there are two columns of data. Column 1 represents the results of modeling within MININEC (3.13), which places the source directly at the ground connection point. The MININEC ground system always uses perfect ground as the basis of the source impedance report, so impedance is listed only for the "perfect" ground entry. Column 2 is the data from the use of the MININEC ground within a NEC-2 system (EZNEC). The numbers given represent the far field gain in dBi and the elevation angle of maximum radiation (TO angle). The slight differences, where they exist, result from the placement of the source in NEC within the lowest segment, rather than at its end, as is done in MININEC 3.13.

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Ground            MININEC                       NEC/w/MIN Gnd
+Perfect            5.14   0  35.9 - j 0.3        5.15   0  36.4 + j 1.7
+Very Poor         -1.76  29                     -1.76  29
+Poor              -0.28  27                     -0.28  26
+Good/Average      -0.04  26                     -0.04  26
+Very Good          1.94  21                      1.94  21
+Salt Water         4.61   9                      4.61   9
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In the following table, we have similar data in the first column, including the source impedance (R +/- jX in Ohms), for the same antenna connected to ground using the Sommerfeld-Norton (S-N) ground calculation system. In the final column is data for the same antenna placed over a 32-radial ground plane that is 2" above ground. This height is close to, but not on, the conservative limit for minimum wire height above ground. The order of data is gain/TO angle/Source Z (if given). The "perfect" line is omitted.

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Ground            NEC/w/S-N Gnd                 NEC/w/Radial System
+Very Poor         -2.20  29  40.1 + j 3.1       -1.15  29  30.7 - j 8.0
+Poor              -1.29  27  45.8 + j 5.5        0.01  26  32.6 - j 5.4
+Good/Average      -1.18  26  47.1 + j 4.9        0.14  26  34.2 - j 5.5
+Very Good          0.89  21  46.3 + j 7.1        1.48  21  37.5 - j 2.8
+Salt Water         4.57   9  36.7 + j 1.5             --------
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NEC does not yield valid data for the "salt water" case for the ground plane system close to ground. Of interest in the tables are the following items.

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1. With no ground plane, the NEC impedance entries are out of line with both the MININEC ground and the ground plane values. This variance represents one reason why some modelers prefer the MININEC ground for "no-radial" modeling.

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2. The source impedance varies somewhat as the ground quality is changed, a feature that the MININEC ground modeling system cannot show.

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3. There is no constant that one can use for all the systems to pre-estimate the change in gain value as one moves from one ground quality to another.

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4. The value for the TO angle for any given ground quality is consistent for all of the ground systems examined.

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The chief use of this data, however, will become apparent with the next exercise. The values shown here represent what a modeler might use as a baseline for estimating the advantages of a more complex array.

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2. Two 1/4 Wavelength Monopoles Fed In-Phase

+
+ +
+

In Fig. 2, we have 2 monopoles spaced just a bit more than 1/2 wavelength apart. For each case that we shall examine, we record the same data as in the first exercise, except that the impedance figures are understood as applying to each of the two sources, which are fed in phase with each other. Although Fig. 2 shows the dual ground radial system, set up to avoid an intersection for this exercise, the first three data sets employ a direct connection of each monopole to ground. Not listed in the tables are horizontal -3 dB beamwidths, which are completely consistent from one model to the next at any ground quality level.

+ 
Ground            MININEC                       NEC/w/MIN Gnd
+Perfect            9.06   0  27.8 - j13.4        9.06   0  28.3 - j11.7
+Very Poor          2.15  29                      2.15  29
+Poor               3.64  27                      3.63  26
+Good/Average       3.88  26                      3.88  26
+Very Good          5.85  21                      5.85  21
+Salt Water         8.52   9                      8.52   9
+
+Ground            NEC/w/S-N Gnd                 NEC/w/Radial System
+Very Poor          1.77  29  31.4 - j 2.3        3.05  29  23.4 - j16.5
+Poor               2.61  27  36.3 - j 2.2        4.22  27  24.7 - j15.1
+Good/Average       2.80  26  36.6 - j 3.3        4.10  26  25.6 - j15.4
+Very Good          4.87  21  35.8 - j 4.2        5.61  21  28.0 - j14.6
+Salt Water         8.50   9  28.5 - j11.7             --------
+

Once more, salt water data for the ground plane system is not valid. However, the more important use that is made of numbers from this chart set is to estimate the advantage of the phase-fed system over a single monopole. Therefore, the next chart compares the gain advantage for each system (combining the MININEC direct ground systems into a single column).

+ 
Ground            NEC/w/MIN Gnd           NEC/w/S-N Gnd           NEC/w/Radial System
+Very Poor          3.91                    3.97                    4.20
+Poor               3.91                    3.90                    4.21
+Good/Average       3.92                    3.98                    4.24
+Very Good          3.91                    3.98                    4.13
+Salt Water         3.91                    3.93                    -----
+

The relative internal consistency of each system as we vary ground quality is interesting. The consistency between the use of the MININEC ground system and the S-N system suggests that for the purposes of gain comparisons, there is no reason to prefer the MININEC system.

+

However, the radial system provides an advantage figure that is 0.2 to 0.3 dB higher than those that emerged from the direct-ground connection systems. This difference is significant. A full analysis would need to survey many more complex arrays than the simple one used here before arriving at any general conclusions. However, the difference is notable. The initial conclusion is that gain advantage claims over a standard (such as the monopole used in this role) must always be given with the full particulars of the modeling conditions that produced them. Moreover, gain advantages produced by different ground systems for the models involved may not be directly comparable.

+

Once more the radial system provides a range of source impedance figures specific to the ground quality.

+

3. A Tilting 1/2 Wavelength Dipole

+
+ +
+

Our third exercise is designed to serve as a reminder of the limitations inherent in the MININEC ground system. As suggested in Fig. 3, we shall use a 1/2 wavelength 2" copper dipole. In successive steps, we shall tilt the vertical by 30, 45, 60, and 90 degrees. In each case, the left end of the dipole will be 1' off the ground. Thus, the final position will place the entire dipole at a height of 1'.

+

As before, we shall compare MININEC ground with S-N ground. We shall omit the separate columns for MININEC and NEC using the MININEC ground, since the results coincide almost exactly. The main differences that we shall examine lie between the MININEC and S-N ground systems in their handling of the tilting element. In each case, we shall use a dipole length that has been resonated within the MININEC ground system and then record the source impedance that results from switching to the S-N system. All values are taken broadside to the dipole, not in line with the tilt.

+ 
A. Dipole Vertical: Length--64.9'; MIN Source Z: 99.8 - j 0.4
+
+Ground            NEC/w/MIN Gnd                 NEC/w/S-N Gnd
+Very Poor         -1.20  22                     -0.88  22   90.0 - j13.9
+Poor              -0.03  20                      0.13  20   94.4 - j 9.1
+Good/Average      -0.21  19                     -0.17  19   96.8 - j 9.3
+Very Good          1.96  15                      1.92  15  100.0 - j 4.9
+Salt Water         5.91   7                      5.91   7   99.9 - j 0.7
+
+B. Dipole 30-Degrees Off Vertical: Length--64.0'; MIN Source Z: 93.0 - j 0.1
+
+Ground            NEC/w/MIN Gnd                 NEC/w/S-N Gnd
+Very Poor         -0.44  29                     -0.38  29   88.4 - j20.8
+Poor               0.33  26                      0.30  26   91.4 - j13.8
+Good/Average       0.31  25                      0.15  25   94.3 - j12.8
+Very Good          1.83  20                      1.66  20   96.0 - j 5.9
+Salt Water         4.96   8                      4.94   8   93.3 - j 0.5
+
+

To a small, but detectable, degree, the MININEC ground is beginning to overestimate the gain of the dipole, especially over better ground qualities.

+ 
C. Dipole 45-Degrees Off Vertical: Length--63.1'; MIN Source Z: 77.3 + j 0.4
+
+Ground            NEC/w/MIN Gnd                 NEC/w/S-N Gnd
+Very Poor          0.74  42                      0.18  42   84.1 - j26.1
+Poor               1.15  40                      0.66  40   84.1 - j17.2
+Good/Average       1.38  43                      0.77  43   86.9 - j14.6
+Very Good          2.12  34                      1.68  34   84.9 - j 5.3
+Salt Water         4.02  10                      3.98  10   78.0 + j 0.0
+

As we move to the 45-degree angle, the over-estimation of gain by the MININEC ground system becomes serious, averaging about a half dB. As well, the sensitivity of the element to the ground quality with respect to source impedance becomes apparent using the S-N ground system, but is invisible with a MININEC ground.

+ 
D. Dipole 60-Degrees Off Vertical: Length--62.6'; MIN Source Z: 49.2 - j 0.2
+
+Ground            NEC/w/MIN Gnd                 NEC/w/S-N Gnd
+Very Poor          2.89  88                      0.73  88   77.6 - j25.4
+Poor               3.09  90                      1.31  90   72.3 - j16.6
+Good/Average       3.63  90                      1.81  90   73.4 - j11.8
+Very Good          4.27  90                      3.12  90   63.9 - j 1.9
+Salt Water         4.37  90                      4.26  90   50.5 - j 0.1
+

As we tilt the element within 30 degrees of ground, almost the entire antenna lies below the so-called 0.2 wavelength limit for MININEC ground accuracy. The inaccuracies show up in two ways. First, the MININEC ground system gain is much too high. Second, the MININEC source impedance is much too low. The figures for the S-N ground for very good ground and better might well bear scrutiny as well.

+ 
E. Dipole 90-Degrees Off Vertical: Length--68.5'; MIN Source Z: 0.2 - j 0.3
+
+Ground            NEC/w/MIN Gnd                 NEC/w/S-N Gnd
+Very Poor         24.26  90                     -4.13  90  147.8 + j132.8
+Poor              21.40  90                     -6.76  90  141.5 + j134.6
+Good/Average      20.91  90                     -6.88  90  130.3 + j137.6
+Very Good         16.95  90                     -8.85  90   78.1 + j107.5
+Salt Water         8.77  90                     -9.38  90   11.4 + j 16.2
+

The MININEC values for the case of the dipole 1' off the ground clearly reveal the inadequacy of the ground system for wires very close to ground. In addition to the wholly unrealistic gain and source impedance values, the length of the required dipole is also a clue to the situation. Using the S-N ground system over very poor ground, the required modeled dipole length for resonance is 58.3' and the source impedance is 104.3 - j 0.5 Ohms, with -4.88 dBi gain. Hence, the use of a MININEC ground does not even provide rudimentary guidance as to the required length of the element.

+

As the antenna becomes more horizontal and as more of its structure moves closer to the ground, the MININEC ground system creates increased errors and serves less and less as an adequate guide to the likely performance of the antenna modeled. Although this lesson is fundamental to almost any modeler when horizontal wires and arrays are in question, the message appears to dim when the antenna bears the label "vertical array" or when sloping wires are part of the antenna structure, whether or not directly driven. Essentially, if any part of an antenna structure has a horizontal component to its radiation field and if that part falls below the threshold of accuracy for the MININEC ground system, then the use of the MININEC ground becomes untrustworthy.

+

4. A Vertical Monopole with a Simple Ground Radial System

+
+ +
+

There is one exception to the general rule just noted. Where a horizontal structure is symmetrical such that its radiation can be viewed as self-cancelling, the MININEC ground system remains quite reasonably accurate. Such an antenna appears in Fig. 4. The monopole with a 4-radial system, if elevated, shows quite similar results over a MININEC and a S-N ground calculation system.

+

The 7.15 MHz model has a set of 34.4' radials, 0.25" in diameter. The 2" diameter main element varies in length to establish resonance at each height. The test heights begin at 1/4 wavelength and halve in steps down to 1/32 wavelength. The following table compares NEC using a MININEC and a S-N ground. As well, figures are included for the same model directly handled in MININEC 3.13.

+ 
Height:  34.4' (1/4 WL)
+Program           Monopole          Gain        TO Angle          Source Z
+                  Length            dBi         degrees           R +/- jX Ohms
+MININEC           34.6'              0.24       15                21.5 + j 0.7
+NEC/w/MIN         34.2'              0.15       15                21.4 - j 0.4
+NEC/w/S-N         34.2'              0.20       15                21.2 + j 1.0
+
+Height:  17.2' (1/8 WL)
+Program           Monopole          Gain        TO Angle          Source Z
+                  Length            dBi         degrees           R +/- jX Ohms
+MININEC           34.6'             -0.15       19                28.8 - j 1.0
+NEC/w/MIN         34.3'             -0.23       19                28.9 - j 0.7
+NEC/w/S-N         34.3'              0.22       19                26.1 - j 0.7
+
+Height:   8.6' (1/16 WL)
+Program           Monopole          Gain        TO Angle          Source Z
+                  Length            dBi         degrees           R +/- jX Ohms
+MININEC           34.4'             -0.27       22                34.4 - j 0.1
+NEC/w/MIN         34.1'             -0.36       22                34.5 + j 0.4
+NEC/w/S-N         34.3'              0.04       22                31.7 + j 0.4
+
+Height:  4.3' (1/32 WL)
+Program           Monopole          Gain        TO Angle          Source Z
+                  Length            dBi         degrees           R +/- jX Ohms
+MININEC           34.1'             -0.25       24                36.7 + j 0.4
+NEC/w/MIN         33.7'             -0.34       24                36.5 - j 0.7
+NEC/w/S-N         34.1'             -0.11       24                35.2 + j 0.9
+

Despite the close approach to ground by the horizontal members of the monopole-plus- radials assembly, the figures comparing MININEC ground--used with either the NEC or MININEC algorithms--and the S-N ground are remarkably consistent. Field-cancelling symmetrical structures are remarkably resistant to the error-producing aspects of the MININEC ground structure.

+

5. A Parasitic Vertical Array with Sloping Parasitic Elements

+
+ +
+

I found a parasitical array that has the general appearance of Fig. 5 in a reputable handbook with the notation that it had been modeled using a MININEC ground because the NEC program lacked sufficient segment capacity to permit modeling the radial system. The present model is only like the original in appearance, since it is not a direct scaling of the MF array for 7.15 MHz. I have placed the lowest wires at the 1' level, corresponding to the lowest height in our third exercise. The parasitic element wires slope somewhat more than the originals. However, all that these modifications achieve is to make the results a bit more dramatic.

+

The following table provides the dimensions of the array used in this example.

+ 
40-m vertical array                            Frequency = 7.15  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1            0.000,  0.000, 29.000  W2E1   0.000,  0.000,  0.167 2.00E+00  28
+2     W3E1   0.000,  0.000,  0.167        34.400,  0.000,  0.167 2.50E-01  33
+3     W4E1   0.000,  0.000,  0.167        33.739,  6.711,  0.167 2.50E-01  33
+4     W5E1   0.000,  0.000,  0.167        31.781, 13.164,  0.167 2.50E-01  33
+5     W6E1   0.000,  0.000,  0.167        28.603, 19.112,  0.167 2.50E-01  33
+6     W7E1   0.000,  0.000,  0.167        24.324, 24.324,  0.167 2.50E-01  33
+7     W8E1   0.000,  0.000,  0.167        19.112, 28.603,  0.167 2.50E-01  33
+8     W9E1   0.000,  0.000,  0.167        13.164, 31.781,  0.167 2.50E-01  33
+9    W10E1   0.000,  0.000,  0.167         6.711, 33.739,  0.167 2.50E-01  33
+10   W11E1   0.000,  0.000,  0.167       2.6E-06, 34.400,  0.167 2.50E-01  33
+11   W12E1   0.000,  0.000,  0.167        -6.711, 33.739,  0.167 2.50E-01  33
+12   W13E1   0.000,  0.000,  0.167       -13.164, 31.781,  0.167 2.50E-01  33
+13   W14E1   0.000,  0.000,  0.167       -19.112, 28.603,  0.167 2.50E-01  33
+14   W15E1   0.000,  0.000,  0.167       -24.324, 24.324,  0.167 2.50E-01  33
+15   W16E1   0.000,  0.000,  0.167       -28.603, 19.112,  0.167 2.50E-01  33
+16   W17E1   0.000,  0.000,  0.167       -31.781, 13.164,  0.167 2.50E-01  33
+17   W18E1   0.000,  0.000,  0.167       -33.739,  6.711,  0.167 2.50E-01  33
+18   W19E1   0.000,  0.000,  0.167       -34.400,5.2E-06,  0.167 2.50E-01  33
+19   W20E1   0.000,  0.000,  0.167       -33.739, -6.711,  0.167 2.50E-01  33
+20   W21E1   0.000,  0.000,  0.167       -31.781,-13.164,  0.167 2.50E-01  33
+21   W22E1   0.000,  0.000,  0.167       -28.603,-19.112,  0.167 2.50E-01  33
+22   W23E1   0.000,  0.000,  0.167       -24.324,-24.324,  0.167 2.50E-01  33
+23   W24E1   0.000,  0.000,  0.167       -19.112,-28.603,  0.167 2.50E-01  33
+24   W25E1   0.000,  0.000,  0.167       -13.164,-31.781,  0.167 2.50E-01  33
+25   W26E1   0.000,  0.000,  0.167        -6.711,-33.739,  0.167 2.50E-01  33
+26   W27E1   0.000,  0.000,  0.167       4.1E-07,-34.400,  0.167 2.50E-01  33
+27   W28E1   0.000,  0.000,  0.167         6.711,-33.739,  0.167 2.50E-01  33
+28   W29E1   0.000,  0.000,  0.167        13.164,-31.781,  0.167 2.50E-01  33
+29   W30E1   0.000,  0.000,  0.167        19.112,-28.603,  0.167 2.50E-01  33
+30   W31E1   0.000,  0.000,  0.167        24.324,-24.324,  0.167 2.50E-01  33
+31   W32E1   0.000,  0.000,  0.167        28.603,-19.112,  0.167 2.50E-01  33
+32   W33E1   0.000,  0.000,  0.167        31.781,-13.164,  0.167 2.50E-01  33
+33    W1E2   0.000,  0.000,  0.167        33.739, -6.711,  0.167 2.50E-01  33
+34           0.853,  0.000, 26.448 W35E1   0.853,  0.000, 29.000 2.50E-01   3
+35   W34E2   0.853,  0.000, 29.000 W36E1  35.000,  0.000,  1.000 2.50E-01  44
+36   W35E2  35.000,  0.000,  1.000        21.500,  0.000,  1.000 2.50E-01  13
+37          -0.853,  0.000, 26.448 W38E1  -0.853,  0.000, 29.000 2.50E-01   3
+38   W37E2  -0.853,  0.000, 29.000 W39E1 -35.000,  0.000,  1.000 2.50E-01  44
+39   W38E2 -35.000,  0.000,  1.000       -19.000,  0.000,  1.000 2.50E-01  15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          28     1 / 98.21   (  1 /100.00)      1.000       0.000       I
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+

The following table lists the results for directly connecting the 1/4 wavelength driver to ground using the MININEC ground system. Direct connection using the S-N system is also shown for reference. The last entry shows the results of placing the monopole on a 32-radial system with the S-N ground. All models use average (good) ground.

+ 
Ground      Gain        TO Angle    Front-to-Back     Beamwidth   Source Z
+System      dBi         degrees     Ratio dB          degrees     R +/- jX Ohms
+
+Direct Connection:
+MININEC      6.28       37          24.99             110.6        9.2 + j  9.1
+S-N         -1.50       34           9.55              98.2       30.1 + j 21.6
+Radial System:
+S-N          1.18       34          11.38              99.5       14.8 + j  3.8
+

Compared to a radial system over S-N ground, the MININEC system not only overestimates performance figures, but as well, provides dimensions that are at odds with those which might yield maximum gain and front-to-back ratio in the radial configuration. If optimization is performed, along with the use of additional radials, available in NEC-4, the performance of the array over radials might show better numbers, but still, nowhere near those provided by the MININEC ground analysis.

+
+ +
+

Fig. 6 provides a view of the MININEC and Radial system elevation patterns for comparison. Fig. 7 provides a similar comparison of the azimuth patterns at the 34-degree elevation angle of maximum radiation.

+
+ +
+

The array uses near ground horizontal portions of the parasitic elements, along with sloping elements at about a 45-degree angle. Both of these conditions incur the typical MININEC ground errors. I have modeled the lowest wires very close to ground to accentuate the error potential of using the MININEC ground in arrays with the listed problematical structures. However, placing any part of the structure below 0.2 wavelengths and having a horizontal component to either driven or parasitic elements will leave the results equally untrustworthy.

+

Conclusion

+

The selection of a ground system for modeling vertical arrays requires considerable care. In general, any serious model--that is, one used for design, analysis, or publication--should employ a radial system as close as possible to the structure of the physical system to be used. If that requires borrowing or upgrading software and the structuring of models with well over 1000 segments, than that is the cost for internal consistency of modeling comparisons. (The largest models in these exercises used close to 2,200 segments.)

+

Models using different ground systems are not especially comparable, at least not on a simple viewing of their report numbers. Even within the same system, there are differences in comparison numbers for larger arrays and whatever simpler standard might be used; hence, such comparisons should be made with reference to the actual ground quality of the antenna site.

+

The MININEC ground shortcut to vertical array modeling should generally be avoided or used sparingly and under very limited conditions. At the very least, the modeler should avoid using the MININEC ground system whenever any part of a radiating structure has a horizontal component and is below the 0.2 wavelength accuracy threshold. Better yet, the model should include the radial system that will be used at the site using the S-N ground calculation system. Although these measures would not guarantee the accuracy of performance figures from vertical array models relative to the actual installation, at the very least, they would ensure that internal consistency among modeled results is sustained.

+
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+

Go to Main Index

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+

38. Radials: Segmentation and Convergence

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Working with radial systems for vertical monopoles and arrays often puts modelers off, since the radials occupy far more wires and segments than the antenna elements themselves. Hence, there is a tendency to be satisfied with results of models that use directly grounded 1/4 wavelength monopoles without a radial system. As well, modelers rarely place radial systems beneath 1/2 wavelength antennas and arrays, especially if the elements make no connection to the ground.

+

In the preceding column, I noted some of the potential inaccuracies that may arise from using a simple MININEC ground with no radial system. The source impedance is calculated for a perfect ground only and hence does not show the range of variation that may be occasioned by placing the antenna system over different soil qualities. Comparisons between an array and a standard antenna, such as a 1/4 wavelength monopole yield different differentials when using the MININEC ground and when using a radial system. Moreover, if the array employs any element, driven or parasitic, with a horizontal component to its radiation field and if the element has any part less than 0.2 wavelengths above ground, the use of the MININEC ground is subject to the known errors of that system for wires close to the ground.

+

Consequently, modelers who are serious about working with vertical antennas and arrays need to increase their familiarity with modeling radial systems using NEC and the attached Sommerfeld-Norton (S-N) ground calculation system. For NEC-2, which does not permit wires either on or below ground level, the radial system should be no closer to ground than about 0.001 wavelength. The use of very thin wires and length tapering is reported to permit placement of the radials even closer to the ground, but for most general modeling purposes, the 0.001 wavelength limit, rounded to a convenient number, should provide a self-consistent foundation for comparing arrays to some standard vertical antenna placed on the same radial system.

+

How Many Radials?

+
+ +
+

The rule of thumb governing the proximity of the radials to the ground in NEC-2 is not the only limitation the modeler should observe. Consider the radial systems in Fig. 1. The upper system uses 32 radials, each with 20 segments per radial. (The choice of 20 will become apparent later on; for now, it represents a relatively high segmentation density.) NEC-2 warns against using more than 30 wires at a single junction. As the angle between wires becomes smaller, the wire segments at the junction interpenetrate. At a certain angle that varies according to the wire diameter, the central portions of the segments will interpenetrate to a degree that introduces errors into the calculations. The NEC core does not specifically check for this limitation, as it does for wire intersections that occur at mid-segment points. Hence, it will not block the completion of the calculation.

+

For radial systems, a 32-radial model does not press the limit significantly. However, we might check the results of using a 64-radial system, shown on the lower part of Fig. 1. As well, we might check both in both NEC-2 and NEC-4 to see if there is any difference of note. In both cases, we shall place a 40-meter copper vertical wire that is 0.25 m in diameter and also using 20 segments over a field of radials, each of which is copper and 2 mm in diameter. (2-mm wire falls between AWG #14 and AWG #12.) The frequency will be 1.83 MHz. The radial system is 0.164 m off the ground (0.001 wavelength). Beneath the radial system is "average ground" (conductivity: 0.005 S/m; dielectric constant: 13) in the S-N calculation system.

+ 
Core        No. of            Gain        TO Angle          Source Impedance
+            Radials           dBi         degrees           R +/- jX Ohms
+NEC-2       32                1.02        22                39.3 + j 7.2
+NEC-4       32                1.02        22                39.3 + j 7.7
+NEC-2       64                1.01        22                38.8 + j 6.6
+NEC-4       64                0.98        22                39.1 + j 7.0
+

The 32-radial systems shows excellent agreement between the two cores. However, as we double the radials, the results from the two cores begin to diverge. Normally, we would expect any gain difference between the cores to give the advantage to the system with the higher number of radials. However, we obtain precisely the opposite results, although hardly to an operationally significant point. The source impedance in both cases decreases, as we might expect of a radial system with lower losses. However, the amount of decrease differs between the two cores.

+

For general purposes, then, 32 radials is a useful level. The model employed in the example required 33 wires and 660 segments. The 64-radial system required 65 wires and 1365 segments. Since run-time for a model increase with the number of segments and also with the number of wires, the smaller system is preferable for the additional reason of human impatience.

+
+ +
+

There are applications that call for exacting replication of radial systems that have more than 32 radials. Fig. 2 shows one scheme that can be used (and expanded as needed) for adding more radials without increasing the junction count. Although many versions are possible, the one in the figure uses a set of 16 inner radial wires, each of which connects to a set of outer radial wires. Creating such a system can be a tedious labor.

+

Simple radial sets can be created by automated radial makers that come with commercial implementations of NEC or by separate equation sets. To create the complex pattern shown in Fig. 2, we can make use of such facilities. First create a 16-radial set at the inner radius, ordinarily a set of 1-segment wires having the same length as the segments lengths in the outer wires. For the 20 segment wires of Fig. 1, a 5% of total length would suffice.

+

Next, create a 64 (or whatever number is desired) using the outer radius for the wires. Then for each group of 4 outer wires, move their inner ends to the correct outer end of one of the set of 16. The result will be the configuration in Fig. 2 with the minimal amount of independent calculation. Do not try to run the model until all of the outer radial wires are correctly placed at their inner ends. NEC will block the run with a message indicating mid-segment wire intersections.

+

Convergence

+
+ +
+

Complex geometries do not answer to the minimum segmentation rules for linear elements. And a radial system with a vertical antenna at right angles to the radials represents a complex geometry. Therefore, it is wise to perform a convergence test on radial systems with their antennas attached. Fig. 3 shows two versions of the same antenna, one using a low segment density, the other a much higher level of segmentation. The question facing the modeler is at what level of segmentation he or she should declare convergence.

+

Let's take the model that we used above. The antenna is a 40-meter long element, 0.25 m in diameter for 1.83 MHz. We shall use 32 radials of 2-mm diameter. Everything is copper. Once more, the radial system is 0.164 m or 0.001 wavelength off the ground for the benefit of NEC-2 restrictions. Hence, the tower top is at 40.164 m. Now let's uniformly segment each wire in steps of 5 from 5 segments per wire to 30 segments per wire. Each antenna model will be over average ground in the S-N system.

+

The results of the convergence test are as follows. The TO angle is omitted, since it is 22 degrees for all cases.

+ 
Segments/   Segment length    Total       Gain        Source Impedance
+Wire        wavelengths       Segments    dBi         R +/- jX Ohms
+ 5          0.0050            165         1.28        37.2 + j 9.4
+10          0.0250            330         1.14        38.2 + j 8.5
+15          0.0167            495         1.07        38.8 + j 8.0
+20          0.0125            660         1.03        39.2 + j 7.7
+25          0.0100            825         1.00        39.5 + j 7.6
+30          0.0083            990         0.99        39.6 + j 7.5
+

Now comes the moment of decision--declaring the level of segmentation at which we arrive at convergence. In one sense, we have not arrived. since the progression of decreasing gain and source reactance, with an increasing source resistance, has not terminated. Ideally, we achieve convergence when the values noted simply vary around a central value with only small changes per increment of increased segmentation.

+

Obviously, holding out for the ideal can drive a modeler crazy. In practical terms, we achieve convergence when the differences between levels of segmentation make no operational difference relative to a real antenna whose properties we might measure after building. In these terms, 10 to 15 segments per wire would certainly suffice. More stringently, but still within the realm of realistic modeling, we can apply this standard: The differential between a given level of segmentation and the next lower level is not significantly larger than the difference between the given level and the next higher level. The 20-segment-per-wire level appears to meet this requirement easily.

+

In the end, however, it is up to the individual modeler to determine--relative to the overall task of which the model is a part--what is a suitable level of segmentation, that is, when convergence is obtained. Although I have shown the total number of segments in the 33-wire models used for the example, this factor should not be among the decision makers for any significant project. In all cases, where the information may be of use to those who might try to replicate the model, the segmentation data should be included in the model description.

+
+ +
+

There is a tendency for newer modelers to assume that, because a radial system is largely self-cancelling with respect to its radiation field, it is satisfactory to use fewer segment in radials than in the main radiator(s). The situation is illustrated in Fig. 4. Therefore, let's take our model and run it through some cases where there is a differential. Once more, the TO angle is a constant 22 degrees for all cases.

+ 
Segments/   Segments/         Total       Gain        Source Impedance
+Radial      Radiator          Segments    dBi         R +/- jX Ohms
+ 5          10                170         1.23        37.4 + j 8.7
+ 5          20                180         1.35        36.4 + j 9.5
+10          20                340         1.14        38.3 + j 8.7
+15          20                500         1.06        38.9 + j 8.1
+

Notice that we do not approach the values of gain and source impedance that attach to the earlier table until we hit the 15-20 case. There is a reason for the variance. The segment lengths on either side of a source segment in NEC should be equal in order to obtain the greatest accuracy. Since the vertical is fed on its lowest segment, only the 15-20 case begins to approximate this condition. For this reason, the 5-20 case shows a higher deviance from the cases in the preceding table than does the 5-10 case, where we have a closer fit between the source segment and the innermost radial segments.

+

The upshot is that, for most purposes, equal segmentation lengths for both radials and radiators is the most accurate route to follow.

+

Length Tapering

+
+ +
+

The 32-radial system using 20 segments per 1/4 wavelength wire remains a large model with respect to some low-end NEC modeling implementations. It requires 660 segments, which can overrun a 500-segment limitation. Although upgrading software to a professional package is wise for serious modeling, there is a technique that the modeler can use to reduce the number of segments in the model without sacrificing accuracy. It is called length tapering and is illustrated in Fig. 5.

+

The practice of tapering the length of segments progressively arose from necessity with the use of MININEC and its initial restriction to a maximum of 256 segments for the entire model. To handle angular junctions, the modeler had to either use very many segments or resort to length tapering. Because NEC cores are segment-limited only by the user's setting of a variable, length tapering is not widely used in NEC-2 or NEC-4 models. However, the technique remains a valid option for the modeler.

+

The principle of length tapering involves setting a lower and upper length limit. One commercial program uses a default lower limit of 0.0025 wavelength and an upper limit of 0.04 wavelength. The user can alter these values to suit a particular set of needs. However, for our example, let's use these values on each wire of the basic monopole model we have been using. We need to taper only the inner junction ends of each wire (although the user has the option to taper either or both ends). In the process of creating tapered-length elements, the program will replace each individual wire with a set of wires meeting the requirements. If we do this for the 32-radial monopole, we obtain a model using 165 wires and 330 segments--well within the program limitation of 500 segments per model. However, here are the results we obtain from the length-tapered model.

+ 
Total       Total             Gain        Source Impedance
+Wires       Segments          dBi         R +/- jX Ohms
+165         330               1.39        35.9 + j 5.6
+

The surprisingly high gain stems from an error we made in constructing the model. The tapered segment length increases when using a default system in a 2:1 ratio. Although the initial radial segments are the same length as the source segment, the segment on the monopole adjacent to the source segment is twice as long as the source segment. Let's go back and try again, using a bit of the data we obtained from our first try.

+

This time, we shall create a new wire that is .0025 wavelength long and running from 0.164 m to 0.574 m in the Z axis. Now we shall finish the vertical portion of the antenna with a second wire from the top of the first to the upper limit of the vertical. When we length taper the model, we shall skip the new wire. In this way, the first segment above the new wire will be the same length, as will be the inner wires of the radials.

+

Because length-tapering may be unfamiliar to some readers, here is the model description in EZNEC format.

+ 
160-meter vertical w/radials:  length tapered         Frequency = 1.83  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+1            0.000,  0.000, 40.164  W2E1   0.000,  0.000,  6.717 2.50E+02   6
+2     W1E2   0.000,  0.000,  6.717  W3E1   0.000,  0.000,  3.440 2.50E+02   1
+3     W2E2   0.000,  0.000,  3.440  W4E1   0.000,  0.000,  1.802 2.50E+02   1
+4     W3E2   0.000,  0.000,  1.802  W5E1   0.000,  0.000,  0.983 2.50E+02   1
+5     W4E2   0.000,  0.000,  0.983  W6E1   0.000,  0.000,  0.574 2.50E+02   1
+6     W5E2   0.000,  0.000,  0.574  W7E1   0.000,  0.000,  0.164 2.50E+02   1
+7    W12E1   0.000,  0.000,  0.164  W8E1   0.410,  0.000,  0.164 2.00E+00   1
+8     W7E2   0.410,  0.000,  0.164  W9E1   1.229,  0.000,  0.164 2.00E+00   1
+9     W8E2   1.229,  0.000,  0.164 W10E1   2.867,  0.000,  0.164 2.00E+00   1
+10    W9E2   2.867,  0.000,  0.164 W11E1   6.143,  0.000,  0.164 2.00E+00   1
+11   W10E2   6.143,  0.000,  0.164        40.966,  0.000,  0.164 2.00E+00   6
+12   W17E1   0.000,  0.000,  0.164 W13E1   0.402,  0.080,  0.164 2.00E+00   1
+13   W12E2   0.402,  0.080,  0.164 W14E1   1.205,  0.240,  0.164 2.00E+00   1
+14   W13E2   1.205,  0.240,  0.164 W15E1   2.812,  0.559,  0.164 2.00E+00   1
+15   W14E2   2.812,  0.559,  0.164 W16E1   6.025,  1.198,  0.164 2.00E+00   1
+16   W15E2   6.025,  1.198,  0.164        40.179,  7.992,  0.164 2.00E+00   6
+17   W22E1   0.000,  0.000,  0.164 W18E1   0.378,  0.157,  0.164 2.00E+00   1
+18   W17E2   0.378,  0.157,  0.164 W19E1   1.135,  0.470,  0.164 2.00E+00   1
+19   W18E2   1.135,  0.470,  0.164 W20E1   2.649,  1.097,  0.164 2.00E+00   1
+20   W19E2   2.649,  1.097,  0.164 W21E1   5.676,  2.351,  0.164 2.00E+00   1
+21   W20E2   5.676,  2.351,  0.164        37.848, 15.677,  0.164 2.00E+00   6
+22   W27E1   0.000,  0.000,  0.164 W23E1   0.341,  0.228,  0.164 2.00E+00   1
+23   W22E2   0.341,  0.228,  0.164 W24E1   1.022,  0.683,  0.164 2.00E+00   1
+24   W23E2   1.022,  0.683,  0.164 W25E1   2.384,  1.593,  0.164 2.00E+00   1
+25   W24E2   2.384,  1.593,  0.164 W26E1   5.108,  3.413,  0.164 2.00E+00   1
+
+(Many radials omitted to compress the model description.)
+
+141  140E2   2.351, -5.676,  0.164        15.677,-37.848,  0.164 2.00E+00   6
+142  147E1   0.000,  0.000,  0.164 143E1   0.228, -0.341,  0.164 2.00E+00   1
+143  142E2   0.228, -0.341,  0.164 144E1   0.683, -1.022,  0.164 2.00E+00   1
+144  143E2   0.683, -1.022,  0.164 145E1   1.593, -2.384,  0.164 2.00E+00   1
+145  144E2   1.593, -2.384,  0.164 146E1   3.413, -5.108,  0.164 2.00E+00   1
+146  145E2   3.413, -5.108,  0.164        22.760,-34.062,  0.164 2.00E+00   6
+147  152E1   0.000,  0.000,  0.164 148E1   0.290, -0.290,  0.164 2.00E+00   1
+148  147E2   0.290, -0.290,  0.164 149E1   0.869, -0.869,  0.164 2.00E+00   1
+149  148E2   0.869, -0.869,  0.164 150E1   2.027, -2.027,  0.164 2.00E+00   1
+150  149E2   2.027, -2.027,  0.164 151E1   4.344, -4.344,  0.164 2.00E+00   1
+151  150E2   4.344, -4.344,  0.164        28.968,-28.968,  0.164 2.00E+00   6
+152  157E1   0.000,  0.000,  0.164 153E1   0.341, -0.228,  0.164 2.00E+00   1
+153  152E2   0.341, -0.228,  0.164 154E1   1.022, -0.683,  0.164 2.00E+00   1
+154  153E2   1.022, -0.683,  0.164 155E1   2.384, -1.593,  0.164 2.00E+00   1
+155  154E2   2.384, -1.593,  0.164 156E1   5.108, -3.413,  0.164 2.00E+00   1
+156  155E2   5.108, -3.413,  0.164        34.062,-22.760,  0.164 2.00E+00   6
+157  162E1   0.000,  0.000,  0.164 158E1   0.378, -0.157,  0.164 2.00E+00   1
+158  157E2   0.378, -0.157,  0.164 159E1   1.135, -0.470,  0.164 2.00E+00   1
+159  158E2   1.135, -0.470,  0.164 160E1   2.649, -1.097,  0.164 2.00E+00   1
+160  159E2   2.649, -1.097,  0.164 161E1   5.676, -2.351,  0.164 2.00E+00   1
+161  160E2   5.676, -2.351,  0.164        37.848,-15.677,  0.164 2.00E+00   6
+162   W6E2   0.000,  0.000,  0.164 163E1   0.402, -0.080,  0.164 2.00E+00   1
+163  162E2   0.402, -0.080,  0.164 164E1   1.205, -0.240,  0.164 2.00E+00   1
+164  163E2   1.205, -0.240,  0.164 165E1   2.812, -0.559,  0.164 2.00E+00   1
+165  164E2   2.812, -0.559,  0.164 166E1   6.025, -1.198,  0.164 2.00E+00   1
+166  165E2   6.025, -1.198,  0.164        40.179, -7.992,  0.164 2.00E+00   6
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     6 / 50.00   (  6 /100.00)      1.000       0.000       I
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+ +
+

Fig. 6 is a view of the length-tapered model above. Since the model begins with the upper end of the vertical element, the new wire is Wire 6, as also indicated by the source entry. The radials were developed by first creating and tapering one radial. Then the radial maker was applied to the substitute wire group to yield the remaining 31. The new model returns the following reports.

+ 
Total       Total             Gain        Source Impedance
+Wires       Segments          dBi         R +/- jX Ohms
+Correctly length-tapered model
+166         331               0.93        39.9 + j 6.2
+20-segment per wire model
+33          660               1.03        39.2 + j 7.7
+10-segment per wire model
+33          330               1.14        38.2 + j 8.5
+

The reports from the length-tapered segment model better approaches the reports for the 20-segment/wire model than does the reported data for the 330-segment (10 segments per wire) model. Moreover, the length-tapered model produces a gain figure in the direction that the progression toward convergence was taking when terminated at 30 segments per wire. Hence, it is in general a better model-type to use than simply reducing the segmentation density to a level deemed to be within program limitations.

+

These notes cover only a few of the elements of adequate radial system modeling. The escape from large models that we effected by length tapering each long wire may be adequate for simple vertical monopole systems. However, there are many larger radial systems used by multi-element vertical arrays. We shall not evade large models with them, although we shall take a look at their construction next time.

+
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Go to Main Index

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+

39. Radials: Complex Radial Systems

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the past two columns, we examined some of the modeling issues surrounding vertical antennas using radials systems. These columns, like all those in this series, were predicated on using a version of NEC-2 as the basic modeling core. We were left with some questions of modeling complex radial systems, which we shall examine in this column. However, it may be useful to begin by reviewing the limitations of NEC-2 with respect to radial systems.

+

NEC-2 does not permit wires either on or below ground. Therefore, radial systems must be constructed above ground, usually at a minimum height of about 0.001 wavelength. NEC-2 also recommends limiting the number of wires at a junction to about 30, making a 32-radial system about the largest that is practical. As noted in pervious columns, there are some work-arounds, but these parameters generally set the limits for vertical antenna radial systems. Model size can be reduced by using length-tapering techniques, which allows many 32-radial systems to be modeled within the 500-segment limit of some commercial implementations of NEC-2.

+

However, modelers should be aware that there are significant differences in reports from above-ground radial system models--even when pressed to the limit of proximity to the ground--and buried radial system models. Of course, buried radials are only feasible in NEC versions above NEC-2. However, without some sense of what NEC-4 might report for a buried radial system, the NEC-2 modeler might uncritically accept a report from the NEC-2 above- ground system model as reflecting accurately what occurs with a buried radial system.

+

Therefore, consider the following simple model: a 40-m element for 1.83 MHz with a diameter of 25 mm (nearly 1"). The diameter for the model was chosen to simplify the modeling of the radial systems, since the length-to-diameter ratio would be better than 4:1 throughout. The radials will consist of 2-mm diameter wires.

+
+ +
+

The ground treatment for separate above-ground and buried radial systems is indicated in Fig. 1. The radials in the above-ground system will be 0.001 wavelength above ground (0.164 m or about 6.5"). A fixed-length 1-segment source wire that is 0.001 wavelength long is at the base of the vertical. The radials and the main element above the source segment are length-tapered from 0.001 wavelength to 0.04 wavelength, which ensures that segments adjacent to the source segment are the same length as the source segment itself.

+

The buried radial system requires a wire junction at ground, so we shall add a 1-segment wire below ground. It is 0.001 wavelength long to match the depth of the radials. The radials and main element above the source wire are length-tapered as in the above-ground model.

+

I constructed radial systems using 4, 8, 16, 32, 64, and 128 radials for the models using NEC-4. The 128-radial system approaches the practical limit of small angles between wires and may result in somewhat dubious results for radial systems of that size. However, the trends in the two types of radial systems are fascinating, as the following tables reveal.

+ 
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Table 1.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength above ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  31 wires; 61 segments
+Very Poor         -1.90       27                41.91 + j 18.38
+Poor              -0.33       25                40.27 + j 22.38
+Good               0.66       22                41.28 + j 23.89
+Very Good          2.45       17                42.26 + j 21.04
+
+8-radials:  55 wires; 109 segments
+Very Poor         -1.47       27                37.49 + j  3.69
+Poor               0.03       25                36.84 + j  6.82
+Good               1.01       22                37.99 + j  8.78
+Very Good          2.81       17                38.89 + j  9.56
+
+16-radials:  103 wires; 205 segments
+Very Poor         -1.34       27                35.91 - j  1.80
+Poor               0.09       25                36.08 + j  0.89
+Good               1.06       22                37.37 + j  2.61
+Very Good          2.92       16                37.91 + j  4.36
+
+32-radials:  199 wires; 397 segments
+Very Poor         -1.29       27                35.09 - j  3.55
+Poor               0.09       25                35.69 - j  1.05
+Good               1.04       22                37.24 + j  0.48
+Very Good          2.92       16                37.83 + j  2.46
+
+64-radials:  391 wires; 781 segments
+Very Poor         -1.23       27                34.36 - j  3.63
+Poor               0.10       25                35.24 - j  1.36
+Good               1.02       22                36.97 - j  0.10
+Very Good          2.91       16                37.91 + j  1.99
+
+128-radials:  775 wires; 1549 segments
+Very Poor         -1.12       27                33.81 - j  3.04
+Poor               0.17       25                34.80 - j  0.95
+Good               1.03       22                36.51 + j  0.04
+Very Good          2.87       16                37.97 + j  1.89
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Table 2.  40-m vertical monopole, 25 mm diameter; 40.96-m (0.25 wavelength) radials, 2 mm
+diameter, tapered segmentation: 0.001 to 0.04 wavelength per wire; radials 0.001
+wavelength below ground; NEC-4.
+
+Soil Type         Gain        TO Angle          Source Impedance
+                  dBi         degrees           R +/- J X Ohms
+
+4-radials:  32 wires; 62 segments
+Very Poor         -4.37       27                87.04 + j 25.31
+Poor              -2.49       25                72.45 + j 19.47
+Good              -0.71       23                60.96 + j 20.42
+Very Good          2.10       17                47.34 + j 14.52
+
+8-radials:  56 wires; 110 segments
+Very Poor         -3.11       28                65.90 + j 18.09
+Poor              -1.51       25                58.63 + j 15.18
+Good              -0.04       23                52.43 + j 15.94
+Very Good          2.60       17                44.34 + j 12.60
+
+16-radials:  104 wires; 206 segments
+Very Poor         -1.61       28                52.71 + j 12.43
+Poor              -0.16       25                49.71 + j 12.18
+Good               0.86       23                46.79 + j 12.83
+Very Good          2.79       16                42.20 + j 11.18
+
+32-radials:  200 wires; 398 segments
+Very Poor         -1.32       27                44.89 + j  7.54
+Poor               0.17       25                43.44 + j  9.55
+Good               1.12       22                42.67 + j 10.46
+Very Good          2.94       17                40.48 + j 10.03
+
+64-radials:  392 wires; 782 segments
+Very Poor         -1.19       27                40.68 + j  4.11
+Poor               0.32       25                39.43 + j  7.08
+Good               1.26       22                39.73 + j  8.50
+Very Good          3.05       17                39.06 + j  9.07
+
+128-radials:  776 wires; 1550 segments
+Very Poor         -1.12       28                38.60 + j  2.18
+Poor               0.17       25                37.32 + j  5.29
+Good               1.03       23                37.91 + j  6.99
+Very Good          2.87       17                37.94 + j  8.27
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+

With better soil quality, the differences in the above-ground and buried radial models are not severe. However, with very poor soil, the 4-radial systems show a great disparity: nearly 2.5 dB. As the graph in Fig. 2 shows, buried radial systems show a rapid rise in gain as radials increase from 4 to 16, but the curves are much shallower after that point. Although the curve for very poor soil continues to rise through 128 radials, the curves for better soils actually decrease in gain from 64 radials upward. Hence, my trepidation over the 128-radial models.

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+ +
+

Perhaps the most telling differences between above-ground and buried radial system models lies in the source impedance reports. Fig. 3 graphs the source resistance of above-ground and buried radial systems for very poor and very good soil through the range of radials used. Note that there is no aberration in the curves, with a steady descent in all cases--hence, a reservation in my trepidation about the 128-radial models. The above-ground and buried radial models for very good soil are quite parallel and not very far apart. However, for very poor soil, the buried radial system model reports much higher values of source resistance with lower numbers of radials.

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+ +
+

The upshot is that above-ground radial systems have severe limitations in their role as substitutes for buried radial systems. If one plans to seriously model buried radial systems, then an investment in NEC-4 is likely the best course.

+

The model that we just used limited the diameter of the main element to an unnaturally low size for 160 meters, and the radials were purposely buried over 6" deep so that a relatively simple model might be used. However, there are many cases of shallower radials and fatter main elements. Either of these cases can press the NEC limits for a good length-to-diameter ratio for the segments.

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The problem has a fairly straightforward solution--and likely not the only one feasible. Fig. 4 sets up a radial system for a main element that is 0.125 m (about 4.92") in diameter, along with a radial system buried only 0.082 m (0.0005 wavelength or 3.3") deep, the dimension D on the sketch. If we use our rule of thumb of keeping the wire lengths in models with complex geometry at a 4:1 length-to-diameter ratio, then the minimum wire or segment length will be 0.5 m, the lengths of A1 and A2 on the sketch.

+

We can start the main element (relative to ground) 0.082 m above ground and use a 1-segment source wire followed by a tapered-length remainder of the element, with the tapering having a 0.5-m minimum length and perhaps a 5-m maximum length for the segments. The first sloping portion of each radial will be from a height of 0.082 m to zero, with the second going from zero to -0.082 m. Since the sine of the angle is 0.082 over 0.5, the angle is 9.44 degrees. The cosine of this angle is .986, so the dimension along the ground is 0.493 m. Little harm would be done in using a round number like 0.5 for this dimension with shallow angles. However, for angles above 30 degrees--which are common in such models--the sloping wire length requires the use of this excursion from dimension to sine to angle to cosine to dimension. Hence, using the full progression of calculations is recommended for all cases.

+

The following table contains partial descriptions (3 of 32 radials in each case) of two models: one is a simple buried radial systems like the one used with the 25-mm main element; the other is a sloping radial model used with a 250-mm main element. The contrast in modeling may reinforce the technique just described.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                     Simple Junction Between Main Element and Radials
+160-m 1/4 wl vertical, tapered radials          Frequency = 1.83  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+1            0.000,  0.000, 40.000  W2E1   0.000,  0.000,  5.242 2.50E+01   7
+2     W1E2   0.000,  0.000,  5.242  W3E1   0.000,  0.000,  2.621 2.50E+01   1
+3     W2E2   0.000,  0.000,  2.621  W4E1   0.000,  0.000,  1.311 2.50E+01   1
+4     W3E2   0.000,  0.000,  1.311  W5E1   0.000,  0.000,  0.655 2.50E+01   1
+5     W4E2   0.000,  0.000,  0.655  W6E1   0.000,  0.000,  0.328 2.50E+01   1
+6     W5E2   0.000,  0.000,  0.328  W7E1   0.000,  0.000,  0.164 2.50E+01   1
+  Tapered-length portion of main element
+7     W6E2   0.000,  0.000,  0.164  W8E1   0.000,  0.000,  0.000 2.50E+01   1
+8     W7E2   0.000,  0.000,  0.000  W9E1   0.000,  0.000, -0.164 2.50E+01   1
+  Fixed wires of main element
+9    W15E1   0.000,  0.000, -0.164 W10E1   0.164,  0.000, -0.164 2.00E+00   1
+10    W9E2   0.164,  0.000, -0.164 W11E1   0.491,  0.000, -0.164 2.00E+00   1
+11   W10E2   0.491,  0.000, -0.164 W12E1   1.147,  0.000, -0.164 2.00E+00   1
+12   W11E2   1.147,  0.000, -0.164 W13E1   2.457,  0.000, -0.164 2.00E+00   1
+13   W12E2   2.457,  0.000, -0.164 W14E1   5.078,  0.000, -0.164 2.00E+00   1
+14   W13E2   5.078,  0.000, -0.164        40.955,  0.000, -0.164 2.00E+00   7
+  First tapered-length radial
+15   W21E1   0.000,  0.000, -0.164 W16E1   0.161,  0.032, -0.164 2.00E+00   1
+16   W15E2   0.161,  0.032, -0.164 W17E1   0.482,  0.096, -0.164 2.00E+00   1
+17   W16E2   0.482,  0.096, -0.164 W18E1   1.125,  0.224, -0.164 2.00E+00   1
+18   W17E2   1.125,  0.224, -0.164 W19E1   2.410,  0.479, -0.164 2.00E+00   1
+19   W18E2   2.410,  0.479, -0.164 W20E1   4.981,  0.991, -0.164 2.00E+00   1
+20   W19E2   4.981,  0.991, -0.164        40.168,  7.990, -0.164 2.00E+00   7
+  Second tapered-length radial
+21   W27E1   0.000,  0.000, -0.164 W22E1   0.151,  0.063, -0.164 2.00E+00   1
+22   W21E2   0.151,  0.063, -0.164 W23E1   0.454,  0.188, -0.164 2.00E+00   1
+23   W22E2   0.454,  0.188, -0.164 W24E1   1.059,  0.439, -0.164 2.00E+00   1
+24   W23E2   1.059,  0.439, -0.164 W25E1   2.270,  0.940, -0.164 2.00E+00   1
+25   W24E2   2.270,  0.940, -0.164 W26E1   4.692,  1.943, -0.164 2.00E+00   1
+26   W25E2   4.692,  1.943, -0.164        37.838, 15.673, -0.164 2.00E+00   7
+  Third tapered-length radial (or 32 total radials)
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     7 / 50.00   (  7 / 50.00)      1.000       0.000       V
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                     Angular-Wire Junction of Main Element and Radials
+160-m 1/4 wl vertical, buried radials                 Frequency = 1.83  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+1            0.000,  0.000, 40.000  W2E1   0.000,  0.000,  4.328 2.50E+02   9
+2     W1E2   0.000,  0.000,  4.328  W3E1   0.000,  0.000,  2.328 2.50E+02   1
+3     W2E2   0.000,  0.000,  2.328  W4E1   0.000,  0.000,  1.328 2.50E+02   1
+  Tapered-length portion of main element
+4     W3E2   0.000,  0.000,  1.328  W5E1   0.000,  0.000,  0.328 2.50E+02   1
+  Fixed length section of main element
+5    W10E1   0.000,  0.000,  0.328  W6E1   0.945,  0.000,  0.000 2.00E+00   1
+6     W5E2   0.945,  0.000,  0.000  W7E1   1.890,  0.000, -0.328 2.00E+00   1
+  Two sloping wires of first radial
+7     W6E2   1.890,  0.000, -0.328  W8E1   2.890,  0.000, -0.328 2.00E+00   1
+8     W7E2   2.890,  0.000, -0.328  W9E1   4.890,  0.000, -0.328 2.00E+00   1
+9     W8E2   4.890,  0.000, -0.328        40.960,  0.000, -0.328 2.00E+00  10
+  Tapered-length portion of first radial
+10   W15E1   0.000,  0.000,  0.328 W11E1   0.927,  0.184,  0.000 2.00E+00   1
+11   W10E2   0.927,  0.184,  0.000 W12E1   1.854,  0.369, -0.328 2.00E+00   1
+  Two sloping wires of second radial
+12   W11E2   1.854,  0.369, -0.328 W13E1   2.834,  0.564, -0.328 2.00E+00   1
+13   W12E2   2.834,  0.564, -0.328 W14E1   4.796,  0.954, -0.328 2.00E+00   1
+14   W13E2   4.796,  0.954, -0.328        40.173,  7.991, -0.328 2.00E+00  10
+  Tapered-length portion of second radial
+15   W20E1   0.000,  0.000,  0.328 W16E1   0.873,  0.362,  0.000 2.00E+00   1
+16   W15E2   0.873,  0.362,  0.000 W17E1   1.746,  0.723, -0.328 2.00E+00   1
+  Two sloping wires of third radial
+17   W16E2   1.746,  0.723, -0.328 W18E1   2.670,  1.106, -0.328 2.00E+00   1
+18   W17E2   2.670,  1.106, -0.328 W19E1   4.518,  1.871, -0.328 2.00E+00   1
+19   W18E2   4.518,  1.871, -0.328        37.842, 15.675, -0.328 2.00E+00  10
+  Tapered-length portion of third radial (of 32 total radials)
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     4 / 50.00   (  4 / 50.00)      1.000       0.000       V
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Sloping radials are not the only complexity that we may encounter when working with radial systems for vertical arrays. Fig. 5 shows two intersecting radial systems for a 2-element array. Only a few wires have been shown in the sketch to preserve some clarity. Between the two radial systems, there is a line of intersection, which for most purposes can be taken as being defined by the midpoint between the two radial systems. Actual radials might well pass over and under each other, as indicated by the dashed extensions in the figure. However, it is also common to join electrically the ends of relevant radials so that the junctions form a line corresponding to the vertical dashed line in the sketch. The junctions along the line of intersection may be connected by wires or simply left open.

+
+ +
+

Fig. 6 shows a 3-system set of intersections. The principles are the same for any number of intersecting radial systems. The key problem in constructing a model is getting rid of overlapping wires, since the NEC core will reject any model with wires that intersect at other than segment junctions. Instead, we need to calculate the coordinates of each intersecting radial so that we end up with true wire junctions.

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+ +
+

The technique is very straight forward, although its execution can be tedious for very large radial systems. Refer to Fig. 7 for guidance. We can find the line of intersection along (let us say) the X axis. Hence, we know the X coordinate of any radial to be shortened for a junction along this line. Since the original and the shortened radial coordinates define a pair of congruent triangles, the ratio of the new (shorter) X-axis coordinate to the original is also the ratio of the new Y-axis coordinate to the original. Of course, both of these numbers are most easily obtained if the origin of the radial system on which we do the original shortening is X=0 and Y=0. (We can always displace the entire system once our calculations and modifications are complete.)

+

If we are using uniform segmentation of the radial wires, then the same ratio that we used to determine the coordinates also tells us the number of segments to use in the shorter radial. The total number of calculations will actually be smaller than we might expect, since we can simply use the values that we get for the positive Y direction in the negative direction with a sign change (assuming an evenly symmetrical radial model). These new radial terminations also become the terminating coordinates for the second radial system where it intersects the first. If a multiple radial system is used and if the junction lines are equally spaced from the center element, the numerical values--with sign adjustments--are applicable to both junction sets. Only the process of entering the values on the wire chart is somewhat tedious and error-prone.

+

The techniques of generating complex radial fields apply equally to those we place above ground and to those we bury. From the notes developed here and using whatever automated facilities may exist within your particular NEC software, you can generate quite reasonable models for virtually any vertical antenna or array that uses a radial system. As we have seen from the preceding columns, such models are much preferable to the all-to-common over-simplifications that we have used in the past.

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Go to Main Index

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4. A Good Start is Half the Trip

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+

L. B. Cebik, W4RNL

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+ Modeling programs are a paradigm of the old saying, "Garbage in, garbage out." However, I prefer to think of this saying in its more positive form: "Good models in, good information out." And getting good information into the NEC or MININEC program is fully half the task in modeling antennas. +

A good model does not begin at the computer, but on a piece of paper. Not just any piece of paper, but some kind of useful form on which you do all the the preliminary work so that you can just transfer the values into the program. (Given the variety of programs, transfer can mean typing up and saving an ASCII input file, entering values in screen tables and entry points, or entering values and selections into a spread-sheet form and pull-down boxes.)

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+ +
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Figure 1 shows a form that I have used for a number of years for common HF and VHF antenna types. Although you can print out the form, you might want to make up your own crisper and more individualized form on a word processor.

+

Let's divide the form into 4 sections and see how it can help our model input work.

+

1. The header: The top lines of the form provide basic information about the model file and the background values within which the antenna will be modeled. The top line forces you to give the model a name--one that is either specific or generic--along with a file name and directory location. The last two items are important once you begin to develop collections of models. It is aggravating to lose ten minutes trying to remember where you stored a file.

+

The second line begins the modeling information. The band(s) entry allows you to specify one or more bands on which the antenna may be used, while the frequency entry is for either the antenna design center frequency or the upper and lower frequencies of a sweep you may intend to perform. The antenna height, even though it may be repeated in the wire table, is a reminder of the intended use of the antenna. Alternatively, if the model is preliminary, you may wish to enter "FS" for free space. Recording the number of elements is a check on the wire table entries below, which may consist of many wires. Recording the units of measure for the antenna elements can save you from trying to mix units later.

+

Recording the ground type and specifications (if other than free space) should be a standard part of your modeling practices. For horizontal antennas, such as dipoles and beams at HF, the use of a ground other than the usual program default may not make significant differences in the data produced by the program for the model. The default for most implementations of NEC and MININEC is "Good" or "Average" soil, with a conductivity of 0.005 S/m and a dielectric constant of 13. These values are taken ultimately from studies performed in the 1930s and often repeated in antenna handbooks.

+

Some programs provide some preset soil types, and the instruction manual will generally describe their values and characteristics--or refer you to the source handbook from which they came. However you obtain the ground values, be sure to enter them both here and in the program. These values are especially important for vertical antennas, whose performance may vary with either or both the ground type directly under the antenna and the ground type at a distance from the antenna. If you plan to use multiple grounds (for example, one in the immediate vicinity of the antenna and another at a distance), you might make an abbreviated entry here and develop the details on unused lines further down the form.

+

Modeling programs may specify the antenna material in one of two ways: either as a material type (such as "copper") or as a specific value. The program may call for either a conductivity or a resistivity value, where one is simply the inverse of the other. For example, copper has a conductivity of 5.8 E 7 (where "E 7" means "10 to the power of 7") S/m, which is equivalent to a resistivity of about 1.7 E -8 Ohms/m. (Some programs will still use "mhos/meter" instead of "Siemens/meter.")

+

As a modeler, you always have the choice to begin your modeling with zero-loss wire. However, it is usually good practice to specify the antenna wire material in terms of the actual material you intend to use (or are using) in order to take its distributed losses into account. In many cases, the differences between zero-loss wire and actual materials may make only insignificant differences in the output data. However, this fact will not be true for all antenna designs. In addition, some programs require a single material for the entire antenna, while others permit material or resistivity/conductivity specification on a wire-by-wire basic. If limited to a single material for some design combination of copper wire and aluminum tubing, you can choose the material that is quantitatively dominant in the design, the one most prominent near the high current regions of the antenna, or simply the one with the higher losses.

+

2. The antenna sketch: To get an understanding of the importance of sketching the antenna to be modeled, let's look at Figure 2, the data sheet for a simple 10-meter aluminum dipole.

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+ +
+

On this data sheet, the header is completely filled in with the basic and background data. Note that for this model, "Free Space" has been selected as the modeling medium. Note also that the material is 6063 aluminum, whose conductivity value may differ from other types of aluminum that might have been used.

+

The sketch itself should be (and this one tries to be) as complete as possible. Not only does the drawing show the overall dimensions, but as well, it displays the lengths and diameters of the individual sections of the dipole elements. Since each change of diameter represents the stop/start point for a wire in the model, complete dimensional data is necessary in order to correctly enter the wire geometry.

+

Although my CAD program has permitted me to overdo the graphical aspects of the antenna sketch, a pencil sketch will normally suffice. However, strive to make it as clear and complete as possible. Remember that it is the fundamental reference for all other modeling work you do.

+

3. The wire chart: NEC and MININEC operate on the basis of wires that are segmented according to rules. A single antenna element may consist of more than one wire, if the diameter changes along the way. In our simple example, we have two 3/16" diameter end pieces and a 1/4" diameter center section.

+

In reality, the center section may consist of 2 pieces of aluminum, slightly separated at a center feedpoint. However, the source (the feedline) is considered to be in series with the segment to which it is connected, and therefore, the wire should be continuous. You can accomplish this by specifying a single 1/4" wire and placing the source at its center. In NEC, you will select an odd number of segments for this wire to ensure source placement at the exact center. In MININEC, you will select an even number of segments to accomplish the same goal. Alternatively, you may choose to create two wires, one for each side of center. By placing a MININEC source at the end of one, it will be correctly placed where the other begins. In NEC, the same task requires selecting or creating a split feed to include the last segment of one wire and the first segment of the next.

+

In this model, I chose a symmetrical arrangement of the element, using the zero point as the center. I also chose to extend the element length along the Y-axis. Since the antenna has only length, the X-axis is always zero, and since it is in free space, the Z or height axis is also zero. (In most programs, the Z axis can be anything when modeling in free space, and you may want to enter for Z the height of intended use for the antenna.)

+

Selecting the Y-axis for the antenna length values over the X-axis may or may not be an arbitrary decision, depending upon the program you are using. Some programs, like AO, have a provision for increasing calculation speed via symmetry. If the antenna elements are centered--but only on the Y-axis--the program can calculate only half the antenna and treat the other half as a mirror image. This feature must be disabled for non-symmetrical antennas or for antennas whose length is specified along the X-axis.

+

In many programs, it makes no difference to calculation speed whether the antenna element lengths appear in either the X-axis or the Y-axis. In some programs, especially when surveying the wire length values of a very complex but linear antenna, it is more visually convenient to scan the left-most X-axis to check for errors. In the end, however, try to adopt one consistent convention for most--if not all--of your models. Swapping axes as you hop from model to model can be a source of unintended errors.

+

Among the most important conventions to adopt is to begin at one end of each antenna element and to proceed from that end to the other without changing directions in mid-stream. In the figure, note that the model proceeds from left to right along the sketch, symmetrically with respect to the zero-point of the Y-axis. Hence, a 16.78' antenna becomes +/-8.39' long.

+

Notice also that end 2 of the first wire becomes the starting point or end 1 of wire 2. For continuous antenna elements, be certain that the X, Y, and Z values of joined ends are the same. Some programs will indicate when wires are connected; others will rely on you to ensure that the junction ends have the same values. NEC connects wires that are within very tiny distances of each other, so also be certain that, if you do not want wires connected, they are far enough apart.

+

Wire entries also require that you specify the wire diameter. Many programs allow you to specify common American AWG wire gauges, which is useful for copper wire antennas. These are converted for the program into actual wire diameters. To be more precise, they are converted in the wire's radius. If you look at the NEC input file in programs that permit this, you will see the converted value of the diameter you entered in the input page or file.

+

You must also specify how many segments the wires will have. In order to make the segments for each wire reasonably close in length, the end wires in Figure 2 have 5 segments (0.78' per segment) and the center wire has 11 (0.82' per segment). Since the center wire containing the feedpoint (source) has an odd number of segments, it is clear that this model is intended for NEC rather than MININEC.

+

4. Source and other data: Missing from the form is any clear specification of the source or feedpoint for the antenna. (Actually, on my own forms, the source specification is on the reverse of the page, along with entry areas for loads, networks, and transmission lines--all subjects of future episodes in this series.) You can and should enter the source specifications on a spare line below the wire lines. For most antennas, this will place the data where it is most usefully compared with the wires themselves.

+

Enter not only the source location, but also the type (voltage or current, single or split) within the limits allowed by the program. We have already seen the utility of split sources. Single voltage sources are the native environment of most modeling programs. However, specifying a current source and giving it a value of 1 is often very useful for comparing current magnitude and phase output data for each segment along the antenna element(s).

+

This model is now ready for conversion into the appropriate program inputs.

+

Some Other Element Entry Considerations: In our fairly simple dipole entry, we had little difficulty in proceeding from element-end to element- end. However, some antenna designs may not make this process so simple in all cases.

+

Having examined numerous antenna models from a wide variety of sources, I am struck by the diversity of ways in which modelers create antenna elements and subdivide them into wires and segments. The variety of ways in which wires are placed into the antenna geometry descriptions often makes it difficult for another modeler to read the wires page. Moreover, many of the models will produce correct far-field data and feedpoint information, but will skew the antenna currents. This latter information can become quite important in analyzing why a complex antenna yields its particular set of performance outcomes.

+

The usual reasons given for the odd collections of wires making up an antenna model are convenience and speed. Many complex antenna element specifications are for half elements, starting at a boom or center point and moving toward the element tip. The specification presumes that other half of the element is a mirror image of the first. So modelers tend to begin in the middle and to work outward. Specification tables usually give the dimensions using positive numbers. Since it is faster to do the positive side, modelers then replicate that side and insert minus signs. Moreover, they tend top go directly from whatever sketch or data sheet they have to the screen entries. I have learned the hard way that slowing down at the beginning saves me a bucket of time later on when I try to troubleshoot my model.

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Let me make some suggestions, scratched with chalk, not etched in stone. They began with my suggestion of always working from one end of the antenna element to the other end, and using the same directional sense for each succeeding antenna element.

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Now consider the element shown in Figure 3. It is one element of a multi- element Yagi. Each element uses many shorter sections of tubing that decreases in diameter as one moves outward from the boom to the end. Let's assume an element that from center outward has these dimensions: 22" at 1.125" diameter; 36" at 1"; 24" at 0.825"; 24" at 0.75"; 24" at 0.625"; and 40.5" at 0.5". The first step is to obtain running totals: 22"; 58"; 82"; 106"; 130"; and 170.5".

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If we follow our conventions, the full element will look like this on paper and in the geometry entry spread sheet (noting that I have in this case chosen to place length values in the X-axis column):

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Wire End 1     x         y    z    End 2     x         y    z    Diameter
+ 1             -170.5    0    0              -130      0    0     .5
+ 2             -130      0    0              -106      0    0     .625
+ 3             -106      0    0              -82       0    0     .75
+ 4             -82       0    0              -58       0    0     .825
+ 5             -58       0    0              -22       0    0     1
+ 6             -22       0    0              22        0    0     1.125
+ 7             22        0    0              58        0    0     1
+ 8             58        0    0              82        0    0     .825
+ 9             82        0    0              106       0    0     .75
+10             106       0    0              130       0    0     .625
+11             130       0    0              170.5     0    0     .5
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(In some programs that permit symbolic entries, the numbers may be replaced by a set of variables indicated by a letter or combination of letters, with a list of values for these variables set out elsewhere.)

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This process may seem like a long way to go, but for an accurate model, all these wires will have to be in the chart anyway. This left-to-right scheme just keeps them well-ordered. Note that wire 6 is the center section and can have the feedpoint specified at its center, with correct segmentation. For NEC, I might assign it 5 segments; for MININEC, 4. The sections with dimensions in the 20s might get 2 segments each, with the 36" section getting 3 segments, and the end sections 4 segments. This procedure keeps segments lengths as close to equalized as this structure permits, while holding the segments lengths well below maximum recommended length.

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Now let's consider a second example: a shortened dipole with wire hats on each end. The hats consist of 4 radial wires and a perimeter wire. Where does the antenna element start and end? Some quick modelers use the horizontal dipole ends and then separately model the wire structures outward and around. However, the wire hat assemblies are part of the antenna. An equally quick second answer is to treat the peaks where the radial wires end as the antenna beginning and ending. Both answers are wrong. The antenna begins and ends where the current goes to zero. MININEC gives a true zero reading, because it takes current nodes to be at the ends of segments. NEC takes current nodes to be at the center of segments, and so the lowest value will never be zero. However, you can get equally low values either side of a correctly chosen wire junction.

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For this example, the antenna begins in four places: at the center of each of the four perimeter lengths. It ends in the comparable places at the other end assembly. Hence, a fully modeled version of this antenna will have, starting on the left end, 8 perimeter wires, each starting mid-length and ending at a radial wire peak. The 4 radial wires come next, working from peak to center, which happens to be the horizontal wire end point. Then we have the horizontal wire, center fed, followed by 4 radial wires working outward from the hub, and finally the 8 perimeter wires, 2 from each peak to common centers.

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In my wire tables, I tend to collect these wires by type so that I can adjust all the radials as a group, adjust all the perimeter wire lengths as a group, etc.

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You can take shortcuts with element structures like the one in the example, but only if a. you can decide in advance that you will never need or want to know the correct current magnitudes and phases on each wire, or b. you are willing to reconstruct the model if you should ever become interested in such matters.

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One More Example: Let's close this exercise with one more example.

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This example is not much more complex than the dipole. However, the differences between the two are interesting. The Yagi design uses inches as the unit of measure and a different type of aluminum from that used for the dipole. Moreover, the antenna is to be modeled over real ground rather than in free space. Both the sketch and the wire table reflect the choice of inches and a ground--the latter evident by the use of a Z-axis value other than zero. (Some programs, such as NEC4WIN, allow you to enter the actual antenna height independently of the Z-axis value.)

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In the wire table, element length values appear in the X-axis column. The element spacing is 57.6" but the reflector is set at the Y-axis value of zero, with the driven element set forward of it. This is one of the two most common conventions for single-driver Yagis. The other convention is to set the driven element at zero, with reflectors given a negative value in the spacing column and directors given positive values in that column. Either convention will work, but once more, it pays to select one convention for all (or at least most) of one's work.

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Finally, the model is set up for MININEC use, since the driver center wire has an even number of segments and runs symmetrically on either side of the feedpoint at its center.

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If racing through the sample models leaves the impression that there are many things to keep track of in correctly setting up even simple models, then the importance of preliminary paperwork should be evident. A good paper model reduces the number of errors and makes the ones that do occur easier to find. The paper model is fully half the trip from antenna idea to useful output data.
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40. Resolution

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L. B. Cebik, W4RNL

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Modelers often seek the shortest run times, the smallest tables, and the least resolution that they can get by with. This somewhat careless practice often begets errors of various sorts. So let's spend a little time looking at the areas of modeling where resolution makes a difference--or at least a potential difference--to the outcome of a modeling session.

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1. Segmentation: Every segment adds more time to each run of the NEC core. Hence, modelers tend to use the least number of segments that they think will do a minimal but adequate job. Of course, the test of whether a model is sufficiently segmented is the convergence test, which we noted in detail in the very first episode of this series.

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There are a number of areas in which we dare not use too few segments. Fig. 1 shows just one sample that should suffice as a reminder for virtually all other cases. In this partial sketch of a common feed for two antenna elements, a single source segment may lead to inaccurate results. Hence, we normally employ at least 3 segments for the common section, and this action may result in quite short segments. The wires moving off from the junctions also require short section, close to a match for the segment lengths in the common wire. With uniform segmentation of the remainder of the antenna, we may end up with a very large model in terms of the number of segments. The modeler can length-taper the elements so that the far ends have longer segments. However, the test of whether a particular scheme of length-tapering (described in discussions of radial is recent episodes) is adequate is a comparison of the results with a uniformly segmented model. Hence, for at least part of our work, very large models for seemingly simple antennas may not be avoidable.

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In some projects, we may be interested in the trends in the current magnitude and phase along elements, for example, in comparing long elements to very short ones or in comparing linear elements to loops of various shapes. Here again, a highly segmented set of elements--with attention to the relative equality of segment length among the items compared--can better reveal the finer details of the trends than truncated versions of the same models.

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Adequate segmentation is also required for precise placement of off-center sources and loads, as suggested in Fig. 2. A dipole that may yield very accurate results with only 11 segments does not provide the modeler with the ability to place an off-center source at exactly 14% of the distance from the element center toward one end. Likewise, a high number of segments are required to place loading inductors 23% of the distance from the element center outward towards the element ends. If one is analyzing an existing antenna that uses such placements, segmentation shortcuts will yield unreliable results.

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Of course, the ultimate model-size cutting exercise occurs with vertical antennas when we attempt to avoid the construction of a radial system. See the last three entries to this series for ways to develop adequate radial systems.

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Segmentation issues affect most of the tabular outputs available from NEC, including the values for currents and far-field strength. Near field and ground wave results are also affected. So it is impossible to over-stress the use of adequate segmentation--both in terms of numbers and in terms of other constraints that we have noted from time to time--in the development of an adequate model. Perhaps the one limitation of some entry-level software is that they place segmentation restrictions on the modeler who takes these notes seriously. Other entry-level software (such as NEC-Win Plus) and upgrades from the entry level, provide more than enough segments for the largest model one might imagine well into one's career.

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2. Pattern Resolution: A second arena in which resolution can make a large difference involves the far-field radiation patterns that we specify. Fig. 3 is a screen grab (from NEC-Win Plus) of an azimuth pattern specification box. Among the matters that we can as users determine is the resolution of the pattern, that is, at what angular increments NEC will produce a table of values out of which the interface program creates a graph of the pattern.

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Three-dimensional patterns, available in some implementations of NEC (for example, NEC-Win Plus and EZNEC 3.0) require a relatively high value for the increment, somewhere between 3 and 5 degrees as the lowest value. Since the program must calculate all values for all bearings in the free-space sphere or the hemisphere over ground, excessive resolution encounters two problems. First, the higher the resolution, the longer the core run time. Second, because the result is presented as a single graphic, the result of maximum resolution would be a solid mass of dots and connecting lines that would obscure the view of useful detail.

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Fig. 4 shows a pair of 3-D patterns of a quad beam over ground, taken from NEC-Win Plus. The 10-degree resolution graphic provides more widely spaced lines for easier identification of portions of the pattern, especially those parts on the far side of the pattern. However, notice the level of distortion to the pattern relative to the 5-degree resolution version. Entire segments of the major lobes appear to be missing from the graphic. In contrast, the 5-degree version show much more detail, but at the expense of blurring the details, especially of the concentrated lobe structure to the rear of the pattern.

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Even the 5-degree 3-D graphic shows strong signs of distortion relative to the actual pattern. The sharp corners taken by lines at intersections are unnatural to normal radiation patterns.

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3-D patterns are both a convenience and often a useful way to cross check our identification of the strongest lobe or the deepest null of a pattern. In addition, we can rapidly survey a pattern for various oddities, such as lobes that increase in strength upward or downward, but which also change the azimuth bearing of maximum strength as we change the elevation angle as well.

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However, the main work of far-field pattern analysis is usually a function of 2-dimension elevation and azimuth patterns. For these patterns, unless we have a special function in mind, we resort to the maximum resolution (or minimum increment) made available to us by a program. For many programs, this is 1 degree. However, some implementations of NEC, such as EZNEC, provide resolutions as fine as 0.1 degree. This degree of fineness requires a table with ten times the number of values as needed with 1-degree resolution, and the graphic calculations naturally take longer. However, the chief question for the modeler is this: when are they useful?

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For most azimuth patterns, a resolution of 1 degree is more than adequate. For very regular patterns with few lobes and nulls, even a 5-degree resolution will yield a satisfactory azimuth pattern. Typical of the antennas able to use lower resolutions in azimuth patterns are the dipole, Yagi, and quad beam.

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Until an wire reaches 10 to 15 wavelengths, a 1-degree resolution captures all of the relevant detail. Non-integer wavelength values (for example, 19.6 wavelengths) that show both emergent and declining lobes and nulls may require a slightly higher resolution to capture every detail of note. As well, complex wire arrays with equally complex phasing conditions among the wires may yield patterns with side and rear structures that benefit from resolutions less than 1 degree. However, these instances are fairly rare.

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More commonly, the modeler requires better than 1-degree resolution with elevation patterns as the antenna height exceeds several wavelength above ground. Let's look at some elevation patterns at different resolution levels and different heights to get a feel for what occurs. We shall use the EZNEC 0.1-degree level, along with the more universal 1.0-degree level. Our subject antenna will be a simple horizontally polarized Yagi set for 299.7925 MHz, so that each wavelength is also 1 meter.

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Fig. 5 shows the elevation patterns for both degrees of resolution at an antenna height of 2 wavelengths. The patterns are indistinguishable to the eye. In fact, both patterns show an elevation angle of maximum radiation (TO angle) of 7 degrees (7.0 in the 0.1-degree system).

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Let's elevate the antenna to 8 wavelengths. For those familiar only with HF antennas, an 8 wavelength height is virtually unthinkable. At 20 meters, we are speaking of 525' or so. However, at 300 MHz, the height is simply 8 meters or about 26' up. As we scan Fig. 6, there appears at first sight to be little difference between the patterns, and the TO angles (2 vs. 1.8 degrees) seem to confirm that the two patterns are virtually identical. However, look closely at the second lobe in the 1-degree resolution pattern. It should be stronger than the third--as shown by the 0.1-degree resolution pattern--but it is not. Slight irregularities in the lobe structure have begun to appear as a result of insufficient pattern resolution.

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If we further elevate the antenna to 10 wavelengths (10 m or 33' at 300 MHz), the irregularities become serious, as shown in Fig. 7. Note that in the 1-degree resolution version of the pattern, many lobes appear as straight-line to points rather than as rounded lobes. Note also that the lowest lobe, which should be the strongest and is the strongest in the 0.1-degree resolution pattern, is weaker than the lobes above it in the 1-degree resolution pattern. In fact, the pattern identifies the TO angle as 7 degrees rather than as the more nearly correct 1.4 degrees.

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Fig. 8 carries the problem still further as we elevate the antenna to 12 wavelengths (12 m or 39'). The 1-degree pattern identifies the strongest lobe at 6 degrees up, whereas the 0.1-degree version places it at 1.2 degrees elevation. Note also that, although all 24 lobes from the ground up to 90 degrees (zenith) are present, the null structure has deteriorated significantly. Compare the two graphs with respect to the interior that shows the depth of nulls. Very often, this structure reveals inadequacies of resolution more evidently than tracing the outer perimeter of the lobes. An adequate pattern for an antenna producing a quite regular far field should show the relatively smooth curve of nulls displayed by the 0.1-degree resolution pattern. If this smooth curve is absent without other known cause, then suspect that the pattern resolution may be inadequate.

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Let's jump to an antenna height of 20 wavelengths (20 m or about 66' at 300 MHz). We can count lobes in Fig. 9 and see that the 1-degree resolution pattern shows only 28 of the 40 total lobes in the 0.1-degree version. Considerable portions of the fine structure of the pattern are missing, and the lower resolution pattern identifies the TO angle as 5 degrees. The more nearly correct value is 0.7 degrees.

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Fig. 10 enlarges the patterns to reveal just how much of the pattern detail has been lost by the 1-degree resolution pattern. Entire sections of the pattern show almost no nulling, and the lobes are irregularly spaced in many areas. Some wider lobes are actually two lobes with the null between having been missed by the lower resolution.

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However, Fig. 10 has a second message for the perceptive viewer. Although the outer limit of the lobe structure appears to form a smooth curve, just as we might expect, the inner structure of nulls is showing the first signs of deterioration. Nothing is seriously amiss yet, and the pattern is perfectly usable for all normal purposes. However, 20 wavelengths is a fairly low height for many UHF antenna installations. Hence, even the 0.1-degree resolution pattern table promises to reach a limit of usefulness at frequencies lower than the limit for the remainder of NEC calculations.

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Vertically polarized antennas tend to show the same signs of inadequate pattern resolution, but in ways whose appearance varies from their horizontally polarized brethren. Therefore, let's look at a 3-element Yagi for 299.7925 MHz that is turned to be vertical. We shall be looking for signs of pattern deterioration that are similar to those we have thus far observed.

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Fig. 11 forms our baseline, with the antenna 3 wavelengths in the air over average ground. Essentially, there is no difference between the two elevation patterns, and the lower (1-degree) resolution version is perfectly adequate for all normal purposes.

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As we raise the antenna to 8 wavelengths (8 m or 26' at 300 MHz), the signs of inadequacy in the 1-degree pattern might elude us, especially if we focus upon the outer edge of the lobes in Fig. 12. However, in the 1-degree resolution pattern, notice the absence of a deep null between the first and second lobes, a sign that the degree of resolution is inadequate to pick up values close to the deepest null. By way of contrast, the interior structure of the 0.1-degree resolution pattern forms a smooth curve. The pattern of lobes and nulls for a vertically polarized antenna is different from that of a horizontally polarized antenna of the same general type. Hence, each polarization will show different outer and inner curves formed by the tips of the lobes and of the nulls.

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By the time we reach an antenna height of 12 wavelengths (12 m or 39'), the 1-degree resolution pattern in Fig. 13 has severely deteriorated to the point of yielding inaccurate information. The higher resolution plot shows the TO angle at 1.2 degrees, with the next major lobe at 3.5 degrees. However, the 1-degree plot--while giving us an accurate 1 degree for the TO angle--reports the next major lobe at 6 degrees. +
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Our last pattern, Fig. 14, taken at an antenna height of 20 wavelengths, shows severe deterioration of both the interior and exterior curves. Contrasting the 0.1 and 1 degree resolution plots should provide ample guidance in detecting when pattern resolution is severely inadequate.

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Conclusion

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The adequacy and accuracy of the information that we derive from NEC models depends to a great degree upon our selections as users. In this episode, we have noted two general areas in which we are prone to use inadequate resolution: segmentation and pattern resolution. Both tendencies can yield unrecognized inaccurate results and should be avoided--without going to the wasteful extreme of using uninformative excess resolution.

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We are also limited to some extent by extant implementations of NEC, only some of which provide either or both the pattern resolution needed for high UHF antennas or the number of segments adequate for large models. Therefore, if we are not going to develop our own interface systems for the available NEC cores, we must use care in selecting the software we buy. As in all such matters, we must match up the software capabilities to the set of anticipated tasks. If entry-level software fails to meet user needs, upgrading is certainly in order.

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41. Multiple-Feedpoint Loop Modeling

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L. B. Cebik, W4RNL

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There are a number of questions that often arise surrounding quad loop modeling. Some of the answers to these question also apply to other antenna models, so it may be worthwhile to spend an inordinate amount of time with the simple quad loop.

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For a single quad loop with a single feedpoint, the conventions of modeling shown in Fig. 1 are very convenient. Essentially, we model "around the horn," taking one wire after the other so that End-2 of the preceding wire matches End-1 of the succeeding wire. We can apply the technique to either square or diamond quad loops--or to any other closed polygon.

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The technique is orderly, giving us a systematic way of keeping track of the wires in complex arrays of which this loop may be one of many. However, the technique has more to recommend it than simple orderliness.

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Fig. 2 shows the current magnitudes and phase angles at selected points around the loop. Each loop side (21.876") for the sample model has 21 segments (in case you want to replicate the exercise). Copper wire and an arbitrary but resonant (+/- j1 Ohm reactance) frequency of 144.4 MHz with #18 wire complete the essential ingredients for the model used here.

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Note that as we begin at the source (the dot in the figure) and move in either direction, we have an orderly progression of current magnitudes and phase angles. Because we have a single feedpoint and a wire that is not perfectly conductive, the midpoints of the vertical wires do not show a relative current magnitude of zero or a phase of exactly -90 degrees. At the upper corners, current magnitude is very slightly less than at the lower corners--not enough to affect antenna operation, but enough to prove that copper has a small amount of resistive loss.

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The figure that may seem oddest to the beginning modeler is the phase angle at the point directly opposite the feed point. However, in most implementations of NEC, phase angle values are run from -179.99 to +179.99. The sudden shift in the phase angle value to +178.1 degrees is the equivalent of having a phase angle of -181.9 degrees. With that mental adjustment, then, we have a seemingly smooth transition of current levels along the quad wires.

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However, appearances--especially when developed by showing only selected values--can be deceiving. Well over half of the current phase transition occurs in the small region around the vertical wire mid-points, where the current magnitude also approaches zero and rises again. This set of transitions is similar to that for a dipole end, except that the dipole end is open.

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In fact, one way to think about a quad loop is as two dipoles with the ends bent toward each other until they touch. The touching ends eliminate the shortening of the so-called end-effect, and a quad loop will have a circumference that is longer than the sum of two dipoles. As well, the effects of changing the wire diameter are opposite each other. For resonance, the fatter the wire of a dipole, the shorter its length must be. For a closed loop, the fatter the wire, the larger the loop circumference for resonance. Despite these behavioral differences, it is often useful to look at a 1 wavelength loop with a single feed as two dipole with touching ends.

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One result of this orientation to the loop is to think of the halves of the overall quad as being in phase and hence additive in their pattern production. In fact, a quad loop of the specifications used in this exercise has a free-space gain of about 3.3 dBi in contrast to the 2.1 dBi gain of a dipole in free space.

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However, if the two halves of the loop, counting from the left side mid-point to the right side mid-point are two dipoles in phase, why does the upper horizontal mid-point show a phase angle about 180 degrees out of phase with the feedpoint? The answer lies partially in the modeling convention we chose and partially in data that we do not see in Fig. 2 (or in any of the usual tables produced by NEC). The wire direction of our continuous loop model is opposite for the upper and lower horizontal wires. Since current values are functions of the End-1 to End-2 orientation of the wires, we find a -180 degree phase angle at the top relative to the zero phase angle at the bottom. What we do not see is that the voltage at the upper mid-point would have a phase angle that is also 180 degrees out of phase with the voltage at the feedpoint. Hence, the combination yields a power that is in phase for the two positions on the wire loop.

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A similar phenomenon occurs with a number of other antennas, some of which are not closed loops. For example, a half square fed at one corner can be thought of as two right angle Vees, each with a quarter wavelength leg vertical. The horizontal quarter wavelength sections join at their ends. The standard and correct way of treating the half square is as two quarter wavelength verticals in phase spaced just about 1/2 wavelength apart. The 1/2 wavelength horizontal wire is often called a phasing line because most of the radiation from it cancels.

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However, if we model two 1/4 wavelength verticals independently, we must provide two sources, each of which have the same current magnitude and phase angle. Only in this way can we obtain a pattern similar to that of the half square. However, if we look at the current tables for the half square, then we find that the current at the corner away from the feedpoint has a phase angle about 180 degrees different from that of the source. Once again, the voltage phase angle at the far corner would also be 180 degrees different from that of the source, establishing an in-phase relationship between the two points.

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For single feed systems, these small mental adjustments make almost no difference in the ways in which we handle loops and half squares in the design or analysis efforts to construct arrays with them. However, the adjustments required begin to make a larger difference--with more room for unseen errors--whenever we begin to look at multiple feedpoints on a single wire structure. For example, we can feed a quad loop at both the upper and lower wire center-points. We might use equal lengths of parallel feedline with a junction to the main feedline directly between the upper and lower loop wires. To feed the loop wires in phase, we would physically run the wires in straight lines, with no twist to either the upper or the lower section from the junction.

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However, our model--if it uses the convention of wire structuring that we started with--will not reflect reality if we feed it as we would when building the physical antenna. Fig. 3 shows two source points, one at the center of each horizontal wire. Both sources are specified for a current magnitude of 1 and a phase angle of 0, as revealed by the designation "No-Twist" on the figure. Relative current magnitude and phase angle values are shown for the same points as in Fig. 2.

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The current magnitude and phase angle values are very much different from those in Fig. 2. In fact, the no-twist sourcing of this model has in fact placed two sources that are 180 degrees out of phase on the model, since a source is in series with its wire. Moreover, the source follows the End-1 to End-2 orientation of the model. Hence, the source on the upper wire is set in the opposite direction as the source on the lower wire. However, we cannot change the voltage phasing, so that the two feedpoints are now out of phase relative to each other.

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A similar situation would occur if we simply placed a second source on the half square at the "other" corner of the array. (In fact, if one draws the open wire ends of a half square together, letting the horizontal wire bend at its center, the result would be a diamond-shaped quad loop.)

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Note that there is no error within NEC in this regard--only an error caused by our not keeping track of the wire directions and making the sources coincide with those directions. Physically, the difference between feeding the two wires in phase and out of phase makes a big difference to the resulting pattern. Fig. 4 shows the patterns for a normal quad with an in-phase dual feed and one that is dual fed out of phase. The "normal" in-phase feed results in pattern lobes broadside to the plane of the loop. In contrast, out-of-phase feeding results in lobes off the edges of the loop--a situation not designed to bring out the best in a multi-element quad beam.

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If we adhere to the initial modeling convention with which we started--remembering that it is most useful for single feedpoint loops--then our model only (and not the physical antenna) will have to place a half twist in one (but not both) of the two sections of feedline from the junction to the antenna wire. Now the model will yield a correct radiation pattern and a set of correct feedpoint values for a dual in-phase feed quad loop.

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However, not everything regarding the model will be in best order. Our artifice, while correcting certain elements of the modeling--the ones of highest interest to most casual modelers--has still left some data out of good order.

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Fig. 5 sketches the dual feed situation with one source set at 0 degrees and the other set at 180 degrees. Around the perimeter are the relative current magnitude and phase angle readouts yielded by NEC for the model. Note initially that each outer corner has a phase angle that is -2.5 degrees relative to the source phase angle. However, their values are very different.

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We may also wish to look at the side mid-point values. Although the current magnitude has gone so close to zero as to not record in limited decimal places, the phase angle is not an anticipated +/-90 degrees. The values differ and depart from 90 degrees by what seems to be a significant amount. However, remember that the closer to the exact mid-point we get, the more rapid is the change of current magnitude and phase angle. At these point--as well as at the open ends of a dipole, NEC calculations may depart by considerable amounts from what we presume (rather than calculate) from theoretical considerations. For the model at hand, the spatial displacement between the calculated +/- 70 degree angles and a true 90 degrees would amount to a very small fraction of an inch at the frequency in question.

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You may establish the correctness of the in-phase feeding as requiring no half twist in reality. Simply construct a small quad loop within the frequency range of whatever antenna analyzer you may have. Use equal lengths of parallel feedline from the two source points to a common junction--and then a length of line about 1 wavelength long to the meter. If you give one section of line a half twist, your source impedance will have a very low resistive component--a few Ohms. With correct in-phase feeding, the resistive component will be moderate to high, depending the length of the two sections of line and where you draw the line between "moderate" and "high."

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If we wish all of our values to be correctly aligned and thus to require no mental adjustments from the modeler, then multiple feed quad loops must employ a different convention from the one with which we started. In short, we must model them as two bent in-phase dipoles. Fig. 6 provides some guidance.

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For a diamond-shaped quad loop, we need add no wires to the model. Instead, we simple model both the upper and lower Vees from left to right, with junctions at the far left and at the far right. (Of course, we might as easily have gone from right to left in both cases, but these notes follow the western convention of reading from left-to-right in most matters.) Now both source points will follow suit and be in phase. However, remember that for highest accuracy, sources at model corners or junctions of wires should use either a short 3-segment wire on which to place the source or use a split source.

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What the square loop gains in simplicity of feeding, it loses in the need to add wires relative to the standard way in which we model quad loops. We must start at the far left mid-point at a junction of two wires, one of which goes down, the other of which goes up. The horizontal wires can be single wires with an odd number of segments in order to center each of the two sources. At the right, we again need two wires, one from the bottom horizontal and the other from the top horizontal--with a junction at the exact center pint between the horizontals. Thus has our 4-wire model of a quad loop grown into 6 wires.

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Segmenting the model also calls for attention. If our horizontal wires have 21 segments apiece, then each of the verticals should use either 10 or 11 segments so that segment lengths will be approximately equal throughout the model. Unfortunately, I still encounter many models that simply give every wire the same number of segments, regardless of the wire length. Sometimes, this practice causes no harm; sometimes it yields significantly flawed modeling results. So I have simply tucked in this reminder.

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Fig. 7 shows the current magnitudes and phase angles that result from the revised model. All four corners of the model are now synchronized. However, do not be fooled by the nicely balanced current values at the mid-points of the sides. The region at the very center of the sides--corresponding roughly to the ends of a dipole--undergoes a very rapid change in current magnitude and phase. You can see this in action by using 100 segments for each of the vertical wires and 201 segments for the horizontals--or as close to this as a software limitation in total segments may permit. Explore especially the current magnitudes and phases for the segments at End 1 of wires 1 and 4 and at End 2 of wires 3 and 6.

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Getting into the habit of modeling dual-feed quad loops (and similar closed polygons) in the way suggested here may not be easy. Of course, since square quad arrays and diamond quad arrays do not differ significantly in performance, you can always simply use diamond-shaped elements and avoid having the 2 extra wires per loop. Or, you can simply model in the old way and make mental adjustments as you go. Or you can simply tell yourself that the current magnitude and phase angle data makes no difference to anything and model in any old way that gets all of the wires roughly in place. None of these options is advisable, although reality tells us that they will be used by some modelers.

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One way to get into the habit of using better conventions in modeling is to annotate models thoroughly. Virtually all software allows for the use of the CM entry--the comment card in the Fortran deck. Besides using this facility to give basic information about the antenna which the model replicates, you should also give yourself a record of any features of the model process that might be subject to memory loss later.

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In addition, if the dual fed quad loop is to be used in an array of loops, it is useful to model each other loop in the same manner as the driven element. This practice will ensure that current magnitude and phase values on the parasitic elements track those on the driver in accurate ways.

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What applies to the quad loop also applies to other types of antennas. Fig. 8 shows the conventional single-feed half square, modeled in typical fashion. However, for a dual feed model that establishes an in-phase feed system, something like the alternative convention should be followed. The vertical wires, as radiators, should be parallel with respect to their End-1 to End-2 orientations. This creates horizontal legs that project toward each other and meet in the middle. Now, when we place separate but in-phase sources at the two corners, the model will perform as it would in reality (apart from the field of sappy pine trees in which we were forced to erect the actual antenna and which are not part of the model).

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Less likely to be done is the alternative method of modeling a folded dipole, as shown in Fig. 9. Note that even with a single feedpoint, the current magnitudes and phases will read differently according to the convention of modeling that we select.

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From these examples, you should have acquired an appreciation for the differences that modeling conventions can make in the data--and sometimes, the pattern--outputs from NEC. In all cases, models should avoid shortcuts. Instead, the conventions adopted for a kind of antenna or array should be those which yield the most correct outputs across the board, whether we intend initially to use some of the data or not. We may often later find occasion to look into the tabular data, and its usefulness without mental or paper conversions--or remaking the initial model--will depend upon the care we use in constructing the initial model.

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42. Moving and Rotating

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L. B. Cebik, W4RNL

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Windows-based facilities make available to the programmer, and the programmer sometimes makes available to the user, the ability to move and manipulate blocks of numbers. Of greatest interest to this series is the ability to move and rotate wires in an antenna model. It is a very handy feature that is often overlooked by users of programs that have it. I tend to use it considerably--even to the point of moving models from one program to another with the facility and back again--if the other program has a feature that I need there.

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So let's tell a short story with lots of pictures to get a handle on moving and rotating the wires of a model.

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Fig. 1 is the outline of a simple 3-element Yagi which happens to be cut for 10 meters. My habitual conventions result in two features of note here. First, I tend to model with the reflector at zero and all other elements having positive spacing values ahead of the reflector. Second, I tend to model element length from -X to +X, which aligns the boom along the Y-axis. Not everybody uses these conventions, so we may wish to translate the model to something in accord with other conventions.

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Fig. 2 shows the main screen of NEC-Win Plus, which happens to have the necessary facilities. The dimensions of the elements appear in the X1 and X2 boxes, with the spacing in the Y1-Y2 boxes. Note the longest element--the reflector--is at Y=0.

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Now move to the "Geometry" box in the upper right corner of the screen. We shall play with only two buttons on the top row. The left button is for rotation, which we shall look at shortly. The middle button is for moving one or more wires, which we shall examine immediately.

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Suppose that we wanted to shift all three wires so that the beam's boom is centered on Y=0. Since the Yagi is 3.41742 m long, we need to move the beam to the rear by -1.70871 m. We can do this by subtracting the movement number from each Y value. However, let's block the entire set of 3 rows and then click on the "Move" button.

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Fig. 3 gives us the resulting screen. The "Move" box is overlaid on the main screen, but you can see the blocking of the relevant wire entries that will allow us to move all three wires at once. In the translation entry area, -1.70871 has been entered for delta-Y. The initial and final positions of the first wired is shown, but the action will affect all of the wires that we have placed in the block.

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Fig. 4 shows the main screen for the finished product. The Y-axis values are now +/-1.70871 m. Note that the driven element for this array is not centered on the boom, but is slightly to the rear of center.

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There are many good reasons for wanting to center a Yagi in this way. For example, if one is modeling a stack of antennas for different bands, one would want the antennas to line up with the mast as the center spot for the array. In some cases, the center of weight will not coincide exactly with the center of the boom, so adjustments may be needed. Nonetheless, the ability to move numerous elements at once by the same precise amount is handy to shorten the work--and to eliminate errors with respect to individual elements.

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Side-by-side stacks are also common. We can use the blocking facility to copy a set of elements from the basic antenna. Then we can move the new elements to their final position by translation in any one or more of the axes. When making up VHF squares of Yagis, for instance, I tend to copy one Yagi. Next, I position each Yagi equal distances on each side of a chosen axis. Then I copy both wire sets to create two more Yagis. These two can be moved together along a single axis to complete the square array.

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Although these actions have been illustrated with NEC-Win Plus, similar movement facilities are available in EZNEC using the "Group" change facilities in that program.

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Now let's suppose that someone prefers to have the Yagi elements extended along the Y-axis, with the boom along the X-axis. The maneuver can be made by going into each wire end entry set and swapping the X1 and Y1--as well as the X2 and Y2--values, wire by wire. However, there is a quicker way using the "Wire Rotate" routine.

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Fig. 5 shows our centered Yagi with all wires within a block. Also in the picture is the rotation box. Since we wish to change the X-Y orientation of the antenna, the rotation will be around the Z-axis. Note the entry of 90 degrees in the "Rotation" area, with the initial and final values for the first wire shown as a check on the work before we commit to it.

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By now, sharp-eyed readers will have noticed that the elements are not perfectly symmetrical relative to the boom axis. As I noted, I often move models from one program to another, and this model originated in another program. Translation from one format to another often requires a bit of clean-up, which has not been performed yet. However, before finalizing a model "for the record," it is important to do the clean-up--not so much because it will change antenna performance reports, but because these small inexactitudes often distract and sometimes confuse others who may examine the model.

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In Fig. 6, we have the rotated antenna wire table--complete with its not-quite-symmetrical elements. However, compare Fig. 6 and Fig. 4 to note the 90-degree reorientation of the beam.

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We could have performed the same rotation on the initial model, which placed that reflector at zero. By rotating the antenna around the Z axis, the reflector would have remained at zero, but on the X rather than the Y axis. The Z-axis is always presumed to have X and Y values of zero. If we had placed the reflector at Y=10 m initially, under rotation, the reflector would end up at X=10 m.

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One convenient use of the rotation facility is to test stacks of Yagis. A common configuration is a stack of 2 Yagis, with one fixed toward a target region (U. S. contesters use Europe as a common target for such arrays). The top beam rotates. Now suppose that we feed both arrays in phase. What happens to the composite pattern as we rotate the upper antenna some angular distance out of perfect alignment.

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Fig. 7 shows the situation. Wires 1-3 represent the lower beam that is fixed. Wires 4-6 represent the upper beam that we intended to rotate. 17 m is a very large spacing for 10-meter arrays, but it will serve for the example. Let's rotate the upper beam 20 degrees and see what happens to the composite pattern.

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The rotation box shows the 20-degree rotation of the blocked wires--the upper Yagi--around the Y-axis. Both beams are otherwise identical. The final position listings in the rotation box may not seem informative at first sight, but they can assist in the prevention of errors before we alter the model itself.

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Fig. 8 gives the final result for the tire upper beam in Wires 4-6. If the coordinates do not seem to let us know that the rotation is correctly done, we can always turn to the antenna view screen.

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Fig. 9 shows the antennas. I have drawn the two arrays closer to each other to reduce the size of the image. However, we can see that the rotated upper array has elements that preserve their alignment with each other. A protractor will confirm that the rotation angle is 20 degrees.

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What we can learn from the exercise may surprise some and be old hat to others. We would want to keep a record for various angular intervals relevant to our concerns--perhaps data and patterns every 20 degrees from in-line to out-of-line (remembering that we will get mirror images as we return from out-of-line back to in-line). Recording gain and front-to-back ratio, and checking the elevation patterns as well as the azimuth patterns will give us a rather complete picture of what happens as we rotate the top beam only.

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In Fig. 10, we can see the pattern for the example. The in-line case would have placed the pattern on a heading of 270 degrees in the plot. With the top beam rotated clockwise by 20 degrees, the maximum forward gain bearing is shifted by only 10-11 degrees. Since this is only a hypothetical exercise, I shall do the unforgivable and leave the remainder of what happens to the gain and front-to-back ratio--as well as to the vertical pattern--to the reader as an exercise well worth doing.

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The ability to rotate several wires at a time in a complex set of wires representing a large stack has further utility. In planning stacks, hams often combine 40-meter beams with multi-band antennas for 20-10 meters. One common technique is to place the 40-meter antenna at right angles to the multi-band array in order to minimize interactions and to permit closer spacing. Assume that the 40-meter array is above the multi-band antenna. Just how much separation is enough for in-line and for 90-degree orientations? A single model with some rotation of one of the two arrays will tell us much.

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We can, of course, combine rotations with movements to try to find the very best position for one array relative to another to minimize unwanted interactions. A similar problem occurs with multi-band quads, but here, the desire is often to place one or more VHF quads in the center region of the larger collection of HF loops. With the rotation facility, we can check performance potential with the VHF quads facing forwards or backwards. Likewise, with the movement facility, we can run the VHF quads forwards and backwards in the quest for perfect, non-interactive placement.

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We can perform similar tests with relative ease for arrays of Yagis or quads formed into squares, triangles, rhombi, etc. Changing separation, forward-rearward alignment, and angular relative positions is made fairly simple by the facilities we have been exploring.

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Let's take a simple example. Suppose we model a square quad for 20 meters. Face-on, it will have the appearance of Fig. 11.

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Now suppose that we wish to convert the square quad into a model of a diamond-shaped quad. One way to do this is to note the length of any one side of each loop in the square quad. From the center of the quad, each unseen support arm will be 0.707 times the length of a side, and this value will determine the plus and minus Z values and the plus and minus X values (or the Y values, if one uses that convention) for the new model. Then we create 8 new wires using these coordinates.

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As the old saying goes, "Stop. There must be an easier way." There is.

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In Fig. 12, we can see the block that encloses the values for the initial square quad. to the right is the rotation box. Our use of it this time will not involve the Z-axis. Instead, we shall use the Y-axis as the axis of rotation. The result will be to turn the elements in terms of the values of X by the amount specified--45 degrees.

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The finished product appears in Fig. 13. Note that the initial quad model had some trailing extra decimal place entries, suggesting once more that I pulled a model from elsewhere and have not cleaned it up yet. Note also that some of the Z values that ought to be zero are calculated to be very tiny numbers (E-5). These certainly should be cleaned up.

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However, except for a little messiness in the fifth decimal place and beyond, the quad has converted to a diamond shape in perfect order, as revealed by Fig. 14. The conversion was much faster than the recalculation of each wire end and reentry from scratch.

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Our work, however, is not finished. Note that the source segment is located along one leg of the driven loop. We need to move the source to one corner. We can implement the source using a split source technique, or we can create a short 3-segment wire at the corner and place the source on the center segment. We connect the ends to each of the adjacent legs of the driven loop that we opened up to make room for the feedpoint wire.

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Rotation in the X and Y axes has many applications beyond the simple case we used as an illustration here. For example, one question raised by operators at both HF and VHF is the effect on skip communications of changing the angle of the antenna relative to the terrain. The ability to rotate the antenna along its boom can provide some provisional answers to these questions--and rotating the entire antenna at once to various angles makes the data gathering process fairly efficient.

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How high must a VHF/UHF beam be to permit its main lobe to accurately track a satellite without undue influence on the elevation of the lobe by ground reflections? Once more, changing both the angle and the elevation of the antenna by rotation and movement actions provides relatively speedy answers.

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How will antennas on separate towers affect each other at various distances and various aiming bearings? The antennas may be at the same or different heights and operate on the same or different frequencies. It is possible to check the current levels of each antenna when one is left unfed while the other is fed. The exercise is never a short one, but the ability to change directions for each antenna, as well a moving them about the hypothetical antenna farm yard, will yield a large batch of data much faster than making changes to the antennas wire by wire.

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Similar analyses can be performed between antennas and wire-grid models of buildings, vehicles, and other objects in the antenna's area. The move and rotation facilities allow the modeler to push buildings around with far greater ease than reinstalling a tower or reconstructing a home or utility building.

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These are only some ways in which the move and rotation facilities in some programs can be used to expedite the gathering of useful data from antenna models. If we master them well, then we may well become interested in tackling larger, more informative projects with our modeling software. I hope these small exercises make you more aware of what is available to you and why it is worthy to become familiar with how to use it.

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I have not focused on scaling elements in this episode largely because we devoted an entire installment to the subject (No. 26). However, it might be useful to note that scaling facilities--whether based on frequency or simple multipliers--add another tool to the collection that can be speed our work and enable us to do more work than we might have initially imagined possible.

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43. Modeling Element Substitutes

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L. B. Cebik, W4RNL

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An under-appreciated property of arrays of many types is the fact that double (and more complex) thin-wire elements can serve as substitutes for impractical fat elements. As we reduce the diameter of an element, the mutual coupling between elements within arrays--both phased and parasitic--decreases, with a consequent decrease in array gain and an offset in frequency of other array properties. Much, but not all, of an array's properties can be fully restored by the substitution for the impractical fat element and the single thin wire element of a double-wire element. For most standard arrays, only the gain will suffer. The double-wire element will restore a good portion of the gain. However, the higher losses of the double wire elements relative to the original fat element will limit the degree of restoration. The larger the number of 1/2 wavelength elements or their equivalents, the lower the percentage of gain restoration. Nonetheless, the use of double-wire elements to preserve such operating parameters as the pattern shape, the front-to-back ratio, and the feedpoint impedance often suffices to make the use of double-wire elements preferable to single thin-wire elements.

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The key question for these notes is how effectively to model double-wire elements so that we meet two criteria:

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  • 1. The substitute element is an effective substitute for the original fat element; and
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The first step in the process is sketched in Fig. 1. We take one representative element from the original array and find its self-resonant frequency. Then we construct a double-thin-wire element model of the same length and place it at the same frequency. We next vary the spacing between the wires each side of a center line until the new element is resonant. Resonance technically means having a purely resistive source impedance with no reactance. There are no task- independent standards for what counts as resonance, but my experience suggests that resonating an antenna within +/-j1 Ohm of reactance is not a difficult task.

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To be exact, we should perform the same exercise with each element within any array. However, unless there are oddities to the array, modeling a single representative element normally suffices to provide a usable uniform wire spacing for double-wire elements throughout the substitute array.

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Critical to the first step and to rebuilding the subject array with double-wire elements is figuring out how to model the substitute elements. Fig. 2 provides one useful technique.

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Assuming a driven element, we need a source wire. For most modeling, the segment with the source should be the same length as the immediately adjacent segments. Hence, the first task is to model a source wire (designated W6 in the sketch) at the element center (assuming for simplicity a symmetrical set of elements in the array). How long we should make the wire and its segments is a function of the wires labeled W4, W5, W7, and W8. The length of each of these wires is one-half the spacing of the double wires in the ultimate substitute element. Hence, the length of the source wire should be close to 1.5 times the spacing of the wires. Arriving at the final number will, of course, require some trial-and-revision modeling in pursuit of the double wire spacing figure in the first step in the process.

+

The end wires (W1 and W11) ideally should be composed of 2 segments each. Equally ideal would be the case of keeping all of the segments in the model the very same length. This practice is the most accurate, but can result in large models even of single elements. The minimum requirement is that the segmentation for each of the 4 long wires (W2, W3, W9, and W10) should be identical to ensure that the segment junctions in parallel wires align with each other. Otherwise, NEC may show some inaccuracies. The level of segmentation along these wires can be determined by experimenting with levels of segmentation on a single element. As the segmentation is reduced from the ideal level, the element reactance will increase. The user must determine at what level the reactance is too high for us to use the element as modeled as a substitute for the original fat-wire element. A few Ohms reactance relative to a resistive value of 70 Ohms is normally acceptable for most design exercises. However, the lower the resistive source impedance values encountered in the array, the higher the need to use more adequate segmentation on the substitute elements.

+

These practices are sufficient for modeling double wire substitute elements for common parasitic arrays, such as Yagis. A 3-element 80-meter Yagi modeled with 4" diameter elements will show considerably more gain than a version made from #12 or #14 AWG wire, even when both are optimized for their wire sizes. Most of the gain--within a few tenths of a dB--can be restored using double-wire equivalents for the 4" elements.

+

A More Complex Case: the Quad Loop

+

Quad beams show relatively narrow operating bandwidth with respect to some parameters, largely because we conventionally construct them from thin wire elements. For most installations, the use of fatter aluminum tubing is impractical. Therefore, the double-wire substitute for a better-performing fat-element version of the quad becomes a desirable alternative.

+
+ +
+

Fig. 3 shows two ways of creating double-wire elements for quads. On the left is the Tee assembly, which places one wire ahead of the original element position and one wire behind the original element position, using a cross or Tee bar attached to the normal quad arm support to hold the wires at a constant distance. Note the use of a shorting wire between the elements at each corner. An alternative to the Tee assembly is the planar arrangement of loops in a double- wire substitute element. The planar assembly places both loops at the same distance from other elements in the array, but one loop must be larger than the other. A good starting point in developing such a loop is to place each loop the same amount larger and smaller than the original element. Extensive modeling with each type of double wire element has shown that in every normal parasitic array tested, there is no performance difference between the two double-loop arrangements so long as the wire spacing is the same within each element.

+

How we then handle the double-wire elements follows the same procedure as for linear elements. See Fig. 4 for the outline of a 2-element quad beam using the Tee arrangement. Of course, the sketch does not show the support structure, which we shall assume is invisible to RF.

+
+ +
+

Especially notable in Fig. 4 is the feedpoint arrangement, which follows the same rules as for the linear elements we examined. The source is on a 3-segment wire at the center of the lower portion of the driven element. The double wire arrangement begins and ends as did the linear element. The only difference is that the elements do not have ends, but form loops. The corner shorting wires are necessary to ensure that each loop in an element has virtually the same current at each corresponding point of each wire. In practice, adding further shorting wires at mid-side points would likely be good building practice.

+
+ +
+

The planar loop structure appears in Fig. 5, a version of the very same quad using the alternative form of loop construction. For many installations, planar loops would be simpler to construct, since they require no addition attachments to the support arms except as necessary to hold the loop corners in place. Likewise, the source treatment for the planar loop driver is the same as for the Tee-assembly. With the planar loop model, it is important to use a level of segmentation that is dictated by the wire spacing in order to keep the segment junctions well aligned. Note at the corners that the outer loop has exactly 2 more segments than the inner loop, which is a function of setting the segment length equal to half the wire spacing. That value is initially directed by the length of the wires from the source wire to each of the longer loop wires.

+

Although linear double-wire elements are quite straightforward to model, loop structures can be sufficiently complex to make it difficult for the modeler to keep his place. Hence, utilizing every available modeling aid, including a good plan on paper before model construction, is always sound advice. However, access to a modeling-by-equation facility can go a long ways toward making the process very easy.

+
+ +
+

Fig. 6 shows the equations page of a NEC-Win Plus model of a 2-element quad. In this simplified version, each of the loop half-sides is defined by a simple equation referenced to the length of a wave at the design frequency (variables A and B). D defines the driver-reflector spacing. H is the user input wire size, corresponding here to #14 AWG wire. We can change the design for other wire sizes by entering the new size and changing the constants in the equations for A, B, and D. We can also change the design frequency in variable G.

+

The essential loop-creation variable is E, which specifies half the distance between #14 wires. The total spacing will be 5"--the selected substitute for the original 0.5" elements upon which the model is based. The rest of the task is simply to set up the wires for the model to make use of these variables.

+
+ +
+

Fig. 7 shows the wire page in symbolic form for the 2-element quad. Wires 1-19 represent the driven element, with the source wire shown in the top place in the listing. Wires 20-33 list the reflector loop, which lacks the need for a source wire and hence uses fewer entries on the wires page. Out of view below the bottom of the figure are the last 4 wires (30-33) which form the corner connectors for the reflector double loop.

+

The length of the source wire is defined in numerical terms so that it is 1.5 times the spacing between wires. Otherwise, the entire structure is set up in terms of variables. The inner and outer loops of each element are set by using the baseline dimensional variable (A or B) and adding to it or subtracting from it half the spacing distance, as represented by variable E. Although the wire page may look complex to newer modelers, consider the ease of introducing errors--if only by transposing digits here and there--should every wire spreadsheet cell need a numeric entry. For example, in the present model, the values of A and B are 51.90357 and 57.3246, which are in fact not used directly on the wire page. Instead, for each entry, we add 2.5 or subtract 2.5 to obtain each of the loop corners.

+

Still, there must be a somewhat easier way to model double-wire elements to arrive at models with fewer segments and even fewer wire entries.

+

Some Simplifications and Cautions

+

We can significantly reduce the level of segmentation if we can do away with the source wire as a separate single wire. There are two ways to accomplish this, as shown in Fig. 8.

+
+ +
+

Below the "standard" treatment of a double-wire assembly, we see an element having two wires and two sources. This wire set might be the center of a linear element or the feedpoint area of a quad loop. By using two sources, we not only eliminate the separate source wire assembly, but as well, we increase the ideal segment length to the actual spacing between the two wires. Once more, we might judiciously reduce segmentation further by sampling a single element as a means of discovering how using few and long segments affects the self-resonant impedance of the element. Once more, the limits of allowable variation depend on the task at hand and are a user-responsibility. For loops, corner shorting wires are required to ensure similar current patterns on the two wires.

+

Calculating the actual source impedance from this virtual parallel feed system requires only a bit of hand-calculator work. Suppose that a quad loop returned values of 165 + j2 Ohms for Source 1 and 138 - j3 Ohms for Source 2. We need not do any fancy vector work to arrive at the final single source value. Instead, use the hand calculator to add the inverses of the two resistances and then take the inverse of the result (75.1). Do the same for the reactance values, taking into account their signs (+j6).

+

Perhaps the only thing that the hand calculation robs us of is using program facilities to determine the SWR and to plot such values over a sweep of frequencies. Only if we can reduce the parallel impedance to a single value within the program can we use these conveniences.

+

The lower portion of Fig. 8 shows one technique that works with good accuracy. We select one of the two wires in the driven double-wire element to be the source wire. From the source segment to the corresponding segment on the other wire within the element, we create a transmission line using the TL facility within NEC. Since the TL line is strictly mathematical, we may choose for it any value of characteristic impedance and any length. The characteristic impedance should be close to the median resistive value between those that would appear on each of the two lines in a parallel source model. Using the figures that we just examined, a characteristic impedance of 150 Ohms would be quite reasonable. Precision is not too critical, since we shall make the line almost impossibly short. Any transmission line effects an impedance transformation continuously down its length. Thus, an extremely short line is needed so that the impedance placed in parallel with the source is as close as possible to that occurring on the second wire of the pair. I have used lines as short as 0.001' with success, although that practice may be a bit fussy. The sample problem return a source impedance of 75.2 + j5.6 Ohms, which is certainly as close as one needs to the calculated parallel values.

+

There are some cautions that must be observed if the TL substitute for a double source is to provide reasonable results--not only in terms of the source impedance, but as well, in terms of the reported far-field pattern. The orientation of the TL line--that is, whether it is "Normal" or "Reversed"--will be a function of how we construct the double wire elements. For example, the portions of the planar quad loops that we connected with a TL line for a single feed both proceeded from -X to +X. Hence, the current direction was the same for both wires. Therefore, we employed the TL as Normal.

+

One convention for constructing continuous loop double wire linear elements is to go around the horn, that is to let the bottom wire move from -X to +X, then to create the end wire, next to make the other long wire move from +X to -X, and finally to close the loop with the other end wire. In this situation, the current direction on the two wires is in opposition. For a single wire element or even such a wire within a parasitic array, there are no negative consequences for the far-field pattern. However, if we had applied the TL line to achieve a simulated parallel source, we would need to use the "Reverse" option, which in fact places a half twist on the line and reorients the sources in parallel.

+

Observing this requirements becomes especially important if we choose to model certain types of driven arrays using double-wire elements as substitutes for single fat elements. The LPDA makes a fine example. It consists of a sequence of linear elements, each of which is connected to the next, both fore and aft, by a phasing line. The line is reversed between each pair of elements.

+
+ +
+

Fig. 9 sketches the forward-most 2 elements of an LPDA array. Assume for the moment that we model each substitute double-wire element as a continuous loop, so that the direction of modeling is reversed for each long wire of each element loop. In order to capture the action of the LPDA, we must parallel the two wires into a virtual single feed point for the phasing line and then we must have a phase reversal between the first element and the second.

+

Using the modeling convention chosen, each element contains within it a phase reversal relative to a parallel feed. Hence, the very short TL we create to connect the two wires within an element must be reversed.

+

We shall connect the "rear" wire of one element to the "forward" wire of the next element. How do we effect the required phase reversal from one element to the next? We do so by making use of the fact that the connected wires already have a reversed phase relative to each other. Hence, we use a phase-line section in its normal mode.

+

It is possible to use an alternative convention in creating the double-wire elements. We can let each wire in the element pair have the same modeling direction, say, from -X to +X. In this case, we would use a normal very short phase line between wires within an element and a reversed phase line to connect one element to the next.

+

Either system will return the same results in terms of array source impedance and far-field pattern values. With careful model construction, both are capable of very useful and accurate results. However, mixing systems tends to yield a bewildering array of meaningless results.

+

Properly and carefully used, the techniques we have explored can allow the modeler to create full models that once seemed too complex to tackle. Often, models use simplified fat-element models for double-wire elements and simply presume that they are "accurate enough." That presumption is wholly unnecessary, since there are a host of techniques, not only to fully model double-wire elements, but as well to do so in reasonably compact models. Therefore, even those having segment-limited NEC modeling programs should be able to handle most of the cases that arise. Moreover, the results obtained--when compared to both fat-wire and single thin-wire models--can be edifying. In fact, they can go a long way toward helping to make design and construction decisions.

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Go to Main Index

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+

44. Designing With NEC: A Case Study
+ Part 1: The 4 Ss

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Recently, I had occasion to design a 4+-element, 5-band quad array. The exercise brought to mind a number of questions that have been sent to me over the last few months, many of which involved ideas that came into play during the process of generating the antenna design. Hence, I thought that making a case study of the design effort might be useful to others who wish to use NEC (or MININEC) to design one or more antennas of the garden variety. By garden variety, I mean antennas of conventional HF and VHF design and structure.

+

The effort begins far from the software itself. Before we are done, we shall be thoroughly involved with NEC, but initially, we start with pencil and paper (or word processor and screen). The first step is deciding and defining what you wish to design.

+

Specifications

+

In any design process, if you do not know what you want to achieve, you will never know when you have achieved it--or why you may be falling short of the goal. Therefore, the first "S" on our list is a set of specification that give a detailed picture of the antenna we wish to design. All such lists involve familiarity with the antenna type so that the specifications are realistic. For the case in hand, the antenna is a 5-band quad on a 26' boom. There will be at least 4 elements per band, arranged in the standard way: a 10' separation of the reflector from the driver, with directors at 8' intervals ahead of the driver.

+

Starting Point

+

Before we complete the list of specifications, let's introduce another "S." Since we do not need to reinvent the large multi-band quad array, we might as well begin with an existing antenna that comes closest to what we wish to design. In this case, it is the "3.5-element" quad array designed by Danny Mees, ON7NQ, and described in some detail in Quad Notes, Vol. 1. For 20, 17, and 15 meters, the antenna has 3 elements that use the 10'-8' spacing. For 12 and 10 meters, Danny inserted an extra element 5' ahead of the reflector (and hence, 5' behind the lower- band drivers). These elements are the drivers for the higher bands, and the remaining two elements become directors. Fig. 1 shows the general outline of the array.

+
+ +
+

By analyzing the ON7NQ array, we can get a fairly good idea of 3+-element performance potentials and put ourselves in a better position to set specifications for the 4+-element array.

+

The following table lists the dimensions of the elements, band-by-band. For the moment, we may ignore the first two columns and focus solely on the side-length and circumference of each element.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ON7NQ 3.5-element 5-Band Quad Dimensions (Inches)
+
+Modeling   Antenna          1/2 Side        Side            Loop
+Variable   Part             Length          Length          Circumference
+A          20 Refl          108.5           217.0           868.0
+B          20 Dri           106.85          213.7           854.8
+C          20 Dir 1         102.5           205.0           820.0
+D          ---
+E          17 Refl          84.25           168.5           674.0
+(F)        (Reserved for Start Frequency)
+G          17 Dri           83.15           166.3           665.2
+H          17 Dir 1         79.9            159.8           639.2
+I          ---
+J          15 Refl          72.4            144.8           579.2
+K          15 Dri           71              142.0           568.0
+L          15 Dir 1         69              138.0           552.0
+M          ---
+N          12 Refl          61.2            122.4           489.6
+O          12 Dri           59.95           119.9           479.6
+P          12 Dir 1         59.1            118.2           472.8
+Q          12 Dir 2         59.35           118.7           474.8
+R          ---
+S          10 Refl          55.34           110.68          442.7
+T          10 Dri           52.9            105.8           423.2
+U          10 Dir 1         52.3            104.6           418.4
+V          10 Dir 2         51.995          103.99          416.0
+(W)        (Reserved for Start Wavelength)
+X          ---
+
+Note:  To convert to meters, divide inches by 39.37.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

These elements were converted into numbers for a NEC-4 model, the details of which we shall shortly address. For now, our main interest lies in the band-by-band performance reports.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  ON7NQ 3.5-element, 5-Band Quad
+NEC-4; Full Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.42       11.83      37.6 - j 18.5    1.66
+14.175     8.29       15.06      44.3 + j  4.4    1.17
+14.35      8.06        9.76      34.8 + j 36.5    2.50
+
+18.068     8.47       21.80      42.7 - j  5.1    1.21
+18.118     8.42       25.52      43.5 - j  0.3    1.15
+18.168     8.36       20.90      43.2 + j  4.6    1.19
+
+21.0       8.43       15.28      49.7 - j 20.1    1.49
+21.225     8.52       20.98      46.4 - j  0.0    1.08
+21.45      8.47       10.24      36.2 + j 30.7    2.16
+
+24.89      9.26       22.72      35.1 - j  2.1    1.43
+24.94      9.22       18.92      41.1 + j  2.3    1.27
+24.99      9.18       16.70      47.6 + j  4.8    1.12
+
+28.0       9.01       18.40      43.8 - j 31.6    1.96
+28.2       9.35       25.89      45.3 - j 11.0    1.29
+28.4       9.62       30.72      51.3 + j  6.8    1.15
+28.6       9.85       22.80      58.7 + j  9.6    1.27
+28.8       9.73       12.38      31.1 + j  8.1    1.68
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The array is a quite good performer of its type, although there are a few areas on which we might like to make improvements as we work toward the larger design. The 20- and 15-meter bands are limited to the lower ends. Whole band coverage would be desirable if possible. It is unlikely that a wire quad array of this order can be made to cover the entire first MHz of 10 meters at the level of performance reported.

+

The antenna also makes evident certain other limits of wire quad arrays. Although monoband Yagis can be designed with better than a 20 dB front-to-back ratio across the band of interest, wire quads have much narrower bandwidth limits. Therefore, a 15 dB front-to-back figure is more likely to be achieved. As well, thin-wire quad arrays are subject to rapid changes in performance characteristics with relatively small changes in frequency. Therefore, it pay to scan the edges as well as the middle of even the narrowest amateur bands to assure adequate performance. Notice, for example, the 6 dB drop in the front-to-back ratio on 12 meters from one edge of the band to the other.

+

Specifications--Again

+

The object of the design process will be an enlarged version of the ON7NQ array, with an extra director 8' in front of the current forward director. The array will retain the extra elements for 12 and 10 meters and place them as in the original. Now we can set some goals derived from the array we have just examined.

+
    +
  • Gain: at least 0.7 dB greater than the existing array
    • +
  • Front-to-Back Ratio: at least 15 dB across each band--if possible
    • +
  • Source Impedance: less than 2:1 50-Ohm SWR for direct feed (individually) on each band with a standard 50-Ohm coaxial cable
    • +
  • Coverage: Full band coverage of all bands, with 800 kHz coverage of 10 meters
    • +
+

Let's see how completely we can realize these goals.

+

Strategy

+

To develop a model with which we can easily work while designing takes some forethought. First, the model will be large--22 elements to be exact, with each element consisting of 4 wires. To meet the general recommendation that segment junctions be aligned as closely as is reasonable possible, the wires for each band will require different levels of segmentation. If 10 meters receives 7 segments per side-wire for each elements, the we should increase the number of segments per side by 2 for each lower band. The 20-meter elements will use 15 segments per side, about twice the number as those in each side of the 10-meter elements. Fig. 2 sketches the segmentation of the reflector elements from the array.

+
+ +
+

The basic model for the array consists of 88 wires and 944 segments. We shall look at the model-size issue momentarily.

+

First, let's examine how design work will proceed. We have the ON7NQ dimensions, but we must allow for the possibility that a larger array will require at least small changes in any of the dimension figures. As well, we must begin with an educated guess at the proper size for the new directors that we shall add. Then, the process will be to optimize the dimensions to achieve the performance specifications.

+

The model will be set in free space so that its dimensions can be set out in terms of both +/-Y and +/-Z. This limits the key dimensional number to one per element. However, manually changing the dimensions of any single element requires up to 16 numerical entries into a wire table, with considerable chance for the usual embarrassing lot of split-key entries and transposed numbers.

+

To simplify the process, I used the model-by-equation facility. The first column of the ON7NQ dimension table lists the variable to which each element dimension is assigned. (Note that the software used, NEC-Win Plus, reserves F for the start frequency and W for the corresponding wavelength.) The variables carry us up through X in the alphabet of available variables. To avoid using up variables on the fixed spacings between elements, these values were entered numerically on the Wires page. Fig. 3 shows a partial page of values.

+
+ +
+

Although not clearly evident from the wires-page graphic, I arranged the wires according to the spacing from the reflector, with all 5 reflectors listed first, from the lowest band to the highest. Then come the two high band drivers, followed by the 5 elements spaced 10' from the reflectors. However, on the equations page, each band's elements are grouped together and labeled, since the optimizing process would proceed one band at a time. Fig. 4 shows the equations page.

+
+ +
+

Segmentation

+

Hand optimizing a design requires many small changes in one or more dimension, followed by a sweep of the band in question to check performance at the band edges and at mid-band. (Of course, more detailed sweeps are occasionally useful to watch the progression of performance characteristics over smaller frequency spreads.) The time required for a NEC run increases with the square of the increase in the number of segments. Anything that might be done to shorten the waiting time would prove useful so long as it did not introduce unacceptable errors in the results.

+

To reduce the size of the model, I reduced the segmentation for each element wire in the following way. 20-, 17-, and 15-meter elements used 7 segments per side, while 12 and 10 meter elements used 5 segments per side. I reached this decision after checking the performance of the ON7NQ array on each band with full segmentation and with the reduced segmentation scheme. Although the numbers did not exactly coincide, the progression of values for each model was sufficiently close to permit initial modeling via the smaller model. However, these results would be considered provisional, pending a recheck using the full segmentation scheme. In that way, only final tweaking--if any should be needed--would require the larger, slower model.

+
+ +
+

The process of hand-optimizing even a complex model like a multi-element, multi- band quad is not completely random. Fig. 5 shows the outline of the new array. The starting point might be anywhere. However, in the development od such arrays, one of the most stable bands turns out to be 15 meters. That is, it tends to be least affected by changes to the other bands. So optimizing 15 meters first is a good way to proceed. Then work outward through 17 meters to 20 meters and inward through 12 meters to 10 meters. As we shall have occasion to note in detail when we evaluate the design, the bands which are not bound by other band elements on both sides tend to be more difficult to set.

+

The development of a design is made easier by attending to details as we proceed. First, although we need to change the source location with every change in band, we can remember where to place the source by annotations on the equations page, as is evident in Fig. 4. Second, we can be alert to patterns that develop on one band and apply them to related bands.

+

A case in point is the fact that for each of the 2 highest bands, the middle director needs to be larger than either the first or the third director. The second director on 20 meters was also larger than the first, although this pattern did not hold for 17 and 15 meters.

+

A second case in point concerns which method to use to arrive at a desired feedpoint impedance. One method involves making changes to the reflector; the other involves work with the directors. In the optimizing process for this array, I quickly learned that enlarging the reflector to increase the feedpoint impedance resulted in more rapid reductions in gain and front-to-back ratio than did the manipulation of the director dimensions.

+

Many of these points are evident in the table of dimensions and variables used for the final version of the design exercise.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+W4RNL 4.5-element 5-Band Quad Dimensions (Inches)
+
+Modeling   Antenna          1/2 Side        Side            Loop
+Variable   Part             Length          Length          Circumference
+A          20 Refl          108.5           217.0           868.0
+B          20 Dri           106.5           213.0           852.0
+C          20 Dir 1          97.5           195.0           780.0
+D          20 Dir 2          98.0           196.0           784.0
+E          17 Refl           84.25          168.5           674.0
+(F)        (Reserved for Start Frequency)
+G          17 Dri            82.8           165.6           662.4
+H          17 Dir 1          79.9           159.8           639.2
+I          17 Dir 2          79.9           159.8           639.2
+J          15 Refl           72.7           145.4           581.6
+K          15 Dri            70.7           141.4           565.6
+L          15 Dir 1          69.75          139.5           558.0
+M          15 Dir 2          69.65          139.3           557.2
+N          12 Refl           61.2           122.4           489.6
+O          12 Dri            60.3           120.6           482.4
+P          12 Dir 1          59.1           118.2           472.8
+Q          12 Dir 2          59.9           119.8           479.2
+R          12 Dir 3          59.3           118.6           474.4
+S          10 Refl           55.0           110.0           440.0
+T          10 Dri            52.9           105.8           423.2
+U          10 Dir 1          52.2           104.4           417.6
+V          10 Dir 2          52.5           105.0           420.0
+(W)        (Reserved for Start Wavelength)
+X          10 Dir 3          52.0           104.0           416.0
+
+Note:  To convert to meters, divide inches by 39.37.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance figures reported by the small model used to manipulate dimensions are as follows.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  W4RNL 4.5-element, 5-Band Quad
+NEC-2; Reduced Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.81       15.13      33.9 - j 20.3    1.86
+14.175     8.57       16.66      52.0 + j 10.3    1.23
+14.35      8.13        9.92      57.7 + j 34.1    1.89
+
+18.068     9.21       21.09      35.6 - j  2.6    1.41
+18.118     9.17       21.91      38.8 + j  5.0    1.32
+18.168     9.09       18.22      41.9 + j 11.9    1.37
+
+21.0       9.41       15.09      41.0 - j 16.6    1.51
+21.225     9.42       17.06      56.3 + j  7.6    1.20
+21.45      9.53       20.97      34.5 + j  8.1    1.52
+
+24.89      10.19      21.88      40.7 + j  4.1    1.25
+24.94      10.21      19.60      42.2 + j  7.3    1.26
+24.99      10.18      16.57      43.5 + j 12.0    1.34
+
+28.0        9.51      12.01      39.7 - j 27.9    1.92
+28.2       10.08      16.81      48.6 - j 12.4    1.29
+28.4       10.54      20.44      47.2 - j  2.8    1.08
+28.6       10.81      19.69      42.2 + j 17.2    1.50
+28.8       10.53      32.57      64.7 + j 15.4    1.45
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Before we comment on the success or failure of the design exercise, let's look at the numbers that emerged from the use of the fully segmented model on NEC-2.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  W4RNL 4.5-element, 5-Band Quad
+NEC-2; Full Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.81       15.02      33.6 - j 20.5    1.88
+14.175     8.58       16.76      51.9 + j 10.0    1.22
+14.35      8.14        9.96      57.8 + j 33.8    1.89
+
+18.068     9.24       22.03      36.0 - j  1.7    1.39
+18.118     9.18       21.26      39.3 + j  5.7    1.31
+18.168     9.10       17.39      42.3 + j 12.5    1.37
+
+21.0       9.49       15.33      41.4 - j 15.6    1.47
+21.225     9.47       17.04      57.0 + j  7.5    1.21
+21.45      9.55       19.16      31.3 + j  9.9    1.70
+
+24.89      10.27      21.77      38.6 + j  5.2    1.33
+24.94      10.29      19.80      40.2 + j  9.1    1.34
+24.99      10.25      16.77      41.9 + j 14.3    1.43
+
+28.0        9.59      12.15      40.7 - j 27.4    1.88
+28.2       10.15      17.00      49.3 - j 12.7    1.29
+28.4       10.60      20.50      47.1 - j  2.8    1.09
+28.6       10.85      19.76      42.6 + j 18.0    1.52
+28.8       10.51      29.74      64.9 + j 12.1    1.40
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The deviations between the two sets of numbers are noticeable, but not large. Perhaps the greatest difference occurs on 12 meters, where the segmentation on the small model shifted to 5 segments per wire from the higher value of 7 used for 20-15 meters. Nonetheless, nothing in the sweeps of the larger model suggested that any modifications to the design were necessary.

+

On occasion, NEC-2 and NEC-4 may differ slightly in values reported for quad arrays. This difference is most noticeable in monoband arrays where an array is set to a precise resonance (less than 1 Ohm reactance) and/or a precise front-to-back peak value at the design frequency. The differences are usually a matter for +/- 10 kHz or so in the frequency of resonance or front-to-back peak. Although the differences are small--perhaps less than operationally significant--a sweep of the design using NEC-4 seemed in order to be certain that some of the more rapidly changing operational characteristics did not yield odd results.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  W4RNL 4.5-element, 5-Band Quad
+NEC-4; Full Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.81       15.02      33.7 - j 20.8    1.88
+14.175     8.58       16.76      51.9 + j 10.0    1.22
+14.35      8.14        9.95      57.8 + j 34.0    1.89
+
+18.068     9.23       22.01      36.1 - j  1.8    1.39
+18.118     9.18       21.24      39.2 + j  5.7    1.32
+18.168     9.10       17.38      42.3 + j 12.5    1.38
+
+21.0       9.49       15.33      41.5 - j 15.6    1.47
+21.225     9.47       17.04      57.0 + j  7.5    1.21
+21.45      9.54       19.13      31.3 + j 10.0    1.70
+
+24.89      10.27      21.79      38.6 + j  5.3    1.33
+24.94      10.28      19.82      40.3 + j  9.1    1.35
+24.99      10.24      16.77      41.9 + j 14.4    1.43
+
+28.0        9.59      12.15      40.8 - j 27.4    1.88
+28.2       10.15      17.00      49.3 - j 12.7    1.29
+28.4       10.60      20.51      47.1 - j  2.8    1.09
+28.6       10.85      19.77      42.6 + j 18.1    1.52
+28.8       10.51      29.75      64.9 + j 12.1    1.40
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Happily, the NEC-2 and NEC-4 results are coincident to the nth degree. I list them here simply to note that, where the software is available, such checks are useful and advisable. The check is especially applicable in this case, where the model-by-equation facility was not available in a NEC-4 version for use from the beginning of the process of design.

+

So now we have a design for a 4.5-element quad on a 26' boom. However, we still have two major question areas left over. First, is the design--as a design--successful relative to the specifications that we set up originally? Second, what relationship does this design--as a model--have to an eventual physical antenna? We shall look at both questions and the collection of data that forms some kind of a set of answers to them next time.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod45-1.gif b/content/amod/amod45-1.gif new file mode 100644 index 0000000..a9a36d0 Binary files /dev/null and b/content/amod/amod45-1.gif differ diff --git a/content/amod/amod45-2.gif b/content/amod/amod45-2.gif new file mode 100644 index 0000000..1337ad8 Binary files /dev/null and b/content/amod/amod45-2.gif differ diff --git a/content/amod/amod45-3.gif b/content/amod/amod45-3.gif new file mode 100644 index 0000000..f14bfd4 Binary files /dev/null and b/content/amod/amod45-3.gif differ diff --git a/content/amod/amod45-4.gif b/content/amod/amod45-4.gif new file mode 100644 index 0000000..e5b7ced Binary files /dev/null and b/content/amod/amod45-4.gif differ diff --git a/content/amod/amod45-5.gif b/content/amod/amod45-5.gif new file mode 100644 index 0000000..8eba95d Binary files /dev/null and b/content/amod/amod45-5.gif differ diff --git a/content/amod/amod45.html b/content/amod/amod45.html new file mode 100644 index 0000000..50d3121 --- /dev/null +++ b/content/amod/amod45.html @@ -0,0 +1,238 @@ + + + + + Designing With NEC: A Case Study + + + +
+

45. Designing With NEC: A Case Study
+ Part 2: Evaluation and Reality

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the first part of the case study, we looked at the 4 Ss of designing by modeling: Starting Point, Specifications, Strategy, and Segmentation. Essentially, we began with a design by ON7NQ and built upon it on the way to developing the following antenna model, shown as a wire assembly:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+W4RNL 4.5-Element, 5-Band Quad Model
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1     W4E2   0.000,-108.50,-108.50  W2E1   0.000,108.500,-108.50 8.09E-02  15
+2     W1E2   0.000,108.500,-108.50  W3E1   0.000,108.500,108.500 8.09E-02  15
+3     W2E2   0.000,108.500,108.500  W4E1   0.000,-108.50,108.500 8.09E-02  15
+4     W3E2   0.000,-108.50,108.500  W1E1   0.000,-108.50,-108.50 8.09E-02  15
+5     W8E2   0.000,-84.250,-84.250  W6E1   0.000, 84.250,-84.250 8.09E-02  13
+6     W5E2   0.000, 84.250,-84.250  W7E1   0.000, 84.250, 84.250 8.09E-02  13
+7     W6E2   0.000, 84.250, 84.250  W8E1   0.000,-84.250, 84.250 8.09E-02  13
+8     W7E2   0.000,-84.250, 84.250  W5E1   0.000,-84.250,-84.250 8.09E-02  13
+9    W12E2   0.000,-72.700,-72.700 W10E1   0.000, 72.700,-72.700 8.09E-02  11
+10    W9E2   0.000, 72.700,-72.700 W11E1   0.000, 72.700, 72.700 8.09E-02  11
+11   W10E2   0.000, 72.700, 72.700 W12E1   0.000,-72.700, 72.700 8.09E-02  11
+12   W11E2   0.000,-72.700, 72.700  W9E1   0.000,-72.700,-72.700 8.09E-02  11
+13   W16E2   0.000,-61.200,-61.200 W14E1   0.000, 61.200,-61.200 8.09E-02   9
+14   W13E2   0.000, 61.200,-61.200 W15E1   0.000, 61.200, 61.200 8.09E-02   9
+15   W14E2   0.000, 61.200, 61.200 W16E1   0.000,-61.200, 61.200 8.09E-02   9
+16   W15E2   0.000,-61.200, 61.200 W13E1   0.000,-61.200,-61.200 8.09E-02   9
+17   W20E2   0.000,-55.000,-55.000 W18E1   0.000, 55.000,-55.000 8.09E-02   7
+18   W17E2   0.000, 55.000,-55.000 W19E1   0.000, 55.000, 55.000 8.09E-02   7
+19   W18E2   0.000, 55.000, 55.000 W20E1   0.000,-55.000, 55.000 8.09E-02   7
+20   W19E2   0.000,-55.000, 55.000 W17E1   0.000,-55.000,-55.000 8.09E-02   7
+21   W24E2  60.000,-60.300,-60.300 W22E1  60.000, 60.300,-60.300 8.09E-02   9
+22   W21E2  60.000, 60.300,-60.300 W23E1  60.000, 60.300, 60.300 8.09E-02   9
+23   W22E2  60.000, 60.300, 60.300 W24E1  60.000,-60.300, 60.300 8.09E-02   9
+24   W23E2  60.000,-60.300, 60.300 W21E1  60.000,-60.300,-60.300 8.09E-02   9
+25   W28E2  60.000,-52.900,-52.900 W26E1  60.000, 52.900,-52.900 8.09E-02   7
+26   W25E2  60.000, 52.900,-52.900 W27E1  60.000, 52.900, 52.900 8.09E-02   7
+27   W26E2  60.000, 52.900, 52.900 W28E1  60.000,-52.900, 52.900 8.09E-02   7
+28   W27E2  60.000,-52.900, 52.900 W25E1  60.000,-52.900,-52.900 8.09E-02   7
+29   W32E2 120.000,-106.50,-106.50 W30E1 120.000,106.500,-106.50 8.09E-02  15
+30   W29E2 120.000,106.500,-106.50 W31E1 120.000,106.500,106.500 8.09E-02  15
+31   W30E2 120.000,106.500,106.500 W32E1 120.000,-106.50,106.500 8.09E-02  15
+32   W31E2 120.000,-106.50,106.500 W29E1 120.000,-106.50,-106.50 8.09E-02  15
+33   W36E2 120.000,-82.800,-82.800 W34E1 120.000, 82.800,-82.800 8.09E-02  13
+34   W33E2 120.000, 82.800,-82.800 W35E1 120.000, 82.800, 82.800 8.09E-02  13
+35   W34E2 120.000, 82.800, 82.800 W36E1 120.000,-82.800, 82.800 8.09E-02  13
+36   W35E2 120.000,-82.800, 82.800 W33E1 120.000,-82.800,-82.800 8.09E-02  13
+37   W40E2 120.000,-70.700,-70.700 W38E1 120.000, 70.700,-70.700 8.09E-02  11
+38   W37E2 120.000, 70.700,-70.700 W39E1 120.000, 70.700, 70.700 8.09E-02  11
+39   W38E2 120.000, 70.700, 70.700 W40E1 120.000,-70.700, 70.700 8.09E-02  11
+40   W39E2 120.000,-70.700, 70.700 W37E1 120.000,-70.700,-70.700 8.09E-02  11
+41   W44E2 120.000,-59.100,-59.100 W42E1 120.000, 59.100,-59.100 8.09E-02   9
+42   W41E2 120.000, 59.100,-59.100 W43E1 120.000, 59.100, 59.100 8.09E-02   9
+43   W42E2 120.000, 59.100, 59.100 W44E1 120.000,-59.100, 59.100 8.09E-02   9
+44   W43E2 120.000,-59.100, 59.100 W41E1 120.000,-59.100,-59.100 8.09E-02   9
+45   W48E2 120.000,-52.200,-52.200 W46E1 120.000, 52.200,-52.200 8.09E-02   7
+46   W45E2 120.000, 52.200,-52.200 W47E1 120.000, 52.200, 52.200 8.09E-02   7
+47   W46E2 120.000, 52.200, 52.200 W48E1 120.000,-52.200, 52.200 8.09E-02   7
+48   W47E2 120.000,-52.200, 52.200 W45E1 120.000,-52.200,-52.200 8.09E-02   7
+49   W52E2 216.000,-97.500,-97.500 W50E1 216.000, 97.500,-97.500 8.09E-02  15
+50   W49E2 216.000, 97.500,-97.500 W51E1 216.000, 97.500, 97.500 8.09E-02  15
+51   W50E2 216.000, 97.500, 97.500 W52E1 216.000,-97.500, 97.500 8.09E-02  15
+52   W51E2 216.000,-97.500, 97.500 W49E1 216.000,-97.500,-97.500 8.09E-02  15
+53   W56E2 216.000,-79.900,-79.900 W54E1 216.000, 79.900,-79.900 8.09E-02  13
+54   W53E2 216.000, 79.900,-79.900 W55E1 216.000, 79.900, 79.900 8.09E-02  13
+55   W54E2 216.000, 79.900, 79.900 W56E1 216.000,-79.900, 79.900 8.09E-02  13
+56   W55E2 216.000,-79.900, 79.900 W53E1 216.000,-79.900,-79.900 8.09E-02  13
+57   W60E2 216.000,-69.750,-69.750 W58E1 216.000, 69.750,-69.750 8.09E-02  11
+58   W57E2 216.000, 69.750,-69.750 W59E1 216.000, 69.750, 69.750 8.09E-02  11
+59   W58E2 216.000, 69.750, 69.750 W60E1 216.000,-69.750, 69.750 8.09E-02  11
+60   W59E2 216.000,-69.750, 69.750 W57E1 216.000,-69.750,-69.750 8.09E-02  11
+61   W64E2 216.000,-59.900,-59.900 W62E1 216.000, 59.900,-59.900 8.09E-02   9
+62   W61E2 216.000, 59.900,-59.900 W63E1 216.000, 59.900, 59.900 8.09E-02   9
+63   W62E2 216.000, 59.900, 59.900 W64E1 216.000,-59.900, 59.900 8.09E-02   9
+64   W63E2 216.000,-59.900, 59.900 W61E1 216.000,-59.900,-59.900 8.09E-02   9
+65   W68E2 216.000,-52.500,-52.500 W66E1 216.000, 52.500,-52.500 8.09E-02   7
+66   W65E2 216.000, 52.500,-52.500 W67E1 216.000, 52.500, 52.500 8.09E-02   7
+67   W66E2 216.000, 52.500, 52.500 W68E1 216.000,-52.500, 52.500 8.09E-02   7
+68   W67E2 216.000,-52.500, 52.500 W65E1 216.000,-52.500,-52.500 8.09E-02   7
+69   W72E2 312.000,-98.000,-98.000 W70E1 312.000, 98.000,-98.000 8.09E-02  15
+70   W69E2 312.000, 98.000,-98.000 W71E1 312.000, 98.000, 98.000 8.09E-02  15
+71   W70E2 312.000, 98.000, 98.000 W72E1 312.000,-98.000, 98.000 8.09E-02  15
+72   W71E2 312.000,-98.000, 98.000 W69E1 312.000,-98.000,-98.000 8.09E-02  15
+73   W76E2 312.000,-79.900,-79.900 W74E1 312.000, 79.900,-79.900 8.09E-02  13
+74   W73E2 312.000, 79.900,-79.900 W75E1 312.000, 79.900, 79.900 8.09E-02  13
+75   W74E2 312.000, 79.900, 79.900 W76E1 312.000,-79.900, 79.900 8.09E-02  13
+76   W75E2 312.000,-79.900, 79.900 W73E1 312.000,-79.900,-79.900 8.09E-02  13
+77   W80E2 312.000,-69.650,-69.650 W78E1 312.000, 69.650,-69.650 8.09E-02  11
+78   W77E2 312.000, 69.650,-69.650 W79E1 312.000, 69.650, 69.650 8.09E-02  11
+79   W78E2 312.000, 69.650, 69.650 W80E1 312.000,-69.650, 69.650 8.09E-02  11
+80   W79E2 312.000,-69.650, 69.650 W77E1 312.000,-69.650,-69.650 8.09E-02  11
+81   W84E2 312.000,-59.300,-59.300 W82E1 312.000, 59.300,-59.300 8.09E-02   9
+82   W81E2 312.000, 59.300,-59.300 W83E1 312.000, 59.300, 59.300 8.09E-02   9
+83   W82E2 312.000, 59.300, 59.300 W84E1 312.000,-59.300, 59.300 8.09E-02   9
+84   W83E2 312.000,-59.300, 59.300 W81E1 312.000,-59.300,-59.300 8.09E-02   9
+85   W88E2 312.000,-52.000,-52.000 W86E1 312.000, 52.000,-52.000 8.09E-02   7
+86   W85E2 312.000, 52.000,-52.000 W87E1 312.000, 52.000, 52.000 8.09E-02   7
+87   W86E2 312.000, 52.000, 52.000 W88E1 312.000,-52.000, 52.000 8.09E-02   7
+88   W87E2 312.000,-52.000, 52.000 W85E1 312.000,-52.000,-52.000 8.09E-02   7
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In order to evaluate the design--while still in its modeling stage--let's review the performance of the smaller ON7NQ design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  ON7NQ 3.5-element, 5-Band Quad
+NEC-4; Full Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.42       11.83      37.6 - j 18.5    1.66
+14.175     8.29       15.06      44.3 + j  4.4    1.17
+14.35      8.06        9.76      34.8 + j 36.5    2.50
+
+18.068     8.47       21.80      42.7 - j  5.1    1.21
+18.118     8.42       25.52      43.5 - j  0.3    1.15
+18.168     8.36       20.90      43.2 + j  4.6    1.19
+
+21.0       8.43       15.28      49.7 - j 20.1    1.49
+21.225     8.52       20.98      46.4 - j  0.0    1.08
+21.45      8.47       10.24      36.2 + j 30.7    2.16
+
+24.89      9.26       22.72      35.1 - j  2.1    1.43
+24.94      9.22       18.92      41.1 + j  2.3    1.27
+24.99      9.18       16.70      47.6 + j  4.8    1.12
+
+28.0       9.01       18.40      43.8 - j 31.6    1.96
+28.2       9.35       25.89      45.3 - j 11.0    1.29
+28.4       9.62       30.72      51.3 + j  6.8    1.15
+28.6       9.85       22.80      58.7 + j  9.6    1.27
+28.8       9.73       12.38      31.1 + j  8.1    1.68
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For comparison, here are the modeled performance figures for the larger design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  W4RNL 4.5-element, 5-Band Quad
+NEC-4; Full Segmentation
+
+Freq.      Gain       Front/Back Impedance        50-Ohm
+MHz        dBi          dB       R +/- jX         SWR
+
+14.0       8.81       15.02      33.7 - j 20.8    1.88
+14.175     8.58       16.76      51.9 + j 10.0    1.22
+14.35      8.14        9.95      57.8 + j 34.0    1.89
+
+18.068     9.23       22.01      36.1 - j  1.8    1.39
+18.118     9.18       21.24      39.2 + j  5.7    1.32
+18.168     9.10       17.38      42.3 + j 12.5    1.38
+
+21.0       9.49       15.33      41.5 - j 15.6    1.47
+21.225     9.47       17.04      57.0 + j  7.5    1.21
+21.45      9.54       19.13      31.3 + j 10.0    1.70
+
+24.89      10.27      21.79      38.6 + j  5.3    1.33
+24.94      10.28      19.82      40.3 + j  9.1    1.35
+24.99      10.24      16.77      41.9 + j 14.4    1.43
+
+28.0        9.59      12.15      40.8 - j 27.4    1.88
+28.2       10.15      17.00      49.3 - j 12.7    1.29
+28.4       10.60      20.51      47.1 - j  2.8    1.09
+28.6       10.85      19.77      42.6 + j 18.1    1.52
+28.8       10.51      29.75      64.9 + j 12.1    1.40
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Design Evaluation

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In this morass of data are some significant figures. First, note that, to a very large degree, the performance curves of the larger array on each band tend to replicate the curves of the smaller array, but with a higher gain. The replication strongly suggests that--with a few exceptions--the array has yielded about all of the performance of which it is capable. But how well did it meet its specifications?

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1. Gain: at least 0.7 dB greater than the existing array

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Although the improvement in gain is not a constant for any individual band, the following average gain advantage/band list suggest the performance improvement provided by the extra set of directors.

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Performance Improvement:  3.5 Elements vs. 4.5 Elements
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+20 Meters             0.25 dB
+17                    0.75
+15                    1.03
+12                    1.04
+10                    0.90
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Only 20 meters fails to show a considerable gain increase. The reasons will be explained in the discussion of "Coverage."

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2. Front-to-Back Ratio: at least 15 dB across each band--if possible

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Only the upper end of 20 meters and the lowest end of 10 meters fail to reach the 15-dB front-to-back ratio. The 10-meter low-end failure stems from the fundamental narrow-band nature of wire quads. The SWR curve is wider than the front-to-back curve in virtually all cases, even when the front-to-back limit is lowered to 15 dB.

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3. Source Impedance: less than 2:1 50-Ohm SWR for direct feed (individually) on each band with a standard 50-Ohm coaxial cable

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The 4.5-element array, unlike the 3.5-element quad, achieves the SWR goal on all bands, with the restriction of 10 meters to the first 800 kHz of the band. The failure of the 3.5-element quad to achieve the SWR goal on 15 meters is correctable with slight shortening of the driven element. The SWR at the low end of the band (1.49:1) suggests that considerably more capacitive reactance can be tolerated at 21 MHz, with a consequent lowering of inductive reactance at the high end of the band. However, this approach does not work on 20 meters, since the low-end resistive component is well below 40 Ohms, indicating a limit to the capacitive reactance increase that might be tolerated. One or the other end of the band ends up with an SWR in excess of 2:1

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4. Coverage: Full band coverage of all bands, with 800 kHz coverage of 10 meters

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This criterion essentially is a replication of the SWR specification. The breadth of 10 meters has already been noted as the source of the cut-off at 28.8 MHz and the low front-to-back ratio and gain in the first 100 kHz of the band. However, 20 meters also calls for comment.

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On a normal (20-10-meter) quad, 20-meters is unbounded on the outside. Moreover, the boom length for 4 elements is exceptionally short. 26' would be about the normal boom length for a 3-element monoband 20-meter quad, although the gain would be similar to the peak value for the large array on 20. To achieve full band coverage with the 4.5-element antenna, considerable changes to the director sizes were needed compared to the 3.5-element array director. As well, the forward director is larger than the inner director.

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It is possible with larger directors to achieve higher gain over part of the 20-meter band. Free-space gain values up to 9.25 dBi were achieved in some versions, but the higher the gain, the narrower the available operating region, as defined by the 2:1 SWR figure. As well, the checkpoint numbers recorded to indicate array behavior tend to gloss over many facets of both gain and front-to-back ratio. For example, on 20 meters, maximum gain occurs just above the lower end of the band, with maximum front-to-back occurring at about 14.1 MHz. Hence, it pays to use checkpoint data with caution and to perform detailed frequency sweeps for each band to assess the performance more thoroughly.

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To achieve an acceptable SWR value for the entire band, it was necessary to accept as well a lower gain value. The performance tapers off at the high end of the band, although operation on that portion of the band is possible. By accepting a bandwidth restriction on 20 meters, the smaller 3.5-element array was able to achieve somewhat higher gain at the low end of the band relative to its size. Therefore, the small average gain increase on 20 for the 4.5-element array results in part from differences in the design specifications for the two different antennas.

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If one were to increase the boom length to 30 feet, changing the forward director spacing from 8' relative to the preceding elements to 12' from that element set, it is possible to elevate 20-meter performance by about 0.2 dB with a very slight decrease in the gain slope and to obtain a very slightly shallower front-to-back curve with small rises in the band edge performance. However, the cost in terms of a longer boom, with consequential loading considerations, may make this small gain somewhat gratuitous. In any event, the potential is there for anyone who wishes to re-tweak the array on all other bands.

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Reality 1: Pattern Shapes

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Some designers expect multi-band arrays to achieve patterns similar to those of monoband directional antennas. The forward lobe will be a single large oval, while the rearward radiation will consist of from 1 to 3 small lobes, each at least 20 dB under the forward gain. Unfortunately, multi-band arrays (with the possible exception of large LPDAs) tend to have patterns that are often far from well behaved. The interaction among the elements--even supposedly inactive elements--remains considerable, as would be evident from an exploration of the current tables produced by NEC. This problem or condition is not exclusively a quad problem, but also attends to large multi-band Yagis as well.

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Not all bands suffer from ill-behaved patterns. As the 20-meter samples in Fig. 1 show, the patterns are quite ordinary. However, as the outside loop set, the 20 meter elements interact least with other elements in the array.

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The sample 15-meter patterns in Fig. 2 show a truer picture of the effects of interactions between the active and inactive elements in the array--where "inactive" means elements for a band other than the one in use. One casualty of the interaction is the front-to-rear ratio, as rearward side lobes grow to considerable proportions. A number of design decisions were made in the process of modeling and optimizing this band. The gain was sacrificed to a small degree in order to obtain the best possible progression of rear lobe formation across the band.

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The single 12-meter pattern in Fig. 3 frames another common element interaction problem--the formation of side lobes. The small side lobes appear from 15 meters on upward in frequency and are likely the result of harmonic operation of larger elements. Under these conditions, currents in the vertical side wires can yield radiation to the array sides in the form of minor side lobes.

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Fig. 4 provides a progression of 10-meter patterns to display how radically a pattern may change across a wide band. The changes to the rear pattern are most evident. However, in the forward direction, note that the minor side lobes develop into considerable bulges with increases in frequency. Of all bands, 10 meter may be the most sensitive to excitation of inactive elements. The 12-meter elements are within the range of reflector size, and the 20 meter elements may operate in a harmonic mode, even though isolated from the 10-meter elements by intervening bands.

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By no means does less-than-perfection in the array patterns count against the use of multi-band, multi-element quads. Rather, the patterns are a simple fact of life that one must take into account both in the design and utilization phases of the antenna.

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Reality 2: Quad Construction

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We have noted the relationship between the design-by-modeling process and the ultimate use of the quad array. Omitted to this point is the relationship between antenna design and modeling on the one hand and antenna construction on the other. Ordinarily, we have passed over this aspect of activity with simple cautions that the model applies accurately within the limitations of the construction process.

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For the present array design, we should add something a little more concrete. Antenna models using bare wire do not take into account construction variables unless the modeler specifically simulates them. The present design is no exception. However, quad construction practices are highly variable, as illustrated simply in Fig. 5.

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The sketch illustrates only 4 among a large number of conditions that may exist at the attachment point between the support arms and the wire elements. Two common methods of attachment are the use of hose clamps and the use of wire loops to fix the position of the element corner. It does not matter whether the element is connected electrically to the metal device that pins the element to the arm. The fixture acts as a simple closed loop connected or coupled to the element at the corner. A quad element has considerable current magnitude at its corners, and such a loop can alter the resonant frequency of the loop when compared to the system in the upper right of the figure, where attachment is made via a wholly non-conductive set of components.

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Metal attachment fixtures can act as loads on the wire loop. For most cases, the loop size can be adjusted to accommodate the fixture. Perhaps the simplest way to do this with any accuracy is to model only the set of driven elements to obtain their independent resonant frequencies, but using the dimensions prescribed by the overall array model. Then construct the drive element set using the proposed construction technique. Measure the resonant frequency of each loop. For a given construction technique, any shift in frequency relative to the model should be consistent, although the amount may vary from one band to the next.

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One may then create reactive loads at each corner of the modeled element until it has the same resonant frequency as the measured drivers. The same load values for each band can be inserted into each corner of each element in the full array. Then, the loop dimensions are adjusted in the model until design performance is restored. The resulting dimensions should prove to be an accurate guide to final construction. For an array of this size and potential performance, the extra modeling and test effort should not be considered excessive.

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Some quads use aluminum arms with fiberglass or similar non-conductive sections for element attachment. The proximity of the aluminum sections of the arms to the elements suggests that the same test procedure is in order as used for the use of metal clamps to wholly insulated arms.

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The quad array described here as a design project for NEC software also reveals another feature that impinges on construction. Many of the performance-improving increments of element adjustment involved changes of a tenth of an inch at a time, especially on the higher bands. Since the change was made to a variable representing 1/8 the loop circumference, some elements of the array may be sensitive to changes as small as an inch in overall wire length for a loop. The designer should flag extra-sensitive elements for special care during construction. Sensitivities of this order are natural to a 5-band array with 22 elements in an elongated cube that is only 18' per side by 26' in length.

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Apart from this specific antenna, the general principle to be observed is that one cannot simply take modeled dimensions and create a physical antenna. One must first correlate the model to the physical conditions of the construction methods used. In some cases, the selection of materials will permit the modeled dimensions to be used as given. I have constructed both wire and tubular element antennas on 10 meters where the modeled dimensions and the physical antenna were under 1" apart.

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However, wherever the physical antenna may have some potential for placing metal within the immediate field of the elements, either the modeler must simulate those objects in the model or one must develop a test regimen to establish a correlation between the design model and the physical prototype. We have illustrated only one of many possible correlation methods. The transition from model to physical antenna should be undertaken with as much care as is put into the modeling design process and into the construction process. Carelessness in any of the three phases of work can yield mediocre communications results.

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The primary subject of these columns is antenna modeling. However, I hope that this foray into a specific design project not only provides some awareness of the modeling work involved, but as well helps one to integrate modeling into the overall process that runs from antenna idea to antenna reality.

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Go to Main Index

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46. A Load in Parallel With a Source

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L. B. Cebik, W4RNL

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One of the examples in my text, Basic Antenna Modeling: A Hands-On Tutorial, involves applying a beta match to a 3-element Yagi. The challenge is to place a reactive load in parallel with the source. Since several of the techniques require a rather high level of segmentation, we shall use a model already set up for the job. Fig. 1 shows the evolution through which we shall go before departing from it.

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The reflector and the director of the Yagi, set up for 14.175 MHz, follow the segmentation pattern in the top driver option. However, the actual driver uses a 3-wire set-up, with the 1-segment wire in the center having the same length as the remaining segments in the driver. In this way, we assure a correct source impedance calculation regardless of what we do in order to place the load in parallel with the source.

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Fig. 2 shows the basic Yagi model in its present form. If we place the source on wire 3 with no matching system, then the impedance will be about 23.4 - j 24.6 Ohms. The impedance is ripe for matching to a 50-Ohm coax line with a beta match. A beta match is made up of an L-network with a reactance in series with the load and a shunt reactance across the source--the coax in this case. The series reactance is already present in the antenna driver source impedance. Hence, the beta match physically consists of the deceptively simple placement of a reactance across the terminals to which the coax connects with the driver.

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Standard L-network calculations, summarized in the equation set (1), provide the level of reactance necessary to effect a good 50-Ohm match. For the case at hand we need just about 50 Ohms (46.9 Ohms, to be more and perhaps spuriously precise) of inductive reactance for the parallel component to go with the nearly 25 Ohms of series capacitance. Indeed, the transformation of 23.4 Ohms to 50 Ohms calls for a series capacitive reactance of 24.95 Ohms, and we have 24.6 Ohms in place--a very close setting of the driver length.

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Essentially, we have two ways to achieve the inductive reactance: a standard inductor or a shorted length of transmission line. Before we finish, we shall look at both methods, but let's start with the coil. It will involve the more complex modeling.

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We cannot simply place a reactive load on the source segment. Every such load will wind up in series with the source, when our goal is to place it in parallel with the source. If we wish to place a reactive load in parallel with the source, one technique is to model the antenna so that there is a physical place for the load to be. To make a place, we must model a set of wires such that they are in parallel with the source segment.

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The lowest portion of Fig. 1 shows the physical arrangement. We simply add three wires to form a square with the 1-segment source wire. The high level of segmentation is designed--well within the limits of NEC's segment length to wire radius limitations--to keep the assembly as small as feasible so that it does not contribute significantly to the radiation pattern of the antenna, thereby distorting the performance reports. Fig. 3 shows the resulting model with its new square.

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To Wire 5, the one that is physically parallel to the source wire, we shall add a load. The next questions are "what kind?" and "how much?" Spot-frequency modeling can use a simple R-X load in which we specify the resistance and reactance of the load. Let's assume a coil Q of 200. With a 46.9-Ohm reactance, the resistance will be 0.2345 Ohms at the specified Q. Fig. 4 shows the entry of the 2 values on the load set-up screen, along with added data on the load magnitude and phase angle.

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With the load specified, the new source impedance is 57.6 + j 1.5 Ohms. This value is correct for 14.175 MHz. However, R-X loads have a limitation. A coil will change reactance for every change in frequency. An R-X load will hold the reactance at the same value for every frequency we might check. Hence, an R-X load will not give a true picture of the source impedance across the 20 meter band.

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We have an easy alternative. On wire 5, instead of using an R-X load, we can employ an R-L-C load. Since there is no capacitance in the load we are applying, we shall leave its value at zero. The resistance remains 0.2345 Ohms. From fundamental equations that appear in every handbook and that are repeated in equation set (2), we can calculate the inductance that provides a reactance of 46.9 Ohms at 14.175 MHz: 0.5266 micro-H.

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Fig. 5 shows the entry screen for R-L-C loads, with the resistance and inductance properly entered. When we run the model, it shows a feedpoint impedance of 57.6 + j 1.4 Ohms, the same as with the R-X load. Where differences will appear is in source impedance reports at a distance from the design frequency. In general, an R-X load will provide too optimistic a portrait of the source impedance and resulting 50-Ohm SWR. A resistance-inductance load is necessary to arrive at a more conservative but more correct set of curves.

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Incidentally, throughout this sequence of models, both the ones covered so far and those yet to be examined, the free-space gain of the Yagi varied by only 0.06 dB and the front-to-back ratio varied by less than 0.1 dB. Since the feedpoint impedance reported so far coincides with L-network calculations within a few Ohms, the techniques are accurate and harmless to the model.

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If we are dissatisfied with the 7-Ohm deviation of the matched model from the calculated nearly perfect 50-Ohm value--perhaps due to some task-driven requirement--then we can check the original model with the addition of the square to see if the square in fact changed the source impedance significantly. To do this, we need only return to version with the R-X load. We can change the values for R and X to 1E10 to simulate an open circuit. With the present driver dimensions (+/-4.947 m), the source impedance in our check model reports as 23.3 - j 24.6 Ohms. The added structure does not significantly affect the source impedance (originally 23.4 - j 24.6 Ohms).

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Nonetheless, the structure is composed of "fat" wire (25 mm or about 1") in order to avoid NEC difficulties with angular junctions of wires having dissimilar diameters. As well, the beta shunt component is placed at a slight distance from the actual source. In order to arrive at a value of source impedance within about 1 Ohm of calculations, it is necessary to juggle two aspects of the model: the driver length and the reactance (or inductance) of the shunted load. For the model that we have been using, I arrived at a source impedance of 50.6 + j 0.3 Ohms with a reactance of 48.5 Ohms and a driver length of +/-4.963 m. The actual values do not necessarily reflect what the physical antenna would require, but the juggling is typical of the adjustment procedure used with beta matches to arrive at an acceptable, if not perfect, match. Modeling does have more than numerical analogs to antenna construction, if we are alert to identify them.

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One limitation of the "added-square" system of putting a load in parallel with the source is that it will disable the use of Leeson corrections, if our model uses a tapered-diameter schedule of tubing. However, the uniform diameter model can be used for analytical purposes, with the tapered diameter version later developed to determine the exact element lengths required for the physical antenna.

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If we wish to avoid the use of a square of wires at the feedpoint, we can still arrive at a model of a beta match. The techniques will employ either a transmission line or a network. Either modeling option requires that we create an "arbitrary" wire at a distance from the antenna. The wire should be far enough away to create no detectable effects on the model. As well, the wire can be perfect or lossless, be a single segment, and be so short and thin that it is virtually invisible to radiated RF energy. Fig. 6 shows the revised model with the square missing but with the arbitrary wire added into the wire set.

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The required shunt or parallel beta inductive reactance can be obtained not only from an actual inductor, but as well from a shorted transmission line stub, the proverbial beta "hairpin." Transmission lines connected to the same segment as a source appear in parallel with the source. Therefore, we can simply create a transmission line using the "TL" facility built into NEC.

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Fig. 7 shows the required transmission line screen. The transmission line goes from the source wire (3) to the new distant wire (6). To make sure that the transmission line appears as a short, we enter very high values of admittance, the equivalent of entering exceptionally low values of impedance. The real and imaginary components are the conductance and the susceptance, the inverse of resistance and reactance. We enter values such as 1E10 in both places. Some programs automate this feature so that the user only needs to enter the request for a shorted (or open) stub.

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Every beta hairpin or stub will have a characteristic impedance based upon the diameter of the wires making up the line and the distance between them. For this exercise, we have arbitrarily set the characteristic impedance at 600 Ohms, indicating a fairly wide spacing between wires. The length is determined from the fact that the inductive reactance of a shorted stub is the product of the line characteristic impedance and the tangent of the lines length in electrical degrees. The ratio of the inductive reactance to the line impedance gives us the tangent of the line length in degrees, which we can then convert into a fraction of a wavelength and from there into a physical length (assuming a velocity factor of 1.0). For this case, the required line length is 0.262584 meters (since the entire dimension set for the model has been in meters). With this length, we obtain a source impedance of 49.2 - j 0.0 Ohms. This value is a few Ohms different from the values using the load applied to the parallel wire square and is likely more accurate, since it involves the addition of nothing physical to the antenna.

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Like the R-L-C type load, the transmission line stub will yield correct results on a frequency sweep. Since the stub is specified as a set of physical dimensions (including the characteristic impedance, which is derived from physical properties of the line), it will correctly modify the source impedance over a wide frequency range. In addition, even if the ultimate antenna will employ a beta shunt inductor rather than a hairpin stub, the transmission line stub can be used with a tapered diameter element set as a substitute for the coil for design purposes--even if the SWR curves will not exactly coincide with those for the coil. Use of the coil to determine the operating SWR bandwidth can be done with the uniform-diameter model. The two significant items that a TL line will not reveal are a. any losses in the line (not usually a problem with short stubs) and b. the effects of the physical line on the radiation pattern.

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We have not yet exhausted the ways in which we can add a parallel load to a source segment. For example, we have not yet employed a "network," the NT function of NEC. We can convert the required values of series resistance and reactance to their equivalents for use in a short-circuit admittance matrix. An example of the network screen appears in Fig. 8.

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The source wire (3) represents the first port, while the "arbitrary" wire (6) represents the second port. Into the Y11 boxes we insert the real and imaginary values required for a parallel or shunt admittance. We leave Y12's values as zeroes. We create a short circuit at the Y22 entry place by using very high values (1E10) for both the real and imaginary components. All we need to do now is determine the real and imaginary components for Y11.

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The equations in set (3) provide us with the conversion formulas to apply to the series resistance (0.2345 Ohms) and reactive (46.9 Ohms) in order to arrive at usable numbers. The resulting values appear in Fig. 8. The result, when the model is run, is a source impedance of 49.0 - j 0.0 Ohms, which is in very close agreement with the transmission stub result we just finished examining. However, the network result is as limited as the R-X load technique: it is correct for only the single frequency for which it is specified.

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Some programs do not provide the user with ready access to the network (NT) facility, but they do permit use of the transmission line (TL) facility. In such as case, we can simulate the network load across the source. Let's examine Fig. 9, the same transmission line screen that we used for the shorted stub. However, we shall approach it from a different angle.

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The line runs from wire (3) to wire (6). Let's set the characteristic impedance at the value of the line to which we wish to effect a match, that is, to 50 Ohms, the value of the coax that we want matched to the antenna. The length of a transmission is independent of the distance between wires (3) and (6) and can be set into the TL call. We do not want the line to create any significant impedance transformation, so we shall make the line very short. The arbitrary length used in this exercise is 0.01 meters.

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Next, let's place the (overly precise) shunt admittance values that we calculated into the real and imaginary (conductance and susceptance) boxes at the "far" end of the very short line. We now have the load across the source. The source impedance that NEC reports from this model is 49.0 - j 0.3 Ohms, almost precisely the value obtained by using the network. However, like the network technique, this application of the transmission line facility is limited to a single test frequency.

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Of the 5 techniques that we have shown for modeling a beta match, the beta inductor on the extra wire square and the transmission line stub are certainly the most useful. Both are responsive to changes in frequency and therefore produce relative accurate impedance and SWR curves for estimating the operating bandwidth of the loaded source antenna. One can change the value of the inductor's Q and develop sets of curves for the operating bandwidth using different values of Q. However, the "added-square" technique is not applicable if tapered-diameter elements are used with the Leeson corrections enabled.

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In spite of this judgment, this exercise has had something of an ulterior motive. The network facility available within NEC (-2 or -4) is rarely used by modelers, especially modelers with less experience in handling shunt admittance networks. Indeed, most amateurs are far more familiar with the concepts of resistance, reactance, and impedance than with their very useful inverse concepts of conductance, susceptance, and admittance. For such reasons as these, some implementations of NEC omit the network facility altogether (along with many other lesser-used facilities) from basic software packages. Other implementations include the facility, but pass over it in silence in manuals. Indeed, the NEC user manual itself is somewhat opaque on the subject for anyone not having significant previous experience with networks. I once asked a mail-list group of NEC users if any would share a few non-proprietary applications of networks to antenna modeling problems. I received one request to share whatever I might receive. Unfortunately, the request brought no sample applications at all. I would still like to receive some samples.

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The examples that I have contrived for this exercise are in many ways unnecessary for effectively modeling a load across a source. However, they do call attention to two facts: 1. the network facility is available and can be put to service, and 2. the transmission line facility is a special case of the network facility.

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Networks can place loads of various orders across any segment. For very large models, an added advantage of the network is that the load can be changed without causing a recalculation of the structure matrix, as is required when using standard loads (the LD facility). As well, networks are in parallel with sources on the same segment, unlike loads (LD), which are in series with sources on the same segment. To offset this advantage, we may note once more that the network value does not automatically scale with frequency changes as does an R-L-C load.

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It may be the case that the increasing speed of desk-top computers and the ease with which one may form a work-around for paralleling a source and a load have largely obviated the advantages of using networks for small to fairly large size models. In any event, we have at least made a passing acquaintance with networks, and that may be enough for one exercise.

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47. So You Want to Read a NEC-Deck

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L. B. Cebik, W4RNL

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Those who develop implementations of NEC for newer users often develop "user-friendly" interfaces between the data that the NEC core requires and what the user sees on screen. The result is very often a more effective first use of the program. However, the interface can obscure the basic structure of the NEC core and its potentials.

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Many users of ELNEC and EZNEC are wholly unfamiliar with the basic elements of a standard .NEC input file, since the program uses a proprietary model file system. The model description bears a close but unclear relationship to a comparable .NEC file. Users of NEC-Win Plus may also be unfamiliar with the terms and layout of an EZNEC antenna description file (called a PD file for the abbreviated keystrokes used to generate it). Some users of Plus may never even look at the available spreadsheet screen that gives the file listing in ASCII .NEC- format terms. As an exercise in correlating user formats and .NEC files, let's compare the data of an EZNEC model description file and the corresponding lines of a standard .NEC file. The exercise will acquaint us with the basic terms of the NEC deck.

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In most advanced implementations, NEC uses a card-deck input file whose format goes back to the early days of FORTRAN, when punch cards provided computational inputs. Nowadays, we simply type in a single line of input-file text as a replacement for the old punch cards--and many current FORTRAN users simply do not make a connection between the line format and the old punch card requirements. For brevity, each card contain a labeled sequence of information, the individual parts separated by a delimiter. Since we Americans use "." as our decimal indicator, we use commas or spaces to separate information. European formats may vary.

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To get us started, let's compare the antenna description file for a simple 2-element Yagi with the corresponding card deck. Then we can explain each type of card we encounter. If you wish, you can try your hand at correlating each element in the NEC deck to elements in the EZNEC antenna description file before reading beyond them.

+ 
                      EZNEC Antenna Description File
+2el Yagi 12M
+Frequency = 24.95  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.-- End 1 (x,y,z : ft)  Conn.-- End 2 (x,y,z : ft)   Dia(in)  Segs
+1         -9.100,  0.000, 40.000       9.100,  0.000, 40.000  1.00E+00   11
+2         -8.800, -4.800, 40.000       8.800, -4.800, 40.000  1.00E+00   11
+3         -0.200,  0.000,  1.000       0.200,  0.000,  1.000     # 14     1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     3 / 50.00   (  3 / 50.00)      1.000       0.000       V
+
+              --------------- LOADS ---------------
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           6     2 / 50.00   (  2 / 50.00)       1.000       100.000
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1      1/50.0  (  1/50.0)    3/50.0  (  3/50.0)  Actual dist  50.0  0.66  N
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+              --------------- MEDIA ---------------
+Medium       Conductivity(S/m)   Dielectric Const.    Ht(ft)   R Coord(ft)
+
+1                5.000E-03            13.00           0 (def)     0 (def)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                         .NEC Input File
+
+CM 2el Yagi 12M
+CE
+GW 1 11 -9.1 0 40 9.1 0 40 .04165
+GW 2 11 -8.8 -4.8 40 8.8 -4.8 40 .04165
+GW 3 1 -.2 0 1 .2 0 1 2.6706E-03
+GS 0 0 .3048
+GE 1
+GN 2 0 0 0 13 .005 0 0 0 0
+EX 0 3 1 0 1 0
+LD 4 2 6 6 1 100 0
+LD 5 1 1 11 2.4938E7
+LD 5 2 1 11 2.4938E7
+LD 5 3 1 1 2.4938E7
+TL 1 6 3 1 50 18.01 0 0 0 0
+FR 0 1 0 0 24.95 0
+RP 0 1 361 1000 76 0 1 1
+EN
+
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The antenna described by these two files is shown in Fig. 1. It is a simple 2-element Yagi of relatively modest performance.

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The main screen of EZNEC 3.0 shows us the basic modeling data in the form illustrated in Fig. 2. Most of the detail resides in sub-screens that the user accesses by mouse-clicking on the entry line in the main screen. The results appear in Fig. 3, which I have shown as an elevation plot, even though the model specifies an azimuth plot.

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NEC-Win Plus uses a different type of main screen, with considerable, but far from total, data entry up front. Frequency, wires, element diameter, and material all may be done from the lead page, although the specifics of the pattern request, ground, source, load, and transmission line require sub-screens. Fig. 4 illustrates the situation. A full readout of the .NEC file, like the one shown below the EZNEC model description file, is available from the "NEC Code" tab of the spreadsheet. +
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Whatever the program, the performance results are the same: Gain: 11.1 dBi; 180-degree front-to-back ratio: 11.1 dB; feedpoint impedance: 42 + j5 ohms. The general azimuth pattern at the take-off angle of 14 degrees appears in Fig. 5. NEC-Win Plus has a data ("Analysis") screen attached to its polar plot, but it has been omitted here.

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I have purposely modified a simple antenna to include an inductive load in the reflector, thus making it physically shorter than the driven element. I have also run a 50-ohm transmission line straight down to within 1' of the ground and created a source wire there. If we had only the simple 2-element Yagi with which to work, our NEC deck would be pretty skimpy.

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Let's look at each card in the deck and read out the information, cross checking it against the EZNEC file. In most cases, I have spread the data units out and labeled them beneath.

+ 
1.  CM 2el Yagi 12M
+

This is a comment card for storing information about the file in ASCII text. It does not enter into the calculations. You may have any number of comment cards, although some implementations limit them. In EZNEC, you may have only one CM card, called the "title." (However, EZNEC 3.0 permits the user to generate a text file to accompany the model with any number of ASCII text comments added. This replaces the CM cards of a standard NEC file.)

+ 
2.  CE
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This card is the "comment end" card, signaling that data for calculation follows.

+ 
3.  GW    1    11   -9.1     0    40     9.1    0    40    .04165
+    GW    2    11   -8.8   -4.8   40     8.8  -4.8   40    .04165
+    GW    3     1    -.2     0     1      .2    0     1    2.6706E-03
+   Type  Tag  Segs  E1 X   E1 Y  E1 Z   E2 X  E2 Y  E2 Z    Radius
+

Type GW cards describe the antenna geometry. Each antenna wire, or "Tag," has a separate numbered card or line (1, 2, and 3). The Segs (segmentation) entry tells how many segments the wire is divided into (11 each for Tags 1 and 2, 1 segment for Tag 3). Then come the Cartesian coordinates for End 1 and End 2 of each straight wire. Here, as in the EZNEC file, they are given in feet. Finally, the wire size is given as a radius (1/2 the diameter given in the EZNEC file. However, the EZNEC file lists the diameter in inches. The NEC deck must use the same units throughout the GW cards, so a 1" diameter become a 0.04165' radius. See also the NEC-Win Plus entry for diameter--also in feet and hence 0.0833. The wire size figure for Tag 3 is the radius of #14 wire, in feet.)

+ 
4.  GS    0    0    .3048
+   Type            Multiplier
+

Although most implementations of NEC, such as NEC-Win and EZNEC, give the user a choice of common units of measure for setting up the antenna geometry, NEC itself calculates only in meters. In the last of its 4 columns, the "geometry scaling" card gives the multiplier needed to convert to meters.

+ 
5.  GE    1
+   Type  End
+

The "geometry end" type card signals the end of the wire set-up and prepares the way for other data that enter into the calculations.

+ 
6.  GN    2      0    0    0    13    .005    0    0    0    0
+   Type  G-type               Die-C.  Cond.
+

The ground parameter card specifies the type of ground calculation system and the necessary parameters to make the calculation. Here, we show a single medium, although a second medium can be set.

+

There are 4 types of ground systems used with NEC: -1 = free space; 0 = a finite ground with a reflection coefficient approximation (the "fast" ground in EZNEC); 1 = a perfectly conducting ground; and 2 (used here) specifies a finite ground using the Sommerfeld-Norton method of calculation for greatest accuracy. (In addition, EZNEC implements the MININEC ground calculation system for users who may find it convenient for some vertical antenna models.)

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Finite ground conditions (cases 0 - 2) require two numbers to implement calculations. The first is a relative dielectric constant, usually given as an integer. Second is the conductivity in Siemens/meter (mhos/meter in older terminology). Both are generally derived from tables. The values shown represent a default presumption of medium earth conditions. Both numbers are omitted for perfect ground.

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As with many cards in the NEC deck, there are unlabled "0" fields. Some of these represent fields simply left blank; others represent input positions for more specialized conditions not relevant to most common ham HF antennas. (Some may be relevant to VHF and UHF antennas.)

+ 
7.   EX     0     3     1     0                1     0
+    Type  S-type Tag   Seg        Voltage:   Real  Imaginary
+

The "excitation" or source information card allows for many types of excitation, of which only voltage sourcing is usual in HF ham use. Hence, the source-type is "0". The next two columns specify the placement of the source in terms of tag number and segment number in that wire. Here, the remote wire has only one segment, and the source is placed at its center. Many programs allow specification of the source at some distance from End-1 of the designated wire, and will then place the source as close to that point as segmentation permits.

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For most ham uses, sources are either voltage or current. The latter is useful for scanning current levels along a wire, since a voltage source of "1" yields small fractions of an amp current, making scanning more difficult. Current sources may also be necessary for some advanced applications.

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Nonetheless, both types of sources are voltage sources ultimately. The current source is generated by a voltage source set on a remote wire and transformed into a current source by a transmission line. The NEC deck for a NEC-Win Plus model will show the wire and line, while EZNEC stores this information internally.

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Voltages are given in terms of X and Y ("real" and "imaginary") coordinates derived from inputs that can be given as a voltage and its phase angle. User current magnitude and phase angle inputs are converted to appropriate voltage values at the remote source wire.

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In general, when converting among programs (for example, between EZNEC Pro and NEC-Win Pro), it is best to use a voltage source to avoid the possibility that one program cannot read the other's remote wire current source technique. Changing back to a current source can be done after file conversion is complete.

+ 
8.    LD      4      2      6           6      1      100      0
+     Type  L-type   Tag   Start Seg   End Seg  R     L or X    C
+

There are two types of loads to consider: concentrated element loading quantities and distributed element material loads. This card illustrates an inductive load added to the center of the reflector. Load types 0 through 3 represent categories of R-L-C combinations that can make up a load. This card shows a type 4 load, which is specified in terms of a series resistance and reactance in ohms.

+

The "tag" and "segment" items locate the load at the midpoint of wire 2. Since there are start and end segment numbers, some loads may be distributed for more than a single section, but most ham antennas employ concentrated loading located within a single segment.

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The final two values (1 and 100) specify the resistance and reactance of the load in ohms. Capacitive reactance, of course, would be entered as a negative number.

+ 
9.    LD       5      1      1         11        2.4938E7
+      LD       5      2      1         11        2.4938E7
+      LD       5      3      1          1        2.4938E7
+     Type   L-type   Tag  Start Seg End Seg    Conductivity
+

Material losses are type-5 loads. As with other loads, the wire (tag) must be identified, along with the first and last segments to which the load applies. Note that these loads apply in addition to any lumped-constant loading of types 0 through 4.

+

To avoid confusion by newer modelers, EZNEC only refers to lumped constants as loads, preferring instead to call material loads "wire losses." EZNEC also expresses these losses as a function of resistivity and relative permittivity. However, the value of resistivity in this case, 4.0E-08 ohms, is simply the reciprocal of the NEC deck conductivity value of 2.4938E7 mhos or Siemens. Additionally, EZNEC restricts antennas to one type of material per model, although the NEC deck permits a specification of a different conductivity value for each wire. Note the NEC-Win Plus entry space for a conductivity value for each wire in the antenna model.

+ 
10.    TL        1    6       3    1    50    18.01    0    0    0    0
+      Type Start tag/seg  End tag/seg   Zo    Length
+

Transmission lines are not physical models in NEC, but mathematical constructs. Hence, they can have any length, regardless of the actual distance between their start and end points on wires. Special techniques are used for shorted and open stubs, but the example here runs a common coax line from the antenna proper to a short segment used a. to terminate the transmission line and b. to serve as the overall source point for the antenna system.

+

By now, the start and end wire and segment numbers are obvious. As in the EZNEC PD file, the next two columns specify the characteristic impedance of the line and its length. In EZNEC, this can be done in several ways, all of which translate into a final characteristic impedance and definite length in meters. In the PD file, the length was given as the actual distance between wires, 39', modified by the velocity factor of the line, .66. This results in an electrical length of 59.1' or 18.01 meters. In NEC-Win Plus and Pro, one must enter the total electrical length and hence Pre-calculate the value from the physical length and the velocity factor of the line used.

+ 
11.    FR     0         1         0     0     24.95     0
+      Type  Stepping   No. of FQs            Start FQ  Increment
+

Antennas are modeled at one or more frequencies. If a single frequency is used, as in this example, the information needed is limited. "Frequency sweeping" requires more information.

+

Stepping can be non-linear (stepping = 1), but normal ham frequency sweeps are linear, changing frequency by the same amount each time. For sweeps, the user specifies the number of frequency steps, the start frequency, and the increment by which to step. For this single frequency model, the number of frequency steps is 1, and the increment is 0, while the modeled frequency is 24.95 MHz.

+ 
12.  RP     0     1           361     1000     76     0     1       1
+   Type   Mode  No. Theta   No. Phi  Special  Theta  Phi  Th Inc  Ph Inc
+

The report card specifies what output data is desired from the calculations. Mode "0" is the normal mode for far field data.

+

Horizontal angular changes are measured as "phi" degrees. Elevation angular changes are measured as "theta" degrees. Although most hams are used to counting elevation from the ground up, NEC counts theta angles from the zenith down.

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This example specifies a report for one theta (elevation) angle, but a full circle of azimuth (phi) angles. Skipping the "Special" column for a moment, the theta angle is 76 (or 90 - 76 for a 14 elevation angle). The figure is a start figure, although only one theta angle has been specified. The azimuth or phi start angle is 0, but will pass through 361 (to ensure a complete circle with a common value at each end of the progression). Both theta and phi are specified for increments of 1 for good resolution.

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The "Special" column contains 4 values that direct the calculations to produce certain types of outputs. 1000 is normally used for vertical, horizontal, and total non-normalized power gains with no averaging. Other outputs are available, and the user is usually interrogated in plain language for the desired output data and form by each program.

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Users of NEC will sometimes be surprised to find that a symmetrical antenna, such as a Yagi, produces a main lobe identified by as much as 2 to 3 less than the expected bearing. Implementations of NEC may identify either the first instance of the maximum power gain as the main lobe or may sample the subsequent headings and center the identified main lobe heading among equal maximum readings. If a program uses the first of these options, then increasing the phi increment will often return the main lobe to its expected position.

+ 
13.    EN
+

EN signals the end of the .NEC file.

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Hopefully, this brief trip through a short NEC deck will orient you to how the input files are constructed for use with NEC. Remember that the card explanations have not covered all the ways in which one may place data on a card of a given type. Only the most common kinds of data inputs for typical ham antenna installations have been illustrated.

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The low-end implementations of NEC-2 omit many of the features and functions available with core in order to create the user-friendly interface that covers the features most needed by the average user. However, high-end programs designed with less "friendliness" and more calculating potential (such as NEC-Win Pro and--for NEC-4--GNEC) tend to make the entire deck available to the user. As a reference, here is a list of NEC-2 cards, some of which we have reviewed and some of which will seem odd. In addition, cards like the RP request have far more options than we have covered, including not only far field patterns, but ground wave patterns as well. EX allows not only for definite voltage sources, but as well for plane-wave excitation for receiving analysis.

+ 
Structure Geometry Input Cards
+
+CM, CE        Comment Cards                        GA            Wire Arc Specification
+GE            End Geometry Input                   GF            Read Num. Greens Function
+GH            Helix-Spiral Specification           GM            Coordinate Transformation
+GR            Generate Cylindrical Structure       GS            Scale Structure Dimensions
+GW            Wire Specification                   GX            Reflection in Coordinate Planes
+SP            Surface Patch
+
+Program Control Cards
+
+CP            Maximum Coupling Calculation         EK            Extended Thin-Wire Kernal
+EN            End of Run                           EX            Excitation
+FR            Frequency                            GN, GD        Ground Parameters
+KH            Interaction Approximation Range      LD            Loading
+NE, NH        Near Fields                          NT            Networks
+NX            Next Structure                       PQ            Print Control for Charge on Wires
+PT            Print Control for Current on Wires   RP            Radiation Pattern
+TL            Transmission Lines                   WG            Write Num. Greens Function File
+XQ            Execute
+

Some programs, like EZNEC, do not generate a NEC deck, but instead communicate with the NEC-2 calculating engine via a number of binary files. (A NEC deck is available in EZNEC Pro with the NEC-4 calculating engine.) Some programs, like NEC-Win Plus, use alternative formatting methods--a spreadsheet file in this case, but also make available the option of saving the mode as a .NEC file. Others, like NEC-Win Pro or GNEC, make the deck an integral part of the modeling process. Getting used to the NEC deck can increase your ability to glean more from whatever program you choose as your basic modeling vehicle. Familiarity may also aid you in interpreting articles that present antenna modeling data in .NEC input file format. Patches, Green's functions, networks, and wire grids are beyond the scope of this introduction, but may be found in NOSC Technical Document 116, Volume 2, Numerical Electromagnetics Code (NEC)--Method of Moments, Part III: User's Guide (1981), which is the source of most of this data.

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48. Radiation Plots: Polar or Rectangular; Log or Linear

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L. B. Cebik, W4RNL

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The user of NEC or MININEC often has choices in how to graphically portray data. The choices (not all of which may be available within a particular program) generally consist of the following.

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1. Polar Plot: Logarithmic Scale

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2. Polar Plot: Linear Scale

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3. Rectangular Plot: Linear Scale

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4. Rectangular Plot: Logarithmic Scale

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I have heard numerous arguments for and against each type of presentation. I shall forego all of them. Instead, let's pick an antenna whose plot has some relatively fine detail (in terms of secondary lobes of interest). Then, let's look at the free-space plots under each of the options listed above.

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Fig. 1 presents the .NEC file of a 12-element Yagi with a test frequency of 148 MHz. The linear elements extend from -X to +X, with the boom extending from a value of zero on the Y axis to positive Y-values. The dimensions are in meters. The boom length is 6.045 m long (about 19.8'). The 4.76-mm diameter (0.00238 m radius) elements are 0.1875" (3/16") rod. The material is standard aluminum (read from the LD lines), and the elements are presumed to be well insulated and isolated from any conductive materials in the boom that supports them. The environment is free space. As is usual for Yagis, the source or feedpoint is at the center of the second element from the rear. Fig. 2 presents an outline sketch of the antenna.

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For the record, when modeled in NEC-4, the array has a free-space gain of 14.27 dBi, a worst-case front-to-back ratio of 23.14 dB, a source impedance of 43.9 - j 4.0 Ohms, and a 50-Ohm SWR of 1.17:1. The -3dB beamwidth is about 36 degrees. However, these figures do not tell us anything of the pattern shape: whether it has very significant secondary forward or rearward lobes or whether the pattern is clean and well controlled. To determine these matters, we can examine the tabular data provided by NEC or we can examine graphical plots of the data. The NEC core yields only the tables. All graphics are added by the programmer.

+

In the following notes, all patterns will be products GNEC by Nittany Scientific. My program choice for this exercise was simple: GNEC has both polar and rectangular plot capabilities. For linear plots, the user has the option of selecting maximum and minimum values for the plotting space.

+

The Logarithmic Polar Plot

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The logarithmic polar plot shown in Fig. 3 was a creation of the American Radio Relay League somewhere in the distant past. This type of logarithmic plot is perhaps the most familiar of the common polar plotting styles used. In some software, plotting beyond the -40 dB point is shown, although in this GNEC plot, the line is cut off at this point. In principle, graphing can go on down to an infinitesimal value.

+

Every polar plot scheme is subject to a set of equations that determines the placement of the data points that make up the curve. The angle at which they occur is fixed by the data itself, but the distance from the plot center is a function of the equations used. The equations may be simple--as they are in linear plots--or complex, as in the present log plot. Note that plotting radiation strength in dB on a log scale results in a form--but not the only possible form--of a double log plot.

+

First, the plot in Fig. 3 is normalized, which is to say that its outer ring is given a value of 1.0 for plot point calculation purposes. The maximum gain of the array is set equal to this value. Hence, the pattern just touches the outer ring. In normalized plots of radiation patterns recorded in dB, the outer ring is usually set to zero dB with inner rings set of -X dB each, where X is another matter of choice--usually of the software writer. Non-normalized plots are possible and often used, although the normalized plot permits the largest pattern that will fit within the outer ring of the graphic.

+

Second, we need to determine the point positions for any heading in terms of their distance from the plot center to the outer ring. Since the plot shows the headings of the -3 dB points for the pattern, we can illustrate the process used to generate the plot in Fig. 3 with good simplicity. By using the -3 dB points, we have already made the first step. Let MG = the maximum gain of the pattern and GH = the gain at some new heading--in this case either 72 or 108 degrees.

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EX is simply the difference between the maximum gain and the gain at the new heading. For our example, the gain at 72 and 108 degrees is close to 11.27 dBi.

+

The position of the dots for 72 and 108 degrees are determined by the next equation, in which VP = the value point as a decimal value relative to 1 and hence the distance away from the center of the plot toward the outer ring.

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The -3 dB points will be about 0.84 of the way from the center toward the outer circle. In a similar manner, we calculate that the worst case front-to-back ratio point, 23.14 dB, will be at about 0.26 of the way from the center to the outer ring. Relative to the outer ring distance on the plot in Fig. 3, you can measure these distances with a ruler. The particular equation shown applies only to values of radiation strength given in terms of dB and requires modification for values given in terms of measured or calculated signal voltage.

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Although the plots on most antenna modeling software mark the reference rings in 10 dB increments, there is nothing fixed about this practice. In fact, ARRL publications use 3 dB increments down through -12 dB with further -18 and -24 dB markers. Moreover, there is nothing fixed (except by tradition) about the equation itself. In non-normalized plots, the user may have a choice of selecting the value of the outer ring. In such cases, the adjustment of the pattern to the selection is simple arithmetic. The gain at every heading is calculated against the value set for the outer ring instead of against the maximum gain of the pattern.

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The logarithmic scale is perhaps the most familiar of the many options for plotting a radiation pattern. It tends to enhance the forward lobe and to emphasize the beamwidth, especially of narrow-beamwidth arrays such as the subject 12-element Yagi. At the same time, it also tends to reduce the resolution of fine detail of weaker portions of the pattern.

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The Linear Polar Plot

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An alternative to the log polar plot is the linear polar plot, shown for our subject antenna in Fig. 4. Note that in this context, "linear" refers to a linear counting of decibels, which is already a logarithmic function relative to power or to voltage and/or current.

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Because the plot steps from the center of the graphic toward the outer ring are linear, the -10-dB ring in Fig. 4 are much closer to the outer ring than with the log plot in Fig. 3. The effect is to broaden the visual pattern and to enhance the detail of the plot with respect to weaker portions of the pattern. Compare the rearward portion of the plots in Fig. 3 and Fig. 4, as well as the secondary lobes. Remember that both plots present the same data. The difference lies in the manner of presentation.

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The plot in Fig. 4 uses a scale that runs from 0 dB for the outer ring to -50 dB at the center. Unlike the log plot, a linear plot must specify both the outer ring and the center values. For a normalized pattern, the outer ring equals the maximum gain of the antenna under study. The minimum or plot-center value is a user choice. In this case, -50 dB provided a good visualization of the secondary lobe structure--and that fact determined the choice. As a point of comparison with the log plot, the -3 dB points on the 50-dB scale are .94 of the way toward the outer ring, while the worst-case front-to-back ratio point is .54 of the way from the center.

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Linear polar plots are not automatically superior to log plots. Indeed, since the center point value is user selected (or in some cases, software selected without user choice), the utility of a linear polar plot depends upon the center value selected. It is possible to create virtually useless linear polar plots.

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Fig. 4A shows a worthless linear polar plot of the subject antenna. It uses a center value of -185 dB and 35-dB steps in the rings. Since the free-space pattern of a horizontally polarized directional antenna with linear elements very often results in very high values of front-to-side ratio, an automated program can make unwise choices for the user. In Fig. 4A, the selected values spread the pattern to such extremes that differentiation of any detail is almost impossible. In short, the linear polar plot is not intrinsically better or worse than a log plot in showing any particular features of a pattern's shape or features.

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Selecting a linear polar plot value set, then, is the most crucial step in generating a plot that does useful work in demonstrating salient points of the radiation pattern. Since the center point is user or software selected, its value must always be made accessible to the plot reader, either by a legend or by a plot-line label. Otherwise, the plot may become seriously misleading.

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In non-normalized plots, the user once more selects the gain value assigned to the outer ring. Then the gain of the pattern at every heading becomes a percentage of the distance from the center to the gain value set into the outer ring. Since computer graphics programs tend to separate the setting of the polar plot space and rings from the assignment of data points within the rings, the value of the outer ring will usually be recorded in a separate alphanumeric entry, with the plot rings retaining the same labels, regardless of the outer ring value.

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The Linear Rectangular Plot

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Fig. 5 shows a rectangular plot of the radiation pattern data using a linear scale for the Y axis. Many analysts prefer the rectangular plot because it allows a comparison of signal strength (whatever the units happen to be) at every heading with only a glance at the reference lines across the plot from the Y-axis. The plot in Fig. 5 has not been normalized. Indeed, normalization is more the exception than the rule with rectangular plots, because the practice often creates odd increments between values on the Y axis. Odd numbering of the Y-axis markers tends to defeat the easy determination of gain values for every heading.

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The generation of a linear rectangular graph requires close attention by the user, especially to the Y-axis minimum and maximum value. Indeed, in some cases, the user may have to experiment with the selection of values to reveal all of the relevant data in sufficient detail. The selected value captures the low-level variations in strength near the front-to-side bearings without going to extremes. There are no further lobes to be revealed by carrying the 0, 180, and 260 degree values below the -50 dB point.

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In the graph shown, the minimum value could have been carried to -100 dB, as it was in Fig. 5A. However, the detail of the pattern for values between -30 and +20 dB would have been obscured by unneeded "scrunching." For example, in Fig. 5A, it is not easy to tell if the smallest side lobes of the forward pattern (between 0 and 180 degrees) show a peak or ar simply level. The determination is easy to make in Fig. 5.

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The rectangular graph also provides the rationale for setting up the original model with the linear elements set on the +/-X axis. The result is to place the main lobe of the array on the Y axis in the wire set-up screen, that is, at a 90-degree heading. Although the other convention of laying elements on the +/-Y axis is often convenient for polar plots, the set-up used here presents the forward and rearward pattern details as complete lobe structures. In Fig. 5, one might have added the labels "forward" and "rear" to the left and right portions of the graph, respectively.

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In short, creating a rectangular plot requires forethought that goes all the way back to the initial model set-up. Of course, this caution applies mostly to cases where one uses the graphic capabilities built into a given piece of software. If one exports the radiation pattern data to a spreadsheet, one can then manipulate either the plotting facility or the angular data. Thus, the resulting rectangular plot can have the appearance of Fig. 5 (or any other that may fit a given antenna pattern), whatever the orientation of the initial model.

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The Logarithmic Rectangular Plot

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The Y-axis of a rectangular plot can be given a log scale. But the results may become "the plot that failed," as in Fig. 6. If you compare Fig. 6 with Fig. 5, you will discover that only the portion of the graph in which gain values exceed 0 dB appear on the new plot. That is a problem with logarithms--they work with positive numbers. Such a problem would not exist if we were plotting signal strength in volts.

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To achieve a proper logarithmic scale for the Y-axis of a rectangular plot would require exportation of the radiation pattern data, followed by a conversion of the entire lot of it into positive numbers. Then one might use that converted data with a log Y axis, although the labels might be reconverted to values corresponding to those on the original data table.

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These last notes have made a small case for exporting data from the NEC output file to programs within which the data may be manipulated for the most effective presentation and study. Even the most competent antenna modeling software will have limitations and cannot anticipate all possible user needs or interesting results that call for special presentation. If it could anticipate all needs, we might simply set up a data bank of results and forget the modeling process itself.

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In the end, the modeler should be prepared to go beyond the modeling software itself to develop effective graphics--whether for radiation patterns or any other facet of the data generated by the core. The forethought required for setting up a model in anticipation of graphing the results carries over into appropriate levels of after-thoughts to apply the best graphing techniques for data that will not fit prescribed patterns.

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In the end, there is more to antenna modeling than can be written into the modeling software itself.

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However, we began our work as a short dash through the various radiation pattern plotting options that we most use. Throughout, we have avoided arguments for or against any one of the many possibilities, since most of those argument presume sets of well-chosen user options for graphic minimum and maximum values. Instead, we have focused on two functions. One is the potential of each plotting scheme for presenting data in a form that is most easily read and most fruitfully studied. The other is the responsibility of the user to select plotting scale values that will achieve the goal of easy reading and useful examination.

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There is no universal best plotting method for radiation patterns. However, for any given plotting goal, one may determine the best way among available methods for achieving a set of goals.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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49. Traps

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L. B. Cebik, W4RNL

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We have not so far had occasion to work with parallel R-L-C loads (LD1). The most notable use of such loads is to model traps, which we install to let an antenna be resonant on more than one frequency of operation. Let's go through an exercise and discover how we may convert traps into parallel R-L-C loads.

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Examine the wire table for a test model, given in NEC-Win Plus form in Fig. 1. You will find a 5-wire assembly for 21.1 MHz that we shall also operate on 14.1 MHz. The wire table is non-standard. Wire 1 is the center section of the antenna--essentially the 15-meter portion. Wires 2 and 3 are the 1-segment wires on which we shall install the traps. Wires 4 and 5 are the outward extensions from the traps to the tip of the elements on 20 meters. Fig. 2 shows the outline of the antenna with a set of dimensions. The overall dimension of 27' 4" corresponds to the wire table tips. However, the inner 22' dimension is the space between the traps themselves and not the space of the center section (wire 1) alone.

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The antenna material is 1" diameter aluminum, and the environment is free space. Note that the trap wires are the same diameter as the remaining wires. Therefore, the model will not account for any effects created by the shape of the traps. We shall construct the 15-meter traps from the mathematical loading facility.

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One problem with a trap is that it is not yet a parallel R-L-C circuit. As shown in Fig. 3, a trap consists of a capacitor in parallel with a series resistance-inductance leg. Before we can create a parallel R-L-C load, we must convert the trap configuration into a true parallel configuration. Moreover, we shall have to do these for each frequency-band of operation.

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In the following notes, we shall set up a procedure for calculating traps and converting them into parallel R-L-C loads. Basic to the procedure is the ability to convert inductances to inductive reactance and back as well as capacitances to capacitive reactances and back. Therefore, as a quick reference, here are the basic equations:

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where XL is the inductive reactance, f is the frequency in hertz, and L is the inductance in henries. The same equations work if we use both MHz and uH.

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where XC is the capacitive reactance, f is the frequency in hertz, and C is the capacitance in farads.

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For our small exercise in converting traps, we shall begin with an inductor only and carry you through the process. The inductor is a 3.3 uH coil with a measured Q of about 235. By standard equation, we can find the inductive reactance. However, we must know the trap frequency. Ordinarily, we design traps to be resonant at or just below the lowest frequency of operation on the upper band. If we set our trap at 21.0 MHz, the inductive reactance is j 435.4 Ohms. Since the Q is 235, the series resistance of the coil is 1.853 Ohms. We can use the capacitive reactance equation to calculate the capacitor, which will be about 17.41 pF to provide the matching reactance for the coil at 21.0 MHz.

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We need to convert the series resistance and reactance values into parallel equivalents. The standard conversions equations for going from a series to a parallel combination of resistance to reactance are

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where RP and XP are the desired parallel equivalents to RS and XS, the original series values of resistance and reactance. The parallel resistance for the trap at its resonant frequency is 102,325 Ohms. The parallel reactance is j 435.4 Ohms, which will return a parallel coil of 3.3 uH.

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However, we do not intend to operate the trap at 21.0 MHz, but at 21.1 MHz. To determine the parallel values at the operating frequency, we need to take a few steps. First, we shall find the inductive and capacitive reactance of the inductor and capacitor at the operating frequency. We may return to basic equations, or we may take this shortcut:

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where XLA and XCA are the reactance values at the resonant frequency, FA, and XLB and XCB are the values of reactance at the new frequency, FB. For operation at 21.1 MHz, we obtain an inductive reactance of j 437.5 Ohms and a capacitive reactance of - j 433.4 Ohms. The required parallel reactance of this combination we may call XNET, which we may determine from this equation:

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Note that the equation uses the absolute values of the reactances, not their originally signed values. For our test model at 21.1 MHz, the net or parallel reactance is - j 45,829 Ohms, although we do not have to enter that value, since we shall use the values of inductance and capacitance, 3.3 uH and 17.41 pF, respectively.

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The parallel resistance for XNET can be derived approximately from the parallel resistance at resonance using this equation:

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where RPB is the parallel resistance at the new frequency, FB, and RPA is the parallel resistance at the resonant frequency, FA. By raising the ratio of 21.1 over 21.0 to the 1.5 power--using the XY function of a hand calculator--we find a new parallel resistance of 103,057 Ohms.

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Now we are ready to install our approximate values into the parallel R-L-C load box for our test model. Fig. 4 shows the NEC-Win Plus version of the entry. Remember that we have two traps and hence two parallel R-L-C loads to create. If we run the model at 21.1 MHz, we obtain a free-space gain of 2.05 dBi with a source impedance of about 71.9 - j 8.0 Ohms. If we check the EZNEC load data output, we find less than 0.1 dB loss from the trap. If we check the NEC-Win Plus power budget table, we find an overall efficiency of almost 98%, despite the use of an aluminum element.

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We may gauge the effectiveness of a trap in part by the degree to which it confines significant current levels to the 15-meter portion of the antenna. Fig. 5 provides the EZNEC antenna view with the relative current magnitude showing. I have expanded the normal curve to show the just visible low currents on the outer ends of the wire, the portions designed to serve 20 meter operation. The fact that the source impedance is so close to the standard resonant 72 Ohms of a regular dipole further confirms the effectiveness of the trap.

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However, we wish to operate the antenna at 14.1 MHz as well. For this operation, we shall need to modify the test model. This version of the model will have loads that approximate the values seen at the lower frequency, well below the trap's resonant frequency. We must recalculate the applicable parallel combination of resistance and reactance that applies to the new frequency. At 14.1 MHz, the reactance of the 3.3-microH coil is about j 292.4 Ohms, and the reactance of the capacitor is about j 648.5 Ohms. Using the same two equations as we did for 21.1 MHz, we obtain for 14.1 MHz a parallel or net reactance of j 532.2 Ohms and a parallel resistance of about 56,297 Ohms. Of course, we shall use the values of inductance and capacitance that we started with, namely, 3.3 uH and 17.41 pF in the parallel R-L-C load, but with the new parallel resistance value.

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For the revised model at 14.1 MHz, Fig. 6 shows the values plugged into the NEC-Win Plus version of the load entry box. There are, of course, two traps to enter in parallel form. If we run the model at 14.1 MHz, we shall obtain a free-space gain of about 1.83 dBi, with a source impedance of about 66.8 + j 0.9 Ohms. EZNEC's load data table shows a loss that slightly over 0.2 dB from the trap equivalent load, while the NEC-Win Plus power budget table shows an efficiency of about 94.7%. Both supplementary values reflect the lower free-space gain at 20 meters.

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Fig. 7 shows part of the reason for the reduced gain. The overall length of the trap dipole is shorter than a full-size version. The shortness is reflected in the source impedance, which is lower than normal for a dipole. In the antenna view, we can also see the sudden decrease in current past the trap positions on the antenna element.

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Part of the reduced efficiency is also due to the fact that the trap Q at 14.1 MHz is not the same as the coil Q that we used to estimate the parallel R-L-C load values. We may obtain the trap Q on 20 meters by reversing our calculations. We shall convert the parallel resistance and reactance into series values, using standard ARRL Handbook equations from Chapter 6:

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where the letters have the same meaning as they had in the series-to-parallel conversion equations. If we process our parallel values through these formulas, we obtain a series resistance of about 5.0 Ohms and a series reactance of about j 532.3 Ohms. Since Q is simply the reactance divided by the resistance, we obtain a value of about 106, somewhat lossier than the value we might obtain considering the coil alone. In fact, the entire trap must be considered at every frequency of use, and we cannot assume that on frequencies below the resonant frequency of the trap that the coil alone determines the effects upon the antenna's performance.

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The ability to transform a trap into a set of series values of resistance and reactance has a further benefit. If our interest in the trap antenna is confined to discreet frequencies, we may calculate the series values of resistance and reactance for each frequency, using the procedure that we have outlined. Then, we may use for each frequency a complex R +/- j X (LD4) load instead of the parallel R-L-C (LD1) loads that we have used in the exercise. However, because LD4 loads do not change reactance with frequency, we cannot perform frequency sweeps with them. Although we can perform frequency sweeps with parallel R-L-C loads, we should limit the frequency excursions that we allow if the load is a trap conversion. Since the value of resistance changes with frequency, a given calculated value will return accurate result only over a limited frequency span.

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Those who may work with traps extensively and who have EZNEC can lighten the burden of modeling traps by using the special entry in the load list provided by the program. Fig. 8 shows the entry box for a trap, using the series resistance and coil inductance, as well as the parallel capacitor value. Note that the frequency of the trap can also be specified. Under these conditions, through a related but somewhat different set of calculations, EZNEC calculates the requisite load values for each frequency at which the trap may be used, even if none of those frequencies happens to be 21.0 MHz.

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EZNEC users may revise the load entry for the test model and run it at both 21.1 and 14.1 MHz. At the higher frequency, the gain should be 2.05 dBi with a source impedance of 71.9 - j 8.0 Ohms. At 14.1 MHz, the corresponding values should be 1.83 dBi and 66.9 + j 0.9 Ohms. The approximation system shown earlier for use with any version of NEC-2, yields output values that are very usable compared to these. However, the appeal of the simple EZNEC trap entry system and of the ability to frequency hop without recalculation of load values is undeniable for individuals whose work requires extensive trap modeling.

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In some ways, the degree of precision of the trap output data is related to more general questions of accuracy with respect to loads placed at some distance from the region in which the current changes slowly from one segment to the next. In our test model, the load is distant on 20 meters from the source, and from Fig. 6, we know that the current is changing fairly rapidly. Hence, the mathematical loads at the trap points will not calculate as accurately as closer in toward the source, and the inductor wire may have at least some affect on the total antenna length. Therefore, when working with trap antennas, allow considerable adjustment capability when moving from your model to the physical antenna.

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We have not exhausted all that might be said about trap loads, but these exercises should enable you to proceed on your own.

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Go to Main Index

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5. Putting Sources Where You Can Find Them

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L. B. Cebik, W4RNL

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+ Very often, a model that approximates a desired antenna is good enough. In some case, we need more precision. Making the antenna dimensions precise is easy work: we simply carry out the length and wire diameter to more decimal places. +

Placing sources and loads precisely can be more work if they do not happen to fall at the center or end of a wire. How can we place them with high precision relative to an existing or proposed antenna?

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There are a few techniques that work very well, although some of them have attached pitfalls that we would want to avoid. We can illustrate the techniques if we contemplate a hypothetical problem demanding great precision. For most of us, the problem will be somewhat unreal, but we will not let that get in the way of seeing how the techniques of source placement work. In this episode, we shall look at sources only, reserving loads and their special requirements for next time.

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Consider a wire antenna for 3.5 MHz made up of #14 AWG copper wire. The antenna will be at 70' above average soil. (For modeling purposes, NEC models were run over the high-accuracy Sommerfeld-Norton ground, which is not available in public-domain MININEC 3.13. The 70' antenna height places the antenna about 0.25 wavelength above ground, within the accepted limits for MININEC. However, in this area of transition, some variance in the resonant length of antenna is to be expected between NEC and MININEC.)

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If this 80-meter antenna were a standard center-fed type, we would simply place the source in the center. With MININEC, this requires an even number of segments; with NEC we need an odd number of segments. If we further suppose that we want to resonate the antenna so that the source impedance showed less than +/-1 Ohm reactance, we would simply adjust the total length until we achieved this goal. If we set the source at the 0,0,70 point, with equal wire lengths extending to either side of this point, then we would play equally with two end values, but keep them equal to each other.

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This is the standard easy case. So lets make the problem a little harder. Suppose we want our wire to be about a half wavelength long, to be resonant within an Ohm or two, and to have the source placed at the point where the resonant impedance is 300 Ohms. Granted, for building purposes, something close to this would do fine, but remember that we are (for some unspecified project reasons) demanding precision.

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The 1-Wire Method

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If your program allows, you can approximate the 300-Ohm feedpoint by moving the source off center, as shown in Figure 1. In MININEC, we select a pulse number, which is always at the junction of two segments. In NEC, we select a segment and visualize the source as being at its center. Of course, we use sufficient segments in each case to ensure convergence.

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To get ahead of myself, I shall specify that the NEC antenna is 136.55' long. Because uncorrected MININEC does not correlate perfectly with NEC, the MININEC antenna will be 136.01' long. These lengths are based on using one of the techniques to come, but for the moment, let us just accept them. Remember also that different implementations of both NEC and MININEC may return slightly different values, based on a host of reasons related to input and output operations, rounding, and other similar factors.

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Since we are trying to be precise, let us choose 136 as the number of segments for our MININEC antenna and 137 segments for the NEC antenna. This move yields segments about 1' long for the two antenna, each segment being about 0.0036 wavelength long, well within limits for each program.

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In MININEC, if I place the source at pulse 23, it is 16.91% in from one end (just about 23.0'). The source impedance report is 317.50 - j1.91 Ohms. Again, this precision is excessive for most practical purposes, but for this example, the numbers will show some things about both the models and the programs. If I move to pulse 24, then the source is 17.65% in from one end (about 24.0'). The impedance report is 295.37 + j1.62 Ohms. Pulse 24 is close to the goal. Moreover, the antenna is close to resonance, and we would expect that the 300-Ohm point to show under 1 Ohm reactance. So we might well estimate the "true" 300-Ohm source point at about 23.6 to 23.7 feet in from one end. However, unless we were to be very lucky in re-segmenting the antenna to find a pulse very close to that point, we cannot get more precise.

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The case with NEC is similar. Using segment 24, we get a source that is 17.15% in from one end or about 23.42 feet (remembering that the NEC antenna model is not the same length as the MININEC model). The source impedance report is 314.3 - j3.32 Ohms. Moving to segment 25, which is 17.88% in from one end or 24.42 feet, we find 292.9 + j0.18 Ohms. The 300- Ohm point is between the two, perhaps at about 24' in from one end. Moreover, we might expect it to show something over 1 Ohm capacitive reactance. Again, we can juggle segmentation and hope to hit the mark.

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Surely there must be an easier way. In fact, there are at least two.

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The 2-Wire Method

Some modelers only create new wires when there is a difference between them--perhaps diameter, direction, or something else that corresponds with visible reality. Within MININEC and NEC, there are no rules against creating separate wires for what is in the real world a single length of copper wire. Therefore, let's rebuild our model of the off-center-fed 1/2 wavelength wire in accord with Figure 2. +
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In MININEC, we shall initially let Wire 1 run from abut -23.6' to 0, with Wire 2 running from 0 to the +112.4' mark. We shall place the source on Wire 1 at the 100% mark, which forces it to the junction of the two wires. We shall leave our segment total at 136, with 24 on Wire 1 and 112 on Wire 2. The aim is to keep the segment lengths on the two wires roughly equal. We might reduce the number of segments on each wire to proportionately lower numbers for speed of running the model. However, the segment lengths might change more significantly if our first estimates prove to be somewhat off.

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Now, by adjusting the end lengths only, we can establish both the 300-Ohm source impedance point and resonance within whatever limits we set for the problem. In fact, the model at hand required that Wire 1 be 23.78' long while Wire 2 had to be 112.23' long to yield a source impedance of 299.87 + j0.54 Ohms with a voltage source.

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Selecting a voltage or a current source in MININEC yields identical source impedance numbers for center-fed (symmetrical) antennas--at least within the limits of the decimal places usually shown. When the antenna is not symmetrical with respect to the source, with identical segments lengths on either side of the source, moving between a voltage and a current source will show a slight, but normally wholly insignificant variance for any desired level of precision. The current source option yielded a source impedance of 299.96 + j0.73 Ohms for this model. The differential also appears to lessen the closer the model is to absolute resonance (for example, when the reactance reaches 0.1 Ohm). I note these phenomena, but repeat that the differential is insignificant in MININEC.

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In fact, the two-wire method is the method of choice for MININEC modeling for precise source placement.

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In NEC, the situation is somewhat different. For our 136.55' long antenna, we can set up the wires as we did for MININEC, with wire 1 having an end coordinate of about -24' and using about +112.5' for the end of Wire 2. The two wires meet at 0,0,70.

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Placing the source for this antenna depends somewhat on the implementation of NEC that you are using. Some versions, such as EZNEC, permit placement of the source by specifying Wire 1, 100%, and choosing a Split Voltage source. The effect of this move is the same as setting up two sources, one on the last segment of Wire 1 and the other on the first segment of Wire 2. The program simply adds the two source impedances, which in other implementations, you might have to do manually.

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For the model at hand, with 2 sources, the end coordinates for resonance and 300-Ohms proved to be -24.1' and +112.45' respectively. The source impedances returned were 152.4 - j0.45 Ohms and 147.1 + j0.36 Ohms. These total to 299.5 - j0.09 Ohms. (A split-voltage-feed option selection produced 299.5 - j0.06 Ohms as its report.)

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Notice that the two impedances are not identical. Although close in length, the segment lengths for Wires 1 and 2 are not identical. Moreover, the currents on each side of the 0,0 point are also not identical, since the feedpoint is off center. If we choose a current source for this model, we should expect some variance from the voltage-source option, since the current source option is generated via a network. In fact, the 2-current- source option produced values of 32.3 - j760.1 Ohms and 259.1 + j734.4 Ohms, for a net impedance of 291.4 - j25.7 Ohms. For precision work, this result is considerably at variance from the voltage source models. In general, where such variations appear with NEC models, the voltage-source option is usually the more accurate.

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The 3-Wire Method

We can avoid any problems in NEC with differentials in reported feedpoint impedances by using a small modification of the two-wire method: the three-wire method. Figure 3 illustrates the idea, along with some problems and corrections we shall note along the way. +
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First, we shall set up Wire 2 by first settling upon a segment length and then centering a 3-segment wire length around the 0,0 coordinate. Since our model uses segment lengths of just about 1' each, we can set up Wire 2 as running from -1.5 to +1.5. Wire 1 then runs from about -24.1 to the junction with Wire 2. Wire 3 runs from the junction of Wire 2 to +112.45. Thus, we maintain our overall length of 136.55' for the antenna. (Note: once more, there is no rule that prevents the modeler from creating the wires from right to left. Nor is there any rule that requires the short end of the off-center-fed antenna to be on the left. My only suggestion is that, whatever conventions you use, you use them consistently in all similar models for the sake of ease of error detection and prevention.)

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Wire 1 and Wire 3 are now shorter than formerly, so they should receive 23 and 111 segments respectively to hold segment length very close to the 1' mark. The total is 137 segments for the model. This arrangement corresponds to part A. of Figure 3. We place a single source of either type at the center of Wire 2.

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The model reports a feedpoint impedance, using either voltage or current source options of 299.5 - j1.21 Ohms. The slight capacitive reactance is just what we expected based on our original estimates derived from the 1 wire model where we inspected the source impedance on segments that bracketed the 300-Ohm point.

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One dangerous temptation of using the 3-wire method is first to arrange Wire 2 as specified and then to decide that the long wires can use fewer segments. Since the antenna is, overall, only about a half wavelength long, we might easily reduce the Wire 1 segmentation to 4 and the Wire 3 segment number to 19, a proportional drop. However, this move makes the segments adjacent to the Wire 2 segments 6 times longer than the segments in Wire 2. The source impedance now reported is 288.6 - j2.29 Ohms, a significant difference from the case where all segments along the wires are close to the same in length.

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If we maintain equal segment lengths with all three wires, we can reduce the center wire to 1 segment and shrink its length to 1' by setting its coordinates at -0.5 and +0.5. This move is suggested in part B of Figure 3. Bringing Wires 1 and 3 to join this new Wire 2 calls for increasing their segment numbers by 1 each to 24 and 112, for a total of 137 segments. The source impedance reported for this model is 299.5 - j1.10 Ohms, the same for even the most critical purposes as the 3-segment wire 2 model produced.

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However, the temptation to reduce the number of segments on the longer wires produces more radically erroneous results with a center wire having only one segment. If we retain the 1' center wire but decrease the number of segments on the end wires to 4 and 19 respectively, the model reports a source impedance of only 260.3 - 2.02 Ohms. Notice that the resistive component is far off the reliable mark, although the reactance has not changed significantly.

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The segments of the end wires in our "temptation" model are about 5.7' long. We may retain this segmentation by increasing the length of the center wire to a like amount by setting its coordinates are -2.85 and +2.85. Then, with 4 segments to Wire 1 and 19 segments to Wire 3, the model reports an accurate source impedance of 299.5 + 0.76 Ohms.

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If the smaller model yields reasonably accurate results, why use the highly segmented model? This fair question has a fair answer. With longer segment lengths, it is easier to develop inequalities of length without either knowing it or being able to correct the inequalities by the simple addition or subtraction of a segment here or there. With short segments, a growing inequality tends to show itself, especially if the lengths have a convenient correlation to the physical dimensions, as they do in this model sequence. Moreover, adding or subtracting a single segment from the end wires has a minimal impact on the length of each segment.

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The 3-wire method of source placement is the most accurate and unambiguous for NEC. Moreover, using 3 segments in the source wire resists the effects of unequal segment lengths in adjacent wires more effectively than using only one segment in Wire 2, although the effects even on the 3-segment center wire can upset precision in some instances. As we noted in the beginning, these methods are applicable only where source placement needs to be as precise as possible.

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I ran the same exercise, with a slight modification on MININEC, even though the 2-wire method is in its simplicity and accuracy the method of choice. For the exercise, the MININEC center wire had 2 segments to ensure placement of the source at the 0,0 point, roughly comparable to part A of Figure 3. In this case, the wire ran from -1.0 to +1.0, with the connecting wires reaching -23.78 and +112.23.

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MININEC returned a source impedance report of 300.20 + j1.35 Ohms (compared to 299.87 + 0.54 for the 2-wire method). Leaving the center wire untouched, the segmentation was reduced to 4 and 19 on the end wires. The source impedance reported was 298.72 + j5.94 Ohms. Although MININEC shows more variance of reactance under these conditions than NEC, the overall MININEC impedance was considerably less affected by radical re-segmentation than was that reported by NEC.

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Returning the center wire to a suitable length relative to the segment lengths on the outer wires, MININEC reported a source impedance of 298.66 - j2.37 Ohms. As expected, the reactance is now closer to the value reported by the 136-segment model, although the resistive part of the impedance remains below the value reported by the more heavily segmented model.

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In general, for this class of cases, MININEC is less sensitive than NEC to changes in wire segmentation for multiple wires making up a single antenna element.

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Applications

The off-center-fed 1/2 wavelength antenna is not the only application requiring fairly precise placement of the source, both in models and in reality. For example, vertically oriented delta loops, used as self- contained vertically polarized antennas on the lower HF bands, call for off-center feeding of one of the vertically angular legs. The proper source point to maximize vertically polarized radiation, relative to the baseline of the antenna, varies with the shape of the delta. (The point is approximately 1/4 wavelength from the apex of the triangle. This dimension, which may be close enough for many building purposes, requires optimization for vertically polarized use of the loop.) +

Moreover, not all uses of antenna modeling software are directly geared toward either the construction of a proposed antenna or the analysis of an existing antenna. There are innumerable exercises one can perform with modeling software to understand better the operation of many types of antennas. For example, off-center-fed ½ wavelength antennas show interesting source impedance curves as the feedpoint is moved outward along the antenna. Moreover, the resonant length of the antenna changes with the feedpoint position and impedance. This is but one of a host of cases in which we can use our modeling software as a very effective self-instruction tool. The more we know about antenna performance in general, the more sense we can make out of the analysis of specific antennas and the more confidence we can have in the models we convert into real antennas.

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In addition, when you pass the 1/2 wavelength mark in antenna size, there are ordinarily options in the placement of the feedpoint. A 1.5 wavelength antenna may be fed at its center or about 1/4 wavelength in from one end. These collinear arrays demand some precision in source placement not only as a guide to construction, but as well to understand the resultant radiation patterns.

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The techniques we have explored here are also applicable to the placement of various type of loads along an antenna element. What a reactive load size needs to be, relative to typical antenna design goals, depends upon precisely where along the antenna element we place it. Moreover, traps require careful placement and design in order to be effective in an antenna element. We shall find (next time) that the techniques of modeling source placement explored in this episode have extensive application to the precise placement of loads.
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50. The NEC-4 IS Card: Insulated Wires

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L. B. Cebik, W4RNL

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From time to time, I shall look at some of the advanced features of both NEC-2 and NEC-4 programs. By "advanced," I mean features not generally included on entry level programs such as EZNEC 3.0 or NEC-Win Plus. Both of these widely used and user-friendly programs reduce the list of available geometry inputs and program control cards in the interest of effectively guiding the user through the modeling process.

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However, both the NEC-2 and the NEC-4 core programs allow a considerable number of additional geometry and control functions. When NEC-4 appeared, it not only improved the accuracy of calculations for tapered-diameter elements, but as well added a number of new inputs. The one in which I am interested this month is the IS card or input. IS stands for "insulated sheath." It provides a way for the user to analyze the performance of antenna wires with insulation.

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For a long time, antenna builders have been aware that insulated antenna element wire has a velocity factor. The electrical length of an insulated wire will be longer than the physical length to a degree that depends upon the type and thickness of insulation. Expressed from a different perspective, a resonant dipole for some given frequency and wire diameter will be shorter if the wire is insulated than it will be if the wire is bare. How much shorter the insulated dipole will be depends on the insulation.

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Unfortunately, there are no handy tables that are generally available to give us the velocity factors (VF) of insulated wires that are commonly used in wire antenna construction. However, experience has taught antenna builders that the values range from 0.99 down to 0.95 or so, depending on the type and thickness of the insulation. Perhaps the IS card of NEC-4 can give us some slightly better feel for insulated wire velocity factors, as well as introduce an advanced feature of a modeling program.

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Modeling the Insulated Wire

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An insulated wire, from the perspective of NEC-4, consists of a wire and an insulating sheath. The program assumes that the insulation begins at the exact surface of the wire and extends to some other point. The "other" point defines the radius of the sheath.

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Fig. 1 shows a sketch of the critical dimensions of an insulated wire and its model. We shall model the illustrated situation in GNEC, perhaps the only currently available commercial implementation of NEC-4 that allows the use of the IS input. Like the core itself, GNEC will expect that its wire geometry inputs list the wire radius and not its diameter. And the first step in setting up a model--without the insulation on the wires--is to set up the wire.

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Fig. 2 shows the wire set-up panel from GNEC. The Tag number is simply the wire number. We shall give the wire 21 segments and place the source at its center (segment 11). In the examples that we shall explore, all dimensions will be metric, the fundamental unit of the NEC core. Hence, the single wire dipole--resonant at 30 MHz--will extend on each side of the X-axis along the Y axis +/-2.416 m. Likewise, the radius is in meters. 0.001 m = 1mm.

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I selected the 0.001-m radius because 2-mm diameter copper wire is a very popular size for European antenna construction. A 2-mm wire is 0.07874" in diameter, just below the 0.0808" diameter of AWG #12 copper wire so popular with U.S. antenna builders.

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Fig. 3 shows the basic antenna model in complete form for a free-space copper dipole resonated at 30 MHz. The CM or comment card is inaccurate because for the purposes of illustration, I have added a line that insulates the wire. However, we should first trace the other lines of the model. The GW line shows the wire we created in Fig. 2, and the following GE line ends the geometry section of the model. The EX lines specifies a voltage source placed at segment 11 of wire 1. The LD5 line provides the conductivity of copper as a material load on every segment of the wire. The FR or frequency request card shows a single frequency request of 30 MHz. The RP 0 line specifies a far-field azimuth (phi) pattern covering all 360 degrees around the antenna.

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If we ignore the IS line for a moment and return to the bare-wire model, the antenna will show a free-space gain of 2.10 dBi and a source impedance of 72.536 + j 0.178 Ohms. I have listed the impedance to many more decimal places than we might make use of operationally. However, at certain points in our work, we shall be interested in numerical progressions, and so I have given the data to the limits provided by the program. The free-space source impedance of the bare-wire model will be important to us in more than one way as we proceed.

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In Fig. 3, we inserted the IS line above the EX line. Let's see how to implement an insulated sheath for a wire.

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Fig. 4 shows the line-assist screen for entering IS information. First, we must identify the wire to which the insulated sheath will apply, namely wire or tag 1 from the first to the last segment. Note that we have options here and may apply a sheath to only some or to all of the segments of a wire. Had we desired to leave the center segment bare, we could have specified 2 IS entries, one to cover segments 1-10 and the other to cover segments 12-21. The only restriction is that we cannot apply two sheaths to any single segment. Hence, we cannot model the multi-layering of different types of insulation.

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Beyond the segment-coverage of the shield, we have 3 significant variables to enter. One of them is the sheath outer radius, as measured from the wire center line to the sheath surface. The depth or thickness of the shield is the sheath radius minus the wire radius. In the illustration, the sheath is 0.0005 m (or 0.5 mm) thick (about 0.0197").

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Note that the IS input is a program control card, not a wire geometry card. Therefore, we must input the value for the sheath radius in meters. If you have used the TL (transmission line) facility within a more basic program, you have sampled inputting dimensional values within a program control card. However, for user convenience, the programmers allow you to use the same units that you specified for the geometry section of your model. The program performs any necessary conversion for you. For NEC itself, the only acceptable input for all such program control entries will be in meters. In contrast, we could have specified the wire coordinates in any units of measure and then used a GS card to scale them to meters for the core run. I set up the basic model in meters so as not to require us to think in multiple systems of units within this exercise.

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The inputs also call for a relative permittivity (or relative dielectric constant). The value shown is hypothetical and for illustration only. As I noted earlier, I do not presently have access to a handy list of relative dielectric constant values for wire insulations that we commonly encounter. One of the few guides available comes from the checking sources like Passive Electronic Component Handbook, 2nd Ed, edited by Charles A. Harper (McGraw-Hill, 1997). The capacitor chapter provides an interesting--although not wholly relevant--list of plastics used as capacitor dielectrics, along with their approximate dielectric constants.

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Material                                          Approx. Permittivity
+Polyisobutylene                                             2.2
+Polytetrafluoroethylene (PTFE)                              2.1
+Polyethylene terepthalate (PET)                             3.0-3.2
+Polystyrene (PS)                                            2.5
+Polycarbonate (PC)                                          2.8-3.0
+Polysulfone (PSU)                                           2.8-3.2
+Polypropylene (PP)                                          2.2
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Common plastics, then, appear to have a range of relative permittivity values between 2 and 3. In contrast, the permittivity of a vacuum is by definition 1.0, and air is 1.0006. If we specify a relative permittivity value of 1.0 for any sheath, no matter how thick, we should obtain the performance of bare wire.

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Note that we earlier specified that the two most interesting variables of insulation were its thickness and its type, which is expressed in the value assigned to the relative dielectric constant. In Fig. 4, we assigned the conductivity entry a very low value of 1E-10 S/m (or mhos/m). The assignment is arbitrary but not without reason. At any frequency of use, we assume that the insulation of an insulated antenna wire is highly effective. How ineffective must the insulating property be for the insulation to show some effect upon antenna performance?

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Fig. 5 suggests a partial answer. I took a particular situation and gradually increased the insulation conductivity. The original bare-wire dipole (+/-2.416 m) has a sheath that is 2 mm thick (for a total diameter of 6 mm or just under 1/4"). This relatively heavy insulation on a 2-mm wire has a permittivity of 3.0, the highest value scanned for these notes. I increased the conductivity in decades to produce the graph of source resistance and reactance in the figure.

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Not until the conductivity passes the 1E-5 S/m level (100,000 Ohms per meter resistivity level) do the values of source resistance and reactance show any change from the values at the lowest level of conductivity. At this level, the material is becoming a semi-conductor more than an insulator. Virtually all insulating materials have conductivities less than 1E-5 S/m when used within their specified frequency and temperature ranges. Hence, setting the conductivity as a constant with the value of 1E-10 S/m poses no problems. As well, it reduces the number of variables with which we must concern ourselves to a manageable value of 2.

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Scanning the Range of Insulation Permittivity and Thickness

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A specific modeling task for analysis might require that we have reasonably exact values for the insulation thickness and relative dielectric constant. Since we do not have access to such figures, let's perform a different sort of modeling task. Let's survey a variety of insulation thicknesses applied to our 2-mm bare wire and see how they affect dipole performance as we systematically increase the relative permittivity from 1.0 to 3.0.

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We shall check 3 insulation thicknesses: 0.5, 1.0, and 2.0 mm (a 1-2-4 progression). A 4-mm thick insulation on a 2-mm wire yields a 6-mm overall insulated-wire diameter, close to 1/4". Here is what the dimensions will look like in tabular form:

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                        Dimensions in Millimeters
+Wire       Wire       Insulation       Sheath          Sheath
+Diameter   Radius     Depth            Radius          Diameter
+ 2.0       1.0        0.5              1.5             3.0
+ 2.0       1.0        1.0              2.0             4.0
+ 2.0       1.0        2.0              3.0             6.0
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+Wire       Wire       Insulation       Sheath          Sheath
+Diameter   Radius     Depth            Radius          Diameter
+ .07874    .03937     .01969           .05906          .11811  (< 1/8")
+ .07874    .03937     .03937           .07874          .15748  (5/32")
+ .07874    .03937     .07874           .11811          .23622  (< 1/4")
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I have repeated the planned survey dimensions in inches for anyone not conversant with metrics.

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We shall portray the results as a series of very similar graphs. Essentially, only the Y-axis will change as we check out various interesting parameters of antenna performance and size.

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Fig. 6 graphs for each of the 3 insulation depths the resonant frequency of the original bare-wire antenna as we increase the permittivity. As expected, assigning a permittivity value of 1.0 to the sheath yields the original 30-MHz resonant frequency. However, for any given insulation depth, increasing the permittivity reduces the resonant frequency. In other words, the antenna becomes electrically longer than its physical length would indicate. Likewise, for any given value of permittivity, increasing the thickness of the insulation also reduces the resonant frequency of the antenna.

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Note that for any insulation thickness, the highest rate of departure from the bare-wire resonant frequency occurs with the initial values of permittivity above 1.0. All three curves gradually flatten, although the thicker the insulation, the slower the rate of flattening. We may also look at the rates of change from the other perspective: for any given permittivity, the highest rates of departure from the bare-wire resonant frequency occur with the initial thickness increases. Each curve represents a doubling of insulation thickness, but the distance between the lower two curves is not twice the distance between the upper two curves.

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Fig. 7 plots for each of the sheath thicknesses the resonant half length of the dipole element versus the increasing permittivity. I re-resonated each dipole by changing its length until the source impedance again reached a value where the reactance with less than +/- 1 Ohm. In fact, all of the checkpoints have reactances less than +/- 0.6 Ohm. This amount of "play" in resonant lengths does limit the precision of the curves, although the general sweep is well within any desired scale of accuracy.

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Since the antenna model extends its element on each side of the X-axis, the element half-length is the most convenient unit of measure. As we might expect, for the insulated dipole to be resonant at 30 MHz, we must reduce its length, with both the insulation permittivity and depth contributing to the shortening effect.

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A convenient rule of thumb used by many antenna builders is to use the ratio of the measured insulated wire resonant frequency and the anticipated bare-wire resonant frequency as the amount by which to multiply the wire length to arrive at an insulated wire antenna that is resonant at the originally desired frequency. For practical purposes within the scope of insulation depths and permittivity values in this exercise, the rule of thumb will work. However, as the permittivity approaches 3.0 and the insulation thickness approaches 2.0 mm on a 2-mm wire, the actual element length needed for resonance will be slightly shorter than the frequency ratio suggests. Therefore, when calculating the insulated wire velocity factor, one should use the resonant wire length rather than the frequency offset.

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In Fig. 8, we have the same data as in Fig. 7, but expressed in terms of a range of velocity factors for the insulated wire antennas. If we take the range of probable insulation permittivity values to run between 1.5 and 3.0, then 0.99 is about the lowest velocity factor that we encounter for wires with very thin, low permittivity insulation. However, wires with higher permittivity insulation that is also thick may have velocity factors that go well below the 0.95 value often cited as the approximate lowest value. Since a number of plastic materials have permittivities above 2.8, the antenna builder should be prepared to shorten the dipole more radically than indicated by rules of thumb wherever the insulation is thick.

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Fig. 9 calls to our attention and often overlooked aspect of the antenna wire's velocity factor. As we shorten a dipole for virtually any reason, the resistive component will decrease relative to its bare-wire resonant value. The bare-wire resonant resistance was just over 72.5 Ohms. All of the re-resonated 30-MHz sheathed dipoles yield resistive impedance values that are lower than the bare-wire value. The curves for the resistive impedance values track the curves in each of the other graphs shown here.

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For low values of relative permittivity or for thin insulations, the amount of impedance decrease is largely insignificant to antenna operation, especially as a dipole. However, the highest decrease shown, about 7 Ohms, may become a noticeable amount if thick wires of the highest permittivity value are used in a complex parasitic array. Such arrays may exhibit low bare-wire impedances, and 6 more Ohms of decrease may become objectionable relative to initial design plans for systems of matching the antenna source to a feedline.

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Nonetheless, the small demonstration using the NEC-4 IS program control card does show a fairly close correlation between experiential rules of thumb and reasonable values of insulation thickness and permittivity as modeled for a dipole. Of course, this exercise has covered only 2-mm diameter wire. Amateur antenna builders very often use other wire diameters, ranging from AWG #18 to AWG #10 or so. Whether we can extrapolate the values from this exercise to these other cases is uncertain unless someone runs the same exercise for a reasonable sampling of the other wire sizes.

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The curves may also serve to answer some questions often posed by those new to antenna work. For example, upon learning that the oxide of aluminum that forms on all antennas made from the material is an insulator, folks often ask whether that oxide has any significant effect on performance. We may use any one of the graphs to perform a crude extrapolation, even knowing that the tabulated permittivity of the material is 2.5-2.8: since the oxide thickness is only a few molecules, the graph line for material would be barely discernable at the top of Fig. 6.

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Although the most common uses of the IS program control card may be connected with the use of insulated wire in antenna structures, these are not the only uses. The wire that we construct as the core around which to model a sheath need not be a highly conductive or even a thin wire. We might assign the wire a fairly low conductivity, and NEC-4 also permits us to assign a value of permeability so that we may account for any effects due to the wire's magnetic properties. We may also sheath the wire, using a uniform depth as a limitation, with any values we might like for conductivity and relative permittivity. Unlike the dipole, we do not need to place a source on the wire itself. Instead, we may use plane-wave excitation with either linear or elliptic polarization.

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I can imagine numerous possible--but not necessarily real--applications for such an arrangement. There are as many applications as there are two-tiered physical structures where our interest may lie in the currents induced in the inner or "wire" layer. Bone-to-marrow, weather-insulation-to-pipe, and sheathing-to-mechanical-lick-cable situations are but 3 possibilities among many.

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The limiting factors for such modes of analysis are two. First, the situation must resemble an insulated wire so that a sheath covers a long inner element. We can create many shapes by linking such wires and sheathing all of them, although not necessarily with the same "material," that is, with the same values of conductivity, permittivity, and thickness. The second--and perhaps more challenging--limitation is our knowledge of the conductivity and relative permittivity of a broad spectrum of materials. However, both conductivity and permittivity are subject to measurement.

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Although not assured, it may be possible to use the IS input in conjunction with a wire and a cylinder created from direct wire inputs to model a coaxial cable. However, there are numerous issues connected with such a structure if it is to simulate an existing coaxial cable. These issues include the effective surface coordinates of the inner side of the cylinder relative to the wire radius, the sensitivity at the test frequency of the structure to close-wire modeling limitations--including closely spaced wires of different diameters, and the relative lengths of segments meeting at junctions within the cylinder structure. However, in principle, the IS entry may be used to simulate the dielectric between the center wire and the cyclinder that represents the outer conductor.

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In the end, antenna modeling software offers a great many more opportunities for RF analysis than the task of designing antennas can contain. The geometry input and the program control cards in the NEC-deck are simply tools to use in those processes. And, like all tools, they are subject to creative applications.

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51. Testing the Fringes of Modeling Programs

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L. B. Cebik, W4RNL

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In episodes 2 and 3 of this continuing series, I outlined briefly the nature and limitations of program using NEC cores and those using MININEC cores for antenna modeling calculations. Special limitations applicable to NEC-4 that do not appear in the core manual were outlined in "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), 3-16, and these limitations also apply to NEC-2 as well. The ARRL NEC-2 antenna modeling continuing education course has two lessons specifically devoted to modeling core limitations. Note that I specifically call them core limitations, since a given limitation would apply to every commercial implementation of a given core unless the programmer adds specific correctives. For example, the NEC-2 difficulty--largely corrected in NEC-4--of handling stepped diameter elements is overcome by the introduction of Leeson corrections (calculated substitute elements of uniform diameter) in both EZNEC and NEC-Win Plus. The correctives are programmer additions to the core.

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Often, it is difficult to appreciate the nature and extent of core limitations without having access to a variety of programs on which to make comparisons. As well, for simple modeling projects in the HF range, almost any one of the program cores will do a good job. If we combine these ideas, then it might be useful to look at a couple of models that press the cores to their limits--and sometimes beyond--in order to see what various programs do with them. The results can be useful in evaluating the suitability of a given program for the particular range of projects that the modeler has in mind.

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The following notes will include these programs:

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  • EZNEC 3.0 Professional Version: NEC-2, NEC-4, and NEC4-D (double-precision)
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  • NEC-Win Plus: NEC-2
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  • NEC-Win Pro: NEC-2
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  • GNEC: NEC-4
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  • ELNEC: MININEC 3.13 (DOS)
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  • AO: MININEC 3.13 (DOS)
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  • Antenna Model: MININEC 3.13 (Windows)
    • +
  • NEC4WIN-VM: MININEC 3.13 (Windows)
    • +
  • MMANA: MININEC 3.13 (Windows) (freeware)
    • +
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Although the NEC-4 and NEC-2 cores may seem to be fixed items, they are not. They continue to evolve as new methods emerge for speeding up routines in the dense matrix calculations in the compiled FORTRAN core. As well, because MININEC 3.13 is a public domain program, it has been translated into compiled BASIC, DOS machine coding, and into C++ for Windows operation. The latter steps have largely removed the older 256-segment limitation of earlier implementations. Hence, we can expect some slight variation in results, since implementing the core code in various ways opens the program to the use of various correctives for its other limitations. Expert MININEC, a proprietary newer version of the code with new algorithms was not accessible for this set of tests.

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A Simple Folded Dipole Test

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Let's begin with a simple antenna that every core can effectively run: a folded dipole that does not press program limitations. Fig. 1 shows the outlines of the model.

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Each long wires is 197.9" (5.0242 m or 0.4776 wl) long at the test frequency of 28.5 MHz. The end wires are 1" (0.0254 m or 0.002415 wl) long. The end wires have 1 segment each, while the long wires each use 111 segments for NEC models and 110 segments for MININEC models. The heavy segmentation essentially overcomes the MININEC tendency to truncate corner junctions. (NEC4WIN limited the number of segments for the long wires to 50.) The odd-even segmentation difference, of course, relates to source placement. A NEC source appears in the middle of a segment, calling for an odd number of segments for center placement. A MININEC source appears on a pulse or junction of two segments, calling for an even number of segments for center placement on the wire. The source type-- voltage or current--makes no difference to the outcome.

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The length of the segments is about 0.004 wl on the long wires and about 0.0024 wl on the end wires, for a segment length ratio of 1.78:1. This value falls within the recommended 2:1 ratio of segment lengths for adjacent segments. The wire diameter is 0.0403", corresponding to AWG #18. This diameter is 1.0236 mm or about 9.73E-5 wl, well within recommended limits.

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The models were set as Y-coordinate values, with the space between the folded dipole wires appearing on the Z-axis. This orientation presents a "broadside" for the azimuth pattern from which I took gain readings. Had I set the wire spacing on the X-axis, the maximum gain readings would have appeared to be about 0.05 dB higher than those in the table, with an approximate 0.1 dB "front-to- back" ratio. This differential occurs because the wires do not have equal current magnitudes and phase angles at corresponding points. The wire conductivity or resistivity value is for copper wire, although NEC4WIN in Version 3.1 of the program does not have user choices for material losses. Hence, its gain values will be for lossless or "perfect" wire.

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The initial model was pruned to resonant length using NEC-4 as the standard. The defined model was then run in programs using other cores. The following table provides the results. Note that AO and NEC4WIN offer several possible combinations of loop and frequency correctives and will have multiple entries. All gain and impedance values are presented in the degree of precision presented by the individual programs. NEC-4D means the double-precision version of the NEC-4 core.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      Standard Folded Dipole at 28.5 MHz
+
+Program and Core        Free-Space        Source Impedance
+                        Gain dBi                R +/- jX Ohms
+A. NEC Cores
+EZNEC 3.0
+  NEC-4                 2.10                    288.6   - j   0.5613
+  NEC-4D                2.10                    288.5   + j   0.1557
+  NEC-2                 2.10                    288.5   + j   0.1875
+NEC-Win Plus
+  NEC-2                 2.10                    288.488 + j   0.1597
+NEC-Win Pro
+  NEC-2                 2.10                    288.488 + j   0.160
+GNEC
+  NEC-4D                2.10                    288.487 + j   0.153
+
+B. MININEC 3.13 Cores
+ELNEC 3.0               2.098                   288.28  - j   4.5420
+AO 6.5
+  No Corrections        2.09                    288     - j   3
+  Frequency Cor.        2.09                    290     + j   7
+  Bent-Wire Cor.        2.09                    288     - j   4
+  Fr. + B-W Cor.        2.09                    290     + j   6
+Antenna Model           2.10                    288.68  + j   0.6826
+NEC4WIN-VM 3.1
+  No Corrections        2.13                    286.13  - j   2.33
+  NEC Freq. Cor.        2.13                    287.76  + j  10.88
+  Loop-Wire Cor.        2.15                    306.61  + j 104.96
+  Fr. + Loop Cor.       2.15                    308.16  + j 111.01
+MMANA                   2.06                    291.158 - j   4.915
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The coincidence of values for both NEC cores illustrates the degree to which the model is well within core guidelines. The ELNEC MININEC result shows a slight capacitive reactance owing to the fact that this program does not implement a frequency corrective. Uncorrected AO results in a similar figure, although with correctives, the impedance values fluctuate around resonance in ways that would be operationally insignificant. The MMANA result appears to reflect a wire conductivity or resistivity assignment that is slightly high, which reduces gain in the hundredths column and increases the resistive component of the source impedance. Although differentials are not operationally significant, the Antenna Model result most closely coincides with the NEC-4 and NEC-4D reports.

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The NEC4WIN-VM numbers require further interpretation, since they are for lossless wire. The basic NEC-4 model returns a gain of 2.14 dBi and a source impedance of 286.4 - j 2.47 for this same condition. The uncorrected NEC4WIN numbers correspond well with this value set. The frequency correction offsets the values in a similar way to the frequency correction in AO. (We shall look at frequency issues in a subsequent model.) Clearly, the loop wire correction is not designed for use with closely spaced wires, such as in a folded dipole.

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Now let us contrast these results with those for a folded dipole that challenges the limits of the cores. Fig. 2 shows the outlines of the new folded dipole model. We shall retain the 28.5-MHz test frequency. However, we shall reduce the wire diameter to AWG #22, that is, 0.0253", 0.6426 mm, or 6.11E-5 wl. As well, we shall reduce the spacing between wires to yield end wires that are much shorter: 0.375", 0.009525 m, or 9.06E-4 wl. The basic NEC-4 model became resonant within +/- j 1 Ohm with a length of 199.04", 5.0556 m, or 0.4806 wl.

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Retaining the 110/111 segmentation density for the long wires and single segments for the end wires, we wind up with segments lengths of 4.33E-3 wl and 9.06E-4 wl, respectively, for a ratio of 4.78:1. This value exceeds the recommended ratio for adjacent segments in both cores. Further limitations of the cores become apparent when we tabulate the results for all programs.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       Narrow Folded Dipole at 28.5 MHz
+
+Program and Core        Free-Space        Source Impedance
+                        Gain dBi                R +/- jX Ohms
+A. NEC Cores
+EZNEC 3.0
+  NEC-4                 2.07                    290.0   - j   0.7181
+  NEC-4D                2.08                    289.8   + j   0.2772
+  NEC-2                 2.08                    289.8   + j   0.3964
+NEC-Win Plus
+  NEC-2                 2.08                    289.808 + j   0.2683
+NEC-Win Pro
+  NEC-2                 2.08                    289.808 + j   0.268
+GNEC
+  NEC-4D                2.08                    289.807 + j   0.264
+
+B. MININEC 3.13 Cores
+ELNEC 3.0               2.074                   289.544 - j   6.4580
+AO 6.5
+  No Corrections        -.09                      7.81  - j   61.5
+  Frequency Cor.        -.27                      7.46  - j   59.8
+  Bent-Wire Cor.        -.09                      7.81  - j   61.5
+  Fr. + B-W Cor.        -.27                      7.46  - j   59.8
+Antenna Model           2.08                    289.459 - j   2.04
+NEC4WIN-VM 3.1
+  No Corrections        2.19                      9.60  - j  73.90
+  NEC Freq. Cor.        2.20                      6.74  - j  62.36
+  Loop-Wire Cor.        2.31                      1.74  - j  46.76
+  Fr. + Loop Cor.       2.32                      1.29  - j  40.10
+MMANA                   -.51                     14.626 - j  58.674
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The NEC core values hold up well under the limit pressure applied in this model. Since the wires have a smaller diameter, the gain reduction relative to the model of a standard folded dipole is reasonable. The source impedance for any pair of wires in a folded dipole is approximately 4 times the value of the source impedance for a single wire of the same diameter. Hence, the impedance values are quite sensible as well.

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For the most part, the implementations of public domain MININEC yield wholly unreliable results, indicating that the model has exceeded core limitations by an excessive amount. The completely unrealistic source impedance values make any inspection of the gain values otiose. However, the fact that the NEC4WIN gain values are out of line with the AO and MMANA values, even for uncorrected MININEC calculations, suggest that in redoing the algorithms for Windows, some alteration has occurred.

+

The ELNEC and Antenna Model value sets, however, are exceptions to the MININEC rule. Both ELNEC and Antenna Model contain close-wire correction factors not used by the other programs. The result are sets of both gain and impedance values that are quite coincident with the values produced by NEC models.

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Although we have looked at only two models--folded dipoles that are within and outside normal core limitations--the exercise does indicate the value of comparative modeling. There are differences between the limitations of the cores surveyed. As well, there are also limitations and correctives within implementations of those cores, some of which involve core reprogramming and some of which involve supplemental correction factors. Even correctives bearing similar names in different programs may operate differently. Therefore, it pays to explore the programs by using a series of models that press the limitations to discover just where a given program's limits actually lie.

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A UHF Model of a 4-Element Yagi

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We have noted a frequency corrective applied to some implementations of MININEC. As we increase frequency, MININEC 3.13 develops a frequency inaccuracy that AO, Antenna Model, and NEC4WIN attempt to correct. ELNEC and MMANA apparently do not have such correction factors.

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Interestingly, the AO MININEC correction factors are calibrated to NEC-2. However, NEC-2 also exhibits a frequency-based deviation from the results obtained from NEC-4 models of the same antenna. The deviation become more pronounced in the upper VHF area and above. It is likely that the differences in reports result from changes made for the NEC-4 core in the treatment of the source "gap" and the element end calculations.

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Let's see to what extent the programs display the deviations. Fig. 3 shows the outline of a 4-element utility Yagi designed to have a very low (under 1.25:1) 50-Ohm SWR across the 420-450 MHz band. Fig. 4 shows the NEC-4 SWR curve for the antenna.

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The following listings of EZNEC wire tables provide the dimensions for the antenna in inches, in meters, and in wavelengths.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+W4RNL 432 WB Yagi               Frequency = 432  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1            0.000, -6.575,  0.000         0.000,  6.575,  0.000 5.00E-01  15
+2            5.807, -6.083,  0.000         5.807,  6.083,  0.000 5.00E-01  15
+3            9.626, -5.453,  0.000         9.626,  5.453,  0.000 5.00E-01  15
+4           15.748, -5.256,  0.000        15.748,  5.256,  0.000 5.00E-01  15
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1            0.000, -0.167,  0.000         0.000,  0.167,  0.000 1.27E+01  15
+2            0.147, -0.154,  0.000         0.147,  0.154,  0.000 1.27E+01  15
+3            0.244, -0.139,  0.000         0.244,  0.139,  0.000 1.27E+01  15
+4            0.400, -0.133,  0.000         0.400,  0.133,  0.000 1.27E+01  15
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : wl)  Conn. --- End 2 (x,y,z : wl)   Dia(wl) Segs
+
+1            0.000, -0.241,  0.000         0.000,  0.241,  0.000 1.83E-02  15
+2            0.213, -0.223,  0.000         0.213,  0.223,  0.000 1.83E-02  15
+3            0.352, -0.200,  0.000         0.352,  0.200,  0.000 1.83E-02  15
+4            0.576, -0.192,  0.000         0.576,  0.192,  0.000 1.83E-02  15
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           8     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The worst case segment length to wire radius ratio is 2.62:1, reasonably well within most program limitations for linear elements with no odd geometric features. The shortest segment is 0.024 wl long (with the longest 0.03231 wl). MININEC models of the same antenna used 16 segments per element to center the source on wire 2.

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In tabulating the results for this model using various programs, it is necessary to sample them at 10 MHz intervals across the 420-450 MHz span. Therefore, each entry consists of four entries forming a progression that will be useful in evaluating the results. Because each data entry is larger, values have been truncated wherever they exceed the column allowance.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   Wide-Band 4-Element Yagi for 420-450 MHz
+
+Program     Freq. Free-Space  Front-Back  Source Impedance        50-Ohm
+ and Core   MHz   Gain dBi    Ratio dB    R +/- jX Ohms           SWR
+
+A. NEC Cores
+EZNEC 3.0
+  NEC-4     420   9.12        11.56       45.81 - j  2.99         1.114
+            430   9.23        12.14       56.30 + j  1.51         1.130
+            440   9.34        12.73       61.22 - j  2.38         1.230
+            450   9.55        14.31       49.46 - j  7.28         1.158
+  NEC-4D    420   9.12        11.56       45.81 - j  2.99         1.114
+            430   9.23        12.14       56.30 + j  1.51         1.130
+            440   9.34        12.73       61.22 - j  2.38         1.230
+            450   9.55        14.31       49.47 - j  7.28         1.158
+  NEC-2     420   9.17        11.69       47.77 - j  1.14         1.053
+            430   9.27        12.20       58.14 + j  1.51         1.166
+            440   9.40        12.92       59.93 - j  4.57         1.221
+            450   9.64        14.99       42.72 - j  6.56         1.236
+
+NEC-Win Plus
+  NEC-2     420   9.17        11.69       47.77 - j  1.14         1.053
+            430   9.27        12.19       58.14 + j  1.50         1.166
+            440   9.40        12.92       59.93 - j  4.57         1.221
+            450   9.64        14.99       42.72 - j  6.56         1.236
+
+NEC-Win Pro
+  NEC-2     420   9.17        11.69       47.77 - j  1.15         1.05
+            430   9.27        12.19       58.14 + j  1.50         1.17
+            440   9.40        12.92       59.93 - j  4.57         1.22
+            450   9.64        14.99       42.73 - j  6.57         1.24
+
+GNEC
+  NEC-4D    420   9.12        11.56       45.81 - j  3.00         1.11
+            430   9.23        12.14       56.30 + j  1.51         1.13
+            440   9.35        12.74       61.22 - j  2.38         1.23
+            450   9.55        14.31       49.47 - j  7.29         1.16
+
+B. MININEC 3.13 Cores
+ELNEC 3.0   420   8.95        10.42       38.11 - j 12.47         1.480
+            430   9.10        11.58       48.22 - j  3.96         1.092
+            440   9.20        12.21       57.67 - j  1.27         1.156
+            450   9.33        13.00       59.82 - j  5.36         1.227
+      (     460   9.58        14.95       46.49 - j  7.08         1.178  )
+
+AO 6.5
+  No Corrections
+            420   8.95        10.74       39.3  - j 11.4          1.44
+            430   9.09        11.81       49.6  - j  3.5          1.07
+            440   9.20        12.39       58.6  - j  1.5          1.18
+            450   9.34        13.24       59.4  - j  5.7          1.22
+  Frequency Cor.
+            420   9.02        11.86       47.7  - j  2.8          1.08
+            430   9.13        12.30       58.4  + j  1.2          1.17
+            440   9.26        12.85       62.6  - j  2.9          1.26
+            450   9.49        14.58       49.3  - j  6.3          1.14
+
+Ant. Model  420   9.00        11.55       44.90 - j  4.87         1.160
+            430   9.12        12.13       55.80 + j  0.92         1.117
+            440   9.24        12.61       62.51 - j  1.39         1.252
+            450   9.44        13.96       53.65 - j  6.89         1.162
+
+NEC4WIN-VM 3.1
+  No Corrections
+            420   8.95        10.43       38.13 - j 12.49         1.48
+            430   9.10        11.58       48.25 - j  3.96         1.09
+            440   9.20        12.21       57.74 - j  1.26         1.16
+            450   9.33        13.00       59.91 - j  5.38         1.23
+  Frequency Cor.
+            420   9.45        10.86       48.22 - j  5.77         1.13
+            430   9.54        11.59       53.32 + j 12.77         1.29
+            440   9.67        12.85       42.13 - j 18.51         1.54
+            450   9.92        15.58       23.44 - j  7.82         2.20
+
+MMANA
+            420   8.94        10.41       38.16 - j 12.53         1.48
+            430   9.09        11.57       48.28 - j  3.99         1.09
+            440   9.19        12.20       57.75 - j  1.28         1.16
+            450   9.32        12.99       59.93 - j  5.35         1.23
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we compare MININEC results to the NEC-2/-4 results, we obtain an interesting picture. Uncorrected MININEC gives consistent results in all implementations. However, as the extra line in the ELNEC entry shows, there is nearly a 10 MHz offset in the 420-450 MHz band relative to NEC values. This amounts to an approximate 2 to 2.5 percent difference.

+

The frequency offset correction operations differ between AO 6.5 and Antenna Model on the one hand and NEC4WIN-VM 3.1 on the other. The AO and Antenna Model corrected values tend to track the NEC-2 figures very well, although there is a slight gain deficit in the MININEC values despite calibration to NEC- 2. In contrast, the NEC4WIN corrected values appear to push the NEC-2 values by a frequency offset that is 10% in the other direction than uncorrected MININEC. For example, the source impedance value for 450 MHz (23.44 - j 7.82 Ohms) is not reached by the NEC models until the frequency is near 470 MHz. As well, the NEC4WIN gain values may be as much as two 10 MHz steps off.

+

However, we should not neglect the fact that there is also a difference between the NEC-2 and NEC-4 figures. Since all NEC-2 values coincide and all NEC-4 (including both single and double precision) values also coincide, we can glimpse the differentials from looking at the EZNEC values, which are clustered in the table. There is about a 5 MHz frequency offset between NEC-2 and NEC-4. The NEC-2 values for 420 MHz approach those reached in NEC-4 at about 425 MHz, and the progression continues through the passband of the antenna. The progression applies to all of the figures for gain, front-to-back ratio, and source impedance.

+

The 1+% frequency offset between NEC-2 and NEC-4 at UHF may not seem like much for a wide-band utility Yagi design. However, for a long-boom, narrow-band array that requires precise dimensions for each element, that degree of offset may prove quite significant.

+

The frequency offset is a function of the fact that the element diameter (0.5") is approaching the length of a segment (average 0.8"). Whenever this condition exists, NEC-2 will return offset results unless one invokes the EK command. This command is not presently available on entry-level software, except for NEC2GO and EZNEC, where (after the initial testing that produced the table above) it is invoked automatically. However, the command is available on advanced NEC-2 software, such as NEC-Win Pro. If we add the "fat-wire" command (actually labeled the "extended thin wire kernel"), which uses a more complex algorithm for the core calculations, we obtain the following results for a NEC-2 model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   Wide-Band 4-Element Yagi for 420-450 MHz
+
+Program     Freq. Free-Space  Front-Back  Source Impedance        50-Ohm
+ and Core   MHz   Gain dBi    Ratio dB    R +/- jX Ohms           SWR
+
+A. NEC Cores
+
+NEC-Win Pro with EK
+  NEC-2     420   9.12        11.52       45.64 - j  2.99         1.12
+            430   9.23        12.11       56.12 + j  1.64         1.13
+            440   9.35        12.72       61.11 - j  1.23         1.23
+            450   9.55        14.29       49.40 - j  7.23         1.16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The end product is a table of values very close to the NEC-4 values. The revised algorithms in NEC-4 resulted in dropping the EK command from the list, since it was no longer required. Whenever the wire diameter is less than half the length of the segments in a NEC-2 model, it is usually wise to invoke the EK command if it is available.

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Returning to the MININEC 3.13 programs, we should note that of all the commercial implementations, only Antenna Model yields results in both the close-spaced wire test and the UHF test that track closely with NEC results. AO has an effective frequency corrective and ELNEC has an effective close-wire corrective: Antenna Model has both, plus reported correctives for both standard (quad-type) corner junctions and very narrow (less than 28 degrees) angular junctions. These latter features would require additional tracking tests, with the caution that for very narrow angular junctions, there may be differences in NEC-2 and NEC-4 results.

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As with all offsets among programs and program cores, the degree of offset allowable relative to a particular standard depends upon the range of tasks, frequencies, and antenna geometry complexities that define our modeling needs. These notes are designed simply to bring some of the fringe-area phenomena into the open for inspection. The relative importance of each differential is, in the end, a user judgment.

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52. Flipping Among NEC Programs

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L. B. Cebik, W4RNL

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As the use of antenna modeling software becomes more and more common, it is becoming less unusual to find modelers who possess more than one program. Some earlier DOS-based programs have been supplanted by Windows programs, not always from the same source. For example, the highly respected AO for MININEC 3.13 was a DOS program that is no longer sold (although still widely used). In its place have emerged, in Windows garb, NEC4WIN and MMANA from Canada and Japan, respectively.

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Among NEC users, the most common programs we encounter are EZNEC 3.0 for Windows from W7EL and NEC-Win Plus (one of a collection of programs from Nittany Scientific, with the others being NEC-Win Pro and GNEC for NEC-2 and NEC-4, respectively). In the following notes, we shall confine ourselves to NEC programs, since our topic will be flipping from one program to another: how to do it and what to watch out for. Most of the MININEC programs use file formats that are not directly convertible from one program to the other. However, NEC4WIN can handle some NEC files, while ELNEC MININEC files can be directly read by EZNEC. Nonetheless, we shall have our hands full just converting from one NEC program to another.

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The basic file format for the NEC core (-2 or -4) has the extension .NEC. It is an ASCII file, a sample of which appears in Fig. 1.

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The file is a simple ASCII file that one can produce on almost any simple text editor. To a large degree--but not completely--NEC-2 and NEC-4 files are interchangeable. NEC-4 introduces some new input potentials and revises a few ways of handling some program control cards. However, mainline work involving the sorts of things new users are likely to do rarely involve the differences between core potentials. Hence, moving files from one core to the other is 90% flawless.

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However, EZNEC and NEC-Win Plus each use proprietary file formats. The .EZ model file is in a format specifically developed by W7EL to fit the needs of his programming of the interface between the model specification and the core. The .NWP file format is based on a spreadsheet input system that allows the program to have some special functions. Bridging the gap requires reversion to a .NEC file.

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NEC-Win Plus permits saving any model in .NEC format. Some things saved in the .NWP files, such as model-by-equation spreadsheet entries, cannot appear in the .NEC file. The .NEC file is always the file of a specific model with a certain wire table having numeric entries, along with program control cards that reflect these values.

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Standard EZNEC 3.0 does not have a provision to import files in .NEC format, nor a provision to save files in this format. However, the Pro version of the program has both potentials. Whether or not one needs the NEC-4 core, if one reaches the point of investing in multiple programs, upgrading to the Pro version of EZNEC may make sense.

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The Utility of Multiple Programs

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Why bother going from one program to the other? For one reason, the tabular and graphical outputs of the two programs have different styles. We might well find one style more suited to certain data collections or presentations than the other, even if we had done the initial work on the other program. For example, EZNEC presents data on current magnitudes and phase angles in tables that subdivide the model elements into wires and segments within those wires. For some purposes, this format may be clearer than the NEC-Win tables that use absolute segment numbers. As well, EZNEC presents current data using RMS values, while NEC-Win adheres to the NEC core use of peak values. Often, we find presentation needs that arise only after we have done some modeling work, and Murphy's Law dictates that we shall have done the initial modeling and data collection in the program that does not meet current presentation needs.

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Fig. 2 and Fig. 3 present partial current data for the model shown in Fig. 1 in EZNEC and NEC-Win format, respectively. The numbers are the same, since the EZNEC source used 1 volt RMS, while the NEC-Win source used 1 volt peak. Hence, the respective RMS and peak values of output data will have the same numerical values.

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There are also reasons of convenience for switching programs. Consider Fig. 4, the wire table from an EZNEC model of a 6-element 2-meter Yagi. My goal was to examine the patterns of this antenna at a height of 20' over real ground with the antenna horizontally oriented and with the antenna vertically oriented. Making the adjustments to the model, initially horizontal, for real ground analysis requires only that I change the antenna height and set up the ground. However, changing the orientation from horizontal to vertical requires a large number of individual wire coordinate value changes in the Y and Z columns at both ends of each wire.

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Fig. 5 shows a simpler solution. I saved the free-space horizontal model as a .NEC file and then opened it in NEC-Win Plus. It is immaterial that EZNEC saves files in .NEC format only in meters. Everything will return to inches when we are done. The key is the simple rotation along an axis permitted by NEC-Win Plus. The figure shows the effect on one of the elements of the rotation, although all elements will follow suit, since all were blocked together for the operation.

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After the operation, I again saved the file in .NEC format from within NEC-Win Plus and reopened it in EZNEC. I then changed the unit of measure back to inches to arrive at the wire table shown in Fig. 6. I then used the same set-up steps to place the boom of the antenna 20' above real ground.

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Not only did I save time, but as well, I saved all of those errors resulting from misplacing and transposing numbers. While the time saving for this model was not great, it mounts up when changing orientations with UHF Yagis up to 43 elements total.

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Another instance in which switching from one program to another makes good sense is in data collections that can be done more readily on one program than the other. For example, EZNEC permits only one RP0 request, that is a single polar pattern request. Suppose we have created a model in EZNEC and wish now to gather free-space data for both azimuth and elevation patterns (in free-space, E-plane and H-plane patterns) over a frequency sweep of considerable proportions. since NEC-Win permits the user to specify multiple pattern requests, transporting the model to this program makes sense. As well, the data set is saved in a durable file, so that the output file for a single frequency sweep run can be recalled later for further examination. Such potentials exist for any .NEC file, whether using NEC-Win Plus, Pro, or GNEC.

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Going the other way, I sometimes have occasion to need to exactly frequency scale a model. If the model has not been set up in NEC-Win Plus using the model by equation facility, then scaling becomes a manual operation. However, by saving the file in .NEC format and opening it in EZNEC Pro, I can use the automated frequency scaling option in that program. Saving again in .NEC format permits a return to NEC-Win for subsequent operations. A 3-element array is no problem for manual re-scaling. However, suppose we wished to scale a 25-element Yagi originally designed for 432 MHz into a version centered on 224 MHz. The benefits of having both programs available becomes evident.

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These applications for program "flipping" only sample the potential available. However, they will suffice to illustrate the benefits and the process.

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Observing Program Limitations

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As important as knowing some of the applications for flipping from one program to another is observing and expecting the limitations of moving a model from one program to the other. The programs each have limitations in accepting a .NEC file from the other source.

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When opening a .NEC file within EZNEC Pro, the file undergoes a conversion into the standard EZNEC format. Some of the unique characteristics of that format and the program structure require the conversion process to set aside some lines and even to reject a file. For example, it is possible to create and save an .NEC file that lacks an EX line, that is a specification of source conditions. EZNEC will reject such files as incomplete. A basically complete file will require a set of wire geometry lines (GW), a source (EX), a frequency (FR), and a pattern request (RP).

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Fig. 7 summarizes for a particular model most of the cases in which EZNEC either ignores or modifies a line to meet its structural needs. Although it is possible to directly create an LD5 line--the line that specifies the material conductivity of a wire--that covers all wires in a model, NEC-Win wire-creation facilities assign conductivity values to each line individually. The user can therefore have difference values of conductivity for each wire in the model. In contrast, EZNEC allows only one loss value for all wires. Therefore, it ignores LD5 entries. Following the conversion process, the user must re-enter the desired material loading value into a special sub-screen in the program.

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Since frequency sweeping is a special function within EZNEC, single frequency core runs are the norm. If the conversion process encounters a sweep step value in the FR entry, it will omit it from the resulting EZNEC file. If the .NEC file has multiple frequency entries, as is common when NEC-Win models request multiple radiation patterns, only one of those frequency steps--modified if necessary to register only the start frequency--will remain in the EZNEC file. The user must set up a frequency sweep from a special screen within EZNEC.

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EZNEC also provides for only one radiation pattern request at a time. Therefore, the program retains only the first request labeled RP and does not accept further such requests. Another small change involves the wire diameter. The original file may specify the wire as an AWG gauge from a special table. However, the .NEC file will register that wire size as a numerical wire radius, and that value will appear as a wire numerical wire diameter within the EZNEC wire table. If the user desires to use the EZNEC AWG entry, he or she must do a single or wire-group modification in the wire table.

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The upshot is simply this: when opening a .NEC format model within EZNEC Pro, the automatic conversion process does not accomplish every necessary model set-up step. The user must survey the main screen and verify that all model values are the ones desired.

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As we earlier noted, saving a model from within EZNEC Pro in .NEC format also has a limitation. All wire dimensions of the saved file will be in meters, the basic unit used by the core for all calculations. NEC-Win will open the files and show metric values.

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The conductivity-resistivity values used for the two programs are not everywhere identical. Therefore, a NEC-Win Plus wire screen will normally show a numerical conductivity value. If the users prefers to specify a value from the program list, he or she must change the individual entries or perform a master block change. If one uses a .NEC file exported from EZNEC from DOS versions of the program, the user should also check the establish the desired type of R-L-C load, since the earlier versions of EZNEC may convert all such loads to R+/-jX loads in the .NEC file.

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Because EZNEC permits only a single pattern request at a time, the .NEC file opened within NEC-Win Plus will show only that single pattern. However, the user should also determine that the pattern meets the NEC-Win pattern request requirements so that the user can request an "Analysis" to determine the maximum gain, front-to-back ratio, and beamwidth data.

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Fig. 8 shows a failed pattern, and provides a reminder of the correct minimum requirements to be able to obtain a pattern analysis. Azimuth patterns must run between 0 and 359 degrees, while elevation patterns must run between 0 and 180 degrees.

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However, since the NEC-Win user may desire multiple patterns, there is a tendency to simply request the missing pattern, as shown in Fig. 9. The added pattern is the elevation pattern, using the default values offered by the program. However, the user will be disappointed in two respects by the resulting elevation pattern. First, it will be at right angles to the axis of the forward lobe. The user must examine the model to determine the orientation of the antenna before accepting or modifying the pattern values. In this case, the requested azimuth angle for the pattern should be along the 90-270-degree line.

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Second, the requested pattern will produce only half a free-space elevation of H-plane pattern. The default value for elevation patterns is a 180-degree sweep to cover all cases over real ground. The range for the elevation pattern requires an increase to 360 degrees for a full free-space pattern. In a similar way, the default elevation angle for azimuth patterns is 1 degree elevation to ensure that the polar plot will yield a pattern over ground. For free-space patterns, this angle should be set at zero degrees.

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As we have noted, standard EZNEC operation is for a single frequency. This situation will be reflected in the .NEC file exported for use with NEC-Win programs. If a frequency sweep is needed, then the user must modify the frequency input data.

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Throughout these notes on flipping from one program to another, we have not mentioned something so obvious that--without mention--it may go unnoticed. File keeping is as important to regular program flipping as any other facet of the process. Suppose that I begin with a file called QUAD.EZ. If I create a QUAD.NEC version of the file and open it in NEC-Win Plus, I shall likely save a file called QUAD.NWP. However, if I wish to transport the file with some modifications back to EZNEC, saving the file as QUAD.NEC will result in a different model than the earlier one.

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Therefore, it is useful to develop some regular scheme for naming the transport .NEC files. A simple way is to designate files saved in .NEC format from EZNEC as QUAD-E.NEC and files saved from NEC-Win Plus in .NEC format as QUAD-P.NEC. This practice honors the tradition of the 8+3 filename. However, current versions of Windows allow for very extended filenames. Therefore, some users have adopted the "complete description" theory of filenames, for example, 2-EL-QUAD-EZ-VER.NEC or 2-EL-QUAD-NWP-VER.NEC, or something similar.

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Adjunct Program and Their Exports

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Adjunct programs to assist in developing NEC models are on the rise. Perhaps the most common one in the U.S. is NEC-Win Synth, a program that allows the user to synthesize complex shapes into wire-grid models. The program is primarily designed to meld with NEC-Win Plus. However, one may do a number of things with the synthesized wire table: save it an import it as a NEC-file into NEC-Win Pro/GNEC or EZNEC Pro, or export it as a wire table in a format acceptable for importation by all versions of EZNEC within the Wire Table.

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However, Synth produces incomplete files, lacking a source (EX) and other data necessary to make a complete model file. Although a program like GNEC will open the file, the user cannot run it until he or she has made the proper additions. Since the file is incomplete, the EZNEC Pro .NEC input conversion system will reject the file. However, the system will accept the file once it is complete as a model.

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Saving the file as a wire table for use with the EZNEC wire table import feature also requires care. Fig. 10 shows a Synth product absorbed into NEC-Win Plus. Note that the wire diameter is in feet, the chosen unit of measure. The diameter corresponds to a value just below 1.2".

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Had we exported the same table to EZNEC for importing within the wire table, we would obtain the partial wire table shown in Fig. 11. Note that all of the numerical values are the same as we found in the NEC-Win Plus table. However, EZNEC always uses inches for wire diameters whatever the selected English unit of measure and always uses millimeters for the wire diameter whatever the selected metric unit of measure.

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Therefore, when importing a Synth wire table into EZNEC as a wire table function, the user must be prepared to change the wire diameter(s). The exceptions, of course, are when the Synth unit of measure is either inches or millimeters.

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This situation is only a sample of the care we must use in moving from one program to another. Not all conversions or importations will work perfectly, nor should we expect them to do so. Importations and conversions are largely a user convenience, and some supplemental effort by the modeler is to be expected. At a minimum, the modeler should always carefully read the imported material to ensure that everything is correct relative to the model design.

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NEC and MININEC Files

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Back in Fig. 1, we looked at a standard-form .NEC file. For the most part, .NEC files are the common thread among almost all implementations of NEC cores. The model files are similar to, but not identical with, MININEC model files. Some MININEC program implementations have limited ability to accept and convert .NEC files to their own formats. However, MININEC model files are not especially interchangeable from one implementation of the public domain core to another--even though most use an ASCII input file (with ELNEC being an exception).

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Fig. 12 shows a typical NEC4WIN model file. The programmer has structured the wire table so that its parts correspond to those of a .NEC file. However, there are numerous functions that NEC handles with program control cards that MININEC handles with verbal entries.

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The MMANA model file, a sample of which appears in Fig. 13, uses a different order for the entries, with only the wire table showing a good correlation to the NEC4WIN file. The MMANA file contains a pattern request, but the NEC4WIN model file does not. This is only one of many major differences between the two implementations of MININEC.

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Classic AO (6.5, for the sample shown in Fig. 14) uses still another format, one permitting the introduction of variables and their definitions. The file may be viewed as perhaps the most compact format of all ASCII MININEC files.

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With a suitable text editor and a template by which to move items around, it is possible to convert most MININEC files from one program to another without re-entering everything from scratch.

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In the end, familiarizing ourselves with more than one program can accrue some benefits in terms of moving a model to the program that will best accomplish a particular task. However, when flipping from one program to another, we must always be aware of all the pitfalls to avoid. If we make the necessary adjustments in advance of running the transported model, we can usually save ourselves considerable time and energy. However, if we must always back track to pick up pieces that we forgot to adjust, we may end spending more time in flipping than in patiently working through a modeling exercise wholly within one program.

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Also see the Antenna Modeling Programs page for more information.

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53. Voltage and Current Sources: How?

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L. B. Cebik, W4RNL

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Programs such as NEC-Win Plus and EZNEC have a special feature that is not inherent to the NEC-2 core: the current source. In past columns, we have reviewed some of the significant uses of a current source. For example, by placing a current magnitude of 1.0 at a phase angle of 0.0 degrees on the source segment of the driver wire of a Yagi antenna, we can conveniently explore the relative current magnitude and phase angle at the center of each parasitic wire. For another example, if we have a phased array, we can simulate its operation by using multiple current sources, each set for the correct magnitude and phase angle. These two applications alone would justify the availability of a current source.

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However, NEC-2 (and NEC-4) do not include a current source of the type used in these examples of applications. In fact, of all the potential modes of excitation, EZNEC and NEC-Win Plus implement only one: the standard voltage source that is in series with the wire segment on which we place it. So the question arises: how do we implement a current source?

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Let's begin with the simplest case, a simple dipole with a single source at its center. Fig. 1 shows an outline of our model.

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To set up this model, say in NEC-Win Plus, we would develop a simple wire entry, such as the one shown in Fig. 2. This particular example happens to be at a frequency of 50.5 MHz, with suitable wire diameter and wire material load values, but these will not play a significant role in this exercise.

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More relevant to our interests is the registry of a single source for the model, at the far right of the wire entry screen. If we click on that entry, we open the source screen, shown in Fig. 3.

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Our entry for this model is a very standard default entry of a voltage magnitude of 1.0 and a voltage phase angle of 0.0 degrees. Indeed, for the model at hand, there is no good reason to use any other value pair.

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The standard .NEC-format file for this model would look like the following lines of ASCII entries:

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+CM 6m dipole
+CE
+GW 1 21 0 -1.41732 5.936485 0 1.41732 5.936485 0.005588
+GS 0 0 1
+GE 0
+EX 0 1 11 0 1 0
+LD 5 1 1 21 5.8001E7
+FR 0 1 0 0 50.5 1
+RP 0 1 361 1000 90 0 1 1
+RP 0 361 1 1000 -270 0 1 1
+EN
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The GW entry is our wire, with the last entry giving the wire size as a radius. The EX entry is the source information, showing a source on segment 11 (out of 21) on wire 1 with a voltage value (at the far right) of 1.0 and a phase angle of 0.0 (minus the decimal places).

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The output data of most relevance for our concerns is the "Antenna Input Parameters" section of the NEC output file. We normally encounter this information in tables that are easier to read, but let's look at the entries as they occur in the NEC-2 output file.

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+                                          - - - ANTENNA INPUT PARAMETERS - - -
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+   TAG   SEG.    VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)       ADMITTANCE (MHOS)      POWER
+   NO.   NO.    REAL        IMAG.       REAL        IMAG.       REAL        IMAG.       REAL       IMAG.     (WATTS)
+     1    11 1.00000E+00 0.00000E+00 1.36049E-02-9.46163E-04 7.31493E+01 5.08723E+00 1.36049E-02-9.46163E-04 6.80244E-03
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This one line of data is the basis for a number of entries that we can find in the output data from NEC-Win Plus and EZNEC. The input or source consists of a voltage of 1.0 + j 0.0 volts. The resultant current is 0.0136 -j 0.000946 amps. Of course, by using the square root of the sum of squares, plus a tangent, we can convert these values into voltage and current magnitudes and their associated phase angles.

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The source impedance is normally given in real and imaginary terms, which translate into a resistance and a reactance: 73.149 + j 5.087 Ohms.

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The utility of using real and imaginary numbers for the impedance is that we can easily estimate the power at the source. Remember that NEC uses peak voltage and current values. NEC-Win Plus follows this procedure, so the source voltage that we entered was 1.0 volts peak. (EZNEC uses RMS entries for voltages and currents and internally correlates these with NEC input and output values.) Since power is I-squared * R, but in RMS terms, we must multiply the current by 0.7071068, or the current squared by 0.5. Hence, the power at the input is 0.00680 watts. (For maximum precision, we should convert the current into a magnitude and phase angle.)

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This data also provides all that we need to determine the SWR relative to any standard impedance that we wish to input. NEC does not provide this data. Instead, the programs we have mentioned do the calculation using the data that we have just given.

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With this much background on using a voltage source, we are ready to change the source to a current source. The input process is simple enough: we simply mark a box or (in EZNEC) change a letter in the source entry line. Fig. 4 shows the relevant source box for our model.

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The user changes from a voltage to a current source with great ease, and sees no visible sign on the wire table that anything but a simple check-mark as changed. However, the model has changed significantly. In fact, if we look at the .NEC-format model generated by NEC-Win Plus, we can see considerable revision of the model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 6m dipole
+CE
+GW 1 21 0 -1.41732 5.936485 0 1.41732 5.936485 0.005588
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 1
+GE 0
+EX 0 30901 1 0 0.0 1.0
+LD 5 1 1 21 5.8001E7
+NT 30901 1 1 11 0 0 0 1 0 0
+FR 0 1 0 0 50.5 1
+RP 0 1 361 1000 90 0 1 1
+RP 0 361 1 1000 -270 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The first revision on the list of lines is the introduction of a new wire, #30901. NEC-Win Plus uses number above 30,000 for wires that will remain hidden from the user's view on the regular screens. However, the wires can always viewed by tabbing to the "NEC Code" page of the spreadsheet input system. In EZNEC, the file remains hidden unless one has the Pro version, which permits saving the model file in .NEC format.

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The wire is a remote wire that is very short, very thin, and has only 1 segment. Like the wires that we use to terminate transmission lines, it is short, thin, and remote enough to not contribute detectably to the overall radiation of the essential wire geometry of the antenna.

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The other new entry in the list is labeled NT, for network. A network is a two-port non-radiating construct that employs short-circuit matrix elements. We place a network between any two wire segments in the overall wire geometry and enter real and imaginary short-circuit admittance values. One of the wire segments may be a remote wires, such as 30901, which the NT line registers at the left as the first of the wires. The other wire is the former source segment on the dipole, segment 11 of wire 1.

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Let's expose the hidden portions of the current source model fully by revising the usual model. Everywhere we see the entry 30901, we shall write 2. This involves the second GW card, the NT card, and the EX card. If we then import this file into NEC-Win Plus, we obtain a main screen that looks like Fig. 5.

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Now the model file looks normal. We see that wire 2 has a source, to which we shall turn momentarily. Although the main screen does not show it, we now have a network whose entries can be viewed.

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The ports of a network are labeled Y1 and Y2. If we place a set of admittance values across the Y1 terminals, we have Y11. Likewise, if we place values across the terminals of Y two, we have a Y22 value. A set of admittance values going from one port to the other bear the label Y12. Fig. 6 shows the conventional sketch for such a port set up for the current source.

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The entries on the NT card following the wire and segment places are, in order, Y11, Y12, Y22, with a real and an imaginary value (conductance and susceptance, in usual electrical terms) for each entry. Note that the current source requires only a Y12 entry, with a value of 1 Mho (or 1 Siemens) in the imaginary slot. Networks, like transmission lines (TL), are in series with the wire segment and any LD load on it, but in parallel with other networks and sources.

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By clicking on the network symbol on the main screen, we can see the network port entries, as shown in Fig. 7. We place zeroes where there are no entries. Since the admittance matrix is symmetric, we need not have an entry labeled Y21. Y12 does all the work. There we find the 1-Mho imaginary admittance entry.

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The current source requires one further revision to the standard voltage source entry, and we find this by opening the source screen for our revised model, shown in Fig. 8. Instead of entering a real value of 1.0 and an imaginary value of 0.0--which is equivalent to entering a voltage magnitude of 1.0 and a phase angle of 0.0 degrees--we enter a real voltage value of 0.0 and an imaginary value of 1.0, yielding a voltage magnitude of 1.0 at a phase angle of 90 degrees.

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The fully revised model in .NEC format has the following appearance:

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 6m dipole
+CE
+GW 1 21 0 -1.41732 5.936485 0 1.41732 5.936485 0.005588
+GW 2 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 1
+GE 0
+EX 0 2 1 0 0.0 1.0
+LD 5 1 1 21 5.8001E7
+NT 2 1 1 11 0 0 0 1 0 0
+FR 0 1 0 0 50.5 1
+RP 0 1 361 1000 90 0 1 1
+RP 0 361 1 1000 -270 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

By standard network theorems, the combination of the specified source and the network will yield a current of 1.0 at a phase angle of 0.0 degrees on the segment of the dipole that the user thought he or she had designated as the source in the original current-source model. Our substitute model has simply shown what goes on behind the scenes in a NEC program offering current sources.

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With a voltage source, we were able to take data on the source voltage, current, impedance, and power directly from the "Antenna Input Parameters" line of the NEC output report. Now everything will surely look different and prevent us from picking up the data so easily without further calculation. In fact, the "Antenna Input Parameter" line of the new current-source model has the following appearance:

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                                          - - - ANTENNA INPUT PARAMETERS - - -
+
+   TAG   SEG.    VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)       ADMITTANCE (MHOS)      POWER
+   NO.   NO.    REAL        IMAG.       REAL        IMAG.       REAL        IMAG.       REAL       IMAG.     (WATTS)
+     2    22 0.00000E+00 1.00000E+00-5.08723E+00 7.31493E+01 1.36049E-02-9.46163E-04 7.31493E+015.08723E+00 3.65746E+01
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The process of picking up data from the NEC output file for redisplay and possible reformatting in a program output is simply a matter of selecting the data needed. In fact, the data needed is fully present on the input parameter line, although not where we expect to find it. Let's do some label swapping. Swap the labels on the admittance and impedance entry pairs--but keep the real and imaginary parts as given. The impedance becomes 73.149 + j 5.087 Ohms.

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Next, reverse the column labels of the voltage and the current. Convert each value into a magnitude and phase angle and subtract 90 degrees. (For our quick look at these tables, we may relabel the voltage as current and the current as voltage. Then, for each of these entry pairs, swap the real and imaginary labels. We would not use this short cut if we were actually calcuating voltages and currents in the program.) The result is a voltage of 73.148 - j 5.087 volts, and a current of 1.0 + j 0.0 amps.

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Since the current is 1.0 peak, to find the power we take half the square of the current (that is, 0.5) and multiply it by the real part of the impedance, for a result of 36.575 watts, which is the value shown in the power column. If you prefer to take the magnitudes of I and E, multiplying them after converting from peak to RMS values, you will also get half of 73.149 or 36.575 watts. (A phase angle difference must also be taken into account, but it is too slight to affect the outcome significantly in this crude check calculation.)

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It is possible to go through the network calculations, but the results will be the same as for our entry label swapping scheme. Although I do not have the internal program coding at hand, it is likely that most programs simply change flags for picking up certain data when a current source has been designated by the user.

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Before leaving the subject, let's see if the system pans out with a few more models. For example, suppose that we have a turnstile antenna composed of two dipoles at right angles. Next, let us feed the two dipoles using current sources. In a perfect turnstile antenna, the two sources should have identical magnitudes and a 90-degree current phase shift between the two dipole sources. Except for a slight displacement owing to the need to make the two dipole wires pass each other without touching, we should obtain the same impedance for each dipole.

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The following model, a hybrid of EZNEC and NEC-Win Plus, shows the structure of our turnstile dipole antenna.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 6m dipole turnstile
+CE
+GW 1,21,0.,-1.4351,6.096,0.,1.4351,6.096,.0008138
+GW 2,21,-1.4351,0.,6.1214,1.4351,0.,6.1214,.0008138
+GW 3,2,593.6486,593.6486,593.6486,593.6605,593.6605,593.6605,5.9365E-4
+GE 1
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+FR 0,1,0,0,50.5
+GN 2,0,0,0,13.,.005
+EX 0,3,1,0,0.,1
+EX 0,3,2,0,-1,0
+NT 3,1,1,11,0.,0.,0.,1.,0.,0.
+NT 3,2,2,11,0.,0.,0.,1.,0.,0.
+RP 0,1,361,1000,76.,0.,0.,1.,0.
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Notice that EZNEC creates only one wire for the termination of the networks, but it has two segments, one for each source. The sources (EX lines) have been converted to 1.0 voltage peak value maximums. Since the current source that we specified as 1.0 at 0.0 degrees requires a remote voltage source of 0.0 at 90 degrees (or 0.0 + j 1.0 volts), the source that we specified as 1.0 at 90 degrees advances a further 90 degrees. Hence, its value is 1.0 at 180 degrees or -1.0 + j 0.0 volts. The network inputs for each source remain constant except for the terminating wire segment numbers.

+

The "Antenna Input Parameter" line of the NEC output report is the following entry:

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                         - - - ANTENNA INPUT PARAMETERS - - -
+
+   TAG   SEG.    VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)        ADMITTANCE (MHOS)     POWER
+   NO.   NO.    REAL        IMAG.       REAL        IMAG.       REAL        IMAG.       REAL        IMAG.    (WATTS)
+     3    43 0.00000E+00 1.00000E+00 2.01009E+00 6.98866E+01 1.42971E-02 4.11214E-04 6.98866E+01-2.01009E+003.49433E+01
+     3    44-1.00000E+00 0.00000E+00-6.96795E+01 1.83212E+00 1.43415E-02 3.77089E-04 6.96795E+01-1.83212E+003.48398E+01
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The impedance for each dipole is about 69.87 and 69.68 Ohms, respectively--as read from the admittance column. With the current magnitude squared and halved (after reading it from the voltage columns), the power is 34.94 and 34.84 watts, respectively, using the real portion of the impedances. Again, reading current from the voltage columns (while reversing the real and imaginary headings) we can see that the currents are 90 degrees apart. If in fact, programs do use the data flagging technique for picking up values (and, as noted, I do not assert that they do in the absence of access to proprietary codes), it is likely that they convert the real and imaginary values as given into a magnitude and phase and for each and then subtract 90 degrees.

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One more example should suffice for our rudimentary demonstration of how we obtain current sources from voltage source. Consider a dipole, just as we have been working with, but having one addition. The center of the dipole connects through a transmission line (TL) to a short source wire. We shall treat the sort wire as a current source segment. The resulting .NEC-format file looks like the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 6m dipole with 1/4-wl TL
+CE
+GW 1 21 0 -1.41732 5.936485 0 1.41732 5.936485 0.005588
+GW 2 1 -0.0127 0 2.54 0.0127 0 2.54 0.000635
+GW 30901 1 9901.0000 9901.0000 9901.0000 9901.0001 9901.0001 9901.0001 .00001
+GS 0 0 1
+GE 0
+EX 0 30901 1 0 0.0 1.0
+LD 5 1 1 21 5.8001E7
+NT 30901 1 2 1 0 0 0 1 0 0
+TL 1 11 2 1 70 1.484122 0 0 0 0
+FR 0 1 0 0 50.5 1
+RP 0 1 361 1000 90 0 1 1
+RP 0 361 1 1000 -270 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The now-familiar remote source wire, 30901, is evident, as are the network and excitation entries. The 70-Ohm transmission line is 1.484 meters long (about 0.25 wavelength), as we read the TL card. The interesting part of this model is the fact that we have two remote wires--a visible one that is the user source wire and a normally invisible one that is the program source because the user has selected a current source. By virtue of the fact that a 70-Ohm line is not a perfect match for a nearly resonant dipole, we should expect some transformation in the impedance at the source.

+

Again, we can turn to the "Antenna Input Parameters" line for values.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                         - - - ANTENNA INPUT PARAMETERS - - -
+
+   TAG   SEG.    VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)       ADMITTANCE (MHOS)      POWER
+   NO.   NO.    REAL        IMAG.       REAL        IMAG.       REAL        IMAG.       REAL       IMAG.     (WATTS)
+ 30901    23 0.00000E+00 1.00000E+00 4.73228E+00 6.66507E+01 1.49283E-02 1.05993E-03 6.66507E+01-4.73228E+00 3.33253E+01
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Reading the impedance from the admittance position, we find a 66.65-Ohm real part and a -4.73-Ohm imaginary part. I-squared-R gives us 33.33 watts of power. We reversed the heading of the voltage and current columns, converting each to a magnitude and phase angle, and then subtracting 90 degrees. However, because the real part of the impedance is more than an order of magnitude greater than the imaginary part, any further calculations we might make with these values would not be seriously hurt by a simplified scan of values. This easy situation, of course, will not always--indeed, not even commonly--be the case for examples more complex than our simple dipole system.

+

The reason for setting forth the last model is that there is another section of the NEC output report that we can sometimes confuse with the "Antenna Input Parameters" portion. The "Structure Excitation" section contains some values the appear to be candidates for our source calculations using a current source. However, they are not suitable for the task.

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If these notes familiarize you with the terms of a current source--as constructed out of a voltage source and a network--then they will have served their purpose.

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Go to Main Index

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54. GC: Wire Segment Length and Radius Tapering

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+

L. B. Cebik, W4RNL

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There are numerous occasions on which we wish to taper either the segment length or the radius (diameter) of a wire along its length. Entry-level programs restrict users to the GW, GS, and GE geometry cards, and this restriction makes tapering a complex procedure involving many wires. However, versions of NEC-2 and NEC-4 that make the entire set of geometry entries available to the user considerably simplify the procedure--and result in faster run times for the resulting model.

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The key is the GC or geometry continuation card. Perhaps the best way to illustrate the use of the card is with a small example.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM bi-conical dipole--tapered radius and tapered segment lengths
+CE
+GW 1 5 0 0 -5.85 0 0 -0.336 0
+GC 0 0 .8 .5 .0833
+GW 2 1 0 0 -0.336 0 0 0.336 .0833
+GW 3 5 0 0 0.336 0 0 5.85 0
+GC 0 0 1.25 .0833 .5
+GS 0 0 .3048
+GE 0
+EX 0 2 1 0 1 0
+LD 5 1 1 5 3.0769E7
+LD 5 2 1 1 3.0769E7
+LD 5 3 1 5 3.0769E7
+FR 0 1 0 0 31.6 1
+RP 0 1 361 1000 90 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In almost all respects, everything about the model is standard. We have a dipole composed of 3 wires, each of which has some material loss (the LD5 entries). Wire 2 in the center has a standard voltage excitation, and the frequency of operation is 31.6 MHz. The model requests a single azimuth/phi pattern. The GS entry conversion constant tells us that the dimensions are in feet, and from the GW entries, we can see that the antenna extends along the Z-axis +/-5.85'.

+

However, we want to look closely at the GW1 and GW3 entries. They have a zero in the final radius column. The zero-entry for radius is NEC's method of alerting the program to a following or continuation card, namely the GC entry. (If you use an entry other than zero and have a following GC line, the core will alert you to a geometry error, but will not tell you exactly what it is.)

+

The GC card permits you to taper both the radius and the segment length within the specified number of segments in the preceding GW line. Both GW1 and GW3 specify 5 segments, mostly to allow me to present short tables in what follows.

+

The GC entry allows three different ways of handling the segment-length tapering, as shown in the triple screen grab of Fig. 1, taken from GNEC.

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+ +
+

Before we explore the differences among the three variations in segment length handling, note that the radius entry is the same for all three. NEC uses a single equation to taper the element radius, and it is not a simple linear taper. Given a starting and end segment radius, along with the number of segments in the wire, the radius will taper according to the following equation:

+
+ +
+

where RRAD is the ratio of two adjacent segment radii, RAD1 is the first specified segment radius, RAD2 is the specified last segment radius, and NS is the specified number of segments. Once the ratio is determined, the program simply multiplies each segment radius by the ratio to arrive at the next in the sequence.

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In the sample .NEC file, the GC entry for GW3 in the final 2 columns shows .0833 and .5. These are the first and last radii values for a wire that increases in diameter along its length. The final two columns for the GC entry following GW1 are in reverse order, indicating a wire that decreases in diameter along its length. For the moment, it is incidental, but note that the radius of GW2, a 1-segment wire, is the same as the end radius for GW1 and as the start radius for GW3.

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With respect to the tapering of segment lengths, we have three options, one of which we specify in the first integer place on the GC line:

+
    +
  • 0 Used to specify a ratio between each adjacent segment on the wire
    • +
  • 1 Used to specify the length of the first segment on the wire, with the remaining segments calculated by the program
    • +
  • 2 Used to specify the length of the first segment and the last segment on the wire, with the remaining segments calculated by the program
    • +
+

The sample program uses Type 0 segment length specifications. Had we desired only to change the wire radius but use equal length segments, we would have specified a ratio of 1.0, which would appear in the third column (first floating decimal place) in the GC line. Fig. 1 shows a ratio of 0.9009 as the requested ratio for a Type 0 GC entry, while the sample program shows a value of 0.8 for GW1 and 1.25 for GW3. A value less than 1 indicates decreasing segment lengths along the wire, while a value greater than 1 indicates increasing segment lengths along a wire. Since 0.8 is the inverse of 1.25, we receive the clue that GW1 and GW3 will vary their segment lengths so that the resulting total dipole element is exactly symmetrical about the source segment/wire.

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Let L be the total wire length, i be the segment number, and Rv be the ratio of adjacent segment lengths. Then the length of the first segment, v1, emerges from the following equation:

+
+ +
+

The program then applies the user-selected ratio to the initial segment length value to determine the remaining segment lengths.

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If we choose a Type 1 GC entry and specify the length of the first segment, we would refer to the middle panel of Fig. 1. The first-segment length selection, if there is one, always goes in the column to the right of the last radius entry in the GC line. The program then solves equation 2 for Rv, the length ratio, by iteration and then proceeds as in a Type 0 GC line to calculate the successive segment lengths.

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Both Type 0 and Type 1 segment length calculations use the value in the GW line for the number of segments on the wire. However, the situation changes if we use a Type 2 GC line and specify the length of the first and last segments. In this case, the GC calculations determine both the ratio of a segment length to the next and the number of segments in the wire. Let v1 be the length of the first segment and v2 be the length of the last segment. Rv will be the ratio of adjacent segment lengths and N will be the number of segments in the wire.

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+ +
+

Since N is rounded to an integer to populate the wire with an integral number of segments, the program recalculates Rv. Thus, the final segment length may depart slightly from the requested value to accommodate the rounding without changing the requested wire length.

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(Note: the NEC manuals employ a delta wherever I have written v to indicate a segment length. The use of a letter simplifies HTML coding.)

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With this background, we may explore a couple of examples of GC use.

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Creating a Bi-conical Dipole

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To a limited degree, we may simulate a bi-conical dipole, that is a wire element whose radius increases continuously from the element center outward. However, the simulation has several restrictions. First, without resorting to wire-cage assemblies, the simulation will use a stepped-diameter element. Instead of decreasing the radius of the wire with each outward movement, we increase the radius. The use of this technique in NEC-2 is subject to the well-known limitation of the program when encountering any stepped-diameter element. It is unreliable. NEC- 4 is more reliable so long as the stepping increment is not too large.

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Second, the source segment should not change radius or length relative to the immediately adjacent segments. By making the last segment of the first wire and the first segment of the third wire the same length and diameter as the single-segment source wire, we preserve this condition. Fig. 2 shows the central portion of a bi-conical simulation using 3 wires and GC entries.

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+

If we specify a Type 0 GC entry for both wires 1 and 3, we might initially set the segment length ratio to 1.0, insuring the production of equal segment lengths. We can easily pre-calculate the resulting segment lengths from the GW1 or GW3 entries and set the center wire to the same length in a reasonable number of iterations. The following chart from the NEC output file shows the resulting segment lengths and radii. The internal units of measure in NEC are meters, but the numbers correspond to our 11.7' dipole.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.00000   0.00000  -1.62098   0.32420   90.00000   0.00000   0.15240     0    1    2      1
+     2   0.00000   0.00000  -1.29678   0.32420   90.00000   0.00000   0.09737     1    2    3      1
+     3   0.00000   0.00000  -0.97259   0.32420   90.00000   0.00000   0.06220     2    3    4      1
+     4   0.00000   0.00000  -0.64839   0.32420   90.00000   0.00000   0.03974     3    4    5      1
+     5   0.00000   0.00000  -0.32419   0.32420   90.00000   0.00000   0.02539     4    5    6      1
+     6   0.00000   0.00000   0.00000   0.32419   90.00000   0.00000   0.02539     5    6    7      2
+     7   0.00000   0.00000   0.32419   0.32420   90.00000   0.00000   0.02539     6    7    8      3
+     8   0.00000   0.00000   0.64839   0.32420   90.00000   0.00000   0.03974     7    8    9      3
+     9   0.00000   0.00000   0.97259   0.32420   90.00000   0.00000   0.06220     8    9   10      3
+    10   0.00000   0.00000   1.29678   0.32420   90.00000   0.00000   0.09737     9   10   11      3
+    11   0.00000   0.00000   1.62098   0.32420   90.00000   0.00000   0.15240    10   11    0      3
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that the program counts segments in absolute numbers. The Tag numbers to the far right indicate the wire to which the segment numbers are assigned. The equality of segment lengths is clear from the near-middle column. As well, we can see the segment radius tapering performed by program calculations in the Wire Radius column.

+

A 3-wire model of the bi-conical simulation is nearly indistinguishable internally in NEC from a model composed of individual wires, each 1 segment long and each having an assigned radius. The following segmentation table shows just such a model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.00000   0.00000   1.62100   0.32420  -90.00000   0.00000   0.15200     0    1    2      1
+     2   0.00000   0.00000   1.29680   0.32420  -90.00000   0.00000   0.12100     1    2    3      2
+     3   0.00000   0.00000   0.97260   0.32420  -90.00000   0.00000   0.08890     2    3    4      3
+     4   0.00000   0.00000   0.64840   0.32420  -90.00000   0.00000   0.05710     3    4    5      4
+     5   0.00000   0.00000   0.32420   0.32420  -90.00000   0.00000   0.02540     4    5    6      5
+     6   0.00000   0.00000   0.00000   0.32420  -90.00000   0.00000   0.02540     5    6    7      6
+     7   0.00000   0.00000  -0.32420   0.32420  -90.00000   0.00000   0.02540     6    7    8      7
+     8   0.00000   0.00000  -0.64840   0.32420  -90.00000   0.00000   0.05710     7    8    9      8
+     9   0.00000   0.00000  -0.97260   0.32420  -90.00000   0.00000   0.08890     8    9   10      9
+    10   0.00000   0.00000  -1.29680   0.32420  -90.00000   0.00000   0.12100     9   10   11     10
+    11   0.00000   0.00000  -1.62100   0.32420  -90.00000   0.00000   0.15200    10   11    0     11
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Almost the only clue that we have a different model appears in the TAG NO. column, where we see 11 different wire numbers. However, we do have a second clue: the assignment to each segment a radius that reflects linear stepping. Simply as a matter of interest, you may wish to compare the radius values in this table to those calculated by using the GC card. The linear steps are each 0.03165 m, and the result is a continuously variable ratio between steps, one that decreases with increasing wire radius. In contrast, the earlier GC-calculated set of steps uses a ratio of about 1.565 for each step larger or smaller.

+

One question to consider when selecting a 1.0 ratio between successive segment lengths concerns the changing segment-length-to-radius ratio along the wire. Some modelers may prefer to use a more nearly constant or at least a slower changing ratio of segment length to radius. In the initial segmentation table, the length-to-radius ratio varies from 12.769 at the center to 2.127 at the outer ends of the dipole.

+

To bring those ratios some distance--but far from all the way--together, we may implement a changing segment length by specifying a ratio value other than 1.0. The original model shows a pair of rates: 0.8 for the decreasing radius side of the dipole and 1.25 for the increasing radius side. These values do not coincide with the radius ratio of 1.565, but they may go some distance in closing the gap. How much they close the distance appears in the following segmentation table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                               - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.00000   0.00000  -1.53310   0.49996   90.00000   0.00000   0.15240     0    1    2      1
+     2   0.00000   0.00000  -1.08314   0.39997   90.00000   0.00000   0.09737     1    2    3      1
+     3   0.00000   0.00000  -0.72316   0.31997   90.00000   0.00000   0.06220     2    3    4      1
+     4   0.00000   0.00000  -0.43519   0.25598   90.00000   0.00000   0.03974     3    4    5      1
+     5   0.00000   0.00000  -0.20480   0.20478   90.00000   0.00000   0.02539     4    5    6      1
+     6   0.00000   0.00000   0.00000   0.20483   90.00000   0.00000   0.02539     5    6    7      2
+     7   0.00000   0.00000   0.20480   0.20478   90.00000   0.00000   0.02539     6    7    8      3
+     8   0.00000   0.00000   0.43519   0.25598   90.00000   0.00000   0.03974     7    8    9      3
+     9   0.00000   0.00000   0.72316   0.31997   90.00000   0.00000   0.06220     8    9   10      3
+    10   0.00000   0.00000   1.08314   0.39997   90.00000   0.00000   0.09737     9   10   11      3
+    11   0.00000   0.00000   1.53310   0.49996   90.00000   0.00000   0.15240    10   11    0      3
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The segment length to radius ratio is 8.067 at the center and 3.278 at the outer end. How much importance this factor may have will depend upon the particular modeling project at hand. Had we doubled the number of segments in GW1 and GW3, adjusting the center segment length accordingly, the outer segments would have violated the conservative recommendation for a 4:1 segment length to radius ratio, and the revised model would not quite meet the recommendations. However, judicious use of the segment length ratio facility would ease the problem of meeting that recommendation--or any other applicable to a particular model.

+

Creating a Buried Radial System

+

NEC-4 offers the user the ability to place wires below the surface of the ground. The buried-wire capability allows more accurate modeling of vertical monopoles and related antennas that use buried ground-plane radial systems. Modeling such systems in the most economic manner relative to core run time without short-cuts that threaten the accuracy of the results is another good exercise for the GC entry.

+
+ +
+

Fig. 3 sketches a radial system of 120-128 radials, as might be used in either an advanced amateur or commercial broadcast antenna system. (Many such systems employ secondary short radial systems close to the antenna base.) Let's set the vertical monopole at a maximum height of 40 m and give it a 25-mm diameter. The radials will be 2-mm in diameter and extend a full 1/4 wavelength from the antenna base or 40.9553 m.

+

The rules for ground penetration of the monopole require that the Z=0 level coincide with a segment junction, and to minimize chances for error, many experts recommend that this also be a wire junction. The radial system will be 0.16382 m below ground, which dictates that the wire length from Z=0 to the radial junction be that length. Equally important for accuracy is that the source segment and the segments adjoining it be of equal length. Since we wish the source to be on the lowest segment above ground, that segment must be 0.16382-m long, and as well, the segment above it.

+

These requirements would suggest that we construct the entire model from segments that are 0.16382-m long. The result would be an exceptionally large model in terms of segment numbers. However, a technique developed for MININEC can reduce the model size to manageable proportions. Some programs, such as EZNEC, implement a form of element length-tapering that calculates from a specified end 1 (or both ends toward the middle) increasing lengths on a 2:1 length ratio, starting from a user-specified shortest length to a user specified longest length. The result is a smaller model with no significant loss of accuracy (assuming judicious application of the tapering feature). The lower half of Fig. 3 shows the general tapering principle involved.

+

The cost of tapering is a very significant increase in the number of individual wires, although this increase in no way matches the decrease in the total number of segments. A 128-radial version of the monopole, with element length-tapering applied to the main element as well as to the radials, results in 776 wires and 1550 segments. This is about the best one might do with an implementation of NEC that uses only the GW, GS, and GE geometry inputs. However, if the basic, pre-tapered, model had been transferred to NEC-4 in a program allowing the use of the GC entry, we might have saved about 645 of the wires. Since run time is an exponential function of both the number of segments and the number of wires, in many very large problems, we might save a significant amount of time.

+

Let's illustrate the differences between a hand-tapered model and a GC-tapered model using a somewhat smaller system. We shall take the same monopole and place it over only 4 radials. This move will shrink the repetitive radial portion of the model to readable proportions. An external tapering of the elements would present the following wire table (without the associated program control entries).

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 160-m 1/4 wl vert-4 bur radial
+CE
+GW 1,7,0.,0.,40.,0.,0.,5.242276,.0125
+GW 2,1,0.,0.,5.242276,0.,0.,2.621138,.0125
+GW 3,1,0.,0.,2.621138,0.,0.,1.31057,.0125
+GW 4,1,0.,0.,1.31057,0.,0.,.6552857,.0125
+GW 5,1,0.,0.,.6552857,0.,0.,.3276435,.0125
+GW 6,1,0.,0.,.3276435,0.,0.,.163821,.0125
+GW 7,1,0.,0.,.163821,0.,0.,0.,.0125
+GW 8,1,0.,0.,0.,0.,0.,-.163821,.0125
+GW 9,1,0.,0.,-.163821,.1638211,0.,-.163821,.001
+GW 10,1,.1638211,0.,-.163821,.4914632,0.,-.163821,.001
+GW 11,1,.4914632,0.,-.163821,1.146747,0.,-.163821,.001
+GW 12,1,1.146747,0.,-.163821,2.457316,0.,-.163821,.001
+GW 13,1,2.457316,0.,-.163821,5.078453,0.,-.163821,.001
+GW 14,7,5.078453,0.,-.163821,40.95526,0.,-.163821,.001
+GW 15,1,0.,0.,-.163821,1.2368E-8,.1638211,-.163821,.001
+GW 16,1,1.2368E-8,.1638211,-.163821,3.7104E-8,.4914632,-.163821,.001
+GW 17,1,3.7104E-8,.4914632,-.163821,8.6577E-8,1.146747,-.163821,.001
+GW 18,1,8.6577E-8,1.146747,-.163821,1.8552E-7,2.457316,-.163821,.001
+GW 19,1,1.8552E-7,2.457316,-.163821,3.8341E-7,5.078453,-.163821,.001
+GW 20,7,3.8341E-7,5.078453,-.163821,3.092E-06,40.95526,-.163821,.001
+GW 21,1,0.,0.,-.163821,-.1638211,2.4736E-8,-.163821,.001
+GW 22,1,-.1638211,2.4736E-8,-.163821,-.4914632,7.4209E-8,-.163821,.001
+GW 23,1,-.4914632,7.4209E-8,-.163821,-1.146747,1.7315E-7,-.163821,.001
+GW 24,1,-1.146747,1.7315E-7,-.163821,-2.457316,3.7104E-7,-.163821,.001
+GW 25,1,-2.457316,3.7104E-7,-.163821,-5.078453,7.6683E-7,-.163821,.001
+GW 26,7,-5.078453,7.6683E-7,-.163821,-40.95526,6.1841E-6,-.163821,.001
+GW 27,1,0.,0.,-.163821,1.9535E-9,-.1638211,-.163821,.001
+GW 28,1,1.9535E-9,-.1638211,-.163821,5.8606E-9,-.4914632,-.163821,.001
+GW 29,1,5.8606E-9,-.4914632,-.163821,1.3675E-8,-1.146747,-.163821,.001
+GW 30,1,1.3675E-8,-1.146747,-.163821,2.9303E-8,-2.457316,-.163821,.001
+GW 31,1,2.9303E-8,-2.457316,-.163821,6.056E-08,-5.078453,-.163821,.001
+GW 32,7,6.056E-08,-5.078453,-.163821,4.8839E-7,-40.95526,-.163821,.001
+GE -1
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The length-tapering of each element uses 32 wires. However, a GC-tapered equivalent model would use only 8 wires (including the untouched wires in the vicinity of the ground penetration).

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 160-m 1/4 wl vert-4 bur radial
+CE
+GW 1,11,0.,0.,40.,0.,0.,.327644,0
+GC 2 0 0 .0125 .0125 13 .16328
+GW 2,1,0.,0.,.327644,0.,0.,.163821,.0125
+GW 3,1,0.,0.,.163821,0.,0.,0.,.0125
+GW 4,1,0.,0.,0.,0.,0.,-.163821,.0125
+GW 5,12,0.,0.,-.163821,40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 6,12,0.,0.,-.163821,0.,40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 7,12,0.,0.,-.163821,-40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 8,12,0.,0.,-.163821,0.,-40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GE -1
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We have added to each long element a GC entry. The main element entry, below GW1, works from the top of the monopole downward, while the radial entries work from the junction outward for GW5 through GW8. The model specifies a Type 2 GC entry, with both the starting and ending segment lengths specified: 0.16281 and 13.5 for the radials. The main element begins with a 13.0-m first segment and works down to the 0.16281-m length.

+

The essential internal calculations appear in the geometry specification section of the NEC output file.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                   - - - STRUCTURE SPECIFICATION - - -
+
+                                     COORDINATES MUST BE INPUT IN
+                                     METERS OR BE SCALED TO METERS
+                                     BEFORE STRUCTURE INPUT IS ENDED
+
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     1    0.00000    0.00000   40.00000     0.00000    0.00000    0.32764    0.00000     11        1    11       1
+         ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS = 13.00000  0.16328
+                                 RADIUS FROM  0.01250 TO  0.01250
+                                 COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  0.67526
+     2    0.00000    0.00000    0.32764     0.00000    0.00000    0.16382    0.01250      1       13    13       2
+     3    0.00000    0.00000    0.16382     0.00000    0.00000    0.00000    0.01250      1       14    14       3
+     4    0.00000    0.00000    0.00000     0.00000    0.00000   -0.16382    0.01250      1       15    15       4
+     5    0.00000    0.00000   -0.16382    40.95530    0.00000   -0.16382    0.00000     12       16    27       5
+         ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS =  0.16328 13.50000
+                                 RADIUS FROM  0.00100 TO  0.00100
+                                 COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  1.49568
+     6    0.00000    0.00000   -0.16382     0.00000   40.95530   -0.16382    0.00000     12       28    39       6
+         ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS =  0.16328 13.50000
+                                 RADIUS FROM  0.00100 TO  0.00100
+                                 COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  1.49568
+     7    0.00000    0.00000   -0.16382   -40.95530    0.00000   -0.16382    0.00000     12       40    51       7
+         ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS =  0.16328 13.50000
+                                 RADIUS FROM  0.00100 TO  0.00100
+                                 COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  1.49568
+     8    0.00000    0.00000   -0.16382     0.00000  -40.95530   -0.16382    0.00000     12       52    63       8
+         ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS =  0.16328 13.50000
+                                 RADIUS FROM  0.00100 TO  0.00100
+                                 COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  1.49568
+
+   GROUND PLANE SPECIFIED.
+
+   TOTAL SEGMENTS USED=   63     NO. SEG. IN A SYMMETRIC CELL=   63     SYMMETRY FLAG=  0
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that each GC request for tapering specifies the same radius for the starting and stopping segments. In this instance, we are interesting only in length-tapering the segments. The result uses shorter segment lengths closer into the junction and longer ones further out than the manual tapered model. To give a one-radial example, the following table tracks the segment lengths of a radial from this model from the geometry structure section of the NEC output file, immediately following the input request section that we have just viewed.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+
+    16   0.08164   0.00000  -0.16382   0.16328    0.00000   0.00000   0.00100   -28   16   17      5
+    17   0.28539   0.00000  -0.16382   0.24422    0.00000   0.00000   0.00100    16   17   18      5
+    18   0.59013   0.00000  -0.16382   0.36527    0.00000   0.00000   0.00100    17   18   19      5
+    19   1.04592   0.00000  -0.16382   0.54632    0.00000   0.00000   0.00100    18   19   20      5
+    20   1.72765   0.00000  -0.16382   0.81712    0.00000   0.00000   0.00100    19   20   21      5
+    21   2.74728   0.00000  -0.16382   1.22215    0.00000   0.00000   0.00100    20   21   22      5
+    22   4.27232   0.00000  -0.16382   1.82794    0.00000   0.00000   0.00100    21   22   23      5
+    23   6.55330   0.00000  -0.16382   2.73400    0.00000   0.00000   0.00100    22   23   24      5
+    24   9.96489   0.00000  -0.16382   4.08919    0.00000   0.00000   0.00100    23   24   25      5
+    25  15.06753   0.00000  -0.16382   6.11610    0.00000   0.00000   0.00100    24   25   26      5
+    26  22.69944   0.00000  -0.16382   9.14771    0.00000   0.00000   0.00100    25   26   27      5
+    27  34.11430   0.00000  -0.16382  13.68201    0.00000   0.00000   0.00100    26   27    0      5
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Whether from idle curiosity or some other purpose, we may contrast this scheme with the manually tapered comparable radial.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+
+    15   0.08191   0.00000  -0.16382   0.16382    0.00000   0.00000   0.00100   -27   15   16      9
+    16   0.32764   0.00000  -0.16382   0.32764    0.00000   0.00000   0.00100    15   16   17     10
+    17   0.81911   0.00000  -0.16382   0.65528    0.00000   0.00000   0.00100    16   17   18     11
+    18   1.80203   0.00000  -0.16382   1.31057    0.00000   0.00000   0.00100    17   18   19     12
+    19   3.76788   0.00000  -0.16382   2.62114    0.00000   0.00000   0.00100    18   19   20     13
+    20   7.64108   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    19   20   21     14
+    21  12.76634   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    20   21   22     14
+    22  17.89160   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    21   22   23     14
+    23  23.01686   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    22   23   24     14
+    24  28.14211   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    23   24   25     14
+    25  33.26737   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    24   25   26     14
+    26  38.39263   0.00000  -0.16382   5.12526    0.00000   0.00000   0.00100    25   26    0     14
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The differences in output reports between the two systems of tapering--one continuous, the other with a user-specified limit to outer segment length--are not great. Both models show a theta angle of 73 degrees (17-degree elevation angle). The manually tapered model shows a gain of 2.10 dBi in contrast to the 2.06 figure for the GC-tapered model. The corresponding source impedance reports are 47.4 + j 14.5 Ohms and 47.5 + j 14.0 Ohms.

+

Although the 4-radial model saves us only 24 wires and hence little time on a modern PC, it is likely that a 128-radial model would save noticeable time. As well, more complex models, perhaps involving the shorter radials as well as the full size ones, might save enough time to make a difference in the course of a project.

+

Nevertheless, our foray into the use of the GC entry has been primarily to examine its capabilities and how to implement them. Ultimately, the aptness of the entry for a particular model is a judgment call by the modeler.

+
+ +

+

Go to Main Index

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55. Parallel Sources, Angular Junctions, and Average Gain: Correcting "Weaknesses"

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L. B. Cebik, W4RNL

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The following notes emerged from conversations with Dean Straw of ARRL over a problematical model. By the time I finished investigating the problem, NEC had involved me with several problems simultaneously:

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  • 1. The parallel sourcing of two wires simultaneously, as the model attempted to capture the geometry that might actually be used in the physical antenna;
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  • 2. The angular junction of the two wires as they might meet at a common wire section on which we might place the source; and
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  • 3. The results of the average gain test and what they might indicate about the model and its improvement.
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Let's begin with a review, starting with the Average Gain Test.

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AGT

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Essentially, we only need two numbers to perform the Average Gain Test: the input power and radiated power. For a lossless antenna, the input power and the average radiated power should be equal. Whatever the gain in one or more favored directions, it will be offset by nulls in other directions. Over the entire sphere of free space, the total amount of radiated power can never exceed the power supplied to the antenna. Hence, the ratio of average radiated power to supplied power should be 1. If the ratio differs by more than a small amount from 1, then the model may be considered suspect.

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The conditions under which an adequate model will show an Average Power Gain (Gave) of 1 also establishes the conditions for performing the Average Gain test. The model is set in free space for a k of 1 and over perfect ground for a k of 2. The wire material must be perfect or lossless. All "real" or resistive parts of loads, networks, and transmission lines must also be set to zero (which may require in a parallel R-L-C load a very high value for the parallel resistance).

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For test purposes, the model is run by taking a regular sample of the radiation pattern every few degrees, and the results are averaged. The result is a fair reading of the average radiated power. To calculate the average power gain, we simply apply the following simple equation:

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where Prad is the radiated power as averaged and Pin is the input power as calculated from source information.

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The average gain figure that results from the test may be higher or lower than 1.0. One proposed gradation of model merit uses the following dividing points:

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Gave Value Range                    Significance
+0.95 - 1.05                   Model is considered to have passed the test
+                                    and is likely to be highly accurate.
+0.90 - 0.95 and 1.05 - 1.10   Model is quite usable for most purposes.
+0.80 - 0.90 and 1.10 - 1.20   Model may be useful, but adequacy can be
+                                    improved.
+<0.80 and >1.20               Model is subject to question and should be
+                                    refined.
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The user may develop more strict limits for the adequacy of a model based on the specific tasks within which the model plays a role.

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Most models that deviate in the test from an average gain of 1 show an inverse correlation between errors in gain and in the resistive component of the source impedance. As the gain climbs, the source impedance decreases, and vice versa. For limited purposes, the average gain value derived from the test can be used to correct both figures, using the following equations:

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and

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Obviously, an average gain values that is greater than 1 will increase the input resistance and decrease the gain. Values less than 1 will do the opposite.

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Parallel-Fed Driven Elements

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When we develop a model of two or more elements that use a common source, the most common modeling configuration appears at the top of Fig. 1. We bring the element wires together at a common wire. Normally, we use 3 segments to ensure that the source segment and the adjacent segments have the same length. This technique is especially apt for center feeding, since the current levels on the segments on either side of the source segment will be equal.

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Fig. 1 also shows an alternative source scheme. We create independent elements, each with its own source wire, with the two wires closely spaced and parallel to each other. However, we place the source on only one wire. From that wire, we run a TL transmission line from one ostensible source segment to the true source segment. By making the TL length very short--for example a fraction of an inch--we obtain negligible impedance transformation, effectively connecting the two source segments in parallel. Moving the actual source from one wire to the other normally yields a difference in impedance that show up only in the hundredths columns of the resistance and reactance. Although the TL length may be only a small fraction of an inch, the actual spacing of the parallel source wires may be somewhat larger. How much larger is part of the story to come.

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The question that emerges from this abstract presentation is this: when do we need to resort to the second mode of feeding parallel sources? The answer is not simple, but the Average Gain Test can help us decide on a case-by-case basis.

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Some NEC Limitations

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The alternative parallel source systems and the AGT come together in guiding our modeling, because NEC has some limitations. Moreover, some of those limitations may affect NEC-2 more than NEC-4. The two most important limitations for the present situation are these:

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  • 1. The sensitivity of NEC to very closely spaced wires, especially where we cannot practically establish exacting parallelism between the segment junctions of the wires; and
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  • 2. Angular junctions of wires, as we decrease the angle between them.
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NEC-2 and NEC-4 appear to be equally susceptible to the first limitation. However, NEC-2 is much more sensitive than NEC-4 to the second limitation. As a foreshadowing of notes to come, in numerous cases of the type we are dealing with, NEC-2 and NEC-4 will yield divergent output reports and AGT values using the upper configuration in Fig. 1. In some cases, we shall be able to achieve a better AGT value and a close coincidence of NEC-2 and NEC-4 reports by using the alternative feed system. Since I have no specific formula to offer as to when we might benefit from moving from one feed system to the other, a set of test cases may have to suffice to give fair warning instead.

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Dipole Elements

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Let's first look at a series of models of dipole elements. Each model will consist of a 28.5-MHz dipole in free space. However, each antenna will have two dipoles fed in parallel. The differences among the models will consist of the angle that each of the two dipoles takes toward the other. In all of the examples, the angular divergence of wires will occur on the X-Y plane.

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Fig. 2 shows our initial case, where the two dipole elements are at 90 degrees to each other. The outline and the wire table show the modeling convention used. A leg from each dipole meets its counterpart at a common section of wire, using the technique at the top of Fig. 1. From this model, we obtained the following NEC-2 and NEC-4 results. (In all dipole listings, gain is the free-space gain and the source resistance is in Ohms.)

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DP10-90     Max Gain          Source            AGT Values
+            dBi               Resistance        Ratio       dB
+NEC-4       1.17              34.62             0.997       -0.01
+NEC-2       1.24              34.07             1.013        0.06
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Both AGT ratings fall well within the highly accurate range. However, let's perform the corrective calculations as an exercise. The NEC-4 reading is 0.01 dB low, for a corrected value of 1.18 dBi. The NEC-2 reading is 0.06 dB high, for a corrected reading of 1.18 dBi. Using the AGT ratio as a multiplier on the resonant source resistance, we get a correct NEC-4 source resistance of 34.52 Ohms and a NEC-2 correct value of 34.51 Ohms. One could not wish for a better starting example.

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In Fig. 3, we have a model that closes the angle between dipole wires to about 60 degrees, with the element lengths adjusted for resonance within +/-1 Ohm of remnant reactance. Again, the model uses the single common wire system of parallel feeding. In this case, we obtain the following results.

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DP10-60     Max Gain          Source            AGT Values
+            dBi               Resistance        Ratio       dB
+NEC-4       1.65              49.37             0.999       -0.00
+NEC-2       1.86              47.05             1.049        0.21
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Although the NEC-2 AGT value of 1.049 appears to fall within the highly accurate range, it represents a 0.21 dB over-estimate of the maximum gain. Corrected, the gain become 1.65 dBi, the same value as reported by NEC-4. Correcting the NEC-2 source resistance yields a value of 49.36 Ohms, a match for the NEC-4 value. Whether or not the differences in NEC-2 and NEC-4 reports makes any operational difference, the example provides some insight into the fact that as we close the angle between the dipole element wires, NEC-2 more rapidly departs from a perfect AGT report than does NEC-4.

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Fig. 4 closes the angle still further--to between 19 and 20 degrees. Once more, the element lengths have changed to obtain resonance. From this model, still using the single common feed wire, we obtain the following reports.

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DP10-20     Max Gain          Source            AGT Values
+            dBi               Resistance        Ratio       dB
+NEC-4       2.32              57.45             1.069        0.29
+NEC-2       2.96              49.62             1.238        0.93
+

The 20-degree angle between element wires yields gain values that exceed the possible gain of a dipole in free space for both cores. Moreover, we see a continuing more rapid departure from an ideal AGT value in the NEC-2 report than the NEC-4 report. However, even the NEC-4 report has fallen out of the ostensible "highly accurate" range.

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Corrected, the NEC-4 maximum gain is 2.03 dBi, the same value as the corrected NEC-2 maximum gain value. The corrected NEC-4 source resistance is 61.41 Ohms, while correcting NEC-2 yield 61.42 Ohms. Once more, the AGT permits us to correct the values listed, but we have a remnant difficulty. The NEC-4 source impedance shows a reactance of +0.33 Ohms, while the NEC-2 report shows +1.40 Ohms. The AGT provides no guidance on handling the reactance.

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The divergence of the initially reported values for the two cores for the 20-degree dipole case suggests that it is time to try the alternative feed system. See Fig. 5.

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The figure shows only the feed portion of the model. The AWG #8 wires are 0.1285" in diameter and are spaced 0.5" apart. Because this model is highly symmetrical, the close spacing is possible, but wider spacing may be necessary for other types of models. The element ends remained at their original positions, even though separating the two feed sections slightly shortens each modeled element's total length. The transmission line length is 0.01". From this model, we obtain the following results.

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DP10-20A    Max Gain          Source            AGT Values              Remnant
+            dBi               Resistance        Ratio       dB          Reactance
+NEC-4       2.07              60.72             1.010        0.04       -j 5.39
+NEC-2       2.07              60.74             1.009        0.04       -j 5.31
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Most notable in the table is the exacting coincidence of NEC-2 and NEC-4 reports, including the AGT values. Correction of the gain to 2.03 dBi and the source resistance to 61.3 Ohms in both cases is simple. However, with slightly wider spacing, one can bring the AGT value close to 1.000 for the model on both cores.

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The alternative parallel source system, then, can overcome some of the divergence in reports between NEC-2 and NEC-4. In this case, the greater sensitivity of NEC-2 to small angular junctions of wires disappears in the alternative system, because it removes the tight angular junctions altogether.

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Closed Geometry Cases

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A second test that we might perform on the angular junction situation occurs with multi-band quad beams that use a common feedpoint. Let's look at two cases, the first of which involves quads for 14 and 28 MHz. Fig. 6 shows the basic layout where the drivers come together in a single 3-segment wire that lies in the plane of the 10-meter driver loop wire. Hence, only the 20-meter loop shows significant departure from a standard square quad loop.

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The wire table reveals that the two quads are concentric and spaced from driver to reflector at 0.16 wavelength. Thus, the 20-meter reflector is behind the 10-meter reflector and the 20-meter driver is forward of the 10-meter driver. The angle made by the lower (fed) 20-meter wire is correspondingly complex.

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The following table of results gives both 14 and 28 MHz values for both cores. Since the antenna is 35' over real ground, the gain value includes a Take-Off angle or elevation angle of maximum radiation. The driven elements are not resonant, so the source impedance gives an R +/- jX value in Ohms.

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QU10-20     Freq.       Max Gain          Source            AGT Values
+            MHz         dBi               Impedance         Ratio       dB
+NEC-4       14          11.49/24           97.6-j43.6       1.005        0.02
+            28           6.57/33          211.4+j14.3       1.006        0.03
+NEC-2       14          11.86/24           90.3-j36.6       1.089        0.37
+            28           6.93/33          195.1+j21.0       1.095        0.39
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According to gradation scales, the NEC-4 model is highly accurate, while the NEC-2 model is reasonably accurate. The corrected gain is 6.54 and 6.55 dBi for NEC-2 and NEC-4 at 28 MHz and 11.49 and 11.47 dBi for NEC-2 and -4 at 14 MHz. Corrected source resistances are about 213 Ohms at 28 MHz and 98 Ohms at 14 MHz for both cores.

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The question we might pose is to what degree we can trust these corrected values, since the model deals with a closed geometry. To perform a test, I developed the alternative feed structure for the drivers, as shown in Fig. 7.

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The trial spacing of the source wires, using AWG #14 (0.0641" diameter) wire, was 0.05' or 0.6". This spacing had proven adequate for the 20-degree dipoles and was worth a try. The TL line was set at 0.01' or 0.12". Swapping feedpoints at the ends of the line yielded difference in the source impedance only in the 4th significant digit. The results that emerged are in the following table.

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QU10-20A    Freq.       Max Gain          Source            AGT Values
+            MHz         dBi               Impedance         Ratio       dB
+NEC-4       14          11.11/24          101.8-j43.2       0.920       -0.36
+            28           6.30/33          247.8-j15.4       0.915       -0.38
+NEC-2       14          11.13/24          101.9-j43.5       0.920       -0.36
+            28           6.29/33          248.4-j15.6       0.915       -0.38
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The coincidence of all reports between the two cores confirms that the use of separate feed wires with a very short TL overcomes the differential sensitivity between NEC-2 and NEC-4 to the angular junction of wires. However, the AGT values suggests that a problem that is common to both cores remains, relative to an ideal report. The most likely culprit is the spacing between the source/TL wires. Therefore, I increased the spacing from 0.6" to 3", while leaving the TL length at 0.12". The reports that emerged were as follows.

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QU10-20B    Freq.       Max Gain          Source            AGT Values
+            MHz         dBi               Impedance         Ratio       dB
+NEC-4       14          11.47/24           93.0-j44.1       1.000        0.00
+            28           6.69/33          228.9-j30.5       1.000        0.00
+NEC-2       14          11.49/24           93.1-j44.4       1.000        0.00
+            28           6.69/33          229.5-j30.8       1.000        0.00
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The 20-meter gain values from this version of the model coincide exactly with the corrected values for the original model and for the first try at using the alternative feed system. The 10-meter gain values are slightly higher than the original model corrected values and in line with the correct values for the first try at the alternative system. As we expected, the NEC-2 and NEC-4 models remained closely coincident.

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As well, the corrected first try and the second try source resistance values are closely aligned. However, they both depart somewhat from the common feed-wire system model, even when corrected. As well, we have no guidance as to what set of reactance values may apply. However, the major changes toward capacitive reactance occur at 14 MHz, and that wire has grown shorter with each alternative feed system maneuver.

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In general, this exercise on the original 14-28-MHz model has aimed to identify aspects of the source situation that are divergent between cores and those that are common to both cores. Nothing in the original model was so far out of line with reality to make it wholly unusable. However, we may sample a more extreme case.

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Fig. 8 shows the driver feed section and wire table for a combined 2-element quad for both 12 and 10 meters. The principles are identical to those of the 14-28-MHz original model with one exception. The angular junction of feed wires is much smaller. The results clearly show what happens. Once more, the antenna is centered 35' above real ground.

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QU10-12     Freq.       Max Gain          Source            AGT Values
+            MHz         dBi               Impedance         Ratio       dB
+NEC-4       24.94       12.04/15          109.9-j 3.0       1.095        0.40
+            28.5        10.43/13          1378 +j1644       1.198        0.78
+NEC-2       24.94       12.96/15           89.8+j15.4       1.356        1.32
+            28.5        11.31/13          1042 +j1315       1.464        1.66
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The corrected gain values for each core show 11.64 dBi at 24.94 MHz and 9.65 dBi at 28.5 MHz. However, the 28.5-MHz impedance values are almost unbelievable. Therefore, I introduced the alternate feed system, shown in Fig. 9.

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The feed-wire spacing is 0.045' or .54", with a TL length of 0.01' or 0.12". Using this system, the model returned the following results.

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QU10-12A    Freq.       Max Gain          Source            AGT Values
+            MHz         dBi               Impedance         Ratio       dB
+NEC-4       24.94       11.67/15          118.9-j30.8       1.002        0.01
+            28.5        12.04/13          134.3+j71.7       1.001        0.01
+NEC-2       24.94       11.65/15          119.7-j31.0       1.002        0.01
+            28.5        12.04/13          134.4+j71.8       1.001        0.01
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The alternate feed system is a necessity in this case to yield values that are sensible. However, had we not had the AGT to alert us to the distortions in the model reports occasioned by the very narrow angle at the driver wire junctions, we might well have interpreted the results as suggesting that interactions among the elements in a physical antenna would make the combination quad impossible to construct.

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The differences show up most clearly in the overlaid NEC-4 azimuth patterns for 28.5 MHz for the two versions of the model, shown in Fig. 10. The disparity between the patterns calls for little comment.

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Conclusion

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The exercises included in these notes only sample the many facets of modeling that we have touched upon so far. We have looked at differential sensitivities between NEC-2 and NEC-4. We have also looked at sample problems common to both cores. We have used the Average Gain Test to uncover both types of difficulties. And we have employed an alternative scheme for parallel feeding elements from a common source as one route to overcoming those problems.

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The variations on the many themes are endless. In the end, the individual modeler must use all of the tests at hand to detect problems and to devise solutions that offer a route to more precise and accurate models. As we have seen in at least one case, a failure to exercise such care may lead to completely misleading results.

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56. When MININEC is Superior to NEC

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L. B. Cebik, W4RNL

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Although NEC (-2 or -4) has become the de facto stand for modeling LF through VHF wire antennas, we should be aware that there are cases in which public domain MININEC, especially in its corrected and improved versions, may yield superior results. In an earlier column, I compared some results using NEC-4 and various implementations of public domain MININEC. However, in that column, I used NEC-4 as a standard against which to compare the various versions of MININEC. The models used were selected on the basis of the known accuracy of NEC-4 relative to the model geometries involved.

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NEC-2/-4 Weaknesses

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There are, however, a number of model geometries which neither NEC-2 nor NEC-4 handle very well. NEC-2 has its well-documented weakness with any stepping of element diameter. When elements are linear, the Leeson corrections provide accurate results. However, the Leeson corrections actually provide the user with a substitute constant-diameter element having the same electrical properties as the original stepped diameter element. Moreover, the use of a Leeson-substitute is applicable only when the element is a. linear, b. within about 15% of half wavelength resonance (1/4 wavelength resonance for vertical monopoles), and c. not loaded except at the element center (if horizontal) or at the element base (if a 1/4 wavelength monopole). Although exceptionally useful for monoband Yagi, the Leeson corrections have limitations when we try to model arrays with loaded elements or arrays that intermix elements for many frequencies.

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NEC-4 has to a major extent overcome the NEC-2 weakness with stepped- diameter elements. However, the results grow more inaccurate as the diameter step grows larger. In most cases, the potential for error shows up on the average gain test as a value that departs considerably from the ideal 1.00 (for horizontal elements--2.00 for monopoles touching the ground). Therefore, when using even NEC-4, running the average gain test after removing all resistive loading from the antenna and placing it in free space (or over perfect ground for monopoles touching the ground) is a crucial step in assessing the appropriate confidence level in a model.

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Both NEC-2 and NEC-4 retain weaknesses in related model geometries where no easy correctives current exist. One such area is an angular junction of wires that have dissimilar diameters. This form of construction is common in LF through VHF antenna construction. At lower frequencies, wire extensions may emanate from a tower. At higher frequencies, antenna elements may begin as aluminum tubing and end as copper wire.

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The errors that accrue to angular junctions of dissimilar diameter wires tend to disappear with at least one type of structure. Consider an element with a symmetrical hat structure (or a ground-plane radial structure). If the structure of wires is truly symmetrical, then the net radiation from the structure is (nearly) zero. With these types of structures, the angular junction errors tend to disappear.

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A second type of error that appears in both NEC-2 and NEC-4 models appears when we closely space elements of different diameters. The common folded dipole may use length-wise wires of differing diameters to control the impedance step-up over a standard dipole. The ratio is 4:1 only if both wires are the same diameter--and NEC handles this case very well if the segment junctions are well aligned for the two wires. However, if the unfed wire is significantly thicker or thinner than the fed wire, then NEC yields results that are prone to error.

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The wires need not be connected at the ends for the errors to appear. In open-sleeve coupling situations, the fed element and the slaved element may be a. in very close proximity and b. of different lengths and diameters. Depending upon the lengths, the diameters, and the spacing, considerable error may creep into the NEC output. The closer the spacing, the higher the error.

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For a more complete review of these weakness, see "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), pp. 3-16.

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MININEC 3.13 Strengths and Weaknesses

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MININEC 3.13 is the public domain version of the program. As such, it has been subject to numerous modifications by those implementing the core within more user-friendly interfaces. In its initial form, MININEC has a series of known weaknesses.

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  • 1. MININEC requires an excessively high level of segmentation to overcome errors at angular junctions of wires.
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  • 2. There is a known limit to the smallest angle that MININEC may handle with a wire junction at any level of segmentation.
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  • 3. As one increases frequency, MININEC shows a frequency offset of increasing proportions.
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  • 4. As one decreases the spacing between wires, inaccuracies increase.
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Each of these inadequacies has been addresses by at least one implementation of MININEC. However, the latest incarnation of public domain MININEC--Antenna Model--has addressed all of them and returns results that are very consistent with NEC-4 models through the lower UHF region (the limits of my testing so far).

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Thus far, no one has managed to weld the highly accurate Sommerfeld ground calculation system to MININEC. Hence, the simple reflection coefficient system remains in all current implementations of the program. Any wire with a horizontal component (meaning both horizontal and tilted wires) will show increasing inaccuracy of results when the wire is less than about 0.2 wavelength high at its lowest point. MININEC thus shows its greatest strengths when the model is in free space or at a relatively high position relative to the ground.

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(We shall by-pass in this column the use of a MININEC ground as a substitute for ground-plane radials for monopoles touching the ground. I did a series of articles "Some Facts of Life About Modeling 160-Meter Vertical Arrays" for The National Contest Journal in 200-2001 the explore this territory in considerable detail.)

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MININEC 3.13 tends to show its strength in just the areas where NEC displays its weaknesses. Linear elements with a stepped diameter produce accurate results without need for any correctives. Indeed, the original Leeson correctives were calibrated to MININEC results using the same elements. (See Chapter 8 of Physical Design of Yagi Antennas by David B. Leeson, especially section 8.5.) Moreover, angular junctions of dissimilar-diameter wires can be routinely handled once correctives are introduced for the basic angular junction difficulty in MININEC. Finally, MININEC shows an ability to yield accurate results with closely spaced wires of differing diameters once the basic close-spaced wire inadequacy has been corrected.

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Note that many of the MININEC strengths--excepting the ability to handle directly stepped-diameter wires--depend upon the introduction of correctives to initial MININEC weaknesses. Hence, the reliability of MININEC 3.13 depends to a great degree upon the adequacy and number of correctives introduced into the calculating core. AO has a good frequency corrective and ELNEC has a good close-wire corrective. As noted, however, Antenna Model has introduced the most thorough-going collection of corrections and will be used as the MININEC program in a couple of sample exercises.

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A VHF Rectangle as a Sample Comparison between MININEC and NEC

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As an exercise for which I have actually built a physical antenna to check models against reality, let's consider a 2-meter rectangle designed for 146.0 MHz. Fig. 1 shows the model, its segmentation, and feedpoint. The model shape was dictated by the task specification of arriving at an antenna having a feedpoint impedance that yield a low SWR with 50-Ohm coaxial cable feedline. The model uses (in the MININEC version) 16 segments in the horizontal legs and 34 segments in the vertical legs.

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The physical construction of the antenna appears in outline form in Fig. 2. The horizontal legs consist of 0.75" diameter aluminum tubing 16.0" long. The lower horizontal leg is split for direct connection of a female UHF connector. The vertical legs each use 33.75" of AWG #14 wires (0.0641" diameter). The wires are bare copper. The test antenna itself used a simple PVC vertical center support and small blocks of wood to support the horizontal legs. The vertical PVC support used two different nesting sizes of PVC to allow for adjustment of the vertical height during tests.

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The free-space pattern for the antenna appears in 3-dimensional form in Fig. 3. For those more used to seeing 2-dimensional patterns for the antenna, Fig. 4 provides the azimuth or E-plane pattern for the antenna. Note that the nulls at 90 degrees to broadside to the antenna are not as deep as those on a dipole placed in free space. There is significant radiation from the vertical legs of any quad loop, square or rectangular--at least enough to diminish the nulls off the edge of the array.

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I ran this antenna at 146.0 MHz using Antenna Model's corrected MININEC and on various implementations of NEC-2 and NEC-4. The following table summarizes the results. There was no difference between single and double precision NEC-4 values.

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Core             Impedance             Free-Space      AGT
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+MININEC (AM)     53.1 + j 0.7          5.04            0.9871/-0.06
+NEC-4            65.2 + j68.6          5.01            0.9780/-0.10
+NEC-2            83.8 + j152           4.82            0.9470/-0.24
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There are several facets to explore in this table. Although one might view some aspects as unnecessarily subtle, the results form an interesting composite.

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First, the average gain test (AGT) values emerge from both EZNEC and NEC- Win Plus for the NEC-2 test--and are consistent in both. EZNEC shares in common with Antenna Model the ability to arrive at an AGT value even if the elements have material loading (LD5 in NEC). These values are of little or no use, since they do not differentiate between material losses and a failure to achieve an ideal 1.0 AGT value due to the antenna geometry in relationship to core calculations. Therefore, one must use care to use perfect or lossless wire for the test. NEC-Win Plus does this automatically in its implementation of the test.

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The AGT value can be translated into a gain deficit (as in the example) or a gain surplus by multiplying the common log of the AGT value by 10. In all three cases, the corrected gain value (the reported value minus the AGT in dB) becomes something very close to 5.1 dBi.

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The AGT value itself may be used to correct source impedances having negligible reactance. Multiply the source resistance by the AGT. The MININEC report becomes about 52.4 Ohms, a difference too small for my instruments to measure. However, the high reactance associated with the NEC source impedance reports voids the use of the AGT to correct the source resistance values.

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In fact, adjusting the vertical legs of the NEC models to yield a source impedance close to resonant provided me with a simple test of which program provided the most accurate results. NEC-4 required vertical legs of 32" to yield a source impedance of about 57 Ohms, while NEC-2 needed vertical legs 29.6" long to report a resonant source impedance of about 65 Ohms. The significant difference between the length of the vertical legs with no change of the horizontal legs allowed a simple test to determine the most accurate modeling result.

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The physical antenna was within about 0.2" of the MININEC results and showed a source impedance very close to 50 Ohms--allowing for instrument error. It is interesting to note that ELNEC, which does not use a frequency corrective for its MININEC core, reported a gain of 5.1 dBi and a source impedance of 50.8 - j 4.0 Ohms, indicating that the frequency drift of raw MININEC has not surpassed usability at the 146-MHz range.

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A Step-Up Folded Dipole as a Sample Comparison between NEC and MININEC

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A folded dipole that is resonant on any given frequency will exhibit the familiar 4:1 impedance set-up relative to a single wire resonant dipole only if the long wires are of equal diameter. If the fed wire is larger in diameter than the unfed wire, then the impedance will increase by less than 4:1, but in no case will it be less than 1:1. If the unfed wire is larger in diameter than the fed wire, then the impedance ratio relative to a single-wire resonant dipole will be greater than 4:1.

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The theoretical impedance transformation is given by the following equation:

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where R is the impedance transformation ratio, s is the wire spacing, center-to-center, d1 is the diameter of the fed wire, and d2 is the diameter of the second wire, and where s, d1, and d2 are given in the same units.

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Suppose that we create a folded dipole using AWG #12 wire (0.0808" dia.) for the fed wire and 0.5" diameter for the unfed wire. Let's also space the wires 3" (0.25') center-to-center. The impedance transformation predicted by the equation is 7.47. If a single wire dipole has an impedance of abut 71 Ohms, then the anticipated folded dipole impedance would be about 530 Ohms. The equation does not take into account the connecting end wires, so we may expect some variance from the value, but not by more than a few percent. As well, the impedance of a dipole will vary slightly depending upon the diameter and type of material, so we should expect perhaps a range of +/-5 Ohms for the set-up folded dipole relative to calculations.

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Now let's make a model of the step-up folded dipole. If we choose 28.5 MHz as the test frequency, we can segment a folded dipole as shown in Fig. 5. The long wires have 68 segments in MININEC and 67 segments in NEC--to ensure proper centering of the feedpoint. The AWG #12 end wires use 2 segments per wire.

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Fig. 6 shows the general physical outlines of the antenna. For the test frequency, the long wires are 16.2' long. For this test, the end wires extend along the Z-axis. If we lay the folded dipole along the X-Y axes, there will be a slight gain difference in the resulting two azimuth lobes amounting to about 0.1 dB. Using the Z-axis for the two long wire displacement equalizes the gain in the lobes.

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Fig. 7 shows the 3-dimensional free-space pattern of the antenna and the familiar donut shape applicable to dipoles, whether folded or unfolded. Those who prefer 2-dimensional patterns may look at Fig. 8, which records the E-plane pattern of the antenna in free space. Incidentally, all patterns and segmentation graphics in this column come from Antenna Model. Hence, the recorded gain is that of the MININEC model.

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The crux of our investigation hinges upon how well MININEC fares over and against NEC-2 and NEC-4 models of the same antenna. The only difference between models will be in the segmentation of the long wires: 68 vs. 67.

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Core             Impedance             Free-Space      AGT
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+MININEC (AM)     530.5 + j 2.0         2.13            0.9988/-0.01
+NEC-4            463.0 + j17.5         1.50            0.8660/-0.62
+NEC-2            375.2 + j25.8         0.60            0.7030/-1.53
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The MININEC model produces highly credible numbers for both the source impedance and the gain. As well, it yields a very good AGT value. In contrast, the NEC-4 and NEC-2 numbers fall well outside the range of credibility. (As with the first test, there is no significant difference between NEC-4 single and double precision values.) Although NEC-4 comes closer to believable numbers, as witnessed by the higher AGT value, the model still falls into the range of the unusable. However, if we adjust the gain values by the AGT deficit in dB, we come close to the value reported directly by the MININEC model.

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Both NEC-2 and NEC-4 provide excellent results when the two long wires of the folded dipole have the same diameter. The limitation faced by NEC lies in its calculations when the wires have different diameters. Indeed, making the end wires equal in diameter to the unfed wire does not change the results. MININEC is the preferred core for antenna design and analysis when antennas have geometries resembling the one in the step-up folded dipole.

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Conclusion

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There are, then, antenna wire geometries for which MININEC is the preferred modeling core, especially if that core has been adjusted to overcome past known weaknesses. This is the case with Antenna Model, although if VHF and upward frequencies are not used, ELNEC will handle close-spaced wires quite well and if no close-spaced geometries are involved, AO will handle VHF and UHF frequencies well. See column #50 for further specific comparisons among MININEC cores.

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These notes are not intended in any way as a criticism or indictment of NEC-2 or NEC-4. Quite the opposite. We obtain the best results in our modeling tasks when we apply the right tool to the right job. For many tasks, NEC-2 and NEC-4 are the right tools. However, corrected MININEC is also available for certain special jobs that NEC-2 and NEC-4 do not do well. And, for a large class of modeling tasks, both NEC and MININEC are equally apt as modeling cores.

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57. Some Comments on Comments

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L. B. Cebik, W4RNL

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NEC (-2 and -4) allows the user to introduce at the very beginning of a model file the CM input or card. CM means comment, and the user can introduce as many CM lines as needed to say anything that he or she wishes to say about the model. Each 80-character line allows 77 text characters (allowing for the necessary CM and space at the beginning of each line). With a virtually unlimited number of lines, one might come close to writing a full report on the model.

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The string of CM cards requires a closing line entry line, CE. This entry terminates the comments and must be followed by a geometry entry, such as a GW wire entry. The NEC output report will print all of the CM lines at the beginning of the file. CM lines have no affect on any computation made by the NEC core.

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Various commercial implementations of NEC handle the CM inputs in different ways. For example, EZNEC has two different CM-relevant entries: the antenna model title, which is saved within the .EZ model file, and the antenna notes, which are saved in a separate .TXT file having the same file name as the model itself. The title is visible whenever the user calls up the model. As shown in Fig. 1, the comments appear in a separate window only when called. In the Pro version of the program, when the user converts an .EZ file to .NEC format, both the title and the notes become CM lines in the converted file.

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NEC-Win Plus also has a special screen for comments, a sample of which appears in Fig. 2. Since this screen contains the file name and location, adding that data to the comments is unnecessary unless conversion of the .NWP file to .NEC format is anticipated. There is no separate model title, so that information must be included in the comments. All of the data in the special "Comments" box becomes a set of CM lines in a file saved in the .NEC format.

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Programs such as NEC-Win Pro and GNEC present the user with a standard ASCII page of lines making up a .NEC-format model file. Hence, the user introduces comments by opening a new line, labeling it CM, and then filling the remaining spaces, as needed, with whatever the user views as an appropriate comment.

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Why Dwell on Comments?

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A natural question is why I should linger over a calculationally non- functional aspect of NEC. Perhaps the answer may become obvious from Fig. 3, a simple model file (of a 3-element 2-meter Yagi) in .NEC format.

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The sole CM line yields a model title, and in highly truncated form at that. Perhaps the only clear information is the design frequency: 146 MHz. Missing is the antenna type--which we may glean from examining the GW lines--and any other data about the antenna.

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This style of model file used to be common in my directories, and is typical of files from others that have come my way. Indeed, I have stored reams of paper with information about the models that I have constructed and evaluated. Correlating the paperwork with an actual model on file has often been a laborious task--even when I remembered to write down the location of the file.

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Gradually, I began to realize that I was passing up a potentially important NEC facility. So over a period of time, I developed a system of using the CM lines to encapsulate the most important model data. The system that I developed is based on the main lines of work that I do. Hence, it will not be satisfactory for every modeler. However, it might set the wheels in motion for the development of your own system.

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The main categories of CM entries that I use are the following ones.

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  • 1. Model file location and file name.
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  • 2. Full modeling task specifications and/or origin of the antenna modeled.
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  • 3. Overview of the basic construction of the model.
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  • 4. Special features of the model.
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  • 5. A basic performance report.
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  • 6. Commentary on the model, including reactions, potential uses, comparisons, etc.
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These categories are fully functional for my work, which focuses on models of antennas with energy sources, where the key data include the source impedance, the far field information, sometimes the near-field information, and sometimes the relative current magnitudes and phase angles on the antenna elements. There are numerous other applications of NEC, including electromagnetic compatibility analyses, radar profiles, receiving tests using plane-wave excitation, etc. These applications may require the development of different categories of information to place within the CM lines of the model.

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The key benefit of developing a standard list of information categories is that one may simply label the information group with the category number and save a good bit of typing. As well, the information will be consistent from one model to the next, allowing direct comparisons.

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Some Details of the Category Contents

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Let's look at each category in a bit more detail.

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1. Model file location and file name: This information may seem otiose, since it is buried in the model itself and not outside of the system of directories where the models lie in storage. Granted, I do keep an external list of models, with a basic title and their locations. However, I often have the occasion to move a model from one directory to another to group it with relevantly similar or comparative models. In each case, I add the new location to the old within the model CM lines, including any file name changes that might occur due to the new use of the model. I also add to the list any direct scalings of a model from one frequency range to another. This series of entries gives me the ability to track the heritage of a model.

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2. Full modeling task specifications and/or origin of the antenna modeled: This category has 2 functions owing to the different reasons for which I may approach a model. One reason for modeling is either to develop a working design or to analyze an existing design. These tasks do not occur in a vacuum, but are often parts of a specific task. Listing both the task and the task parameters provides insight into later remarks in category 6, the reactive commentary to the model. Hence, the task specification should be as complete as possible within the limitations of truncated entries. If the task involves analysis for the achievement of certain levels of gain, beam width, bandwidth, rear pattern performance, etc., all of these should be noted. Comparing two models many moons later becomes simpler when the performance of the models is read in the context of the original tasks that generated the models.

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Many models have their basis in existing antennas or antenna designs. Listing the essential particulars of the design origin is critical to avoiding errors in model reports, to re-inventing already existing designs, and to finding other details about the antenna design. Notes should also include revisions to an original or basic design, so that a sequence of models--perhaps versions A through G--reveal the evolution of a modified design.

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3. Overview of the basic construction of the model: An overview of the model's basic construction can save a good bit of time ferreting out the information from the lines of a model (or from the various windows in some implementations of NEC). The data should include the units of measure used in the GW lines. These units may be different from the units used to express construction details and, hence, may allow correlations of numbers without calculation between some source material for the antenna and the actual model entries. The basic data should also include the element diameter, if that is the most usual wire measure used in your design work, since the .NEC wire entries will use the radius. (Numerous implementations of NEC provide a wire construction table that employs the wire diameter.) The element material should find a place in this list as a check on subsequent LD5 entries. As well, one should note the level of segmentation used, whether expressed in terms of the number of segments per element or segments per (half-)wavelength.

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Of course, we should not omit a set of element dimensions. The format that we use for these dimensions may vary with the system that we use to enter coordinates. For free-space simple (1 antenna) models, one might use element lengths expressed in terms of the "+/-" values of half lengths. If we model a system of antennas where the overall dimensions might be opaque due to scattering the multiple antennas throughout a coordinate system, full length measurements of elements may prove more useful. The separation of elements in a multi-element antenna can follow whatever convention one uses for constructing the model. Some modelers center such antennas equally behind and ahead of one of the coordinate system axes. Others count from zero for the rearmost element, with positive values for the other elements. Still others place the driven element at zero and count fore and aft of that element. A consistent convention from one model to the next--or a second data set if a certain task forces one to use a non-normal convention--generally saves interpretation time. Amassing data is only useful if it simplifies interpretation. If the data concentration complicates interpretation, it is likely time for a re-evaluation of system of recording it.

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4. Special features of the model: Every data collection system needs a catch-all bin for data that just seem to have no home but are important to a model. The lack of a home is usually a function of the fact that the data involved are model-specific and do not appear with all models within a roughly coherent collection. So I created a home for all such data.

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The data that I almost always include in this category range from the antenna environment (free-space, x WL above y ground, etc.), structural aspects of the antenna (such as the element relationship to a supporting boom), and the specified feed system and any matching systems used to obtain a specific feedpoint impedance. However, many antennas have specific data applicable almost only to them.

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For many models, there are special data pertaining to sources, loads, and/or transmission lines that may be apt for this category. To give just one example, consider Fig. 4, the outline of a 5-band 2-element quad beam using a separate feedpoint for each band.

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Quad loops require 4 wires each, and there are two sets of loops per band. Keeping track of the source wires and segment numbers for each band can be daunting, especially if the model does not use a strictly progressive mode of construction. In this case, the wire order is 20, 15, and 10 meters (driven, then reflector wires) followed by 17 and 12 meters (driven and director wires). I know this instantly from the comments, where I stored the requisite source information, recorded in Fig. 5. Gleaning this information from the GW wires would take a good bit of time, especially if I had not worked with the model for some months.

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Of course, there is more than one way of handling the sources in cases like this. We may keep a single EX (excitation) input line and change the requisite details. However, in some programs, such as EZNEC, one enters the source information in a table. In such cases, we might wish to use the lower portion of Fig. 5 as a means of source entry. We enter the location of all of the sources and then activate only one of them by assigning a source magnitude that is greater than zero.

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Load data for load types LD0 and LD1 show the value of inductance or capacitance. We might wish to enter in category 4 the corresponding reactance value at the center design frequency. Alternatively, a load type LD4 uses a reactance value, and we might enter here the corresponding value of inductance or reactance.

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Transmission lines have many functions, including their use simply as transmission lines. However, open and shorted stubs are often common features of models used for impedance matching and phasing lines in collinear arrays. Horizontal and vertical phased arrays also require transmission lines. Category 4 is a convenient place to record the functions of each transmission line (TL) in the model, with such other particulars as may be useful to sort out a potentially confusing morass of TL constructs.

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Although our original sample model Yagi is in free space, it might well be placed at a specific height in terms of a wavelength above a ground of a certain type, whether simple or complex. Entries in category 4 can obviate the need to interpret the numeric entries on GN or GD lines in the model.

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How many more special entries you might need depends on the model particulars. The useful data will emerge in part from the model parameters and in part from the overall modeling task. However, if a large series of models that are part of a long-term general task have consistently used data elements, then you might consider creating an additional regular or major CM data category.

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5. A basic performance report: The CM lines are not likely the best place to store complete frequency sweep data for a given model. However, a truncated performance report at the center design frequency may be useful when surveying models. For the class of antennas that I typically model, far field and source data generally form the core of my needs. For the Yagi in Fig. 3, the gain, front-to-back ratio, beamwidth at -3 dB points, source impedance, and 50-Ohm SWR comprise the central data. Since the antenna is a wide-band unit, my interest would extend to the band edges as well as including the mid-band frequency. Hence, I might record a short data table for 144, 146, and 148 MHz.

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The results of all of our data summarizing appear in a revision of Fig. 3, shown in Fig. 6. The CM lines now occupy more space in the file than the geometry and control inputs that affect calculations. However, ASCII files are very small, and the added data requires very little storage space. Hence, adding the information costs little more than the time it takes to record it.

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Having the data within the model file allows me to re-learn what I originally learned by running the model. Now I need to run the model only if there are additional data that I find a need to accumulate. Whether to include some of the new data in the CM lines becomes a real time decision based upon an estimate of my later needs for seeing that new data.

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6. Commentary on the model, including reactions, potential uses, comparisons, etc.: We have so far omitted category 6. from the list to this point, because it is perhaps the most task-driven entry of all. The comment shown in Fig. 6 indicates my initial interest in the Yagi, as a possible directional utility antenna for the 2-meter amateur band. The boom length (under 28") promised a light-weight antenna that one might construct using a non-conductive boom material and supporting from the rear. Hence, with a suitably flexible support system, one might easily change the orientation from horizontal to vertical and back again, a desirable feature in a utility antenna. I might also add to the simple remark in Fig. 6 open questions about transforming the model into a real antenna. For example, any implementation of the antenna would require a split driven element for direct feed, and this fact promises to complicate construction relative to the simple mounts required by the parasitic elements.

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Since the exact information suited to this category is task specific, it is impossible to say in general what sorts of entries would be most useful. In a series of models set up for comparison, one might record the ranking of the given model--or a series of rankings within the series based upon a list of critical parameters. It likely is also useful to record reactions, especially if they result from surprise--perhaps at how well or how poorly an antenna performs in one or another department of concern. As well, one might enter here what model modifications are envisioned, and the file name and location of the model that incorporates those revisions.

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Equally important to recording evaluative remarks that fit within the task at hand is to enter comments that are relevant to the model but which fall outside a defined task. To see a potentially new use for an antenna type is significant, even if not within the scope of work.

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Printing

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The utility of the CM lines as a basic data storage medium can be lost if we only save the model file and never refer to it again. Therefore, my practice has been to print a copy of the model file and include it in the sheaf of papers recording output data. This practice requires attention to the provisions of the modeling program used. In EZNEC, one may print the comments from one screen and print an antenna model description from another. NEC-Win Pro permits saving a model in .NEC format, and thus printing can be a single step. Generic NEC programs would use the input file as the basis for printing.

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Very often, printing the input file can save reams of paper often necessary to print the NEC output file. A number of programs permit one to print selected sections of the output file and thus avoid having to waste paper on portions of the NEC output file that serve little function relative to an assigned task. Of course, in very large models, the input file itself may run to many pages, especially if one does not take legitimate short-cuts. For example, a 200-wire model with all wires having identical material loads (type LD5) requires in many set-ups an extra 200 lines of LD entries. We may truncate these to a single line using techniques spelled out in the NEC manuals. (Not all programs permit conversion of LD5 lines into a single line, while others permit only a single material load entry for an entire antenna structure.)

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We have explored one systematic way of using the CM lines as an aid to modeling. The system shown is one that suits a specific modeler, namely, me. It may require anywhere from minor to major revision to be suitable to some other modeler. In a departmental setting, I can imagine the situation devolving into a series of interminable meetings trying to decide the best set of categories for everyone involved in the modeling enterprise. One can only hope that simple rationality will prevail over modern group dynamics.

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Nevertheless, the sample system that we have explored does demonstrate that the CM lines represent a resource that we can too easily overlook. If these notes make you aware of the potential for these lines, then they will have done their work.

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58. Some Basic Guideline Graphics for NEC

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L. B. Cebik, W4RNL

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Over the years since I started this column, I have had requests for a listing of basic guidelines and limits applicable to NEC. I have had occasion to create some presentation graphics covering some of this information, and I shall present them in this column.

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The .GIF graphics can be extracted from the text and placed in a Word or Word Perfect document, one per page at full paper width. Then the result may be printed or saved. Only the ones useful to you should be extracted. As well, you may run them through a graphic program. such as Paint Shop Pro or equivalent, for printing--and even revising to suit your specific needs. Alternatively, you may take notes on aspects of NEC limitations and guidelines as they apply to your projected modeling work.

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The set of graphics is neither comprehensive nor complete in detail. Most of the sheets are taken from the NEC-2 manual, but apply also generally to NEC-4. The key exception is the fact that NEC-4 permits wires underground, with rules for the penetration of a wire into the ground. Fig. 7 below covers the NEC-4 situation in an example of a monopole with buried radials.

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Since the graphics themselves contain the text, little commentary is required. Actually, each graphic requires a full column of commentary, but that has mostly appeared in past columns.

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For fuller information, there are several useful sources. Of course, the NEC-2 and NEC-4 user manuals are the primary sources. For modeling with NEC-2, Basic Antenna Modeling: A Hands-On Tutorial As well, ARRL offers an on-line course in modeling with NEC-2. Both of these latter sources offer exercise model files.

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Fig. 1: Some Absolute NEC Limits for Wires and Segmentation: Although few MF and HF models will approach these limitations, they become especially important in the modeling of antennas for VHF and upward, where the anticipated element diameter may become a very appreciable fraction of a wavelength. See column #3 for more information on NEC limitations.

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Fig. 2: Some Conservative Wire and Segmentation Recommendations for Newer Modelers: The experienced modeler may safely by-pass these recommendations, although most models should remain within these guidelines in order to achieve an AGT (Average Gain Test) value that is close to ideal. See Fig. 11 for further information on the AGT.

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Fig. 3: Some Modeling Practices to Embrace: Not all good practices appear in this brief set of guidelines, but the listed suggestions may help you develop your own extended list of good practices. Good practices do not ensure a good model, but they do help to eliminate oversights that seem to defy detection once the full model is complete.

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Fig. 4: Some Modeling Practices to Avoid: As with the list of good practices, this list of practices to avoid is incomplete, but a potential foundation for a user-specific list of things to avoid. Some practices, such as using a stepped-diameter element, have correction features in some implementations of NEC-2. NEC-4 has overcome much of the inaccuracy involved in stepped diameter elements, but AGT values for large diameter changes may still be disappointing. The remaining practices to avoid apply equally to NEC-2 and NEC-4, with the exception of the ground warning, which applies to NEC-2 only.

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Fig. 5: Limits for Wires Near the Ground: The Sommerfeld-Norton ground calculation system is very accurate for wire very near the ground, and the limits for wire proximity to ground are small. However, a ground radial system very near the ground in NEC-2 provides only a crude indication of the buried ground radial system for which it may substitute and which is available in NEC-4. See column #11 for more on ground radial systems. The increased speed of current-generation PCs has largely made the use of the reflection coefficient method of calculating ground effects irrelevant, since the S-N ground calculations do not significantly slow the calculation process down.

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Fig. 6: Selecting the Right Ground for the Right Job: In NEC-2, a wire (vertical monopole) touching the ground may not yield correct results with either the S-N or the reflection coefficient ground. Hence, resorting to a perfect ground for comparative results between models may be necessary. However, for more accurate results that take into account the properties of the ground, NEC-4 is preferred, since one may directly model a buried ground radial system.

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Fig. 7: NEC-4 Ground Penetration Rules, Using a Vertical Monopole and Radials as a Sample Case: The sample in this figure combines the rules for ground penetration in NEC-4 with an example of element length tapering to avoid adjacent segments that differ too much in length. The method shown uses manual tapering with separate wires for each segment length. However, it is possible to use the GC input to automate the process within sngle wires for each element. Whichever system is used, the source wire and the wire between Z=0 and the junction of the radials should be individual wires to allow for maximum control over the model and to avoid junction errors as one modifies the model. Although the wire penetrating ground may have a segment junction at the required Z=0 point, users achieve maximum model control by making Z=0 a wire junction.

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Fig. 8: Transmission Line (TL) Limitations: As non-radiating elements of the model, transmission lines are subject to many limitations. Where a model requires transmission lines outside regions of high current and low rates of current change, many lines may be modeled using physical (GW) wires. See column #21 and #22 for more on transmission lines.

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Fig. 9: Connections of Loads, Sources, and Transmission Lines on the Same Segment: Applying mutliple loads, sources, and/or transmission lines on a single segment is often a source of confusion. (In addition, some implementations of NEC may permit only a single load and/or a single source on a chosen segment.) See columns #4 and #5 for more on sources. See columns #6, #13-#17, and #46 for more on loads. Since a load is in series with a transmission line, placing a load on the wire used to terminate a transmission line will not place the load in parallel with a source at the near end of the transmission line. One must use the admittance facilties of the TL entry, although these values are not frequency nimble. To obtain a load in parallel with a source that will change reactance as the frequency changes requires other types of work-arounds.

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Fig. 10: The Convergence Test: For a fuller account of the convergence test, see column #1. The convergence test, like the AGT, is a necessary but not a sufficient condition of model adequacy.

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Fig. 11: The Average Gain Test: For a fuller account of the average gain test, see column #20. Since both the convergence test and the average gain test are necessary but not sufficient conditions of model adequacy, they together yield at best a good indication of model adequacy, but not a decisive judgment. The use of experimental results as well as a full evaluation of the model in terms of all program limits remain recommended additional checks on models.

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Converting the AGT number into a value in decibels is simply a matter of 10 times the common log of the AGT value. Use only the AGT value obtained in free-space (or over perfect ground) for lossless wires and no resistive components to any loads in the model. If the source impedance is very close to have no reactance, then the basic AGT value times the reported source resistance value will provide a more correct source resistance value. The positive AGT value in dB may be subtracted from the reported gain value and a negative AGT value in dB may be added to the reported gain value to yield a more nearly correct gain figure for many models.

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There are additional rules and provisions within NEC. There are, as well, numerous very specific situations that might create a problem if not modeled carefully. Nevertheless, I hope this collection of graphics--whether in whole or in part--provides a few handy reminders that help you avoid potential pitfalls.

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59. MININEC and NEC: A Design Case Study

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L. B. Cebik, W4RNL

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In past columns, I have occasion to suggest that, within the limitations of wire antenna modeling as a whole, one should select the program best suited to a design or analysis task. Of course, the generic choices are NEC (-2 or -4) on the one hand, and MININEC on the other. The choice of programs rests on working to the strengths of a core and away from its weaknesses.

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NEC, of course, has the Sommerfeld-Norton ground, and wherever wires with a horizontal far field component must reach below the 0.2 wavelength level, NEC is the obvious selection. The MININEC ground system inflates gain values below the 0.2 wavelength level and only calculates the source impedance based on a perfect ground. Likewise, NEC is the obvious choice for antenna structures involving coaxial or other low-impedance transmission lines. The TL facility creates non-radiating (non-wire geometry) lines that do not add to the segment burden of the model. MININEC lacks this feature.

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NEC-4 improves upon NEC-2 in several ways. First, it can better handle linear elements with stepped diameter schedules than can NEC-2. However, both tend to have access to the Leeson substitute constant diameter element correction feature that has proven very accurate. Still, that feature applies only to linear elements that (when horizontal) meet certain standards with respect to load and transmission-line placement.

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NEC-4 also permits wires underground and is the current default standard for the simulation of buried ground radial system. NEC-4 is also more accurate at mid-VHF frequencies and upward. As well, NEC-4 has improved surface patch facilities and the ability to handle wire permeability, as well as conductivity. The core also accepts insulated sheath and upper medium inputs for greater flexibility in modeling.

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In contrast, MININEC 3.13 (the public domain version) has lost many of its limitations through creative programming. While NEC-2 cores and NEC- 4 cores tend all to yield very similar results within their types, MININEC cores tend to vary in results, depending upon the correctives introduced by the programmer. At present, Antenna Model by Teri Software yields results that most closely correlate with those of NEC-4 over a range of models falling well within the capabilities of both types of programs. See column 51 of this series for a detailed comparison of MININEC programs in current use by many modelers.

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Virtually all Windows implementations of MININEC have lost the DOS-based limitation of 256 segments (or double that number for programs implementing symmetry). As well, MININEC needs no correction factor for stepped-diameter elements. Indeed, the Leeson corrections were initially calibrated against MININEC modeling results. MININEC does require correction factors for very closely spaced elements, for frequencies above about 30 MHz, and for wires forming tight angles. Not all implementations are equally successful in providing such correctives.

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Angular junctions of wires of different diameter form a limitation on NEC that is worse in NEC-2 than in NEC-4. See column #56 in this series for some test cases. I want to return to this type of model to present a design case study. It will reveal some temptations to think that a model is OK, when it may not be. It will also show some ways to tell the difference. Those ways may not all be inherent in the modeling process when we examine that process in isolation.

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A "Large" Triangle Omni-Directional Antenna for 2 Meters

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The search for a horizontally polarized omni-directional antenna has persisted over many years. The triangle came into being in the 1950s and has recently been re-developed by Par Electronics for VHF and UHF use. These triangles are of the "small" variety, and a sample version is included in the AO software package by K6STI. "Small" means that the total circumference is under 0.6 wavelengths, with a feedpoint impedance in the 8-12 Ohm range, with an inductive reactance running from 70 to 170 Ohms, depending upon the exact design. The loop is interrupted and has a gap opposite the feedpoint of about an inch.

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There is also a larger version of the triangle, with a circumference of about 0.75 wavelength. It uses a larger gap--something in the 3-4" range. The benefits of the larger interrupted loop include a feedpoint resistance close to 50 Ohms, but still offset by an inductive reactance in the 350-Ohm range. The disadvantage of the larger loop is about a 0.1 dB gain deficit relative to the small loop, although one would not likely notice that deficit in operation. Both types of triangles tend to surpass the more traditional turnstiled dipole array by about a dB in gain and by achieving a much more circular pattern. Unlike a turnstile, the pattern of which quickly devolves into a distinct oval even when only a small amount off the design frequency, the triangle tends to preserve its nearly perfect omni-directional pattern over it operating bandwidth.

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The design issue facing the triangle builder is supporting the antenna. Ordinarily, one would support the structure at the feedpoint, using a large diameter element for the main arms and thinner material for the legs that extend to the gap. The basic mechanical structure results in a design model that requires two angular junctions of wires having dissimilar diameters. Fig. 1 provides the key dimensional elements of the antenna.

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The overall arm length (dimension A) for the design exercise uses 0.625" (5/8") diameter aluminum. At element diameters used, there is no performance difference among any of the alloys of aluminum. The legs will use 0.1875" (3/16") diameter rods. The model requires us to calculate on the basis of dimension B, but it is simple to move between the arm length (dimension C) and the required coordinates indicated by dimension B.

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The key is to find a set of dimension, including the gap between leg tips, that yields an omni-directional pattern. Only with a tightly designed combination of arm length, leg length, and gap will the array yield a circular polar plot. This requires a balance between the radiation from the arms and the legs. Since the current and the consequential field strength are not constant along the element, a simple symmetrical arrangements, such as an equilateral triangle, will not achieve the goal. The best way to determine the exact element dimensions is by trial-and-error modeling. (Remember that we also must adjust the gap along the way to achieve a 50-Ohm resistance at the feedpoint.)

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The MININEC model of the antenna appears in Fig. 2. The white crosses represent pulses or segment junctions. The arm wire of the model uses and even number of segments to ensure that the source is placed at the exact center of the wire. A fuller description of the model, in AM format, appears at the end of the column.

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The NEC model is shown in Fig. 3. EZNEC Pro/4 is the software I used for this exercise, although any version of NEC-4 would do as well. The models are not distinguishable from the graphic views provided by the software. However, what is apparent is that when a user moves from one software package to another, he or she must become familiar with the graphic conventions used in the current software. The EZNEC antenna view is shifted laterally by 180 degrees relative to the Antenna Model view. With the axes showing, the shift is not problematical.

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The key differences between the models surround the dimension required to obtain as close to a perfectly circular pattern as possible. The MININEC model in AM results in the following values--referenced to Fig. 1. Recall that the arms (A) use 5/8" diameter tubing and the legs (C) use 3/16" rod.

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Dimension        Length in Inches
+  A                22.8
+  B                16.2
+  C                18.9
+ Gap                3.2
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Using these dimensions, the AM model yields a feedpoint impedance of 49.5 + j357.3 Ohms. Eliminating the reactance for a 50-Ohm feedline is an exercise beyond the scope of this modeling study.

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Fig. 4 shows in polar form the free-space E-plane pattern of the resulting antenna. Maximum gain occurs approximately at a 90-degree angle to the line running from the feedpoint through the center of the gap. The antenna feedpoint is to the left, with the gap to the right, with the arms pointing straight up and down relative to the figure plane.

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The maximum free-space gain is 0.72 dBi, with about a 0.2 dB maximum variation in gain around the circle. The gain to the antenna "rear," that is, behind the feedpoint, is slightly higher than the gain in the direction of the gap, although the difference is about 0.1 dB. The rectangular plot on Fig. 5 provides a slightly greater resolution of the pattern variations.

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The pattern centerline from the feedpoint to and through the gap is centered on the X-axis. Note that as we move in either direction away from this center line by about 20 degrees, we reach a double "null" in the pattern at about 0.2 dB down from the maximum or 0-dB line. (The nulls would be more exacting with higher resolution, but -10 dB is the highest resolution permitted by the program.) The double null means that the actual maximum-gain points are not at precise right angles, but further back in the vicinity of 100 degrees off the center line. As a consequence, the radiation in the direction of the feedpoint is only about 0.1 dB down from the maximum gain.

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The NEC-4 model of the same antenna, optimized as closely as possible to a perfectly circular E-plane pattern, results in the following dimensions.

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Dimension        Length in Inches
+  A                23.6
+  B                15.75
+  C                18.75
+ Gap                3.2
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The feedpoint impedance reported by NEC-4 is 53.2 + j 390.4 Ohms.

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The free-space E-plane pattern derived from EZNEC appears in Fig. 6. I have moved data into the polar plot field for easier reference. The data includes in tabular form much of the information that we gleaned from the AM rectangular plot. The maximum reported gain is 0.76 dBi, and the two maximum gain points lie on bearings further to the rear of the antenna, given an orientation identical to the one used with the AM model. Hence, the 0.26-dBi gain deficit in the direction of the gap is halved in the direction of the feedpoint.

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There are two indicators that tell use something about which of the two models is the more accurate. First, NEC-4 improves upon the performance of NEC-2 with respect to angular junctions of wires having different diameters. The NEC-2 report on the model using NEC-4 dimensions shows a maximum gain of 0.72 dBi and a minimum gain of 0.32 dBi, a variation of 0.4 dB. Second, the reported feedpoint impedance is 57.1 + j 411.7 Ohms. If we are aware in advance of the deficit in accuracy of NEC-2 relative to NEC-4 under the modeling parameters used in this structure, and if we know as well that NEC-4 advances accuracy without attaining full precision, then we have an indication of potential problems with the NEC-4 dimensions.

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The average gain test (AGT), which is available in all three programs used in this case study, provides a means of turning suspicions into a measure of model adequacy. A perfect model would yield an AGT value of 1.0 with the model in free space and using zero-loss wires. The NEC-2 model returns a value of 0.947, while the NEC-4 model shows a value of 0.977. The AM MININEC model returns a value of 0.9955.

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Some charts of AGT values suggest that the range from 0.95 through 1.05 represents very adequate and accurate models, remembering that the AGT is a necessary but not a sufficient condition of model adequacy. (None of the factors that tends to produce models with high AGT values but known inadequacies occur with these models. Many of the model types that show good AGT results but remain inadequate models involve parallel wire structures with essentially self-canceling radiation or inequalities of current on each side of the source position.)

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In essence, the a priori charts recording model quality by reference to AGT values would show that both the AM and NEC-4 models are fully accurate, despite the differences in their dimensions. For some purposes, the charts might be adequate, but in this instance, the precision that we have imposed on the modeling task requires that we use a higher standard. For example, using a contrast between a perfect 1.0 AGT value and a 0.95 values yields more than a 0.22 difference in the gain report, which is as great or greater than the gain variations we have discussed relative to pattern perfection.

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The acid test for the models involves a different exercise, suggested by the fact that the dimensions for the triangle indicated by each program are different. Let's apply these dimensions across programs.

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Fig. 7 shows both the polar and the rectangular E-plane plots for the free-space model using the dimensions developed in the NEC-4 portion of the exercise. The maximum gain of 0.74 dBi is accompanied by an increase in imperfection in the plot that now is approaches 0.3 dB. As well, the maximum and minimum gain positions have now reversed, with minimum gain at right angles to the line running from the feedpoint through the triangle's gap. The reported feedpoint impedance is 50.9 + j 355.2 Ohms. Although the resistive portion of the impedance is only about 2 Ohms different from the NEC-4 report, the inductive reactance shows a 10% difference from the NEC-4 figure.

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For the sake of contrast, the NEC-4 report on the dimensions developed via MININEC appears in Fig. 8. The maximum reported gain is 0.98 dBi and occurs at right angles to the line from the feedpoint through the gap. Minimum gain occurs along the feedpoint-gap line and is least in the direction of the gap. The maximum variation in gain is over 0.5 dB. The reported feedpoint impedance is 51.2 + j 389.1 Ohms. Once more, the resistive component difference is about 2 Ohms. but the difference in reactance approaches 10%. However, the differences are less than those we encountered when running the NEC-4 dimensions on MININEC.

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It is interesting to note that the NEC-4 model using MININEC dimension shows a greater pattern difference but a smaller feedpoint impedance difference than the MININEC model using NEC-4 dimensions. Of greater significance for the modeler are the indications offered by the dimensional changes. If the arms are too long relative to the legs, the pattern distorts along the line from feedpoint to the gap. If the legs are too long relative to the arms, the pattern distorts at roughly right angles to the line.

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Although it may be a bit gratuitous, Fig. 9 shows a 3-dimensional pattern for the triangle when we place it 1 wavelength above real ground, the height that generally corresponds to a mobile installation. Relative to a turnstiled-dipole array, the triangle exhibits higher gain within the lower elevation lobe. This gain is largely the result of a reduction in the gain of the higher-angle lobe. A stack of 2 such triangles with 1/2- wavelength spacing and fed in phase is capable of about 2.4 dB further gain with the lower one at 1 wavelength above ground.

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What, If Anything, Does the Case Study Show?

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The importance of the differences between using NEC-4 and corrected- MININEC for the design of the triangle may vary from insignificance to high import. The weight of the differences depends upon two major factors: the operational parameters assigned to the design effort and the degree to which manufacture can replicate the model.

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If variations of as much as 1 dB in the omni-directional pattern are acceptable, then the differences in the design results make little or no difference. Either program's dimensions will yield a pattern within the assigned specification limit.

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However, if the design specifications call for the least possible variation in the pattern gain, then the higher AGT score of the MININEC model (when derived from an adequately corrected version of MININEC 3.13) yields higher confidence in the dimensions produced by that model. Note, however, that the adequacy of the version of MININEC used must be established in advance.

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A very tight design specification is only relevant where the construction of the actual antenna is capable of replicating the modeled conditions very closely. Every model is subject to differentials between model and reality that result from a manufacturing process and a modeling process that can only approximate each other. The differentials become an ever- growing burden as we model in the VHF and UHF range. Nuts and bolts that make no difference to the HF performance of an array become more appreciable factors at much higher frequencies.

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For a home-brew or garage type assembly, it is likely that the differences between models make no difference at all. For a precision shop with the goal of producing many such antennas with repeatable performance from unit-to-unit, beginning with the most reliable design may be more crucial.

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There are several factors that the models do not show. For example, the models do not show any projections of either the arms or the legs beyond the corresponding portion of the element at the corners. Such projections would be almost inevitable for most proto-types, although one might eliminate them in final production models. Moreover, the models do not show the effects of splitting the feedpoint region of the arms and adding a feedline connector (as well as adding any type of matching components). The fatter the conductor, the greater the capacitance at the feedpoint split. Hence, its dimensions may affect the remnant inductive reactance. As well, feedline connectors and the leads from the connector to the element will also have an affect on the impedance.

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The final factor in the mix involves the ability to test the pattern precisely. The average backyard builder is unlikely to have more than a receiver with an S-meter as a guide to the omni-directionality of the pattern. Chamber tests used by engineering and manufacturing firms are much more likely to uncover small variations in the pattern's circularity.

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For the backyard builder and casual user, then, there is likely to be no discernable difference between antennas built up from each of the models. For the precision shop, the corrected-MININEC model is more likely to yield the better results. What is clear, however, even for the casual modeler and builder, is that the use of NEC-2 is more likely to result in an antenna that falls far short of the desired results. Its ability to handle angular junctions of wires having different diameters falls far short of NEC-4, which the AGT values suggest is still shy of corrected MININEC.

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One last question might arise here: why is the differential between MININEC and NEC models so much less dramatic than the types of case examined in column #56 of this series? The answer is straightforward. The greater the differential of wire diameters at the junction, the greater the error level in NEC. The differential between wires in this design exercise is 2:1. In column #56, the differential was 6.2:1. In that exercise, it was clear that the NEC models were seriously deficient. In this exercise, we have been working with borderline differences the weight of which depends upon factors external to the modeling process itself. Clear deficiencies show themselves vividly once we know what to look for. However, the borderline cases are less self-evident. It is important to understand the borderline cases and what is involved in their evaluation. That has been part of the design case study.

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+=================================================================================================
+                                 ANTENNA MODEL
+                   Copyright (C) 1992-2002 Teri Software Co.
+                   05-04-2002                        3:39 PM
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+                            Antenna File: il6fs.def
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+                  2-meter interrupted loop hor. pol. antenna
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+                                  Free Space
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+               Lowest Frequency of Operation: 144.0000 megahertz
+               Center Frequency of Operation: 144.5000 megahertz
+              Highest Frequency of Operation: 145.0000 megahertz
+
+             Dimensions below are in inches unless otherwise noted
+
+Wire Statements
+
+                  End Coordinates, Wire #1             Wire
+               X             Y             Z         Diameter      Segments     Material
+
+  End 1:   0.000000     -11.40000      0.000000      0.625000         16        6063-T832
+  End 2:   0.000000      11.40000      0.000000                                 Alloy
+
+                  End Coordinates, Wire #2             Wire
+               X             Y             Z         Diameter      Segments     Material
+
+  End 1:   16.20000     -1.600000      0.000000      0.187500          8        6063-T832
+  End 2:   0.000000     -11.40000      0.000000                                 Alloy
+
+                  End Coordinates, Wire #3             Wire
+               X             Y             Z         Diameter      Segments     Material
+
+  End 1:   0.000000      11.40000      0.000000      0.187500          8        6063-T832
+  End 2:   16.20000      1.600000      0.000000                                 Alloy
+
+  Approximate near-field/far-field boundary is 3.55210 meters or 1.71211 wavelengths
+
+Source Statements
+     Source #1
+                 Pulse               Voltage             Phase
+                  No.                (Volts)             (Deg)
+
+                    8                1.00000            0.00000
+
+=================================================================================================
+EZNEC/4 ver. 3.0
+
+2-m large triangle 144.5 MHz                                               5/4/02     3:44:58 PM
+
+                       --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 144.5 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1          W3E2        0,  -11.8,      0      W2E1        0,   11.8,      0     0.625   17
+2          W1E2        0,   11.8,      0              15.75,    1.6,      0    0.1875    8
+3                  15.75,   -1.6,      0      W1E1        0,  -11.8,      0    0.1875    8
+
+Total Segments: 57
+
+                             -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       1        50.00      50.00    12       1           0         I
+
+                        -------------- LOADS (RLC Type) --------------
+
+Load     Specified Pos.     Actual Pos.         R          L          C       R Freq    Type
+       Wire #  % From E1  % From E1  Seg      (ohms)      (uH)       (pF)      (MHz)
+1       1        50.00      50.00    12       Short      Short      2.82415    0        Ser
+
+No transmission lines specified
+
+Ground type is Free Space
+=================================================================================================
+
+ +

+

Go to Main Index

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+

6. Modeling Loads: What Kind, How Much, and Where?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Both NEC and MININEC permit you to add "loads" to the antenna at virtually any point along the wires composing the model. Loads are simply reactances (and associated loss resistances) inserted into the antenna to change its characteristics. +

Let's look at loading in several steps, beginning with real-life loads, moving to model loads, and finally applying what we discussed last time (with respect to sources) to place the loads properly in our models.

+

Loads and Their Applications

Figure 1 suggests several applications for loads. What they have in common is that capacitively reactive loads make an antenna element electrically shorter than it is without the load and inductively reactive loads make the antenna element electrically longer than it is without the load. +
+ +
+

We often find inductive loads used to shorten linear antenna elements. We place coils along a dipole anywhere from the center outward. Once we pass about the 50-60% point outward along the element, the coils of wire act more like lengths of wire than as inductors with reactance. Hence, we cannot model element end-loading with reactive loads, but must find a way to model those antenna extensions with wires.

+

An alternative to the use of coiled or solenoid inductors is the use of parallel transmission line as the inductive loading element. A shorted transmission line less than 1/4 wavelength long will have an inductive reactance that is a function of the length of line and its characteristic impedance. Its characteristic impedance is a function of the wire diameter and spacing. Standard antenna references have the right equations (as does the HAMCALC collection by VE3ERP).

+

Every inductive load has a Q, a ratio of reactance to resistance (in the wire). Standard coils used in antennas have Qs that run from about 100 to 300 (with some specially made coils running higher), while parallel transmission line loads (also called linear loading) general have a Q of over 1000. These numbers will have high interest for us in modeling.

+

Capacitive loading is less used, since there are fewer cases in which we want to make an antenna physically long and then shorten it. One application is fine tuning the reflector of a quad beam. Capacitive loading is often easier to adjust than the inductive loads on short reflector loops. The Q of capacitors at HF is usually high enough that modelers ignore the resistive losses.

+

Coil losses are predominantly series resistance losses, so we can think of the coil as a resistor and an inductor (or inductive reactance in series). Capacitor losses tend to be in the form of parallel resistance across the capacitance (or capacitive reactance). Figure 2 shows the basic schematic forms that we need to keep in mind as we model loads.

+
+ +
+

Modeling Loads

In an antenna model, loads are not physical structures. They are mathematical elements factored into the calculations. If an inductor used as a load in a real antenna has a diameter many times that of the element it is loading, we do not try to model the physical structure. Modeling programs view reactive loads as non-radiating elements. For all practical purposes this is true, although there is always some radiation from the physical structure of a coil, capacitor, or linear loading line. +

Modeling offers three basic ways to model a loading device: as a series circuit composed of a resistance and a reactance (+ for inductive, - for capacitive), as a series circuit composed of a resistor, an inductor and a capacitor (with units in Ohms, Henrys, and Farads), and as a parallel circuit composed of a resistor, an inductor and a capacitor (with units in Ohms, Henrys, and Farads). If you use either of the latter entry modes, and your circuit lacks one of the elements, put a zero in its place. The zero is not a short circuit: instead, the program knows to treat the zero as a missing element. See Figure 3.

+
+ +
+

1. Resistance-Reactance Loads: It is tempting to use the series resistance-reactance mode of loading for single loading elements such as coils and capacitors. In many programs, we have direct access to inserting a series resistance and reactance, but inserting values for inductance and capacitance may be more complex. In many cases, the source impedance gives us clues to the reactance values needed. For example, in a shortened dipole, the reactance at the source point gives us the reactance value for a center-loading coil and approximately the value of each of two coils placed near mid-element.

+

If we know the required reactance for a loading coil, we can derive the series resistance from a measurement or a decent estimate of the coil Q. Never omit the coil resistance. If we need 200 Ohms of inductive reactance and estimate the Q at 200, then the series resistance is 1 Ohm. (As small as it seems, that 1 Ohm does affect antenna performance and needs to be included in the model.) At HF, you may ignore resistance with respect to capacitive reactances.

+

However, the series resistance-reactance load has a limitation. If we check the performance of an antenna across an amateur band, that is, away from the central design frequency, the load resistance and reactance in the model stay the same. Real coils do not act this way. They change their reactance as we change frequency. Therefore, the series resistance- reactance model may give an unrealistic picture of antenna performance.

+

For example, here is a 40-meter dipole with mid-element loads modeled with R-X loads and with R-L-C loads when viewed across the 40-meter band. The load design is a coil of about 12.93 uH, which has a reactance of 581 Ohms at the design frequency of 7.15 MHz. The coil Q is about 166, for a series resistance of 3.5 Ohms.

+ 
Frequency      R + X Load                    R-L-C Load
+ MHz      Source Z       50-Ohm SWR     Source Z       50-Ohm SWR
+ 7.00     45.4-j33.5      2.003         44.3-j50.2      2.791
+ 7.05     46.5-j20.6      1.536         45.7-j32.1      1.945
+ 7.10     47.5-j 7.5      1.177         47.1-j13.6      1.330
+ 7.15     48.5+j 5.6      1.123         48.6+j 5.4      1.119
+ 7.20     49.7+j18.8      1.455         50.2+j24.8      1.634
+ 7.25     50.8+j32.1      1.873         51.8+j44.8      2.352
+ 7.30     52.0+j45.6      2.383         53.6+j65.4      3.299
+
+

Notice the overly optimistic report of the 2:1 VSWR operating bandwidth that the frozen R + X load gives to the antenna. The actual 2:1 VSWR operating bandwidth is not over 250 kHz, but a little over 150 kHz, as reported by using the R-L-C load.

+

2. Series Resistance-Inductance-Capacitance Loads: Simple loads using a single inductor or capacitor can also be modeled in terms of their inductance or capacitance (along with the resistance, as applicable). This is shown in the right-hand columns of our sample table, which used loads inserted in this way. By using values for inductance and capacitance, the program automatically calculates the reactance for each frequency checked, and a more realistic picture of antenna performance emerges.

+

The conversion equations for moving from reactance to inductance/capacitance and back to reactance are well known, but they are so important to modeling loads, that I shall repeat them here for reference. L = inductance in Henrys, XL = inductive reactance in Ohms, C = capacitance in Farads, XC = capacitive reactance in Ohms, R = resistance in Ohms, F = frequency in Hertz, and 6.28 is the value of 2 times PI.

+
    +
  • XL = 6.28 F L----from inductance to inductive reactance
    • +
  • L = XL / (6.28 F)----from inductive reactance to inductance
    • +
  • XC = 1 / (6.28 F C)----from capacitance to capacitive reactance
    • +
  • C = 1 / (6.28 F XC)----from capacitive reactance to capacitance
    • +
+

You will be working in basic units, even though the most common units required by antenna circuits for HF are in terms of microHenrys and picoFarads. Since most modeling programs use engineering notation, get used to expressing 65 picoFarads as 65E-12 and 5.5 microHenrys as 5.5E-6.

+

Suppose you use mid-element loads for a shortened rotatable 40-meter dipole, coming up with a reactance of 510 Ohms for each coil at the mid- band design frequency of 7.15 MHz. The coils have an estimated Q of 200, so we know the series resistance must be 2.55 Ohms. The required value of inductance is 11.4E-6 Henrys. We would enter the series resistance- inductance-capacitance values as 2.55,11.46E-6,0 (with the zero meaning no capacitor). These are entered as a string in some programs or plugged into spaces in a dialog box in other programs.

+

3. Parallel Resistance-Inductance-Capacitance Loads: For most amateur applications, parallel R-L-C loads have one primary use: for antenna traps. A trap is a parallel tuned circuit used to terminate a portion of an antenna element at a particular frequency by placing a high impedance reactance circuit at a particular place along the element, with the circuit acting like an inductive reactance at lower frequencies, where the outer portion of the element comes into play again. Traps are normally tuned to a frequency just below the lower edge of the band for which they function as traps. A 15 meter trap, for example, is normally tuned to about 20.5 to 20.7 MHz or thereabouts.

+

How to calculate the operative values of resistance and reactance of traps for all frequencies of interest in an antenna will be the subject of a future column. For now, let's focus on getting the trap into the antenna as a load on the band for which it is a trap.

+
+ +
+

Figure 4 shows our problem. The trap consists of a coil and a capacitor in parallel, but the coil is actually an inductor and a resistor (for its losses) in series. Let's set the coil Q at 200 and tune the trap to 28.0 MHz. The coil is 1.1 uH and the capacitor is 29.4 pF. By the conversion equations above, we get a reactance of 193.5 Ohms, and using the value of Q, we find the series resistance of the coil to be 0.9675 Ohms. We cannot directly enter these values into a model parallel circuit load because not all of the values are in parallel.

+

Hence, we must convert the series values for the coil reactance and resistance into parallel form. Let RP = equivalent parallel resistance, XP = equivalent parallel reactance, RS = original series resistance, and XS = original series reactance. ^2 means a number is squared.

+
    +
  • RP = (RS^2 + XS^2) / RS
    • +
  • XP = (RS^2 + XS^2) / XS
    • +
+

For our example, summing the squares of RS (.9675) and XS (193.5) gives 37442. Dividing this number by the series resistance gives 39938 as the parallel resistance. Dividing 37442 by the series reactance gives 193.5 as the parallel reactance. Converting 193.5 into an inductance at 28.0 MHz returns a value of 1.1 uH. (The resistance was so small that it nudged the inductive reactance and inductance figures by too small an amount to show--less than 1/2 of 1%. However, the series and parallel equivalents for resistance are very different.)

+

Now we can enter our parallel values for R and L, along with the original value for C, for a parallel R-L-C load as 39938,1.1E-6,29.4E-12.

+

We may use these values at 28 MHz and throughout the 10 meter band. However, if the antenna has an extension for use at 15 or 20 meters, perhaps, the trap will have to be calculated for each of those bands. Although the values for L and C will stand, the fact that the reactance changes for the lower bands means that the equivalent parallel resistance will also change, and that requires a separate set of calculations.

+

Since our aim here is to create loads we can insert into antenna structures, this example will do until we can spend more time on the subject of traps.

+

Placing Loads

There is a fundamental difference in the placement of loads in MININEC and in NEC. If you are only a casual modeler and only want a trap approximately correct in its placement, then you may look at the placement question as being the same for both programs. Create a wire and place the load on the nearest pulse or segment, depending on whether you are using MININEC or NEC. Some programs give you an option of placing the load at a certain percentage along a wire, and this is handy. The exact placement will be on the pulse or segment nearest the one specified. +

However, changing the length of the wire, for example, to bring it to resonance, will change the length of the segments. The load will be moved--slightly or significantly, depending upon the number of segments and hence on the length of each one. Figure 5 shows the problem.

+
+ +
+

For more precise modeling, lets return to separate discussions of MININEC and NEC and see what we can do to set loads more exactly where we want them.

+

1. MININEC: Loads in MININEC go onto pulses, which occur at the junction of segments. This fact tells us more than one thing about loads.

+
+ +
+

First, to place a load precisely, we can create two wires which meet at the load position, as in Figure 6. This maneuver permits us to independently change the length of the wires. For simple loads, such as loading coils, we can vary the length of the outer wire (or outer wires, in the case of a dipole) without moving the load as we fine tune the antenna model for resonance or some other characteristic.

+

If the load is a trap, we can separately change the lengths of the inner wire for 10-meters and the out wire for 15 or 20 meters. Only changes in the length of the inner wire will affect the trap position, which is exactly what we want to do. Changes in the outer wire leave the trap position unaffected.

+

The only caution in the procedure is to makes the segment lengths on each of the wires approximately equal. This is not too critical with MININEC, but it is good practice in all modeling. The procedure we are describing here coincides with the procedures for precisely setting non-centered sources in MININEC.

+

Second, since MININEC loads occur at points along the modeled wire, they have no dimension. Trying to model a bulge in the antenna to account for the load's physical diameter is a largely superfluous effort, given the normal margins of error within modeling. However, if you wish to try it, you will need to create 2 more wires. End the inner wire by 1/2 the length of the load. Create a new wire of this length and the load's diameter. Set the load at the end of this wire. Create a second wire of the same diameter and length, with one end joined to the first new wire. To the second end of this wire connect the old outer end, which has been shortened by 1/2 the length of the load. Be sure that the inner and outer wires are segmented so that all of the segments are now about 1/2 the length of the load, that is, approximately equal in length all along the wires composing the element.

+

In MININEC, there are techniques length-tapering to reduce the total number of segments required, and these are features of ELNEC, AO, and NEC4WIN. Moreover, NEC4WIN can handle the increased segmentation directly. However, in most cases, the exercise will yield no significant improvement in either the analysis of the antenna or in guidance for building a modeled antenna design. Real-world adjustment of the final product will still be required.

+

2. NEC: NEC places a load on a particular segment, and you may view the load as distributed along the segment, even though some modeling program graphics may show the load as a dot in the middle of the segment. In placing the load and structuring our model element, let's be guided by Figure 7.

+
+ +
+

As with our initial attempt to place a load in MININEC, we may use a simple estimate in NEC along a single wire element. Then we simply place the load on the nearest segment to the exact position we may desire. Just as before, if we vary the length of the wire to achieve some antenna characteristics, such as resonance, we inadvertently change the load position slightly with each adjustment. For casual modeling, this procedure may suffice, but it may equally fall far short of the precision we might sometimes require.

+

An alternative is the use of the two-wire system used with MININEC. There is a difference, however. Placing the load on the last segment of the inner wire does not position it at the junction of the wires. Instead, the load will be on the last inner wire segment itself.

+

In most instances, end-of-inner-wire placement will be a correct placement, especially for traps. Traps are a part of the inner wire which they terminate when operated in the trap frequency band. Whether using a simple load or a trap, the placement on the inner wire will lock the load in place. Adjustments on the outer wire will leave the load placement unaffected.

+

As with the MININEC version of the two-wire system, good practice dictates that the segment lengths on the inner wire and the outer wire be approximately equal.

+

You may also use a 3-wire system, placing the load on a separate wire of 1-segment length. Here the segment may simulate the length of the load or trap (with due caution for the segment lengths in adjoining wires). As with the two-wire system, the load is locked in position. The natural tendency will be to use this system in order to set the diameter of the 1-segment loaded wire equal to the diameter of the load. This procedure is not disallowed, but must be used with extreme care. If the element diameter tapering correction does not function when the element has loads or when the diameters do not follow some regular progression, then NEC-2 will give erroneous results. In NEC-4, which does not require the correction system for tapered diameter elements, too large a shift in diameter will require either that a very large number of segments be used to achieve convergence as a test of the reliability of the results--or that convergence may not be achieved. In either case, trying to model the load diameter usually proves to hold more problems than it solves.

+

In the End. . .

For both MININEC and NEC, the 2-wire system of load placement is adequate for almost every modeling situation that may occur with amateur radio antennas. With this settled, the modeler can focus on other important questions surrounding loads. Learn to create series and parallel R-L-C loads in order to go beyond the more restrictive R-X loads--and to use each in its proper place in the development of antenna designs and analyses. Load creation and placement together form a single enterprise that can enrich your modeling work.
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Go to Main Index

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+

60. NVIS Antenna Models and the Ground Type

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+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In past columns, we have noted some of the deficiencies of the systems of ground calculations associated with MININEC and with the fast or reflection coefficient system in NEC (-2 and -4). These two ground calculation systems both use (although not in exactly the same way) a simplified algorithm for the rapid calculation of ground effects on the far field of a signal. The NEC reflection coefficient system also applies the ground calculations to the source impedance calculations. However, MININEC always calculates the source impedance as if the antenna is over perfect ground.

+

The simplified calculation systems for ground effects emerged for various reasons. The original MININEC system had to do its calculations within the restrictions of early desk-top computer systems with as little as 640 KB of RAM. The NEC reflection coefficient system held a speed advantage over a more complete ground analysis system, a strong consideration with large models in the days of CPU speeds below 10 MHz.

+

NEC also incorporates the Sommerfeld-Norton (S-N) ground calculation system, which is the most accurate calculation system available on wire-based antenna simulation packages. While very accurate, it requires considerably more time to execute within a model, relative to the reflection coefficient system. However, for any NEC implementation, modern CPU speeds ranging from 200 MHz to 2 GHz tend to make the extra time required for execution of the S-N system less than significant. Indeed, perhaps the only use remaining for the reflection coefficient system in NEC is to make comparisons among ground effect calculation systems. For a comparison of the mathematical foundations of the various ground systems, the appropriate NEC manuals contain full information.

+

The limitations of the MININEC ground system and the NEC ground reflection system are matters of the height of the antenna wires above ground. Both systems begin to yield inaccurate results when any wire in the antenna system is at or below about 0.2 wavelengths and has any horizontal component to the radiation. Because the error gradually develops as we lower the wire closer to the earth, we may easily overlook it. As well, we cannot mark a clear and distinct point or height at which errors begin. Nonetheless, well below the boundary region, the errors are vivid, if one has some experience with what values are sensible at very low antenna heights.

+

In episode 37 of this series, we performed a small exercise with tilted dipoles with one end very close to the ground. As we tilted the dipole away from the vertical and toward the horizontal, the disparity between MININEC results and NEC-4 S-N results grew in proportion to the horizontal component of the tilted dipole radiation. The S-N system in either NEC-2 or NEC-4 is considered accurate down to several wire radii from the earth's surface.

+

NVIS Antennas and Models

+

Near Vertical Incidence Skywave (NVIS) propagation makes use of the fact that near-vertical signals do not all penetrate the ionospheric layers and disappear into space. Instead, a usable amount of signal is ordinarily reflected or refracted downward. A good brief account of the general parameters of NVIS propagation appears in Jaques d'Avignon, VE3VIA, "The NVIS Propagation Mode and the Ham," The ARRL Antenna Compendium, Vol. 5, pp. 129-134.

+

The most common form of NVIS antenna is a simple wire array placed relatively close to the earth's surface. The antenna types used include dipoles, loops, and in-phase fed pairs of dipoles or folded dipoles. Heights range from a few feet to about 1/4 wavelength. Above that height, the elevation angle of maximum radiation lowers enough to reduce the vertical radiation significantly. The object of a NVIS antenna is to radiate vertically as strongly as possible.

+

Antenna modelers are always interested in how much gain and what feedpoint impedance an antenna has. Hence, curiosity about NVIS antenna models goes back to the early days of MININEC. The models are simple--well within the 256 segment limitation of the original DOS-based MININEC program. Although Windows implementations of MININEC have removed the segmentation limit on models, they have not yet overcome the limitations of the MININEC ground calculation system.

+

Virtually by definition, all NVIS antennas use a height that places horizontal wires below the threshold for accurate results using the MININEC or NEC reflection coefficient ground systems. Hence, it is not out of place to present two modeling rules for NVIS antennas.

+

1. NEVER use MININEC to model a NVIS antenna.

+

2. NEVER use the NEC reflection coefficient ground system to model a NVIS antenna.

+

By default, we are left with a third rule:

+

3. Always use the NEC S-N ground system when modeling NVIS antennas.

+

The question these rules leave us is this: how much error can we expect if we use the "forbidden" ground or modeling systems with a NVIS antenna? Since a NVIS antenna may have wires ranging from virtually at the earth's surface to about 1/4 wavelength above the ground, there is no single answer. However, we can perform a series of exercises to show the growth of the error under varying conditions with various kinds of models. Since this column is finite, we can only sample a few cases. For convenience, all examples will use 3.9 MHz as the operating frequency.

+

A Wire Dipole

+

One common antenna that amateurs press into service for NVIS operations is the simple dipole. Fig. 1 shows the basic outline of a #14 copper wire dipole, cut to 121' for the test frequency.

+
+ +
+

At 3.9 MHz, a wavelength is 252.2', placing a quarter wavelength just below the 70' height mark. We can test the antenna at 10, 30, 50, and 70 feet above ground and compare the results that we get using different ground systems. EZNEC allows one to use NEC-2 (or NEC-4 in the Pro version) with not only the reflection coefficient and S-N systems, but as well with the MININEC ground system. The MININEC ground results correlate extremely well with the same ground system in its MININEC antenna property calculation environment. Therefore, we may conveniently make comparisons among ground system effects of reported antenna properties without leaving a single program.

+

The following table lists the results of modeling our NVIS dipole at the test heights using each of the ground systems.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+MININEC Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                9.40         89                   5 - j 36
+ 30                8.04         90                  30 + j  0
+ 50                6.91         86                  66 + j  9
+ 70                5.90         52                  91 - j  6
+
+NEC Reflection Coefficient Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                1.78         88                  31 - j 35
+ 30                6.15         88                  47 - j  4
+ 50                6.47         86                  72 - j  1
+ 70                6.03         52                  87 - j 15
+
+NEC S-N Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                -.51         88                  53 - j  8
+ 30                5.64         88                  52 - j  4
+ 50                6.40         87                  73 - j  3
+ 70                6.04         52                  87 - j 16
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we model the NVIS dipole using a MININEC ground, we shall draw all of the wrong conclusions. The antenna height for maximum gain appears to be as close to the ground as we can manage and certainly no higher than about 10'. As well, we shall have a very low feedpoint impedance to consider when developing a system to match the antenna to the feedline and the feedline to the equipment.

+

However, even the reflection coefficient system of NEC shows how inaccurate the MININEC ground is under these circumstances. It correctly shows that the optimum height is somewhere around 50' or about 0.2 wavelengths above ground. The S-N system is more dramatic in its results (and more accurate). The gain of the dipole at a 10' height at 3.9 MHz is about 10 dB lower than the MININEC ground illusion. As well, the feedpoint impedance is an easily managed 50 Ohms.

+
+ +
+

Fig. 2 shows the comparative elevation patterns for the dipole at the 4 heights sampled in this modeling test. For NVIS work, the 50' height is closest to the optimum value in terms of radiation directed vertically. At slightly lesser gain, the 30' height is also usable--and, of course, anything between and around these values. The 70' height sacrifices vertical radiation for radiation at a lower angle. The 10' height is simply deficient in gain from any perspective.

+
+ +
+

Fig. 3 shows the azimuth patterns of the dipole with an elevation angle of 60 degrees. Although the gain deficit of the 10' height is clear, perhaps the more important aspect of the azimuth patterns is their oval shape. Even though one thinks about NVIS work in terms of a circular pattern, operating needs in terms of target stations or areas may make an oval pattern more desirable on occasion than a purely circular one.

+

A Wire Loop

+

One technique used to obtain a more circular pattern in NVIS operation is to use a 1 wavelength loop instead of a dipole. Fig. 4 shows the rudiments of such an antenna.

+
+ +
+

The dimensions shown are somewhat arbitrary but close to correct for the 3.9-MHz operating frequency. The diagram shows a side-fed loop, although we might as easily have chosen a feedpoint at the loop corner or anywhere between. The results of comparing ground systems for this antenna at the test heights appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+MININEC Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                10.15        90                   10 + j  8
+ 30                 8.60        90                   58 + j  2
+ 50                 7.48        90                  124 - j  4
+ 70                 6.05        101                 167 - j 45
+
+NEC Reflection Coefficient Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                4.46         90                   36 - j 52
+ 30                7.11         90                   81 - j 16
+ 50                7.17         90                  132 - j 27
+ 70                6.26         101                 158 - j 63
+
+NEC S-N Ground
+Height             Gain         TO angle           Feedpoint Impedance
+(feet)             (dBi)        (degrees)          (R +/- jX Ohms)
+ 10                0.42         90                   95 + j 48
+ 30                6.32         90                   98 - j 12
+ 50                7.04         90                  136 - j 30
+ 70                6.26         102                 158 - j 65
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Once more, the MININEC ground system yields unbelievably optimistic reports of antenna performance at very low heights. The loop gain is reportedly almost 10 dB higher than the same antenna calculated using the S-N system. As well, the feedpoint resistance reported by the MININEC system is about a tenth of the value yielded by the S-N system. Of course, there is a relationship between the errors produced by the MININEC ground system at very low heights. The extremely low source impedance indicates erroneously high current levels that yield a high gain value.

+

Unfortunately, the ground errors cannot show themselves in the average gain test, since this test requires the use of free space (or a perfect ground for ground-mounted monopoles). All of these tests place the NVIS antennas above average ground (conductivity: 0.005 S/m; dielectric constant: 13).

+

The reflection coefficient system in NEC lowers the amount of error for any given low height, but still yields inaccurate results. If we compare the excess gain at 10' with the low feedpoint impedance, relative to the S-N report, we find the same pattern as in the MININEC results. The S-N system finds the best height for the loop to be in the vicinity of 50' at 3.9 MHz or about 0.2 wavelength above ground.

+
+ +
+

The elevation patterns in Fig. 5 show that same general properties as those for the dipole. the 50' height gives us the highest gain straight up of all of the test heights. 50' shows its highest gain somewhat off vertical, and 10' simply yields insufficient gain relative to what it might be at a better height.

+
+ +
+

The azimuth patterns in Fig. 6 reveal that the use of a loop does indeed circularize the pattern compared to the pattern of a dipole. The 60-degree elevation angle applies to these patterns as well as to those of the dipole in Fig. 3. The departure from a circle is a little over 1 dB for heights from 30' to 70', with the stronger directions being in line with the feedpoint.

+

A Dipole and a Low Reflector

+

One type of antenna recommended by some for NVIS service consists of a dipole at about 1/4 wavelength above ground, with a low wire in line with the driven dipole. To simulate this type of antenna, I took the dipole we previously examined, placed it at 70' above average soil, and added a second wire the same length (121') at a height of 5' above ground. Fig. 7 shows the general outline of the model.

+
+ +
+

The results for the antenna appear in the following table, which includes both NEC-2 and NEC-4 reported values and the values for the earlier dipole at 70' without a parasitic wire below it.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+MININEC Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              5.75         52                  92 - j  8
+NEC-2              5.75         53                  92 - j  8
+Dipole only        5.90         52                  91 - j  6
+
+NEC Reflection Coefficient Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              5.67         50                  81 - j 20
+NEC-2              6.22         55                  88 - j 11
+Dipole only        6.03         52                  87 - j 15
+
+NEC S-N Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              6.09         53                  79 - j 11
+NEC-2              6.09         53                  79 - j 11
+Dipole only        6.04         52                  87 - j 16
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In the case of the dipole with its low parasitic reflector, the MININEC results are at odds with the NEC-4 S-N results in showing a lower gain with a higher source impedance. As noted earlier, these error directions are consistent with each other. The reflection coefficient results are interesting insofar as there are more distinct differences between NEC-2 and NEC-4 than for the other two cases.

+
+ +
+

Fig. 8 shows the azimuth and elevation patterns for the array, which are remarkable similar to those for the dipole alone at 70' without the extra wire. The extra wire does little that the average ground beneath the driven element cannot do with respect to the far field radiation pattern or the feedpoint impedance.

+

The tightness of the figures for NEC-2, NEC-4, and the dipole alone in NEC-4 contrast with the somewhat wider span of numbers between the two-and one-wire arrays using a MININEC ground. The differential suggests that even if the driven wire is above the region of inaccuracy for MININEC ground, the almost functionless second wire close to the earth in the array does have an affect on the reported results.

+

A correspodent took me to task for using an example with the reflector wire the same length as the driver wire. So I surveryed the situation by leaving the driver as is and gradually lengthening the reflector wire. The following chart shows the results of the survey.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+NEC-4 S-N Ground:  70' and 5':  Driver 121'
+Refl. Length (ft)  Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+121'               6.09         53                  79 - j 11
+122'               6.14         52                  80 - j 10
+123'               6.18         52                  82 - j 10
+124'               6.20         52                  83 - j  7
+125'               6.21         53                  84 - j 10
+126'               6.21         52                  85 - j 10
+127'               6.21         53                  85 - j 11
+128'               6.21         53                  86 - j 11
+129'               6.20         53                  86 - j 11
+130'               6.20         54                  86 - j 12
+131'               6.19         53                  86 - j 12
+132'               6.19         53                  86 - j 16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The reflector plays a very small role in increasing the gain of the dipole + reflector combination--0.12 dB relative to the initial model and 0.17 dB relative to the dipole alone, as modeled in NEC-4 using the SN ground system. Of course, this survey is in many ways beside the point, which is to compare the performance of modeling software with respect to the ability to adequately model various types of NEVIS arrays when one or more of the wires is close to the ground.

+

A Wire Loop and a Low Reflector

+

I repeated the modeling experiment using the 1 wavelength perimeter wire loop at 70' with a second loop at the 5' level. Fig. 9 shows the general outlines of the model.

+
+ +
+

The following table follows the reflected-dipole format, but with data for the reflected loop.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+MININEC Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              6.90          92                164 - j 34
+NEC-2              6.90          95                164 - j 34
+Loop only          6.05         101                167 - j 45
+
+NEC Reflection Coefficient Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              5.76         108                144 - j 66
+NEC-2              6.50         100                159 - j 57
+Loop only          6.26         101                158 - j 63
+
+NEC S-N Ground:  70' and 5'
+Model              Gain         TO angle           Feedpoint Impedance
+                   (dBi)        (degrees)          (R +/- jX Ohms)
+NEC-4              6.47          97                159 - j 51
+NEC-2              6.47         100                159 - j 51
+Loop only          6.26         102                158 - j 65
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The loop situation shows something significant to modeling: once a source impedance has a relatively high reactive component, the pattern that we have observed of gain moving in one direction while the resistive part of the impedance moves in the other may no longer hold. The MININEC ground model shows excess gain relative to the NEC-4 S-N ground version, but the resistive impedance relationship does not hold. Nevertheless, the considerable size of the low reflector apparently increases the gain above the S-N model by a greater amount than the reflector did with the dipole.

+

The reflection coefficient model again shows significant variations between NEC-2 and NEC-4 core runs of the model. These variations apply both to the gain and to the source impedance. As well, the 8-degree difference in the elevation angle of maximum radiation occasion differences between the far field patterns, although the amount of variation would not likely be measurable in the field.

+
+ +
+

Fig. 10 shows the S-N azimuth and elevation patterns for array with its reflector, patterns that do not differ noticeably from those for the loop alone.

+

Conclusion

+

The lower the wires of a NVIS antenna, the more unreliable will be the results from a model using either a NEC reflection coefficient ground or a MININEC ground. The inaccuracies of the MININEC ground system affect mainly the gain and feedpoint impedance reports, although those errors will also show up in the reported currents on the antenna elements. In some cases, the errors may slightly affect the far field pattern shape, although such distortions will normally be very slight.

+

The level of error becomes very seriously misleading with a MININEC ground in two respects. First, when the wires of a MININEC model are brought below about 0.1 wavelength, the gain increases and the source impedance decreases so that the result is wholly unrealistic. Second, the MININEC ground system error curve is such as to lead the idea that the lowest possible antenna height yields the strongest signal. Even the unreliable reflection coefficient system in NEC more correctly identifies the best height as falling in the region of about 0.2 wavelengths.

+

Those who wish to pursue studies of modeled ground calculation systems and low wires with a horizontal component may use the model descriptions below as starters.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                      EZNEC/4 ver. 3.0
+
+75-meter NVIS dipole                         5/18/02     10:40:54 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 3.9 MHz
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (ft)              End 2     Coord. (ft)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,  -60.5,     50                  0,   60.5,     50       #14   51
+
+Total Segments: 51
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       1        50.00      50.00    26       1           0         V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Real, High-Accuracy
+
+              --------------- MEDIA ---------------
+
+No.    Cond.    Diel. Const.  Height    R Coord.
+       (S/m)                  (ft)      (ft)
+1      0.005     13           0         0
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                      EZNEC/4 ver. 3.0
+
+75-m loop for NVIS                           5/18/02     10:43:12 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 3.9 MHz
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (ft)              End 2     Coord. (ft)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1          W4E2        0,      0,     30      W2E1        0,64.2564,     30       #14   51
+2          W1E2        0,64.2564,     30      W3E1  64.2564,64.2564,     30       #14   51
+3          W2E2  64.2564,64.2564,     30      W4E1  64.2564,      0,     30       #14   51
+4          W3E2  64.2564,      0,     30      W1E1        0,      0,     30       #14   51
+
+Total Segments: 204
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       1        50.00      50.00    26       1           0         I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Real, High-Accuracy
+
+              --------------- MEDIA ---------------
+
+No.    Cond.    Diel. Const.  Height    R Coord.
+       (S/m)                  (ft)      (ft)
+1      0.005     13           0         0
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                      EZNEC/4 ver. 3.0
+
+75-m dipole/parasitic NVIS                   5/18/02     10:42:10 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 3.9 MHz
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (ft)              End 2     Coord. (ft)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,  -60.5,     70                  0,   60.5,     70       #14   51
+2                      0,  -60.5,      5                  0,   60.5,      5       #14   51
+
+Total Segments: 102
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       1        50.00      50.00    26       1           0         V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Real, High-Accuracy
+
+              --------------- MEDIA ---------------
+
+No.    Cond.    Diel. Const.  Height    R Coord.
+       (S/m)                  (ft)      (ft)
+1      0.005     13           0         0
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                      EZNEC/4 ver. 3.0
+
+75-m loop + parasitic NVIS                   5/18/02     10:44:11 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 3.9 MHz
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (ft)              End 2     Coord. (ft)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1          W4E2        0,      0,     70      W2E1        0,64.2564,     70       #14   51
+2          W1E2        0,64.2564,     70      W3E1  64.2564,64.2564,     70       #14   51
+3          W2E2  64.2564,64.2564,     70      W4E1  64.2564,      0,     70       #14   51
+4          W3E2  64.2564,      0,     70      W1E1        0,      0,     70       #14   51
+5          W8E2        0,      0,      5      W6E1        0,64.2564,      5       #14   51
+6          W5E2        0,64.2564,      5      W7E1  64.2564,64.2564,      5       #14   51
+7          W6E2  64.2564,64.2564,      5      W8E1  64.2564,      0,      5       #14   51
+8          W7E2  64.2564,      0,      5      W5E1        0,      0,      5       #14   51
+
+Total Segments: 408
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       1        50.00      50.00    26       1           0         I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Real, High-Accuracy
+
+              --------------- MEDIA ---------------
+
+No.    Cond.    Diel. Const.  Height    R Coord.
+       (S/m)                  (ft)      (ft)
+1      0.005     13           0         0
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +

+

Go to Main Index

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+

61. GM: Coordinate Transformation

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Most NEC-2 readers of this series employ entry level programs, such as EZNEC or NEC-Win Plus. These programs limit the wire inputs available to the user to GW (Wire Geometry), GS (Scale Structure Dimensions), and GE (End Geometry Inputs) for the geometry portion of the model. Moreover, to one degree or another, these lines are invisible, as the user focuses on a wire table, supplemented by a "unit of measure" input. The end result, however, is a standard NEC input file (or its equivalent).

+

Consider a dipole made from AWG #14 (0.0641" diameter) wire set up as a model using +/-7.96' as the length. We shall arbitrarily use 21 segments for the wire and place the voltage source on segment 11 of our one wire. For those who have not read the NEC manual itself, wire numbers are called "tags." The tag number is a convenience, since the program itself will calculate according to absolute segment numbers. Hence, the first segment of wire or tag 3 would have an absolute segment number of 22.

+
+ +
+

Fig. 1 shows the NEC input file for our dipole, taken from NEC-Win Pro. The GW input line specified the coordinates of the wire and the radius in the same unit as the unit of length. Hence, out #14 wire have a radius of 2.67E-3 feet. The GS input provides the scaling factor to translate these values into meters, the basic unit used by NEC. Any input line beyond the GS card that scales for a coordinate, length, or radius dimension must be specified in meters. The GE card ends the geometry section of our simply model.

+

The geometry information from the input file appears in the NEC output file (extension .NOU in NEC-Win Pro). The following lines are extracted from the output file as a point of reference for what is to come.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1    0.00000   -7.96000   30.00000     0.00000    7.96000   30.00000    0.00267     21        1    21       1
+      STRUCTURE SCALED BY FACTOR   0.30480
+
+   GROUND PLANE SPECIFIED.
+
+   TOTAL SEGMENTS USED=   21     NO. SEG. IN A SYMMETRIC CELL=   21     SYMMETRY FLAG=  0
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.00000   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0    1    2      1
+     2    0.00000   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081     1    2    3      1
+     3    0.00000   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081     2    3    4      1
+     4    0.00000   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081     3    4    5      1
+     5    0.00000   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081     4    5    6      1
+     6    0.00000   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081     5    6    7      1
+     7    0.00000   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081     6    7    8      1
+     8    0.00000   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081     7    8    9      1
+     9    0.00000   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081     8    9   10      1
+    10    0.00000   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081     9   10   11      1
+    11    0.00000    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    10   11   12      1
+    12    0.00000    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    11   12   13      1
+    13    0.00000    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    12   13   14      1
+    14    0.00000    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    13   14   15      1
+    15    0.00000    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    14   15   16      1
+    16    0.00000    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    15   16   17      1
+    17    0.00000    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    16   17   18      1
+    18    0.00000    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    17   18   19      1
+    19    0.00000    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    18   19   20      1
+    20    0.00000    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    19   20   21      1
+    21    0.00000    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    20   21    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The structure specification serves as a check on the entries in the input file. The segmentation data provides a listing of the wire segments created by this structure. Although we tend normally to overlook these basic features of the NEC output file, we shall have occasion to make significant use of them before we complete our work.

+

As a further reference, the model--set over average S-N ground--yields a source impedance of 77.4 + j 0.4 Ohms.

+

We have in past columns looked at some supplementary geometry input cards, most notably, the GC input that allows tapering the segment lengths or the radius of the wire. See column #54. These cards are normally available only on more advanced programs, such as NEC-Win Pro (NEC-2) or GNEC (NEC-4). In this episode, we shall examine the basics of using the GM input, labeled in the NEC Manual as "Coordinate Transformation." We shall confine ourselves to NEC-2 because the NEC-4 input equivalent has a few differences relative to its NEC-2 predecessor. The differences result from the fact that NEC-2 restricted itself to 7 floating decimal entry places, while NEC-4 observes no such limit. With 10 floating decimal entry positions in the GM line, it is able to allow the user some finer divisions of the GM work. However, if we become clear on some basic ways in which we can use the NEC-2 entry, we can easily master the NEC-4 counterpart.

+

The GM line is subdivided as follows:

+ 
GM  ITG1  NRPT  ROX  ROY  ROZ  XS  YS  ZS  IMOV
+    I1    I2    F1   F2   F3   F4  F5  F6  F7
+

I1 and I2 are integer entries, and the series, F1 through F7 are floating decimal entries. Not all floating decimal entries necessarily function as the decimal values of one or another parameter. As we shall see, the F7 entry will use the decimal to separate two integers as a means of expanding the number of entries allowed by the line.

+

The meanings of the entries follow from the general functional definition of the GM entry: to translate or rotate a structure with respect to the coordinate system or to generate new structures translated or rotated from the original. In other words, we may set up a structure in very simplified terms relative to the coordinate system and then follow one of two main options. 1. We may move the structure from its starting points to another set of coordinates based either on rotating the structure around one or more of the axes or upon incrementing all X or all Y, or all Z values by a specified amount. 2. We may create a structure identical to the original, but displaced along one or more axes or rotated (or both), leaving the original in its specified position. Of course, with multiple GM cards, we may do both.

+

Within this context, the entries take on the following meanings:

+

ITG1: This entry specifies the tag (wire) number increment to be applied either to the present structure or to the created structure. If we leave everything else in the line at zero, we simply increase the tag numbers by the indicated amount.

+

NRPT: The second integer entry specifies the number of new structures to be generated. If NRPT is zero, then any other instructions apply to the original structure. Since the instructions will either rotate or displace the structure, nothing will remain in its original place. If NRPT is 1 or higher, then the instructions apply to the new structure, and the original structure remains in its original place.

+

ROX, ROY, ROZ: These floating decimal entries specify the angle in degrees through which the structure (new or original, depending on the value of NRPT) will be rotated around the indicated axis. A positive value causes a right-hand rotation. Since rotation is around a specified axis, a set of values displaced from a centered position across a given axis will rotate around the axis, not around the center of the structure.

+

XS, YS, ZS: These entries specify the amount be which the structure is translated or moved along or parallel to a given axis with respect to the coordinate system.

+

Note: The order of operation always begins with rotation in the order X, Y, and Z, followed by translation in the order X, Y, and Z. If you wish to move a structure before rotating it, use two GM entries.

+

IMOV: IMOV uses the decimal point to separate two separate integer fields: IMOV1 and IMOV2. IMOV1 indicates the first tag/wire number to which the instructions apply. IMOV2 indicates the ending tag/wire.

+

Note: I am indebted to Arie Voors for calling my attention to the fact that early versions of the NEC-2 core used ITS for F7, with a seemingly different procedure. Hence, if using a public domain core of unknown vintage, check the applicable edition of the NEC-2 manual for applicable instructions.

+

NEC-4 introduces a refinement to this system of specifying the start and stop tag numbers for the geometry rotation and translation maneuvers within the GM input. Floating decimal entry places 7 through 10 are used to specify individually the start tag and segment numbers and the stop tag and segment numbers.

+

Once we grow familiar with the GM card capabilities, using it gradually becomes second nature. A couple of simple transformations may help us move from just reading the manual to actually using the input line.

+

GM-1: A Simple Rotation and Translation

+

Suppose that we wish to perform two operations on our original dipole. First, we want to rotate the dipole so that it extends along the X-axis rather than as at present along the Y-axis. This maneuver requires a 90-degree rotation around the Z-axis, since the antenna is centered at 0, 0, 0 on the coordinate system.

+

Second, suppose that we wish to change the antenna height by 10'. This move requires a translation of +10 feet along the Z-axis.

+

Before we make a move to create a GM line, we should ask whether the order of operations will make a difference to the outcome. Without our center dipole, we determine that the order of operations will not affect the outcome. Therefore, we may use a single GM card. It will have the general appearance of the following line:

+ 
GM   0     0     0    0    90   0   0  10   0
+GM  ITG1  NRPT  ROX  ROY  ROZ  XS  YS  ZS  IMOV
+    I1    I2    F1   F2   F3   F4  F5  F6  F7
+

I have adjusted the entry spacing so that I can repeat the identification of the entries below the actual GM line that we would type to show clearly that we are rotating around the Z-axis (ROZ) and translating along the Z-axis (ZS). The combination of the integer entries and IMOV specify that the operations will not create a new structure, but will involve the entirety of the existing structure.

+
+ +
+

Some implementations of NEC-2 offer line-aides, that is, windows that permit the user to enter data without concern for the spacing and separation of the entries in the final line. Fig. 2 shows the NEC-Win Pro GM window, with our data entered. When we OK the window, it creates the desired line in our model, which appears in its entirety in Fig. 3.

+
+ +
+

Note that the only difference between this model and the one we used earlier is the insertion of the GM line. since the GM line appears before the GS (scaling) line, we enter the desired translation moves in the same units as we used for the GW or wire line. In this case, we are using feet. (Getting used to the requisite scaling factors shown in the GS line provides the necessary data to determine what the unit of measure is in the GW line, since the scaling factor will always be the value necessary to translate the GW units into meters.)

+

To see what actually happened to our model, we must refer to the NEC output file. The following extracts give us the information, especially when we compare this data to the data for the original model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1    0.00000   -7.96000   30.00000     0.00000    7.96000   30.00000    0.00267     21        1    21       1
+      THE STRUCTURE HAS BEEN MOVED, MOVE DATA CARD IS -
+        0    0   0.00000   0.00000  90.00000   0.00000   0.00000  10.00000   0.00000
+       GM command acting on tag #'s            0 through            0
+  inclusive.
+      STRUCTURE SCALED BY FACTOR   0.30480
+
+   GROUND PLANE SPECIFIED.
+
+   WHERE WIRE ENDS TOUCH GROUND, CURRENT WILL BE INTERPOLATED TO IMAGE
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    2.31067    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     0    1    2      1
+     2    2.07961    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     1    2    3      1
+     3    1.84854    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     2    3    4      1
+     4    1.61747    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     3    4    5      1
+     5    1.38640    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     4    5    6      1
+     6    1.15534    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     5    6    7      1
+     7    0.92427    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     6    7    8      1
+     8    0.69320    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     7    8    9      1
+     9    0.46213    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     8    9   10      1
+    10    0.23107    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081     9   10   11      1
+    11    0.00000    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    10   11   12      1
+    12   -0.23107    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    11   12   13      1
+    13   -0.46213    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    12   13   14      1
+    14   -0.69320    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    13   14   15      1
+    15   -0.92427    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    14   15   16      1
+    16   -1.15534    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    15   16   17      1
+    17   -1.38640    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    16   17   18      1
+    18   -1.61747    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    17   18   19      1
+    19   -1.84854    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    18   19   20      1
+    20   -2.07961    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    19   20   21      1
+    21   -2.31067    0.00000   12.19200    0.23107    0.00000-180.00000   0.00081    20   21    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

There are a few items in the extract worth noting. First, the input structure specifications simply note the presence and parameters of the GM input but do not alter the original line in this section of the report. Instead, the transformations appear in the segmentation data that follows.

+

Second, we note that the values that formerly were in the Y-column of the original model are now in the X-column. However, note that the segment-1 value is positive, whereas it had been negative in the initial model. Had we needed to specify a negative value for segment-1, then we would have entered -90 under ROZ. The difference makes no difference for this simple file. However, with more complex structures, it might make a difference. Hence, growing accustomed to the conventions governing the rotation entries and their consequences is important.

+

Third, our original model showed Z-values of 9.144 (meters). The new Z-value is 12.192 m or 3.048 meters higher than the original model, that is, 10'. The segmentation data this provides confirmation that our GM entry has indeed done what we intended to request.

+

For reference, the output report returns a source impedance of 72.9 + j 9.1 Ohms. This value is sensible in light of the 1/3 wavelength by which we increased the antenna height above average ground.

+

Translating a structure has many rationales. With the GM line, we may revise the height of the antenna with a single numerical revision. Although this does not represent much of a saving for our simple dipole, it certainly might shorten the work of evaluating a 5-band 4-element quad (80 wires) at a series of heights above ground. Similarly, the rotation might not seem significant for the dipole. However, suppose that we had a stack of two Yagis and wished to evaluate the influence of one upon the other at different and divergent angles of orientation. We can use the GM line to rotate one of the Yagis by any angle whatsoever--and change that angle by simply altering one entry within the line. We may also rotate an antenna along its bore sight (assuming that it is centered on an axis) in order to evaluate the antenna's performance over ground when both horizontally and vertically polarized. If we have an array of 4 long-boom Yagis for weak-signal use, we may alter the spacing among them to obtain the best results using GM entries. As well, we can change from a flat square to a diamond arrangement by rotating the arrays about a common center line. These are but a few of the potential applications for rotating and translating part or all of a wire structure using the GM entry.

+

GM-2: A Simple Replication Example

+

We may also use the GM entry to replicate wire structures without further GW lines in the input model. Let's try a simple case: we shall replicate our dipole 3 more times at 16' intervals from the original model. We might do such things to create phased arrays or for any number of other reasons.

+
+ +
+

Fig. 4 shows the help screen. We have chosen to create 3 new complete structures and to translate each of them by an interval of 16 (feet) along the X-axis. When we OK this screen, we obtain the input model shown in Fig. 5.

+
+ +
+

The only difference between this model file and the one for the original dipole is the GM line. In this case, we are leaving the original structure intact and creating 3 additional structures, each one a dipole having the same dimensions and wire radius. A view of the total wire structure appears in Fig. 6.

+
+ +
+

If we look at the NEC output file, we obtain the following extract of data.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1    0.00000   -7.96000   30.00000     0.00000    7.96000   30.00000    0.00267     21        1    21       1
+      THE STRUCTURE HAS BEEN MOVED, MOVE DATA CARD IS -
+        0    3   0.00000   0.00000   0.00000  16.00000   0.00000   0.00000   0.00000
+       GM command acting on tag #'s            0 through            0
+  inclusive.
+      STRUCTURE SCALED BY FACTOR   0.30480
+
+   GROUND PLANE SPECIFIED.
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.00000   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0    1    2      1
+     2    0.00000   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081     1    2    3      1
+     3    0.00000   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081     2    3    4      1
+     4    0.00000   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081     3    4    5      1
+     5    0.00000   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081     4    5    6      1
+     6    0.00000   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081     5    6    7      1
+     7    0.00000   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081     6    7    8      1
+     8    0.00000   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081     7    8    9      1
+     9    0.00000   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081     8    9   10      1
+    10    0.00000   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081     9   10   11      1
+    11    0.00000    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    10   11   12      1
+    12    0.00000    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    11   12   13      1
+    13    0.00000    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    12   13   14      1
+    14    0.00000    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    13   14   15      1
+    15    0.00000    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    14   15   16      1
+    16    0.00000    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    15   16   17      1
+    17    0.00000    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    16   17   18      1
+    18    0.00000    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    17   18   19      1
+    19    0.00000    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    18   19   20      1
+    20    0.00000    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    19   20   21      1
+    21    0.00000    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    20   21    0      1
+    22    4.87680   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   22   23      1
+    23    4.87680   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    22   23   24      1
+    24    4.87680   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    23   24   25      1
+    25    4.87680   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    24   25   26      1
+    26    4.87680   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    25   26   27      1
+    27    4.87680   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    26   27   28      1
+    28    4.87680   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    27   28   29      1
+    29    4.87680   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    28   29   30      1
+    30    4.87680   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    29   30   31      1
+    31    4.87680   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    30   31   32      1
+    32    4.87680    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    31   32   33      1
+    33    4.87680    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    32   33   34      1
+    34    4.87680    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    33   34   35      1
+    35    4.87680    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    34   35   36      1
+    36    4.87680    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    35   36   37      1
+    37    4.87680    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    36   37   38      1
+    38    4.87680    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    37   38   39      1
+    39    4.87680    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    38   39   40      1
+    40    4.87680    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    39   40   41      1
+    41    4.87680    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    40   41   42      1
+    42    4.87680    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    41   42    0      1
+    43    9.75360   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   43   44      1
+    44    9.75360   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    43   44   45      1
+    45    9.75360   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    44   45   46      1
+    46    9.75360   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    45   46   47      1
+    47    9.75360   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    46   47   48      1
+    48    9.75360   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    47   48   49      1
+    49    9.75360   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    48   49   50      1
+    50    9.75360   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    49   50   51      1
+    51    9.75360   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    50   51   52      1
+    52    9.75360   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    51   52   53      1
+    53    9.75360    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    52   53   54      1
+    54    9.75360    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    53   54   55      1
+    55    9.75360    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    54   55   56      1
+    56    9.75360    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    55   56   57      1
+    57    9.75360    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    56   57   58      1
+    58    9.75360    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    57   58   59      1
+    59    9.75360    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    58   59   60      1
+    60    9.75360    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    59   60   61      1
+    61    9.75360    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    60   61   62      1
+    62    9.75360    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    61   62   63      1
+    63    9.75360    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    62   63    0      1
+    64   14.63040   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   64   65      1
+    65   14.63040   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    64   65   66      1
+    66   14.63040   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    65   66   67      1
+    67   14.63040   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    66   67   68      1
+    68   14.63040   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    67   68   69      1
+    69   14.63040   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    68   69   70      1
+    70   14.63040   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    69   70   71      1
+    71   14.63040   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    70   71   72      1
+    72   14.63040   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    71   72   73      1
+    73   14.63040   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    72   73   74      1
+    74   14.63040    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    73   74   75      1
+    75   14.63040    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    74   75   76      1
+    76   14.63040    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    75   76   77      1
+    77   14.63040    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    76   77   78      1
+    78   14.63040    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    77   78   79      1
+    79   14.63040    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    78   79   80      1
+    80   14.63040    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    79   80   81      1
+    81   14.63040    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    80   81   82      1
+    82   14.63040    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    81   82   83      1
+    83   14.63040    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    82   83   84      1
+    84   14.63040    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    83   84    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We easily note that the structure replicates itself along the Y-axis, but at 4.8768 m (16') intervals along the X-axis. If we run this model, we obtain a source impedance of 89.7 - j 11.1 Ohms.

+

We have possibly forgotten something, especially if we intended to make the total structure into a phased array of 4 dipoles fed in phase. Our model in Fig. 5 showed a single source (EX line). The GM entry replicates only the wire structure. It does NOT replicate any sources or loads applied to that structure. Let's correct part of that situation, as shown in Fig. 7.

+
+ +
+

The model now contains 4 sources or EX entries, each a voltage source having the same magnitude and phase angle. We may use the antenna view function to check on the placement of the sources, as shown in Fig. 8.

+
+ +
+

Note that we did not revise the LD line. Therefore, only the original structure is copper and has that less-than-perfect conductivity. The new wires have perfect conductivity. Therefore, when we run this model, we should not expect perfect symmetry among the source values. Indeed, we obtain the following values for sources 1-4:

+
    +
  • 1. 69.7 - 33.9 Ohms
    • +
  • 2. 50.7 - 49.8 Ohms
    • +
  • 3. 50.4 - 50.0 Ohms
    • +
  • 4. 69.0 - 34.1 Ohms
    • +
+

The model has another peculiarity. We did not increment the tag number for each new structure. Therefore, the segmentation data shows a "1" for the tag number throughout. This result has several implications.

+

First, there is a difference between a tag number and a wire number. The two are the same only when, after all operations in the geometry section, there is a different tag number for each length of wire having open ends of junctions with other wires in the model. Many geometry input cards use a single tag number for a collection of wires that, if we had entered each one separately, they would have had different tag numbers. The GC, GH, and GA inputs are typical. The equation of tag and wire numbers applies only if all wires are GW entries.

+

Second, we might have specified copper conductivity for all wires by a simple revision of the LD5 entry. Instead of ending the load at segment 21 (in Fig. 7), we could have specified segment 84.

+

The loading specification just noted would not work had we replicated the dipole with an increment in the tag number. See Fig. 9.

+
+ +
+

The help screen in Fig. 9 is identical to the one in Fig. 4 with one exception. Note that the Tag Number Increment is now 1 (rather than zero). The result of this change appears in the GM line in the model shown in Fig. 10.

+
+ +
+

For simplicity, I have left the LD5 entry as it was. Thus the only change required in addition to the GM line is a re-specification of the positions of the sources in the EX entries. Each one now specifies the same segment number, but for different wire/tag numbers. The antenna view would be identical to the one shown in Fig. 8, which serves as a quick check in advance of running the model. Once we do run the model, we come up with the following data extract.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1    0.00000   -7.96000   30.00000     0.00000    7.96000   30.00000    0.00267     21        1    21       1
+      THE STRUCTURE HAS BEEN MOVED, MOVE DATA CARD IS -
+        0    3   0.00000   0.00000   0.00000  16.00000   0.00000   0.00000   0.00000
+       GM command acting on tag #'s            0 through            0
+  inclusive.
+      STRUCTURE SCALED BY FACTOR   0.30480
+
+   GROUND PLANE SPECIFIED.
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.00000   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0    1    2      1
+     2    0.00000   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081     1    2    3      1
+     3    0.00000   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081     2    3    4      1
+     4    0.00000   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081     3    4    5      1
+     5    0.00000   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081     4    5    6      1
+     6    0.00000   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081     5    6    7      1
+     7    0.00000   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081     6    7    8      1
+     8    0.00000   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081     7    8    9      1
+     9    0.00000   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081     8    9   10      1
+    10    0.00000   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081     9   10   11      1
+    11    0.00000    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    10   11   12      1
+    12    0.00000    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    11   12   13      1
+    13    0.00000    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    12   13   14      1
+    14    0.00000    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    13   14   15      1
+    15    0.00000    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    14   15   16      1
+    16    0.00000    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    15   16   17      1
+    17    0.00000    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    16   17   18      1
+    18    0.00000    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    17   18   19      1
+    19    0.00000    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    18   19   20      1
+    20    0.00000    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    19   20   21      1
+    21    0.00000    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    20   21    0      1
+    22    4.87680   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   22   23      1
+    23    4.87680   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    22   23   24      1
+    24    4.87680   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    23   24   25      1
+    25    4.87680   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    24   25   26      1
+    26    4.87680   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    25   26   27      1
+    27    4.87680   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    26   27   28      1
+    28    4.87680   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    27   28   29      1
+    29    4.87680   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    28   29   30      1
+    30    4.87680   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    29   30   31      1
+    31    4.87680   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    30   31   32      1
+    32    4.87680    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    31   32   33      1
+    33    4.87680    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    32   33   34      1
+    34    4.87680    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    33   34   35      1
+    35    4.87680    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    34   35   36      1
+    36    4.87680    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    35   36   37      1
+    37    4.87680    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    36   37   38      1
+    38    4.87680    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    37   38   39      1
+    39    4.87680    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    38   39   40      1
+    40    4.87680    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    39   40   41      1
+    41    4.87680    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    40   41   42      1
+    42    4.87680    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    41   42    0      1
+    43    9.75360   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   43   44      1
+    44    9.75360   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    43   44   45      1
+    45    9.75360   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    44   45   46      1
+    46    9.75360   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    45   46   47      1
+    47    9.75360   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    46   47   48      1
+    48    9.75360   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    47   48   49      1
+    49    9.75360   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    48   49   50      1
+    50    9.75360   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    49   50   51      1
+    51    9.75360   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    50   51   52      1
+    52    9.75360   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    51   52   53      1
+    53    9.75360    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    52   53   54      1
+    54    9.75360    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    53   54   55      1
+    55    9.75360    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    54   55   56      1
+    56    9.75360    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    55   56   57      1
+    57    9.75360    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    56   57   58      1
+    58    9.75360    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    57   58   59      1
+    59    9.75360    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    58   59   60      1
+    60    9.75360    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    59   60   61      1
+    61    9.75360    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    60   61   62      1
+    62    9.75360    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    61   62   63      1
+    63    9.75360    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    62   63    0      1
+    64   14.63040   -2.31067    9.14400    0.23107    0.00000  90.00000   0.00081     0   64   65      1
+    65   14.63040   -2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    64   65   66      1
+    66   14.63040   -1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    65   66   67      1
+    67   14.63040   -1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    66   67   68      1
+    68   14.63040   -1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    67   68   69      1
+    69   14.63040   -1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    68   69   70      1
+    70   14.63040   -0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    69   70   71      1
+    71   14.63040   -0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    70   71   72      1
+    72   14.63040   -0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    71   72   73      1
+    73   14.63040   -0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    72   73   74      1
+    74   14.63040    0.00000    9.14400    0.23107    0.00000  90.00000   0.00081    73   74   75      1
+    75   14.63040    0.23107    9.14400    0.23107    0.00000  90.00000   0.00081    74   75   76      1
+    76   14.63040    0.46213    9.14400    0.23107    0.00000  90.00000   0.00081    75   76   77      1
+    77   14.63040    0.69320    9.14400    0.23107    0.00000  90.00000   0.00081    76   77   78      1
+    78   14.63040    0.92427    9.14400    0.23107    0.00000  90.00000   0.00081    77   78   79      1
+    79   14.63040    1.15534    9.14400    0.23107    0.00000  90.00000   0.00081    78   79   80      1
+    80   14.63040    1.38640    9.14400    0.23107    0.00000  90.00000   0.00081    79   80   81      1
+    81   14.63040    1.61747    9.14400    0.23107    0.00000  90.00000   0.00081    80   81   82      1
+    82   14.63040    1.84854    9.14400    0.23107    0.00000  90.00000   0.00081    81   82   83      1
+    83   14.63040    2.07961    9.14400    0.23107    0.00000  90.00000   0.00081    82   83   84      1
+    84   14.63040    2.31067    9.14400    0.23107    0.00000  90.00000   0.00081    83   84    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The tag numbers increment according to the GM-line instruction. Otherwise, the structure and segmentation data is identical to the preceding model. So, too, is the source data for sources 1 through 4. Incrementing the tag number is useful, but not always necessary to obtain correct results from the model using a GM entry.

+

These simple models function only to acquaint the new modeler with the facilities of the GM entry. Many more applications are possible. We can create a cube with a single wire and then a least-necessary number of GM lines. What we can do to a cube, we can also do to virtually any geometric shape that we simulate with straight lines.

+

The exercise has also aimed at revealing a few cautions about the use of the GM facility, especially with respect to control inputs, such as EX and LD, that we may have to replicate along with the geometry structure.

+

In the final analysis, how useful the GM entry is may depend upon the imagination of the modeler. However, we should remember that each wire created by a GM entry is in fact a wire that participates in the matrix calculations. We may save a considerable amount of modeling time with the GM card, but we do not effect a savings in the calculation time.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod62-1.gif b/content/amod/amod62-1.gif new file mode 100644 index 0000000..0a17204 Binary files /dev/null and b/content/amod/amod62-1.gif differ diff --git a/content/amod/amod62-2.gif b/content/amod/amod62-2.gif new file mode 100644 index 0000000..1a6642f Binary files /dev/null and b/content/amod/amod62-2.gif differ diff --git a/content/amod/amod62-3.gif b/content/amod/amod62-3.gif new file mode 100644 index 0000000..d99710f Binary files /dev/null and b/content/amod/amod62-3.gif differ diff --git a/content/amod/amod62-4.gif b/content/amod/amod62-4.gif new file mode 100644 index 0000000..63810cc Binary files /dev/null and b/content/amod/amod62-4.gif differ diff --git a/content/amod/amod62-5.gif b/content/amod/amod62-5.gif new file mode 100644 index 0000000..c2059bb Binary files /dev/null and b/content/amod/amod62-5.gif differ diff --git a/content/amod/amod62-6.gif b/content/amod/amod62-6.gif new file mode 100644 index 0000000..4c7c5c4 Binary files /dev/null and b/content/amod/amod62-6.gif differ diff --git a/content/amod/amod62.html b/content/amod/amod62.html new file mode 100644 index 0000000..14ae8f8 --- /dev/null +++ b/content/amod/amod62.html @@ -0,0 +1,403 @@ + + + + + GH: Helix-Spiral Specification + + + +
+

62. GH: Helix-Spiral Specification

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In episode 29 of this series, we explored the construction of a model of a helical dipole for 28.5 MHz. The techniques used there combined the model-by-equation facility of NEC-Win Plus with its spreadsheet blocking capabilities to produce the model solely by using the GW (wire geometry) input. In entry level programs, such as EZNEC and NEC-Win Plus, the GW input is the only way to create the individual wires and segments out of which a NEC model emerges.

+

Advanced NEC-2 and NEC-4 programs sacrifice some of the convenience of the spreadsheet functions in order to provide the user with all of the core input capabilities. So we shall examine a new way to create our helical dipole using the GH input--and then combine it with the GM input that we examined in the preceding episode.

+

The Old Helical Dipole

+

If we translate the NEC-Win Plus model into a standard ASCII format .NEC file, we shall obtain the following model:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 28,5-MHz helical dipole
+CM radius 4", length 112", 1t=12"
+CE
+GW 1 3 0 4 0 2 2 3.4641 0.0404331
+GW 2 3 2 2 3.4641 4 -2 3.4641 0.0404331
+GW 3 3 4 -2 3.4641 6 -4 0 0.0404331
+GW 4 3 6 -4 0 8 -2 -3.4641 0.0404331
+GW 5 3 8 -2 -3.4641 10 2 -3.4641 0.0404331
+GW 6 3 10 2 -3.4641 12 4 0 0.0404331
+GW 7 3 12 4 0 14 2 3.4641 0.0404331
+GW 8 3 14 2 3.4641 16 -2 3.4641 0.0404331
+GW 9 3 16 -2 3.4641 18 -4 0 0.0404331
+GW 10 3 18 -4 0 20 -2 -3.4641 0.0404331
+GW 11 3 20 -2 -3.4641 22 2 -3.4641 0.0404331
+GW 12 3 22 2 -3.4641 24 4 0 0.0404331
+GW 13 3 24 4 0 26 2 3.4641 0.0404331
+GW 14 3 26 2 3.4641 28 -2 3.4641 0.0404331
+GW 15 3 28 -2 3.4641 30 -4 0 0.0404331
+GW 16 3 30 -4 0 32 -2 -3.4641 0.0404331
+GW 17 3 32 -2 -3.4641 34 2 -3.4641 0.0404331
+GW 18 3 34 2 -3.4641 36 4 0 0.0404331
+GW 19 3 36 4 0 38 2 3.4641 0.0404331
+GW 20 3 38 2 3.4641 40 -2 3.4641 0.0404331
+GW 21 3 40 -2 3.4641 42 -4 0 0.0404331
+GW 22 3 42 -4 0 44 -2 -3.4641 0.0404331
+GW 23 3 44 -2 -3.4641 46 2 -3.4641 0.0404331
+GW 24 3 46 2 -3.4641 48 4 0 0.0404331
+GW 25 3 48 4 0 50 2 3.4641 0.0404331
+GW 26 3 50 2 3.4641 52 -2 3.4641 0.0404331
+GW 27 3 52 -2 3.4641 54 -4 0 0.0404331
+GW 28 3 54 -4 0 56 -2 -3.4641 0.0404331
+GW 29 3 56 -2 -3.4641 58 2 -3.4641 0.0404331
+GW 30 3 58 2 -3.4641 60 4 0 0.0404331
+GW 31 3 60 4 0 62 2 3.4641 0.0404331
+GW 32 3 62 2 3.4641 64 -2 3.4641 0.0404331
+GW 33 3 64 -2 3.4641 66 -4 0 0.0404331
+GW 34 3 66 -4 0 68 -2 -3.4641 0.0404331
+GW 35 3 68 -2 -3.4641 70 2 -3.4641 0.0404331
+GW 36 3 70 2 -3.4641 72 4 0 0.0404331
+GW 37 3 72 4 0 74 2 3.4641 0.0404331
+GW 38 3 74 2 3.4641 76 -2 3.4641 0.0404331
+GW 39 3 76 -2 3.4641 78 -4 0 0.0404331
+GW 40 3 78 -4 0 80 -2 -3.4641 0.0404331
+GW 41 3 80 -2 -3.4641 82 2 -3.4641 0.0404331
+GW 42 3 82 2 -3.4641 84 4 0 0.0404331
+GW 43 3 84 4 0 86 2 3.4641 0.0404331
+GW 44 3 86 2 3.4641 88 -2 3.4641 0.0404331
+GW 45 3 88 -2 3.4641 90 -4 0 0.0404331
+GW 46 3 90 -4 0 92 -2 -3.4641 0.0404331
+GW 47 3 92 -2 -3.4641 94 2 -3.4641 0.0404331
+GW 48 3 94 2 -3.4641 96 4 0 0.0404331
+GW 49 3 96 4 0 98 2 3.4641 0.0404331
+GW 50 3 98 2 3.4641 100 -2 3.4641 0.0404331
+GW 51 3 100 -2 3.4641 102 -4 0 0.0404331
+GW 52 3 102 -4 0 104 -2 -3.4641 0.0404331
+GW 53 3 104 -2 -3.4641 106 2 -3.4641 0.0404331
+GW 54 3 106 2 -3.4641 108 4 0 0.0404331
+GW 55 3 108 4 0 110 2 3.4641 0.0404331
+GW 56 3 110 2 3.4641 112 -2 3.4641 0.0404331
+GS 0 0 .02540
+GE 0
+EX 0 28 3 0 1 0
+EX 0 29 1 0 1 0
+LD 5 1 1 3 5.8001E7
+LD 5 2 1 3 5.8001E7
+LD 5 3 1 3 5.8001E7
+LD 5 4 1 3 5.8001E7
+LD 5 5 1 3 5.8001E7
+LD 5 6 1 3 5.8001E7
+LD 5 7 1 3 5.8001E7
+LD 5 8 1 3 5.8001E7
+LD 5 9 1 3 5.8001E7
+LD 5 10 1 3 5.8001E7
+LD 5 11 1 3 5.8001E7
+LD 5 12 1 3 5.8001E7
+LD 5 13 1 3 5.8001E7
+LD 5 14 1 3 5.8001E7
+LD 5 15 1 3 5.8001E7
+LD 5 16 1 3 5.8001E7
+LD 5 17 1 3 5.8001E7
+LD 5 18 1 3 5.8001E7
+LD 5 19 1 3 5.8001E7
+LD 5 20 1 3 5.8001E7
+LD 5 21 1 3 5.8001E7
+LD 5 22 1 3 5.8001E7
+LD 5 23 1 3 5.8001E7
+LD 5 24 1 3 5.8001E7
+LD 5 25 1 3 5.8001E7
+LD 5 26 1 3 5.8001E7
+LD 5 27 1 3 5.8001E7
+LD 5 28 1 3 5.8001E7
+LD 5 29 1 3 5.8001E7
+LD 5 30 1 3 5.8001E7
+LD 5 31 1 3 5.8001E7
+LD 5 32 1 3 5.8001E7
+LD 5 33 1 3 5.8001E7
+LD 5 34 1 3 5.8001E7
+LD 5 35 1 3 5.8001E7
+LD 5 36 1 3 5.8001E7
+LD 5 37 1 3 5.8001E7
+LD 5 38 1 3 5.8001E7
+LD 5 39 1 3 5.8001E7
+LD 5 40 1 3 5.8001E7
+LD 5 41 1 3 5.8001E7
+LD 5 42 1 3 5.8001E7
+LD 5 43 1 3 5.8001E7
+LD 5 44 1 3 5.8001E7
+LD 5 45 1 3 5.8001E7
+LD 5 46 1 3 5.8001E7
+LD 5 47 1 3 5.8001E7
+LD 5 48 1 3 5.8001E7
+LD 5 49 1 3 5.8001E7
+LD 5 50 1 3 5.8001E7
+LD 5 51 1 3 5.8001E7
+LD 5 52 1 3 5.8001E7
+LD 5 53 1 3 5.8001E7
+LD 5 54 1 3 5.8001E7
+LD 5 55 1 3 5.8001E7
+LD 5 56 1 3 5.8001E7
+FR 0 1 0 0 28.5 1
+RP 0 1 360 1000 89 0 1 1
+RP 0 181 1 1000 -90 0 1 1
+EN
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I have purposely listed the entire set of 56 wires and 56 loads, since assigning a material conductivity to individual wires is standard for programs such as NEC-Win Plus. Once in .NEC form, I could replace all of the LD5 lines with a single line, since the entire helical dipole is constructed from AWG #12 copper wire. The length is 112", which yields 9.33 turns of the helix. The helix is uniform throughout, using 12" per complete turn. Since each of the 56 wires has 3 segments, we end up with a total segment count of 168.

+

The model uses a split source which yields a free-space source impedance of 25.4 + j 5.4 Ohms and a gain of 1.74 dBi.

+

Recreating the Helical Dipole with GH

+

Initially, we shall use a single line to create the basic free-space helical dipole. The only entry will look like the top line of the following entry.

+ 
GH  1    168  12  106  4   4   4   4   .0404
+GH  ITG  NS   S   HL   A1  B1  A2  B2  RAD
+    I1   I2   F1  F2   F3  F4  F5  F6  F7
+

The line structure, like most other NEC-2 geometry entries, consists of 2 integer places and 7 floating decimal places. The use of integers in many of those entries is simply a function of using rounded numbers to keep the example easy-to-read and to have the new model correspond as closely as possible with the old. Here is a list of the entries and their explanations.

+

ITG: This entry assigns a tag number to all of the segments making up the helix (or spiral). For simplicity, we assign a 1 here.

+

NS: The number of segments into which the helix (or spiral) will be divided. Note that the new helical dipole will be constructed of a single wire composed of many segments. We shall retain the 168 value from the old model.

+

S: The turn spacing, as measured from a consistent point on successive turns. In NEC-2, the turn spacing for helixes and spirals will be constant or linear. The model assigns a 12" spacing between turns, the same value as used in the old model.

+

HL: The total length of the helix. Here we assign--for reasons that we shall discover--a value of 106" instead of the 112" of the initial model. If HL is zero, then we obtain a flat spiral. Some implementations of NEC-2 may yield a division-by-zero error if HL=0. However, one may always give HL a very low value to avoid this problem and retain an essentially flat spiral. If HL is negative, the output is a left-handed spiral; if positive, the helix is right-handed. Since the helical dipole does not care about its hands, we have assigned a positive number.

+

The following 4 entries rest on the fact that NEC-2 grows its helices along the Z-axis. For a free-space model, this presents no problems, even for our HF helical dipole, since we can always use a theta pattern instead of a phi pattern to obtain the typical dipole figure-8 pattern. As well, we shall look at ways to reorient the helix once we have finished constructing it.

+

A1: The radius of the helix along the X-axis at Z=0 (the helix starting point). Since we used a "radius" of 4" from center to hexagon point in our old model, we shall use 4 as the radius.

+

B1: The radius of the helix along the Y-axis at Z=0 (the helix starting point). Once more, we assign a 4.

+

A2: The radius of the helix along the X-axis at Z=HL (the terminating point of the helix). Since our helix is uniform in radius, we assign another 4.

+

B2: The radius of the helix along the Y-axis at Z=HL (the terminating point of the helix). Since our helix is uniform in radius, we assign another 4.

+

RAD: The wire radius. Since we are using AWG #12, the radius is 0.0404.

+

If we were designing a flat spiral, then HL would be zero or virtual zero, and A2 and B2 would not have the same values as A1 and B1. However, A2 and B2 must grow or shrink together to prevent intersecting wires within the spiral. In a helix, it is not necessary to maintain a constant radius, although that is the most common form. We can create a spiral helix by using different values for A1/B1 and A2/B2 while using a non-zero value for HL. The result will be roughly conical, with the more open end higher or lower depending on our selection of A and B values.

+

A limitation of the NEC-2 helix creation line is that it does not permit variation of the pitch as we move along the helix. This limitation has no effect on our simple model.

+

The GH input does not appear in the original (1981) NEC-2 user's manual. It is classified as a non-official addition to NEC-2. Nonetheless, it is a highly useful addition.

+
+ +
+

Fig. 1 shows the complete simple helix model. since the wire units are in inches, we add the scaling line (GS) to convert them to meters. As well, since we specified a total of 168 segments in the model to coincide roughly with the original model, we use a split-feed system. However, rather than occurring on adjacent wires, as in the original, they occur on adjacent segments of our single tag: segments 84 and 85, specifically. As well a single load (LD5) line suffices to give the model wire copper's conductivity. The RP0 line specifies a theta pattern.

+
+ +
+

Fig. 2 places the two helices side by side, but not perfectly to scale. The old model has 9.33 turns, while the new one has 8.83 turns, given the fixed 12-inch turn spacing in each model. If the new model curves seem smoother than the old, that is no illusion. The old model uses 3 segments per straight line, while the new model has a new angle for each segment.

+

The new model returns a free-space gain of 1.73 dBi and a source impedance (combining the split-feed in series) of 22.6 - j 1.9 Ohms. But it does so with a length of 106" rather than the original 112".

+
+ +
+

We can capture something of the reason for the length difference from the views of Fig. 3. The original model used a hexagon to simulate a circle. For general building guidance, the simulation is reasonable. However, with a radius to a point of 4", the circumference of the hexagon is somewhat shorter than that of a circle with the same radius. Hence, we would require greater length to equal the total wire in the much more circular helix created by the GH entry.

+

One modeling benefit of using the GH facility is that we can prune our helix model to length simply by changing 1 number in the GH line (HL). Changing the length of the original model requires that we add, remove, or modify one or more GW entries.

+

The NEC output report on the helix provides some useful information not readily available from the original model. The following extract from the output file for our simple "GH" model is helpful in checking our design or finding out some of its properties.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     HELIX STRUCTURE-   AXIAL SPACING BETWEEN TURNS =  12.000 TOTAL AXIAL LENGTH = 106.000
+  1  RADIUS OF HELIX =     4.000     4.000     4.000     4.000           0.04040     168        1   168       1
+     THE PITCH ANGLE IS   25.5228
+     THE LENGTH OF WIRE/TURN IS   27.8506
+      STRUCTURE SCALED BY FACTOR   0.02540
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.09885    0.01648    0.00801    0.03706   25.62438  99.46429   0.00103     0    1    2      1
+     2    0.08816    0.04765    0.02404    0.03706   25.62438 118.39286   0.00103     1    2    3      1
+     3    0.06794    0.07368    0.04007    0.03706   25.62438 137.32143   0.00103     2    3    4      1
+     4    0.04036    0.09173    0.05609    0.03706   25.62438 156.25000   0.00103     3    4    5      1
+     5    0.00842    0.09986    0.07212    0.03706   25.62438 175.17857   0.00103     4    5    6      1
+     6   -0.02443    0.09719    0.08814    0.03706   25.62438-165.89286   0.00103     5    6    7      1
+     7   -0.05463    0.08402    0.10417    0.03706   25.62438-146.96429   0.00103     6    7    8      1
+     8   -0.07893    0.06175    0.12020    0.03706   25.62438-128.03572   0.00103     7    8    9      1
+     9   -0.09470    0.03280    0.13622    0.03706   25.62438-109.10715   0.00103     8    9   10      1
+    10   -0.10022    0.00031    0.15225    0.03706   25.62438 -90.17857   0.00103     9   10   11      1
+    11   -0.09490   -0.03221    0.16828    0.03706   25.62438 -71.25000   0.00103    10   11   12      1
+    12   -0.07932   -0.06126    0.18430    0.03706   25.62438 -52.32143   0.00103    11   12   13      1
+-----
+    80    0.04264    0.09070    1.27408    0.03706   25.62438 154.82140   0.00103    79   80   81      1
+    81    0.01091    0.09962    1.29011    0.03706   25.62438 173.74997   0.00103    80   81   82      1
+    82   -0.02200    0.09777    1.30613    0.03706   25.62438-167.32145   0.00103    81   82   83      1
+    83   -0.05252    0.08535    1.32216    0.03706   25.62438-148.39288   0.00103    82   83   84      1
+    84   -0.07737    0.06370    1.33819    0.03706   25.62438-129.46431   0.00103    83   84   85      1
+    85   -0.09385    0.03516    1.35421    0.03706   25.62438-110.53574   0.00103    84   85   86      1
+    86   -0.10018    0.00281    1.37024    0.03706   25.62438 -91.60717   0.00103    85   86   87      1
+    87   -0.09567   -0.02984    1.38627    0.03706   25.62438 -72.67860   0.00103    86   87   88      1
+    88   -0.08082   -0.05926    1.40229    0.03706   25.62438 -53.75003   0.00103    87   88   89      1
+    89   -0.05723   -0.08227    1.41832    0.03706   25.62438 -34.82146   0.00103    88   89   90      1
+-----
+   157    0.01339    0.09932    2.50810    0.03706   25.62438 172.32138   0.00103   156  157  158      1
+   158   -0.01955    0.09829    2.52412    0.03706   25.62438-168.75005   0.00103   157  158  159      1
+   159   -0.05038    0.08663    2.54015    0.03706   25.62438-149.82148   0.00103   158  159  160      1
+   160   -0.07576    0.06561    2.55618    0.03706   25.62438-130.89291   0.00103   159  160  161      1
+   161   -0.09294    0.03748    2.57220    0.03706   25.62438-111.96434   0.00103   160  161  162      1
+   162   -0.10008    0.00531    2.58823    0.03706   25.62438 -93.03577   0.00103   161  162  163      1
+   163   -0.09639   -0.02744    2.60426    0.03706   25.62438 -74.10720   0.00103   162  163  164      1
+   164   -0.08227   -0.05723    2.62028    0.03706   25.62438 -55.17862   0.00103   163  164  165      1
+   165   -0.05926   -0.08082    2.63631    0.03706   25.62438 -36.25005   0.00103   164  165  166      1
+   166   -0.02984   -0.09567    2.65233    0.03706   25.62438 -17.32148   0.00103   165  166  167      1
+   167    0.00281   -0.10018    2.66836    0.03706   25.62438   1.60709   0.00103   166  167  168      1
+   168    0.03516   -0.09385    2.68439    0.03706   25.62438  20.53566   0.00103   167  168    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I have left only 3 turns--the two ends and the turn in the source region- -in this report to reveal the segment-by-segment change of angle in a GH helix. The helix extends from Z=0 to Z=2.6924 m (106"). The values in the Z column do not match these terminal values, since they are values for the center of each segment.

+

Among the useful data provided in the NEC output report is the pitch angle (25.522 degrees) and the length of wire per turn (27.8506"). From the latter value, knowing that we have 8.833 turns, we can derive the total length of wire in the helix: 246". (Since each wire in the original model is 4.47" long--allowing for the pitch of the turns--and we have 56 wires, the total wire length in that model is 250".)

+

Manipulating the Helical Dipole

+

The helical dipole that we just created is vertical and extends from Z=0 to Z=HL. It is unlikely that this position is what we might desire for the finished product. However, we may change a number of positional features of the structure by using the GM input that we reviewed in the preceding episode.

+

Let's begin by rotating the structure reactive to the X-axis. Our goal will be to set the structure into what would be a horizontal orientation extending from Y=0 to Y=HL. A single entry on a GM card placed just after the GH card will do the job.

+
+ +
+

Fig. 4 shows the revised model. Note that we have entered a -90-degree rotation in order to come up with positive values for the Y-axis entries. The following extract from the NEC output file gives us a view of what we accomplished.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+                                     COORDINATES MUST BE INPUT IN
+                                     METERS OR BE SCALED TO METERS
+                                     BEFORE STRUCTURE INPUT IS ENDED
+
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     HELIX STRUCTURE-   AXIAL SPACING BETWEEN TURNS =  12.000 TOTAL AXIAL LENGTH = 106.000
+  1  RADIUS OF HELIX =     4.000     4.000     4.000     4.000           0.04040     168        1   168       1
+     THE PITCH ANGLE IS   25.5228
+     THE LENGTH OF WIRE/TURN IS   27.8506
+      THE STRUCTURE HAS BEEN MOVED, MOVE DATA CARD IS -
+        0    0 -90.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
+       GM command acting on tag #'s            0 through            0
+  inclusive.
+      STRUCTURE SCALED BY FACTOR   0.02540
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.09885    0.00801   -0.01648    0.03706  -62.79489 108.92291   0.00103     0    1    2      1
+     2    0.08816    0.02404   -0.04765    0.03706  -52.48438 134.75235   0.00103     1    2    3      1
+     3    0.06794    0.04007   -0.07368    0.03706  -37.67732 146.87851   0.00103     2    3    4      1
+     4    0.04036    0.05609   -0.09173    0.03706  -21.29291 152.34449   0.00103     3    4    5      1
+     5    0.00842    0.07212   -0.09986    0.03706   -4.34627 154.29633   0.00103     4    5    6      1
+     6   -0.02443    0.08814   -0.09719    0.03706   12.69518 153.68493   0.00103     5    6    7      1
+     7   -0.05463    0.10417   -0.08402    0.03706   29.44213 150.22438   0.00103     6    7    8      1
+     8   -0.07893    0.12020   -0.06175    0.03706   45.24815 142.10108   0.00103     7    8    9      1
+     9   -0.09470    0.13622   -0.03280    0.03706   58.42714 124.31185   0.00103     8    9   10      1
+    10   -0.10022    0.15225   -0.00031    0.03706   64.37504  90.37230   0.00103     9   10   11      1
+    11   -0.09490    0.16828    0.03221    0.03706   58.62722  56.17144   0.00103    10   11   12      1
+    12   -0.07932    0.18430    0.06126    0.03706   45.52954  38.12186   0.00103    11   12   13      1
+-------------
+    80    0.04264    1.27408   -0.09070    0.03706  -22.55676 152.07639   0.00103    79   80   81      1
+    81    0.01091    1.29011   -0.09962    0.03706   -5.63323 154.24218   0.00103    80   81   82      1
+    82   -0.02200    1.30613   -0.09777    0.03706   11.41387 153.81986   0.00103    81   82   83      1
+    83   -0.05252    1.32216   -0.08535    0.03706   28.19972 150.61245   0.00103    82   83   84      1
+    84   -0.07737    1.33819   -0.06370    0.03706   44.11424 142.96058   0.00103    83   84   85      1
+    85   -0.09385    1.35421   -0.03516    0.03706   57.60257 126.18023   0.00103    84   85   86      1
+    86   -0.10018    1.37024   -0.00281    0.03706   64.32867  93.34651   0.00103    85   86   87      1
+    87   -0.09567    1.38627    0.02984    0.03706   59.40185  58.17066   0.00103    86   87   88      1
+    88   -0.08082    1.40229    0.05926    0.03706   46.64632  39.04739   0.00103    87   88   89      1
+    89   -0.05723    1.41832    0.08227    0.03706   30.98812  30.29621   0.00103    88   89   90      1
+    90   -0.02744    1.43434    0.09639    0.03706   14.29458  26.50571   0.00103    89   90   91      1
+-------------
+   155    0.07152    2.47605   -0.07020    0.03706  -40.05297 145.59858   0.00103   154  155  156      1
+   156    0.04488    2.49207   -0.08960    0.03706  -23.81736 151.78846   0.00103   155  156  157      1
+   157    0.01339    2.50810   -0.09932    0.03706   -6.91952 154.17381   0.00103   156  157  158      1
+   158   -0.01955    2.52412   -0.09829    0.03706   10.13116 153.93953   0.00103   157  158  159      1
+   159   -0.05038    2.54015   -0.08663    0.03706   26.95272 150.97652   0.00103   158  159  160      1
+   160   -0.07576    2.55618   -0.06561    0.03706   42.96780 143.77073   0.00103   159  160  161      1
+   161   -0.09294    2.57220   -0.03748    0.03706   56.74142 127.94738   0.00103   160  161  162      1
+   162   -0.10008    2.58823   -0.00531    0.03706   64.20849  96.30074   0.00103   161  162  163      1
+   163   -0.09639    2.60426    0.02744    0.03706   60.13300  60.27703   0.00103   162  163  164      1
+   164   -0.08227    2.62028    0.05723    0.03706   47.74811  40.02946   0.00103   163  164  165      1
+   165   -0.05926    2.63631    0.08082    0.03706   32.21882  30.74262   0.00103   164  165  166      1
+   166   -0.02984    2.65233    0.09567    0.03706   15.57208  26.67626   0.00103   165  166  167      1
+   167    0.00281    2.66836    0.10018    0.03706   -1.44899  25.63317   0.00103   166  167  168      1
+   168    0.03516    2.68439    0.09385    0.03706  -18.43868  27.12110   0.00103   167  168    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The entries make it clear that the extension of the helical dipole that formerly appeared in the Z-column now appears in the Y-column.

+

Since it is also unlikely that we would want the helical dipole to lie partially above and partially below ground when we add a ground system to the model later on, we should likely raise the antenna in the Z-axis. Perhaps 30' or 360" will do as a start. As well, many modelers prefer to have their antennas centered, with equal amounts extending + and - relative to the axis at right angles to them. This move would require that we move the structure along the Y-axis by -53 (a 53" move toward the negative portion of the Y-axis).

+

We need not add a second GM card. Our total revision involves a rotation first, followed by two translations. Since the GM card rotates before translating--our desired order of operation--we may include all 3 requests on a single card, as shown in Fig. 5.

+
+ +
+

Since the GM card will precede the GS or scaling card, we may make all entries in the unit of measure that we used for the GH line. The final model (at least for this exercise) appears in Fig. 6.

+
+ +
+

We need only look at an extract from the NEC output file to see if we succeeded in all of our moves.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     HELIX STRUCTURE-   AXIAL SPACING BETWEEN TURNS =  12.000 TOTAL AXIAL LENGTH = 106.000
+     1  RADIUS OF HELIX =     4.000     4.000     4.000     4.000           0.04040     168        1   168
+1
+     THE PITCH ANGLE IS   25.5228
+     THE LENGTH OF WIRE/TURN IS   27.8506
+      THE STRUCTURE HAS BEEN MOVED, MOVE DATA CARD IS -
+        0    0 -90.00000   0.00000   0.00000   0.00000 -53.00000 360.00000   0.00000
+       GM command acting on tag #'s            0 through            0
+  inclusive.
+      STRUCTURE SCALED BY FACTOR   0.02540
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.09885   -1.33819    9.12752    0.03706  -62.79489 108.92291   0.00103     0    1    2      1
+     2    0.08816   -1.32216    9.09635    0.03706  -52.48438 134.75235   0.00103     1    2    3      1
+     3    0.06794   -1.30613    9.07032    0.03706  -37.67732 146.87851   0.00103     2    3    4      1
+     4    0.04036   -1.29011    9.05227    0.03706  -21.29291 152.34449   0.00103     3    4    5      1
+     5    0.00842   -1.27408    9.04414    0.03706   -4.34627 154.29633   0.00103     4    5    6      1
+     6   -0.02443   -1.25806    9.04681    0.03706   12.69518 153.68493   0.00103     5    6    7      1
+     7   -0.05463   -1.24203    9.05998    0.03706   29.44213 150.22438   0.00103     6    7    8      1
+     8   -0.07893   -1.22600    9.08225    0.03706   45.24815 142.10108   0.00103     7    8    9      1
+     9   -0.09470   -1.20998    9.11120    0.03706   58.42714 124.31185   0.00103     8    9   10      1
+    10   -0.10022   -1.19395    9.14369    0.03706   64.37504  90.37230   0.00103     9   10   11      1
+    11   -0.09490   -1.17792    9.17621    0.03706   58.62722  56.17144   0.00103    10   11   12      1
+    12   -0.07932   -1.16190    9.20526    0.03706   45.52954  38.12186   0.00103    11   12   13      1
+--------
+    80    0.04264   -0.07212    9.05330    0.03706  -22.55676 152.07639   0.00103    79   80   81      1
+    81    0.01091   -0.05609    9.04438    0.03706   -5.63323 154.24218   0.00103    80   81   82      1
+    82   -0.02200   -0.04007    9.04623    0.03706   11.41387 153.81986   0.00103    81   82   83      1
+    83   -0.05252   -0.02404    9.05865    0.03706   28.19972 150.61245   0.00103    82   83   84      1
+    84   -0.07737   -0.00801    9.08030    0.03706   44.11424 142.96058   0.00103    83   84   85      1
+    85   -0.09385    0.00801    9.10884    0.03706   57.60257 126.18023   0.00103    84   85   86      1
+    86   -0.10018    0.02404    9.14119    0.03706   64.32867  93.34651   0.00103    85   86   87      1
+    87   -0.09567    0.04007    9.17384    0.03706   59.40185  58.17066   0.00103    86   87   88      1
+    88   -0.08082    0.05609    9.20326    0.03706   46.64632  39.04739   0.00103    87   88   89      1
+    89   -0.05723    0.07212    9.22627    0.03706   30.98812  30.29621   0.00103    88   89   90      1
+    90   -0.02744    0.08814    9.24039    0.03706   14.29458  26.50571   0.00103    89   90   91      1
+--------
+   156    0.04488    1.14587    9.05440    0.03706  -23.81736 151.78846   0.00103   155  156  157      1
+   157    0.01339    1.16190    9.04468    0.03706   -6.91952 154.17381   0.00103   156  157  158      1
+   158   -0.01955    1.17792    9.04571    0.03706   10.13116 153.93953   0.00103   157  158  159      1
+   159   -0.05038    1.19395    9.05737    0.03706   26.95272 150.97652   0.00103   158  159  160      1
+   160   -0.07576    1.20998    9.07839    0.03706   42.96780 143.77073   0.00103   159  160  161      1
+   161   -0.09294    1.22600    9.10652    0.03706   56.74142 127.94738   0.00103   160  161  162      1
+   162   -0.10008    1.24203    9.13869    0.03706   64.20849  96.30074   0.00103   161  162  163      1
+   163   -0.09639    1.25806    9.17144    0.03706   60.13300  60.27703   0.00103   162  163  164      1
+   164   -0.08227    1.27408    9.20123    0.03706   47.74811  40.02946   0.00103   163  164  165      1
+   165   -0.05926    1.29011    9.22482    0.03706   32.21882  30.74262   0.00103   164  165  166      1
+   166   -0.02984    1.30613    9.23967    0.03706   15.57208  26.67626   0.00103   165  166  167      1
+   167    0.00281    1.32216    9.24418    0.03706   -1.44899  25.63317   0.00103   166  167  168      1
+   168    0.03516    1.33819    9.23785    0.03706  -18.43868  27.12110   0.00103   167  168    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The average Z value is 9.144 m or 30'. The model extends from Y=-1.3462 m to +1.3462 m (that is, -53" to +53"). The values shown for segments 1 and 168, of course, represent the Y coordinates of the segment center, so their values will be just shy of the tag end coordinates.

+

Conclusions and Cautions

+

This little exercise set in using the GH entry--along with the GM entry-- to create helical structures has aimed at familiarization with some of the modeling economies that are available in implementations of NEC-2 that make all of the geometry cards available to the user. The original model of our helical dipole used 56 GW entries, while the revised model used only 1 GH and eventually 1 GM entry to do the same work. As well, we need only one LD5 entry to provide the dipole with copper's conductivity throughout.

+

For our efforts, we received the benefit of having a helix that better simulates a spiral curvature. The angle changes with every segment, rather than with every third segment, as in the original. The result is a structure that yields a slightly different required length for resonance and a slightly different source impedance.

+

When constructing models of helical structures, we need to remain aware of all NEC limitations. If we make the radius of the helix too small for the wire radius used, then we may run against the segment-length-to-wire- radius limits of NEC. If we confine the space required by 1 turn to a value that is too low, then the wire proximity may violate NEC limitations. Proximity errors may increase if the parallel segment junctions are not in very close alignment. Most of these problems will show up within one of two tests. First, most NEC implementations have some sort of error checking routine to pre-test a model relative to many of the NEC guidelines. Second, we can perform an average gain test as a check on model adequacy.

+

The limitations on helical models do not impinge on the design and modeling of most helical antenna designs for the VHF region and above. In these antennas, turns are relatively widely spaced with a large radius to the spiral. However, the limitations will often be approached and surpassed in attempts to model compact helical dipoles for HF service. Typically, such dipoles use fairly closely spaced wires on forms with under a 2" diameter. The GH facility can create the requisite wire structure, but the user must be cautious with the results.

+

These notes apply only to the NEC-2 implementation of the GH entry. The NEC-4 version of the entry has a different format, so that a NEC-2 model with a GH entry does not import directly into NEC-4. By shrinking the helix radius entries into single values for the start and end, the entry opens room for specifying differential start and stop wire radii. As well, instead of asking for the spacing of a full turn and the total length of the helix, the NEC-4 entry asks for the total length and the number of turns. Finally, the NEC-4 version of GH allows two different types of spirals. Since both NEC-2 and NEC-4 use only 7 floating decimal entries, entry meanings will change when moving from one program to the other.

+
+ +

+

Go to Main Index

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+

63. GH and GM: The NEC-4 Versions

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

We have examined in the past two episodes the basic uses of the GH (Helix-Spiral Specification) and the GM (Coordinate Transformation) inputs in their NEC-2 incarnations. Along the way, we had occasion to briefly note that in certain particulars, the NEC-4 versions of these geometry in[put lines differed from the NEC-2 counterparts. Some modelers may have occasion to use NEC-4, and so it may be useful to trace the way in which this core employs these input lines.

+

Although the inputs are a function of the NEC-2 and NEC-4 cores, implementing software provides the user with certain helps. Therefore, we shall examine the GH and GM cards through NEC-Win Pro (NEC-2) and GNEC (NEC-4), both by Nittany Scientific. The screens of these programs will have similar appearances, since they are roughly counterpart programs. However, it will be the differences that most interest us.

+

The Helical Dipole for 28.5 MHz

+

Let's begin be re-creating the helical dipole from the preceding column. In Fig. 1, we have the ASCII inputs that define this model.

+
+ +
+

There are only two lines in the model version that differ. One is the LD5 material conductivity line. In the NEC-2 version, places 2, 3, and 4 specify the tag number, the start segment, and the stop segment of the wire to be loaded. The NEC-4 version uses a shortcut: these same places all contain zeroes, indicating that all segments in the model will be loaded by the conductivity value (in S/m) listed in the last entry position. We have noted this shortcut in past columns, but likely have not illustrated its use until now.

+

The more germane difference lies in the GH line that defines the helical dipole. The basic design consists of AWG #12 wire (0.0808" diameter) would in a helix in which the turns occupy 12" each. The radius is 4", and the overall length is 106" or 8.8333 turns.

+

NEC-2 enters the data in this format:

+ 
GH  1    168  12  106  4   4   4   4   .0404
+GH  ITG  NS   S   HL   A1  B1  A2  B2  RAD
+    I1   I2   F1  F2   F3  F4  F5  F6  F7
+

Note that we use the space between turns and the total length to define the helix, where both values are in the unit of measure chosen for the model and transformed to meters by the GS line.

+

In contrast, the basic defining data required by the NEC-4 version is the number of turns, where the number of turns may be a decimal value rather than a simple integer, and the total length of the helix. Hence, the line input format undergoes a reshaping.

+ 
GH  1    168  8.3333  106    4    4    .0404  .0404  0
+GH  ITG  NS   TURNS   ZLEN   HR1  HR2  WR1    WR2    ISPX
+    I1   I2   F1      F2     F3   F4   F5     F6     F7
+

The integer entries retain the same meanings to indicate the tag number of the spiral and the total number of segments with the helix. F1 and F2 contain the number of turns and the total length. The length is designated ZLEN, because--common to both cores--the initial helix is grown along the Z-axis from zero to a positive limit. If ZLEN is negative, the output is a left-handed spiral; if positive, the helix is right-handed. Since the helical dipole does not care about its hands, we have assigned a positive number.

+

Whereas in NEC-2, we might assign different values to the radius along the X-axis and the Y-axis (allowing an oval), HR1 and HR2 assign a single radius value to the Z=0 end and to the Z=ZLEN ends of the spiral, respectively. WR1 and WR2 refer to the wire radius at each end of the helix. If we enter different values for two entries, then the program automatically scales the radii of the segments logarithmically.

+

The final entry, ISPX is effective only when HR2 and HR1 are not equal-- which creates a spiral structure. When HR1=HR2, values of 0 or 1 make no difference. However, when we have a spiral, 0 defines a log spiral and 1 defines an Archimedes spiral.

+
+ +
+

Fig. 2 shows the NEC-2 and NEC-4 GH-help screens to further identify the differences between the GH geometry input lines. The help screens simply provide places to enter the line data in order (or to revise individual entries), so correlation to the respective model lines should be straightforward.

+

In the original model, we were not content to leave the helix extending from Z=0 to Z=106 (inches). Therefore, we rotated the helix -90 degrees on the X-axis, displaced it by -53" on the Y-axis, and elevated it 360" on the Z-axis. We accomplished all of this with a single GM line input. For operations that act upon the entirety of the tags and segments within a model, there is no difference between the NEC-2 and the NEC-4 GM inputs. Therefore, in the final helical dipole model, the NEC-4 version will appear as in Fig. 3.

+
+ +
+

To verify that the resulting model is identical to the one we produced in NEC-2 in the preceding column, we may take a truncated look at the NEC output file.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1      THIS WIRE IS A LOG-SPIRAL OR HELIX                                          168        1   168       1
+ SPIRAL DATA: TURNS=    8.8333  LENGTH=  1.0600E+02  H.RAD=  4.0000E+00  4.0000E+00  W.RAD=  4.0400E-02  4.0400E-02
+          TOTAL LENGTH OF WIRE IN THE SPIRAL =  2.45104E+02
+      THE STRUCTURE HAS BEEN MOVED, GM COMMAND DATA IS -
+        0    0 -90.00000   0.00000   0.00000   0.00000 -53.00000 360.00000    0    1    0  168
+      STRUCTURE SCALED BY FACTOR   0.02540
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.09885  -1.33819   9.12752   0.03706  -62.79489 108.92291   0.00103     0    1    2      1
+     2   0.08816  -1.32216   9.09635   0.03706  -52.48438 134.75235   0.00103     1    2    3      1
+     3   0.06794  -1.30613   9.07032   0.03706  -37.67732 146.87851   0.00103     2    3    4      1
+     4   0.04036  -1.29011   9.05227   0.03706  -21.29291 152.34449   0.00103     3    4    5      1
+     5   0.00842  -1.27408   9.04414   0.03706   -4.34628 154.29633   0.00103     4    5    6      1
+     6  -0.02443  -1.25806   9.04681   0.03706   12.69518 153.68493   0.00103     5    6    7      1
+     7  -0.05463  -1.24203   9.05998   0.03706   29.44213 150.22438   0.00103     6    7    8      1
+     8  -0.07893  -1.22600   9.08225   0.03706   45.24814 142.10108   0.00103     7    8    9      1
+     9  -0.09470  -1.20998   9.11120   0.03706   58.42714 124.31186   0.00103     8    9   10      1
+    10  -0.10022  -1.19395   9.14369   0.03706   64.37504  90.37231   0.00103     9   10   11      1
+    11  -0.09490  -1.17792   9.17621   0.03706   58.62722  56.17145   0.00103    10   11   12      1
+    12  -0.07932  -1.16190   9.20526   0.03706   45.52955  38.12187   0.00103    11   12   13      1
+------------
+    80   0.04264  -0.07212   9.05330   0.03706  -22.55679 152.07638   0.00103    79   80   81      1
+    81   0.01091  -0.05609   9.04438   0.03706   -5.63326 154.24218   0.00103    80   81   82      1
+    82  -0.02200  -0.04007   9.04623   0.03706   11.41384 153.81986   0.00103    81   82   83      1
+    83  -0.05252  -0.02404   9.05865   0.03706   28.19970 150.61245   0.00103    82   83   84      1
+    84  -0.07737  -0.00801   9.08030   0.03706   44.11422 142.96060   0.00103    83   84   85      1
+    85  -0.09385   0.00801   9.10884   0.03706   57.60255 126.18027   0.00103    84   85   86      1
+    86  -0.10018   0.02404   9.14119   0.03706   64.32866  93.34658   0.00103    85   86   87      1
+    87  -0.09567   0.04007   9.17384   0.03706   59.40187  58.17071   0.00103    86   87   88      1
+    88  -0.08082   0.05609   9.20326   0.03706   46.64635  39.04741   0.00103    87   88   89      1
+    89  -0.05723   0.07212   9.22627   0.03706   30.98815  30.29622   0.00103    88   89   90      1
+    90  -0.02744   0.08814   9.24039   0.03706   14.29461  26.50571   0.00103    89   90   91      1
+-------------
+   157   0.01339   1.16190   9.04468   0.03706   -6.91958 154.17381   0.00103   156  157  158      1
+   158  -0.01955   1.17792   9.04571   0.03706   10.13111 153.93953   0.00103   157  158  159      1
+   159  -0.05038   1.19395   9.05737   0.03706   26.95266 150.97653   0.00103   158  159  160      1
+   160  -0.07576   1.20998   9.07839   0.03706   42.96775 143.77077   0.00103   159  160  161      1
+   161  -0.09294   1.22600   9.10652   0.03706   56.74138 127.94746   0.00103   160  161  162      1
+   162  -0.10008   1.24203   9.13869   0.03706   64.20848  96.30087   0.00103   161  162  163      1
+   163  -0.09639   1.25806   9.17144   0.03706   60.13303  60.27713   0.00103   162  163  164      1
+   164  -0.08227   1.27408   9.20123   0.03706   47.74816  40.02950   0.00103   163  164  165      1
+   165  -0.05926   1.29011   9.22482   0.03706   32.21887  30.74264   0.00103   164  165  166      1
+   166  -0.02984   1.30613   9.23967   0.03706   15.57213  26.67627   0.00103   165  166  167      1
+   167   0.00281   1.32216   9.24418   0.03706   -1.44894  25.63317   0.00103   166  167  168      1
+   168   0.03516   1.33819   9.23785   0.03706  -18.43862  27.12109   0.00103   167  168    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The values are essentially the very same as those we developed in the NEC-2 model for the helical dipole. Indeed, NEC-4 returned a source impedance of 22.6 - j 2.1 Ohms, with a free-space gain of 1.73 dBi. The NEC-2 model returned the same gain with a source impedance of 22.6 - j 1.9 Ohms.

+

Log vs. Archimedes Spirals

+

If we set HR1 and HR2 to different values, we obtain a spiral structure. Only if we set the helix length (ZLEN) to zero will we obtain a flat spiral. Just for the exercise, lets create a flat spiral with a starting radius of 4" and a final radius of 20". In fact, either HR1 or HR2 may be the larger or the smaller figure. However, if HR2=0, then its values becomes the value of HR1. Hence, for a nearly closed end to HR2, we must use a very low number, but one greater than zero.

+

For the sake of simplicity, we shall use a constant wire radius throughout and retain the 168 total segment count. In addition, we shall specify 9 turns for our spiral. The resulting help screen version of the new GH line will look like Fig. 4.

+
+ +
+

The only remaining option is whether to choose a log spiral (entry = 0) or an Archimedes spiral (entry = 1) in the ISPX position. The differences in the ways of calculating rate of spiraling lie in the development of a new radius based on the preceding radius using a program-calculated constant.

+
+ +
+

In practical terms, alternately selecting between the two spirals and leaving the other spiral-determining factors constant results in the two spirals shown in Fig. 5.

+
+ +
+

The differential in spacing between the successive rings of the two spirals is clearly apparent. However, there are other features worth noting. In both spirals, the segment lengths increase at the same rate from the innermost point to the outer limit. The selection of the number of turns and the number of total segments results in segment junctions that do not align particularly well. For the highest accuracy when using closely spaced wire segments, segment junction should be aligned as closely as possible. With 171 segments, the junctions would align at 19 segments per turn.

+

All other recommendations and limitations applicable to wires set up with the GW input apply to the GH input. The user should be specially aware of these limitations when using closely spaced spiral rings in conjunction with sizable wire radii. The log spiral may prove tricky unless the modeler pays close attention to the innermost rings and their spacing. The following extract from the NEC output report tracks the first 2 and the final 2 rings of the log spiral in our example as a sample of the ring-spacing differentials that may emerge.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1      THIS WIRE IS A LOG-SPIRAL OR HELIX                                          168        1   168       1
+ SPIRAL DATA: TURNS=    9.0000  LENGTH=  0.0000E+00  H.RAD=  4.0000E+00  2.0000E+01  W.RAD=  4.0400E-02  4.0400E-02
+          TOTAL LENGTH OF WIRE IN THE SPIRAL =  5.59747E+02
+      STRUCTURE SCALED BY FACTOR   0.02540
+
+   TOTAL SEGMENTS USED=  168     NO. SEG. IN A SYMMETRIC CELL=  168     SYMMETRY FLAG=  0
+
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   0.09921   0.01694   0.00000   0.03421    0.00000  98.02802   0.00103     0    1    2      1
+     2   0.08890   0.04923   0.00000   0.03454    0.00000 117.31374   0.00103     1    2    3      1
+     3   0.06830   0.07655   0.00000   0.03488    0.00000 136.59945   0.00103     2    3    4      1
+     4   0.03956   0.09573   0.00000   0.03521    0.00000 155.88516   0.00103     3    4    5      1
+     5   0.00578   0.10442   0.00000   0.03555    0.00000 175.17088   0.00103     4    5    6      1
+     6  -0.02931   0.10143   0.00000   0.03589    0.00000-165.54341   0.00103     5    6    7      1
+     7  -0.06176   0.08689   0.00000   0.03624    0.00000-146.25769   0.00103     6    7    8      1
+     8  -0.08783   0.06221   0.00000   0.03659    0.00000-126.97198   0.00103     7    8    9      1
+     9  -0.10444   0.03000   0.00000   0.03694    0.00000-107.68626   0.00103     8    9   10      1
+    10  -0.10953  -0.00624   0.00000   0.03730    0.00000 -88.40055   0.00103     9   10   11      1
+    11  -0.10230  -0.04247   0.00000   0.03765    0.00000 -69.11484   0.00103    10   11   12      1
+    12  -0.08333  -0.07459   0.00000   0.03802    0.00000 -49.82912   0.00103    11   12   13      1
+    13  -0.05454  -0.09886   0.00000   0.03838    0.00000 -30.54341   0.00103    12   13   14      1
+    14  -0.01900  -0.11240   0.00000   0.03875    0.00000 -11.25769   0.00103    13   14   15      1
+    15   0.01937  -0.11345   0.00000   0.03913    0.00000   8.02802   0.00103    14   15   16      1
+    16   0.05629  -0.10166   0.00000   0.03950    0.00000  27.31374   0.00103    15   16   17      1
+    17   0.08754  -0.07810   0.00000   0.03988    0.00000  46.59945   0.00103    16   17   18      1
+    18   0.10947  -0.04524   0.00000   0.04027    0.00000  65.88516   0.00103    17   18   19      1
+    19   0.11941  -0.00661   0.00000   0.04065    0.00000  85.17088   0.00103    18   19   20      1
+    20   0.11599   0.03352   0.00000   0.04105    0.00000 104.45659   0.00103    19   20   21      1
+    21   0.09936   0.07062   0.00000   0.04144    0.00000 123.74231   0.00103    20   21   22      1
+    22   0.07114   0.10043   0.00000   0.04184    0.00000 143.02802   0.00103    21   22   23      1
+    23   0.03430   0.11943   0.00000   0.04224    0.00000 162.31374   0.00103    22   23   24      1
+    24  -0.00714   0.12525   0.00000   0.04265    0.00000-178.40055   0.00103    23   24   25      1
+    25  -0.04857   0.11698   0.00000   0.04306    0.00000-159.11484   0.00103    24   25   26      1
+    26  -0.08529   0.09529   0.00000   0.04347    0.00000-139.82912   0.00103    25   26   27      1
+    27  -0.11305   0.06236   0.00000   0.04389    0.00000-120.54341   0.00103    26   27   28      1
+    28  -0.12853   0.02173   0.00000   0.04431    0.00000-101.25769   0.00103    27   28   29      1
+    29  -0.12973  -0.02215   0.00000   0.04474    0.00000 -81.97198   0.00103    28   29   30      1
+    30  -0.11625  -0.06437   0.00000   0.04517    0.00000 -62.68626   0.00103    29   30   31      1
+    31  -0.08931  -0.10011   0.00000   0.04561    0.00000 -43.40055   0.00103    30   31   32      1
+    32  -0.05173  -0.12518   0.00000   0.04605    0.00000 -24.11484   0.00103    31   32   33      1
+    33  -0.00756  -0.13654   0.00000   0.04649    0.00000  -4.82912   0.00103    32   33   34      1
+    34   0.03833  -0.13264   0.00000   0.04694    0.00000  14.45659   0.00103    33   34   35      1
+    35   0.08076  -0.11362   0.00000   0.04739    0.00000  33.74231   0.00103    34   35   36      1
+    36   0.11485  -0.08135   0.00000   0.04784    0.00000  53.02802   0.00103    35   36   37      1
+----------------------------
+   133   0.29053   0.20650   0.00000   0.12117    0.00000 123.74231   0.00103   132  133  134      1
+   134   0.20801   0.29367   0.00000   0.12234    0.00000 143.02802   0.00103   133  134  135      1
+   135   0.10030   0.34922   0.00000   0.12352    0.00000 162.31374   0.00103   134  135  136      1
+   136  -0.02087   0.36624   0.00000   0.12471    0.00000-178.40055   0.00103   135  136  137      1
+   137  -0.14201   0.34206   0.00000   0.12591    0.00000-159.11484   0.00103   136  137  138      1
+   138  -0.24940   0.27862   0.00000   0.12712    0.00000-139.82912   0.00103   137  138  139      1
+   139  -0.33057   0.18235   0.00000   0.12834    0.00000-120.54341   0.00103   138  139  140      1
+   140  -0.37583   0.06354   0.00000   0.12958    0.00000-101.25769   0.00103   139  140  141      1
+   141  -0.37934  -0.06477   0.00000   0.13082    0.00000 -81.97198   0.00103   140  141  142      1
+   142  -0.33991  -0.18822   0.00000   0.13208    0.00000 -62.68626   0.00103   141  142  143      1
+   143  -0.26116  -0.29271   0.00000   0.13335    0.00000 -43.40055   0.00103   142  143  144      1
+   144  -0.15127  -0.36603   0.00000   0.13464    0.00000 -24.11484   0.00103   143  144  145      1
+   145  -0.02210  -0.39926   0.00000   0.13593    0.00000  -4.82912   0.00103   144  145  146      1
+   146   0.11208  -0.38785   0.00000   0.13724    0.00000  14.45659   0.00103   145  146  147      1
+   147   0.23614  -0.33223   0.00000   0.13856    0.00000  33.74231   0.00103   146  147  148      1
+   148   0.33582  -0.23787   0.00000   0.13990    0.00000  53.02802   0.00103   147  148  149      1
+   149   0.39934  -0.11470   0.00000   0.14124    0.00000  72.31374   0.00103   148  149  150      1
+   150   0.41881   0.02386   0.00000   0.14260    0.00000  91.59945   0.00103   149  150  151      1
+   151   0.39115   0.16239   0.00000   0.14398    0.00000 110.88516   0.00103   150  151  152      1
+   152   0.31861   0.28519   0.00000   0.14536    0.00000 130.17088   0.00103   151  152  153      1
+   153   0.20852   0.37802   0.00000   0.14676    0.00000 149.45659   0.00103   152  153  154      1
+   154   0.07266   0.42978   0.00000   0.14817    0.00000 168.74231   0.00103   153  154  155      1
+   155  -0.07407   0.43379   0.00000   0.14960    0.00000-171.97198   0.00103   154  155  156      1
+   156  -0.21524   0.38869   0.00000   0.15104    0.00000-152.68626   0.00103   155  156  157      1
+   157  -0.33473   0.29864   0.00000   0.15250    0.00000-133.40055   0.00103   156  157  158      1
+   158  -0.41857   0.17298   0.00000   0.15396    0.00000-114.11484   0.00103   157  158  159      1
+   159  -0.45656   0.02527   0.00000   0.15545    0.00000 -94.82912   0.00103   158  159  160      1
+   160  -0.44352  -0.12817   0.00000   0.15694    0.00000 -75.54341   0.00103   159  160  161      1
+   161  -0.37992  -0.27003   0.00000   0.15845    0.00000 -56.25769   0.00103   160  161  162      1
+   162  -0.27201  -0.38402   0.00000   0.15998    0.00000 -36.97198   0.00103   161  162  163      1
+   163  -0.13116  -0.45666   0.00000   0.16152    0.00000 -17.68626   0.00103   162  163  164      1
+   164   0.02729  -0.47892   0.00000   0.16307    0.00000   1.59945   0.00103   163  164  165      1
+   165   0.18570  -0.44730   0.00000   0.16464    0.00000  20.88516   0.00103   164  165  166      1
+   166   0.32612  -0.36434   0.00000   0.16623    0.00000  40.17088   0.00103   165  166  167      1
+   167   0.43228  -0.23845   0.00000   0.16783    0.00000  59.45659   0.00103   166  167  168      1
+   168   0.49146  -0.08309   0.00000   0.16944    0.00000  78.74231   0.00103   167  168    0      1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Another advantage of aligning the segment junctions is that one can more easily calculate the spacing between rings by using aligned segment centers from the table.

+

A Reversible Yagi: The NEC-4 GM Input

+

We have so far overlooked the final 4 entry positions in the NEC-4 GM card. The structure of the GM input follows this model:

+ 
GM  ITG1  NRPT  ROX  ROY  ROZ  XS  YS  ZS  IT1  IS1  IT2  IS2
+    I1    I2    F1   F2   F3   F4  F5  F6  F7   F8   F9   F10
+

Up through floating decimal input F6, the GM input line is identical to the NEC-2 version. However, NEC-4 uses 4 final places to input the start and stop tag numbers and segments numbers for the structure to be copied and replicated at a new position (and orientation). Omission of these 4 entries results in the movement or duplication of all segments in the model. We used this feature in out first example.

+

If IT1 is zero, then IS1 refers to the absolute segment number in the model. If IT1 is greater than zero, then IS1 refers to the relative (tag-number-related) segment number specified, except that an IS1 value of zero in this case becomes a value of 1. Similar rules apply to IS2, with IT2 referring to the last tag number in the range. If IT2 and IS2 are both zero, the range extends to the last segment defined in the model up to the entry of the GM line.

+

Let's use a simple example of a reversible 2-element Yagi. such antennas are sometimes used in the lower HF range and made from wire. A permanent installation would not be rotatable, and so one might install alternative driver elements, one on each side of a common reflector wire. The unused driver would have small effects on the overall pattern of the antenna, relative to its omission.

+
+ +
+

Fig. 6 shows the model to be used for this antenna. We create two wires by standard GW entries. The longer wire (GW 1) is obviously the reflector. The shorter wire (GW 2) defines one driver, spaced 168" from the reflector for this 10.125-MHz array.

+

Although we save no modeling space, let's use the GM input to define the third wire, that is, the alternate driver. We shall want this driver to be a new structure and to have its own tag number. There, we specific a tag increment of 1 and also 1 new structure. Since we wish to space the wire equally distant from the reflector, but on the opposite side, we order a translation of 336" along the X-axis.

+

The final 4 entries show the tag and segment numbers for the start and stop of the existing wire to be duplicated and moved. If we look at the antenna view graphic, we get a picture of the total final model shown in Fig. 7 (minus the identifications of the element functions).

+
+ +
+

The addition of the 4 places to the GM line offers some interesting possibilities for the modeler. In NEC-2, we could only duplicate and move entire structures defined by a tag number. However, NEC-4 permits us to duplicate partial structures within the limits of a given tag number. Indeed, there is no restriction against beginning in the middle of one tag number and ending in the middle of another.

+
+ +
+

Fig. 8 shows the GM help screen with the start-stop entries opened. We might have begun with tag 1, segment 11 and ended with tag 2, segment 8 (although in the context of our example, I cannot think of a reason for doing so). (Those interested may wish to open the help screen for the GM line in our first example. There we only rotated and translated an existing structure. The differences between that help screen and the present one may be useful in becoming accustomed to the differing appearances of the GM lines in that example and this one.)

+

Since we have only specified a single source, we may run the model both with and without the GM input line. Fig. 9 compares the free-space E- plane pattern for the original 2-element wire Yagi and the new reversible model. The effects of the undriven alternate driver are clear in its slight addition to gain and the slight decrease in front-to-back ratio.

+
+ +
+

In order to obtain the reverse-direction pattern, we need only alter the source location on the EX input line. Instead of specifying tag 2, we would enter tag 3 in the second entry position. (See Fig. 6.)

+

Conclusion

+

We have used simple models in this exercise because our aim was to illustrate the differences between the NEC-4 and the NEC-2 formats and functions for the GH and GM entries. The true utility of these geometry entry lines begins to emerge when our structures become far more complex. Consider creating a rectangular grid of wires. First, create 3 sides of one grid square with 3 GW entries. Then duplicate the second 2 wires in a single GM line as many times as it takes to make a single row of grid squares, each with an open bottom edge. Now, with a second GM line, duplicate the entire row as many times as it takes to fill the rectangular plane. Since the bottoms of the last row of squares are all open, let's enter a GW line to close the first square. Now add a final GM line to duplicate this line and close the remaining square bottoms. The model remains at a constant ASCII input size whether we are creating a 5-by-5 grid or a 50-by-50 grid. However, since every new GM structure replicates wires and segments, the core run times will be quite different for the two sizes of wire grids.

+

One common practice among modelers is to run the same model on both NEC-2 and NEC-4, sometimes to detect any differences between results and thereby catch any sensitivity of the model to limitations of the programs. We may perform such tests only where the entry lines for the model are the same for both NEC-2 and NEC-4. A model using only GW entries for the wire geometry and simple control input entries are amenable to being run in both programs without modification.

+

However, there are many subtle differences in the advanced input structures for lines having the same identification letters within NEC-2 and NEC-4. We have sampled a few of those differences as they relate to the GH and GM inputs. There are many others, and numerous ones apply to the control inputs. If these small exercises have made you a bit self- conscious about the input line differences among the NEC cores, then they will have done some useful work.

+

Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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64. An Orientation to the NEC Output File

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+

L. B. Cebik, W4RNL

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+
+ +

+
+

Most beginning NEC modelers employ one of the entry-level programs, such as EZNEC or NEC-Win Plus. These programs are amazing pieces of software for a number of reasons. They ease the task of inputting the information necessary to create a model. As well, the provide a mass of distilled output data that the user most wants and re-forms it into tables and graphics that make it the most readable. One cost of having so much convenience is that the entry-level programs must restrict the number of wire geometry and control inputs made available to the user.

+

Because the entry-level programs are so convenient, many users have little idea of what is going on behind the scenes to create the graphics and tables. They may never look at the output file produced by the NEC core which is doing the calculating (except for some post-run additional calculations for user convenience). So I thought that we might take a look at an output file and see what it can tell us--or at least show us from where the output functions of our modeling program gets their information.

+

EZNEC (short of the Pro version) does not give the user access to the NEC output file. However, that file is always accessible in NEC-Win Plus and in advanced programs. So we shall be looking at NEC-Win programs in this exercise. We shall use both NEC-Win Plus and NEC-Win Pro, although both produce an output file with the extension .NOU to save the core-run output. (A core "run" is simply the operation of the NEC calculating portion of the overall program, which shows only as thermometer bars in EZNEC and as a temporary sub-screen in NEC-Win software.)

+
+ +
+

Let's begin with a small model, the one shown in NEC-Win Plus format in Fig. 1. The wire layout consists of 2 wires for a 30-meter Yagi. The wire has a diameter of 2 mm (0.0787"), and the dimensions are all in meters. The wire is copper, and the source is at the center of wire 1. The upper left corner let's us know that we shall run the antenna at 10.125 MHz only. The "No Ground" label tells us the antenna is in free space. We have requested 2 radiation patterns. Modeling conventions designate them as azimuth and elevation patterns, but in free space, they are best termed E-plane and H-plane patterns, respectively.

+
+ +
+

Fig. 2 shows the modeling outline of the array. Each element has 21 equal-length segments. The red source segment is at the center of the element designated as the driver. Since the remaining element is longer, it functions as a reflector. NEC functions with neither of these forms of model set-up. The .NWP file for the model in Fig. 1 is in spreadsheet format, while the outline is a graphic. NEC requires a simple ASCII file consisting of lines of characters meeting certain standards. The standard for input data vary according to the type of line.

+
+ +
+

NEC-Win Plus creates an input file for the model that has the very same form as one that we might create by typing into a simple text editor. This file has the format used by NEC-Win Pro and other advanced programs that give the user access to all of the geometry and control inputs that are usable with NEC. (See Fig. 3.) The GW lines provide the coordinates of the wires, the number of segments in them, and the wire radius (1 mm). Since all dimensions are already in meters, the GS or scaling line uses a factor of 1.

+

The EX line provides data for the voltage source, specifying its location on wire or tag 1, segment 11, with a magnitude of 1.414 and a phase angle of zero. Each wire or tag has a corresponding LD5 line to specify that the wires have the conductivity of copper (5.8E7 s/m). The FR line sets the single frequency of the calculations, while the two RP0 lines request standard azimuth and elevation patterns. The former is at zero degrees elevation, while the latter is at an azimuth angle of zero degrees. However, these patterns--in basic NEC terms--are really phi and theta patterns. The give-away is the "90" entry, which specifies the theta angle for the phi, counting from overhead to the horizon. In the theta pattern itself, the 90-degree entry simply specifies the starting point for the pattern data. Both patterns request 361 data points so that the total pattern will close on itself and not leave a 1-degree gap.

+
+ +
+

Fig. 4 shows the resulting E-plane and H-plane (azimuth/phi and elevation/theta) patterns that emerge from the core calculations. The E-plane pattern counts degrees in a counter-clockwise direction, indicating a phi rather than a true azimuth pattern. The H-plane pattern shows 90 degrees at the virtual horizon, with 0 degrees at the top, indicating its true identity as a theta and not an elevation pattern.

+
+ +
+

Most programs provide the user with selected tabular data. Fig. 5 shows the VSWR report from NEC-Win Pro. Invisible to the user is the fact that only some of the reported data comes from the NEC calculations directly: the information on the input impedance. The VSWR figure comes from a post-run calculation made by the program and dependent upon the user's insertion of an impedance reference figure.

+

What the Core Output Looks Like and Tells Us

+

With this much orientation, let's turn to the actual NEC output file for this model and see what it looks like and what it has to tell us--and where it is silent. The report is an ASCII document, making it convenient for moving part or all of the data into other programs for viewing or manipulation. The best place to begin is at the beginning of the file created by the core run.

+ 
 **********************************************
+    NUMERICAL ELECTROMAGNETICS CODE (NEC-2D-P)
+ **********************************************
+
+ Enhanced version, copyright 1997-2001 Nittany Scientific
+
+ Run date:  08:39:25 on 04-JUN-2002
+
+ Parameter dimensions:
+
+   NEC2D Version:  2.5
+   Maximum # of segments:            42
+   Maximum # of segments in core:            42
+   Maximum # of new connections to NGF segments:           180
+   Maximum # of sources:             1
+   Maximum # of degrees of symmetry:             1
+   Maximum # of networks:             0
+   Maximum # of segments at a junction:             1
+   Maximum # of loads:             2
+   Maximum # of frequencies or angles:           361
+
+ **********************************************
+

The NEC calculation core operates best when certain parameters are at least as large as required by the size of the model but not so much larger that they slow down the speed of the matrix and other calculations made by the core. Originally set by a separate file, most implementations of NEC use an automated system of setting the parameters.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - STRUCTURE SPECIFICATION - - -
+
+                                     COORDINATES MUST BE INPUT IN
+                                     METERS OR BE SCALED TO METERS
+                                     BEFORE STRUCTURE INPUT IS ENDED
+
+
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+  1    0.00000   -7.06000    0.00000     0.00000    7.06000    0.00000    0.00100     21        1    21       1
+  2   -4.30000   -7.52500    0.00000    -4.30000    7.52500    0.00000    0.00100     21       22    42       2
+      STRUCTURE SCALED BY FACTOR   1.00000
+
+   TOTAL SEGMENTS USED=   42     NO. SEG. IN A SYMMETRIC CELL=   42     SYMMETRY FLAG=  0
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The first entry in the output file is a record of the wire geometry of the model. This section serves as an important check for the modeler to discover whether the intended model actually materialized. Note that the core assigns each wire a tag number. These will normally be the same as the wire numbers, but not when implementing certain complex structures.

+

As well, the structure section of the report assigns to each segment in the model an absolute segment number. The tag number serves as a way of tracking the location of the absolute segments within the model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1    0.00000   -6.72381    0.00000    0.67238    0.00000  90.00000   0.00100     0    1    2      1
+     2    0.00000   -6.05143    0.00000    0.67238    0.00000  90.00000   0.00100     1    2    3      1
+     3    0.00000   -5.37905    0.00000    0.67238    0.00000  90.00000   0.00100     2    3    4      1
+     4    0.00000   -4.70667    0.00000    0.67238    0.00000  90.00000   0.00100     3    4    5      1
+     5    0.00000   -4.03429    0.00000    0.67238    0.00000  90.00000   0.00100     4    5    6      1
+     6    0.00000   -3.36190    0.00000    0.67238    0.00000  90.00000   0.00100     5    6    7      1
+     7    0.00000   -2.68952    0.00000    0.67238    0.00000  90.00000   0.00100     6    7    8      1
+     8    0.00000   -2.01714    0.00000    0.67238    0.00000  90.00000   0.00100     7    8    9      1
+     9    0.00000   -1.34476    0.00000    0.67238    0.00000  90.00000   0.00100     8    9   10      1
+    10    0.00000   -0.67238    0.00000    0.67238    0.00000  90.00000   0.00100     9   10   11      1
+    11    0.00000    0.00000    0.00000    0.67238    0.00000  90.00000   0.00100    10   11   12      1
+    12    0.00000    0.67238    0.00000    0.67238    0.00000  90.00000   0.00100    11   12   13      1
+    13    0.00000    1.34476    0.00000    0.67238    0.00000  90.00000   0.00100    12   13   14      1
+    14    0.00000    2.01714    0.00000    0.67238    0.00000  90.00000   0.00100    13   14   15      1
+    15    0.00000    2.68952    0.00000    0.67238    0.00000  90.00000   0.00100    14   15   16      1
+    16    0.00000    3.36190    0.00000    0.67238    0.00000  90.00000   0.00100    15   16   17      1
+    17    0.00000    4.03429    0.00000    0.67238    0.00000  90.00000   0.00100    16   17   18      1
+    18    0.00000    4.70667    0.00000    0.67238    0.00000  90.00000   0.00100    17   18   19      1
+    19    0.00000    5.37905    0.00000    0.67238    0.00000  90.00000   0.00100    18   19   20      1
+    20    0.00000    6.05143    0.00000    0.67238    0.00000  90.00000   0.00100    19   20   21      1
+    21    0.00000    6.72381    0.00000    0.67238    0.00000  90.00000   0.00100    20   21    0      1
+    22   -4.30000   -7.16667    0.00000    0.71667    0.00000  90.00000   0.00100     0   22   23      2
+    23   -4.30000   -6.45000    0.00000    0.71667    0.00000  90.00000   0.00100    22   23   24      2
+    24   -4.30000   -5.73333    0.00000    0.71667    0.00000  90.00000   0.00100    23   24   25      2
+    25   -4.30000   -5.01667    0.00000    0.71667    0.00000  90.00000   0.00100    24   25   26      2
+    26   -4.30000   -4.30000    0.00000    0.71667    0.00000  90.00000   0.00100    25   26   27      2
+    27   -4.30000   -3.58333    0.00000    0.71667    0.00000  90.00000   0.00100    26   27   28      2
+    28   -4.30000   -2.86667    0.00000    0.71667    0.00000  90.00000   0.00100    27   28   29      2
+    29   -4.30000   -2.15000    0.00000    0.71667    0.00000  90.00000   0.00100    28   29   30      2
+    30   -4.30000   -1.43333    0.00000    0.71667    0.00000  90.00000   0.00100    29   30   31      2
+    31   -4.30000   -0.71667    0.00000    0.71667    0.00000  90.00000   0.00100    30   31   32      2
+    32   -4.30000    0.00000    0.00000    0.71667    0.00000  90.00000   0.00100    31   32   33      2
+    33   -4.30000    0.71667    0.00000    0.71667    0.00000  90.00000   0.00100    32   33   34      2
+    34   -4.30000    1.43333    0.00000    0.71667    0.00000  90.00000   0.00100    33   34   35      2
+    35   -4.30000    2.15000    0.00000    0.71667    0.00000  90.00000   0.00100    34   35   36      2
+    36   -4.30000    2.86667    0.00000    0.71667    0.00000  90.00000   0.00100    35   36   37      2
+    37   -4.30000    3.58333    0.00000    0.71667    0.00000  90.00000   0.00100    36   37   38      2
+    38   -4.30000    4.30000    0.00000    0.71667    0.00000  90.00000   0.00100    37   38   39      2
+    39   -4.30000    5.01667    0.00000    0.71667    0.00000  90.00000   0.00100    38   39   40      2
+    40   -4.30000    5.73333    0.00000    0.71667    0.00000  90.00000   0.00100    39   40   41      2
+    41   -4.30000    6.45000    0.00000    0.71667    0.00000  90.00000   0.00100    40   41   42      2
+    42   -4.30000    7.16667    0.00000    0.71667    0.00000  90.00000   0.00100    41   42    0      2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The segmentation information is useful in determining whether all aspects of the geometric structure wind up where you intend. The present straight-wire model offers no question marks, but catenary wires, arcs, and helices can present many questions that an examination of the segmentation can answer. Note, however, that the information specifies the center point of each segment on the Cartesian coordinate system--not the segment ends or junctions. However, the +/-I list provides a list of connections, which can be useful in determining whether all segments having a desired junction actually hit the junction point.

+

The presence of a GE entry indicates the end of the geometry section. At this point, the output report records the control inputs as a series of line entries. Note that all of the integer entries that fall into floating decimal positions take on engineering notation. Hence, the frequency in the FR line is no longer 10.125, but 1.01250E+01.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ ***** DATA CARD NO.   1 EX     0     1    11     0  1.41421E+00  0.00000E+00  0.00000E+00  0.00000E+00
+0.00000E+00  0.00000E+00
+ ***** DATA CARD NO.   2 LD     5     1     1    21  5.80010E+07  0.00000E+00  0.00000E+00  0.00000E+00
+0.00000E+00  0.00000E+00
+ ***** DATA CARD NO.   3 LD     5     2     1    21  5.80010E+07  0.00000E+00  0.00000E+00  0.00000E+00
+0.00000E+00  0.00000E+00
+ ***** DATA CARD NO.   4 FR     0     1     0     0  1.01250E+01  1.00000E+00  0.00000E+00  0.00000E+00
+0.00000E+00  0.00000E+00
+ ***** DATA CARD NO.   5 RP     0     1   361  1000  9.00000E+01  0.00000E+00  1.00000E+00  1.00000E+00
+0.00000E+00  0.00000E+00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The frequency holds sufficient significance to receive a separate region of the output report to itself.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 - - - - - - FREQUENCY - - - - - -
+
+                                    FREQUENCY= 1.0125E+01 MHZ
+                                    WAVELENGTH= 2.9610E+01 METERS
+
+ APPROXIMATE INTEGRATION EMPLOYED FOR SEGMENTS MORE THAN   1.000 WAVELENGTHS APART
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Following the frequency, the report lists any loads, whether they specify RLC, R-X, or simple element conductivity.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                               - - - STRUCTURE IMPEDANCE LOADING - - -
+
+       LOCATION          RESISTANCE   INDUCTANCE  CAPACITANCE       IMPEDANCE (OHMS)     CONDUCTIVITY    TYPE
+    ITAG FROM THRU          OHMS        HENRYS       FARADS        REAL      IMAGINARY    MHOS/METER
+
+       1    1   21                                                                       5.8001E+07     WIRE
+
+       2    1   21                                                                       5.8001E+07     WIRE
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The report will also record the antenna environment, which is simple in this model (free-space). As well, it records the time expended so far on basic matrix calculations--a very brief time for this simple model. Often, examining the timing--especially of a model that has been left unattended during its run--can provide clues either to the adequacy of the model or to the computer set-up on which one runs the model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                  - - - ANTENNA ENVIRONMENT - - -
+
+                                            FREE SPACE
+
+                                - - - MATRIX TIMING - - -
+
+                        FILL=    0.110 SEC.,  FACTOR=    0.000 SEC.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The core has so far calculated the mutual impedances among all of the segments in the model. However, before it can calculate the currents on each segment--a necessary prerequisite to determining the antenna power gain in any chosen direction--it must account for the source or excitation. Therefore, it records all of the source input data, along with calculations predicated on the source and factors already calculated. Only then can the program calculate the segment currents.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                          - - - ANTENNA INPUT PARAMETERS - - -
+
+TAG   SEG.    VOLTAGE (VOLTS)         CURRENT (AMPS)         IMPEDANCE (OHMS)        ADMITTANCE (MHOS)      POWER
+NO.   NO.    REAL        IMAG.       REAL        IMAG.       REAL        IMAG.       REAL        IMAG.     (WATTS)
+1    11 1.41421E+00 0.00000E+00 2.85369E-02-9.87696E-04 4.94981E+01 1.71318E+00 2.01786E-02-6.98406E-04 2.01787E-02
+
+                             - - - CURRENTS AND LOCATION - - -
+
+                                 DISTANCES IN WAVELENGTHS
+
+
+  SEG.  TAG    COORD. OF SEG. CENTER     SEG.            - - - CURRENT (AMPS) - - -
+  NO.   NO.     X        Y        Z      LENGTH     REAL        IMAG.       MAG.        PHASE
+     1    1   0.0000  -0.2271   0.0000  0.02271   2.5339E-03 -1.9134E-04  2.5411E-03   -4.318
+     2    1   0.0000  -0.2044   0.0000  0.02271   7.0345E-03 -5.1543E-04  7.0533E-03   -4.191
+     3    1   0.0000  -0.1817   0.0000  0.02271   1.1146E-02 -7.8904E-04  1.1174E-02   -4.049
+     4    1   0.0000  -0.1590   0.0000  0.02271   1.4929E-02 -1.0156E-03  1.4963E-02   -3.892
+     5    1   0.0000  -0.1362   0.0000  0.02271   1.8343E-02 -1.1912E-03  1.8381E-02   -3.716
+     6    1   0.0000  -0.1135   0.0000  0.02271   2.1338E-02 -1.3112E-03  2.1378E-02   -3.516
+     7    1   0.0000  -0.0908   0.0000  0.02271   2.3866E-02 -1.3714E-03  2.3905E-02   -3.289
+     8    1   0.0000  -0.0681   0.0000  0.02271   2.5881E-02 -1.3682E-03  2.5917E-02   -3.026
+     9    1   0.0000  -0.0454   0.0000  0.02271   2.7347E-02 -1.2979E-03  2.7378E-02   -2.717
+    10    1   0.0000  -0.0227   0.0000  0.02271   2.8238E-02 -1.1534E-03  2.8262E-02   -2.339
+    11    1   0.0000   0.0000   0.0000  0.02271   2.8537E-02 -9.8770E-04  2.8554E-02   -1.982
+    12    1   0.0000   0.0227   0.0000  0.02271   2.8238E-02 -1.1534E-03  2.8262E-02   -2.339
+    13    1   0.0000   0.0454   0.0000  0.02271   2.7347E-02 -1.2979E-03  2.7378E-02   -2.717
+    14    1   0.0000   0.0681   0.0000  0.02271   2.5881E-02 -1.3682E-03  2.5917E-02   -3.026
+    15    1   0.0000   0.0908   0.0000  0.02271   2.3866E-02 -1.3714E-03  2.3905E-02   -3.289
+    16    1   0.0000   0.1135   0.0000  0.02271   2.1338E-02 -1.3112E-03  2.1378E-02   -3.516
+    17    1   0.0000   0.1362   0.0000  0.02271   1.8343E-02 -1.1912E-03  1.8381E-02   -3.716
+    18    1   0.0000   0.1590   0.0000  0.02271   1.4929E-02 -1.0156E-03  1.4963E-02   -3.892
+    19    1   0.0000   0.1817   0.0000  0.02271   1.1146E-02 -7.8904E-04  1.1174E-02   -4.049
+    20    1   0.0000   0.2044   0.0000  0.02271   7.0345E-03 -5.1543E-04  7.0533E-03   -4.191
+    21    1   0.0000   0.2271   0.0000  0.02271   2.5339E-03 -1.9134E-04  2.5411E-03   -4.318
+    22    2  -0.1452  -0.2420   0.0000  0.02420  -8.7033E-04  1.1146E-03  1.4141E-03  127.985
+    23    2  -0.1452  -0.2178   0.0000  0.02420  -2.4453E-03  3.1118E-03  3.9576E-03  128.161
+    24    2  -0.1452  -0.1936   0.0000  0.02420  -3.9163E-03  4.9537E-03  6.3148E-03  128.329
+    25    2  -0.1452  -0.1694   0.0000  0.02420  -5.2948E-03  6.6605E-03  8.5086E-03  128.483
+    26    2  -0.1452  -0.1452   0.0000  0.02420  -6.5590E-03  8.2103E-03  1.0509E-02  128.620
+    27    2  -0.1452  -0.1210   0.0000  0.02420  -7.6828E-03  9.5767E-03  1.2278E-02  128.738
+    28    2  -0.1452  -0.0968   0.0000  0.02420  -8.6411E-03  1.0734E-02  1.3780E-02  128.835
+    29    2  -0.1452  -0.0726   0.0000  0.02420  -9.4114E-03  1.1659E-02  1.4984E-02  128.911
+    30    2  -0.1452  -0.0484   0.0000  0.02420  -9.9753E-03  1.2334E-02  1.5863E-02  128.965
+    31    2  -0.1452  -0.0242   0.0000  0.02420  -1.0319E-02  1.2744E-02  1.6398E-02  128.998
+    32    2  -0.1452   0.0000   0.0000  0.02420  -1.0435E-02  1.2882E-02  1.6578E-02  129.009
+    33    2  -0.1452   0.0242   0.0000  0.02420  -1.0319E-02  1.2744E-02  1.6398E-02  128.998
+    34    2  -0.1452   0.0484   0.0000  0.02420  -9.9753E-03  1.2334E-02  1.5863E-02  128.965
+    35    2  -0.1452   0.0726   0.0000  0.02420  -9.4114E-03  1.1659E-02  1.4984E-02  128.911
+    36    2  -0.1452   0.0968   0.0000  0.02420  -8.6411E-03  1.0734E-02  1.3780E-02  128.835
+    37    2  -0.1452   0.1210   0.0000  0.02420  -7.6828E-03  9.5767E-03  1.2278E-02  128.738
+    38    2  -0.1452   0.1452   0.0000  0.02420  -6.5590E-03  8.2103E-03  1.0509E-02  128.620
+    39    2  -0.1452   0.1694   0.0000  0.02420  -5.2948E-03  6.6605E-03  8.5086E-03  128.483
+    40    2  -0.1452   0.1936   0.0000  0.02420  -3.9163E-03  4.9537E-03  6.3148E-03  128.329
+    41    2  -0.1452   0.2178   0.0000  0.02420  -2.4453E-03  3.1118E-03  3.9576E-03  128.161
+    42    2  -0.1452   0.2420   0.0000  0.02420  -8.7033E-04  1.1146E-03  1.4141E-03  127.985
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The excitation data is needed for the current calculations. If you look closely at the impedance entries, you will see--in slightly different notation--the impedance report that went into the VSWR table shown in an earlier figure. NEC does not calculate VSWR values, but those are simple enough to implement in a post core-run action.

+

I have included the entire current listing for this small model to provide you with a sense of how the internal parts of the output report interrelate. Note that the entries list the center coordinates for each segment, corresponding to the list we viewed in the segmentation data. For each segment, we find a current given in two forms: by the real and imaginary components and by a magnitude and phase angle. Some programs provide facilities for creating a rectangular plot of the current along a wire or sequence of wires. This data--in either tabular or graphical form-- can be useful in determining the properties of elements within an antenna array. As well, the current level at the center of each wire is often useful data for understanding especially the operations of arrays using elements in the neighborhood of 1/2 wavelength. Hence, it is important to be able to locate a wire center segment by reference to its absolute segment number. (Some programs, such as EZNEC, translate the current table into a format that restores the original wire and segment numbers used in the creation of GW entries.)

+

Note that the current levels are very low, making it difficult in some cases to clearly see the relative current level along an element. Using a current source (discussed in an earlier column in this series) can provide a basis for showing all current levels relative to a source current magnitude of 1.0. Such a source is also convenient in phased arrays for setting each source with a specific current magnitude and phase angle. As we have shown in earlier columns, we may also calculate for a voltage source the magnitude necessary to produce a power of a given level--taking into account that NEC uses and reports peak values of voltage and current, whereas power is always an RMS calculation. This calls for a revision of the user-input for the voltage magnitude and a rerun of the core--unless the program has a provision for calculating this value after the user specifies a desired power level (EZNEC). Using different power levels or equalizing them for all revisions of the model does not effect the power gain calculations that appear in the radiation patterns under an RP0 request. However, setting a power level is very useful to near field and ground wave calculations.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 2.0179E-02 WATTS
+                                           RADIATED POWER= 1.9644E-02 WATTS
+                                           STRUCTURE LOSS= 5.3508E-04 WATTS
+                                           NETWORK LOSS  = 0.0000E+00 WATTS
+                                           EFFICIENCY    =  97.35 PERCENT
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Some programs omit some aspects of the power budget. However, the total input power is useful as a check on any manual adjustment of the voltage magnitude to achieve a desired power level. The radiated power is subject to two types of subtractions from the input power. Structure losses are those losses owing to LD5 (wire conductivity) loads. One reason that I chose a wire array is to let you change the wire conductivity from a perfect or lossless wire to a copper wire to an aluminum wire, etc. You will observe changes in the radiated power and the overall efficiency of the antenna.

+

Network losses owe to the use of any RLC or R-X loads that have a resistive component. As well, networks with less than unlimited conductance will also create losses. Since such loads and networks may be anywhere along the elements, the same load will not necessary show the same overall loss at every position. Any loads created by the use of transmission lines (such as open or shorted stubs) will be lossless (in contrast to the same types of loads in their physical implementations). In addition, external losses created by matching networks that are not part of the model will not show up in the efficiency report.

+

We are finally ready to read out the pattern requests. However, I shall truncate the two reports to only a few lines each.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+[Phi pattern]                                   - - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -           - POWER GAINS -       - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.              VOLTS/M    DEGREES      VOLTS/M    DEGREES
+   90.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10773E+00   -64.63
+   90.00     1.00    -999.99    5.65    5.65    0.00000   -90.00  LINEAR    1.87706E-13   115.37    2.10715E+00   -64.63
+   90.00     2.00    -999.99    5.64    5.64    0.00000   -90.00  LINEAR    3.75218E-13   115.38    2.10542E+00   -64.62
+   90.00     3.00    -999.99    5.63    5.63    0.00000   -90.00  LINEAR    5.62342E-13   115.39    2.10254E+00   -64.61
+   90.00     4.00    -999.99    5.61    5.61    0.00000   -90.00  LINEAR    7.48885E-13   115.41    2.09851E+00   -64.59
+   90.00     5.00    -999.99    5.59    5.59    0.00000   -90.00  LINEAR    9.34656E-13   115.43    2.09334E+00   -64.57
+   90.00     6.00    -999.99    5.56    5.56    0.00000   -90.00  LINEAR    1.11946E-12   115.45    2.08703E+00   -64.55
+   90.00     7.00    -999.99    5.53    5.53    0.00000   -90.00  LINEAR    1.30312E-12   115.48    2.07961E+00   -64.52
+   90.00     8.00    -999.99    5.50    5.50    0.00000   -90.00  LINEAR    1.48545E-12   115.52    2.07107E+00   -64.48
+   90.00     9.00    -999.99    5.46    5.46    0.00000   -90.00  LINEAR    1.66625E-12   115.56    2.06143E+00   -64.44
+   90.00    10.00    -999.99    5.41    5.41    0.00000   -90.00  LINEAR    1.84536E-12   115.60    2.05070E+00   -64.40
+-----
+   90.00   351.00    -999.99    5.46    5.46    0.00000    90.00  LINEAR    1.66625E-12   -64.44    2.06143E+00   -64.44
+   90.00   352.00    -999.99    5.50    5.50    0.00000    90.00  LINEAR    1.48545E-12   -64.48    2.07107E+00   -64.48
+   90.00   353.00    -999.99    5.53    5.53    0.00000    90.00  LINEAR    1.30312E-12   -64.52    2.07961E+00   -64.52
+   90.00   354.00    -999.99    5.56    5.56    0.00000    90.00  LINEAR    1.11946E-12   -64.55    2.08703E+00   -64.55
+   90.00   355.00    -999.99    5.59    5.59    0.00000    90.00  LINEAR    9.34656E-13   -64.57    2.09334E+00   -64.57
+   90.00   356.00    -999.99    5.61    5.61    0.00000    90.00  LINEAR    7.48885E-13   -64.59    2.09851E+00   -64.59
+   90.00   357.00    -999.99    5.63    5.63    0.00000    90.00  LINEAR    5.62342E-13   -64.61    2.10254E+00   -64.61
+   90.00   358.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    3.75218E-13   -64.62    2.10542E+00   -64.62
+   90.00   359.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    1.87706E-13   -64.63    2.10715E+00   -64.63
+   90.00   360.00    -999.99    5.65    5.65    0.00000   -90.00  LINEAR    2.19582E-22   115.37    2.10773E+00   -64.63
+=====================
+[Theta pattern]                                 - - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -           - POWER GAINS -       - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.              VOLTS/M    DEGREES      VOLTS/M    DEGREES
+   90.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10773E+00   -64.63
+   91.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10762E+00   -64.62
+   92.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10729E+00   -64.62
+   93.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10673E+00   -64.61
+   94.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10596E+00   -64.59
+   95.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10496E+00   -64.57
+   96.00     0.00    -999.99    5.63    5.63    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10374E+00   -64.54
+   97.00     0.00    -999.99    5.63    5.63    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10230E+00   -64.51
+   98.00     0.00    -999.99    5.62    5.62    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10064E+00   -64.47
+   99.00     0.00    -999.99    5.61    5.61    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.09876E+00   -64.43
+  100.00     0.00    -999.99    5.60    5.60    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.09665E+00   -64.39
+------------
+  441.00     0.00    -999.99    5.61    5.61    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.09876E+00   -64.43
+  442.00     0.00    -999.99    5.62    5.62    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10064E+00   -64.47
+  443.00     0.00    -999.99    5.63    5.63    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10230E+00   -64.51
+  444.00     0.00    -999.99    5.63    5.63    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10374E+00   -64.54
+  445.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10496E+00   -64.57
+  446.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10596E+00   -64.59
+  447.00     0.00    -999.99    5.64    5.64    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10673E+00   -64.61
+  448.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10729E+00   -64.62
+  449.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10762E+00   -64.62
+  450.00     0.00    -999.99    5.65    5.65    0.00000    90.00  LINEAR    0.00000E+00     0.00    2.10773E+00   -64.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The radiation reports--whether for phi or theta--offer a variety of data for each bearing defined by a combination of phi and theta angles. The format for the reports selected here is for a 2-dimensional pattern in which one angular system is progressively calculated while holding the other constant. Other patterns are possible, including 3-dimensional patterns that sample the entire sphere around the antenna at specified intervals.

+

The reports offer, of course, the total power gain--recorded in dBi using an isotropic radiator as a comparator--and its vertical and horizontal components. The report also offers polarization information, which is not especially useful in this particular model using linear elements. Finally, we find a record of the electrical fields tangential to the X-Y axes (theta) and parallel to it (phi). Although many general modelers focus only upon the antenna power gain, the other data has extensive applications, depending upon the type of antenna and upon the properties of highest interest.

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We should note a few seeming oddities in the report. First, the theta pattern ends at an angle of 450 degrees. This ending point stems from the starting point on the virtual horizon (90 degrees) and the fact that the core counts in a positive direction. The polar H-plane plot that we earlier observed has done a post-run reset of the angles to correspond to something more familiar.

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Since the antenna is in free space and is composed of linear elements, it is polarized in parallel to the X-Y axes. There is no significant radiation at right angles to this orientation. Hence, the vertical power gain is virtually zero. NEC records such a power gain--in dBi--as -999.99, an insignificantly low but non-zero value.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ ***** DATA CARD NO.   7 EN     0     0     0     0  0.00000E+00  0.00000E+00  0.00000E+00  0.00000E+00
+0.00000E+00  0.00000E+00
+
+ RUN TIME =     0.330
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The EN entry marks the end of the core run. Note that we obtain a registration of the total run time. This value happens for the present entry to be 3 times the value of the matrix fill and factor value recorded earlier. Those who implement version of NEC commercially are ever on the search for ways of compiling the original FORTRAN program so that it calculates faster. In conjunction with the latest 2 GHz, fast memory bus machines, these techniques have converted runs that took overnight into runs that barely allow one to inhale properly.

+

We have taken you through the structure of the NEC output report for a simple model on which we placed equally simple demands. However, I hope the exercise orients you to the output report sufficiently well so that you can navigate around more complex reports--perhaps involving plane wave sources, requests for ground waves or near field data, and those making use of one or more of the supplementary geometry inputs. The next step is to transfer the output report to a spreadsheet on which you may manipulate the data in further useful ways. The output tables and graphics of any given implementation of NEC may cover most of the important data, but they cannot cover all possible present and future interests. The only way to make full use of the NEC output data is to return to the output report itself. The more comfortable you are in navigating that report, the more interesting and useful information you can draw from it.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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65. The 1/2-Wavelength Resonant Dipole as a Core Test Instrument

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L. B. Cebik, W4RNL

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+

In the course of creating models, we occasionally enter into gray areas that border upon the limitations of the calculating core, whether that is NEC-2, NEC-4, or MININEC. Very often we simply plunge ahead with the model, despite that fact that it may be quite complex. We hope that any difficulties will show themselves.

+

Actually, the more complex the model, the more likely it is to mask the difficulties that we encounter. Consider a model of a log periodic dipole array (LPDA) that uses physical wires as the phase line. For normal phase lines using wires ranging from AWG #18 to AWG #10 or so, the phase line separation will be under 2". However, some element sections of the LPDA may be over 2" in diameter.

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+ +
+

As shown in Fig. 1, the most ordinary way to model an LPDA with physical wires as the phase line is to set the two wires of the line vertically. Each LPDA element is split in the center, with half connected to each line. For thinner LPDA elements, we encounter no potential problems, as evidenced by the upper portion of the sketch.

+

However, large-diameter center sections of an element can result in the case shown in the lower half of the figure. The element centerlines are separated by a large enough space that the core does not interpret them as forming a wire junction. However, the surface boundaries of each element pass each other and touch at the ends.

+

Modeling rules prohibit wires which penetrate the surface area of another wire. Had we use crossing wires, the surfaces of the two wires would have penetrated each other and we would have had an error in geometry. Even if we have a core which allows the run, the results would have been useless. I once encountered a model of an antenna with such errors that seemed to yield over 35 dBi gain. Only when I examined the model did I find the surface penetrations. The AGT for the model was over 1,000.0 (when perfection would have been 1.0), indicating that the true gain was minuscule.

+

However, our present case uses wires that abut at the ends. There is no end cap invoked, since the wires make a junction with another wire. The situation invokes no warnings or errors, and the core runs look sensible at first sight. Our question is whether these results are reliable.

+

To answer that question, we should go back to the simplest model possible and perform a series of tests on the situation itself. For that purpose, the dipole is ideal.

+

Some NEC Tests

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The construction of a modeling test scenario requires some thought. Just making a resonant dipole will not do the job. There are numerous questions to pose.

+

1. What type of test will do the job? Since the initial problem involves an LPDA phase line, which is an application of a transmission line, we shall eventually need to construct a physical transmission line connected to the center of a dipole. If we compare the source impedance of a simple model of a dipole of a given diameter with the impedance of any transmission line that is 1/2 wavelength long, we should be able to detect any significant problems created by the situation in Fig. 1.

+

2. What transmission line and what diameter dipole elements? We need to be able to approach and then pass the limit of the two dipole halves abutting at the centerline of the dipole. If we use 0.5", 1.0", and 1.5" dipoles, we shall need a transmission line whose wires are separated by perhaps a little over an inch. If we use AWG #16 (0.0508" diameter) wire for the lines, we can obtain an impedance of 450 Ohms with a spacing of about 1.084". With a vertically oriented transmission line, the 0.5" dipole will be well short of overlap. The 1" element will almost but not quite touch. The 1.5" diameter element will overlap. For reference, we shall add a #16 wire dipole to the list as a baseline.

+

We shall use perfect or lossless wires for all parts of the test dipole models. A lossless transmission line wire will most closely approach a true velocity factor of 1.0, allowing us to use calculated values of 1/2 wavelength.

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3. What frequency? Since the problem arose in connection with models of LPDAs in the HF range, we may arbitrarily select 14 MHz as the test frequency. The test is not frequency dependent, but a middle HF frequency has some modeling advantages. First, it allows us to make fine discriminations in length simply by measuring everything in inches. Second, for the element diameters used, we have potentially sufficient numbers of segments available, given the recommended limit that the length of a NEC segment should be at least as large as the element diameter. For some tests, 1" long segments to match the separation of the transmission line wires will be possible. Since a dipole model converges far below this level of segmentation, we may use fewer segments for some initial models.

+

A wavelength at 14 MHz is 843.061". We shall use 1/2 wavelength transmission lines that are 421.531" long. The resonant length of the perfect-wire dipole, of course, will vary with the diameter of the element.

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4. What test models should we generate? Fig. 2 shows the range of models that we shall examine.

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+ +
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Since we are working initially with NEC--specifically NEC-4--we shall look at two ways of feeding a dipole for reference. The simple dipole model will have 41 segments with the feedpoint or source at the center segment, in accord with the NEC system wherein the current center is the segment center. We shall also examine the same dipole using a dual-feed or split-feed system. Here, we shall use 42 segments, feeding the segments on either side of the centerline. This test will tell us something about the sensitivity of the model to minor changes in segmentation and feed arrangements.

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We shall then apply to our simple single-feed dipole a 1/2 wavelength transmission line which we shall terminate in the shortest practical wire. We shall place the source on this 1-segment wire.

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Finally, we shall construct two types of physical transmission lines. The first will be a vertically oriented or Z-axis line corresponding to modeling practices for LPDAs. The element inner ends will be displaced by 1.084" at their wire centerlines, and each inner end will terminate at 0.0 on its axis. This set-up will ensure that the 1.5" diameter elements will overlap as they touch at their ends, but will not form a wire junction. The second type of physical transmission line--used only as a check--will consist of two wires spaced horizontally in the plane of the length of the dipole. This line will effect a center spacing of 1.084" in the dipole.

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The simple model results: The following table summarizes the results obtained for the simple models of a dipole using both single and split feed systems. Each dipole was resonated to under +/-0.01 Ohm reactance, and the dipole length (listed as a +/- value in inches) is carried out to more decimal places than we would ever need in practical modeling. However, we are not modeling a practical antenna, but checking the modeling system for certain sensitivities. Hence, the excess precision is warranted.

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The table lists the dipole length, the resonant source impedance, and the Average Gain Test (AGT) value, given as both a relative gain value and in dB. The AGT value gives us both a relative merit rating, where 1.0 indicates perfection, and a set of correctives. The test is a necessary but not a sufficient condition of model adequacy. Hence, a perfect AGT rating suggests but does not guarantee an adequate model. For AGT values less than 1.0, the conversion of the value into a value in dB indicates how much the reported gain is below the likely actual gain value. An AGT greater than 1.0, when converted, indicates how much higher than the likely actual gain value the reported gain may be. As well, if the source reactance is very low, then multiplying the AGT numerical value by the reported source resistance will closely approximate the likely actual source resistance. (However, when the reactance grows higher, this latter corrective gradually fails.)

+ 
El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
+
+#16 Single        +/- 204.900       72.10 - j 0.006         1.0         0.0
+#16 Split         +/- 204.874       72.17 + j 0.006         1.0         0.0
+
+0.5" Single       +/- 202.408       71.92 + j 0.001         1.0         0.0
+0.5" Split        +/- 202.350       71.95 + j 0.003         1.0         0.0
+
+1.0" Single       +/- 201.122       71.88 - j 0.006         1.0         0.0
+1.0" Split        +/- 201.040       71.89 - j 0.001         1.0         0.0
+
+1.5" Single       +/- 200.168       71.89 - j 0.003         1.0         0.0
+1.5" Split        +/- 200.060       71.86 - j 0.005         1.0         0.0
+

With segment lengths varying from 9.53" to 9.99", these simple models give a fair account of NEC-4 modeling (and by extension, NEC-2, since nothing in them presses any of the problem areas in the earlier version of NEC). The difference in resonant length between the single and split feed versions of the model are most likely due to the additional segment needed to center the split source. As expected, such simple models show no calculable departure from a perfect AGT value.

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The next table attaches to the center of the 41-segment model a 450-Ohm, velocity-factor=1.0 transmission line that is 421.531" long. It terminates in a perfect/lossless 1 segment wire that is about 2" long and has 1 segment. We place the source on this wire. The transmission line uses the TL facility of NEC. This facility creates non-physical, non-radiating mathematical lines that are lossless. (Perhaps future versions of NEC may replace this system with lossy line calculations by introducing the proper algorithms and allowing the user to introduce appropriate loss values.) Hence, the transmission line wires do not create any effects that would alter the radiation pattern. If the source wire is sufficiently small and distant from the dipole itself, it will have a completely negligible effect on the radiation pattern. The following table lists the resultant values for these runs.

+ 
El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
+
+#16 Single        +/- 204.900       72.10 - j 0.063         1.0         0.0
+
+0.5" Single       +/- 202.408       71.92 - j 0.061         1.0         0.0
+
+1.0" Single       +/- 201.122       71.88 - j 0.068         1.0         0.0
+
+1.5" Single       +/- 200.168       71.89 - j 0.063         1.0         0.0
+

These tests introduce a systematic decrease in the source reactance of about 0.06 Ohm. The most likely cause is imprecision in the length of the transmission line. Other than this one change, the transmission line alters nothing else.

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These result are exactly what we should have expected. Indeed, they comprise one reason why NEC modelers use the TL facility for most modeling enterprises involving transmission lines, including the modeling of LPDAs.

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Finally, we are ready to model the dipole using physical wires for the transmission line. If you think that I expect difficulties, you are correct. However, in a test, we let those difficulties emerge where they might rather than imposing any preconceptions upon them.

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The first transmission line consists of two parallel AWG #16 wires separated vertically by 1.084". The dipole consists of two halves, each joining one of the transmission line wires at a 90-degree angle. The far end of the transmission line has a 1-segment wire connecting the two wires. The source is placed on this wire.

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For the 4 element diameters, we obtained the following NEC-4 results. Note that each entry shows at least two levels of segmentation. The smaller numbers follow the segmentation of the simple dipole models, using about 42 segments per half wavelength. This condition results in two segments--one on each transmission line adjacent to the source wire/segment--that are radically different in length than the source segment. NEC recommendations call for segments each side of the source segment having lengths about the same as each other and as the source segment. Therefore, the second entry shows the entire assembly segmented to produce segments about 1" long. We shall discuss procedures used for the the 1.5" diameter elements after reviewing the overall results.

+ 
El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
+
+#16 21/42/1       +/- 204.900       57.64 + j 0.909         1.251       0.97
+#16 205/421/1     +/- 204.900       77.38 - j 2.812         0.933       -0.30
+
+0.5" 21/42/1      +/- 202.408       60.65 + j 0.511         1.185       0.74
+0.5" 205/421/1    +/- 202.408       105.5 - j 1.382         0.684       -1.65
+
+1.0" 21/42/1      +/- 201.122       63.24 + j 0.291         1.135       0.55
+1.0" 205/421/1    +/- 201.122       151.2 - j 2.821         0.477       -3.22
+
+1.5" 21/42/1      +/- 200.168       65.87 + j 0.060         1.089       0.37
+1.5" 205/421/1*   +/- 200.168       137.4 - j 4.17          0.524       -2.81
+1.5" 133/281/1    +/- 200.168       170.7 - j 2.836         0.421       -3.76
+*  See text for an explanation of why this entry has a special difficulty.
+

This table calls for a number of comments:

+

1. The 1.5" diameter case: The program warned of a condition that many modelers overlook and under-appreciate: the penetration at an angular junction of the surface of one wire into the center of another wire. See Fig. 3.

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+ +
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The 1.5" wire surface penetrates along the last segment of the #16 wire for 0.75". With a segment length of about 1", the surface of the large element extends beyond the center of the #16-wire segment. The core itself does not stop the run, even though this condition is considered highly problematical to any model.

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As a result, I developed the segmentation in the third line, keeping the segment lengths of the dipole and the transmission line roughly equal and using the shortest segment length that would avoid the warning. Indeed, the segment length in the transmission line wires is just over 1.50".

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2. Angular junctions of wires having dissimilar diameters: Once we go past the #16 wire model, we begin to see a pattern of results that reveals another shortcoming of NEC. NEC-2 produces worse results than NEC-4, but the NEC-4 results show that the models are highly unreliable. In some circumstances, an AGT value less than 0.95 or greater than 1.05 is considered beyond the realm of reliability, while in other situations, the limits might be set as 0.99 and 1.01. In almost all cases where we have a ratio of diameters greater than about 2:1, the AGT value falls outside of virtually any set of limits.

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The situation has an interesting abnormality relative to our usual expectations for convergence testing. In a normal situation, we anticipate increasing the number of segments until we reach a reasonable level of convergence between one level of segmentation and the next. Once we achieve this goal, we consider the model converged and that the results will be as reliable as possible.

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In the case of angular junctions of wires having dissimilar diameters, we encounter a reverse convergence situation. The lower the level of segmentation, the more accurate the results are relative to an actual antenna using the physical counterparts of the modeled wires. However, since we do not have, in most modeling exercises, the external standard against which to measure the adequacy of the results, we must rely upon the AGT. In this case, the values are wholly beyond the limits of confidence.

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3. The case of #16 wire: The reported values for the model composed wholly of #16 wire show better AGT ratings for the highly segmented model than for the model using fewer segments. Indeed, the larger model has a uniform diameter throughout, segment lengths very close to the length of the source segment, very adequate segment length to wire diameter ratios, and generally no other perceptible problems. However, the AGT rating of the "205/421/1" model is only 0.933. Something must be amiss.

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NEC does have a sensitivity to closely spaced wires. We obtain the highest accuracy when we perfectly align the segment junctions, as is the case in the present model. However, the core is not perfectly comfortable with the parallel run of 1/2 wavelength wires. Exactly what constitutes the "imperfect comfort" I do not know except that it represents a limitation of NEC models.

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The upshot of the exercise is this point: NEC models attempting to employ physical wires for both the elements and connecting transmission lines are likely to be less accurate than those using the TL facility available within the program. This point applies not only to cases like the dipole with the remote source at the end of a transmission line, but as well to LPDAs and other phased arrays.

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Before we depart NEC models of dipoles with 1/2 wavelength transmission lines, let's briefly pause to look at the second type of line: one that splits the element but leaves it on a single plane. The gap created is once more 1.084" for our #16 450-Ohm line that is 1/2 wavelength or 421.531" long. Although we do not have to concern ourselves with the touching overlap of element wire ends, the results may be useful as a comparison in other respects with the vertically oriented transmission line.

+ 
El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
+
+#16 21/42/1       +/- 204.900       56.00 - j 3.970         1.282       1.08
+#16 205/421/1     +/- 204.900       76.29 - j 7.717         0.947       -0.25
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+0.5" 21/42/1      +/- 202.408       58.89 - j 3.310         1.216       0.85
+0.5" 205/421/1    +/- 202.408       99.49 - j 6.399         0.723       -1.41
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+1.0" 21/42/1      +/- 201.122       61.14 - j 3.184         1.170       0.68
+1.0" 205/421/1    +/- 201.122       131.3 - j 7.628         0.547       -2.62
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+1.5" 21/42/1      +/- 200.168       63.32 - j 3.164         1.129       0.53
+1.5" 205/421/1    +/- 200.168       135.8 - j 8.688         0.528       -2.77
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In all cases, the AGT values are very comparable to those we met when looking at the vertically oriented transmission line. Making the transmission line horizontal does not overcome any of the difficulties previously encountered. We may add to those difficulties--for both types of transmission line--that for the 1" and the 1.5" diameter elements, using the higher level of segmentation, the segment length to wire diameter ratio is deficient. The 1" element yields a ratio of 0.98:1, while the 1.5" element shows a ratio of 0.65:1. Both of these cases are above the absolute minimum ratio of 0.5:1, but a well into the region of growing unreliability.

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The interesting phenomenon with these models is the systematic increase in capacitive reactance. The models all use the same lengths as the ones we found to be resonant in the single-feed simple models. Still, they show up as short. Before we attribute the shortness to any particular cause, we should review other models, namely, ones that we might develop using MININEC 3.13, the public domain version of the alternative core.

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Some MININEC Tests

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Raw MININEC 3.13 would be wholly inadequate to the task of modeling a dipole with a 1/2 wavelength transmission line and a remote feedpoint/source. However, the core calculating program has undergone extensive modification by a number of implementers. Perhaps the most thorough-going set of modifications belongs to the Antenna Model package by Terisoft. The program has revised the algorithms to overcome limitations involving sharp angle at wire junctions, closely spaced wires, and increasing frequency. Over a set of models for which NEC-4 has known accuracy, Antenna Model has closely matched the reported outputs.

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Like all MININEC programs, Antenna Model lacks the NEC TL facility and the Sommerfeld-Norton ground calculating system. The latter want has no relevance to the present set of tests, but the former absence does limit the number and type of tests that we may perform. Fig. 4 shows the three tests that we can perform.

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The simplest set of models is a single-wire dipole fed at its center and resonated to the standards used for the NEC models. Since MININEC counts pulses, which occur at segment junctions and specified ends, we require 42 segments to feed that dipole at the exact center. As a check on the adequacy of the segmentation, we shall also increase the number of segments by 50% to 64. The following table provides the results of our initial work.

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El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
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+#16 42 Segs       +/- 204.9185      72.11 + j 0.002         0.9991      -0.004
+#16 64 Segs       +/- 204.9185      72.18 + j 0.247         0.9994      -0.003
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+0.5" 42 Segs      +/- 202.475       72.02 - j 0.001         0.9981      -0.008
+0.5" 64 Segs      +/- 202.475       72.11 + j 0.252         0.9985      -0.007
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+1.0" 42 Segs      +/- 201.231       72.06 - j 0.004         0.9974      -0.011
+1.0" 64 Segs      +/- 201.231       72.15 + j 0.243         0.9979      -0.009
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+1.5" 42 Segs      +/- 200.280       72.14 + j 0.005         0.9966      -0.015
+1.5" 64 Segs      +/- 200.280       72.23 + j 0.202         0.9973      -0.012
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The simple dipole models appear to be sufficiently well converged to be useful for our further tests. The increase in segmentation yields a systematic increase in the feedpoint resistance and in the reactance in an inductive direction. Improvements in the AGT values are completely marginal. (All values would be 1.0 if carried out to only 2 decimal places.)

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Based on the resonant lengths of the dipoles, we may now construct vertically oriented transmission lines using AWG #16 (0.0508" diameter) wire space 1.084". The lines will be 1/2 wavelength long or 421.531". We shall use three levels of segmentation for all tests. 21/42/2 indicates that each side of the dipole has 21 segments, each transmission line wire has 42 segments, and the connecting feedpoint wire has 2 segments in order to center the source. We shall also use a 42/84/2 scheme to check convergence. Finally, we shall use a 205/421/2 scheme to provide a high segmentation level. In MININEC, it is recommended that adjacent segments have no more than a 2:1 length ratio, which this scheme achieves.

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However, we have limitations using the 1" and the 1.5" diameter elements. The recommended minimum segment length should not be less than 1.25 times the diameter of the wire. To achieve this standard, it was necessary to perform revised tests for maximum segmentation. The 1" diameter element used a 160/421/2 scheme, while the 1.5" diameter element used a 106/421/2 scheme. The results appear in the following table.

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El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
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+#16 21/42/2       +/- 204.9185      72.05 - j 21.69         0.9991      -0.004
+#16 42/84/2       +/- 204.9185      72.15 - j 9.874         0.9995      -0.002
+#16 205/421/2     +/- 204.9185      72.24 - j 0.867         0.9998      -0.001
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+0.5" 21/42/2      +/- 202.475       71.98 - j 16.71         0.9981      -0.008
+0.5" 42/84/2      +/- 202.475       72.06 - j 7.456         0.9989      -0.005
+0.5" 205/421/2    +/- 202.475       72.21 - j 0.176         0.9994      -0.003
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+1.0" 21/42/2      +/- 201.231       72.03 - j 15.38         0.9974      -0.011
+1.0" 42/84/2      +/- 201.231       72.11 - j 6.779         0.9984      -0.007
+1.0" 205/421/2    +/- 201.231       72.24 - j 0.256         0.9989      -0.005
+1.0" 160/421/2    +/- 201.231       72.24 - j 0.220         0.9989      -0.005
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+1.5" 21/42/2      +/- 200.280       72.11 - j 14.70         0.9966      -0.015
+1.5" 42/84/2      +/- 200.280       72.16 - j 6.578         0.9979      -0.009
+1.5" 205/421/2    +/- 200.280       72.28 - j 0.456         0.9985      -0.007
+1.5" 106/421/2    +/- 200.280       72.24 - j 0.533         0.9985      -0.007
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Violating the length to diameter recommendation turns out to have no significance for the tests run here. More significant is the overall segmentation used. Segmentation levels that approach a level that allows the source wire segment to maintain the recommended margin with the segment lengths on the transmission line yield the most accurate results, using the simple dipole tests as a standard. Inadequate segmentation tends to introduce growing values of capacitive reactance into the source impedance and to yield slightly lower AGT values.

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Overall, at every level of element diameter, the corrected MININEC algorithms yield highly usable results when we create dipoles with attached wire transmission lines. Unlike the NEC results, which strongly suggest that we avoid this route to modeling the dipoles (and by extension, other phased arrays with elements and transmission lines), an adequately corrected MININEC can easily and adequate model these situations. The AGT values strongly suggest--without guarantees, since the test is a necessary but not a sufficient condition of model adequacy--that the resulting models will be highly adequate in free space.

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The NEC models showed enough deficiencies that they were unable to answer the initial question of this investigation. Does the overlap of element diameters that only touch at their ends create any danger of jeopardizing the adequacy of a model? The table above shows no signs that such problems will arise. The 1.5" elements yield results that fall very exactly in the progression of values for the element diameters that do not have any end-touching. For this class of cases, the touching of the inner element ends--where a wire junction does not form--appears to have no effect upon the outcome. Since MININEC uses pulses (appropriate segment ends) as the current centers, the special penetration problem that appears in NEC does not re-appear here.

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Before we leave MININEC and our dipole tests, we should also test a horizontally oriented transmission line model. As with the NEC models, we shall split the dipole element and separate the two halves with a transmission line using #16 wire and a spacing of 1.084". The remaining dimensions of the model will be the same as in the previous model. As well, we shall employ the same set of segmentation levels as used previously. Here are the results.

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El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
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+#16 21/42/2       +/- 204.9185      71.72 - j 27.85         0.9992      -0.003
+#16 42/84/2       +/- 204.9185      71.83 - j 15.54         0.9996      -0.002
+#16 205/421/2     +/- 204.9185      71.90 - j 6.654         0.9998      -0.001
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+0.5" 21/42/2      +/- 202.475       71.63 - j 21.66         0.9981      -0.008
+0.5" 42/84/2      +/- 202.475       71.72 - j 11.91         0.9989      -0.005
+0.5" 205/421/2    +/- 202.475       71.84 - j 4.699         0.9994      -0.003
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+1.0" 21/42/2      +/- 201.231       71.66 - j 19.89         0.9974      -0.011
+1.0" 42/84/2      +/- 201.231       71.74 - j 10.83         0.9984      -0.007
+1.0" 205/421/2    +/- 201.231       71.88 - j 4.164         0.9989      -0.005
+1.0" 160/421/2    +/- 201.231       71.86 - j 4.178         0.9989      -0.005
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+1.5" 21/42/2      +/- 200.280       71.73 - j 18.89         0.9966      -0.015
+1.5" 42/84/2      +/- 200.280       71.78 - j 10.34         0.9979      -0.009
+1.5" 205/421/2    +/- 200.280       71.89 - j 4.034         0.9985      -0.007
+1.5" 106/421/2    +/- 200.280       71.85 - j 4.124         0.9985      -0.007
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Between the horizontal and vertical transmission line models, there is scarcely a change in any of the AGT values. The significant changes appear in the reactance at the source for each type of model. The higher the level of segmentation, the closer the model approaches resonance.

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Perhaps the most comparable models between the NEC and the MININEC set are the highly segmented #16 AWG models using physical transmission lines. The following small table compares the NEC and MININEC models for horizontal transmission lines.

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El. Dia.          El. Length        Source Impedance              AGT
+Inches            Inches            R +/- jX Ohms           Relative    dB
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+MININEC
+#16 205/421/2     +/- 204.9185      71.90 - j 6.654         0.9998      -0.001
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+NEC
+#16 205/421/1     +/- 204.900       76.29 - j 7.717         0.947       -0.25
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Both models show the remnant capacitive reactance. In the NEC model, there is a modifying algorithm that handles the effects of a feedpoint gap wherever one places a source. That calculation is not a part of the separation of the element wire halves when we place a transmission line in the picture. The gap adjustment occurs at the remote source. It is possible that the difference creates the resulting capacitive reactance in the source impedance of the models, although I am at present uncertain whether there is a comparable calculation present in the MININEC algorithms.

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The MININEC model achieves a higher AGT value, largely as a result of the corrections for closely spaced wires. At present, NEC cores do not have a correction or adjustment for errors that may e creep in due to the close spacing of long wire runs.

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Conclusion

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Our foray into modeling dipoles and transmission lines has turned up a number of interesting facets of modeling in both NEC and MININEC. All of the results are relevant to modeling any set of elements and associated transmission lines. The pursuit of an answer to a single question gradually yielded at least partial answers to a larger set of questions.

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Although we focused the exercise on a single question, the general procedure is relevant to any complex modeling task that may press one or more of the limitations inherent in the available modeling cores. Wherever a model type is complex and the modeling strategies approach the fringes of the core capabilities, it is worthwhile to develop a test procedure to assess in advance the adequacy of the strategy. The results can save us from inadvertent misrepresentations of the potentials of an antenna design. As well, they may also give us fuller confidence in a particular strategy that passes all of our tests. Either way, testing modeling techniques in advance with relevant but simplified models is a worthwhile enterprise.

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Go to Main Index

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66. State of the Art?

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L. B. Cebik, W4RNL

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The following notes represent a set of ruminations on the state of development of both NEC and MININEC from their inception to the present. My interest as a user is not in the actual algorithms inside the calculating core, but rather with the efforts that have gone into developing the cores to their fullest potentials for accurate modeling of difficult antenna geometries.

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An Initial Limitation

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Both NEC and MININEC are wire-modeling programs at root (even though NEC has a surface patch capability). Hence, we likely should except the limitations imposed be a necessary segment-length-to-wire-radius value will ultimately not be eliminated without changing the entire basis of the modeling core. The core uses a thin-wire calculation scheme, and hence, the radius can only be enlarged so far before one exceeds the limits of the thin-wire equations.

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This limitation has consequences related to the maximum frequency for which one may model accurately. For a true wire size within the normal range of construction, there will be a frequency frontier or region at which the wire radius increases toward the segment length so that result become untrustworthy. I call this region a frontier because it appears to be dependent upon at least two variables: the wire radius and the complexity of the geometric structure. The more complex the structure, the more segments per wavelength are required to converge results.

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Of course, we have a work-around for those willing to do the detailed modeling required. We may use very thin wires and simulate solid wires with a cylindrical wire-grid structures. Under usual modeling conditions, the amount of effort required to create the cylindrical substitute and finding the most reliable means of giving the resulting antenna a source will together make this work-around untenable in practical terms.

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Both NEC and MININEC are subject to this initial limitation. Hence, it is likely that there will always be an upper frequency limit--variable though it may be--for both types of cores. Above that limit, other modeling core techniques become dominant.

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However, NEC-2 and MININEC 3.13 are both public domain software cores. Hence, both find a place in inexpensive entry-level software. Hence, they are both in very wide use--and that is part of the story.

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Other Limitations

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When MININEC 3.13 became available out of the work of Rockway and Logan and entered public domain use, it became the core of choice for early DOS-based commercial programs, such as MN by Brian Beezley and ELNEC by Roy Lewallen. When NEC-2, developed largely under the leadership of Jerry Burke at LLNL, finally became public domain (as NEC-3 and NEC-4 supplanted it at LLNL), it entered commercial programs such as NECWires by Beezley and EZNEC by Lewallen. These DOS-based programs eventually took a back seat to Windows-based program, as EZNEC converted to Windows and NSI's NEC-Win Pro and Plus appeared. Windows versions of MININEC began to appear in both free and commercial ware, such as NEC4WIN by Orion and most recently Antenna Model by Terisoft.

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Before we assess some of the significance of these progressions of software, let's make a short listing of some of the limitations that each core suffers in its native form.

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MININEC 3.13 Limitations

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MININEC 3.13 uses a simplified ground system, making use of a reflection coefficient to determine the effects of ground on the far field. However, the reported source impedance is always taken over perfect ground--and that value may or may not be sufficiently accurate for a given modeling task. (In contrast, NEC-2 accesses a Sommerfeld-Norton ground calculation scheme that provides in NEC-2 very accurate result within a few wire radii of the ground. NEC-4, of course, permits buried wires, that is, wire below Z=0.)

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MININEC 3.13 has what some call a frequency bias, that is, an error factor that increases with frequency. At VHF and higher, the error is significant. MN provided a correction for this bias. MININEC 3.13 also has a closely-spaced wire problem in its native form. ELNEC provided a corrective for this difficulty. MININEC 3.13 also showed errors when wires met at angle from a right angle down to very small angles. Two routes were generally used to overcome this problem. Since the initial MININEC was limited in the number of total segments that a model might have--a limit removed in Windows versions that usually code in C (however many the following + signs)--one technique was the system of length tapering used in ELNEC. This system ensured that the segment lengths at the angular corner were very short, thus eliminating the clipping effect that results from the use of pulses (at segment junctions) to form the center of current. Core modifications were a second route to overcoming this limitation. Early attempts at corrections have evolved into a rather sophisticated scheme in Antenna Model that produces very accurate results.

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NEC-2 does not suffer the angular junction problem until the angles between wires become very small--small enough that the center of the joined wires inter-penetrate. In the most general terms, the middle third of a wire segment is critical to model accuracy, and all junction penetrations should fall outside this area. The thinner the wire and the longer the segment, the narrower the angle may be without incurring model inaccuracies that show up on an average gain test.

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MININEC has one more limitation relative to NEC-2/-4: it runs very slowly for a model of a given size relative to the comparable model in NEC. The latest core revisions and Windows programming languages have not yet allowed MININEC to catch up in speed to NEC. Indeed, for very large models, it is not even a race.

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Unlike NEC-2 and -4, MININEC 3.13 does not have a "TL" or transmission line facility. This forces one to model all transmission lines as real (potentially radiating) wires, which can become a tedious task for arrays such as a very large and well-populated LPDA. However, the junctions between the thinner phase-line wires and the fatter element wires presents no problems--as they would for NEC-2 and -4.

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We should note in passing that Rockway and Logan have moved on to a complete revision of MININEC to overcome a number of the limitations of 3.13. The result is a sequence of programs called generally "Expert MININEC." Since the programs are proprietary and have considerable cost for versions that permit a high segment count, I do not have a current version and hence must exclude these developments from consideration here. However, a relatively full description of the program foundations has been available at the EM Scientific (web.archive.org) web site.

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NEC-2 Limitations

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NEC-2 (and -4) place the center of current in the mid-segment region and thus are subject to limitations quite unlike those of MININEC 3.13. The original programming is in Fortran, which has seen a number of run-speed improvements as those implementing the core make use of the latest compilers. With the increase in computer speed and RAM size as adjuncts to these speed improvements, the need for using the fast or reflection- coefficient ground calculation system has largely passed, and the S-N ground system is generally recommended for all antenna models requiring placement over ground. As well NEC calculates the source impedance of a model over the actual ground specified in the model, whichever type of ground that the user selects.

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There are two ways to look at NEC-2 limitations. One is by way of comparison with what MININEC 3.13 does well. The other is by way of comparison with what NEC-4 does better. To be fair, we shall have to make both types of comparisons.

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The primary example of a comparison between NEC-2 and NEC-4 is perhaps the ability of the latter version to handle wires placed below ground. Although numerous modelers have tried to determine vertical monopole performance by placing NEC-2 ground radials very close to the ground, modeling the same structures in NEC-4 with buried radials have shown these approximations to be very limited.

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NEC-4 also offers a few possibilities included in neither MININEC 3.13 nor NEC-2. An obvious example is the NEC-4 control card IS, that allows the user to evaluate wires having insulated sheathes with user-specifiable thicknesses, conductivities, and dielectric constants.

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NEC-4 improvements over NEC-2 range from the well-advertised to the relatively unknown. In the latter group belongs an emergent frequency offset between NEC-2 and NEC-4 as one goes into and through the UHF range. In general, NEC-4 is considered more accurate in this regard. It also appears that NEC-4 handles tight angles between joined wires, especially in radial sets and similar structures, somewhat better than NEC-2.

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The most widely advertised improvement in NEC-4 is the ability to handle with reasonable accuracy antenna elements composed of stepped-diameter model wires, a common feature of upper HF arrays. NEC-2 models of such elements are wholly unreliable. There emerged some schemes for overcoming this limitation. The one used in both EZNEC and NEC-Win Plus involves the Leeson corrections. Essentially, the program calculates a uniform-diameter element of the correct length and diameter to serve as a substitute for the stepped-diameter element. The calculations have restrictions, for example, the requirements that the element be symmetrical (if not a monopole touching the ground) and that all sources and loads be at the element center (or monopole base). Since these restrictions are no problem for Yagi, LPDA, and similar upper HF elements, the substitute uniform-diameter work-around has performed very successfully.

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However, even the work-around has limitations. There will be a difference in the reported NEC-2 output for such an element with uniform segmentation vs. one with highly variable segmentation, especially if the segment lengths differ close to the source.

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NEC-4 requires no substitute elements, as it handles stepped-diameter directly. However, the core does not yield identical results with those of substitute uniform-diameter elements, and the more radical the stepping of the original elements, the further NEC-4 results depart from those obtained by Leeson substitutes. In contrast, Leeson substitute elements correlate very precisely with the native stepped-diameter element directly handled by MININEC. MININEC 3.13 does not suffer the large limitation of NEC-2 and the smaller one of NEC-4, and hence yields accurate results without correction factors (other than those notes earlier for frequency and the like).

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Related to the stepped-diameter element limitation is another: NEC yields erroneous result when there are junctions of wires having dissimilar radii. As one might expect, the difficulty is worse in NEC-2 than in NEC-4. However, a well-corrected MININEC program produces more accurate results in such cases than even NEC-4.

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Both NEC-2 and -4 require for greatest accuracy that closely spaced wires have the best possible segment-junction alignment. However, even adhering to this condition yields erroneous results if the wires--even though not touching--have dissimilar diameters and the error increases as the wires are brought closer to each other. The degree of divergence from accuracy tends to show clearly in average gain tests. Once more, a well-corrected MININEC 3.13 does not share this difficulty. However, note the qualification that the MININEC core must be well-corrected. With suitable correction, MININEC will show poor accuracy with closely spaced wires of any diameter, including standard folded dipoles.

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NEC-2 and -4 do have a TL or transmission line facility which enables the user to construct non-radiating lines of virtually any characteristic impedance and length. However, despite having been around since at least the early 1980s, the TL facility remains restricted to lossless lines, with no way of handling real lossy lines. At the same time, constructing real-wire simulations of transmission lines to account for losses in them falls prey either to NEC's difficulty with very closely spaced wires or to its inability (without massive and mostly impractical wire-grid constructs) to handle concentric coaxial cables. Only NEC-4 would be able to handle the dielectric within a coaxial cable, if one tried to create such a cable as a wire-grid structure.

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Some Common Limitations

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Both NEC and MININEC permit the user to place resistance-reactance or resistance-inductance-capacitance loads on a modeled wire. In both cases, the loads are non-radiating or, in other terms, mathematical only. As such, they are, like transmission lines, most accurate when placed at current maximums, where the current at both ends of the loaded segment is roughly equal. Placed away from these positions, the current at one end of the load differs from the current at the other end, and the load less accurately reflects the performance of a real component. An inductor, for example, performs as almost solely an inductor only so far as the current at each end is equal. Any differential will show up in the form of the wire acting partly as a length of the antenna wire. The non-radiating loads of modeling programs cannot show this non-inductive activity of a load placed on a wire in a region of significantly changing current level.

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MININEC 3.13 has another limitation in its native form. It permits load and source placement only at the wire ends or at the center. Some implementations of MININEC, such as ELNEC, have overcome this limit, while others have not. Although the models--by judicious subdivision of an element into separate wires--can overcome the limitation, its persistence does complicate modeling.

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As we have noted, of the cores under consideration, only NEC-4 permits the use of wires lower than Z=0. For a perfect ground, a monopole just touching ground will yield virtually identical results in both MININEC 3.13 and NEC-2. However, if we assign the ground values of conductivity and relative dielectric constant (permittivity), we obtain considerably different results. In general, NEC-2 results are without merit. MININEC 3.13 results are usable, but with limitations that have not been appreciated until comparisons were made between those results and the outputs obtained in NEC-4 with buried radial fields of various sizes. The resulting correlations were spotty at best. The usefulness of the MININEC ground had been sufficiently superior to use of either form of NEC-2 ground to encourage EZNEC to provide that ground system as an addition to the ones within the NEC-2 core.

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However, in the end, the adequacy of using a MININEC ground with vertical monopoles and variants depends in large part on the degree of accuracy required by the modeling task. There is a vast difference in the demands placed on a modeling system when we desire precision from those we impose when we are looking a general trends. As well, the MININEC system has been misused in the analysis of monopole arrays where one or more of the elements is sloping. Any horizontal component to the radiation of the element, when the elements is in whole or part less than 0.2 wavelengths above ground will result in errors. Still, the results may be only as erroneous as those produced on a simulated buried field in NEC-2 that is composed of wires close to ground--assuming that a buried radial field is the actuality to be modeled.

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I am Surprised. . .

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The sum of this incomplete review of MININEC 3.13 and NEC limitations is not what one might initially expect. The point is not at all to compare the two core types in an effort to assess superiority. As previous columns have suggested, which core is superior depends to a very great extent on the parameters of the modeling task.

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Rather, my ruminations on the limitations of the cores bear an element of surprise that more has not been done in certain directions of potential development.

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1. MININEC 3.13: The MININEC core lacks three things achieved by NEC-2: speed of run-time, the presence of the S-N ground calculation system, and the presence of the TL facility. In terms of the user's encounter with the best of current MININEC 3.13 implementations, these shortcomings are the most pronounced. I cannot say what the future may hold for speeding up MININEC runs and for adding the two facilities to the programs available to the user. However, having noted these hoped-for developments, let's turn to the other side of the coin.

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Since its release as a public domain program, MININEC 3.13 has been under continuous development by a number of individuals. Corrections have emerged for most of the geometry-related and frequency-related aspects of core performance. As well, initial segmentation limits have disappeared in Windows implementations of the cores so that now computer memory is the chief limiting factor in model size.

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While user interfaces have emerged to ease both the input side of modeling and to make the output side more readable and interesting, the bottom line remains this one: the core itself has undergone considerable evolution in the decades since it became public domain.

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2. NEC-2: NEC-2 is no less a public domain core than is MININEC 3.13. The code is readily available. Indeed, there have been a few core modifications to customize it for use with various interfaces, if for no other purpose than to set the maximum limit on the number of allowable segments in a model.

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However, most of the major work of commercial developers has been in the region of the input and output interfaces. Input systems have become sophisticated, even to allowing modeling by equation in NEC-Win Plus or modeling in MathCAD, as in SuperNEC. Model viewing--with accessible geometry data--is commonplace, and modeling with a reliable transfer from a graphic to a wires table is not far off. Output tables and graphics have grown more numerous and content-rich, and the NEC outputs gradually become more easily accessed and transferred to a medium of preference.

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However, the NEC-2 core has remained relatively inviolate. For example, EZNEC permits the specification of TL physical lengths and velocity factors. However, what enters the core is a pre-calculation of the electrical length. The core remains as is. Similarly for EZNEC and NEC- Win Plus Leeson corrections. The core uses the substitute element, but has not been altered internally to better handle stepped-diameter elements.

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NEC-4 has emerged as the best of NEC, but even it has limitations, such as those suggested earlier. Although it is proprietary, its remaining limitations seem significant enough to encourage developers to work with the public domain NEC-2 core to yield a core that is as accurate as MININEC is in the regions where its accuracy is both known and high. Curiously, such developments have either not occurred or not been made public--even in the form of an improved commercial implementation of NEC- 2. Improved versions of NEC-2 either rest on improved run times or upon improved user interface facilities.

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I do not know if the existence of NEC-4--however proprietary it may remain--discourages wrestling with NEC-2 to improve it. Likely such development would have only limited commercial attractiveness within the U.S., where NEC-4 is readily available to those who can pay for both the license and the software. However, since NEC-4 still has export restrictions, refinement of the NEC-2 core seems to be a task that might appeal to developers outside the U.S.

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It may well be that many of those who might be capable of undertaking the further development of NEC cores are awaiting a NEC-5. There have been hints from time to time of emergent cores using the method of moments in conjunction with a different set of algorithms.

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So the state of the art is that NEC users either work with a 20-year old core having severe limitations or that they qualify to work with a decade-old core that is not limitation-free. MININEC 3.13 users face equal limitations in the absence of certain features that NEC users enjoy, despite continuous and intensive development efforts over the years.

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Little wonder that I am surprised.

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Also see Antenna Modeling Programs page for more informationon.

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Go to Main Index

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67. Wire Grids 1: Plane and Simple

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L. B. Cebik, W4RNL

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Except for the use of surface patches--which are not generally available on entry level NEC software--the method of simulating a solid or closely meshed surface is through the use of wire grids. Note that I am including closely spaced meshes--such as window screening--along with solid planar surfaces in the wire-grid pool. Fig. 1 gives us the initial story.

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NEC is based upon round conductors and thus cannot directly model a flat surface. This limitation shows up vividly in UHF modeling, where NEC has difficulty simulating integrated antenna elements and transmission lines composed of flat thin strips of copper on a glass or similar substrate. At lower frequencies, from VHF downward, we can simulate flat planes by constructing a grid of interconnected wires having the same outline area as the solid surface. In fact, for basic modeling of rectangular surfaces, some entry-level software--such as NEC-Win Plus and EZNEC Pro--provide semi-automated systems. The user inputs certain dimensions and the program creates the requisite wires and intersections for the plane in the form of a set of wires or GW entries.

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In fact, the two software packages just cited illustrate two different ways in which we can go about creating a wire grid. Fig. 2 illustrates the difference.

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On the left, we find a small number of wires, just enough to populate the two directions of the plane. The intersections of the grid, except for the 4 corners, consist either wholly of segment junctions or of combinations of wire and segment junctions. Although beginning modelers are often cautioned to use a wire junction for every crossing pair of wires that touch, it is legal to NEC's rules to have wires joined at segment junctions.

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The advantage of this systems revolves around the fact that the run time for a model depends upon both the number of segments in the model and the number of wires. Although the total number of segments in the left construct equals the number of segments in the construct to the right, the number of wires is considerably lower--and the run time is accordingly shorter. However, the advantage is accompanied by a disadvantage. If we move either end coordinate of any one of the wires, the entire set of junctions along the wire (except for the unmoved end) becomes a set of either non-junctions or illegal wire crossings at other than a wire end or a segment junction.

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For this reason, one might equally create the same wire grid using the system at the right. Here, every junction is a wire end. The result is somewhat greater flexibility in model revision. We can take a given wire and move it a bit. Then we need only revise the end coordinates of a few other wires (from 1 to 3) to restore the integrity of the grid. We can take a simple rectangle and fold down the corners or make other simple geometric revisions with fair ease. The price that we pay for this flexibility is to have as many wire as we have segments, thus extending the run time for the core.

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Wire grids are subject to some rules--actually, more like some rules of thumb. For example, the most common wire/segment length used in most wire grids is 0.1 wavelength. This value is about twice as long as the recommended length for a segment in a dipole (about 0.05 wavelength). Wherever the current levels are high or change rapidly from one wire-grid element to the next, the modeler should use a shorter segment length. However, when wire grids simulate planes that are not very active in the antenna system, that is, they have relatively low and nearly uniform currents, some modelers have used segments lengths longer than 0.1 wavelength. Even the 0.1 wavelength baseline segment length yields a sizable model, since the number of segments in the wire grid will be about 220 times the area of the plane when measured in square wavelengths.

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Ideally, the surface area of the grid should approximate the surface area of the plane being modeled. This often leads to the use of fairly "fat" wires, since the grid wire diameter should equal the grid spacing or segment length divided by PI. Obviously, the more wires in a grid of a certain set of outside dimensions, the smaller the segment length becomes and hence, the smaller the wire diameter needs to be.

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These basic rules of thumb are subject to numerous variations according to the kind of surface that we are trying to simulate with a wire grid. A screen mesh may vary in its opening size and may not need the wire diameter required by a simulation of a flat plane. Likewise, a plane with a very coarse surface may more adequately model with thinner wires or longer segments. There is no simple infallible route to wire-grid modeling.

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In this episode, we shall restrict ourselves to relatively simple wire grids that we can create using automated wire-grid facilities within modeling programs. All of our examples will focus on rectangular planes. In fact, all will serve as reflectors for various kinds of arrays. We shall eventually return to wire grids used to create other types of shapes. But in the beginning, simple planes or combinations of planes will alert us to some fundamentals of wire-grid modeling.

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A Corner Reflector

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One of the simplest high-performance arrays available for UHF service is the corner reflector. The antenna consists of a dipole and two flat surfaces joined along one edge. The apex of the tent-like reflector is behind the dipole at a certain distance that is largely a matter of the desired feedpoint impedance. Performance is a periodic function of the reflector dimensions, with larger reflector planes (up to a point) yielding higher gain. The corner reflector array is a wide-band antenna with stable performance values for a 25% bandwidth (at least). Some designers have used fan dipoles and other geometries to further increase the operating bandwidth.

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Fig. 3 shows two model outlines for a corner reflector. They correspond to typical ways of constructing the antenna. One style of construction uses a series of rods or tubes arranged to simulate a flat plane, with each rod being considerably longer than the dipole element and in the same plane. The other style of construction makes use of either a solid surface or a rigid screen to form the reflector planes. A screen tends to show less wind resistance than a solid surface and is popular in larger reflectors used at lower frequencies.

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There is a tendency on the part of modelers to use the rod model as a substitute for the wire-grid version. The rod model uses (in this particular case) only 24 wires and 586 segments. The wire-grid version, for reflector planes having an identical overall area as the rod-planes, requires 613 wires and 622 segments. (The slightly higher segment count is a function of the dipole using several segments in its single wire, while each element of the wire grids uses 1 segment per wire.)

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When joining two independently created planes along one edge, be sure to delete the duplicate edge wire at the junction.

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In this example, whether or not the rod model can substitute for the wire-grid model depends on the degree of refinement we require for the output data. The following brief table will illustrate the point. It presents the reported performance figures for the two models, which use identical dipoles at identical distances from the apex of the two planes of the reflector, each plane having the same outer dimensions.

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+Model            FS Gain         180-Deg          Feedpoint Impedance
+                 dBi             F-B dB           R +/- j X Ohms
+Rod              11.25           29.90            92.6 - j 4.0
+Wire-Grid        11.80           30.52            88.2 - j 0.3
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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For many purposes, the output data of each model is adequate. However, we can notice some difference. Note that each model is most likely adequate as a model of the particular construction type that it simulates. The question we posed was whether the simpler rod model might suffice as a model of a solid surface corner reflector that the wire-grid simulates. In general, the answer seems to wobble on a fence.

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The wire grid used in our initial comparison employed 0.1 wavelength segments. So we might also ask whether that model is adequate or whether we should use a reflector model with shorter segment lengths, perhaps 0.05 wavelength. Fig. 4 illustrates the difference between the low-density and high-density planes.

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While the low-density model required 613 wires and 622 segments, the new model demands 2279 wires and 2289 segments. Doubling the segment density results in a total wire count that is 4 times the original, minus some segments for the edges. Obviously, one's software must have a segment capacity able to handle the number of segments and wires.

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Let's compare the performance results.

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+Model            FS Gain         180-Deg          Feedpoint Impedance
+                 dBi             F-B dB           R +/- j X Ohms
+Low Density      11.80           30.52            88.2 - j 0.3
+high Density     11.71           31.62            88.4 - j 0.8
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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For this particular application, increasing the segment density yielded no significant change in results. Unfortunately, about the only way to determine whether we need to use a wire grid with shorter segments is to actually model the antenna using both density levels. Of course, once you have the larger model, you might as well use it.

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Fig. 5 shows the design-frequency E-plane patterns for the three models. It is clear that the two wire-grid models have very similar patterns. However, there are noticeable differences in the rearward portions of the pattern for the rod model. Although they make only a slight difference in this case, let's not forget them as we look at further examples.

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A Flat Plane Reflector with a Double-Quad Driver

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Although it has a fairly long history, the double-quad has re-emerged as a high-performance UHF antenna when placed ahead of a flat-plane reflector. Fed across a gap at the center, the antenna is capable of a 50-Ohm impedance, convenient for conventional coax feeding. However, the exact impedance is also a function of the double-quad dimensions and the spacing from the reflector without much alteration of performance. Like the case of the corner reflector, the antenna is more sensitive to the size of the reflector plane.

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As we did for the corner reflector, let's create both a rod and a wire-grid reflector. All we need is a single plane, so our work is much simplified. We shall use identical outside dimensions for both types of reflector planes. The modeling results appear in sketch form in Fig. 6.

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Neither reflector is optimally sized necessarily. For our purposes, it is only necessary that we make them the same size, use the same double quad, and place the driven element the same distance from the reflector. The rod model shows vertical rods, since the double quad is essentially a side-driven pair of quads in parallel.

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The next step, of course, is to compare the reported outputs from NEC-4.

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+Model            FS Gain         180-Deg          Feedpoint Impedance
+                 dBi             F-B dB           R +/- j X Ohms
+Rod Ref. D-Q      9.65           21.59            55.5 - j 3.4
+W-G Ref. D-Q     10.06           29.48            48.6 - j 10.7
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Whether or not differences in gain and impedances reports are significant or trivial depends upon the modeling task at hand. What is undeniable is the very large difference in the reported front-to-back ratio--about 8 dB. We may wish to ask why there is so much larger a difference in the front-to-back ratios for this case and so little for the corner reflector.

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The answer lies in the nature of the driven elements. The corner reflector used a dipole that was aligned with the rods in the reflector. However, our double-quad array uses a driven element ,which is not polarized wholly in a plane parallel to the rods. The side-fed quad loop has only a dominant vertical component (if we take a perspective on the antenna as if it were above a ground surface), but retains a small but significant amount of radiation with a horizontal component. Hence, the wholly vertical reflector rods are less effective than the full mesh of a screen or a solid surface reflector.

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My goal in presenting this particular model is to make a simple point: just because a simplified rod model (22 wires, 381 segments for the double quad) is adequate for some cases, we may still require the bulkier wire-grid model (1013 wires, 1245 segments of 0.05 wavelength for the double quad) in other cases. One must always analyze the nature of the driving antenna rather than assuming the a smaller rod model is "good enough."

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Fig. 7 displays the E-plane patterns for the two models. The differences in rearward performance show up clearly.

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A Tri-Plane Reflector Array

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The tri-plane reflector is only sparingly used, although it has some interesting properties. Not the least of these properties is the fact that it uses a monopole driven element, where one plane of the reflector is also the "ground plane" for the monopole. A second interesting feature is that the main lobe of the antenna emerges in a direction roughly equidistant angularly from each of the reflecting surfaces.

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The interesting part of these phenomena for the modeler is how to obtain a model over ground of the antenna when we aim it so that the signal is a parallel to the ground as possible. Let's make the game more interesting by desiring to have a version that is horizontally polarized and a version that is vertically polarized. Fig. 8 shows the steps in the set of transitions. Let's see how we moved from one to the next.

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In any automated system of wire grid generation, it is usually easiest to develop a set of rectangular planes by using the axes of the coordinate system as one of the edges. Hence, the initial set of three sides for the tri-plane reflector are oriented in this manner, as shown in the top sketch of the three views. The driven monopole shows faintly inside the reflector as the line connecting the green segment-junction dots. Since 3-sided corner reflector theory is based upon reflector and monopole dimensions given in terms of wavelengths, I constructed the model in these terms. The grid wires are 0.1 wavelength, and the overall dimensions of each side of the reflector are 2.0 by 2.0 wavelengths. The model used 2461 wires and 2468 segments, with an 8-segment monopole driven element.

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The performance of the array is somewhat better than that of a corner reflector with its reflector planes optimized. The free-space gain is about 16.2 dBi, with a front-to-back ratio of 35.7 dB. Fig. 9 provides the E-plane pattern of the array.

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The more important performance feature for this exercise is the fact that the direction of radiation at its maximum is about 45 degrees from any of the 3 planes. Since I had constructed the planes in a positive direction from the coordinate center (0, 0, 0), the pattern in Fig. 9 is taken at a phi (azimuth) and a theta (elevation) angle of 45 degrees.

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The original wire grid structure emerged from the EZNEC system. However, if I wanted to have vertically and horizontally polarized version of the antenna for use over ground, I would have had to build the array from scratch for each orientation. Instead, I converted the model into a standard .NEC format file and imported it into NEC-Win Plus. There, I used the rotation capabilities to rotate the entire array to the correct positions. Then, in order to have three corresponding patterns. I re-opened the file in EZNEC Pro.

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The two lower figures show the resulting models. The driving monopole will not be parallel to the Z-axis for the vertically polarized model. The driver is parallel to one of the seams of the reflector, and hence will be at a 45-degree angle to the Z-axis. Likewise, the horizontally polarized version shows a driver that is at 45 degrees to the axis along which we find the maximum radiation.

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The point of using the tri-plane reflector array as an example in this context is to alert you to the fact that various modeling programs have different facilities for manipulating the collection of wires that form wire-grid planes. In this case, by some judicious exportations and importations, I was able to easily re-develop the array wire-grid structure to a favorable orientation within the strictures of entry-level programs that use only the GW or basic wire creation input for the task.

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Those using a more generalized NEC core may lack some of the automated wire-grid building features, but these users have a powerful feature absent in the entry-level programs. After building a single plane, one may use the GM input--described in past columns--to replicate and re-orient the initial plane to form and place the 3 sides of the overall reflector. The caution to exercise here is to omit the edge wire along one side of the initial plane. When you create a new plane with the GM card, be sure that its edge with a missing wire (or wire set) meets the next plane along an edge having the wire (set) in place. When you have the entire set of 3 planes constructed, fill in any missing wire edges with a final wire or wires. In general, this procedure is simpler than trying to remove duplicate wires later. As well, it is normally easier to create one plane, replicate it twice, with rotation to set the joining edges together, and finally to rotate the entire structure to the final desired position than it is to build the entire structure in its final orientation. To go from a horizontally polarized to a vertically polarized version of the array requires only changes to the final GM input line.

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Other Planar Structures

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The last of our examples, the tri-plane reflector, is, of course, half a cube. Extending our development to produce a solid cube 2 wavelengths along any edge would require about 4500-4800 wires and segments, using a wire or segment length of 0.1 wavelength.

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Many wire-grid structures do not demand such densities. Many buildings require that we model only the conductive steel frames. However, when doing such modeling, it is important to keep in mind basic NEC requirements. We should strive for equal-length adjacent segments, especially those having higher current levels or rapid changes of current level from one segment to the next. As well, the wire diameter used in each wire of the grid should be about the same as the wire in any adjacent wire. This latter requirement is more stringent in NEC-2 than in NEC-4. However, even NEC-4 has limitations with respect to the amount of stepping in wire diameter along a straight line and at angular junctions. Finally, be certain not to use wire diameters and segment lengths such that an angular wire junction will let one wire penetrate too far into the center area of the other wire.

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Wire-grid planes have proven highly effective in modeling solid and closely meshed surfaces well into the UHF range. We have only sampled one use of the wire-grid, namely, to model reflector planes. However, this simple introduction to wire-grid structures has given us a platform from which to remind beginning wire-gridders of some of the restrictions on such structures and some of the software facilities available for creating and manipulating wire grids.

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Advanced wire-grid development is a special talent requiring both a drafting and an antenna background. There are detailed wire-grid models of exceedingly complex structures, such as ships, airplanes, helicopters, ground vehicles, and even human bodies. Most of these models are proprietary, that is, they are privately held by the firms that developed them for various antenna and EMI/RF compatibility studies. Nonetheless, some of the principles and the difficulties of modeling complex structures can be organized into some useful tips. That is for next time.

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As well, there are software packages that can ease the process of developing a wide variety of common shapes. For example, making a wire-grid horn or parabola can be a very time-consuming task unless one has a program that synthesizes the shape and needs only some basic data, such as certain critical dimensions. Similar remarks apply to generalized vehicle shapes, even if we do not require all of the fine detail of an in-house proprietary model. For many purposes, we can evaluate antenna placements on a vehicle using a generic shape, such a the shape of a van, an SUV, or a pick-up truck, each having correct main dimensions.

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In a future column, we shall return to wire grids as we move from the plane and simple to the angular and awkward.

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68. Wire Grids 2: Angular and Awkward

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L. B. Cebik, W4RNL

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In the last episode, we looked at some simple rectangular wire-grid structures in order to set forth some of the rules of thumb that guide wire-grid construction. We saw that there are guides, but no completely firm rules for the process, although we always have the AGT and convergence tests that we may apply to the entire model in order to assess its adequacy.

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In this episode, I want to look at more advanced wire-grid construction. We shall examine both very specific structures and more generic structures, and when each may be applicable to a modeling task. However, we shall have to speak in far more general germs than those used in the previous discussion. The more detailed and complex the wire-grid structure, the less absolute are the rules of construction.

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Fig. 1 illustrates with clip-art a number of the types of structures that engineers have had to wire-grid. Some structures, like buildings, only need their skeletons modeled, since the remainder may be largely non-conductive. By far, the largest wire-gridding enterprise encompasses the many types of transportation devices to which we attach antennas or which may play a role in RF compatibility studies. If the Navy (or merchant marine) has a new vessel on the drawing boards, then antenna placement--including interactions among antennas--is a prime concern. It is no less a concern for the Saturday sailor who may directly or indirectly use part of his rigging for his antennas. Aircraft--both winged and helicopters--present new challenges to antenna placement as a function of both the use of new materials and the development of new RF-based services. Land motor vehicles ranging from compact cars to personal SUVs to medium and large carrier trucks remain a prime target for wire-grid construction. Some investigators are even wire-gridding the human body--with special attention to the head--in their studies of the effects of new communications technologies on human health.

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The elements of Fig. 1 would be more vivid had I been able to present samples of wire-grid structures capturing at least a sample of each type of subject. However, most of the very specific wire-grid models belong to the companies within which they have been created. Hence, unlike models of Yagis, quads, and other common antenna types, there are few available and meaningful samples of the wire-gridder's art.

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Specific Wire-Grid Models

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The development of an adequate wire-grid model of any structure requires a number of skills and knowledge bases. First, one must have an intimate knowledge of the structure itself. The size and composition of the elements of the structure determine to a very large degree the parameters of the wire-grid model. One must also understand how RF energy interacts with the structure in order to place grid elements correctly, especially in areas likely to have high or changing currents. Indeed, the construction of a wire-grid model of a complex structure, like a war ship, may require more than one iteration before the model is fully adequate to its use in reliable analyses.

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Some argue persuasively that wire-gridding is an art, since it resembles in many ways the production of a realistic sculpture of a given subject. The modeler must decide what is significant and how to go about ensuring that what is significant is prominent in the model. To illustrate the point crudely, let's examine a few steps in the process, using 2-D graphics to illustrate (inadequately) what essentially is a 3-D task.

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Fig. 2 gives us one type of starting point. We see a planar shape of modest complexity composed of curves and lines, where the lines are not parallel. A wire-grid model of the shape must use straight lines, for example, those connecting the dots in the lower part of the sketch. These points will not necessarily have the same distance from adjacent points throughout the model. Hence, the wire-gridder is faced from the outset with decisions concerning segment length inequalities and their consequences upon the adequacy of the final model.

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Even with a 2-D shape, we must fill in the model with wires and their junctions to simulate (in this example) a solid surface. Fig. 3 shows a few of the questions we must answer. The density of segmentation will determine to a large degree the final model size. A very complex structure may occupy 10s of thousands of segments. The higher the frequency of the RF, the shorter that we must necessarily make the segments, at least in areas that we might classify as sensitive.

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How we fill in the structure is as important as specific segment lengths, since the angles of the wires may play a role in how well the model serves as a tool for the specific analyses tasks at hand. In some cases, like a wire-gridding El Greco, the modeler may have to distort the model relative to the real structure in order for it to perform its function. Each case of wire-gridding a specific structure presents its unique challenges.

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We have not addressed issues such as wire diameter and conductivity (and permeability). A building skeleton may consist of many different sizes of conductive frame members. Yet, NEC works best when adjacent wire segments have the same diameter. The requirement is relatively critical to NEC-2, although even NEC-4 requires close scrutiny when wire diameters of adjacent segments change too abruptly. As well, each wire in the assembly requires in many cases of very specific modeling its own conductivity (and permeability) value. Although steel vehicles and aluminum aircraft still abound, modern materials scattered in the latest designs have complicated both the real and modeled structures. (Note that we are not speaking here of minor conductivity differentials among materials, such as those among steel, aluminum, and copper. Instead, composites can be engineered for virtually any level of conductivity, and that value may differ as we change positions along a structure.)

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Except for relatively straight forward cases of creating wire-grid structures, the modeler requires fully-featured software for developing the final model. The core segmentation limit must be adequate to the model (rather than letting the segment limit drive the model size). If the conductivity issue is complex, then the software must allow for individual assignment of those values to each wire or group of wires.

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Those who are heavily engaged in wire-grid work use a variety of adjunct software. Perhaps the most common type is some form of CAD software so that one can construct the model as a drawing--in 3 dimensions, of course. The output of the CAD file--perhaps in .DXF or a proprietary format--can then be transferred to a NEC input system and result in the requisite set of GW entries to form the model. Unless the adjunct software is very much customized, the modeler will still need to assign conductivity values (LD5 inputs) within the framework of NEC. As well, one must also introduce the frequency parameters, one or more sources, any R-X or R-L-C loads, and appropriate output requests in order to complete the model. As well, one may need to add further wires to the model to count as antennas placed upon the structure.

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Finally (at least for this brief description), the modeler must place the structure within its operating environment. Sea-going vessels, of course, are among the simplest to place, as are buildings--IF they are composed of solid conductive exterior surfaces. However, even these examples may present occasional problems. A building frame with many sub-basements--sometimes filled with parked cars, sometimes not--may not show a working ground level that corresponds to the land surface within which the building stands. If the building frame has an earth ground, it may consist of the lowest level of construction, while an antenna on the roof may show its far field performance relative to the surface ground. Whether these features make a difference is usually not completely assured in advance of actually modeling and running the entire model.

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The wire-grid model is therefore not complete just by developing a set of wires to create a structural framework in NEC-model form. Diagnostic analyses of the model, using whatever data may be available from real tests, is as much a part of the process as any other step.

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We have described in outline form some of the parameter's of the wire-grid art and science when applied to critical analyses of very specific structures. The challenges are sufficient that there should be little wonder that advanced wire-gridders hold their techniques close to the vest. As well, the subjects of these models may include proprietary designs, such as future automobiles, or security-sensitive designs, such as new weapons platforms or vehicles. Hence, the general modeler should not expect to see many of these advanced wire-grid structures being shared among modelers.

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More Generic Wire-Grid Models

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Many tasks that require wire-grid structures need not have all of the detail demanded by the most highly refined models that we have been discussing. A generic model of a vehicle, building, or other shape may suffice to yield adequate data for a given design of analysis project. To that end, modelers can benefit from adjunct software already available. For example, a South African firm produced Wiregrid, which they characterize as "a graphical interface for NEC." More recently, Nittany-Scientific released its NEC-Win Synth software for graphically creating wire-grid structures, either free-hand or using a number of pre-set general shapes. Whether such packages are suitable to a particular modeling project is always a user-decision based in part upon the task specifications. However, for a large number of investigations, such software aids can be very useful. Let's focus on one such package--NEC-Win Synth--in order to see what may be involved in creating wire-grid structures using such aids. We shall be as interested in the limitations as in the opportunities afforded by the software.

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NEC-Win Synth produces only a set of wires, that is, ultimately a set of GW input lines to a NEC file. The output is directly accessible in the proprietary .NWP format used in NEC-Win Plus, but may also be saved in .NEC format for use with other software packages. As well, the user may also create a wire table that can be imported by the EZNEC wire table facility. However, in all of these cases, one must keep track of the total wire and segment count to ensure that the package used to run the final NEC model will handle the wire-grid structure and its supplements.

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Fig. 4 shows the main screen that is available for the user if he wishes to create his own wire grid be specifying the wires involved. The graphic display area is available for checking the model at every step, which consists of adding wires, one at a time. Note that the user specifies not only the wire end coordinates, but the number of segments and wire diameter as well. For the model as a whole, the users sets a design frequency and the unit of measure.

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Although this screen is available, its largest use is perhaps to construct adjunct structures to one or more of the pre-set shapes available within the program. How one handles a pre-set shape is quite different from building a wire-grid one wire at a time.

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Fig. 5 displays one of the full pre-set screens available, in this case, an SUV. Like modeling from scratch, the user establishes a design frequency, along with the number of segments per wavelength and the wire diameter for the wire grid. However, the program itself determines how many wires and where they are placed. The user inputs critical dimensions--in the selected units of measure--from a chart to the right. If one is perhaps trying to decide where to place antennas on a new SUV, then he needs only a tape measure to obtain the relevant dimensions. As with all construction projects, measure twice and enter once.

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The NEC-Win Synth system of wire-grid creation uses segment junctions wherever relevant for wire intersections. The system reduces the ultimate file size and run time relative to wire grids that use a separate wire between each junction. However, the user will almost always need to go back to the Synth software to create a new model from scratch if he desires to revise features of the initial wire-grid structure. Not to take this step can all too easily result in a collection on unjoined or illicitly joined wires.

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+CE Generated by NEC-Win Synth 1.0
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+GW  1 6 0.0000000000 0.0000000000 0.0000000000 0.0000000000 1.0000000000 0.0000000000 0.0050000000
+GW  2 6 0.0000000000 0.0000000000 0.1750000000 0.0000000000 1.0000000000 0.1750000000 0.0050000000
+GW  3 6 0.0000000000 0.0000000000 0.3500000000 0.0000000000 1.0000000000 0.3500000000 0.0050000000
+GW  4 6 0.0000000000 0.0000000000 0.5250000000 0.0000000000 1.0000000000 0.5250000000 0.0050000000
+GW  5 6 0.0000000000 0.0000000000 0.7000000000 0.0000000000 1.0000000000 0.7000000000 0.0050000000
+GW  6 4 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.0000000000 0.7000000000 0.0050000000
+GW  7 4 0.0000000000 0.1666666667 0.0000000000 0.0000000000 0.1666666667 0.7000000000 0.0050000000
+GW  8 4 0.0000000000 0.3333333333 0.0000000000 0.0000000000 0.3333333333 0.7000000000 0.0050000000
+GW  9 4 0.0000000000 0.5000000000 0.0000000000 0.0000000000 0.5000000000 0.7000000000 0.0050000000
+GW 10 4 0.0000000000 0.6666666667 0.0000000000 0.0000000000 0.6666666667 0.7000000000 0.0050000000
+GW 11 4 0.0000000000 0.8333333333 0.0000000000 0.0000000000 0.8333333333 0.7000000000 0.0050000000
+GW 12 4 0.0000000000 1.0000000000 0.0000000000 0.0000000000 1.0000000000 0.7000000000 0.0050000000
+GW 13 6 1.8000000000 0.0000000000 0.0000000000 1.8000000000 1.0000000000 0.0000000000 0.0050000000
+GW 14 6 1.8000000000 0.0000000000 0.1750000000 1.8000000000 1.0000000000 0.1750000000 0.0050000000
+GW 15 6 1.8000000000 0.0000000000 0.3500000000 1.8000000000 1.0000000000 0.3500000000 0.0050000000
+GW 16 6 1.8000000000 0.0000000000 0.5250000000 1.8000000000 1.0000000000 0.5250000000 0.0050000000
+GW 17 6 1.8000000000 0.0000000000 0.7000000000 1.8000000000 1.0000000000 0.7000000000 0.0050000000
+GW 18 4 1.8000000000 0.0000000000 0.0000000000 1.8000000000 0.0000000000 0.7000000000 0.0050000000
+GW 19 4 1.8000000000 0.1666666667 0.0000000000 1.8000000000 0.1666666667 0.7000000000 0.0050000000
+GW 20 4 1.8000000000 0.3333333333 0.0000000000 1.8000000000 0.3333333333 0.7000000000 0.0050000000
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I have presented the resultant wire table only through wire #20, since the entire model of the SUV has 253 wires. The segment count is in the 1500 range at 5 segments per wavelength, with no antennas yet added. A higher segment density will increase the model size exponentially.

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The user will have to add applicable antennas, wire conductivities, model frequency scanning limits, and output requests before running it through the NEC core. Some of the operations can be handled as block operations in some programs, so the finishing time is not excessive by any means. As well, compared to modeling an SUV from scratch, wire by wire, or even by combining semi-automated wire-grid planes, the model construction time is very small.

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Nevertheless, the model does have limitations. The vehicle has a shape the reflects the general shape of an SUV having the same dimensions. However, it does not have all of the bumps and indents that are typical of specific SUV models. For most general modeling, these differences between reality and model will make little or no difference. However, they might make a difference in some particular investigation. Hence, the modeler should never assume without evaluation whether or not the synthesized model is adequate to any particular modeling task.

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A modeler need not employ a pre-set shape for a particular object when creating a wire grid. The program contains an number of interesting geometric shapes, as illustrated in Fig. 6.

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The illustration exhibits only 3 shapes. The conic section and the circular section, of course, can be combined in a single file to create a radiating ice cream cone--or anything else having that shape. Since the circular cap can be oriented as the user desires, he can cap either end of the cone.

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The closed cylinder has been used in a number of cases to simulate each half of a very fat dipole. Another form develops an open-ended cylinder, allowing the modeler to cap the ends with circular sections. The caution each modeler must observe in combining shapes is to be certain that overlapping shape-edge wires are reduced to a single wire in each case.

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Fig. 7 illustrates some shapes that are useful for UHF and microwave antenna work. The corner reflectors used as illustrations in the preceding episode can now be fabricated--in model form--more simply, with the apex already set as a single wire. The horn and parabola are of obvious use. Indeed, if one pre-calculates the parabola's geometry to yield a set of dimensions, forming one is simple. However, the wire spreadsheet accompanying the graphical user interface also has provision for modeling by equation, so that a modeler can set up the parabola with variables and revise its shape from within the synthesizing program. Which generation scheme works best depends upon the user's needs.

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Our final illustration, Fig. 8, shows the currently available vehicle shapes in terms of the necessary dimensional inputs necessary to fabricate a desired wire-grid model.

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Note that the collection does not include generic tanks, planes, ships, or helicopters. What the future may hold for additional pre-set models I cannot say at this time. However, the modeler is not left solely to wire-by-wire modeling of such structures in wire-grid form. Rather, one can combine preset wire-grid shapes--especially the geometric shapes--and develop specialized constructs in less time than a wire-by-wire technique would yield. However, the process is likely slower than other techniques to which I referred earlier, such as the use of CAD drawings exported as NEC wires lists.

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Conclusion

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In many ways, this episode has been cursory and vague, providing only a general idea of what advanced wire-gridding requires. At the same time, I see no way around this situation, since wire-gridding requirements cover such a wide span of purposes and needs. Whether one views wire-grid construction as an inviting challenge or a daunting necessary evil depends as much upon individual temperament as upon the nature of the specific task at hand. There are aids to wire-gridding, such as the program that we sampled, and these can assist one to get started into complex shapes, even if only at the generic level. However, the inveterate wire-gridder combines a wide variety of skills in developing the most refined structures that yield the most accurate analyses. Developing those skills takes time and energy and more than a little talent.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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69. 4-8-16-Infinite Sided Loops

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L. B. Cebik, W4RNL

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Suppose that we have a conventional quad loop, that is a square (in either the flat or diamond configuration) loop of approximately 1 wavelength circumference at resonance. In fact, such a square will be considerably larger than 1 wavelength, although the exact resonant circumference will depend upon the wire size as measured in fractions of a wavelength.

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A question posed every now and again is what circumference is required if we use a circular form. Since most loops have taken a square form, the question is usually asked in terms of the adjustment needed, if any, to transform the loop into a circle and still be resonant.

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Actually, the question is often set out in the context of a multi-element parasitic beam. However, the number of variables involved in an answer to a beam question is initially too great to deal with. We need a simpler starting point, and a single loop is the reasonable initial focus of inquiry. Here, we can eventually use near-resonance (plus or minus a very few Ohms of reactance) to determine that a given circle is the counterpart of a square or vice versa. Since we tend to measure loops by their circumference, we have a means of direct comparison and the possibility of coming up with an "adjustment factor."

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Once we establish that two loops are counterparts, we can also determine the gain of each shape for a direct comparison. Theoretically, a circular loop form has a higher gain than a symmetrical square--indeed, a higher gain than any regular polygon. However, we rarely hear how much gain. Hence, it is difficult to know whether it is worth the effort of fabricating a circular loop in preference to the fairly easy construction associated with the square.

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Antenna modeling software provides us with a means of exploring the questions that we have listed. However, NEC and MININEC cannot take us all the way to a circle. Every curved geometric shape must consist of straight wires. So that best that we can do is approximate a circle with a suitable complex polygon. Some say that a hexagon is good enough; others prefer an octagon. Still others think that a hexadecagon or 16-sided polygon is required. Therefore, let us begin with a little geometry and trigonometry.

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Geometry and Trigonometry

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Finding counterpart polygons and circles with equal circumferences is mostly a matter of finding appropriate counterpart dimensions. Circumference will be one of those dimensions. We need another, and we shall call it a focal line. A focal line is a line drawn from the center of a figure to its outermost point. In the case of a polygon, that point will be a corner. For a circle, the line is a radius.

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Fig.1 shows a circle, a square, an octagon, and a 16-sided polygon. These will be the members of our progression of polygons that ever more closely approximate a circle, in 2:1 steps in terms of the number of sides. The 16-side limit is appropriate, since it limits the complexity of the models we use and it fairly closely approaches a circle as determined by the ratio of the circumference to the length of the focal line.

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The figure shows the relationship of C to fn (where n may be an s for a square, an o for an octagon, and 16 for the 16-sided figure) for each of our polygons. The ratio of C to Fs is only 0.9003 of the ratio of C to fc (or r for radius). However, the ratio of C to f16 is 0.9936 of the ratio for the circle. Hence, although we cannot attain a true circle, we can approach it well within 1 percent geometrically with the most complex of our polygons.

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We can calculate the ratios between C and fn simply by knowing the angle between 2 adjacent focal lines. Obviously, the square has 90-degree angles. The octagon has 45-degree angles, and the 16-sided polygon has 22.5-degree angles: simple arithmetic that is a function of the 2:1 ratio of sides in our set of polygons.

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Fig. 2 helps us calculate the ratio of circumference to focal line length for any of our polygons. If we set one side of the polygon vertical, as in the figure, then a line bisecting the angle between adjacent focal lines will create a right triangle. The angle of concern is now 1/2 the total angle, and the sine of that angle times the length of the focal line will give us 1/2 the length of the side. Twice that length times the number of sides gives us the circumference or sum of the lengths of all sides. The inverse of that number gives us the length of the focal line as a function of the circumference.

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Hence, we may use circumference as an initial measure that two figures are counterparts, that is, they have the same circumference. From the circumference comes the length of the relevant focal line, and combining that value with the sine and cosine of the half-angle between focal lines, we can derive all of the necessary coordinates to create a model of our polygon. (The 16-sided polygon will need the sine and cosine of either one or two intermediate angles, but that is a small matter.)

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Modeling the Loops

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Our interest in the basic questions and the project that they inspire lies in the modeling issues associated with trying to derive an answer using NEC or MININEC. We shall restrict ourselves to entry-level software, where only the GW input line is accessible for creating our polygons. In advanced software that makes available all of the NEC input possibilities, we might set up a single wire and then complete the circle using the GM input to replicate and move new wires. We might also use the GA (arc) input line. However, anything that we can do with those inputs, we can also do with GW lines--and a little more manual labor in the set-up. Indeed, going through the exercise of using an input line per wire may be useful in giving modelers with programs like NEC-Win Pro or GNEC some ideas for simplifying the process--or at least the appearance of the input file. (Unless we invoke symmetry--the GX input--NEC will treat each internally generated wire resulting from the GM or GA lines as a segmented wire, and the total run time will not materially change. So it will be largely a matter of showing a given amount of set-up work within the model or hiding that same amount of work, used in the pre-modeling stage, behind a shorter input file. One might well debate, as we shall not do here, which is better: an elegantly short input file that is far from self-explanatory or a full input file that one might read at a glance.)

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We shall begin with the square loop as the most conventional shape. Indeed, our selection of starting points has a second rationale. We have a perfectly good calculating program that will determine the dimensions of a single loop to near resonance solely by entering the design frequency and the wire diameter in the units of measure used in the model. Fig. 3 shows the equations and wire set-up screen for this model. This model is available from the Nittany Scientific (web.archive.org) web site and is a NEC-Win Plus model. Alternative calculation programs are available for the same results, although they would require manual entry to create a model.

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Since the question of square vs. circular loops arises almost exclusively in VHF antenna design, we shall use 146 MHz as our standard frequency. To limit the number of models that we need to examine, we shall use the following wire diameters in inches: 0.0625, 0.125, and 0.25. 0.0625" is close to the diameter of AWG #14 wire, while 0.25" is a useful diameter for soft copper tubing that we might press into quad-loop use. 0.125" is close to the diameter of AWG #10 wire. As with the sequence of polygons, the wire sizes step in 2:1 ratios.

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The square quad loop model automates the generation of dimensions for the first step in our trials. However, we need models for the other polygons. If we externally calculate the length of the focal line for each of them, using the circumference of the square version as a starting value, then we can construct a simplified equation-based model for the more complex polygons (again, using NEC-Win Plus as our platform).

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Fig. 4 shows the variables and wire set-up needed for the octagon. By making the starting side parallel the Z-axis, we can use the sine and cosine of 22.5 degrees to determine the coordinates of the corners, adding plus and minus signs as necessary for the quadrant within which the coordinates lie. With allowances for those signs, the set-up work is simply repetitious.

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In Fig. 5, we find the comparable information for the 16-sided figure. To minimize the number of trig functions, this model places a focal line along the X-axis. Hence, we may reuse the sine and cosine of 22.5 degrees and only need to add the sine/cosine of 45 degrees to complete the variable set for the model. The wire set-up reflects the change of orientation.

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The square quad loop uses 11 segments per wire for a total of 44. The octagon uses 5 segments per wire for a total of 40. The 16-sided figure uses 3 per wire, for a total of 48. NEC, of course, requires an odd number of segments per wire if we wish to center the source on a given wire. Once we settle on the segmentation of the source wire, it is a good habit to make all of the segments in the model as close to the same length as possible. In the case of regular polygons, achieving that goal is simple. As well, when comparing models of different shapes but very comparable sizes, it is normally useful to have similar segment lengths in all of the compared models. However, these rules of thumb are no substitute for performing convergence and average gain tests on each model of a sequence.

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Fig. 6 shows the numerical values for the coordinates of the 16-sided figure using the alternative set-up. You may locate the value of f16 by looking at the very first end-1 X coordinate. In some cases, having the points arranged so that they parallel the coordinate system axes may be inconvenient. In that event, you may set up the figure in the same manner that we used for the octagon. You will need the sines and cosines of 11.25, 33.75, 56.25, and 78.75 degrees. However, in terms of varables, we may reduce the set to a pair of angles, because 11.25 and 78.75 degrees form one pair whose sines and cosines reverse, while 33.75 and 56.25 degrees form the second pair with the same property.

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An alternative procedure is to accept the model as is initially and then to rotate it by 11.25 degrees. Fig. 7 shows the results of global rotation around the Y-axis. The rotation gives us the same result as setting up the polygon with sides parallel to the X- and Z-axes. Fig. 8 shows the difference.

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Why select one orientation over the other? The procedure that results in Fig. 7 is a bit quicker to develop. However, in some cases, one may wish to have a source that is centered within a wire and also on a wire parallel to the ground--if one were to further develop the models to place them over a ground surface.

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For any model, we can check the circumference. In the case of the square and the octagon, the absolute value of the second end-1 X coordinate is also the length of a half-side. Hence, the circumference of the square is 8 times that values and the circumference of the octagon is 16 times its half-side value. The initial 16-sided polygon uses the full length of the focal line as an X coordinate, so its circumference is 6.2428903 times that value (to be spuriously precise). The alternate or rotated 16-sided figure uses the same calculation as the square and the octagon.

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Almost all of the set-up steps may also be accomplished with Multi-NEC, AC6LA's NEC adjunct program. As well, Antenna Model--among well-corrected MININEC implementations--would allow much the same set up, but with an even number of segments per source wire.

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Some Sample Results

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The initial values for the 8- and 16-sided figures do not yield resonance. Indeed, the more sides that we add, the lower the self-resonant frequency. However, once we obtain the self-resonant frequency, we may re-scale the loop to 146 MHz. We must take care to return the scaled wire size to its original value and recheck the impedance at 146 MHz to assure ourselves that it is within reasonable limits, since we wish to know by how much a resonant near circle circumference differs from the circumference of a resonant square.

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In fact, the ratio of loop circumferences is also the ratio of the initial resonant frequency to 146 MHz, the design frequency.

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In all cases, I performed an average gain test (AGT) on each test model to assure myself that the result would be comparable. The AGT values ranges from 0.998 to 1.005, for a range of gain errors totaling 0.03 dB. The worst case AGT value was 1.005, which is equivalent to a gain error of 0.02 dB. The resistive component of the feedpoint impedance would be off in this case by 1/2 of 1%. Since most builders work with perhaps 1% tolerances, the AGT margins are well within limits. All models used perfect or lossless wire, but the differences in outcome for copper or aluminum would be insignificant. The following table summarizes the results of the test models, with all values for 146 MHz and all dimensions in inches. Gain values are free space. The tests and re-scaling were performed using NEC-4 (in this instance, EZNEC Pro/4).

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+            Model Test Results for 4-, 8-, and 16-Sided Loops
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+0.0625" Diameter Wire (0.00077 wavelength)
+# Sides          Gain       Feed Z          Circumference   Ratio/Square
+                 dBi        R+/-jX Ohms     Inches
+ 4               3.35       128.0 + j 0.3   87.040          ----
+ 8               3.59       137.2 + j 0.2   85.579          0.9832
+16               3.63       139.4 - j 0.2   85.043          0.9771
+Gain increase:   0.28
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+0.125" Diameter Wire (0.00155 wavelength)
+# Sides          Gain       Feed Z          Circumference   Ratio/Square
+                 dBi        R+/-jX Ohms     Inches
+ 4               3.39       130.2 + j 2.5   88.143          ----
+ 8               3.62       139.1 + j 1.9   86.453          0.9808
+16               3.66       141.2 + j 1.5   85.849          0.9740
+Gain increase:   0.27
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+0.25" Diameter Wire (0.00309 wavelength)
+# Sides          Gain       Feed Z          Circumference   Ratio/Square
+                 dBi        R+/-jX Ohms     Inches
+ 4               3.45       133.3 + j 4.2   89.664          ----
+ 8               3.67       141.9 + j 3.3   87.699          0.9781
+16               3.71       143.9 + j 2.9   87.023          0.9705
+Gain increase:   0.26
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There are several characteristics of the progressions worth noting:

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1. As we approach a true circle, the gain increases over that of a square quad loop. However, the increase is less than 0.3 dB, which is operationally unnoticeable. In a multi-element array, this gain will not accrue to each added element, but instead will represent the total gain increase for the entire array. Hence, if moving from a square to a circular element quad invokes considerable construction complexities, it may not be worth the effort.

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2. As we approach a true circle from the square starting point, the near-resonant feedpoint impedance increases. The increase is between 7% and 8%. Although not a truly serious increase, it is sufficient to bring a note of caution relative to SWR curves based on calculations for a square loop starting point. The change may also require some re-optimizing of multi-element quads that move from square to circular elements.

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3. As is well known among quad builders, the larger the element diameter, the larger the required loop circumference for resonance. This fact does not change as we move from square elements to circular ones.

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4. The fatter the wire diameter, the greater the adjustment required in the loops. Using the 16-sided polygon as a reasonable approximation of a circle, it requires a circumference nearly 98% of the size of a square loop with 0.0625" diameter wire but only about 97% of the square's circumference when the wire is 0.25" in diameter.

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A Caution

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The adjustment factors developed based on models up through 16 sides apply only to independent loop elements. For this situation, simple re-scaling is a sufficient technique for returning the loop to resonance as we increasingly round it.

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However, multi-element parasitic beams have other considerations that make the situation far more complex. Establishing resonance through loop adjustment may not suffice to ensure that the performance of the array replicates a square-quad original. Element spacing may require changes. As well, one must consider not only centering the impedance or SWR curve at the design frequency, but as well the curves for the forward gain and the front-to-back ratio.

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A 16-sided polygon is within 1% of being a good approximation of a circle, considering the ratio of the circumference to the length of a focal line. Hence, for individual quad loops, the adjustment factors developed by the models should be quite reliable. As the figures derived from octagons show, the 8-sided figure may not be as reliable as a guide to circularizing elements. As well, in the adjustment of loops from a square original to a circular final product, the change in resonant impedance may be as important as the loop circumference. On the other hand, it is unlikely that the gain differential will ever be noticed.

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In terms of modeling approximations of circles, the polygon that we select for the approximation depends upon the degree of precision that we require. For tracking some general trends or where we know in advance that there are features of the physical antenna that we cannot model, even a hexagon may serve as an approximation (where the circumference C equals 6 times fh, the hexagon focal line length). Increasing requirements for precision, however, makes the 16-sided figure a very adequate choice in most cases. Even if we cannot model a true circle in NEC or MININEC, we may still come very close. The answer to whether "very close" is "satisfactorily close" is always a task-driven judgment.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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7. Maximizing Your Data

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L. B. Cebik, W4RNL

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+ Now that we can pick and place loads to best advantage, do we have a good handle on how best to use them? Many newer modelers restrict themselves to trying to design an antenna, analyzing the performance of a given antenna, or modifying an antenna. Rarely do they develop methods for teaching themselves some very useful things about antennas, using the modeling program as a foundation. +

We can teach ourselves much about antennas if we learn to do some systematic modeling. What "systematic modeling" means is best told by way of an example. We can think of it as a model of modeling. It is adaptable to any number situations in which we want to maximize our knowledge and understanding in order to make intelligent decisions about antenna construction options. In this instance, however, we shall focus on the loads we have learned to use.

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The Task and Its Start

We want to construct a shortened, loaded antenna element. What is the best loading scheme? Where is the best place to position the load? Figure 1 illustrates part of our quandary. +
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To make the task more specific, let's use 7 MHz as our target frequency region. The element will be aluminum. For study purposes, we can set a diameter of 1" as being about midway between beefy construction and wire construction. The exact dimensions may differ if we choose a different materials, but the trends will all hold true.

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The best way to begin the task is by modeling a 1/4 wl vertical antenna above and in contact with perfect ground. Use about 25 segments, feeding the antenna in the segment closest to ground (in NEC) or at the ground pulse (in MININEC). Adjust the length to resonance. With NEC (from which all of the following numbers were derived), you should obtain from an elevation plot a gain of about 5.14 dBi with a source impedance of about 35.97 Ohms for a 33.7' vertical. Exact numbers will vary from program to program, but they should be very close to these. We shall assume that all cases of resonating an antenna bring the source impedance to less than +/- 1 Ohm of reactance.

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Even if we plan to use a dipole element, modeling over perfect ground is useful and reliable. Although a real vertical over imperfect ground will show a different gain, the trends derived from our perfect ground model will be accurate. Moreover, a vertical over perfect ground also provides data for a dipole in free space. Simply subtract 3 dB from the gain and double the source impedance. A test 67.4' free space dipole with 51 segments (to place the source at exact center in NEC) yields a gain of 2.13 dBi and an impedance of 71.87 Ohms. From the free space dipole, we can then adjust results for dipole elements over real ground.

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So, we shall save half the time it takes to create and modify both the antenna geometry and the load placement simply by modeling the situation over perfect ground with a ground-mounted vertical.

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What Happens When we Shorten a Vertical?

Understanding the practical dimensions of loading a shortened antenna element begins by understanding what happens when we just shorten the element. Suppose we take our 1/4 wl vertical and begin shortening it in 10% increments, adjusting the number of segments to prevent them from getting too short. +
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The graph in Figure 2 shows what happens for our 7 MHz vertical--and for any other 1/4 wl vertical, as well as for any free space dipole. The gain begins to drop from its peak of 5.14 dBi down to 4.69 dBi at the 10% of original length mark (3.4'). Equally notable is the drop in feedpoint impedance from nearly 36 Ohms down to a fraction of an Ohm. As the resistance at the source drops, the capacitive reactance rises from zero for the full length antenna to over 1400 Ohms for the antenna that is only 10% of that length.

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At this point, we must make some study decisions. Ideally, we should explore loading with every length of antenna. Since we do not have room for that ideal in this column, I shall choose a particular antenna length to explore: about 70% of full length. In fact the antenna is 23.4' long--of course, using the same 1" diameter aluminum we started with. With no load, this antenna shows a gain of 4.93 dBi, only about 0.2 dB down from the full size antenna, but with a source impedance of 13.49-j176.3 Ohms.

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The capacitive reactance tells us what compensating value of inductive reactance a base loading coil must have to resonate the antenna: 176.3 Ohms (just about 4.008 microHenrys at 7 MHz). However, if we want to look at options for loading the element at other than the base (or, with double the reactance and inductance values, at the center of a dipole), we must look systematically at what values of reactance will do the job. For this task, we can specify a type 4 (complex impedance) load consisting of a resistance and series reactance, and initially set the resistance to zero. (We shall change that zero later.)

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So let's move the load from the antenna base (segment 1 in NEC, or the 2% mark for a 25-segment antenna). We shall for space economy move the load successively to segments 5, 10, 15, 20, and 25 (18, 38, 58, 78, and 98% up the antenna). Then we shall adjust the amount of reactance to bring the antenna to resonance.

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The graph in Figure 3 shows part of the results of our work. The source resistance climbs steadily from its low of 13.49 Ohms up to 29.21 Ohms with the load very near the tip of the antenna element. However, note the curve for the required value of inductive reactance. Near the element tip. the required reactance is 8680 Ohms, or a seeming inductance of 0.197 milliHenrys. The real antenna would be resonant just from added wire length in the solenoid long before that high an inductance was reached.

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There is a reason for this situation. NEC loads are pure (mathematical) reactances and not physical coils. In the classic relationships between reactance and inductance, a coil with equal input and output current is assumed. However, on an antenna, the coil replaces a section of linear antenna element. On that "missing" piece of antenna, the standing current magnitude changes so that the input and output currents levels are not equal. The differential is an indicator of how much a real coil radiates and to the same degree acts as a length of wire rather than a solenoid.

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The further out the antenna you move, the greater the current level change per unit length. A center-loading coil shows far less than 1% change and hence acts strictly as an inductance. At the tip, the coil acts almost exclusively as a length of wire and very little as an inductance.

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In addition to the declining effectiveness of coils as inductive reactances as you move away from the source, the required reactance for resonance increases. At the 58% point, the necessary reactance is over double that required at the source. Expressed in other terms, for a dipole, each mid-element loading coil must be as big (in reactance and inductance) as a single center loading coil. For our antenna, a loading coil mounted exactly half way up the element must have 330 Ohms reactance compared to a base loading coil of 176.3 Ohms.

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However, as the load moves outward along the element, two advantageous things happen. The source resistance rises--from 13.49 Ohms for a base loading coil to 21.79 Ohms for a mid-element loading coil. This rise in source resistance has implications for the ease of matching the antenna to common feedlines. (Remember to double these values if you are thinking of a dipole.) Second, the antenna gain rises slowly as the load moves outward, from 4.93 dBi with a base load to 5.02 dBi with our impractical load near the tip. With the load exactly mid-element, the gain is 4.95 dBi, which is not a significant difference from the gain of the antenna with a base load.

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Q

Once you obtain systematic data about the required reactance to achieve resonance with the load positions you are considering, it is time to factor Q into the effort. Every inductor has a series resistance, and the reactance divided by the resistance is the component Q. However, the resistance is pure loss, and we need to see the magnitude of these losses. +

Again, it would be useful to know the effect of Q on loads for every antenna length possible and at every load position along each of the antennas. However, for this example, let's stick with our 23.4' long vertical (corresponding to a 46.8' dipole) and explore the effects of Q upon just the base load and the mid-element load models.

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The first question is this: what is a sensible range of Q to explore? It is certainly feasible to construct a loading coil with a sustainable Q of at least 100. ("Sustainable Q" means the Q after the coil has been immersed for months or years in the chemical soup that we call our atmosphere.) At the other extreme, the highest coil Q I have seen claimed for an antenna loading coil is about 600. Whether or not such a high value is actually feasible or sustainable in use, I cannot say, but exploring the Q-range from 600 down to 100 should be instructive.

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Therefore, in two sets of modeling runs, let's explore what happens to the antenna with base loading and with mid-element loading as we vary the Q. We can do this by simply using the Type 4 load we have been using for reactance insertion and adding a series resistance appropriate to the Q. Since the reactance value of the mid-element load is over double that of the base load, you will have to expect resistance values to parallel that ratio for equivalent Q values.

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The graph in Figure 4 shows the effects of decreasing Q on the antenna gain. From a value of 600 down to a value of 300, the loss is slight. However, from that Q value downward, the curve gets increasingly steep. As the Q of the base load decreases, the resistance of the coil shows up as an increase in source resistance. The increase is in the range of 0.3 Ohms at Q=600 to 1.75 Ohms for Q= 100.

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The results for mid-element loading appear in Figure 5. The curve is virtually identical to that for base loading. Once more, a Q of 300 seems to be the dividing point between modest losses and more extreme losses with mid-element loading coils. Because the coil is further out, the source resistance changes only by about the same amount as it does with a base loading coil, although the series resistances are more than double. The source resistance with a Q of 100 is about 2.5 Ohms higher than it is with an infinite Q.

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Throughout the range of Q values for both the base loading and the mid- element loading models, the difference in gain between the models is never greater than about 0.3 dB. This very slight difference belies some common recommendations often heard that give mid-element loading grandiosely higher marks than base loading. We have a case here of remarks being taken out of their original context and becoming unwarrantedly general. Nothing in the physics of a loaded antenna warrants them.

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The recommendation for mid-element loading arose from very short mobile antenna practice. In this situation, the antenna must contend with significant amounts of auto body metal and other surrounding objects to absorb or reflect in uncontrolled ways the radiation from the antenna. If the advice has any application, it is not to the general theory of loaded antennas, but to antennas located where external conditions affect their performance. For any given Q, there is no significant difference in the anticipated performance of base loaded or mid-element loaded antennas that are free and clear of such clutter.

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Operating Bandwidth

The investigation would not be complete without exploring the operating bandwidth of loaded antennas. Once more, we shall restrict ourselves here to just our two examples. We shall specify a Q of 300 for both models, even though a complete study would want to explore operating bandwidth for every increment of Q checked in the preceding section of the study. +

To check the operating bandwidth of the antennas, we must change the type of load to a type 0 load having a series resistance, inductance, and capacitance (the last of which we set to zero to show that it is missing). The resistance-inductance combination for the base-loaded antenna is .5877 Ohms and 4.008E-6 Henrys. For the mid-element loaded model, the combination is 1.1 Ohms and 7.503E-6 Henrys. This change in load type ensures that the antennas will show the correct complex impedance at every frequency.

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We may make a frequency check every 100 kHz for two increments above and below the resonant frequency to ensure that we cover the width of the 40-meter ham band. Here are the results from my NEC run.

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Base-loaded model:  R = 0.5877 Ohms; L= 4.008E6 H
+Frequency      Gain      Source Impedance    VSWR
+relative to     dBi         R+/- jX Ohms     relative to
+Resonance                                    14.08 Ohms
+-0.2 MHz       4.72      13.16 - j 18.83     3.645
+-0.1           4.73      13.61 - j  9.36     1.944
+ 0             4.75      14.08 - j  0.01     1.001
++0.1           4.76      14.56 + j  9.22     1.886
++0.2           4.77      15.05 + j 18.37     3.293
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+Mid-element-loaded model:  R = 1.10 Ohms; L= 7.503E6 H
+Frequency      Gain      Source Impedance    VSWR
+relative to     dBi         R+/- jX Ohms     relative to
+Resonance                                    22.68 Ohms
+-0.2 MHz       4.76      20.30 - j 28.17     3.446
+-0.1           4.77      21.45 - j 14.43     1.907
+ 0             4.78      22.68 - j  0.42     1.019
++0.1           4.79      24.00 + j 13.88     1.802
++0.2           4.80      25.43 + j 28.55     3.104
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Figure 6 graphs the SWR curves relative to the resonant impedance of each antenna. Although the SWR operating bandwidth of the mid-element loaded model is slightly wider than that of the base-loaded model, the difference is unlikely to make a difference in operation. Both antennas have 2:1 operating bandwidths in the vicinity of 200 kHz, or less than the span of the 40-meter band.

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The operating bandwidths, of course, are those at the antenna source terminals. The application of matching systems and losses in the feedline may make these bandwidths appear wider by virtue of taking SWR readings at the transmitter location. For our purposes, it is an open question whether that widening of the operating bandwidth comes with a low or high cost in losses.

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The tabular data shows as a graph cannot the changes in both the resistance and the reactance at the feedpoint of the respective antennas. The ratios in the source resistances of the two antennas is reflected also in the total change in reactance across the checked bandwidth. Hence, the SWR curves turn out to be very similar.

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Interestingly, the key significant difference in the two loading systems appears to be the source resistance. For most purposes, the higher source resistance of mid-element loading would yield higher efficiency with the same set of external losses due to such things as connection resistance and the like. Other variables, such as construction advantages of one system over the other, fall outside what modeling can indicate. However, we have not modeled our last load with our 23.4' vertical over perfect ground.

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"Capacity" Hat Loading

As we observed when moving loads outward along the antenna element, by the time we pass the mid-element point, loads act more and more like lengths of wire and less like pure inductances. If we place a coil on the very end of the element, it acts like a simple extension of the antenna element, but with tight coupling and consequent cancellation of some radiation. A more effective end-loading scheme is the so-called "capacity" hat. +

A capacity hat is an wholly symmetrical structure added to an element end at right angles to the main element. The symmetry ensures cancellation of any radiation from the structure. The name "capacity" hat arose from a method of calculating the size of the hat, a method which is useful at low and medium frequencies, but which grows increasingly inaccurate throughout the HF range. Physically, the hat is simply an extension of the antenna element that does not produce significant radiation.

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Figure 7 shows the general scheme, along with several hat types. The square, hexagon, and octagon shown all have a perimeter wire, which reduces the required size of the support spokes. However, hats can be composed solely of spokes (a few or many), can have intermediate as well as perimeter connecting wires, or can even be disks.

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There are some rules for creating hats. The thinner the hat wire, the longer the spokes, for any given geometry. The fatter the main element, the longer the spokes.

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Any hat that passes the symmetry test will work as well as any other such hat. For example, here are gain and source impedance figures at resonance for 3 hatted 23.4' verticals: a square, a hexagon, and an octagon, all with perimeter wires. As you increase the number of spokes further, the rate of spoke length decrease goes down. Spoke length indicates the distance from the main element outward.

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               Square:             Hexagon:            Octagon:
+                3.11' spokes        2.78' spokes        2.6' spokes
+Gain           5.03 dBi            5.03 dBi            5.03 dBi
+Source Z       29.5 - j 0.6        29.7 + j 0.9        29.7 + j 0.9
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There are two very notable sets of values in this small table. First, the gain of the antenna is higher than with either system of inductive loading at a Q of 300. The gain is about mid-way between the inductively loaded models and the full length antenna. Second, source impedances at resonance are significantly higher than even those of the mid-element loaded model.

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The SWR graph in Figure 8, based on the resonant impedances of each antenna type, compares the curves of the inductively loaded models with the curve of any one of the hat-loaded models. The 2:1 SWR points are more than 500 kHz apart, well beyond what is needed to cover 40 meters. + 
"Capacity"-hat loaded model:  hexagon
+Frequency      Gain      Source Impedance    VSWR
+relative to     dBi         R+/- jX Ohms     relative to
+Resonance                                    22.68 Ohms
+-0.2 MHz       5.01      27.26 - j 14.42     1.663
+-0.1           5.02      28.44 - j  6.73     1.265
+ 0             5.03      29.66 + j  0.91     1.031
++0.1           5.04      30.94 + j  8.58     1.330
++0.2           5.05      32.26 + j 16.22     1.690
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The chart reveals that the rate of change of reactance across the frequency sweep is the smallest of all three types of loading we have investigated. The tables for the other two types of hats are too close to this one in all values to merit display.

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The upshot is this: if mechanical problems do not override performance figures, hat loading deserves serious consideration in the development of shortened antennas.

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Summary 1: the Example

We can summarize our work on the shortened 40-meter vertical in a small table. + 
Loading scheme      Gain      Source         2:1 VSWR
+                    dBi       Resistance     Bandwidth
+Base:  Q=300        4.75      14.08          <250 khz
+Mid-el.:  Q=300     4.78      22.68          <250 khz
+"Capacity" hat      5.03      29.67          >500 kHz
+Full-size           5.14      35.97          >500 kHz
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A more complete study would yield much more data. However, this much is enough to reveal some of the design decisions facing us. Gain, bandwidth, and source impedance form the elements of the final compromise, after adding in all of the external factors to which modeling cannot contribute.

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Summary 2: the Method

More important than the particular example that we probed is the method used to probe it. Beginning at a fundamental point in the study--the shortening of antennas before loading them back to resonance--we used the facilities of the program (either NEC or MININEC) to generate a relatively rapid means of developing comparative data, data that will carry over to real antennas--both vertical and horizontal--placed over real ground. The use of free space and of perfect ground is not restricted to preliminary antenna design work. It is also an important tool in systematic studies designed to increase our knowledge and understanding of antenna behavior under a wide variety of conditions. +

A little aimless modeling every now and then can be entertaining and occasionally useful. However, the more systematic you make your modeling efforts, the more profitable the output and the program become.

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70: Refining Physical Transmission-Line Models

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L. B. Cebik, W4RNL

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There are numerous occasions when we need to model transmission lines as physical-wire or GW entries. The advantage of physically modeling a transmission lines is the fact that it will show the losses found in reality. Using the TL facility produces lossless or ideal lines. (Perhaps some future version of NEC will modify the core to accept loss factors to expand the utility of this facility.)

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However, for most purposes, the modeler is faced with certain limitations. Fig. 1 shows one example.

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Coaxial cables are likely to defy physical modeling for almost all applications. The close-spacing of the wires within common cables (RG-8, -8X, -11, -17, -28, -58, etc.) even makes impractical modeling a cylinder with another wire along the center. For NEC-4, the dielectric between the wire and the cylinder is perhaps the smallest part of the problem, given the IS control entry.

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However, it is possible to model physically many types of 2-wire parallel transmission lines. With a vacuum or dry air dielectric between and around the wires, parallel transmission lines answer to the equation

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where Zo is the characteristic impedance of the line, S is the center-to-center spacing of the wires, and d is the diameter of the wire. Fig. 2 illustrates the elements of the calculation. If the two wires have different diameters, some references replace the element d with the square root of the product of the two individual diameters.

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If we create a parallel transmission line from 2 AWG #14 (0.0641" diameter) wires, calculations show a spacing of 1.367" for a 450-Ohm line. We can model this transmission line and check the calculation against NEC reports. We shall use NEC-4.1 in the program GNEC for the illustrations in this set of notes.

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We must pay reasonably careful attention to the model that we use for correlating NEC to standard calculations. First, as suggested by Fig. 3, the segment lengths should all be about 1.367" to correspond with the short source and load wires at the end of the transmission line. Second, the end wires do change the overall effective line length by a small amount. Therefore, the length selected for the check is 3/2 wavelengths, which minimizes the amount of error per half wavelength. For a test frequency of 14 MHz, the resulting model has 1852 segments.

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The source is a standard voltage source of 1 volt at 0 degrees phase angle. The load is 450-Ohm and is purely resistive. At exactly 3/2 wavelengths, the source impedance should be exceptionally close to the load impedance if the model captures adequately the standard calculation method for parallel transmission lines.

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The standard calculation for the relationship among the line characteristic impedances and the key physical line dimensions makes no reference to wire losses. Therefore, the initial trial of the model used a perfect or lossless line. The resulting source impedance was 450.003 + j 0.466 Ohms. Replacing the ideal wire with copper yielded an impedance reports of 450.979 + j 1.349 Ohms.

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Since this is an exercise, I have reported the results using all decimal places provided by the program. In an exercise, there are no task-related specifications of the required precision, so using all of the data seems appropriate. However, it does appear that differences in the CPU and/or the operating system used in a computer may result in slight variations in reports. Most of these variations are confined to the second, third, or later decimal places. For practical purposes, the differences make no difference. However, they can be disconcerting to one experiencing them for the first time when moving from one computer to another, even when using the same program.

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Even with copper wire, the modeled result is within about 0.2% of the calculated value. The obvious conclusion is that for purely air-dielectric lines, a physical model is quite adequate, so long as one does not try to bring the wires too close to each other.

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The type of transmission line so far modeled at best reflects the actual parallel line that we call ladder line. This style of line consists of two wires held parallel by periodic spacers that are too small to create a significant velocity factor (VF), where a factor becomes significant as it grows lower than 1.0. Ladder line is but one of many styles of parallel transmission line, a few of which appear in Fig. 4.

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Far more commonly used by radio amateurs and general consumers are vinyl-covered lines, such as those shown in the lower part of Fig. 4. TV twin lead usually has a characteristic impedance (Zo) of 300 Ohms. The cheaper sorts use a solid flat area between the wires. To reduce losses, some varieties use a tubular form with air in the center hollow area. Since the strongest fields exist directly between wires, the tubular line tends to have a higher VF than the common type, perhaps 0.9 vs. 0.8. Another technique used to raise the VF is to cut windows in the flat vinyl area between wires. The technique also tends to raise the VF to about 0.9 and is most common in 400-450-Ohm lines.

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Physically modeling a transmission line is limited to crude approximations unless it can also model the line's velocity factor. Many transmission line sections occur as parts of antennas, and the dimensions of those parts often account for the velocity factor of the line used in the assembly. Hence, an accurate model should be able to replicate or approximate the line's VF.

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NEC-2 is limited to modeling parallel lines in an air/vacuum environment only. NEC-4, however, includes the IS (Insulated Sheath) control input that allows the user to specify for any given wire in the model an insulated covering. We explored the basics of using the IS input in column #50. Essentially, we specify a radius greater than that of the wire, along with a conductivity and a relative permittivity (dielectric constant).

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Suppose that we wished to develop a 450-Ohm transmission line having a VF of 0.90. The development process begins with the fact that a physical wavelength of line will be 0.90 times the electrical wavelength. So we may take our original 3/2 wavelengths test transmission line and shorten it to 1.35 wavelengths. At 14 MHz, our test frequency, the length is 1138.13". Of course, to maintain the correct segment lengths, we shall reduce the number of segments on each long wire from 925 down to 833.

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Before we make any other changes to the model, we may check the source impedance at the new length. The report was 493.005 - j 35.816 Ohms.

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Fig. 5 shows the GNEC assist screen with labels upon all of the required entries. Perhaps the one entry that initially catches most modelers is the radius number. Although we were able to specify the wire coordinates in inches and then use a scaling entry (GS) to convert those coordinates into meters, as required by the core, control cards require direct entry in meters. Hence, the radius, which will be in the general vicinity of 0.09", must be entered in terms of meters, that is, about 0.002286. The entry shown is a bit smaller (0.882").

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Assuming that we have an excellent insulating material, we may enter 1E-10 for the conductivity (0.0000000001 S/m). For single wires, there is little change in the performance of wires with conductivities from 1E-10 down to 1E-7 S/m. Much more influential on the performance will be the relative permittivity or relative dielectric constant. The value shown, 3.25, falls in the general range for vinyl plastics (2.5 to 3.5) in the HF range.

+

The following two brief model descriptions in ASCII entry form show the difference between the pre-insulated (VF = 1.0) and post-insulated (VF = 0.9) condition of the long transmission-line wires. Note that we have insulated only the long wires, leaving the source and load wires bare.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Parallel 450-Ohm TL Simulation
+CM cu AWG #14 wire
+CE
+GW 1 925 0 0 0 0 0 1264.59 .03205
+GW 2 1 0 0 1264.59 0 1.367 1264.59 .03205
+GW 3 925 0 1.367 1264.59 0 1.367 0 .03205
+GW 4 1 0 1.367 0 0 0 0 .03205
+GS 0 0 .02540
+GE 0
+EX 0 4 1 0 1 0
+LD 4 2 1 1 450 0 0
+LD 5 1 1 925 5.8001E7
+LD 5 2 1 1 5.8001E7
+LD 5 3 1 925 5.8001E7
+LD 5 4 1 1 5.8001E7
+FR 0 1 0 0 14 0
+RP 0 1 361 1000 90 0 1 1
+EN
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Parallel 450-Ohm TL Simulation
+CM cu wire + .9 VF via IS cards GW 1 & 3
+CE
+GW 1 833 0 0 0 0 0 1138.13 .03205
+GW 2 1 0 0 1138.13 0 1.367 1138.13 .03205
+GW 3 833 0 1.367 1138.13 0 1.367 0 .03205
+GW 4 1 0 1.367 0 0 0 0 .03205
+GS 0 0 .02540
+GE 0
+EX 0 4 1 0 1 0
+LD 4 2 1 1 450 0 0
+LD 5 1 1 833 5.8001E7
+LD 5 2 1 1 5.8001E7
+LD 5 3 1 833 5.8001E7
+LD 5 4 1 1 5.8001E7
+IS 0 1 1 833 3.25 1e-10 .00224
+IS 0 3 1 833 3.25 1e-10 .00224
+FR 0 1 0 0 14 0
+RP 0 1 361 1000 90 0 1 1
+EN
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The rest of the development effort is to find--using a constant conductivity value--a radius and a permittivity value that together bring the transmission line to resonance at, hopefully, 450 Ohms. In fact, any number of combinations will do the job as well as it can be done by this method. The following table shows eligible combinations of sheath radius and permittivity that yield reasonably close tallies. Remember that the length is preset to 90% of the air-dielectric length, so that the only changes being made are to the two IS entries.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      IS Radius and Permittivity Values for a 450-Ohm, 0.90-VF Line
+
+      Sheath Radius         Relative        Source Impedance
+      inches     meters     Permittivity    (R+/-jX Ohms)
+      0.09       0.002286   3.1             452.431 - j 0.967
+      0.09       0.002286   3.15            452.462 + j 0.461
+      0.0882     0.002240   3.25            452.437 - j 0.617
+      0.088      0.002235   3.25            452.430 - j 1.033
+      0.088      0.002235   3.3             452.456 + j 0.237
+      0.0878     0.002230   3.3             452.446 - j 0.186
+      0.0866     0.00220    3.4             452.442 - j 0.342
+      0.0858     0.00218    3.5             452.454 + j 0.153
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The inverse relationship between the sheath radius and the permittivity value is readily apparent. Somewhat less noticeable is the fact that the resonant (more accurately, the near-resonant) condition of the source resistance is about 2 Ohms higher than for the air-dielectric case. (Again, more precisely, about 2.5 Ohms higher than the perfect-conductor model and about 1.5 Ohms higher than the copper-wire case. The present model also uses copper wire.)

+
+ +
+

Fig. 6 illustrates the situation. We have a combination of insulated sheathing plus an air dielectric between the wires. The greater part of the spacing uses an air dielectric, but the insulated sheathing of the wires is sufficient to change the Zo of the line itself. In a more complete form, the equation for calculating the characteristic impedance of a parallel transmission line is

+
+ +
+

where the added factor is the square root of the relative permittivity of the material between and around the lines. Hence, the Zo of the line is slightly different from our originally calculated 450 Ohms. However, since most of the space is air, we are only off by about 0.5%, with is close enough for most purposes. Nevertheless, further development can refine the characteristic impedance, if necessary.

+

For our purposes in this exercise, I shall declare that we are close enough. Our goal was to establish a means by which to model transmission lines having a desired velocity factor (0.90) and a selected characteristic impedance (450 Ohms). By the correct selection of a radius and a relative permittivity for a parallel transmission line, we can develop the necessary model within reasonably close tolerances.

+

If we need a lower value for the velocity factor, we shall find that the required IS entry--keeping the conductivity constant at 1E-10 S/m--requires nearly a doubling of both the sheath radius and the relative permittivity. For our sample line a radius of 0.0039 m (0.1535") and a permittivity of 7.0 yielded a source impedance of 454.316 - j 0.353 Ohms. The new source value continues to climb by another 2 Ohms. However, the doubling is not quite linear, since we obtained resonance with a 0.90 VF with a permittivity of 3.5 and a sheath radius of 0.00218 m (which would have yielded, if doubled, 0.00436 m).

+

Indeed, the non-linearity shows more clearly if we take the wire radius into account, since it is the sheath thickness--and not simply its outer radius--that is effective in establishing a given velocity factor. The thickness of the 3.5-permittivity sheath for a 0.90 VF was 0.00137 m, while the thickness of the 7.0-permittivity sheath for a 0.80 VF is 0.00309 m.

+

Nevertheless, the exercise does provide some guidance in the development of lines with any desired velocity factor. At least it does so by a trial-and-error method within the modeling software.

+

We have used a sample transmission line consisting of a pair of AWG #14 (0.0641" diameter) wires spaced 1.367" center-to-center. The use of this sample is not without reason. The wire size and spacing fall well within the ability of the NEC-4 core to model accurately if the segment junctions are well aligned. Of course, with parallel wires, we may obtain perfect alignment simply by assigning the same number of segments to each wire. With a segment length that is equal to the wire spacing, we assure that the source and load wires adjoin segments of the same length.

+

A further reason for using the specified sample line stems from the fact that the transmission line wire diameter can be the same as the diameter of the antenna wire to which it might be attached in a sample antenna + transmission line model. AWG #14 copper or copperweld wire is a very common value used in many installations, especially those designed for use in the amateur HF bands. However, if all we were concerned with was the feed line for a center-fed doublet, then we would not require all of the effort to establish a line velocity factor. We might with greater ease use the TL facility and externally adjust the required physical line length to achieve a set of electrical conditions.

+

Not all uses of transmission lines in antenna systems are so simple as modeling the main feedline of a center-fed doublet. Let's look at a different application and see what the modeling opportunities and limitations might be.

+
+ +
+

Fig. 7 shows the basic outlines of a 3/2 wavelengths center-fed doublet for the 20-meter amateur band. The difference between this antenna design and an ordinary doublet is the use in the center region of each half-element a 1/4 wavelength shorted stub, where the short occurs 1/2 wavelength from the feedpoint.

+

The interesting question surrounding the design proposal concerned the effects of the stubs on the pattern and gain of the antenna. The top portion of Fig. 8 shows the pattern of the same antenna treated simply as a 3/2 wavelength doublet. At the prescribed length of 99', the antenna shows a typical 6-lobe pattern with a maximum strength of about 8.4 dBi, as modeled at an elevation angle of 14 degrees, based on its height of 50' above average ground. The antenna uses AWG #14 copper wire and extends left-to-right (or right-to-left) across the pattern plot.

+
+ +
+

The center section of the figure shows the azimuth pattern when we create the parallel transmission-line stub using AWG #14 wire. The model for this azimuth pattern uses the very type of transmission line sampled earlier in the exercises, but with no insulated sheath. Hence, the velocity factor is very close to 1.0. As the pattern shows, there is a slight shift in the power distribution among lobes. The strongest lobes are now--by a slight margin--the 4 angling lobes relative to the wire, with a small reduction in the broadside lobes. By dividing power among 4 lobes, the overall maximum gain decreases fractionally to about 8.2 dBi, using the same elevation angle.

+

In the design proposal, however, the 1/4 wavelength stub section used material having a velocity factor of about 0.8. Hence, it seemed appropriate to investigate whether the antenna performance would change by assigning a velocity factor less than 1.0 to the modeled stub section. One stage in the modeling insulated the stub wires with insulation radii and permittivities consistent with the 0.9-VF line shown earlier. The result was the pattern in the lowest portion of Fig. 8. This pattern changes the relative strength of the lobes to increase the power in the broadside lobes and decrease it in the angling lobes, resulting in a maximum gain of about 9.2 dBi. Among the models tried, this one yields the strongest broadside lobe strength.

+

At best, the models in this series suggest some trends in performance, none of which offer much optimism that going to the extra lengths of construction complexity for the antenna will yield a comparable improvement in performance as compensation. However, the models--as limited as they are--do suggest trends and hence fall among a whole class of modeling efforts that I tend to classify as "suggestive" rather than definitive. Since they are not a decisive confirmation or refutation of the claimed principles of construction, they do not qualify as "proof-of- principle" models. Each of these categories of models has utility in a domain of modeling that is well shy of a definitive "analytical" model or a definite "design" model. Each category of model has functions within a task-defined set of limitations.

+

One of the limitations inherent to the evaluation of the design proposal is the fact that the physical antenna uses coaxial cable as the shorted stubs. Its physical length is as specified in the model, which means that its velocity factor makes the stubs--as stubs--electrically longer than the physical length.

+

The key factor of variance between the model and the physical antenna is the fact that when a shorted stub is not exactly 1/4 wavelength long, the reactance differs between a 50-Ohm stub and a 450-Ohm stub by a 9:1 ratio. Since the shorted stubs are longer than 1/4 wavelength, the reactance is capacitive, indicating a resonant or 1/4 wavelength frequency well below the 14-MHz test frequency. Fig. 9 provides some graphic data on the reactances of shorted stubs from 10 through 80 degrees of electrical length.

+
+ +
+

The proposed antenna was to operate at a variety of frequencies, some far removed from the 14-MHz test frequency. Hence, it is not possible in the simplified exercise to substitute the 450-Ohm line--at any VF supplied by the use of an insulated sheath--for the coax line at all frequencies.

+

Had the antenna been differently designed, the differences reported by using the 450-Ohm line stub with and without an insulated sheath would have been far more dramatic. Let's move the short from the outer ends of the stubs to the inner ends. Now the distance from the center feedpoint to the far end of the stub--the open end--is about 1/2 wavelength, while the inner end is about 1/4 wavelength distant from the feedpoint. Then let's repeat our experiment of modeling the stub sections without sheathing--giving us a VF close to 1.0--and with a sheathing corresponding to the 0.9-VF transmission line sample.

+
+ +
+

Fig. 10 shows the results. In this case, there is almost a full 2-dB increase in gain and a corresponding narrowing of the beamwidth for the sheathed version. As in the first version, we cannot claim that we have a definitive model, but we may be moving from a suggestive to a proof-of-principle model, relative to using transmission-line sections--even of coax--to tailor the performance of a wire antenna.

+

What principle applies to this particular antenna lies beyond the scope of the exercise. We have examined the use of the IS or insulated sheath control input of NEC-4 to simulate a transmission line with a velocity factor other than 1.0. There may be modeling occasions on which it is worthwhile to use this facility in more than a haphazard way to check out an actual design, the principles of a design, or the trends that would likely emerge from design variations. So long as we do not overstate the claims from a model, all of these goals are worthwhile.

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Go to Main Index

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71: The Average Gain Test Revisited

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L. B. Cebik, W4RNL

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+
+ +

+
+

In column 20, we examined the basic parameters of the Average Gain Test (AGT) as a test for model adequacy. This test is built into such commercial implementations of NEC as EZNEC and NEC-Win Plus, and has been adapted to the Antenna Model implementation of MININEC 3.13. However, a number of modelers do not use these programs, but instead use one of the public domain versions of the NEC-2 core. Hence, they must set up their own AGT, a fairly simple but elusive process unless one has some detailed instructions. Let's begin by reviewing some basic information from the earlier column.

+

AGT Basics

+

Essentially, we only need two numbers to perform the test: the input power and average radiated power. For a lossless antenna, the input power and the average radiated power should be equal in an ideal model. Whatever the gain in one or more favored directions, it will be offset by nulls in other directions. Over the entire sphere of free space, the total amount of radiated power can never exceed the power supplied to the antenna, and if the antenna is lossless, can never be lower than the input power. Hence, the ratio of average radiated power to supplied power should be 1. If the ratio differs by more than a small amount from 1, then the model may be considered suspect.

+

The conditions under which an adequate model will show an Average Power Gain (Gave) of 1 also establishes the conditions for performing the Average Gain test. The model is set in free space. (We shall look at setting the model over perfect ground in a moment.) The wire material must be perfect or lossless. All "real" or resistive parts of loads, networks, and transmission lines must also be set to zero.

+

For test purposes, the model is run by taking a regular sample of the radiation pattern every few degrees, and the results are averaged. (Note: for these tests, the sample is taken as a power and not as a power ratio, although one can be easily converted to the other.) The result is a fair reading of the average radiated power. To calculate the average power gain, we simply apply the following simple equation:

+
+ +
+

where Prad is the radiated power as averaged and Pin is the input power as calculated from source information.

+

What about k? For a free space model, k = 1. However, if the test lossless model is placed over perfect ground, then k = 2.

+

The results will not vary by much if the only loss in the antenna is wire loss for high conductivity materials of reasonably large diameters. However, for the most reliable figure of merit, the test is best run on a wholly lossless version of the model being tested.

+

The average gain figure that results from the test may be higher or lower than 1.0. One proposed gradation of model merit uses the following dividing points:

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Gave Value Range                   Significance
+0.95 - 1.05                   Model is considered to have passed the test
+                              and is likely to be highly accurate.
+0.90 - 0.95 and 1.05 - 1.10   Model is quite usable for most purposes.
+0.80 - 0.90 and 1.10 - 1.20   Model may be useful, but adequacy can be
+                              improved.
+<0.80 and >1.20               Model is subject to question and should be
+                              refined.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The user may develop more strict limits for the adequacy of a model based on the specific tasks within which the model plays a role.

+

Most models that deviate in the test from an average gain of 1 show an inverse correlation between errors in gain and in the resistive component of the source impedance. As the gain climbs, the source impedance decreases, and vice versa. For limited purposes, the average gain value derived from the test can be used to correct both figures, using the following equations:

+
+ +
+

and

+
+ +
+

Obviously, an average gain values that is greater than 1 will increase the input resistance and decrease the gain. Values less than 1 will do the opposite. One may simplify the gain correction by converting the AGT value into an equivalent value in dB:

+
+ +
+

If the resulting value in dB is positive, it is an amount by which the model reports are high and must be subtracted from the reports. If the converted gain value in dB is negative, it is the amount by which the reports are low and its absolute value must be added to the reports.

+

The list of suggested categories of adequacy of a model place the most ideal models in the AGT range from 0.95 to 1.05. An AGT value of 1.05 yields a conversion value of 0.21 dB, while a value of 0.95 converts to -0.22 dB. For some purposes, these differentials may be well within task limits, while for others, they may fall outside task limits. Hence, whether we use raw NEC report data or corrected values--even for quite adequate models--remains a user responsibility based upon the nature of the modeling task at hand.

+

The key limitations in the use of the correctives are two. First, if the AGT value is very high or very low, then the corrections are unlikely to give more than a suggestion of the corrected gain. The closer to a perfect value, the more likely the corrections will yield values that are reliable relative to a physical implementation of the modeled antenna.

+

The utility of the AGT test in warning of on inadequate model are obvious for large departures from the ideal values of 1.0 for a free-space run and 2.0 for a monopole array set over perfect ground. Large departures from the ideal call for a careful inspection of both the model and the many published limitations of NEC in order to detect and correct errors in the model. There are many conditions leading to error which the core will not call attention to by stopping its run. As well, some of these conditions may not be detected by the error-detection systems in commercial implementations of NEC. For example, closely spaced wires that do not inter-penetrate may have mis-aligned segments that will create errors in the NEC results. Ultimately, it is up to the modeler (and not the software) to develop the most reliable possible model and to establish that reliability.

+

Second, the corrective to the source impedance is reliable only if the reactance is very low. In other words, the antenna must be at or relatively close to resonance if the AGT value is to yield a reasonably accurate value for the source resistance. When reactance is high at the source segment, the source resistance correction may be suggestive, but is inadequate to be treated as reliable.

+

When AGT values are close to ideal, but depart by more than a very few percent from the ideal, individual models are often presented as yielding actual values of gain and impedance. In a perfect world, the reports should be adjusted by reference to the AGT, but usually, the differences are too small to make a significant difference for either analysis or for translating a model design into a physical reality. Unmodeled "lumps and bumps" in the physical antenna normally swamp such small variations between corrected and uncorrected model results.

+

However, reference to AGT values may be important in several types of modeling enterprises. For example, when modeling a series of related antennas for certain comparisons, it is wise to determine the AGT value of each model to ascertain that trends in gain and impedance are accurate, with no anomalous values that result from variations in the AGT values for the sequence of models. As a second type of example, I recently had occasion to compare the same model(s) using NEC and using MININEC. The initial results, using raw report data, produced gains over a half-dB apart, with similar differences in the source impedance. However, for the models in question, NEC AGT values were systematically high (averaging about 1.06), while MININEC results were equally systematically low (averaging about 0.94). When I compared corrected gain and source impedance values, they fell within 1% of each other.

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Setting Up an Average Gain Test

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Obtaining an AGT value is matter of reviewing the existing model and then setting up an RP 0 (Request for Pattern) input as a substitute for whatever other output request might be made. Suppose that we start with the following simple dipole model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Simple dipole antenna in Free Space
+CM Optimized for resonance at 300 MHz
+CE
+GW 1 9 0 -.2418 0 0 .2418 0 .0001
+GS 0 0 1
+GE 0 -1 0
+EX 0 1 5 0 1 0
+FR 0 1 0 0 300 1
+RP 0 181 1 1000 -90 0 1 1
+RP 0 1 360 1000 90 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model has already eliminated all resistive loading. Indeed, there are no load (LD) entries at all. As well, the model is in free space. However, it still retains its requests for E-plane and H-plane patterns (AZ/phi and EL/theta patterns in modeling terms). It is not necessary to remove these lines or other properly structured output requests from a model to obtain an AGT value. However, for clarity, we shall substitute the requisite RP 0 entry for the ones in the initial simple model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Simple dipole antenna in Free Space
+CM Optimized for resonance at 300 MHz
+CE
+GW 1 9 0 -.2418 0 0 .2418 0 .0001
+GS 0 0 1
+GE 0 -1 0
+EX 0 1 5 0 1 0
+FR 0 1 0 0 300 1
+RP 0 181 361 1002 0 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Now let's extract the RP0 line and explore its necessary and optional properties.

+ 
RP   0    181      361    1002   0      0      1      1
+    Type  # theta  # phi  XNDA   theta  phi    theta  phi
+          angles   angles see    start  start  incr.  incr.
+                          text
+

The XNDA entry differs from the most common far-field pattern request only in the last or "A" integer. (In an RP request, the first 4 numeric entries are integers, and the remaining are floating decimals. XNDA is therefore not a single number, but a set of 4 integer entries in one.) A "0" indicates no request for averaging, while a "1" or a "2" requests averaging. The difference between "1" and "2" is that the latter suppresses printing to the output file of the individual values making up the total field defined by the phi and theta entries, while a "1" yields a sizable table of values. Which you choose depends upon the need for those values.

+

There are two dimensions to the theta and phi entries: their formulation and the increment used within that formulation. Let's look at them individually, beginning with the number of angles.

+
+ +
+

Fig. 1 shows what we wish to obtain from each azimuth increment: an "orange" slice that samples each increment for theta from the zenith to its polar opposite. The number of theta angles will thus form a semicircle, and each new phi angle increment will produce another "orange" slice until we have sampled the entire free-space sphere.

+

For the sample line, we have chosen 1-degree increments for our fair sample. We might have chosen 91 theta angles and 181 phi angles, using a 2-degree increment in the last floating-decimal positions. Equally, we might have selected 0.5 as the angular increment, resulting in 361 theta angles and 721 phi angles. The object is always to create a complete sphere without repetition of angles, a problem that will cause erroneous results by counting some samples more than once. You may compare the results of the suggested line with another that simply doubles the theta angles from 181 to 361 to see what error might emerge. (The extra "1" is to ensure that we include both points at the limits of the slice.)

+

For a hemisphere, used when evaluating monopole arrays over perfect ground, use a theta value of half that required for a full sphere. Be sure to include the extra point, for example, 91 instead of 90) to include both end points. By starting with theta = zero, you assure that the hemisphere will just reach the perfect ground surface.

+

In fact, the selection of sampling increments (and the consequent number of sampled angles) does make a small difference in the AGT value--so small as to be numerically but not operationally interesting. For antennas with highly varied pattern shapes, very narrow beamwidths, many secondary lobes, etc., changing the sampling increment may make a much bigger difference than it does for our simple dipole with its "figure-8" pattern.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             AGT Values as a Function of the Number of Samples
+                          Test Dipole:  9 Segments
+
+     Angular Increment        Reported AGT        Common Form
+     2 Degree (Phi/Theta)     9.95720E-01         0.9957
+     1                        9.95696E-01         0.9957
+     0.5                      9.95690E-01         0.9957
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In general, the smallest increment that the modeler can use yields the most accurate figure for the AGT and for any correctives used in the analysis of multiple models. However, for simple geometric shapes, a 1 or 2 degree angle is quite adequate in virtually all cases. In the days of slow PCs, one often heard the advice to use the largest angle applicable to the beamwidth of the antenna. As well, those slower days suggested making use of antenna pattern symmetry to reduce number of sampling points and the run time for an average gain test pattern, especially when recording the sampling point values. However, since the amount of time required for an AGT test of the simple dipole by the current generation of PCs is under 30 seconds on an "old" 400-MHz P-2 machine for the smallest increment in the table above, there is little reason not to use small angles for all antennas. The more complex the antenna geometry, the smaller will be the percentage of run time devoted to the AGT pattern, with or without a print- to-file of the sampled positions.

+

As a reference, here is the sort of report lines that you will receive from a NEC-4 output file (reduced to only the AGT lines) for an 11-segment dipole.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+AVERAGE POWER GAIN= 9.97119E-01
+                     SOLID ANGLE USED IN AVERAGING=( 4.0000)*PI STERADIANS.
+
+POWER RADIATED ASSUMING RADIATION INTO 4*PI STERADIANS = 6.91679E-03 WATTS
+
+
+                         - - - POWER BUDGET - - -
+
+                     INPUT POWER   = 6.93677E-03 WATTS
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Make sure that the solid angle used in the averaging is equal or very close to 2*pi steradians for a hemisphere over perfect ground or equal or very close to 4*pi steradians for a full free-space sphere. (Including both limits is essential in obtaining a true 2.0 or 4.0 value for the solid angle.) NEC-2 does not yield the radiated power report entry. However, I have listed the Power Budget Input Power line, which is actually a rounded (by 1 place) version of the power reported by the Antenna Input Parameters power entry. Multiplying the Average Power Gain times the Input Power will provide the Power Radiated value.

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There is one more set of numbers that is interesting before we leave our over-kill of AGT. Our initial dipole was modeled using 9 segments. Let's see what happens as we increase the number of segments, each time moving the source position to center it.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 AGT Values as a Function of Segmentation
+                     Test Dipole: 1-Degree Increments
+
+     Number of Segments       Reported AGT        Common Form
+       9                      9.95696E-01         0.9957
+      11                      9.97119E-01         0.9971
+      15                      9.98451E-01         0.9985
+      21                      9.99212E-01         0.9992
+      31                      9.99640E-01         0.9996
+      51                      9.99871E-01         0.9999
+      71                      9.99937E-01         0.9999
+     101                      9.99973E-01         1.0000
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For some tasks, the differences will make no difference. For others, up to a point, increased segmentation may be advisable when measured against the parameters of a modeling task. However, note the decrease in the rate of increasing AGT value toward 1.0 with the higher levels of segmentation. Hence, even for the most exacting modeling task, there will be a cut-off, beyond which increasing the number of segments--even on this model with a very thin wire (radius = 0.1 mm) relative to total length (about 0.484 m)--will yield nothing useful.

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In this regard, remember that there is a convergence test that is also useful in evaluating the adequacy of a model. With NEC, there is a region of segmentation density that yields the least change in output report values as we increase and decrease the density by small increments. For most purposes, this region represents the converged model. In the end, balancing the two tests provides the best measure of an adequate model.

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However, there are two limitations in this generalization. First, not all models that yield close-to-ideal AGT numbers will converge, and not all models that converge will yield close-to-ideal AGT values. Second, there are models that will neither converge nor yield a satisfactory AGT value. Both tests represent necessary but not sufficient conditions of model adequacy. Hence, the final responsibility for producing an adequate model within the much-published limitations of the core software remains squarely on the shoulders of the modeler.

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Go to Main Index

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72. The GX or Symmetry Geometry Input

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L. B. Cebik, W4RNL

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NEC-2 and NEC-4 have a useful geometry input card labeled GX . Often called the Symmetry Card, its actual title is "Reflection in Coordinate Planes." A typical input line suggests extreme simplicity:

+ 
GX    5     110
+      I1    I2
+

Note that there are no floating decimal positions for this input. The I1 entry indicates by how much to increment the tag numbers for each new construct created by the card. This maneuver helps prevent overlapping tag numbers for the wires of the model. The next entry is actually three binary entries, one each for the X, Y, and Z axes around which a reflection would occur: a "1" means "yes, reflect in this plane (across this axis)," and a "0" means "do not reflect."

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A reflection is a symmetrical replication of the existing structure created by GW and other entries preceding the GX card. Since the sample line has reflections in two planes, we shall end up with 3 new constructs for a total of 4 constructs and 4 times the total number of wires and segments as are in the geometry preceding the GX line. The 3 planes in the I2 entry indicate the X, Y, and Z axes. However, replication or reflection occurs in reverse order. In this case, we have no Z-axis replication. The Y-axis "1" creates a replica on the "other" side of the Y-axis. Then, the X-axis "1" creates a reflection of the two structures on the other side of the X-axis. Obviously, to use this card effectively requires careful planning to avoid ending up with a tangled jungle of illicitly overlapping and intersecting wires.

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The user's question is obvious: what do we get for all of our careful planning? The answer is a reduction of the core run-time. The NEC manuals provide a chart of the relative run-times for the matrix storage, fill-time, and factor-time elements of the core run, but the bottom line is that a single reflection can reduce a run-time to about half of the same model created by other means. Two reflections cuts the time to about a fourth, and 3 reflections to about an eighth. The values show up most graphically on very large models (several thousands of segments), where the overhead for pre- and post-matrix work is a very small part of the total run-time. Hence, most advanced modelers save the GX card for very large models.

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A Working Example: 3 Ways to Analyze a Square of 4 Yagis

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Any account of the GX card faces a problem. Either the illustrations will be too large to show and the run-time improvements will be easy to see, or the models will be small, but the run-time differences will be hardly significant. Since these notes aim to orient the newer modeler to the use of the GX card, we shall use the small-model avenue and look at run-times in more detail later on.

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Let's begin with a simple 6-element Yagi designed for 146 MHz, where a wavelength is about 80.84" or 2.0533 meters. The total model, with all dimensions in meters, appears in Fig. 1. We shall stay in free space for this exercise, since eventually we shall want to create a GX version with symmetry relative to to the X and the Z axes. For simplicity throughout this exercise, we have modified the LD5 (material load) line so that it always encompasses all segments, no matter how many wires segments we add to the model by any of the means that we shall explore. The vital NEC output report data for this little antenna appears in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           Single 6-Element 146-MHz Yagi
+
+     Gain       Front-to Back         Feedpoint Impedance        Run-Time
+     dBi        Ratio dB              R +/- j X Ohms             Sec
+     10.23      35.39                 49.97 + j 9.53             1.20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The only unusual bit of data in the listing is the core run-time taken from the NEC output report. It includes all core operations, which include the modification of values for the conductivity of aluminum and the E-plane or azimuth/phi pattern request as well as the matrix work.

+

This is our base-line data against which we shall make comparisons as we modify the model to create a square array of 4 such beams with their booms separated by 1 wavelength in each direction. (We do not here have to concern ourselves as to whether the spacing is optimal, so the convenient measures will work well for us.)

+

There are at least 3 ways to create our square of 3 models. The method that is available on entry-level programs is simply to replicate the first Yagi 3 more times and to space each one at the required distances apart to make the square. Using copy and move functions for blocks of GW or wire entries simplifies the process somewhat, but the final model is somewhat large visually and not too easy to scan rapidly. Fig. 2 verifies this fact.

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Note the we need not add any new LD5 inputs, since the I1 and I2 entries cover all segments in the total model. Otherwise expressed, everything is aluminum. However, we did add new EX lines so that each beam has a source. Fig. 3 shows the NEC-Vu graphic of the square.

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The output data appears in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                Square of 4 6-Element 146-MHz Yagis:  GW Construct
+
+     Gain       Front-to Back         Feedpoint Impedance        Run-Time
+     dBi        Ratio dB              R +/- j X Ohms             Sec
+     16.25      26.23                 50.96 + j 7.29 (x4)        9.50
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance is interesting, but the run-time is the more crucial figure to examine. The run-time is 7.9 times longer than for the single Yagi.

+

A second formation technique is available to the user of more advanced programs, such a NEC-Win Pro (NEC-2) or GNEC (NEC-4). Instead of replicating with modifications all of the GW lines, we may employ the GM or Coordinate Transformation card instead. So let's reuse our 6 GW lines for a single Yagi and then make the moves indicated by the GM lines that follow in Fig. 4.

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+ +
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The first GM line moves the existing Yagi into the -X and -Z region. The amount of each move is 1/2 wavelength, as indicated by the 1.026668 (meter) values. This move will simplify the required moves for both this and the third alternative square.

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The second GM line creates a second Yagi 1 wavelength above the first one and assigns it tag numbers 7-12.

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The third GM line creates a new pair of Yagis 1 wavelength in the +X direction and assigns them the tag numbers 13-24.

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We end up with the same square of Yagis that we viewed in Fig. 3. The output report appears in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                Square of 4 6-Element 146-MHz Yagis:  GM Construct
+
+     Gain       Front-to Back         Feedpoint Impedance        Run-Time
+     dBi        Ratio dB              R +/- j X Ohms             Sec
+     16.25      26.23                 50.96 + j 7.29 (x4)        9.45
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The only difference in the reported data is the run-time. In this instance, it is 0.05 seconds shorter than the run-time for the GW construct. However, such times will show natural variations for the individual models that are larger than the difference in the two recorded values, depending upon the myriad of variables within the computer.

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If we know how to read the GM cards, the GM model is simpler to scan. Although the model uses NEC-4, it will also run in NEC-2, at least using the version of NEC-2 employed by NEC-Win Pro. The Imov entries may be missing if we are moving or replicating the entirety of the structure that so far exists. However, because there are so many cores of various ages and variation, if you are using something like Multi-NEC with a public domain core, be certain that you adhere to that core's requirements for setting up the GM lines.

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Fig. 5 records the E-plane (phi) pattern for the free-space square of 4 Yagis. Since the output reports for the two different models are identical, the pattern applies equally to both.

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Now let's create the same models with mirrors but no smoke, that is, with the GX reflection input. We shall add a GM card to move the initial Yagi into the same -X, -Z position that we used with the GM construct. However, this time, we shall create the other 3 Yagis with a single GX line, as shown in Fig. 6.

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+ +
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Note that by incrementing the tag numbers by 6, we shall create a total of 24 tags. The GX line indicates replication across the Z-axis and then total replication across the X-axis. The NEC-Vu result is identical to the square of Yagis shown in Fig. 3. We also have added the EX lines to make sure that we have a source for each reflection. So why does the resulting pattern emerge as shown in Fig. 7?

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The answer lies in how NEC creates reflections in coordinate planes. The new structures are indeed mirror images. The following abbreviated table compares the first and last segments of each of the 4 reflector wires from the GM construct (which is identical to the GW construct) and from the GX construct, as recorded in the Segmentation Data in the NEC output file.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Partial Segmentation Tables From NEC-4 Output Files
+
+2m6-GM4a:  GM Construct
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1  -1.51677   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238     0    1    2      1
+    21  -0.53657   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238    20   21    0      1
+
+   127  -1.51677   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238     0  127  128      7
+   147  -0.53657   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238   146  147    0      7
+
+*  253   0.53657   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238     0  253  254     13
+*  273   1.51677   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238   272  273    0     13
+
+*  379   0.53657   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238     0  379  380     19
+*  399   1.51677   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238   398  399    0     19
+
+====================================================================================================
+
+2m6-GX4:  GX construct
+
+  SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1  -1.51677   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238     0    1    2      1
+    21  -0.53657   0.00000  -1.02667   0.04901    0.00000   0.00000   0.00238    20   21    0      1
+
+   127  -1.51677   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238     0  127  128      7
+   147  -0.53657   0.00000   1.02667   0.04901    0.00000   0.00000   0.00238   146  147    0      7
+
+*  253   1.51677   0.00000  -1.02667   0.04901    0.00000 180.00000   0.00238     0  253  254     13
+*  273   0.53657   0.00000  -1.02667   0.04901    0.00000 180.00000   0.00238   272  273    0     13
+
+*  379   1.51677   0.00000   1.02667   0.04901    0.00000 180.00000   0.00238     0  379  380     19
+*  399   0.53657   0.00000   1.02667   0.04901    0.00000 180.00000   0.00238   398  399    0     19
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we compare the entries for the 3rd and 4th reflectors, which emerge from translations or from reflections across the X-axis, we can see that the order from first to last segment is reversed in the GX construct. As well, the beta orientation angle is not 0, but 180 degrees. However, if we return to Fig. 6, the model description, and examine the EX lines, we set up all four sources with the same phase angles: 1.414 real and 0 volts imaginary. The result is a square of four Yagis with the left pair fed out of phase with the right pair.

+

To restore the in-phase feed for the two pair of Yagis, we need to reverse the phase of the right-most beam sources or EX entries (or, alternatively, of the left-most pair). We achieve this simply by adding a minus sign to the real component of the voltage at the source, as shown in Fig. 8.

+
+ +
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When we make the change, the following data emerge from the model after running the core.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                Square of 4 6-Element 146-MHz Yagis:  GX Construct
+
+     Gain       Front-to Back         Feedpoint Impedance        Run-Time
+     dBi        Ratio dB              R +/- j X Ohms             Sec
+     16.25      26.23                 50.96 + j 7.29 (x4)        4.40
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Obviously, almost nothing changes relative to the GW and GM constructions, except for the run-time. In this trivial-sized model, the run-time is about half that of the other two models, and most of that time is taken up in pre- and post- matrix calculations and file generation. A truly large model would show a far greater reduction in core run-time.

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A Different Type of Reflection Model

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A second type of example may better illustrate the run-time savings that symmetry yields. We shall develop a simple doublet at 15 MHz, where a wavelength is close to 20 meters. We shall use segments close to 1-meter long so that there are about 20 segments per wavelength. The first model uses 2001 segments in a 2000-meter length. The second uses 4001 segments and twice the length of the first model. The third model uses 2001 segments with the same lengths as the first model. However, we set the 2001 segments from a position of Y=-2000 to Y=0. Then we set the GX input as follows.

+ 
GX  1  010
+

This entry creates a reflection across the Y-axis. The reflection runs from Y=+2000 to Y=0. The result is a single continuous wire-pair running 2000 meters each side of Y=0. To center the source, we create two EX lines, each in the segment closest to Y=0. The sum of the two source impedance reports should equal the impedance we would achieve in the 4001-segment model at the same overall length (4000 meters). The values will not be precisely the same, because the sources are located in a low current, high voltage region of the antenna, where the impedance changes rapidly in a very small distance. However, we are here less interested in the output reports for the models--except to ensure that each model is accurately constructed--and more interested in the run times. Fig. 9 shows the two large models. The half-size initial doublet is simply the left half of the lower sketch without a GX card and with only one source centered (segment 1001).

+
+ +
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Fig. 10 is a composite of all three models. (If you test them, use only one at a time.)

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The following table summarizes the run times with double-precision NEC-4 on a 1.8-GHz machine running under XP. The parameters were set so that the entire operation in each case required no file-swapping to the hard drive.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                              Larger Model Run Times
+
+           Model                                 Run-Time
+           D2001 (2001 segments)                  27.73 seconds
+           D4001 (4001 segments)                 179.01 seconds
+           D4002GX (2001 segments + GX)           55.43 seconds
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The models are perhaps medium-size and simple enough not to require excessive run-times regardless of the method of construction. However, they are large enough that the overhead becomes insignificant compared to the matrix time. Hence, their relative times are useful in developing an expectation of run times on models of this size and larger. A single reflection requires about twice the run-time of virtually the same model without the reflection. However, the GW version of the same model requires over 3.2 times the run-time of the GX version of the same wire antenna. The run-times shown are averages of runs of the same models after various periods of computer operation. However, in this case, the times varied by less than 0.1 seconds per model.

+

The doubling of the number of segments in the two GW-only models results in a 6.45 increase in run-time. Reducing that time to merely double the smaller-model run-time represents a considerable savings, especially when extrapolated (roughly) to even larger models. Since I did not exclude to the degree possible all overhead time, these numbers will be imprecise relative to all of the possible variations in model construction. But they do provide an indication of the orders of savings possible whenever a GX input is relevant to a large model.

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Run-times are not the only notable feature of the model. The ability to bring a wire to a zero value, that is, to a position on an axis, can be multiplied indefinitely within the limits of array dimensions allowed by the core and the operating system. Hence, one might build 1/2 of a wire-grid ship, plane, or ground vehicle and create the other half via the GX entry. Similarly, a free- space sphere may begin with 1/8th of the structure and reach completion via the GX entry specifying reflection in all three planes. An oval may require only 1/4 of the structure for completion in two reflections.

+

Some GX Cautions

+

Here are some cautions in using the GX card.

+

1. Do not locate segments in the plane (axis-value=0) or crossing the plane around which the reflection occurs. The result will be intersecting or overlapping wire segments, an illicit NEC condition.

+

2. Do not add a wire or patch after the GX card; that is, do not add on a GW, GH, CW, or SP entry. Such additions will destroy at least one plane of symmetry, and the program will reset to whatever symmetries may exist prior to the ruined one (or more).

+

3. Do not use a GM card with a number of new structures greater than zero, or symmetry will be destroyed. As well, a GM card acting on only part of a structure will also destroy symmetry.

+

4. Avoid second GX entries, since they will negate the symmetry established by the prior GX entry. A following GR (Generate Cylindrical Structure) card will also negate the symmetry of a prior GX card.

+

5. If the GE card indicates a ground plane by setting I1 to 1 or to -1, then symmetry across the Z-axis (otherwise expressed, symmetry parallel to the X-Y plane) will be destroyed, although any other specified symmetry will be used. As a practical example, if one wishes to use symmetry for the square of 4 Yagis, but above a real ground, then the most direct way to accomplish this goal is to set a vertical pair of Yagis either as a pair of GW constructs or a GW + GM construct, and then to use the GX card to create the second pair across (in our examples) the X-axis. A following GM card may be used to rotate a structure about the Z- axis, so long as it includes the entire structure and does not create new structures.

+

Most of the listed cautions or limitations on the GX entry reset the core to either non-symmetry or to the highest level of symmetry allowable in light of the fault. There are other conditions, such as placing non-symmetrical lumped loads (LD1 through LD4) on the structure, that simply destroy symmetry without any resetting of the core. However, non-radiating networks (NT or TL entries) will not adversely affect a symmetry specification.

+

For the novice to the use of the GX card, making it the last entry prior to the geometry end (GE) card is perhaps the wisest route. Like sources (EX), one must also specify lumped loads in separate lines in the model. During the learning curve, it may prove useful to develop an over-simplified model having the same essential features as the eventual complex or very large model to ensure that you have introduced no symmetry-destroying features. Further information on the GX entry appears in the user-sections of the NEC-2 and NEC-4 manuals.

+

Our foray into the GX card has been to introduce both its features and its restrictions. In general, for small to medium size models, it is likely best to avoid using the card, since the time saved on the current crop of 1- to 2-GHz machines is small. However, for exceedingly complex and large models, symmetry may be the only course to take to achieve acceptable run-times.

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73. Source-to-Feedline Matching Techniques

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L. B. Cebik, W4RNL

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With most antenna designs that we model, the source segment is as far as we need to model to fairly represent the characteristics of the antenna. If the source impedance does not match the characteristic impedance of a proposed feedline, we leave the matching network for calculation external to the actual modeling process. In most cases, the addition of the matching network has no affect upon the properties of the antenna itself as a radiating system.

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There are simple matching systems that we can incorporate into the antenna model. However, more complex matching networks may lie beyond the modeler's experience or the facilities built into entry-level implementations of NEC-2. Some of these programs do not make available the NT or network facility. As well, the NT facility calls for values of shunt admittance (conductance plus or minus susceptance), and calculating these values calls for a bit of external effort relative to one's initial modeling experience with series impedance (resistance plus or minus reactance) loads. Finally, the shunt admittance values that we may insert into an NT command are fixed and do not change with frequency.

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For this reason, modelers are sometimes interested in seeing if there is a way to create matching networks at the ostensible antenna source using LD load values that we may insert as series (or parallel) R-L-C values. These values are frequency nimble, changing their reactance with frequency changes assigned to the model.

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In fact, there is a fairly straightforward technique for accommodating standard matching networks to the ostensible antenna source. (I used the qualifier "ostensible" because in the process of adding these networks, we shall change the location of the source segment.) To arrive at the general network solution, we shall have to review a few modeling fundamentals relative to sources, transmission lines, and loads.

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A Few Source-Load-Transmission-Line Basics

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Fig. 1 shows the standard diagram that describes the relationship among sources (EX0), lumped loads (LD0 through LD4), and transmission lines (TL). EX0 is a voltage source and here covers the implementation of current sources in programs like EZNEC and NEC-Win Plus. LD4 loads are impedance specifications in terms of resistance and reactance. LD0 through LD3 are lumped R-L-C loads in series or parallel form.

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We are working with EX, LD, and TL commands that we assign to the same segment. The key relationships to note in Fig. 1 are these. First, an LD load is always in series with both a source and a transmission line assigned to the segment. This applies no matter how short the segment or where we may locate it. (I sometimes receive questions as to why a load assigned to the terminating wire of a TL transmission line does not significantly affect any antenna parameter, including the source impedance value. If we created a stub with a terminating wire, any load we assign to the terminating wire falls outside the region that we might represent as the portion of the wire between the transmission line wires. The only way to place a load between the wires is to create a transmission line from parallel (GW) wires and place the load on the physical wire (GW) that connects the two wires at their termination.)

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Second, a voltage source (EX0) always is in series with the segment to which we assign it. In essence, it creates a mathematical gap in the segment and places the assigned source voltage and the resultant current in series with the segment wire. (Hence, any assigned lumped load falls outside the "gap.") So the source will be in series with any load.

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Third, a TL transmission line is also in series with the segment to which we assign it, and it will be in series with a load and in parallel with a source placed on the same segment. All TL transmission lines are non-radiating structures, that is, they are not represented by geometry commands that add to the radiating structure of the model. As well, such lines are lossless. The fact that a TL is in parallel with a source and in series with a load opens the way to both potentials and to limitations.

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The Simplest Matching Situation

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The simplest case of matching that faces a modeler is bringing a non-resonant source impedance, that is, one containing reactance, to a resonant condition. If we make a center-fed doublet (actually, a redundant expression) that is too long or to short for some designated frequency of operation, the source impedance will appear as a resistance plus or minus a reactance. We may bring the doublet to resonance by inserting on the source segment a load with a reactance that is equal in magnitude but opposite in type to the reactance reported for the source.

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We sometimes forget what we are doing relative to the model, because the technique is so simple and because we tend to express what we are doing in physical terms, such as "adding a loading coil." However, the coil has an inductance which we may convert at the operating frequency to a reactance. NEC gives us the option of inserting either an LD0 series R-L-C load in which we specify the inductance or an LD4 load in which we specify the reactance. LD0 (and their counterpart parallel LD1) loads have the advantage of changing reactance with frequency and so give more accurate results for the progression of source impedance values across a frequency sweep.

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It is significant to understand that Fig. 2 is an appropriate reformulation of Fig. 1. For inductive loads added to the source segment, the source and any TL that we may add are mathematically at the center of whatever physical structure we may use to implement them in a real antenna. Therefore, we may assume that the source is at the middle turn of a loading coil. Likewise, we may physically implement each half of the loading inductance with a shorted transmission line stub and each side of the physical feedpoint. We call such implementations of center loading "linear loads," and they are subject to fields of the antenna itself that may slightly disrupt the equal magnitude but opposite polarity currents we assume for transmission lines. Hence, it is normally most accurate to model linear loads using physical wires rather than the TL facility, which cannot show the influences of the radiated fields.

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If our doublet is too long, it shows an inductive reactance at the feedpoint. In a model, we may add a capacitive reactance or a capacitor value in an LD load on the source segment to bring the doublet to resonance, that is, to a source impedance that is solely resistive. Our physical implementation of the load in most wire antennas would involving placing capacitance at the feedpoint assembly, between the antenna wire ends at the feedpoint gap and the transmission line ends. Since we are dealing with a series reactance situation, we may wish to use equal value capacitors, one for each side of the feedpoint gap. Each capacitor will need to provide half of the series reactance, which means choosing capacitors with twice the capacitance of the value specified in a single load assigned to the model source segment.

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The Beta or Hairpin Match

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A common system of matching a low (20-30-Ohm) Yagi feedpoint impedance to a 50-Ohm main feedline involves the use of a beta or hairpin match. A beta match is not only a simple matching system, it is also easily modeled. See Fig. 3.

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In most cases, we set the length of the driver element--the element that we model with a source--slightly short of resonance. Hence, the source impedance prior to matching will show a resistance plus a degree of capacitive reactance. Note that the source impedance specification is in the form of a series circuit value of R - jX. In effect, the reactance is the equivalent of a component in series with resistive component of the impedance.

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From the perspective of the feedline, we are trying to match the higher feedline characteristic impedance to a low resistive impedance at the antenna. An L-network that will achieve this goal consists of a shunt or parallel inductive reactance on the higher-impedance side and a series capacitive reactance on the low impedance side. We already have the series capacitive reactance built into the feedpoint segment. All that we need to do is to add the appropriate inductive reactance across the feedpoint.

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In modeling terms, this means placing an inductive reactance across the source gap. Of course, we cannot directly achieve this with an LD load, since it will always be in series with the source. (If we are willing to highly segment the antenna structure, we can create a wire bridge across the source segment/wire, and insert the required inductive reactance or an inductor having that reactance at the design frequency on the bridge wire. If the segment lengths are very short relative to a wavelength, the bridge wire construct will not materially affect the array performance. The need for high segmentation arises not only because we must keep the bridge-wire construct very small, but as well because the segments adjacent to the source segment need to be the same length as the source segment for highest NEC report accuracy.)

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The beta inductive reactance can be either in the form of a coil or a shorted transmission line stub, so long as each has the correct value of inductive reactance. In fact, the hairpin match received its name from the shape of a shorted transmission line stub using parallel transmission line. Since a TL line is in parallel with the source, we may model a beta match using a shorted TL stub placed on the source segment. All that we need to do is to calculate the required stub length. (Depending upon the implementation of NEC-2, the program may create a "hidden" stub terminating wire or it may require that the user create his own terminating wire and values of admittance for a short circuit. A TL is actually a form of NT or network set up to simulate transmission lines.)

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We often forget that the terms of a down-converting L-network are reversible. We may use a series inductive reactance in combination with a parallel or shunt capacitive reactance to achieve the very same goal. I have used this technique to match phased arrays showing series inductive reactance but a low resistive component at the feedpoint to common coaxial cable. In this case, the physical implementation was a capacitor across the feedpoint terminals, but the model used an open TL stub with a length to yield the same capacitive reactance.

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Equivalent Single-Ended and Balanced Networks

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We have worked our way through simple and specialized matching situations toward a more general solution to the feedline matching and modeling problem. Many of the networks that we physically implement are unbalanced or single-ended. In fact, their names are derived from unbalanced forms of the network: the L, the PI, and the Tee, to name the most common ones. (Of course, we may create more complex combinations of these networks, such as the PI-L, once common in vacuum tube power amplifiers. However, we must remember that the PI and the Tee are simply L-networks back-to-back.)

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As noted in Fig. 4 for the PI and the Tee unbalanced networks, every single-ended network has a balanced equivalent. We calculate the values using the single-ended equations, which appear in a myriad of utility programs to save us the hand-calculator work. Then, we simply divide the reactances for the series elements in half, place one portion in each of the two lines of the balanced system.

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Converting networks into balanced forms relieves us of a major limitation relative to NEC and single-ended networks. An unbalanced network presumes a virtually lossless ground buss to terminate components, as well as a source and a load (the old antenna feedpoint) that also run between the "hot" line and ground. NEC has a limitation in this regard. Simply bringing a wire to Z=0, except for a perfect ground, will not achieve a virtually lossless interconnection with other wires brought to Z=0 unless they all terminate at the same point. Two wires connected to a real ground (Sommerfeld or reflection coefficient) at any distance will always show a resistance between the two Z=0 points. In most instances, this limitation precludes modeling a single-ended network in NEC.

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A balanced network is independent of any ground connection. We can implement Ls, PIs, and Tees in balanced form without regard to ground and arrive a relatively accurate modeled results. All that we need to do is to figure out how to attach our network to the antenna's former feedpoint. After all, we have a single segment with the former source point at its center, but two terminals of a 4- terminal network.

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The TL Connection

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The creation of a network using LD0, LD1, or LD4 loads for the reactive components requires that we construct a grid of wires matching the network needs. Fig. 5 shows such a network for a balanced PI network. For the moment, let's concentrate on the wire grid in the lower portion of the graphic.

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Because the network terminating components of the balanced PI are shunt reactances, each end of the grid shows a bridge section of only wires connected on one end to a cross wire to which the TL is joined and at the other network end to a bridge wire to which we assign the source. Had we used a balanced Tee network, the "empty legs" of the parallel parts of the wire grid would hold LD loads, and we would need one less crossing section for shunt or parallel components. An L-network would also be smaller, since we would need only a single pair of series components across from each other and a single shunt component.

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The point is to make the wire-grid no large than it has to be to hold the components and to establish the parallel connection to the grid of both the source (on one end) and the TL (on the other). As well, make the grid as small as possible. By using extremely thin lossless wire for the grid, we can shorten the length of the individual grid wires to the limits of NEC--about .001 wavelength. Each wire in the grid--contrary to the graphic--whether crossing or parallel--should be exactly the same length.

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Now we are ready to examine the upper portion of the graphic. We want the physical structure of the grid to be as far distant as feasible from the antenna wires in the model. The goal is minimal influence on the network grid by the antenna's radiation. However, we want to have the grid as electrically close as is feasible to the former source segment. The TL facility allows us to achieve this goal. We may place the grid wires anywhere we wish in terms of the Cartesian coordinates that specify the physical structure. However, the electrical length of the transmission line depends upon the entry that we make for it, regards of the location of the terminals of the line.

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The TL acts like a source in that it creates a series connection to a wire segment. Hence, we may specify only one segment for each end of the TL line (or any other NT command). We may set the wire-grid end a few or many wavelengths from the antenna wire. We specify the electrical length of the TL to something very short--perhaps an inch or less in the upper HF range.

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The best characteristic impedance (Zo) to use for the TL is the feedpoint impedance (resistive component) of the antenna prior to adding the TL and the wire grid. Almost any Zo will do, since the impedance transformation for the line length will normally not by significant. However, the higher the reactive component of the impedance, the shorter we need to make the line and the more critical the value of Zo.

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Once we have set up the antenna structure, the TL, and the wire grid for the intended network, all that we need to do is to calculate the network values or to obtain them by trial and error.

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Does This System Really Work?

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Let's set up a model and see if this system of feedpoint matching in models really works. Our worked example will consist of a near-resonant folded dipole made from lossless AWG #18 wire with a spacing of 3" between wires on a frequency of 28.5 MHz. For the folded dipole in question, in free space, with a total length of 196", the reported source impedance is 286.7 + j 0.6 Ohms.

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What I wish to obtain is a match to 50-Ohm feedline. So I shall implement a balanced L-network in the model. Calculations show the required antenna-side shunt capacitor to be 42.4 pF (-j 131.7 Ohms) and the required pair of series inductors to be 0.304 uH (+j 54.4 Ohms). Now we can create the total model, with the wire grid about 1000" or more in any direction from the model. I chose "up." The result resembles Fig. 6, although the folded dipole and the network grid are not in scale, since I combined two separate views to make this one.

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The red circle represents the source location, while the red squares indicate the load locations. The wires in this grid are 1" long, or about 0.0012 wavelength at 28.5 MHz. They also use lossless AWG #18 wire (0.0403" diameter). The 290-Ohm transmission line is 0.1" long electrically, despite the 1000" separation of the network from the antenna wires. The following table shows the EZNEC model description for anyone wishing to replicate the exercise.

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+                      EZNEC/4 ver. A4.0
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+Folded Dipole with Matching Network
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+         --------------- ANTENNA DESCRIPTION ---------------
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+Frequency = 28.5 MHz                              Wire Loss: Zero
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+              --------------- WIRES ---------------
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+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1          W4E2      -98,      0,      0      W2E1       98,      0,      0       #18   99
+2          W1E2       98,      0,      0      W3E1       98,      0,      3       #18   1
+3          W2E2       98,      0,      3      W4E1      -98,      0,      3       #18   99
+4          W3E2      -98,      0,      3      W1E1      -98,      0,      0       #18   1
+5          W7E2        0,   -0.5,   1000      W6E1        0,    0.5,   1000       #18   1
+6          W5E2        0,    0.5,   1000      W8E2        1,    0.5,   1000       #18   1
+7          W8E1        1,   -0.5,   1000      W5E1        0,   -0.5,   1000       #18   1
+8          W9E2        1,   -0.5,   1000     W10E1        1,    0.5,   1000       #18   1
+9         W11E1        2,   -0.5,   1000      W7E1        1,   -0.5,   1000       #18   1
+10         W6E2        1,    0.5,   1000     W11E2        2,    0.5,   1000       #18   1
+11         W9E1        2,   -0.5,   1000     W10E2        2,    0.5,   1000       #18   1
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+Total Segments: 207
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+              -------------- SOURCES --------------
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+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       11       50.00      50.00    1        1           0         I
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+          -------------- LOADS (RLC Type) --------------
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+Load     Specified Pos.     Actual Pos.         R          L          C        Type
+       Wire #  % From E1  % From E1  Seg      (ohms)      (uH)       (pF)
+1       9        50.00      50.00    1        Short      0.27       Short      Ser
+2       10       50.00      50.00    1        Short      0.27       Short      Ser
+3       8        50.00      50.00    1        Short      Short      42.2       Ser
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+                -------- TRANSMISSION LINES ---------
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+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF  Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      1           50.00     50.00    5           50.00     50.00    0.1          290     1      N
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+Ground type is Free Space
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Note that the values of inductance and capacitance do not precisely coincide with the calculated values. We shall examine the variables in the system in a moment. However, with the values shown, the reported source impedance is 49.5 + j 0.1 Ohms.

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The system does work--but within limits. Here are some of those limits based on the fact that the wires in the grid will interact with each other.

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1. Wire size will make a difference to the results, although the affect tends to be small compared to some other affects. #12 wire yielded an impedance of 49.1 - j 0.9 Ohms, while #22 gave 49.6 + j 1.0 Ohms.

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2. The TL Zo for the very short (0.1") line can vary considerably without significant change in the new source impedance value. Values between 250 and 300 Ohms occasioned no change in the reported impedance within the decimal limits shown here. As well, extending the line length from 0.1" to 1.0" also produced no source impedance change.

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3. Grid wire length makes a large difference to the adjusted network values to achieve a near-50-Ohm source impedance. Doubling the wire length in both directions to 2" required 0.24-uH coils and a 40.9-pF capacitor. A second doubling to 4" wires required 0.155-uH coils and a 39.8-pF capacitor. The progression is clear, and the smallest feasible wire grid yields results closest to calculated values.

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4. The wire grid presses NEC limits. Hence, it is essential to obtain an Average Gain Test value and to correct the reported system gain accordingly. The free-space folded dipole reported a gain of 2.14 dBi and an AGT of 1.0. The version with the matching network yielded a gain of 2.26 dBi, but with an AGT value of 1.029. Correcting the gain requires a 0.12-dB subtraction, for a net gain of 2.14 dBi. With the calculated values of matching network components, the reported impedance was 49.3 + j 12.7 Ohms. The resistive component corrected (AGT * reported value) is 50.7 Ohms, although the reported reactance is not accounted for by any known corrective measures.

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Note that the LD values make no assumption about coil Q, although this factor may be important in some (but not necessarily all) models. I purposely used lossless wire and components to be able to compare the results with standard L-network computations. In general, the series inductance is more sensitive to change than the shunt capacitor (or, properly speaking, their respective reactance values).

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Nevertheless, since component measuring techniques rarely surpass +/-5% for gear outside of precision laboratories, the modeled values are certainly within the limits of what is measurable by most experimenters. With due modeling of known cases, one can calibrate a given wire grid structure at a design frequency to know in advance the modeling offset.

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The benefit of this technique, of course, is that it permits the use of R-L-C loads and hence returns relatively accurate results as one checks the performance across a frequency span. The limitation of the technique is that the requirements for maximum load accuracy are at odds with the limits of NEC itself for a perfect AGT value. Longer wire grid wires reduces the AGT variation, but creates sufficient wire interaction to throw off the network values by much more significant amounts.

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In the End. . .

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There likely is no perfect or limitless method for replicating networks used to match a given antenna feedpoint impedance to a given feedline characteristic impedance. However, this one comes as close as I have so far been able to develop for using standard series R-L-C loads that are frequency nimble in a way that closely approximates calculated values for such networks. Used within its limits, it may be of service in a variety of applications.

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The remote wire-grid technique is, of course, adaptable to many configurations, even to adding a component in parallel to a series component and source situation. Not all configurations will require a full grid of the sort used with L-circuits and PI-networks. However, the same generals rules of formation and the same limitations should be observed for all such structures.

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74. Some Numerical Green's Function Rudiments

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L. B. Cebik, W4RNL

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Suppose that you need to use a geometric structure over and over, each time varying some relatively simple appurtenance. We might have a wire-grid model of a ship, plane or ground vehicle and wish to know the best type of antenna and placement for a certain purpose. We might even have a fixed-size reflector--again constructed as a wire-grid assembly--and wish to find the best drive element for it, as well as the best place to put the driver.

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We always have the option of running new models of the entire geometric structure composed of GW, GM, etc. entries. Very often, we can make the necessary changes using cut and paste methods within whatever ASCII editor we happen to use to create .NEC files. However, each run takes the same amount of time, plus or minus a little for variations in the new model sections that we introduce.

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There is a better way--at least better in the sense of saving some time. How much time we save will vary not only with our computer speed, but as well with certain ratios between the size of what we create to use many times and the size of what we add to the model. The modeling technique involves Numerical Green's functions, which pre-calculate certain portions of the modeling problem and then use the results as substitute elements in the final set of matrix solutions. Mathematical details appear (for NEC-4) in section 6.3 of the program description and theory portion of the manual. NEC-2 handles these functions in essentially the same way as NEC-4. However, the feature is only available on advanced version of implementing programs and is generally omitted from entry level programs.

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For the user, the task is a double one: first, learning the rudiments of incorporating Green's functions into a model. and second, learning when it is useful to employ them. If we take first things first, then we need to start with a little big model, that is, a model eligible for Green's function treatment but small enough to handle within the confines of these notes.

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A Planar Reflector and a Double-Diamond-Quad Driver

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If we begin with a complete model, we can then more easily sort out the elements of a Green's function version of it. So let's begin with a double-quad driver in front of a planar reflector. The reflector uses a wire-grid in standard ways. Fig. 1 shows a portion of the model: the driver and the start and end of the reflector.

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The model also shows the commands necessary to complete the model. For simplicity, I have set all of the wires to the same conductivity in one LD5 line. The ground setting is for free space. The frequency (FR) is 435 MHz only. The pattern request (RP0) is a simple azimuth or phi request at 0 degrees elevation or 90 degrees theta. If I run this example, I obtain the pattern shown in Fig. 2.

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My sample has only 450 wires and 678 segments, so it is not all that large. It took 22.03 second for the core run on my slower machine. The model shows 11.25 dBi forward gain and a 180-degree front-to-back ratio of 21.28 dB, with a source impedance (at the center of the diamonds) of 45.11 - j 6.40 Ohms. I cite these reference figures only for comparison with those that we get from running the model in a different way: the Green's function way.

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Green's Functions: the File

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Operationally, there are two steps to using Green's functions in a model: the structure for which we create a file and the model that calls up the file so that we can get a final result. We shall take them one at a time.

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In our example, the portion of the model that we may wish to use many times is the wire-grid reflector that runs from GW 10 through GW 446. So we shall include those lines in the file part of the Green's function model without even changing the wire numbers. You can see an abbreviated portion of the structure in Fig. 3.

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The file portion of our work must also include a few other items. If we wish to assign a conductivity to the wire-grid wires, then we must have an LD5 entry in this unit. As well, we specify the frequency, the FR entry. (A Green's file may not use multiple frequencies.) Since lumped loads, networks, and transmission lines do not affect the basic matrix calculations done within the file that we are creating, we may omit them. The file created would only ignore such entries anyway. We also specify ground conditions (GN) (or free-space, as in this example) within the file part of the effort.

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The last line (before EN) in this example is a request to write the result to a file. We can specify any filename, but the .WGF extension is what the core recognizes as a Green's file. If there are other output requests, such as RP, NE, or NH, they come after the WG (write Green's file) command. However, in most cases, the modeler will save such requests for the other part of the modeling process.

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Note: early versions of NEC-2 do not permit the addition of a user-created filename. Rather, the earliest--unmodified--versions of the core automatically assigned the file the name TAPE20. NEC-2 Programs such as NEC-Win Pro have added the ability of the user to specify filenames, since one may wish to maintain a collection of Green's files for any number of modeling tasks.

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When we run this model, that we can save as a regular .NEC model file, we may discover no noticeable return. That is, we created a .WGF file, but not a complete model. The process is not a storage of what the modeler has written, but a filling and factoring of the matrix for the structure, along with a reservation of array space in memory for the matrix in subsequent runs when the users calls the file. That is step two.

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Green's Functions: the Model

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To use the Green's function file that we just created, we must create one or more models that call on the file. The file will consist of a GF entry to call up the file, followed by whatever else we may add to complete the model. Fig. 4 shows the model file for our complete planar reflector and double-diamond-quad driver.

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In the new model, we begin (after the CM and CE lines) with a GF, a call for the Green's file that we have created. Note that besides mentioning the filename, the line also has a zero. That zero indicates a call for normal printing in the NEC output file. A 1 in this position would have been a call for a list of wire ends, in case we wanted to join a new wire to an wire within the Green's file structure. We do not need that feature for our examples, since our driver elements do not make contact with the wire-grid reflector.

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Note: early versions of NEC-2 do not permit the addition of a user-created filename. Rather, the earliest--unmodified--versions of the core automatically assigned the file the name TAPE20. Therefore, be sure to use the procedure that applies to the core that you are using.

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Following the GF entry, we add whatever geometric structure we may need to complete the full antenna model. In this case, we enter the 9 lines that form the double-diamond-quad driver assembly. It does not matter whether the GW tag numbers precede or follow the tag numbers in the Green's function file, so long as the numbers are unique.

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The new modeling file does not contain either frequency (FR) or ground (GN) commands. When the model runs, it will take these commands from the Green's file.

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In this file, we need to add an LD5 entry if we wish the wires in the GW lines to have a different conductivity from those in the Green's file. I arbitrarily assigned copper values to these lines. Even though the LD5 card specifies all wires in the model, an LD in this part of the model will not reflect back into the Green's file, where the wires are aluminum.

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No matter where we may place the Excitation (EX), it goes into this part of the model. The last major entry is the output request, in this case, a simple RP0 phi-pattern request. We may use any of the legitimate output requests within the model. As well, if we had an lumped loads (LD0 - LD4), networks (NT), or transmission lines (TL), we would place them in this portion of the total model.

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Once we have our model complete, let's run it. If we do, again using my slow machine, we obtain 11.25 dBi free-space gain, 21.28 dB 180-degree front-to-back ratio, and 45.06 - j 6.44 Ohms source impedance. The slight difference in source impedance results from the change of material conductivity that I imposed to illustrate the separation of file and model values. Otherwise, the result is identical. If you look into the NEC output file, you will see all segments listed, with the notation "241 new unknowns."

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The double-diamond-quad driver has so many segments because the source segment is very short as it forms a common link between the two quad loops. But we still have the same total number of wires (450) and the same total number of segments (678) that we had in our single model containing everything in one file. The total number of new unknowns does have an important consequence: the total run time for the model was 19.88 seconds, just a bit over two seconds shorter than the run time for the single complete model.

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With that sort of run time, one might well ask why one should use a Green's function file. For this small model, where overhead, patterns requests, etc. occupy a significant portion of the run time, it may make no great sense to use a Green's file. However, we have only begun to scratch the surface of NGF use.

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Re-Using the .WGF File

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The total structure of the double-diamond-quad plus planar reflector looks like the views shown in Fig. 5.

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If we wish to look at other candidates for antennas using planar reflectors, we might well wish to save the wire-grid structure and simply replace the driver portion of the overall model. (The antenna view is actually for the original full model because in many systems, the antenna view facility may not show the contents of the Green's file.)

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Suppose that I wished to find out how well a horizontal dipole might perform ahead of the given planar reflector. (In the real world, I would recognize that the double-diamond-quad driver is vertically polarized and also that the optimal size for a planar reflector may vary with the driver in front of it. However, in this context, we may by-pass such matters.) Suppose that I select a wire radius. I still have to find the right length so that the dipole is nearly resonant (or perfectly resonant, if I am lucky or patient). As well, I shall set myself the task of finding a dipole length and position ahead of the reflector so that the source impedance is very close to 50-Ohms at resonance. My final model will look like Fig. 6. The face view is slightly tipped, since the dipole lines up with the center horizontal wires in the reflector structure.

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The model for the dipole plus planar reflector appears in Fig. 7. Note that we simply re-use the Green's file. In fact, we re-used that file about a dozen times before arriving at this final model, since the X and Y coordinates required considerable shifting to achieve our goals.

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The model showed a free-space gain of 8.83 dBi, with a 180-degree front-to-back ratio of 24.14 dB. The reported source impedance was 49.93 + j 1.53 Ohms. The run time for this model was 4.12 seconds.

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Two aspects of the model and its run time are important here. First, the model has 458 segments, of which only 21 represent new unknowns--the 21 segments of the dipole. Note the much larger ratio of total segments to new unknowns than we found in our double-diamond model.

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The second important aspect of the model is called to our attention by creating a full model of the antenna using only GW entries for the wires. You need not always create such a check model, but for this column, I had no choice. He who cites time must take time to run the models.

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The non-Green's-file model reported 8.83 dBi free-space gain, 24.14 dB 180-degree front-to-back ratio, and 49.95 + j 1.55 Ohms impedance. However, the full model had all aluminum wires, whereas the Green's version used a copper dipole. Hence, we obtained a 0.02 difference in both resistance and reactance at the source. (Of course, these differences are not operationally significant, but in this exercise, we are comparing calculation results for the sake of establishing confidence in the modeling technique.)

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The run time for the non-Green's version was 13.95 seconds. The Green's version took less than 30% of that amount of time to run. If I had had to make my dozen or so runs to zero in on the targets of the modeling design exercise, it would have taken me well over 3 times as long per run.

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Fig. 8 shows the phi pattern for the dipole plus planar reflector, not at all a bad pattern for such a simple antenna. Although 2.5 dB lower in gain that the double-diamond, the dipole version may be that much easier to construct. Turned the other way for vertical polarization and translated into the region just below a GHz, the antenna might be suitable for use in a back-to-back pair of passive repeating antennas for use when one's phone site is in a hollow of other area shielded from normal line-of-sight contact with the cell tower. (Of course, the vertical positioning of the antenna will show a wider beamwidth.)

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Some Potentials and Some Cautions

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The use of a Green's functions file can save time in model formation. Instead of using cut and paste methods to patch a set of GW lines into a model, we merely need to repeat the GF or file call line of the model. The resulting model, as the dipole example illustrates, is very much easier to read, since the added structure is so much simpler than the full model. In addition, the load, source, and output request lines are more immediately at hand. For example, it was easy for me to see that I had initially placed my source on the wrong segment of the dipole model. Separating the dipole GW line from the EX line by 400+ other lines of model might have made the error search a longer one.

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However, with every potential comes a caution. If the added structure is to contact the structure within the Green's file, it may be important to print the wire-end file. The error to avoid is either having no contact when one is desired or having the new wire intersect an existing wire in the Green's file at other than a segment or wire junction. There is always a big difference between saving time and becoming careless. The latter often requires much more time in the hunt for the errant entry.

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The use of a Green's file may also save run time for the model. However, as we saw from the two examples, the relative time that we save appears to be a function of how much we can pack into the Green's file and how little is left over for the variable new structures that we wish to test. The lower the number of new unknowns relative to the total number of segments in a model, the more run time that we are likely to save, all other aspects of our model being equal.

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Of course, there is no objection to having a collection of Green's files and calling them up sequentially in certain types of tests. For example, with our planar reflector, we might have up to a dozen or more wire-grid reflector files, each with a different shape or size. To find the one closest to optimal for a given driver system, we need only change the GF line of the model. The utility of the collection depends in part on having a constant test frequency for all of the members of our collection so that moving from one file to the next yields reliable results.

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Do not expect to build up a collection of multiple-use Green's files overnight--unless you have a graduate student or other indentured servant to whom you can assign the task. (And if your work based on these models results in a publication, at least give the grad student a footnote, if not co-authorship.) The collection will emerge with time. Hence, it pays to think from the first use of such models what the test frequency should be for the most profitable work. Then, design each Green's file for that frequency. As well, from the start, give some thought to properly descriptive filenames so that you can sort out the files and know at a glance what is in each of them.

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Green's files are especially useful where an overall structure may have a symmetrical portion and another portion that is non-symmetrical. For example, one may use symmetry (the GX entry) to create ships, planes, and ground vehicles with half the wires, using a centerline and symmetry to complete the overall structure. Placing this structure in a Green's file gives you the ability to place--in the model that calls the file--an antenna of any shape anywhere on or about the structure without harming the symmetry. In fact, we can place structures that are mostly, but not completely, symmetrical into two files, the Green's file for the symmetrical portion, and a regular modeling file with a GF line for the portions that are not symmetrical. We can then evaluate such structures not only for antenna placement using voltage sources, but as well using plane-wave excitation to see the consequences for the structure.

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The use of Green's functions is not a means of increasing the overall number of segments in a model. MAXSEG needs to be set at or above the total number of segments, including those held in the Green's file. As well, a Green's file does not relinquish the memory space needed by the model. Although it omits the fill and factor times, it retains the matrix storage time--and the memory space needed for that function.

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(As an aside, the key limiting factor for model size is not the NEC-4 core itself. The core can be and has been modified by various implementations to expand the number of allowable segments in a model. Moving the region reserved for SP entries from above 10,000 to above 80,000 theoretically raises the number of allowable segments beyond anything that almost any modeler might imagine. However, it appears that the 32-bit Windows operating system is limited to about 4 GB, divided between system operations and applications. Hence, the practical limit for the number of segments on a Windows platform with about 2GB maximum available memory for a run that does not involve file-swapping with the hard drive is just above 11,000 (if there are no surface patches). The run time for hard-drive file swapping depends on the input and output speeds of the drive--as the slowest procedure in the process--and may take 10 or more times as long as runs wholly within memory. The ability of a machine to handle such runs varies with the machine set-up, what may be running in the background, and a host of other factors outside the control of an implementing program for NEC-4. NEC-2, which handles Green's files in the same way as NEC-4, tends to be limited at most to 10,000 segments or less by most implementations of the core.)

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Wisely used, Green's function files may save a modeler both time and error-hunting energy. These notes are designed only to introduce the rudiments of the process of using them. Modeler task assignment and creativity will in the end determine if they are worth the development time.

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Go to Main Index

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75. NEC: Power Efficiency vs. Radiation Efficiency

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L. B. Cebik, W4RNL

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There seems to be a semi-pervasive mystery about what NEC may report by way of "efficiency" with respect to an antenna under test. So let's examine what the NEC output report may tell us in this regard. We shall use a series of simple examples to illustrate the information.

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Power and Radiation Efficiency Reports and Calculations

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First, every NEC output report provides a Power Budget report. The general form of the budget looks something like the following (without regard to the specific model that generated the numbers involved.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           INPUT POWER   = 6.8603E-02 WATTS
+                                           RADIATED POWER= 5.6868E-02 WATTS
+                                           WIRE LOSS     = 1.1735E-02 WATTS
+                                           EFFICIENCY    =  82.89 PERCENT
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The input power is a calculation based upon the source level (normally, voltage magnitude at 0 degrees phase angle) and the calculated source impedance. The radiated power is the input power minus the sum of all losses. Wire losses include losses due to the material conductivity (LD5) assigned to the model's wires as well as losses associated with lumped loads (LD0 - LD4). A category of loss not present in the given model are the "NETWORK LOSSES," that is, losses associated with network (NT) and transmission line (TL) commands. In all cases, losses are calculated relative to the resistive portion of any impedances (or, for networks, the conductive portion of any admittances). The example allows a simple subtraction of the loss from the input power to arrive at the radiated power.

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Power efficiency (as we shall call it here) is simply (Radiated Power / Input Power) * 100, and is given as a percentage.

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Numerous modelers are also interest in another figure, a radiation efficiency. This value would give a measure of some sort for the effectiveness of the antenna as a radiator within the actual operating environment. Hence, if there are ground losses associated with the antenna, radiation efficiency (again, as we shall call it) would take them into account. A number of experimenters try many techniques to arrive at this value, ignoring the fact that NEC will yield such a value with the correct output call.

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Of course, the NEC report will be limited in the same way that any other output data are limited. NEC will use level ground, and the only objects within the field of the antenna will be those modeled by the program user. On the other hand, these limitations may also become an advantage, since one may compare antenna radiation efficiencies under conditions in which all "other" things are equal.

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The required call is an RP0 (far-field) request for the same sort of pattern that we need for an Average Gain Test. We set the XNDA entry to either 1001 (if we wish the pattern data to appear in the output report) or 1002 (if we are interested only in the required information for calculating the radiation efficiency). There are two cases of note: free space (no ground) and all other cases having a ground that may range from perfect to very lossy (using either the refection coefficient or Sommerfeld ground systems). We set up the RP0 request to fairly sample the sphere or hemisphere at reliably constant intervals in degrees. So the two possible lines will look something like the following ones:

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Free Space @ 5-degree Intervals                   RP 0 37 73 1002 -90 0 5 5
+Over any ground @ 5-degree intervals              RP 0 19 73 1002 -90 0 5 5
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In both cases, we have suppressed the printing (to file) of the radiation pattern. However, one may use this data for generating a surface or 3-D pattern for the antenna model in question. The angles follow the phi and theta conventions, which may differ from azimuth/elevation starting points that may be built into an implementation of NEC.

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The 5-degree interval may not always be sufficient to track precisely the pattern undulations of a given far-field pattern. In such cases, one may reduce the interval for both phi and theta to 2 degrees or even 1 degree. The number of steps for theta (37 for free space) and phi (73 for free space) will increase accordingly, reaching 181 and 361, respectively, for 1 degree intervals. However, it will be rare that we need a value for radiation efficiency that approaches that level of precision.

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As noted, we must calculate the value of radiation efficiency. We based what amounts to a super-simple calculation on the data the emerges when we set the final digit of XNDA to 1 or 2, both of which request "gain averaging." The raw data line has the following appearance at the end of the RP0 request portion of the NEC output report.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+   AVERAGE POWER GAIN= 4.99152E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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First, examine the solid angle data. For free space, the value within (--) will be 4. If that is the case, the radiation efficiency will be the value of the average power gain * 100 and will be a percentage. In this case, which applies to the case of a hemisphere created over any ground type, the value in (--) is 2. For all such cases, the radiation efficiency is the (average power gain / 2) * 100 %. Since the reported power gain is 0.4992, the radiation efficiency is 24.96% (using at least 1, if not 2, too many decimal places for most purposes).

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There are some short-cuts to arrive at the desired average power gain for patterns of known symmetries. However, on modern computers, using the RP0 calls shown will not create delays for most model runs.

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Some Case Studies

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When we wish to give weight to a set of examples, we re-name them "case studies." Let's look at a few and see what we get for our efforts by way of reports. We shall begin with a vertical monopole with 4 radials, all of AWG #12 wire. We shall set the base of the monopole and its radials at 5' above ground level. The set-up has the outline shown in Fig. 1.

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Initially, we shall use perfect or lossless wire, no loads, and a perfect ground to run out test. The model appears in the following lines.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM radiation efficiency test vertical/4 radials
+CM full length
+CM perfect conductor
+CM perfect ground
+CM no loads
+CE
+GW 1 21 0 0 13.7 0 0 5 0.0033695
+GW 2 21 0 0 5 8.7 0 5 0.0033695
+GW 3 21 0 0 5 0 8.7 5 0.0033695
+GW 4 21 0 0 5 -8.7 0 5 0.0033695
+GW 5 21 0 0 5 0 -8.7 5 0.0033695
+GS 0 0 .3048
+GE 1 -1 0
+GN 1
+EX 0 1 21 0 1 0
+FR 0 1 0 0 28.5 1
+RP 0 19 73 1002 -90 0 5 5
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The relevant power and average gain report data follows.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 1.7441E-02 WATTS
+                                           RADIATED POWER= 1.7441E-02 WATTS
+                                           WIRE LOSS     = 0.0000E+00 WATTS
+                                           EFFICIENCY    = 100.00 PERCENT
+
+   AVERAGE POWER GAIN= 1.94882E+00       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Using our handy calculation method, we obtain a radiation efficiency of 97.45%. One would think that we should obtain 100%, since there are no losses anywhere in the model. However, we did not sample the hemisphere at close intervals. The perfect-ground pattern for the monopole appears in Fig. 2.

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Note the lobe structure near the zenith angle. It varies rapidly--more rapidly than our 5-degree interval can precisely track. The two small peaks (actually, circles of peak value on a true hemispherical display) occur between our 5-degree sampling intervals. So our rule of thumb must be this: the more irregular the pattern shape, the smaller the required interval between sampling steps.

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Now let's add wire loss to the model by inserting an LD5 line into the model.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+LD 5 0 0 0 5.8e7 0
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Now our report takes the following appearance.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 1.7119E-02 WATTS
+                                           RADIATED POWER= 1.6890E-02 WATTS
+                                           WIRE LOSS     = 2.2951E-04 WATTS
+                                           EFFICIENCY    =  98.66 PERCENT
+
+   AVERAGE POWER GAIN= 1.92198E+00       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The power efficiency is 98.66%, due to the small losses of copper for the antenna elements. Our radiation efficiency is 96.10%, again off the mark by virtue of the sampling interval.

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It is now time to revise the GN (ground specification) entry to place the antenna over a real ground. We shall use the standard default values for average ground (conductivity = 0.005 S/m, permittivity = 13). (Some programs call these values "good" ground.) The required revised GN line appears below.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+GN 2 0 0 0 13 .005
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

After running NEC (-4 for these examples), the resulting report appears.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 1.8126E-02 WATTS
+                                           RADIATED POWER= 1.7858E-02 WATTS
+                                           WIRE LOSS     = 2.6748E-04 WATTS
+                                           EFFICIENCY    =  98.52 PERCENT
+
+   AVERAGE POWER GAIN= 5.72269E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power efficiency changed slightly as a function of the fact that the source impedance upon which the power calculations are based also changed with the revision to the ground beneath the antenna. The average power gain over average ground is 0.5723, for a radiation efficiency of 28.62%. (Given the number of small influences on the values that result from calculations, it is usually most profitable to take radiation efficiencies as whole numbers, even though this exercise shows them to 2 decimal places.)

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Now let's change the antenna. I shall arbitrarily alter the length of the monopole to 5' (at 28.5 MHz), but retain all other properties. Eventually, I want to check out the radiation efficiencies of two ways of loading the antenna inductively back to near resonance. The two ways appear in Fig. 3.

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Before we add either a mid-element or base loading inductor, let's run our revised model that has no loading at all. The model has this structure:

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM radiation efficiency test vertical/4 radials
+CM short length
+CM copper conductor
+CM SN-Ave ground
+CM no loads
+CE
+GW 1 21 0 0 10 0 0 5 0.0033695
+GW 2 21 0 0 5 8.7 0 5 0.0033695
+GW 3 21 0 0 5 0 8.7 5 0.0033695
+GW 4 21 0 0 5 -8.7 0 5 0.0033695
+GW 5 21 0 0 5 0 -8.7 5 0.0033695
+GS 0 0 .3048
+GE 1 -1 0
+GN 2 0 0 0 13 .005
+LD 5 0 0 0 5.8e7 0
+EX 0 1 21 0 1 0
+FR 0 1 0 0 28.5 1
+RP 0 19 73 1002 -90 0 5 5
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

When we run NEC, we obtain this report.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 3.0774E-05 WATTS
+                                           RADIATED POWER= 2.9852E-05 WATTS
+                                           WIRE LOSS     = 9.2238E-07 WATTS
+                                           EFFICIENCY    =  97.00 PERCENT
+
+   AVERAGE POWER GAIN= 5.79608E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For a copper wire short monopole with full-length radials over average ground, our power efficiency has dropped by merely 1.5%. Since the average power gain is 0.5796, the radiation efficiency has actually increased (allowing for sampling interval error) to 28.98%. (Actually, the difference is not supportable without a much tighter sampling interval.) If you revise this model and the full-length monopole that preceded it, you will discover that the gain difference is also not too significant (0.72 dBi at 20 degrees elevation for the full-length monopole, 0.69 dBi at 21 degrees for the short model).

+

Next, let's add a mid-element loading coil to bring the short monopole to near resonance. The required new LD4 line shows an R-X load of 1.89 + j 568 Ohms. In this and the next example, I shall use inductive reactances with a Q of 300.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+LD 4 1 11 11 1.89 568
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

By adding the loading coil, we obtain near resonance, but show the following power and radiation efficiencies.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 3.8337E-02 WATTS
+                                           RADIATED POWER= 3.2516E-02 WATTS
+                                           WIRE LOSS     = 5.8202E-03 WATTS
+                                           EFFICIENCY    =  84.82 PERCENT
+
+   AVERAGE POWER GAIN= 4.99152E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Wire loss now includes not only the copper material losses, but also the mid-element loading coil losses. Our power efficiency is 84.82%. The average power gain is 0.4992, for a radiation efficiency of 24.96%. The loading coil has cost us only 4% in radiation efficiency, but about 2/3-dB in gain. The antenna shows a gain of -0.04 dBi at 21 degrees elevation.

+

There is a wide-spread mythology that mid-element loading improves antenna performance properties by noticeable amounts over a base loading coil. There is an improvement in feedpoint impedance (in these examples, from 7 Ohms to about 13 Ohms), but the jury is out on performance until we look at the models. First, let's replace the mid-element LD4 line with an alternative base-loading line.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+LD 4 1 21 21 1.06 318.05
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The required inductive reactance to bring the initial short monopole to resonance is j 318.05 Ohms. The corresponding series resistance for a Q of 300 is 1.06 Ohms. With all other factors unchanged, we obtain the following efficiency reports.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 6.8603E-02 WATTS
+                                           RADIATED POWER= 5.6868E-02 WATTS
+                                           WIRE LOSS     = 1.1735E-02 WATTS
+                                           EFFICIENCY    =  82.89 PERCENT
+
+   AVERAGE POWER GAIN= 4.95310E-01       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power efficiency has dropped 2 percentage points. However, the radiation efficiency has dropped only 0.2 percentage points to 24.77% (based on an average power gain of 0.4953). As well, the gain dropped only from -0.04 dBi to -0.06 dBi at 20 degrees elevation. What most folks overlook in the comparison of base loading and mid-element loading is that a mid-element loading coil must be considerably larger than a base loading coil, and for the same value of Q, that means an increase in the series resistance as well. Hence, except for the differential in feedpoint impedance--which can be useful in itself--the performance difference falls in the range of the operationally unnoticeable.

+

We have noted that there is no great correlation over small ranges of change between directional gain and radiation efficiency. Here, directional gain applies at least in the theta plane for our omni-directional monopole. The following table compares reported gain and radiation efficiencies of the base- loaded monopole as we change the soil type beneath it.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Soil          Cond.          Perm.         Far-Field      Ave. Pwr      Rad. Eff.
+Type          S/m                          Gain dBi       Gain          %
+Very Good     0.0303         20            +0.04          0.4766        23.83
+Average       0.005          13            -0.06          0.4953        24.77
+Poor          0.002          13            +0.13          0.5209        26.05
+Very Poor     0.001           5            -0.42          0.4931        24.66
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

There are mathematical accounts for the changes shown in the table, but the values defy glib or simplistic generalizations.

+

To avoid any mis-impression that the determination of radiation efficiency involves only vertical antennas, let's set up a horizontal dipole at 1 wavelength above ground, as shown in Fig. 4. We shall use AWG #12 copper wire for the antenna and select a near-resonant length.

+
+ +
+

Before we establish the antenna over ground, we shall first check it in free space. The free-space model has this appearance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Copper #12 Dipole
+CM Free Space
+CE
+GW 1 41 0 -100 420 0 100 420 0.0404331
+GS 0 0 .02540
+GE 0
+EX 0 1 21 0 1 0
+LD 5 1 1 41 5.8001E7
+FR 0 1 0 0 28.5 1
+RP 0 37 73 1002 0 0 5 5
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that we employ the RP0 call for a complete sphere of samples to arrive at the average power gain.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 6.9136E-03 WATTS
+                                           RADIATED POWER= 6.8595E-03 WATTS
+                                           WIRE LOSS     = 5.4029E-05 WATTS
+                                           EFFICIENCY    =  99.22 PERCENT
+
+   AVERAGE POWER GAIN= 9.92175E-01       SOLID ANGLE USED IN AVERAGING=( 4.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power efficiency is 99.22%, allowing for the loss involved in using copper wire. The average power gain is 0.9922. Since we used a complete sphere, the radiation efficiency is 99.22%. We show no variance between power and radiation efficiencies, because the free-space pattern of a dipole is so regular.

+

Next, let's place the dipole 35' (1 wavelength at 28.5 MHz) above average ground. Our model changes in several respects.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Copper #12 Dipole
+CM Average Ground
+CE
+GW 1 41 0 -100 420 0 100 420 0.0404331
+GS 0 0 .02540
+GE 1 -1 0
+GN 2 0 0 0 13 .005
+EX 0 1 21 0 1 0
+LD 5 1 1 41 5.8001E7
+FR 0 1 0 0 28.5 1
+RP 0 19 73 1002 -90 0 5 5
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Besides changes in the GN entry, we also have a different RP0 call, since we shall now work with a hemisphere of samples. Here is the report that we obtain.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                        - - - POWER BUDGET - - -
+
+                                           INPUT POWER   = 7.0811E-03 WATTS
+                                           RADIATED POWER= 7.0243E-03 WATTS
+                                           WIRE LOSS     = 5.6826E-05 WATTS
+                                           EFFICIENCY    =  99.20 PERCENT
+
+   AVERAGE POWER GAIN= 1.47681E+00       SOLID ANGLE USED IN AVERAGING=( 2.0000)*PI STERADIANS.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power budget remains essentially unchanged, despite the slight change in the source impedance that yields slightly different input and radiated power values. However, our average power gain is 1.4768, for a radiation efficiency of 73.84%. Unlike the vertical monopole, the horizontal dipole shows much more regular changes of radiation efficiency with changes of soil type, ranging from 80.01% over very good soil to 65.93% over very poor soil.

+

Conclusion

+

NEC will indeed yield a value for radiation efficiency, if we set up the proper RP0 call and select a sampling interval adequate to the level of precision that we may require from the report and subsequent calculation. The values produced may be surprising to some modelers, because for many types of analysis and design tasks, we are normally unconcerned over radiation efficiency. However, in the design of vertical monopoles and arrays, as well as in the design of "mini- antennas," radiation efficiency may be a more important concept.

+

Depending upon the antenna design, there may be slight differences in the reports yielded by NEC-2 and NEC-4. All of the examples used here used NEC-4. The procedures remain the same in both programs, and the NEC models used here will run in NEC-2, but slight mathematical differences in the outputs may occur. So far, I have encountered none that reach the level of being significant relative to other data we may derive from our models.

+

Correlating radiation efficiency values to directional gain reports, soil type, and other data derived from models is neither simple nor automatic. Hence, the interpretation of relatively small changes in radiation efficiency (in contrast to very large changes) is the responsibility of the investigator and should rest upon appropriate considerations in addition to the data reports that emerge from the models.

+

At most, these notes show you how to get a radiation efficiency report. They do not show you what to do with it.

+
+ +

+

Go to Main Index

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+

76. Developing Antenna Expectations Using Modeling Software
+ 1: Horizontal Wires in the Lower to Medium HF Range

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Preamble

+

On numerous occasions, I have suggested that antenna modeling software (using either NEC or MININEC) is a good self-instruction tool for learning to have proper expectations of many type of antennas. In this and the next few columns, I shall illustrate how you can accomplish this goal. Each column will focus on a basic antenna type and develop a set of modeling exercises for exploring the basic properties of that type of antenna. Most of the exercises will be simple and in no way challenge either your software or your modeling ingenuity. However, the lack of challenge does not make the exercises any less important if you have not already been through them (or any number of variations on them).

+

Modeling software continues to grow easier to obtain for the individual who is relatively new to antennas, that is, who has not done systematic studies in basic antenna properties. I have discovered over the years that this group of folks includes many old-time as well as new radio amateurs, short-wave listeners, and others. This group of individuals is my target for these exercises. Modeling itself will not tell you exactly why--in terms derived from Maxwell's laws and supplemental research and engineering findings--antennas act as they do. Still, easily accessed modeling programs will help you develop a reasonable and extensive set of correct expectations from the types of antennas that you may encounter.

+

For the most part, our notes will by aimed at the antenna under discussion. I shall assume that you have mastered the basic operation of your software program. As well, I shall assume that you are familiar with the basic terminology that such programs use, although I shall include a few brief reminders as we go along. However, each basic type of antenna has many variables attached to it, each of which deserves exploration. So I shall remain focused on the modeling application rather than on the programs themselves.

+

The Center-Fed Horizontal Wire at Low to Medium High Frequencies

+

Let's begin by thinking about a particular type of antenna and the number of variables that attach to it. Our subject is the center-fed wire antenna, commonly used at lower to medium high frequencies (HF). Here is a list of basic variables that we shall explore.

+
+ A. The antenna environment (free space or over ground) +

B. The length

+
+
+
+
1. Resonant vs. non-resonant lengths
+
2. Physical length vs. electrical length
+
+
+
a. Changing the physical length
+
b. Changing the frequency of operation
+
+
+
+
+
C. Wire diameter +
+
+
+
1. Effect on the feedpoint impedance
+
2. Length required for resonance
+
+
+
D. Height above ground +
+
+
+
1. Effect on the feedpoint impedance with a constant length
+
2. Length required for feedpoint resonance
+
+
+
+

E. Ground quality

+

F. Wire conductivity

+

G. Operating (SWR) bandwidth vs. wire (element) diameter

+
+

In each case, I have paired up common variables encountered in basic antenna work, and the method of pairing means that we shall overlook some potential combinations. Nevertheless, with this beginning, you may go on to pair other sets of variables and explore more of the territory on your own.

+

Antenna modeling software has many forms and implementations, despite the fact that NEC-2 and MININEC are the most common calculating cores. Therefore, I shall not present models so much as describe them. They are all simple, so you may create your own model within the set-up of the software that you have. You will encounter minor differences between the results that you obtain from your model and the sample results that I shall show. Nevertheless, you will be able easily to see the same trends in the results, and that is the most important factor in developing correct expectations of an antenna. For this initial exercise set, the models will be super-simple, consisting of a single horizontal wire. We shall specify all lengths in terms of both feet and meters. Wire diameters will use AWG gauge numbers, along with their diameters in inches and millimeters. Heights above ground will be listed in wavelengths, feet, and meters. Except where I shall try to focus your attention on some special aspect of a unit of measure, pick the one most comfortable for you.

+

With so many variables attached to the horizontal center-fed wire, we need to move from these preliminaries to the actual work involved.

+

A. The Antenna Environment (Free Space or Over Ground)

+

Let's begin by setting our software for free space (or "no ground"). We shall create a 1/2 wavelength resonant dipole for 3.6 MHz. The wire will be AWG #12 (0.0808" or 2.052 mm). We shall set the conductivity of the wire for copper, using either a pre-set value in the program of a user-inserted conductivity of about 5.8E7 S/m (or a resistivity of 1.7E-8 Ohms/m). We may specify a source (feedpoint) voltage of 1.0 at 0 degrees phase angle at the center of the 11-segment NEC wire (10 or 12 segments in MININEC). To set up the wire, as shown in Fig. 1, we shall run it from -Y to +Y, leaving both the X values and the Z values at zero. On my version of NEC-4, the Y-coordinates were -66.55 and +66.55 feet (+/-20.284 m).

+
+ +
+

The first step is to learn why I used the length indicated. If I look at the source impedance, it reads 73.73 - j0.27 Ohms. Since we want resonance, we need to define the term. For our purposes, we can set resonance as any source impedance where the reactance (or imaginary term) is less than +/-1.0. This limit is much tighter than you would need in a practical antenna and much looser than we can obtain by juggling the length value. However, it is just about right for determining trends in the source (feedpoint) impedance. Depending on your program, you may have to adjust the values of +/-Y to obtain resonance within the limits indicated, and your remaining impedance value may drift a bit from the result listed.

+
+ +
+

Having established a resonant center-fed wire at 3.6 MHz in free space, let's examine the patterns. Modeling programs use the terms "azimuth" and "elevation" for all patterns. However, the terms strictly apply only when we have a ground surface against which to measure an elevation angle. In free space, for a horizontal wire, the azimuth pattern corresponds to the E-plane pattern, and the elevation pattern corresponds to the H-plane pattern. Both appear in Fig. 2. The E-plane pattern is the figure-8 that we see in texts, while the H-plane pattern is a perfect circle. For reference, we can record the maximum free-space gain as 2.03 dBi (where your program my show a smidgen more or less, and where we remember that we are using copper wire, not a perfect conductor). We shall explore this value further on when we take up different values of wire conductivity.

+

Now let's make a few changes and re-run the model. First, we shall insert in each of the Z boxes a value of 1 wavelength (273.214' or 83.276 m). Next, we shall specify the use of a real ground. If using NEC, specify the Sommerfeld or "high accuracy" ground. Set the values for this ground at "good" (sometimes called "average"), that is, with a conductivity of 0.005 S/m and a permittivity (relative dielectric constant) or 13. Now set the pattern for elevation.

+

Run the model and check the source impedance. You should discover that the antenna is no longer strictly resonant, with an impedance of 71.34 - j6.42 Ohms. It is merely near-resonant. Next, check the elevation pattern at an azimuth bearing of 0 degrees. It is no longer circular, but shows the effects of ground reflection. Hence, the pattern breaks into elevation lobes and nulls. Since the lowest lobe is the one of main interest, we can record its elevation angle (14 degrees) and its strength, 7.85 dBi. (We shall take a closer look at that elevation angle a bit further onward.) Now check the azimuth pattern at the elevation angle of maximum radiation--the Take-Off (TO) angle. The pattern is no longer a tightly pinched figure-8, but more of a peanut. Ground reflections not only increase the azimuth gain at the TO angle, they also reduce the side nulls relative to a free-space pattern. See Fig. 3.

+
+ +
+

B. The Length: 1. Resonant vs. Non-Resonant Lengths

+

Let's use the 3.6-MHz wire antenna model that is 1 wavelength above good or average ground as our starting point. First, we should make it resonant within the limits we have set for that term. With the Y-values at +/-66.8' (20.361 m), we can obtain resonance. Next, let's see what happens as we change the wire in 1' (0.3048 m) increments, going up two notches and then down two notches. Hence, our total antenna length will change by 2' (.6096 m) for each change. Within the limits of program differences, your table of results should resemble the one that follows.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           Changing Antenna Length
+
+       Length        Length                Source Impedance             Gain at 14-deg.
+       +/-feet       +/-meters             R +/- jX Ohms                Elevation dBi
+       64.8          19.751                66.29 - j51.74               7.82
+       65.8          20.056                69.13 - j25.89               7.83
+       66.8          20.361                72.09 - j 0.07               7.85
+       67.8          20.665                75.16 + j25.74               7.86
+       68.8          20.970                78.35 + j51.56               7.87
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Each 2' of antenna length change is about a 0.007 wavelength change--not a lot, but noticeable. Despite that fact that the total change in length from the shortest to the longest wire is 8' (2.438 m), the antenna gain has changed by only 0.005 dB--a truly insignificant amount. This explains why, for antennas using antenna tuners, we do not need lengths to be precise. Only when the exact source impedance is of some importance do we need to concern ourselves with precision pruning.

+

Our example presumes that some precision is useful, as shown by the changing values of the source impedance. But the table of values also has more to tell us. First, note the change in reactance. Allowing for the fact that we had j0.07 Ohm reactance at the so-called resonant point, we can see that the reactance curve would be very nearly equal each side of resonance over the small span that we have covered. The very slightly higher change below the resonant length is due to the fact that each 1' (0.3048 m) of change below the resonant length is a slightly higher percentage of length reduction relative to the preceding length than each increment is a percentage of length increase above the resonant length.

+

The resistive portion of the source impedance tells a different story. The resistance increases more rapidly above the resonant length than below it. As the resistance decreases, it has only a small range to cover. However, as we increase the length toward 1 wavelength, the range over which the resistance may climb is monumental, suggesting that even for our small changes, we should expect more change per increment. Both the resistance and reactances changes--and their differences above and below the resonant antenna length--do not amount to anything noticeable for a broadband antenna like a center-fed wire, but for other antenna types with more rapid changes in source impedance with element length changes, we often clearly see non-symmetrical changes in the impedance curves. When we see reversals in the non-symmetry, we have a good occasion to examine the antenna in order to understand why.

+

B. The Length: 2. Physical Length vs. Electrical Length

+

Let's now see what happens to the performance parameters when we increase the electrical length of our center-fed wire. We have sometimes referred to our wire as a dipole. This term is shorthand for a more complete but very unwieldy label: a resonant (or near-resonant) 1/2 wavelength center-fed dipole. The question of resonance, of course, refers to the feedpoint impedance and to what degree it is contained wholly in the resistive component, with no reactance. The antenna is about 1/2 wavelength long. A wavelength at 3.6 MHz is 273.214' (83.276 m) long, so a true half wavelength will be 136.607' (41.638 m). Our actual wire length was 133.6' (40.721 m) for the version that is resonant at 1 wavelength above average ground. We know that the physical length is less than the electrical length, which is--by the standard of resonance--almost exactly 1/2 wavelength. The physical length is 97.80% of the electrical length.

+

We shall look again at the amount of shortening later, but for now we need only note that the difference results from what some call "end-effect." The surface at the end of the wire adds electrical length to the wire without adding any further physical length.

+
+ +
+

Since we feed the antenna at its precise center, it is center-fed. We call the antenna a dipole because there are exactly two transitions from maximum current (at the wire center) to minimum current (at the wire ends). When we change the length of the wire so that there are more than two such transitions, we technically no longer have a dipole. Center-fed antennas used on frequencies where they are no longer have only two transitions go under an unofficial but useful label: doublets. See Fig. 4 for the contrast between a dipole and a doublet. A wire antenna becomes a doublet even if some frequencies at which we use it might qualify for the dipole label.

+

a. Changing the physical length

+

Now here is the exercise--or at least the first of two. Let's exactly double the length of the antenna. Then let's triple it. Finally, let's quadruple the original length. We shall retain the frequency and the height above ground. We need only be certain that the feedpoint remains in the exact center and that we have enough segments for the new length. To preserve the segment length, lets increase the NEC segments from 11 to 21 to 31 and finally to 41. MININEC segmentation, using even numbers, calls simply for multipliers of 2, 3, and 4.

+

We shall record the source impedance for each step. When it comes to looking at patterns and finding maximum gain, we shall have to go back and forth between elevation and azimuth pattern to find the azimuth heading as well as the elevation angle of maximum radiation. If we do the job correctly, we shall end up with a table like the one that follows. Note that the lengths shown are for my resonant model. Apply the multipliers to the length of your own resonant dipole when 1 wavelength above ground. All wires remain AWG #12 copper.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                     Performance of Wire Antennas 1 Wavelength Above Average/Good Ground
+
+Length        Length         Length        Az hdg         TO angle      Gain          Source Impedance
+wl*           feet           meters        degrees        degrees       dBi           R +/- jX Ohms
+0.5           133.6           40.72         0             14            7.85          72.09 - j 0.07
+1.0           267.2           81.44         0             14            9.62          6629 + j 1367
+1.5           400.8          122.16        49             14            8.56          105.0 - j 69.08
+2.0           534.4          162.88        34             14            9.15          4488 + j 1324
+
+* Since we are multiplying times the physical length, the lengths in wavelengths are approximate.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Without looking at the patterns themselves, the table already tells us something important about them. For antennas in the range of 1/2 wavelength to 1 wavelength, the pattern is bi-directional, with the strongest (only) lobes broadside to the wire. However, as we further increase the length, the strongest lobe is at an angle relative to the broadside heading. How much depends on the wire length.

+
+ +
+

Fig. 5 shows the patterns for the three new wire lengths. A 1 wavelength wire acquires its gain mostly from narrowing the beamwidth. We still have a 2-lobe pattern. Let's skip to the pattern for the 2 wavelength antenna. Now we have 4 lobes, each quartering (but not exactly) to the broadside heading. Radiation broadside to the wire is negligible. This pattern gives you an intuition of what happens if we extend the wire to 3 wavelengths: 6 lobes. You can check this for yourself and find that you are correct. In fact, with wire close to a any multiple of a full wavelength, the number of lobes will be double the element length in wavelengths.

+

However, let's move back to the case where the wire is 1.5 wavelengths long. We find 6 azimuth lobes. Lobes do not suddenly appear and disappear as we increase a wire's length. They grow and shrink. At a length of 1.5 wavelengths, the pair of lobes for a 1 wavelength wire are shrinking and the ones for a 2 wavelength antenna are growing. Hence we see all six lobes. (A 3.5 wavelength antenna would have the 6 lobes for 3 wavelengths and the 8 for 4 wavelengths, for a total of 14 lobes.) As we increase the number of lobes, the beamwidth for each one tends to become narrower.

+

Since the 1.5 wavelength wire has more lobes that either the 1 wavelength or the 2 wavelength wire, but only the same amount of power, we would expect the power in the strongest lobe to be somewhat less than for either of the other cases. If we look in the gain column, we can see the fulfillment of our expectation. The differential is not especially operationally significant, but it is noticeable.

+

Now let's turn to the feedpoint impedance column. The impedances for the lengths close to a multiple of a full wavelength are high, while those close to an odd multiple of a half wavelength are low. But in all three cases, the antenna plays shorter than resonance. (As we approach but do not reach resonance for a multiple of a full wavelength, the inductive reactance indicates the antenna's shortness. As a side exercise, try to play with the length of the 1 wavelength antenna to achieve resonance as defined for our exploration. The range is extremely narrow, as the reactance changes from a very high value of inductive reactance to a very high value of capacitive reactance just past the resonant point.) The reason for the antenna being short is, again, the end effect. By simply multiplying our physical length, we effectively added in an end effect for each new length. However, the wire itself has only one set of ends. Hence, it needs to be longer than shown for true resonance.

+

Special note: although we changed the length of the wire radically, we did not change its height above ground. Therefore, the TO angle remained constant throughout the exercise. Increasing the length of a single wire does not lower (or raise) the elevation angle of maximum radiation.

+

b. Changing the frequency of operation

+

We can perform the same exercise in a second way. Instead of doubling the length of the antenna, we may instead simply double the frequency. If we use the 2, 3, and 4 multipliers, we obtain frequencies of 7.2, 10.8, and 14.4 MHz. If we perform the experiment in this manner, we shall have to change the physical height of the antenna each time so that it is exactly 1 wavelength up for each new frequency. As we did in the first experiment, we shall increase the number of segments for each trial to the same value used the first time (11, 21, 31, and 41 for the NEC model).

+

If we perform the trials in the manner just described, our new table will look like the one that follows.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                     Performance of Wire Antennas 1 Wavelength Above Average/Good Ground
+
+Frequency     Length         Az hdg        TO angle       Gain          Source Impedance
+MHz           wl*            degrees       degrees        dBi           R +/- jX Ohms
+ 3.6          0.5             0            14             7.85          72.09 - j 0.07
+ 7.2          1.0             0            14             9.49          5886 + j 703.2
+10.8          1.5            49            14             8.45          103.5 - j 56.48
+14.4          2.0            34            14             9.02          3644 + j 528.7
+
+* Since we are multiplying frequency relative to the physical length, the lengths in wavelengths
+are approximate.)
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Some things did not change at all. The TO angle remained the same, because it is a function of the wire's height above ground as measured in wavelengths. The patterns that we produced are virtually identical to those from the previous exercise, and Fig. 5 remains a proper portrayal of both the elevation and azimuth patterns.

+

We can notice a few changes in the table. For example, the impedance values appear to be a bit closer to resonance for each of the steps above the original frequency, relative to the values for doubling the wire length. The wire diameter is the source of this phenomenon. As we multiplied our frequency, we also divided the wavelength so that it became a smaller quantity. However, we kept our AWG #12 copper wire. Hence, relative to a wavelength, the wire became fatter with each multiplication. For straight-wire elements, the fatter the wire, the shorter the required physical length for resonance. Even though the frequency-multiplied versions of the antenna are the same relative physical lengths as in the first trials, they are electrically longer due to element fattening.

+

The second change to notice is the set of gain values. They are lower than in the earlier table. Wire size cannot be the culprit, since we would expect a fatter wire to have slightly lower losses than a thinner one. In fact, the radiation efficiency of the 14.14 version of the antenna appears as 98.83% in the NEC output file, whereas the efficiency of the 2.0 wavelength 3.6-MHz model shows as 97.70%. So we cannot even blame skin effect, which increases with frequency.

+

The source of the lower gain in the models that multiply frequency is actually the ground. Although we did not change any of the ground constants, losses due to the ground increase with frequency (as well as with proximity to it). Once more, even though the differentials make no operational difference that anyone could detect, they are numerically visible and give us indications of the influence of various factors on the actual gain of a given antenna.

+

C. Wire Diameter: 1. Effect on the Feedpoint Impedance

+

We noted in passing that changing the diameter of a wire had an effect upon its resonant length. We can get a small handhold on this phenomena in two ways, and we shall sample them both. This is a good exercise to perform with a wire in free space to minimize the number of possible variables at work. So let's return to our resonant 3.6-MHz center-fed wire that was +/-66.5 feet (20.284 m) long in Fig. 1. (Of course, you should begin with whatever length turned out to be resonant in free space within your own software.) The AWG #12 copper wire will be our center-point for the chart. Let's sample AWG wire sizes from #4 through #20 in steps of 4 gauges. We shall preserve the wire length and see what happens to the source impedance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                            Changing Wire Diameter:  Effect Upon Source Impedance
+
+       AWG #                 Diameter             Diameter              Source Impedance
+                             Inches               mm                    R +/- jX Ohms
+        4                    0.2043               5.189                 73.22 + j 3.57
+        8                    0.1285               3.264                 73.34 + j 1.53
+       12                    0.0808               2.052                 73.73 - j 0.27
+       16                    0.0508               1.290                 74.53 - j 1.73
+       20                    0.0320               0.813                 75.99 - j 2.64
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Over the 6.38:1 diameter range in our set of trials, we find a small but definite progression of impedance values. As we increase the copper wire diameter, the resistance component of the source impedance goes down. The reactive component becomes less capacitive and more inductive, indicating that the diameter increase is also increasing the electrical length for the same physical length of wire.

+

C. Wire Diameter: 2. Length Required for Resonance

+

We may alter the trial by aiming toward the wire length that will yield a resonant 3.6-MHz antenna. If we do the job, the results will look similar to those in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Changing Wire Diameter:  Effect Upon Resonant Wire Length
+
+       AWG #         Diameter       Diameter      Resonant Length       Source Impedance
+                     Inches         mm            Feet           Meters        R +/- jX Ohms
+        4            0.2043         5.189         132.80         40.477        72.76 + j 0.05
+        8            0.1285         3.264         133.00         40.538        73.19 + j 0.29
+       12            0.0808         2.052         133.10         40.569        73.73 - j 0.27
+       16            0.0508         1.290         133.20         40.599        74.69 - j 0.36
+       20            0.0320         0.813         133.30         40.630        76.31 + j 0.23
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Between the largest conductor and the smallest, we find about 0.5' (0.153 m) difference in length. The trend is perfectly visible, but the effect on a practical 80-meter antenna in terms of selecting #12 or #14 wire is negligible. The change in the resistive (resonant) impedance is also quite visible as it changes by nearly 4 Ohms. Once more, the change is more visible than significant for practical antenna building. Still, we need to be aware of small systematic changes as well as large ones.

+

The changes are a guide to the likely consequences of using fatter wires. We may simulate widely space wire pairs (with either open or closed ends) and of cages of wires used by some lower HF antenna designers to simulate truly fat elements and to obtain a wider operating bandwidth. However, the concept of operating bandwidth is farther down the list of properties that we wish to examine in our systematic survey of properties.

+

In fact, we have run out of space for this column. So we shall have to reserve the remaining exercises for next month.

+
+ +

+

Go to Main Index

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+

77. Developing Antenna Expectations Using Modeling Software
+ 1: Horizontal Wires in the Lower to Medium HF Range (continued)

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the first half of our exploration of the modeled characteristics of horizontal wire antennas, we examined a number of basic properties. Starting with the differences that we encounter when placing the antenna in free space or over a specified ground, we moved on to look at the effects of selecting a resonant or non-resonant wire length. We continued our investigation of length by extending the wire's electrical length in two ways: by multiplying the initial length while staying at the initial frequency (3.6 MHz) and by multiplying the frequency while retaining the initial length. Finally, we examined differences made by changing the wire diameter from its initial AWG #12 value to a range from AWG #4 through AWG #20. We saw the difference that wire size made in the source impedance of a constant length antenna and also the difference in resonant antenna length as we changed the wire size.

+

In each case, we focused upon two features of the properties. First, we wanted to see what trends developed--and, if possibly, why. Second, we made note of those trends that might make a significant operating difference, separating them from those that were numerically interesting but not operationally significant.

+

In this continuation of the investigation, we should complete our preliminary study. As you may recall, we set up a list of modeling tasks.

+
+ A. The antenna environment (free space or over ground) +

B. The length

+
+
+
+
1. Resonant vs. non-resonant lengths
+
2. Physical length vs. electrical length
+
+
+
a. Changing the physical length
+
b. Changing the frequency of operation
+
+
+
+
+
C. Wire diameter +
+
+
+
1. Effect on the feedpoint impedance
+
2. Length required for resonance
+
+
+
D. Height above ground +
+
+
+
1. Effect on the feedpoint impedance with a constant length
+
2. Length required for feedpoint resonance
+
+
+
+

E. Ground quality

+

F. Wire conductivity

+

G. Operating (SWR) bandwidth vs. wire (element) diameter

+
+

Having completed items A through C, we may move on to items D through G. As was true in the first half of our work, each modeling task is quite simple, although most involve several repetitions, each time making a small specified change in the model. As well, we shall begin with a resonant AWG #12 copper wire center-fed dipole 1 wavelength above good ground (conductivity 0.005 S/m, permittivity 13). Fig. 1 outlines the model. In most cases, we shall retain the minimal but adequate segmentation, using 11 segments for the half wavelength antenna in NEC models and 10 or 12 segments in MININEC models.

+
+ +
+

Perhaps the only term for which we need a reminder is the idea of resonance. For our exercises, we shall treat an antenna as resonant if the source reactance is less than +/-j1 Ohm. As always, slight differences between programs may make slight differences in the actual numbers you find in your program reports. This situation applies not only to the differences between NEC and MININEC programs, but also to different implementations of each calculating core. However, the trends that we discover should not change.

+

D. Height Above Ground: 1. Effect on the Feedpoint Impedance with a Constant Length

+

A number of erroneous generalizations pervade introductory literature on center-fed dipole antennas. We saw from our look at the effects of wire diameter on resonant length that the simplified cutting formulas that inhabit handbooks are very imprecise. In addition, I often hear that, as we reduce the height of a dipole toward ground, the impedance goes down. Now we have a way to find out. Let's begin with our older free-space resonant dipole and run it up and down a ladder of height. That dipole was 133.1' (40.57 m) long and reported a source impedance of 73.73 - j0.27 Ohms.

+

To see what happens to the source impedance at various heights, let's check it every 0.1 wavelength from 0.25 wavelength up to 1.25 wavelength. We shall start at a 1/4 wavelength height because MININEC programs are generally inaccurate in reporting both the gain and the source impedance for antennas with a horizontal radiation component when they are 0.2 wavelengths or lower. If we perform the exercise, we shall obtain a table like the one that follows. Of course, we are retaining our 3.6-MHz test frequency.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                             Dipole Source Impedance Changes with Height Changes
+
+                     Height                                      Source Impedance
+                     WL             Feet          Meters         R +/- jX Ohms
+                     0.25            68.30         20.82         87.61 + j 17.01
+                     0.35            95.63         29.15         90.40 - j  4.69
+                     0.45           122.95         37.47         75.47 - j 14.13
+                     0.55           150.28         45.80         63.36 - j  5.76
+                     0.65           177.59         54.13         66.26 + j  6.55
+                     0.75           204.91         62.46         77.23 + j  7.86
+                     0.85           232.23         70.78         81.55 - j  0.87
+                     0.95           259.55         79.11         75.50 - j  7.08
+                     1.05           286.88         87.44         68.38 - j  3.85
+                     1.15           314.20         95.77         69.07 + j  3.34
+                     1.25           341.52        104.09         75.54 + j  4.44
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

The data form a complex pattern that may be clearer in graphical form. Fig. 2 shows the changes in both resistance and reactance, with reference to left and right scales, respectively. Note the both the resistance and the reactance cover two complete cycles of peaks and nulls within the 1 wavelength span of antenna heights. The height of peaks and the depth of nulls diminish as we increase height, but the cycle continues indefinitely as we further increase height (until we reach a height at which succeeding differences are too small to detect or calculate).

+

More interestingly, the peaks and nulls for resistance do not occur at the same heights as corresponding peaks and nulls of reactance--where we may temporarily define a peak reactance as the maximum inductive value and a reactive null as the maximum capacitive value. Resistive peaks and nulls occur about 1/8 wavelength higher than their closest reactive counterparts. Moreover, the amount of change is actually greater than most folks expect from a simple wire antenna.

+

D. Height Above Ground: 2. Length Required for Feedpoint Resonance

+

There is a second way to examine these changes. Let's reformulate our question into this one: what is the resonant length of a wire dipole of the same composition for each height on the list? To this question, we may add, what is the corresponding resonant source impedance? We may start with our free space model and place it over good ground at the various heights. Then we may juggle the length until we achieve resonance. Finally, we may record the resulting wire length and the resonant feedpoint impedance to obtain a table like the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                              Dipole Resonant Wire Lengths with Height Changes
+
+       Height                                     Resonant Length              Source Impedance
+       WL            Feet           Meters        Feet           Meters        R +/- jX Ohms
+       0.25           68.30          20.82        131.84         40.18         85.27 + j 0.15
+       0.35           95.63          29.15        133.46         40.68         91.09 - j 0.05
+       0.45          122.95          37.47        134.22         40.91         77.24 + j 0.13
+       0.55          150.28          45.80        133.54         40.70         63.94 - j 0.07
+       0.65          177.59          54.13        132.60         40.42         65.56 - j 0.06
+       0.75          204.91          62.46        132.50         40.39         76.25 - j 0.07
+       0.85          232.23          70.78        133.18         40.59         81.69 + j 0.17
+       0.95          259.55          79.11        133.64         40.73         76.36 - j 0.12
+       1.05          286.88          87.44        133.40         40.66         68.81 + j 0.03
+       1.15          314.20          95.77        132.84         40.49         68.70 - j 0.08
+       1.25          341.52         104.09        132.72         40.45         74.93 - j 0.16
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Over the span of heights in the table, the range of resonant lengths varies by over 2' (0.6 m). As well, the resonant source impedance ranges from 64 to 91 Ohms, a span of 27 Ohms. The length reaches its maximums at greater heights than the maximums of source impedance. Fig. 3 shows the relationship clearly. Note that, like the numbers in Fig. 2, the required resonant length for our wire undergoes two complete maximum-minimum cycles for each wavelength change of height.

+
+ +
+

The cycles that we have witnessed are not unique to simple dipoles. You will find similar phenomena in parasitic arrays based on the horizontal dipole, although with smaller excursions of resistance and reactance. Should you wish to pursue this aspect of horizontal antenna behavior further, examine the maximum gain values for each height. You will discover gain peaks at about 0.625 wavelength and 1.125 wavelength heights, with minimums near the 0.375 wavelength and 0.875 wavelength marks. Like the other dipole properties, both peaks and nulls are about 1/2 wavelength apart from the next peak or null. However, with respect to gain, there is another property to consider: the elevation pattern shape. Track the gain of the dipole at high elevation angles for both maximum and minimum gain values as you change antenna heights.

+

Since the gain and pattern shapes are applicable to our first table of values, using a constant antenna length, you may fairly conclude that the differences throughout the exercise are functions of the antenna's interaction with the ground. Even though that ground remained a constant in terms of its conductivity and permittivity, the antenna's height above it changed, resulting in altered patterns of ground reflections at a distance to add to or subtract from the direct radiation. As well, ground reflections in the immediate vicinity of the antenna resulted in variations in the source impedance as we changed heights. We saw the effects on resonant wire length and source impedance grow smaller with increasing height. We might well conclude that the effects will continue to diminish with further height increases until differences from step-to-step become too small to call for notice.

+

E. Ground Quality

+

Since the basic source of the changes that occur with dipole performance as we vary the height of the antenna above ground are a function of the antenna's interaction with the ground, a new question arises: will the performance of a dipole change (or change significantly) as we alter the characteristics of the ground beneath it. Of course, modeling software provides the means for reaching an answer.

+

Although there is no absolutely systematic reason for doing so, sampling of the effects of ground conditions on antennas typically uses four traditional categories of soil: very poor, poor, good, and very good. In fact, these categories perform quite well in providing a fair sampling of ground effects. Taken from FCC charts that date to the 1930s, we may define each ground quality level in terms of the associated conductivity and permittivity (relative dielectric constant).

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           Some Useful Soil Types
+
+              Soil Type                    Conductivity                 Permittivity
+                                           S/m                          (Dielectric Constant)
+              Very Poor                    0.001                         5
+              Poor                         0.002                        13
+              Good                         0.005                        13
+              Very Good                    0.0303                       20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

To create some trials, let's begin with our resonant dipole over good ground at a height of 1 wavelength at 3.6 MHz. Then we need only change the ground constants to obtain the simple table that follows.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       Changes of Dipole Performance with Ground Quality: 1-WL Height
+
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             7.45          14                    72.35 + j 2.20
+              Poor                  7.66          14                    72.60 + j 0.76
+              Good                  7.85          14                    72.09 - j 0.07
+              Very Good             8.03          14                    72.28 - j 1.72
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Between the worst and best of the soil types listed, we find only a 0.6 dB difference in maximum gain. As well, the TO angle does not change at all. The resistive portion of the source impedance changes by well under 1 Ohm, and the reactance varies by less than 4 Ohms. All in all, the trial suggests that for a horizontal wire antenna, the ground quality will make little difference to the antenna performance.

+

MININEC users, of course, may track the far field gain values and TO angles. However, since MININEC reports the source impedance as if the antenna were over perfect ground, it cannot track the changes in the source impedance with changes in ground quality. For the present test, those changes are not significant to operation of the antenna.

+

However, the changes that we saw result from an antenna height of 1 wavelength above ground. Suppose that we simply drop the antenna height to a half wavelength, that is a height of 136.61' (41.64 m). Without readjusting the antenna length, let's repeat the trials we just performed to see what happens.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      Changes of Dipole Performance with Ground Quality:  1/2-WL Height
+
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             7.02          26                    69.58 - j 0.82
+              Poor                  7.38          27                    69.77 - j 3.69
+              Good                  7.74          28                    68.58 - j 5.20
+              Very Good             8.11          29                    68.61 - j 8.48
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Immediately we see that the gain differential between the worst and best soils has grown to about 1.1 dB. This level of difference is sufficient to show up in overlays of the elevation patterns for the antenna above the 4 different soil types, as shown in Fig. 4. As well, the TO angle is no longer constant, but actually increases with improved soil quality. Although the range of resistance change in the source impedance remains about 1 Ohm, the reactance change has increased.

+
+ +
+

The overall changes remain small, but the closer we bring the antenna to the ground, the greater the effect of soil quality upon the performance figures. You may wish to examine the antenna using other heights than the 2 that we have sampled. As well, you may wish to check performance at various heights using the ground constants for salt water (5 S/m, 81).

+

F. Wire Conductivity

+

The range of materials that we employ as antenna element materials ranges from silver-coated conductors to stainless steel. All of the materials are conductors, but with various levels of conductivity. Most implementations of NEC and MININEC permit the user to specify the material in order to account for losses that result from the fact that no conductor is perfect (since super-conductive wires for lower HF use are not available).

+

In fact, the most general procedure for the modeler is to introduce a value for conductivity. The program then calculates the losses incurred by each segment assigned that value and adjusts the results accordingly. Losses, of course, reduce far-field gain and near-field strength. As well, since these losses are resistive, they tend to increase the resistive portion of the source impedance slightly. Since the losses also have a very small but calculable effect on the resonant length of a wire element, the reactance will also show a small change from one level of conductivity to another. A few programs, such as EZNEC, call for the entry of values of resistivity, the inverse of conductivity. The following table lists the values of conductivity and resistivity that we shall use. However, different sources provide different numbers--usually only slightly different--so these numbers are not absolute by any means. However, they provide enough diversity for our purposes.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Some Values of Conductivity and Resistivity for Representative Conductors
+
+Material                            Conductivity                 Resistivity
+                                    S/m                          Ohms/m
+Perfect                             ----                         ----
+Silver                              6.289E7                      1.590E-8
+Copper                              5.747E7                      1.740E-8
+6061-T6 Aluminum                    2.500E7                      4.000E-8
+Brass                               1.563E7                      4.099E-8
+Zinc                                1.667E7                      6.000E-8
+Phosphor Bronze                     9.091E6                      1.100E-8
+Tin                                 8.772E6                      1.140E-7
+Type 302 Stainless Steel            1.389E6                      7.200E-7
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The values that we introduce are bulk values, which are adjusted relative to the wire surface area and skin effect into actual values per unit length. Hence, the effects of wire conductivity will vary with the surface area of the wire (as well as the frequency of use). To better see the effects of using different wire materials for antenna elements, we should not simply sample our AWG #12 wire (diameter 0.0808" or 2.05 mm). Instead let's use a range of material diameters. At the bottom end, we may sample AWG #20 wire (diameter 0.032" or 0.81 mm). The ratio of #12 to #20 wire is about 2.5:1. At the opposite end of the scale, let's specify a conductor 1" (25.4 mm) in diameter, about 12.4 times fatter than the #12 wire.

+

We shall use our #12 dipole at 1 wavelength above ground as the test vehicle. Because the source impedance will change so little, we shall be interested only in the maximum gain of the antenna. Since the maximum gain of a dipole does not change much as we move a little off the resonant frequency, we may perform the tests casually, retaining the initial dipole length throughout. The trends and degrees of performance change per change in material will not be altered by the procedure. However, you may refine the procedure to whatever degree you find most informative. The results of our runs appear in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      Changes in Maximum Dipole Gain with Changes in Wire Conductivity
+
+       Material                            Maximum Gain for Each Wire Diameter
+                                           AWG #20               AWG #12              1"
+       Perfect                             7.94                  7.94                 7.95
+       Silver                              7.70                  7.85                 7.94
+       Copper                              7.60                  7.85                 7.94
+       6061-T6 Aluminum                    7.56                  7.79                 7.94
+       Brass                               7.55                  7.79                 7.94
+       Zinc                                7.47                  7.76                 7.93
+       Phosphor Bronze                     7.29                  7.69                 7.93
+       Tin                                 7.28                  7.69                 7.93
+       Type 302 Stainless Steel            6.22                  7.29                 7.90
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The results have much to tell us. We expected the maximum gain to decrease with the increasingly poor conductivity of the materials as we move down our list of samples. For AWG #20 wire, the expectation seems to follow a nearly ideal pattern. The conductivity value for silver is nearly 3.8 times that for stainless steel, and there is a 1.5-dB net difference in gain. However, as we move up to AWG #12 wire, the difference between silver and stainless drops to just over 0.5 dB. With a 1" conductor, the difference is a mere 0.04 dB.

+

For each frequency, there is a diameter of element such that any larger diameter fails to improve the gain. In effect, the surface area of the conductor per unit length is sufficiently large that the conductor approaches the status of a perfect conductor. For our test frequency of 3.6 MHz, that diameter is in the vicinity of 1" (25.4 mm). Since there is no existing standard of just how well an element must perform to be accorded the "near-perfect" status, you will have to determine your own standard, most likely based on whatever design or analysis task you are performing.

+

The required diameter for near-perfection compresses the gain level of dipoles ranging from silver to stainless steel into a tight group without significant gain differential from the lowest to highest values. In part, the required diameter is a function of its ratio to the wavelength at the frequency of use. Although a 1" diameter stainless steel element for a 3.6-MHz dipole is impractical, much smaller diameters of "near-perfect" stainless steel conductors become feasible at VHF and UHF frequencies with insignificant loss relative to the more usual element material, aluminum. Where durability under extreme conditions may be necessary, antennas in this range often use stainless steel.

+

G. Operating (SWR) Bandwidth vs. Wire (Element) Diameter

+

The concept of "operating bandwidth" begins with the question of over what frequency range a given antenna will perform to specification. The specifications may include any of the operating parameters that we have come to associate with antenna use: gain, front-to-back ratio (if relevant), beamwidth, pattern "purity" (as defined for a given task), and source impedance. In some cases, source impedance is not a significant concern, as in the use of a doublet over a wide frequency range with an antenna tuning unit to effect a match to the equipment involved. However, in many circles, operating bandwidth and 2:1-SWR bandwidth have come to be nearly synonymous.

+

Dipoles are a good case in point. Our AWG #12 copper dipole at a height of 1 wavelength shows the following properties at 3.5, 3.6, and 3.7 MHz.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                              Operating Properties of an AWG #12 Copper Dipole
+
+Property                                                  Frequency in MHz
+                                           3.5                   3.6                  3.7
+Maximum Gain dBi                           7.67                  7.85                 7.99
+TO Angle degrees                           14                    14                   14
+Horizontal Beamwidth degrees               80.2                  79.6                 79.0
+Pattern purity                             fig-8                 fig-8                fig-8
+Source Impedance (R+/-jX Ohms)             68.80-j48.85          72.09-j0.07          75.86+j49.19
+72-Ohm SWR                                 2.376                 1.002                2.397
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Only 1 set of numbers suggests any limitation to the operating bandwidth of the antenna: the 72-Ohm SWR, as derived from the source impedance across the 3.5- to 3.7-MHz passband.

+

For other type of antennas, any of the operating properties may stray from specifications and hence defeat the use of an antenna for a given application over the desired passband. Mono-band quads very often have a wider SWR bandwidth than they do a front-to-back bandwidth, perhaps defined as a ratio of 20 dB or better. Other antenna may change pattern shape to undesirable forms. Some UHF long-boom Yagis suppress forward sidelobes by 20 dB or more only over a narrow bandwidth, even though the forward gain and SWR bandwidths are much wider.

+

With these cautions in mind, we may look at the SWR bandwidth of our dipole. We shall use the same set of dipoles that we employed for the conductivity studies, although we shall bring each to resonance at 3.6 MHz. The following table sets up the 3 copper dipoles for our exercise,

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                 3 Dipoles Used for SWR Bandwidth Exercises
+
+Material                                   AWG #20               AWG #12              1"
+Length feet (meters)                       133.76 (40.77)        133.60 (40.72)       132.54 (40.40)
+3.6-MHz Source Impedance
+       (R +/- jX Ohms)                     74.58 - j 0.06        72.09 - j 0.07       70.58 - j 0.02
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For convenience, we shall set the reference value for our SWR curves at 72 Ohms.

+
+ +
+

Fig. 5 presents the three 72-Ohm SWR curves together. The curves show clearly the relationship of element diameter to the SWR bandwidth of a simple center-fed antenna. The 1" diameter version has a significantly wider bandwidth in terms of an SWR value below 2:1 than either of the wire dipoles. The #20 version has the worst of the 3 SWR bandwidths.

+

However, 1" elements are difficult to erect and maintain at 3.6 MHz, given their length in excess of 133' (40 m). Therefore, wire antenna users in the lower HF region often simulate larger elements with pairs (or cages) of wires. For example, we can simulate the large element with a pair of AWG #12 wires spread apart by about 12" (0.30 m). Fig. 6 shows some of the modeling techniques used to capture this antenna.

+
+ +
+

For the model, run both long wires in the same direction, a move necessary to use the feeding technique. Use enough segments so that the end wires (1 segment each) are about the same length as the segments in the long wires. Be sure to use the same number of segments in both long wires, since the close spacing requires good segment-junction alignment for maximum accuracy.

+

Place a source at the center of one of the long wires. From the source segment, run a TL-type transmission line to the center of the other wire. Specify a negligible length, for example 0.01' (3 mm). Assign the transmission line a characteristic impedance (Zo) of about twice the value expected at the source. In this case, a dipole would generally have an impedance between 70 and 75 Ohms, so a Zo of 150 Ohms will do. Let the velocity factor be 1.0, if applicable to your software. Unfortunately, this technique does limit the model to NEC-based software, since implementations of MININEC do not have a TL facility.

+

NEC gives the transmission line its assigned length, regardless of the physical distance between the terminal points. The effect of the minuscule TL length is to electrically join the source segment and its counterpart on the other wire as if the two were in a tapering junction. However, it saves the complexities involved in physically modeling the taper and often produces more accurate results, since it does not press NEC limits for angular junctions. The following small table gives the results of the modeling in comparison to the 1" dipole previously modeled.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                A Comparison of a 1" Copper Dipole vs. Paired AWG #12 Copper Wires at 3.6 MHz
+
+Property                     Antenna       1" Element            2xAWG #12
+
+Length feet (meters)                       132.54 (40.40)        131.60 (40.11)
+Maximum Gain dBi                           7.93                  7.91
+TO Angle degrees                           14                    14
+Horizontal Beamwidth degrees               79.8                  79.8
+Pattern purity                             fig-8                 fig-8
+Source Impedance (R+/-jX Ohms)             70.58-j 0.02          71.18-j 0.41
+72-Ohm SWR                                 1.020                 1.013
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The two antennas are virtually identical in performance. The paired AWG #12 wires do not quite reach the gain of the 1" element because their combined surface areas are still shy of what the single fat element achieves. However, the paired-wire dipole is more likely to be supportable in practice.

+
+ +
+

Fig. 7 combines the 72-Ohm SWR curves for both antennas from 3.5 to 3.7 MHz. Actually, the dual-wire version has a slightly wider SWR bandwidth, suggesting that a wire separation of about 10" (0.25 m) would have achieved the initial goal.

+

Conclusion

+

We have covered a wide swath of properties associated with lower-HF wire horizontal dipoles and doublets, all of which are accessible via judicious modeling. Nevertheless, we have only scratched the surface. Many exercises remain for you to invent and develop to further refine your expectations from horizontal elements and antenna based upon them. You can replace assumptions, presumptions, and mythology with data derived from systematically modeling every aspect of the performance of basic antennas. From that data emerge more nearly correct expectations of the antennas that you design, build, or analyze.

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+ +

+

Go to Main Index

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+

78. Developing Antenna Expectations Using Modeling Software
+ 2A: Vertical Dipoles

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The second basic antenna type that we should systematically investigate through our modeling software is the vertical dipole. We shall look at the vertical monopole in the next column, but for now, the familiar dipole--turned on end--will be our subject. Although the exact parameters that we shall look at will differ in part from those we explored with the horizontal wire, we shall follow a similar procedure. The antenna properties that will interest us fall into the following categories.

+
+ A. Model convergence +

B. Element diameter

+

C. Element material

+

D. Height above ground

+

E. Element length

+

F. Ground quality

+
+

As we have done before, we shall define resonance as a source impedance whose reactance is less than +/-j1 Ohm.

+

A. Model Convergence We may begin with a free-space model. Because we shall be working with the antenna--when we place it over ground--in wholly positive numbers that indicate its length, we may construct our free-space model in the same manner. Fig. 1 shows the general outlines of the model.

+
+ +
+

The figure does not indicate a specific length, because we shall soon look at several element diameters. However, to begin the process, let's consider the number of segments we need to use in the model. We shall begin by specifying a 1" (25.4-mm) element made from copper. (We shall look at alternative materials shortly.) Although the exact resonant free-space length may vary slightly depending upon the program used, we should also note that it may vary slightly with the number of segments used in the model--at least until the models converge. The following table shows the lengths and source impedance reports for the use of 11, 21, and 31 segments in a NEC-4 model. All models in this exercise will use 7.15 MHz as the test frequency.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                      Vertical Dipole Model Convergence
+
+No. of               Resonant Length              Free-Space            Source Impedance
+Segments             Feet           Meters        Gain dBi              R +/- jX Ohms
+11                   66.10          20.147        2.12                  71.96 - j 0.08
+21                   66.06          20.135        2.13                  71.95 - j 0.09
+31                   66.05          20.132        2.13                  71.99 + j 0.02
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Convergence is fairly simple, but worth looking at anyway. The 21-segment model is sufficiently converged with models using more segments to suffice for our purposes. Although the degree of convergence demanded is greater than would be operationally necessary under any conditions, it serves to indicate how model reports may vary slightly among otherwise identical models using different levels of segmentation.

+

I based my judgment of convergence upon the gain and the relative constancy of the resonant length. The impedance shows variations in resistance that are consistent with the different resonant points between the last two models. Because the second version shows a reactance slightly more negative than the first, we expect the resistance also to be slightly lower. In contrast, the reactance of the 31-segment model is (in relative terms) considerably higher than for either preceding model, and we expect the resistance to by a bit higher. Had I used 1 more decimal in the length determination, we could have easily brought the reactance to a level comparable to the 11- and 21-segment models. All such further maneuvering would likely have been of little value, since we shall simply adopt the 21-segment standard for all vertical dipole in these notes. However, we shall note in passing that the more complex the geometry of any antenna, the more important it becomes to go through the convergence process early on during the modeling task to ensure the greatest reliability possible for our results.

+

There is no need to show free-space E-plane and H-plane patterns for the vertical dipole, since they are the same as those shown for the free-space horizontal dipole. Relative to modeling software, there is a slight change of labels. For a horizontal wire, the E-plane pattern corresponds to the software designation of the azimuth pattern, while the H-plane pattern occurs on what the software calls the elevation pattern. However, we must reverse the software labels--and software place to look--for the patterns. For a vertical dipole, the E-plane pattern shows up when we request the elevation (or theta) pattern, while the H-plane pattern emerges when we call for the azimuth (or phi) pattern.

+

B. Element Diameter

+

While we are in free space, we may also confirm our expectations regarding changes in element length as we change the diameter of our vertical dipole element. Verticals for 40 meters come in many versions--some using tower structures and others using stepped-diameter tubing. Some even use wires suspended beneath tree limbs or other supports. For our checks, we may confine our sample to just a few sizes, perhaps 1" (25.4 mm), 0.5" (12.7 mm), and AWG #12 wire (0.0808" or 2.05 mm). For the test, we shall stay at 7.15 MHz and use 21 segments per element. Your results should resemble the ones in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                      Varying Vertical Dipole Diameter
+
+El. Dia.                     Resonant Length                     Free-Space           Source Impedance
+" (mm)               Feet           Meters        WL             Gain dBi             R +/- jX Ohms
+1" (25.4 mm)         66.06'         20.135 m      0.480 wl       2.13                 71.95 - j 0.09
+0.5" (12.7 mm)       66.37'         20.230 m      0.482 wl       2.12                 72.11 - j 0.05
+AWG #12              66.88'         20.385 m      0.486 wl       2.07                 73.18 - j 0.04
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Consistent with our experience derived from looking at horizontal wires, the fatter the element, the shorter the resonant length. As well, fatter wires have slightly lower resistance values, since their losses are less than for thin wires. The effects are almost negligible for the move from a 1" to a 0.5" element. However, the differences are much more noticeable with the move from either of those two elements down to the thin #12 element.

+

The table lists the element length in 3 forms, adding the wavelength-measure to our normal lengths in feet and in meters. The underlying reason is that we shall be performing some essential tests of the vertical dipole in height increments measured in fractions of a wavelength. Knowing the antenna length as a fraction of a wavelength will let you easily calculate how far the bottom of the antenna is above the ground.

+

C. Element Material

+

Before moving our vertical dipole out of free space, let's examine the effects of selecting different materials for the element. Performing the exercise in free space will accustom you to seeing the differences in a different context than the one used for the horizontal dipole (which was 1 wavelength above good ground). We may also shrink the table of materials to give us a few widely separated materials from the longer list.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Some Values of Conductivity and Resistivity for Representative Conductors
+
+Material                            Conductivity                 Resistivity
+                                    S/m                          Ohms/m
+Perfect                             ----                         ----
+Copper                              5.747E7                      1.740E-8
+6061-T6 Aluminum                    2.500E7                      4.000E-8
+Tin                                 8.772E6                      1.140E-7
+Type 302 Stainless Steel            1.389E6                      7.200E-7
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we look at both the free-space gain and the source impedance, we can tabulate the values. However, in examining the following table, remember that the resonant length of each vertical dipole came from the copper model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       Changes in Dipole Performance with Changes in Wire Conductivity
+
+Material                            Maximum Gain for Each Wire Diameter
+                                    Source Impedance (R +/- jX Ohms)
+                                    AWG #12               0.5"                 1"
+Perfect                             2.14                  2.14                 2.13
+                                    71.97 - j 1.11        71.91 - j 0.22       71.85 - j 0.85
+Copper                              2.07                  2.12                 2.13
+                                    73.18 - j 0.04        72.11 - j 0.05       71.95 - j 0.09
+6061-T6 Aluminum                    2.03                  2.12                 2.13
+                                    73.81 + j 0.52        72.21 + j 0.04       72.00 - j 0.05
+Tin                                 1.96                  2.11                 2.12
+                                    75.12 + j 1.63        72.41 + j 0.22       72.10 + j 0.04
+Type 302 Stainless Steel            1.69                  2.06                 2.10
+                                    80.26 + j 5.73        73.19 + j 0.88       72.48 + j 0.36
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table shows us everything that we should have expected. The thinner the element, the greater the loss in gain (from a perfect or lossless conductor) due to the lower conductivity value. With a 1" element, the losses through stainless steel are insignificant. However, the losses of an AWG #12 stainless steel wire become significant.

+

We may also notice a pattern to the impedance values in the table. First, the greater the material losses, the higher the source resistance. Second, as we increase the level of material losses, we also may notice a move to positive values of reactance, which would translate into a very slightly shorter resonant length for each element diameter. These effects are also related to the element diameter.

+

The final item for notice in the table is the gain of the dipole, even when using a perfect conductor. Both the AWG #12 and the 0.5" diameter dipoles show a gain of 2.14 dBi, but the 1" element shows a gain of 2.13 dBi. Because of the very small difference, it is easy to pass off the difference as a simple function of mathematical processing procedures for the core used. Indeed, in some programs, all 3 gains may be the same and in others, the 1" and 1/2" elements may show the same value.

+

However, the difference is real, even if not operationally significant. Dipole gain is also a function of the wire length. We saw with horizontal dipoles that if we lengthened a dipole beyond resonance, we encountered a slight increase in gain--and shrinking the dipole below resonance yielded a slightly lesser gain. Now compare the resonant lengths of the three vertical dipoles in free space. The 1" dipole is more than a quarter-foot shorter than the AWG #12 version, just about enough to make numerically visible the dependency of a dipole's gain on the dipole's length.

+

Perhaps a more important lesson emerges from the exercises. The gain of a wire element is not a function of its being resonant or non-resonant. Resonance is handy for numerous purposes, such as matching an antenna directly to a coaxial cable or--as in these exercise--for establishing a certain order of equivalence among models or for seeing clearly the effects of certain changes that we can make in the antenna or its operating environment. But the property of antenna gain is independent of the source impedance.

+

D. Height Above Ground

+

For our remaining trials, we shall place the 1" (25.4-mm) vertical dipole over good ground (with changes in ground quality coming a bit later). We shall not change the length from its free-space resonant value (66.06' or 20.135 m). However, we shall be placing the antenna at different heights above ground, as shown in Fig. 2.

+
+ +
+

To effect the height changes, we need only add or subtract the required amount from both ends of the dipole. The key point in the height designations will be the source position, which is the center of the dipole. To ascertain that the source position is exactly where we need it, we can employ a second wire. The wire should be short--perhaps 0.001 wavelength long--and very thin--about AWG #20 or thinner. The wire position is at least 5' (1.52 m) away from the test antenna, but even with the source height. This wire is at right angles to the vertical dipole and too small to affect any of the performance report data from the main model. However, by changing the height of both the short wire and the vertical dipole together, we obtain a confirmation that the dipole center is precisely where we want it.

+

We shall move the vertical dipole from a source or center height of 0.25 wavelength above the ground to 1.25 wavelengths above the ground. Because not all software can move a model in terms of wavelengths, the following table provides the 7.15-MHz source-point heights for the trials. For reference, 1 wavelength at 7.15 MHz is 137.56' or 41.93 m.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                         Trial Source-Point Heights
+
+              Height in      Wavelengths          Feet           Meters
+                             0.25                  34.39         10.48
+                             0.35                  48.15         14.68
+                             0.45                  61.90         18.87
+                             0.55                  75.66         23.06
+                             0.65                  89.42         27.25
+                             0.75                 103.17         31.45
+                             0.85                 116.93         35.64
+                             0.95                 130.69         39.83
+                             1.05                 144.44         44.03
+                             1.15                 158.20         48.22
+                             1.25                 171.95         52.41
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The lowest height is sufficient to place the bottom of the dipole less than a half-meter (1.36') above ground, since each side of the dipole is about 0.24 wavelength long. Since the azimuth pattern of the vertical dipole will be a circle, we may confine our interest in patterns to elevation. We shall record the maximum gain, the TO angle, and the source impedance of the antenna at each new source-point height. Results should resemble the following NEC-4 table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                   Vertical Dipole Trial Performance Data
+
+              Height         Gain          TO angle              Source Impedance
+              WL             dBi           degrees               R +/- jX Ohms
+              0.25           -.11          18                    98.16 + j 5.20
+              0.35           0.32          15                    73.52 - j 7.43
+              0.45           0.30          14                    68.44 - j 1.80
+              0.55           0.67          46                    70.32 + j 1.72
+              0.65           1.97          41                    72.82 + j 1.33
+              0.75           2.72          36                    73.13 - j 0.39
+              0.85           3.20          32                    72.00 - j 1.03
+              0.95           3.45          29                    71.26 - j 0.36
+              1.05           3.52          26                    71.57 + j 0.36
+              1.15           3.48          23                    72.21 + j 0.31
+              1.25           3.43          21                    72.34 - j 0.20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Let's begin with the source impedance data, since it is perhaps the simplest. Fig. 3 shows the data in graphical form. Once we elevate a vertical dipole's center above about 0.4 wavelength, the impedance curves smooth out. In fact, for any height above about 0.4 wavelength, it would make no operational sense to adjust the length of the dipole to effect a more precise resonance. Only when the center of the dipole is lower than about 0.4 wavelength does the impedance show significant change, and the difference from resonance (within +/- j1 Ohm) remains small. Contrast this impedance behavior with the behavior of a horizontal dipole at comparable heights, as noted in the preceding episode of this series.

+
+ +
+

Much more interesting is the gain and TO angle information in the table. If we examine only the gain column, we see a steady rise in gain until we reach 1.05 wavelengths above ground. However, if we combine the gain and TO data, we discover a much more varied situation. Between the 0.45- and 0.55 wavelength level, the TO angle jumps from 14 degrees to 46 degrees. Since very little in antenna work shows a sudden large change, there must be an explanation to account for the change in the numbers, one that shows an evolution to the elevation pattern of the vertical dipole as we increase its height.

+
+ +
+

Fig. 4 samples the elevation pattern at various interesting heights, and you may fill in the missing heights with your own software. Only at 0.25 wavelength does the vertical dipole elevation pattern show a single lobe. At 0.35 wavelength, a second lobe emerges, initially as a bulge that is just recognizable as a second lobe. However, by 0.45 wavelength, the lobe has grown to serious proportions. We may pause here to note that this type of pattern evolution is common to many, if not most, vertically polarized antennas, not just to the vertical dipole. Many of the users of such antennas have two goals for the installation: to emphasize the low angle radiation (and reception), and to eliminate as much interferences as possible arriving at high angles from shorter distances. Hence, they prefer patterns like those at the two lower levels over the pattern for 0.45 wavelength, despite the lower gain level. The exact wire height required for a given vertically polarized array may differ somewhat from the one required for a vertical dipole. Hence, each vertical array needs careful planning (and modeling) to assure that it is at a height within the range of desirable heights.

+

If we extrapolate from the 0.45 wavelength level, we can imagine the secondary lobe continuing to grow until it becomes the lobe with maximum gain. Fig. 4 skips to the 0.75 wavelength level to illustrate a second elevation pattern phenomenon: the merging of elevation lobes. As the elevation angle of the secondary lobe decreases, its vertical beamwidth does not narrow appreciably. Nor does the beamwidth of the lowest lobe decrease either in angle or beamwidth by any large amount. (Again, contrast this lobe behavior with lobe behavior for the horizontal wire in the preceding column.) The result is a merging of lobes into a "butterfly wing" appearance, which reaches it peak for 2 lobes at about 0.75 wavelength for our vertical dipole.

+

Above 0.75 wavelength, we see the emergence of a 3rd lobe, already well developed in the 1.05 wavelength pattern. This height, relative to our trial heights, shows the maximum gain for the second lobe. By 1.25 wavelengths above ground, the 3rd lobe is large enough that the gain in the second lobe is reduced by a small amount. However, we should note one more phenomenon. The lower two lobes are merging almost into one. The differential in gain between the two lobes is very small. At 10 degrees above ground, the gain is 2.61 dBi, well above the gain levels with the antenna closer to ground. Of course, elevating a vertical dipole to a center height of 1.25 wavelengths is not practical at 40 meters. However, much higher center heights are common at VHF, where a vertical dipole gives a good account of itself in omni-directional point-to-point communications.

+

Let's return to heights closer to the ground. We saw two interesting items in the table below the 0.55 wavelength mark. First was the sudden transition of maximum gain from the lower lobe to the upper lobe, a transition we now know to be a gradual transition in lobe development. Second, was the fact that at a height of 0.45 wavelength, the gain was lower than at 0.35 wavelength. Whenever we encounter such phenomena, we should take a more detailed look at the region. The following table gives the results every 0.05 wavelength from 0.25- to 0.50 wavelength above ground.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                            Vertical Dipole Trial Performance Data at Low Heights
+
+              Height         Gain          TO angle              Source Impedance
+              WL             dBi           degrees               R +/- jX Ohms
+              0.25           -.11          18                    98.16 + j 5.20
+              0.30           0.12          17                    81.52 - j 7.39
+              0.35           0.32          15                    73.52 - j 7.43
+              0.40           0.35          14                    69.62 - j 4.78
+              0.45           0.30          14                    68.44 - j 1.80
+              0.50           0.22          13                    68.98 + j 0.50
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The source impedance information follows the curves shown in Fig. 3. Let's focus on the gain and TO angle data and graph it. See Fig. 5. The gain peaks at a height of 0.4 wavelength. Although the TO angle continues to descend slowly above that level, the gain decreases.

+
+ +
+

Fig. 6 provides 3 elevation patterns that show why this decrease occurs. The second lobe of a vertical dipole does not emerge as a narrow-beamwidth lobe, but instead as a large region of radiation (or reception sensitivity). At a height of 0.5 wavelength, the second lobe--even though weaker in terms of maximum gain--contains a great deal of the antenna's energy, as indicated by its large area. Remember that this elevation pattern would be the same regardless of the azimuth bearing, so in 3-dimensional terms, the second lobe already dominates the vertical dipole radiation pattern. The only source for that large increase in energy is from the lower lobe.

+
+ +
+

Lobe development for vertically polarized antennas is so different from the lobe development of horizontally polarized antennas that it requires detailed study, if one is to acquire reasonable expectations of vertical antenna behavior. These initial systematic exercises only form a start to the process.

+

E. Element Length

+

When we examined horizontal wires, we explored length changes in small increments. For our vertical dipole, we shall use much larger increments. First, set the center of the 1" (25.4-mm) dipole at a height of 0.8 wavelength (110.05' or 33.54 m). This height will allow us to extend each end of the antenna in 0.125 wavelength (17.20' or 5.24-m) increments, thus extending the total antenna length in quarter wavelength increments. We shall start with the free-space resonant length, which is 0.48 wavelength, just shy of the perfect 0.5 wavelength mark, but using the resonant length will start us on familiar ground. The longest antenna length that we shall examine, 1.5 wavelength, will still clear the ground by 0.05 wavelength without moving the antenna center point.

+

For each change of length, we shall increase the number of segments by 10. The resulting segment lengths will therefore be close to the same for each new model. If we perform the exercise, we obtain a table that should resemble the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                    Extending the Vertical Dipole Length
+
+                     Length         Gain          TO Angle       Source Impedance
+                     WL             dBi           degrees        R +/- jX Ohms
+                     0.50           2.99          34             72.62 - j 0.09
+                     0.75           2.45          32             497.0 - j 829.9
+                     1.00           2.05          10             1922  - j 1621
+                     1.25           2.62           9             144.6 - j 612.8
+                     1.50           5.65          41             135.8 + j 35.85
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Fig. 7 can assist us in interpreting the data by relating it to the corresponding elevation patterns. The first two antenna lengths have high elevation angles, indicating that the maximum gain is in the second lobe. However, by a length of 1 wavelength, the maximum gain lies in the lowest lobe. Maximum low-angle gain appears with a length of about 1.25 wavelengths. When we extend the length further, the lowest lobe almost disappears, and virtually all of the energy appears in the upper lobe that we just saw emerging with the 1.25 wavelength version of the antenna.

+

We may correlate in a general way the information in this table and figure with what we may already know about horizontal wires. In that arena, antennas maintained a broadside azimuth lobe up through and past a length of 1 wavelength. As we increase the length of the horizontal antenna, the broadside lobe continues to increase in strength and to narrow in beamwidth, although new lobes gradually appear at angles to the main broadside bearing. By the time we reach a length of 1.5 wavelengths, the broadside lobe has severely diminished as the angular lobes dominate the pattern.

+

Turning the array on end to make a center-fed vertical antenna creates a comparable set of radiation phenomena, but translated to the elevation pattern and taking ground reflections into account in lobe formation. We achieve maximum low-angle gain at about 1.25 wavelengths. At a length of 1.5 wavelengths, the antenna becomes almost useless for low angle communications. Since vertical doublets are sometimes used as multi-band antennas, the lesson is not to use one that is longer than about 1.25 wavelengths at the frequency of operation. If you find it necessary to operate where the antenna would be longer, it is likely time to set up a second vertical dipole.

+

F. Ground Quality

+

Because vertically polarized radiation tends to enter more deeply into the ground than horizontally polarized antenna radiation, verticals tend to be more sensitive to changes in the quality of the ground. Therefore, let's do a small survey of the effects of ground quality on antenna performance with our 1" (25.4-mm) vertical dipole. We shall use the same categories of ground quality that we employed for the horizontal wire.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           Some Useful Soil Types
+
+              Soil Type                    Conductivity                 Permittivity
+                                           S/m                          (Dielectric Constant)
+              Very Poor                    0.001                         5
+              Poor                         0.002                        13
+              Good                         0.005                        13
+              Very Good                    0.0303                       20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

To see whether height above ground makes a difference in the range of performance from the best to the worst soils, we shall perform the trial twice, once with the center of the dipole at a height of 0.25 wavelength, and again with the center at a height of 0.5 wavelength (the highest level at which the lower lobe dominates over good ground). We shall record the gain, TO angle, and source impedance and arrive at a table that resembles the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                         Changes of Vertical Dipole Performance with Ground Quality
+
+Center Height: 0.25-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -.74          21                    91.80 + j 1.63
+              Poor                  0.22          19                    96.04 + j 5.35
+              Good                  -.11          18                    98.16 + j 5.20
+              Very Good             1.94          15                    101.7 + j 8.80
+
+Center Height: 0.5-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             1.37          16                    69.97 + j 0.60
+              Poor                  1.13          14                    69.26 + j 0.35
+              Good                  0.22          13                    68.98 + j 0.49
+              Very Good             1.25          10                    68.13 + j 0.21
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

At the lower height, the source impedances show a maximum variation of 10 Ohms resistance and j7 Ohms reactance. At the higher level, the source impedance differences are under 2 Ohms resistive and less than j0.5 Ohm reactive. This data provides the suggestion that the higher above ground that we place a vertical dipole, the less the effect of the ground in the immediate area of the antenna on the source impedance.

+
+ +
+

To gain a handhold on the gain and TO angle data, Fig. 8 provides overlaid patterns of the lower-level antenna over the 4 ground types. We can clearly see the increase in TO angle with a decrease in soil quality. The gain is another matter, since the table shows shifts above and below 0 dBi. However, except for the gain over very good soil, the actual patterns are tightly clustered. However, the gain over good soil is lower than the gain over poor soil, which may initially seem unexpected. NEC calculates the effects of ground quality by creating a single composite value from the conductivity and permittivity values in the tables. The method of combining them results in a slightly higher far-field loss for good soil than for poor soil. Operationally, the difference could not be noticed, assuming that we could ascertain that our soil in fact met the condition for either good or poor soil in the table.

+
+ +
+

Fig. 9 overlays the elevation patterns for the upper-level antenna over each of the 4 soil types. The entire series is interesting, since it samples patterns with two elevation lobes. Perhaps the first notable feature is the face that, if the soil is very good, then the lobe structure of the elevation pattern is more distinct than for any of the lesser soil qualities. We see the familiar increase in TO angle with decreasing soil quality. As well, the good soil pattern has lower gain than the poor soil pattern. However, what may surprise us most is that the highest gain occurs with the antenna over very poor soil. The advantages of finding a location with very good soil dwindle as we elevate the antenna further above the ground.

+

We may fairly ask whether a ground radial system beneath the vertical dipole will improve its performance. Unfortunately, neither NEC-2 nor MININEC permit buried radials. The closest that we can come in these programs is to place a radial system at about 0.001 wavelength above ground, a procedure available in NEC, but generally not recommended for MININEC. We shall use 64 radials to create a radial system about as large as amateurs ever use, larger than most in operation, but shy of commercial broadcast standards. Smaller radial systems will have lesser effects than those shown, but larger ones will not change the results significantly. With the radials in place, we can re-run the trials for both the lower and higher antenna positions over the 4 soil types. The table we develop will be similar to the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Changes of Vertical Dipole (Plus Radials) Performance with Ground Quality
+
+Center Height: 0.25-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -.20          21                    85.88 + j 11.60
+              Poor                  0.56          19                    90.60 + j 10.75
+              Good                  0.18          18                    91.68 + j  8.88
+              Very Good             1.95          15                    98.69 + j  8.00
+
+Center Height: 0.5-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             1.41          16                    70.33 + j 0.71
+              Poor                  1.17          14                    69.50 + j 0.44
+              Good                  0.26          13                    69.17 + j 0.64
+              Very Good             1.25          10                    68.14 + j 0.32
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In no case did the radial system model change the TO angle of any of our trials. At the higher level, the maximum impedance difference made by the radials was about 1/3-Ohm. The maximum gain difference was 0.04 dB. Hence, the radials prove to be ineffective in improving the performance of a vertical dipole placed a half wavelength over ground at its center, with the tip about 1/4 wavelength above ground.

+

The lower antenna shows some signs of improvement for soils worse than very good, where differences are not significant with and without the radials. Gain increases with decreasing soil quality, with a maximum improvement of about 0.5-dB for very poor soil. We would expect more significant changes in source impedance, since it is largely a function of soil in the immediate antenna area. Here we find that the source resistance decreases by about 6 Ohms on average, suggesting lower ground losses.

+

As a side note, we may re-run the lower-level antenna over a 64-radial field buried a half-foot under the soil, if we have NEC-4. I am adding this exercise, since it provides a check on the adequacy of the model that uses a slightly elevated field to simulate buried radials. Our buried radial version produces the following results.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              Changes of Vertical Dipole (Plus Buried Radials) Performance with Ground Quality
+
+Center Height: 0.25-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -.02          22                    89.42 + j 15.40
+              Poor                  0.71          19                    95.29 + j 15.00
+              Good                  0.35          18                    96.14 + j 13.16
+              Very Good             2.09          15                    100.7 + j 11.75
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The buried radial system show less change in source resistance relative to the antenna with no radials than did the system with elevated radials. However, the effects upon the reactance result in a relatively uniform "detuning" effect, with similar reactance levels for all 4 soil types. Gain increases vary from 0.15 dB for very good soil to 0.72 dB for very poor soil. These values do not change for moderate changes in the depth of the radial field.

+

The result is that the NEC-2 simulated buried radial field only partially captures the effects of buried radials as modeled in NEC-4. For some operational planning and analysis needs, the NEC-2 radials may be perfectly satisfactory; for other needs, they may fall short. A final reminder is in order: the 64-radial field is large. Any smaller fields will have lesser affects upon the performance of the low-level vertical dipole.

+

Conclusion

+

We have run a number of systematic modeling studies on vertical dipoles to become familiar with their properties. A more complete set of exercises would include the same trials for vertical dipoles for many frequencies, from MF through at least high HF. As well, the are numerous other systematic tests that are possible with the modeling software for this basic antenna. This episode simply shows a few of the many paths of study that are possible in the process of developing reasonable expectations of the vertical dipole--and antennas based upon it.

+

However, as incomplete as the work may be, we shall move on. There is another basic vertical antenna type that needs attention long before we look at more complex antennas: the vertical monopole. That will be our subject next time.

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+

Go to Main Index

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+

79. Developing Antenna Expectations Using Modeling Software

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Last month, we examined the vertical dipole. This month, we shall explore its half-brother, the vertical monopole. Actually, we shall divide our work in two, examining fraternal twins: the elevated vertical monopole with an attached ground plane and the ground-mounted vertical monopole with a ground plane on or under the soil. By starting with the elevated monopole, we can begin the sampling as we did for every other episode in this series: in free space.

+

As always, we shall look systematically at a number of antenna properties that modeling software can unfold for us.

+
+ A. Elevated vertical monopole +
+ 1. Monopole development +

2. Height above ground

+

3. Ground quality

+
B. Ground-mounted monopole +
+ 1. Perfect vs. lossy ground +

2. Radial density

+

3. Buried radials

+

4. Radial length

+

5. Vertical length

+
+
+

Coverage will be incomplete, but by combining our explorations with those you have acquired from past episodes, you can produce your own complete survey.

+

A. Elevated Vertical Monopoles

+

Elevated vertical monopoles generally consist of a vertical element approximately 1/4 wavelength long. To the base of this element goes the center conductor of a coaxial feedline cable. The braid of the cable connects to a symmetrical set of radials extending usually at right angles to the vertical element. Because we think of the coaxial cable braid as being grounded and serving as a shield, we often think of the antenna as consisting of a vertical radiating element and a relatively inert "counterpoise." Nothing could be farther from the truth. Every part of the antenna structure radiates and is active in yielding the performance that emerges from a vertical monopole.

+

1. Monopole Development

+

To understand the elevated vertical monopole, we may begin where we left off last month: with a vertical dipole. Then we can proceed to develop the vertical monopole out of that antenna, as suggested by Fig. 1.

+
+ +
+

Let's begin our work on 2-meters, 146 MHz, to be more precise. Verticals are used at all frequencies, from LF through UHF, so a VHF example is suitable for our work. We shall use 0.25" (6.35-mm) aluminum as our material for both the vertical element and, eventually, for ground plane radials. Since we wish to have a baseline against which to compare our development, let's use the vertical dipole. In free space, a resonant 1/2 wavelength vertical dipole will have the properties shown in the following brief table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                          Vertical Dipole:  146 MHz
+
+                             Diameter:                    0.25"         6.35 mm
+                             Length:                      38.1"         967.74 mm
+                             Free-space gain              2.13 dBi
+                             Source impedance
+                               R +/- jX:                  72.11 + j 0.35 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For all of our work on 2 meters, we shall expressed dimensions in inches and millimeters. My tables emerge from NEC-4 models, so the exact figures produced by your model may differ slightly. But as always, the trends will remain good for any version of NEC-2 or MININEC. The patterns for the free-space vertical dipole are identical to those we discussed in the preceding column.

+

We may view a vertical monopole with a ground plane attached as simply an adapted vertical dipole. We retain the upper portion of the dipole--about 1/4 wavelength long--and revise the lower half of the vertical element. Instead of a single wire, we construct a symmetrical set of spokes or radial elements, connected together at the source and extending at right angles to the upper portion of the element. We may use any number of radial elements, but 4 has proven sufficient for highly predictable performance.

+

In constructing our initial vertical monopole, we shall use a fixed vertical length that is 1/2 the length of the vertical dipole. Then we shall add 4 radials. The radial lengths will be equal and set to achieve 2 goals. First, we wish to achieve resonance. Second, we wish the current to divide equally, not only among the radials, but also between the two halves of the assembly. The current at the base of the vertical element, where we place the modeling source, should equal the sum of the currents on the innermost segments of the radials. The result of our work will resemble the following model in both dimension and performance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           First Model: Vertical Monopole with 4 Radials:  146 MHz
+
+                     Diameter:                            0.25"         6.35 mm
+                     Vertical Length:                     19.05"        483.87 mm
+                     Radial length:                       23.7"         601.98 mm
+                     Free-space gain                      1.01 dBi
+                     Relative radial current:             0.249
+                     Source impedance
+                       R +/- jX:                          23.17 + j 0.12 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table should raise many questions. The first concerns a mythology attaching to vertical monopoles that lists their resonant source impedance as about 35-36 Ohms. That value holds true of 1/4 wavelength vertical radiators over and connected to perfect ground. However, the elevated vertical monopole with ground plane has a much lower impedance. What we build, we can rebuild as soon as we examine a second question: Why is the gain so low?

+

A conventional and wrong answer to this question is that only the vertical portion of the antenna is radiating. In fact, all parts of the antenna radiate. However, the symmetrical portion of the assembly radiates in such a way, due to the symmetry of the radials, that the radiation almost cancels. See Fig. 2.

+
+ +
+

The "azimuth" or H-plane pattern shows the total far field along with its horizontal and vertical components. The vertical component is invisible behind the black line showing the total field. The horizontal component appears in blue at the center of the pattern in the form of 8 very small lobes. It is the remnant calculable radiation after cancellation among the fields produced by each of the 4 radials. Over ground, the horizontal component of the total field will be slightly stronger, but never strong enough to alter the dominantly vertical polarization of the antenna.

+

Our initial model of the vertical monopole actually has radials that are longer than the vertical element. We can approach more conventional dimensions by lengthening the vertical element a bit and shortening the radials. The work would result in the following model--and its performance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Second Model: Vertical Monopole with 4 Radials:  146 MHz
+
+                     Diameter:                            0.25"         6.35 mm
+                     Vertical Length:                     20.15"        511.81 mm
+                     Radial length:                       19.00"        482.60 mm
+                     Free-space gain                      1.34 dBi
+                     Relative radial current:             0.250
+                     Source impedance
+                       R +/- jX:                          24.66 - j 0.30 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model achieves an almost perfect current equality between the upper and lower halves of the assembly. It also yields a vertical element a bit longer than the radials. However, the source impedance remains under 25 Ohms at resonance.

+

We did increase the gain by about a third of a dB, a function of lengthening the vertical portion and shortening the radials. Perhaps we can further lengthen the vertical element and achieve the "ideal" 35-Ohm vertical monopole. The results appears in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           Third Model: Vertical Monopole with 4 Radials:  146 MHz
+
+                     Diameter:                            0.25"         6.35 mm
+                     Vertical Length:                     23.45"        595.63 mm
+                     Radial length:                       10.00"        254.00 mm
+                     Free-space gain                      1.68 dBi
+                     Relative radial current:             see text
+                     Source impedance
+                       R +/- jX:                          34.94 + j 0.51 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The vertical element is longer and achieves a higher gain than the preceding vertical monopole models. However, the vertical portion of the assembly is not a resonant 1/4 wavelength element. Rather, it is longer than 1/4 wavelength, as indicated by the fact that the current peaks above the feedpoint segment in the model. Note that to do this analysis, we are examining data that we have not checked with other models in this series of exercises: the element current. There is no intrinsic harm or fault attached to this situation--only a name change. Rather than being the analog of a vertical dipole, the new monopole is an analog of an off-center-fed 1/2 wavelength element.

+

Since we have a procedure for producing a 35-Ohm monopole assembly, we may as well go all the way to a 50-Ohm assembly. The results should resemble those in the following table, as we continue to extend the vertical element and shrink the length of the radials.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Fourth Model: Vertical Monopole with 4 Radials:  146 MHz
+
+                     Diameter:                            0.25"         6.35 mm
+                     Vertical Length:                     26.30"        668.02 mm
+                     Radial length:                        6.25"        158.25 mm
+                     Free-space gain                      1.83 dBi
+                     Relative radial current:             see text
+                     Source impedance
+                       R +/- jX:                          50.55 - j 0.09 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The antenna is highly off-center-fed, since the current reaches its peak value about 20% of the way up the vertical element. We achieved a 50-Ohm source impedance. However, you may find that the dimensions are a bit more finicky to pick out as we shorten the radials to about a third of the length of those used in the initial model.

+

The exercise is designed to remove some common misconceptions about elevated vertical monopoles. The vertical monopole can be derived from the vertical dipole without reference to ground, either real or perfect. The H-plane pattern establishes that all parts of the assembly are active radiators, although the radiation from the radials almost cancels completely. We can make the monopole--within the initial 1/2 wavelength total size--any length we wish in order to effect a desired source impedance, and the resulting increase in vertical element length tends to increase the overall gain of the assembly.

+
+ +
Before we leave free space for an environment closer to the ground, let's examine an intermediate step between the vertical dipole and the vertical monopole with radials extending at right angle from the vertical element. We may slope the radials at any angle downward from the right-angle plane, as suggested by the middle portion of Fig. 3. If we select an angle of about 45 degrees, we can obtain a vertical monopole that takes up less radial room while using a shorter vertical element. As well, the array will have a 50-Ohm resonant impedance, equal current division between upper and lower parts, and a slightly higher gain than we have so far obtained. The following table summarizes the design. + 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                             Vertical Monopole with 4 Sloping Radials:  146 MHz
+
+                     Diameter:                            0.25"         6.35 mm
+                     Vertical Length:                     18.70"        474.98 mm
+                     Radial length (see text):            18.50"        469.90 mm
+                     Free-space gain                      1.98 dBi
+                     Relative radial current:             0.251
+                     Source impedance
+                       R +/- jX:                          51.24 + j 0.48 Ohms
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the radials are 18.5" (469.9 mm) long, they use only 13.08" (332.23 mm) distance from the vertical centerline of the assembly. Of course, they also extend downward by the same distance, since we set them at a 45-degree downward angle. Sloping radials are a standard technique in vertical monopole construction to obtain a system that shows a good match to common 50-Ohm coaxial cables.

+

Even though the vertical element is shorter than the other 50-Ohm model, we obtain slightly higher gain. Actually, the vertical element in this model does not end at the feedpoint or base of the exactly vertical element. It extends downward to the lower tips of the sloping radials.

+
+ +
+

As Fig. 4 shows, the horizontal component of radiation from the radials remains well-canceled. However, the radials also have a vertical dimension, and the radiation in that plane does not cancel. Rather, it contributes to the overall vertically polarized radiation of the entire assembly from top to bottom. Not only are the radials not an inert counterpoise, they are an essential active ingredient in the vertical monopole and necessary to make it function in the desired manner.

+

2. Height Above Ground

+

We shall omit from these notes certain exercises that you should perform for yourself. For example, check the performance of the vertical monopole in free space using various materials, as we did for the vertical dipole. In addition, perform frequency sweeps across the 4 MHz of the 2-meter band for each model to determine the operating bandwidth, not only relative to SWR, but also with respect to other performance parameters. To save a bit of column space for ground-mounted vertical monopoles, we shall leap to an examination of the vertical monopole at various heights above ground.

+

For the exercise, we shall use the version of the monopole with a 20.15" (511.81-mm) vertical element. From that model, we obtained a free-space gain of 1.34 dBi and a source impedance of 24.66 - j 0.30 Ohms. Our first test will cover a broad swath: from 0.5 to 5 wavelengths in height in 0.5 wavelength increments. This coverage reflects the fact that VHF vertical monopoles are used at many heights, depending upon operating circumstances. For reference, 1 wavelength at 146 MHz is 6.737' or 2.053 m. We shall use good ground (conductivity: 0.005 S/m; permittivity: 13). The antenna height will reflect the distance between ground and the base or feedpoint of the assembly. The results yield the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       Vertical Monopole Performance vs. Height Above Ground:  146 MHz
+
+       Height Above Ground                 Gain           TO Angle      Source Impedance
+       WL     Feet           Meters        dBi            degrees       R +/- jX Ohms
+       0.5     3.368          1.027        1.42           45.3          25.04 + j 0.43
+       1.0     6.737          2.053        2.61            9.1          24.72 - j 0.08
+       1.5    10.105          3.080        3.65            7.0          24.69 - j 0.19
+       2.0    13.474          4.107        4.33            5.6          24.68 - j 0.23
+       2.5    16.842          5.133        4.81            4.7          24.67 - j 0.26
+       3.0    20.210          6.160        5.16            4.1          24.67 - j 0.27
+       3.5    23.579          7.187        5.42            3.6          24.67 - j 0.28
+       4.0    26.947          8.213        5.63            3.2          24.67 - j 0.28
+       4.5    30.316          9.240        5.79            2.8          24.67 - j 0.29
+       5.0    33.684         10.267        5.93            2.6          24.66 - j 0.29
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table of performance values vs. height uses an elevation angle increment of 0.1 degrees rather than the more usual 1.0-degree increment. As we raise an antenna above 1 wavelength, the rate of change of TO angle with each change of height decreases. If we want to know the maximum gain, using 1-degree angle intervals may not yield a reliable answer, since the width of the lobe may be narrow, and a few tenths of a degree difference in angle may show as much as a half-dB difference in gain. The higher the antenna, the more critical it becomes to use the finest elevation angle increment available on the software.

+

The vertical monopole shows nothing unexpected. The source impedance is virtually constant, regardless of height within the table's range. The lowest lobe is strongest for all but the 0.5 wavelength height, and the progressions of gain and TO angle are normal in every way.

+

We should investigate the performance of the same vertical monopole in the lower height region, using heights comparable to those used with the vertical monopole in the preceding column. The results appear in the following table, although the physical heights are listed in terms of inches and millimeters. For reference, at 146 MHz, a wavelength is 80.8415" or 2053.37 mm.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       Vertical Monopole Performance vs. Height Above Ground:  146 MHz
+
+       Height Above Ground                 Gain           TO Angle      Source Impedance
+       WL     Inches         mm            dBi            degrees       R +/- jX Ohms
+       0.25    20.21          513.3        1.25           16.0          23.19 - j 2.06
+       0.35    28.29          718.7        1.26           14.1          23.28 + j 0.08
+       0.45    36.38          924.0        1.19           13.2          24.55 + j 0.67
+       0.55    44.46         1129.4        1.79           42.4          25.28 - j 0.03
+       0.65    52.55         1334.7        2.29           37.6          25.06 - j 0.65
+       0.75    60.63         1540.0        2.57           33.7          24.51 - j 0.68
+       0.85    68.72         1745.4        2.63           35.9          24.33 - j 0.29
+       0.95    76.80         1950.7        2.53           27.7          24.58 - j 0.05
+       1.05    84.88         2156.0        2.71            8.7          24.83 - j 0.16
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As we did in the first table, we used good ground beneath the vertical monopole for the test. The range of source resistance values is only 2.09 Ohms, and the range of source reactance is only 2.73 Ohms, despite the great range of heights. The antenna shows a high TO angle from a height of 0.55 wavelength through a height of 0.95 wavelength. You may wish to compare this table with the corresponding table for the vertical dipole in the last episode, understanding that the heights in the two tables mean two different things. The vertical dipole heights mark the height of the dipole center, while the monopole heights mark the base of the antenna. However, in both cases, the height represents the antenna feedpoint.

+

For both antennas, 0.55 wavelength marks the beginning of the high TO angle or the dominance of the second elevation lobe. However, the vertical dipole does not return to the dominance of the lowest lobe within the limit of the table, 1.25 wavelength. Still, the tables are not directly comparable in detail, since one antenna is for 7.15 MHz and the other is for 146 MHz. You may wish to create either a 146-MHz vertical dipole or a 7.15-MHz vertical monopole to produce a more exacting comparison.

+

3. Ground Quality

+

The are some correlations between the behavior of a vertical dipole and an elevated vertical monopole, but they are not universal. Hence, we cannot assume that the behavior of the vertical monopole over different ground qualities will replicate the work we did with the dipole. We need to give the monopole its own trials.

+

For this test, we shall alter the vertical monopole to one for which the trials might be more useful in guiding practical antenna work. We shall use a 10-meter (28.4-MHz) vertical monopole with a vertical element that is 8.75' (2.667 m) long with a 1" (25.4-mm) diameter. The radials will be 0.25" (6.35 mm) in diameter and 8.0' (2.438 m) long. The material is aluminum. At 28.4 MHz, a wavelength is 34.63' (10.56 m), and we find 10-meter verticals mounted at all heights from near the ground to a full wavelength above the ground (usually on rooftops). Therefore, we shall check our vertical monopole at base heights of 0.25, 0.5, 0.75, and 1.0 wavelength.

+

We shall use the same ground qualities as in the past, as shown in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           Some Useful Soil Types
+
+              Soil Type                    Conductivity                 Permittivity
+                                           S/m                          (Dielectric Constant)
+              Very Poor                    0.001                         5
+              Poor                         0.002                        13
+              Good                         0.005                        13
+              Very Good                    0.0303                       20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

With these soil qualities, we obtained the following results for the 10-meter vertical monopole.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                        Changes of Vertical Monopole Performance with Ground Quality
+
+Base Height: 0.25-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             1.11          19                    23.24 - j 0.70
+              Poor                  1.29          16                    23.05 - j 1.34
+              Good                  1.04          16                    22.95 - j 1.34
+              Very Good             0.73          14                    22.63 - j 1.76
+
+Base Height: 0.5-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             2.01          15                    24.72 + j 0.96
+              Poor                  1.54          46                    24.75 + j 1.21
+              Good                  1.64          45                    24.79 + j 1.21
+              Very Good             2.57          44                    24.89 + j 1.38
+
+Base Height: 0.75-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             3.09          12                    24.29 + j 0.01
+              Poor                  2.70          34                    24.28 + j 0.10
+              Good                  2.76          33                    24.26 + j 0.10
+              Very Good             3.83          32                    24.21 + j 0.23
+
+Base Height: 1.0-Wavelength
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             3.81          10                    24.46 + j 0.62
+              Poor                  2.71           9                    24.46 + j 0.69
+              Good                  2.64          26                    24.47 + j 0.69
+              Very Good             3.83          25                    24.50 + j 0.74
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the source impedance is stable at every height over the range of soil types, it grows perceptibly more stable as we increase the height. The chief interesting elements in the table are the gain and corresponding TO angle values. At 0.25 wavelength, the lower lobe dominates for every soil types. However, above the height, only over very poor soil does the lower lobe dominate. As we move upward with the antenna base, we see a gradual return to lower lobe domination from worse to better soils, but the picture is only suggested by the table. You may wish to do further trials at 1.25 wavelength and above to discover at what point the lower lobe returns to domination for good and very good soils.

+

The gain values are also interesting, since they do not correlate directly with soil type. At heights from 0.5 wavelength to 1.0 wavelength, the antenna over very poor soil is superior to all but very good soil, and at the lowest height shown, poor soil takes gain honors. The differences are of only marginal operational interest--much less interest than the TO angle--but the trends will likely seem surprising relative to common assumptions about vertical monopoles.

+
+ +
+

To better gauge the importance of the tabular data, you may wish to overlay elevation patterns at each height for the 4 soil types. Fig. 5 shows the patterns at a height of 0.25 wavelength above ground. As in all of the overlays that you will obtain from these trials, the patterns for good and poor soil are virtual clones of each other. The pattern for very good soil shows the more distinct differentiation of the lower and the emerging second lobe. In contrast, the pattern for very poor soil does not show a distinct second lobe at all. In all cases, the vertical beamwidth is large enough that there is likely to be little detectable difference in the performance of the antenna with a change in soils.

+
+ +
+

As we move to a height of 0.5 wavelength above ground, Fig. 6 provides the relevant elevation patterns. Only over very poor soil is the development of the second lobe sufficiently retarded to allow the lower lobe to dominate in terms of maximum gain. As we improve soil quality, the upper lobe increasingly dominates over the lower lobe. Over poor and good soils, there is not a very great difference in the maximum gain for each lobe. However, over very good soil, the high-angle lobes has a considerable advantage over the lower lobe. As well, since all of the plots use the same gain scale, the lower lobe of the "very-good soil" pattern is weaker than for the other antenna environments.

+
+ +
+

In Fig. 7, we can find the first emergence of the third lobe, although it is not clearly identifiable in the pattern for very poor soil. In that pattern, the lowest lobe continues to have the maximum gain. In all of the patterns, the lower two lobes have begun to merge. Over poor and good soil, the two parts of the merged lobe have nearly the same strength. However, over very good soil, the lower component of the merged elevation lobe remains considerably weaker than the upper lobe. Hence, higher-angle radiation (and reception) dominates the antenna's performance.

+
+ +
+

In our final set of overlaid patterns--Fig. 8--at 1.0 wavelength above ground, we find that the third lobe has become very distinct in all of the patterns. Over good and poor soil, the merged lower lobes have very nearly equal strength--too near to make a difference. However, the pattern for very poor soil continues to show the clear dominance of the lowest lobe--virtually to the same degree that over very good soil, the upper lobe continues to dominate. Indeed, one must wonder how high one might have to raise the antenna over very good soil before the TO angle comes down to the level of the lower lobes of the patterns over other soil types.

+

These patterns should accomplish two goals. First, they should serve to question some of the assumptions that we may be inclined to bring to the study of vertical monopoles. With the proper systematic use of our modeling software, we may set aside assumptions and allow the data to develop as it will. Second, the patterns should prepare us for the highly complex sets of elevation lobes that we encounter when taking patterns of antennas set at considerable heights, when measured in terms of wavelengths.

+

We have spent considerable space looking at elevated vertical monopoles, and still many questions remain for you to explore on your own. What is the effect of using either fewer or more radials in the ground-plane system? What is the effect of the relative diameters of the vertical element and the radials on the required lengths of each for resonance? How would a vertical monopole with sloping radials perform at various heights and over different soils? Would it perform more like a vertical dipole or like the vertical monopoles that we have explored in this column? Are there differences of performance that are directly frequency related that we might detect by using directly scaled antennas? These are only a few of the questions unanswered by this small beginning in the systematic study of elevated vertical monopoles.

+

I had hoped to include in this episode a considered look at ground-mounted vertical monopoles. There are not only questions of performance expectations to develop, but as well a host of modeling questions to consider. Hence, to be fair to the ground-mounted vertical monopole, I shall have to wait until next time. Until then, you have time to work on the unanswered questions that I left behind for elevated vertical monopoles.

+
+ +

+

Go to Main Index

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+

8. Modeling Wire Arrays

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Wire arrays present the modeler with some challenges and some opportunities to overlook obvious errors in modeling. They also tend to make us use almost all of the resources available within antenna modeling programs. So let's look at this class of antennas and explore a few useful techniques and cautions. +

Basic Concepts

Bi-directional wire arrays comprise a class of antennas composed of multiple 1/2 wl antenna elements arranged to produce antenna patterns that serve specific purposes. If we adopt the 1/2 wl resonant length of wire as our basic unit, then we can make sense out of the operative vocabulary of bi-directional wire arrays. The key questions are 2: a. How are the elements arranged relative to each other? b. With a given arrangement, what is the main axis of radiation? +
+ +
+

Figure 1 shows three basic arrangements that yield the fundamental categories within which these arrays are specified. Elements are collinear when they are arranged end-to-end so that the main radiation lobes are tangential to the wire. The ends may touch, as in the illustration, or they may be separated by a phasing section, a length of wire or transmission line that alters the current phase and magnitude at the point of junction. Ordinarily, these lines are used to increase the strength of the main radiation lobes.

+

When elements are parallel to each other, in a plane that is parallel to the ground surface, and the strongest radiation lobes are tangential to the wires, we have an End-Fire array. Most commonly for bi-directional arrays, the two elements are fed 180 degrees out of phase with each other.

+

A Broadside array places elements (normally) in a vertical plane, with the main radiation lobe again tangential to the wires. In this configuration, we feed the wire elements in phase with each other.

+

Most bi-directional wire arrays use combinations of these techniques. For most applications, a 1 wl wire is the shortest collinear element having sufficient gain to use in either a broadside or end-fire array. Longer elements, such as the 1.25 wl extended double Zepp (EDZ), are commonplace. Moreover, we may combine both end-fire and broadside techniques into single arrays. For many of the bi-directional array designs, absolute precision of wire length is less important than with other types of antennas. A 5% variation in the length of a 1/2 wl element may make little difference to the performance of the array. Indeed, as arrays grow larger, modeling does not so much determine an exact construction version as it looks at trends in both performance and source impedance to guide field adjustment of the physical antenna. In addition, we should not expect source impedances that are ready matches to a 50-Ohm system feedline. Instead, we shall find a wide variety of source impedances that challenge us to develop feed networks.

+

Although bi-directional arrays date from the earliest days of radio communications, they reached a zenith of design effort in the 1930s as short wave broadcasting became commonplace. Great "antenna farms" involving acres of land emerged as stations built multiple fixed-position antennas beaming power with narrow beamwidths at selected reception areas. Although new ideas in bi-directional arrays surface more slowly today, designing an antenna of this type to serve a specific communications need is still a significant engineering enterprise.

+

In some applications, especially in the upper HF range, the Yagi and other rotatable parasitic antennas have supplanted the bi-directional array. However, up to about 10 MHz, the bi-directional array is still the antenna of choice for most fixed stations. Moreover, even above 10 MHz, these antennas offer a cost-benefit ratio that make them attractive alternatives to other techniques.

+

Feeding the End-Fire and Broad Side Arrays

One of the most common errors in modeling common arrays is forgetting which array requires out-of-phase feeding and which requires in-phase feeding. This usually occurs with NEC-2 programs, where we set and forget the transmission lines we use to create the feeding system. +
+ +
+

Figure 2 shows the top view of a flat-top or 8JK and a broadside view of a Lazy-H.

+

Virtually all flat-top arrays of 2 elements are fed 180 degrees out of phase. The simplest means of achieving this goal is to create two transmission lines of equal length to an added central source wire (junction). One line is reverse connected to its element. Since the current magnitude and phase shift along each line is identical, the reverse connection on one of the lines ensures the out-of-phase condition.

+

Virtually all vertically-stacked 2-wire arrays are fed in-phase. Once more, the simplest feed system is to use equal lengths of transmission line to an added common junction wire, but normal connections are used for both lines. Ordinarily, the slight differences in the source impedance of the two wires, given their different distances from the earth's surface, is not sufficient to disturb the relative phasing. However, in very sensitive systems, networks may be used to achieve critical phasing adjustments.

+
+ +
+

For all arrays, it is best to develop models in step-wise fashion, rather than throwing together all the elements and then wondering what might be wrong with the overall result. Figure 3 shows the steps.

+

1. First, create the wires and use a separate source for each. With the simple expedient of alternately feeding one wire 180 degrees out of phase with the other wire and then in phase, you will see the pattern results appropriate to your design. You will also have a record of the wire source impedances, should you decide to do some independent calculations for a feed system.

+

2. Next, try the most direct feed system possible. This step involves creating a very short, thin wire in the model physically located exactly between the two antenna wires and along the center line of those elements. If you are using NEC-2, you can create two transmission lines, one from each antenna wire to the common or junction wire. Place the source on this third wire (remembering to remove the two formerly independent sources). Use the connections appropriate to the antenna type.

+

Record the composite source impedance. The key question at this point is whether that impedance is acceptable in terms of the system feed from that point back to the transmitting/receiving equipment. Within the scope of this step, you have the option of changing the characteristic impedance of the line, most usually within the 300/450/600 Ohm set of commercially available transmission lines. However, you can always construct your own.

+

Be certain to allow for the velocity factor (VF) of the line. Some programs permit direct entry of this value; others require that you pre-calculate the longer line length with a VF of 1.0 equivalent to a direct connection with a lines whose VF is less than 1.0.

+

In some cases, you will be "stuck" with the composite source impedance that emerges. Often, the direct line feed is the only physically feasible system of routing the feedlines. In some other cases, you may have the option of running longer lines to a common junction point.

+

3. If you can manage longer lines, you may experiment with them to see if they yield a more desirable composite source impedance than direct feed.

+

The following table illustrates the process, using a 1/2 wl spaced flat-top with 180-degree out-of-phase feeding. The frequency is 14.175 MHz, resulting in each line having a minimum length of about 17.5 feet.

+ 
Line length              Composite source impedance
+(each leg)          600-Ohm line             450-Ohm line
+ 17.5'               44.4 - j  4.4            25.0 - j  1.7
+ 20.0'               46.5 + j 63              26.2 + j 50
+ 22.5'               54.1 + j137              30.7 + j106
+ 25.0'               71.3 + j228              40.7 + j176
+ 30.0'              216   + j556             129   + j444
+

For a coax match, the most direct feed with 600-Ohm coax seems best. However, other feed systems may direct the use of other lengths. While you are at it, do a frequency sweep of the antenna to check the rate of change of both the resistive and reactive components of the composite source impedance. You may also change the wire lengths to place the resonant point of the system at a different resistive value of impedance.

+

Patterns and Frequency Sweeps

While you are exploring feed systems, also explore the elevation patterns. Many broadside systems have one or more lobes at very high angles, making the system more susceptible to atmospheric noise inputs. Flat-top systems, although generally of lower gain, naturally null the most vertical lobes, reducing sensitivity to high angle radiation. Figure 4 provides a sample pattern for an end-fire system fed 180 degrees out-of-phase. +
+ +
+

On the other hand, in-phase fed broadside systems, such as the Lazy-H, often permit multi-band service with usable gain and patterns extending from 0.5 F to 1.25 F, where F is the frequency for which each element is 2 half wavelengths. Consider the Lazy-H cut for about 21 MHz, with 44' wires spaced vertically by 22' (about 1/2 wl). If the lower wire is at 35' up, the upper wire will be 57' high. (This system might also be called an EDZ Lazy-H cut for 28 MHz and spaced about 5/8 wl at that frequency.) The following table records the modeled performance on various amateur frequencies.

+ 
Frequency      T-O Angle      Gain dBi       Source Impedance
+10.1           28              7.38           50 + j  91
+14.0           20              9.04          572 - j 394
+18.1           16             10.56           49 - j 142
+21.0           13             12.15           24 - j  36
+24.9           11             14.31           17 + j  94
+28.0           10             14.78           39 + j 291
+

If the source impedances are not an issue, this antenna might be useful as a multi-band antenna serving 30 through 10 meters with minimally dipole performance at the lowest frequency. You may verify that all patterns are broadside to the antenna, in contrast to the many-lobed patterns that would appear on 10 meters had we started with a 30-meter dipole. You may also wish to experiment with other line lengths from the center source junction to the antenna elements to see if you can arrive at a length more favorable to your own feed system ideas.

+

Modeling Collinear Elements with Phase Lines

Collinear antenna elements that employ phasing stubs often tempt us to automatically use NEC-2 transmission line capabilities in our initial models. While this technique sometimes works, it very often leads us into endless trials (and errors) searching for the correct length to make the antenna model at its performance of record. +

With phasing lines and NEC-2 we always have 2 options, as shown in Figure 5, a representation of collinear EDZ antenna elements. (Of course, only the physical modeling option is open to those who use MININEC. However, it is the initial option of choice for all modeling.)

+
+ +
+

Only some types of arrays are amenable to the substitution of non-radiating transmission-line models for their stub elements. A few depend upon the incomplete cancellation of currents to yield their final performance figures. Therefore, it is usually wise to begin with a physical model of a collinear element and ten later to convert it to a transmission line model.

+

Physical modeling is straight forward, as the figure indicates. All wires should run continuously, from end 1 of wire 1 to end 2 of wire 9. Use a segmentation density high enough that the horizontal shorting lines of the stubs are not radically different in length from the wire segments immediately adjacent to them. In developing the model, make use of either the current tables or a graphical aid to show relative current magnitudes. See Figure 6.

+
+ +
+

The aim of the collinear EDZ design is to place equal magnitude currents at each of the phasing lines. Unequal currents result in radiation from the phasing lines, which can disrupt overall performance. The current magnitude graphics represent two stages on the way to perfecting a model of the antenna in question.

+

This design, which dates back to the 1930s work of Hugo Romander, W2NB, is actually fairly forgiving, with 2-3% errors in length yielding only a drop of a few tenths of a dB in gain. The beamwidth of this antenna is only about 17 degrees between -3 dB points, so it is best suited to point-to- point communications rather than casual amateur work.

+

Wide-spaced physical stubs do not change their length rapidly as they are made narrower, since the characteristic impedance of these shorted stubs changes slowly as the spacing is increased beyond a couple of inches. Therefore, they provide a starting point for replacement with transmission line sections. The easiest procedure in many cases is to use 600-Ohm line for initial replacement trials. Once a working length value is found, you may convert it to an inductive reactance and from there to any transmission line value with a length appropriate to its characteristic impedance and velocity factor. Place the transmission line stubs on the first and last segment of the center wire (relative to the model in Figure 6), and use a segmentation density high enough to closely approximate the center wire ends.

+

More Complex Arrays, Such as the Sterba Curtain

Arrays are not always as simple as the models with which we have been working. A few seem to defy adequate modeling, especially if we insist upon using transmission line facilities in our programs. The Sterba curtain is one of these antennas. Yet, it models physically with remarkable ease--if you know some tricks of the trade. +
+ +
+

Figure 7 shows a side view of a Sterba curtain, similar to the typical sketch shown in many an antenna manual. The twisted vertical line pairs seem to beg for transmission line treatment. If we contemplate using physical lines, we often bog down in the thought of trying to keep them at a constant spacing and still effecting the "half-twist."

+

The top view shows a simple solution. Offset two wires by a small space. 0.5' will do at 40 meters without creating the slightest distortion in antenna performance for this 2.5 wl antenna. Run one wire from end to end, using vertical lengths to let it alternate between the top and bottom positions. Run the other wire the same way, but start at the far end and opposite corner. The result will be a set of wires correctly oriented to each other in both the horizontal and vertical planes. Connect the near and far ends with "near-vertical" wires (offset from the vertical only by the space between the horizontals). Make the connections to keep the wire continuous from its start to finish.

+

Here is a typical table of wires, with the wire offset in the Y-axis.

+ 
Sterba curtain:  Frequency = 7.2  MHz.
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft) Dia(in) Segs
+
+1   W20E2   0.000,  0.500, 67.000  W2E1   0.000,  0.000,134.000  # 12   15
+2    W1E2   0.000,  0.000,134.000  W3E1  33.500,  0.000,134.000  # 12    8
+3    W2E2  33.500,  0.000,134.000  W4E1  33.500,  0.000, 67.000  # 12   15
+4    W3E2  33.500,  0.000, 67.000  W5E1 100.500,  0.000, 67.000  # 12   15
+5   W21E1 100.500,  0.000, 67.000  W6E1 100.500,  0.000,134.000  # 12   15
+6    W5E2 100.500,  0.000,134.000  W7E1 167.500,  0.000,134.000  # 12   15
+7    W6E2 167.500,  0.000,134.000  W8E1 167.500,  0.000, 67.000  # 12   15
+8    W7E2 167.500,  0.000, 67.000  W9E1 234.500,  0.000, 67.000  # 12   15
+9    W8E2 234.500,  0.000, 67.000 W10E1 234.500,  0.000,134.000  # 12   15
+10   W9E2 234.500,  0.000,134.000 W11E1 268.000,  0.000,134.000  # 12    8
+11  W10E2 268.000,  0.000,134.000 W12E1 268.000,  0.000, 67.000  # 12   15
+12  W11E2 268.000,  0.000, 67.000 W13E1 234.500,  0.500, 67.000  # 12    8
+13  W12E2 234.500,  0.500, 67.000 W14E1 234.500,  0.500,134.000  # 12   15
+14  W13E2 234.500,  0.500,134.000 W15E1 167.500,  0.500,134.000  # 12   15
+15  W14E2 167.500,  0.500,134.000 W16E1 167.500,  0.500, 67.000  # 12   15
+16  W15E2 167.500,  0.500, 67.000 W17E1 100.500,  0.500, 67.000  # 12   15
+17  W21E2 100.500,  0.500, 67.000 W18E1 100.500,  0.500,134.000  # 12   15
+18  W17E2 100.500,  0.500,134.000 W19E1  33.500,  0.500,134.000  # 12   15
+19  W18E2  33.500,  0.500,134.000 W20E1  33.500,  0.500, 67.000  # 12   15
+20  W19E2  33.500,  0.500, 67.000  W1E1   0.000,  0.500, 67.000  # 12    8
+21   W4E2 100.500,  0.000, 67.000 W16E2 100.500,  0.500, 67.000  # 12    1
+

For this particular model, the source is placed in wire 21, which corresponds to the alternate source point. You may omit wire 21 and employ a split feed system, using the last segment on wire 20 and the first segment on wire 1 as the source positions. There are minor differences in current equality on the horizontal sections between the two source systems, as you may see from the current tables or the graphical current magnitude facility in your program. These differences will alter the gain slightly and also the degree to which the 26-degree beamwidth main lobe is offset from being directly broadside to the wire array. However, the source impedance at the end position may be more convenient, being closer to 600 Ohms. You may undertake many modeling experiments, especially with the vertical spacing between the top and bottom wires of the system, to effect the most equal current distribution possible.

+

Conclusion

We might extend these notes indefinitely, since there are dozens more basic and variant types of wire arrays, each with its own set of modeling challenges. However, those challenges will be mostly variations on those we have encountered in this set of exercises. +

If these notes have a message, it is something like this: model slowly and progressively toward the final complete antenna package (to the degree that your program permits modeling it). Double check all input values before running the model at each stage. Along the way, make use of all of the data provided by the program (and not just gain and source impedance results) to perfect the model.

+

The more we learn about using the vast array of data provided by antenna modeling programs, the better--and quicker--and more informative our models become.
+

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+

Go to Main Index

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+

80. Developing Antenna Expectations Using Modeling Software
+ 2B: Vertical Monopoles (continued)

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the preceding episode, we began our investigation of vertical monopoles by looking at elevated versions of the antenna. However, as our general work outline showed, the elevated vertical monopole is but one of the two ways we use the antenna. At lower frequencies ranging from LF and VLF up through the lower HF region, we often use them with one end at ground level and with a buried system of radials. So we still have half a project to finish.

+

The overall project had this structure:

+
+ A. Elevated vertical monopole +
+ 1. Monopole development +

2. Height above ground

+

3. Ground quality

+
B. Ground-mounted monopole +
+ 1. Perfect vs. lossy ground +

2. Radial density

+

3. Buried radials

+

4. Radial length

+

5. Vertical length

+
+
+

Even though we could only sample some of the many systematic questions relating to the properties of elevated vertical monopoles, we have to move onward. This series is not designed to answer all questions that contribute to a set of reasonable expectations of antenna types. Instead, it is designed to show some of the principles of systematic study that will let you continue the process of gathering data in ways that make sense of antenna performance patterns. We shall be similarly incomplete this month.

+

B. Ground-Mounted Monopole

+

The ground-mounted vertical (monopole) was once considered one of the most basic of all antennas. More recently, we have come to see it as an extension or a modification of the dipole, with the radial system substituting for the lower half of the dipole. However, because the ground plays such a significant role in the performance of the antenna, we shall not start in the same place that we began with all of the other antennas that we have so far explored. Instead of beginning in free space, we shall begin with a perfectly reflecting ground.

+

1. Perfect vs. Lossy Ground

+

In both NEC and MININEC, if we place a vertical element in contact with a perfect ground, the program will calculate the properties of the antenna by creating an image antenna that extends mathematically below the ground surface by an equal length. The left sketch in Fig. 1 shows the general situation.

+
+ +
+

A perfect ground will totally reflect the radiation striking it, thus doubling the power in the radiated field. To see the image antenna effects in action, let's create a 7.05-MHz vertical monopole made from 2" (50.8-mm) aluminum. We shall give it a length of 33.25' (10.135 m). For this exercise, let's use 30 segments. NEC-4 returns a maximum gain of 5.14 dBi with a source impedance of 35.94 - j 0.13 Ohms.

+

As shown in the middle portion of Fig. 1, the 1/4 wavelength vertical element plus its image is equivalent to a 1/2 wavelength vertical dipole in free space--except for the source impedance. If we create such a dipole for 7.05 MHz from the same materials, making it 66.5' (20.27 m) long, we obtain a source impedance of 71.84 - j 0.58 Ohms. The very slight difference between the reported impedance and double the 1/4 wavelength impedance stems from the slight shift we had to make in the position of the source. The monopole source is on the lowest segment of the physical antenna, which places it slightly above ground. We assigned the dipole 61 segments, placing the source at its exact center, which corresponds to the ground level (Z=0) for the monopole.

+

Because the dipole has no reflections to double the radiated power of its far field, we should expect the field strength to be 1/2 the level of the monopole over perfect ground. So, instead of a field strength of 5.14 dBi, the dipole in free space reports 3 dB less, or 2.13 dBi.

+

To simplify models of vertical monopoles, modelers have in the past simply placed the monopoles in contact with the ground using MININEC. (NEC-2 and NEC-4 return completely useless reports under the same conditions.) The practice was so widespread that the EZNEC version of NEC incorporated the MININEC ground as a user-selected option. To understand the operation of the MININEC ground, let's place our monopole from the ground up using the MININEC ground system. As in past episodes, we shall use the following samples of ground quality as trials for our simple monopole model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                           Some Useful Soil Types
+
+              Soil Type                    Conductivity                 Permittivity
+                                           S/m                          (Dielectric Constant)
+              Very Poor                    0.001                         5
+              Poor                         0.002                        13
+              Good                         0.005                        13
+              Very Good                    0.0303                       20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Running the model through these sample ground qualities, we obtain the following performance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                Changes of Vertical Monopole Performance with Ground Quality:  MININEC Ground
+
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -1.76         29                    35.94 - j 0.13
+              Poor                  -0.28         27                    35.94 - j 0.13
+              Good                  -0.03         26                    35.94 - j 0.13
+              Very Good             1.95          21                    35.94 - j 0.13
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We obtain a plausible-looking chart of gain values and TO angles. However, the source impedance remains the same for every value. The MININEC ground system always uses the source impedance for a perfect ground as one of its simplifying features, remembering that it was developed for early PCs with very limited memory resources. Hence, it cannot tell us whether the source impedance changes with ground quality. We cannot know from the MININEC ground system whether we need to adjust the length of the monopole to bring it to resonance for a given ground quality.

+
+ +
+

The MININEC ground system does let us make an important contrast, one that will hold true for every trial in this episode. Fig. 2 shows the difference between a pattern taken over perfect ground and one taken over a real (MININEC) ground. The lower part of the figure represents all of the elevation patterns that we shall encounter. The only differences will be in the maximum gain and the TO angle as we move from one trial to another. As long as we stick to our 1/4 wavelength vertical monopole, we shall see the lower elevation pattern.

+

2. Radial Density

+

The use of a MININEC ground cannot capture the fact that the performance of a vertical monopole will change according to the size of the radial field that we add to the base of the monopole, as shown in the far right portion of Fig. 1. The radials, normally at or below the ground surface of a ground-mounted vertical monopole, are an essential ingredient to the antenna's performance with respect both to its source impedance and its far-field strength. We should now be on the verge of appreciating that the performance of a ground-mounted vertical monopole is a function of a complex interaction among the physical properties of the antenna, the ground quality, and the number and type of radials that we place at its base.

+

NEC-2 does not permit a wire to extend below ground level (Z=0). Therefore, the program cannot directly model a buried radial system. However, to simulate a buried radial system, the standard procedure is to create the radial set with the antenna and its radials raised about 0.001 wavelength above ground. This level is at or close to the absolute proximity permitted under NEC for wires above a Sommerfeld ground calculating system. (Do not use the simpler reflection coefficient system.)

+

For our 7.05-MHz monopole, we shall raise it by only 0.4" (10.16 mm) above ground. To the antenna base, we shall add radial systems using various numbers of radials. To be systematic about the matter, we shall use the progression 4, 8, 16, 32, and 64 radials. Broadcast systems use 120 radials with shorter radials between the longer ones, but a 64-radial system is about as large as amateur systems get. Besides, 64 radials, set up as we shall prescribe, will result in models with more than 1900 segments.

+

We shall not change the length of the monopole, but instead track what happens as we change the number of radials and the soil quality. We need to set a length for the radials. Each one will be--for the sake of our initial trials--0.25 wavelength long, that is, 34.88' or 10.63 m. (We shall look at the question of radial length before we have finished the episode.) For reasons having to do with subsequent trials, we shall assign 30 segments to each radial, as well as to the monopole, so that all segments are about the same length, close to 12" (0.3 m).

+

If we create the models using each of the specified number of radials and run the model over the 4 sample ground qualities, we obtain a table that resembles the following one.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+               Vertical Monopole Performance with Ground Quality and Number of Radials: NEC-2
+
+4 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -2.64         29                    46.57 + j 27.66
+              Poor                  -2.13         27                    59.43 + j 64.93
+              Good                  -3.31         26                    81.51 + j 63.16
+              Very Good             -3.09         21                    114.0 + j 97.64
+
+8 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -1.67         29                    36.19 + j  4.73
+              Poor                  -0.65         27                    40.48 + j 20.35
+              Good                  -1.40         26                    49.86 + j 21.27
+              Very Good             -1.01         21                    69.18 + j 43.57
+
+16 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -1.28         29                    33.44 - j  3.90
+              Poor                  -0.18         27                    35.55 + j  3.53
+              Good                  -0.59         26                    40.06 + j  3.94
+              Very Good              0.20         21                    51.69 + j 14.66
+
+32 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -1.05         29                    30.61 - j  6.90
+              Poor                   0.08         27                    33.16 - j  2.89
+              Good                  -0.15         26                    35.54 - j  3.14
+              Very Good              1.09         21                    41.64 + j  1.37
+
+64 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -0.89         29                    29.66 - j  7.48
+              Poor                   0.24         27                    32.08 - j  4.73
+              Good                   0.06         26                    33.70 - j  4.99
+              Very Good              1.51         21                    47.39 - j  2.82
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table shows that for any number of radials, the elevation angle of maximum radiation--the TO angle--varies only with the soil quality. As we add radials, the source resistance descends and compresses, so that the wide range we see with few radials becomes a narrow range with many radials. The source reactance, which was always inductive with only 4 radials, is always capacitive with 64 radials. However, we should also note that some of the source impedance values drop below the 35-Ohm level that we encountered with a perfect ground. There is an old rule of thumb that suggests a way to account for losses to ground in a vertical monopole. Any portion of the source resistance that is above 35-36 Ohms is simply a loss function. However, the models suggest to the contrary that the relationship may not be so simple as that, since some source resistance values are below the ideal level. In fact, the source resistance for very poor soil and 64 radials begins to approach the level that we encountered for an elevated monopole with radials.

+
+ +
+

Of course, the gain reports will not support a suggestion that very low source resistance values mean high efficiency from our vertical monopole. Fig. 3 tracks the gain values from the table for each of the ground qualities as we increase the number of radials. Note that the gain performance of the monopole over poor soil is always slightly better than over good soil. As well, the performance over very good soil shows a much steeper curve so that, with fewer than 16 radials, the gain is lower than with some of the worse soil qualities.

+

If we remember that we created these models as an above-ground simulation of a buried radials system, we can pose a valid question: how reliable is this simulation? This question is not so simple as it seems. The effects of ground on vertical monopoles has been under continuous study since the earliest days of radio. Even the best modeling systems are under scrutiny in the quest for a more perfect understanding of ground effects and the ideal radial system. At best, in our trials, we can only demonstrate a superior model of the monopole and its radials. We cannot reach an absolutely final answer.

+

3. Buried Radials

+

Unfortunately, the only way to create a superior model of the ground-mounted vertical monopole with a buried radial system is to use NEC-4, which is outside the reach of most casual modelers. However, NEC-4 does permit the use of wires below ground. In conjunction with the Sommerfeld ground calculating system, the model promises to yield more accurate results than a scarcely elevated substitute. However, should the Sommerfeld (S-N) system undergo refinement as a means of calculating ground effects, then even these models will yield better results in future modeling software.

+
+ +
+

Fig. 4 shows what is necessary to develop a buried radial system. NEC requires that a wire or segment junction coincide with the ground (Z=0). The wire or segment from ground down to the level of the junction of radials plays a critical role in the model. The segment just above ground is where we place the source, and to obtain reliable results, this segment should be the same length as the segments adjacent to it. If we do not use segment length tapering, the distance from the ground down to the radials thus determines the length of the segments in the vertical monopole. We shall use 66 segments, since we shall place the buried radials 0.5' (0.15 m) below ground. In fact, moving the radial depth tends to change the results by insignificant amounts for a fairly wide range of depths. Hence, the half-foot depth represents a reasonable compromise between reflecting actual practice in setting radials and relatively manageable model sizes. Because the radials are symmetrical, we can use a reduced segmentation density. In fact, we shall retain the 30-segment-per-radial density that we used for the elevated system.

+

If we set up the models according to this scheme and run them through the sample soil qualities, we obtain the following table of results.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+               Vertical Monopole Performance with Ground Quality and Number of Radials: NEC-4
+
+4 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -4.62         30                    97.95 + j 27.77
+              Poor                  -2.85         27                    69.26 + j  6.64
+              Good                  -2.53         26                    67.02 + j 12.35
+              Very Good              0.35         21                    52.55 + j 12.79
+
+8 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -2.49         29                    57.61 + j 22.66
+              Poor                  -1.73         27                    57.59 + j  8.47
+              Good                  -1.49         26                    54.66 + j 11.89
+              Very Good              0.81         21                    47.47 + j 10.82
+
+16 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -1.32         29                    40.34 + j 11.40
+              Poor                  -0.63         27                    46.71 + j 10.16
+              Good                  -0.64         26                    45.81 + j  9.69
+              Very Good              1.19         21                    43.76 + j  9.23
+
+32 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -0.91         29                    34.52 + j  4.58
+              Poor                   0.09         27                    38.55 + j  7.91
+              Good                  -0.07         26                    39.69 + j  7.38
+              Very Good              1.50         21                    40.89 + j  7.99
+
+64 Radials
+              Soil Type             Gain          TO Angle              Source Impedance
+                                    dBi           degrees               R +/- jX Ohms
+              Very Poor             -0.78         29                    32.47 + j  1.54
+              Poor                   0.34         27                    35.00 + j  5.20
+              Good                   0.16         26                    36.53 + j  5.12
+              Very Good              1.70         21                    38.76 + j  6.91
+
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We may first notice that the TO angles have not changed, with the one exception of 4 radials with very poor soil. Our second notice should go to the source impedances. With few radials, the buried-radial model reverses the source impedance situation with respect to values for very good and very poor soil. Internally to the table, the 16-radial level marks a turning point in the source resistance reports. With fewer radials, the source resistance goes up as soil quality goes down. With more than 16 radials, the trend reverses. All reactances are inductive for two reasons. First, the height above ground of the vertical is unchanged, even though we added a small subterranean section to the antenna. Second, the source position is slightly higher up on the total vertical length from the radials to the tip. Nonetheless, as we add more radials, the ground-mounted vertical monopole comes very close to resonance over any soil quality, with under j 7 Ohms reactance as the 64-radial worst case.

+
+ +
+

Fig. 5 extracts the gain data for a visual presentation. When we compare it to the data from the above-ground radial models, we see some clear differences. Even though the above-ground version did not record the cross-over in gain advantage between poor and good soils at the 16-radial mark (corresponding to the changeover point for the source resistance values), these two soil levels show the highest correlation between the two graphs. The most significant changes occur with respect to very good and very poor soil. The values for very good soil maintain an advantage over other soil qualities and the curve is much shallower than with the above-ground reports. In contrast, with buried radials and very poor soil, we find a steeper curve and values always at the bottom of the scale.

+

It is likely that the buried-radial models return more reliable results than their NEC-2 above-ground simulation. The gain and source impedance reports tend to be closer to intuitions, although intuition would be a poor guide with respect to the middle of the scale, where poor soil sometimes outperforms good soil by a small margin (that is not operationally significant). We should note once more that the inter-relationship among the physical antenna structure, the soil quality, and the number of radials is further complicated by source resistance values that fall noticeably below the perfect-ground value. Finally, you may wish to compare the results in both sets of tables with the recorded when using a MININEC ground without a radial system.

+

4. Radial Length

+

Throughout the trials that we have been performing, we used radials that were exactly 1/4 wavelength at 7.05 MHz. One continuing discussion concerning ground-mounted vertical monopoles concerns the ideal length for radials. As we have seen, we cannot obtain absolute answers to such questions, but we can see what models have to report on the subject. Let's take the 16-buried-radial model and test it for radials of varying length, ranging from 0.10 wavelength to 0.40 wavelength. We can, for demonstration purposes only, use only good and very poor soils for our sampling, leaving other options for further exploration as something you can do yourself. We shall retain our 0.25" (6.25-mm) radials and segmentation density, which means that the models will grow larger with every increase in radial length. The results should resemble the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Effects of Radial Length on Vertical Monopole Performance
+
+Good Soil
+                     Length         Gain          TO Angle       Source Impedance
+                     WL             dBi           degrees        R +/- j X Ohms)
+                     .10            -1.30         26             47.12 - j  0.85
+                     .15            -0.87         26             43.92 + j  4.80
+                     .20            -0.72         26             44.58 + j  8.29
+                     .25            -0.74         26             45.82 + j  9.69
+                     .30            -0.57         26             46.95 + j 10.17
+                     .35            -0.51         26             47.83 + j 10.07
+                     .40            -0.48         26             48.36 + j  9.63
+
+Very Poor Soil
+                     Length         Gain          TO Angle       Source Impedance
+                     WL             dBi           degrees        R +/- j X Ohms)
+                     .10            -3.10         29             46.94 - j 17.96
+                     .15            -2.40         29             40.94 - j  7.64
+                     .20            -1.76         29             37.77 + j  1.90
+                     .25            -1.32         29             40.33 + j 11.40
+                     .30            -1.18         30             47.76 + j 15.52
+                     .35            -1.13         30             53.84 + j 13.71
+                     .40            -1.06         31             56.34 + j  9.68
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In both trials, we see a regular and smooth improvement in gain performance with longer radials, although the range is less with good soil than with very poor soil. There are in the models no special lengths within the range tested. The TO angle over good soil remains constant, although over very poor soil, the angle begins to increase slowly as we extend the radial length above 0.25 wavelength.

+

Both tables show that with radials about 0.30 wavelength, the inductive reactance reaches a maximum. Source resistance shows minimum values, but at slightly different radial lengths: for good soil, at 0.15 wavelength, for very poor soil, at 0.20 wavelength. These are minor phenomena, more of numerical interest than operational significance. Indeed, IF the models are reasonably accurate predictors of antenna behavior with varying radial lengths, then it is likely that the exact radial length will not affect antenna performance significantly so long as all radials are the same length and as symmetrically laid out as feasible.

+

5. Vertical Length

+

When we encounter initial textbook discussions of ground-mounted vertical monopoles, the authors treat us to graphical elevations patterns related to the length of the vertical monopole above ground. Inevitably, the patterns show a significant gain advantage to using a monopole that is 0.625 wavelength. Let's replicate those patterns over perfect ground. Then let's go a step farther and perform the same set of trials over good ground with our 16-radial buried system. We shall not change general parameters of the model, using 1/4 wavelength radials. Our goal will be to understand why some broadcast antenna engineers prefer in fact not to use the longer monopole (beyond the fact that such a monopole represents a very tall structure to maintain in the AM broadcast frequency range). The results of our trials at 7.05 MHz will look like those in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                         Effects of Vertical Length on Vertical Monopole Performance
+
+Perfect Ground
+                     Length         Gain          TO Angle       Source Impedance
+                     WL             dBi           degrees        R +/- j X Ohms)
+                     .25             5.14         --             35.94 - j  0.13
+                     .375            5.83         --             269.9 + j 372.4
+                     .50             6.95         --             6762. - j 664.9
+                     .625            8.04         --             64.09 - j 253.9
+                     .75             6.61         46             59.14 + j 26.59
+
+Good Soil
+                     Length         Gain          TO Angle       Source Impedance
+                     WL             dBi           degrees        R +/- j X Ohms)
+                     .25            -0.64         26             45.83 + j  9.71
+                     .375           -0.06         22             308.3 + j 380.0
+                     .50             0.53         18             5859. - j 669.4
+                     .625            0.73         15             64.65 - j 235.5
+                     .75             4.14         45             73.26 + j 34.47
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

With an aluminum vertical, the 5/8 wavelength vertical over perfect ground shows a 2.9-dB advantage over the 1/4 wavelength vertical. However, when we transplant the verticals to merely good soil, the gain advantage of the longer version shrinks to less than 1 dB. We may note the lower TO angle of the longer vertical and still think that we should use it. For that reason, we should also explore the elevation patterns themselves over both perfect and merely good ground.

+
+ +
+

We can trace the pattern development in Fig. 6. From a vertical length of 1/4 wavelength up to 1/2 wavelength, the patterns over good soil track well with the patterns over perfect ground. However, at a length of 5/8 wavelength, the very modest secondary lobes of the pattern over perfect ground take a different turn. They become very large regions of high angle radiation. Much of the energy that--over perfect ground--extended the lower lobe has now moved into the second lobe. Little wonder that engineers who do not wish to cause interfering skip signals at night in the AM BC band opt for a shorter length of vertical monopole. Even for amateur use, the 5/8 wavelength monopole may increase short-range noise and interfering signals without commensurate improvements in long-range performance.

+

The 0.625 wavelength vertical monopole is the analog of the 1.25 wavelength vertical dipole. Two episodes ago, we saw that increasing the dipole length to 1.5 wavelengths virtually eliminated low angle radiation and redirected energy at very high angles. The same effect holds true for ground-mounted vertical monopoles that we extend to 0.75 wavelength. As the bottom patterns in Fig. 6 show clearly, even the version over perfect ground shows the angle of the main lobes to be very high. The version over good soil eliminates virtually all low angle radiation.

+

Conclusion

+

Although we seem to have covered a wide territory in our investigation of ground-mounted verticals, we have omitted many facets of what a truly thorough study might accomplish. We did not look at the effects of using different combinations of vertical element diameters with equally varied radial diameters. We did not investigate the effects of different materials on monopole performance. Even where we sampled different soil qualities, we often left gaps in the coverage.

+

However, we have progressed far enough for you to proceed individually to do a more thorough exploration. Indeed, the principles of systematic exploration of antenna properties via models apply to any number of antenna types, both simple and complex: parasitic arrays, phased arrays, closed geometries (vertical and horizontal loops, etc.), and even systems of multiple antennas. In some cases, such as horizontal arrays that are well elevated above ground, the results will be as authoritative as one might wish. In other cases, such as ground-mounted verticals, they will be useful, suggestive, and helpful, without necessarily being without contest from new developments in the understanding of how complex factors combine to yield antenna performance.

+

In virtually all cases, the exercises will not only contribute to our understanding of the subject antenna types. As well, they will help us overcome numerous misconceptions, presumptions, myths, and assumptions that we carry to our antenna work. These are some of the key roadblocks to developing reasonable expectations of antenna performance, the goal of using modeling as a means to understanding better what antennas can do.

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Go to Main Index

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+

81. Appreciating EK

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+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In episode 51, we encountered the inaccuracies that result in NEC-2 from too low a ratio between the segment length (Ls) and the wire radius (R). In the example, we used the following model, outlined in Fig. 1, to track the differences between NEC-4 results and NEC-2 results.

+
+ +
+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+W4RNL 432 WB Yagi               Frequency = 432  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1            0.000, -6.575,  0.000         0.000,  6.575,  0.000 5.00E-01  15
+2            5.807, -6.083,  0.000         5.807,  6.083,  0.000 5.00E-01  15
+3            9.626, -5.453,  0.000         9.626,  5.453,  0.000 5.00E-01  15
+4           15.748, -5.256,  0.000        15.748,  5.256,  0.000 5.00E-01  15
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The average segment length is about 0.8", while the diameter is 0.5", for a length-to-radius (Ls/R) ratio of 3.2:1. The following table records the modeled performance data from 420 to 250 MHz for the 4-element wide-band Yagi design.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                  Wide-Band 4-Element Yagi for 420-450 MHz
+
+  Core        Freq.  Free-Space     Front-Back    Source Impedance             50-Ohm
+              MHz    Gain dBi       Ratio dB      R +/- jX Ohms                SWR
+
+  NEC-4D      420    9.12           11.56         45.81 - j  2.99              1.114
+              430    9.23           12.14         56.30 + j  1.51              1.130
+              440    9.34           12.73         61.22 - j  2.38              1.230
+              450    9.55           14.31         49.47 - j  7.28              1.158
+
+  NEC-2       420    9.17           11.69         47.77 - j  1.14              1.053
+  w/o EK      430    9.27           12.20         58.14 + j  1.51              1.166
+              440    9.40           12.92         59.93 - j  4.57              1.221
+              450    9.64           14.99         42.72 - j  6.56              1.236
+
+  NEC-2       420    9.12           11.52         45.64 - j  2.99              1.120
+  w EK        430    9.23           12.11         56.12 + j  1.64              1.130
+              440    9.35           12.72         61.11 - j  2.20              1.230
+              450    9.55           14.29         49.40 - j  7.23              1.160
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The last portion of the table records the data we obtain when we implement the EK or extended thin-wire kernel command (EK). The use of this command restores the performance reports to good alignment with NEC-4 results. Hence, we should learn how, when, and why to use the EK command in NEC-2, as well as why it is unnecessary in NEC-4.

+

How: The easiest step in the process is implementing the EK command. Immediately following the GE (geometry end command), we may write a new line:

+ 
EK 0
+

The line changes the approximation of the electrical field integral equation in the core calculations from the thin-wire kernel to the extended thin-wire kernel. Unfortunately, some entry level versions of NEC-2 do not give the user the option of using the extended kernel, although NEC2GO does implement it automatically whenever the wire radius exceeds a certain ratio to the segment length. The most recent (Version 4) EZNEC programs also appear to implement EK automatically. Programs that allow the user to write his or her own model file, such as NEC-Win Pro, provide for the use of the extended thin-wire kernel whenever the modeler deems it necessary. For a simple sample dipole, the model file will have the following appearance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM NEC-WIN Example
+CM Simple dipole antenna in Free Space
+CM Optimized for resonance at 300 MHz
+CE
+GW 1 9 0 -.2418 0 0 .2418 0 .0537
+GS 0 0 1
+GE 0 -1 0
+EK 0
+EX 0 1 5 0 1 0
+FR 0 1 0 0 300 1
+RP 0 181 1 1000 -90 0 1 1
+RP 0 1 360 1000 90 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Why: The information necessary to appreciate the significance of the extended thin-wire kernel in NEC-2 appears early on in the user portion of the manual. "In the thin-wire kernel, the current on the surface of a segment is reduced to a filament of current on the segment axis. In the extended thin-wire kernel, a current uniformly distributed around the segment is assumed. The field of this current is approximated by the first two terms in a series expansion of the exact field in power of aa [where a is the wire radius]. The first term in the series, which is independent of a, is identical to the thin-wire kernel, while the second term extends the accuracy for larger values of a. Higher order approximations are not used because they would require excessive computation time."

+

"In either of these approximations, only currents in the axial direction on a segment are considered, and there is no allowance for variation of the currents around the wire circumference. The acceptability of these approximations depends on both the value of a/wavelength and the tendency of the excitation to produce circumferential current or current variation. Unless (2*pi*a)/wavelength is much less than 1, the validity of these approximations should be considered." One potential arena in which the validity of these approximations may be tested is the modeling of a boom connected directly to the parasitic elements of a Yagi antenna. In practice, the connection or the very close proximity of a boom to the parasitic elements alters the required length of the elements to preserve array performance. However, in NEC-2 and NEC-4--when modeled within the other limitations of the software--the boom has no effect upon the parasitic elements. The result strongly suggests that boom-to-element effects are functions of variations in circumferential currents, which NEC does not take into account. A fuller account of this phenomenon is a subject for another episode in this series.

+

The NEC-2 manual goes on. "The accuracy of the numerical solution for the dominant axial current is also dependent on [the ratio of segment length to radius or Ls/R]. Small values of [Ls/R] may result in extraneous oscillation in the computed current near free wire ends, voltage sources, or lumped loads. Use of the extended thin-wire kernel will extend the limit on [Ls/R] to smaller values than are permissible with the normal thin-wire kernel." In general, Ls/R must be greater than 8 for errors under 1% for the normal thin-wire kernel. This amounts to a segment length-to-wire-diameter ratio of 4:1, for programs that input wire thickness as a diameter. The manual notes that "reasonable solutions" have been obtained for the normal thin-wire kernel for Ls/R values down to about 2, with equally "reasonable solutions" for the extended thin-wire kernel for Ls/R values down to about 0.5. However, exact specification of the geometries involved does not appear. Hence, the most general guidance one might give is to use the EK command to implement the extended thin-wire kernel whenever the value of Ls/R goes below 8 (or a segment-length-to-wire-diameter ratio of 4). For straight-wire elements, the limit to Ls/R may be between 2 and 1 for very reliable results.

+

There are numerous other facets of extended thin-wire kernel implementation noted in the manual. For example, the normal thin-wire kernel is used--even if the EK command is implemented--at wire bends, such as those encountered in closed and nearly closed antenna geometries. Delta, quad, and Moxon rectangle geometries are samples of such antennas. At bends, the modeler should avoid very small values of Ls/R so that the surface of one wire at the junction does not penetrate into the central region of the other wire, a condition that "generally leads to severe errors."

+

Why EK is not used in NEC-4: The NEC-4 manual provides a chapter outlining the differences between NEC-3 and NEC-4. Over the range of considerations relevant to the use of EK in NEC-2, NEC-3 is essentially the same as NEC-2--but is different in other respects. In NEC-4, "the thin-wire approximation is now implemented with the current treated as a filament on the wire surface and the boundary condition enforced on the wire axis."

+

"With the boundary condition enforced on the wire axes, the openings at wire ends should be closed with end caps. This is particularly important when the ratio of segment length to radius is on the order of 2 or less. Wire ends are closed with flat caps in NEC-4, with the current and charge density assumed continuous from the wire onto the cap." NEC-4 also includes optional caps for use with voltage sources with equally low values of Ls/R. "This approximate treatment was found to be about as effective as the extended thin-wire kernel included as an option in [NEC-2 and] NEC-3. The extended thin-wire kernel option (EK card) has been dropped from NEC-4.

+

The NEC-4 thin-wire kernel appears at first sight to replicate the extended thin- wire kernel of NEC-2 and NEC-3. Hence, results seemingly should be identical. However, the implementation of wire end caps and other alterations to the solution algorithms for wires tells us otherwise. Rather, expect results to be very close.

+

For relatively thin, straight wires having long segment lengths, where Ls/R is more than 8, there will be almost no difference between NEC-2 and NEC-4, even without implementing the extended thin-wire kernel in NEC-2. For values of Ls/R between 8 and 2, NEC-2 with EK and NEC-4 will normally show very close results. However, as the value of Ls/R passes 2 on its way downward, expect larger differences.

+

I have quoted directly from the NEC-2 and NEC-4 manuals because many users of antenna modeling software simply do not read them. As well, the self-consistent language within those manuals is guidance against misinterpretation of what the manuals record about the basis for NEC core operations. However, what we have been reviewing are simply the most relevant extracts from the fuller treatment provided by the manuals to cover not only the situation surrounding the EK card, but as well overall core operations. Hence, I fully recommend that every user of NEC-2 or NEC-4 (or even NEC-3) gradually become fully conversant with the provisions of the manuals. They were not written for the purpose of being supplanted by a series of one-line or more-easily remembered summary statements. Such statements may be useful as the beginning, but are never the ultimate end of understanding both the capabilities and the limitations of the cores.

+

When: I have provided some general recommendations on when to invoke the EK card, where "when" means "at what Ls/R value." However, we might pause to go through a pair of small exercises in order to better appreciate the high generality of those recommendations.

+
+ +
+

The first exercise involves a simple dipole, the model for which I showed earlier. Fig. 2 outlines the dipole. Nothing in the dipole will change except the radius of the one wire that makes up the model. Beginning with a radius of 0.0001 meters (0.1 mm), we shall increase the radius until we reach levels that allow us to create segment-length-to-radius values in the range from 4:1 down to 1:1. Since we shall not change the wire length, every increase in radius will carry us theoretically further from the initial resonance of the antenna. This move is intentional, since once we have significant reactance in the source impedance, differences created by running the model under various conditions will become more graphic.

+

Because we shall begin with a 1/2 wavelength resonant dipole, we should not expect much change in the gain or variation among models with respect to gain. Resonant dipoles change gain only very slowly with changing conditions, a common feature of most simple antennas resonated for a high source current. Therefore, the source impedance values will be our primary window on the differences. We shall run them without the EK card in both NEC-2 and NEC-4, and also with the EK card in NEC-2. All models were run on NSI's GNEC package, which contains both NEC-2 and NEC-4 cores. The following table captures the results.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                             A Dipole in NEC-4 and in NEC-2 With and Without EK
+
+Constants:           Free-Space Environment; Frequency: 300 MHz
+                     Length: 0.4836 m; Segments: 9; Segment Length: 0.5373 m
+                     Ls = segment length; R = radius
+
+Wire Radius: 0.0001 m               Ls/R: 537
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.12                  72.080 - j 0.001
+NEC-2 w/o EK         2.12                  72.079 - j 0.002
+NEC-2 w EK           2.12                  72.079 - j 0.002
+Wire Radius: 0.001 m                Ls/R: 53.7
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.13                  75.629 + j16.514
+NEC-2 w/o EK         2.13                  75.628 + j16.515
+NEC-2 w EK           2.13                  75.222 + j16.490
+Wire Radius: 0.01 m                 Ls/R: 5.37
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.18                  91.469 + j32.379
+NEC-2 w/o EK         2.18                  92.039 + j33.316
+NEC-2 w EK           2.18                  90.677 + j31.667
+Wire Radius: 0.0134 m               Ls/R: 4.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.20                  95.680 + j30.113
+NEC-2 w/o EK         2.20                  97.272 + j32.149
+NEC-2 w EK           2.20                  94.637 + j30.042
+Wire Radius: 0.0179 m               Ls/R: 3.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.22                  99.783 + j23.974
+NEC-2 w/o EK         2.22                  103.832 + j27.652
+NEC-2 w EK           2.22                  98.657 + j25.572
+Wire Radius: 0.0269 m               Ls/R: 2.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.26                  102.414 + j 5.134
+NEC-2 w/o EK         2.27                  114.262 + j 9.213
+NEC-2 w EK           2.27                  102.410 + j12.229
+Wire Radius: 0.0537 m               Ls/R: 1.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                2.38                  51.890 - j46.292
+NEC-2 w/o EK         2.43                  54.146 - j58.430
+NEC-2 w EK           2.47                  86.345 - j31.830
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Certain results appear incontestable. First, wherever there are differences among the results, the NEC-2-with-EK data are closer to the NEC-4 data than are the data from NEC-2-without-EK. Second, the values for a ratio of segment length to radius of 1.0 are sufficiently variable as not to be able to say which values are more reliable than the others. From the table alone, without external verification, it would even be presumptuous to assert that the NEC-4 values are the most reliable. At all other values, we have much more confidence in the coincidence between NEC-4 and NEC-2-with-EK.

+

The more difficult question to answer is when to implement the EK card in NEC-2. For Ls/R values above 5.37, the EK card is certainly unnecessary for the dipole. Even at the radius of 0.01 m, the NEC-2 results seem equally separated from the NEC-4 results, although in opposite directions. There is a change when we simply reduce the Ls/R value from 5.37 down to 4.0: the NEC-2-with-EK results are clearly more coincident with the NEC-4 results than NEC-2-without-EK. Hence, a segment-length-to-radius ratio in the range of 6 down to 4 seems an appropriate changeover to the use of EK for NEC-2 users.

+
+ +
+

Coincidence between NEC-2-EK results and NEC-4 is not always a decisive reason for implementing the EK card in NEC-2. Consider, for example, a simple quad loop, such as the one outlined in Fig. 3. The EK version of the model follows.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM Quad Loop
+CE
+GW 1,11, -0.1324,0,-0.1324, 0.1324,0,-0.1324, 0.0001
+GW 2,11, 0.1324,0,-0.1324, 0.1324,0,0.1324, 0.0001
+GW 3,11, 0.1324,0,0.1324, -0.1324,0,0.1324, 0.0001
+GW 4,11, -0.1324,0,0.1324, -0.1324,0,-0.1324, 0.0001
+GS 0 0 1
+GE 0
+EK 0
+EX 0 1 6 0 1 0
+FR 0 1 0 0 300 1
+RP 0 1 360 1000 89 0 1
+RP 0 181 1 1000 -90 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The loop is set for 300 MHz, with initial side lengths that are 0.2648 m, with 11 segments per side. With the initial wire radius of 0.0001 m, the segment lengths are 0.0241 m. As we increase the radius of the wire, the loop will drift farther from resonance. Since the geometry is closed, the loop will show capacitive reactance as we enlarge the wire (in contrast to the increasing inductive reactance of a straight wire under similar conditions). We can tabulate the results of modeling in NEC-2, NEC-2-without-EK, and NEC-2-with-EK.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                            A Quad Loop in NEC-4 and in NEC-2 With and Without EK
+
+Constants:           Free-Space Environment; Frequency: 300 MHz
+                     Side Length: 0.2648 m; Segments: 11; Segment Length: 0.0241 m
+                     Ls = segment length; R = radius
+
+Wire Radius: 0.0001 m               Ls/R: 241
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.30                  125.46 - j 1.213
+NEC-2 w/o EK         3.30                  125.46 - j 1.207
+NEC-2 w EK           3.30                  125.46 - j 1.207
+Wire Radius: 0.001 m                Ls/R: 24.1
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.29                  119.53 - j52.554
+NEC-2 w/o EK         3.29                  119.58 - j52.323
+NEC-2 w EK           3.29                  119.58 - j52.322
+Wire Radius: 0.0048 m               Ls/R: 5.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.28                  106.48 - j86.861
+NEC-2 w/o EK         3.26                  107.84 - j83.170
+NEC-2 w EK           3.26                  108.21 - j83.076
+Wire Radius: 0.006 m                Ls/R: 4.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.28                  102.50 - j91.561
+NEC-2 w/o EK         3.25                  104.60 - j86.457
+NEC-2 w EK           3.25                  105.33 - j86.268
+Wire Radius: 0.008 m                Ls/R: 3.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.29                  95.571 - j97.117
+NEC-2 w/o EK         3.20                  99.146 - j89.857
+NEC-2 w EK           3.22                  100.91 - j89.398
+Wire Radius: 0.012 m                Ls/R: 2.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.31                  80.679 - j102.15
+NEC-2 w/o EK         3.20                  87.361 - j92.323
+NEC-2 w EK           3.16                  93.264 - j90.958
+Wire Radius: 0.0241 m               Ls/R: 1.00
+Core                 Gain (dBi)            Source Impedance (R+/-jX Ohms)
+NEC-4                3.32                  37.507 - j80.703
+NEC-2 w/o EK         3.11                  43.091 - j78.095
+NEC-2 w EK           2.58                  81.412 - j80.556
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Variations of both gain and source impedance begin to appear with a segment- length-to-radius ratio of 5:1. Down to a ratio of about 2:1, the pair of NEC-2 results are closer to each other than either is to the NEC-4 result. The most likely reason for this divergence from the type of results we obtained from the straight dipole is the conditions of the model and how each core handles them. The NEC-4 applies its revised algorithm to all segments and junctions of the loop. The simplified thin-wire kernel of NEC-2 also applies to each segment and wire junction. Hence, we expect some divergence of results relative to NEC-4. The EK version of NEC-2 does not apply the extended thin-wire kernel to junctions of wires that are at an angle--the bent-wire case. As a consequence, its reports will coincide with neither NEC-4 nor NEC-2-without-EK.

+
+ +
+

As we increase the wire radius, the surface of one wire at a junction penetrates farther into the central region of the other wire segment forming the junction, as suggested by the simple sketch in Fig. 4. As the penetration reaches a region where it alters the current calculation, the results grow less reliable. Between ratios of 5:1 and 3:1, we encounter a growing variance among the reports, with no internal guidance as to which may be the more nearly correct. In just the region that the EK card in NEC-2 provided significant modeling assistance in terms of the accuracy of results, it proves to be of little assistance with closed geometries and other bent-wire configurations without external means of verification.

+

The use of the EK card with NEC-2 thus finds its best range of uses with straight-wire elements of uniform diameter. For segment-length-to-radius ratios between 8:1 and 2:1, it yields results that are consistent with those emerging from NEC-4. Perhaps one day we shall see the EK facility appear as a user option on most entry-level NEC-2 software.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod82-1.gif b/content/amod/amod82-1.gif new file mode 100644 index 0000000..c2b411f Binary files /dev/null and b/content/amod/amod82-1.gif differ diff --git a/content/amod/amod82-2.gif b/content/amod/amod82-2.gif new file mode 100644 index 0000000..d9e7a68 Binary files /dev/null and b/content/amod/amod82-2.gif differ diff --git a/content/amod/amod82-3.gif b/content/amod/amod82-3.gif new file mode 100644 index 0000000..50dfc1f Binary files /dev/null and b/content/amod/amod82-3.gif differ diff --git a/content/amod/amod82.html b/content/amod/amod82.html new file mode 100644 index 0000000..0f32867 --- /dev/null +++ b/content/amod/amod82.html @@ -0,0 +1,191 @@ + + + + + The Nature and Adequacy of NEC Correctives + + + +
+

82. The Nature and Adequacy of NEC Correctives

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

NEC has a number of correctives for special situations. The most notable of these situations involves the ratio of segment length to wire radius. In NEC-2, whenever the radius is greater than about 1/4 the segment length, the NEC-2 manual recommends the use of the EK command, which invokes the extended thin-wire kernel. We examined that feature of NEC-2 in the last episode. We also noted that NEC-4 revised the algorithms for determining the currents on wire segments so as to do away with the need for the EK command.

+

The most noted external corrective for NEC-2 involves the inherent weakness of the program for dealing with elements having a tapered diameter, as illustrated in Fig. 1.

+
+ +
+

The most commonly used corrective system was developed by Leeson and involves the use of substitute uniform-diameter elements. The substitute elements involve a reasonably complex procedure that begins with the detection of the element ends and hence the determination of the range of wires over which the corrective will be applied. The wires must be linear and symmetrical about a center coordinate. The exception is a monopole wire in contact with the ground with its source (if any) on the segment adjacent to the ground. The wire with two ends must place any sources or loads on the center segment. Moreover, the corrective is valid for only a restricted frequency range, usually prescribed as being within about 15% of the element being 1/2 wavelength. Most programs (such as EZNEC and NEC-Win Plus) simply refuse to invoke the correctives if the element does not meet any one of the limiting criteria. Although the standard case for the application of Leeson correctives is the downward taper of element diameter, as portrayed in Fig. 1, the correctives will also work with bi-conical antennas composed of stepped diameter elements.

+

The adequacy of the Leeson correctives is dependent upon a number of factors. One of those factors is the uniformity of segment length along the substitute element. If we model a physical element exactly, we often find a mixture of long, short--and sometimes very short--sections of element for the various element diameters. There is a tendency among modelers to under-segment the longer wires in the element relative to the shorter wires. Consider the situation in Fig. 2.

+
+ +
+

In this example, the short center section uses a single segment, followed in the next wire by longer segments, etc. The application of the Leeson correctives normally pre-calculates a total element length for the substitute element, using the calculated uniform diameter that achieves an element having the same electrical characteristics as the original tapered-diameter element. Then the program will calculate the length of wires that substitute for each of the original wires. The program will normally use for each new wire the same number of segments as specified for the tapered diameter wire. The resulting element will be as uniform or non-uniform in segment length as the originally specified element.

+

The new algorithms of NEC-4 ostensibly did away with the need for using the Leeson corrections. For many cases, NEC-4 produces virtually identical results as does NEC-2 with the Leeson correctives invoked. However, NEC-4's new algorithms are not without limits. If the rate of diameter change is too great or if the overall decrease in diameter is too large along the overall length of the element, NEC-4 will tend to over estimate the gain of the element and underestimate the source impedance, if that element is driven.

+

We may illustrate the situation for virtually all of the limitations by running a pair of contrasting elements through all of the available options. We shall begin with a "low-taper" element that I extracted from a multi-element Yagi design for 20 meters. I isolated the driven element of the array, but made no attempt to resonate it in isolation, relative to its resonant length within the array. Hence, the element will show some feedpoint reactance.

+

The following EZNEC description of the element shows the free-space environment used for the comparisons. However, it was necessary to run the element in a variety of programs, including NEC-Win Pro, GNEC, and EZNEC, in order to cover all of the possibilities.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+lo-taper element                                          Frequency = 14.175 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                -205.95,   79.8,      0      W2E1     -156,   79.8,      0     0.625   4
+2          W1E2     -156,   79.8,      0      W3E1     -120,   79.8,      0      0.75   3
+3          W2E2     -120,   79.8,      0      W4E1      -72,   79.8,      0     0.875   4
+4          W3E2      -72,   79.8,      0      W5E1       72,   79.8,      0         1   13
+5          W4E2       72,   79.8,      0      W6E1      120,   79.8,      0     0.875   4
+6          W5E2      120,   79.8,      0      W7E1      156,   79.8,      0      0.75   3
+7          W6E2      156,   79.8,      0             205.95,   79.8,      0     0.625   4
+
+Total Segments: 35
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       4        50.00      50.00    7        1           0         I
+
+Ground type is Free Space
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The segmentation along the element is relatively uniform. For wires 1-4, the segment lengths are 12.49", 12", 12", and 11.07". As well, the long center section of the element with 13 uniform length segments ensures that the segments adjacent to the source segment are the same length as the source segment. The diameter steps are a uniform 0.125" drop per step.

+

Now let's run this element through all of the available combinations of corrected and uncorrected situations that we can generate with the NEC-2 and NEC-4 cores. Our results should resemble those in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           Low-Taper Element Free-Space Gain and Source Impedance
+
+Core and Condition                                        Gain (dBi)           Impedance (R+/-jX Ohms)
+
+NEC-2
+1.  No internal or external correctives                   2.20                 76.49 + j 19.23
+2.  EK command invoked                                    2.20                 76.78 + j 19.21
+3.  Leeson correctives invoked                            2.14                 74.68 + j 11.85
+4.  Resubstitution of a single wire with the Leeson
+       diameter, length, and total number of segments     2.14                 74.69 + j 11.94
+
+NEC-4
+1.  No internal or external correctives                   2.17                 76.14 + j 12.84
+2.  Resubstitution of a single wire with the Leeson
+       diameter, length, and total number of segments     2.14                 74.69 + j 11.94
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In NEC-4 programs that permit the use of Leeson corrections (such as EZNEC Pro/4), there is rarely any difference between corrected NEC-2 and corrected NEC-4. The Leeson corrections apply only to modeling situations in which there is no inherent difference in the performance of the two cores.

+

Given the relatively gentle taper of the element, even the NEC-2 results are not dramatically off the mark. However, note that the "raw" NEC-4 results are only about halfway home in the estimation of gain, although they are quite close in the estimation of the source impedance. Of course, the standard for these remarks is the Leeson correction result, which is presumed accurate here and has tested accurate in innumerable physical antenna designs.

+

For our second example, let's use a much more highly tapered element, extracted from another multi-element array. The element model employs a short, fat center section simulating the boom-to-element assembly. Our concern in this exercise is not the adequacy of that technique, but its consequences for the element model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+hi-taper element                                          Frequency = 14.175 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                 -203.5,     72,      0      W2E1     -138,     72,      0       0.5   8
+2          W1E2     -138,     72,      0      W3E1      -96,     72,      0     0.625   6
+3          W2E2      -96,     72,      0      W4E1      -48,     72,      0      0.75   6
+4          W3E2      -48,     72,      0      W5E1       -4,     72,      0     0.875   5
+5          W4E2       -4,     72,      0      W6E1        4,     72,      0     3.419   1
+6          W5E2        4,     72,      0      W7E1       48,     72,      0     0.875   5
+7          W6E2       48,     72,      0      W8E1       96,     72,      0      0.75   6
+8          W7E2       96,     72,      0      W9E1      138,     72,      0     0.625   6
+9          W8E2      138,     72,      0              203.5,     72,      0       0.5   8
+
+Total Segments: 51
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       5        50.00      50.00    1        1           0         V
+
+Ground type is Free Space
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Ideally, the segment lengths adjoining the source segment (Wire 5) should be the same length as the source segment. However, the segment lengths for wires 1 through 5 read as follows: 8.19", 7", 8", 8.8", 8". Achieving the desired result would require additional segments on an already large model (when we add all of the other elements of the original array). We are blocked from further segmenting the short, fat source wire, because the segment-length-to-radius ratio is already 4.68:1. Adding a segment each to wires 4 and 6 would have resulted in a segment length as much below the segment length on Wire 5 as the present segmentation places the length above that of the center segment in the element.

+

Let's see what happens to the results for this model when we run it through the same set of core runs that we used for the low-taper element.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           High-Taper Element Free-Space Gain and Source Impedance
+
+Core and Condition                                        Gain (dBi)           Impedance (R+/-jX Ohms)
+
+NEC-2
+1.  No internal or external correctives                   4.30                 45.33 + j  2.51
+2.  EK command invoked                                    4.37                 44.56 + j  2.48
+3.  Leeson correctives invoked                            2.16                 68.88 - j 11.44
+4.  Resubstitution of a single wire with the Leeson
+       diameter, length, and total number of segments     2.12                 69.59 - j 11.52
+
+NEC-4
+1.  No internal or external correctives                   3.06                 59.14 - j  6.17
+2.  With the VC command invoked                           2.95                 60.57 - j  6.26
+3.  Resubstitution of a single wire with the Leeson
+       diameter, length, and total number of segments     2.12                 69.58 - j 11.53
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The wholesale inability of raw NEC-2 to handle the highly tapered element is evident. I invoked the EK command in the NEC-2 sequence of results simply to demonstrate that the EK command is not a substitute for the Leeson corrections. If we skip to the NEC-4 results, we find that the very high taper and other limitations of the element model also yield results that are well off the mark set by invoking the Leeson corrections. Once more, the gain report is about halfway between the NEC-2 report and the Leeson report. However, the source impedance report is about 2/3 the way home--a function of the fact that one figure is recorded in dB while the other uses a non-logarithmic adjustment. Raw NEC-4 shows an average gain test value of 1.235 for the element. The adjusted gain would be 2.14 dBi, much closer to the Leeson value.

+

Unlike the low-taper element case, the high-taper element does show a difference between the results for the modeled element and for a one-wire substitute element with the same length, diameter, and total number of segments as the programmed set of wires. The difference is not great, since some pains were taken to equalize segment lengths as best one could within the original model. Less careful segmentation--as is commonly used in casual modeling of large arrays with tapered diameter elements--would have yielded a higher disparity between the programmed Leeson element and the 1-wire equivalent element.

+

Because the highly tapered element has a short, fat center section with a segment-length-to-radius ratio of only 4.68:1, I added an entry to the NEC-4 list. One run of the model invokes a new command in NEC-4 labeled VC, for voltage cap. For the element that we have been testing, the invocation of the new command produces noticeable but not very large differences relative to raw NEC-4.

+

NEC-4 introduces wire-end caps as a standard part of the overall calculations. At a voltage source segment or at segments with impedance loads, NEC-4 makes it optional for the user to introduce segment end caps "to reduce the excitation of the inside of the wire at these points." Fig. 3 shows the general situation at a voltage source.

+
+ +
+

The sketch is adapted from Part II (page 29) of the NEC-4 manual and does not show all mathematical detail. Its purpose is to acquaint you with the general situation at the voltage source with respect to the caps forming the inside ends of the wire segments on either side of the source segment. See the NEC-4 manual for full mathematical details.

+

To employ these end caps, we need only place a simple program control card in the deck:

+ 
VC
+

The end caps become important for small segment-length-to-radius values. As the ratio goes below 2:1 and continues to shrink, the imaginary part of the current and the real part of the charge will go into oscillation without the use of end caps. Because a source that is near to the end of a wire may show an error in the source voltage, the end caps have been made optional by introducing them via the VC command.

+

For the average user of NEC, the question that is often preliminary to matters of mathematical refinement is at what point the use of the VC command will begin to show differences from the same model without using the VC command. To provide a sample answer, we may return to the simple dipole that we have used in other episodes. The NEC input file for this dipole is quite simple.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM NEC-WIN Example
+CM Simple dipole antenna in Free Space
+CM Optimized for resonance at 300 MHz
+CE
+GW 1 9 0 -.2418 0 0 .2418 0 .0001
+GS 0 0 1
+GE 0 -1 0
+VC
+EX 0 1 5 0 1 0
+FR 0 1 0 0 300 1
+RP 0 181 1 1000 -90 0 1 1
+RP 0 1 360 1000 90 0 1 1
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 9-segment free-space dipole is initially resonant at 300 MHz. Let's catalog the gain and source impedance reports as we enlarge the radius of the antenna without altering any other factors. The only difference between the non-VC and VC models is the absence of the VC line in the former.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    Gain and Source Impedance of a Dipole With and Without the VC Command
+
+Wire Radius   Segment-Length-to-           Without VC                          With VC
+(meters)      Radius Ratio          Gain (dBi)    Source Z              Gain (dBi)    Source Z
+0.0001        537:1                 2.12          72.08 - j 0.00        2.12          72.08- j 0.00
+0.001         53.7:1                2.13          75.63 + j16.51        2.13          75.63 + j16.52
+0.01          5.37:1                2.18          91.47 + j32.38        2.15          91.57 + j33.10
+0.0134        4:1                   2.20          95.68 + j30.11        2.15          95.71 + j31.69
+0.0179        3:1                   2.22          99.78 + j23.97        2.14          99.71 + j27.48
+0.0269        2:1                   2.26          102.41 + j5.13        2.10          103.60 + j15.82
+0.0537        1:1                   2.38          51.89 - j46.29        1.93          99.00 - j17.25
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As the ratio reaches the 4-6:1 level, we can clearly see an effect upon the gain report with and without the use of the VC command. Without the VC command, the gain report increases steadily. In contrast, with the VC command invoked, the gain reaches a peak value and then descends. Except for the 1:1 segment-length-to-radius ratio value, there is little difference in the source impedance reports. However, for the very small ratio, the source impedance difference is considerable. The non-VC report represents a precipitous drop in resistance and a rapid shift in the reactance. With the VC command invoked, the resistance remains in the general range of the preceding reports, with a milder shift in reactance.

+

The test dipole used only 9 segments, a segmentation density one might consider below true convergence. So we may reset the dipole example for a segment-length-to-radius ratio of 1.5:1. We may sample a number of different levels of segmentation by simply altering the radius so that it is always 2/3 the segment length. The results of this exploration form an interesting table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Constant Dipole Length and Segment-Length-to-Radius Ratio
+
+No.    Segment       Radius                Without VC                          With VC
+Segs   Length (m)    (m)            Gain (dBi)    Source Z              Gain (dBi)    Source Z
+
+ 9     0.0537        0.0358         2.30           95.83 - j 17.52      2.05          104.00 + j  3.81
+15     0.0322        0.0215         2.20          129.68 - j 34.52      2.09          141.40 - j  8.96
+25     0.0193        0.0129         2.13          182.40 - j118.85      2.09          224.11 - j 92.56
+41     0.0118        0.0079         2.11          215.06 - j258.65      2.09          292.31 - j262.77
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With the VC command invoked, the gain stabilizes very rapidly with the increase in the number of segments and a constant segment-length-to-radius ratio. Without the VC command in use, the gain descends with increasing numbers of segments toward the "with-VC" value. The source impedance values follow the same general trends, but show noticeably different values are each level.

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At the same time as the results appear to be converging, the average gain test (AGT) values also approach closer to 1.000. However, with the lowest segmentation level and no VC command, the AGT value is 1.0148. With the AGT command in use, the corresponding AGT value is 0.9591. The two sets of AGT values approach 1.000 from opposite directions, and the use of the VC command results in a slightly poorer AGT value than without the command in use. A similar pattern holds for the first sample that we took. Without the VC command in use, we obtained a gain report of 2.38 dBi with a source impedance of about 52 - j46 Ohms. With the VC in use, the gain report was 1.93 dBi with an impedance of 99 - j17 Ohms. Although the VC report appeared more closely tied to the preceding ratios of segment length to radius, the non-VC AGT value was 1.0315, while the VC value was 0.9330, about twice as distant from the ideal value.

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The VC command, then, yields results that are not self-interpreting or wholly consistent with other markers that one normally uses to develop a sense of model adequacy. In general, then, the VC source wire-end cap command should only be used where there are experimental results with which to correlate the results. The NEC-4 manual notes that the "voltage-source end caps have been made optional until their effect is better understood."

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83. Insulated Wires: The NEC-2 Way

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L. B. Cebik, W4RNL

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In episode #50 of this series, I called attention to the IS (Insulated Sheath) card introduced into NEC-4. The program control command provides a means to factor into a model the effects of the conductivity and permittivity of insulation wrapped around a wire. Assuming a high insulating effect--that is, a very low conductivity--the physical shortening effects of insulation on a wire for a given frequency are functions of the permittivity (relative dielectric constant) and thickness of the insulation.

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NEC-4 and IS

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Fig. 1 shows the situation of an insulated wire. For NEC modeling, there are two radii of interest. One is the radius of the conducting wire (WR). The second is the radius of the wire-plus-insulation (SR). The difference in the two radii is the thickness of the insulation (D). In NEC-4, we can enter the required data in the IS command and obtain automatic calculation of the effects of the insulation. By comparing, for example, the resonant length of a bare wire and a wire with a given type and thickness of insulation, we can obtain the velocity factor of the insulated wire in antenna (not in transmission-line) service. See column 50 for some ranges of velocity factors that apply to typical types and depths of insulation.

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I do not presently have access to a handy list of relative dielectric constant values for wire insulations that we commonly encounter. One of the few guides available comes from the checking sources like Passive Electronic Component Handbook, 2nd Ed, edited by Charles A. Harper (McGraw-Hill, 1997). The capacitor chapter provides an interesting--although not wholly relevant--list of plastics used as capacitor dielectrics, along with their approximate dielectric constants. Some of these same plastics are used for wire insulation.

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Material                                                         Approx. Permittivity
+Polyisobutylene                                                                2.2
+Polytetrafluoroethylene (PTFE)                                                 2.1
+Polyethylene terepthalate (PET)                                                3.0-3.2
+Polystyrene (PS)                                                               2.5
+Polycarbonate (PC)                                                             2.8-3.0
+Polysulfone (PSU)                                                              2.8-3.2
+Polypropylene (PP)                                                             2.2
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Common plastics, then, appear to have a range of relative permittivity values between 2 and 3. In contrast, the permittivity of a vacuum is by definition 1.0, and air is 1.0006. If we specify a relative permittivity value of 1.0 for any sheath, no matter how thick, we obtain the performance of bare wire.

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Fig. 2 shows--at the top--the model for a resonant 30-MHz dipole using 2-mm diameter copper wire in free space. In this model, the wire has a 2-mm-thick insulating sheath with a permittivity of 2.25. The model shows the length of the dipole when brought to resonance. The dipole half-length of 2.302 m contrasts to the bare-wire half-length of 2.416 for resonance. The result is a velocity factor of 0.957.

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In episode 50, I cataloged a considerable mass of baseline data for the IS command using the 30-MHz dipole. I took three cases involving a 2-mm diameter wire: with 0.5-mm, 1.0-mm, and 2.0-mm thick insulation. I then systematically ran each physical situation through permittivities from 0 through 3 in 0.25 steps. My goal was to develop a series of curves for various ways of looking at the data for the progression of insulation thickness that had a 1-2-4 progression. Part of that work was to develop data on the 30-MHz dipole's resonant length and resonant impedance for each permittivity level.

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These two data categories will be useful to us when we examine an alternative means of handling insulated wires that is equally applicable to any form of NEC.

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Insulation through LD2

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Although NEC-2 does not have anything to equal the simplicity of an IS command, it is possible to simulate the effects of wire insulation by using the LD 2 command. The use of the LD 2 command has a limited application to dipole-type geometries, but may prove useful to NEC-2 users with unmodified cores. The commands LD 0 through LD 3 specify lumped loads of either series or parallel R-L-C types. (LD 4 is the R-X load, while LD 5 is the command used to specify the conductivity of the wire, where no entry indicates a perfect or lossless wire.) In early episodes of this series, we have worked in detail with the use and limitations of both series and parallel loads that specify the capacitance or the inductance in basic units--the LD 0 and LD 1 commands. However, for most modeling situations, there seems to be little application for the LD 2 and LD 3 commands, which also specify either series of parallel R-L-C circuits. However, these commands use distributed values, specified as farads/meter or henrys/meter.

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We shall be employing the LD 2 series circuit, but use only one value: the inductance value in distributed form. The premise is simple: an insulated sheath around a wire acts very much like a distributed inductance along the wire in terms of shortening the required physical length for a given electrical length. Since LD loads are non-radiating, whether lumped or distributed, the use of the LD 2 load has no affect on the performance pattern of the antenna except as the physical wire length has an affect.

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The middle portion of Fig. 2 shows the direct substitution of an LD 2 command card for the IS command.

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LD         2    1       1         21    0  1.033e-7   0
+Command  Type  Tag  Start Seg  End Seg  R      L      C
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The expanded version of the LD 2 line identifies the individual entries. Note that for this type of entry, we select all of the segments on the wire to apply the following series R-L-C values uniformly along the length. The value of the required inductance in H/m is in the order of E-07, that is, in the ballpark that surrounds a tenth of a uH/m. The exact amount that I placed in the LD 2 line was the amount required to resonate the dipole at the same length and frequency as the IS card. I called the dipole resonant if the reactance was under +/-0.2 Ohms. By a series of modeling exercises, I was able to replace all of the IS commands from episode 50 with LD2 commands with L/m values for the three cases and for all permittivities from 0 through 3. Then I made a table.

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The table actually has more data than we yet have use for, but we may examine most of the lines. The "Permittivity" line in each of the 3 sections lists the range and increments of dielectric constants covered by the exercise. The "DP Length" line shows the half-length in meters. The "Zres IS" line records the resonant impedance or feedpoint resistance for each dipole length and permittivity level.

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The next line--"A:L/m"--records the value of distributed inductance required to bring the dipole back to resonance after removing the IS line. The following line lists the resonant impedance recorded from the model that used that specified value of L/m. As you will note, there is a slight but no where close to debilitating difference in the Zres numbers that emerge from the use of the IS command and from the use of the LD 2 command to simulate wire insulation.

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You may create from the specified lines of the table a chart that correlates insulation permittivity and thickness on the one hand and usable model values for LD 2 commands to simulate in NEC-2 the increments of insulation covered. 2-mm diameter (1-mm radius; 0.0787" diameter) wire is about half way between AWG #14 (0.0641") and AWG #12 (0.0808"). The indicated L/m value should cover both wire sizes and associated insulation. Remember to use the center portion of Fig. 2 as a model-construction guide. It should especially remind you to multiply each of the values shown in the table by E-07.

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You can roughly approximate these values by knowing the insulation thickness, the wire size, and the relative permittivity of the insulation. You can pre-calculate the required values from the following rough equation:

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where L/m is the distributed inductance in henrys/meter, epsilon is the permittivity of the insulation, R is the radius of the wire-plus-insulation, and r is the radius of the wire itself. The equation is especially good for permittivity values between 2 and 3, the normal range of insulation dielectric constant for most wire used by radio amateurs. However, the final constant (2.267) is an average between the lowest and highest values required to cover all of the required values of L/m in the table. Within the range of the table, calculated values at the extremes reach an error of +/-6%. However, a 6% error in the LD 2 command inductance entry still provides a model that is off resonance only by about 3 to 4 Ohms of reactance. Hence, the calculation may still be quite serviceable for practical applications.

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The value of L/m actually undergoes an inflation with increases in both the ratio of radii and permittivity. The approximate rate of expansion is roughly equal to the product of those 2 values to the 12th root. So you may obtain a further bit of accuracy by using this variant of the roughest equation:

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The use of the expansion factor on the equation's constant results in maximum errors for L/m of less than 2% across the range of calibration. For most combinations of radii ratios and permittivities, the error is less than 0.5%.

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Of course, the error notes for equations 1 and 1A are not a comparison to a physical antenna, but a correlation of LD 2 values of L/m to NEC-4 IS results for the range of radii and permittivity in the original table for a 2-mm copper dipole at the test frequency. In both the initial approximation and the version of the equation with the expansion adjustment, the second term ensures that the value of L/m goes to zero when the permittivity goes to 1, the condition of a bare wire. As well, the final term ensures that the value of L/m goes to zero when R and r are equal, again, the condition of a bare wire.

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Equations 1 and 1A are ad hoc adjustments of a somewhat different equation developed by Alexander Yurkov, RA9MB. We shall look at his alternative as our next step in providing a substitute for the IS command for NEC-2 users.

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The RA9MB/UA3AVR Insulated Wire Simulation

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Yurkov took a different tack in developing his modeling aid for insulated wires. He calculated the effect of insulation, taking the entire wire-plus-insulation radius as his basic unit. Examine the lowest model in Fig. 2. Note that the wire radius is not the copper wire radius of 1 mm, but the insulation outer radius of 3 mm. In the LD 2 line, note that the value of distributed inductance is considerably different from the value used in the middle model. (The middle model retained the wire size as originally specified.)

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Equation 2 uses the same terms as equation 1. However, the Yurkov adds a term, the square of kabs. The term "kabs" stands for an "absolute velocity factor" and uses the value 0.95 in applications of the equation. Yurkov's original equation also employs a complex first term that he labels µ0. However, Dimitry Federov, UA3AVR, modified the equation for use in NEC models by dividing that term by values that simplified the left-most term of the equation to the form used in equation 2. For further information on the Yurkov equation and its foundations, you may visit www.qsl.net/ua3avr/Read_me_Eng.htm.

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As an exercise, I took the models used in the first two steps of the data table and modified the GW lines to reflect the larger wire radius required by the Yurkov equation. I then varied the value of "B:L/m" until the dipole was once more resonant for each case and increment of permittivity. I recorded the resulting resonant impedance as "Zres 1.5" (or "Zres 2" or Zres 3", depending upon the case).

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The final line of the data table lists "C:L/m," the values of distributed inductance calculated directly from equation 2.

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We can summarize the differences between the Yurkov equation and my rough variant in this way. Yurkov's equation is based on solid foundations. However, it requires that the user alter the wire radius from its wire value to a value equal to the insulation radius. For most real cases, that change will make no significant difference to the reported data. However, it does result in a requirement to introduce a negative inductance for permittivity values of 1 and just above 1 in order to restore the dipole to resonance. Thickening the wire changes both the skin effect and the resonant length so as to require a capacitive reactance for resonance with the fixed dipole lengths used. Note that NEC will handle at least small values of inductance in negative numbers. On the other hand, my initial rough equation has a narrower range within which it yields accurate values, although the version including expansion is at least as accurate as the Yurkov equation over the test range in correlations with the results of NEC-4 models using the IS command. In addition, equations 1 and 1A retain the original wire radius in the model. Which version you employ will make little difference practically and may well turn out to be a function of which equation you are most comfortable solving and which modeling technique (applying the original or the adjusted wire radius) you are most comfortable using.

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How Confident Should We Be in the NEC-2 LD 2 Simulation of Insulated Wires?

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Tabular data often does not lend itself to evaluations indicated by our lead question. Perhaps we can better judge our confidence level in the Yurkov substitution method by graphing the data. Note that we have no external baseline of empirical data. So we shall be comparing the results obtained by the NEC-4 IS command with the substitute methods of handling insulated wires in dipole-type antennas. We shall proceed on a case-by-case basis, beginning with the thinnest insulation.

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Fig. 3 has 3 lines. The redline indicates the required values for L/m to restore the dipole to resonance based on the original use of the IS command in NEC-4. These values are based on retaining the specified wire radius as it was in the original NEC-4 IS model. The green line indicates the values of inductance required if we increase the wire radius to the value indicated by the insulation radius. In this case, the radius increases from 1 mm to 1.5 mm. The blue line records the values of L/m calculated from the Yurkov equation.

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Two trends are equally important in this graph. First, all three curves are closely parallel, indicating the general validity of either procedure in simulating an insulated wire. However, at very low values of permittivity, the enlarged conductor radius of the Yurkov method results in required values of L/m that are less than zero. This situation represents a limit to the application of the Yurkov equation, since a permittivity of 1 should yield the same results as a bare wire (under the condition that the conductivity is so low as to be negligible). However, most applications will never encounter this situation.

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The second trend involves the modeled values of L/m and the values of L/m calculated from the Yurkov equation. The two lines are too close together to yield differences in modeling results that could be called significant.

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Fig. 4 tracks the 30-MHz dipole resonant impedance under three conditions. The red line indicates the resonant impedance using the original NEC-4 model with the IS command. The green line indicates the resonant impedance using the 1-mm radius wire and the associated LD 2 command entries. The blue line provides values of resonant impedance using the increased radius and the required values of L/m in the LD 2 command. The three lines correspond to the upper, middle, and lower models in Fig. 2.

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Perhaps the most telling note that we can make for this graph is this one: at widest divergence, the modeled resonant impedance values vary among all three lines by less than 0.25-Ohm relative to a median value of nearly 70 Ohms.

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Fig. 3 and Fig. 4 tracked the data for the thinnest insulation--0.5 mm. Fig. 5 and Fig. 6 track the data for the next level of insulation thickness: 1.0 mm. Fig. 5 provides information on the values of L/m for the same three situations described for Fig. 3. Once more, the curve for the 1-mm wire parallels the curves for the 2-mm wire, with the latter pair of curves dipping below an L/m value of zero for the lowest permittivity level. Again, the calculated and modeled values of L/m for the Yurkov case are too close together to represent any significant difference.

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Fig. 6 tracks the three defined resonant impedance cases, in parallel to Fig. 4, but for the middle insulation thickness. Once more, the three lines are within about a quarter-Ohm of each other at their widest divergence. However, there is a systematic variance between the values that emerge from using the IS command and those emerging from use of the LD 2 simulation when using the same wire radius in the GW line. This condition suggests a difference between the two methods for simulating the effects of insulation, but not a difference that should create a level of variance that has practical implications for the average wire antenna builder.

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Fig. 7 and Fig. 8 track the same two data sets for the thickest insulation: 2 mm. The L/m traces show the same parallel development. However, the values calculated from the Yurkov equation and the values required by the model to restore the 3-mm radius wire to resonance begin to diverge at both ends of the permittivity range covered. The final sets of values for the green and blue lines at a permittivity of 3 differ by about 6%. However, for the 30-MHz dipole, that divergence yields an impedance that is off-resonance by only about 3.5 Ohms of reactance. For practical applications, construction variables would normally mask this difference.

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In Fig. 8, we have the traces for the three resonant impedance situations: the original IS model, the direct substitution of an LD 2 command for the IS command, and the use of the insulation radius as in the Yurkov equation. The latter two cases parallel each other with a maximum separation of about a third of an Ohm. Interestingly, the original IS model shows resonant impedance values that begin by tracking the direct replacement model and end by tracking the Yurkov model.

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Conclusion

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We began the series of graphs with the question of to what degree we might have confidence in using either equation 1 (or 1A) or equation 2 as NEC-2 substitutes for the IS command that is available in NEC-4 for dipole-type antenna elements. Over the range of tests covered by this exercise, the general answer is that we can have high confidence in the use of the LD 2 simulation for virtually all practical dipole applications. It yields results that are--to a high degree--consistent with those produced by the NEC-4 IS command.

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However, we need to enter a caution here. These initial tests cover only a single dipole. They do not cover all frequencies at which we generally use insulated wire for antennas--generally the HF range. Nor do the tests cover closed loops. These notes are not designed to fully validate the method, but only to show some of the procedures that might be used to validate the method for a given modeling situation. As well, these notes do not validate the substitute method against the physical realities of antennas, but only against the NEC-4 results when using the IS facility.

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We should also be aware of a second caution. We noted that equation 1 shows about a 6% potential error in the value of L/m at the extremes of its range of application. Equation 1A, of course, shows a much lower level of potential error, a maximum of 2% for the test range. The Yurkov equation shows limitations at the upper end of application to the same degree as equation 1. At the lower end of application--with very low values of permittivity--it also has a limit. Within the range of insulation thicknesses used in this exercise and within the range of permittivities covered, the limitations are no barrier to practical applications. Indeed, practical values of both insulation permittivity and insulation thickness generally fall within the limits of the exercise.

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There are, however, specialized applications that fall well outside the limits of the exercise. The general confidence that we can place on these simulation techniques may not carry over to such applications. Since both equations show trends toward divergence from the IS command models at the extremes of the test range, it is probable that further divergence will appear as we move well outside the test range of values. Hence, all such applications would require independent validation of whatever modeling technique is used to simulate insulated wires against the physical realities of antenna construction.

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Addendum: Why the Technique Has Limited Application

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Jack Louthan of TeriSoft has provided a simple and direct explanation of why the technique illustrated above has limited application. For example, it provides in the form given a reasonable output impedance value for a simple dipole, but the results for a closed loop show a significant divergence between IS-based and workaround-based results. In calculating the E-field for each segment in a model NEC calculates a "cosine" component, a "sine" component, and a "constant" component. NEC then sums the three fields to arrive at a total field value for each segment.

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LD commands modify the "constant" component of the E-field calculation, whereas IS commands (in NEC-4) modify the "cosine" component. As a consequence, any workaround formulation will result in satisfying only a limited range of geometries. The workaround shown is applicable only to linear elements--and likely only to applications in which the element is in the vicinity of 1/2 wavelength.

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These notes are directed toward users of existing NEC-2 codes. NEC-2 exists under numerous modifications, since it is readily available in the public domain. NEC-4 remains proprietary. Some software writers have adapted the NEC-4 IS command input to the NEC-2 framework and thus provide direct insulated wire or sheath inputs. Wherever the IS input is available, you should use it, since the results will be considerably more accurate for more antenna geometries than any workaround.

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84. GA: Creating and Moving Arcs

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L. B. Cebik, W4RNL

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In episode 69 of this series, I showed a way to create approximations of circles that used up to 16 sides via the equations facility of NEC-Win Plus. In that exercise, I was not only showing some easy techniques of polygon formation, but as well comparing the quality of circle approximations. The basic equations-page facet of the model appears in Fig. 1. Note that I have translated the dimensions from the original ones in inches for 146 MHz into meters for 300 MHz.

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Although the equations page appears simple enough, the model itself requires 16 wire and 48 segments, at 3 segments per wire. A standard ASCII NEC input file for the formulation appears in Fig. 2.

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You may wish to review column #69 for further details of the technique, especially if you do not have access to a version of NEC-2 having the complete command set. In this column, I want to review one of those seemingly more esoteric commands. As a sample, examine Fig. 3, which contrasts the 16-sided simulation of a circle with one having 90 sides with 1 segment per side. Obviously, the right-hand view of the antenna is much closer to a "perfect" circle--perhaps even more perfect than anything we might build. The question for this column is how we can build the circle.

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The requisite command is GA, Wire Arc Specification. The line is the same in both NEC-2 and NEC-4 and has the following appearance:

+ 
GA    1    5    10    50    75    .001
+      I1   I2   F1    F2    F3    F4
+      ITG  NS   RADA  ANG1  ANG2  RAD
+

The line begins (after the identification of the command) with the tag (or wire) number, followed by the number of segments: the two occupy the two integer places. All of the segments will have the same tag number, although constructing the arc with just the GW facility would give each segment a new wire or tag number, since each segment will have a different angle as well as coordinate set.

+

RADA specifies the radius of the arc relative to a perfect circle with its center at 0, 0, 0 on the coordinate system. The radius axis is relative to the Y-axis and hence will take a positive X value. The arc extends from ANG1 through ANG2 as measured relative to the X axis in the +/-Z direction around the Y-axis. Both ANG1 and ANG2 are in degrees. The angles move clockwise relative to the X-axis. RAD is the radius of the wire.

+

Therefore, the sample line specifies Tag 1 with 5 segments. The arc radius is ten (units of measure). The arc extends between 50 and 75 degrees "vertically," that is from 50 degrees from the X-axis to 75 degrees relative to the X-axis. You may, if you wish in a free-space model, begin with a negative angle.

+

Since we are not limited in segment length, except by the rules governing segment-length-to-wire-radius ratios, we can in principle create very close approximations of smooth arcs simply by increasing the number of segments in the GA command. The GA command gives us the ability to fabricate some interesting structures, so let's take a few steps in that direction.

+
+ +
+

First, we shall create a simple 90-degree arc using the specifications shown in the GA line in Fig. 4. Here we create a simple arc with 11 segments. Note that the arc extends from -45 to +45 degrees. The radius of 0.303 meters is not accidental. It yields a nearly resonant dipole when fed at segment 6 at the frequency specified in the FR line. In the E-plane, the gain is just under 2 dB, with a feedpoint impedance of about 65 Ohms. These values will be sensible to anyone who has modeled an inverted-Vee wire antenna, which brings its ends toward each other, but with straight-line legs.

+

The individual segments within Tag 1 are more interesting than the straight-line segments of an inverted-Vee, as evidenced by the extract from the NEC output report.

+ 
                                - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+ SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+ NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+   1   0.22841   0.00000  -0.19792   0.04323   49.09091   0.00000   0.00100     0    1    2      1
+   2   0.25425   0.00000  -0.16340   0.04323   57.27273   0.00000   0.00100     1    2    3      1
+   3   0.27492   0.00000  -0.12555   0.04323   65.45455   0.00000   0.00100     2    3    4      1
+   4   0.28999   0.00000  -0.08515   0.04323   73.63636   0.00000   0.00100     3    4    5      1
+   5   0.29915   0.00000  -0.04301   0.04323   81.81818   0.00000   0.00100     4    5    6      1
+   6   0.30223   0.00000   0.00000   0.04323   90.00000   0.00000   0.00100     5    6    7      1
+   7   0.29915   0.00000   0.04301   0.04323   81.81818 180.00000   0.00100     6    7    8      1
+   8   0.28999   0.00000   0.08515   0.04323   73.63636 180.00000   0.00100     7    8    9      1
+   9   0.27492   0.00000   0.12555   0.04323   65.45455 180.00000   0.00100     8    9   10      1
+  10   0.25425   0.00000   0.16340   0.04323   57.27273 180.00000   0.00100     9   10   11      1
+  11   0.22841   0.00000   0.19792   0.04323   49.09091 180.00000   0.00100    10   11    0      1
+

Note that the X-coordinate for the center of the 6th segment is 0.30223, although we specified a radius of 0.303. The deficit is due to the fact the segment 6 is a straight wire that cuts off very slightly the curve of a true arc. As the Seg. Length column shows, the command calculates the arc so that all segments have the same length.

+

The orientation of the arc is not especially useful. However, we may move it anywhere we wish via the GM command. Suppose that we wish to point the open side of the arc straight up and bring the bottom of the arc to a ground or Z=0 level. We can do so by using the GM command shown in Fig. 5.

+
+ +
+

The GM line specifies that we rotate the arc 90 degrees around the Y-axis so that the wire ends are upward. That rotation will bring the bottom of the arc below Z=0, so we may raise it on the Z-axis by the radius of the arc. The resulting segmentation table appears in the model output report.

+ 
                                - - - - SEGMENTATION DATA - - - -
+
+                                        COORDINATES IN METERS
+
+                         I+ AND I- INDICATE THE SEGMENTS BEFORE AND AFTER I
+
+
+ SEG.   COORDINATES OF SEG. CENTER     SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+ NO.       X         Y         Z       LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+   1  -0.19792   0.00000   0.07459   0.04323  -40.90909   0.00000   0.00100     0    1    2      1
+   2  -0.16340   0.00000   0.04875   0.04323  -32.72727   0.00000   0.00100     1    2    3      1
+   3  -0.12555   0.00000   0.02808   0.04323  -24.54545   0.00000   0.00100     2    3    4      1
+   4  -0.08515   0.00000   0.01301   0.04323  -16.36364   0.00000   0.00100     3    4    5      1
+   5  -0.04301   0.00000   0.00385   0.04323   -8.18182   0.00000   0.00100     4    5    6      1
+   6   0.00000   0.00000   0.00077   0.04323    0.00000   0.00000   0.00100     5    6    7      1
+   7   0.04301   0.00000   0.00385   0.04323    8.18182   0.00000   0.00100     6    7    8      1
+   8   0.08515   0.00000   0.01301   0.04323   16.36364   0.00000   0.00100     7    8    9      1
+   9   0.12555   0.00000   0.02808   0.04323   24.54545   0.00000   0.00100     8    9   10      1
+  10   0.16340   0.00000   0.04875   0.04323   32.72727   0.00000   0.00100     9   10   11      1
+  11   0.19792   0.00000   0.07459   0.04323   40.90909   0.00000   0.00100    10   11    0      1
+

We can see from the table that the ends of the arc are stretched symmetrically across the Y-axis from -X to +X. Segment lengths remain unchanged by the translation and rotation exercise. However, note the Z-value for Segment 6. Instead of being zero, it is 0.00077. A true arc would rest at Z=0. However, because segment 6 is a straight line, it remain shy of zero by the same amount that the identical position in the first model remained shy of the specified arc radius. For both models, note that the alpha orientation angle increases by 8.18182 degrees with each segment. Fig. 6 provides NEC-Vu representations of the two arcs. Note that in the right-hand case, the axes are conventionalized to the center of the sketch and do not show the fact that the entire arc is above Z=0.

+
+ +
+

So far, we have been exercising the GA and GM commands only far enough to orient us to their use to create and position a desired arc. We have not yet built anything interesting. Let's build something.

+
+ +
+

Fig. 7 shows the model of an "umbrella" reflector with a dipole driver. We recognize the GA line. The only difference between this line and our first model is that the number of segments is 10. The reduction is to place a segment junction at the center of the arc. The significant line is the GM command. It specifies that we shall increment the tag numbers by 1 and create 4 new structures identical to the entirety of the first. The third entry in the line specifies a rotation angle of 36 degrees for each new structure around the X-axis. By this means, we can create 5 full arcs or a 10-spoke "umbrella." Since we gave each arc 10 segments, each arc will join at the junction of segments 5 and 6. Fig. 8 shows the results of our modeling.

+
+ +
+

For this model, the umbrella ribs represent a reflector. Hence, the GW line with the tag number of 6 sets a near-resonant dipole ahead of the umbrella. for this exercise, I have not optimized the position of the driver relative to the reflector. Nor have I experimented with optimizing the arc size for maximum performance from the array.

+
+ +
+

Nevertheless, even this rough and ready construct exhibits a reasonable 2-element parasitic beam pattern, as revealed by Fig. 9. The free-space gain is 5.1 dBi, with a 9.9-dB front-to-back ratio. The feedpoint impedance is 61 Ohms resistive, since the spacing between the reflector and the driver center is about 0.75 wavelength.

+

Note that we have achieved this performance even though the reflector is circular rather than parabolic and is even smaller across then the dipole driver. The possibilities for experimenting with other radii of reflector arcs as well as different distances between the reflector and driver centers are nearly endless. Included in these experiments would be the reduction in the number of ribs or arcs, since only the two arcs most closely aligned with the driver carry significant current.

+

It is now time to use GA to create a complete circle, as promised at the beginning of this exercise. To make a complete circle with 90 segments, we need only modify our very first model, as shown in Fig. 10.

+
+ +
+

In this GA line, we specify a full 360-degree arc, that is, a circle. For simplicity, I specified ANG1 as 0 and ANG2 as 360. The arc has the 90 segments shown back in Fig. 3, with a source on the bottom-most segment (Segment 68, as noted in the EX line of the model). Let's run this model and compare the results with those that we obtained from the 16-sided approximation of a circular quad elements.

+ 
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Comparison of a 16-Sided and a 90-Sided Approximation of a Resonant Circular Loop
+
+       Model                 Free-Space           Feedpoint Impedance
+                             Gain dBi             R +/- jX Ohms
+       16 sides              3.63                 140.2 + j 0.0
+       90 sides              3.68                 142.3 - j 0.7
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+

Given that a square loop shows a gain of about 3.39 dBi with a resonant feedpoint impedance of about 125 Ohms, we see that the closer approximation of a true circle continues the upward progression of values. However, the values differ by under 1.5%, making the 16-sided approximation a fair representation of a circle. On the other hand, given the simplicity of the circular loop using the GA command, the original method of creating the 16-sided figure now seems cumbersome.

+

Single quad loops have applications, but multi-element quad beams are more common, at least for amateur-band operations. Let's take one final construction step and compare a pair of typical 2-element quad beam models.

+
+ +
+

Fig. 11 shows a NEC model of an optimized 2-element square quad beam for 299.8 MHz in free space with no element loading. The square quad beam model requires 8 wires (with 21 segments each in this model). For ease of modification, the model driver element is centered at X=0, Y=0, and Z=0, with the reflector spaced along the Y-axis. Modifying this array requires that we change at least 8 values to change the length or circumference for each element.

+

Alternatively, one might develop a set of equations and use variables for the element corner positions and for the reflector position relative to the driver. However, the modeling software must have a model by equation facility to do this. In fact, this model was derived from a more complex set of equations for which the user need enter only the design frequency and the element diameter. However, those equations do not cross over into the .NEC format input file. So the user must employ (at the time of writing) 2 programs--one with equation and variable facilities and one able to work in NEC-4 in this case.

+
+ +
+

In Fig. 12, we have a circular quad that uses the GA command to create the two requisite circles of wires. The driver line is simply a revision of our earlier single element circular loop. The reflector line begins with a circular loop created by the GA command and then uses the GM command to move the loop (Tag 2) the proper distance from the driver. Each loop has 90 segments.

+
+ +
+

Fig. 13 compares the two structures. The square quad beam has 168 segments using 8 wires or tags. The circular quad beam has 180 segments in two tags. However, as the models indicate, the circular structure has only 3 values that might require modification after the initial formation of the model. To change the driver circumference--and the length of every wire segment within it--we need change only the value of the driver (Tag 1) radius. A similar operation on Tag 2 changes the reflector size. We can change the element spacing simply by altering the GM card Y-axis translation value. In effect, we may easily optimize the design of circular quad beams because the variables are built into the GA and GM commands.

+

In episode 69, I suggested that the slight (0.3-dB) gain advantage of a circular loop over a square loop would be a 1-time matter. We should not expect to see the gain advantage increase arithmetically with every parasitic loop that we might add to a more elaborate quad. The following table tends to confirm the suggestion, since it presents the result of hand optimizing the circular quad beam for driver resonance and for maximum front-to-back ratio (in excess of 40 dB) at the design frequency.

+ 
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+               Comparison of 299.8-MHz 2-Element Square and Circular Quad Beams in Free-Space
+
+Quad          Driver Cir.    Reflector Cir.       Space          Gain   Front-Back    Feedpoint Impedance
+              meters         meters               meters         dBi    Ratio dB      R +/- j X Ohms
+Square        1.0233         1.1159               0.1657         7.17   46.25         142.2 - j 1.3
+Circular      0.9877         1.0820               0.1665         7.37   42.17         160.2 - j 0.4
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+

Immediately apparent is the fact that the circumference of the circular elements is smaller than the circumference of the square elements for equivalent performance properties. If you examine the current distribution on the square elements, you may discover part of the reason. At the square quad loop corners, we find a higher current level than would be found on a pair of 1/2 wavelength linear elements at equivalent positions. In contrast, the current distribution takes on a smoother curve with the circular loops. In addition to using elements with smaller circumference values, the circular loop requires slightly wider spacing than its square counterpart. Both models use a 0.001-m wire radius.

+

As was the case with the single loops, the circular array has a higher resonant feedpoint impedance than the square quad beam, about 13% higher. The 180-degree front-to-back ratios are comparable. The circular quad beam has a gain advantage of only 0.2 dB over its square comparator. Fig. 14--the free-space E-plane patterns for both arrays--suggests that the difference is operationally insignificant.

+
+ +
+

The performance of a parasitic array is a complex interaction of element diameter, size (circumference), and spacing. Hence, one might be able to tweak the values for slightly better performance out of either quad. However, such improvements would not likely translate into actual performance from a physical version of the antenna, since construction variables would tend to be larger than the percentage of change made to any of the variables in the design. The bottom line is that the shape we choose for a quad beam is more a function of mechanical demands at any given frequency than it is of the electrical superiority of one shape over another.

+

However, deciding quad array matters is secondary in this exercise. Our basic premise was that the GA command--especially when combined with the GM command--gives us the ability to construct interesting and potentially useful structures. It does so in a manner that allows easy user control over design modifications, which is always a desirable feature of a model. The umbrella reflector and the 2-element circular quad beam are but two samples that help demonstrate the ease of construction and modification.

+

In the course of this series, we have had occasion to cover many of the geometry commands that are not normally available on entry-level software. However, several still remain as potential subjects for future columns.

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+

Go to Main Index

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+

85. Electrical Fields at a Power Level and Distance

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

There are occasions on which the modeler needs to know the strength of a radiated electrical field using a specific power level and a specific distance from the antenna. If the antenna structure is centered at the coordinate system origin, that is, where X, Y, and Z equal zero, we can develop this information within NEC in a straightforward manner. However, the task requires more than one step.

+

The following exercises will develop those steps in two ways, paying special attention to the RP (pattern request) and the EX (excitation) commands.

+

Consider the following simplified model of a 1/4 wavelength monopole with 4 buried short radials.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 1/4-wl gp 4r
+CE
+GW 1,30,0.,0.,10.135,0.,0.,0.,.0254
+GW 2,1,0.,0.,0.,0.,0.,-.1524,.0254
+GW 3,10,0.,0.,-.1524,3.292,0.,-.1524,.003175
+GW 4,10,0.,0.,-.1524,0.,3.292,-.1524,.003175
+GW 5,10,0.,0.,-.1524,-3.292,0.,-.1524,.003175
+GW 6,10,0.,0.,-.1524,0.,-3.292,-.1524,.003175
+GE -1
+FR 0,1,0,0,7.05
+GN 2,0,0,0,13.,.005
+EX 0,1,30,0,1.414214,0.
+RP 0,181,1,1000,90.,0.,-1.,0.,0.
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The dimensions are in meters, with a 2" diameter main element and 0.25" diameter radials. Fig. 1 shows the outline of the antenna from two perspectives.

+
+ +
+

If we run this model over average ground, the gain is -2.29 dBi at a TO angle of 27 degrees elevation (63 degrees theta). The feedpoint impedance is about 59.4 + j0.4 Ohms. This is the typical data collection that many modelers are satisfied to collect, and Fig. 2 shows the theta (elevation) pattern that accompanies this omni-directional antenna.

+
+ +
+

However, many modelers are interested in the electrical fields from a given antenna. We may examine a portion of the data for the present model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+**** Electric Field: Theta Pattern ****
+Phi=0, Freq=7.05, File=vr4-ff.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+ Theta     Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+  90.00   7.1434E-008   -107.82   2.6078E-024    -93.92
+  89.00   9.5624E-002   -106.35   3.6393E-018    -94.28
+  88.00   1.7909E-001   -105.08   7.1385E-018    -95.44
+  87.00   2.5231E-001   -103.95   1.0497E-017    -95.92
+  86.00   3.1683E-001   -102.95   1.4097E-017    -95.36
+  85.00   3.7390E-001   -102.06   1.7780E-017    -94.98
+  84.00   4.2453E-001   -101.26   2.1636E-017    -95.05
+  83.00   4.6955E-001   -100.54   2.4428E-017    -96.02
+  82.00   5.0965E-001    -99.88   2.8494E-017    -94.71
+  81.00   5.4540E-001    -99.29   3.1561E-017    -95.20
+  80.00   5.7729E-001    -98.74   3.5149E-017    -95.08
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 90-degree theta angle (0-degree elevation), of course, is not usable for anything, since results at the horizon are not usable. However, the other angles illustrate the sort of values that one will encounter in a typical scan of the e-fields when calling a standard far-field pattern.

+

In most instances, the values are useful only for comparative purposes. They do not provide any useful information directly about the e-field values at a given distance and a given theta (elevation) angle or height above ground.

+

One way to overcome this problem is to make an RP 1 ground-wave request. In this type of request, one sets a distance from the coordinate system origin using the (F5) position. Instead of specifying an initial theta angle in (F1), the user specifies a height above ground (Z) in meters. One may select for (F3) an increment for multiple readings. The number of theta values in (I2) will now become the number of heights for observation of the e-field, beginning at the value in (F1) at intervals determined by (F3). However, all values will lie along a cylinder extending from the surface upward at the distance set into (F5).

+

The following lines show a typical simple model using RP 1 at a distance of 1000 meters and a single height of 2 meters.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 1/4-wl gp 4r
+CE
+GW 1,30,0.,0.,10.135,0.,0.,0.,.0254
+GW 2,1,0.,0.,0.,0.,0.,-.1524,.0254
+GW 3,10,0.,0.,-.1524,3.292,0.,-.1524,.003175
+GW 4,10,0.,0.,-.1524,0.,3.292,-.1524,.003175
+GW 5,10,0.,0.,-.1524,-3.292,0.,-.1524,.003175
+GW 6,10,0.,0.,-.1524,0.,-3.292,-.1524,.003175
+GE -1
+FR 0,1,0,0,7.05
+GN 2,0,0,0,13.,.005
+EX 0,1,30,0,1.414214,0.
+RP 1 1 361 1000 2 0 1.00000 1.00000 1000
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that only the RP line has changed relative to the initial model that made a far field request. However, we obtain what is essentially a limited data phi (azimuth) pattern output for the specified distance and height.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+**** Electric Field: Phi Pattern ****
+Z=2, Freq=7.05, File=vr4-rp1.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+  Phi      Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+   0.00   1.9180E-004    -19.95   1.6350E-022    119.22
+   1.00   1.9180E-004    -19.95   5.1436E-012    134.30
+   2.00   1.9180E-004    -19.95   1.0262E-011    134.30
+   3.00   1.9180E-004    -19.95   1.5331E-011    134.30
+   4.00   1.9180E-004    -19.95   2.0325E-011    134.30
+   5.00   1.9180E-004    -19.95   2.5219E-011    134.30
+   6.00   1.9180E-004    -19.95   2.9991E-011    134.30
+   7.00   1.9180E-004    -19.95   3.4617E-011    134.30
+   8.00   1.9180E-004    -19.95   3.9074E-011    134.30
+   9.00   1.9180E-004    -19.95   4.3341E-011    134.30
+  10.00   1.9180E-004    -19.95   4.7397E-011    134.30
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The data must appear promising, but before we do anything with it, let's examine the EX line of the model. We specified a value of 1.414214 as the voltage magnitude (the peak value corresponding to 1 volt RMS). If we are interested in the power level that yields these values, we must also examine the power budget.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ - - - POWER BUDGET - - -
+
+ INPUT POWER   = 1.6842E-02 WATTS
+ RADIATED POWER= 1.6842E-02 WATTS
+ WIRE LOSS     = 0.0000E+00 WATTS
+ EFFICIENCY    = 100.00 PERCENT
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The antenna input power is 0.016842 watts. This is not likely to be a power level that is useful for taking e-field readings. As well, the input power with a standard EX 0 voltage source will vary from model to model according to the source impedance, since P = (E^2/R), where E is an RMS value.

+

Suppose that we are interested in the e-field values at 1,000 meters using an antenna input power of 1 kw. To arrive at these values, we must adjust the source voltage to a value that will yield them. The required voltage multiplier will be the SQRT (desired power/modeled power), or in this case, SQRT (1000/0.016842). The multiplier is 243.6706, for a new voltage entry on the EX 0 line of 344.6024. If we revise the model, we arrive at the following power budget and sample e-field lines.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ - - - POWER BUDGET - - -
+
+ INPUT POWER   = 9.9999E+02 WATTS
+ RADIATED POWER= 9.9999E+02 WATTS
+ WIRE LOSS     = 0.0000E+00 WATTS
+ EFFICIENCY    = 100.00 PERCENT
+
+**** Electric Field: Phi Pattern ****
+Z=2, Freq=7.05, File=vr4-rp1k.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+  Phi      Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+   0.00   4.6736E-002    -19.95   8.3783E-020    -55.87
+   1.00   4.6736E-002    -19.95   1.2533E-009    134.30
+   2.00   4.6736E-002    -19.95   2.5006E-009    134.30
+   3.00   4.6736E-002    -19.95   3.7356E-009    134.30
+   4.00   4.6736E-002    -19.95   4.9525E-009    134.30
+   5.00   4.6736E-002    -19.95   6.1452E-009    134.30
+   6.00   4.6736E-002    -19.95   7.3080E-009    134.30
+   7.00   4.6736E-002    -19.95   8.4352E-009    134.30
+   8.00   4.6736E-002    -19.95   9.5213E-009    134.30
+   9.00   4.6736E-002    -19.95   1.0561E-008    134.30
+  10.00   4.6736E-002    -19.95   1.1549E-008    134.30
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power budget confirms that the input power is now 1,000 watts. The e-field values now reflect the increased power, as well as the established distance of 1,000 meters at a height of 2 meters above ground. Fig. 3 provides rectangular plots of the magnitude and phase of the vertical components of the fields.

+
+ +
+

The limitation of the RP 1 request is that it requires increments of height in meters. Hence, it does not give a ready angular read out of the e-fields at a distance. There is also a way to overcome that limitation using the far-field request (RP 0). We simply insert a distance from the coordinate system origin into the (F5) position. Let's continue using the 1,000-meter distance we specified in the RP 1 request. However, we shall preserve the theta pattern request that we made in the initial model in order to obtain values at 1-degree intervals from the ground upward. The model will have the following appearance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 1/4-wl gp 4r
+CE
+GW 1,30,0.,0.,10.135,0.,0.,0.,.0254
+GW 2,1,0.,0.,0.,0.,0.,-.1524,.0254
+GW 3,10,0.,0.,-.1524,3.292,0.,-.1524,.003175
+GW 4,10,0.,0.,-.1524,0.,3.292,-.1524,.003175
+GW 5,10,0.,0.,-.1524,-3.292,0.,-.1524,.003175
+GW 6,10,0.,0.,-.1524,0.,-3.292,-.1524,.003175
+GE -1
+FR 0,1,0,0,7.05
+GN 2,0,0,0,13.,.005
+EX 0,1,30,0,1.414214,0.
+RP 0 181 1 1000 -90 0. 1.00000 1.00000 1000
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The only difference between this model and the one with which we started is that the RP 0 line has an extra number, the 1000-meter distance specification. This distance does not change the power gain pattern or value set, as evidenced by Fig. 4, a rectangular version of the pattern shown in Fig. 2.

+
+ +
+

The relevant data that we obtain from the tabular files has this appearance.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ - - - POWER BUDGET - - -
+
+ INPUT POWER   = 1.6842E-02 WATTS
+ RADIATED POWER= 1.6842E-02 WATTS
+ WIRE LOSS     = 0.0000E+00 WATTS
+ EFFICIENCY    = 100.00 PERCENT
+
+**** Electric Field: Theta Pattern ****
+Phi=0, Freq=7.05, File=vr4-rfld.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+ Theta     Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+ -90.00   7.1434E-011    246.54   2.6078E-027     80.44
+ -89.00   9.5624E-005    248.00   3.6393E-021     80.08
+ -88.00   1.7909E-004    249.28   7.1385E-021     78.92
+ -87.00   2.5231E-004    250.41   1.0497E-020     78.44
+ -86.00   3.1683E-004    251.40   1.4097E-020     78.99
+ -85.00   3.7390E-004    252.30   1.7780E-020     79.38
+ -84.00   4.2453E-004    253.10   2.1636E-020     79.31
+ -83.00   4.6955E-004    253.82   2.4428E-020     78.34
+ -82.00   5.0965E-004    254.47   2.8494E-020     79.65
+ -81.00   5.4540E-004    255.07   3.1561E-020     79.16
+ -80.00   5.7729E-004    255.61   3.5149E-020     79.28
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Once more, the data appears ok, but before we adopt it, let's re-examine the model on which we based it. Note that the model uses the same initial voltage source magnitude: 1.414214. Since the power input has not changed from the initial model (0.016842 w), we may use the same voltage adjustment ratio and replace the original source voltage with 344.6024.

+

If we make the change, we obtain a somewhat different tabular set of values.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ - - - POWER BUDGET - - -
+
+ INPUT POWER   = 9.9999E+02 WATTS
+ RADIATED POWER= 9.9999E+02 WATTS
+ WIRE LOSS     = 0.0000E+00 WATTS
+ EFFICIENCY    = 100.00 PERCENT
+
+**** Electric Field: Theta Pattern ****
+Phi=0, Freq=7.05, File=vr4-rfld1k.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+ Theta     Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+ -90.00   1.7406E-008    246.54   3.5717E-025    335.99
+ -89.00   2.3301E-002    248.00   4.9539E-019    337.96
+ -88.00   4.3638E-002    249.28   9.9617E-019    336.98
+ -87.00   6.1479E-002    250.41   1.4985E-018    336.03
+ -86.00   7.7202E-002    251.40   2.0201E-018    334.85
+ -85.00   9.1108E-002    252.30   2.5282E-018    336.04
+ -84.00   1.0345E-001    253.10   2.8632E-018    337.87
+ -83.00   1.1442E-001    253.82   3.4424E-018    335.74
+ -82.00   1.2419E-001    254.47   3.7840E-018    338.19
+ -81.00   1.3290E-001    255.07   4.2623E-018    336.94
+ -80.00   1.4067E-001    255.61   4.8567E-018    335.49
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power budget confirms that we have an input power of 1,000 w. The following table then provides the key values of the electrical field at a distance of 1,000 meters for each increase in elevation of 1 degree. Given that we have a vertical monopole, the e-theta values are the most significant ones. The lowest usable value--89 degrees or 1 degree above the horizon--is lower than the 2-meter height value given by the RP 1 request, even though the actual height at 1,000 m is close to 17.5 meters. However, the far-field output does not include the surface wave component. Notice that in the RP 1 data, the e-phi values are several orders of magnitude higher than those in the RP 0 data, even though both levels are operationally insignificant.

+

Remember that the reported values for the e-field are in peak volts. Multiply by 0.707 to obtain RMS values. (EZNEC provides all current and voltage output values in RMS. Version 2 of the NEC-Win software packages will provide a switch so that the user will have the option on inputting and outputting either peak or RMS values.)

+

The distance of 1,000 m or 1 km is one of the standards used in common engineering exercises involving antennas. An alternative to the km is the mile. However, the RP 0 and RP 1 lines require inputs as meters, so 1 mile = 1609.344 m. (Again, EZNEC provides flexibility of input and output units for the RP 1 request. It does not allow access to the RP 0 request to set a distance. However, it will provide tabular outputs in terms of 1 kw / km and 1 kw / mile.)

+

Although the 1-mile and 1-km distances are most commonly used, advanced modelers may have occasion to select other distances. As well, it may on some occasions be useful to compare the e-fields using different power levels. Consider the following model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 1/4-wl gp 4r
+CE
+GW 1,30,0.,0.,10.135,0.,0.,0.,.0254
+GW 2,1,0.,0.,0.,0.,0.,-.1524,.0254
+GW 3,10,0.,0.,-.1524,3.292,0.,-.1524,.003175
+GW 4,10,0.,0.,-.1524,0.,3.292,-.1524,.003175
+GW 5,10,0.,0.,-.1524,-3.292,0.,-.1524,.003175
+GW 6,10,0.,0.,-.1524,0.,-3.292,-.1524,.003175
+GE -1
+FR 0,1,0,0,7.05
+GN 2,0,0,0,13.,.005
+EX 0 1 30 0 24.36700  0.00000
+RP 0 181 1 1000 -90 0. 1.00000 1.00000 1000
+EN
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we compare this model to the one using 1000 w, we can see that the only difference is in the EX 0 line. The voltage magnitude is now 24.367 v (pk). To arrive at this value, I used the same calculation scheme, but set the desired power at 5 w instead of 1000 w. The adjustment factor was 17.2301. At 5 w, we obtain the following output data.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+  - - - POWER BUDGET - - -
+
+ INPUT POWER   = 4.9999E+00 WATTS
+ RADIATED POWER= 4.9999E+00 WATTS
+ WIRE LOSS     = 0.0000E+00 WATTS
+ EFFICIENCY    = 100.00 PERCENT
+
+**** Electric Field: Theta Pattern ****
+Phi=0, Freq=7.05, File=vr4-rfld5w.NOU
+
+            ---E (Theta)---     --- E (Phi) ---
+ Theta     Magnitude     Phase     Magnitude     Phase
+Degrees     Volts/m     Degrees     Volts/m     Degrees
+ -90.00   1.2308E-009    246.54   9.7188E-026    325.03
+ -89.00   1.6476E-003    248.00   1.3963E-019    324.60
+ -88.00   3.0856E-003    249.28   2.7620E-019    324.84
+ -87.00   4.3472E-003    250.41   4.1454E-019    324.53
+ -86.00   5.4590E-003    251.40   5.5021E-019    324.48
+ -85.00   6.4423E-003    252.30   6.7638E-019    325.11
+ -84.00   7.3146E-003    253.10   8.0686E-019    325.08
+ -83.00   8.0903E-003    253.82   9.3937E-019    324.72
+ -82.00   8.7813E-003    254.47   1.0841E-018    323.95
+ -81.00   9.3973E-003    255.07   1.1981E-018    324.34
+ -80.00   9.9467E-003    255.61   1.3289E-018    324.25
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The power budget confirms the 5-w input power level. The sample theta pattern lines provide a direct comparison of those for the 1-kw power level. With this simple exercise, one can compare the e-fields at selected distance between what amateur radio operators refer to as QRP and QRO. The 200-times power differential boils down to a 14.14-times difference in e-field strength over the specified distance. (Since P = (E^2/R) and R has not changed, we would expect the square of the e-field difference to equal 200--and it does.) Such exercises are interesting ways to expand our understanding of the consequences of selecting different power levels relative to the strength of field at a receiving site. However, all such calculations done within modeling software omit the effects of propagation phenomena.

+

Too few modelers make use of the F5 entry position in the RP 0 pattern request line. By a simple double run, one may derive far-field e-field reports for any distance (even non-sensible ones) using any desired power level. Sometimes, that is very useful information indeed.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod86-1.gif b/content/amod/amod86-1.gif new file mode 100644 index 0000000..cb8619a Binary files /dev/null and b/content/amod/amod86-1.gif differ diff --git a/content/amod/amod86.html b/content/amod/amod86.html new file mode 100644 index 0000000..9cb2c8b --- /dev/null +++ b/content/amod/amod86.html @@ -0,0 +1,253 @@ + + + + + NEC-2 Manual Sample Files + + + +
+

86. NEC-2 Manual Sample Files

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The NEC-2 User Manual contains a series of examples designed to familiarize the NEC-2 user with many of the facets of the program outputs. Unfortunately, many NEC-2 users restrict themselves to the subset of outputs provided by entry-level programs, such as far-fields, near-fields, segment currents, etc. As well, many users employ only voltage sources (or indirectly provided current sources).

+

NEC-2 offers a command structure that is considerably more sophisticated than entry-level programs display. One way to approach the refinements that are possible is to work one's way through the sample models. The pages of sample output files generally strike users as unfathomable. However, if one runs the model for oneself, the output file generated by one's own core tends to make more sense and become infinitely more interesting. For example, the user can make small but significant variations in the initial sample and see what happens to the output data as a result of these changes. Suddenly, relatively opaque manual pages become transparent vehicles of illuminating data.

+

To ease the process of testing the examples from the NEC-2 User's Manual, I have transscribed them into this text. To use a file, simply block copy the model file text and insert it as an ASCII file to the input of your core. If you encounter any stray codes from this HTML version, you may run the models through Notepad, cleanse them, and then save them in .txt format, but with a .NEC extension--or whatever the proper input file extension may be for your program.

+

Alternatively, you may download from my web site a zipped file containing all of the examples, called NEC2-EXAMPLES. Unzip the file and store the example models in the directory/folder of your choice.

+

Virtually all of the examples contain codes that the common entry level programs may not recognize. Therefore, it is best to use them with full-featured programs or with cores having input sections that recognize all of the NEC command structure.

+

In the NEC User's Manual, Examples 1-4 are combined into one input file, as are Examples 7 and 8. I have separated them here as a convenience. However, by referring to the manual for the NX (Next Structure) command, you may recombine the files into their original format.

+

The introductions to each file come from the NEC-2 User's Manual, pp. 95-153. Quotation marks ("..") indicate material from the Manual. There are occasional references to discussions in other sections of the Manual. I have omitted here the referenced material for brevity.

+

Example 1

+

"Examples 1 through 4 are simple cases intended to illustrate the basic formats. Example 1 includes a calculation of near-electric-field along the wire. When the field is computed at the center of a segment without an applied field or loading, the Z-component of electric field is small since the solution procedure enforces the boundary condition at these points. This is a check that the program is operating correctly. The values would be still smaller if the field points were more precisely at the segment centers. The radial, or X, components of the near-field can also be compared with the charge densities at the segment centers (rho = 2 PI alpha epsilono Ex). If the fields were computed along the wire axis, the radial field would be set to zero. For a nonplanar structure, however, computation along the axis is the only way to reproduce the conditions of the current solution and obtain small fields at the match points."

+ 
CE EXAMPLE 1. CENTER FED LINEAR ANTENNA
+GW 0 7 0. 0. -.25 0. 0. .25 .001
+GE
+EX 0 0 4 0 1.
+XQ
+LD 0 0 4 4 10. 3.000E-09 5.300E-11
+PQ
+NE 0 1 1 15 .001 0. 0. 0. 0. .01786
+EN
+

Example 2

+

"In example 2 the wire has an even number of segments so that a charge discontinuity voltage source can be used at the center. The symbol "*" in the table of antenna input parameters is a reminder that this type of source has been used. Three frequencies are run for this case and the EX card option is used to collect and normalize the input impedances. At the end of example 2 the wire is given the conductivity of aluminum. This has a significant effect since the wire is relatively thin."

+ 
CM EXAMPLE 2. CENTER FED LINEAR ANTENNA.
+CM CURRENT SLOPE DISCONTINUITY SOURCE.
+CM 1. THIN PERFECTLY CONDUCTING WIRE
+CE 2. THIN ALUMINUM WIRE
+GW 0 8 0. 0. -.25 0. 0. .25 .00001
+GE
+FR 0 3 0 0 200. 50.
+EX 5 0 5 1 1. 0. 50.
+XQ
+LD 5 0 0 0 3.720E+07
+FR 0 1 0 0 300.
+EX 5 0 5 0 1.
+XQ
+EN
+

Example 3

+

"Example 3 is a vertical dipole over ground. Since the wire is thick, the extended thin-wire approximation has been used. Computation of the average power gain is requested on the RP cards. Over a perfectly conducting ground the average power gain should be 2. The computed result differs by about 1.5%, probably due to the 10-degree steps used in integrating the radiated power. For a more complex structure, the average gain can provide a check on the accuracy of the computed input impedance over a perfect ground where it should equal 2 or in free space where it should equal 1. Example 3 also includes a finitely conducting ground where the average gain of 0.72 indicates that only 36% of the power leaving the antenna is going into the space wave. The formats for normalized gain and the combined space-wave and ground-wave fields are illustrated. At the end of example 3, the wire is excited with an incident wave at 10-degree angles and the PT card option is used to print receiving antenna patterns."

+ 
CM EXAMPLE 3. VERTICAL HALF WAVELENGTH ANTENNA OVER GROUND
+CM 1. PERFECT GROUND
+CM 2. IMPERFECT GROUND INCLUDING GROUND WAVE AND RECEIVING
+CE PATTERN CALCULATIONS
+GW 0 9 0. 0. 2. 0. 0. 7. .3
+GE 1
+EK
+FR 0 1 0 0 30.
+EX 0 0 5 0 1.
+GN 1
+RP 0 10 2 1301 0. 0. 10. 90.
+GN 0 0 0 0 6. 1.000E-03
+RP 0 10 2 1301 0. 0. 10. 90.
+RP 1 10 1 0 1. 0. 2. 0. 1.000E+05
+EX 1 10 1 0 0. 0. 0. 10.
+PT 2 0 5 5
+XQ
+EN
+

Example 4

+

"Example 4 includes both patches and wires. Although the structure is over a perfect ground, the average power gain is 1.8. This indicates that the input impedance is inaccurate, probably due to the crude patch model used for the box. Since there is no ohmic loss, a more accurate input resistance can be obtained as

+ 
Radiated power  = 1/2 (avg. gain) x (computed input power)
+                = 1.016 (10^-3) W
+
+Radiation resistance = 2 (radiated power)/|I source|^2
+                     = 162.6 ohms.
+

"Since the input power used in computing the gains in the radiation pattern table is too large by 0.46 dB, the gains can be corrected by adding this factor."

+ 
CE EXAMPLE 4. T ANTENNA ON A BOX OVER PERFECT GROUND
+SP 0 0 .1 .05 .05 0. 0. .01
+SP 0 0 .05 .1 .05 0. 90. .01
+GX 0 110
+SP 0 0 0. 0. .1 90. 0. .04
+GW 1 4 0. 0. .1 0. 0. .3 .001
+GW 2 2 0. 0. .3 .15 0. .3 .001
+GW 3 2 0. 0. .3 -.15 0. .3 .001
+GE 1
+GN 1
+EX 0 1 1 0 1.
+RP 0 10 4 1001 0. 0. 10. 30.
+EN
+

Example 5

+

"Example 5 is a practical log-periodic antenna with 12 elements. Input data for the transmission line sections is printed in the table "Network Data." The table "Structure Excitation Data at Network Connection Points" contains the voltage, current, impedance, admittance, and power in each segment to which transmission lines or networks connect. This segment current will differ from the current into the connected transmission line if there are other transmission lines, network ports, or a voltage source providing alternate current paths. Thus, the current printed here for segment 3 differs from that in the table antenna "Input Parameters." The latter is the current through the voltage source and includes the current into the segment and into the transmission line. Power listed in the network-connection table is the power being fed into the segment. A negative power indicates that the structure is feeding power into the network or transmission line."

+

"With 78 segments, file storage must be used for the interaction matrix. The line after data card number 14 shows how the matrix has been divided into blocks for transfer between core and the files. The line "CP TIME TAKEN FOR FACTORIZATION," gives the amount of central processor time used to factor the matrix excluding time spent transferring data between core and the files. Hence it is less than the total time for factoring printed below."

+

"The EX card option has been used to print the relative asymmetry of the driving-point admittance matrix. The driving-point admittance matrix is the matrix of self and mutual admittances of segments connected to transmission lines, network ports, or voltage sources and should be symmetric."

+ 
CM EXAMPLE 5. 12 ELEMENT 10G PERIODIC ANTENNA IN FREE SPACE.
+CM 78 SEGMENTS. SIGMA=D/L RECEIVING AND TRANS. PATTERNS
+CM DIPOLE LENGTH TO DIAMETER RATIO=150.
+CE TAU=0.93, SIGMA=0.70, BOOM IMPEDANCE=50. OHMS.
+GW 1 5 0. -1. 0. 0. 1. 0. .00667
+GW 2 5 -.7527 -1.0753 0. -.7527 1.0753 0. .00717
+GW 3 5 -1.562 -1.1562 0. -1.562 1.1562 0. .00771
+GW 4 5 -2.4323 -1.2432 0. -2.4323 1.2432 0. .00829
+GW 5 5 -3.368 -1.3368 0. -3.368 1.3368 0. .00891
+GW 6 7 -4.3742 -1.4374 0. -4.3742 1.4374 0. .00958
+GW 7 7 -5.4562 -1.5456 0. -5.4562 1.5456 0. .0103
+GW 8 7 -6.6195 -1.6619 0. -6.6195 1.6619 0. .01108
+GW 9 7 -7.8705 -1.787 0. -7.8705 1.787 0. .01191
+GW 10 7 -9.2156 -1.9215 0. -9.2156 1.9215 0. .01281
+GW 11 9 -10.6619 -2.0662 0. -10.6619 2.0662 0. .01377
+GW 12 9 -12.2171 -2.2217 0. -12.2171 2.2217 0. .01481
+GE
+FR 0 0 0 0 46.29
+TL 1 3 2 3 -50.
+TL 2 3 3 3 -50.
+TL 3 3 4 3 -50.
+TL 4 3 5 3 -50.
+TL 5 3 6 4 -50.
+TL 6 4 7 4 -50.
+TL 7 4 8 4 -50.
+TL 8 4 9 4 -50.
+TL 9 4 10 4 -50.
+TL 10 4 11 5 -50.
+TL 11 5 12 5 -50.00 0 0 0 .02 0
+EX 0 1 3 10 1.
+RP 0 37 1 1110 90. 0. -5. 0.
+EN
+

Example 6

+

"The geometry data for the cylinder with attached wires was discussed in section III-2 [of the Manual]. The wire on the end of the cylinder is excited first and a radiation pattern is computed. The CP card requests the coupling between the base segments of the two wires. Hence after the second wire has been excited, the table "ISOLATION DATA" is printed. The coupling printed is the maximum that would occur when the source and load are simultaneously matched to their antennas. The table includes the matched load impedance for the second segment and the corresponding input impedance at the first segment. The source impedance would be the conjugate of this input impedance for maximum coupling."

+ 
CE EXAMPLE 6.  CYLINDER WITH ATTACHED WIRES.
+SP      0       0       10.     0.      7.3333  0.      0.      38.4
+SP      0       0       10.     0.      0.      0.      0.      38.4
+SP      0       0       10.     0.      -7.3333 0.      0.      38.4
+GM      0       1       0.      0.      30.
+SP      0       0       6.89    0.      11.     90.     0.      44.88
+SP      0       0       6.89    0.      -11.    -90.    0.      44.88
+GR      0       6
+SP      0       0       0.      0.      11.     90.     0.      44.89
+SP      0       0       0.      0.      -11.    -90.    0.      44.89
+GW      1       4       0.      0.      11.     0.      0.      23.     .1
+GW      2       5       10.     0.      0.      27.6    0.      0.      .2
+GS      0       0       .01
+GE
+FR      0       1       0       0       465.84
+CP      1       1       2       1
+EX 0    1       1       0       1.
+RP 0    73      1 1000  0.      0.      5.      0.
+EX 0    2       1       0       1.
+XQ
+EN
+

Example 7

+

"Examples 7 and 8 demonstrate the use of NEC for scattering. The columns labeled "gain" are, in this case, scattering cross section in square wavelengths (rho/lambda^2)."

+ 
CM EXAMPLE 7. SAMPLE PROBLEMS FOR NEC - SCATTERING BY A WIRE.
+CM 1. STRAIGHT WIRE - FREE SPACE
+CM 2. STRAIGHT WIRE - PERFECT GROUND
+CM 3. STRAIGHT WIRE - FINITELY CONDUCTING GROUND
+CE (SIG.=1.E-4 MHOS/M., EPS.=6.)
+GW 0 15 -55. 0. 10. 55. 0. 10. .01
+GE 1
+FR 0 1 0 0 3.
+EX 1 2 1 0 0.
+RP 0 2 1 1000 0. 0. 45. 0.
+GN 1
+EX 1 1 1 0 45. 0. 0.
+RP 0 19 1 1000 90. 0. -10. 0.
+GN 0 0 0 0 6. 1.000E-04
+RP 0 19 1 1000 90. 0. -10. 0.
+EN
+

Example 8

+

"Example 8 is a stick model of an aircraft as shown in figure 19."

+
+ +
+ 
CM EXAMPLE 8. SAMPLE PROBLEM FOR NEC
+CE STICK MODEL OF AIRCRAFT - FREE SPACE
+GW 1 1 0. 0. 0. 6. 0. 0. 1.
+GW 2 6 6. 0. 0. 44. 0. 0. 1.
+GW 3 4 44. 0. 0. 68. 0. 0. 1.
+GW 4 6 44. 0. 0. 24. 29.9 0. 1.
+GW 5 6 44. 0. 0. 24. -29.9 0. 1.
+GW 6 2 6. 0. 0. 2. 11.3 0. 1.
+GW 7 2 6. 0. 0. 2. -11.3 0. 1.
+GW 8 2 6. 0. 0. 2. 0. 10. 1.
+GE
+FR 0 1 0 0 3.
+EX 1 1 1 0 0. 0. 0.
+RP 0 1 1 1000 0. 0. 0.
+EX 1 1 1 0 90. 30. -90.
+RP 0 1 1 1000 90. 30.
+EN
+

Example 9

+

"Example 9 shows scattering by a sphere with ka of 2.9 (ka = circumference/ wavelength). Bistatic scattering patterns are computed in the E and H planes, followed by near E and H field. The near fields within the sphere should be the negative of the incident field to produce zero total field. This condition is approximately satisfied in the example."

+

"If the frequency is changed to ka = 2.744, however, large internal fields will exist in the TM101 mode of the spherical cavity which is resonant at this ka. Such internal resonances may occur in any closed structure and result in severe errors. The errors may be avoided by placing wires inside the sphere to destroy the resonance condition at a given frequency. Since the magnetic field integral equation enforces zero tangential magnetic field on the inside of the surface, the surface acts as a perfect magnetic conductor on the inside. Hence, the resonant fields are the dual of those that would exist in a perfect electric conductor. Unfortunately, while the correct magnetic currents for the internal fields would not radiate externally, the electric currents radiate strongly."

+ 
CM EXAMPLE 9. BISTATIC SCATTERING BY A SPHERE.
+CM PATCH DATA ARE INPUT FOR A SPHERE OF 1. M. RADIUS
+CM THE SPHERE IS THEN SCALED SO THAT KA=FREQUENCY IN MHZ.
+CM THE PATCH MODEL MAY BE USED FOR KA LESS THAN ABOUT 3.
+CE FOR THIS RUN *-* KA=2.9 ***
+SP 0    0 .13795 .13795 .98079  78.75   45.     .11957
+SP 0    0 .51328 .21261 .83147  56.25   22.5    .17025
+SP 0    0 .21261 .51328 .83147  56.25   67.5    .17025
+SP 0    0 .80314 .21520 .55557  33.75   15.     .16987
+SP 0    0 .58794 .58794 .55557  33.75   45.     .16987
+SP 0    0 .21520 .80314 .55557  33.75   75.     .16987
+SP 0    0 .96194 .19134 .19509  11.25   11.25   .15028
+SP 0    0 .81549 .54490 .19509  11.25   33.75   .15028
+SP 0    0 .54490 .81549 .19509  11.25   56.25   .15028
+SP 0    0 .19134 .96194 .19509  11.25   78.75   .15028
+GX 0 111
+GS 0 0 47.71465
+GE
+FR 0    1 0     0       2.9
+EX 1    1 1     0       90.     0.      0.
+RP 0    19      1 1000  90.     0.      -10.    0.
+RP 0    1       19 1000 90.     0.      0.      10.
+NE 0    1       1       11      0.      0.      0.      0.      0.      5.
+NE 0    1       11      1       0.      0.      0.      0.      5.      0.
+NE 0    11      1       1       0.      0.      0.      5.      0.      0.
+NH 0    1       1       11      0.      0.      0.      0.      0.      5.
+NH 0    1       11      1       0.      0.      0.      0.      5.      0.
+NH 0    11      1       1       0.      0.      0.      5.      0.      0.
+EN
+

Example 10

+

"Example 10 is a monopole antenna on a sparse radial wire ground screen using the Sommerfeld/Norton ground method. Part of the interpolation grid from SOMNEC is reproduced so that the user can check that his code is operating correctly."

+

"The NGF has been used to take advantage of the symmetry of the ground screen before adding the monopole on the axis of rotation. The addition of the monopole results in 12 new unknowns. This includes the six segments in the monopole and segments at the junction of the six radial wires. The basis functions for these junction segments are modified and have become new unknowns. The currents represented by these new unknowns are printed in their normal locations in the table of currents."

+

"The NGF can be tested on any of the other examples in this section by splitting the structure at some point. The results should be unchanged, although small differences may occur on computers with less than a 60-bit word length."

+

Note: Depending on the core or program used to test this example, you may be able to (and wish to) give the .WGF file a unique name, especially useful if you have other NGF files within the same directory/folder.

+ 
CM EXAMPLE 10. Green's Function for Radial-Wire Screen over Finite Ground
+CM Screen Radius = 30 m (1. wavelength radius)
+CE Screen height = .01 m  6 radial wires
+GW 0 12 0. 0. .01 30. 0. .01 .003
+GR 0 6
+GE 1
+FR 0 1 0 0 10.
+GN 2 0 0 0 4. .001
+WG
+NX
+CE Monopole on radial wire ground screen from the NGF file.
+GF
+GW 1 6 0. 0. 0.01 0. 0. 7.51 .003
+GE
+EX 0 1 1 0 1.
+RP 0 19 2 1001 0. 0. 5. 90.
+EN
+

These model files are provided to encourage newer users of raw cores or of programs above the entry level to familiarize themselves with the complete scope of what NEC can do. As well, since many of the example narratives point to limiting factors, the user can familiarize himself or herself with NEC limitations and correctives or work-arounds.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod87-1.gif b/content/amod/amod87-1.gif new file mode 100644 index 0000000..2191055 Binary files /dev/null and b/content/amod/amod87-1.gif differ diff --git a/content/amod/amod87.html b/content/amod/amod87.html new file mode 100644 index 0000000..909ebe1 --- /dev/null +++ b/content/amod/amod87.html @@ -0,0 +1,320 @@ + + + + + NEC-4 Manual Sample Files + + + +
+

87. NEC-4 Manual Sample Files

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Last month, we presented the examples models that occur in the 2-decade-old NEC-2 User's Manual. This month, we shall meet the example models that appear in the 1992 NEC-4 User's Manual (pp. 100-181). A number of the models are identical to those in the earlier manual, while some others vary only to the degree required by revisions in some few of the command line structures. However, the NEC-4 Manual adds two new models covering features unique to NEC-4 (relative to NEC-2).

+

To ease the process of testing the examples from the NEC-4 User's Manual, I have transscribed them into this text. To use a file, simply block copy the model file text and insert it as an ASCII file to the input of your core. If you encounter any stray codes from this HTML version, you may run the models through Notepad, cleanse them, and then save them in .txt format, but with a .NEC extension--or whatever the proper input file extension may be for your program.

+

Alternatively, you may download from my web site a zipped file containing all of the examples, called NEC4-EXAMPLES. Unzip the file and store the example models in the directory/folder of your choice.

+

In the NEC User's Manual, Examples 1-4 are combined into one input file, as are Examples 7 and 8. I have separated them here as a convenience. However, by referring to the manual for the NX (Next Structure) command, you may recombine the files into their original format.

+

The introductions to each file come from the NEC-4 User's Manual, pp. 100-181. Quotation marks ("..") indicate material from the Manual. There are occasional references to discussions in other sections of the Manual. I have omitted here the referenced material for brevity.

+

Example 1

+

"Examples I through 4 are simple cases intended to illustrate the basic formats. In Example 1, a A/2 dipole is excited at its center. The XQ command requests only the calculation of current. After "ANTENNA INPUT PARAMETERS", a table shows the value of current at the center of each segment. Next, the antenna is loaded at its center with a series R-L-C circuit. Since the load coincides with the source segment, the effect on input impedance is simply to add the load impedance in series. If the load had been on another segment, the effect on input impedance would have been more complex."

+

"The PQ command requests a listing of the linear charge density at the center of each segment. In addition, the charge density is printed at the free ends of segments 1 and 7, with "E" following the segment number to indicate a free wire end. The values obtained for charge density at wire ends will be very dependent on the segment lengths. As more segments are added to reduce the segment lengths, the charge densities at the ends will increase, approaching the singular behavior expected at an edge. However, the values printed give some indication of the charge in the vicinity of the end."

+

"The NE commands request computation of near electric fields, first along the wire axis and then along the wire surface. Ideally, the z component of electric field would be zero along the wire axis and on the surface, except over the source region. On the wire axis the field is very small at the centers of segments away from the source, since these values are enforced in the moment-method solution. When the field is evaluated along the wire surface, the z component is small, but considerably larger than on the axis. Evaluating the z component of field on the wire surface is the worst case for the thin-wire approximation in NEC-4. This calculation illustrates a difference between NEC-4 and NEC-3. In NEC-3, the solution was obtained by matching the boundary condition on the wire surface, with the current treated as a filament on the axis. Hence NEC-3 would give very small tangential fields on the surface at the match points. When the near field is requested at a point on the wire axis in NEC-3, it is actually computed on the wire surface. The radial electric field (Ex) computed on the wire surface can be compared with the charge densities at the segment centers. For charge density rho and wire radius a the field is Ex = rho/2 PI alpha epsilon0."

+ 
CE EXAMPLE 1. CENTER FED LINEAR ANTENNA
+GW 0 7 0. 0. -.25 0. 0. .25 .001
+GE
+EX 0 0 4 0 1.
+XQ
+LD 0 0 4 4 10. 3.000E-09 5.300E-11
+PQ
+NE 0 1 1 15 0. 0. 0. 0. 0. .01786
+NE 0 1 1 15 .001 0. 0. 0. 0. .01786
+EN
+

Example 2

+

"In Example 2 the wire has an even number of segments, so a bicone voltage source model has been used to excite the wire at its center. The symbol '*' in the table of antenna input parameters is, a reminder that this type of source has been used. The wire radius is very small for this problem, since the bicone source is only accurate for thin wires and small radius to segment-length ratios. A safer way to excite the center of this wire would be to use applied-field voltage sources on segments 4 and 5, each with half of the total voltage."

+

"Three frequencies are run in Example 2, and the option on the EX command is used to collect and normalize the input impedances. At the end of Example 2, the wire is given the conductivity of aluminum. This has a significant effect, since the wire is relatively thin."

+ 
CM EXAMPLE 2. CENTER FED LINEAR ANTENNA.
+CM CURRENT SLOPE DISCONTINUITY SOURCE.
+CM 1. THIN PERFECTLY CONDUCTING WIRE
+CE 2. THIN ALUMINUM WIRE
+GW 0 8 0. 0. -.25 0. 0. .25 .00001
+GE
+FR 0 3 0 0 200. 50.
+EX 5 0 5 1 1. 0. 50.
+XQ
+LD 5 0 0 0 3.720E+07
+FR 0 1 0 0 300.
+EX 5 0 5 0 1.
+XQ
+EN
+

Example 3

+

"Example 3 is a vertical dipole over ground. The average power gain has been computed using the option on the RP command. For the first result, with perfectly-conducting ground, the average gain is close to the ideal value of 2. For a more complex structure, the average gain can provide a check on the accuracy of the computed input impedance. The value of average gain should be 1.0 for a model in free space and 2.0 over perfectly conducting ground. Acceptable differences from the correct value may range from a few percent for a simple model to ten percent or more for large, complex models."

+

"Example 3 also includes a solution for finitely conducting ground using the reflection coefficient approximation. With a finitely conducting ground the average gain cannot be used as a check on solution accuracy, but shows the radiation efficiency of the antenna, taking into account ground loss. Since the average gain has dropped from 2.0 for perfectly conducting ground to 0.72, the radiation efficiency is 36 percent."

+ 
CM EXAMPLE 3. VERTICAL HALF WAVELENGTH ANTENNA OVER GROUND
+CM 1. PERFECT GROUND
+CM 2. IMPERFECT GROUND INCLUDING GROUND WAVE AND RECEIVING CE PATTERN CALCULATIONS
+GW 0 9 0. 0. 2. 0. 0. 7. .3
+GE 1
+FR 0 1 0 0 30.
+EX 0 0 5 0 1.
+GN 1
+RP 0 10 2 1301 0. 0. 10. 90.
+GN 0 0 0 0 6. 1.000E-03
+RP 0 10 2 1301 0. 0. 10. 90.
+RP 1 10 1 0 1. 0. 2. 0. 1.000E+05
+EX 1 10 1 0 0. 0. 0. 10.
+PT 2 0 5 5
+XQ
+EN
+

Example 4

+

"Example 4 is a simple model to demonstrate the connection of a wire to a surface patch. Although the structure is over a perfectly conducting ground, a value of 1.8 is obtained for average gain. This result indicates that the input impedance is inaccurate, probably due to the crude patch model used for the box. In a case such as this, the average gain can be used to compute corrected values for the radiated power, input resistance and antenna gain. The total radiated power from integrating the radiated field, 9.623(10-4) watts, is printed after the average gain. In earlier versions of NEC, this value must be obtained by multiplying the average gain by the total input power. The radiation resistance can then be computed as

+ 
Radiation resistance = 2 (radiated power)/|I source|^2
+                     = 167.8 ohms.
+

where Isource is the source current, and the factor of 2 is necessary because values printed by NEC for current, voltage and field are peak rather than rms. Since the value of input power used in computing gains for the radiation pattern table is too large by 0.46 dB (10 log10[2/1.8]), the gains can be corrected by adding this amount."

+ 
CE EXAMPLE 4. T ANTENNA ON A BOX OVER PERFECT GROUND
+SP 0 0 .1 .05 .05 0. 0. .01
+SP 0 0 .05 .1 .05 0. 90. .01
+GX 0 110
+SP 0 0 0. 0. .1 90. 0. .04
+GW 1 4 0. 0. .1 0. 0. .3 .001
+GW 2 2 0. 0. .3 .15 0. .3 .001
+GW 3 2 0. 0. .3 -.15 0. .3 .001
+GE 1
+GN 1
+EX 0 1 1 0 1.
+RP 0 10 4 1001 0. 0. 10. 30.
+EN
+

Example 5

+

"Example 5 is a practical log-periodic antenna with 12 elements. Input data for the transmission line sections is printed in the table "NETWORK DATA." The table "STRUCTURE EXCITATION DATA AT NETWORK CONNECTION POINTS" contains the voltage, current, impedance, admittance and power at each segment to which the transmission lines or networks connect. The currents printed in this table are the currents in the segments at the connection points, and will differ from the current into the connected transmission line if there are other transmission lines, network ports or a voltage source providing alternate current paths. Thus, the current printed for segment 3 differs from that in the table "INPUT PARAMETERS." The latter is the current through the voltage source and includes the current into the segment and into the transmission line. Power listed in the network-connection table is the power being fed into the segment. A negative power indicates that the structure is feeding power into the network or transmission line."

+

"This example was run with the parameter MAXMAT set to 64 to illustrate the output format when file storage must be used for the matrix. The line after the listing of input line 14 shows how the matrix has been divided into blocks for transfer between memory and file storage. The line "CP TIME TAKEN FOR FACTORIZATION" shows the amount of central processor time used to factor the matrix, excluding I/0 time. This will be less than the total factoring time printed below in the output."

+ 
CM 12 ELEMENT 10G PERIODIC ANTENNA IN FREE SPACE.
+CM 78 SEGMENTS. SIGMA=D/L RECEIVING AND TRANS. PATTERNS
+CM DIPOLE LENGTH TO DIAMETER RATIO=150.
+CE TAU=0.93, SIGMA=0.70, BOOM IMPEDANCE=50. OHMS.
+GW 1 5 0. -1. 0. 0. 1. 0. .00667
+GW 2 5 -.7527 -1.0753 0. -.7527 1.0753 0. .00717
+GW 3 5 -1.562 -1.1562 0. -1.562 1.1562 0. .00771
+GW 4 5 -2.4323 -1.2432 0. -2.4323 1.2432 0. .00829
+GW 5 5 -3.368 -1.3368 0. -3.368 1.3368 0. .00891
+GW 6 7 -4.3742 -1.4374 0. -4.3742 1.4374 0. .00958
+GW 7 7 -5.4562 -1.5456 0. -5.4562 1.5456 0. .0103
+GW 8 7 -6.6195 -1.6619 0. -6.6195 1.6619 0. .01108
+GW 9 7 -7.8705 -1.787 0. -7.8705 1.787 0. .01191
+GW 10 7 -9.2156 -1.9215 0. -9.2156 1.9215 0. .01281
+GW 11 9 -10.6619 -2.0662 0. -10.6619 2.0662 0. .01377
+GW 12 9 -12.2171 -2.2217 0. -12.2171 2.2217 0. .01481
+GE
+FR 0 0 0 0 46.29
+TL 1 3 2 3 -50.
+TL 2 3 3 3 -50.
+TL 3 3 4 3 -50.
+TL 4 3 5 3 -50.
+TL 5 3 6 4 -50.
+TL 6 4 7 4 -50.
+TL 7 4 8 4 -50.
+TL 8 4 9 4 -50.
+TL 9 4 10 4 -50.
+TL 10 4 11 5 -50.
+TL 11 5 12 5 -50.00 0 0 0 .02 0
+EX 0 1 3 10 1.
+RP 0 37 1 1110 90. 0. -5. 0.
+EN
+

Example 6

+

"The structure data for the cylinder with attached wires was discussed in section 3.4 [of the Manual]. In this example, the wire on the end of the cylinder is excited first, and a radiation pattern is computed. The CP command requests the coupling between the base segments of the two wires. The coupling printed is the maximum that would occur when the source and load are simultaneously matched to their antennas. The table includes the matched load impedance for the second segment and the corresponding input impedance at the first segment. The source impedance would be the conjugate of this input impedance for maximum coupling."

+ 
CE CYLINDER WITH ATTACHED WIRES.
+SP      0       0       10.     0.      7.3333  0.      0.      38.4
+SP      0       0       10.     0.      0.      0.      0.      38.4
+SP      0       0       10.     0.      -7.3333 0.      0.      38.4
+GM      0       1       0.      0.      30.
+SP      0       0       6.89    0.      11.     90.     0.      44.88
+SP      0       0       6.89    0.      -11.    -90.    0.      44.88
+GR      0       6
+SP      0       0       0.      0.      11.     90.     0.      44.89
+SP      0       0       0.      0.      -11.    -90.    0.      44.89
+GW      1       4       0.      0.      11.     0.      0.      23.     .1
+GW      2       5       10.     0.      0.      27.6    0.      0.      .2
+GS      0       0       .01
+GE
+FR      0       1       0       0       465.84
+CP      1       1       2       1
+EX 0    1       1       0       1.
+RP 0    73      1 1000  0.      0.      5.      0.
+EX 0    2       1       0       1.
+XQ
+EN
+

Example 7

+

"Examples 7 and 8 demonstrate the use of NEC for scattering calculations. The normalized cross sections (rho/lambda2) for bistatic scattering are printed in the radiation-pattern tables."

+ 
CM SAMPLE PROBLEMS FOR NEC - SCATTERING BY A WIRE.
+CM 1. STRAIGHT WIRE - FREE SPACE
+CM 2. STRAIGHT WIRE - PERFECT GROUND
+CM 3. STRAIGHT WIRE - FINITELY CONDUCTING GROUND
+CE (SIG.=1.E-4 MHOS/M., EPS.=6.)
+GW 0 15 -55. 0. 10. 55. 0. 10. .01
+GE 1
+FR 0 1 0 0 3.
+EX 1 2 1 0 0.
+RP 0 2 1 1000 0. 0. 45. 0.
+GN 1
+EX 1 1 1 0 45. 0. 0.
+RP 0 19 1 1000 90. 0. -10. 0.
+GN 0 0 0 0 6. 1.000E-04
+RP 0 19 1 1000 90. 0. -10. 0.
+EN
+

Example 8

+

"Example 8 is a stick-model of an aircraft, as shown in figure 21."

+
+ +
+ 
CM SAMPLE PROBLEM FOR NEC
+CE STICK MODEL OF AIRCRAFT - FREE SPACE
+GW 1 1 0. 0. 0. 6. 0. 0. 1.
+GW 2 6 6. 0. 0. 44. 0. 0. 1.
+GW 3 4 44. 0. 0. 68. 0. 0. 1.
+GW 4 6 44. 0. 0. 24. 29.9 0. 1.
+GW 5 6 44. 0. 0. 24. -29.9 0. 1.
+GW 6 2 6. 0. 0. 2. 11.3 0. 1.
+GW 7 2 6. 0. 0. 2. -11.3 0. 1.
+GW 8 2 6. 0. 0. 2. 0. 10. 1.
+GE
+FR 0 1 0 0 3.
+EX 1 1 1 0 0. 0. 0.
+RP 0 1 1 1000 0. 0. 0.
+EX 1 1 1 0 90. 30. -90.
+RP 0 1 1 1000 90. 30.
+EN
+

Example 9

+

"Example 9 shows the calculation of scattering by a sphere with ka of 2.9 (ka = 2 PI alpha/lambda = circumference/lambda.) Bistatic scattering patterns are computed in the E and H planes. Then near electric and magnetic fields are computed, starting at the center of the sphere and going out along the z, y and x axes. The fields within the sphere should be the negative of the incident field to produce zero total field. This condition is approximately satisfied in the example."

+

"If the frequency is changed so that the internal cavity of the sphere becomes resonant (ka = 2.744 for the TM101 mode) large fields will be found inside the sphere. Such internal resonances may occur in any closed structure, and will result in large errors in the computed currents and radiated fields. Since the magnetic-field integral equation used in NEC enforces the boundary condition of zero tangential magnetic field on the inside of the surface, the surface acts as a perfect magnetic conductor on the inside. Hence, the resonant fields that are seen will be the dual of those that would exist in a perfect electric-conducting sphere. Unfortunately, while the correct magnetic currents for the internal fields would not radiate externally, the electric currents in the NEC solution radiate strongly."

+

"A number of ways have been developed for avoiding internal resonances, one being to solve combined electric and magnetic field integral equations. The only solution to the problem in NEC is to place wires inside the sphere to destroy the resonance condition at a given frequency. Three orthogonal dipoles might be placed at the center of a sphere. If the wires are perfectly conducting the resonance would be shifted to a different frequency. However, if lossy wires are used, resonances could be reduced at all frequencies."

+ 
CM BISTATIC SCATTERING BY A SPHERE.
+CM PATCH DATA ARE INPUT FOR A SPHERE OF 1. M. RADIUS
+CM THE SPHERE IS THEN SCALED SO THAT KA=FREQUENCY IN MHZ.
+CM THE PATCH MODEL MAY BE USED FOR KA LESS THAN ABOUT 3.
+CE FOR THIS RUN *-* KA=2.9 ***
+SP 0    0 .13795 .13795 .98079  78.75   45.     .11957
+SP 0    0 .51328 .21261 .83147  56.25   22.5    .17025
+SP 0    0 .21261 .51328 .83147  56.25   67.5    .17025
+SP 0    0 .80314 .21520 .55557  33.75   15.     .16987
+SP 0    0 .58794 .58794 .55557  33.75   45.     .16987
+SP 0    0 .21520 .80314 .55557  33.75   75.     .16987
+SP 0    0 .96194 .19134 .19509  11.25   11.25   .15028
+SP 0    0 .81549 .54490 .19509  11.25   33.75   .15028
+SP 0    0 .54490 .81549 .19509  11.25   56.25   .15028
+SP 0    0 .19134 .96194 .19509  11.25   78.75   .15028
+GX 0 111
+GS 0 0 47.71465
+GE
+FR 0    1 0     0       2.9
+EX 1    1 1     0       90.     0.      0.
+RP 0    19      1 1000  90.     0.      -10.    0.
+RP 0    1       19 1000 90.     0.      0.      10.
+NE 0    1       1       11      0.      0.      0.      0.      0.      5.
+NE 0    1       11      1       0.      0.      0.      0.      5.      0.
+NE 0    11      1       1       0.      0.      0.      5.      0.      0.
+NH 0    1       1       11      0.      0.      0.      0.      0.      5.
+NH 0    1       11      1       0.      0.      0.      0.      5.      0.
+NH 0    11      1       1       0.      0.      0.      5.      0.      0.
+EN
+

Example 10

+

"In Example 10, a horizontal dipole antenna 16 m long is modeled near the surface of a ground using the Sommerfeld solution. A file of Sommerfeld-integral values was generated by running the SOMNTX program for the ground parameters epsilong = 10, rho = 0.01 S/m and 5 MHz. The file from SOMNTX was given the name SOMEX10.NEC"

+

In the first data set the wire is modeled in free space and then at a height of 0.01 m over the ground. The input impedance is considerably closer to resonance when the wire is over ground, but the average gain of 1.59E-2 shows that only 0.795 percent of the input power is being radiated into the upper half space, with the rest absorbed by the ground."

+

"In the second data set, the dipole is modeled in an infinite medium with the same ground parameters, and then buried 0.01 m below the ground surface. When the wire is in a conducting medium the segment coordinates and segment lengths in the table "CURRENTS AND LOCATION" are normalized by the quantity |lambdag| = lambda0|epsilong - jrho/omega epsilon01/2 where lambda0 is the wavelength in free space. The normalized segment lengths should satisfy the criteria for solution accuracy as discussed in section 2.1."

+

"In computing the radiated field in the infinite medium, a factor of e-jkR/R is omitted, as is always done when the distance R is not specified on the RP command. Since the actual field has an exponential decay when k is complex, the radiated field, defined as the component of field falling off as 1/R, is zero in a lossy medium. By omitting the exponential, NEC obtains a non-zero value that indicates the relative strength of field in any direction at a finite distance, but it should not be considered radiated field. Likewise, the average gain and radiated power cannot be interpreted in their usual senses. All power is absorbed in the medium and not radiated. While the interpretation of these values is open to question, the computed values seem more useful than printing zero. When the field is computed in a lossy medium with a ground interface, zero will be printed for the radiated field and gain, since then it is not possible to remove the exponential attenuation."

+

"With the dipole buried 0.01 m below the ground surface, the average gain is slightly larger than when the wire was above ground. This difference is probably due to the change in current distribution when the wire is in the ground. The attenuation through 0.01 m of this ground is negligible."

+

"In the final case, two dipoles are modeled, with one above the ground surface by 0.01 m and the other buried by the same distance. Both dipoles are driven by 1 volt sources, but opposing currents are set up in a transmission-line mode. The input resistance of the upper dipole is negative, indicating that it is absorbing power from the buried wire. The average gain and radiated power are smaller than for a single wire above or below ground, probably as a result of the large fields generated in the ground with this two-wire configuration."

+ 
CM Horizontal 16 m dipole
+CM 1. Dipole in free space
+CM 2. Dipole above ground - Ground: E = 10., SIG 0.01 S/M,5 MHz
+CE Sommerfeld gound option
+GW 1    11      -8.     0. 0.01 8.      0.      0.01    .001
+GE -1
+FR      0       1       0       0       5.
+EX      0       1       6       0       1.
+RP      0       10      2       1000    0.      0.      10.     90.
+RP      0       10      10      1002    0.      0.      10.     10.
+GN      2       0       0       0       10.     0.01    SOMEX10.NEC
+RP      0       10      2       1000    0.      0.      10.     90.
+RP      0       10      10      1002    0.      0.      10.     10.
+NX
+CM Horizontal 16 m dipole
+CM 1. Dipole in an infinite lossy medium
+CM 2. Dipole below the ground surface
+CE      Sommerfeld gound option - E = 10., SIG = 0.01 S/M, 5 MHz
+GW 1    11      -8.     0. -0.01        8.      0.      -0.01   .001
+GE -1
+FR      0       1       0       0       5.
+EX      0       1       6       0       1.
+UM      0       0       0       0       10.     0.01
+RP      0       10      2       1000    0.      0.      10.     90.
+RP      0       10      10      1002    0.      0.      10.     10.
+CM NOTE: The above calculation of average gain in a lossy medium cannot
+CM      be interpreted in the usual sense. A factor of EXP(-jkR)/R
+CM      has been omitted from the field so that a non-zero value can
+CM      be  obtained for R --> infinity with complex k. However, by the
+CM      usual definition, the far-field gain is zero in a lossy medium.
+CM      Set upper medium to free space, then use Sommerfeld ground.
+GN 2    0       0       0       10. 0.01 SOMEXIO.NEC
+RP 0    10      2       1000    0. 0. 10. 90.
+RP 0    10      10      1002    0. 0. 10. 10.
+NX
+CM TWO HORIZONTAL 16 M DIPOLE ANTENNAS ABOVE AND BELOW GROUND
+CE SOMMERFELD GOUND OPTION - E = 10., SIG = 0.01 S/M, 5 MHz
+GW 1    11      -8.     0. 0.01 8.      0.      0.01    .001
+GW 2    11      -8.     0. -0.01        8.      0.      -0.01   .001
+GE -1
+FR      0       1       0       0       5.
+EX      0       1       6       0       1.
+EX      0       2       6       0       1.
+GN      2       0       0       0       10. 0.01 SOMEXIO.NEC
+RP      0       10      2       1000    0.      0.      10.     90.
+RP      0       10      10      1002    0.      0.      10.     10.
+EN
+

Example 11

+

"In example 11, a 15 m monopole is modeled on a ground stake 2 m deep. Separate GW commands are used to define the monopole and ground stake to ensure that the junction will occur exactly at the interface. The average gain computation shows that the radiation efficiency of this antenna over ground is 16 percent. NE and NH commands are used to compute the electric and magnetic fields at a distance of 5000 m with the surface wave included. When the Sommerfeld ground option is in use, the near magnetic field is computed from a finite-difference evaluation of V x E. The increment for evaluating differences is ±10-3 A0. Hence, if the near magnetic field had been evaluated at a height of less than 0.06 ra in this example an incorrect value would have been obtained due to the negative increment in z falling on the wrong side of the interface." [Note: in the lines above, V is a stand-in for an inverted delta, not available for this transcription.]

+

"If the lower medium had a conductivity of zero, the average gain could be computed over both upper and lower half spaces (0° < 0 < 180°) and should have a value of 1.0. This can serve as a necessary, but not sufficient, check on the solution accuracy for a dielectric ground. In integrating the power in a dielectric ground, it may be necessary to use increments in theta of a degree or less to accurately sample the field near the totally reflecting or critical angle in the ground (theta = 180° - sin-1 epsilon-1/2 = 162° for epsilontau = 10, rho = 0.) The steepness of this near discontinuity increases with increasing height of the antenna above the ground."

+ 
CM 15 m monopole antenna on a ground stake 2 m deep.
+CE Ground: E = 10., SIG = 0.01 S/m, 5 Mz.
+GW 1    8       0.      0.      -2.     0.      0. 0.   0.01
+GW 2    10      0.      0.      0.      0.      0. 15.  0.01
+GE -1
+FR 0    1       0       0       5.
+GN 2    0       0       0       10. 0.01 SOMEX10.NEC
+EX 0    2       1       0       1.
+RP                      0       19      2       1002 0. 0.      5.      90.
+NE 0    1       1       21 5000.        0.      0.1     0.      0.      10.
+NH 0    1       1       21 5000.        0.      0.1     0.      0.      10.
+EN
+

Example 12

+

"The monopole antenna from Example 11 is now modeled on a ground screen of six radial wires, with a screen radius of 12 meters. The Numerical Green's Function option was used to take advantage of the rotational symmetry of the ground screen. The monopole is added on the axis of rotation in the second part of the run."

+

"The screen was buried 5 cm below the surface of the ground. Since a segment cannot penetrate the interface, the junction of the monopole and the radial wires was located on the interface at the origin. The inner segment of each radial wire descends at an angle to the 5 cm depth, and the remainder of the radial is horizontal. The inner segment was chosen to have approximately the same length as the horizontal segments. The complete ground screen is generated with a GR command to set the code to use symmetry in the solution."

+

"The monopole is added to the NGF solution in the second part of the run. The summary of segment data includes all segments from the NGF file and those added for the monopole. After the summary of segment data, a line shows the number of new unknowns in the NGF solution. This number includes the new segments plus one new unknown for each segment from the NGF file that connects to a new segment. Segments in the NGF file that connect to new segments contribute new unknowns since they need new basis functions due to the changed junction condition. Since there are 10 segments in the monopole and six radials each connecting to the base of the monopole, the number of new unknowns is 16. The code must also recompute the field from the second ring of segments from the center of the screen, since the basis functions for the first segments extend onto the second segments. This additional integration can significantly reduce the advantage of using the NGF to take advantage of symmetry when many NGF segments connect to new segments."

+

"The computed results include a radiation pattern and average gain. From the average gain, it is seen that the radiation efficiency has increased to 29 percent from the 16 percent obtained with a ground stake. A better ground screen would increase the efficiency still further. The NEC-GS program is much more efficient than NEC-4 [11] for modeling monopoles on large radial-wire ground screens. However, at the present time there is no version of NEC-GS using the NEC-4 solution algorithms."

+ 
CM 6-Wire Radial-Wire Ground Screen.
+CE An NGF file is written to take advantage of symnetry of the screen.
+GW 1    14 12.  0. -.05 0.8     0.      -.05    .01
+GW 1    1 0.8   0. -.05 0.      0.      0.      .01
+GR 0    6
+GE
+FR 0    1       0       0       5.
+GN 2    0       0       0       10. .01 SOMEX10.NEC
+WG
+NX
+CE 15 m Monopole added to the ground screen from the NGF file.
+GF
+GW 2    10      0.      0.      0.      0.      0. 15. .01
+GE
+EX 0    2       1       0       1.
+RP 0    19      2       1001    0.      0.      5. 90.
+EN
+

These model files are provided to encourage newer users of NEC-4 to familiarize themselves with the complete scope of what NEC can do. As well, since many of the example narratives point to limiting factors, the user can familiarize himself or herself with NEC limitations and correctives or work-arounds.

+
+ +

+

Go to Main Index

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+

88. EX and PT

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Most newer NEC antenna modelers and even experienced antenna designers have little occasion to use any other form of excitation than EX 0, the voltage source. Some software packages simulate a current source by placing--either overtly or covertly--a voltage source and a network (NT) between the actual excitation segment and the segment that the modeler wishes to call the source. Other packages allow split sources by exciting two adjacent segments in series and calculating the resulting source impedance for the user.

+

A typical model in .NEC format would look like the following simple 6-element Yagi in free-space. (The LD5 line assigns the aluminum material loss to the entire set of model segments. The last entry in the line is a permeability value of 1, indicating that this model is set up in NEC-4.) The dimensions are in meters.

+ 
CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0 1 0 0 146. 0
+GN -1
+EX 0 2 11 0 1 0.
+RP 0 1 361 1000 90. 0. 1.00000 1.00000 0.
+EN
+

From a model such as this one, perhaps the most used output is the E-plane pattern, in this case, a Phi or Azimuth pattern, according to the names assigned by the software. Fig. 1 shows a sample for the present model, along with the data for the pattern. Not shown is the other most desired piece of information, the source impedance: 50.0 + j9.5 Ohms at 146 MHz for this model.

+
+ +
+

Plane-Wave Excitation

+

There are occasions when a modeler may seek other information from the model, information that may emerge from the use of plane wave excitation. The EX command has three significant options for the modeler:

+
+

EX 1: incident plane wave, linear polarization

+

EX 2: incident plane wave, right hand (thumb along the incident vector) elliptic polarization

+

EX 3: incident plane wave, left hand (thumb along the incident vector) elliptic polarization

+
+

Both of the elliptical polarization options are useful when simulating signal sources from helical and similar antennas. Linear polarization simulates line-of-sight signal sources. These notes do not pretend to provide a compendium of uses for the various signal sources. Instead, they are designed to introduce the rudiments of using incident plane-wave sources, as well as a few tips on making incident plane-wave models do what the modeler wants them to do in terms of data output.

+

For anyone not acquainted with incident plane-wave excitation, the first item to understand is that these sources do not excite a specific wire segment on the model. Instead, they simulate an external signal source that excites the entire antenna structure. The entry-line structure for them has a number of interesting properties that differ from the line structure of a simple voltage source.

+ 
+Com  I1   I2     I3     I4   F1        F2        F3         F4    F5   F6    F7
+ID   Type # Thta # Phi  Not  Th angle  Ph angle  Eta        Theta Phi  Axis  El. field
+          angles angles used to vector to vector pol. angle step  step ratio V/m
+EX   1    1      8      0    90        0         90         0     45   0     0
+
+

The sample entry is for a linear plane wave. Hence, F6 is 0 by non-relevance. F7 also has a 0, but that value indicates a default value of 1 V/m. In some problems designed to ferret out coupling potentials among wires, you may use a specific value that closely approximates the value from the source signal at the structure being examined in model form.

+

Most of the remaining entries define incident plane waves as a calculation loop within NEC (with some properties resembling the loop operation of frequency sweeps using the FR command). In the sample, for the sake of clarity, there is only one theta angle: 90 degrees. This angle is parallel to the plane of the antenna elements. The sample specifies 8 phi-angle (azimuth-angle) steps at 45-degree increments, thus providing samples evenly spaced in the element plane.

+

The F3 entry, called Eta, under linear polarization is easy to memorize. With a value of 0, the polarization is in the +/-Z direction--vertically polarized for antennas over ground. If F3 is 90, the polarization is in the X-Y plane--horizontally polarized for antennas over ground. The sample in free space uses horizontal polarization for simplicity, but there is no restriction against checking results when cross-polarized or with the polarization set to intermediate angles. When using EX 2 or EX 3, elliptical polarization, the entry changes its meaning and defines the major ellipse axis. (Remember that true circular polarization is simply a special case of elliptical polarization having equal axes.)

+
+

[Special Note for NEC-2 Users: The structure of the NEC-2 plane-wave excitation entry is slightly different than the NEC 4 entry. It has the following structure:

+ 
+Com  I1   I2     I3     I4   F1        F2        F3         F4    F5   F6
+ID   Type # Thta # Phi  Not  Th angle  Ph angle  Eta        Theta Phi  Axis
+          angles angles used to vector to vector pol. angle step  step ratio
+EX   1    1      8      0    90        0         90         0     45   0
+
+

Note that the NEC-2 version lacks the F7 floating point entry for the electrical field strength, and the default value of 1 V/m always applies. Only 1 incident plane wave is allowed at a time (that is, before a succeeding execution step). If excitation types are mixed before a succeeding execution step, then the program will use only the last excitation type encountered.]

+
+

Let's replace the lines of our original model from EX onward with the following (NEC-4) lines

+ 
EX 1 1 8 0 90 0 90 0 45 0 0
+RP 0 1 361 0000 90. 0. 1.00000 1.00000 0.
+EN
+

The EX entry is the one used in the sample. The RP 0 request calls for far field patterns, and the EX 1 loop will produce 8 of them, each one with a plane wave source spaced 45 degrees from the preceding one. Although unnecessary for linear polarization, the RP 0 request varies the XNDA entry. In the original model, the request used 1000 for XNDA, indicating that the output report would be printed in terms of the vertical, horizontal, and total gain. The replacement entry beginning with 0 prints the output in terms of major-axis, minor axis, and total gain. This option is significant for elliptical plane waves. For a total-gain-only output desire, the initial digit is not important, but it can become important as one explores the components of the total gain report value.

+

Receive Patterns

+

Plane-wave excitation is particularly important to the modeling of structures that do not themselves have an energy source, but which receive radiation from external sources. In some cases, they may re-radiate the energy, such as the case of a cell phone tower that is the right size and too close to a broadcasting tower. At a minimum, such a tower may change the pattern of the broadcast signal from its original shape that was certified to the licensing agency. In other cases, we may be interested in the scattering radiation from an object--a boat, aircraft, or other vehicle, for instance--illuminated by a radar or other signal. The number of potentially interesting and important cases that call for plane-wave excitation is as unending as the growing list of our concerns for the effects of radiation on animal, vegetable, and mineral objects around us.

+

Under these conditions, we are interested in structures as receiving devices, meaning recipients of energy. For our sample, we shall use the 6-element Yagi antenna as a receiving antenna. The question that next arises is how to derive useful data from the structure. For that purpose, NEC has an interesting command: PT. The PT command has a number of options.

+

PT -2: All current printed. This also occurs if PT is omitted altogether.

+

PT -1: Suppress printing of all wire-segment currents.

+

PT 0: Current printed for specified segments only.

+

PT 1: Currents printed in a format designed for a receiving pattern.

+

PT 2: Currents printed in a format designed for a receiving pattern, plus a normalized value for the last segment's current.

+

PT 3: Only the normalized current is printed.

+

The PT -1 option is useful when we only need 1 set of current data, but modeling circumstances would normally yield multiple sets of current tables. For example, a frequency sweep for which we need a collection of both theta and phi patterns would require a repetition of the FR command above each RP 0 request. Hence, the FR loop would repeat and normally yield two sets of the current data. Inserting a PT -1 command after the second FR command will suppress the printing of the second set of current data. PT 0 is useful in large models to isolate the current data on specific portions of a model.

+

However, our present interest lies in the PT entries followed by positive integers. The general format is as follows.

+ 
+Com  I1    I2     I3       I4
+ID   Type  Tag #  1st Seg  Last Seg
+PT   2     2      1        11
+
+

The I2 through I4 entries are necessary only for PT 0 through PT 3. In this instance, the sample request asks both for the data on Tag 2, Segments 1 - 11, and for the normalized value of the data on segment 11. To make sense of this entry, refer to the initial model. Tag 2 represents the Yagi driver, and segment 11 is the segment connected to the feedline--a source segment in the transmitting mode and the focal segment in the receiving mode.

+

A single value of normalized current level would not be of much use. In fact, a very normal use of the PT 1 through PT 3 commands is in conjunction with an EX 1 command. Let's combine these lines into a different set of concluding lines for our initial model.

+ 
PT 2 2 1 11
+EX 1 1 37 0 90 0 90 0 10 0 0
+XQ
+EN
+

The EX 1 line specifies a loop of 37 excitations, each 10 degrees apart on the phi coordinates, and all at a theta angle of 90 degrees throughout. We might have selected any portion of the coordinate system sphere by specifying both phi and theta increments and steps. In that case, theta changes would occur before phi changes. However, for illustrative simplicity, theta remains constant in this introduction. Note that without a self-executing command to follow the EX 1 line, we need to insert XQ to execute the calculation of the specified currents.

+

The output file for the PT 2 request has two parts. The first is a list of all currents on the specified segments in terms of relative magnitude and phase angle, given the excitation level of 1 V/m. A PT 1 entry using the same form would produce this first data set. The data table has the following appearance--carried only through the first two excitation coordinates.

+ 
+                         - - - RECEIVING PATTERN PARAMETERS - - -
+                                   ETA=  90.00 DEGREES
+                                      TYPE -LINEAR
+                                   AXIAL RATIO= 0.000
+
+           THETA      PHI          -  CURRENT  -         SEG
+           (DEG)     (DEG)       MAGNITUDE    PHASE      NO.
+
+            90.00      0.00     1.3360E-26     14.58       22
+            90.00      0.00     3.2918E-26     15.61       23
+            90.00      0.00     4.9538E-26     16.58       24
+            90.00      0.00     6.4222E-26     17.45       25
+            90.00      0.00     7.6951E-26     18.24       26
+            90.00      0.00     8.7620E-26     18.95       27
+            90.00      0.00     9.6115E-26     19.61       28
+            90.00      0.00     1.0234E-25     20.21       29
+            90.00      0.00     1.0625E-25     20.75       30
+            90.00      0.00     1.0782E-25     21.25       31
+            90.00      0.00     1.0708E-25     21.70       32
+            90.00     10.00     6.9810E-05   -125.22       22
+            90.00     10.00     1.7385E-04   -122.98       23
+            90.00     10.00     2.6449E-04   -120.90       24
+            90.00     10.00     3.4657E-04   -119.02       25
+            90.00     10.00     4.1959E-04   -117.32       26
+            90.00     10.00     4.8257E-04   -115.76       27
+            90.00     10.00     5.3448E-04   -114.32       28
+            90.00     10.00     5.7442E-04   -112.97       29
+            90.00     10.00     6.0169E-04   -111.71       30
+            90.00     10.00     6.1584E-04   -110.51       31
+            90.00     10.00     6.1671E-04   -109.36       32
+
+

We can plot the data for any of the selected segments around the complete phi circle. In fact, we used 37 steps in the model in order to be able to have a graph that started and finished at the same level. If we plot the data for Segment 32 (the absolute segment number for segment 11 on tag 2), we obtain the traces in Fig. 2. The magnitude and the phase angle have separate plots, since plotting them with a single Y-axis would have given us a virtually flat line for the small changes in magnitude.

+
+ +
+

The graph for phase, of course, does not give us the perfect match between 0 degrees and 360 degrees. The result stems from two facts. First, the 0/360-degree point is in a region where the phase angle is changing very rapidly. So too is the magnitude, but it is in both cases too close to zero to show any variation between the graph-line ends. Second, NEC is subject to a number of occurrences of rounding in the course of its calculations. Hence, what it calls 360 degrees may be fractionally off. In most cases, this variation makes no difference, even visually, to a result. However, in this case, the combination of circumstances yields a visually divergent set of graph-line ends. The reported data for the two points is as follows.

+ 
Angle     Magnitude     Phase Angle
+0 deg.    1.34E-26       14.58 deg
+360       8.39E-14      158.30
+

With a initial electrical field magnitude of 1 V/m, values below 1E-10 are subject to seemingly wide variations in magnitude and phase angle. However, the actual voltage levels are too low to be significant, whichever level and angle one selects.

+

The second set of data produced by the PT 2 entry (and the only data produced by a PT 3 entry) includes the normalized values for Tag 2, Segment 11, or absolute segment 32. There will be 37 entries on this list.

+ 
+                        - - - NORMALIZED RECEIVING PATTERN - - -
+                            NORMALIZATION FACTOR= 2.6983E-02
+                                   ETA=  90.00 DEGREES
+                                      TYPE -LINEAR
+                                   AXIAL RATIO= 0.000
+                                   SEGMENT NO.=   32
+
+                     THETA      PHI         -  PATTERN  -
+                     (DEG)     (DEG)        DB        MAGNITUDE
+
+                      90.00      0.00    -999.99     3.9686E-24
+                      90.00     10.00     -32.82     2.2856E-02
+                      90.00     20.00     -26.60     4.6774E-02
+                      90.00     30.00     -18.80     1.1475E-01
+                      90.00     40.00     -12.15     2.4691E-01
+                      90.00     50.00      -7.32     4.3037E-01
+                      90.00     60.00      -3.94     6.3530E-01
+                      90.00     70.00      -1.70     8.2236E-01
+                      90.00     80.00      -0.42     9.5310E-01
+                      90.00     90.00       0.00     1.0000E+00
+                      90.00    100.00      -0.42     9.5310E-01
+                      90.00    110.00      -1.70     8.2236E-01
+                      90.00    120.00      -3.94     6.3530E-01
+                      90.00    130.00      -7.32     4.3037E-01
+                      90.00    140.00     -12.15     2.4691E-01
+                      90.00    150.00     -18.80     1.1475E-01
+                      90.00    160.00     -26.60     4.6774E-02
+                      90.00    170.00     -32.82     2.2856E-02
+                      90.00    180.00    -236.16     1.5553E-12
+                      90.00    190.00     -31.35     2.7077E-02
+                      90.00    200.00     -26.29     4.8478E-02
+                      90.00    210.00     -24.51     5.9467E-02
+                      90.00    220.00     -24.35     6.0584E-02
+                      90.00    230.00     -25.47     5.3265E-02
+                      90.00    240.00     -28.13     3.9206E-02
+                      90.00    250.00     -32.55     2.3572E-02
+                      90.00    260.00     -35.65     1.6502E-02
+                      90.00    270.00     -35.30     1.7187E-02
+                      90.00    280.00     -35.65     1.6502E-02
+                      90.00    290.00     -32.55     2.3572E-02
+                      90.00    300.00     -28.13     3.9206E-02
+                      90.00    310.00     -25.47     5.3265E-02
+                      90.00    320.00     -24.35     6.0584E-02
+                      90.00    330.00     -24.51     5.9467E-02
+                      90.00    340.00     -26.29     4.8478E-02
+                      90.00    350.00     -31.35     2.7077E-02
+                      90.00    360.00    -230.14     3.1105E-12
+
+

As we did for the raw magnitude information, we can plot the normalized data as well. As a first move, let's look at a plot of the feedline segment relative magnitude of current normalized to a maximum value of 1.0. Fig. 3 shows us the plot.

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The resulting graph is virtually identical to the upper portion of Fig. 2, with the exception that the new graph fills the space from bottom to top. This type of graphical and tabular information may be very useful in some cases, but it seems to lack much informative power for our simple example.

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Therefore, let's give our illustrative model a question for which the data may be able to yield an answer. Does the pattern shape change between transmit and receive, or is the basic antenna essentially reciprocal, that is, does it have the same pattern regardless of whether it is transmitting or receiving? Note that this question excludes any factors applying to propagation phenomena between transmitting and receiving antennas.

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First, we need to convert the polar plot of Fig. 1 into a rectangular plot--only because my software presently only has rectangular plot facilities for receive patterns. The data on such a plot will still be in dB. In fact, let's set the plot limits (Y-axis) at +10 dB and -40 dB to allow the overall pattern variations show themselves with some clarity. The maximum gain of the Yagi is 10.23 dBi, so the peak value will not over-extend the top line by any significant amount.

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Second, let's plot the normalized receiving data over a similar 50-dB span: from 0 dB down to -50 dB. While we set this up, let's also note that the normalized receiving plot data uses a 10-degree increment, while the radiation plot uses a 1-degree increment. The difference is due to further limitations of the rectangular plot facility in the software that I used.

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Fig. 4 shows the two plots, and their agreement is clearly evident within the limits of the different increments used in this simple demonstration. There is no evidence that the transmitting and receiving plots are any different. Of course, one might expand at least the tabular receiving results to a full 360 degrees using 1-degree increments and then compare that table with the values in the transmit version radiation table. That, as they say in all of those math texts, is an exercise I am content to leave to the reader.

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Combining Modeling Goals in a Single Model

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In this exercise, we have looked at two different types of projects involving linear incident plane-wave excitation. The first involved generating patterns--which tend to be of little use here, but in some cases might be useful as re-transmission or scattering patterns--and the second developed tabular data and rectangular plots of received patterns. Each called for a different increment in the phi circle. For patterns, we do not need either the full current set or the restricted set called out by the PT 2 command. For the receive rectangular plots, we need only the current data shown.

+

The easiest way to achieve these ends is to separate them within the model with the XQ command for the currents and a new EX 1 line before the RP 0 command.

+ 
CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0 1 0 0 146. 0
+GN -1
+PT 2 2 1 11
+EX 1 1 37 0 90 0 90 0 10 0 0
+XQ
+EX 1 1 8 0 90 0 90 0 45 0 0
+PT -1
+RP 0 1 361 0000 90. 0. 1.00000 1.00000 0.
+EN
+

The techniques shown in the sample model are also useful in other models, even when we wish to use the same EX 1 line but for both theta and phi patterns. We would lose all but the last of the second set of patterns if we do not repeat the EX 1 line, and we can omit the repetitious data with the PT -1 command.

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If we want to frequency sweep both sets of results, we must also include a second FR line, and both should reflect the desired sweep. The following lines that revise the end of the model illustrate the principle with a 2-step sweep. Had we omitted the second FR entry, we would obtain far-field plots only for 147 MHz, the last frequency in the FR loop.

+ 
+FR 0 2 0 0 146. 1
+GN -1
+PT 2 2 1 11
+EX 1 1 37 0 90 0 90 0 10 0 0
+XQ
+FR 0 2 0 0 146. 1
+EX 1 1 8 0 90 0 90 0 45 0 0
+PT -1
+RP 0 1 361 0000 90. 0. 1.00000 1.00000 0.
+EN
+
+

These notes are not designed to be comprehensive in the treatment of either the EX command or the PT command. However, they do illustrate how the two work together to yield receive data and patterns. That is enough to get you started. Undoubtedly task specifications will let you modify the elements of this simple example so that you can obtain the desired results for most modeling efforts that require plane wave excitation and/or receive patterns.

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Go to Main Index

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89. A Note on Archimedes and Log Spirals for the NEC-4 GH Command

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L. B. Cebik, W4RNL

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The GH command in NEC-4 permits two kinds of spirals having different initial and terminal radii: Archimedes and log spirals. The user makes his or her selection by a simple choice in the last floating point decimal entry, F7. The following notes are for those who have never encountered spirals of different type or who may have cut the class in which they were introduced. To see what sort of coordinates NEC will produce for each type of spiral requires only that we have a hand calculator with a y^x (y to the x-power) key in addition to the other usual keys. A spreadsheet will be handier in the long run, especially for log spiral calculations.

+

In columns 61 and 62, we examined the basic formation of helices with regular structures in both the NEC-2 and the NEC-4 versions of the GH command. NEC-2 permitted regular spirals of a single sort, along with the potential for oval turns in which the radius along the X-axis differed from the radius along the Y-axis. NEC-4 reduced the options to circular turns, but offered a choice between spiral types. NEC-4 is able to create flat spirals by setting the height to zero. However, many implementations of the NEC-2 GH command, which was an unofficial addition to the command set, do not allow truly flat spirals.

+

A typical but simple helical antenna over perfect ground might result in the following model. Note that NEC builds a helix under a single tag #, with all individual segments using the same tag number, whatever the number of segments. As well, NEC builds the helix from Z=0 upward to some positive value of Z. If the modeler desires a different orientation or a wholly different position, the GM command is available to move or rotate the structure--or both.

+ 
+CM General Helix over Perfect Ground
+CE
+GH 1 100 5 1 1 2 .001 .001 0
+GE 1 -1 0
+GN 1
+EX 0 1 1 0 1 0
+FR 0 1 0 0 299.7925 1
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
+
+

The GH line has the following structure.

+ 
+    I1    I2    F1     F2      F3      F4     F5       F6       F7
+GH  1     100   5      1       1       2      .001     .001     0
+Cmd Tag   # of  No of  Length  Initial Final  Initial  Final    Spiral
+    #     Segs  Turns          Radius  Radius Wire Rad Wire Rad Type
+
+

Most of the command entries are self-explanatory with the brief notations. However, F1, the number of turns, is a bit special. The number of turns need not be an integer, but may be fractional. As well, if the value for F1 is positive, the helix is right-handed, and if negative, the helix is left-handed. (In NEC-2, the left vs. right option is implemented in F2, the total length of the helix.) If the initial and final helix radii and wire radii are the same, then the entry in F7 makes no difference. However, if F3 and F4 are different, then the spiral-type entry makes a considerable difference in the resulting helix. Here is a table of values for the start-end radii of each turn in terms of coordinates (where Y=0 in all cases) for the sample model shown earlier.

+ 
+Turn--Seg       Archimedes                Log
+Numbers         X          Z              X          Z
+  1      1      0.0        0.0            0.0        0.0
+1-2  20-21      1.2        0.2            1.14869    0.14869
+2-3  40-41      1.4        0.4            1.31950    0.31950
+3-4  60-61      1.6        0.6            1.51571    0.51571
+4-5  80-81      1.8        0.8            1.74110    0.74110
+5    100        2.0        1.0            2.0        1.0
+
+

Note that the rise in value along the Z-axis is exactly proportional to the increase in radius. Of course, the two spirals do not have the same electrical properties as radiators. However, the purpose of our model and its two variations is not to establish a working antenna, but to sample the two types of available spirals.

+

The simpler spiral is the Archimedes, with its arithmetically regular structure. In an Archimedes spiral, the radius (R) at any wire junction is given by a simple equation:

+
    +
  • R = Ri + (a * theta)
    • +
+

where R is the radius under consideration, Ri is the initial radius, a is a constant, and theta is an angle.

+

Because the change of radius is uniform, we can formulate values for a and theta in a variety of ways, so long as the product of the two yields a progression of values that steps by an increment of 0.01 per segment. (In the model, the units are meters, but the same considerations apply to any system of units.) Theoretically, we should devise a single value for the constant a and vary the value of theta in radians to continuously increase from zero through 5 * 2 * pi or 31.415927. However, our interest in the spiral is only to check the coordinates that the NEC core will assign to wire junctions. So we can change procedures without loss. Every turn has 20 segments in the model, so every radius will occur in increments of 0.05 (turn) of a complete circle. The entire helix will reach a value of 1.0 (turn) at the start of each new turn. The radius will increase by 0.01 per segment or 0.2 per turn (a). At the start of turn 3 (end 1 of segment 41), the angle will have increased through 2.0 cycles (turns) or 40 segments. Theta is 40 * 0.05 = 2.0, and a*theta is 2.0 * 0.2 = 0.4. Added to the initial radius, 1.0, the new radius is 1.4, and the new Z value is 0.4. (In this simple example, I have set the total height to equal the total increase in radius. The change in height, however, will always be proportional to the change in radius.)

+

We can short-circuit the complexities even further once we know how much the radius and height change for each segment. With 100 segments and a total radius increase of 1.0, along with a total height of 1.0, each segment will increase the radius and the height by 0.01 of the total. Hence, 40 segments times 0.01 = 0.4. Since the height begins at zero, the new height is 0.4. Since the radius begins at 1.0, the new height is 1.0 + 0.4 or 1.4. If all that we ever use are Archimedes spirals, then the simplified method of checking coordinates will suffice.

+

For those who have lost--or never had--an introduction to log spirals--the basic formulation may seem deceptively simple:

+
    +
  • R = Ri*a^theta
    • +
+

where R is the radius under consideration, Ri is the initial radius, a is a constant, and theta is an angle. The constant, a, is not the same constant as it is for an Archimedes spiral with its regular or uniform variation along the length of the helix. Fig. 1 compares the appearance of both types of spirals. Both spirals have the same initial and end radii and the same overall length from bottom to top. The uniformity of the increase of the Archimedes spiral is readily apparent both in the top view (or the bottom, depending on your position) and in the side view. In contrast, the log spiral not only increases in diameter as we move upward, but the rate of radius increase and the rate of height increase also go up along the progression from bottom to top.

+
+ +
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As a side note, we shall maintain a GH-orientation in all that follows. GH helices initially form from the plane of the X and Y coordinates, that is, from Z=0. In addition, GH helices in NEC-4 have radii centered at X=0 and at Y=0. The GM command is available in NEC to allow the modeler to move the helix or to turn it to any angle possible within the Cartesian coordinate system, so we shall make a like assumption. Hence, all spirals that will appear in these notes will begin with their initial or minimum radius at the bottom and the maximum radius at the top, and the spiral length will be measured from Z=0 upward.

+

A modeling caution to observe is that both types of spiral increase the length of segments as they move upwards toward a larger radius. The increase from one segment to the next is normally quite small for helices with at least 20 segments per turn. In many cases is is more critical to keep the segments aligned from turn-to-turn, especially if the spiral is tight.

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Fig. 2 shows a well-aligned spiral with an even number of segments along side a less-well aligned spiral. In all spirals, performing an average gain test (AGT) will reveal whether segment misalignment introduces any significant degree of model inadequacy. The very close spacing of turns in the sample model results in rather inadequare models over perfect ground, with the bulk of the poor AGT values resulting from placing the source (EX) on the segment adjacent to ground. It fails to have segments on each side of the source segment that are as equal in length to the source segment as possible, and the segment meets the perfect ground at an oblique angle rather than vertically. Nevertheless, these faults do not affect our calculation of the running dimensions of a spiral of either the log or Archimedes sort. To check the effects of the spiral itself, without the effects of the source position, place the source on a segment other than the first segment.

+

The calculation of both a and theta in the equations for the radius at any point along a log spiral is intrinsically interesting, especially if we adapt it to models of such spirals formed from straight wires under the NEC-4 GH command. The procedure to follow is independent of the system used within the core itself. Any system of calculations that yields values for a and theta should yield radius values or their equivalent in X and Y coordinates that are numerically precise relative to those produced by the core To obtain a complete report on the spiral, we need to be prepared to enter the following information (all within the same units of measure, of course).

+
    +
  • Rmax--the maximum radius of the spiral.
    • +
  • Rmin=Ri--the initial or minimum radius of the spiral.
    • +
  • s--the number of segments per turn of the helix.
    • +
  • t--the total number of turns in the helix.
    • +
  • Lt--the total length of the spiral.
    • +
  • theta--the segment of interest, using end 2 of the segment.
    • +
+

Since end 1 of the first segment is at a helix length of zero, and the radius at zero length is Rmin, extended along the +X direction. Therefore, all further segment references apply to end 2 of the segment. Hence, the last segment calculated will yield the final radius and the final height of the spiral.

+

To obtain a progression of radii, we need to obtain values for both a and theta. Finding theta is the easier task, since we have already entered it as the total number of segments in the spiral. However, we may also define theta' as the increment or step around the circle taken by each segment. Because we are working with increments of the circle defined by the segments, we may bypass degrees and radians and take theta' in terms of the amount of the circle intersected by the ends of any given segment.

+
    +
  • theta' = 1/s
    • +
+

This is one step in the process of finding the value of a from the data that we are ready to enter. The next step requires that we find the ratio of maximum to minimum radius, Rr.

+
    +
  • Rr = Rmax/Rmin
    • +
+

We also need the ratio of the segments per turn (s) to the total number of turns (t) to define an intermediate term, n.

+
    +
  • n = s/t
    • +
+

Now let m be a function of Rr and n.

+
    +
  • m = Rr^n
    • +
+

Then a becomes a function of m and theta'. We use the square of theta' as the exponent for m to arrive at a, which is also the radius increment for the first segment of the series forming the spiral.

+
    +
  • a = m^(theta'^2)
    • +
+

The composite form of the equation sequence is

+
    +
  • a = ((Rmax/Rmin)^(s/t))^((1/s)^2)
    • +
+

I have used spreadsheet notation because progressive superscripts are almost impossible to read and because the form allows direct transfer to a spreadsheet of your choice. Having values for all of the needed terms, Ri (or Rmin), a, and theta, we may calculate the new radius anywhere along the spiral. All that we need to do is to enter theta, the segment number in which we are interested.

+
    +
  • R = Ri*a^theta
    • +
+

As well we can easily determine at what turn (or fraction of a turn) the segment occurs.

+
    +
  • turns = theta'*theta
    • +
+

For any spiral length, we can determine the length up to segment theta (Lth) by beginning with the total length of the spiral, Lt, which we entered initially. Theoretically, the spiral rises in height in exact proportion to the increase in the radius.

+
    +
  • R-Rmin/Rmax-Rmin = L-Lmin/Lmax-Lmin
    • +
+

R is the radius at any segment, theta, and L is the spiral length up to that same segment. Lmax is the total length, Lt. Since Lmin is zero in the GH formation of a spiral, then Lth, the length at segment theta, is readily determined.

+
    +
  • Lth = ((R-Rmin)*Lt)/(Rmax-Rmin)
    • +
+

The calculations given for the radius in these notes result in values that exactly coincide with those generated by the NEC-4D core that I use. However, the values produced by that core for the length of the spiral up to end 2 of any segment sometimes show a slight variance, suggesting that the core uses another approach to length determination (or the Z coordinate). The variance is greatest in the first turn of the spiral and appears in the third significant digit. Beyond that point, the variance appears in the fourth significant digit. There are certain ratios of Rmax to Rmin where no variance appears at all. Functionally, the differences do not make a difference, but the numerical variance needs to be noted.

+

Finally, we can easily calculate the end-2 coordinates of the segment that we have entered as theta. First define the angle (A) of the specified segment in radians.

+
    +
  • A = 2*pi*theta*theta' = (2*pi*theta)/s
    • +
+

Then the X, Y, and Z coordinates follow.

+
    +
  • X = R cosA
    • +
  • Y = R sinA
    • +
  • Z = Lth
    • +
+
+ +
+

If it were not easy to place this progression of straightforward calculations into a spreadsheet page, the exercise would perhaps have only academic interest as a means to checking some particular set of coordinates of a modeled log spiral formed by the GH command. Fig. 3 shows a typical spreadsheet from my collection. I normally keep two working columns of data for entry and calculation, where a label indicates the entered data. I could lock the column marked sample, since I do not vary it. Instead, I use it for reference, that is, to remind myself of the calculation procedures and what data that I need to enter for a spiral under analysis. I also retain the Sample model on file to refresh myself from time to time. Those who deal daily with spirals can, of course, omit these memory aids. The following two lines are the GH entries for the Sample and the Work spirals in Fig. 3. The remaining model lines are identical to those in the initial example.

+ 
+Sample:  GH 1 120 6 1 1 3 .001 .001 0
+
+Work:    GH 1 300 6 4 3 4 .001 .001 0
+
+

The added utility of the spreadsheet is for modelers who wish to model a spiral but who have only the GH entry of NEC-2 with which to work. Most helix-makers attached to NEC-2 programs only create uniform helices in which the radius at the top and the bottom are the same. However, one might expand the spreadsheet to create a list of wires and coordinates for each value of theta, that is for each segment comprising a spiral of any size whatsoever. Since the equations for creating an Archimedes spiral are so straightforward, I did not include them in this spreadsheet, but if the modeler is interested in both Archimedes and log spirals, the additions are simple enough to make. With judicious spreadsheet planning, one might even create columns for either direct or indirect transfer to a NEC file as a set of wire coordinates. Of course, such a construct would consist of a separate 1-segment wire for each new straight-wire section of the spiral. (In contrast, the GH entry produces a new wire segment for each spiral section, all under a single tag number.) However, the end result would not differ in appearance from the helices created by existing uniform-radius helix makers associated with commercial implementations of NEC--except, of course, for the coordinates that transform a helix into a spiral.

+

The spreadsheet table of wires might have the following appearance, with variations customized to the input system of the version of NEC being used.

+ 
+                             Transfer Data                      Reference
+                     End 1                   End 2               Radius
+Cmd   Wire#   X       Y       Z       X       Y       Z       End 1   End 2
+GW    1       1.0000  0.0000  0.0000  0.9598  0.3119  0.0046  1.0000  1.0092
+GW    2       0.9598  0.3119  0.0046  0.8240  0.5986  0.0092  1.0092  1.0185
+GW    3       0.8240  0.5986  0.0092  0.6042  0.8315  0.0139  1.0185  1.0278
+GW    4       0.6042  0.8315  0.0139  0.3205  0.9865  0.0187  1.0278  1.0373
+GW    5       0.3205  0.9865  0.0187  0.0000  1.0468  0.0234  1.0373  1.0468
+etc. . . .
+
+

Transfer of the spread sheet data will depend upon the input system of the NEC implementation. A standard ASCII input system will require entry of the command name (GW) as well as the wire number, the number of segments for each wire (1), the End-1 and End-2 coordinates, and a wire radius. You can place these on the spreadsheet list and transfer complete lines of entry without need for later "touch-up." Other systems may not need either the command name or the wire number, although almost all will need the number of segments and a wire radius or diameter. In some systems, you can add these later with block operations.

+

Most spreadsheets separate data columns with Tabs. Some NEC implementations will accept Tabs; others will not. If you need to get rid of the Tabs, you can transfer the blocked data to a word processor. Often, the "unformatted text" or similar option will prevent the inclusion of the spreadsheet cell outlines while preserving the Tabs. Whether the word processor retains the Tabs or replaces them with multiple Spaces, you may use the global replace function to convert either one to a single space between entries on a line. (Using the same number of digits per entry, even if zeroes, simplifies the replacement procedure.) If some of these steps sound involved, compare the process to hand entering dozens of individual numbers without error. The bottom line is that it is possible to create wire lists that form either Archimedes or log spirals (flat or extended) in NEC implementations that lack the NEC-4 GH command.

+

Since each application is likely to differ in needs, I shall leave further extensions of the spreadsheet calculations to you. If these notes have acquainted you with the differences between an Archimedes and a log spiral in both visual and calculation terms, they have served their purpose. The NEC-4 GH entry offers considerable flexibility in creating helical shapes. Having a choice of spiral types is an advantage over the usual NEC-2 GH entry offerings, although the NEC-4 entry did give up the ability to directly create oval helices in the process.

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Go to Main Index

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9. Modeling Ground Planes and Other Radial Systems

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+

L. B. Cebik, W4RNL

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+ +

+ Vertical monopoles require a ground plane for the completion of the antenna, whether at ground level or elevated. Other types of antennas also call for ground radial systems. Modeling radial systems presents a numbers of challenges, especially if we are creating one for the first time. So let's see what is involved. +

Of course, modeling a vertical monopole over perfect ground requires no ground plane, because the program (NEC or MININEC) creates the requisite image antenna necessary for completion of the overall structure. Hence, our focus will be upon modeling vertical monopoles over real ground.

+

The Radial System

+
+ +
+

The standard ground plane system consists of a set of wires arranged radially about a single point. In real systems, the number general ranges from 4 to 120. If the number is only 4, as in Figure 1, the system is simple. Let L be the length of the radial. Then take 4 wires, all with one end at a certain point, usually at the coordinate 0, 0, Z, where Z may be some number greater than zero. For each of the 4, keep the same value of Z. Then alternatively assign the length to positive and then negative values of alternating X and Y. Then our wire chart looks like this.

+ 
Wire #    End 1     X    Y    Z         End 2     X    Y    Z
+ 1                  0    0    Z                   L    0    Z
+ 2                  0    0    Z                   0    L    Z
+ 3                  0    0    Z                   -L   0    Z
+ 4                  0    0    Z                   0    -L   Z
+

Beyond 4 radials, the required values for X and Y become a little more complex. Perhaps the greatest temptation in modeling vertical monopoles is always to use perfect ground in order to avoid having to create large models involving many radials. However, modeling a radial system is a straightforward task with simple rules which are amenable to symbolic model entry or to advanced calculation to determine the radial end-points. Figure 2 shows a typical radial system with 8 radials surrounding a center antenna that passes through the page. To construct or symbolize a set of radials, you may use any system similar to the following:

+
+ +
+

Set the X-axis as the reference line. Let L be the length of each radial (so that a sample radial might have the values at end 1 of X=0 and Y=0 and at end 2 of X=L and Y=0). If 8 is the number of radials, then the angle (A) between each radial is A=360/8. The radials will then have end-2 coordinates as follows:

+ 
Radial Number            End-2 X                  End-2 Y
+     1              X1 = L                   Y1 = 0
+     2              X2 = cos A * L           Y2 = sin A * L
+     3              X3 = cos (2 * A) * L     Y2 = sin (2 * A) * L
+
+     8              X2 = cos (7 * A) * L     Y2 = sin (7 * A) * L
+

In this example, radial 1 is the one which will extend from the center point to the values X=L and Y=0. You may set this table into a modeling program offering symbolic dimensional notation, or you may prepare the table and its results as a preliminary exercise on a prepared form to keep your work systematic and traceable. Symbolic entry does allow revision of the length of the entire radial system with a single change for the value of L. You must, however, have an entry for each radial in the system. Hence, changing the number of radials in a system requires the introduction of the correct number of wires to complete the array.

+

Once you have modeled radial systems with various numbers of wires, you should save your collection under some system of filenames. You may pull them from the files, scale them to the frequency of a present project as well as to the desired wire size and type, adjust X, Y, and Z values to position them for the new project, and then construct the new radiating wires atop them.

+

What Some Programs Offer

Various versions of NEC and MININEC offer us different ways of setting up the wires for a radial system. Here are a few examples. +

AO offers symbolic wire data entry. Hence, you may simply plug in the equations for each radial coordinate and present the value of A and L. If you have these preset into a number of files for each desired radial set size, you can join the relevant file to your proposed antenna file externally to AO and give the new file an .ANT extension. Then you can complete the radial system by adding 1. an antenna element wire (or more than one, if needed), 2. a value for L, which itself may be symbolic and determined by some other factor, such as frequency.

+

EZNEC offers an automated radial maker. From the wire description page, you enter the first wire of the radial set, ordinarily specifying the length along either the X or the Y axis. Then the program will ask which wire forms the basic radial (and it always uses end 1 as the pivot point). Finally, it will ask how many radials. The result that appears will be a set of radials with the correct angular spacing and the correct end coordinates. Because the operation is so fast, it does not usually pay to save radial files as separate entities in EZNEC.

+

NECWin will offer its "Plus" version around the beginning of 1999. It will contain an interesting spread sheet that permits flipping from a symbolic data page to an actual value page, so that you can see a radial set both ways. In this program, it will definitely pay to save sample radial set models as separate files for later reuse.

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+ +
+

If you have a sloping ground plane system, as illustrated in Figure 3, you can back up the calculations in symbolic entry on step and add a rotational component to take the final length at its level coordinates and rotate them downward by the appropriate number of degrees. Within EZNEC, you may group rotate the wires in the radial set downward in one command set. The following table, drawn from a 40-meter model, illustrates the wires of a sloping radial system with the radial length set at 9.8 meters, but sloping downward ar a 45-degree angle. (You can verify this length by taking any one of the X or Y values (6.93) and adding its square to the square of the difference between the End 1 and End 2 Z values (6.93). The square root of the sum is the leg length (9.8), via our old friend, the Pythagorean theorem.)

+ 
Wire  End 1    X       Y       Z    End 2    X       Y       Z
+ #    Conx                          Conx
+1            0.000,  0.000, 50.135  W2E1   0.000,  0.000, 40.000
+2     W1E2   0.000,  0.000, 40.000         6.930,  0.000, 33.070
+3     W1E2   0.000,  0.000, 40.000         0.000,  6.930, 33.070
+4     W1E2   0.000,  0.000, 40.000        -6.930,  0.000, 33.070
+5     W1E2   0.000,  0.000, 40.000         0.000, -6.930, 33.070
+

A wise exercise is to familiarize yourself with the coordinate values you might expect using a free-space model centered in the "0, 0, 0" coordinates. Create on paper or as models some flat radials systems using 4, 8, and 16 radials, as well a some 4-radial sloping systems at 30, 45, and 60 degrees. Set the radial length at some round number, such as 10 (any units will do). Make a chart of the coordinate values you obtain for each system. Then, when you construct actual radial systems, you can compare the results to the chart to see if all the values appear to be reasonable. Making a further cross check with the antenna structure viewing system of your software will likely ensure a correct model--or at least one that is set up as you intend it to be.

+

As a sample, my 16-wire reference table, with an arbitrary radial length of 10, looks like this:

+ 
Radial               End 1                         End 2
+Wire No.       X       Y       Z             X       Y       Z
+1            0.000,  0.000,  0.000        10.000,  0.000,  0.000
+2            0.000,  0.000,  0.000         9.239,  3.827,  0.000
+3            0.000,  0.000,  0.000         7.071,  7.071,  0.000
+4            0.000,  0.000,  0.000         3.827,  9.239,  0.000
+5            0.000,  0.000,  0.000         0.000, 10.000,  0.000
+6            0.000,  0.000,  0.000        -3.827,  9.239,  0.000
+7            0.000,  0.000,  0.000        -7.071,  7.071,  0.000
+8            0.000,  0.000,  0.000        -9.239,  3.827,  0.000
+9            0.000,  0.000,  0.000       -10.000,  0.000,  0.000
+10           0.000,  0.000,  0.000        -9.239, -3.827,  0.000
+11           0.000,  0.000,  0.000        -7.071, -7.071,  0.000
+12           0.000,  0.000,  0.000        -3.827, -9.239,  0.000
+13           0.000,  0.000,  0.000         0.000,-10.000,  0.000
+14           0.000,  0.000,  0.000         3.827, -9.239,  0.000
+15           0.000,  0.000,  0.000         7.071, -7.071,  0.000
+16           0.000,  0.000,  0.000         9.239, -3.827,  0.000
+

Core Limitations

Because ground plane wires, even sloping ones, have a horizontal component, MININEC ground planes should not be lower than 0.2 wl, the same accuracy restriction imposed on all horizontal wires. Similarly, the quick ground system attached to NEC-2 is limited in accuracy below about the same minimum height. DOS MININEC is further limited by the low number of total segments that a model may include. Using the provisions of symmetry in AO can increase the effective number of segments. However, only the Windows implementations of MININEC have broken this barrier within the calculating core. +

The Sommerfeld-Norton ground system in NEC-2 permits the modeler to place radials very close to the surface, so long as the radials are at least 0.001 wl above the ground and the height is equal to or greater than the diameter of the radial wire. Although most recommendations suggest that no special treatment is needed for the radial wires at this level, some difference in results appear between identical radials with equal segmentation and with tapered length segmentation. (Tapered length segmentation involves using very short segment lengths closest to the junction, with increasing segment length outward until some preset segment length is reached or the radial ends.) If the modeler attempts to place thin radials lower than 0.001 wl, but never lower than 0.0001 wl, then length tapering techniques must be used.

+
+ +
+

NEC-2 recommends a maximum of 30 wires to a junction. Although this limitation can be judiciously violated to a small degree, larger radials systems require special techniques. Figure 4 suggests a route to overcoming the limit. Some radials join together at a wire junction shy of the main junction, so that the hub sees no more than the recommended maximum number of wires.

+

Since radials usually form symmetrical patterns, structuring them with tapered diameter materials requires no corrective replacements (such as those we might need with linear Yagi elements). Like a capacity hat at the top of an element, the fields cancel due to the symmetrical arrangement of radials, resulting in the introduction of no errors.

+

An Example of a "Near-Ground" Radial System Model

Let's examine a typical model of a near-ground radial system. The frequency is 7.05 MHz or a wavelength of 42.55 meters. 0.001 wl is about 0.043 meters. Let's round this to 0.05 meters for the example. We can make the ground plane from 6.34 mm diameter (about 0.1") wire. We shall also place the ground plane beneath a 50 mm (nearly 2") diameter 1/4 wl monopole and above average Sommerfeld-Norton ground conditions (conductivity = 0.005 s/m; dielectric constant = 13). If we restrict ourselves to a 4-radial model initially, we have room to print the standard NEC file for such a model. It includes 6061-T6 material conductivity constant in the type 5 load (LD) entries. The final entry (RP) is a pattern request for an elevation plot. The file looks like this: + 
CM 1/4 wl vert: 7.05 MHz
+CM 4 radials, 0.05 m
+CE
+GW 1 10 0 0 10.1846 0 0 .05 .025
+GW 2 10 0 0 .05 11.796 0 .05 .00317
+GW 3 10 0 0 .05 0 11.796 .05 .00317
+GW 4 10 0 0 .05 -11.796 0 .05 .00317
+GW 5 10 0 0 .05 0 -11.796 .05 .00317
+GS 0 0 1
+GE 1
+GN 2 0 0 0 13 .005 0 0 0 0
+EX 0 1 10 0 1 0
+LD 5 1 1 10 2.4938E7
+LD 5 2 1 10 2.4938E7
+LD 5 3 1 10 2.4938E7
+LD 5 4 1 10 2.4938E7
+LD 5 5 1 10 2.4938E7
+FR 0 1 0 0 7.05 0
+RP 0 181 1 1000 -90 0 1 1
+EN
+

A 32-radial version of the same antenna would simply be much longer, with 33 wires total (and 33 corresponding LD entries). Interestingly, the gain of the 4-radial antenna is -1.57 dBi with a take-off angle of 64 degrees (zenith, or 26 degrees elevation), and the source impedance is 49 + j 52 Ohms. In contrast the 32-radial antennas shows a gain of 0.12 dBi at the same take-off angle, with a source impedance of 33 - j 0 Ohms. As we raise the ground plane to twice the height, both antennas show a rise in gain and a very slight lowering of the take-off angle, although the 32-radial version change is very small indeed. The 4-radial antenna reports a significant drop in both the feedpoint resistance and reactance, while the change in the 32-radial impedance values is about 1 Ohm in each category.

+

What are we to make of these reports? First, the larger ground plane exhibits much more stable characteristics by nearly a 10:1 factor. Second the reported feedpoint impedance of the larger array is much closer to free space values expected from the antenna than is the report from the 4-radial model. On the other hand, the values continue to change with small adjustments in the height of the ground plane, even for the larger model. We would be hard pressed to know precisely which values at which height to use for more than general guidance.

+

Is the Model Accurate?

Assessment of a model of a surface or buried radial system using radials that are in close proximity to ground is a complex question. In general, comparative values between different versions of the antenna and its ground radials will be correct. However, absolute values of far field gain and of source impedance are subject to several limitations of the NEC modeling system in addition to slight variability we encountered with the larger ground plane. +

First, the ground type (in terms of conductivity and of dielectric constant or permittivity) specified for the model presume a uniform or homogenous soil. Since the soil at levels most influential on antenna performance may be stratified, the model may not accurately reflect reality. The potential inaccuracy may be especially acute at lower frequencies, where the field may penetrate the soil to a considerable depth, for example, several feet in the lower HF range.

+

Second, ground conductivity may vary with frequency. Data on local soil susceptibility to this factor is often difficult to obtain. Even when the soil value is known for one frequency, sweeping the frequency over a large range may introduce errors relative to real conditions.

+

Note that these limitations are functions of the NEC-2 core and the Sommerfeld-Norton ground calculation system. They are not limitations of any particular implementation of NEC and should not be held against a vendor's product.

+

So Where Does All of This Leave Us?

For modeling radial systems at least 0.2 wl above the ground, both MININEC and NEC-2 will do a very satisfactory job on small ground plane systems. The limitation of segments in MININEC restricts such radial systems to a quite small size, but highly elevated systems usually are small--3 to 4 radials at most. NEC-2 can safely model systems of up to 30 radials or so without the use of special techniques. +

Modeling ground plane verticals close to the ground--as a stand-in for modeling radials systems either on or under ground--is a less certain enterprise. Because we lack assured data for such systems against which to compare the models, our efforts can provide only general guidance and comparative measures. (Even NEC-4 suffers from this same absence of data.) The complexities of the ground on and in which we place radials preclude the level of confidence we give modeling numbers for well-elevated horizontal arrays.

+

Nevertheless, do not discount altogether near-ground modeling of vertical monopoles with ground planes. Comparative data and trends provide valuable information that can be used to improve many antenna systems. Meanwhile, a new generation of work is underway to tighten the correlation of modeling and experimental results.

+

Other Applications for Radials

Radials have, of course, their second most common use at the far end of shortened linear elements in structures traditionally called "capacity hats." These symmetrical, field-canceling structures, shown by example in Figure 5, simply supply the linear element with the missing length to achieve resonance or some other specified condition. Although shown applied to the top of a vertical monopole in the sketch, they work in the very same manner at the ends of a shortened dipole element. +
+ +
+

The principles of modeling hats are identical to those of modeling radials. Because the fields of a hat cancel, we introduce no significant errors into the model by using wire diameters different from that of the main element. The only construction difference in the model will be that for dipoles, the axes on which we place the radials will not always be X and Y, but will involve Z plus either X or Y.

+

Perimeter wires are often part of the hat structure. In working with the model to determine the best radial length, we should take one extra step of care to ensure that the perimeter wire remains attached to the spoke ends. If we enter the radial dimensions in symbolic form, as we would with AO or NECWin Plus, the attachment is easy: simply specify the terminating points of each perimeter wire in the same coordinate notation as the appropriate radial ends.

+

In a program such as EZNEC, where all wires are entered numerically, the task is no harder. When modifying the radial length of an existing hat model that has a perimeter wire, first activate the "preserve connection" feature. Then modify the outer radial end coordinates as a group function, using the "l" or length specification option. The entire hat system of radials and perimeter wires will grow or shrink according to the selected length value. For model development, it is useful to list all of the radial wires in one batch (which would occur naturally, if you used the automated radial maker) and then add the perimeter wires as a second batch.

+

Although we have been most concerned with the construction of radial systems for use in ground plane modeling, the same modeling techniques apply wherever we need a radial structure.
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Go to Main Index

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+

90. An Orientation to NEC Near Fields
+ Part 1. NEC-2 Input Basics and Simple Outputs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Beginning modelers tend to focus on the far-field properties of antennas and to overlook near-field data. There are both good and bad reasons for this situation. First, not every entry-level program makes the near-field data available. Second, reading and using the inherent NEC-2 data output can be daunting in the absence of an adequate orientation to that data. Third, compromises in some programs relative to the Cartesian coordinate system and the inherent NEC output angle system can generate some confusions. Fourth, little effort has gone into making the near-field interface more user friendly. Fifth, outside of one piece of data, not inherent to the NEC-2 core, the remainder of the near field data is relatively foreign and therefore useless to the beginning modeler. These are not the only reasons we might give for the disuse into which near field data falls among relatively new modelers, but the list is long enough for an introduction to a partial corrective for the situation.

+

Most practical applications of antennas tend to follow compass headings and elevation angles. We record heading in a clockwise fashion around a compass rose to derive azimuth bearings. Similarly, we count degrees upward from the horizon to arrive at elevation angles. However, NEC employs a true Cartesian system of coordinates that defines points by reference to X, Y, and Z axes. When we translate the coordinates to headings and angles, we count in a counterclockwise direction in which 0 degrees lies along the X-axis of the coordinate graph. Hence, +Y is at 90 degrees, -X at 180 degrees, and -Y at 270 degrees. NEC does not inherently use an elevation system that counts from the ground up, but instead uses theta angles measured from the zenith downward. Fig. 1 shows the correct system. Note that since a standard theta angle would run from the zenith downward, it would be correct to count both horizon points as 90 degrees. The continuous count for a 360-degree theta circle is only one of several schemes used.

+
+ +
+

Fig. 1 uses two separate circles to sort out the elements of the coordinate and angle systems. It is difficult to adequately present the 3-dimensional system on a flat or 2-dimension surface. However, Fig. 2 provides an often-used 3-diminsional conventionalization.

+
+ +
+

My reason for not using the type of sketch shown in Fig. 2 is that it takes an expert graphic artist to select just the correct angles for the three axes in order to portray the observation point at a position that is intuitively correct to the reader. Lacking the services of such a skilled artisan, I shall rely on the simpler 2-circle sketch to portray positions.

+

One of the reasons that NEC users sometimes never get clear on how to manipulate the inputs for near fields is that entry-level programs try as best they can to accommodate the user's likely orientation toward azimuth (compass rose) headings and elevation angles. The conversion to elevation angles is simple enough, since the elevation angle = 90 (degrees) - theta (or theta = 90 - elevation). Azimuth is another matter. Some entry level programs simply switch the outer ring number without altering the phi pattern and call the result an azimuth pattern. Other programs use a phi pattern, but label it as an azimuth pattern. Still other programs simply use and label the patterns as phi patterns as they emerge from the NEC output file. Given the morass of potentially confusing orientations, and the fact that near-field entries require a single clear and unambiguous orientation, let's take a problem and work through it.

+

Entry Using Cartesian or Rectangular Coordinates

+
+ +
+

Fig. 3 shows one of the two ways of locating an observation position for a near-field request. Following Cartesian convention, the observation location is located by values for X, Y, and Z. Now let's translate that into an actual model using these conventions.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 0 1 1 1 5 10 5 1.0 1.0 1.0
+NH 0 1 1 1 5 10 5 1.0 1.0 1.0
+EN
+
+

The NE and NH lines provide the near-field entry requests for electrical and magnetic field strengths. The preceding lines define a simple 2-mm-diameter vertical dipole that is 0.5 wavelength long, with its base 0.25 wavelength above average ground, as specified by the GN entry. The frequency is 299.7925 MHz. Since we are requesting only a pair of single-frequency near-field reports, they will self-execute.

+

Notice that the near field requests separate the electrical and magnetic field solution requests. Otherwise, they are identical in form. Let's expand the form so that we can separate the NEC-2 entries in this model. Since the NE and NH commands occur after the closure of the geometry section of the model, the dimensions must be in meters, regardless of the units used and scaled within the geometry section of the model.

+ 
+Cmd  Cart/  No. of Points    Coordinate        Step Size
+     Spher  X     Y     Z    X     Y     Z     X     Y     Z
+NE   0      1     1     1    5     10    5     1.0   1.0   1.0
+NH   0      1     1     1    5     10    5     1.0   1.0   1.0
+
+

With respect to the entry of Cartesian or rectangular coordinates to specify the NE and NH requests, NEC-2 and NEC-4 use identical command entries.

+
+ +
+

Fig. 4 shows a help screen used by NEC-Win Pro to form one of the near-field command entries. The use of "1" for the number of points in each of the three coordinate directions does not yield 3 observation points, but only a single point defined by the three coordinates. (We shall briefly examine multiple points before we quit.) One of the uses made of single-point near-field requests is to satisfy certain government regulations regarding the magnitudes of electrical and/or magnetic fields in the vicinity of antennas used by various services, including the amateur service. The output report--if within limits set by regulations--will satisfy the requirements of those regulations for a large variety of well designed antenna models. We can glean the requisite data from the output table for the near-field request, as sampled below for the model just displayed.

+ 
+**** NEAR ELECTRIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-6.nec
+
+            -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+     5.000000  10.000000   5.000000     6.6689E-03    25.21    1.3338E-02    25.21    3.8323E-02  -149.78    4.1105E-02
+
+**** NEAR MAGNETIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-6.nec
+
+            -  LOCATION  -                     -  HX  -               -  HY  -               -  HZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS         AMPS/M   DEGREES       AMPS/M   DEGREES       AMPS/M   DEGREES      AMPS/M
+     5.000000  10.000000   5.000000     9.7519E-05  -150.52    4.8760E-05    29.48    5.0538E-11    18.32    1.0903E-04
+
+

For the simple purpose of the presumed near-field requests, we are interested in 2 parts of the output report. First, the observation location coordinates appear in the report and serve as a check on the accuracy of our input. In more extensive reports, the coordinate locations would define separate observation points within the range of our request.

+

Second, the last entry in each line lists the peak field magnitude in volts/meter for the electric field and in amperes/meter for the magnetic field. Since this report emerges directly from the NEC output file, the values are in peak volts/meter. Compare those lines with the following ones from an identical EZNEC model.

+ 
+         --------------- NEAR-FIELD PATTERN DATA ---------------
+
+Frequency = 299.793 MHz
+Power = 0.0046119 watts
+Max field = 0.0290653 V/m RMS
+ at X,Y,Z = 5, 10, 5 m
+
+Electric (E) Field (V/m RMS)
+
+X (m)      Y (m)      Z (m)       Ex Mag     Ey Mag     Ez Mag     Etot
+5          10         5          .00471558  .00943117  0.0270987  0.0290653
+
+
+Frequency = 299.793 MHz
+Power = 0.0046119 watts
+Max field = 7.84369E-05 A/m RMS
+ at X,Y,Z = 5, 10, 5 m
+
+Magnetic (H) Field (A/m RMS)
+
+X (m)      Y (m)      Z (m)       Hx Mag     Hy Mag     Hz Mag     Htot
+5          10         5          7.0156E-5  3.5078E-5  0          7.8437E-5
+
+

The "Etot" and "Htot" columns correspond to the "Peak Field" columns in the first report, but the values under those columns differ radically. Actually, they differ not at all once we realize that the peak voltage/meter (and current/meter) of the NEC output report have been converted into RMS values in the EZNEC report. The SQRT(2) or 1.4142 times the RMS values will yield values very close to those of the NEC-Win Pro output, allowing for the slight differences in actual numbers that results from using different FORTRAN compilers.

+

We shall note in passing that the original NEC-2 core did not yield a total or peak magnitude column. However, many implementations of NEC-2 have added that calculation because it is fundamentally useful to even casual modelers.

+

Although these calculations yield values called near-field reports, they differ from those shown in most basic texts under near-field calculations. In most texts, near-field equations extract from the total field equations those terms most relevant to strict near-field phenomenon calculation. The result is a simpler set of equations to manipulate. Since NEC must ultimately deal with the total field, including all components, the near-field reports are for the total solution, including surface-wave components.

+

Entry Using Spherical Coordinates

+

Let's now enter the same problem using the spherical coordinate entry option. The rudiments of this option appear in Fig. 5.

+
+ +
+

The key ingredients of the alternative entry system are the radius-line from the coordinate center to the observation location, the phi angle pf the observation point, and the theta angle of that point. If we wish to use the same observation position, we shall have to do some calculating. I shall show all results to the display limits of my hand calculator, since I wish the output report to coincide as precisely as possible with the first model. You may round numbers as your task dictates or permits.

+

1. Beginning with the original X, Y, and Z coordinates, we can calculate the radius in standard vector form, Hence, the radius r = SQRT(X^2 + Y^2 + Z^2). For X=5, Y=10, and Z=5, r=12.247449.

+

2. The phi angle is a function of the X and Y coordinate, such that Y/X = tan(phi). Hence, phi = arctan(Y/X) or 63.434949 degrees--and NEC wants the angle in degrees.

+

3. The theta angle is a function of the radius R and the Z coordinate. It tends to be easier to start with an elevation angle, such that el=arcsin(Z/r) degrees, and theta=90-el degrees, that is 65.905157 degrees.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 1 1 1 1 12.247449 63.434949 65.905157 1.0 1.0 1.0
+NH 1 1 1 1 12.247449 63.434949 65.905157 1.0 1.0 1.0
+EN
+
+

The sample model uses the same antenna and varies only the NE and NH requests to coincide with the coordinate system for entry. The following lines expand the entries with notations for the meaning of each entry in each line.

+ 
+Cmd  Cart/  No. of Points      Coordinate                         Step Size
+     Spher  r     phi   theta  r (radius) phi angle  theta angle  r     phi   theta
+NE   1      1     1     1      12.247449  63.434949  65.905157    1.0   1.0   1.0
+NH   1      1     1     1      12.247449  63.434949  65.905157    1.0   1.0   1.0
+
+

Note that for each sequence of r, phi, and theta, phi precedes theta in the entry. This order applies to NEC-2. However, NEC-4 reverses the phi and theta positions so that the order is r, theta, phi. For now, we shall restrict ourselves to NEC-2.

+
+ +
+

Fig. 6 presents the entry set-up screen for the present model to correspond with the earlier model using Cartesian coordinates. Both screens request data inputs that track exactly what will appear in the entry line. However, there is an alternative way to request the input data that some users find more convenient if their request involves more than one point along an axis or other line. Instead of requesting the starting values, the increment, and the number of points, the system requests the start values, the stop values, and the number of points. EZNEC uses such as system, as shown in Fig. 7, and then internally converts the request to the form required by the core.

+
+ +
+

To see if we have done our set-up calculations correctly, lets examine the output report for this new model in NEC-Win Pro format.

+ 
+**** NEAR ELECTRIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-6.nec
+
+            -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+     5.000000  10.000000   5.000000     6.6689E-03    25.21    1.3338E-02    25.21    3.8323E-02  -149.78    4.1105E-02
+
+**** NEAR MAGNETIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-6.nec
+
+            -  LOCATION  -                     -  HX  -               -  HY  -               -  HZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS         AMPS/M   DEGREES       AMPS/M   DEGREES       AMPS/M   DEGREES      AMPS/M
+     5.000000  10.000000   5.000000     9.7519E-05  -150.52    4.8760E-05    29.48    5.0538E-11    18.32    1.0903E-04
+
+

The first thing to notice is that the "Peak Field" magnitude reports are identical to those produced using the Cartesian coordinate system for entry. The result is expected the moment that we also examine the observation location data at the left end of each line. The values for X, Y, and Z are identical to those in the Cartesian output report. That is the second notable feature of near-field reports: regardless of which input system we use, the output report is always in terms of Cartesian coordinates for the distinct observation points.

+

For single-point reports, it makes no difference which input system we use, and so the best advice is to choose the simplest based on the data available. Suppose that we are calculating the field intensity of an antenna at a certain height above ground with an observer some specified distance away in a clear field. In such a case, we can often simplify the problem by placing the line from the antenna support along a model geometry axis for either an X or a Y entry on the Cartesian system. The height of the antenna above ground becomes a simplified Z-axis entry. We do not have to pre-calculate the angular distance from the antenna down to the observer. Hence, for many simple cases, the Cartesian entry system is the easier to use.

+

However, let's attend to the limitations of the model. It presumes that the antenna is oriented correctly relative to the observation point. For a vertical dipole in a clear field, the presumption may hold. However, if the antenna is directional in any way, the presumption may not hold unless the orientation is modeled into the geometry. Note also that the hypothetical case presumes a clear field with no absorbing, refracting, or reflecting objects within a relevant distance from either the antenna or the observation point. In the situations of real antennas, we rarely encounter this ideal condition. A fully adequate model would require us to model reasonable approximations of all such objects along with the antenna itself.

+

Which Input System?

+

It would be easy to summarize the cases for the use of each input system in a couple of lines.

+

Use the Cartesian coordinate input system wherever you require a field of observation points spaced apart by equal or otherwise specified increments of distance.

+

Use the spherical coordinate input system whenever you need a field of observation point separated by equal angular increments or when you need a set of observation points along equal increments in the direction of the radius line.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 0 3 3 3 5 10 5 1.0 1.0 1.0
+EN
+
The initial test model uses Cartesian coordinates for the electric field only to illustrate the "box" effect produced by their use in multiple steps. Fig. 8 shows to entry formation screen to clarify what the model requests. +
+ +
+

For each axis, the NE requests wants 3 steps at the indicated increment of 1.0-meter each. Hence, the output report will yield 27 lines. For some purposes, this type of report, as illustrated by the following lines, may be just what a task dictates. However, we may need only a few of the values produced out of the entire set of lines.

+ 
+**** NEAR ELECTRIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-4-3.nec
+
+            -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+     5.000000  10.000000   5.000000     6.6689E-03    25.21    1.3338E-02    25.21    3.8323E-02  -149.78    4.1105E-02
+     6.000000  10.000000   5.000000     7.4387E-03  -136.47    1.2398E-02  -136.47    3.8370E-02    48.47    4.0987E-02
+     7.000000  10.000000   5.000000     7.9924E-03    40.01    1.1418E-02    40.01    3.8327E-02  -135.21    4.0767E-02
+     5.000000  11.000000   5.000000     5.8165E-03    81.69    1.2796E-02    81.69    3.8346E-02   -93.49    4.0826E-02
+     6.000000  11.000000   5.000000     6.5235E-03   -69.28    1.1960E-02   -69.28    3.8250E-02   115.36    4.0590E-02
+     7.000000  11.000000   5.000000     7.0459E-03   118.42    1.1072E-02   118.42    3.8054E-02   -57.17    4.0243E-02
+     5.000000  12.000000   5.000000     5.0622E-03   131.45    1.2149E-02   131.45    3.8072E-02   -44.11    4.0272E-02
+     6.000000  12.000000   5.000000     5.7020E-03   -10.04    1.1404E-02   -10.04    3.7853E-02   174.19    3.9932E-02
+     7.000000  12.000000   5.000000     6.1871E-03  -172.23    1.0607E-02  -172.23    3.7536E-02    11.75    3.9485E-02
+     5.000000  10.000000   6.000000     6.4090E-03  -114.92    1.2818E-02  -114.92    3.1057E-02    68.49    3.4195E-02
+     6.000000  10.000000   6.000000     7.1580E-03    86.85    1.1930E-02    86.85    3.1200E-02   -89.38    3.4151E-02
+     7.000000  10.000000   6.000000     7.7435E-03   -92.96    1.1062E-02   -92.96    3.1394E-02    91.08    3.4164E-02
+     5.000000  11.000000   6.000000     5.6244E-03   -52.12    1.2374E-02   -52.12    3.1349E-02   131.88    3.4158E-02
+     6.000000  11.000000   6.000000     6.3577E-03   159.88    1.1656E-02   159.88    3.1508E-02   -15.99    3.4180E-02
+     7.000000  11.000000   6.000000     6.9433E-03    -9.14    1.0911E-02    -9.14    3.1666E-02   175.05    3.4194E-02
+     5.000000  12.000000   6.000000     4.9841E-03     3.65    1.1962E-02     3.65    3.1656E-02  -172.16    3.4194E-02
+     6.000000  12.000000   6.000000     5.6705E-03  -135.22    1.1341E-02  -135.22    3.1757E-02    48.97    3.4184E-02
+     7.000000  12.000000   6.000000     6.2275E-03    65.52    1.0676E-02    65.52    3.1831E-02  -110.35    3.4136E-02
+     5.000000  10.000000   7.000000     6.4443E-03    85.40    1.2889E-02    85.40    2.6446E-02   -93.43    3.0116E-02
+     6.000000  10.000000   7.000000     7.0583E-03   -68.31    1.1764E-02   -68.31    2.6269E-02   113.41    2.9633E-02
+     7.000000  10.000000   7.000000     7.5220E-03   116.39    1.0746E-02   116.39    2.6219E-02   -61.32    2.9313E-02
+     5.000000  11.000000   7.000000     5.4786E-03   156.26    1.2053E-02   156.26    2.6218E-02   -21.57    2.9368E-02
+     6.000000  11.000000   7.000000     6.1422E-03    11.69    1.1261E-02    11.69    2.6247E-02  -165.72    2.9209E-02
+     7.000000  11.000000   7.000000     6.6806E-03  -153.71    1.0498E-02  -153.71    2.6351E-02    29.27    2.9135E-02
+     5.000000  12.000000   7.000000     4.7962E-03  -141.18    1.1511E-02  -141.18    2.6341E-02    41.76    2.9138E-02
+     6.000000  12.000000   7.000000     5.4556E-03    82.77    1.0911E-02    82.77    2.6459E-02   -94.04    2.9129E-02
+     7.000000  12.000000   7.000000     6.0079E-03   -73.40    1.0299E-02   -73.40    2.6614E-02   109.99    2.9156E-02
+
+

Note that NEC uses an order of precedence in the rate of change of each coordinate, with the X-coordinate changing value most rapidly, followed by the Y- and finally the Z-coordinate.

+

Suppose that we wish only a line of reading along the axis of the radius line. For this type of task, the spherical coordinate system is usually the most apt, as illustrated by the following revision to our basic spherical-coordinate model.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 1 4 1 1 12.247449 63.434949 65.905157 1.0 1.0 1.0
+EN
+
+

Once more, I have restricted the model to only an NE entry for simplicity. Fig. 9 shows the NE entry screen to clarify the maneuver of requesting 4 points along the radius line.

+
+ +
+

The model requests 4 observation point spaced 1 meter apart along the radius line. The core returns the following report.

+ 
+**** NEAR ELECTRIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\amod90-6-3.nec
+
+            -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+     5.000000  10.000000   5.000000     6.6689E-03    25.21    1.3338E-02    25.21    3.8323E-02  -149.78    4.1105E-02
+     5.408248  10.816497   5.408249     6.2225E-03    25.84    1.2445E-02    25.84    3.5339E-02  -149.52    3.7965E-02
+     5.816497  11.632993   5.816497     5.8311E-03    26.38    1.1662E-02    26.38    3.2787E-02  -149.30    3.5273E-02
+     6.224745  12.449490   6.224745     5.4853E-03    26.85    1.0971E-02    26.85    3.0581E-02  -149.11    3.2939E-02
+
+

For our limited purposes, the most notable part of the output report is the set of coordinates. If we take a vector sum of the coordinates for each observation point, we shall find that each differs by exactly 1.0 meter from the preceding or following point.

+

The End of the Beginning. . .

+

The exercises in this episode have tried to develop a bit of comfort with the alternative near-field input systems available in NEC-2. We looked mostly at single observation point situations to make the input systems clear, and we essentially examined only one part of the output data.

+

I have not tried to replicate the mathematical background of near fields as calculated NEC, since the theory portions of the manuals do a far better job than I can in these columns. Instead, my task has been to orient the modeler toward using the NE and NH inputs to obtain the information needed for observation points of choice. Nevertheless, we have left some questions open. How does the data within each report line integrate? How does the NEC-4 input system differ from the NEC-2 system? Finally, how does the new request command, called LE and LH, differ from the present set of request commands that we have so far surveyed? Those are enough questions to occupy another entire episode.

+
+ +

+

Go to Main Index

+ + diff --git a/content/amod/amod91-1.gif b/content/amod/amod91-1.gif new file mode 100644 index 0000000..c662485 Binary files /dev/null and b/content/amod/amod91-1.gif differ diff --git a/content/amod/amod91-2.gif b/content/amod/amod91-2.gif new file mode 100644 index 0000000..3562c14 Binary files /dev/null and b/content/amod/amod91-2.gif differ diff --git a/content/amod/amod91-3.gif b/content/amod/amod91-3.gif new file mode 100644 index 0000000..5588c30 Binary files /dev/null and b/content/amod/amod91-3.gif differ diff --git a/content/amod/amod91.html b/content/amod/amod91.html new file mode 100644 index 0000000..a648c75 --- /dev/null +++ b/content/amod/amod91.html @@ -0,0 +1,270 @@ + + + + + Orientation to Near Fields + + + +
+

91. An Orientation to NEC Near Fields
+ Part 2. Some Refinements and NEC-4 Additions

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The preceding episode had a simple goal: to orient you to the specifications of a location for a near-field reading using either Cartesian or spherical coordinates. The reading can be for either the electric or the magnetic field. In the process, we also explored the basics of setting up the reading or observation location at multiple points. As indicated in Fig. 1, we learned that if we need multiple observation points at linear intervals, the Cartesian coordinate system of entry may be more useful. If we need observation points at equal-angle increments, then spherical coordinates may prove simpler.

+
+ +
+

Once we have become oriented to obtaining near-field readings, we are in a better position to appreciate some refinements in the command and its output. We hinted at a number of these items, but the time has come to set them forth explicitly.

+

1. Near-Field Execution: When we request a far-field radiation pattern (RP0), NEC automatically executes the request. If we need a frequency sweep for a single RP0 request, the RP0 automatically executes it. However, if we make multiple RP0 requests and wish the same frequency sweep for each pattern, then we must repeat the FR command specifications prior to each RP0 entry.

+

Near-field request operate differently. As we saw in the preceding episode, when we request a single frequency, the NE and NH commands will self-execute, similarly to the RP0 request. The following model provides us with a concrete example of this situation. You may extract and run the model. Then check the output tables to ensure that results for both the NE and NH command appear.

+ 
+CM NE/NH test
+CM 1-step, Cartesian coordinates
+CM 1 Frequency
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 0 1 1 1 5 10 5 1.0 1.0 1.0
+NH 0 1 1 1 5 10 5 1.0 1.0 1.0
+EN
+
+

Let's modify only the FR command to set up a 2-step frequency sweep. As the extract from the model shows, we retain the NE and the NH commands, but ask for a 2-step sweep. If you run the model, no near-field outputs will appear.

+ 
+FR 0 2 0 0 295 10
+NE 0 1 1 1 5 10 5 1.0 1.0 1.0
+NH 0 1 1 1 5 10 5 1.0 1.0 1.0
+EN
+
+

When we request multiple frequencies, each NE or NH command must have a request for execution (normally XQ) somewhere after each request. So the following model puts the requests in place.

+ 
+FR 0 2 0 0 295 10
+NE 0 1 1 1 5 10 5 1.0 1.0 1.0
+XQ
+NH 0 1 1 1 5 10 5 1.0 1.0 1.0
+XQ
+EN
+
+

However, we are still deficient, since the output will show near electric field readings for both frequencies, but near magnetic fields only for the higher frequency. What we forgot was that the FR command forms a loop relative to the most immediately following execution command (such as XQ or RP). Subsequent execution requests make use only of the highest or final frequency in the sweep. In order to obtain data for both frequencies for both near-field requests, we must repeat the FR loop, as in the final model of this series.

+ 
+FR 0 2 0 0 295 10
+NE 0 1 1 1 5 10 5 1.0 1.0 1.0
+XQ
+FR 0 2 0 0 295 10
+NH 0 1 1 1 5 10 5 1.0 1.0 1.0
+XQ
+EN
+
+

Now the output report will show a pair of entries each for the near electric and magnetic fields.

+

2. The Peak Field Value Reading: Because many beginning modelers are interested only on the peak field value reading from a given set of near-field requests, we called attention to that entry in the near-field output tables in the preceding episode. We also noted in passing that the value is not the simple vector sum of the values specified in the X, Y, and Z columns. Let's pause a moment to see what that remark meant. We may begin with the single entry tables for our basic model at the beginning of this episode.

+ 
+**** NEAR ELECTRIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\91-1.nec
+
+            -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS        VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+     5.000000  10.000000   5.000000     6.6689E-03    25.21    1.3338E-02    25.21    3.8323E-02  -149.78    4.1105E-02
+
+**** NEAR MAGNETIC FIELDS ****
+**** Frequency = 299.79, File: C:\ant\NE-NH\91-1.nec
+
+            -  LOCATION  -                     -  HX  -               -  HY  -               -  HZ  -       - PEAK FLD -
+        X          Y          Z          MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS     METERS     METERS         AMPS/M   DEGREES       AMPS/M   DEGREES       AMPS/M   DEGREES      AMPS/M
+     5.000000  10.000000   5.000000     9.7519E-05  -150.52    4.8760E-05    29.48    5.0537E-11    18.32    1.0903E-04
+
+

If we create vector sums for EX, EY, and EZ, and then for HX, HY, and HZ, we arrive at two values: 4.1122E-2 V/m for the electric field and 1.0903E-4 A/m for the magnetic field. The fact that the square root of the sum of the squares of the magnitudes appears to give a precise result for the magnetic near field often leads us to believe that something must be wrong with the core when it calculates the value for the other field.

+

What is wrong is our geometric interpretation of what is essentially a temporal calculation. If the phase angles were identical or if one component dominates, then the simple vector sum would be a good approximation of the peak voltage or current. Otherwise, the peak value will be equal to or less than the result of the geometric calculation. The phase differences among the component values tell us that each reaches its magnitude at a different time during a cycle, and so the calculation of a peak value must take that fact into account.

+

The actual calculation of the peak value is a multi-step procedure found in the NEC routine called NFPAT. It proceeds approximately as follows:

+

For either NE or NH, for a given field point defined by X, Y, and Z, let

+
    +
  • EXM, EYM, EZM = magnitude of EX, EY, EZ (given in peak volts/m or peak amps/m)
    • +
  • EXP, EYP, EZP = phase angle of EX, EY, EZ (degrees or radians)
    • +
+

"E" is a stand-in for either the voltage or the current. There is no difference in the calculation procedures. Next, let's calculate some intermediate terms involving the phase angles, finally arriving at a term called "TP."

+
+ +
+
+ +
+
+ +
+

Now we may include TP in the final calculation involving the squares of the component magnitudes.

+
+ +
+

The resulting peak voltage or current reading (called "Epeak") in V/m or A/m is also in peak units.

+

3. NEC-2 vs. NEC-4 Spherical Coordinate Entries: When entering rectangular coordinates (NE0/NH0), there is no difference between the NEC-2 and NEC-4 entries. However, there is an important difference between the two cores when entering spherical coordinates. The two cores swap places between the phi and theta entries. Consider the following model in NEC-2 format.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 1 1 1 1 12.247449 63.434949 65.905157 1.0 1.0 1.0
+NH 1 1 1 1 12.247449 63.434949 65.905157 1.0 1.0 1.0
+EN
+
+

The format for the NE and the NH lines is as follows:

+ 
+     I1     I2    I3    I4     F1         F2         F3           F4    F5    F6
+Cmd  Cart/  No. of Points      Coordinate                         Step Size
+     Spher  r     phi   theta  r (radius) phi angle  theta angle  r     phi   theta
+NE   1      1     1     1      12.247449  63.434949  65.905157    1.0   1.0   1.0
+NH   1      1     1     1      12.247449  63.434949  65.905157    1.0   1.0   1.0
+
+

To achieve the same goal in NEC-4, we must use the following model.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 .25 0 0 .75 .001
+GE 1 0 0
+GN 2 0 0 0 13.0000 0.0050
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 1 1 1 1 12.247449 65.905157 63.434949 1.0 1.0 1.0
+NH 1 1 1 1 12.247449 65.905157 63.434949 1.0 1.0 1.0
+EN
+
The terms of the NE and NH lines have changed position with respect to phi and theta. + 
+     I1     I2    I3    I4     F1         F2           F3           F4    F5    F6
+Cmd  Cart/  No. of Points      Coordinate                           Step Size
+     Spher  r     phi   theta  r (radius) theta angle  phi angle    r     phi   theta
+NE   1      1     1     1      12.247449  65.905157    63.434949    1.0   1.0   1.0
+NH   1      1     1     1      12.247449  65.905157    63.434949    1.0   1.0   1.0
+
In programs like GNEC and NEC-Win Pro, the assist screens will appear identical, as in Fig. 2. +
+ +
+

However, each screen will create the required NE or NH entry correctly for the core in use. Since there is nothing in the NE or NH entries to create an error in the core run, NEC will not warn you if you accidentally mis-enter the phi and theta angles when creating the line without assistance. The results will simply be wrong. You may block copy the two versions of the model and run them on the same core to examine the disparity of the results.

+

4. The Antenna Structure and the Ground: The safest procedure to obtain controlled results is to ensure that no selected field point falls within the wires of the antenna, that is, along the segment line or within its radius. If a field point does fall within these confines, NEC will move it an amount equivalent to the wire radius outside the wire in a direction normal to the plane for a reading and along the vector from the source segment to the observation point. Because the results may not include that segment's contribution to the H field or to the radial component of the E field, it is always wise to pre-plan the observation points so that they all fall outside the wire segments of the model.

+

The preferred ground calculation system for near-field analysis is the Sommerfeld-Norton (SN) system. However, there are restrictions. To minimize errors that tend to appear at very low frequencies, no observation point should be exactly at ground level. In fact, the minimum distance above ground in NEC-2 should be 0.001 wavelength. The reflection coefficient approximation (RCA) system, sometimes called the "fast" ground calculation system, may produce errors in the magnetic field calculations for observation points at some distance from the source. The RCA system does not include surface-wave contributions for this calculation and so may underestimate the field strength.

+

As noted in the previous episode, NEC differs from textbook treatments of near field calculations. Most texts introduce near-field calculations by extracting from a total field equation those elements that are most influential relative to the near field strength and then ignoring the remaining elements. NEC includes the near-field and the total field elements and so will take into account influences by the near field and the ground-wave factors.

+

NE/NH and LE/LH

+

NEC-4 introduced a new pair of near-field commands to the pair that it inherited from NEC-2. So you have a choice between using the pair that best suits the requirement of the modeling task. (Of course, you have no requirement to use either NE and NH or LE and LH in pairs, and you may use both within the same model.) NE and NH are general abbreviations for near-electric and near-magnetic fields. LE and LH indicate near-electric and near-magnetic fields along a line. The differences between the two systems of calculating near fields may prove useful, not only in understanding the new NEC-4 commands, but as well in better appreciating the terms of the NE and NH output reports.

+

The NE/NH command set calculates its observation positions based upon either Cartesian or spherical coordinates, but it always reports its results in terms of field strength in Cartesian coordinates. However, it does not initially yield a single field strength value for the X, Y, and Z coordinate marking the observation position. Instead, it yields 3 values, each of which applies to that position in a plane parallel to the indicated axis. The components of the peak field strength are individual field strengths related to the axes of the coordinate system itself. See the left side of Fig. 3 for a rough representation.

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+ +
+

On the right in Fig. 3 is a similar situation. An observation point has a bearing from the source that is identical to the one on the left. However, the LE and LH command pair request output data along a defined line, in this case, running from the source to the final observation point. The data returned by the request provides electric or magnetic field strength using the axial direction of the line as the primary field component. Also provided are two transverse components, one horizontal and the other vertical. If we define the axial vector as a-cap, and we may let h-cap and v-cap be the horizontal and vertical transverse components, respectively, as roughly represented on the right side of Fig. 3. The actual vectors use the following equations.

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+ +
+

The key entry data for both the LE and LH command are the number of points along the line to use for field strength reports and the starting and ending coordinates of the line. Hence, the pair of commands has the following structure.

+ 
+CMD     I1     I2     I3     I4     F1     F2     F3     F4     F5     F6
+        RSET   NPTS   0      0      X1     Y1     Z1     X2     Y2     Z2
+LE      0      16     0      0      0      0      0      0      1.5    .5
+LH      0      16     0      0      0      0      0      0      1.5    .5
+
+

Both of the sample lines request a report using 16 points along a line defined by 0, 0, 0 at end 1 and by 0, 1.5, and 0.5 at end 2. The command uses the same execution rules as the NE/NH pair. It will self execute if there is only one frequency requested. However, for multiple frequencies in the FR command, it requires either a following RP or XQ command to execute. As well, if there are multiple requests as well as multiple frequencies, then the FR command requires repetition before each LE or LH command to ensure that data is available for all requests at all frequencies. As well LE and LH are subject to the same ground and boundary conditions as NE and NH.

+

It is possible to set up NE/NH models so that they cover the same observation points as corresponding LE/LH models. Consider the following conventional near-field model. It uses spherical coordinates and is set up for NEC-4.

+ 
+CM NE/NH test
+CE
+GW 1 11 0 0 -.5 0 0 .5 .001
+GE 0 0 0
+GN -1
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+NE 1 16 1 1 0 71.565051 90 .10540932 0 0
+NH 1 16 1 1 0 71.565051 90 .10540932 0 0
+EN
+
+

The model requests 16 observation point along a line defined by a phi angle of 90 degrees and a theta angle of 71.565 degrees. The selection is not accidental, since the line formed has regularly spaced observation points that terminate at round numbers. The electric field report from NEC-4 is as follows.

+ 
+***************************************** NEAR ELECTRIC FIELDS *****************************************
+**** Frequency = 299.79, File: C:\ant\NE-NH\91-3.nec
+
+              -  LOCATION  -                     -  EX  -               -  EY  -               -  EZ  -       - PEAK FLD -
+        X           Y           Z           MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE     MAGNITUDE
+      METERS      METERS      METERS         VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES     VOLTS/M
+      0.000000    0.000000    0.000000     0.0000E+00     0.00    0.0000E+00     0.00    1.1000E+01  -180.00    1.1000E+01
+      0.000000    0.100000    0.033333     3.3698E-09    -3.88    2.7694E-01    -3.88    8.1373E-01   147.90    8.5038E-01
+      0.000000    0.200000    0.066667     1.0570E-09    -4.90    8.6864E-02    -4.90    3.9996E-01   101.89    4.0078E-01
+      0.000000    0.300000    0.100000     2.9706E-10    20.67    2.4413E-02    20.67    3.0347E-01    58.81    3.0408E-01
+      0.000000    0.400000    0.133333     2.9407E-10    79.32    2.4168E-02    79.32    2.5943E-01    21.14    2.5974E-01
+      0.000000    0.500000    0.166667     4.0556E-10    75.92    3.3330E-02    75.92    2.2690E-01   -14.38    2.2690E-01
+      0.000000    0.600000    0.200000     4.5147E-10    56.32    3.7103E-02    56.32    1.9972E-01   -49.58    1.9999E-01
+      0.000000    0.700000    0.233333     4.5907E-10    31.00    3.7728E-02    31.00    1.7694E-01   -85.08    1.7774E-01
+      0.000000    0.800000    0.266667     4.4839E-10     2.55    3.6850E-02     2.55    1.5796E-01  -120.99    1.5932E-01
+      0.000000    0.900001    0.300000     4.2974E-10   -27.93    3.5317E-02   -27.93    1.4217E-01  -157.27    1.4399E-01
+      0.000000    1.000001    0.333334     4.0824E-10   -59.84    3.3550E-02   -59.84    1.2897E-01   166.13    1.3114E-01
+      0.000000    1.100001    0.366667     3.8636E-10   -92.79    3.1752E-02   -92.79    1.1785E-01   129.29    1.2026E-01
+      0.000000    1.200001    0.400000     3.6526E-10  -126.55    3.0018E-02  -126.55    1.0840E-01    92.25    1.1097E-01
+      0.000000    1.300001    0.433334     3.4543E-10  -160.93    2.8389E-02  -160.93    1.0029E-01    55.07    1.0296E-01
+      0.000000    1.400001    0.466667     3.2706E-10   164.19    2.6879E-02   164.19    9.3273E-02    17.77    9.5988E-02
+      0.000000    1.500001    0.500000     3.1014E-10   128.92    2.5488E-02   128.92    8.7149E-02   -19.63    8.9880E-02
+
+

A corresponding LE/LH model set up for the same observation points has the following appearance.

+ 
+CM LE/LH test
+CE NEC-4 only
+GW 1 11 0 0 -.5 0 0 .5 .001
+GE 0 0 0
+GN -1
+EX 0 1 6 00 1 0
+FR 0 1 0 0 299.7925 1
+LE 0 16 0 0 0 0 0 0 1.5 .5
+LH 0 16 0 0 0 0 0 0 1.5 .5
+EN
+
+

It produces (on NEC-4 only) the following electric field report.

+ 
+********************************** NEAR ELECTRIC FIELDS ALONG A LINE ***********************************
+**** Frequency = 299.79, File: C:\ant\NE-NH\91-3a-nec4.nec
+
+ Unit Vectors:      X        Y        Z
+ Axial       =   0.00000  0.94868  0.31623
+ Transverse1 =  -1.00000  0.00000
+ Transverse2 =   0.00000 -0.31623  0.94868
+
+              -  LOCATION  -                    - Axial -           - Transverse1 -       - Transverse2 -
+        X           Y           Z           MAGNITUDE   PHASE      MAGNITUDE   PHASE      MAGNITUDE   PHASE
+      METERS      METERS      METERS         VOLTS/M   DEGREES      VOLTS/M   DEGREES      VOLTS/M   DEGREES
+        0.0000      0.0000      0.0000     3.4785E+00  -180.00    0.0000E+00     0.00    1.0436E+01  -180.00
+        0.0000      0.1000      0.0333     1.2688E-01    69.64    0.0000E+00     0.00    8.5015E-01   150.69
+        0.0000      0.2000      0.0667     1.2948E-01    64.35    0.0000E+00     0.00    3.8826E-01   105.77
+        0.0000      0.3000      0.1000     1.1507E-01    51.67    0.0000E+00     0.00    2.8186E-01    59.78
+        0.0000      0.4000      0.1333     9.6121E-02    32.83    0.0000E+00     0.00    2.4217E-01    19.60
+        0.0000      0.5000      0.1667     7.8259E-02     9.45    0.0000E+00     0.00    2.1557E-01   -17.18
+        0.0000      0.6000      0.2000     6.3321E-02   -17.26    0.0000E+00     0.00    1.9302E-01   -52.93
+        0.0000      0.7000      0.2333     5.1490E-02   -46.44    0.0000E+00     0.00    1.7343E-01   -88.62
+        0.0000      0.8000      0.2667     4.2284E-02   -77.42    0.0000E+00     0.00    1.5660E-01  -124.54
+        0.0000      0.9000      0.3000     3.5128E-02  -109.74    0.0000E+00     0.00    1.4222E-01  -160.75
+        0.0000      1.0000      0.3333     2.9527E-02  -143.07    0.0000E+00     0.00    1.2995E-01   162.77
+        0.0000      1.1000      0.3667     2.5097E-02  -177.16    0.0000E+00     0.00    1.1945E-01   126.06
+        0.0000      1.2000      0.4000     2.1553E-02   148.14    0.0000E+00     0.00    1.1039E-01    89.16
+        0.0000      1.3000      0.4333     1.8685E-02   112.98    0.0000E+00     0.00    1.0254E-01    52.12
+        0.0000      1.4000      0.4667     1.6337E-02    77.44    0.0000E+00     0.00    9.5684E-02    14.95
+        0.0000      1.5000      0.5000     1.4395E-02    41.59    0.0000E+00     0.00    8.9652E-02   -22.32
+
+
+ Line integral of E       = -1.45652E-01 3.06530E-02 Volts
+ Cumulative line integral = -1.45652E-01 3.06530E-02 Volts
+
+

The coordinates of each observation point are the same. However, the electric field strength values are nowhere the same, due to the differences in the way in which each command calculates the field component values. The only conditions that will yield the same values for both commands is a model in which the observation point extend along one of the axes.

+

Note that within the LE (and LH) report are supplemental data. At the top of the report, we find the axial, horizontal, and vertical vectors that define the components listed as axial, transverse 1, and transverse 2. For each line, the square root of the sum of the squares of the values is, of course, 1.0. You may use the arc-cosine of axial Z value to obtain the theta angle used in the NE/NH version of the model (71.656 degrees). Given that we have a vertical dipole in free space, the zero-readout for the horizontal vector should not be surprising.

+

At the end of the report, we find the line integral of E, as well as a cumulative integral. We may add to this model additional LE and LH requests so that the end of one line is the beginning of the next. The next line may run in any direction and even return to the series starting point. Each subsequent LE or LH command, as appropriate, will show its own line integral and a new cumulative value. However, the lines must form a continuous string with no breaks; that is, the end-2 coordinates of one line must be the end-1 coordinates of the next line. In addition, the LE and LH commands must form a group with no intervening control commands.

+

These models will serve to both introduce the LE and LH commands within NEC-4 and to show some of the differences between them and the NE/NH commands that are common to both NEC-2 and NEC-4. By no means is this a complete treatment of near-field analysis. In fact, we have not mentioned such fundamental textbook matters as the limit of the near field and the relationship of that limit to the longest dimension of the antenna. These are matters for study outside of the context of the ways to obtain near-field strength calculations within NEC-2 and NEC-4.

+

Instead, our goal has been to orient you to the near-field commands in terms of locating observation points relative to the input options and the output data. In most cases, you will wish to set the voltage source (EX0) for a value that will provide a set input power in order to make the near-field strength data more relevant. We covered such adjustments in past episodes. Indeed, the more you delve into the wide array of available control commands within NEC, the more you realize how inter-related they are in terms of making the most of a modeling endeavor.

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Go to Main Index

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92. Calculating Circular Gain

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In its RP0 or far-field output report, NEC provides a good bit of information. To illustrate, I have extracted a single line from a 180-degree theta (elevation) report.

+ 
+                              - - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -          - POWER GAINS -        - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.               VOLTS     DEGREES       VOLTS     DEGREES
+
+    0.00    90.00    10.39     3.84   11.261    0.46544    -3.89  RIGHT     1.00721E+00   -99.56    4.73544E-01   163.94
+
+

Most users rely upon the polar plot facilities built into their implementations of NEC for the relevant data and overlook the valuable information in the tabular report. However, the report is an extremely useful tool as well as a source of data. It will always be in basic NEC formulation using phi and theta angles, although some implementations of NEC convert or quasi-convert the angles to azimuth and elevation. A theta angle of zero degrees is the zenith directly overhead, while the phi angle of 90 degrees indicates a heading along the Y-axis.

+

The next three entries are the ones most printed along with polar plots: the power gains in dBi for the total field, the horizontal component and the vertical component. Allowing for rounding, the component powers add up to the total field power level, however, not by direct addition of dB. Rather, we must first convert the values in decibels into dimensionless power gain, using the standard procedure of dividing the value in dB by 10 and taking the antilog (base 10) of the result. The horizontal gain is 10.94, while the vertical gain is 2.42, for a total of 13.36. The dimensionless power pain of the total field is 13.37, although this simple exercise must allow for rounding of the original double-precision calculation numbers.

+

The central columns are relevant to elliptically polarized antennas. Although very important to numerous application involving elliptical polarization, we shall pass over them in this exercise. Basic explanations of the terms "axial ratio" and "tilt angle" appear in many basic college antenna texts, for example, Balanis, Antenna Theory: Analysis and Design, 2nd Ed. (Wiley, 1997), pp. 64-73. Perhaps the most important function of this data within this exercise is to remind us that even circular helices yield elliptically rather than circularly polarized patterns, where a perfectly circularly polarized pattern would have an axial ratio of 1.0. Although ideally, a linearly polarized pattern would have an axial ratio of zero, NEC will classify a pattern as linear when the minor axis is many orders of magnitude smaller than the major axis so that a practical calculation of the value results in a zero value. Apparently, to avoid excessively large numbers, NEC inverts the classic or textbook definition of axial ratio to "minor axis over major axis." Considerable effort is presently underway in many quarters to improve the circularity of polarization of antennas for special applications, with the quadrifilar design receiving extensive design scrutiny.

+

Relative to the central set of three columns, our interest is in the last entry, the sense. It tells us whether a circularly or elliptically polarized antenna has right-hand (clockwise) or left-hand counterclockwise) polarization. Since virtually no antenna will produce a pure circularly polarized signal that is only one or the other hand, the sense tells us which pattern will dominate--the left-hand or the right-hand pattern. Some newer modelers are often surprised that one can produce patterns for the respective circular polarizations, but Fig. 1 shows in the EZNEC example that we certainly can.

+
+ +
+

In fact, the patterns are drawn for the model from which the RP 0 report line has been drawn. In NEC format, the model appears in the following lines.

+ 
+CM General Helix over Perfect Ground
+CE
+GH 1 100 5 .6959 .191 .191 .0005 .0005 0
+GE 1 -1 0
+GN 1
+EX 0 1 1 0 1 0
+FR 0 1 0 0 299.7925 1
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

The third numeric entry on the GH line is positive (and records the number of turns in this NEC-4 version). Hence, the helix formed is a right-hand helix with a dominant right-hand polarization. Fig. 2 shows the outlines of the helix over perfect ground to show the correspondence of the model and the patterns in Fig 1, where the right-hand pattern dominates.

+
+ +
+

The RP 0 request in this model produces the report from which I drew the sample line. All other lines in the model are very standard.

+

Returning to our sample report line, the final columns provide the Etheta and Ephi field intensities. These values are simply proportional measures, since we have not specified in the request any specific distance from the coordinate system center. As a result, many modelers treat these entries as idle relative to the first order business of finding the total field gain of the antenna. The specific sample line is for the zenith angle overhead and the helix is pointed straight up. Hence, we might believe that the total field value is the maximum gain. However, because the pattern is a combination of left-hand and right-hand components, the actual maximum total field gain heading is a degree off the zenith or 0-degree theta angle heading.

+

We can calculate the pattern values for both the left-hand and right-hand patterns using the previously ignored Etheta and Ephi data. Some implementations of NEC, such as EZNEC Pro, GNEC, NEC-Win Pro, and NEC-Win Plus, already perform these calculations. EZNEC Pro offers the patterns and a tabular form of the calculations as a pattern option. The Nittany-Scientific programs provide circular polarization data and patterns in its MultiPlot feature. If you are using a generic NEC core, you can also calculate the information and apply it to almost any polar plotting module to which you may have access.

+

In order to see how the calculation proceeds, let's repeat the relevant parts of our sample line.

+ 
+  - - ANGLES - -  - POWER GAIN -  POLARIZATION    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI       TOTAL       SENSE          MAGNITUDE     PHASE      MAGNITUDE     PHASE
+ DEGREES  DEGREES      DB                        VOLTS         DEGREES    VOLTS         DEGREES
+
+    0.00    90.00   11.261        RIGHT          1.00721E+00   -99.56     4.73544E-01   163.94
+
+

The procedure begins by taking the real and imaginary components of each value of E (theta and phi), which appear in terms of magnitude and phase angle in the sample line.

+
+
    +
  • vetr = EthetaMag * cos(Ethetaphase); theta real
    • +
  • veti = EthetaMag * sin(Ethetaphase); theta imaginary
    • +
  • vepr = EphiMag * cos(Ephiphase); phi real
    • +
  • vepi = EphiMag * sin(Ephiphase); phi imaginary
    • +
+
+

Depending upon your calculating medium, you may have to convert the phase angles to radians to arrive at the correct values for the sines and cosines, for example in many spreadsheets. These initial values are simply intermediate steps. We next must re-combine the collection into units that reflect the polarization of the antenna.

+
+
    +
  • velr = 0.5*(vetr + vepi); left real circular component
    • +
  • veli = 0.5*(veti - vepr); left imaginary circular component
    • +
  • verr = 0.5*(vetr - vepi); right real circular component
    • +
  • veri = 0.5*(veti + vepr); right imaginary circular component
    • +
+
+

Now we can combone the circular components into values of magnitude by standard "SQRT of SQRs" techniques.

+
+
    +
  • elm = sqrt(velr*velr + veli*veli); left magnitude
    • +
  • erm = sqrt(verr*verr + veri*veri); right magnitude
    • +
+
+

What we now have are the magnitudes of the left-hand and the right-hand electrical fields in volts (peak). The move from these voltage magnitudes to pattern data in dBic (dBi circular) requires a few more steps. The following are the calculations required for the conversion.

+

a. Power Gain: Convert the Total Field Gain into a dimensionless gain measure:

+
+
    +
  • PwrGn = antilog (base 10) (TtlFldGn/10)
    • +
+
+

Note: My spreadsheet does not return antilogs to base 10, but does return antilogs to base e. The spreadsheet formulation compensates for that limitation. The @EXP function returns the antilog to the base e, and the multiplier is the standard log-ln conversion.

+
+
    +
  • @EXP((TtlFldGn*2.3025851)/10)
    • +
+
+

b. Voltage Gain Ratio vs. Power Gain Ratio: Square the ratio of the right voltage magnitude (erm) to the left voltage magnitude (elm). This squared ratio is the ratio of the dimensionless power gains for right and left patterns.

+
+
    +
  • RatSq = (erm/elm)^2
    • +
+
+

The next steps are predicated on the assumption that the sum of the two dimensionless circular power gains is the dimensionless total field power gain.

+

c. Right Gain: Right Gain and Left Gain are 2 unknowns subject to simultaneous equations. Selecting Right Gain first, we obtain the following.

+
+
    +
  • GnRt = RatSq * PwrGn/(1 + RatSq)
    • +
+
+

d. Right Gain dBi: Conversion to dBi is standard.

+
+
    +
  • GnRtdBi = 10 * log(GnRt)
    • +
+
+

e. Left Gain: Left Gain is simply the power gain minus the right gain (all dimensionless).

+
+
    +
  • GnLf = PwrGn - GnRt
    • +
+
+

f. Left Gain dBi: Conversion to dBi is standard

+
+
    +
  • GnLfdBi = 10 * log(GnLf)
    • +
+
+

For our single sample line of RP 0 reporting, we obtain the following values.

+ 
+Theta     ERM     ELM     Sense   RatSq   PwrGn   GnRt     GnRtdBic   GnLf     GnLfdBic
+0         .7393   .2697   right   7.516   13.369  11.799   10.718     1.570    1.959
+
+

A spreadsheet or other program can be set-up to handle as many entries as we might need to encompass a full pattern for the range of angle that we choose. In fact, let's compare a fuller range of values for our sample helix and see what the RP 0 lines look like when sampled every 10 degrees in a theta pattern from one horizon to the other.

+ 
+GH5-08-1a                              - - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -          - POWER GAINS -        - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.               VOLTS     DEGREES       VOLTS     DEGREES
+  -90.00    90.00    -9.36  -148.77   -9.357    0.00000     0.00  LINEAR    1.03655E-01    70.66    1.10934E-08   -51.70
+  -80.00    90.00    -7.05    -6.59   -3.801    0.40133   -47.10  RIGHT     1.35220E-01    83.37    1.42590E-01   -52.82
+  -70.00    90.00    -3.56    -3.67   -0.607    0.20487   -44.61  RIGHT     2.01953E-01    99.75    1.99439E-01   -57.10
+  -60.00    90.00    -2.80    -6.54   -1.269    0.06595   -32.93  LEFT      2.20486E-01   116.54    1.43387E-01   -71.72
+  -50.00    90.00    -5.07   -10.68   -4.018    0.35876    21.30  LEFT      1.69708E-01   157.82    8.90534E-02  -151.60
+  -40.00    90.00    -1.02    -2.59    1.275    0.56022    35.00  RIGHT     2.70616E-01  -135.73    2.25904E-01   164.19
+  -30.00    90.00     4.83     1.49    6.483    0.68079     1.68  RIGHT     5.30634E-01  -112.46    3.61516E-01   158.86
+  -20.00    90.00     8.19     3.33    9.421    0.56596    -4.79  RIGHT     7.81870E-01  -104.15    4.46826E-01   160.14
+  -10.00    90.00     9.89     3.99   10.887    0.50102    -4.55  RIGHT     9.50856E-01  -100.57    4.81993E-01   162.68
+    0.00    90.00    10.39     3.84   11.261    0.46544    -3.89  RIGHT     1.00721E+00   -99.56    4.73544E-01   163.94
+   10.00    90.00     9.83     2.93   10.635    0.44749    -3.71  RIGHT     9.43675E-01  -100.68    4.26509E-01   162.74
+   20.00    90.00     8.05     1.20    8.865    0.45047    -3.45  RIGHT     7.69033E-01  -104.32    3.49384E-01   159.62
+   30.00    90.00     4.56    -1.46    5.530    0.49995     0.19  RIGHT     5.14647E-01  -112.48    2.57304E-01   157.80
+   40.00    90.00    -1.65    -4.82    0.060    0.50176    27.07  RIGHT     2.51829E-01  -135.28    1.74695E-01   165.86
+   50.00    90.00    -6.13    -6.49   -3.297    0.35333    43.47  LEFT      1.50288E-01   152.44    1.44159E-01  -168.60
+   60.00    90.00    -3.18    -5.19   -1.059    0.74593   -18.59  LEFT      2.11052E-01   109.98    1.67502E-01  -149.83
+   70.00    90.00    -3.54    -5.01   -1.201    0.56213   -35.58  LEFT      2.02554E-01    94.54    1.70983E-01  -145.53
+   80.00    90.00    -6.46    -8.74   -4.441    0.42198   -34.22  LEFT      1.44683E-01    81.98    1.11320E-01  -145.85
+   90.00    90.00    -8.48  -151.11   -8.476    0.00000     0.00  LINEAR    1.14726E-01    73.72    8.47569E-09  -146.31
+
+

Notice that the pattern changes its sense along the selected sampling path. At the horizons, the Etheta values dominate to a degree the allows NEC to classify the pattern as linear. The left-hand and right-hand reversals may be less apparent until we perform the circular pattern calculations on them.

+ 
+       Values Calculated by the Listed Equations                   Reference
+Theta    ERM    ELM     Sense      GnRtdBic    GnLfdBic         R-H Gn    L-H Gn
+-90      .0518  .0518   linear     -12.367     -12.367          -12.37    -12.37
+-80      .1278  .1105   right      -4.529      -11.916          -4.53     -11.91
+-70      .1675  .1105   right      -2.178      -5.786           -2.18     -5.79
+-60      .1226  .1399   left       -4.891      -3.743           -4.89     -3.74
+-50      .0578  .1226   left       -11.414     -4.891           -11.42    -4.89
+-40      .2399  .0676   right      0.943       -10.056          0.94      -10.06
+-30      .4460  .0847   right      6.329       -8.100           6.33      -8.10
+-20      .6136  .1701   right      9.100       -2.045           9.10      -2.04
+-10      .7153  .2378   right      10.432      0.866            10.43     0.87
+0        .7393  .2697   right      10.718      1.959            10.72     1.96
+10       .6841  .2611   right      10.044      1.679            10.04     1.68
+20       .5585  .2116   right      8.283       -0.148           8.28      -0.15
+30       .3860  .1287   right      5.072       -4.469           5.07      -4.47
+40       .2057  .0682   right      -0.393      -9.977           -0.40     -9.98
+50       .0635  .1329   left       -10.605     -4.190           -10.61    -4.19
+60       .0274  .1885   left       -17.890     -1.150           -17.88    -1.15
+70       .0506  .1805   left       -12.578     -1.529           -12.58    -1.53
+80       .0486  .1196   left       -12.924     -5.105           -12.93    -5.10
+90       .0574  .0574   linear     -11.486     -11.486          -11.49    -11.49
+
+

The higher gain in the Left-Hand Gain column for the entries sensed as left becomes much more apparent. Of course, the table--or any enlargement of it--becomes suitable for creating a polar or rectangular plot of the two circular components of the overall helix pattern. The reference columns are taken from the tabular output of EZNEC Pro, version 4, and serve to demonstrate that the calculation method shown here is consistent with techniques currently in use. Note that I do not say that the method is in fact the method used in EZNEC, since I did not reference that code when working out these calculations. Rather, the results of the calculations are consistent with those of EZNEC (and of the other programs mentioned early on in this exercise.)

+

As one final exercise, let's see what happens for a helix that is left-handed, as in the following example.

+ 
+CM General Helix over Perfect Ground
+CE
+GH 1 100 -5 .6959 .191 .191 .0005 .0005 0
+GE 1 -1 0
+GN 1
+EX 0 1 1 0 1 0
+FR 0 1 0 0 299.7925 1
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
The only difference between this model and the one that we have previously used is the minus sign in the third entry of the GH or helix-forming line. The negative value for the number of turns creates a left handed helix, as shown in Fig. 3. +
+ +
+

The sample RP 0 line that corresponds to the one for the previous example appears in the NEC output file.

+ 
+                              - - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -          - POWER GAINS -        - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.               VOLTS     DEGREES       VOLTS     DEGREES
+    0.00    90.00    10.39     3.84   11.261    0.46544     3.89  LEFT      1.00721E+00    80.44    4.73544E-01   163.94
+
+Reference:  Corresponding line for the right-hand helix
+    0.00    90.00    10.39     3.84   11.261    0.46544    -3.89  RIGHT     1.00721E+00   -99.56    4.73544E-01   163.94
+
+

Very little has changed, but the changes make a world of difference. Only the tilt angle and the Etheta phase angle have different numbers. However, those numbers alter the circular polarization calculations.

+ 
+Theta     ERM     ELM     Sense   RatSq   PwrGn   GnRt     GnRtdBic   GnLf     GnLfdBic
+0         .2697   .7393   left    0.133   13.369  1.570    1.959      11.799   10.718
+
+Reference:  Corresponding line for the right-hand helix
+0         .7393   .2697   right   7.516   13.369  11.799   10.718     1.570    1.959
+
+

The values for the zenith angle show a flip-flop that is not true of the values for the entire pair of left- and right-hand patterns. Fig. 4 shows some of the detail.

+
+ +
+

Below the zenith angle, the patterns for the left- and right-handed versions of the helix differ considerably--at least when examining them for fine detail. A comparison of the two model views in Fig. 1 and Fig. 3 will uncover the basic reason. The left-hand helix uses the same phi angle as the right-hand helix, but departs the ground plane at essentially a 90-degree angular difference to produce a true mirror image of the right-hand helix patterns. The left-hand patterns are a mirror image of the patterns we might obtain for the other helix by giving it a 90-degree phi-angle adjustment.

+

This exercise has provided a procedure by which you can calculate your own circular power gain patterns, if you are using an implementation of NEC that does not include them. Since they involve only data within the RP 0 section of the output report, the calculations are equally applicable to NEC-2 and NEC-4, even though the sample model is from NEC-4. If you already have provision for obtaining circularly polarized power gain patterns in your implementation of NEC, then perhaps the exercise will provide some insight into at least one way to obtain them.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +

+

Go to Main Index

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+

93. Convergence Revisited

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the very first column in this series, we examined the convergence test of model adequacy. The convergence test actually emerged from the development of MININEC, in contrast to NEC. However, the test generally carries over to NEC (-2 or -4) as one of two necessary but not sufficient conditions of model adequacy. The other test, of course, is the Average Gain Test (AGT), which has become a special function in some implementations of NEC, for example, in EZNEC, NEC2GO, and the NEC-Win/GNEC series of programs from Nittany Scientific. We examined the AGT test in three past columns, #20, #55, and #71.

+

Under limited conditions, the AGT allows the user to correct the reported gain for a model, and under even more restricted conditions, to correct the reported source resistance. The correctives are most accurate when the AGT value is not far off an ideal value (1.00 for free space and 2.00 over a perfect ground) and when the source impedance has a relatively low reactive component. In contrast, the convergence test gives the modeler information on the best level of segmentation to use in order to obtain the most accurate results.

+

In passing, I have had occasion to note that the convergence test works somewhat differently when using a NEC core than when using a MININEC core. This statement is not always true--at least not always true within the limits of the levels of segmentation that a modeler is likely to be willing to use. This seemingly small nuance suggests that we might spend a little time with a set of examples to illustrate what the qualification means in practical terms.

+

A Pair of Test Yagi Models

+

Let's explore two distinctly different Yagi models. The first will be an OWA 6-element Yagi, shown in the right in Fig. 1. OWA Yagis are optimized for wide-band performance with usable performance and impedance properties that extend for about a 7% bandwidth. Another type of Yagi is the narrow-band NBS design, sketched in outline on the left in Fig. 1. Jim Breakall used a similar design when he wrote "A Validative Comparison of NEC and MININEC Using NBS Experimental Yagi Antenna Results" for The Applied Computational Electromagnetic Society Journal, November, 1986. So it is fitting to resurrect this antenna--even with some modifications--in this re-visit of the convergence test.

+
+ +
+

For this test, I modeled both antennas at 299.7925 MHz, where 1 meter = 1 wavelength. The two antennas perform in significantly different ways. The shorter OWA Yagi has slightly lower gain, as one might expect from the boom-length reference. It uses a master and slave driver set (the fed driver and director 1) to increase the operating bandwidth. In conjunction with the second and third directors, the array has its maximum gain, maximum front-to-back ratio, and its SWR passband center all on or veryv close to the same frequency. Fig, 2, at the top, shows a 3-D pattern on the test frequency.

+
+ +
+

The NBS Yagi uses fewer elements on a longer boom to achieve its higher forward gain. In addition, it uses equal spacing between the successive elements. As a result, its pattern (Fig 2, bottom), is less "well-behaved" than the OWA pattern. The array has a significant rear main lobe. (In this contest, "significant" means only highly noticeable. Whether the rear lobe is significant to any particular potential use of the array requires the introduction of task criteria outside the scope of this exercise.) In addition, the NBS Yagi shows very significant radiation in the region around 90 degrees to the line along the main forward and rearward lobes. The magnitude of this band of radiation would not show up in a 2-diemensional E-plane pattern, since the dimples in the 3-D pattern are very deep. In an E-plane pattern, they would show up as very deep nulls with seemingly small secondary lobes both forward and aft of the null headings. However, the 3-D pattern shows to what degree the nulls are operationally illusory, since at all other headings that form the band around the pattern, the radiation is significant. In contrast, the OWA pattern shows no secondary forward lobes and only the standard H-plane pattern broadening at right angles to the plane of the elements.

+

The two modeled antennas have other differences, as well. The OWA Yagi is designed to directly match a 50-Ohm feedline. However, the NBS antenna displays a low impedance. For this exercise, I shortened the driver from its NBS-specified 0.5 wavelength size. At the NBS length, the feedpoint impedance is highly inductively reactive. Shortening the driver does not significantly change other performance values, but it does allow one to derive a meaningful SWR curve referenced to the resonant feedpoint impedance: 17 Ohms. Fig. 3 overlays the 50-Ohm OWA SWR curve and the 17-Ohm NBS curve for comparison, using NEC-4 models of each. X-axis frequency increments are 2.5 MHz.

+
+ +
+

The OWA 2:1 SWR curves extends from just above 285 MHz to just above 306 MHz, for a 21-MHz passband: just about the advertised 7%, using the design frequency as the divisor. In contrast, the NBS Yagi has a 2:1 SWR curve that extends from about 293 MHz to 302 MHz, for a 6-MHz or 2% passband. In both cases, and typical of Yagi design, the SWR rises more rapidly above the design frequency than below it.

+

We may note as well that the NBS design requires considerably fatter elements to achieve its narrow operating bandwidth than the OWA needs for its wider passband. The OWA elements are 2.5-mm in diameter, while the NBS elements are 8.5 mm, a 3.4:1 ratio. It is possible to widen the OWA passband even further by optimizing the design for fatter elements, although a wider passband is unnecessary for our purposes here.

+

The data on these two interesting Yagi designs is useful as background, but the information seems distant from the subject of model convergence. That impression is not a true one. We shall have occasion to call attention to the antenna differences as we gradually get a better handle on convergence as applied to both NEC and MININEC.

+

The OWA Yagi and Convergence

+

To permit you to replicate the OWA Yagi and the convergence exercise for which it is one test subject, the following table provides the relevant dimensions. Element lengths appear in two forms: as half lengths for modeling +/- to one of the axes and as full lengths for reference. All dimensions are in meters except for the diameter and radius, which are in mm. The models using these dimensions prescribe perfect or lossless wire and are in free space.

+ 
+              Dimensions of the 6-Element OWA Yagi for 299.7925 MHz
+
+Element        Half-Length     Full Length    Space from Reflector     Diameter/Radius
+Reflector      0.250           0.500          ----                     2.5/1.25
+Driver         0.247           0.494          0.125                    2.5/1.25
+Director 1     0.231           0.462          0.177                    2.5/1.25
+Director 2     0.225           0.450          0.321                    2.5/1.25
+Director 3     0.225           0.450          0.461                    2.5/1.25
+Director 4     0.216           0.432          0.671                    2.5/1.25
+
+

The OWA Yagi does not show its lowest SWR value at the design frequency. The lowest value occurs close to the point where the SWR rises rapidly. Hence, design-frequency impedances values always show a small inductive reactance. Nevertheless, I designed the original model using 15 segments per element in NEC and 14 segments per element in MININEC. The different algorithms used by the two types of cores have different requirements for calculating currents and hence for source placement. NEC uses the center of each segment as its foundation. To place a source at a segment center and have it also be centered on the element requires an odd number of element segments. In contrast, MININEC calculates from pulses, which generally occur on segment junctions. To place a source on a pulse requires that we use an even number of segments on the element. Since all of the elements in the model have similar lengths, we adhere to the same number of segments per element throughout the model.

+

To observe the numerical trends in convergence within the broadband OWA model, I stepped each core through 7 levels of segmentation. I began the NEC models at 11 segments with increments of 4 segments per element and stopped at 35 segments. The MININEC version of the same model used the same increment, but ran from 10 through 34 segments per element.

+

For the test, I used NEC-4D (double-precision) as found in version 4 of EZNEC. Actually, the use of a single or double precision core makes no differences to the progression. The practical performance of the antenna changes in no significant way through the progression. However, we shall be interested in the numerical trends. The reason that I mention the core and the program used for the runs is that the exact numbers you obtain depend in part on the FORTRAN compiler used with the core for running it on a standard PC. Hence you may find that your own NEC core (-2 or -4, single or double precision) may give a slightly different result. Nevertheless, the trends should remain true.

+

Since the test frequency is at the border between VHF and UHF, I selected Antenna Model (AM) for the MININEC runs. Only the MININEC frequency offset is at stake in these models, since they have no odd geometries to challenge other MININEC limitations. Therefore, your should obtain the same results using any version of MININEC that has been adequately corrected for the frequency offset that emerges as we increase the design frequency of a model. AM also calculates the AGT value, which will be useful in the comparisons.

+

The table of results for NEC-4D and for corrected MININEC appear below. They contain the usual information on free-space gain in dBi, the 180-degree front-to-back ratio in dB, and the reported source impedance in terms of resistance and reactance in Ohms. In addition, the tables provide some supplementary information, namely, the AGT score, along with the length of an average segment and the ratio of this length to the element radius. We shall have occasion to explore all of these data along the way.

+ 
+OWA Yagi Convergence Tests:  NEC-4D Results
+
+# Segments    Gain     Front-to-Back    Source Impedance     AGT     Ave. Seg.   Seg. Len. to
+per element   dBi      Ratio dB         R +/- jX Ohms                Length      Radius Ratio
+11            10.26    32.17            51.83 + j9.43        0.992   0.0422      33.8:1
+15            10.28    32.33            51.83 + j9.01        0.996   0.0311      24.8:1
+19            10.29    32.24            51.93 + j8.65        0.998   0.0245      19.6:1
+23            10.29    32.08            52.02 + j8.37        0.998   0.0202      16.2:1
+27            10.29    31.91            52.10 + j8.14        0.999   0.0172      13.8:1
+31            10.29    31.77            52.16 + j7.95        0.999   0.0150      12.0:1
+35            10.29    31.64            52.21 + j7.79        0.999   0.0133      10.6:1
+
+OWA Yagi Convergence Tests:  MININEC (AM) Results
+
+# Segments    Gain     Front-to-Back    Source Impedance     AGT     Ave. Seg.   Seg. Len. to
+per element   dBi      Ratio dB         R +/- jX Ohms                Length      Radius Ratio
+10            10.27    32.12            49.86 + j9.51        1.0005  0.0465      37.2:1
+14            10.28    32.22            51.05 + j9.01        0.9998  0.0332      26.6:1
+18            10.28    32.24            51.60 + j8.69        0.9996  0.0258      20.7:1
+22            10.28    32.19            51.91 + j8.44        0.9995  0.0211      16.9:1
+26            10.28    32.13            52.10 + j8.26        0.9994  0.0179      14.3:1
+30            10.28    32.06            52.22 + j8.10        0.9994  0.0155      12.4:1
+34            10.28    31.99            52.31 + j7.98        0.9994  0.0137      10.9:1
+
+

Perhaps the most notable feature of the NEC-4 and MININEC tables is how little they differ from each other. The gain value quickly levels off (by 19 segments per elements), while the front-to-back ratio shows a very slow descent as we increase the segment density. The source resistance climbs slowly, while the reactance decreases slowly. Any slowing of the rate of change from one segmentation level to the next is largely a function of the fact that as we increase the density in increments of 4 segments per element, each step in the progression is a smaller percentage of increase over the preceding step.

+

In a very real and practical sense, the models are fully converged by no later than 14/15 segments per element. In terms of a numerical progression, neither core shows full convergence, that is, no change from one step to the next. These results are quite unsurprising in view of the fact that the smallest ratio of segment length to wire radius is over 10:1. The models in no way stress or stretch the thin-wire algorithms at the hearts of the cores. Perhaps the only anomalous data between the two tables occurs in the AGT column. The MININEC values decrease with increasing segmentation, while the NEC values increase as the segmentation rises in density. However, the amount of change is truly insignificant. My only point in noting the reverse trends is to show that the AGT value need not parallel the convergence progression.

+

The goal of the OWA example is to show that there are cases in which the two different cores--NEC and MININEC-- will show very close, if not coincident, convergence tracks. Two properties of the OWA having an impact on this parallelism are the broadband characteristics of the OWA and the use of relatively thin elements. The NBS Yagi differs from the OWA in both categories.

+

The NBS Yagi and Convergence

+

The NBS Yagi is a narrow-bandwidth array that uses relatively fat elements: 8.5 mm in diameter. The elements are about 3.4 times larger in diameter than the ones used in the OWA array. The parasitic beam itself is a highly usable design. With adjustment of the driver length, a gamma or beta match will allow the use of a 50-Ohm coaxial cable as the feedline. More specifically, the following table lists the dimensions of the NBS array, using the same conventions as for the OWA Yagi. Element lengths appear in two forms: as half lengths for modeling +/- to one of the axes and as full lengths for reference. All dimensions are in meters except for the diameter and radius, which are in mm. The models using these dimensions specify perfect or lossless wire and are in free space.

+ 
+              Dimensions of the 5-Element NBS Yagi for 299.7925 MHz
+
+Element        Half-Length     Full Length    Space from Reflector     Diameter/Radius
+Reflector      0.241           0.482          ----                     8.5/4.25
+Driver         0.2225*         0.445*         0.200                    8.5/4.25
+Director 1     0.214           0.428          0.400                    8.5/4.25
+Director 2     0.212           0.424          0.600                    8.5/4.25
+Director 3     0.214           0.428          0.800                    8.5/4.25
+
+*The driver lengths shown is for the NEC-4 model.  The driver of the MININEC model has
+a half length of 0.223 (full length 0.446) m to achieve resonance on the test frequency.
+Resonance for this exercise means a reactance of under +/-j1 Ohm at the test frequency.
+
+

The NBS Yagis longer boom yields almost a full dB of gain over the OWA Yagi, with 1 less element. The cost for this added gain is less control over the source impedance and a significantly narrower bandwidth. These attributes do not count for or against the NBS Yagi without review in the presence of the criteria of intended use.

+

I ran the NEC-4 and MININEC models through the same exercise that I used on the OWA Yagi. The NEC-4 models increased the segmentation density from 11 to 35 segments per element in 4-segment increments. The MININEC model used the same increment in moving from 10 to 34 segments per elements. The following table records the results.

+ 
+NBS Yagi Convergence Tests:  NEC-4D Results
+
+# Segments    Gain     Front-to-Back    Source Impedance     AGT     Ave. Seg.   Seg. Len. to
+per element   dBi      Ratio dB         R +/- jX Ohms                Length      Radius Ratio
+11            11.20    13.72            17.10 - j1.15        0.997   0.0401       9.4:1
+15            11.22    13.28            17.02 + j0.33        0.998   0.0294       6.9:1
+19            11.22    13.10            17.00 + j0.96        0.999   0.0232       5.5:1
+23            11.22    13.06            17.01 + j1.08        1.000   0.0192       4.5:1
+27            11.22    13.10            17.03 + j0.94        1.000   0.0163       3.8:1
+31            11.22    13.18            17.06 + j0.64        1.000   0.0142       3.4:1
+35            11.22    13.29            17.08 + j0.28        1.000   0.0129       2.9:1
+
+NBS Yagi Convergence Tests:  MININEC (AM) Results
+
+# Segments    Gain     Front-to-Back    Source Impedance     AGT     Ave. Seg.   Seg. Len. to
+per element   dBi      Ratio dB         R +/- jX Ohms                Length      Radius Ratio
+10            11.14    14.58            17.51 - j2.28        0.9980  0.0441      10.4:1
+14            11.17    14.09            17.52 - j0.84        0.9982  0.0315       7.4:1
+18            11.18    13.83            17.53 - j0.04        0.9984  0.0245       5.8:1
+22            11.18    13.70            17.55 + j0.40        0.9985  0.0201       4.7:1
+26            11.19    13.64            17.58 + j0.60        0.9987  0.0167       4.0:1
+30            11.19    13.63            17.61 + j0.68        0.9988  0.0147       3.5:1
+34            11.19    13.63            17.64 + j0.68        0.9988  0.0130       3.1:1
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There is more divergence between the NEC-4 and MININEC trends with respect to the NBS Yagi than with respect to the OWA Yagi. However, the AGT values track each other very well relative to the two cores. As noted, the segment-length-to-radius ratio is much lower for the NBS model, and the antenna is narrow banded with regard to both performance and source impedance. The narrow-band characteristic of this antenna largely accounts for intrinsic differences in the gain and front-to-back readings, which are numerical (but not practically) more distant that the comparable OWA value pairs. It is likely a combination of the two characteristics that accounts for the half-Ohm difference in the source resistance.

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The characteristics are precisely what we need to show a convergence phenomenon in NEC, one that occurs often--but not so often as not to be disconcerting to someone who encounters it. The MININEC results are almost perfectly in accord with those for the thin-element wide-band Yagi. Like the preceding example, the MININEC model is practically converged at the 14 or 18 segment per element level. For the most finicky numerical analysis, we find virtually complete convergence between the 30 and 34 segment per element levels, with identical values of gain, front-to-back ratio, source reactance, and AGT. (However, the preceding example taught us that the AGT and convergence progressions need not coincide, so we may view the last element of convergence as accidental.) The source resistance difference between the two steps is 0.03 Ohm.

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The NEC-4 model is somewhat different. Convergence does not occur at the highest levels of segmentation. Rather, it occurs in the region between 19 and 27 segments per element. For almost all data, the increments of change from step-to-step within the region are equal to or smaller than the incremental steps outside the region. In addition, we find that many of the progressions of values actually change direction. The fact that NEC models often converge at a segmentation level below the maximum possible level (without violating the minimum segment-length-to-radius ratio) appears to be unique to NEC models--at least in the range of models that I have so far encountered. Normally, it will show up only at levels of segmentation density far beyond what may be practical for a given model and beyond what is necessary for results that meet every canon of practical need. But it remains a notable difference from the manner in which convergence tends to work with MININEC models.

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Conclusion

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The sample models that we have used in this exercise are the best of all possible models and the worst or all possible models. They are the best because they have allowed us to see some of the major factors that contribute to the differences in convergence testing in MININEC and in NEC models. At the same time, they are the worst of models because--for all practical and almost all theoretical purposes--we would never reach the level of segmentation density that shows a full converged NEC model of the NBS Yagi, let along full convergence of the MININEC version of the NBS model.

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Putting those concerns aside, there are differences in the manner in which NEC models converge relative to the way in which MININEC models converge. Although the matter may fall among the minor details of the differences between the two types of cores, the more that we understand these minor differences, the better use we may make of each of them.

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Also see the Antenna Modeling Programs page for more information.

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Go to Main Index

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94. GR: The "Generate Cylindrical Structure" Command

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L. B. Cebik, W4RNL

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The GR command is a specialized rotational device that may use symmetry for rapid calculation of the replication of an initial structure. View the initial structure as vertical and offset from the center (X = 0, Y = 0) position. Invoking the GR command will then created rotated versions of the initial structure the number of times (NR) specified by the command with each new version rotated around the Z-axis by 360°/NR. The result is a cylindrical structure with the added property of running much faster than a similar structure produced by the GM command due to the use of symmetry. All of models in this exercise are run in NEC-Win Pro, a NEC-2-based program that makes available all of the commands.

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Like the GX command, GR is deceptively simple, since it employs only the first two integer positions on the command line. It does not use any of the floating decimal positions. Due to its simplicity, the command carries with it a host of restrictions, some of which have led modelers to by-pass the command in favor of others. Like GX, GR is identical in both NEC-2 and NEC-4.

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+Cmd        I1                I2
+           Tag No.           Total No.
+           Increment         of Occurrences
+GR         1                 6
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Like GX, the I1 entry should specify an increment such that each new occurrence of the initial structure takes on a previously unused tag number. In some commands, such as GM, you will specify the number of new structures beyond the initial structure. However, in GR, you specify the total number of structures, including the initial structure. Now let's sample the restriction list.

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  • 1. Avoid using GR when segments lie on or cross (at other than junctions) the Z-axis to prevent the occurrence of overlapping segments.
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  • 2. Avoid adding a GW entry following GR or symmetry may be defeated (or "destroyed").
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  • 3. Use a following GM command only if the number of new structures is set to zero and if the command acts only on the entire structure. Also avoid rotating the structure with GM around the X- or Y-axis when a ground is specified.
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  • 4. A following GX or GR entry will destroy the previously established symmetry.
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  • 5. Avoid non-symmetrical lumped loads. However, non-radiating networks and sources will not affect symmetry.
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The GR command differs from the corresponding GX command in several important ways, even though both make use of symmetry during the core run. First, GX allows symmetry in all 3 planes--X, Y, and Z--and the modeler can select from 1 to 3 planes of symmetry for any model. See column #72 of this series for the rudiments of applying the GX command. In contrast, the GR command applies symmetry around the Z axis only.

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Second, the GX command applies symmetry once per option, although with multiple planes of symmetry, we may end up with up to 8 total objects. One is the original and the other 7 are replications created in a cube if we select the maximum level of symmetry available. The GR command uses symmetry rotationally relative to the original structure. Hence, in principle, there is no limit to the number of replications (one less than the total number of occurrences that we specify within the command itself). However, there are very practical limitations on the number of successful replications we may have. That number depends upon the X-Y dimensions of the original structure. Specifying too many occurrences will result in overlapping or inter-penetrating structures that yield a defective model.

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Third, the reflections in the GX command are essentially linear across a specified plane of reflection. For the plane in question, we arrive at the same absolute values for the coordinates, but with the signs reversed. The GX command uses symmetry rotationally, separating each occurrence of the structure by an angular distance, but at the same distance from X=0 and Y-0 as the original structure.

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We shall sample the formation of GR structures using the simplest possible structures. Fig. 1 shows the structures that result from the sample models.

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Despite the seeming complexity of some of the structures, formation is very straightforward. To create the set of 6 vertical dipoles in the left-most portion of Fig. 1, we need only 2 geometry commands (plus the obligatory GE command to terminate the geometry portion of the model). Fig. 2 shows perhaps the simplest of GR models.

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GW1 sets up a vertical dipole in this free-space model. It extends equally above and below the Z = 0 level. As well, the dipole is displaced 1 m along the X-axis. However, a starting structure may begin with any values of X and Y so long as they are not both zero. Since we have only one tag number, we need increment it only by 1 in the GR line. Then we specify 6 total structures to form the cylinder at the left in Fig. 1.

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+                                 - - - STRUCTURE SPECIFICATION - - -
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+                                     COORDINATES MUST BE INPUT IN
+                                     METERS OR BE SCALED TO METERS
+                                     BEFORE STRUCTURE INPUT IS ENDED
+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     1   -1.00000    0.00000   -2.80000    -1.00000    0.00000    2.80000    0.00100     11        1    11       1
+      STRUCTURE ROTATED ABOUT Z-AXIS  6 TIMES.  LABELS INCREMENTED BY    1
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+   TOTAL SEGMENTS USED=   66     NO. SEG. IN A SYMMETRIC CELL=   11     SYMMETRY FLAG= -1
+ STRUCTURE HAS   6 FOLD ROTATIONAL SYMMETRY
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The sample structure specification portion of the output file for the model shows how the core sets up the GR command. The segmentation data provides a full set of the 66 segments within the overall cylinder of wires. Note that in the original model, there is an EX0 entry for each wire. In the source impedance report, the actual value is not especially meaningful to any real antenna structure. However, observing that all the values are the same is good modeler evidence that the geometry has a correct set-up.

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We may easily change the number of wires in the model by altering only the GR line of the model. Examine the GR line for the model in Fig. 3.

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The new version of the model produces the structure in Fig. 1 just left of center. The command automatically recalculates the proper angular displacement for the 12-wire cylinder. Note also in the model that there are now 12 EX0 entries to make this model comparable to the first one. One caution to observe when increasing the number of occurrences of the initial structure is not to add so many that the individual wires are too close together. Although not a problem with our standard 0.001-m radius wire, inaccuracies may result if the individual wire radii are too large for the spacing between them.

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Examine the model in Fig. 4. This model adds an allowable post-symmetry rotation and movement of the 6-wire structure in the very first model.

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Since the GM entry affects the entire structure, it will run on both NEC-2 and NEC-4. The first motion entry in the command rotates the structure 30°. You can see the rotation by referencing the Y-axis line in the inner right-of-center view in Fig. 1. Compare its orientation to the un-rotated left-most view within the figure. The second maneuver within the GM command elevates the entire cylinder 2.8-m along the Z-axis. Since neither motion disturbs the symmetry of the structure, the moves show up correctly in the segmentation data of the output report. Compare the data--especially the Z-axis values--for this model with the comparable values in the report for the first model. Here is a small sample from each model's segmentation data.

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Unmoved model.

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+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   -1.00000    0.00000   -2.54545    0.50909   90.00000   0.00000   0.00100     0    1    2      1
+     2   -1.00000    0.00000   -2.03636    0.50909   90.00000   0.00000   0.00100     1    2    3      1
+     3   -1.00000    0.00000   -1.52727    0.50909   90.00000   0.00000   0.00100     2    3    4      1
+     4   -1.00000    0.00000   -1.01818    0.50909   90.00000   0.00000   0.00100     3    4    5      1
+     5   -1.00000    0.00000   -0.50909    0.50909   90.00000   0.00000   0.00100     4    5    6      1
+     6   -1.00000    0.00000    0.00000    0.50909   90.00000   0.00000   0.00100     5    6    7      1
+     7   -1.00000    0.00000    0.50909    0.50909   90.00000   0.00000   0.00100     6    7    8      1
+     8   -1.00000    0.00000    1.01818    0.50909   90.00000   0.00000   0.00100     7    8    9      1
+     9   -1.00000    0.00000    1.52727    0.50909   90.00000   0.00000   0.00100     8    9   10      1
+    10   -1.00000    0.00000    2.03636    0.50909   90.00000   0.00000   0.00100     9   10   11      1
+    11   -1.00000    0.00000    2.54545    0.50909   90.00000   0.00000   0.00100    10   11    0      1
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Moved model.

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+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   -0.86603   -0.50000    0.25455    0.50909   90.00000   0.00000   0.00100     0    1    2      1
+     2   -0.86603   -0.50000    0.76364    0.50909   90.00000   0.00000   0.00100     1    2    3      1
+     3   -0.86603   -0.50000    1.27273    0.50909   90.00000   0.00000   0.00100     2    3    4      1
+     4   -0.86603   -0.50000    1.78182    0.50909   90.00000   0.00000   0.00100     3    4    5      1
+     5   -0.86603   -0.50000    2.29091    0.50909   90.00000   0.00000   0.00100     4    5    6      1
+     6   -0.86603   -0.50000    2.80000    0.50909   90.00000   0.00000   0.00100     5    6    7      1
+     7   -0.86603   -0.50000    3.30909    0.50909   90.00000   0.00000   0.00100     6    7    8      1
+     8   -0.86603   -0.50000    3.81818    0.50909   90.00000   0.00000   0.00100     7    8    9      1
+     9   -0.86603   -0.50000    4.32727    0.50909   90.00000   0.00000   0.00100     8    9   10      1
+    10   -0.86603   -0.50000    4.83636    0.50909   90.00000   0.00000   0.00100     9   10   11      1
+    11   -0.86603   -0.50000    5.34545    0.50909   90.00000   0.00000   0.00100    10   11    0      1
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The 30-degree rotation shows up in the X and Y coordinates for the first tag. The elevation become clear from the all-positive Z values for the same tag number.

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The right-most view in Fig. 1 shows a 6-wire cylinder that is close top and bottom by circular structures. The NEC-2 model in Fig. 5 shows how we can perform the operation. (Because the structure development involves GM commands that affect individual tags and not the entire structure, there are separate NEC-2 and NEC-4 versions of the model, due to difference in the GM command structure between the cores.)

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After creating the initial vertical wire, we enter two separate GA commands to create 60° arcs, the angular distance between the wires in the ultimate set. However, GA initially creates each arc vertically, so we must rotate each one by 90°, while moving it to the proper end of the initial wire. We assign to the GA structures a number of segments so that the segment length within that structure is approximately the same as the segment length within the vertical wires but with enough segments to form an adequate arc. The result is an initial structure consisting of a vertical wire with an arced wire attached to each end. The GR command finishes the full cylinder with its closed top and bottom ends.

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The following sample lines from the segmentation data show the 3 tags of the initial structure and the same data for the last replication in the overall model. To orient yourself, note the source assignments in Fig. 5 to Tags 1 and 16 and find those tags in the partial table.

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+  SEG.     COORDINATES OF SEG. CENTER       SEG.     ORIENTATION ANGLES    WIRE    CONNECTION DATA   TAG
+  NO.        X          Y          Z        LENGTH     ALPHA     BETA      RADIUS    I-   I    I+    NO.
+     1   -1.00000    0.00000   -2.54545    0.50909   90.00000  90.00000   0.00100   -66    1    2      1
+     2   -1.00000    0.00000   -2.03636    0.50909   90.00000   0.00000   0.00100     1    2    3      1
+     3   -1.00000    0.00000   -1.52727    0.50909   90.00000   0.00000   0.00100     2    3    4      1
+     4   -1.00000    0.00000   -1.01818    0.50909   90.00000   0.00000   0.00100     3    4    5      1
+     5   -1.00000    0.00000   -0.50909    0.50909   90.00000   0.00000   0.00100     4    5    6      1
+     6   -1.00000    0.00000    0.00000    0.50909   90.00000   0.00000   0.00100     5    6    7      1
+     7   -1.00000    0.00000    0.50909    0.50909   90.00000   0.00000   0.00100     6    7    8      1
+     8   -1.00000    0.00000    1.01818    0.50909   90.00000   0.00000   0.00100     7    8    9      1
+     9   -1.00000    0.00000    1.52727    0.50909   90.00000   0.00000   0.00100     8    9   10      1
+    10   -1.00000    0.00000    2.03636    0.50909   90.00000   0.00000   0.00100     9   10   11      1
+    11   -1.00000    0.00000    2.54545    0.50909   90.00000 -90.00000   0.00100    10   11   63      1
+    12    0.96985   -0.17101    2.80000    0.34730    0.00000-100.00000   0.00100    31   12   13      2
+    13    0.85287   -0.49240    2.80000    0.34730    0.00000-120.00000   0.00100    12   13   14      2
+    14    0.63302   -0.75441    2.80000    0.34730    0.00000-140.00000   0.00100    13   14  -45      2
+    15    0.96985   -0.17101   -2.80000    0.34730    0.00000-100.00000   0.00100    34   15   16      3
+    16    0.85287   -0.49240   -2.80000    0.34730    0.00000-120.00000   0.00100    15   16   17      3
+    17    0.63302   -0.75441   -2.80000    0.34730    0.00000-140.00000   0.00100    16   17   35      3
+---------------
+    86   -0.50000    0.86603   -2.54545    0.50909   90.00000-150.00000   0.00100   -49   86   87     16
+    87   -0.50000    0.86603   -2.03636    0.50909   90.00000   0.00000   0.00100    86   87   88     16
+    88   -0.50000    0.86603   -1.52727    0.50909   90.00000   0.00000   0.00100    87   88   89     16
+    89   -0.50000    0.86603   -1.01818    0.50909   90.00000   0.00000   0.00100    88   89   90     16
+    90   -0.50000    0.86603   -0.50909    0.50909   90.00000   0.00000   0.00100    89   90   91     16
+    91   -0.50000    0.86603    0.00000    0.50909   90.00000   0.00000   0.00100    90   91   92     16
+    92   -0.50000    0.86603    0.50909    0.50909   90.00000   0.00000   0.00100    91   92   93     16
+    93   -0.50000    0.86603    1.01818    0.50909   90.00000   0.00000   0.00100    92   93   94     16
+    94   -0.50000    0.86603    1.52727    0.50909   90.00000   0.00000   0.00100    93   94   95     16
+    95   -0.50000    0.86603    2.03636    0.50909   90.00000   0.00000   0.00100    94   95   96     16
+    96   -0.50000    0.86603    2.54545    0.50909   90.00000  30.00000   0.00100    95   96   46     16
+    97    0.33682   -0.92542    2.80000    0.34730    0.00000-160.00000   0.00100    14   97   98     17
+    98    0.00000   -0.98481    2.80000    0.34730    0.00000-180.00000   0.00100    97   98   99     17
+    99   -0.33682   -0.92542    2.80000    0.34730    0.00000 160.00000   0.00100    98   99  -28     17
+   100    0.33682   -0.92542   -2.80000    0.34730    0.00000-160.00000   0.00100    17  100  101     18
+   101    0.00000   -0.98481   -2.80000    0.34730    0.00000-180.00000   0.00100   100  101  102     18
+   102   -0.33682   -0.92542   -2.80000    0.34730    0.00000 160.00000   0.00100   101  102   18     18
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By locating the coordinates of each segment junction in the original wire, you may add arcs at each junction and create a cylinder that is closed at all available intermediate points. Note in the sample model that the 6 EX0 entries now use new tag numbers to reflect the 3-tag initial structure. When creating structures by symmetry, it is useful to keep track of the ways that geometry modifications will affect other parts of the total model. If a scratch pad will not suffice, you may consult the Necvu segment identification feature or the segmentation data to track these affects.

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I placed sources at the center of each wire in the structures as a convenience when checking the accuracy of each model. The result is a structure that performs similarly to a simple fat dipole, as shown by the 3-dimensional pattern in Fig. 6. (The red lines are a conventionalized representation of the capped cylinder oriented at corresponding angles relative to the field lines. Without the end caps, the maximum free-space gain is 2.08 to 2.10 dBi, about the same as that of a dipole. The beamwidth of the E-plane pattern is consistently about 83 degrees.

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Even though these small sample models do not fairly show the core-run timesaving, the largest model (132 segments) required less than twice the time of the smallest (66 segments). Wire cylinders also offer some advantages when modeling large diameter tubular structures, since the radii of the individual wires forming them via GR may have the same size as wire attached to them (so long as those wires do not destroy the symmetry). A disadvantage is that GR-formed cylinders are not suitable for antennas such as slotted cylinders, since there is no way to remove selected wires from the finished product.

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For very large models, both GX and GR (but not in the same model) can speed core runs. Although the sample models are small in order to make them clear, symmetry's true home is the model that otherwise would press the core in terms of required matrix space or the time it takes a PC to process the model.

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A Special Note on the "Destruction" of Symmetry

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A number of modelers have read NEC manual warnings about the conditions in which symmetry is "destroyed." Unfortunately, these warnings appear in unqualified form. As a result, some modelers do not use the GR command when another wire (GW) command must appear afterwards for fear that the structure created by the GR command simply will not appear in the model.

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In fact, the structure does appear and becomes just a set of wires specified by the geometry function of the GR command. The symmetry mode of calculation, however, does not function. Hence, if we have a following GW command or another condition that defeats or destroys symmetry, we do not lose the modeled structure created by GR. We only lose the increased speed of the run that symmetry would permit.

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To illustrate the correct situation, examine the model in Fig. 7. The model is the same as the very first model in this episode, with one addition. The initial GW command established a wire, and the GR command creates the resulting circle of 6 wires. In this model, GW 11 adds a new wire.

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To the right of the model file, I have inserted the Necvu rendering of the model that emerges from the wire specification section of the NEC output report. The 6 wires in the circle emerge from GW 1 and the GR command. To see how NEC handles this case, we may examine the first section of the NEC output report.

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+                                - - - STRUCTURE SPECIFICATION - - -
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+                                     COORDINATES MUST BE INPUT IN
+                                     METERS OR BE SCALED TO METERS
+                                     BEFORE STRUCTURE INPUT IS ENDED
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+  WIRE                                                                               NO. OF    FIRST  LAST     TAG
+  NO.        X1         Y1         Z1          X2         Y2         Z2      RADIUS   SEG.     SEG.   SEG.     NO.
+     1   -1.00000    0.00000   -2.80000    -1.00000    0.00000    2.80000    0.00100     11        1    11       1
+      STRUCTURE ROTATED ABOUT Z-AXIS  6 TIMES.  LABELS INCREMENTED BY    1
+     2   -5.00000    0.00000   -3.00000    -5.00000    0.00000    3.00000    0.00100     10       67    76      11
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+   TOTAL SEGMENTS USED=   76     NO. SEG. IN A SYMMETRIC CELL=   76     SYMMETRY FLAG=  0
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Note the very last entry that sets the symmetry flag at 0. If symmetry had been in effect, the flag would read -1. Hence, the model will run with all 7 wires in place, but will not use symmetry in the calculation process. Since GR is a highly functional geometry command, even apart from its potential to invoke symmetry, we should keep it in mind for many purposes, for example, when modeling radial systems, cylinders, and numerous other shapes.

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Conclusion

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Our brief foray into cylindrical rotation does not capture everything that we may do with the GR command. However, I hope that these notes make the command somewhat more accessible than it might otherwise have been.

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Go to Main Index

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95. Some Basics of the NT Command

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L. B. Cebik, W4RNL

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The NT command allows you to implement 2-port networks in a model using non-radiating methods, much like the TL command. In fact, the TL command is a specialized implementation of more general networks. However, use of the TL command presumes a basic mastery of handling short circuit admittance matrix parameters. As a result, the command has little general use among the total body of those using NEC. Short circuit admittance matrix parameters and their calculation from more conventional antenna parameters is a subject well beyond the scope of this series. However, there are a number of applications of NT networks that admit of some approximations and hence some short cuts in the calculation procedure. They will suffice to allow us to illustrate the fundamental uses of the command, as well as its entry structure.

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The NT command will let you perform easily some difficult modeling tasks, such as placing a loading element in parallel with a source or creating a parallel connection between segments on different wires within a model. It also allows you to incorporate extremely complex networks into a model so long as you can reduce them to the short circuit admittance parameters required by a 2-port network. In virtually all cases, the command is less troublesome than calculating the values to fit its entry positions. The problem facing the modeler who has not previously used networks is less a matter of understanding the command entries than it is in knowing what entries to make in the floating decimal positions.

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The command structure itself is very straightforward. As the sample line below shows, the integer entries specify the specific tag and segment numbers between which we connect the network. In some cases, one of the tags will be a remote wire, and occasionally, it will serve as a "place-holder" to terminate the network. However, there are many applications in which both wires will be active parts of the structure geometry.

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+CMD     I1      I2      I3      I4      F1      F2      F3      F4      F5      F6
+        TAG1    SEG1    TAG2    SEG2    Y11R    Y11I    Y12R    Y12I    Y22R    Y22I
+NT      2       1       1       6       5.8e-5  -7.3e-3 -5.8e-5 1.7e-2  5.8e-5  -4.8e-3
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The floating decimal entries call for port values according to the standard 2-port labeling. See Fig. 1.

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End 1 corresponds to tag 1-seg1, and end 2 to tag 2-seg2. Since the entries that go into the network are usually non-symmetrical, it is important to keep the ends straight. In the sample to the right, we wish the Y element to be in parallel with the assigned tag and segment. Therefore, we must assign its value to the Y11 real and imaginary component positions in the command and be certain the I1 and I2 specify the segment to which the Y element is parallel.

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Y11 is the short circuit input admittance, expressed in terms of real and imaginary components. In other contexts, we might call the real component the conductance (G) and the imaginary component susceptance (B). Both use Siemens or mhos as the unit of measure, and they are the inverse of resistance and reactance, respectively. Hence, admittance (Y), also measured in mhos is the reciprocal of impedance (Z). Y22 is the output short circuit reverse-transfer admittance, as indicated by the arrow in the sketch. Since each port has balanced currents, the net current transferred between port 1 and 2 is zero. Hence, Y12 does not represent a physical connection between ports. Rather, it is the short circuit transfer admittance. Since the matrix is symmetric, it is unnecessary to specify Y21, since the forward transfer admittance and the reverse transfer admittance are equal. Y12 and Y22 are also specified in terms of real and imaginary components.

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Besides being specific to an assigned frequency, multiple NT entries must be grouped together. You may intermix them with TL commands, but the group must have no other commands separating the members of the group. Intervening commands other than NT or TL will result in the next TL or NT entry destroying previous NT and TL commands. If your NEC core does not employ auto dimensioning, you must set the parameter MAXNET high enough to include the total number of NT and TL commands to be used in the model. For most models, this setting is trivial. However, there may be a large number of driven elements in an array, each with a current source. Since each current source invokes a network, some assemblies may require a very high number of NT commands.

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In an earlier episode, we examined a technique for creating parallel sources, but requiring only 1 source assignment. By using a very short transmission line, we effected a virtual short circuit between the specified segments, but with the connections in parallel with the source. The technique proves useful when close space wires might yield inaccuracies if drawn to a single source wire due to very small angles between wires at the junctions. See Fig. 2.

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The following lines show the excitation and transmission line commands for the parallel-wire dipole.

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+CM Parallel-Wire Dipole
+CE TL method
+GW 1 79 0 -.47 .006 0 .47 .006 .0005
+GW 2 79 0 -.47 -.006 0 .47 -.006 .0005
+GW 3 1 0 -.47 -.006 0 -.47 .006 .0005
+GW 4 1 0 .47 -.006 0 .47 .006 .0005
+GE
+FR 0 1 0 0 150 1
+EX 0 2 40 00 1 0
+TL 1 40 2 40 140 .001
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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The reported source impedance of the dipole is 71.427 - j1.873 Ohms. For comparative purposes, the impedance report has far more decimal places than practical applications would require. Now let's suppose that we would like to create the virtual short circuit between wires using the NT command. Like TLs, NTs are in parallel with sources and in series with loads on the same segment.

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Fig. 3 compares the entry assist screens for the required TL and NT entries. The TL entry uses a very short length: 1 mm. By using an electrical length entry as short as 1e-10, the impedance specification would have become wholly arbitrary. Now examine the right side of the figure and the following model.

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+CM Parallel-Wire Dipole
+CE NT method
+GW 1 79 0 -.47 .006 0 .47 .006 .0005
+GW 2 79 0 -.47 -.006 0 .47 -.006 .0005
+GW 3 1 0 -.47 -.006 0 -.47 .006 .0005
+GW 4 1 0 .47 -.006 0 .47 .006 .0005
+GE
+FR 0 1 0 0 150 1
+EX 0 2 40 00 1 0
+NT 1 40 2 40 1e10 -1e10 -1e10 1e10 1e10 -1e10
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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Creating a virtual short circuit with an NT command is seemingly complex, but once you have the formula, you may copy it as many times as you need it. In fact, there is a pattern to the entries. Let us set the conductance of the connecting wire (G) to 1e10 and the susceptance (B) to the same value. To create a short circuit with these initial values, we need to set the admittance matrix of the NT command as follows.

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+Parameter       Real                    Imaginary
+Y11             +G      1e10            -B      -1e10
+Y12             -G      -1e10           +B      1e10
+Y22             +G      1e10            -B      -1e10
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We shall later see that this entry set views the short circuit as a special form of a PI network translated into admittance matrix entries. For the moment, we may simply memorize the form--of course, after running the model and confirming that it yields the correct source impedance: 71.430 - j1.868 O. Both the TL and NT versions of the parallel-wire dipole return free-space gain values of 2.13 dBi. You may also wish to examine the currents on various corresponding segments of the model to establish their virtual identity.

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A second relatively simple use of the NT command that we have already encountered appears in an earlier episode: the current source. Examine the following model, a basic dipole with a current source.

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+CM dipole with current source
+CE 0 deg at antenna source
+GW 1 11 0 -.2375 0 0 .2375 0 .001
+GW 2 1 9999 -.005 9999 9999 .005 9999 .001
+GE
+FR 0 1 0 0 299.7925 1
+EX 0 2 1 00 0.00000 1.00000
+NT 2 1 1 6 0 0 0 1 0 0
+XQ
+EN
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In this case, we create the required dipole (GW1) and add a second remote 1-segment wire (GW2) located too far away from the key element to have any affect on the pattern data. The remote wire is very short, very thin, and never given a material load. Next, we place a network (NT) between the dipole source segment and the remote wire, using the standard set-up of the NT command for a current source. Using the NT assistance screen in the software, as shown on the left in Fig. 4, will ease the burden of remembering which entry point receives the value of 1 for the Y12 imaginary position. Finally, we add an EX0 command, placing the source on the remote wire and phase shifting the value by 90°.

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By entering a Y12-imaginary value of 1.0 mho in the network, we obtain a 90° phase shift in the current at the element relative to the phase of the voltage at the source on the other side of the network. As well, whatever value the source shows as its voltage will appear at the other side of the network on the element as the current value. The technique of "forcing" current values is widely used in phased array design, but here, it functions to provide a current source with a known value at the true feedpoint of the antenna. One very significant use of current sources is to allow rectangular plots of the element currents reference to a standard value, such as 1.0. The right side of Fig. 4 shows such a plot for the dipole.

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For easy extraction of the required data that applies to the antenna feedpoint (in contrast to the model source on the remote wire), we must learn how to "read" the data. The first key output report entry is the antenna input parameters, shown below for our current-source dipole.

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+- - - ANTENNA INPUT PARAMETERS - - -
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+TAG   SEG.    VOLTAGE (VOLTS)          CURRENT (AMPS)         IMPEDANCE (OHMS)         ADMITTANCE (MHOS)       POWER
+NO.   NO.    REAL        IMAG.        REAL        IMAG.       REAL        IMAG.        REAL        IMAG.      (WATTS)
+  2    12  0.00000E+00 1.00000E+00 -1.16117E-01 7.17602E+01 1.39353E-02 -2.25490E-05 7.17602E+01 1.16117E-01 3.58801E+01
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1. The phase-shifted voltage value--1.0 v imaginary--is the real current level at the element feedpoint. You may verify this from the current table for segment 6.

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+SEG.  TAG           - - - CURRENT (AMPS) - - -
+NO.   NO.      REAL        IMAG.       MAG.        PHASE
+ 6    1      1.0000E+00 -2.2205E-16  1.0000E+00    0.000
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2. The impedance at the element feedpoint appears as an admittance (and its inverse as an impedance). If you create a standard dipole model using a voltage source, its impedance with a voltage source is 71.76 + j 0.12 Ohms, the value that now appears under the admittance entry.

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3. The power report is accurate for the current-source model. Hence, by the technique of power adjustment shown in earlier episodes, we would adjust the imaginary voltage value as the square root of the ratio of new power to old to arrive at the correct source for the desired power level. A value of 5.279 volts imaginary will yield a 1000-watt power level.

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The NT command also offers use the potential for having one more alternative way to perform a specific task. Consider the following model, a simple 3-element Yagi designed for 14.175 MHz and using 1" (0.025 m) aluminum elements.

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+CM 3-el Yagi with beta match
+CM Pre-match version
+CE
+GW 1 101 -5.292 0 0 5.292 0 0 0.0125
+GW 2 50 -4.947 3.024 0 -0.049 3.024 0 0.0125
+GW 3 1 -0.049 3.024 0 0.049 3.024 0 0.0125
+GW 4 50 0.049 3.024 0 4.947 3.024 0 0.0125
+GW 5 101 -4.786 6.049 0 4.786 6.049 0 0.0125
+GS 0 0 1
+GE 0
+EX 0 3 1 0 1 0
+LD 5 0 0 0 2.5E7
+FR 0 1 0 0 14.175 1
+RP 0 1 360 1000 90 0 1 1
+EN
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The elements employ a high segmentation density, with the driver element (GW2 - GW4) subdivided. The left side of Fig. 5 shows the evolution of the element, along with the first alternative that we shall use in our quest to match the antenna to a 50-Ohm feedline. However, run this pre-match version of the antenna to obtain its "natural" source impedance: 23.42 - j24.59 Ohms. The reported antenna gain is 7.84 dBi with an AGT value of 0.99977, indicating a very adequate model and accurate output reports (as always, within the limits of the AGT test).

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Our matching goal has several options, but we shall choose to add a beta match. The beta match is a version of an L-network with down conversion from the source (50 Ohms) to the load. This system requires a series impedance element on the load side of the network, already in place in the form of the capacitive reactance of the source. The other element of the network consists of a shunt reactance of the opposite type (relative to the series reactance) on the source side of the network. To achieve this goal, we need to be able to place a load in parallel with the source. However, LD loads appear in series with the source and thus are not applicable.

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One tactic that we can use is to create a physical structure to give a parallel position for the load. The last part of the sketch in Fig. 5 shows a way to accomplish this feat. By using 1-segment wires around the 1-segment source wire, we create a box. Since the wires are short, they contribute very little to the radiation pattern. However, they provide a place for the desired shunt reactance. Examine the additional wires for the box in the following model. Note that they place the box at right angles to the plane of the antenna, although an in-line orientation would work as well. The new wires appear between the original driver entry and the director, which is now GW8. As well, the final end of the driver (GW7) follows the box structure. Excitation remains on GW3.

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+CM 3-el Yagi with beta match
+CM vertical placement
+CE
+GW 1 101 -5.292 0 0 5.292 0 0 0.0125
+GW 2 50 -4.947 3.024 0 -0.049 3.024 0 0.0125
+GW 3 1 -0.049 3.024 0 0.049 3.024 0 0.0125
+GW 4 1 -0.049 3.024 0 -0.049 3.024 0.098 0.0125
+GW 5 1 -0.049 3.024 0.098 0.049 3.024 0.098 0.0125
+GW 6 1 0.049 3.024 0.098 0.049 3.024 0 0.0125
+GW 7 50 0.049 3.024 0 4.947 3.024 0 0.0125
+GW 8 101 -4.786 6.049 0 4.786 6.049 0 0.0125
+GS 0 0 1
+GE 0
+EX 0 3 1 0 1 0
+LD 4 5 1 1 0.2345 46.9
+LD 5 0 0 0 2.5E7
+FR 0 1 0 0 14.175 1
+RP 0 1 360 1000 90 0 1 1
+EN
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The required value for the shunt element derives from standard L-network equations:

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The term "delta" is the loaded Q of the network and derives from the high and low resistance values at the circuit terminals. The required series reactance is delta times the low resistance and appears in series with it. The shunt or parallel reactance is of the opposite type from the series reactance and is the high resistance divided by delta. There are numerous utility programs available for calculating the required values. By using the natural source resistance and the feedline characteristic impedance to determine delta, we discover that the existing series capacitive reactance is almost precisely what the equations calculate. Hence, we need only calculate a corresponding shunt or parallel reactance: 46.9 Ohms inductive. Based on experience, we may assign the shunt element a Q of about 200. The final values appear in the LD4 entry for the model.

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We might run the model to obtain its performance values: 7.86 dBi gain, 57.58 + j1.51 Ohms impedance, 1.008 AGT, 0.036 AGT-dBi, and an adjusted gain of 7.82 dBi. The AGT value shows that the wire box has a small affect on model adequacy, and the adjusted gain value suggests that the box also has a small affect on performance of the driver. The fact that we did not arrive at precisely 50 Ohms impedance is a measure of how far off from ideal the series reactance is, as well as the affects of the wire box. Perhaps one of the chief advantages of this system of adding a parallel load is that it allows the simulation of inductors (in contrast to beta hairpin assemblies). By converting the load to a type 0 using the same series resistance, but an inductance of 0.527 µH, the model becomes perfectly frequency nimble, with accurate output values for frequency sweeps across the operating passband.

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Although subsequent alternative shunt loads will not require the driver scheme used for the box version, we shall retain it so that the core model remains constant in all of our trials. In the following model, we see a version of the antenna using a technique that we met in previous episodes when exploring the use of transmission lines. This model employs a standard shorted transmission line stub calculated to provide the required reactance. Then, we trimmed the stub to a length that yielded the most satisfactory source impedance.

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+CM 3-el Yagi with beta match
+CM TL 600-Ohm stub
+CE
+GW 1 101 -5.292 0 0 5.292 0 0 0.0125
+GW 2 50 -4.947 3.024 0 -0.049 3.024 0 0.0125
+GW 3 1 -0.049 3.024 0 0.049 3.024 0 0.0125
+GW 4 50 0.049 3.024 0 4.947 3.024 0 0.0125
+GW 5 101 -4.786 6.049 0 4.786 6.049 0 0.0125
+GW 6 1 1.001 1.001 1.001 1 1 1 0.000322
+GS 0 0 1
+GE 0
+EX 0 3 1 0 1 0
+LD 5 0 0 0 2.5E7
+TL 3 1 6 1 600 0.262584 0 0 1e10 1e10
+FR 0 1 0 0 14.175 1
+RP 0 1 360 1000 90 0 1 1
+EN
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GW6 provides the remote termination wire for the shorted stub. The TL command specifies a 600-Ohm line with a length of 0.263 m, simulating an open or ladder line stub assembly. Run the model to obtain its output reports: 7.84 dBi gain, 49.23 - j0.005 Ohms impedance, 0.999 AGT. The near-ideal value of AGT requires no gain report adjustment, and the gain value coincides with the report from the pre-matched model. Although the TL line cannot show losses within it, they should be negligible. Like the use of an LD0 load in the box model, this version of the beta-matched Yagi is also frequency nimble.

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Fig. 6 shows the assist screen for the TL stub in the model that we just examined. However, it is not the only way in which we might use the TL command to effect a parallel load on the Yagi source segment. The right side of the figure shows an alternative set of entries. Examine the next model. You will note that the geometry remains unchanged from the previous model. However, the TL line reflects the values shown in the figure.

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+CM 3-el Yagi:  14.175 MHz
+CM TL + shunt admittance beta match
+CE
+GW 1 101 -5.292 0 0 5.292 0 0 0.0125
+GW 2 50 -4.947 3.024 0 -0.049 3.024 0 0.0125
+GW 3 1 -0.049 3.024 0 0.049 3.024 0 0.0125
+GW 4 50 0.049 3.024 0 4.947 3.024 0 0.0125
+GW 5 101 -4.786 6.049 0 4.786 6.049 0 0.0125
+GW 6 1 2000 2000 2000 2000.001 2000.001 2000.001 0.000814
+GS 0 0 1
+GE 0
+EX 0 3 1 0 1 0
+LD 5 0 0 0 2.5E7
+TL 3 1 6 1 50 0.01 0 0 0.0001066 -0.0213214
+FR 0 1 0 0 14.175 1
+RP 0 1 360 1000 90 0 1 1
+EN
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As a special form of a network, the TL command allows the use of shunt admittance values at either end of the line for various simulation purposes. In this case, instead of using a stub, we specify a very short line length. The line is so short that no significant transformation of voltage, current, or impedance can occur. On the "far" end of the line, we insert the shunt admittance equivalents of the series values of resistance and reactance that we need for the match. The real component of an admittance (Y) is conductance (G), and the imaginary component is susceptance (B). Since the conversion requires converting a series impedance into a shunt or parallel admittance, we may use these equations:

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The subscripts "S" and "P" indicate series and parallel values, respectively. Using the original values of the required impedance for a coil with a Q of 200, we convert 0.2345 + j49.6 Ohms to 1.066E-4 - j2.132E-2 mhos. These values go on end 2 of the line.

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If you run the model, you will obtain the following reports: 7.82 dBi gain, 48.98 - j0.32 Ohms impedance, 0.999 AGT. The resistive component of the impedance is slightly low because we did not adjust the coil reactance for a closer approach to 50 Ohms before converting the reactance to a susceptance. The limitation of this method of creating a beta match is that it is frequency specific and does not yield highly accurate values in a frequency sweep.

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We are not quite done with our beta matched Yagi. We have painlessly slipped into the realm of admittances, and so we might as well create the parallel matching element using the NT command. Examine the following model and its NT command that replaces the TL commands.

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+CM 3-el Yagi:  14.175 MHz
+CM NT + shunt admittance values
+CE
+GW 1 101 -5.292 0 0 5.292 0 0 0.0125
+GW 2 50 -4.947 3.024 0 -0.049 3.024 0 0.0125
+GW 3 1 -0.049 3.024 0 0.049 3.024 0 0.0125
+GW 4 50 0.049 3.024 0 4.947 3.024 0 0.0125
+GW 5 101 -4.786 6.049 0 4.786 6.049 0 0.0125
+GW 6 1 2000 2000 2000 2000.001 2000.001 2000.001 0.000814
+GS 0 0 1
+GE 0
+EX 0 3 1 0 1 0
+LD 5 0 0 0 2.5E7
+NT 3 1 6 1 0.0001066 -0.0213214 0 0 1e10 1e10
+FR 0 1 0 0 14.175 1
+RP 0 1 360 1000 90 0 1 1
+EN
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To place a load in parallel with a source on a specific segment, we may use the system shown in model and in Fig. 7. We place the shunt admittance values on the end of the network connected to the target segment. These are the Y11 values, which are identical to those used for the short-TL version of the model. Y12 remains blank, as indicated by the zero entries. The other end of the network requires a short circuit, normally created by the use of very high values of real and imaginary admittance for Y22. The network short circuit adds nothing to the structure geometry of a model, and so the short-circuited end of the network may connect to any wire without affecting antenna performance. Since GW6 is left over from the TL models, we used that 1-segment wire as the network terminus.

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You may run the model for its reports: 7.82 dBi gain, 48.98 - j0.01 Ohms impedance, 0.999 AGT. The reduced reactance results from not having a 0.01-m line between the source segment and the load. Since we are using admittance values (comparable to using impedance values in an LD4 load), the model is frequency specific. Its chief advantage lies in the place it occupies in our progression of beta-matched models. Hopefully, by revealing its relationship to other techniques that we may use to achieve relatively the same goal, the function and nature of NT networks is somewhat clearer.

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In this episode, we have looked at some fairly simple applications of the NT command and their relationship to alternative ways of achieving the same goals. Indeed, the more commands that we master, the more ways that we may create modifications to the geometry of a model. The flexibility lets us select the means that best suits the need.

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There are further applications of the NT command that more directly involve us in the 2-port-network nature of the command. In the next episode, we shall examine how to add to our antenna models the matching networks that bring the source impedance from its natural value to that ubiquitous 50-Ohm value. Along the way, we shall also show some short cuts to the required calculations, although a hand-calculator will still be a necessary adjunct to our modeling efforts.

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Go to Main Index

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96. Some Further Applications of the NT Command

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L. B. Cebik, W4RNL

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In the last episode, we examined the basics of the NT or network command, along with some specialized uses. The command itself is straightforward in its structure.

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+CMD     I1      I2      I3      I4      F1      F2      F3      F4      F5      F6
+        TAG1    SEG1    TAG2    SEG2    Y11R    Y11I    Y12R    Y12I    Y22R    Y22I
+NT      2       1       1       6       5.8e-5  -7.3e-3 -5.8e-5 1.7e-2  5.8e-5  -4.8e-3
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The integer entries identify the terminal tags and segments for the network, while the 6 floating point positions take the admittance values for the 2-port network. In this episode, we shall probe a bit further into the use of the NT command to simulate complex real networks of components. Note that we shall have to be careful when we use the term "network." With respect to the NT command's contents. The term refers to a 2-port admittance parameter network. At the same time, these handy networks serve to capture the key ingredients of all manner of passive arrays of components that we more traditionally call networks. In theory, the 2-port network can stand in for any component network, no matter how complex.

+
+ +
+

The terms of a 2-port network, shown in Fig. 1, have names with meanings:

+
    +
  • Y11: short circuit input admittance
    • +
  • Y22: short circuit output admittance
    • +
  • Y12: short circuit reverse transfer admittance
    • +
  • Y21: short circuit forward transfer admittance
    • +
+
+ +
+

Consider a real component network, such as the central part of Fig. 2. One form of analysis that we can perform (A) is to short-circuit the output and apply a voltage to the input. Then we can reverse the procedure (B), applying a voltage to the output side with the input side short circuited. Under these conditions, the following relationships will hold.

+
+ +
+

With the output shorted, we can calculate the values of Y11 and Y21:

+
+ +
+

With the input shorted, we can likewise calculate the values of Y22 and Y12:

+
+ +
+

Since we have restricted ourselves to passive networks, we need not calculate both Y12 and Y21, because

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+ +
+

Perhaps the only special thing we must do is get used to the fact that NEC nomenclature puts the admittance terms in capital letters, while textbooks shown them in the lower case. Those same textbooks have also replaced--in most cases--the traditional E with a V for voltage, as in the above equations. As well, we shall also have to remember that admittance parameter networks involve calculations based on shunt or parallel admittance, not on series admittance.

+

Impedance Matching a Folded Dipole to a 50-Ohm Source

+

In order to see some practical cases using the NT command, let's set up a folded dipole at 28.5 MHz, as in the following model.

+ 
+CM Folded Dipole
+CM Pre-match version
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GE 0
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 1 50 00 1 0
+XQ
+EN
+
+

The key parameter for our work will be the source impedance: 286.705 + j0.651 Ohms. That is why the model uses the XQ command rather than an RP command. In episode 73, we reviewed a technique for adding a component network to the model in order to match the folded dipole to a 50-Ohm source. See Fig. 3.

+
+ +
+

To create this antenna plus matching network (an L circuit), we ended up with a model like the following one.

+ 
+CM Folded Dipole
+CM TL + LD matching network to 50 Ohms
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GW 5 1 0. -.0254 1 0. .0254 1 .0005119
+GW 6 1 0. .0254 1 .0254 .0254 1 .0005119
+GW 7 1 .0254 -.0254 1 0. -.0254 1 .0005119
+GW 8 1 .0254 -.0254 1 .0254 .0254 1 .0005119
+GW 9 1 .0508 -.0254 1 .0254 -.0254 1 .0005119
+GW 10 1 .0254 .0254 1 .0508 .0254 1 .0005119
+GW 11 1 .0508 -.0254 1 .0508 .0254 1 .0005119
+GE 0
+TL 1 50 5 1 290 .001
+LD 0 9 1 1 0. 2.6E-07 0.
+LD 0 10 1 1 0. 2.6E-07 0.
+LD 0 8 1 1 0. 0. 4.19E-11
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 11 1 00 1 0
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
+

The added lines or GW entries provide a wire framework to hold the components, indicated by the LD0 entries. A very short transmission line (TL) makes a virtual direct connection to the normal folded dipole feedpoint while the actual wire grid structure is at a considerable distance from the main antenna structure to prevent unwanted interactions among the two groups of wires. The model returns a matched source impedance of 50.231 + j1.412 Ohms.

+

The wire-grid system holds both advantages and disadvantages. On the plus side, it is accurate within general limits and is amenable to frequency sweeps. On the minus side, the extra wires do have an affect on the network and require great care to achieve reasonable results.

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In contrast, if we replace the wire grid with the NT command, we vastly simplify the model. At the same time we can achieve considerable accuracy, since the NT network is a non-radiating structure that does not interfere with the structure geometry of the model. However, an NT replacement for the component network has 2 drawbacks: it is frequency specific (like an LD4 load that specifies resistance and reactance), and it requires some external work to arrive at the values for the 6 floating decimal positions in the command.

+

Those who have little or no experience using 2-port networks usually have two stages of learning curve to endure. The first involves getting used to converting component values into shunt admittance values rather than using the more familiar impedance terms. In isolation, of course, conductance (G) is the inverse of resistance (R), and susceptance (B) is the inverse of reactance (X). Originally, to signify the inverse relationship, the unit of conductance, susceptance, and admittance was the mho, more recently changed to the Siemen (S). G and B occur together, just as do R and X. As well, we tend to think of R and X in series form: R +/- jX Ohms. However, admittance normally appears in shunt or parallel form: G +/-jB S. To convert a series-form impedance to a shunt-form admittance requires that we combine the inversion with a series-to-parallel operation, so that the actual conversions look like the following:

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+ +
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Note the reversal of sign on the susceptance equation, due to the change of phase angle when changing from a series to a parallel form.

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The second stage of the learning curve involves deriving the correct values for Y11, Y12, and Y22 when converting a component network into a 2-port network. Depending on the complexity of the component network, along with our adeptness at working with nodal equations, etc., the work can become tedious. However, for many tasks, there is no way around the work.

+

For our illustrations, we can simplify the entire operation by setting up a few restrictions. First, capacitors will have an indefinitely high Q, and so we may safely ignore their conductance. This holds true only of good quality capacitors used in the HF region, and so we shall continue to work below 30 MHz. Second, if an inductor has a sufficiently high Q (perhaps 200 or so and up), then under conversion, the low series resistance will not alter the susceptance value of the resulting admittance. We may then directly calculate capacitor and inductor shunt admittance values from the following equations:

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+ +
+

We should recognized the first 2 simplified forms as the negative inverse of forms that we would use to calculate reactance values. The third form is a handy way to arrive at the conductance of the inductor: by dividing its absolute value of susceptance by the coil Q. For uniformity in this exercise, all component network inductors will have a Q of 300.

+

Under the simplifying assumptions, we may then calculate the real and imaginary components of the 2-port network for L and PI networks using the following simple equations:

+ 
+Parameter          Real              Imaginary
+Y11                Gp1 + Gs           Bp1 + Bs
+Y12                -Gs                -Bs
+Y22                Gp2 + Gs           Bp2 + Bs
+
+

The p1 and p2 subscripts refer to the shunt or parallel components in a real network, while s refers to the series component. Let's apply these procedures to a few matching networks that we might calculate (usually from a utility program) to match our original folded dipole to a 50-Ohm source. We may always compare our results to the source impedance obtained from our wire grid model.

+

Three Networks

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Let's begin with an up-converting L circuit using a series inductor and a shunt capacitor on the load side of the L circuit. The arrangement would appear like the left-hand side of Fig. 4. The component values come from one of my utility programs.

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+ +
+

This may be as good a time as any to note some differences among network-calculating utilities. Some programs offer you the choice of both coil and network Q (called "delta" in Terman's classical work). Other programs calculate the components for the lowest possible value of delta or working Q, which achieves the highest network efficiency. The latter types of programs are best, since you may not know what the lowest feasible value of working Q may be. Hence, you may select a Q that is too high in the sense of resulting in a less efficient network. In any event, always use the highest component (coil) Q and the lowest network Q that you can, while having manageable components. You may wish to calculate the network Q or delta from the following conventional equations for calculating L circuits (about 2.17).

+
+ +
+

The calculated components are a 0.608 uH series coil and a 42.4 pF shunt capacitor. We need to convert these values first into shunt admittance values and then into parameter entries. We shall use basic units throughout.

+ 
+Component          Value          G (Conductance)          B (Susceptance)
+P1                 None           0                        0
+S                  0.608E-6       3.0616E-5                -9.1848E-3
+P2                 42.4E-12       0                        7.5926E-3
+
+Parameter                   Real                                 Imaginary
+Y11                Gp1 + Gs      3.0616E-5              Bp1 + Bs      -9.1848E-3
+Y12                -Gs           -3.0616E-5             -Bs           9.1848E-3
+Y22                Gp2 + Gs      3.0616E-5              Bp2 + Bs      -1.5922E-3
+
+

You can recognize the calculated values of Y11-Y22 in Fig. 4 within the NT assistance screen from NEC-Win Pro. The total model has the following appearance.

+ 
+CM Folded Dipole
+CM Ls-Cp L-network version: NT
+CM Ls = 0.608 uH, Q = 300; Cp = 42.4 pF
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GW 5 1 -.001 0 1000 .001 0 1000 .00005
+GE 0
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 5 1 00 1 0
+NT 5 1 1 50 3.0616e-5 -9.1848e-3 -3.0616e-5 9.1848e-3 3.0616e-5 -1.5922e-3
+XQ
+EN
+
+

The model requires only 1 wire in addition to the folded-dipole wires. It serves to provide a new source segment for the input end of the 2-port network. The NT entries follow the order shown in the conversion table. Be certain to orient the terminating wires so that the network operates in the correct direction.

+

If we run the model, it returns a source impedance of 50.410 + j0.042 Ohms. Since the network includes a conductance value, the network does show losses. The folded dipole itself uses perfect wire, so that the GW parts of the model have no loss. Hence, the reported efficiency of 99.28% gives us a sense of the relative losses incurred by adding an actual L matching circuit to the antenna.

+

Why did the circuit not show a perfect 50-Ohm resistive impedance? There are 2 factors which are not clearly separable within the model. First, the external L circuit calculator rounds value to a maximum of 3 significant digits. Second, we used a considerable number of simplifying assumptions. Finally, the fact that we carried out the impedance calculation to 3 decimal places is a function of our desire to compare calculations, not to arrive at a practical matching solution. Rounded to "whole" Ohms, the result is practically perfect.

+

We may equally use the same L-circuit with the reactances (or susceptances) reversed, as in the left side of Fig. 5.

+
+ +
+

As we work our way through the calculations, the susceptance values will be close to those of the first example. However, their signs will be reversed. Numerical differences result from the reported component values having only 3 significant digits. As well, because we have swapped places for the capacitor (indefinitely high Q) and the coil (Q = 300), the shunt conductance values in the component network (and the resulting 2-port network) will also differ from the first example. The initial calculations call for a 51.3-pF series capacitor and a 0.737 uH shunt inductor.

+ 
+Component          Value          G (Conductance)          B (Susceptance)
+P1                 None           0                        0
+S                  51.3E-12       0                        9.1863E-3
+P2                 0.737E-6       2.5257E-5                -7.5772E-3
+
+Parameter                   Real                                 Imaginary
+Y11                Gp1 + Gs      1E-10                  Bp1 + Bs      9.1863E-3
+Y12                -Gs           1E-10                  -Bs           -9.1863E-3
+Y22                Gp2 + Gs      2.5257E-5              Bp2 + Bs      1.6091E-3
+
+

When working with NEC, unless specifically instructed otherwise, entering zero is not usually wise. Hence, the real components of Y11 and Y12 become exceedingly low numbers (1E-10) that still have calculational value. At this value level, the sign become meaningless. The entries appear in the assistance screen on the right side of Fig. 5 and are evident in the NT entry in the model itself.

+ 
+CM Folded Dipole
+CM Cs-Lp L-network version: NT
+CM Cs = 51.3 pF; Lp = 0.737 uH, Q = 300
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GW 5 1 -.001 0 1000 .001 0 1000 .00005
+GE 0
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 5 1 00 1 0
+NT 5 1 1 50 1e-10 9.1863e-3 1e-10 -9.1848e-3 2.5257e-5 1.6091e-3
+XQ
+EN
+
+

Note that, except for the NT entry, the model is identical to the one used in the first example. One advantage of using NT networks is that, if you can calculate the Y11 - Y22 entries, you may try many networks with minimal model revision. Running the model yields a source impedance of 50.293 - j0.317 Ohms, well within the limits set by our rounded component values and our initial assumptions. The efficiency remains 99.28%, since the delta of our L circuit did not change with the alteration of the components.

+

There is no reason why we cannot calculate a true 3-legged PI network to serve as our matching circuit. Fig. 6 shows on the left the resulting components that we shall need.

+
+ +
+

Our calculation scratch pad will have the following appearance.

+ 
+Component          Value          G (Conductance)          B (Susceptance)
+P1                 41.87E-12      0                        7.4977E-3
+S                  0.668E-6       2.7866E-5                -8.3599E-3
+P2                 45.89E-12      0                        8.2176E-3
+
+Parameter                   Real                                 Imaginary
+Y11                Gp1 + Gs      2.7866E-5              Bp1 + Bs      -8.622E-4
+Y12                -Gs           -2.7866E-5             -Bs           8.3599E-3
+Y22                Gp2 + Gs      2.7866E-5              Bp2 + Bs      -1.423E-4
+
+

The assistance screen shows the values, as does the following model for this situation.

+ 
+CM Folded Dipole
+CM C-L-C PI-network version: NT
+CM Cp1 = 41.87 pF; Ls = 0.668 uH, Q = 300; Cp2 = 45.89 pF
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GW 5 1 -.001 0 1000 .001 0 1000 .00005
+GE 0
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 5 1 00 1 0
+NT 5 1 1 50 2.7866e-5 -8.622e-4 -2.7866e-5 8.3599e-3 2.7866e-5 -1.423e-4
+XQ
+EN
+
+

The 2-port NT version of our matched folded dipole shows a source impedance of 50.340 - j0.301 Ohms. The efficiency is down to 99.10%, indicating the inherently higher losses for a 3-component network than for a 2-component network that performs the same impedance transformation.

+

In general, then, for the class of network applications with which we have been dealing, the simplifying assumptions have created no noticeable problems for the use of the NT command to simulate 2- and 3-component matching networks in the HF region.

+

A Harder Case: The T

+

So far, we have worked with the PI network and incomplete forms of it in converting component networks into shunt admittance values and then into Y11 - Y22 entry values for the 2-port network of the NT command. We have not attempted an analysis of another popular matching network, the T. In its most common form, the C-L-C T is a high-pass network as well as an impedance transformer. We can easily calculate values for a fixed-component version to serve our folded dipole, as shown on the left in Fig. 7.

+
+ +
+

The figure shows the component values, which result in the following initial shunt admittances.

+ 
+Component          Value          G (Conductance)          B (Susceptance)
+Cs1   (Y1)         51.3E-12       0                        9.1863E-3
+Lp    (Y3)         0.706E-6       2.6366E-5                -7.9099E-3
+Cs2   (Y2)         200.0E-12      0                        3.5814E-2
+
+

We may develop a new set of conversion formulas, or we may convert the admittance-based T network into an equivalent PI network, using standard conversion equations. The crossover labels for the components have conventional designations, as shown in Fig. 8.

+
+ +
+

The conversions equations are very straightforward.

+ 
+Conversion Formula       Label         Values Based on the Example
+Yt = Y1 + Y2 + Y3                      3.7090E-2
+Yc = Y1 Y2 / Yt          Ls            8.8702E-3
+Ya = Y1 Y3 / Yt          Cp1           -1.9591E-3
+Yb = Y2 Y3 / Yt          Cp2           -7.6377E-3
+
+

Not included in the conversion is the conductance. For a Q of 300, the original inductor conductance is 2.6366E-5. If we divide the conductance into the series component susceptance, we obtain a virtual Q of 336.5. We may use this value with each of the imaginary values in the following table to arrive at an approximation of the appropriate real entry. In general, the 2-port paths all involve the T inductor, but the virtual Q for each of the shunt legs of our conversion PI will likely be higher than the Y12 value. Nevertheless, the error will create little or no harm. With this in mind, we can create the final table of entries for the NT command.

+ 
+Parameter                   Real                                 Imaginary
+Y11                Gp1 + Gs      2.0539E-5              Bp1 + Bs      6.9111E-3
+Y12                -Gs           2.6366E-5              -Bs           -8.8702E-3
+Y22                Gp2 + Gs      3.6628E-6              Bp2 + Bs      1.2325E-3
+
+

The assistance screen reproduced in Fig. 7 shows these entries, as does the model itself.

+ 
+CM Folded Dipole
+CM C-L-C T-network version: NT
+CM Cs1 = 51.3 pF; Lp = 0.706 uH, Q = 300; Cs2 = 200.0 pF
+CE
+GW 1 99 -2.4892 0. 0. 2.4892 0. 0. .0005119
+GW 2 1 2.4892 0. 0. 2.4892 0. .0762 .0005119
+GW 3 99 2.4892 0. .0762 -2.4892 0. .0762 .0005119
+GW 4 1 -2.4892 0. .0762 -2.4892 0. 0. .0005119
+GW 5 1 -.001 0 1000 .001 0 1000 .00005
+GE 0
+FR 0 1 0 0 28.5 1
+GN -1
+EX 0 5 1 00 1 0
+NT 5 1 1 50 2.0539e-5 6.9111e-3 2.6366e-5 -8.8702e-3 3.6628e-6 1.2325e-3
+XQ
+EN
+
+

If we run the listed model, we obtain a source impedance of 49.681 + j0.016 Ohms, a value that is as close to perfect as any other the other results in this exercise. As well, the efficiency value is comparable to those for the other NT examples in this set.

+

These samples provide you with a starting point in expanding your use of the NT command beyond the kinds of special cases that we reviewed on the previous episode of this series. However, beware of extending the simplified calculations beyond the type of non-critical HF situation that we presumed at the start. Full exploration of NT potentials requires some exercises in mastering the techniques of converting all manner of component networks into terms sutable for use with the 2-port admittance parameter network of the NT command.

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At the other extreme, for those who do not wish to make any calculations externally to the modeling program, one implementation of NEC-2 may be useful. NEC2GO contains a special matching network module. It begins with the source impedance of an unmatched antenna. Then it gives you the choice of available networks to match the antenna's impedance to a source impedance of your choice. As well, you may choose both the coil and the network Q. Your network choices include applicable L, PI, and T circuits. The program then creates a new source wire and the NT command to implement the network selected. The only caution you need to exercise is to select a working Q that will yield the best combination of efficiency and manageable component values.

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Go to Main Index

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97. Integrating Commands: A Case Study

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L. B. Cebik, W4RNL

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In past episodes, we have examined some of the commands available on more advanced implementations of NEC. In each case, we looked at the command in relative isolation, with only enough of a model to illustrate how we enter and basically use the command. Although such guidance is a necessary step on the road to mastery of the command, it does not reveal the full power of the commands. That power only becomes apparent as we gradually learn how to integrate the commands into a model so as to achieve a goal.

+

There is no set of examples that will fully illustrate how we may effectively integrate commands for more effective modeling. The number of structure geometry and control commands is simply too large to sample every potential combination that we might effectively use. At most, we can look at a case study to see the thinking process that goes into setting up a model. Then, the rest is up to your own ingenuity in developing the most effective model for the task specifications that oversee the work.

+

The case study that I shall present involves a relatively recent innovation in AM broadcast antenna design. The antenna is called the Star-H, and has been developed by Kinstar, a joint partnership between the Star-H Corporation and Kintronic Laboratories. For more information, see the July issue of antenneX or the web sites indicated in that article. The article author, Dave Cuthbert, WX7G, adapted the antenna--at least in model form--to 160 meters and introduced a further space-reduction technique.

+

The basic star-H divides the vertical portion of the array into 4 parallel vertical wires, on the premise that each wire will have 4 times the impedance of a single vertical, a desirable situation for easier impedance matching and lower power losses in the resistive connections from part-to-part. A second feature of the antenna is converting each vertical leg into an inverted-L configuration. Since each of the 4 folded sections will form a symmetrical horizontal collection with the same current magnitude and phase angle everywhere along each wire, the horizontal fields will cancel, leaving only the radiation from the base-fed vertical wires. The effect is comparable to a 4-spoke top hat arrangement, except that each leg of the array will have its own higher source impedance. Fig. 1 shows the general outline of the array. Since the view is broadside, you will have to visualize the horizontal legs projecting into and out of the page that correspond to the ones going from side to side.

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The object of the design is to reduce the height required by the array to about 1/3 the height of a full size 1/4 wavelength monopole. Each inverted-L section thus requires a very long horizontal section. Since the center 4 wires and the end of each horizontal wire require support--presumed to be a power pole or similar--the antenna needs considerable real estate. In scaling the antenna to the 160-m amateur band, Cuthbert folds each horizontal end toward but not to an adjacent corner. The result is an array that might fit a reasonable plot of ground without either excessive vertical or horizontal demands.

+

The resulting model that I created used AWG #12 wire throughout (without loss, since the model is for illustration of some modeling principles). The vertical sections are 50' high, with the initial parts of the horizontal portions 35' long. Hence, the tip-to-tip distance is a maximum of 70'. The fold-overs are about 45' long and approach the tip of the next corner. Fig. 2 shows the Cuthbert design as adapted here.

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The Star-H developers recommend an industry-standard 120-radial system beneath the antenna and the ground. My interest in the design was to find out its potential when used over such a radial system. In outline, the system has the appearance of Fig. 3, if we could view it with X-ray vision from overhead.

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Of course, a buried radial system requires the use of NEC-4 software, so the following modeling exercise uses GNEC. Each radial is 1/4 wavelength long at 1.8 MHz. A wavelength at that frequency is about 166.6-m or 546.6' long, so the radials are each 136' long. Hence, the entire structure of the antenna itself, including the bent inverted-L legs, will fit well within the limits of the field, which is 272' from tip-to-tip.

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In the process of testing various constructs for the field, I confirmed the fact that a truly symmetrical arrangement of wires in a radial pattern does not need to have the same segmentation density of wires that do not result in mutually canceling fields. Hence, while the other portions of the array use a segment length of about 1', the buried ground plane structure uses only 25 segments per radial. I raised the number of segments per radial from 10 to 25 using a test 1/4-wl monopole, and the impedance change was minuscule: delta R was 0.02 Ohm and delta X was 0.05 Ohm. Further increases in the segments per radial seemed unjustified, although you can add a GC command and taper the segment lengths along the radial.

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Even with the sparse segment population, a 120-radial field requires 3000 segments to go with 120 wires or GW tag entries. Software having only GW or individual wire entry facilities thus results in very large model files, even before entering the upper portions of the antenna. However, NEC has two commands well worth using on this model:

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The WG or "write a numerical Green's function file" command allows us to separate the radial system portion of the model from the upper structure. By including the companion GF or "re-call a numerical Green's function file" in a separate model containing the upper portion of the structure, we can run the radial system once for a given frequency and use its output with any number of antenna structures. When the NEC core runs with the second file, it need not perform the entire set of matrix calculations over again, but calls up the results from the Green's file saved with an .NGF extension and combines them with the added structural elements in the new file. The result is a very great savings in run time, although the actual saving depends on the ratio of added segments to those handled by the initial model that created the Green's function file. In the present case, the radial system will use 3000 segments, but the additions will use no more than 530 more.

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A 3000-segment radial system, if composed solely of GW entries, would require considerable run time before it wrote the .NGF file. However, we can shorten that run time to something insignificant by using another available command. The GR or "rotational symmetry" command requires only the establishment of the first wire. Then, we simply specify that we wish a total of 120 structures at 3-degree intervals to arrive at a fully symmetrical and complete ground radial system. If nothing disturbs the symmetry, then we end up with a rapid-fire run. In fact, it required under 10 seconds on a 1.8 GHz PC.

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The following lines shows the radial portion of the antenna model at 1.8 MHz.

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+CM 160-m radial system: 1/4 wl long/radial, #12 wire
+CE
+GW 1 25 0 0 -1 0 136 -1 .00673
+GR 1 120
+GS 1 0 0
+GE
+FR 0 1 0 0 1.8 1
+GN 2 0 0 0 13.0000 0.0050
+WG radials.ngf
+EN
+
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The geometry section is a paradigm of simplicity, with only the first radial and the rotational symmetry commands. Since the dimensions are in feet, we need to add a scaling factor, which uses the automated feet-to-meters option available in NEC-4. The "plain" GE command and a more complex entry (GE -1 -1 0) yield the same results. The presence of a ground does not disturb rotational symmetry since the model makes no attempt to rotate the symmetrical structure from its initial orientation.

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The actual ground is the usual entry for average soil conditions, with a conductivity of 0.005 S/m and a dielectric constant or permittivity of 13. If you change either the frequency (set at 1.8 MHz) or wish to use a different set of ground conditions, you will have to make a decision. You may alter the entries in the model that writes the .NGF file and re-run an unchanged model with the added structure. Alternatively, you may save the results of changing the frequency or ground conditions under a different file name with the .NGF extension and make similar changes in the model with the antenna structure. Each .NGF file for the 120 radials uses about 1.7 MB of hard drive storage, which is greater than the sum of all other input, output, and temporary files combined for the model with the antenna structure, but still a very small file of its type.

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The alternative method of creating the radials would use the GM command.

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+CM 160-m radial system: 1/4 wl long/radial, #12 wire
+CE
+GW 1 25 0 0 -1 0 136 -1 .00673
+GM 1 119 0 0 3 0 0 0
+GS 1 0 0
+GE
+FR 0 1 0 0 1.8 1
+GN 2 0 0 0 13.0000 0.0050
+WG radials.ngf
+EN
+
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The GM command creates all of the necessary radials. However, it requires 320 seconds (on the same computer) to run and requires an .NGF file storage space of 141 MB. Those numbers represent 32 times the run time and 82 times the storage space of the GR version of the radial system.

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The corresponding antenna structure file that recalls the radial system results will have an appearance that depends on the complexity of the superstructure. The following model is for a test monopole that is full length, but still uses AWG #12 wire.

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+CM 160-m monopole over radials
+CM call radials.ngf
+CE
+GF radials.ngf
+GW 201 1 0 0 -1 0 0 0 .00673
+GW 202 1 0 0 0 0 0 1 .00673
+GW 203 131 0 0 1 0 0 132 .00673
+GS 1 0 0
+GE -1 -1 0
+EX 0 202 1 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
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The first structure entry is a call for the .NGF file contents. Then we add the monopole structure. GW201 is a 1' wire connecting the hub of the radials to the surface (Z = 0). GW202 is a 1' 1-segment wire from the ground up and serves as the source segment (see the EX0 entry). GW 203 handles the rest of the vertical monopole. In this case, the height worked out to exactly 1' per segment. Since the model that wrote the .NGF file uses 120 tag numbers, the antenna structure begins with a higher number. In this case, the number was chosen for easy tracking of more complex antenna structures above ground. Note the use of the more elaborate GE command to ensure that the model records that a ground plane is present, but that the current expansion should undergo no modification, since there are buried wires within the total structure.

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The model that calls and uses an .NGF file holds the excitation and radiation pattern requests. However, it contains no ground specification (GN) for frequency setting (FR). Those commands appear in the model that wrote the .NGF file. Since those specifications are necessary to both parts of the model and must be self-consistent, they begin life in the earlier model.

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Despite the fact that we have 3133 total segments in the monopole and its radial system, the model required under 1 minute to complete the calculations. This speed proved very useful, since a number of experimental heights were required before the antenna achieved near-resonance. The model showed a gain of 1.30 dBi at a take-off angle of 23 degrees elevation (theta = 67 degrees). The reported impedance for lossless wire was 36.028 - j2.021 Ohms. These values become reference marks for models of the Cuthbert version of the Star-H for 160 meters.

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Above the 1' above ground level, the new array requires 4 identical structures. For each leg of the array, there is a short (2') wire running horizontally away from center. Then there is a vertical section that I set at 50'. Next, there is another horizontal wire at the 50' level running 35' away from the vertical leg. Finally, we have a 45' wire running from the end of the previous wire toward the corner of the next structure.

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In some implementations of NEC, we would have to repeat the 4-wire set for each leg of the modified Star-H. However, implementations using the full command set allow us to simplify the set-up. The following model--using a single source of excitation--shows how we can minimize the number of GW entries.

+ 
+CM 160-m star-H over radials
+CM call radials.wgf
+CE
+GF radials.ngf
+GW 201 1 0 0 -1 0 0 0 .00673
+GW 202 1 0 0 0 0 0 1 .00673
+GW 203 2 0 0 1 0 2 1 .00673
+GW 204 50 0 2 1 0 2 50 .00673
+GW 205 35 0 2 50 0 35 50 .00673
+GW 206 45 0 35 50 32 3 50 .00673
+GM 10 3 0 0 90 0 0 0 203 1 206 45
+GS 1 0 0
+GE -1 -1 0
+EX 0 202 1 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
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It is possible to use the GR command in the antenna model. We would need to move the first two GW entries to follow the GR command, which applies to the structure as it departs the center line (X = Y = 0). GR will create the wires, but not use symmetry in the calculation. The GR version of the model has the following appearance.

+ 
+CM 160-m star-H over radials
+CM call radials.wgf
+CE
+GF radials.ngf
+GW 203 2 0 0 1 0 2 1 .00673
+GW 204 50 0 2 1 0 2 50 .00673
+GW 205 35 0 2 50 0 35 50 .00673
+GW 206 45 0 35 50 32 3 50 .00673
+GR 10 4
+GW 201 1 0 0 -1 0 0 0 .00673
+GW 202 1 0 0 0 0 0 1 .00673
+GS 1 0 0
+GE -1 -1 0
+EX 0 202 1 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
+

The use of GR in the upper portion of the antenna does not gain anything significant in terms of run time. Both models require just over 124 seconds to run. Because the bulk of the run time involves loading and processing the results of the 3000-segment .NGF file, the remaining 530 segments of new geometry require only a small part of the run time. To effect a significant saving of run time (apt perhaps to larger models than the present example), we would need to design the upper structure so that the GR command had no following GW lines.

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The single-feed version of the Cuthbert-modified Star-H reports a gain of 1.05 dBi (in both the GM and GR versions of the model) with an TO elevation angle of 25 degrees (65 degrees theta). The source impedance report is 13.183 + 0.548 Ohms. We may also provide the model with 4 separate feedpoint, using the first segment of GW 204 (and its counterparts, GW 214, GW 224, and GW 234). We do not change the model otherwise, since the feedpoints appear in series with the structure. Hence, they need completion to ground and use the same routes through GW201 and GW202 on the way to the radial system below ground.

+ 
+CM 160-m star-H over radials
+CM call radials.wgf
+CE
+GF radials.ngf
+GW 201 1 0 0 -1 0 0 0 .00673
+GW 202 1 0 0 0 0 0 1 .00673
+GW 203 2 0 0 1 0 2 1 .00673
+GW 204 50 0 2 1 0 2 50 .00673
+GW 205 35 0 2 50 0 35 50 .00673
+GW 206 45 0 35 50 32 3 50 .00673
+GM 10 3 0 0 90 0 0 0 203 1 206 45
+GS 1 0 0
+GE -1 -1 0
+EX 0 204 1 0 1 0
+EX 0 214 1 0 1 0
+EX 0 224 1 0 1 0
+EX 0 234 1 0 1 0
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+EN
+
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The 1.80-MHz performance report includes a gain of 1.10 dBi at a TO elevation angle of 25 degrees (65 degrees theta), and individual source impedances of 52.421 + j2.004 Ohms. Fig. 4 provides a comparison of the patterns of the two modified Star-H antennas (solid line) and the reference 1/4 wavelength monopole.

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The 2-degree difference in the TO angle and the 0.2-dB difference in gain is a function of the full-size monopole's greater length and the resulting current distribution. For high power BC application, the basis for the use of 4 feedlines lies not only in the lower losses associated with the higher impedances. As well, the system distributes the total source current among 4 feedlines, further reducing the stress on each cable due to heating. For local stations using power levels up to a few thousand watts, high power coaxial cables would likely serve well and avoid problems of routing and spacing from other objects that parallel feedlines involve. A carefully tuned 4-source system might easily avoid the use of any matching components at the individual sources, simply by "pruning" the 4 wires to achieve matching conditions.

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Even in amateur service, a 4-port coaxial system is usable, although amateurs operate across a span of frequencies within each assigned band. One advantage of the 4-source feed system is the simplicity of extending the 2:1 SWR range of the antenna while sustaining the lower losses of the higher impedance. The key is to adjust the height of the array so that the resistive portion of the impedance extends from perhaps 35 Ohms to perhaps 80 Ohms as we move the frequency above 1.8 MHz. The rate of change of the resistive portion of the impedance is about 8 Ohms per 100 kHz in the 50-Ohm region. The second part of the balancing act is to use a horizontal length that is slightly long at the lowest frequency. Then the antenna exhibits inductive reactance everywhere within the band. A series capacitor at each feedpoint can compensate for the reactance, leaving only a resistive impedance for the individual cables. The rate of change of the reactance is nearly 80 Ohms per 100 kHz and shows a nearly linear curve. Selecting a capacitor with a suitably wide range to match the reactance range to be compensated is both possible and feasible. The only update to this very old technique is that the remote capacitors require careful ganging and equally careful weather-proofing.

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At the equipment end of the 4 lines, you may change the impedance of each line to 200 Ohms using a 1:4 UNUN. The 4 higher impedances then require only parallel connection to match 50-Ohm equipment outputs and inputs. In more critical situations, such as BC service, where the exact pattern shape makes a licensing difference, the system must have means of ensuring that the balance of power is correct at the antenna terminals.

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These notes on matching systems are secondary to the main focus of this column: the use the NEC resources to produce the most efficient and effective model. By integrating a number of commands into a model, we produced a 120-radial system and an .NGF file that we can apply to an unlimited number of antennas. To modify the model for other frequencies, we need only make two small maneuvers. First, we would reset the frequency in the FR command. Second, we would change the length of the radial to suit the frequency and whatever other design specifications might be relevant to the project. Since the model invokes the rotational symmetry (GR) command, the radial revision effort requires a change to only a single GW entry. We might make the radial system one step more complex by entering a GC command following the single GW entry. In that command, we might length-taper the radial from the center outward so that the innermost segment has a length to match the depth of the field (1'). We may also change the size of the system simply by altering the angle and total number of structures within the GR command. The result is a model that runs extremely rapidly and requires minimal storage space for the resulting .NGF file.

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The antenna structure file that calls upon the radial system .NGF file is also compact. For symmetrical systems, we may create only one of the upper structures and use either the GM and GR command to replicate the initial structure the require number of times. In the present project, if we wished to alter the balance between the vertical and horizontal portions of the upper structure, we would need to enter only a single set of new coordinates. The GM command would replicate the first as many times as might be necessary to finish the task. In addition, the use of the .NGF file for the radial system shortens the run time between design revisions from somewhere in the 6- to 10-minute range down to 2 minutes on the PC used for this exercise. As a result, the entire design perfection procedure takes a matter of hours rather than days.

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There are other commands that we might have incorporated into our integrated model. For example, we might design and add a matching network to the single-source version of the model, using NT-command techniques explored in the two most recent columns. We can easily calculate the required components for a down converting L-circuit and from that point find usable entries of Y11, Y21, and Y22 in the 2-port NT command. By estimating the value of the coil Q, we can get a measure of the network losses. Of course, we may add into the final design a material loading value (LD5) for both the radials and the upper antenna structure.

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Antenna modeling, then, is not just a matter of learning the terms of each command. It is also a matter of learning to see opportunities for integrating the commands into a model (or, in this case, a pair of models) so as to yield the most effective combination that will minimize unnecessary work (as well as work time) and maximize flexibility. Since these tasks tend to be task specific, there is no single general rule that will cover all cases. Rather, there are only case studies--like the present one--that may alert you to the possibilities. At that point, your own ingenuity must take over.

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Go to Main Index

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98. Planar Reflectors: Wire Grid vs. SM Patches

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L. B. Cebik, W4RNL

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In previous episodes of this series, we have by-passed one set of geometry commands: SP, SM, and SC. These commands are not available on the most popular entry level commercial versions of NEC-2 (such as NEC-Win Plus and EZNEC), although other versions of NEC-2 that a beginning or intermediate modeler might use (such as NEC2GO and 4NEC2) do allow access to the complete NEC-2 command set. In general, SP and SM, along with necessary extensions via SC, create surface patches and are found in specific advanced modeling problems tackled by relative advanced modelers using such programs as NEC-Win Pro, GNEC, or custom versions of NEC-2 and NEC-4.

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However, a number of applications of SM (and its necessary extension card, SC) have begun to appear. For example, I have recently seen planar reflector and UHF horn models employ the SM command. Therefore, it may be useful to explore the simplest of the surface patch commands in order to grasp some of the requirements, advantages, and limitations of using it.

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Surface Patch Basics

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We create a surface patch with the SM command by defining its corner coordinates. The more general SP command permits a range of specific regular patch shapes, such as triangular, rectangular, and quadrilateral geometries, as well as a shapeless patch description. Wherever the specification of X, Y, and Z coordinates exceeds the 6 floating decimal places in a NEC-2 command line (unchanged in NEC-4), we must add an SC command to complete the coordinates. In addition, SP allows a succession of SC cards to complete complex structures with relative efficiency.

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SM is a simpler command. It creates only a rectangular patch, but that patch consists of a user-specified number of patches defined in terms of the number of patches for both width and height. The SM command allows only the single SC command necessary to complete the coordinate entry. The following sample command lines provide an example of SM/SC structure.

+ 
+Cmd   I1                I2                 F1    F2     F3     F4     F5     F6
+      # Patches-Width   # Patches-Height   C1-X  C1-Y   C1-Z   C2-X   C2-Y   C2-Z
+SM    12                12                 0.    -.6    -.6    0.     .6     -.6
+
+Cmd   I1        I2        F1    F2    F3
+      Not Used  Not Used  C3-X  C3-Y  C3-Z
+SC    0         0         0.    .6    .6
+
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Defining a rectangular shape requires that we define three consecutive corners of the rectangle. Hence, we must use the SC entry for the third corner (C3), while the coordinates for the first two corners (C1 and C2) appear in the SM command. The integer entries of the SC card are unused and hence receive automatic zeroes. However, the integer entries of the SM command specify how many patches will exist along the width and height of the overall patch. For purposes of modeling, "width" means the line between corners 1 and 2, while height means the line between corners 2 and 3, regardless of the actual orientation of the patch within the Cartesian coordinate system.

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We can find the fundamentals of using patches within the NEC-2 and NEC-4 manuals. The patch "formulation uses the Magnetic Field Integral Equation [MFIE], and is restricted to closed surfaces with non-vanishing enclosed volume. It is not applicable to a conducting plate or shell of zero thickness." Essentially, proper use of surface patches requires modeling the entire volume, even of a thin plate. "Theoretically the MFIE can be used for a thin box or cylinder, but the solution may become inaccurate due to the decreasing condition number of the matrix and the simple point matching and pulse current expansion used in the solution in NEC."

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"As with wire modeling, patch size measured in wavelengths is very important for accuracy of the results. A minimum of about 25 patches should be used per square wavelength of surface area, with the maximum size for an individual patch about 0.04 square wavelengths." For a square patch, these terms translate into a minimum of about 5 patch widths per wavelength of edge dimension. A higher patch density up to reasonable numbers is usually desirable.

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"In general, the use of surface patches is restricted to modeling voluminous bodies. The surface modeled must be closed since the patches only model the side of the surface from which their normals are directed outward." See Fig. 1 for a simplified representation of a surface patch and its outward-directed unit normal vector. The arrow represents the outward-directed normal, the foundation for patch calculations. The complete NEC output file contains in the early geometry section a listing of surface patches created by an SM command. Included in the listing are the "COMPONENTS OF UNIT TANGENT VECTORS." The patches also have a current distribution table.

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The NEC manual also points out that "if a somewhat thin body, such as a box with one narrow dimension, is modeled with patches, the narrow sides (edges) must be modeled as well as the broad surfaces. Furthermore, the parallel surfaces on opposite sides cannot be too close together or severe numerical error will occur." The manual also strongly suggests that models employing new shapes be compared to experimental outcomes in order to establish the validity of the patch modeling.

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Since we shall not use the SP command itself or attempt to attach a wire directly to a patch structure, we may use these extracts from the manual notes as a basis for our next steps into the use of SM commands.

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Planar Reflectors: Wire-Grid or SM Patches

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Let's begin our efforts with a single dipole that uses a planar reflector to provide directivity, that is, gain and a usable front-to-back ratio. The general outline--shown only in a facing view--appears in Fig. 2. The dipole is resonant at 300 MHz and the reflector dimensions are 1.2 by 1.2 meters (or wavelengths).

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The reflector consists of 12 units both horizontally and vertically. Ordinarily, we would construct the reflector with a wire-grid structure. The maximum length of each wire segment in the grid is 0.1 wavelength, and the wire diameter is the cell-wire length divided by PI. The radius is half this value, 0.0159 meter (or wavelength). The following model captures these elements.

+ 
+CM Dipole .175 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.2 m;  Z = 1.2 m
+CM standard wire-grid:  Seg L = 0.1 m; redius = L/PI = 0.0159 m
+CE
+GW 1 12 0 -.6 0 0 .6 0 .0159
+GM 1 6 0 0 0 0 0 -.1 1 1 1 12
+GM 1 6 0 0 0 0 0 .1 1 1 1 12
+GW 12 12 0 0 -.6 0 0 .6 .0159
+GM 1 6 0 0 0 0 -.1 0 12 1 12 12
+GM 1 6 0 0 0 0 .1 0 12 1 12 12
+GW 24 11 .175 0 -.218 .175 0 .218 .004
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+EX 0 24 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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The geometry entries up to but not including GW 24 define the planar reflector. You can simplify the structure, but the present model is one of a system of planar reflector models having a uniform horizontal and vertical center line set. Hence, the necessary wire replications occur on each side of these center wires.

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The technique being applied to patch versions of the planar reflector is interesting because it directly violates the manual recommendation that requires the modeling of the reflector as a closed geometrical shape with volume. The operative theory behind the use of patch-based reflectors is that the surface is a perfect tangential reflecting surface. Hence, on this account, we need not be concerned with the remaining 5 surfaces of the reflector, but may deal only with the surface facing the driver element (or elements, in more complex planar reflector arrays).

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If we accept this account, then we may replace the wire-grid structure with a simpler array of patches. The corresponding surface-patch or SM version of the model has the following appearance.

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+CM Dipole .175 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.2 m;  Z = 1.2 m
+CM SM patch: 10 patches/meter
+CE
+SM 12 12 0. -.6 -.6 0. .6 -.6
+SC 0 0 0. .6 .6
+GW 24 11 .175 0 -.218 .175 0 .218 .004
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+EX 0 24 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+
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We may enter the patch lines manually or use such help screens as may be available. The following sample help screen from GNEC allows entry of all of the 3 corner coordinate sets on one screen and it then creates both the SM and SC lines necessary for the NEC input file. The sample entries in Fig. 3 apply to a model that we shall examine a little further on in this discussion.

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Our fundamental question is how well the wire-grid and SM reflectors track each other. The answer to this question depends on how accurate the SM assumption is, namely, that the only relevant outward-directed normal vector for a planar reflector is from the surface directly facing the driving element(s). One way to approach that question is to overlay the resulting E-plane (theta) and H-plane (phi) patterns for the array. See Fig. 4. Note in the models that the driver dimensions and the driver spacing from the reflector do not change between models.

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In the forward direction, there is no major difference, although the dashed lines for the wire-grid model show a slightly higher gain. The key differences lie in the rearward structure. In the theta pattern especially, the patch reflector does not show the full development of the quartering rearward sidelobes and may give an erroneous impression of the worst-case front-to-back ratio.

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Nevertheless, the simple models used here suggest that the two types of reflectors are viable alternatives for at least preliminary modeling. I ran both models through a small range of reflector sizes, varying the width from 1.0 m to 1.4 m and then the height through the same range. The wire grid model shows a distinct peak using the 1.2 by 1.2 meter reflector. The following table compares the results for both the wire-grid and the patch reflectors. In the model designations, H means the horizontal reflector length at right angles to the dipole, while V means the vertical reflector length parallel to the dipole.

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The gain for the SM-patch 1.2 by 1.2 reflector is also the highest value among the set. However, the gain change from one reflector vertical width to the next, for a given horizontal length, is not as great as with the wire-grid models. The shallowness of the patch curves shows up clearly in Fig. 5.

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The gain values used in the table are corrected for the average gain test (AGT). For the patch models, the AGT values ranged from 0.974 up to 0.989. In contrast, the wire-grid models had AGT values of about 0.998 or better (where 1.0 is perfect, since the test was run with free-space models with no resistive losses). The AGT scores, plus an understanding of the ways in which using the SM-patch reflector violates the prescribed handling of patch constructs, strongly suggests that the SM-patch reflector models are secondary in precision to the wire-grid variety.

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Nevertheless, the SM-patch models do afford reasonable first approximations of planar reflector results from wire-grid reflectors. They run about 4 times faster than wire-grid reflectors, and the input files are somewhat simpler.

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Patch density within the SM/SC command lines does make some difference in the output reports. To check this aspect of the patch reflector, I varied the patch density of the basic 1.2 by 1.2-meter (wavelength) reflector from 10 patches/meter up to 15 patches/meter (with added check values of 6 and 20 patches/meter). The following table summarizes the reported values.

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+  Variations in Performance Reports Due to Variations in Patch Density
+            Reflector: 1.2 by 1.2 Meters (Wavelengths)
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+Patches/     Reported   Front-to-Back   Impedance         AGT      AGT-
+1.2 Meter    Gain dBi   Ratio dB        R+/-jX Ohms                dBi
+ 6           9.12       18.98           50.85 - j1.65     0.966    -0.14
+10           9.14       19.11           50.03 - j1.72     0.975    -0.11
+11           9.14       19.13           50.00 - j1.70     0.976    -0.10
+12           9.13       19.16           50.00 - j1.70     0.976    -0.11
+13           9.13       19.17           50.00 - j1.67     0.976    -0.10
+14           9.13       19.18           49.99 - j1.66     0.976    -0.10
+15           9.13       19.19           49.99 - j1.65     0.976    -0.10
+20           9.12       19.22           49.98 - j1.63     0.976    -0.10
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The significance of these variations depends on the uses to which we try to put the SM patch reflector models. The patch density of 10 per dimension is about 3 times the recommended minimum per unit area as measured in wavelengths. As a result, changes from one step to the next are small. As we increase the patch density above 10.dimension, gain decreases very slowly, while the front-to-back ratio increases at an equally slow rate. Increasing patch density has very little effect on the AGT value for the model.

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While these facts are significant to the understanding of how SM-patch reflector models tend to respond to changes in the reflector geometry commands, they do not yield results that would impact a design or analysis situation. Given that SM-patch planar reflector models are at best first approximations of more accurate but more complex wire-grid models, we may consider the models fully converged at a patch density of 10 patches per linear wavelength.

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Corner Reflectors: Wire-Grid or SM Patches

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The SM-patch planar reflector illustrates the use of a single patch structure that simulates a single physical (conductive) plane structure. The SM/SC command set has also been used to simulate more complex structures, such as horns. Hence, the structure requires the use of multiple SM/AC command pairs to include all planes of the structure. In each case, the operating presumption (assuming that the modeler has appreciated the restrictions on the use of patches) is that the single outward-normal unit vector of the incomplete volume provides an adequate basis for the modeling effort.

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We may test a multiple-SM structure using one-sided techniques with a model far simpler than a horn. A corner reflector of conventional design consists of 2 identical planes joined along one edge, usually called the apex. The angle between the planes is conventionally 90 degrees, although other angles are both feasible and desirable if we wish to optimize the gain potential of the array. Fig. 6 outlines the basic construction of the corner array using a single dipole driver, regardless of whether we employ a wire-grid or an SM-patch model for the reflector surfaces.

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Our purposes involve only comparing one form of modeling with another, so we may select smaller reflector planes as illustrative models. In fact, each of the two reflector planes will consist of 1.0 by 1.0 meter wire or patch grids. Since the test frequency remains 300 MHz, the use of 10 units per linear dimension of the planes will yield 10 segments or 10 patches per wavelength. The wire-grid version of the model has the following appearance.

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+CM Dipole .324 m from corner reflector
+CM Basic Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM T1 = center line, T2, T3 = verticals + GM
+CM T4, T5 = horizontal centers + GM
+CM Density = 0.1 m x 0.1 m
+CM Size = 1.0 m x 2.0 m
+CE
+GW 1 10 0 0 -.5 0 0 .5 .0159
+GW 2 10 0 -.1 -.5 0 -.1 .5 .0159
+GM 0 9 0 0 0 0 -.1 0 2 1 2 10
+GW 3 10 0 0 0 0 -1 0 .0159
+GM 0 5 0 0 0 0 0 -.1 3 1 3 10
+GM 0 5 0 0 0 0 0 .1 3 1 3 10
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 4 10 0 .1 -.5 0 .1 .5 .0159
+GM 0 9 0 0 0 0 .1 0 4 1 4 10
+GW 5 10 0 0 0 0 1 0 .0159
+GM 0 5 0 0 0 0 0 -.1 5 1 5 10
+GM 0 5 0 0 0 0 0 .1 5 1 5 10
+GM 0 0 0 0 -45 0 0 0 4 1 0 0
+GW 101 11 .324 0 -.2119 .324 0 .2119 .004
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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The CM lines show some of the particulars of the structure, including the dipole distance from the apex of the corner reflector. This value will not change when we arrive at the SM/SC version of the model. As with the planar wire-grid reflector, the reflector plane modeling uses a horizontal center wire line in order to be able to change with ease the vertical height of the reflector, adding the same amount to the top and bottom. The vertical wires begin with an apex wire and an initial wire on each side of the apex. Then the initial side wires are replicated the proper number of times to arrive at the horizontal dimension for each plane. Of course, we rotate each plane 45 degrees to yield the 90-degree final angle. From the dipole (GW 101) onward, the model is straightforward. Note that the comment on reflector size gives the total size of the pair of reflector planes as if they were laid out in a single plane.

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The SM/SC version of the corner reflector is deceptively simple.

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+CM Dipole .324 m from corner reflector
+CM Basic Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM SM panels
+CM Density = 0.1 m x 0.1 m
+CM Size = 1.0 m x 2.0 m
+CE
+GW 1 11 .324 0 -.2119 .324 0 .2119 .004
+SM 10 10 0 0 -.5 .7071068 .7071068 -.5
+SC 0 0 .7071068 .7071068 .5
+SM 10 10 .7071068 -.7071068 -.5 0 0 -.5
+SC 0 0 0 0 .5
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+EX 0 1 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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As we might expect, the same corner reflector requires only 2 SM/SC entry pairs to form the reflector planes. Of course, we must do some initial calculations to establish the corner points for each of the two planes so that each one is 45 degrees each side of the X-axis for this model. The only change to the dipole is to give it a tag number of 1, since there are no other wires in this version of the corner reflector.

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However, the SM/SC entries deserve a bit closer attention. From the perspective of model symmetry, they do not use the same set of corners. However, from the perspective of patch construction, they do. Fig. 7 illustrates the "right-hand rule" according to which we need to construct joining patches.

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If we do not adhere to the right-hand rule, the resulting patterns yielded by the overall model will lead us to conclude that we cannot construct single-surface SM/SC corner reflectors at all. When properly constructed, the SM/SC model will produce comparable but not identical results relative to the wire-grid version of the array. Fig. 8 provides an overlay of the theta (E-plane) and phi (H-plane) patterns for the subject structure.

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As with the single planar reflector, the SM/SC corner reflector does not show very significant differences in the forward gain. Rather, the key difference is that the SM/SC construct does not show the full development of the rearward lobes. Due to the operation of the corner array, there are also differences in the reported beamwidth, especially in the phi (H-plane) pattern. The following table shows the differences in numerical terms.

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+       Variations in Performance Reports of Wire-Grid and Patch-Based Corner Reflectors
+                    Each Reflector Plane: 1.0 by 1.0 Meters (Wavelengths)
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+Version     Reported   Front-to-Back   E-plane     H-plane     Impedance         AGT      AGT-
+            Gain dBi   Ratio dB        Beanwidth   Beamwidth   R+/-jX Ohms                dBi
+Wire-Grid   10.98      26.57           56 deg.     48 deg.     49.94 + j0.14     0.999    -0.01
+SM-Patch    10.75      24.15           56          52          47.37 - j1.65     0.970    -0.13
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As was the case with the single plane reflector, the corner reflector shows a significantly lower AGT value than we obtain for the wire-grid model. If we correct the gain value, it climbs to 10.88 dBi, somewhat closer to the wire-grid model value. However, using the AGT to correct the resistive portion of the source impedance results in 45.95 Ohms, a value that is further distant from the wire-grid value. Increasing the source resistance would require increasing the distance of the dipole from the reflector apex, which might correspond roughly to the radius of the wires in the wire-grid reflector.

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Nevertheless, due to the fact that single-sided SM-SC planes can only partially simulate the operation of a physical structure, we must treat the SM-patch version of the corner reflector as a first approximation. It has the advantage of faster run times and simpler input models, but it does show lower AGT values and deficiencies in the development of certain parts of the array pattern, relative to wire-grid models.

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Because the SM-patch reflector model is based on the assumption that only a single plane surface is relevant to array performance, the SM/SC model of plane reflective surfaces will always have limitations. First, it cannot apply at all to any array in which the assumption is not close to being correct. Second, as we have seen, even where the assumption is close to being correct, it is rarely if ever precisely correct.

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However, as a speedy method of constructing first approximations of arrays and arriving at reasonable performance values, one-sided SM/SC planar surfaces have a useful role to play in some modeling enterprises. They can play that role well so long as we remember that the world of multiple surface patches is right-handed.

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Go to Main Index

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99. S-N, RCA, and MININEC Grounds

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L. B. Cebik, W4RNL

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We have in past episodes discussed the ground calculation systems associated with the most common antenna modeling cores, MININEC and NEC. A development in one of the commercial MININEC packages (Antenna Model) brings those ground calculation systems back into focus.

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The Basic or Native Ground Calculation Systems

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The MININEC ground calculation system is perhaps the most rudimentary, since its development paralleled the original intent of MININEC: to offer reasonably accurate round-wire antenna modeling in a Basic package that would run on early PCs with very limited RAM and disk storage. Over the years, the latest public domain version of MININEC (3.13) has undergone various degrees of modification to achieve two major goals. One aim of redevelopment was to extend the 128-segment and later 256-segment limit for models. Conversion of the package to a Windows format and a compatible programming code system has yielded MININEC versions with almost unlimited segments, although almost all such packages make their core runs more slowly than the compiled FORTRAN that is common to most NEC packages. The second goal was to correct some of the modeling weaknesses that included an error that increased with frequency, problems with very close-spaced wires, and potential errors associated with angular structures. Various software packages have addressed individual limitations, but Antenna Model has achieved the most thorough set of correctives.

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Perhaps the one enduring feature of MININEC that resisted alteration for the longest period is the ground calculation system. As far back as 1991, Roy Lewallen, W7EL (author of ELNEC and EZNEC programs) provided careful warnings about the use of the MININEC ground calculation systems with horizontal wires closer to ground than about 0.2 wavelength. (See "MININEC: The Other Edge of the Sword," QST, Feb., 1991.) Since then, warnings have emerged concerning errors ranging from small to large with sloping wire constructs where one end is at ground or close to ground. These constructs have a horizontal component and to that degree suffer the MININEC ground calculation limitation. Vertical wires do not have the same limitation as horizontal wires. When a vertical wire touches the ground, it will return a plausible antenna pattern and gain report. However, the source impedance does not change with changes in the assigned ground quality. Rather, MININEC always returns the source impedance over perfect ground. Hence, it is not possible to track variations of source impedance due to ground losses with the MININEC native ground calculation system. If the modeler constructs radials, then all wires must be above ground, and the radials are subject to the horizontal-wire limitation that we have already noted.

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NEC (both -2 and -4) offer two real-ground calculation systems. The use of 2 separate systems results again from the early days of slower computers. The Reflection Coefficient Approximation (RCA) system produces faster core run times, but it suffers from a minimum height restriction for horizontal wires. Various sources give different values for the recommended minimum height above ground, ranging from 0.1 to 0.2 wavelength. The error introduced into horizontal wires below the recommended limit does not follow the same trends as MININEC ground calculation errors under the same circumstances. Vertical wires touching the ground also produce errors. However, NEC's RCA system does have a mode of operation that simulates ground radial systems using the number of radials and radial length specified by the user. It is available only in packages that make the full set of NEC commands available. Like the MININEC ground calculation system, the RCA system in the radial mode produces plausible patterns and gain reports. However, it responds to differences in the ground quality and the number and length of radials. Still, in this mode of operation, the RCA system returns source impedance reports based on perfect-ground or image calculations.

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The second NEC ground calculation system is usually called the Sommerfeld-Norton (S-N) system. It runs more slowly than the RCA system, but that factor has largely become a superfluous concern with the speed of modern PCs. With respect to horizontal wires, the S-N ground calculation system provides accurate gain and source impedance reports with wires very close to ground. If h is the height above ground in wavelengths and a is the wire diameter in wavelengths, then the closest approach to ground for a wire (in wavelengths) should be as follows:

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+ If a is very small relative to h, then we may use the recommended closest approach for the height alone. +

With respect to vertical wires, the S-N ground calculation system suffers the same limitation as the RCA system. Vertical wires touching the ground will yield erroneous results. As a result, models dealing with vertical monopoles and arrays based upon them must construct radial systems in accord with other limitations of their NEC core. For NEC-2, all wires must be above ground, although with the S-N ground calculation system, the vertical and radial wires may approach the ground in accord with the recommended equation. In NEC-4, we may model buried radials. Radials may converge below ground or may have sloping sections that converge above ground. In either case, a wire that passes Z=0 may do so only at a segment or a wire junction.

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Packaged Ground Calculation Systems

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Most antenna modeling packages provide the user with the ground calculation systems native to the core used in the package. MININEC packages provide the user with the MININEC ground. NEC-2 and NEC-4 packages make the S-N and RCA ground calculation systems available. However, there are 2 known exceptions to this general trend.

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EZNEC (in all its version-4 forms: regular, Plus, and Pro) gives the user a choice between the S-N and the MININEC ground systems with either the NEC-2 or NEC-4 cores. The premises behind this set of options are straightforward. First, modern PCs do not need the speed advantage that was once a main reason for using the RCA system. The time saved between ground calculation systems at the original PC CPU speed of 2 MHz was significant, but almost undetectable with current 2 GHz CPUs. S-N system calculations can still be saved to a file to free the RAM in successive runs for mutual impedance and currents calculations, but current RAM capabilities have largely obviated the need for this step. Therefore, for all antenna models with horizontal components, the S-N ground calculation system's greater accuracy dictates its use.

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Second, there are still a number of modeling applications in which the user will wish to connect a vertical wire directly to ground without employing a radial system. Preliminary performance comparisons of various sorts become highly efficient using this technique. However, neither the S-N nor the RCA systems return plausible results in NEC using this technique, especially with respect to the source impedance. Although less than perfect relative to models using buried radial systems in NEC-4 plus the S-N system, a MININEC ground provides quite reasonable values for initial comparisons, along with the source impedance that applies to the use of a perfect ground.

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There is a qualification that we must note on this account. The RCA system, when set up for buried radials, would offer the advantages for initial comparisons with a MININEC ground, with the added advantage of showing some sensitivity to the conditions of the radial field. However, the set-up for this option involves a somewhat interesting relationship between the ground specifications command and the pattern request command. The ground specification command is divided between 2 possible commands, GN and GD.

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If the GN command's I2 (NRADL) entry is greater than zero, then you must use the GD command to enter a second medium. If NRADL is 1 or more, then the meanings of F3 through F6 change from a more basic set-up of the command. Let's see what happens to the GN command under these conditions.

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+Cmd   I1     I2     I3   I4   F1    F2    F3    F4    F5    F6
+      IPERF  NRADL  0    0    EPSR  SIG   RADS  RADW  --    --
+GN    0      8      0    0    13    .005  .237  .001
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I2 shows a request for 8 radials. The single-medium ground quality values go into F1 and F2 as always. However, F3 and F4 have new meanings. RADS is the radius of the screen, or the length of the individual radials in the screen. RADW indicates the radius of the individual wires composing the set of radials. Both values are in meters.

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In NEC-2, the RP command must have an I1 assignment of 4 for a simple set of radials. If there are GN and GD commands requesting both a screen and a second medium, then the NEC-2 RP command must let I1 = 5 for a screen and a linear cliff or let I1 = 6 for a screen and a circular cliff. NEC-4 uses I1 = 0 in the RP command for all these cases, since the type of cliff will be set in the GD command. NEC-4 will read a NEC-2 model with only a screen request by treating the RP4 request as RP0.

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The radial screen option in the GN command applies only to the RCA real ground type (I1 = 0) and is not allowable with a request for an SN ground (I1 = 2). The calculations are based upon a modified reflection coefficient, and the resulting source impedance report will be the same as for a perfectly conducting ground (I1 = 1). Despite this limitation, the system is more versatile than simpler ground systems (such as those used with MININEC cores), since it will show differences in far-field patterns due to changes in the ground quality and changes in the number of radials.

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As currently implemented, EZNEC has no provision for setting the RP pattern request command to the values required by the RCA ground radial set-up. Hence, the facility that the program makes available for verticals without modeled wires for a radial system is the MININEC ground. Packages that make the complete set of NEC-2 or NEC-4 commands available to the user may substitute the RCA ground radial set-up for the MININEC ground calculation system for initial comparisons of vertical antennas and arrays.

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Special Note: As with all comments on the current capabilities of an existing program, the notes are believed to be accurate as of the time of writing. However, software developers tend to continuously upgrade and modify their offerings. Hence, what is true at the time of writing may prove to be outdated by the time of publication.

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The second package to provide the user with non-standard ground calculating systems is a version of MININEC: Antenna Model. We have noted on more than one occasion that this package provides the most thorough set of correctives to the shortcomings of the raw MININEC version 3.13. As noted in previous columns, for comparable models, Antenna Model's MININEC core tracks very well with NEC-4. As well, MININEC offers the added advantage of showing no limitations wherever we have junctions (angular or linear) of wires having different diameters. However, like other MININEC offerings, Antenna Model lacks some features that are standard in NEC, such as the TL transmission-line and the NT network facilities.

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Antenna Model shared one limitation with all versions of MININEC: the use of the MININEC ground calculation system. However, the software developers found a way the graft both the RCA and the S-N ground calculation systems to their MININEC package. Hence, with two qualifications, Antenna Model offers the same ground calculation advantages as NEC. The first qualification is that MININEC is like NEC-2 in that all wires must be above ground level. Second, MININEC offers no provision for setting up the complex interaction of commands that allows the RCA ground calculating system to add radials. Hence, the chief benefit of the addition of NEC ground calculating systems to the Antenna Model MININEC package lies in the realm of an improved ability to handle horizontal or slanted wires close to the ground. For example, Antenna Model is the only MININEC offering that is capable of producing accurate models of NVIS antennas that ordinarily have one or more wires within 0.2 wavelength of the ground.

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Some Comparisons

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Whenever we encounter a new modeling program feature, we should make a set of test runs in order to establish whether or not the claimed specifications of the feature are as accurate as we need for our work. The exact dividing line between acceptable and unacceptable will, of course, vary with the specifications for the modeling work that we do.

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Since the addition of the NEC ground calculating systems to MININEC in Antenna Model benefit low-lying horizontal wires the most, I set up a series of small tests, of which the following one is an example. I created a simple dipole for 29.97925 MHz, where a wavelength is exactly 10 meters. I used 31 segments for a NEC-4 model and 30 segments for the corresponding MININEC model. The dipole used a perfect or lossless wire with a diameter of 1 mm. With a length of 0.485 wavelength (4.85 meters), the model produced resonant dipoles in free space on both NEC-4 and MININEC. Resonance here means a remnant reactance of under +/-j 1.0 Ohm. The source impedance in NEC-4 was 71.99 - j0.43 Ohms, while in Antenna Model's MININEC, the source impedance was 71.84 -j0.56 Ohms. The differences fall well within what we would expect with a simple 1-segment change in segment density. The change, of course, reflects the difference in the position of the source relative to the segments themselves (MININEC at a junction, NEC within a segment). In both cases, the free-space gain was 2.14 dBi.

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With this model, I then created all of the ground calculation system variation that I might compare, using the so-called "standard" or "average" ground quality: conductivity: 0.005 S/m, relative permittivity: 13. I then set the dipole at a series of heights, beginning at 0.5 wavelength above ground. Each successive step brought the antenna 0.05 wavelength closer to ground down to a height of 0.05 wavelength. To simulate the closest approach to ground permissible, I set the final step at 0.001 wavelength above ground. The values for this height appear in the tables, but not in the graphs, since the increment is not linear and since some of the values would have obscured variations among the other steps in the sequence. Fig. 1 outlines the test set-up.

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The first test directly compared the Antenna Model MININEC use of the S-N system against the NEC-4 version of the antenna. The NEC-4 test employed EZNEC Pro/4, but there is no detectable difference among the core outputs of NEC-4 offerings. Indeed, running the same NEC-4 compiled Fortran core on different CPUs and operating systems generally shows a wider variation in results than running two different NEC-4 cores on the same CPU and operating system.

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Table 1 shows the results of the test. From 0.5 wavelength down to 0.05 wavelength, the correlation of results is as exact as we may expect from models with slightly different segmentation densities. The only variant result is the source impedance at a height of 0.001 wavelength (1 cm). Antenna Model certifies its results only to 0.01 wavelength, although the variance in source impedance is only about 7% at 1/10 the minimum recommended height of use. For all practical cases, Antenna Model's MININEC with the S-N ground is the equal of NEC's results with the S-N ground calculating system.

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Since Antenna Model also implements the NEC RCA ground calculation system, we might as well perform the same set of modeling steps using it. However, we cannot find our NEC-4 counterpart models in EZNEC. So this set of models uses NSI's GNEC. See Table 2. Note that the correlations between both the gain and the impedance reports are quite tight down to a height of about 0.2 wavelength. Then we see a drifting apart of values that becomes more extreme from 0.1 wavelength down to the minimum height. For reasons that we shall see shortly, it is unlikely that we would uses this ground below 0.2 wavelength for horizontal wires, so the divergence of reported values between the NEC-4 and the MININEC cores is more artifactual than significant.

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We can find the MININEC ground calculation system both in the MININEC-based Antenna Model and in the NEC-4-based EZNEC Pro/4. Therefore, we might as well complete the picture by comparing the reports for the same set of models using what most experts consider to be the least adequate system for horizontal wires. In fact, as shown in Table 3, the two cores yield as close to identical results as we can expect from the models involved, given the slight difference in segment density. The numerical differences between the MININEC ground results and the RCA ground results suggest that, while both use reflection coefficient approximations, they do not operate in exactly the same manner. The fact that the MININEC ground yields the same results whether attached to NEC-4 or to MININEC, while the RCA ground does not, is another indicator of differences between the two fast-running ground calculation systems.

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There are alternative ways of viewing the same data. For example, we can compare in NEC-4 the reported gain values for both the S-N and RCA ground calculation systems. Fig. 2 connects the data dots, omitting the values for a height of 0.001 wavelength.

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The chart shows that below 0.2 wavelength, the RCA system supplies gradually inflated gain values for the horizontal wire gain values. This is the same height at which we found some divergence between the NEC-4 and MININEC reported gain values and represents a rough limit for the reliability of the RCA system. Fig. 3 shows the corresponding source resistance information over the same range of wire heights.

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At 0.2 wavelength wire height, we find the same divergence of S-N and RCA values. However, there is a fair tracking down to 0.1 wavelength. At that point, the RCA source impedance reports continue downward, while the S-N values turn upward. This divergence has caused some users to consider 0.1 wavelength to be the minimum usable height for RCA ground calculation system results. However, if you examine Table 1 and Table 2. you will see that the NEC-4 reports for the lowest height show a lower source resistance for the RCA system than for the S-N system. The indication is that the turn upward in source resistance occurs at a lower height in the RCA system than in the S-N system. The net result is that the safest position at which to limit the use of the RCA system with horizontal wires is about 0.2 wavelength above ground.

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Since 2 out of the 3 ground systems available in the Antenna Model implementation of MININEC are "imports," we might as well include all three systems in graphing the gain and source resistance reports. Fig. 4 compares the three reported values drawn from the right-hand columns of the 3 tables. Once more, I have omitted the lowest height, since it is not a linear increment and because its values would obscure changes in other values in the graph.

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The S-N and RCA lines track well down to a height of 0.2 wavelength. The RCA terminal value at 0.05 wavelength is lower than for its counterpart using NEC-4, as shown in Table 2. However, the split from the S-N reported value sets 0.2 wavelength as a practical limit for using the RCA value. The major surprise may lie in the comparison of the S-N and RCA curves on the one hand and the MININEC ground curve on the other--throughout the complete range of values. Except for a coincidence of gain report at 0.5 wavelength, the MININEC ground curve diverges from the two other curves all along the range of heights, describing a shallow parabola. The coincidence of values near 0.2 wavelength is mostly coincidental, since the upward progression at heights below that level is a simple continuation of the questionable curve across its entire range from 0.5 wavelength downward.

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The graph of source resistance values in Fig. 5 shows a similar curve, but reversed. The inflation or deflation of source resistance values, relative to the S-N and RCA curves, is inversely proportional to the gain divergence. Hence, the MININEC ground system reports the highest gain values with the lowest source resistance values. In the end, for horizontal wires below 0.5 wavelength, the MININEC curves suggest that the formulation of the ground calculation was likely crude, over-simplified, or hasty, if not some combination of all three. That Antenna Model has grafted the S-N and RCA systems to its implementation of MININEC (especially when combined with its extensive correctives for most of the other MININEC weaknesses) provides the user with more assured results for any antenna structure having horizontal wires below 0.5 wavelength. The only redeeming function of the MININEC ground system is its ability to handle vertical antennas and arrays without demanding a radial system for at least initial comparisons. However, implementing the RCA radial command would allow the removal of the MININEC system altogether. This last remark, of course, is made with total ignorance of the programming difficulties that might be involved.

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As a final reminder, we might also attend to Fig. 6. Each of the sloping wires has a horizontal as well as a vertical component. Hence, using either the MININEC or the RCA ground calculation systems, we shall encounter errors in both the gain and source impedance reports when part or all of the structure is below 0.2 wavelength. The error will be proportional to a. the amount of the wire that is below 0.2 wavelength and b. the relative preponderance of the horizontal component relative to the vertical component. This factor is often ignored by modelers of complex vertical arrays that may use sloping (guy) wires as active elements, whether directly or parasitically excited. Ignoring this situation imperils accuracy of the results.

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+ +
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MININEC is still widely used by numerous antenna modelers, especially since very cheap or free software using the core is readily available. However, not all public-domain MININEC implementations are equal. Indeed, the extensive modifications of the core--and now the ground calculating system--within Antenna Model almost remove it from the realm of MININECs except as a record of its genetic heritage.

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Of course, Antenna Model is limited in the same manner as NEC-2: all wires must be above ground. For the most accurate round-wire modeling of arrays using buried radials, NEC-4 remains the core of choice. Nevertheless, the addition of the S-N and RCA ground systems within Antenna Model has given us a good occasion on which to compare low horizontal wire results for all of the extant ground calculation systems. Those comparisons are the main focus of these notes.

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Go to Main Index

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+
+

AntenneX Antenna Modeling Column Index

+

L. B. Cebik, W4RNL

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+
+
+

Because computerized antenna modeling has become widespread, and its popularity as a design tool continues to increase, this series will be devoted to helping you get the most from the design software you use. The articles will focus upon the use of NEC and MININEC, along with useful adjunct software. There are twin goals: to help you get the most out of your modeling efforts and to help you avoid the pitfalls and temptations built into modeling systems and their use. In the process, you may even come to understand your antennas a little better.

+

This series appears as a monthly column in antenneX, and is available in PDF book format with some model sets on the Books Page.

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
No.Title
147Warnings and Errors: What Does NEC Do and What Should You Do?
146Unequal Serial Feedline Connections
145Serial Feedline Connections
144Receiving Directivity
143Modeling Radiating Surfaces
142VOACAP Type 13 Files
141Circular R-X Graphs
140Antenna Matching with EZNEC Version 5 Part 2. L-Networks
139Antenna Matching with EZNEC Version 5 Part 1. Transformers and Shunt Loads
138Types of Substitute Models
137NEC Implementations Cores, Limitations, and Work-Arounds
136AM BC Modeling with NEC Part 6. Grounds
135AM BC Modeling with NEC Part 5. Multiple Tower Arrays
134AM BC Modeling with NEC Part 4. Square, Sloping, and Tapered
133AM BC Modeling with NEC Part 3. The Long and the Short of It
132AM BC Modeling with NEC Part 2. Quandaries: How Many Legs? How Good is Good?
131AM BC Modeling with NEC Part 1. Basic Considerations
130Models vs. Prototypes: Why Field Adjustments Will Always be Necessary
129Some Rudiments of Receiving Pattern Modeling
128When Not to Use NEC for Antenna Modeling
127A Potpourri of Modeler Miscellanea
126"Ideal" Polar Plots
125When to Worry and When Not to Worry: A Case Study
124Modeling (with) Parabolic Reflectors
123Radiating and Transmission Line Currents
122 + Reciprocity: Home on the Range +
121 + Radiation Patterns and Propagation +
120 + Back on the Ground +
119 + Modeling Odd Structures: the Gamma Match
+ Part 2. Gamma Assembly Variables +
118 + Modeling Odd Structures: the Gamma Match
+ Part 1. Gamma Modeling Basics +
117 + Modeling and the Logic of Question Resolution +
116 + Insulation Revisited +
115 + Single, Bifilar, and Quadrifilar Helices +
114 + Modeling Folded Monopoles +
113 + When Simple Geometries Become Complex: A Rhombic Case Study +
112 + Wires Meeting Ground: 2 Cases +
111 + Dipoles: Variety and Modeling Hazards
+ 4. Zigzag, Fold-Back, and Fan Dipoles +
110 + Dipoles: Variety and Modeling Hazards
+ 3. Tapered-Diameter, Bent, and Hatted Dipoles +
109 + Dipoles: Variety and Modeling Hazards
+ 2. Linear, V, and Folded Dipoles in MININEC +
108 + Dipoles: Variety and Modeling Hazards
+ 1. Linear, V, and Folded Dipoles in NEC +
107 + Scaling Models +
106 + Refining Our Notions of Azimuth Patterns +
105 + Models, Symmetry, and Loads: A Couple of Reminders +
104 + PS: I Change +
103 + True Azimuth Models: EZNEC Software +
102 + True Azimuth Models: NSI Software +
101 + Modeling the Un-Modelable +
100 + The Dipole and the Coax +
99 + S-N, RCA, and MININEC Grounds +
98 + Planar Reflectors: Wire Grid vs. SM Patch +
97 + Integrating Commands: A Case Study +
96 + Some Further Applications of the NT Command +
95 + Some Basics of the NT Command +
94 + GR: The "Generate Cylindrical Structure" Command +
93 + Convergence Revisited +
92 + Calculating Circular Gain +
91 + An Orientation to NEC Near Fields
+ Part 2. Some Refinements and NEC-4 Additions +
90 + An Orientation to NEC Near Fields
+ Part 1. NEC-2 Input Basics and Simple Outputs +
89 + A Note on Archimedes and Log Spirals for the NEC-4 GH Command +
88 + EX and PT +
87 + NEC-4 Manual Sample Files +
86 + NEC-2 Manual Sample Files +
85 + Electrical Fields at a Power Level and Distance +
84 + GA: Creating and Moving Arcs +
83 + Insulated Wires: The NEC-2 Way +
82 + The Nature and Adequacy of NEC Correctives +
81 + Appreciating EK +
80 + Developing Antenna Expectations Using Modeling Software
+ 2B: Vertical Monopoles (continued) +
79 + Developing Antenna Expectations Using Modeling Software
+ 2B: Vertical Monopoles +
78 + Developing Antenna Expectations Using Modeling Software
+ 2A: Vertical Dipoles +
77 + Developing Antenna Expectations Using Modeling Software
+ 1: Horizontal Wires in the Lower to Medium HF Range (continued) +
76 + Developing Antenna Expectations Using Modeling Software
+ 1: Horizontal Wires in the Lower to Medium HF Range +
75 + NEC: Power Efficiency vs. Radiation Efficiency +
74 + Some Numerical Green's Function Rudiments +
73 + Source-to-Feedline Matching Techniques +
72 + The GX or Symmetry Geometry Input +
71 + The Average Gain Test Revisited +
70 + Refining Physical Transmission-Line Models +
69 + 4-8-16-Infinite Sided Loops +
68 + Wire Grids 2: Angular and Awkward +
67 + Wire Grids 1: Plane and Simple +
66 + State of the Art? +
65 + The 1/2-Wavelength Resonant Dipole as a Core Test Instrument +
64 + An Orientation to the NEC Output File +
63 + GH and GM: The NEC-4 Versions +
62 + GH: Helix-Spiral Specification +
61 + GM: Coordinate Transformation +
60 + NVIS Antenna Models and the Ground Type +
59 + MININEC and NEC: A Design Case Study +
58 + Some Basic Guideline Graphics for NEC +
57 + Some Comments on Comments +
56 + When MININEC is Superior to NEC +
55 + Parallel Sources, Angular Junctions, and Average Gain: Correcting "Weaknesses" +
54 + GC: Wire Segment Length and Radius Tapering +
53 + Voltage and Current Sources: How? +
52 + Flipping Among NEC Programs +
51 + Testing the Fringes of Modeling Programs +
50 + The NEC-4 IS Card: Insulated Wires +
49 + Traps +
48 + Radiation Plots: Polar or Rectangular; Log or Linear +
47 + So You Want to Read a NEC-Deck +
46 + A Load in Parallel With a Source +
45 + Designing With NEC: A Case Study: Part 2: Evaluation and Reality +
44 + Designing With NEC: A Case Study: Part 1: The 4 Ss +
43 + Modeling Element Substitutes +
42 + Moving and Rotating +
41 + Multiple-Feedpoint Loop Modeling +
40 + Resolution +
39 + Radials: Complex Radials Systems +
38 + Radials: Segmentation and Convergence +
37 + Verticals: Using the MININEC Ground +
36 + Getting a Grip on AZ/EL and Phi/Theta +
35 + Notes on Using AZ-EL Plots Effectively +
34 + The Second Ground Medium +
33 + A Clean Sweep +
32 + A Case Study: Rotating a Beam +
31 + A Case Study: a 90' Wire +
30 + Modeling By Equation
+ D. Scratch Pads and Coordinates +
29 + Modeling By Equation
+ C. Formulas and Blocks +
28 + Modeling By Equation
+ B. Bigger and Better Things +
27 + Modeling By Equation
+ A. A Beginning +
26 + The Scales of Equivalence +
25 + Bringing Up the Rear: Front-to-Back Ratios +
24 + The Power and the Source +
23 + Modeling LPDAs +
22 + Physical Models of Parallel Transmission Lines +
21 + The NEC TL Facility +
20 + The Average Gain Test +
19 + What Can We Learn From Tables? +
18 + Why Tri-Banders Are Hard to Model +
17 + Notes on Reactive Antenna Loads and Their NEC Models:
+ E. Some Unfinished Business on Modeling Loads +
16 + Notes on Reactive Antenna Loads and Their NEC Models:
+ D. Some Solenoid Loading Basics +
15 + Notes on Reactive Antenna Loads and Their NEC Models:
+ C. Some Linear Loading Basics +
14 + Notes on Reactive Antenna Loads and Their NEC Models:
+ B. Some Mid-Element Loading Basics +
13Notes on Reactive Antenna Loads and Their NEC Models:
+ A. Some Center Loading Basics
12 + Verticals At & Over Ground: Sensible Expectations +
11 + A Ground is Just a Ground: Unless It Is a Model of a Ground! +
10 + Tapering to Perfection +
09 + Modeling Ground Planes Other Radial Systems +
08 + Modeling Wire Arrays +
07 + Maximizing Your Data +
06 + Modeling Loads: What Kind, How Much & Where? +
05 + Putting Sources Where You Can Find Them +
04 + A Good Start is Half the Trip +
03 + Within the Lines: NEC-2 +
02 + Under the Limits: MININEC +
01 + Converging Toward Excellence +
+
+

+

Topics: Magazine Columns, Modeling


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+

Antenna Options

+
+
+

L. B. Cebik, W4RNL

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+
+ +
+

When asked to become a contributing editor for QEX, ARRL's technical experimenter's journal, I developed the "antenna options" theme as a foundation for my irregular contributions. Each episode in the series tries to lay out the options that an antenna builder, designer, or user has over some defined territory. Sometimes the options are purely practical--as practical as selecting element or boom materials. Sometimes the options match antenna designs to operating goals. Sometimes the options involve modeling software and its use. Occasionally, a topic requires more than one episode to finish (although we never really exhaust our options). However, the irregular publication schedule limits the number of columns devoted to a single topic. All items on the list below appear with permission, although they are copyrighted by ARRL. The material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex). The episodes will appear at this site only after they have appeared in QEX.

+ +

The versions of the episodes that appear here are in HTML format. Hence, they will diverge in appearance from the versions appearing in QEX. Occasionally, I shall have to change some wording to suit the arrangement and progression of graphics and tables.

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+ +
+

Updated 03-05-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author and ARRL.

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Return to Amateur Radio Page

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Topics: Magazine Columns


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A Yagi Case Study
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L. B. Cebik, W4RNL

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"This antenna is the best thing since sliced bread." Such is too often the claim made for antennas by individual builders and commercial makers alike. I'll bet those who make this and similar claims have not stopped to consider that for many meals, sliced bread is exactly the wrong bread to serve. I know a nice little restaurant that serves excellent soups in freshly baked bread bowls. I would not eat there if they tried to serve the soup in sliced bread.

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So, too, with antennas. For any general application, we have options. Only when we evaluate those options against our specific requirements and our situational limitations can we decide on the best antenna for the circumstances. Notice that the result is not simply "the best antenna." It is the best antenna for the given job and the conditions under which it will have to do that job.

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Since I cannot know every circumstance in which amateurs set up antennas, I cannot say what the best antenna is for any amateur activity. But I can use the space that QEX has allotted to me to discuss some options and alternatives for specific tasks. In small spaces, I cannot cover every possible option and certainly not all of the details that attach to each option. However, I can (hopefully) begin a thinking process that may ultimately let you make the best final decisions for yourself. The options that I have in mind are not brand-A vs. brand-B commercial offering. I do not have the appropriately rated test range for this kind of discussion. Instead, I shall look at options among antenna types, antenna construction, matching systems, etc. that one might face in deciding what to build for oneself.

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In virtually all areas of antennas, there are facets of design and performance that we easily overlook, and many of them have an important place in our decision-making processes. To make the process even more concrete, let's look at the myriad of options that attach to a seemingly simple case study that I call "A Tale of 3 Yagis."

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Yagi arrays require the antenna-builder to make three major decisions on the way from idea to reality.

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  • 1. What design is best?
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  • 2. What material is best for the elements?
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  • 3. What assembly method is best?
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These three questions ultimately rest on another: what are the uses, purposes, or goals for the antenna? How all of these questions inter-relate is part of the motivation for this set of notes.

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To keep our work confined within a space that we can control, I shall examine only 2-meter Yagis. Within that space, I shall further assume that the user will take the antenna into the field for one or more of a variety of portable operations. To make matters even simpler, I shall restrict the discussion to 3-element Yagis with 30" boom lengths or less.

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Even with these restrictions, we still have design choices. We may select a narrow-band, high-gain design to maximize potential for point-to-point communications. Alternatively, we may select a design with a very high 180-degree front-to-back ratio for direction finding uses. Finally, we may select a design that covers the entire 2-meter band with an exceptionally low 50-Ohm SWR. For each design, there are trade-offs that we shall examine along the way.

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Once we select a design, we need to select the material for the elements. If we choose to use rod or tubing for the elements, we may simply optimize the design for the element diameter we wish to use. In fact, the design information provided in the tables will cover most common 2-meter rod and tubing sizes. However, my e-mail regularly poses questions about the use of non-standard materials, such as flat stock, L-stock, whips, and tape. Therefore, we shall spend a bit of time looking at a technique for determining what adjustments we might have to make for some of these materials. I shall provide some data that emerged from my own use of these techniques, but the techniques themselves will be your better guide to handling materials that I have not imagined.

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Finally, we shall look at a few methods of overall assembly that are suitable for the element material, the overall size of the antenna, and the intended use. For such a short boom, there is no reason not to use a non-conductive boom. In most cases, the choice will be between PVC and fiberglass, with PVC being easier to find and somewhat more versatile.

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In the end, these notes are just a sample of a thought process you can and should extend to other bands, other designs, and other operating purposes.

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Part 1: The 3 Yagi Designs

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The first step in our tale of 3 Yagis is to describe the Yagis themselves. There is a high-gain, narrow-band version, a maximum-front-to-back ratio version, and a very-wide-band version. A papa bear, mama bear, and chubby baby bear analogy in these characterizations is likely not accidental.

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For each antenna design, the tables will provide detailed dimensions for a variety of element diameters from 1/8" up to 1/2", in readily available rod and tube sizes. The material may be aluminum (recommended for its low weight and high strength), brass, and copper. The performance figures are based upon aluminum, although changing the material will not alter the performance in any detectable way.

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The tables also provide performance data from NEC-4 models at the design frequency. All designs attempt to achieve a minimum of 20-dB 180-degree front-to-back ratio across the listed passband. However, the particular design will reveal variations in where, within the operating passband, the maximum front-to-back ratio occurs. All 3-element Yagi designs show a gradual increase in gain across the operating passband.

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Fig. 1 shows the relative proportions of the 3 Yagi designs, using the 3/8"-diameter element versions as the basis for the sketch. The high-gain version has nearly equal spacing between elements and an almost uniform taper of the element outer tips. (The departure of the spacing and taper from uniformity is essential to achieving the performance.) The maximum 180-degree front-to-back ratio design preserves a similar driver-reflector structure, but shortens the length and spacing of the director to achieve the deep rear null. Both antennas have feedpoint impedance near 25 Ohms. The very wide-band version requires a 50-Ohm feedpoint and therefore widens the reflector-to-driver spacing. Note also the relatively short director.

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1. High Gain: 144.5 MHz high gain 3-element Yagi: The high-gain Yagi is designed for maximum gain with a reasonable boom length and modest bandwidth. It will cover about 2 MHz of the 2-meter band if the design frequency is moved from 144.5 MHz to 145 MHz. However, its present design recognizes that most point-to-point activity is in the first MHz of the band. So the design frequency is set at 144.5 MHz. Within the first MHz, the SWR is less than 1.2:1 for any listed element diameter. Although horizontal operation is the norm for the low part of 2 meters, the antenna is equally operable horizontally or vertically.

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We should note here that we can obtain higher gain from 3 elements with a longer boom and by setting aside the desired 20-dB front-to-back ratio. However, such designs usually also have much lower feedpoint impedances that may be difficult to match to a 50-Ohm cable without undue loss in the connections. The high-gain design used here is therefore a compromise among the many operating parameters involved in the directional antenna.

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The feedpoint impedance is resonant at about 25 Ohms. This arrangement is intentional to avoid the need for excessive numbers of mechanical connections at the antenna proper. A 1/4 wavelength section of RG-83 (35-Ohm) or a parallel section of RG-59 (or similar 70-Ohm) coax will provide a match to the 50-Ohm main cable. Cut the section for 144.5 MHz, allowing for the cable's specific velocity factor. Alternatively, one may modify the design to shorten the driver so that it shows about 25 Ohms of capacitive reactance. Then, a hairpin or gamma match becomes applicable.

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It is not possible to let the maximum front-to-back ratio of the high-gain, narrow-band design coincide with the design frequency for all element diameters. The smaller the element diameter, the more likely the maximum front-to-back ratio is to fall below the design frequency. However, the front-to-back ratio exceeds 22 dB from 144 to 145 MHz for all versions of the design.

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Table 1 provides dimensions for the design using round elements from 1/8" up to 1/2" in diameter. Table 2 shows the modeled free-space performance at the design frequency--144.5 MHz--for each size material. Simplified figures for the edges of the 1-MHz operating passband appear in Table 3, while Table 4 suggests the overall usable operating bandwidth with 25-Ohm SWR values at 144, 145, and 146 MHz. If the builder uses a 1/4 wavelength matching section for a 50-Ohm coaxial feedline, the 50-Ohm SWR at the junction of the matching section and the main feedline will be similar. Fig. 2 shows free-space E-plane and H-plane patterns for the array at the design frequency. These patterns replicate the pattern shapes when the antenna is used over ground in the horizontal and vertical positions, respectively.

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The charts show clearly that the bandwidth for any particular characteristic tends to increase with an increase in element diameter. However, note that each increase in element diameter requires a change in element spacing as well as element length to sustain the performance curves over the 144-145-MHz passband. Most of the change in element spacing occurs with respect to the driver and reflector, since this spacing, relative to a given element diameter, largely determines the feedpoint impedance of the array, once we have set the performance values with the spacing and length of the director.

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To change the design frequency, scale both element lengths and element spacing. Take the ratio of the old (144.5 MHz) frequency to the new frequency and multiple all dimensions in the tables by the result. If the scaling is within the 2-meter band, no element-diameter adjustment is necessary. If the frequency ratio is greater than about 1.2:1 or less than 0.8:1, then element-diameter scaling is necessary to retain the performance characteristics.

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2. Maximum Front-to-Back: 146 MHz maximum front-to-back 3-element Yagi: The applications for a high-gain design are obvious. A maximum front-to-back ratio design has more limited application, for example in the field of amateur radio direction finding. The antenna should have sufficient gain to locate the desired signal and a sufficiently sharp and deep rear null to provide a reliable bearing toward the target transmitter. Although the horizontal pattern for any parasitic beam will include rear, quartering lobes, the vertical pattern will show a clear single null. Most direction-finding activities use vertical polarization.

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I have set the design frequency for the maximum front-to-back ratio at 146 MHz, because there is no absolute standard for direction-finding frequencies. However, for operation within the 2-meter band, one may scale the dimensions according to previously given principles without concern for scaling the element diameter. However, for scaling outside the limits of the 2-meter band, one should also scale the element diameter.

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Although not radically finicky, the maximum front-to-back ratio for a Yagi design is a narrow-band phenomenon. Hence, one should construct the antenna for the frequency of intended use. As the performance tables will show, the front-to-back ratio decreases steadily off-frequency until the design shows no distinct null. However, the design has sufficient gain and front-to-back ratio to make it a useful performer for other purposes.

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The feedpoint impedance for this design is set for about 25 - j 25 Ohms. The models all use an identical shorted transmission line stub across the feedpoint to simulate a hairpin match. Hence, the SWR curves are for 50 Ohms. The modeled feedpoint resistance is actually close to 27 Ohms, and the required inductive reactance of the hairpin is 54 Ohms. You may construct a U-shaped hairpin for the antenna by calculating the characteristic impedance for the spacing and wire diameter used. Then the length follows standard shorted-transmission line equations found in The ARRL Antenna Book, Chapter 24. A normally good construction method for the hairpin it to choose a distance between the parallel lines that is equal to the spacing between the driver terminals.

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As an example, AWG #14 wire (0.0641" diameter) has a 400-Ohm characteristic impedance at a center-to-center line spacing of 0.901". A shorted stub or hairpin made from this line would need to be 1.73" long to achieve 54 Ohms inductive reactance at 146 MHz. The final adjustment requires care, since the terminal structure at the feedpoint normally introduces some reactance that may add to or subtract from the amount provided by the hairpin. Lower characteristic impedances yield longer stubs for the same reactance. Narrowing the line spacing or fattening the conductor will lower the characteristic impedance. The goal is a hairpin that is short enough to be sturdy in field use but not so short as to make the final feedpoint adjustment too finicky.

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If you build this design for its intended purpose, general field adjustment also requires care. Contrary to most received wisdom, the reflector is not chief source of the front-to-back ratio in the design. The reflector is relatively insensitive and serves primarily to establish the feedpoint impedance by virtue of its length and spacing from the driver. The most sensitive element relative to establishing the ideal front-to-back ratio will be the director. The director length will be more sensitive than its spacing from the driver, although both dimensions deserve the label "sensitive."

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Table 5 provides dimensions and Table 6 supplies performance figures based on NEC-4 models for element sizes ranging from 1/8" to 1/2". In all of the designs in these notes, the dimension values presume a non-conductive boom or the use of mountings that insulate and isolate the elements from the influences of a conductive boom. See "Scaling and Adjusting VHF/UHF Yagis" at my web site for notes on adjusting element lengths for insulated through-boom construction (Scaling and Adjusting VHF/UHF Yagis). However, for boom lengths under 30" or so, and for direct-feed drivers, there is little reason to use a conductive boom.

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The performance figures show the increasing performance--although very gradually increasing--as we increase the element diameter and also adjust both element length and spacing to optimize performance for each new element size. This clear picture emerges largely because the design aligns the design feedpoint impedance and the maximum front-to-back ratio at the same frequency. The only performance figure for which variations make no difference is the 146-MHz front-to-back ratio: I ceased optimizing when this value exceeded 50 dB.

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Fig. 3 shows free-space E-plane and H-plane patterns, which replicate the patterns you will obtain when using the antenna in a horizontal or vertical orientation, respectively. Over ground, expect the vertical pattern to have less gain but a wider beamwidth than the horizontal pattern. However, when used vertically, the rear quadrants will show a single deep, sharp null.

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3. Very Wide-Band: 146 MHz very wide-band 3-element Yagi: The third design stresses smooth performance over the entire 2-meter band with a 50-Ohm SWR of less than 1.2:1. The design achieves this goal by using a variation of a W6SAI design from the 1980s, modified for 2 meters and for the full range of rod and tube diameters. Although the gain is about a full dB less than the high-gain model, the wide-band Yagi will provide roughly equal performance anywhere in the band. Thus, it is fit for flipping from horizontal to vertical and back again as we change to and from point-to-point and FM repeater operations.

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The Yagi uses a direct 50-Ohm feedpoint with no matching network required (although common-mode current suppression measures are advisable). The need to establish the SWR curve as the primary design goal has consequences as we increase the element diameter. The front-to-back ratio shows improvement with each larger element, but the low end of the band does not quite make the 20-dB level. Very quickly in the sequence, the gain ceases to increase with increasing element diameters. Although not clearly apparent in the performance figures, both the peak gain and the peak front-to-back ratio occur at ever higher frequencies. Above the smallest element size, the peak front-to-back ratio occurs above the upper end of 2 meters.

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Nevertheless, the very wide-band 3-element Yagi is a true general utility antenna for use anywhere in the band. Table 7 provides the dimensions for elements ranging from 1/8" to 1/2" in diameter. Table 8 supplies the modeled performance figures. Fig. 4 gives us the shape of patterns when we use the antenna horizontally and vertically. All previous notes about scaling this antenna to other frequency bands are applicable with the very-wide-band Yagi.

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The very wide-band version of the 3-element Yagi completes the family of designs that we shall consider. Other variations may be possible, but these 3 cover the major performance parameters with which amateurs are most concerned: gain, front-to-back ratio, and operating or SWR bandwidth. One might further optimize the designs, but the level of optimizing used here gets the most out of each design that we can for each size element.

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The next step--assuming that one of these designs will meet an operating need--is deciding upon the element material. Our choices are not merely the material type, for example, copper, aluminum, or brass. They also include materials other than the uniform round tubes that our initial design models have used. We shall explore some of our options next time.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jul/Aug, 2004, pp. 55-59. Reproduced with permission. Copyright ARRL (2004), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: VHF / UHF, Yagi


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Horizontal Bi-Directional Wires

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L. B. Cebik, W4RNL

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In the last set of notes, we discussed some of the options for bi-directional wire broadside arrays based on the vertical dipole. Since we should be fair to horizontal wires, this collection of notes will focus on bi-directional wire arrays that have their roots in the horizontal dipole. Just as the last collection was incomplete, so this one will be even further from exhaustive. Once we have some basic arrays available to use, the permutations and combinations form an endless progression. However, we can look at the various types of arrays.

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To be effective, a horizontal array should be well above ground. Although we might disagree on the minimum height for horizontal arrays, placing all arrays at 1 wavelength above ground for the top wire (if the array has a vertical dimension) will keep us well above the minimum. In the preceding notes, I set a height of 50' as a limit of sorts, since most serious array users can usually arrange 60' support posts, trees, or surplus telephone poles. The physical height restriction leads us to 15 meters, more specifically, a uniform test frequency of 21.225 MHz for all comparative horizontal array data. A wavelength at this frequency is 46.34'. To unify further the modeling conditions, the ground will be average, that is, have a conductivity of 0.005 s/m and a relative permittivity of 13. All antenna elements will use AWG #12 (0.0808" diameter) copper wire. As a result, we can more directly compare the reported performance characteristics for the antennas included in these notes.

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Traditionally, we categorize arrays as collinear, end-fire, or broadside. These categories are not mutually exclusive, but they do give us a convenient way of grouping our subject antennas. However, we must begin with a baseline.

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The Standard Antennas

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No antenna is more fundamental to amateur (and other) antenna work than the 1/2 wavelength resonant dipole. Fig. 1 shows the outline of the antenna. Superimposed on the antenna is the distribution of the current magnitude along the wire's length. (Adding the current phase would create difficult viewing problems with some of our antennas.) Note that the dipole is electrically resonant, which requires a physical length that is 0.486 wavelength for #12 copper wire at the specified height above average ground. The resonant length of a dipole will vary with the height above ground, especially below about 1.25 wavelengths.

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Horizontal wire antennas tend to have an elevation angle of maximum radiation (or TO angle) that depends on the antenna's height more than any other factor. Hence, all of the basic antennas whose performance reports appear in Table 1 have a TO angle of 14°. The dipole data in the table give numerical meaning to the plots on Fig. 1. Note the wide (79°) beamwidth for a standard dipole. A triangle of dipoles would suffice to cover the entire horizon. The dipole gain of 7.6 dBi becomes the baseline against which we may measure the gain of all subsequent arrays.

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The second standard antenna can go by several names. The table and Fig. 2 both refer to a 1 wavelength center-fed doublet. An equally apt way to refer to the antenna is as a collinear array of 2 half wavelength wires. The current magnitude curve on the antenna outline shows why this name has good sense, since we observe two complete cycles of current rise and fall. Like the dipole, the physical length will be shorter than the electrical length. For the test conditions, we obtain resonance with a length of 0.956 wavelength of wire. Finding the resonant length of a center-fed 1 wavelength wire is tedious in modeling and virtually impossible with real wire. The resonant point occurs at a very high value of resistive impedance, where the reactance changes in a very short space from very inductive to very capacitive. Hence, there is an air of artificiality about the reactance number in the table, although the resistive part is a good indicator of what to expect at the feedpoint. One way to bring the impedance down to a value that is more amenable to our coaxial ways is to use a 1/4 wavelength section of 450-Ohm line.

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The pattern and the gain value are both very real and usable. The 1 wavelength wire provides about 1.6 dB additional gain relative to a dipole under equal conditions, but at a cost in the beamwidth. The longer wire has a beamwidth of about 51°. A triangle of 1 wavelength wires will not cover the horizon.

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The third standard wire antenna is the extended double Zepp (EDZ). We operate this antenna off resonance. We sometimes say that the antenna is non-resonant, but there is another use for this term. Many traveling wave and frequency-independent antennas show no cyclical appearance of resonant frequencies as we operate the antenna over a large frequency range. Many texts call these antennas non-resonant in contrast to antennas like a center-fed wire of fixed physical length. This antenna is resonant in the sense of showing cyclical re-appearance of zero reactance at the feedpoint as we sweep through a wide frequency range. So we may be content in calling the EDZ an off-resonance antenna. Fig. 3 shows the current magnitude distribution for a physical length of 1.25 wavelength. The antenna qualifies as a collinear array.

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As we increase the length of a center-fed wire beyond 1 wavelength, we find that the gain increases until the length passes the 1.25 wavelength mark. However, the azimuth patterns and the tabular data show us other dimensions of what is occurring. As we move from about 1.2 wavelengths to 1.25 wavelengths, the resistive and capacitively reactive components of the feedpoint impedance decrease. (The gain changes only by about 0.1 dB.) Offsetting the reduction in the feedpoint impedance is the growth of the sidelobes that give an EDZ azimuth pattern its distinctive look. With a length of 1.2 wavelengths, the sidelobes are about 13 dB lower in gain than the main lobe. By a length of 1.25 wavelengths, the sidelobes have grown by 3 dB. At a total length of about 1.5 wavelengths, the side lobes would be as strong as or stronger than the main or broadside lobe. As well, the beamwidth continues to shrink as we lengthen the wire and increase the peak gain. Hence, the EDZ represents a sort of limit to the length of collinear arrays unless they employ techniques to correct phasing along the wire.

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Collinear Arrays

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One technique that allows us to obtain increased gain with straight wires is to introduce at critical points along the wire a phase-changing stub. Consider a 2 wavelength center-fed wire, such as the one shown in Fig. 4. We see 4 complete half wavelength current cycles. However, if we had just used a continuous length of wire. The phasing of the current at the outer half wavelength sections would have been 180° out of phase for producing a simple broadside pattern. Indeed, we would see for such a wire a 4-lobe pattern that forms a cloverleaf. By introducing 1/4 wavelength shorted transmission-line sections, we change the phase of the current at the beginning or inner end of the outer sections so that the radiation adds to the radiation of the center section. The result is a narrow main beam (the width is 26°) with over 1 dB gain over the EDZ. The tabular data for the collinear arrays appears in Table 2, for comparison with the patterns in the relevant figures.

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Like a 1 wavelength wire, which is what we find at the center of our collinear array that uses 1/2 wavelength sections, the feedpoint impedance is very high. As well, the azimuth pattern shows small EDZ-like sidelobes that are normal to very closely spaced 1/2 wavelength sections--in this case, the end sections relative to the longer inner section of the array.

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We need not limit ourselves to using 1/2 wavelength sections as the basis for a collinear array. As shown in Fig. 5, 5/8 wavelength section will work as well and provide additional gain. The collinear array shown uses such sections and has a total length of 2.78 wavelengths to achieve a peak gain of 13.5 dBi, about 1.5-dB higher than the comparable array using 1/2 wavelength sections. However, the beamwidth has shrunk to 16°. This array is for point-to-point communications.

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The array shows twice as many sidelobes because we have--in effect--a doubled EDZ structure. The inner section is slightly over 1.5 wavelengths, which seems long for an EDZ. However, if you examine the current magnitude curve on the outline sketch, you will see that it requires the added current rise not only at the feedpoint, but also at the location of the phasing lines. Because these regions are already reactive, the phasing lines can be shorter to effect the required phase reversal--in this instance, about 0.15 wavelength. The feedpoint impedance is normal for an EDZ-type antenna. Moreover, despite the high increase in array complexity, it still shows a TO angle of 14° that owes to its 1 wavelength height above ground.

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In the models for both of the collinear arrays, the phase lines are physical wire structures and not NEC TL constructs.1 The non-radiating TL lines are most accurate at high current regions of an antenna where the current changes very slowly over appreciable distances along the wire. They become less accurate in regions of the antenna in which the current changes rapidly over short distances. Since both collinear arrays show relatively low currents at the phase-line locations, physical lines are necessary for best accuracy in the models. The modeled line wires should be the same diameter as the antenna element wire, and the spacing should not be excessively close.

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The final sample of a collinear array takes an odd turn--upward. The bi-square array is a center-fed 2 wavelength wire with the ends turned upward to form a square that is 1/2 wavelength on a side. However, the wire ends do not meet, but leave a gap. Fig. 6 shows the general outline and the current magnitude curves for each of the 4 wires. Because we have set a 1 wavelength limit for the top structure, the low point for the array is about 0.3 wavelength above ground. The net effect is to raise the TO angle of the array as a whole. A useful rule of thumb for any array consisting of multiple wires in the vertical plane is that the effective height of the array is about 2/3 the way up the array from the low point to the high point. Hence, the effective height of the bi-square in the illustration is about 0.75 wavelength.

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The bi-square has a beamwidth of about 63°, although its gain is about halfway between the values for the 1 wavelength and the EDZ arrays, both of which antennas exhibit narrower beamwidths. If you compare the elevation pattern for the bi-square with those for the other two relevant wires, you will discover that the bi-square lacks most of the upper structure or second elevation lobes that characterize the elevation patterns of the single wire antennas. The bi-square lends itself to single-support mounting, and you may place two such antennas at right angles on the support, switching to the one that yields best signal strength.

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End-Fire Arrays

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If a set of elements radiates in the plane of the elements with the lobes broadside to the element wires, then we have an end-fire array. Among basic arrays, we need only one sample: the W8JK "flat-top" array, developed by John Kraus, W8JK. The antenna has many incarnations using various element lengths and forms and using many spacing distances. In general, the longer the elements, for a given spacing, the higher will be the gain. Equally generally, the closer the spacing, the higher the gain will be. Hence, every W8JK is a compromise based on best achieving a particular set of goals for the antenna.

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Fig. 7 shows the outline of the 15-meter version that we shall examine. It uses a pair of 1 wavelength elements (or collinear 1/2 wavelength elements) spaced 1/2 wavelength apart. Between the elements, we find two phase lines of equal length meeting at a central point where we attach the main feedline. Note that the elements require a 180° phase difference, so one and only one of the phase lines receives a single half-twist. The modeled impedance data in Table 3 rests on the use of 450-Ohm phase lines with a velocity factor of 0.9. Other line values will produce other impedances. The 15-meter patterns in Fig. 7 are very clean with a bi-directional gain similar to that of a 2-element reflector-driver Yagi.

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The selection of the element length and spacing for this sample becomes apparent from the patterns in Fig. 8. As we raise the operating frequency, the spacing increases to lower the gain, but the element lengths increase to raise it. Lowering the operating frequency produces opposite effects. The result is an array that one might use over several bands with remarkably similar performance. The remaining gain changes are largely a function of the antenna's changing height when measured in wavelengths.

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The W8JK first emerged in 1937. For other configurations, see Kraus' Antennas, 2nd Ed., p. 458, as well as innumerable articles in QST over the years since the antenna first appeared. The array also lends itself to becoming part of more complex array systems.

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Broadside Arrays

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If the main radiation lobes of an antenna are at right angles to the plane of the elements, then we have a broadside array. Standard HF horizontally polarized arrays tend to require a vertical plane for the elements for broadside use, although NVIS operations might set the element in a horizontal plane for straight-up radiation. The most common simple 2-element broadside array for 15-meter and other upper HF bands is the Lazy-H, shown in Fig. 9. Like the W8JK, the elements are 1 wavelength long and spaced vertically 1/2 wavelength apart. However, we feed the elements in phase, so we do not twist either of the two phase-lines. (An alternative feeding system brings the main feedline to the bottom element. The line connecting the elements receives a half twist to produce a 360° phase change in the 180° phase line. The resulting feedpoint impedance is very high and requires a matching section.) Table 4 provides the modeled data for the center-fed version of the array. The impedance reports rest on the use of 600-Ohm phase lines having a velocity factor of 1.0.

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With elements at 1/2 wavelength and 1 wavelength above ground, the lazy-H out-performs the W8JK on 15 meters, even though the effective height is only a bit over 0.8 wavelength. The increased gain is partly a function of suppressing the upper lobe structure that we see in the W8JK pattern as a result of the lazy-H's vertical stack of elements at a 1/2 wavelength spacing. Like the W8JK, we can use the lazy-H on other bands, as shown both in the tabular data and the patterns of Fig. 10. Even though the elements are not spaced for maximum vertical lobe suppression on other bands, the elevation patterns show good reduction in higher angle lobes compared to a flattop array. As we lower the operating frequency, the height of the lower wire in the lazy-H grows closer to the ground when measured as a fraction of a wavelength. Hence, the bi-directional pattern for 30 meters does not appear, since it would be weaker than a simple dipole at 46' above ground and have a higher TO angle. Nevertheless, the antenna is operable on that band. Unlike the W8JK, the lazy-H shows considerable variation in gain as we move from one band to the next.

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The pattern for 28.5 MHz calls for a brief note. Using elements that are 1 wavelength long for 15 meters produces a 10-meter pattern with very strong sidelobes, since the elements are over 1.3 wavelengths long on that band. Instead of beginning with a standard 15-meter design, we might have design for 10 meters a lazy-H that uses 1.25 wavelength elements with 5/8 wavelength spacing--about 44' and 22', respectively. The result would not change the 10-meter gain significantly, but it would yield an EDZ-type pattern with lower sidelobe content. As well, the antenna would operate over the same frequency range as our sample. This is the so-called expanded or extended lazy-H.

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The lazy-H is the foundation for many more complex arrays. In principle, we may combine the lazy-H and the W8JK into a 4-element array. The lazy-H also finds extensive use in commercial array construction for short-wave broadcasting. Consider a vertical bay of elements fed in phase, with as many element at 1/2 wavelength spacing as vertical supports will allow. Now place further columns of such arrays next to each other. Finally, place a large screen between 1/4 wavelength and 1/2 wavelength behind the rows and columns of antennas. In the late 1920s, we would have called the antenna a billboard array. If we reduce the element lengths to about 1/2 wavelength and use special wide-band forms of dipole elements, we end up with the modern dipole directional array. By staggering the feed current phase angle from one vertical bay to the next, we can actually slew the direction of the main lobe without ruining the overall characteristics of the antenna pattern. This brief account of modern dipole arrays overlooks a myriad of both electrical and mechanical engineering feats necessary to implement such an array, but it does show the fundamental place of the lazy-H among broadside arrays.

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Our final sample broadside array is a curtain, one that passed out of use long ago. Nevertheless, it serves well as a sample of an antenna that continues to attract amateur attention for its pattern properties. In Fig. 11 we have the outline of a 3-section Sterba curtain, first reported in antenna literature in 1931. Basic to the design are the 1/2 wavelength by 1/2 wavelength inner sections, with end sections that are 1/4 wavelength wide by 1/2 wavelength high. We may use as many inner sections as we desire, but a centered feedpoint requires an odd number. The lines between sections are critical: they must be 1/2 wavelength long parallel transmission lines with a half-twist in each line to keep the top and bottom wires in phase with each other. The sample places the bottom wire 1/2 wavelength above ground to keep the array within our maximum height limits.

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Table 5 provides the modeled data to accompany the patterns in Fig. 11. Like the lazy-H, the elevation pattern shows good suppression of higher-angle lobes. The figure shows two azimuth patterns to accommodate the two most common feedpoints for Sterba curtains: the center of the lower element structure and the corner. The table includes only one data set, since there is no significant difference in the gain, the beamwidth, or the feedpoint impedance. A 600-Ohm feedline would handle either central or corner feeding very effectively. With central feeding, we have a bi-directional pattern that is exactly broadside to the array itself. However, if we feed that antenna at a corner, we bend the pattern by nearly 5° in the direction of the feedpoint. For such a large array (even though only 2 wavelengths or about 92' long), copper losses are sufficient to distort the pattern direction, although one might compensate through a tedious task of making slight dimension alterations.

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Like a lazy-H that uses a bottom feedpoint and a 1/2 wavelength half-twist phase-line, the Sterba curtain is a monoband antenna. On other frequencies, it becomes simply a semi-random collection of wire. As well, the Sterba requires a great quantity of wire. Consider once more the collinear array that used half wavelength sections. If we stack a pair of these antennas vertically, the total array length and height will be the same as for a Sterba curtain. However, we require only a single phase-line between the two to connect the feedpoints to the main feedline. The resulting array (with wires at 1/2 wavelength and 1 wavelength heights) will have a gain of nearly 15 dBi, but with a very great saving in wire.

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Another Interim Conclusion

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For the wire fans, horizontal bi-directional arrays offer considerable potential in the form of relatively simple, reliable, and inexpensive arrays. In the upper HF region, such antennas have a long-term home if we use care in the ones we select. The lazy-H and the W8JK may be the most flexible arrays in terms of potential multi-band use. However, we must consider the impedances at the tuner end of the main feedline. In some cases, a low antenna feedpoint impedance may create significant line losses, even in parallel lines. We may need to change dual phase-line lengths and impedances to arrive at the best compromise efficiency level on all bands. Monoband arrays with very high impedances will likely require matching sections to arrive at the lower impedances of common coaxial or parallel transmission lines. Simple antennas can present not-so-simple feeding challenges.

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Likewise, we must use care in our selection of an array in terms of the gain-vs.-beamwidth question. If we had just one friend with whom we wish to communicate (or two friends at 180° separation), then we might use gain alone as our desideratum. However, in most cases, we shall want to balance gain against coverage. Hence, it is likely that we shall have to trade some gain to obtain adequate beamwidth.

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Just when we might think we have reached an ending, someone has whispered to me, "How do we convert a bi-directional array into a directional array?" It turns out that, even here, we have options.

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ao10-models.zip.

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Updated 08-27-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Sep/Oct, 2006, pp. 55-61. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Bruce Array / Sterba Curtain, Collinear, Dipole, Doublet, EDZ / Zepp, HF Upper, Lazy H, Phased Array, W8JK


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From Two to One

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L. B. Cebik, W4RNL

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In the preceding two episodes, we examined clusters of options for vertical and horizontal bi-directional wire arrays based on the dipole as the root antenna. Each cluster only sampled the options available, and we might easily add to the number of clusters. However, our goal was to present each cluster in an internally consistent environment to ease some of the difficulty in decision-making. Within each group, the individual can now use consistent performance data in combination with dimensional data, installation challenges, and budgetary cautions when deciding on the next antenna to build.

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Very early on, a perennial question arose: how does one convert a bi-directional array into a directional beam? Once more, we have options. Most handbooks treat the options in different chapters, so we rarely receive any kind of overview of available techniques. Although our space is small and therefore our samples will be few, we can partly correct the oversight.

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Consider two elements of similar size, at least one of which would serve as a bi-directional antenna. To create a directional end-fire beam from these two elements, we have to provide each element with the correct relative current magnitude and phase angle to yield the strongest possible forward lobe and the weakest possible rearward lobe. Similar considerations apply to both multi-element arrays and to large collinear arrays. As a convenience in sorting out how we accomplish the goal, we can separate the techniques into 4 general groups: parasitic methods, phasing methods, screen reflection, and traveling-wave termination. Not all techniques are equally apt to all antenna types and situations, but all have a place in the option set.

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Parasitic Methods

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Many hams associate parasitic elements almost solely with Yagi-Uda arrays based on the half wavelength antenna element. However, designers have long realized that parasitic elements will work with almost any bi-directional antenna. A parasitic element approximates the conditions that we may achieve directly by complex phasing systems, but it does its work solely by virtue of its length, diameter, and spacing from the original element. For a given spacing and diameter, if we shorten an element relative to the original one with a feedpoint (now called the driver), the new element will show a negative relative phase angle for its current and the main forward lobe will form in its direction. It has become a director. If we lengthen the element relative to the driver, then its current will show a positive phase angle relative to the current on the driver and the main forward lobe will be in the direction of the driver. The new element has become--by convention--a reflector. Reflector-driver arrays tend to show a wider operating bandwidth but poorer gain and front-to-back characteristics than optimized driver-director arrays. Hence, reflector-driver arrays are easier to tame, that is, easier to field-adjust into acceptable performance. We may fairly use these basic principles of parasitic element operation to create a large variety of directional beams.

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Consider the half-square array, essentially a broadside array consisting of 2 vertical dipoles in an easily reproduced wire antenna. See Figure 1. The sketch shows the single half square along with 2 parasitic variations. The dimensions differ slightly from those used in our first array episode to yield a near-50-Ohm feedpoint impedance. However, we are still using AWG #12 copper wire, average ground, and a maximum height of 50'. The left-most plot shows the azimuth pattern with its slight misalignment due to the corner feedpoint. Table 1 supplies the modeled data.

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We may add to the original array a reflector and optimize the vertical lengths for maximum front-to-back ratio with the selected spacing. The forward gain increases by about 3.2 dB with only a small narrowing of the beamwidth. The 180° front-to-back ratio is excellent. The rearward quartering lobes show a very slight imbalance, but not to a point of creating problems in using the array. The structure is very simple to replicate, and the feedpoint impedance remains "coax-ready."

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Rather than lengthen the reflector physically, we may also lengthen it electrically. One convenient method is to use a shorted length of transmission line to add to a driver-length element enough inductive reactance to create an effective reflector element. The sample uses 50-Ohm line at an electrical length of 17'. Suppose now that we add such a length (adjusted physically for the velocity factor of the selected coax) to the driver and bring it to a central point between the elements. We can install a remotely operated switch that converts one side into just an extension of the feed cable and the other side into the required shorted-stub. (Use a DPDT switch or relay to isolate the braids as well as the center conductors.) We now have a reversible half-square beam with virtually the same gain as the fixed version and a very useful rearward lobe set. The need to place the load and the feedpoint on the same side of the array creates a bit more imbalance in the pattern, but nothing fatal to the array's use.

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We can also apply parasitic methods to collinear arrays, for example, the extended double Zepp (EDZ) shown in Figure 2. The sample EDZ uses a length just above 1.2 wavelength to reduce the sidelobes. Like our earlier horizontal bi-directional arrays, the sample uses AWG #12 copper wire and is 1 wavelength above average ground. Table 2 provides the modeling data for both the single EDZ and two versions of a parasitic beam.

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The first version uses a full-size reflector element. Since the element will be capacitively reactive, we can incorporate electrical lengthening into the center loading inductive reactance and tune the element for maximum front-to-back ratio. We also have the option of adding a coil to the center of the driven element to achieve resonance and simplify matching. For example, with the same parasitic array set for resonance, we might use a 1/4 wavelength section of 75-Ohm cable as a matching section for a 50-Ohm main feedline. Providing the driver with inductive reactance at a normal Q range of 200 to 250 has its costs in terms of a slightly lower forward gain. However, the forward gain shows well over a 3-dB increase relative to the single EDZ element.

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We may also simplify the structure somewhat by using a split reflector element, with a section for each outer half wavelength of the driver. The front-to-back ratio will not be as high as with a full-size element properly loaded, but we save the trouble of having to field adjust a reflector inductor for maximum front-to-back ratio.

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Figure 3 shows two ways of obtaining reversible EDZ beams from the same reflector options. In both cases, we find decreases in the reported data from the model in one or another performance category, as shown in the bottom lines of the table. Mutual coupling between the active and inert drivers is stronger than in the case of comparable reversible-direction wire Yagis. Nevertheless, some combination of elements may satisfy a given set of operating needs.

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Phasing Methods

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We often employ phasing methods to improve the rearward null performance of an array. Rarely do phasing methods show very marked gain increases over parasitic methods applied to essentially the same array. In some cases, such as the fixed half-square beam, resorting to phasing techniques would only add considerable complication for little, if any, detectable improvement. In other cases, however, phasing treatment may show marked improvement.

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Phasing techniques essentially add an energy source to what we may achieve with parasitic methods. Parasitic techniques achieve the goal of setting the relative current magnitudes and phase angles to create a beam by virtue of mutual coupling between the elements. A driver-reflector Yagi, for example, rarely surpasses 12-dB front-to-back ratio. If we phase feed the two elements, we can create current magnitude and phase relationships that can easily raise the front-to-back ratio to 20 dB. Indeed, if we are willing to sacrifice some gain, we can create 180° front-to-back values as high as 50 dB--but only for the narrowest of bandwidths.

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Many hams have a restricted view of phasing techniques. ON4UN's Low-Band DXing has perhaps the largest collection of practical phasing techniques. We may usefully but incompletely categorize the techniques into 3 groups, as shown in Figure 4. On the left are methods that use transmission-lines to achieve the requisite splitting of current and transforming the current magnitudes and phase angles to optimal values. The ZL-Special technique of using a single 1/8 wavelength line with a half-twist misled many builders into believing that line impedance transformation was the critical factor. However, the rate of current transformation along a line may not coincide with the impedance transformation. Particular set-ups of elements may require a forward, a rear, or an intermediate feedpoint. One part of the line may require a half-twist or not. Indeed, there are many situations in which available transmission lines or those we might construct simply will not provide the required current magnitude ratio and the phase angle difference that yields an effective beam.

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The most direct route around this problem is to employ phase-changing networks at each element, as suggested by the middle sketch. Due to the weight of such networks, we ordinarily employ them with ground-mounted vertical monopole systems. An alternative is shown on the far right. We may employ ground-mounted networks and use measured transmission-line lengths to each element. Current undergoes a full cycle in 360° of line (not in 180°, as is the case for impedance). However, the lines may have different lengths to add additional current and phase angle transformations to the output of the network or networks.

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Network calculations require more space than we have for this overview, but we can demonstrate the potential benefits of a transmission-line-based phasing system with a single example. Consider 2 vertical dipoles set up for parasitic operation, as shown in Figure 5. The element center points are at equal heights, and the lowest approach to average ground for this 7.15-MHz array is 15'. With the 1" diameter aluminum elements used for the array, we obtain the patterns shown in the figure and the modeled performance figures that appear in Table 3. Like virtually all good 2-element driver-reflector parasitic systems, we obtain about 3.2-dB gain over a single vertical dipole. As we might expect from such an array, the maximum front-to-back ratio is just over 12 dB. With the element dimensions shown, the feedpoint impedance is close to 50 Ohms.

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Without changing any of the array dimensions, we may improve performance, especially with respect to the front-to-back ratio, as shown on the right side of Figure 5. The required phase line has two sections. The short section goes to the forward element. The longer section goes to the rear element and uses a half twist. The phase line sections consist of a foam dielectric coaxial cable with a 50-Ohm impedance and a velocity factor of 0.78. (A 0.66 velocity factor would yield physical lengths too short to handle the spacing between elements.) The net feedpoint impedance is about 30 + j13 Ohms, hence the need for a section of 35-Ohm cable (or parallel sections of 70-Ohm cable) to yield an impedance close to 50 Ohms. The specified length entails a velocity factor of 0.66. For the effort of figuring or finding a usable phasing system, we obtain a very small increase in gain and a very large improvement in the front-to-back ratio. At the same time, we maintain a coax-ready array.

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Planar or Screen Reflector Techniques

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Screen or planar reflectors date back to the 1920s and the billboard array. Once considered ungainly at HF, they find extensive use in the UHF region. The reflector is largely untuned, although extensive modeling has shown that gain reaches maximum when the limits of the screen at about 0.5 wavelength beyond the limits of the driving array in all dimensions. The screen is unlike the parasitic reflector, which does not reflect but instead has a size to yield the correct current magnitude and phase angle to yield a maximized forward and a minimized rearward lobe. The screen is a reflecting surface that acts largely (but not exclusively) according to principles derived from optics.

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In the HF region, the short-wave broadcast industry makes extensive use of screen reflector arrays with banks of dipoles fed in phase for a main beam that is broadside to both the screen and the driving array. Figure 6 shows the outlines of a very large array consisting of 3 rows and 3 columns of dipoles. Only a few of the support cables appear in the sketch. To have shown them all would have obscured the essential electrical elements of the array. It is possible to construct far smaller screen arrays to good effect. For example, a lazy-H is a bi-directional array that corresponds to a 1V-2H scheme in terms of the designations in Figure 6. Not only would a screen that is 2 wavelengths high by 2 wavelengths wide yield a directional signal, it would produce about 5 dB gain over the maximum gain of the basic lazy-H.

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The models used to test the capabilities of the dipole array with a screen reflector use commercial standards. Commercial dipole arrays strive to be broad-banded. The wire is AWG #10 copper (although many arrays use aluminum-coated steel). A combination of folded dipoles and a spacing of 0.3 wavelength yields a wider operating bandwidth, although it produces less than absolutely maximum gain. Table 4 shows the modeled free-space performance of screened arrays from 1V-1H up to 3V-3H. Corresponding to the data entries are the azimuth patterns that appear in Figure 7. Each pattern rests on the use of a screen with dimensions optimized for the driving array size. (Commercial HF dipole arrays may skimp a bit on the screen size, and because the elements are horizontally polarized, the screen may use only horizontal wires. When a screen uses only horizontal wires, some reflector elements may exhibit parasitic properties, including high-than-normal current magnitude excursions.)

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The data and patterns are notable in several different ways. As we add elements vertically, the beamwidth does not change, although for each column, we find about the same gain increase with each added vertical bay. When we read the table and the patterns horizontally, we discover that each horizontal bay that we add reduces the beamwidth and increases the front-to-back ratio. One major advantage of the dipole array is that it allows the operator to select the best compromise between gain and beamwidth just by opting for an array size. In addition, by phasing each vertical bay in equal increments (for example, 30°, 60°, 90° for a 3-bay array), it is possible to slew the signal angle with respect to the plane of the array without major distortion to the pattern shape.

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In amateur use, a planar or screen reflector accepts a wide variety of drivers. The drivers may be either vertically or horizontally polarized and range from simple dipoles to more complex bi-directional arrays. Half-squares, rectangles, and side-fed quads are all applicable to a planar reflector to increase the forward gain and to yield a very good front-to-back ratio. In addition, for these single-feedpoint drivers, we can often find a spacing between the reflector and the driver that yields a desired feedpoint impedance, such as 50 Ohms, without sacrificing significant gain. One caution to observe is not to bother using an end-fire array in front of the screen. The screen will dominate so that the phased elements will not provide any significant further gain.

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Traveling-Wave Termination

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Long-wire technology arose in the late 1920s and more especially in the 1930s in answer to the need for very precise trans-oceanic point-to-point communications. Edmond Bruce stands at the head of the class of antenna engineers for his invention of the "king" of long-wire antennas. Although these collinear arrays have largely passed out of service as installations strive to save real estate, amateurs still dram of wire antenna farms. Indeed, one humorist from past decades once specified his ideal DX antenna as a very large rhombic installed on a rotatable island. The basic long-wire shapes are the single long wire, the V, and the diamond or rhombic. Each of these shapes is essentially bi-directional. We obtain a directional beam by adding a terminating impedance at the array end opposite the feedpoint. In doing so we convert a standing-wave antenna into a traveling-wave antenna, although the conversion is imperfect.

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We measure the basic single long-wire in wavelengths. The sample shown in Figure 8 is 4 wavelengths long. As the patterns show, the long-wire has a split lobe. As we make the antenna longer, the lobes in each direction grow closer to the axis of the wire itself, but they never meet for almost all practical lengths. The sample long-wire antennas in these notes use 0.16" diameter (AWG #6) wire and are 1 wavelength above average ground at a test frequency of 3.5 MHz. The end-fed single wire has a lobe count that is twice the number we would expect of a center-fed wire of the same length. As the data in Table 5 show, an unterminated or standing-wave long-wire has a natural imbalance of nearly 2 dB away from the feedpoint.

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When we add a terminating impedance (in this case 800 Ohms), we obtain the directional pattern shown in Figure 8. The gain drops significantly, not only because of the terminating resistor, but as well because each end of the array must have a wire to a common ground. The two vertical lines tend partially to fill the pattern nulls and thereby prevent the array from obtaining full gain. Nevertheless, we also obtain a very wide operating bandwidth. In fact, the SWR bandwidth is significantly wider than the practical bandwidth for the pattern shape.

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The V array in Figure 9 rests on the long-wire. The angle between the two legs is a function of the lobe angle of each leg--as shown by the lobes of the single long wire. Two lobes coincide down the centerline between lobes, resulting in a bi-directional pattern that is close to equal strength in both directions. The feedpoint is in series with the legs at their junction. If we wish to add a termination, we must run lines to ground, where we place separate terminating impedances, or we must run a line between the far ends of the V with the termination centered. In either case, we discover a decrease in gain relative to the unterminated array. However, the pattern is very strongly directional, and the SWR bandwidth far outstrips the practical operating bandwidth. With a V array, changing operating frequency changes the leg length as measured in wavelengths. Hence, the angle for an acceptable pattern has a limited frequency range of about 2:1.

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With the possible exception of VK3ATN's moon bounce 2-meter rhombic in the 1960s, I am unaware that anyone has ever bothered to use an unterminated rhombic, as shown in Figure 10. However, I have included data on it in Table 5 to compare with the far more common terminated version. A rhombic with 4 wavelength legs is, of course, twice as long overall as a V with 4 wavelength legs, but the width is about the same, since the same angle-based construction is involved. The terminating impedance of a rhombic (850 Ohms in this sample) is in series with the collinear array wires. Therefore, we see far less difference between the gain of the unterminated and the terminated versions. However, we can achieve very high front-to-back ratios.

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For commercial service, the major failing of all long-wire technology was the high level of the sidelobes, clearly evident on all of the patterns. The correct V or rhombic angle might combine two or more long-wire lobes, but it did little to suppress the other lobes in the long-wire pattern. For amateur serve, optimized V-beams and rhombics have two major drawbacks. Acreage is one of them. The other is the extremely narrow beamwidth. Nevertheless, the technique of using a termination to convert a bi-directional array into a directional beam deserves its place among the options available to us.

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Conclusion

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These notes have taken a somewhat different approach to converting a bi-directional array into a directional beam by providing an overview of the major techniques available to us. Not every technique is applicable to every bi-directional array that we might wish to convert into a directional beam. As well, in some cases, a technique might be applicable in principle but highly impractical to implement. In most cases, however, we likely will find more than one potential method of conversion and can weigh each against the other factors (for example, complexity, finickiness, budget, etc.) that go into our final building decisions.

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ao11-models.zip.

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Updated 11-01-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Nov/Dec, 2006, pp. 51-59. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Broadcast, Dipole Curtain Array, EDZ / Zepp, HF Lower, Half Square, Phased Array, Rhombic, Vertical


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Narrowband NVIS Antennas

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L. B. Cebik, W4RNL

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Dean Straw, N6BV, wrote an article for QST in December, 2005: "What's the Deal About 'NVIS'?" The article provides some excellent guidance for obtaining the best results from Near Vertical Incidence Skywave (NVIS) operation. The discussion limits itself to using a simple inverted-V antenna, which prompted the following notes. We have a number of options for potentially effective NVIS antennas. In this episode, we shall look at antennas that are narrow band, that is, antennas that cover one or part of one amateur band. We have enough to learn about them to occupy us fully.

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Figure 1 sketches the NVIS situation in the most general terms. Regular amateur operations seek to elevate antennas to provide low-angle radiation. Ionospheric refraction results in a skip zone, an area between the central station and the nearest communications target. In addition, many central stations have obstructions that limit the range of point-to-point communications methods. In both cases, directing a lower HF signal upward can result in a sufficient return to provide short to intermediate range communications. Many government services consider the NVIS frequency range to extend from 2 to about 10 MHz. As Straw notes, the 7-MHz region is most suitable for nighttime work, while the 80/75-meter band provides the best results for daytime operation by radio amateurs.

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Although you may set up many antennas for somewhat directional patterns, most operators strive to have an omni-directional antenna. Unfortunately, pure omni-directionality is hard to obtain with simple antennas. However, you can approximate a circular azimuth pattern by choosing the right antenna, as shown on the left in Figure 2. The elongated azimuth pattern shown on the right may also be useful. For simple wire antennas, the broader pattern is off the ends of the wire. If the installation area permits, you can go some distance in planning your coverage. The figure also shows a convention that I shall use in these notes: listing the broadside and the endwise half-power beamwidth. The closer these numbers are to each other, the more circular will be the pattern. The greater the difference, the more elongated that the oval pattern becomes. The ratio of one to the other is a useful measure of pattern circularity.

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The final preliminary note concerns the antenna environment. We shall be looking at narrow-band antennas for use at the central station. In amateur terms, that generally means a durable home installation for which one may plan and then construct with care. The short-masted AS-2259 antenna is designed for field use, which might be a central station on a military battlefield. The antenna is useful to amateurs in Field Day and similar exercises. However, for long-term NVIS antennas, we can do far better.

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The Lowly Dipole

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The standard AWG #14 copper wire dipole will be our starting point for these NEC-4 modeling tests. All antennas will use average ground (conductivity = 0.005 S/m, relative permittivity = 13). The test frequency will be 3.9 MHz. A wavelength is about 252.2' at this frequency. The tabular data will be in fractions of a wavelength, so this number is handy for translating the information into numbers for physical planning. The trends that we uncover will be applicable throughout the lower HF range. Figure 3 sketches the 4-dipole configurations that we shall examine.

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The first case of a dipole over bare ground has two goals. One aim is to see at what antenna height we obtain maximum upward gain. The second purpose is to put to rest a certain persistent myth about NVIS dipoles, namely, that a super-low height provides a gain advantage. Table 1 provides expanded information on the performance of a dipole over bare ground at heights ranging from 0.05 wavelength (about 12.5' at 3.9 MHz) up to a quarter wavelength (63'). The table provides gain values from NEC-4 using the Sommerfeld-Norton ground calculation system (referred to as "high accuracy" in EZNEC). It also provides gain numbers reported by the only modeling program readily available during the early days of NVIS antenna analysis in the late 1980s and very early 1990s. That program was MININEC. As early as February, 1991, Roy Lewallen, W7EL, provided warnings to QST readers about the limitations of the MININEC simplified ground calculations system in his article "MININEC: The Other Edge of the Sword." Unfortunately, even today, many beginning modelers do not heed the warning. As the table shows, when we place a horizontal antenna below about 0.2 wavelength, MININEC reports an ever-inflating gain value. At the lowest height used in the table, the actual gain is 8 dB lower than the MININEC report. See the Straw article for the safety concerns and the supposed noise advantage of very low antennas.

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The table shows a gain peak with the antenna about 0.175 wavelength above ground. Although this height will be consistently the peak gain height for all of our simple antennas, heights from about 0.125 wavelength up to about 0.225 wavelength are perfectly acceptable. As we raise the antenna in small increments, we notice a slow rise in the endwise beamwidth, but a more rapid rise in the broadside beamwidth. Hence, we can go some way toward tailoring the circularity or elongation of the pattern simply by varying the height without seriously subtracting from the available gain.

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The remaining 3 configurations for a NVIS dipole reflect methods that some operators use or should use to improve performance. Table 2 supplies the corresponding modeling data, but restricts the height range to values from 0.125 wavelength to 0.225 wavelength. The first supplemented dipole uses a single 1/2 wavelength wire at ground level below the dipole. This wire and all other antenna supplements use modeled heights of 0.001 wavelength above ground so that the models will run on both NEC-2 and NEC-4. The installer's goal is to create a virtual Yagi pointed upward. Contrary to expectations, the table shows a very limited improvement in maximum gain, with the best improvement at the lowest height. Ground reflections do not occur just below the antenna wire, but over a very wide area in all directions from the antenna.

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Studies of HF dipole arrays used for short-wave broadcasting and of VHF/UHF planar reflector arrays show that a conductive screen forms a very useful reflecting surface based on principles derived from optics. Such screens perform best when they extend at least 1/2 wavelength beyond the driven elements in all directions. The model with the screen in Figure 3 and in Table 2 uses a screen that is 1 wavelength by 1 wavelength on a side. The cells are 0.1 wavelength on a side. To simulate a solid screen, the wire would have to be very thick and using that wire would prevent the screen from sitting 0.001 wavelength above ground. So I reduced the wire size to a 1" diameter. The reduced wire size leaves the screen "holy" and reduces the reported gain. However, it may also better reflect the likely amateur use of inexpensive materials like chicken wire in which the junctions are not durably connected. The tabulated data shows a nearly constant improvement over the dipole and single-wire reflector. It also shows a decreasing improvement over the dipole above bare average ground. Still, the peak gain height remains at 0.175 wavelength. The broadside beamwidth shows a 4°-5° reduction with the screen in place, but the endwise beamwidth does not change at all.

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We can simulate a full screen with a series of wires at ground level if we use enough of them. The final configuration uses 9 AWG #14 copper wires at a height of 0.001 wavelength. The wire spacing is 0.1 wavelength. Each wire is only slightly longer than the dipole itself. With the 9 wires forming a field that is 0.8 wavelength long, the final section of Table 2 shows performance virtually identical to the performance with a full screen. Smaller numbers of wires or total field sizes produce lesser performance levels. (Since the single reflector proved so ineffective and since the screen is simpler to model than the 9-wires, analyses of other simple antenna will contrast bare-ground and screen performance. However, the 9-wire field is always available as an alternative to a screen and may be easier to install.)

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Let's pause here to look at an important side question: how does ground quality affect the improvement level offer by the screen or the 9-wire field? I modeled the dipole at a height of 0.175 wavelength over bare ground and over the screen using several ground quality levels, all of which appear in Table 3. The worse the soil quality, the greater the improvement offered by the ground-level screen. Over very poor soil, the gain improvement is nearly 2 dB, but over very good soil, the improvement drops to only 0.2 dB. In no case of solid ground does the use of a screen seriously approach the level of a perfect ground, although at sea, one might come very close. The conclusion is that NVIS antennas over poorer grades of soil may benefit significantly from a screen or a 9-wire reflector. The Inverted-V

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Testing NVIS inverted-V antennas adds another variable to our modeling efforts. Let's assume that we use a fixed height for the ends of the V. For safety, I placed the ends 0.05 wavelength (about 12.5' at 3.9 MHz) above ground. As I surveyed changing top heights, I restored the antenna to near resonance, which drew the ends in toward the center and increased the angle of the wire relative to the ground. Figure 4 shows the bare ground and screen configurations. Table 4 presents the test results, including the wire angle.

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The inverted-V over bare ground shows much less gain than a dipole. The effective height of the entire wire is about 2/3 the distance between the lower and the upper ends. Hence, the peak gain is approximately the same as the dipole over bare ground at a height between 0.1 wavelength and 0.125 wavelength. Consistent with the dipole models, the peak gain for the inverted-V occurs at a top height of 0.175 wavelength.

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One advantage of an inverted-V is that the endwise beamwidth increases by from 10° to 20° relative to the dipole. In fact, the higher that we place the V, the more circular the pattern becomes. At a height of 0.225 wavelength, we find only a 23° difference between the broadside and the endwise beamwidth reports. The wire angle at this height is about 46°, a value that we cannot safely achieve at lower top heights. Obviously, the greater the wire angle relative to ground, the more omni-directional the pattern becomes.

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For any given top height, an inverted-V's effective height will be lower than a linear dipole at the same height. As a consequence, the inverted-V tends to benefit more from the presence of a ground-level screen (or its 9-wire substitute). The lower part of Table 4 shows a 1-dB or greater improvement in gain. As well, it shows a slight improvement in the circularity of the azimuth coverage due to a small shrinkage in the broadside beamwidth.

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One strategy for setting up a NVIS antenna system is to use a pair of inverted-V antennas--one for 80/75 meters, the other for 40 meters--using a common center support and a common feedpoint. If the antennas are at right angles to each other, interactions between the two sets of wires will be minimal. The limitation of such a system is that we end up with both bands using heights that are not optimal. 0.125 wavelength at 3.9 MHz is close to 0.23 wavelength at 7.2 MHz. While both heights fall within the scanned range for our test cases, one or the other may yield a pattern shape that is not ideal. We may use the same center support for both bands, but setting up separate antennas optimized for the best height and wire angle (over a reflector screen) may let us achieve near circularity of coverage or just the degree of pattern elongation that we need for the intended coverage area.

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The 1-Wavelength Loop

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An overlooked antenna for NVIS work is the 1 wavelength loop. Each side of the loop is only about half the length of a dipole for the same frequency. If we plan to supplement the antenna with a screen or other reflection means, the loop may prove to be more compact than a dipole or a V with a screen below. As well, we can nest loops for each lower HF band that we wish to cover. Figure 5 shows the bare-ground and the screened configurations, the data for which appear in Table 5.

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Compared to a dipole, the 1 wavelength loop provides slightly higher maximum gain levels and slightly more circular patterns. At the height of maximum gain, the loop pattern is about 24° less oval than the dipole pattern, as measured by the difference between the broadside and the endwise beamwidth values. For the loop, the broadside direction passes through the mid-side feedpoint and the midpoint of the opposite side. The endwise pattern passes through the two opposing two sides without a feedpoint. The use of a 1 wavelength by 1 wavelength screen below the loop at ground level provides slightly less added gain than it does for a dipole.

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In some respects, the 1 wavelength loop provides the best of the dipole and the inverted-V worlds. It has the dipole's gain and the V's nearly circular pattern. However, it does require 4 corner supports, and the feedpoint is well above the range for a good match to common 50-Ohm coaxial cable. The latter problem disappears if we add a 1/4 wavelength section of 70-75-Ohm cable.

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High-Gain NVIS Arrays

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The simple antennas that we have explored offer a balance between gain and beamwidth. Since we are dealing with nearly circular azimuth patterns with only one main lobe, the only way to increase upward or maximum gain is to decrease the beamwidth in one or both directions. Hence, high-gain arrays are not necessarily for everyone. The operator who needs to use elevation angles down to say 45° may obtain better results with one of the simple antennas. However, a central station that requires only short-distance communication may find an advantage in concentrating his or her signal upward. In fact, by using a common wire array configuration, we may obtain up to 6-dB additional gain.

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Perhaps the two most common NVIS arrays used to increase upward gain are the "Jamaica" and the "Shirley" array. Actually, both arrays are forms of the lazy-H facing the sky. Moreover, for raw upward gain, these arrays overlook the best of the lot: the extended (or expanded) lazy-H. Let's quickly sample all 3 antennas both with and without a screen (or multi-wire) supplement. In each case, the antenna itself will use the same AWG #14 copper wire common to the simple antennas. We feed each antenna element in phase with equal length lines to a central feedpoint. The feedpoint impedance will vary according to the element length, the spacing, and the characteristic impedance of the phasing lines. Table 6 provides the modeled data for all 3 antennas.

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The Shirley array, shown in Figure 6 uses 1/2 wavelength elements spaced about 0.65 wavelength apart. Some versions use folded dipole elements for presumed match to the phase lines, but that aspect of the antenna construction plays no role in establishing the basic gain and pattern data. At a height between 0.175 wavelength and 0.2 wavelength, the antenna shows a little over 4-dB gain over a dipole. The price that we pay for the gain is a very significant reduction in the broadside beamwidth (by nearly 70°), but not in the endwise beamwidth. See the lower part of Figure 6. The result is a highly elongated oval that favors the directions off the ends of the elements. The use of a 1 wavelength by 1 wavelength screen adds nearly a dB to the gain without altering the beamwidth values. +
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The Jamaica array, shown in Figure 7, uses a standard lazy-H configuration: two 1 wavelength elements with a 1/2 wavelength space between them. Over bare ground, it improves upward gain by a full dB over the Shirley array, but the addition of a 1.5 wavelength by 1 wavelength screen adds less than a half-dB more. In both cases, the Jamaica height is the same as the Shirley height. One way to view the circularity of the patterns is to take the ratio of the broadside to endwise beamwidth values. The dipole over bare ground shows a broadside-to-endwise ratio of 1.7:1. In contrast, the Jamaica array has a ratio of less than 1.3:1 over bare ground, as illustrated by the patterns in the lower half of Figure 7. Both numbers are drawn from the height of maximum gain. (In contrast, the Shirley array showed a broadside-to-endwise ratio of 0.6:1.) Note that the use of collinear half wavelength elements and half wavelength spacing yields no sidelobes. The wider spacing of the Shirley elements revealed the emergence of low-angle broadside lobes.

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For raw gain, we can do little better than increase the element length to 1.25 wavelength and use a 0.65 wavelength space between the elements. Figure 8 shows the results, along with patterns that reveal the emergence of sidelobes in both the broadside and endwise directions. The user will have to determine whether the lower-angle sidelobes present a danger of increased noise pick-up based on the level and types of noise sources for the given location.

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If the sidelobes do not pose a problems, then the extended lazy-H array adds nearly 2 dB to the gain offered by the Jamaica beam, without a screen or with the requisite 2 wavelength by 1 wavelength screen needed by the extended lazy-H. (Of course, a field of wires about 1.5 wavelength long and extending about 0.4-0.5 wavelength beyond the broadside limits of the active array may substitute for the screen.) The screen adds only about 0.4-dB gain to the bare ground version of the antenna. Essentially, the extended lazy-H configuration provides 12.5-13 dBi maximum gain over average ground, compared to 6.4 to 7.1 dB for a dipole at roughly the same height. In exchange, as shown by the lower part of Figure 8, we further narrow the beamwidth--down to 44° broadside and 31° endwise. The 1.4:1 ratio shows fairly good azimuth circularity.

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Assuming that we can handle the Lazy-H array feedpoint impedance values with an antenna tuner, the extended version of the array offers a further unadvertised benefit that stems from its higher gain level. We can afford to place an extended lazy-H a bit higher than the optimal height and set the element length at 1.25 wavelength on 7.2 MHz, with a 40-meter spacing of about 0.6 wavelength to 0.65 wavelength. The gain deficit relative to an optimal height will be small. At 3.9 MHz, the array will be a little over half as high, and the element lengths and the spacing will be half as much. The array will still perform well, with a gain level intermediate between a dipole and a full extended lazy-H. At the lower frequency, we would find no sidelobes.

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The lure of additional gain often blinds us to other considerations that may affect our operation. Throughout these notes, I have tried to give equal strength to gain and beamwidth comparisons. Which factor requires greater weight in deciding on a NVIS antenna requires an operator decision. If operations require more than short range, then the added gain of the lazy-H configurations may not be an advantage. Therefore, Figure 9 may be of interest. It shows overlaid patterns for a 1 wavelength loop and for the extended lazy-H array, both over bare ground. The increased gain potential of the lazy-H captures our initial attention. However, if we count upward to the 45° elevation angle, we discover that the loop has a significantly higher gain in that elevation direction. In fact, at that angle, the lazy-H has almost no gain, since it is the angle for the null between the main lobe and the sidelobe in both the broadside and the endwise patterns.

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Conclusion

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We have looked at a variety of central-station NVIS antennas for amateur use with an eye toward finding the optimal height of maximum gain (between 0.175 wavelength and 0.2 wavelength). We also examined the level of pattern circularity achieved by these simple designs. We also explored a few high-gain NVIS arrays, as well as the level of benefit offered by ground screens or multi-wire substitutes. Which antenna might be correct for you depends on your available space, your access to supports, and also the type of operating that you do. For casual chats with a neighbor who lives beyond yon hill (or even beyond the hill beyond yon hill), a high gain array may be a nearly ideal NVIS antenna.

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For the emergency operator, high gain alone may not solve all challenges, especially if there is a need to reach beyond short range into the intermediate range that still falls within the skip zone. One of the simpler antennas may better serve the requirement. In his article, Straw noted the need for multiple relays to route important messages outward and then back inward toward targets, many of which required NVIS-type propagation. Under these conditions, the right antenna--abetted by high operator skill and experience--proved invaluable. In fact, it gave a contemporary rationale for continuing to call our national organization the American Radio Relay League. Indeed, an operator who copies precisely and relays accurately is as important as the antenna that he or she uses.

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ao12-models.zip.

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Updated 01-01-2007. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jan/Feb, 2007, pp. 55-61. Reproduced with permission. Copyright ARRL (2007), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Dipole, HF Lower, Horizontal Loop, Inverted V, Loading, NVIS


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NVIS Antennas for Special Needs

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L. B. Cebik, W4RNL

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Our last episode dealt with basic and advanced monoband NVIS antennas. Although we found a number of differences among the antennas, most of them showed reasonably circular azimuth patterns as determined by the ratio of the broadside to endwise half-power beamwidth. Virtually all of the antennas achieved their maximum upward gain at heights between 0.175 wavelength and 0.2 wavelength. We also saw clearly the relationship between gain and beamwidth, especially when we compared antennas like the dipole, the inverted-V, and the 1 wavelength loop with more complex arrays based on the lazy-H configuration.

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In this follow-up set of notes, we shall look at two special needs within the overall NVIS scene: a desire for directional NVIS communications and the requirement--largely a function of newer ALE potentials--for very wide-band communications. To simplify our discussions, we shall place all antennas over bare average ground (conductivity = 0.005 S/m, relative permittivity = 13).

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Directional NVIS Communications

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Curiously, a few years back, I received within a fairly short time period two notes via e-mail. One correspondent wished to know if there might be an effective NVIS antenna for his coastal location, since he wished to direct as much as possible of his signal inland. The second note, a few weeks later, asked is there might be an antenna for his coastal location that would allow NVIS communications out to sea with enough front-to-back ratio to quiet signals from land-based stations in the other direction. Not only do both inquiries have an affirmative response, they both might use the same antenna.

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Figure 1 shows two candidates composed of AWG #12 copper wire and set at 45' about 0.175 wavelength) for 3.9-MHz operation. The upper left sketch shows a conventional 2-element driver-reflector Yagi. The element spacing provides a feedpoint impedance close to 50 Ohms. As we lower the height of a directional antenna, the main forward lobe angles ever more upward. The Yagi shown has a TO angle of about 49°, with an elevation beamwidth that extends to nearly overhead. The maximum gain approaches 8.2 dBi at the TO angle, with a 7.5-dB front-to-back ratio. The radiation directly upward from the Yagi is only down about 3.5 dB or so from the maximum gain, so NIVS communications at the shortest ranges will be similar in strength to using a dipole or inverted-V. However, receiving sensitivity to the rear of the array will be well down from maximum gain. The result is directive NVIS operation, whether out to sea or inland from the sea.

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The way to improve the NVIS directional pattern is not with more antenna gain, but with less. The more compact Moxon rectangle--consisting of AWG #12 copper wire--has a lower maximum gain value: about 7.9 dBi. However, the TO angle is about 55°, with a smoother pattern curve from front-to-rear. Hence, the zenith angle falls within the elevation pattern's beamwidth. As well, the rectangle's configuration provides an additional 2-dB of front-to-back ratio, resulting in further quieting in the unwanted direction. We might obtain similar results from the Yagi by lowering its height somewhat.

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Because both antennas are horizontal directional beams, even at low heights, we have a limited horizontal beamwidth. NEC-4 reports a value of 94° for the Yagi and 120° for the Moxon rectangle. These reports derive from the azimuth patterns that we took using the TO angle as the pattern elevation angle. Since both TO angles are quite high, we must use caution in accepting the reported values.

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Every azimuth pattern over ground specifies an elevation angle for the pattern. Only if the elevation angle is 0° (illicit in NEC-2) will the pattern itself be circular. Azimuth-equivalent patterns in free-space may use 0° elevation and also yield a far-field tracing that is flat and circular. Every non-zero elevation angle entry in fact produces a pattern based on a conical surface, as suggested by the radically high elevation angle in Figure 2. Let's assume that the figure has sliced the cone from tip to base and therefore shows only the main forward lobe and not the rearward lobes. The actual half-power beamwidth on the surface of the cone is the angular distance between the points on the lobe that are 3 dB down from the peak gain value.

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Unfortunately, limitations of software force us to project the pattern onto a flat circular plotting form. World maps suffer a similar problem when we project the features of a globe onto a flat page. The problem is distortion. With azimuth patterns, we do not notice the problem with antennas that we use for long-distance communication, because we normally us fairly low elevation angles. Hence, the cone and the plotting form are very similar. However, for NVIS operations, we are interested in high to very high angles, that is, elevation angles from 45° to 90°. At these angles, the distortion can be high, and it increases as we increase the elevation angle. The right side of Figure 2 may seem to create only mild distortion, but the sketches show a 2:1 ratio between the angles on a flat surface and on the conical surface at the left.

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We may quickly calculate an approximate corrected horizontal beamwidth value using a simple equation:

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BWa = BWr * cos(elevation angle) or BWa = BWr * sin(theta angle)

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BWa is the actual horizontal beamwidth, BWr is the NEC report of the beamwidth, and the indicated angles are the elevation or theta angles at which we take the phi/azimuth pattern. The use of an elevation angle or a theta angle will depend on the operative convention of your antenna modeling software. NEC operates using theta angles counting from the zenith downward. We convert theta angles to elevation angle by subtracting from 90°. The equation is only a handy approximation because it does not account for the fact that the pattern has side-to-side curvature on the surface of the cone, but it provides results that are as close as we need for virtually all applications.

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One reason that we do not question beamwidth reports for lower angle azimuth patterns relative to the values that occur in free-space patterns is that the cosine of the elevation angle is 0.9 or higher for all such angles that are 25.8° or lower. However, the cosine of the elevation angle decreases ever more rapidly toward zero as we raise the elevation angle. The Yagi reported a beamwidth of 94° at a TO angle of 49°. The cosine of 49° is 0.646 and so the adjusted beamwidth is about 62°. The Moxon reported a beamwidth of 120° at an elevation angle of 55°. The corrected value is about 69°. Although the initial reports seemed to give the Moxon a large horizontal beamwidth advantage over the Yagi, the corrected values tell us that there is not much difference. Since wire NVIS directional antennas require aiming, correcting the high-angle azimuth beamwidth reports is essential if we are to know what coverage we can expect from it. Of course, coverage does not suddenly end beyond the beamwidth limit, but it may weaken rapidly.

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Wide-Band Terminated NVIS-ALE Antennas

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Automatic Link Establishment (ALE) equipment has become almost standard in military circles. By very rapid scanning and synchronization of codes and return codes, the central station can select the most promising frequency for successful communications. Other governmental agencies have seen a potential for adapting this system to emergency communications. Since the scanning central transceiver does its work so rapidly, it does not have time for the delays associated with changing matching networks to effect a match between the equipment and the antenna. As a result, antennas that exhibit a constant impedance over a very wide frequency range have once more become very popular government acquisition items.

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Unfortunately, radio amateurs have also become enamored with these antennas. One of the most common misconceptions associated with these antennas is that they perform in all respects as smoothly across the frequency spectrum as the very low SWR value suggests. In general, we can rarely obtain such smooth performance over a 2:1 frequency range using an inverted-V configuration. Let's perform a small experiment. We can use the 3 antennas shown in Figure 3 as samples. Each antenna is 42.5' high at the center and 2.5' above average ground at the ends. The distance between the center pole and the wire end is 50'. Each leg is therefore 64' long, for a total AWG #12 wire length of 128'. These dimensions apply to all three variations on the inverted-V installations. The operating range is 3.75 MHz to 7.5 MHz. Each antenna is initially a bit shorter than 1/2 wavelength electrically so that we may obtain adequate NVIS patterns throughout the passband.

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The single-wire unterminated V forms a performance baseline for our comparisons. At the antenna feedpoint, we shall expect (and ignore in this context) a wide set of excursions for the resistive and reactive components. The resistance will begin quite low and reach a very high value at or near the upper frequency limit. The reactance begins as a moderate capacitive value and climbs to a very high inductive value. These progressions are normal for an antenna that begins at just under 1/2 wavelength and reaches about 1 wavelength at the upper frequency limit.

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More significant for the present context are the data in Figure 4, which graphs the maximum gain and the broadside and endwise beamwidth values. The gain declines at the lower end of the spectrum as the antenna reaches 1/2 wavelength and then becomes even shorter. Otherwise, the gain level is relatively smooth and consistent with values that we saw for the inverted-V in the last episode. The broadside beamwidth shows a continuous climb with increasing frequency. In contrast, the endwise beamwidth remains relatively constant until we near the upper end of the passband.

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The middle sketch in Figure 3 shows perhaps the most popular terminated wide-band antenna used by amateurs: the terminated folded dipole. There are many versions and a number of myths surrounding the antenna. The spacing between the AWG #12 conductors can vary from an inch to a foot or two with no modelable difference in the basic performance. Far more critical to any application is the length. An ideal terminated wide-band folded dipole antenna will be at least 1/2 wavelength long at the lowest operating frequency to remain above the performance "knee." The knee represents an electrical length below which performance falls off precipitously as the antenna feedpoint resistance without the termination would decrease from about 70 Ohms toward zero. The series termination would provide a stable feedpoint impedance, but also dissipate more and more of the energy. In the inverted-V configuration, the baseline non-terminated impedance would be closer to 50 Ohms. Above the knee region, the impedances undulate around the value of the terminating resistor. A resistor in the vicinity of 800 to 900 Ohms tends to yield the smoothest SWR curve. Of course, the antenna must include an effective method of converting the high terminal impedance down to a conventional coaxial-cable value.

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Like the single wire unterminated inverted-V, the terminated folded version is slightly short relative to the knee in order to produce acceptable patterns for NVIS operation within the 3.75- to 7.5-MHz passband. Because the amount of shortening below 1/2 wavelength is small, we should see only the start of the gain decline below about 4.5 MHz. The graph in Figure 5 confirms this suspicion. Below about 4.5 MHz, the curve takes a sharper downward direction than the corresponding gain curve for the unterminated inverted-V. Equally significant in Figure 5 are the beamwidth curves for broadside and endwise directions from the wire antenna. Compare these curves to the corresponding set in Figure 4. The fundamental similarity is inescapable.

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An alternative method of developing a wide-band terminated antenna is to place the terminating resistors at the wire ends. These resistors require a ground-return line to provide them with a low impedance common point. The model for this basic configuration uses a wire that is 0.001 wavelength above ground so that the model will run on both NEC-2 and NEC-4.1 Commercial versions of the antenna show variations on the basic theme. Some use fans of different-length elements joined at the terminated ends. Others bring the common line back up to the feedpoint. Most of the variations tend to yield somewhat smoother SWR curves. The modeled basic version uses a 500-Ohm resistor at each end of the wire, with a 1000-Ohm reference impedance. As with the folded dipole type of terminated antenna, the system needs an effective impedance transformation device to allow a coaxial feedline. One difference between the end-terminated system and the folded-dipole type occurs with the SWR performance below the knee region. Whereas the folded version shows a smoother SWR curve, the end-terminated version tends to show a rise in SWR. Hence, the SWR provides a warning apart from gain performance to tell the user when the antenna is too short.

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Figure 6 graphs the maximum gain and the beamwidth values for the end-terminated antenna in its simplest form. The gain curve roughly parallels the folded-dipole curve, but with a slightly lower knee-frequency region--closer to 4 MHz than to 4.5 MHz. More interesting are the beamwidth curves. The broadside beamwidth is very close to what we found for the unterminated and the folded-dipole antenna types. However, the endwise beamwidth shows a greater variation across the passband than we found with the other two antennas. As well, the average endwise beamwidth is perhaps 25° greater and exceeds the broadside beamwidth throughout the passband. One consequence of this behavior difference is that commercial versions of the antenna tend to favor flatter installations than the 38° slope of the wires in these test models. The more level the wire, the lower the endwise beamwidth of the end-terminated wire, with a resulting equalization of beamwidths for NVIS operation.

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We cannot escape an ultimate comparison of the gain curves for the 3 sample antennas. See Figure 7. The gain differential between the two terminated antennas is inconsequential compared to the deficit relative to the unterminated wire. The gain difference runs from a minimum of 5+ dB up to over 6.5 dB across the 2:1 frequency span. Since NVIS operations often call for working at the margins of acceptable transmitted and received signals, a central station using a terminated antenna loses 3/4 of its transmitted power and over an S-unit of received signal strength compared to a simple unterminated wire. While terminated antennas might be used at field installations to simplify operation, they do not appear to offer the amateur operator any significant benefits for a durable installation.

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The reason for limiting the 3 antennas to a 2:1 frequency span results from the fact that terminating a given length antenna does not change the far-field pattern shape. To illustrate this basic fact, Figure 8 presents some samples of overlaid endwise elevation patterns. Only the terminated folded-dipole antenna appears as the lower-gain entry for comparison with the unterminated antenna. Adding the end-terminated antenna would only create murky pattern outlines for the inner or weaker patterns. The essential feature of these patterns is the strict congruence between the stronger and the weaker patterns across the passband. Termination affects the radiated energy of an antenna, but not its patterns. I have included a pattern for 10 MHz to establish the reason for limiting the antenna passband. However smooth the SWR curve may be for a given terminated design, the bell-shaped pattern at 10 MHz indicates an endwise beamwidth that is usually too narrow for most NVIS operations.

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The Search for a Wide-Band Unterminated NVIS Antenna

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ALE has added a fresh incentive to find a NVIS antenna that provides full unterminated wire antenna gain but with an exceptionally wide operating bandwidth. A more ideal antenna would exhibit relatively uniform gain directly upward with equal beamwidth values, that is, with a virtually circular azimuth pattern at any elevation angle. The half-power beamwidth values should fall within a range from 70° to perhaps 110° to assure adequate energy and receiving sensitivity at about a 45°-elevation range to allow intermediate as well as short-range communications by this mode. The search for such an antenna has taken two basic directions--one relatively futile, the other more promising.

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Both directions share a common feature: the use of frequency-independent design techniques. The most obvious technique is to apply LPDA design equations to a dipole array that points straight upward (or downward). In general, an LPDA design with linear elements fails to achieve the desired results due to a conflict between LPDA design criteria and the height range within which NVIS antennas perform best. For any number of elements covering any frequency range, the best height falls within the 0.125 wavelength and the 0.225 wavelength range. To obtain the best LPDA performance in terms of gain and feedpoint impedance we must increase the value of one of the calculation constants (sigma) to a value higher than we find in most horizontally oriented arrays. For the 2.5-11-MHz range (a 4.4:1 frequency span), the result would be an exceptionally tall array. As well, the gain would yield beamwidths well below the desired 70° minimum value.

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If we shorten the array by reducing the value of sigma and reduce the number of elements, then LPDA performance over wide frequency range tends to collapse. Numerous anomalous frequencies will appear. At these frequencies, the pattern will show multiple lobes in unwanted directions and the main lobe will not be upward. As well, the impedance curve tends to vary widely. In general, the wider the frequency span for an LPDA, closer that the design constants of tau and sigma must come to the highest permissible values. As a result, if we try to place each element at a height that favors NVIS operation, we end up with an array that fails completely in its mission.

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An alternative array that also uses basic LPDA principles in an expanded format has become popular among some commercial antenna makers for the corporate and government market: the log-spiral doublet array. Figure 9 shows the general outline for one such design. The spiral uses a factor of atheta to define the rate of radius increase with each wire segment. The design shown uses a pair of 4-turn spirals 180° apart to end up with the full structure.

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Log-spiral antennas have their greatest use in the UHF region where the design can attend to the element diameter (or strip width on a substrate). A wire version in the HF range that uses a single wire diameter will thus be less ideal and subject to numerous finicky requirements. Most commercial designs to not use an inner limiting radius for the spiral. As well most use a conical or modified conical shape (with 4 or 6 sides). Some offerings use outer-end resistive terminations, although this practice seems to defeat the point of using such a complex structure, namely, to achieve full wire gain over a wide frequency span. Hence, the state of the art relative to log-spiral NVIS potentials remains uncertain. Nevertheless, Table 1 shows the modeled performance of the flat log-spiral design and thus suggests what may be possible some time in the future. Note that at only 2 frequencies does the beamwidth drop to less than 70° in one of the sampled planes. Patterns do not go completely askew until we pass 10.5 MHz. The sample array used here requires a 50-meter diameter just to contain the wire, with additional space needed for supports.

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Conclusion

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We began by identifying two special needs sometimes associated with NVIS operation. Obtaining a directional NVIS array proved to be the simpler project, since any number of relatively low-gain horizontal arrays might meet the operational criteria for an installation. Very-wide band NVIS operation across a large frequency spread presented the more difficult challenge. If we require relatively slow frequency changes, then we can easily press an inverted-V into service over a 2:1 frequency range for acceptable NVIS patterns. However, the higher rates of ALE frequency change require an antenna that requires no alteration of the impedance matching network in the course of operation. Some typical wide-band terminated antenna types can meet the need, with 2 restrictions. First, for many antennas that we might set up as inverted-Vs or as linear doublets, the operative frequency range for acceptable NVIS patterns remains about 2:1. Second, termination yields considerable loss of gain. Achieving a wide-band unterminated antenna design capable of covering 2.5 to 10 MHz with roughly similar gain levels and acceptable NVIS patterns without a need to switch networks remains a future goal for amateurs and an expensive project for commercial and government installations.

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ao13-models.zip.

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Updated 05-01-2007. © L. B. Cebik, W4RNL. This item first appeared in QEX, May/Jun, 2007, pp. 50-55. Reproduced with permission. Copyright ARRL (2007), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Doublet, HF Lower, Inverted V, Moxon, NVIS, Yagi


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Reversible Wire Beams for Lower HF Use

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L. B. Cebik, W4RNL

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Rotatable directional beams for the lower HF region (from 30 meters downward) tend to be rare, heavy, and expensive. Many operators choose instead to use wire beams, despite their fixed orientation. One partial way around the limitation is to build a reversible wire beam. We can accomplish this feat with varying degrees of electrical complexity by switching sections of elements or using loading components.

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In these notes, we shall examine 5 different but inter-related ways of achieving the goal of reversibility with the minimum of complexity. Some designs may require more real estate, but basic construction will only involve stringing and supporting elements. Any remote switching that we do will occur outside the antenna geometry. We shall look at two designs that use shorted stubs to load driver elements to become electrically long enough to serve as reflectors in 2-element beams: one Moxon rectangle and one Yagi. Then we shall look at an alternative reversible 2-element Yagi that requires 3 wires. The next step is to extend that technique to a 3-element Yagi with 5 wires. Finally, we shall reduce the wire count to 4, using an idea passed along to me by Bill Desjardins, W1ZY.

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Some Directional Beam Basics

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Although we may apply the general ideas in these notes to any of the bands in the lower HF region (or even to 160 meters), we shall focus on 40 and 30 meters, using test frequencies of 7.15 and 10.125 MHz. 30 meters is a band that is ideal for a reversible wire beam, because we can usually manage a 50-foot height. However, the band is so narrow that we do not receive a full impression of wire-beam capabilities and limitations unless we also include 40 meters.

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One limitation of horizontal beams is strictly frequency-related. The height of a beam determines to a significant measure its performance potential, and we measure the height in wavelengths. In the lower HF region, height is normally a fraction of a wavelength, since even at 30 meters, a wavelength is about 100'. At 40 meters, that same 100; is only about 0.7 wavelength. Figure 1 shows selected elevation patterns at different heights from 0.25 wavelength up to 1.0 wavelength for a 2-element Yagi. At the lowest height, the beam is best used as a directional NVIS antenna. The lowest usable height for reliable DX work may be about 3/8 wavelength Table 1 provides performance data at 0.125 wavelength increments.

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Note that the rise in forward gain is not smooth as we increase height. As well, the front-to-back ratio fluctuates with height, reaching its maximum value at 1/2 wavelength intervals beginning at 3/8 wavelength (with the second maximum value at about 7/8 wavelength. The value curves grow ever smoother as we exceed a 1 wavelength height, but such heights are impractical for most reversible wire beam builders.

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The performance that we can obtain depends on the beam that we select. Most wire antenna beam builders choose a directional beam over a bi-directional antenna to obtain freedom from rearward QRM. Different beam designs are better or worse in this department. Figure 2 shows the elevation and azimuth patterns of 3 different beams at a height that maximizes the front-to-back ratio: 3/8 wavelength. The standard 2-element Yagi barely achieves 12 dB. The Moxon rectangle and the 3-element Yagi do far better. Similar relationships would show up at all heights, but the patterns for a height of 3/8 wavelength are simply more vivid. As we shall see, however, the front-to-back ratio will not be our only consideration if we choose to build a reversible beam.

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All wire beams will fail to cover a band as wide as 40 meters. Figure 3 overlays 50-Ohm SWR patterns for the 3 subject beams. The Moxon rectangle and the 2-element Yagi have natural 50-Ohm feedpoint impedances. For greater gain in the 3-element Yagi, I selected a design with a 30-Ohm feedpoint impedance and fitted it with a Regier series matching system using 50-Ohm and 75-Ohm cables to arrive at 50 Ohms. However, the SWR curve does not significantly change its 2:1 SWR bandwidth in the conversion. All three beams manage to cover a little over half of 40 meters. Hence, for most bands (with the exception of the 50-kHz 30-meter band), the builder will have to select the preferred portion of the band. Unlike simple dipoles, the directional beams will change their gain and front-to-back properties with frequency within any of the wider bands. 2-element (reflector-driver) beams shows a descending gain value with rising frequency, while a beam with at least one director will show a rising gain value with increasing frequency. Perhaps the more critical parameter is the front-to-back ratio, which tends to go to pot for the subject beams at about the limits of the 2:1 SWR values.

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The final factor that limits the utility of a reversible beam is geographic. Reversible beams are useful only if there are desired communications target areas at approximate 180° bearings relative to the beam. In Tennessee, a reversible beam would cover most of Europe on one side and the VK and ZL regions in the other. Only if you are comparably situated should you consider a reversible beam.

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The Survey Elements

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Our short survey of techniques of easily reversing beams will use 4 elements. Of course, there will be text, along with a general outline of the beam under discussion. The outline graphic will also show a free-space E-plane pattern for reference and comparison apart from any particular height above ground. We shall also examine parts of two tables. Table 2 lists the dimensions of each beam, while Table 3 provides free-space performance data at the design frequencies.

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All modeled wire beam designs in Table 2 use AWG #12 copper wire. Design techniques call for slightly different dimensions for the 30- and 40-meter Moxons, even when one measures the elements in terms of wavelengths. However, for the wire Yagis, you may use the same dimensions in wavelengths on both bands. If you design the Yagis for 40 meters, you may simply scale the element lengths and the spacing values for 30 meters. The failure to compensate for the constant element diameter only lowers the resonant frequency a bit on 30 meters, but the 50-Ohm SWR does not reach 1.5:1 on this narrow band. On 40 meters, the design frequency is 7.15 MHz. You may rescale the design upward or down ward within the band without regard to the element diameter and not incur any adverse effects.

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The free-space performance values in Table 3 allow a direct comparison from one beam's potential to another's. The top section of the table provides data on the modeled performance of non-reversible forms of each beam to permit an evaluation of the performance of reversible versions. You may revise the EZNEC models for the options to place each beam at the height that you plan to use before you reach any final conclusions. The Yagi performance data include some special entries labeled "Unused Driver Open" and "Unused Driver Shorted." We shall explain those notations as we move through the various Yagi designs.

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The Stub-Loaded 2-Element Moxon Rectangle

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The Moxon rectangle is a 2-element driver-reflector parasitic beam that uses two forms of element coupling to arrive at the design-frequency patterns shown in Figure 4. Not only do we have coupling between the parallel portions of the elements, but as well between the ends of the element tails. For versions of the rectangle requiring a 50-Ohm feedpoint impedance and using a uniform element diameter throughout, a design aid is available in the form of a spreadsheet at Antenna Design. (The spreadsheet also contains design aids for monoband quad beams and 3-element Yagis.)

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Ordinarily, the Moxon rectangle reflector tails are longer than shown in Figure 4 and in Table 2. However, to make the beam reversible, we use two identical driver elements along with the prescribed gap between element tails. To the center of each element we connect a section of 50-W coaxial cable. At any one time, one section of cable connects to the main feedline, also a 50-Ohm cable. The other section we short to form a j65-Ohm inductive reactance. At 40 meters, the stub's electrical length is 240.4", while at 30 meters, the electrical length is 169.8". Both lengths of coax are more than long enough to reach a center point, even using a cable with a 0.66 velocity factor (and shortening the physical length accordingly). Since the cables are for independent elements, a remote DPDT switch or relay changes each coax function. It is possible to use long lines that reach the shack for these functions. By careful calculation (including the line's velocity factor), we can determine long line lengths that will serve as the required stub. In fact, we can also make the lines long and tune out the excess inductive reactance with a capacitor. This type of system would place all switching inside the warmth of the shack. However, these refinements are beyond the scope of these introductory notes.

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As shown in the performance data in Table 3, the one drawback of using stubs to reverse the direction of a wire Moxon rectangle is a decrease in the feedpoint impedance. The resistive impedance drops by about 8 Ohms relative to an independent version of the antenna. Squaring the rectangle a small amount by shorting dimension A and increasing the tail length, C, of both elements would raise the impedance, but at a slight cost in forward gain, plus a refiguring of the required shorted stub reactance.

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The Stub-Loaded 2-Element Yagi

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We may apply the same technique to a 2-element Yagi, as shown in Figure 5 and in the tables. Because we wish to preserve the 50-Ohm impedance of the array once we install a coax section on each driver element, we increase the element spacing from 0.146 wavelength to 0.155 wavelength. The shorted reflector stub provides j75 Ohms inductive reactance. On 40 meters, the coax (electrical) length is 258.8", while on 30 meters, the length is 182.3". The two coaxial cable lengths allow an easy mid-point meeting for switching cable functions from driver to stub and back again, even allowing for the line velocity factor.

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The switched version of the antenna slightly outperforms the independent 2-element Yagi for interesting reasons. First, the physical proportions of the elements differ. Second, a loaded reflector provides slightly better front-to-back values than a full-size reflector. Nonetheless, we would be very hard pressed to notice the difference in operation.

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Whether you choose a Moxon rectangle or a Yagi, the stub-loaded switched beam provides the most compact route to a reversible beam. I have seen 3-element Yagis with switched elements, normally a function swap between the director and the reflector. Often such beam use open stubs for the director to provide capacitive reactance to shorten the element's electrical length. The driver remains unswitched. Hence, each parasitic element switches between open and shorted modes, with potential length changes for each mode. Since these cables are weighty, some designs have used lumped components. In most cases, the switch systems are more complex than the ones used for the 2-element beams. As well, few Yagi 3-element designs provide peak performance with equal spacing between each pair of elements, and very often they also require a matching network to raise a low feedpoint impedance (perhaps 25 Ohms) to the main feedline value. We may keep our switching simple if we have enough land to add some further wire elements.

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The 3-Wire 2-Element Yagi

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One way to simplify switching is to begin with a common reflector element. For 2-element Yagis, we then add a driver on each side of the reflector. As shown in Table 2, the spacing of the elements returns to the value of the independent beam. The net result, as shown in Figure 6, is essentially two 2-element Yagis with a common reflector. Instead of switching loading stub lines, this design simply switches the feedline. We can handle this task at the antenna level or we can bring the two feedlines to the shack and use a simple mechanical switch.

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The 2-element reflector-driver Yagi has a limitation. As shown by the modeled data in Table 3, the performance changes according to whether the unused driver is shorted across the feedpoint or left open. The open connection provides the better front-to-back ratio. (The free-space E-plane pattern in Figure 6 shows the results of an open unused driver.) When the front-to-back ratio depends wholly on a reflector element, the unused element exerts a greater effect on the reflector performance (that is, on the current magnitude and phase angle), than when we have a parasitic beam with at least one director.

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Obtaining an open condition in the unused driver is a simple matter electrically if we switch at the antenna level. However, the arrangement may prove to be mechanically complex. We may also achieve the desired condition with a switch at the shack end of the feedlines if we attend to the cable lengths. If the feedlines are an odd multiple of a quarter wavelength, then shorting the unused line will produce an open circuit at the feedpoint. An even multiple of a quarter wavelength will require an open line end to yield an open circuit at the feedpoint. (In calculating the line lengths, of course, be sure to include the line's velocity factor.)

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The 5-Wire 3-Element Yagi

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The 3-wire reversible beam for 2-element Yagis becomes a 5-wire reversible beam for 3-element Yagis. Such an array requires considerable open ground, as the dimensions in Table 2 and the outline in Figure 7 reveal. In the process, we gain an advantage but acquire a disadvantage.

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The "bad" news first: to make the effort of installing a 3-element wire beam worthwhile, we need to select a design that provides significant gain over the 2-element Yagis. The data in Table 3 show that the design provides 1.5 to 2 dB additional forward gain over either 2-element beam. In the process, the feedpoint impedance drops to about 30 Ohms. Therefore, we require a matching system to reach 50 Ohms in order to achieve the widest possible operating bandwidth. We can easily achieve the match using common 50-Ohm and 75-Ohm coaxial cable sections in a Regier series match. We shall not go into the required calculations for this type of match in this set of notes. However, you can download a spreadsheet that includes the Regier series match within a collection of common matching systems at Antenna Matching. (The collection includes 3 types of series matches, the beta match, 2 versions of gamma-match calculations, and the matchline-and-stub system. Like the antenna design aid, the spreadsheet appears in both Quattro Pro and Excel formats.) The series matching system transfers matching complexities from the feedpoint junction to the transmission line itself. Therefore, it adds no further weight to the system.

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The "good" news is that the front-to-back ratio of a 3-element Yagi is largely a function of the director and not the reflector element. Therefore, as is clear from the data in Table 3, the state of the unused feedpoint makes almost no difference to the array performance in either direction. With a series match in place, it is likely that switching at the shack may be the easiest way to handle directional changes for the array.

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The 4-Wire 3-Element Yagi

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W1ZY determined that he did not have the real estate needed for the 5-wire beam. He also reasoned that he could feed the driver with parallel transmission line and use his antenna tuner to arrive at the impedance needed by his equipment. Therefore, he opted for the scheme shown in Figure 8. As the free-space E-plane pattern suggests, he lost no performance in his truncated 4-wire version of the reversible 3-element Yagi.

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The dimensions in Table 2 reveal that the elements consist of 2 directors and 2 "reflectors." I place the word reflector in quotation marks, because each of these two elements trades functions as we swap directions. One of the two elements becomes a reflector. The element between it and a director becomes the driver. The driver length makes little difference to beam performance. (In fact, J-poles have been used as 3-element Yagi drivers.) Driver length becomes critical only if we are seeking a particular feedpoint impedance. In this design for a reversible beam, parallel feedline allows the use of a driver impedance with a considerable reactive component. Therefore, we may do the work of 5 elements with only 4 and still obtain full 3-element Yagi performance in each direction.

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For optimal performance, we must observe some cautions with the 4-wire reversible beam. First, in order to function correctly as a reflector, the unused driver must be shorted across the feedpoint by a relay or by a precisely cut line. With the reflector open at the center, the beam loses almost a full dB of forward gain and most of the high front-to-back ratio shown in the free-space E-plane pattern in Figure 8.

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Second, as the SWR increases at the feedpoint, even low-loss parallel lines begin to show detectable losses. The values at the feedpoint (about 35 + j50 Ohms) are not fatal. But losses over a 100' length of line may exceed 0.5 dB. As well, the values that appear at the tuner terminals may exceed the matching range. At 40 meters, the use of one of the modern low-loss coax cables may prove to match parallel line loss with an easier match at the tuner. In addition, the low-loss coax lines need no spacing between each other to prevent unwanted coupling. Nevertheless, in both cases, the lines require cutting to a length that-with the switching system used-will ensure a closed circuit at the active reflector (inactive driver) center.

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Conclusion

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We have looked at 5 of many variations on the theme of creating a reversible horizontal wire beam for the lower HF region. The options that we explored are among the simplest electrically, although some of them required a considerable open area for implementation. The chief goal of these notes has been to show that for the budget-minder operator with a penchant for using wire, a reversible beam is not only possible, but both feasible and practical.

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However much we tried to simplify the designs, we could not eliminate all electrical complexities. A reversible beam requires a switch somewhere along the line to change directions. As well, the unused element or the loading stub require attention to both line length and the switched condition at the line end. These matter are generally considerations that we wrestle with during installation. When operating, we may change directions as quickly as we can flip a switch.

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There are numerous variations on the design shown as examples. Perhaps the most common tendency would be to think of the elements in the form of inverted-Vs. This option has two constraints and one advantage. The advantage is the ability to provide a strong support along the centerline for the cable hanging from the elements. One of the constraints is the necessity to redesign the elements to suit the new configuration. To base the design on a few guesses derived from the linear designs shown here or elsewhere seems a bit careless when good design tools are readily available.

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The second constraint concerns performance. Inverted-V elements will reduce the front-to-side ratio of the beam patterns. In addition, V elements will also lower the effective height of the antenna. In the lower HF region, we are already height challenged with respect to obtaining a low-enough elevation angle for superior DX performance. At a certain (unspecified) point, lowering the ends of a horizontal beam may elevate the TO angle too much. In such cases, one might wish to consider one of the many directional vertical arrays, especially below 40 meters. Reversible beams are both possible and practical, but they will not overcome the limits that we briefly examined at the beginning of these notes.

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ao14-models.zip.

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Updated 07-07-2007. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jul/Aug, 2007, pp. 52-57. Reproduced with permission. Copyright ARRL (2007), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: HF Lower, Loading, Moxon, Reversible, Yagi


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Circularly Polarized Aimed Satellite Antennas

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L. B. Cebik, W4RNL

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Among aimable satellite antennas, we generally have two options. The axial-mode helical antenna has become a favorite among some satellite and other operators, especially at UHF (435 MHz and up). However, the crossed and turnstiled Yagi remains in favor among other operators. Let's explore these options, at least to a small extent, on common ground.

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The Axial-Mode Helical Antenna

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The following notes on axial-mode helices summarize parts of my longer study, "Notes on Axial-Mode Helical Antennas in Amateur Service," which appeared in the 2005 Proceedings of the Southeastern VHF Society. There I examined NEC-4 models of 5-, 10-, and 15-turn helices both over perfect ground and over ground-plane wire-grid screens. Figure 1 shows the general outline of the models, as well as their relative sizes, using a 1.2-wavelengh-by-1.2-wavelengh screen that is 1-wavelengh above ground. The test frequency is 299.7925 MHz, where 1 meter = 1-wavelengh. You may scale the designs for other frequencies by using the ratio of 300 to the new frequency times each of the critical dimensions, including the wire diameter but excluding the pitch angle. For uniformity, all models point straight up.

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The need for such a study is a function of the classical literature on axial-mode helices. Researchers tend to treat the antenna as a broadband array, and extrapolating data useful to amateur spot-frequency use is somewhat daunting. (See the final notes for some references, especially VE3NPC's more recent empirical measurements.) Modeling this type of antenna also requires considerable care.

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Perhaps the two most critical dimensions are the pitch angle and the circumference. In fact, basic helix theory tends to restrict axial-mode operation of the helix to pitch angles between 12° and 14°. The smaller the pitch angle (within limits), the higher will be the gain of a helix with a fixed number of turns. As well, various texts restrict the circumference to ranges from either 0.8-wavelengh to 1.2-wavelengh (Kraus) or from 3/4-wavelengh to 4/3-wavelengh (Balanis). The number of turns in a helix is a builder selection, as gain (for any given pitch and circumference) rises with the number of turns. As well, selection of a wire diameter is also a builder choice. Although not mentioned in any serious way in most literature, conductor size does make a difference to helix performance. The larger the wire diameter as a fraction of a wavelength, the higher the gain for an otherwise fixed helix size. The sample models that we shall explore use 2-mm diameter wire.

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There are two major issues with modeling an axial-mode helix. The first issue arises from the fact that NEC must use straight wires to simulate a circle. The difference between the circumference of a circle and that of a polygon inscribed within the circle only reaches relative insignificance as the number of sides on the polygon passes about 16 or so. A 16-sided regular polygon inscribed within a circle has a circumference that is about 99.4% that of the circle. For a more rounded number in my NEC-4 helix models, I used 20 segments per turn. Using 2-mm diameter wire, the segment length-to-radius ratio remained well above modeling minimums.

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The second major issue involves the reported vs. the actual gain of the helix models. For both the perfect-ground and the wire-grid-plane models, I assigned the source to the first segment, the one in contact with the ground surface. Because this segment does not have equal length wire segments on either side of the source segment, the initial reports of gain and source resistance will be erroneous but correctable. By moving the source segment to other segments, I ascertained that applying standard Average Gain Test (AGT) adjustments to the gain values would yield very reasonable corrected reports.

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Figure 2 shows the results of gradually increasing the circumference of 5-, 10-, and 15-turn helices (12° pitch, 2-mm diameter wire) over wire-grid planes that are 1.2-wavelengh on a side and 1-wavelengh above average ground. The gain curves are similar to those produced by the NEC-2 models created by Paolo Antoniazzi, IW2ACD, and Marco Arecco, IK2WAQ, in "Measuring 2.4 GHz Helix Antennas," QEX, May/June, 2004. The major difference is that the ground beneath the helix in my models yields a moderate rise in gain below the generally accepted optimal circumference range. Both sets of curves show that as the helix grows longer, the optimum circumference for maximum gain decreases. Exceeding the optimal circumference results in a steep loss of gain potential. With a constant pitch angle (12°), the peak-gain circumference decreases by about 0.05 wavelength with each 5-turn increase in helix length.

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The dimensions for 3 sample axial-mode helical directive arrays appear in Table 1. The arrays correspond to 12° pitch 5, 10, and 15 turn antennas at 299.7925 MHz, where 1 m = 1 wavelength. The modeled performance data appears in Table 2. The gain values have been corrected for the average gain test (AGT) score, and raw reports will be somewhat lower. The peak gain of the helices is about 11.7, 13.0, and 14.2 dBi for the 5-, 10-, and 15-turn antennas, respectively. Note that the gain increases almost linearly with the increase in the number of turns. This fact is important to keep in mind when comparing axial-mode helices with alternatives to them as circularly (or nearly circularly) polarized antennas.

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Modeling the helix itself is simplified by the GH entry in NEC. However, the NEC-2 and the NEC-4 versions of that geometry command differ radically. Therefore, modelers need to consult the appropriate manual for guidance. (The commands are available in NEC-Win Pro and in GNEC, by Nittany-Scientific, with entry-formation assistance screens.) An alternative method of creating a helix appears in EZNEC Pro, which allows helix creation as a set of individual wires batch created by entries similar to those used in the GH command. The termination of the helix on perfect ground is simple enough, but mating the lowest wire end to a wire-grid junction may call for the modeler to displace the wire end to meet the closest junction. The size of the elevated ground-plane surface for a given helix does make a difference in the performance of the antenna, although gain changes are small. There is an optimal size that varies with the length of the helix. The ground screens in the sample models are close to optimal.

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An axial-mode helical antenna rarely yields perfect circular polarization. Instead, it yields elliptical polarization with a major and a minor axis and a tilt angle. The antennas approach perfect circularity most closely along the axis of the helix. Applications needing something closer to circular perfection tend to work with quadrifilar designs, although they are impractical for amateur satellite service. The sample models improve their circularity with increased length. More pertinent to amateur use is the fact that an axial-mode helix does not produce a perfect single-lobe pattern. Figure 3 shows the total field patterns of the 5-, 10-, and 15-turn helices over an elevated ground screen. In each case, we can see a considerable collection of side lobes. Each model uses the circumference that produces the best gain, but that circumference does not yield the lowest level of side lobes. Reducing the circumference produces lower gain (from 1 to 2 dB, depending upon the length of the helix), but results in a cleaner pattern. Circumferences below about 0.85 wavelength rarely have any sidelobes at all through the 15-turn limit to my investigation.

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As well, there are remnants of opposite-direction polarization within the total field of the axial-mode helix. Figure 4 shows the dominant right-hand polarized component of a 15-turn helix over a ground-screen elevated above average ground. The left-hand component is down by 25 dB, with some of the lower lobes being composed mainly of left-hand components. All of these facets of axial-mode helix performance have a bearing on the sensitivity of such antennas to off-axis signals, whether at high or low angles relative to the axis that marks the centerline of the helix. How much side-lobe and oppositely polarized lobe suppression is enough, of course, is a user determination based upon the application and the local circumstances of use.

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These notes have not addressed the question of constructing a helical antenna. Chapter 19 of The ARRL Antenna Book provides some of the general schemes used. For UHF, the most common technique is to use a non-conductive central shaft with periodic side-projections to support the helix turns at critical points. (Fowler also uses a conductive center support rod with no degradation of performance.) The number of supports per turn depends upon numerous factors, including the inherent stiffness of the wire or tubing used to form the helix. A central shaft has a mechanical advantage by allowing attachment to the ground-plane screen, cup, or grid. Hence, the wire turns do not experience much stress, except for the inevitable attachment to a connector. Standard references give the impedance as 140 times the helix circumference in wavelengths. However, the impedance will vary with the helix structure at the terminating end and with the diameter in wavelengths of the element wire. As the impedance varies, so too will the matching method selected for use with the coaxial cable. In such applications, the coax used for the main feedline may be 50 Ohms or (for those using surplus solid sheath varieties) 75 Ohms.

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The dimensions for an axial-mode helical array are implicit in the set of design criteria to which we build. Hence, I have given only overall dimensions, although you may easily derive more specific dimensions from the graphs shown and the basic trigonometry for the design work. The following dimensions--many of which are inter-dependent--define a helix.

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+R = radius of the helix, wire-center to wire-center
+C = circumference of the helix            C = 2 p R
+S = spacing between turns                 S = C tana
+a = pitch angle                           a = tan-1 (S/C)
+N (or n) = number of turns
+L = axial length of helix                 L = n S
+D = conductor diameter
+L' = conductor length for a single turn   L' = SQRT(C2 + S2) = C/cosa = S/sina
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All dimensions refer to center-to-center distances relative to the wires. The last two items in the list are relevant to the physical planning of the helix design.

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If these notes give the impression that the axial-mode helix is somewhat imperfect, the impression is correct. However, it is not so far from perfect to bar its effective use in satellite applications. The antenna originated as a broadband array and has been pressed--sometimes uncritically--into spot frequency or narrow-band uses. Understanding the fundamental properties of axial-mode helices in this context is an essential ingredient to producing an antenna that fulfills its promise to the limits of its ability.

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Alternative Parasitic Arrays

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An alternative to the axial-mode helical array is a parasitic array with turnstiled or quadrature fed drivers. Up to a point--but not necessarily beyond that point--such arrays offer some advantages over helical arrays. Not the least of these advantages is our familiarity with the construction techniques involved in building them and matching them to standard coaxial cable feedlines.

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Unlike the helix and its design equations, most parasitic arrays are designed by model or experiment--or both--for a certain level of performance at a given frequency within some overall size constraint. Therefore, we shall offer some dimension tables for our samples without in the least claiming them as the best possible designs. The goal will be to note some significant differences between parasitic and helical arrays designed for circular polarization. The design models are for 299.7925 MHz to coincide with the helix designs that we have so briefly surveyed. Like the helices, the parasitic arrays can be scaled to other frequencies.

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When most folks think of parasitic arrays with circular polarization (or an approximation thereof), the crossed Yagi comes to mind. Although that antenna is certainly one of our alternatives, it is not the only one. Neglected is the quad beam, which one may convert to circular polarization without adding any further elements beyond those needed for ordinary or linear polarization.

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Figure 5 shows 3 of our samples to illustrate their comparative sizes. For moderate gain levels, the parasitic arrays have boom lengths that are much shorter than corresponding helical arrays. For example, a 10-turn helix with a gain of about 13 dBi is almost a half wavelength longer than a 10-element Yagi with about a half-dB higher gain. However, we have noted that helices tend to increase in gain almost (but not quite) linearly with added turns, while adding more directors to a parasitic array results in a decreasing gain-per-new-element value. Hence, there is a crossing point at which the helix may show more gain than a parasitic array of the same overall length. That crossover point most likely occurs when the arrays approach 5 wavelength in overall length.

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The first non-helical candidate is a 4-element quad, the dimensions for which appear in Table 3. The quad is only 0.91 wavelength long from reflector to the forward-most director. Using 1-mm diameter wire for the elements, it has a gain of 10.6 dBi when placed 1 wavelength above average ground. The quad's beamwidth is 58°. The performance of the quad is more completely summarized in Table 5, along with the other sample candidates as alternatives to the helix. Two sets of values are especially significant. One is the high value of front-to-sidelobe ratio (listed as a negative value of dB below the main lobe gain value), when compared to the much smaller ratio shown by the helices. In fact, Figure 6 shows the elevation patterns for the quad overlaid with two of the Yagis for direct comparison with the helix patterns shown in Figure 3.

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Because a quad allows some flexibility in the placement of the driver without undue adverse effects on the array gain, we may arrive at a single-source impedance of about 95 Ohms resistive. Hence, a 1/4 wavelength section of 93-Ohm cable forms a proper phase line run between successive corners of the driver. The result is a circularly polarized antenna. This technique first came to my attention in a sample model that Brian Beezley, K6STI, included in the model collection that accompanies his AO program. We should not run the phase-line coax parallel to the active element. Hence, it is likely that we would use a 3/4 wavelength section of line running from one corner to the center non-conductive boom and back to the adjacent corner. We may reverse the polarization simply by connecting the main feedline at one or the other end of the phase line. Higher isolation feeding methods have appeared from time to time. For this simple system, the result is a 50-Ohm impedance for the main feedline. The 4-element quad in the outline sketch has a 2:1 50-Ohm SWR bandwidth of more than 25 MHz, which eases the problems associated with construction variables. (Redesigning the antenna for fatter elements would yield a larger bandwidth.) Obviously, longer versions are possible for the quad if one desires more gain. However, in our survey of alternatives, let's turn to some Yagi designs.

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Table 4 provides the dimensions of 3 sample Yagis, all derived indirectly from normal Yagis of DL6WU vintage. The short 8-element version is 1.42 wavelengths long, while the 10-element version has a boomlength of 2.05 wavelengths. The 12-element version is 2.60 wavelengths long. The last sample Yagi appears mostly to demonstrate that as we add new directors, the increase in gain dwindles per added element. Nevertheless, the 14.2-dBi gain of the 12-element Yagi compares well to the peak gain of the 15-turn helical antenna with a total length of over 3.6 wavelengths.

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Since NEC uses only axial currents in calculating the antenna fields, one may model crossed Yagis with each crossed parasitic element pair joined at the center. If there are any interactions, they will not show in the model. In practice, it is likely that one will use a pair of independent linear elements. Since the drivers require separation, if only by a small distance, to establish their independence, it will not harm construction to use the same separation between parasitic elements. The modeled dimensions in Table 4 presume the use of a non-conductive boom.

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Table 5 summarizes the potential performance of the Yagis. The total field patterns for the 8- and 10-element versions appear in Figure 6, along with the quad. I omitted the 12-element Yagi lest the morass of pattern lines become unreadable. Each Yagi shows close to the same front-to-sidelobe ratio--about 15-16 dB. As well, all of the Yagis show the same high ratio of right-hand gain to left-hand gain. Figure 7 shows the polarized components of the 10-element Yagi for illustration of the difference. You may wish to compare this pattern with Figure 4, the comparable pattern for a 15-turn helical design.

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All of the Yagis use identical feed systems to establish quadrature and a match to a 50-Ohm feedline. In this particular design, the single driver source impedance is 50 Ohms. Hence, the turnstile phase-line is also 50 Ohm. The resulting impedance presented to the main feedline is close to 25 Ohms. A length of 35-Ohm line (or a pair of 70-Ohm lines in parallel) provides the required match for a 50-Ohm main feedline. As with the quad, one may change polarization simply by swapping phase-line ends for the junction with the matching section and main feedline. Removing the phase-line altogether converts the array to linear polarization, with the un-fed elements having little if any effect on operation in this mode.

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To center the design frequency within the overall 2:1 50-Ohm SWR passband, the line lengths for both the phase line and the matching line are not true quarter wavelengths electrically. The electrical length of the phase-line is a bit over 0.22 wavelength, while the matching line is close to 0.215 wavelength. The 2:1 SWR passband, as illustrated in Figure 8, runs between 270 and 330 MHz, a 60-MHz spread that should make home construction less critical. However, as with any antenna based upon turnstiled dipoles, the SWR bandwidth will be far wider than the operating bandwidth for which the patterns hold their desired shape. Hence, it remains good design practice to optimize the performance of the crossed Yagis for the desired range of operation. An SWR meter alone is not sufficient to optimize any circularly polarized antenna.

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The physical implementation of a parasitic design will require considerable effort. Never assume, but actually measure the actual velocity factors of the lines. Construction will require close attention to line dress and to the potential effects of any connector installed. For UHF and upward, one should use certified connectors rather than hamfest specials and bargains. Even the solder lumps that close the wire loops of the quads can create detuning effects from 70 cm upwards. Whether you are building a helix or a Yagi, the casual and careless construction techniques that are harmless at HF become potential plagues to UHF antennas.

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Conclusion

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As always, we have looked at alternatives for antennas meeting a certain set of needs. In this case, we selected satellite communications, with its need for circular polarization--or as closely as we may approximate circular polarization using standard construction techniques. The key alternatives for antennas that we steer with respect to both azimuth and elevation are axial-mode helical arrays and turnstiled parasitic arrays.

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Both techniques will produce able arrays. Our survey and samples do not exhaust the designs that we may bring to bear on the communications need. However, they should open the door to relevant considerations in making a choice between the two major routes to circularly polarized antennas and to some of the considerations when designing an antenna within either general category.

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Reference Note

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There are a number of background sources for information on axial-mode helices. The following list is a start, with most of the items having extensive bibliographies. John D. Kraus, Antennas, 2nd Ed. (1988), pp. 300-310.
+ H. E. King and J. L. Wong, "Helical Antennas," Chapter 13 of Antenna Engineering Handbook, 3rd Ed., R. L. Johnson, Ed. (1993), pp. 13-1 ff.
+ Darrel Emerson, AA4FV, "The Gain of an Axial-Mode Helix Antenna," The ARRL Antenna Compendium, Vol. 4 (1995), pp. 64-68.
+ C. A. Balanis, Antenna Theory, 2nd Ed. (1997), pp. 505-512.
+ W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd Ed. (1998), pp. 231-239.
+ Paolo Antoniazzi, IW2ACD, and Marco Arecco, IK2WAQ, "Measuring 2.4 GHz Helix Antennas," QEX, May/June, 2004, pp. 14-22.
+ L. B. Cebik, W4RNL, "Notes on Axial-Mode Helical Antennas in Amateur Service," Proceedings of the 2005 Southeastern VHF Society Meeting, pp. 82-121.
+ Clare Fowler, VE3NPC, "Real World Helix Antenna Measurements," The AMSAT Journal, May/Jun, 2006

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ao15-models.zip.

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Also see the Antenna Modeling Programs page for more information.

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Updated 08-27-2007. © L. B. Cebik, W4RNL. This item first appeared in QEX, Sep/Oct, 2007, pp. 51-56. Reproduced with permission. Copyright ARRL (2007), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Helix, Quad, Satellite, VHF / UHF, Yagi


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Horizontally Polarized Omni-Directional Antennas: Some Compact Choices

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L. B. Cebik, W4RNL

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Obtaining omni-directional coverage with vertical polarization is simple: use a version of the many vertical antennas including the 1/4 wavelength ground-plane monopole, the vertical dipole with or without a J-pole matching section, or any number of collinear variations on these antennas. However, if we wish to have omni-directional coverage with horizontal polarization, solutions are less automatic. In fact, the search for a perfect horizontally polarized omni-directional (HPOD) antenna goes back into the dim recesses of antenna history. We shall examine a number of options, their limitations, and, in some cases, ways to overcome those limitations. We shall divide the work into two parts, looking at some of the more compact choices in this episode. Next time, we shall examine a few larger omni-directional horizontal arrays and take a longer look at stacking them.

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The search has two dimensions. The first is obtaining a perfect circle for an azimuth radiation pattern. How far from circular you may be willing to accept a pattern may determine how much work you will put into the antenna design and construction-or vice versa. The second dimension is field strength or the antenna gain at low angles. As we shall see, some designs with good patterns unfortunately send a goodly part of their energy in useless directions, such as straight up or down. While helpful for satellite reception, these antennas are less than ideal for some VHF point-to-point applications.

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All of the antennas in these notes use 144.5 MHz as the test frequency. Patterns and performance values assume a height of 20' above average ground.

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Turnstile or 90° Phase Fed Systems

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Perhaps the oldest HPOD antennas employ one or another form of phase feeding, using at least 2 elements. Figure 1 shows the most common form of feeding one element with the same current magnitude but phase-shifted 90° from the other. Both elements are identical, but are at right angles to each other. The phase line characteristic impedance is the feedpoint impedance of the directly fed element. However, with both elements connected, the net feedpoint impedance is one-half of the impedance of an isolated element. There are alternative feed systems to arrive at the same goal, but a few of them concern themselves with impedance matching rather than obtaining the correct current magnitude and phase angle at the center of each element.

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The simplest version of this antenna also gave birth to the generic names for the feed system. A pair of resonant dipoles at right angles to each other presents the appearance of a turnstile. Figure 2 provides the general outline of the antenna. The version from which we drew the patterns uses 0.125" aluminum for the 38.96" elements. The model places the elements 0.25" apart, center-to-center. Each dipole presents a 70-Ohm impedance. With the 70-Ohm 1/4 wavelength phase line in place, NEC-4 reports a net feedpoint impedance of 35 Ohms. Since the impedance does not change over a very broad frequency range, we may accept the 1.43:1 50-Ohm SWR or we might use a series matching system to match more exactly a 50-Ohm feedline.

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The azimuth patterns show a slight squaring, but the gain range is only about 0.5 dB, less than we could detect in operation. The chief limitation of the turnstiled dipoles is revealed in the elevation pattern. We find more energy broadside to the dipole pair than off its edges. Hence, the maximum gain at 20' and a 4.8° TO (take-off) angle is only 5.06 dBi.

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Ott Fiebel, W4WSR, pointed out to me an interesting variation on the standard turnstile by placing two 1/2 wavelength elements at a 90° angle, but using one end of each element to form the apex. A simple 1/4 wavelength parallel line matching section connected in series with the ends at the apex allows a 50-Ohm match. Although the pattern is not quite as clean as the standard turnstile pattern, the construction is simple and reliable.

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Figure 3 shows one way to overcome the broadside radiation of turnstiled dipoles: create a stack with 1/2 wavelength separation. In the model, the lower antenna is at 20', with the upper antenna about 80" above it. The elevation pattern shows a radical reduction in high-angle radiation. The maximum gain of the antenna pair is 9.14 dBi, with a 0.9-dB range of gain around the perimeter of the azimuth pattern. However, we cannot use the same dipoles that we used in the single turnstile. Mutual coupling between the bays requires that we lengthen the dipoles to 40.2". Without this adjustment, the pattern becomes very distorted. We would not notice the distortion from the SWR. For all turnstiles, the SWR bandwidth is very much wider than the operating bandwidth measured in terms of an acceptable pattern. For further information on the performance behavior of turnstiled antennas, see "Some Notes on Turnstile Antenna Properties," QEX, March/April, 2002, pp. 35-36.

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We may also turnstile 1 wavelength quad loops at right angles to each other. A single quad loop has an impedance of about 125 Ohms, for a net feedpoint impedance of 62.5 Ohms for the turnstiled pair. RG-63 (125-Ohm) coax is suitable as a phase line. Figure 4 shows the outline and patterns for one version of the antenna using a diamond configuration for simplified construction. (See "A 6-Meter Quad Turnstile," QST, May, 2002, pp. 42-46, for one version of this antenna.) The elements are AWG #12 copper wire, with each loop having a circumference of 87.7". Alternatively, one might equally use quad loops in a square configuration, the so-called eggbeater. In either configuration, we may leave a gap between the top wires at the crossing point or connect them together. Performance does not change.

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The elevation pattern shows a significant improvement in the direction of radiation from the antenna, with the lowest lobe as the strongest. The maximum gain of the modeled turnstiled quad is 6.21 dBi, with a gain range of about 0.5 dB, as shown by the not-quite-perfect circle of the azimuth pattern. The TO angle is 4.8°. All of the patterns in these notes will use the maximum gain at the TO angle as a measure of performance. It serves as a stand-in for our real concern with HPOD antennas: the signal strength for point-to-point communications over some fixed distance and a fixed observation or reception height.

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Once we overcome the basic turnstile's broadside radiation that robs energy from the desired edgewise signal path, matching becomes the most obvious construction hurdle. However, the turnstile antenna has a hidden limitation. The pattern shape is highly dependent upon the magnitude and phase relationship between the two feedpoints. Most common feed systems provide a correct relationship at only one frequency, and the values change as we move away from that frequency. Small inequalities in the current magnitude and departures from the required 90° phase-angle result in considerable distortion to the nearly circular pattern at the design frequency.

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We might easily turnstile or phase-feed a number of other antennas. However, most of them would serve better for satellite communications than for horizontally polarized direct communications. Therefore, we may let the dipole and quad loop turnstile pairs serve as examples of our initial technique for obtaining omni-directional patterns.

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Halos

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The second common category of antenna for obtaining at least a semblance of a circular azimuth pattern is one or another version of the halo. More correctly, this class of antenna rests on a 1/2 wavelength dipole bent so that the ends almost meet. The most tempting form for the halo is either a circle or a square. However, as Figure 5 shows, a symmetrical halo with a single element yields a highly non-circular pattern. The model uses 0.5" aluminum for the element that is 10" on a side with a 0.52" gap. The azimuth pattern gain varies by nearly 3 db. To boot, the impedance is only about 8.3 Ohms.

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One way to circularize the pattern is to add a surface on each element end to increase the capacitance between ends. The model outlined in Figure 6 simulates plates be using 4 facing 6" wires on each side of the gap. A normal halo would employ a disk. We see an obvious improvement in the pattern shapes, with a maximum gain of 7.35 dBi and a gain variation of less than 0.4 dB. As well, the feedpoint resistance is about 49 Ohms. However, the plates have added an inductive reactance of j1000 Ohms. Hence, we need a series capacitance at the feedpoint of 1.1 pF. This requirement creates a considerable matching difficulty, since very small changes in the capacitance will create large changes in the feedpoint impedance.

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To overcome this difficulty-at least to some extent-we may use a double loop, as shown in Figure 7. The double loop is essentially a halo version of a folded dipole, which raises the feedpoint impedance. At the same time, the design uses a rectangular form to circularize the azimuth pattern without the need for a large capacitive structure. The sample model uses AWG #12 copper wire. Across the feedpoint, the side is 8.8", while the long sides are 14.3". The gap between ends is 0.35", and the spacing between wires is 1.34".

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The double rectangle shows a maximum gain of 6.7 dBi (at 20' above average ground), with a variation of only about 0.5 dB around the azimuth pattern. The feedpoint resistance is 64 Ohms, but there remains a considerable inductive reactance. To compensate for the 721-Ohm reactance, we require a series capacitor at the feedpoint (1.53 pF), which complicates effective and efficient matching. Alternatively, we may adjust the capacitance across the gap by reshaping the wires that face each other.

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The halo need not be either circular or rectangular to form an interrupted half wavelength loop. One interesting alternative shape is a triangle with a gap at the apex, across from the feedpoint. With the correct ratio of leg-length to feedpoint-side leg and the correct gap, we can obtain a very circular azimuth pattern. In general, we find two versions of the triangle, a smaller version with a circumference that is less than 0.6 wavelength and a larger version with a circumference greater than 0.75 wavelength.

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Figure 8 shows the outline of a small triangle that uses a 0.125" diameter aluminum element. The feedpoint side is about 14" long, while the angled legs are each 16.8". The circumference is 47.5". The apex gap is quite small in the model: 0.12". At 144.5 MHz, the maximum gain is 6.59 dBi, with less than 0.1-dB variation in the gain. However, the resonant feedpoint impedance is only 8.4 Ohms. Hence, we require an impedance transformer to use the antenna effectively.

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The large triangle is an alternative to the smaller one. The modeled sample in Figure 9 has a circumference of 64.3", with a 23.8" feedpoint side and 20.3" angled legs. The large triangle achieves about 6.37-dBi gain at the test height. Like the small triangle, the gain variation around the azimuth pattern is under 0.1 dB. The ostensible advantage of the large triangle is the feedpoint resistance: 58 Ohms. However, the feedpoint impedance also shows a remnant inductive reactance of 525 Ohms. Hence, we require once more a series capacitance (1.85 pF) or other treatment to arrive at resonance.

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In general, accurately constructed halos exhibit very circular azimuth patterns. Unlike the turnstiles, the pattern shape is quite stable over frequency spreads within the SWR bandwidth of the antenna. Nevertheless, halos have their own limitations for the home builder. Prototypes that I have built of various halos-both rectangles and triangles-in my modest shop suggest that the antenna type presents us with two significant hurdles. The elimination of remnant reactance is the more obvious of the challenges. The second difficulty lies in the susceptibility of these antennas to changing resonant frequency with only minor flexing of the elements. The interrupted-loop construction adds the size and alignment of the gap to the list of dimensional concerns. An effective halo must freeze both the size of the gap and the alignment of the element at the gap. As well, the remaining lengths of element material should not be susceptible to flexing that would change the design shape.

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The Uniform or Constant Current Loop

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An overlooked design emerged in 1944 in Donald Foster, "Loop Antennas with Uniform Current, IRE, Oct, 1944. Recently, Robert Zimmerman, NP4B, resurrected the idea in "Uniform Current Dipoles and Loops," in antenneX for April and May, 2006. The principle is to divide the circumference of a loop into sections such that the inductance of each wire length is offset by a periodic capacitor and so that the loop exhibits a 50-Ohm impedance--without need for any form of matching. Let's divide a square of wire into 7 sections. Each section will be 0.12-wacelength long, for a total circumference of 0.84 wavelength. At each wire junction, we shall insert a capacitor. The capacitor size will vary with the wire diameter. AWG #12 calls for 4.11-pF units.

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In physical terms for 144.5 MHz, each AWG #12 wire section is 9.8" long. The square is 17.15" on a side for a circumference of 68.6". The number of sections (7) does not correspond to the number of sides (4), which is no hindrance to effective antenna operation. Although the component arrangement yields omni-directional patterns, the appearance of the antenna, as shown in Figure 10, may seem initially strange.

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It does not matter if the feedpoint is placed mid-side or near a corner, so long as the feedpoint is in the middle of a wire section. The relative current magnitude along the circumference of the loop changes by less than 4% all along the perimeter. (Initially, this phenomenon appears to have been the goal of the open-ended CCD long doublet, but the open ends preclude obtaining that result.).

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The uniform current square loop provides horizontally polarized radiation. Although only a little larger than the triangles, the results are equal in omni-directionality and superior in gain. At 20' above average ground (close to 3 l), the maximum antenna gain is 7.76 dBi, with a total variation in gain of about 0.8 dB. The gain is about a dB better than the best triangle. The elevation pattern reveals one significant reason for the improved gain from the loop. If you compare the elevation pattern with the one's shown for the triangles, you will see that the loop produces virtually no radiation straight upward, leaving more energy for the lower lobes.

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Since the antenna does not need to compensate for rapidly changing reactance values, it shows a reasonable SWR bandwidth. However, the design is sensitive to the capacitor value within very close tolerances. The resonant impedance (50.7 Ohms) of the model using 4.11-pF capacitors changed to an impedance of 45.4 - j39.1 Ohms simply by using a 4.0-pF capacitor value. However, Zimmerman uses an interesting technique involving parallel transmission line for his loops. See "Uniform Current Loop Radiators," QEX, May/June, 2006, pp. 45-48. By cutting alternative positions on the wire length, he allows the facing wires to form the capacitors. Field adjustment consists of slowly widening the gaps until you achieve the desired capacitance.

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If you prefer a more symmetrical arrangement, you might increase the number of capacitors to 8, placing them at corners and at the center of each side. Without altering the loop size, the capacitor size increases slowly as you add capacitors. For 8 capacitors, models suggest a value of 4.7 pF for each one. The feedpoint remains centered between two capacitors. In addition, the radiation performance does not change. The chief hurdle in constructing a constant-current loop is still obtaining the correct capacitance value, a matter for careful construction.

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Conclusion

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We have looked as some of the basic options for horizontally polarized omni-directional antennas, including turnstiled elements, halos of various shapes, and the constant-current loop. Our concern has been less to look at specific construction ideas than to see the basic principles, as well as the limitations and challenges, presented by each class of antenna. Which one you may decide to build will likely rest as much on local shop skills as upon basic needs for the antenna. Commercial versions exist for some of the antennas discussed, with halos especially popular. For the inveterate antenna builder, there are many additional options. Next time, we shall examine a few larger arrays and the stacking question.

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ao16-models.zip.

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Updated 10-23-2007. © L. B. Cebik, W4RNL. This item first appeared in QEX, Nov/Dec, 2007, pp. 54-58. Reproduced with permission. Copyright ARRL (2007), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Closed and Interrupted Loop, Quad Loop, Turnstile, VHF / UHF


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Horizontally Polarized Omni-Directional Antennas: Some Larger Choices

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L. B. Cebik, W4RNL

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In the last episode, we explored some of the more compact choices for omni-directional, horizontally polarized (HPOD) antennas. Each had some advantages and each had some limitations. In this episode, we shall continue the exploration by examining a few larger arrays using more than 2 independent elements, that is, elements fed in phase. Stacking HPOD antennas is a familiar technique of increasing the gain in all directions, so we shall also spend a little time on that question.

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In the first part of this safari, we employed uniform element sizes to all models. The elements in this episode will be a bit more diverse in diameter, ranging from 1/8" to 1/2", since the models are based on prototypes. However, we shall retain the 144.5-MHz design frequency, because on 2 meters, the first MHz is the prime territory for horizontally polarized antennas. It is possible to adapt almost any of the designs for field or hilltop service using locally available materials.

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The Big Wheel

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An interesting and misunderstood semi-constant-current antenna is the Big Wheel, first published in QST in September, 1961 (see "The Big Wheel on Two" by R. H. Mellen, W1IJD, and C. T. Milner, W1VFY, pp. 42-45). Originally described as three 1 wavelength loops fed in phase, the antenna is actually a complete circle fed by parallel transmission lines at three equidistant points on the circumference. The outline and patterns appear in Figure 1. Between each transmission line, we find a current peak along the circumference, simulating the constant-current loop action. The model for this antenna uses a 3/8"-diameter element with 600-Ohm NEC-TL lines from a central feedpoint. The model has a radius of 17.3" for a circumference of 108.7".

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The maximum gain is about 7.3 dBi at 20' above average ground, with less than 0.4-dB variation around the horizon. Note the similarities between the elevation patterns of the constant-current loop (in the preceding episode) and the big wheel. However, the big wheel requires care in construction, because obtaining a usable feedpoint impedance for common coaxial cables involves interrelationships among the element diameter, the element radius, and the characteristic impedance of the connecting transmission lines. The goal is to obtain a pre-match impedance of about 25 - j 25 Ohms, so that the addition of a beta or hairpin transmission line stub provides the impedance transformation to 50 Ohms. Once obtained, however, the SWR should be less than 2:1 across the entire 2-meter band with very good retention of azimuth pattern circularity.

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The original big wheel employed an all-tubular construction method that allowed some element warping to arrive at the desired feedpoint impedance. Nevertheless, because the connections to the rim occur at high-impedance points, the parallel or nearly parallel lines to the hub perform an impedance transformation that demands somewhat finicky adjustment. The antenna remains very popular in Europe, but is perhaps nowadays less well known in the U.S. There may be arrays of three elements with equivalent performance, but simpler matching schemes.

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The Dipole Triangle and Wheel

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One very straightforward array that yields a very circular horizontal azimuth pattern is a combination of three linear dipoles arranged in a triangle. Figure 2 shows the outline of such an array for 144.5 MHz using 0.5"-diameter elements. The success of the array in achieving a true HPOD far-field pattern rests on three factors: the distance of the dipole feedpoints from the assembly hub, the length of each dipole, and the method used to match the triangle to a standard coaxial cable feedline.

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The modeled antenna uses a feedpoint-to-hub distance of 15.6", with dipoles that are 34.7" long. The shortness of the dipoles (relative to the 40.8" half wavelength at the design frequency) does not result simply from the element diameter. Even though the dipole end tips are about 9.6" apart, there is considerable interaction between any one dipole and its two mates. Varying the distance of the dipoles and their individual lengths also varies the distance between element tips. However, for this example, judicious juggling of the variables produced individual dipole feedpoint impedance values very close to 50 Ohms. A 50-Ohm cable to the hub thus performs essentially no impedance transformation and therefore does not restrict the available operating bandwidth of the array.

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As the patterns in Figure 2 demonstrate, the triangle is capable of producing an almost identical set of patterns to those yielded by the big wheel. In fact, the modeled deviation from perfect circularity is about 0.1-dB. (The maximum gain for the big wheel seems superior by a small amount, but the average gain around the big-wheel azimuth pattern is closer to 7.15 dBi due to a slightly greater range between maximum and minimum gain values.) Perhaps the only two disadvantages of the triangle are physical: it requires more area than a circle, and the free ends may be more susceptible to local wind and weather.

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We may curve the dipole elements and form a circular version of the same array. Figure 3 shows the outline of a 3-dipole wheel and thus return us to a truly interrupted loop. With 0.5"-diameter elements, the radius is 15.7" for the 144.5-MHz antenna. The resulting circumference is 98.6". With dipole tip spacing of about 1.1", each dipole occupies 31.7" of the circumference of the circle. Like the dipoles of the triangle, the dipoles are set for close to a 50-Ohm feedpoint impedance to allow the use of 50-Ohm lines to the hub without significant impedance transformation. Note the shorter lengths of the dipole compared to those in the triangle, largely due to both the curvature and the close coupling of dipole ends.

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The 3-dipole wheel requires somewhat more planning than the simple triangle, since we need 3 support arms. A non-conductive arm leading to a T at the end would allow the support to fit into the dipole ends to permit a bit of tip-spacing adjustment. At the feedpoint gaps, the dipoles will also require insulated plugs, which should be as small as feasible. If we add tube-bending into the construction equation, the 3-dipole wheel may be more complex to construct than the triangle, but the final product will form a closed circle and occupy considerably less area. Despite these differences, as shown in the elevation and azimuth patterns, the performance of the wheel is virtually identical to the performance of the triangle.

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The remaining question involves matching the set of 3 50-Ohm impedance values at the hub to a 50-Ohm transmission line. Figure 4 shows us two alternatives. A parallel connection of the lines will yield an impedance in the vicinity of 16 Ohms to 17 Ohms, a difficult value to match without employing a network. As well, any remnant or stray reactance will further complicate matching. Less often employed but perfectly usable under the circumstances of this array (three identical dipoles and connecting lines) is a series connection. (In fact, the models for these arrays use a series connection system, and the patterns shown are no different from those applying separate sources to each connecting line.) The resulting impedance will be in the vicinity of 150 Ohms to 155 Ohms, and any stray reactance will be too small to seriously affect the final result. A 1/4 wavelength section of 93-Ohm RG-62 performs the final transformation of the impedance to about 55 Ohms. Even tuned to the low end of 2 meters, the SWR only reaches 1.5:1 at the highest end of the band. The system has enough broadband capability to allow adjustment of the lowest SWR value anywhere in the band simply by lengthening or shortening the matching line slightly.

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The Lindenblad

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In one sense, our last option is not a true HPOD, that is, a horizontally polarized omni-directional antenna. The Lindenblad is actually a circularly polarized array with equal horizontal and vertical components within the point-to-point radiation pattern. Its origins lie in the pioneering work of N. E. Lindenblad, who first proposed the antenna design almost off-hand in a broad article on television transmitting antennas. (See N. E. Lindenblad, " Antennas and Transmission Lines at the Empire State Television Station," Communications, vol. 21, April, 1941, pp. 10-14 and 24-26.) After World War II, Brown and Woodward (who made numerous contributions to VHF and UHF antenna design) developed the idea in detail from Lindenblad's patent papers. (See G. H. Brown and O. M. Woodward, "Circularly Polarized Omnidirectional Antenna," RCA Review, vol. 8, June, 1947, pp. 259-269.) They envisioned possible aviation uses for the antenna. The overall goal for the antenna was omni-directional coverage in the X-Y plane (parallel to ground) with circular polarization.

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Figure 5 shows two ways of looking at the Lindenblad. The left side shows face views and an overhead view of the array. We have four slanted dipoles, each equidistant from a center point. For circular polarization in the X-Y plane, that is, for equal horizontal and vertical components to the radiation pattern, the degree of dipole slant and the distance from the center point are interdependent. At a distance of about 1/4 wavelength, the required slant angle is 45°. (There are refinements to the calculations. See Appendix 1, "Some Overlooked Antenna Basics for DX and Off-World Communications," Proceedings of the 2006 Southeastern VHF Society Conference, pp. 250-252, for further information. See earlier portions of the article for information on the modified Lindenblad that may be more useful for lower angle satellite communications.)

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The right side of the sketch shows the dipoles and their required interconnections for an effective array. Since the dipoles are fed in phase and have individual feedpoint impedances close to 105 Ohms in the arrangement shown, 4 RG-62 1/2 wavelength lines provide a net parallel junction impedance of about 25 Ohms. A 1/4 wavelength length of 35-Ohm cable (usually composed of parallel sections of 70-Ohm cable) completes the final impedance transformation to 50 Ohms. The 0.125" diameter aluminum dipoles are each 40.1" long. Other feeding arrangements are certainly possible.

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The single elevation pattern in Figure 6 shows a pattern quite unlike the earlier elevation patterns. The combination of vertical and horizontal lobes, even at a height as low as 20', tends to fill the outline of the total radiation pattern in the plot. At the TO angle of 4.6°, the maximum gain is 6.15 dBi, with an overall gain variation of about 0.9 dB. Note that the total pattern is a bit squared off, mostly as a result of the combined horizontal components of the slanted dipoles. However, unlike the previous antennas that we have examined, the Lindenblad's point-to-point performance is not strictly proportional to the far-field radiation pattern. For example, notice the differing strengths of the horizontal and vertical components in the far-field pattern at the lower left. The lower right corner pattern is a ground-wave plot using a distance of 1 mile and a receiving height of 20'. In this pattern, the vertical and horizontal components are nearly equal.

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Since the Lindenblad maintains its pattern over a considerable bandwidth and since the antenna has a usable SWR bandwidth that is wider than the 2-meter amateur band, the array is suitable for use as an omni-directional antenna for both ends of the band. The major disadvantage is that each component of the array's radiation (and reception) pattern is weaker than most of the other antennas in our selection of options. A second Lindenblad between 0.5 wavelength and 1 wavelength above the first and turned 45° will not only improve performance (to a maximum gain of over 8 dBi), but will also circularize the pattern.

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Stacking Larger Omni-Directional Arrays

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One popular configuration for any of the larger omni-directional antennas is a vertical stack of 2. Because we may be tempted to misapply some rules of thumb derived from other antenna types, we should devote a small space to this topic before we close. Like horizontal dipoles, the horizontally polarized arrays with circular patterns increase gain when we stack two such antennas an optimal distance apart and feed the two antennas in phase. At the design frequency, 144.5 MHz, a wavelength is about 81.7", which makes stacking fairly convenient.

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We need to know what separation distance is optimal for these arrays. One popular separation value is a half wavelength. The temptation to use this value arises from and is applicable to special circumstances. On the left, in Figure 7, we find the elevation patterns of a single pair of turnstiled dipoles. Because radiation is stronger at high elevation angles, the use of 1/2 wavelength spacing in a stack of 2 pairs of turnstiled dipoles is very productive. The use of 1/2 wavelength spacing with horizontal antennas tends to attenuate very high angle radiation and to make the energy available at lower angles. The maximum gain of a single turnstile pair is about 5.5 dBi (with a 20' height above average ground) in the lowest lobe. With 1/2 wavelength spacing, the lowest lobe shows better than 9-dBi gain when the lower turnstile is at 20' over the same type of ground.

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On the right in the same figure, we have elevation patterns for the 3-dipole wheel. The single antenna pattern uses a 20' height. However, by nature, the 3-dipole configuration does not shows very high-angle energy levels. In fact, the lowest lobe has a gain of about 7.25 dBi. Therefore, the automatic use of a stacking space of 1/2 wavelength is not necessary, and we are free to seek out the separation that yields maximum gain in the stack's lowest lobe, as pictured in the lower elevation plot. Table 1 provides modeled data for various stacking distances when the height of the lower 3-dipole wheel is 20' above average ground.

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Gain honors go to a stack spacing of 7/8 wavelength, and the elevation plot in Figure 7 uses this value. However, stacking distances between 3/4 wavelength and 1 wavelength would not show any detectable differences in performance. Noticeable in the table is the fact that the two antennas interact so that the impedance values shift with each change in stacking height. Obtaining a closer impedance value to 50 Ohms may require us to change the lengths of the 93-Ohm match sections.

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The 3-dipole wheel exhibited virtually no fluctuation in the gain around the perimeter. However, construction variations may create very small distortions in the pattern. The variations remain in a stack of 2 such antennas at any stacking distance. One way to smooth the azimuth pattern is to orient the spokes at a 60° offset between the upper and the lower antennas for a 3-element array and at a 45° offset for a 4-element array. The offset technique will smooth the azimuth patterns of stacks having up to 1-dB or greater fluctuations in gain around the horizon. For example, Figure 8 shows the azimuth pattern differences when we stack Lindenblads without and with a 45° offset. The squarish pattern of a single Lindenblad reappears in the aligned stack. However, with the offset, the pattern is perfectly circular.

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The offset technique of circularizing azimuth patterns applies only to arrays using independent elements fed in phase. Phase-fed elements, such as those in a turnstile, may suffer from the same treatment in a stack of two.

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In-phase feeding of two HPOD antennas in a stack uses the same general rules and procedures employed in any stacking situation. For 50-Ohm feedpoints, the most widely used procedure is to employ a pair of 1/4 wavelength 75-Ohm lines to a parallel junction. The 100-Ohm transformed impedances together form a close match for the usual 50-Ohm main feedline in most amateur installations.

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However, the 3-dipole HPODs that we have examined in these notes offer an alternative potential if the main feedline happens to be a length of surplus 75-Ohm hard-line. Since the individual dipole impedances match the 50-Ohm connecting lines, we may bring these lines all the way to a central position before we wire them in series. Figure 9 shows the general scheme. The two resulting 150-Ohm impedance values in parallel provide a close match for the hard-line. A secondary function of the sketch in Figure 9 is to suggest an alternative method of routing the support elements for the 3-dipole wheels in the stack. As a support system, the idea is less applicable to the dipole triangle.

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Conclusion

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In our voyage through the land of horizontally polarized omni-directional antennas, covering this and the preceding episode, we have encountered many schemes. One common feature of most of them is the presence of one or more features that calls for precise, if not downright finicky adjustment, with a resulting narrowing of the region in which we may obtain a nearly perfect circular azimuth pattern. The smaller the array, the more problematical some of the critical features become. Of the lot, perhaps the larger 3-dipole arrays are the least problematical: once we obtain the proper physical dimensions, the matching becomes routine. As well, the larger arrays best maintain their circular azimuth patterns over a broad bandwidth. That feature may be less important during operation than it is during construction. With a broader design bandwidth, small variations in construction precision create fewer problems in the antenna's performance.

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Nonetheless, our survey has unearthed many older and newer designs for the HPOD at VHF. One or more of the options should serve almost any need.

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Updated 01-12-2008. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jan/Feb, 2008, pp. 40-44. Reproduced with permission. Copyright ARRL (2008), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Big Wheel, Dipole, Lindenblad, VHF / UHF


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Beam Matching

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L. B. Cebik, W4RNL

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Most modern HF and VHF beams present the builder with modest matching problems, relative to the antenna impedance and the impedance of the main feedline. Rarely does the impedance difference exceed an SWR of 3:1. Under these conditions, the builder has numerous options among matching systems. These notes provide a very brief overview of the main systems.

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Series Matching

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Series matching includes 3 systems, ranging from the most specific to the most general. All series matching systems presume that the matched element is insolated and isolated from any conductive boom.

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1. The 1/4 Wavelength Transmission-Line Transformer: The 1/4 wavelength transmission-line transformer is perhaps the best known of the series matching systems. Figure 1 outlines the basic application of the system.

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We may insert a 1/4 wavelength section of transmission line between a resonant antenna impedance and a feedline if the transformer section Zo is the geometric mean between the antenna and the feedline impedance. For example, if a beam has an impedance of 25 Ohms and we have a 50-Ohm feedline, then a transformer section of 35-37 Ohms will effect the required impedance transformation. We may use RG-83 or parallel sections of RG-59 to create the transformer. We may also step up or step down: the only requirement is that the transformer Zo be roughly the geometric mean of the two end values.

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If the feedpoint impedance is slightly reactive or if the available transformer line is not quite the exact geometric mean between the antenna and the cable impedance, the system will still work, although the lowest SWR may not be 1:1. Perhaps the simplest way to determine the optimal line length under these conditions is to use an antenna modeling program and experiment with line lengths, taking SWR sweeps for each trial length of line.

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2. The Bramham System: The Bramham system of series matching tackles a special problem: matching a resonant antenna impedance to a different feedline Zo. The basic problem and solution appear in outline form in Figure 2. In Electronic Engineering for January, 1961 (pp. 42-44), B. Bramham published a paper on "A Convenient Transformer for Matching Coaxial Lines," based on work he had done for a CERN report in 1959. Bramham's solution was to develop a means for calculating equal lengths of the two lines, Z1 and Z2, which would effect the impedance transformation for a given frequency. The solution is elegantly simple.

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First, let's define a special term, M:

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Z1 and Z2 are the values of the two lines to be joined in the scheme shown in Figure 2. The required lengths (L1 and L2) of the two is a function of M:

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L1 is the length if the matching line Z1 and L2 is the length of the matching line Z2. The lengths are in degrees relative to a 360° wavelength for simple translation into electrical line lengths, which then translate into physical line lengths taking the line velocity factor into account.

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3. The Regier General Series-Matching Solution: 3 decades ago, Regier developed a general solution for series matching any antenna impedance to a given line with a single line insertion. The details of Regier's solution can be found in the following references:

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  • "Impedance Matching with a Series Transmission Line Section," Proceedings of the IEEE (July, 1971), 1133-1134
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  • "The Series-Section Transformer," Electronic Engineering (August, 1973), 33-34
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  • "Series-Section Transmission-Line Impedance Matching," QST (July, 1978), 14-16.
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The general outline of the Regier system appears in Figure 3. Regier's solution is best used in "normalized" form, where the ratios of one impedance to another are first reduced to single values. Otherwise, the calculation equations tend to look terribly opaque. So let's define a few quantities.

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The load impedance is specified as RL +/- jXL and Z1 is the selected impedance of the special matching section. We shall let L1 be the electrical length in degrees of the line Zo between the load and the special matching section, while L2 is the electrical length in degrees of the special matching section.

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Now we can calculate the two lengths, starting with L2, since it plays a role in calculating L1.

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Although this equation looks a bit forbidding, it can be handled on a calculator or with a spreadsheet. The equation produces two good results, plus and minus. The positive result gives a shorter length for L1 and hence is preferred. If the result is an imaginary number, then the value of n must be changed. You can do this by increasing the value of Z1, the characteristic impedance of the special matching section. Remember that the series matching technique can use parallel transmission line sections as well as coaxial cables, so using a length of 300-Ohm or 450-Ohm line as the special matching section is perfectly appropriate.

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In some cases, a calculator will return a negative value for the electrical length of L1. To arrive at the correct positive value, simply add 180° to the calculated result. For example, should L2 return a value of -62°, the correct result will be 118°.

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There are limits to what combinations of Zo and Z1 we may use and still obtain a desired match. In general, the closer the values of Zo and Z1, the smaller the range of antenna impedance values that we can match.

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The Beta or Hairpin Match

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Essentially, the beta match is a form of L-network specifically arranged to transform a higher line Zo to a lower antenna impedance. In the process, the network usually uses a shortened element that has capacitive reactance in the feedpoint impedance as one of the reactive components in the L-network. Figure 4 shows the general evolution of the typical beta or hairpin match. Let's begin our treatment of the L-network with the designation, delta, lower case. The designation appears in Terman's 1943 classic, Radio Engineers Handbook (page 213 and elsewhere), but a number of more recent publications have preferred to use terms such as "working Q," "network Q," or "loaded Q (QL) (in contrast to the "unloaded Q or QU) in preference to the older term. However, delta will do nicely for our work.

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In an L-network, we may express the relationships that define delta in two ways:

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The ratio of the input or source resistance (Rin) to the output or load resistance (Rout) defines the value of delta. I have chosen this starting point for our treatment as a tribute to George Grammer, whose classic volume A course in Radio Fundamental makes use of the concept (pages 69-70). The fact that this starting point simplifies the calculation of the reactance components of the network adds some substance to the reference. In fact, the calculation of the reactive components is very easy.

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For our down-converting version of the L-network, the series component is simply the product of delta and the load resistance. The parallel or shunt reactance is the ratio of the source or input resistance to delta. Both results are in Ohms, but-as noted earlier, the reactances are of opposite type. For the highest level of effectiveness for a given resistive component of feedpoint impedance, the beta match requires a certain series reactance. Other reactance values can be matched but may result in higher values of delta and hence in slightly higher losses. We obtain the optimal value of delta by adjusting the element length. The only component that we need to add to the system is the parallel or shunt element. If the element has a capacitive reactance, the shunt element must be inductive (and vice versa).

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Some folks distrust the beta match because one form of shunt inductance seems to be a short circuit across the feedpoint. Figure 5 shows 3 typical forms of adding inductive reactance across the feedpoint terminals, which are insulated and isolated from any conductive support boom. A solenoid inductor is feasible and generally has little loss, since its reactance will normally be quite low. However, shorted transmission-line stubs may generally provide the same inductive reactance with even lower loss. The hairpin or shorted parallel transmission line section is the version that most worries new users. However, the beta match in any form is as effective as virtually any other system in effecting a low-loss match between the element and the feedline--when the element resistive component is less than the feedline Zo. In addition, one may also lengthen an element to make it inductively reactive. Then the shunt component becomes a capacitance. Both versions of the beta match have undergone extensive modeling confirmation and physical confirmation. Like the series matching systems, the beta match presumes an element that is insulated and isolated from any conductive boom.

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The Gamma Match

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The third major system for matching the impedance of beam driven elements to a standard feedline, such as 50-Ohm coaxial cable, is called the gamma match. H. H. Washburn, W3MTE, introduced the amateur community to the gamma match in his September, 1949, QST article, "The Gamma Match" (pp. 20-21, 102). D. J. Healey, W3PG, provided the first mathematical analysis of the match in "An Examination of the Gamma Match," QST, April, 1969 (pp.11-15, 57). Healy's treatment, however, required the use of nomographs and a Smith chart.

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Since these seminal articles, several alternative analyses have appeared in amateur journals. H. F. Tolles, W7ITB, presented a purely mathematical analysis in "How to Design Gamma Matching Networks" in Ham Radio for May, 1973 (pp. 46-55). Because the Tolles equations proved tedious to many gamma designers, R. A. Nelson, WB0IKN, set them into a Basic program in "Basic Gamma Matching," Ham Radio, January, 1985 (pp. 29-33). ARRL converted Nelson's Apple-Basic program into a version suitable for IBM computers, and a listing appears in The ARRL Antenna Book, 16th Ed. (p. 26-20). In 2000, Dave Leeson, W6NL, corrected portions of the program so that it is perhaps the most accurate of the available means to calculate gamma matches. This program is also available within the HamCalc collection of Basic utilities edited by George Murphy, VE3ERP.

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Since the work of Tolles and Nelson, two alternative mathematical analyses have appeared. Ron Barker, G4JNH, presented "A New Look at the Gamma Match" in QEX, May/June, 1999 (pp. 23-31). Barker changes some of the fundamental assumptions about the key factors in a gamma match to arrive at his results. Unfortunately, his work is less amenable to easy placement in a Basic utility or a spreadsheet, since the calculations require the solution to simultaneous equations. In contrast, R. Wheeler, G3MGW, returned to the Healey analysis and converted the graphical techniques back into mathematical methods that allow a straightforward spreadsheet set of calculations. Wheeler's 2-part "Re-Examination of the Gamma Match" appeared in RADCOM (September, 2004, pp. 35-37, and October, 2004, pp. 54-56, with reprints appearing in antenneX for October and November, 2006. Both of these later analyses rely on something that was unavailable to earlier gamma calculations. In most cases, the determination of the initial or pre-match driver feedpoint impedance rested on assumption, guesswork, or rudimentary measurement. Measurement became difficult if the builder connected the driver to the boom and did not allow for a feedpoint gap, even if it would later be closed. Both Barker and Wheeler require the use of antenna modeling software to determine the pre-match driver impedance.

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The gamma match differs from the previous matching systems in that the calculations are not precise. Rather, they produce starter values that will require careful field adjustment (the gentler sounding term for trial and error). Figure 6 shows some of the reasons why the calculations are less than fully precise. The gamma system begins with a larger number of variables, some of which are the physical dimensions of the assembly components. We need to know or decide upon the main element diameter, the gamma rod diameter, and the center-to-center spacing between these two parts. Calculations usually proceed (although there have been variations) by treating the gamma assembly as a section of parallel transmission line, shorted at the far end. The end result is a change in the position of the antenna feedpoint relative to the element without the gamma assembly. Most calculation systems do not take into account the far-end shorting bar structure or the structure that supports the feedline connector.

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Practical gamma matches also include a number of variations on the ideal situation used in calculations. The rod may extend beyond the shorting bar. The required series capacitor may not be at the feedpoint, but be somewhere along the gamma rod. The change of placement alters the structure relative to the ideal form used for calculations, but not so much as to prevent you from devising a highly successful match. Figure 7 provides a photo of a practical gamma match that uses a tubular capacitor within the central part of the rod. The gamma system is the only matching system in this group that permits a direct connection of the main element center to the boom. However, we cannot easily obtain the initial feedpoint impedance when we connect the element to the boom, and the boom will have an affect upon the feedpoint impedance.

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The two major calculation systems have different sources but similar starting points. Both begin by calculating the characteristic impedance of the presumed parallel transmission line formed by the main element and the gamma rod or tube. The next step is to calculate the impedance step-up created by treating the gamma section as a short folded dipole or monopole. The following steps involve calculating the impedance of the gamma section at the outer end. The impedance at the feedpoint then becomes a parallel combination of the transformed end impedance and the stepped feedpoint impedance. The Healey-Wheeler requires the user to insert trial values of the gamma rod length until the resulting resistive component at the new feedpoint matches the target line Zo. The Tolles-Nelson-Leeson system calculates the gamma rod length.

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The two systems do not produce identical results. As well, the results differ from the results of antenna modeling. Because NEC cannot effectively handle the gamma match, only a highly corrected version of MININEC (such as Antenna Model) is adequate to the modeling task. However, even MININEC cannot show the required variations that emerge from connecting the element to a central boom. Since gamma matches receive only spot checks rather than systematic comparison of calculations and/or models with physical antennas, all three methods are tentative guides, useful for beginning the process of designing a gamma match, but always needing extensive field adjustment.

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I have omitted the detailed equations used in the progression of gamma calculations because they are too numerous for our short space. For a more systematic look at the two major gamma calculation schemes, see "Notes on the Gamma Match," (parts 1 and 2), antenneX, September and October, 2006. The notes also include an extensive but inexhaustive set of comparisons with MININEC models of the gamma match.

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In many ways, the gamma match is far more flexible than the series or beta matching systems. It works for elements connected to a conductive boom or for isolated driven elements. Within limits, it can handle impedance both higher and lower than the cable impedance. Nevertheless, the system always requires field adjustment (otherwise known as trial and error), since the calculations are only approximations.

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Conclusion

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We have surveyed a number of options open to the modern beam builder for matching the impedance values at driven elements to the feedline and equipment. Series and beta calculations are both precise, under the condition that we know the actual velocity factor of the lines used in the matching efforts. However, both series and beta matching systems require that we use insulated driven elements relative to any conductive boom that may support the elements. (Of course, the parasitic element center points may be grounded to the boom.) An additional restriction on the beta match is that the driver impedance must be below the line impedance. The Bramham system requires a resonant feedpoint impedance that matches one of the two line lengths used.

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The gamma match system allows (but does not require) the builder to use what we once called "plumber's delight" construction methods with all elements connected to the boom. It matches a wide range of impedances. However, the main calculation systems for the gamma match achieve only working approximations that require field adjustment.

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Many other matching methods exist. We may conduct beam matching at the shack-end of the line. As well, we may install more complex networks at the antenna feedpoint, so long as the assembly will support them easily. Match-line and stub methods also exist. These alternatives plus the ones that we have discussed still only list some, but certainly not all, of our options.

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For a spreadsheet program (in either Quattro-Pro or Excel format) that includes the matching calculations, see Antenna Matching. There are separate pages for the Healey-Wheeler and the Tolles-Nelson-Leeson systems. In addition, the sheet contains a page for the match-line and stub system, which is useful for antennas such as the extended double Zepp. The sheets serve only to increase your options for easy calculation of the matching systems, since utility programs are also available from other sources.

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Updated 03-05-2008. © L. B. Cebik, W4RNL. This item first appeared in QEX, Mar/Apr, 2008, pp. 58-61. Reproduced with permission. Copyright ARRL (2008), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Matching


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Reflections on Reflectors

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L. B. Cebik, W4RNL

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Some reflectors reflect-and others do not. Consider the two different beams in Figure 1. One uses a planar reflector, while the other uses a parasitic reflector. The planar reflector actually reflects. In important ways, the parasitic reflector does not-at least not in the way we usually imagine the situation with parasitic beams.

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The most common mental picture that we generate when first encountering the conventional names of Yagi elements is something like a lighthouse beacon. Each light has a reflector to determine the beam direction and a lens to direct and focus the light signal from the structure. So we link the lighthouse's Fresnel lens to the parasitic director or directors of a beam and we associate the beam's reflector with the lighthouse's reflector. Indeed, some lighthouses do not use reflectors, and so, too, we can actually construct parasitic beams without a reflector element. The mental picture is simple, straightforward, coincident with the beam-element names-and mostly wrong.

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Some beam types do reflect energy in the conventional lighthouse or flashlight sense. These beams differ in some important respects from parasitic beams, of which the Yagi-Uda array is the most common form. Since I have received numerous questions about the differences between-and the potential interchangeability of-the two types of reflectors, it seems useful to look briefly at these two options for creating directional antennas.

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Reflectors that Reflect

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Let's begin with reflectors that reflect: the planar (or curtain or sheet) reflector, the corner reflector, and the parabola. Each type has special needs and many variations, and we shall confine our discussion to the planar reflector as perhaps the simplest form of reflector screen. Planar reflectors are very old and often went under the name "billboard" reflectors in the 1920s. Figure 2 shows the basic principles of the planar reflector's operation, largely derived from optical principles applied to RF energy. The basic unit for understanding the sketch is the ray. If we think of a dipole element, shown on end in the sketch, as emitting rays in all directions, we can trace the patterns that emerge. Some rays are completely reflected forward, where they add to or subtract from the rays from the dipole itself in standard interference patterns. Some rays to the side have no reflected rays for such combinations and hence form partially shadowed areas. Behind the reflector sheet is an area where almost no rays go, creating a full shadow. However, at the reflector edges, we encounter diffraction, with some energy scattered in virtually all directions. Hence, a planar reflector with finite dimensions cannot create an infinite front-to-back ratio.

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Ahead of them, we can place arrays of phase-fed driver elements, both simple and complex. For example, a common UHF beam uses a planar reflector with a double-diamond element. However, for clarity, we shall use a simple dipole as the driver. As shown in Figure 3, we place the dipole ahead of the reflector plane, and the forward radiation consists of the direct rays from the dipole and the reflected rays from the sheet. The reflector size and the placement of the dipole are not arbitrary. The sketch shows most of the critical dimensions for making such a beam.

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Let's begin by assuming that we wish to set the dipole's feedpoint impedance at 50 Ohms. We shall remove this limiting assumption later. However, it will serve us to illustrate one or two points about planar reflectors. First, as shown in the top portion of Table 1, the size of the reflector does make a difference in planar beam performance. If our main concern is the front-to-back ratio, then the size of the screen may grow indefinitely, especially off the ends of the dipole, to increase the ratio. If our concern is gain, then there is an optimal reflector size for maximum gain. As a rule of thumb, the reflector should extend from 0.4 wavelength to 0.6 wavelength beyond the limits of the driving element or array. The larger the driver assembly that we use, the larger that the screen must be to achieve maximum gain from the total assembly. As a side note, in the range of reflector sizes shown, using a constant dipole length and spacing from the reflector, the feedpoint impedance does not change significantly as we change the size of the planar reflector.

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For the simple dipole driver, the 1.2 wavelength-by-1.2 wavelength reflector provides maximum gain. A double-diamond or a bobtail curtain drive might provide up to 2 dB additional gain. As well curtain arrays exist that set vertical and horizontal bays of drivers before very large screens for additional gain. We may increase the front-to-back ratio by increasing the E-plane dimension, that is, the dimension of the reflector parallel to the driving element. If the screen is about 2 wavelength in this direction, the 180° front-to-back ratio will approach 30 dB. However, the worst-case front-to-back ratio will tend to remain relatively constant in the 22-24-dB range despite high 180° values. Only the rear lobe in line with the axis of the beam undergoes radical reduction.

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A second factor is the spacing of the dipole from the reflector plane. As shown by the sample modeled data in Table 1, we can achieve higher gain values and higher front-to-back ratios by moving the dipole closer to the screen. The closer spacing results in more complete illumination of the reflector by the dipole source. As the dipole approaches the reflector, its resonant length slowly changes. As well, the resonant impedance decreases. Whether the performance improvements are worth the inconvenience of requiring more complex matching methods for the amateur's standard 50-Ohm cable is a user decision. Different driver assemblies have different optimal spacing values for a direct 50-Ohm match to the feedline, and as driver assemblies grow more complex, the best match spacing may not be close to the best performance spacing.

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When deciding between a planar reflector array and a parasitic beam, we must measure our communications needs against the likely performance of the potential antennas. Table 2 lists some of the key modeled performance characteristics in free-space of the medium-size reflector with a dipole driver and of two types of Yagis: a 2-element driver-reflector array with the element spacing close to the value that yields the best front to back ratio and a 3-element relatively long boom (0.345 wavelength) Yagi. The 2-element Yagi often serves as a seeming analog to the planar reflector array, but its performance does not approach either the gain or the front-to-back ratio of the true reflector antenna. The 3-element Yagi in the list beats the planar reflector in the front-to-back category, but not in gain. Of course, we can always add an almost indefinitely large number of directors to the Yagi to improve its gain and to narrow its beamwidth in both the E-plane and the H-plane. See Figure 4 for free-space patterns in both planes for all three antennas.

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The ultimate decision on whether to use a Yagi or a planar reflector does not normally rest on small differentials in gain and the front-to-back ratio. The Yagi, exemplified by the 3-element version in these notes, has by nature a fairly narrow operating bandwidth in which the performance values remain stable. We sometimes talk of broadband vs. narrow band Yagis, but such discussions are relative to Yagis alone. Compared to the planar reflector array, all Yagis are narrow band antennas. Figure 5 provides data on the modeled gain and front-to-back performance of the 3-element Yagi and the simple planar reflector array. The planar array values are very nearly flat from 420 to 450 MHz. The degree of increasing gain is comparable to the increase that we associate with the dipole alone as it grows longer as a function of a wavelength. In contrast, the Yagi gain shows a continuous rise with frequency. Just above the band edge, it will peak and then the Yagi will reverse its direction. The Yagi front-to-back ratio peaks at mid-band and declines toward the band edges.

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Paralleling the performance curves are the SWR curves. Figure 6 shows three curves, each referenced to the self-resonant impedance of each antenna. The broadest curve belongs to a simple dipole, in this case, using a 4-mm-diameter element like all other elements in these notes. The planar array curve comes next and shows that the antenna provides impedance service almost as wide as the gain and front-to-back curves. In contrast, the 3-element Yagi provides less than a 2:1 SWR only over about half of the 70-cm band.

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Table 2 has a special final entry. We may simulate a solid planar reflector by using a series of rods in the plane of the driver. Obtaining the performance of a solid or screen reflector has several requirements. As shown in Figure 7, the total area of the rod reflector, much used in the past for television antennas, must equal the area of the screen reflector. In addition, the simulated solidity of the screen depends upon using a number of rods and an individual rod diameter that together fill in the screen. The fewer the rods that we use, the fatter we must make each rod. The present example uses 13 rods, each 0.036 wavelength (25-mm at 435 MHz). In most applications, the performance of a rod reflector is the same as an equal-size screen. However, in other optically based reflector forms, such as corner reflectors, the rod reflector will show hybrid characteristics, partially parasitic and partially optical.

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Parasitic "Reflectors"

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Applied to a parasitic array, the term reflector is simply a conventionalized term used to locate the appropriate element. The fact that it is normally-but not always-longer than the driver element leads to misimpressions about how it works. In fact, parasitic arrays are special forms of phased element sets in which we let the geometry of the elements determine the correct relative current magnitudes and phase angles of the elements for directional operation. For arrays based on half wavelength elements, we normally measure the current magnitude and phase angle at the element center, where the current reaches its peak value.

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When we have only two elements of equal or nearly equal length, we can find relative current magnitude and phase angle combinations that yield a maximum front-to-back ratio and other combinations that yield maximum gain. The values for each combination vary with the spacing and the exact length of the elements involved. Let's turn to a 10-meter portable beam that I built a number of years ago. Table 3 shows the dimensions of the array, and the two lower angles provide the ideal figures for either a very high 180° front-to-back ratio or for maximum gain (with a front-to-back ratio in the 7-8-dB range).

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Figure 8 provides outlines of two forms for the same element set. The first form employs the beam as a standard driver-reflector Yagi. As the tabular values show, confirmed generally by the free-space E-plane pattern, the beam has modest performance, but is typical of the genre. The second form of the beam adds a harness of transmission lines that improve the current magnitude and phase angle relationships between the forward and the rear elements relative to the beam direction. (It is somewhat of a mistake to label phased array elements as a driver and a reflector.) The gain increases slightly, but the most noticeable operational improvement is the front-to-back ratio. As the E-plane pattern shows, the entire rearward radiation has decreased very significantly.

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The exercise simply points to two significant facts about parasitic reflectors. First, we use a reflector size and spacing to obtain as best we can within physical geometry limits a current magnitude and phase angle combination to enhance the directivity of a beam. Second, relative to the driver, the reflector phase angle will normally be positive. As we add directors to a Yagi array, the role of the reflector changes. Although we may adjust its position and length to enhance performance slightly, it serves largely to set the driver's impedance. How much of a role the reflector element plays in obtaining a desired level of gain or front-to-back ratio depends upon the particular Yagi design.

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As we increase the number of elements in a parasitic beam, the simple relationships in the current and phase angle among the elements tend to shift. The reflector remains at a positive phase angle relative to the driver in almost all cases, while the first director ahead of the driver will have a negative phase angle relative to the driver. (For exercises in this regard, we normally set the driver current magnitude at 1.0 and a phase angle of 0.0°. The normalized set-up eases the process of comparing values among beam designs.) As soon as we use even one director, the idealized 2-element relationships become void relative to specific values.

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Table 4 provides the element-center current magnitude and phase angle values for 3 Yagi beams: a 2-element driver-director array, a 3-element antenna, and a 6-element OWA (optimized wide-band antenna) design. Figure 9 shows the current magnitudes and phase angles in graphical form. The length of each line is proportional to the relative current magnitude, while the angle is proportional to the phase angle relative to the vertical line for the driver current. Some of the lines have perceptible curves, indicating the change in the current phase angle along the element from the center peak to the element end that intersects with the edge dot representing the element. In this set of examples, a counterclockwise direction indicates a negative phase angle, while a clockwise direction indicates a positive phase angle. (If you model antennas and replicate this exercise using parasitic beams of your choice, be certain that all elements-and sections of elements in stepped-diameter element designs-use the same orientation. Universally reversing the element direct will reverse the clockwise-counterclockwise orientation of the graphs, while randomly changing element and element section directions will yield a largely unreadable graph.)

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The 2-element Yagi shows a relative director current that is nearly identical to the value of the driver, with a relative phase angle of -156°. At the design frequency (435 MHz), the two elements have nearly ideal conditions for achieving a high front-to-back ratio. Maximum front-to-back values would require a relative current magnitude of about 1.025 with a phase angle of -154° at the element spacing shown (0.08 wavelength). (Note that with two elements, the required ideal current magnitudes and phase angles will be the same relative to the forward and rearward elements. However, in a parasitic design, which element we feed makes a considerable difference in our ability to find a geometry that will produce desirable results. The present design produces excellent performance, but only over a very narrow bandwidth.)

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The current magnitudes and phases angles associated with the 3-element Yagi coincide roughly with at least the phase-angle rules of thumb. The reflector phase angle is positive, while the director phase angle is negative. However, the exact values are functions of the element lengths and their spacing from the driver. There are numerous configurations for 3-element Yagis, each suited to a specific performance task. In each case, the exact values will be different from those shown for the same beam. The 6-element Yagi illustrates how complex the pattern of current magnitude and phase-angle values may become as we add directors and configure them for desired performance levels. The sample beam has a wide bandwidth (relative to Yagis as a whole) in part controlled by the close spacing of the driver and the first director. Above the design frequency, the first director's current magnitude will actually exceed the magnitude on the driver and form a secondary driver to control performance at the higher end of the operating spectrum. Hence, the current magnitude and phase-angle values on the array element will shift with the operating frequency.

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In fact, we normally design parasitic beams by reference to the performance they yield, letting the current magnitudes and phase angles be whatever they must be to obtain that performance. Antenna modeling software abets this process, since the performance values generally appear with polar plots of anticipated radiation patterns. Hence, many beam designers never look at the current values on the elements. This process helps us forget that parasitic reflectors do not reflect in the optical sense. Rather, they remain part of the phasing system for a directional set of elements.

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The Interchangeability of Planar and Parasitic Reflectors

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The idea of replacing a parasitic reflector with a planar reflector is natural, but filled with questions. The key question is whether we gain anything in the process. Long-boom Yagi enthusiasts have pondered this question since (at least) DJ9BV's use of a reflector plane consisting of 4 reflector elements. The spacing between the reflectors was too wide to form a true planar reflector, but the builder claimed additional performance relative to a single reflector.

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The feasibility of replacing a single parasitic reflector with a planar reflector depends in large part on the radiation directed toward it. Therefore, the key test is whether the set of elements from the driver forward and with no reflector element has a large rearward lobe or set of lobes. In such cases, a planar reflector or some other system of reflectors may improve performance over a single parasitic reflector. Figure 10 outlines a series of arrays that use a driver with 10 identical directors. The sketches show a single parasitic reflector, a system of three reflectors, and a planar reflector. Table 5 shows the results of the experiment.

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A single reflector element provides good performance from the array. The free-space gain is over 14 dBi, and the front-to-back ratio is greater than 20 dB. The second step adds two further reflectors, each about 2 mm longer than the original and space 15 mm behind the central reflector element. The vertical distance between these reflectors is 420 mm. The augmented parasitic system increases the gain by less than 0.2 dB. The 180° front-to-back ratio gives us an illusion of a high improvement in the rearward direction, but the pattern in Figure 10 shows that there are quartering rear sidelobes that are down by only about 5 dB relative to the single-reflector version.

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The final step in the progression replaces the system of reflector elements with a planar reflector. To obtain the performance of the 3-reflector model, the screen required 500-mm by 500-mm dimensions. Whether either "improved" reflector system is worth the construction effort may depend as much on mechanical factors as on performance benefits. The 3-reflector system is complex, requiring a boom extension and a vertical support for the elements. The planar reflector might consist of light screen material, but it would require bracing to maintain its shape. Both augmented reflector system would add to the wind forces on the antenna. Hence, the decision to use an augmented reflector system must weigh performance against potential mechanical disadvantages.

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A planar reflector may give the illusion of improving the performance of a small Yagi. Consider the 2-element driver-director array that we used to show current magnitudes and phase angles on the elements. Since it has no reflector, perhaps adding a planar reflector might improve performance. Figure 11 shows the outline and free-space patterns of the two arrays. The pattern with the higher gain belongs to the version with the planar reflector. In this case, the presence of the reflector appears to improve performance-at least with respect to gain-by almost 2 dB. The key pattern modification is the reduced beamwidth of the planar version.

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However, consult Table 6. The first two entries confirm the impression that we gleaned from the patterns. The final entry shows what is actually happening. With only a dipole, a planar array has virtually the same performance as the reflector with 2 elements ahead of it. The director adds nothing to the planar array performance, but does reduce the feedpoint impedance. For the best performance, we might keep the planar reflector and do away with the parasitic director.

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Planar and other optically based reflectors depend upon the illumination provided by the source. Planar arrays are most effective with either single drivers or collections of phase-fed drivers properly spaced ahead of them. Corner arrays tend to require single dipole drivers or end-to-end arrays of drivers, since the illumination of a corner reflector with a 60° to 90° angle is quite complex. In contrast, parabolic reflectors operate best when the total driving source energy points toward and illuminates the entire the parabolic surface. Ray-tracing graphs and equations best describe the function of each type of reflector.

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In contrast, parasitic reflectors require positions and lengths that determine the optimal current magnitude and phase angle for directional beam operation. However, the exact values depend upon the complex interaction of all of the antenna elements. Although we can certainly design Yagi and other parasitic beams without reference to element current magnitudes and phase angles, reference to these parameters may help us understand why a Yagi is not a flashlight.

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ao18-models.zip.

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Updated 05-05-2008. © L. B. Cebik, W4RNL. This item first appeared in QEX, May/Jun, 2008, pp. 58-61. Reproduced with permission. Copyright ARRL (2008), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Dipole, Dipole Curtain Array, Planar Reflector, VHF / UHF, Yagi


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A Yagi Case Study
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L. B. Cebik, W4RNL

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In the first episode of this "Tale of 3 Yagis," we explored the design options for a 3-element 2-meter Yagi with intended field use and restricted to a 30" boom or smaller. Our options included high-gain, high-front-back, and wide-band versions of the antenna. Each option provided design dimensions for round-tubing elements ranging from 0.125" up to 0.5" in diameter. In this episode, we shall examine some of the element materials other than round tubing that we may use and how we may go about the process of correlating these materials to the dimensions in the first part of this exercise on antenna options.

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However, let's make no mistake: the design options presented do not represent a comprehensive view of all of the Yagi design variations that we might bring to the planning table. There are designs with wider bandwidths and designs with higher gain--all generally within the initial guidelines for the exercise.

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For example, we may develop a very-wire-band Yagi by slaving a second driver to the original driver. Technically, this becomes a 4-element Yagi if we view the driver as a parasitic element, but it is not a true director except at the very low end of the operating passband. Table 1 shows the dimensions for such a very-wide-band Yagi using 0.125" diameter elements. The performance figures appear in Table 2 and in Fig. 1 and Fig. 2. As the table shows, the antenna is capable of very acceptable performance for at least the 140- to 150-MHz range, with lesser performance beyond. The first graph--taken from an EZNEC frequency sweep and displayed on AC6LA's EZPlot--shows the relatively even gain, which varies by only 0.4 dB across the passband. The line marked "front/sidelobe ratio" actually provides the worst-case front-to-back value, in contrast to the 180-degree front-to-back ratio that shows higher values across part of the operating passband. The second graph records the modeled feedpoint resistance, reactance, and 50-Ohm SWR values from 140 to 150 MHz. Note that the SWR does not rise to 1.3:1 within the passband. The performance overall is comparable to the wide-band design in Part 1, but with a much wide passband. However, in exchange for the extended passband, the design requires an extra element and exceptionally careful construction and field adjustment to achieve the performance promised by the model. In the rigors of field operation, the chances of maladjustment due to bumps and other accidental deformations are too great for inclusion in the design pool.

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There are ways to achieve higher gain from the same boom length as our 3 original designs. One technique is to use a pair of phased elements as a driver, as exemplified by the design in Table 3. The antenna is essentially a "phagi," that is, a phased horizontal array with one or more parasitic elements. We may also call this a log-cell Yagi, although the phased driver set is not large enough to constitute a true LPDA on its own. The dimensions specify 0.1875" diameter elements for 2 meters. The phase line between the two rear elements consists of a 50-Ohm line with a reversal between elements. The electrical length is 20.26", allowing lines with a 0.66 velocity factor to meet the need. The native feedpoint impedance at the 146-MHz design frequency is about 15 + j23 Ohms. Since the impedance is inductively reactance, we may apply beta-match techniques to raise the impedance to 50 Ohms resistive--or close to that value. A shunt capacitor with about -j35.5 Ohms reactance across the feedpoint gap will do the job. At 146 MHz, this amount to about 30.7 pF, the equivalent of a 12.27" electrical length of 50-Ohm transmission line used as an open stub.

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Table 4 tabulates the performance between 145 and 147 MHz, while Fig. 3 and Fig. 4 provide a graphical view of the same data. The design provides almost an extra dB of forward gain relative to the high-gain design in Part 1, while preserving a high front-to-back ratio within the listed passband. Once more--and typical of most Yagi designs--the worst-case front-to-back ratio is relatively even across the passband, while the 180-degree value tends to peak at a high value. As with many higher gain Yagi designs, the SWR and impedance curves suggest that the antenna may be useful below the lower limit of the passband, but the performance graphs suggest that the use is limited by decreasing gain and front-to-back ratios.

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Once more, I have not included this design in our general pool because it involves phasing techniques. To construct the phagi would require extensive measurement and adjustment, for example, in determining the precise velocity factor of the line used for phasing the rearward elements. Listed velocity factor values are simply not accurate enough from one batch of line to the next to ensure proper line length to achieve the modeled performance. As well, the phase line becomes an extra element to carry into the field, not to mention the need for connectors at each end as part of the antenna structure.

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Nevertheless, these two brief examples of alternative designs are reminders that we do not exhaust the full set of design options in the ones that we included on Part 1. Rather, these options only scratch the surface of a wide variety of Yagi and related designs. We chose them only because they form a relevant collection of straightforward designs that promise relative ease of replication in most home shop settings. As a final design reminder, all of the designs in both this part and the first episode involve elements that are insulated and isolated from a metallic boom and indeed prefer a non-metallic boom. However, to say more about boom materials would leap into the last part of this series and skip our trips to the home improvement center or survey element materials.

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Part 2: Element Materials for the 3 Yagi Designs

It would seem on the surface that the range of rod and tubing sizes reported in the dimension tables of Part 1 would cover the territory indicated by the Part 2 subtitle. We have already noted that one may use aluminum, brass, or copper tubing or rods for the elements with no significant change in performance. Once an element reaches a certain diameter for a given frequency, the differential in material losses for common conductive materials no longer makes a difference to performance. At 2 meters, that semi-critical element size is about 1/8". +

I have not included common metric sizes of tubing and rod material. For example, the common 4-mm material used in Europe for VHF arrays is about 0.1575" in diameter, half way between 1/8" and 3/16" U.S. sizes. As well, I have omitted AWG wires sizes, although AWG #8 (0.1285") would make a usable substitute for 1/8" elements with no design modification. Elements smaller than 1/8" tend to be flimsy, while those larger than 1/2" tend to be physically impractical. As a result, the range of sizes that we have provided in the dimension tables covers most of the reasonable materials for 2-meter Yagi construction.

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. . .Assuming that builders want to use elements having a circular cross section. I have learned over the years that we should never make this assumption. Antenna builders will latch onto almost any material at hand, including dime-store collapsible whips, flat stock, L-stock, and even channel and square stock. For special purposes, some antenna builders will use the metal tape that comes in spring-loaded tape measures.

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Proposals to use these materials come with one question: with what round element size does each size of each variant material equate? The notes in this section will present a few of my findings for some of the materials at 146 MHz. More important than the results is the procedure that I used to determine them. I shall outline a very practical procedure for use on 2 meters that will allow anyone to replicate my experiments and to find the best approximation of a round conductor that matches a novel material proposal. All that we require is a reasonably accurate antenna analyzer, a standardized center hub for a dipole, and a mast-stand fixture on which to perform the experiments.

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The method that I used to compare a variety of materials was to create dipoles resonant at 146 MHz. Using an MFJ-259B analyzer, first calibrated to my station receiver, I made and pruned dipoles for each round conductor listed in the dimension tables of Part 1 and then made and pruned dipoles for each variant material that I could think of and easily obtain. I added a round 0.75" diameter dipole to the group, because many substitute materials are close in performance to this size round element. The key feature of the procedure is not absolute agreement with modeled predictions for the round conductors, but instead a method that would ensure consistency from one dipole to the next.

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The dipole hub assembly that I used is designed to provide a consistent dipole-center environment from one test to the next. Fig. 5 shows the general outline of the plate, which I made from an existing scrap of 1/4"-thick polycarbonate. Hence, there is no magic, but only convenience, in the plate length and width. Each dipole candidate mounts both physically and electrically by way of the two 6-32 nuts and bolts at the upper plate center. For each dipole, I used a bolt length to have the least excess threaded length beyond the limits of the dipole material. The two outer holes in the plate use nylon screws into threaded plastic tubes that sit within holes in the dipole for support of the element. I removed the support tubes for the tape elements, since they are too thin to support drilling 1/4" holes. For the rod elements, I used square washers at the inner screws to electrically clamp the inner rod ends, while the rod itself rested on top of the outer tubes.

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The plate mounts to a section of PVC with a pair of sheet-metal screws. Because the assembly is only temporary, you can use any clean hardware. The area above the support stub and behind the dipole center is clear so that I could mount a length of coax with solder lugs, avoiding the use of a connector at this point. The coax length is 1/2 wavelength, allowing for the velocity factor of the RX-8X that I used. (Note that RG-8X has different velocity factors from different makers. However, do not rely on manufacturer's specifications for velocity factor. Measure the line for an electrical half wavelength. My line had a listed velocity factor above 0.8, but measured about 0.735. The distant line end should replicate the feedpoint impedance at the dipole terminals, while minimizing body effects during measurements.)

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I have a wood test stand that I use for various purposes. It appears in the photos. It holds a 5' section of 1-1/4" Schedule 40 PVC for this test. The upper section of the mast, using an un-cemented coupling, is a 2' section of the same material, and that is the support stub to which I attached the dipole plate. For pruning, I simply lifted the upper section off, carried it into the shop, and sawed, clipped, or sanded the element ends, according to which material was under test.

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The 7' total height of the assembly placed the antenna about 1 wavelength above ground, a sufficient height to minimize ground effects on the dipole's resonant frequency. As well, for each test, I placed the test stand in the same position with the dipoles oriented the same way. The goal was not laboratory precision, but usable consistency from one test to the next.

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+ Photo A. The complete test assembly with a tubular dipole attached and the antenna analyzer stationed closer to the ground. +
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Photo A shows the complete assembly with a tubular dipole attached and the antenna analyzer stationed closer to the ground. Photo B is a close-up of the center plate with a thin rod element clamped in place and supported by the outer posts. The last picture in this series, Photo C, shows the same assembly with an L-stock element: the outer support posts pass though holes in the element.

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+ Photo B. A close-up of the center plate with a thin rod element clamped in place and supported by the outer posts. +
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+ Photo C. The same assembly as in Photo B, but with an L-stock element--the outer support posts pass through holes in the element. +
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You may replicate this type of system--adding your own improvements--to test any number of materials for comparison with the round elements presumed by antenna modeling software. In the interim, the following notes record the results that I obtained.

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1. Round Conductors: Table 5 shows the results of tests with round conductors that form the reference values for all of the subsequent tests. Also included in the table are the NEC-4 modeled values for the lengths of each size of tubing.

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Round conductors offer the best combination of strength-vs.-weight and ability to slip the wind to minimize loading from that source. As well, they tend to resist ice build-up better than most flat or L-stock elements. Hence, for a long-term station installation, I would recommend them. For most purposes 6061-T6 and 6063-T832 aluminum stock, available by mail order if not in stock locally, are the best antenna element materials. Nevertheless, there are reasons and occasions for using other materials.

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Interestingly, the round elements all measure well within 0.5% of the NEC-4 modeled lengths, except for the 3/4" tubing, which comes in with under 1.0% variance relative to the modeled value.

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Table 6 provides the measured data on all of the tested alternatives to round conductors. The table lists not only the length of the dipole that turned out to be resonant on 146 MHz, but as well the size of the most nearly equivalent measured round conductor. This value permits the builder to refer to the dimensions in Part 1 that most closely approximate the dimension needed for the alternative material.

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2. Flat Stock: Flat stock holds two advantages for home construction. First, it is readily available at home centers. Second, it is flat. Hence, we can drill it easily on any equally flat surface and avoid the difficulty of drilling a round surface. The disadvantage of this stock is that the 1/16" thick type is very flimsy and bends all too easily. The 1/8" stick is sufficiently sturdy for a permanent installation, but may be needlessly heavy for field use.

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The flat stock plays very close to its measured round counterparts. Some modelers advocate using round wires having the same surface area as the flat stock. The closest round wire to 1/2"-by-1/16" flat stock is 0.375" tubing. However, the measured lengths for both the 1/16" and 1/8" flat stock is 0.5" tubing, which has about 1.4 times the surface area per unit length. As well, the 3/4"-by-1/16" flat stock measures closest to the 0.75" round tube.

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3. L-Stock: 1/16" thick L-stock combines the benefits of offering flat surfaces to drill with excellent rigidity and easy access at home centers. In addition to Yagi service, builders have used the stock for both the horizontal element-portions of quads and for Moxon rectangles. It is half the weight of square stock with equal outer dimensions. The down side of L-stock is that it offers considerably more wind resistance than a round conductor. It also is prone to snagging in field exercises, such a fox hunts in wooded areas.

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Like flat stock, L-stock appears to approximate its round counterpart element material in both the measured half-inch wire and the modeled 3/4" wire. Within the limits of my measurements (1/6"), there is no significant difference between the flat stock and the L-stock.

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4. Collapsible Whips: For field antennas, collapsible whips offer a certain convenience, since we can shorten the elements to the whip's minimum length for transport. In addition, most whips adapted from TV and cell-phone replacement service have a plug in the lower end. The plug has a mounting hole, which permits the builder to swivel the elements in line with the boom for an even more compact assembly during transport to and from the working site.

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For this test, I salvaged whips from very old TV rabbit ears as a test of larger diameter versions. Since the whips extended to about 48", I performed two tests: one with the larger section dominating the element length at 146 MHz, the other with the thinnest sections fully extended. I also obtained two Radio Shack cell-phone whips that extend only to 28" per unit. These whips give an indication of equivalent lengths for the thin-whip style. In both cases, I used the square washer clamp method of fastening that I used with aluminum rods in the initial tests.

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With the large whips using their fattest sections, the dipole length is closest to 3/8" round wire. The same whip using its inner largest-diameter section (about 0.25") and its smallest section (about 1/16") requires a length of 40.0", which is longer than needed for 0.125" uniform-diameter material. The small whip required a dipole length of 38.88", also longer then needed by the smallest round element tested.

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The excess length required by collapsible whips, even with fat button ends, owes to the stepped-diameter structure on each side of the dipole centerline. The first test used the fattest large-whip sections, resulting in the smallest step, and the result is the shortest of the required whip lengths. The second large-whip test had the greatest step in diameter, and yields the longest resonant overall length. The cell-phone replacement begins with a smaller diameter, from which we might expect a longer overall length. However, the steps in diameter are small and regular so that its length is shorter than required for the second large-whip test. All of these results coincide with fundamental theory regarding elements that taper from the center to their tip.

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5. Measuring Tapes: The final group of tests involves a material used almost exclusively by fox hunters: cannibalized measuring tape. Although the tape is steel, it is satisfactory for field antennas. By judiciously buying a few bargain tapes and replacing some very worn tape measures in the shop, I managed to find 4 tape widths. Measuring tape is very thin, but the exact thickness may vary with brand and age. Hence, the values shown in the table are indicative, but not absolute for each width.

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The advantage of a tape-measure element is its ability to bend at a field snag and to bounce back to position with no damage (at least, no damage in the short run). Because a 3-element, 2-meter Yagi, perhaps of the maximum front-to-back design, requires about 10' of tape for its elements, a single long tape measure provides material for many replacement elements or for several individual Yagis. Replacement tapes without the cases and mechanisms are difficult to find locally these days, so expect to destroy a complete tape-measure unit if you opt for this element material. However, bargain tape measures abound.

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The measured resonant lengths for tape-measure material all indicate an equivalence to round conductors about half as much in diameter as the tapes were wide. Unlike the flat stock, which had a significant thickness, the tapes are very thin. Hence, their wide surfaces alone did not suffice to bring them close to the resonant lengths of round conductors with the same cross dimension.

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The measured values for the alternative materials held a few surprises. Perhaps the performance of flat-stock was the most dramatic. Nevertheless, I would not claim that the near-equivalencies at 2-meters would hold up at HF, where one might trade the greater difficulty of constructing the requisite number of long dipoles for finer gradations of measurement.

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The survey of alternative element materials is not by any means complete or ultra-precise. However, the technique used to find their nearest equivalent round conductor has proven quite reliable in adapting designs. Reliability here means that the results are usable for the adaptation of round wire designs to alternative stock used in the home-construction of antennas. Neither my tape measure nor my antenna analyzer meets anything like laboratory standards, and the testing circumstances are not of calibrated range or chamber quality.

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One final caution is in order. With non-round conductors, the inter-element coupling between adjacent elements may not by identical to the coupling from round elements. Hence, some final field adjustment of element lengths may be necessary, even for materials listed as equivalent to a round conductor. This caution is especially true of the driver-director relationship, where small director length adjustments tend to yield considerable changes in the Yagi performance curves at 2 meters.

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Field adjustment, of course, presumes that we have already built our Yagi design of choice. Even within the constraints of this exercise, we have options. Some of those options will be the subject of Part 3, building 3-element Yagis for different uses.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Sep/Oct, 2004, pp. 49-54. Reproduced with permission. Copyright ARRL (2004), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: VHF / UHF, Yagi


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A Yagi Case Study
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L. B. Cebik, W4RNL

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In the first episode of this "Tale of 3 Yagis," we explored the design options for a 3-element 2-meter Yagi with intended field use and restricted to a 30" boom or smaller. Our options included high-gain, high-front-back, and wide-band versions of the antenna. Each option provided design dimensions for round-tubing elements ranging from 0.125" up to 0.5" in diameter. In the second episode, we examined some of the element materials other than round tubing that we may use for the Yagis. As well, we looked at the process of correlating these materials to the dimensions in the first part of this exercise on antenna options.

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In this final portion of the exercise, we shall explore some of the construction options involved in building the small 3-element Yagi--whatever the selected design and element material. Our perspective will not be commercial construction, but rather what we can accomplish within a typical home shop.

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Part 3: Building 3-Element Yagis for Different Uses

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A commercial antenna designer might begin with a set of operating or use specifications and then select materials and construction methods that will achieve those goals. However, the average home antenna-builder often begins from a different position. He or she has some materials, some shop abilities and limitations, and some uses for the final product. The next step is usually reaching a physical design that combines these starting points into one antenna. Therefore, let's examine a few building options for both permanent (long-term) installations and for field antennas.

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Long-term construction techniques: Utility antennas on 2 meters can make good use of 1/2" to 1" nominal PVC pipe as the boom material. The elements are light enough that you can place a Tee fitting off center (to avoid the driver position) and still have a stable mounting. Indeed, you may even extend the boom rearward so that the boom-to-mast assembly is behind the reflector. This system is especially suitable for vertically oriented Yagis to suppress interactions between the mast and the array. The non-conductive boom also means that you may use the dimensions in Part 1 as a direct guide to construction without adjustment for the use of a metallic boom.

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The typical white PVC is variable around the U.S. with respect to its UV resistance. If the white plumbing PVC in your area is UV susceptible, then the gray electrical conduit version is usable and tends to be more uniformly UV resistant. Other alternatives include fiberglass and other resin-based non-conductive tubular materials.

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For long-term installations, I recommend round elements, either aluminum tubes or rods. All of the designs that appear in Part 1 use split drivers to minimize the number of mechanical connections on the driver assembly. The low-impedance drivers are either resonant (the high-gain version) for use with a 35-37-Ohm 1/4 wavelength matching section, or they are designed for about 25 Ohms of capacitive reactance for use with a beta or hairpin match (the maximum front-to-back ratio version). The very wide-band design requires direct connection to a 50-Ohm coaxial cable (the very wide-band version). In each case, the design places the antenna connections at the split-driver terminals.

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Fig. 1 gives us several alternatives for assembling the driver to the boom. Although the graphic shows alternatives A and B, we actually have 4 major combinations, plus any number of adaptations you may create based on local materials. Alternative A uses a small plate (Plexiglas, polycarbonate, or acrylic) with the drive tube anchored to it. A non-conductive insert (fiberglass, CPVC, or similar) aligns the two halves of the driver and strengthens the tube against crushing during bolt tightening. Even if the parasitic elements pass through the boom, the very slight misalignment of elements relative to their ideal plane will create no operational difficulties.

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Alternative A also shows a direct connection to coaxial cable without the use of a connector. This technique allows you to use a length of cable of your choosing to dress the lead to the boom and as much farther as you choose during antenna assembly. The open end of the coax, with its implicit ring connectors for attachment to the driver terminals, requires sealing. Plasti-Dip and similar products have proven reliable in this service and are less bulky than coax sealant and tape. Indeed, over the years, I have come to prefer this system over the alternative shown in B.

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If you prefer a connector, alternative B shows a simple mounting bracket that not only holds the connector, but also extends to one side of the element. 1" by 1/16" L-stock will handle either the BNC connector shown in the sketch or a standard UHF connector. Do all drilling before trimming the L-stock to final size for easier handling while creating the required holes. The sketch also shows the bracket with rounded upper edges. The easiest way to arrive at this shape is to use a disk sander. (Do not use a grinder designed for steel.) Clearly, you may adapt the connector bracket for use with the plate assembly in alternative A. Likewise, you may use direct coaxial cable connections to each side of the driver that passes through the boom.

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The through-boom driver shown in the sketch uses 1/2" tubing with a 3/8" fiberglass or similar rod or tube that actually passes through the boom PVC pipe. There is a limit for minimum effective insulating rod size to support the driver, since a hardware hole will pass through both the element and the rod. However, you may use this larger driver with any of the dimension sets in Part 1, using thinner material for parasitic element diameters. The "fat" driver will require a reduction in length to bring the beam to its proper SWR curve, but it will not otherwise affect performance.

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There is no good reason why the parasitic elements for a simple 3-element Yagi should not pass though the PVC boom. There are three (or more) different suitable systems for holding the elements in place. See Fig. 2. The top option works well with rods and tubes at least 3/16" in diameter. It uses minimum-size hitch-pin clips on either side of the boom to secure the element. Some builders use C- or E-clips, relying upon their spring action to hold the element in place against the boom. However,, all such hardware should be non-corroding. The middle sketch shows the use of a setscrew. If you under-drill the hole, most stainless steel bolts (#6 to #10, depending on the element diameter and the boom diameter) will self-tap the material for a firm seating. You may install a nut below the setscrew head and tighten it to the boom after securing fixing the element. For larger tube sizes, you may use the final option, a sheet metal screw that penetrates both the PVC boom and a hole at the center of the element.

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Both the hitch-pin mount and the setscrew mount benefit from a small bit of filing. The hitch-pin clips require holes through the round rods or tubes. A small jeweler's file can create a flat spot no great than about 3/32" diameter without weakening the element. The flat spot eases the drilling if you do not have a drill press. A similar flat spot at the element center gives a setscrew a good surface for the bite necessary to secure the element.

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The techniques suggested here have resulted in numerous solid Yagis up to 6 elements, with boom lengths up to 5' or more. (The longer the boom, the less suitable that rear mounting becomes.) All of the designs in Part 1 use under 30" of boom for the elements and are suitable for the hardware-store materials noted along the way. The one place not to use hardware-store materials is in the elements themselves. High-grade 6063 or 6061 aluminum tubing or rod is the best element choice for a long-term installation.

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Construction of field-antennas: Antennas for the field call for some special notes. Of course, you may take an antenna built according to the preceding suggestions into the field. However, that antenna has a permanent size, about 40" by 30". Hence, it is a bit ungainly for transport in an auto trunk or other confined space. One of the hallmarks of a good field antenna is that it stores compactly for transport and is ready for use with minimal field assembly. The ideal situation is one that requires no tools to transform the transport package into a working antenna.

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You can achieve this goal in a variety of ways. There are as many ways to successfully build a good field antenna as there are alternative materials for antenna elements. To demonstrate what is possible (in local talks for clubs and other functions), I created a hybrid Yagi using separate techniques for each of the 3 elements. The design uses the very wide-band design as its basis, although there is no reason not to use any of the other versions. Since you will likely use a single material best suited to your operating goals, you own field antenna will pick the design that is also most apt to those goals.

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My hybrid begins with a length of 1/2" nominal PVC pipe. The actual outer diameter of this pipe is a little over 7/8". I placed a Tee fitting just behind the driver position. The fitting is aligned for horizontal mounting of the antenna on a boom, using PVC screw fittings to increase the boom diameter until it matches the mast on which the antenna will sit. For many field uses, you need not cement the fitting in place. Press fitting the Tee will provide a secure and durable connection between the boom sections for most field operations. You may use a sheet-metal screw to secure the un-cemented side of the Tee, but that requires a screwdriver. The forward end of the boom also has a cap to keep out bugs and debris.

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Fig. 3 shows the general arrangement of the boom, along with the special rear section. At the rear end of the boom, there is an in-line coupler. It attaches to the forward boom sections with a large hitch-pin clip. I drilled the end of the boom with two holes at 90-degree angles. Hence, I can change the orientation of the antenna from horizontal to vertical and back again simply by removing the hitch-pin clip, twisting the boom, and re-installing the clip. You can use the same system with a rear boom-to-mast attachment system rather than the funny handle shown in the sketch.

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Most fox-hunting antennas that I have seen use rubber hand-grips in line with the antenna. These grips are most suitable to point Yagis at satellites, but are not ergonomically suitable for aiming the antenna straight ahead. Therefore, I took the pistol grip handle from a defunct electric weed cutter and replaced the steel tube with a short length of PVC. Since the in-line coupler bears the lever-force of the entire antenna ahead of it, I cemented the coupler to the handle-end pipe. Fig. 4 reveals that I left the trigger in place, since it is smooth, while the bare opening without it has sharper, less comfortable edges. You can store the entire antenna as a 3' long storage unit that is only about 4" wide, plus the handle. Alternatively, you can remove the handle and break the boom at the Tee for even more compact storage. Fig. 4 shows the pieces in full storage mode.

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Fig. 5 show the elements, each half-ready for use and half-stored for transport. The photo in Fig. 6also shows the demonstration elements. The driver uses collapsible whips taken from TV rabbit ears. The reflector uses flat stock, and the director uses a length of steel measuring tape.

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The 1/2"-wide flat-stock reflector would not store well if we used a full half-element length each side of the boom. Instead, I used #8 bolts and wing nuts for the outer section so that it could fold back on itself and fit entirely behind the driver during storage. For the reflector, I used a #10 wing nut and bolt that passes entirely through the boom to secure the reflector in place for both use and transport. 1/16"-stock seemed a bit flimsy initially, but has held up well during use.

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The driver whips retract for storage and extend for use. Setting them requires a tape measure or other measuring strip to get the correct length each side of center. (I wrote the measurement on the boom.) #8 hardware secures the position of the driver. I ground shallow grooves with a rotary tool in the small Plexiglas plate so that the driver stays in either the use or storage position once I tighten the wing nuts. The feedpoint bolts also hold the length of coax that I have devoted to the antenna.

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The director uses a length of steel measuring tape. A single sheet metal screw is usable as an element-to-boom fastener, although I placed a few thin washers between the tape and the boom to maintain the tape curvature. The tape does not require re-positioning for storage. Instead, wrap the tape around the boom and secure it with a piece of duct tape or similar. In fact, you can use sections of cardboard tubing from a roll of paper towels to slide over the coiled elements. In either case, guard your face when opening the element, since it will spring to position very rapidly.

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Does the hybrid field antenna work? Since I selected materials for the director and reflector that are very close equivalents to 1/2"-diameter round elements. I used the spacing for the very wide-band design for those elements. Then, I simply adjusted the driver length to give the 50-Ohm impedance curve for that design. I used the two fattest sections of the whip, and the resulting length was not much longer than the value shown in the Part-1 tables, about 19.25" each side of center.

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For field use, especially if you plan to use the antenna in a hand-held activity like fox hunting, you will need to determine the correct driver length for a normal use position well in advance of going into the field. You may also discover that for different orientations and heights above ground, the required driver lengths may differ.

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If you prefer the design security of using tubular elements, Fig. 10 shows one method of achieving a compact storage package and a full-size array of the type that you choose. You may construct the boom in the same manner as for the alternative element materials, using the 3-piece break down for transport. However, the element positions will have stubs protruding about 1.5" on each side of the boom. The reflector and director stubs will be 3/8"-diameter aluminum tubes, while the driver stub will be a length of 3/8"-diameter fiberglass or other non-conductive rod or tube. Secure each stub through the boom with a sheet metal screw as a permanent mounting.

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Although you may believe in thinner rods for field use, 1/2" 6063-T832 tubing weighs very little more than 3/16" solid rod. Table 1 provides some comparative weight of rods and tubes used in common amateur antenna construction. The material is drawn from the web site maintained by Texas Towers. It applies to aluminum tubing with a wall thickness of 0.058". Alternative materials with thicker or thinner walls will, of course, change the weight per foot. For the project at hand, the elements are between 3.0' and 3.3', so totaling the element weight is easy math.

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In most cases, the boom will outweigh the sum of the elements and their hardware by a good margin. So using larger materials adds little to the antenna weight, but allows the use of nuts and bolts as fasteners. The half-elements use 1/2" diameter tubes, none of which will be longer than about 20". You may attach the reflector and director outer element halves to the stubs with #6 or #8 nuts and bolts or with hitch-pin clips. (Do not exceed #8 size hardware, or the necessary hole may weaken the stub.) The driver uses nuts and bolts, plus solder lugs, to attach the element halves and to form connection points for the coax cable and any matching device (such as a hairpin).

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The advantages of using aluminum tubes as elements for the field antenna include general strength. Overgrown fox-hunting field sites that can snag the elements may still test the antenna's sturdiness. However, use of the antenna at an emergency or Field-Day site for FM or similar applications is unlikely to encounter such tests. The disadvantages include the need for small hardware to assemble the antenna. If you opt for this type of field antenna, be sure that the transport package includes both extra hardware to replace pieces lost in the grass and tools for assembly. A dedicated screwdriver and nut-driver are essential.

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In the end, the decisions concerning the methods of construction will rest upon your intended uses, the availability of materials, and your own assessment of your construction skills. However, somewhere in this collection of ideas--and other ideas that you develop--will be a Yagi that you can build yourself.

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Conclusion

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The hybrid demonstration antenna is simply a potpourri of ideas that you can adapt to both field and long-term antennas for 2 meters. In fact, we have surveyed a wide variety of factors that go into a home-brew utility Yagi for this band.

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  • 1. We examined three different Yagi designs: a high-gain version, a maximum front-to-back ratio model, and a very wide-band unit.
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  • 2. We also saw 2 ways of matching a 25-Ohm driver impedance to a 50-Ohm coax line using a 1/4 wavelength matching section with a resonant driver and a potential hairpin match with a driver that is capacitively reactive.
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  • 3. We explored a variety of alternative materials that builders of field antennas use instead of rods and tubes, and we measured them at 146 MHz to find their nearest round equivalents.
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  • 4. Finally, we explored various ideas for constructing both long-term and field antennas using common materials from hardware outlets.
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Now, you have no excuse for not building your own 3-element 2-meter Yagi, whatever your operating goals. In fact, I would expect you to have some building ideas that yield an antenna better than any of the samples that you have seen in these notes. Those ideas increase the number of options we have. The greater the number of options, the closer that we can match our antenna to the job for which we need it.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Mar/Apr, 2005, pp. 52-56. Reproduced with permission. Copyright ARRL (2005), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index Page

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Topics: VHF / UHF, Yagi


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Modeling Software, Part 1

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L. B. Cebik, W4RNL

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A regular question that appears in my e-mail is what antenna-modeling program to buy or use. The question takes many forms, but the nub usually boils down to matching the options offered by one or more particular programs with the modeling needs of the potential user. So let's examine some of the alternatives in the available array of programs, beginning with the calculating cores that underlie the available implementations. In these notes, I shall assume that you are familiar with the basic terms of antenna modeling using round wires and can handle such terms as wire, segment, source, load, etc. If these terms are still a mystery, see the 4-part series, "A Beginner's Guide to Modeling with NEC," QST, November, 2000, through February, 2001.

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We shall discuss only NEC and MININEC modeling software, both of which are readily available in low cost or entry-level implementations. Table 1 provides a list of such software, along with Internet addresses for those who wish further information. The list is not absolutely complete, and it contains two entries that we shall not discuss. Expert MININEC is a proprietary revision of the original MININEC core, while SuperNEC uses a MatLab interface. Since I do not own either program, they will not figure significantly in the discussion. The "feel" of a program is a highly personal facet of modeling software. Therefore, examining the web sites of the program makers is the best route to determining if you will be comfortable using any of the programs. As well, the web sites can provide up-to-date information on features and price. Programmers are continuously adding features to programs, so these notes are technically out-of-date as soon as I write them.

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1. NEC or MINNINEC

There are two classes of cores that perform the "method of moments" calculations comprising the analysis of an antenna design. For a more complete history of the development of these two strains of cores, see Bob Haviland, W4MB, "Programs for Antenna Analysis by the Method of Moments," The ARRL Antenna Compendium, Vol. 4, pp. 69-73. NEC emerged from main-frame FORTRAN work, while MININEC was developed to work on early desktop computers having very limited memory resources. Both cores have undergone extensive upgrades. For example, re-programming MININEC in one of the Windows-compatible languages has eliminated the early segment restriction on that core. Likewise, newer FORTRAN compilers for PC use have speeded up the runtimes of NEC models. +

MININEC 3.13 is a public domain program. As a result, it has undergone significant modification to overcome some of its initial limitations in addition to removing the upper limit on the number of segments in a model. All of the Windows implementations listed in Table 1 have no upper limit on the number of segments that a model may have. Two older DOS-based programs, AO (or MN) by Brian Beezley, K6STI, and ELNEC, but Roy Lewallen, W7EL, did have limits of about 256 segments. Expert MININEC by EM Scientific employs a different algorithm set from the ones used in the public domain version. As well, "raw" MININEC has a number of inherent limitations that may or may not be relevant to your modeling needs. All versions (with one exception, Antenna Model) use a ground simulation that becomes highly inaccurate if wires with any horizontal component are closer than about 0.2 wavelength above ground. As well all wires must be above ground, with only vertical wires allowed to touch the ground. The unmodified core is also sensitive to wire spacing, and such simple antennas as a folded dipole may give erroneous results. Sharp corners in the antenna geometry can also yield inaccurate results unless the wire segments are very short or the program has introduced a correction feature. Finally, the MININEC core has a frequency offset that becomes larger with increasing frequency. It becomes noticeable in the 10-meter region of the amateur spectrum.

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Unlike NEC cores, which have undergone very limited modification, the MININEC core has seen extensive modification by individual programmers to overcome these limitations. Over a series of benchmark tests where NEC-4 has shown proven accuracy, the various implementations of MININEC show variable results, each according to the modifications introduced and the success of those modifications. I ran all of the MININEC programs available to me through a series of benchmark tests, and only Antenna Model passed them all. (See 51. Testing the Fringes of Modeling Programs for details of the benchmark comparisons.) This fact does not mean that the other programs are not useful; instead, it means that they must be used within the frequency or structure limits built into them. There are many lower-frequency modeling tasks with relatively simple antennas for which any of the MININEC implementations will work well.

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What MININEC does very well that NEC does far less well is handle wire junctions with different diameters, whether linear or angled. Indeed, the Leeson correction process, which some implementations of NEC include, used MININEC as the standard during its development.

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NEC cores use a quite different set of algorithms. The cores will handle without modification over 10,000 segments, although software vendors may set a segment limit to various versions of the programs they sell. In addition, NEC has a number of additional features, the most prominent of which is the Sommerfeld-Norton (S-N) ground simulation routine. The S-N ground system is highly accurate, even for wires only fractionally above the surface. (Among MININEC implementations, only Antenna Model has grafted the S-N ground calculation system to its core.) The compiled FORTRAN routines used by many implementations are much faster for similarly sized models than most of the MININEC cores. In addition, NEC includes both networks and (lossless) transmission lines as part of the non-radiating accessories to models. In general, NEC cores have become a de facto standard for round-wire antenna modeling. NEC has a number of unique outputs (relative to MININEC), such as near-field analysis, received currents and scattering patterns from both linear and elliptical plane-wave excitation, and mutual coupling between specified wire segments. As well, NEC includes true ground wave analysis that includes near fields and surface waves.

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Entry-level programs generally limit the user to the basic wire geometry command. For example, EZNEC (Fig. 1 and Fig. 2) and NEC-Win Plus (Fig. 3) limit wire geometries to straight segmented wires.

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A full NEC core implementation includes a considerable collection of geometry commands that permits the construction of complex antenna and allied structures with minimal input file size. There are commands to create arcs, circles, helices, and catenary wires. Another command permits both length and diameter tapering along a specified wire. There is a command for rotating, replicating, and moving a wire already created. A large rectangular wire-grid structure might take as few as 4 entry lines for a model in the format (but not the detail) shown in Fig. 4. NEC also includes provision for the creation of surface patches.

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The key limitation to NEC cores is the inability to handle precisely elements having a changing diameter at wire junctions. For linear elements having no loads, transmission lines, or networks, the Leeson correction system has worked very well. (See David B. Leeson, W6QHS, Physical Design of Yagi Antennas (ARRL, 1992), Chapter 8, for details.) However, where loads, lines, or networks are present along the element length or where the element is not linear, these correctives do not apply. Both EZNEC and NEC-Win Plus include the correctives.

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NEC comes in two generally available versions: NEC-2 and NEC-4. (There is a NEC-3 that saw limited distribution.) We shall discuss the differences between these cores, but first, we should pause to look at file formats.

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2. File Formats

NEC cores require, in unmodified condition, the use of an ASCII file of the sort on the main GNEC screen shown in Fig. 4. (The NEC-Win Pro main screen would be virtually identical.) The model file contains all parameters of the model in terms of the geometry that describes the wires, the modifications to the geometry (such as the specification of element material loading and a source or excitation), and requests for outputs (the RP command in the illustration). The user may create a full model on a text editor as an input to the NEC core. The standard input file extension is .NEC, although any text editor, such as Notepad, will read the file and permit editing. +
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A number of NEC implementations use proprietary model file formats that are not ASCII. For example, the NEC-Win Plus files (see Fig. 3) use a spreadsheet format. EZNEC, shown in Fig. 1 and Fig. 2, uses its own file format (and transfers data to its cores in binary form). Unlike many other programs, EZNEC uses separate screens for the main data and the individual collections of data that describe the wires, loads, sources, ground values, and other constituents of a model. NEC2GO uses a basic file system derived from but not identical to its progenitors, AO and NEC-Wires (Fig. 5). Nevertheless, all three programs--either in all or in advanced versions--include facilities for converting files constructed in their native file formats into a .NEC file. 4NEC2 (Fig. 6), NEC-Win Pro, and GNEC save files in the basic .NEC format. The bottom line is that a file created under one system with a NEC core is convertible into a file to be saved under another system.

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One limitation that likely has limited the use of MININEC among antenna modelers is the fact that there is no standard file format.

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Fig. 7, Fig. 8, and Fig. 9 present the main screens of Antenna Model, NEC4WIN, and MMANA. They suggest--correctly--that each program uses a different file format that is not directly convertible from one program to the next. In addition, the user must plug some model parameters directly into the program, although some implementations attach these parameters to the individual model file. As a result, it is generally the case that the modeler has to re-construct a model from scratch when moving from one program to the next.

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MultiNEC, illustrated in Fig. 10, while not a NEC program in itself, can read many formats, including NEC-Win Plus, EZNEC, and the MININEC program, Antenna Model. Multi-NEC is an Excel application that works with the core of an existing modeling program and adds a considerable number of features on both the input and output side of the core.

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3. NEC2 or NEC-4

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The relative popularity of NEC as the basic calculating core for round-wire antenna modeling has resulted in the development of a larger body of modeling assistance than is available for MININEC. Perhaps the most notable training aid is the ARRL Antenna Modeling Correspondence Course, which comes with exercise models in EZNEC, NEC-Win Plus, and basic .NEC formats. However, other volumes (such as Basic Antenna Modeling: A Hands-On Tutorial and Intermediate Antenna Modeling: A Hands-On Tutorial) and article series (for example, "Antenna Modeling" that appears monthly in antenneX) are available.

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NEC-2 is the most widely used core and has become a public domain item. It is therefore available worldwide. The basic algorithms for the core treat only the axial currents, a fact that provides some of the core's limitations. It will not register the influence of a boom that intersects element wires at right angles. It requires a set of substitute uniform diameter elements for accurate calculation of linear elements having a changing diameter along their length. Non-radiating loads, transmission lines, and networks are most accurate in regions of an element that have a high and stable current, and such additions to the wire structure become less accurate as one moves into regions where the current level changes more extremely from one segment to the next. As we bring wires of different lengths and diameters into close proximity, the accuracy of the result may suffer. All wires must be above ground.

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Fortunately, NEC-2 contains a self-testing ability that will detect many model inadequacies. The average gain test is a necessary but not sufficient test of adequacy, and there are some inadequate models that the test will not detect. Although the convergence test is applicable to NEC models, it is the most used test for determining the adequacy of MININEC models. (Antenna Model incorporates the average gain test into its implementation of MININEC.) Hence, modelers who use NEC have a way to determine to a high, although incomplete, degree of confidence the quality of their models.

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NEC-4 represents a further development of and revision to NEC-2. The current calculations use a different algorithm that gives higher accuracy to antenna structures that use a tapering diameter. However, for very steep tapers, the results do not fully mesh with MININEC or Leeson correction results. Since the new algorithms treat only axial currents, some of the same limitations affecting NEC-2 still apply, although in some cases, to a lesser degree. For further details, see "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), pp. 3-16.

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However, NEC-4 adds a considerable number of new features that enhance modeling. The core permits wires below ground for accurate modeling of ground radial systems and similar subterranean structures. The core allows the modeler to specify insulating sheaths for wires. Besides the near-field analysis available in NEC-2, NEC-4 also uses a second form of near-field analysis along the axis of a line specified by the modeler. Although the standard above ground medium is a vacuum or dry air, NEC-4 allows specification of a different upper medium, with constant supplied by the modeler. The newer core also permits plot data file storage directly rather than via facilities provided by the commercial implementation.

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NEC-4 has another important difference from NEC-2: it is not public domain. Instead, it is proprietary with the Lawrence Livermore National Laboratory and the University of California. It requires a separate license before a commercial implementation (GNEC or EZNEC Pro/4) can be sold. In recent years the cost of a license to an individual--such as a radio amateur--for non-commercial purposes has come way down, but may still be significant in deciding whether to invest in a NEC-4 package. You may obtain the license materials on line at LLNL

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For many applications, there are "work-arounds" available so that NEC-2 results will reasonably replicate what you would obtain using NEC-4. However, for many other types of applications, NEC-4 is necessary. For example, simulating a buried radial system for a vertical monopole was once believed to be possible using either a MININEC-type ground (available in EZNEC) or a system of radials placed very close to the ground. Subsequent modeling in NEC-4 using buried wires has shown some serious shortcomings of the NEC-2 work-arounds. Hence, for critical applications, NEC-4 is the core of choice, if available.

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Throughout these initial descriptions of both NEC and MININEC, I have referred to "round-wire" modeling. Both cores use algorithms based on the thin round wires, normally in a vacuum or dry air and well separated from other materials. A considerable amount of current antenna design uses elements with other cross-section geometries and other environments. For example, laying (or etching) copper strips on a substrate is a common construction method for antennas in the UHF region and upward. Without extensive external calculations of the adjustment for the changed geometry and the substrate, NEC cannot accurately model such structures. Those structures require the use of what some call hybrid programs that combine method-of-moments techniques with other means of accounting for altered current distribution and the influence of the base material. For even the well-heeled amateur interested in modeling, the cost of such programs--virtually all of which are proprietary--can be daunting, if not downright forbidding.

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4. Segment Limitations

Thus far, we have been looking primarily at differences among the calculation cores available for round-wire antenna modeling. The major implementation-specific differences that we have explored are the file formats for storing antenna models. However, among the commercial implementations of NEC, there is another more fundamental limitation: the number of segments permitted by the core. The procedure--from a programming perspective--for setting the maximum number of segments allowed is straightforward. Therefore, some commercial versions of NEC have segments limits below the maximum possible values. +

The most notable of programs with segment limitations is EZNEC, now in version 4. Regular EZNEC limits the number of segments to 500, while EZNEC Plus allows 1500. EZNEC Pro (in both NEC-2 and NEC-4 versions), allows up to 20,000 segments by controlling the utilization of virtual memory. An allied decision made by commercial implementations of NEC is whether to use a single-precision or double precision core. Single precision cores run faster, although double-precision results are normally more precise. The speed difference does not show up in small models, while the precision difference does not appear until a model becomes highly complex.

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NEC2GO claims its NEC-2 core has no segment limitation. In contrast, the NEC-2D (meaning double precision) core in both NEC-Win Plus and NEC-Win Pro set the limit at 10,000 segments. GNEC's NEC-4D core allows up to a little over 11,000 segments, since it does not internally control the use of virtual memory during a run. In addition, cores may automatically set their dimensions, including the allowable number of segments, memory, and wires to a junction, by programming pre-sets, or by manual user settings. EZNEC sets the segmentation limits and memory allocation automatically by virtue of the model size, and NEC-Win Plus uses a similar system. However, NEC-Win Pro and GNEC have a parameter file to allow the user to set values for the most efficient core operation.

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When new to antenna modeling, 500 segments may seem to be enough for the biggest imaginable problem. However, it is wise to consider both present and future uses of a modeling program before opting for the least expensive and most segment-limited version. Of course, economics may prove to be a decisive factor in decision-making, in which case, one may have to obtain simply the best program for the price. If you can take future potential modeling activities into account, the following brief examples may be of interest.

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  • 1. Adhering to appropriate modeling guidelines for either NEC or MININEC, a 5-band quad may require as many as 220 segments per set of loops for each band.
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  • 2. A 5 wavelength, 3-wire rhombic may require up to 600 segments.
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  • 3. A 160-meter 4-square array with a full buried radial system with 32-radials per monopole may require nearly 1600 segments.
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  • 4. A VHF or UHF corner reflector of considerable size and composed of a wire-grid structure may require over 2200 segments.
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How large your models might someday become as you refine your modeling efforts presents you with some interesting match-ups with available software.

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I began these notes with the vain hope of compressing the options facing the potential antenna modeler into a single session. However, that goal is not realistic, so we shall have to spend one more episode on the subject. With the transition into options involving the number of available segments, we are moving from general considerations of the NEC and MININEC cores into choices among the features and facilities offered by the available implementations. We shall continue in this vein next time.

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Also see the Antenna Modeling Programs page for more information.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Sep/Oct, 2005, pp. 54-59. Reproduced with permission. Copyright ARRL (2005), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Modeling


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Modeling Software, Part 2

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L. B. Cebik, W4RNL

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In Part 1 of this parade through the options facing the new modeler or the modeler wishing to upgrade his or her capabilities, we examined a number of fundamental choices among the available calculating cores for round-wire modeling activities. Besides noting a few (but certainly not all) of the differences between NEC and MININEC programs, we also looked at some differences between NEC-2 and NEC-4. As we came ever closer to sorting among the available commercial implementations of each core, we found variations in the model file formats used among programs. Finally, we explored the need for a modeler to consider both short- and long-range modeling activities when deciding on the segmentation limitations that attach to some programs.

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As if these were not enough options for one to consider when investing in modeling software, we shall explore in this episode a number of other options and what they may (or may not) mean to the modeler. Throughout, we are by-passing explanations of how modeling programs do what they do, since that information appears in many other articles and books. As well, we are not recommending any one or more individual program, but trying to set forth the considerations that each program purchaser should think about when exploring the available programs at their web sites. Last time, we presented a table of programs and the URLs to use when exploring the possibilities.

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5. The Availability of Commands

MININEC appeared with an abbreviated set of commands relative to NEC-2. The available implementations of both public domain MININEC and the proprietary version known as Expert MININEC have added to the original command list. In general, however, the number of added commands is small. +

NEC is another matter. New modelers often select entry-level software that internally restricts the number of commands relative to the full list accepted by the core. The general purpose in the restriction is to provide the modeler with a user-friendly interface for setting up a model and for examining the output. Among the most notable examples of this practice are standard EZNEC and NEC-Win Plus, although each program uses a unique interface.

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To get a handhold on the range of commands that are usable by the NEC cores, examine Table 1. It presents a complete list of commands for NEC-2 and NEC-4. Note that some commands are specific to each core and that some commands change formats when moving from one core to the other. The NEC manuals for both versions tend to divide the commands into those that specify the geometry structure of the antenna and those that control the model afterwards, either by introducing modifications--such as loads or transmission lines--or by specifying the desired output data.

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Entry level programs tend to restrict the number of geometry commands to just 3: GW, GS, and GE. GW specifies a wire's coordinates, number of segments, and radius (although a program may list the entry as the wire diameter). In most cases, the actual user entry is invisible with respect to the command name. GS is a necessary entry that many entry-level programs automatically insert to convert the user's unit of measure into meters, the unit required by the core for calculation. GE simply marks the end of the geometry portion of the model.

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However, full NEC programs that permit ASCII entry of commands allow the use of all of the commands applicable to the core in use. Such programs are 4NEC2, NEC-Win Pro, and GNEC. Some of these programs permit multiple modes of entry. For example, the listed Nittany Scientific programs have an assist screen for each new command so that the user does not need to worry about the line format. In addition, they have an insert--essentially, the NEC-Win Plus program--to allow wire, source, and load creation in a manner identical to the entry-level program. Finally, the programs have a wire-assist function that aids in transferring model geometries created on spreadsheets into the NEC model format.

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The command set is useful in creating complex geometric structures in a compact form. Some programs--EZNEC especially--has wire-formation functions that replicate many of the commands in the geometry list. For example, one can form length-tapered elements (GC), helices (GH), along with wire-grids and radials systems (GM). The results are a list of individual wires, each equivalent to a GW entry. Consider a set of monopoles spaced 1/2 wavelength apart above a wire-grid simulation of a ground-plane surface. Depending on the number of monopoles and the outer dimensions of the rectangular wire grid, the EZNEC construct might have from hundreds to thousands of individual wire entries. In contrast, using the GW entry for the first wire in each group and the GM command to replicate it the required number of times, we might set up any monopole array and its ground surface in no more than 6 entries. However, mastering the full command set for either NEC-2 or NEC-4 requires a far longer learning curve than becoming able to produce useful results from the core with a more restricted command set.

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The control commands are equally restricted in entry-level programs. Among the structure modifying commands, the EX or source command used in entry-level programs is least versatile. The user may specify a voltage source placed on a segment of the geometry. These programs do create an indirect current source, if the user wishes, a function not directly available in range of selections available under the EX label. Among the excitation variations unavailable to the entry-level program user are those involving plane wave excitation--both linear and elliptical. These commands are useful in modeling activities that analyze the receiving and scattering properties of antennas,

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At the lowest entry level, the user has access only to far-field data in both tabular and graphical forms. The graphics are not a function of the core, but are fairly standard functions that programs provide to ease user understanding of the data. Some programs provide tabular near-field data, and others provide--at a more advanced level--surface-wave data. Missing from the list are other options attached to the RP command, and totally missing are the receiving (PT) and mutual coupling (CP) options for output requests. These options are only available in full NEC-2 and/or NEC-4 programs.

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The GF and WG commands associated with reading and writing Numerical Green's Files are especially useful to those who must repetitively use portions of large model files. Consider a series of wire-grid reflector structures having various dimensions. Then consider having to test each reflector with a variety of driver structures, each of which may require changes of position relative to the reflectors. The modeler can initially create a series of reflectors and create (WG) Green's files for each one. Then, by recalling the appropriate file (GF), the modeler can add the driver and run the entire model in a fraction of the time needed to re-run the entire reflector portion from scratch.

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Whether your modeling--both now and in the future--requires the additional commands available in the full NEC programs is more than an idle consideration. As well, you may not need to make a very long-term decision at the beginning. Software makers do offer discounts for upgrading, but only when the move is from one program to another in a single product line.

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6. Input/Output Style and Presentation

The input and output systems of coordinates often take some users by surprise. The surprise factor is often a function of the system with which the user is most familiar: the compass rose vs. the Cartesian coordinate system. Fig. 1 shows the Cartesian coordinate system as used by both NEC and MININEC. In all cases, the +X-axis corresponds to the 0° heading used in the output reports for radiation patterns. +Y corresponds to 90 degrees. Of course, -Z values are valid only for free space models in all of the cores and only in NEC-4 for models using a ground. +
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Note that the system effectively counts counterclockwise. For most antenna structures, the direction of counting presents no problem. However, when constructing arrays of multiple antennas, such as an AM broadcast tower set, not only are directions from one tower to the next important, but as well, the modeler may be used to employing a compass rose or clockwise orientation for the field geometry. So far as I know, only Expert MININEC offers an option for inputting values using true compass or azimuth headings.

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Fig. 2 shows the circles for the output conventions. Inherently, NEC and MININEC use the phi or counterclockwise system for headings in the X-Y plane, along with a Z-axis theta system that counts from the overhead or zenith angle downward. Some software systems offer only this option for the presentation of radiation patterns, but other implementations also offer (and refer to) azimuth and elevation headings. In most cases, conversion of theta angles to elevation angles (angles above the horizon) is simple. However, the phi-to-azimuth (clockwise) conversion is more complex. Hence, some software simply calls the phi patterns azimuth patterns. Other software, like the sample standard 2-D azimuth pattern in Fig. 3 from NEC-Win Plus, modifies only the outer ring values without flipping the pattern itself. For symmetrical patterns, this practice makes no difference, but may create confusion for non-symmetrical patterns if the user forgets what conversion process is at work.

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In the realm of 2-D patterns, there are many more options for presentation than simply the total pattern. Post run calculations can sort out the left-hand and right-hand circular components of a pattern, as in the EZNEC sample shown in Fig. 4 and also available in the Nittany Scientific software Multi-Plot facility. Besides showing a pattern, the software may also make available in various forms supplementary data, as shown in the side-box in Fig. 3. Of special interest is the NEC4WIN presentation in Fig. 5; it adds a supplemental calculation of the headings for each lobe in the pattern.

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Most modeling software provides a 3-D pattern for the user, and the presentation will vary slightly with each software package. Fig. 6 shows the Nittany Scientific version, which allows a conventionalized but not scaled representation of the antenna in the typical line pattern. The antenna view and pattern change together as one rotates the image. Some packages use a standard separation of lines, representing increments (in degrees) between points in the far-field sample. Other programs allow user control of the increments, although one must always strike a balance between wide line spacing and little pattern definition on the one hand, and small increments for detail that may create an unreadable dark graphic. Antenna Model adds color to the pattern for easier reading, as shown in Fig. 7.

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Although virtually all antenna modeling software packages offer graphical far-field representations that show the same data, some presentations may be better suited to specific applications than others. Hence, the prospective user should consider the options in the appearance of pattern graphics as well as the number of different patterns types that may be available. Far-field patterns have major and minor axes, and the RP0 command allows the user to specify these data in place of the more conventional vertical and horizontal components of the total field. We have also noted that one can calculate the circular components of a total field. Some programs, such as EZNEC Pro, may also allow the presentation of surface-wave (RP1) fields, while others may plot near-field (NE or NH) data.

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In addition to polar plots, some software implementations provide an array of rectangular plots. At the low end of the scale, EZNEC provides an SWR plot across a specified frequency range, while NEC-Win Plus plots both SWR and the impedance components. NEC2GO provides a graph with multiple data lines for frequency sweeps. Antenna Model supplies separate gain, 180° front-to-back ratio, worst-case front-to-back ratio, resistance, reactance, and SWR curves for its frequency sweeps. At the upper end of the range of available rectangular plots are NEC-Win Pro and GNEC, which provide not only graphs for frequency sweeps, but as well, current and receiving data plots.

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To increase the available graphical representations of data from entry-level programs, there are supplemental programs. For example, EZPlots from AC6LA provides extensive graphing of EZNEC frequency sweep data, which emerges from the core program in tabular form only. More flexible is AC6LA's Multi-NEC, which works with a considerable number of NEC and MININEC programs to provide versatility on both the input and outside sides of the core. It allows batch runs and the use of variables on the input side, and produces a number of polar and rectangular plots for the output data. Both of these programs are Excel applications rather than stand-alone programs.

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7. Auxiliary Functions

Rigorously, any calculation made by an antenna-modeling program outside of the core is an auxiliary function. Since the SWR corresponding to a reported source impedance requires a user specification of a reference impedance, it is technically an auxiliary calculation. Likewise, calculation of the circular components of a total far field fits the same category. However, these calculations are so intimately connected to the core calculations that we tend to think of them as inherent to the modeling process. +
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A more clearly auxiliary function is the "model-by-equation" facility or the use of variables, represented by the NEC-Win Plus "equations" page shown in Fig. 8. (Part 1 showed a sample--Fig. 3--of the NEC-Win Plus "wires" page revealing the use of variables rather than numbers.) In NEC-Win Plus, the equations are preserved only in the .NWP format file, but saving the model in .NEC format saves only the resulting numbers.

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Some auxiliary functions are extensions of existing commands that the core already provides. Fig. 9 shows the screen from EZNEC in which the user would specify loads using R-X, or series or parallel R-L-C values. Placing a trap in an antenna element normally requires external calculation of a parallel L and C value, where the inductor also has a series resistance (calculated from the known or estimated coil Q). Hence a series-to-parallel conversion is in order. As well, the trap is designed to be resonant at a certain frequency. Hence, the net resistance and reactance at other frequencies varies in accord with how far off resonance the trap may be. Rather than calling for an external recalculation of the load assembly for each new frequency, EZNEC recalculates the load value for that frequency based on the input data provided by the user.

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NEC2GO provides a different type of integrated auxiliary calculation. Fig. 10 shows the matching network selection screen. The user selects the desired line impedance and the network type--where only viable networks are active relative to the source impedance derived from an initial core run. There are other matching network programs available, but the unique part of the NEC2GO system is that it converts the selected network and values into an NT command and adds it to the model, moving the source to a new wire created by the auxiliary function.

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We have noted in passing the facility in some programs to create various wire structures within some programs. Radial systems (whether used for a ground plane or as a "top hat") and wire-grid rectangles are the most common, although in EZNEC, one can also create helices and circles (or, more correctly, straight-wire approximations of circles). For more complex structures, Nittany Scientific offers a package called NEC-Win Synth to synthesize the geometry section of models. The output can be saved in both .NWP and in .NEC formats for use in a wide variety of NEC software. The package includes over 50 preset shapes ranging from simple geometric shapes, like an open or closed cylinder, to generic vehicle shapes, such as a sedan, van, or pick-up truck.

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True auxiliary functions are integrated into the software package that implements a given calculation core. Numerous programs have independent modules to perform various calculations, but often, they are conveniences more than integrated parts of the modeling process. For most of the independent calculation modules, one can find external programs to perform the same calculations. Hence, these functions may have lesser status than integrated auxiliary functions when evaluating one's options in the selection of antenna-modeling software.

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Our samples of auxiliary functions, like every other aspect of this survey of options, incompletely represent what is available in the commercial implementations of NEC and MININEC. The goal is to make you aware of the range of enhancements that may be available to the antenna modeler. In deciding what software is best for both immediate and future needs, you will have to decide which features of which software best mesh with those needs.

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8. Cost

I would be remiss if I did not take cost into account as one of the option sets facing the antenna modeler. Software is an inherently unstable commodity, with both the available features and the cost changing over time. As operating systems evolve, changes in software are inevitable. The PC software that we have sampled is generally compatible with operating systems up through XP. What the near future may bring, such as 64-bit CPUs, etc., and the effects that future developments may have on antenna modeling software appear in a crystal ball that I do not have. Therefore, these notes are necessarily dated and subject to change. +

In thinking about cost, the prospective user must consider the program capabilities that come with the price and the support available from the program developer. Typically, but not always, free programs come without any commitment to support. Support has at least two dimensions: bug fixes and tutorial material. All of the developers noted in this exploration of options want to know about bugs and are interested in user suggestions. However, suggestions for change and enhancement are always subject to programming feasibility, and a given suggestion might not show up in a software package until many versions down the line--if at all.

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Tutorial materials take many forms. Many packages have attached tutorials to guide the user through at least the initial stages of modeling with the software. Manuals come in two forms: via the "help" facility and/or in a printed manual. In some cases, the program developer may provide or update a manual with documents that require user printing. Articles appear from time to time in various journals, such as QST. My own series on Antenna Modeling appears monthly in antenneX and covers topics relevant to the use of both NEC (-2 and -4) and MININEC. Of all the cores, NEC-2 enjoys the most tutorial support. The ARRL antenna modeling correspondence course is a 31-lesson introduction to antenna modeling with exercise models provided. Nittany Scientific offers both basic and intermediate modeling tutorials, also with exercise models provided.

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Nevertheless, the bottom line is dollars for digits. Table 2 provides the software prices as derived from on-line sources at the time of writing. Remember that NEC-4 requires a prior license from LLNL as well as the implementing software, so include all costs when counting your resources. The numbers are for general guidance and are rounded. Be certain to get exact prices, including shipping and handling, from vendors before making your investment in antenna modeling software.

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Whether you are considering an entry-level program or an advanced version of the latest software, these notes are aimed to expand the range of factors that you should consider as you approach a decision. Not all of the available options would fit the space available for these notes, so expect to do much more detailed analyses in preparing to write a check.

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Also see the Antenna Modeling Programs page for more information.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Nov/Dec, 2005, pp. 50-56. Reproduced with permission. Copyright ARRL (2005), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Modeling


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Do I Need More Gain?

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L. B. Cebik, W4RNL

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On 2 meters, we find both horizontally polarized and vertically polarized antennas in keeping with the 2 main activity clusters on that band. At the lower end of the band, point-to-point communication dominates, along with some E-M-E reflected-wave communication. In the main, these activities use horizontal polarization. In the upper part of the band, repeater and related mobile activities dominate, with a reliance on vertically polarized antennas. Near the middle of the band, we find a narrow frequency spread used for satellite communications. The variety of antennas used for this service tends to be a mixture, with some circularly polarized antennas. Similar patterns apply to most of the amateur VHF and UHF bands.

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Unfortunately, many amateurs carry over HF antenna experiences into the VHF and UHF bands. Hence, there seems to be only one question that dominates poor results with an existing antenna: how do I obtain more gain? Longer Yagis and exotic antennas come to mind as the sure fire answers to all inadequate communications problems. (We shall bypass the "more power" answer to the same question.)

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For some situations, an antenna with more forward gain might be the answer. But higher gain may not always imply a longer Yagi with more elements. For many cases, the answer to our need for effective communication may lie elsewhere. In these notes, we shall review some information that is readily available but scattered. In the end, we may opt for more antenna gain, but only as a secondary feature of other antenna properties that we too often overlook. We shall confine ourselves to ordinary communication on 2 meters--as a band on which we can focus attention and make comparisons. Extreme terrestrial DX and E-M-E communications will have to be topics for another day.

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Height

Sometimes the answer to an antenna problem is not gain but height. There are two immediate clusters of reasons for needing more height. +

Local Clutter: Local clutter consists of all objects that may block, absorb, refract, and reflect RF energy so that it cannot reach its target. Fig. 1 provides a simplified sketch of the situation. Both organic and inorganic structures can get in the way of RF energy that we want to reach a certain station, regardless of whether we are using a vertically or horizontally polarized antenna. Trees and shrubs vary in their energy deflection abilities, depending on local weather, type of flora, and the season. Wet wood is usually more ionized than dry wood. Some species of trees have a higher metallic content than others.

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The more modern a human-built structure, the more likely it is to have more metal that can block our communications attempts. On old Victorian mansion might have a single AC circuit and wires in the floor of the upper story. A modern house has computer, telephone, TV, and other cables adding to extensive house wiring that likely comes down the walls from an attic area. As well, foil-lined attic insulation is common. Finally, structural steel is working its way into the modern home, not only as support beams, but also as a replacement for the traditional 2-by-4. We do not have to move to a high-rise apartment structure to be surrounded by metal.

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In these kinds of situations, raw antenna gain may not help us much at all. As the figure suggests, we need to place our antenna above the clutter. If the clutter is at a moderate distance from our antenna location, we can sometimes move the antenna site laterally to clear most of the problematical signal deflections. However, in most cases, nothing succeeds like height. We shall return to the local-area height question, but first, we should note the second category of concerns.

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The Horizon: How close the radio horizon is to us often surprises newer VHF and UHF operators. Since VHF and UHF communication normally is line of sight (and just a little more), the height of the antennas at both ends of the line determines how far apart we may be and still effectively communicate. Fig. 2 shows the most basic outline of the situation.

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If the 2 antennas have different heights, each will have a different distance to the grazing point, that is, the point at which the RF energy encounters the ground. We can estimate either D1 or D2 from a standard equation (shown in The ARRL Antenna Book, 20th Ed., p. 23-6).

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The equation shown is actually a short form of a slightly more complex equation, a version of which appears in Reference Data for Engineers, 8th Ed., p.33-14.

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The equations are easily converted from miles of distance and feet of height to kilometers and meters. However, let's look more closely at the new element in the second version of the equation. K is the effective earth radius. The value is about 1.333 for the temperate latitudes, but may vary from 0.6 to 5.0 depending on where in the world we may be. The simplified equation produces accurate results only for the latitudes in which the value of K is 4/3.

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We may easily turn the equation around to see how high an antenna must be for a given distance to the radio horizon.

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Lest we think that achieving a significantly greater distance to the radio horizon is a linear matter of raising the antenna by so many feet, notice the fact that the equation uses the square root of height in finding the distance. Doubling the antenna height will only increase the distance to the radio horizon by a factor of 1.4. Table 1 correlates some common antenna heights and the distance to the radio horizon.

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Of course, the distance to the horizon (D1) is not the distance to the most remote distant station that we can contact. That station will also have an antenna height and resulting distance (D2) to its radio horizon. So the actual communications distance is D1 + D2. Atmospheric bending of signals may add perhaps 10% to the raw calculation. However, broadcast antennas (for example, FM or television) usually add a factor to their height plans so that station signals clear the Fresnel zone, the region in which diffraction from objects in the signal path may yield interfering waves. Nevertheless, for point-to-point communications, the average amateur is severely limited in efforts to increase the communications range by adding more tower sections. Little wonder that FM repeater work relies heavily on placing the repeater antennas on the highest tower with space for rent or donation.

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In most cases, achieving enough antenna height to clear most local clutter takes precedence over adding to the antenna gain. Only if we can establish at least marginal communications with the desired target station will added antenna gain provide significant signal strength to convert marginal signals into reliable ones.

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Gain and Beamwidth

We often overlook an important property of antennas in our quest for maximum gain and front-to-back ratio. Antennas also exhibit a beamwidth that can be very useful to us in obtaining the coverage that we desire and the blocking of signals from undesired directions. We shall deal eventually with all four of the antennas in Fig. 3, but initially we shall look most intently at the 3 Yagis in the group. The outlines are to scale. Table 2 lists the dimensions for the Yagi antennas in inches. The dimensions assume that the beams use either a nonconductive boom or that the elements are well insulated and isolated from a conductive boom. The EZNEC models of these antennas are available from the ARRL web site. The models use a free-space environment and the elements will form a horizontally polarized antenna if we place them over ground. However, you may rotate the elements to create a vertically polarized antenna and adjust the array height as desired. +
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All three Yagis are credible performers for their boomlengths and number of elements, and all use 1/2" diameter elements for uniformity. I have selected Yagis that cover the entire 2-meter band so the comparisons are fair throughout. The change of gain across the band is minimized, and the front-to-back ratio is at least 20 dB for all models at all frequencies sampled. The two larger Yagis have feedpoint impedance values very close to 50 O. The 3-element version has a natural driver resonance between 25 and 30 O. The model uses a 1/4 wavelength matching section to bring the model source impedance above 40 O at the design frequency (146 MHz). The 36-O transmission line can be composed of parallel sections of 72-O coax cable. Should you wish actually to construction the antenna, you may also shorten the driver and add a beta (hairpin) matching component. In all cases, the beams cover the band with under 2:1 50-O SWR. Table 3 lists the modeled performance of the Yagis at 144, 146, and 148 MHz in free space to provide some fundamental data.

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We should first review some common information about Yagis with different lengths. The most significant physical fact is that the boomlength tends to increase faster than the element count. The 7-element Yagi has 2.3 times the number of elements as the 3-element Yagi, but the boom is 3.4 times longer. The 11-element Yagi has 3.7 times the elements of the 3-element Yagi, but on a boom 8.1 times longer. Gain does not keep pace with the increases in either the element count or boomlength. Moving from 3 to 7 elements nets us a 3.9-dB gain increase, but adding a similar number of elements to wind up with 11 nets us only about 2.6-dB additional gain.

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Next, let's examine some data that many VHF Yagi users overlook. The data tables include the E-plane and H-plane beamwidth values, that is the number of degrees between the half-power points on the radiation pattern. The E-plane beamwidth is very close to what we would obtain operating the beam horizontally over the ground, while the H-plane value is close to what we can expect for beamwidth when operating the antenna vertically over ground.

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If we begin with the 11-element Yagi, shown in Fig. 4 for all three sampled frequencies in both planes, we find no great difference between the E-plane and H-plane beamwidth values--about 3°. However, if we shorten the beam to 7 elements, as shown in the overlaid patterns of Fig. 5, the beamwidth difference grows to 9°. When we clip 4 more elements from the Yagi, as in the patterns in Fig. 6, the difference between the E-plane and H-plane beamwidth values climbs to about 43°.

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To make the information even more graphic, Fig. 7 overlays all 3 beam patterns in each plane for 146 MHz. The E-plane patterns show the gain increases with boomlength. However, the beamwidth decreases by only 27° as we move from 3 to 11 elements. In the H-plane, the differential in beamwidth values is 67°. When using the Yagis over ground in the horizontal position, the change in beamwidth usually signals only greater ease or difficulty in aiming a rotatable installation. In contrast, the much larger change in beamwidth presents us with some interesting potentials for vertically oriented Yagis over ground, even if we create a fixed installation.

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Before we explore that potential, let's add one more beam to the collection, the Moxon rectangle. This compact 2-element array has some interesting properties in conjunction with the Yagis in our collection. Table 4 lists the dimensions, with reference back to Fig. 3, which shows the outline of the beam. Dimension A represents the two parallel long element sections. B is the driver tail length, while D is the reflector tail, where "tail indicates the portion of the elements that point toward each other. Dimension C is the gap between tails. The sample Moxon uses 1/4" diameter elements.

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Table 5 provides the modeled performance data for the Moxon rectangle. The gain is modest, but the front-to-back ratio is very high for a 2-element wide-band beam. The direct 50-O feedpoint covers the entire 2-meter band easily. More significant perhaps are the patterns in Fig. 8. The E-plane beamwidth is 79° at mid-band, about 13° wider than for the 3-element Yagi. However, the greatest growth in beamwidth occurs in the H-plane pattern, which is 34° wider than the corresponding 3-element Yagi pattern. The cardioidal pattern provides a 144° beamwidth at 146 MHz.

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Where we do not require much gain, the Moxon rectangle provides some very promising potentials. Horizontally, the antenna makes a good field unit that we might hand-steer without much difficulty. However, the final promise for the antenna may well lie in its service as a fixed vertically polarized antenna for certain types of home-station repeater operations.

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Beamwidth as a Primary Property

At many locations, omni-directional antennas for repeater operations may be the wrong choice. Fig. 9 presents only two such scenarios. The left portion of the figure shows a situation in which there may be a repeater station to the east that either causes interference or which we simply do not wish to access while working with one or more of the repeaters to the west. The situation calls for a directional antenna with a reasonably good front-to-back ratio to reduce signals to and from the east. At the same time, the beamwidth of the antenna should be wide enough to permit contact with the entire set of repeater stations to the west. +
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On the right, we have a hill or other major terrain obstruction that prevents operation to the east. In this case, we might use an omni-directional antenna. However, such an antenna will provide lower gain. As well, reflections from the hill may create interference patterns. The use of a directional antenna with the proper pattern shape would permit us to control the reflections in a useful way.

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We have surveyed 4 different antennas in terms of the H-plane beamwidth. Which one will serve best in a given application depends on the operational needs. Fig. 10 presents overlaid H-plane patterns for all 4 antennas at 146 MHz. There are 4 different sets of needs indicated by the dots or locations of the desired repeater stations. (Note that, although I am working in terms of repeaters, any vertically polarized station within the active field may be included.)

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The upper left situation shows 4 widely spaced stations, two of which fall outside the beamwidth of any of the Yagis. If gain is not a major consideration, then the Moxon rectangle may best fulfill this need. Indeed, one need not use this antenna design only when there is a need for a very wide beamwidth. The upper right portion suggests a situation calling for somewhat more gain but a lesser demand on beamwidth. Hence, the 3-element Yagi may be the antenna of choice. The two lower scenes present calls for still higher gain and decreasing beamwidth requirements. The 7- or 11-element Yagis may best fill these roles.

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The lessons from this exercise are two. First, for any proposed antenna, we should understand not only the potentials for gain and front-to-back ratio. We should also understand both the E-plane and H-plane beamwidths. Second, once we understand the beamwidth capabilities of antennas, we may select one that will provide us with designer-coverage for a given communications situation. In many cases, we may avoid the expense and maintenance worries of using a rotator by selecting the right antenna for the desired field of coverage.

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More Gain, Same Beamwidth

So far, we have resolved antenna issues by relying on antenna properties other than forward gain. There may be cases in which we need height, beamwidth, and additional gain. As we saw in comparing the Yagis, the higher the gain potential, the narrower the beamwidth. Suppose we need to meet the demands of one of the top two scenes in Fig. 10, but with more gain than we can obtain from a single Moxon rectangle or 3-element Yagi. +

The answer does not lie in making a longer Yagi. For every increment of boomlength that we add, we lose a proportional amount of beamwidth. For vertically polarized Yagis, the rate of decreasing beamwidth is greater than for horizontally polarized Yagis. Of course, we can accept the narrower beamwidth and resort to the rotator. However, we should first explore a strategy that allows us to enjoy the simplicity of a fixed installation.

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One effective strategy is to use a 2-stack of whichever antenna we select. The mechanical trade-offs between a longer-boom Yagis with 3-dB higher gain and a stack of 2 shorter Yagis are about even at 2-meters and above. To create a stack, we shall have to extend the mast by about 7' (1 wavelength), but the individual antennas will place less stress on the mast than a single Yagi with a boom perhaps 3 times as long. Since we would have to rotate the longer Yagi to cover the same field, let's try the stacking route.

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A good separation between vertically polarized stacked beams is about 1 wavelength, center-to-center (or, for reference, feedpoint-to-feedpoint), as shown in the outlines in Fig. 11. Since all of the feedpoint impedances are 50 O, you may use a pair of 75-O cables, one from each feedpoint to the midpoint between them. Each line should be an odd multiple of 1/4 wavelength at about 146 MHz (taking the velocity factor of the line into account). The two resulting 100-O impedances in parallel match the main 50-O cable. Other schemes are possible, but this one is time-tested. Phase-line losses require the use of the best quality coax that you can afford.

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Table 6 provides comparative information on the modeled performance of the two types of antennas, with information on single-unit and 2-stack versions. With a 1 wavelength separation between the two antennas in each stack, we net about 3.2-dB of added gain over single-units at the lower height. As well, the 2-stack has a slightly lower TO angle, and that fact has positive implications for point-to-point use of the array. The antennas are each far enough above ground and far enough apart that the feedpoint impedance values for the 2-stack do not significantly change relative to the impedance of a single unit.

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For the present discussion, perhaps the most important fact is that neither beam loses any horizontal beamwidth when placed in the 2-stack just described. Fig. 12 compares the single-unit and 2-stack azimuth patterns for each antenna type. 2-stack gain in each case marks the outer limit of the patterns. Hence, the Yagi may give the illusion of showing a pattern that is smaller in area. However, the real difference lies in the narrower beamwidth for the higher-gain Yagi, relative to the Moxon rectangle.

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Our exercise presumed that we needed vertical polarization for the desired communications. It also set up scenarios in which we wanted to null out a general direction and direct our transmitted energy (and our receiving sensitivity) over part or all of the remaining horizon. The techniques that emerged gave priority to the H-plane beamwidth of the antenna candidates in devising a way to meet the need. Gain became a secondary property. Within the limits of the scenario, attaining more gain required methods other than simply making a longer Yagi with more gain.

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Conclusions

At VHF and UHF, there are numerous communications activities that call for the highest gain possible. Long-distance point-to-point work may call for stacks and squares of the longest-boom antennas feasible installed as high as possible. E-M-E work may call for similar antennas, but height is less of a problem, since we shall point the antennas upward. Still, the quest for gain rules these activities. +

However, we may fail to meet most basic communication needs if we only think of gain, and especially, if we think of gain only in terms of longer Yagis with more elements. The first task is to employ all of the ingenuity at our disposal in raising the antenna above the local ground clutter. The next step is raising the antenna to a height that places our signal above the radio horizon relative to our targets.

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As we move into special needs--such as those presented by home-station contacts via repeaters--gain may once more take a back seat to other antenna performance parameters. In the sample case, the horizontal beamwidth of various antennas proved to be more important than raw gain in developing a solution. Even when we needed more gain, a longer antenna was not the best route to achieving it.

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These notes are not in any way final answers to the questions that we have explored. Instead, they are initial options designed to expand thinking about point-to-point communications. For example, Yagis and Moxon rectangles are not the only antenna types that might meet our needs. Planar and corner reflector arrays are available and might allow easier construction, especially at 432 and 1296 MHz. Even the broadband batwing dipole array might meet some needs.

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The first step in choosing the option that is correct for a given situation is an analysis of the situation itself. The second step is a full understanding of the antenna performance properties relevant to the needs of the situation. The more complete our understanding of available antenna designs, the more likely that we shall be to select a workable option as a solution.

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ao6-models.zip.

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Updated 01-12-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jan/Feb, 2006, pp. 47-53. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Moxon, VHF / UHF, Yagi


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Wire and the HF Horizon
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L. B. Cebik, W4RNL

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The 1/2 wavelength dipole and its kin (the inverted-V, the quadrant, etc.) are far more competent antennas than many folks give them credit for being. They provide good gain with a fairly wide beamwidth and are bi-directional. In fact, if we rotate a 1/2 wavelength dipole in 120° increments, we obtain full horizon coverage with only a small gain deficit in the pattern overlap region, as shown on the left in Fig. 1. With an antenna tuner and parallel feedlines, we can use the antenna at higher frequencies. Up to about 1.5 times the resonant frequency, the beamwidth is still great enough to give us less than a 3-dB gain deficit in the pattern overlap region. See the right side of Fig. 1. For full-horizon coverage with no more than a 3-dB gain deficit (about 1/2 S-unit), we need a half-power beamwidth of about 60° from each of the 3 antenna positions.

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Now let's give ourselves a limitation. We shall take away the rotator and use wire for the dipole. We end up with a very inexpensive but fixed antenna. For full-horizon coverage, we shall need at least 3 dipoles at approximate 120° angles. The question then becomes how to arrange the 3 dipoles. The arrangement must activate one dipole, leaving the other 2 inert or inactive. Fig. 2 shows full-Y and triangular (or delta) arrangements. The sketches assume that each dipole has a feedline, and that all feedlines are the same length. They run from the feedpoints to a central location. That location may be at the station equipment or a remote switch at the center of the arrays.

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The full-Y array requires 4 supports, with one at the center and 3 for the far dipole ends. The triangle only needs 3 supports, since each support handles 2 dipole ends. However, if we wish to use the arrays at or very near to their resonant frequencies, we hit a snag in the form of very non-dipole patterns. Since the antennas are near their resonant frequencies on the lowest frequency of use, the two most obvious schemes fail us.

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On the left in Fig. 3, the full-Y array produces a bi-directional pattern with a narrow beamwidth. Interaction with the inactive dipoles produces north-south bulges and narrows the east-west pattern. In contrast, the inactive dipoles in the triangular array form reflectors to produce a spade-shaped pattern in one direction. In other applications, we might capitalize on this pattern, but for our project, it defeats the goal of covering the entire horizon. Most of the interactive effects disappear if the operating frequency is more than about 30% distant from resonance. However, that requirement would defeat our desire to have a 3-dipole array that is highly usable on several ham bands and able to cover the horizon.

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There are alternative array configurations that do not result in interactions of the type we obtain from the full-Y and delta arrays. In the 1930s, some operators used a half-Y formation. The Y was full, but each element was half of a dipole. Each half-dipole leg came together at a center point and each had 1 of the feedlines already connected. Hence, the array ended up with 3 feedlines. To select a dipole, we simply used 2 of the 3 lines. Many of these early operators used the antenna on a single band. Therefore, they created twisted triplets for the feedline. The close spacing and wire insulation on the feedlines gave a reasonably constant and fairly low characteristic impedance for any wire-pair in the group. Determining the correct dipole to use simply required selecting the feedline pair that yielded the strongest signal.

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Fig. 4 provides an outline sketch of the wire portion of the array cut for 20 meters. The dimensions are overly precise, since we shall be using the array with parallel feedline and an antenna tuner. However, the dimensions are based on first resonating the dipoles in free space and then transferring those dimensions to a model over ground. Any equal wire lengths within a few inches of the values in the figure will work as well. Table 1 provides a recap of the critical dimensions, along with the dimensions of some other versions of the half-Y array.

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The pair of wires that we select forms a dipole that is bent to include a 120° angle. Like any slightly Vee'd antenna, we lose a bit of gain and some of the side null depth of a standard dipole. As shown in the top lines of Table 2, that gain loss relative to a standard dipole is under a half dB at 20 meters. However, in exchange for the maximum gain deficit, we obtain very workable patterns for many bands. The left portion of Fig. 5 overlays patterns from 20 through 10 meters. The gain is remarkably consistent from one band to the next. Only on 10 meters do we find sufficient interaction between the 2 actives wires and the inactive wire to produce a 0.9-dB front-to-back ratio.

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10-meter operation presses the array to its limits as a means of covering the entire horizon with 3 bi-directional patterns. The right side of Fig. 5 shows the deeper nulls in the overlap region between maximum gain points. As well, there are other cautions to observe when using the half-Y array in multiband service. Table 4 lists some of the modeled performance figures, as well as indicating the bands most likely to yield excellent performance. Below 20 meters, we obtain an even broader beam. However, the source impedance has a low resistance and a very high reactance. With the standard high impedance lines that we tend to use for the array, this situation will likely result in a challenging matching situation for most tuners and introduce significant line losses. On 12 and 10 meters, the source impedance values reach levels that may challenge tuners in the other direction, depending upon the impedance components that exist at the terminals as a result of the line length and characteristic impedance. However, consistent operation on 20 through 15 meters--with 12 meters also a possibility--should be easy.

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For the upper HF region, installing the half-Y should require only 3 supports, one at each dipole end. The triple feedline that forms an equilateral triangle as a cross-section can simply drop from the center point. If the curve that the line forms on its way to the shack entry is shallow enough, you can maintain equal-length lines along the entire feedline run. Under these conditions, you should not need significant retuning when switching from one pair of dipole legs to the next. Hence, a simple switching scheme should give instant recognition of which dipole pair yields the strongest signal.

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There will be a temptation to use a center support and to place the feedline wires symmetrically around the support. This method will work if the support does not form a conductor or semi-conductor. Trees and telephone poles notoriously change their conductive properties with the weather and the seasons. They can create losses along the line that take up much of the energy before it ever reaches the antenna. Unless the center support is certifiably non-conductive for the HF region in all weather, it may be better to offset the three feedlines from the support and to maintain sufficient distance to minimize interactions between the support and the lines.

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The half-dipole Y is not the only possible form for the array. Ron Wray, WB5HZE, wrote me about some interesting possible variations to suit his needs. Instead of using 1/4 wavelength legs for each branch of the Y, he considered using half loops. In effect, the active pair of half loops would form a 1 wavelength quad loop with a 120° Vee. He also suggested that we need not replicate the isolation of the inactive element at the top or unfed point. The result would be a set of loops that had special advantages. First, for the same top height as the dipoles, they would yield additional gain. Second, a single top junction would simplify construction. Third, the entire array would occupy only half the lateral space required by the 1/4 wavelength dipole legs. Finally, if a builder desired to use tubing or similar materials, a single center support could hold the entire array.

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I modeled the revised system and ended up with the dimensions shown in the remaining lines of Table 1 for a 20-meter version of Ron's antenna. In addition to the standard square loop, we can also form a rectangle with a 50-Ohm impedance on the fundamental band. The table also shows the dimensions for such a loop, with reduced lateral spread. The rectangle is only 40% as wide as the version using linear dipole legs. However, it is significantly longer from top to bottom. See Fig. 6

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Table 2 shows the free-space and 50' modeled 20-meter performance data for the 3 versions of the half-Y array. The square and rectangular loop versions lose about a quarter dB relative to flat versions of those antennas. The loops both form in-phase fed pairs of horizontal elements and show gain over the single dipole. As well, the loops show slightly higher beamwidth values. I chose a certain maximum height (50') for the comparisons because that is likely to be the factor limiting most antenna builders. With a maximum top-wire height, the loops show slightly higher TO angles than the dipole version, since the element with the feedpoint is lower than for the linear element antenna. For any loop, the height that determines the TO angle--when referenced to a single linear element--is about 2/3 the way from the lower to the upper loop wire. (The same approximation applies also to stacks of Yagis.)

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The source of the added gain for the loops on the fundamental frequency becomes apparent from Fig. 7. The graphic overlays the elevation patterns for the 3 versions of the loop with the 50' top-wire height. The square loop shows considerable suppression of high-angle radiation due to the use of 2 wires, one above the other. As we move toward the rectangle, the horizontal portions of the antenna come closer to a 1/2 wavelength spacing, at which point, radiation toward the zenith would disappear. It is not possible to reach a full 1/2 wavelength and still have a loop. However, the 50-Ohm rectangle has about 10 dB lower levels of zenith radiation than the linear dipole. As a result, there is more energy for the lowest lobe.

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You may choose any fundamental band for a half-Y array in any of the 3 forms shown in these notes. Table 3 provides a starting point by giving the free-space resonant dimensions for the arrays using #12 copper wire as a material. Obviously, the higher the fundamental frequency of the loop, the easier it will be to form an array that requires only a single support. With some adjustment of the loop size, you can use tubular horizontals and wire vertical elements. You may also create a 1-support structure by using a set of non-conductive horizontal supports with all-wire loops stretched between them. The variations are as unlimited as your creative adaptation of locally available materials.

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Any of the 3 versions of the half-Y array will provide horizonal coverage on the primary bands because the unfed element is largely inert. The horizontal portions of the third element are at right angles to the active loop or dipole, despite the 120° Vee. Since the inactive element is also not fed, the current level remains near zero all along its length. Fig. 8 shows an EZNEC portrayal of the relative current magnitude on the elements of both the Y-dipole and the Y-rectangle versions of the array on 20 meters, the fundamental frequency. Note that, for both versions of the antenna, the current level on the inactive element is completely insignificant, compared to the current on the active wires.

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Table 4 provides the modeling data for all three versions of the array for a top-wire height of 50' above average ground. We have already noted the caution about operating the antennas at 30 meters, due to the low feedpoint resistance and the high ratio of source reactance to resistance in all 3 antennas. For multi-band operation, the dipole version of the half-Y array shows lower gain than the square and rectangular versions on 20 and 17 meters. However, the loop versions of the array lose any significant gain advantage on 15 meters. On 12 and 10 meters, the dipole array produces usable patterns, although the high feedpoint resistance and reactance may present some antenna tuners with a challenge.

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The loop versions of the Y-array show a steep decline in gain as the frequency climbs above 21 MHz. The situation is considerably worse on 12 and 10 meters than the gain values in the performance table indicate. Fig. 9 shows the elevation and azimuth plots for the rectangular Y-array on both 15 and 12 meters. Similar patterns emerge for the square array and for the same set of reasons. At 21 MHz, the loops still show mainly broadside radiation, which is natural to a loop with a circumference in the vicinity of 1 wavelength. However, by the time the operating frequency reaches 24.94 MHz, the array is operating like a 2 wavelength loop, with strong radiation off the edges rather than broadside to the loop face. As a result of the change in operating conditions, the loop patterns show a very strong component directed straight upward as well as strong side-to-side radiation. In terms of total coverage of the horizon, the loop-based forms of the Y-array lose their utility as the loop circumferences grow to about 1.75 wavelength or larger.

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The potential Y-array builder thus has to decide whether he or she wants more gain on 20 and 17 or the possibility of extended operation to include 12 and 10 meters. Since the final decision will likely also contain strong consideration of what will fit within a given antenna space and how many supports are available, I can only suggest careful planning before attempting to construct any version of the Y-array.

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The planning should also include careful attention to the method of handling the triple feedline. If you plan the system as a monoband array, you can create your own twisted triplet of wires using well-insulated AWG #12 or larger wires. If you use good quality wire with one of the modern plastics for insulation, the feedline will likely have low--or at least acceptable--losses in the HF range. Do not use computer cabling, since the wires are likely too thin for even QRP power levels. The low-impedance line may not be a match for the source impedance, so you will still need a tuner. However, tuners built into modern transceivers may be all that you need to effect an adequate match.

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For multi-band use, the situation changes. Fig. 10 shows the basic system of feeding the antenna with homemade transmission lines that have a relatively high characteristic impedance. With 1" spacing, AWG #12 or AWG #14 wire will show close to 400 Ohms as the characteristic impedance. It is possible to make periodic spacers from plastic discs. The goal is to hold all three wires in perfect alignment from the antenna source to the antenna tuner terminals or to some intervening switching system. If there is a center support, the wire-spacing disc can be the end portion of a larger piece of plastic material used to space the entire set of wires well away from the support. The plastic should have good RF properties in the upper HF region and be resistant to UV radiation. UV-protected polycarbonate is readily available from plastic supply houses and other sources.

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If the run of line is fairly long and the spacers are anchored, you may also move the wire positions by one hole with each new spacer. Make each position shift in the same direction, either clockwise or counterclockwise, so that the resulting line has a stiffening twist along its total length. The ultimate goal is a set of 3 possible line combinations such that, when switching from one combination to the next, no antenna tuner changes are necessary. The result will be the ability to switch from one combination to the next to determine instantly which one produces the strongest signal. The strongest received signal normally indicates the best setting for the strongest transmitted signal.

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You may switch the system manually or remotely anywhere along the line. The top portion of Fig. 11 shows a simplified manual switching system suitable for use in the shack near the tuner output terminals. The numbered lines are the 3 wires from the loop or dipole halves. The lines marked A and B represent the 2-wire parallel feed line from the switch to the antenna tuner. Because the impedance at the switch may be either very high or very low, use as large a ceramic rotary switch (2-pole, 3-position) as you can obtain, depending on the power that you plan to use. The terminals should be well spaced and heavy to handle either high voltage or high currents. You may add a third wafer to ground the inactive line. A metal enclosure is not necessary, but the entire assembly should adhere to all safety precautions concerning unwanted contact by either the operator or shack visitors.

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The lower portion of Fig. 11 shows the bare bones of a remote relay-controlled switching system. In the sketch, the normally closed contacts are upward to simplify the drawing. The relay control switch is in the shack, while the relays might normally live very close to the array feedpoints. The schematic does not show the normal reversed diode across each relay and the extensive use of by-pass capacitors and other components needed to keep the relay control lines free of RF. Like the manual switching sections, the relays need widely spaced contacts to handle high voltage and large contact surface areas to handle high currents. The remote system allows the use of one of the commercial parallel transmission lines for the run from the switching box to the antenna tuner. The relay system requires careful weather proofing. I prefer a double-shell system, with weep holes well separated. If one shell has a hidden leak, the second shell sustains protection. Debug the relay housing(s) at least once or twice per season.

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The half-Y array is not an answer to every upper-HF operating need. Its goal is to provide full horizon coverage for the general operator with limited space and a budget that does not include a rotator. Antenna and feedline switching with less expensive components substitutes for an expensive and high-maintenance rotator system. One or another version of the antenna may be suitable for potential use on any of the HF amateur bands as the fundamental frequency.

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The triangular or Y-array concept is adaptable to many variations. For example, if you have a need for diverse target areas rather than whole horizon coverage, you might consider a triangle of extended lazy-H antennas. With sufficient separation, you can create a switchable triangle of Lazy-H arrays targeted by the best compromise relative to the broadside pattern of each one. The extended Lazy-H uses 1.25 wavelength elements on the highest frequency of use, with 1/2 wavelength to 5/8 wavelength spacing between the upper and lower elements. A perfect triangle is not necessary, so you can modify the broadside direction of each Lazy-H to accommodate the narrower beamwidth that gives you the higher gain. As well, the longer elements will be more immune to interaction with the inactive antennas. If you begin with 1.25 wavelength elements and a vertical spacing of 5/8 wavelength at 10 meters, you can cover several lower bands with good patterns and significant gain before the array approaches the size at which interactions with the inactive wires creates pattern distortions. However, the array trades beamwidth for gain, so full horizon coverage cannot be a goal. However, you can obtain good signal strength to up to 6 target communication areas.

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Alternatively, especially for the lower bands, you can create triangles of vertical dipoles. By judicious switching, you can drive one dipole and let the other 2 form a set of reflectors. The leads to a central remote switch can comprise inductively reactive loads for the reflectors to create the right amount of lengthening for optimum parasitic reflector service. Vertical antenna patterns normally have a larger beamwidth than horizontal antenna patterns, and a 120° beamwidth is not difficult to obtain. Therefore, you can cover the entire horizon with just 3 vertical dipoles.

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The Y-arrays and some of the possible triangles provide examples of what we can do with wire when faced with a limited budget and limited installation space. The basics for the arrays that we discussed have very old roots, but are ripe for re-use, refreshment, and contemporary adaptation to increase our antenna options. "Why" is a question, but for some operators, "Y" may be an answer.

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A Special Appendix

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Correspondence arrived at QEX asking the following question. "One can make W4RNL's Y antenna omni-directional by driving the 1, 2, 3 feedpoints with three-phase power (where the 1, 2, 3 feedpoints are driven with RF power at 0-degree, 120-degree, and 240-degree phases respectively)." "I guess I'm curious to figure out how I can take my RF signal and turn it into a 3-phase RF signal."

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My reply was informal.

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Although the idea is intriguing, I do not know if its is practical. I took the 20-meter Y model at 600" (50') and modified it to have 3 short feed wires, with simultaneous 0, 120, and 240 degree phased sources. The modeling plan and the elevation/azimuth plots are in Fig. 12.

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The original switched Y had bi-directional gain of a little over 7 dBi at 19 degrees elevation. The phase-fed Y has a max gain of a little over 6 dB--straight upward. There is a moderately strong triangular pattern at 19 degrees elevation, with a gain only a little under the upward maximum value. (Note that the pattern is not truly omni-directional, since the individual patterns do not add smoothly.)

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The impedance of each source point is about 85 Ohms. One would need 3 identical twisted pairs of about that impedance as a Zo and sufficiently separated so as not to interact. Back at the shack end of the line one could set up delay lines for 120 degrees and 240 degrees, but that is a lot of line. And it is good only for one band. One might also install delay lines at the antenna hub with a single main feedline back to the shack. However, such lines might be difficult to route to prevent undesired interactions. In the shack, double shielded coax might do the trick, with a 1:1 balun for the twisted pair runs. Coiling delay-line coax in old large metal popcorn cans would likely serve the added shielding needs, although the usual decorations on such cans might need disguising to maintain proper station dignity.

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However, all is not lost. If we scale the design for 40 meters and adjust for practical height considerations, then we might have a workable combination of a NVIS and longer distance antenna. MARS and other military affiliate and related operations often look for antennas that would serve both shorter range and longer-range regional needs, and such an antenna pattern might fit their needs. But due to the need for delay lines, the antenna would be frequency or fairly narrow-band specific. I have not looked into what lower heights as measured in wavelengths will do to the pattern, but this may be a start in the design process if one has a need for such an antenna.

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It is likely that the junction of the 3 lines (1 direct and 2 delay) at the TX end of the line would need a transmission-line transformer at about a 2:1 ratio to raise the parallel connection composite impedance of a little over 25 Ohms up to 50 Ohms.

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Those are my off-the-shelf thoughts. At least the picture may be interesting.

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ao7-models.zip.

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Updated 03-01-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Mar/Apr, 2006, pp. 51-57. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Dipole, HF Upper


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How Wide is Wide?

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L. B. Cebik, W4RNL

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Unlike the question, "How high is up?" our question has an answer. In fact, the question has many answers. The first step is deciding what we are referring to by the word "wide." Since our subject is antennas, there are two possibilities: beamwidth and bandwidth. Let's choose the latter as the more intriguing. Let's further refine the expression with a qualifier and call the operative term "operating bandwidth." That expression should give us room to get into trouble.

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The Width of the U.S. Amateur Bands

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As background, we may look at the U.S. amateur bands from 160 meters through 70 cm and define the bandwidth of each. One common way to arrive at the width of each band is to divide the width of the band from the lowest frequency to the highest by the band's center frequency--and multiply by 100 to arrive at a percentage. 20 meters is 350 kHz wide, with a center frequency of 14.175 MHz (or 14175 kHz to use constant units of measure). The result is 2.47%. Table 1 provides bandwidth values for each of the amateur bands within the indicated scope of our survey.

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The bandwidth numbers are useful in some contexts. For example, a precisely scaled antenna from one band would have the same coverage in terms of the bandwidth on the new band. Precision scaling means scaling the element length(s), diameter(s), and spacing (if relevant). If we scale an antenna known to cover one of the wider bands for a narrower band, we can be sure that the antenna will cover the new band. If we begin with an antenna for a narrower band, we cannot be certain that a scaled version will cover a wider band.

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Next, with a bit more trepidation, let's subdivide the range of bandwidths that emerged for the U.S. amateur bands. The following categories have no validity in general antenna literature, but will be useful for discussion within these notes. If the bandwidth is less than 1%, we may refer to a narrow bandwidth. If the bandwidth is between 1% and 4%, we may refer to a medium bandwidth. In the table, we may call bandwidths greater than 4% wide bandwidths.

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Our concern over bandwidth derives from a subset of the antennas that we typically use. For example, someone who uses a center-fed (or off-center-fed or end-fed) wire cares very little about bandwidth. He or she simply "dials in" the correct settings of a tuner for maximum effectiveness (usually meaning a good SWR match at the transceiver). The operator measures bandwidth in terms of how many times the tuner requires resetting as the frequency moves up or down one of the bands.

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The bandwidth categories evolve from general expectations that we have for relatively standard Yagi antenna designs, where the elements are aluminum tubes in the upper HF range. A 0.5" 10-meter element for 10 meters would require a 2.0" diameter on 40 meters. The normal tapered-diameter schedules for full-size 40-m elements in amateur installations virtually never approach this value. So practical antenna scaling may not meet the table's presumption of perfect antenna scaling. As a result, horizontal 40-meter antennas based on designs that easily cover 20 or 15 meters usually suffer declining performance or full failure to perform at one or the other 40-meter band edge.

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A combination of practical material limitations and total bandwidth has established conventions for band utilization. We find the 80-meter band subdivided into the 80-meter CW band and the 75-meter phone band, each requiring separate antennas (or antennas with switched element lengths, loads, or other means of changing the range). On 160, we find a relatively narrow DX window, with antennas designed to cover only that region. 10-meter antennas tend to cover the first MHz of the band--and sometimes, only the first 800 kHz of the band. In the VHF and UHF region, we find many high performance narrow-band antennas for use only within specific small parts of the bands. FM repeater users generally expect to use relatively simple, omni-directional, vertical antennas. Hence, high performance horizontal antennas on 6 meters tend to cover only a half MHz at the low end of the band. The upper 3 MHz of the band call for ground-plane monopoles, J-poles, and a few collinear vertical designs.

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How we handle the wider amateur bands thus has at least two dimensions: operator decision or preference on the one hand and design capability on the other. We shall be interested in what various antenna designs--especially parasitic beams--can achieve by way of operating bandwidth.

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Operating Bandwidth

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Before we look at antenna types that will cover the various amateur bands, let's probe the idea of operating bandwidth for a parasitic beam. For many amateurs, the 50-Ohm SWR seems to be the only factor involved in setting the operating bandwidth. For general-purpose communications, a 2:1 SWR maximum serves as a usable standard. Avid DXers and contest operators tend to prefer a 1.5:1 limit to prevent fold-back circuits in high power amplifiers from reducing or cutting off the power output.

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There are numerous other considerations that go into a final judgment of an antenna's operating bandwidth. We can focus on just two aspects of antenna performance and enlarge our thinking considerably. How well the front-to-back ratio holds up across a given band contributes to many decisions about whether to use a particular antenna design. Amateurs tend to use a 20-dB standard for the front-to-back ratio of Yagis with at least 3 elements. The figure represents a minimum value that we expect to achieve at all frequencies within the band. (I shall pass over the question of which front-to-back figure to use: 180°, worst-case, or average front-to-rear ratio.)

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Matters of gain can be even more complex. Much commercial antenna literature cites only a single number. It does not matter whether the number is the peak gain or the average gain, because neither figure tells us anything about the antenna's gain behavior across the intended passband. Only a detailed table of samples or a graph for the entire band will give us an adequate portrait of the gain performance. Very likely, these ideas will grow more meaningful as we look at some sample designs. The samples will emerge from my stock of antenna models. All make use of very standard techniques, even though the models themselves may not be in final form, ready for the home workshop. For example, some HF Yagis will use uniform-diameter elements rather than tapered-element schedules. However, all present very reasonable pictures of actual antenna performance.

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Example 1: A 4-Element Yagi and a 3-Element Quad Beam for 20 Meters. We may begin with a pair of contrasting parasitic beams for the medium width 20-meter band. The 4-element Yagi uses a 437" boom, while the quad's boom is about 387" long. The Yagi uses 1" diameter elements, while the quad uses AWG #12 wire elements. We expect most extant beam designs to cover all of 20 meters. Both the standard 4-element Yagi and the 3-element quad provide SWR values of less than 2:1 across the band, as shown in Figure 1. The quad uses a 75-Ohm standard, while the Yagi uses a beta match to arrive at a 50-Ohm SWR reference. Table 2 provides sampled data from the models across the band.

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At mid-band, both antennas show a free-space forward gain of above 8.55 dBi. However, the two antennas have very different gain curves, as revealed in Figure 2. Like most standard-design Yagis with at least one director, the 4-element beam shows a rising gain characteristic as we increase frequency within the passband. In contrast, the quad shows a decreasing gain value as we increase frequency. I chose these particular models because they pass at the middle of the band. Hence, neither has any particular average gain advantage.

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Still, we may concern ourselves with two aspects of these curves. First, what is the total change in gain across the band. For the Yagi, the gain difference is just above 0.4 dB, while for the quad, the difference is a little over 0.5 dB. Only a particular operator with a good sense of what the desired operation requires can decide if these numbers are acceptable or not. Second, we may note where the highest gain values occur. Apart from other reasons for selecting one of the 2 antennas, the quad favors the CW end of the band, while the Yagi favors phone operation. Note that the questions we may usefully pose about antenna gain performance are simple, and the answers may be easy--if only we take the time to pose them.

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The front-to-back performance of the 2 sample antenna designs appears in Figure 3. The Yagi just about meets the front-to-back standard of 20-dB minimum, using the 180° values across the band. However, the quad meets the standard only for about half the total bandwidth. The quad design used here emerged from a series of 3-element quad designs expressly aiming for maximum operating bandwidth. As with most quad beams, the SWR bandwidth--when measured against our normal amateur standard--exceeds the front-to-back bandwidth by a considerable margin. Whether or not a particular operation needs a 20-dB minimum front-to-back ratio is once more an operator decision.

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Example 2: A 5-element Standard-Design Yagi and a 6-Element OWA Yagi for 28-29 MHz. When we design parasitic beams for 10 meters, we usually design them only for the first MHz of the band--from 28.0 to 29.0 MHz. The reduced passband still has a bandwidth of 3.51%, making it considerably wider than 20 or 15 meters. Many highly capable designs for 20 meters strain to achieve a good set of performance values across the most active part of 10 meters. Let's compare a 5-element Yagi of standard design to a 6-element OWA design. Both antennas use 0.5" elements. The 5-element array has a 333" boom, partly because it increases the driver-reflector spacing to produce a near-50-O feedpoint impedance. The OWA design, pioneered by NW3Z and WA3FET, packs its elements onto a 288" boom.

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The boom lengths and the number of elements call for a small comment. Ever since the appearance of the groundbreaking work of Jim Lawson, W2PV, a sound bite has pervaded Yagi articles: gain is a function of boomlength rather than the number of elements. As true as this statement may be, it is no excuse for using too few elements to achieve all of the characteristics that one needs from a given Yagi design. As we shall see in the OWA design, extra elements may not increase gain over the longer-boom 5-element Yagi, but they can shape the performance curves across the operating bandwidth of the antenna.

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As shown in Figure 4, the 5-element design achieves a very acceptable 50-Ohm SWR curve. However, by judicious spacing among the reflector, the driver, and the first director, the OWA SWR curve is superior and meets the most stringent fold-back circuit requirements. Table 3 provides sample numbers for the rest of the performance categories on which we are focusing. Note that the 5-element design has a very good front-to-back ratio, but tails off in this category at the upper end of the 10-meter activity region.

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More important than the front-to-back behavior is the shape of the gain curves that appear in Figure 5. Nothing in the 5-element standard-design Yagi controls the steep gain increase with rising operating frequency. The total gain differential across the band is nearly a full dB. In contrast, the extra OWA element and the arrangement especially of the second and third directors place the gain peak within the passband. One result is more even gain across the band. The total gain range is a mere 0.23 dB.

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Example 3: A Log-Cell Yagi for the Entire 10-Meter Band. The OWA design is only one of many techniques for increasing the operating bandwidth of a parasitic beam. Suppose that we wanted a beam that would cover the entirety of 10 meters, that is, cover nearly a 6% bandwidth. The OWA design would strain at the 60+% increase in required bandwidth. However, a well-designed log-cell Yagi can handle the task with relative ease. Our sample uses a 5-element log cell designed according to LPDA rules. It adds parasitic elements, namely, a reflector and a director. The resulting 7-element array uses a 337" boom with 0.75" diameter elements. Table 4 provides sample modeling results across the band. The band-edge 50-Ohm SWR values mark the highest values for the array.

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Figure 6 provides the gain and front-to-back curves for the antenna design. The peak in the front-to-back ratio may give the impression that the bulk of the band shows a poor ratio until we read the right-hand Y-axis and discover that the minimum front-to-back ratio is 27.15 dB. The use of a log cell as a driver does not generally enhance array gain relative to standard-design Yagis of the same boom length. However, it does provide strong control of the gain curve. As the graph shows, the antenna's peak gain occurs close to the band's center. As well, the gain changes by only 0.16 dB across the entire 1.7 MHz spread.

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Example 4: A Short-Boom 3-Element Yagi with Phased Drivers for 6 Meters. We tend to call parasitic arrays with driver cells designed according to LPDA principles and equations "log-cell Yagis." However, we often use 2 or 3 phased driver elements that we arrive at by trial and error (or success, as the case may be). Such antennas often bear the label "phagi," in keeping with our penchant for snappy antenna names. Let's look at one example to see what a casually designed phased driver pair might be able to do to enlarge the operating bandwidth of an antenna. 6 meters is a good band for a compact simple Yagi used vertically to provide some gain and wide directivity within the 3 MHz used for FM operations.

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Standard-design wide-band Yagis that will cover all of 6 meters already exist. The two samples shown in Figure 7 are adaptations of 10-meter designs that Bill Orr, W6SAI, first presented in Ham Radio during the 1980s. The 3-element version is interesting because it uses a boom length that one might find in a higher-grain, narrower-bandwidth Yagi. However, as evident in the data in Table 5, the gain of the wideband Yagi is about a full dB lower--the price paid for increased operating bandwidth.

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The smaller 3-element Yagi with the phased pair of driver elements on the far right of Figure 7 is actually an extension of a 2-element driver-director Yagi. This class of Yagi has a high peak gain but a very narrow beamwidth. I tend to recommend them for use on the narrow amateur bands, such as 30, 17, and 12 meters, although they have other specialized uses as well. The enlargement of the driver section of the antenna does not materially increase the boom length ahead of the drivers, and so the overall length is less than the boom needed by the 2-element wide-band driver-reflector Yagi. All three Yagi designs use a tapered-diameter schedule consisting of 0.5" and 0.375" element sections.

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The data table shows that the phased drivers do not quite equal the performance of the wide-band 3 element Yagi. However, the performance curves are closer to that antenna than to the 2-element curves. As well, the 2-element gain shows its downward progression with rising frequency, in contrast to the nearly parallel upward gain curves of the 3-element Yagis. Hence, for the intended application--FM simplex and repeater operation--the phase-fed dual driver of the sample short-boom Yagi seems a natural. Unlike either the OWA Yagi or the log-cell Yagi, the 3-element phagi has too few elements to control all of the relevant operating parameters.

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Example 5: An 8-Element Utility Yagi for 70 cm. Almost as wide as 6 meters, the 70-cm band has a bandwidth of 6.9%. Very long-boom Yagis, such as the DL6WU "trimming" series and other comparable designs, manage to cover the entire band with something to spare. The undulations of gain, front-to-back ratio, and SWR are fascinating to observe, but all three aspects of operation remain under relatively good control. Wide operating bandwidth is a boon to the home antenna builder, since limitations of precision tend not to void the basic performance of the antenna. The question that we might pose here is whether we can cover all of 70 cm with a relatively short utility antenna, say, using 8 elements. In this frequency range, the boom length would be about 53".

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The project is quite feasible under 2 conditions. First, we should use fat elements, about 0.5" or so. Second, we should expect some variability of performance across the band. Other than that, we may use a fairly standard Yagi design. Figure 8 shows the 50-Ohm SWR curve of our sample antenna, which reflects the application of OWA principles stretched about as far as I dare.

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Sample data from across the band appear in Table 6. The gain and front-to-back curves are in Figure 9. The gain curve shows that it is possible to place the gain peak within the passband and to control the range of variation within about 0.5 dB. The gain level is close to what is standard for narrower-band Yagis with the same number of elements. However, over the wide operating bandwidth, we cannot fully control all facets of performance to the same level. The front-to-back curve dips to slightly less than 15 dB, which is adequate for the designated use as a utility beam for either horizontal or vertical installation.

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Example 6: An 8-Element Wire LPDA for 3.5-4.0 MHz. Yagi designs are capable of considerably wider-band performance than we generally give them credit for--if we are willing to pay the price in terms of using more elements for a given boom length or using special driver sections. I have stretched one design to cover a 26% bandwidth with an acceptable SWR curve and modest, though usable performance. However, when we turn to the 80-meter amateur band, the 13% bandwidth combined with a need to use relatively thin wire presents a daunting challenge. One solution is to use a full LPDA for the band. With 8 special wire elements and an 86' virtual boom length, such an array can provide about 7 dBi free-space gain with a front-to-back ratio that remains above 20 dB across the band. Since such an array is a major undertaking, I have not hesitated to use virtual 2" elements composed of dual wires (shorted at the phase-line and the outer end) spaced anywhere from 8" to 12" apart along their length.

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Figure 10 shows the modeled 50-Ohm SWR curve, and sample data appears in Table 7. The gain and front-to-back curves are in Figure 11. All of the curves show a particular trait inherent to LPDAs. The curves undulate across the passband, but the peaks and nulls do not coincide with each other. Many newcomers to phased element design (including LPDAs) believe that the phase line provides a direct source of energy to the elements. While this belief is true, it is equally true that the elements exhibit mutual coupling. Hence, an LPDA (and any phased-fed collection of elements) is a form of parasitic array, at least in part. The balance among the energy sources for the elements undergoes continuous change as we change frequency. As one consequence, the operating parameters change with frequency. A good LPDA design is one that minimizes the level of change, although some change is inevitable in even the most ideal designs.

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Our sample antennas have had two goals. One purpose was to show that it is possible by a variety of techniques to enlarge the operating bandwidth of a directional array. We have only touched a few of the many techniques available. The second aim was to expand our appreciation of the concept of operating bandwidth so that SWR becomes only one of many equal parts in the equation. We have many options in deciding which aspect of performance deserves primary attention, and equally many options in the techniques by which we achieve acceptable performance over a wide operating bandwidth.

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ao8-models.zip.

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Updated 05-01-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, May/Jun, 2006, pp. 54-59. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: HF Lower, HF Upper, VHF / UHF, Yagi


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A Broadside of Vertical Wires

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L. B. Cebik, W4RNL

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We often misunderstand the quest for more gain. The instant picture is a directional beam rotated by a heavy motor at the top of a large steel tower. That is only one version of robbing energy from unused directions and focusing it in the direction of our communications targets. Very often, we can do the required job with a bi-directional antenna. If we can limit our target areas, we can often do away with the tower and the rotator. Wire still works very well, especially in bi-directional arrays.

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The set of options that we shall explore in these notes consists entirely of vertical arrays, which are especially apt to the lower HF and upper MF regions. All of the antennas that we shall examine are garden-variety arrays, with many variations in the literature. What may give this treatment a small bit of uniqueness is the fact that we shall level the playing field. To keep everything full size, we shall put every antenna on 40 meters--specifically 7.15 MHz. As well, each antenna will be above average ground, that is, ground with a conductivity of 0.005 S/m and a relative permittivity of 13. Once we examine some basic standards against which to measure array performance, all antennas will use AWG #12 copper wire. As a result, any changes of ground, frequency, and element size will apply roughly equally to all of the antenna types in the group.

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In addition, we shall bypass the potential long list of monopole arrays and thereby evade questions surrounding ground radial systems and end-fire directional phasing schemes. We shall limit ourselves to antennas based on the vertical dipole and broadside arrays of dipoles that give us bi-directional patterns. The excluded antennas all are good candidates for service in amateur communications, but we have only limited space to conduct a review of some of the possibilities.

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A Standard: the 1/2 Wavelength Vertical Dipole

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The fundamental standard against which to measure the performance of all of the other related antennas on our incomplete list is the vertical dipole. Fig. 1 provides a snapshot of the antenna's outline and both the elevation and azimuth patterns that emerge under the modeled test conditions. The sample antenna is a 1.25" diameter aluminum center-fed vertical that approximates what we might find in actual practice. Real antennas in amateur use might consist of anything from wire suspended from an overhanging limb to large well casings or even light tower sections.

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The base of the dipole is about 15' above ground. Since a wavelength at 7.15 MHz is just about 140' long, you can change the numbers in feet to a fraction of a wavelength. From that point, conversion to metric measures is simple. The importance of the base height shows up in the elevation pattern for the dipole. For any vertical antenna or array that we do not attached directly to ground and a radial system, two performance values interaction in opposite directions. As we raise the antenna, the elevation angle of maximum radiation (TO angle) decreases slowly and the gain increases. The same increase in height will also enlarge the higher-angle lobe. At a certain height--which varies with each array--all further energy will go into the second or higher elevation lobe. The heights that I have selected may not coincide with what your own physical conditions permit or with your preferences, so I recommend that you reproduce the exercise using your own set-ups.

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My selections rest on several conditions. First, the base height must be at least 10'-12' above ground for safety. The outer end of any dipole or wire array holds an injurious voltage level. Lowering the base of the vertical dipole would require additional protection measures for people and animals. Second, the higher-angle lobe should be as small as practical to reduce sensitivity to higher angle signals. The resulting pattern disqualifies these antennas from NVIS service, but provides quieter background levels for the DX operator. Third, the combination of gain and TO angle must be optimal. This last condition is a judgment call and will vary with the needs and preferences of each operator. Table 1 provides a summary of modeled performance data for my selections for all three vertical dipole antennas and arrays.

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The vertical dipole itself is not yet a broadside array, since we have no plane of elements against which to measure the broadside directions. However, one simple array consists of two 1/2 wavelength vertical dipoles fed in phase. Fig. 2 provides the outline and the patterns for the dipole pair. Note that mutual coupling requires that we lengthen the dipoles slightly to obtain resonance. For the test conditions, the bi-directional maximum gain at the 15° TO angle is about 4.5-dB greater than the gain of a single dipole. In exchange, the half-power beamwidth is 58° in each prime direction. Do not underestimate the importance of the beamwidth value in planning a broadside array. Feeding the array is simple in this case, since the dipole feedpoint values are close to 50 Ohms. Equal lengths of coax provide equal feedpoint currents. However, if we wish to have 50 Ohms at the junction of the two lines, then we must resort to 3/4 wavelength 70-75-Ohm lines (since the velocity factor of ordinary coax lines will not allow electrical quarter wavelength lines to reach a common junction).

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The azimuth pattern in Fig. 2 shows another interesting fact about pairs of vertical dipoles fed in phase. The separation shown is 73', slightly greater than 1/2 wavelength. As we increase the spacing beyond 1/2 wavelength, the gain continues to increase, but we find sidelobes emerging. At what spacing we terminate the quest for gain because the sidelobes are too large is again a judgment call.

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Fig. 3 shows what we can obtain from 3 vertical dipoles in phase. We obtain nearly 1.5-dB additional gain, but with a beam that is over 15° narrower. To achieve near resonance at the feedpoints, we must make the outer dipoles slightly longer than the center dipole. However, the factor that hinders most antenna builders from implementing a 3-dipole array (besides space) is the need for binomial current distribution. To produce the desired pattern, the center dipole must show twice the feedpoint current as each of the outside dipole feedpoints. One advantage that accrues to the wire arrays that we shall sample is the use of a single feedpoint for the entire array.

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Hatted Dipoles

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Before we look at the wire arrays, we should examine a technique that can overcome to some degree the height requirements of the simple vertical dipole. We can add hats to each end of each dipole and reduce the vertical length without jeopardizing the performance by very much. The hats can be any symmetrical wire extensions at right angles to the vertical. The extensions permit the antenna to reach a resonant length, but the symmetry of the extensions tends to cancel the horizontal component of the far fields. Fig. 4 shows the outline (and patterns) of a 1.25" diameter vertical dipole shortened to 32'. Each AWG #12 hat wire is 16' long. The hat in this case takes the form of a T with the wires in the plane of the dipoles. Hence, we may lash the extension wires to a pair of non-conductive lines at the top and bottom of the dipoles to simplify overall construction. If we raise the feedpoint level above ground to nearly the same height as the full dipole feedpoints, we obtain close to the same TO angle and very close to full gain. However, we significantly reduce the near-resonant feedpoint impedance. The same considerations would apply to all-wire hatted dipoles, although the vertical dimensions would be somewhat longer. See Table 2 for the modeled performance data for all three hatted arrays.

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Fig. 5 demonstrates the hatting technique applied to a pair of dipoles fed in phase. 50-Ohm 3/4 wavelength lines would satisfactorily transform the impedances for a common-junction match to a 50-Ohm main feedline. The gain, TO angle, and beamwidth are comparable to the values for full-size dipoles in the same arrangement. The azimuth pattern shows the consequences of closing the spacing slightly: the sidelobes have virtually disappeared. By holding the hat extension wires at a constant 16', we can see the consequence of mutual coupling in the vertical section of the two dipoles. Like the full-size dipole array, the individual elements require lengthening to restore a near-resonant condition.

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A 3-hatted-dipole array appears in Fig. 6. It uses the same spacing (72') as used in the 2-dipole array to reduce sidelobes. The results once more are very similar to those for full-size dipoles. However, this array requires binomial feeding, just like the full-size counterpart, with the feedpoint current at the center element reaching twice the value of the feedpoint currents on the outer elements. I have included the 3-dipole arrays not as a recommendation for construction, but instead to provide performance standards against which we may compare the performance of wire arrays that simulate 3-dipole arrays.

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Wire Arrays

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Almost any antenna handbook contains the names of vertically polarized wire arrays that do not and need not touch the ground: half-squares, bobtail curtains, deltas, and rectangles. Physical constraints often dictate which among the candidates that we can implement. How we categorize the entire collection depends on the perspective from which we approach them. I once called the entire group "self-contained verticals" or SCVs, since they do not require ground radial systems. We may also view them from the feedpoint perspective. Each antenna has one feedpoint but presents vertical wires in phase. Hence, we might call them "self-phasing arrays." By bending and connecting parts of each dipole element so that they touch, we create lines that change the phase of both the voltage and the current to leave the vertical wire sections essentially in phase with each other at close to optimal spacing.

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In our effort to create a level field for comparisons, all of the wire arrays that we shall explore use AWG #12 copper wire at 7.15 MHz over average ground. The heights will aim at maximum gain commensurate with a reasonable TO angle, but in no case will the top height exceed 50'. Table 3 provides the modeled performance data for

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Perhaps the purest form of SCV is the half-square array. Interestingly, this antenna emerged later than its doubled big brother, the bobtail curtain. (See Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," CQ (March, 1948), 21-23 and 92-95, and Ben Vester, K3BC, "The Half Square Antenna," QST (March, 1974), 11-14, for the seminal articles on each antenna.) However, the half square is electrically more fundamental, corresponding roughly to a pair of vertical dipoles fed in phase. Fig. 7 shows the general outline and the plots for a half square at roughly the optimal operating height. We can picture two vertical dipoles. The upper halves of each dipole bend toward each other until they just touch. These touching lines not only complete each dipole, but also form a phasing line between the two corner points. At the center, the voltage and current undergo a phase reversal, so the two vertical wires remain in phase. Hence, we need only a single feedpoint at one of the two upper corners. (We can also extend one vertical leg to the ground and use voltage-feeding techniques).

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For best performance the horizontal wire must be shorter than 1/2 wavelength, while the vertical wires are longer than one-half of a resonant vertical dipole. For common copper wire sizes, the ratio of vertical to horizontal is about 5:8. Because the resulting array does not use full 1/2 wavelength spacing (about 70') and only half of the virtual dipoles contribute to the effective far field, the gain is about a dB shy of the gain of two vertical dipoles fed in phase. At maximum gain, the TO angle is slightly higher, since the bottom ends of the elements are closer to ground. These factors also contribute to the 80° beamwidth of the array.

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The bobtail curtain appeared earlier, but is electrically the double of the half-square array. Fig. 8 presents the outline and the patterns for a roughly optimized bobtail curtain. The dimensions closely correspond to those worked out empirically by SM4CAN. The vertical elements are shorter than those of the half square, but the phase lines in each of the 2 sections are longer. To obtain a 50-Ohm impedance, the feedpoint is about 60% of the way up the center element. However, bringing the center element to the ground and using voltage-feeding techniques is very common. Still, we lack the radiation from the upper portions of the vertical dipoles and the spacing remains shy of a more ideal 1/2 wavelength. Hence, the maximum gain is lower than for 3 half wavelength dipoles in phase, and the beamwidth is greater. In fact, the bobtail curtain performance figures more closely resemble the values associated with 2 half wavelengths in phase. Nevertheless, the bobtail's single feedpoint produces a very close approximation of binomial feed with its 1-2-1 current magnitude ratios at the upper corners of the array.

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There are two configurations that many hams use largely to overcome site constraints. One is the delta and the double delta. Table 3 provides data on the single right-angle delta, when we feed it about 15% up one side to maximize the vertical component of the far-field pattern. This compact form that requires only a single upper support falls short of the ideal vertical element spacing and hence shows the lowest gain of any of the wire arrays. Its cousin, the double delta, appears in Fig. 9. We feed the array across the upper and lower (or base) wires at the center for vertical polarization. Although the feedpoint impedance is close to ideal, the gain is less than the gain of 2 vertical dipoles in phase--with a corresponding increase in beamwidth.

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The side-fed rectangle and double rectangle provide higher gain than single and double deltas largely because the end elements are vertical and closer to 1/2 wavelength apart. Table 3 provides data on the single rectangle. It optimum dimensions represent a compromise between spacing and the required length of the end elements. Element spacing dominates the equation until the vertical end elements become too short to provide a strong far field pattern. The low feedpoint impedance of a single rectangle tends to reduce the utility of this version of the antenna despite the fact that the spacing of the horizontal wires is relatively small. The double rectangle, shown in Fig. 10, is more practical, despite its greater horizontal dimension. The gain and beamwidth approximate the values for 2 ideal vertical dipoles fed in phase although the antenna only requires 2 50' tall non-conductive end supports. The diagram shows the array fed at the center of one end. The 31-Ohm impedance is far more workable than would be the very low impedance at the middle of the center vertical wire, on which we find twice the current magnitude of the end vertical wires.

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Of the double arrays, the bobtail curtain and the dual rectangle may be the most popular for those with the required space. The double rectangle is a bit shorter and presents the fewest safety problems. However, the bobtail curtain has a bit more gain and its loose ends provide a means for voltage-feeding techniques. (Bringing the bobtail center wire to ground and using a tank circuit for impedance matching does not alter the position of the high current point at the corner with the two horizontal phase lines. Nor does it alter the required current magnitudes and phase angles at each of the array's outer corners.) Half squares and single deltas remain popular among those with more limited space. With a change of feedpoint, each antenna is adaptable to use as a general all-band wire.

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The Bruce Array

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The Bruce array or curtain derives its name from Edmond Bruce, one of the legends of antenna developments in the late 1920s and through the 1930s. The array that bears his name is not, according to reports traced to John Kraus, W8JK, the antenna that he would have preferred to bear his name. The preferred antenna is the rhombic (originally named the diamond by Bruce). In fact, the Bruce-type curtain fell out of favor among wire-fans in the amateur community until resurrected by Rudy Severns, N6LF, and given prominence in Chapter 8 of the 20th edition of the ARRL Antenna Book. We shall briefly examine two forms of the Bruce array: a 5-element "innie" and a 7-element "outie." A Bruce array requires 1/8 wavelength end sections, and the navel reference refers to how we handle them. Table 4 provides the modeled data for the two sample arrays.

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As suggested in Fig. 11, a Bruce array consists of a set of parallel vertical dipoles with a vertical height of about 1/4 wavelength. The separation between vertical sections is also about 1/4 wavelength. Hence, each horizontal wire represents the completion of a vertical dipole. Unlike the half square and the bobtail curtain, the Bruce verticals presume a high current region at the center of the vertical wire sections. Unlike the rectangle, the bottom wire does not return to the position of the top wire, but extends in the opposite direction to connect to the next vertical dipole. The ideal length both vertically and horizontally for wire sections (excluding the shorter end sections) is actually about 1.05 times a quarter wavelength, although the antenna admits of considerable variation. The 5-element version represents an attempt to squeeze out the maximum gain from the number of elements, which required slightly more spacing horizontally and slightly less vertical length. However, the benefits are very small for the exercise.

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The most interesting fact about the 5-element version is the inward turn of the end sections. The resulting array is 148' long, only slightly longer than longest of the doubled wire arrays. Using a centered feedpoint on the center wire (other feedpoint positions are possible), the array produces just over 6 dBi gain, close to the maximum that we can encourage from 3 vertical dipoles fed in phase. The modeled feedpoint impedance is close to 300 Ohms, a handy value for available transmission lines. The one major difference from other arrays occurs in the azimuth pattern. It shows uneliminable sidelobes that result from spacing vertical elements at 1/4 wavelength intervals. The differential in the sidelobe sizes results from one end section occurring at the array top and the other existing at the array bottom.

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The alternative form of the Bruce array--shown mostly in college texts such as Kraus' Antennas--points the end sections outward. The seven-element version of the array appears in Fig. 12 and requires the horizontal span that the inward turn version would need for 8 sections. Using 7 elements allows a central wire for the feedpoint. It uses a more conventional set of element dimensions, with equal vertical and horizontal lengths. Nevertheless, adding 2 more sections has two consequences. First, the impedance is close to 460 Ohms, another convenient impedance for available transmission lines. Second, the larger version shows increased gain over the smaller version. The increase is about 1.25 dB, with a commensurate shrinking of the beamwidth. The progression of gain-vs.-beamwidth ratios provides a glimpse at the original use for curtain-type arrays. In the 1930s, point-to-point communications with specific cities across the ocean comprised a significant set of commercial enterprises. Hence, both Bell Labs and RCA gave high emphasis to more directive wire arrays. Unless one is very favorably positioned between two major target areas 180° apart, it is possible to set up a wire array with too much gain and too little beamwidth. The azimuth pattern for the 7-element Bruce array shows the diminishing beamwidth when compared to other azimuth patterns in the series.

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An Interim Conclusion

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We have not examined every vertically polarized wire array that we might use on 40 meters, indeed, not even every wire array based on the vertical dipole. However, we have subjected enough types to comparable modeling conditions to allow some evaluation of performance potential vs. mechanical requirements for installation. All of our samples except the original full-size vertical dipoles might easily suspend from sturdy ropes between non-conductive 60' end support posts, trees, or even surplus telephone poles. Scaling the arrays to 80/75-meter size would likely require lower bottom wires or elements ends in addition to taller posts. The results would include increased TO angles and slightly lower maximum gain levels. Even so, vertically polarized wire arrays offer a large number of options for bi-directional lower-band antennas.

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These notes have omitted the many bi-directional horizontal arrays of use to radio amateurs. I shall partially fill the void next time. In the meantime, be sure to obtain for your library not only a current edition of The ARRL Antenna Book, but as well a copy of ON4UN's compendious Low-Band DXing.

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ao9-models.zip.

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Updated 07-01-2006. © L. B. Cebik, W4RNL. This item first appeared in QEX, Jul/Aug, 2006, pp. 53-60. Reproduced with permission. Copyright ARRL (2006), all rights reserved. This material originally appeared in QEX: Forum for Communications Experimenters (www.arrl.org/qex).

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Return to series index page

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Topics: Bobtail Curtain, Bruce Array / Sterba Curtain, Delta Loop, Dipole, HF Lower, Half Square, Loading, Rectangle, Vertical


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Adjusting Near-Perfect Broadband Antennas for 80-75 Meters

+ hr +

Adjusting Near-Perfect Broadband Antennas for 80-75 Meters

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This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Dipole, HF Lower, Matching


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Antenna Systems

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Antenna Systems

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This page exists to include the PDF in the topic index

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Part of An Antenna Potpourri

+

Topics: Hardware, Matching, Transmission Line


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A Trap 2-Band 2-Element Beam for 17 and 12 Meters

+ hr +

A Trap 2-Band 2-Element Beam for 17 and 12 Meters

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This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HF Upper, Traps, Yagi


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Basic Operating Needs of the Radio Shack

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Basic Operating Needs of the Radio Shack

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This page exists to include the PDF in the topic index

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Part of An Antenna Potpourri

+

Topics: Hardware


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Design of a 2-3-Element Full-Performance Yagi for Portable and Field Use (3 Parts)

+ hr +

Part 1: Electrical Design

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Part 2: Mechanical Design

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Part 3: Improving 20- and 17-Meter Performance

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This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HF Upper, Portable, Yagi


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Designing Multi-Band Parasitic Beams (6 Parts)

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Part 1: General Design Considerations

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Part 2: A Small 15-10-Meter Design Example

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Part 3: A 3-Element 15-Meter, 4-Element 10-Meter Design Example

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Part 4: Alternative 15-Meter Moxon, 10-Meter Yagi Design Examples

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Part 5: Alternative 15-Meter-10-Meter Yagi Design Examples

+

Part 6: Small Yagi-Yagi Alternatives to the Moxon-Yagi 2-Band Beam

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This page exists to include the PDF in the topic index

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+

Part of An Antenna Potpourri

+

Topics: HF Upper, Matching, Moxon, Traps, Yagi


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Forming Reasonable Expectations of Modern Tri-Band Beam Designs

+ hr +

Forming Reasonable Expectations of Modern Tri-Band Beam Designs

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HF Upper, Yagi


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Home-Brew Design and Construction

+ hr +

Home-Brew Design and Construction

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This page exists to include the PDF in the topic index

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Part of An Antenna Potpourri

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Topics: Hardware


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An Antenna Potpourri

+ hr +
+

Note (2024): These appear to be articles that were prepared but not published or put online, they were later made available by antenneX. These were retrieved from www.on5au.be and re-orgnaized with some duplicate items that exist elsewhere removed.

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+ hr
+ + diff --git a/content/ap/myr101520m.html b/content/ap/myr101520m.html new file mode 100644 index 0000000..e9ca7f9 --- /dev/null +++ b/content/ap/myr101520m.html @@ -0,0 +1,18 @@ + + + + + + Monxon Yagi Rectangle for 10m 15m 20m + + + +

Monxon Yagi Rectangle for 10m 15m 20m

+ hr +

Monxon Yagi Rectangle for 10m 15m 20m

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HF Upper, Moxon, Yagi


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Notes on 2-Band (2-M, 70-CM) LPDAs (2 Parts)

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Part 1. Narrow-Band LPDAs

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Part 2. Wide-Band LPDAs

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This page exists to include the PDF in the topic index

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Part of An Antenna Potpourri

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Topics: LPDA, VHF / UHF


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Notes on Ribbons, Cages, Parasites, and Lines
+ Broadband Coverage of the 80-75-Meter Band with AWG #12 Copper Wire

+ hr +

Notes on Ribbons, Cages, Parasites, and Lines
+ Broadband Coverage of the 80-75-Meter Band with AWG #12 Copper Wire

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Dipole, HF Lower, Matching


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Nulling an Unwanted Station
+ Worse and Better Solutions

+ hr +

Nulling an Unwanted Station: Worse and Better Solutions

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HB9CV / ZL Special, Moxon, Phased Array, VHF / UHF, Yagi


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Reinventing the (Big) Wheel

+ hr +

Reinventing the (Big) Wheel

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This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Big Wheel, Dipole, VHF / UHF


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The Dual-Element Wideband Dipole
+ Some Preliminary Notes

+ hr +

The Dual-Element Wideband Dipole: Some Preliminary Notes

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Dipole, HF Lower, HF Upper, Loading, VHF / UHF


+ + \ No newline at end of file diff --git a/content/ap/tdewdspn.pdf b/content/ap/tdewdspn.pdf new file mode 100644 index 0000000..bcea51a Binary files /dev/null and b/content/ap/tdewdspn.pdf differ diff --git a/content/ap/tilzx80mv.html b/content/ap/tilzx80mv.html new file mode 100644 index 0000000..3faec7e --- /dev/null +++ b/content/ap/tilzx80mv.html @@ -0,0 +1,18 @@ + + + + + + The IL-ZX as an 80-Meter Vertical + + + +

The IL-ZX as an 80-Meter Vertical

+ hr +

The IL-ZX as an 80-Meter Vertical

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Closed and Interrupted Loop, HF Lower, Vertical


+ + \ No newline at end of file diff --git a/content/ap/tilzx80mv.pdf b/content/ap/tilzx80mv.pdf new file mode 100644 index 0000000..5774ea4 Binary files /dev/null and b/content/ap/tilzx80mv.pdf differ diff --git a/content/ap/tpl.html b/content/ap/tpl.html new file mode 100644 index 0000000..1d6c7ee --- /dev/null +++ b/content/ap/tpl.html @@ -0,0 +1,18 @@ + + + + + + The Practical Lindenblad + + + +

The Practical Lindenblad

+ hr +

The Practical Lindenblad

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Lindenblad, Satellite, VHF / UHF


+ + \ No newline at end of file diff --git a/content/ap/tpl.pdf b/content/ap/tpl.pdf new file mode 100644 index 0000000..22e6eca Binary files /dev/null and b/content/ap/tpl.pdf differ diff --git a/content/ap/tsl.html b/content/ap/tsl.html new file mode 100644 index 0000000..e3b7481 --- /dev/null +++ b/content/ap/tsl.html @@ -0,0 +1,18 @@ + + + + + + The Shack Layout + + + +

The Shack Layout

+ hr +

The Shack Layout

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Hardware


+ + \ No newline at end of file diff --git a/content/ap/tsl.pdf b/content/ap/tsl.pdf new file mode 100644 index 0000000..ba9a01b Binary files /dev/null and b/content/ap/tsl.pdf differ diff --git a/content/ap/tvdlpda.html b/content/ap/tvdlpda.html new file mode 100644 index 0000000..08bf9ab --- /dev/null +++ b/content/ap/tvdlpda.html @@ -0,0 +1,18 @@ + + + + + + The V-Dipole LPDA + + + +

The V-Dipole LPDA

+ hr +

The V-Dipole LPDA

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: HF Upper, LPDA, VHF / UHF


+ + \ No newline at end of file diff --git a/content/ap/tvdlpda.pdf b/content/ap/tvdlpda.pdf new file mode 100644 index 0000000..c98bdb8 Binary files /dev/null and b/content/ap/tvdlpda.pdf differ diff --git a/content/ap/ydalfdq.html b/content/ap/ydalfdq.html new file mode 100644 index 0000000..3638ae4 --- /dev/null +++ b/content/ap/ydalfdq.html @@ -0,0 +1,18 @@ + + + + + + Yagi Driver Assemblies: Linear, Folded Dipole, and Quagi + + + +

Yagi Driver Assemblies: Linear, Folded Dipole, and Quagi

+ hr +

Yagi Driver Assemblies: Linear, Folded Dipole, and Quagi

+

This page exists to include the PDF in the topic index

+ hr
+

Part of An Antenna Potpourri

+

Topics: Dipole, Quad, VHF / UHF, Yagi


+ + \ No newline at end of file diff --git a/content/ap/ydalfdq.pdf b/content/ap/ydalfdq.pdf new file mode 100644 index 0000000..2aa81d8 Binary files /dev/null and b/content/ap/ydalfdq.pdf differ diff --git a/content/bookant.html b/content/bookant.html new file mode 100644 index 0000000..089e66f --- /dev/null +++ b/content/bookant.html @@ -0,0 +1,135 @@ + + + + + + Some Antenna Books by L. B. Cebik, W4RNL + + + +
+ + + + + + +
+

Some Antenna Books by
+ L. B. Cebik, W4RNL

+
+

+
+
    +
  • Basic Antenna Modeling: A Hands-On Tutorial is a step-by-step course in modeling with NEC-2, including well over 100 different exercise models with numerous variations. There are many exercises for student entries, with check-tables to confirm the results.
    • +
  • Intermediate Antenna Modeling: A Hands-On Tutorial provides over 450 pages of illustrated text and about 300 exercise models and variants as a means of introducing virtually the entire command sets of both NEC-2 and NEC-4. The self-study course is designed for use in conjunction with advanced software packages. The major division are The Geometry Commands; Far-Field and General Control Commands; and Special Outputs, Control Commands, and Techniques. +
    +
  • + Antenna Modeling Notes - Volumes 1 through 7: The long-running series of monthly columns in antenneX as been converted into book form, with 25 columns covered in each of four volumes. Information on sources of modeling programs and program capabilities has been updated. In addition, each volume includes a selection of NEC models in .EZ, .NWP, and .NEC format to permit you to examine the concepts under discussion. Volume 1 (columns 1 - 25), Volume 2 (columns 26-50), Volume 3 (columns 51-75), and Volume 4 (columns 76-100) contain about 400 pages each: + +

    • +
  • Antennas From the Ground Up: An introduction to antennas and related ideas (with a special focus on wire antennas) for the newer antenna enthusiast, originally appearing as columns for Low Down, but heavily supplemented.

    • +
  • + Antennas Made of Wires: + +

    • +
  • + An-Ten-ten-nas: The first 58 episodes of this long-running 10-meter antenna column in 10-10 News is now available in a cooperative venture with 10-10 International. +

    • +
  • + Antennas and Feedlines for QRP consists of presentations to the annual FDIM symposium at Dayton, with new material added in this cooperative venture with QRP ARCI. Available through the QRP ARCI. +

    • +
  • Cubical Quad Notes: Volume 1: A Review of Existing Designs: This first volume reviews many existing designs of both monoband and multi-band quad arrays to assess both the potentials and the limitations of these antennas and their feed systems.

    • +
  • Cubical Quad Notes: Volume 2: Rethinking the Quad Beam: The second volume examines the most fundamental properties that determine quad performance and develops computer design programs for a number of monoband quad beam types, from 1 to 4 elements.

    • +
  • + Cubical Quad Notes: Volume 3: Multi-Band Quad Questions: The third volume begins with a detailed analysis of element intereactions in 2-element 2-band quads and expands to triband and larger beams as well, including quads with up to 6 elements covering all 5 upper HF bands.
    + Volume 3 includes a set of model files: Cubical-Quad-Notes-Vol-3-Models.zip. +

    • +
  • + Ground-Plane Notes: This volume explores the subject of ground planes, with primary emphasis upon the modeled behavior of buried radial systems. It examines in detail the concepts of soil conductivity and relative permittivity, as well as providing what NEC-4 modelxs report about a large number of questions, including the number of radials, their length and depth, the effects of monopole height above them. the use of insulated wire, the the effects of frequency. As well, the volume answers a number of modeling questions, from how to set up radial system models to the adequacy of substitutes for buried radials, such as the use of near-ground radial NEC-2 models and the use of a MININEC ground system. In addition, the volume treats elevated radial system for the lower HF, upper HF, and VHF/IHF ranges.
    + Includes set of model files Ground-Plane-Notes-Models.zip. +

    • +
  • Long-Boom Yagi Studies: This large CDROM volume explores many series of long-boom Yagis from 2 to 14 wavelengths, including the classic DL6WU series and others, with a sequence of optimized Yagis in the same range provided by N6BV. The aim is to replace the scattered sampling of specific designs with systematic data from many series of Yagis, element-by-element, to find the data trends. The work covers single units and vertical stacks of 2, spaced either for maximum gain or for the best combination of sidelobe suppression. The volume also includes a 14 wavelength long Yagi with 20-dB sidelobe attenuation for almost the entire 70-cm band. Appendices contain sweep graphs for almost all of the Yagi series, element by element, and 360 EZNEC models used as the basis for data generation.

    • +
  • + Long Wire Notes: Long-wire technology may be ancient, but it still has much to teach about the behavior of directional antennas. This volume covers single (straight) long wires, V arrays, and rhombics in both terminated and unterminated forms. The latter forms are among the first traveling-wave and frequency-independent antennas. Although the book makes constant reference to classical references in the field, it uses modern computer antenna modeling software to refresh the analysis, check older design data, and establish some facts about long-wire antennas that lay outside the boundaries of early calculations. The book also provides details and cautions on modeling certain forms of long-wire antennas, especially multi-wire terminated rhombic designs.
    + Includes set of model files Longwire-Notes-Models.zip. +

    • +
  • LPDA Notes - Volume 1: Pure LPDAs: Volume 1 looks at the basic properties of pure log periodic dipole arrays, with special emphasis upon the types of antennas usually created by radio amateurs.

    • +
  • LPDA Notes - Volume 2: Hybrid LPDAs: Volume 2 begins with a detailed analysis of the strengths and weaknesses of various traditional and long-boom designs for the log-cell Yagi. Part 3 explores a number of practical LPDAs, including lower HF vs. UHF designs, narrow-band vs. very wide-band designs, and split-band vs. continuous-band designs.

    • +
  • LPDA Notes - Volume 3: A Potpourri of LPAs: Volume 3 begins with astudy of shorted stubs used with LPDAs with a following exploration of the patterns of element currents. Part 2 examines LPDA predecessors, the 2-bat zigzag LPA to determine its capabilities relative to LPDAs. Part 2 examines the potential of extended aperture LPDAs (EALPDAs, while the last section explores the V-element LPDA and the log-spiral LPA.

    • +
  • + Moxon Rectangle Notes: This one-volume effort collects and organizes information on the Moxon rectangle, beginning with the history and principles of the antenna and moving to practical wire and tubular versions for HF, VHF, and UHF. The book includes a complete set of antenna models mentioned in the text, as well as a Moxon rectangle design program (in several formats) developed by the author.
    + Includes a set of model files: Moxon-Rectangle-Notes-Models.zip. +

    • +
  • Planar and Corner Reflector Arrays: Resting on optical rather than parasitic or phased-element principles, planar (flat) and corner reflectors suffer undeserved neglect by a large portion of the amateur community (and others). The planar reflector turns out to have an ideal size based on the size of the driver, which can be simple or complex. Corner reflectors accept fewer driver variations, but are capable of high performance levels, although rod-based and screen-based reflectors have interesting differences. The book includes information of 3-dimensional reflectors as well as on the more standard 2-dimensional corner reflector.

    • +
  • + Self Contained Vertical Notes: Nearly a decade has gone by, and I still receive questions about these interesting antennas. Therefore, I decided to return to ground zero and re-formulate the information in those articles and much, much more to create this volume. I have expanded coverage in terms of several factors: the fundamentals upon which SCVs operate, antenna types that fit within the group, frequency coverage, and special applications and opportunities.
    + Includes a set of model files: SCV-Notes-Models.zip +

    • +
  • + Some Basics of Multi-Band Beam Design: There is among some amateur radio beam designers a special art: the art, since, and craft of designing multi-band parasitic beams. Sometimes the work of an individual, sometimes the work of a team, designing directional antennas that cover more than one amateur band is not as easy as it may seem on the surface. We cannot simply interlace a collection of monoband beams, since all of the off- band elements will be active, at least at a low level, on all bands. The interactions are sufficient to complicate the process of deriving on all bands adequate gain, respectable front-to-back ratios, clean radiation patterns, and an acceptable feedpoint impedance.
    + Includes a set of model files: Some-Basics-of-Multi-Band-Beam-Design-Models.zip +

    • +
  • + Two Element Horizontal Beams Volume 1 - Phased Arrays: If one element is good, then two must be better. This credo underlies most amateur understanding of 2-element (and n-element) arrays. In Volume 1 of this set, we explore the nature and types of 2-element directional and bi-directional phased arrays. We call an array phased when we provide energy directly to each element in the array.
    + Includes a set of model files: Two-Ele-Horizontal-Beams-Vol-1-Phased-Arrays-Models.zip +

    • +
  • + Two Element Horizontal Beams Volume 2 - Parasitic Arrays: Feeding a single element creates the most popular form of 2-element array. This longer look results in a completely new volume because there are so many variations on the basic 2 element parasitic scheme. Of course, we call an array parasitic when we feed one element (usually) and allow the other elements to arrive at the conditions for directional service solely by the mutual coupling between elements.
    + Includes a set of model files: Two-Ele-Horizontal-Beams-Vol-2-Parasitic-Arrays-Models.zip +

    • +
  • Two older volumes (written about 1980) are available in .PDF format. One is Seven Steps to Designing Your Own Ham Equipment, and the other is Setting Up and Using Your Own Ham Shack. Although the specific details have changed over the last two decades of rapid electronic evolution, the general principles involved in both enterprises may still prove useful.

    • +
  • Wide-Band Yagi Notes (2 Volumes): +
      +
    • Volume 1, Basic Principles, introduces and reviews the fundamentals of wide-band Yagi design, including classic DL6WU features, OWA principles and special properties, and the principles of adapting a given design to different materials.
      • +
    • Volume 2, Practical Antennas, provides a potpourri of practical (that is buildable) OWA and other wide-band Yagi designs on a band-by-band basis from 10 meters to 70 cm, with a special chapter on 40 meters. Includes antenna models of all antennas mentioned in the text.
      • +
    +

    • +
+


+

Return to Home Page

+

Topics: Books, Modeling


+ + diff --git a/content/classes/Random_LB.zip b/content/classes/Random_LB.zip new file mode 100644 index 0000000..a11d8ab Binary files /dev/null and b/content/classes/Random_LB.zip differ diff --git a/content/classes/aids.html b/content/classes/aids.html new file mode 100644 index 0000000..e40e1ff --- /dev/null +++ b/content/classes/aids.html @@ -0,0 +1,101 @@ + + + + + + Antenna Modeling Aids + + + + + + + + + +
+
+

Antenna Modeling Aids

+
+
+

L. B. Cebik, W4RNL

+
+
+

+

Antenna modeling via method-of-moments and related software has become a major part of antenna design and analysis activity at every level of effort, from amateur radio to professional research and engineering. Although software is widely available, education in the effective use of these computer aids has been lacking. Part of my effort to remedy this difficulty has included a monthly column in antenneX called simply Antenna Modeling.

+

To further assist antenna modelers, I have prepared some other materials which are available from commercial sources. The list of links below will more fully describe each item and provide additional links to places where the items may be obtained.

+


+

Basic Antenna Modeling: A Hands-On Tutorial.

+

A sizable volume of 21 chapters introducing antenna modeling in NEC-2. Written to accompany the Nittany-Scientific NEC-Win Plus software implementation of NEC-2, the principles of modeling presented by the book are nonetheless perfectly general. The book is designed to be used in a wide variety of contexts, ranging from self-study to short-courses and seminars to formal college classroom instruction in antenna modeling. Accompanying the book is a disk of antenna models for the 150+ exercises to give the user detailed hands-on experience and guidance in model construction for a wide variety of antennas. The title link provides further information on the book, as well as a link to Nittany-Scientific for pricing and ordering.

+

Intermediate Antenna Modeling: A Hands-On Tutorial

+

Provides over 450 pages of illustrated text and about 300 exercise models and variants as a means of introducing virtually the entire command sets of both NEC-2 and NEC-4. The self-study course is designed for use in conjunction with advanced software packages. The major division are The Geometry Commands; Far-Field and General Control Commands; and Special Outputs, Control Commands, and Techniques.
+

+

Exercise Models in EZNEC and NEC Format

+

Some modelers may wish to use Basic Antenna Modeling with EZNEC software, which uses a proprietary format for model files. Therefore, I have prepared a disk of the exercise files in the .EZ format. The disk contains all 150+ exercises, with variants used in the exercises, for a total of over 350 model files. The disk may also be used as a sampling of some of the many types of MF to UHF antennas that one may model with NEC-2. The title link provides fuller information on the disk, including a link to the source of purchase and a partial list of the models included.

+ + + + + + + + + + + + + + +
+

PART A:
+ Basic Modeling & Model Testing

+ 		+

PART B:
+ Common Modeling Techniques, Limitations, and Work-Arounds

+ 		+

PART C:
+ Practical Antenna Modeling

+
~ NEC-2
+ ~ Modeling Preparations
+ ~ Basic Antenna Models
+ ~ NEC Output Data
+ ~ Careful Model Construction
+ ~ Convergence Testing
+ ~ Frequency Specification		~ Source Types and Placement
+ ~ Tapered-Diameter Elements
+ ~ Geometry Limitations
+ ~ Grounds and Applications
+ ~ Resistive Loads
+ ~ Reactive Loads
+ ~ Transmission Lines		~ Monopoles and Ground Planes
+ ~ Vertically Polarized Antennas and Arrays
+ ~ Bi-directional Wire Arrays
+ ~ Yagis
+ ~ Horizontal Parasitic and Phased Arrays
+ ~ VHF/UHF Antennas
+ ~ Special Structures
+

Plus APPENDIX:  Some Useful Data for Antenna Modelers (missing)

+

+

+

Models for Antenna Modelers in .EZ and .NEC Formats: 2nd Edition

+

There has been a need for exemplary models for newer antenna modelers to use to gain experience. As well, experienced modelers have no wish to reinvent models already in existence. To serve both groups, I have gleaned--from my accumulation of over 4000 models--sets of models that may serve as a foundation for modelers to build upon. Each set in the second edition consists of over 100 models focused around a central antenna category. The available sets (which contain the same models in both .EZ and .NEC formats) are these:

+
    +
  • 102 HF Yagis
    • +
  • 130 HF and VHF Quads
    • +
  • 111 HF-UHF LPDAs
    • +
  • 103 Vertical and Horizontal Phased Arrays
    • +
  • 103 HF Horizontal Wire Antennas/Arrays
    • +
  • 108 HF and VHF Vertical Antennas/Arrays
    • +
  • 144 VHF/UHF Antennas
    • +
+

The title link provides fuller information on the content of each set and a download link at the bottom of the page.

+

+

Antenna Modeling Programs - more information about modeling software (Updated 2024 - NEC5 info, NEC-Win downloads).

+

Random Models - 2803 models, some of these appear to have been used in website articles (Added 2024 from ON5AU site).

+

Antenna Modeling Books - A listing of more than a dozen books in PDF format (some include zipped model sets) by L. B. Cebik, W4RNL.

+

+

Updated 12-25-2007.

+

Return to Home Page

+

Topics: Modeling


+ + diff --git a/content/classes/models.html b/content/classes/models.html new file mode 100644 index 0000000..14b4f5a --- /dev/null +++ b/content/classes/models.html @@ -0,0 +1,56 @@ + + + + + + Models for Antenna Modelers: 2nd Edition + + + +
+ + + + + + +
+

Models for Antenna Modelers: 2nd Edition

+

L. B. Cebik

+
+
+

+

There has been a need for exemplary models for newer antenna modelers to use to gain experience. As well, experienced modelers have no wish to reinvent models already in existence. To serve both groups, I have gleaned--from my accumulation of over 4000 models--sets of models that may serve as a foundation for modelers to build upon. The antenna designs consist of published or shared work or of original work by the collection compiler. To the best of my knowledge and by intention, the collections includes no commercially available antennas.

+

A few years back (1999), I made available over 400 models from my personal collection of non-commercial antennas. Both the response to those models and the elapsed time since their release has suggested that a new and expanded edition is in order. The new edition aims to be more useful to users in at least two major ways.

+
+

1. The number of categories has shrunk by one, since 10-meter antenna models are now distributed throughout the other categories. However, each of the 7 categories of antennas has doubled in size. There are from 100 to 140 models in each set. The total number of models in the complete collection is over 800, with no more than about 10% maximum overlap among sets. (For example, I could not have a Yagi set without a wire beam for 75 meters, which also must be in the wire-array collection.)

+

2. The first edition used a code for filenames to hold them within the old 8-character filename limit. The 2nd edition uses long filenames to more fully describe the antenna type, variation, frequency of use, and--if known--the designer. You will still have to work your way through some abbreviations in the compacted filenames, but these names will give you a better clue as to what you are likely to see.

+
+

As with the first edition, each collection comes in two forms: a set in EZNEC (.EZ) format and the same set in generic NEC (.NEC) format. Virtually all programs besides the entry-level EZNEC can read the generic NEC ASCII text format file. However, I have added to the collection a few files that are larger than the 500-segment entry-level EZNEC limit in order to provide a glimpse at some very large quads, adequately sized planar and corner reflectors, and very large radial systems.

+

Each set consists of over 100 models focused around a central antenna category. The available sets are these:

+
    +
  • 102 HF Yagis
    • +
  • 130 HF and VHF Quads
    • +
  • 111 HF-UHF LPDAs
    • +
  • 103 Vertical and Horizontal Phased Arrays
    • +
  • 103 HF Horizontal Wire Antennas/Arrays
    • +
  • 108 HF and VHF Vertical Antennas/Arrays
    • +
  • 144 VHF/UHF Antennas
    • +
+

Virtually every model can be effectively scaled from the frequency of design to a desired frequency, with care to adjusting the element diameter(s) as well as element lengths. These models are not finished products. While a few may translate directly into antennas that might be constructed at home, the primary intention is to provide models that allow you to study antenna types and their performance. As well, they may form the basis for design improvements that you may make as you perfect your modeling skills. In short, these models are not a substitute for a thorough knowledge of the modeling software or fundamental antenna principles. Additional information on each collection appears in the individual set descriptions.

+

HF Yagis: 102 Models

The collection includes both wire and tube models, with tubular elements including some stepped-diameter versions and some uniform-diameter versions. Models cover all of the HF bands: 80, 75, 60, 40, 30, 20, 17, 15, 12, and 10 meters. If you see a design for one band without a counterpart for another band, you may scale the element lengths, spacing, and diameters to create the desired beam. There are 85 true Yagis, although there are a few V-Yagi designs that combine parallel-element coupling and element-end coupling. As well, the collection includes 15 Moxon rectangles, which also use both parallel-element and element-end coupling. See the VHF-UHF antenna collection for Yagis covering these higher frequencies. +

Quad Antennas: 130 Models

The models cover quad sizes from 1 element up to 6 elements for 3.6 MHz through 1296 MHz. The set of 10-meter models especially shows a wide variety of variations, especially for diamond-shaped and square models with loading at the high-voltage points. The models with "opt" included in the filename are the products of a set of equation-based models in .NWP-format that cannot be included here. However, the calculation instruments are available at numerous sources. AWG #12 copper wire sample optimized quads appear for all bands from 80 meters to 1296 MHz. Besides monoband quad beams, the collection also includes a good number of 2-, 3-, and 5-band models ranging in size-per-band from 2 elements to 6-elements. +

LPDAs: 111 Models

The collection of LPDAs includes both log periodic dipole arrays and log-cell Yagis, which use LPDA structures for their drivers. The log-cell Yagi models (labeled LC) are mainly on the very wide 10-meter band. The LPDAs proper (labeled LP) cover a very wide frequency range beginning at 3.5 MHz and ending at about 2 GHz. There are 3+ octave models, but most examples cover a 1-octave (2:1-frequency) range. Models also vary widely in size, with a preference for relatively high-performance LPDAs. Many include performance-enhancing modifications. The collection also contains some special purpose or non-amateur range models, including 3 FM LPDAs, some single-band LPDAs, and some government and commercial communications band versions. +

Verticals: 108 Models

The collection of verticals includes both vertical element antennas and antennas with predominantly vertically polarized radiation. The models tend to focus on the 160-meter through 30-meter bands. For those bands, there are simple monopoles over radial systems, shortened monopoles with a variety of hat structures, and numerous wire structures whose dominant radiation is vertically polarized. This group includes rectangles, hentennas, delta loops, quad loops, half-squares, bobtail curtains, Sterba curtains, and Bruce arrays. There are also a few parasitic and phased monopole structures. Besides these basic vertically polarized HF antennas, there are a number of others, including J-poles, the L-antenna, the collinear vertical, and a trio of dipole arrays. +

Wire Arrays: 103 Models

The collection of wire arrays covers perhaps the widest territory of any of these collections, since there are collinear, end-fire, and broadside arrays. Hence, you will find extended double Zepps, 8JKs, and lazy-Hs among the offerings. The collection also includes some wire Yagis for the low HF range. As well, you will discover loops oriented both vertically and horizontally. Indeed, you will find rectangles, double rectangles, hentennas, half-squares, and bobtail curtains for the vertical radiation aficionado. Among the larger arrays are collinear extended double Zepps, Sterba curtains, and Bruce arrays. In addition, there are a number of wire loops potentially usable on several bands. The collection even includes a few long wires, Vee-beams, a rhombic, and some challenging NVIS arrays. Virtually all of the antennas use either AWG #12 or AWG #14 copper wire as the main ingredient. +

Phased Arrays: 103 Models

The collection of phased-array models covers the HF spectrum from 80 through 10 meters, with a few models at VHF and UHF frequencies. Phased arrays (for the purposes of this collection) include any antenna that provides a feed to more than one element. Many are vertical arrays--especially in the MF and lower HF range, and some models are for the AM broadcast range. Upper HF designs are mostly horizontal, although some of these antennas may be used vertically to good effect. Among the antenna types included are collinear, broadside, and endfire wire arrays, 2-element horizontal phased arrays (ZL Specials, HB9CVs, and variations), stacked beams, dipole arrays, and turnstiles. Some models use the TL facility of NEC-2 to provide one or more phasing lines, while others use separate feedpoints. +

VHF-UHF Antennas: 144 Models

The collection has samples of many kinds of antennas, including Yagis, quads, corner reflectors, planar reflectors, simple and collinear verticals, and dual rhombics. However, Yagis dominate the collection, since there are so many sizes, designs, and variations on them. The collection only touches on quads, since the separate collection of quad designs includes both HF and VHF/UHF quad beams. Some designs, like the DL6WU Yagi, may only have a small sample on a particular band, because you may create other lengths simply by removing directors one-at-a-time from the forward end. As well, many designs for 50 through 432 MHz scale readily to the upper UHF region. There are also a few FM band antennas, including a triplet of LPDAs. However, most VHF/UHF LPDAs appear in the separate LPDA collection. +

+

The complete set of models can be downloaded here, 801 models in eznec and nec format (2 MB zip).

+

The files in these collections are copyright by L. B. Cebik. All original designs, that are not already the property of others, are also copyright by L. B. Cebik and may not be used for the production of any commercial or proprietary product without prior written agreement with the designer. +

+

Updated 08-10-2003.

+

Return to Antenna Modeling Aids

+

Topics: Modeling


+ + diff --git a/content/classes/models.zip b/content/classes/models.zip new file mode 100644 index 0000000..bbdab62 Binary files /dev/null and b/content/classes/models.zip differ diff --git a/content/download/1elqd.vbs b/content/download/1elqd.vbs new file mode 100644 index 0000000..10d19c8 --- /dev/null +++ b/content/download/1elqd.vbs @@ -0,0 +1,24 @@ +MSGBOX "Program to calculate the perimeter length of a resonant quad loop." & CHR(13) & "All equations correlated to NEC antenna modeling software." & CHR(13) & CHR(13) & "L. B. Cebik, W4RNL",,"Resonant Quad Loop" + +Sub Calculate + + F = INPUTBOX ("Enter Desired Frequency in MHz:","Desired Frequency") + U = INPUTBOX ("Select Units for Wire Diameter in 1. Inches or 2. Millimeters","Wire Diameter") + WD = INPUTBOX ("Enter Wire Diameter in your Selected Units","Wire Diameter") + IF U=1 THEN WLI=11802.71/F:D=WD/WLI + IF U=2 THEN WLI=299792.5/F:D=WD/WLI + L=.4343*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413 + WL=299.7925/F + PM=LN*WL + WF=983.5592/F + PF=LN*WF + + 'MSGBOX "Wire Diameter in Wavelengths:" & Round(D,4) & CHR(13) & "Perimeter Length in Wavelengths =" & Round(LN,4) & CHR(13) & "Wavelength in Meters =" & Round(WL,4) & CHR(13) & "Perimeter Length in Meters =" & Round(PM,4) & CHR(13) & "Wavelength in Feet =" & Round(WF,4) & CHR(13) & "Perimeter Length in Feet =" & Round(PF,4),,"Dimensions" + + MSGBOX "Wire Diameter in Wavelengths:" & Round(D,4) & CHR(13) & "Perimeter Length in Wavelengths =" & Round(LN,4) & " Meters: " & Round(PM,4) & " Feet: " & Round(PF,4) & CHR(13) & "Wavelength in Meters =" & Round(WL,4) & " Feet " & Round(WF,4),,"Dimensions" +End Sub + +Do Until P = 7 + P = MSGBOX ("Calculate Quad Demensions",4,"Yes or No") + if P = 6 then Calculate +Loop \ No newline at end of file diff --git a/content/download/2elqd.vbs b/content/download/2elqd.vbs new file mode 100644 index 0000000..b5a284c --- /dev/null +++ b/content/download/2elqd.vbs @@ -0,0 +1,42 @@ +MSGBOX "Program to calculate the dimensions of a resonant square 2-element quad beam." & CHR(13) &"All equations calibrated to NEC antenna modeling software for wire diameters"&CHR(13) & "from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz." & CHR(13) & CHR(13) & "L. B. Cebik, W4RNL",,"2 Element Quad" + +Sub Calculate + +F = INPUTBOX ("Enter Desired Frequency in MHz:","Operating Frequency") +U = INPUTBOX ("Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths","Wire Diameter") +WD = INPUTBOX ("Enter Wire Diameter in your Selected Units","Wire Diameter") +IF U=1 THEN WLI=11802.71/F:D=WD/WLI +IF U=2 THEN WLI=299792.5/F:D=WD/WLI +IF U=3 THEN D=WD +MSGBOX "Wire Diameter in Wavelengths: " & Round(D,6),,"Wire Diameter" +L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D) +IF D1<-4.5 then MSGBOX "Wire diameter less than 3E-5 wavelengths: results uncertain." +IF d1>-2 THEN MSGBOX "Wire diameter greater than 1E-2 wavelengths: results uncertain." +AD=.00336:BD=.04966518519:CD=.2731955556:DD=.6716364021:ED=1.644147937 +DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED +AR=.003173333333:BR=.0508237037:CR=.3081977778:DR=.8663851852:ER=2.040064444 +RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER +AS1=-.003:BS=-.03551851852:CS=-.1553055556:DS=-.2902116402:ES=-.02540079365 +SP=(AS1*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES +AZ=1.976333333:BZ=30.84751852:CZ=172.4909722:DZ=419.5162831:EZ=519.8747579 +ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ +AG=-.06333333333:BG=-.7203703704:CG=-3.010277778:DG=-5.381375661:EG=3.738769841 +GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG +AW=1.688666667:BW=23.76837037:CW=124.9339444:DW=295.8872328:EW=281.2755159 +SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW +AF=-.00266666667:BF=.388:CF=4.790666667:DF=19.55485714:EF=28.76628571 +FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF +AN=-.08333333333:BN=-.9462962963:CN=-3.943055556:DN=-7.582671958:EN=-5.23234127 +DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN +WL=299.7925/F +WF=983.5592/F +MSGBOX "Wavelength in Meters = "& Round(WL,4) & CHR(13) & "Wavelength in Feet = "&Round(WF,4),,"WaveLength" +MSGBOX "Quad Dimensions in Wavelengths, Feet, and Meters:" & CHR(13) & CHR(13) & "Driver Side = "&Round((DE/4),4)&" WL or "&Round((DE/4)*WF,4)&" Feet or "&Round((DE/4)*WL,4)&" Meters" & CHR(13) &"Driver Circumference = "&Round(DE,4)&" WL or "&Round(DE*WF,4)&" Feet or "&Round(DE*WL,4)&" Meters" & CHR(13) & "Reflector Side = "&Round((RE/4),4)&" WL or "&Round((RE/4)*WF,4)&" Feet or "&Round((RE/4)*WL,4)&" Meters" & CHR(13) & "Reflector Circumference = "&Round(RE,4)&" WL or "&Round(RE*WF,4)&" Feet or "&Round(RE*WL,4)&" Meters" & CHR(13) & "Reflector-Driver Space = "&Round(SP,4)&" WL or "&Round(SP*WF,4)&" Feet or "&Round(SP*WL,4)&" Meters" & CHR(13) & "Approximate Resonant Feedpoint Impedance = "&Round(ZR,3)&" Ohms",,"Dimensions" + +MSGBOX "Approximate Free-Space Gain = "&Round(GN,4)&" dBi" & CHR(13) & "Approximate 2:1 VSWR Bandwidth = "&Round(SW,4)&"% of Design Frequency" & CHR(13) & "Approximate >20 dB F-B Ratio Bandwidth = "&Round(FB,4)&"% of Design Frequency" & CHR(13) & "Approximate Rate of Gain Change = "&Round(DG,4)&"dB per 1% of Design Frequency",,"Calculations" +End Sub + +Do Until P = 7 + P = MSGBOX ("Calculate Quad Demensions",4,"Yes or No") + if P = 6 then Calculate +Loop diff --git a/content/download/3el-highgain-yagi.nwp b/content/download/3el-highgain-yagi.nwp new file mode 100644 index 0000000..e5ecb1a Binary files /dev/null and b/content/download/3el-highgain-yagi.nwp differ diff --git a/content/download/3el-maxfb-yagi.nwp b/content/download/3el-maxfb-yagi.nwp new file mode 100644 index 0000000..430c2e6 Binary files /dev/null and b/content/download/3el-maxfb-yagi.nwp differ diff --git a/content/download/3el-wideband-yagi.nwp b/content/download/3el-wideband-yagi.nwp new file mode 100644 index 0000000..ec0921f Binary files /dev/null and b/content/download/3el-wideband-yagi.nwp differ diff --git a/content/download/3elhgqd.vbs b/content/download/3elhgqd.vbs new file mode 100644 index 0000000..34663e2 --- /dev/null +++ b/content/download/3elhgqd.vbs @@ -0,0 +1,56 @@ +MSGBOX "Program to calculate the dimensions of a resonant square (High Gain) 3-element quad beam. All equations calibrated to NEC antenna modeling software for wire diameters from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz." &CHR(13) & CHR(13) &"L. B. Cebik, W4RNL",,"3 Element Quad Calculations" +DIM f, U, WLI, WD, D, L, LL, LM, D1, AD, BD, CD, DD, ED, DE, AR, BR, CR, DR, ER, RE +DIM AI, BI, CI, DI, EI, IR, AS1, BS, CS, DS, ES, AP, BP, CP, DP, IP, EP, AZ, BZ, CZ, DZ, EZ +DIM ZR, AG, CG, BG, DG, EG, GN, AW, BW, CW, DW, EW, SW, AF, BF, CF, DF, EF, FB, WS, WF +SUB Calculate + F = INPUTBOX ("Enter Desired Frequency in MHz:","Desired Frequency") + U = INPUTBOX ("Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths","Select Units") + 'U = INPUTBOX ("Choose 1. or 2. or 3.") + WD = INPUTBOX ("Enter Wire Diameter in your Selected Units","Wire Diameter") + IF U=1 THEN WLI=11802.71/F:D=WD/WLI + IF U=2 THEN WLI=299792.5/F:D=WD/WLI + IF U=3 THEN D=WD + + L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D) + IF D1<-4.5 then MSGBOX "Wire diameter less than 3E-5 wavelengths: results uncertain." + if d1>-2 THEN MSGBOX "Wire diameter greater than 1E-2 wavelengths: results uncertain." + AD=.000266666667:BD=.00506666667:CD=.03633333333:DD=.1221904762:ED=1.183285714 + DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED + DE = Round(DE, 3) + AR=.0037333333333:BR=.05362962963:CR=.29275555556:DR=.7424529101:ER=1.814412698 + RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER + RE = Round(RE, 3) + AI=-.00266666667:BI=-.033244444444:CI=-.1550666667:DI=-.3222793651:EI=.7283809524 + IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI + IR = Round(IR, 3) + as1=.00033333333:BS=.004837037037:CS=.02552777778:DS=.05643756614:ES=.2191230159 + SP=(as1*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES + SP = Round(SP, 3) + AP=-.002333333333:BP=-.03128148148:CP=-.15586111111:DP=-.3417669312:EP=-.05499206349 + IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP + IP = Round(IP,3) + AZ=4.4029:BZ=53.43954444:CZ=239.2408583:DZ=462.3614437:EZ=373.3035655 + ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ + ZR = Round(ZR,3) + AG=-.15:BG=-1.768518519:CG=-7.763055556:DG=-14.78592593:EG=-.609722222 + AG=Round(AG,3) + GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG + GN = Round(GN,3) + AW=.16666666667:BW=2.265925926:CW=11.706111111:DW=27.93058201:EW=28.88753968 + SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW + SW = Round(SW, 3) + AF=.11933333333:BF=1.671777778:CF=8.9885:DF=22.45931746:EF=23.68797619 + FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF + FB = Round(FB,3) + WL=299.7925/F: WL = Round(WL,3) + WF=983.5592/F:WF = Round(WF,3) + d = Round(D,5) + MSGBOX "Wire Diameter in Wavelengths: " & D & chr(13) & "Wavelength in Meters =" & WL & chr(13) & "Wavelength in Feet =" & WF,,"Characteristics at " & F & " Mhz" + MSGBOX "Quad Dimensions in Wavelengths, Feet, and Meters:" & chr(13) & chr(13) & "Driver Side =" & (DE/4) &" WL or "&(DE/4)*WF &" Feet or "&(DE/4)*WL&"Meters" &CHR(13) & "Driver Circumference ="&DE&" WL or "&DE*WF&" Feet or "&DE*WL&"Meters" &(CHR(13))& "Reflector Side ="&(RE/4)&" WL or "&(RE/4)*WF&" Feet or "&(RE/4)*WL&"Meters" & CHR(13) & "Reflector Circumference ="&RE&" WL or "&RE*WF&" Feet or "&RE*WL&"Meters" & CHR(13) & "Reflector-Driver Space ="&SP&" WL or "&SP*WF&" Feet or "&SP*WL&"Meters" & CHR(13) & "Director Side ="&(IR/4)&" WL or "&(IR/4)*WF&" Feet or "&(IR/4)*WL&"Meters" & CHR(13) & "Director Circumference ="&IR&" WL or "&IR*WF&" Feet or "&IR*WL&"Meters" & CHR(13) & "Director-Driver Space ="&IP&" WL or "&IP*WF&" Feet or "&IP*WL&"Meters" & CHR(13) & "Approx. Feedpoint Impedance ="&ZR&" Ohms ",,"Quad Dimensions" + MSGBOX "Free-Space Gain ="&GN&"dBi" & CHR(13) & "Approximate 2:1 VSWR Bandwidth ="&SW&"% of Design Frequency" & CHR(13)& "Approximate >20 dB F-B Ratio Bandwidth ="&FB&"% of Design Frequency",,"Gain, Bandwidth and F/B Ratio" +End Sub + +Do Until P = 7 + P = MSGBOX ("Calculate Quad Demensions",4,"Yes or No") + if P = 6 then Calculate +Loop diff --git a/content/download/3elwbqd.vbs b/content/download/3elwbqd.vbs new file mode 100644 index 0000000..c89f71a --- /dev/null +++ b/content/download/3elwbqd.vbs @@ -0,0 +1,50 @@ +MSGBOX "Program to calculate the dimensions of a resonant square 3-element quad beam." & CHR(13) & CHR(13) & "All equations calibrated to NEC antenna modeling software for wire diameters" & CHR(13) & "from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz." & CHR(13) & CHR(13) &"L. B. Cebik, W4RNL",, "WideBand 3 Element Quad" + +Sub Calculate + +F = INPUTBOX ("Enter Desired Frequency in MHz:","Operating Frequency") +U = INPUTBOX ("Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths", "Wire Diameter") +WD =INPUTBOX ("Enter Wire Diameter in your Selected Units","Wire Diameter") +IF U=1 THEN WLI=11802.71/F:D=WD/WLI +IF U=2 THEN WLI=299792.5/F:D=WD/WLI +IF U=3 THEN D=WD +MSGBOX "Wire Diameter in Wavelengths: " & Round(D,6),,"Wire Diameter" +L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D) +IF D1<-4.5 then MSGBOX "Wire diameter less than 3E-5 wavelengths: results uncertain." +IF d1>-2 THEN MSGBOX "Wire diameter greater than 1E-2 wavelengths: results uncertain." +AD=.00064:BD=.01044148148:CD=.06484444444:DD=.1886626455:ED=1.232080635 +DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED +AR=.0009333333333:BR=.01915555556:CR=.13983333333:DR=.4587492063:ER=1.64042381 +RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER +AI=-.0012:BI=-.0209037037:CI=-.13021111111:DI=-.3498137566:EI=.5941126984 +IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI +AS1=-.0033:BS=-.03927777778:CS=-.1724583333:DS=-.3239603175:ES=-.04951547619 +SP=(AS1*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES +AP=-.004866666667:BP=-.06262962963:CP=-.29347222222:DP=-.6174457672:EP=-.2289269841 +IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP +AZ=-2.227066667:BZ=-26.75247407:CZ=-115.9142556:DZ=-217.8183323:EZ=-79.59203175 +ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ +AG=-.07:BG=-.7877777778:CG=-3.350833333:DG=-6.143888889:EG=5.104166667 +GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG +AW=-.05847333333:BW=-.5028392593:CW=-.4586494444:DW=6.080227037:EW=17.61091389 +SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW +AF=.11695666667:BF=1.717985556:CF=9.6510925:DF=25.23848992:EF=27.78167988 +FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF +AN=-.04666666667:BN=-.5414814815:CN=-2.302777778:DN=-4.364074074:EN=-3.092777778 +DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN +WL=299.7925/F +WF=983.5592/F + +MSGBOX "Wavelength in Meters ="& Round(WL,4) & CHR(13) & "Wavelength in Feet ="& Round(WF,4),,"WaveLength" + + +MSGBOX "Quad Dimensions in Wavelengths, Feet, and Meters:" & CHR(13) & CHR(13) & "Driver Side = "&Round((DE/4),4)&" WL or " & Round((DE/4)*WF,4) & " Feet or "&Round((DE/4)*WL,4)&" Meters" & CHR(13) & "Driver Circumference = "&Round(DE,4)&" WL or "&Round(DE*WF,4)&" Feet or "&Round(DE*WL,4)&" Meters" & CHR(13) & "Reflector Side = "&Round(RE/4,4)&" WL or "&Round((RE/4)*WF,4)&" Feet or "&Round((RE/4)*WL,4)&" Meters" & CHR(13) & "Reflector Circumference = "&Round(RE,4)&" WL or "&Round(RE*WF,4)&" Feet or "&Round(RE*WL,4)&" Meters" & CHR(13) & "Reflector-Driver Space = "&Round(SP,4)&" WL or "&Round(SP*WF,4)&" Feet or "&Round(SP*WL,4)&" Meters" & CHR(13) & "Director Side = "&Round((IR/4),4)&" WL or "& Round((IR/4)*WF,4)&" Feet or "&Round((IR/4)*WL,4)&" Meters" & CHR(13) & "Director Circumference = "&Round(IR,4)&" WL or "&Round(IR*WF,4)&" Feet or "&Round(IR*WL,4)&" Meters" & CHR(13) & "Director-Driver Space = "&Round(IP,4)&" WL or "&Round(IP*WF,4)&" Feet or "&Round(IP*WL,4)&" Meters" & CHR(13) & "Approx. Feedpoint Impedance = "&Round(ZR,3)&" Ohms",,"Dimensions" + + +MSGBOX "Free-Space Gain = "& Round(GN,5)&" dBi" & CHR(13) & "Approximate 2:1 VSWR Bandwidth = " & Round(SW,5) & " % of Design Frequency" & CHR(13) & "Approximate >20 dB F-B Ratio Bandwidth = "& Round(FB,5) & "% of Design Frequency" & CHR(13) & "Approximate Rate of Gain Change = "& Round(DG,5) & "dB per 1% of Design Frequency",,"Characteristics" +End Sub + +Do Until P = 7 + P = MSGBOX ("Calculate Quad Demensions",4,"Yes or No") + if P = 6 then Calculate +Loop \ No newline at end of file diff --git a/content/download/4elqd.vbs b/content/download/4elqd.vbs new file mode 100644 index 0000000..ed6df13 --- /dev/null +++ b/content/download/4elqd.vbs @@ -0,0 +1,57 @@ +MSGBOX "Program to calculate the dimensions of a resonant square 4-element quad beam." & chr(13) & "All equations calibrated to NEC antenna modeling software for wire diameters" & " from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz." & CHR(13) & CHR(13) & "L. B. Cebik, W4RNL",,"Wide Bandwidth 4 Element Quad" + +Sub Calculate + F = INPUTBOX ("Enter Desired Frequency in MHz:","Operating Frequency") + U = INPUTBOX ("Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths","Wire Diameter") + WD = INPUTBOX ("Enter Wire Diameter in your Selected Units","Wire Diameter") + IF U=1 THEN WLI=11802.71/F:D=WD/WLI + IF U=2 THEN WLI=299792.5/F:D=WD/WLI + IF U=3 THEN D=WD + D = Round(D,5) + + L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D) + IF D1<-4.5 then MSGBOX "Wire diameter less than 3E-5 wavelengths: results uncertain." + if d1>-2 THEN MSGBOX "Wire diameter greater than 1E-2 wavelengths: results uncertain." + AD=-.00018:BD=-.002359259259:CD=-.01090277778:DD=-.01971296296:ED=.1174938889 + DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED:DE=DE*8 + DE = Round(DE, 3) + AR=.0002666666667:BR=.004237037037:CR=.02554444444:DR=.07158756614:ER=.2119230159 + RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER:RE=RE*8 + RE = Round(RE,3) + AI=-.0002:BI=-.002525925926:CI=-.01182777778:DI=-.02473915344:EI=.1008246032 + IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI:IR=IR*8 + IR = Round(IR,3) + AT=-.0006:BT=-.009059259259:CT=-.04912777778:DT=-.1152343915:ET=.01678174603 + TT=(AT*(D1^4))+(BT*(D1^3))+(CT*(D1^2))+(DT*D1)+ET:TT=TT*8 + TT = Round(TT,3) + SP=.1635:IP=.481 + ATT=.0026666666667:BTT=.036888888889:CTT=.177:DTT=.3386587302:ETT=1.046738095 + TTP=(ATT*(D1^4))+(BTT*(D1^3))+(CTT*(D1^2))+(DTT*D1)+ETT + TTP = Round(TTP,3) + AZ=1.2:BZ=13.92592593:CZ=60.777777778:DZ=113.9177249:EZ=132.618254 + ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ + ZR = Round(ZR,2) + AG=-.1:BG=-1.184444444:CG=-5.228333333:DG=-9.831507937:EG=4.045238095 + GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG + GN = Round(GN,3) + AW=-.06663333333:BW=-.6539148148:CW=-1.677836111:DW=1.361137831:EW=9.502790079 + SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW + SW = Round(SW,3) + AF=-.03:BF=-.27666667:CF=-.4475:DF=2.348809524:EF=7.853214286 + FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF + FB = Round(FB,3) + WL=299.7925/F + WF=983.5592/F + WL = Round(WL,4) + WF = Round(WF,4) + + MSGBOX "Wire Diameter in Wavelengths: " & D & CHR(13) & "Wavelength in Meters = " & WL & CHR(13) & "Wavelength in Feet = " & WF,,"Wire Diameter" + + MSGBOX "Quad Dimensions in Wavelengths, Feet, and Meters:" & CHR(13) & CHR(13) &"Driver Side ="&(DE/4)&" WL or"&(DE/4)*WF&"Feet or "&(DE/4)*WL&"Meters" & CHR(13) & "Driver Circumference ="&DE&" WL or"&DE*WF&"Feet or "&DE*WL&"Meters" & CHR(13) & "Reflector Side ="&(RE/4)&" WL or "&(RE/4)*WF&"Feet or "&(RE/4)*WL&"Meters" & CHR(13) & "Reflector Circumference ="&RE&" WL or "&RE*WF&"Feet or "&RE*WL&"Meters" & CHR(13) & "Reflector-Driver Space ="&SP&" WL or "&SP*WF&"Feet or "&SP*WL&"Meters" & CHR(13) & "Director 1 Side ="&(IR/4)&" WL or "&(IR/4)*WF&"Feet or "&(IR/4)*WL&"Meters" & CHR(13) & "Director 1 Circumference ="&IR&" WL or "&IR*WF&"Feet or "&IR*WL&"Meters" & CHR(13) & "Director 1-Reflector Space ="&IP&" WL or "&IP*WF&"Feet or "&IP*WL&"Meters" & CHR(13) & "Director 2 Side ="&(TT/4)&" WL or "&(TT/4)*WF&"Feet or "&(TT/4)*WL&"Meters" & CHR(13) & "Director 2 Circumference ="&TT&" WL or "&TT*WF&"Feet or "&TT*WL&"Meters" & CHR(13) & "Director 2-Reflector Space ="&TTP&" WL or "&TTP*WF&"Feet or "&TTP*WL&"Meters" & CHR(13) & "Approx. Feedpoint Impedance ="&ZR&" Ohms ",,"Quad Demensions" + MSGBOX "Free-Space Gain ="&GN&"dBi" & CHR(13) & "Approximate 2:1 VSWR Bandwidth ="&SW&"% of Design Frequency" & CHR(13) & "Approximate >20 dB F-B Ratio Bandwidth ="&FB&"% of Design Frequency",,"Gain/SWR and Bandwith" +end sub + +Do Until P = 7 + P = MSGBOX ("Calculate Quad Demensions",4,"Yes or No") + if P = 6 then Calculate +Loop \ No newline at end of file diff --git a/content/download/a2dbs.zip b/content/download/a2dbs.zip new file mode 100644 index 0000000..e8f5c29 Binary files /dev/null and b/content/download/a2dbs.zip differ diff --git a/content/download/a2dil.zip b/content/download/a2dil.zip new file mode 100644 index 0000000..320a654 Binary files /dev/null and b/content/download/a2dil.zip differ diff --git a/content/download/a2mbs.zip b/content/download/a2mbs.zip new file mode 100644 index 0000000..29b31e4 Binary files /dev/null and b/content/download/a2mbs.zip differ diff --git a/content/download/a2mil.zip 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b/content/ebook.html new file mode 100644 index 0000000..9af44a6 --- /dev/null +++ b/content/ebook.html @@ -0,0 +1,493 @@ + + + + + + Electronics Books + + + +
+

Electronics Books

+
+
+
+ 
+
+Electronics Books of Interest to QRP Enthusiasts           Version 1.2
+                                                       August 20, 1996
+Compiled by L. B. Cebik, W4RNL
+
+Contents:  This file contains basic information on electronics books
+of especial interest to QRP enthusiasts.  It lists QRP Operating,
+Technique, and History Books; Basic Project Books; Advanced Design and
+Text Books; and General Reference Works. These listings provide
+something for the beginner through the advanced QRP enthusiast and for
+both operators, and designer-builders.
+
+Except for certain basic reference works, the list does NOT include
+standard, general interest amateur radio books.  There are many such
+works that will be of interest to the QRP enthusiast.  However, some
+limit has had to be imposed upon the list to keep it within useful
+boundaries.  For this same reason, books on antennas are not included
+in this listing:  the number of antenna books of interest to QRP
+enthusiasts is too large.
+
+Periodicals of interest to QRP enthusiasts and antenna books of
+interest to QRP enthusiasts will be found in separate listings.
+
+Each entry in this book list provides the following information:
+author, title, publisher, year of publication, cost, ISBN #, numbers
+of pages, and a brief description of the contents.
+
+Special thanks go to DL8MFQ, WA8MCQ, AK0B, W6EMD, N2CX, KC4EWT, N3LSB,
+and WA6AHL for their assistance in compiling this list.
+
+The individual items in this list are believed to be reasonably
+complete and accurate as of the date of this notice.  Corrections and
+additions may be e-mailed to me at the listed address.  I shall be
+pleased to add to the list any publication omitted if it is of high
+interest to QRP operators and builders.  And, of course, I shall be
+pleased to correct any errors and update the information listed.
+
+Permission to reproduce this list is hereby granted on condition that
+a full reference to its source is included.
+
+Good reading, good building, and good operating to you.
+
+                                          L. B. Cebik, W4RNL
+
+======================================================================
+              ==========================================
+                 Books of Interest to QRP Enthusiasts
+              ==========================================
+
+                              ==========
+              QRP Operating, Technique, and History Books
+                              ==========
+
+Author:        Adrian Weiss, W0RSP
+Title:         History of QRP in the U.S., 1924-1960
+Publisher:     Milliwatt Books (526 N. Dakota, Vermillion, SD 57069)
+Year:          1987
+Cost:          $15.00 (includes 1st class postage)
+ISBN #:        0-9614139-1-3
+Pages:         200
+Contents:      A rigorous but personalized history of QRP by a
+               professional historian and longtime QRPer, with
+               extensive extracts from the original records published
+               in QST and elsewhere.
+
+Author:        Adrian Weiss, W0RSP
+Title:         The Joy of QRP
+Publisher:     Milliwatt Books
+Year:          1984
+Cost:          (out of print)
+ISBN #:        ---
+Pages:         151
+Contents:      An informal overview of QRP that emphasizes operating,
+               but with a few projects; considered a classic.
+
+Author:        Dave Ingram, K4TWJ
+Title:         How to Get Started in QRP
+Publisher:     National Amateur Radio Association (NARA)
+               (P.O. Box 598, Redmond, WA  98073)
+Year:          1992
+Cost:          $9.95
+ISBN #:        ---
+Pages:         131
+Contents:      A beginners guide to QRP, touching on operating,
+               commercial and home brew gear, accessories, antennas,
+               VHF/UHF QRP, battery and "natural" power.
+
+Author:        Brad Wells, KR7L
+Title:         Your QRP Operating Companion
+Publisher:     ARRL
+Year:          1992
+Cost:          $6.00
+ISBN #:        0-87259-376-2
+Pages:         96
+Contents:      An introduction to QRP operating, including ragchewing,
+               DXing, and contesting, with lists of QRP clubs and
+               organizations, as well as net and calling frequencies.
+
+Author:        Richard Arland, K7YHA
+Title:         Low Power Communications, Vol. 1
+Publisher:     Tiare Publications
+               (P.O. Box 493, Lake Geneva, WI 53147)
+Year:          1992
+Cost:          $14.95
+ISBN #:        0-936653-33-7
+Pages:         93
+Contents:      A basic book on QRP, focusing on the newcomer to the
+               QRP arena, helping him/her get off on the right foot;
+               includes lots of the author's personal philosophy.
+
+Author:        Richard Arland, K7YHA, Ed.
+Title:         Low Power Communications, Vol. 2
+Publisher:     Tiare Publications
+Year:          1994
+Cost:          $19.95
+ISBN #:        0-936653-53-1
+Pages:         130
+Contents:      A more advanced volume featuring many top names in the
+               QRP hobby (AA2U, N4BP, WB8VGE, etc.) telling how they
+               pursue various facets of QRP, such as DXing,
+               contesting, DXpeditions, antennas, satellites,
+               milli/microwatting, and solar power.
+
+Author:        Richard Arland, K7YHA
+Title:         Low Power Communications, Vol. 3
+Publisher:     Tiare Publications
+Year:          1995
+Cost:          $14.94
+ISBN #:        0-936653-66-3
+Pages:         95
+Contents:      Devoted to equipment evaluations:  commercial, kit,
+               new, used; how to buy used gear; also includes software
+               and antennas.  Author warns:  "this book is extremely
+               opinionated."  (Vol. 1, 2, & 3 may be available as a
+               set from the publisher.)
+
+Author:        Dick Pascoe, G0BPS
+Title:         Introducing QRP:  An Introduction to the History and
+               Skills of Low Power Operating in the UK
+Publisher:     R. A. Pascoe
+Year:          1996
+Cost:          $8.00
+ISBN #:        ---
+Pages:         84
+Contents:      A succinct introduction to the history of QRP, the
+               basic equipment for QRP, and the operating techniques
+               needed for QRP.  Available in the US from Kanga, USA
+
+
+                              ==========
+                          Basic Project Books
+                              ==========
+
+Author:        Joel Kleinman, N1BKE, and Zack Lau, KH6CP/1, Editors
+Title:         QRP Power
+Publisher:     ARRL
+Year:          1996
+Cost:          $12.00
+ISBN #:        0-87259-561-7
+Pages:         175
+Contents:      "The best recent QRP articles from QST, QEX, and the
+               ARRL Handbook."  Designed to update QRP Classics for
+               the 1990s, with chapters on QRP operating, construction
+               practices, tranceivers, receivers, and accessories.
+
+
+Author:        Paul Harden, NA5N
+Title:         The Electronic Data Book for Homebrewers and QRPers
+Publisher:     Five Watt Press
+Year:          1996
+Cost:          $20.00
+ISBN #:        0-913945-57-9
+Pages:         150
+Contents:      QRP rig circuit analysis, component specification
+               sheets, QRP operating aids, and QRP rig lab tests. Also
+               includes the QRP Yellow Pages, by Rich High, W0HEP
+
+
+Author:        Doug DeMaw, W1FB
+Title:         W1FB's QRP Notebook, 2nd Ed.
+Publisher:     ARRL
+Year:          1991
+Cost:          $10.00
+ISBN #:        0-87259-365-7
+Pages:         179
+Contents:      Construction projects for QRP transmitters, receivers,
+               and accessories; most projects have circuit boards
+               available.
+
+
+Author:        Doug DeMaw, W1FB
+Title:         W1FB's Design Notebook:  Practical Circuits for
+               Experimenters
+Publisher:     ARRL
+Year:          1990
+Cost:          $10.00
+ISBN #:        0-87259-320-7
+Pages:         198
+Contents:      Practical circuits that use readily available
+               components and hand tools.
+
+Author:        Bob Schetgen, KU7G, Ed.
+Title:         QRP Classics
+Publisher:     ARRL
+Year:          1990
+Cost:          $12.00
+ISBN #:        0-87259-316-9
+Pages:         274
+Contents:      QRP projects from ARRL publications of the 15 years
+               preceding publication of this book; transmitters,
+               receivers, transceivers, accessories, most easy to
+               build.  Later printings include a design omitted in
+               first printing.
+
+Author:        Dave Ingram, K4TWJ
+Title:         Golden Classics of Yesteryear:  A Super Collection of
+               Rigs, Circuits, and Keys from Amateur Radio's Romantic
+               Past
+Publisher:     MFJ
+Year:          ---
+Cost:          $9.95
+ISBN #:        ---
+Pages:         60
+Contents:      Combines QRP and classic radio interests; schematics
+               and construction details for QRP and QRO TX and RX from
+               the 20s to the 50s with emphasis on historical accuracy
+               and fun.
+
+Author:        Doug DeMaw, W1FB, & Jay Rusgrove, W1VD, Eds.
+Title:         Solid State Basics for the Radio Amateur
+Publisher:     ARRL
+Year:          1978
+Cost:          (out of print; check local libraries)
+ISBN #:        ---
+Pages:         160
+Contents:      A short course in semiconductors with practical
+               projects for radio amateurs, with chapters on receiver
+               and transmitters circuits, as well as basic linear and
+               digital IC information.
+
+Author:        Michael Bryce, WB8VGE, Editor
+Title:         The HW-8 Handbook
+Publisher:     (Available from Kanga USA, Bill Kelsey, N8ET, 3521
+               Spring Lake Drive, Findlay, OH 45840)
+Year:          1991
+Cost:          $11.00
+ISBN #:        ---
+Pages:         56
+Contents:      A compilation of articles and modifications for the
+               Heathkit HW-7, HW-8, and HW-9 transceivers.
+
+Author:        Rev. George Dobbs, G3RJV, Ed.
+Title:         G-QRP Club Circuit Handbook
+Publisher:     RSGB (Available from Kanga USA)
+Year:          1983
+Cost:          $12.00
+ISBN #:        1-872309-00-3
+Pages:         ---
+Contents:      A compilation of QRP circuits from the pages of SPRAT
+               from 1974-1982; considered a classic.
+
+Author:        Drew Diamond, VK3XU
+Title:         Radio Projects for the Amateur
+Publisher:     RSGB
+Year:          1995
+Cost:          $12.00
+ISBN #:        0-646-24547-3
+Pages:         130
+Contents:      30 chapters of projects and techniques for the QRP
+               builder from the Australian point of view, but with
+               parts available almost anywhere.
+
+Author:        Ed Noll, W3QFJ
+Title:         Solid State QRP Projects
+Publisher:     MFJ
+Year:          ---
+Cost:          $12.95
+ISBN #:        ---
+Pages:         ---
+Contents:      52 QRP projects using transistors, FETs, and ICs
+               without requiring extensive electronics knowledge.
+
+Author:        Phillippe Bajcik
+Title:         Reussir ses recepteurs toutes frequences (Successful
+               receivers at all frequencies)
+Publisher:     ---
+Year:          1994
+Cost:          145 French Francs
+ISBN #:        ---
+Pages:         ---
+Contents:      A combination of fundamental theory and construction
+               projects that lean heavily on ICs such as the NE602/4/5
+               and the MC3362.
+
+
+                              ==========
+                    Advanced Design and Text Books
+                              ==========
+
+Author:        Wes Hayward, W7ZOI, & Doug DeMaw, W1FB
+Title:         Solid State Design for the Radio Amateur
+Publisher:     ARRL
+Year:          1986 (originally, 1977)
+Cost:          $15.00
+ISBN #:        ---
+Pages:         256
+Contents:      Advanced fundamentals of solid state design for RF
+               circuitry needed for transmitters, receivers, and
+               allied accessory and control circuits.
+
+Author:        Wes Hayward, W7ZOI
+Title:         Introduction to Radio Frequency Design
+Publisher:     ARRL
+Year:          1994
+Cost:          $30.00
+ISBN #:        0-87259-492-0
+Pages:         383
+Contents:      Fundamental methods of RF circuit design combining math
+               and intuitive methods for practical applications.  ARRL
+               reprint of this 1982 Prentice-Hall publication includes
+               software for solving various design problems.
+
+Author:        Chris Bowick
+Title:         RF Circuit Design
+Publisher:     Sams
+Year:          1982
+Cost:          $22.95
+ISBN #:        0-672-21868-2
+Pages:         176
+Contents:      Practical advanced approaches to the design of RF
+               amplifiers, impedance matching networks, and filters,
+               including Smith chart techniques.
+
+Author:        Doug DeMaw
+Title:         Practical RF Design Manual
+Publisher:     Prentice-Hall
+Year:          1982
+Cost:          ---
+ISBN #:        0-13-693754-3
+Pages:         ---
+Contents:      A systematic treatment of designing practical RF solid
+               state circuits
+
+Author:        Krauss
+Title:         Solid State Radio Engineering
+Publisher:     Bostian, Raab, Wiley
+Year:          1980
+Cost:          ---
+ISBN #:        0-471-03018-X
+Pages:         ---
+Contents:      Considered a very good design book for RF solid state
+               amplifiers
+
+Author:        Ulrich L. Rhode & T. T. N. Bucher
+Title:         Communications Receivers:  Principles and Design
+Publisher:     McGraw-Hill
+Year:          1988
+Cost:          $59.50
+ISBN #:        0-07-053570-1
+Pages:         583
+Contents:      Comprehensive engineering of receiver systems, their
+               characteristics, and their stages, including coupling,
+               amplification, mixing, frequency control, demodulation,
+               and accessory circuits.
+
+Author:        Doug DeMaw
+Title:         Ferromagnetic Core Design & Application Handbook
+Publisher:     Prentice-Hall
+Year:          1981
+Cost:          (out of print)
+ISBN #:        0-13-314088-1
+Pages:         256
+Contents:      Fundamental information on core and inductors using
+               ferrites and powdered iron mixes; rumors of reprint
+               possibilities.
+
+Author:        Jerry Sevick, W2FMI
+Title:         Transmission Line Transformers, 2nd Ed.
+Publisher:     ARRL
+Year:          1990
+Cost:          $20.00
+ISBN #:        0-87259-296-0
+Pages:         247
+Contents:      The fundamental textbook on the theory, design, and
+               construction of transmission line transformers.
+
+Author:        Jerry Sevick, W2FMI
+Title:         Building and Using Baluns and Ununs
+Publisher:     CQ Communications
+Year:          1994
+Cost:          $19.95
+ISBN #:        ---
+Pages:         ---
+Contents:      Construction and application of practical transmission
+               line transformers based on a series of articles in CQ.
+
+Author:        Anatol I Zverev
+Title:         Handbook of Filter Synthesis
+Publisher:     Wiley
+Year:          1967
+Cost:          ca $100.00
+ISBN #:        0-471-98680-1
+Pages:         ---
+Contents:      Considered the basic text on filter synthesis.
+
+Author:        Williams & Taylor
+Title:         Electronic Filter Design Handbook (LC, Active, and
+               Digital Filters), 2nd Ed.
+Publisher:     McGraw-Hill
+Year:          1988
+Cost:          ---
+ISBN #:        0-07-070434-1
+Pages:         ---
+Contents:      A modern network theory approach to filter design
+               covering a wide variety of filter types.
+
+
+                              ==========
+                        General Reference Works
+                              ==========
+
+Author:        Many:  Bob Schetgen, KU7G, General Editor
+Title:         The ARRL Handbook for Radio Amateurs
+Publisher:     ARRL
+Year:          1995
+Cost:          $30.00
+ISBN #:        0-87259-172-7
+Pages:         1200+
+Contents:      A comprehensive reference ranging from basic electronic
+               ideas through advanced amateur techniques; includes
+               over 1000 drawings and photos, with many reference
+               tables and charts; revised annually; completely
+               rewritten for 1995
+
+Author:        William I. Orr, W6SAI
+Title:         Radio Handbook, 23rd Ed.
+Publisher:     Sams
+Year:          1987
+Cost:          $39.95
+ISBN #:        0-672-22424-0
+Pages:         600+
+Contents:      A basic reference (and successor to the Jones Handbook)
+               of longstanding reputation on most facets of radio
+               electronics for amateurs.
+
+Author:        RSGB
+Title:         Radio Communication Handbook
+Publisher:     RSGB
+Year:          1982
+Cost:          $35.00
+ISBN #:        ---
+Pages:         600+
+Contents:      The respected British counterpart of US handbooks for
+               radio amateurs containing broad coverage from basic
+               concepts to practical circuits.
+
+Author:        Frederick E. Terman
+Title:         Radio Engineers' Handbook
+Publisher:     McGraw-Hill
+Year:          1943
+Cost:          (out of print; see library or used book stores)
+ISBN #:        ---
+Pages:         1019
+Contents:      "Essential theory, standards, practice, and data for
+               the radio and electronics engineer;" a classic of
+               fundamentals.
+
+
+

+
+
+ Go to Amateur Radio Page
+ Return to Home Page
+
+
+

Topics: Books


+ + diff --git a/content/edu/edu.html b/content/edu/edu.html new file mode 100644 index 0000000..67e190f --- /dev/null +++ b/content/edu/edu.html @@ -0,0 +1,47 @@ + + + + + + Amateur Radio Continuing Education Index + + + +
+

Amateur Radio Continuing Education

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Some 35 years of teaching have given me an abiding interest in the continuing education of radio amateurs. As an Educational Advisor to the ARRL, I have prepared since 1992 an article for each of the annual Proceedings of the National Education Workshop. Because these volumes do not see a wide circulation, and because the articles I have contributed might have a useful note or two within them, I am placing them here. Readers should make an attempt to look through the entire contents of the series for other very useful and insightful articles, full of tips and techniques to make ham teaching--both before and after licensing--more effective.

+

A number of the articles contain references to web sites, periodicals, vendors, clubs, and other sources having addresses. Such information grows stale and outdated fairly quickly. However, ARRL and QST are 2 enduring sources for updated information. Web search engines are another good source of what is current.

+

The published items are linked from the bibliographical list below.

+

"A Short Tale About the Family, the Fox, and the Moxon" Proceedings of the 2002 National ARRL Education Workshop, (Newington: ARRL, 2002), pp. 95-99

+

"Youth Teachers and Tutors; or Elmer Does Not Have to Be an Adult" Proceedings of the 1999 National ARRL Education Workshop, (Newington: ARRL, 1999), pp. 81-84

+

"The Internet as a Teaching Tool: Using It Well" Proceedings of the 1999 National ARRL Education Workshop, (Newington: ARRL, 1999), pp. 76-80

+

"QRP: A Newcomer's and Old-Timer's Challenge" Proceedings of the 1998 National ARRL Education Workshop, (Newington: ARRL, 1998), pp. 30-38

+

"Introducing the "All-Band" Doublet: What the Student and the Instructor Should Keep in Mind" Proceedings of the 1998 National ARRL Education Workshop, (Newington: ARRL, 1998), pp. 39-46

+

"Antenna Modeling Programs as Teaching Tools," Proceedings of the 1996 National ARRL Education Workshop, (Newington: ARRL, 1996), pp. 28-35

+

"Why 0.707? Teaching R.M.S. Values of AC Voltage and Current," Proceedings of the 1995 National ARRL Education Workshop, (Newington: ARRL, 1995), pp. 33-40

+

"Beyond the License: Teaching the Principles of Effective Station Design," Proceedings of the 1994 National ARRL Education Workshop, (Newington: ARRL, 1994), 15-22

+

"The Blackboard Jumble," Proceedings of the 1993 National ARRL Education Workshop, (Newington: ARRL, 1993), 27-34

+

"Continuing Ham Education," Proceedings of the 1992 National ARRL Education Workshop, (Newington: ARRL, 1992), pp. 34-41

+
+ +
+

Updated 09-06-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

The availability of on-line information varies with time, with some sites appearing and others disappearing. One of the more durable and useful sites is the following one from Australia;

+

Radio Electronics School (web.archive.org): a many-section course on the fundamentals of electronics for new amateur radio operators.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Education


+ + diff --git a/content/edu/edu1.html b/content/edu/edu1.html new file mode 100644 index 0000000..abc18c5 --- /dev/null +++ b/content/edu/edu1.html @@ -0,0 +1,74 @@ + + + + + + Continuing Ham Education + + + +
+

Continuing Ham Education

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Since the advent of the VEC program, there has been a dramatic reduction in the availability of quality technical self-instructional materials for radio amateurs. Part of the decline owes to the concentration of instruction upon the licensing process, which involves only rudimentary technical information presented in fragments. Although this presentation parallels the structure of the license examinations, it fails to give students any sense of the fact that communications electronics consists of a coherent and interrelated set of ideas, formulas, and techniques. Another part of the decline in available self- instructional material derives from concerns about the growing median age of licensed hams. Consequently, great and appropriate effort has gone into recruiting potential hams from among the nation's youth. The program, whose success is becoming apparent in license statistics, has taken energy from the next step in amateur education: post-licensing education in the basics of communications electronics. +

THE CLIENTELE

The consequences of the lack of suitable instructional materials are many. Recently licensed amateurs have difficulty understanding the technical articles in QST and other amateur radio journals. Many of these amateurs feel that the space is wasted and clamor for more general interest articles. At one time, hams raised an equal clamor for more technical articles and more thorough technical articles. With few resources to ease the way into understanding the technical fundamentals of amateur radio, quality assurance of amateur signals rests more with the manufacturer's ability to make foolproof equipment and less with the individual amateur's ability to correct technical difficulties. Accompanying the reduced ability comes a potentially reduced appreciation of the importance of bringing signals into line with regulatory specifications. None of these situations, however, should be interpreted as meaning that hams, in general, do not want to know. +

Despite the absence of suitable materials for amateur instruction beyond the requirements of licensing, significant numbers of hams do wish to learn the technical aspects of their avocation. Informal questioning of amateurs in my local region has produced some interesting facts about the desire to learn. At least 1 percent and perhaps as many as 5 percent of the hams in the area at any one time wish they could participate in some form of electronics education related to their interests in amateur radio. If one were to extrapolate from these figures that in any one year 1 percent of U.S. hams would participate in self-instruction or local classes, sales of instructional texts would number almost 5,000 per year, enough to ensure a suitable return on the investment in publishing such materials. If consciousness-raising and recruitment of interest are added to these unsolicited expressions, then sales and activity would be considerably higher.

+

The potential clientele for amateur instruction shows little demographic differentiation. Hams of all ages, from teens to retirees, equally express interest in further ham education. In real classes that extend for several weeks, the drop-out rate is highest among those in their 30s, who have a combination of jobs and children to divert them from their interest. Otherwise, attendees remain loyal to the class if instruction is good and if interest in the student as an individual is a key ingredient in the teaching. Classes for amateur licensees show little, if any, signs of socio-economic differentiation beyond that encountered among the amateur population as a whole. The understanding of a mystery--a very appealing mystery of how something magical works--has much of the appeal that it had in the early days of radio. It is an appeal without the boundaries that separate many other activities in society. I personally have taught college professors and plumbers in the same class, and they had much the same attitude and interest.

+

If these informally gathered data hold true over the amateur population as a whole, then the success in fulfilling the need for post-licensing amateur radio education will depend upon the quality of the materials and assistance we provide.

+

THE NEEDS

Individual and informal group instruction in radio fundamentals requires one or more texts written expressly for this purpose. Modern circumstances both of communications technology and of activities permitted under amateur service licenses strongly suggest that the older practice of combining all radio fundamentals in a single text is no longer practical or effective. In addition, the goals of self-study or small group informal education suggest that a single volume might be self-defeating, overwhelming the ham who wishes to increase his or her know-how. Therefore a series of texts, each covering a significant segment of the fundamentals of communications technology, appears best to describe the need. +

Existing self-instructional materials do not meet the needs of amateur radio licensees. Current licensing manuals consist largely of questions and answers from the examination pool. In almost all such manuals, excluding the A.R.R.L. study guides, the only text is a brief explanation of the correct answer to a given question. Only League guides provide connected text to introduce ideas in a reasonably coherent manner, but the scope of these guides precludes the development of crucial basic ideas in radio communications. For example, the General Class guides have yet to introduce the concept of Q and its importance to many facets of radio work. Resonance, too, is missing. Wave conditions on feedlines is nowhere seen. Little wonder new licensees have many misconceptions of how things actually work if all they have read is a license guide. This is no criticism of such guides. They were never intended as substitutes for appropriate instructional materials.

+

Perhaps the two best basic texts for hams were Bob Shrader's Amateur Radio: Theory and Practice and George Grammer's A Course in Radio Fundamentals. Both are unavailable, and neither may be truly apt to the contemporary need. Shrader's book was keyed to older FCC study questions and was only as comprehensive as that question pool. As a one-volume coverage of amateur electronics, it could not address crucial points as leisurely as might be desirable. Yet, its thickness gives it a formidable appearance. Grammer's book is an A.R.R.L. classic and is still a model of lucidity and important detail. However, its World War II origins show, as the world of amateur radio electronics has widened almost beyond belief. The development of amateur radio instructional materials requires rethinking to capture the best of these books while meeting today's new circumstances.

+

Self-instructional materials in electronics abound. NRI and CIE have offered home instruction courses for as long as most hams can remember reading electronics magazines. Heath transformed its excellence in writing kit-building manuals into equally excellent self-instructional materials. However, commercial materials aim at a general electronics education sufficient to prepare the student for work as a technician across a broad spectrum of the overall field. Topics of special interest to hams occur only as advanced or specialized instruction, or they do not appear at all. Although these self-instruction courses are excellent at what they do, they do not immediately meet the needs of amateur radio licensees.

+

Even if there were suitable self-instructional texts, continuing ham education would have other needs as well. If the texts are to serve small group informal instruction as well as self-study, volunteer instructors would greatly benefit from instructor guides. Volunteer instructors very often have insufficient background or time to develop lesson plans, to create classroom-size visual reinforcement materials, or to design effective classroom demonstration experiments. The cause of good instruction creates a need for guides to assist instructors in their efforts.

+

The development of materials requires oversight and coordination. The use of those materials in group situations also calls for assistance and coordination. The fulfillment of these needs creates its own need for an effective organization of volunteers and others to ensure the successful production of materials and the establishment of classes for hams.

+

THE PLACE OF THE LEAGUE IN CONTINUING HAM EDUCATION

Fulfilling the needs of post-licensing amateur radio self-instruction and informal classes will require two coordinated developmental efforts: 1. creation of written instructional materials and supplements, and 2. organization of the people who are committed to and involved in various aspects of the instructional program. No organization inside or outside amateur radio is qualified to take on such a task except A.R.R.L. With access to writing and teaching talents, with access to clubs and other potential sponsoring groups, with experience in recruiting, teaching, and licensing new hams, with publication experience and facilities, with a staff experienced in dealing with amateur radio licensees, and with a membership that includes the single largest collection of U.S. hams, the League is positioned as no other commercial or nonprofit organization to undertake such an effort. +

The activities required to develop a continuing ham education program represent a major addition to the current primary challenge given to the A.R.R.L. Educational Activities Department. It is possible to implement such a program in stages, reevaluating each stage before beginning the next. 1. The first stage, which is key to the entire program, is the development of texts. This stage requires oversight, recruitment of writers, determination of the basis of writer efforts--pay, volunteer, other--and coordination of publishing efforts. 2. The second stage would be the development and publication of instructional guides for use with the texts in classes. This stage might be undertaken solely as a service to affiliated clubs and potential instructors, even if the League determines to limit its activity in this field. 3. The third stage--which includes active recruitment of Educational Advisors to serve this effort, continuing assistance to sponsoring groups, and other activities associated with a continuing education enterprise--requires the greatest commitment of long-term League energy. Division of the project into stages represents one way in which the League may cautiously enter into such a program of post-licensing technical education.

+

BOOKS

Without adequate written materials, no educational program can succeed. The fundamental materials necessary for post-licensing amateur education are a series of texts which segment basic communications electronics into logical teaching units. The specific units chosen should reflect practical as well as theoretical considerations. For example, in the following proposed scheme, the subject of digital information techniques precedes basic VHF and UHF techniques. The reason for this progression stems from the tendency of newer Technician class amateurs to enter into packet and other digital modes early on. They use commercial equipment for RF generation and reception, while developing interfaces or interconnections with their computers and packet modems. Thus, understanding packet and its requirements is a more immediate need than understanding the nonadjustable transceiver that sends and receives packet. Similar considerations apply to the exact placement of every volume in the series. +

There are numerous subdivisions one might use to teach electronics, but the following scheme has several advantages. First, each text presents a coherent topic which permits the student to increase his or her knowledge in a systematic way. Each avoids the temptation to collect a hodge-podge of information that lacks the proper connective threads. Second, the series of texts as a whole shows a similar developmental pattern. Third, the topics parallel in numerous ways the material in the A.R.R.L. Handbook, which allows students to read more deeply into a subject. Should an alternative scheme be chosen for a collection of texts, it should be educationally defensible in similar terms.

+

1. Basic DC, AC, and RF Circuit Concepts: This is the basic volume of the series and covers fundamental circuit concepts and the action of most major passive components. It would introduce Ohm's Law and related topics, AC and RF phenomena, reactance and Q, resonance, filters, transformers and coupling, and impedance matching.

+

2. Analog Circuit Concepts and Amplifier Devices: The second volume would introduce the concepts of amplification and oscillation, along with the basic amplifying components: the transistor, the FET, and the vacuum tube. It would thoroughly cover low and high power amplifying circuitry and biasing amplifiers for each class of operation, along with adjunct topics such as positive and negative feedback, spurious oscillation, frequency limitations, amplifier types, and the op amp.

+

3. Digital Devices and Techniques: Volume three introduces the reader to digital integrated circuit functions and to the dominant lines of digital ICs. Beginning with gate functions, the volume would not only provide insight into the available functions and combination of functions, but would demonstrate practical circuits for ham applications. It would also cover specialized digital ICs found in amateur use and explain basic computer and memory chips.

+

4. Basic Antenna and Feedline Concepts: If one considers the A.R.R.L. Antenna Book a reference manual and Maxwell's Reflections a special purpose advanced text, then a truly basic introduction to the fundamental concepts of antennas and feedlines does not exist. Such a volume would introduce antenna energy conversion independently of antenna type, later relating the properties of practical antennas to basic concepts. The text would also introduce transmission line concepts independently of past misconceptions. These fundamentals would expand to include specialized antennas, such as ground-mounted verticals (and arrays), beams (both parasitic and driven), and others; impedance transformation; and transmitter-to-line impedance matching.

+

5. Digital Information Techniques: This volume introduces digital information techniques ranging from CW to RTTY, AMTOR, and Packet, along with information on specialized telemetry and other modes of encoding RF signals with decodable data. Included would be information on the principles of encoding and practical techniques for accomplishing the goal, with supplemental details to prepare the amateur to participate intelligently and successfully in each mode of operation.

+

6. Voice and Picture Modulation: Analog information encoding upon RF signals is a companion to the preceding volume and would explain the dominant methods of modulating and demodulating RF with decodable voice and picture information. Double side-band AM, SSB, and FM would dominate the volume, although the volume should permit the reader to appreciate the entire spectrum of modulation types included in FCC regulations, along with practical circuits and techniques for implementing them.

+

7. Basic Transmitter and Receiver Design: With the conceptual building blocks established so far, the reader is prepared to understand the basic concepts used in the design of modern transmitters and receivers (or transceivers). Historical designs (such as regenerative receivers and frequency-multiplying transmitters) could well illustrate both design objectives and limitations. However, the circuits and overall functional flow of modern units would be stressed to encourage understanding of equipment typically used by amateurs.

+

8. Basic VHF, UHF, and Microwave Techniques: This volume would introduce hams to the special considerations common to VHF, UHF, and relevant microwave equipment, circuits, and devices encountered by radio amateurs. The coverage would include receivers and converters, transmitters and transverters, and antennas and feedlines, with appropriate mention of safety precautions applicable to frequencies above HF.

+

9. Basic Test Equipment and Techniques: Completing the series would be an introduction to the basic concepts, circuits, and instruments used to measure electronic phenomena. The text would emphasize instruments reasonably available to amateurs and techniques amateurs might use to measure relevant but special parameters, such as reactance and impedance.

+

The overall format of the proposed texts might well be the current A.R.R.L. standard: 8.5 by 11 inches in size with two columns of text and variable size graphics to sustain interest in the page. Each volume would run 100 to 150 pages, divided into several chapters. Wherever possible, photographs should complement graphics and circuit diagrams to familiarize the reader with the appearance of components, circuits, and instruments. Each text chapter would include the following: 1. presentation and illustration of basic concepts and relationships, 2. extended explanations of critical ideas, 3. notes on the relationship of the current concepts to others in electronics, 4. sample practical applications with actual and usable circuits, 5. experiments the reader can perform, where applicable, and 6. references to other books for further information on the subject.

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Mathematics is inevitable in any electronics text: in these texts, formulas may run to reasonable complexity so long as explanations of the terms and relationships are given. However, for mathematics beyond high school second-year algebra (for example, polar notation, complex trigonometry, and statistical notations), an appendix or a side bar in the chapter should explain the rudiments of notation and procedure to orient the reader. Calculus should not be necessary.

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ADJUNCT INSTRUCTIONAL MATERIALS

As an adjunct to the texts, it might well be possible to design or adapt computer programs in BASIC to perform calculations demonstrated in each text. There are many public domain programs covering basic electronic formulas up through calculations of amplifier parameters and transmission line functions. There are two ways of presenting these programs: 1. as a collection of independent programs, and 2. as a coherent program under a single master menu per text. Without much difficulty, a programmer of moderate experience could write a master menu program to link the program collections in each text. The result would be a reasonably comprehensive computer program for basic amateur radio mathematics. +

The use of the proposed texts in informal classes taught by volunteers sponsored by local radio clubs or similar groups requires little more of the student than attentive reading and listening, abetted by hands-on experience. However, much is required of the average volunteer instructor who often has little teaching background. Therefore, instructors need guidance in the use of the texts in classes, which calls for a series of instructor guides. The current A.R.R.L. guides for Novice/Technician classes and for General classes are two variations on the guidance theme. The guides should be keyed to individual texts in the series and contain lesson plans for each unit of material. Each plan should include a teaching time estimate, a set of objectives, requirements for teacher preparation, a list of required materials, and a list of classroom demonstrations and experiments. The last element, the demonstrations, should be outlined in detail, with hints on how to make them effective in a classroom. In addition to these detailed lesson plans, the instructor guides should also have a master plan for the entire volume and other information to assist prospective instructors to estimate and plan for the duration of the class term. Each guide should also contain graphics that the instructor can use in the classroom, either by photocopying pages from the guide or by transferring the graphic to an overhead projector transparency.

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In addition to the specific guidance needed to teach each text, instructors should have access to more general assistance in teaching classes of this type. Such material may be appended to each volume, or a master instructor's manual might be produced. Such a manual would be similar in relevant content to the current League Instructor's Manual, with adjustments made for the differences between conducting licensing classes and teaching continuing education classes. Among the new material might be how to retain student interest and loyalty in a longer term class, how to master mathematical operations, how to use hands-on experiments in class to reinforce the relationship of theory and practice, how to learn the needs of individual students to make teaching more effective, and a number of other topics.

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OVERSIGHT, ASSISTANCE, AND RECRUITMENT

However modest or extensive, a ham continuing education program requires human effort. Some person-hours will be volunteer; others will be paid staff; still others will be by contract or other temporary paid vehicle. The organization of the program to ensure the most efficient and effective use of all personal exertions also has ramifications for program costs. Even if the initial stages of the program are small, they require the definitive assignment of an A.R.R.L. staff member. The most logical placement of the program is within the Educational Activities Department. The need for a full- or part-time assignment to the program will vary with the workload as the commitment and the program develop. +

For the text phase of the program, the staff member would coordinate writing and publishing efforts to ensure a set of worthy League publications. The staff member would work directly with authors or with a series editor. Similar considerations apply to the writing of instructor guides, although the sources of materials may be more diverse and require extensive contact with instructors and possibly with Educational Advisors in the field. If the program extends (either sooner or later) to extensive field efforts with club or group sponsorship of classes and volunteer instructors, then staff coordination responsibilities will grow almost exponentially. Part of that task will include extensive informational assistance to ensure that groups and instructors have the best and most complete set of materials possible. Another part of the task may well be the recruitment of club sponsors and volunteer instructors to initiate and enlarge educational programs at a local level. Although precise activities may differ from those presently undertaken by the Educational Activities Department to recruit youthful new hams, they will be no less extensive or demanding.

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Any program as extensive as a continuing ham education program requires general oversight. First, the program must meet the terms of League policy as determined by its Board of Directors. Second, the program must be expert, meeting the highest standards of publication and continuing education. Third, the program must be responsive to real needs expressed by individuals and groups of hams throughout the country. Fourth, the actions and products of the program and its personnel must come under periodic review.

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Perhaps the best means of meeting these needs would be a volunteer program planning and oversight committee composed of several different types of members. 1. The committee should include one or more Directors to ensure that all detailed plans meet the terms set by Board policy. Director members would also ensure knowledgeable and regular reporting to the Board on the progress of the program. 2. The staff member(s) assigned to the program should participate fully in the committee's work. Most feedback and problems will likely come first to the attention of a staff member. Too, staff members are most likely to be thoroughly conversant with practical and temporary problems, such as publication delays. 3. Volunteer experts in education and in writing technical materials who are also radio amateurs should be members of the committee. Whether in planning, review, or evaluation, these members can best assure that the elements of the program meet the highest standards of technical continuing education. Indeed, part of their task may be to establish these standards.

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The extensive series of texts suggested for the continuing ham education program presents a major writing challenge. To ensure the highest quality writing, each volume should be prepared by a writer of known quality. Coordination of production would be handled by the League staff member assigned responsibility for the program. However, the staff member should not be expected to be responsible also for the accuracy of the technical content and the consistency and quality of the writing style of each volume in the series. Rather, the program requires a series editor for this duty. Consistency of graphics (both type and quantity), terminology, chapter and paragraph size and style, index considerations, allowable volume-to-volume repetition of material, amount and type of mathematical material, and numerous other tasks that contribute to making the series a cohesive whole strongly suggest the need for a series editor whose work would be no less than that of the individual volume authors.

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The associated instructor guides may be a function assigned either to a staff member or to one or more experts in such matters. The requirements for lesson plans built around the texts and the requirements for usable classroom graphics may suggest a collaborative effort. A master teaching guide that would include recruiting and teaching aids may be otherwise assigned. The final products, however, require oversight and editing by a single hand to ensure consistency of style, level, and format.

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A relatively small number of volunteer Educational Advisors (EAs) currently serve the efforts of the Educational Activities Department. Most of these dedicated teachers and teaching experts are concerned with the recruitment and training of youth for entry into the ranks of radio amateurs. If a program of continuing ham education comes into existence and includes assistance for clubs and other groups which sponsor classes, then further recruitment of specialized EAs seems in order. Continuing education of people of all ages and levels of background presents problems somewhat different from those facing teachers of licensing classes. The term of student commitment is longer. The technical level of the material is higher. The balance of understanding and mastering the mathematics of various principles differs from that associated with basic licensing. The required sophistication of classroom demonstrations is much greater. These and other differences strongly suggest the recruitment of specialized EAs with expertise and interest in post-licensing continuing education to supplement the current array of EAs. These volunteers could go a long way toward easing the burden of the program on the League staff member assigned to shepherd it.

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Recruiting clubs and other groups to sponsor continuing education classes for hams requires a continuing effort. In the area of recruiting and teaching potential hams, the Educational Activities Department is already familiar with the formidable task of acting as a liaison with these groups and providing them with timely and effective services. Similar, but largely distinct, activities would be required to assist groups who may take an interest in teaching classes over the material in any of the texts in the proposed series. Servicing instructors and sponsoring groups and making them part of the League family would require a significant commitment of staff time and energy. Nonetheless, providing such services would be as crucial a step to program success as it is in the present programs of the Educational Activities Department.

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BENEFITS OF A POST-LICENSING CONTINUING HAM EDUCATION PROGRAM

The primary benefit of a program of continuing ham education would be, overall, an amateur community whose technical knowledge more closely approximates regulatory expectations. Although amateur radio will always hold an important place for the individual whose principal, if not sole, interest is communications, encouraging and making possible further technical expertise is an equally important aspect of the traditions and the potentials of the service. The joy of understanding may be sufficient reward for some hams. For others, the ability to engage in building or servicing equipment may be the result. Some younger hams may proceed from amateur continuing education efforts into careers in electronics. Hams of many ages may begin to participate in the more experimental aspects of amateur radio, whether these involve digital signal processing, new modulation methods, greater computer-radio interface capabilities, VHF-UHF-microwave experimentation, or satellite activity. The baseline measure of success, however, is simply a closer adherence to and appreciation of the technical requirements of amateur transmitted signals. +

The proposed program of continuing ham education does not compete with any existing educational program. Rather, in a manner consistent with the traditions of amateur radio, the program might help to increase the number of people entering technical electronics careers. In the end, however, such a program--while not applicable to every ham--would raise the general level of technical know-how among individuals and groups throughout amateur radio. That accomplishment would suffice to justify the energy and resources required by the program of continuing ham education. With the VEC program and its associated recruitment and educational activities well-established, the time may be ripe to give full deliberation to this next important step in educational services to the amateur community.

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From Proceedings of the 1992 National ARRL Education Workshop, (Newington: ARRL, 1992), pp. 34-41 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Educational Notes Index
+ Return to Amateur Radio Page
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Topics: Education


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A Short Tale About the Family, the Fox, and the Moxon

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L. B. Cebik, W4RNL

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The number of amateur radio activities in which one can involve all family members, whether or not licensed, is quite large. Field Day comes to mind, with a strong communal sense pervading the operating positions, the picnic tables, and the play area for children. However, my thoughts are drawn to the idea of some special activities in which there is mutual activity between parent and child, to the near exclusion of all else. The activities should let the child participate and give plenty of time for simple togetherness between the family members. Of course, "simple togetherness" is never simple, but involves all of the details of living that make family relationships so natural in their complexity and so complex in their naturalness.

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One such activity is fox-hunting: seeking out the hidden transmitter on VHF--usually 2 meters--by direction finding techniques that range from the simple to the sophisticated. There are periods of detection, in which one listens for and finds the direction of the hidden transmitter. Then there are periods of driving toward it--or at least thinking that one is driving toward the transmitter. These periods are perfect for that combination of ham and non-ham conversations that weave together a hobby and whatever is most important to the family members at the moment. The alternating detection and driving periods build toward a climax: the approach and actual discovery of the transmitter location. Finally, there is family triumph, as all shore the successful climax of the effort. Even if the work does not fall into the prize-winning category, the success is sufficient for all to share.

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+ If this little account sounds a bit glorified, let me share a bit of correspondence: Just a quick note to say thanks for your contribution to the Amateur Radio Community. I built a variation of your 2-meter Moxon antenna design and used it at the local Amateur Radio Club fox hunt - on Saturday, May 5, 2001. +
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+ My son (who has Downs Syndrome) and I came in second place in only 35 minutes! This was our first Fox Hunt. We were beat only by a team of engineering students who do this sort of thing as a regular pass time. The third place team came in at three times the time. +
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+ Much of our success was due to the Moxon antenna, which I scaled to the exact fox frequency using EZNEC. I was actually startled at the depth of the null. Your antenna design and my son's compass brought us to within 20 feet of the "fox" with only 4 readings! +
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+ Thanks again. My son is very proud of the second place award he was given for our effort! +
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I have removed the names of the individuals, but left in all of the other details. Similar parent-child mutual activities are certainly possible, and the benefits--for fully able and for challenged children--are likely impossible to catalog. Even sharing the frustration of not winning a prize and demonstrating the will to try again next time can benefit a youngster of any age.

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Building a Fox-Hunt Moxon Rectangle

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For those who might like to try fox hunting as a family adventure, here is a run down on one way to build a good Moxon rectangle. Fig. 1 shows the basic outline of a Moxon rectangle for 146 MHz using 3/16" aluminum rod elements. The most critical dimension is the gap between the driver and the reflector. It is desirable to set the element pieces to the correct length as the first act in building. +
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The antenna and support details appear in Fig. 2. Looking at details B-B and C-C, we can see the plan of assembly and feeding. The antenna will consist of 4 rods, each threaded to 10-24 on one end. The driver will have pairs of 10-24 stainless or aluminum nuts to hold terminal rings from the feedline. The reflector half-elements will join in a stainless steel coupling nut (a short piece threaded all the way through). You can purchase these or make one from a small piece of 1/2" by 1/2" aluminum stock. Simply drill though the piece from end to end and tap the required 10-24 threading.

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My favorite antenna support material is Schedule 40 PVC. As frequency increases, I like to minimize contact with the material. It would appear that Schedule 40 PVC varies in exact composition from one part of the US to another. In some places, UV retardants are effective, while in others, they are either ineffective or non-existent. Likewise, RF characteristics may vary from one manufacturer to another. By minimizing contact with the elements, any RF deficiencies in the PVC have little or no effect on the antenna.

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In

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, you can see the scheme I used. 1/2" nominal PVC is glued into a T, with elbows pointing upward in the sketch. The elements pass through end caps. These caps and the pipe stubs necessary to cement them to the elbows permit the use of set screws that pass through threaded holes in the double thickness of PVC. With threading that deep, set screws work well, although other methods can be used to ensure that the element do not move. One system that also works is to use short pieces of plastic tubing over the rods between the PVC supports and the nuts.

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Fig. 2 also shows a center Tee fitting for connection to a mast. This fitting is optional and would be suited more to the horizontal use of the antenna. Lets look at the alternative that I actually used in Fig. 3. When vertically orienting the Moxon, a rear support system is very useful. We can make one up out of more PVC fittings and pipe. For my test antenna, I used a single PVC pipe section between elements, with the reflector center point holding a 4-way cross fitting. Another pipe stub proceeds rearward and friction fits into the Tee in the support. I drilled two sets of holes through the stub so that I could change the antenna's orientation from vertical to horizontal and back by removing only a single bolt.

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The support consists of a straight section and an angular section, forming a strong triangle. The terminating sections are 1.25" to 1/2" adapters sections. The antenna support pipes fit into the 1/2" side ports, while the 1.25" through sections receive piping of the same size to fit over a standard TV mast. Clamps mounts are shown, although one might also use set screws. The space between the upper and lower adapters can consist of the short clamps pipe sections shown, or the space can be filled with a single section of 1.25" nominal PVC. The resulting structure has a bit of flexibility, but stands up to abuse very well.

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One of the keys to building a good PVC structure is to be prepared in advance for aligning portions of the structure that must be at right angles or parallel to each other. PVC cement may give you as little as 15 seconds before glued parts become immovable. I have cataloged a number of right-angle junctions in my shop that are suitable for aligning PVC pieces. Among them are legs and other supports for the work bench. If a Tee or an elbow requires fitting, I usually put a scrap of pipe dry into the open end. The longer section makes alignment much easier than a junction stub. I simply glue the junction in question and then press it against my sturdy pre-formed angle.

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For the element mountings in their caps, I first cemented the junction pipe stubs in the caps. (These stubs will be glued into the elbows later.) Then I drilled the caps and stubs together. A drill press makes easy work of centering the holes on both sides of each cap. Next, I pushed each pair of caps over a scrap of 3/16" diameter rod to keep them aligned while cementing each one into its corresponding elbow joint. These and similar techniques simplify making almost any conceivable structure from PVC parts.

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Bending rod elements is most simply done with a copper tubing bender, a small device that can be found at most hardware depots. The bender will make a 1" radius bend. 3/16" rod and smaller will easily handle bends of this radius with no noticeable weakening or visible cracks. I first cut each element section to length and mark the point (away from the threaded end) that corresponds to one half the side-to-side width. I placed this point in the middle of the 90-degree bend. This technique has yielded results identical to those predicted by sharp-cornered computer models of the antenna.

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There are many ways to construct the Moxon for VHF use. The sample shown here is only one of them. For an alternative construction method, with many useful additional notes on the design, see "A Compact Two-Element, 2-Meter Beam" by Lee Lumpkin, KB8WEV, and Bob Cerrito, WA1FXT. The article appeared in the January, 2000, QST, pp. 60-63. Their version used #10 AWG wire, which is just over 0.1" in diameter.

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The Moxon can be scaled for 220 or 440 MHz use--so long as one remembers also to rescale the element diameter or to make appropriate adjustments in dimensions if a scaled element cannot be used. The thinner the wire relative to the original, the smaller the gap; the fatter the element, the wide the gap. And other dimensions will also alter slightly to obtain the maximum null at the new design frequency, with the resonant point slightly lower to obtain full operational coverage of a band or the subsection of interest.

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Why a Moxon?

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The basic azimuth pattern of a Moxon shows, at its design frequency, a deep null, with some forward gain. For most VHF uses, it is the pattern shape, with its very high front-to-rear ratio, that holds more interest than the antenna's gain. Fig. 4 reveals the azimuth pattern of a 2-meter Moxon when the antenna is vertically oriented and, hence, vertically polarized. The model is designed for 146 MHz and the deepest null occurs only in the vicinity of the design frequency. Hence, you may wish to scale the antenna for the precise frequency on which fox hunts are conducted in your area. +
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For general use--horizontally or vertically, the front-to-rear ratio--accounting for the full rear quadrant--is very good anywhere in the band. Moreover, as Fig. 5 shows, the antenna has a very broad operating bandwidth. The SWR curve never reaches 1.4:1 anywhere in the band.

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The first task after placing all of the Moxon element pieces in their PVC holders and attaching the feedline is to adjust and temporarily lock the gaps between element ends. The first rod Moxon showed a 50-Ohm resonance at about 145.75 MHz, just about where the design placed it.

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It is usually dangerous to assume that, because an antenna is tuned to provide a good match for the feedline, it will also show the modeled gain and front-to-back ratio. However, in this case, the antenna geometry that determines the source impedance also determines the pattern shape. Since the elements were uniform in diameter, there was no reason to expect any performance surprises. Therefore, I locked the assembly tight and moved on to performance tests.

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The Knoxville, TN, area has repeaters from close to 145 MHz up to nearly 148 MHz. All of them are easily accessed and heard at full quieting from my location with only a low elevation ground-plane vertical. In fact, a telescoping whip on my hand-helds will access all of our main repeaters. On a 15' mast, the Moxon made "telephone" copy of all of the repeaters when the antenna pointed anywhere near the forward direction to them. A distant repeater that I hear poorly on a vertical was now full quieting. The Moxon's gain can make a difference for signals at the FM threshold.

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When the antenna faced away from the repeaters, only 1 of 6 repeaters that I checked could still be heard, and then at far less than full quieting. I could not access any of the repeaters with 5 watts of power--the limit of my gear at the time. I ran additional tests using two hand-helds on simplex across the FM portion of the band. Differences in the patterns at the band edges and at the design frequency were not especially detectable at distances of a quarter mile. Face forward, communications was easy and full quieting. With the antenna pointed in the other direction, communications was virtually impossible.

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The proto-type vertical rod Moxon has proven a very effective antenna at blocking unwanted signals from the rear. In fox-hunting, it is precisely the deep null to the rear that let's us take a bearing on the hidden fox transmitter. Whether distant from the fox or close in, the deep null--combined with a compass--will serve well in locating the fox's direction without any ambiguity.

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I shall leave the details of setting up the Moxon for mobile fox-hunting to your ingenuity. Some folks use a system involving a auto-window mount support, and it may also contain a large compass rose. Set the compass rose with a compass at each stop or reading period and then take the null of the fox. Using an antenna backwards takes a little getting used to, but quickly results in accurate bearings on the fox. Now if only the roads went to the fox as the crow flies, we could win every fox hunt in a flash (well, a slow flash within the speed limits).

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Back to the Family

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I have dwelt on building a Moxon for fox-hunting to show that with a little effort, one can set up a family activity without much cost. It takes equal effort to set up the activity so that it accomplishes your family goals. You may wish to try an initial fox-hunt alone to get used to the the antenna and the other aspects of how the hunt is conducted. Then you can concentrate on the total activity, including the involvement of any children, when the family takes to the fox's trail. +

As in the communications that I received, you can let the child operate the antenna and compass, building their confidence in their abilities to contribute to family success. I remain convinced that the self-confidence of children as they grow older stems not solely from succeeding in games and activities with their peers. It also grows with every successful contribution they make to the success of any activity that the family deems to be important. As well, successful contributions to the fox hunt may also intensify their interest in amateur radio as a life-long means of making contributions to the larger family that we call community and society.

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Fox-hunting is not the only way to achieve such goals, but it is a good case in point. Amateur radio is filled with opportunities for service and for full family participation that includes both the licensed and non-licensed members. I am indebted to a father and son for reminding me of this important aspect of our avocation.

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From Proceedings of the 2002 National ARRL Education Workshop, (Newington: ARRL, 2002), pp. 95-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Educational Notes Index

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Return to Amateur Radio Page

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Topics: Education, Moxon, PVC


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The Blackboard Jumble

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L. B. Cebik, W4RNL

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+ Teaching aids for amateur radio classes are within easy reach of almost every instructor. Less easily reached is an understanding of how to make the very best use of each kind of device to help students absorb, retain, and interconnect the bewildering array of wonderful information handed out in class. From the point of view of the ham instructor, who may not have long experience in the classroom, choices among teaching aids may seem arbitrary. Use the chalk, if it is handy. Make up a batch of overhead transparencies or large charts to save class time. Photocopy or create reams of handouts so students can carry home reinforcements of the class lessons. Box up a collection of components, power sources, and meters to demonstrate various principles. Such is the stuff of teaching. +

After a few classes, an idea begins to develop: each kind of teaching aid has its own best use. If only I had realized this before my first class, I might have been more effective in getting my students to truly understand the things I take for granted in amateur radio. Even the ubiquitous blackboard that is available in most classrooms (although it is often green today) has its own special strengths in teaching. The jumble of writing crammed into every corner of the surface, with circuit and block diagrams plopped here and there, just has to stop and get organized. But how?

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My own experience in 30 years of teaching both ham radio and other subjects suggests that the answer to this question comes in two parts. First, we need a general idea of the best way to use each of the generic types of teaching aids. Just as our wood shops have many different tools, each with its own set of purposes, so too, not every teaching tool is good for every teaching job. Once we understand these basics, then we can begin the main task: to make the blackboard something more than a catch-all for everything that does not seem to have a better home. We shall discover that, despite its reputation for being old-fashioned, the blackboard is an excellent teaching tool for special tasks that none of the more modern teaching aids can do quite as well.

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COMMON TYPES OF TEACHING AIDS

There is such a large assortment of teaching aids that we cannot possibly deal with all of them here. Let us specify that the kinds of teaching aids of most concern here are those that help us along in the course of teaching a certain lesson plan, perhaps something about basic electrical principles. Films and videotapes that might teach the whole lesson for us are thus set aside for now. So too are numerous other learning activities that might also have a place in the teaching schedule, for example, guest experts on certain modes of operating, hands-on lessons in soldering circuit boards or making wire antennas, and many others. +

Still, there are at least four general categories of teaching aids we might use in everyday fashion: handouts, overhead transparencies and other pre-prepared charts, demonstrations, and our old friend, the chalkboard. Each of these has a place in reinforcing lessons and in supplementing the class textbook. Let's take a brief look at each category.

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1. Handouts. With easy access to photocopy machines and services and with a computer to invent new collections of ideas, instructors are often tempted to inundate their students with handouts. Too many sheets, however, can be as bad as none at all. The student drowns in a sea of words, overwhelmed rather than enlightened. Reprints, extracts, outlines, and charts--usually handed out at either the beginning or the end of class- -fill the student's notebook. But does the information fill his or her head in a useful way? The object of a handout should be to organize special information, either in class or later.

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My own preference (and certainly there is much room for other ways of doing things) is to use handouts for two main purposes: to outline the lesson so that students can follow along and keep their place and to provide special collections of information that organize data in useful ways that our classroom text does not. The idea of a class-organizing outline is fairly straightforward and may include references to the text pages covered, exam questions covered (if relevant), and possibly suggestions for further reading, study, or experimentation. Special collections of data require a word or two more.

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+ Fig. 1. Sample partial handout on electrical phenomena and units of measure. The actual handout would include more entries and additional information. +
Electrical PhenomenonAbbrev.Basic Unit of MeasureAbbrev.Common Fractional Units
Voltage; or electromotive force (e.m.f.); also called Tension or PressueEVoltVmV (milliVolts), µV (microVolts) [both common in receiver work]; kV (kiloVolts) [common in power amplifier work and in electrical power transmission line work]
CurrentIAmpere (Amp for short)AmA (milliAmps), µA (microAmps) [again, both common in receiver and other low power work]
ResistanceROhmOhmkOhm (kilOhms), MOhm (MegOhms) [common resistance values in all work]
CapacitanceCFaradFµF (microFarads) [power supply, audio, and timing capacitors when in whole numbers; by-pass capacitors when expressed as 0.XX values]; pF (picoFarads) [most common in HF tuned circuits and filters]
InductanceLHenryHmH (milliHenries) [common in audio frequency circuits and some RF chokes]; µH (microHenries) [HF and VHF RF circuits]
+

Consider Fig. 1, a partial table of basic electrical phenomena, units of measure, and abbreviations. Anyone can extend and complete this table to the exact degree needed by the students of any particular class, which is one important dimension of handouts: gear them to the exact needs of the students, not to some general parameters of electronics. Different classes, say, for novices and technicians as opposed to extras, may need different information or levels of information.

+

Handouts are also useful for including important bits of information passed out verbally in the classroom, and they can key a remembrance of explanations. For example, listing the alternative words for voltage might help a student remember that the British like the word "pressure" and thus prevent a confusion if that person reads an R.S.G.B. publication. The student might also remember what is "tense" about a high tension line. In this way, the student begins to draw into a more comprehensive circle the bits and pieces of electrical terminology he or she has met along life's way.

+

2. Preprepared Charts. Charts that the instructor brings to class, whether on paper or as overhead transparencies, should have a different look than handouts. They have a different purpose, namely, hitting and organizing the critical high points in any body of information. Comparing Fig. 1 and Fig. 2 shows something of the difference in appearance. The transparency has less information on it, but the information it does have stands out in higher relief.

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ Fig. 2. Sample of a partially finished table used as an overhead transparency or as developed on a blackboard. See text for techniques of development. +
Electrical PhenomenonAbbrev.Basic Unit
+ of Measure		Abbrev.Common
+ Fractional Units
Voltage or electromotive
+ force (e.m.f.)		EVoltVmV, µV, kV
CurrentIAmpereAmA, µA
ResistanceROhmOhmkOhm, MOhm
CapacitanceCFaradFµF, pF
InductanceLHenryHmH, µH
+
+

Of course, a good chart or transparency should have lettering large enough for all to see. That is why photocopying book pages onto transparencies often fails to help students in class: they just cannot read the text comfortably. However, computers with bold, large, vivid print fonts let you create truly striking transparency masters.

+

Moreover, the chart or transparency is never a substitute for the presence and activity of the teacher. Only the teacher can look the students in the eye and see confusions and questions the person is too shy to ask. Also, it takes a teacher to show the students how to navigate a chart or table full of information. As a matter of personal preference, I would use a finished table like Fig. 2 only as a review sheet, not as my primary aid to teaching the information. For that task, I prefer a blackboard (for reasons that will appear in just a few more paragraphs).

+

For more excellent information on using transparencies, see an earlier volume of this series, The ARRL National Educational Workshop, specifically, 1992. Chester S. Bowles, KD1AP, does an excellent job of providing tips on making and using these charts in his article, "Creating and Using Overhead Transparencies," on pages 21-25.

+

3. Demonstrations. Demonstrations come in many forms, from showing amateur communications techniques with real equipment to giving students the chance to practice soldering circuits. The keys to effective demonstrations are simplicity and size. First, do not try to cover too many things in one demonstration. Teaching the entire instruction language of Packet on the first demonstration repels rather than attracts future users. Likewise, introducing students to vector calculations of resultant currents in AC-powered circuits with resistance and reactance as their first encounter with Ohm's Law will create more fog than light.

+

Demonstrations must also be sized to the class. A teacher's desktop demonstration of Ohm's law should not use an AAA battery, 1/8-watt resistor, and a pocket VOM, unless the students can each spend some time peering at the setup, hopefully through a magnifying glass. Demonstrations for the class must be large, so that everyone can see well. Or, they must be rigged for passing around the room or being viewed by each student in turn. Rush no one and be ready to answer every question.

+

Review past editions of the Workshop proceedings and other instructional aides produced by the League for some excellent ideas on demonstrations. Many, if not most, of the ideas have come from teachers in the field.

+

4. Blackboards. Is there any work left for the board? The answer is yes. In fact, even if an instructor spends months in preparing his or her ideas, handouts, transparencies, and demonstrations, he or she will spend more time working with the black-, green-, or chalkboard (or the whiteboard with its marker pens) than with all the other teaching aids combined.

+

The most striking feature about a blackboard is that it begins blank (and hopefully cleanly erased by the preceding user). It is ready for anything, whether or not anticipated. No matter how many calculations you prepare for the class on Ohm's Law or resistors in parallel, someone may ask a question that requires one more example. No matter how complete a chart of schematic diagram symbols you give the class, someone will ask about the one not on the list. There are words you thought everyone knew, until you discover a few students spelling "mho" as "mo." Names and addresses of parts and equipment dealers will inevitably be needed one week prior to their planned introduction into the class. Even if you think that there are better methods for presenting certain information, very often the blackboard is the only handy way.

+

The other most striking feature about blackboard work is that you create it as you go. The blackboard is an ideal tool for developing ideas and information in a well-calculated progression, one element at a time. With a marker pen and a blank transparency, we can capture some of this special talent on an overhead projector. I have known wheelchair-bound instructors who have successfully taught everything from math to political science this way. But they have all wished they could have a blackboard instead.

+

The reasons for their blackboard fantasy are two: the position and the eraser. Blackboard writers stand in front of the class and can keep an eye on students to see their responses. Moreover, the chalk eraser corrects errors and permits modifications with the greatest of ease. Combined with some forethought about where on the board to put things and with a sense of neatness to keep material in good order, the blackboard, its chalk, and its eraser provide a tool that permits students to see ideas develop, whether in terms of words, in terms of calculations, or in terms of pictures.

+

THE BOARD AS A DEVELOPMENTAL TOOL

A table saw is an excellent device for ruining perfectly good pieces of wood until we learn how most effectively to use it. Likewise, a blackboard can ruin perfectly good information if we let the data pour forth in a jumble with little rhyme or reason. One of the best ways to avoid blackboard jumble is to think about the board as a method of showing how ideas develop, how they emerge, how they combine to make more complete packages. +

The blackboard, however, cannot substitute for the teacher. Rather, the teacher develops ideas, with the blackboard as his or her developmental partner. Words, together with pictures or writing, provide a reinforced presentation of ideas in the order needed by students for understanding. One of the beauties of the blackboard is that the picture or the writing can precede, follow, or be simultaneous with the talk, according to which order produces the strongest response. There is no general rule here, but experience will gradually give one a sense of the correct order.

+

To see more clearly what good board use requires and to gain a better appreciation of what blackboards can do for teachers, let's take three examples, one each from the worlds of words, calculations, and diagrams. From these examples will spring all the extrapolations you need to use your board more effectively.

+

1. Tables of Terms. Fig. 1 and Fig. 2, shown earlier, represent partial views of complete charts of basic electrical terms for Novices and Technicians. Both the handout and the transparency versions had good uses, but neither seems best for the act of teaching the terms themselves in the context of a classroom. One purpose of the exercise is to teach students to avoid confusing the name of the phenomenon and its abbreviation with the name of the unit of measure and its abbreviation. That requires a student to hear and see each type of term used in its own context. That way, each type of term forms the right language linkages for later confident use and recognition.

+

For this reason, I prefer to develop the table of terms in the figures on the blackboard. The order of development goes something like this:

+

Step 1. Put the column headings on the board, along with explanations of why the chart requires 5 columns. This task involves distinguishing phenomena from units of measure, with analogies to common measures. For example, length has more than one basic unit of measure (feet or meters), and we might see a blueprint with the notation "L (meaning length) = 3'6" or something similar. When terms are brand new, as they often are for potential hams, this sorting process may be critical for preventing confusions before they occur.

+

Step 2. Introduce the first term, in this case, voltage or electromotive force. As I explain e.m.f., with some sense of what the phenomena is, I introduce the abbreviation, E, so students will see its connection. Then I add some remarks on tension and pressure so that students can coalesce similar ideas with multiple names under a single heading.

+

Step 3. Introduce the unit of measure, here the volt. Mentioning Volta and the naming of electronic units (but not many phenomena) after pioneers in the field gives students a handle for distinguishing unit terms from phenomenon terms. Most abbreviations come naturally.

+

Step 4. Introduce common fractional units, saying something about the contexts in which each might most commonly appear. In this case, each subunit can be explained with or without reference to a complete table of prefixes. Generally, I prefer not to get two tables going at once, since the development of each can interfere with the development of the other.

+

Repeating the process for each term allows the table to grow on the board. If lessons on the basics of capacitance and inductances occur at a future class, I often prewrite the old elements of the table on the board just before class, leaving room to develop the new ones.

+

Working with the developing table is just as important as developing it in the first place. Leave it on the board while you proceed to a related topic, perhaps Ohm's Law. Be sure to ask of your voltage source, "What is the voltage?" Someone is bound to answer, "6." That gives you the perfect opportunity to explain that numbers in electronics (excepting Q) require units of measure. In short, thinking developmentally about using the blackboard as an aid to teaching also allows you to unfold other important and related ideas.

+

2. Calculations. Calculations are a natural for blackboard work. We can put up and erase example after example until students catch on to the idea. Nevertheless, we often do not use the board to full advantage from the teaching point of view. The student needs to understand every little--as well as big--step of a problem. What experience can take for granted and do automatically, teaching cannot. Developing a calculation is not just applying a formula, but as well it is a systematic process of thinking through a problem and reflecting that thinking in an orderly way on the board. Let's assume that we wish to show how to use Ohm's Law with all calculations made in basic units. The development might look like this:

+

Step 1. Lay out the sample measurements and the quantity we wish to find. Be consistent with units, either spelling them out or using the proper abbreviations. For example:

+ 
     Measured voltage:   6 V
+     Measured current:   3 mA
+     Needed:             Resistance in kOhms
+

Step 2. Since we wish to make the calculation in basic units, that is, using Volts and Amps, we have a conversion step here. Whether we place the conversion next to the current entry or as another line of entry is optional so long as the work is neat and the student can see exactly what needs to be done.

+ 
     Measured Current:   3 mA = 0.003 A
+

Step 3. Calculate the resistance in basic units. Until students have mastered the algebraic transforms of Ohm's Law, place the correct form ahead of the fairly simple calculation. Then, let the students call out the answer.

+ 
     R = E   /   I
+     R = 6 V / 0.003 A
+     R = 2000 Ohms
+

Step 4. Finally, add the conversion step to put the answer in the correct units. Again, it is optional whether you use a new line or add the step to the numerical answer line, so long as students are clear about what you did and why.

+ 
     R = 2000 Ohms or 2 kOhms
+

No law requires you to use a vertical scheme for developing classroom calculation, although it does permit alignment of critical elements in the calculation process. Call attention to these alignments to ensure that the student notices them. In other words, take nothing for granted about the naturalness of seeing things in the "common" way. That way is not yet common to most potential hams, but it will become common as a result of your teaching. Thus, it may prove most helpful to students to style your developing calculations to coincide with those the student is likely to see in his or her text and in amateur magazines and books.

+

Once you have constructed enough calculations on the board, you may wish to provide students with some handouts with others: use worked, partially worked, and unworked samples. You can guide them through the process of finishing or making some of the calculations by labeling lines. To make the handout more effective, instruct the student to use a strip of paper to cover all the lines below the one he or she is reading. He or she should move to the next line only when the current one is fully understood. If understanding eludes the student, there is a question for the next class. Tell the student to mark the item and ask about it at the beginning of the next class.

+

Many students are inclined to ask these questions in private, because they are embarrassed about not understanding. Unless the student is especially shy, encourage him or her to ask within the class. That way, everyone benefits from the explanation. My experience has taught me two important lessons. First, for everyone who asks a question, there are five others who refrain, even though they need to ask the very same question. Second, the only foolish question is the one unasked. Try to give your classes the sense of community in which everyone helps everyone else. That more than any other technique seems to break the barrier of silence.

+

Of course, good answers contribute to a student's willingness to ask questions. When you can point to the developing progression of a calculation or a table of ideas to show precisely where something went wrong and how to make it right, you have a key ingredient of some very good answers.

+

3. Diagrams. Most instructors (including me) tend to draw too fast on the blackboard. The simpler the diagram, the faster we draw. In turn, the faster we draw, the less students learn. Speed makes messy drawings. Even more importantly, speed turns our diagrams into mysteries: instead of clarifying principles, speedy drawings obscure them.

+

Developmental thinking can change all that. By treating the drawing or schematic diagram as an orderly, emerging set of ideas, we can use it to familiarize students with the crucial elements that go into circuits and systems, all the while relating each step to basic principles, such as Ohm's Law. To see how this works, let's assume that we wish to illustrate Ohm's Law for a Novice class. We shall use a combination of ingredients, each developing the ideas in parallel. First, there is an experiment on the table using batteries or power supplies, some "unknown" resistors (say, 5-watters, with tape over the value markings), a voltmeter, an ammeter (or milliammeter), and an ohmmeter on the side to check our results.

+

Second, there will be a set of calculations. For this example, we may use the ones just completed. Finally, we shall develop one or more circuit diagrams to help students relate schematic drawings to both real-world components and to the fundamental formulas of electronics. The one thing we shall leave out of this exercise is any sense of hurry.

+

Even without the calculations and the experiment, the principles of developing diagrams still apply. Adding in the other elements reinforces the importance of letting diagrams emerge rather than just appear as a whole. The sample exercise might look like this:

+

Step 1. Start by setting up the power source, perhaps a battery. Then, begin the diagram by showing only the battery or power source. We shall follow this procedure at each step so that students can associate components with their schematic representations. Even if we have previously presented a list of schematic symbols and samples of their live counterparts, showing the correspondence in action can augment that past lesson and add to it a new dimension. Here, students will see the connections that make components into circuits.

+

The first stage of our diagram on the board will thus look like this:

+
+ +
+

Step 2. Add a switch to both the experiment and the diagram and explain its use. Not only will it make and break current flow for our tests, but it will also contribute to our safety in handling the components. So our diagram grows a bit:

+
+ +
+

Step 3. Add a resistor to complete the circuit. This addition shows the basic units involved in our prospective calculation, even though we have yet to add the measuring devices.

+
+ +
+

Step 4. If the students understand the basic idea of a complete circuit, we can then show and explain how the meters fit into the overall scheme. Place a meter across the resistor while explaining why voltmeters are used that way. Then interrupt the line near the resistor with a small erasure to insert the (milli)ammeter. It pays to ensure that students understand that current travels through the meter without significant resistance and hence does not materially affect the accuracy of our work.

+
+ +
+

Step 5. You are now ready to switch on power and make some measurements. With the touch of an eraser and chalk, close the diagramed switch as you turn on the experiment. With the measurements, start the calculation procedure previously outlined. Add the values to the diagram, with the resistor value left open.

+
+ +
+

Step 6. Moving through the steps of the calculation, we can arrive at the value of the resistor. To complete the task, we can erase the question mark and replace it with the value of the resistor. Now to check our work.

+

Step 7. Switch off the power, remove the resistor, and check its value with the ohmmeter. If the resistor was well marked, you can strip the tape to reveal its value. An explanation of tolerances may also be in order. You may even wish to diagram the ohmmeter hook-up.

+
+ +
+

You can now run through a collection of unknown resistors with the ease of placing them into the experimental circuit (with the power off) and going back to a question mark for the resistor value on the diagram. Make a mental note that you owe the students a later explanation of ohmmeters as devices that usually measure current with a preset voltage and only have a scale calibrated in Ohms.

+

One advantage of developing our very simple diagram so carefully is that we can make changes without creating confusion. Suppose, for instance, we wish to illustrate the fact that Ohm's Law works equally well for DC and AC. In our experiment, we would replace the DC source with an AC source. Ideally, the source would be capable of an R.M.S. voltage that is equal to the voltage of the DC source. Then, students could expect the same current to flow as in the first experiment. We need, of course, meters for AC voltage and current.

+

Changing our well-developed diagram is as easy as erasing the DC source and plugging in the AC source:

+
+ +
+

The technique also applies to replacing resistors with capacitors and with inductors to illustrate their ability to limit the flow of alternating current. Note, however, that although we can show the action of DC with a capacitor, if we use a sufficiently large electrolytic to demonstrate turn- on current, we cannot demonstrate the action of an inductor with DC without a current-limiting resistor in the circuit. Blown fuses generally do not make good demonstrations, although with the right preparation (being certain that only fuses will blow in our DC source), they can make a vivid demonstration of DC current through an inductor.

+

Our look at the steps in the development of even the simplest circuit diagram has been patiently slow for two reasons. First, students need to see diagrams emerge in order to understand every aspect of the circuit they are seeing--often for the first time. Remember, the diagram is for the student, not for the instructor.

+

Second, every step in the development of a diagram is a teaching opportunity, even if it may seem that the instructor is repeating something already said. The repetition, surrounded by something new to the student, reinforces the earlier lesson by connecting it to additional information and ideas. In this way, the student's understanding grows and develops in ways quite parallel to the development of our charts, our calculations, and our diagrams.

+

Just as with any set of techniques, there are effective and ineffective ways of applying them. The ineffective way to use a chalkboard developmentally is simply to parrot the procedures mechanically. Or, one can get so wrapped up in replicating the procedure that one's attention is diverted from the students. Good principles become bad ideas if we do not use them wisely.

+

Making the most of the developmental potential of a blackboard requires creativity and a bit of a flourish annexed to an understanding of the principles behind the procedures outlined here. For all the teaching aids available to us, instruction remains a person-to-person enterprise. Good procedures plus the best of the teacher's personality tend to make the best instruction and the best learning. Of course, a little neatness on the blackboard has never been known to hurt a thing. It is the first step to avoiding the dreaded blackboard jumble.

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+ +

+
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From Proceedings of the 1993 National ARRL Education Workshop, (Newington: ARRL, 1993), pp. 27-34 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ Go to Educational Notes Index
+ Return to Amateur Radio Page
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Topics: Education


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+

Beyond the License:
+ Teaching the Principles of Effective Station Design

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+
+

L. B. Cebik, W4RNL

+
+
+ +

+ The most numerous questions ham students ask before and after class or during breaks concern equipment and antennas. The third most popular group of questions relate to station design, everything from finding a source of AC to running cables through the walls, from operating desks to special lighting. Every new ham wants an effective station, however modest the investment in equipment. +

As an adjunct to preparing students for the license exams, we can teach station design more systematically than we currently do. Better teaching is often a matter of collecting and organizing material under a coherent set of principles. Ergonomics, the study of the human dimensions of the workplace, is not as organized as electronics. Hence, the principles are not absolute. However, we can organize the subject so that the student has a mental checklist of things to consider.

+

The following notes are a step in the direction of organizing station design ideas in a way the student can use, master, and adapt to his or her particular circumstances. Their importance lies in the contribution they can make to the new ham's operating satisfaction and success. In some ways, then, they can be as important as a ham's selection of equipment and antenna and his or her knowledge of electronics and the regulations.

+

We can group the basic principles of ham ergonomics into four major groups:

+
    +
  • Safety,
    • +
  • The Operating Position,
    • +
  • Personal Ergonomics, and
    • +
  • The "Shack."
    • +
+

Each category collects a number of subsidiary principles. Moreover, each idea requires adaptation to different types of operation and personal circumstance. For example, the operating position of an exclusive VHF packet operator will look quite different from that of a CW DXer. In these notes, we can cover only the high points of each category and hope they are clear enough to be applied to the new ham's real world and to the ham teacher's encounter with his or her student's questions.

+

SAFETY

Safety should override every other thought about the ham shack, especially since amateur equipment is nowadays an integral part of the household. The matrix of safety has two dimensions. In one of them, we can divide the subject between safety to the operator and safety to others who may be nearby. In the other dimension, we can divide ham shack safety into electrical and mechanical components. For brevity, we shall focus on this latter dimension here. +

1. Electrical Safety. Electrical safety has three major components: AC and DC power, RF currents, and RF radiation.

+

a. AC and DC Power Lines: Since most equipment is well housed today, AC and DC power lines and junctions are generally well protected from casual and fatal contact. However, component failure does occur, and dangerous situations can arise at the operating position. Shorted bypass capacitors can make the equipment cases hot, and protective circuits may operate only if the house ground is effective.

+

Every station, therefore, should have an effective ground, a short wide conductor connected to a deep ground rod or copper water pipe. The house ground should be periodically checked for effectiveness by measuring the voltage between the station ground and the third wire and the neutral wire of the station's AC outlet.

+

All power cords--AC and also DC lines from independent power supplies to transceivers or amplifiers--should be completely insulated with no exposed contacts. Cords should be out of reach and not kinked in ways that promote insulation wear and eventual wire exposure.

+

The wall sockets that supply AC power to the equipment should never be overloaded. Ideally, the station should have a separate 110-volt line with its own circuit breaker. In practice, this is usually not feasible. However, be certain that the circuit used by amateur equipment is not shared by heavy current users among the household appliances. If you add or plan to add a high-power amplifier requiring 220 volts, be sure it has its own circuit and breaker.

+

There should be a master AC switch for the station, one that cuts power to all equipment. This may require building a master AC panel for the shack and instructing family members in its use. The panel must meet wiring codes, but the components are usually inexpensive. Such a panel with a master plug as well as switch once saved my life.

+

b. RF Currents: RF currents can be exposed at terminals, cable junctions, open equipment, and antennas. The principles of solution are straightforward. Just as antennas should be high and out of reach of any person, so too, terminals should be inaccessible. Cable junctions should be inaccessible or shielded, or both. Open equipment should be closed.

+

The dangers here are similar to those of contact with power lines: electrical shock and burns. In this respect, we can think of the antenna balun as a safety device in addition to its other functions. Antenna currents flowing on the outside of coax cables that make the equipment cases "hot" are not merely annoyances; they are dangers, especially to the uninitiated.

+

c. RF Radiation: Related to, but not identical to, RF current dangers are potential dangers from exposure to RF radiation. The exact dangers are still under study, but safety dictates that all radiating structures (antennas) be as far away from human bodies as possible. The more power they radiate, the farther away from humans they should be. The higher the frequency, the more probable the danger for a given power and a given distance from the body.

+

Expressed in these blank terms, the basic ideas can cause unnecessary fear of amateur operation. The proper way to present these ideas is as a search for better solutions to antenna placement challenges and for good decisions as to equipment power. Sensitizing new hams to radiation safety includes stirring their interest in reading the latest developments and findings in QST and other reputable journals.

+

2. Mechanical Safety. As important to safe operation are the mechanical factors in a station. We can divide our thinking into two departments: physical dangers and security.

+

a. Physical Dangers: A complete catalog of potential physical safety problems would require a book. The basic principle is simultaneously to protect people and equipment from damage by accidental contact with each other.

+

One of the most common dangers is cable maze: the looping and twisting of cables under and near the equipment. Not only do people trip over cables, cables often attack the operator's feet, wrapping themselves around like vines. The equipment has crashed to the floor or the cables have broken before they turn loose. The solution to this problem is a cable trough at the rear of the operating table or under its rear lip. Hardware stores are full of hook-like devices that will hold cables in a free but neat bundle out of the way of unwary feet.

+

Often overlooked by experienced as well as new hams is the physical danger that sharp corners and precariously balanced heavy equipment may present. It pays to recess all equipment so that bumps cannot knock the gear loose, damaging either the person who bumps it or the gear itself. Likewise, recessing equipment into consoles or shelves protects unwary body parts from cuts and gashes as they pass over sheet metal corners or sharp projections.

+

b. Security: If you are lucky enough to be able to devote an entire room to the ham station, consider adding a lock to the door. If there are small children in the family, a sliding bolt well above their reach may be enough to keep small hands from getting into danger when no one is looking. Security also dictates a fire extinguisher in the station. It should be mounted in a handy location and be rated for electrical fires.

+

More commonly, the modern ham station is located in a room that is shared with other family functions. As equipment shrinks, a very versatile set-up may require little more room than a personal computer. In this case, security moves from the door to the operating position. Consider putting the equipment in a unit with doors that you can lock when the station is not in use. You may even wish to build special ducts for the cables. The primary object is to secure the station from any entry that might remotely harm the innocent invader. The secondary--but also very important--goal is to protect the equipment from uneducated and unauthorized handling.

+

Of course, the most safe and secure station is the one surrounded by educated adults and children. Not every family member may become a ham, but everyone in the family can learn to respect the station equipment, to know what to do in the event of an emergency, and to share both the successes and frustrations of amateur operations.

+

THE OPERATING POSITION

The operating position consists of the arrangements of equipment and the supporting surfaces that permit the arrangement. There are innumerable individual variables that play a part in good station decisions: available space; funds; woodworking or finishing skills; and the modes, bands, and types of operation. However, a few general principles apply to almost all situations. They require that we look at the operating position from different angles. +

1. Furniture. Since equipment is not self-supporting (the days of 6' rack panels are mostly gone), it requires a desk or console for support. Furniture fulfills at least two functions: support and storage. Desks have one support surface and usually many storage drawers. Computer consoles with upper shelving provide more support surfaces, but usually fewer storage drawers and shelves. Some consoles have doors that can safely secure the equipment and keep the electronics out of sight in a multi-purpose room.

+

For larger layouts, unfinished doors supported by pedestals with shelves, cabinets, or drawer units provide up to 7' of operating room. I personally prefer wider doors (up to 36") to leave plenty of writing, keyboard, and elbow room in front with space for a cable trough behind. However, 30" doors work well for many installations.

+

Of course, hams with extensive woodworking skills can develop custom furniture to support and protect their equipment functionally and beautifully. The U-shaped console is perhaps the most accessible arrangement for an extensive array of equipment. Plywood or laminated panels with cutouts and support shelves can shield equipment and cables from curious fingers while allowing good panel access in front and good air flow behind. A wheeled swivel chair is a must. More linear L-shaped arrangements are also serviceable.

+

Effective operating requires not only that the furniture support the equipment, but that it supports it correctly relative to the operator. Correct support has two dimensions: the vertical and the horizontal (or elevation and azimuth, if you prefer).

+

2. Equipment and Accessories. Equipping the station is a function of the primary operating interests of the new licensee. Although these notes are devoted to everything except the primary equipment, the best possible advice for the new ham is to leave room at the operating position for growth. New interests, hamfest bargains, and a host of other incentives will cause a station to grow.

+

The other basic principle concerns our usual neglect of the space taken by station accessories. Telephones, microphones, keys and keyboards, logs, note paper, and many other operating needs often end up competing with elbow room at the operating position. Planning for these items in advance can make the difference between a discouraging mess and a clean, effective set-up that even has a safe corner for a coffee cup.

+

In addition, every station needs close at hand a number of operating aids. Most of them are paper. Spare scratchpads, repeater directories, antenna bearing charts, ham magazines to read during quiet band times: these are typical of the paper aids that need both storage and access at the operating position. Spare fuses, an extra microphone, patch cable, and headsets are among the bulkier items that often need storage at the operating position. Desk drawers or shelves are a necessity.

+

3. The Vertical Perspective. Seated at the operating position, we scan our equipment vertically. Fig 1 shows a general outline of the situation. There are three major areas of concern.

+
+ +
+

First, the heaviest equipment with the most used controls should be in the prime sight line and hand line. Auxiliary equipment with less used controls should be in the next tier, with visual monitors above. This arrangement is most relaxing for both the eyes and the arms. Note the room for a cable trough behind the equipment.

+

Second, visual angles should be as natural as possible. Note that the main piece of gear presents a flat face to the operator in his or her natural seated position. This facilitates reading out frequency, meter, and control settings. The equipment on the elevated shelves should not be higher than a lifted head can easily see.

+

Third, the controls of the main gear are elevated for ease of adjustment with elbows on the table top. Achieving this goal often requires a sloped console base, since equipment bales are usually not long enough to do the job. The space under the base console is useful for storing papers, CW keys, and other items, for housing a master AC safety panel, and for meters and accessories.

+

3. The Horizontal Perspective. Horizontally, equipment should ideally be laid out according to principles of focus, quadrant, and halo. Fig. 2 illustrates the three concepts with a typical modest HF station. VHF, SSTV, RTTY, packet and other specialized operations will have their own layouts, but three focus-quadrant-halo principles will still apply. Of course, most of us can only approximate the ideal.

+
+ +
+

a. The Focal Area: Central to the position is the main equipment of the operation, the gear that requires the closest attention to readouts and controls. Its centerline position and vertical placement where both eyes and hands can reach it are crucial to effective operation. In the HF illustration, the focal gear is the transceiver. In a VHF packet station, it might be the rig and the computer keyboard right in front of it.

+

b. The Quadrants: Surrounding the focal area should be quadrants of related pieces of equipment. Around the center of Fig. 2 are 4 quadrants for transmitting, computer, antenna control, and speaker functions. Note that each functional quadrant groups together related equipment.

+

Every quadrant assignment will be a compromise between operating needs and ideal equipment spacing. The weight of the amplifier with its power transformer demands support, while the lighter transmatch can be placed higher. If we assume that the computer is central to station operation, it needs a central position for monitor viewing, even though that may separate the transmatch from antenna control functions. If the computer is a peripheral device for occasional use, then it might go on the right, with the antenna functions moved to the center. In this example, the vertical computer case goes to the far left, with the monitor positioned centrally for easy reading. All of this, of course, presumes that the cables exit the station to the right of the position.

+

The objectives of the quadrant principle are many. Related gear belongs together for minimal cable runs. The most handled equipment requires easiest, most direct access. Crucial monitors and readouts require the most direct eye contact. Power and RF cable directions can modify quadrant placement. Even being left- or right-handed can make a difference in deciding the best placement for each quadrant.

+

c. The Halo: Around the quadrants, and beneath them, is a halo for all the miscellaneous items that go into operating a particular station. These include the telephone, the log, the mike, the key, the keyboard, operating aids, and often- used pieces of test equipment. Whatever the support system you use for your equipment, leave a little extra surface, shelf, and drawer space to keep needed extras close at hand. At my own station, a world globe sits atop the gear, and file drawers hold all sorts of paper work, including some magazines to read while waiting for a band to open. Finally, find a safe place in the halo area for your coffee cup or soft drink glass, well away from the rig and the keyboard.

+

Combining furniture ideas along with vertical and horizontal perspectives of equipment placement is best done on paper first. Paper is light and cheap compared to the other items and permits a dozen changes without a single strained muscle. A little planning goes a long way toward comfortable and effective operation.

+

PERSONAL ERGONOMICS

Many personal factors can affect the effectiveness of operation either positively or adversely. Only three will appear here, but they may suggest others to you. +

1. Seating. A good chair is a must for any operating position. A good chair must support the base of the shoulders and the lower back. The length of the seat pad should support the legs, but not cut off circulation to the calves. The seat should be just high enough to support the thighs while leaving the feet on the floor, again, so as not to cut off blood in the back of the thighs. Fig. 3 illustrates these points.

+
+ +
+

Well-designed office chairs with seat and back adjustments often work well as ham operating chairs. The wheels are handy for turning as well as moving, but the base should be broad enough to prevent the chair from tipping over. If the chair has arms, they should not interfere with the operator's arms.

+

These design features, of course, are idealizations. Some operators are only happy if they can hunker down in an old overstuffed chair, while others require a hard-bottom straight chair to help them stay alert. Whatever the choice, be sure to check yourself periodically to see if your chair is unnecessarily fatiguing you or interfering with what you want to do.

+

If the shack area is large enough, leave room for an additional chair for observers and visiting operators. In part, that is a matter of ham hospitality. Additionally, the chair may be a good place for a potential ham in the family--spouse, sibling, child--to get close to the operation and feel a part of it. With attention to just a few details, every ham station can be a recruitment center for new hams.

+

2. Light. Room lighting often leaves the operating position in the dark, or--what may be worse, in sharp dark shadows. If the operating position is near a wall, a central ceiling fixture often will not suffice to prevent eye strain. Yet, an equipment-filled operating desk or table often cannot find room for a lamp.

+

Supplemental lighting may consist of either lamps at the operating position or a new ceiling fixture overhead. Either system will work if you attend to some basic principles. Lighting should be adequate, but diffused to prevent harsh shadows and blinding reflections on readout panels. Lamp shades should protect you from having to look directly at the light source. Since diffusers on light fixtures and lamps cut down on the light going in any given direction, start with a larger bulb, perhaps as much as 200 watts.

+

The perfect lamp or fixture may not exist. Most lamps with diffusers stand straight up, but you may need a swing arm to place the light over the space between you and the equipment. In such cases, you may have to be inventive, combining elements from more than one source to create the perfect lamp or lamps.

+

Use care both with fluorescent fixtures and with high-intensity lamps. Be sure you can withstand the type of light they produce for long periods before making either kind of fixture a permanent part of the shack. Remember: the goal is both good illumination and long-term eye comfort.

+

3. Ventilation. Good air flow and temperature control are essential to operating comfort and good health. You should not sit in either a hot or a cold draft. Hence, do not place the operating desk or table over a heating or air conditioning vent. If the walls have air registers, be sure the air flow does not pass directly over you on its way either in or out.

+

On the other hand, be sure that air can move around the operating position. Ventilation is necessary to carry heat from the equipment, and it must have somewhere to go. Likewise, operating comfort and efficiency are best if the temperature and humidity are reasonably constant without the air going stale. Hot or cold cul-de-sacs within a house or its basement are not the best places for an amateur station.

+

Other amenities of personal comfort are largely a matter of taste. Places for a sink, coffee pot, cold drink storage, snacks, pillows, etc. have no general planning principles. Indeed, only two principles apply to these refinements: 1. if something is important to you, have it at hand or accessible; 2. if it can cause harm to the equipment by way of spillage, sharp points, and the like, do not make it too accessible.

+

THE "SHACK"

The "shack" is an honorable and traditional word for wherever the operating position is. Long ago, the shack was a rough out-building, or an equally rough part of an attic or basement, known for its messy, smelly, and dangerous appearance. In modern times, the shack is most often a room or portion of a room where we set up our equipment, run our power and antenna cables, and do our operating. Every possible shack site needs a full evaluation to ensure it will work in the context of both our operating desires and our family's needs. Although these principles stress amateur operation, the family circumstances within which we enjoy our hobby require and deserve as much, if not more, attention. While making new friends around the area, the country, or the world, we should not alienate those who are closest to our hearts and responsibility. +

1. Site Inventory. The first step in evaluating a room as a prospective shack is to diagram everything relevant to our operation. Fig. 4 illustrates a hypothetical room.

+
+ +
+

The sketch in Fig. 4 provides information on everything in the room: heat registers, AC sockets and switches, existing lighting, window placement, and even door swing. It includes all the important dimensions. Additionally, the drawing says something about what adjoins the room, in this case a front room along one wall and a bathroom along the other. (The adjacent bathroom might well be an advantage to a contest operator.)

+

The drawing does not limit itself to one floor of the house. In this case, the sketch shows relevant parts of the basement. These (or attic) details may be important when considering where to place the operating desk or table.

+

For example, suppose your operating desk is 5'10" long by 2'8" wide. Antennas will be in the back yard. The outer wall with windows is not a good site, since the desk would cover the heat register. The 6' by 3' alcove is tempting, because it would snugly place the equipment in its own space. However, sounds from the equipment would reach the front room, and the cable runs would be a problem. Hence, the best position might be along the rear windowless outer wall with a basement window just below.

+

The sketch does not tell us everything we need to know about the room. Be sure the walls have a pleasant appearance, since you will be seeing a lot of them while operating. Test the walls and ceiling for acoustics, and add sound dampening materials if appropriate. Measure window sill heights before placing furniture. Determine the clearance needed for passage though the room to and from the door. Check the walls for their ability to support any shelving or other construction you intend. Check the floor: Can you drill through unobtrusively for your cables? Do you need mats to dampen foot noise? It is easier to modify and perfect the station room before installing furniture and equipment than afterwards.

+

2. Cables. To the room in Fig. 4, you may wish to add a 220 v. AC line to power the amplifier. Power cables must meet all applicable codes. Indeed, it will be wise to test the existing 110 v. AC socket. It should be a #12 2- wire plus ground circuit with a 20-Amp fuse or circuit breaker. Additionally, it should be as isolated as possible, with a minimum of other household equipment using the same breaker or fuse.

+

Antenna cables may be the greatest challenge in the shack. One goal is to use the shortest feasible run of cable to the antennas. Assume for the sake of example that the antennas are in the back yard. Placing the operating table along the rear wall of Fig. 4 permits the cables to leave the shack through the floor and out the rear basement wall either through the basement window frame or through the perimeter joists. Alternatively, they may leave through the rear wall using PVC or other tubes packed with thermal insulation around the coax.

+

The second goal is to make as few modifications as possible to the house. Save plugs from the hole cuts for reinstallation if you sell the house. In any event, be sure the cables have easy passage with no binding. Use enough cable to allow looping turns rather than sharp bends. Support the cable every few feet to prevent deformation from sagging.

+

3. The Rest of the Room. Our 9' by 12' room would make an ideal shack if we could put all our radio activity and nothing else in the room. A quiet test bench with tools and an array of meters might go into the 3' by 6' alcove next to the door. Book and magazine shelves could go along the wall between the door and the operating position. Some comfortable chairs and reading lamps could go next to the windows. Or, a separate desk and computer station might go on either side wall for correspondence, QSLing, and other ham paperwork. The possibilities are nearly endless.

+

As noted earlier in the discussion of the principles of security, only some of us are lucky enough to be able to devote an entire room to ham activities. In many instances, amateur radio will have to share space with other family enterprises. In that event, strive to keep the shack separated by a real or imaginary barrier. The barrier should keep objects and instruments --things like toys, tools, and small appliances--from entering the operating area. The barrier should also be a sound cushion to keep the bustling clatter of family life outside and the odd chatter of ham radio inside. If everyone in the family is educated to respect the barrier, it may work better than any wall. However, amateur radio is just one facet of family life. Sometimes it must give way to more pressing needs.

+

4. Maintenance. Although shack maintenance deserves extensive discussion all by itself, perhaps a very few words here can alert the new ham to the need for continuing preservation of his or her ham investment. Maintenance has three major dimensions: clean-up, performance checks, and service. Cleaning up the operating position on a daily basis is somewhat of a drudge, but essential to the long life and neat appearance of the equipment and furniture. Gummy dust is an enemy to equipment, but easily avoided by routine wiping.

+

Equipment ages and often loses performance so slowly that we do not notice. Periodically checking performance and keeping a record of those checks can often spot a problem before it becomes catastrophic. Received signal strength of local stations and power output measurements are the beginning of a good performance checklist. Although modern solid state digitalized equipment often requires less periodic servicing and alignment than older tube-type completely analog gear, plan some service money into the ham budget. These smaller amounts can save the cost of premature equipment replacement later on.

+

THE HUMAN DIMENSION

Every list of principles for station design must be customized to the individual situation of the station designer. This brief introduction to the human and personal dimensions of station design is only a beginning. However, it should be sufficient to get any new ham started down the right road to effective operating--apart from the selection and mastery of the right equipment for the shack. +

The shack is a composite of technical requirements and personal factors. The latter includes ourselves in terms of what we want out of a shack, our physical environment, our human environment, and--of course--our finances. For the lifelong ham, there never comes a time when something better cannot be done with or to the station.

+

Shacks change with time, just as do operating interests and family circumstances. A dozen years down the road, the sophisticated customized station layout will surely be better than the first assemblage of equipment. But the first shack will linger in memory as the most exciting. It will be that place for the first contacts, the first successes, and the first frustrations. Therefore, the more instructors can do to pass along fundamental principles for good shack design, the more likely will be the prospect for that complex and refined station of the future.

+

At the same time, putting together a ham shack draws upon skills and talents that go far beyond the technical electronics, the rules and regulations, and the good operating procedures we teach in licensing classes. And every classroom full of potential hams and upgrading licensees brings together an abundance of ability and knowledge, some of which may contribute to improving our own shacks. In the end, then, teaching the precepts of shack design involves as much listening as it does talking. Some of the best features in my own shack have come from the students I supposedly taught.

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+ +

+
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From Proceedings of the 1994 National ARRL Education Workshop, (Newington: ARRL, 1994), pp. 15-22 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ Go to Educational Notes Index
+ Return to Amateur Radio Page
+

Topics: Education


+ + diff --git a/content/edu/edu4-1.gif b/content/edu/edu4-1.gif new file mode 100644 index 0000000..34b036c Binary files /dev/null and b/content/edu/edu4-1.gif differ diff --git a/content/edu/edu4-2.gif b/content/edu/edu4-2.gif new file mode 100644 index 0000000..d2d26aa Binary files /dev/null and b/content/edu/edu4-2.gif differ diff --git a/content/edu/edu4-3.gif b/content/edu/edu4-3.gif new file mode 100644 index 0000000..7227778 Binary files /dev/null and b/content/edu/edu4-3.gif differ diff --git a/content/edu/edu4-4.gif b/content/edu/edu4-4.gif new file mode 100644 index 0000000..9689bff Binary files /dev/null and b/content/edu/edu4-4.gif differ diff --git a/content/edu/edu4-5.gif b/content/edu/edu4-5.gif new file mode 100644 index 0000000..3999a2b Binary files /dev/null and b/content/edu/edu4-5.gif differ diff --git a/content/edu/edu4-6.gif b/content/edu/edu4-6.gif new file mode 100644 index 0000000..68e0257 Binary files /dev/null and b/content/edu/edu4-6.gif differ diff --git a/content/edu/edu4.html b/content/edu/edu4.html new file mode 100644 index 0000000..9348012 --- /dev/null +++ b/content/edu/edu4.html @@ -0,0 +1,225 @@ + + + + + + Teaching R.M.S. Values of AC Voltage and Current + + + +
+

Why 0.707?
+ Teaching R.M.S. Values of AC Voltage and Current

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Introducing students to AC voltages and currents inevitably leads to a discussion of r.m.s. values. 1 volt r.m.s. or 1 amp r.m.s. equals 0.707 of 1 volt or amp peak voltage or current. When students ask, "Why 0.707?" we usually do as most of our texts did: we treat the student to a discussion of the root mean square of all the infinitesimal segments under a sine curve. The student memorizes the 1 unit r.m.s. = 0.707 unit peak relationship, but does not clearly tie together basic concepts in alternating current. +

Granted, some students are content to memorize the relationship and let matters go. However, some want to get a handle on the relationships between peak and r.m.s. values of voltage and current. When I sense this, here is how I proceed. I turn around the explanation, starting with power and never mention r.m.s. until it is necessary to name the unit of measure. The task is not as easy as it appears. Many ham students have never mastered basic ideas in math and geometry. Therefore, the process of putting together the needed ideas often requires a few time-outs for reviewing or teaching some essential skills.

+

However, the results are often startling: the exercise of tying together ideas on this topic often triggers repeat performances by the students with more advanced ideas in electronics. Seeing the student consolidate ideas on his or her own produces a feeling of teacher satisfaction that justifies the time and energy of taking the student on a detailed trip through basic ideas in alternating current.

+

The following notes reflect how I generally proceed, including how I try to lead students around the pitfalls and hazards along the way. Although there is no magic in this step-by-step procedure, it does seem to work. The methods may be usefully adapted to other teaching efforts, both in basic subjects and in more advanced topics for license upgrades.

+

START WITH DC

The first step in achieving a good understanding of AC is to be certain the student understands completely both Ohm's Law and the power law for DC. For our purposes, the most important form of Ohm's Law is
+
+ R = E / I (1) +

+ If we let R be some constant value, such as 1, then the ratio of E to I must be 1:1 or any other paired values, such as 2:2, 3:3, or 4:4. +

To be sure the student understands this, use a schematic diagram or a test set-up configured as in Fig. 1. Since it is difficult to work out a test jig that allows both E and I to be equal without serious straining batteries, the schematic is often the best teaching aid, especially if supplemented by numerous sample calculations.

+
+ +
+
+ Fig. 1 Basic DC circuits +
+

For the DC lesson on Ohm's Law, digital voltmeters and ammeters can help plant the understanding that negative values of voltage and current are also proper for the E to I ratio. Value combinations of -2:-2, -4:-4, and -6:-6 all yield an R of 1 ohm, just as did the positive numbers. The only difference is the direction of electron travel through the meter and resistor.

+

It is also important to stress that the values read from the meters are the levels of voltage and current at the instant of the reading. Neglecting real-instrument delays, every instantaneous reading represents an equally instantaneous level of voltage and current.

+

Power, of course, is the rate of energy use. In transferring DC understanding to AC, we need also to be certain the student grasps the relationship of power to work or total energy use. Work is the rate of energy use multiplied by the time of usage. Whether we measure work in watt-seconds, watt-hours, or kilowatt-hours, the total electrical energy used by our circuit in Fig. 1 is reflected by the total heat generated and dissipated by the resistor. The longer we do work at a constant rate, the more energy we use. Ignoring the actual means used to measure house power use, the longer we run the electric heater, the more we pay the power company, which charges us for the total energy we use. If we ran that same heater off of batteries, we would see the same increase in cost by having to buy replacement batteries periodically.

+

If the time factor is the same for every calculation, then power will be directly proportional to work. For a steady direct current through a constant value resistor with a constant voltage, power will be proportional to work. However, the student needs to get a grasp of the importance of time before approaching AC.

+

For one thing, the DC-equivalents of AC phenomena depend on averaging certain values over at least one cycle. For another, energy use and its rate are also averages over time. The power formula,

+
+ P = E x I (2) +

+ will be crucial to converting an understanding of DC into an equivalent understanding of AC. In fact, now is the time to begin labeling the elements of formulas so that the student can easily sort out ideas. So lets convert the form of our DC formulas to these:
+
+ R = Edc / Idc (3) +

+ and
+
+ Pdc = Edc x Idc (4) +

+ R, of course, is simply anything that converts electrical energy into heat (or another form of energy) and therefore is not properly either AC or DC. +

Note that in these formulas, I use the symbols for multiplication and division most familiar to ham students. With calculators and computers, students understand "/" to mean division, but if necessary, use the other division symbol.

+

GENERATING AC

If the student is thoroughly at ease with the important concepts of DC given in the first step, then he or she is ready for the second step: the generation of standard forms of AC voltage and currents. Of course, an alternating current is any current that changes direction periodically. As teachers, we know of sine waves, square waves, triangle waves, and composite waveforms impossible to capture in a word. However, fundamental to AC concepts is circular motion, and the student will not be comfortable with AC without mastering its basic elements. +
+ +
+
+ Fig. 2 AC generation +
+

To introduce circular motion, I generally use a hypothetical generator which goes through one electrical cycle for every mechanical cycle. Fig. 2 illustrates how I use the generator. As the generator passes through the time-instant T0, its position vertically is also 0. The voltage and the current available to the load resistor is also 0. As the generator passes through T30, indicating the 30-degree point of travel around the circle, its elevation above 0 is a certain value. Here is where we must introduce just the amount of trigonometry needed to find out how high the arm is.

+

Whether or not a student has had trigonometry, it is not difficult to convey the idea that the relationship of the side opposite to an angle of interest divided by the hypotenuse is a constant for any given angle. Then we can name the relationship the sine of the angle. Next, we can calculate the values of voltage for each of the indicated angles by punching out the sine of the angle on an inexpensive "scientific" calculator. If we let the hypotenuse of the triangle be 1 for all cases, then

+
+ E(angle) or I(angle) = sin(angle) (5) +

+ If the hypotenuse has a value other than 1, then the voltage or current become the sin of the angle multiplied by the actual value of the hypotenuse. +

For these introductory examples, it is convenient to let both the hypotenuse of the triangles be 1 and the load resistor be 1 ohm. Numbers other than 1 will obscure the relationship of the sines of angles to the values of voltage and current, as well as to the value of power. When the lesson is over, you can inform the student that he or she has just had his or her first experience with the supposedly advanced concept of "normalized values."

+

When introducing the idea of the instantaneous voltage or current, I try to use angles of 30 and 60 degrees, avoiding 45 degrees as much as possible. The aim here is to be sure the student is comfortable with circular motion and sines without prematurely including a half-developed notion of r.m.s. in the explanation.

+

Although Fig. 2 shows only the first quadrant of motion, I generally take examples from all four quadrants. This shows that the values of voltage and current (with a purely resistive load) take both positive and negative values, and that they take them together. Here, we can relate these calculations of instantaneous voltage and current values to the DC measurements we made when reversing the direction of current flow.

+

In fact, we can now show that Ohm's Law applies to instantaneously measured or calculated values of AC. At any given point in the path of motion,

+
+ R = Einst / Iinst (6) +

+ Additionally,
+
+ Pinst = Einst x Iinst (7) +

+

One of the most interesting sets of instantaneous values is the one produced by doing Ohm's Law at 90 degrees and again at 270 degrees. Since we let the hypotenuse be 1,

+
+ E90 = I90 = sin 90 = 1 (volt or amp), +

+ and
+
+ P90 = E90 x I90 = 1 x 1 = 1 watt. +

+ Likewise,
+
+ E270 = I270 = sin 270 = -1 (volt or amp), +

+ and
+
+ P270 = E270 x I270 = -1 x -1 = 1 watt. +

+ Since the voltage, current, and power never reach any higher values, we can rename these special values as the peak values. Thus, we have defined Epk, Ipk, and Ppk. At this moment, it is important to bring the student back to the diagram in Fig. 2 to relate the values the special points in the circular travel of the generator. +

Just here, we can open some questions yet to be answered. Since the peak voltage, current, and power occur at only two points along the entire travel within the generator, they do not alone define the total energy produced by the generator and used by the resistor during an entire cycle. That value must be something less than the peak value. But how much less? Is there a systematic relationship between the peak voltage, current, and power and the total energy generation and use over time? These questions take us to step 3.

+

Each step in the lesson purposefully ends with some questions to teach by example to students a way of teaching themselves. By noticing details that lead to questions and then by posing good question, the student can guide himself or herself to good answers. Proceed slowly to let the method sink in.

+
+ +
+
+ Fig. 3. AC Power Curve +
+

AC POWER AND WORK

One of the difficulties I have encountered with most explanations of AC power is that the curve for that power over a complete generator cycle is rarely, if ever, shown. Fig. 3 at the top of this page rectifies the situation. Some experienced hams I have met never realized that the curve was symmetrical relative to its peaks and valleys. This curve can simplify the explanation of average AC power and its relevance to r.m.s. voltage and current. +

The curve, of course, is simply a sine-squared curve with a maximum value of 1. If you have access to a spreadsheet program, you can produce full-page curves to assist students in working with the next set of ideas. My procedure began with setting up spreadsheet columns for every 5 degrees from 0 to 360 degrees. The next row converts them to radians. (Use @RAD(X) formula on column A and copy it for the remaining columns as a block.) The third row takes the sine of the angle (@sin(X)) (using the same do-it-once-and-block-copy procedure). Row four uses the formula "A3 * A3" (with block copy for the remainder) to produce the values for a sine- squared curve. Graphing the results produces an accurate curve, labeled to taste. The curves shown here are flattened to take less vertical space, but spreadsheet programs with excellent graphing ability (such as Quattro Pro 7.0 used here) will proved full 8.5" by 11" graphs with fine resolution.

+

The curve is very useful. First, it shows the variations in instantaneous power over time. The student can now see that the actual energy generated and used will be a function of time as he or she imagines the curve repeated over and over through many cycles. The resistor is going to warm up and reach a pretty constant temperature with AC, just as it did with DC.

+

Discovering how much energy is used per unit of time will require more than an instantaneous readout. It will require that we average the power of the cycle, meaning a time period of 360 degrees. Thinking of degrees as time units is important in the understanding of AC, and many students never catch on to this fundamental notion. If it helps, you can convert each degree (or five degrees) into a period of milliseconds. However, to keep the student from thinking these ideas apply only to American house current, use several AC frequencies in the power range. At 60 Hz, a cycle takes about 16.7 milliseconds or about 46 microseconds per degree. In Europe, where 50 Hz is fairly standard, a cycle takes 20 milliseconds at about 55 microseconds per degree. That is fast, but finite.

+

Returning to Fig. 3, we can by visual inspection alone see that the 0.5 line represents the average of all the values on the curve. The student should draw a line across the page on this 0.5 dotted line to emphasize it. The area inside the peaks above the 0.5 line equals the area outside the peaks and below the 0.5 line: the missing power and the present power are the same. Cutting up a graph to show this can take any distrust out of the student's inspection. Of course, rudimentary integration techniques would confirm the visual findings, but we shall not presume of the student any math we cannot easily teach along the way.

+

The result of this exercise is the convincing confirmation of the fact that the average power is half the peak power. Otherwise expressed.

+
+ Pave = Ppk / 2 (8) +

+ Therefore, if every cycle beyond this first one is the same, the total energy generated and used is a function of the average power multiplied by the time of generation and use. +

PDC AND PAVE

The fourth step in our process takes us back to DC. Suppose we want to heat the resistor in both the DC and AC circuits to the same temperature, indicating an equivalent conversion of electrical energy into heat energy. In this case, the average energy use--and hence the average power--must be the same in both cases. For DC, this rate of use is a constant, the same at every instant. For AC, it is the average rate of use across at least a half cycle of many identical cycles. Otherwise expressed,
+
+ Pave = Pdc (9) +

+ Since, the average AC power is equal to the constant DC power, the peak AC power must be twice the DC power, or
+
+ Ppk = 2 x Pdc (10) +

+

Before we leave Fig. 3 behind, let's take one more look at it. There are four points on the graph where the instantaneous AC power equals the average AC power. Those are the points where the graph of instantaneous power crosses the 0.5 horizontal line. Along the time or 0-to-360-degree axis, those points are 45, 135, 225, and 315 degrees. Looking back at Fig. 2, we can see that these points are the half-way points along the arc from 0 to 90 degrees, from 90 to 180 degrees, etc. Whether we look at the circular diagram or the power curve, we can conclude that the power is below the 45-degree point for half the time and above it for half the time.

+

We now have a fairly clear picture of electrical energy doing work, whether that electrical energy is AC or DC. Doing the same work indicates an equivalence between the two forms of electrical energy.

+

However, we still have a question or two left over. If the DC power equivalent of AC power is the average AC power or half the peak AC power, what will be the values of AC voltage and current relative to peak voltage and current that will be equivalent to their DC counterparts?

+

EDC-EQUIV AND IDC-EQUIV

Our fifth step will be to find the voltage and current that produce the average AC power that is one-half the peak power. We have several routes by which to do this. The best effect on students occurs when we use all of them, for then we can show the interrelationship of numerous basic AC ideas. Here, we shall show only two. +

1. Remembering that the peak power is 1 watt produced by a peak voltage of 1 volt and a peak current of 1 amp, we can ask what voltage and current are needed to produce a current equal to half the peak power. We are specifically looking for a voltage and current with the same numeric value. Other voltage and current values that produce the same power can be derived with a single constant, k, such that

+
+ (k x E) x (1/k x I) = P (11) +

+

Therefore, Edc-equiv = Idc-equiv for the problem at hand. We are seeking a numeric value which, when multiplied by itself, produces the desired power value. This, of course, is simply the square root of the power value. However, some students may well have lost track of the concept of square roots and require an explanation of this order.

+

The DC-equivalent voltage and current are both the square root of the average or dc-equivalent power. We might formalize this as

+
+ Edc-equiv x Idc-equiv = 0.5 Ppk (12) +

+ or
+
+ Edc-equiv x Idc-equiv = 0.5 x (Epk x Ipk) (13) +

+ To find a multiplier to apply equally to the peak voltage and to the peak current, we simply take the square root of 0.5, that is, we find a number which when multiplied by itself equals 0.5. The result can be pressed out of any calculator:
+
+ Edc-equiv x Idc-equiv = 0.707 Epk x 0.707 Ipk (14) +

+ or
+
+ Edc-equiv = 0.707 Epk (15) +

+ and
+
+ Idc-equiv = 0.707 Ipk (16) +
+

Of course, from our discussion of the basic generator and resistor circuit, both the voltage and current may be negative, but only at the same time.

+
+ +
+
+ Fig. 4 Sine curve of circularly generated AC voltage or current. +
+

2. The graph of the instantaneous values of voltage and current form sine waves, as shown in Fig. 4. It is possible to compare this graph with Fig. 3 to derive some valuable data, but combining graphs can make the comparison easier. Fig. 5 combines the voltage-current sine wave with the graph of instantaneous values of power using separate axes, one on the left, the other on the right. Fig. 6 takes a different approach. If the student understands that a negative voltage times a negative current yields a positive power, then we can graph the absolute values of the voltage or current to produce the graph in Fig. 6. To graph absolute values on a spread sheet, simply add a new line in column A, using the @ABS(X) function. Then, block copy the new line in A for all columns from 0 to 360 degrees.

+
+ +
+
+ Fig. 5. Combined AC voltage/current and AC power graph with separate Y axes. +
+
+ +
+
+ Fig. 6. Combined AC voltage/current and AC power graph using absolute E and I values. +
+

Whichever graphing system you use, call attention to the number of degrees at which the power crosses the 0.5 horizontal line. Then ask what the voltage and current are at these degree points. You can read approximate values from the graph at the 45, 135, 225, and 315 degree points: a little over 0.7.

+

Taking the sine of any of these points produces a value of 0.707 for 45 and 135 degrees and -0.707 for 225 and 315 degrees. For a power of 0.5 Ppk, the resultant voltage and current are 0.707 Epk and 0.707 Ipk, respectively.

+

Fig. 6 also demonstrates that except for the 0 and 1 points on the graph, both the voltage and the current must have values greater than the numerical value of the power (when voltage and current are equal, before multiplying one by k and the other by 1/k).

+

Finally, the graph demonstrates that the value of voltage or current that is 0.707 times the peak value of each represents the same time division line as the 0.5 peak power point. That is, for half the time of each cycle, the value of voltage, current, or power is less than the indicated value and for half the time of each cycle, the value of voltage, current, or power is more than the indicated value.

+

The graphic ideas dovetail with the straight arithmetic ideas perfectly. That is the goal of teaching the same lesson from more than one point of view. Some students learn best by seeing the calculations; others learn best from examining the graphs. Some will even combine ideas from the two perspectives before catching on. Do not rely on mere repetition.

+

REVERSING THE PROCEDURE

Whichever route we use, the result is the same. We have established that the DC equivalents of AC voltage and current are 0.707 of the peak values of AC voltage and current. Now we let 1 AC voltdc-equiv = 1 volt DC and 1 AC ampdc-equiv = 1 amp DC. This procedure is proper since these values in both AC and DC circuits produce equal energy generation and use. +

What then is the value of the peak voltage and current relative to the DC equivalent values. Since 1 DC equivalent volt or amp = 0.707 the peak voltage or current, the peak voltage or current must equal the DC equivalent voltage or current divided by 0.707, or

+
+ Epk = Edc-equiv / 0.707 (17) +

+ and
+
+ Ipk = Idc-equiv / 0.707 (18) +
+

At this point, you can introduce the student to the magic of the square root of 2. 1 divided by 0.707 = 1.414 and vice versa. 0.707 equals half the square root of 2 or 1.414 / 2. If your students are interested, you may wish to return to the basic ideas of trigonometry and geometry to trace the use of the square root of 2 in connection with the sides and the hypotenuse of right triangles. Familiarity with these relationships will pay dividends to the student in his or her later study of electronics.

+

Or you may just give as a memory exercise the conventional formulas:

+
+ Epk = Edc-equiv x 1.414 (19) +

+ and
+
+ Ipk = Idc-equiv x 1.414 (20) +
+

RENAMING DC-EQUIVALENCE

Let's return to Fig. 4, which so far has done very little work alone. Using the middle or "0.0" line as our referent, we can ask what the value is of all of the instantaneous values of voltage or current for either the top or bottom part of the curve. Since the voltage and current are constantly changing, each instant is infinitesimally small. We can sample the process by taking the values at each 5-degree interval, using a calculator with trig functions and an accumulating memory. (Using the first 90 degrees of the curve cuts the calculation to 19 data points. However, the trade-off is a slightly greater departure from the correctly derived value.) The result is about 0.629 of the peak value. The student is not stretched very far to learn that the average of all the instantaneous values is 0.637 of the peak value. This "average" AC voltage or current value, of course, is useful for understanding circuits where the alternating current has been rectified to provide pulses in only one direction. +

Let us try another method of "averaging." First, take the square of each instantaneous value. Next, add up all the squares. Third, take the average (or the mean) of all the squares by dividing the total of the squares by the number of instantaneous values. Finally, take the square root of the result.

+

This "root mean square" (r.m.s.) method of taking the square root of the mean of the squares of all the values of the voltage or current under the curve, ranging from 0 to 1, yields a value identical to the DC equivalent value of voltage and current. We can approximate the process by checking all values at 5-degree intervals. The result, using 19 data points (like the result of using all possible instantaneous values), is 0.707 of the peak value. The full r.m.s. calculation simply expands our earlier arithmetic derivation of DC equivalent values.

+

From this fact, Edc-equiv and Idc-equiv get their common names: Erms and Irms, where "rms" means "root mean square." Hence, we may take the final step of relabeling earlier formulas:

+
+ Erms = 0.707 x Epk (21) +

+
+ Irms = 0.707 x Ipk (22) +

+ Conversely,
+
+ Epk = 1.414 x Erms (23) +

+
+ Ipk = 1.414 x Irms (24) +

+ Now the student has in his or her possession precisely the relationships required by the exams. In addition, he or she also has a grasp of the interrelationships of many of the fundamental ideas relating to AC and DC voltage, current, and power. In the long haul, the latter understanding is more important. +

The process of thoroughly teaching r.m.s. values of AC requires patience. It may not be for every new amateur student. It requires helpful analogies and lots of teacher personality. But, when a student really catches on, the effect is rewarding to teacher and student alike.

+
+ +

+
+

From Proceedings of the 1995 National ARRL Education Workshop, (Newington: ARRL, 1995), pp. 33-40 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +

+
+ Go to Educational Notes Index
+ Return to Amateur Radio Page
+

Topics: Education


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+

Antenna Modeling Programs as Teaching Tools

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+ Among all the new phenomena to which we introduce new ham students, antennas may leave them least comfortable. Even experienced hams have trouble understanding this deceptively simple transducer that converts electrical energy at radio frequencies into electromagnetic radiation. The sample whips, dipoles, and VHF Yagis we bring to class may not help. I can hear the facial expressions: they say, "That bunch of wire does WHAT?" +

At the Novice and Tech level, antenna questions are few, but cover a surprisingly sophisticated array of concepts. Most students have little choice other than to commit correct answers to memory. Those who want to know more, however, can fix in mind a number of important ideas abetted with a well-guided tour of one of the numerous antenna modeling programs now available.

+

Some Advantages

For those uninitiated to antenna modeling programs, here is a very cursory description. Both MININEC and NEC-2 use different implementations of a mathematical technique called the method of moments to model the performance of antennas. The user constructs an antenna model by specifying its element dimensions and height. The program provides a sketch of the modeled antenna and pictures of the resulting radiation pattern (the far field), along with data about electrical conditions at the antenna feedpoint and along the elements. This is not all the programs do, but it is enough for basic instruction. Likewise, each program has limitations, but none will be pressed in the course of basic antenna instruction. +

Here are some advantages of using an antenna modeling program:

+

1. Economic availability: Antenna modeling programs are available at a very reasonable cost, given their long term benefits. Of course, the program owner can also use it to good purpose outside the classroom. At this level, it does not matter whether the teacher chooses a version of MININEC or of NEC-2: both are more than adequate to the task of vividly guiding students through some basic ideas.

+

Programs useful for teaching are available from many sources. EZNEC (NEC-2), available from Roy Lewallen, W7EL and NEC-Win Basic (NEC-2) from Nittany-Scientific, Inc. are but 2 of numerous NEC programs. Terisoft produces Antenna Model, a MININEC program. Program prices range from about $50 to $150, a bargain for what you get.

+

2. Dynamic instruction: Antenna modeling programs are dynamic. Basic concepts can be taught statically, using chalkboard, models, and various graphics. However, antenna modeling programs permit the instructor to guide the student through some basic comparisons, overlaying one pattern on another. They also permit real variation of antenna variables, such as dipole length, to connect real wire dimensions to real consequences. Students can ask questions about variations on an instructional model and watch their variations yield results.

+

3. Small group instruction: The programs, being PC-based, encourage small group instruction. Four or five students gathered around the instructor create a good learning environment. When numbers are small, students tend to ask more questions than they do in large classes. They feel freer to offer comments that reveal how well they do or do not understand the ideas involved. Responses can be tailored to individual needs. Of course, the instructor may need to repeat the procedure in order to serve everyone in class, but he or she will discover that no two sessions are alike, a pleasing challenge for most teachers.

+

4. Scripting: Antenna modeling programs permit careful scripting of the guided tour. All programs permit the user to save each antenna model as a separate small file. The instructor can organize a progression of files by names or numbers. In class he or she can then keep track of what comes next with a simple list of topics and filenames.

+

Of course, it also pays to have on hand a number of supplementary models designed to anticipate probable student questions. Constructing a good model of even such a basic antenna as a 2-meter quarter-wave vertical with a sloping set of ground plane radials can take a good bit of time. Preplanning keeps the class running smoothly. However, every class will likely add new models to the list of supplements.

+

Even experienced lesson plan writers who organize teaching material by expert second nature should not expect to purchase a program and instantly use it in the classroom. Antenna modeling programs need to be mastered carefully. They contain numerous variables that surround the situation of an antenna, and the user must learn how to set them and the best values to use. Modeling the antenna itself requires mastery of the program's key words, such as "wire," "segment," "source," and "load," and what each means to a good antenna model. If using a three axis coordinate system (X, Y, Z) for antenna dimensions is unfamiliar, it will require practice to handle smoothly. If elevation and azimuth patterns are not second nature, they will require some study so that the instructor can select the relevant patterns and speak about them usefully.

+

All of these (and other) preparation steps take a bit of time. Fortunately, the manuals that accompany antenna modeling programs are quite detailed and thorough. Additionally, all of the listed programs provide the user with pre-modeled antennas to familiarize him or her with modeling conventions and practices. For a bit of initial guidance, you might look at the following item: "A Beginner's Guide to Using Computer Antenna Modelling Programs," The Antenna Compendium, Vol. 3 (Newington: ARRL, 1992), pp. 148-155; reprinted in Vertical Antenna Classics, ed. R. Schetgen (Newington: ARRL, 1995), pp. 10-17.

+

Some Basic Modeling Exercises

Before introducing students to anything a modeling program might do, be certain they are familiar with some basic concepts. Among them are "element," "vertical antenna," "horizontal antenna," "Yagi," and "SWR." They do not have to have a highly technical knowledge of the last two ideas, so long as they understand that a Yagi antenna has multiple elements, feeds only one of them, and is directional. They should also understand that SWR (VSWR) is an indication of the degree to which the antenna and the feedline are well matched, with a 1:1 reading indicating as good a match as can ever be obtained. +

Bring some model antennas to the session, including a ground plane vertical, a dipole, a 2-element Yagi, and a 3-element Yagi. You can make miniature models from wire, wood dowels, and the like. Their purpose is both visual identification and orientation to what the antenna modeling patterns show.

+

Using the miniature models, orient the students to the ideas of elevation pattern and azimuth pattern by having them look down the ends of the horizontal antennas and then from above. You will also need the miniatures later to demonstrate what it means to look at an azimuth pattern at an angle above horizontal and to look at patterns of antennas that are vertically and horizontally polarized.

+

For these exercises, it is likely best to keep all models over real ground rather than trying to explain the difference between free space and real ground. Students will be more intuitively familiar with antennas a certain height above ground.

+

1. 80-Meter Dipole: A #14 wire dipole for 3.7 MHz about 50' above real ground makes a good starting exercise. You can begin by showing them the model file with the wires (about 62.3' each side of center). Since the angle of highest radiation for this low dipole (relative to a wavelength at 80 meters) is straight up, preset the azimuth pattern angle at about 45 degrees Make this model as resonant as you can, hopefully with a feedpoint reactance under 1 Ohm.

+
+ +
+
+ Fig. 1. The elevation pattern of a typical 80-meter wire dipole 50' above ground. Note that maximum radiation is nearly straight upward. +
+

There are three major items this model can illustrate. a. By showing students the elevation pattern, you can explain what a pattern shows, namely, that at some distant points (but not skip distance), the signal strength would be the same at each point along the perimeter of the pattern. This is a measure of the strength of the radiated field in the transmit mode and the sensitivity of the antenna to received signals. You can also explain that because the antenna is so low in height compared to the length of a wave (80 meters long), much of its energy is radiated straight upward, but with plenty going off at angles for good ham communications.

+
+ +
+
+ fig. 2. The azimuth pattern, at 45 degrees above horizontal, for the same dipole antenna. The antenna wire runs left to right at the pattern center. +
+

b. Next you can show them the azimuth pattern at 45 degrees upward. Not only will this verify that there is good energy for communications, but as well, it will show that the classic figure-8 pattern of a dipole applies only to antennas with greater height relative to a wavelength.

+

c. Show the students the feedpoint conditions report, including the feedpoint impedance and the SWR. Even though the books place the resonance impedance of a straight dipole at 70-72 Ohms, our low antenna shows an impedance of 57-58 Ohms resistive. Now note the good match to standard 50-Ohm coax with an SWR of about 1.15:1.

+

This is a good opportunity to introduce the student to how to refine his or her own antenna. Construct a second version of this model lengthened so that it shows about a 2:1 SWR at 3.7 MHz. 64.9' each side of center should do the trick. Construct a third model of the antenna shortened to achieve the same 2:1 SWR; 62.3' will be quite close. Again, sow the student each model and the feedpoint report, noting the inductive (+) reactance for the long model and the capacitive (-) reactance for the short one.

+

If the student has only an SWR meter to make measurements, he or she cannot initially tell from a 2:1 SWR that the antenna is too long or to short. Typical advice to new antenna builders includes finding the lowest SWR point for the antenna. You can use the long and short models to make this point more real to students. The short antenna will show resonance (less than 1ê reactance) at about 3.775 MHz, while the long antenna will resonate at about 3.625 MHz. Obviously, we lengthen the short one and prune the long one, but not to the model dimensions. Instead, we strive with simple antennas for lowest SWR at or near the frequency we want to call the design center.

+

One final note: you can also compare the gain numbers. It is not important whether you use dBi or dBd. Here, it is important for the student to note that the SWR figures do not significantly change the gain of the antenna at all. Make sure they do not get caught up in any numbers past the first two digits, even though programs often give more decimal places. And be sure they understand that a difference of one decimal place is operationally meaningless.

+

2. Dipoles and Yagis: Because the programs permit you to save and then overlay various patterns developed by the numerical analysis, it becomes convenient to demonstrate to students the basic principles of gain. Perhaps 10 meters is the best place to perform this comparison, since this is a band for both dipoles and Yagis.

+

Start by bring on screen the pattern of a typical dipole, a little over 16' long. Use the azimuth pattern at the proper take-off angle. If you place the dipole about 30-35' up in the air over real ground, students can see that, compared to the 80-meter dipole, the classic figure-8 pattern is reappearing because the antenna is now closer to a full wavelength up in the air.

+
+ +
+
+ Fig. 3. comparative azimuth patterns for a 10-meter dipole, a 2-element Yagi, and a 3-element Yagi, each 35' above ground. All patterns were taken at an angle of 14 degrees above the horizontal. Most programs will have on-screen indicators of which pattern belongs to which antenna. +
+

Now call up the pattern of a 2-element Yagi that you have previously saved and let it overlay the dipole pattern. Having a miniature physical model on hand and orienting it in the same plane as the miniature dipole will let you bypass any steps needed to show the antenna on screen and thus let you go straight to the azimuth pattern. Again, use the same antenna height above ground and the proper take-off angle.

+

You are now in a position to show students the modest, but real gain of the Yagi over a dipole, as well as demonstrating the basic idea of front-to-back ratio as an aid in reducing QRM. Teach them also to scan the entire rear lobe of the antenna to note its shape and the relative QRM reduction from all rear quadrants (what some call the front-to-rear ratio). When counting the grid layout rings, labeled in dB, remember that a full S- unit on the student's receiver will be about 6 dB.

+

If your program permits, add a third pattern from your saved files, this time for a 3-element Yagi. Again, use a physical miniature to orient the students to the antenna. Students should instantly note the further, but small increase in gain. However, they should also note the more significant increase in Front-to-back ratio and the improvement in the overall front-to-rear ratio. Well designed Yagis, and their models, should show another S-unit of improvement in rear rejection.

+

You should also stress that the humble dipole begins with good gain over real ground. For all the advertising claims and impression left by the claims, the dipole remains a good antenna for making excellent contacts across the country and world. Directional antennas like the Yagi are helpful in many ways, but they are not absolutely necessary for enjoying amateur radio.

+
+ +
+
+ Fig. 4. Elevation patterns of the same antennas as in Fig. 3. +
+

Unless students have specific questions about the feedpoint conditions, you should avoid burdening them with the numbers associated with the Yagis. The lower numbers require that one use a matching system, an advanced topic. If the student buys a beam, the manufacturer will explain the tune-up procedure for that system. Is a student wants to build a beam, you can give that individual a little one-on-one instruction on the side.

+

3. A 40-15 Dipole: A misconception many students pick up is that if they use a dipole, it must have something like the figure-8 pattern. A little exercise with a 40-meter dipole can correct that impression very quickly. The first step is to construct a model of a 40-meter dipole, perhaps 50' high. Make it a little long, perhaps 68.8' long with #14 copper wire. At 7.1 MHz, show the azimuth pattern at about 39 degrees take-off angle. The very oval shaped 80-meter dipole pattern for an antenna at the same height in feet is now just beginning to pinch in its sides, since the antenna is twice as high relative to a full wavelength at its frequency.

+
+ +
+
+ Fig. 5. Azimuth patterns of a 40-meter dipole used at 7.1 MHz and at 21.2 MHz. +
+

Next, simply change the frequency to about 21.2 MHz, on the pretext of showing them that a 40-meter dipole can be used at 15 MHz also. Let the 6- petal pattern emerge. You can then explain that an antenna's pattern depends in part on how long the antenna is relative to the length of a radio wave. If they prefer the figure-8 pattern, they will have to construct a half-wave dipole specifically for 15 meters. If they are interested, you might use the miniature antennas to add some practical notes on orienting the antenna so that maximum radiation goes in the most desirable directions. In my part of the country (TN), running the wire North-South gives good 40-meter coverage East and West, while placing the strongest 15-meter lobes on some of the best DX paths.

+

These simple active exercises have introduced students to concepts they need to understand to pass the license test. In addition, they have enabled some very practical instruction on the side. That aspect of the instruction makes the test questions far more meaningful to the student. Once you start the process of developing models for class, you will discover many more useful workouts with models.

+

Some VHF Exercises

VHF is a good place to introduce vertical antennas to the student, since repeater operations are virtually all vertically polarized. In your collection of miniature antennas should be a quarter-wave vertical with ground plane, a 5/8ths wavelength vertical with ground plane, and perhaps a 3-element Yagi that you can orient both horizontally and vertically. Of course, at 2 meters, you can bring in full-size antennas to assist the learning process. +

4. Quarter-wave and 5/8ths-wave Verticals: Although handheld 2-meter rigs use rubber duck antennas, the student may wish to use an outdoor antenna at home. Some version of a ground-plane vertical will likely be the first choice, perhaps atop a 25' roof peak. It is fairly easy to model a 146 MHz version of such an antenna with 4 radials. Make the radials about 20.2" long each on a flat plane and the radiator about 20.05" straight up, all using #12 copper wire. This is a ground plane the student can actually build.

+

First show the students an azimuth pattern (take-off angle about 3ø) to confirm that they understand that vertical antennas provide a uniform pattern of radiation in all directions (unless interrupted by nearby objects). Then switch to an elevation pattern. The elevated vertical antenna provides a certain signal strength in its lowest lobe. Just for reference, have the students record the gain figure for the antenna (about 5.4 dBi or 3.3 dBd).

+

Also call attention to the complex pattern of upper lobes. Caused by interactions between the basic (incident) radiation of the vertical and reflections from the ground plane, these lobes are hardly ever useful at VHF for repeater work. Finally, call attention to the feedpoint report, noting the low feedpoint impedance and SWR (a little greater than 2:1). Have students record this with the gain number.

+

Next, start a new model, this time a 5/8ths wavelength vertical. Using the same ground plane, simply extend the length of the vertical element to about 45 inches. Go through the same steps, first verifying the uniform azimuth pattern and then showing an elevation pattern. Students have heard that 5/8th wavelength antennas are supposed to have a theoretical gain over a quarter-wave vertical of about 3 dB. Hence, they may be surprised to learn that with such a simple ground plane, they are unlikely to achieve more than something over a half dB of gain.

+

Finally, show them the feedpoint condition report. If they have wondered why 5/8th wavelength antennas have a little tapped coil at the base, they can at least partially understand why. The base coil is a matching circuit to permit the use of 50-Ohm coax with the complex impedance of the longer antenna.

+

As a final exercise in the series, return to a quarter-wave vertical with its 4 ground plane radials, all of #12 copper wire 25' high. In the model, bend the radials down 45 degrees. You can use the Pythagorean theorem to calculate the outer end coordinates (about 14.3" out and the same down). The shift in ground plane position will require that you shorten the vertical whip to about 18.67" long. This should resonate close to 146 MHz.

+

You may wish to start the run of this model with the feedpoint conditions report. Compare the results with the flat ground plane model. The sloping ground plane yields a very good match for 50-ohm coax--so close that any difference does not make a difference. If a home-made antenna is not a perfect match, the student can always add more or take away from the bend of the radials to perfect the match.

+
+ +
+
+ Fig. 6. The elevation pattern of a 2-meter ground-plane vertical antenna at 25' above ground. The shape of the pattern applies to all three antennas discussed in the text, with only small differences in the gain of the lowest lobe. +
+

If students trust by now that the vertical radiates uniformly in all horizontal directions, go straight to an elevation pattern. While all three elevation patterns have similar features, including the complex array of high lobes, this pattern shows a bit more gain than the flat plane quarter-wave vertical and perhaps an insignificant amount more than the model of the 5/8ths wavelength vertical.

+

If you wish the students to think about this situation, you might ask them how we could get more gain when we actually shortened the vertical whip by a tiny bit. The answer, of course, lies in the sloping ground plane elements. Now they operate not only as a ground plane, but as an approximation of a vertically oriented dipole. That is, the ground plane elements add to the radiation of the antenna. Hence, more power is radiated than with the flat plane quarter-wave vertical, whose ground plane added virtually nothing to the power radiated.

+

If any of these antennas is well matched to the feedline, it will perform quite well for the student. The gain differences are too small to make a practical difference. More significant differences emerge from changing the height of these antennas. At 6' off the ground, they all perform comparably to each other, but all at reduced gains, reductions that may make a difference in practical operations.

+
+ +
+
+ Fig. 7. Elevation pattern of the same ground-plane vertical antenna at a height of 6' above ground. +
+

If you run this supplemental exercise, you will note that the 5/8ths wavelength vertical provides somewhat more gain than either of the other two models (but still under 1 dB). That little extra may account for the popularity of the 5/8ths wavelength antenna as a mobile antenna.

+

2. Horizontal and Vertical Yagis: Many students will be tempted early after receiving their licenses to put up a small beam for extended repeater coverage. From advertisements, they are perhaps used to seeing the azimuth patterns of horizontally polarized Yagis. However, they may be surprised by the azimuth pattern of a vertically polarized Yagi.

+

First, model a small, 3-element 2-meter Yagi. These dimensions, set for 146 MHz, may be useful to you:

+ 
     Reflector length:        39.8"
+          Space:                   18"
+     Driven Element length:   37.25"
+          Space:                   14.5"
+     Director length:         33.4"
+

This compact beam has a front-to-back ratio around 20 dB, and its 40-Ohm feedpoint impedance matches well to short runs of coax. With half-inch diameter aluminum elements, it is a distinct candidate for homebrewing.

+

Construct the model for this beam in the horizontal plane. Bring up the azimuth pattern (4 degree take-off angle at a 25' height). From the HF exercises, students will recognize the typical Yagi pattern.

+

Next construct in advance the same beam oriented vertically. In class, simply overlay the pattern of the same beam at the same height (measured at the boom) in its new orientation. Now explain the "eyeball" pattern.

+

Miniatures are useful in helping students grasp why the pattern spreads, with slightly less gain. Horizontally, ground reflections strengthen the lowest lobe and create some high lobes (visible on an elevation pattern). The beamwidth is a function of the antenna's geometry of tapering element lengths. Vertically, the radiation that bounced off the ground in the horizontal mode now can spread to its fullest extent, for a beamwidth almost double the horizontal orientation. Only the weaker side (element end) radiation now reflects off the ground; hence, slightly less gain.

+
+ +
+
+ Fig. 8. Azimuth patterns of the same 3-element 2-meter Yagi oriented horizontally and vertically at a height of 25' above ground. +
+

Operationally, these facts mean that a Yagi set up vertically for repeater and other FM work need not be moved as often to catch stations slightly off the beam's axis. Although the wider beamwidth of the vertical orientation may occasionally permit some QRM, the ease of finding a heading that permits full quieting operation on FM will usually outweigh the uncommon irritation.

+

Students are likely to notice that the beam offers very significant gain over a vertical. You should therefore remind them of the other costs involved in putting up a beam, including the need for a rotator. Get them from the start to think about how an antenna relates to the kind of operating they envision doing, and how the entire communications system fits into a budget. The models of beams may not only explain some basic concepts to students, but may also attract them. Part of the lesson should be to help the student put everything in perspective.

+

These sample exercises only scratch the surface of uses to which you may put an antenna modeling program in the classroom. I have purposely kept the samples close to the basic concepts students should master for the Novice and Tech licenses, along with some practical material so that they can have realistic expectations from their new stations.

+

However, there are many features of these programs which you may use to good advantage according to your plans and style of teaching. Most programs provide rotatable views of the antenna model for comparison with miniatures or full-size VHF antennas. Some programs provide 3-dimensional views of the far field radiation patterns as a webbing: use these with caution, since they can both clarify and confuse. In the program reporting systems, there lies a wealth of data, most of which is best saved for more advanced students.

+

Finally, there is the program itself. Some students will not be satisfied merely watching the demonstrations. They will want to learn how to use the program to understand other types of antennas and possibly one day to design their own. You may find yourself staying after class to teach a new generation of antenna modelers.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +
+

From Proceedings of the 1996 National ARRL Education Workshop, (Newington: ARRL, 1996), pp. 28-35 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +

+
+ Go to Educational Notes Index
+ Return to Amateur Radio Page
+

Topics: Education, Modeling


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Introducing the "All-Band" Doublet:
+ What the Student and the Instructor Should Keep in Mind

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+

Perhaps too many new hams embarking on their first HF adventures think only of resonant dipoles fed with coaxial cable and plugged directly into the transceiver's output connector. Many end up with a mass of wires in the back yard as they try to make separate antennas for 80, 40, 15, and 10 meters. Others think that they are restricted to only one band because they have room for only one antenna. Too few modern Elmers have the personal experience to guide new HFers into one of the oldest ham antennas of all: the all-band doublet.

+

It may be useful to review what it takes to get the doublet on the air effectively. The data comes in two parts: 1. information that every doublet user should have initially, whether a student or an experienced ham, and 2. opportunities for the instructor to assist students and new hams in gaining some practical knowledge about problem solving, parts acquisition, and a number of other areas that stop some newcomer projects in their tracks. An all-band doublet is a rather refined antenna system when looked at in detail, but it is also relatively easy to get on the air with it. If the student runs into difficulties or has questions, the instructor can help him or her work out the answers. There are many opportunities for advanced Elmering with the all-band doublet

+

The Basic Doublet Antenna System

+
+ +
+

As shown in Figure 1, the basic all-band doublet antenna system consists of 3 parts: the antenna proper, the feedline, and the antenna tuning unit (or transmatch).

+

1. The Antenna: The antenna proper consists of a length of copper or copperweld wire, with a center feedpoint. Three popular lengths for the antenna are these:

+

a. 130-140' (best, if you have the room and want the strongest results on 80 meters.

+

b. 90-110' (works second best on 80 meters, with good results on all other bands).

+

c. 65-75' (good for 40 meters through 10 meters, but not for 80).

+

Notice that the precise length is not critical. Much more critical is getting the doublet as high as you possibly can. Although the antenna will work at low heights in the 20-25' range, it does much better (especially on 80 and 40) when it is higher than 35' up. You can use available trees for support, or you can even build your own support poles or trusses from designs in the ARRL Antenna Book.

+

Many inexperienced hams will need guidance in the selection of materials. Obviously, #14 stranded wire, readily available at stores like Radio Shack, will fill the bill. However, if there is a local hamfest, you may want to guide the new ham in the purchase of copperweld wire. You may also have to guide him or her in its peculiarities, especially how to keep it straight while trying to assemble the antenna. Insulated copper wire will also work well if it is sufficiently strong. The inner ends will require insulation stripping to make connections, but the far ends may be left insulated. The twisting of wires at these ends to make a loop for the support line will introduce no significant changes to the antenna's operation.

+

A second area where guidance can be critical is in the selection and use of antenna supports. Home-made trusses and their guying are not simple matters. Neither is trying to get a line over a branch 40' or more up a tree. The many techniques for launching a line often depend on local talent, whether that talent is tree climbing, bow-and- arrow, fishing rod, or slingshot. Guide the new ham to the local talent and be sure that safety lessons accompany the talent.

+

Of course, the ends of the wire need to be insulated from the support, so you will need end insulators and rope for the job. A good 1/4" sun (UV)-resistant synthetic fiber rope will hold up most antennas unless they are stressed too tightly.

+

Suppose that the antenna will not quite fit the space available. One standard technique of reducing the real estate needed is to set up the doublet in the inverted-Vee configuration. This version of the doublet tends to circularize the pattern, but reduce overall gain of the antenna at almost every frequency of use.

+

Consider bending the elements instead (if supports are available). Drooping ends are the most common version of this arrangement. However, setting up the antenna as a "Z," with all parts of the antenna wire as high as possible, often provides better performance. Drooping ends, and even ends bent in the same direction, provides some radiation cancellation, especially on the lowest bands of use, while the zig-zag version--if not too radically Z-ed--tends only to bend the pattern's directions.

+

Once more, a newcomer may need some guidance--or even just a second pair of eyes--to see clearly all the possibilities and potential problems of laying out an antenna within the confines of his or her yard. What makes a good support, what directions the wires should go for maximum communications, and what hazards to avoid are all questions calling for experienced advice. However, try not to take over the entire job from the newcomer.

+

2. The Feedline: The second element is the feedline. For this antenna, we use a parallel transmission line because it has very low losses, no matter what the SWR (within reasonable limits). 300-Ohm TV ribbon line will work, but it is not the strongest. Most ham dealers can get 400-Ohm or 450-Ohm vinyl-coated transmission line with larger wires. Completely open ladder line, with only insulated spaces, also works well but is less common.

+

Guidance in the selection of feedline may also be needed, especially in knowing which cheap and weak lines to avoid. If there is a local hamfest that is likely to draw a reputable antenna wire and feedline dealer, helping the new ham make his or her purchases is an act likely to be appreciated for years to come.

+

Unlike coaxial cable, which you may run close to any object, parallel transmission line should be as free and clear of objects as possible. If the line must be brought down parallel to an object, such as the wall of a house, use insulated spacers to keep the line several inches away from the object. Avoid bringing the line near metal gutters and down spouts, power lines, conduits, or other metallic objects. Close proximity to metal can disrupt the balance between the wires of the feedline, adversely affecting its performance. Wherever the line must change directions, keep the angles shallow and, if at all possible, keep the line at right angles to the antenna wire.

+

Use special care when attaching the feedline to each side of the antenna wire center feedpoint insulator. Be sure that connections are mechanically secure, and then solder the feedline wires to the antenna wires. Test the connections for movable wire bends that may cause a break while swaying in the wind. Recently, some ladder-line "grabber" center fixtures have appeared on the market to secure the ladder line to the antenna wire and reduce the danger of breakage: they are well worth the investment.

+

One special problem deserves special attention: getting parallel feedline into the shack and over to the antenna tuner. There are almost as many ways to solve this problem as there are all-band doublet installations. The type of solution used depends largely on where the feedline enters the house.

+

If the feedline enters at a window, one can bring it through the window frame or through a board installed at the base of the window. Both have advantages and disadvantages. Bringing the line though the wooden window frame defaces the frame. Using a board on which the bottom section of the window closes requires special means to ensure insulation and security around the window. In each case, one can use a pair of bolts spaced about the same distance apart as the wires and make separate indoor and outdoor attachments. This feature is important, since it permits detachment of the feedline when electrical storms are imminent or when going on vacation.

+

Feeding a parallel transmission line through a wall calls for even greater care. One simple system (among many) uses a short length of PVC run through the wall and weather sealed around the edges. Some hams center the transmission line in the tube and hold it in place with fiberglass insulation. Others use plastic spacers with a center cutout to hold the line in place and seal the tube. There are many variations on this theme, but the old idea of simply slamming a window frame down on the transmission line at the window should be discouraged, especially with metal window frames. In all cases, there should be a way of disconnecting the transmission line out of doors and grounding it.

+

Routing the feedline within the house or shack calls for equal care. Ideally, the tuner should be as close to the line exit point as possible. Feedline should not be simply drooped on the floor or haphazardly tacked to the walls and ceiling. Spacing from invisible metal in the wall cavities is as essential indoors as is spacing from outdoor metallic objects.

+

Helping new hams analyze where duct work, house wiring, telephone wires, and metal plumbing pipes may be located in house walls is another arena of assistance too often overlooked. Many new hams are as initially uneducated about house structures and utilities as they are about amateur electronics. Showing the student how to look at house fixtures, outlets, switches, telephone and cable connections, and plumbing routes and to use these signs to make good estimates of their routings through the house may be a really enlightening experience for the student.

+

3. The Antenna Tuning Unit or Transmatch: The "antenna tuner" is a network for transforming the impedance that is present at the shack end of the transmission line to another value, normally 50 ohms. An all- band doublet shows a different feedpoint impedance at each frequency of operation. The exact length of the antenna relative to the frequency will largely determine that impedance. The feedline will transform that impedance continuously along its length, repeating values every half wavelength of line. Since most transmission lines have a velocity factor, a half wavelength of line will be shorter than a true half- wavelength for the frequency of interest.

+

All of this together means that the exact impedance presented to the antenna tuner will vary from band to band and from one antenna installation to another.

+
+ +
+

Most antenna tuners use unbalanced networks. The most popular network used in commercial tuners is the series C, parallel L Tee network, schematically shown in Figure 2. The popularity of this network stems largely from the fact that it is the most economical to produce and from the relative ease of tuning it to an adequate low-SWR match.

+

Unbalanced networks employ a 4:1 transformer or balun to allow for the use of balanced feedlines. This feature often means that the antenna tuner settings that produce a low SWR between the tuner and the transceiver may not give the highest efficiency of power transfer. However, for most general purpose communications, efficiency will be adequate.

+

Building one's own antenna tuner or transmatch is a good introduction into the satisfactions of home construction. Students may need guidance in the selection of parts, many of which are available these days only from surplus outlets or at hamfests. Helping the student select parts that are suitable in their range of values and their power-handling ratings without paying too much is an invaluable service. Another avenue of help is asking local club members to search their junk boxes for components they may be willing to sell or donate to the cause of aiding a new ham.

+

A second avenue of guidance is helping the new ham select a suitable commercial tuner, if that is his or her favored route. Interpreting specifications, evaluating features, and teaching the student to look at the tuner as a long-term investment that can be useful many years down the road are all important activities that teach by example the practiced art of reading ads and brochures and making the best possible choice of equipment for one's present and future needs.

+

Since antenna tuners do not wear out unless severely abused, used transmatches should be as good as new ones, and perhaps less expensive. Once more, helping a new ham scour a hamfest for the best used equipment available--showing him or her what to look for and what to look out for--may be a real service that has long-term benefits. New hams also need a little help in learning how to bargain down a price.

+

If the all-band doublet is to be a long-term antenna for the new ham, and if home-brewing is an interest, then the best antenna tuner may not be the C-L-C network with a balun to handle balanced lines. Instead, there are circuits in the ARRL Antenna Book and elsewhere for link-coupled antenna tuners that have balanced outputs ready for the parallel feedline. Finding the right coil stock and capacitors, however, may be a fair-sized challenge these days.

+
+ +
+

Adjusting the All-Band Doublet

Using the all-band doublet requires just a little more work than using a resonant dipole. The first job is to find the correct antenna tuner settings for each band you plan to use. However, once you have established these settings, you can make a chart and return to the settings, with only a moment's tweaking to set up the antenna perfectly. +

Since the most common tuner is the C-L-C Tee with a balun for balanced transmission lines, let's see what the set-up for it consists of. First, use a low power setting for initial tune-up. Second, for each band, find an empty place to do your tuning in order to minimize QRM. Third, read the tuner manual to see if there are any recommended initial settings for the controls.

+

The next step is to apply low power and find the settings of the controls that allow you to achieve a 1:1 SWR. Record the setting. Now increase power to the level at which you intend to operate. You may have to tweak the settings just a bit.

+

Repeat the process for each of the bands. If you have never used this kind of set-up before, you might practice moving from band to band so that you do not forget to check the settings and make final adjustments before going to full power.

+

For each band, also check how far up and down the band you can move the transmitter frequency without exceeding a 2:1 SWR. Make notes on whether the settings are broad or sharp for each band. Sharp tuning often indicates either of a high SWR or a high level of reactance at the tuner antenna terminals--or both.

+

On some bands, you may find more than one set of control settings that will give a 1:1 SWR. For C-L-C tuners, the rule of thumb is to use the setting with the higher output capacitance, which usually coincides with a lower value of inductance. These settings are normally higher in efficiency. However, you should listen to signals on the band with each set of control positions and use the ones that yield the stronger signals--if any difference can be detected.

+

At the other extreme, you may discover that on some bands, there are no settings that will produce a 1:1 SWR. This condition normally means that the impedance at the antenna terminals of the tuner has too much reactance, either capacitive or inductive, and the tuner cannot both compensate for it and also end up with a correct value to make the match perfect.

+

The easiest method of overcoming this problem is to change the feedline length by patching in a 6' to 10' section of line between the tuner terminals and the "regular" line. Since a transmission line is an impedance transformer along which the values of resistance and reactance are constantly changing (if the SWR is initially greater than 1:1), changing the length of the line changes the values of resistance and reactance presented to the tuner.

+

Sometimes, the new line length will work with all bands. In other cases, keeping the "patch-in" section handy is necessary for a few bands.

+

For new hams, these procedures are often mysterious, and a "doom-and-gloom" factor can set in as soon as they discover that everything is not perfect on the first try. Reassuring them and showing them a few tricks of the trade can go a long toward increasing their confidence that they can tackle new challenges and overcome them. As always, however, let the newcomer handle the controls as much as possible.

+

What to Expect from the Doublet

Initially, newcomers are simply overjoyed to hear signals on the bands and to be able to make contact with some of them. Eventually, however, they will come up with a variety of questions. Why can I hear the 1s and 2s, but not the 4s and 5s? Why do I hear near-by stations on 80 and 40, but lots of DX on 15 and 10? +

Part of the answer lies in the nature of the ham bands, but part of the answer also lies in the antenna itself. An all-band doublet produces a different radiation and reception pattern for each of the ham bands. In addition, the angle at which the radiation goes out and comes in most effectively varies from band to band, with the higher bands generally having lower angle radiation than the lower bands. (This accounts in part for better DX results on the upper bands.)

+

Although providing a complete set of patterns for all versions of the doublet would require lots of space, I can at least provide a small rogue's gallery of some patterns.

+

Let's assume that we have a 135' doublet (plus or minus 10') at about 50' in the air. What sort of patterns would this antenna make for each of the Novice CW bands? Making allowances for the highly variable effects of terrain in the general region and the ground clutter that surrounds most homes, we can expect something like the following patterns for each band. Remember that the upper azimuth pattern in each set assumes the doublet is aligned from left to right. It is taken at the elevation of maximum radiation (except for 80 meters). The lower elevation patterns are taken along the strongest lobe of the antenna's pattern on that band, whichever way that lobe might be pointed. Azimuth patterns generally tell us in which direction over how broad a span our signals go, while elevation patterns tell us at what angle most of our signal hits the ionosphere, to be reflected back toward earth and a receiving station.

+
+ +
+

The 80-meter azimuth pattern is taken at an elevation angle of 45 degrees. As the elevation pattern shows, most of the radiation is above this angle. Some hams call the relatively low dipole a cloud- burner. Although this is not a DX antenna, there is plenty of useful radiation for all kinds of excellent 80-meter QSOs.

+
+ +
+

On 40 meters, the all-band doublet has a narrower pair of lobes, but the radiated signals in the primary directions will be stronger (and reception more sensitive). The elevation angle of maximum radiation is 39 degrees. However, note that there is a lot of energy being sent out (and received) at lower angles. Hence, the possibilities for DX improve. However, the antenna proves most useful for cross-country QSOs ranging from 800 to 2400 miles, depending on the time of day. These will mostly be broadside to the antenna wire.

+

If we had installed the antenna as an inverted-Vee, with the wires sloping downward from a central support, there would be a few modifications to the pattern. Instead of a peanut, the azimuth pattern would be more oval, giving more reception and less rejection off the ends of the antenna. The angle of maximum radiation would also be just a bit lower, although maximum signal strength at the peaks of the major lobes would be down just a bit. For general operating, the differences are not likely to be noticed without a side-by-side test.

+
+ +
+

On 15 meters, the antenna is 3 wavelengths long. Note that there are 3 major lobes on each side of the wire. The stronger outer lobes are about 45 degrees off broadside. The elevation angle of maximum radiation is about 13 degrees, well down into DX territory. Since 15 is a good DX band, it would be nice to align the antenna so that one of the major lobes points at a desired DX territory.

+
+ +
+

On 10 meters, the doublet is 4 wavelengths long, and there are 4 major lobes on each side of the wire in the azimuth pattern. The elevation angle of maximum radiation has dropped to 10 degrees, and the antenna is capable of allowing us to work a lot of DX--if one of the main lobes is pointed in the right direction. The main lobes are about 35 degrees from the ends of the antenna wire.

+

Newcomers are becoming more and more sophisticated about antenna patterns, since a few appear in almost every issue of the amateur radio magazines. However, what the patterns really mean may not be clear. Instructing newcomers in how to use azimuth and elevation patterns will help them make better use of the large amounts of antenna information available these days.

+

One especially important lesson to teach is that all of these patterns have limitations, since they are generated by computer rather than by actual measurements made of the performance of actual antennas. First, the computer modeling programs use a level ground, which is not the terrain for many hams in the U.S. Hilly or mountainous terrain may vary antenna patterns by a significant margin. Second, the patterns assume a level antenna wire, with none of the droops, zigzags, and other shape imperfections we mentioned earlier. However, none of those imperfections will have a significant negative effect on antenna performance. They will just shift a lobe or two by a little bit.

+

The best use of patterns like these is to establish some very general expectations about antenna performance. For example, we might expect an azimuth pattern of the 100' version of the doublet to have only 3 lobes on each side of the wire; and the 67' long version would show only two lobes on each side. However, if the antennas are all at the same height, we would expect the elevation patterns to be similar for each band.

+

Antenna Maintenance

Every piece of amateur radio equipment deserves regular preventive maintenance. The antenna system is no exception. In fact, the antenna system--including the antenna proper, the feedline, and the antenna tuner--require special attention just because they seem so immune to harm. +

However, here is a list of things that can happen to your antenna system that can adversely affect performance:

+ 
1.  Antenna:
+          wire corrosion
+          wire breaks inside strong insulation
+          wear on support ropes or lines
+          wear or corrosion of solder joints at the feedpoint
+2.  Feedline:
+          build-up of dirt
+          hidden breaks
+          changes in the nearby metals
+3.  Antenna Tuner:
+          dust, dirt, tarnishing of the coil
+          dirt between capacitor plates
+          dirty switches
+

All of these items assume that we have taken generally good care of everything.

+

The cure for all these evils is a regular maintenance program to examine and clean everything before it causes trouble. In addition, items showing wear can be replaced while the situation is under control, not during a contest or field day.

+

Good maintenance begins at the time of building the antenna and feedline system. Raising the antenna should also mean that it can be lowered. Hence, the use of pulleys, eye-bolts, and other means of passing the rope or support line is essential to a good antenna installation. Passing the rope over a crotch of a tree is a good method for finding the rope immovable in a couple of years, as the tree grows right over it.

+

Be certain that all connections between the feedline and the antenna wire are mechanically solid and well soldered. Do not rely on solder for the mechanical connection. In some parts of the country, it may be useful to seal the solder connection, since chemical salts in the air may break down the solder joint.

+

Even if you use a ladder-line "grabber" device, be sure that there are no sharp edges against which the line may rub and break. In fact, the first maintenance should be about 4 months after initial construction as a check to ensure that all work was well done. Thereafter, a check at least once a year is wise.

+

Many hams wax antenna wires with one of the automotive waxes designed to go on metals. They also contain cleaners that remove dirt, grime, and some tarnish to the wire during reapplication.

+

Similar measures also apply to feedlines. Some doublet users have noticed that the antenna tuner settings require a little change during rain showers. While the water on the line may not create significant losses, it nevertheless pays to clean the feedline during a regular maintenance session. Again, automotive polish applied to vinyl-coated feedlines not only helps shed water, but also cleans dirt build-ups from particulates and chemicals in the air.

+

One often neglected area of maintenance is the point where the line enters the house. Because the temperature may be vastly different indoors relative to outdoors, the line and its insulation can undergo stress and wear. If the passage is filled initially with fiberglass or a similar insulation to protect from drafts, the material can become packed with dirt and insects. Periodically changing the insulation-- and even the line section in this area--can help maintain the antenna system at full efficiency.

+

The antenna tuner also needs a good periodic cleaning to remove dust and coatings that accumulate just from sitting in the living environment. A fine bottle-type brush (electric shaver type?) is good for catching dust between capacitor plates, as is some contact cleaner on a lintless rag. However, be sure the cleaner is non-toxic.

+

Coils require special care. Many have tinned or silvered coatings, and tarnish can be a problem. It can even degrade the contact between the turns of a rotary coil and the wheel that contacts the turns. Try to clean the coil with non-abrasive materials to avoid removing the finish, since the copper underneath may tarnish even faster.

+

While doing a general cleaning, inspect all connections. A good- looking solder joint to a coax connector might reveal a weakness after a period of time. Switch contacts may need cleaning and even replacement. Tightening all chassis and case screws (unless the instruction book explicitly says not to in some instance) is usually good practice, especially those screws that form part of the ground common of the tuner.

+

Instructing newcomers in good maintenance practices is essential in this world in which almost all consumer electronics are marked "Do not open, No user parts inside." The entire amateur station represents a new level of responsibility for the licensee. He or she is responsible for the care and upkeep of the equipment to ensure that it meets technical specifications set by regulation. The only way for many to meet this need with respect to transceivers is to send them back to the factory for periodic servicing. However, almost every ham is able to perform many of the maintenance needs of the antenna system. Setting good habits as the new ham walks into the door of his or her new shack is to set a good habit for a lifetime.

+

The all-band doublet is so deceptively simple an antenna that it seems to beg for neglect--until it quits working or falls down. Yet, a regular schedule of maintenance once or twice a year can make the antenna operate reliably for many years.

+

Of course, if the antenna does become a victim of weather, falling trees, or other accidents, replacing it is a straightforward exercise, made easier by having done it once already. Not only that, but replacement is easy on the budget. In fact, it may be impossible to find an antenna that does so much for so little as the all-band doublet.

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From Proceedings of the 1998 National ARRL Education Workshop, (Newington: ARRL, 1998), pp. 39-46 © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ Go to Educational Notes Index
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Topics: Doublet, Education


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+

QRP
+ A Newcomer's and Old-Timer's Challenge

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+

QRP is a very old radio-telegrapher's Q-signal meaning "Reduce power." If followed by a "?" the signal means "Shall I reduce power?" There are literally thousands of amateurs throughout the world who answer with a resounding "Yes!"

+

In the world of QRP operators, the term is defined loosely as operating with a power of 5 watts on CW and 10 watts PEP on SSB. If you think that you cannot do much with that little power, consider these facts. QRPers regularly earn DXCC and other DX awards. QRPers have made contacts garnering thousands and sometimes tens of thousands of miles per watt. QRPers regularly accumulate scores in the larger amateur radio contests that rival or exceed the scores of high power stations.

+

QRPers often repeat a longstanding slogan: "Power is no substitute for skill." For newcomers and old timers alike, the slogan presents a special challenge. With the amateur bands becoming ever more crowded and with more of what The Old Man (Hiram Percy Maxim, the original W1AW) would have called "rotten operators" using more space, we must all increase our skills in every aspect of amateur radio in order both to enjoy our hobby and to effectively render public service through it.

+

No better means of perfecting skills in every aspect of amateur radio exists than making the decision to forego power for QRP operation. There are, of course, operating skills to be mastered and honed. QRP also offers the chance to develop our building skills through a wide variety of compact but highly competent kit transceivers. With a few batteries, one can take QRP to the field (and not just on Field Day) to enjoy that special challenge. It includes not only the ability to operate and to keep the station going, but as well to install an antenna that is easy to carry, is easy to put up and take down, and is effective.

+

For both newcomer and old timer, QRP offers one other significant benefit: it can be very economical. It is not unusual to find an operator whose single-band transceiver, antenna tuner, keyer, paddles, and antenna have left him a good bit of change from a $200 bill.

+

However, the first steps into QRP are often (and perhaps unnecessarily) the source of fear and trepidation. We have become so used to the modern 100-watt output transceiver that the thought of making lots of contacts with 1/20th that amount of power seems almost impossible. And how is one to be able to compete on the air with the so-called "big guys?"

+

Introducing the newcomer to QRP therefore takes considerable sensitivity and patience, as well as good practical guidance. The following notes are not designed to be a tutorial on QRP itself so much as a small and incomplete set of suggestions for helping someone over the threshold into QRP.

+

Step 1: Making a QRP Contact

There is an old theory in amateur radio that is akin to antique ways of teaching kids to swim: throw them in and let them sink or swim. In this case, the parallel would be to tell the newcomer to just go ahead and make a contact using low power. +

However, there are a number of things we can do to help the newcomer get his or her feet wet and learn what to expect of QRP. This assumes that the newcomer has a fairly standard transceiver in the 100- watt output class.

+

First, we can help the student to learn what QRP sounds like. If possible, make arrangements with a local who can control rig power reasonably accurately and who has a strong signal (without overload) at the student location. Have the other station reduce power in definite steps, starting at 100 watts and ending up at about 5 watts (or even 1 watt). The 20:1 power reduction between 100 and 5 watts will show up as between 2 and 3 S-units, depending on the meter calibration (or lack of it).

+
+ +
+

If the local was S9 before, then S6-7 will still be quite strong. The newcomer has learned that QRP signals are not quite so weak as he or she might have suspected. Having the student then practice copying very weak signals (as QRM and QRN permit) is a good way to build confidence that he or she can copy a QRP signal.

+

Next, have the newcomer start reducing power in definite increments, again with the local using 5 watts or less. Have the local give signal reports at each level. It is important here also to use honest readability reports, rather than the standard R5. However, for this experiment, the R-report should not change by much, if anything.

+

When the newcomer hits 5 watts and exchanges signal reports with the local--also running 5 watts--interrupt the proceedings. Congratulate the newcomer on making his or her first QRP-to-QRP contact. Try to ensure that the local QSLs with a QRP notation for the newcomer's records and long-term memories.

+

This exercise can be repeated, but without pre-arrangement, until the newcomer is comfortable making his or her own contacts. After a while, a new thought sets in: why should one consume all the electrical energy it takes to keep the big rig running when all that QRP requires is a low power transmitter and a sensitive, stable receiver with a good QRM filter? At this point, most hams asking this question become QRPers for life.

+

Step 2: Finding Other QRP Newcomers

Many folks do not realize that there are both þregularþ and Novice QRP calling frequencies in the U.S. Here is a list of the Novice frequencies for reference. + 
 Band             CW           SSB
+   80           3.710
+   40           7.110
+   15          21.110
+   10          28.110         28.385
+

Have (and help) the newcomer to listen on or near these frequencies for signals. Weak signal strength is not always a sign that the station is QRP. Some low power stations add QRP after signing their calls; others do not.

+

Not only Novices appear at these calling frequencies, but experienced operators call CQ there also. They are anxious to help the newcomer make QRP contacts to build both skills and confidence. So a newcomer should not be afraid to answer a station that is obviously not a Novice. The other operator will be glad to adjust his or her code speed to the level of the newcomer. This is an old and honored tradition among experienced hams on CW and applies at all power levels.

+

On 10 meters, there are Novice privileges on SSB. At the present time, SSB QRP is just beginning to draw more attention. One factor influencing this increase is the availability of SSB kits. I suspect that once the initial surge of 10-meter DXing and 10-10 work calms down as 10 meters opens up on a regular basis, we shall hear 10-meter QRP on the Novice calling frequency. I have worked a number of 10-meter QRP SSB stations, most notably a completely solar-powered station using about 1 watt. He was S5 or better and completely competitive with the QRO stations.

+

When the newcomer advances past the Novice to the General level, a large world of QRP will be opened to him or her. There are QRP calling frequencies in the U.S.A. on all of the ham bands from 160 meters through 2 meters. One incentive toward advancement is for the newcomer to understand what will be opened for use. Therefore, for reference, here are the remaining US QRP calling frequencies for each band:

+ 
  Band                CW             SSB
+  160                1.810          1.910
+   80                3.560          3.985
+   40                7.040          7.285
+   30               10.106
+   20               14.060         14.285
+   17               18.096
+   15               21.060         21.385
+   12               24.906
+   10               28.060         28.885
+    6               50.060         50.885
+    2               144.060       144.285
+                                  144.585 (FM)
+

European QRP calling frequencies differ from those used in the U.S. due largely to differences in amateur radio frequency assignments. For those wishing to chase QRP DX, the European QRP calling frequencies are these:

+ 
  Band                CW             SSB
+  160                1.810          1.843
+   80                3.560          3.690
+   40                7.030          7.090
+                     7.060
+   30               10.106
+   20               14.060         14.285
+   17               18.096
+   15               21.060         21.285
+   12               24.906
+   10               28.060         28.360
+    6               50.060         50.285
+

Step 3: Getting Involved in QRP

QRP is more than just operating at 5 watts or less. It is almost a frame of mind that encompasses many different activities. One of the best ways to identify or even generate one's interests is to become involved with local, area, or even national QRP organizations. +

If there is a local or area QRP club, the newcomer should be encouraged to attend meetings or get-togethers, depending on the groupþs nature. Some clubs, like the Michigan and Colorado QRP Clubs, hold regular meetings. These are often informal, often with a meal, program, and some show-and-tell. The show-and-tell may involve some new kit just built, some QSL cards for significant contacts, or even some old-time gear that was used for QRP before the days of solid state.

+

Other groups hold nets or on-the-air meetings. Still others meet once or twice a year, sometimes at a picnic, sometimes at hamfests.

+

At last report (which is not likely to be too accurate), there were QRP clubs in Arizona, Arkansas, California, Colorado, Georgia, Illinois, Michigan, Missouri, New England, New Jersey, Ohio, Oklahoma, Pennsylvania, Texas, Washington, and Wisconsin.

+

One good way to meet other QRPers is to join one of the e-mail lists devoted to QRP. QRP-L (@Lehigh.edu) is the largest QRP list. On one side of the coin, it can overwhelm someone not used to receiving 50 messages a day via e-mail. However, it does represent the entire spectrum of QRP interests: operating, building, problem solving, field operations, and helping newcomers.

+

Subscription instructions appear in the section of this article devoted to QRP resources. Learning how to make the best use of an e- mail list is itself an art. Knowing when to send a message to the entire list and when to address one to a specific individual takes a little practice. However, once a person has had a few questions answered, the process grows more natural.

+

Another avenue of involvement is to join one or more of the clubs sponsoring regular journals. A list of some of those organizations also appears within the resource section of this article. Also given are costs, contact people, and a brief note on what to expect from the journal.

+

QRP ARCI is the QRP Amateur Radio Club International, a venerable US-based QRP organization that began many years ago when dropping power to 100 watts was considered a big step in the right direction. Today, QRP ARCI adheres to the 5-watt philosophy, and many members encourage milliwatting, the reduction of power to levels below 1 watt so that power may be given in milliwatts. Microwatting is not uncommon among members.

+

The QRP Quarterly, the journal of QRP ARCI, is one of the most diverse of all in its content. It not only offers technical articles, but also has information on operating, club awards, and club-sponsored operating activities.

+

Each of the other journals listed (and others not listed) in the resource section has something unique to offer. Many QRPers support as many of them as possible (if only to be sure that something new does not slip by unread). Every newcomer should be encouraged to support at least one of them. Reading new things about QRP on a regular basis is not only a good way to increase one's knowledge; it is also an excellent pathway to developing new interests.

+

Step 4: Selecting One or More Interests

QRP is not one world within ham radio; it is many. The beauty of the situation is the fact that anyone can inhabit as many (or as few) of these worlds as he or she has time and interest to give. Here is a short list of some of the activity areas within QRP. +

1. Operating: General operating to make QRP contacts remains the focal interest of most QRPers. However, there are some special operating arenas that deserve note.

+

a. Field Operation: Since QRP equipment is so compact and can often be operated from batteries, many QRPers like to take to the field and set up portable stations on hilltops, campgrounds, and similar locations. Part of the fun lies in developing an ever-improving station for this purpose, including antennas that are light to carry, easy to assemble, and effective on the air. Many field operators would enjoy the company and help of a newcomer as he or she learns the ropes (sometimes literally) of operating this way in exchange for helping to carry things, assemble the station, and help with the operating and logging.

+

Here is a list of what an ardent field operation QRPer might take with him or her:

+
    +
  • 1. Single-band rig for favorite band.
    • +
  • 2. Compact antenna tuning unit (ATU or transmatch).
    • +
  • 3. Wire antenna--often a random length wire to toss over a tree limb, a wire dipole, or a doublet.
    • +
  • 4. Transmission line--for the dipole, thin coax; for the doublet, TV twinlead.
    • +
  • 5. 2 batteries--main and back-up, usually 1 to 6 Ampere-hour gel cels.
    • +
  • 6. Hand key or keyer paddles--keyer itself is usually inside the transceiver case.
    • +
  • 7. Log book and 2 pens or pencils (one always breaks).
    • +
  • 8. Something on which to rest the rig and ATU--may be a table, a converted packing case, or even a large piece of foam with cutouts: the object is to keep the equipment mechanically stable during operation.
    • +
  • 9. Something to sit on, ranging from a foam pillow to a camping stool.
    • +
  • 10. Refreshments
    • +
  • 11. Safety equipment--depending on the remoteness of the site.
    • +
+

b. Contest Operation: Many QRP organizations sponsor a number of different types of contests, from short þsprintsþ to longer efforts. Rarely are QRP contesters so abbreviated in their operating ways that they will not take time out to make sure a newcomer has every part of the required exchange. And when a QRPer wishes you "Good luck!" at the end of the contact, he or she means it.

+

An alternative to strictly QRP contests are the "big" contests, many of which have a special QRP category. Here the challenge is to compete for contacts with higher power stations. Most QRP contesters do not sit and call CQ, but instead search for other stations calling CQ. This "search and pounce (SAP)" method, as Rich Arland, K7YHA, once called it, has run up scores for QRP operators that would have been respectable in any category of the contest.

+

c. Fox-hunting: A recent QRP phenomenon is the fox hunt. Everybody knows who the fox is, where he is, and what his frequencies will be and at what times he will be on the air. The trick is to catch him. Everything is informal, so even failure to get the fox this time brings a determination to get the next one.

+

d. Milliwatting and microwatting: Eventually, 5 watts becomes too small a challenge for some QRPers. They reduce power first to 1 watt and then even lower. One of their major challenges is to measure accurately the actual amount of power they are sending to the antenna. A second challenge is to be heard at all. Schedules with like-minded low power operators are a way of life, and sometimes they use special code words to be sure they were actually heard. Those who engage in this portion of QRP work usually have well-trained ears, which are often a better signal discriminator than the very best DSP filters available. Good ears and a good fist are important skills for all QRP operators.

+

2. Building: Many QRPers are lifelong builders of ham gear and accessories. One of the appeals of QRP is that rigs can be simple enough for the average ham to build from a kit and for the more technically inclined to design or redesign. Letþs break this area down into several areas to see how a newcomer might be transformed from an appliance operator into a home brewer.

+

a. Kit Building: Kit building from Heath and other now-departed sources was once a routine part of amateur radio. The complexity of modern transceivers has largely ended this trend, except in one area: QRP. A number of large and small companies have devoted considerable effort to designing a variety of transceivers that the average ham can build and successfully use. A partial list of kit-makers appears in the resource section.

+

For the newcomer, even a fairly simple kit can seem mysterious without guidance. Helping the newcomer to select his or her first kit and then guiding the person through the building process so that the result is something successful and useful for the station are two important areas of effective Elmering. However, once the first kit is done, a third area becomes important: guiding the newcomer to the next stage in challenge rather than to the most challenging kit on the market.

+

One very important set of lessons that almost demands the aid of an Elmer is the art of testing the gear that one is building. Only a very few of the simplest kits can be built, smoke-tested, and then found to work or not. Whenever there are two or more stages, each can be tested as they are built, so that any problems are discovered early on, when they are easy to identify and relatively easy to fix. Some kit instructions proceed in this manner; other kits require experienced intervention for such testing. Helping the newcomer to understand this process is a piece of teaching likely to last a lifetime in the student.

+

b. Tinkering: The term "tinkerer" was once a highly respectable word for the basement, garage, or shop builder and inventor. Many QRPers are avid tinkerers. Some like to modify and improve the kit they have just finished building and testing. Others like to build and revise circuits they find in magazines. Still others like to build from scratch.

+

SPRAT, the journal of the G-QRP Club is more than 50% devoted to tinkering in the best traditions of modifying and improving circuits and gear. In the issue I happen to have in hand, there are two complete fairly complex projects, with a fistful of small circuits--one an ultra-simple transmitter, some simple test detectors, a junk-box filter, a modification of an existing circuit, and a couple of handy circuits that a builder might use in his or her own more complete design.

+

In contrast, but not too much contrast, is QRPp, the journal of the Northern California QRP Club (NORCAL). NORCAL has become very well known for its club-designed and produced transceiver kits. The particular issue of QRPp that I happened to pick up has three complete projects, plus two more extensive articles on both the electronic and mechanical details of modifications to two rigs--plus the start of a multi-part tutorial. It also has a good collection of short items.

+

Is one journal preferable to the other? It depends on one's interests and the emphases within those interests as to which journal might be more useful or valuable.

+

Whatever the special nature of one's interest in tinkering, the beginning tinkerer needs help getting started. Learning where to get parts, which parts to get, how to handle the parts, when to use which of similar parts are all lessons needing a good source of information and advice. There are dozens of pitfalls to the process of designing and building a prototype, and a little help in avoiding even a few of them can transform discouragement into the persistence that brings success.

+

3. Antennas: There is a debate within the ranks of QRP operators: whether it is proper to use sophisticated high gain antennas atop tall towers or whether the QRPer should use the simplest antennas possible to go along with the simple gear he or she may be using. The debate really describes two kinds of QRPers. First, there are those who simply wish to use the least power possible as a means of reducing QRM. Their goal is to achieve as much as possible with the lowest reasonable power. These folks tend to use the best antennas they can obtain or build. Second, there are QRPers who are committed to doing the absolute most with the absolute least, perhaps with the idea that someday they will be able to do everything with absolutely nothing. These dedicated minimalists tend to insist on simple antennas. Since many of them are also lovers of field operation, their desire for simple antennas also has a practical side. Whatever the reason or direction, QRPers tend to experiment with antennas more than most folks. Wire is the favorite antenna material, and the lighter the better. However, the variety of materials used to support the wire ranges from fishing rods to PVC to towers to whatever will hold it in position.

+

Since a good antenna--however defined--is crucial to effective QRP operation in any of the categories we have listed, good instruction in antenna basics is absolutely essential for the newcomer to QRP.

+

But antenna basics also come in two parts: antennas as electronic components and antennas as mechanical devices that require good construction and maintenance. Even learning to analyze the antenna possibilities and restrictions of one's own yard can benefit from a practiced eye, plus a little help in getting the antenna in the air.

+

Step 5: Learning More

A brief article like this can do little more than sample the opportunities for helping the newcomer to master QRP. Indeed, this one arena of amateur radio often masters the ham, becoming a life-long compulsion. +

Nevertheless, it would be inappropriate to suggest that QRP is the exclusive interest of amateur radio. Even the major QRP organizations recognize that there are conditions, needs, and services that may call for higher power levels from time to time. And all of these areas also call for effective Elmering.

+

However, QRP can become so consuming an interest that the practitioner always desires more information about one or another thing in the field. Therefore, the resources section also contains a starter list of books, some devoted to QRP operating, others devoted to QRP circuitry and equipment. Only antennas are not included, since the QRPers antenna books are also every ham's antenna books.

+

In the end, all of ham radio is enriched by whatever it is that each ham learns. And it is enriched even more by whatever we pass on to others.

+

QRP Resources

The following lists are not complete, but are intended to get both the newcomer and the instructor started in the adventure of QRP operating and building. [Special Note: Since the time that I wrote this article, many of the resources in terms of periodicals, web-based lists, parts and kit supplier etc., have changed. However, QRPARCI and G-QRP remain enduring focal points for obtaining updated information.] +

Periodicals

1. QRP Quarterly: Published quarterly by QRP ARCI (QRP Amateur Radio Club, International), QQ comes with annual membership ($15 US, $18 CA, $20 DX). The 40 8.5x11" pages contain a good mix of technical articles on construction, circuits, antennas, modifications, and test equipment, along with operating and award information, editorial views, QRP philosophy, contest dates and results, and member news. The "Idea Exchange," compiled by Mike Czuhajewski, WA8MCQ, has been a long- standing favorite. Editor Ron Stark, KU7Y, is backed by 8 contributing editors to maintain a diverse publication. Membership dues- subscriptions go to Ken Evans, W4DU; 848 Valbrook Court; Lilburn, GA 30047 USA. +

2. SPRAT: The "Small Powered Radio Amateur Transmitter" or SPRAT is published by the G-QRP Club 4 times each year. Under the editorship of Rev. George Dobbs, G3RJV, each 44-page issue in 5.75x8.5" format contains 60% construction articles in each issue (circuits, antennas, test equipment, etc., both basic and advanced, with some pcb layouts) from many different countries. Each issue also contains award, operating, contest, G-novice, SSB, VHF, and member columns and news. SPRAT comes with membership in G-QRP Club, which can be obtained by U.S. residents for $14 per year from Bill Kelsey, N8ET, Kanga US, 3521 Spring Lake Drive, Findlay, OH 45840, USA

+

3. QRPp: NORCAL, the QRP Club of Northern California, publishes a feature-packed 72-page quarterly in 5.75x8.5" format. Edited by Doug Hendricks, KI6DS, the journal features over 20 articles per issue, mostly devoted to technical and construction topics, including new designs, conversions, improvements, and modifications. Some issues feature NORCAL club projects, such as the NORCAL 40(A), the Sierra, and the recent "38 Special." Cost is $15 per year from The QRP Club of Northern California; Jim Cates, WA6GER; 3241 Eastwood Road; Sacramento, CA 95821 USA. Make subscription checks payable to Jim Cates, not NORCAL.

+

4. Low Down: This award-winning journal of the Colorado QRP Club appears 6 times per year. Each 40-page 5.75x8.5" issue, edited by Rich High, W0HEP, contains technical articles, rig profiles and other equipment reviews; overseas QRP operating features, club member profiles, and CQC activities news. Technical Editor Paul Harden, NA5N, provides a regular circuitry or technical feature, while W4RNL supplies "Antennas From the Ground Up." Low Down comes with membership for $15 per year from the Colorado QRP Club; P.O. Box 371883; Denver, CO 80237-1883 USA.

+

5. Lo-Key: Published 4 times each year, this 32-page 5.75x8.5" journal comes with membership in the CW Operators QRP Club of Australia. Annual cost is $14 A from Kevin Zietz, VK5AKZ; 41 Tobruk Avenue; St. Marys, SA 5042 Australia. As a service to U.S. hams, N8ET accepts subscription money at Dayton and forwards it in order to assist with currency conversion. Edited by Don Callow, VK5AIL, each issue contains two to three construction articles/issue, including advanced ideas, equipment modifications, keyers, etc. (some with parts kits available); along with awards, contest, and net program news.

+

Some Books of Special Interest

Adrian Weiss, W0RSP, History of QRP in the U.S., 1924-1960 (Milliwatt Books: 526 N. Dakota, Vermillion, SD 57069), 1987, $15.00 (includes 1st class postage), 200 pp. A rigorous but personalized history of QRP by a professional historian and longtime QRPer, with extensive extracts from the original records published in QST and elsewhere. +

Adrian Weiss, W0RSP, The Joy of QRP (Milliwatt Books), 1984, $23.00 (includes 1st class postage), 151 pp. An informal overview of QRP that emphasizes operating, but with a few projects; considered a classic.

+

Brad Wells, KR7L, Your QRP Operating Companion (ARRL), 1992. $6.00, 96 pp. An introduction to QRP operating, including ragchewing, DXing, and contesting, with lists of QRP clubs and organizations, as well as net and calling frequencies.

+

Dave Ingram, K4TWJ, How to Get Started in QRP (National Amateur Radio Association [NARA], P.O. Box 598, Redmond, WA 98073. 1992, $9.95, 131 pp. A beginners guide to QRP, touching on operating, commercial and home brew gear, accessories, antennas, VHF/UHF QRP, and battery and "natural" power.

+

Richard Arland, K7YHA, Low Power Communications, Vol. 1-3 (Tiare Publications; P.O. Box 493, Lake Geneva, WI 53147), 1992, about 100 pages per volume. Price varies from $14.95 to $19.95 per volume. Volume 1 is a basic book on QRP, focusing on the newcomer to the QRP arena, helping him/her get off on the right foot. Vol. 2 is a more advanced volume featuring many top names in the QRP hobby (AA2U, N4BP, WB8VGE, etc.) telling how they pursue various facets of QRP, such as DXing, contesting, DXpeditions, antennas, satellites, milli/microwatting, and solar power. Vol. 3 is devoted to equipment evaluations: commercial, kit, new and used; how to buy used gear; also includes software and antennas.

+

Dick Pascoe, G0BPS, Introducing QRP: An Introduction to the History and Skills of Low Power Operating in the UK (R. A. Pascoe), 1996, $8.00, 84 pp. A succinct introduction to the history of QRP, the basic equipment for QRP, and the operating techniques needed for QRP. Available in the US from Kanga, USA (see address under the kits listings).

+

Joel Kleinman, N1BKE, and Zack Lau, KH6CP/1, Editors, QRP Power (ARRL), 1996, $12.00, 175 pp. "The best recent QRP articles from QST, QEX, and the ARRL Handbook." Designed to update QRP Classics for the 1990s, with chapters on QRP operating, construction practices, transceivers, receivers, and accessories.

+

Paul Harden, NA5N, The Electronic Data Book for Homebrewers and QRPers (Five Watt Press), 1996, $20.00, 150 pp. QRP rig circuit analysis, component specification sheets, QRP operating aids, and QRP rig lab tests. Also includes the QRP Yellow Pages, by Rich High, W0HEP.

+

Doug DeMaw, W1FB, W1FB's QRP Notebook, 2nd Ed. (ARRL), 1991, $10.00, 179 pp. Construction projects for QRP transmitters, receivers, and accessories; most projects have circuit boards available.

+

Rev. George Dobbs, G3RJV, Ed., G-QRP Club Circuit Handbook (RSGB: Available from Kanga USA), 1983, $12.00. A compilation of QRP circuits from the pages of SPRAT from 1974-1982; considered a classic.

+

Drew Diamond, VK3XU, Radio Projects for the Amateur (RSGB), 1995, $12.00, 130 pp. 30 chapters of projects and techniques for the QRP builder from the Australian point of view, but with parts available almost anywhere.

+

Ed Noll, W3QFJ, Solid State QRP Projects (MFJ), $12.95. 52 QRP projects using transistors, FETs, and ICs without requiring extensive electronics knowledge.

+

Of course, standard amateur radio reference books, such as The ARRL Handbook for Radio Amateurs and The ARRL Antenna Book, are recommended for every ham's bookshelf. However, if the newcomer is to make best use of these materials, special guidance by a long-term Elmer may be needed.

+

Kits and Equipment

The following list of QRP kit and equipment makers is not complete, but will get you started in your exploration of inexpensive but challenging building projects. Listed are makers of multi-band and single-band transceiver kits, mostly CW, but some SSB, as well as some modular boards that can be combined into a full transceiver. Construction difficulty ranges from very easy to challenging. A number of station accessories, such as keyer and antenna tuner kits, are available from these and other makers. + 
EMTech
+3641A Preble Street
+Bremerton, WA 98312 USA
+
+Kanga US
+3521 Spring Lake Drive
+Findlay, OH 45840 USA
+(Note:  Kanga US handles British Kanga and Hands kits, as well as other
+US kits.)
+
+Oak Hills Research
+20879 Madison Street
+Big Rapids, MI  49307 USA
+
+Small Wonder Labs
+Dave Benson, NN1G
+90 East Robbins Avenue
+Newington, CT 06111 USA
+
+Ten-Tec
+1185 Dolly Parton Highway
+Sevierville, TN 37862 USA
+
+Wilderness Radio
+P.O. Box 734
+Los Altos, CA 94023-0734 USA
+

Internet Resources

The most significant QRP e-mail list for U.S. hams is QRP- L@LEHIGH.EDU. To subscribe to this list, send a message to LISTSERV@LEHIGH.EDU with no subject line entry and only the text SUBSCRIBE QRP-L [firstname] [lastname] [call] where you substitute your information for each [] and do not use the [] in your message. You will receive a verification message and should reply as instructed. QRP-L is a very active list, with well over a thousand subscribers. Exchanges range from operating notes to circuitry inquiries, with any topic relating to QRP operation being permitted. The G-QRP Club maintains an e-mail list in the UK for use by its members, and membership is certainly open to U.S. QRPers. +

The World-Wide Web holds a basic resource for QRP that will provide many links to other pages of both relevance and interest. The URL is http://qrp.cc.nd.edu/QRP-L/ and the pages are maintained by Steve Hideg. Of special interest to the newcomer will be photographs Steve has taken of a wide variety of assembled kits for QRP work. Links to kit-maker pages will show additional photos of kits, both inside and out. The Web site is also linked to many of the archival documents of QRP-l, including a world-wide list of QRP clubs, an expanded list of periodicals, an equally expanded list of electronics books of interest to QRPers, and a list of antenna books.

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The abbreviated list of resources has only scratched the surface of what is available in each of the categories. Nonetheless, Elmers should be very selective in recommending materials, offering new resources only at the rate the newcomer can effectively absorb them.

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From Proceedings of the 1998 National ARRL Education Workshop, (Newington: ARRL, 1998), pp. 30-38. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ Go to Educational Notes Index
+ Return to Amateur Radio Page
+

Topics: Education


+ + diff --git a/content/edu/edu8.html b/content/edu/edu8.html new file mode 100644 index 0000000..769eb5b --- /dev/null +++ b/content/edu/edu8.html @@ -0,0 +1,58 @@ + + + + + + Youth Teachers and Tutors + + + +
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Youth Teachers and Tutors
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+ Elmer Does Not Have to Be an Adult

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L. B. Cebik, W4RNL

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There is an old picture of Elmer that may need a bit of retouching sometime soon. We show him (usually "him) as an older, kindly fellow looking over the shoulder of a youthful ham-to-be, gently guiding the youngster's preparations for the exam. Perhaps we can revise the picture this way: Elmer is a more experienced peer of the newcomer, sitting across a table, conversing with the newcomer eye-to-eye. In school rooms and school-sponsored clubs, where guidance into the role of an Elmer is available, recruiting youth teachers and tutors is both possible and desirable.

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Developing youth teachers and tutors is possible because the practice is already used in many programs. School systems throughout the country have introduced under various names the use of slightly older students to assist younger students in the mastery of many curricular skills. As well, we have long experience in many levels of student teaching, ranging from simple "show-and-tell" to formal individual and group reports.

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Developing youth teachers and tutors is desirable for several reasons. First, it develops a firmer commitment to amateur radio in all its aspects within the youth teacher or tutor. By exercising what we have learned so far in the service of helping others to learn the same thing, we tend to learn more fully and deeply--if for no other reason than the challenging questions from those we help. Moreover, we tend to prize more permanently those activities in which we have successes, and helping others learn is a very impressive sign of success.

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In addition, youth teachers overcome in the newcomer many of the barriers to learning occasioned by age and status differences. Questions we hesitate to ask the mature Elmer for fear of looking stupid become part of the normal conversational flow with our experienced peers. The net result is an enhanced view of the class or club as "ours," instead of being "their" (the older Elmers') activity. While certainly not a cure-all for everything that interferes with long-term commitments to amateur radio classes, clubs, and activities, the development of youth teachers and tutors can make a positive contribution to those commitments.

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Teaching

Many folks who are thrust into teaching situations take a wrong view of what "teaching" means. The most common misconception is that teaching means preparing a presentation to a group to inform them on some topic or another. While such presentations are often quite valuable, they miss the focus of teaching: the student. +

Over my own years of teaching (35), I have picked up a different slant on teaching. "Teaching" means "helping to learn." Once we make the transition to this idea, our focus changes to those things that help our students to learn. This very thought gives us much more flexibility in trying to figure out how to get the job done, for we are no longer thinking primarily of ourselves as teachers. We are thinking of the student and what he or she is trying to learn. Whatever helps that process becomes useful, whether or not we happen to be the active ingredient in the teaching process.

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From this perspective, youth teachers and tutors are not simply ways to distribute our personal work load. They are instead excellent means of facilitating the learning process. Employed carefully, youth teachers and tutors can not only convey information and provide a patient vehicle for practicing the knowledge until it is firmly grasped, but as well experienced peers can pass along to the newcomer some intangible aspects of amateur radio. Among these are the spirit of challenge, the excitement of communications, and the dedication to service. Parental lessons and values that we come to appreciate only later in life are absorbed more naturally from those our own age who share more immediately in the difficulties of growing.

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Carelessly utilized, youth teachers and tutors who are unprepared for their roles or who are unwilling to exercise them can do more harm than good in the teaching process. Rather than these dangers being a reason to avoid using youth teachers and tutors, they are simply reasons to spend the extra effort to develop these members of the teaching team.

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The concept of the teaching team--the team that helps the newcomer to learn--is crucial in figuring out the best ways to utilize effectively and productively every resource to help learning happen. One of the ways that we can keep the youth members of the group returning for further service is to help them understand that they have special roles to play and that those roles are vital to the success of the team. The team may have a captain or a coach, but its achievements belong to everyone.

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Youth Teachers

The idea of giving our youth a significant teaching role seems at first daunting in light of the differential between their limited experiences and our far more extensive seasoning. However, if we look at the many small steps they have taken in the process of becoming teachers, we can gather some confidence in them. From their earliest school days, they have participated in one or another form of show-and-tell. Even in the elementary grades, they prepared and presented reports of educational value to their classmates. Finding appropriate teaching roles is simply a matter of using these experiences as a model and then finding appropriate units of material for them to teach. +

Without probing into educational theory, here are some practical guidelines for developing and employing youth teachers.

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  • 1. Give youth teachers small units of material to present in a finite time period that is only part of the group session.
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  • 2. Help them organize their presentations, but do not block their creativity. They may come up with more ingenious visual aids than their leader.
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  • 3. Select topics that they can master. First efforts might concentrate on operating subjects or general overviews, with the leader available to fill in technical detail.
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  • 4. Support and supplement the teaching session. If you spot an error, do not correct it while the session is occurring or even immediately afterwards. Remember, you are not grading the youth teacher, but encouraging him or her. Simply incorporate a correction in a follow-up note later in the overall session.
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  • 5. Let the youth teacher grow, encouraging but not demanding further refinements of knowledge and technique. Likewise, do not insist that everyone be a youth teacher. Some individuals will realize only later that they want to play a role in the formal teaching part of the team.
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As the overall leader, you can begin the process of developing both the skills and the confidence it takes to teach. One easy method is to regularly reserve time for folks to express their recent achievements, whether in the learning process toward a license or in the world of ham operations. You may spot reports that deserve fuller treatment and ask (apart from the group session to remove any pressure) the individual to make a longer report. You can also use well-placed questions in these sessions to aid the members in better articulating both the facts and the excitement of the achievement.

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You can also remove some of the barriers to good teaching, such as the use of adult-size tables and podiums, having specified places for reporters and teachers to stand, and other practices best reserved for later in life. Sitting comfortably around a table or in some other group arrangement, with the youth teacher situated in a comfortably familiar way, can do wonders for overcoming stage fright. And, by all means, be a good example.

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Youth Tutors

Teaching a group is only one half of the task. The best Elmering is a one-on-one affair in which the newcomer becomes a full person with highly individualized talents and weaknesses. Developing the spirit of individual assistance within the class or club can go a long way toward making it a permanent part of each member's natural way of thinking. +

The process of developing a tutorial system can begin with something as simple as dividing the group into pairs for code practice, for prelicensing drill on question, or any number of other similar activities. These can be either mutual help sessions or activities in which the more experienced help the newcomers. Besides their primary function of reinforcing learning, these sessions will also help you identify potential tutors. Some of the group members will show a genuine enthusiasm for the task. You may detect that some of the experienced members do better in assisting with certain subjects or skills. These are observations you can capitalize on in developing the tutorial system within the group.

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There are many ways to organize a tutorial system more formally, and your choice may depend on circumstance. The range of options generally runs, on the one hand, from having a "big buddy" for each newcomer to follow through the entire initial licensing process, and on the other, to having topical specialists available for special help on demand. Tailor the style of the tutoring to the nature of the group and its special needs. Since needs may change over the years, so too might the tutoring system.

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In general, youth tutoring works best when there is a common study unit the tutor and the newcomer can work through together. This feature allows the session to have focus. However, encourage tutors to have some pure conversation time with the newcomer in order to let each person know the other. In addition, encourage tutors to let you know of any special circumstances that may arise in the course of tutoring. These may range from a unique problem facing the newcomer to the need for additional technical information to answer questions raised by the newcomer. Often, youth tutors will be more forthcoming with such notes if they contribute to the formulation of new things to teach that are for everyone.

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Youth tutors require guidance, especially is maintaining a suitably modest approach to the newcomers. Learning how to be proud of what we have learned well enough to pass on to the next newcomer, while not flaunting the achievement, is a difficult task, even for very experienced teachers. Therefore, guidance sessions for youth tutors should include continuous attitude training as well as the other elements necessary for success. (These other elements include comprehension of the study unit, good tutorial techniques, and feedback on newcomer progress.)

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Conclusion

These brief notes on youth teachers and tutors cannot hope to cover the entire subject. They are only an introduction designed to encourage their use in class and club situations where there is long-term contact among group members. Setting up a system of youth teachers and tutors requires more energy and involvement than merely making presentations. However, that effort translates into more energy and involvement expended by group members in helping each other. The end result is often a life time of dedication by more hams to amateur radio and to radio amateurs. +
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From Proceedings of the 1999 National ARRL Education Workshop, (Newington: ARRL, 1999), pp. 81-84. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Educational Notes Index

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Return to Amateur Radio Page

+

Topics: Education


+ + diff --git a/content/edu/edu9.html b/content/edu/edu9.html new file mode 100644 index 0000000..bf9b31f --- /dev/null +++ b/content/edu/edu9.html @@ -0,0 +1,175 @@ + + + + + + The Internet as a Teaching Tool + + + +
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The Internet as a Teaching Tool
+ Using It Well

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L. B. Cebik, W4RNL

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The internet contains a wealth of opportunities to enhance the education of prospective hams and new licensees of all ages. The trick is to use it selectively and wisely. Like every other teaching tool, internet resources require careful evaluation, sometimes for deciding whether or not to use one at all, sometimes to find the best use for a good resource.

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What's Available on the Web: The World Wide Web (WWW or simply the Web) contains a vast array of personal, commercial, organizational, and informational materials, some strictly text (with or without graphics), some embellished with audio and moving images. As teaching tools, we are most interested is the information available to us. In the amateur radio arena, what we can access would fill a library. Here is a partial list arranged by categories:

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Operating Modes:Activities:Operating Aids:
CWYouth RadioRST
RTTY/PSK31Emergency ServicesQ-signals
SSTVARES/RacesTime Standards
FMField DayMaps/Headings
ATVFox HuntingGrid Squares
PacketDXingCall Look-up
FAXNetsSolar Flux
SatellitesMARSRepeater Guides
.VECs/ExaminationsQSL Information
Technical:County HuntingBeacons
Amplifiers..
DSPEquipment:Organizations:
RFIManufacturersFCC
RF SafetyDealersARRL
AntennasReviews(Other National Organizations
Transistors.in Canada, Great Britain,
AttenuatorsHistory:Japan, South Africa, etc.)
Transmission LinesAntique RadiosAMSAT
ToroidsCall Signs10-10
MicrowavesOrigins of "73", etc.TAPR
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This highly abbreviated listing is derived from one of several "ham link" sites: "AC6V Amateur Radio and DX Reference Guide" (https://www.ac6v.com). The actual main index page fills 4 complete sheets, and even includes separate references for the Wouff-Hong and the Rettysnitch.

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Notice that the ARRL is listed only once in the table. Actually, there are extensive references to the ARRL site, which has a long index of its own covering virtually every aspect of League activities and services. Not the least of these services are the special ones available to ARRL members.

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With so much available, the big task is becoming familiar with the resources and figuring out how best to use them.

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Print Supplements: Some web pages can be downloaded in print form and then reproduced for students as class supplements. Not every web page is suitable for this use. Here are a few cautions to observe.

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  • 1. Be very selective, so that you do not overload the student with paper. Familiarize yourself with a wide variety of selections on any topic so that you can select the very best available.
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  • 2. Evaluate each potential paper supplement for clarity of writing and graphics, relative to the age group and background of the students. The key is to challenge students to increase their knowledge without making the challenge impossible to meet.
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  • 3. Be sure you have permission to use the material. Most folks who place materials on the web are happy for you to use them, but obtain permission, regardless of whether the web page or site contains a copyright notice.
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  • 4. Decide whether it is better to distribute an item to everyone or to keep it in a class reading file--to be handed out when there is a clear need and/or interest.
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  • 5. Recheck the source site periodically for revisions and updates to the material presented. Technical information often requires corrections, while activities and regulatory information is subject to regular revision.
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Print reproduction allows an instructor to control student contact with material. Amid the many excellent presentations on various topics, there are items that display misconceptions and errors. Hence, the control afforded by print reproduction can usefully guide students to correct as well as readable material.

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Student Browsing: As we approach Y2K, most students are likely to have direct access to the web, whether at home, in school, or through activity centers. This offers the student a special educational dimension beyond ordinary print materials: the excitement of discovering information for himself or herself. At the same time, this new dimension reduces the amount of control an instructor has over the absorption of misinformation or disinformation.

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Despite this danger, the instructor can take a few steps to limit damage and enhance the positive directions of discovery. All are based on having a good familiarity of what is available.

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  • 1. Suggest specific sites with known quantities of good and accurate information--geared to the degree possible to the level and background of the student. Do not just give the student a general ham-link site. (Students will discover these sites fairly quickly.)
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  • 2. Select specific URLs (web page addresses) within sites that take the student to the most relevant material. For example, at my own site-- devoted to antenna theory and practice--there are advanced articles that might not be informative to newcomers. However, there is also a series of articles designed for relative beginners, and one can directly access this series. (For example, Antennas From the Ground Up leads directly to the while bypassing the main index page.) +
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  • 3. Encourage students to discuss with you what they have been reading on the web, and to give you the web site address. This offers you the opportunity to supplement the material, to help the student see its relevance and application, and to overcome errors and misinterpretations. The web materials should be only a start toward productive conversations.
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  • 4. Offer the student additional or alternative web pages to investigate relative to those he or she brings to you.
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  • 5. Relate the web site material directly to licensing and other classroom materials at hand to reinforce important ideas and concepts.
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Ultimately, the existence of general ham-link sites cannot be hidden. Therefore, it is better to approach them head-on, informing students of typical URLs. However, also offer guidelines for their use, lest the student get caught in a maze of links that interferes with the learning process. Show them how to extract useful information without printing everything in sight. Let them bring one or two key pieces of information to class for individual or group discussion. Help them to distinguish casual interesting reading from useful reference material. Reference material may not be just technical or regulatory information, but as well may include how hams live and operate around the world. This latter type of data can be useful when students make their first DX contacts.

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In short, teach students to be as selective in their web browsing and searches as you are.

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Lists, Chatrooms, and New Groups: Whether in paper or on-line form, web sites are generally one-way instruments of teaching and learning--from the site to the student. Interaction is largely after the fact in the form of student-teacher or classroom discussion. When not in class, students often want to pose questions or share information. Lists, chatrooms, and news groups offer three different opportunities for doing so.

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Chatrooms are web creations for real-time conversations. News groups and distribution lists are e-mail creations that allow conversation on a somewhat slower basis, but still with less than a 1-day turn-around in most instances.

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Of the three conversational modes, the distribution list is, in my experience, the most productive for learning. Some lists are monitored, which means that inappropriate subject matter and behavior are detected and corrected. Some lists are moderated, so that inappropriate material is blocked from the list. These practices tend to reduce the occurrence of "flame wars" and other distractions from the main purposes of each list. Hence, the level of information transfer tends to be much higher than on other conversational modes.

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The means by which a student becomes part of a distribution list is by e-mail subscription to the "listserver" or the "majordomo" of the list. One list of special note is QRP-L, a list once based at the lehigh.edu site. Since the list has moved, it is used here only as a sample of procedures that may vary slightly from one list to another. QRP-L focused on QRP activities and construction and afford subscribers a chance to ask question and pass along news to other subscribers. It is one of the best places for relative beginners to HF operation to ask questions about equipment and antennas, although holding to the low-power focus is important as well. We may use this list as an example of how a distribution list works.

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In this example, the message data is shown in capital letters for clarity, although either upper or lower case will do in the real message. Sentence ending punctuation has been omitted so that it will not be confused with punctuation used within the addresses and message texts. To subscribe to this list, an individual sends a message to LISTSERV@LEHIGH.EDU using no subject line and only a simple text (here using my information as an example): SUBSCRIBE QRP-L LB CEBIK W4RNL

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The procedure might vary a bit from list to list, and some lists may have a confirmation procedure (to exclude commercial automated advertising systems from mass distributing advertisements on the list). Once subscribed, the individual should read carefully and keep at hand the welcome message, which will contain any procedural rules and limits to be observed. To send a message to the group, use the list address, in this case QRP-L@LEHIGH.EDU The automated list server distributes a copy of the message to everyone who subscribes. On active lists, replies begin to emerge almost immediately. Some may go to the entire list. Others will come directly to the person who posed the question.

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Lists require special attention to courtesies, such as not simply including the original message in the reply message. That maneuver wastes reader time and mail-box space. Also important are staying within the subject area of the list and speaking respectfully in all messages.

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There are numerous special interest distribution lists, such as ANTENNAS and TENTEN-L. As the student refines his or her interests, other lists will become attractive as a place to be helped and to render help from one's own experiences, not to mention sharing both achievements and hard-won lessons.

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This very brief introduction to the teaching and learning opportunities available on the internet cannot do justice to what is available. Nor can this note cover all the points of guidance that an instructor should give to students in order to make their internet ventures both pleasant and productive. However, if the ideas here capture only a little bit of your attention and interest, then you may already be headed down a road of new opportunities in teaching the next generation of radio amateurs.

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From Proceedings of the 1999 National ARRL Education Workshop, (Newington: ARRL, 1999), pp. 76-80. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Educational Notes Index

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Return to Amateur Radio Page

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Topics: Education


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The "Ideal" Back-Up Antenna for 80-20 Meters

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L. B. Cebik, W4RNL

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Everyone needs a back-up antenna in case one or more of the main arrays at the antenna farm becomes inoperative. The requirements for the back-up antenna are very straightforward:

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  • 1. It should be a simple, multi-band design--in order to replace any one or more of the main systems. We shall accept the need for an antenna tuner (ATU).
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  • 2. It should also be mechanically simple--to make maintenance a relatively easy matter.
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  • 3. It should cover all bands of main interest--here defined arbitrarily as 80 through 20 meters.
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For this exercise, I shall confine myself to horizontal antennas, with the proviso that they be as high as possible. 70' is not very high on 80 meters for a horizontal antenna, and I shall use that as my minimum height. However, if the back-up is to replace wounded high-altitude horizontal beams, 100' is not unrealistic. If you live in the right kind of forest, these heights can be attained using trees instead of towers as the end support points.

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These notes do not imply that a vertical does not make a good back-up for the main antenna systems. In fact, I use a multi-band vertical myself for just such purposes. However, it is too difficult to cover both vertical and horizontal possibilities in one small article, so I shall confine the discussion to horizontal antennas.

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The "Best" Single Wire

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If we begin with a single horizontal wire, placed as high as we can achieve, only one question remains: how long? Figure 1 suggests the answer I would give.

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Notice that I have by-passed the standard multi-band doublet lengths of 135' and 102' (or thereabouts). The reason is simple. As we increase frequency, the azimuth patterns for these antennas break into many lobes, with much reduced radiation broadside to the wire. I shall take the following condition to be desirable for a back-up antenna: we know where the main lobes of the pattern go. The best way to guarantee consistency for all the bands we wish to cover with the back-up antenna is to ensure that the lobes on every band are broadside to the wire.

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88'--plus or minus a non-critical bit--is the longest wire we can use to ensure broadside lobes on 20 meters. The antenna length is about 1.25 wavelengths on 20, which makes it an extended double Zepp. At the same time, the chosen length is between one- third and three-eighths wavelength on the low end of 80 meters. With care, that length is usable at a lower level of performance than for the other bands.

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Figure 2 shows the free-space azimuth patterns for the back-up antenna for 80 through 20 meters. You may correlate the patterns with the data in Table 1.

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Table 1.  Free-Space Performance of an 88' #12 Copper Wire Doublet
+            Freq.       F-S Gain    Horizontal        Feedpoint Z
+            MHz           dBi       B/W (deg.)        R +/- jX Ohms
+             3.6        1.77        85                  25 - j 615
+             3.9        1.82        84                  30 - j 500
+             5.37       2.05        79                  71 - j 20
+             7.0        2.38        71                 185 + j 510
+            10.1        3.36        53                3360 + j2245
+            14.0        5.03        32                 155 - j 805
+

Of course, these NEC-4 modeling numbers are more precise than would be operationally significant. However, they do clearly show the trends in performance. An often overlooked figure of merit is the beamwidth, which gives us a measure of relative coverage for an antenna. Note that the 60-meter values place the antenna at close to resonant-dipole length on this band.

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No one has ever decreed that we cannot make an 88' doublet out of aluminum tubing. Before we dream of rotating such an antenna, let's examine the free-space performance figures for a version with an average effective diameter of 1". Table 2 tells the story.

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Table 2.  Free-Space Performance of an 88' 1" Aluminum Tubing Doublet
+            Freq.       F-S Gain    Horizontal        Feedpoint Z
+            MHz           dBi       B/W (deg.)        R +/- jX Ohms
+             3.6        1.90        85                  24 - j 425
+             3.9        1.93        84                  29 - j 340
+             5.37       2.13        78                  72 - j 2
+             7.0        2.44        71                 197 + j 385
+            10.1        3.43        53                2560 + j 220
+            14.0        5.02        31                 125 - j 495
+

There are some interesting differences between the numbers in the two tables. First, the trend with the fatter element is higher (but not significantly higher) gain--except for 20 meters. Here, the gain actually decreases (although insignificantly), because the fatter wire more closely approaches an electrical length where the EDZ ears come to dominate the azimuth pattern. At an electrical length of 1.5 wavelengths, the antenna would show 6 nearly equal lobes.

+

Second, the fatter wire tends to reduce the feedpoint impedance, especially the reactive components. This effect can be very useful in easing the burden on the ATU. On 80 and 75, there is a disproportionately high ratio of reactance to resistance in the feedpoint impedance. Hence, even with very high efficiency parallel lines, expect line losses to add to the reduced performance from the already short antenna length (about 1/3 wavelength). That is an important reason why I call this antenna a back-up rather than a prime station antenna.

+

One of the limiting factors for every ATU is the range of reactance it is able to compensate for at any given frequency. Of course, if we choose the "wrong" line length, we may encounter such cases due to the impedance transformation properties of every transmission line. One easy solution is to change the line length until we reach the best compromise setting. This technique--plus tuning up using very low power--can be critical on the lowest band (80/75 meters).

+
+ +
+

For those who would like the benefits of tubing but the low cost and lighter weight of wire, Figure 3 offers a couple of the many alternatives. We can simulate the diameter of any size tubing with a pair of wires spaced by a certain distance. The spacing would have the value that allows the antenna to be naturally resonant on the same frequency at which the tubular antenna is resonant. This is an easy modeling task that takes the work out of field adjustment.

+

An alternative to the paired wire arrangement (shorted at both the outer end and at the feedpoint) is the old-fashioned cage. Since everything old becomes new again, cage antennas for low-band dipole use have gained a certain popularity, especially as the newer polycarbonate plastics have become generally available. As these figures suggest, the cage may also have some utility for multi-band doublets.

+

Even more significant are the figures for the doublet's performance over ground. Table 3 and Table 4 list the figures for heights of 70' and 100'. Added to the table is the TO angle (the take-off angle or elevation angle of maximum radiation) and the vertical beamwidth. Together, these figures give us a view of the range of incoming and outgoing skip angles over which we may effect communications. Like the horizontal beamwidth, the vertical beamwidth is a much overlooked valuable piece of data.

+ 
+Table 3.  70' Performance of an 88' #12 Copper Wire Doublet
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         5.90       59          130         180           30 - j 610
+ 3.9         5.86       53          134         180           35 - j 495
+ 5.37        6.41       37           51          97           80 - j 30
+ 7.0         7.84       28           33          79          165 + j 485
+10.1         8.66       19           21          55         3810 + j2160
+14.0        10.81       14           15          33          155 - j 820
+
+Table 4.  100' Performance of an 88' #12 Copper Wire Doublet
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         6.12       38           57         107           30 - j 620
+ 3.9         6.40       36           47         102           35 - j 505
+ 5.37        7.93       25           29          85           60 - j 25
+ 7.0         7.83       20           21          74          185 + j 530
+10.1         9.16       14           14          54         3115 + j2450
+14.0        10.50       10           10          32          165 - j 810
+

The feedpoint impedances at the two levels fall well within the margins of rough equality. The most important differences show up in the gain and TO angle columns. Although usable, the 70' model shows very high TO angles and lower gain on 80 meters. The 180-degree beamwidths on 80 meters indicate nearly circular patterns. In contrast, the TO angles and vertical beamwidths for 80 meters in the 100' model promise significantly better DX performance, with much more oval patterns. On 40 through 20 meters, the gain differentials disappear, but the higher model shows the expected lower TO angles.

+
+ +
+
+ +
+

In order to get a better perspective on the significance of these figures, examine Figure 4 and Figure 5. They show the elevation patterns of the antenna at the two heights: 100' and 70', respectively. Besides illustrating the notes just given, they also reveal the growth of secondary lobes at the upper frequencies as we raise the antenna by 30' or so. 20 meters has grown a third elevation lobe. The high dome pattern gravitates from 10.1 MHz down to 7 MHz in the move from 70' to 100'. The shape difference at the two heights in the 80/75 meter patterns is self-evident.

+

I have not added the azimuth patterns, since they resemble too closely the patterns in Figure 2. The key difference is that as we reduce the frequency of use, the side rejection decreases. The decrease is more radical at the lower height, where it disappears almost completely at 80 meters. In addition, the high X:R ratio at 80 meters tends to yield higher line losses that do not appear in the basic antenna patterns. The gain of the antenna along remains unchanged, although a high-loss line situation means that less power will reach the antenna.

+

A Pair of Semi-Eternal Triangles

+

Although it is not likely to be true, let me assume that I have convinced you that an 88' doublet is the best single-wire back-up antenna for 80 through 20 meters. Once we have gone this far for the sake of the argument, we can pose the question of how to derive the best world-wide coverage with such a wire antenna. The answer is as simple as the triangle.

+

Actually, I want to explore two versions of the triangle: a Y-array and a true triangle. For no particular reason, I shall begin with the Y-array, shown in Figure 6.

+
+ +
+

As the figure shows, the ends of the wires are set 12' from a center-point for the array. The array would require a rectangle about 100' by 175' for implementation. A 4- post construction method seems most obvious (1 at the center and three on the perimeter). However, those with special skills in high-strength wire trussing might manage with only the perimeter posts. A slight dip in antenna height toward the center point would create no significant performance problems

+

There is no special magic to my choice of element separation from the center point. The goal was to minimize interaction between the active element and the inactive ones. 18' between adjacent ends is sufficient to achieve this goal, as evidenced by the modeled data in Table 5. The data are for a 100' array height.

+ 
Table 5.  100' Performance of a Y-Array of 88' #12 Copper Wire Doublets
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         6.11       38           58         108           31 - j 620
+ 3.9         6.38       36           47         104           35 - j 505
+ 5.37        9.18       26           29         135          130 - j 30
+ 7.0         7.87       19           21          73          185 + j 535
+10.1         9.14       13           14          55         3110 + j2470
+14.0        10.39       10           10          33          165 - j 810
+

The data are insignificantly different from those of Table 4, which gives modeled values for an independent 88' doublet. 60 meters is the exception. On that band, the near-resonance of the elements yields a beam pattern with an 11-dB front-to-back ratio. The main lobe is away from the inactive elements, which form a composite parasitic reflector. The significantly different feedpoint impedance relative to the value for a single 88' wire at the same height is another indicator of the odd behavior on this band. Whether that odd behavior is an advantage or a disadvantage depends upon operating needs.

+
+ +
+

To effect world wide-communications, we should understand how the patterns for the triangle overlap. As well we should examine the nulls in the pattern. As Figure 7 attests, on 80 meters, there is no significant null (<1 dB). On 40 meters (Figure 8), the nulls are only about 2 dB, which is likely small enough not to occasion any repositioning of wires.

+
+ +
+
+ +
+

The first band on which we discover nulls deep enough to cause concern is 30 meters (Figure 9). The nulls become very much deeper on 20 meters (Figure 10), where the EDZ narrow beamwidth becomes quite significant in antenna planning.

+
+ +
+

In modeling exercises, no negative effects resulted from warping the Y array from its perfect 120-degree separation. Changes up to 20 degrees appear not to create any noticeable consequences for the radiation patterns from the individual antenna wires. Consequently, the array designer can position the three wires in an approximate Y, with each wire broadside to the most favored contact directions, whether those are domestic or DX.

+

It would be incorrect to say that the wires do not interact at all. Figure 10 shows the very slight interaction by the manner in which the secondary lobes of the three patterns overlap in slightly irregular ways. In fact, the main lobes depart from the true broadside by about 1 degree in the direction of the other wires. These facts, however, do no more than complete the record. Their operational significance is negligible, and the three wires may be considered as aiming in a true broadside direction for all practical purposes. As well, the wires more severely interact on 60 meters so that the result is a directional pattern with an 11-dB front-to-back ratio. The interaction level is a function of the near-resonant length of the wires in the triangle.

+

The Y-array presumes that all of the parallel feedlines will be brought to a central switching point, from which a single parallel feedline will proceed to the shack. Switching would be by a remote system (unless the shack is located approximately under the center-point of the array. Figure 11 provides the basic elements of such a remote switching system.

+
+ +
+

The system shown can be considered a "bare-bones" version that can be embellished in innumerable ways. Since the array shows no significant differences between open and closed centers for the inactive antennas, shorting the transmission lines of the unused antennas can serve useful functions. For example, you might want to add RF chokes to the shorted contacts with a subsequent lead to ground. The result will be to bleed off any static charges on these wires.

+

In fact, you may wish to add a fourth "Off" position to the switching system, for use when the array is wholly inactive. This option would simply remove all power from the relays and bleed all three wires of static charges that may build up from winds and other weather forces. (I shall assume that there will be provisions nearer to the shack for a total disconnect and grounding of both the relay power lines and the parallel transmission line coming from the switching unit. Add other safety features as the spirit moves you.)

+

In addition to safety features, it also pays to decouple the relay power lines from RF right at the switching unit. You may add rf chokes and by-pass capacitors to each power lines inside the weatherproof relay box. Alternatively, you can place ferrite cores over each power lines. Be sure to include the common in this treatment. Although shown with a ground connection at the shack, this line at the remote switching unit is ripe for RF pick-up and distribution. Additional decoupling at the shack end of the line is also a wise precaution.

+
+ +
+

The same switching unit can be used with the second configuration of the array: the true triangle shown in Figure 12. This arrangement requires only 3 posts, about 112' apart. The outer dimensions allows for a 12' spacing of the wire from the post, which results in 12' of separation between adjacent wire ends. The true triangle requires less space than the Y-array. A rectangle about 112' by 97' will contain all of the wires. Like the Y- array, I shall assume that the feedlines are brought to a central point for switching among the antennas.

+

The true triangular array in theory shows more tendency toward interaction between the active antenna and the inactive wires. Hence, there is likely to be a more significant difference in performance based on whether the center points of the inactive wires are open or shorted.

+

The interaction does not greatly affect the overall performance of the antenna, as shown in Table 6 and Table 7. With the unused centers closed or shorted, there is a very slight front-to-back ratio. It is never greater than 0.3 dB and the "stronger" lobe is in the direction of the unused wires. With the unused wire centers open, the front-to-back effect drops to less than 0.1 dB on all but 30 meters.

+ 
+Table 6.  100' Performance of a Triangle-Array of 88' #12 Copper Wire Doublets
+                                  (Unused Centers Closed)
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         6.25       38           55         109           28 - j 615
+ 3.9         6.57       35           46         103           32 - j 500
+ 7.0         7.61       20           21          71          185 + j 525
+10.1         9.31       13           14          56         3320 + j2655
+14.0        10.22       10           10          32          165 - j 820
+
+Table 7.  100' Performance of a Triangle-Array of 88' #12 Copper Wire Doublets
+                                   (Unused Centers Open)
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         6.14       38           57         108           29 - j 620
+ 3.9         6.42       35           47         101           34 - j 505
+ 7.0         7.88       19           21          76          185 + j 535
+10.1         9.38       13           14          62         3050 + j2490
+14.0        10.16       10           10          32          170 - j 820
+
+ +
+

In reality, a noticeable difference in pattern shape occurs only on 30 meters. Figure 13 compares the 30-meter patterns for a. the Y-array (which is virtually identical to the pattern of the independent doublet), b. the triangle with the unused centers closed, and c. the triangle with the unused centers open. I chose a different orientation for each antenna, since the key pattern alteration occurs near pattern center. The side "bulges" in the 30-meter patterns for the true triangle do not materially affect the gain of the main lobes. However, the open condition does yield a front-to-back ratio of 0.6 dB, which can be noticed on patterns, but not in operation.

+

In the end, then, you may take your choice of open or closed unused elements. Since the choice is so close in performance, my own preference would be to opt for the safest choice: lines closed at the remote switching center. Whether that choice results in electrically closed or open feedpoints for the unused elements depends on the exact length of the line used between the elements and the switching box. Quarter wavelength lines will result in open centers, while half wavelength lines will yield shorted centers. Shorted lines that are longer than 1/4 wavelength will add capacitive reactance to the wires and possible increase the directive effect in the direction of the unused wires. Shorted lines shorter than 1/4 wavelength or longer than 1/2 wavelength will likely add inductive reactance to the unused wires, converting them into reflectors of sorts. The effect, of course, will vary from band-to-band, since the line length to the switching box will change its electrical length with changes of frequency.

+

For many applications, minor directive and reflective effects may be no hindrance, and the smaller footprint of the true triangle will be the overriding consideration. For some applications, maximum isolation of each antenna will be the dominant concern: in such cases, the Y-array should be the configuration of choice. Before making this decision, it would likely be wise to model the system--with the proposed feedline as part of the model--to gain a better view of actual effects.

+

The "Expanded" Lazy-H

+

Before leaving the field of back-up wire antennas that are about 88' long and that cover 80 through 20 meters, we should take note of the expanded lazy-H, which likely first appeared in print in CQ in an article by W2EEY. Figure 14 shows the essential elements of the array: wires vertically spaced 44' apart. Although there are monoband schemes for bottom feeding the array, multi-band use tends to require balanced in phase feeding of the system, as shown in the sketch.

+
+ +
+

As we did with the independent doublet and the triangular arrays, let's place this antenna at a top height of 100', with the lower wires at 56'. For the data in Table 8, I used a 450-Ohm phasing line and took that feedpoint impedance readings from the junction of the two 22' lines.

+ 
+Table 8.  100' Performance of an Expanded Lazy-H of 88' #12 Copper Wire Doublets
+Freq.       F-S Gain    TO Angle    Vertical    Horizontal  Feedpoint Z
+MHz           dBi       (deg.)      B/W (deg.)  B/W (deg.)  R +/- jX Ohms
+ 3.6         5.95       46          138         131           10 - j  95
+ 3.9         6.05       43          141         118           15 - j  60
+ 5.37        8.81       30           37         137          150 - j 115
+ 7.0         9.02       23           27          76          455 - j 445
+10.1        11.69       16           18          56           20 - j  45
+14.0        14.87       11           12          32           50 + j 385
+

We should divide our discussion of the performance between the lower bands and the upper bands for this antenna. The lower bands show lesser gain and higher TO angles than the independent doublet. This phenomenon results from the fact that the elevation angle at any frequency is a composite angle of the upper and lower wires. The lower wire at 56' significantly increases the 80/75-meter TO angle. The vertical beamwidth is very wide, which may compensate to a degree by offering low angle performance not far down from maximum. However, on the lowest band, the high angle reception is likely to increase the overall noise in relationship to signal strength. Hence, for 80 and 75 meters, finding a way to disable the lower wire and using only the upper wire would make good operating sense. On 40 meters, the added gain compared to a single doublet may more fully compensate for the slightly higher TO angle.

+

The performance on 60 meters is similar to the performance of a single wire triangle. The front-to-back ratio is 13 dB and the main forward lobe is in a direction away from the "inactive" reflector wires.

+

Upper band performance of the Lazy-H is marked by very significant increases in gain over a single doublet without decreases in the horizontal beamwidth. Where the gain comes from appears in Figure 15, an elevation plot for 30 meters.

+
+ +
+

Compare this plot to the 30-meter trace in Figure 4. That plot shows a very strong second elevation lobe at about a 45-degree elevation angle, along with the "dome" that indicates the development of third lobes. The expanded Lazy-H (which is a little under 1 wavelength long on 30 meters) shows strong first elevation lobes with second lobes about 10 dB lower in strength. The 20-meter elevation pattern would show a similar plot, with more ripples but no added strength above the first lobe. The added gain in the lowest lobes comes from the reduction in high angle gain--a very nice trade indeed.

+

The impedances of the triangle of lazy-H arrays suggest the use of a lower-impedance parallel line. Due to the variation in values from band to band, you can expect some tuning difficulties with common tuner designs. You may use inserts of added line length to arrive at the best set of impedance values for each band. On any band where the tuning is very sharp at the recommended low-power initial tune-up point, raise the power level slowly, checking for any necessary returning as you go. 20 and 80 meters may present the most difficulties due to the relatively high ratio of reactance to resistance.

+

I have not modeled a Y-array of three expanded lazy-Hs, but I would suspect that the end-to-end isolation of the antennas would be similar to that of the doublets. If we have three (or 4) tall poles, towers, or trees for the support of a doublet array, we might wish to think about the expanded lazy-H as an alternative--at least for all of the bands except 80/75 meters.

+

Updating the Expanded Lazy-H for 80-20 Meters

+

Some of the impedance values for the feedpoint junction of the phasing lines to the elements show similarities to those of the basic 88' doublet, although with a somewhat smaller X:R ratio. The most troublesome feedpoint impedance values occur when the resistive component is very low and the line impedance is quite high. The result is en exceptionally high SWR that even the low-loss reputation of parallel lines cannot overcome. That is, the line losses will be very considerable and in some cases prohibitive.

+

The are several strategies to lower the line losses. One route is to lower the impedance of the feedline to the lowest practical level while maintaining an open-wire construction to preserve the very low level of matched-line loss. 300-Ohm lines will go a long way toward reducing line losses to a more (but not completely) acceptable level when the feedpoint resistance is very low and the reactance is significant. Vinyl-coated lines aqre most common in this category, although we must use two precautions with them. First, the loss level of a vinyl coated line is higher than for open wires. Second, we must use line that is rated for transmitting duty and not the inexpensive low-power TV reception line.

+

We may also use other techniques to modify the arrangement of the antenna (including phase lines). One relatively easy technique is to raise the impedance of the phase line to the highest practical level, perhaps 600 Ohms. Table 9 compares the 88' lazy-H at a top height of 100' for 450-Ohm and 600-Ohm phasing lines with respect to the feedpoint impedance.

+ 
+Table 9.  Feedpoint Impedanceof an Expanded Lazy-H of 88'
+#12 Copper Wire Doublets at 100'
+              450-Ohm Line             600-Ohm Line
+Freq.         Feedpoint Z              Feedpoint Z
+MHz           R +/- jX Ohms            R +/- jX Ohms
+ 3.6           10 - j  95               15 - j  95
+ 3.9           15 - j  60               20 - j  50 
+ 5.37         150 - j 115               90 + j 215
+ 7.0          455 - j 445              990 - j 260
+10.1           20 - j  45               40 - j 100
+14.0           50 + j 385               60 + j 450
+
+

In most cases, the ratio between the resistance and reactance changes very litttle, but the 80- and 75-meter resistance values do rise slightly.

+

An alternative is to use a slightly longer element length. Chuck Gerarden, W0DLE, has constructed a lazy-H of the present type on a tall tower using 92' elements. Chuck's elements use an interesting techniques of employing aluminum tubing for the inner sections and thin-wall fiberglass tubing with aluminum wire inside for the outer sections. Fig. 16 shows the antenna. At present, only the upper element rotates, although he will add a rotator for the lower element. He also has the ability to switch between upper-only, lower-only, and both elements in phase. For the present, he has the array aligned for bi-dirctional coverage of both coasts, but can rotate the upper element on the lower bands where the single element gain exceeds that of the combination of upper and lower elements. When he activates only the upper element, he can use the tower as a top-hat loaded vertical for 160 meters.

+
+ +
+

If we combine the higher-Z phase-line with the longer element, we obtain the probable feedpoint impedances shown in Table 10. Note that the table does not account for the fatter elements used in Chuck's antenna.

+ 
+Table 10.  Feedpoint Impedanceof an Expanded Lazy-H of 92'
+#12 Copper Wire Doublets at 100'
+              600-Ohm Line             
+Freq.         Feedpoint Z              
+MHz           R +/- jX Ohms            
+ 3.6           15 - j  75             
+ 3.9           25 - j  30           
+ 5.37         125 + j 265             
+ 7.0          865 - j 595            
+10.1           40 - j  75           
+14.0          130 + j 670            
+
+

We can extend both techniques--raising the phase-line impedance and elxtending the element length--and effect some further small improvements. We might try for 100' elements and check phase-lines of 600 Ohms and 800 Ohms for this type of lazy-H. Table 11 provides the results of this experiment.

+ 
+Table 11.  Feedpoint Impedanceof an Expanded Lazy-H of 100'
+#12 Copper Wire Doublets at 100'
+              600-Ohm Line             800-Ohm Line
+Freq.         Feedpoint Z              Feedpoint Z
+MHz           R +/- jX Ohms            R +/- jX Ohms
+ 3.6           25 - j  20               30 + j  26
+ 3.9           35 + j  35               40 + j  92 
+ 5.37         320 + j 435              295 + j 585
+ 7.0          240 - j 450              555 - j 745
+10.1           30 + j  30               55 + j  45
+14.0          320 - j 810              225 - j 895
+
+

The effects are small, but may make the difference between whether a tuner can handle the resulting impedance at the shack end of the line. Of course, for tower-mounted elements, the user can mount a remote weatherproofed tuner at the feedpoint and eliminate all line losses except a. the small losses in the phase lines and b. the matched-line losses of coax running from the feedpoint to the equipment in the shack.

+

Extending the length of the element has a drawback on 20 meters. Remember that the premise of the 88' back-up antenna was to have the main lobes of the bi-directional pattern broadside to the element. Fig. 17 shows that about 100' is the absolute limit of an element length that will cover the 20-meter band in this fashion. Even so, the sidelobes that we see at the 88' length grow until they are about equal in strength to the broaside lobes. As well, the broadside lobes suffer further reduction in their beamwidth.

+
+ +
+

These alternatives to the 88' lazy-H for 80-10 meters with a standard 450-Ohm line prove the old saying that there may be no such thing as a perfect antena--or at least a perfect simple antenna. As we squeeze out a slightly more convenient feedpoint impedance at 80 meters, we begin to see a decay of the desired 20-meter performance.

+

Conclusion

+

The horizontal wire back-up antennas and arrays I have described depend on height for good performance on all bands. If you have the structures in place--or if you are thinking about how to place towers for a major antenna farm for the lower bands, you might seriously consider setting them up so as to support one or more of the suggested antennas as the system back-up. They offer to take up the slack in operations when the main systems are down.

+

However, if you only have the trees or poles with no present antennas, you may wish to give one of these arrays another kind of serious consideration. Although I have called the 88' doublet (and its variations) a good back-up antenna relative to larger systems, there is no reason that it cannot form the basis of a very good main system on its own, at least from 60 meters on up through 20. It is at least worthy of thoughtful investigation during the planning stages of a low-band antenna farm.

+

The key to the system is the property of the 88' doublet to have true bi-directional patterns on all of the bands from 80 through 20 meters. (We can do--and I have elsewhere done--a similar exercise with a 44' doublet to cover 40 through 10 meters.) Pattern control is a key element in serious operation, and the 88' doublet offers flexibility and reliability if we are willing to dust off that old link-coupled tuner and invest in some high quality parallel transmission line. Whether you keep it simple with an independent doublet, get bold with a Y-array or triangle, or go totally wild with the expanded lazy-H--alone or in an array--the performance is likely to be surprisingly good. However, do not develop high expectations from 80 and 75 from the short wire element and possible line losses. However, as a back-up antenna or array, the 88' length may prove serviceable as a single compromise length with determinate pattern directions.

+

Updated 04-14-2000, 11-01-2004, 09-08-2005. © L. B. Cebik, W4RNL. This item first appeared in volume 2 of the Top Band Anthology, pp. 19-33. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Doublet, HF Multi Band, Lazy H


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Suppose I Could Have Only One Wire Antenna. . .

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+
+

L. B. Cebik, W4RNL

+

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+ +

+
+

. . .What would I choose? Let me be a bit more specific. Suppose I wanted to work 40 through 10 meters. And further suppose that I want to know where my signal is going. Now what would I choose.

+

The 40-Meter Dipole Starting Point

+

The most common answer to the problem I just posed is a 40-meter #12/#14 copper wire dipole, fed with parallel transmission line for use as a multi-band doublet. Fig. 1 tells the simple construction tale.

+
+ +
+

Placed high enough in the air, the 67' doublet performs very well. Its bi-directional pattern on 40 has good side QRM rejection, and with enough altitude, the elevation angle makes DX a real potential with every band opening. Let's place the antenna at a height of 66' (about 20 m) up and see what the models tell us that we can expect by way of performance.

+ 
Freq.     Max. Gain      TO        VBW       HBW       Feedpoint Z
+MHz        dBi           Deg       Deg       Deg       R +/- jX Ohms
+ 7.15      7.3           28        35        86          70 - j  10
+10.1       8.1           20        23        70         275 + j 800
+14.15      9.0           15        16        51        4670 - j 345
+18.1      10.5           11        12        33         175 - j 860
+21.2       8.4           10        10        33         100 - j 115
+24.95      9.3            8         9        33         375 + j 730
+28.5       9.5            7         8        28        3265 + j 375
+

The TO angle is the elevation angle of maximum radiation. I have also provided information on the vertical and horizontal beamwidths (measured to the -3 dB points from the maximum strength bearing). We often neglect this information, but the data tell us some important facts. The vertical beam width is a rough measure of the range of elevation angles that we can count on for good communications. The horizontal beamwidth tells us how broad or narrow our signal is and hence how careful we must be in aiming the antenna--either when we build it or when we rotate it. (One of the amusing facets of reading lots of e-mail is discovering how many beam users demand 1-degree aiming accuracy when their beamwidths are well over 50 degrees.)

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The 67' doublet shows the anticipated lowering of the TO angle as we increase frequency. As we increase the frequency, the antenna is increasing in electrical height, that is, its height as a fraction of a wavelength. So we expect the beam angle to be lower on the upper bands. The beam widths--both vertical and horizontal--narrow with rising frequency. Still, the vertical beamwidth is wide enough on all bands to catch the main stream of long-range skip. And the horizontal beamwidth is sufficiently broad to make aiming non-critical (but not unimportant).

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The range of impedances at the antenna suggests that with a parallel transmission line and an ATU, we should be able to effect a match on all bands. 20 and 10 meters might present slight problems, but changing the line length will likely solve them by presenting the ATU with impedance values it can handle.

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However, the gain column presents us with a small problem. The maximum gain of the 67' doublet occurs on 17-meters, takes a large dip above that band, and then slowly rises once more. For a simple wire, the actual gain numbers are not the problem. The question we want to ask is this: why does the dip occur?

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Fig. 2 can help us figure out what has occurred. The azimuth patterns overlaid on the plot are for 40, 15, and 10 meters. The 40-meter pattern is the typical oval. As we increase frequency, the oval grows narrower (decreasing horizontal beamwidth) while the gain increases--up to 17 meters. On this band, the 67' doublet is about 1.25 wl long: an extended double Zepp (EDZ). We expect about 3 dB gain over a dipole from an EDZ, and if we compare the 40-meter and 17-meter gain figures, we can see that we get it.

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Above 17 meters, the antenna is longer than 1.25 wl. At 15 meters, the antenna is about 1.5 wl long. The main lobe is no longer broadside to the antenna, but, as shown in Fig. 2, it is broken into 6 distinct lobes. The lobes broadside to the wire are no longer the strongest. As we move into the 10-meter region, where the antenna is 2 wl long, we have a pattern composed of 4 lobes at roughly 40-degree angles to the wire.

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For those unfamiliar with pattern development as an antenna becomes multiple wavelengths long, the following rules of thumb apply. For an antenna that is N wavelengths long, where N is an integer (like, 1, 2, 3), the number of lobes is twice the value of N. So a 2 wl antenna has 4 lobes, and a 1 wl antenna has only 2. For antenna lengths that are N.5 (like 1.5, 2.5, etc.), the number of lobes will be the sum of the number of lobes we get at N and at N+1. At 15 meters, where the antenna is 1.5 wl long, 1 wl gives us 2 lobes and 2 wl gives us 4 lobes, for a total of 6. The higher number at N.5 wl values arises because the new lobes are growing and the old ones shrinking--and they are nearly equal strength at the N.5 wl points.

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The 44' Wire Solution

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The problem with wire lengths over 1.25 wl is that we are no longer sure that we have a good signal broadside to our antenna. Suppose I put up a wire in Tennessee, running it NW to SE. That makes it broadside to Europe in one direction and to VK/ZL-land in the other. Not a bad set up. However, the main lobes for frequencies from 21 MHz up are no longer going where I want them to go. (Where they go may result in interesting contacts, but we set up our problem at the beginning so that it includes the need to keep our signals where we want them.)

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There is a simple solution to this problem, but it may not be the one some folks would expect. Conventional wisdom tells us always to make antennas bigger and longer. However, the solution to our problem is to make our doublet shorter. Let's try a doublet that is 44' long, as in Fig. 3. Again, #14 or #12 AWG copper wire will do just fine for the antenna.

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The first question we may now ask is whether we lose anything with the shorter wire. Let's find part of the answer in another table, modeled with the copper wire (#14 AWG) antenna 66' above average ground.

+ 
Freq.     Max. Gain      TO        VBW       HBW       Feedpoint Z
+MHz        dBi           Deg       Deg       Deg       R +/- jX Ohms
+ 7.15      7.0           29        35        94          25 - j 580
+10.1       7.6           20        23        83          55 - j 100
+14.15      7.7           15        16        72         195 + j 485
+18.1       8.6           12        12        60         920 + j1565
+21.2       9.0           10        10        51        4160 + j 155
+24.95     10.4            8         9        40         520 - j1545
+28.5      10.4            7         8        31         140 - j 650
+

The gain figures begin about a quarter dB below the figures for the 67' doublet on 40 meters and climb steadily. The elevation angles of maximum radiation and the vertical beamwidths are virtually identical to those for the longer doublet. The shorter antenna provides a broader horizontal beamwidth on every band, which makes aiming less critical. The pattern of impedances offered at the feedpoint differs in detail from that of the longer doublet, but the values are manageable. However, see the cautionary note below.

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To see one of the major advantages of our short doublet, we should look at Fig. 4.

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The composite azimuth patterns for the doublet on all of the bands for which it is intended have their major lobes exactly broadside to the wire. The 44' length was no accident. On 10 meters, this length is about 1.25 wl long, the standard EDZ length. The 10-meter pattern shows the anticipated strong main lobes plus the emerging "ears," secondary lobes that will become the major lobes at higher frequencies. On 15 meters, the antenna is about 1 wl long, and on 30 meters it is just under the right length for a half wl dipole (which is indicated by the low resistive impedance and the capacitive reactance for 10.1 MHz). On 40 meters, the antenna is between 1/3 and 3/8 wl long, about the minimum length we should use. Anything shorter would show very low resistance values and very high reactance values--a difficult situation for any ATU to handle.

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If I wanted to aim at both Europe and at Australia and New Zealand on all bands from 40 through 10 meters, then the 44' doublet is the superior antenna to the longer 67' doublet. Of course, larger (102' or 135') all-band doublets break into fragmented lobe patterns at lower frequencies than the 40-meter dipole with which we started. So, if we make aiming one of the criteria for our antenna, the 44' doublet may be the way to go.

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Two side notes. First, if we want to cover the bands only up through 20 meters, but want to include 80 and 75 meters within the frequencies for which we are well-aimed, then an 88' doublet might meet our needs. Of course, there is nothing magic in the precise length numbers chosen, since a length change of a foot or two will change almost nothing in terms of performance. The bands with the highest reactances at the feedpoint might show the greatest change in value as we alter the antenna length, but the feedpoint values on the other bands would hardly change enough for an ATU to notice.

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For either the 88' or the 44' doublet, the lowest band of use (80/75 and 40, respectively) present challenges in line losses and matching at the shack end of the line. Hence, the short doublet--only 1/3 to 3/8 wavelength on the lowest band--should be considered as a back-up antenna on those bands.

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Second, height is a major consideration with this sort of antenna. Perhaps 66' is not feasible for everyone. However, every foot of (safe) height that you can add to the antenna, the better it will work. This principle goes back to the days of George Grammer of ARRL, who preferred to add height rather than elements to his antennas. The idea is no less true today, although there are some limits. Once we get above 1 wl, there may be some holes in our DX elevation-angle coverage at certain antenna heights. However, in Grammer's day, only on 10 meters and VHF did most hams think about heights above 1 wl or so.

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The Aluminum Alternative

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There is no good reason why a single element antenna must be constructed from thin wire--excepting cost and ease of construction. If there is only one support that is high enough, then we might well consider constructing an aluminum tubing version of the 44' doublet. Fig. 5 shows one of many possible schemes for constructing the element. The wind survival rating for this scheme is about 70 mph.

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In tabular form, the element structure looks like the following partial antenna model description.

+ 
              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1        -22.000,  0.000, 66.000  W2E1 -19.000,  0.000, 66.000 5.00E-01   3
+2   W1E2 -19.000,  0.000, 66.000  W3E1 -15.250,  0.000, 66.000 6.25E-01   4
+3   W2E2 -15.250,  0.000, 66.000  W4E1 -11.500,  0.000, 66.000 7.50E-01   4
+4   W3E2 -11.500,  0.000, 66.000  W5E1  -7.750,  0.000, 66.000 8.75E-01   4
+5   W4E2  -7.750,  0.000, 66.000  W6E1  -4.000,  0.000, 66.000 1.00E+00   4
+6   W5E2  -4.000,  0.000, 66.000  W7E1   4.000,  0.000, 66.000 1.25E+00   9
+7   W6E2   4.000,  0.000, 66.000  W8E1   7.750,  0.000, 66.000 1.00E+00   4
+8   W7E2   7.750,  0.000, 66.000  W9E1  11.500,  0.000, 66.000 8.75E-01   4
+9   W8E2  11.500,  0.000, 66.000 W10E1  15.250,  0.000, 66.000 7.50E-01   4
+10  W9E2  15.250,  0.000, 66.000 W11E1  19.000,  0.000, 66.000 6.25E-01   4
+11 W10E2  19.000,  0.000, 66.000        22.000,  0.000, 66.000 5.00E-01   3
+

The construction shown in the figure should be designated light to medium for the element length involved. It is based upon purchasing 8' lengths of aluminum and cutting them in half. Prices for 6061-T6 aluminum tubing from sources such as Texas Towers and others are quite reasonable. The tapering scheme allows for about 3" of tubing overlap at every junction. Any less overlap would jeopardize physical strength, while too much more overlap will unnecessarily increase the element weight. The double section of 1.25" and 1.125" diameter tubing at the center provides reinforcement for most mounting schemes.

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Some builders prefer to alternate longer and shorter sections of tubing for greater overall strength. Whatever scheme one uses, analyzing it through a program such as YagiStress by Kurt Andress can go a long way toward ensuring a mechanically sound antenna. Nonetheless, the 44' doublet is only about 9' longer than most 20-meter Yagi reflectors and a good bit shorter than the elements used for 30-meter and 40-meter Yagis. Hence, the use of an aluminum tubing element is certainly feasible.

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Special Note: Some time after I placed this note at the site, Carroll Allen, AA2NN, pointed out the the taper schedule suggested would have a wind survival rating of only about 70 mph. He developed a spread sheet for EXCEL to calculate the stress on the tubing. For commonly used antenna tubing, such as 6061-T6, with a wall thickness of 0.058", the maximum stress for each section should be 40,000 psi or less. He kindly redesigned the sections for a 100 mph wind survival rating. The following table presents the revised taper schedule. Like the original schedule, the 1.125" diameter section is presumed to run all the way through the 1.25" section, but also to have its own exposure length.

+ 
      44' Aluminum Doublet Half-Element Structure
+             for 100 MPH Wind Survival
+Diameter (")    Section L (")   Cumulative L (")
+  1.25              72                  72
+  1.125             19                  91
+  1.0               20.5               111.5
+  0.875             21.5               133
+  0.75              23                 156
+  0.625             24                 180
+  0.5               84                 264
+

The use of aluminum tubing provides a small but determinate increase in electrical performance for the doublet. As we increase the diameter of an element, the RF resistance decreases considerably. Although copper wire is certainly efficient enough for most purposes, the tubing version of the antenna shows an increase in efficiency, despite the fact that the tubing version user aluminum, which has a higher resistivity than copper.

+ 
Frequency           #14 Copper Wire          Stepped-Dia. Aluminum
+  MHz               Efficiency (%)           Efficiency (%)
+ 7.15                    96.98                    99.70
+28.50                    98.35                    99.77
+

Notice that the differential in efficiency grows less as the frequency increases, that is, as the wire diameter becomes a greater fraction of a wavelength. Nonetheless, the tubing version shows systematically higher gain values for each band than the wire version of the 44' doublet. Compare the following table with the copper wire table given earlier.

+ 
Freq.     Max. Gain      TO        VBW       HBW       Feedpoint Z
+MHz        dBi           Deg       Deg       Deg       R +/- jX Ohms
+ 7.15      7.2           29        35        94          20 - j 410
+10.1       7.7           20        23        83          50 - j  85
+14.15      7.8           15        16        72         195 + j 295
+18.1       8.7           12        12        60        1005 + j 845
+21.2       9.1           10        10        51        1700 - j 705
+24.95     10.5            8         9        40         285 - j 795
+28.5      10.5            7         8        31         100 - j 375
+

The gain differences are certainly not large enough to make any kind of operational difference in using the 44' doublet. At most, they help us better understand some of the variables involved in antenna structures.

+

Notice also that the feedpoint impedance figures vary from the wire values more radically as the frequency increases--and also where the resistance or reactance values are high to begin with. The values shown--which will vary considerably as one changes the precise length of the finished antenna--are nonetheless quite manageable by most ATUs.

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Supporting an aluminum doublet of the size we are suggesting is a considerable project. Fig. 6 shows the main aspects of the things we should consider.

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+ +
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1. We shall need a support tower or pole as tall as we can safely make it. Although I know some inveterate climbers much older than I am who regularly scale high towers, my own experience tends to decrease my tower height by one section for every decade older I get. Safety comes first; antenna height second.

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2. As I doodled the sketch in Fig. 6, I added a rotator for the fun of the prospect. We only need about 180 degrees rotation for this doublet, so a side mounting on an existing tower would likely be good enough. For sample photos of one version of this antenna constructed from tubing and able to rotate with a CD44 rotator, see the web site of Adam, N4EKV. (Today's cheap TV rotators are no longer able to handle this antenna, but 25 years ago. . .)

+

3. For elements 40' and longer, consider adding a top-mounted truss to help support the element. A truss system will require a longer mast than truss-less elements. The exact position on the element to place the ends of the truss depends a great deal on the precise element diameter schedule chosen. Use a weather and UV resistant material for the truss rope.

+

4. Since the antenna will use parallel transmission line, stand-off insulators will be necessary. If the antenna is to rotate, the position of the line from the feedpoint to the stationary supports on the pole will require considerable planning. The line should avoid close proximity to any metal in the mounting region.

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5. The parallel transmission line is low loss inherently when the runs follow standard handbook recommendations. However, for lowest losses, consider true open-wire line rather than vinyl-coated lines. Even lines with "windowed" openings in the vinyl between the wires tend to show higher losses when wet than when dry. Line losses will generally be low except for the lowest band in the range shown.

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6. When the antenna feedpoint impedance is disproportionately reactive, you can expect difficulties effecting a match with an antenna tuner. On the lowest band, the 3/8 wavelength wire has an impedance where the reactance is 20 times the resistance. Under these conditions, the ability of a tuner to effect a match between the impedance at its terminals and the standard 50-Ohm coax to the rig will depend both on the line and the tuner configuration. Line concerns involve an interaction between the line length and the characteristic impedance. As well, even high-efficiency parallel lines will add losses to the already lower performance on the lowest band in the usable antenna range. To avoid tuner damage, tune up using low power and then raise power to the operating level.

+

Like all antennas, preventive maintenance at least once per year (every 6 months is better) will go a long way toward preventing unexpected catastrophic failures.

+

However, you decide to construct a single-element antenna, the 44' doublet has some interesting properties that provide advantages over other types of multi-band doublets. It is an antenna worth considering--if you can have only one wire.

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The use of the 44' length--or more properly, the approximate length of a 1.25 wavelength wire at 10 meters--is not new. It dates back to at least the middle of the 20th century. For example, Gene Fuller, W2LU, in the July, 1966, issue of CQ wrote an article on using 42' wires in a set of phased arrays ("Beam Antennas for the H.F. Range," page 12).

+

The 44'-wire exercise is designed mainly to encourage antenna builders to think "outside the box" of antennas that are naturally resonant at some operating frequency or at the lowest operating frequency. Resonance is not a requirement of good performance. Hence, we are free to set some one or more other goals for our antenna. In this case, we have set the goal of having radiation patterns that are broadside to the wire. For 40-10 meters, the 44' wire fulfills this goal, however, close to or far from resonance its length may be on any one of the bands covered.

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Updated 03-01-2000, 07-01-2002, 03-26-2003, 07-30-2003. © L. B. Cebik, W4RNL. This item appeared in AntenneX, February, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Doublet, HF Multi Band


+ + diff --git a/content/edz/edz.html b/content/edz/edz.html new file mode 100644 index 0000000..264a390 --- /dev/null +++ b/content/edz/edz.html @@ -0,0 +1,98 @@ + + + + + + Some Notes on EDZ Beams + + + +
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Some Notes on EDZ Beams

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L. B. Cebik, W4RNL

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Some time back, I wrote a piece for Communications Quarterly on the Extended Double Zepp ("Modeling and Understanding Small Beams: Part 3: The EDZ Family of Antennas," Fall, 1995, 53-71). My hope was to improve our understanding of the EDZ and look at some of its possibilities.

+

The EDZ in its simplest form is a non-resonant wire antenna about 5/4 wavelengths long. Being non-resonant, exact length is non-critical. Shorter versions have smaller side lobes but higher capacitive reactance; longer versions the reverse. Feedpoint impedance ranges from 100 to 150 ohms resistive with well over 600 ohms capacitive reactance. The chief reason for using the EDZ is its 1.5+ dB gain over a dipole comparably situated.

+

Brian Egan, ZL1LE and I had been discussing EDZ potentials since about 1991. He initially suggested a 2-element beam consisting of an EDZ driven element plus two Yagi-type reflector elements spaced a few feet behind the driven element and each pushed sideways to the wire end limits of the driven element. Modeling this configuration seemed to make a different arrangement preferable. From this arose the 2-element (driven element- reflector) beam noted in the article. The center of each element is inductively loaded, one for matching the feedline, the other for optimizing the rear element as a reflector. With 1/2 wavelength parallel lines down to near ground level, the two matching/loading units could be reversed, reversing the direction of the beam. This installation was tested for a couple of years at W4RNL and worked quite credibly.

+

Well, folks, as the old song says, "Everything old is new again." Bill McDowell, K4CIA, sent me a copy of an article from the June, 1938, QST, "The Extended Double-Zepp Antenna." In the back pages is a description of how to add a parasitical element to the EDZ. Author Hugo Romander, W2NB, describes a 0.2 wavelength spaced array. The driven element is stub matched to the source feedline. The other element is stub loaded inductively, but at two points: one for use as a reflector, the other for use as a director. Hence, a different system for a reversible beam--and a perfectly competent one. W2NB's system has the advantage of simplicity, while ours has the advantage of convenience. It can be fun to discover that one has reinvented the wheel. Fortunately, the information I added to the end of my article reviewing the principles of stub matching and loading would aid one to replicate the W2NB EDZ beam, so I do not feel totally disconnected from the 1938 work.

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From time-to-time, folks discuss the possibilities for a 3-element EDZ beam. Henry Pollock, WB4HFL, is actually planning to build one. The idea led me to try to verify his modeling results and to compare his configuration to an alternative.

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As with the 2-element EDZ, one has two main choices of configuration: 3 long elements or a long driven element with pairs of Yagi elements (directors and reflectors) at the extreme limits of the EDZ driving element.

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+

Henry has chosen the double-Yagi version, and very likely wisely so. Since he plans to put it at 60' for 10 meters, let's look at modeling results for both arrangements centered at 28.5 MHz.

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The 3-wire EDZ beam can be built from 3 41'8" lengths of #12 wire, each with a center load. The director requires about 800 ohms, the reflector 1150 ohms, and the driven element 980 ohms. The resulting antenna has a resonant feed resistance of about 90-95 ohms, just about right for a 1/4 wl matching section of 70 ohm coax to the regular 50-ohm feedline. You can make the director and reflector inductive loads from coils or from 450-ohm parallel vinyl covered feedline stubs 5.5' and 6.25' long each. If you do not use a split coil for the driven element feed point, you may wish to design a stub matching system--or perhaps use an ATU and parallel line all the way.

+

The potential beam performance at 60' is quite good: 15.5 dBi gain with about 30 dB front-to-back ratio. Adding the director to our old 2-element EDZ beam really improves the front-to-back ratio more than it helps raw gain.

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But here is the rub:

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The 3-wire EDZ beam is quite narrow-band in pattern--and even more so in feedpoint impedance and loading. At 28 and 29 MHz, the front-to-back ratio drops to the 7-9 dB range. The feedpoint shows a 250-ohm reactance change across the band. This is a beam that needs adjustment of all 3 elements if one hopes to cover more than 100 kHz of 10 meters. (For lower band versions, narrow the bandwidth in proportion of the ratio of the desired lower frequency to 28.5 MHz.)

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The double Yagi EDZ tells a somewhat different story. WB4HFL did not give me detailed dimensions, so I modeled my own version, with directors and reflectors spaced 5' from the driven element. Parasitical elements had outer limits in line with the end of the EDZ element (41'8"). Reflectors were 17'1" and directors were 16'0.5" long. #12 wire, of course, for consistency throughout.

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The results at the design center frequency were interesting: 16.0 dBi gain with a front-to-back ratio of 38 dB at 60' height. The front-to-rear quadrants had a minimum ratio of about 21 dB. What the 3-wire gives us in a slightly better front-to-rear ratio at design center is offset by the added gain of the double-Yagi version. Feedpoint impedance of the double Yagi version is about 90 - j1000 ohms, calling for a stub match or an ATU feed system.

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However, the WB4HFL-style design has two hidden advantages, partially revealed by a frequency sweep:

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First, the double-Yagi version retains a better figure from 28 to 29 MHz, never sinking below 11 dB front-to-back ratio at those extremes. While not superlative, the ratio climbs to nearly 20 dB at the 28.25 and 28.75 marks. These numbers are far superior to the 3-wire beam.

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Second, the only adjustment needed across the band is the driven element tuning. Like its counterpart, the double-Yagi version shows a 250-ohm reactance excursion across the band, along with a 75-ohm change in the resistive component. However, parallel feedline and a good ATU would take care of the problem. Because of the high reactance-to-resistance ratio, one might have to carefully select the line length in order to present the ATU with a load it can handle most efficiently. Nonetheless, no other adjustments are necessary, a plus for the double-Yagi design.

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Now why does the double-Yagi version work?

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If you look at the current distribution along the EDZ, it consists of a small central peak with outward dips. The outer 1/2 wavelength of the EDZ wire on either side is a perfect dipole current distribution pattern. Parasitical elements aligned with these peaks perform just as they would with independent in-phase separate driven elements. The 3-element double Yagi EDZ beam is actually a form of two in-phase-fed side-by-side 3-element Yagis with ¼ wavelength tip-to-tip spacing. And the performance is just about the same.

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One question that often arises with EDZ beams is how do we get rid of the ears in the pattern, those quartering side lobes. W1GQL, David Billheimer, sent me a design that accomplishes just that--an ear-less EDZ beam. Figure W1GQL-1 shows the azimuth pattern of this 20-meter 2-element wire beam.

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Dave's technique is to create what looks to me like a "gull-wing" design: the driven element is drawn in to midway between the 2 elements, while the parallel sections are drooped like a Vee. See Figure W1GQL-2.

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Dave's 20-meter CW beam has a 50' maximum height. The elements are about 5' apart. The two reflectors begin about 14.5' apart and droop to the 33.6' level at a maximum width of 39.4' each side of center. The driven element legs (beginning at center) move outward and forward to a little over 8' each side of center and then parallel the reflectors. (I have rounded the dimension numbers.)

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The natural feedpoint of this ear-less EDZ beam is about 60 ohms resistive and -j1000 ohms reactive. Dave uses stub-tuning to match 50-ohm coax for his narrow-band CW needs. However, the pattern of the beam holds up across 20-meters and can be fed with parallel feedline and an ATU quite effectively.

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I have added Dave's beam to demonstrate that we have not yet exhausted all the possibilities with either EDZs or wire beams. Among these notes and two articles, we have look at EDZs, stacked EDZs, parasitical EDZs, bent EDZs, and phased EDZs. I must be overlooking something. . .

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Of course: co-linear EDZs.George Goldstone, W8AP, sent me some correspondence he had with Hugo Romander, W2NB (W6CH in the 1960s), and Henry Pollock, WB4HFL, sent me a copy of a Ham Radio article by Alvan Mitchell, W6QVI. The article was an update on Hugo's co-linear EDZ array, which the ARRL Antenna Book of 1943 still carried. Since few folks have access to either Hugo's 1938 article or the 1943 Antenna Book, let's take a look at this version of the EDZ, outlined in the figure below.

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The antenna is given in terms of electrical degrees. The phasing lines are shorted parallel-line stubs. Here are Hugo's 20 meter dimensions and Alvin's 15 meter dimensions as samples: dimensions are in feet.

+ 
+Band     A         B         C
+14      43        53.5      11.5
+21      27.5      35.5       7.7
+
+

The 15 meter version, which I modeled extensively, is 126' long, about the length of a 75-meter dipole. So what do you get for all that linear space on 15 meters.

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You get almost precisely what Hugo predicted in 1938: about 7 dB gain over a dipole similarly place in a bi-directional pattern that is very narrow: 16°-17° between -3 dB points to be as exact as my model will permit. Modeled gain is about 14.3 dBi in a pattern like this one:

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The best points for installing the parallel line stubs in the 15-meter model were actually 1.5' farther inboard than W6QVI suggests: about 29' from the ends and 34' from the antenna center. 67° proved the length required for maximum gain. The feedpoint impedance is about 170 - j740 ohms, requiring an ATU, stub matching, or something similar.

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As W2NB pointed out, careful aiming is required. (The EDZ beams earlier noted had beamwidths between 32 and 38 degrees, while a standard Yagi or quad has a beamwidth between 50 and 60 degrees, depending on the number of elements.) This is no antenna for casual worldwide DXing. Rather, it is a serious point-to-point antenna. Within that context, it is an antenna that proves that narrow beamwidths are not impossible at HF. I have expensive flashlights with wider beamwidths.

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If you want a bi-directional antenna with a gain of about 18 dBi each way, while retaining the narrow (16-17°) beamwidth, try stacking two of these antennas at 5/8 wl separation. For the 15-meter sample, that places the two at 50' and 79' respectively. The feedpoint impedance, when fed in phase with 450-ohm line at the midpoint between the two, is about 65 + j350 ohms. A pair of series capacitors would cancel the reactance, providing a direct connection to 70-75-ohm cable (through a choke balun).

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Let's carry the experiment one step further. To each of the vertically stacked EDZ arrays, one might arrange a series of 1/2 wl reflectors to achieve some further forward gain and reduce the rear lobe. Alternatively, one might place a second vertically stacked array 1/8 wl behind the original vertical stack. Then, feed the rear array with a current magnitude and phase to maximize forward gain and front-to-back ratio. At 21.2 MHz, the spacing would be just about 5.8'. With proper feeding of the rear elements, we might achieve an azimuth pattern like this:

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21 dBi forward gain, over 26 dB front-to-back ratio, and a 16-17° beamwidth are figures that amateur radio operators rarely see from antenna arrays whose bases are about 1 wl up and whose tops are 1.7 wl up. Of course, for most operations, such figures are contrary to what is need for effective ham operation, but they might be useful for some specialized operations.

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Antennas spaced 1/8 wl apart call for 135° phase differences in the elements on the currents: this is the received wisdom. Unfortunately, it is wrong. Dipoles with this spacing might call for something close to this figure. However, for any two elements spaced more than a small fraction of a wavelength but less than 1/4 wl, there will be for each spacing a relative current magnitude and phase for the rear element that will yield maximum gain and maximum front-to-back ratio. With real materials, these two maxima may occur on very slightly different frequencies. For the array shown here, the maxima occurred with the rear elements fed at 0.75 the forward element current at a phase angle of 142 degrees. Slightly better performance might have been obtained if the upper and lower phased pairs had been individually optimized.

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It is unlikely that standard ZL Special techniques would achieve perfect phasing. Instead, one should most likely use phasing networks to establish the operating conditions. Since the arrays are identical, one could use this method to flip the direction of the beam electronically. "But in the end, this is all hypothetical, isn't it? No one could or would build such an array." Given that all the techniques needed are standard in the field, I am not so sure of this. Some folks might engineer such an array just to say that they have an array with 21 dBi forward gain and to listen to the long-path echoes of their own signals. Hams have done far stranger things in the history of the service. I wonder what might be heard if one of these reversible arrays were aimed directly toward one of the poles.

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We are still far from done with the EDZ. I am looking forward to the next step. These notes are simply the update so far. I'll add more as soon as I learn more about this interesting antenna. If I read enough old articles, I could learn more very shortly.

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Updated 5-10-97 © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

+

Topics: Doublet, HF Upper


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Feeding the EDZ

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L. B. Cebik, W4RNL

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Typically, Extended Double Zepp (EDZ) users employ one of two methods in feeding this higly capacitively reactive 1.25 wl long antenna. Some users, especially those who employ the antenna as a simple center-fed long wire on bands other than the design band, simply use parallel feedline and an ATU. Others, with single-band use in mind, use a matching stub arrangement to find a 50-ohm point for a coax feedline. Of course, one can also place a split coil at the feedpoint to provide the inductive reactance necessary to cancel out the antenna's inherent capacitive reactance, although the resulting resistive impedance will still be 100 ohms or greater.

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In the Summer, 1997, issue of Communications Quarterly, Rick Littlefield, K1BQT, presents a 2-meter EDZ that bears close examination. Besides an interesting construction method, designed to make a very durable EDZ for vertical use in hearing 2-meter repeaters, the key unique feature of Rick's design is the match and feed system that eliminates the usual center inductor to cancel out the heavy capacitive reactance at the feedpoint.

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An EDZ at almost any frequency has a variable feedpoint impedance and capacitive reactance, depending on the exact length to which it is cut. However, without altering performance by more than a tenth or so of dB gain, one can cut the antenna for a feedpoint impedance in the 100-140 ohm resistive range, which gives a capacitive reactance in the 500-600 ohm range.

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Rick applied a technique used with 5/8 wl vertical gp antennas: instead of an inductor, he uses a length of coax about 10.875" long, with a rod element beyond that point. Let's think of a 5/8 wl vertical and then simply place 2 of them feedpoint to feedpoint to get the final EDZ. The feed goes to the center conductor of the coax length. At the feed end, the braid is not connected to anything. At the far end, the center conductor and the braid are connected together and this junction goes to the 38" rod element. Rick calls this a delay line.

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When two of these assemblies are put end to end, the coax center conductors are the two terminals making up the feedpoint. The braid ends are about an inch or two apart (and must NOT be connected together). The result is a nearly purely resistive feedpoint impedance of 100 ohms in the 2-meter model. Rick uses a 75-ohm 1/4 wl (+ 1/2 wl added) to make a combination matching section and balun for a 50-ohm coax feedline.

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The delay line is interesting, because the name does not describe its function. Actually, it is a simple shorted feedline stub providing the inductive reactance necessary to cancel the antenna's capacitive reactance. Let's look at the figure to see the evolution of the arrangement.

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Part A shows the conventional split coil arrangement so familiar to EDZ builders (who do not use either open feedline to an ATU or a stub tuning method for a 50-ohm match). Part B replaces the inductors with a pair of shorted feedline stubs calculated to provide the same inductive reactance as the coil sections. Note that I have designated the outer part of the antenna line as "a" and the inner part as "b" in the sketch. When I substituted the parallel feedline, I designated on side of it as "c." "C" is as long as "b".

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There is no rule that says you cannot sometimes make a wire do double duty. There is no incompatibility between wire "c" and wire length "b" so that we can combine them together as in Part C of the sketch. And Part C is essentially the arrangement used in Rick's coax "delay" line. Because the coax is now doing double duty, the exact length may change from simple calculations for stubs, but it is very close.

+

Although the final arrangement looks like a Tee match, it is not. The center must have a gap, forming at best a split-T top. The open ends of the non-feedpoint center are actually the ends of the inductive stubs away from the feedpoint and thus must be kept independent of each other by a gap.

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The use of coax was possible in the original model, because the resistive portion of the feedpoint impedance was near 50 ohms on each side of center (for the 100-ohm total). Hence, the use of 50-ohm coax did not alter the feedpoint impedance.

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If we use feedlines of higher impedance, two things will happen. First, the feedpoint impedance will be reduced. Second, the length of the stub will increase, placing the junction of "c-b" and "a" farther outward on each side of center. The next figure is a sketch of a model I developed while exploring this subject.

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To create as reliable a NEC model as possible, I used 0.125" diameter aluminum for all parts. This kept the diameter constant, thus allowing a greater reliability of the result with NEC-4. I modeled the parallel lines 1" apart, give about a 330-ohm characteristic impedance for the resultant line. With a connection point about 14.5" outward from center and a 2" gap between the open ends, the stub/line or split-T match provides about 54 ohms resistive impedance and no reactance at the feedpoint. Hence, direct 50-ohm coax feed is now possible.

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The revised feed provides both capacitive reactance cancellation and resistive impedance transformation together. The length of the section is about the same as the combination of a 330-ohm shorted stub plus a length of the same line necessary to transform the overall impedance to nearly 50 ohms on its own, although treating this way of looking at the sections as a correct analysis of actions and interactions involved is far from certain at this point.

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However, the model's parallel feedline section is close enough to 300 ohms to suggest that experiments may be useful with twinlead, taking into account the line's velocity factor of 0.8, of course. The technique may also be applicable using 450-ohm window line or 600 ohm ladder line, experimentally finding the correct length to use. And the technique is likely applicable at all HF and VHF frequencies at which EDZs are in use.

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One advantage of the technique is that it is fairly broad-banded, giving full 2-meter coverage either in Rick's coax version or in the modified parallel line version shown here. I have not explored the consequences of this feed for use of the EDZ as a simple long wire on other HF bands--yet.

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Henry Pollock, WB4HFL, took up the challenge of creating a #14 copper wire HF version of the impedance transformation "delay" line EDZ. His initial version was 42' long with 450-ohm match lines either side of center, each 66.5" long. The antenna resonated at 28.9 MHz on this first try. Modeling the exercise suggested that lengthening the antenna a bit (to 44.7') and shortening the match sections to about 65.5" (adjusted after physical modeling for velocity factor) would likely bring the antenna closer to a 28.5 MHz target. The 2:1 SWR bandwidth of the model appears to be about 600 kHz, although the use of a coax feeder will likely widen the bandwidth operationally at the shack end of the line. These figures are not unlike the bandwidth numbers for stub-tuned versions of the EDZ.

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As a general rule, lengthening the antenna wire tends to reduce the resistive component of the feedpoint impedance, while lengthening and shortening the match section changes the reactance without affecting the resistance much. In general, it appears that the higher the characteristic impedance of the feedline used to effect the impedance transformation, the narrower the 2:1 SWR bandwidth of the antenna.

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So here is one more experimental way to feed an EDZ. The K1BQT and WB4HFL experimental antennas prove that the principle works, yielding an EDZ with no need for stubs or ATUs: matching is built into the antenna structure itself. Have fun creating some interesting prototype EDZs for 50-ohm feeds.

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Updated 8-27-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Return to Amateur Radio Page

+

Topics: Doublet, EDZ / Zepp, HF Multi Band


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+

An Almost Universal HF Back-Up Antenna
+ For the Antenna Farm That Has Everything Else:
+ Some Preliminary Notes

+

+
+

L. B. Cebik, W4RNL

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+

I have had occasion in the past to write on the W2EEY Expanded/Extended Lazy-H array that first appeared in the 1960s as a mono-band wire array. W6SAI later discovered that the antenna had available gain on frequencies in a range of at least 2:1. In other words, a 10-meter version of the antenna might be still useful on 20 meters.

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My own looks into this antenna suggest an even wider range of utility, even though performance tapers off steadily as one lowers frequency. The chief drawback of the antenna has so far been the fixation on wire construction. I wondered what tubular elements might do, and the result is this preliminary note.

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Large antenna farms for serious DX and contest use often have far more than one antenna per band. Hence, back-up on many bands is almost a matter of course. However, there is often only on antenna for each of the following bands: 40, 30, 17, and 12.

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Now suppose there were a single rotatable antenna of relatively easy maintenance (compared to a 5-element Yagi or similar) that might provide emergency performance on 40 through 10 meters, performance that was not stellar, but usable in a crunch. Further suppose that the antenna had a top height of not more than say 70' (about 1/2 wl on 40 meters) and has elements no longer than some of the half-size 40-meter beams that are commercially available. Finally, suppose that the antenna required no boom, but looked more like one of those 40-meter beams flopped over to point straight up.

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Such an antenna is not a mechanically simple installation, since 44' foot aluminum elements are not for the beginner. However, once installed, the antenna poses fewer stress problems than horizontally positioned arrays that require a boom. If it happened also be to bi-directional, then it might be laid close in to a pole or tower, since the total required rotation is 180 degrees.

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There might be a niche for such an antenna, so the performance potentials and the installation challenges seem worth exploring, at least on a preliminary basis.

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The W2EEY Expanded/Extended Lazy-H

The basic array is an extension of the Lazy-H: two 1 wl elements vertically separated by 1/2 wl and fed in phase. The W2EEY innovation was to extend the elements to 1.25 wl, extended double Zepp length. He also expanded the separation to 5/8 wl to maximize in-phase gain. +
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Fig. 1 shows the outlines of a typical extended Lazy-H in typical wire form. For many years, the Editors and Engineers Radio Handbook (edited by W6SAI) has carried that standard Lazy-H, fed at the bottom with a stub for coax matching for mono-band use. However, for multi-band use, a center junction of equal lengths of feedline is the simplest route to in-phase feeding on many bands.

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The dimensions of the array for 10 meters are a modest 44' element length and 22' vertical separation. The EDZ element lengths represent the practical limit for use on HF bands, including 10 meters. Longer elements will yield a multi-lobe pattern on 10 meters.

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The antenna height selected for study was a 66' top height. It can be mounted higher or lower with standard changes in the elevation angle of maximum radiation. However, a height of at least 66' seems advisable for reasonable 40-meter use.

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From Wire to Tubing

I have elsewhere looked at the performance of the W2EEY version of the antenna across many bands. The question that came to mind regarding rotating the array required a change in element material. So I redesigned the antenna for aluminum tubing having an aggressive tapering schedule. +
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Fig. 2 shows the arrangement used to develop models. There is no assurance that this particular schedule meets appropriate standards. Any actual elements that one might contemplate constructing should be taken through an exercise or two on YagiStress to determine their mechanical feasibility. Although the schedule used here has proven very useful in comparing wire versions of the antenna to the most severe gradations I could think of, the element design is hypothetical only in mechanical terms.

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Special Note: Some time after I placed this note at the site, Carroll Allen, AA2NN, pointed out the the taper schedule suggested would have a wind survival rating of only about 70 mph. He developed a spread sheet for EXCEL to calculate the stress on the tubing. For commonly used antenna tubing, such as 6061-T6, with a wall thickness of 0.058", the maximum stress for each section should be 40,000 psi or less. He kindly redesigned the sections for a 100 mph wind survival rating. The following table presents the revised taper schedule. Like the original schedule, the 1.125" diameter section is presumed to run all the way through the 1.25" section, but also to have its own exposure length.

+ 
      44' Aluminum Doublet Half-Element Structure
+             for 100 MPH Wind Survival
+Diameter (")    Section L (")   Cumulative L (")
+  1.25              72                  72
+  1.125             19                  91
+  1.0               20.5               111.5
+  0.875             21.5               133
+  0.75              23                 156
+  0.625             24                 180
+  0.5               84                 264
+

The chief differences between the wire and tubing versions of the antenna were two. First, the models had many more wires. Second, the source impedances (as taken at the junction of the two feedlines from the elements to a center small segment) varied somewhat from those associated with the wire version.

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For those unfamiliar with the extended Lazy-H, let's run a series of tabular entries and some patterns to check the potential performance. As with all models, these assume level, uncluttered terrain (average Sommerfeld-Norton ground) in NEC-4.1. Any serious antenna farmer has already run terrain analysis using N6BV or K6STI software and can therefore adjust the numbers for gain and elevation angles accordingly.

+

The figures in the first table focus on performance. The frequencies are band centers. Gain is maximum at the elevation angle of maximum radiation (TO angle). note that gain is bi-directional. The horizontal beamwidth is to the -3 dB points on the maximum gain curve.

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+Frequency      Gain      TO Angle       Horizontal          Notes
+  MHz          dBi       degrees        Beamwidth (deg)
+28.5           15.2       8             37             EDZ-type side lobes
+24.94          14.7      10             41
+21.225         12.6      11             52             Standard Lazy-H
+18.118         11.0      13             61
+14.175          9.1      17             73
+10.125          8.2      24             85
+ 7.15           6.5      33             99
+ 7.15           7.2      29             89             Using top wire only
+

As the table shows, gain decreases steadily with frequency, since the elements grow shorter and the spacing narrower. The 10-meter gain is similar to a long-boom 5-element Yagi (without the front-to-back ratio). On 15, gain performance is similar to some 3-element Yagis, dropping to 2- element performance on 17. Below that frequency, the antenna becomes the equivalent of a rotatable dipole.

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The patterns to follow, band by band, show the elevation patterns along the axis of maximum gain. Only spot azimuth patterns (for 10, 15 and 30 meters) are shown, since the evolution of the azimuth pattern with frequency changes is perfectly normal. One key advantage for the array is the relative absence of very strong high angle radiation, especially on the upper bands, thus reducing a potential noise source.

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+ 10-Meters +
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+ 12-Meters +
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+ 15-Meters +
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+ 17-Meters +
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+ 20-Meters +
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+ 30-Meters +
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+ 40-Meters +
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The 40 meter graphic shows two patterns, one for the use of both wires in phase, the other for the use of only the top wire. The latter is harder to implement in practice, but increases gain while lowering the take-off angle. On 30 meters, the use of only the top wire gives the appearance of lowering the take-off angle, but in fact, the bottom lines of the two patterns overlap, with the 2-wire system showing more gain. The seemingly unexpected result comes from a difference between vertical beamwidths for the two arrangements. Hence, on 30, the phased 2-wire system appears to offer superior overall performance.

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The decrease in gain for each reduction in frequency is clearly apparent. given the array of antennas that inhabit some of the most extensive antenna farms, one might judge 20-meter performance to be the weakest in comparative terms. WARC band antennas tend to be simpler, and relative to them, the array is down by only a couple of dB at most. (If one has designed against these tendencies, then the differentials will also be different.) From 15 meters upward, the array gain is quite good--indeed, competitive might be a reasonable term. However, on 20, 5-element Yagis are fairly common (as are stacks of beams that give similar performance). The array on 20 yields performance similar to that of a 1 wl wire, perhaps 2 S-units weaker than the high-performance main antenna(s).

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Nonetheless, the overall performance of the array relative to all of the antennas in use for every band must be accounted quite good in view of what the antenna is in this application: it is an emergency back-up capable of being switch in to replace any antenna system that goes dead when Murphy dictates. With a size similar to a half-size 40-meter 2-element Yagi pointing straight up, it is also much simpler than its most cogent competitor: a log-periodic for 40-10 meters.

+

Phase Lines

The models developed here used 600-Ohm, VF=1.0 lines for phasing. Each line was cut to 14' even though the distance to the center point was 11' only. A 3' buffer was allowed for each line to account for routing that would clear any metallic structures that might disrupt standard performance of the lines. +

With these constraints, the models yield the following source impedance calculations.

+ 
+Frequency      Source Impedance         Notes
+  MHz          R +/- jX Ohms
+28.5           140 - j 655         Highly variable with change of Zo
+24.94          335 + j 655         Somewhat variable with changes of Zo
+21.225         110 + j  85         Decreases with Zo decreases
+18.118         165 - j 135         Decreases with Zo decreases
+14.175         880 - j 136         Highly variable with change of Zo
+10.125          65 + j 250         Reasonably stable
+ 7.15           14 + j  10         Low and stable
+ 7.15           14 + j  30         Top-wire only in use, with line.
+

The number of cases in which the source impedance decreases with lower characteristic impedance phasing lines suggest that the highest feasible value of Zo be used for the antenna. Indeed, with lower values of Zo, the 40-meter source impedance can decrease below 10 Ohms, rapidly escalating the negative effects of loss sources in any installation.

+

High variability with changes in phasing line type tend to indicate that the builder of any antenna of this type may encounter quite different source impedances owing to minor local variations. Although the phased pair of 44' doublets yields lower ratios of reactance to resistance, relative to a single 44' doublet, the low impedance at 40 meters may prove difficult to match at the tuner end of the line. The reactance will vary more widely than the resistance over a greater section of each half wavelength of line. Hence, careful line-length selection may prove necessary, although this factor will vary with the particular tuner configuration and internal components.

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On the basis of these results (typical of several different models), there appear to be three initially plausible feed systems.

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1. Parallel feedline and an ATU: The simplest feed system is to use parallel feedline from the juncture of the phasing lines to the operating position, with an ATU providing the requisite matching. for minimum loss in the matching system and for maximum isolation of equipment from common mode currents, a link-coupled tuner is recommended (with due construction precautions against unintended common mode paths). Without careful measurement of the actual source impedances encountered and equally careful measurement of the feedline length, there may be cases in which the impedance presented to the tuner terminals falls outside the range for which the tuner can effect a match while compensating for reactances at that point. Ordinarily, changing the line length in small increments will overcome this problem without incurring significant losses.

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2. Remote switching of matching circuits--Version 1: A box of fair proportions installed at or very near the junction of the two phase lines might contain an array of circuits matching the source impedance on each band to standard 50-Ohm coaxial cable (or 75-Ohm hardline). The system would require a power source to control separate input and output sides of each network. The design of such a system would have to be a custom installation based on the actual source impedances of the system.

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3. Remote switching of matching circuits--Version 2: A remotely switched matching network box mounted precisely at the junction of phase lines may present mechanical problems if the installation has a rotating mast joining the two elements. Moreover, the impedances to be matched may not be the most desirable. A length of open-wire parallel feeder from the phase line junction to some point further down the support structure may provide more desirable values and a more convenient mechanical installation. Since the variables of this modified system are so many, I have not explored any particular line lengths to check feasibility. Hence, electrically, this system can only be classed as equivalent to the first version.

+

Either remote matching system serves a certain preference among antenna farmers: the desire to present sensitive rigs and amplifiers with loads that require no in-shack tuning during intensive operations. All adjustments are made during installation and remade during routine maintenance. Those willing to make real-time adjustments and who can correctly install open-wire feeders may wish to use the simplest of the systems outlined here.

+

Of the three systems, only the remote box at the phase-line junction is amenable to easy switch-over to using only the top wire on 40 meters. Adapting the other systems to such use will be an exercise in ingenuity.

+

Mechanical Considerations

+

+

The basic elements of the antenna structure appear in Fig. 3.

+

No support structure is shown, since this aspect of the installation is subject to so many variations. The antenna itself consists of two 44' long elements of considerable weight. The top one will be 22' above the lower one, which might be considered a moderate stacking challenge to those with large antenna farms. Since the elements are mounted close to the line of the rotating support mast, the stresses they impose upon the assembly may be less than those of elements at the ends of a boom. A mast extension to handle a truss system to add support farther out along the elements is certainly feasible and may well be advisable.

+

If the lower element is (or both elements are) are side-mounted relative to a supporting pole or tower, then there will be a dead zone in the rotation. The size of this zone in degrees will vary inversely with the distance of the mast from the support structure. If we assume that there is a direction from the station that can be ignored, side-mounting may offer a means of installing the emergency antenna on an existing tower or pole. However, the elements may well interfere with existing guy wires.

+

These mechanical notes are offered on the premise that anyone thinking about this antenna has considerable experience with tall installations and can integrate the structure into a considerable backlog of diverse variables involved in high pole and high tower work. Those who may be reading these very preliminary notes without requisite experience should perhaps review some of the very considerable stack of reprints offer by Champion (K7LXC) before becoming too much attracted to the ideas noted here.

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The aluminum extended Lazy-H is a bi-directional array with rotational capabilities that may make use of its reasonably narrow horizontal beamwidth on 40 through 10 meters. As such, it may fill a special niche, which I have termed the nearly-universal back-up for giant antenna farms. The feed system challenges are more electronic than they are mechanical--except for mounting and water-proofing a box for two of the suggested systems. Otherwise, the array presents fewer mechanical problems than most very large Yagis.

+

Still, the array not a cure-all for whatever ails. Nor is it a magic elixir for all antenna installations. The notes presented here simply suggest that for some installations, the antenna may provide that nearly universal back-up which is ever handy: ready to go on 40 to 10 meters when Murphy strikes down the primary antenna(s). Just do not tell Murphy you have installed one of these or he will take down your antennas two at a time.

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Updated 2-12-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

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Topics: HF Multi Band, Lazy H


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Not Everything Good is New:
+ The Expanded Lazy-H

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+

L. B. Cebik, W4RNL

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Very effective antennas do not have to be exceptionally large or expensive. The latest designs and construction methods have their advantages--and also their costs. They tend to obscure some older designs of high merit as we forget to remember them.

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Rotatable antennas are very effective, but for those unwilling or unable to put a tower, rotator, and sizable aluminum structure in the air, fixed position wire arrays can provide excellent gain. Most designs are bi- directional, but the side rejection is often sufficient to eliminate most QRM. If we have the trees or the poles to support the ends, and if we take the trouble to align the antenna in the most favorable directions for our intended operation, a wire array can work wonders. For example, a great circle drawn through my QTH in Tennessee with one end in VK-ZL land will have its other end in Europe. A bi-directional array might be just the ticket for much of my operating.

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Many broadside arrays are flat-tops--that is, they require at least two wires with considerable horizontal space between them. For most purposes, I would need 4 supports. However, a design that has been around since wire became popular is the Lazy-H, a vertical stack of two wires fed in phase. The standard Lazy-H consisted of two 1 wl wires spaced 1/2 wl apart and elevated so that the lower wire was 1/2 wl above ground.

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John Schultz, W2EEY, wrote in the November, 1968, CQ of the "Expanded Lazy-H Antenna." Bill Orr, W6SAI, recalled this antenna in one of his many columns during the 1980s. Another 15 years has gone by, so let's recall this effective array one more time. The key to expanding the Lazy-H is to increase both the horizontal and vertical dimensions by just a little bit.

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If we increase the wire lengths from 1 wl to 1.25 wl, we have stacked extended double Zepps in our Lazy-H. The effect is to give us a bit more gain per wire and a significant amount more from the pair. Then, if we increase the spacing from 1/2 wl to 5/8 wl, we achieve approximately the maximum stacked gain possible with two simple wires.

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Now, let's build one of these expanded Lazy-Hs for 10 meters.

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Fig. 1 shows the antenna outline. For 10 meters, a length of 44' per wire is satisfactory and not critical: 40' to 50' will work, but the pattern on 10 meter begins to split up as we lengthen the antenna too far beyond 1.25 WL. Vertical spacing between the two wires need not be too fussy, but the recommended 22' gives us not only 5/8 wl at 10 meters but a usable spacing at other frequencies.

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The recommended minimum of 1/2 wl at 10 meters is a bit low for optimal performance. I would recommend that a lower-wire height of about 44' be used, which places the top wire at 66' up. Lower heights will reduce the gain and elevate the TO angle from the figures I shall present as we think about this simple array.

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The mechanical beauty of the Lazy-H design is that it requires only two supports--although fairly tall ones. The electrical beauty of the antenna is that it provides excellent bi-directional performance from 10 meters through at least 17 meters, with good performance down to 30 meters. It can also be pressed into service on 40 meters without much difficulty.

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Fig. 2 shows the azimuth pattern of the antenna on 10 meters at an elevation angle of 8 degrees. The phase-fed array still retains the EDZ "ears." These ears are the beginnings of the multi-lobe pattern that emerges as the antenna wire length grows toward the 1.5 wl mark.

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On all bands below 10 meters, the length of the antenna is under the EDZ mark, so the pattern is bi-directional with single lobes each way. In fact, at 15 meters, the antenna becomes a standard Lazy-H: two 1 wl wires spaced 1/2 wl apart vertically.

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In Fig. 3, we see the 17-meter pattern at its elevation angle of maximum radiation of 13 degrees. As the tables below will show, the lobes become wider as we reduce frequency and narrower as we increase frequency.

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For a more systematic view of anticipated performance on all of the possible bands on which we might use this one Lazy-H, here is a table of modeled performance over average ground, with the lower wire 44' up. The table lists the usual gain and TO angle data, but also adds numbers for the vertical and horizontal beamwidths between the -3 dB (half-power) points. This date is useful in determining the azimuth coverage of the antenna in each direction and in estimating the elevation angles to catch the skip for varying circumstances.

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Freq      Max. Gain      TO angle       Vert. BW       Hor. BW
+MHz       dBi            degrees        degrees        degrees
+28.5      15.1            8              9             31
+24.9      14.6           10             11             41
+21.2      12.5           11             12             52
+18.1      10.9           13             14             61
+14.15      9.0           17             18             73
+10.1       8.1           24             27             85
+ 7.15      6.4           33             44             99
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By the time the antenna's operating frequency is lowered to 40 meters, the pattern becomes a broad oval with a fairly high TO angle, as shown in Fig. 4. However, sufficient radiation occurs at lower angles to make it usable for general purpose communications on that band.

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How good is the antenna's performance? I could use any number of comparators here, but the simplest would be a single 44' wire placed 66' up in height, the same height as the top wire of the array. The usefulness of this comparison is that it helps reveal something of the array's characteristics.

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Freq      Max. Gain      TO angle       Feedpoint Z
+MHz       dBi            degrees        R +/- jX Ohms
+28.5      10.5            7              150 - j 695
+24.9      10.4            8              620 - j1700
+21.2       9.0           10             4200 + j 850
+18.1       8.6           12              835 + j1560
+14.15      7.7           15              190 + j 490
+10.1       7.6           20*              56 - j 105
+ 7.15      7.0*          29*              24 - j 600*
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The starred gain entry for 40 meters indicates that the single wire at this frequency shows more gain than the array (by about 0.6 dB). In the TO angle column, the starred entries indicate that the single wire shows a significantly lower angle than shown for the array. Both phenomena are related. The array elevation angle of maximum radiation is a composite from radiation from both wires, with the lower wire radiation raising the angle of the final composite pattern. The difference is slight until the very lowest bands on which we might press this antenna into service. On 40 meters, the lower wire is just over 1/4 wl above ground, so that it raises the overall pattern angle of the array by a goodly amount and provides slightly less gain than the single wire that is about 1/2 wl up. As well, The high ratio of reactance to resistance in the feedpoint impedance suggests that there may be difficulty in obtaining a good low-loss match.

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From 20 meters on up, the Expanded Lazy-H shows good gain over a single wire. The benefits increase the higher one goes in frequency, up to the break-up of the pattern when the wires are longer than 1.25 wl. It is certainly possible to scale the antenna for maximum benefits at a lower frequency, but that lower frequency of maximum gain will become the highest frequency at which one can use the array and still have a bi-directional pattern with a single main lobe off each side of the wires.

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The single 44' wire also shows a wide variation in feedpoint impedance according to the length of the wire. The 10-meter value is typical for an EDZ. The 15-meter value is also typical, but of a 1 wl center-fed wire. Parallel feeders and a highly competent antenna tuner would be needed for this antenna. However, careful analysis of the impedance excursions along the chosen feedline can minimize the chances that the tuner antenna terminals will see either a resistance or a reactance value outside its range of adjustment.

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So far, I have given no figures for the feedpoint impedance of the Expanded Lazy-H. The two elements in Fig. 1 are fed in phase by the simple expedient of using equal lengths (11') of line to a center point to which we attach the parallel feeders going to the antenna tuner. There are two controllable variables that will affect the feedpoint impedance at the junction with the main line to the shack. One is the length of the lines, which we have set at 11' each. The other is the characteristic impedance and velocity factor of the phasing lines. I shall not here explore other phasing line lengths, but instead shall show some anticipated feedpoint impedances for each band using three different phasing lines. One will be a 450-Ohm, 0.95 VF line, typical of windowed vinyl-covered lines. Another will be 300-Ohm, 0.8 VF line, typical of good quality TV line. The third will be 600-Ohm, 1.0 VF line, which might be bought or built from wire and spacers.

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                    Feedpoint Impedance (R +/- jX Ohms)
+Freq      450-Ohm             300-Ohm             600-Ohm
+MHz       0.95 VF             0.8 VF              1.0 VF
+28.5       65 + j 425         115 + j 570          105 + j 610
+24.9       17 + j 115*         11 + j 140*          30 + j 140
+21.2       22 - j  15*         10 + j  38*          40 - j  50
+18.1       45 - j 125          16 - j  26*          90 - j 230
+14.15     385 - j 395          75 - j 150         1050 - j 350
+10.1       50 + j 105          40 + j  65           50 + j 155
+ 7.15      10 - j  95*          6 - j  80*          13 - j  90*
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Starred entries represent very low resistive components to the feedpoint impedance which might present larger excursions along whatever line is chosen as the main feedline to the shack. Note that the starred entries are fewest with the 600-Ohm phasing line. Once more, it is worth noting that these numbers are derived for general guidance from models. Variations will emerge from the actual construction of the antenna and from conditions and clutter at the antenna site.

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One question that almost always emerges with respect to comparing the single wire and the array gain figures for 10 meters is this: how can the array deliver over 4.5 dB gain over the single wire? The answer is straightforward if we compare elevation patterns for the two antennas. Fig. 5 tells the tale.

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Like any single-wire antenna, the EDZ at 66' on 10 meters shows an array of nearly equal-strength vertical lobes: 4 to be exact. In contrast, the upper lobes of the Expanded Lazy-H are suppressed leaving a single dominant lobe and a secondary lobe well over 4 dB weaker. All other lobes are down by 12 dB or more. The array tends to waste far less power at very high angles of radiation compared to the single wire. This comparative pattern, with variations, tends to hold true down through 20 meters.

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On 20, the effect is less pronounced but still easily measured, as shown in Fig. 6. The area enclosed by the upper lobes of the single wire at the top of the figure is distinctly greater by a considerable margin than the area enclosed by the upper lobe (barely discernable as a double lobe) of the array. The difference in area (assuming that the azimuth patterns are comparable, as they happen to be in this case) is a rough measure of the added power appearing in the lower lobes. In this case, that additional power shows up not only in the maximum gain, but as well in the vertical beamwidth. The phased feeding of vertically stacked horizontal wires has benefits hard to match in a typical flat-top wire array.

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Along side the benefits come some limitations. The Lazy-H requires a pair of tall supports and is suited to the antenna farm with more tall trees than money. It is possible to lay out more than one of these inexpensive antennas in order to cover additional regions along the horizon. It is likely that no special treatment will be needed to detune unused arrays to prevent them from altering the pattern of the array in use. Either leaving the shack end of the unused feedline open or shorting it will introduce to the wire feedpoints sufficient reactance to detune the wires. However, this is a facet of multiple array installation that the builder should keep in mind. Sometimes Murphy dictates that nothing will work to prevent interaction short of greater physical separation of the arrays.

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The Expanded Lazy-H is an outstanding bi-directional array for 10 meters in the design given here. Its performance holds up well down through 20 meters, and we can press it into service on lower bands. It takes up very little room horizontally in the yard, although a couple of optimally spaced tall trees certainly can aid the installation process. The wires for the elements and the phasing lines, as well as the feedline to the shack and the UV-resistant support ropes, are certainly inexpensive compared to the cost of a tower, rotator, coax, and commercial aluminum antenna. It is a design worth recollecting every 15 years or so just to make sure that we do not forget it.

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Can the extended Lazy-H be converted into a directional beam for some or all of the bands that it covers? To find out--at least in principle--see "Curtains for the Extended Lazy-H."

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Updated 4-5-1999; 04-15-2003. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Mar., 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Multi Band, Lazy H


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Not Everything Good is New:
+ Curtains for the Extended Lazy-H

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L. B. Cebik, W4RNL

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The Basic Expanded/Extended Lazy-H

A few years ago, I called attention to a wire array that receives notice only about every fifteen years--despite its excellent performance as a fixed bi-directional array of modest proportions. With two 44' long wires spaced 22' apart, the extended or expanded Lazy-H provides primary service on 20 through 10 meters, with quite adequate service on 30 and even 40 meters. From each element center, we run a parallel feedline--in phase--to a center position, which then becomes the primary feedpoint. We may use any feedline from 300 Ohms to 600 Ohms, although any figures shown in these notes will apply to 450-Ohm line with a 0.95 velocity factor. These notes also presume AWG #14 or #12 copper wire for the elements. +

The base of the antenna ideally should be about 44' or more above ground for the lowest elevation angles of maximum radiation (take-off or TO angles). However, if necessity prevent the top wire from reaching 66', then a lower height and higher elevation angles are tolerable.

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"The Expanded Lazy-H," at this site provides a set of representative elevation and azimuth patterns for the antenna. The following table summarizes the performance when set at a 44'-66' height. The gain is the maximum gain at the TO angle. The Beamwidth is the angle between half-power or -3 dB points away from the bearing for maximum gain. The feedpoint impedance (Feed Z) is at the junction of the two 11' lengths of 450-Ohm parallel line.

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+                  Extended Lazy-H Performance Potential
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+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.5       15.1        8         31                64 + j 425
+24.95      14.6       10         41                17 + j 115
+21.1       12.5       11         52                22 - j  18
+18.118     10.9       13         61                43 - j 125
+14.1        9.0       17         73               403 - j 395
+10.125      8.1       24         85                49 + j 105
+7.1         6.3       33         99                10 - j 100
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The impedances are all quite manageable for a wide-range balanced antenna tuner, with the possible exception of 40 meters and 12 meters. However, the impedance at the tuner will also be a function of the line length in wavelengths from the feedpoint to the tuner, so adjustment of the values to be matched is feasible.

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Planar Reflectors

My reason for returning to the extended/expanded Lazy-H grew out of an inquiry from Bill Burton, T88BA of Pelau. He had assembled the pieces for the antenna. However, he had also seen some commercial arrays that used a curtain-style reflector. Hence, he asked whether such a reflector was feasible for the big Lazy-H. +

I have seen a number of schemes for multiple extended double Zepps of about 44' and even for the Lazy-H, all designed to use parasitic elements or phased elements to convert the bi-directional array into a directional beam. Their complexity could be daunting, often with the result that only the builder knew the correct adjustments for each band. On the other hand, a planar or curtain reflector is a broad-band passive addition that might be serviceable.

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In UHF work, a planar reflector generally exceeds the dimensions of the active element or array by perhaps 3/8 to 1/2 wavelength on all four sides. Such a curtain would be somewhat ungainly for the extended/expanded Lazy-H. So I somewhat arbitrarily selected a set of dimensions that seemed close to feasible for someone with sufficient land to erect the basic antenna at the ideal minimum height. The modeled screen is 50' wide by 30' high. This is only 6' wider than the element lengths and 8' larger vertically. In many ways, it is a minimalist planar reflector.

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Fig. 1 shows the parts of the array, although not to scale. The extended/expanded Lazy-H remains unchanged from independent use which results in its bi-directional characteristics. The screen is centered behind the active array. Although the modeled screen uses a grid-square assembly, it is possible to use a sequence of wires parallel to each other. For this horizontal array, the wires must also be horizontal.

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The 10' spacing was my initial trial spacing for the reflector--just a bit shy of 1/4 wavelength at 15 meters. After looking at numerous other spacings, I returned to my intuitive selection, since it provides approximately equal front-to-back ratios at the array limits, namely 10 meters at the high end and 30 meters at the low end.

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To see how the curtain or planar reflector changes array performance, examine the following table and compare various values to the ones for the array alone.

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+             Curtained Extended Lazy-H Performance Potential
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+Freq.      Gain       TO angle   Beamwidth  F-B Ratio       Feed Z
+MHz        dBi        degrees    degrees    dB              R+/-jX Ohms
+28.5       18.4        8         30         13.7            112 + j 430
+24.95      17.1       10         40         15.5             29 + j 125
+21.1       15.5       11         50         17.1             25 - j   3
+18.118     14.4       13         56         16.8             33 - j 100
+14.1       13.1       17         63         14.2            175 - j 460
+10.125     12.2       23         69         13.8             21 + j 140
+7.1        10.0*      30         75          8.3              2 - j 100
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The gain increase in the favored direction is between 3 and 4 dB, depending upon the band, with peak increases in the 17 and 20 meter bands. The gain improvement values are consistent with those for any casually designed 2-element driver-reflector Yagi. Peak front-to-back ratio occurs on 15 meters and decreases slowly above and below that band.

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The impedance values are interesting. No great change occurs in the reactance values. However, the resistive component shows an interesting pattern. On 15 meters, its value is about the same as the value for the array alone. Above 15 meters, where the spacing is greater than 1/4 wavelength, the resistive component of the impedance is higher than for the array alone. Below 15 meters, the resistive component is less than for the array alone, while the spacing is less than 1/4 wavelength.

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Fig. 2 through Fig. 7 provide azimuth and elevation patterns for the array on each band. They require no individual comment. However, the trends in the rear lobe formations should be reasonably clear. In all cases, the patterns are well-behaved, with no spurious lobes--other than the emergent secondary lobes inherent to the array when the active element length approaches 1.25 wavelengths.

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Before leaving our patterns, we must take special note of 40 meters. The gain value for that band is starred. That star indicates that the pattern shows maximum gain in the reverse direction relative to all of the other bands. See Fig. 8 for azimuth and elevation details.

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The reason for pattern reversal is simple. The horizontal dimension for the reflector (50') is 1/2 wavelength or more for all bands from 30 to 10 meters. However, on 40 meters, the reflector horizontal dimension is only about 3/8 wavelength. Hence, despite its vertical dimension, the screen acts like a director at less than 0.1 wavelength spacing. The very low resistive component of the feedpoint impedance reflects this condition. It is unlikely that one would be able to take advantage of the reverse pattern, given the potential difficulty in achieving a low-loss match.

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Physical Realities

The proof-of-principle exercise suggests that a minimalist planar reflector or curtain behind an expanded/extended Lazy-H will yield a competent directional beam with a noticeable improvement in gain and quite usable front-to-back characteristics. However, the requirements for the reflector are sufficiently challenging to make this array an antenna with a somewhat small niche. +

Planar reflectors require both vertical and horizontal dimension for highest effectiveness. Too narrow a vertical dimension will degrade the array characteristics as much as too short a horizontal dimension. Since the reflector is untuned, it must be at least 1/2 wavelength at the lowest frequency used, with additional length up to about 1 wavelength wherever feasible. Vertically, we improve performance with height greater than those used here, although the vertical dimension will reach its limits of helpfulness more quickly than the horizontal dimension.

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Assuming that we can erect vertical supports of the needed height, I recommend some form of halyard assembly to raise and lower the reflector screen. Even an extremely open "chicken-wire" screen reflector will show considerable aggregate wind resistance in violent storms. However, if one desired beaming in both broadside directions, then a pair of screens--with only one raised at a time--will yield a reversible beam. If the user has only one primary target region, lowering a single screen will return the array to its inherent bi-directional pattern, and that may suffice for other operations.

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For raising and lowering, we need an open-weave metal "fabric" that will resist snagging when it is crumpled on the ground. However, one might wind the screen around a ground-level cylinder instead of lowering it into a heap directly on the ground. One might even use a combination of horizontal wires and vertical ropes to create a more flexible screen for this purpose. The final product is suited to the skills of one who has experience with square-rigged sails, with the sail and spar arrangement inverted from those we find at sea. Of course, we shall invert another matter as well: we shall seek to slip the wind rather than catching it.

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The curtained Lazy-H is a fixed position wire array of considerable mechanical size and requires equal mechanical ingenuity to implement. However, it holds promise of providing multi-band gain and front-to-back ratio so that the operator can use the upper HF band on which propagation is nearest to optimal for a desired path. The beamwidth on the upper bands is narrow enough to require careful siting. Although the values in the charts emphasize the amateur bands, the general arrangement may be suitable for short-wave listening in the intervening spectrum--and possibly even for an economical short-wave broadcast installation.

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The curtained Lazy-H is certainly not an antenna for everyone. But it may be an antenna for someone.

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Updated 04-15-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Multi Band, Lazy H, Planar Reflector


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Some ABCs of A-B-C: Notes on Triangles of Doublets

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L. B. Cebik, W4RNL

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On occasion, folks have asked me questions of this sort:

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+ My all-band doublet doesn't seem to be doing the job. So what if I replace it with a longer one, a loop, or whatever. Or suppose that I add an antenna of a different kind to the existing doublet. What should I do? +
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In many cases, I recommend a second or third antenna of the same type. It struck me that perhaps some short background on why I make that recommendation on some occasions--but not all--might be useful to those who do not have much experience with all-band wire doublets.

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The Single Doublet

Every wire antenna has a length (in feet, meters, etc.) and a height. We shall use a center-fed doublet throughout these notes. Since our question does not directly involve elevation angles of radiation for the best DX, etc., I shall use a constant height of 50' above average ground for this discussion. Those constants will allow us to make direct comparisons. Anyone with lower or higher wires can read other notes at this site to make any adjustments in the comparisons. +

A difference of height will make little or no difference in the azimuth patterns of a doublet as we move from band-to-band (as long as the antenna is not too close to the ground). The pattern is mostly a function of the antenna length in terms of wavelength at each operating frequency. Small changes of frequency do not materially affect the pattern, so we can use a single frequency on each band as a sample that holds true for the whole band.

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Let's start with a 135' center-fed doublet. 135' is about (and "about" is plenty good enough here) 1/2 wavelength long on the 80-75-meter band. At 40 meters it is 1 wavelength. On 20, it is 2 wavelengths, and on 10 it is 4 wavelengths.

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Any center-fed doublet will have only 2 lobes for any length in wavelengths up to and just beyond 1 wavelength--1 lobe on each side of the wire, broadside to the wire. When the antenna is 2 wavelengths long, there will be 4 lobes--2 on each side of the wires--and they will angle away from the wire leaving a null directly broadside to the wire. A 4 wavelength antenna will have 8 lobes--4 on each side--and the strongest ones will be angled further away from the broadside directions.

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Fig. 1 provides snapshots of the azimuth patterns that reflect the notes I just gave. In addition, it shows the 15-meter situation. The antenna is 3 wavelengths long, so we get 6 lobes. For all of the patterns, the antenna runs from left to right (or right to left) across the center line of the plots. So broadside is up and down on the patterns.

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The first thing we can do with these patterns is explain why a given doublet gives good results in certain directions on some bands but not on others. Assume that we set the wire in the U.S. so that broadside goes to Europe and to Australia. By the time we operate on 15 to 10 meters, our strongest lobes are no where near the headings for those two major target areas.

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So our first lesson is in wire antenna orientation. By knowing the antenna length, we can roughly determine the directions of lobes on our favorite bands and set up the wire to give the strongest performance in those directions by how we orient the wire. We cannot obtain a perfect setting on all bands, but we can (assuming that we do not need to move any supporting trees) obtain good settings on our favorite bands.

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Before we look further at the matter of direction, we have a few more preliminaries to note. For example, what band should I choose as the basic one for DX in my favorite directions? Here is where a small performance table may help for the bands illustrated in Fig. 1.

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+135' Doublet Performance at 50' Up
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+           Freq. MHz        Max Gain dBi    TO Angle deg
+           3.75              3.2            30 (arbitrary)
+           14.175            9.4            19
+           21.225            9.8            13
+           28.5             10.6             9
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The TO or take-off angle is the elevation angle of maximum radiation. It is correct for 20-10 meters, but is not for 80 meters, where the height of the antenna is low enough to direct most radiation at very high angles. So I chose a reasonable short-skip angle to take the gain reading.

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Since the gain on 80 is so low and the radiation angle so high, 80 is not a good candidate for use in orienting the antenna for DX directions. The gain on 20, 15, and 10 are similar, so one of those bands is a better candidate. However, if we prefer local rag chewing, then the 80-meter broadside should aim at our target areas. Remember that the 40-meter pattern will also be a 2-lobe broadside affair, but the strength will be higher and the beamwidth narrower (since the added gain has to come from somewhere).

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There are, of course, a number of other amateur bands on which the antenna is not close to an integral number of wavelengths long. What happens when the antenna is X.5 wavelengths long, where X is any integer? The answer is a function of how lobes appear. They do not pop into existence, but grow and shrink as we change the length of the antenna (or as we raise and lower the operating frequency, which achieves the same change in antenna length when measured in terms of wavelengths). At X.5 wavelengths, the azimuth pattern will show two sets of lobes in approximately equal strength: the set for wavelength X, longer than which we now are, and the set for wavelength X+1, which we are approaching.

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On 17 meters, a wavelength is about 54' long and our 135' doublet is about 2.5 wavelengths long (give or take a little). (A wavelength is about 984/f feet long, where f is the frequency in MHz.) We shall have 4 lobes for the 2 wavelengths that we passed in length. We shall have 6 lobes for the 3 wavelengths that we are approaching. So the pattern will be composed of 10 lobes total. That sounds good, since we get lobes in so many different directions. However, for every lobe, there is also a null. So we have 10 blank directions and each lobe is narrower than its counterpart in a 2 wavelength or a 3 wavelength wire.

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This note on nulls gives us the second lesson concerning wire doublets and their azimuth patterns. Study the azimuth patterns twice. First, look at the lobes that tell you where the radiation is going. Second study the nulls that tell you where performance will be very weak. Only then should you make decisions about how to orient the antenna.

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What happens when a wire is X.25 or X.75 wavelengths long. Since lobes grow and shrink, the answer is almost obvious. At X.25 wavelengths, the wire is not long enough for strong lobes from the X+1 length, but will show some smaller lobes derived from that length. At X.75 wavelengths, the wire is too long to support full scale lobes from the X length, but will have smaller lobes (meaning lower gain) still present. In either case, as some lobes show low development, the larger ones are that much larger, since the radiated power is relatively constant (ignoring external variables) across all frequencies.

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Now suppose that you have studied the azimuth patterns and decide that you cannot place a strong lobe every where that you want to communicate. It is precisely here that folks immediate jump to thoughts of other antennas. But virtually every other horizontal wire antenna, whether straight or looped, has a pattern of lobes and nulls. Most of them are more complex to install. So what is a solution to our quandary?

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Now wire is relatively cheap. Antenna supports are not. So any solution that we come up with should have the desirable property of involving a minimum of new supports.

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The 135' Doublet Triangle

There is no perfect solution to the problem of working everywhere we want to work with an array of horizontal wire doublets. However, we can go a good distance toward that solution by adding only one more antenna support. We shall create a triangle of wire doublets, something like the idealized sketch in Fig. 2. +
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The drawing shows an equilateral triangle, but almost any shape will do. In fact, a better ideal is to angle each antenna so that its lobes--on your favorite bands--hit your favorite targets. Just give yourself a little separation at the wire ends--perhaps 10' on the end of a 135' doublet--to minimize interactions among the wires.

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The sketch also shows two different means of feeding the antenna. You can run 3 feedlines, each the same length as the others, to a central point where you install a weather-proof relay box to switch among the wires. A single feedline runs to the shack, along with a relay power line and switching lines via an A-B-C switch to activate one of the 3 antennas at a time.

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The alternative is to run three lines, again, all the same length, to the shack for use with a manual A-B-C switch at that location. Since the lines will be parallel transmission lines, follow the usual precautions about keeping them free and clear of anything that might disrupt their balance.

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The point of using equal-length lines in each case is so that you can switch between antennas and determine by ear the strongest signal. If they are not the same length, you will have to do some rapid re-adjustment of the tuner settings for each switch position. With identical antennas and feedlines, you should be able to pick out the strongest one and then only do a final tweaking of the settings on the tuner.

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As Fig. 3 shows, you may not always have a good choice as to exactly where you position the supports for the antenna. Fitting the triangle to available yard space is an eternal amateur antenna problem. However, as we shall see, we can effect some improvement on our operation, even if we cannot perfect it.

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Notice that we were able to add two antennas for the cost of wire and with only one extra support. We may well trade any remaining imperfections in the system for that major simplification of structure.

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Now the question is simply this: what do we get for our pains? The easiest way to show what we get is by overlaying azimuth patterns for each antenna in one massive plot for each band covered in Fig. 1. We shall note both the advantages that we accrue from the new arrangement and the remaining problems that we could not solve.

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Fig. 4 shows the three antenna patterns at the same 30-degree angle that we used in Fig. 1. It is immediately apparent that we can cover more of the horizon with our signal (and reception) than with a single antenna. However, since the antenna is close to 1/2 wavelength, there is some interaction between the antennas so that the inactive ones act as reflectors. The 2-dB difference should not affect performance too much. You will find the same phenomenon on 40-meters, where the wires are all nearly 1 wavelength.

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The 20-meter situation appears in Fig. 5. We still have some nulls, but count the major directions that we can cover, letting overlapping lobes count as 1. We have 6 directions, not just the 4 that a single wire would give us. As well, the overlaps are not perfect, so that a signal that is on the fringe of one lobe may be centered in overlapping one. Of course, by carefully planning of your triangle, you can minimize the overlap and spread the area of coverage. The patterns shown simply use our equilateral triangle as their basis.

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In Fig. 6, we find 15-meter quite well covered by the 3 antennas and their strongest lobes. Indeed, 15 meters is a band that really benefits from a triangle of 135' doublets.

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If you look at Fig. 5 and Fig. 7, you may get the impression that when an antenna is an even number of wavelengths, it leaves more nulls than when it is an odd number of wavelengths, as in the 15-meter case. In general, this is a correct conclusion, although as we further increase the antenna length, the number of lobes becomes high enough to make it difficult to tell the difference. 10-meters is a good band for which to redesign the triangle to place a lobe in the direction that you want it.

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The 88' Doublet Triangle

If you lack yard space for 135' doublets in a triangle, you might try 88' doublets. Here is a performance table for a single doublet on the same bands that we surveyed for the longer doublet. + 
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+88' Doublet Performance at 50' Up
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+           Freq. MHz        Max Gain dBi    TO Angle deg
+           3.75              2.8            30 (arbitrary)
+           14.175           10.1            19
+           21.225            9.1            13
+           28.5             10.3             9
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The performance figures for each band are not very much different than for the 135' doublet, but the patterns are considerably different. Remember that the 88' doublet is only about 1/3 wavelength at 3.75 MHz. Fig. 8 shows the 88' doublet azimuth patterns when we place the antenna 50' above ground.

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The 80-meter pattern is similar to the one for the longer wire. However, the 20-meter pattern shows the typical "ears" of an extended double Zepp, since that is exactly what the antenna is at 14 MHz. It is 1.25 wavelengths, which means that the 2 wavelength lobes are just beginning to emerge. On 15 meters, the wire is 2 wavelengths long and shows the same sort of pattern that the 135' doublet showed on 20 meters. The 10-meter 88' doublet pattern is an example of a 10-lobe pattern for a 2.5 wavelength antenna.

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Besides taking less space, the triangle of 88' doublets also shows less interaction among the wires. Hence, we can use somewhat smaller separations of the wire ends in making the triangle. However, in exchange for spatial economy, we shall encounter differences in the ability of the triangle to fill in the nulls on the single-wire patterns.

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On 80 meters, as shown in Fig. 9, the absence of pattern distortions created by interactions among the wires yields almost complete horizon coverage. However, remember that this pattern is at an elevation angle of 30 degrees, and most radiation is upward. We can improve long-haul performance of the triangle by "merely" raising the supports to the 90-100 foot level.

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Fig. 10 shows us the 20-meter combined patterns. The azimuth plot provides a good model for a hex symbol to embroider for good luck. More importantly, it shows some nulls that may call for careful design of the triangle to ensure the desired target-area coverage.

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Like its counterpart 20-meter pattern, the 15-meter patterns in Fig. 11 add up to fairly complete coverage, but with nulls and overlapping lobes. Hence, one might wish to design the triangle to spread the lobes a bit. However, you will discover that with 4 lobes per wire, every spread in one direction increases an overlap somewhere else.

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The situation grows both better and worse on 10 meters, as shown in Fig. 12. The null areas are wider, but often not as deep, since minor 10-meter lobes fill the null at about 1.5 S-units lower strength. Once more, designer triangle formation seems the order of the day.

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It would be difficult in a general discussion to provide samples of designer triangles, since each would prove useful for only one region of the U.S.--and likely be useless outside the U.S. However, one can experiment most easily with altering the triangle orientations with modeling software. There are inexpensive packages, and even some free MININEC programs. It may pay to master them well enough to go with your self-study geography lessons in order to give yourself the bast chance of placing doublet supports at the correct locations.

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In the end, there are no perfect solutions. However, at a cost of one extra support and a bale of wire--plus feedlines and an A-B-C switch--you cannot get much better horizontal coverage much more cheaply than with a triangle of doublets.

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An additional caution or two: The doublet lengths used here place the lowest band at 80 meters. You can use a 70' doublet if you wish to cover 40-10 meters. In that case, the 80-meter and the 20-meter patterns shown in Fig. 1 become the patterns for 40 and 10 meters, respectively. As well, you can use a 44' doublet in place of the 88' version used in these notes. The same adjustments then apply to the patterns in Fig. 8. In both cases, the performance data in the tables would apply with band adjustments to an antenna at about 25' above ground.

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Xs and Ls

Some folks ask what happens when we have only two doublets. They envision crossing or end-to-end arrangements like those in Fig. 13. However, they often have in mind to use something other than a right angle. +
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The first thing that happens is a requirement for either 1 or 2 more support posts. If you have plenty of Douglas Firs handy, a 4-post system is no problem. But if you have to construct or erect your own supports, then the support work either matches or exceeds the work required by a triangle. The L-configuration is like the triangle, but only lacks 1 wire and its associate feedline. Of course, you can now get away with an A-B switch, rather than having to figure out how to make an A-B-C switch.

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Let's put up 2 135' doublets that cross at the center (with a separation to keep the wires apart) and see what we can achieve with only 2 antennas on each of our sampling bands.

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Fig. 14 shows the 3.75-MHz results. Since the deepest null is now only about -3 dB or about 1/2 S-unit, it is likely that performance will be satisfactory within the height limitations that we discussed earlier.

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On 20 meters, as shown in Fig. 15, we have deep nulls and considerable lobe overlapping. Hence, for this band, adjusting one antenna by at least 25-30 degrees off a right angle will likely produce better coverage. For an individual antenna, the lobes are only about 35 degrees each side of a broadside tangent line relative to the wire, so some angling to enhance coverage seems in order.

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Fig. 16 gives us the 15-meter story. Once more, the main lobes heavily overlap, but each is about 40 degrees off the line tangential to the antenna wire. Finding a compromise angle for both 20 and 15 meters will require some thought, especially when we add in the need to be aiming at communications target areas.

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The most thorough coverage occurs on 10 meters, due to the multiplicity of lobes. See Fig. 17. Despite the gaps or nulls that remain on each of the bands, the level of coverage with just two 135' doublets is significantly greater than with a single doublet. Conclusion: if you cannot swing 3 antennas, at least try for two.

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The 88' doublet does not fare quite as well in a 2-wire system as the 135' doublet. Indeed, the 88' doublet seems best suited to a triangular environment.

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80 meters appears in Fig. 18. As is evident, there is no significant difference between the 135' and 88' 80-meter situation with respect to coverage.

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The 20-meter patterns are in Fig. 19. The extended double Zepp patterns simply give us two different bi-directional options. Hence, careful broadside aiming of the wires seems the order of the day.

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If we wish to target areas on 20 meters, they will be broadside to the antenna. However, on 15 meters, as shown in Fig. 20, we cannot target the same areas, since the lobes on that band angle away from broadside by about 35 degrees. Unlike the situation with a triangle of doublets, the 2-wire system of 88' doublets appears to force us to declare that either 20 or 15 meters is our favorite band, but not both--at least not into the same parts of the world.

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Fig. 21 gives us the 10-meter picture. At 2.5 wavelengths, the antenna yields fairly solid coverage, although there likely is room for wire aiming on this band.

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However we construct the doublets, the triangle provides superior coverage and more versatility than a crossed or L-ed doublet system. Obviously, 2 wires are better than 1, but 3 is significantly better than 2 without requiring any further supports.

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I have omitted construction details, since they are so variable with the circumstances of the individual builder. As well, I have omitted inverted Vees, which will tend to change the situation on the lower bands more than on the higher, since the patterns will be broader ovals.

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Nevertheless, the switched doublet triangle offers flexibility that takes advantage of the strongest lobes--especially on the upper bands--in the antenna pattern. A switched-doublet system is cheaper than a rotator and tower system, and repair costs are reduced usually to the cost of antenna wire and possibly some parallel transmission line. However, the performance of a wire--when you can place one of its main lobes on the desired station--can be surprisingly good.

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Nothing here is intended to compare the doublet with other wire antennas--or even non-wire antennas. These notes are intended only to show some possibilities that we often overlook when thinking about wire doublets.

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A love triangle is usually a disaster. However, a triangle of doublets is often a happy marriage of economy and performance.

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Updated 05-15-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Doublet, HF Multi Band


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Resurrecting the Y-Doublet

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L. B. Cebik, W4RNL

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After presenting some notes on triangles of doublets of various lengths, I received more than one message recalling an old Y-configuration from the 30s and 40s. The basic scheme was designed for a given band and consisted of three 1/4 wavelength wires at 120-degree angles coming together at a center point. There, according to recollections, the old timers used a 3-wire twisted feedline to the shack. At any one time, the operator hooked up two of the 3 wires to the antenna tuner (or, in more remote past times, to the rig output terminals). The result was a steerable doublet.

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Essentially, the operator was selecting the pair of feed wires that created a doublet, with the third antenna wire relatively inert. We normally think of a doublet as linear, but bending it by 30 degrees does not especially harm its performance. So that part of the system is quite sound.

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More foreign to current practice is the twisted feedline. In the 1930s, many hams commonly feed their dipoles with low-impedance parallel line. A 72-Ohm transmitting parallel line used to be available, but apparently the high power version is no longer made. 72-Ohm parallel lines made from round wires are not feasible with open-wire construction, since the required center-to-center spacing would require contact between the wires. However, by using a carefully calculated thickness of an insulating material with a known dielectric constant on each wire, the desired impedance is achievable.

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Amateur practice tended to rely on two factors. First, the resulting parallel line resembled ordinary line cord, sometimes called zip cord. Second, properly configured antenna tuners or even amplifier output circuits were capable of handling a fairly wide range on impedances. Therefore, amateurs used to simply twist pairs of insulated wires together to form a low impedance parallel feedline. The wires might be line cord or they might be other insulated wires twisted and taped together.

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Adding a third wire to the set and leaving it disconnected from the RF source was relatively harmless. If the wire was equally spaced from the other two hot wires, it would have negligible current on it. The antenna wire would be at essentially right angles to the main pattern and hence induce a minimum of coupled antenna current into the inert feeder. Since the currents on the other two feeder wires would be equal in magnitude but opposite in phase, any induced currents in the third wire would cancel, leaving no current in the third wire.

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Overall, the system effects a space savings over three doublets in a triangle. With good solid AWG #12 wire for the elements, one can use only three corner supports and let the triangle of antenna wires support the center assembly. (One can always add a center support, if convenient or necessary.) With that promise and the potential for having a steerable doublet, the idea is worth further exploration.

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The Steerable Y-Doublet Array

Let's begin by looking at the antenna wires and their potential performance. We shall look more closely at the feed system later on. The basic configuration of the Y-doublet appears in Fig. 1. +
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We shall use as our test array a Y cut for 3.6 MHz. My free-space model used 67' legs for initial checks. Hence, ignoring the necessary insulating end ropes to the support trees or posts, we get a triangle about 116' on a side and capable of fitting within a rectangular back yard that is about 101' by 116'. The figure shows the three feed wires, of which we shall use only two at a time. For modeling, that means terminating each leg short of the exact center point. Then we connect a short wire between 2 of the 3 wires. I used a separation between inner leg ends of about 3' so that I could use a 3-segment wire for the source and use segment lengths of about 1' on the antenna wire legs.

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Fig. 2 shows the overlaid free-space patterns for the Y-doublet at 3.6 MHz using different pairs of legs to form each of 3 doublets. The patterns indeed promise full horizon coverage as we switch pairs of feedlines at the shack end of the feeder lines.

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I also checked the antenna's performance on each of the bands above 80 meters. All of the traditional ham bands (40, 20, 15, and 10 meters) yielded very high feedpoint impedances. Since we are working with a low-impedance feedline, I set these bands aside as not especially feasible for use with the system. (We shall review this decision before we are finished.) However, 30, 17, and 12 meters showed feedpoint impedances sufficiently low to potentially allow use of the antenna on these bands using the low-impedance feeder system employed in first half of the 20th century. The following table shows the free space performance potential of the array.

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+               Y-Doublet Modeled Performance:  Free Space
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+           Freq.            Gain            Feed Z
+           MHz              dBi             R+/-jX Ohms
+           3.6              1.70             59 - j   6
+           10.125           5.16            106 - j 375
+           18.118           4.62            134 - j 103
+           24.94            4.92            171 - j 291
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The free-space patterns are generally only applicable for a real horizontal antenna over ground if the height is at least 1 wavelength. 80-meter doublets at 270' or more are rare. Therefore, I remodeled the antenna at a 50' height to reflect a more realistic scenario. At that height, the maximum gain of the antenna has an elevation angle that is nearly straight up. So I chose for that band an angle of 34 degrees to reflect typical skip angles. The resulting 3.6-MHz patterns, shown in Fig. 3, are a good bit more oval than their free-pace counterparts.

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On the upper bands, I used the take-off (TO) angle for gathering potential performance data. The antenna promises performance as shown in the following table, with the leg-length adjusted to 66.5' to bring the array close to resonance at 3.6 MHz. (Wire doublets tend to vary their feedpoint impedances with height in noticeable ways when the doublet is less than 1 wavelength above ground.)

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+        Y-Doublet Modeled Performance:  50' Above Average Ground
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+      Freq.           Gain             TO Angle        Feed Z
+      MHz             dBi              degrees         R+/-jX Ohms
+      3.6              3.43            34*              56 + j   8
+      10.125           9.98            26              110 - j 424
+      18.118           9.59            14              135 - j 153
+      24.94           10.23            11              182 - j 365
+* 80-meter elevation angle arbitrary.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The patterns on the upper bands are not ovals by any means. Fig. 4 shows these patterns, but only one pattern per band for clarity. As we increase frequency, we find two especially interesting pattern properties. First, as the legs become longer in terms of wavelengths, the patterns develop growing side "wings." Eventually, by 12 meters, the main lobe has split into two forward lobes. Second, as we increase frequency, the array becomes more directional, with a growing differential between the forward and the rearward gain.

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Still, the patterns may be usable for general amateur operations. The question left is why we get reasonably low impedances at 30, 17, and 12 meters. Fig. 5 shows part of the reason.

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The graphics display the relative current magnitude distribution along the doublet for each of the 4 bands. On 80 meters, we have a somewhat typical dipole current distribution, with the current peak at the feedpoint. On the other bands, we approximate a 3/2-, 5/2-, and 7/2 wavelength doublet current distribution. Each of these configurations places a current peak at the doublet center, resulting in a relatively low feedpoint impedance.

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We should also note that the unused wire shows a flat current line. The current on it models out (in its perfectly spaced geometry) at about 4 orders of magnitude less current than on the active wires. That is, if the current at the source is 1.0, then the current on the inert wire shows a value of 0.0001 or 1E-4 or less.

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The Feeder Question

The original system was designed for use with a twisted trio of feedline wires, in other words, a twisted pair plus one. Fig. 6 shows the general hook-up, but without any poor attempt on my part to sketch a braid of 3 wires. +
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There are several questions about the feasibility of using such a system in modern times. The first quandary is whether we can build such a feeder system.

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Modern insulated wire tends to use higher quality (lower loss) insulation than did the wire of yore. I would steer away from line cord, but modern wires use plastics with better RF characteristics, even if the only intend use is carrying DC. Since the system is designed for a low characteristic impedance, but with considerable SWR on the higher bands, I would recommend a heavy gauge wire, perhaps #12 or so. The actual characteristic impedance will depend on the thickness of the wire, the dielectric constant of the insulation material, and how tightly we hold the wires together. Consequently, I can give no exact figures.

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However, you can make up lengths of a proposed feedline and check the impedance in a number of ways with a variety of dummy loads and a low-level signal source. Any one of the current crop of antenna analyzers will give you a fairly accurate reading. Given the relatively high dielectric constant of the insulating material, expect to find a significant velocity factor, something in the 0.6 to 0.7 region.

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The next inquiry has to do with the effective inertness of the unused 3rd feeder wire. I re-created the model of the Y-doublet using parallel feedlines. Since twining the leads is not feasible in a physical model, I simply dropped the three leads straight down from the 50' level to 1' above ground. At that point, I connected two of the feeder ends with a 3-segment source wire. Again, all wires used a 1' segment length.

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The resulting feedpoint impedances are not accurate to the low-Z feeder system. However, that was not the point of the tests using the feeders with something over 800 Ohms as the characteristic impedance. The question was whether the unused antenna and feeder wires would remain inert relative to the active wires.

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As one measure, the following performance table shows the effects of the added copper losses of the physically modeled feedlines.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            Y-Doublet Modeled Performance:  50' With Feeders
+
+           Freq.            Gain            TO Angle
+           MHz              dBi             degrees
+           3.6              3.35            34
+           10.125           9.74            26
+           18.118           9.60            14
+           24.94            9.85            11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Gain remains virtually unchanged. So, too, do the patterns, and the outlines shown in Fig. 3 and Fig. 4 remain valid for the reconfigured model.

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A second test is to check the current distribution along both the unused antenna wire and the ostensibly inert feeder. I actually performed two tests, one with the unused feeder simply left open and another with the feeder extended 1 foot to touch the ground. The 12-meter current distribution graphic in Fig. 7 remains valid for both.

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Note that the current line on the unused feeder and antenna wires is flat. The relative current magnitude under either test condition on all of the bands remained less than 1E-4 relative to a source current of 1.0.

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The modeling test, of course, has limitations relative to an actual twisted trio of wires. In the test, the modeled wires are widely separated and perfectly spaced along the entire 49' feeder run. How well the twisted trio performs may turn out to be as much a careful-construction issue as any other kind of issue.

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However, the tests suggest an alternative feed system that just might open up the Y-doublet to use on all of the HF bands. Fig. 8 tells the story.

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+ +
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The Y-doublet on the traditional upper ham bands, 40 through 10 meters, can show feedpoint impedances in the thousands of Ohms, with considerable reactance. Indeed, shrinking or expanding the basic 80-meter legs may prove useful in reducing the high reactance levels that accompany lengths that are close to even numbers of half wavelengths. Commonly, we try to select for a doublet a feedline characteristic impedance that is about the geometric mean between the feedpoint impedance extremes that we are likely to encounter. There is a practical limit to this effort, since lines above 600-800 Ohms are difficult to produce. Hence, 600-Ohm or so open wire becomes typical for such applications.

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We can create a trio of pairs by using circular spacers of the type shown in the figure. For HF work, Plexiglas or polycarbonate spacers should be satisfactory. We can cut a hole in the center of each to reduce the weight. The holes can actually be slots if we add bridge wires to hold the spacers in place. In essence, we are adapting techniques normally used to create caged elements and applying them to the feedline. Such lines might permit the use of the antenna on all bands with a wide-range antenna tuner and will go a long distance in maintaining something close to the modeled ideal geometry we used in the test cases.

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Of course, should you choose to work with a system of this order, you can replace the alligator and crocodile clips of yore with an in-shack switching system to change the orientation of the pattern on all bands.

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The resurrected Y-doublet as some potential of still being serviceable today. There are many variables beyond the limits of this initial feasibility check, so success is not assured. However, for some hams who are restricted to backyard wire systems but who wish some directional flexibility, the system may be worth a try.

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With the wide spaced feeder system, the system may also be adaptable to 102', 88', 67', and 44' doublet lengths discussed in other notes at this site and in mountains of other literature. However, as with all horizontal doublets, the rule of thumb that calls for the maximum feasible height remains in play for effective operation.

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Updated 05-16-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Doublet, HF Multi Band


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+ Title graphic +

Horizontally Oriented, Horizontally Polarized Large Wire Loop Antennas

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This talk was originally prepared for the 1999 Atlanticon Symposium

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Large wire antennas are deservedly popular among QRP operators who have room for them. They are cheap and effective: the two favorite words among hams.

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Among the more usable of the large wire antennas is the loop that is at least 1 wl long at the lowest frequency of operation. However, large loops belong to three different families, each with distinct characteristics.

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Fig. 1 shows the three families of antennas. VOVPLs are vertically oriented, vertically polarized wire loops, such as the delta and the rectangle when we feed them along the side. They stand upright and vertically polarized radiation is broadside to the antenna plane. Ordinarily, VOVPLs are monoband antennas and perform less well than their relatives when pressed into service on other bands.

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VOHPLs are vertically oriented, horizontally polarized wire loops. The quad loop fed along a horizontal wire is the most popular member of this group, although horizontally polarized triangular antennas are also common. VOHPLs show significant superiority over VOVPLs in all band use. However, they have two limitations. First, if we can place a wire doublet at the top height of the VOHPL, it will usually show a lower angle of maximum radiation, because the VOHPL's radiation is a combination of the upper and lower wires. Second, to be a truly large loop of 1 wl or greater, the VOHPL requires exceptionally tall supports.

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For the ham with more area than height in his yard or field, a more frequent selection is the HOHPL: the horizontally oriented, horizontally polarized large wire loop antenna. The standard installation is to place the loop as high as one can, with only the placement of supports and the overall yard size as restrictions on the loop length. Loops up to several wavelengths long around their perimeter are in use on 80 meters--and on all of the bands above.

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(We should note in passing that there is no known HOVPL, that is, a horizontally oriented, vertically polarized large loop antenna.)

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HOHPLs can be strung around the edge of a yard, meaning that even a city lot whose perimeter is at least 280' long can support a 1 wl version at 80 meters. Such a lot is about 70' by 70' if square. If the yard width is only 50', then the yard need only extend 90' back to hold the antenna. With allowance for sidewalks, flower beds, trees, and the like, there is still room for a HOHPL in many more ham homesteads than we might think. Therefore, the entire class of HOHPLs deserves a longer look to discover their strengths and their weaknesses.

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Let's develop a plan of attack for understanding HOHPLs. The first part of our work will include some answers to the most pressing questions about HOHPLs:

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  • 1. How big should we make HOHPLs?
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  • 2. What shape should we make them?
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  • 3. Where and how should we feed a HOHPL?
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  • 4. At what height should we place the antenna?
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  • 5. On what frequencies can we use the HOHPL?
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  • 6. How does the HOHPL compare to other all-band antennas?
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The second part of our effort will be devoted to a compendium of modeled antenna patterns to give you some idea of what to expect from HOHPLs. Some of the answers we give to questions just outlined will become graphically clear when we peak at a number of antenna patterns.

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1. How big should we make HOHPLs?

Ideally, a HOHPL should include at least 1 wl of wire at its lowest frequency of operation. For 80 meters, that means about 280' defines the antenna perimeter. In a pinch, we can make the antenna shorter and still effect a match using parallel feeders and an antenna tuner. However, let 3/4 wl be about the absolute minimum for the antenna. +
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The circular HOHPL outlines in Fig. 2 show my best suggestion: make the loop larger than 1 wl. A 1 wl horizontal loop that is less than 1/2 wl above ground tends to be a cloud burner. NVIS (near vertical incidence skywave) antennas are certainly useful--and desirable to certain types of operation. But they have very poor DX potential.

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By the time a loop is at least 2 wl long at its fundamental frequency of operation, it looses its ability to warm the clouds and becomes an antenna with some potential for longer distance communications. so the general rule for HOHPLs is this: make them as long as you can support in your yard.

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These notes apply to the use of a HOHPL at the lowest desired operating frequency. However, longer is not always better if our main interests are at the upper end of the HF spectrum. As we shall see, a desire to operate on both 80 and 10 meters with a HOHPL may provide us with a bit of a dilemma.

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Although I shall be speaking in terms of 1 wl and 2 wl HOHPLs, there are no rules against making them even larger or against making them some non- integral multiple of a wavelength. In some respects, we can say with assurance that performance of a 1.5 wl HOHPL will be intermediate between a 1 wl and a 2 wl version. However, as we shall discover, there are enough variations in the performance of a 1 wl HOHPL to make my claim fall among the world's most vague statements.

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2. What shape should we make a HOHPL?

Ideally, a circular HOHPL would likely be best from a theoretical perspective. However, a circular at 80 or 160 meters is usually impractical for most ham installations. Therefore we must turn to polygons, that is, shapes with straight lines that compose the perimeter. +

Before we speak in geometric terms, let's note a mechanical issue that will be involved in the shape decision. Besides the position of the supports for corners, we must also take into account the length of each side vs. the strength of the wire used to form the HOHPL. Assuming the availability of supports, we would normally place supports at distances to protect the antenna from undue stress, especially stress due to weather. Wind and ice are the major enemies of large loop antennas with long wire runs.

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Copperweld is a good material for a long wire loop and may call for fewer supports than soft-drawn copper wire. Although heavier than pure copper, quality copperweld wire has many times the strength. However, another reality of HOHPL construction is that hams tend to use whatever bargain wire they can find at hamfests, close-outs, and other inexpensive sources. If you choose the economic route, be prepared to splice breaks during the life of the antenna.

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Realities of ham antenna farms usually breed irregular shapes for HOHPLs. These shapes are not only usable, but as well they can be modeled and analyzed. However, we can only do this on a case-by-case basis. For our work today. we must confine ourselves to regular polygons. You may think of any regular polygon as a greater or lesser approximation of a circle: the more sides to the polygon, the closer the approximation to a perfect circle.

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Fig. 3 Illustrates some of the typical geometries used in constructing making HOHPLs of both regular and irregular shape. We shall from here on confine ourselves to the regular shapes. Our reason is a matter of both the general application of the ideas and the ease of making calculations.

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Regular polygons have some dimensions that are especially useful in planning and calculating the various antenna dimensions. Fig. 4 shows them in outline form for the triangle through the octagon. Note the Side (S), radial to a peak (A), and radial to a side (H).

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Table 1 lists some of the relationships among S, A, H, and C (the overall circumference or total wire length of the loop. Note that the more numerous the sides, the closer the lengths of A and H to each other. A circle, with an infinite number of sides from a geometric perspective, finds A and H to be equal.

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                                Table 1.  Figuring a Regular HOHPL
+
+                                   A.  Deciding the Wire Length
+
+L = wire length = 300 / Fl (meters) = 984 / Fl (feet)            Fl = lowest frequency used in MHz
+L (1.8 MHz) = 167 m = 547'                                               L (3.5 MHz) = 86 m = 281'
+
+                               B.  Figuring the Layout (See fig. 4)
+
+C = length of circumference             S = length of side        A = length of radial from center
+                             H = length of X or Y from center of loop
+
+I.  Triangle                                        III.  Hexagon
+S = C / 3                                           S = C / 6
+H = 0.29 S          (= 0.10 C)                      H = 0.87 S          (= 0.14 C)
+A = 0.58 S          (= 0.19 C)                      A = S               (= 0.17 C)
+A + H = 0.87 S      (= 0.29 C)
+
+II.  Square                                         IV. Octagon
+S = C / 4           (= 0.25 C)                      S = C / 8
+H = 0.5 S           (= 0.13 C)                      H = 1.2 S           (= 0.15 C)
+A = 0.7 S           (= 0.18 C)                      A = 1.3 S           (= 0.16 C)
+
+V.  Circle                                          VI.  "Irregular"
+A = H = 0.16 C                                      String wire along ground and adjust
+

The table of relationships is especially handy when you begin the process of planning a HOHPL with a paper sketch of your yard space. They are also handy if you wish to calculate the wire end coordinates on an antenna modeling program. The main shapes that we shall focus on in generating patterns for possible HOHPLs will be the square, the hexagon, and the octagon--the last because it most closely approximates a circle.

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3. Where and how should we feed a HOHPL?

Since the HOHPL is a multiband antenna, the feedpoint impedance will vary from band-to-band. Therefore, the only practical feed system is a parallel transmission line to an antenna tuner. The line can be anything from TV lead to commercial or home brew bare wires spaced every so often with almost any weather- resistant insulating rod. Even segments of plastic coat hangers will do for insulators, since the spacing will keep the rods from undergoing undue electrical stress. +

You may locate the feedpoint of a HOHPL at any point along its length. Mechanically, this usually means intersecting the antenna at the position that allows the straightest line from the antenna to the shack entry point. For some installations, the feedpoint may be at a corner (or junction of sides); for others, the feedpoint may be centered on a side--or even off- center on a side.

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One of the surprises that modeling the HOHPL produced is this: at what point you feed the antenna does make some difference in the resulting pattern on at least some of the bands in the HF region. As we shall see, when we explore the antenna over many ham bands with several geometric configurations, even the octagon fails to act like a circle on some of the upper HF bands. When we look at the patterns of the various antenna versions, keep in mind where you want the lobes and nulls to be relative to your own possible installation. A less direct feedline might yield a superior pattern relative to your operating desires.

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At this point I shall make a brief pitch for every serious antenna buff to acquire at least one of the antenna modeling programs. There is no reason for us to simply accept what a roughly constructed antenna might give us. We can plan and tame the beast-- whether by relocating wires or relocating the feedpoint--to give us the best compromise of lobes going just where we want them.

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4. At what height should we place a HOHPL?

Like all of the questions surrounding large loops, this question has two dimensions: the mechanical and the electrical. Therefore, the simple answer ("As high as possible") does not tell us everything we need to know or think about in constructing an antenna that consists of hundreds of feet of wire and a system of at least 3 and up to 8 support structures. +
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The most ideal and yet practical arrangement for supporting a HOHPL corner appears in Fig. 5. Note that the system includes a pulley and rope for raising and lowering the wire. A cleat near the ground is useful for tying off the rope. I have also used rope loops and clip rings at the cleat level. I disconnect the extra rope used only when lowering the antenna and store it out of the weather. I clip the upper rope to a hook instead of a cleat. When I need to lower the antenna, I add the extra section, which is long enough to reach but not pass through the pulley.

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A slip ring can be made from almost any plastic, although I tend to prefer Schedule 40 PVC Tee fittings for their durability. Their smooth interiors also tend to minimize wire kinking and rubbing, thus prolonging the life of the antenna. I do not offer these mechanical notes as a final and best answer to every situation. Instead, I hope that they get you to think about the mechanical details of your antenna as being just as important to its successful performance as the electrical details.

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Electrically, the question of HOHPL height is a matter of the elevation angle of the radiation. We can best picture what height means to use if we select an antenna design, a set of heights, and a few test frequencies. So let us take a square HOHPL that is 1 wl long at 80 meters and place it 35' up, 50' up, and 75' up--all typical ham installations. Now let's see, with the aid of computer modeling, what happens. But first, be sure to understand that antenna modeling presumes flat terrain with no ground clutter. Hence, the results will be very general.

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Fig. 6 demonstrates the difficulty of using a HOHPL at its lowest frequency (where it is 1 wl long). The 1 wl loop radiates predominantly broadside to the plane of the wire, which is straight up and down. Even at 75' up, the antenna is a "cloud-burner," or a suitable candidate for NVIS (Near Vertical Incidence Skywave) service.

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On 40 meters, as the patterns in Fig. 7 show, the antenna begins to form patterns that are suited to normal sky wave communications. However, the antenna is still a bit low when under 75' up, so the angles of maximum radiation are 37° at 50' up and 44° for 35' up. Longer distance effectiveness is enhanced by raising the antenna to 75' up, where the angle is about 26°.

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On 20 meters, as illustrated in Fig. 8, the same antenna begins to show excellent DX potential. At 35' up, the elevation angle of maximum radiation is 26°, with angles of 19° and 14° appearing at heights of 50' and 75', respectively. The emergence of higher angle secondary lobes becomes apparent, but these lobes are generally not as large as those that form with doublets at the same height.

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On 10 meters, as revealed by the patterns in Fig. 9, the HOHPL become an excellent DX antenna, with very low elevation angles of radiation: 12°, 9°, and 6° for heights of 35', 50', and 75' respectively. (Remember that the lobes have a vertical beamwidth so that the angles cited represent the center points of reasonably broad angular spreads that can handle propagation angles somewhat distant from the center line.)

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If the HOHPL has a significant weakness, it lies in the operation of the antenna at its fundamental frequency. To some extent, this weakness can be ameliorated by further elevating the antenna. A better solution, if land area is available, is to build a longer antenna, so that the fundamental frequency is lower. When the antenna is operated at its 2nd harmonic (when it is 2 wl long), the primary radiation is mostly in the same plane as the wire loop. Elevation angles at 80 meters will still be high, but not nearly as high.

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Compare Fig. 10 to Fig. 6. Although the elevation angle on 80 meters for the 2 wl loop is not ideal, it is considerably better than the elevation angle of the 1 wl version.

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5. On what frequencies can we use the HOHPL?

The answer to this question is simple: on any HF frequency. With parallel feedlines and an antenna tuner--hopefully a link-coupled tuner--we can load the antenna and produce useful signals on every band, whether traditional or WARC. What we get for radiation, however, depends on many factors, including the shape of the antenna, the length of the wire, and where we feed the antenna. +

Therefore, let's look at a compendium of azimuth patterns for the HOHPL using a variety of configurations to sample the territory. (Remember that a full set of patterns would use up a book, so we must restrict ourselves to a relevant sample.) We shall look at 1 wl antennas in the square and the octagon configurations, each fed at the center of a side and at a corner. Then we shall repeat the process with a 2 wl long hexagon as a sample of a longer HOHPL. From these examples, you can likely extrapolate what might happen with a large loop placed in your own yard.

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In all cases, the feedpoint of the antenna is placed at the left-most point on the antenna relative to the pattern shown. This procedures gives you a fair comparison, especially of patterns that are too complex to place in a single figure by laying one pattern on top of the other. In some cases, it would be impossible to keep track of which lobe belonged to which antenna. Therefore, we shall use separate figures and devote one page to each of the amateur bands for the 80-meter antennas--and a column to each band for the 160-meter model.

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80 Meters

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Any differences of performance among the loops shown here are too small to detect in operation, amounting to only 0.07 dB. The basic pattern of the loop at its fundamental frequency is a broad oval, stretched in the direction through an axis running from the feedpoint to a point on the opposite side of the loop. The loop "sides" are only a little over 2 dB down from the gain maxima.

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All of the loops in this long sequence of azimuth patterns have been modeled so that the feedpoint is to the far right, whether that point is in the middle of a side or the point where the wire takes a new direction. The orientation of the loop is shown only for the 80-meter azimuth patterns. However, the loop and feedpoint positions do not change as the modeling runs increase in frequency on succeeding pages. You can draw your own North line on each pattern.

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For all of the loops shown here, the 3.5 MHz azimuth patterns have been taken at an arbitrary 45° elevation angle. The actual elevation angle of maximum radiation on 80 meters is 90° or straight up for these loops, which are 1þ long. If you compare these patterns with Fig. 6, you will see that there is very little low elevation angle radiation on 80 meters, since the basic radiation pattern is broadside to a 1 wl loop.

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On 80 meters, an 80-meter loop arranged as a HOHPL makes a very good NVIS (near vertical incidence sky wave) or cloud burner antenna. Long- distance contacts will likely be rare on 80 meters, although contacts within a 300-500 mile radius may be stronger than with some other types of antennas, such as verticals and inverted Vees. See the 80-meter patterns of Fig. 15 and Fig. 16 for an alternative, composed of 2 wl loops at 80 meters.

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40 Meters

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Both the loop shape and the feed position begin to make themselves evident on the 40-meter azimuth patterns. Elevation angles of maximum radiation run from 37° to 43° for these 1 wl loops at 7 MHz, which allows direct comparisons among the azimuth patterns. Beginning with the square loops, we can examine them a pair at a time.

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The square loops show a very distinct difference in shape and gain that depends upon the feed point. The side-fed model shows stronger lobes (by almost 0.8 dB) and deeper nulls. In contrast, the corner-fed model is a round-cornered diamond, with a bit less gain in the direction of the feedpoint. Moreover, the points of maximum gain for the corner-fed model are to the sides, that is at right angles to the axis passing through the antenna feedpoint and the point opposite it on the antenna loop.

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In contrast to the differences between patterns depending on the feedpoint for the square loops, the octagon loops show an almost insignificant difference in pattern, whether the antenna is fed at a corner or in the middle of one side. The smaller differences also show up in the feedpoint impedances, with the squares showing a large difference as the feedpoint is moved.

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The simultaneous change in both pattern and feedpoint impedance in the square models indicates that the diamond and square configurations make a difference in the current distribution and interaction as the turned with the change in feedpoint. At 40 meters, the effect is much less for the octagon, since the difference in length between a radial to a corner and a radial to a side is much smaller. Whatever the differences, all four of these loops would make very good omni-directional antenna for 40 meters.

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30 Meters

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On 80 and 40 meters, the loops are close to resonance. Sometimes, differences show up most graphically when an antenna is operated at a frequency for which it is not resonant. For all of the loops, the feedpoint reactance is in the vicinity of 600 Ohms at 10.1 MHz. Once again, the squares show a stronger pattern difference that depends solely on the feedpoint selection.

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When fed at the corner, the 30-meter square pattern becomes very bi-directional, with about a 2 dB front-to-back ratio and about 8 dB or more front-to-side ratio. The distance from the feedpoint to the opposite peak is about 3/8 wl. In contrast, the side-fed square feedpoint is only about 1/4 wl from the opposite point across the square. Radiation remains strongest off the corner peaks, and the gain along the feedpoint axis is nearly 7 dB down from the forward gain of the corner-fed model.

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Once more, the octagon-shaped models show much less difference that can be attributed to the selection of the feedpoint position. Although there is little operational difference between the two octagons, it is interesting to note minor pattern tendencies. For example, absolute gain maxima do not appear in corresponding positions.

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In addition, the nulls of the side-fed octagon are slightly deeper than those of the corner-fed model. This feature shows a kinship between the side-fed square and octagon models.

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In all, three of the four arrangements make very respectable omni- directional antennas. Only the corner-fed square arrangement is less suited to this service and better suited to bi-directional operation that requires careful antenna orientation for effective use.

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20 Meters

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On 20 meters, the elevation angle for the loop, whatever its shape or feedpoint position, has decreased to about 20°. This angle (a product of the 50' height for all of the models) places the antenna radiation into the DX range, although signals would be stronger with the antenna even higher. On 20 meters, the antenna planner is faced with further decisions.

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The square loop shows major lobes near or above 10 dBi off each of the four corners. The lobes of the side-fed model are broader, which would lessen the problem of orienting the antenna toward desired areas of the world. In contrast, the narrower but stronger lobes of the corner-fed square would provide a gain advantage, especially in three of the four directions that the antenna favors. The cost of the added gain is a collection of very wide and deep nulls in the pattern, which would effectively limit communications in many directions.

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In contrast, the octagons seem once more to have very similar patterns to each other, regardless of the feedpoint position. However, note the fact that the lobes are a function of feedpoint position and not of whether there is a side or a corner at the lobe location. This factor shows up in the differential in the feedpoint impedances for the two octagon models.

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What the octagons lack in maximum gain, they make up for in omni- directional potential. Although nulls can be as deep as 10 dB below the lobes, they cover less territory and are shallower than most of the nulls in the patterns for the square models. The lesson here is simple: if 20 meters is a desired band for operation of a HOHPL and if one wishes to work in every possible direction, then the HOHPL should be as round as one's terrain permits. The squarer the shape, the larger and deeper the pattern nulls.

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17 Meters

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The patterns for 17 meters appear to have no rhyme or reason--indeed, they seem to suggest an error in modeling. However, they are as correct as NEC-4 can make them. Once more, nonresonant operation of the loop permits the current distribution to change radically with small changes of configuration. The result is a diverse set of patterns.

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The corner-fed square shows a high-gain bi-directional pattern that is similar to and in line with the 30-meter pattern for the same model. Maximum gain is off the corners that are in line with the feedpoint. The side-fed square also shows its maximum gain off the corners. However, since the feedpoint is between corners, the gain is more evenly distributed among all four corners. Hence, the apparent major difference in the operation of the loops turns out to be smaller than at first sight, but very significant for planning.

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The corner-fed octagon pattern shows its affinity to the corner-fed square with a noticeable but less extreme bi-directional pattern. The greater "side" gain results in a lower gain along the major axis of the antenna, compared to the square. However, the "side" gain is not sufficient to qualify this arrangement as having good omni-directional potential.

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The pattern for the side-fed octagon may seem initially mysterious. Twisting the antenna and moving the feedpoint by only 22.5° alters the axis of highest gain by 90°. Part of the mystery begins to clear up when we note that the antenna is attempting to produce 10 lobes from 8 sides and 8 corners. Since the antenna is over 5 wl long at 18.1 MHz, current distribution and resultant gain distribution can change rapidly with small changes in antenna configuration. Since 17 meters is less widely used, these difficulties are usually minor.

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15 Meters

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The tendency of a square loop to radiate with maximum gain from its corners continues on 15 meters. The elevation angle is in the 13-14° region, which gives the antenna significant DX potential. The strongest lobe of the corner-fed square has a gain rivaling a 3-element Yagi, but over a much narrower beamwidth. (We should especially note this fact, because wire antenna makers often advertise their wares as equal to beams. The illusion only persists if we ignore beamwidth.)

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With corner feed, current magnitude and phase combine to yield 4 strong, narrow lobes with corner feed. With side feed, the major lobes become many (12, to be exact), well spread around the horizon, but at loss of over 3 dB of maximum gain. (Note that the corner-fed version also has 12 lobes, but 8 are very minor.) The side-fed square becomes the configuration of choice if we desire maximum coverage on 15.

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Like the 17-meter model, the 15-meter models of the octagon show far greater similarity than do the square models. The corner-fed version retains a bit of the 4-lobe dominance found in its square counterpart, but the minor lobes have grown into major ones, giving the antenna better potential for omni-directional contacts. However, the side-fed octagon has the most even pattern of all, with only a small tilt of the pattern away from the feedpoint.

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As has been the case on other bands, the feedpoint impedance differs most widely between the two square models, with considerable less difference between the two octagon models. The corner-fed square has a lobe with the highest gain of the four models. In contrast, the highest gain of the very even-lobed side-fed octagon is about 4 dB lower than the corner-fed square. Even lobes usually means lower maximum gain.

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12 Meters

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The 12-meter corner-fed square continues the pattern of bi-directionalness on this model on the non-harmonically related bands. As was the case with lower band models, the highest gain is along the axis from the corner feedpoint through the corner opposite. When side fed, the square once more shows maximum gain from the four corners of the loop.

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The loop which is 1 wl long on 80 meters has 14 lobes, or 7 per half loop on 12 meters. This is no accident, since the length of the loop at 24.9 MHz is a little over 7 wl. (On 80 meters, the loop showed only two lobes in the oval pattern, 1 per half wavelength.) As the side-fed pattern shows, some lobes may be very small. In other cases, lobes may merge to become almost indistinguishable from a single lobe. However, you can always count on them being present as a function of the length of the wire at one lobe per half wavelength.

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The 14 lobes of the 12-meter octagons are clear and distinct in both the corner and side fed versions of the antenna. In the octagons, the lobes are functions of the feedpoint in terms of direction. However, the difference between the two feed positions shows up in the minor differences in the relative strengths of the individual lobes, except for the one directly opposite the feedpoint.

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Interestingly, the 12-meter models are as a group closer to resonance than any other group. The bi-directional corner-fed square shows the highest reactance. The other models, with there more even collection of lobes, show between 20 and 75 Ohms reactance. You may track the feedpoint impedances in the reference table that immediately follows this compendium of azimuth patterns. You may find it useful to correlate the pattern descriptions, the maximum gains, and the feedpoint impedances of the models.

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10 Meters

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28 MHz is exactly 8 times 3.5 MHz. since the loops at 80 meters had two lobes, we should be able to count 16 lobes in the 10-meter models. In fact, the square models only show 12 lobes. What has happened to 4 lobes? In principle, two things can occur. One is that the lobes merge. In most instances, merges lobes show some aberration of the normal cigar shape of a lobe. No such odd shape appears in the square models.

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The other possibility is that lobes cancel each other due to the presence of equal but opposite radiation from symmetrical points across a loop. In the corner-fed model, notice the wide and very deep nulls at the 45° angles, and in the side-fed model, notice similar nulls at the 90° points. Both sets of nulls correspond to the middle points along the sides of the squares. In effect, the lobes for these positions have cancelled each other out across the antenna loop.

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The relative positions in the octagon that might correspond to those in the squares are not quite right for complete cancellation of any lobes. Hence, the full complement of 16 lobes appears in each of these models. The corner-fed octagon shows its strongest lobes on either side of the position where the corner-fed square has its strongest lobe. The side-fed octagon positions its strongest lobes like those of the corner-fed square.

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The side-fed octagon also illustrates lobe merging and the consequent distortion of lobe shape as two or more lobes come together. The "mittens" at 135° and 225° are good examples of merging lobes.

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It is clear from this compendium that loop shape can make a difference in how the loop performs on various bands. If you plan to build an irregular loop, by all means, anticipate its performance through modeling.

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Azimuth Patterns of Hexagon 160-Meter Loops, Corner and Side Fed

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80 Meters

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Because the 160-meter loop is about 2 wl long at 3.5 MHz, the pattern resembles that of the 80-meter loop when used on 40 meters. However, the antenna height is proportionately lower (about 0.18 wl for the 160-meter loop on 3.5 MHz vs. 0.35 wl for the 80-meter loop on 7 MHz), so the elevation angles of maximum radiation are higher: in the 48° to 49° range. Nevertheless, there is far more radiation at lower elevation angles than with the 1 wl loop on 80 meters. The additional low angle gain holds the promise (but not the guarantee) of more regular longer distance contacts on 80 meters. Although the radiation pattern is fairly even all the way round the loop, it is slightly stronger at 90° to the feedpoint axis. There is virtually no difference between the patterns for the version using a corner feedpoint or for the one using a side feedpoint. +
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40 Meters

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On 40 meters, the 160-meter loop becomes quite bi-directional with either corner or side feeding. Maximum gain occurs off opposite points of the hexagon. with corner feeding, the axis of maximum gain is through the feedpoint to the opposite corner. However, if we side-feed the hexagon, the axis of maximum gain is at right angles to the feedpoint-to-opposite side axis.

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Both of the 40-meter patterns of the 160-meter loop are exercises in finding hidden lobes. We expect 8 lobes. In the corner-fed model, we can almost count them in terms of small bumps in the pattern. The side-fed model appears to be missing a lobe--the one to the rear of the feedpoint. In fact, this lobe is highly suppressed and would appear only if there were deeper nulls on each side of it.

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30 Meters

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The patterns for the 160-meter hexagon at 10.1 MHz are roughly bi-directional along the axis from the feedpoint to the opposite position on the loop. However, the side-fed version achieves an almost rectangular pattern, which is somewhat of an oddity.

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Of equal significance with the pattern shape are the high values of resistance and reactance at the feedpoint of either version of the 160-meter hex. The 80-meter loop showed only a few values of reactance above 500 Ohms, and no resistance values reached that level. In contrast, the 160-meter loop will show values in excess of that level for many bands. The length of the feedline used may require careful selection with the larger loop to ensure that the values presented to the antenna tuner are within the range of available adjustment. Some feedline length-switching may be required as one moves from one band to another.

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20 Meters

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The 20-meter patterns for the larger loop show a combination of most of the pattern characteristics we have already seen: bi-directionalness, merged lobes, and a number of others. Primary radiation is off opposing sides, as with the 40-meter patterns, but with a greater complexity of lobe structure. As well, the feedpoint resistance and reactance values are fairly high.

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Of interest is the fact that maximum gain values fall only in the middle of the span of those exhibited by the 80-meter loop when run at 14 MHz. On this band--and on others as well, the antenna offers little to justify the added complexity of running a wire twice as long as the 80-meter loop. One might well argue for some installations that the benefits derived on 80 meters from the larger loop are offset by the disadvantages on some of the higher bands. Indeed, the shorter loop and a separate 80-meter antenna might be easier to use.

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17 Meters

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The 17-meter patterns for the 160-meter loop bear a striking resemblance to those for 40-meter operation if we do two things. First, we have to smooth the peaks of the narrower and more numerous 17 meter lobes. Second, we have to notice the movement of the peak gain regions a small angular distance away from their axes on 40 meters so that a narrow weak area develops along the precise axes of 40 meter peak gain.

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As curious as the patterns are, the 17-meter impedance values are also interesting because they come closer to resonance than the values on any other band. However, there will still be considerable excursions of voltage and current on the feedline, because the high values of feedpoint impedance on other bands almost dictate the use of 600-Ohm open parallel feeders as the best compromise among all the impedance levels encountered.

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15 Meters

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At a certain level of lobe multiplication, azimuth patterns tend to lose their identify as guides to antenna radiation and become more like Rorschach ink blot tests. With the 15-meter patterns of our large loop, we may have reached that stage. Local ground clutter, terrain irregularities, and simple blowing of the antenna wire in the wind may lessen the utility of following out each pencil-thin lobe of the azimuth pattern.

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Nonetheless, we can gain something from observing the azimuth patterns, if only by gaining a general impression of regions of strength and weakness. For example, between the corner-fed and the side-fed patterns, the former seems to have more lobes of higher strength in more directions, thus promising contacts in both the morning and the evening hours of the daily skip cycle (assuming that the antenna is set up on a rough East-West axis).

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12 Meters

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The patterns for both 12 meters and 10 meters share some interesting characteristics. Regardless of the feedpoint, there are very few lobes that are less than 8 to 10 dB down from the peak gain lobes, and almost all of them have very narrow beamwidths. Therefore, the effective gain of the antenna is not given by the maximum gain figures, which happen to range in the vicinity of 14 to 15 dBi. Rather, the average gain over the 360° horizon is more like 5 to 8 dBi. These are gain values more akin to a multiband quarter wavelength vertical with a ground plane mounted on a roof top than they are to typical gain antennas.

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There is a strong possibility that, if your interests are in upper HF operations, the large 160-meter loop will prove to be a disappointment. Its true virtue lies in the lower HF region, especially on 80 meters, with reasonable good performance through 20 meters.

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10 Meters

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Although the 80-meter loop shows poor performance on 80 meters for every application other than NVIS, the smaller loop has distinct advantages over the larger loop on almost every other band. The patterns are smoother, with reasonable gain in most directions. The feedpoint impedances are moderate and amenable to the use of inexpensive and readily available 300-Ohm or 450-Ohm parallel feedlines. The values of impedance presented to antenna tuners are more likely to be within the adjustment range of inexpensive units.

+

Size alone, then, is not the sole determinant of HOHPL performance. Smaller can be better for some operational purposes. As important as size is the antenna shape and the feedpoint position in the determination of the antenna patterns that will most benefit our operational needs. A HOHPL that best fits our needs is a blend of many factors.

+
+ +
+

Reference Tables of Modeled Antenna Performance for Antenna Azimuth Patterns Shown

+ 
80-Meter Square Loop, Corner-Fed:  Fig. 11
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    dBi     Deg     R +/- jX Ohms
+3.5     4.4     45*     120 - j 100
+7       6.0     43      95 - j 230
+10.1    10.4    29      280 - j 650
+14      11.3    20      245 - j 240
+18.1    14.1    15      375 + j 245
+21      14.2    13      250 - j 170
+24.9    14.7    10      345 + j 125
+28      13.7    9       260 - j 220
+
+80-Meter Square Loop, Side-Fed:  Fig. 12
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    dBi     Deg     R +/- jX Ohms
+3.5     4.3     45*     120 - j 100
+7       6.7     37      290 - j 105
+10.1    8.0     27      280 - j 610
+14      10.7    19      215 - j 265
+18.1    11.7    15      415 + j 210
+21      10.8    13      410 - j 215
+24.9    11.7    11      380 + j  20
+28      12.2    9       280 - j 250
+
+80-Meter Octagon Loop, Corner-Fed:  Fig. 13
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    Bi      Deg     R +/- jX Ohms
+3.5     4.3     45*     135 - j  55
+7       6.3     41      205 - j 150
+10.1    7.9     29      250 - j 580
+14      9.3     21      155 - j 250
+18.1    11.6    15      310 + j 250
+21      11.9    13      275 - j 230
+24.9    10.5    11      300 + j  40
+28      11.4    10      310 - j 310
+
+80-Meter Octagon Loop, Side-Fed:  Fig. 14
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    dBi     Deg     R +/- jX Ohms
+3.5     4.3     45*     135 - j  70
+7       6.3     41      200 - j 180
+10.1    7.7     25      250 - j 610
+14      9.8     19      270 - j 230
+18.1    9.8     16      295 + j 150
+21      10.0    14      275 - j 335
+24.9    10.8    11      265 - j  70
+28      11.8    10      300 - j 415
+
+160-Meter Hexagon Loop, Corner-Fed:  Fig. 15
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    dBi     Deg     R +/- jX Ohms
+3.5     5.4     49      145 - j 265
+7       10.5    36      350 - j 505
+10.1    10.9    23      2810- j 1140
+14      10.8    21      815 - j 1010
+18.1    13.2    15      415 - j  90
+21      13.0    14      1830- j 370
+24.9    14.8    11      870 - j 540
+28      14.9    10      1300+ j 635
+
+160-Meter Hexagon Loop, Side-Fed:  Fig. 16
+
+Freq.   Gain    TO      Feedpoint Z
+ MHz    dBi     Deg     R +/- jX Ohms
+3.5     5.5     48      145 - j 260
+7       9.2     33      285 - j 495
+10.1    8.9     25      2205- j 1105
+14      10.3    18      655 - j 920
+18.1    11.7    15      385 - j 130
+21      12.5    14      1570- j 687
+24.9    15.0    11      735 - j 585
+28      14.6    9       1455+ j 125
+

Notes:

+

1. * beside a TO entry means that the angle used is arbitrary. Maximum gain is straight up (elevation angle = 90°).

+

2. Feedpoint impedance figures are representative and will vary with the exact length and layout of the antenna loop. The impedance presented to the antenna tuner will also be a function of the exact length, characteristic impedance (Zo), and velocity factor (VF) of the transmission line used for each particular installation.

+

3. Gain figures represent the maximum gain of the strongest lobe in the azimuth pattern and should not be interpreted as the sole basis for deciding among HOHPL designs. Equally important are the distribution of the lobes, the depth of the nulls, access to all desired communications directions, and other factors.

+

4. TO angles are the elevation angles of maximum radiation from the strongest lobe. The vertical structure of lobes may vary.

+

6. How does the HOHPL compare to other all-band antennas?

Although it would be impossible to do a detailed comparison with every possible contender against the HOHPL, we can sample one case: the standard 135' center-fed doublet. For fairness, we shall place both antennas at 50 feet and overlay azimuth patterns for 80, 40, 20, and 10 meters, as representative of a fuller comparison. +
+ +
+

On 80 meters, there is no major difference between the doublet and the square HOHPL. The HOHPL shows a higher radiation angle, giving the doublet about 1.2 dB more gain (5.6 vs. 4.3 dBi at the arbitrary 45° elevation angle).

+
+ +
+

There is a distinct difference between the HOHPL and doublet 40-meter patterns. The doublet is 1þ long and shows a bi-directional pattern. The HOHPL loop is 2 wl long and displays major lobes in four directions, although at lesser gain (8.1 vs. 6.7 dBi at about 36° elevation). Which antennas has the advantage depends on one's operating needs.

+
+ +
+

On 20 meters, the 1wl HOHPL shows enough tilt in the pattern away from the feedpoint to give it a small gain advantage at similar elevation angles. Although the patterns seem otherwise fairly similar, with only small offsets in the lobes, the doublet shows some deep nulls broadside to the antenna, nulls that can adversely affect communications in certain quadrants. Although the "side" nulls of the HOHPL are deep, they do not differ as much from the doublet wire-end nulls.

+
+ +
+

The 10-meter patterns, while a bit confusing at first sight, also show that the HOHPL has somewhat fewer nulls of great depth than the doublet. Moreover, especially in the direction away from the feedpoint, the HOHPL lobes are stronger (by about 1.5 dB) and more even in gain. In contrast, the doublet is beginning to show greater strength in lobes that are further from the broadside direction and more towards the antenna ends.

+

Conclusion

Summing up all of the patterns for the HOHPL shows it to be a somewhat better performer over a full azimuth circle than the 135' doublet. A 2 wl HOHPL would show an even greater evenness in the lobe structures, since its 80-meter pattern is already like the 4-lobe pattern we saw above for 40 meters. In this summary comparison, I have not stressed matters of raw gain, but instead, I have placed emphasis upon the nature and position of the lobes and nulls. For nation-wide and world-wide communications, evenness of pattern may often be more important than the gain of one or more individual lobes. +

As a consequence of this behavior, the advantage of the HOHPL will not show itself in any one contact or in a short period. Satisfaction with the antenna grows with time and changes in the propagation paths, a successful communications almost everywhere shows up in the log.

+

Still, the HOHPL, even in its smaller 1 wl form, requires a considerable investment in real estate, supports, wire, and accessories compared to the simpler doublet. Only the potential user can decide if it is the right antenna for his or her installation. If it is, then in about a year, you will be able to scan your log and chuckle the famous chuckle:

+
+

"Ho, ho, HOHPL!"

+
+
+ +
+

Updated 1-19-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +

+
+ Return to Amateur Radio Page +

Topics: HF Multi Band, Horizontal Loop


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+ Title graphic +

Coils, Linear Loads, and Capacity Hats:
+ An Overview of Small Loaded Yagis

+

This talk, originally prepared for the 1996 FDIM Symposium in Dayton, summarizes material drawn from the studies called "Modeling and Understanding Small Beams," which appeared in eight installments in Communications Quarterly.

+ +

+

Many QRPers and other hams operate within limited spaces. Others simply do not want to erect or maintain full-size beams that span 35' or more on 20 meters. So there will always be interest in shrunken beams and other arrays.

+

In this overview of small, 2-element Yagis, we shall compare the modeled performance of several size-reduction schemes, otherwise known as loaded elements. First, however, we need to look at the general performance of shortened radiators relative to resonant dipoles for a given frequency. How short does it make sense to go? If we know the answer to that question, we can then ask what is the best way to get there.

+

Inductive or coil loading is the most familiar form of element shortening, and placing the coils at the element centers is mechanically most convenient. However, we can replace the coils with linear loads, which are nothing more than shorted transmission line stubs. Finally, we can "load" the other end of the element with a capacity hat. For orientation, Figure 1 shows each of these options applied to dipoles elements. Each scheme has certain advantages and disadvantages that I shall try to lay out so you can select your own preference.

+
+ +
+
+

How Short Should I Go?

+
Everything Yagi begins with the half wavelength dipole. As the dipole goes, so goes the beam. So our first question is what happens when we shorten a dipole by loading it. Answers are not hard to come by if you do a little systematic antenna modeling with one of the numerous Method-of- Moments programs available. For our purposes, either MININEC or NEC will do, since we shall not come close to violating their limitations. Those unfamiliar with these programs should understand that when used within their limitations, they are exceptionally accurate, well beyond the abilities of home-built antennas to test.1 +

We shall look first at center-loaded dipoles with inductive loads. Moving the inductors outward, up to about the middle of each quarter wave leg of the dipole, can improve performance, but somewhat marginally. For center- loaded dipoles, the element gain is a function of two factors: element length and load Q. Figure 2 is a graph of dipole gain in dBi in free space of shortened, loaded dipoles compared to a full size dipole at 10 meters (28.5 MHz). Virtually identical figures emerge at other frequencies by shortening the element by an equal percentage.

+
+ +
+

A full size dipole for 10 meters is just over 16' long. That makes shortening in 2' increments a handy gauge of performance. If we assume a lossless load, needed to compensate for the shortened length, we uncover the amount of loss in gain directly attributable to element shortening. Although the graph does not make the loss of gain look serious, there is about a 15% loss between the full size element and the exceptionally short 6' element. In contrast, the 12' element, about 3/4ths full-size, losses only about 9% gain.

+

However, no load is without some resistive loss: hence, the rest of the graph. The moment we assign a value of Q, the load's reactance divided by its heating resistance, differentials among the shortened elements grow more pronounced. Even at the unrealistic Q-value of 500, losses in the 6-, 8-, and 10-foot elements grow serious.

+

Do not overestimate the Q you may maintain in an antenna loading element, whether it is a coil or a linear load. Hypothetically, you might calculate Q's up to 300 for leadless coils of optimal length-to-diameter ratios of fresh, clean materials. When you add leads, connectors, and-- especially--the action of the chemical soup we call our atmosphere, you will rarely achieve Qs above 100 in antenna coils. Even a perfect coil will weather down to that Q very quickly after you place the antenna in the air. Physically modeled linear-loading elements have Qs from about 300 to over 1000, and they are nothing more or less than the touted ultra-low-loss transmission-line sections. However, realizing very high Qs in linear loads is a complex and somewhat tricky business. So be very conservative in your estimates of inductor Q for antenna loads.

+

In terms of our graph, conservativism means going to the right-hand edge of the graph. Here we find a break in the gain-efficiency of our shortened dipole between the 10' and 12' models, 5/8ths and 3/4ths normal length respectively. That break coincides with longstanding broadcast antenna engineering rules of thumb that use 60 degrees electrical length (2/3rds resonant length) for verticals as the break-point between acceptable and unacceptable efficiency.2

+

What kind of load and where we put it do make some difference in the performance of a dipole element and any Yagi we make from such dipoles. Figure 3 gives us a basis for comparing short dipoles (12' long) using center loads, mid-element loads, and capacity hats. The strength of the electrical field is a function of the current along the element, which, for a dipole, is highest at the center or feedpoint and lowest at the element ends. The figure provide current levels in a 10-meter dipole with center loading (Q=300), mid-element loading (same Q) and capacitive hat "loading." All main elements are 0.75" diameter aluminum.

+
+ +
+

Compared to the full-size dipole, the two inductively-loaded antennas display sharp current drops beyond the loading point, in essence, the missing antenna segment made up for by the coil. The free space gain of the midelement-loaded dipole is only marginally better than that of the center-loaded dipole: 1.84 dBi vs. 1.82 dBi. The free space gain of the full-size dipole is 2.13 dBi. Interestingly, the capacity-hat loaded dipole shows a free space gain of 2.03 dBi. However, notice that the current along the capacity-hat element parallels the values for the full-size dipole right up to the hat itself. The nonradiating structure at the end of the antenna uses only the lowest levels of antenna current. The other loads are placed in high-current regions of the element, but yield insignificant radiation in the tight fields of the coils.

+
+ +
+

For reference, Figure 4 provides free-space azimuth patterns for a full-size dipole, along with 12' capacity hat, midelement-loaded, and center-loaded dipoles, working downward in gain. The pattern differences are so slight that any of the 4 would make a working dipole. However, those differences will have a significant effect upon Yagis that use them.

+

The feedpoint impedance of a shortened dipole will affect the feedpoint impedance of any Yagi in which it is used. A full-size 2-element Yagi has a feedpoint impedance of approximately 35 ohms, depending upon design, using a full size dipole with a natural impedance of about 72 ohms. A 12' center-loaded dipole has a feedpoint impedance of about 32 ohms, while a 12' midelement-loaded dipole's feedpoint is about 44 ohms. The feedpoint impedance of a capacity hat dipole of the same length is nearly 60 ohms. Consequently, expect 2-element Yagis using inductive loading to have lower feedpoint impedances (10-20 ohms) compared to Yagis using capacity-hat elements (30 ohms).

+

Let me add a word about helical elements. A helical element is a continuous coil, like a slinky, wound in one direction, and fed in the middle. It radiates well because the turns are spread apart and the field is not as self-enclosed as with a normal coil. I have modeled a few, using simplified geometry (square and hexagonal turns). They perform well so long as the turns are not overly compressed. An 11 and a half foot model dipole of 12 turns with a 6" diameter provided 1.94 dBi free space gain and a resonant feedpoint impedance of about 38 ohms. However, do not expect such performance if you wind the coil over a support structure, such as PVC. PVC is a fairly good RF performer at HF for small lengths and supports, but it is not air, and it will reduce inductor Q. Moreover, using smaller turns and more of them will reduce gain. Compressing turns to further shorten the antenna element will begin to reduce gain radically, as the antenna begins to act more like a coil than a linear element. In the end, helical elements may be more trouble than they are worth in Yagi applications.

+

The upshot of this investigation is a series of recommendations:

+
    +
  • +

    1. Wherever possible, use elements at least 2/3rds normal resonant length.

    +
    • +
  • +

    2. Mid-element loading provides such a small improvement over center loading that the choice should be made on grounds of mechanical factors, such as ease of construction and durability.

    +
    • +
  • +

    3. Capacity-hat loading is a viable alternative to inductive loading for dipoles and Yagi elements in a monoband beam.

    +
    • +
  • +

    4. For center-loaded dipoles and beams, consider linear-loading as a higher-Q option to center loading coils.

    +
    • +
+

Remember that these are ideal recommendations: local circumstances may always dictate that you violate one or more of them.

+
+

Center-loaded Yagis: Coils or Linear Loads?

+
We have spent nearly half our time on dipoles, because understanding dipole performance is 90% of the game of understanding Yagi performance. Proof of this is in the following rule of thumb: if he driven element Q goes down, gain decreases; if the reflector Q goes down, front-to-back ratio decreases. Using this rule backwards is a guide to trouble shooting your antenna. If your gain is down, look for problems in the driven element (or directors, if you can afford them); if the front-to-back ratio goes down, look for the problem in your reflector. If all else fails, check your feedline. +

90% of the rest of the game is understanding full-size Yagi performance. So let's begin with a simple 2-element, driven element and reflector, Yagi. Again, figures are for 10 meters, but you scale them up to 20 or down to 6 with fair ease and reliability.

+
+ +
+

Figure 5 provides the dimensions of the antenna I shall use as a standard. A 16' driver and a 16.5' reflector are 4.25' apart, using 3/4" diameter aluminum. The antenna shows a balance between gain and front-to-back ratio. You can squeeze more of one or the other out of the antenna, but not both. The feedpoint impedance is quite reasonable at about 30 ohms, and a beta match or a gamma match works well. I prefer to reserve the gamma match for all metal construction and use the beta match for insulated feedpoints.3 The latter are common in center-loaded construction, so we shall specify them, but without bias against the gamma match.

+
+ +
+

Figure 6 gives an idea of performance, referenced to free space. The gain over a dipole in free space is about 4.1 dB, and the front-to-back ratio of about 11+ dB is 2 S-units. Nothing stellar here, but it is a good antenna for round tables, contests, and the like, where you want to suppress QRM but do not want to totally miss contact with someone behind you.

+

We can shorten the elements of this antenna to about 11.6' and 12.16' respectively for the driven element and reflector, while retaining the same spacing. All we need to do is place high-Q inductors at the center of each element. Of course, we shall have to insulate the elements from the boom (unless the boom is PVC), and we shall also have to split the driven element coil at the center for the matching and feed network. All this is shown in Figure 7.

+
+ +
+

What do we get for our pains? A very usable antenna, as shown in Figure 8. Let us assume that weather and other factors have set the loading coil Q at 100. We shall have lost about 1 dB of gain overall from coil losses and shorter elements. However, we do gain in the front-to-back ratio department by almost a full S-unit (6-dB). In fact, you can play with the reflector and achieve something over 20 dB front-to-back ratio for outstanding rejection of QRM. However, these figures come at a cost.

+
+ +
+

The first cost is a low feedpoint impedance. The full size 2-element Yagi had a feedpoint impedance of 30 ohms, while the center-loaded version is down to 20 ohms. Increasing the front-to-back ratio further lowers the feedpoint impedance to below 10 ohms. Maintaining a good efficiency, reflected in the ratio of feedpoint impedance to loss resistance, becomes very difficult at very low feedpoint impedances. A 1-ohm loss at a 50-ohm feedpoint impedance is about a 2% loss. When the feedpoint impedance hit 10 ohms, that 1-ohm loss consumes 10% of your power.

+

There is a lower-loss alternative to loading coils. It is the linear load that for a long time has simply not been understood in ham circles.4 A linear load is a simply a pair of inductive (shorted) transmission-line segments. Shorted transmission line lengths less than a quarter wavelength show inductive reactance. We can precisely calculate the length of line of any construction needed for a given reactance at any frequency. There is a program in George Murphy's HAMCALC that does precisely this job.5 We place two lines, each with half the overall required inductive reactance under each element and throw away the coils.

+

The center loading coil required for our model antenna showed about 248 ohms for each element. Each transmission line will have about 124 ohms reactance. #12 wire spaced about 1.25" in a long hairpin will provide the required reactance if it about 1.6' long each side of center. Figure 9 shows 2 possible layouts for linear loads. What has probably kept linear loading in a state of confusion is that the symmetrical triangular system--where the effects of the antenna's radiation apply equally to both wires of the linear load--is the only one where the length can be calculated reliably from standard transmission-line formulas.6

+
+ +
+

The flat-plane layout, which is often mechanically handier, especially for field antennas, is not quite a true transmission line. The radiation from the antenna affects each line slightly differently so that currents are not equal and opposite at corresponding points on the line. That, in turn, makes the line radiate as part of the antenna. The bottom line is that the linear load needs to be a bit longer to do its work--close to 2' each side of center. Figure 10 shows a graph of modeled lengths for a 12' 3/4" diameter aluminum element and flat-plane linear loads of #12 and other size conductors.

+
+ +
+

As a side side note, if we move the linear load sections outward--toward midelement loading points--we encounter a second unbalancing force that operates even if we use great care in placing the linear load lines in a symmetrical arrangement with the main element. Near the element center, current levels change very slowly, so that the small space between one terminal of the load and the other terminal of the load show almost identical current levels. Farther out the element, the current level changes more rapidly so the a small space can show a much larger current difference. Hence, even symmetrically built lines will show significant current imbalance. This imbalance, in turn, disrupts easy calculation of the line length and makes empirical experimentation necessary.

+

The final dimensions for my test antenna using a flat-plane are shown on Figure 9. I used the same old 11.6' and 12.16' 3/4" diameter aluminum elements spaced 4.25' apart. The linear loads are #12 wire evenly spaced below the main element in 1.25" increments. The reflector linear load (actually load pair) is 4' long, while the driver load is 3.8' long total. Note that the driven element linear load has been shortened to let the element show a capacitive reactance, necessary to permit the use of a beta match. Contrary to a gamma match, where we purposely lengthen the element to make it appear inductive, with a beta match, we shorten it to provide a built-in series capacitive reactance. Then a coil across the feedpoint provides the parallel inductive reactance necessary to complete our L-circuit matching system. Standard L-circuit formulas apply to this matching system. You can replace the small beta-match coil with a shorted piece of transmission line and you have what has been dubbed the "hairpin" match. Figure 11 compares our usual picture of an L-network matching a higher source resistance to a lower load resistance to the situation when it is used with an antenna.

+
+ +
+

The linear-loaded version of our center-loaded antenna is equivalent to raising the Q of the center load to a reliable and durable value of 300. Gain is improved by about 2/3rds of a dB, closer to the gain of a full size Yagi, and the front-to-back ratio is improved for any given value of reactance chosen for the reflector. Although the test antenna sacrificed a little front-to-back ratio for the sake of a higherr feedpoint impedance (about 20 ohms), 20 dB front-to-back ratios with feedpoint impedances above 15 ohms are not hard to achieve or hard to match with the beta match scheme. Figure 12 compares the free space azimuth patterns of the inductive and linear load version of the center-loaded antenna.

+
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We mentioned one cost of center loading (whether one uses coils or linear loads): lower feedpoint impedance. There is a second cost: narrower SWR bandwidth. Figure 13 compares the SWR bandwidths of a full-size Yagi with our three-quarter size center- loaded version. Curves for center inductors and for linear loads are insignificantly different, so read the second line up as covering both for all practical purposes. The third or top line gives the SWR bandwidth for a modeled version of the loaded antenna using 8' elements. Such antennas are both possible and, in some cases, necessary. However, be aware that you lose more than bandwidth with them. If we arbitrarily allow the center load Q to be 300, the gain will decrease to less than 4.5 dBi. If a center inductor has, after weathering, a Q of 100, the gain is barely more than that of a dipole, about 2.5 dBi. However, such antennas do offer signal and QRM discrimination, with front-to-back ratios approaching 18 to 20 dB. A half-size 2-element, linearly-loaded Yagi for 40 meters may be a very good antenna indeed, compared to whatever else is available. However, do not shorten the required 17-20' boom (four times the length of the 10-meter model), or you will lose even this performance.

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The differences in inductively-loaded and linear-loaded antennas of the same physical dimensions are not overwhelmingly great, even if noticeable. Construction and maintenance considerations may well dictate which version you build. For 10 meters, a strip of 3/8" thick plywood, coated for weather protection, makes a good insulated element base. Suspend the element and the linear load below the plate, using strips from 4" square freezer boxes as a good weather-resistant set of insulators. A 5' section of 1 1/4" diameter nominal Schedule 40 PVC makes a good boom. Alternatively, you can run half-inch nominal PVC through holes cut in the ends of the PVC boom. PVC glue will weld the pieces together. With just a bit of tape wrapped around the smaller PVC, 1" diameter aluminum tubing with fit tightly over the PVC. With this construction, you can also mount coil sections over the smaller PVC and come up with a durable inductive center load. Obviously, for 20 meters, you will need hardier construction methods.

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Capacity Hats

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We have not exhausted the means of shortening antenna elements and still maintaining fairly efficient performance. It is time to tip our capacity hats. Unfortunately, capacity hats are ill-understood in much of the ham literature. Often thought of solely in the context of vertical antennas, they can be useful for horizontal antennas and even for quad loops. +
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Figure 14 shows some variations on the capacity hat applied to different types of elements. If nothing else shows up, the symmetry of hat constructions does. It is there for good reason.

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We can look at hats from two points of view, but only if we are willing to keep them well-separated. First, we can look at them as physical structures that permit current flow. If we start with a shortened main element, the hat structure completes the length needed by the antenna current at some given frequency to reach zero while the antenna is resonant. What makes the hat different from the main element is that its symmetrical construction yields no radiation, since the currents in the various legs cancel each other out in terms of field generation.

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Now let's take a different look at the same antenna. From this perspective, each leg of a shortened dipole is like a shortened quarter wave vertical. We can look at it as if it were a single-wire transmission line. The antenna (minus the hat) will have a certain length-to-diameter ratio which determines its average characteristic impedance. Since it is short, as Figure 15 suggests, we can lengthen it to a resonant length, or we can add to the end away from the feedpoint the missing capacitive reactance in the form of a nonradiating "stub." That stub is the capacity hat, so named because of its function to add capacitive reactance to the far end of the antenna element.

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There is an old technique of calculating the size of the hat needed by any given shortened element at any given frequency. Unfortunately, it is not particularly accurate above 80 meters. First, it was generated for very thin wire antennas that approximate skinny conical sections of wire on which the theory is based. Above 80 meters, almost all ham antennas represent fat wires. Second, hat size has been predicated on the solid conductive disk with no thickness.7 Hams almost always use thick open- frame hats, which do not come close to approximating the disk. At low and very low frequencies, almost any antenna diameter is very thin and almost any hat material is of little thickness relative to the length of a wave of RF energy. But we HF hams have to live with being both fat and thick-- antenna-wise, at least.

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One can construct a series of ad hoc correctives to the classical calculations and come up with reasonable approximations of hat size, close enough to start experimental construction. In fact, HAMCALC also contains a program designed to do this.8 However, an antenna modeling program is the final planning step before construction, since it treats hats as physical objects along which currents flow, a much more accurate method of calculation.

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Typical ham hats come in two generic types: a series of spokes radiating from the element end and a closed version of those spokes that includes a perimeter wire. As Figure 16 shows, the major variants in these types of hats are the square, the hexagon, and the octagon. Hats have traditionally been applied to verticals, but they can be applied to 2- element Yagi construction with success. In fact, a dipole in free space is nothing more than a quarter-wave vertical and its modeled image: equal antenna leg lengths call for the same size hats, except that a dipole requires one on each end.

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Figure 17 shows the dimensions of a 10-meter capacity-hat Yagi I designed and built over the winter. It uses the same 11.6' and 12.16' elements spaced 4.25' apart that were used in center-loading experiments. For this band, the required square, perimeter-enclosed hats of #12 wire had spokes just over 10" long. Since the original elements were designed for equal center loading inductive reactance while giving the required Yagi driven element-to- reflector relationship for the 4.25' boom length, we should expect equal size driven element and reflector hats.9

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If a 10-meter beam calls for a square with perimeter 20" fromt point to point (and correspondingly smaller hexagons and octagons), then a 20-meter Yagi, 3/4th's full size, would call for squares about 40" from point to point. This is not as radical a weight and wind load on the element end as one might at first sight believe. My thin #12 structure, soldered at the corners and hose-clamped in place at the element ends has withstood standard weather blasts with no ill-effects. The real question is whether we gain anything by going to capacity hats. The current distribution shown way back in Figure 3 suggests that we do.

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Figure 18 shows the azimuth pattern in free space of the 10-meter beam in question. Note that its gain and front-to-back ratio closely approximate those of the full size 2-element Yagi. The gain loss is insignificant in practical operating terms, and the front-to-back ratio is much the same. However, the capacity hat Yagi cannot approach the front- to-back ratio of the center-loaded antenna, which--of course, was purchased at the cost of a greater reduction of gain and much narrower SWR bandwidth.

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Figure 19 compares the SWR bandwidth of the full size antenna, the capacity hat model and the center-loaded models, all normalized to their inherent feedpoint impedances. The merits of the capacity-hat model in this respect show themselves clearly. In fact, the driven element of the capacity-hat Yagi shows a feedpoint impedance between 30 and 35 ohms, with remnant inductive reactance. A pair of series capacitors between the element connections and the coax connector cancels the inductive reactance and permits direct connection of 50-ohm coax with under 2:1 SWR over the first MHz of 10-meters.

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The SWR bandwidth of an antenna does not just indicate the ease or difficulty of matching the antenna to a certain feedline. Narrow bandwidths usually indicate some other potential problems. In a Yagi antenna, maximum gain and maximum front-to-back ratio do not coincide at the same frequency. Maximum gain occurs at a lower frequency than maximum front-to-back ratio, and gain decreases steadily across the band. When the SWR bandwidth is wide, both maxima usually occur within the 2:1 SWR portion of the curve, and the gain decrease across the band is slow. When the SWR bandwidth is narrow, maximum gain may occur at a frequency of very high SWR, and the gain may decrease more rapidly across the band. Too, the front-to-back ratio, which may be high at the design center frequency, may deteriorate swiftly away from that frequency. Compared to center-loaded Yagis, the wider SWR bandwidth of the full-size and capacity hat Yagis is indicative of greater stability among other antenna properties.

+

Moreover, do not take SWR figures above an antenna's design center frequency too seriously. SWR figures below the antenna design center frequency are more indicative of antenna performance. Above design center, the SWR may remain low--or at least acceptable--but both the gain and front-to-back ratio may decrease to the point of making the antenna little better than a dipole.

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Result: the capacity-hat 2-element Yagi is--or should be--a contender in your thinking about small beams for the small QRP city lot.

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Summary

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No one can make your antenna building decisions for you. Your specific situation has too many variables that only you can know and weight in the final summary. However, we can summarize some of the advantages and disadvantages of center-loaded and capacity-hat Yagis. +
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    1. Center-loaded Yagis: These antennas have the disadvantage of lower gain and narrower SWR bandwidths. The latter is a problem on 20, 15, and 10, but not on 12 or 17 meters. They have some mechanical advantage in offering less wind loading and weight at element ends. They can also be tuned for high front-to-back ratios.

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    2. Linear-loaded Yagis: Similar to inductively-loaded Yagis in mechanical advantage, SWR bandwidth, and front-to-back ratio, linear-loaded Yagis have high gain figures due to a higher loading element Q.

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    3. Capacity-hat Yagis: Of all types of shortened Yagis, capacity hat models offer performance closest to a full size Yagi in terms of gain, SWR bandwidth, and front-to-back ratio (less than that of a center-loaded Yagi). Hats on the element ends can add to element stress and wind loading.

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    4. General: Shortened antennas with elements at least 2/3rds normal length offer good gain, good front-to-back ratios, and reasonable to good SWR bandwidths. When element lengths are less than 2/3rds normal, expect low gain and very narrow SWR bandwidths, although the front-to-back ratio can be sustained. It is unwise to use boom lengths less than 0.1 wavelength, with about 1/8th (0.125 - 0.16) wavelength preferable.

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Although I have not tried the experiment, there is no reason why techniques cannot be combined. For example, I can imagine a 40 meter beam with half-normal element lengths that uses a combination of linear loading and capacity hats. When too long, linear loads can become loss factors, and without linear loading, the capacity hat might be very ungainly. A combination might yield smaller center loads and smaller hats, while still giving a little gain and good directionality across at least part of 40 meters.

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In short, do not use my findings as gospel. Instead, model and experiment. The fun you have may be your own.

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Notes

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1. Among the most ready sources for NEC and MININEC are the following: a. Roy Lewallen, W7EL, for ELNEC (MININEC) and EZNEC (NEC-2); b. Brian Beezley, K6STI, for AO (MININEC) and NEC/Wires (NEC-2); and c. Nittany Scientific, Inc. for NEC-Win Basic (NEC-2). The W7EL and K6STI programs are DOS, while NEC-Win is for Windows. For an introduction to programming with MININEC, see "A Beginner's Guide to Using Computer Antenna Modeling Programs," pp. 10-17, and Roy Lewallen, "MININEC: The Other Edge of the Sword," pp. 18-22, both in Vertical Antenna Classics, ed. Robert Schetgen, KU7G (Newington: ARRL, 1995). (Note: all articles and programs without an author reference are by the author of this paper.)

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2. Walter Schulz, K3OQF, "Designing a Vertical Antenna," QST (September, 1978), 19-21, reprinted in Vertical Antenna Classics, pp. 7-9.

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3. For information on the beta or hairpin match, see recent editions of The ARRL Antenna Book, pp. pp 26-21 to 26-23; "The Hairpin Match: A Review," by Thomas Cefalo, Jr., WA1SPI, Communications Quarterly, Summer, 1994, pp. 49-54; and "Some Further Notes on the Beta Match," Communications Quarterly, Winter, 1995, pp. 51-52.

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4. See, for example, the description of linear loading in The ARRL Antenna Book, and recent edition, pp. 6-7 to 6-8, where matters are left to "cut and try."

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5. HAMCALC is available as free ware from George Murphy, VE3ERP, 77 McKenzie Street, Orillia, ONT, Canada L3V 6A6. Although the program may be shared freely, if you write Murph for the latest version, he asks a $5 donation to cover the costs of Canadian postage and disks. Any excess, he donates to a Canadian ham-related national charity. The program for calculating linear loads and other transmission line segments as reactances is call "Transmission Line Stubs." WA1SPI's program for beta matches is also in the collection under the title, "Hairpin Match for Yagi Antennas."

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6. For further information on linear-loaded Yagis, see "Modeling and Understanding Small Beams, Part 4: Linear-Loaded Yagis," Communications Quarterly, Summer, 1996, 85-106.

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7. For basic information on capacity hat theory and calculations, see the following: Walter Schulz, K3OQF, "Designing a Vertical Antenna." Schulz's graphs have been replaced by equations in recent editions of The ARRL Antenna Book, 17th Ed. (Newington: ARRL, 1994), p. 2-40. For additional treatments, see E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems, 2nd Ed. (Englewood Cliffs: Prentice-Hall, 1968), pp. 384-88; R. C. Johnson, Antenna Engineering Handbook, 3rd Ed. (New York: McGraw-Hill, 1993), p. 24-8; or E. A. Laport, Radio Antenna Engineering (New York: McGraw-Hill, 1952), Chapter 1 ("Low Frequency Antennas"). Laport notes that even using these equations at low frequencies, we must be "contented" with approximations (p. 28). See also F. E. Terman, Radio Engineers' Handbook (New York: McGraw-Hill, 1943), p. 113. For an update with an extensive bibliography, see John S. Belrose, "VLF, LF, and MF Antennas," in Rudge, et al., Editors, Handbook of Antenna Design, Volume 2 (London: Peregrinus, 1983), pp. 553-662.

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8. The HAMCALC program for this purpose is called "Capacity Hats."

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9. For further information on capacity hats and this model antenna, see "Modeling and Understanding Small Beams, Part 8: Capacity Hats," Communications Quarterly, Fall, 1997, 61-79.

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Also see the Antenna Modeling Programs page for more information.

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Updated 1-17-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Amateur Radio Page
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Topics: HF Upper, Loading, Yagi


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Symposium 2005 Dayton
+ Straightening Out the Inverted-L

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Straightening Out the Inverted-L

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This page exists to include the PDF in the topic index

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Topics: HF Multi Band, Inverted L


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Symposium 2006 Dayton
+ Welcome to Yagi-World

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Welcome to Yagi-World

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This page exists to include the PDF in the topic index

+ hr
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Topics: HF Upper, Yagi


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Back to Basics An Antenna Primer for New QRP Operators

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Back to Basics An Antenna Primer for New QRP Operators

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This page exists to include the PDF in the topic index

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+

Topics: Dipole, Doublet, G5RV / ZS6BKW, Inverted L, Inverted V, Traps, Vertical


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Wi're We Using Wire?

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This talk, originally prepared for the 1997 Dayton FDIM Symposium, summarizes material discussed at greater length in the series "Antennas From the Ground Up," which appears in Low Down. Published episodes in this series are available at this site, should you wish greater detail on various points

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For lower HF-band antennas, the reason for using wire antennas is simple: they work; they are cheap; and there is nothing better for most of our wallets. Understanding the dollar and work economy of wire antennas only requires that we look at Figure 1, a simplified sketch of typical wire antenna construction. There is not a lot of mechanical complexity in a wire antenna of the sorts we use on 80, 40, and 30 meters.

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The more difficult answer to our question involves understanding what wire antennas do and why and how they do it. In fact, most hams have very little idea of how wire antennas work. Of course, once we master wire antennas, we have also mastered the hardest part of all antennas, so perhaps it pays to go back to basics and take a closer look at these marvels of simplicity.

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After getting a few terms squared away, we shall look at three types of linear (straight-line) wire antennas: a. the center-fed wire; b. the off- center-fed wire, and c. the end-fed wire. It would be nice to add some loops, fans, fractals, and wire beams to our agenda, but there is so much to say about these three simple antennas, that the fancy wires will have to await another day.

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I am always amazed by how many wrong things we teach new hams to believe about antennas. Hence, I have no choice but to begin all over again. Inevitably, I shall repeat things you already know, but that is necessary to provide a framework for a few things you may not yet have encountered. For example, antennas do not radiate, at least not in the sense most folks think about radiating. For example, that 80-meter dipole you are using on 40 meters is no longer a dipole. For example, no matter what shape you make a horizontal antenna, the elevation angle of maximum radiation will change hardly at all. For example, as I lower a resonant half wavelength dipole below a height of a half wavelength, the feedpoint impedance will exceed 75 ohms part way down and be lower than 75 ohm part of the way. If these teasers have not attracted your attention, then you just do not like wire.

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The 1/2 Wavelength Resonant Center-Fed Dipole Wire Antenna

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We are often taught that antennas are special devices, transducers that convert radio frequency alternating current energy into radiating electromagnetic fields. This teaching is only relatively true: antennas do the job better than most other electronic devices, but they all try. In fact, "conversion' is not really a precise word at all. Every instance of electrical energy has a field, and every field has associated electrical energy. +

Moreover, antennas do not radiate outward in that sparky sense which we find in cartoons. Rather, they permit fields to expand from the wire without limit. A transmission line can be thought equally 1. as a waveguide confining electromagnetic fields or 2. as a conveyor of electrical energy from the source to the load. Figure 2 takes a field perspective on the transmission line and antenna situation. And if you do not believe electronic components radiate, think about why iron and ferrite toroidal cores are all the rage in RF circuitry.

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All of this preamble brings us to the 1/2 wavelength resonant center-fed dipole antenna. By shortening the name of the antenna to "dipole," we can make most new hams believe that it is the most basic antenna of all. When we give the antenna's full pedigree, its true nature appears: it is a rather sophisticated and complex device. To be certain we are all on the same wavelength, let's review what each part of the name means (see Figure 3).

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    1. Dipole: the antenna is a dipole because it has two "poles," that is, regions of the antenna where the current goes from maximum to minimum.

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    2. Center fed: The antenna is fed at its exact center.

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    3. Half wavelength: the antenna is approximately 1/2 wavelength long.

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    4. Resonant: the feedpoint impedance, Z, which is ordinarily composed of resistive and reactive components (R +/- jX), is purely resistive.

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What we think we know about dipoles is not much, but then we seem not to think we need to know much. The proper length in feet of a half wavelength resonant wire dipole is 468/F in MHz, and the feedpoint impedance is close to 70 ohms, with some decrease as we lower the antenna height. If you are content to live in the clouds, these old saws are fine; if you require more precision in your understanding, these bits of tradition do not live up to a half truth.

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The following information is predicated on NEC-2/4 models, which means that they do not account for the terrain slopes in your area or the ground clutter in your yard. However, they are relatively accurate, even when translated to other frequencies, since antenna heights above ground are given as fractions of a wavelength. My examples will use #14 copper wire, so adjust longer for thinner wire and shorter for fatter wire.

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1. The length of a resonant half wavelength dipole never gets down to the formula. See Figure 4. But it does vary by a total of about 3' at 3.6 MHz as you change height above ground from 1/20th of a wavelength to a full wavelength. Precise resonance is not significant to the wire's performance as a radiator, but it is nice to know where resonance really is.

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2. The feedpoint impedance at resonance also varies with height, going well above and well below the standard 70-ohm value as we move from 1 wavelength downward. See Figure 5. Again, your ground clutter may obscure this curve, but you can now see how the progression goes.

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3. We all believe that low-angle radiation is important to making contact with distant stations. How well does a low dipole do? See Figure 6, a 40-meter dipole. (Remember, we can translate the numbers to other frequencies, since heights are in units of a fraction of a wavelength.) The resonant half wavelength dipole begins to do quite well as we increase its height from 3/8 wavelength to 1/2 wavelength. (Higher-angle radiation continues to dominate, which is why some folks prefer certain kinds of loops or beams for quieter DXing.) Note the dip in gain around the 3/4 wavelength height point. As we move an antenna upward, the lobe structure changes, and new lobes appear, often straight up. +
+ +
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See Figure 7, which compares the elevation pattern of a dipole at 1/2 and at 7/8 wl. Much of the wire's energy at 7/8 wl is aimed at higher angles, nice for locals, but less helpful for DX.

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4. The traditional figure-8 pattern we associate with dipoles is mostly an illusion at low antenna heights. Figure 8 provides a graph of the front- to-side ratio of dipoles as we increase antenna height. Only above about 1/2 wavelength does the peanut shape of good side rejection appear. You do not need an inverted Vee at low heights on the low HF bands to have omnidirectional radiation; the dipole will do just fine. See Figure 9 for paired azimuth patterns at 22 degrees elevation for a graphic display of this fact.

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All this must mean that the dipole is a pretty bad antenna, right? WRONG! The resonant half wavelength dipole, even at relatively low antenna heights competes very well with everything folks have invented to compete with it. And usually at a fraction of the cost. Let's look at only two examples of the antenna's competitiveness.

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Most dipole competitors demand that you place their antennas just so or the maker will not be responsible for the performance. Already I am suspicious, because with an ordinary dipole, you can twist and turn as necessary and still have almost all of the dipole's performance. There are two ways of bending a dipole, one a bit better than the other. See Figure 10. We can bend both elements in the same direction, whether down or to the same side. However, we lose a little of the antenna's radiation this way due to cancellation. The problem is insignificant until the horizontal main part of the element approaches 70% or less of the full length of the dipole.

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Zig-zagging the wire horizontally maintains most of the antenna's radiation more efficiently, but at a cost, as shown in Figure 11. The antenna pattern tilts toward the outside corners of the wire. Remember, though, that one person's cost is another person's profit. Suppose you can almost but not quite get the main lobe of your dipole broadside to Europe. Perhaps you can create a zig-zag that will move the pattern without requiring that you move the trees in your yard.

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Of course, you can Vee the dipole in any direction, or slope the whole wire down a hill. In estimating the probability that the antenna will still act like a dipole, just be very honest with yourself. Ask yourself, "Does the antenna still look like a dipole?" If the answer is an honest, "Yes," then your likelihood of good dipole performance is high.

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And, do NOT sell the performance of a dipole short. Top-wire-height for top-wire-height, among competitive wire antennas, the dipole can make a case for itself as top dog. Figure 12 displays the outlines of 5 antennas. One is our old friend the half wavelength resonant center-fed dipole. Three are loop antennas often proposed as alternatives to the dipole. All four are shown as side views, face-on to the antenna wire. The last is a simple wire Yagi, thrown in because it makes use of about 1 wl of wire, the same as the loops. (Incidentally, my model of this #14 copper wire antenna for 40 meters has a driven element 66' long, a reflector 70' long, and a spacing of 20', with a feedpoint impedance close to 50 ohms.)

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The rules of the following exercise are simple: all the antennas have their top wires (or the apex of the triangle) at the same height. This is based on the premise that with low wire antennas on the lower HF bands, we put them just as high as we can get them, not at some theoretical height.

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On these terms, Figure 13 tells an interesting story. The elevation angle of maximum radiation of the right-angle delta is highest because so much of the high-current high-radiation part of the antenna is so low compared to the top height. The square and rectangular loops have comparable performance, better than the triangle, but worse than the dipole. In fact, the only antenna of the group with a consistently lower elevation angle of maximum radiation is the wire Yagi. Of course, the Yagi maintains a special parasitical relationship between elements that tends to hold the elevation angle of maximum radiation lower.

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In the end, then, the only good reason for choosing one of the loops, vertically oriented, but fed as horizontally polarized antennas, is because one lacks the full length needed for a dipole at the top height available. (Feeding the loops as vertically polarized antennas is another matter calling for another full session or a chapter in ON4UN's book on low band DXing.) The dipole holds its own and surpasses many of its competitors.

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The Center-Fed "Dipole" on All Bands

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Dipoles as resonant antennas are monoband affairs. To convert an 80- meter dipole to an all-band antenna (sometimes called a "doublet," but no longer a dipole except on one band), throw away the coax (or do not buy it in the first place). Run 450 ohm parallel feedline (or 300 ohm line, if that is more convenient) to an antenna tuning unit (ATU) and work all bands. This is an old and very successful tradition among hams. +

What you can expect for performance at heights between 35' and 50' is shown in an article in the "Antennas From the Ground Up" series for Low Down ("5. 8-to-1 Odds, or a 135' Center-Fed Multi-Band Dipole Data Compendium"). See that article for the contents of Figure 14. The higher the band, the higher the antenna in terms of fractions of a wavelength at the operating frequency--and hence, the lower the take-off angle. The 80-meter oval breaks up into an increasing number of lobes, and the gain in the strongest lobes increases. On 10-meters, it exceeds 10.5 dBi, but not broadside to the antenna wire. Patterns for 35' and 50' are shown, with the higher wire height being better, but only marginally so above 30 meters.

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Installing an all-band doublet requires one of two things: either careful planning to set the main lobes where you want them on the bands of special interest, OR a willingness to take what you get based on the fact that you have only two tall supports. (If you have three supports, put up two or three of these antennas facing different directions and use an antenna switch for the strongest signal. They are cheap antennas!)

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The exact length of the antenna no longer matters within broad limits, since the ATU will match to the parallel feedline with quite decent efficiency. I recommend a balanced ATU, using either a Z-match (for low power) or one of the pre-SSB inductively coupled units once so popular in handbooks. With a basic antenna like this, get back in touch with coupling basics as well.

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Suppose you do not have 135' of space between supports but still want to work 80 meters and up. Try the 102' doublet. Again, exact length is unimportant, since we shall use parallel feedline and a balanced coupler. (That is why we do not call it a 'G5RV" here; 100' was a popular length long before Gil put his head on the chopping block trying to help some coax users effect an easier match on pre-WARC bands.) The 102' doublet is at least 3/8 wl long on 80, which makes it a reasonably efficient radiator there--and a very good one on all bands above 80.

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See the "Antennas From the Ground Up" series for Low Down ("6. But My Yard's Too Small, or a 102' Center-Fed Multi-Band Dipole Data Compendium") for the contents of Figure 15, which tells the story, again at 35' and 50' heights. Note that compared to the longer 135' doublet, the 102' doublet expands its lobes more slowly, since it is shorter in terms of number of wavelengths long at each frequency. However, the gain is comparable on the upper bands. Ignore any differences under a dB. Once again, you can preplan the lobes by where you set your supports or you can accept what you get, or you can build more than one facing this-a-way and that-a-way and switch to the stronger signal.

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In Figures 14 and 15 you have a compendium of patterns to establish your baseline expectations of these two popular multiband antenna arrangements. Your terrain and ground clutter will, of course, modify the reality you experience, but not so much in most cases, that the patterns are invalidated. Keep them as a reference file for future antenna thoughts. Thoughts like: "Gee. 10+ dBi gain on 10 meters with a hunk of wire no more than 3 or 4 wavelengths long. Wire is not such a bad option after all."

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Off-Center-Fed Wire Antennas

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A wire antenna is cheap and easy. Buy a roll or two of #14 stranded antenna wire from Radio Shack or similar outlet. Or buy some copperweld from someone as reputable as the Wireman. Get two end insulators and some UV resistant dacron rope to support the ends. Buy a center insulator or try one of the ladder-line grabbers from EMTech. Purchase some good quality 450-ohm parallel feedline from a good outlet. Total cost: $30 to $40 dollars or so.

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The next question for someone like me who wants to make a buck is this: "How can I sell these materials at a larger profit?" One good answer is to advertise them as convenient: everything you need in one place and package.

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Now here is a bad answer: combine some trivial statements with some questionable statements that are hard to disprove, and add some easily obtainable rave notices from users who have never before used even a half- decently constructed wire antenna. The result: instant success, but I hope a batch of nightmares occasioned by twinges of conscience. Unfortunately, this is the impression that the off-center-fed wire antenna scene left me with after doing my own modeling investigations.

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Figure 16 shows the general layout of an off-center-fed half wavelength wire antenna. As is the case with resonant center-fed dipoles, formulas for cutting the antenna abound--and occasionally work for someone. However, they are as imprecise as ever, so I shall not even list them. Instead, let's look at some results of modeling off-center-fed (OCF) antennas at 7.15 MHz.

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1. As shown in Figure 17, the resonant length of an OCF varies both with the antenna height and the distance from center it is fed. Hence, there is no magic length for an OCF.

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2. Two popular points of feeding an OCF are the 100 ohms and the 300 ohms points. These points exist only if we do not model the feedline attached to the antenna wire. As Figure 18 demonstrates, these point vary considerably as antenna height is varied, even if the antenna is resonated for each test point. Notice that the hypothetical 300 ohms feedpoint occurs on a quite steep portion of the curve, and actually hitting this point is a test of luck, not skill. Hitting something close to 100 ohms is easier, but something of an illusion.

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The reason I call the feedpoints illusory is that the feedline of an OCF will always be unbalanced. Therefore, it becomes a part of the antenna, at least to the degree that the feedline radiates. A large portion of the feedline currents are equal and opposite, so the feedline contributes only in small ways to overall radiation, but even a little radiation will throw the anticipated impedance point well off its mark.

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3. The resonant lengths of an OCF on even harmonics are different than the resonant length of an OCF on its fundamental frequency of operation. The result is an antenna that exhibits considerable reactance at harmonics of the fundamental.

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To create an OCF that provides a reasonable match to coax at the fundamental and even harmonics requires some significant efforts to smooth out the impedance problems. It is possible to do this advertently or inadvertently. B&W offers a doublet with a coax match on all HF bands by the express use of a parallel resistance across the feedpoint. This resistive element trades loss (around half power) for convenience, a trade that may fit military QRO needs, but which is not especially apt to QRP operations. It is also possible to insert matching or isolating elements at the feedpoint, elements which one may never realize are as lossy on some bands as B&W's resistor. The safest rule of thumb to follow appears to be this: if the match claim is too good, the matching system likely ain't.

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4. Feedline radiation contributes little to the radiation pattern of the OCF on most frequencies. Most modeling studies of feedline radiation are flawed, because they assume that the feedline or the jacket of a length of coax is as much a part of the antenna element system as the main wire itself. This is easily disproved by the number of folks who successfully run coax to dipoles without a balun. Only under certain conditions, usually involving the angle between the wire and the feedline, does significant energy become coupled to the outside of a coax feedline.

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For the OCF, the only way to model the system required modeling both the antenna wire and the parallel feedline. This produced very large models with long calculation periods. Nonetheless, the results showed a little modification of the basic patterns on some harmonics, but likely less than yard clutter was likely to induce.

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Well, then the OCF is a bad wire antenna, right? Wrong, again! But, let us start all over again. Begin with a 135' long piece of wire, or thereabouts. Feed it off center--far enough off to be convenient to your shack but not so far off that you are nearly end-fed. Note that convenience to the shack is likely the best guide to the feedpoint. Use 300 ohm or 450 ohm feedline with no isolators, baluns, transformers, "special couplers," or other devices. Bring the feedline to a balanced tuner. Now operate. What can you expect?

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See the "Antennas From the Ground Up" series for Low Down ("6. Unbalanced But Sane, or a 135' Off-Center-Fed Multi-Band Dipole Data Compendium") for the contents of Figure 19, which presents a compendium of patterns for a 135' OCF model fed about 50' from one end (D1) and 85' from the other (D2) about 35' above average ground. Some patterns will differ as the feedpoint is drawn farther away from center, since the lengths on either side of the feedpoint will approach or depart from special relationships. (For example, on some band, the off-center feedpoint may approximate a full wavelength antenna fed 1/4 wl in from one end. This would be true for one possible feedpoint value, but not for others.) Feedpoint values shown are ballpark values and should not be used for precise guidance, since they do not take into account the effects of feedline radiation.

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The patterns for multiband use of the OCF are not vastly different from those for the center-fed doublet of the same length, except where the special length relationships may be in effect on upper bands. Gain is within a dB of that for the doublets. (Note that calling the antenna a "beam" or even "better than a beam" is simply not justified, since it produces only what one expects a wire antenna to produce, given length and frequency.)

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The bottom line on the OCF is that it is a highly usable wire antenna with multiband capability. Its most efficient performance is likely to result from the simplest possible construction. The performance is plenty good for a wire antenna of its length, but more than good wire performance is unlikely. It will remain unlikely so long as detailed modeling set-ups and labs tests remain hidden, if they exist at all, and as long as what does exist falls into the realm of advertising hype.

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Let's End With the Zepp

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We have fed in the middle. We have fed to the side. Let's now take the final step and feed at the end. The antenna has been called the Zepp, Zeppelin, or end-fed Zepp. (The last arose when some writers called the 135' doublet a "center-fed Zepp.") Initially, the antenna was just a long piece of wire, end fed and trailing out the rear of the zeppelin. Feeding was relatively easy with direct connections to the output tanks of high impedance tube amplifiers. Ground operators added feedlines and produced the antenna that appears in Figure 20. Some argue on theoretical grounds that the antenna cannot work, but folks keep on building and successfully using this odd little antenna that never wants to get near to a piece of low impedance coax. +
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Actually, the antenna wire part is simple. It is a half wavelength of wire on its fundamental frequency, and the current distribution is identical to that of a center-fed antenna of the same length. The low-current, high- voltage feedpoint presents a very high impedance, requiring the use of parallel feedline.

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How can you feed an antenna when one side of the line is connected to nothing and the other is connected to an antenna of finite length? The lines must be radically unbalanced! Actually, the imbalance is not at all severe. First, the connection to nothing is not to absolute nothing, so the end of the open side of the line exhibits an extremely high but finite impedance. Likewise, the connected side of the line sees a super high impedance--and two highs make a pretty good balance.

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Pretty good, but not perfect. However, precisely the imbalance remaining on the line--which yields some minor line radiation--permits the antenna to be matched at the shack end of the feedline. If the balance had been perfect, the feedpoint impedances on most bands would consist of thousands of ohms of resistance combined with thousands of ohms of reactance. Under these conditions, the impedance along most of the feedline would look like a more extreme version of Figure 21. The reactance would be low for much of each half wavelength of line, but the resistance would be even lower, with values less than 1 ohm in many instances.

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Fortunately, the balance is not perfect. What the ATU is likely to see are values that are quite reasonably matched. Again, a good old-fashioned inductively coupled tuner is likely the best bet for the end-fed Zepp.

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See the "Antennas From the Ground Up" series for Low Down ("12. A Tiger by the Tail, or a 135' End-Fed Multi-Band Dipole Data Compendium") for the contents of Figure 22. What do we get for our end-fed trouble? Figure 22 tells most of the story: we get a multiband wire antenna where the lobes increase with frequency and the gain moves from broadside to off the end of the wire as the frequency increases. This familiar motif differs only in detail from the summary remarks about the other two 135' antennas we have examined in detail.

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Summary

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We have looked at low-lying dipoles and at wires used for multiband purposes for two good reasons. First, basic information is necessary to dispel novice mythology about dipoles and other wire antennas. Second, we have wanted to leave behind some compendia of antenna patterns to set some proper expectations for future antenna building. +

We could go on for days looking at all the many ingenious wire set-ups that hams have invented over the years. Most of these antennas are designed to overcome circumstantial limitations. Whatever their designers have thought of them, they have brought no real improvements upon the dipole and its multiband counterparts. In fact, it is difficult to beat a wire doublet as high as one can get it--difficult, that is, without access to federal grants, crown jewels, or Superman's cape.

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Wire does have some disadvantages that we just have to admit. It is very difficult to rotate a wire dipole or beam--something like pushing rope. However, I can install three wire antennas for far less than the cost of one modest rotator, let along the cost of the tower and beam. Wire looks--well, so Novice! It lacks all the electromechanical glint and sophistication that we associate with beams. Of course, a broken wire antenna is invisible on the ground, while a broken beam transforms a backyard into a junk yard of embarrassment. And I do not have to take a bank loan to replace my wire antenna.

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Just be sure you construct your antenna well. I am convinced that people believe that some of the commercial wire antennas work "better" simply because they did not spend the same construction care on their $30 home brew job that they spent on the $150 prepackaged antenna of the same design. A wire antenna has three dimensions. First is the electrical: make sure all connections are electrically sound and durable. Second is the mechanical: use sound principles of mechanical security at physical connections and stress points. Third is maintenance: erect your antenna with an eye toward lowering it a couple of times a year to check both electrical and mechanical connections, and to clean the wire and transmission line. Some folks like auto polish on both to shed the rain and to restore a little glint in the setting sun.

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The basic wire is long. The basic wire is as full size as we can make it. It is so basic that it does not need magic to make it work. But work it does. And when it falls down--despite our best maintenance efforts--it is cheap to reinstall. And it goes on working. Now you know why we are using wire--at least until the ship comes in carrying the professional installers and the 200' tower, rotator, and combined 80-40-30 meter quad.
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Updated 1-19-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Topics: Delta Loop, Dipole, EDZ / Zepp, HF Multi Band, Off Center Fed Dipole, Quad Loop, Yagi


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+ Title graphic +

12 Ways to See and Love Your Feeders

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This talk, on the basics of understanding feedlines, was originally prepared for the 1998 Dayton FDIM Symposium

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+

Transmission line have been a big mystery because we have never been told how to look at them. We look at a capacitor and know instantly all about it. Same goes for coils, resistors, and switches. But a transmission looks for all the world like some ordinary pieces of wire--and in a pinch, we can use them as a source of wire.

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Do not be fooled. Transmission lines--or feeders, feedlines, cable, etc.--are not ordinary wire. They have conductors, but so too do capacitors, coils, switches, etc. But like all those components, transmission lines use conductors to do a job--actually a lot of jobs.

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So I shall not tell you anything new about transmission lines. It is all in the books. What I want to do is simply reorganize all that information so that we have some good ways to look at transmission lines. Once we have that fixed in our heads, transmission lines will never be mysterious again. In fact, they will become our friends, if not the love of our lives.

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We shall along the way note some handy and some not-so-handy formulas for calculating stuff. You should be familiar with what they are trying to tell us, but at the same time, you should not have to fill pages with calculator outputs. Let two programs do that. One is HAMCALC (Version 32 or higher) from VE3ERP has a number of programs to do all the work for you. Another handy program is TLA, from N6BV of ARRL. We shall note how to use these cheap but rich resources along the way.

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1. The first way to look at transmission lines: with a tape measure

The most fundamental property of transmission lines is length. Know how long your transmission line is. It does not matter if you use feet or inches, meters or centimeters, cubits or furlongs: they all convert back and forth. +

Oddly, the majority of hams I know cannot tell me how long their transmission line is within 6 inches. This vacuum proves that no one ever told them that measuring is the first step to making friends with the line.

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Obviously, the best time to measure a transmission line is before you install it. Include the connectors--they are part of the overall length.

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Why know the length? First, the obvious: the line has to reach from your shack to the antenna. Second reason: if it breaks or goes bad, you need to know how much replacement to buy.

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Third reason: there is a lot that just knowing the length will tell us--when we are ready to learn it and need to know it. Every other piece of information about transmission lines gets used some of the time, but length gets used all the time. So always know how long every piece of transmission line is in your system. Short pieces: measure to some fraction of an inch. Long pieces, measure within a couple of inches or so.

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Now make a sketch and a chart, as suggested in Figure 1. Note that every sub-length is listed, as well as totals for a given run between points. Revise the chart whenever you make any changes in the feedline system. Store this chart where you keep all of the instructions and other plans for your station equipment, but keep it handy for reference.

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2. The second way to look at transmission lines: with an protractor

Notice that there is a blank line on form. The length in feet (or meters) is not all the length information we want on our chart. We also want the electrical length of the feeder. Electrical length is normally given in electrical degrees (sometimes radians, which we shall skip today). Getting the electrical length is a 3-step process, once you know the physical length. + 
                                   Typical Feeder Values
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+1.  Coaxial Cables
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+RG #           Belden #       Zo          Velocity    Loss in dB
+                              Ohms        Factor      per 100' @ 3.5 MHz
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+RG-58A         8529           50 -j1.29   0.66        0.762
+RG-59A         8241           75 -j1.81   0.66        0.711
+RG-8X          9258           50 -j1.03   0.78        0.511
+RG-8A          8237           50 -j0.60   0.66        0.351
+RG-213         8267           50 -j0.60   0.66        0.351
+RG-8 (foam)    8214           52 -j0.60   0.78        0.289
+               9913           50 -j0.52   0.84        0.242
+               9086           50 -j0.52   0.84        0.242
+RG-11A         8267           75 -j0.89   0.66        0.351
+RG-17A                        50 -j0.24   0.66        0.140
+RG-218                        50 -j0.24   0.66        0.140
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+2.  Hardlines (solid jacket coaxial cables)
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+Type                          Zo          Velocity    Loss in dB
+                              Ohms        Factor      per 100' @ 3.5 MHz
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+1/2" hardline                 50 -j0.23   0.81        0.111
+1/2" hardline                 75 -j0.41   0.81        0.132
+3/4" hardline                 50 -j0.15   0.81        0.074
+3/4" hardline                 75 -j0.31   0.81        0.098
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+3.  Parallel 2-wire feedline
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+Type                          Zo          Velocity    Loss in dB
+                              Ohms        Factor      per 100' @ 3.5 MHz
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+300-ohm tubular xmt           300-j2.14   0.80        0.173
+450-ohm "window" ladder       450-j2.16   0.95        0.098
+600-ohm open wire             600-j0.95   0.97        0.032
+                                                      from TLA by N6BV
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+Table 1.  Some characteristics of typical transmission lines.
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1. Velocity Factor (VF): Look at Table 1, which provides some significant data on a few common types of feeders, both coaxial and parallel. For the moment, we are interested only in the column labeled "velocity factor." This column tells us how long that a length of the feeder is in terms of its relationship to a wavelength of RF energy. Since the example in Figure 1 uses RG-213, we need only a glance at the table to see that its velocity factor is 0.66.

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VF tells us that any wavelength of energy in the cable at any frequency is only 0.66 as long as the same wavelength in free space. Conversely, the effective length of the cable is simply its physical length divided by VF. 74.875' (or 22.82 m) divided by 0.66 is about 113.45' (34.58 m) long.

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2. A Wavelength at a Desired Frequency: Since a free space wavelength at 1 MHz is about 299.8 m or 983.6' long, we can find the length of a wave at any frequency in MHz by dividing the base number by the desired frequency. Let's say that our 40 meter dipole is cut for 7.15 MHz. 983.6 (299.8 m) divided by 7.15 yields 137.56' (41.93 m).

+

3. Converting to Degrees: To change the result into electrical degrees, just divide the effective length from step 1. by the length of a wavelength in step 2. and multiply by 360 (the number of degrees in one cycle). So 113.45/137.56 (34.58/41.93) equals 0.825, times 360 equals 296.9 degrees.

+
+ +
+

Let's enter this data in our record chart, as in Figure 2. For the moment, this is for curiosity, but soon we shall make use of the information.

+

For our notebooks, we can combine the 3 steps into one big formula. The only difference between the two version is that for a physical length in feet, we divide 360 by 983.6 to get a constant of 0.366; while for physical lengths in meters, we divide 360 by 299.8 to get a constant of 1.20.

+
+ +
+

Of course, if we know the electrical length of a feeder and its velocity factor and frequency of operation, we can turn these formulas around to get the physical length:

+
+ +
+

where K = 1.20 for a result in meters and K = 0.366 for a result in feet. Do not lose this, because it will come in handy later. If you do lose it, you can get the results from one or more of the programs on HAMCALC.

+

3. The third way to look at transmission lines: with a lost power meter

Everyone seems to hate transmissions lines, if for no other reason than that they eat up some of the transmitter's power. Well, if that is what bugs you, Figure 3 shows a way to avoid the power losses of transmission lines. The final amplifier is directly coupled to the antenna (with an RF preamp for receive, all automatically switched). The losses in the interstage feeder cable are made up for by setting the gain of either the ground amplifier or the final amplifier just a bit higher so that the output achieves a set level. We should not have to redesign the output filter of the amplifier too much to make it match most common 50-ohm ballpark antennas. We do, however, have to feed DC power to the amplifier, along with the signal. +
+ +
+

If this scheme is impractical for your situation, then you must resign yourself to using feedlines from your transmitter-output/receiver-input to your antenna. With that act of resignation comes a job: understanding feeder line losses and reducing them to a practical minimum.

+
+ +
+

The first step in the process is understanding what power loss means in practical terms. Figure 4 is designed to help. It graphs actual power loss with the loss registered in decibels (dB). If we arbitrarily let 6 dB equal 1 S-unit, then you have to lose about 75% of your power before your signal goes down by 1 of those S-units.

+

All of this is fine for the QRO operator, who has power to spare. However, QRP operators often work on the differences between no registration on the S-meter and a faint tick of the needle, that is, in the 1 dB differential between no signal and something that can be heard and copied. Even though 1 dB represents about a 20% power loss, that 20% can be composed of lots of little losses that add up. Hence, it pays--within certain practical limits--to minimize every potential power loss.

+

Let's peek back at Table 1, our list of typical feeders. Starting with the coaxial cables, we notice that the fatter the cable, the lower the loss, for any given characteristic impedance (Zo). Hence, if you want to use coaxial cable, try RG-218 or one of the hardlines.

+

The other option is to use one of the parallel feedlines, which are quite light and have low losses. Since their Zos are not the semi-standard 50 ohms, you will need an ATU to match whatever impedance the line presents to your transceiver.

+

Notice that the loss figures are given for perfectly matched systems at 3.5 MHz and use 100' of line. Now, the line length calculations is very linear. Double the length of line and you lose twice as much power; halve the line length and lose half the power.

+

Suppose we freeze the line length at 100' and change frequency or change SWR. What happens? We are told that the losses increase with frequency and with SWR, but by how much?

+
+ +
+

Figure 5 shows the losses from 80 to 10 meters for RG-213 for SWR ranging from 1:1 to 5:1. This will give you an idea of the rate of loss increase from both frequency and from SWR for a standard 0.4" diameter coaxial cable.

+
+ +
+

Compare Figure 5 with Figure 6. The second graph is for standard 450- ohm plastic covered window line over the same frequency spread and SWR range. Incidentally, 5:1 is about the SWR for a low-hanging dipole (80-90 ohms feedpoint impedance). First, notice that the shape of the curves are quite similar to those for the coax. This means you can use these curves to extrapolate reasonable loss values from other cables you use, knowing the matched loss value.

+
+ +
+

However, let's not neglect the loss figures on the vertical axis of the graph. They are quite different for the two types of cables. Figure 7 shows the 1:1 and 5:1 SWR figures for the two cables. Note that the parallel transmission line has a lower loss per 100' at a 5:1 SWR than RG- 213 with a 1:1 match. In fact, the parallel transmission line losses would be less, even with a 10:1 SWR (except under certain rare conditions that your ATU could not handle anyway). Referring back to Table 1, only hardline rivals parallel transmission line for low losses, but with a large penalty in handling difficulty and weight.

+

Lowest-loss recommendations:

+

1. Use parallel feedline unless physical situations dictate otherwise.

+

2. Use the shortest feedline possible (consistent with solid installation).

+

3. Do not throw away expensive coax recently installed: save any change- over for the next time lines get old.

+

4. The fourth way to look at transmission lines: with an X-ray machine

What makes transmission lines lossy? What makes them work? These are the same question. To answer it, we must step back and take a brief look at common 2-wire transmission line construction. (There are multi-wire transmission lines, but hams rarely encounter them.) Contrary to some ancient ideas, it takes 2 wires minimally to make a transmission line. +
+ +
+

Figure 8 shows a cross section of some common parallel transmission lines. The basic idea is to keep the two lines exactly parallel for their entire length. So we use spacers or some windowed or closed insulating material to lock the wires in place.

+
+ +
+

Figure 9 shows some common coaxial cable construction, where the two wires are not identical. Rather, there is a center conductor, solid or stranded, and a concentric outer conductor. What is in between can be a solid or foam dielectric, air, or an inert gas. The outer conductor can be a braid or solid. Needless to say, a stranded center conductor with a braid is more flexible than the same size coax with a solid conductor and a solid outer conductor.

+

Note that as long as I am treating the cable as a transmission line, I try never to use the word "shield." Too, the outer jacket serves no electrical purpose, but may serve both physical and chemical purposes. All jackets hold the outer conductor tightly in place and keep it from corroding. Some jackets protect from moisture, others from UV sunlight, others from chemical salts, and a very few from all three. In fact, the jacket alone can change the prices of identical transmission lines inside by a factor of three.

+

5. The fifth way to look at transmission lines: with a ruler and LCR meter

Every transmission line has some physical dimensions. They are not accidental. They determine the characteristic impedance of the transmission line. Let's look at the two types of line and see how we determine the Zo. +

First, any length of wire has a inductance. For two wires parallel or concentric to each other, the total inductance for any arbitrary length is the sum of inductances of the two lines in series.

+

Second, any two lengths of wire parallel to each other show a capacitance, like plates. The capacitance of a fixed arbitrary length of parallel wires is a function of the wire sizes, the space between them, and the nature of the insulation or dielectric between them.

+
+ +
+

Figure 10 shows the two phenomena and prepares us for some old fashioned formulas.

+

First, for any transmission line, it is primarily the L and C per unit length that determine the characteristic impedance, Zo:

+
+ +
+

However, this equation is only approximate. for the record, let's look at the "big" formula:

+
+ +
+

where R is the series resistance per unit length and G is the shunt conductance per unit length--the unit lengths used for L and C. For most calculations, ignoring R and G does little harm, but for maximum precision, they are needed. They actually tell us that the Zo of virtually any line is not 100% resistive, but has a slight phase angle that shows up as those little remnant reactances in the Zo column of Table 1.

+

Because L and C are functions of the physical sizes of the conductive materials from which we make our transmission lines, we do not need to know the actual values of L and C per unit length to make a transmission line. We can use sizes and distances apart instead.

+

For parallel transmission lines, we calculate with the formula

+
+ +
+

where S is the center-to-center spacing of the conductors and d is the diameter of the conductors, both in the same units. The term "e" is the dielectric constant of the material between the lines, where a vacuum has a value of 1 and most solid material have higher values.

+

Too often, the version of this equation that we see in books leaves out the dielectric constant, and that leaves some gaps in our understanding. For example, with only air as a wire spacer, we cannot make a 50 or 75 ohm parallel transmission line, since it would require that the wires overlap. However, if we divide 276 by a higher number, resulting from the use of a dielectric with a high constant, then we can build our 75-ohm parallel line. However, even though we can, no one in the US does.

+

For a coaxial transmission line, we use this formula:

+
+ +
+

where D is the inner diameter of the outer conductor and d is the outer diameter of the inner conductor, both in the same units.

+

Both these formulas are handy. However, it is more likely that you would build a parallel transmission line (with an air dielectric with a constant of 1) than it is that you will build a coaxial cable.

+

6. The sixth way to look at transmission lines: with a thermometer

So why is transmission line lossy? Because the wires and the dielectrics are not perfect. Wire has resistance. The larger the wire diameter, the smaller the resistance, but it never goes to zero. Some energy is always lost as heat in the wire. Remember that we are using HF/VHF frequencies with our feedlines, so the skin effect has a marked influence on the current-carrying capabilities of the line. According to researchers, most of the losses in transmission lines up through UHF frequencies are a function of the current-carrying capacity of the wires. +

Conclusion: whatever the type of feeder, use the largest wire diameter your system can physically withstand.

+

There is a second reason for power loss: Every dielectric leaks. Energy get across the space between the wires, trying to bake the insulation instead of proceeding to the end of the line. However, dielectric losses begin to dominate only above UHF frequencies.

+

How do we know lines leak and resist? Because we can measure the increase in temperature, even with a perfect match.

+

But why does SWR increase losses? We have not even said what SWR is, but we do know that when the SWR is 1:1, the voltage and current are everywhere the same along the line, except for the basic resistance and leakage losses. However, when the SWR is greater than 1:1, voltage and current change along the line, reaching peaks and nulls, as shown in Figure 11.

+
+ +
+

Even with a mild SWR of 3:1, the current reaches peaks 3 times the 1:1 value. Because wire has a certain resistance per unit length, the higher current results in higher resistive losses for a given voltage.

+

7. The seventh way to look at transmission lines: with a field detector

Having seen how transmission lines lose some energy, let's understand how they deliver so much of it to the antenna--the load. +

First, remember that the characteristic impedance of a transmission line is not its resistance. It is a resistive impedance, meaning that it is a product of two reactance so situated that they result in a zero phase angle (or darn close). The only energy dissipation is through the loss mechanisms described.

+
+ +
+

Second, resistive impedances control energy but do not dissipate it. Figure 12 shows how. Think of each wire as trying to be like the antenna at the end of the line. The antenna is a transducer that permits the development of a field that can spread without limit. All of the energy in the current distribution along the antenna wire is lost, since the field is in a form that allows no retention or recapture.

+

It is not incidental that every conductor in every circuit is trying to establish and maintain a field that spreads without limit. Hence, we have to shield, shorten leads, bypass, and take other measures to keep our circuits from radiating--or from radiating prematurely.

+

The wires in the transmission line are trying to do the same thing. However, the two conductors, with equal and opposite polarity voltages and currents confine the field to very narrow spaces, mostly between the conductors. The energy stands on the line and is propagated down the line. The transmission line is a field (or wave) guide that is highly efficient.

+

If you terminate the line with an antenna--any device that permits the field to expand without limit, all but the little dissipated energy in the lines reaches the antenna. If you short circuit or open circuit the line instead, it all returns to the source.

+
+ +
+

Figure 13 shows us once more the cross section of a coax cable and a parallel transmission line so that we can compare the fields. Because the outer conductor of the coax cable encloses the field between conductors, we get the so-called "shielding effect." All this means is that very near metallic objects have little or no effect on the fields between the transmission line conductors.

+

The parallel transmission line is not so fortunate. Although the fields are narrowly confined, they are not perfectly confined. Hence, bringing a conductive object near one line can disrupt the balance in currents and voltages that are crucial to proper operation of the line. Energy coupled to this external object is energy not in the nearer line, which leaves an excess in the other line. This is a good way to convert both the nearby object and the feedline into an unintended antenna.

+

Hence, keep parallel transmission lines away from conducting objects. Do not nail them through their insulation to posts. Instead, invent nonconductive clamps. Do not clamp them down to the window sill with aluminum window frames. You might get away with it, but you might also turn your window frame into an inefficient antenna and rob the efficient antenna in the trees of valuable power. Space the parallel transmission line several times its widest dimension from nearby conductive or unknown objects. How many is "several?" The more, the better.

+

8. The eighth way to look at transmission lines: with an SWR meter

By this point, I can feel the impatience growing. A shout is welling up in your throats. you can almost not restrain yourself. Well, let it out: +
+ "WHAT ABOUT SWR?" +
+

I give up. Let's see what SWR really is. SWR is one way to register the mismatch between the ultimate load and the transmission line characteristic impedance. If the load impedance and the characteristic impedance of the transmission line are the same, then the SWR (or VSWR, more correctly) is 1:1.

+

SWR is not a measure of how well the antenna works. Low or high SWR numbers can occur for antennas with identical far field patterns operating with essentially the same efficiency.

+

SWR is a measure of what conditions exist on the transmission line. Those conditions exist all along the transmission line (with a little allowances for the losses we have seen). Hence, those condition appear in one or another form at the end of the transmission line you wish to connect to the transmitter. When the SWR is 1:1, those conditions presented to the transmitter are easily predicted. When the SWR is not 1:1, all bets are off.

+

Except: remember that we had you measure your transmission line. That will come in handy in just a bit.

+

Here I want to clear up just one common misconception and then move on to stuff more important than SWR. SWR is not simply the ratio of the antenna impedance to the Zo of the transmission line. Sometimes that ratio is not even close to the SWR.

+

Consider the following antenna impedances, all of which are presented to a 50-ohm coaxial cable: 1. 100 ohms resistive; 2. 70.7 ohms resistive and 70.7 ohms reactive (inductive for convenience; and 3. 100 ohms reactive. All cases result in an impedance magnitude of 100 ohms, one at zero degrees phase angle, the second at 45 degree phase angle, and the last at 90 degrees phase angle.

+

Although we are not yet sure why, we know the 100 ohms resistive case results in an SWR of 2:1. However, some may be surprised to learn that the second case shows an SWR of 3.27, while the third shows an SWR of -209.6 (yes, really a negative number) in some computerized SWR calculating systems. (Note: the "pure" answer to the third example is an indeterminately large number, but to avoid division by zero, most calculating programs substitute a very tiny number for the zero. Hence, they will yield a value--one often as meaningless as a negative SWR value.) Why? The correct equations for SWR and impedance tell why.

+

To calculate SWR, let's define two arbitrary terms, A and B. In doing so, we shall let RL be the load or antenna resistance, XL be the load or antenna reactance, and Zo be the characteristic impedance of the line, ignoring that little reactance remnant in Table 1.

+
+ +
+

and

+
+ +
+

The only difference (although it is a big difference) is the + vs. - at the resistive ends of the expressions.

+
+ +
+

Actually, equation 9 is less interesting than equations 7 and 8. They tell us that the resistive and reactive parts of the load impedance are separately handled within the equations, so that the reactive portion is not part of the standard way in which we calculate impedances.

+

9. The ninth way to look at transmission lines: without a Smith Chart

Do not misunderstand me: the Smith chart, invented and improved by P. H. Smith between 1939 and 1944, is a very useful tool. Some folks have gone so far as to claim that it is indispensable and the only thing they need to understand transmission lines. Were Smith around today, he would be the first to say that you have to understand transmission lines first before you can understand what the Smith chart is telling you. In fact, everything that a Smith chart can tell you can be independently calculated without knowing the SWR. Most computerized Smith Chart programs actually perform independent calculations and then convert them to graphical- geometric Smith chart plots. +

We can calculate the voltage, current, and impedance along any length of transmission line, obtaining both the magnitude and phase angle. In fact, any two of the three will do, since the impedance is simply the voltage divided by the current (with due attention to the phase angle).

+
+ +
+

Figure 14 provides a view of the excursions of voltage, current, and impedance magnitudes (without reference to phase angles) along a 450-ohm transmission line from an extended double Zepp antenna. Its purpose is only to demonstrate that these values do not vary in many instances in nice, clean sine waves--nor even symmetrically within a half wavelength span of line. For simple matching purposes, pure impedance curves tend to be most helpful. If we know the impedance and its phase angle, we can easily convert that to series values of resistance and reactance.

+

I shall bypass the temptation to toss out three more equations at you. Besides the fact that they are messy, all of the work has been done for lossless lines in one of the programs in the HAMCALC collection. There, you can specify any feeder Zo and VF, along with antenna-end values of R and X and some desired power level, and then see the value of voltage, current, and impedance (in both Z and R+/-jX forms) at any distance from the antenna or in a chart taken every 5 degrees along a line. If you can do without the chart and want losses thrown in, then use TLA by Dean Straw.

+

The big chart is handy for checking out what happens along a transmission line and for graphing the results. We are all taught that the impedance values repeat themselves every 180 degrees or half wavelength of transmission line. Unfortunately, most sources fail to teach us that voltage and current repeat their values only once every 360 degrees or full wavelength of feedline. That sort of neglect kept us in the dark about a number of interesting questions for nearly a half century, for example, how the element phasing of the ZL special really works.

+

10. The tenth way to look at transmission lines: with a calculator and a graph

Because we can vary the length of our feedline, even if lengthening it creates just a little more loss, we may often find it useful to understand what happens to the resistance and reactance as they continuously change every 180 degrees of line. The program, "Transmission Line Performance" in HAMCALC will provide figures for 180 degrees, and if you want to see what happens in the next 180 degrees, take the last figures in the columns, and plug them in as initial figures for a new chart. +

Let's look at a few graphs made up from the tables to see what happens to the resistance and reactance in some typical scenarios. But first, let's go back to Figure 2, where we entered the electrical length of our hypothetical RG-213: 296.9 degrees. Since this is close to 300 degrees and my graphs use values for each 10 degrees, we shall use that nice round number. However, the graphs cut off at 180 degrees. Since all impedance phenomena repeat every 180 degrees, we simply subtract 180 from 300 to get 120 degrees. The values that appear at the 120-degree mark are the one's most likely to show up at the end of our coax.

+
+ +
+

We can begin with Figure 15, a graph of resistance and reactance for an antenna impedance of 150 +/- j0 ohms. This is a resonant antenna with an SWR of 3:1 relative to our RG-213, with its characteristic impedance of 50 ohms. Because the antenna is resonant, note the nice symmetry of the curves--and be sure to read each from the correct Y axis: left for resistance and right for reactance.

+

First, it is not the case that everywhere along the lines, the R +/- jX values yield an impedance of 150 ohms. Instead, everywhere along the (lossless) line, the SWR is 3:1. Second, note that the reactance can reach well above 60 ohms (capacitive or inductive, depending on the length of the line). Third, at the 120-degree mark, we read an impedance of about 21 + j25 ohms.

+

This last figure tells us something important. The reactance figure is one that most network tuners can handle with ease, while the 2.5:1 ratio of source resistance (50 ohms) and presented resistance is fairly easily handled by almost any common tuner. So, if we can stand the cable loss of a 3:1 SWR, along with the slight tuner losses, we can easily match our antenna-feedline to the transmitter.

+
+ +
+

Now consider Figure 16. Here we also have a 3:1 SWR with our RG-213. Note that this SWR occurs with an antenna impedance of 70 + j66 ohms. At the 120-degree mark, we find an impedance of about 17 + j6 ohms. Although the reactance is low, so too is the resistance. Most network tuners will handle the job, but at slightly less efficiency than the previous case. Same SWR, but different tuning conditions and different impedance value.

+

Actually, Figure 15 and Figure 16 present the same curves, shifted by the reactance on the line. For a given line Zo, every curve with the same SWR will overlap every other curve of the same SWR, with only an adjustment down the line according to the relationship of R to jX at the antenna. Note the peak resistance of 150 ohms near the 20-degree mark, at which point the reactance is close to zero (the slight variance being a result of using 10-degree increments for our marks). Note that inductive reactance pushes peak resistance down the line away from the antenna.

+
+ +
+

In Figure 17, we see the resistance and reactance curves for a resonant 500-ohm antenna with a 50-ohm coax feeder--a 10:1 SWR situation. As with all resonant antennas, the curves are symmetrical through the 180- degree line span. It is most important to note for how much of the span (120 degrees or two-thirds) that the resistance is below 20 ohms. Our tendency is often to think of high SWR being associated with high values of impedance, when precisely the opposite is generally true: for most of the line length, the resistive component of the impedance is very low.

+
+ +
+

The same 10:1 SWR applies to Figure 18, with an antenna feedpoint impedance of 300 + j243 ohms. It may not be readily apparent that this curve overlays Figure 17 exactly. The peak resistance value of 500 ohms occurs at the 5-degree mark. Hence, the automated resistance Y-axis does not replicate. However, the reactance Y-axis scale shows the overlap of those curves.

+
+ +
+

Suppose that our 74' 10.5" of feedline had been 450-ohm "window" line with a VF of 0.95. Our line would be 206 degrees long, and we would look at the 26-degree mark on any relevant charts. The closest 10-degree point is, of course, 30 degrees. Using that number, lets see what happens if we use this parallel feeder with an antenna whose feedpoint impedance is 1000 - j100 ohms. Figure 19 tells the story. Because the impedance is slightly capacitive, the graph is shifted toward the antenna end, with the first graphable resistance peak between the 175 and 180 degree marks. Although the reactance at the antenna is only -100 ohms, the reactance value along the length of line varies from +400 to -400 ohms. At the end of the line we ran (the 30-degree mark), the impedance presented to the ATU is about 450 - j375 ohms--a fairly easy matching situation for any truly balanced ATU.

+

There are numerous matching schemes that do away with the ATU proper. Instead, they try to use calculated or experimentally determined line lengths to intercept something close to a 50-ohm resistive point on the line and then add enough reactance across the line to yield a net reactance of zero. Unfortunately, here is an antenna and feedline combination on which that technique would fail. Notice that the resistive component of the antenna never falls below 200 ohms. However, since this value occurs just about where the reactance crosses the zero line, a 4:1 balun might work with a line length just under 90 degrees (or 270 degrees, etc.). Direct reactance cancellation at or near the point along a 450-ohm line of a current maximum works best if the SWR is middling (4:1 to 6:1) or the reactance holds a 2:1 (or lower) ratio to the resistance for higher resistance values. Otherwise, the resistance along the line may not approach 50 ohms or may occur in a region of very rapidly changing values, making tuning excessively sharp.

+
+ +
+

More common with antennas near (but not at) a multiple of a wavelength long is the situation exemplified by Figure 20. The antenna impedance of 1000 - j2000 ohms yields an SWR of 11.47. Notice the very brief spike in the resistance curve, with the remainder of the curve at a low resistance. This curve graphically demonstrates the danger of using a 4:1 balun between the feedline and a network tuner. Let's examine our 30-degree mark. Ignoring the 200-ohm reactance, which tends to disrupt normal transmission- line transformer operation, the 90-ohm resistive component would simply be reduced to 22.5 ohms, a worse situation than would be the case with a 1:1 ferrite bead choke in place of the toroidal balun. At some points along the line, the resistive component will fall to under 10 ohms with the 4:1 system. Antenna situations like this one--which is quite common--make a good case for hauling out the old link-coupled antenna tuner.

+
+ +
+

We can close our series of examples with Figure 21, a 450-ohm line feeding an Extended Double Zepp (EDZ). Typically, these antennas show a feedpoint impedance of about 120 - j800 ohms (plus or minus about 20 percent, depending on the exact length of the antenna). Notice the very high spike in resistance and the very long series of very low resistance values. Also notice that there are two regions to the graph: a. a region from about 20 to 120 degrees where values change slowly and b. a region from 120 to 180 degrees where they change almost wildly. If you want freedom from ATU matches that change with weather conditions such as rain, ice, or even wind, choose a line length that ends up in the "slow-change" area.

+

The series of graphs can be extended indefinitely. However, if you study the examples given, you will begin to develop a fairly good intuitive feeling for what happens to impedance along a continuous impedance transformer called a transmission line. Add a program to calculate actual values for you, and you can convert your intuitions into intelligent decisions in the selection of feeder lines and line lengths for your installation.

+

11. The eleventh way to look at transmission lines: with pruning shears

As we have noted, a transmission line is a continuous impedance transformer. Impedance values repeat the value at the antenna feedpoint every 180 degrees (with a little adjustment for line losses). There is another magic mark along the way: the 1/4 wavelength or 90-degree point. At this point, however much the impedance departs in one direction from the line Zo at the antenna, it now departs by the same degree in the other direction. +

Arithmetically, the relationships look like this:

+
+ +
+

where Zo is the characteristic impedance of the quarter wavelength matching section of line needed or chosen to do the matching job, Z1 is the impedance at one end of the section, and Z2 is the impedance at the other end of the line.

+

This property of transmission lines is most useful with essentially resistive loads (very low reactances). With coaxial cable, it solves the problem of matching some common antennas to our ubiquitous 50-ohm feedline.

+

Some common quad beam design have feedpoint impedances of 100-ohms. One can purchase an expensive 2:1 balun, but that is unnecessary. Since the two impedances, 100 ohms and 50 ohms have a product of 500, the square root is 70.7 ohms. A quarter wavelength section of any common 70-ohm cable, cut with respect for its VF, will effect the transformation.

+

Many good Yagi designs have feedpoint impedances of about 25 ohms. To use a 50-ohm coax cable as our feedline, we need a quarter wavelength section of the square root of 1250, or 35.4 ohms. We can make such a line with parallel sections of 70-ohm feedline.

+
+ +
+

In fact, the quarter wavelength magic matching section is a special case of the more general series-section matching technique worked out by Frank Regier, OD5CG, about 1970. It appeared in QST in 1978 and has had a place in the ARRL Antenna Book ever since. As shown in Figure 22, the quarter-wave section match is simply a series match where the length of L1 is zero. Interestingly, the match-line and stub system is also a special case of the series match system, where the series section is replaced by a parallel capacitive or inductive stub.

+

12. The eleventh way to look at transmission lines: with a trigonometer

If we do not understand transmission line stubs, the last sentence in the preceding section will seem mysterious. However, whenever we place a shorted or open-circuit length of transmission line in series with or in parallel across another line (or even an antenna), it acts like a capacitor or an inductor. +
+ +
+

Figure 23 shows the basic relationships between transmission line length and its function as a circuit component. If the line is exactly 1/4 or 1/2 wavelength long, then it is resonant and has no reactance. However, at all other lengths, the line is either a capacitive reactance or an inductive reactance, depending upon whether it is open-circuited of closed- circuited (shorted). Notice that the lines change reactance types as they pass the 1/4 wavelength point.

+

The actual reactance is easy to calculate. For a closed-circuit line,

+
+ +
+

where XC is the reactance of a closed-circuit length of transmission line, Zo is the characteristic impedance of the line, and L is the length in electrical degrees. Note that we shall have to use the conversion process we learned in section 2 to convert electrical length to and from physical length.

+

For an open-circuit line, we use

+
+ +
+

where XO is the reactance of the open-circuit length of transmission line. Again, we use the standard conversion process to go between physical and electrical line lengths.

+

In both cases, the sign of the X-term will specify the type of reactance: positive for inductive and negative for capacitive.

+
+ +
+

We use actual capacitors and inductors to produce desired reactances in circuits. In principle, we can substitute transmission lengths in every case, although the practice is bulky except in the microwave region. At HF, some of the most common uses for transmission line stubs are illustrated in Figure 24. The beta-match hairpin is simply a transmission- line version of the beta-match coil. Linear loaded antenna elements are transmission-line substitutes for loading coils. One-quarter wavelength stubs can replace lumped components in the formation of frequency-specific, high-Q filters.

+

The match-line-and stub system of matching an antenna to a feed line is especially interesting. Although there are some conditions that will not permit a match, wherever one is possible, four are possible. HAMCALC has a program that will calculate matches for possible cases. Let's use such a match on our EDZ example with a feedpoint impedance of 100 -j800 ohms. Suppose we wish to connect this to a 50-ohm coaxial cable at 7.15 MHz. Let's specify 450-ohm, VF-0.95 window line for both the match line and the stub.

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If we use a match line length of 21.02' (6.41 m), then we can attach a 2.65' (0.81 m) shorted stub or a 35.32' (10.77 m) open stub to effect our match to 50-ohm coax. With a length of 23.312' (7.11m), we can use a 62.69' (19.11 m) shorted stub or a 30.02' (9.15 m) open stub. All will work, but--of course--we normally choose the shortest combination of matchline and stub that will achieve the goal. For monoband antennas with odd feedpoint impedances, the match-line and stub system is a handy tool indeed. Incidentally, the stub reactances are all (+/-) 57.7 ohms, and we could apply a capacitor or inductor across the line in place of the open or shorted stub, respectively.

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A Baker's Dozen. More ways to look at your feeders

We have to end our story somewhere, and a dozen ways to look at your feeders (and love them) is a nice even number. However, we could go on (and on and on). For example, we need to look at transmission lines with kid gloves to make sure we do not mistreat them. We also need to look at feeders with a field strength meter to see if they are radiating like antennas. We should additionally look at feedlines with an underwater scope to get further depth in our coverage. +

However, these 12 ways of looking at feeders will hopefully provide you with the means to sort out all the kinds of things you already know about feedlines so that you can feel more comfortable with them. The 12 ways are just a means of making sense out of a lot of information. I have said nothing new on the subject. Except, perhaps, that my feeders like to know that I love them.

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A Note on More Advanced Equations

Although we have used only as many basic equations as may be needed to develop an intuitive feeling for transmission line operation, the reader should not assume that the omitted equations are unimportant. Rather, they would have bogged down the flow of this particular discussion. +

For reference, here are a few equations of use. In the following, Er is the voltage at the antenna, Ir is the current at the antenna, Zr is the impedance at the antenna, Zo is the characteristics impedance of the transmission line, and L is the length in electrical degrees.

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1. To determine the voltage (Es) anywhere along a transmission line from the antenna:

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2. To determine the current (Is) anywhere along a transmission line from the antenna:

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3. To determine the impedance (Zs) anywhere along a transmission line from the antenna:

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Each of these equations has a real and an imaginary (j) part, which can be solved separately and recombined to yield a magnitude and a phase angle. Morover, the voltage, current, and impedance at the antenna may also be a magnitude at a phase angle, thus requiring further subdivision of the equations. The techniques described by Keucken in Exploring Antennas and Transmission Lines by Personal Computer can be useful in setting these equations up in one or more of the common programming languages.

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These equations are for lossless lines. Similar equations exist for lossy lines and involve the use of the value of Zo derived from the series impedance per unit length and the shunt admittance per unit length, along with sinh and cosh functions. For lossy lines, the impedance at some distance from the source is given by

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+ +
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where "gamma" is a complex loss coefficient comprised of the matched-line loss attenuation constant and the line phase constant and L is given in units matching those of gamma. These equations lend themselves to computer solution to speed computation and ensure precision, although the elegance of the Smith Chart lies in its ability to handle them graphically.

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The relationships among the line characteristic impedance, Zo, and the voltage and current along the line (treated variously as forward and reflected voltage or current, or as maximum and minimum voltage or current) are too numerous to cover here. However, using Zo as the characteristic impedance of a lossless line, we can define the reflection coefficient, rho, as follows:

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where Rr and Xr are the resistive and reactive components of the impedance Zr as used in the preceding equations. SWR (voltage or current standing wave ratio) is simply

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which may make apparent the direct calculation of SWR given in the main text. The fact that the reflection coefficient, and hence SWR, are circular functions is the key to understanding the construction of the Smith Chart, a simplified version of which is shown in Figure 25.

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As you delve into the variety of literature, you will encounter variations of both notation and form of the equations shown here for reference and others related to them. It is useful to keep a log of the variations in the texts to which you refer most often to ensure ease in following a set of calculations or discussion of the phenomena described by these equations.

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References

+

The following software may be useful in calculating various problems with transmission lines:

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HAMCALC, version 32, by George Murphy, VE3ERP, 77 McKenzie Street, Orillia, ONT L3V 6A6, Canada. Murph requests that users send him $5.00 to cover the cost of the disk, a mailer, and postage from Canada. Any excess over costs is donated to the Canadian National Institute for the Blind amateur radio program.

+

TLA, by Dean Straw, N6BV, comes with the current edition of the ARRL Antenna Book or can be obtained from the ARRL BBS.

+

MicroSmith, by Wes Hayward, W7ZOI, available from ARRL.

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The following books and chapters may be useful to you in furthering your understanding of transmission lines.

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R. Dean Straw, N6BV, ed., The ARRL Antenna Book (Newington: ARRL, 1997), Chapter 24.

+

Joseph J. Carr, Practical Antenna Handbook, 2nd Ed. (New York: TAB Books, 1994), Chapter 3.

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Wilfred N. Caron, Antenna Impedance Matching (Newington, ARRL, 1989): one of the finest tutorials on Smith Chart use.

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M. Walter Maxwell, Reflections: Transmission Lines and Antennas (Newington, ARRL, 1990): perhaps the best source book for overcoming misconceptions about transmission lines and SWR.

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Jerry Sevick, Transmission Line Transformers, 2nd Ed. (Newington: ARRL, 1990): this and other of Sevick's books are authoritative on the subject.

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For advanced reading, I recommend the following:

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Richard C. Johnson, ed, Antenna Engineering Handbook, 3rd Ed. (New York: McGraw-Hill, 1993), Chapter 42.

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John A. Keucken, Antennas and Transmission Lines (Starkeville, MS: MFJ, 1996), Chapters 16-25 (a reprint of a fine text). See also Keucken's Exploring Antennas and Transmission Lines by Personal Computer.

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Frederick E. Terman, Radio Engineers' Handbook (New York: McGraw-Hill, 1943), Section 3. Ronold W. P. King, Transmission Line Theory (New York: Dover, 1965); a highly theoretical work for the exceptionally curious.
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Updated 5-19-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Amateur Radio Page
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Topics: Matching, Transmission Line


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10 Questions You Always Wanted to Pose to Your Vertical, But Were Afraid to Ask

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This talk, on the basics of vertical antennas, was originally prepared for the 1999 Dayton FDIM Symposium

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Horizontal antennas are simple. Verticals, on the other hand, are complex, mysterious beasts around which we have spun horror stories, myths, and gobs of misinformation. We live in terror of the dreaded ground plane, not knowing if we need one or, if we do, what will work and what will not. We fear to load them, for we know not where to place a coil or how to hang a hat.

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Verticals look innocent enough. Like a skeleton with one bone, they sit erectly, so prim and properly military in their posture and bearing. But at night, when the wind howls, we have nightmares in which the vertical writhes and bends into pretzel shapes, choking the communications life out of our precious RF.

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Books abound on the vertical antenna.1 However, most appear to be exercises in black magic. Often it seems less that the author has mastered the vertical antenna than that the vertical has mastered the author. Have you ever noticed the reverence with which aficionados of verticals approach their subject? The mystique of verticals is enough to make anyone dizzy.

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I wish I were overstating the case, but--alas--I am not. Among all antennas, verticals evoke the largest number of disputes and the most desperate question of all: how do they work?

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Quite frankly, I cannot answer that one question-- just because it includes everything there is to know about verticals. However, we can explore a number of smaller questions--10 in all--that might give us a hand- hold on vertical antennas. Once we have looked at these 10 questions, I hope the myths and misinformation about verticals will dissipate like a rain cloud and let us progress on our own toward filling in the gaps I leave behind. For my goal is to bring verticals down to earth- -and at the same time, to bring them up from the murky depths. My aim is to make the vertical antenna as ordinary as the horizontal.

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As with any mystery, we clear it up by asking the right questions. The ones I shall pose are not the only ones we might ask--and the approach is not the only one we might take. However, the following questions are good ones and just might lead us to a little more clarity than before.

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1. What makes an antenna a vertical antenna?

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2. Why do we even bother using verticals?

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3. Why are verticals so much harder to understand than horizontal antennas?

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4. Why is "counterpoise" such a dirty word?

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5. What makes a vertical either a monopole or a dipole?

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6. What is a ground plane?

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7. How can we make a short vertical work well?

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8. How can we make verticals directional?

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9. How can we make verticals out of wires that are mostly horizontal?

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10. Just how "good" is a vertical?

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If that is not enough work for one foray into vertical antennas, then I have lost the meaning of the word "work."

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1. What makes an antenna a vertical antenna?

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Antennas are inherently and by themselves neither vertical nor horizontal. The technique of studying a antenna by itself is to place is in free space, with no other object in its field in any direction whatsoever.

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Unless an antenna is a dot or a sphere, the antenna will have identifiable planes of radiation. The traditional names for these planes are the E-plane (associated with the antenna's electrical field) and the H-plane (associated with the antenna's magnetic field). Consider Fig. 1 at the top of the next page. For the Yagi antenna--a very planar antenna--the E-plane is in line with the elements. The H-plane is at right angles to the elements. The fields can use arrow heads to indicate direction a. because the antenna is very directional and b. because the elements define a major plane.

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Except for element and object coupling, the magnetic field is far less important to antenna performance at a distance than the electrical field.

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Although we shall return to the magnetic antenna field or H-plane before we are done, let's focus on the E-plane or the electrical field of the antenna. This is the field primarily responsible for long distance communications (although one field could not exist without the presence of the other at the antenna).

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A simple antenna, like a dipole, has many possible E-planes. In Fig. 2 below, the left figure shows the shape of any one of them, since it cuts a cross section in a plane with the element. The right figure looks at the element from the end and sees an indefinitely large number of cross-sections or E-plane figures we might make--all just alike. So if we tilt the left figure progressively upward, it will turn into the right figure-- and vice versa.

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To see the transition, look at Fig. 3, a 3-D representation of the same patterns.

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The antenna is exaggerated immensely to shows its orientation relative to the field pattern. However, these fields are represented at arbitrarily huge distances from the antenna, so that if I drew the antenna to scale, it would be invisibly small.

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The familiar donut shape pattern can only materialize in free space. If we place any objects of significant size anywhere in the field, some radiation will reflect from them or refract around them, distorting the pattern and at least taking a bite from the donut. With all antennas we use--except in outer space, perhaps--we live with reflections and refractions and distorted patterns. In fact, we have learned to make use of the distortions to make our antennas to a better job of placing radiation fields where we need them.

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Until further notice, we shall concern ourselves only with the E-plane fields of antennas. If we think E-plane only, then we can understand why we call antennas vertically and horizontally polarized--or vertical and horizontal for short. All we have to do is to bring them down to earth, as we do in Fig. 4. Now we have a reference plane, namely the surface of the earth, against which to compare the E-plane fields of an antenna. If those fields are parallel to the earth's surface, the antenna is horizontally polarized. If the fields are at right angles to the earth's plane, then they are vertically polarized.

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The scheme is so simple that you would think that no one could confuse it. However, antennas themselves give us good reason to get confused sometimes. In the real world, hardly any antennas are purely vertical or purely horizontal. Instead, even antennas that we think of a purely one or the other have some remnant (E- plane) radiation of the opposite polarity. Fig. 5 provides a couple of samples.

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The top antenna is a horizontal dipole. As purely horizontal as we like to think of the dipole, it retain a tiny vertically polarized component, mostly caused by ground reflections which interact with the element. The amount is insignificant in terms of having any affect on the overall antenna pattern. The horizontally polarized field is not distinguishable from the total antenna field.

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The bottom antenna happens to be a half-square, which has a larger horizontally polarized radiation component to go with the predominantly vertically polarized radiation. The remnant does have a small but determinant affect on the overall antenna pattern, as evidenced by the slight smudge in the larger pattern outline: the total field and the vertically polarized field are not absolutely coincident.

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So when we call an antenna a vertical, what are we saying? We are simply noting that the dominant orientation of the electrical fields from the antenna are at right angles to the earth's surface. Nothing more, nothing less.

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2. Why do we even bother using verticals?

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There is a myth that says inherently verticals are inferior to horizontals. Consequently, they are always the last option, perhaps when you are faced with using a vertical or not using any antenna at all. although there is a way in which we can give this claim some truth, in fact it is not event a half truth--more like about an 8th truth at best.

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Verticals have their best use when we define some total communications picture. Then their use makes eminent sense. So let's construct some communications scenarios.

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1. From lower HF down through VLF, the surface wave component of an antenna's radiation is important. From lower HF on up, the surface wave is too weak and dissipates too soon for more than community communications. In the AM broadcast band, a surface wave can cover a radius of 50 miles with modest power (relative to broadcast powers). At VLF, with enough power, a surface wave will go around the world.

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Surface waves are most efficient when vertically polarized. Hence, AM broadcast antennas are vertical to enhance their surface wave propagation.

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2. Mobile antennas from HF through UHF are vertical for two major reasons. First, moving objects, like cars and boats, do not have much surface area to support horizontal antennas. (The 6 and 2 meter halos are exceptions.) Second, vertical antennas tend to be omnidirectional. For local communications, where a vehicle may undergo many changes of orientation, the vertical means a more even signal strength relative to the other terminal of the path. In most cases of local communications, we are using ground wave, but not the surface wave subdivision. Instead, we are using point- to-point communications.

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The other terminal within this local communications ring employs an antenna which offers the highest promise of maximum signal strength. In point-to-point communications, signal polarity is largely sustained along the path. Some polarity skewing occurs because of signal refraction from objects, but not in the main. Hence, to avoid the signal path loss occasioned by cross polarization--which can run from 3 to 20 dB, depending on circumstances--the other terminal uses a vertical antenna as well.

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3. Skywave propagation results in polarization skewing, thus voiding in large (but not total) measure the polarization differences between vertical and horizontal antennas. However, some operations dictate that they be able to receive from and transmit to all directions equally well and simultaneously. Since vertical antennas (but not necessarily vertical arrays) are omnidirectional, they are often the only antennas suited to the communications need.

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4. In the war between vertical and horizontal antennas, most horizontally polarized antennas do not have an elevation angle of maximum radiation that is low enough to match long distance propagation angles until those antennas are at least 1/2 wl up--or higher. Above that height, going horizontal is seldom a bad choice, but below that height, long-distance communications may suffer with a horizontally polarized antenna. Vertically polarized antennas at or near ground level (as well as those mounted some distance above the ground) inherently have low elevation angles of maximum radiation.

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Every installation has its own special concerns that determine the maximum height (and horizontal spread) for antennas. Since 1/2 wl at 40 meters is about 70' and 135' at 80 meters and 275' at 160 meters, achievement of significant radiation at low elevation angles is often impossible for feasible horizontal antennas. Hence, the vertical antenna becomes the antenna of choice.

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5. Some installations lack the horizontal space needed to handle a horizontally polarized antenna. In such cases, a vertical antenna with compact horizontal dimensions may be the only feasible antenna.

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This last case may be the only one in which one should think that they are using second best. However, it is likely much more productive to devote one's thinking to improving the vertical installation to make it the most effective possible. The items in our list are all very good reasons for using verticals. Although the list is not complete, you can fill in the rest of the possible entries yourself.

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3. Why are verticals so much harder to understand than horizontal antennas?

Unless a vertical antenna is very high above the ground--perhaps a wavelength between the earth and the antenna bottom--the antenna will interact with the earth in ways more complex than the simple interactions involved with horizontal antennas. Hence, there is a larger set of terms we have to master in order to fully appreciate what is going on with a vertical. +
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We can illustrate the complexity by a simple demonstration. Fig. 6 shows a series of elevation patterns along the main axis of radiation from a horizontal dipole placed 1/2 wl above ground. The horizontal antenna is concerned with ground quality mostly at a distance from the antenna--the region sometimes called the Fresnel region at several wavelength distance from the antenna. Here, the ground quality has an affect on the reflection of radiation to combine with the direct radiation to form the main elevated beam. Note that from perfect to very poor ground, the increments of signal strength change are quite small and very regular. They progress downward from perfect to very poor in neat steps.

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Fig. 7 shows a vertical dipole that begins 10' off the ground and is 1/2 wl long. If we could have perfect ground, the antenna would provide very significant gain. Salt water (not illustrated here because it would bring tears to the eyes of most land-locked vertical users) approximates the perfect pattern quite closely. However, over typical soils, the skywave signal strength is reduced considerably from its ideal. Notice also that the changes are not as regular as with the horizontal antenna. Poor soil produces a slightly stronger skywave signal than does the supposedly better average soil.2 This phenomenon does not occur at every height at which we might mount the vertical.

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Because verticals--whether or not they are self- contained or use ground planes--are so interactive with soils, we must acquaint ourselves with soil behavior and peculiarities. For example, at lower HF, RF penetrates the soil much deeper than at upper HF. Since soils are very often layered, with each layer having difference conductivity properties, we may not be able to predict or to model with precision the performance of a vertical antenna at 80 meters, although the same antenna at 20 meters might be very predictable. Likewise, some soils- -such as those in desert areas with sandy salts--may change with the weather--becoming more conductive for a while after a ran storm--the performance of a vertical may change from day to day.3

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Even though some vertical designs--those we shall eventually classify as self-contained--are dependent for the most part only on soils in the Fresnel region, vertical monopoles that use ground planes are also dependent upon soils immediately beneath the antenna.4 Hence, we must not only concern ourselves with general soil properties, but as well, we must be able to distinguish between local and distant soils, as sketched roughly in Fig. 8.

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As complex a subject as soil is when juxtaposed with antennas, the major hindrance to the understanding of vertical antenna behavior are the partial truths that parade as universal generalizations. Here are a few, given without much comment:

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1. Verticals always need a ground plane. Wrong.

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2. Verticals are omnidirectional. Not all are.

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3. Verticals are always weaker than horizontals. Not always, and it depends at which elevation angles you look. Besides, the stronger reception might be mostly noise.

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4. A short vertical is next to useless. Very wrong.

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5. If you cannot put down a large ground plane, you had better add lots of copper sulphate to your yard soil. Only if you are seeking to kill the grass.

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6. Verticals are dangerous to other people in the area. Actually, this can be true, if one installs the antenna carelessly, without due attention to safety. We could spend an entire hour on the subject of differentiating RF exposure (usually not a problem, especially at QRP levels) from RF contact (and the inevitable RF burn). It is the latter that forms the chief danger to folks in the area, but preventing contact is a simple matter to fix by any of a dozen different techniques, ranging from fencing beyond touching range to elevating the antenna out of reach.

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7. Every vertical needs a counterpoise. A what?? Let's spend a few moments on this term.

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4. Why is "counterpoise" such a dirty word?

The term "counterpoise" comes from mechanical systems contexts. It means a counter-balancing force, ordinarily a weight on the other side of a fulcrum. It wormed its way into antenna work as a term that covered up ignorance under impressive sounds. If some hank of wire seemed necessary to make an antenna work, but it had no name officially condoned as the name of an antenna part, it was dubbed a counterpoise. This name was reserved mostly, but not always, for antenna parts that did not seem to contribute to radiation. +

There is nothing in the world of antennas that corresponds to the dead weight facet of the concept of a counterpoise. Every part of an antenna contributes to the antenna far field pattern (except those parts that we specifically design to have self-cancelling radiation). Hence, there is no such thing as a mere counterpoise. We should do our best to expunge the term from the language of antennas.

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Fig. 9 illustrates three recent applications of the term in ham literature.

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Case A involves a wire running for some specified number of feet from the ground terminal of an antenna tuner to ground. However, The entire length of wire from ground to the far elevated end is the antenna, with the feedpoint at the ATU simply off center.

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Case B. treats the lower wire from a 1/4 wl vertical as a counterpoise, even though--in its vertical position--it constitutes the other half of a common vertical dipole.

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The third case (C) is a modern adaptation of a very old scheme of running a second wire at or near the ground under a horizontal wire, ostensibly to improve some mysterious relationship between the upper wire and the earth. Actually, the horizontal antenna performance remains unchanged, and the wire becomes a trip for anyone careless enough to walk through it. At best, it serves as a parasitic reflector, possibly converting a general purpose antenna into an NVIS (Near Vertical Incidence Skywave) special.

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In every case, the so-called counterpoise can be analyzed (and modeled) as a part of the antenna. Hence, let us simply set the term aside as one we no longer need and replace it with specific terms that correctly identify the parts of antennas.

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5. What makes a vertical either a monopole or a dipole?

Having spent a good bit of time clearing away problematic ideas that get in the way of understanding verticals, let's make some positive progress. One of the most confusing question we can get our hands on is when a vertical is a monopole and when it is a dipole. +

The question is not difficult if the antenna wire is 1/4 wl long or shorter. A quarter wavelength wire fed at its end in free space presents an impossible situation that has no resemblance to a real antenna, like one we might stick in the ground. It always wants some form of completion, whether as a real or a simulated ground plane, so that we can feed it at or near a current maximum.

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The problem that boggles our minds is when the vertical antenna element is longer than 1/4 wl. We can in fact have vertical monopoles that are anywhere from 1/4 wl to at least 5/8 wl long. We can also have vertical dipoles that range from short (1/3 wl to 3/8 wl long) to well over the standard 1/2 wl length.

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The way to figure out which is which lies in the feedpoint and system: where are you feeding the antenna and how. As to positions, we have roughly two choices. We can feed the antenna at the lower end or we can feed it in the middle. (The upper end is theoretically available as a feedpoint, but somewhat inconvenient except in some nearly vertical sloper designs.)

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Our choices as to the method of feed are also a pair. We can feed the antenna at a point at or near a current maximum. We may also feed the antenna at a voltage maximum. We are accustomed to matching a high- current, low voltage, low impedance source to a low impedance antenna feedpoint. We think of such points as the base of a vertical monopole or the center or near center of a dipole. Voltage feeding involves the use of high-Q tank circuits with the power coupled in and the antenna attached at or near the "hot" end of the tank.

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It is sometimes easier to make out the antenna type by analyzing the feed from the bottom rather than the top. In the left example in Fig. 10, the feedpoint is 1/4 wl from the end of the radial. If the remainder of the antenna is also 1/4 wl long, then the feed is similar to that of a dipole, with a lower impedance since the radiation from the radials is self-cancelling. If the vertical portion is longer than 1/4 wl, then the antenna operates similarly to an off-center-fed wire. The feedpoint remains a current feed, although one should watch out for current imbalance on the feeder. Although the vertical part of the antenna, when separated from the radials, is an unbalanced monopole, when the radials are reconnected, balance is restored for a current feed.

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The sketch in Fig. 11, shows the current magnitude along both the vertical and each of the (4) radials for a sample 1/4 wl monopole with ground plane. The current in the radials at the junction is 0.25 of the source value of 1.0. Note the current peaks in the radials near the junction of elements.

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The middle case of Fig. 10 is clear enough on its own. The antenna is current fed for lengths between 1/3 wl and nearly 3/4 wl. Because the antenna is balanced about a current maximum at its center, it requires no ground radials to establish that balance.

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In the model sketched in Fig. 12, the 1/2 wl antenna has been placed over a system of 4 radials, each 1/4 wl long. The current magnitude curves reveal that the current in each radial never rises above 0.1 of the current at the antenna source (1.0), and the current peaks about mid-way down each radial. The gain difference between this little model, with the antenna about 2' above the radial system, is less than 0.25 dB relative to the same antenna in the same position, but with no radial system.

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The last case in Fig. 10 strikes many as similar to the first, since the feedpoint is at the base. However, the tank circuit makes this a voltage-fed antenna, and the current maximum is at roughly the center of the antenna. For proper operation, the antenna requires no radials, but does demand a good RF ground return to the source. If we do lay down a radial system, it is not for propagation, but for the enhancement of the RF ground of the tank circuit. Of course, the link for the low- impedance feeder system could be replaced by a tap on the main coil.

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With the end of a 1/2 wl antenna at the same position above ground as the model used in Fig. 12, the antenna shows the same gain, within about 0.1 dB, as the center fed version. Fig. 13 shows the current magnitude distribution along the element, with its peak at the center of the antenna, almost identically to the magnitude pattern of the center-fed version. As an end fed antenna, the feedpoint impedance is high: about 1400 Ohms resistance and 4000 Ohms reactance. However, before we leave our 1/2 wl vertical, let's perform one more experiment.

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Compare the current magnitude curves of Fig. 13 and Fig. 14 below. Shape is more important than absolute value of the maximum shown.

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In Fig. 14, the 1/2 wl element was placed above 4 radials and fed against them. The result was similar to that of the 1/2 wl center-fed element placed above the same radial set. Gain differences are less than 0.1 dB, and the maximum current region remains at the element center. The source impedance is high, and the current in the radials reaches about 0.1 of the value at the vertical element center.

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This exercise is not designed to show that radials do not help, since we used only 4. However, it does demonstrate that the end-fed 1/2 wl element remains exactly what it is whether or not placed above and fed against radials.

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6. What is a ground plane?

One of the enduring misnomers of all antenna work is the phrase "ground plane." We cannot get rid of it (in the way that we can simply stop using the term "counterpoise"). However, we can do as much as possible to eliminate drawing some of the wrong conclusions that abound. +
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Let's first treat the "plane" part of the phrase. As revealed in Fig. 15, the typical plane consists of a symmetrical arrangement of spokes extending from one side of the feedpoint, where the other side is essentially a vertical element. For the common 1/4 wl vertical antenna, the plane spokes are also approximately 1/4 wl long. Almost any number of spokes may be used so long as we arrange them symmetrically.

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The lower half of Fig. 15 shows the function of the plane: to replace the radiating lower half of a vertical dipole with a structure that 1. lets the assembly be resonant on some desired frequency, 2. permits the feedpoint at the element-plane junction to be a current- feed point, and 3. eliminates radiation from the plane by cancellation. That is, radiation from one plane spoke is cancelled by radiation from one or more spokes in the assembly. (Hence, we may in fact use an odd number of radial spokes to make up the plane, and as few as three will preserve the circular vertical pattern that we prize.

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Notice that this description of the plane makes no reference to ground. In fact, one can model the antenna just described in free space with no theoretical problems rearing their troublesome heads. A ground-plane vertical requires no ground to operate perfectly well.5

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There are actually a large number of subquestions concerning the radial plane of a vertical monopole. Let's look at them, one at a time.

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a. How many radials do I need to achieve maximum performance from my vertical + plane? The answer to that question depends on the proximity of the antenna to the earth. The closer to the earth-- including being in the earth, the more radials are needed.

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However, it is not very far above the earth that the use of many radials instead of a few fails to help the antenna. As shown in Fig. 16, at a height of 10' (about 0.07 wl at 7 MHz) for the base of a vertical + radial plane, performance is not enhanced by doubling the number of radials up to 32 from an initial set of 4. When those radials lay on the earth, as in the lower curve, performance increases continuously with each doubly of the number of radials. And it would continue to improve up to at least 120 radials. (Because there is some question about the accuracy of absolute value values yielded by NEC models for planes near the ground, but not about the accuracy of performance trends, the graph uses the gain with 32 radials as a reference in both cases, showing the lesser gain with fewer radials. 0 dB is an arbitrary reference point.)6

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To the graphed gain, we can also add data concerning the feedpoint impedance as we change the number of radials. For the elevated antenna, source impedance changes by less than 1 Ohm across the range of radials. With surface radials, the impedance changes considerable, with a resistive component variation of 24 Ohms and a reactance variation of 65 Ohms. Hence, the received wisdom for earthed radials holds good: the more radials, the better up to about 120, with about 30 being the minimum number for a long-term, serious installation. For an elevated system, whether on a pole,tower, or roof, 4 to 8 is enough.

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b. What difference, if any, does sloping the radials make to the installation? Fig 17 shows several degrees of sloping we might typically use.

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The sloping-radial question implies an elevated vertical because it is difficult to slope 160-meter radials at a 45-degree angle into most kinds of ground. The answer involves two aspects of antenna performance: the gain and the feedpoint impedance. Each answer is partially dependent on the height of the antenna assembly.

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Fig. 18 gives part of the answer in terms of the gain of a 4-radial vertical at two very different heights: 1.0 wl and 0.2 wl. The higher antenna shows a continuous progression of gain increase (although just barely) as the radial angle relative to a flat plane parallel to the earth continues to increase. When sloped, the plane is no longer a purely non-radiating symmetrical system. The horizontally polarized radiation is balanced and self-cancelling. However, the vertically polarized radiation--which grows significantly the greater the slope to the radials--simply adds to the radiation from the upper vertical section. In short, a roof-top vertical with sloping radials is actually a form of vertical dipole.

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0.2 wl for the vertical feedpoint is about the lowest height for this modeling test, because at lower heights, the radials drag the ground. However, the approach of the radial ends toward the ground with steeper slopes actually produces less gain than the max gain angle of 30 degrees.

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Not only does the gain change with the degree of radial slope, but so too do the elevation angles of maximum radiation (TO or take-off angles) and, of course, the source or feedpoint impedance. The following small table makes the changes clear.

+ 
Radial             TO              Feedpoint Z
+Slopes          angle           (Resistance)
+degrees         degrees         Ohms
+Height:  1 wl
+ 0              26              21.3
+30              27              41.3
+45              28              49.7
+60              28              55.9
+Height:  0.2 wl
+ 0              15              19.4
+30              17              43.1
+45              18              56.3
+60              18              68.6
+

Evident is the more rapid rise in the source resistance as the radial slope angle increases for the antenna whose radials more closely approach the earth. At a slope of 60 degrees, the 0.2 wl base height of a 40-meter version of this antenna places the radial tips within 2' of the ground with significant vertically polarized radiation from the lower portion of the antenna.

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Equally evident is the small but definite increase in take-off angle as the radials approach the position where the antenna would become a vertical dipole. This latter phenomenon occurs because the growing vertically polarized radiation from the bottom wires comes from a position that is lower than the upper wire, and this portion of the radiation has a higher take-off angle. The overall elevation angle of maximum radiation is a composite of the two angles.

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c. What differences, if any, does absolute height of the antenna base make to performance? We can only provide a sample modeling test for this question, so the answer will only be partial. However, the results reveal an interesting facet of vertical antenna operation. I placed 40-meter vertical antennas at base heights of 10, 20, and 30 feet. (Base height refers to the lowest extent of the antenna wire or wires.) I used both a vertical monopole with an 8-wire radial system and a full-size vertical dipole. Of course, the top of the dipole was much high (1/4 wl higher, to be more precise). The models for the vertical + radial plane used a plane with no slope, that is, with the radials at right angles to the vertical element.

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Fig. 19 shows the basic test configuration, with the results in several performance categories tabulated below the figure.

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Base Height        Gain    T-O Angle       Feedpoint Resistance
+  feet          dBi     degrees                 Ohms
+A.  Vertical Dipole
+  10            0.22    16                      79.5
+  20            0.34    15                      70.8
+  30            0.28    14                      68.5
+B.  Vertical Monopole with Radial Plane
+  10            0.20    22                      26.0
+  20            0.27    18                      21.8
+  30            0.18    16                      19.8
+

There is little to choose between any of the antennas or configurations with respect to gain. The maximum gain differential is 0.16 dB. The vertical dipoles exhibit a lower elevation angle of maximum radiation for each height because their feedpoints are always 1/4 wl higher than those of the monopoles in this test. As with all of our test models, the higher the vertical antenna base from the ground, the lower the feedpoint resistance. The low value of the feedpoint resistance may surprise some folks, since we are often told that the inherent resonant resistance at the feedpoint of a vertical monopole is 36 Ohms. It is not. Above about 20' in height, the feedpoint resistance will fluctuate periodically for this antenna between 20 and 22 Ohms. The antenna is modeled with a 2" diameter aluminum tube and 0.25" aluminum radials.7

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More significant is the peak gain within each antenna type at the 20' base height. In fact, the peak for the monopole occurs at a slight higher height than 20' and drops more rapidly when the antenna is placed 10' higher. Why the gain exhibits this behavior becomes clear from Fig. 20.

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The pattern of a vertical antenna at a low height shows a single lobe when viewed with respect to the field elevation. Notice that the antenna is relatively insensitive to radiation coming from higher elevation angles. As we increase the height of the vertical, a second lobe emerges at a higher elevation angle. This lobe peaks in the vicinity of a 60 degrees elevation angle--too high for the reception of almost anything except atmospheric noise.

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Those who use vertical antennas by choice rather than the necessities of a particular antenna site often select them knowing that the gain will not compete with a horizontally polarized antenna they might use instead. However, the signal-to-noise ratio is often improved because atmospherics received from high elevation angles are reduced. Some of that reception advantage disappears if we place the antenna too high. and the second lobe of the elevation pattern achieves full development.

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There is a counterweight to this facet of vertical antenna behavior that is especially apt to urban, suburban, and wooded locations. I cannot demonstrate it with a model, but only from the collective experience of many vertical users, including myself. The phenomenon is the dreaded "Rf-eating shrubbery." In the open fields of America's great farming states, a ground-mounted vertical has its best home, with nothing but open fields for many wavelengths in any direction. In crowded locations, the presence of significant structures--both natural and man-made--appears to prevent a ground-mounted vertical from achieving its full performance potential. Therefore, the elevated location of a vertical monopole--for example, a roof-top- -becomes a better location. The higher location is especially apt to the compact, multi-band vertical monopoles produced by many commercial companies.

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A second reason for elevating a vertical antenna is the presence of nearby noise sources such as machinery and other instruments that create RF from sparks. Much of this noise is vertically polarized, but hugs the ground in a surface wave. Elevating a vertical can often, but not always, reduce the noise level from these sources. Since noise sources can be very complex, the tactic is not universally successful, but it is worth a try in noisy urban areas.

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d. What makes a monopole's radial plane a ground plane? A ground plane, then, is simply the completion of the monopole, in effect making it a dipole with a lower half that yields little or no radiation. It only becomes a ground plane when in close proximity to or contact with the earth itself. As the numerous examples have shown, one effect of contact with the earth is a higher feedpoint impedance value, which most analysts have traditionally interpreted as being the sum of the antenna's natural impedance and something called ground losses.

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There may be a better way to think about the ground than as a loss-center. This view gives us no idea of how the losses occur. We think of the ground as a big resistor spread out over some amorphous surface area. The picture, of course, makes no sense whatever.

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A better way to think about the earth's surface is as a large area that is a semiconductor. A semiconductor is defined in solid state electronics as a material with neither the high conductivity of the best metals nor the low conductivity of the best insulators. What is in between is a broad territory.

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Placing a monopole with a radial plane in the air sets it into a very effective insulating medium. Under these conditions, the fields from the individual radials combine to yield a net of no field at all--assuming a symmetrical radial pattern. If we place the same radial plane in the earth, we cannot talk about fields until we examine all of the conducting material making up the plane. We may insulate the radials, but that does not change anything, except in the local area of the insulation: the radial current yields a field which instantly becomes a current in the adjacent conducting medium. Because soil may be composed of particles, some of which conduct and some of which insulate, the overall situation of a surface radial plane is a mix of fields and currents, both of which are detectable and measurable.

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What forms the plane of a vertical monopole when the radials are in the earth is the entire region about the monopole, as suggested in Fig. 21.

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The outline of the region is only a dotted line, because the region has an indefinite boundary. The radial lengths actually show little modeled difference in performance over a 25% change in length, whereas the length of the vertical in air is critical to resonance. Likewise, the lengths of radials that are away from the earth also have a much more marked affect on resonance. Burial of the radials is unnecessary for the earth itself to become part of the plane, since radials very close to the ground show the same effects.

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Increasing the number of radials in the earth increases the role of high conductivity material in forming the radial plane of the antenna. This shows up not only as increased gain, but as well in a tighter correlation in the feedpoint impedances between the free space and the at-ground versions of the same structure.

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7. How can we make a short vertical work well?

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For the 40-meter band down through 160 meters, many of us cannot erect a full-size vertical, even of the quarter wavelength variety. So we look for ways to shorten the antenna. Fig. 22 shows the most common methods: a base-loading inductor, a mid-element loading inductor, a top hat, and a hybrid of inductance and a hot. We shall skip the hybrid, since it should be reserved for mobile use, when the antenna length is super-short.

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The loading methods present us with a dilemma. The best method electrically is the most difficult to implement mechanically. Loading coils are fairly straightforward, but the top-loading hat is a heavy wind- catcher. Nonetheless, let's look quickly at some facets of hat loading.

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To examine the various loading schemes, I took a full-size 40-meter radial-plane monopole within 0.1' of earth using 16 radials for the test. I then reduced the height to 1/2 full size without changing the radial system. Next, I introduced various loading methods. The base load called for 282.2 Ohms or 6.28 uH. The mid- element load called for 456 Ohms or 10.15 uH. I assumed for the test a Q of 300 as an achievable intermediate range value. The top-hat consisted of 4 0.25" diameter spokes, each 9.1' long. In the table below, the gain is relativized to a value of 0 dB for the full-size monopole, since absolute gain figures for near-earth monopoles have not been fully validated.

+ 
Antenna              Relative             TO Angle             Resonant Source
+                     Gain dB              degrees              Impedance Ohms
+Full-size             0.00                26                   38.8
+Base-loaded          -3.03                28                   18.5
+Mid-el. load         -1.52                28                   21.3
+Hat-loaded           -0.47                27                   24.7
+

The table should contain no surprises, relative to preconceptions we tend to hold about vertical antennas. However, the difference in relative gain between the base-loaded and the mid-element-loaded monopoles ought to have taken us by surprise. Free space models and models of dipoles using center-loading compared to mid-element loading show far less differential in gain, in fact, too small a differential to make a difference in use. Because mid-element coils have a much higher resistive loss for the same Q, due to the necessity of using larger values of inductive reactance, the overall losses tend to nearly equalize with those of a center-load antenna.

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What produces the differential in gain between the base-loaded and the mid-element-loaded monopoles is the proximity of the loading system to the earth and to the right angle plane. Mutual coupling between parts or (or segments of, in models) the main element and the radials differs between the two cases far more than with a linear dipole using center-loading or mid-element- loading inductive reactances. It is thus sound for mobile whips to place loading coils as high as possible.

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The higher gain and source impedance of the hat-loaded model relative to the other forms of loading is clearly apparent. What is less well understood is that a hat may be composed of any number of spokes and that these spokes may be used alone or with a perimeter wire connecting their tips. Fig. 23 shows the results of a study I did with a 3 MHz monopole and hats of both types. Since the effective length of a spoke + perimeter wire is the length of the spoke plus approximately half the length of the wire connecting two tips, the spoke length of the perimeter system starts and remains shorter than using spokes alone. The two systems converge at about 60 spokes or so, beyond which, the radials simulate a solid disc.

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Fig. 24 shows modeled SWR sweeps across 40 meters for the antennas earlier tabulated. Each curve is referenced to the antenna's resonant impedance at 7.15 MHz. Of course, the full-size antenna shows the broadest SWR curve, followed closely and desirably by the curve for the top-hat model.

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I have on other occasions already warned you to be ready for surprises, for example, in connection with verticals over different soil types. Here is another case. The narrowest operating bandwidth of the collection occurs with the mid- element-loaded model, not the base-loaded model, despite the reputation of mid-element-loading for providing a wider operating bandwidth than base-loading.

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Every radial-plane vertical monopole placed close to or on the earth holds the potential for surprises, including the surprise of working quite well. The worst case of our collection, the base-loaded model, is down by only 3 dB relative to a full size monopole, which amounts to just about 1/2 S-unit.

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We encounter similar surprises when analyzing shortened vertical dipoles. We can still obtain very usable performance from a vertical dipole as small as 25% full length. The trick is to minimize losses in both the loading assembly and in the connections associated with low-impedance terminals.

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Fig. 25 shows several methods of loading a vertical dipole. Evident are the familiar center and mid-element loading systems that we have already noted. Also at the bottom of the sketch is the Moxon short-radial-plus- reactance system, which has come in for debate. All of these systems are quite usable, even if proponents of various systems cannot fully agree on their relative merits.

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The top systems are examples of double hats, one on each end of the dipole, which remains center-fed. Shortening elements by equal amounts at both ends through the use of hats having any number of radials is a tried and true technique for either vertical or horizontal dipoles. It deserves a bit more attention.

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As an experiment, I designed a 7 MHz vertical dipole about 1/4 normal length: 17.5' long, composed of 1.25" diameter aluminum, which might be a typical ham installation. The base of the antenna was 4.5' above ground, with the top at 22' up, a workable assembly for most sites. Then, I modeled 4 different ways of loading the antenna:

+

1. Center loading inductor: 1201 Ohms or 27.3 uH, with a 4-Ohm series resistance for a Q of 300.

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2. Mid-element loads at about half-way between the center feedpoint and the ends, each 1096 Ohms or 24.9 uH, with a series resistance of 3.65 Ohms for a Q of 300.

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3. Top and bottom hat loads composed of 4 spokes, each 9.35' long, and a perimeter wire, with all aluminum hat assembly wires 0.125" in diameter.

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4. Top and bottom "Tee" wires of 0.125" diameter aluminum, each wire 46.6' long.

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The results are in the table, with the gain of each antenna version referenced to a value of 0 dB for the double-Tee model.

+ 
Antenna              Relative             TO Angle             Feedpoint Z
+                     Gain dB              degrees              R +/- jX Ohms
+Center load          -2.3                 26                   11.6 - j 0.1
+Mid-el. load         -2.1                 26                   18.0 + j 0.1
+4-spoke hat          -0.3                 27                   28.2 - j 0.3
+Double-Tee            0.0                 27                   26.9 + j 0.4
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The inductively loaded versions of the antenna are significantly down in gain from the hatted versions. Most of the loss is in the inductors of finite Q. If truly lossless inductors could be used, the total spread of gain would amount to about 0.5 dB. However, the center- load antenna impedance would be about 7.5 Ohms, while the mid-element-loaded version would be about 18 Ohms. The higher feedpoint impedances shown in the chart reflect the losses in the inductors.

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Between the hatted versions there is little to choose except the most convenient installation method for a particular site. As shown in Fig. 26, the gain difference reflects a slight ovalizing of the double-Tee pattern in the direction of the wire ends. (The very slight departure from a circular pattern also shows up in a single Tee monopole over a ground plane. A full 1/4 wl monopole over a 16-radial plane at ground level, incidentally, shows about the same gain and take-off angle as these slightly elevated vertical dipoles.) Other end-loading arrangements are possible. These samples simply demonstrate the feasibility of the technique.

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8. How can we make verticals directional?

I have not stressed any particular gain figure for the sample vertical antenna systems shown because actual gain will depend on too many variables for any generalized figure to make any sense. 1/4 wl monopoles with ground plane at or near the earth's surface require large numbers of radials for maximum efficiency. Slightly elevated radial systems require close attention to symmetry to avoid pattern distortion. Gain also varies with the soil in the immediate antenna location for near-ground monopoles. The gain of both monopoles with highly elevated radial systems and vertical dipoles depends as well upon the soils in the Fresnel or reflection zone. +

Whatever our initial gain for a single vertical antenna, we can improve upon it by applying standard techniques for creating directional antennas from two or more vertical elements. In the process, we may gain a significant reduction of gain to the rear of the array of elements. In short, we may create vertical beams.

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The two most common techniques for creating vertical arrays involve either phasing the current among the elements or using parasitic elements. Fig. 27 shows in a broad way the differences in anticipated performance. Phased elements can deliver a deep null to the rear, often exceeding 30 dB relative to the maximum forward gain. However, the deep phased array null extends only over about 60 degrees of the horizon. The front-to-back ratio of parasitic arrangements rarely exceeds about 10-12 dB. In exchange for accepting a lesser front-to-back ratio, the builder of parasitical arrays has a simpler building task, since phasing techniques require extensive calculations and careful construction.8

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A 2-element array gives a broad forward lobe. Even with beam reversal techniques, much of the horizon remains outside of the main lobes. The simplest technique for covering the entire horizon with fixed vertical elements is to use 3 in a triangle and to switch them. Let's briefly examine a full-size and a shortened array of vertical dipoles to see what is involved.

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Fig. 28 sketches the outlines of three vertical dipoles set 10' above ground at their bases. For 40 meters, the dipoles ar 65.9' long, and for 30 meters they are 46.3' long. The 40-meter triangle is 22' on a side, while the 30-meter triangle is 15.5' on a side. From each dipole, a 50Ω coax stub (RG-213, VF=0.66) extends to a center junction box. The 40-meter stub is 16.4' long, while the 30-meter stub is 11.7' long.

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For each direction, one stub is connected to the shack feedline. The other two stubs are shorted to form inductive reactances that electrically lengthen the elements to proper reflector size. A typical switching box is shown in Fig. 29.

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The result is a 3-direction switchable array that can cover the entire horizon, as shown in Fig. 30.

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The array gain is about 3 dB greater than a single vertical dipole at the same height. The dual reflector system provides about 12 dB of front-to-back ratio. Although the array is about as simple as one might imagine, its chief drawback is finding supports for the tall vertical dipoles.

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We can also make an array from the short hatted vertical dipoles we briefly examined, using essentially the same 22' per side spacing of elements employed for the full size array. However, the elements can be supported from below, as suggested in Fig. 31. The sketch also hints at another change in arrangements.

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The feedpoint impedance for the driven element will be about 25 Ohms. By setting the length of the vertical (or of the hat spokes) a bit short, the driver impedance becomes capacitively reactive. If we introduce a hairpin (a shorted transmission line section) or a coil across the feedpoint, we effect a beta match to bring the impedance to 50Ω for coaxial feed.

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We leave the beta hairpins or coils across each feedpoint. Using the same switchbox that we used for the full sized array, we switch in a 1/4 wl section of coax from the box to the driver. The 1/4 wl sections from the other elements are shorted at the box, creating an open circuit at the element. The hairpin or coil now become a small inductively reactive load, electrically lengthening the element for reflector service.

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Once more, we can cover the horizon with a 3- position switch. The gain of this short array is about 2.5 to 3 dB over the gain of a single short vertical, with better than 12 dB front-to-back ratio. Although the short array cannot match the forward gain of the much taller vertical array, it can certainly be useful with respect to adding a directional dimension to one's operating.

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More complex arrays are certainly possible using 5 elements for a 4-cornered, 3-element parasitic beam system. The center element can be a voltage-fed 1/2 wl tower used to support upper HF beams, with the guy wires used for parasitic elements under proper switching conditions for electrically lengthening and shortening them. In fact, directional vertical arrays for lower HF use are limited only by the electrical and mechanical ingenuity of the builder.

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9. How can we make verticals out of wires that are mostly horizontal?

Vertically polarized radiation patterns need not come only from vertical elements. We can construct vertically polarized antenna from wire loops, generically known as SCVs (self-contained vertically polarized large wire loops). Fig. 33 shows the out line of several different types. +
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Each of these single loop versions of the SCV produce a bi-directional pattern, ranging from a broad oval for the delta loops to a peanut-shaped pattern for the rectangle and the half square. All of the antennas have a feedpoint 1/4 wl from the top center, which maximizes vertically polarized radiation. The connecting wire between the feedpoint and a point exactly opposite it on the opposing side structure acts as a phasing line by being a 1/2 wl line in which the current phase reverses. The voltage and current at the opposing points are equal in magnitude and opposite in phase, creating a pair of quarter wavelength verticals in phase. Radiation is broadside to the array. The antennas are self-contained and require no ground plane or soil treatment beneath the antenna structure.

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If space permits, the builder can develop "double- wide" version of some SCV configurations for additional gain and directivity, as shown in Fig. 34. Some names originally given to SCV configurations are misnomers. The table below provides a very general indication of relative performance by listing the gains of some common configurations at 7 MHz with a 50' maximum height.

+ 
Antenna              Gain          Front-Side           TO Angle             Feed Z
+Name                 dBi           Ratio dB             degrees              Z = R Ohms
+
+Equi. Delta          1.5           - 3                  18                   135
+R.-A. Delta          1.9           - 5                  20                    60
+Dbl R-A Delta        3.7           -12                  20                    40
+Sq. Quad             1.6           - 4                  18                   145
+Dia. Quad            1.5           - 4                  16                   135
+Rect. (MS)           3.0           -12                  17                    15
+Dbl MS               3.3           -12                  17                    80
+Open DMS             4.5           -25                  16                    30
+Half Square          3.4           -15                  18                    65
+Bobtail              5.0           -28                  18                    40
+

In the charted figures, not all of the antennas are at optimal height. Each type of SCV has an optimal height range. Below that range, ground interactions reduce gain significantly; above that range, the gain of the lowest lobe drops as a new higher-angle second lobe forms. Since SCV's are employed to take advantage of the low angle of radiation with rejection of higher-angle QRM and QRN, the secondary lobe actually reduces the desired performance.

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Two cautions about SCVs are necessary to get the most from them. First, do not have improper expectations of them. They are capable of gain and directivity relative to a vertical monopole or a vertical dipole. However, that gain is not the gain of a horizontal dipole that is at least 1/2 wl above ground. Instead, because the elevation pattern is typically the low-angle, single lobe pattern associated with monopoles, wise users expect better signal-to-noise ratios from DX signals, but not necessarily a more power signal.

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Second, design carefully. Casual design and construction of an SCV may yield disappointment. Besides having a optimal height range, each SCV type also has a optimal shape for maximum gain. In some cases, the ratio of the vertical to horizontal measure may vary with frequency.9

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Although any of the basic SCVs is already an array of 2 elements phased, it is fairly straightforward to create a parasitic beam from a pair of SCVs. Fig. 35 shows an example, a 3.6 MHz reversible half-square pair. The length of coax from the reflector is match with a similar line from the driver feedpoint to a center junction box. By switching from direct feed to a short, the line changes from a simple feedline to an inductively reactive shorted stub that electrically lengthens the non- driver to reflector status. Similar schemes can be applied to any of the SCVs to obtain a reversible beam.

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Fig 36 shows the anticipated performance from such a beam when placed at an optimum height above ground. With a forward gain of about 3 dB over a single half square and a worst-case front-to-rear ratio of over 18 dB, the antenna offers excellent low angle (DX) performance for the amateur with the space and supports for the array. This last statement presumes, of course, that we point the antenna in the right directions.

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Because SCVs require only wire and accessories, they form an attractive alternative for some locations to erecting complex aluminum structures. For each band, their height requirements are modest compared to the height needed for an equally effective horizontal antenna. On the other hand, we still need some tall trees or structures to hold up the wire.

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10. Just how "good" is a vertical?

The answer to this question depends on what is going to count as good. If what we want is an antenna for the lower HF bands that maximizes low angle radiation and reception to yield a higher signal-to-noise ratio--but not necessarily more power--for DX operation, then one or another of the vertical antennas we have surveyed may prove a superior candidate. For example, the half-square beam we have just examined will outperform a Yagi placed at the same 95' maximum height relative to DX, although not for shorter skip contacts. Fig. 37 tells the story. +
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The Yagi has more raw gain, but most of its power is at too high an angle for most DX, since the antenna height is only about 1/3 wl. The half-square beam at the same height promises more power at the lower angle.

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More modest installations can expect lesser performance, but similar patterns of performance: better contacts over longer paths and weaker signals closer in. However, even these installations must use careful construction and well-designed structures to achieve all that a vertical can give. For a monopole that is ground- mounted, 4 radials will yield something, but 30 radials will yield a lot more--and 60 or more will yield the most that the antenna can give.

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Installation also requires close attention to surroundings. Ground and near-ground mounted verticals tend to be susceptible to signal absorption by ground clutter and to noise from man-made sources. A clear field for at least a wavelength--and hopefully a lot more--is necessary for best results. Moreover, a naturally quiet location is a big help.

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For the city and suburban dweller, an elevated mounting may be best, if feasible. A roof top at least 20 to 30 feet up can reduce local noise and improve signal strength on both transmission and reception, especially for multi-band trap verticals. However, if the antenna is a 1/4 wl monopole, one must use a radial system. I personally recommend at least 4 radials for each band (using something like multi-wire flat rotor cable, or similar, or a radial fan of single wire radials spread across the roof) arranged as symmetrically as possible.

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Elevated city and suburban installations must give attention to system grounding for lightning and static charge protection, but for most elevated verticals, providing RF isolation from the ground line will prevent diversion of signals into the ground. Simple RF chokes of sturdy construction usually suffice.

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Whether circumstance forces us to use a vertical antenna or whether we choose to use one to achieve certain operational goals, the key to successful construction and operation is a better understanding of how verticals work and how various competing vertical possibilities compare in potential. My goal in these notes has been to cut away some outmoded ways of thinking about verticals, including some downright harmful and ignorant ways of talking about them.

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Even when approached with thoughtfulness, vertical installations still remain subject to an array of variables that will normally defy precise analysis short of long- term operating experience. Soils that affect far field patterns are often beyond analysis for most ham installations. Some aspects of the operation of ground planes are undergoing re-analysis and re-measurement. In the interim, certain facets of ground planes are vocally disputed, as if loud voices could make the measurements come out as desired. Alas, we must wait patiently for results to emerge before making any final pronouncements--for example, on how Christman elevated radial systems compare with surface ground plane systems.

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That does not mean that we cannot learn more about verticals. And it does not mean that we cannot use them effectively. Clear thinking goes a long way to avoiding that dizzying vertigo that has in the past infected the study and use of vertical antennas.

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Notes

1. If you are serious about studying vertical antennas, begin with any recent edition of The ARRL Antenna Book, although the information is scattered in many chapters. The ARRL Antenna Compendium series has many good articles as well. The Amateur Radio Vertical Antenna Handbook, by Paul Lee, N6PL, is by now a classic, as is All About Vertical Antennas, by Bill Orr, W6SAI, and Stuart Cowan, W2LX. Vertical Antenna Classics from ARRL is a collection of relevant articles. For lower HF applications, the most complete study remains Antennas and Techniques for Low-Band DXing, by John Devoldere, ON4UN. +

2. The following table may help you appreciate soil differences better. The table represents an adaptation of values found in The ARRL Antenna Book (p. 3-6), which are themselves an adaptation of the table presented by Terman in Radio Engineer's Handbook (p. 709), taken from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. Terman's value for the conductivity of the worst soil listed is an order of magnitude lower than the value shown here.

+ 
Soil Description                           Conductivity    Permittivity    Relative
+                                                in S/m          (Dielectric     Quality
+                                                                Constant)
+Fresh water                                     0.001           80
+Salt water                                      5.0             81
+Pastoral, low hills, rich soil, typical from
+Dallas, TX, to Lincoln, NE                      0.0303          20              Very Good
+Pastoral, low hills, rich soil, typical of OH
+and IL                                          0.01            14              Good
+Flat country, marshy, densely wooded, typical
+of LA near the Mississippi River                0.0075          12
+Pastoral, medium hills, and forestation, typical
+of MD, PA, NY (exclusive of mountains and
+coastline)                                      0.006           13
+Pastoral, medium hills, and forestation, heavy
+clay soils, typical of central VA               0.005           13              Average
+Rocky soil, steep hills, typically mountainous  0.002           12-14           Poor
+Sandy, dry, flat, coastal                       0.002           10
+Cities, industrial areas                        0.001           5               Very Poor
+Cities, heavy industrial areas, high buildings  0.001           3               Extremely Poor
+

3. The best compact treatment of soils and antennas is Chapter 3 of The ARRL Antenna Book.

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4. See Antennas and Techniques for Low-Band DXing, by John Devoldere, ON4UN, pages 9-30 to 9-31.

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5. Here is a convenient, but neither authoritative nor exhaustive, set of ground types or classifications that may be useful in sorting out various aspects of ones antenna system:

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G1. The DC and static discharge ground

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G2. Circuitry common bus (ground)

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G3. Lightning ground

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G4. RF ground

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G5. Far field reflective ground

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G6. Antenna-completion ground

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Only the last type of ground is under discussion, and it does not require THE ground to function. It is in the near field of the antenna, but is not itself the near field ground in the same sense in which we speak of the far field ground. The only time THE ground comes into play is when the antenna-completion ground--or plane--is under, on, or very near THE ground.

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6. All models of verticals with ground planes have gone through a thorough development to avoid some modeling pitfalls. They originate with free space dipoles, with their standard 72-Ohm feedpoint impedance. Then, the model replaced the lower leg of the dipole with a set of radials (ranging from 2 through 64 in various steps), in each case, with the radial lengths adjust for resonance. At each step, the models were convergence tested (that is, the number of segments per unit length increased in steps) to establish the internal coherence of the model. Models were also checked to assure that the feedpoint represented as closely as possible the maximum current position on the antenna, with the sum of the adjacent segment currents equal to the source current.

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7. The notion that a radial-plane monopole has a feedpoint impedance of 36 Ohms arises from the theoretical exercise of modeling a monopole as a simple vertical element above a perfect ground, thus automatically giving an impedance of 1/2 that of a dipole. In fact, modeling programs will yield the same result, since they create a mathematical image antenna beneath the modeled one. In fact, the source impedance of a real radial-plane monopole varies considerably due to factors not accounted for in the dubious image-antenna calculational convenience. The ratio of diameters of the main element and the radials plays an important role in the feedpoint impedance, as it also does in determining the length of radials for resonance. We obscure these facts with assumptions carried into the field site and also be laying radials and them adjusting the monopole height to achieve resonance. Under these conditions, one rarely if ever achieves maximum current at the feedpoint.

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8. The best sources for basic information on phased vertical arrays is The ARRL Antenna Book, Chapter 8, and Low Band DXing, Chapter 11.

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9. More complete details on the SCV family of antennas can be found in a series of articles appearing in 1998 and 1999 issues of The National Contest Journal. The articles can also be found at SCVs: A Family Album.

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Updated 5-19-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, HF Lower, Half Square, Loading, SCV, Vertical


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Do the VOMBA! Vertically Oriented Multi-Band Antennas

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This talk, on the basics of vertically oriented multi-band antennas, was originally prepared for the 2000 Dayton FDIM Symposium

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Among the more popular antennas used by QRP enthusiasts is the VOHPL, the vertically oriented, horizontally polarized loop, consisting of about 1 wl of wire at the lowest frequency used. Within this group of antennas are the delta--both equilateral and right-angle--the square and diamond quad loop, and the rectangle. When vertically oriented, we must feed them at the top or bottom center to make sure they are horizontally polarized. Fig. 1 shows just one of the many VOHPL configurations.

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Fig. 1 also shows a second vertically oriented array: the Lazy-H. One of a number of in-phase-fed arrays, the Lazy-H is also horizontally polarized. In traditional terms, this is a broadside array, since radiation is strongest perpendicular to the plane defined by the two radiating wires. (In contrast, a Yagi is an end-fire array, since radiation is in the plane of the elements.)

+

We often operate either type of antenna on more than one band. Hence, we obtain a bigger category of antennas: the VOMBA: the vertically oriented multi-band antenna.

+

We can also feed the loops on their sides and arrive at vertically polarized antennas (VOVPLs), but they tend not to be good performers on bands other than the one for which they are cut. Yet, we still have an interesting question. Suppose that we take a loop and move the feeder to the corner. It is not at the center of a horizontal wire, so it is not purely horizontal. It is not up the antenna side, so it is not purely vertical. So what is it? It is a hybrid with the properties of both a horizontal and vertical antenna. Before we are finished, we shall look at one especially interesting version of this hybrid: the W6RCA right triangle.

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The next question is a simple one. What do we want to accomplish in our exploration of VOMBAs? Essentially, we want to know which--if any--of the many types of VOMBAs makes the best multi-band antenna. We have to have a baseline, and I shall arbitrarily select 40 meters for that reference point. Except for a couple of specific antennas, we shall cut the VOMBAs for 40 meters and see how they do on bands above 40 meters.

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Why 40 meter? A wavelength at 40 meters is about 140' long. We can make rectangles and triangles with top heights of 35 to 70 feet and still squeeze most of the loop into the space below. Since space is at a premium in most urban and suburban station locations these days, 40 meters is the most common loop we would discover in a survey.

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Here is we shall proceed. First, we shall look at the most tempting antenna group--the loops. Then we shall take a quick look at the 40 meter doublet as a standard of comparison by which to judge the loops. Third, we shall examine the W6RCA corner-fed triangle to see how it differs from the loops and the doublet. Finally, we shall explore the expanded Lazy-H to see if a phase-fed array can compete with the loops.

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Along the way, as is my habit, I shall present a lot of information in the form of antenna model patterns and tables of modeled output data. In all cases, the antennas are perfectly amenable to modeling, since their structures do not come close to the limits of NEC or MININEC. The one major limitation is the average ham's cluttered environment. Models usually use a clear horizon, but we hams live in object-filled yards. The end result is always a slight adjustment to the numbers when you actually build a VOMBA.

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The VOHPL on Many Bands

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Many would-be loop builders want to use VOHPLs on frequencies above their fundamental. With parallel transmission line and an ATU, multi-band operation is certainly possible. The key question is this: what do we get for our trouble? And how does the VOHPL stack up against other possible multi-band antennas. Patterns and performance data for the 135' center-fed antenna, the 102' center-fed antenna, the 135' end-fed Zepp, and the 135' off-center-fed antenna have been presented in past FDIM sessions, and a complete set of patterns for all of the HF bands are available at my web site. The compendiums of patterns for these antennas will make excellent comparative references for you as you try to decide which multi-band wire to build. Developing this reference library of patterns and data is one of the reasons for the web site and for the series of articles in Low Down called "Antennas From the Ground Up."

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For the VOHPLs, we shall vary the procedures that I have used for the other antennas. For most antennas, I have simply presented each antenna, its pattern, and its data. Among VOHPLS, there are simply too many variants to analyze one pattern at a time. Therefore, we shall begin with a collection of types of patterns that occur on various bands with the VOHPLs, labeling each with a letter. Then, we shall tabulate the modeling results for each type of VOHPL on each band, referring to a pattern by letter (if one exists in our collection). We shall also list other data, such as maximum gain, elevation angle of maximum radiation, and approximate feedpoint impedance.

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All antennas in the VOHPL collection will have a maximum top wire height of 66' as representative of a maximal backyard ham installation. All of the modeled data emerge from EZNEC (using NEC-4.1, although NEC-2 is perfectly adequate to modeling these antennas). The modeled antennas are constructed of #14 copper wire over average ground (conductivity = 0.005 S/m; permittivity [also called relative dielectric constant] = 13). Since these antennas are all horizontally polarized, the actual ground or soil quality will have minimal affect on performance.

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Let's begin our catalog of antenna pattern types.

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A1: The Rounded Oval

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The oval azimuth pattern in Fig. 2 is typical for horizontal wire antennas at heights under 1/2 wavelength (wl). The lower the height, the more circular the pattern. As we increase the height, the radiation off the ends or edges of the antenna decreases. Gradually, the pattern becomes dimpled and fades into the next pattern type (A2).

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We should not neglect the elevation portion of Fig. 2. The egg-shaped pattern just touches the out ring at a high angle. Maximum signal strength for this example is around 60 degrees above the horizon, the "take-off" (TO) angle. For distant signals, we are much more interested in radiation at much lower levels. The 40-meter range of most- desired elevation angles might be from 15 to 30 degrees, while the 10 meter range might be 5 to 15 degrees. You can interpolate values for the bands between. These rules of thumb (which often have exceptions) apply not only to this pattern, but as well to every other pattern in this group.

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A2: The Peanut

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The peanut, shown in Fig. 3, is a natural evolution from the oval. With doublets, this pattern is what happens when you elevate the antenna.

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Notice not only the deeper side nulls, but also the lower TO angle of the elevation pattern.

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B. The High Oval

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The high oval in pattern B (Fig. 4) is distinct, but not because of the shape of the azimuth pattern. This portion of the pattern can range from a near circle to an indented square. It occurs usually at frequencies above the baseline frequency for which a VOHPL is designed.

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The key to the high oval is the elevation pattern. Note that the strongest radiation is straight up--or nearly so. What emerges at lower angles is relatively weak. In general, this is not a desirable pattern for an antenna on any of our favorite bands.

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C1: Very Small Wings

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With VOHPL loops operated above their fundamental frequency, patterns do not always break up in the ways typical of doublets. We do not obtain cloverleaf or daisy-petal azimuth patterns. One of the variations for lobe formation (shown in Fig. 5) is the development of side "wings" off the edges of the antenna. In most cases, when these wings are small, antenna performance tends to be good. If you examine the elevation pattern for C1, you will see that its TO angle is in the vicinity of the elevation pattern we called the peanut (A2). This is a pattern with which we can easily live in a multi-band antenna.

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C2: Large Smooth Wings

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Large smooth wings, shown in Fig. 6, develop as we change the loop shape or increase the frequency somewhat further. Notice that now the radiation is off the edges of the loop and is no longer broadside to it. In addition, the elevation pattern is marked by multiple lobes. For any given case, either the lower or the upper lobe may be stronger--or they may both be at about the same strength.

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If we note on which bands this type of pattern occurs, it may be quite usable. We simple have to remember that signals will be stronger off the edges of our loop.

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C3: High-Angle Wings

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Sometimes, the development of side-wings in the azimuth pattern is accompanied by an almost complete loss of low-angle radiation. Fig. 7 shows the patterns for such a case, which is common on the upper HF bands for some 40-meter loops. Although the azimuth pattern may show a high gain figure, the gain is often at angles too high in the upper HF region to do more than bring in an occasional E-layer signal. For general operation, C3 is not at all a desirable pattern.

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Virtually all of the radiation patterns of 1 wl VOHPLs will fit one of these general patterns, although the gain and precise elevation angle of maximum radiation will vary widely. However, with this catalog in hand, we can efficiently characterize the radiation pattern of a VOHPL on every band of operation.

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Now we are ready to look at the individual possible vertical loop antennas of the VOHPL collection. The following tables--for two kinds of deltas and for two kinds of rectangles--provide data on take-off angle, maximum gain, approximate feedpoint impedance, and pattern type.

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1. The Right-Angle Delta

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The right-angle delta appears in Fig. 8. With a top height of 66', it has a lower horizontal wire at about 36.6' up. In the table following the sketch of the right-angle delta, the lowest angle data are shown if the lowest lobe is either dominant or if it is close to equalling a higher more dominant lobe.

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In addition to the data shown, it is useful also to examine modeled data on the -3 dB beamwidth both horizontal and vertical. This information gives clues to the shape of the lobes.

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        40          5.9          240 -j   5       A1
+10.1        28          7.6         2150 +j2055       A2
+14.15       36          7.1          120 -j  20       A2
+18.1        22          8.5         1055 -j 910       C1
+21.15       13          7.5          215 +j 130       C2*
+24.95       65          8.1         1515 -j1700       B
+28.5        15          8.0          405 +j 195       C3
+*  15 meter patterns vary depending on elevation angle.
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The B and the C2-C3 patterns on the upper bands on a 40-meter right-angle delta limit the effectiveness of this loop above about 30 meters.

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2. The Equilateral Delta

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An equilateral delta (Fig. 9) is taller but narrower than its right-angle cousin. With a 66' top, the equilateral delta is about 12' closer to the ground at the bottom. This makes a difference in the performance, especially above 40 meters.

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        46          5.3          135 -j   5       A1
+10.1        33          5.7         2380 +j1160       A1/2
+14.15       43          6.1          265 +j  70       A2-B
+18.1        43          6.4         1255 -j2135       B
+21.15       30          4.3          110 +j 160       C2/3
+24.95       14          5.4         2055 -j1655       C2
+28.5        20          6.6          315 +j 305       C3
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For the same top height as a right angle delta, the equilateral delta has a lower gain on every band, accompanied by generally higher TO angles. The exceptions to this trend appear on the upper bands, where the length of the sides exceeds 1/2 wl and thus changes the patterns more radically relative to the slightly shorter sides of the right-angle delta.

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The presence of B through C3 patterns from 20 meters upward limits the effectiveness of the equilateral delta as a multi-band antenna.

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3. The Square Quad Loop

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A square quad loop (Fid. 10) cut for approximate resonance on 40 meters at about 66' high places its lower wire at about the 30' level. The square shape makes this VOMBA among the most compact of those we have so far examined. Again, the change in length and orientation of the sides will give this version some distinct performance trends, compared to the deltas.

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        35          6.3          145 -j   5       A1/2
+10.1        24          7.6         2900 +j2760       A2
+14.15       48          6.7          290 +j  65       B
+18.1        35          7.2         1215 -j1640       B
+21.15       14          5.0          255 +j  50       A*
+24.95       16          6.8         1520 -j1400       A**
+28.5        45          7.9          295 +j 185       C3
+* Very "square" oval
+** Very narrow beamwidth
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For the lower HF bands, the quad loop offers generally lower TO angles and higher gain than the deltas. However, its utility on 20 meters and up is very limited by B and C3 patterns, as well as a very narrow beamwidth on 12 meters.

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4. The Rectangular Quad Loop

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A horizontally fed quad loop increases in gain at its fundamental frequency when stretched vertically. However, the more common ham configuration is to stretch the loop horizontally. For multi-band operation, this stretch-mode is not necessarily a disadvantage, since it places the bottom wire higher, promising at least a lower elevation angle for signals. If the top wire of the model in Fig. 11 is at 66', the lower wire will be 46' up for this particular rectangle. (Since we can make rectangles with any ratio of height to length, this model is just a random sample.)

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A second feature of stretching the loop horizontally is to raise the feedpoint impedance on the fundamental frequency. If we had the room to stretch the quad up and down, we would have seen a drop in the feedpoint impedance. In either case, the impedances for bands above the fundamental are not greatly affected by any of our reshapings.

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        37          6.2          285 +j  10       A1
+10.1        26          7.6         2655 +j1135       A2
+14.15       40          3.3          135 -j  30       B
+18.1        19          8.4         1930 -j2365       A1
+21.15       12          9.4          155 -j  75       C2
+24.95       11          7.6         2505 -j 555       C2
+28.5        43          7.9          385 +j  60       C3
+

On the lower bands, the performance of the rectangle is generally comparable to the square quad loop. On the upper HF bands, there is a trend toward higher gain and lower TO angles, but, it does not extend to all of the bands. 20 and 10 meters remain under the weight of B and C3 patterns, which limits the effectiveness of the antenna on these bands.

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Overall, the VOHPL group does not show outstanding characteristics in multi-band service. On at least two bands per antenna, we encounter either B or C3 patterns. The high TO angles of these patterns limit long-range skip performance on just the bands where we want it. Moreover, lower angle radiation tends to be weaker than for other pattern types.

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These problems are not fatal to enjoying one of the loops as the multi-band antenna for a station. Effectiveness depends also on other factors. 1. Is this the only antenna my yard can support? If so, then we can tailor our operation to use the antenna on the bands where it is most effective. 2. What are my favorite bands? If the list coincides with the bands on which one of the loops is quite effective, then we have a match that will be hard to beat. On the other hand, if our favorite bands fall where the loops are least effective, it is time to think of other antenna possibilities.

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Before we leave the VOHPL group altogether, let's pose one more question: What is an appropriate standard of comparison to use in trying to decide if a vertically oriented loop has enough performance to justify its existence in my yard? There is not single answer to this question. However, we can provide a reasonably fair comparison with a rather basic antenna.

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Our top height is 66' for this exercise. Suppose that we also have 67' for the length of a wire antenna. Why not try a simple 40-meter doublet as our multi-band antenna?

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The 66' Doublet

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A 67' doublet is approximately resonant on 40 meters (Fig. 12). At a height of 66', it is also about a half wavelength up, which is a reasonably good height for dipole performance. Above 40 meters, the antenna become a doublet for open wire transmission line and ATU use. As the table shows, it acquits itself quite well.

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        28          7.3           70 -j  10       A2
+10.1        20          8.1          275 +j 800       A2
+14.15       15          9.0         4670 -j 345       A2
+18.1        11          10.5         175 -j 860       D
+21.15       10          8.4          100 -j 115       E
+24.95        8          9.3          375 +j 730       E-F
+28.5         7          9.5         3265 +j 375       F
+

Overall, the doublet displays a lower TO angle on every HF band compared to the entire collection of loops having the same top height. This fact is not hard to explain. Even with a favorable pattern, the loop elevation angle of maximum radiation is a composite function of the low angle off the top wire and the higher angle off of the bottom wire. The doublet, with only a top wire, does not have its TO angle lowered by the presence of a lower wire.

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The doublet also exhibits a very different pattern of feedpoint impedances across the bands relative to the entire collection of loops. Since the doublet starts out only 1/2 wl long, rather than 1 wl for the loops, the feedpoint impedances will reflect its total length on any given band. On 20 and 10 meters, it is an even number of wavelengths and hence shows very high feedpoint impedances. These impedances need not defeat use of the antenna, since the exact values of R and X will vary along the open-wire feedline. Careful length selection can present the antenna tuner with easily handled values.

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The gain of the doublet also tends to exceed that of the loops on all bands. For the lower three bands, the A2 peanut patterns assure a signal direction perpendicular to the wire length. However, on the upper four bands, the patterns will differ from anything we have so far examined.

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D. The EDZ Pattern

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Fig. 13 shows a typical set of azimuth and elevation patterns for an extended double Zepp--or EDZ. On 17 meters, the 40-meter doublet is about 1.25 wl long and hence exhibits these patterns. The azimuth pattern main lobe is considerably narrowed relative to our typical peanuts (A2), and new lobes are beginning to show up as a set of "ears" on the azimuth pattern. However, the elevation pattern remains very well behaved, with much of the energy concentrated at low elevation angles.

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As we increase the frequency still further, we can expect the new lobes to increase in size. An equivalent move would be to keep the frequency at 17 meters and to increase the length of the antenna wire. In either case, we would be setting the antenna at something approaching 1.5 wl. At this length, that antenna pattern shows us something new.

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E. The 6-Petal Pattern

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When the antenna is about 1.5 wl long, the 6-petal pattern of Fig. 14 emerges. Here, we have radiation lobes of roughly equal strength in 6 different direction. This is the 40-meter doublet pattern on 15 meters. Since the elevation patterns of the doublet are so well-behaved, I have omitted them in these figures.

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F. The 4-Petal Pattern

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On 10 meters, the 40-meter doublet is 2 wl long. Its azimuth pattern, as shown in Fig. 15, becomes as 4-petal affair.

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Someone may ask how we lost 2 petals when "everyone" knows that making doublets longer tends to increase the number of lobes. Perhaps a useful way to look at the situation is with a simple bit of arithmetic.

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If the doublet is an integral number of wavelengths long (that is, 1, 2, 3, . . .), then the number of lobes will be exactly twice the length in wavelengths. However, lobes do not simply appear and disappear as we change the antenna length. Rather, they grow and shrink. As we grew from 1 wl to 2 wl, the 1-wl broadside lobes shrunk, while the 2-wl lobes emerged and grew. At about 1.5 wl, both sets were the same size. Hence, 6 lobes. The general rule is something like this: at any half wavelength point between integral numbers of wavelengths, the doublet will show a number of lobes that is the sum of those for the lower integer and those for the upper integer. Hence, the 1.5 wl doublet had 2 lobes for a 1-wl antenna and 4 lobes for a 2-wl antenna, for its total of 6.

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With these easy formulas in mind, you can readily imagine the 40-meter doublet on 12 meters, where the pattern is listed as E-F. We would expect to find the 2 wl lobes dominating the overall azimuth pattern, with traces of the broadside 1 wl lobes still visible, but not too strong. This situation is just the opposite case from the EDZ pattern, which is closer to 1 wl long. With the EDZ, the 1-wl broadside lobes were dominant, with traces of the emerging 2-wl lobes visible as "ears."

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Our small safari into the jungle of lobe formation for doublets has a point. We have noted that, in general, the performance of the doublet is superior to that of the loops in terms of gain and elevation angles of maximum radiation. However, that improvement comes at a price. On the upper HF bands (15 through 10 meters), the main lobes of the pattern are no longer broadside to the antenna wire. Therefore, as we change bands in this high frequency region, our radiated energy tends to go in different directions. What we gain in gain, we lose in terms of controlling where our signals go. The question of control is a potential problem (but not for everyone) to which we shall return before ending the exercise.

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However, at this point in our journey, I must reach a conclusion that no VOHPL fan wishes to hear. Given the choice of a 1 wl vertically oriented horizontally polarized loop and a doublet at the height of the loop's top wire, I would choose the doublet. Of course, that decision assumes two high support points. Deltas remain the choice of hams with only one high support point.

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The Hybrid Triangle

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Let us not, however, give up wholly on 1-wl loops. The results we have examined so far characterize loops that are fed at a center point along one of the loop's horizontal wires. The centered feedpoint ensures that the loop will maximize its horizontally polarized radiation.

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In other places, I have extensively discussed a class of antennas called SCVs, the self-contained, vertically polarized 1-wl loops. Although this group includes the half-square and the bobtail curtain, let's confine ourselves to loop versions. Any of the four loops we have examined can be converted to an SCV. For the rectangle and the square quad loop, we simply move the feedpoint to the middle of the vertical leg. For the two deltas, we move the feedpoint to a position 1/4 wl down from the apex of the triangle. In the process, we shall likely have to alter the delta dimensions a bit to restore resonance.

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SCVs show patterns in which the vertically polarized radiation field dominates. The horizontal field tends to cancel itself. Gain is not high, but the radiation angle is very low--a boon to low HF band DXing. However, as a group, SCVs tend to be poor performers as multi-band antennas. Once more, I would prefer a simple doublet to an SCV on the upper HF bands.

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What we have not so far considered is a hybrid loop: a 1 wl antenna that is not fed for either horizontal or vertical polarization. Instead, it is fed somewhere between those two extremes. If we do not go too far toward the purely horizontal feedpoint, we might retain some of the low elevation angle of the SCV. At the same time, if we go far enough, we might obtain some gain from the growing horizontal radiation pattern that no longer cancels itself out.

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To test this idea, let's look at one interesting example of an antenna designed to achieve just these goals. The sample is the corner-fed triangle developed by W6RCA and shown in the sketch in Fig. 16. With #12 AWG copper wire, the antenna is 55' long at the top, which is set at a 60' height. The vertical dimension is 30', which places the feedpoint (the "dots" in the lower right corner) 30' above ground. Dimensions are not critical, but every variation will alter the performance a little bit.

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One of the conveniences Cecil Moore designed into his wire creation is an accessible feedpoint. At the corner, the feedpoint is easier to support than when we place it at the center of a wire. As well, the feedpoint is at the lowest point of the antenna.

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Now we have only two questions to ask. How well is it likely to perform? How does it achieve the performance? We can answer the first question with another model data table.

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+Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        18          2.2           41 +j   5       A1
+10.1        26          6.2         8000 +j 525       Fig. 17
+14.15       17          7.6          150 +j 145       Fig. 18
+18.1        14          8.6          695 -j1125       Fig. 18
+21.15       12          8.5          295 +j 310       Fig. 18
+24.95       10          9.2          625 -j 955       Fig. 19
+28.5        25          8.0          445 +j 525       Fig. 20
+
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On 40 meters, the behavior of the W6RCA triangle is similar to that of an SCV. The gain is limited, but the TO angle of 18 degrees promises quiet reception for hearing DX signals. Note that the feedpoint impedance for this band is also similar to what we expect from SCVs.

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On the other bands, the triangle exhibits a somewhat unique pattern of feedpoint impedances, including the very high value on 30 meters. These values for the vertical and horizontal components of the total far field patterns result from side lengths and their mutual coupling on each of the bands above 40 meters. As we change bands, the horizontal field comes to play an increasingly dominant role in the total pattern--hence, the improved gain values above 40 meters.

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To understand the remainder of the modeled performance predictions, we must look at some more azimuth patterns. In this case, we shall show both the vertical and horizontal far fields along with the total field. How the two "sub-fields" combine to produce the overall field is interesting in its own right.

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As an side note, let's look briefly at the relationship among the vertical, horizontal, and total field components of the far field patterns that have become so familiar to us from articles based on antenna modeling. For any given heading from the antenna, the total field is a function of the vertical and horizontal fields. How they relate involves logarithms to the base 10. Using antilogs (the reverse of logs), we extract the power ratios from each subfield and add them together. Finally, we take 10 times the log of the sum. The result is summarized in an equation that looks like this.

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This is not an equation to be memorized or put on a 3x5 card by the computer--such as we do with SWR formulas. Instead, I have noted it in passing to remind you that there is a very clear relationship among the components of the far field patterns we use to indicate the potential performance of antennas. With this in mind, we can better understand the composite azimuth patterns of the W6RCA triangle as we move to frequencies above 40 meters.

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Fig. 17 shows the azimuth pattern of the triangle on 10.1 MHz, where the TO angle is 26 degrees. In general, the pattern qualifies as an A pattern, but with a difference. The left side is a peanut, while the right side is an oval, giving us a kidney bean. The feedpoint and the vertical leg of the triangle are at the right, as shown in the sketch in Fig. 16. The antenna is 30' above ground, for a top-wire height of 60'.

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Although the horizontal field is relatively well formed, the vertical field is stronger in the direction away from the wires extending from the vertical leg. The resulting composite total pattern shows a null to the left and almost a bulge to the right. But, the main strength of the field is broadside to the triangle.

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Fig. 18 shows the pattern at a 14-degree TO angle for 18.12 MHz.

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This pattern is a stage in the evolution of the pattern as we move further upward in frequency. The 4-lobe 2-wl pattern is evident in the horizontal component. The vertical component is once more stronger away from the more horizontal legs of the triangle, making the null to the right much more shallow. Note, however, that the vertical component also has 4 lobes, even if not well-formed. (In some patterns, especially for antennas having complex geometric shapes, identifying lobes can be difficult, since the null between lobes may not be evident.) Moreover, the vertical pattern lobes are roughly where the horizontal component has nulls.

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Fig. 19 makes the relationship of the vertical and horizontal components even more graphic. The pattern is for 12 meters with a TO angle of 10 degrees. In this 6-petal pattern, the locations of lobes and nulls of the component patterns are very clear. Note that, except for the new lobes that are emerging with the rise in frequency, the trend in pattern development follows that of the preceding two figures. The notable difference is in the vertical component field: at 12 meters, the field is slightly stronger in the direction of the horizontal wires, not away from them. +

On 10 meters, the pattern grows even more complex. From the table, we can note the higher than expected TO angle. Once more, the mutual coupling and lengths of the three wires of this antenna form a complex set of relationships as we move to a frequency that is now 4 times the original 1 wl resonant frequency of the antenna on 40 meters. Fig. 20 illustrates the results of these relationships with the 10-meter elevation pattern, where the right side of the pattern represents the direction from the vertical side of the triangle.

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Had the field in Fig. 20 not been a complex composite of both vertical and horizontal components, we might have classified it as a type B or C3 pattern, with only high-angle radiation. The third lobe from the horizon on the right side might have been the strongest. The composite field, however, yields an intermediate TO angle at about 25 degrees above the horizon, with a weaker lobe at about 7 degrees. Since this lobe is only about 2 dB down from the strongest lobe, we may still find some long distance skip signals.

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Looking at the component fields of a total far field can help us understand just how the total field emerges. The vertical and horizontal components are also indicators of likely signal strength for clear path point-to-point communications with either vertical or horizontal antennas. However, these clear paths occur only for local communications--and even then, the clutter and terrain may modify them. Hence, locally, we often achieve better signal strength than cross-polarization might predict.

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For distant or skip communications, we are most interested in the total far field pattern of radiation (or receiving sensitivity) with respect to any antenna design. Refraction of signals within the layers of the ionosphere tends to skew polarization, so that for most communications purposes, we may concern ourselves only with the total field.

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Despite the limitations of the W6RCA triangle, it represents a perfectly usable general-purpose wire antenna for 40 through 10 meters. As we increase frequency, the total pattern comes more and more to resemble that of the 67' doublet at about the same top height. In some ways, the performance figures for the doublet are marginally superior. However, the triangle offers two mechanical advantages. First, it requires a span of only 55' or so (for support ropes). Second, the feedpoint connection is only 30' above ground rather than 60' plus. The cost is this: the triangle requires twice as much wire.

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If you alter the dimensions of the triangle--for example, making it taller and shorter, then the patterns we have shown will vary somewhat. Local ground clutter may also create some differences. The patterns are for general guidance, and do not predict performance perfectly.

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The EDZ and the Lazy-H

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Gain is not everything in wire antennas. One of the shortcomings that we encountered with the VOMBAs we have so far explored is that the radiation patterns do not maximize in the same direction on all bands. Hence, if we align the wires north and south, hoping for east-west communications, we do not achieve our goal on all bands. This situation is not a problem for everyone, but let us suppose for a short while that consistent pattern direction from 40 through 10 meters is a major goal. Is there an antenna that will let us reach this goal--and still have reasonably good gain on all of the bands?

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The answer is yes, although it may come as a bit of a surprise. Let's make a doublet that is only 44' long. Since we have been putting our VOHPL top wires at 66' up, let's use that height for our new short doublet. Fig. 21 shows the super simple arrangement.

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Notice that the sketch bears a second name for the antenna: the 10-meter extended double Zepp or EDZ. On 10 meters, the antenna is about 1.25 wl long, the standard EDZ length. On 15 meters, the antenna is just about 1 wl long. On 30 meters, it is just a bit short of a 1/2 wl dipole. On 40 meters, the antenna is in the vicinity of 3/8 wl long.

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A doublet length of between 1/3 and 3/8 wl is about as short as we would wish to go. As we shorten the doublet further, the feedpoint impedance shows a very low resistance and a very high reactance--a combination that may challenge our antenna tuners. At the 3/8-wl mark, we still have most of the gain of a 1/2 wl dipole, with feedpoint resistance and reactance values that most tuners can handle. We might have to adjust the feedline length to put a favorable combination of resistance and reactance at the tuner terminals, but this is standard practice.

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As a little exercise, lets' tabulate the modeled performance from the 44' doublet and compare the numbers to those from the 67' doublet at the same height.

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a.  The 44' Doublet
+Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        29          7.0           25 -j 580       A1/2
+10.1        20          7.6           55 -j 100       A2
+14.15       15          7.7          195 +j 385       A2
+18.1        12          8.6          920 +j1565       A2
+21.15       10          9.0         4160 +j 155       A2
+24.95        8          10.4         520 -j1545       A2-D
+28.5         7          10.5         140 -j 650       D
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+b.  The 67' Doublet
+Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        28          7.3           70 -j  10       A2
+10.1        20          8.1          275 +j 800       A2
+14.15       15          9.0         4670 -j 345       A2
+18.1        11          10.5         175 -j 860       D
+21.15       10          8.4          100 -j 115       E
+24.95        8          9.3          375 +j 730       E-F
+28.5         7          9.5         3265 +j 375       F
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Overall, the gain picture favors neither antenna. Gain on the lower HF bands favors the 67' doublet, but on the upper bands, the 44' doublet shows its advantage. Part of the reason for the higher gain in the upper HF region appears in the tables, where the 67' doublet patterns are labeled E and F. Compare those patterns with Fig. 22.

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By setting the maximum length of the doublet at the 1.25-wl mark on the highest frequency we plan to use, we obtain bi-directional patterns for all of the bands (40 through 10 meters). The same principle can be applied for any 4:1 frequency ratio: for example, an 88' EDZ/doublet to cover 80 through 20 meters with bi-directional patterns.

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For every antenna advantage, there is a potential disadvantage to consider. As we increase the operating frequency with our 44' doublet, we encounter a narrowing beamwidth. We also acquire deeper nulls off the ends of the antenna. For some operators, these are desirable properties; for others, they limit the sphere of communications. Let's catalog the evolution of the beamwidth and front-to-side ratios.

+ 
Freq.       TO          Beamwidth   Front-to-Side
+MHz         Ang         degrees     Ratio- degrees
+7.15        29          94           9
+10.1        20          83          15
+14.15       15          72          20+
+18.1        12          60          30
+21.15       10          51          40
+24.95        8          40          35
+28.5         7          31          20
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Beamwidth generally means the distance in degrees between points on the pattern that are 3 dB lower in gain than the maximum gain. Although a 31-degree beamwidth (on 10 meters) is perfectly adequate for covering all of Europe from points within the US, a 44' doublet broadside to Europe would have some difficulty on paths to Africa on 10 meters.

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The chart also answers the question of from where the 44' doublet gets its upper HF gain advantage over the 67' doublet. The narrower beam width and the 2-lobe pattern place more power in the primary direction for the antenna pattern. This answer covers most of the gain, but remember that it represents 2-dimensional thinking. Antenna patterns have a third dimension. Although not too important in the present case, that third dimension will become very important shortly.

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For the person whose objectives include knowing just where his or her signal is going, the 44' doublet is an elegantly simple solution to having a single element that covers 40 through 10 meters. There are no rules that demand that we make the antenna from wire. If we are up to the mechanical task, we might make the element out of aluminum tubing and mount it atop a tower. We would need a mast extension to hold some truss ropes. We would also have to use great care in routing the parallel feedline around the rotator to the element and then away from the tower leg on the way toward the shack. However, if you can put a 66' tower in place and construct a 44' aluminum element, these extra tasks will seem minor.

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Before we get carried away in grand plans for a rotatable 44' doublet, let's remind ourselves that our subject is VOMBAs, vertically oriented multi-band antennas. The 44' doublet, like the 67' doublet, is not a true VOMBA, since it lacks a vertical dimension. However, the 44' doublet forms the basis for a true VOMBA, the extended Lazy-H.

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The classical Lazy-H consists of two wires, each 1 wl long and separated vertically by a 1/2 wl distance. Both wires are center fed by equal-length phasing lines to a center point, from which we bring the main feedline back to the shack and its ATU. Various schemes have been developed to allow for feeding the array from the bottom with 50-Ohm coax, some of which can be found in the Editors and Engineers Radio Handbook.

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The earliest reference I have found to the expanded version of the Lazy-H is in a November, 1968 article in CQ by John Schultz, W2EEY. Bill Orr resurrected the antenna in the 1980s in one of his regular Ham Radio columns. The key to the array lies in increasing the element length to 1.25 wl and the spacing to 5/8 wl, as shown for a 10-meter version in Fig. 23.

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We have some options in how we think about the expanded Lazy-H for 10 meters. Actually, the antenna is a standard 1-wl by 1/2-wl Lazy-H for 15 meters. Alternatively, it is an array of 2 10-meter EDZs, each 44' long. However, we think about the antenna, the spacing is 22', so if we place the top wire at 66' up, the bottom wire is at the 44' mark. If we have the ability to put up a 44' wire doublet, the odds are that we can also construct an expanded Lazy-H.

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How well will the expanded Lazy-H perform across the 40 through 10 meter range?

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Freq.       TO          Gain        Impedance         Ptn
+MHz         Ang         dBi         R ± jX
+7.15        33          6.4           10 +j  95       A1/2
+10.1        24          8.1           50 +j 105       A2
+14.15       17          9.0          385 -j 395       A2
+18.1        13          10.9          45 -j 125       A2
+21.15       11          12.5          20 -j  15       A2
+24.95       10          14.6          15 +j 115       A2-D
+28.5         8          15.1          65 +j 425       D
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Let's notice a few special features of the table of modeled performance values. First, we do not need to add a table of the horizontal beamwidths, since they would be almost exactly the same as those for the 44' doublet. Second, the TO angles for the Lazy-H are very slightly higher than those for the single EDZ. The Lazy-H has a second wire at a lower height, and its overall TO angle will be a composite of the TO angles for each wire alone. The differences, however, are not operationally significant.

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Third, the gain is higher on all bands except for 40 meters. The gain also exceeds the gain of the 66' doublet on all bands except 40. The lower wire on 40, where the two wires are too close to derive any gain, tends to reduce gain on that band. However, the final figure is only about a dB less than that of the 67' doublet on the same band. The higher gains on all other bands give this array an advantage worth considering--especially since the patterns are bi-directional on every band of operation.

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The feedpoint impedances call for some comment. The models for this antenna were constructed with 450-Ohm parallel line with a velocity factor of 0.95, similar to what would be obtained from common vinyl-covered windowed 450-Ohm line. In addition, the lines are exactly 11' long each, meeting at the midpoint between the elements. (For wire versions of this antenna, I would recommend that you use a rope between elements to support the line and provide strengthening where the two phasing lines meet the main feedline to the shack.)

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If you change the length of the phasing lines or change the characteristic impedance (for example, by using open-wire 600-Ohm lines), you will not change the antenna performance. However, you will change the impedance at the junction where the main feedline joins the phasing lines. Some combinations will yield lower impedances at the junction; others will yield higher impedances. Since there are almost innumerable combinations we might use, be prepared to experiment with main feedline lengths that provide values at the ATU terminals which fall within the component range of the tuner.

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As a sample of the range over which feedpoint values might run, here are comparative feedpoint values for three types of line, each of which is arranged as a pair of 11' phasing lines to the midpoint between elements.

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                            Feedpoint Impedance (R ± jX Ohms)
+Freq        450-Ohm                 300-Ohm                 600-Ohm
+MHz         0.95 VF                 0.8 VF                  1.0 VF
+28.5         65 + j425              115 + j570               105 + j610
+24.9         17 + j115*              11 + j140*               30 + j140
+21.2         22 - j 15*              10 + j 38*               40 - j 50
+18.1         45 - j125               16 - j 26*               90 - j230
+14.15       385 - j395               75 - j150              1050 - j350
+10.1         50 + j105               40 + j 65                50 + j155
+ 7.15        10 - j 95*               6 - j 80*               13 - j 90*
+

Starred entries represent very low resistive components to the feedpoint impedance which might present larger excursions along whatever line is chosen as the main feedline to the shack. Note that the starred entries are fewest with the 600-Ohm phasing line. Once more, it is worth noting that these numbers are derived for general guidance from models. Variations will emerge from the actual construction of the antenna and from conditions and clutter at the antenna site.

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To get a sense of how the expanded Lazy-H performs, let's look at a few selected azimuth patterns on various bands. For all patterns, the top wire is 66' up, as always, above average ground.

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Fig. 24 gives us the basic EDZ pattern for 10 meters--with one modification. The gain is considerably higher than for a single EDZ at 66'. On 10 meters, the 5/8-wl spacing of the wires provides the highest possible increase in gain for a broadside array. As a rough comparison, the gain is equal to that of a 5-element 24' boom Yagi on 10 meters, although the Yagi, of course, will use considerably shorter elements. The Yagi will also have a wider beamwidth, but its pattern will be in only one direction.

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As we decrease frequency, the beamwidth will become wider and the EDZ "ears" will diminish. Below 12 meters, we obtain only a 2-lobe pattern. Fig. 25 shows the pattern for 17 meters, where it is now wide enough to provide broad coverage. However, the nulls of the ends of the wires are greater than 25 dB down from the main lobe, making the antenna highly directional.

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On the lowest band of operation, 40 meters (Fig. 26), the pattern has become an oval, with just a trace of the peanut shape. As we earlier noted, the gain is less than that of the single 10-meter EDZ or the 67' doublet, but it is still high enough to provide excellent coverage.

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One question that almost always emerges with respect to comparing the single wire and the array gain figures for 10 meters is this: how can the array have 4.5 dB gain over the single wire with just about the same horizontal beamwidth? The answer is straightforward if we think in 3 dimensions. Since we know that the horizontal patterns are very similar, we can compare elevation patterns for the EDZ and the expanded Lazy-H. Fig. 27 tells the tale.

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Like any single-wire antenna, the EDZ at 66' on 10 meters shows a set of nearly equal-strength vertical lobes: 4 to be exact. In contrast, the upper lobes of the Expanded Lazy-H are suppressed, leaving a single dominant lobe and a secondary lobe well over 4 dB weaker. All other lobes are down by 12 dB or more. The array tends to waste far less power at very high angles of radiation compared to the single wire. This comparative pattern, with variations, tends to hold true down through 20 meters.

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On 20, the effect is less pronounced but still easily measured, as shown in Fig. 28. The area enclosed by the upper lobes of the single wire at the top of the figure is distinctly greater by a considerable margin than the area enclosed by the upper lobe (barely discernable as a double lobe) of the Lazy-H array. The difference in area (assuming that the azimuth patterns are comparable, as they happen to be in this case) is a rough measure of the added power appearing in the lower lobes. In this case, that additional power shows up not only in the maximum gain, but as well in the vertical beamwidth. The phased feeding of vertically stacked horizontal wires has benefits hard to match in a typical flat-top wire array.

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Along side the benefits come some limitations. The Lazy-H requires a pair of tall supports and is suited to the antenna farm with more tall trees than money. The expanded Lazy-H is an outstanding bi-directional array for 10 meters in the design given here. Its performance holds up well down through 20 meters, and we can press it into service on lower bands. It takes up very little room horizontally in the yard, although a couple of optimally spaced tall trees certainly can aid the installation process. The wires for the elements and the phasing lines, as well as the feedline to the shack and the UV-resistant support ropes, are certainly inexpensive compared to the cost of a tower, rotator, coax, and commercial aluminum antenna.

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Before we leave the Lazy-H, let's consider a few of its further potentials. For example, we might consider a pair of 88' doublets in a configuration for 80 through 20 meters.

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Such an array as shown in Fig. 29 deserves as much height as we can obtain. Let's look at performance figures for only 2 versions. The first will have a top wire at 80 feet, with the bottom wire at 35', for full 5/8-wl element spacing on 20 meters. The second version lowers the top wire to 70', which is near the top height we have been using. The lower wire remains at 35' for 1/2-wl on 20 meters. The comparison is instructive. In each case, direct 450-Ohm, 0.95 velocity-factor lines have been used for phase feeding the elements from a central point.

+ 
a. 35-80' (5/8-wl Spacing)
+Freq.       TO          Gain        Beamwidth         Impedance
+MHz         Ang         dBi         degrees           R ± jX
+3.6         66          5.8         130                 9 -j  90
+3.9         56          5.8         129                13 -j  55
+7.15        28          7.9         78                310 -j 380
+10.1        20          11.1        57                 22 -j  35
+14.15       15          13.7        32                 61 +j 430
+
+b. 35-70' (1/2-wl Spacing)
+Freq.       TO          Gain        Beamwidth         Impedance
+MHz         Ang         dBi         degrees           R ± jX
+3.6         80          6.0         135                10 -j 125
+3.9         69          6.0         131                15 -j  85
+7.15        32          7.2         81                585 -j 290
+10.1        23          10.1        58                 36 -j 120
+14.15       16          13.6        33                 23 +j 150
+

Even the smaller and lower of the two arrays has good potential on all of the bands covered. From 7 MHz upward, there is little to choose between the two versions of the larger expanded Lazy-H. On 80 and 75 meters (3.6 and 3.9 MHz), the lower version seemingly has a very high TO angle. However, if we choose an arbitrary elevation angle, such as 45 degrees, both arrays have gain in the 5.2 to 5.3 dBi region. This gain level is not bad, considering that the height of the upper wire is in the 1/4-wl region.

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Whether we work with the single 44' or 88' doublet or with the expanded Lazy-H, we have obtained directional control of our antenna patterns. We also obtained gain on most bands and acceptable performance on all. If we cannot somehow manage a rotatable 88' Lazy-H array, we are faced with the question of directing our main lobes in all--or at least many--desired directions.

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Fig. 30 shows one way to accomplish the desired goal. If we have the room and the supports--in short, if we live in a forest--we can set three Lazy-H arrays in a Y pattern. The sketch shows the larger version, but you can always directly scale the dimensions for the smaller 40-10 meter version.

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With a 12' gap from the antenna wire ends to the array center-point, there is virtually no interaction among the wires. A 6' gap would do for the version using 44' doublets. Within plus or minus 10-15 degrees, any of the individual Lazy-Hs can be moved from perfect symmetry in order to better align it with desired communications targets.

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Besides the space required for 3 Lazy-H arrays, the one drawback to the Y-array is the need for 4 supports. One might get away with only 3 supports if one is knowledgeable about rope-based trussing systems. However, there is an alternative to the Y.

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A standard triangle (Fig. 31) offers a more compact arrangement of the antennas and needs only three supports--just one more than a single Lazy-H would require. Once more, scale the space down for the smaller array. As with the Y, variations in the exact angles of each array will not be noticed except in the better aim we obtain for each Lazy-H relative to our communications targets.

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The two arrays of arrays are often the cheapest ways to obtain world-wide coverage with minimal gaps. The lower the frequency within each range, the fewer the gaps in coverage for the 6 possible main lobes.

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The triangular arrangement does not offer the nearly perfect absence of interaction among the arrays. The worst case pattern distortion amounts to under 5 degrees along the horizon, whether the unused antennas are open or shorted at their feedpoints. Hence, for all practical purposes, interaction among the arrays can be ignored.

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Controlling the arrays requires a remote switching box unless we wish to bring three sets of feedlines into the shack. A weatherproof box with a series of relays capable of handling high voltages and currents in their contacts can be placed in the center of the arrangement, with a single feedline back to the shack.

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Fig. 32 shows one possible switching system for remotely controlling which antenna is active. The in-shack controller can use almost any indicator system the user might imagine. Therefore, I shall leave further refinements to the reader's sketch pad.

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Conclusion

In our quest for the perfect VOMBA, we have covered a large territory, ranging from simple doublets to arrays of arrays. We began with the popular 1-wl loops, vertically oriented. These turned out to be far from the best we might do for a vertically oriented multi-band antenna. We looked at simple 67' doublets and hybrid triangles. When we added pattern direction control to our list of desires, we ended up with the 10-meter EDZ and the derivative expanded Lazy-H. Then we dared to dream much bigger dreams. +

If my goals were 40 to 10 meters with all patterns broadside to my antenna wire, and if I could have but one wire, I would likely choose the 44' doublet and get it as high as I could manage. If I could manage 60 to 70 feet of height, I would add the second wire and make an expanded Lazy-H. If I could use a square that was 50 by 50 feet or so, I would erect 3 expanded Lazy-H arrays in a triangle. If I has another square that was a little over 100 by 100 feet, I might erect a second low-band set of Lazy-H arrays. All this planning, of course, assumes that I already have the supports or that I have the patience to watch my newly planted Douglas firs grow.

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If I have only one tall support, then I would likely opt for some form of delta. However, I would not stop planning for a second tall support and the day I could replace the delta with a Lazy-H.

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Every antenna decision, however, is a compromise between the antenna types that perform best and the kind and size of space we have to erect them. Consequently, my concluding statement of my own "druthers" is likely to be highly modified by whatever places I may live in the future. And your evaluation of the potentials of the VOMBAs we have examined must be moderated and modified by the realities of your own unique circumstances.

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However, in your quest for a vertically oriented multi-band antenna, it pays to look beyond whatever may be a current fad in wire antennas. Some of the "older models," like the Lazy-H, may have more to offer than first meets the eye. In addition, do not be put off by that fact that we call antennas like the Lazy-H a "phased" array. If you can cut two pieces of parallel transmission line to the same length--and long enough to meet in the middle of the array--then you can successfully build something like a Lazy-H.

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In addition, while you resign yourself to present circumstances that force you to build small, continue to dream big. You never know when you might be transferred to a big forest where you can support an array of Lazy-Hs for 160 meters.

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Updated 5-19-00. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Delta Loop, Dipole, Doublet, EDZ / Zepp, HF Multi Band, Lazy H, Quad Loop


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Mastering Some Mysteries of 2-Element Beams Part 1

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This talk was originally prepared for the 2001 Dayton FDIM Symposium

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The decision to upgrade a single wire antenna into a multi-element beam marks a major step in QRP station sophistication. Whatever the band, whatever the material, a 2-element array is more than a simple doubling of elements. It represents additional gain, additional directivity, and additional responsibility to know how the thing works.

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This small presentation is designed to remove some of the mystery from the 2-element directional beam. I shall not in this space be able to answer every question or treat every possible design. However, I do hope to accomplish two things. First, I want to look at the basic electronics of 2-element beams so that you can have a qualitative understanding of why things work like they do. Second, I want to provide you with a compendium of designs for 20 through 10 meters that will let you build some 2-element beams with confidence.

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In the following pages we shall address a series of topics relating mostly to horizontal 2-element beams, with the hope that they have good order:

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  • 1. How 2-element beams work;
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  • 2. 2-element driver-reflector Yagis (with dimensions) for 20-10 meters;
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  • 3. 2-element driver-director Yagis (with dimensions) for 17-12 meters;
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  • 4. More geometric possibilities;
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  • 5. Horizontal phased directional arrays;
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  • 6. Wire beams (with dimensions) for 80 and 40 meters.
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These topics cover a lot of ground, so we had best hitch the mules (a team of 2, of course) and begin plowing. Even so, we shall only cover the first 3 topics today. But there is always FDIM 7.

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1. How 2-Element Beams Work

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Let's begin with my title: 2 X 1 = 4. What does it mean? The answer lies within the common resonant 1/2þ dipole. If we place a dipole made from common materials, such as copper or aluminum, in free space, it will show a gain of about 2.1 dBi (dB over an isotropic source). When placed at least 1/2 wl over average ground, the same dipole will show a gain of about 7-8 dBi due to reflections from the ground. Fig. 1 shows the typical dipole pattern, a near-figure 8.

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The gain of the dipole comes from the fact that radiation is concentrated broadside to the wire, with little radiation off the wire ends. The dipole is bi-directional. Now suppose that we could reduce one major lobe and enhance the other. Then we would have a directional beam with QRM reduction in 3 of the 4 major quadrants. No longer would that G station QRM our U.S. attempt to contact the VK or ZL.

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Fig. 2 provides one of many typical 2-element directional beam patterns--with the antenna placed at the same height as the dipole. The beam consists of 2 elements, each of which is close to being a resonant 1/2 wl dipole--close but for many good reasons not quite. Note that the end nulls are just as strong as with the dipole, but as well, the rear lobe is reduced by many dB. The reduction in rear gain shows up as an increase in forward gain. A well-designed 2-element beam will have about 6 - 6.5 dBi free-space gain or about 11 - 12 dBi gain if placed at least 1/2 wl above average ground. The net gain over a dipole is about 4 dB. So, multiplying 1 dipole by 2 gives us 4 dB advantage--somewhere between 1 and 2 S-units. Add the rear QRM and QRN reduction, and you have a very worthy improvement to station performance.

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Yes, you can get more gain and a higher-front-to-back ratio by going to more elements, stacked arrays, and so forth. However, the big step is going from 1 element to 2.

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Now the question before us is simple: how do we shrink one lobe and expand the other one? To answer that question, we have to consider first how elements get their energy. Then we can turn to the question of how much energy per element in what exact form.

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+ +
+

In Fig. 3 we have set two elements close to each other--close enough to lie in each other's "near field." The near field for our purposes represents the region where the elements closely interact, exchanging energy. Some call it inter-element coupling; others call it inductive coupling; still others call it mutual coupling. Whatever the name, some important things are happening relative to how energy is supplied and distributed.

+

First, we have a choice in supplying energy to the 2 elements. We can apply energy to both elements or to just 1 of the 2. Whichever way we choose, the elements both receive energy, either from the source or from each other. If we feed only one element, the unfed element receives energy by virtue of its close coupling to the fed element. It radiates the energy it receives and hence the fed element receives energy from the unfed element. If we feed both elements energy, each element both receives and re-radiates energy to each other. In either case, inter-element coupling determines to a very large measure the properties of the resulting antenna.

+

For any given set of near-resonant 1/2 wl elements at fairly close spacing (say, between 0.05 wl to about 0.5 wl), there will be an "ideal" energy relationship between the two elements. Now all we have to do is to define "ideal." Let's consider two definitions. First, we shall look at the ideal of having the maximum front-to-back ratio in the direction that is 180ø opposed to the maximum forward gain direction. We can call this the ideal of a maximum rear null. Second, we shall look at the ideal of obtaining maximum forward gain from the two elements. We can call this, quite obviously, the ideal of maximum gain.

+

To achieve either ideal, at the center of each of the 2 elements, there will be a certain current magnitude and phase angle combination. What that combination is will differ for each ideal. As well, it will differ as we change the lengths of the two elements, making one longer than, shorter than, or equal to the other. Third, the combination will differ as we change the spacing between elements. Finally, the combination will change as we alter the physical shape of the elements, perhaps by bending the ends toward each other.

+

Let's explore for a moment one of these variables that determines the combination of current magnitude and phase: spacing. As a little experiment, let's look at what happens when we phase both elements of two different array pairs, shown in Fig. 4. At a spacing of about 0.125 wavelength, the unequal element pair makes up a very workable 2-element Yagi for 28.5 MHz, when only the forward element is fed. At the same spacing, the equal-length pair is close to resonant, but with a typical dipole pattern.

+
+ +
+

Let's first set as our operating goal achieving a maximum rear null 180 degrees from the peak of the forward lobe. We can define the null as adequate if it exceeds -50 dB relative to the forward lobe. This value would exist only over a tiny bandwidth, but for study purposes, it is a goal that modeling programs, such as NEC-4, can easily show. We shall vary the distance between the elements in 0.05 wl increments. For each distance, we shall change the current magnitude and phase on the rear element until the desired null is achieved.

+

Table 1 shows the results for both element pairs. For this case, the current phase for each step is virtually the same for both types of arrays, but the required current magnitude on the rear element is different according to whether the elements have the same or different lengths. Other element lengths we might have chosen would have resulted in other values.

+

For each increase in spacing, the current magnitude changes very little, no matter which type of array we choose. However, the required phase angle on the rear element shows a continuous decrease, with the highest gain at the closest spacing of the elements. Some other considerations will limit our ability to use the very highest gain and still have the maximum null. In the end, there is no single ideal spacing for achieving a deep rear null. Instead, for any spacing, there is a current magnitude and phase angle that will achieve the null.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Phasing 2 Elements for Maximum Rear Null
+Equal vs. Unequal Element Lengths
+
+                                                Rear Element Current
+Spacing                 Mag.        Phase       F.S.        F-B
+ wl         inches      (rel-       deg.        Gain        Ratio
+                        ative)                  dBi         dB
+
+Designed for Maximum Rear Null:
+Equal-Length Elements (196.8" x2 at 28.5 MHz)
+ 0.05        20.7       1.035       163         6.55        >50
+ 0.1         41.4       1.07        145         6.46        >50
+ 0.15        62.1       1.09        125.5       6.18        >50
+ 0.2         82.8       1.09        106         5.76        >50
+ 0.25       103.5       1.07         87         5.14        >50
+ 0.3        124.2       1.045        69         4.26        >50
+ 0.35       144.9       1.02         51         2.72        >50
+ 0.4        165.7       1.00         34         0.31        >50
+
+Unequal-Length Elements (192" forward, 208.1" rear at 28.5 MHz)
+ 0.05        20.7       0.925       163.3       6.57        >50
+ 0.1         41.4       0.945       145         6.45        >50
+ 0.15        62.1       0.955       126.0       6.19        >50
+ 0.2         82.8       0.95        106.7       5.77        >50
+ 0.25       103.5       0.94         88         5.16        >50
+ 0.3        124.2       0.92         69.5       4.21        >50
+ 0.35       144.9       0.90         51.8       2.73        >50
+ 0.4        165.7       0.88         34.5       0.28        >50
+
+Note 1:  All forward element currents set at a relative magnitude of 1.0 at 0 degrees
+phase angle.
+Note 2:  All values of rear current relative magnitude and phase angle taken when
+the rear null passed -50 dB relative to the forward lobe.
+Note 3:  Elements are 1" diameter aluminum.
+
+Table 1:  Phasing 2 elements for maximum rear null using equal and unequal
+element lengths.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Much of antenna element phasing theory is devoted to the achievement of rearward nulls. Little attention has been given to achieving maximum gain from the array. Let's look at Table 2 to see what the effects of changing space might have on the required rear element relative current magnitude and phase for this goal. For spacing from 0.05 through 0.25 wavelengths, the required current magnitude for each array remains relatively constant. However, the required phase angle decreases with increased spacing, but at far less than the rate for achieving a maximum rearward null. Maximum gain does not occur with the closest spacing, but in the vicinity of 0.1 wl. As one might expect, the front-to-back ratio of two elements becomes mediocre (at best) when the goal is maximum gain.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Phasing 2 Elements for Maximum Forward Gain
+                       Equal vs. Unequal Element Lengths
+
+                                                Rear Element Current
+Spacing                 Mag.        Phase       F.S.        F-B
+ wl         inches      (rel-       deg.        Gain        Ratio
+                        ative)                  dBi         dB
+
+Designed for Maximum Rear Null:
+Equal-Length Elements (196.8" x2 at 28.5 MHz)
+ 0.05        20.7       1.02        173         7.32        7.64
+ 0.1         41.4       1.03        165         7.35        7.19
+ 0.15        62.1       1.02        158         7.23        6.90
+ 0.2         82.8       1.03        152         7.03        6.00
+ 0.25       103.5       1.03        147         6.76        5.03
+
+Unequal-Length Elements (192" forward, 208.1" rear at 28.5 MHz)
+ 0.05        20.7       0.91        173         7.33        7.70
+ 0.1         41.4       0.92        166         7.36        7.22
+ 0.15        62.1       0.92        159         7.24        7.03
+ 0.2         82.8       0.92        150         7.04        6.59
+ 0.25       103.5       0.93        147         6.77        5.13
+
+Note 1:  All forward element currents set at a relative magnitude of 1.0 at 0 degrees
+phase angle.
+Note 2:  All values of rear current relative magnitude and phase angle taken when
+the forward lobe reached a peak gain, beyond which gain fell off.
+Note 3:  Elements are 1" diameter aluminum.
+
+Table 2:  Phasing 2 elements for maximum forward gain using equal and unequal
+element lengths.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The differences in the azimuth patterns for the same antenna geometry, but set up for each of the ideal phasing conditions, are dramatic indeed. Fig. 5 shows the maximum forward gain ideal and the maximum rear null ideal in free-space azimuth patterns, using the unequal-element model and a spacing of 0.1 wavelength at 28.5 MHz.

+
+ +
+

Amateur 2-element beams strive for a workable compromise between maximum gain and excellent front-to-back ratio. As well, we demand coverage of a band of frequencies and not a single frequency. The little experiment resulted in arrays that achieve their impressive values only over a very tiny portion of even a WARC band. As well, amateur 2-element beams also strive for an operating impedance that yields a good match--either directly or through a simple network--to 50-Ohm coaxial cable. When we add up all of out demands, we are bound to hit some limitations. In fact, in the following sections of these notes, we shall be talking mostly in terms of limitations.

+

2. 2-Element Driver-Reflector Yagis (with Dimensions) for 20-10 Meters

The Yagi-Uda array, in its most simple form, consists of a driven element and an undriven reflector. Fig. 6 shows the general outline of this configuration. The reflector element is called parasitic because its sole source of power is the energy coupled from the driven element. It achieves a directional pattern solely by virtue of our selection of the element lengths and their spacing (for any given element diameter). +
+ +
+

The sketch should familiarized you with the parts of a typical driver-reflector Yagi. As well, it will help to make you comfortable with some of the terms used in connection with such antennas. Note that when we have a single feedpoint, thus creating a driver or driven element, a reflector element will necessarily be longer than the driver in an optimized design. The main lobe of radiation (the forward lobe) will be ahead of the driver.

+

Before we plunge into further details of Yagi designs, let's establish a few facts of life. If we strive for maximum gain, we can achieve it--or something very close to it. However, the feedpoint impedance will be unreasonably low (under 10 Ohms), and the operating bandwidth over which we achieve the maximum gain will be far less than the bandwidth of any amateur band--with the possible exception of the WARC bands. So, for 20, 15, and 10 meters we shall have to settle for well under 7 dBi free-space gain.

+

Second, since the driver-reflector Yagi derives its properties from the geometry of the antenna, it also is limited by what we can do with 2 parallel linear elements, whatever their relative lengths or their spacing. With this configuration, it is not possible to achieve more than about 15 dB front-to-back ratio. If we add demands for a usable feedpoint impedance and a good operating bandwidth, we shall achieve some between 10 and 12 dB front-to-back ratio.

+

We can illustrate what is possible for a 2-element driver-reflector Yagi with some patterns and graphs for 10 meters, where the tested bandwidth is 28-29 MHz (or 28-29.7 MHz for a certain wide-band model). I chose 10 meters because the desired 1 MHz bandwidth of 3.5% is wider than the bandwidth of 20 meters (2.5%) or 15 meters (2.1%). Hence, if a given design is satisfactory for the 10-meter band, it will--when properly scaled--be satisfactory for 20 or 15 meters. However, remember that scaling involves changes of element length, elements spacing, and element diameter. If you forget to scale the element diameter, your design may be well off the mark.

+

We shall encounter some graphs and numbers in working with Yagis, and sometimes their significance can be elusive. For example, how much operational advantage do I gain by adding 1 dB of front-to-back ratio? Is a half dB of added forward gain significant? Fig. 7 shows the free-space azimuth patterns of a narrow-band (1 MHz) 10-meter Yagi at the band edges and at center band. In the forward (graphical upward) direction, the spacing between lines is about 1/2 dB. In the rear, directly opposite the main forward direction, the front-to-back ratio shows a 1.5 dB total change. For the antenna portrayed, the operator would not be able to tell the difference with sophisticated test equipment--and he would lose many QSOs setting up that equipment.

+
+ +
+

For basic comparisons among antenna designs, we often use "free-space" models and performance figures. Compare Fig. 7 to Fig. 2: note that the azimuth pattern taken over ground show more gain--the result of adding ground reflections to the basic gain level--and shallower side nulls than the free space model. In general, a given design does not restore all of its side rejection until it is much higher than 1 wavelength above ground.

+

Actually, we shall look at two basic driver- reflector designs. One is a narrow-band version designed to cover 28-29 MHz with under 2:1 SWR when properly matched to a 50-Ohm coaxial cable. The antenna uses elements spaced about 1/8 wavelength apart, a distance the represents a good compromise between gain and a usable feedpoint impedance (about 35 Ohms resistive). The second design strives for two goals: coverage of the entire 10-meter band and a direct 50-Ohm feed that requires no matching network. The elements are spaced about 0.175 wavelength apart. Table 3 presents the dimensions for the two antennas using 0.5" aluminum elements.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                     Narrow-Band 2-Element Yagi Design
+Design Range:                                      28.0 - 29.0 MHz
+Element Diameter:                                  0.5"
+Driver Length:                                     16.1'
+Reflector Length:                                  17.4'
+Element Spacing:                                    4.32' (1/8 þ)
+
+                                      Wide-Band 2-Element Yagi Design
+Design Range:                                      28.0 - 29.7 MHz
+Element Diameter:                                  0.5"
+Driver Length:                                     15.9'
+Reflector Length:                                  17.3'
+Element Spacing:                                    6.0' (0.175 þ)
+
+Table 3.  2-element driver-reflector dimensions for 10 meters.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Unless you use 1/2" aluminum tubing, the required dimensions will not be identical for your version of these beams. We shall discuss the effects of real materials at length momentarily. We shall also look at some construction alternatives and what they mean for the builder's final dimensions. Before getting that specific, let's look at the relative performance of these two antennas, which differ mostly in the element spacing. The 1.7' difference may not be much on 10 meters, but it becomes a 3.4' difference on 20 meters. However, we may not need a wide-band design for 20 and 15 meters. +
+ +
+

Fig. 8 graphs the gain of both antennas across all of 10 meters. Let's note several features of the graph. First, for all driver-reflector designs with reasonable feedpoint impedances and decent front-to-back rations, the peak gain will occur below the lower band edge. As you go down the band, the resistive portion of the feedpoint impedance decreases, which coincides with the gain curve. (The gain curve properties will change if we use a director instead of a reflector.)

+

Second, note that the narrow-band Yagi does not simply go to pot above its highest operating frequency. The gain curve parallels that of the wide-band version, even though the user is unlikely to get a low SWR above 29.0 MHz. When thinking about operating bandwidth, always consider what the limiting factors are. In some cases, it may be the SWR curve. In other cases, it may be a steep curve for the front-to-back ratio.

+
+ +
+

The two Yagi designs exhibit rather modest slopes to their front-to-back curves, as shown in Fig. 9. There is only about a 0.5 dB difference in the peak values for the two designs. More important is the fact that the narrow-band version is designed to peak about 28.5 MHz, while the wide-band version is set to peak somewhat higher in frequency. The goal in both cases is to have reasonably equal front-to-back ratios at the limits of the respective operating passband.

+
+ +
+

Similar design considerations go into setting the SWR curves, shown in Fig. 10. The narrow-band version has an SWR under 2:1 for the 28-29 MHz region, while the wide-band version shows under 2:1 SWR for the entire 10-meter band.

+

However, to fully understand the curves, let's note that each is based on a different resonant impedance. The resonant feedpoint impedance increases as we separate a driver and reflector. The wide-band version is based on a direct 50-Ohm feed and uses 50-Ohm resistive impedance as the baseline. The gradual curves--which almost always are steeper below the design frequency than above it--result from the increasing reactance that occurs off resonance: capacitive below resonance, inductive above it.

+

The narrow-band antenna shows a resonant impedance of about 35 Ohms resistive. The same levels of reactance--when added to the lower resistance--result in steeper SWR curves. We use these curves because they generally trace the performance you will get relative to 50-Ohms once you place a proper matching network at the feed point.

+

Let's take up 4 questions related to these Yagi designs before moving on to other types of 2-element beams:

+
    +
  • 1. Why don't I get 50 dB front-to-back ratio or 7+ dBi free-space gain?
    • +
  • 2. What can I do to match the narrow-band antenna to my coaxial cable?
    • +
  • 3. What happens if I use a combination of aluminum tubing for the elements?
    • +
  • 4. How do I build versions of these antennas for 20 or 15 meters?
    • +
+

1. Why don't I get 50 dB front-to-back ratio or 7+ dBi free-space gain? There is a limit to the ability of paralleled linear elements to obtain the ideal relative current magnitude and phase, whether "ideal" means a deep rear null or maximum gain. Although the comparison is not absolutely precise, we can look back at the ideal numbers for the experimental models using unequal element lengths and compare them with the mid-band values for each of our designs.

+

Table 4 lists the ideal numbers from the experimental models for element separations ranging from 0.1 to 0.2 wavelengths. The two actual Yagi designs have element spacings that fall between these limits. In all cases, the forward element is assigned a current magnitude of 1.0 and a phase angle of 0 degrees.

+

Immediately apparent is the fact that the current magnitude for the actual designs is well below the optimal level for either the maximum rear null or the maximum forward gain ideal. The current phase is within the "ballpark" of what is ideal. However, paralleling two elements while obtaining a usable front-to-back ratio and a usable feedpoint impedance requires a spacing (as well as element lengths) that prevents us from reaching the required near-equality of current magnitude on the two elements. Geometry limits what we can do with only two elements to achieve the ideal--and still have an antenna that we can easily use.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                                Rear Element Current
+Spacing                 Mag.        Phase       F.S.        F-B
+ wl         inches      (rel-       deg.        Gain        Ratio
+                        ative)                  dBi         dB
+
+Maximum rear null:
+ 0.1         41.4       0.945       145         6.45        >50
+ 0.15        62.1       0.955       126.0       6.19        >50
+ 0.2         82.8       0.95        106.7       5.77        >50
+Maximum gain:
+ 0.1         41.4       0.92        166         7.36        7.22
+ 0.15        62.1       0.92        159         7.24        7.03
+ 0.2         82.8       0.92        150         7.04        6.59
+Narrow-Band design at 28.5 MHz:
+ 0.125       51.8       0.67        143         6.20        11.12
+Wide-Band design at 28.6 MHz:
+ 0.175       72.0       0.60        129         6.05        10.68
+
+Table 4.  A comparison of relative current magnitude and phase between ideal and
+real Yagi designs.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Nevertheless, the added 4 dB of gain over a dipole and the 2 S-units of front-to-back ratio are highly useful. We can add more elements, but the increment of improvement for each new element will not equal the improvement we have made by adding just one element to a dipole.

+

2. What can I do to match the narrow-band antenna to my coaxial cable? The wide-band Yagi has served us well for several demonstrations. It showed us how increasing the element spacing increases the feedpoint impedance of a 2-element driver-reflector Yagi. It also showed us that complete coverage of 10 meters is possible. However, we shall turn away from this design in favor of the narrow band design. The narrow-band design is suitable for scaling to 20 and 15 meters with complete band coverage in each case.

+

Before we leave the wide-band design, let us remember that it is intended for direct connection to a 50-Ohm coaxial cable. However, the potential for common-mode currents on the cable strongly suggests that we insert a 1:1 choke--sometimes called a choke balun--at the antenna feedpoint. Whether we choose the W2DU design of placing ferrite beads on a 1' length of coax or some other design, the use of a choke is a wise precaution to prevent pattern distortion that might occur under certain conditions due to some antenna current being present on the outside of the coax braid. As well, the choke tends to suppress RF that gets back into the shack, distorting the SWR readings and possibly disrupting some sensitive circuits in our transmitters. Some folks wait until trouble shows itself before adding a choke at the 50-Ohm feedpoint. My preference is good preventive engineering, so I add one as a matter of course.

+

The narrow-band version of the antenna has a resonant feedpoint impedance of only about 35 Ohms. We can run the antenna with a direct feed, but the SWR will be fairly high across the band, never dropping below 1.4:1 and exceeding 2:1 at one band edge or the other.

+

If the natural feedpoint impedance had been about 25 Ohms, we might leave the driven element resonant and use a 37-Ohm 1/4 wavelength matching section, made up from 2 parallel sections of 75-Ohm cable. (RG-59 is close enough, but be sure to adjust the 1/4 wavelength requirement by the velocity factor of the line used: about 0.67 for solid dielectric and about 0.78 for foam.) However, the matching section is not especially apt to our narrow-band 2-element Yagi.

+

There are 3 popular matching techniques. The gamma match and the Tee match both work and both permit the driven element to be directly connected to the boom. However, both add considerable mechanical complexity to the driver, especially in the number of component part connections, each of which has a small resistive loss and the sum of which can rob power by turning it into heat. If it does not happen on installation day, it usually grows as the antenna ages in place.

+

My personal preference for HF matching is the beta match. Let's take a brief look at what it is and what it does.

+

The beta match appears to be simply a small coil or hairpin placed across the terminals of an antenna, most often a Yagi. Some folks mistake the coil for an RF choke, while others mistake the hairpin for a short circuit.

+

Actually, the beta coil or hairpin is one part of an impedance matching circuit, where the remaining elements are invisible, if you do not know what to look for. Many Yagi antennas have feedpoint impedances in the 20 to 35 Ohm range, somewhat low for feeding directly with coaxial cable. We need to raise the impedance to 50 Ohms--and that is what the beta match system does. The coil is not the only element in the circuit. There is also a capacitor--or, more correctly, some capacitive reactance. We get that part of the circuit from the antenna element itself.

+
+ +
+

Fig. 11 shows how we move from a resonant driven element to a beta match. Let the resonant antenna impedance be low, say about 25 Ohms. If we shorten the element, the resistance does not change significantly, but the antenna becomes capacitively reactive, as the middle part of the figure shows.

+

If we shorten the element by the right amount, we get the right capacitive reactance in series with the antenna resistance to go together with an inductance across the coil to make an L-circuit. An L-circuit is one of the fundamental impedance transformation circuits, and in this case, -Xa and XL together change the 25-Ohm antenna resistance to 50 Ohms.

+

We can calculate the needed values if we know the antenna feedpoint resistance (Ra). (We know that coax has a characteristic impedance (Ro) of 50 Ohms.) First we calculate a value called "delta" by some and "working Q" by others. Delta = the square root of [(Ro/Ra)-1]. Now we can easily calculate the necessary values of capacitive reactance in the antenna (-Xa) and of inductive reactance to place across the terminals (XL). Xa = Delta times Ra. XL = Ro / Delta.

+

Since these values are given as reactances, you need to convert the inductive reactance into a component value. The capacitive reactance will be developed by simply shortening the antenna element until the beta match gives us 50 Ohms.

+

For reference, Table 5 presents some of values we commonly encounter with beta matches with 50-Ohm coax for various values of antenna feedpoint resistance (Ra):

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Ra               35               33               25               17                12.5
+Delta            0.6              0.7              1.0              1.4               1.7
+Xa               22.9             23.6             25.0             23.6              21.7
+XL               76.4             70.7             50               35.4              28.9
+
+Table 5.  Some common values encountered in beta matching networks for antennas.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Notice that the capacitive reactance reaches a peak when delta = 1, while the inductive reactance gets smaller as the feedpoint resistance gets smaller.

+

We have not yet converted these inductive reactances (XL) into a component value, because there are two distinct ways to achieve the required reactance across the coil. Fig. 12 shows them both:

+
+ +
+

The beta inductor is simply a coil with the value of inductance that provides the inductive reactance at the operating frequency. If you divide the required inductive reactance by the product of the operating frequency (in Hz) and twice pi, you get the right inductance.

+

The hair pin version of the beta inductor is actually a small shorted stub of parallel transmission line. Rather than go through the calculation procedure, I shall simply once more recommend that you obtain a recent copy of HAMCALC, a suite of handy ham calculation programs in GW Basic. You can get a copy for $7 to cover CD-ROM and mailing costs from George Murphy, VE3ERP, 77 McKenzie Street, Orillia, ON L3V 6A6, Canada. Among the selections on the disk is an excellent program that will calculate the dimensions of a hairpin for the match. It was written by Thomas Cefalo, Jr., WA1SPI. The program will also tell you the equivalent inductance in case you want to wind a coil. Other programs in HAMCALC will help you wind an accurate coil.

+

Many antenna builders use the experimental technique of adjusting the driven element for a beta match. After calculating the beta coil or hair pin, they install it and then adjust the element length for a low SWR. Antenna modelers tend to determine the required element length in advance from their software and save some time fumbling for the right element length.

+

Either way, the beta match results in a very low loss match. For inductor Qs over 100 (easy to obtain, but some maintenance is required to maintain the Q), losses will be well under 1%--and even less for the hairpin.

+

If you like to build antennas, you should become familiar with the beta match. Some folks actually avoid the beta match because it is "too simple to really work." However, it does work, and very well indeed for antennas with moderately low feedpoint impedances. Since there are easy-to-use utility programs for calculating everything you need, there is no need to avoid either the beta match or antennas that require one.

+

Our narrow-band antenna for 10 meters, with a 35-Ohm impedance requires that we shorten the driven elements from 16.1' to about 15.7' to supply the 22-23 Ohms of capacitive reactance. Then we place a coil or hairpin (shorted stub) with 76 Ohms of inductive reactance at 28.5 MHz across the feedpoint. As just one example among many, a hairpin made from #12 AWG wire (0.0808" diameter) and spaced 1.5" will require a length of 11.2" to do the job, while a coil of 0.43 microH will do the same job. Of course, every good builder leaves himself some room for final adjustment.

+

3. What happens if I use a combination of aluminum tubing for the elements? Before we look at the answer to this question, let's begin with a word of caution. Many new antenna builders go to the hardware store and buy aluminum conduit to use for beam antenna elements--mostly because it is cheap and available. My suggestion is to avoid this material. It is heavy and tends to be soft. Purchase 6063-T832 or 6061-T6 tubing from a reputable dealer (Texas Towers is one of many). It is much better suited to the task and is not very expensive. By mail, it comes in 6' lengths, and many ham antenna designers tailor their designs to this length.

+

If we use tubing such as this, we shall have to taper the element diameter as we move out from the center of each element. The key question is what this move does to the required element lengths for a given spacing.

+
+ +
+

Fig. 13 is designed to give us some idea of how various element shapes affect the resonant length of antenna elements. If the element flares outward, as with the bi-conical, the resonant length is shorter than for a uniform diameter element. If the element diameter grows smaller as we move outward--either in a smooth or stepped taper--it must be longer than a uniform diameter element. And what applies to a resonant element also applies to a parasitic element.

+

Therefore, if you simply take the element lengths that we have given for the 10-meter beams but use a set of nested tubes, it is likely that the result will not perform to standards. With no standard antenna with which to compare the home-brew Yagi, you may never be aware of how far from peak performance the array is.

+

To save you the trouble of buying a complete modeling software program to develop tapered element designs, I have taken a pair of standard ARRL Antenna Book element taper schedules for each band (20-15-10) and refigured the element lengths in advance. Element tapering uses fairly complex equations developed by Dave Leeson and incorporated into the best commercial modeling software. So please do not think that you can do the job just be averaging the element diameters--or by guessing. If you want to use an element diameter taper schedule that does not match one of these versions, you will have to go back to the model-drawing boards and refigure the element lengths from scratch.

+

In each case, a basic uniform-diameter model serves as the basis for each design that is modified for a tapered element schedule. For each of the three wide HF bands, we shall present a graphic of the taper schedules used, followed by a table of values for the outer section and the total (1/2-element and full-element) lengths. The lengths given assume that all elements are insulated from the boom.

+

10-Meters

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                              Element Lengths
+Element                           Outer                             1/2-El.           Element
+                                  Section                           Length            Length
+Narrow-Band Version:  0.5" Uniform Diameter
+Driver                                                               96.6"            193.2"
+Reflector                                                           104.4"            208.8"
+Medium Duty Taper Schedule Version
+Driver                            61.6"                              97.5"            195.0"
+Reflector                         69.6"                             105.6"            211.2"
+Heavy Duty Taper Schedule Version
+Driver                            55.9"                              97.9"            195.8"
+Reflector                         64.5"                             106.5"            213.0"
+Wide-Band Version:  0.5" Uniform Diameter
+Driver                                                               95.4"            190.8"
+Reflector                                                           103.8"            207.6"
+Medium Duty Taper Schedule Version
+Driver                            60.4"                              96.4"            192.8"
+Reflector                         69.0"                             105.0"            210.0"
+Heavy Duty Taper Schedule Version
+Driver                            54.6"                              96.6"            193.2"
+Reflector                         64.0"                             106.0"            212.0"
+
+Table 6.  Element lengths for 10-meter tapered-diameter 2-element Yagis.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the differences between the uniform-diameter and the tapered diameter versions of the same beam appear to be small, they are critical if the builder wants to achieve the level of gain, the front-to-back ratio, and the SWR curve that has been shown. Unlike casual wire antenna building, constructing a Yagi requires considerable care and reasonable precision. Nest each tube size about 3" inside the next larger size. Less nesting length weakens the element; more nesting increases weight unnecessarily.

+

4. How do I build versions of these antennas for 20 or 15 meters? The basic process of transferring a successful antenna design from one frequency to another is to scale the design. Divide the old frequency by the new one. Then use this ratio to multiply each element length, the element spacing, and the element diameter. A 190" 0.5" diameter element for 28.5 MHz wants to be 1.343 times larger in every way when scaled for the middle of the 15-meter band (21.225 MHz). The length becomes 255.1" and the diameter will be 0.67".

+

Obviously, we must use either 5/8" or 3/4" diameter tubing, which means that the scaling will not be precise. Some adjustment will be needed to the element lengths (which are more sensitive to change than the element spacing) in order to bring the design to the exact results that we want.

+

To save you some work, I have scaled and adjusted the narrow-band version of the 2-element driver-reflector Yagi for use on 15 and 20 meters. We do not need the wide-band version unless we simply wish to have a 50-Ohm direct feed system. Each beam has a band center resonant feedpoint impedance of about 35 Ohms. For use with a beta match, each driver will need to be shortened proportionally to the shortening used for the 10-meter version. A useful figure is to shorten each driver by 2.5% to achieve the correct capacitive reactance to go with the beta reactance to form the L-network. Of course, you will have to recalculate the beta coil or beta hairpin (shorted stub), since the inductance or line length required changes for a given inductive reactance as we change frequency. If you use materials or wire-spacing other than the #12 wire in the 10-meter example, the required hairpin length will also change. It pays to have a handy program like HAMCALC around to help calculate the hairpin.

+

Table 7 provides the basic dimensions for a uniform-diameter 2-element Yagi for both 20 and 15 meters. Following these dimensions are graphics showing the taper schedules for medium duty and heavy duty versions of the antenna. The difference between medium and heavy duty is a wind speed of 75 miles per hour for the lighter version and about 100 miles per hour for the heavier version. Then, for each band, there is a table of construction values.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                      15-Meter 2-Element Yagi Design
+Design Range:                                      21.0 - 21.45 MHz
+Element Diameter:                                  0.75"
+Driver Length:                                     21.5'
+Reflector Length:                                  23.4'
+Element Spacing:                                    5.80' (1/8 þ)
+
+                                      20-Meter 2-Element Yagi Design
+Design Range:                                      14.0 - 14.35 MHz
+Element Diameter:                                  1.0"
+Driver Length:                                     32.2'
+Reflector Length:                                  35.0'
+Element Spacing:                                    8.7' (1/8 þ)
+
+Table 7.  2-element driver-reflector dimensions for 15 and 20 meters.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As a side note, we can use a PVC boom for the 10-meter Yagi. However, the length and element load for 15 and 20 meters makes PVC impractical, due to its tendency to sag. For 2-element beams, you can use 0.58" wall tubing in a size about 1.25" to 1.5" outside diameter. However, for better strength, insert another section of tubing the next 1/8" outside diameter smaller in the larger boom tube. The added strength will also help to prevent tube crushing by the U-bolts used to secure the element plates and the mast plate.

+

If you purchase 6' tubes by mail, you can join them to form a longer (20-meter) boom using the double tubing method. The 8.7' element spacing calls for a 6' and a 3' section of tube. Just be certain that the junctions are reversed so that the "3+6" outer tube has a "6+3" arrangement of the inner tube. Obviously, if you have access to 1/8" wall aluminum tubing (or 1" to 1.25" nominal [1.25" to 1.4" actual outside diameter] aluminum [6061- T6] pipe used for scaffolding), you can save a bit of work for the long boom. Avoid the softer aluminum electrical conduit if possible, although for the 10 meter and 15 meter beams, it should be adequate if the actual outside diameter is at least 1.25".

+

The lesson is simply this: select materials for the boom as carefully as you would for the elements. The load on a boom increases rapidly as it grows longer and the elements also grow longer.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Element Lengths
+Element                 Outer                   1/2-El.     Element
+                        Section                 Length      Length
+Narrow-Band Version:  0.75" Uniform Diameter
+Driver                                          129.0"      258.0"
+Reflector                                       140.4"      280.8"
+Medium Duty Taper Schedule Version
+Driver                  71.5"                   131.5"      263.0"
+Reflector               82.9"                   142.9"      285.8"
+Heavy Duty Taper Schedule Version
+Driver                  48.8"                   132.8"      265.6"
+Reflector               59.9"                   143.9"      287.8"
+
+Table 8.  Element lengths for 15-meter tapered-diameter 2-element Yagis.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Immediately apparent is the fact that the elements have grown to more sizable proportions. Hence, they will be more ungainly and harder to handle when raising the beam to full operating height. Hence, it pays to have proportionately more helpers around when erecting the beam. As well, the desired height of at least a half wavelength (and much more, if accessible) has risen from 16 to 22 feet, while a full wavelength height has stretched from 35' to about 22' up.

+

You may also notice that the medium duty taper schedule for 15 meters uses the same element sizes employed in the 10-meter heavy duty design shown earlier. We shall very shortly discover that the 20-meter medium duty design uses the same element sizes that were for heavy duty use on 15 meters. However, achieving the duty rating is not simply a matter of tubing diameter. In addition, the length of each tube in the sequence also contributes to the duty rating. Therefore, do not change the lengths for each size tubing without recalculating the load--a task for which there are some programs, such as YagiStress by Kurt Andress. As we increase the beam size, mechanical factors become as important as electrical factors in the total design.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                              Element Lengths
+Element                           Outer                             1/2-El.           Element
+                                  Section                           Length            Length
+Narrow-Band Version:  1.0" Uniform Diameter
+Driver                                                              193.2"            386.4"
+Reflector                                                           210.0"            420.0"
+Medium Duty Taper Schedule Version
+Driver                            61.0"                             199.0"            398.0"
+Reflector                         77.3"                             215.3"            430.6"
+Heavy Duty Taper Schedule Version
+Driver                            47.8"                             201.8"            403.6"
+Reflector                         64.5"                             218.5"            437.0"
+
+Table 9.  Element lengths for 20-meter tapered-diameter 2-element Yagis.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Perhaps the only new notable item in the 20-meter beams is the heavy-duty element structure. The element diameter jumps from 1.25" at the element center down to 1.0" for the next section. For strength, the schedule assumes that center piece is actually two pieces of tubing--a 1.25" and a 1.125" diameter section, used together.

+

The remaining elements of construction can be gleaned from any recent copy of the ARRL Antenna Book and the myriad of beam articles that have been written in any of the amateur magazines in the last decade. I would not go back too much beyond 1990, especially for beam designs. Before 1990, much of Yagi design done by amateurs was by-guess-and-by-gosh, with inflated performance claims made in the absence of good measurements or good modeling software.

+

3. 2-Element Driver-Director Yagis (with Dimensions) for 17-12 Meters

+

Although the driver-reflector 2-element Yagi has an important place among amateur beams, it is not the only kind of 2-element parasitic beam available. In stead of using a reflector behind the driven element, we may also use a director ahead of the driver. Fig. 17 shows the outline and main components of such an array.

+
+ +
+

Although I shall not ultimately recommend this kind of design for 10 meters, except in very specific cases, it may be useful to develop a 10-meter version of this antenna in order to compare it with the 10-meter driver-reflector antennas that we have examined in detail. Table 10 provides us with the general dimensions of very usable 10-meter beams of both designs, where the reflector model is the one we called the narrow-band version.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                         Driver-Reflector Yagi Design
+Design Range:                       28.0 - 29.0 MHz
+Element Diameter:                   0.5"
+Driver Length:                      16.1'
+Reflector Length:                   17.4'
+Element Spacing:                     4.32' (1/8 wl)
+                          Driver-Director Yagi Design
+Design Range:                       28.0 - 29.0 MHz
+Element Diameter:                   0.5"
+Driver Length:                      17.1'
+Director Length:                    16.1'
+Element Spacing:                     2.8' (0.08 wl)
+
+Table 10.  2-element driver-reflector and driver-director dimensions for 10
+meters.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Since the driver has become the rear element in the director-beam, we can easily see that the lengths of the forward and rear elements are quite similar for the 2 designs. However, one crucial dimension is very different: the element spacing.

+

When we place a director ahead of a driven element, the gain increases as we shrink the element spacing until we reach about 0.05 wavelength distance. The design we have selected uses a wider spacing. Remember that all amateur beams are compromises. As we shrink the element spacing of the driver-director design, the feedpoint impedance becomes very low. I have drawn a line at about 20-Ohms resistive impedance as a means of reducing power loss due to the inevitable slight losses in connections between component parts of the antenna. Hence, I use the 0.08 wavelength spacing, which yields a resonant feedpoint impedance of about 22-23 Ohms with the half-inch diameter elements in the example. In general, a spacing of 0.07 to 0.08 wavelength is usable and lends itself to a simple beta match.

+
+ +
+

Fig. 18 gives us a partial perspective on what we get with a driver-director Yagi: a bit more gain and a lot more front-to-back ratio at the design frequency. Given that the boom length is shorter than for the driver-reflector design, it would seem that we should abandon the lower performance Yagi version and adopt the driver-director beam as our standard. This hasty conclusion is why I called the azimuth pattern only a partial view of the director-beam's performance potential. In order to see a fuller picture, we should compare the performance of the two candidates across the first MHz of 10 meters.

+
+ +
+

Fig. 19 compares the free-space gain of the two types of Yagis, each with a design frequency of 28.5 MHz. The reflector version gain picture--with its descent as we increase frequency--is already clear to us. The driver-director version shows just the opposite sort of curve. Gain increases with frequency. In fact, the rate of increase is higher than the rate of decrease for the driver-reflector beam type. As a result, the director version almost reaches its peak possible gain before we cross the 29 MHz point in the graph. Note that the director version has a lower gain at the low end of the passband than the reflector version has at the upper end of the passband. Those who wish to have a relatively even performance across the 28-29 MHz span would likely be better off with the reflector version of the antenna.

+
+ +
+

Where the driver-reflector Yagi holds the greatest superiority is in the front-to-back ratio department. As Fig. 20 clearly shows, the director-type Yagi has a higher front-to-back ratio than the reflector type across almost all of the passband. Had I been willing to move the peak value a bit higher in frequency, I might have made the claim to superiority apply to the entire passband. However, I chose to set the peak front-to-back ratio very close to the design frequency. Notice that the front-to-back ratio exceeds 20 dB for nearly 200 kHz, but it falls off rapidly when we move above or below that frequency region. The steep performance curve, like the one for gain, is a consequence of the very close element spacing.

+

For a moment, let us dwell on the high performance that we can obtain from the driver-director design at the design frequency. As we mentioned very early in these notes, 2-element Yagi performance is intimately related to the relative current magnitude and phase of the currents at the centers of the two elements. We saw that the driver-reflector design was limited by the inability of widely spaced parallel linear elements to achieve values close to those of either the rear-null or maximum-gain ideals.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                                   Rear Element Current
+Spacing                           Mag.             Phase            F.S.              F-B
+ wl              inches           (rel-            deg.             Gain              Ratio
+                                  ative)                            dBi               dB
+
+Maximum rear null:
+ 0.05             20.7            0.925            163.3            6.57              >50
+ 0.1              41.4            0.945            145              6.45              >50
+Maximum gain:
+ 0.05             20.7            0.91             173              7.33              7.70
+ 0.1              41.4            0.92             166              7.36              7.22
+Driver-Director design at 28.5 MHz:
+ 0.08             33.1            1.02             154.5            6.56              20.93
+
+Table 11.  A comparison of relative current magnitude and phase between ideal and real Yagi designs.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As Table 11 shows, the driver-director design comes considerably closer to the ideals. Although the relative rear element current is a bit high, its phase angle is close to the mean between the 0.05 and 0.1 wavelength spacing values for the experimental model. As we might expect, the front-to-back ratio of the driver-director array shows the higher level of improvement over the values for the driver-reflector array.

+
+ +
+

The improvement comes at the cost of operating bandwidth. We have already seen that the front-to-back curve is steep, meaning that performance falls off rapidly above and below the design frequency. As Fig. 21 reveals, the SWR bandwidth is equally narrow and steep. Whereas the reflector design can yield full coverage for the 28-29 MHz span, the director design covers only about half the band with under 2:1 SWR. In the graph, both SWR curves are taken relative to the resistive impedance at resonance at or very near to the design frequency of 28.5 MHz.

+

The effective range of use for a high-performance 2-element driver-director Yagi is a bit under 1% of the design frequency with normal sized materials. For 10 meters, such an array would be suitable as a CW-only or a 300-500 SSB antenna. However, the design type has better homes than the wide amateur bands.

+

The so-called WARC or non-harmonic HF ham bands are very narrow frequency allocations. 12 and 17 meters are each 100 kHz wide. Driver-director Yagis can easily cover these bands while maintaining better than a 20 dB front-to-back ratio and under 1.5:1 SWR after matching. The gain over each range will vary by about 0.4 dB. Given the fairly simply construction and load offered by these short-boom arrays, a driver-director Yagi may be just the ticket to open these bands.

+

Therefore, I have scaled and adjusted the basic driver-director design for each of the two highest WARC bands. Each design has had its driver length adjusted for a beta match network--that is the coil or the hairpin. If you wish to use parallel RG-59 as a 35-37 Ohm 1/4 wavelength matching section with a resonant driver, increase the driver lengths by about 2.5%. Either system has more than enough low-loss bandwidth to handle these narrow bands.

+
+ +
+

Fig. 22 shows three separate element tapering schedules. The medium duty versions should handle 75 mph winds, while the heavy duty structure should survive 100 mph winds. (Survival, of course, is also a function of all of the elements of construction, not to mention regular preventive maintenance.) The top tapering schedule is the one I used for a 12-meter version of the antenna that appeared in QST in August of 2000. The other two schedules are taken from Yagi designs in the ARRL Antenna Book.

+

Table 12 provides the dimensional data necessary to supplement the tapering schedules shown in Fig. 22. The values shown for the beta-match hairpin (shorted stub) are for a 600-Ohm transmission line. Such a line requires a very wide spacing (6" using #12 AWG wire). For narrower hairpins, you can either recalculate the length using the WA1SPI program or you can multiply the given length by the inverse of the ratio between the old and new line impedance values. The lower the line impedance (usually associated with narrower spacing), the longer the hairpin must be.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Element Lengths
+Element                 Outer                   1/2-El.     Element
+                        Section                 Length      Length
+Basic Design:  0.5" Uniform Diameter
+Driver                                          114.0"      228.0"
+Director                                        110.6"      221.2"
+Medium Duty Taper Schedule Version (A)
+Driver                  10.8"                   115.8"      231.6"
+Director                 7.3"                   112.3"      224.6"
+Medium Duty Taper Schedule Version (B)
+Driver                  67.5"                   115.5"      231.0"
+Director                63.8"                   111.8"      223.6"
+Heavy Duty Taper Schedule Version
+Driver                  62.6"                   116.6"      233.2"
+Director                58.8"                   112.8"      225.6"
+
+Beta stub:  4.8-5.0" 600 Ohm shorted line
+
+Table 12.  Element lengths for 12-meter tapered-diameter 2-element driver-
+director Yagis.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Despite the larger average element diameter, the heavy duty element taper requires the longest elements of the set. This result is a further warning not to take short cuts when figuring the revised element lengths needed for a given element taper schedule. The amount of taper and where it occurs has a bearing on the final required dimensions, and simple averaging will rarely yield a correctly figured beam.

+

In the same QST issue containing the 12-meter Yagi, there is also a 17-meter version of the driver-director array. The design is perfectly satisfactory for use on this band. As shown in Fig. 23, we can adjust a basic design for numerous usable element taper schedules. The first, called a light-duty design for up to 50 mph winds, is the version in the article. (A true confession: the taper schedule permitted me to change bands just by moving the elements apart and by changing the 3/8" diameter tip sections.) Note that a medium duty taper schedule at 12 meters becomes no more than a light duty schedule when the element are significantly lengthened. The remaining taper schedules are once more drawn from the ARRL Antenna Book. They should be good for 75 mph and 100 mph winds, if everything else in the assembly is well-constructed.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                              Element Lengths
+Element                           Outer                             1/2-El.           Element
+                                  Section                           Length            Length
+Basic Design:  0.625" Uniform Diameter
+Driver                                                              157.2"            314.4"
+Director                                                            152.3"            304.6"
+Light Duty Taper Schedule Version
+Driver                            56.0"                             161.0"            322.0"
+Director                          51.1"                             156.1"            312.2"
+Medium Duty Taper Schedule Version
+Driver                            82.5"                             160.5"            321.0"
+Director                          77.5"                             155.5"            311.0"
+Heavy Duty Taper Schedule Version
+Driver                            54.4"                             162.4"            324.8"
+Director                          49.0"                             157.0"            314.0"
+
+Beta stub:  7.0" 600 Ohm shorted line
+
+Table 13.  Element lengths for 17-meter tapered-diameter 2-element driver-director Yagis.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Needless to say, all of the construction hints we have mentioned in connection with the driver-reflector array also apply to the driver-director array. In addition, consult as many amateur Yagi books and articles as you can to develop your final construction strategy. Pay as much attention to the support and rotating system as you do to the beam antenna on top of the tower. A properly based tower with correct guying is not a simple or casual installation. Also, be sure to read up on lightning protection.

+

Conclusion

I wish we had the time to cover the remaining topics on the original list. For example, we may have left the impression that we can only go so far in achieving the ideal rear-null relative current magnitude and phase relationship with a geometric arrangement of elements. However, if we judiciously bend the element ends toward each other, we can achieve very nearly ideal current conditions--about 30+ dB worth of front-to-back ratio. By now, almost everyone knows the bent-element array as the Moxon rectangle. +

If we had more time and space, we might also look at a number of practical wire Yagis (and Moxon rectangles) for 80, 40, and 30 meters. In the process, we would learn how to at least make these non-rotating parasitic arrays become reversible.

+

And if we had still more time and space, we might also learn how to combine the performance of the driver-director array with the broad-banded characteristics of the driver-reflector array--all through the use of phasing lines. Interestingly, it is not too difficult to overcome the limitations of the ZL Special (very low feedpoint impedance) and the HB9CV (complex matching system) with a much more general phase line system made from common coaxial cables.

+

But my time and space have disappeared. However, I hope that the exercise leaves you a little more comfortable with 2-element beams, both in terms of understanding how they work and in terms of supplying you with versions of these parasitic arrays for 20-10 meters that you can in fact build successfully.

+

When you fully understand the dipole, you are 70% of the way toward understanding the 2-element beam. After you have mastered the 2-element beam, you are 90% of the way to understanding all larger arrays. For once you have added that second element, everything else is just a little more of mostly the same. However, upon reaching that point, you will find that those little differences become mighty intriguing.

+
+ +
+

Updated 5-19-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Upper, Matching, Stepped Diameter, Yagi


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+ Title graphic +

Mastering Some Mysteries of 2-Element Beams Part 2

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This talk was originally prepared for the 2002 Dayton FDIM Symposium

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The decision to upgrade a single wire antenna into a multi-element beam marks a major step in QRP station sophistication. Whatever the band, whatever the material, a 2-element array is more than a simple doubling of elements. It represents additional gain, additional directivity, and additional responsibility to know how the thing works.

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Last year, I presented a list of topics that seemed to be the most important ones in understanding horizontal 2-element beams:

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  • 1. How 2-element beams work (done);
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  • 2. 2-element driver-reflector Yagis (with dimensions) for 20-10 meters (done);
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  • 3. 2-element driver-director Yagis (with dimensions) for 17-12 meters (done);
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  • 4. More geometric possibilities (to be done);
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  • 5. Horizontal phased directional arrays (to be done);
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  • 6. Wire beams (with dimensions) for 80 and 40 meters (to be done).
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Unfortunately, space let me only cover 3 of the topics. That leaves three to go--and my promise to cover them in FDIM 7. Since FDIM 7 is here, so are the final 3 topics--with an addition.

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1. The Human Response to a First Beam

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If you have previously used only a dipole, double, vertical, or other basic antenna from your operating site, then your first beam will surprise you. Wherever pointed and however simple or modest the design, the beam will seem almost like magic, as the stations you listen to become so much stronger than they used to seem. Indeed, you will almost be inclined to rave over your new antenna--whether commercially built or home-brew--to the point of telling others that no better antenna has ever been designed, sold, built, or used. You may even wish to classify it as a "killer," although this expression leaves me cold, since I know of a few former hams who were in fact killed by their antennas. +

Notice that I predict this reaction to your first beam, even without asking what kind of beam you might have. How can we explain such uniform response?

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Perhaps Fig. 1 can help us. Overlaid on the polar plot are the azimuth patterns of 3 antennas, each 1 wavelength above ground. The dipole pattern is obvious. The two 2-element Yagi patterns represent a full size Yagi and a smaller, highly loaded version that is not dissimilar in performance to a number of Yagi and non-Yagi designs on the market. As we noted last year, loading a reflector can increase the front-to-back ratio, while loading the driver reduces forward gain.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                          Performance of 3 Sample Antennas
+
+Antenna                           Forward Gain                      Front-to-Back
+                                  in dBi at 14                       Ratio in dB
+                                  Deg. TO Angle
+Dipole                             7.9                              ---
+Full-Size                         11.9                              12.3
+Loaded                            10.3                              17.5
+
+Table 1.  A comparison of the performance of three antennas.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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All three antennas provide good nulls 90 degrees off line, thus cutting QRM from the antenna sides. Relative to the dipole, both beams show a marked reduction in signal strength to the rear, and here is our first piece of magic. What comes from the front seems stronger to our ears in part because it is no longer competing so heavily with signals from the rear. Regardless of the presence or absence of forward gain, the reduction of QRM and QRN from the rear will always make the signal in the forward direction easier to copy.

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Let's add up what we obtained from each of the two beams. The loaded beam gives us nearly 3 S-units of rearward quieting (17.5 dB) relative to the dipole, while providing another half-S-unit (2.4) dB of forward gain, for a seeming net of nearly 3.5 S-units of improvement on reception. The full-size 2-element Yagi only gives us 2 S-units of rearward quieting (12.3 dB), while providing over a half-S-unit forward gain (4.0 dB): 2.5+ S-units total apparent receiving advantage. So far, the small, loaded beam seems to have the advantage.

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Unfortunately, our installations never have ways to tell which antenna has the advantage on the transmitting side of the coin. However, we know that the front-to-back ratio has no bearing on the signal we send forward. Hence, the full size beam has a 1.6 dB advantage over the loaded beam. Since 1 dB is the minimum discernable difference between signal strengths to the human ear, the full-size beam's slightly higher gain might make a difference at the other end of the line. Indeed, it might make the difference between whether our QRP QSO succeeds or fails.

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Rarely do we lack receiver sensitivity and bandwidth filtering. However, a commitment to QRP always carries with it a limitation to our transmitted power. Hence, despite the slight reduction in overall receiving advantage, the slightly higher gain of the full size beam is advisable (unless limited by our yard size, support structure, or money).

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However, most first-beam users rely only on what they hear to determine what they claim about their beams. If general use is all we have in mind, then perhaps nothing is wrong in this response. However, I have heard mediocre designs extolled as the finest antennas ever built solely on the user's first response to listening to signals on a beam. In fact, all that we can glean from such reports is that the beam is directional, but not that it is comparatively good relative to other designs.

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The lesson: just because you have invested $300 to $500 in your first beam (with equal or greater amounts in support and rotating abilities), do not inflate its performance to match the economic situation. Be modest and let your accomplishments with the new antenna speak for you.

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2. Alternative Geometries

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Since the 1920s and 1930s, antenna experimenters have worked with alternative shapes for their antennas in an effort to find one or more that provide the best performance in the minimum space. Fig. 2 shows a few of the shapes, but not necessarily to scale. Each driver element with a dot indicating a feedpoint is about 1/2 wavelength long. +
+ +
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The X-beam was one of the earliest, with the Roman-X following, and finally the folded X-beam as the most compact version. Unfortunately, folded Xs tend to have low gain and large rear quartering lobes, despite the fact that they fit inside a quad loop laid flat.

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The VK2ABQ square is related to experiments done on similar squares in the 1930s. Derivative from it is the diamond and the hex beam, the latter combining the pinched center of the X with the close proximity of the element ends. Of the 6 alternatives, only the hex- beam is in commercial production, accompanied by a plethora of maker and user claims. Perhaps what is most significant about the hex is that it is a compact and relatively light- weight design that is directional--whatever the level of performance--and fits small yards or roof tops with a TV rotator for turning power.

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What the hex and the square have in common is that they employ two forms of element coupling: the mutual coupling between parallel or nearly parallel elements that we saw in last year's standard Yagi designs and additional coupling between the element ends. Some writers distinguish the coupling forms by calling them inductive and capacitive, respectively.

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Perhaps the most refined version of the dual-coupled parasitic array is the Moxon rectangle, a personal favorite, even though I have no monetary interest in the design. It is simply intriguing to me--enough so that I have developed a computer program that yields designs that are compatible with 50-Ohm coax. You need only enter the design frequency and the element diameter--whether wire or tubing--to get working dimensions on any frequency from the AM BC band to lower UHF. Fig. 3 gives the key to the dimension reports.

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You can find the program for these dimensions in a number of places: my website (Moxon Rectangles and Online Calculator), VE3ERP's HAMCALC suite of GW Basic utilities, and even a NEC-Win Plus equation-based model. However, to save you searching time, the following tables present dimensions of Moxon rectangles with elements that range from AWG #14 copper wire to 1" aluminum tubing, for 20 through 10 meters. All dimensions are in inches. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                        10-Meter (28.37-MHz) Moxon Rectangle Dimensions
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+Element          A                B                C                D                 E
+#14                               151.4            22.8             4.2               22.3             55.3
+#12                               151.3            22.6             4.4               28.3             55.3
+0.5"                              150.0            20.6             6.3               28.7             55.6
+0.625"           149.8            20.3             6.6              28.7              55.6
+0.75"            149.6            20.0             6.8              28.7              55.5
+0.875"           149.5            19.7             7.0              28.8              55.5
+1.0"                              149.4            19.5             7.2               28.8             55.5
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+                        12-Meter (24.94-MHz) Moxon Rectangle Dimensions
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+Element          A                B                C                D                 E
+#14                               172.3            26.0             4.7               32.1             62.8
+#12                               172.2            25.8             4.8               32.2             62.8
+0.5"                              170.7            23.6             6.9               32.6             63.2
+0.625"           170.5            23.3             7.3              32.6              63.2
+0.75"            170.3            23.0             7.6              32.6              63.2
+0.875"           170.2            22.7             7.8              32.7              63.2
+1.0"                              170.1            22.4             8.1               32.7             55.2
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+                        15-Meter (21.20-MHz) Moxon Rectangle Dimensions
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+Element          A                B                C                D                 E
+#14                               202.8            30.8             5.3               37.7             73.8
+#12                               202.6            30.5             5.5               37.8             73.8
+0.5"                              201.0            28.1             7.9               38.3             74.3
+0.625"           200.8            27.7             8.3              38.3              74.3
+0.75"            200.6            27.3             8.6              38.4              74.3
+0.875"           200.4            27.0             8.9              38.4              74.3
+1.0"                              200.3            26.7             9.1               38.5             74.3
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+                        17-Meter (18.12-MHz) Moxon Rectangle Dimensions
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+Element          A                B                C                D                 E
+#14                               237.4            36.1              6.1              44.2             86.4
+#12                               237.2            35.9              6.3              44.2             86.4
+0.5"                              235.4            33.2              8.9              44.7             86.8
+0.625"           235.1            32.7              9.4             44.8              86.9
+0.75"            234.9            32.3              9.7             44.9              86.9
+0.875"           234.7            32.0             10.0             44.9              86.9
+1.0"                              234.5            31.7             10.3              44.9             86.9
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+                        20-Meter (14.13-MHz) Moxon Rectangle Dimensions
+
+Element          A                B                C                D                 E
+#14                               304.7            46.6              7.5              56.5             110.6
+#12                               304.5            46.3              7.8              56.7             110.8
+0.5"                              302.2            43.1             10.9              57.3             111.3
+0.625"           301.9            42.6             11.3             57.4              111.3
+0.75"            301.6            42.1             11.8             57.4              111.3
+0.875"           301.4            41.7             12.2             57.5              111.4
+1.0"                              301.1            41.3             12.6              57.5             111.4
+
+Table 2.  Moxon rectangle Dimensions:  20-10 meters.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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We shall look briefly at other Moxon dimensions when we touch on lower HF wire beams. The most critical dimension is the gap between element ends. Combined with the general shape--either more square or more rectangular--the gap sets the operating impedance of the array. The other dimensions--except perhaps for the driver tail lengths to bring the array to resonance on the design frequency--change slowly. The overall front-to-back dimension (E) changes very slowly with wide differences in element diameter.

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Before we look at how to build a Moxon and how it performs across a full ham band, let's see what reasons we might have for selecting a Moxon. First, for a given band, the side-to-side dimension is about 70% of the same dimension on a full size Yagi. Hence, the 35' elements of a 20-meter Yagi shrink to about 25' in the Moxon.

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Second, the pattern of a Moxon is desirable in some circumstances.

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Fig. 4 compares the azimuth pattern of a Moxon with that of a full-side Yagi, with both antennas 1 wavelength above ground and an elevation angle of 14 degrees. The Moxon sacrifices about 0.5 dB of gain, but gives it back in the form of a wider beamwidth. Note that the Moxon does not shows its deepest pattern nulls at 90 degrees off the forward heading. The angle is closer to 120 degrees each side of the forward bearing. For a simple installation, we obtain wider coverage without turning the beam. The high front-to-back ratio of the Moxon is obvious: 20 dB is a normal average across a ham band, with the peak at the design frequency. The originator of the rectangle, Les Moxon, G6XN, subscribed to the good ears theory of operation: if you cannot hear them, you cannot work them. He also used a fixed installation.

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Fig. 5 shows two ways to install a wire version of a Moxon. We can make a cheap fixed installation using 4 posts and ropes. We can set and preserve the gaps between tails by running a cord from the front corner to the rear corner. If we use a piece of PVC instead of rope, with the tails taped to it, we might get by with just a post on either end of the array. For further thoughts on wire installations, see my QST article on "Having a Field Day with the Moxon Rectangle," in the June, 2000 issue.

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My original Moxon was described along with a brief history of the design's evolution from VK2ABQ squares in "Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and The Modified Moxon Rectangle," Communications Quarterly, (Spring, 1995), 55-70. That version used nonconductive support rods from a central plate to hold the wire in place--again, with a cord from front-to-back on each side to keep the tails and gap fixed in position. This version permitted me to rotate the beam.

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Fig. 6 outlines the basic parts of a Moxon with tubular elements. The boom--conductive or non-conductive--supports plates made from varnished plywood or polycarbonate, and the plates support the elements. To preserve the gap, insert a small length of rigid tubing, such as CPVC, into each tail end and fasten in place.

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You can make rounded corners by carefully bending sections of aluminum tubing. Alternatively, you can use small triangular plates to join the main and tail portions of the elements. One enterprising Australian builder used the corners of defunct lawn chairs for his Moxon. Ingenuity is the key. You can find additional construction hints in "An Aluminum Moxon Rectangle for 10 Meters," The ARRL Antenna Compendium, Vol. 6 (Newington: ARRL, 1999), pp. 10-13.

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If you use stepped diameter tubing, here is how to compensate. First, select the dimensions for the average size of the tubing that you plan to use, taking into account the length of each size used. Then, use the gap dimension for the size tubing that forms the gap. The results will by very close to precisely on target.

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Good precision in construction is always sound advice, but the Moxon plays very well without undue fussiness. The impedance performance is very broad, as shown by the 50-Ohm SWR curve for 28.0-29.0 MHz in Fig. 7. The curve is for a tubular model, and the angles will be more extreme for a thin-wire version. Nevertheless, there is plenty of room for a wire version to cover 1 MHz of 10 meters with under 2:1 SWR, and if the beam covers 10, then scaled versions will easily cover all of the bands from 20 through 10 meters.

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As you can see from the curve, the SWR below the design frequency rises more rapidly than above the design frequency. Therefore, for the wide ham bands, I set the design frequency a little over 1/3 the way up the band.

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Peak front-to-back ratio--whether interpreted as the 180-degree ratio or the worst-case ratio--occurs on the design frequency. As shown in Fig. 8, it remains well above 15 dB at the band edges and averages more than 20 dB across the band. Like all 2-element driver-reflector parasitic arrays, the forward gain decreases as frequency increases. In common with other arrays with shorter side-to- side lengths, the gain decrease curve is steeper than for a full size Yagi with the same front-to-back element spacing. However, the gain is highest in the most used part of the band, from 28.0 to 28.6 MHz.

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The Moxon can be redesigned for other impedances. At my website are notes on designing 95-Ohm versions of the antenna to simplify making turnstile pairs for satellite communications. Turned on edge, the Moxon rear null makes a fine detector for direction finding (fox hunting). Although Moxons do not do well when we nest them for several bands, it is possible to use a 20 meter Moxon in place of a 20-meter Yagi in such commercial tri-banders as the Force 12 C-3. If the C-3 does not fit our property, perhaps a 25' wide Moxon-ized version might.

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In the end, the Moxon serves us here as a prime example of possibilities for using alternative geometries for our 2-element beams. What we may lose in gain, we might more than make up for in terms of other advantages that may suit some specific operating needs.

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3. Phased 2-Element Arrays

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The 2-element phased array goes under various names, the most common of which are the ZL-Special and the HB9CV. Actually, these two names can now be used as labels for generic types of horizontal phased arrays: the direct-phased array and the matched-phased array. For a detailed study of these antenna types, see "Some Notes on Two-Element Horizontal Phased Arrays," Parts 1-4, in The National Contest Journal, Nov., 2001, through May, 2002. +

Originally, these antennas competed with primitive Yagi designs that had not yet been optimized by computer simulations. The phased 2-element arrays received a highly inflated gain estimate based on the poor performance of the Yagis. To this day, they sustain a numerical reputation that has no justification. However, they do have some interesting advantages over the standard 2-element Yagi.

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With element spacing in the vicinity of 1/8 wavelength, 2 elements with any configuration have limits to their gain, no matter whether we phase them for maximum gain or maximum rear null. See Fig. 9.

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The maximum free-space gain in the maximum-null situation is about 6.2 dBi, about the same or slightly less than the standard 2-element Yagi. In the maximum-gain situation, the gain might rise to about 7.3 dBi, about the same as a 2-element quad. However, the front-to-back ratio goes to pot.

+

It is possible to find an intermediate situation in which we raise the maximum gain to about 6.6-6.7 dBi while sustaining a 20 dB front-to-back ratio. The added gain is useful although marginal. The increased front-to-back ratio--about 6-7 dB higher than a standard full-size Yagi--is the source of the phased array's reputation, since we tend to judge with our ears and not with test instruments. However, if you hear of gain claims for a 2-element phased array that claim a free-space forward gain above 7 dBi, try not to believe them.

+

The 2-element horizontal phased array has sufficient advantage over a 2-element Yagi that it bears a quick investigation. We shall look at the basic design of each generic type and some variations of each. Our goal will be to find one or more that we might build for ourselves. That goal turns out to be harder than it appears.

+

A. Direct-Phased or ZL-Special Arrays: The original ZL-Special appeared in the late 1940s and early 1950s, and came in several styles, all of which rested on a mistake. Fig. 10 surveys some of the early breeds of ZL-Specials.

+
+ +
+

All of the versions of the ZL-Special labored under the belief that the phasing of two elements depended on the length of the transmission line between the two elements in its function to transform impedance. Designers sought a 135-degree impedance transformation, so they used a 45-degree (1/8 wavelength) line with a half twist. The trombone tries to account for the velocity factor of the line.

+

In fact, phasing is a function of the relative current magnitudes and phases on the two elements--not the impedance at the element feedpoints. As well, the rear element when spaced about 1/8 wavelength from the forward element needs a phase angle close to -45 degrees. The difference between 135 and -45 degrees makes no difference to impedance, since the impedance repeats itself every 180 degrees. However, current repeats itself only once per 360 degrees, and the -45-degree value is a better guide to what adjustments have to be made to a given design.

+
+ +
+

Fig. 11 shows the basic elements of a fundamental ZL-Special design. The key questions are these: how long are the elements for a given element diameter? How far apart do we space the elements? What value of transmission line will work to transform the current magnitude and phase from the forward element to the rear? How long should we make the line? What treatment do we need at the combined feedpoint to match a 50-Ohm main feedline to the antenna?

+

Let's roughly design a workable ZL-Special. We shall use 28.5 MHz as our design frequency and keep all dimensions in terms of wavelengths. The elements will be 1/2" in diameter, or 0.00121 wavelength. Now let's select a forward element length of 0.465 wavelength and a rear element length of 0.506 wavelength, with a 0.125 (1/8) wavelength spacing. From last year's notes, we know that we could choose other element spacings, as long as we selected the correct relative current magnitude and phase angle for the elements--and assuming that we might obtain it with existing transmission lines.

+

Early tubular-element ZL-Specials tended to use 75-Ohm line for phasing work. Actually, to achieve the required current phase relationships, a line nearer to 25 Ohms works best. Since such a line is not available, let's see what happens if we use RG-83, a 35-Ohm line (available from the Wireman of South Carolina). An electrical length of 0.197 wavelength will work, and since this length translates into a physical length of 0.13 wavelength with the line's 0.66 velocity factor, it will fit the space between elements. The pattern that results appears in Fig. 12 and is highly promising.

+
+ +
+

The gain is a bit above a 2-element Yagi, but the front-to-back ratio is superlative. However, we have one more obstacle to overcome. The feedpoint impedance at the junction of the first element and the phase line is 20 Ohms. We can fix this problem by using a 0.197 electrical wavelength (0.13 physical wavelength) of the same RG-83 to form a matching section. With this line in place, we obtain the SWR curve of Fig. 13.

+
+ +
+

Compared to a directly fed system, the 50-Ohm SWR curve is backward, sloping more gently below the design frequency. That phenomenon is a function of the matching section. We easily obtain under 2:1 SWR across the first MHz of 10 meters, and what works on 10 scales nicely for the other upper HF bands.

+
+ +
+

Fig. 14 shows the anticipated gain and front-to-back curves across 10 meters. A phased array usually shows the gain curve of a Yagi with 1 or more directors: it rises with frequency. The ends and middle of the curve are about a quarter dB higher than the curve for a full-size Yagi.

+

The front-to-back curve--shown as 180-degree values--is better than virtually any full size 2-element Yagi, dipping below 20 dB only at the upper end of the band.

+
+ +
+

Fig. 15 shows the free-space patterns near the band edges to demonstrate that the antenna in fact performs well across the band. However, that fact does not mean that the antenna is easy to build. RG-83 costs $3/foot, but that is its least problem. If we wish to build this antenna, then we will need a non-conductive boom--perhaps PVC. Such booms are practical only on 10 and perhaps 12 meters due to weight and sag.

+

We need the non-conductive boom due to the fact that the phase line has a reversal along the way. Under these conditions, the line may unevenly couple energy to a metallic boom, which is normally connected to the mast and ultimately to ground. Any such coupling disrupts the current magnitude and phase relationships between elements. We might try some large ferrite decoupling shells over both ends of the coax to suppress currents on the outer portion of the phaseline, but quickly our little array takes on more weight than we might wish.

+

Let's try a variant that is easier to build. Roy Lewallen, W7EL, introduced what he called the Field-Day Special. For more details than we have room for here, see his original article: "Try the 'FD Special' Antenna," QST (Jun., 1984), 21-24. The outlines of a 10-meter version appear in Fig. 16.

+
+ +
+

Roy wanted a Field Day antenna that he could roll up and carry to mountain sides and tops, so he used common parallel line with folded dipole elements and a 300-Ohm feedline. The element lengths show two sizes: the shorter is for common 450-Ohm line, which is stronger, and the longer is for 300-Ohm line, which is lighter. Actual lengths may be 1-2% shorter due to the insulation on the wire. In the analytical model, the phase line is 4.9' long (0.142 wavelength) and accounts for the 0.8 velocity factor of the phaseline material. This length is slightly longer than the 4.27' (0.124 wavelength) spacing of the elements. The feedpoint impedance is between 40 and 50 Ohms resistive, but has some inductive reactance. Hence, Roy added series capacitor on a small plate at the feedpoint. 90-110 pF per capacitor will compensate and yield a mostly resistive feedpoint impedance for a coax feedline.

+
+ +
+

Fig. 17 shows free-space patterns for the middle and ends of the 10-meter band (first MHz) to demonstrate that the antenna has potentially the same properties as a ZL-Special composed of tubular elements. The actual curves are very similar to those in Fig. 13 and Fig. 14. You may scale the antenna for any of the ham bands and expect similar results. Tied to supports (like those for a wire Moxon), the antenna is a simple and inexpensive field antenna--and not a shabby home antenna as well. See Roy's article for the stub techniques he used to switch directions for the array.

+

Although it is conventional in a directly phased ZL-Special to join the phase line to the forward element, there is no rule that says we must do the job this way. All we want to obtain is a set of current magnitude and phase values on the two elements that will give us the best compromise between gain and front-to-back ratio for a set of elements and a certain spacing between them. Fig. 18 shows an alternative arrangement for the phase line and the feedpoint.

+
+ +
+

The elements of this design are identical to those of the original tubular ZL-Special. The diameter is 0.5" (0.00121 wavelength), with the forward elements 0.465 wavelength long and the rear element 0.506 wavelength long. The element spacing is 0.125 wavelength. The key difference is that we shall presume that RG-83 is unavailable, but we do have some RG-8X with a velocity factor of 0.78.

+

As we noted early in our exploration of ZL-Specials, higher impedance lines do not achieve the correct relative current magnitudes and phase angles that we need. Now we must add the qualification that they fail if we use the junction of the phaseline and forward element as the feedpoint. However, we can alter the relative phasing by using a short length of phaseline between the forward element and the junction that forms the feedpoint.

+

For the current design, the forward length is physically 0.015 wavelength (electrically 0.019 wavelength), while the rearward section is physically 0.13 wavelength (electrically 0.167 wavelength)--both made of RG-8X. The net impedance is just about 25 Ohms. Hence, a 1/4 wavelength section of paralleled RG-59--adjusted for the velocity factor of the foam or solid core line used--gives us a close match to our 50-Ohm main feedline.

+
+ +
+

Fig. 19 shows the performance patterns at the middle and ends of the first MHz of 10 meters--very similar to those of the other 2 variants on the ZL-Special. Like the initial ZL-Special design, the phase line requires a non-conductive boom or a method of decoupling the phase line outer braid. For construction details of one such array, see "Two Hilltoppers for 10 Meters: a Dipole in a Tube and a Beam in a Boom," The ARRL Antenna Compendium, Vol. 6 (Newington: ARRL, 1999), pp. 1-9.

+

B. Matched-Phased or HB9CV Arrays: Although the English-speaking world tends to favor ZL-Special phased arrays, the European continent finds greater favor in the HB9CV horizontal phased array. However, proponents of the design are no less prone to inflating the performance potential. The HB9CV and its variants differ from the ZL-Special only on the technique of phasing, not in performance potential. However, the matched-phasing system of the HB9CV and its variants does offer a degree of flexibility in design so that the end product--although more difficult to build--tends to yield more reliable results.

+
+ +
+

As shown in Fig. 20, the HB9CV phased array comes in two major varieties, with many variations. By pure experimentation, the developer came up with elements lengths that are 0.46 wavelength forward and 0.50 wavelength rear, with a spacing of 0.125 wavelength. The prescribed element diameter range is 0.004 to 0.007 wavelength, much too fat for modern building: 1.5" at 10 meters. Hence, some adjustment is necessary.

+

The key to the HB9CV is the Tee or Gamma match system applied to each element. The separate functions of these sections has often been overlooked. The rear element matching section alters the rear element feedpoint impedance until it is a close match with the phase line. The match will not be 300 Ohms for the Tee or 75 Ohms for the gamma. Instead, it will be whatever impedance a physical 1/8 wavelength line will show when we take the line's velocity factor into account. Once matched, the current transformation of magnitude and phase angle along the line will track very closely with the impedance transformation, resulting in close to optimal values on the rear element.

+

The forward element matching section in the version shown has a different function. The junction of the phase line and the forward elements will normally show a low impedance. The forward gamma provides a match to the main feedline. These two functions lie at the heart of all of the variants on the HB9CV. They also allow the designer to customize a design to a set of building blocks--element sizes, element spacing, and phase-line type--and still obtain the desired patterns.

+

The HB9CV is capable of broad-band performance with consistent properties across any upper ham band (including versions up to at least 2 meters), as evidenced by the patterns in Fig. 21 for the Tee version of the array. The 50-Ohm SWR is well under 2:1 across the band.

+
+ +
+

The HB9CV has the advantage of permitting direct boom-to-element mounting. However, for the newer home builder, it holds a disadvantage: the exact dimensions of the element lengths and the matching sections will very from one selection of material size to the next. Hence, casual building of an HB9CV often results in a relatively mediocre antenna that fails to achieve the patterns shown. However, if we apply the matching principles in somewhat different ways, we can come closer to something that we can build and adjust in the backyard.

+

A recent design has emerged from Eric Gustafson, N7CL, and is available from CAL-AV in 30- and 40-meter versions. Let's look at the basics of the design in Fig. 22 and adapt them to upper HF regions.

+
+ +
+

The N7CL design makes use of beta matches at each element feedpoint. We described the principles of the beta match in the FDIM-6 presentation. Briefly, we shorten each element until it shows a capacitive reactance of about -j20 to -j40 Ohms, depending on the matching needs. We then add a shunt inductive reactance to raise the impedance to a desired level. So we expect the N7CL elements to be a bit shorter than the corresponding HB9CV or ZL-Special elements. For 1/2" elements, the forward elements is 0.445 wavelength and the rear element is 0.477 wavelength. The spacing is also closer: 0.111 wavelength.

+

The elements require insulated mounting--using plates such as those shown for the Moxon rectangles. The 100-Ohm phaseline will be isolated from the metallic boom: we shall build it from two sections of 50-Ohm cable. RG-8X has a velocity factor of 0.78, so the required line length will not show the same value physically as it does electrically. A physical length of 0.131 wavelength allows us to pass the cable through the boom and connect it to the elements at each end.

+

The rear stub must raise a natural impedance of about 16 Ohms resistive with nearly -j40 Ohms of capacitive reactance to about 100 Ohms resistive. A 50-Ohm shorted stub with an electrical length of about 0.111 wavelength will do the job. The combined phase-line/forward-element impedance at the feedpoint is also low and capacitively reactive: about 21 - j22 Ohms. So we need another beta shorted stub of 50-Ohm cable, this time, about 0.126 wavelength electrically. Now we have a pretty good match to a 50-Ohm feedline across 10 meters. We may tuck these stubs into the boom ends to keep them out of the weather.

+
+ +
+

Fig. 23 shows the potential performance of the N7CL design. Because the rear element has an impedance transformation that reverses the reactance transformation across the band as seen by the forward elements, the gain curve is the reverse of all of the other phased arrays that we have observed. However, like all of the other phased arrays, it out-performs a reflector-driver Yagi by about a quarter dB. The front-to-back ratio drops below 20 dB only at the upper end of the first MHz of 10 meters. It should be a straightforward task to scale this design to the other upper HF bands so that the peak performance ends up in the best part of the band.

+
+ +
+

The 50-Ohm SWR curve shown in Fig. 24 shows one slight limitation of the N7CL design on 10 meters: the array just barely makes the 2:1 limit that we normally use as a standard. However, this limitation will not be a problem on the narrower 20 and 15 meter bands.

+
+ +
+

Fig. 25 samples the performance of the N7CL design at checkpoints across the band.

+

What HB9CV does with gamma and Tee matches and N7CL does with beta matches, we can also achieve in other ways. For example, if we lengthen the elements, the naturally low impedance of an all-fed array will slowly rise. At a certain length and spacing the rear element will show a 100 Ohm impedance, accompanied by a inductive reactance. With a 100-Ohm phase line, the combined forward element and phase line junction will show a 50-Ohm impedance, also accompanied by an inductive reactance. Fig. 26 shows the outline of such an array.

+
+ +
+

In this array, the rear elements is 0.622 wavelength, with a 0.601 wavelength forward element, using our standard half-inch 10-meter elements. The spacing is 0.145 wavelength, wider than the other arrays. The phaseline will be the same dual RG-8X that we used in the N7CL array.

+

The physical line length in the example is 0.145 wavelength (0.186 wavelength electrically), although minor changes in length have little effect on performance. On the plate used to insulate the rear element from the boom, we add a 50 pF capacitor to each side of the line (for a net 25 pF of reactance compensation). At the forward end of the line, we need a pair of 30 pF capacitors (net 15 pF, since they are in series) to compensate for the feedpoint reactance. The result is a broadband response across the 28.0-29.0-MHz span that makes SWR a matter of little significance. In fact, the antenna is sufficiently broadband to allow the use of twin 75-Ohm cable for a phase line with little change in performance.

+
+ +
+

The sample patterns in Fig. 27 reveal that the capacitively matched phased array has a little more gain than the other phased arrays. This bonus results from the use of elements that are about 20% longer than standard. Indeed, we can continue to squeeze more gain from the array while maintaining the front-to-back ratio properties by increasing the element diameter and length, and by further increasing the spacing.

+

I have presented this array of phased arrays mostly to show what is possible (and reasonable) for 2-element arrays. The arena of 2-element phased arrays still resounds with excessive claims and more than a little unsubstantiated rationales. In the end, however, with the 2-element phased array, we get a little more because we put a little more into them by way of obtaining more optimal relationships between the element current magnitudes and phases.

+

The following table will give you a summary view of the situation. It compares the performance of a narrow-band driver-director Yagi, a broad-band driver-reflector Yagi, a standard ZL-Special array, and the N7CL phased array, when all antennas are 1 wavelength above average ground.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   Comparative Performance Figures of 2-Element Arrays
+                      All Arrays 1 Wavelength Above Good Ground at 28.5 MHz
+
+1.  Reflector-Driver Yagi
+Dimensions in wavelengths:
+Reflector        Driver           Element            Element
+Length           Length           Spacing            Diameter
+0.5028           0.4620           0.1250             0.001207 (0.5")
+Performance:
+Gain             TO Ang.          2nd Lobe           Angle          Main-             Front
+                                                                    2nd               -Back
+dBi              degrees          Gain dBi           degrees        Lobe              Ratio
+                                                                    Ratio dB          dB
+11.61            14               9.35               46             -2.26             12.52
+
+2.  Driver-Director Yagi
+Dimensions in wavelengths:
+Driver           Director         Element            Element
+Length           Length           Spacing            Diameter
+0.4972           0.4670           0.0750             0.001207 (0.5")
+Performance:
+Gain             TO Ang.          2nd Lobe           Angle          Main-             Front
+                                                                    2nd               -Back
+dBi              degrees          Gain dBi           degrees        Lobe              Ratio
+                                                                    Ratio dB          dB
+11.83            14               9.49               46             -2.34             19.58
+
+3.  ZL-Special
+Dimensions in wavelengths:
+Rear El.         Fwd El.          Element            Element        Phaseline--Note 1
+Length           Length           Spacing            Dia.           Length        Zo      VF
+0.5060           0.4650           0.1250             0.0012         0.1300        35      0.66
+Performance:
+Gain             TO Ang.          2nd Lobe           Angle          Main-         Front
+                                                                    2nd           -Back
+dBi              degrees          Gain dBi           degrees        Lobe          Ratio
+                                                                    Ratio         dB
+11.68            14               9.51               47             -2.17         31.62
+
+2.  N7CL Phased-Array with Rear-Element-Matching
+Dimensions in wavelengths:
+Rear El.         Fwd El.          Element            Element        Phaseline--Note 2
+Length           Length           Spacing            Dia.           Length        Zo      VF
+0.4972           0.4670           0.0750             0.0012         0.1314        100     0.78
+Performance:
+Gain             TO Ang.          2nd Lobe           Angle          Main-         Front
+                                                                    2nd           -Back
+dBi              degrees          Gain dBi           degrees        Lobe          Ratio
+                                                                    Ratio         dB
+11.74            14               9.49               46             -2.25         31.44
+
+Note 1:  ZL-Special uses a feedpoint impedance matching section.
+Note 2:  N7CL array uses shorted stubs for rear-element matching and for feedpoint matching.
+
+Table 3.  Comparative performance figures of sample 2-element arrays with all arrays 1 wavelength above good ground at 28.5 MHz.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table reveals several facts of interest. First, the phased array extra gain is not especially significant in operation. Second, the phased array shines in obtaining the front-to-back ratio associated with the narrow-band driver-director array, but spreading it over the broad frequency span associated with the driver-reflector array. Third, there is no significant difference among all of the elevation data relative to second lobe-first lobe comparisons.

+

The 2-element phased array is a distant cousin of the log periodic dipole array (LPDA). There are designs for larger arrays and for multi-band arrays that use 2 or three phased elements for drivers, along with some parasitic elements. Since many of the designs do not follow LPDA formulas or follow any of the design principles shown here, but instead emerge from experimental work, precisely classifying these hybrid driver sets is an exercise in futility.

+

Because 2-element phased arrays tend to be specialized monoband antennas, I shall not provide a set of building tables as I did last year for the Yagis. However, you may develop your own dimensions using a fairly straightforward technique that employs antenna modeling software such as EZNEC or NEC-Win Plus. These programs use NEC-2 and a set of substitute uniform-diameter elements for cases where a linear element near resonance uses stepped-diameter construction. Here is how to adapt the basic designs shown here to your proposed band of operation and tubing schedule.

+

1. First, scale the design from the 10-meter design frequency (28.5 MHz) to the new design frequency in one of the other upper HF ham bands. Take the inverse of the frequency ratio and multiply it times the present element lengths and spacings. (EZNEC contains an automatic scaling function which will calculate the new element lengths, spacing, and transmission line lengths.)

+

2. Record the new element lengths. Now replace the elements by the more complex collection of tubing lengths that make up the stepped-diameter elements. For the outer or tip element limit, start with the original tip limit. However, check the substitute element chart and find what the outer dimensions are for each element. Adjust the tapered tip until the substitute element yields the same uniform substitute element length as you determined from the simple scaling.

+

3. Check the modeled performance and make any fine adjustments necessary to obtain the performance curves of the original scaled model--or to improve on them.

+

If you have always been a little fearful of modeling antennas, you may wish to explore the new ARRL on-line NEC-2 modeling course. By the end of the course, the technique that I just described will seem simple and obvious.

+

Now build your favorite 2-element phased array.

+
+

Some Wire Yagis and Arrays

+
In our exploration of upper HF 2-element parasitic and phased arrays, I have neglected the lower HF region. Operators do want to obtain some gain and directivity on 80, 40, and 30 as much as they wish it on 20 through 10 meters. so let's do a quick survey of some 2-element horizontal array ideas for the low bands. I shall assume that you do not have towers, massive rotators, etc. and restrict myself to some wire ideas. +
+ +
+

Let's begin by specifying dimensions for 2-element reflector-driver Yagis for 80, 40, and 30 meters. Fig. 28 shows the general outline of the antenna so that you may correlate the dimensions to a plan. All of the antennas use a direct coax feed for simplicity of construction. In Table 4, all dimensions are in feet and the wire size is either AWG #12 or #14 copper.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                           #12/#14 Wire Yagis
+
+Element                           Length                            Spacing
+3.6 MHz
+Reflector                         138.0                             -----
+Driver                            130.2                             39.4
+3.9 MHz
+Reflector                         127.4                             -----
+Driver                            120.2                             36.4
+7.1 MHz
+Reflector                          70.0                             -----
+Driver                             66.0                             20.0
+10.125 MHz
+Reflector                          49.0                             -----
+Driver                             46.2                             14.0
+
+Table 4.  Wire Yagi dimensions for 80-30 meters.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

To use these dimensions, we must keep in mind some of the design elements behind them. First, the dimensions are for bare wire. Insulated wire elements will be anywhere from 1% to 4% shorter due to an antenna velocity factor (which is not the same as a transmission line velocity factor). The physical length of an insulated wire will be shorter than the physical length of a bare wire of the same size for the same electrical properties. Unfortunately, the amount of required shortening depends upon the dielectric constant of the insulating material and the thickness of the insulation. Since hams obtain their wire from many sources, almost all of which do not clearly specify either property, I cannot give you a table of values to guide the required adjustments.

+

Second, the spacing of the wires is about 0.144 wavelength, which yields a feedpoint impedance between 40 and 50 Ohms for these beams. Had I used 1" diameter elements, the element lengths would have been 2% shorter, which we would expect. However, to achieve a near-50-Ohm feedpoint impedance, I would have had to increase the spacing to about 0.160 wavelength--a considerable increase. The difference stems from the increased fat-element mutual coupling (or the decreased thin-wire mutual coupling) for a given spacing of wires. One of the consequences of this difference is a narrowing of the SWR bandwidth of a thin-wire Yagi, as shown in the 40-meter SWR comparison of SWR curves in Fig. 29.

+
+ +
+

Third, thin copper wire will have higher losses than fat aluminum, despite the conductivity advantage of copper. The driver losses result in a gain reduction of about 1/2 dB when we compare #12 to 1" elements, an 8:1 diameter difference. Hence, a 6.2 dBi free-space gain drops to the 5.7 dBi level. However, reflector losses tend to increase the front-to-back ratio, and the wire Yagi has a slight advantage over the tubular version. The pattern in Fig. 30 shows the differentials in both directions for our sample beams.

+
+ +
+

Fourth, wire beams for the lower HF region are normally constructed at heights well below 1 wavelength. Most such antenna are between 1/3 and 2/3 wavelength up, with many 80/75-meter antennas well below 1/3 wavelength. Such mounting heights have a number of properties to which we must adjust when we make a wire beam. Below 1/3 wavelength, a horizontal antenna--including a Yagi--has such a high elevation angle of maximum radiation (Take-Off or TO angle) that if we cannot get the antenna higher, then we may wish to consider other beam types--such as a parasitic half-square. The lesser gain but lower radiation angle may give us better results. For reference, Table 5 gives us the heights for the lower bands for 0.375, 05, and 0.625 wavelength. Except for tower owners or North Woods operators, 5/8 wavelength is about as high as we shall mount even a 30-meter wire beam.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                      Height in Feet of Some Beam Levels
+
+Wavelength                                         Frequency
+                                  3.6              3.9              7.1           10.125
+0.375                             102.5             94.6            51.9          36.4
+0.5                               136.6            126.1            69.3          48.6
+0.625                             170.8            157.6            86.6          60.7
+
+Table 5.  Heights in feet for typical beam mounting heights in wavelengths for some lower HF
+frequencies.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

On 80 and 75 meters especially, a wire Yagi will be difficult to elevate even to the 3/8 wavelength level.

+

Below 1/3 wavelength, most Yagis shows wide excursions in the feedpoint impedance with small changes in height. Between 3/8 and 5/8 wavelength, the feedpoint impedance changes slowly, but still may require adjustment of the driver length from planned dimensions. However, not only does the feedpoint impedance change significantly with height in this low mounting region, but so do the operating characteristics. Any horizontal antenna will show a gain peak at about 0.625 and 1.125 wavelength, and a gain low at about 0.375 and 0.875 wavelength. At higher mounting levels, these phenomena become very slight, but at low levels, the changes are noticeable in operation. In contrast to gain, the front to back ratio changes in much the opposite direction, with higher values near the 3/8 wavelength mark and lower values higher up.

+

Of course, to this list of changes with height, we must add the TO angle. That angle is in the 34-35-degree level--with a single vertically fat lobe--when the antenna is at 3/8 wavelength and drops to about 22 degrees with a single vertically thinner lobe as we move to the 5/8 wavelength level. Understanding all of these effects of changing antenna height is critical to making the right decisions as we plan a wire beam for one of the lower HF bands. Fig. 31 summarizes many of these differences by showing typical azimuth patterns for a 2-element Yagi at the various heights that we have discussed.

+
+ +
+

One Yagi variant--the Moxon rectangle--shows some resistance to these changes at low heights. The feedpoint impedance of a Moxon rectangle changes very little from about 1/4 wavelength above ground on upward. As well, the Moxon rectangle, even when built from wire as thin as AWG #14 (0.0641" diameter), can cover all of 40 meters (see Fig. 32).

+
+ +
+

For reference, Table 6 lists some dimensions for 50-Ohm Moxon rectangles for the lower HF region, with dimensions in feet. The side-to-side dimension remains at about 70% of the corresponding Yagi dimension. Use Fig. 3 as a guide to the application of these dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                             Lower HF Moxon Rectangle Dimensions
+
+Freq.            A                B                C                D             E
+3.6              99.98            15.47            2.16             18.33         36.96
+3.9              92.28            14.28            2.00             16.92         33.20
+7.1              50.69             7.82            1.15              9.35         18.32
+10.125           35.47             5.45            0.84              6.56         12.85
+
+Table 6.  Some Moxon rectangle dimensions (in feet) for lower HF bands for AWG #14 copper wire.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the Moxon rectangle cannot lower the TO angle relative to a Yagi, it begins to shine in other comparative categories at low mounting heights, as suggested by the typical azimuth plots in Fig. 33. The gain meets or exceeds the corresponding Yagi gain (in Fig. 31), and the front-to-back ratio is at least 9 dB better--a full 1.5 S-units.

+
+ +
+

Since we cannot normally rotate a wire beam, one common technique for working in at least two main directions is to create a reversible beam. There are more ways than one to achieve this goal, but let's explore a pair of typical designs. The first technique is applicable to both the Yagi and the Moxon rectangle. We simply create two driven elements instead of one. Then we load one of the elements with a transmission line stub. The stub--when on the driver--becomes a part of the overall transmission line from the shack, so we shall use 50-Ohm cable for our stubs.

+
+ +
+

Fig. 34 shows the general outline of Yagi and Moxon rectangles set up for reversal of direction. Whatever the band, the Yagi uses the driver dimension already shown for both elements. Each element center comes down via a 50-Ohm cable to a central remote switching box. The Moxon rectangle uses the driver dimensions including A, B, and C (gap) in the charts and then repeats the A and B dimensions for the other element.

+

The switch changes both the center and braid connections to keep the stubs totally independent of each other. The Yagis need a stub reactance of about 75 Ohms (whatever the band) to load the element into reflector service. The Moxon rectangle need about 70 Ohms for similar service. Table 7 lists the electrical lengths of two kinds of stubs: shorted stubs less than 1/4 wavelength long and open stubs greater than 1/4 wavelength long. You may also add exactly 1/2 wavelength to either type of stub if you need additional stub length to reach the switch position. Be sure to multiply the electrical lengths in the chart by the velocity factor of the line you might use for the stub. In most cases, solid dielectric lines have a velocity factor close to 0.66, while foam lines have a value close to 0.78. Table values are in feet.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                        Basic Stub Lengths to Load Reflectors
+
+75-Ohm Stubs
+Freq.                             Shorted                           Open
+MHz                               Length                            Length
+3.6                               42.8                              111.0
+3.9                               39.5                              102.5
+7.1                               21.7                               56.3
+10.125                            15.2                               39.5
+70-Ohm Stubs
+Freq.                             Shorted                           Open
+MHz                               Length                            Length
+3.6                               41.4                              109.7
+3.9                               38.2                              101.3
+7.1                               21.0                               55.7
+10.125                            14.7                               39.0
+
+Table 7.  Some open and shorted stub electrical lengths.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

You can find equations for calculating stubs in most antenna manuals. Remember that transmission line stubs are not without some loss, and the longer the stub line, the greater the losses. The chief effect will be a slight loss of gain (added to the loss we experienced by going from fat to thin elements). However, the front-to-back ratio will give our beam some good directional properties, and we shall still have very usable forward gain.

+

In addition to adding switching complexities and some losses to our array, the direction-reversing scheme will also narrow the operating bandwidth of the beam somewhat. However, the array will remain a direct-feed 50-Ohm beam. Fig. 35 shows the anticipated 50-Ohm SWR curves for reversible Yagis and Moxons. Note that the loading affects the Yagi curve slightly more than it alters the Moxon curve.

+
+ +
+

For those who may have only 1 or 2 tall supports, Carrol Allen, AA2NN, has developed a diamond-Vee version of the Moxon. In fact, when thinking about making either a Yagi or a Moxon into something like an inverted Vee for simpler construction, it is wise to think of the diamond-Vee instead. See Fig. 36.

+
+ +
+

Let me describe the 40-meter version of this antenna, and you can do whatever scaling may suit your own location and operating desires. The top of the antenna is about 51' above ground, with the element ends at 35.5'. The gentle slope allows some variation in the actual mounting height, although the top is close to the 0.375 wavelength level.

+

The top center of the two elements shows a spacing of 24.6', with the element tips separated by about 9.4'. Drawing the tips toward each other introduces some degree of element end coupling, so the antenna is not a pure Yagi, but the level of coupling is not as extreme as in the Moxon. Drawing the elements toward each other also allows the builder to use ropes at the element ends and a common tie point for the structure on each side. The wire length on each side of center is about 33.2' for each half element in the array.

+

To load one of the elements for reflector duty, we need about 65 Ohms of inductive reactance. A shorted stub of about 20.2' or an open stub of about 54.8' (or increases in 1/2 wavelength increments for either) will do the job. A switching system like the one described earlier will create a reversible array.

+
+ +
+

Fig. 37 gives us some idea of how well the antenna will perform at its low Vee height in terms of both azimuth and elevation. The TO angle is about 36 degrees, slightly higher than a Yagi at a 3/8 wavelength height, due to the drooping ends. Likewise, the gain is about a half-dB lower. However, the front-to-back ratio is typical Moxon, with a value of better than 20 dB. Fig. 38 shows the anticipated 50-Ohm SWR curve, which is also typical Moxon.

+
+ +
+

If you wish to see more of Carrol's 40-meter reversible beam ideas, including improvements on the stub system outlined here, see "Two-Element 40-Meter Switched Beam," ARRL Antenna Compendium, Vol. 6 (Newington: ARRL, 1999), pp. 23-25.

+

Let's close with one more idea--something that you can do with a Yagi but not a Moxon rectangle. Suppose that you want a simpler switching arrangement, something that you can do in the shack. Then examine Fig. 39.

+
+ +
+

With driver-reflector Yagis, you can layout 2 of them using the same reflector. The dimensions in the Yagi table will work fine, because the unused driver has almost no effect at all on the performance of the reflector and the active driver. Separate lines to an in-shack switch also mean that the line lengths are not at all critical, and the lines may be closely paralleled structurally on their way from the shack to the antenna. All of the Yagi data will apply to this simple reversible Yagi, whatever the band you choose. Its only demerit is the need for a third wire and the spacing from the reflector. So a 20' front-to-back 40-meter Yagi becomes 40'. But if you have the space in this dimension, the ease of tune-up may offset the work of stringing the third wire.

+

We have not covered all of the many ways to work with 2-element wire beams on the lower HF bands. For example, we can make an open-sleeve coupled pair for covering both ends (but not the middle) of the 80/75-meter band using 4 wires and only 1 feedpoint. (If you are interested, see Some Notes on Lower HF Wire Beams for details.) The total space is only about 3' larger than needed for an 2-element Yagi for 3.6 MHz alone. I toss this note in only to demonstrate that once you get started, the possibilities are nearly endless.

+

We have focused--both in this set of notes and in Part 1 at the last FDIM--on the principles as well as the practicalities of 2-element arrays. As well, we have focused on uni-directional arrays and by-passed the fascinating world of bi-directional arrays, such as the 8JK and the lazy-H. The more you understand about 2-element directional performance--whether in the form of a parasitic Yagi, a phased array, or a parasitic alternative beam like the Moxon rectangle, the better your position to either build or buy successfully.

+

We have not focused in the main upon construction, except for the exercises last year on stepped-diameter Yagi elements and on some casual notes in this session. You will want to examine as many articles and books as you can find on good construction techniques. Your objectives should be twofold: 1. Find out what techniques offer the best probability of a safe, durable, and electrically effective array; 2. Discover which techniques best suit the materials and building skills that you have or want to develop. Combine the two, and you are ready to step up from a single element antenna to the world of 2-element arrays.

+

Once you have successfully mastered a 2-element antenna, can 3 or more elements be far behind?

+
+ +
+

Updated 5-24-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

+

Topics: HB9CV / ZL Special, HF Upper, Moxon, Phased Array, Yagi


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+ Title graphic +

Some Principles of Portable Antennas to Strive For

+

This talk was originally prepared for the 2003 Dayton FDIM Symposium

+ +

+

2003 marks the 8th FDIM symposium to which I have tried to make a contribution to our array of antenna ideas. This year, I want to present some principles that apply to portable antennas. We may not be able to achieve them all, but the more of them that we can implement, the greater success we are likely to have in our portable and field operations.

+

Unfortunately, I have seen too many operations (many documented with published photos) showing folks using the finest QRP equipment with some of the worst antennas imaginable. Sometimes, circumstances force us to load up the proverbial bedsprings, and we can make contacts--at least a few. However, when you have only 5 watts of power--or less--you owe it to yourself to develop the finest field antenna you can imagine--and then carry. Of course, that last qualification is the limiting factor. You must be able to get the antenna to the site, erect it, and then take it down and home again. Before we are done, I shall pass along a few techniques to help make that possible--at least in some circumstances.

+

Since this is not a mystery story, I shall list the basic principles that I have in mind right here--and then expand upon them.

+
    +
  1. Look before you leap.
    2. +
  2. The higher, the better.
    3. +
  3. The bigger, the better--up to a point.
    4. +
  4. As the guy said, safety above all else.
    5. +
  5. Avoid nuts (and bolts).
    6. +
+

My 6th principle is simply that no presentation should have more than 5 principles.

+

Look before you leap. The first principle simply says to reconnoiter the territory that you will be using before you go there to operate. Find out what is there that may be useful, what is there that may get in the way, and what is not there that you will need. I knew an operator who carefully prepared a doublet and an end-fed wire for his vacation, which sent him into the New Mexican wastelands, where there was not a tree or shrub more than 4' high to tie off the ends.

+

My example is extreme, but not so far fetched as it sounds. If you will use a horizontal wire or even an inverted-L, you need at least a pair of tall supports and a way to reach them to tie off the ends. If you will use a vertical, you should know that you can set it up reliably. A base pipe that works well in clay and loam is not necessarily adequate in sand or rock. Even a guy-wire/rope needs soil that will handle the anchor.

+

The more complex the field operation, the more important it becomes to do advanced planning. Too often, even in seemingly well-planned Field Day operations, the first person to arrive with an antenna selects the best spot for his/her antenna and all others arriving later must squeeze themselves into any remaining space. Little wonder why scores are not higher.

+

The planning process is mostly a thinking and paper operation, which is not very exciting compared to the actual effort to make contacts. However, it can make actual operation even more exciting by improving the chances for more successful contacts. The process is very straightforward.

+
    +
  1. Catalog the antennas that will go on the expedition.
    2. +
  2. Visit the site and records all details, including trees (and limbs eligible as supports); relative heights of areas within the site; unusable places due to water, ant colonies, etc.; and any other feature that might affect the operation or its layout.
    3. +
  3. Make many sketches of potential site layouts before deciding on the one to use.
    4. +
  4. After deciding on the layout, accumulate all of the pieces needed to make that layout become an operating reality.
    5. +
+

+

Fig. 1 sketches the very same area twice. It has 4 trees, each with a pattern of eligible limbs. I have omitted some potential details to keep the sketch from getting too crowded. I shall assume that the most convenient place from which to approach the site is the lower left corner. It may be nearest to a trail or a parking area. As you can see from the left version of the sketch, the initial plan is to dump all of the heavy gear as near to the approach as possible. Then the antenna field can take shape using the spaces left over. The operative principle behind the antenna arrangement is to keep the antennas as far from the equipment as feasible within the limits of the site.

+

It seems reasonable to use the nearly aligned trees on the right edge of the site to support the doublet, even if one end must hang down. To give the vertical antenna clearance from the doublet, the plan calls for placing it near the left edge of the site, even if that means reducing the radial field to only 3 effective radials stretched out on the grass. The ATUs, one for each antenna, go on the operating table, with feedlines to the individual antennas.

+

Now let's re-plan the site. Let's move the operating table to a more central location. Yes, it is nearer the doublet, but we shall let height provide separation and take advantage of the shorter feedline run that goes upward from the ATU with less chance of encountering objects that might disrupt balance. Our next move is to run the doublet between trees 1 and 4. This arrangement allows the doublet to be horizontal throughout, with no vertical end to couple into the vertical antenna. The increased angle will have little effect on patterns. We shall also move the vertical to the open area that formerly held the operating table. It has no immediately nearby tree to absorb its energy. The radials extend for their full length in each direction. Note that the ATU is at the base of the vertical, a better position if there will be significant SWR levels at any operating frequency. The cable to the table is a length of matched coax.

+

I only label the right-side plan as possibly better, because the sketches lack significant details that you would enter into your real planning drawings. A boulder where you want to place the operating table could ruin everything. As well, high and low spots in the area might dictate some right and wrong places to set the vertical antenna. A hornet's nest on the limb from which you wish to hang the doublet might call for last minute revisions. Nevertheless, the right-hand sketch does widely separate the antennas and, to the degree possible, account for the most efficient transfer of power--both incoming and outgoing--from the antennas to the operating position, while minimizing the potential for unwanted interactions.

+

Once you have reconnoitered the site and planned its layout, your next task is to gather all of the materials needed to make it a reality. Everyone thinks of the equipment, the antennas, and the feedlines. However, have you thought about the materials necessary to get the antennas in place and to keep them there throughout the event? It usually pays to have at least 2 means of getting lines over limbs, because trees have a habit of coming in odd shapes. As well, it also pays to not let the antenna wire contact a limb, but to suspend it below the limb with a rope and ring. A vertical antenna may require guying, even if the maker declares that no guying is necessary. Loose soil and careless wanders can defeat such claims in a flash. Do not forget the equipment anchors. QRP gear tends to be small and light. Hence, it crawls off operating tables and finds it way to the ground when no one is looking. In general, plan on having as much (or more) weight devoted to set-up and maintenance materials as to the operating equipment, antennas, and feedlines.

+

The bottom line is a modification to the basic principle: Look--and think and plan--before you leap.

+

The higher, the better. When it comes to antennas, this principle is as old as radio itself. We often think of the principle as applicable to horizontal antennas, like dipoles and multi-band doublets. However, it also applies to many types of vertical antennas. Let's look at what happens when we take a few representative vertical antennas that you might carry to the field and elevate them. We shall compare antenna base heights of 0, 5, 10, 15, and 20 feet--the last height likely only being available to those with significant equipment. Our samples will consist of a vertical monopole with radials and a vertical dipole without radials. Fig. 2 shows the general outlines of what we shall do with a few models. Although the samples will be full-size, while the vertical antennas that you carry to the field may be shortened and loaded, the general patterns of the analysis will apply.

+

+

The variations in patterns created by elevating a vertical antenna may seem subtle, but they can become important under certain operating assumptions. For our small sample, we shall take vertical monopoles using 4 radials--about the average size radial field used for most field expeditions. As we elevate the antenna base from ground level past 5, 10, 15, and up to 20 feet above average ground, we shall droop the radials back toward the ground. In part, this move reflects using the radials also as part of the guying system. The drooping radials also let us set the impedance close to 50 Ohms for a direct match with coax. Let's look at the information in tabular form and as a series of overlaid elevation patterns. The abbreviation 'wl' means wavelength.

+ 
+4-Radial Vertical Monopoles over Average Ground
+
+Band:  10 Meters (28.4 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---             -0.17           27                      42 + j 38
+ 5              0.14             0.73           22                      54 + j  3
+10              0.29             1.32           17                      52 + j  6
+15              0.43             1.50           14                      46 - j  1
+20              0.58             1.63           45                      49 + j  0
+ 1.47           13
+Band:  20 Meters (14.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---             -0.32           26                      44 + j 35
+ 5              0.07             0.20           24                      46 + j  4
+10              0.14             0.49           22                      56 + j  4
+15              0.22             0.80           19                      50 + j  1
+20              0.29             0.97           17                      41 + j  4
+Band:  40 Meters (7.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---             -0.43           25                      46 + j 35
+ 5              0.04            -0.15           24                      45 + j  3
+10              0.07             0.06           23                      50 + j  5
+15              0.11             0.21           22                      54 + j  1
+20              0.14             0.32           21                      59 - j  0
+
+
+ +
+

Clearly, the greatest change in pattern shape (Fig. 3) and performance occurs on 10 meters, because each 5' of height is twice the change on 20 and 4 times the change on 40 in terms of wavelengths. On 40 meters, we acquire about a dB of gain and a lower elevation angle of maximum radiation, also called the take-off or TO angle. On 20, the gain increment is greater, as is the lowering of the elevation angle. On 10 meters, we see more radical changes in the elevation pattern, most notably the emergence of the higher lobe until it becomes also the strongest lobe.

+

Whether the 10-meter pattern at 20' is useful depends upon the operating goals. On DXpeditions, the pattern only brings in noise to a remote island. However, for landlocked field operations looking for shorter- and longer-range contacts, the higher-angle radiation may be beneficial. The double entry for 20' on 10 meters indicates the angle and strength of both the lobes of the pattern.

+

We may perform a similar analysis for vertical monopoles, which will be twice as long above the base height as the monopoles. Still, they are usable and generally require no radials. So let's see what happens. Remember that the feedpoint of a vertical dipole with the same base height as a corresponding monopole is about where the tip of the monopole falls. Therefore, we should expect to find lower TO angles. As well, the vertical dipole, when sufficiently above the ground, will show a typical dipole feedpoint impedance of about 70 Ohms. The feedline should come away from a dipole at right angles for as far as may be feasible. However, I have heard of successful vertical dipoles that run the coax inside the lower end (assuming the use of a tube), with a 1:1 choke/balun at the point of exit. As with all field antennas, you should test all assembly, disassembly, and operating details long in advance of carrying the antenna to the field.

+ 
Vertical Dipoles over Average Ground
+Band:  10 Meters (28.4 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---              0.40           19                      96 + j 49
+ 5              0.14             1.23           16                      71 - j  4
+10              0.29             1.42           13                      70 + j  2
+15              0.43             1.59           12                      73 + j  2
+20              0.58             2.38           35                      74 + j  5
+ 2.07           11
+Band:  20 Meters (14.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---              0.03           19                      100 + j 14
+ 5              0.07             0.56           17                      80 - j  2
+10              0.14             0.84           15                      72 - j  0
+15              0.22             0.93           14                      70 + j  4
+20              0.29             0.94           13                      71 + j  7
+Band:  40 Meters (7.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+ 0              ---             -0.24           19                      111 + j 22
+ 5              0.04             0.08           17                      90 + j  3
+10              0.07             0.24           16                      81 + j  0
+15              0.11             0.32           15                      76 + j  1
+20              0.14             0.35           14                      72 + j  3
+
+

Once more, we find the greatest variation in operation on 10 meters, with lesser changes on 20 and 40 meters. The gain of the dipoles is slightly higher than that of the monopoles, except at the highest altitude. Indeed, we can see a diminishing gain advantage as we raise each dipole higher. That phenomenon occurs because each of the monopoles is becoming a dipole the higher that we raise it. The drooping radials are no longer a symmetrical horizontal affair that cancels out its own radiation. To the degree that the radials have a vertical component to their slope, they also contribute to the vertically polarized radiation of the entire antenna. The VHF Ringo Ranger, with its conical lower section, is actually a form of a vertical dipole.

+
+ +
+

The patterns in Fig. 4 show that the vertical dipole's greater overall height and higher feedpoint create pattern variations more quickly than do the corresponding monopoles. Even the 10-meter dominant lobe at a base-height of 20' has a lower TO angle than the corresponding lobe of the monopole. As usual, the changes are less severe on 20 and 40 meters.

+

Even with a base near ground level, the vertical dipole has one more advantage over a monopole with the same base height, especially where the operating field is not a completely clear plane. There is a widely reported phenomenon that goes under many names. I tend to call it "RF-eating shrubbery," based on my own experience of moving an old Hy-Gain 14AVQ from ground level to the rooftop of a one-story home. With only 4 radials per band, performance improved dramatically, far more than the tables would suggest. A vertical dipole tends to avoid the RF absorbers by having its feedpoint elevated to begin with. Hence, commercial antennas that are vertical dipoles or simulate them by having the high current area of the antenna elevated for each band, have become very popular.

+

+

Although the effects of height on verticals may seem somewhat subtle, they become dramatic applied to horizontal dipoles and doublets. Fig. 5 shows a small sample of dipoles at heights of 10, 20, 30, and 40 feet above average ground. We shall sample near-resonant dipoles at 10, 20, and 40 meters at each of these heights, and then show the corresponding elevation patterns. In this case, however, the patterns are taken along the axis of maximum gain, since a dipole pattern at field heights may range from a broad oval to, at best, a bi-directional peanut at the maximum height.

+ 
Horizontal Dipoles over Average Ground
+
+Band:  10 Meters (28.4 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+10              0.29             5.68           51                      85 + j  6
+20              0.58             7.67           24                      64 - j  5
+30              0.87             7.09           16                      78 - j  4
+40              1.15             7.84           12                      69 - j  0
+Band:  20 Meters (14.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+10              0.14             5.33           87                      61 + j 11
+20              0.29             5.72           50                      86 + j  1
+30              0.43             6.59           32                      77 - j 17
+40              0.57             7.33           24                      63 - j  9
+Band:  40 Meters (7.1 MHz)
+Height (ft)     Height (wl)     Gain (dBi)      TO Angle (deg)          Feed Z (R +/- jX Ohms)
+10              0.07             2.55           88                      53 + j  1
+20              0.14             5.71           87                      61 + j 10
+30              0.22             6.02           75                      78 + j  9
+40              0.29             5.86           50                      88 - j  4
+
+
+ +
+

As the tables and Fig. 6 show, height is a necessary ingredient in maximizing the performance of a dipole or any other horizontally oriented antenna. The higher the antenna in terms of wavelengths above ground, the lower the TO angle of the lowest lobe and the more complex the lobe structure. The 10-meter patterns clearly show this phenomenon. In fact, a horizontal antenna does not become truly competitive with a good vertical until it is at least 3/8 wavelength above ground. In addition, if you examine the tables, you will discover that the feedpoint impedance of a dipole does not begin to stabilize until we reach the 3/8 wavelength or greater height. For heights below about 1 wavelength, there are heights less favored. If you examine the 10-meter patterns, you will discover that the 20' height shows a higher maximum gain than the 30' height. The 30' height is close to 7/8 of a wavelength, where so much energy goes upward that the lowest lobe suffers a bit.

+

We have performed our rudimentary examination of the effects of height on antenna performance using full-size dipoles and monopoles. However, for the sake of weight and convenient assembly, many field operators have obtained multi-band, shortened antennas. So our next question is whether size makes a significant difference, that is, significant enough for us to rethink our field antennas.

+

The bigger, the better--up to a point. In fact, size can make a sizable difference. As we did for our look at height, we shall explore the effects of size for both vertical and horizontal antennas. The vertical will be a 20-meter vertical monopole at ground level. We shall use the full-size antenna as our baseline data and then shorten the antenna in two steps to 3/4 full size and to 1/2 full size. For each of these two cases, we shall place the load both at the base and about halfway up the vertical element, using full-length radials throughout. Then we shall do the same for a horizontal 20-meter dipole at a height of 20'. We shall use center and mid-element loading for lengths that are 3/4 and 1/2 of the full-size antenna.

+

Normally, we use inductors (coils) to shorten an antenna, and coils have some losses that are a function of the Q or ratio of series reactance to series resistance. Most loading coils have a Q of 200 to 250, but I shall use a Q of 300 for our test models. Since the required loading will differ for the vertical and horizontal antennas, let's take them one at a time. Fig. 7 shows in sketch form the vertical tests.

+

+

The following table summarizes the results of the test models, using the full-size monopole as a basic reference and then proceeding to the 3/4 and 1/2 size versions with base and mid-element loading coils. The mid-element coils were placed exactly half-way up the monopole, although a practical antenna may vary this position considerably. The coil reactances were varied until re-establishing resonance within +/-j1 Ohm.

+ 
+Monopole Size Tests: 14.1 MHz
+
+All antennas use 1" diameter verticals with 15' long, 0.2" diameter radials.
+Length refers to the vertical element.  All loading coils have a Q of 300.
+
+Antenna         Length (ft)     Load:   L (uH)          R (Ohms)        X (Ohms)
+                        Gain (dBi)              TO Angle (deg.)                 Feed Z (R +/- jX Ohms)
+Full-Size       17.5                    ---             ---             ---
+                        -0.56                   27                              42 + j 2
+3/4, Base       13.125                  1.422           0.42            126
+                        -0.78                   28                              19 - j 0
+3/4, Mid-El     13.125                  2.427           0.72            215
+                        -0.78                   27                              29 + j 0
+1/2, Base       8.75                    3.240           0.96            287
+                        -1.59                   29                               9 + j 0
+1/2, Mid-El     8.75                    5.395           1.59            478
+                        -1.31                   29                              17 - j 0
+
+

The move from full size to 3/4 size results in a gain reduction of about 0.2 dB. However, a further reduction to half-size increases the loss of gain to around a full dB. The rate of gain reduction increases more rapidly as we get still shorter than half-size. You can estimate the effects of these losses from the patterns in Fig. 8. The advantage of using mid-element coils is less a matter of gain than it is a matter of having a higher, easier-to-match feedpoint impedance than we get with base loading coils. However, to obtain that advantage, we normally encounter greater mechanical complexity, which often translates in the field to a greater tendency to break in the middle of an operating session.

+

+

Reduced size vertical monopoles are certainly usable, but full-size versions are somewhat better and have a broader bandwidth. In fact, the operating bandwidth--using the usual 2:1 SWR standard--decreases according to the loaded element length. However, since we assume the use of an ATU at the base of the antenna, SWR will not normally be a problem, and added losses will be only those inherent to the particular type of network used in the tuner. (If you simply use coax to the antenna base and place tuner at the operating table, you will have a small additional loss due to the SWR level on the cable, and the total loss from this source will be a function of the cable length. Such cable losses will vary with the frequency of operation, increasing as one increases frequency.)

+

The dipole tests all used AWG #12 (0.0808" diameter) copper wire at a test height of 20' above average soil. The antennas were level, something that may not be completely feasible in most field situations if we tie off the ends of the antenna using available structures. Fig. 9 shows the layout of the tests, followed by the tabular results.

+

+ 
+Dipole Size Tests: 14.0 MHz
+
+All antennas use AWG #12 wire.  All loading coils have a Q of 300.  Center loading coils are single units.
+However, mid-element loading uses 2 coils each of the size listed.  Hence, the total loading is twice the values shown.
+
+Antenna         Length (ft)     Load:   L (uH)          R (Ohms)        X (Ohms)
+                        Gain (dBi)              TO Angle (deg.)                 Feed Z (R +/- jX Ohms)
+Full-Size       33.88                   ---             ---             ---
+                        5.74                    50                              85 + j 0
+3/4, Center     25.41                   4.309           1.26            379
+                        5.42                    51                              40 + j 0
+3/4, Mid-El     25.41                   3.968           1.16            349
+                        5.45                    51                              59 + j 0
+1/2, Center     16.94                   9.947           2.92            875
+                        4.66                    50                              18 - j 1
+1/2, Mid-El     16.94                   9.095           2.67            800
+                        4.76                    52                              34 + j 1
+
+

We see the same pattern in the loaded, shortened dipole that we saw in the monopole. Total mid-element loading requirements are nearly twice the center-loading requirement in terms of coil size and losses. Hence, for any given level of shortening, mid-element loads to not significantly increase gain, although they do set the feedpoint impedance at a more usable value if we do not use a tuner. Both center-loading and mid-element loading coils present mechanical challenges by adding to the complexity and weight of the antenna structure. The more complex the mechanical structure of a field antenna, the greater the likelihood of difficulties during an extended field operation.

+

Nevertheless, as the patterns in Fig. 10 show, we do not lose much by way of pattern. The worst-case gain is about 1 dB lower than the gain for a full-size dipole, about the same drop that we encountered with the vertical monopole. Do not try to directly compare the patterns for the monopoles with those for the dipole, since the outer ring in each case refers to a different gain level. However, you may wish to estimate the dipole gain at an angle of 25 degrees and compare that estimate to the maximum gain of the monopoles at their TO angles. The dipoles are down by about 2 dB or so and thus have more strength along the axis of maximum bi-directional gain than the monopoles have in their omni-directional patterns.

+

+

We can effect considerable simplicity in compact dipole design by eliminating the loading coils. Instead, let's complete the antenna simply by dropping the elements downward once we have created a half-length dipole. The arrangement, which we can call an inverted-U, looks like the outline sketch in Fig. 11.

+

+

The general dimensions shown for a 20-meter inverted-U are for AWG #12 wire, although they tend not to change much for any size elements. A single mast would support a tubular horizontal element with drooping end wires. Perhaps the one disadvantage of this design is that it requires a 20' mast to keep the ends of the elements well above the level that people can reach. Even at QRP power levels, the voltage on the ends of a dipole can reach uncomfortable, if not dangerous, levels.

+

The inverted-U performs a little better than a half-size dipole at the same height when that dipole uses loading coils. The performance is a little less robust than a 3/4-size or a full-size dipole. The elevation pattern shown in Fig. 12 provides the relevant data. It also shows the -3-dB or half-power points for the antenna. You may generally apply these angle values to any of the dipoles that we have examined.

+

+

The azimuth pattern shows that the inverted-U has significant, but not overriding vertically polarized radiation from the drooping ends. Hence, for any given height, its azimuth pattern--to the right in Fig. 12--will be a bit more oval than corresponding patterns for loaded dipoles.

+

The design frequency for the inverted-U modeled here is 14.175 MHz, the center of the band. The reason that I used this frequency rather than some frequency closer to the CW end of the band is simple. Using linear elements rather than loading coils provides a very broad SWR curve, while the drooping elements reduce the feedpoint impedance from the 70 Ohms that we associate with a full-size linear dipole down to just about 50 Ohms. Fig. 13 shows the modeled SWR curve for the inverted-U.

+

+

Before we close the book on our five principles of field antennas, we shall return to the inverted-U to show you how to build a 5-band version, suitable for 20 through 10 meters, an antenna that will be about 36" long for carrying. And the cost will be well under $50, even if you buy all of the parts (excluding the mast) new. However, before we go there--and perhaps to create a mood of suspense--let's return to the general issue that surrounds my note to keep the ends of the inverted-U element well above the hands of even the tallest person at the field operation site.

+

As the guy said, safety above all else. Safety is often a remote thought at remote field operations. However, it is much easier to plan safety into a field operation than it is to transport an injured person from the remote site back to civilized territory that has medical care. Hence, it must be an integral part of every planned field operation.

+

+

Fig. 14 sums up some of the most overlooked safety matters in a field set-up. The safety principle that we have mentioned is illustrated by the stick figure and the antenna end: a safe spacing between the furthest reach of a person and the end of an antenna. Antenna ends are normally high-voltage points and must not be touchable, even accidentally, during operation.

+

The figure also points to a few other safety features. The simple word "guys" signals the need to make sure that everything you erect in the field should be mechanically secure from any anticipated breeze. The proper location of an antenna is sufficiently remote from the operating site so that if the antenna falls, it cannot fall on anyone--or on any expensive equipment. Having taken that precaution, you should also brace the installation so that it has the least chance to fall. In most cases, 3 or 4 guy ropes will adequately stabilize anything tall, including masts and vertical antennas. If the vertical structure is more than 20' tall, then use two sets of guys, one every 10' upward. 3/16" nylon rope is light enough for you to carry extra in the field pack to replace worn guys. Also carry a cigarette lighter to seal the rope ends to prevent fraying.

+

No guy rope or wire is any better than its tie-down. Do not depend upon finding rocks or limbs at the field site to use as tie-down weights. Bring long stakes that you can drive into the ground. The longer--within carrying limitations--the better. As well, learn one or two good knots that do not slip, and apply those knots to the rope-to-stake junctions.

+

Fig. 14 also shows several pennant-shaped items called flags. It does not require the dark of night or a morning fog to make the visible invisible. There is a fog caused by the excitement of the venture that blinds every participant at one time or another. Murphy's Law says that the fog will strike when an individual is nearest to something that will stop the field operation in its tracks. You may not be able to totally defeat Murphy, but you can make his task more difficult. Place flags on the guys at the most visible level. An added flag on the tie-down stake is not a bad idea to prevent a trip that will bring down the antenna.

+

Add flags on short stakes along any cable run to forewarn wanderers of its presence. A snagged cable can break--usually at the connectors. As well, it can drag down the antenna. On the other end of the line, it can drag the equipment off the operating table. The figure only shows a ground-level coax run. You should add flags to any twinlead rising from an ATU up to a doublet overhead. Indeed, make a general rule for yourself that anything that you may encounter from toes up to outstretched hands gets a flag.

+

Flags need not be formal pennants. At a fabric store, look for remnants of the brightest, most iridescent cloth that you can find. A yard of this material will be light to carry and allow you to rip strips for flags that only the absolutely color-blind person can miss.

+

Our focus on making the site elements safe from accidental encounters should not exclude the other safety factors that we normally think about. All equipment must be electrically safe, with no exposed electrical contacts. If a power supply or battery has such contacts, invent a cover for them to prevent accidental contact--either by a person's fingers or the wandering screwdriver shaft. A shorted battery means a short field trip, not to mention damage to your favorite screwdriver.

+

Do not overlook the mechanical security of your equipment. Much low-power equipment is also very light. Add a power and RF cable, and you have situation that we can call a drag--right off the operating table to the ground. You may use any number of techniques to prevent gravity from making your equipment disappear. Some field operators develop compartmentalized cases to hold all of the gear in place during use. You may also create a base-plate and use L-brackets to hold down the gear. You may also create a table-top with shallow bins into which each item fits. The exact system that you create will vary with the type of operation and the amount of equipment to be anchored.

+

Anchoring equipment requires pre-trip planning. In fact, every facet of making a field operation safe and secure demands as much time devoted to thought in advance of the trip as will be taken by the trip itself. These brief notes are only designed to alert you to the possible issues and a few ways of handling them. The actual number of ways of making a field operation safe and secure are as many and varied as the creative minds of field operators.

+

Pre-planning should include two important steps. The first is to clean everything that will go on the trip. This activity should focus on anything in the set-up that will make metal-to-metal contact, including connectors and joints in any antenna structure. The second step follows onto the first: test everything at home to ensure that it has the highest probability of working at the site.

+

Nothing blunts a safety principle like too many words. As incomplete as this listing may be, I shall bring it to an end here, hoping that I have said just enough for you to carry on from this point. Forethought is your greatest weapon against Murphy's Law that reads "If it can happen and it ain't good, then it will."

+

Avoid nuts (and bolts). Accidents are not the only events that bring field operations to a screeching halt. One of the most trivial but effective ways to stop an operation is to lose a nut or bolt in the grass or dirt and never find it again. So invent ways of preventing that loss. I use two rules.

+
+

1. Any nut or bolt used in the field set-up must be permanently tightened and never loosened.

+
+

2. Every field connection must use something other than a nut and bolt.

+

There are a few wing-nut connections for ground wires and the like that may be unavoidable. For these, I add a dab of Plasti-Dip to the end of the threaded contact to prevent the wing nut from coming off completely.

+

However, let's use this final principle to do two things. First, I shall introduce you to two of my favorite field connectors. They are not the last word in connections for field antennas, but they may inspire you to more closely examine the available hardware to develop even better ones for your type of field operations.

+

Second, to give you an idea of how we can apply at least one of these field connection-makers, we shall return to the inverted-U antenna and see what it may have to offer. Again, it is not the last word in field dipoles, but it has some features well worth considering, including its light weight, common materials, and low cost.

+

+

Fig. 15 shows two of my favorite hardware items for any type of field antenna using aluminum tubing. The data includes a reference to the McMasters-Carr catalog (http://www.macmasters.com). However, many sizes may be available in the specialty hardware section of home centers. The catalog will present you with a quandary. The hardware is available in both stainless steel and plated versions. Stainless steel offers a rust-proof finish, but plated hardware has more sizes and is half the cost.

+

Suppose that we are constructing an antenna using aluminum tubes and need to bridge a gap with a component, such as a coax connector or a loading coil. Of course, we mechanically plug the electrical gap by using a short length of fiberglass rod or tube, or a CPVC tube. The tool clip, sometimes sold as a "broom-handle" clip, solves our bridging problem, as shown in Fig. 16.

+

+

With a small piece of Plexiglas, we can create a plate to hold a connector or coil. The clips form the mechanical connection to the tubing and the component terminals. Use 3/16" to 1/4" thick Plexiglas, because the flat end of the clip is not really flat. In fact, it is curved and springy, so that when you (permanently) nut and bolt it to the plate, it exerts considerable bending pressure on thinner plastics. Flattening the mounting portion presses the clip portion together so that it makes excellent mechanical and electrical contact with the tubing.

+

My preference for home-made antennas is already showing, and wherever possible, I like to use aluminum tubing. However, I long ago learned not to use just any tubing, just as I learned to build my own antennas to be as good or better than anything on the commercial market. So I use 6063-T832 tubing for almost every antenna project, except when I need aluminum rods, which are available in 6061-T6. The aluminum stock is available, if not locally, from mail order houses, such as Texas Towers, and comes in 6' lengths. 6063-T832 tubes have 0.58" walls, which means that you can nest the tubes in 1/8" diameter increments. Fig. 17 shows a typical nest of tubes from 0.75" diameter down to 0.375" diameter, with a quarter-inch rod thrown in for good measure.

+

+

If we carefully de-burr and clean both the inside and outside of the tubes, they will slide together when not in use to make a compact single item to carry for a monopole--or a pair of transportable items for a dipole. Do not file the cut tube edges. Instead, sand them smooth with fine aluminum oxide sandpaper to avoid leaving particles of another metal on them. Periodically clean the outsides with a plastic pad and clean the insides with a long-handle bottle-brush. Do not use a lubricant to facilitate nesting, since we shall depend on the metal-to-metal contact of clean aluminum for electrical contact between sections of an element.

+

Some folks who have only used heavier aluminum conduit for antenna elements do not realize how light a 6063-T832 element can be. The following table lists the weight per foot of each size of tubing, along with the weight of some aluminum rods. From the table, you can estimate the weight of almost any kind of element you may wish to make and then add in the weight of any loading or center-structure that you add.

+ 
Table of Aluminum Tubing Weight Per Linear Foot
+
+6063-T832 Tubing                        6061-T6 Rods
+Diameter        Lb/ft                   Diameter        Lb/ft
+0.375"          0.044                   0.1875          0.032
+0.5"            0.095                   0.25            0.058
+0.625"          0.104
+0.75"           0.127
+0.875           0.150
+1.0"            0.202
+1.125"          0.229
+1.25"           0.255
+1.375"          0.283
+1.5"            0.309
+
+

I included some larger tubing sizes, because someone might wish to design a nested mast composed of tubing sections. However, such a mast can hold only the lightest dipole assembly and requires guying at least every 10' above ground.

+

To form the basic element for our inverted-U, let's create a full-size 10-meter dipole. Fig. 18 shows the basic structure.

+
+ +
+

The 3/4" section to the far left will be part of the center-plate assembly that we shall show separately. We only need to note here the hole for the hitch-pin clip that we shall use at each junction to fasten the sections together. Nested, each half-element is only 36" long, using a 3" overlap at each junction. Open, we use hitch-pin clips to mechanically fasten the sections. Each hole requires that we carefully drill through both section of tubing on one operation to ensure a tight-fitting hole and accurate alignment. You may wish to mark each hole on the joining tubes in a way that does not interfere with nesting. A jig made from scrap wood and some form of drill press makes the drilling of perfectly aligned holes much easier.

+

The element--composed of 2 half-elements and the center plate--will cover the first MHz of 10 meters with less than 2:1 SWR using the tubing sizes and lengths shown. For each of the bands from 12 through 20 meters, we need to add wire extensions that hang down and that we can readily change. However, let's first complete the dipole with a center plate assembly that is permanently assembled and hence, has a few nuts and bolts.

+

+

I used a scrap of 1/4" thick polycarbonate that I happened to have as a based for the center assembly, as shown in Fig. 19. I also had stainless steel U-bolts, so I pressed them into service to fasten the plate to the mast. However, you may substitute a short mast section--either metal or PVC--and use single bolts and self-locking nuts to fasten the mast and plate together. In fact, you may develop an entirely different dipole center assembly, so long as it has a means of connecting the cable to the antenna and a way of connecting the element halves to the center gap and junction.

+

1/2" nominal CPVC fits inside the short lengths of scrap 0.75" tubing. The tubing keeps the element halves aligned and minimizes the necessary hardware to fasten the element to the plate. I used a short section of 1" by 1" by 1/16" aluminum L-stock to hold the female coax connector. The entire assembly weighs under 1 lb, including U-bolts. The entire remainder of the element, including hitch-pin clips weighs less than 2 lb. So we have a 3-lb 10-meter dipole.

+

Before going any further, let me note an additional advantage of hitch-pin clips as a mechanical fastener. They are considerably larger than any screw or nut or bolt that you might use to join element sections. As a result, they do not get lost on the ground quite so easily. However, let's go one step further in the hardware preservation plan. You can add brightly colored tape flags to the loop of each pin. With that added precaution, you will have to dig a hole and bury a clip before you can lose it.

+

However, the clips provide mechanical fastening of the sections. Electrical contact is a matter of clean aluminum meeting clean aluminum. If you clean the element sections before each field adventure, you will have no problems at all. However, do NOT use this technique for a home antenna that will stay in the weather for months and years. The oxide build-up will gradually increase the resistance between tube sections and degrade antenna performance.

+

Now we are ready to expand the coverage of the antenna for all bands from 10 through 20 meters. For 12-20 meters, you can add vertical wires to the ends of the 3/8" diameter end pieces of tubing. Almost any wire from AWG #18 up to AWG #14 will do. A convenient wire to use is AWG #17 fence wire, which is cheap, plentiful, and very adequate to the task. Fig. 20 shows how I attached my wires to the end of the 10-meter element, once more using a hitch-pin clip.

+

+

I drilled a pair of holes through the tube at right angles to each other. One through-hole is the size of the straight section of the hitch-pin clip. The other is just large enough to pass the end wire. With the wire in place and bent over slightly, I install a hitch-pin clip, pressing the wire to one side as the clip goes through its holes. The combined bends make a very secure mount and good electrical contact. However, when I remove the clip, the end wire pulls right out.

+

I have pairs of end wires for each band wound on empty plastic ribbon spools. I tug them straight before installation, but slight curves remaining in the wires have no affect on the antenna performance. The wires are remarkable consistent in length, whatever the wire size, since the tubing sections dominate the high-current section of the antenna. The following table provides the length needed for each band, using the dimensions set for the 10-meter basic dipole. I have added the modeled performance on each band for reference, assuming a height of 20' above average soil. Remember that the 20' height is necessary on 20 meters as a safety measure.

+ 
End-Wire Lengths need for the Inverted-U
+
+Band    Wire Length             Modeled Performance             Gain    Elevation       Impedance
+           (inches)             at 20' Above Average            (dBi)   Angle (deg)     R +/- jX
+                                Ground:                                         (Ohms)
+10         -----                                                7.6       24            65 - j 2
+12          16                                                  7.2       27            67 - j 8
+15          38                                                  6.4       32            69 - j 8
+17          62                                                  5.7       38            65 - j 4
+20         108                                                  4.9       49            52 + j 4
+
+

A spool of aluminum fence wire contains an endless supply of replacement end wires, in case you break one, step on another, and inadvertently use a third as a tie-down. I recommend a non-conductive mast, if you have one, to prevent an accidental resonance on one or another band. With a 20' mast, 15-meters is the band most likely to show some SWR anomalies due to coupling between the end wires and the mast. As noted in the safety section, use guys on whatever mast you take to the field. Do not rely on tripod bases if you plan to have the antenna up more than a few minutes.

+

The inverted-U will perform as well as any commercial field dipole on the market. The big difference is that you will have a difficult time spending $50 on the inverted-U, even if you have to buy a double pocket full of hitch-pin clips to meet the minimum order requirement for a mail-order house.

+

I present the invert-U as only one of many possible light-weight field antennas that you can build yourself. Using the same techniques, you can build vertical monopoles, including loaded versions for 80, 40, and 30 meters. Tool clips can hold separate loading coils for each band. You can construct base supports from PVC. (See recent issues of QRP Quarterly for the application of these techniques to vertical monopoles. QST will eventually publish a complete background and construction article on the inverted-U. The basic idea is not new, but the use of hitch-pin clips to make it work is relatively recent.)

+

I respect the major commercial portable/field antennas on the market--and I have systematically modeled some of them. Still, there is no reason why the budget-minded QRP field operator cannot have a first-rate set of antennas to use on his trips and still have a few dollars left over to pay for the gas and some food for the adventure. At the same time, there is also no good reason why those antennas must depend on field assembly using easily lost nuts and bolts when there is so much hardware available that is both secure and hard to lose.

+

I have come to the end of my list of principles. They are all ideals, and the real circumstances of a portable or field operations may dictate that you have to violate one or more of them. With respect to performance, you at least will know what to expect by the amount that you violate principles like being high and large. If there is one principle that you should not violate under any but the most dire emergency circumstances, it is the principle of safety. We can replace good equipment, but not good operators and friends.

+
+ +
+

Updated 5-24-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Dipole, HF Lower, HF Upper, Loading, Vertical


+ + diff --git a/content/fdim/fdim9.html b/content/fdim/fdim9.html new file mode 100644 index 0000000..f9f2583 --- /dev/null +++ b/content/fdim/fdim9.html @@ -0,0 +1,18 @@ + + + + + + Symposium 2004 Dayton: My Top Five Backyard Multi-Band Wire HF Antennas + + + +

Symposium 2004 Dayton
+ My Top Five Backyard Multi-Band Wire HF Antennas

+ hr +

My Top Five Backyard Multi-Band Wire HF Antennas

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: Dipole, Doublet, HF Multi Band, Horizontal Loop, Inverted L, Lazy H, W8JK


+ + \ No newline at end of file diff --git a/content/fdim/fdim9.pdf b/content/fdim/fdim9.pdf new file mode 100644 index 0000000..9a77b71 Binary files /dev/null and b/content/fdim/fdim9.pdf differ diff --git a/content/gp/58-1.gif b/content/gp/58-1.gif new file mode 100644 index 0000000..790d533 Binary files /dev/null and b/content/gp/58-1.gif differ diff --git a/content/gp/58-1.html b/content/gp/58-1.html new file mode 100644 index 0000000..27027a1 --- /dev/null +++ b/content/gp/58-1.html @@ -0,0 +1,183 @@ + + + + + + The 5/8-Wavelength Mystique Part 1: 80-Meter Monopoles With Buried Radials + + + +
+

The 5/8-Wavelength Mystique
+ Part 1: 80-Meter Monopoles With Buried Radials

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

For the lower-HF portion of the study, I selected 3.75 MHz as a reasonable test frequency, even though it is unlikely that anyone would have the wherewithal to construct a 164' 5/8 wavelength monopole. I also used 0.1" diameter copper wire throughout the 80-meter portion of the study. First, the wire size is quite reasonable for a radial system. A large radial system of 128 wires creates a major junction, and the use of relatively thin wire ensures that the shortest wire length (0.5') will create no significant problems of segment inter-penetration at the junction of the radials. Second, the use of 0.1" diameter wire throughout ensures that there are no angular junctions of wires having dissimilar diameters in the model. Moreover the losses of 0.1" diameter wire at 80 meters a quite low, allowing the results to stand for those which might be obtained with the much larger-diameter elements used in actual 80-meter monopoles.

+

Modeling a buried radial system requires attention to several constraints of NEC-4. First, the vertical elements must pass through the ground surface at a segment junction. This requirement is most easily met by using a 1-segment wire from the ground level to the radial junction, which is 0.5' below the ground surface. As well, the source segment should be of the same length as the segment immediately adjacent to it for maximum accuracy. Therefore, I used a 0.5', 1-segment wire for the source wire, the lower end of which is at ground level. Above the source segment, the vertical radiator was developed using segment length-tapering, a convenient facility on EZNEC software. The 1-segment wire above the feedpoint is 0.5' long, the one above that is 1.0' long, and so on until a maximum segment length of 8' was reached. Fig. 3 provides a partial sketch of the technique.

+
+ +
+

Angular wire junctions are most accurate if the segments that meet are the same length. Therefore, the radials were also created using segment length-tapering techniques, with the inner-most segment 0.5' long, as shown in Fig. 3. Model creation was speeded by another convenience of EZNEC, the ability to select the group of wires composing an initial radial and then simply specifying the total number of radials required by the model. For comparative purposes, I explored models using a MININEC ground with no radials as well as buried radial systems using 32, 64, and 128 radials per model. Fig. 4 shows an outline sketch of the 32- radial model. For a discussion of the history and mathematics of classical ground calculations, see Rudy Severns, N6LF, "Verticals, Ground Systems, and Some History, " QST (July, 2000), 38-44. For a discussion of the techniques used in NEC-4 for the evaluation of the Sommerfeld/Asymptotic model, see Gerald J. Burke, Numerical Electromagnetics Code--Nec-4: Method of Moments; Part II: Program Description--Theory (LLNL: 1992), pp. 32-56.

+
+ +
+

To provide a cross section of the performance of the 1/4 wavelength and 5/8 wavelength monopoles, I used 4 different types of ground conditions, as shown in Table 1. As I demonstrated in Part 2 of the series, "Some Facts of Life About Modeling 160-Meter Vertical Arrays," in The National Contest Journal (2000 and 2001 in a 5-part sequence), the use of the traditional sequence of ground conditions called "very poor," "poor," "good," and "very good" provides a fair sampling of soil varieties for most lower HF purposes. As well, the modeling techniques for buried radial system using NEC-4 are described in more detail in that series. Also included are demonstrations of limitations in using the MININEC ground and the NEC-2 close-to-ground radial systems as substitutes for a fully modeled buried radial system.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Soil types used in the study.
+
+Soil Type           Conductivity              Permittivity
+                    Siemens/meter             dielectric constant
+Very Poor           0.001                      5
+Poor                0.002                     13
+Good (Average)      0.005                     13
+Very Good           0.0303                    20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Many antenna analysts use MININEC or a version of NEC with a MININEC ground in order to simplify the modeling of vertical monopoles. Since EZNEC provides the MININEC ground as a user option, I produced a set of reference materials for the 64' 1/4 wavelength and the 164' 5/8 wavelength monopoles. Table 2 provides data for the two verticals for the various soils. There is a single feedpoint impedance value listed, since MININEC calculates the impedance over a perfect ground, regardless of the soil type specified for the far field pattern.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  1/4 and 5/8 wavelength vertical monopoles over MININEC ground.
+
+                       1/4 WL Monopole                    5/8 WL Monopole
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor        -1.73    28           37.0+j2.2     1.07     19            83.7-j477
+Poor             -0.26    26                         1.09     15
+Good              0.46    25                         0.47     13
+Very Good         2.51    19                         2.86     19
+
+Note:  Since use of a MININEC ground results in the calculation of the source impedance over
+a perfect ground, the single value of feedpoint impedance applies to all cases.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The shorter monopole gain values follow what I shall term "naive" expectations: with improvements in soil quality, gain increases and the take-off (TO) angle (or elevation angle of maximum radiation) decreases. In contrast, the 5/8 wavelength radiator shows a decreasing gain value from very poor soil through good soil, with an increase only as we approach very good soil. This difference is explicable by reference to Fig. 2, which showed the difference in the position of maximum current along the radiator. (To be brief, the less conductive the soil, the higher the effective height of the 5/8 wavelength monopole current maximum above ground at the region of reflection that forms the far-field pattern. The 1/4 wavelength current maximum remains at ground level for any soil type.)

+
+ +
Most evident is the lower TO angle of the longer monopole for all soil qualities. Fig. 5 places the patterns of the two monopoles over good ground, where the maximum gain is virtually the same. Evident is the lower TO angle for the longer antenna, along with the secondary high-angle lobe of radiation. For reception, it would appear that the quarter wavelength monopole would be somewhat quieter relative to high-angle QRN. +
+ +
+

If general pattern shape were the only interesting factor in the comparison of 1/4 and 5/8 wavelength monopoles, the MININEC ground models might serve. However, The ability to model fully buried radial systems of various sizes leads to a number of questions concerning the effect of field size upon monopole performance. Therefore, I constructed models using 32, 64, and 128 radials for both monopoles, retaining the initial heights of 64' and 164', selected during the MININEC-ground modeling. The 64' height of the shorter antenna was nearly resonant under MININEC ground analysis. The 164' height is 5/8 wavelength at the test frequency of 3.75 MHz.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 3.  1/4 wavelength vertical monopoles over Sommerfeld-Norton ground with a buried radial
+             system of various sizes (3.75 MHz).
+
+Soil Type    No. Radials         Gain         TO Angle        Feedpoint Impedance
+                                 dBi          degrees         R +/- jX Ohms
+Very Poor
+                  32             -1.16        29              36.4 + j  8.8
+                  64             -0.43        30              34.0 + j  9.9
+                 128             -0.28        29              32.0 + j  8.0
+
+Poor              32             -0.07        26              39.4 + j 10.4
+                  64              0.53        27              36.6 + j 10.5
+                 128              0.70        26              34.2 + j  8.9
+
+Good              32              0.26        24              40.3 + j 10.0
+                  64              0.71        25              37.6 + j  9.7
+                 128              0.87        25              35.5 + j  8.4
+
+Very Good         32              2.20        19              40.0 + j  9.7
+                  64              2.39        19              38.6 + j  9.3
+                 128              2.53        19              37.3 + j  8.6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Table 3 shows the results for the 1/4 wavelength monopole. For each soil quality, the addition of radials up to the tested limit, there is the expected gain increase. The increment of gain increase itself is most evident in the move from 32 to 64 radials and is most effective with the worst of the soil qualities used. The increment of improvement in the move from 64 to 128 radials is much smaller and is least over good soil.

+

The table shows a fluctuation in the TO angle, never more than one degree. This phenomenon is a function of rounding values to the nearest whole degree and is insignificant. More notable is the fact that modeling the buried radial system shows a set of progressions that a MININEC ground cannot show. For any given soil quality, the more numerous the radials, the lower the feedpoint impedance. (Due to the construction of the model, the feedpoint position is invariant throughout the sequence of models.) However, with one exception (32 radials over very good soil), the feedpoint impedance for any size radial field increases with improvements in soil quality.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 4.  5/8 wavelength vertical monopoles over Sommerfeld-Norton ground with a buried radial
+             system of various sizes (3.75 MHz).
+
+Soil Type    No. Radials         Gain         TO Angle        Feedpoint Impedance
+                                 dBi          degrees         R +/- jX Ohms
+Very Poor
+                  32              0.82        18              81.6 - j 445.5
+                  64              0.87        19              81.0 - j 447.0
+                 128              0.88        18              80.9 - j 447.6
+
+Poor              32              0.99        15              80.9 - j 446.4
+                  64              1.03        15              80.3 - j 447.9
+                 128              1.04        15              80.2 - j 448.6
+
+Good              32              0.47        13              80.4 - j 446.8
+                  64              0.51        13              79.8 - j 448.2
+                 128              0.53        13              79.6 - j 448.9
+
+Very Good         32              2.98        10              80.2 - j 448.8
+                  64              3.01        10              79.7 - j 449.8
+                 128              3.02        10              79.6 - j 450.9
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Table 4 shows comparable information derived from the model of the 5/8 wavelength radiator over the same radial systems. Radials were held to 1/4 wavelength (65.6') for all 80-meter models. Once more, there is a gain increase for any soil type with increasing numbers of radials, but the increments are much smaller and would be operationally insignificant. The general gain pattern for the long vertical varies in accord with the MININEC ground values, but at a lower level except for the use of a good ground. A good ground yields the lowest gain of the test group owing to the particular composite ground conductivity-permittivity phase angle in the calculation of ground effects in the Sommerfeld-Norton (S-N) system, a factor first noted (to the best of my knowledge) by Jack Belrose. Good ground is not always best for a vertical radiator. In passing, one should note that the ground used in modeling is homogenous and cannot take into account affects of stratified changes in ground quality with depth. Since radiation penetration at MF and lower HF is considerable, real conditions for a vertical monopole for 80 meters might vary considerably from the conductivity measurements made near the surface. Although the radial system may respond according to the model, the far field may vary in strength and TO angle from the modeled result.

+
+ +
+

The use of a buried radial system does not alter one major result of the study, despite considerable variance between MININEC-ground and S-N ground. As shown in Fig. 6, there is no significant variation of gain between a 1/4 wavelength and a 5/8 wavelength radiator over good ground. The chief edge for the longer radiator lies in the lower elevation angle of the main lobe of radiation, but with the drawback of having a fairly strong higher lobe of radiation. Any advantage in gain for the longer radiator shows up over worse quality soils. With the largest radial fields, the 5/8 wavelength radiator shows a 0.5 dB advantage over a 1/4 wavelength radiator when the soil approximates the poor level and a full dB advantage when the soil is very poor. Over very good soil, the longer radiator again shows a half-dB advantage.

+
+ +
+

An interesting aspect of the 5/8 wavelength radiator is its pattern when we compare different soil qualities. For reference, Fig. 7 shows the 1/4 wavelength patterns for very poor and very good soil using the 32-radial field. As we might expect, there is little to distinguish the pattern shapes. Essentially, only the signal strength and the TO angle have changed significantly. Making a similar comparison of 5/8 wavelength patterns yields a feature that has not been well-noted in amateur literature. In Fig. 8, we find the same decrease in signal strength and TO angle for the pattern taken over very poor soil. However, the angle and strength of the secondary lobe in the region of 50-55ø elevation does not change over the range of soil qualities. Both conditions yield about the same susceptibility to high-angle QRN. Of course, if we speak in relative terms, the high-angle QRN over very poor soil will be stronger in comparison to the received signal strength from low-angle radiation.

+
+ +
For the purposes of comparison, I modeled a vertical dipole with the same top height s the 5/8 wavelength monopole. The model achieved resonance with the base 35.7' above ground. Although impractical to implement, the dipole was center-fed. The goal was to find out whether the 5/8 wavelength monopole showed any superiority over the dipole, since both antennas would show a current maximum at just about the same height. The dipole was modeled over a MININEC ground, over an S-N ground with no radials, and over an S-N ground having 32 radials. We can compare the results in Table 5 with those for the long monopole in Table 4. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 5.  1/2 wavelength vertical dipole over MININEC and Sommerfeld-Norton ground (with and
+             without a 32-radial ground plane) (3.75 MHz).
+
+Soil Type    Ground Type/        Gain         TO Angle        Feedpoint Impedance
+             No. Radials         dBi          degrees         R +/- jX Ohms
+Very Poor
+             MININEC/0           -0.27        18              75.3 + j 0.2
+             S-N/0               -0.11        17              72.8 + j 3.5
+             S-N/32               0.02        18              73.8 + j 4.7
+
+Poor         MININEC/0            0.36        15              75.3 + j 0.2
+             S-N/0                0.47        15              73.5 + j 2.5
+             S-N/32               0.55        15              74.5 + j 3.0
+
+Good         MININEC/0            0.11        13              75.3 + j 0.2
+             S-N/0                0.22        14              73.5 + j 1.6
+             S-N/32               0.28        14              74.1 + j 2.1
+
+Very Good    MININEC/0            3.04        11              75.3 + j 0.2
+             S-N/0                3.09        11              74.4 + j 0.6
+             S-N/32               3.10        11              74.6 + j 0.7
+
+Note:  Dipole was set for the same top height (164') as the 5/8 wavelength monopole, resulting
+in a bottom height of 35.7' for a near-resonant length of 0.1" diameter copper wire.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Over very good ground, there is no practical difference in performance between the elevated dipole and the 5/8 wavelength monopole, regardless of the presence or absence of radials beneath the dipole. However, with soil worse than very good, the monopole shows an increasing gain advantage over the dipole--nearly a full dB over very poor soil. As well, the presence of a buried radial system (using 1/4 wavelength radials) beneath the dipole shows a small but definite performance improvement over a no-radial condition, and the effect becomes greater with worsening soil conditions. Whether the performance improvement is significant enough for the investment of resources in putting the radial system in place would be a user judgment.

+

The upshot of these studies into the performance of a 5/8 wavelength monopole over and against a 1/4 wavelength monopole can be summarized this way,

+
    +
  • 1. The 5/8 wavelength radiator shows significant gain advantage over a 1/4 wavelength monopole only over soils that are poor or worse, but in any event, the gain advantage is far less than the theoretical 3 dB that yielded the 5/8 wavelength mystique.
    • +
  • 2. The 1/4 wavelength monopole, besides its considerable mechanical simplicity, has an advantage in the absence of a secondary high-angle lobe of considerable strength relative to the main lobe; hence, the quarter wavelength radiator may be quieter in most installations.
    • +
  • 3. The chief advantage of the 5/8 wavelength monopole lies in the lower TO angle for the main lobe.
    • +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 6.  Ground wave strength of 1/4 wavelength and 5/8 wavelength monopoles at 10
+             wavelengths from the antenna at ground level with 1000 watts (3.75 MHz).
+
+Soil Type        1/4 WL Gnd Wave       5/8 WL Gnd Wave        Difference
+                 milliVolts/meter      milliVolts/meter       percent
+Very Poor            54.04                 84.81                 57%
+Poor                 99.61                147.49                 48%
+Good                161.60                222.92                 38%
+Very Good           319.33                437.77                 37%
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The last point in part explains the preference--when feasible--for a 5/8 wavelength radiator in MF applications where ground wave strength is a design goal. Table 6 provides ground wave values in mV/m at a distance of 2623' (10 wavelengths at 3.75 MHz) from the two types of monopoles, taken at ground level. The 5/8 wavelength radiator shows a significantly higher field strength. The percentage of increase in the field strength over that produced by the 1/4 wavelength radiator increases with decreasing soil quality.

+
+ +
+

I must add one final note before turning to VHF applications of these radiators. Although there is no magic to using a precise 5/8 wavelength radiator relative to imprecisely approximating that height, there is a danger in letting the radiator become too long. As is the case with the related extended-double Zepp (the EDZ, a 1.25 wavelength center-fed radiator), further increases in radiator length reduce field strength perpendicular to the radiator and increase the strength of lobes at oblique angles to the radiator. The EDZ pattern in horizontal use devolves into 6 lobes of approximately equal strength when the radiator reaches 1.5 wavelengths. Fig. 9 shows what happens when we let the monopole grow to a corresponding 3/4 wavelength height. The low-angle radiation disappears, and the strongest radiation is in the vicinity of a 45ø elevation angle. This note is perhaps unnecessary for experienced antenna designers planning to use a monopole at its fundamental frequency. However, such antennas are often pressed into service on higher frequencies, where they are correspondingly longer in terms of wavelengths. Users often wonder at the absence of low-angle radiation without considering the effects of vertical length on the radiation pattern.

+
+ +
+

Updated 04-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: 2-Meter Elevated Ground-Plane Antennas

+

Return to Index

+

Topics: HF Lower, Vertical


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+

The 5/8-Wavelength Mystique
+ Part 2: 2-Meter Elevated Ground-Plane Antennas

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

At VHF, both the 1/4 wavelength monopole and the 5/8 wavelength monopole are widely used, but in circumstances quite different from those applicable to an 80-meter monopole. Some 15 years ago, Don Reynolds, K7DBA, looked at "The 5/8-Wavelength Antenna Mystique" (in The ARRL Antenna Compendium, Vol. 1 [Newington: 1985], pp. 101-106). I knew my title had to have a source other than pure creativity. In any event, although the article must be read in the context of affiliations with AEA, which began back then marketing an effective telescoping 1/2 wavelength antenna for handhelds, the measurements used as the basis of the article will interest those who read further into this modeling study.

+

The VHF monopole is designed for elevated use, normally with 4 symmetrical 1/4 wavelength radials. We shall not here deal with monopoles of any length without radials, although radial-less dipoles will be noted. To understand the relative performance potential of these antennas, it was necessary to construct a number of models to account for the variety of configurations. Fig. 10 shows the span of models considered, where all models used 0.25" diameter aluminum for every element.

+
+ +
+
    +
  • 1. A 1/4 wavelength (20.15") radiator and 4 19" radials at right angles to the vertical.
    • +
  • 2. A 1/4 wavelength (18.7") radiator with 4 18.5" radials sloping downward 45°.
    • +
  • 3. A 1/2 wavelength (38.14") vertical dipole.
    • +
  • 4. A 5/8 wavelength (50.5") radiator and 4 19" radials at right angles to the vertical.
    • +
  • 5. A 5/8 wavelength (50.5") radiator with 4 18.5" radials sloping downward 45°.
    • +
+

The test frequency was 146 MHz, where a wave is 80.84" long, making the selection of the length of the longer monopole obvious. The 1/4 wavelength monopoles were adjusted for resonance, with adjustment also to the sloping radial length to bring the radiator and radial lengths into rough alignment.

+

Each model was run over the standard soil varieties. Given that VHF antennas are used under varying circumstances, I approximated two major ones. For roof and tower mounting, I used a height of 25' (300") at the base of the monopoles and the center of the dipole. Further height increases would not have altered the results significantly in terms of operational trends. Vertical monopoles are also used in mobile and temporary installations. For that case, I used a base height of 5' (60").

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 7.  146 MHz 1/4 wavelength vertical monopole with 4 90° radials at 5' and 25' base height.
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         2.76    12.2         26 - j 1      5.83     3.4           26 - j 0
+Poor              2.32    34.3         26 - j 1      5.28     3.4           26 - j 0
+Good              2.32    33.9         26 - j 1      5.28     3.4           26 - j 0
+Very Good         2.90    33.5         26 - j 1      4.90     3.3           26 - j 0
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Table 7 summarizes the results for the 1/4 wavelength monopole with 4 radials at right angles to the radiator. At a height of 60", the radiated field strength of the antenna is best over very poor and very good soils. However, note that the TO angle for all but the worst soil is not the expected very low angle. The low angle corresponding to the strongest lobe over very poor soil has a reduced signal strength, although not down by more than about 1 dB or so from the higher-angle lobe. Fig. 11 shows the changing balance between the lower and higher lobes of the array as we change the soil quality beneath it at a base height of 5'.

+
+ +
+

At a height of 300", the expected low radiation angle for the major lobe is present. However, note the decreasing gain with increasing soil quality. Although the amount is not operationally significant, the trend is interesting.

+

A further factor to note is the lower-than-expected feedpoint impedance for the 1/4 wavelength monopoles. Received wisdom anticipates a feedpoint impedance of about 35-36 Ohms, based on ground mounted monopoles over perfect ground. An elevated monopole does not easily answer to this conception. The monopoles constructed for this model began with a free-space 1/2 wavelength dipole. One half of the dipole was replaced with 4 radials, with lengths adjusted until two conditions were achieved. First, the maximum current level is at the feedpoint, and the sum of the currents on the first radial segment of each of the four radials was close to the source segment current value. Second, the lengths of the radiator and the radials were adjusted to achieve resonance and to retain the current maximum position.

+

A useful technique for establishing a reasonable equality between the current level on the source segment of the monopole and the sum of the current levels on the first segment of the four radials is to use a maximum of segments consistent with maintaining a reasonable segment-length-to-radius ratio. As well, a close equality should be maintained between the segment lengths on the monopole and on the radials, since the source segment will be immediately adjacent to the first segments on the radials. For the 90° and sloping radial 1/4 wavelength monopoles, 31 segments per element provides a very usable figure while still maintaining a small enough model that does not require segment length-tapering to run on basic NEC-2 software. Small deviations from the goal of equal currents did not produce significant changes in the feedpoint impedance, which is about 38% lower than image-based conceptions of a monopole would dictate. Changing the number of radials does not materially affect the impedance or the vertical radiator length, if the radial lengths are adjusted to bring the assembly back to resonance.

+

The 1/4 wavelength monopole with sloping radials was constructed in the same manner. The length of the radiator and the lengths of the 45°-sloping radials were adjusted to place the maximum current at the feedpoint and to have a division of current among the radials so that sum of the currents in the 4 radials at their junction equaled the current level at the feedpoint, with the assembly as close to resonance as feasible. Consequently, both the radiator and the radial lengths are different from those used in the 90° radial model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 8.  146 MHz 1/4 wavelength vertical monopole with 4 45° radials at 5' and 25' base height.
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         3.24    13.0         51 - j 0      6.74     3.5           50 + j 0
+Poor              2.47    37.5         51 - j 0      6.18     3.4           51 + j 0
+Good              2.48    37.5         51 - j 0      6.18     3.5           51 + j 0
+Very Good         3.03    36.7         51 - j 0      5.79     3.4           51 + j 0
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Table 8 collects the results of running the model at both high and low levels. At 5', the sloping-radial monopole shows the same pattern of high-angle main lobes except over very poor soil. At 25', the pattern of decreasing gain with increasing soil quality also reappears. The chief difference in performance is a noticeable increase in gain at all levels and soils relative to the 90° radial monopole. At 25', the difference amounts to nearly 1 dB.

+

The reason for the gain increase is simple: the sloping radials have both a horizontal and a vertical component to their radiated fields. The horizontal components cancels (if the radials are identical in length and symmetrically distributed). However, the vertical component--non-existent in the 90° monopole--contributes to the overall radiation of the antenna, yielding a small gain increase.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 9.  146 MHz 1/2 wavelength vertical dipole at 5' and 25' (feedpoint height).
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         3.08    13.2         72 - j 0      6.79     3.6           72 - j 0
+Poor              2.19    11.0         73 - j 0      6.22     3.5           72 - j 0
+Good              2.14    11.1         73 - j 0      6.22     3.5           72 - j 0
+Very Good         2.42    38.0         73 - j 0      5.83     3.4           72 - j 0
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If the sloping radials increase gain, then a true vertical dipole should show additional increases in antenna gain. Therefore, I modeled a reference dipole for the test frequency--with the dipole center at the test heights so that the maximum current position would be consistent among the models. Table 9 reports the modeling results. At 25'. the dipole shows a minor (and operationally insignificant) increase in gain over all soils relative to the 45°-radial monopole. At the lower height, the dipole shows a reduction in gain--largely as a function of the closer proximity of the lower antenna end to the ground. However, except over very good soil, the TO angle of the strongest lobe is now at the expected low angle. Hence, for poor and good soils, the gain comparison is not especially valid, since the radiation is headed in different directions. Nonetheless, the dipole can be considered to have a slightly weaker signal, but one more likely to be directed at a favorable elevation angle. Fig. 12 compares elevation patterns of the three antennas so far considered at a height of 25' above good ground. In practical terms, the low- angle lobes of the dipole and the 45° sloping-radial monopole overlap, with the 90°-radial monopole slightly weaker.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 10.  146 MHz 5/8 wavelength vertical monopole with 4 90° radials at 5' and 25' base
+             height.
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         3.74     9.9         65 - j 227    5.78     3.2           65 - j 227
+Poor              2.87    25.2         65 - j 227    5.28     3.2           65 - j 227
+Good              2.87    25.2         65 - j 227    5.28     3.2           65 - j 227
+Very Good         3.36    24.5         65 - j 227    4.94     3.2           65 - j 227
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The key question is whether a 5/8 wavelength radiator will have any advantage over the array of monopoles and dipoles we have so far explored. Table 10 tells the story for a 50.5" radiator over quarter wavelength radials set at 90° to the radiator. At a base height of 5' above ground, the 5/8 wavelength monopole shows the same progression of gain values and the same relatively high-angle main lobes as the 45° sloping-radial monopole, the better of the two 1/4 wavelength monopole arrays. Fig. 13 reveals, as do the tabular numbers, that the 5/8 wavelength monopole has a slightly lower-angle lowest lobe and slightly greater strength, with the elevation pattern taken over good ground.

+
+ +
+

Notable in the comparison of patterns is the fact that the elevation pattern of the longer monopole has one more lobe than the pattern for the 1/4 wavelength antenna. Hence, while the lowest lobe is stronger than that of the shorter antenna, the longer monopole also has stronger radiation at considerably higher angles than the 1/4 wavelength monopole. The consequence of the third lobe is to increase the complexity of the lobe structure variations as we change the soil type over which we operate the antenna at a height of 5'. Fig. 14 shows the elevation patterns for the 5/8 wavelength monopole for very poor, good, and very good soils in order to demonstrate the changing balance among lobes. (Poor soil is omitted since its pattern overlaps the pattern for good soil.)

+
+ +
+

Although the 5/8 wavelength monopole shows a very slight advantage over the 1/4- wavelength monopole with sloping radials, the advantage disappears when we raise the longer antenna to 25' at its base. Comparing the numbers in Table 8 and Table 10 sets the stage for examining Fig. 15. With both antennas over good soil, the 1/4 wavelength monopole with sloping radials shows nearly a full dB additional gain over the 5/8 wavelength model.

+
+ +
+

In the end, it is dubious whether a 5/8 wavelength monopole has any significant operating benefit over a 1/4 wavelength monopole, each with 4 radials. Perhaps the higher top height of the longer antenna will yield some benefit when its base is very close to the ground. However, the 5/8 wavelength monopole always requires some form of matching system for use with a 50- Ohm coaxial cable, and matching systems at VHF are not without loss. At rooftop and higher levels, the sloping radial monopole with a 1/4 wavelength radiator or a half wavelength dipole will do as well--or better.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 11.  146 MHz 5/8 wavelength vertical monopole with 4 45° radials at 5' and 25' base
+             height.
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         3.02    50.2         65 - j 191    3.95     36.2          65 - j 191
+Poor              3.83    51.1         65 - j 191    4.90     36.1          65 - j 191
+Good              3.84    51.0         65 - j 191    4.90     36.1          65 - j 191
+Very Good         4.21    51.1         65 - j 191    5.30     36.1          65 - j 191
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

One tendency of those who home brew VHF monopoles is to attempt to replicate the advantages of the sloping radial system that adds to the performance of a 1/4 wavelength monopole. Hence, they slope the radials of a 5/8 wavelength monopole. In principle, the radiation resistance goes down, requiring only a series inductance as a means of compensating for the capacitive reactance at the feedpoint. Unfortunately, the maneuver results in a major change in the elevation pattern of the antenna over all qualities of soil, as revealed in Table 11. Radiation from the lowest lobe is over 2 dB down from the flat-radial system. Fig. 16 shows the situation graphically over good soil at a height of 25'. The number of lobes in the pattern does not change with the change in radial angle, but the power distribution changes very significantly. In general, a 5/8 wavelength monopole with sloping radials cannot be recommended for general communications.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 12.  146 MHz 1.25 wavelength vertical EDZ at 5' and 25' (feedpoint height).
+
+                       5' Base Height                     25' Base Height
+Soil Type        Gain     TO Angle     Feed Z       Gain      TO Angle      Feed Z
+                 dBi      degrees      R+/-jX       dBi       degrees       R+/-jX
+Very Poor         4.31    10.5         115 - j 389   9.49     3.5           108 - j 385
+Poor              3.70     9.3         118 - j 390   8.93     3.4           108 - j 385
+Good              3.65     9.4         118 - j 390   8.93     3.5           108 - j 385
+Very Good         3.22     8.7         120 - j 391   8.54     3.4           108 - j 385
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

There is one more antenna that deserves passing recognition before we summarize the results of the VHF use of monopole. Although completely impractical at 80 meters, a vertical EDZ can be effectively used at VHF in many circumstances. Table 12 summarizes the results of modeling a 111" center-fed EDZ at the center heights used for the dipole: 60" and 300". At the lower height, the antenna is only 10" above the ground, but it outperforms any of the monopoles and the dipole. It shows a consistent low angle for the main lobe, a fact illustrated in the 5' outline of the elevation pattern in Fig. 17. As well, the antenna shows the decreasing gain with improvements in soil quality so that with very good soil, the gain drops just below the level achieved by the 5/8 wavelength monopole with its base at 60" above ground.

+
+ +
+

With the antenna center at 25' above ground, the EDZ provides just under 3 dB additional gain relative to the best of the other antennas in the collection examined here. The elevation pattern is also shown in Fig. 17. The feedpoint impedance of the vertical EDZ will be a challenge to transform to what a 50-Ohm cable requires, but there are both network and linear transmission line methods of achieving the match. Even allowing for the losses in such systems, the vertical EDZ may be worth considering for some applications. See, for example, Rick Littlefield, "The 2-Meter PVC-EDZ Antenna, Communications Quarterly (Summer, 1997), pp. 104-106. As well, see "Feeding the EDZ" at this site for additional notes on this general technique, sometimes called using "delay lines."

+

Whatever the advantages of using a straight vertical radiator, the question that formed the basis for this VHF study was whether there is any profit in using a 5/8 wavelength monopole in preference to a 1/4 wavelength monopole when each is equipped with 4 radials. The results of our investigation might be summarized as follows.

+
    +
  • 1. At heights well above 1 wavelength, the 5/8 wavelength monopole is no better than a 1/4 wavelength monopole--and the shorter antenna may have a slight advantage when its radials are sloped 45°. In addition, the sloping-radial short monopole may offer matching benefits.
    • +
  • 2. At low heights, the longer monopole offers very slight gain advantages, but like the 1/4 wavelength monopole, the elevation of maximum radiation over most soil types tends to be quite high.
    • +
  • 3. For lower operating heights, a vertical dipole or EDZ offer more consistent low angle performance over most soil types, although the mounting and matching questions may present the builder with considerable challenges.
    • +
+

The modeling application to house-top mounted monopoles is--except for nearby metallic structures--applicable to reality without much adjustment. However, the results for lower mounting heights would need adjustment for the effects of the antenna surroundings. Hand-held antennas are almost impossible to predict relative to surrounding influences on radiated signals. However, Dan Richardson, K6MHE, is performing some studies of typical monopoles and other antennas mounted on various types of vehicles, as simulated by a series of detailed wire-grid structures. I shall await the results of his work to see if the greater height of the current maximum for a 5/8 wavelength monopole mounted on the trunk of a car makes a significant difference relative to the lower current maximum of a 1/4 wavelength monopole mounted in the same position. In short, a final decision on which type of antenna may be best (including both vertical dipoles and EDZs) must rest on a full analysis of the operating circumstances. At best, these general notes are indicators, but they are not final or universal judgments.

+

Before we can complete the overall picture of 5/8 wavelength monopole performance relative to the more familiar 1/4 wavelength monopole, we must look at one more frequency region: the upper HF bands.

+
+ +
+

Updated 04-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: Upper HF Monopoles

+

Return to Index

+

Topics: VHF / UHF, Vertical


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+

The 5/8-Wavelength Mystique
+ Part 3: Upper HF Monopoles and
+ a "Poorly Grounded" Speculation

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

From various sources, the idea persists that it is possible to create a "gain" vertical monopole for the upper HF bands by using a 5/8 wl radiator instead of the more usual 1/4 wl radiator. From various books, the idea tends to migrate on occasion into magazine articles, where new generations of amateurs accept the premise as gospel. The purpose of this final section of our investigation is to see what truth, if any, lies in this persistent notion.

+

To accomplish the investigation, I modeled monopoles with 4 1/4-wl radials at 20 and 10 meters--specifically, at 14.15 MHz and 28.5 MHz. The 20-meter monopoles used 1" diameter radiators, while the 10-meter models used 0.5" vertical elements. All radials were #12 AWG wire.

+

The 20-meter radials were 199.4" long, with a 211" 1/4-wl vertical and, alternatively, a 41.5' 5/8-wl vertical. For the 1/4-wl monopoles, I used the same standard as with the VHF monopoles: the sum of the currents on the first segments of each radial added up to the value of the source current on the main radiator. The one exception to these dimensions is the last section of Table 13, where I revised the dimensions of the 1/4-wl monopole with radials that sloped at a 45-degree angle to bring the system to resonance and to effect the "equal current" standard. In this revised monopole, the radiator is 200" long, with 191" radials. No such revision was made to the non-resonant 5/8-wl radiator.

+

Similarly, at 10 meters, I used a 104.75" radiator with 99" radials for the 1/4-wl monopole system. Since there was no significant change in any parameter except the feedpoint impedance when revising the 20-meter sloping-radial model, I did not perform the same operation on the 10-meter antenna. The 5/8-wl monopole used the same radials, but with a 255" vertical radiator.

+
+ +
+

Fig. 18 shows the 4 types of models for each band. Both the 1/4-wl and 5/8-wl monopoles were modeled with radials at 90 degrees to the radiator and with radials sloping 45 degrees downward. Each 90-degree monopole was modeled at heights of 1, 5, and 25 feet to simulate ground, low, and roof-top positioning of the antenna base. Only the 25' high monopole was adapted to sloping radials. Since the fixed physical heights for test modeling represent different heights in terms of wavelengths for each of the two bands, I modeled each band separately.

+

As with all other antennas--and subject to some speculative discussion at the end of this section--the antennas were modeled over the standard spectrum of soil quality samples: very poor, poor, good, and very good. See part 1 of these notes for full details on the conductivity and permittivity of each soil grade.

+

20 Meters

In a partial way, Table 13 and Table 14 sum up the results for 1/4-wl and 5/8-wl monopoles. However, there is a cursory and misleading way to read the tables and a more accurate method of digesting them. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 13.  20-Meter 1/4-wl monopoles over various soils.
+
+Soil Type      Gain     TO Angle    Lobe        Feedpoint Impedance
+               dBi      degrees     No.         R +/- jX Ohms
+
+1/4-wl Monopole, 90-degree radials, 1' above ground
+Very Poor      -1.03    28          1           35.8 + j 6.7
+Poor            0.00    26          1           38.5 + j 10.2
+Good           -0.24    25          1           37.6 + j 9.9
+Very Good       0.76    22          1           42.8 + j 12.1
+
+1/4-wl Monopole, 90-degree radials, 5' above ground
+Very Poor      -0.39    25          1           29.2 + j 0.4
+Poor            0.43    22          1           31.3 + j 0.7
+Good            0.16    22          1           31.3 + j 0.2
+Very Good       1.05    19          1           33.6 + j 0.3
+
+1/4-wl Monopole, 90-degree radials, 25' above ground
+Very Poor       1.37    17          1           23.2 + j 4.2
+Poor            1.11    14          1           22.8 + j 4.1
+Good            0.55    14          1           22.8 + j 4.2
+Very Good       1.00    33          2           22.4 + j 4.3
+
+1/4-wl Monopole, 45-degree radials, 25' above ground
+Very Poor       1.43    18          1           55.3 + j 35.8
+Poor            1.54    15          1           54.9 + j 34.7
+Good            1.05    15          1           54.6 + j 34.7
+Very Good       1.17    12          1           53.8 + j 33.6
+
+1/4-wl Monopole, 45-degree radials, 25' above ground (revised dimensions)
+Very Poor       1.40    18          1           47.5 + j 0.8
+Poor            1.54    15          1           47.2 - j 0.2
+Good            1.05    15          1           46.9 - j 0.3
+Very Good       1.19    12          1           46.3 - j 1.2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Table 14.  20-Meter 5/8-wl monopoles over various soils.
+
+Soil Type      Gain     TO Angle    Lobe        Feedpoint Impedance
+               dBi      degrees     No.         R +/- jX Ohms
+
+5/8-wl Monopole, 90-degree radials, 1' above ground
+Very Poor       1.70    19          1           107 - j 366
+Poor            1.74    16          1           107 - j 366
+Good            1.29    16          1           107 - j 366
+Very Good       1.26    14          1           107 - j 366
+
+5/8-wl Monopole, 90-degree radials, 5' above ground
+Very Poor       1.98    18          1           106 - j 370
+Poor            1.81    15          1           106 - j 369
+Good            1.33    15          1           106 - j 369
+Very Good       0.96    12          1           105 - j 369
+
+5/8-wl Monopole, 90-degree radials, 25' above ground
+Very Poor       3.00    14          1           108 - j 369
+Poor            2.67    38          2           109 - j 369
+Good            2.87    37          2           109 - j 369
+Very Good       3.95    37          2           109 - j 369
+
+5/8-wl Monopole, 45-degree radials, 25' above ground
+Very Poor       3.29    36          2           104 - j 351
+Poor            4.18    37          2           105 - j 351
+Good            4.31    36          2           106 - j 352
+Very Good       5.27    35          2           107 - j 352
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

According to the modeling analysis, at 1' above ground, the 5/8-wl antenna shows a 1.37 dB average gain advantage over the 1/4-wl monopole. As we raise the base height to 5', the advantage on average remains about 1.31 dB--very consistent with the advantage at the lower height. However, when we place that antenna atop a 25' roof, the 5/8-wl vertical outstrips the 1/4-wl assembly by 2.11 dB with 90-degree radials and by 2.96 dB with sloping radials. From this quick readout, it would appear that the 5/8-wl vertical has finally achieved the 3 dB advantage so many claim for it relative to the shorter vertical.

+
+ +
+

However, for the elevated 5/8-wl monopole, we must pay special attention to the "Lobe Number" column in the tables. For the 1/4-wl antenna, as partially illustrated by Fig. 19, the elevation patterns show their strongest radiation from the lowest lobe--if there is more than one. The 1' high antenna (1-90 in the figure) and the 5' high antenna (5-90 in the figure) have only a single lobe in their elevation patterns due to the very low mounting heights. The higher versions with 90-degree or 45-degree radials (25-90 and 25-45 in the figure) show the emergence of a second lobe at a higher angle. Only for the 90-degree radial 25' high monopole over very good ground does the second lobe grow stronger than the lower lobe. In all other cases, the lower lobe dominates the pattern. Hence, the recorded signal strength of maximum gain is almost always for the lowest lobe (#1) for the 1/4-wl monopole at all heights.

+

When we turn to the 5/8-wl monopole, partially illustrated in Fig. 20, we discover that the situation is not at all the same. For almost all cases where the antenna is mounted at 25', the strongest lobe is not the lowest one, but instead is the higher-angle second lobe. The only exception among angles tested is the 90-degree-radial 5/8-wl monopole when placed over very poor soil. This particular case is the basis for some speculations on ground quality at the end of this study.

+
+ +
+

As Fig. 20 reveals, there is something curious about the patterns for 5/8-wl monopole. The lowest lobe remains at a relatively constant angle and strength. Lowest-lobe signal strength varies between 1.29 and 1.51 dBi over good soil as we change the base height, and the lobe TO angle is between 12 and 16 degrees above the horizon. The higher maximum gains reported by the models when the antenna has a base height of 25' are wholly a function of the upper lobe, the TO angle of which ranges above 35 degrees. If we use the lower lobe of the 5/8-wl pattern as a guide (instead of the stronger upper lobe), then the 5/8-wl monopole advantage over the 1/4-wl monopole at the same base height drops to the 0.5 to 1.0 dB range--far below the desired 3-dB advantage.

+
+ +
+

Fig. 21 shows what the gain advantage amounts to, using the 90-degree radial versions of the two monopoles, each with a base height of 25' above good ground. In operation, there would be little to choose between the two antennas. The very slight gain advantage of the longer monopole is offset by its greater sensitivity to high-angle QRN. Whether a 41.5' rooftop radiator is sufficiently easy to maintain relative to the standard 17.6' 1/4-wl radiator to go for the extra partial dB is a user judgment.

+
+ +
+

As shown in Fig. 22, a set of elevation plots for the 5/8-wl monopole with 90-degree radials at a base height of 25', the vertical antenna exhibits some of the same properties as the VHF verticals. As we improve the soil quality both beneath the antenna and in the ground-reflection region, the lower lobe shrinks and the upper lobe increases in strength. Contrary to the expectations of many, the strongest lowest lobe occurs over very poor soil.

+

The 20-meter monopoles at a 25' base height are only about 1/3 wavelength above ground. That same physical base height is above 2/3 wavelengths on 10 meters. Therefore, the 10-meter versions of our monopole sets deserves independent attention.

+

10 Meters

The 10-meter monopoles used the same range of physical base heights as those for 20: 1, 5, and 25' up, with the highest versions using both a 90-degree radial set and a sloping 45-degree set. Table 15 and Table 16 summarize the results of the modeling. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 15.  10-Meter 1/4-wl monopoles over various soils.
+
+Soil Type      Gain     TO Angle    Lobe        Feedpoint Impedance
+               dBi      degrees     No.         R +/- jX Ohms
+
+1/4-wl Monopole, 90-degree radials, 1' above ground
+Very Poor      -0.66    27          1           33.4 + j 4.2
+Poor            0.23    25          1           36.1 + j 6.1
+Good            0.07    25          1           36.4 + j 5.8
+Very Good       0.43    23          1           38.8 + j 6.2
+
+1/4-wl Monopole, 90-degree radials, 5' above ground
+Very Poor       0.43    22          1           25.2 + j 1.3
+Poor            0.95    19          1           26.1 + j 0.5
+Good            0.75    20          1           26.0 + j 0.3
+Very Good       0.81    17          1           26.5 - j 0.5
+
+1/4-wl Monopole, 90-degree radials, 25' above ground
+Very Poor       2.99    13          1           24.1 + j 4.0
+Poor            2.67    35          2           24.2 + j 3.9
+Good            2.73    34          2           24.2 + j 3.9
+Very Good       3.78    33          2           24.1 + j 3.8
+
+1/4-wl Monopole, 45-degree radials, 25' above ground
+Very Poor       3.11    13          1           59.3 + j 38.3
+Poor            2.42    38          2           59.6 + j 38.2
+Good            2.51    37          2           59.6 + j 38.1
+Very Good       3.52    36          2           59.8 + j 38.0
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Table 16.  10-Meter 5/8-wl monopoles over various soils.
+
+Soil Type      Gain     TO Angle    Lobe        Feedpoint Impedance
+               dBi      degrees     No.         R +/- jX Ohms
+
+5/8-wl Monopole, 90-degree radials, 1' above ground
+Very Poor       2.13    19          1           82 - j 307
+Poor            1.97    16          1           82 - j 307
+Good            1.72    16          1           82 - j 307
+Very Good       1.05    13          1           82 - j 308
+
+5/8-wl Monopole, 90-degree radials, 5' above ground
+Very Poor       2.43    17          1           83 - j 307
+Poor            1.88    14          1           83 - j 307
+Good            1.63    14          1           83 - j 307
+Very Good       2.21    46          2           83 - j 307
+
+5/8-wl Monopole, 90-degree radials, 25' above ground
+Very Poor       4.13    10          1           84 - j 308
+Poor            3.16    26          2           84 - j 308
+Good            3.19    25          2           84 - j 308
+Very Good       4.19    24          2           84 - j 308
+
+5/8-wl Monopole, 45-degree radials, 25' above ground
+Very Poor       3.02    10          1           83 - j 283
+Poor            3.57    25          2           84 - j 283
+Good            3.54    25          2           84 - j 283
+Very Good       4.26    23          2           84 - j 282
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

If we again begin with a casual reading of the tabular data, we find that the 5/8-wl monopole has an advantage over the 1/4-wl antenna at every height. At the 25' level, the advantage is about 0.6 to 0.7 dB. The reason for this low figure, compared to what we initially encountered on 20 meters at the same height, is that both the 1/4-wl and the 5/8-wl antennas show maximum strength in the second, higher lobe. The common exception is once again when the antenna is over very poor soil, where the lower lobe dominates.

+
+ +
+

On 10 meters, even the 1/4-wl monopole shows a strong development of the second elevation lobe when the base of the antenna is 25' up. As shown in Fig. 23, over good ground, the differences between the flat-radial and sloping radial systems are minimal. Similarly, the there are no highly significant differences in the patterns for 90-degree and sloping 45-degree radial systems when we turn to the 5/8-wl monopole. With respect to the two lower lobes, as shown in Fig. 24, the structures are similar. However, note that the 5/8-wl monopole has developed a third elevation lobe near the 50-degree elevation angle. With sloping radials, this lobe is stronger than the lowest lobe. With the 90-degree radial set, the situation is reversed, even though the second lobe remains the strongest in both cases.

+
+ +
+

At a 25' height, the lowest lobe for either version of the 5/8-wl monopole is between 1.7 and 1.8 dBi. The lowest lobe of the 1/4-wl vertical with the same base height is about 1.5 dB whether the radials are straight or sloping. Hence, at the most desired angles of radiation, the 5/8-wl monopole advantage drops to a small fraction of a dB--hardly worth the extra 12' feet of vertical radiator in most cases.

+

We have tended to focus on the performance of the antennas at roof-top height. However, the two types of monopoles are also worth comparing at lower base heights. Here the 5/8 wl gain advantage is in the 1.3 to 1.7 dB range on 10 meters. Perhaps of equal importance is the fact that elevation angle of maximum radiation is 6 to 8 degrees lower than for the 1/4-wl monopole--indeed, it sits squarely in the most desire elevation-angle region for effective DX operation. Note as well that the 1/4-wl monopole shows its highest gain over poor soil, while the 5/8-wl version has its highest gain over very poor soil. That phenomenon accompanies another: the 5/8-wl monopole at a 5' base height already has sufficient second lobe development over very good ground to place the maximum gain at a high angle.

+

Summary--So Far

The results of the analysis of upper HF monopoles may well be summarized in two statements: +
+

1. At roof-top heights, the advantage of the of an upper HF 5/8-wl monopole over a 1/4-wl version is well under 1 dB, while the added radiator length above the roof-top may create significant mechanical challenges to offset the small gain in signal strength.

+

2. At base heights near the ground, the 5/8-wl monopole advantage may sometimes exceed 1 dB at lower angles of radiation, but does not reach 2 dB, even on 10 meters. The lower TO angle of the 5/8-wl monopole may prove to be of some advantage in such situations. Although each advantage of the longer monopole may be individually somewhat marginal, together, the advantages may add up to a noticeable improvement in performance over a 1/4-wl vertical.

+
+

Although I have used good ground for most of the illustrative patterns in this study, we should take note of the performance of all of the monopoles over very poor soil. On 10 meters, we can show the effects by comparing 25' high 5/8-wl monopoles with 90-degree and 45-degree radial sets. See Fig. 25.

+
+ +
+

The 10-meter patterns show once more that the use of sloping radials is marginal or detrimental, just as it was in the VHF region when the antenna was several wavelengths above ground. The flat-radial monopole has the greater signal strength at the lowest elevation angles. However, what may be more important is the fact that for either case, the poorer the ground, the better the antenna performance, both in terms of gain and in terms of pattern shape.

+

Now, if we only knew how good or bad the ground was beneath and around our antenna. . .

+

Some Poorly Grounded Speculations

+

This section of the investigation is somewhat speculative and based on inadequate evidence. However, it may have some use in fostering further investigations that might better resolve the questions we shall raise.

+

In some 7 MHz investigations of vertical antenna performance in concert with Dave Bowker, W1FK, he measured the soil conductivity of his Maine antenna site at 0.0002 to 0.00025 S/m. The readings were not only repeatable with good equipment, but as well showed the proper trends for rainy and dry spells. Using these values and some careful measurements of a 7-MHz vertical with a number of different elevated radial fields, we developed a permittivity value of about 7 for the area. First, this value of dielectric constant turned out to be assigned to shale, which is not unlike the constitution of the antenna site sub-soil. Second, using the value permitted careful models of the antenna and radial system to track all variations such that the modeled resonant impedance and the measured resonant impedance were always within 1 Ohm of each other--or less.

+

This anecdote--and that is all it can be at this stage--is coincident with reports that soil conductivity decreases with increases in frequency. (This claim is not the same as saying that for a given conductivity, ground losses increase with increasing frequencies. This other principle is already accounted for in the Sommerfeld-Norton ground calculation algorithms used by NEC. The new claim is not, since the user enters values--presumably measured or accurately estimated--of conductivity and permittivity (relative dielectric constant) into the S-N ground calculation system.) The measured value of the Maine antenna site is well below any value listed in standard soil quality charts--most of which were generated for AM broadcast antenna use. Indeed, a conductivity value of less than 1 mS/m is no where in such charts associated with a dielectric constant as high as 7.

+

The sum of these considerations is a question: just how poor is the soil beneath our upper HF vertical antennas? Although I cannot answer that question directly, I can look at some models using very low values of conductivity and permittivity. In fact, we can look together at the results of some speculative modeling. I used an initial value of 0.0002 S/m for conductivity and reduced the value to 0.0001 S/m. For a constant dielectric constant of 7, there was no significant change in the modeled performance of the subject antennas for the 2:1 change in soil conductivity. However, at low values of conductivity, changes in permittivity have a stronger influence on performance. See Part 2 of Some Facts of Like About Modeling 160-Meter Vertical Arrays: Part 2: Appreciating Conductivity and Permittivity. Therefore, using the 0.0001 S/m value of conductivity, I reduced the permittivity in steps from 7 to 1.

+

The modeled antennas were the 20-meter and 10-meter 1/4-wl and 5/8 wl monopoles at 25' above ground using 90-degree radial sets. The results of the modeling tests appear in Table 17.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 17.  20-Meter and 10-Meter 1/4-wl and 5/8-wl monopoles over low-quality
+soils.
+
+Soil Cond.     Gain     TO Angle    Lobe        Feedpoint Impedance
+& diel. const. dBi      degrees     No.         R +/- jX Ohms
+
+1/4-wl 20-Meter Monopole, 90-degree radials, 25' above ground
+.0002/7         1.54    16          1           23.1 + j 4.1
+.0001/7         1.57    16          1           23.1 + j 4.1
+.0001/5         1.72    17          1           23.2 + j 4.0
+.0001/3         1.98    18          1           23.5 + j 4.0
+.0001/1         3.01    14          1           24.0 + j 3.8
+
+5/8-wl 20-Meter Monopole, 90-degree radials, 25' above ground
+.0002/7         2.86    13          1           109 - j 369
+.0001/7         2.88    13          1           108 - j 369
+.0001/5         3.19    14          1           108 - j 369
+.0001/3         3.61    15          1           108 - j 369
+.0001/1         4.30    11          1           108 - j 370
+
+1/4-wl 10-Meter Monopole, 90-degree radials, 25' above ground
+.0002/7         2.71    12          1           24.2 + j 4.0
+.0001/7         2.72    12          1           24.2 + j 4.0
+.0001/5         3.06    12          1           24.2 + j 4.0
+.0001/3         3.52    13          1           24.2 + j 4.1
+.0001/1         3.72     9          1           24.2 + j 4.3
+
+5/8-wl 10-Meter Monopole, 90-degree radials, 25' above ground
+.0002/7         3.86    10          1           84 - j 308
+.0001/7         3.87    10          1           84 - j 308
+.0001/5         4.18    10          1           84 - j 308
+.0001/3         4.56    11          1           84 - j 308
+.0001/1         4.50     8          1           84 - j 308
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For all of the models, there is a significant increase in gain as we decrease the dielectric constant, using a very low value of conductivity. To gain a sense of what the table shows, we can turn to some illustrations.

+
+ +
+

Fig. 26 shows the tabular extremes for the 20-meter antennas. Note that the lower lobe of the best 1/4-wl monopole performance coincides closely with the lowest lobe of the 5/8-wl monopole using the starting values of the progression. The improvement on 20 as we decrease the dielectric constant is about 1.5 dB total.

+
+ +
+

In Fig. 27, we see the same data in pattern form for 10 meters. The increment on this band is only about 1 dB, possibly due to the more complex lobe structure that results from the antenna being higher in terms of wavelengths than the 20-meter models.

+

The upshot of the speculative modeling is simply this: the worse the soil, the better that most verticals perform. This statement has some assumptions built into it. The most important is that we are not located near a large body of salt water and that the soils with which we are making comparisons are not any better than that which we classified as very good. However, the pattern continues to repeat itself: lowest lobes dominate over the poorest soils, while with better soils (poor to very good), higher lobes often take over, to the detriment of low-angle radiation.

+

It would be glib to jump to conclusions. However, I do not know the answer to the question of how well our upper HF vertical perform, since I do not have decent data at hand for the conductivity and permittivity of the usual soils at the upper HF frequency range. All that I can do is draw from these notes a conditional conclusion: if any of this speculative material has relevance to real antenna performance, then we may one day have to re-evaluate our judgments of the performance of vertical antennas in the upper HF range.

+
+ +
+

Updated 04-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Topics: HF Upper, Vertical


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+

The 5/8-Wavelength Mystique

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The 5/8 wavelength vertical monopole has long held the reputation of providing about a 3-dB gain advantage over the 1/4 wavelength vertical monopole. The foundation of that reputation rests upon theoretical calculations that show the longer monopole to have the derived gain increase when both monopoles are set over a perfect ground. Fig. 1 shows the modeled elevation patterns of the two subject antennas under the prescribed conditions. Both antennas are set up as 0.1" diameter copper elements, which have negligible losses. At the 3.75 MHz test frequency, the 1/4 wavelength monopole showed a gain of 5.08 dBi, compared to the 8.01 dBi figure for the 5/8 wavelength monopole.

+
+ +
+

For an example of the claim or illustrations of the theoretical gain of the 5/8 wavelength monopole over the 1/4 wavelength monopole, see Terman's Radio Engineers' Handbook (McGraw-Hill, 1943), pp. 793-795. Recent college antenna texts fold vertical monopole concepts into more general considerations, although many antenna texts through at least 1970 present the theoretical relationship of a 1/4 wavelength radiator to a 5/8 wavelength radiator in the classic terms of Fig. 1. This idea persists in amateur radio literature. For examples, see Orr and Cowan, Vertical Antennas (RAC, 1986), p. 162, and by the same authors, Simple and Low-Cost Wire Antennas (RAC, 1990), p. 115.

+

A second factor contributing to the reputation of the longer monopole for higher gain is the current distribution along the element. Fig. 2 shows the distribution for both the long and short monopoles, with the ground plane elements omitted for clarity. The 1/4 wavelength antenna presents its "half-dipole" current distribution curve, while the 5/8 wavelength antenna provides a "half-EDZ" distribution curve. The peak current at a position well above the top of the short antenna is said to give the longer monopole a lower-angle of radiation and additional gain.

+
+ +
+

Although the claim of "3 dB more gain" for a 5/8 wavelength vertical radiator has considerably quieted in recent years, little by way of systematic exploration of the claim has appeared in amateur literature. Therefore, a little study seemed in order. However, the examination is complicated by the fact that the 1/4-vs.-5/8 question arises in two ot three different contexts. In the lower HF region of the spectrum, vertical monopoles are implemented with their bases normally at ground level, with a buried set of ground-plane radials. In the VHF region, vertical monopoles and their radials are elevated at least 1 wavelength above ground and often up to several wavelengths. The third main but lesser used region for monopoles are the upper HF bands from 20 through 10 meters, where they are sometimes employed by space-restricted hams. Consequently, our look into the 5/8 wavelength monopole question will require three related but relatively independent investigations, one for each frequency region and antenna assembly.

+

The three-part investigation appears in the following items:

+ +

The exploration proceeded using NEC-4 as a suitable modeling vehicle for examining the question of relative gain. The VHF and upper HF portions of the study might well have been undertaken with NEC-2 in any of its basic commercial implementations, since the number of elements are few and the antenna geometry does not challenge any of the software limitations. However, NEC-2 cannot directly model a buried radial system, and many basic NEC software packages are limited in the total number of segments a modeler can use. Therefore, professional software using NEC-4.1 becomes the necessary tool for buried ground-plane systems involving up to 128 radials.

+
+ +
+

Updated 04-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: Vertical


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+ +


+ 1 MHz Ground-Wave Analysis
+
+ A Comparison Among MININEC and NEC Modeling Implementations

+
+
+ L. B. Cebik
+
+

Ground-wave analysis in the frequency region of 0.5 to 1.5 MHz is crucial within the AM broadcast industry. Recent recommendations to the FCC would permit the use of antenna modeling calculations to replace some (but not all) field measurements. To provide an inter-program basis for comparing ground-wave calculations, a comparative data gathering exercise was undertaken using various implementations of MININEC 3.13, "Expert" MININEC (EM Sci), NEC-2, and NEC-4. This report provides the results of the work.

+

1. Ground-wave analysis for vertical antennas and arrays. The basic unit of measure for ground-wave analysis is the Volt/meter (V/m), although many common applications call for figures in milli-Volts/meter (mV/m). The parameter measured is the vertical component of the radiation field (sometimes designated E-theta), using a specified power and distance. The most common power used is 1,000 W (1 kW). The most common distances are 1 mile (1609 m) and 1 km (1,000 m or 0.6214 mi). Often, readings are rechecked at further distances. For this study, distances of 1, 3, and 5 km are used for modeled calculations.

+

To make the comparisons, a single near-resonant 1/4 monopole was modeled. Ground selection was dependent on the program used, since not all cores or all implementations of modeling cores permit access to the same types of ground system calculations. For example, in MININEC and NEC, the monopole was modeled with a direct connection to ground and no buried radials, since such radials are not available in most versions of these programs. However, NEC-4 permits a model using a buried radial system, and one such model was developed for this study.

+

Ground-wave analysis in all forms of MININEC is limited to the use of a perfect ground, since there is no provision for a ground-wave analysis other than the determination of far-field values at 0 elevation angle (90 theta or zenith angle) and a specified distance. NEC-2 and NEC-4 have provisions for a separate ground-wave output via request by the RP1 card. The results may be specified as a radial distance and an observation height. The provision of a ground-wave analysis output permits the specification of soil qualities in terms of conductivity and permittivity for the model, in addition to the use of a perfect ground.

+

One implementation of both NEC-2 and NEC-4 (EZNEC Pro) provides a MININEC ground calculation system for use in conjunction with the specified NEC core. By employing a MININEC ground and specifying soil quality values, the modeler obtains the ability to make ground-wave calculations that cannot be done within MININEC itself. As well, the use of the MININEC ground is said to overcome the inaccuracies inherent in the use of either the reflection-coefficient or Sommerfeld-Norton ground calculations with simple "no-radial" models. Whether this assertion is validated by comparison among models will become part of the data from this study.

+

A third method of ground-wave analysis involves the use of a buried ground radial system, a possibility within NEC-4. The ground-wave output from this modeling structure may use any permissible soil quality values. However, the model may not use a perfect ground, since part of its structure is below the ground surface.

+

2. Models used in this study. The basic vertical monopole antenna used in this study consists of a single wire 0.0254 m (1.0") in diameter. The reason for this selection involves the ease of modeling this thin diameter using a buried radial system in NEC-4, to be explained shortly. The resistivity of the wire was 1.72E-08, the approximate value for copper.

+

The length of the monopole for NEC-2, NEC-4, and Expert MININEC is 72.771 m (2865") to yield an antenna that is resonant within +/-j1 reactance over perfect ground. For versions of MININEC 3.13, the requisite length was 72.898 m (2870"). One version of MININEC 3.13 (NEC4WIN95) contains a "NEC-correction" feature, which returned the monopole length to the shorter value for resonance as here defined.

+

Models connected directly to ground and using no radials initially employed 21 segments, a value that places all critical dimensions well within the convergence and other boundaries of modeling. MININEC models place the source at the junction of the ground and the wire segment adjacent to ground. NEC models place the source within the segment adjacent to ground. No deleterious effects were noted from the differential in source placement between the two types of cores.

+

The NEC-4 model calls for special comment, due to the requirements for establishing a buried radial system. Such models must meet two major requirements. First, there must be a wire segment junction at the point where the wire enters ground. This requirement is usually met by specifying a wire end at Z=0. Second, wire segments adjacent to the segment on which the source is placed should be the same length as the source segment for greatest accuracy.

+
+ +
+

Fig. 1 provides a simplified sketch of the rudiments of the model used in this study. The radial system was placed 0.152 m (6") below ground. Other studies have shown that there is very little difference in the outcome of models with identical radial systems buried from about 3" to about 24" below ground.1 The radial placement yields a single segment wire between the radial junction and the ground surface. A second single-segment wire of the same length extends above the surface and becomes the source wire. Above the source wire, a series of length-tapered wires extends, the shortest being the same length as the source segment. The height above ground was set at 72.771 m (2865"), the same as the other NEC monopole models that use no radials. All monopole wires have a diameter of 0.0254 m.

+

The radial system consists of 120 2mm (0.0787") diameter, 74.948 m (2950.7") long copper wires, with equal angular spacing between them. Each of these wires is also length tapered, with the shortest wire being equal to the monopole wire forming the junction. No problems of accuracy have been encountered in the use of large radial systems in NEC-4 if all radials are thin and have the same length, despite the angular junction of wires having dissimilar diameters.

+

The model just described meets all requirements, however conservative, for length-to-diameter ratios for even the shortest wires in any element. One reason for the selection of the thin monopole (relative to what is commonly found in AM broadcast antenna installations) is that the modeling is greatly simplified. However, there are usable techniques for modeling thicker monopoles and/or shallower radial fields.2

+

A significant question is whether the length-tapered monopole is equivalent within relevant limits to the 21-segment monopoles with which it is being compared. That comparison proves to be more than 1-dimensional and is part of the data gathered in the course of the study.

+

3. Modeling cores and programs used in this comparison. The cores and programs compared in this study are the following.

+
    +
  • MININEC 3.13 ELNEC (Lewallen)
    + NEC4WIN 95 (Orion)
    + AO 6.5 (Beezley)
    • +
  • Expert MININEC (EM Sci, Inc.)
    + Expert MININEC Broadcast Professional
    • +
  • NEC-2
    + EZNEC Professional (Lewallen)
    + NEC-Win Pro (Nittany-Scientific)
    • +
  • NEC-4
    + EZNEC Professional (Lewallen)
    + GNEC (Nittany-Scientific)
    • +
+

Except for the unique ability of EZNEC Professional to provide ground-wave analysis over a MININEC ground using either NEC-2 or NEC-4, there was no difference in the values provided using the NEC cores with either Nittany-Scientific or Lewallen implementations.

+

4. MININEC 3.13 results. The Table 1 lists the results of ground-wave analysis obtained--insofar as was possible--from implementations of MININEC 3.13. The models are single-wire monopoles with no modeled radial system. All ground-wave calculations have been expressed in mV/m, even if program outputs registered V/m. The ground-wave calculation, where available, is based on a distance of 1,000 m and a power level of 1,000 W.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
ProgramELNECAONEC4WIN unc.NEC4WIN cor.
Height (m)72.89872.89872.89872.771
Impedance (Ohms)36.15 - j0.1736.0 - 0.438.08 + j0.1836.17 - j0.83
Gain (dBi)5.145.125.145.14
Field Strength (mV/m)312.85312*not availablenot available
+
+
+ Table 1. A comparison of MININEC 3.13 results +
+

Only values for 1 km are available from EZNEC, while AO allows the specification of a distance. However, AO provides somewhat truncated values, since it rounds extensively. For example, it rounded the conversion of 1,000 m into 0.6 miles. I found no way to extract field strength data from NEC4WIN. These values are in themselves of academic interest, although they may be useful in comparisons with other values enumerated in later tables. Internally, perhaps the most interesting aspect of the numbers is the consistency of calculated source impedance for all uncorrected models.

+

5. Expert MININEC Broadcast Professional and NEC-2/-4 results over perfect ground. Expert MININEC provides the user with the ability to specify virtually any power level and any distance when taking field strength readings, within the limitations of using the far field computation at 0 elevation over perfect ground. Therefore, it is possible to arrive at field strength values for 1, 3, and 5 km.

+

In addition, one can obtain comparable results from both NEC-2 and NEC-4 using virtually any implementation of these cores. Therefore, one may combine the results into a single table, since all three employ a 21-segment 72.771 m monopole, and none of the models uses a radial system.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Perfect Ground ValuesExpert MIN.NEC-4NEC-2
Source Impedance (R +/- jX Ohms)36.09 - j0.2736.22 + j0.2636.22 + j0.26
Ground Wave @ 1 km (mV/m rms)312.78312.75312.74
Ground Wave @ 3 km (mV/m rms)104.26104.25104.25
Ground Wave @ 5 km (mV/m rms)62.5662.5562.55
+
+

Table 2. A comparison of ground-wave field strength values for Expert MININEC Broadcast (EMB), NEC-4, and NEC-2 (Nittany-Scientific or Lewallen).

+

The results shown in Table 2 are remarkably clear. For the test model, there is no significant difference in calculated performance within any entry on the table. Expert Mininec Broadcast and NEC-2/-4 calibrate coincidentally for the class of cases involved in this study using exactly vertical wires when the calculations are made over perfect ground. As well, comparison with Table 1 shows that there is no significant difference in the available field strength readings between MININEC 3.13 and the cores recorded in Table 2.

+

6. NEC-4 results using buried radials over various soils. Evaluating the results of a modeled vertical monopole of the type used in this study must eventually involve a comparison with a version that modeled a buried radial system to complete the monopole antenna. The 120-radial system of 0.025 radials (74.948 m or 2950.7") using 2 mm diameter copper wire was chosen because it replicates common practice in the frequency range (1.0 MHz) and allows relatively accurate modeling results.

+

However, comparing the results of such a model in NEC-4 to other models over perfect ground is not without some issues, since there are limitations to the comparison. The NEC-4 model with buried radials cannot be modeled with a perfect ground, since part of the essential structure is below ground level. The question that will arise is whether one can reasonably extrapolate from the buried-radial model to those over perfect ground with attention to the ground-wave field strength values. The question will require some attention to differences in ground-wave calculations produced by NEC-4 and NEC-4D (single and double precision versions of the core).

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NEC-4 with 120 Buried RadialsNEC-4NEC-4D
Very Poor (0.001 S/m; 5)
Gain (dBi)/TO Angle (degrees)-0.80 / 25-0.80 / 25
Source Impedance (Ohms)41.46 - j 2.9241.46 - j 2.92
GW: 1 km189.49189.50
GW: 3 km36.3336.33
GW: 5 km14.2014.20
Poor (0.002 S/m; 13)
Gain (dBi)/TO Angle (degrees)0.67 / 230.67 / 23
Source Impedance (Ohms)38.75 - j 0.6338.75 - j 0.63
GW: 1 km229.68229.68
GW: 3 km54.7654.76
GW: 5 km25.2225.22
Good (0.005 S/m; 13)
Gain (dBi)/TO Angle (degrees)1.86 / 211.86 / 21
Source Impedance (Ohms)37.87 + j 0.9837.87 + j 1.00
GW: 1 km276.10276.08
GW: 3 km79.7879.78
GW: 5 km42.4642.46
Very Good (0.0303 S/m; 20)
Gain (dBi)/TO Angle (degrees)3.44 / 153.44 / 15
Source Impedance (Ohms)36.90 + j 1.5736.90 + j 1.58
GW: 1 km304.79304.80
GW: 3 km99.0199.00
GW: 5 km58.1858.18
+
+
+ Table 3. Ground wave and other values deriving from NEC-4 and NEC-4D models. +
+

Therefore, Table 3 provides data for both core outputs, using the same 1, 3, and 5 km standard distances at a power of 1 kW. In addition, the model has been placed over a variety of soils, according to the widely used standard listing in Terman's Radio Engineer's Handbook (p. 709), which derives from "Standards of Good Engineering Practice Concerning Standard Broadcast Stations," Federal Register (July 8, 1939), p. 2862. In other studies, the use of the chosen categories of soil quality constants for Sommerfeld-Norton ground calculations has been found to be a fair, if not perfect, sampling of the range of possible soil conditions.3 The first listed value in each portion of the table is conductivity in S/m, while the second value is the permittivity or relative dielectric constant.

+

Of first notice in the table is the spread of values of ground-wave field strength for any given distance at the set power as we change the soil quality. Although the ground-wave field strength values over very good soil approach those from models placed without radials over perfect ground, over very poor soil the values are only about 60% of the perfect ground values. In addition, there is a progression of decreasing source impedance as soil quality improves which cannot show up when calculations are made solely over perfect ground.

+
+ +
+

Of second notice is the tendency to extrapolate from the values for very good soil to the values for perfect ground calculations on the basis of the general tendencies shown in the output results. Although such an extrapolation is probably satisfactory for many applications, a more precise version of the process is beset with problems relating to the complexity of the calculations involved.

+

One problem involves the fact that a 120-radial system may approach the performance of a solid surface, but it does not reach that level. Fig. 2 shows graphically the increase in ground-wave field strength at 1 km with 1 kW of power over poor soil (0.002 S/m; 13) as we increase the number of radials in a NEC-4 model. As is readily apparent, the curve has not reached a final plateau.

+

A second problems involves the extension of the soil quality into higher values. Perhaps the standard of quality is salt water, with a conductivity of 5 S/m and a dielectric constant of 81. Table 4 provides values for NEC-4 and NEC-4D models of the system in use over salt water.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NEC-4 with 120 Buried RadialsNEC-4NEC-4D
Salt Water (5.0 S/m; 81)
Gain (dBi)/TO Angle (degrees)5.29 / 075.28 / 06
Source Impedance (Ohms)32.72 - j 2.5832.72 - j 2.57
GW: 1 km400.48328.14
GW: 3 km135.89109.36
GW: 5 km123.3365.60
+
+
+ Table 4. Ground wave values deriving from NEC-4 and NEC-4D models over salt water. +
+

The NEC-4 values are wholly unreliable and stem from unreliable calculation behavior that actually begins as the soil quality approaches the level listed as very good. At these values of conductivity and permittivity, calculated ground-wave field strength values show variability when listed in 1 increments. Although the differential between maximum and minimum values is small (about 0.02 mV/m rms), it varies from the anticipated uniform value at all compass points. NEC-4D provides uniform values. As conductivity reaches a value of about 0.5 S/m, the maximum-minimum spread in NEC-4 output values grows to over 4 mV/m, and for each doubling of conductivity above that level, the spread nearly triples. Increasing the dielectric constant over this range from 20 to 50 does not change the spread from maximum to minimum very much, but it does change the maximum and minimum values themselves. Therefore, above a conductivity of about 0.1 S/m and a dielectric constant of about 20, NEC-4 values of ground-wave field strength for the type of model used here become quite unreliable.

+

In contrast, the ground-wave field strength values produced by NEC-4D always provide a uniform value at every azimuth bearing for a vertical monopole of the type used in this study. For several echelons of increase beyond the soil quality called very good, the results are generally reliable. However, the reliability is not perfect. The results for the subject model with "salt-water" ground constants exceed the result of every model surveyed, when the monopole is placed over perfect ground without radials. The 1-km ground-wave value is over 4% greater than any of the perfect ground values.

+

Whether or not the differentials have any practical significance, it remains the case that one cannot numerically extrapolate with any degree of precision from the radial model to the perfect ground model or vice versa. Moreover, more deeply burying the radial system will not resolve the issue. In a series of models using 60 radials, it was found that increasing the depth to 12" increased the 1 km field strength by 6 mV/m rms. The values remained constant within 1 mV/m thereafter until at least a depth of 24".

+

The NEC-4 and NEC-4D results for soil qualities that are very good or worse are too close for repetition in further tables in this study. However, whatever the ground type, with or without a radial system, as soil quality approaches very good, the NEC-4D ground-wave field strength readings will begin to decrease relative to those produced by NEC-4.

+

7. NEC-2/-4 results over a MININEC ground. One implementation of NEC-2 and NEC-4 (EZNEC Professional from Lewallen) provides the user with the option of employing a MININEC ground calculation while using one or the other of the NEC cores. This option enables the user to employ the RP1 option to develop ground-wave field strength readings. As well, it permits the user to select any set of soil quality constants. The limitation of this option is that the source impedance is calculated as it would be in MININEC 3.13, that is, only over perfect ground. Consequently, although the ground wave values will vary with the soil constants selected, the source impedance will remain the same for all cases.

+

The assumption underlying the use of MININEC ground with NEC calculations on a monopole with no radials is that the MININEC ground calibrates well to a full NEC-4 model with radials. Other studies have shown that this assumption is not adequate for systems with few radials, but for purely vertical antenna structures, it may hold well enough to simplify some orders of modeling.4 Models that employ any horizontal or sloping elements, whether directly fed or parasitic, may encounter erroneous results if any portion of a sloping or horizontal wire is below about 0.2 above ground.

+

Table 5 provides a listing of results using NEC-2 and NEC-4 with a MININEC ground within EZNEC Pro. The entries parallel those in Table 3, which records the outputs for the full 120-buried radial model. In addition, the table provides for each core 2 listings, one of which corresponds to the standard 21-segment models used over perfect ground, and the other of which corresponds to the length-tapered element used in the 120-radial model. The length-tapering for these new models is identical to that portion of the 120-radial model that is above the surface of the ground. For both models, the source is on the wire segment that joins the ground.

+

Table 5, then, provides the data necessary to perform two tasks: a. to discover if the length-tapered model is a reasonable correlate of the 21-segment standard model monopole, and b. to determine if the use of NEC with a MININEC ground provides, with a simplified model, usable results with respect to treating a 120-radial model as a standard.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NEC Core, MIN Gnd, No RadialsNEC-4; 21 Segs.NEC-4; L-TaperedNEC-2; 21 Segs.NEC-2; L-Tapered
Very Poor (0.001 S/m; 5)
Gain (dBi)/TO Angle (degrees)-0.80 / 260.00 / 26-0.08 / 260.00 / 26
Source Impedance (Ohms)36.22 + j 0.2635.48 - j 0.2436.22 + j 0.2635.47 - j 0.26
GW: 1 km206.41208.14206.25208.04
GW: 3 km39.5239.8539.8040.14
GW: 5 km15.4415.5715.6015.74
Poor (0.002 S/m; 13)
Gain (dBi)/TO Angle (degrees)1.01 / 231.09 / 231.01 / 241.09 / 24
Source Impedance (Ohms)36.22 + j 0.2635.48 - j 0.2436.22 + j 0.2635.47 - j 0.26
GW: 1 km239.39241.43238.52240.60
GW: 3 km57.0257.5157.1757.67
GW: 5 km26.2626.4826.3626.59
Good (0.005 S/m; 13)
Gain (dBi)/TO Angle (degrees)2.11 / 212.18 / 202.11 / 212.18 / 21
Source Impedance (Ohms)36.22 + j 0.2635.48 - j 0.2436.22 + j 0.2635.47 - j 0.26
GW: 1 km284.46286.89282.60285.07
GW: 3 km82.1682.8681.9982.71
GW: 5 km43.7344.1043.6744.05
Very Good (0.0303 S/m; 20)
Gain (dBi)/TO Angle (degrees)3.53 / 153.61 / 153.54 / 163.61 / 16
Source Impedance (Ohms)36.22 + j 0.2635.48 - j 0.2436.22 + j 0.2635.47 - j 0.26
GW: 1 km308.37310.96306.82309.53
GW: 3 km100.13101.0099.99100.87
GW: 5 km58.8559.3458.7959.31
+
+
+ Table 5. NEC-2 and NEC-4 with MININEC ground. +
+

Within the table, the maximum variation among ground-wave field strength calculations is about 1.3%. The lower source resistance values for the length-tapered models in both NEC-2 and NEC-4 is partly attributable to the closer proximity of the source to the actual ground. For most purposes, the data from either the standard 21-segment model or the length-tapered model would be interchangeable.

+

Relative to the 120-radial NEC-4 model, these models show higher values for ground-wave field strength calculations, ranging from under 2% for very good ground to nearly 10% for very poor ground. The differentials have sufficient pattern to them to suggest that the variations may be systematic. The range of values in mV/m (rms) runs from a little over 5 for very good ground to well above 18 for very poor ground. Therefore, it is unlikely the setting the buried radial system to a lower level would increase the field strength calculation outputs sufficiently to reach the levels resulting from the use of a MININEC ground.

+

The precise differential that represents a threshold between a usable and an unusable correlation of values between the two ways of modeling monopoles is, in the end, a task driven judgment. The task will contain, implicitly or explicitly, the appropriate criteria for determining the adequacy of a no-radial substitute model for a fully-modeled buried radial system.

+

8. NEC-2/-4 results over reflection coefficient and Sommerfeld-Norton grounds with no radials. Every implementation of NEC-2 and NEC-4 cautions against using the output values from a model that places a monopole in direct connection with ground with no radial system when employing either the Sommerfeld-Norton or the reflection coefficient approximation ground calculation methods. However, little exemplary evidence for the dangers of this procedure appear in software or other literature. Within the present context, it might be useful in developing an appreciation of the sound advice to present ground-wave field strength values and related data as they emerge from the standard and the length-tapered models misplaced on the ground with no radials.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NEC Core, RCA Gnd, No RadialsNEC-4; 21 Segs.NEC-4; L-TaperedNEC-2; 21 Segs.NEC-2; L-Tapered
Very Poor (0.001 S/m; 5)
Gain (dBi)/TO Angle (degrees)-11.1 / 26-25.4 / 260.83 / 261.53 / 26
Source Impedance (Ohms)420.0 - j 6738620 - j 1481029.42 - j 0.4924.96 - j 2.79
GW: 1 km57.9011.23229.14248.25
Poor (0.002 S/m; 13)
Gain (dBi)/TO Angle (degrees)-8.69 / 24-22.5 / 241.67 / 232.20 / 23
Source Impedance (Ohms)317.2 - j 4946342 - j 1090031.17 - j 0.3027.51 - j 2.27
GW: 1 km77.9715.84258.15274.38
Good (0.005 S/m; 13)
Gain (dBi)/TO Angle (degrees)-6.75 / 21-20.1 / 212.54 / 212.90 / 20
Source Impedance (Ohms)267.0 - j 3125211 - j 687532.81 - j 0.5430.07 - j 2.38
GW: 1 km101.8921.70298.89311.60
Very Good (0.0303 S/m; 20)
Gain (dBi)/TO Angle (degrees)-2.61 / 16-15.2 / 163.71 / 153.90 / 15
Source Impedance (Ohms)146.6 - j 1242514 - j 274034.78 - j 0.2333.19 - j 1.43
GW: 1 km151.2035.59314.67321.48
+
+
+ Table 6. NEC-2 and NEC-4 with a reflection coefficient approximation ground. +
+

In Table 6 and Table 7, field strength values for 3 and 5 km are omitted, since the 1 km figure provides adequate evidence that the values are not usable. In Table 6, the NEC-2 figures are obviously far off the mark. However, it is interesting to note that the length-tapered model--which was stable in relationship to the standard model over a MININEC ground--has become highly unstable with results that little resemble those of the standard model.

+

At first sight, the results from NEC-4 appear to be more reasonable. Had one taken only a single model over a single set of soil quality values, one might have been tempted to accept the results. However, both sets of values result in 1 km field strength values that are higher than those from placing the monopole on a perfect ground. In addition, the progression of source impedance values proceeds in the wrong direction, showing the appearance of higher ground losses as the soil quality improves.

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NEC Core, S-N Gnd, No RadialsNEC-4; 21 Segs.NEC-4; L-TaperedNEC-2; 21 Segs.NEC-2; L-Tapered
Very Poor (0.001 S/m; 5)
Gain (dBi)/TO Angle (degrees)-8.52 / 26-21.2 / 26-1.40 / 25-1.28 / 25
Source Impedance (Ohms)249.9 - j 63.714499 - j 150248.92 + j 4.7547.48 + j 2.59
GW: 1 km78.0318.13177.37179.77
Poor (0.002 S/m; 13)
Gain (dBi)/TO Angle (degrees)-5.02 / 24-16.9 / 24-0.16 / 24-0.06 / 23
Source Impedance (Ohms)144.5 - j 32.702197 - j 838.047.40 + j 5.6546.23 + j 4.55
GW: 1 km119.0230.27209.14211.51
Good (0.005 S/m; 13)
Gain (dBi)/TO Angle (degrees)-1.80 / 21-12.3 / 211.14 / 201.22 / 21
Source Impedance (Ohms)89.0 - j 1.111013 - j 146.745.26 + j 5.7644.37 + j 5.24
GW: 1 km180.1653.29254.47256.69
Very Good (0.0303 S/m; 20)
Gain (dBi)/TO Angle (degrees)2.26 / 16-3.98 / 162.98 / 153.05 / 15
Source Impedance (Ohms)48.7 + j 3.78203.9 - j 2.4041.19 + j 3.6940.40 + j 3.60
GW: 1 km264.81129.18298.19291.58
+
+
+ Table 7. NEC-2 and NEC-4 with a Sommerfeld-Norton ground. +
+

As Table 7 shows well, the NEC-2 values are beyond the pale of credibility, and the instability between the standard and length-tapered models shows itself, although perhaps not to the extremes revealed by the use of a reflection coefficient ground. In contrast, the NEC-4 results more closely approach credibility with a reasonably close coincidence between the standard and the length-tapered models. Nevertheless, for most purposes, the values throughout the table are too distant from either the models over perfect ground or the 120-radial model for practical use.

+

The purpose of this last exercise was not to simply state the obvious, namely, that values derived from monopole models connected directly to a reflection coefficient or Sommerfeld-Norton ground are not generally reliable. The tables focus attention on the degree of departure from reliable figures and the ways in which the modeling results go astray under the specified conditions.

+

9. Conclusions. The data presented in this study provides an inter-program comparison of the expected results from modeling 0.25 vertical monopoles over a number of ground systems ranging from perfect ground to a full 120-radial buried system. The data are relevant to evaluating various modeling schemes that might be employed in the calculation of ground-wave field strength values applicable to MF (AM broadcast) antennas and arrays.

+

MININEC 3.13, Expert MININEC, and NEC (-2/-4) produce well-correlated output values of ground-wave field strength when the models are simple monopoles connected to a perfect ground.

+

The NEC-4 120-radial buried system model correlates reasonably closely to both MININEC and NEC models that are simple monopole connected directly to perfect ground--so long as the NEC-4 model soil quality is very good or better. Lesser soil quality leads to greater disparity between the model outputs. Wherever soil quality is a significant consideration and the quality may be less than very good, a model over perfect ground may not prove fully adequate.

+

Over the span of soil qualities usually encountered, the use of a MININEC ground with a simple monopole model correlates to a fair degree with the outputs from the NEC-4 120-radial buried system model. However, the two types of models increasingly diverge in output values as soil quality becomes worse.

+

In all cases, the acceptability of a model depends upon the criteria of evaluation employed. since these criteria are determined by the project goals and specifications, no conclusion can be drawn generally about the acceptability of using one model in preference to another. The exceptions to this conclusion are models connecting a monopole directly to a reflection coefficient or Sommerfeld-Norton ground: for most purposes, the outputs of such models are wholly unreliable.

+
+ Notes +
+

1 See Part 4 ("A Potpourri of 160-Meter Vertical Antennas and Modeling Issues") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays," forthcoming in The National Contest Journal.

+

2 See Part 3 ("Complex Radial Systems and Limitations of the MININEC (No-Radial) Ground") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."

+

3 See Part 2 ("Appreciating Conductivity and Permittivity") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."

+

4 See Part 1 ("Some Baseline Data") of "Some Facts of Life About Modeling 160-Meter Vertical Arrays."

+

This four part series can be found on the Some Facts of Life About Modeling 160-Meter Vertical Arrays page.

+

Also see the Antenna Modeling Programs page for more information about modeling software.


+
+ +
+

Updated 02-23-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +

+ Go to Main Index
+

Topics: Broadcast, MF, Vertical


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+

Counterpoises, Capacity Hats, and A Standard
+ for Comparing Antennas Suspected of Radiation from the Feedline

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Investigators have suspected that a number of very small antennas do not themselves have significant radiation. Instead, the so-called antenna structures form non-radiating or very low-level radiating structures, and the main radiation from the antenna assembly as a whole occurs from the outer surface of the braid of the coaxial cable feedline.

+

Most of the tests so far performed lack one essential ingredient to an unambiguous test result: one or more standards against which to compare the system under study. These notes are designed to suggest a standard against which to compare subject antennas.

+

At the outset, I shall suggest that 50 MHz may be a good test frequency. It is within an amateur band, allowing the use of legal transmitters. The structures are large enough not to require ultra-finicky adjustments either for tune-up or for measurement. As well, upper-HF construction techniques work well. At the same time, they are small enough to be inexpensive and physically manageable. For example, the suggested mounting height will be 1/2 wavelength. At 50 MHz, a half wavelength is 2.998 meters, 9.836', or 118.03". A ten-foot mast of non-conductive material--such as PVC--serves well with a home-made tripod mount. Careful backyard testing becomes very feasible.

+

The immediate problem is that many subject antennas are designed for other frequencies. Therefore, the subject antenna will normally require that the tester construct a 50-MHz version for tests. However, since it is the antenna principles that are under test--and not a specific antenna device--the substitution presents no theoretical problems.

+

Before setting up the suggested standard, let's examine some candidates for the task. In the process, we can perhaps get rid of a few common terminological problems that may inhibit either good testing or good reader understanding of the test results.

+

Vertical Dipoles and Ground-Plane Radial Monopoles

+

Essentially, our basic choice for a test antenna standard will be a vertically polarized antenna. If, as the test suspicion indicates, it is the feedline that is radiating, that line normally proceeds downward from the antenna structure under test. This situation provides another reason for using 50 MHz as a test frequency. With a 1/2 wavelength non-conductive mast, the feedline will be able to drop vertically from the antenna assembly. At low HF frequencies, the feedline may have to bend, twist, coil, or crawl along the ground for most of the first quarter wavelength from the antenna. A definitive test requires that we use a single orientation for the suspected actual radiator.

+
+ +
+

Fig. 1 shows 3 antenna configurations. The vertical dipole is electrically the simplest structure. However, because we need to feed the antenna at its center, the feedline should run horizontally for a considerable distance from the antenna. In practice, we use such antennas along with as many decoupling devices as a given situation needs to prevent pattern distortion due to unwanted coupling to the feedline.

+

The center vertical monopole uses 4 radials to form a nearly non-radiating ground plane for the antenna. Largely because the radiation from the horizontal radials is nearly zero, early texts on these antennas introduced two expressions into the antenna lexicon, one more dangerous than the other. The expression "ground-plane" radial system is itself not always accurate, because the horizontal radials do not necessarily form a ground plane, where we take the term "ground" seriously. Common practice is to connect the coaxial feedline braid to the radials and the center conductor to the vertical element. Hence, we have the illusion of the radials somehow being connected to ground. However, those radials function even when the antenna is many wavelengths from the energy source and form a ground conductor only for static build-up on the elements. In this context, we sometimes connect an RF choke between the vertical element base and the radial system in order to bleed static build-up from the vertical element as well. However, the antenna radial system may make no connection to the earth and still perform its function within the antenna perfectly well.

+

A second term is even more insidious: "counterpoise." This term entered antenna work from the world of mechanics in which some machinery required well-balanced counterweights in order to perform its function. Early thought about antennas led to underground wires paralleling horizontal antennas, buried and elevated radial systems, etc., and all received--for want of an understanding of their actual function--the vague label "counterpoise." Today, we find uses for the term that range from highly refined and defined applications to vague and ambiguous uses. Unfortunately, a large number of readers may not be tuned into the more rigorous uses within an article and carry away the idea that whatever constitutes the counterpoise requires less stringent standards of construction or analysis than the so-called antenna proper. I have read an advertisement for an antenna that uses a very long piece of wire as a "counterpoise," with the advice to kick it around until the antenna achieves resonance. In an article within a respected journal, I read about a portable monopole for use on balconies, and the author advised the reader simply to drop a counterpoise downward, with no concern for where it went or in what environment it operated. I have even seen the term used to characterize the coaxial cable feedline of antennas in which the tester suspected that the cable or counterpoise did the radiating.

+

In fact, in antenna work, there is no such thing as a counterpoise. Every part of the antenna system performs a function that we may directly analyze and calculate--and measure as well. The carelessly dropped "counterpoise" wire was actually the lower half of a vertical dipole. It exhibits a current distribution comparable to the distribution on the upper section, the so-called antenna proper. Radiating coaxial cables are susceptible to measurement and adjustment either to maximize or minimize the radiation. Finally, the radial system of the monopoles in Fig. 1 also show appropriate current distributions along their lengths, and they do radiate. They just happen to be horizontal and their far-field radiation is mostly self-canceling.

+

Let's compare the 3 configurations as physical NEC-4 models and see what we obtain in free space. Free space has no other object in its universe other than the antenna structure modeled. Hence, there is no ground. We shall note something else that is lacking shortly.

+ 
+Dimensions of Free-Space Models of Vertical Dipoles and 4-Radial Vertical Monopoles
+
+Vertical Dipole
+Element Length     WL         Inches          Millimeters     Diameter     WL          Inches          Millimeters
+                   0.474      111.891         2842.04                      2.118e-3    0.5             12.7
+4-Radial Vertical Monopole (both versions)
+Element Length     WL         Inches          Millimeters     Diameter     WL          Inches          Millimeters
+                   0.245      57.834          1468.98                      2.118e-3    0.5             12.7
+Radial Length      WL         Inches          Millimeters     Diameter     WL          Inches          Millimeters
+                   0.255      60.195          1528.94                      1.059e-3    0.25            6.35
+
+

There is a reason for the element diameters used in the model. Ultimately, we want a standard that will reasonably replicate a main element composed of large diameter (low-loss) coaxial cable, that is, a cable whose braid approaches 1/2" in diameter. Also note that the monopole length is slightly greater than 1/2 the length of the vertical dipole. That maneuver results from the fact that the virtual position of a source is in the center of a model segment. The vertical dipole uses 31 segments with the source assigned to segment 16 at the center of the wire. The vertical element in the monopoles uses 16 segments, with the source assigned to the segment nearest the junction with the radials. By lengthening the vertical element about half the length of a segment, the monopole has a source position that is about the same distance from the vertical element tip as in the dipole.

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We recognize that the right-most portion of Fig. 1 is simply the center antenna turned upside down. In free space, the orientation makes no difference, so long as we select the correct polar plot to show the resulting pattern. In all cases, I selected E-plane plots, which in modeling terminology means azimuth plots. The results appear in Fig. 2.

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The gain of the dipole is 2.13 dBi (using aluminum elements throughout, although that hardly matters, given the large diameter of the elements). Both of the monopoles show a gain of 1.35 dBi. Note that the horizontal structure of each monopole creates no difference in the elevation angle of maximum radiation. It remain perpendicular to the vertical element.

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If you explore the current distribution on the antennas, you will easily discover that that vertical dipole current decreases slowly at first as we move away from the source. A similar distribution occurs on the vertical section of the monopoles and is identical for both versions. The radials also participate in the current distribution. However, the current divides into 4 equal components at the junction, with each radial's first segment showing about 1/4th the source current. The radials are active parts of the antenna and critical to its proper operation.

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In fact, the radial length was selected to bring the monopoles to near resonance, defined as a remnant source reactance of less than +/-j1 Ohm. Hence, they are slightly longer than the vertical element. Radial length is a function in part of the few radials used. I have elsewhere shown on a number of occasions that the higher the number of radials, the shorter the radial length needed to achieve system resonance. Somewhere in the region of 60 to 70 radials in free space, the radial length closely approaches the radius of a thin solid surface.

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The modeled source impedance of the vertical dipole is, as we would anticipate, 72.04 + j0.35 Ohms. A persistent error in much literature would have the monopole impedance be 1/2 half that value, since the vertical element of the monopole is half the length of the dipole. Unfortunately, this easy derivation holds true only if we use a perfect ground, that is, if we mathematically recreate the missing half of the dipole with no radials in the model. When we place the monopoles in free space, we obtain a source impedance of 23.19 - j0.24 Ohms. To arrive at 36 Ohms, we must lengthen the vertical element considerably with a consequential shortening of the radials to return to near resonance. The result is an off-center-fed vertical element with its maximum current well above the feedpoint on the segment that joins with the radials.

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We are now in a position to look more closely at the upside-down monopole. Suppose that we had inserted 2 or 3 segments of vertical wire between the present source segment and the radials. To achieve resonance, we would have shortened the radials to compensate for the added vertical length. As well, we would have dubbed the radial structure a "capacity hat." As long ago as the 1950s, Laport's classic text clearly notes that the name is based not on solid electronic theory, but on an analogy that is useful for approximate calculations of the required hat size based on the capacitive reactance of short vertical monopoles at ground level used in the low frequency region of the spectrum. Nevertheless, the name and idea persisted in amateur circles due to an article in QST in the 1970s, and the article was reprinted often in various antenna books. I have elsewhere shown that the calculations are seriously off in the HF region and above. As well, there is a complex relationship between the vertical element diameter and the diameter of the radials (or spokes, when speaking of hats).

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In the end, the so-called capacity hat has nothing to do with capacity. We do not have one plate of a capacitor, the other plate of which is presumed to be the universe itself. Our free-space universe for the model has nothing in it to form the other plate of the so-called capacitor. Rather, the spokes of a top-hat structure provide the element length necessary for a normal current distribution such that the source impedance is whatever the designer needs it to be, normally, near to resonance. Because the hat spokes are at right angles to the main radiator and are symmetrically arranged, they contribute nearly nothing to the overall element radiation. The element end is actually 4 ends: the tips of the radials, not the flat plane created by the right-angle structure.

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In point of fact, our upside-down monopole is simply an extreme form of top-hat. If we place the virtual source at the center of the source segment, then the radials are already displaced slightly from the source and constitute a top-hat. However, we have already seen that the free-space operation of the antenna is identical to the right-side up version, for which we are not in the least inclined to apply the term capacity-hat to the radials. In fact, the radials complete the antenna structure--relative to dipole current distribution--and do not form either a ground or a capacitor. Hence, it is likely that calling the structure a "top-hat" (or "end-hat" on horizontal elements) may be preferable to continuing the use of the label "capacity hat."

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We can illustrate the relative identity of the ground-plane radials and the top hat by bringing the monopoles closer to earth--dragging the vertical dipole along for the ride. As a first step. let's use the so-called average ground for our earth (conductivity = 0.005 S/m; relative permittivity = 13). Next, let's set the source at 1/2 wavelength above ground. This is not yet a fair test, because the right-side-up monopole extends from 1/2 wavelength upward, while the upside-down monopole extends from 1/2 wavelength downward. If we take elevation plots of the three antennas in their new positions, we obtain the patterns shown in Fig. 3. The figure also shows the maximum gain and take-off angle for each configuration.

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The first thing to notice about vertical antennas is that their source impedances do not change much until we bring them very close to the ground. The antennas in Fig. 3 are at the border of this region. The vertical dipole remains within a half-Ohm of its free-space value with an impedance of 69.45 + j0.72 Ohms. The right-side-up monopole shows a modeled impedance of 23.63 + 0.44 Ohms, again within a half-Ohm of its free-space value. Only the up-side-down monopole, with its tip about 1/4 wavelength from ground shows a slightly larger deviation: 22.02 - j2.09 Ohms.

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The right-side-up monopole shows a very high TO angle, largely due to the fact that all of its radiating structure is above 1/2 wavelength. If we drop the antenna to a base height of 0.25 wavelength, the gain is 1.16 dBi at a TO angle of 16.2 degrees. The source impedance also changes to 21.59 - j1.77 Ohms. These values closely parallel those of the upside-down monopole, which has very similar top and bottom height values relative to the revised position of the right-side-up version. In short, the two monopoles remain the same antenna, even when we bring the earth into the picture.

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I have noted that the radiation from the radials is nearly zero. However, it does not go completely to zero. We may observe remnant radiation from the radials by taking azimuth plots of the vertical dipole and either of the monopoles--and we may use the models in free space or over ground. For each type of antenna, there will be no difference due to the presence or absence of a ground surface. As Fig. 4 shows, the vertical dipole has no detectable horizontal component to the overall radiation pattern. The monopoles, however, have an 8-lobe pattern that shows up at the -40 dB level. For all practical purposes, we can ignore this small horizontal component. Nevertheless, the horizontally polarized component does establish that the radials--whether at the top or bottom of the monopole structure--do radiate. Most of that radiation is self-canceling, taking the symmetrical arrangement into account. But some radiation does emerge.

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Transforming the Upside-Down Monopole into a Testing Standard

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The upside-down monopole represents an example of an antenna wherein the top structure radiates as little as possible, and for practical measurements, not at all (unless the measuring equipment is capable of detecting -40 dB radiation relative to the main field). Hence, it is suitable as a standard of comparison with antennas suspected of feedline radiation as the main source of far fields. However, the radials are 5' long and may sag a good bit in their top position. Therefore, we should try to shrink the assembly without changing its basic operation.

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One way to shrink the top hat assembly is to add more radials. However, we may use a more efficient means. We can add a perimeter wire from radial tip to radial tip. Fig. 5 shows the general outline. Note the lines that indicate the path of current distribution. Now they extend from the radial hub to the center of each perimeter wire. For the 50 MHz monopole using 0.25" radial assembly wires, the total path length is about 0.253 wavelength, in contrast to the radial-only length of 0.255 wavelength. The slight shortening of the path is due to the sharp corner at the radial tips.

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Fig. 6 compares the relative current magnitudes in the standard 4-radial top-hat and the version that uses a perimeter wire in an EZNEC graphic that overlays the current curves on the outline of the models. If you place a ruler on the graphic, you will see on both outlines that the distance between the radial hub and the current line is about 1/4 the distance between the vertical monopole and its current maximum. In the version using the perimeter wire, the current at the tip of each radial is about twice the current in the connecting perimeter wires. Of cources, we have at those points a second splitting of the current paths. The decrease of the current to zero at the exact centers of the perimeter side shows clearly.

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The radials themselves have decreased to a length of 0.148 wavelength (34.93" or 887.39 mm). The overall hat assembly is only 58% as large as the radial-only version. The modeled free-space performance data shows a gain of 1.59 dBi, with a source impedance of 21.47 - j0.49 Ohms. With the top-hat 1/2 wavelength above average ground, the gain is 1.20 dBi at a TO angle of 15.5 degrees, with a source impedance of 20.43 - j1.83 Ohms. The horizontal component has shrunk to the -50 dB level relative to the main elevation lobe of the antenna.

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It is likely that any version of the standard top hat antenna using a perimeter-wire top-hat will employ a perimeter wire that is considerably thinner than the radials: perhaps AWG #12 or #14 or 2-mm wire. Because NEC (even NEC-4) becomes less accurate when we have non-symmetrical junctions of wires having different diameters, it is not possible to provide a precise design. However, modeling suggests that for AWG #12 perimeter wire, the radials should be about 0.156 wavelength (36.82" or 935.35 mm).

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The entire purpose of setting up a standard is to measure it on the test site using all available test equipment. The measurements include--besides the obligatory source impedance record--near-field and ground-wave measurements at distances clearly marked for replication. Do not use hand-held instruments, but devise mounting brackets so that each measurement uses an identical position. You may also generate current probes using a multi-turn winding around a toroidal core and letting the antenna element form the other 1-turn winding of the resulting transformer. By rectifying and filtering the induced voltage or current, you may derive relative current readings along the length of any portion of the array. All of these readings together form the base-line of data for further comparisons. In this set-up, the feedline should operate only as a feedline. If necessary (due to the odd angle of departure from the assembly top), add a choke-balun (common-mode choke) at the feedpoint.

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Fig. 6 shows the basic top-hat monopole along side an adaptation to determine the radiating properties of coaxial cable. The cable serves as both the feedline and the main vertical radiator. It is similar in principle to feeding the cable through the center of the driven element tube, except that the role of the tube is played by the outer surface of the coaxial braid. The cable should be at least 1/2 wavelength long, that is, long enough to reach from the top of the 1/2 wavelength non-conductive mast to the ground.

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The diagram shows two possible ways to connect the cable: with the center conductor to the hat or with the braid to the hat. In theory, with a perfectly balanced line, there should be no difference in any measurements applied to the system, since any imbalance created by the hat on one side of the line will couple through to the outer surface of the braid. However, practice may show otherwise. The diagram also shows the presence of a ferrite bead choke. At 50 MHz, you may use about a dozen FT-43 toroid cores that have an inner diameter just large enough slide over the coax jacket. Because toroids are available in different lengths, about 6-8 inches of cores is about right for 6 meters. The so-called bead-balun choke is most useful in this application because you can move its position to one in which a. you obtain the maximum radiation and b. you obtain the minimum radiation from the cable. The diagram shows various positions for the coax line on the source side of the bead-balun. Varying the line position below the vertical length needed for maximum radiation is a good way to find out if other forms of coupling to the line may occur.

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Measure the same set of parameters as for the basic antenna. Include relative current readings from both the main vertical length of coax that forms the prime radiator and from positions beyond the choke-balun to determine if there is coupling to the line by direct radiation. In theory, it should be possible to obtain just about the same performance from the coax + hat assembly as from the basic antenna in which the feedline operates solely as a feedline. Not shown in either case is the matching network that you may need to raise the low impedance of the assembly (20-25 Ohms) to the 50-Ohm level required by the coax. A quarter wavelength section of parallel 70-75-Ohm cable (taking the line's velocity factor into account) is a simple way to match the top-hat monopole to the line, although a simple L-circuit will also work well.

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Now you may take the third step and replace the hat assembly with any desired test antenna assembly that you suspect may rely on the feedline for radiation. Since many of these top assemblies may not allow easy measurement of their radiation or their current levels due to the shape of their parts. you may estimate better the degree to which they radiate and to which the feedline radiates by comparing measurements with the two base-line antennas. As well, you may compare near-field and ground-wave readings with the choke in various positions on the coax, after ensuring that there is no significant coupling by direct radiation to the coax beyond the choke.

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The hat assembly is an example of a half dipole that radiates only about 40-50 dB below the level of the vertical radiator--plus whatever radiation may occur from the feedpoint connection mechanical components. Its very low level of radiation is partly a function of the symmetry of its construction and its size, where the "right" size is determined by resonance when using a vertical main element that is 1/2 the length of a resonant dipole. It is part of the antenna assembly--as determined by the current distribution along its radials and perimeter wire--but unlike some other assemblies that call themselves antennas, the hat is not supposed to radiate significantly.

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If the current distribution along the coax feedline substitute for the main vertical element matches the current distribution with a test antenna and if the near-field and ground-wave measurements also match up, then we have strong evidence that the test antenna is little more than a "hat-substitute" and has about the same radiation properties. If the current distribution along the coax outer surface is different for the test antenna, but the near-field and ground-wave readings are the same, then it is likely--subject to more detailed analysis--that the test antenna presents the feedpoint with a different set of impedance conditions, but does not contribute significantly to radiation. If the radiation levels increase with the subject antenna, then it is likely that the antenna assembly is radiating to some degree. (For further comparisons, you may wish to make reference near-field and ground-wave readings with a vertical dipole.) If the overall near-field and ground-wave readings are lower with the subject antenna in place, it is likely that the subject antenna is creating a resistive load that is converting some supplied energy into heat rather than radiation. The comparative measurements do not provide definitive final answers, but they do provide both probable answers and pointers toward the system elements that may need further analysis.

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Conclusion

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I have dwelt at a bit of length establishing that the top-hat monopole as simply a different but highly usable standard for comparing test results with antennas suspected of relying on feedline radiation for their far fields. It seemed necessary to clear the field of potential misconceptions attaching to notions like "ground plane," "counterpoise," and "capacity hat." The top-hat monopole and its smaller cousin that uses a perimeter wire to shrink the top-hat spread are simply inverted ground-plane monopoles and operate in exactly the same manner.

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As a test standard, the top-hat monopole is useful because the hat structure--whether only radials or radials plus a perimeter wire--is designed to minimize radiation. Hence, it provides a standard of comparison by which one can obtain data to determine if a subject antenna radiates better or worse. I have suggested a battery of tests that include ground-wave, near-field, and relative current readings to provide a sufficiently complete portrait of antenna operation by which to reach conclusions supported by evidence with a minimum of assumptions. Refined test equipment is desirable, but rudimentary test instruments based on handbook designs are likely satisfactory if well constructed and if the test set-up is carefully handled to provide consistent results. Moreover, the test set-up requires very little more than a roomy backyard at 50 MHz.

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Although a calibrated test range or chamber is superior, the test set-up described that includes standards of comparison as well as a reasonable compliment of measurements should go a long way to determining whether some of the suspected antennas in fact rely wholly, partially, or not at all on feedline radiation as their main mode of operation. If the reliance on the feedline is sufficiently strong, then we can save much effort and money by simply creating a hat to replace the complex and often expensive non-radiating antenna.

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Updated 11-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Dipole, Loading, VHF / UHF, Vertical


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Counterpoise?
+ On the Use and Abuse of a Word

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L. B. Cebik, W4RNL

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The term counterpoise has a long history in antenna engineering and amateur practice. Today, it may be among the most misused terms in amateur circles. Indeed, if we examine both the history of the term, its meaning, and its misuses, we might reach an interesting conclusion: there is no such thing as a counterpoise in antenna analysis, even though the term has a long and somewhat respectable use in antenna engineering.

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Although my bookshelf has many gaps and covers antenna history in fits and spurts, we can detect some trends in the use of the terms, along with the seeds of misuse. Therefore, let's begin with a small informal history of the term counterpoise.

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The Rise and Fall of the Counterpoise

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I have several texts and popular books on radio and on antennas dating to the 1920s. In none of them do I find the term counterpoise. However, I do find references to a venerable antenna type that shall prove significant in these notes: the inverted-L. Fed at its base and strung between the equipment building and a far-end support, the antenna was once the most popular home antenna for those experimenting with radio receivers in the early 1920s. In Chapter 3 of Practical Radio by Henry Smith Williams (1922), we find the antenna name along with diagrams and instructions on how to arrange it. Part of the discussion involves grounding. However, the concern is for lightning protection to meet the requirements of the Board of Fire Underwriters. Hence, we meet such new ideas as the lightning arrestor (a gap mechanism) and old ideas such as the knife switch to short the antenna terminals to a ground connected either (ideally) to a ground rod or (practically) to a water piper. (My local cable system still--for convenience--uses a water-pipe ground connection out of doors.)

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My earliest ARRL book is The Radio Amateur's Handbook for 1930. Chapter 11 covers antennas. This chapter makes no reference to a counterpoise. However, it does divide antennas into two categories. "Those in which the ground is an essential part are known as Marconi antennas." "The second type of antenna is the Hertz antenna, in the operation of which the ground does not play an essential part." (Page 159) Although few people still refer to a Hertz antenna in general categorical ways, the term "Marconi antenna" still makes its appearance, some times referring generically to a vertical monopole system (with or without a top hat structure) and sometimes referring to a specific design. The referent to the term requires a scorecard.

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The idea of a counterpoise worked its way into amateur radio literature largely from AM broadcast practice, although references to the counterpoise rarely reveal the term's source. Instead, we have to follow indirect clues. For example, many references to the term appear in descriptions of antennas for 160 meters. Indeed, many earlier (pre-1960) uses of the term do not include references to 80- and 40-meter antennas, strongly suggesting that early writers took the 1.8- to 2-MHz band to be an extension of the AM broadcast band. However, not all references are quite so specific.

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In the Frank C. Jones Radio Handbook for 1937 (p. 39), we find the critical distinction derived from AM broadcast practice.

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+ A counterpoise which consists of one or more wires in a network insulated from the ground wil often reduce loss resistances which might occur when the quarter wave antenna is connected to poorly conducting earth. The counterpoise in the case of a network of several wires acts as a condenser plate with high capacity to earth, with the result of lower loss in the antenna system; for this reason the counterpoise should be fairly close to the ground. [See Fig. 1.] +
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Fig. 2 shows a vertical antenna with an elaborate ground wire system buried under the surface of the earth for the purpose of obtaining low loss resistance connection to the ground. This system is more generally used than the counterpoise.

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The Jones handbook of course eventually became the famous Editors and Engineers Radio Handbook so ably edited for decades by Bill Orr, W6SAI. However, the last edition (the 23rd) contains no mention of the counterpoise. Nevertheless, Jones captures the critical distinction that gave the term counterpoise its good sense. It distinguished the buried radial system from a system of radials very slightly elevated from the ground. The entire radial system is insulated from the ground so that the only electrical connection occurs by virtue of the capacitance between the radials and the earth.

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The sketch of the counterpoise system in Fig. 1, which is adapted from figure 6 in Jones' handbook and contains the essential features, also contains the seeds of some later misuses of the term. The antenna is the inverted-L, a necessity for most amateurs with limited yard space. More relevant is the drawing of the counterpoise wires. We find a few wires that do not form a full radial structure, and they all go in the direction of the horizontal portion on the inverted-L. An uncritical reader might well get some odd ideas. For example, perhaps we do not need a full set of radials in a counterpoise. In addition, perhaps it is important that the wires appear beneath the horizontal leg of the inverted-L. Finally, perhaps a counterpoise wire or set of wires is important to horizontal antennas. Following Windom's 1929 QST article, we might treat the vertical portion of the inverted-L as simply a one-wire feedline to the true element, the horizontal portion of the antenna.

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Following the end of World War II, the amateur market once more received a spate of books on all facets of radio practice including antennas. Antenna Manual by Woodrow Smith, appeared in 1948. Unfortunately, it did not result in the periodic updates that marked the other Editors and Engineers offering by Orr. However, it remains a classic in amateur literature. On p. 154, Smith repeats the Jones statement about the counterpoise, in contrast to the buried radials ground system.

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+ In the case of very rocky or poorly conducting soil a counterpoise often is substituted for a buried network of wires. A counterpoise is a network of wires place above the earth a slight distance and insulated from it, so arranged to produce a very high capacity to the earth. +
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In the same post-war era, ARRL developed a continuing series that has become as well-known as its Handbook. The earliest The ARRL Antenna Book on my shelf is the 5th edition from 1949. On page 62 we find a discussion of elevated vertical monopole radials, followed by this statement:

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+ The lengths of wires and the configuration used are not especially critical. . ., particularly when the ground plane is close (in terms of wavelengths) to the actual ground. The ground plane is usually called a counterpoise when so used. +
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The first and seemingly casual statement about counterpoises actually marks the beginning (or close to it) of another misuse of the term as it folds together all forms of elevated radial systems. As we shall see, there may be good reason to separate the elevated radials from a counterpoise system as understood by AM broadcast engineers of the period.

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On pages 220 and 221 of the same volume, in a discussion of antennas for 160 meters (Chapter 10), we find a more extended discussion of "The Counterpoise."

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+ The counterpoise is a form of capacity ground which is often quite effective. Its use is particularly beneficial when a extensive buried system is not practicable, or when an ordinary pipe ground cannot be made to have sufficiently low resistance, as in rocky or sandy soils. +

The shape of the counterpoise may be made anything convenient; square or oblong arrangements are usually easy to construct and will work satisfactorily.

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To work properly, a counterpoise must be large enough to have considerable capacity to ground, which means that it should cover as much ground area as the location will permit. . . .The capacity of the counterpoise will be approximately equal to that of a condenser consisting of two plates, each of the same area as that of the counterpoise, with spacing equal to the height of the counterpoise above ground.

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The height of the counterpoise is not particularly critical. . .from 6 to 10 feet [0.01 wavelength to 0.02 wavelength] above ground.

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[T]he best performance will be secured as a general rule, when the counterpoise is insulated from ground.

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The discussion contains further details on the construction of a 160-meter counterpoise system. Indeed, it is one of the most extensive discussions in amateur radio literature. Interestingly, The Radio Amateur's Handbook for 1952, especially in connection with 160-meter antennas, in Chapter 14, on p. 342, under the heading of 160-meter monopoles that are usually inverted-Ls, repeats the kernel of the Antenna Book account.

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+ The use of a counterpoise is recommended where a buried system is not practicable or where a pipe ground cannot be made to have low resistance because of poor soil conditions. A counterpoise consists of a number of wires supported from 6 to 10 feet above the surface of the ground. Generally, the wires are spaced 10 to 15 feet apart and located to form a square or polygonal configuration under the vertical portion of the antenna. +
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The 1952 Handbook reason for using a counterpoise does not jibe completely with engineering practice in the same year. In fact, we may turn to an engineering classic, Radio Antenna Engineering by Edmund A. Laport, which appeared in 1952. The full discussion of radial system alternatives is too long to quote extensively, but Laport describes the basic idea succinctly on p. 52.

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+ The counterpoise is an insulated net of radial wires assembled above the ground to form a large capacitance with the ground. From the earliest days of radio, the merits of the counterpoise as a low-loss ground system have been recognized because of the way in which the current densities in the ground are more or less uniformly distributed over the area of the counterpoise. Any tendency toward nonuniformity of current distribution in the ground will increase the portion of the ground current toward the edge of the counterpoise. It is inconvenient structurally to use very extensive counterpoise systems, and this is the principle reason that has limited their application. The size of the counterpoise depends upon the frequency. It should have sufficient capacitance to have a relatively low reactance at the working frequency so as to minimize counterpoise potentials with respect to ground. +

There should not be any connection to actual ground in the antenna circuit when a counterpoise is used.

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See Fig. 3 for a sketch adapted from Laport's volume. My version is simplified in omitting the antenna control box ("tuning house" below the wires) and, more significantly, in only showing a few of the wires that make up the counterpoise system. As Laport notes, the counterpoise system is preferable to a buried radial system in terms of loss reduction in the AM broadcast band. However, for ground-mounted installations, it is usually impractical. Hence buried wires in AM broadcast antenna systems are more common. However, the counterpoise system remains necessary in urban situations, when such antenna must be mounted atop buildings with somewhat dubious conductive structures below the ground-plane system.

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However, the extensive references to the details of a counterpoise system begin to dwindle after Laport's work. (In many ways, Laport's volume is a compendium of engineering practices in antennas for the 2 decades prior to the release of his text in the early 1950s.) For example, in Wave Propagation and Antennas by George B. Welch, 1958, we find on p. 183 only a small reference to the counterpoise in connection with increasing the efficiency of short vertical monopoles.

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+ A ground system mounted in insulated supports a short distance above the earth is called a counterpoise. +
+

By 1974 and the 13th edition of The ARRL Antenna Book, the extended account of the counterpoise system has disappeared from the discussion of 160-meter antennas. Instead, we have a somewhat vague mention of raising the antenna and radials off the ground, although some reference to the capacitances involved still occur.

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+ Such a system is sometimes called a counterpoise. +
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The absence of detail on the counterpoise, as understood in the 1949 to 1952 period, was bound to result in some potential confusions. Just when they begin is dim, but by 1991 and the 16th edition of The ARRL Antenna Book, they are in relatively full force. On pages 2-36 to 2-37, we find a detailed account of the work of Doty, Frey, and Mills, who used a 64-radial system 5' above ground at 27-30 MHz to test the effectiveness of a vertical monopole. Despite that fact that the large radial system is 0.12 to 0.15 wavelength above ground, a relatively great height for such systems, the text still calls the assembly a counterpoise system. In addition, on page 3-11, we find an additional statement.

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+ The effect of a perfectly conducting ground (for radiation resistance purposes) can be simulated under an antenna by installing a metal screen or mesh such as poultry netting (chicken wire) or hardware cloth on or near the surface of the ground. The screen or counterpoise system should extend at least a half wavelength in every direction from the antenna. +
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The use of a densely packed ground screen has been common practice in AM broadcast work for many decades, although it often shows up in the form of short radials placed between the longer radials on the standard 120-radial broadcast buried ground plane. However, texts like Laport's do not call this a counterpoise. It lacks the required elevation above the ground.

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By the appearance of the 20th edition of The ARRL Antenna Book in 2003, the departure from engineering practice in the use of the term counterpoise is relatively complete. For example, on page 2-16, we find the following statement.

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+ The term ground planeis also used to describe a vertical antenna employing a 1/4 wavelength vertical radiator working against a counterpoise system, another name for the ground plane that supplies the missing half of the antenna. The counterpoise for a ground-plane antenna usually consists of four 1/4 wavelength radials elevated well above the earth. +
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Of course, this use of the term flies in the face of the history of the term to refer to radial systems that are close enough to the ground to exhibit a relatively high capacitance between the radials and the ground. As well such systems would contain many radials or other wires to simulate to the degree possible a solid plate for maximum capacitance. To further the confusion on the use of the term counterpoise, we find on page 3-2 a repetition of the statement quoted from page 3-11 of the 16th edition, referring to the ground screen on or in the ground at the antenna base. Finally, on pages 6-8 to 6-9, we find reference to the work of Al Christman, KB8I (now K3LC), who has perhaps done the most research with monopoles using elevated radial systems. Christman is clear in noting that the height of the radials that allows the use of only a few radials (compared to the large radial systems needed in buried systems) introduces a change in the way in which we view the radials. Whereas the counterpoises of Laport and others contained many wires of somewhat indefinite length (up to perhaps 1/2 wavelength), the elevated radials in his study required attention to the combined lengths of the radials and the vertical section to obtain resonance. Fig. 4 outlines the differences.

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Nevertheless, on page 6-8, we find the following statement.

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+ A counterpoise is most commonly a system of elevated radials, where the radial wires are interconnected with jumpers. . .. +
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With respect to systems using vertical monopoles, the confusion or conflation is now complete. At one time, the notion of a counterpoise distinguished a certain kind of ground system from the typical system of buried radials. The counterpoise consisted of radials (ideally) or other shapes (practically in restricted spaces) insulated from the ground and placed relatively close to ground as measured in terms of wavelengths. The theory of the counterpoise involved creating sufficient capacity between the ground radial system and the ground itself to increase the efficiency of the monopole system, and as reported by Laport and others, it yielded higher efficiencies in some cases than buried radials.

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One consequence of the engineering use of the term counterpoise was a 3-part distinction. Below the ground, we have buried radial systems with the wire in direct (or nearly direct, if the wires are insulated) contact with the ground. Next, we have the counterpoise alternative to buried radials. The counterpoise size and wire density equaled that of the buried radial system for maximum efficiency. Third, we have elevated radials, where the capacitance between the radials and the ground is too small to be effective in the determination of antenna efficiency. Rather, the radials become part of the antenna structure sufficiently independent of the ground that antenna resonance is a function of the overall antenna size at the operating frequency. Under these conditions, of course, the required element and radial lengths will change according not only to antenna height, but as well with the number of radials used and whether we leave the tips open like spokes or connect them together with a perimeter wire. The general properties of elevated radials apply regardless of the height of the antenna above ground once we pass through the frontier between the counterpoise and genuinely elevated radials.

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Unfortunately, current literature available to radio amateurs blurs the distinction among these three relatively distinct cases, only one of which corresponded to the traditional engineering use of the term. If the term now covers every type of antenna with radials, then we may completely drop the term and simply say that an antenna needs radials to work. Or we might even resurrect the term "Marconi" antenna, although that option might itself create more confusions than it resolves.

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Practical Consequences and Recent Aberrations

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As "they" say in television advertisements, "But wait. There's more."

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The conflation of the traditional engineering use of the term counterpoise with monopole radial systems in general leaves the would-be antenna builder with massive decisions and no way to answer them. The counterpoise itself, as described in the literature, requires complete insulation from the ground. A buried radial system is already in direct contact with the ground. An elevated radial system may use without harm a single safety lead connected to the hub of the radials and a ground rod. For static discharge and lightning safety, the counterpoise requires different safety switching and discharge methods relative to the other systems.

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More intriguing is the question of at what height to place, respectively, the counterpoise and the elevated radials. For convenience and safety of individuals using the ground-plane space, most literature recommends a height of 6 to 10 feet for a 160-meter counterpoise. However, that height may in fact be greater than optimal for maximum capacitance between the counterpoise and the ground. Heights closer to perhaps 1 to 1.5 meters (3.3 to 4.9 feet) may be more satisfactory, with proportional reductions when using a counterpoise on either 80 or 40 meters.

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In contrast, the minimum height at which elevated radials become very effective is between 2 and 3 meters (6.5 and 9.8 feet), almost regardless of which band one uses in the lower HF spectrum. In this region, 6 to 8 radials generally suffice for an elevated system, but the length of the radials requires adjustment in concert with the length of the vertical section to obtain resonance and a stable feedpoint reactance over small changes in system height above ground. The physical distances represent heights that average about 0.15 wavelength at 160 meters, 0.3 wavelength on 80, and 0.6 wavelength on 40 meters. As well, these are only heights where the performance and the feedpoint impedance stabilize. Some additional height is possible before the far-field radiation pattern begins to show signs of deterioration. For further information on lower-HF elevated radial systems, see any of Al Christman's articles or see Chapter 6 of Ground Plane Notes, available from antenneX.

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In its engineering form, the counterpoise emerged as an alternative to buried radials systems for AM broadcast use. We may model both systems using equivalent monopoles and radials systems. Let's use a test frequency of 1 MHz, in the middle of the AM broadcast band. For a buried radials system, let's lay down 128 radials, each 0.003-m in diameter (about the same diameter as AWG #10 wire). The radials will be 1/2 wavelength long, since that is one of the recommended values for a counterpoise system, and buried radials are not extremely sensitive to length. The radials will be 0.1-m (about 4") below the surface of average ground (conductivity 0.005 S/m, relative permittivity 13).

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We may use the same set of radials for a counterpoise by raising them to a height of 2-m (6.56' or 0.0067 wavelength) above the same ground, with no connection between the radials and ground. Otherwise, the radials are identical to the buried set. Let us assume for at least a moment that 128 radials composed of wires with the specified diameter form a very reasonable approximation of a solid surface. We may calculate a capacitance value for the virtual capacitor of which the counterpoise is one plate. The calculated capacitance is about 3.5e-7 Farads, which yields a capacitive reactance at the design frequency of about -j4.5e-1 Ohms. The reactance is under 1/2 Ohm, although the initial assumption may be shaky. The actual reactance is likely some higher figure due to the open-end structure of the modeled counterpoise radial system. Nevertheless, the calculation shows the general range of values toward which counterpoise designers aimed.

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Fig. 5 overlays elevation patterns for the two monopole installations. Both patterns have a TO elevation angle of 21 degrees. The buried-radial system yields a maximum gai of 2.24 dBi, while the counterpoise system shows a maximum gain of 1.93 dBi, about a 0.3-dB difference. One might change the counterpoise system gain by solidifying the radial structure, perhaps with cross wires linking the radials, especially in the outer regions in which the radials show maximum separation.

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Despite the similarity of antenna performance, the current distribution along buried radials is not the same as along the slightly elevated counterpoise wires. Fig. 6 shows graphs of the current magnitude along the radial wires. Both parts of the figure use the same maximum current value (red) in order show the variations. The monopole current will appear wholly red, since the currents in the individual radials begin in the feedpoint segments at 1/128 the source current.

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The currents in the buried radials begin at a relatively low level and continually decrease along the length of the radials. Because buried radials are in a medium of limited conductivity and significant relative permittivity, the current distribution is not the same as in wires in air. The level of segmentation in the model does not permit us to view small fluctuations in the radial currents, but the overall progression is typical of radials systems of all sizes.

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In contrast, the counterpoise radials show an interesting pattern with a current peak roughly 1/4 wavelength from the monopole and then a relatively smooth current magnitude decrease toward the radial ends. Although the current progression is smooth along the radial wires of the counterpoise system, it is not symmetrical on each side of the peak (red) values. An adequately sized counterpoise system is one in which the radials or other structures are large enough to allow the current distribution its full progression. Nevertheless, the monopole alone plays the dominant role in setting system resonance, just as it does with a buried radial system.

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Counterpoises, as understood in mid-20th century engineering literature and some amateur literature of the same period, then, are far different electronic devices than true elevated radials that are part of the antenna's resonant length. Elevated radials, ranging from Christman's research subjects to VHF ground-plane radials, are intrinsically more similar to each other than elevated lower-HF radials are to counterpoises.

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Unfortunately, radio amateurs, even those who write about their successful antennas, are subject to impressions and truncated sound bites. Let's combine elements of less adequate treatments of the counterpoise that have occurred in the last quarter of the 20th century. We may begin with one enduring picture, sketched in Fig. 1. The antenna shown is an inverted-L, with a truncated 3-wire counterpoise extending under the horizontal portion of the antenna wire. Let's add the sound bite that virtually any wire extending from the base of a monopole is a so-called counterpoise wire. In this combination we have the makings of some serious misuses of the idea of a counterpoise.

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Fig. 7 outlines 3 antennas that I have encountered in amateur radio magazines over the lest decade or so. I am purposely omitting the identities of the antenna builders. What the antennas share is a common claim that at least one wire in the system is a counterpoise. The first case involves a field antenna, either in the form of an inverted-L or in the form of a sloping wire. Since the antenna is end fed, we normally require an antenna tuner to match the impedance at the wire's end to the transceiver in use. Normal practice would show as direct a connection between the tuner's ground terminal and the earth. What the innovator adds is a somewhat long wire that he terms a counterpoise, and this wire leads to the earth connection.

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The second antenna comes from a number of sources. In one article, the innovator creates a monopole and then uses a so-called counterpoise wires to dangle off the edge of his apartment balcony or deck. Having heard that the counterpoise wire length is not critical, he cuts it casually. The third case involves a horizontal wire antenna end fed with parallel transmission line. Adhering to the apparent picture in Fig. 1, he adds a wire underneath the horizontal aerial wire and claims that this counterpoise improves performance.

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All three claimed antenna parts called counterpoises emerge from the murkiness that has come to surround the term. The term "counterpoise" comes from mechanical systems contexts. It means a counter-balancing force, ordinarily a weight on the other side of a fulcrum. This name, as it has been conflated in amateur literature to suggest anything with radials, has acquired the additional meaning of an antenna part that does not itself radiate but permits the radiating parts to radiate better than they would without it. There is nothing in the world of antennas that corresponds to the dead weight facet of this misshapen version of the concept of a counterpoise. Every part of an antenna contributes to the antenna far-field pattern (except those parts that we specifically design to have self-canceling radiation). Hence, there is no such thing as a mere counterpoise.

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+ +
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Fig. 8 shows both the claimed and the actual antenna on the left in Fig. 5. The actual antenna runs from the earth connection through the tuner to the far end of the wire, whether it is sloping or bent. Since the tuner is effectively in series with the wire, it forms an off-center feedpoint for the antenna. Of course, the current in the wire running close to or one the ground contributes little if anything to the antenna's far-field pattern. At most, it may present the terminals of the ATU with an impedance that more easily fits within the tuning range of the components.

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+ +
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The claimed version of the antenna in Fig. 9 is among the most insidious because of the market for commercially made mini-monopoles. One such antenna comes with a bale of wire that the user is supposed to unroll. He then tunes his antenna and kicks around the wire bale until he achieves a satisfactory match. What the user does not realize (since he has already purchased the antenna) is that most of his antenna is lying at his feet. In the less problematical version shown in the figure, the entire antenna constitutes a vertical dipole. The length of the upper and lower ends together contribute to the overall resonant length, and the lower portion of the antenna--if we mount it from an elevated support--does as much of the radiating as the upper portion. In most circumstances, it will not matter whether the actual feedpoint position is slightly off-center with respect to the peak current position on the overall antenna. Since the current level changes very slowly in the vicinity of its peak value on a dipole element, the feedpoint impedance will also change very slowly.

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+ +
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The third case (C) is a modern adaptation of a very old scheme of running a second wire at or near the ground under a horizontal wire, ostensibly to improve some mysterious relationship between the upper wire and the earth. Actually, the horizontal antenna performance remains unchanged, and the wire becomes a trip for anyone careless enough to walk through it. At best, it serves as a parasitic reflector, possibly converting a general-purpose antenna into an NVIS (Near Vertical Incidence Skywave) special, as suggested by Fig. 10. However, single wires close to the ground do virtually nothing to improve even the performance of NVIS antennas. A ground screen that exceeds the elevated antenna's dimension by about a half wavelength in every direction is necessary to create an effective planar reflector.

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In every case, the so-called counterpoise can be analyzed (and modeled) as a part of the antenna.

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Where Does All of the Discussion Leave Us?

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On the one hand, we have the information left to us by the history of radio antennas before the concept of a counterpoise lost its meaning. On the other hand, we have the collection of misunderstandings (a collection larger than the samples shown here) that have resulted from the conversion of the term counterpoise into a general-purpose word having little import. The fuzzy, blurry current use has been the source of many an egregious error by casual writers about antennas that they have built. Indeed, the present use is only a malevolent ghost of the original.

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One major option is to restore the term to its traditional meaning alone to indicate a large radial or screen insulated from the ground but close to it to serve as a capacitively coupled ground for monopoles. That option would force upon writers of articles and handbooks several responsibilities.

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1. The treatment of the counterpoise would need restoration to the length at least of the version found in the 1949 edition of The ARRL Antenna Book or in sources like Laport's Radio Antenna Engineering in order to give the term clear sense.

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2. Such writers would also have to clearly distinguish between a true counterpoise and monopole radials elevated far enough off the ground to lose enough of their capacitive coupling to ground to act as the simple completion of a dipole, with one end composed of a symmetrical set of elements whose radiation is largely self-canceling.

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3. The same writers would have to overcome the temptation to refer to any set of monopole radials as a counterpoise. Indeed, they would have to overcome the temptation to call anything other than the traditional counterpoise by that name.

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Now let us suppose that we find fault in either the correctness of the theory that underlay the traditional antenna engineering concept of a counterpoise or that we determine it no longer has relevance in that meaning to current antenna practice. Because confused and conflated alternative meanings for the terms tend to create greater misunderstandings than they resolve, this option leads to only one action: that we drop the term altogether from the antenna lexicon.

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Updated 01-01-2007. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Dec., 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index +

Topics: Broadcast, Inverted L, MF, Vertical


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Some Techniques for Building a QRP Field Vertical

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L. B. Cebik, W4RNL

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The requirements for a QRP field vertical--usually base-loaded--are few but critical. It must be sturdy and easy to handle in the field. The field may be anything from a hotel room to an actual meadow. The parts must be easy to hold but hard to lose. The entire structure should breakdown into a set of pieces that fit within a small bag or case.

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Over the years, I have seen a wide variety of parts used for such antennas, some better than others. These notes simply add to the collection of techniques available to the QRP field operator, as he or she designs a personal field vertical.

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+ Fig. 1. Basic elements of a vertical with base loading. +
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Fig. 1 shows the basic elements of a field vertical intended for base loading. We must have a main radiator. The height of this radiator is caught between two demands. On the short end, it should be usable within the 8' high ceiling of a hotel or motel room. On the long end, it should be as tall as we can manage for the sake of efficiency. The shorter the radiator, the greater the size of the loading coil and, hence, the lower the radiated power for a given amount of power fed to the system.

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The antenna requires a support system that will keep it vertical and stable (even in a modest breeze). The larger the support spread, the sturdier the mount. However, once more we encounter conflicting needs. The support system should break down or collapse into manageably short pieces for transport and not be unreasonably heavy. The support system may also form the hub of the radials that we use to complete what is essentially a shortened vertical monopole. The better the radial system, the better the performance.

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Finally, we need a way to feed the antenna. For this type of antenna, feeding also includes loading and matching. A shortened vertical has a low resonant impedance: the shorter the antenna, the lower the resonant impedance and the higher the inductive reactance required to offset a high capacitive reactance. We need a small assembly-- consistent in size with the pieces of the system--and a means of connecting it to the antenna and the radials.

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With these essentials in mind, let's look at a few of my personal preferences for the pieces of the system.

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The Main Radiator. Fig. 2 shows how I prefer to make up the main radiator for a field vertical. T6063-832 aluminum tubing is light and readily available from sources such as Texas Towers (http://www.texastowers.com). It comes in 6' lengths to avoid UPS excess shipping charges, but we shall use shorter sections than this length. The figure shows the largest diameter as 0.75". This specification depends on two major factors. First is the question of weight. The larger the tubing, the higher the weight. For a home ground- mounted vertical, I might start with 1.25" diameter tubing, but this antenna is for the field.

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+ Fig. 2. A radiator made up of nested aluminum sections. +
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I use certified 6063-T832 aluminum with a wall thickness of about 0.05" for a reason: the interior will be smooth, allowing me to nest the tubing easily. Hardware depot tubing sometimes has a seam that roughens the interior. (At the end of these notes, I shall make some maintenance suggestions, including keeping the tubing interiors clean.) All of the sections shown in the figure collapse into a single unit that is still light, not to mention compact.

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The section lengths are all equal, and we have a choice for that length. Ignoring the top rod, 4 sections of 2' tubing will make a 7' 3" radiator, which fits nicely under a room ceiling, if we overlap the section by 3" for strength. 5 sections of 3' pieces, including the top rod, make a 14' vertical, which is significantly more efficient as a ground-plane antenna. The choice depends on your intended operations and the length of your carry-bag.

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+ Fig. 3. Key hardware items for the portable vertical. +
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For field use--but not for permanent installations--we may simplify the junctions. The figure shows small holes about 7/64" to 1/8". These holes are for hitch pins, shown in Fig. 3. The figure also shows the source: page 2971 of the McMasters-Carr on-line catalog (http://www.mcmasters.com). Hitch pin clips, also called hairpin cotter pins, come in a variety of sizes and materials. Stainless steel is best, but cheaper plated pins are adequate if never subjected to rain. The main radiator uses a pin size intended to hold 1/2" to 3/4" diameter rods or other similar fixtures. They also have large round ends for easy gripping. However, I hot-glue ribbons through the round ends so that the pins cannot hide in the grass.

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Now we can return to the optional top rod of the main radiator. A pin of the size specified is a bit large for the 3/8" tube to 1/4" rod junction, adding a different hitch pin size to our hardware. As well, the weight per unit length of the rod is higher than that of the 3/8" tube. The difference will not make the rod unusable, but only a bit troublesome relative to our otherwise simple structure.

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Drill the hitch pin holes through both pieces to be joined in one operation to assure alignment. Be sure to deburr the holes so that the drilled aluminum tubes still nest smoothly for storage. Since it is likely that the holes will be only close to perfectly centered, make a pencil line from one section to the next for easy field alignment. Renew the line after every few uses of the antenna. The hitch pin clips are easy to use and mechanically sound for this application. However, the antenna relies on the metal-to-metal contact between tube sections for electrical continuity in the antenna. The practice is satisfactory for short-term field use, but not for long-term permanent home installation. The condition of using this system is guaranteeing clean aluminum for the junctions.

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The Support Stand. A 4-legged stand provides good stability for the field vertical under indoor or gentle weather conditions. The stand that I built from scrap PVC appears in Fig. 4. It consists of 5 separate parts. 4 of the parts are 2' long legs of Schedule 40 1/2" nominal diameter PVC (Part A in the figure). Each leg has an in-line junction cemented on the outer end (Part B). This junction allows you to insert additional lengths of tubing for longer legs and added stability. As well, you can drill the junction to accept aluminum tent pegs to hold the legs firmly to the soil in the field. Alternatively, you can bend stiff steel wire into Us that fit over the legs near the outer ends: press these Us into the soil.

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+ Fig. 4. Details of the 5-piece PVC support stand +
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The hub of the legs is a 4-way junction of the same PVC material (Part C). However, I modified the hub by drilling a 5/8" hole through the center. Into this hole, I cemented an 18" length of 1/2" nominal CPVC tubing, which has a 5/8" outside diameter (Part D). Because CPVC has a thinner wall than Schedule 40 material, I inserted a 3/8" wood dowel and then filled the interior of the tube with fiberglass resin used in auto repairs (Bondo). This addition stiffens the vertical section against stresses created by the main radiator.

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At the base of the CPVC is a 1.5" length of 1" diameter aluminum tubing (Part E). On opposing sides of the short tube, I installed 1/2" long #10 stainless steel bolts, with the heads inside the tube. A little filing flatted the round heads so that the tub fit over the CPVC. The figure shows one of the bolts aligned with one leg of the stand, but that is a function of my limited drawing skills. The bolt actually is aligned between the legs on opposite sides of the tube. To center the tube and provide an insulated separation between the 1" tube and the main radiator, I added a very short section of 3/4" nominal diameters CPVC (Part F). The 3/4" CPVC fits inside the 1" aluminum tube and over the 1/2" CPVC. I cemented the CPVC separator in place, thus locking the short base aluminum tube in place as well. The main radiator simply slips over the CPVC and slides down to the separator.

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The small base aluminum tube serves two purposes. With a wing nut on each bolt, the tube forms the hub of any radials used with the antenna, as well as for any special ground rod connection. I recommend a full set of radials for each band. You can construct these from flat 4-wire TV rotator cable, cutting each strand to a quarter wavelength for 10, 15, 20, and 40 meters. The exact length is less important than the presence of as many radials as possible, with a field minimum of 4 recommended for adequate efficiency. Connect the 4 strands together at the inner end and use a ring connector under the wing nut and over the hub bolt. Above the hub bolts, we may connect the match/load/feed system base, with its top end going to the main radiator.

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The Match/Load/Connector System. Fig. 3 showed not only a sketch of the hitch pin clip, but also the outline of a handy tool clip. The clip is also available from McMaster-Carr (page 2726) and comes in numerous sizes in both plated and stainless types. Once more, stainless steel is best for durability, but plated clips will last well if not subjected to rain. The size shown (1/2" to 3/4") will work, even with the 1" base tube, but a larger size is also dandy for a base coil and feed system.

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+ Fig. 5. Mounting plate for the loading and matching components. +
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Fig. 5 shows the outlines of a plate that holds the loading and matching components. I recommend 3/16" thick (or thicker) Plexiglas or polycarbonate. The part of the clips with a mounting hole (which uses #6 hardware) comes arched. As you tighten the hardware, the section flattens against the plate, forcing the spring section to close very tightly. When fully tightened, the arch exerts considerable force on the plate and can deform 1/8" thick material over the span of a few hours. The stiffness of the tool clips makes excellent electrical contact with the tubing.

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The plate shows a sketch of a simple loading system using two coils. The high-band coil covers 10-20 meters with an 8-10-foot vertical. An added plug-in 10 micro-Henry coil allows loading on 40 meters. A lead from the coax center pin to coil taps does the tuning for the simplest version of this base-loaded vertical.

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However, finding a tap that gives a low SWR is often difficult with higher levels of loading. The resonant impedance gets lower and lower, and by the time we find a tap near 50 Ohms, the reactance is considerable. To overcome this problem, you may add a capacitor across the coax terminals. A receiving variable with about 1200 pF total capacity should work with all but the shortest verticals on 40 meters. (Higher bands are less problematical.) The physical size of the capacitor depends on the desired power handling capabilities. For an old-fashioned multi-section receiver capacitor, you can offset the tool clips toward the coax connector side of the plate. There will be about 1/2" of space between the plate and the main radiator, due to the shape of the tool clips.

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Adding the capacitor converts the simple base loading system into an L-network for matching low load resistances to 50 Ohms while compensating for the capacitive reactance of the short vertical. Jumpers can use banana plugs and chassis jacks to simplify the overall set-up. How much of the assembly consists of plug-in components and how much you permanently mount to the plate depends on your operating needs and the sizes that you choose for the main radiator sections.

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I have not given any specific values on a band-by band basis for some components, especially for the loading coils and the L-network capacitor. My reasons are many. First, the required values will vary with your selection of the main vertical length. Second, they will vary with the height of the antenna base above the real ground. Third, they will also vary with the number and length of the radials that you use--and somewhat with variations in how you arrange them. Two 10 microHenry coils--one for the upper bands and tap-able, the other a fixed coil added in series for 30 meters and below--should handle most cases, along with a 1200 pF shunt capacitor on the coax side of the coils, if you choose the L-network option. (You may parallel a 100 pF capacitor with the big one to provide a fine-tuning control.) Nevertheless, there are too many variables involved in the personalized versions of this system to guarantee a good match in every circumstance.

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+ Fig. 6. Other ways to use the tool clips. +
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The tool clips are handy in a variety of circumstances that range from field antennas to prototype experimental designs. Fig. 6 illustrates a couple of situations where they work well. The simple plate and its coax connector are useful for feeding a dipole center, illustrated by the left side of the vertical sketch in the figure. By using a fiberglass rod inside two sections of tubing--fixed in place with hitch pins--the center connector simply snaps into place. For mid-element loading coils in field or trial use, the plate and tool clip system, along with a fiberglass separator, allows one to develop the exact loading coil or trap needed for a given design, all without having to remove and replace screws in the element.

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Maintenance. The system just described requires no tools in the field. The tool clip hardware is shop-tightened and requires no further field work. Everything simply snaps into place, whether a hitch pin or a tool clip. This feature allows for quicker assembly and disassembly, leaving more operating time. The entire collection of parts (nested main radiator, 5-part support, and matching/loading/connector plate) fits into a bag as short as 24" long. (Extras, such as additional field braces, SWR meters, etc., are the user's responsibility.)

+

However, the system will only work well if you give it the required pre- and post-use maintenance.

+

1. Before use: Test assemble the antenna to ensure that all parts fit together as prescribed. Perform any adjustment necessary (such as burr removal). If the aluminum has become cloudy during storage due to oxidation, clean the surfaces with a plastic scouring pad. (Do not use steel wool or course sandpaper.) Check all coils for electrical and structural soundness. Count parts to ensure that everything is available.

+

2. After Use: Clean all parts of the antenna thoroughly. Remove any dirt from the stand, using any good cleaner or detergent. Check for use damage to the vertical section of the stand to ensure a smooth fit with the lower aluminum tubing at the next use. Clean the outer surface of the aluminum tubes with a mild cleanser to remove field dirt and stains. Clean the inner surfaces of the tubes with a stiff long-handled bottlebrush. Recheck the coils for any damage--and repair immediately. Re-wrap components together to restore a factory-like presentation. Count components to ensure nothing is missing. Replace any missing component immediately.

+

With these measures, the antenna should provide many years of satisfactory service. However, I fully suspect that long before the antenna wears out, you will be experimenting with other improved field antennas.

+

The ubiquitous base-loaded vertical is far from the most efficient antenna that you can use. However, it is cheap, compact, and reliable, even if the gain goes down with the frequency and the amount of loading required. The system shown here uses a longer main radiator than most whip-based systems for a modicum of higher efficiency. The L-network can provide a somewhat better match for the rig. Even with these improvements, the system remains light for easy field transport. It requires no tools for assembly and disassembly. Allowing for leftover aluminum tubing and hardware bought in excess quantities (all useful for other projects), the net cost is about $25 to $35, depending on the sources used and the size of your junk box. (If you purchase components for the matching/loading system, the cost may go up accordingly.)

+

Even if you do not build your own field vertical, perhaps the use of hitch pin clips and tool clips will give you some ideas for other projects.

+

Updated 05-25-2002. © L. B. Cebik, W4RNL. This item originally appeared in QRP Quarterly, April, 2002, pp. 17-20. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

Go to Amateur Radio Page

+

Topics: Hardware, Matching, Vertical


+ + diff --git a/content/gp/gp.html b/content/gp/gp.html new file mode 100644 index 0000000..dc4065a --- /dev/null +++ b/content/gp/gp.html @@ -0,0 +1,52 @@ + + + + + + Modeling Perspective on Ground Planes Index + + + +
+

A Modeling Perspective on "Ground" Planes

+
+
+

L. B. Cebik, W4RNL

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+ +

+
+ Most of what we have learned about ground planes beneath vertical antennas arose from LF and MF practice. There is another perspective from which we can approach the subject: modeling in programs like NEC and MININEC. Moreover, there is an alternative point of departure for investigations to the normal survey of landscape and subsoil properties. The alternative is free space. The combination of the two underlies the notes in this collection. +

My aim is not to replace classic vertical antenna theory. Instead, it is to see what antenna modeling might add to the array of considerations we give to vertical monopole antennas and their ground planes. To that end, I have let the modeling lead where it may. At most, the notes may guide some of our expectations, but they are not likely to alter our explanations.

+

This is all background. There are no practical antennas in these notes, although there may be a practical idea or two. For one of the best arrays of practical applications combined with recent insights into vertical antenna pattern analysis and elevated radials, see ON4UN's Low-Band DXing. This book is still the current standard, as are the continuing investigations of Jack Belrose, VE2CV. But if I list every classic and worthy study, this index will be longer than the notes. ON4UN has an excellent bibliography.

+

Since there have been numerous recent developments in the understanding of elevated ground planes, the following references are suggested:

+

Arch Doty, K8CFU, John Frey, W3ESU, and Harry Mills, K4HU, "Efficient Ground Systems for Vertical Antennas," QST (February, 1983), 20-25

+

Al Chrisman, KB8I, "Elevated Vertical Antenna systems," QST (August, 1988), 35-42

+

Al Chrisman, KB8I, "Elevated Vertical Antennas for the Low Bands," ARRL Antenna Compendium, Vol. 5 (1966), 11-18

+

KB8I and professional colleagues have also published a numbers of studies on this subject in the IEEE Transactions on Broadcasting.

+

L. A. Moxon, G6XN, "Ground Planes, Radial Systems and Asymmetric Dipoles," ARRL Antenna Compendium, Vol. 3, (1992), 19-27

+

Dick Weber, K5IU, "Optimal Elevated Radial Vertical Antennas," Communications Quarterly (Spring, 1997), 9-27

+

Rudy Severns, N6LF, "The Lazy-H Vertical," Communications Quarterly (Spring, 1997), 31-40

+

Rick Littlefield, K1BQT, "Build a 20-Meter DX Pole," Communications Quarterly (Spring, 1997), 98-102

+

Note: By the conclusion of this series of notes, you should understand fully why the last three articles are essentially about the same antenna.

+
+

1. Part 1: Some Preliminary Notes on the Ground

+

2. Part 2: "Capacity" Hats

+

3. Part 3: Planes in Space

+

4. Part 4: Down to Earth Verticals

+

5. Part 5: Regional Differences

+

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+
+ +

+

Updated 6-6-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Lower, MF, Vertical


+ + diff --git a/content/gp/gp1.html b/content/gp/gp1.html new file mode 100644 index 0000000..0e90ae5 --- /dev/null +++ b/content/gp/gp1.html @@ -0,0 +1,69 @@ + + + + + + Modeling Perspective on Ground Planes Part 1: Some Preliminary Notes on the Ground + + + +
+

Part 1:
+ Some Preliminary Notes on the Ground

+
+
+

L. B. Cebik, W4RNL

+

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+ +
+

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+

We are very careless with the ground. We tend to treat it as a single homogenous entity. In simplest terms, that means that we think about the ground in the same way, no matter in what radio context it appears.

+

We are not as careless as we used to be. When forced by circumstance, we do sort out the following grounds.

+

G1. The DC and static discharge ground: This is the ground of long ground rods by which we ensure that DC, small static charge build-ups, and power line AC are shunted to ground. Our station ground strap gets into the act here, because we make a common ground for all cases, keeping them at the same potential, hopefully ground potential if our distance from the rod into the earth is not too long.

+

G2. Circuitry common bus (ground): We have also learned that there is a difference between a circuitry common and an earth ground. Sometimes we have learned this the hard way with shocks and tingles.

+

G3. Lightning ground: We have also learned that lightning strokes and other sudden high voltage and high current impulses require more attention than G1-type grounds. The details of a satisfactory, equipment-protecting grounding system for lightning are more complex than those required for simply preventing the wind from building a static charge on our dipoles.

+

G4. RF ground: Effective RF ground also requires attention to many details. Deep rods, while useful, may be less effective as RF grounds than we previously thought, and the U.S. Army developed a system of perimeter straps and a sequence of shorter rods to effect a satisfactory overall station RF ground. RF paths to and from ground via transmission lines, circuitry-to-case connections, common mode paths, and numerous other sources are receiving increased attention both by those who build equipment and by those who assemble operating stations.

+

We might extend this list--not to mention subdivide it. But let's turn to a couple of new categories created out of one old one. Both have to do with antennas.

+

We tend to think of the ground relative to an antenna as a single ground. Hence, we tend to lump together the ground from which signals reflect to contribute to antenna far field patterns and the ground directly under a monopole antenna. The "only" difference is their relative distance from the antenna itself. However, let's see where separating the two ideas leads.

+

G5. Far field reflective ground: The ground quality is usually specified in terms of conductivity (given in Siemens or milli-Siemens per meter) and a dielectric constant (permittivity). ON4UN did some modeling with some vertical radiators that suggests the ground kicks in as a reflective medium somewhere around 2 and a half wavelengths from the antenna--possibly more for highly elevated antennas. Although the ground immediately under the antenna has some effect on antenna effectiveness relative to far field patterns, the effect is small (unless the ground is needed to complete the antenna). Dipoles, for example, exhibit only small gain changes as the quality of soil is ranged from very poor through very good.

+

Do not confuse ground quality with terrain considerations. The quality of ground at varying distances from an antenna is only one factor among many with which terrain evaluation is concerned. Slope and interfering objects are samples of other factors that go into terrain evaluation for determining the ultimate elevation pattern for a given antenna and site.

+

Self-contained vertically polarized antennas, running from the vertical dipole to complex arrays like the bobtail curtain, exhibit the same far field radiation properties with respect to ground as do dipoles and other horizontally polarized antennas at HF. The surface wave of an HF antenna is small, relative to the sky wave. Losses may be slightly higher than with a high horizontal antenna, but generally are not significant.

+

G6. Antenna-completion ground: Monopole antennas are generally analyzed as having their missing pole (relative to a dipole) within the ground. This is often pictorially presented as an "image" antenna sticking straight into the earth. While this portrayal allows the solution to certain basic equations, it is actually a very poor picture of what is going on.

+

It is the surface volume of the ground that provides the completion of the antenna. Signals penetrate the ground to depths that vary directly with wavelength and inversely with frequency. However, even with a monopole, the penetration does not act like a spear into the ground.

+

A more correct picture is a surface area (with some depth) around the monopole. The conventional radius of this surface is about 1/4 wl. Since even the best soil is lossy compared to conductors, we lay screens and radials under the soil to improve its conductivity. Somewhere between 60 and 120 radials approaches the conductor saturation point of most soils. This is the most traditional ground plane.

+

Of course, we can also elevate the ground plane. A number of investigators (nicely referenced by ON4UN) have discovered that even a few feet of elevation can improve the performance of a monopole over that obtainable with buried radials.

+

Another interesting phenomenon is that rooftop monopole vertical antennas do not seem to benefit from littering the roof with 60 to 120 radials. 4 to 8 seems to be enough to achieve all the performance of which the antenna design is capable.

+

Let's add one more phenomenon: Experimenters have discovered that the best length for radials is slightly less than 1/4 wl. Of course, these were elevated radials.

+

And one more: If we model a monopole with radials in free space, it does not care what its orientation is.

+

If we construct a monopole with the feedpoint high, and then if we add another monopole atop the first, we have a vertical dipole. Now let us shorten the upper monopole and compensate with a hat. A hat is a symmetrical array of wires ranging from 2 to very many, with or without a perimeter ring or inner rings. Its function is to complete the current path necessary to achieve some specified state at the feedpoint, usually resonance. We used to call this a "capacity" hat based on the way we calculated its size at LF and VLF, but those methods go to pot at HF. (I know this from having written a very convoluted program to calculate them from 3 to 30 MHz for antenna length reduction only down to 70% full size.) So let's just call our structure a hat. Because it is at right angles to the antenna, and because it is symmetrical, it ideally does not radiate. All the field from one leg is cancelled by a field equal in magnitude but opposite in phase from an opposing leg.

+

Now continue to shorten the upper monopole until it is very short, perhaps even insignificantly short. The hat has to grow in order to provide an ever longer current path to maintain resonance (or some other specified condition) at the feedpoint. In fact the hat grows to nearly 1/4 wl in radius. Since it is a very fat wire indeed, it does not grow to a full 1/4 wl.

+

What we have is an upside down conventional monopole. Turn it right side up at many wl above the ground, and the far field pattern is indistinguishable from the upside down version. Tilt the legs making up the hat, and they are no longer at right angles to the single-wire monopole end: hence, they partially radiate and partially cancel--as every maker of simple 2-meter sloping GP antennas knows. Upside down, we called the structure a hat; rightside up, we call it a ground plane. The antenna does not care because an antenna-completing structure by any other name performs just as sweetly.

+
+ +
+

Now bring the antenna closer to the dirt ground. The fields from the hat-plane begin intersecting the ground in earnest, and those intersections yield interactions that may alter the required size of the hat-plane. But the basic function of the hat-plane is to complete the antenna. In short, the antenna-completing ground is not a ground at all.

+

Instead, we sometimes use the ground to do the work of the hat-plane. More precisely, we have used the conductivity of dirt ground materials to do the work of the hat plane. Everyone who has ground-mounted a vertical in the middle of a septic tank drain field has gotten decent performance without radials.

+

So, what about that class of self-contained vertically polarized wire antennas (SCVs)? This group includes a number of 1 wl loop and open antennas, such as the delta, the square, the rectangle, and the half- square. All these antennas produce vertically polarized radiation independently of the dirt ground by virtue of the fact that part of the antenna structure acts as a phasing line in which horizontal structure radiation is cancelled, while radiation from the vertical elements is phased for additive field production.

+

SLVs model nicely in free space with properties that carry over into models and real antennas mounted several wavelengths above ground. Up and down make no difference to these antennas under the given conditions. Such antennas depend only on the far field reflective ground with respect to their patterns.

+

Brought closer to the dirt ground--which is inevitable when we use SCVs on the lower HF bands--the antenna fields intersect with the "semi-conductive" ground materials--just as they might if we sandwiched one of the antennas between two sheets of metal. The results are modifications to antenna performance. But, the antenna does not depend upon the ground for its basic performance as an antenna--that is, the ground does not complete the antenna. The ground is not a ground plane.

+

In fact, the so-called ground plane is never a GROUND plane, but always a hat-plane. Hence, the so-called antenna-completing ground is not a ground at all--even though we sometimes use the ground to do the work of the plane. This is not the first time we have misnamed something in radio. It took a long time to weed out the term "condenser." It will likely take even longer to drop the term "ground" from ground plane.

+

But do we not always connect the braid of the coax to the plane and the center to the monopole? Most of us do, but it is not required if we separate our DC and RF grounds from the antenna end of the transmission line. We can feed a monopole through an inductively coupled balanced ATU and then connect either side of the line to either antenna terminal. Once again, we collect a number of functions into a single configuration, like connecting the case to the coax braid and the braid to the monopole ground rod as our station ground: then we forget to sort out the functions, and the configuration makes it hard to separate them. Nonetheless, the antenna, as an antenna alone, does not need a ground for its ground plane. (But add one anyway for lightning, static discharge, RF, and DC grounding.)

+

By sorting out our grounds--and further sorting real grounds from planes we only call grounds--we can achieve a better understanding of a. how monopoles work and b. why some vertically polarized antennas do not need a ground plane. But I doubt if the term "hat-plane" will ever gain currency.

+

Eventually, we shall add pictures and quantifications to these initial notes. Nonetheless, I hope they prove useful as a start in sorting out the many grounds of radio work, especially if you, like Karl Mannheim, ever say, "Ich habe meine Grunde vergessen." ("I forgot where I started.")
+

+
+ +

+

Updated 5-20-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Return to Amateur Radio Page

+

Topics: HF Lower, MF, Vertical


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+

Part 2:
+ "Capacity" Hats

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ If we are to succeed in looking at ground planes in a different way, as suggested in Part 1, then we must first understand some things about so- called capacity hats. While this discussion may seem initially to be a digression, we shall see in later parts that almost all of what can be said about hats can also be said about so-called ground planes--except this: hats go on top, planes go on the bottom. +

A true hat is a symmetrical conductive structure that we place on the end of an antenna element, and at right angles to it, so that two effects occur. First, the net radiation from the hat is zero, due to the cancellation of radiation from one part of the structure by that from another part. Second, by using the hat as a path for antenna currents, we may shorten the main element length and still achieve resonance or some other specified condition.

+

We may also use slightly non-symmetrical structures to achieve, what is usually called top-loading. So long as the structure does not radiate a field more than about -30 dB relative to the field from the main element, the radiation from the field will not materially affect the overall pattern or the feedpoint impedance of the antenna. Non-symmetrical top loading may, however, have an affect on the operating bandwidth and gain of the antenna element.

+

Although we refer to these methods as top-loading, they are quite distinct from base or mid-element loading. All the two forms of loading have in common is that they allow us to use a shorter main element in our antenna. Base-loading and mid-element loading normally use either solenoid inductors or shorted transmission line stubs to introduce into the antenna an inductive reactance that compensates for the capacitive reactance that emerges as the element is shortened. Inductive reactance comes at the cost of resistance that transforms some of the energy reaching the antenna into heat. Every mode of inductive loading, including the use of inductive transmission line stubs, has a finite Q, and that means a source of gain loss in addition to the loss of gain which is natural to the shortening of an antenna element.

+

A hat is simply a form of antenna length completion so that the current has a path of a correct length to achieve resonance, despite the use of a shortened main element. The only losses are those associated with the shortening of the element and the materials used to construct the hat.

+

From the perspective of modeling, we may drop the word "capacitive" when referring to hats. That term arose from a method of calculating the size of hats for LF and VLF and rests on using an open transmission line analogy for antennas. From the beginning, the technique was considered only an approximation, and it breaks down severely at HF, where the diameter and relatively uniform diameter of antenna elements violates the fundamental terms of the analogy. Hence, from this point forward, I shall simply refer to hats or top hats.

+

We may construct hat structures in many forms. The most common form is a series of radials extending from the end of the main element outward. The radials are spaced at equal angles to each other. Hats require a minimum of 2 opposing radials, but may have any large number until they form a solid disk. Along the way, we shall examine an alternative to this structure that has some interesting properties.

+

The length of a hat radial (or "spoke," as it is sometimes informally called) depends on many variables: the length of the main element relative to the frequency of interest, the diameter of the main element, the diameter of the radial wire, and the number of radials. Let's freeze the element and radial diameters for a moment at 2" and 0.25" respectively, and let's make them aluminum. That will simplify some modeling exercises by not varying everything at the same time. Let's also make our frequency of interest 7.05 MHz.

+
+ +
+

We shall start with the arrangement shown in Figure 1. Here we have a vertical monopole atop perfect ground. We shall use a top hat consisting of 4 spokes, and then shorten the antenna 10% at a time and see what length the spokes must be to reresonate the antenna. Gain and feedpoint impedance figures are included to see what shortening the element does to them.

+ 
+Length (%)     Length (ft)    Radial         Gain (dBi)     Feedpoint Z
+                              Length (ft)                   (R +/- jX ohms)
+100%           33.25          ---            5.14           35.97 - 0.63
+ 90%           29.925          2.060         5.13           35.19 + 0.70
+ 80%           26.6            3.800         5.08           32.76 - 0.66
+ 70%           23.275          5.570         5.02           29.08 - 0.71
+ 60%           19.95           7.600         4.96           24.34 + 0.13
+ 50%           16.625          9.900         4.88           18.81 - 0.66
+ 40%           13.3           12.700         4.80           13.07 + 0.19
+ 30%            9.975         16.100         4.71            7.83 - 0.42
+ 20%            6.65          20.700         4.59            3.67 - 0.62
+ 10%            3.325         27.100         4.29            1.00 - 0.42
+
+

Although the shortening progresses linearly, the rate of decrease in gain and feedpoint impedance increases more rapidly past the 70% mark. Historically, commercial antenna engineers have used 2/3 full size as a bench mark for minimum efficient antenna operation. However, the gain over a perfect ground decreases by less than a full dB down to the 10% mark, making very short amateur antennas feasible, if the feedpoint impedance can be overcome.

+

The use of hats is not restricted to vertical monopoles. We may employ them on dipoles with equal results. NEC programs model vertical monopoles over perfect ground by the use of the antenna image, essentially a copy of the antenna below the ground level. If we move each of these resonant antennas along with its image into free space, we obtain a resonant dipole whose feedpoint impedance is simple twice the figure for the monopole. Gain reductions will parallel those for the vertical monopole (although starting in the vicinity of about 2.13 dBi in free space for the dipole). In the end, a short dipole with a hat on either end will still have very usable gain. A 2-element Yagi with hatted elements about 70% full-size will rival its full-size cousin in both gain and front-to-back ratio, although the feedpoint impedance will be lower. Indeed, the failure of the hatted 2-element Yagi to achieve the kinds of front-to-back ratio that are achieved by linear and coil loaded Yagis is further evidence of the difference between the two routes to shorter elements.

+

Hat spoke length decreases as we add more radials to the structure. If we double to number of radials to 8 with the same main antenna, here is what we get.

+ 
Length (%)     Length (ft)    Radial         Gain (dBi)     Feedpoint Z
+                              Length (ft)                   (R +/- jX ohms)
+100%           33.25          ---            5.14           35.97 - 0.63
+ 90%           29.925          1.505         5.13           35.18 - 0.06
+ 80%           26.6            2.730         5.08           32.84 - 0.40
+ 70%           23.275          4.000         5.03           29.27 + 0.23
+ 60%           19.95           5.400         4.97           24.49 + 0.73
+ 50%           16.625          7.000         4.90           18.87 - 0.02
+ 40%           13.3            9.000         4.83           13.10 - 0.45
+ 30%            9.975         11.650         4.77            7.81 - 0.61
+ 20%            6.65          15.500         4.69            3.62 - 0.03
+ 10%            3.325         22.000         4.52            0.95 - 0.20
+

There are several things to notice about this table. First, radial lengths range from about 75% to 80% of those required for a 4-radial hat. Second, there is no significant change in gain between the two hat sizes until the antenna length is less than 70% full-size. At shorter lengths, hats with more radials yield slightly higher gains, but that advantage quickly diminishes to the level of the unnoticeable. Third, the feedpoint impedance does not change as the number of radials in a hat increase; it is a function of the main antenna element length.

+

We can plot the decrease in radial length with the increasing number of radials more readily by spot checking antenna. The following three tables use antenna elements of 90, 70, and 50 percent full size (2" diameter aluminum) with 0.25" hat radials that double with each step.

+ 
Length         Number         Radial         Gain (dBi)     Feedpoint Z
+(% and ft)     of Radials     Length (ft)                   (R +/- jX ohms)
+ 90% 29.925     4              2.060         5.13           35.18 - 0.06
+                8              1.505         5.13           35.18 - 0.06
+               16              1.235         5.13           35.21 + 0.10
+               32              1.090         5.13           35.19 - 0.19
+               64              1.022         5.13           35.19 - 0.07
+
+Length         Number         Radial         Gain (dBi)     Feedpoint Z
+(% and ft)     of Radials     Length (ft)                   (R +/- jX ohms)
+ 70% 23.275     4              5.620         5.02           29.24 + 0.57
+                8              4.000         5.03           29.35 + 0.82
+               16              3.150         5.03           29.35 + 0.48
+               32              2.720         5.03           29.32 + 0.12
+               64              2.500         5.03           29.25 - 0.52
+
+Length         Number         Radial         Gain (dBi)     Feedpoint Z
+(% and ft)     of Radials     Length (ft)                   (R +/- jX ohms)
+ 50% 16.625     4              9.900         4.88           18.81 + 0.66
+                8              6.950         4.90           18.86 - 0.31
+               16              5.450         4.91           18.98 + 0.66
+               32              4.650         4.91           18.99 + 0.29
+               64              4.250         4.91           19.00 + 0.12
+

I would have carried the exercise out to 128 radials, except for three factors. First, even with the shortest antenna element, the gain and feedpoint impedance values had stabilized well before the 64-radial mark. Second, a well-converged model for the 50% full size 64-radial antenna had already exceeded 1,000 segments. And third (the reason I did not have to run the big model more than once), the radial lengths for larger arrays are completely predictable.

+
+ +
+

Figure 2 is a graph of the values charted above. If you examine the data by taking the decrease in length for each doubling of the number of radials, you will discover that for each doubling, the length decrease halves. The 50% model with 128 radials will therefore have radials just about 4.05' long. (Moreover, we already know the antenna gain and feedpoint impedance.) The exact increment to be halved with each step will, of course, vary as we change the diameters of the main element and of the radials.

+

There is a second popular way to construct top hats. Instead of using radials alone, we may use radials and connect them together with a perimeter wire. Figure 3 illustrates the difference. With a perimeter wire, the required length of the radials decreases significantly. In the table below are figures for a 4-radial assembly with a perimeter wire. Compare the radial lengths with those required by the radial-only structure.

+
+ +
+ 
Length (%)     Length (ft)    Radial         Gain (dBi)     Feedpoint Z
+                              Length (ft)                   (R +/- jX ohms)
+100%           33.25          ---            5.14           35.97 - 0.63
+ 90%           29.925          1.320         5.13           35.17 - 0.11
+ 80%           26.6            2.380         5.05           33.02 + 0.62
+ 70%           23.275          3.400         5.03           29.29 + 0.19
+ 60%           19.95           4.500         4.96           24.38 - 0.91
+ 50%           16.625          5.800         4.90           18.89 - 0.15
+ 40%           13.3            7.350         4.83           13.15 + 0.28
+ 30%            9.975          9.200         4.76            7.83 + 0.05
+ 20%            6.65          11.400         4.68            3.62 - 0.94
+ 10%            3.325         14.400         4.45            0.96 + 0.43
+

Compared to the spoke-only version of the 4-radial top hat, the radial + perimeter model creates no changes in feedpoint impedance. The slightly elevated gains of the perimeter model suggest that adding the outer wire allows the hat to perform with an equivalence to a hat with twice the number of radials. Finally, required spoke length of the hat decreases more rapidly as the antenna is shortened. The degree of shortening decreases as the basic number of radials is increased, but never diminishes to zero.

+

The use of a perimeter wire permits more compact hat structures than are possible with the open radial structure. However, no weight savings are gathered this way. In very approximate terms, the current path for a perimeter model is equal to the length of the radial plus one-half the length of the perimeter segment to the next radial. Hence, one will use more wire in the perimeter version, but will be able to place it more securely closer to the main element.

+

Understanding the behavior of top hats is important in itself, since hatted vertical monopoles are growing more common as hams use ingenuity in finding ways to support such structures and as they learn of the reduced losses and wider operating bandwidth possible with such antennas in comparison to base-loaded verticals. Moreover, since we have finally learned that hats are simply antenna current pathways and not capacitor plates, we may be in a position to use them wisely in dipole assemblies (both vertical and horizontal).

+

However, for our purposes, a short study of hats is a preliminary to inverting them to form planes--which we are ready to do, if you will join me in free space.
+

+
+ +

+

Updated 5-20-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Return to Amateur Radio Page

+

Topics: HF Lower, Loading, MF, Vertical


+ + diff --git a/content/gp/gp24-1.gif b/content/gp/gp24-1.gif new file mode 100644 index 0000000..04c53ec Binary files /dev/null and b/content/gp/gp24-1.gif differ diff --git a/content/gp/gp24-2.gif b/content/gp/gp24-2.gif new file mode 100644 index 0000000..8c42701 Binary files /dev/null and b/content/gp/gp24-2.gif differ diff --git a/content/gp/gp24-3.gif b/content/gp/gp24-3.gif new file mode 100644 index 0000000..548b3c0 Binary files /dev/null and b/content/gp/gp24-3.gif differ diff --git a/content/gp/gp24-4.gif b/content/gp/gp24-4.gif new file mode 100644 index 0000000..0052989 Binary files /dev/null and b/content/gp/gp24-4.gif differ diff --git a/content/gp/gp24-5.gif b/content/gp/gp24-5.gif new file mode 100644 index 0000000..ce95495 Binary files /dev/null and b/content/gp/gp24-5.gif differ diff --git a/content/gp/gp24.html b/content/gp/gp24.html new file mode 100644 index 0000000..7806634 --- /dev/null +++ b/content/gp/gp24.html @@ -0,0 +1,132 @@ + + + + + + NEC-2 and NEC-4: Reading Trends with Caution 7 MHz Vertical + Ground Plane + + + +
+

NEC-2 and NEC-4: Reading Trends with Caution
+ A Case Study with a 7 MHz Vertical + Ground Plane

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ When doing some systematic modeling, it is often useful to read trends in values, even if the actual differences would make no operational difference for a given antenna design. However, one must use great care when interpreting results as a trend: the progression of differences may not in fact represent a trend of antenna performance so much as a trend in the manner in which the modeling program calculates various values. +

A case in point came to light while doing some work with NEC-2 on some simple 1/4 wl vertical monopoles with ground planes of various sizes--both as free space models and as highly elevated antennas. The test frequency was 7.05 MHz, and all antenna elements were specified as aluminum (6061- T6). The 1/4 wl vertical section remained constant: 10.1346 m long with a diameter of 50 mm. The test radials systems included 4, 8, 16, and 32 radials, all of 6.35 mm diameter. 32 radials is at the limit of wires to a single junction recommended for NEC-2.

+

As an interesting side note, the length of the radials, when uniformly adjusted to achieve resonance without changing the length of the vertical element, underwent changes as the table below shows.

+ 
Number of Radials        Length of Radials in meters
+      4                       11.796
+      8                       12.314
+     16                       12.588
+     32                       12.863
+

Both NEC-2 and NEC-4 showed resonance (within the limits of +/- j 1 Ohm) with these lengths both in free space models and with models whose base was 40 m high (with a vertical top height of 50.1346 m). In this regard, the two programs are well-calibrated to each other.

+
+ +
+

Figure 1 shows one version of the model used, this one with 16 radials. Since the object of the exercise was not extreme precision relative to an actual antenna, simplified modeling procedures were used. Each element has 10 segments (resulting in a 330-segment model with 32 radials). The source is placed on the lowest segment of the vertical element. (Somewhat greater accuracy might be obtained by length tapering all wires toward the junction, although it is advisable to create a separate wire for the source and length taper the vertical wire above it so that the source segment and all adjacent segments are as close to the same length as feasible.)

+

For the examination of trends, the simple model sufficed. It had been run in two implementations of NEC-4 (EZNEC Pro from W7EL and GNEC from Nittany Scientific) with no differences of either gain or source impedance that amounted to anything more than rounding conventions unique to each implementation. The maximum difference in reported source resistance was 0.02 Ohms, and the maximum reported difference in source reactance was 0.03 Ohms (with this last difference occurring only once). Gain figures coincided exactly to 2 decimal places, and TO values were exact to 2 significant figures, the limits checked.

+

NEC-2 is another matter. The NEC-2 core has been around for many years and has been updated and customized by those offering full implementations. The are 16-bit and 32-bit versions as well. The same models were run on the version of NEC-2 included with EZNEC Pro and with the 32-bit version provided with NECWin Pro. As one might expect, output data from NEC-2 does not replicate that from NEC-4. However, for a given model and situation, all source values among the 2 versions of NEC-2 and the NEC-4 versions were within 0.3 Ohms resistance and 0.5 Ohms reactance. Gain values were within 0.07 dB.

+

These differences are all operationally insignificant. However, the object of the test was to study the trends in values, especially gain, for the increasing number of radials in the models, both in free space and 1 wl over various types of ground. The types of ground used were those classified as "very good" (cond.=0.0303 S/m; D.C=20), average (cond.=0.005 S/m; D.C=13), and very poor (cond.=0.001 S/m; D.C=5).

+

The charts below compare the gain output for both versions of NEC-2 (NWP=NECWin Pro; EZ-2=EZNEC Pro) with the gain output for NEC-4 (the same in both implementations).

+

Also see the Antenna Modeling Programs page for more information.

+

1. Free space values

+
+ +
+

Note that, in Figure 2, the NEC-4 decrease in gain is nearly linear for a geometric increase in the number of radials. The curves for NEC-2 for each program show the same trends and are nearly parallel to the NEC-4 curve. These are the curves which might set up some anticipations of values in other contexts for all NEC programs.

+

2. Very good ground values

+
+ +
+

The NEC-4 curve in Figure 3 shows the same type of decreasing gain pattern as it did in free space. However, the EZNEC-2 values are flat--or nearly so, since the hump in the curve represent a gain change of 0.01 dB, which might be an artifact of rounding. The NWP curve, however, shows a distinct and almost linear increase in value, although the values themselves are closer to those yielded by NEC-4. (Elevation angle of maximum radiation is 24 degrees. for all curves.)

+

3. Average soil values

+
+ +
+

Although the NEC-4 curve in Figure 4 is not visually linear, the degree off linear is only 0.01 dB, again, possibly due to rounding. The NWP curve is again closer in value to the NEC-4 curve, but it ascends. The EZNEC-2 figures are flat within a 0.01 dB range. The elevation angle of maximum radiation moved from 26 degrees to 25 degrees as the number of radials increased.

+

4. Very poor soil values

+
+ +
+

The curves in Figure 5 all show descending tendencies, with the NEC-4 curve being the most linear. The elevation angle of maximum radiation was 11 degrees for all cases. (Those who insist that good soil is a necessity in the territory of a highly elevated vertical monopoles should study the effects of soil more thoroughly. Although the gain values for average soil and for very poor soil are quite close, with the 1 wl base height of the antenna, the very poor soil allows the gain to appear in the lowest lobe, while with average soil, the highest gain appears in the next lobe upward.)

+

If one asks the question, "What are the trends in values as we add more radials to a free space or highly elevated ground plane antenna system model?" no single answer emerges that is wholly reliable. The NEC-2 curves show sufficient variation from one implementation to another and from one soil type to another, that it would be untenable to insist upon any trend from the data. What one implementation gives, the other takes away, whether in terms of curve shape or coincidence of values with NEC-4.

+

Even the NEC-4 curves must be treated with caution. The curves are internally consistent from one case to the next, which increases the confidence that they exhibit a general trend. However, nothing in the models identifies the trend as being either an accurate reflection of reality or simply a calculational trend of the computational core.

+

Since this exercise was performed without access to the codings of either the core or the specific implementations of the input and output systems used, one is left without means of settling the disjunction. This situation is the one most common to users of NEC-2 and NEC-4. Hence, reading trends from small variations in program outputs must be done with extreme caution, whether those variations are regular or irregular.

+

It is easy to read too much into visually apparent numerical differences below the level of operational significance. Hopefully this exercise may provide a sufficient cautionary note in the opposite direction. If the question of whether or not a trend is simply an artifact of the computational system cannot be settled, the claim of a trend may be dubious at best. Moreover, it pays to cross check one implementation of a computational system with another before before deciding that one has a trend in the first place.

+

For reference, here are descriptions of 2 of the models used, given in EZNEC form for compactness.

+ 
1/4 wl w/GP: 7.05 MHz                        09-12-1998     06:34:16
+Frequency = 7.05  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+1            0.000,  0.000, 10.135  W2E1   0.000,  0.000,  0.000 5.00E+01  10
+2     W3E1   0.000,  0.000,  0.000        11.796,  0.000,  0.000 6.35E+00  10
+3     W4E1   0.000,  0.000,  0.000         0.000, 11.796,  0.000 6.35E+00  10
+4     W5E1   0.000,  0.000,  0.000       -11.796,  0.000,  0.000 6.35E+00  10
+5     W1E2   0.000,  0.000,  0.000         0.000,-11.796,  0.000 6.35E+00  10
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          10     1 / 95.00   (  1 /100.00)      1.000       0.000       V
+
+Ground type is Free Space

+
+ 
1/4 wl w/GP: 7.05 MHz                        09-12-1998     06:35:05
+Frequency = 7.05  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+1            0.000,  0.000, 50.135  W2E1   0.000,  0.000, 40.000 5.00E+01  10
+2     W3E1   0.000,  0.000, 40.000        12.588,  0.000, 40.000 6.35E+00  10
+3     W4E1   0.000,  0.000, 40.000        11.630,  4.817, 40.000 6.35E+00  10
+4     W5E1   0.000,  0.000, 40.000         8.901,  8.901, 40.000 6.35E+00  10
+5     W6E1   0.000,  0.000, 40.000         4.817, 11.630, 40.000 6.35E+00  10
+6     W7E1   0.000,  0.000, 40.000         0.000, 12.588, 40.000 6.35E+00  10
+7     W8E1   0.000,  0.000, 40.000        -4.817, 11.630, 40.000 6.35E+00  10
+8     W9E1   0.000,  0.000, 40.000        -8.901,  8.901, 40.000 6.35E+00  10
+9    W10E1   0.000,  0.000, 40.000       -11.630,  4.817, 40.000 6.35E+00  10
+10   W11E1   0.000,  0.000, 40.000       -12.588,  0.000, 40.000 6.35E+00  10
+11   W12E1   0.000,  0.000, 40.000       -11.630, -4.817, 40.000 6.35E+00  10
+12   W13E1   0.000,  0.000, 40.000        -8.901, -8.901, 40.000 6.35E+00  10
+13   W14E1   0.000,  0.000, 40.000        -4.817,-11.630, 40.000 6.35E+00  10
+14   W15E1   0.000,  0.000, 40.000         0.000,-12.588, 40.000 6.35E+00  10
+15   W16E1   0.000,  0.000, 40.000         4.817,-11.630, 40.000 6.35E+00  10
+16   W17E1   0.000,  0.000, 40.000         8.901, -8.901, 40.000 6.35E+00  10
+17    W1E2   0.000,  0.000, 40.000        11.630, -4.817, 40.000 6.35E+00  10
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          10     1 / 95.00   (  1 /100.00)      1.000       0.000       V
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+              --------------- MEDIA ---------------
+Medium          Conductivity(S/m)   Dielectric Const.    Ht(m )   R Coord(m )
+1                   5.000E-03            13.00           0 (def)     0 (def)

+
+
+ +

+
+

Updated 9-12-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Lower, Modeling, Vertical


+ + diff --git a/content/gp/gp3-1.gif b/content/gp/gp3-1.gif new file mode 100644 index 0000000..7ae94b7 Binary files /dev/null and b/content/gp/gp3-1.gif differ diff --git a/content/gp/gp3-2.gif b/content/gp/gp3-2.gif new file mode 100644 index 0000000..6430750 Binary files /dev/null and b/content/gp/gp3-2.gif differ diff --git a/content/gp/gp3-3.gif b/content/gp/gp3-3.gif new file mode 100644 index 0000000..b5a1b7c Binary files /dev/null and b/content/gp/gp3-3.gif differ diff --git a/content/gp/gp3-4.gif b/content/gp/gp3-4.gif new file mode 100644 index 0000000..547dd8a Binary files /dev/null and b/content/gp/gp3-4.gif differ diff --git a/content/gp/gp3.html b/content/gp/gp3.html new file mode 100644 index 0000000..af8807c --- /dev/null +++ b/content/gp/gp3.html @@ -0,0 +1,155 @@ + + + + + + Modeling Perspective on Ground Planes Part 3: Planes in Space + + + +
+

Part 3:
+ Planes in Space

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ We are very comfortable modeling dipoles in free space. We use such models as the starting point for many a disquisition on dipole properties. So let us begin our journey just here. +

We should note that in free space, we may model a dipole along any of the three Cartesian coordinates (or even traversing them at an angle). Free space has nothing in any direction and in every direction. Wherever the dipole broadside is, off that broadside will be maximum gain.

+

This reminder of free space properties is to remove any initial anxiety about modeling our dipole along the Z axis--which would be height, if we had a ground below. Since we are interested in vertical antennas relative to ground, this strategy will be handy for modeling over ground.

+

Let's not be too hasty in getting close to the ground. For present purposes, we shall stay 2 wavelengths above ground. At this height and above, antennas show virtually the same feedpoint impedance they show in free space, and some basic gain comparisons will be instructive as we move from full size dipoles toward monopoles with planes.

+

We shall retain our 2" diameter aluminum main element. If we add a plane or a hat, it will be composed of 0.25" aluminum radials. This procedure will preserve consistency throughout the exercise. Moreover, we shall continue to list gain and feedpoint values to 2 decimal places. Although this level of reporting the modeling program output has little if any practical antenna building significance, it occasionally reveals some numerical trends that might be obscured by rounding the numbers to a construction level.

+

Building a full size dipole in free space means nothing more than doubling the full size monopole over perfect ground. NEC does the same thing for us with the monopole as it constructs an image during calculations. The only difference shows up in the feedpoint impedance: values will be twice those reported for the monopole. Let's compare the monopole and the dipole. Gain figures list the monopole over perfect ground and the dipole in free space. They are not significant here, but will become so later.

+ 
Antenna        Length         Feed Z              Gain
+               (ft)           (R +/- jX ohms)     (dBi)
+
+Monopole       33.25          35.97 - 0.06        5.14
+Dipole         66.50          71.92 - 0.27        2.13
+
+ +
+

As shown in Figure 1, we may place hats at the ends of a dipole in a manner identical to placing one at the top of a vertical monopole. Moreover, we may construct a hatted dipole in the same way we constructed the dipole: simply by joining two monopoles with hats in the center and keeping the main elements in a line. Once more, we may expect the dipole feedpoint impedance to be twice that of the monopole. "Gain loss" is referenced to the gain of the corresponding full size antenna above. The hats on each end of dipoles consist of 4 wires of the same lengths used for the monopoles: 70%: 5.57' each; 50%: 9.90' each; and 20%: 20.7' each.

+ 
Antenna        Length         Feed Z              Gain      Gain loss
+               (ft)           (R +/- jX ohms)     (dBi)     (dB)
+
+70% Full-size
+Monopole       23.275         29.08 - 0.71        5.02      -0.12
+Dipole         46.550         58.15 - 1.50        2.01      -0.12
+
+50% Full-size
+Monopole       16.625         18.81 + 0.66        4.88      -0.26
+Dipole         33.250         37.63 + 1.39        1.87      -0.26
+
+20% Full-size
+Monopole        6.650          3.67 - 0.61        4.59      -0.55
+Dipole         13.300          7.34 - 1.41        1.58      -0.55
+

The relatively precise feedpoint impedance doubling is obvious. Now here is where the gain figures acquire some importance. The differences in gain of each shortened monopole relative to the full size monopole are exactly reflected in the differences in gain of each shortened dipole relative to the full size dipole. A hatted dipole (or monopole) 20% of full size, relative to a full size dipole, loses only 0.55 dB of gain--or about 1/10 of an S-unit as such measures are loosely reckoned.

+

Similar results accrue over ground. Since we are limiting ourselves to approaching only 2 wavelengths from ground, let's set the feedpoints of the vertical dipoles at 280' up and see what happens.

+ 
+Antenna        Length         Feed Z              Gain      Gain loss
+               (ft)           (R +/- jX ohms)     (dBi)     (dB)
+
+Full-size
+Dipole         66.50          71.83 - 0.79        4.44
+
+70% Full-size
+Dipole         46.550         58.02 - 1.43        4.34      -0.10
+
+50% Full-size
+Dipole         33.250         37.53 + 1.45        4.21      -0.23
+
+20% Full-size
+Dipole         13.300          7.32 - 1.13        3.94      -0.50
+
+

Again, the dipole only 20% of full size loses only a half dB relative to a full size dipole, as do equivalently shrunken monopoles. If we can handle the low feedpoint impedances involved, these antennas can be useful.

+

The shortest of the hatted antennas has hat radials far longer than the main element itself. However, the radiation from these hats fully cancels so that all radiation in the far field pattern is vertically polarized. Moreover, the hats do not interact, as evidenced by the fact that the shortest dipole reflects the same feedpoint impedance doubling and gain reduction amount as the monopole over perfect ground. Each hat is the antenna current completion path for each of the monopoles forming the dipole.

+

The symmetrical hat at right angles to the main element does not radiate. However, if the radials of the hat are angled, significant radiation does occur. In general, if the antenna is vertical, and we construct a so- called sloping ground plane of wires, horizontally polarized radiation from the plane wires does cancel while vertically polarized radiation adds to the radiation of the antenna. In essence, as we split one monopole into 4 wires, leaving the other as a single element, we can bend the wires through the arc of 90 degrees and end up with a monopole and plane, as shown in Figure 2

+
+ +
+

Modeling this progression requires a caution: The wires resulting from splitting the main element yield a fatter wire than the former end of the one-wire dipole. This fatter 4-part wire carries slightly higher currents closer to the feedpoint, which raises the overall gain of the antenna in a near-dipole configuration. This shows up as a shorter length for the 4- part wire than for the 1-wire upper end. With this in mind, we can construct some models of the transition using angles of 5, 45, and 90 degrees, in order to look at both the gain and the pattern of the antenna. In all case, the upper end is 33.25' of 2" aluminum, while the lower part is 4 0.25" wires of the length given in the table.

+ 
+Antenna             Radial Length       Feedpoint Z         Gain
+                    (feet)              (R +/- jX ohms)     (dBi)
+
+Simulated dipole:  5-deg from vertical
+Free space          27.5                57.27 - 0.79        2.58
+2 wl up                                 57.16 - 0.71        4.91/7 deg
+
+Sloping plane:  45-deg from vertical
+Free space          29.5                48.33 + 0.51        2.08
+2 wl up                                 48.26 + 0.62        4.47/7 deg
+
+"Ground" plane:  90-deg from vertical
+Free space          38.7                21.38 - 0.66        1.32
+2 wl up                                 21.42 - 0.59        3.85/6 deg
+
+

We can look at the gain figures in two ways. First, we can view the sloping plane antenna as reduced in gain by about 0.5 dB from a true vertical dipole of similar materials. Second, we can view the sloping plane antenna as providing about 2/3 dB gain over a similarly situated monopole with a level plane. Although the gain may not be much, it is real. However, we often throw it away by being careless with the placement of sloping radials or by not attending to the matter of resonating the entire antenna, including the sloping radials. We shall discuss the importance of resonance in a later episode. By way of preview, the importance lies not in any special property of resonance itself, but instead by what it indicates with respect to the high current position on the entire antenna, where antenna includes both the main element and the radials.

+

In free space, we cannot accurately model only half the antenna. The model consists of both the main element and the radials, whether those radials are pointed straight down, sloped at an angle, or placed at right angles to the main element to form a plane. Adding the term "ground" to the expression "plane" adds nothing to the model. With respect to free space modeling, the plane is simply the other half of the dipole so constructed as not to add to the overall radiation. In fact the plane does not even bend or distort the free space radiation pattern of the antenna in any way, as the elevation pattern in Figure 3 indicates. The plane acts just like a hat--or a hat acts just like a plane. In free space, the only distinction seems to be this: we use the term "hat" when the structure replaces some of the main element length, and we use the term "plane" when the structure replaces all or virtually all of the main element length, where "length" is referred to each monopole making up a dipole. electrically, there is no difference: hat and plane differences are functions of the variables we discussed in the last episode: main element diameter, main element length, radial diameter, and number of radials.

+
+ +
+

Moreover, as indicated in Figure 4, there is no rule that prevents the construction of asymmetrical hatted/planed antennas. Indeed, many short verticals for the lowest HF bands are precisely such constructions: hatted, planed vertical antennas.

+
+ +
+

Before we return to earth to muddy up the situation a bit, let's look at a problem attached to modeling dipoles that consist of one linear monopole and a plane. NEC has a limitation in that it will not permit placement of a split feedpoint at a multiple wire junction. The standard view of a vertical antenna and its plane seems to require precisely this move. One temptation is to move the feedpoint to the wire segment immediately adjacent to the junction with the radials. This can lead to problematical results, as shown in the next table. All main elements are 33.25' long.

+ 
Antenna        Radial length       Gain           Feedpoint Z
+               (feet)              (dBi)          (R +/- jX ohms)
+4-radials
+Free space     38.7                1.32           21.38 - 0.66
+2 wl up                            3.85/6 deg     21.42 - 0.59
+
+8-radials
+Free space     40.4                1.24           21.90 - 0.22
+2 wl up                            3.79/6 deg     21.95 - 0.30
+
+16-radials
+Free space     41.3                1.18           22.30 - 0.50
+2 wl up                            3.74/6 deg     22.36 - 0.43
+
+32-radials
+Free space     42.2                1.11           22.73 - 0.26
+2 wl up                            3.69/6 deg     22.80 - 0.19
+

The descending gain and increasing feedpoint impedance indicate that the antenna is being feed increasingly off center. With a dipole whose halves are identical, the physical center is also the electrical center. With an antenna whose two halves are of different construction, the electrical center may well be elsewhere. The electrical center of the antenna (dipole) is the point of highest current. As we add more radials, we increase the working diameter of the monopole we call the plane. The point of highest current moves further out away from the junction, calling for more wire on the other side of the electrical center, namely, in the radials, to return the system to resonance.

+

Moving the region of highest current further into the plane moves it also into the region of cancelled radiation. Although the loss may not be very large, it is definite, as the progressively lower gains of the models demonstrates.

+

To overcome this modeling problem and permit the exercise to continue, I have adopted a convention for further models of planes. To the base of the upper 33.35' main element, I have added a single wire 1' long. The plane radials join at the base of this section. The feedpoint is a split feed at the junction of the in-line wires. The procedure does not end the slight movement of the electrical center of the antenna toward the radials, but it effectively limits the movement to within the 1' wire. The sum of currents on the radials never exceeds the current on the added wire.

+

In addition, the revised model reflects at least one of the more common construction practices on the lower HF bands. Many builders join their radials in a single "wad" that rises out of the ground to meet a slightly elevated upper main element. Whatever the practice, a table of models built along the revised pattern yields the following data.

+ 
+Antenna        Radial length       Gain           Feedpoint Z
+               (feet)              (dBi)          (R +/- jX ohms)
+4-radials
+Free space     35.6                1.38           22.88 - 0.18
+2 wl up                            3.88/6 deg     22.91 - 0.22
+
+8-radials
+Free space     34.5                1.34           23.03 - 0.06
+2 wl up                            3.85/6 deg     23.06 - 0.02
+
+16-radials
+Free space     32.5                1.38           22.81 + 0.06
+2 wl up                            3.88/6 deg     22.82 + 0.13
+
+32-radials
+Free space     30.0                1.45           22.39 - 0.37
+2 wl up                            3.94/6 deg     22.42 - 0.31
+
+

The gain of the models has largely stabilized, as has the feedpoint impedance. Radial lengths decrease as the number of radials increases. Although the models do not precisely locate the electrical centers of each antenna, they are perhaps accurate enough for us to bring the vertical antenna with a plane down to earth. Two wavelengths is a long way, and we shall want to pay attention to our landing patterns.
+

+
+ +

+

Updated 5-20-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Return to Amateur Radio Page

+

Topics: HF Lower, Loading, MF, Vertical


+ + diff --git a/content/gp/gp4-1.gif b/content/gp/gp4-1.gif new file mode 100644 index 0000000..563e711 Binary files /dev/null and b/content/gp/gp4-1.gif differ diff --git a/content/gp/gp4-2.gif b/content/gp/gp4-2.gif new file mode 100644 index 0000000..bc4028c Binary files /dev/null and b/content/gp/gp4-2.gif differ diff --git a/content/gp/gp4-3.gif b/content/gp/gp4-3.gif new file mode 100644 index 0000000..7f3708b Binary files /dev/null and b/content/gp/gp4-3.gif differ diff --git a/content/gp/gp4-4.gif b/content/gp/gp4-4.gif new file mode 100644 index 0000000..ca84f0b Binary files /dev/null and b/content/gp/gp4-4.gif differ diff --git a/content/gp/gp4-5.gif b/content/gp/gp4-5.gif new file mode 100644 index 0000000..5bbbb31 Binary files /dev/null and b/content/gp/gp4-5.gif differ diff --git a/content/gp/gp4-6.gif b/content/gp/gp4-6.gif new file mode 100644 index 0000000..e863359 Binary files /dev/null and b/content/gp/gp4-6.gif differ diff --git a/content/gp/gp4.html b/content/gp/gp4.html new file mode 100644 index 0000000..41c04d4 --- /dev/null +++ b/content/gp/gp4.html @@ -0,0 +1,308 @@ + + + + + + Modeling Perspective on Ground Planes Part 4: Down to Earth Verticals + + + +
+

Part 4:
+ Down to Earth Verticals

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Most accounts of elevated ground planes begin with wires under the ground and proceed to elevate them. Since we started in free space and skimmed the atmosphere at a height of 2 wavelengths, let's continue our top-down progression. In figures and tables, and with a minimum of words, we can find some very interesting phenomena. +

For example: many hams are familiar with the elevation patterns of horizontal antenna and can speak with assurance of take-off angles, secondary lobes, etc. But few are familiar with the patterns created by elevated vertical antennas. Therefore, as a small compendium, here are a few patterns taken with a model of an 8-radial 1/4 wl vertical. All patterns are over medium earth. Exact gain numbers are omitted (they will appear in tables later) because it is pattern shape that is our focal interest.

+
+ +
+

Figure 1 gives a representative high-altitude elevation pattern--280' on 40 meters. Patterns for antennas above and somewhat below this height are similar.

+
+ +
+

At 1 wavelength up, in Figure 2, the vertical begins to show the domination of a higher angle lobe. This pattern appears from grounds as good as salt water to poor earth.

+
+ +
+

In Figure 3, at a half wavelength up, high angle radiation dominates, although over salt water, there is a strong lower lobe.

+
+ +
+

As is evident if Figure 4, when the base of the plane reaches about 0.25 wl, the lower lobe again dominates, although high angle radiation is readily apparent. A similar pattern appears as self-contained vertical 1 wl wire antennas are raised "too high."

+
+ +
+

At about 0.15 wl between the ground and the base of the plane, as shown if figure 5, secondary lobes are virtually absent, with radiation concentrated in a single main lobe whose angle increases as soil conditions worsen.

+
+ +
+

Below 0.1 wl, the pattern simply grows more bulbous, with lower gain and a higher elevation angle of maximum radiation. This pattern holds good as the plane is brought to ground and even below ground.

+

The patterns are typical of any ground plane antenna. A vertical dipole, however, presents some interesting variations--or perhaps compressions may be a better description. The vertical dipole has a widely separate feedpoint and element end. For feedpoint heights down to about 0.5 wl, the corresponding figures apply. Pattern changes compress below about 3.8 wl feedpoint height. At this height, the element end is about 20' off the ground at 40 meters, and the pattern resembles that if Figure 4 (ground plane at 0.25 wl). With the antenna end only 5' off the ground and the feed point nearly 40' up, the pattern is like Figure 4-5. Lowering the antenna just another 3' yields a pattern similar to Figure 4-6. Without bends or end hats, the true vertical dipole is just about at its lower limit.

+

We have already seen that the natural free space feedpoint impedance in ohms) of a quarter wavelength vertical with a plane is in the lower 20s, a value that also holds good at a 2-wl height. This feedpoint impedance value is at odds with experience when verticals are placed on or just above the ground. Additionally, ground and near-ground verticals do not exhibit the gain shown by the models at 2 wl up.

+

How do we account for the discrepancy? To see the answer to this, we need to look at models of ground plane verticals gradually lowered from their lofty heights to the earth. Fortunately, NEC-4 makes it possible not only to bring the plane close to earth, but--with the Sommerfeld-Norton ground system--to take the plane below ground.

+

It is important in looking at various planed-vertical models to seek out both differential and parallel alterations of fields and of feedpoint impedances as the models are lowered. Therefore, I have run several models through successive steps over four kinds of earth: perfect (which does not permit penetration), salt water with a conductivity of 5 S/m and a dielectric constant of 81 (for which height values within about 0.2' above the surface return faulty results, but for which sub-surface values of height are functional), very good earth with a conductivity of 0.0303 and a dielectric constant of 20, and medium/average earth with a conductivity of 0.005 and a dielectric constant of 13.

+

The tables list for each level both feedpoint impedance and elevation pattern values (maximum gain and take-off angle for that gain). It is important to remember that these are separate data. Feedpoint impedance is a function of the earth conditions just below the antenna and in its most immediate vicinity. Far field data are functions of earth conditions beginning at some distance (something at least over a wavelength, if not farther) from the antenna. If the conditions under the antenna have been improved, then the feedpoint impedance of "very good ground" might apply, but the far field might still be no better than that shown for "medium" earth. Conversely, island operations might show "medium" earth impedances while giving salt water far field results.

+

Table heights are listed in feet, and are given for the feedpoint. The tables must be read with two understandings. First, a wavelength at the target frequency of 7.05 MHz is about 140' long, so that the table begin at 2 wl, with check point at 1.5, 1.0, 0.5, 0.375, 0.25, 0.15 wl and lower. Second, in accord with the model construction technique described in the last episode, the plane will be 1' below the feedpoint. At upper heights, this difference makes no difference, but becomes increasingly important at the lowest heights, e.g., 20 10, 5, 1.5, 1.2, 1.1, and 0 feet up. There are two zero feet feedpoint values, one with a modified model for plane wires buried 0.5' down; the other unmodified with plane wires 1.0' below the surface. The modified model appears not to have introduced unreasonable numbers for the plane 0.5' below surface.

+

Commentary on the tables will appear afterwards.

+ 
Vertical Dipole (for reference):  2" dia.  al. element, 66.5' long
+Free space:  Gain:  2.13 dBi; Feed Z:  71.98 - 0.85 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   71.75 - 0.82   8.16 / --           71.75 - 0.82   7.54 / 14
+210-1.5   71.56 - 0.81   8.17 / --           71.57 - 0.81   7.31 / 19
+140-1wl   71.02 - 0.81   8.21 / --           71.03 - 0.80   6.45 / 28
+ 70-0.5   67.82 - 1.10   8.40 / --           67.85 - 1.07   7.22 /  5
+ 52.5     73.02 - 8.99   8.05 / --           72.97 - 8.95   7.06 /  5
+ 43.25    83.92 - 8.03   7.46 / --           83.81 - 8.06   6.59 /  6
+ 38.25    93.00 - 1.17   7.07 / --           92.90 - 1.28   6.25 /  6
+ 35-.25   101.3 + 11.0   6.80 / --           101.8 + 10.7   6.02 /  7
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   71.78 - 0.79   5.18 / 13           71.83 - 0.79   4.44 /  7
+210-1.5   71.62 - 0.76   5.45 / 18           71.71 - 0.75   3.43 /  9
+140-1wl   71.14 - 0.68   5.21 / 27           71.34 - 0.63   3.52 / 27
+ 70-0.5   66.21 - 0.48   1.25 / 14           68.99 - 0.15   0.20 / 13
+ 52.5     71.79 - 8.39   2.09 / 12           71.00 - 7.05   0.35 / 15
+ 43.25    82.01 - 9.07   2.15 / 13           79.21 - 8.90   0.23 / 16
+ 38.25    91.25 - 3.82   2.07 / 14           87.86 - 5.76   0.07 / 17
+ 35-.25   101.0 + 6.95   1.98 / 15           97.89 + 3.14   0.11 / 18
+

Notes: The pattern of feedpoint impedance does not change significantly as one changes the soil type beneath the antenna. The greatest change occurs close to the ground with the transition from very good to medium earth, and a similar change will likely be noted in the transition from medium to poor earth.

+

Variable in antenna gain and take-off angle are noticeable with changing far field earth conditions. However, most notable is the sudden decrease in gain over very good and medium earth between 1 wl and 0.5 wl heights. Low-mounted vertical dipoles with salt-water paths are capable of approximately 6 dB better performance than the same antenna with medium earth paths.

+ 
1/4 wl Vertical (2" dia.  al. element, 33.25' long), with 4 0.25" radials
+each 35.6' long, set 1' below the feedpoint
+Free space:  Gain:  1.38 dBi; Feed Z:  22.88 - 0.18 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   22.90 - 0.18   7.39 / --           22.90 - 0.18   6.94 / 13
+210-1.5   22.92 - 0.94   7.39 / --           22.92 - 0.10   6.87 / 18
+140-1wl   22.96 + 0.12   7.38 / --           22.97 + 0.11   6.53 / 26
+ 70-0.5   23.30 + 1.01   7.33 / --           23.30 + 0.99   5.98 /  4
+ 52.5     20.90 + 0.49   7.80 / --           20.93 + 0.50   6.63 /  5
+ 35-.25   21.14 - 3.55   7.71 / --           21.12 - 3.49   6.75 /  6
+ 20-.15   27.08 - 5.53   6.62 / --           26.95 - 5.51   5.86 /  7
+ 10       33.72 - 2.05   5.71 / --           33.53 - 2.19   5.08 /  8
+  5       37.46 + 3.37   5.31 / --           37.30 + 3.09   4.73 /  9
+  1.5     40.03 + 12.9   5.09 / --           41.21 + 14.2   4.40 /  9
+  1.2     39.94 + 14.8   5.10 / --
+  1.1     39.82 + 15.4   5.12 / --
+  0-.5                                       37.23 + 1.09   4.45 /  9
+  0-1.0                                      38.31 + 1.96   4.33 /  9
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   22.91 - 0.20   5.07 / 27           22.91 - 0.22   3.88 /  6
+210-1.5   22.94 - 0.13   4.85 / 17           22.94 - 0.17   3.21 / 36
+140-1wl   23.01 + 0.05   5.09 / 25           23.01 - 0.04   3.24 / 24
+ 70-0.5   23.42 + 0.79   3.49 / 44           23.42 + 0.51   2.33 / 44
+ 52.5     21.26 + 0.68   1.71 / 52           21.68 + 0.66   0.73 / 52
+ 35-.25   20.84 - 2.90   1.86 / 12           20.91 - 2.16   0.14 / 15
+ 20-.15   25.73 - 5.69   2.02 / 15           24.49 - 5.13   0.19 / 18
+ 10       32.40 - 3.87   1.81 / 18           30.36 - 4.48   0.02 / 22
+  5       37.14 + 1.01   1.64 / 19           34.82 - 0.44   -.13 / 24
+  1.5     43.72 + 22.6   1.24 / 21           40.64 + 21.1   -.46 / 25
+  1.2     45.84 + 37.3   1.04 / 20           42.94 + 35.5   -.65 / 25
+  1.1     49.03 + 52.1   0.75 / 21           46.61 + 49.0   -.94 / 25
+  0-.5    52.63 + 12.9   0.33 / 21           67.38 + 13.7   -2.6 / 26
+  0-1.0   54.11 + 17.4   0.21 / 21           68.62 + 18.6   -2.6 / 26
+

Notes: There are numerous things to notice about this table set. With respect to feedpoint impedance, note the slight rise at 70' (1/2 wl), just where the vertical dipole impedance dipped. Although NEC-4 does not return sensible values for planes set at distances of 0.2' and 0.1' above the surface, the values for the plane set below ground provide an indication of the standard monopole feedpoint impedance values when the antenna is mounted without a plane but in contact with perfect earth. However, these values increase rapidly with a degradation in earth quality immediately under the antenna. Moreover, the resonance of the system is also disturbed--with a further shortening of the radials as the indicated need. Shortening the radials will also slightly lower the value of the resistive component of the feedpoint impedance. The progression of increase in feedpoint impedance begins as the antenna is lowered below the 0.25 wl point, whatever the ground type.

+

The far field pattern displays a variability in the angle of the lowest lobe, depending on the type of far field ground. In the region from 0.375 wl through 1 wl over very good and worse earth, high angle radiation dominates the pattern. Over these same earths, the gain takes a sudden nose-dive below the 0.5 wl antenna height, but progresses more smoothly down over slat water and better. At a certain height which varies with the level of earth quality, the take-off angle of low-mounted antennas reaches a minimum and then rises as the antenna is brought lower, including with the plane below the surface. The differential in gain between the value for a 2 wl height and for the lowest height modeled increases as the earth condition values decrease.

+ 
1/4 wl Vertical (2" dia.  al. element, 33.25' long), with 8 0.25" radials
+each 34.5' long, set 1' below the feedpoint
+Free space:  Gain:  1.34 dBi; Feed Z:  23.03 - 0.06 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   23.05 - 0.06   7.36 / --           23.05 + 0.06   6.91 / 13
+210-1.5   23.06 - 0.14   7.36 / --           23.06 + 0.14   6.84 / 18
+140-1wl   23.11 + 0.36   7.35 / --           23.11 + 0.35   6.49 / 26
+ 70-0.5   23.42 + 1.25   7.30 / --           23.43 + 1.23   5.95 /  4
+ 52.5     21.03 + 0.69   7.77 / --           21.06 + 0.70   6.60 /  5
+ 35-.25   21.34 - 3.35   7.66 / --           21.33 - 3.30   6.71 /  6
+ 20-.15   27.38 - 5.26   6.56 / --           27.26 - 5.24   5.80 /  7
+ 10       34.08 - 1.84   5.66 / --           33.89 - 1.99   5.02 /  8
+  5       37.81 + 2.76   5.26 / --           37.59 + 2.40   4.69 /  9
+  1.5     40.45 + 9.97   5.04 / --           40.38 + 9.71   4.48 /  9
+  1.2     40.25 + 11.8   5.07 / --
+  1.1     39.95 + 13.1   5.10 / --
+  0-.5                                       37.23 + 1.09   4.45 /  9
+  0-1.0                                      38.32 + 1.95   4.33 /  9
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   23.06 + 0.04   5.04 / 27           23.06 + 0.02   3.85 /  6
+210-1.5   23.08 + 0.11   4.82 / 17           23.08 + 0.07   3.17 / 36
+140-1wl   23.15 + 0.29   5.06 / 25           23.15 + 0.21   3.21 / 24
+ 70-0.5   23.55 + 1.03   3.44 / 45           23.56 + 0.76   2.27 / 44
+ 52.5     21.39 + 0.89   1.63 / 52           21.81 + 0.88   0.65 / 52
+ 35-.25   21.02 - 2.71   1.82 / 12           21.08 - 1.96   0.11 / 15
+ 20-.15   26.03 - 5.47   1.96 / 15           24.76 - 4.93   0.15 / 19
+ 10       32.74 - 3.84   1.76 / 18           30.65 - 4.60   0.03 / 22
+  5       37.17 - 0.44   1.64 / 20           34.80 - 2.36   -.14 / 24
+  1.5     40.66 + 10.3   1.55 / 21           37.87 + 7.47   -.19 / 25
+  1.2     40.93 + 19.5   1.53 / 20           38.54 + 16.0   -.23 / 26
+  1.1     41.84 + 28.0   1.43 / 21           39.84 + 22.9   -.34 / 26
+  0-.5    47.37 + 11.1   0.81 / 21           54.61 + 12.6   -1.5 / 26
+  0-1.0   49.19 + 16.3   0.66 / 21           56.33 + 18.5   -1.6 / 26
+

Notes: For all values over perfect earth and salt water, and for all values down to a low antenna height, the differences in numerical values between the 4-radial and 8-radial models parallel those between the respective free space models.

+

At heights below 5' (plane at 4' or less), the 8-radial model shows significant improvements. with the plane above the earth, the impedance does not rise as fast as that of the 4-radial model. The seeming anomaly of a lesser increase at low heights for the model over medium earth relative to the model over very good earth is more apparent than real. With smaller increases in reactance at those levels, the overall non-resonant condition is less radical than that of the model over very good earth. Bringing the model over very good earth back to resonance will lower the resistive component and make the values more comparable.

+

With the plane below the surface, feedpoint reactances are similar to those for the 4-radial model, but the resistive component values are significantly less.

+

With the plane below 5' (0.035 wl), the 8-radial model begins to exhibit significant improvements in gain over the 4-radial model over very good or worse earth. With the planes below the surface, the improvement is greater than 1 dB. With the planes higher than 5' above ground, gain differences are insignificant.

+ 
1/4 wl Vertical (2" dia.  al. element, 33.25' long), with 16 0.25" radials
+each 32.5' long, set 1' below the feedpoint
+Free space:  Gain:  1.38 dBi; Feed Z:  22.80 + 0.06 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   22.81 + 0.17   7.40 / --           22.81 + 0.17   6.94 / 13
+210-1.5   22.82 + 0.25   7.40 / --           22.82 + 0.25   6.87 / 18
+140-1wl   22.86 + 0.47   7.40 / --           22.86 + 0.46   6.51 / 26
+ 70-0.5   23.12 + 1.35   7.36 / --           23.13 + 1.33   6.01 /  4
+ 52.5     20.82 + 0.69   7.81 / --           20.84 + 0.70   6.64 /  5
+ 35-.25   21.33 - 3.28   7.66 / --           21.31 - 3.22   6.71 /  6
+ 20-.15   27.48 - 4.82   6.54 / --           27.36 - 4.82   5.79 /  7
+ 10       34.15 - 0.92   5.64 / --           33.97 - 1.08   5.01 /  8
+  5       37.84 + 3.92   5.25 / --           37.64 + 3.46   4.68 /  9
+  1.5     40.59 + 9.50   5.02 / --           39.93 + 8.42   4.53 /  9
+  1.2     40.60 + 10.0   5.03 / --
+  1.1     40.23 + 11.1   5.07 / --
+  0-.5                                       37.25 + 1.08   4.45 /  9
+  0-1.0                                      38.34 + 2.49   4.33 /  9
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   23.82 + 0.15   5.05 / 27           22.82 + 0.13   3.88 /  6
+210-1.5   22.84 + 0.22   4.86 / 17           22.84 + 0.18   3.16 / 36
+140-1wl   22.90 + 0.40   5.08 / 25           22.91 + 0.32   3.24 / 24
+ 70-0.5   23.25 + 1.14   3.40 / 45           23.27 + 0.88   2.24 / 44
+ 52.5     21.15 + 0.90   1.53 / 52           21.56 + 0.91   0.57 / 52
+ 35-.25   20.98 - 2.67   1.84 / 12           20.99 - 1.93   0.13 / 15
+ 20-.15   26.16 - 5.13   1.96 / 15           24.86 - 4.70   0.14 / 19
+ 10       32.99 - 3.04   1.75 / 18           30.96 - 4.01   -.06 / 22
+  5       37.52 + 0.52   1.61 / 20           35.32 - 1.73   -.20 / 24
+  1.5     40.61 + 5.86   1.57 / 21           38.15 + 2.87   -.24 / 25
+  1.2     39.38 + 9.51   1.71 / 20           37.55 + 7.21   -.15 / 26
+  1.1     39.17 + 15.0   1.73 / 21           38.21 + 11.3   -.21 / 26
+  0-.5    43.41 + 9.01   1.20 / 21           44.90 + 10.3   -.63 / 26
+  0-1.0   45.41 + 15.2   1.04 / 21           46.88 + 16.9   -.74 / 26
+

Notes: Once more, most differences in numerical values parallel the differences in free space models. The most notable differences occur over very good or worse earth at antenna height below 5' (plane below 4'). Doubling the number of radials to 16 drops the very good earth impedance by about 5 ohms and the medium earth impedance by 10 ohms, the same rate of change as between 4 and 8 radials. Reactance at low levels also decreases further, except as the plane goes below the surface.

+

Above ground gain, even at very low heights, increases only marginally. However, there is nearly a 0.9 dB increase in gain for the models with the plane below the surface--a 1.9 dB increase over the 4-radial models.

+ 
1/4 wl Vertical (2" dia.  al. element, 33.25' long), with 32 0.25" radials
+each 30.0' long, set 1' below the feedpoint
+Free space:  Gain:  1.45 dBi; Feed Z:  22.39 - 0.37 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   22.40 - 0.28   7.47 / --           22.40 - 0.28   6.99 / 13
+210-1.5   22.41 - 0.21   7.47 / --           22.41 - 0.21   6.93 / 18
+140-1wl   22.43 + 0.01   7.47 / --           22.43 + 0.01   6.55 / 26
+ 70-0.5   22.63 + 0.88   7.44 / --           22.64 + 0.87   6.10 /  4
+ 52.5     20.44 + 0.11   7.87 / --           20.47 + 0.12   6.72 /  5
+ 35-.25   21.19 - 3.73   7.68 / --           21.17 - 3.68   6.73 /  6
+ 20-.15   27.41 - 4.86   6.54 / --           27.30 - 4.87   5.79 /  7
+ 10       34.00 - 0.42   5.66 / --           33.84 - 0.58   5.03 /  8
+  5       37.63 + 4.99   5.27 / --           37.46 + 4.62   4.70 /  9
+  1.5     40.39 + 11.0   5.04 / --           39.63 + 9.68   4.56 /  9
+  1.2     40.60 + 11.0   5.02 / --
+  1.1     40.42 + 10.9   5.05 / --
+  0-.5                                       37.25 + 1.07   4.45 /  9
+  0-1.0                                      38.35 + 1.92   4.33 /  9
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   22.41 - 0.29   5.09 / 27           22.42 - 0.31   3.94 /  6
+210-1.5   22.43 - 0.23   4.92 / 17           22.44 - 0.27   3.18 / 37
+140-1wl   22.48 - 0.04   5.12 / 25           22.49 - 0.12   3.29 / 24
+ 70-0.5   22.77 + 0.69   3.38 / 45           22.81 + 0.44   2.22 / 44
+ 52.5     20.74 + 0.33   1.44 / 53           21.15 + 0.38   0.48 / 51
+ 35-.25   20.81 - 3.17   1.90 / 12           20.76 - 2.45   0.17 / 15
+ 20-.15   26.15 - 5.28   1.98 / 15           24.83 - 4.96   0.15 / 19
+ 10       33.05 - 2.63   1.75 / 18           31.11 - 3.83   -.07 / 22
+  5       37.70 + 1.53   1.60 / 20           35.70 - 1.07   -.24 / 24
+  1.5     41.47 + 6.44   1.49 / 21           39.32 + 2.54   -.39 / 25
+  1.2     40.09 + 7.45   1.65 / 21           38.59 + 4.60   -.30 / 26
+  1.1     38.41 + 10.1   1.82 / 21           38.49 + 6.85   -.28 / 25
+  0-.5    40.54 + 7.19   1.48 / 21           38.83 + 6.15   -.17 / 26
+  0-1.0   42.51 + 14.1   1.33 / 21           40.34 + 13.4   -.24 / 26
+

Notes: Above ground mounting of the antenna and plane yields performance that improves slightly in only one area: the degree of reactance induced at the feedpoint by close mounting to the ground. Performance actually degrades in other categories, but by amounts that are either insignificant or not especially reliable. Indeed, the improvement in gain between the 4- radial model and the 32-radial model at plane heights of 4 to 9 feet is only about 0.1 dB

+

When the plane is below the surface, the feedpoint reactance continues to drop, but by lesser amounts than with other radial doublings. Gain improvements amount to less than 0.3 dB over very good ground and by less than 0.5 over medium earth. Doubling the number of radials once more may be dubious if the far field earth is very good, but may bring about further gain improvements (in the neighborhood of 0.25 dB) if the path ground is medium or worse. Because of time constraints, 64-radial plane modeling has not been more than sampled.

+

All of these antennas constitute tuned systems (in the sense noted in passing by Moxon): they are resonant (or at very low heights, near resonant) antennas. Planes have been modeled just as would any open-spoke hat system for shortening the length of an antenna elements.

+

Since hats can be modeled with spokes plus a perimeter wire, I decided to model a 1/4 wavelength vertical with a plane of this design. A 4-spoke + perimeter model was constructed and run through the same exercise as all of the open-spoke models.

+ 
1/4 wl Vertical (2" dia.  al. element, 33.25' long), with 4 0.25" radials
+each 19.4' long, with a perimeter wire forming a square, all set 1' below
+the feedpoint
+Free space:  Gain:  1.70 dBi; Feed Z:  20.76 - 0.60 ohms
+
+          Perfect Earth                      Salt Water
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   20.75 - 0.51   7.72 / --           20.75 - 0.51   7.20 / 14
+210-1.5   20.74 - 0.45   7.72 / --           20.74 - 0.45   7.11 / 18
+140-1wl   20.71 - 0.27   7.73 / --           20.72 - 0.28   6.65 / 26
+ 70-0.5   20.65 + 0.51   7.75 / --           20.66 + 0.50   6.43 /  4
+ 52.5     18.99 - 0.72   8.11 / --           19.00 - 0.70   6.98 /  5
+ 35-.25   20.76 - 3.89   7.68 / --           20.74 - 3.87   6.76 /  6
+ 20-.15   27.25 - 3.00   6.51 / --           27.17 - 3.03   5.77 /  7
+ 10       33.54 + 4.46   5.69 / --           33.47 + 4.29   5.06 /  8
+  5       37.04 + 13.7   5.34 / --           37.02 + 13.4   4.76 /  8
+  1.5     39.54 + 25.4   5.14 / --           40.73 + 26.5   4.46 /  9
+  1.2     39.74 + 28.6   5.13 / --
+  1.1     39.76 + 29.5   5.13 / --
+  0-.5                                       37.34 + 0.95   4.44 /  9
+  0-1.0                                      38.38 + 1.85   4.32 /  9
+
+          Very Good Earth                    Medium Earth
+Height    Feed Z         Gain/TO angle       Feed Z         Gain/TO angle
+(feet)    (R +/- jX)     (dBi/degrees)       (R +/- jX)     (dBi/degrees)
+280-2wl   20.76 - 0.52   5.15 / 27           20.77 - 0.53   4.16 /  7
+210-1.5   20.76 - 0.46   5.13 / 17           20.77 - 0.49   3.27 /  9
+140-1wl   20.76 - 0.31   5.25 / 25           20.79 - 0.37   3.43 / 25
+ 70-0.5   20.82 + 0.39   3.11 / 45           20.91 + 0.19   1.97 / 45
+ 52.5     19.17 - 0.45   1.20 / 10           19.50 - 0.30   -.01 / 13
+ 35-.25   20.27 - 3.56   2.07 / 13           19.99 - 2.96   0.30 / 16
+ 20-.15   26.32 - 3.82   2.02 / 16           25.01 - 4.06   0.15 / 19
+ 10       33.57 + 2.00   1.76 / 18           32.22 - 0.09   -.16 / 23
+  5       38.67 + 10.5   1.58 / 20           37.83 + 6.84   -.40 / 24
+  1.5     44.55 + 32.0   1.27 / 21           43.86 + 26.2   -.71 / 25
+  1.2     46.65 + 49.4   1.08 / 20           46.14 + 41.7   -.90 / 25
+  1.1     49.88 + 68.4   0.79 / 21           49.66 + 56.6   -1.2 / 25
+  0-.5    52.13 + 12.7   0.35 / 21           63.87 + 8.36   -2.5 / 26
+  0-1.0   53.53 + 17.0   0.25 / 21           64.35 + 14.8   -2.5 / 26
+

At high mounting points, the perimeter plane offers slightly improved performance over a corresponding open radial system of 4 wires--up to about 0.25 dB over medium earth. This technique offers little advantage to HF operators, but could make a VHF plane vertical more compact. Why this technique is not used (besides a general failure to be aware of it) is subject to speculation. One might cite the feedpoint impedance. But that would lead us to suggest that the array of plane verticals available to the amateur community are being fed somewhat distant from their electrical centers in order to achieve a 50-ohm feedpoint impedance. since the plane is started at this point, the electrical center of the antenna may well lie in the plane, where radiation is self-cancelling.

+

At low mounting heights (less than 5 feet, but above ground), differences between the perimeter and the open-spoke 4-radial models are marginal, being in the main 0.2 dB or less. However, the feedpoint impedance-- especially the reactive component--of the perimeter model is subject to much greater increases as the antenna approaches the earth than open-spoke models.

+

With the plane below ground, the perimeter model equals or exceeds the open-spoke 4-radial model with respect to both the increases in reactance and the antenna's gain. Those who have limited property on which to place a radial system with 64 to 128 spokes may wish to investigate further the possibilities of a simple perimeter ground plane with spokes under 0.14 wavelength. Systems with 8, 16, 32, or any number of radials can be designed. However, the larger the number of spokes, the less the shortening factor for adding a perimeter wire.

+

Despite the potential for reader boredom, I have reproduced the entirety of the modeling result tables, rather than making spot comparisons. I have not noted every interesting feature of the emergent patterns. Nor have I made specific recommendations other than for further investigation into certain possibilities. Hence, you may find your own interesting results in them, including a decision to buy a Caribbean island as a mounting station for your next vertical antenna.

+

However, there is a distinct difference between the dimensions of the modeled radial systems and those in general use. Moreover, we have some remnant questions about the electrical centers of these antennas and their potential feed points. All of these matters suggest that at least one more exercise is in order.
+

+
+ +

+

Updated 5-22-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Return to Amateur Radio Page

+

Topics: HF Lower, MF, Vertical


+ + diff --git a/content/gp/gp5-1.gif b/content/gp/gp5-1.gif new file mode 100644 index 0000000..650a2ab Binary files /dev/null and b/content/gp/gp5-1.gif differ diff --git a/content/gp/gp5-2.gif b/content/gp/gp5-2.gif new file mode 100644 index 0000000..684965c Binary files /dev/null and b/content/gp/gp5-2.gif differ diff --git a/content/gp/gp5-3.gif b/content/gp/gp5-3.gif new file mode 100644 index 0000000..93de673 Binary files /dev/null and b/content/gp/gp5-3.gif differ diff --git a/content/gp/gp5.html b/content/gp/gp5.html new file mode 100644 index 0000000..fbdd500 --- /dev/null +++ b/content/gp/gp5.html @@ -0,0 +1,195 @@ + + + + + + Modeling Perspective on Ground Planes Part 5: Regional Differences + + + +
+

Part 5:
+ Regional Differences

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ From the tables in the last episode, it should be clear that when talking about vertical antennas, it is misleading to think that they are everywhere the same and that one account for all verticals leads to a clear set of expectations of them. The tables lead me to want to distinguish several regions of interest for vertical antenna investigators. There is nothing absolute about these distinctions, especially the lower ones, since antenna interaction with the lossy but conductive medium called earth changes with frequency. With that reservation in mind, let's tentatively distinguish the following regions. +

1. Subsurface plane: As the name implies, this region includes antennas with their planes below the surface of the earth--and, needless to say, their main elements above the surface.

+

2. Close to earth: We may loosely define this region as including about heights greater than zero up to about 0.07 to 0.1 wavelength. In this region, we find that antenna-earth interaction creates the greatest detuning of a free-space designed vertical antenna with a plane. The upper boundary is more a frontier than a line, just as "greatest" detuning cannot be defined as a distinct line.

+

3. Transition: 0.1 to 0.5 wavelength forms a region in which the gain of a vertical antenna drops precipitously with height decreases over lossier mediums, but descends in an orderly fashion over highly conductive media like salt water. Regardless of the medium in this region, the feedpoint impedance tends to meander.

+

4. Free Space: From 0.5 wavelengths upward, the properties of a vertical antenna with a plane (and vertical dipoles as well) most closely adhere to the properties of models in free space.

+

Let's see if we can summarize some of the features of each region, with attention to some distinctive phenomena that occur in each region.

+
+

Subsurface Plane

+
When the plane of a 1/4 wl vertical is below the surface, the feedpoint of the antenna begins to approach its "half-dipole" value of about 35 ohms. The more subsurface radials we add up to about 32 or so, the closer the approximation. (With salt water, we can achieve an even closer approximation with as few as 4 radials.) This situation most clearly approaches the perfect-earth and image-antenna picture that is fundamental to classic vertical antenna theory. +

Gain, which involves the quality of earth at a distance from the antenna, is another matter. To a considerable degree, it also depends on the size of the subsurface ground plane in terms of the number of radials. Literature suggesting that 64 to 128 radials yields the best gain coincides with the progression of models (which was arbitrarily cut off at 32 radials except for spot checks at 64 radials).

+

When the plane in question uses an open-spoke assembly of radials, unless the number of radials is very great, there will be only slight differences in gain between systems using standard 1/4 wl radials and those using lengths to create a "tuned" system. In fact. models suggest that especially with perimeter-wire systems, trimming the main element for resonance is not only physically easier, but electrically sound as well. The following table of antennas and their gain tells the story.

+

All antennas us a plane 0.5' under the surface and adhere to the models used previously: Main element = 2" dia. al.; radials = 0.25" dia. al.; Frequency = 7.05 MHz; medium earth (C=0.005 S/m; DC=13)

+ 
Gain      TO angle       Feed R         Feed X
+dBi       degrees        ohms           ohms
+
+4 Radials:
+free space design:  Main = 33.25'; radials = 35.6'
+-2.56     26             67.38          + 13.67
+radials resonated:  Main = 33.25'; radials = 10.8'
+-2.25     26             59.86          - 0.12
+main el resonated:  Main = 32.30'; radials = 35.6'
+-2.68     26             63.73          + 0.01
+
+8 Radials:
+free space design:  Main = 33.25'; radials = 34.5'
+-1.50     26             54.61          + 12.62
+radials resonated:  Main = 33.25'; radials = 12.6'
+-1.68     26             51.66          + 0.10
+main el resonated:  Main = 32.40'; radials = 35.6'
+-1.57     26             51.44          + 0.20
+
+16 Radials:
+free space design:  Main = 33.25'; radials = 34.5'
+-0.63     26             44.90          + 10.32
+radials resonated:  Main = 33.25'; radials = 15.0'
+-1.23     26             46.44          - 0.37
+main el resonated:  Main = 32.50'; radials = 35.6'
+-0.66     26             42.30          - 0.76
+
+4 Radials + perimeter wire:
+free space design:  Main = 33.25'; radials = 19.4'
+-2.48     26             63.87          +  8.36
+radials resonated:
+Note:  no resonant point shorter than 19.4' found
+main el resonated:  Main = 32.50'; radials = 35.6'
+-2.55     26             61.78          + 0.52
+

The 4-radial plus perimeter plane proved interesting because shortening the radials dropped the reactance to about 7.0 from which point it rose again with further shortening of the radials.

+

For all cases except the 4-radial open-spoke plane, resonating the antenna decreased the gain relative to the designs generated to resonate in free space. Shortening the radials to achieve resonance created a larger decrease in gain than shortening the main element. The decreases in gain occasioned by shortening the main element are largely academic and of no practical import.

+

For the 4-radial open-spoke design, shortening the radials actually produced a 0.43 dB increase in gain relative to the free space design. Whether this is achievable in practice with the radically shortened radials (-24.8') is unknown.

+

It is interesting to note that, even as an idle impracticality, the free space design yielded the highest gain of the variant models tested. It is tempting to suggest that the 1/4 wl subsurface plane vertical is essentially a non-resonant antenna.

+
+

Close to Earth

+
In the region below 10 feet at 7 MHz, but still above ground, we discovered that using more than 4 radials added little if anything to planed verticals. In the 5-10' region, where most amateur place their elevated radials, the feedpoint impedance was in the mid 30s with little reactance when a free space model was used as the basis for design. Although performance improves with the condition of the medium, mounting elevated radials over salt water for the low HF bands is normally impractical except on the largest ships. +

For this region of use, the perimeter plane is especially significant, since it shortens the wire structure needing elevation, adding to a relative freedom from safety and maintenance concerns. Initial and later adjustment is also eased relative to buried radials.

+

Although a full-size vertical dipole cannot be operated in this region, hatted dipoles certainly can. Below is a comparison among the standard open-spoke 4 radial vertical, the perimeter 4 radials vertical, and a vertical using hats on each end. The comparison is interesting:

+ 
Antenna             Main el   Radials   Gain TO angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi  degrees   R +/- jX ohms
+Bottom 10' off the ground
+4 radial vertical   33.25     35.6      0.02   22      30.36 - 4.48
+4 radials + per.    33.25     19.4      -.16   23      25.01 - 4.06
+30% dipole/hats     19.95     16.1      -.37   24      27.72 + 4.88
+
+Bottom 5' off the ground
+4 radial vertical   33.25     35.6      -.13   24      34.82 - 0.44
+4 radials + per.    33.25     19.4      -.40   24      32.22 + 6.84
+30% dipole/hats     19.95     16.1      -.75   26      33.42 + 17.1
+

Although the hatted vertical dipole needs a bit of design perfection, it is only down by about 0.6 dB from the better of the two competitors in this medium earth comparison. The hats, of course, may be replaced with perimeter hats with under 7.8' spokes. (See the section on "Free Space" below for reference to a commercial antenna using a similar technique.) All in all, we have not appreciated the place of hatted dipoles in the near-earth-mount vertical antenna category.

+
+

Transition

+
The region from 0.1 to .05 wl up is a transitional region in which antenna gain drops rapidly as the feedpoint height is decreased. It is also the lowest region in which one can mount a full-size vertical dipole. +

For the test frequency of 7.05 MHz, this region also host most verticals with drooping radials. Let us therefore compare briefly the vertical dipole, the drooping radial vertical, and the flat plane vertical. As usual, all antennas are 2" dia. aluminum main elements, with 0.25" dia aluminum radials. As a test, we shall compare the antennas over medium earth at heights of 35' (1/4 wl) and 52.5' (3/8 wl) up at the feedpoints. The sloping-radial models will use a 45-degree angle for the 4 radials.

+ 
Antenna             Main el   Radials   Gain TO angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi  degrees   R +/- jX ohms
+3/8 wl up
+Dipole              66.5'     ---       0.35   15      71.00 - 7.05
+Sloping radials     33.25     30.0      0.41   14      46.60 + 0.91
+Flat plane          33.25     35.6      0.73   52*     21.68 + 0.66
+
+1/4 wl up
+Dipole              66.5'     ---       0.11   18      97.89 + 3.14
+Sloping radials     33.25     31.0      0.39   17      56.16 + 0.60
+Flat plane          33.25     35.6      0.14   15      20.91 - 2.16
+

The vertical with the sloping radials (or the dipole with the split and spread lower end) shows a superiority to both the flat plane vertical and the vertical dipole in varying degrees ranging from small to very significant. At 3/8 wl up, the gain of the flat plane vertical is at a very high elevation angle, which is suppressed to a considerable measure in the dipole and sloping radial antenna. However, a significant secondary lobe remains at the higher angle.

+

When 1/4 wl up, the sloping radial vertical is superior to either of the alternatives, if for no other reason than the closer match to 50-ohm coaxial cable. Moreover, the elevation pattern, even though 3 degrees higher at maximum than its corresponding 3/8 wl antenna, is devoid of the high secondary lobe. Figure 5-1 overlays both patterns so that the reader can determine whether the secondary lobe is a help or a hindrance to intended operation.

+
+ +
+

It should be noted in passing that this transitional region is also the natural home to many forms of self-contained vertically polarized 1-wl wire loop antennas (including the half-square), all of which have bi-directional gain greater than any of the half wavelength antennas discussed here.

+
+

Free Space

+
+

From a half wavelength upward, plane verticals retain their free space characteristics at the feedpoint and show gain levels commensurate with their height above ground, regardless of the nature of the medium. Although gain over medium earth is less than that over salt water, the progression of gain figures is orderly, and the level of gain is in all cases useful. Moreover, the gain level of the antenna does not vary significantly with the number of radials.

+

As viewed from the perspective of free space modeling, the planed vertical is simply a hatted dipole. With a feedpoint impedance ranging from 20-23 ohms at resonance, the hatted dipole does not present the most favorable match to 50-ohm coaxial cable. However, this problem is easily solved is we remember that a dipole can be fed virtually anywhere along its length. As the feedpoint is moved well away from center, a slight adjustment may be necessary to re-resonate the antenna. For our hatted, this may be done either to the main element or to the radials/hat spokes.

+
+ +
+

In general, we have three options for feeding the hatted dipole: at the electrical center, usually called the base of the vertical; up the main element to a point where the feedpoint impedance at resonance is near 50 ohms; and off-center in the opposite direction. Figure 2 illustrates the options. Since we cannot easily feed all 4 radials (or 8, 16, 32, etc.) at the same time, we may simply lengthen the main element and shrink the radials until the desired point appears at the "base of the vertical." As we shall see, off-center feed yields a modicum of gain as a tiny bonus. Since we have seen that drooping radials add to the antennas vertical radiation, we shall also include versions of the 3/8 wl vertical with radials dropping at a 45-degree angle.

+

The following table provides a comparison among the three types of feed for free space and at a height of 1 wl (140' for 7.05 MHz). As always, we retain the 2" dia. al. main element and the 0.25" al. radials.

+ 
Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms
+
+4 Radial:  standard base feed:
+Free Space          33.25     35.6      1.38      ---       22.88 - 0.29
+1 wl up                                 3.24      24        23.01 - 0.04
+4 Radial:  feedpoint 55% from center
+Free Space          33.25     35.6      1.53      ---       49.24 - 0.25
+1 wl up                                 3.39      24        49.53 + 0.31
+
+4 Radial:  3/8 wl with base feed
+Free Space          45.00     13.6      1.88      ---       53.51 + 0.46
+1 wl up                                 3.45      24        53.75 + 0.86
+
+4 Radial:  3/8 wl with 45-degree drooping radials and base feed
+Free Space          45.00     12.1      2.06      ---       68.85 - 0.17
+1 wl up                                 3.59      24        68.99 + 0.37
+

Either of the off-center feed systems improves the design of the antenna. Since the basic 4-radial system may be shrunken by the use of a perimeter wire, I ran the same exercise on the basic antenna model.

+ 
Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms
+
+4 Radials with perimeter:  standard base feed
+Free Space          33.25     19.4      1.70      ---       20.76 - 0.60
+1 wl up                                 3.43      25        20.79 - 0.37
+4 Radials with perimeter:  feedpoint 55% from center
+Free Space          33.25     19.5      1.74      ---       47.50 + 0.35
+1 wl up                                 3.47      25        47.57 + 0.87
+
+4 Radials with perimeter:  3/8 wl with base feed
+Free Space          45.00     7.75      1.91      ---       51.30 + 0.30
+1 wl up                                 3.48      24        51.49 + 0.68
+
+4 Radials with perimeter:  3/8 wl with 45-degree drooping radials and base
+feed
+Free Space          45.00      7.80     2.08      ---       66.19 - 0.61
+1 wl up                                 3.61      24        66.33 - 0.09
+

Gains might well be greater over real ground at a different antenna height. With little effort, the feedpoint impedances of the drooping radial models can be altered to 50 ohms.

+

The antenna elevation pattern, which is the same for all the antennas excepting maximum gain, appears in Figure 3. Note the higher lobe and its ability to obscure gain at lower elevations. It is likely the at 2 wl the main lobe would show the free space gain improvement of over 1.2 dB.

+
+ +
+

As one last comparison, let's throw in the vertical dipole:

+ 
Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms
+
+Vertical dipole:  center feed
+Free Space          66.50     ----      2.13      ---       71.92 - 0.24
+1 wl up                                 3.53      27        71.34 - 0.63
+

Perhaps it is time to view the half wavelength dipole rather than the quarter wave vertical as the basic vertical antenna, especially at VHF, where inattention to dipole possibilities has limited antenna design. Since VHF antennas are used almost exclusively from 1 wl upward, application of these principles should be a natural development.

+

In addition, at any HF or VHF frequency, we may hat both ends of a dipole with little gain loss. The limiting factor tends to be the feedpoint impedance. As an example, here is a dipole 30% of full length with hats at either end and vertically oriented:

+ 
Antenna             Main El   Radial    Gain      TO Angle  Feedpoint Z
+                    L (ft)    L (ft)    dBi       degrees   R +/- jX ohms
+
+Vertical hatted dipole:  30% of full-length and center feed
+Free Space          19.95     16.1      1.70      ---       15.65 - 0.99
+1 wl up                                 3.56      28        15.46 - 0.91
+

The 4-wire open-spoke hat may be replaced with either a many-spoked version or a perimeter model to shrink the end arrays considerably. Versions for HF and VHF using a different end loading system are already commercially available (The ZR family from Force 12), with one model having been adjusted for near ground use.

+

Since the 3/8 wl antenna with the small drooping radials is both compact and quite superior to the quarter wavelength model, I suspect VHF designers may eventually discover it. In the interim, for VHF, take two quarter wavelength pieces of hardware store tubing, find some PVC for a center insulator and a mount for one end. Shove coax up the lower tube and attach to each side of the insulator-tube junction. Presto: instant vertical dipole (even if the older literature misnames it something else--which I won't repeat, since I try to avoid reinforcing misconceptions even by naming them). With 1" tubing at 2 meter, the feedpoint impedance will be closer to 50 ohms than to 70. Thanks to N6BT for reminding me that I forgot something here: the need to decouple with beads the feedpoint and a choke at the point where the coax emerges from the lower half of the dipole. Alternatively, you can use a PVC Tee and bring the coax out to the side for side-mounting to a pole or tower. (Schedule 40 and related PVC, although not UV rated, is quite durable, cheap, and easily worked--almost Tinker Toys for adults.)

+

Of course, there is nothing to prevent you from adapting one of the designs above to VHF use. Experimentation will be necessary, since there is a small but distinct discrepancy between these 7.05 MHz models, all done on NEC-4, and models done with MININEC--about 2.5%. At that size of discrepancy, and with limitations within both programs, it is not possible with home workshop building techniques to say definitively which is closer to the mark. However, the discrepancy is dimensional only and does not affect the progressions of data drawn from the models.

+
+

Conclusion

+
+

Free space design of flat plane verticals as hatted dipoles has proven its relevance from the very highest mounting altitudes to the very lowest. Perhaps the exercise has also given us some appreciation of the different characteristics of verticals as we move them up and down through the regions we have marked out for purely pragmatic reasons. Whichever may be our main interest, the exercise has been useful (at least to the writer).
+

+
+ +

+

Updated 5-26-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Return to Amateur Radio Page

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Topics: HF Lower, MF, Vertical


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Models with Buried Radials: A Small Compendium

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L. B. Cebik, W4RNL

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I have written a number of notes in the past on modeling verticals antennas with buried ground radials using NEC-4. Nevertheless, I still receive numerous questions about buried ground radials. It appears that most inquirers have read all but the one item addressing their question.

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So I thought I might combine a number of facets of modeled monopoles with buried radials into one note as a series of modeling tests. After developing our basic 2-MHz model of a near-resonant 1/4 wavelength monopole, we shall examine 6 different tests. In all tests, one of the variables will be the number of radials. I have chosen to use the geometric progression of 4-8-16-32-64-128 radials as the X-axis of virtually all graphs in this note, since it forms a logarithmic progression.

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With one exception, we shall be looking at 3 different properties of each monopole as a Y-axis variable: gain in dBi, the feedpoint resistance in Ohms, and the feedpoint reactance in Ohms. The remaining test variable will appear as different lines on each graph. Here are the tests that you will encounter in this note.

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  • 1. Radial wire size: 2, 4, and 8 mm diameter
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  • 2. Radial length: 0.15 through 0.40 wavelength in 0.05 wavelength increments
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  • 3. Radial insulation: separate insulation thickness and insulation permittivity tests
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  • 4. Monopole length: 0.20 through 0.60 wavelength in 0.1 wavelength increments
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  • 5. Soil conditions: Very poor, average, and very good soil
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  • 6. Frequency: 0.5, 1.0, 2.0, and 4.0 MHz
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For the last test only, we shall add one more survey: the field strength for a power of 1 kW at a distance of 1 km. The terms of this test should alert you to the fact that all measurements will be metric for the exercise.

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The Basic Model

Unlike NEC-2, NEC-4 permits the use of buried wires, that is, wires that both are at and penetrate Z=0. As a wire penetrates the ground level, there must be either a segment or a wire junction at Z=0, along with a number of other restrictions. For example, the Geometry End or GE command must use a value of -1 as its first entry so that the command indicates a coming ground specification and prevents modification of the current expansion in the core calculations. +

Because the monopole and the radials normally have different diameters, with the base of the monopole close to ground, setting up a radial system usually requires 1 or more sloping wires to reach the depth of the radials, with the remaining radial length specified as a level wire. The sloping wire system, shown in Fig. 1, also allows the modeler to use a reasonable number of segments per wire and to keep the lengths of all segments close to equal throughout the model.

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For the models in this note, the segment length is as close to 0.05 wavelength as is feasible in each case. For most models, we shall use a 2-MHz test frequency. I am not in this note interested in developing a 160-meter antenna, but the 2-MHz frequency is convenient for the geometric progressions that it allows with mostly integers. The monopole diameter is 10 mm (0.3937") by decision. That diameter is 5 times larger than the basic radial diameter (2 mm or 0.07874"), which itself splits AWG #12 and #14 wire diameters (0.0808" and 0.0641", respectively), the most commonly used radial sizes for amateur installations. AM BC work tends to use AWG #10 copper wire (0.1019" or or 2.59 mm).

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The radial system itself will consist of 3 wires per radial. The first 0.05 wavelength wire slopes from the monopole base to ground, while the second wire of the same length slopes from ground to the level at which the remainder of the radial lives. For simplicity, the monopole base will be above ground by as much as the radials are below ground: 0.15 m (or 5.91"). The actual ground depth for radials is an insensitive matter, and depths from 3" to nearly 2' yield essentially the same performance figures for models that are otherwise alike.

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Throughout the model exercise, I shall use the Sommerfeld-Norton ground calculating system available in both NEC-2 and NEC-4. This system has proven to be the most accurate so far committed to major antenna modeling software, although research continues in the effort to make ground calculations as precise as antenna structure calculations. The system is capable of replicating classic Brown-Lewis-Epstein results within fairly close tolerances, although it is not clear that the limits of the 1930s treatment are fully appreciated in all circles. NEC calculates the electrical length of the segments in the radial system according to the medium surrounding the wire, so the current distribution may vary from the same wires in a vacuum or dry air. For most tests, except the one in which I specifically vary the soil quality, the standard ground properties are a conductivity of 0.005 S/m and a relative permittivity of 13, the so-called average soil.

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For baseline models using a near-resonant monopole and 1/4 wavelength radials, the system just described allows maximum economy of segments while falling well within recommended limits for NEC-4 models and providing considerable flexibility for models calling for non-standard monopole or radial lengths. Indeed, only in a few special cases will we examine plots of the models, since they all look like the sample in Fig. 2. The only differences will be in the far field maximum gain and sometimes the TO or Take-Off angle (the elevation angle of maximum radiation). In all cases in which the TO angle is listed, it will appear as a theta angle, the angle from the zenith down to the TO angle. 90 - theta will give you the elevation angle in more familiar terms.

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The modeling process becomes much simplified by modeling the radials and the monopole separately. The radial models use a combination of rotational symmetry and Numerical Green's files to provide a very compact way of both describing the radials and storing the radial matrix data. The following sample specifies 8 radials. However, to specify 128 radials requires only 2 changes. In the GR line, change 8 to 128. In the WG line that stores the data, change the file name, again by replacing 8 with 128. The 3 GW entries describe the 2 sloping and 1 level wire for the first radial, while the GR line replicates the radial the desired number of times at equal angular intervals.

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+CM GRn 2-mm radials
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+GW 1 1 0 0 .15 7.5 0 0 .001
+GW 1 1 7.5 0 0 15 0 -.15 .001
+GW 1 3 15 0 -.15 37.47 0 -.15 .001
+GR 1 8
+GE -1 -1 0
+GN 2 0 0 0 13.0000 0.0050
+LD 5 0 0 0 5.8e7 1
+FR 0 1 0 0 2 1
+WG gr8-2.ngf
+EN
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Note the the .NGF file will also contain applicable ground, loading, and frequency information. For consistency, the ground values in the sample model remain the same in most tests. All radials use copper wire. The largest .NGF files (128 radials) require only about 440 KB, a fraction of the storage space required for a model that uses wire repetition or replication rather than symmetry for the radial system. The largest file requires under 10 seconds to create using a relatively slow computer.

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The companion final execution file is very simple, as the following sample shows.

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+CM 10-mm vertical monopole
+CM grn-m
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+GF 0 gr8-2.ngf
+GW 201 5 0 0 .15 0 0 36.515 .005
+GE -1 -1 0
+EX 0 201 1 0 1 0
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
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The geometry section begins by calling up the relevant .NGF file, followed by any additional structures. In this case, there is only a vertical monopole with its base at the hub of the radials. Since loading within the .NGF file does not extend beyond that file, the monopole for all test cases uses perfect or lossless wire. The monopole length is approximately the length of a resonant 1/4 wavelength monopole using a perfect ground. This measure gives us a reasonably automatic readout of how well each size of radial system approximates a perfect ground at 2 MHz with respect to the feedpoint impedance. Since the far field gain is largely a function of the uniform soil quality from the Fresnel region onward, differences in far field gain relative to radial system size give a measure of losses associated with sparse radial systems. The completion file also contains excitation and pattern request data, but uses the ground and frequency specifications from within the .NGF file. To call up a different size of radial system, simply modify the file name in the GF command.

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The use of .NGF files for the radials not only yields small and easy to read model descriptions, it also creates fast run times, even on a slow computer. The largest combination of long monopole and 128 radials requires less than a minute to run on a 400 MHz machine. The limitation of this system of performing large numbers of test models is that you must have access within your version of NEC-4 to the entire command set for the core.

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Test 1: Radial Wire Size vs. Number of Radials

A frequently asked question is whether the size of wires in a radial system makes any difference to monopole performance. Hence, it seemed reasonable to set up 1/4 wavelength radial systems using various wire sizes: 2, 4, and 8 mm in diameter. 2-mm wire is most common, but the progression should indicate something of an answer as to whether increasing the wire size will improve performance. The relevant data from the test runs appears in the table labeled Test 1. +
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There is a slight difference in gain using 128 radials over the 4:1 diameter ratio from the smallest to the largest wire: 0.05 dB. Where there are few radials, for example 4, the difference is larger: 0.22 dB. The situation is amenable to graphing to give a better sense of the differences along the way, as illustrated by Fig. 3.

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In no case does the improvement by using fat radial wires equal the improvement of doubling the number of radial wires. The net difference in gain for the thinnest wire in the set is 1.22 dB from a 4-wire to a 128-wire radial system. For the fattest wire, the difference is 1.05 dB. In no case does the TO angle vary from 67 degrees theta (23 degrees elevation). Hence, the use of very fat wires in a radial system may involve more work to handle the materials than it returns in performance benefits. As well, the increase even to 4-mm wire is impractical for non-commercial installations, since 4 mm is about 0.1575", just a bit smaller than AWG #6 wire.

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The feedpoint resistance information provides us with a snapshot of two different phenomena. First, the feedpoint resistance decreases as we raise the number of radials from 4 to 128. The amount of that difference averages about 12.5 Ohms for the 3 sample wire sizes. The ratio of the difference in feedpoint resistance for a given radal system size to the value for the largest filed provides us with an estimate of losses that we might eliminate by radial system improvements. Note in Fig. 4 that after we pass the 8-radial mark, the decrease is quite linear for all wire sizes.

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The second phenomenon to note is how close to each other the 3 wire sizes are with respect to the feedpoint resistance for any wire size. For 128 radials, feedpoint resistance varies by about 0.6 Ohms, while for the smallest field size (4 radials) the difference is under 2.7 Ohms when comparing the thinnest and the thickest wires.

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Charting the feedpoint reactance for each model provides a measure of how close to or far from resonance the antenna system is with each size of radial field. This chart (Fig. 5) provides only general guidance, since the model has limitations. The monopole length (about 36.4 m) derives from a monopole of the same diameter with a perfect ground. The model was brought to near resonance, defined for our purposes as within +/-j1 Ohm of reactance. In the models using a radial system, the base of the monopole is 0.15-m above ground at the hub of the radials. Hence, the monopole and its radial system together do not form a perfect analog of the initial model. However, for each of the 3 radial wire sizes, the model using 128 radials approaches resonance within the same +/-j1 Ohm reactance limit.

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The three chart lines parallel each other very closely with little difference between wire sizes. Beyond 16 radials, the approach to resonance with a fixed monopole length is nearly linear for all radial wire sizes. Once more we find that doubling the number of radials effects a greater improvement than doubling or quadrupling the radial wire size. However, keep one fact in mind: the radial fields for all increments are exactly symmetrical. To model non-symmetrical fields would require a wholly different type of model in which each radial receives individual attention. That work would need a wholly new study.

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Test 2: Radial Length vs. Number of Radials

The second most asked question about radial systems involves the length of the buried radials. Classic literature suggests that longer (than 1/4 wavelength) is better, while some recent literature suggests that shorter (than 1/4 wavelength) is better. So let's devise a small modeling experiment to see what NEC-4 might add to the array of suggestions. +

We shall use our 2-MHz, 10-mm diameter, near resonant 1/4 wavelength monopole over radial fields that use 2-mm diameter copper radials. The first variable, as always, will be the number of radials: 4 to 128. The second variable will be the physical length of the radials. The following table lists the tested lengths, recorded both as a fraction of a wavelength and in meters. In each test, as the radial length grew, so too did the number of segments so that the physical length of each segment remained relatively constant.

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+Radal Lengths Tested with a 1/4 Wavelength Monopole over Average Ground
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+Length  Wavelengths     Meters
+          0.15          22.48
+          0.20          29.98
+          0.25          37.47
+          0.30          44.97
+          0.35          52.46
+          0.40          59.96
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The results of the test runs yielded the table of values labeled as Test 2.

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One of the more interesting results emerges from the portion of the table recording the gain of the monopole. All gain values are for a TO theta angle of 67 degrees (23 degrees elevation). The pattern shows itself clearly in Fig. 6. For small radial fields, such as 4 or 8 radials, there is virtually no difference in system performance, regardless of radial length within the limits of the test runs. However, gain differences begin to appear as we increase the number of radials. By the time that we arrive at the largest field, we find over 3/4-dB difference in gain as a function of radial length.

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Radial length makes very little difference to the feedpoint resistance, although the pattern shown by the gain graph also holds for the resistance graph, at least for radials up to 0.25 wavelength. Above that radial length, the values form a nearly random pattern of crossing lines. See Fig. 7.

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The effects of radial length on the resonant frequency of the system, as recorded by the feedpoint reactance values, are quite small. Fig. 8 displays the tightly grouped curves as we change the length from 0.15 up to 0.40 wavelength. With only 4 radials, we find virtually no difference in the reactance values. At 128 radials, there are graphically visible differences, but the total range is only about j5 Ohms. It is likely that for any given design, construction variables will create a larger variability.

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Although NEC calculates the electrical length of the segments based on the medium within which the wires are situated, the longer electrical lengths do not results in radial resonances or other phenomena that yield significant variations in current distribution. In general, as shown in Fig. 8a, the current shows its highest radial values within the first 0.1 wavelength as measured from the radial hub. The current patterns shown in the 3 sample graphs use red for the highest value, in this case approaching 5E-4 A. The lowest value--approached by the blue portions of the radial lines is 2E-4A. The 3 radial fields are not to scale, but the intermediate colors indicate the length of a segment on each radial. One might increase the number of segments per radial for a more sensitive readout, but the general trend is clear from the simplified treatment of these graphs.

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The conclusion that we might draw from the exploration of radial lengths is that the larger the number of radials, the greater the advantages of using radials at least up to 0.40 wavelength. However, even with 128 radials, the 60% length increase between 0.25 wavelength and 0.40 wavelength radials yields only about 1/3-dB additional gain. Hence, the models suggest that the increase in radial length for a large radial field may not be very cost- and effort-effective. As the number of radials decreases, the advantage of longer radials disappears.

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Test 3: Insulated Radials vs. the Number of Radials

Another frequently asked question concerns the use of insulated radials in place of the more common bare-wire radials. The builder's thought involves the lifetime of the radial, based on the assumption that insulated radials are better protested from wire-consuming effects of the soil in which they are buried. The question that remains is whether the insulation has any significant effect on the performence of the radial field as measured by overall system performance. +

To see what NEC-4 might report about insulated wires, I created 2 tests in accord with the 2 major variables involved in the use of insulated wires. For both tests, I retained the same 1/4 wavelength 10-mm diameter monopole with fields of 2-mm diameter copper radials that are a physical quarter wavelength buried 0.15 meter in average soil. As usual, the field sizes ranged from 4 to 128 radials.

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Technically, there are 3 variables associated with wire insulation. The first is the insulation resistance. Modern plastic insulations have very high resistance values, far higher than would show any effect on overall insulation performance. So I set the conductivity value at 1E-10 S/m for all test runs. This move left us with the insulation thickness and the insulation's relative permittivity as variables.

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For the thickness test (3a), I chose a permittivity value of 2.5, which is about midrange in the general span of current wire insulations. Then I used insulation thicknesses of 0.5, 1.0, and 1.5 mm to surround the 2-mm wire at the center. The resulting total diameters were 3-mm, 4-mm, and 5-mm for the test wires.

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To test the effects of the insulation's permittivity (3b), I used a 2-mm diameter wire covered in insulation that is 1-mm thick, resulting in a 4-mm diameter wire assembly. Since the general range of plastic-based insulation is 2.0 to about 3.0, I tested the assembly with permittivity values of 2.0, 2.5, and 3.0. The center values for each test are the same, allowing us a frame of reference to see the variations occasioned by each variable. The results of the test runs appear in the table marked Test 3.

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We shall not try to present any graphs of the resulting data, because we would end up with a single blurred line for both test 3a and test 3b. There is no significant variation in the gain, the feedpoint resistance, or the feedpoint reactance over the range of each test. The tiny variations that do occur are associated mostly with the smallest number of radials, where the gain range is about 0.1 dB maximum. Values of feedpoint resistance and reactance fluctuate in a tiny meander that has no practical significance.

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The results of these tests suggest that the use of insulated wires for radials--over the range of common insulation values--has no significant effect upon the performance of a quarter wavelength monopole over quarter wavelength radials. Hence, for an amateur installation, the selection of wire for the radial set may likely continue to be a matter of what is convenient and economical to obtain. As with all of the tests so far, the number of radials has an effect that outstrips all of the variables that we have so far examined.

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Test 4: Monopole Length vs. the Number of Radials

Test 4 changes the trend as it examines monopole length in relation to the number of radials. In this set of tests, all radial systems will use 1/4 wavelength radials with a 2-mm diameter. The vertical radiator will be 10-mm in diameter. However, we shall vary its height from 0.20 wavelength to 0.60 wavelength in 0.10 wavelength increments. Because the test parameters require us to change the vertical monopole height in a uniform manner, none of the heights will replicate the performance of the near-resonant radiator used in other tests. All monopoles use the same segment lengths and the source or feedpoint is the lowest monopole segment. +

The test results appear in the table labeled Test 4.

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The feedpoint resistance and reactance listings are present as a reference. The wide divergence of the values prevents effective graphing, since variations within each monopole lengths would not show up as the number of radials increases. However, the feedpoint resistance does show a reverse trend for some lengths and a bit of meandering for other lengths. A similar meandering is also apparent in the values for the feedpoint reactance. The moderately high inductive reactance for the 0.5-waveloength monopole shows that--with the 1/4 wavelength radials--the antenna has not quite reached an electrical height of 0.5 wavelength.

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Perhaps the most interesting facet of this test series is the list of gain values for the individual heights. In this case, a graph is both possible and illuminating. See Fig. 9.

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The chart shows more than one interesting trend. As the monopole grows longer, the models show less and less increase in gain with the increasing number of radials. For the 2 longest monopoles (0.5 and 0.6 wavelength), there appears to be no clear relationship between the gain value and the number of radials. Across the range of radials, the 0.5 wavelength monopole gain varies by only 0.08 dB, while the 0.6 wavelengthmonopole gain varies by 0.18 dB. In contrast, the gain of the shortest monopole varies by 1.65 dB as we increase the number of radials from 4 to 128.

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The chart shows the TO theta angle of the individual monopoles. The listed angle remains constant across the full span of radial numbers. Translated into elevation terms, the taller the monopole, the lower the elevation angle of maximum radiation. Fig. 10 shows some sample patterns.

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The secondary upper-angle lobe of the pattern for the 0.6 wavelength monopole is interesting when we realize that there is essentially no gain difference between the 0.5 and 0.6 wavelength antennas, even with 128 radials. Over a real ground (average in this test sequence), monopoles between 0.6 and 0.7 wavelength do not show the gain advantage that accrues to theoretical calculations that use a perfect ground as a foundation. Fig. 11 shows the patterns for 1/4, 1/2, and 5/8 wavelength monopoles over perfect ground. The maximum gain for the shortest monopole is just above 5.1 dBi. The half wavelength monopole achieve about 6.9 dBi. The 5/8 wavelength monopole reaches a value just over 8.1 dBi. Hence, in theory, the 5/8 wavelength monopole should show a 3-dB superiority to the 1/4 wavelength monopole, with a 1.25-dB advantage over the half wavelength monopole.

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Over real, lossy grounds, the difference between the 5/8 wavelength monopole over the 1/4 wavelength version drops to about a half-dB. There is no significant difference between the gain of a 1/2 wavelength monopole and a 5/8 wavelength monopole over real ground. However, the 1/2 wavelength monopole has a clean, single-lobe pattern without the high-angle lobe. For this reason, many BC engineers remain at the 1/2 wavelength level to avoid any untoward consequences of having secondary lobe radiation. At VHF and UHF, amateur installations may use a 5/8 wavelength radiator with an elevated ground plane in order to place the monopole region of highest current and maximum radiation at a slightly higher position--enough sometimes to clear portions of the vehicle or other metallic objects in the immediate region of the antenna.

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A ground radial systems may in fact perform other functions than just completing the radiating antenna structure. Many, if not most, installations require a matching network at the antenna terminals. A large radial system provides a very low impedance ground path for the network relative to a power source installation--which often may fall within the overall radial field. The radial system may serve as the overall RF ground or as a supplement to large bus or strap connections among elements of the power distribution and matching system. This facet of radial system functioning does not show up in the models within this sequence of tests.

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Test 5: Soil Conditions vs. the Number of Radials

For tests of various soil conditions, we may return to our quarter wavelength 2-mm radials and our near-resonant 10-mm diameter vertical radiator. At the 2-MHz test frequency, the variable will be the soil quality. We shall only sample the range of soil qualities, using our average or good soil as a center point. + 
+Soil Qialities Used in Test 5
+Label             Conductivity       Relative Permittivity
+Very Good         0.0303 S/m         20
+Average           0.005 S/m          13
+Very Poor         0.001 S/m           5
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As the brief table suggests, the conductivity of the average soil is nearly the geometric mean between the conductivities of very poor and very good soil. (The actual geometric mean is 0.0055.) The permittivity of average soil is very nearly the arithmetic mean between the values for very good and very poor soil. (The actual arithmetic mean is 12.5.) Under these test conditions, we ought to see clear differences among the performance values produced for each soil condition. As well, we ought to see clearly the effects of using the range of radials included in the test sweep. The results of the test runs appear in the table labeled Test 5.

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The test models show significant differences not only in the gain for each soil quality, but as well in the TO theta angle, listed in the table. Fig. 12 overlays the elevation patterns, showing the differences in relative strength and shape. The patterns use 128 radials. The higher elevation angles for the progressively poorer soils appears clearly in the graphic.

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With respect to far-field gain, as shown in the table and in Fig. 13, soil quality has more to do with the gain value than does the number of radials in the ground system under the antenna itself. The worse the soil, the wider the gain range within the span of the radial fields sampled. Very poor soil produces a difference of over 2.6 dB between 4 and 128 radials, whereas average soil produces a difference of about 1.2 dB. Very good soil shrinks that difference to 0.5 dB. However, the worst gain for the smallest radial system over average soil is nearly a full dB greater than the best value for the largest radial field with very poor soil. Likewise, the worst gain for the smallest radial system over very good soil is well over a full dB greater than the best value for the largest radial field with average soil.

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Feedpoint resistance is a reasonable indicator of the losses occasioned by soil quality. Again, the spread of values between a 4-radial field and a 128-radial field suggest the effects of soil. For very poor soil, that spread is over 40 Ohms. Over average soil, that spread drops to 14 Ohms, while over very good soil, the differential is only 6 Ohms. Nevertheless, as we increase the size of the radial field, the feedpoint resistance converges toward 40 Ohms. Fig. 14 shows the curves.

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One reason that the 3 curves of feedpoint do not fully converge is that fact that the monopole used in all cases is the same height, rather than being tailored to each soil condition. We find a similar situation with respect to feedpoint reactance, as illustrated by Fig. 15.

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In this case, it is the line for very poor soil that crosses the nearly parallel lines for the other two soil qualities used in this test sequence. Very good and average soil show spreads of about j50 Ohms for the range of radial field sizes, whereas the worst soil in the study shows a span of about j70 Ohms.

+

The values shown in this test sequence may be more reliable relative to reality for the feedpoint resistance and reactance than for the far-field gain. NEC assumes a uniform soil quality for both the immediate vicinity of the antenna and the more distant regions. In some areas, the region where principle reflections occur to form the far-field pattern may differ from the immediate vicinity of the antenna. However, in most cases measurements are confined to the immediate area occupied by the radial field. (In non-critical cases, these values may simply be lifted from existing tables for a region.) Nevertheless, these tests--and similar ones that might be performed using smaller increments between soil quality classifications--suggest that the ground quality may have as much to do with monopole performance as the radial field size. Indeed, the most evident trend is that the worse the soil, the more important it becomes to use a radial field size that allows the antenna to achieve its best performance for that soil. As well, while we normally cannot alter the soil quality under and around our antennas, we can make changes in the size of the radial field--at least until we hit a practial upper limit.

+

Test 6: Frequency vs. the Number of Radials

+

A less frequent but significant question often posed about models relates to frequency. Most sample modeling, such as the set of tests that we have so far run, use a constant frequency. However, from one set of sample runs to another, the test frequency may change, all for good reason within the context of each set of sample runs. Very often, without sufficient experience, a reader cannot correlate the results of one set of models with another set's output. What these readers do not fully appreciate is the fact that the losses due to soil quality are frequency specific.

+

To sample this phenomenon, I scaled the basic test model for 2 MHz up to 4 MHz and down to 1 MHz and 0.5 MHz. The basic system uses a 10-mm diameter near-resonant monopole and 2-mm 1/4 wavelength radials. Each scaled version uses the same proportions for both length and diameter of the system elements. As well, the sloping portions of the radial model were scaled to maintain the same proportions as the basic model and to ensure that all models used the same number of segments per radial, regardless of frequency. All tests used the standard, that is, the average soil quality constants.

+ 
+Dimensions of Test Models for Frequency Checks
+Frequency           Monopole                  Radial
+   MHz         Length      Diameter     Length      Diameter
+   0.5         146.06 m    40 mm        149.88 m    8 mm
+   1.0         73.03 m     20 mm        74.94 m     4 mm
+   2.0         36.515 m    10 mm        37.47 m     2 mm
+   4.0         18.2535 m   5 mm         18.735 m    1 mm
+
+

To the usual catalog of gain and feedpoint values, I added a new category that may be useful in the context of the frequency tests: field strength using a power of 1 kW at a distance of 1 km from the antenna at ground level. The listed values appear at the bottom of the table labeled Test 6.

+
+ +
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As we change frequency, we obtain variations in both the maximum far-field gain and the TO theta angle. As the frequency increases, the elevation angle of maximum radiation also increases, as shown in the right-most column in the gain listings. However, regardless of the radial field size, the angle does not change for any of the test frequencies. Reflections that are crucial to far-field formation, of course, occur beyond the limits of the 1/4 wavelength radial systems used.

+

As we raise frequency, the maximum gain of which a near-resonant monopole is capable decreases, as shown both in the table and in Fig. 16. As well, as we raise the frequency, the greater that we find the difference in gain between the limits of the radial field sizes. At 0.5 MHz, the difference is only about 0.6 dB between 4 and 128 radials. However, at 4 MHz, the difference increases to nearly 1.8 dB. The difference increases with each frequency doubling, but not either in a strictly linear or a strictly geometric manner.

+
+ +
+

As an indication of the higher soil losses with increased frequency, we may examine the feedpoint resistance data, shown in Fig. 17. The higher the frequency, the more dependent the antenna system is upon the number of radials in order to approach the lowest feedpoint resistance. Otherwise expressed, the higher the frequency, the greater the spread of feedpoint resistance values between 4 and 128 radials.

+
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+

Feedpoint reactance, however, does not show the same trends as feedpoint resistance. As Fig. 18 illustrates, the reactance curves form a tight bunching with only a slight divergence at the level of the largest radial fields. I this regard, the reactance values are a measure of the accuracy of the frequency scaling, with allowance for the skin effect changes with frequency for the copper radials.

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As an added exercise, I performed ground-wave modeling calculations for each model in the sequence. I specified a distance of 1 km at ground level for each calculation. The standard excitation for each model was 1 V peak. I recorded the input power to the antenna as well as the field strength calculation in peak V/m. The square root of the ratio between the desired power (1 kW) and the recorded power gives us a multiplier to adjust the original field strength reading to the values corresponding to the uniform power level. (Since the feedpoint resistance changes for each model in each sequence, the model's input power will also change. Hence, the post-run calculation is necessary to obtain field strength values for a uniform power level. Some software has this facility built into the overall program structure.) Fig. 19 provides a graphical view of the resulting field-strength values.

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The graph provides an illustration of a principle often passed over hastily in texts and handbooks: as we increase frequency with a vertical antenna, the ground wave grows increasingly weaker at an exponential rate. NEC calculates the sum of surface and point-to-point waves. At the frequencies sampled in this test, it is the surface wave that diminishes most rapidly. Two of the frequencies of this test series fall in or very close to the AM BC band. Although the field strength differences are less at these lower frequencies than at the higher frequencies in the tests, they do show significant differences (about 8% with 128 radials).

+

As we increase frequency by doubling, the difference between readings at the extremes of the radial field sizes grows more pronounced. The difference as a percentage of the median field strength value increases nearly linearly as we move upward from one frequency to the next, growing by about 5% per frequency jump. At 1 MHz, the spread is under 10% from 4 to 128 MHz, while at 0.5 MHz, the spread is closer to only 5%. As a consequence, the lower the frequency, the more difficult it is to determine potential radial field degradation over time via field strength readings. An initial 128-radial field established to the strictest standards might degrade to a field equivalent to half or a quarter of the initial size with only a 2% drop in field strength at 1 MHz. This simplistic calculation, of course, presumes uniform degradation. Selective degradation of areas of the field may produce non-uniformities in the field of a single radiator. For multiple-tower arrays, determining the differences between selective field degradation pattern distortions and field distortions emerging from other sources (such as incorrect power distribution among the array towers) may prove to be an immense challenge.

+

The End of the Beginning

The sequence of tests in this brief compendium is designed to provide some answers to questions that have been posed to me, mostly by amateur radio operators. That question source provided the basis for setting the basic test frequency at 2 MHz: a nice round number that is also close to the 160-meter MF amateur band, where ground radial systems are matters of considerable concern. The basic question, often posed in other words to avoid transmitting a sense of either penury or laziness, is this: how few radials can I get away with and still have a maximally effective system? As we have seen, the answer is not simple. The span of tests that we have modeled suggests that for the common 1/4 wavelength monopole over average to poor soil, the number of radials in the field may be the most significant factor in reducing losses and improving performance. +

However, these modeling tests only illustrate some principles and do not provide final answers to the challenges of specific situations. As well, we have not run all of the tests for all of the possible interesting frequencies and physical arrangements we might generate as possible solutions. For example, we might develop models that sample radial lengths and monopole lengths together to find the best combination. We might also sample the effects of soil conditions that change at some specified distance from the monopole. In short, this brief collection of tests is a beginning and not an end to the development of a better understanding of the performance of monopoles and their associated radial systems. Finally, of course, we have not at all addressed the conditions surrounding phased arrays of towers with highly complex radial systems.

+

Nevertheless, these notes have attempted to address in one place a collection of questions frequently posed to me over the years. I hope the modeling data is useful as a start toward answering some of them.

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Updated 08-31-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: HF Lower, MF, Modeling, Vertical


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Notes on Hatted Vertical Dipoles for 10 Meters

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L. B. Cebik, W4RNL

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+

The search for compact antennas--especially vertically polarized antennas--has taken many turns. However, one of the simplest and cheapest to construct is the vertical dipole with so-called "capacity hats" on each end. Let's look at what is involved in designing and building such an antenna. The design is based on others that I have built, including horizontally polarized 2-element Yagis.

+

The dipole will be shorter than normal, and the hat assemblies provide the missing length to bring the dipole to resonance. Formerly called "capacity hats," it is now recognized that the terms grew out of a very loose calculating analogy and has no literal meaning relative to relevant antenna properties. In fact, the analogy produces results that are accurate only at VLF and LF. Several years ago, I developed a correction program for calculating hats for 4, 6, and 8 arms or spokes, with and without a perimeter wire, for HF (included with HAMCALC by VE3ERP). I have designed several antennas and arrays using vertical dipoles with hat assemblies. The 10-meter that we shall examine is simply a modified scaling of 40- and 30-meter models.

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Fig. 1 shows several different styles of symmetrical hats that we may use. Note that we can use a number of spokes, a set of spokes plus a perimeter wire, or even a flat solid disk. We rarely use solid disks below the VHF range, because they tend to trap wind. A spoke system lets the wind pass through, almost unobstructed.

+

For a given shortened dipole length and a given frequency, the required length of the spokes/arms needed to bring the assembly to resonance depends on a number of variables. Foremost is the number of spokes. As the number of spokes increases, their required length decreases. In the vicinity of 64 radial spokes, the assembly approximates a solid disk. For any given number of spokes, if we add a perimeter wire, the spoke length decreases. The amount of decrease, relative to the length required without a perimeter wire, is close to (but not exactly) 1/2 the distance between spoke tips. As we approach the spoke limit of about 64 radials, the spoke lengths approach each other relative to the two types of assemblies. Intermediate perimeter wires--say halfway out each spoke--may serve mechanical functions but do not materially affect the required spoke length. Fig. 2 will give some indication of the relative curves for hat system with and without perimeter wires. Each entry is for a resonant 3-MHz vertical monopole, but the same principles of hat structures apply equally to monopoles and to dipoles. In fact, one may design a hatted dipole by first modeling a monopole and then simply tacking two of the resulting designs together at the feedpoint.

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The required length for the spokes also depends upon the ratio of the main element diameter and the spoke diameter. The current at the junction of the main element and the spokes divides into the individual spokes arithmetically. However, the actual current level in the section of main element immediately adjacent to the spokes will vary somewhat according to the circumference of the main element vs. the sum of the circumferences of the spokes. Hence, dimensions modeled for one set of elements may require change with changes of element diameters.

+

The spoke-and-perimeter structure of the hats that we have examined so far is not the only way to create a symmetrical hat. We may also use a spiral structure, such as the one outlined in Fig. 3. Note that not just any spiral will do. The 4 spiral arms all originate at the element and maintain complete symmetry at every point. A square shape is just a modeling convenience. Many applications--especially at VHF and up--may use continuous spiral curves.

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As one shortens a dipole by any means of loading, the feedpoint impedance decreases. A true symmetrical hat assembly yields the highest impedance for any type of loading with a fixed overall length. There are studies of various types of loading for a half-length monopole for 80 meters that will demonstrate this fact. As well, a true symmetrical hat assembly preserves the widest possible bandwidth of all loading means (except, of course, resistive loading, which is not relevant here). Finally, a true symmetrical hat assembly yields the highest gain level, since it preserves the distribution of current along the dipole up to the end, with the decreases associated with the tip region falling on the radiation-canceling hat assembly.

+

Because the net radiation from the hat assembly is negligible due to field cancellation, a hatted assembly will model accurately in both NEC and MININEC. NEC's weakness relative to angular junctions of wires of different diameters does not apply to situations where there is field and radiation canceling. However, if one wishes to model spokes with one diameter and a perimeter of another diameter, problems may arise in NEC, although they will generally be slight.

+

For further background on the subject of hats, you may wish to see one or more of the following items at my web site:

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The subject antenna, shown in outline form in Fig. 4, was modeled in NEC-4. It consists of a main element 79" long with a 1" diameter. The spokes and perimeter wires are AWG #12. The spokes or arms are 24" long, resulting in a 4' corner-to-corner dimension or a side dimension of about 34". There is a reason for the selection of these dimensions.

+

For any dipole diameter, the feedpoint impedance will decrease as we shorten the dipole. To hold resistive losses at the feedpoint to a minimum, it is usually wise to use an impedance in the region of 25 Ohms as a practical minimum. This value is also convenient, since one may make a matching system for a 50-Ohm coax feedline from parallel 1/4 wavelength sections of 70-75-Ohm cable.

+

The subject antenna's 79" length with a 1" diameter provides the requisite 25-Ohm impedance at resonance, as determined by the dimensions of the hat assembly. The hat assembly will grow smaller if we add further radial spokes, but the impedance of the dipole will not significantly changes with such changes in the hat. (There will be very small length changes due to the current distribution and division situation described above.)

+

The free-space gain of the antenna is 1.82 dBi, about 0.3 dB less than a full size dipole. This is for a length comparison of 79" for the hatted version and about 200" for a full size version. Over ground, the gain is 0.57 dBi at 20 degrees elevation angle with a 5' base height and 1.19 dBi at 16 degrees for a 10' base height. Fig. 5 shows the elevation patterns for the 2 heights.

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With a 37-Ohm matching section, the free-space model of the antenna supplies the 50-Ohm SWR curve shown in Fig. 6. The 50-Ohm resonant impedance at 28.5 MHz changes to 42 + j 3 Ohms if the antenna base is 5' above average ground and to 54 + j 3 Ohms if the base is 10' above average ground. The basic SWR curve shows that there is adequate room for displacement for these different positions of the antenna while sustaining an SWR well under 2:1.

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+ +
There are as many ways to construct a vertical dipole as there are builders. Fig. 7 shows one simple way to pre-solder a 4-arm hat assembly from #12 copper wires and then to attach it to the main mast--both top and bottom--with hose clamps. Use one of the bi-metal protective compounds where the copper meets the aluminum. The hose clamp should be stainless steel throughout. The use of the hose clamp mounting system permits you to adjust the exact position of the hats as a means of adjusting the center frequency for maximum band coverage. +
+ +
+

Of course, you may choose to use aluminum tubing or wire for the structure to avoid bi-metal contacts. However, fastening the corners at the spoke and perimeter-wire junctions may become more complex.

+

Ideally, the 1/4 wavelength matching section should come off the feedpoint at right angles and meet a 1:1 choke balun--perhaps a W2DU bead choke--and continue at right angles to the vertical for as far as possible. You may wish to try running the 1/4 wavelength matching section down the lower section of the dipole. However, depending on a number of situational variables, you may find it more difficult to eliminate currents from the braid of the main coax line. For a short (5') mast, Schedule 40 or 80 PVC is very good--if it is adequately UV protected in your area. A 10' mast is likely to call for a section of TV mast. You can create the needed spacing and insulation between the antenna element and the support mast with a series of PVC screw couplings.

+

The footprint and volume of the antenna puts it in the small category. The height (under 8' or less than 1/8 wavelength) make it easy to hide in restrictive neighborhoods. You can even work out a mounting so that you can raise it to about 20' and use it horizontally. A hand-rotated horizontal dipole can work the world when 10 meters is open.

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Updated 01-14-2003. © L. B. Cebik, W4RNL. This item appeared in AntenneX, December, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Dipole, HF Upper, Loading, Vertical


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+ Where Do I Hang My Hat?

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L. B. Cebik, W4RNL

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Since my first study in "capacity hats" ("Modeling and Understanding Small Beams: Part 8 Capacity Hats," Communications Quarterly [Fall, 1997], 61-79), a number of questions have come my way. One of the more recent ones is where to place a hat for maximum efficiency (electrically). The answer to the question is quite brief. However, making the answer believable requires an understanding of hats in general. In order to develop an trustworthy answer via modeling on any of the version of NEC or MININEC, let's start by summarizing what may be inaccessible because the original article is not at hand.

+

Some Hat Basics

1. Capacity is irrelevant to hats. The name "capacity hat" arose from a technique of approximating their size with VLF and LF antennas. However, this technique breaks down at HF, where the main element diameter becomes a significant percentage of a wavelength in size and departs too far from the conical section presumed in the calculation scheme. There are numerous "fixes" on the scheme, including one in HAMCALC for which I am responsible, but these contain many ad hoc factors and yield limited accuracy, even when the range of variation is severely limited. +

2. A hat is an extension of the antenna element. As such, one can read the current curve in continuity with the remainder of that curve on the main element. Depending on the hat structure, the current may divide, but the sum of the individual currents in the hat segments immediately adjacent to the last main element segment is the natural continuity of the main element current curve.

+

Consequently, the simplest and yet most adequate view of a hat is as a simple mechanical extension of the main element.

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3. Hats come in two general types: symmetrical and non-symmetrical. As shown in the figure, the physical size of each type of hat need not differ to achieve the same goal of bringing a given antenna element to resonance (or to some other specified condition). However, the operation of the two types of hats is quite different.

+

A non-symmetrical hat provides a single current curve extending from contact with the main element to its end. For variations of shape, see Half-Length 80-Meter Vertical Monopoles: the Best Method of Loading Parts 1-5. The simplest non-symmetrical hat is very likely the inverted L, where the upper horizontal portion of the antenna brings the vertical portion to resonance, but supposedly adds little to the desired pattern. However, as any model will show, the upper portion does radiate and thus has an influence on the overall far field pattern of the antenna.

+

Symmetrical hats have structures the sum of whose parts yields a cancellation of virtually all radiation. Therefore, they do not contribute more than negligibly to the radiation pattern of the antenna. The main element essentially supplies the far field pattern shape and strength.

+

4. Of all hat structures and other loading schemes applied to shortened antenna elements, symmetrical hats provide a. the highest gain, b. the highest source impedance, and c. the widest operating bandwidth for both performance characteristics and source impedance. The 80-meter monopole study is a good reference for seeing the relationship of symmetrical hats to various non-symmetrical alternatives with respect to all three categories of antenna properties. However, the following graph can give some indication of the symmetrical hat's superiority to other loading schemes.

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The graph shows the results of modeling 4 antennas. One is a full size monopole over perfect ground, about 78.75' long. The graph carries out the current magnitude curve only to the 60' point, which is the length of the other 3 loaded elements. The full size element, of course, has a current magnitude curve that continues to descend toward a value of zero at the end, and these further portions contribute to the radiation. The shortened elements terminate at the 60' mark.

+

The current in the symmetrical hat model closely parallels that of the full size antenna up to the 60' point, and in fact slightly exceeds the current of the full-size element at the 60' mark. The mid-element inductively loaded model uses a lossless load. However, the load (253 Ohms) represents a replacement of the main element that would have radiated with a high current magnitude had it been linear. Beyond the load, the element shows a rapid drop in current and a current magnitude curve similar to that appropriate to the low-current-magnitude outer end of a full-size element. The base or source loaded element begins with a rapid drop in current magnitude and descends from that point, even though the load is about half that of the mid-element load (137 Ohms).

+

The performance of the various models, all with 2" aluminum main elements and referenced to perfect ground, can be seen in this table:

+ 
Model               Gain (dBi)          Source Z (R +/- jX)
+Full-Size           5.14                36.0 - j 0.1
+Hat Load            5.06                31.7 - j 0.1
+Mid-XL Load         4.99                25.0 - j 0.5
+Base-XL Load        4.97                16.7 + j 0.2
+

Of course, both forms of loading with inductive reactance would show additional losses once a finite Q is assigned to the inductors. The lesser gain of the reactively loaded elements in these lossless inductor models relative to the hat-loaded element is solely due to the position of the loads and their replacement of high-current magnitude element areas with low-current magnitude areas. Hat losses are already included in the material losses (aluminum) of its structure. It is the superiority of performance promise that brings designers back to the hat as a means of loading shortened elements, despite the obvious mechanical difficulties of implementing this means of loading on either vertical or horizontal elements.

+

Modeling Considerations

For many, drawing conclusions from models--even the latest NEC-4 method-of- moments models--is a bit tenuous. Therefore, it may be useful to review the modeling considerations involved in working with hats. +

1. Both NEC and MININEC models coincide with each other and with reality. For adequately segmented models, I have seen at most a 2% variance in hat sizes between NEC and MININEC models. Both, in turn, have yielded physical specifications for resonant vertical (monopole) and horizontal (dipole) antenna elements that are well within the normal variances encountered in antenna construction.

+

Although both NEC-2 and NEC-4 usually show erroneous results when there are angular junctions of wires having dissimilar diameters, this problem tends to disappear when the radiation field from one of the elements or element sets is self-canceling. Symmetrical hats meet this requirement. Moreover, even non-symmetrical hats, where there is considerable radiation cancellation due to the physical layout, provide usable guidance in the construction of a physical version of the model.

+

Consequently, NEC and MININEC models are generally trustworthy, especially for analyzing trends in hat construction variables that are treated systematically.

+

2. For many studies of trends, modeling monopoles over perfect ground is a compact method of investigation. Since the NEC and MININEC modeling systems create an image antenna, they replicate what one might construct for a hatted dipole in free space, but with half the required segments. This move, in turn, permits high segmentation density for maximum accuracy and for reading out small changes in current along the length of the elements, all without exceeding a programs total segment count limit or without incurring long run times.

+

A monopole over perfect ground will bear the following relationships to an equivalent dipole in free space. a. The free space dipole will be exactly twice as long as the perfect-ground monopole. NEC models should use an odd number of segments in the dipole to permit exact center-placement of the source.

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b. The source impedance of the monopole will be half the source impedance of the dipole. The figure might be slightly off in a NEC pair of models because the source position of the monopole is in the middle of the first segment above ground, while the dipole source is perfectly centered. With adequate segmentation, the differential will be insignificant.

+

c. As shown in the figure, the monopole gain will be 3 dB higher than that of the free space dipole due to the reflection of the ground. Hence, for calculating the gain of a horizontal dipole over a ground with a known reflection gain, one simply subtracts 3 dB from the monopole gain and then adds the appropriate reflection gain for a final value.

+

In all of this, the use of monopoles over perfect ground is perfectly adequate to tracking trends of performance and of changes to the hatted antenna's structure. Essentially, the difference between the perfect- ground monopole and antennas at heights over real ground are a set of arithmetic constants.

+

Hat Geometry

Virtually any hat geometry is the electrical equal of any other hat geometry. So long as the hat structure is symmetrical, radiation cancels, leaving only the effect of the main element. One type of antenna, sometimes called a Marconi, consists of a vertical element with a Tee-top, that is equal lengths of wire extending in opposite directions. Hams often make these antennas by shorting the feedline of an 80-meter dipole and pressing the antenna into service as a 160-meter monopole (usually with an inadequate ground plane). +

For another study, I ran models of a 16-meter long vertical monopole at 3 MHz with a variety of wire hats ranging from 3 to 32 spokes and using 2 different designs. One design used only spokes, while the other used spokes plus a perimeter wire that connected the spoke tips. In every case, the length of the spokes and other hat dimensions were adjusted for resonance over perfect ground. The figure shows a few of the possible variations, but not to scale.

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We can show the performance of the various hats in a pair of tables. First, the models using only spokes:

+ 
Number         Spoke-Length        Gain           Source Z
+of Spokes      Meters              dBi            R +/- jX Ohms
+ 3             5.994               4.96           27.9 _ j 0.7
+ 4             4.966               4.98           27.8 - j 0.7
+ 6             3.848               4.99           27.9 + j 0.4
+ 8             3.239               4.99           27.9 + j 0.4
+12             2.611               5.00           27.9 - j 0.2
+16             2.297               5.00           27.9 - j 0.9
+24             2.007               5.00           27.9 - j 0.3
+32             1.861               5.00           28.0 - j 0.2
+

For models using a spoke-plus-perimeter-wire construction, the table looked like this:

+ 
Number         Spoke-Length        Gain           Source Z
+of Spokes      Meters              dBi            R +/- jX Ohms
+ 3             2.985               4.97           28.1 + j 0.1
+ 4             2.591               4.98           28.1 + j 0.6
+ 6             2.280               4.99           28.0 + j 0.8
+ 8             2.096               4.99           27.9 - j 0.5
+12             1.918               5.00           28.0 + j 0.1
+16             1.808               5.00           27.9 - j 0.8
+24             1.701               5.00           27.9 - j 0.3
+32             1.640               5.00           28.0 - j 0.2
+

Clearly, there is no significant difference in the source impedance regardless of the hat construction method or the number of spokes in the hat structure. Likewise, there is a maximum difference of 0.04 dB in the gain figures. The only difference of significance is the length of the spokes, which define a virtual "radius" for the various hat structures.

+

One cannot combine all of the hats into a single graph, since there are two different geometric progressions at work. However, we can graph one of the progressions. Let us use the 4-8-16-32 spoke progression.

+
+ +
+

As the graph shows, there is a regular curve to the reduction of spoke lengths as the number of spokes increases. The spoke-plus-perimeter-wire hat form effects large size reductions for low spoke number structures. You can estimate the reduction by considering that the true element end is not a spoke tip, but instead a point along the perimeter wire halfway between spoke tips. Adding this length to the spoke length very roughly approximates the spoke length of the counterpart spoke-only design. As the number of spokes increases, the distances between spoke tips shrinks, bringing the two designs closer to coincidence of effective radius.

+

At some point beyond the right edge of the graph, the curves for the spoke- only and the spoke-plus-perimeter-wire design will come together. At that same point, the addition of further spokes will not significantly decrease the radius of the hat further. In effect, the hat will simulate a solid surface.

+

What distinguishes wire and disc hats from other symmetrical hat forms, such as the cylinder, is the fact that wire and disc hats have no linear dimension along the axis of the main linear element. Cylinders have such a linear dimension, and as such actually comprise less a hat structure than a change of element diameter, even if the change is very large.

+

Element vs. Hat-Wire Diameter

+

In the exercise just noted, the main element and the hat wires had different but constant diameters. However, there are some hat-size variations occasioned by changes in the ratio of the main element diameter to the hat wire diameter. To sample these variations, let us use a 60' long monopole over perfect ground, but change its diameter in regular steps from 0.5" to 2.0". Then, let us use different size wires for the hat structure. #12 AWG (0.0808"), 0.25", and 1" hat wire diameters will suffice for illustration.

+

We shall explore two hat structures. One is a 4-spoke (only) hat, and the other is a 4-spoke-plus-perimeter-wire hat. Let's record the required spoke lengths for each type of hat throughout the combinations of main element diameters and hat wire diameters.

+ 
#12 AWG (0.0808") diameter hat wire
+Element Diameter         Spoke-Only          Spoke + Perimeter
+in inches                Length - inches     Length - inches
+     0.5                  99.2               57.2
+     0.75                103.8               60.0
+     1.0                 107.4               62.1
+     1.25                110.4               63.9
+     1.5                 112.9               65.4
+     1.75                115.1               66.7
+     2.0                 117.1               67.9
+
+0.25" diameter hat wire
+Element Diameter         Spoke-Only          Spoke + Perimeter
+in inches                Length - inches     Length - inches
+     0.5                  90.3               54.0
+     0.75                 94.9               56.8
+     1.0                  98.4               58.9
+     1.25                101.3               60.7
+     1.5                 103.7               62.2
+     1.75                105.9               63.5
+     2.0                 107.9               64.7
+
+1.0" diameter hat wire
+Element Diameter         Spoke-Only          Spoke + Perimeter
+in inches                Length - inches     Length - inches
+     0.5                  77.4               49.6
+     0.75                 81.8               52.3
+     1.0                  85.2               54.4
+     1.25                 88.0               56.1
+     1.5                  90.3               57.6
+     1.75                 92.4               58.9
+     2.0                  94.3               60.1
+
+ +
+

The first graph shows the same data as in the table, but makes clear the regularity involved. For the spoke-only design, where the hat wire is a constant diameter, the greater the ratio of main element diameter to hat wire diameter, the larger the required spoke length or hat radius.

+
+ +
+

The second graph shows essentially the same story for the spoke-plus- perimeter hat design. Even for this design, with naturally shorter spokes, the increases are significant.

+

Interestingly, there is no significant difference in the main element current magnitude in the segment adjacent to the junction with the hat structure, regardless of element diameter. For a #12 wire hat diameter, the current magnitude (relative to 1) in the last main element segment for a 0.5" diameter element is 0.463 and for a 2.0" diameter element is 0.464, both for 60' long elements. The first segments in the 4 spokes show 0.110 and 0.111, respectively for the two element diameters. The longer spokes, however, do show a slower decrease in current, as one might expect, since the terminating value is zero in both cases.

+

Hat Placement

I have reviewed a number of variables involved in hat construction so that they do not interfere with conclusions to be drawn about hat placement on a shortened element. Each of the variables noted will change the numbers involved in hat placement, but not the trends, which will apply to each equally. +
+ +
+

The original question was whether it makes a difference where along a shortened element one places a hat, so long as the hat is generally out toward the end somewhere. The answer is yes. For any given combination of main element length and diameter and a given hat wire diameter, where the hat is sized to achieve resonance (or some other specified condition), end placement is always electrically the most efficient. Any other placement requires either a. for a constant hat size, a lengthening of the overall element, or b. for a given element length, an increase in the hat size. Moreover, every alternative position yields less gain than an end hat, although option b. with the set length and growing hat yields less gain than a constant hat size and lengthening element.

+

To reach this conclusion, I ran a series of models, of which we shall sample just a few. Consider a 60' long 3 MHz vertical element over perfect ground with an end hat. Then in successive steps (we shall use 5' steps), move the hat down. Then check resonance and a. increase the element length to achieve it or b. increase the hat size to achieve it.

+ 
Hat Place      Element        Spoke          Gain      Feed Z
+               Length "       Length "       dBi       R +/- jX
+End Hat        720            109            5.06      31.7 - j 0.1
+5' Down        720            127            5.03      29.4 - j 0.9
+               782            109            5.04      30.3 + j 0.6
+10' Down       720            144            5.00      27.2 + j 0.1
+               808            109            5.04      29.3 + j 0.6
+15' Down       720            160            4.97      24.8 - j 0.9
+               830            109            5.04      25.5 + j 0.5
+
+

Clearly the movement of the hat inboard relative to the element end demands an increase in one or another dimension to restore resonance. Lengthening the element itself beyond the hat maintains the higher gain, but at the expense of ending up with little or no saving in element length, which was the initial motivation for hat loading in the first place. (A full-size element is about 945" long.) The constant length element has a decreasing gain curve, but a rapidly enlarging hat radius--nearly 50% in the example.

+
+ +
+

The relative futility of moving the hat inboard relative to leaving it at the element's end appears in current graphs of the constant-length models in this sequence. The hat occupies a significant length of main linear element, wherever it appears. The current levels beyond the hat are those appropriate to a linear element's end, and thus have little current to contribute to radiation. Placing the hat at the outermost point along the element allows it to function with the smallest size and to occupy the element portion with the lowest current (relative to any other possible position).

+

The exact dimensions, hat growth, and wire length growth will, as noted vary with the exact set of structural dimensions chosen. However, the trend will not change. Whatever the mechanical difficulties involved, hats are physically smallest and electrically most efficient (or detract least from the antenna's performance) when located at the outermost limit of a proposed antenna element. This applies not only to vertical monopoles, but as well to dipole structures. Perhaps the only two operative reasons for placing a hat inboard on a monoband antenna are these: a. the inboard placement is mechanically dictated by support requirements; b. the inboard hat placement is designed solely to change the frequency of a secondary resonance of the element.

+

The conclusions prompted the modeling survey have been for a long time a part of antenna lore, which is replete with tales of silly things people supposedly have done, like clipping off the wire remnant from someone's hatted mobile whip. The claim was that the unrequested modification did not adversely affect radiation. However, as the table shows, it did adversely affect radiation--although in a minuscule manner--and, more significantly, it did affect system resonance. The clipping culprits in this legend turned out to be only 1 fact less ignorant than the victim of their (undoubtedly Halloween) vandalism.

+

Legends aside, these exercises in modeling do more than set up an additional support for placing hats as far outboard as the antenna's physical structure permit. They provide a body of data about source impedance, gain, and current magnitude along the element to clarify somewhat the overall understanding of hat properties. The project has been as much an exercise in using all of the data provided by modeling programs as it has been a demonstration of hat properties. (There is, in fact, further data available that goes beyond the scope of this particular set of notes.)

+

Time to go. Now where did I leave mine--hat, that is. It was hanging on the end of an antenna when I came in.

+
+ +
+

Updated 10-31-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/ir-1.gif b/content/gp/ir-1.gif new file mode 100644 index 0000000..41594e1 Binary files /dev/null and b/content/gp/ir-1.gif differ diff --git a/content/gp/ir-2.gif b/content/gp/ir-2.gif new file mode 100644 index 0000000..26bfe34 Binary files /dev/null and b/content/gp/ir-2.gif differ diff --git a/content/gp/ir-3.gif b/content/gp/ir-3.gif new file mode 100644 index 0000000..3f6b53a Binary files /dev/null and b/content/gp/ir-3.gif differ diff --git a/content/gp/ir-4.gif b/content/gp/ir-4.gif new file mode 100644 index 0000000..26320e4 Binary files /dev/null and b/content/gp/ir-4.gif differ diff --git a/content/gp/ir.html b/content/gp/ir.html new file mode 100644 index 0000000..bb6207f --- /dev/null +++ b/content/gp/ir.html @@ -0,0 +1,295 @@ + + + + + + The Insulated Radial Question + + + +
+

The Insulated Radial Question

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

One common question posed by radio amateurs on the verge of installing their first ground plane (GP) antenna for 160, 80, or 40 meters runs something like this:

+
+ I can obtain miles of insulated wire cheaply from the local home center. Will the use of insulated wire make any difference in the performance of my vertical, relative to bare wire? +
+

Most experienced GP users usually say that the answer is "no." However, they then qualify the answer by adding something to the effect that in their experience or via the grape-vine, no adverse effects of insulated wire radials has been reported. Something in the reply puts a note of uncertainty on the answer.

+

NEC-4 can shed some additional light on the question and add a small note of greater confidence in the reply. Since this is not a mystery novel with a surprise ending, let's set forth the general conclusion: operationally, the use of buried insulated radials of common wire with common insulations will result in no detectable performance difference relative to a bare wire buried radial system. The NEC-4 performance figures, including the Sommerfeld-Norton ground calculations, will show some interesting numerical wiggles, but the sum of those wiggles will be far below the threshold of the construction variables involved in implementing a ground radial system.

+

With the conclusion out of the way, we can turn to a more interesting question: how did I reach that conclusion?

+

NEC-4 and Buried Radials

+

NEC-4 permits the modeler to place wires below the surface of the ground. Hence, NEC-4 can do what NEC-2 cannot: model a vertical monopole with a buried radial system. However, the model must adhere to certain NEC-4 guidelines, which will make the model somewhat more complex than just placing a wire for the vertical and a number of radial wires. Fig. 1 shows something of the requirements.

+
+ +
+

Although we shall not work with 128-radial GP systems, the general outline looks impressive and is actually an exercise in repetitive model entry. The key elements for both the vertical element and the radials appears in the lower part of the graphic.

+

Here are some of the constraints:

+
    +
  • 1. A radial system is normally only a small distance below the ground surface.
    • +
  • 2. The vertical wire that penetrates the ground must do so on a segment junction. To insure that a segment junction occurs at Z = 0, most experts recommend that we use a wire from the surface to the junction of the radials, and another wire for the vertical portion of the monopole from the ground upward.
    • +
  • 3. We wish to feed the monopole at the lowest segment above ground to simulate base feeding. However, the source segment and the segments adjacent to it should be the same length to assure an accurate source impedance report.
    • +
  • 4. The short wire from the ground down to the radial junction determines the length of the source segment and the segment above it. Since these wires are very short, the main vertical element wire would require a massive number of segments if it were uniformly segmented.
    • +
  • 5. The wire segments joining at the radial junction should also be the same length as the short wire that meets them. Again, the radials, if uniformly segmented, would create a massive model in terms of the total number of segments.
    • +
+

Fig. 1 shows how we can meet the criteria and still have a model size of reasonable proportions. We length-taper the wires forming both the radials and the vertical element above the source segment. We use short wire segment lengths where required and gradually increase the segment lengths outward towards the wire ends--well beyond the portion of the sketch shown. The results show a close correlation to those derived from a uniformly segmented model, but in a fraction of the run time.

+

Note: the same techniques of length tapering are applicable to numerous models within the scope of NEC-2.

+

There are more complex cases than the simple one that we set up here, but for examining the insulated radial question, we do not have to create a very complex model. Instead, we shall set up a 1.83-MHz vertical monopole exactly 40 meters long and 25-mm in diameter. We shall also explore systems of 4 and 8 radials, each exactly 1/4-wl long (40.955 m). The radials will be 2 mm in diameter, which is between AWG #14 and #12 wire.

+

One limitation of NEC-4 is normally a set of erroneous output reports wherever we have angular junctions of wires with dissimilar diameters. However, these errors disappear wherever we have a completely symmetrical arrangement of wires such that the net radiation from them is roughly zero. Top hats and radial systems fall into this category.

+

2 Systems of Length-Tapering Wires

+

Since the days of the first ELNEC MININEC programs, W7EL has offered users the ability to length taper elements. Fig. 2 shows an 8-radial system using the ELNEC/EZNEC technique.

+
+ +
+

In the figure, the circles represent wire junctions, while simple dots indicate segment junctions within wires. Essentially, EZNEC substitutes for each wire being length-tapered a series of wires. The user sets the shortest and the longest desired segment lengths for an existing uniformly tapered wire. Then the program creates at the designated wire end a single 1-segment wire of the shortest length. The next wire created is twice that length, and so on until we reach the longest desired segment length. The program creates the final wire using segments equal to or shorter than the specified longest segment length.

+

In the interests of space, we shall illustrate the principle using a 4-radial model, where both the radials and the vertical element use tapered-length wires and segments:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 160-m 1/4 wl vert-4 bur radial
+CE
+GW 1,7,0.,0.,40.,0.,0.,5.242276,.0125
+GW 2,1,0.,0.,5.242276,0.,0.,2.621138,.0125
+GW 3,1,0.,0.,2.621138,0.,0.,1.31057,.0125
+GW 4,1,0.,0.,1.31057,0.,0.,.6552857,.0125
+GW 5,1,0.,0.,.6552857,0.,0.,.3276435,.0125
+GW 6,1,0.,0.,.3276435,0.,0.,.163821,.0125
+GW 7,1,0.,0.,.163821,0.,0.,0.,.0125
+GW 8,1,0.,0.,0.,0.,0.,-.163821,.0125
+GW 9,1,0.,0.,-.163821,.1638211,0.,-.163821,.001
+GW 10,1,.1638211,0.,-.163821,.4914632,0.,-.163821,.001
+GW 11,1,.4914632,0.,-.163821,1.146747,0.,-.163821,.001
+GW 12,1,1.146747,0.,-.163821,2.457316,0.,-.163821,.001
+GW 13,1,2.457316,0.,-.163821,5.078453,0.,-.163821,.001
+GW 14,7,5.078453,0.,-.163821,40.95526,0.,-.163821,.001
+GW 15,1,0.,0.,-.163821,1.2368E-8,.1638211,-.163821,.001
+GW 16,1,1.2368E-8,.1638211,-.163821,3.7104E-8,.4914632,-.163821,.001
+GW 17,1,3.7104E-8,.4914632,-.163821,8.6577E-8,1.146747,-.163821,.001
+GW 18,1,8.6577E-8,1.146747,-.163821,1.8552E-7,2.457316,-.163821,.001
+GW 19,1,1.8552E-7,2.457316,-.163821,3.8341E-7,5.078453,-.163821,.001
+GW 20,7,3.8341E-7,5.078453,-.163821,3.092E-06,40.95526,-.163821,.001
+GW 21,1,0.,0.,-.163821,-.1638211,2.4736E-8,-.163821,.001
+GW 22,1,-.1638211,2.4736E-8,-.163821,-.4914632,7.4209E-8,-.163821,.001
+GW 23,1,-.4914632,7.4209E-8,-.163821,-1.146747,1.7315E-7,-.163821,.001
+GW 24,1,-1.146747,1.7315E-7,-.163821,-2.457316,3.7104E-7,-.163821,.001
+GW 25,1,-2.457316,3.7104E-7,-.163821,-5.078453,7.6683E-7,-.163821,.001
+GW 26,7,-5.078453,7.6683E-7,-.163821,-40.95526,6.1841E-6,-.163821,.001
+GW 27,1,0.,0.,-.163821,1.9535E-9,-.1638211,-.163821,.001
+GW 28,1,1.9535E-9,-.1638211,-.163821,5.8606E-9,-.4914632,-.163821,.001
+GW 29,1,5.8606E-9,-.4914632,-.163821,1.3675E-8,-1.146747,-.163821,.001
+GW 30,1,1.3675E-8,-1.146747,-.163821,2.9303E-8,-2.457316,-.163821,.001
+GW 31,1,2.9303E-8,-2.457316,-.163821,6.056E-08,-5.078453,-.163821,.001
+GW 32,7,6.056E-08,-5.078453,-.163821,4.8839E-7,-40.95526,-.163821,.001
+GE -1
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+LD 5,3,0,0,5.7471E+7,1.
+LD 5,4,0,0,5.7471E+7,1.
+LD 5,5,0,0,5.7471E+7,1.
+LD 5,6,0,0,5.7471E+7,1.
+LD 5,7,0,0,5.7471E+7,1.
+LD 5,8,0,0,5.7471E+7,1.
+LD 5,9,0,0,5.7471E+7,1.
+LD 5,10,0,0,5.7471E+7,1.
+LD 5,11,0,0,5.7471E+7,1.
+LD 5,12,0,0,5.7471E+7,1.
+LD 5,13,0,0,5.7471E+7,1.
+LD 5,14,0,0,5.7471E+7,1.
+LD 5,15,0,0,5.7471E+7,1.
+LD 5,16,0,0,5.7471E+7,1.
+LD 5,17,0,0,5.7471E+7,1.
+LD 5,18,0,0,5.7471E+7,1.
+LD 5,19,0,0,5.7471E+7,1.
+LD 5,20,0,0,5.7471E+7,1.
+LD 5,21,0,0,5.7471E+7,1.
+LD 5,22,0,0,5.7471E+7,1.
+LD 5,23,0,0,5.7471E+7,1.
+LD 5,24,0,0,5.7471E+7,1.
+LD 5,25,0,0,5.7471E+7,1.
+LD 5,26,0,0,5.7471E+7,1.
+LD 5,27,0,0,5.7471E+7,1.
+LD 5,28,0,0,5.7471E+7,1.
+LD 5,29,0,0,5.7471E+7,1.
+LD 5,30,0,0,5.7471E+7,1.
+LD 5,31,0,0,5.7471E+7,1.
+LD 5,32,0,0,5.7471E+7,1.
+FR 0,1,0,0,1.83
+GN 2,0,0,0,20.,.0303
+EX 0,7,1,0,1.414214,0.
+RP 0,181,1,1000,90.,0.,-1.,0.,0.
+EN
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The file appears in generic NEC format. The model requires 32 wires for just 5 elements (a vertical plus 4 radials). As well, EZNEC creates a material loading entry for each wire, although these do not materially increase the model run time.

+

An alternative technique is available within NEC (2 or 4). It consists of the GC or geometry continuation card that we can apply to each wire. Fig. 3 outlines that same model using this system.

+
+ +
+

Note that there are no wire junctions except at the hub of all of the radials. Instead, the GC card allows us to specify the length tapering, and the NEC core does the work of producing the required segments. We have options that include specifying the ratio of one segment to the next or of specifying the longest and shortest segment lengths and letting the core calculate the required ratio. Unlike the EZNEC system, which doubles the wire/segment length with each step and ends with a wire usually having 2 or more uniform segments lengths, the GC option provides a continually increasing segment length throughout the element being length-tapered.

+

Let's illustrate the look of such a model, again using a smaller 4-radial GP with a tapered vertical element:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 160-m 1/4 wl vert-4 bur radial
+CE
+GW 1,11,0.,0.,40.,0.,0.,.327644,0
+GC 2 0 0 .0125 .0125 13 .16328
+GW 2,1,0.,0.,.327644,0.,0.,.163821,.0125
+GW 3,1,0.,0.,.163821,0.,0.,0.,.0125
+GW 4,1,0.,0.,0.,0.,0.,-.163821,.0125
+GW 5,12,0.,0.,-.163821,40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 6,12,0.,0.,-.163821,0.,40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 7,12,0.,0.,-.163821,-40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 8,12,0.,0.,-.163821,0.,-40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GE -1
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+LD 5,3,0,0,5.7471E+7,1.
+LD 5,4,0,0,5.7471E+7,1.
+LD 5,5,0,0,5.7471E+7,1.
+LD 5,6,0,0,5.7471E+7,1.
+LD 5,7,0,0,5.7471E+7,1.
+LD 5,8,0,0,5.7471E+7,1.
+FR 0,1,0,0,1.83
+GN 2,0,0,0,20.,.0303
+EX 0,3,1,0,1.414214,0.
+RP 0,181,1,1000,90.,0.,-1.,0.,0.
+EN
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model requires only 8 wires--5 for the main parts of the elements and 3 in the ground entry region. The total number of segments is about the same for the 2 version of length-tapered GP antennas (63-64), but the number of wires is reduced by letting NEC do the tapering. While the run time difference is not significant on a 4-radial GP, it becomes significant for full AM BC radial systems. The difference lies in the fact that model calculation times climb exponentially with both the number of segments and the number of wires.

+

The following extract from a NEC output file illustrates just what NEC does internally with the GC card data applied to the appropriate GW card above it.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+5    0.00000    0.00000   -0.16382    40.95530    0.00000   -0.16382    0.00000   12       16    27       5
+          ABOVE WIRE IS TAPERED.  REQUESTED INITIAL AND FINAL SEG. LENGTHS =  0.16328       13.50000
+               RADIUS FROM  0.00100 TO  0.00100
+               COMPUTED NUMBER OF SEGMENTS =    12   LENGTH RATIO =  1.49568
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+    16   0.08164   0.00000  -0.16382   0.16328    0.00000   0.00000   0.00100   -28   16   17      5
+    17   0.28539   0.00000  -0.16382   0.24422    0.00000   0.00000   0.00100    16   17   18      5
+    18   0.59013   0.00000  -0.16382   0.36527    0.00000   0.00000   0.00100    17   18   19      5
+    19   1.04592   0.00000  -0.16382   0.54632    0.00000   0.00000   0.00100    18   19   20      5
+    20   1.72765   0.00000  -0.16382   0.81712    0.00000   0.00000   0.00100    19   20   21      5
+    21   2.74728   0.00000  -0.16382   1.22215    0.00000   0.00000   0.00100    20   21   22      5
+    22   4.27232   0.00000  -0.16382   1.82794    0.00000   0.00000   0.00100    21   22   23      5
+    23   6.55330   0.00000  -0.16382   2.73400    0.00000   0.00000   0.00100    22   23   24      5
+    24   9.96489   0.00000  -0.16382   4.08919    0.00000   0.00000   0.00100    23   24   25      5
+    25  15.06753   0.00000  -0.16382   6.11610    0.00000   0.00000   0.00100    24   25   26      5
+    26  22.69944   0.00000  -0.16382   9.14771    0.00000   0.00000   0.00100    25   26   27      5
+    27  34.11430   0.00000  -0.16382  13.68201    0.00000   0.00000   0.00100    26   27    0      5
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As the extract shows, NEC internally converts the entry notation of a wire number and a set of segments within the wire into absolute segment numbers. For the first radial, wire #5, we have segment 16 through 27, each with a separate length according to the ratio that NEC calculated from our entry of start and end segment lengths.

+

Since the two length-tapering systems differ, we can ask which is more accurate. Here are results for bare-wire radials for 4 and 8 radial systems from the EZNEC results and from the GC results, as run on GNEC.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+GP Size           Gain        TO Angle          Source Impedance
+(# Radials)       dBi         degrees           R +/- jX Ohms
+
+4  EZNEC          2.10        17                47.33 + j 14.52
+4  GC             2.06        17                47.52 + j 13.97
+
+8  EZNEC          2.39        17                44.33 + j 12.60
+8  GC             2.35        17                44.48 + j 12.03
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Besides showing that the report differences fall well below operational significance, these numbers will also serve as references for our next step: the investigation of what happens when we insulate the radials.

+

Insulating Wires

+

NEC-4 adds a few new features absent in NEC-2. For example, NEC-4 allows an entry in the material loading line (LD5 in the above models) for permeability, which is 1 for non-magnetic wire materials like copper.

+

A most interesting addition is the IS card, where IS means an insulating sheath. What we can do with that card appears in the single annotated entry line that follows:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+IS     0       0        16       63         2            1e-10      .00125
+ID  New Data Tag #  Start Seg  End Seg  Permittivity  Conductivity  Radius
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

After the line identification, the first entry is 0 if we are entering new data. Then we specify the wire/tag number, along with the starting and ending segments for the insulated sheath. If we enter 0 for the tag number, we can use absolute segment numbers, a move that allows us to insulate all of the radials in one line. Segment numbers 16 through 63 cover all of 4 radials on the simpler model.

+

Just as we might for a ground quality specification, we enter a relative dielectric constant (or permittivity) value and a conductivity value. For this test case, the conductivity is very low to indicate excellent insulating properties: 1E-10 s/m. Most wires today use some form of plastic covering and most common plastic have permittivity values between 2.0 and 3.0. for the series of checks that we shall perform, I used values of 2.0, 2.5, and 3.0.

+

The radius must be greater than the wire radius: 0.001 m or 1 mm. For the series of checks, I used sheath radii of 0.00125, 0.0015, and 0.002. The first value gives a relatively thin insulation, which the last value results in an insulation diameter twice that of the wire itself.

+
+ +
+

Fig. 4 illustrates the relationship between the IS entry and the wires that we have just insulated.

+

The resulting model is little changed from the GC version we examined earlier. Here is a sample:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+CM 160-m 1/4 wl vert-4 bur radial
+CE
+GW 1,11,0.,0.,40.,0.,0.,.327644,0
+GC 2 0 0 .0125 .0125 13 .16328
+GW 2,1,0.,0.,.327644,0.,0.,.163821,.0125
+GW 3,1,0.,0.,.163821,0.,0.,0.,.0125
+GW 4,1,0.,0.,0.,0.,0.,-.163821,.0125
+GW 5,12,0.,0.,-.163821,40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 6,12,0.,0.,-.163821,0.,40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 7,12,0.,0.,-.163821,-40.9553,0.,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GW 8,12,0.,0.,-.163821,0.,-40.9553,-.163821,0
+GC 2 0 0 .001 .001 .163281 13.5
+GE -1
+IS 0 0 16 63 2 1e-10 .00125
+LD 5,1,0,0,5.7471E+7,1.
+LD 5,2,0,0,5.7471E+7,1.
+LD 5,3,0,0,5.7471E+7,1.
+LD 5,4,0,0,5.7471E+7,1.
+LD 5,5,0,0,5.7471E+7,1.
+LD 5,6,0,0,5.7471E+7,1.
+LD 5,7,0,0,5.7471E+7,1.
+LD 5,8,0,0,5.7471E+7,1.
+FR 0,1,0,0,1.83
+GN 2,0,0,0,20.,.0303
+EX 0,3,1,0,1.414214,0.
+RP 0,181,1,1000,90.,0.,-1.,0.,0.
+EN
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We can look at the results of our exploration using both 4- and 8-radial systems with insulated wires. The following table gives the results of GNEC runs, with the reported TO angle converted from GNEC's native theta angle into the more familiar elevation angle.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Dielectric.       Radius      Gain        TO Angle          Source Impedance
+Constant           mm         dBi         degrees           R +/- jX Ohms
+
+4 Radials
+2.0               .00125      2.13        18                46.81 + j 14.56
+                  .0015       2.26        18                45.63 + j 15.77
+                  .002        2.15        17                46.28 + j 12.36
+2.5               .00125      2.17        17                46.31 + j 14.02
+                  .0015       2.21        18                46.12 + j 14.56
+                  .002        2.42        17                43.67 + j 13.11
+3.0               .00125      2.16        18                46.73 + j 14.65
+                  .0015       2.21        18                46.06 + j 14.83
+                  .002        2.41        18                43.93 + j 15.54
+
+8 Radials
+2.0               .00125      2.34        18                44.60 + j 12.59
+                  .0015       2.45        17                43.61 + j 13.38
+                  .002        2.33        17                44.44 + j 11.77
+2.5               .00125      2.35        17                44.41 + j 12.16
+                  .0015       2.40        17                44.18 + j 12.80
+                  .002        2.51        17                42.80 + j 11.76
+3.0               .00125      2.36        18                44.31 + j 12.38
+                  .0015       2.39        17                44.21 + j 12.78
+                  .002        2.53        17                42.74 + j 13.08
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
If we compare the range of numbers with the values for a bare wire radial system, then we can see that, first of all, the variations make no operational difference that would not be masked by the ground and construction variables involved in a given installation. Relative to the modeled numbers, the bare wire model values for resistance fall into the high end of the range of insulated wire values, while the bare-wire reactance value falls about mid-range. +

We might have carried this investigation further into larger radial systems, but there is no need to do so. One condition of the study was to place all the test models over very good ground with a conductivity of 0.0303 and a permittivity of 20. This move tends to maximize any effects of radial insulation, and the results have shown quite minimal effects. There are interesting "wiggles" in the values as we change the sheath permittivity and radius, but these must await a different kind of study for proper interpretation.

+

A second reason for not extending the study emerges if we examine the range of variation of the od the values. The reported gain varies a total of 0.29 dB for the 4-radial model but only by 0.20 dB for the 8-radial model. The resistance varies a total of 3.15 Ohms and 1.85 Ohms for the 4- and 8-radial models, respectively. For those same models, the reactance varies a total of 2.66 Ohms and 1.63 Ohms.

+

In short, as we add more radials, the range of variation of values decreases. By the time we would reach 120 or 128 radials, we should expect little or no variation among values.

+

Conclusion

+

The ability of NEC to handle buried length tapered radials with insulation on them adds some measure of confidence to the general proposition that insulated radials of common wire and insulation types and thicknesses will not materially change the performance of a ground plane vertical antenna, relative to using bare wire radials. Modeling confirms common experience, at least over common soils.

+

There are several directions in which one might expand the investigation. Obviously, one might test the models over a myriad of soil quality combinations. As well, one might expand the range of insulation permittivity values for alternative insulation types, as well as explore higher values of conductivity to simulate what happens as insulation become corrupt with age. And, as the final test, one might cover a much larger range of radial system sizes, just to be sure that the trends indicated do hold true. It is a project out of which an engineering graduate student might generate a thesis or two. It has all of the earmarks of a good engineering thesis: minimal text and gobs of tables and graphs.

+

However, until such a thesis comes along to develop a comprehensive compendium of insulated radial data, perhaps this preliminary study will suffice to give GP builders confidence in that mile-long role of insulated wire from the surplus shop.

+
+ +
+

Updated 05-01-2003. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Apr., 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Lower, MF, Modeling, Vertical


+ + diff --git a/content/gp/linvert.html b/content/gp/linvert.html new file mode 100644 index 0000000..b027b7f --- /dev/null +++ b/content/gp/linvert.html @@ -0,0 +1,57 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Index + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ the Best Method of Loading

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+
+

Summary

+
In the pursuit of obtaining the most compact and efficient 80- meter monopole antenna, numerous loading schemes have been proposed, including based lumped constant loading, base linear loading, top (capacity) hat loading, and a number of antenna element extension-and-fold-back systems. Modeling these systems is difficult due to the various limitations of existing modeling software, including MININEC, NEC-2, and NEC-4. +

Preliminary work is best done in MININEC, because (with due caution) it is best capable of modeling nonlinear geometries employing wires of different diameters, a necessary condition of a compact 80-meter monopole. A monopole 37.5' long, corresponding to a common commercial height, is the constant main element used, with other parameters varied to achieve the following goals:

+
    +
  • a. Maximum gain within the limits of the antenna type;
    • +
  • b. True vertically-polarized circular pattern;
    • +
  • c. Highest feedpoint impedance for maximum efficiency;
    • +
  • d. Flattest SWR curve between 3.5 and 3.7 MHz; and
    • +
  • e. Most compact and mechanically practical assembly.
    • +
+

The range of models compared covered the following types of monopoles: full-length, 37.5' unloaded, lumped constant base- loaded, linear-base-loaded, "capacity" hat loaded; top linear loaded; zigzag fold-back loaded, and helically loaded. Figures are provided on gain and feedpoint impedance at 3.6 MHz, as well as on feedpoint impedance and SWR at 0.05 MHz intervals from 3.5 to 3.7 MHz. Other data can be obtained from these models by rerunning them using the descriptions provided in an Appendix. Especially recommended is a study of current levels along the antenna wires.

+

No single model antenna achieves all of the goals listed above. However, the helical fold-back element extension model achieves goals a. through c., and perhaps holds promise of achieving e. The zigzag fold-back element extension model excels in achievement of goals b, c. and d., with only slightly less gain than the helix and with some promise of meeting goal e. The capacity hat model shows excellent gain, bandwidth, and feedpoint impedance, but may be mechanically problematical except in a Marconi configuration. All other models show lesser performance in one or more categories. Unless mechanical constraints preclude further work on them, the helical and the zigzag foldback models appear to be the best candidates for further study and testing. However, before hats are discarded as too large or too fixed or too unwieldy, the spiral hat noted in the last segment (Part 5) should be examined. It was modeled in NEC-4 because the model was too large of standard MININEC.

+
+

Part 1: Goals, and Methods of the Study

+

Part 2: Baseline Data: Full-Size and Capacity-Hat Verticals

+

Part 3: Base-Loading: Lumped-Constant and Linear Loading

+

Part 4: Top (Element-Extension) Loading: Linear, Zig-Zag, and Helical Loading

+

Part 5: Summary Comparisons and Conclusions; With an Alternative Suggestion

+

Part 6: Descriptions of Models Reported

+

+
+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert1.html b/content/gp/linvert1.html new file mode 100644 index 0000000..44ee7ca --- /dev/null +++ b/content/gp/linvert1.html @@ -0,0 +1,77 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 1: Goals, and Methods of the Study + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 1: Goals, and Methods of the Study

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

The development of a compact and efficient 80-meter monopole has yielded numerous schemes of loading. To the present, no published studies known to me have systematically addressed the relative merits of these schemes in terms of overall antenna performance. Obviously, a short monopole will perform less well than a full-length resonant monopole (using the same constant ground and ground plane conditions). First, the gain of the shortened monopole will be less than that of the full-length monopole. Second, the shorter monopole will have a lower feedpoint impedance, thus increasing the ratio of ohmic (loss) resistance to radiation resistance.

+

A. Goals of the Study

Within these constraints and with a target frequency of 3.6 MHz, one can establish the following goals for any project to yield a workable short 80-meter monopole: +

1. The antenna should have the maximum gain achievable within the limits of the antenna type. In general, this gain is limited by the theoretical gain of the shortened monopole prior to the addition of any loading scheme to bring it to resonance. However, some schemes may in fact marginally (and perhaps insignificantly) increase the gain beyond that point.

+

2. The antenna should exhibit a true vertically-polarized circular radiation pattern. Any horizontally-polarized field component should be sufficiently small that it does not affect the overall antenna field shape or strength.

+

3. The antenna should have the highest possible feedpoint impedance at resonance for maximum efficiency. Given a constant set of ohmic losses, presumed for the sake of this study, the higher the radiation resistance, the higher the antenna efficiency.

+

4. The antenna should exhibit the flattest SWR curve possible between 3.5 and 3.7 MHz. A flat SWR curve indicates a wider operating bandwidth before adjustments to the antenna must be made.

+

5. The antenna should promise the most compact and mechanically practical assembly possible. An antenna must have mechanical properties that enable it to withstand reasonable handling and weather conditions. Moreover, it must be reproducible within the normal manufacturing and economic limits of current practice.

+

This preliminary study cannot assure that its final recommended antenna configurations can meet every goal, even if a model seems to promise that achievement. However, every effort has been made to formulate configurations that hold reasonable promise of being both good performers and practical manufacturing products.

+

B. Methods of the Study

The evaluation of the results of the modeling exercise require an understanding of the methods used and the rationale for selecting these methods. These considerations have two significant aspects: the selection of the modeling software and the selection of the modeling parameters. +

1. Modeling Software

There are four major antenna modeling calculation engines potentially relevant to this study: NEC-4, NEC-2, MININEC 3.13, and Proprietary MININEC. Currently, these are implemented in the following commercially available packages: EZNEC-Pro (NEC-4 and NEC-2), ELNEC (MININEC 3.13), AO (MININEC 3.13), NEC-Wires (NEC-2), NEC-Win Pro (NEC-2, with GNEC-NEC-4 soon to appear), NEC4WIN (MININEC 3.13, with a NEC-2 version under beta test), and MININEC for Windows (Proprietary MININEC of Rockway and Logan). Other versions of the same software have more or less user features offered by the same sources are not here listed. +

NEC-2 has the well-know limitation of being unable to handle with any reliable accuracy antenna elements whose diameter changes along the length. In addition, it also yields unreliable outputs for antenna elements of complex geometry, where the antenna diameter changes at a corner. NEC-2 is also limited in accuracy wherever it encounters very tight angles so that regions of presumed current impinge on each other. Since all of these factors are essential to the modeling of short, loaded vertical monopoles, NEC-2 is unusable.

+

I have recently discovered conclusive evidence that NEC-4, while an improvement in all these areas over NEC-2, is nevertheless unreliable in the same areas of concern to modelers of loaded vertical monopoles. In general, both gain and feedpoint impedance figures are inconsistent for the modeling requirements. Some of the limitations of NEC-4 are published at my personal website. (See http://funnelweb.utcc.utk.edu/~cebik/radio.html for an index of relevant notes.)

+

The proprietary revised FORTRAN MININEC recently issued by Rockway and Logan has yet to be tested for accuracy in these areas of concern. The present user interface has made testing a laborious task, and this software was set aside for the present modeling exercise.

+

MININEC 3.13, used by AO, ELNEC, and NEC4WIN, handles closely spaced wires of differential diameters without significant problem. Moreover, segments of different diameters meeting at angles are also routinely handled within the limits imposed by the scheme of placing pulses at segment ends. This requires the use of very short segments at junctures of this type to ensure minimal effective element length shortening. The modeler can achieve this goal by the use of sufficient equi-length segments or be the use of a segment-length tapering schedule. Tapering schedules are built into both AO and ELNEC.

+

MININEC also requires that the modeler avoid very tight angles, where required segmentation for accuracy would exceed program limits. This limitation can be overcome by flattening the apex of very sharp angles so that the resultant angles approach right angles. This yields no large problems in modeling or in extrapolating those models to real "pointed" structures. Whenever this is done, the text indicates the alternative procedure used. In the end, the inaccuracies are no greater than those imposed by straight-wire modeling, common to all forms of available modeling software. The errors yielded by meeting the requirements of MININEC 3.13 are systematic. Therefore, trends produced by the figures are reliable, even if frequency shifted.

+

Therefore, all modeling for this study was done on ELNEC 3, a version of MININEC 3.13 with a user interface permitting the rapid alteration of antenna configuration and reasonable calculation times. Segmentation, where possible, was held at a limit just below a total of 128 model segments in order to avoid additional time penalties imposed by calculation of larger matrices. Cross checks with larger models show no significant differences in absolute values generated or in the trends.

+

2. Modeling Parameters

The overall goal of this study is to compare general loading configurations for short vertical monopoles. The general properties of these schemes can be explored in simplified form by standardizing certain modeling parameters. Among the standardization features are the following items: +

1. Use of perfect ground: All antennas a modeled over perfect ground so that gain figures become directly comparable. Real ground and modeled ground planes lie beyond the scope of the present study, but may be advisable in later studies.

+

2. Use of lossless wire: Initial studies suggest that the two most common materials used for antenna element components produce few changes in key output figures. Although some material selection is predictable (aluminum for tubing, copper for thin wire), these decision belong to an advanced stage of study. The use of lossless wire permits one to sort out the general configuration potentials from limitations later introduced by actual materials.

+

3. Restriction of "main" element size: Main element diameters of 1" and 2" are used throughout, with occasional reference to 1.5" diameter elements. These elements general encompass the range of manufacturing possibilities and suffice to indicate appropriate trends in gain and feedpoint impedance.

+

4. Restriction of main-element length: commercial half-size monopoles are general in the range of 30 to 40 feet long. One commercial short, loaded 80-meter monopole is 37.5' long. For mechanical reasons, this length is judged to be a practical maximum for most amateur radio purposes. Therefore, it has been adopted as the standard length for all models (except the full-size resonant quarter wavelength model used for comparison) in this study. A single main element length makes it possible to compare directly the effectiveness of the loading schemes examined.

+

5. Restriction of output data taken: The key indicators of antenna performance within the limitations of this study are gain in dBi, feedpoint impedance in R+/-jX ohms, and SWR referenced always to the antenna impedance at 3.6 MHz and resonance. For the purposes of this study, resonance is defined as less than 1 ohm reactance, a necessary condition for producing reliable SWR curves at low resonant feedpoint impedances.

+

Restrictions specific to a given model will be reported when that model is given detailed examination.

+

The model coding used in this study deserves an explanation. All file extensions are .EN, indicating an ELNEC file. All such files are readable and convertible by EZNEC into .EZ files. All model file names begin with 35 to indicate an 80-meter vertical antenna. The following codings distinguish among antenna types:

+ 
     File name           Antenna Type
+
+     35Vxx.         Unloaded vertical monopole
+     35VSxx.        Short, unloaded vertical monopole
+     35VCxx(A).     "Capacity" hat vertical monopole
+     35BLxxxx(A).   Base lumped-constant loaded antenna
+     35LLxxxx.      Base linear-loaded antenna
+     35LHxxxx.      Top linear-loaded antenna
+     35VTxxxx.      Top Zig-Zag loaded antenna
+     35VZxxxx.      Top helically-loaded antenna
+

The "xxxx" in each file name is a group of four numbers. The first pair is restricted to 10, 15, or 20, indicating main element diameters of 1", 1.5", or 2" respectively. The second pair is used where appropriate to indicate the spacing of the loading structure from the main element, center-to-center in feet, where 30 indicates 3.0' spacing. Wherever spacing is variable, detailed explanations are provided. Each subsequent chapter of this report begins with a list of file names of models reported in the chapter.

+

Figures are provided for antenna structures that may be unclear from verbal descriptions. Since all patterns are visually similar, only one such pattern is provided for the reference antenna in the following chapter. Data presentation will largely be confined to tables, with occasional graphs to clarify trends and curves in the data.

+

An appendix of file descriptions is included for ease in replicating the models used in this study.
+

+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 2: Baseline Data: Full-Size and Capacity-Hat Verticals
+
+ Return to Index
+
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert2.html b/content/gp/linvert2.html new file mode 100644 index 0000000..96f243b --- /dev/null +++ b/content/gp/linvert2.html @@ -0,0 +1,120 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 2: Baseline Data: Full-Size and Capacity-Hat Verticals + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 2: Baseline Data: Full-Size and Capacity-Hat Verticals

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Models used:

+ 
      35V10       35V15       35V20
+      35VS10      35VS15      35VS20
+      35VC10      35VC15      35VC20
+      35VC10A     35VC15A     35VC20A
+

A. Full-Length Verticals

The baseline for all short monopole comparisons is the full length resonant quarter wave vertical over perfect ground. ELNEC/MININEC models of full-size quarter wavelength verticals show the following properties: + 
Antenna     Diameter    Length      Gain       Feedpoint Impedance
+Filename    in inches   in feet     in dBi     in R ± jX ohms
+
+35V10       1.0"        65.97'      5.15       35.98 - 0.32
+35V15       1.5"        65.9'       5.15       36.03 - 0.54
+35V20       2.0"        65.8'       5.15       36.09 - 0.19
+

Figure 2-1 shows the elevation pattern for this model (35V20), which is standard for all subsequent models, except those specifically noted. As expected, the horizontal field component is nonexistent.

+
+ +
+

The SWR curves for a full-size vertical show little variation with changes in element diameter. SWR and feedpoint impedance (Z=R±jX in ohms) are rounded to one decimal place.

+ 
Antenna     Feed  3.5 MHz     3.55 MHz   3.6 MHz     3.65 MHz    3.7 MHz
+
+35V10       SWR   1.7         1.3        1.0         1.3         1.6
+            Z     32.9-17.8   34.4-9.1   36.0-0.3    37.6+8.4    39.4+17.1
+35V15       SWR   1.6         1.3        1.0         1.2         1.5
+            Z     32.9-16.9   34.4-8.7   36.0-0.5    37.7+7.7    39.5+15.9
+35V20       SWR   1.6         1.3        1.0         1.2         1.5
+            Z     32.9-15.7   34.5-8.0   36.1-0.2    37.8+7.6    39.6+15.5
+

Note that, with changes in element diameter, the resistive component of the feedpoint impedance does not change significantly, while the reactive component changes from resonance grow smaller with increasing diameters. This pattern will hold generally true for all models in this study.

+

B. 37.5' Verticals

When the monopole is shortened to 37.5' long, it shows reduced gain. In addition, the feedpoint impedance becomes highly reactive, and its resistive component becomes very low. The height selected for the short vertical is about 57% of full-size or about 0.14 wavelength, relative to the full-size verticals examined above. + 
Antenna     Diameter    Length      Gain       Feedpoint Impedance
+Filename    in inches   in feet     in dBi     in R ± jX ohms
+
+35VS10      1.0"        37.5'       4.885            7.94 - 286.97
+35VS15      1.5"        37.5'       4.886            7.89 - 265.62
+35VS20      2.0"        37.5'       4.886            7.85 - 250.44
+

The numbers on the short verticals without loading are provided as references against which to evaluate the various loading schemes. In some cases, a given loading scheme can actually increase the gain beyond these numbers, but not by very much (up to about 0.05 dB).

+

C. "Capacity" Hat Verticals

A true so-called capacity hat is any assembly at the top of an antenna element that lengthens the current path to permit the attainment of a specific condition, such as resonance, but which is so arranged that the radiation from the assembly is zero to negligible. The ordinary way of achieving this effect is to place a symmetrical assembly of wires, with or without perimeter connecting wires, at the antenna top. The current divides among the wires. However, for every radiating wire, there are one or more other wires so positioned that their radiation field(s) is exactly equal and opposite the one in question, canceling it. Arrangements of any number of wires, even or odd numbers of them, are possible, up to and including a solid flat circular plate. +

The method of calculating the size of capacity hats is predicated on low frequency models in which the diameter of a radiator is an insignificant percentage of a wavelength. Under this condition, a wire with parallel surfaces can be said to approximate the actual conic section needed to allow the antenna to be viewed as an open transmission line. However, at HF, the wire diameter is an appreciable percentage of a wavelength and the analogy with transmission lines breaks down. The calculated capacitive reactance of the missing antenna section is no longer a reliable indicator of the size of the hat needed using standard low frequency calculations of the capacitance of a single circular flat plate. since the method of calculation is not perfectly general and requires a mass of ad hoc corrections, the transmission line analogy (originally characterized as an approximation only) is no longer applicable, and the hat should not be called a capacity hat.

+

The subject of hats holds many complexities. Here we may simply note that the length of required wires in any configurations of hat is a complex relationship among the main antenna element diameter, the hat wire diameter, and the frequency of interest, with added complexities from a perimeter wire and any other inter-wire connections within the hat.

+

Any properly sized hat meeting the definition at the beginning of this section which is used to provide for antenna element current path completion, whatever it configuration, produces the same results: a vertically polarized radiation pattern with no horizontal component. Hat sizes grow smaller with increasing numbers of wires in the symmetrical structure, reaching the minimal size of a solid circular plate at about 60 wires. (It is no accident or coincidence that this number corresponds closely with the number of elements in an elevated ground plane for maximum vertical antenna efficiency.) However, the performance characteristics of the antenna do not change significantly whether than antenna hat has 60 shorter wires or 2 opposed longer wires, as in the classic Marconi antenna.

+
+ +
+

To sample the characteristics of hatted short vertical monopoles, a Marconi model was constructed. Figure 2-2 shows the general outline of the antenna as modeled. For simplicity, the hat wires were made the same diameter as the main element wire. The models yielded following characteristics:

+ 
Antenna     Diameter    Each hat         Gain        Feedpoint Impedance
+Filename    in inches   wire in feet     in dBi            in R ± jX ohms
+
+35VC10      1.0"        19.0'            4.940             22.75 - 0.33
+35VC15      1.5"        19.0'            4.940             22.75 - 0.92
+35VC20      2.0"        19.05'           4.940             22.79 - 0.73
+

Smaller diameter hat wires would have required significantly greater length per wire. However, it is possible, under almost any other loading scheme to provide an antenna user with sufficient wire to use as a substitute for the other loading scheme, wherever local circumstances permit. The hat-loaded antenna does show good gain and a reasonably high feedpoint impedance. Its SWR characteristics are as follows:

+ 
Antenna     Feed  3.5 MHz     3.55 MHz   3.6 MHz     3.65 MHz    3.7 MHz
+35VC10      SWR   2.1         1.5        1.0         1.4         1.9
+            Z     20.9-16.1   21.8-8.3   22.8-0.3    23.7+7.5    24.7+15.3
+35VC15      SWR   2.0         1.5        1.0         1.3         1.8
+            Z     20.9-15.7   21.8-8.3   22.8-0.9    23.7+6.5    24.7+13.9
+35VC20      SWR   2.0         1.4        1.0         1.3         1.8
+            Z     21.0-14.8   21.9-7.8   22.8-0.7    23.8+6.3    24.8+13.4
+
+ +
+

Figure 2-3, using 35VC20 and 35V20 as line generators, compares the hatted short vertical and the full-size vertical with respect to SWR bandwidth. Among the models in this study, only these two exceed a true 200 kHz 2:1 SWR bandwidth.

+

The series of models 34VC10A through 35VC20A demonstrates the similarity of performance of all hatted verticals having the same main element length and diameter. In common, all models in this series have a 4-wire hat made of #12 lossless wire, as sketched in Figure 2-4. Individual leg lengths are noted in the table. Note that as the diameter of the main element increases, so too does the required leg length in the hat, although the relationship is not linear.

+
+ +
+ 
Antenna     Diameter    Each hat         Gain        Feedpoint Impedance
+Filename    in inches   wire in feet     in dBi            in R ± jX ohms
+
+35VC10A     1.0"        15.8'            4.947             22.83 + 0.24
+35VC15A     1.5"        16.8'            4.945             22.83 - 0.15
+35VC20A     2.0"        17.6'            4.943             22.86 - 0.11
+

Note that the gain decreases (insignificantly in practical terms, but in a numerically noticeable manner) as the element diameter and the leg lengths increase. SWR figures follow:

+ 
Antenna     Feed  3.5 MHz     3.55 MHz   3.6 MHz     3.65 MHz    3.7 MHz
+
+35VC10A     SWR   2.0         1.4        1.0         1.4         1.9
+            Z     21.0-15.4   21.9-7.6   22.8+0.2    23.8+8.0    24.8+15.7
+35VC15A     SWR   2.0         1.4        1.0         1.4         1.8
+            Z     21.0-14.8   21.9-7.5   22.8-0.2    23.8+7.2    24.8+14.5
+35VC20A     SWR   1.9         1.4        1.0         1.3         1.8
+            Z     21.0-14.1   21.9-7.1   22.8-0.1    23.8+6.9    24.8+14.0
+

Most of the numerical differences in the SWR and feedpoint impedance table figures can be attributed to the slight differentials in reactive offsets at resonance, when expanded over the test frequency range.

+

Virtually identical performance can be obtained from any hat configuration. The 23-ohm feedpoint impedance of the hatted vertical requires only a 2:1 matching section or similar scheme to permit the antenna to be used with 50-ohm coax. The chief drawback to this scheme is the mechanical unwieldiness of large hat assemblies and the likely unavailability of attachment points for the Marconi wire ends (let alone 4-wire system ends) that would preserve symmetry. A minor drawback is the fact that these antennas exhibit a secondary resonance in the range of 13.5 to 13.9 MHz, possibly making them subject to close-by 20 meter interference. However, hatted short verticals are an option that should never be far out of mind in monopole design.
+

+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 3: Base-Loading: Lumped-Constant and Linear Loading
+
+ Return to Index
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert3.html b/content/gp/linvert3.html new file mode 100644 index 0000000..a2aa12c --- /dev/null +++ b/content/gp/linvert3.html @@ -0,0 +1,126 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 3: Base-Loading: Lumped-Constant and Linear Loading + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 3: Base-Loading: Lumped-Constant and Linear Loading

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Models used:

+ 
     35BL10    35BL15    35BL20
+     35BL10A   35BL15A   35BL20A
+     35LL1015  35LL1515  35LL2015
+

A. Base Loading

Standard base-loaded short vertical monopoles place lumped-constant non-radiating loads, normally inductive, at the feedpoint of the antenna-- or more exactly, immediately between the feedpoint and the main element. Although solenoid inductors do radiate some energy, it tends to be insignificant compared to the radiation of an equivalent linear radiator. Since the region of a quarter wavelength resonant antenna immediately adjacent to the feedpoint carries the highest current, it is most influential upon the overall field strength of the antenna. If a 37.5' antenna is only 0.14 wavelengths long and the missing section relative to a 0.25 wavelength antenna is replaced at the high current region with a non-radiating load, then even apart from losses inherent in the loading element, the antenna's field strength will be seriously diminished. +

Moreover, the feedpoint impedance of the antenna, relative to a full- size monopole, will also be significantly lowered, approaching the feedpoint impedance of the shortened antenna without the base load. Whatever resistive losses may exist in the antenna structure will then occupy a greater proportion of the power fed to the antenna, power that is lost to radiation.

+

These well-known phenomena are aptly illustrated in models that place lossless inductive loads at the feedpoint to compensate for the reactance.

+ 
Antenna   Diameter  Base Load      Gain           Feedpoint Impedance
+Filename  in inches in +jX ohms    in dBi         in R ± jX ohms
+
+35BL10    1.0"      287            4.885          7.94 + 0.03
+35BL15    1.5"      266            4.886          7.89 + 0.38
+35BL20    2.0"      250            4.886          7.85 + 0.06
+

The gain figures are identical to those of the antenna without the load, since the load inductance has been assigned no loss.

+

Standard forms of base loading inherently narrow the operating bandwidth of an antenna. Below operating frequency, a higher inductive reactance is needed to bring the antenna to resonance, but an inductor in fact provides less reactance at the lower frequency. The opposite effect occurs above the design center frequency, with the same rapid rise in SWR.

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35BL10    SWR  5.5       2.5       1.0       2.4       4.8
+          Z    7.4-14.7  7.7-7.3   7.9+0.0   8.2+7.2   8.5+14.2
+35BL15    SWR  4.8       2.2       1.0       2.3       4.6
+          Z    7.4-13.3  7.6-6.4   7.9-0.0   8.2+7.0   8.4+13.6
+35BL20    SWR  4.7       2.2       1.0       2.2       4.1
+          Z    7.4-12.9  7.6-6.3   7.9+0.1   8.1+6.3   8.4+12.5
+

Although the actual values for reactance for each frequency along the sweep are lower than with some other antennas, for example, the capacity hat examples noted above, they are much higher in relationship to the values of feedpoint resistance, thus resulting in higher SWRs. The other item of note with respect to this model is that two familiar phenomena clearly reveal themselves: the small increase in gain and the increase in operating band width with increases in the main element diameter.

+

Base-loading using lossless loads can give a misleading impression of potential antenna performance, especially when compared with antenna models whose loading features are physically modeled. Therefore, as a more proper standard of comparison, the inductive base loads were assign an arbitrary Q of 300. This represents the limit of what may be practically possible and may exceed that limit when the physical coil is subject to prolonged atmospheric exposure.

+ 
Antenna   Diameter  Base Load      Gain      Feedpoint Impedance
+Filename  in inches in R+jX ohms   in dBi         in R ± jX ohms
+
+35BL10A   1.0"      0.96 + 287     4.390          8.90 + 0.03
+35BL15A   1.5"      0.89 + 266     4.422          8.78 + 0.38
+35BL20A   2.0"      0.84 + 250     4.445          8.69 + 0.06
+

The coil loss that results in lower gain and a 1-ohm increase in feedpoint impedance, also yields a slightly wider operating bandwidth:

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35BL10A   SWR  4.7       2.3       1.0       2.2       4.2
+          Z    8.4-14.7  8.6-7.3   8.9+0.0   9.2+7.2   9.4+14.2
+35BL15A   SWR  4.2       2.1       1.0       2.2       4.0
+          Z    8.3-13.3  8.5-6.4   8.8-0.0   9.0+7.0   9.3+13.6
+35BL20A   SWR  4.1       2.1       1.0       2.0       3.7
+          Z    8.2-12.9  8.4-6.3   8.7+0.1   9.0+6.3   9.2+12.5
+

It is against these numbers, and not against those of a lossless load, that one must compare base linear loading.

+

B. Base Linear Loading

An alternative to lumped constant base loading is base linear loading. A base linear load consist of a length of shorted, inductively reactive transmission line to achieve the required loading reactance. In principle, transmission lines are inherently less lossy than lumped inductors and therefore yield an antenna of higher efficiency and radiation strength. +

Contemporary antenna construction tends to modify the action of linear loads by using a portion of the main element as one wire of the parallel transmission line. Since this wire ordinarily has a much larger diameter than the pair of supplemental wires making up the other wire of the transmission line section and the initial section of the radiator, radiation in the high current region of the antenna proper is less efficient. To some degree, this inefficiency is compensated for by the imbalance between the lines of the transmission line. Further imbalance is introduced by the placement of the transmission lines at differential distances from the radiating segment. Figure 3-1 identifies the structural and electrical elements of a contemporary linearly loaded vertical antenna.

+
+ +
+

The illustration also reflects the model used to test these antennas. Because all forms of NEC have difficulties with very small angles between wires that join, a model was made of a set of parallel wires with cross wires. The structural main element was modeled at 1, 1.5, and 2 inch diameters. The supplemental wires are spaced 1.5' on either side of the main structural element and are #12 AWG wire. Horizontal connecting wires are also #12 AWG. Adjustments to resonance were made by altering the length of the 3-wire section while maintaining an overall 37.5' length. The gap between structural main element sections was arbitrarily set at 0.05 feet (0.6"). The lower horizontal member is set 0.5' above ground. The height of the gap is thus the length of the linear load plus 0.5'. The results of the modeling for lossless wire are these:

+ 
Antenna   Diameter  Linear Load    Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35LL1015  1.0"      12.5'          4.891          8.20 + 0.75
+35LL1515  1.5"      11.4'          4.891          8.51 + 0.22
+35LL2015  2.0"      10.6'          4.892          8.72 + 0.43
+

Because transmission lines are inherently high Q structures, we should expect base linear loaded models to exhibit a narrow operating bandwidth. The models do not disappoint this expectation.

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35LL1015  SWR  9.7       3.5       1.0       3.8       9.3
+          Z    7.5-22.0  7.9-10.8  8.2+0.8   8.6+12.1  9.0+23.4
+35LL1515  SWR  8.9       3.3       1.0       3.4       7.9
+          Z    7.8-21.6  8.2-10.5  8.5+0.2   8.9+11.2  9.3+21.8
+35LL2015  SWR  7.9       3.1       1.0       3.2       7.3
+          Z    8.0-20.5  8.4-10.2  8.7+0.4   9.1+10.9  9.5+21.2
+

The figures for lossless wire, like those of the lumped-constant base- loaded models, are excessively optimistic with respect to gain and excessively pessimistic with respect to operating bandwidth. More realistic would be figures using a real material. For present comparisons, we may use copper as the modeling material, with the understanding that actual losses would be somewhat higher in a real antenna, since a significant portion of the structure would be aluminum.

+ 
Antenna   Diameter  Linear Load    Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35LL1015  1.0"      12.5'          4.419          9.15 + 0.56
+35LL1515  1.5"      11.4'          4.461          9.40 + 0.08
+35LL2015  2.0"      10.6'          4.491          9.56 + 0.45
+

As predicted, the gain figures for base linear loading with copper wire are lower than those for the corresponding base loaded models with lossless loads. However they are comparable and very slightly more favorable than figures for a base loading inductance with a Q of 300. Moreover, the feedpoint impedance increases with main element diameter rather than decreasing, as with lumped-constant base loading. However, this last fact is accounted for by the decreasing size of the linear load and the resultant reduced interaction with the main element.

+

The results of imbalance among the lines of the transmission line and between those lines and the main radiator show up in several ways. The feedpoint impedances are noticeably higher than with the base-loaded models, although they still fall in the very low range. Second, the length of the linear loads differ somewhat from independently calculated linear loads. Since transmission line stub calculations normally use wires of the same diameter, the independent calculation used #12 AWG wire as a basis and used the base-loading values as targets. Line lengths of 16.3, 15.2, and 14.4 feet were calculated for the three antenna diameters. These lengths are systematically about 3.8 feet longer than the modeled values.

+

Besides imbalances created by position and wire size, another factor accounts for the length differential. Standard calculations of transmission line stubs do not account for the horizontal connecting wire at the shorted end or for connecting wires to the stub's point of application. For narrow spaced normal transmission lines, these distances are normally an insignificant fraction of the length. In the present case, where wires are space 1.5' apart, these connecting lines are a part of the overall length. Hence, to some degree, not determined in this exercise, the physically modeled horizontal wires must be added to the physical line lengths used in the model. With that in mind, the figures come much closer to agreement.

+

It may be useful to address briefly the question of treating the linear loads as mid-element loading structures. This mode of visualizing the #12 wire structure is not feasible for several reasons. First, the required mid-element loading reactance is much higher than the base loading reactance, about 1.4 times the base value, although the relationship is not identical for the three main element diameters. Second, the required 36"- wide transmission line stubs would run from nearly 21' for the 1" element to 17.5' for the 2" element. These values are far too long to correlate with the physical models. Third, the feedpoint impedances range from nearly 13.5 ohms for the 1" element to 12.8 ohms for the 2" element. The values differ considerably more from the models by than do the base-loaded values. Consequently, and with due regard to uncalculated variables created by wire-size differentials and wire placement, treating the linear load as a base-loading substitute remains the best model available.

+

Although transmission lines are inherently high Q structures, they are not lossless. Consequently, real linear loads exhibit a wider operating band width than do models using lossless wire.

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35LL1015  SWR  8.2       3.1       1.0       3.4       7.8
+          Z    8.4-22.0  8.8-10.8  9.2+0.6   9.5+12.0  9.9+23.3
+35LL1515  SWR  7.6       3.0       1.0       3.0       6.8
+          Z    8.7-21.7  9.0-10.6  9.4+0.1   9.8+11.1  10.2+21.8
+35LL2015  SWR  6.9       2.8       1.0       2.9       6.5
+          Z    8.8-20.5  9.2-10.0  9.6+0.5   10.0+10.9 10.4+21.4
+
+ +
+

Figure 3-2 compares SWR curves for the 2" diameter models of base loaded (with zero losses and with a Q of 300) and linear loaded models. The figures are more suggestive than precise, since inductors are not physical models and the linear loads have copper wire losses to moderate their values of Q. However, they do suggest that the operating bandwidth of either case, when translated into physical realities with real losses will fall within the range of the curves. Tests with other linear loaded elements shows very little operating bandwidth difference between a well- designed linear load and a high-Q coil.

+

Any form of base loading, whether in the form of a lumped inductor or a linear transmission-line inductive reactance results in a low feedpoint impedance and narrow operating bandwidth, relative to other forms of short monopole loading. In addition, the base linear loaded models exhibited a high impedance resonance within the 20-meter band.
+

+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 4: Top (Element-Extension) Loading: Linear, Zig-Zag, and Helical Loading
+
+ Return to Index
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert4.html b/content/gp/linvert4.html new file mode 100644 index 0000000..f8a3f07 --- /dev/null +++ b/content/gp/linvert4.html @@ -0,0 +1,213 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 4: Top (Element-Extension) Loading: Linear, Zig-Zag, and Helical Loading + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 4: Top (Element-Extension) Loading: Linear, Zig-Zag, and Helical Loading

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Models used:

+ 
     35LH1030  35LH1530  35LH2030
+     35VT1010  35VT1510  35VT2010
+     35VT1020  35VT1520  35VT2020
+     35VT1030  35VT1530  35VT2030
+     35VZ1025  35VZ1525  35VZ2025
+               35VH1525
+

Virtually all forms of top-loading are forms of element extension loading, that is, means of extending the element length electrically without adding physical height to a given monopole. So-called capacity hats form a special case in which two or more extensions are symmetrically arranged to minimize radiation from the assembly. This measure is considered desirable whenever the designer wishes to preserve an essentially vertically polarized field from the monopole. With this in mind, we may overlook the inverted-L configuration, since the horizontal extension of the monopole element provides substantial horizontally polarized radiation to the overall pattern, thus disrupting the essentially circular, low angle pattern of a true vertical radiator.

+

However, there are a number of techniques of element extension loading that are not true hats and which do not add significant horizontally polarized radiation to the pattern. The pattern remains circular, low angle, and the horizontal component is at least 30 to 35 dB below the level of the overall radiation pattern.

+

A. Top Linear Loading

A top linear load represents a fold-back of the antenna element and a refold forward. The resulting assembly is visually similar to the base linear load. However, because it does not occur in the high current portion of the antenna element, it cannot be treated as a transmission line stub with inductive reactance. Indeed, inductive reactance grows progressively less influential on antenna performance the farther outward it is placed along the element. The top linear load should be treated as a simple fold-back whose overall length will be somewhat longer than the linear extension of the element to resonance. The lengthening is due to interaction with the nearby "lower" portion of the antenna it parallels, with consequential current cancellation. Since the current along the element is sinusoidal rather than linear, cancellations do not yield an easily calculable remainder apart from method-of-moments techniques. +

One common form of top linear loading is the addition of a Tee element across but insulated from the top of the antenna. Supplementary wires from the ends of the conductive Tee connect to either side of an insulated break in the main element. Figure 4-1 illustrates the general principle.

+
+ +
+

Modeling the linear top load as in part A. of the figure would require a very tight acute angle, a difficulty for all method-of-moments software. To evaluate the general principle of top loading, an alternative model was developed with angles more closely approaching right angles, as shown in part B of the figure. A top bar at the 37.5' mark extends 3.0' either side of the main element. Supplementary wires (#12 AWG) drop to the 19.9' mark and to a mark 0.05' lower, connecting to horizontal extension rods from each side of the split main element. Interestingly, it was only necessary to extend or contract the length of this lower bar to adjust the configuration for main element diameters of 1 to 2 inches. The figure in the table is the length of the lower bar on one side of the antenna, with the other lower bar being of equal length.

+ 
Antenna   Diameter  Lower Bar      Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35LH1030  1.0"      1.5'           4.911          16.71 - 0.46
+35LH1530  1.5"      1.25'          4.913          16.84 - 0.26
+35LH2030  2.0"      1.0'           4.913          16.94 - 0.38
+

The decreasing length of the lower bar indicates that less supplementary wire length was needed as the main element increased in diameter. Gain exceeds either form of base loading and approaches the gain of a capacity-hat monopole. Horizontally polarized radiation is down by at least 40 dB, and the vertical characterization of the field is thus undisturbed. The feedpoint impedance is considerably higher than that of base-loaded models, but still significantly lower than the capacity-hat models.

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35LH1030  SWR  4.7       2.3       1.0       2.1       4.2
+          Z    15.1-26.9 15.9-13.8 16.7-0.5  17.6+13.2 18.6+27.3
+35LH1530  SWR  4.6       2.3       1.0       2.1       4.3
+          Z    15.1-26.9 16.0-13.7 16.8-O.3  17.8+13.5 18.8+28.3
+35LH2030  SWR  4.7       2.3       1.0       2.1       4.3
+          Z    15.2-27.1 16.0-14.0 16.9-0.4  17.9+13.6 19.0+28.4
+

The operating bandwidth of the top linear loaded monopole is slightly under 100 kHz with the lossless wire used in these models. With aluminum and copper materials, the bandwidth is likely to expand slightly to reach the 100 kHz mark.

+

B. Zig-Zag Top Loading

One alternative to using a single linear load element extension that eliminates some of the current cancellation as below the 20' mark of the main element is to use multiple folds. These folds, of uniform length, would surround the main element symmetrically in a 2-down-2-up pattern, resulting in four wires. A simple insulated cross at the antenna top and at the lower extremity of the element extension assembly could provide proper spacing. Figure 4-2 illustrates the general principle behind this zig-zag element extension. +
+ +
+

In principle, the zigzag assembly should result in a shorter overlap than the single linear top load. As a result, the antenna should exhibit additional gain, although this figure might well be marginal from an operational perspective.

+

A fairly large number of models were constructed, using different main element diameters and differing spacings from the main element of the supplemental wires (#12 AWG). In each table, the Zig-Zag length entry represent the length in feet of the wire assembly as measured from the top downward.

+ 
1.  1' center-to-center spacing from main element to zigzag assembly wires
+
+Antenna   Diameter  Zig-Zag        Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35VT1010  1.0"      16.55'         4.914          16.55 + 0.24
+35VT1510  1.5"      16.9'          4.913          16.47 - 0.10
+35VT2010  2.0"      17.1'          4.913          16.42 - 0.70
+
+2.  2' center-to-center spacing from main element to zigzag assembly wires
+
+Antenna   Diameter  Zig-Zag        Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35VT1020  1.0"      13.25'         4.924          17.78 + 0.41
+35VT1520  1.5"      13.75'         4.923          17.66 + 0.13
+35VT2020  2.0"      14.1'          4.923          17.57 + 0.32
+
+3.  3' center-to-center spacing from main element to zig-zag assembly wires
+
+Antenna   Diameter  Zig-Zag        Gain      Feedpoint Impedance
+Filename  in inches length (feet)  in dBi         in R ± jX ohms
+
+35VT1030  1.0"      10.7'          4.933          18.71 + 0.32
+35VT1530  1.5"      11.26'         4.932          18.56 + 0.38
+35VT2030  2.0"      11.62'         4.932          18.43 - 0.45
+

The series of models exhibits several important traits. First, as the separation of the zigzag assembly grows larger, so too does the gain and the feedpoint impedance, while the required zigzag assembly length decreases. Second, within each group of models, increasing the main element diameter decreases gain and feedpoint impedance, while lengthening the required zigzag assembly. Figure 4-3 compares the required zigzag assembly length for each level of spacing and main-element diameter. The progressions are regular, but not precisely linear. Increasing the main element diameter actually decreases slightly the spacing of the assembly from the radiating surface of that element. Within each group, best performances comes from the smallest diameter main element, which may not be consistent with mechanical requirements for such antennas.

+
+ +
+

The overall length of the 4-wire zigzag assemblies may be compared with the length of the single top linear load: 17.6' from the antenna top downward at a top spacing of 3' from the main element. With equivalent 3' spacing from the element, the 4-wire zigzag assembly length is approximately two-thirds that of the 2-wire fold-back. The models using 1' spacing result in an assembly almost as long as the top linear load. However, had the top linear load been more closely spaced than 3' from the main element, it would have extended several feet farther down the element. In mechanical terms, the 1' spacing of the 4-wire zigzag assembly may be more mechanically sound than the 2-wire assembly spaced at 3' for very similar performance.

+

Although the gain increase of the zigzag loading method is operationally marginal, garnering the highest feedpoint impedance possible is of operational importance. Moreover, the assemblies spaced 3' from the main element exhibit another advantage over more closely spaced zigzags and linear top-loads: a wider operating bandwidth.

+ 
1.  1' center-to-center spacing from main element to zigzag assembly wires
+
+Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35VT1010  SWR  6.4       2.7       1.0       2.8       6.5
+          Z    14.7-33.2 15.6-17.0 16.5+0.2  17.6+18.5 18.8+37.9
+35VT1510  SWR  7.1       3.0       1.0       3.0       7.4
+          Z    14.5-35.3 15.4-18.4 16.5-O.1  17.6+19.6 19.0+41.4
+35VT2010  SWR  7.9       3.3       1.0       3.2       8.2
+          Z    14.3-37.5 15.3-19.9 16.4-0.7  17.7+20.7 19.2+44.6
+
+2.  2' center-to-center spacing from main element to zigzag assembly wires
+
+Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35VT1020  SWR  4.1       2.1       1.0       2.1       4.1
+          Z    16.0-25.9 16.9-13.0 17.8-0.4  18.8+14.2 19.8+28.5
+35VT1520  SWR  4.3       2.2       1.0       2.2       4.2
+          Z    15.8-26.6 16.7-13.5 17.7+O.1  18.7+14.4 19.8+29.4
+35VT2020  SWR  4.4       2.2       1.0       2.2       4.5
+          Z    15.6-27.0 16.6-13.6 17.6+0.3  18.7+15.0 19.9+30.7
+
+3.  3' center-to-center spacing from main element to zigzag assembly wires
+
+Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35VT1030  SWR  3.4       1.9       1.0       1.9       3.3
+          Z    16.9-23.3 17.8-11.7 18.7+0.3  19.7+12.5 20.7+24.9
+35VT1530  SWR  3.5       1.9       1.0       1.9       3.4
+          Z    16.7-23.2 17.6-11.6 18.6+O.4  19.6+12.7 20.7+25.5
+35VT2030  SWR  3.6       2.0       1.0       1.9       3.4
+          Z    16.5-24.1 17.5-12.4 18.4-0.5  19.5+12.0 20.6+25.0
+

The trends in the general performance figures are replicated in the SWR and impedance sweeps. Within each group, the large the main element diameter, the narrower the operating band width. The greater the spacing of the zigzag assembly from the main element, the greater the operating bandwidth. A spacing of 1' does not achieve 100 kHz between 2:1 SWR figures. Figure 4-4 compares SWR curves for the 2" diameter main element models at the three spacings.

+
+ +
+

Although the 2' spaced assemblies exhibit a bandwidth similar to that of the 3' spaced top linear load, the 3' spaced zigzag assemblies show a clearly superior operating bandwidth. Added to the higher feedpoint impedance, this structure may be worth considering, despite its greater mechanical difficulties.

+

For all these models, horizontal components to the total field were greater than 35 dB down from the total pattern and virtually without effect on pattern strength and shape.

+

C. Helical Loading

An alternative to either the linear of zigzag top loading arrangements is the use of a helical loading extension. Such an arrangement is most effective when spaced some distance from the main element: a standardized 3' spacing was adopted for these models. Additionally, for efficiency and in anticipation of mechanical requirements for such a system, a coil-wire diameter of 0.25" was selected for the test loading elements. +

When placed on an antenna far from the feedpoint, a loading helix shows little inductive reactance effect. Rather, the wire forms a coiled element extension to provide a current path sufficient for resonance. The inductive effect of the coil appears mostly in the fact that the total length of wire required for resonance is greater that for linear systems. On the other hand, the assembly can be quite compact. In the test models, the assembly was about 2' long. This figure may be best appreciated when compared to the 11' assemblies required for zigzag structures spaced 3' from the main element. Figure 4-5 illustrates the principle.

+
+ +
+

For test purposes, models were constructed using a square helix form, with each turn held at the same level and only the last of the 4 wires in the turn dropped to the next lower level. turns were spaced 0.5' apart. In the model table, the length of the coil is indicated by the number of turns and can be converted into feet by dividing by 2. Since spacing is a standard 3' from the coil, the last pair of numbers in the file name indicates the wire diameter. One constraint on the model due to the use of a square model coil is that part of each quarter turn passes as close as a little over 2' from the main element. A truly circular coil will require fewer turns for the same effect.

+ 
Antenna   Diameter  Number    Gain      Feedpoint Impedance
+Filename  in inches of turns  in dBi         in R ± jX ohms
+
+35VZ1025  1.0"      3.98      4.954          22.10 + 0.10
+35VZ1525  1.5"      4.05      4.953          22.07 - 0.80
+35VZ2025  2.0"      4.13      4.953          22.08 - 0.94
+

Shortening the length of the top-loading assembly has two beneficial effects. First, it reduces the amount of interaction between the assembly and portions of the main element carrying higher currents, with a consequential increase in antenna gain. Indeed, lossless wire gain figures are higher even than those for a capacity hat vertical (4.940 dBi vs. 4.953 dBi), although marginally so. The horizontal component of the total radiation field of the helical loading system is greater than 35 dB below the total field value.

+

Second, the same decrease in interaction raises the resonant feedpoint impedance to the 22-ohm range. This figure is second only to the capacity hat verticals (22.75 ohms) among the shortened monopole models and several ohms greater than corresponding zigzag and top linear loaded models (about 18.5 ohms). However, a relatively high resonant feedpoint impedance does not guarantee the widest operating bandwidth.

+ 
Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35VZ1025  SWR  4.0       2.1       1.0       2.1       4.1
+          Z    19.5-31.5 20.7-16.2 22.1+0.1  23.6+17.3 25.3+36.0
+35VZ1525  SWR  4.4       2.2       1.0       2.1       4.3
+          Z    19.3-33.1 20.6-16.0 22.1-O.8  23.7+17.3 25.7+37.3
+35VZ2025  SWR  4.5       2.3       1.0       2.2       4.2
+          Z    19.1-34.0 20.5-18.1 22.1-0.9  23.9+18.0 26.0+39.3
+

The 2:1 SWR operating bandwidth is less than 100 kHz (in these lossless wire models). The higher sweep limit SWRs are due to higher reactance components than in corresponding models of top loading using linear of zigzag assemblies.

+

Because the models used flat turns, the results were checked against several alternative models. Reversing the direction of the helix produced identical output figures. Bending the last turn in the helix toward the main element and using a vertical wire closely spaced to the main element as a means of resonance adjustment also had no effect upon the gain, the feedpoint impedance, or the SWR curve, although this arrangement may have significant mechanical implications. Finally, a model was created using a 0.125' per quarter turn descent rate. A model corresponding to the 1.5" flat turn model is presented for comparison:

+ 
Antenna   Diameter  Number    Gain      Feedpoint Impedance
+Filename  in inches of turns  in dBi         in R ± jX ohms
+
+35VH1525  1.0"      4.14      4.952          21.95 - 0.09
+
+Antenna   Feed 3.5 MHz   3.55 MHz  3.6 MHz   3.65 MHz  3.7 MHz
+
+35VH1525  SWR  4.3       2.2       1.0       2.2       4.5
+          Z    19.2-32.7 20.5-17.1 22.0-0.1  23.6+18.3 25.5+38.6
+

These figures are virtually indistinguishable from those for the corresponding flat turn model, so further modeling of constant rate descent helical top loads and other similar configurations was judged unnecessary at this stage of the investigation.

+

Among the top-loading methods examined here, the wide-spaced helical method offers the highest gain and highest feedpoint impedance. The wide- spaced zig-zag assembly offers the greatest operating bandwidth. Figure 4- 6 compares the SWR curves of a sample (using 1.5" diameter main elements) of each top-loading method with the same main element diameter. Whether either is equally or more mechanically feasible than top linear loading is a judgment beyond the scope of this modeling study.

+
+ +
+

Using lossless wire against perfect ground permits a detailed comparison of the theoretical possibilities of element extension top loading. However, it is also fair to ask to what degree the use of real materials will moderate the promise shown by some of these models. The answer to this question is complicated by the fact that a real structure of any of these sorts is likely to be a composite of copper and aluminum in differing proportions, according to the load type. However, some indication may be given by looking at models of samples of each type of antenna. For an initial comparison with models using lossless wire, models were constructed of both all-copper and all-aluminum antennas using 1" diameter main elements. Given are the gain in dBi and the resonant feedpoint impedance.

+ 
File Name Antenna Description      Gain Feedpoint Impedance
+                                   dBi  Z = R ± jX in ohms
+
+1.  Linear top-loaded model
+35LH1030  17.6x1.5' load, 1" mast  4.91      16.71 + 0.46   Lossless
+                                   4.72      17.51 + 0.47   Copper
+                                   4.62      17.92 + 0.45   Aluminum
+
+2.  Zig-Zag top-loaded models
+35VT1010  16.55' load, 1" mast     4.91      16.55 + 0.24   Lossless
+          1' spacing               4.61      17.76 + 0.19   Copper
+                                   4.45      18.40 + 0.17   Aluminum
+
+35VT1020  13.25' load, 1" mast     4.92      17.78 + 0.49   Lossless
+          2' spacing               4.76      18.47 + 0.46   Copper
+                                   4.68      18.83 + 0.45   Aluminum
+
+35VT1030  10.7' load, 1" mast      4.93      18.71 + 0.24   Lossless
+          3' spacing               4.82      19.22 + 0.22   Copper
+                                   4.76      19.49 + 0.20   Aluminum
+
+3.  Helically top-loaded model
+35VZ1025  3.98 turn load, 1" mast  4.95      22.10 + 014    Lossless
+          3' spacing               4.89      22.41 + 0.13   Copper
+                                   4.86      22.57 + 0.11   Aluminum
+

For further comparison, aluminum antennas falling into the full-size and capacity hat categories do not decrease gain or significantly change feedpoint impedance relative to lossless wire models. Gain reductions are of the order of 0.01 to 0.02 dB and impedance factor changes are less than 0.1 ohm.

+

Of the selected models, the 1' spaced zigzag model shows the greatest change of gain when modeled in aluminum. This occurs because the length of #12 wire is so long and the interaction with the main element extends farthest down the antenna. By way of contrast, the helical model, with only 2' of interactive length and 0.25" wire shows the least change of gain and feedpoint impedance of all the element extension top-loaded models.

+

Wide-spacing of the element extension load along with minimal load length appear to offer the most promise among models of this type for the best balance of gain, feedpoint impedance, and operating bandwidth. None of the top-loaded element extension models showed any type of resonance in or near the 20-meter band.
+

+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 5: Summary Comparisons and Conclusions; With an Alternative Suggestion
+
+ Return to Index
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert5.html b/content/gp/linvert5.html new file mode 100644 index 0000000..20c1501 --- /dev/null +++ b/content/gp/linvert5.html @@ -0,0 +1,137 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 5: Summary Comparisons and Conclusions + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 5: Summary Comparisons and Conclusions

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

In order the clarify the basis upon which the conclusions of this study are drawn, the initial goals of this study are apt for review:

+

1. The antenna should have the maximum gain achievable within the limits of the antenna type.

+

2. The antenna should exhibit a true vertically-polarized circular radiation pattern.

+

3. The antenna should have the highest possible feedpoint impedance at resonance for maximum efficiency.

+

4. The antenna should exhibit the flattest SWR curve possible between 3.5 and 3.7 MHz.

+

5. The antenna should promise the most compact and mechanically practical assembly possible.

+

Goal 2. is achieved by every model studied, with all horizontal field components sufficiently suppressed to yield essentially true vertically polarized circular patterns. Goal 5. requires a separate discussion for each model after examining the results with respect to goals 1., 3., and 4.

+

For the sake of compactness, some of the data described in detail in the preceding chapters may be summarized in tabular form. "Mast" means the main element. All antenna are 37.5' tall. Except for the special case of base-loading with a Q=300 inductance, all models are listed in terms of lossless wire.

+ 
File Name   Antenna Description     Gain  Feedpoint Impedance ±50 kHz SWR
+                                    dBi   Z = R ± jX in ohms
+1.  Capacity-hat models
+35VC10      2-wire hat, 1" mast        4.940 22.75 - 0.33           1.5 - 1.4
+35VC15      2-wire hat, 1.5" mast      4.940 22.75 - 0.92           1.5 - 1.3
+35VC20      2-wire hat, 2" mast        4.940 22.79 - 0.73           1.4 - 1.3
+35VC10A     4-wire hat, 1" mast        4.947 22.83 + 0.24           1.4 - 1.4
+35VC15A     4-wire hat, 1.5" mast      4.945 22.83 - 0.15           1.4 - 1.4
+35VC20A     4-wire hat, 2" mast        4.943 22.86 - 0.11           1.3 - 1.3
+
+2.  Inductive base-loaded models
+
+2.1  Lossless inductive loads
+35BL10      0-loss load, 1" mast       4.885  7.94 + 0.03           2.5 - 2.4
+35BL15      0-loss load, 1.5" mast     4.886  7.89 + 0.38           2.2 - 2.3
+35BL20      0-loss load, 2" mast       4.886  7.85 + 0.06           2.2 - 2.2
+
+.1  Lossy inductive loads:  Q=300
+35BL10      Q-300 load, 1" mast        4.390  8.90 + 0.03           2.3 - 2.2
+35BL15      Q-300 load, 1.5" mast      4.422  8.78 + 0.38           2.1 - 2.2
+35BL20      Q-300 load, 2" mast        4.445  8.69 + 0.06           2.1 - 2.1
+
+3.  Linear base-loaded models
+
+35LL1015    12.5' load, 1" mast        4.891  8.20 + 0.75           3.5 - 3.8
+35LL1515    11.4' load, 1.5" mast      4.891  8.51 + 0.22           3.3 - 3.4
+35LL2015    10.6' load, 2" mast        4.892  8.72 + 0.43           3.1 - 3.2
+
+4.  Linear top-loaded models
+35LH1030    17.6x1.5' load, 1" mast    4.911 16.71 - 0.46           2.3 - 2.1
+35LH1530    17.6x1.25' load, 1.5" mast 4.913 16.84 - 0.26           2.3 - 2.1
+35LH2030    17.6x1' load, 2" mast      4.913 16.94 - 0.38           2.3 - 2.1
+
+5.  Zig-zag top-loaded models
+
+5.1  1' mast-to-load spacing
+35VT1010    16.55' load, 1" mast       4.914 16.55 + 0.24           2.7 - 2.8
+35VT1510    16.9' load, 1.5" mast      4.913 16.47 - 0.10           3.0 - 3.0
+35VT2010    17.1' load, 2" mast        4.913 16.42 - 0.70           3.3 - 3.2
+
+5.2  2' mast-to-load spacing
+35VT1020    13.25' load, 1" mast       4.924 17.78 + 0.41           2.1 - 2.1
+35VT1520    13.75; load, 1.5" mast     4.923 17.66 + 0.13           2.2 - 2.2
+35VT2030    14.1' load, 2" mast        4.923 17.57 + 0.32           2.2 - 2.2
+
+5.3  3' mast-to-load spacing
+35VT1030    10.7' load, 1" mast        4.933 18.71 + 0.32           1.9 - 1.9
+35VT1530    11.26' load, 1.5" mast     4.932 18.56 + 0.38           1.9 - 1.9
+35VT2030    11.62' load, 2" mast       4.932 18.43 - 0.45           2.0 - 1.9
+
+6.  Helically top-loaded models:  3' spacing
+35VZ1025    3.98 turn load, 1" mast    4.954 22.10 + 010            2.1 - 2.1
+35VZ1525    4.05 turn load, 1.5" mast  4.953 22.07 - 0.80           2.2 - 2.1
+35VZ2025    4.13 turn load, 2" mast    4.953 22.08 - 0.94           2.3 - 2.2
+35VH1525    4.14 turn load, 1.5" mast  4.952 21.95 - 0.09           2.2 - 2.2
+

Without question, the capacity hat models represent the best performance with respect to gain, feedpoint impedance, and operating bandwidth. Unfortunately, they present mechanical problems for the construction of a single, self-supporting (with or without guys) vertical antenna for 80-meters. Hat wires are simply too long and require end supports suited to specialized installations. For more on this subject, see the special section at the end of this chapter.

+

Surpassing the capacity hat verticals (marginally) in gain and only slightly lower in feedpoint impedance are the helically top-loaded monopoles using 3' spacing between the main element and the coil. Although these antennas have an operating band width approximating that of the 2-foot spaced zigzag top load and the linear top load, it is anticipated that, when translated to real materials and feedlines, the effective bandwidth would reach 100 kHz. However, the mechanical questions are significant: can a light, stiff 0.25" wire 6' diameter 4-turn coil assembly be developed that will withstand wind loads at the top of the antenna. It is likely that such an antenna will require an insulated coil-bracing spider and special consideration of the bending characteristics of the main mast at various wind levels.

+

Among non-hat top loads, the 3-foot spaced zigzag models provide the widest operating band width: well over 100 kHz at the 2:1 SWR points. Additionally, antenna gain is quite good, only slightly less than the helical and hat models. However, feedpoint impedance drops to the 18.5 ohm range, considerably less than the 22+ ohms offered by the hat and helical models. Because these antennas require an 11' long 6' wide set of load wires, special care must be taken to maintain spacing along a wind-bent antenna. This problem may be less severe than with the helical load due to the fact that much lighter wire can be used for the load assembly.

+

Top linear loading offers greater mechanical simplicity in its two wire, 17.6' assembly. However, its gain is less, its feedpoint impedance is lower, and its operating bandwidth is narrower than the models noted above.

+

Base-loading, whether in the form of an inductor or a linear load offers a very low feedpoint impedance (under 10 ohms) with no compensating qualities, such as high gain or wide operating bandwidth. Therefore, despite the mechanical simplicity of such models, they have little else to recommend them, especially when compared to the potentials of top-loaded short vertical monopoles.

+

This phase of the study has reached the conclusion that the top-loaded models of short vertical monopoles deserve further investigation in terms of potential performance using the real materials (aluminum and copper) over real ground and ground planes. A viable standard against which such performance potentials can be measured is the capacity-hat model.

+

One advantage held by this preliminary study is that it could be conducted within the modeling limits of a single method-of- moments program, MININEC 3.13. Since further studies will require ground planes and real grounds, they must employ one or more versions of NEC, both to take advantage of the Sommerfeld-Norton ground modeling algorithms and to allow for the large number of wires and segments utilized by extensive ground planes and complex antenna geometries. However, NEC--in both versions 2 and 4--is limited with respect to handling nonlinear geometries with wires of different diameters will require. This will require the construction of substitute models. Although absolute reported values will therefore become unreliable, models can be evaluated against suitable standards. In the present case, top-loaded short vertical monopole models may be measured against a combination of the full size quarter wavelength vertical and the capacity-hat shorter monopole to permit correlations that cross modeling program lines.

+

Special Section: The Top-Hat Revisited

Because modeling top hats with MININEC is limited by the restriction on the number of segments allowed in any one model, a fuller exploration of possibilities was conducted in NEC-4. The figures given for gain and feedpoint impedance are not directly comparable to those appearing for MININEC models. Therefore, this section is separated for consideration on its own. +

I modeled a number of top-hat configurations, including those using only spokes and those using spokes plus a perimeter wire. All models use aluminum as the antenna and top-hat material, so comparison with lossless wire model shown above is inappropriate. In all cases, the antenna diameter is 1", and radials are 0.25" in diameter.

+ 
Antenna     Number      Radial          Gain        Feedpoint Impedance
+Filename    of radials  length, feet    in dBi            in R ± jX ohms
+
+35SC1025    16           7.2'            4.95              23.02 - 0.75
+35RC1025    32           6.1'            4.95              23.07 - 0.35
+35EC1025    8 w/perim    6.7'            4.94              23.08 + 0.50
+

All of these antennas had SWR curves like those shown for the hatted models developed with MININEC. NEC-4 returns very slightly higher values at the +/-100 kHz extremes: 2.0 to 2.1 at 3.5 MHz and 1.9 at 3.7 MHz.

+

Increasing the number of radials or adding a perimeter wire permits a very significant reduction in the radius of the hat required. However, such hats a structurally very restrictive. A first consideration is weight, which is proportional to the total wire required by a given hat structure. The 32-wire hat required more than 190' of hat wire. The 16-radial version cut that to about 115' at a cost of a larger overall radius. The 8-spoke with perimeter wire model used the least wire (92').

+

A second consideration is ease of adjustment for the constructor. A perimeter model hat is normally fixed in construction. Large numbers of hat wires are not cost-effectively pruned. Hence, most builders simply change the antenna height until it matches the chosen hat.

+

There is an alternative structure for hats that verges on falling into the category of top loads that are not true hats. One may spiral as few as 4 wires for several equi-spaced turns in a flat plane. The turns may be curves or straight lines with regular expansions in distance from the main element with no change of performance. Figure 5-1 shows a squared turn model.

+
+ +
+

The squared-turn model used 1+ spiral turn per wire with a 6.4' maximum distance from the main element at the corners. Using shorter wires to simulate curved spirals yielded no change in ultimate radius of wire length. The final product reported here required about 112' of wire, with 4 easily trimmed or extended ends.

+

The aluminum antenna produced a modeled gain of 4.94 dBi over perfect ground, suggesting true capacity-hat performance an superiority over the best of the top-loaded models when using other than lossless wire. Figure 5-2 shows an elevation pattern, including the remnant -40 dB horizontal component created by the fact that the spiral hat does not achieve absolutely perfect symmetry.

+
+ +
+

The SWR curve suggests a 2:1 SWR operating bandwidth of at least 200 kHz:

+ 
Antenna     Feed  3.5 MHz     3.55 MHz   3.6 MHz     3.65 MHz    3.7 MHz
+
+35HC1025    SWR   2.1         1.5        1.0         1.4         1.9
+            Z     21.3-16.8   22.2-8.7   23.1-0.5    24.0+7.5    25.0+15.7
+

It is quite likely that operational models of an antenna such as this might be designed for 3 ranges: 3.5-3.65; 3.65-3.8; and 3.8-4.0 with only a height adjustment in the main element. Using the same hat required a mast length of 32.8' to cover the upper 200 kHz of the band. Alternatively, hat adjustment can be easily made. A third alternative would be set the antenna for the lowest range and to switch in series capacitors (between the antenna and a 2:1 matching network or device) to cancel the inductive reactance as the operating frequency is increased.

+

Mechanically, a spiral offers another advantage in addition to the limited number of wires. An insulated 4-spoke structure might be developed for assembly at the top of the main element. Each spoke might be physically independent but interlocking at the main mast with the adjacent spoke support(s). The hat wires might fall into grooves in each spoke to assure long term alignment. However, the disassembled support system would lie in a flat stack of 4 pieces for ease of transport. I suspect a main element large than 1" would be required to handle such an assemblage.

+

Just because I have not previously seen hats designed either as spirals or as any of the non-standard configurations noted in the last chapter does not mean that they have not been used or that they have not appeared in the lengthy literature on short verticals. nonetheless, I thought it worth reporting as one more way to break preconceptions about what hats must look like to do their job of producing relatively efficient and wide-band short verticals for 80 meters.
+

+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 6: Descriptions of Models Reported
+
+ Return to Index
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


+ + diff --git a/content/gp/linvert6.html b/content/gp/linvert6.html new file mode 100644 index 0000000..99ceda4 --- /dev/null +++ b/content/gp/linvert6.html @@ -0,0 +1,1307 @@ + + + + + + Half-Length 80-Meter Vertical Monopoles Part 6: Descriptions of Models Reported + + + +
+

Half-Length 80-Meter Vertical Monopoles:
+ Part 6: Descriptions of Models Reported

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

As a reference, the following pages provide descriptions of the antenna models reported. The descriptions involve a conversion of the file from the ELNEC-MININEC form used in the modeling to the EZNEC-NEC format in which they can be downloaded as text files. However, each file should be easily translatable into a form sufficient for antenna construction under any common antenna modeling program. For ease of reading, antenna descriptions are not split across pages. Numbering categories refer to chapters in the preceding report.

+ 
+2.   Baseline Data:  Full-Size and Capacity-Hat Verticals
+
+
+2.1  Full-size vertical monopoles:
+
+35V10
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 65.970     G   0.000,  0.000,  0.000 1.00E+00  60
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          60     1 / 99.17   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35V15
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 65.900     G   0.000,  0.000,  0.000 1.50E+00  60
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          60     1 / 99.17   (  1 /100.00)      1.000       0.000       I
+
+
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+35V20
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 65.800     G   0.000,  0.000,  0.000 2.00E+00  60
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          60     1 / 99.17   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+2.2  Short (37.5') 80-meter vertical monopoles
+
+35VS10
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+35VS15
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VS20
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+
+2.3  Capacity Hat Monopoles:  Marconi
+
+
+35VC10
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2          -19.000,  0.000, 37.500  W3E2   0.000,  0.000, 37.500 1.00E+00  20
+3           19.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 1.00E+00  20
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+35VC15
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2          -19.000,  0.000, 37.500  W3E2   0.000,  0.000, 37.500 1.50E+00  20
+3           19.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 1.50E+00  20
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+35VC20
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2          -19.050,  0.000, 37.500  W3E2   0.000,  0.000, 37.500 2.00E+00  20
+3           19.050,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.00E+00  20
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+2.4  Capacity Hat Monopoles:  4-wire
+
+35VC10A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2          -15.800,  0.000, 37.500  W3E2   0.000,  0.000, 37.500    # 12   10
+3           15.800,  0.000, 37.500  W4E2   0.000,  0.000, 37.500    # 12   10
+4            0.000, 15.800, 37.500  W5E2   0.000,  0.000, 37.500    # 12   10
+5            0.000,-15.800, 37.500  W1E1   0.000,  0.000, 37.500    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+
+35VC15A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2          -16.800,  0.000, 37.500  W3E2   0.000,  0.000, 37.500    # 12   10
+3           16.800,  0.000, 37.500  W4E2   0.000,  0.000, 37.500    # 12   10
+4            0.000, 16.800, 37.500  W5E2   0.000,  0.000, 37.500    # 12   10
+5            0.000,-16.800, 37.500  W1E1   0.000,  0.000, 37.500    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VC20A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2          -17.600,  0.000, 37.500  W3E2   0.000,  0.000, 37.500    # 12   10
+3           17.600,  0.000, 37.500  W4E2   0.000,  0.000, 37.500    # 12   10
+4            0.000, 17.600, 37.500  W5E2   0.000,  0.000, 37.500    # 12   10
+5            0.000,-17.600, 37.500  W1E1   0.000,  0.000, 37.500    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+3.   Base-Loading:  Lumped-Constant and Linear Loading
+
+3.1  Lumped-constant base loading:  lossless loads
+
+35BL10
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.000       287.000
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35BL15
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.000       266.000
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35BL20
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.000       250.500
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+3.2  Lumped-constant base loading:  load Q = 300
+
+35BL10A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.960       287.000
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35BL15A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.890       266.000
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35BL20A
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)       0.840       250.500
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+3.3  Linear base loading
+
+35LL1015
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 13.050 1.00E+00  25
+2     W7E2   0.000,  0.000, 13.000     G   0.000,  0.000,  0.000    # 12   20
+3     W1E2   0.000,  0.000, 13.050  W4E1   1.500,  0.000, 13.050    # 12    2
+4     W3E2   1.500,  0.000, 13.050  W5E1   1.500,  0.200,  0.500    # 12   20
+5     W4E2   1.500,  0.200,  0.500  W6E1  -1.500,  0.200,  0.500    # 12    4
+6     W5E2  -1.500,  0.200,  0.500  W7E1  -1.500,  0.000, 13.000    # 12   20
+7     W6E2  -1.500,  0.000, 13.000  W2E1   0.000,  0.000, 13.000    # 12    2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          20     2 / 97.50   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35LL1515
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 11.950 1.50E+00  25
+2     W7E2   0.000,  0.000, 11.900     G   0.000,  0.000,  0.000    # 12   20
+3     W1E2   0.000,  0.000, 11.950  W4E1   1.500,  0.000, 11.950    # 12    2
+4     W3E2   1.500,  0.000, 11.950  W5E1   1.500,  0.200,  0.500    # 12   20
+5     W4E2   1.500,  0.200,  0.500  W6E1  -1.500,  0.200,  0.500    # 12    4
+6     W5E2  -1.500,  0.200,  0.500  W7E1  -1.500,  0.000, 11.900    # 12   20
+7     W6E2  -1.500,  0.000, 11.900  W2E1   0.000,  0.000, 11.900    # 12    2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          20     2 / 97.50   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35LL2015
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 11.150 2.00E+00  25
+2     W7E2   0.000,  0.000, 11.100     G   0.000,  0.000,  0.000    # 12   20
+3     W1E2   0.000,  0.000, 11.150  W4E1   1.500,  0.000, 11.150    # 12    2
+4     W3E2   1.500,  0.000, 11.150  W5E1   1.500,  0.200,  0.500    # 12   20
+5     W4E2   1.500,  0.200,  0.500  W6E1  -1.500,  0.200,  0.500    # 12    4
+6     W5E2  -1.500,  0.200,  0.500  W7E1  -1.500,  0.000, 11.100    # 12   20
+7     W6E2  -1.500,  0.000, 11.100  W2E1   0.000,  0.000, 11.100    # 12    2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          20     2 / 97.50   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+4.  Top (Element-Extension) Loading:  Linear, Zig-Zag, and Helical Loading
+
+4.1  Linear loading
+
+35LH1030
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 19.900 1.00E+00  30
+2     W7E2   0.000,  0.000, 19.850     G   0.000,  0.000,  0.000 1.00E+00  25
+3     W1E2   0.000,  0.000, 19.900  W4E1   1.500,  0.000, 20.050    # 12    3
+4     W3E2   1.500,  0.000, 20.050  W5E1   3.000,  0.100, 37.500    # 12   25
+5     W4E2   3.000,  0.100, 37.500  W6E1  -3.000,  0.100, 37.500    # 12    8
+6     W5E2  -3.000,  0.100, 37.500  W7E1  -1.500,  0.000, 20.000    # 12   25
+7     W6E2  -1.500,  0.000, 20.000  W2E1   0.000,  0.000, 19.850    # 12    3
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          25     2 / 98.00   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35LH1530
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 19.900 1.50E+00  30
+2     W7E2   0.000,  0.000, 19.850     G   0.000,  0.000,  0.000 1.50E+00  25
+3     W1E2   0.000,  0.000, 19.900  W4E1   1.250,  0.000, 20.050    # 12    3
+4     W3E2   1.250,  0.000, 20.050  W5E1   3.000,  0.100, 37.500    # 12   25
+5     W4E2   3.000,  0.100, 37.500  W6E1  -3.000,  0.100, 37.500    # 12    8
+6     W5E2  -3.000,  0.100, 37.500  W7E1  -1.250,  0.000, 20.000    # 12   25
+7     W6E2  -1.250,  0.000, 20.000  W2E1   0.000,  0.000, 19.850    # 12    3
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          25     2 / 98.00   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35LH2030
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,  0.000, 37.500  W3E1   0.000,  0.000, 19.900 2.00E+00  30
+2     W7E2   0.000,  0.000, 19.850     G   0.000,  0.000,  0.000 2.00E+00  25
+3     W1E2   0.000,  0.000, 19.900  W4E1   1.000,  0.000, 20.050    # 12    3
+4     W3E2   1.000,  0.000, 20.050  W5E1   3.000,  0.100, 37.500    # 12   25
+5     W4E2   3.000,  0.100, 37.500  W6E1  -3.000,  0.100, 37.500    # 12    8
+6     W5E2  -3.000,  0.100, 37.500  W7E1  -1.000,  0.000, 20.000    # 12   25
+7     W6E2  -1.000,  0.000, 20.000  W2E1   0.000,  0.000, 19.850    # 12    3
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          25     2 / 98.00   (  2 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+5.2  "Zig-Zag" loading
+
+35VT1010
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2     W3E2   1.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   1.000,  0.000, 20.950  W2E1   1.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  1.000, 20.950  W3E1   1.000,  0.000, 20.950    # 12    4
+5     W6E2   0.000,  1.000, 37.500  W4E1   0.000,  1.000, 20.950    # 12   10
+6     W7E2  -1.000,  0.000, 37.500  W5E1   0.000,  1.000, 37.500    # 12    4
+7     W8E2  -1.000,  0.000, 20.950  W6E1  -1.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -1.000, 20.950  W7E1  -1.000,  0.000, 20.950    # 12    4
+9            0.000, -1.000, 37.500  W8E1   0.000, -1.000, 20.950    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VT1510
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2     W3E2   1.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   1.000,  0.000, 20.600  W2E1   1.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  1.000, 20.600  W3E1   1.000,  0.000, 20.600    # 12    4
+5     W6E2   0.000,  1.000, 37.500  W4E1   0.000,  1.000, 20.600    # 12   10
+6     W7E2  -1.000,  0.000, 37.500  W5E1   0.000,  1.000, 37.500    # 12    4
+7     W8E2  -1.000,  0.000, 20.600  W6E1  -1.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -1.000, 20.600  W7E1  -1.000,  0.000, 20.600    # 12    4
+9            0.000, -1.000, 37.500  W8E1   0.000, -1.000, 20.600    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT2010
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2     W3E2   1.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   1.000,  0.000, 20.400  W2E1   1.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  1.000, 20.400  W3E1   1.000,  0.000, 20.400    # 12    4
+5     W6E2   0.000,  1.000, 37.500  W4E1   0.000,  1.000, 20.400    # 12   10
+6     W7E2  -1.000,  0.000, 37.500  W5E1   0.000,  1.000, 37.500    # 12    4
+7     W8E2  -1.000,  0.000, 20.400  W6E1  -1.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -1.000, 20.400  W7E1  -1.000,  0.000, 20.400    # 12    4
+9            0.000, -1.000, 37.500  W8E1   0.000, -1.000, 20.400    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT1020
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2     W3E2   2.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   2.000,  0.000, 24.250  W2E1   2.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  2.000, 24.250  W3E1   2.000,  0.000, 24.250    # 12    4
+5     W6E2   0.000,  2.000, 37.500  W4E1   0.000,  2.000, 24.250    # 12   10
+6     W7E2  -2.000,  0.000, 37.500  W5E1   0.000,  2.000, 37.500    # 12    4
+7     W8E2  -2.000,  0.000, 24.250  W6E1  -2.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -2.000, 24.250  W7E1  -2.000,  0.000, 24.250    # 12    4
+9            0.000, -2.000, 37.500  W8E1   0.000, -2.000, 24.250    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT1520
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2     W3E2   2.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   2.000,  0.000, 23.750  W2E1   2.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  2.000, 23.750  W3E1   2.000,  0.000, 23.750    # 12    4
+5     W6E2   0.000,  2.000, 37.500  W4E1   0.000,  2.000, 23.750    # 12   10
+6     W7E2  -2.000,  0.000, 37.500  W5E1   0.000,  2.000, 37.500    # 12    4
+7     W8E2  -2.000,  0.000, 23.750  W6E1  -2.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -2.000, 23.750  W7E1  -2.000,  0.000, 23.750    # 12    4
+9            0.000, -2.000, 37.500  W8E1   0.000, -2.000, 23.750    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT2020
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2     W3E2   2.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   2.000,  0.000, 23.400  W2E1   2.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  2.000, 23.400  W3E1   2.000,  0.000, 23.400    # 12    4
+5     W6E2   0.000,  2.000, 37.500  W4E1   0.000,  2.000, 23.400    # 12   10
+6     W7E2  -2.000,  0.000, 37.500  W5E1   0.000,  2.000, 37.500    # 12    4
+7     W8E2  -2.000,  0.000, 23.400  W6E1  -2.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -2.000, 23.400  W7E1  -2.000,  0.000, 23.400    # 12    4
+9            0.000, -2.000, 37.500  W8E1   0.000, -2.000, 23.400    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT1030
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   3.000,  0.000, 26.800  W2E1   3.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  3.000, 26.800  W3E1   3.000,  0.000, 26.800    # 12    4
+5     W6E2   0.000,  3.000, 37.500  W4E1   0.000,  3.000, 26.800    # 12   10
+6     W7E2  -3.000,  0.000, 37.500  W5E1   0.000,  3.000, 37.500    # 12    4
+7     W8E2  -3.000,  0.000, 26.800  W6E1  -3.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -3.000, 26.800  W7E1  -3.000,  0.000, 26.800    # 12    4
+9            0.000, -3.000, 37.500  W8E1   0.000, -3.000, 26.800    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT1530
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   3.000,  0.000, 26.240  W2E1   3.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  3.000, 26.240  W3E1   3.000,  0.000, 26.240    # 12    4
+5     W6E2   0.000,  3.000, 37.500  W4E1   0.000,  3.000, 26.240    # 12   10
+6     W7E2  -3.000,  0.000, 37.500  W5E1   0.000,  3.000, 37.500    # 12    4
+7     W8E2  -3.000,  0.000, 26.240  W6E1  -3.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -3.000, 26.240  W7E1  -3.000,  0.000, 26.240    # 12    4
+9            0.000, -3.000, 37.500  W8E1   0.000, -3.000, 26.240    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+35VT2030
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500    # 12    3
+3     W4E2   3.000,  0.000, 25.880  W2E1   3.000,  0.000, 37.500    # 12   10
+4     W5E2   0.000,  3.000, 25.880  W3E1   3.000,  0.000, 25.880    # 12    4
+5     W6E2   0.000,  3.000, 37.500  W4E1   0.000,  3.000, 25.880    # 12   10
+6     W7E2  -3.000,  0.000, 37.500  W5E1   0.000,  3.000, 37.500    # 12    4
+7     W8E2  -3.000,  0.000, 25.880  W6E1  -3.000,  0.000, 37.500    # 12   10
+8     W9E2   0.000, -3.000, 25.880  W7E1  -3.000,  0.000, 25.880    # 12    4
+9            0.000, -3.000, 37.500  W8E1   0.000, -3.000, 25.880    # 12   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+Ground type is Perfect
+
+
+4.3  Helical loading
+
+35VZ1025
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.50E-01   3
+3     W4E2   0.000,  3.000, 37.500  W2E1   3.000,  0.000, 37.500 2.50E-01   4
+4     W5E2  -3.000,  0.000, 37.500  W3E1   0.000,  3.000, 37.500 2.50E-01   4
+5     W6E2   0.000, -3.000, 37.500  W4E1  -3.000,  0.000, 37.500 2.50E-01   4
+6     W7E2   3.000,  0.000, 37.000  W5E1   0.000, -3.000, 37.500 2.50E-01   4
+7     W8E2   0.000,  3.000, 37.000  W6E1   3.000,  0.000, 37.000 2.50E-01   4
+8     W9E2  -3.000,  0.000, 37.000  W7E1   0.000,  3.000, 37.000 2.50E-01   4
+9    W10E2   0.000, -3.000, 37.000  W8E1  -3.000,  0.000, 37.000 2.50E-01   4
+10   W11E2   3.000,  0.000, 36.500  W9E1   0.000, -3.000, 37.000 2.50E-01   4
+11   W12E2   0.000,  3.000, 36.500 W10E1   3.000,  0.000, 36.500 2.50E-01   4
+12   W13E2  -3.000,  0.000, 36.500 W11E1   0.000,  3.000, 36.500 2.50E-01   4
+13   W14E2   0.000, -3.000, 36.500 W12E1  -3.000,  0.000, 36.500 2.50E-01   4
+14   W15E2   3.000,  0.000, 36.000 W13E1   0.000, -3.000, 36.500 2.50E-01   4
+15   W16E2   0.000,  3.000, 36.000 W14E1   3.000,  0.000, 36.000 2.50E-01   4
+16   W17E2  -3.000,  0.000, 36.000 W15E1   0.000,  3.000, 36.000 2.50E-01   4
+17   W18E2   0.000, -3.000, 36.000 W16E1  -3.000,  0.000, 36.000 2.50E-01   4
+18           2.800, -0.200, 35.500 W17E1   0.000, -3.000, 36.000 2.50E-01   4
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VZ1525
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.50E-01   3
+3     W4E2   0.000,  3.000, 37.500  W2E1   3.000,  0.000, 37.500 2.50E-01   4
+4     W5E2  -3.000,  0.000, 37.500  W3E1   0.000,  3.000, 37.500 2.50E-01   4
+5     W6E2   0.000, -3.000, 37.500  W4E1  -3.000,  0.000, 37.500 2.50E-01   4
+6     W7E2   3.000,  0.000, 37.000  W5E1   0.000, -3.000, 37.500 2.50E-01   4
+7     W8E2   0.000,  3.000, 37.000  W6E1   3.000,  0.000, 37.000 2.50E-01   4
+8     W9E2  -3.000,  0.000, 37.000  W7E1   0.000,  3.000, 37.000 2.50E-01   4
+9    W10E2   0.000, -3.000, 37.000  W8E1  -3.000,  0.000, 37.000 2.50E-01   4
+10   W11E2   3.000,  0.000, 36.500  W9E1   0.000, -3.000, 37.000 2.50E-01   4
+11   W12E2   0.000,  3.000, 36.500 W10E1   3.000,  0.000, 36.500 2.50E-01   4
+12   W13E2  -3.000,  0.000, 36.500 W11E1   0.000,  3.000, 36.500 2.50E-01   4
+13   W14E2   0.000, -3.000, 36.500 W12E1  -3.000,  0.000, 36.500 2.50E-01   4
+14   W15E2   3.000,  0.000, 36.000 W13E1   0.000, -3.000, 36.500 2.50E-01   4
+15   W16E2   0.000,  3.000, 36.000 W14E1   3.000,  0.000, 36.000 2.50E-01   4
+16   W17E2  -3.000,  0.000, 36.000 W15E1   0.000,  3.000, 36.000 2.50E-01   4
+17   W18E2   0.000, -3.000, 36.000 W16E1  -3.000,  0.000, 36.000 2.50E-01   4
+18   W19E2   3.000,  0.000, 35.500 W17E1   0.000, -3.000, 36.000 2.50E-01   4
+19           2.200,  0.800, 35.500 W18E1   3.000,  0.000, 35.500 2.50E-01   2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VZ2025
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 2.00E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.50E-01   3
+3     W4E2   0.000,  3.000, 37.500  W2E1   3.000,  0.000, 37.500 2.50E-01   4
+4     W5E2  -3.000,  0.000, 37.500  W3E1   0.000,  3.000, 37.500 2.50E-01   4
+5     W6E2   0.000, -3.000, 37.500  W4E1  -3.000,  0.000, 37.500 2.50E-01   4
+6     W7E2   3.000,  0.000, 37.000  W5E1   0.000, -3.000, 37.500 2.50E-01   4
+7     W8E2   0.000,  3.000, 37.000  W6E1   3.000,  0.000, 37.000 2.50E-01   4
+8     W9E2  -3.000,  0.000, 37.000  W7E1   0.000,  3.000, 37.000 2.50E-01   4
+9    W10E2   0.000, -3.000, 37.000  W8E1  -3.000,  0.000, 37.000 2.50E-01   4
+10   W11E2   3.000,  0.000, 36.500  W9E1   0.000, -3.000, 37.000 2.50E-01   4
+11   W12E2   0.000,  3.000, 36.500 W10E1   3.000,  0.000, 36.500 2.50E-01   4
+12   W13E2  -3.000,  0.000, 36.500 W11E1   0.000,  3.000, 36.500 2.50E-01   4
+13   W14E2   0.000, -3.000, 36.500 W12E1  -3.000,  0.000, 36.500 2.50E-01   4
+14   W15E2   3.000,  0.000, 36.000 W13E1   0.000, -3.000, 36.500 2.50E-01   4
+15   W16E2   0.000,  3.000, 36.000 W14E1   3.000,  0.000, 36.000 2.50E-01   4
+16   W17E2  -3.000,  0.000, 36.000 W15E1   0.000,  3.000, 36.000 2.50E-01   4
+17   W18E2   0.000, -3.000, 36.000 W16E1  -3.000,  0.000, 36.000 2.50E-01   4
+18   W19E2   3.000,  0.000, 35.500 W17E1   0.000, -3.000, 36.000 2.50E-01   4
+19           1.500,  1.500, 35.500 W18E1   3.000,  0.000, 35.500 2.50E-01   2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+35VH1525
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Zero
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.50E+00  40
+2     W3E2   3.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.50E-01   3
+3     W4E2   0.000,  3.000, 37.375  W2E1   3.000,  0.000, 37.500 2.50E-01   4
+4     W5E2  -3.000,  0.000, 37.250  W3E1   0.000,  3.000, 37.375 2.50E-01   4
+5     W6E2   0.000, -3.000, 37.125  W4E1  -3.000,  0.000, 37.250 2.50E-01   4
+6     W7E2   3.000,  0.000, 37.000  W5E1   0.000, -3.000, 37.125 2.50E-01   4
+7     W8E2   0.000,  3.000, 36.875  W6E1   3.000,  0.000, 37.000 2.50E-01   4
+8     W9E2  -3.000,  0.000, 36.750  W7E1   0.000,  3.000, 36.875 2.50E-01   4
+9    W10E2   0.000, -3.000, 36.625  W8E1  -3.000,  0.000, 36.750 2.50E-01   4
+10   W11E2   3.000,  0.000, 36.500  W9E1   0.000, -3.000, 36.625 2.50E-01   4
+11   W12E2   0.000,  3.000, 36.375 W10E1   3.000,  0.000, 36.500 2.50E-01   4
+12   W13E2  -3.000,  0.000, 36.250 W11E1   0.000,  3.000, 36.375 2.50E-01   4
+13   W14E2   0.000, -3.000, 36.125 W12E1  -3.000,  0.000, 36.250 2.50E-01   4
+14   W15E2   3.000,  0.000, 36.000 W13E1   0.000, -3.000, 36.125 2.50E-01   4
+15   W16E2   0.000,  3.000, 35.875 W14E1   3.000,  0.000, 36.000 2.50E-01   4
+16   W17E2  -3.000,  0.000, 35.750 W15E1   0.000,  3.000, 35.875 2.50E-01   4
+17   W18E2   0.000, -3.000, 35.625 W16E1  -3.000,  0.000, 35.750 2.50E-01   4
+18   W19E2   3.000,  0.000, 35.500 W17E1   0.000, -3.000, 35.625 2.50E-01   4
+19           2.000,  1.000, 35.420 W18E1   3.000,  0.000, 35.500 2.50E-01   2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+
+
+5.  Spiral Top-Hat Loading
+
+35HC1025
+
+Frequency = 3.6  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E2   0.000,  0.000, 37.500     G   0.000,  0.000,  0.000 1.00E+00  40
+2     W3E2   0.000,  1.000, 37.500  W8E2   0.000,  0.000, 37.500 2.50E-01   2
+3     W4E2   2.000,  1.000, 37.500  W2E1   0.000,  1.000, 37.500 2.50E-01   4
+4     W5E2   2.000, -3.000, 37.500  W3E1   2.000,  1.000, 37.500 2.50E-01   8
+5     W6E2  -4.000, -3.000, 37.500  W4E1   2.000, -3.000, 37.500 2.50E-01  12
+6     W7E2  -4.000,  5.000, 37.500  W5E1  -4.000, -3.000, 37.500 2.50E-01  24
+7            2.200,  5.000, 37.500  W6E1  -4.000,  5.000, 37.500 2.50E-01  16
+8     W9E2  -1.000,  0.000, 37.500 W14E2   0.000,  0.000, 37.500 2.50E-01   2
+9    W10E2  -1.000,  2.000, 37.500  W8E1  -1.000,  0.000, 37.500 2.50E-01   4
+10   W11E2   3.000,  2.000, 37.500  W9E1  -1.000,  2.000, 37.500 2.50E-01   8
+11   W12E2   3.000, -4.000, 37.500 W10E1   3.000,  2.000, 37.500 2.50E-01  12
+12   W13E2  -5.000, -4.000, 37.500 W11E1   3.000, -4.000, 37.500 2.50E-01  24
+13          -5.000,  2.200, 37.500 W12E1  -5.000, -4.000, 37.500 2.50E-01  16
+14   W15E2   0.000, -1.000, 37.500 W20E2   0.000,  0.000, 37.500 2.50E-01   2
+15   W16E2  -2.000, -1.000, 37.500 W14E1   0.000, -1.000, 37.500 2.50E-01   4
+16   W17E2  -2.000,  3.000, 37.500 W15E1  -2.000, -1.000, 37.500 2.50E-01   8
+17   W18E2   4.000,  3.000, 37.500 W16E1  -2.000,  3.000, 37.500 2.50E-01  12
+18   W19E2   4.000, -5.000, 37.500 W17E1   4.000,  3.000, 37.500 2.50E-01  24
+19          -2.200, -5.000, 37.500 W18E1   4.000, -5.000, 37.500 2.50E-01  16
+20   W21E2   1.000,  0.000, 37.500  W1E1   0.000,  0.000, 37.500 2.50E-01   2
+21   W22E2   1.000, -2.000, 37.500 W20E1   1.000,  0.000, 37.500 2.50E-01   4
+22   W23E2  -3.000, -2.000, 37.500 W21E1   1.000, -2.000, 37.500 2.50E-01   8
+23   W24E2  -3.000,  4.000, 37.500 W22E1  -3.000, -2.000, 37.500 2.50E-01  12
+24   W25E2   5.000,  4.000, 37.500 W23E1  -3.000,  4.000, 37.500 2.50E-01  24
+25           5.000, -2.200, 37.500 W24E1   5.000,  4.000, 37.500 2.50E-01  16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          40     1 / 98.75   (  1 /100.00)      1.000       0.000       I
+No loads specified
+
+No transmission lines specified
+
+Ground type is Perfect
+

+
+
+ +

+
+

Updated 5-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Return to Index
+ Go to Amateur Radio Page
+

Topics: HF Lower, Loading, Vertical


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The Pseudo-Brewster Angle Revisited

+ hr +

The Pseudo-Brewster Angle Revisited

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: HF Lower, HF Upper, VHF / UHF, Vertical


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+

The 40-Meter 3-Way Special

+
+
+

A Small, Simple Triangular Vertical Array

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ This note is about a short, simple 3-way vertical array for 40 meters. There is nothing new in the concepts underlying the array. But you might not have seen them arranged quite this way. +

The array consists of a triangle of three off-center-fed vertical dipoles close to the ground and no more than 22' above ground at their peaks. Each vertical dipole is end loaded with an element extension device--hats and near-hats. Each element has an inductive reactance at its off-center break. The driven element inductor acts as a beta-match shunt inductance, while the reflector inductor acts as a loading element to electrically lengthen the element. Quarter wavelength coax lines to each vertical act as a power carrier for the driven element and as an open circuit for the reflectors through a remotely switched bank of three relays centered in the triangle of verticals. No ground plane is needed.

+

The result is an array with modest gain (which varies with the method of element end loading), better than 10 dB front-to-back ratio, a low elevation angle of maximum radiation (about 24 degrees, with a wide vertical lobe for lower angle signals), and little high angle radiation. Switching provides complete 360-degree coverage at nearly full gain, divided into three quadrants.

+

Let's divide the concepts underlying this array into easy-to-digest chunks.

+
+

1. 1 vs. 2 Reflectors for Verticals

+
Any vertical antenna--ground-plane or dipole--becomes directional if one adds a slightly longer antenna of the same sort 1/4 wl behind the driven antenna. The ultimate in rearward nulls occurs if we use a carefully pruned phasing line between the two elements. However, good gain and adequate front-to-rear response occur if we make the reflector about 3-4% longer than the driven element or if we inductively load the reflector to an equivalent electrical length. +

We can add a modicum of gain and extra front-to-rear nulling by using three verticals, arranged in an equilateral triangle, 1/4 wl per side. The reflector verticals are tuned in the same way as a single reflector. The sketch shows the basic layout and direction of the main lobe.

+
+ +
+

The following azimuth patterns compare the performance of 1- and 2- reflector arrays. Note that these patterns might be individually improved by careful tweaking of values, while the rearward nulls might be deepened by the use of a phasing line system. For a simplified, non-phasing-line system, the 1/4 wl per side triangle is important to further steps in the final array developed here.

+
+ +
+
+

The 3-Way Array

+
If we can selectively make each vertical a driven element and the other two reflectors, we can create a switchable beam. The broad forward lobes nicely cover just about 1/3 of the horizon with a full-strength signal, with a significant reduction of signal strength from the rear. +
+ +
+

This array has been used, although with 1/4 wl monopoles, it requires extensive ground planing. Typically, the means used to convert driven elements into reflectors and back tend to be complex. Most examples have used phasing networks to produce the deepest possible nulls to the rear. See for example, the section (4.11) in ON4UN's Low Band DXing (pages 11-48 to 11-54) for techniques used to phase feed triangular arrays from 0.145 to 0.29 wl per side.

+

If 10-12 dB front-to-rear performance for a 3-way array is sufficient, we may omit the phasing line and use the phasing that results from the parasitical arrangement of elements. However, vertical monopoles with ground planes (not to mention full size vertical dipoles) are very tall on 40 meters. So let's rethink the antenna elements.

+
+

Capacity Hat Dipoles

+
Instead of using 35' vertical monopoles or base-loaded shortened versions of them, let's think about vertical dipoles instead. We can add capacity hats to the ends of dipoles and shorten them considerably without losing much gain. Hats are simply symmetrical arrays of wire at right angles to the dipole ends. The symmetry results in radiation cancelling and hence does not yield significant horizontally polarized radiation. +

As described in other notes in this series concerning the top-end loading of half-size 80-meter verticals, a hat does not have to be perfectly symmetrical to yield insignificant horizontal radiation. For most purposes, a horizontal pattern that is down by 30 dB from the total far field pattern has an insignificant effect on antenna performance. However, such non-symmetrical element extensions usually reduces the operating bandwidth and gain by a small (but not insignificant) amount.

+

Here is a small sample of possible hat arrangements.

+
+ +
+

For a 1/4-size dipole (about 17.5'), standard capacity hat assemblies will have a radius well over 7 feet, and the simple square with a perimeter requires a spoke length of about 8.5 feet. Spirals and solenoids can be made much smaller, although they will require just about the same overall length of wire. For example, a helix of 2 full turns plus a little can be arrange with a radius of about 2 feet, for easier mechanical construction. See the notes on linear loaded half size verticals for other possible element extension ideas.

+

Hat size will also vary with the exact distance from the ground of the dipole bottom end. The models used here placed the lower end about 4.5' off the ground with the tops at 22' up.

+

Each vertical dipole will be identical. For 7 MHz, they should be resonated without any attachments at about 100 kHz higher than the desired center frequency of operation. This will produce an independent feedpoint impedance of about 27 - j40 ohms at the target frequency. This impedance is of some importance to the array's operation.

+
+

Where to Feed the Dipole

+
Feeding the dipole at its center is the standard, but is not necessary. This feedpoint will be some 13' off the ground, a very unhandy place for handling coaxial feedlines. +

So let's feed the dipole off center, namely, at the lowest point before entering the lower hat assembly. The small distance from the element's electrical center (0.06 wl) makes about a 1-ohm difference in feedpoint resistance. The radiation pattern difference and the currents on the antenna element are virtually unaffected. (If you model the dipole using center and off-center feed, be sure to switch to a constant power option rather than using a voltage or current source. Otherwise, the current readings will not be comparable.)

+

With our off-center feed, the coax is now only 4.5' off the ground, a much more manageable position from a mechanical standpoint.

+
+

Loading the Verticals

+
Across the feedpoint of each vertical, attach a 50-ohm inductive load. This can be a shorted transmission line stub. A 450-ohm line stub will be about 2.35' long, while a 300-ohm line stub will be almost 3' long. Sturdy stubs of 1/8" rod can be made in any line width. Programs such HAMCALC have stub calculating programs for home brewing almost any kind of stub imaginable. +
+ +
+

The figure illustrates the stub and coil options. A coil of about 1.15 microH is required for the inductive reactance of about 50 ohms. A coil 1" long and 1" in diameter with about 8 turns of #12 wire will satisfy this requirement. A slightly smaller coil of 1/8" diameter aluminum wire would also work well and not incur bi-metallic effects common to aluminum-copper junctions, but at a slight cost in Q due to the slightly higher resistance of aluminum.

+

For the reflectors, the loading inductance makes the element electrically longer--just about the right amount to act as a first-rate reflector for the driven element.

+

When the three verticals are arranged as an equilateral triangle about 35.1' on a side, the driven element shows an impedance of about 30 - j 25 ohms. This figure is just about ideal for using a shunt beta inductive reactance in the 50-60 ohm range. This is the function of the inductor at the feedpoint of the driven element.

+
+

Connecting and Switching the Array

+
Each inductor is across the feedpoint of its vertical dipole. Also across each feedpoint is a coax connector. A piece of 50-ohm coax 1/4 wl long runs from the connector to the center point of the array. This point is about 20.3' from each vertical. Solid dielectric coax commonly has a velocity factor of 0.66, and a 1/4 wl section will be about 23.1' long. This length will reach, but not permit much droop to the coax. To allow the coax to reach the ground comfortable, consider foam dielectric coax, with a velocity factor near 0.8, for a rough length of 28.1 feet. +

A 1/4 wl length of transmission line is useful in switching. If we ground the end at the center of the array, the end at the antenna element will show a very high impedance, essentially an open circuit. The high impedance in parallel with the inductor at the element feedpoint means that the currents distributed along the element will see only the loading inductance. This condition is perfect for the element to function as a reflector.

+

However, if we connect the coax at the array center end to a source of RF, then the 1/4 wl section simply acts as a continuation of the 50 ohm line. The shunt beta inductor in conjunction with the series capacitive reactance at the antenna feedpoint form an L-circuit that converts the low resistive component to 50 ohms (or thereabouts).

+

If we place three SPDT relays in a weather-proof box, we can remotely switch which vertical receives power while the other two act as reflectors. The simplified diagram shows the scheme.

+
+ +
+
+

Anticipated Results

+
This array provides broad, but low gain coverage of a full 1/3 of the horizon. Its chief advantages are low angle radiation combined with quite decent reduction in signal strength off the rear. It will not compete with even a 2-element Yagi that is nearly a half wavelength up, but that is not its purpose. It will compete quite nicely with delta loops and similar self-contained vertically polarized wires (SCVs). Some SCVs may have greater gain, but the front-to-back ratio of the triangular array will compensate in many situations. Moreover, the triangular array requires a smaller and tidier piece of real estate. +

System gain for the triangular will vary from 1.5 dBi to 4.5 dBi depending on the quality of the ground in the region most affecting the far field pattern. (Gain will be even higher near salt water, but few of us live on an island.) The front-to-back ratio will usually be better then 10 dB and often exceed 12 dB (2 S-units).

+
+

Reality

+
Although this system is almost elegant in its simplicity, adapting it to local conditions of terrain, height above ground, etc. will require considerable experimentation before settling upon the exact operating conditions. If you aim for the desired independent feedpoint impedance of the independent dipoles--adjusting the element extensions accordingly--then the remaining steps are likely to be routine. Routine does not mean automatic, and considerable patience will be required to get everything just right. +

The operating bandwidth is likely to be fairly narrow, so the antenna may be best suited for CW operators (who seem more comfortable with favorite operating frequencies that are fairly narrow in scope).

+

The models used here used vertical elements of 1.25" diameter aluminum. One might use larger diameter elements for both structural and bandwidth improvements. The physical model under development here will likely use PVC and CPVC for all nonconductive elements, including the vertical pipes that keep the elements at least 4.5' off the ground. The short verticals should be easily supported without the use of concrete if the base PVC section is capped with drainage holes and a gravel counter-weight filling below the soil level. Other construction ideas abound.

+

The principles of this array are adaptable to longer dipoles and even to antennas considered to be monopoles with elevated ground planes (which are- -whatever we choose to call them--still dipoles). This has been an exercise in putting fundamentals together. Hence, I claim no originality for the array--and indeed, it may well have been published many times before. It is such a natural, that I would be surprised if it has not appeared numerous times in print--even if in different rubric.

+

But if I have been clear enough in saying how these pieces go together, then perhaps you are a step closer to being able to put your own favorite pieces together to make your own ideal array.
+

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+
+

Updated 7-20-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
+

Topics: Dipole, HF Lower, Loading, Vertical


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3 Wires = The Whole World

+

+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+ Many folks are fond of vertical antennas, especially below 14 MHz. These antennas take up little horizontal real estate. With a little ingenuity, we can make them from wire. By using vertical dipoles, we can save the pain of laying a ground plane. And we can work the world without a rotator. The low elevation angle of maximum radiation is not only good for DX, it is also a natural filter from QRM and QRN originating closer in. +

If there are problems, they number two: 1. The antennas have low gain, and 2. We need either a braced vertical or something high from which to hang the long wires. I can help a bit with the first problem, but the second is yours. If you have some tall trees, you might consider hanging support ropes as high as you can go and suspending your vertical dipoles from them. Tall towers for upper HF beams can also serve as anchors for a vertical array.

+

However, let's keep the gain requirements modest--say about 3 dB more gain than from a single vertical dipole. But let's also keep active our aim of working the world. Assuming that we can hang 3 wires, we can make a nice little triangular parasitic array that will do just the job we need.

+

The Basic Layout

For 40 and 30 meters, wire vertical dipoles become quite practical. At about 10' off the ground, they show a take-off angle of about 16 degrees, and have something over 1 dBi gain. But they are tall, with a 40-meter vertical reaching almost 80 feet and a 30-meter vertical stretching above 55' up. +

If we can manage the height, we can build a switchable directive parasitical array from 3 wires. Figure 1 shows the general layout. Essentially, the system consists of three verticals laid out so that two form parasitical reflectors for the third, which is a driven element. The parasitical arrangement is capable of about 3 dB gain over a single vertical and yields between 15 and 16 dB front-to-back ratio without any effort expended on calculating and pruning a phasing system. If these benefits are sufficient, then we can proceed.

+
+ +
+

The right side of Figure 1 shows the way to calculate the positions of the three elements in an equilateral triangle. If we know the face length, A, then the others will fall in place this way:

+ 
B = .577 A
+C = .289 A
+D = .5 A
+

How large shall we make A? Actually, the length of A depends on two factors, neither of which is some special fraction of a wavelength taken from theory. Letting the distances between verticals run from 0.12 wl to about 0.25 wl yields nearly the same gain with about the same front-to-back capability (using parasitical arrangements). So what might set our distance?

+

First, the driven element will have to be shortened from its natural resonant length when isolated as a dipole. We shall shorten all three legs accordingly, since each will serve in its turn as the driven element. However, reducing the length of all the wires will require us to load the two legs to make them act as reflectors. We can do this the hard way with loading coils, or we can do it the easy way with shorted coax stubs. We shall bring the stubs to a central junction box, where the reflector stubs will be shorted and the driver stub becomes just another short length of the feed system. In this way, we can use a remote switch and some relays to change the direction of the array. So, the length of the feedline used as a shorting stub helps to determine the length B, since we may wish to bring the line directly to an elevated box centered among the 3 wires.

+

Second, the face length A determines the feedpoint impedance of the driven element. When the face length A is about 0.16 wl, the source impedance of the driver approaches 50 Ohms, a very handy value indeed. At 7.1 MHz, this distance is about 22 feet. With this face length, the distance B becomes about 12.7 feet. Will the loading stubs be at least this length for the assembly? Actually, we get a little length to spare. The required stub for 50-Ohm, 0.66 velocity factor line will be 16.4' long, enough to allow some play in the line for a direct connection.

+

For those unfamiliar with calculating the length of shorted stubs, the basic equation for determining the inductive reactance from the length of transmission line is

+
+ +
+

where L is the line length and WL is a wavelength, both in the same units, VF is the velocity factor of the line, ZO is the line's characteristic impedance, and XL is the inductive reactance. Solving for L, the line length, we get

+
+ +
+

where the terms have the same meaning as in equation 1. If we want to place the junction box on the ground, we can add a half wavelength of line (taking the velocity factor into account) and achieve the same reflector loading goal.

+

Here are some starter dimensions for both 40 and 30 meters, assuming that each antenna starts 10' off the ground.

+ 
Triangle factors (measured in feet):
+
+Frequency      A         B         C         D
+7 .1           22'       12.7'     6.35'     11'
+10.1           15.5'      8.95'    4.47'      7.75'
+
+Antenna wire (#12) and cable factors (measured in feet):
+
+Frequency      Vertical Length     Top height     Stub length (RG-213)
+ 7.1                65.9'             75.9'          16.4'
+10.1                46.325'           56.325'        11.7'
+

If you move up or down from the given vertical positioning, expect some small changes in the required dimensions, but none so great that you cannot make the system work.

+

The Switching System

The beamwidth of the triangle array is between 128 and 130 degrees wide between -3 dB power points. Since 120 degrees is one third of the horizon, switching the elements around between driver and reflector functions will cover the horizon in three switch positions. +
+ +
+

Figure 2 shows a simple switching system for the array involving three DPDT relays. The schematic shows antenna 1 as the driver, with verticals 2 and 3 having shorted stubs. Note that the stub shields or braids are isolated from the main feedline braid when the stubs is shorted. When a stub becomes an extension of the feedline, its braid is connected to the feedline.

+

The relays can be anything from small items purchased locally for low power use to beefy units for high power operation. The components require a waterproof box, but the coax connectors should not be directly grounded to the case, since that would defeat braid isolation. In addition to the usual coax feeder to the shack, a 4-wire rotator cable (or a similar cable suitable for outdoor use) carries power to energize the relays, according to the switch position in the shack. Of course, at the shack end of the line, you can make up any desired indicator system, from a simple row of LEDs to a small map with the lamps showing the part of the world at which the array is aimed.

+

In the schematic, when no power is applied (that is, when the station is idle), all relays revert to the shorted stub mode, and the feedline is disconnected from the three vertical wire dipoles. You may add whatever other safety features you deem appropriate to the junction box system.

+

Performance

How well can we expect this very simple array to perform? The answer lies in some properly interpreted far field plots. +
+ +
+

Figure 3 shows an overlay of the three possible azimuth plots, one for each switch position. However, do not take these plots completely at face value.

+

First, note that there are slight nulls in the coverage. Although they are shallow, you may wish to orient the array so that the nulls point at places where no ham lives.

+

Second, the gain figure holds only for placement of the antenna over average ground. As the soil gets either better or worse in the general category scheme, the gain will rise. (The actual pattern of gain vs. height above various soils grows more complex as we take into account more varieties of coil conditions.) However, the improvement over a single vertical wire will remain about constant. Although "average soil" yields nearly the lowest gain figures of any soil (depending upon the exact vertical height over it), the take-off angle will decrease as the soil improves and will rise as the soil condition grows worse, almost wholly independent of the gain.

+

Third, the figures show the slightly higher gain figures yielded by the 30- meter version of the array. 40-meter gain figures are about 0.15 dB lower due to the lower effective height of the antenna, since we placed each at a minimum height of 10 feet.

+
+ +
+

The elevation plot shown in Figure 4 shows the vertical array benefits to their best advantage. The low take-off angle favors DX skip angles, while the front-to-back ratio is very useful, if somewhat short of astounding.

+

The absence of significant high angle lobes, including the total absence of one directly overhead, is also beneficial for communications, since QRM and QRN originating at short skip distances are naturally attenuated, relative to a horizontal dipole or similar antenna. (However, this feature does not affect local area noises, many of which are vertically polarized.)

+
+ +
+

The SWR curves for the arrays are good (but not perfect) for 40. Sliding the design center frequency a bit higher or lower than 7.1 MHz will allow coverage of a desired band edge. As you move lower than the design center frequency, the pattern loses some front-to-back ratio, but adds a bit of gain. Higher up, the gain drops, but the front-to-back ratio is sustained.

+
+ +
+

Within the narrow confines of 30 meters, SWR is no problem at all. The band is not wide enough for the pattern to change significantly.

+

Conclusion

The triangular array can be scaled and adjusted for many bands. For example, a 10-meter version might be mounted on a single mast with three 5' PVC arms supporting the 3 vertical dipoles. In this case, the dipoles might use some combination of 3/4" through 1" hardware-store aluminum tubing. VHF versions can be even more compact. When the antenna is several wavelengths above ground, the low-angle gain increases considerably while retaining the wide beamwidth that offers full-horizon coverage in 3 switch positions. +

ON4UN, in his justly famous Antennas and Techniques for Low Band DXing, devotes an entire chapter (11) to phase-fed vertical arrays. However, vertical Yagis, that is, parasitical arrays, receive scarcely 1 column of attention (in Chapter 13). Granted, a correctly phase-fed vertical array is capable of a very deep 180-degree null. However, the overall front-to-rear ratio may not for many operators be sufficiently superior to that of a parasitical array to justify the effort of perfect phasing. In addition, the perfect null does not occur at the same phasing among elements as maximum gain, and the gain difference may approach a full dB.

+

Those who prize the silent rear will continue to phase-feed their systems carefully. However, those who prefer simplicity in their installations may wish to explore parasitic techniques to achieve a compromise between gain and front-to-back ratio. Ted Hart, W5QJR, showed a 5-wire design a few months back in antenneX. You might consider this 3-wire array the little brother of his system, since it is essentially a 2-element vertical Yagi with a double reflector. Like the bigger system, with proper switching, it will cover the entire horizon with a bit of gain and some useful front-to-back ratio.

+

Of course, for many, the required height to implement this system may be out of reach. Many of us use verticals that are considerably shorter than a full 1/2 wl long. As I shall try to show in a later item, all is not lost: there are triangular possibilities for the short vertical operator.

+
+ +
+

Updated 2-5-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Nov., 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, HF Lower, Vertical


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A Vertical Doublet for 30-10 Meters

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+

L. B. Cebik, W4RNL

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+
+ +

+
+

One common problem faced by many of today's hams is a total lack of space for an antenna system. Sometimes land restrictions prevent construction of the ideal antenna farm. Sometimes family objections get in the way. Multi-family dwellings also defeat antenna farm dreams.

+

Suppose that you can put up only one antenna and that it must be vertical in order to use the minimum space possible. One common solution to the problem is to buy a trapped multi-band vertical and place it on the roof, with the minimum number of radials tacked down to the roofing shingles or draped over the eaves. Most of the available trapped monopoles are good antennas of their type, but they are initially costly.

+

Is there a cheaper alternative? In fact, there is a much cheaper alternative that is also less visible. However, there will be several kinds of work involved, and you will need an antenna tuner.

+

Although an antenna tuner (ATU) is part of any antenna system where it is used, I tend to separate the cost of the ATU from the cost of the antenna. In a lifetime, one will wear out many antennas, but a good tuner should last forever. So I shall assume that you have--or will obtain--the best ATU for your operating needs.

+

A 20-Meter Vertical Dipole

+

Any dipole, when placed horizontally over the ground, shows the familiar figure-8 pattern broadside to the wire, even if we change its length from about 3/8 wl to about 1 wl long. (The lower the antenna height, the more "thick-waisted" the pattern gets.) As we lengthen the wire, the beamwidth gets narrower while the peak gain gets a bit stronger.

+

If we turn the dipole to a vertical position and elevate it off the ground by a few feet, we obtain an omni-directional pattern quite similar to that of a standard ground-plane monopole. The same tendencies that kept our horizontal dipole showing its two lobes broadside to the wire now keep the elevation angle of radiation low as we change the length of the vertical dipole from 3/8 wl up to 1 wl long.

+

Now let's fix the length, using a standard 20-meter dipole as our vertical antenna. As shown in Fig. 1, we might place this antenna 10' (3 m) off the ground and support its upper end, which is now about 43.5' (13.25 m) off the ground.

+
+ +
+

At this point, the only change from standard ham practice that we shall make is to substitute parallel feedline for our usual coax. Although this move will require a bit of special attention--to be discussed further on-- the basic run should be brought as straight away from the vertical as possible for as long as possible before routing it to the station. We shall use our ATU to provide a match between whatever impedance appears at the ATU and the station equipment.

+

Our 20-meter vertical dipole is nearly 3/8 wl long at 30 meters. It is 1 wl long on 10 meters. For the bands between 20 and 10, the antenna is somewhere between 1/2 and 1 wl long. It meets the conditions for having a decently low radiation angle on all of these bands.

+
+ +
+

Fig. 2 shows the elevation patterns of our vertical dipole for all bands from 30 meters through 10 meters. As we expected, if we increase frequency, the main lobe gets a bit lower, ranging from 18 degrees on 30 to 10 degrees on 10. Of course, as we might also expect, the gain is much lower than that of a beam, but then, we are contemplating this antenna for locations where a beam is impossible anyway. The following table shows the modeled gain and elevation angle for a 1" diameter aluminum version of the antenna on each of the bands.

+ 
Band           Gain           Elevation Angle
+30 meters      0.9 dBi        18 degrees
+20             1.4            15
+17             1.8            13
+15             2.1            12
+12             2.7            11
+10             3.3            10
+

Even wire versions of the antenna (#12-#14 AWG) will show almost identical gain and elevation figures.

+

Construction

+

Since we are not seeking an exact match to a 50-Ohm coaxial cable, the dimensions of the 20-meter vertical dipole shown in Fig. 1 are not at all critical within a few inches or centimeters. The antenna can be wire or tubing, depending on what the available support systems will allow.

+
+ +
+

Three of many possible support systems appear in Fig. 3. On overhead limb of a tall tree can support the wire antenna, with a rope holding the bottom end in place. If the transmission line is very securely attached to the wire, a little tension will keep the vertical from flapping in the breeze. If you have 2 support structures separated by a space, you can support the top and bottom of the antenna with cross ropes. Of course, you can also mix and match the two top and bottom support means shown in the sketch.

+

Equally effective will be a self-supporting version of the antenna, although developing a 10' support may be more difficult. As well, the antenna--if made from standard tubing--may wave mightily in stiff breezes unless guyed with light ropes about 2/3 the way up the tubing.

+

It is impossible to analyze in the abstract all of the difficulties that may be faced by individuals trying to get an antenna in place in very restricted spaces. So the best advice is to give your situation careful study, looking for support possibilities in everything you see. For example, if the roof or chimney top is not quite high enough, but a tree in the area is more than tall enough, you can use a sloping rope to connect the two and support the wire antenna.

+

There is no magic about the 10' minimum height selected for this antenna. Safety is the foremost concern. The end of the antenna on some bands will carry a very high voltage that can create RF burns if someone touches it while you are transmitting. Although the top height provides good performance, you can lower it if you bend the bottom wire to the side at a safe distance above everyone's head. The change in performance is small enough that it is unlikely to be noticed.

+

Matching the Antenna to the Station Equipment

+

The impedance that your ATU sees at its terminals depends on several factors:

+
    +
  • 1. The band of operation;
    • +
  • 2. The length and characteristic impedance of the parallel transmission line you use; and
    • +
  • 3. The imbalance the occurs from routing the transmission line so that the antenna field couples to it.
    • +
+

Let's take up the first two considerations together. The impedance of the antenna at its center feedpoint will change from band to band. From any given impedance at the antenna terminals, the impedance will vary along the feedline depending on the characteristic impedance of the line, the line length, and the velocity factor of the line. 300-Ohm twinlead has a velocity factor of about 0.8 due to the solid vinyl insulation between wires. Almost all other parallel lines have velocity factors above 0.95, and home-made line with periodic spacers has a velocity factor of just about 1.0.

+

Impedance, recorded as resistance and reactance in series, repeats itself every electrical half wavelength (taking into account the velocity factor) along a transmission line. As a test, I modeled the antenna with various physical feedline lengths, using a 3" spacing between #12 wires to simulate a home-made line. With lengths of 1/8, 1/4, 3/8, and 3/4 wl of transmission line at 20 meters, I obtained the following impedances.

+ 
                    Transmission line length at 20 Meters
+Band Antenna        1/8 wl         1/4 wl         3/8 wl         1/2 wl
+30     35 - j 465**   20 - j  95     25 + j 225     60 + j 175   4250 - j6720*
+20     70 - j  30    120 + j 450   2880 + j1950*   170 - j 625     74 - j  50
+17    165 + j 420   1950 - j1310*   125 - j 235    155 + j 360   2740 - j 465*
+15    340 + j 830    235 - j 650    105 + j 150   2215 + j 135*   130 - j 305
+12   1310 + j1720*    90 - j 200    300 + j 870    135 - j 440    135 + j 440
+10   4200 + j 110*    65 + j   5   4300 - j 175*    70 + j  10   4250 + j 105*
+

The repetition points will vary from band to band, since they occur as a function of wavelength. Within in the limits of this small test, I have flagged very high impedance values that might exceed the range of the tuner controls to match easily. Notice that as the line length changes, the values appear on different bands. Hence, for any given line length, only 1 or 2 of the bands are likely to present a difficult matching situation.

+

The double-star entry shows a potential weakness of the system on 30 meters. The very high ratio of reactance to resistance, along with the low resistive component, indicates a very high SWR on high-impedance transmission lines, and even these lines will show significant losses under these conditions. As well, note the very slow change of impedance and the sudden spike in values as we change the length of the transmission line. Hence, finding a set of values at which the tuner can provide a satisfactory match at low losses may also be difficult.

+
+ +
+

The solution is sketched in Fig. 4. Adding a 6-10' (2-3 m) length of line- -either manually or with a knife switch--will under most circumstances change the impedance values enough on a troublesome band to let you obtain a desired match. The extra line should form a wide loop and not be folded back on itself too tightly.

+

The third circumstance which can alter the impedance that appears at the tuner terminals is the degree to which the transmission line is coupled to the antenna field. This can occur whenever the line forms an angle other than 90 degrees with the vertical antenna wire. The closer to the antenna that the angled transmission line is, the stronger the coupling. Antenna field coupling to the transmission line appears as common mode currents-- that is, currents that are the same in magnitude and phase on both wires. These currents add and subtract from the normally equal magnitude but opposite phase currents on a transmission line, upsetting the desired balance. The currents also show up in the shack as RF that can disrupt equipment operation or give minor RF shocks at any metal corner. They may also cause RF interference with household devices. Ordinarily, they are not strong enough to reradiate in ways that seriously disrupt the antenna pattern itself.

+

The cures require a little work. First, re-examine the transmission line routing to see if the right angle to the antenna can be maintained farther away from the antenna wire. Second, you may install a 1:1 balun at the entry point to the house and use coax from that point to the ATU--if the ATU is a network-type tuner. (This treatment is not needed with a link tuner if the input and output sides do not have a common ground path.) If the coax run is short enough, losses due to high SWR will not be great. A ground wire--as short as possible--to a good earth ground should go from the balun end of the coax. Third, you may also install a balun at the input end of the ATU or use brute-force ferrite split blocks over the coax on the input side of the ATU (and on the output side, if using the second suggested system).

+

The suggested routes of cure are given in the recommended order of implementation. Only the most stubborn cases require all three techniques. The exercise will teach you much about how RF gets from an antenna into the shack--and how to block it most effectively. The presence of common mode currents does not mean that the antenna is not performing correctly or that the pattern shape and strength are ruined. It only takes a little RF in the shack to disrupt matters.

+

One question that often crops up with multiband antennas is whether one might use coax instead of parallel line all the way from the antenna to the ATU. If the coax run is very short, one might use this technique of feeding the vertical doublet, but some of the impedances at the antenna terminals will present a very high SWR to a 50-Ohm coaxial line. As frequency increases, so to do coax losses, and performance on the highest bands may suffer from appreciable power being turned into heat in the line. For this type of application, parallel feeders are far more efficient.

+

How "Good" is the Multiband Vertical Doublet

+

When a dipole is pressed into service on bands other than the one for which it is near resonance, it often becomes other than a dipole. The old name "doublet" is more properly used with such antennas. In assessing how good such an antenna is, of course, we must compare it to the right group of antennas. Comparing it to a beam is unreasonable, since we already agreed that the antenna is for use where no beam is feasible.

+

A fairer comparison is with a 20-meter ground plane monopole elevated to about the same top height as the vertical doublet. This antenna represents a roof top mounting, such as one might use with a trap monopole. For this test, the ground radials of the monopole were sloped, as they might be on a rooftop, and the antenna was resonated to give a 50-Ohm resistive impedance on 20 meters.

+
+ +
+

Fig. 5 compares the 20-meter elevation patterns of both the vertical doublet and the monoband monopole with a sloping ground plane. Although there are slight differences in the two patterns, performance of the two antennas is close enough that the user would detect no operational differences.

+

If you have the space and resources for a better antenna, by all means use it. However, for the ham with limited space and resources, a vertical doublet for 30 through 10 meters--based on the 20-meter dipole--makes an effective antenna for general communications.

+
+ +
+

Go to Amateur Radio Page

+

Topics: Dipole, Doublet, HF Multi Band, Vertical


+ + diff --git a/content/gp/vdgp-1.gif b/content/gp/vdgp-1.gif new file mode 100644 index 0000000..88f3223 Binary files /dev/null and b/content/gp/vdgp-1.gif differ diff --git a/content/gp/vdgp-2.gif b/content/gp/vdgp-2.gif new file mode 100644 index 0000000..7bcb63b Binary files /dev/null and b/content/gp/vdgp-2.gif differ diff --git a/content/gp/vdgp-3.gif b/content/gp/vdgp-3.gif new file mode 100644 index 0000000..c428132 Binary files /dev/null and b/content/gp/vdgp-3.gif differ diff --git a/content/gp/vdgp.html b/content/gp/vdgp.html new file mode 100644 index 0000000..23d2f1d --- /dev/null +++ b/content/gp/vdgp.html @@ -0,0 +1,255 @@ + + + + + + Vertical Dipoles and Ground Planes What Antenna Modeling Reports + + + +
+

Vertical Dipoles and Ground Planes
+ What Antenna Modeling Reports

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ A number of positions have been expressed from different perspectives relative to the need for a ground plane beneath a self-contained vertical antenna, that is, an antenna that does not require the ground plane to serve as the other half of a dipole. A typical self-contained vertical antenna is the vertical dipole. +

This note is not intended to resolve the question. Its only function is to report the results of some systematic modeling to see what modeling programs such as NEC-2 and NEC-4 have to say on the question. Whether the modeling program outputs reflect reality is a question that requires additional work to determine.

+

The situation cannot be effectively modeled in MININEC, since that core will not handle wires close to the ground, and a ground plane must be very close to the ground. I also decided against using buried wires, since the work could not be then replicated by users of NEC-2. However, Jack Belrose has established that a ground plane set as low as 0.001 wl above ground will replicate the typical on-the-ground and shallow-buried ground plane very well.

+
+ +
+

Therefore, I created a model of a 2" diameter aluminum vertical dipole for 7.05 MHz, which is resonant within +/- j1 Ohm. The required vertical dipole length was 66.6 feet. For half the runs, I added a radial system consisting of 32 0.25" wires, the center of which was directly below the vertical dipole, as shown in Figure 1.

+

To set the length of the radials, I began with a 1/4 wl monopole over perfect ground, setting its length to achieve resonance. I then moved the 1/4 wl monopole to free space and created a 32-radial ground plane that would restore resonance in that medium. The required radials length was 42.2 feet.

+

Since the system of radials is independent of the antenna, there is no precise reference length or test to use to set the length of the radials. Moreover, typical amateur installations rarely use precision measures for radials. Indeed, they even more rarely use 32 radials, so the radial system implies a degree of perfection greater than would typically be used. This fact should be kept in mind when evaluating the results of the modeling runs.

+

Past modeling over various types of soil has suggested that modeling solely over average soil, even in the high accuracy Sommerfeld-Norton system, can give misleading results. Therefore, runs were made over 4 soil types:

+ 
 Type               Conductivity        Dielectric Constant
+"Very Good"          0.0303 s/m               20
+"Average"            0.005                    13
+"Poor"               0.002                    13
+"Very Poor"          0.001                     5
+
+

The array of soil types should give a better picture of performance.

+

I modeled the antenna itself at center feedpoint heights of 2 wl (280'), 1 wl (140'), 1/2 wl (70') and 1/4 wl (35'). This last height placed the antenna 1.7' above ground and less than 1.6' above the ground plane. The ground plane, for runs using it, was placed at a constant height of 0.164' (about 2" or 0.05 m) above the ground, which is very slightly higher than 0.001 wl.

+

Here in tabular form are the results, giving the gain (dBi), take-off angle (degrees), and source impedance (R +/- jX Ohms) for each run with and without a ground plane beneath the antenna.

+ 
Height                             Soil Type
+               Very Good      Average        Poor           Very Poor
+2 wl/280'
+No GP          5.18 / 13      4.44 /  7      4.78 /  6      5.70 /  7
+               71.7 + j0.1    71.8 + j0.1    71.8 + j0.1    71.8 + j0.1
+With GP        5.18 / 13      4.44 /  7      4.78 /  6      5.70 /  7
+               71.7 + j0.1    71.8 + j0.1    71.8 + j0.1    71.8 + j0.1
+1 wl/140'
+No GP          5.21 / 27      3.52 / 27      2.92 / 28      3.77 / 12
+               71.1 + j0.3    71.3 + j0.3    71.3 + j0.2    71.5 + j0.3
+With GP        5.21 / 27      3.53 / 27      2.93 / 28      3.76 / 12
+               71.1 + j0.3    71.3 + j0.3    71.4 + j0.3    71.5 + j0.3
+1/2 wl/70'
+No GP          1.26 / 10      0.20 / 13      1.12 / 14      1.37 / 17
+               68.1 + j0.5    69.0 + j0.7    69.2 + j0.6    70.0 + j0.8
+With GP        1.27 / 10      0.28 / 13      1.19 / 14      1.44 / 16
+               68.2 + j0.7    69.4 + j0.9    69.7 + j0.7    70.7 + j0.8
+1/4 wl/35'
+No GP          1.96 / 15      -.09 / 18      0.22 / 19      -.74 / 21
+               101.7+ j7.4    97.7 + j4.2    95.8 + j4.0    91.4 + j0.8
+With GP        1.99 / 15      0.32 / 18      0.71 / 19      0.04 / 21
+               97.0 + j7.2    90.3 + j11     90.0 + j13     85.6 + j15
+Delta Gain      0.03 dB        0.40 dB        0.49 dB        0.78 dB
+

With the end of the antenna at least 1/4 wl above the ground plane, the maximum gain improvement os 0.08 dB, as reported by NEC-4. with the end of the antenna in close proximity to the ground plane, the improvement in gain is directly related to the quality of the soil beneath the antenna. For soil ranging from poor to average, the additional gain provided by the 32- radial ground plane is less than half a dB. For very poor soil, the improvement is about 3/4 dB.

+
+ +
+

Of immediate notice to those who have not modeled verticals extensively is the fact that the worst performance, as calculated by the modeling program, occurs over average soil. Poor relative performance shows up as both lesser gain and a higher angle of maximum radiation. Figure 2 shows why. The development of elevation lobes can be a squared-edge field, the result of two lobes mixed. The lower or the higher may dominate, and this may be by a small amount or a large amount. Therefore, in evaluating the potential performance of a vertical antenna, one should always investigate not just the angle of maximum radiation, but as well all of the elevation lobe structure.

+

Whether the added gain for any situation justifies the creation of a significant ground plane is a user decision. Whether the model reflects reality accurately is a question requiring independent investigation. However, it seemed useful as the beginning of a running investigation to present some NEC-4 modeling results in this regard. NEC-2 results are perfectly consistent, so one may replicate the exercise with ease. A copy of the EZNEC description of the test antenna for one test is attached as a reference. The EZNEC "radial-maker" is an easy way to create the required radial system.

+

Three directions of further analysis are indicated. First, the ground plane is fairly extensive. Would a few radials--4, for instance--achieve the same gain improvements? Second, is the gain increase relatively linear as the antenna center moves from 1/2 wl up down to 1/4 wl up? Third, would longer or shorter radials materially affect the improvement in gain? These are questions I hope to get to--at least so far as modeling is concerned-- as time permits.

+ +
+ 
                      EZNEC/4  ver. 2.5
+vert dipole w/gp: 7.05 MHz                   09-18-1998     08:09:22
+Frequency = 7.05  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1          0.000,  0.000,313.300         0.000,  0.000,246.700 2.00E+00  21
+2   W3E1   0.000,  0.000,  0.164        42.200,  0.000,  0.164 2.50E-01  10
+3   W4E1   0.000,  0.000,  0.164        41.389,  8.233,  0.164 2.50E-01  10
+4   W5E1   0.000,  0.000,  0.164        38.988, 16.149,  0.164 2.50E-01  10
+5   W6E1   0.000,  0.000,  0.164        35.088, 23.445,  0.164 2.50E-01  10
+6   W7E1   0.000,  0.000,  0.164        29.840, 29.840,  0.164 2.50E-01  10
+7   W8E1   0.000,  0.000,  0.164        23.445, 35.088,  0.164 2.50E-01  10
+8   W9E1   0.000,  0.000,  0.164        16.149, 38.988,  0.164 2.50E-01  10
+9  W10E1   0.000,  0.000,  0.164         8.233, 41.389,  0.164 2.50E-01  10
+10 W11E1   0.000,  0.000,  0.164         0.000, 42.200,  0.164 2.50E-01  10
+11 W12E1   0.000,  0.000,  0.164        -8.233, 41.389,  0.164 2.50E-01  10
+12 W13E1   0.000,  0.000,  0.164       -16.149, 38.988,  0.164 2.50E-01  10
+13 W14E1   0.000,  0.000,  0.164       -23.445, 35.088,  0.164 2.50E-01  10
+14 W15E1   0.000,  0.000,  0.164       -29.840, 29.840,  0.164 2.50E-01  10
+15 W16E1   0.000,  0.000,  0.164       -35.088, 23.445,  0.164 2.50E-01  10
+16 W17E1   0.000,  0.000,  0.164       -38.988, 16.149,  0.164 2.50E-01  10
+17 W18E1   0.000,  0.000,  0.164       -41.389,  8.233,  0.164 2.50E-01  10
+18 W19E1   0.000,  0.000,  0.164       -42.200,  0.000,  0.164 2.50E-01  10
+19 W20E1   0.000,  0.000,  0.164       -41.389, -8.233,  0.164 2.50E-01  10
+20 W21E1   0.000,  0.000,  0.164       -38.988,-16.149,  0.164 2.50E-01  10
+21 W22E1   0.000,  0.000,  0.164       -35.088,-23.445,  0.164 2.50E-01  10
+22 W23E1   0.000,  0.000,  0.164       -29.840,-29.840,  0.164 2.50E-01  10
+23 W24E1   0.000,  0.000,  0.164       -23.445,-35.088,  0.164 2.50E-01  10
+24 W25E1   0.000,  0.000,  0.164       -16.149,-38.988,  0.164 2.50E-01  10
+25 W26E1   0.000,  0.000,  0.164        -8.233,-41.389,  0.164 2.50E-01  10
+26 W27E1   0.000,  0.000,  0.164         0.000,-42.200,  0.164 2.50E-01  10
+27 W28E1   0.000,  0.000,  0.164         8.233,-41.389,  0.164 2.50E-01  10
+28 W29E1   0.000,  0.000,  0.164        16.149,-38.988,  0.164 2.50E-01  10
+29 W30E1   0.000,  0.000,  0.164        23.445,-35.088,  0.164 2.50E-01  10
+30 W31E1   0.000,  0.000,  0.164        29.840,-29.840,  0.164 2.50E-01  10
+31 W32E1   0.000,  0.000,  0.164        35.088,-23.445,  0.164 2.50E-01  10
+32 W33E1   0.000,  0.000,  0.164        38.988,-16.149,  0.164 2.50E-01  10
+33  W2E1   0.000,  0.000,  0.164        41.389, -8.233,  0.164 2.50E-01  10
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          11     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+No loads specified
+No transmission lines specified
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+              --------------- MEDIA ---------------
+Medium        Conductivity(S/m)   Dielectric Const.    Ht(ft)   R Coord(ft)
+
+1                 5.000E-03            13.00           0 (def)     0 (def)
+

+ +
+

Phase 2: From 1/2 WL down to 1/4 WL

The range of heights from 1/2 wl (70' source point) down to 1/4 wl (35' source point) is quite interesting. Although one can see for each type of soil a general progression, the curves are not at all so smooth as we might expect. +

Here in tabular form is the result of modeling the vertical dipole both without and with a ground plane at 0.164' for each 5' increment.

+ 
Height                             Soil Type
+(top/ctr/bot)   Very Good       Average         Poor            Very Poor
+103.3/70/36.7
+No GP           1.26 / 10       0.20 / 13       1.12 / 14       1.37 / 17
+With GP         1.27 / 10       0.28 / 13       1.19 / 14       1.44 / 16
+Improvement     0.01            0.08            0.07            0.07
+98.3/65/31.7
+No GP           1.57 / 10       0.26 / 13       1.11 / 14       1.19 / 17
+With GP         1.58 / 10       0.35 / 13       1.19 / 14 +     1.29 / 17
+Improvement     0.01            0.09            0.08            0.10
+93.3/60/26.7
+No GP           1.83 / 11       0.31 / 14       1.08 / 15       0.98 / 17
+With GP         1.84 / 11       0.42 / 14       1.18 / 15       1.12 / 17
+Improvement     0.01            0.11            0.10            0.14
+88.3/55/21.7
+No GP           2.02 / 11       0.34 / 14 +     1.02 / 15       0.75 / 18
+With GP         2.02 / 11       0.46 / 15       1.15 / 15       0.94 / 18
+Improvement     0.00            0.12            0.13            0.19
+83.3/50/16.7
+No GP           2.13 / 12       0.33 / 15       0.92 / 16       0.48 / 18
+With GP         2.13 / 12       0.47 / 15 +     1.08 / 16       0.74 / 19
+Improvement     0.00            0.12            0.16            0.26
+78.3/45/11.7
+No GP           2.15 / 13 +     0.26 / 16       0.76 / 17       0.16 / 19
+With GP         2.15 / 13 +     0.45 / 16       0.98 / 17       0.52 / 20
+Improvement     0.00            0.19            0.22            0.36
+73.3/40/6.7
+No GP           2.10 / 14       0.13 / 17       0.54 / 18       -.23 / 20
+With GP         2.09 / 14       0.39 / 17       0.85 / 18       0.28 / 20
+Improvement     -.01            0.26            0.31            0.51
+68.3/35/1.7
+No GP           1.96 / 15       -.09 / 18       0.22 / 19       -.74 / 21
+With GP         1.99 / 15       0.32 / 18       0.71 / 19       0.04 / 21
+Improvement     0.03            0.41            0.49            0.78
+

Quite clearly, the poorer the soil, the greater overall improvement is effected by a ground plane beneath the vertical dipole. However, that improvement does not become something worth the investment in a uniform manner. With very good soil, it is unlikely that a ground plane effects an improvement worth the effort. If we arbitrarily set 0.2 dB gain as the minimum improvement, then over no soil does the ground plane effect significant improvement until the antenna center is below 3/8 wl.

+

Moreover, the gain curves are neither smooth nor the same shape for each soil type. Over very poor soil, the gain shows a relatively smooth decrease with each decrease in antenna height whether or not there is a ground plane. Over better soils, the gain shows a peak value at center height between 1/2 and 1/4 wl (indicated by a + in the table). The better the soil, the lower the height of the gain peak. Over very good soil, the gain peaks at the same height, with or without a ground plane. Over average or poor soil, the peaks with and without a ground plane occur at different heights.

+

Once more, these are modeling results only--and only for a comparison between the absences of a ground plane and the use of a 32-radial ground plane of the size specified earlier. One cannot extrapolate to reality. Moreover, until the other questions posed earlier are tested, one cannot even extrapolate to other ground plane sizes, whether the variance is in number of radials or in radial length.

+ +
+

Phase 3: The Effect of the Number of Radials

Even though the improvements that modeling reports are marginal and significant only at the lowest heights over the worst soils, the 32-radial standard lies beyond the system size of most amateur installations. Most amateur installations are likely to have only 4 radials. +

The 4-radial system was developed in the same manner as the 32-radial system. A 1/4 wl monopole was resonated over perfect ground. When placed in free space, a 4-radial ground plane system was developed to re-resonate the antenna. The elements of this system were 37.7' long (shorter than the radials in the 32- radial system by about 0.5'). This system was placed 0.001 wl above ground (about 2" or 0.05 m).

+

We may look at the potential for small radial systems--at least as modeling would show them, by inserting the 4-radial data into the previous table of values for the height range of 1/2 wl to 1/4 wl relative to the center of the vertical dipole above ground.

+ 
Height                             Soil Type
+(top/ctr/bot)    Very Good        Average          Poor             Very Poor
+103.3/70/36.7
+No GP            1.26 / 10        0.20 / 13        1.12 / 14        1.37 / 17
+4 radials        1.26 / 10        0.21 / 13        1.13 / 14        1.38 / 16
+32 radials       1.27 / 10        0.28 / 13        1.19 / 14        1.44 / 16
+
+98.3/65/31.7
+No GP            1.57 / 10        0.26 / 13        1.11 / 14        1.19 / 17
+4 radials        1.57 / 10        0.27 / 13        1.12 / 14        1.21 / 17
+32 radials       1.58 / 10        0.35 / 13        1.19 / 14        1.29 / 17
+
+93.3/60/26.7
+No GP            1.83 / 11        0.31 / 14        1.08 / 15        0.98 / 17
+4 radials        1.83 / 11        0.33 / 14        1.10 / 15        0.79 /17
+32 radials       1.84 / 11        0.42 / 14        1.18 / 15        1.12 / 17
+
+88.3/55/21.7
+No GP            2.02 / 11        0.34 / 14        1.02 / 15        0.75 / 18
+4 radials        2.02 / 11        0.35 / 14        1.04 / 15        0.79 / 18
+32 radials       2.02 / 11        0.46 / 15        1.15 / 15        0.94 / 18
+
+83.3/50/16.7
+No GP            2.13 / 12        0.33 / 15        0.92 / 16        0.48 / 18
+4 radials        2.13 / 12        0.34 / 15        0.94 / 16        0.53 / 19
+32 radials       2.13 / 12        0.47 / 15        1.08 / 16        0.74 / 19
+
+78.3/45/11.7
+No GP            2.15 / 13        0.26 / 16        0.76 / 17        0.16 / 19
+4 radials        2.15 / 13        0.28 / 16        0.79 / 17        0.22 / 19
+32 radials       2.15 / 13        0.45 / 16        0.98 / 17        0.52 / 20
+
+73.3/40/6.7
+No GP            2.10 / 14        0.13 / 17        0.54 / 18        -.23 / 20
+4 radials        2.09 / 14        0.16 / 17        0.58 / 18        -.13 / 20
+32 radials       2.09 / 14        0.39 / 17        0.85 / 18        0.28 / 20
+
+68.3/35/1.7
+No GP            1.96 / 15        -.09 / 18        0.22 / 19        -.74 / 21
+4 radials        1.95 / 15        -.04 / 18        0.30 / 18        -.56 / 21
+32 radials       1.99 / 15        0.32 / 18        0.71 / 19        0.04 / 21
+

The improvement that a 4-radial ground plane system is likely to produce is for the most part insignificant. The increase in gain according to the modeling software, is greater than 0.1 dB only for the worst soil and at the lowest antenna height. Nevertheless, there is a certain proportionality to the slight improvements, insofar as they tend to reveal the beginnings of a steady curve of increased performance up through the 32-radial level. It is likely that this trend reflects reality, even if the actual numbers may vary (or not) between real antenna systems and models.

+ +
+

Phase 4: The Effect of the Length of Radials

To test the effects of the lengths of radials, I selected the antenna and ground plane configuration where the 32-radial ground plane had the greatest impact on antenna gain--that is with the antenna centered at 1/4 wl above ground. I then changed the length of the ground plane radials in 1/16 wl (0.0625 wl) increments from 3/16 to 8/16 wl. +

The results of the modeling runs are given in the following table.

+ 
Radial Length                       Performance
+L in feet   L in WL     Gain dBI    T-O angle         Source Z
+0 (no GP: ref.)         -.74        21           91.4 + j 0.1
+26.25       .1875       -.53        21           88.5 + j 5.0
+35.00       .2500       -.28        21           86.2 + j 9.1
+43.75       .3125       0.12        22           85.9 + j16.5
+52.50       .3750       0.54        22           91.3 + j24.7
+61.25       .4375       0.83        23          102.7 + j28.9
+70.00       .5000       0.95        24          117.0 + j23.9
+

It is clear that under the modeled circumstances, increasing the length of the radials detunes the antenna relative to its resonant length with no ground plane. In terms of resonance alone, the peak detuning or maximum reactance occurs in the vicinity of a radial length of 7/16 wl. The resistive component of the source impedance continues to climb throughout the tested range of radial lengths.

+
+ +
+

Gain and take-off angle are most clearly shown when graphed. Figure 3 shows the two parameters as they vary with the length of radials. Gain rises almost linearly if we exclude the two limiting values of radial length in the test. Above 7/16 wl (0.4375 wl), gain increases at a much slower rate.

+

It is also clear that the ground plane itself plays a second role in determining the elevation pattern of the vertical dipole. As the length of the radials increases, the take-off angle also increases. The stepped nature of curve is an artifact of taking angular reading a 1-degree increments. The curve can be read in both a positive and a negative manner: the ground plane length offers some control over the take-off angle, but on the other hand, for applications requiring the lowest achievable take-off angle, long radials become a deficit.

+ +
+

Conclusion

This completes the introductory survey of the effects of a ground plane beneath a self-complete antenna such as a vertical dipole. The modeling has shown some of the tendencies in the calculated outputs for such antenna systems in terms of antenna height, low height variations, number of radials, and radial length. The study is by no means complete, since one may fill in some of the gaps, extend the progressions, and replicate the work for other frequencies and antenna types. +

As repeated throughout, this rudimentary study does not speak directly to real antenna systems, but only shows what modeling calculations within NEC-2 and NEC-4 try to say about vertical dipoles over ground planes. Except for vertical dipoles in very close proximity to very poor soils, the addition of a ground plane has minimal benefit to offer vertical dipoles--and by extension other vertically polarized antennas that are not dependent upon the ground plane to complete the antenna itself.

+

Because the ground plane in this study was constructed above the ground itself, the work can be replicated and extended using any version of NEC available (excluding MININEC). Those with NEC-4 capabilities may wish to compare the results shown here with a carefully constructed ground plane system below the surface of the ground at various depths. Although vertical antennas are extensively used at 7 MHz, the frequency is at the high end of the range of frequencies for which the questions posed are relevant. Hence, replication of the study at lower frequencies is advisable before extrapolating to many conclusions from this effort, even within the context of modeling.

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In short, this study has more "phases" than I am ever likely to have time for in the near future.

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For additional information on work done in this area on 20 meters, you may download a paper from the Rick Karquist, N6RK, site. The paper is in .pdf format and thus requires Adobe Acrobat to read or print.
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Updated 9-22-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
+

Topics: HF Lower, Vertical


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A Triangle for the Short Vertical Operator

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+

L. B. Cebik, W4RNL

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+ Last month, I described a triangle array of three full-size vertical dipoles for 40 meters (with 30 meters as a bonus). Since these wires require that we have access to supports around 80' up, I promised a triangular array composed of short vertical elements. Time to keep my promise. We shall design a 40-meter triangular array of three hatted dipoles having a total height of 22' above ground, with the bases 4.5' off the ground. Even if you do not need such an array, the techniques involved may be useful to you somewhere else down the road. +

For some of the background material, I shall rely on last month's item. We need the space this month for current detail. So I hope you saved a copy of the tall triangle.

+

Hatted Dipoles

When a dipole is shortened, it maintains far more of its gain potential than most folks realize. Of course, in its shortened condition, it is no longer at or near resonance. Hence, we load it. Inductive loading of a dipole, whether placed at the feedpoint or moved to a mid-element position, creates the greatest loss, since either method converts high current areas of the linear element into tightly confined inductive fields, leaving lower current on the linear element beyond. Even with no resistive coil losses, the gain drops well below that of a "hatted" dipole. +
+ +
+

Figure 1 shows a very short hatted vertical dipole next to its full-size counterpart. In free space, the hatted dipole has a gain of only 0.35 dB less than the full size dipole. Since the radiation pattern strength is a function of the current on the antenna, and since the hatted dipole preserves undisturbed the high current portion of the dipole element, it also preserves most of the dipole's far field pattern strength.

+

Brought near the ground, as we propose to do in this exercise, the hatted dipole shows some further far field weakening compared to the full size dipole. With a base of 10' from the ground and a feed point about 32-35' above that point, the full size dipole has a 1.3 dB gain over the hatted dipole set only 4.5' above ground with its feedpoint less than 9' above that point. The difference also shows up in the elevation angle of maximum radiation: 16 degrees for the full-size dipole vs. 26 degrees for the hatted dipole.

+

A triangular array of hatted vertical dipoles is capable of a forward gain of about 2.5 dBi, about 2 dB less than a similar array of full-size dipoles. Most of the gain decrease comes from the lowered height of the feedpoint and the element region immediately surrounding it. But remember that the entire hatted dipole array vertically does not even reach the feedpoint of the full size dipole array. Moreover, the array shows a gain of abut 3.6 dB over a single hatted dipole. If we can only manage short verticals, then the triangle offers significant gain and directionality over the single short vertical.

+

A triangular array of dipoles only 17.5' long, with bases about 4.5' off the ground, gives us something we might control mechanically without upper support requirements. We might construct the elements from 1.25" aluminum or similar material. Of course, we shall need to consider the hats for both the top and bottom ends before we are done.

+

For the present design, I enlarged the triangle face to about 35' for element spacing that is closer to 1/4 wavelength. The center point amid the elements is 20.25' from each element. The reason for increasing the spacing is to broaden the operating bandwidth of the array, since shortened elements tend to decrease operating bandwidth, even with symmetrical hats which preserve operating bandwidth better than any other short element loading form.

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+ +
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The pattern characteristics of the triangular array remain quite good across 40 meters, as illustrated in Figure 2. The anticipated front-to- back ratio varies between 11 and 16 dB across the band, while the gain varies by less than 1/2 dB. Therefore, if the lower gain and somewhat higher elevation angle of maximum radiation are acceptable, then this array is worth further consideration.

+

Each element will consist of a 17.5' conductor of moderate diameter. 1.25" is a good design start, although you will use what is most conveniently obtained. You will also need insulated pipe or tubing for the center or feedpoint separator and for the base mounting support.

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Figure 3 provides some of the rough details for a hatted vertical dipole. Each dipole will have a loading/beta inductor at its center. When the element functions as a reflector, the inductance loads the element to the correct electrical length for nearly optimal reflector functioning. When the element operates as a driven element, the same inductor functions as a beta match reactance. The elements are cut specifically to a length that, when set in a triangle of the size prescribed, shows a feedpoint impedance of 30-35 Ohms resistance and about 20 Ohms capacitive reactance at the center of 40 meters. The reactance at the center of each element is about 60 Ohms.

+

The original design used 1/8" rods for the capacity hats, with similar material used as a perimeter wire. The hat structures use an 8.4' spoke length. The large 4-spoke hats are only one possible hat design. There are numerous ways to fasten rods to the main mast. You can drill through the main element. Alternatively, you can create a bracket to both support the rods and fit over the main element. Construction details are largely a matter of locally available materials and builder comfort in using them.

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The array provides three-way coverage that is essentially the same as the full size-array, as shown in Figure 4. Half-power points are separated by about 130 degrees so that little is lost to the nulls between peaks. Although the take-off angle is somewhat higher than with a full size dipole, there is considerable gain at lower angles for solid DX skip angle coverage on 40 meters. The antenna system provides full horizon coverage at a gain level similar to the fixed bi-directional gain of an optimized delta SCV.

+

Feeding the Short Triangle

Let's spend a little time looking more closely at the load and feed system of the shortened elements. As noted, each element has a permanent 60-Ohm loading inductive reactance permanently attached across the insulated center of the element. The reactances are loads only when the element functions as a reflector, which occasions less loss than when a driven element is inductively loaded at its center. When the reactance is across the driven element, it is part of a beta matching system. Figure 5 shows the two styles of loading reactance that we can use. +
+ +
+

The hairpin is nothing more or less than a shorted section of parallel transmission line. You can fabricate your own, perhaps of #10 aluminum wire (to avoid bi-metallic effects at the junction). With a 2" spacing, the hairpin will need to be a little over 2.9' long. A 4" spacing between wires shortens the length to about 2.5' on the assumption of a velocity factor of 1.0 for these self-supporting lines. You may also use 450-Ohm parallel line, which would require nearly 2.8' if the velocity factor is 0.95. 300-Ohm TV ribbon with a velocity factor of 0.8 calls for nearly 3.5' of line.

+

For this application, a solenoid coil may be the most compact solution. There is insignificant loss if the Q is over 200, which is easily obtained from a coil that has well spaced turns and a diameter that is nearly equal to the coil length. 7 turns of #10 wire spread to a length of about 1.6" will provide adequate "squeeze and spread" adjustment range for tuning up the system.

+

The next step is to control the elements so that each knows when it is a reflector and when it is a driven element. For this purpose, we can use 1/4 wl sections of 50-Ohm feedline. A 1/4 wl section of RG-213, and similar lines with a 0.66 velocity factor, figures to be about 22.6' long when cut for the center of 40 meters. Since the distance from the element to the center of the triangle is 20.25', these lines leave no room for flex and might require a central control box to be mounted at the 13.25' feedpoint height--which is bound to be inconvenient. Foam lines, like RG- 8X, have a velocity factor of about 0.79, resulting in a 1/4 wl section that is about 27.2' long. This length permits a nice slope to a few feet off the ground, with a bit of flex to spare. However, I have found foam lines to vary considerably is actual velocity factor, with one batch measuring at just over 0.73. Hence, test the 1/4 wl lines you cut before using them.

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+ +
We shall press into service the very same control box we used for the full size array described last month and shown in Figure 6. The remotely switched relays connect the coax from the shack to one of the three 1/4 wl lines. Since, this makes the element a driver, the section from the box to the element is just another part of the feedline, and the reactance across the element feedpoint is a beta matching coil. +

The other two 1/4 wl lines are shorted at the control box and not connected to either the center conductor or the braid of the shack feedline. When shorted at the control box, a quarter wavelength line section show a very high impedance--essentially an open circuit--at the element end. Now the coils at the center of each element provide continuity for the element and load it to the correct electrical length for use as a reflector.

+

Switching directions is as easy as with the full-size array. However, be sure to note the different electrical principles involved for the full and short arrays. All switches look alike, but what they switch may be very different things.

+

Hatting the Dipoles

The short dipole array is designed to set each element 4.5' off the ground, for a maximum element height of 22'. Hence, each 17.5' dipole is just about one-fourth of full dipole length. Hat structures may require as much horizontal room as the dipole takes up vertically. The original design used 4 spokes and a perimeter wire to connect the tips of the spokes. +
+ +
+

However, hats come in many variations, from as few as 2 spokes set precisely in opposite directions to 60 or more symmetrically spaced spokes. As Figure 7 shows, the design may use spokes only or use a connecting wire from tip-to-tip. Each of these hats is symmetrical so that the radiation from one part is cancelled by radiation from elsewhere in the hat.

+

The relationship of the spoke length (which establishes a virtual hat "radius") and the number of spokes is quite regular, although not simple. First, spokes are shorter, for any set number of them, if a perimeter wire is employed. The true element end is not at the tip of the spoke, but half way between spokes on the perimeter wire. Very roughly, the effective spoke length is the sum of the spoke and the half-length of perimeter wire.

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Figure 8 shows a graph of what happens to the required spoke length as the number of spokes is increased--for both the spoke-only design and for the spoke-plus-perimeter-wire design. Although this study was done at 3 MHz, the trends are perfectly applicable at any HF frequency. For small numbers of spokes, the perimeter wire shortens the hat radius fully by half. However, as the number of spokes increases, the shrinkage benefit of the perimeter wire is reduced, since the length between tips is much shorter.

+

At the same time, more spokes means shorter spokes, but probably not beyond a limit of about 60 spokes, when the system begins to simulate a solid disc. You can draw out both curves on the graph until they intersect and level well beyond the right edge of the graph. Notice also that there is a minimum spoke length limit. This limit is about 70% of the spoke length of the 4-spoke-plus-perimeter design. Hence, for the triangular do not expect spokes much less than about 5.5' long, no matter how many you add.

+

Actual spoke system construction once more is a local effort and depends on available materials and construction techniques you have mastered. You can, of course, use an insulated extension for the element to provide truss support for the upper spokes, and replicate something similar for the lower hat.

+

Alternative Hat Systems

If full 40 meter coverage is not required and slightly less gain is acceptable, you may construct more compact non-symmetrical hats to replace the symmetrical ones used in the original design. A non-symmetrical hat does not provide complete field cancellation from the hat structure, although tight coupling can reduce horizontally polarized radiation to levels 25 dB or more below the overall field strength. +
+ +
+

Figure 9 shows some, but by no means all, options available for non- symmetrical hat design. The spiral, if very carefully constructed, can become a nearly symmetrical hat, although coupling between different points along the same wire prevents true symmetrical hat performance.

+

The solenoid, shown as a large spread coil, can also be compacted into a length of wire resembling a normal inductor. However, at the high-voltage, low-current end of the element, there are radically unequal currents at the coil ends, defeating the conditions required for an inductance of appreciable magnitude. Instead, the solenoid functions as simply a length of wire so configured as to minimize its physical size and to allow the element to reach resonance. (A measure of how little the end-loading solenoid acts as an inductor can be seen by comparing the actual coil of wire required to produce resonance with an inductor that might be used as a source of inductive reactance. Inductive reactance values in the 10s of thousands of Ohms are needed near antenna element ends to effect reactive loading, while the wire coil achieves resonance with only a small fraction of the wire length needed to make a coil with the high reactance. In antennas, not everything that looks like an inductor functions as an inductor. Similar things can be said of apparent capacitors.)

+

The zig-zag hat is simply a variant of extending the wire outward, but bringing it inward and then back and forth (up and down for a vertical element) until resonance is achieved. (The dotted lines in the sketch represent insulated supports.) The close coupling extends the total length of wire required to make this type of hat, but the wire can be light and held within about 2' of the main element for fairly good efficiency.

+

Every form of non-symmetrical end loading offers both advantages and disadvantages. On the plus side is the fact that non-symmetrical end loading can result in quite compact antenna structures that are mechanically easier to fabricate and maintain. However, all such structures result in less gain, lower feedpoint impedances, and a narrower operating bandwidth for both the antenna characteristics and the feedpoint impedance. Wherever physically feasible, symmetrical hats are superior.

+

Conclusion

The array lends itself to considerable experimentation. One direction might be to off-center feed the dipole at the junction with the lower hat. Little change to the feedpoint impedance occurs in the few feet from center, and the reflector loading reactances and beta inductor will be about the same. However, there is a price to pay for the convenience of having the feedpoint and 1/4 wl lines so close to earth. There may be considerable current on the outside of the coax lines. Therefore, W2DU chokes may be needed, and the length of each one will be part of the 1/4 wl lines. +

The short, hatted three-dipole array is certainly not for everyone with the backyard space for it. The array presents some construction challenges that may be beyond what a given situation permits. However, it does offer a number of design ideas that are worth stowing in the notebook for future reference. Hatted dipoles (and monopoles) offer superior performance to elements of equal length using other forms of loading. Elements, even with loads at their centers, can be made to perform different functions in a given array depending upon their connection--and that may be remotely controlled by fairly simple means. Triangles offer one of the least expensive steerable arrays for the lower bands.

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While you may not build this array, I'll bet at least one of these ideas works its way into your future antenna construction projects.

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Updated 2-5-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Dec., 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, HF Lower, Loading, Vertical


+ + diff --git a/content/gup/groundup.gif b/content/gup/groundup.gif new file mode 100644 index 0000000..f8827a1 Binary files /dev/null and b/content/gup/groundup.gif differ diff --git a/content/gup/groundup.html b/content/gup/groundup.html new file mode 100644 index 0000000..6ae2843 --- /dev/null +++ b/content/gup/groundup.html @@ -0,0 +1,165 @@ + + + + + + Antennas From the Ground Up Index (42 Articles) + + + +
+ Antennas From The Ground Up +
+
+

L. B. Cebik, W4RNL

+

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+ +
+

The following series of articles was originally prepared for publication in Low Down, the journal of the Colorado QRP Club. The series is designed to present fundamental antenna information, concentrating most fully on lower HF band wire antennas and related topics, to QRP operators. Since Low Down has devolved into a small newsletter, I have terminated the series and will place the remaining pre-prepared items here.

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+ +

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+ Note: This series (with revisions and enhancements) are available in book form under the titles from MFJ: + +

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  1. + Where Do Antennas Fit in Your Communications System? +
    2. +
  2. + The Resonant Half-Wavelength Center-Fed Antenna +
    3. +
  3. + Azimuth, Elevation, and Antenna Modeling +
    4. +
  4. + Making a Dipole Fit the Space Available +
    5. +
  5. + A 135' Center-Fed Multi-Band Dipole Data Compendium +
    6. +
  6. + A 102' Center-Fed Multi-Band Dipole Data Compendium +
    7. +
  7. + How to Make Your Tuner Work on Every Band +
    8. +
  8. + Horizontal vs. Vertical Antennas on the Low HF Bands +
    9. +
  9. + Fundamentals of Off-Center-Fed Dipoles +
    10. +
  10. + Harmonic Operation of OCFs +
    11. +
  11. + A 135' Off-Center-Fed Multi-Band Dipole Data Compendium +
    12. +
  12. + A 135' End-Fed Multi-Band Dipole Data Compendium +
    13. +
  13. + What Happens Along a Length of Feedline +
    14. +
  14. + ATUs, Delta, and Tuner Losses +
    15. +
  15. + More on ATUs, Delta, and Losses +
    16. +
  16. + Noise, Antennas, and Receiving Systems +
    17. +
  17. + Vertically-Oriented, Horizontally Polarized 1 wl Loops +
    18. +
  18. + Multiband Use of VOHPLs +
    19. +
  19. + Vertically Oriented, Vertically Polarized 1 wl Loops +
    20. +
  20. + Some Facts and Fantasies About Standing Wave Ratios +
    21. +
  21. + A Short Look at Wire Beams +
    22. +
  22. + A Horizontal 80-Meter Multi-Band Loop Data Compendium +
    23. +
  23. + Where to Place Your Impedance Matching Efforts +
    24. +
  24. + The 75-Ohm 1/4 Wavelength Matching Section +
    25. +
  25. + A 1/2 Wavelength Inverted-L Multi-Band Antenna Data Compendium +
    26. +
  26. + A 3/8 Wavelength Inverted-L Multi-Band Antenna Data Compendium +
    27. +
  27. + Differentiating Among Many Types of Grounds +
    28. +
  28. + Why Parasitic Beams Work +
    29. +
  29. + Interesting Alternatives to the Yagi +
    30. +
  30. + A Collection of Inverted-Vee Patterns +
    31. +
  31. + Handling Parallel Feedlines +
    32. +
  32. + When and Which Parallel Feedline to Use +
    33. +
  33. + Unwanted Currents and Their Suppression +
    34. +
  34. + The 44' Doublet as a 40-10 Meter +
    35. +
  35. + Sorting Out Bi-Directional Phased Arrays +
    36. +
  36. + The Dual Expanded Lazy-H for 80-10 Meters +
    37. +
  37. + A Potpourri of Bent Dipoles +
    38. +
  38. + A Collection of Quadrant Antenna Patterns +
    39. +
  39. + A Nearly All-Band Vertical Doublet +
    40. +
  40. + The Terminated Wide-Band Folded Dipole Antenna +
    41. +
  41. + The Terminated (Very) Longwire Antenna +
    42. +
  42. + The Terminated Vee-Beam and Rhombic +
    43. +
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+ +

+

Return to Amateur Radio Page

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Topics: Magazine Columns


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+

ANTENNAS FROM THE GROUND UP

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1. Fantastic Feedlines,
+ or Where Do Antennas Fit in Your Communications System?

+
+
+

L. B. Cebik, W4RNL

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+ +

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+ We can all buy or build a box full of parts called a radio, or a transceiver, if we want to be precise. Then we add accessories: headphones, keyers, paddles, computers, antennas. . . +

Antennas? Unfortunately, feedlines and antennas are too often looked at as accessories, as if the "rig" was the most important thing in the world in a communications system. And that has blocked our attention to and understanding of antennas. So let's start all over again by looking at a communications system. See Figure 1 for a sketch of a basic system.

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As you can see, a true communications systems consists of at least two stations: either a minimum of two or no communications will occur. Each station receives and transmits. Each needs devices to receive and to transmit. What transmitting and receiving have in common--usually, but not absolutely always--is a transmission line and antenna. For some special purposes, like working 160 meters, some folks use separate receiving and transmitting antennas, and separate feedlines.

+

Although this may seem very basic, let's review the functions of these components of the communications system:

+

Transmitter: a collection of circuits (composed of components) that generates RF electrical energy and modifies it to include intelligence.

+

Receiver: a collection of circuits (composed of components) that separates the intelligence from the incoming RF electrical energy for station use.

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Transmission line: transfers RF electrical energy from the transmitter to the antenna with minimal loss. Also transfers RF electrical energy from the antenna to the receive with minimal loss. Required only when the antenna is remote from the transmitter.

+

Antenna: a transducer that converts RF electrical energy into electro- magnetic radiation or fields and which converts intercepted electro- magnetic radiation into RF electrical energy.

+

Interestingly, if we connect the transmitter and receiver directly to the antenna, as we virtually do with VHF handhelds (walkie-talkies?), we can eliminate the most interesting part of the communications system: the transmission line. Transmission lines are not interesting just because they seem mysterious. They are especially interesting because they are the key to everything else. Some traditional treatments of communications electronics begin with transmission line theory. From there, they derive lumped components (capacitors and inductors) and then they also derive antennas.

+

Notice that I said "lumped components (capacitors and inductors)." I did not say "capacitance and inductance. One of the things we have to do to understand antennas and transmission lines is to separate in our minds the ideas of things--the capacitors and inductors--from the basic phenomena-- capacitance and inductance. Capacitors and inductors are just the things we use to implement controlled amounts of capacitance and inductance when and where we want them.

+

Transmission lines also exhibit capacitance and inductance. Every length of wire exhibits inductance, and every pair of surfaces (like wire surfaces) exhibit capacitance. Although transmission lines come in many varieties ranging from one wire to many, the two wire line--coax or parallel--is most familiar to us. Two wires with a finite length equals capacitance and inductance.

+

Transmission lines have something else of note: standing waves. A standing wave is nothing more than the variations in voltage and current along a transmission line. When measured and plotted on a graph, they replicate an electrical wave as we are accustomed to picturing it: something more or less like a sine wave with many possible variations.

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Standing waves are functions of basic electrical properties: If we pass a current through a wire, it generates an electro-magnetic field. If the electrical energy is alternating current (AC) and high enough in frequency (RF), then that field will radiate, that is, be detectable at a distance. It will be detectable unless we can control and confine it. Transmission lines confine the field by having equal but opposite voltages and currents on each wire in a two wire system in close enough proximity so that the fields cancel each other.

+

For a full account of the parameters of coaxial transmission lines, see QEX, August, 1996, pp. 3-10.

+

Now let's look at our lumped components: If they were large enough, they would have standing waves. They still have fields. If they did not, the grid-dip oscillator would not work. Of course, we try to control and confine component and interconnection-wire fields by a lot of methods. We confine inductor fields with iron or ferrite coil cores. We position components relative to each other for minimum coupling. We install shielding to keep inside fields from interacting with outside fields. Remember, however, that we can make use of component radiation. For example, we can make a large planar coil for the plate circuit of a tube and use it simultaneously as a lumped component in the circuit and as a loop antenna not especially less efficient than those used externally to the transmitter. (See, for example, Communications Quarterly, Winter, 1994, pp. 7-8.)

+

Since every capacitor exhibits some inductance and every inductor exhibits some capacitance (again, controlled to a minimum for predictable circuit use), every lumped component is a sibling of a transmission line. Just ask VHF designers who use transmission line components instead of inductors.

+

What about the other end of the transmission line: the antenna? Are they transmission lines? According to a traditional analysis, still very useful for low and very low frequencies, we can visually and mathematically picture an antenna as a transmission line spread apart so that the wires are collinear (end to end) rather than parallel. See Figure 2 for a very simplified sketch of the antenna and one of its several types of fields. A lot of stuff happens if you do open up the transmission line in this way.

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First, the fields around the wires are no longer confined by equal but opposite adjacent fields. Second, the intensity of the field and its phase may be just far enough away so that they add to the total field intensity in some directions and subtract from it in others.

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In a transmission line, only enough power is consumed to overcome the losses of the wire system relative to establishing the fields of the standing wave. The remainder of the power supplied by the source is available at the other end of the line for the load. Of course, if we manage to unbalance the transmission line, it will act like an opened transmission line for that part of the voltage and current not in balance. In other words, it will act like an antenna.

+

The antenna is the transmission line's load in a transmitting situation because its fields are no longer confined. The current along the line yields fields that may spread without limit (with respect to the system). In short, the electrical energy is transformed into electro-magnetic radiation, and it must be resupplied from the source to maintain the ever-expanding fields.

+

If you are ready for a little surprise, the energy of an antenna does not in fact travel in the antenna wire or tubing. It travels along the field lines in Figure 2 outside the wire or tube. In addition, the energy in a transmission line exhibits the same property. We shall look deeper into this mystery in another installment.

+

On the receiving side, the antenna is always intercepting electro-magnetic fields, which set up currents in (or along) the antenna elements. The pattern of interception is the same as transmission, so that maximum current is generated from intercepted fields in the same direction as the maximum radiation of transmitted fields. The transmission line is in series with the currents, acting as the antenna's load and setting up equal but opposite polarity voltages and currents along its wires, voltages and currents that are amplified and processed by the receiver as radio frequency electrical energy..

+

Or, to put it another way, the opened transmission line converts currents to fields and fields to currents. Antennas have capacitance and inductance, just as do transmission lines. More nearly correctly, antennas have capacitive and inductive reactance, from which we can calculate equivalent capacitances and inductances. Antennas of certain lengths show no reactance (we call them resonant), while antennas of other lengths show either an inductive or capacitive reactance at the feedpoint. We can cancel out the reactance with a lumped component having an equal amount of the opposite type of reactance. What is handy is that we can do the canceling right at the antenna terminals or remotely with an antenna tuning unit (ATU). Yes, we shall look at how ATUs work in a future column.

+

So, what's your point? Any antenna theorist might well object to this account as too simplified (and hence distorting to some degree). In fact, for a more accurate account of how antennas fundamentally work, see Kenneth McCleish, W7TX, "Why an Antenna Radiates," QST, November, 1992, pp. 59-63. His account is traceable to Maxwell's Laws (whereas mine may be traceable only to Murphy's Laws).

+

Actually, there are several points. First, the account does capture an essential interrelationship at basic levels among every part of the communications system. Second, it is important to every operator with any technical inclination to develop an interest in and appreciation of how the seemingly separate elements of a communications system interrelate.

+

Third, learning about antennas and transmission lines requires exactly the same concepts we have to master to learn about circuits and components. We just use them in a different pattern of priority. For example, we match one circuit's output to another's input, and that is a matter of impedance matching and transformation--just like antenna work. We cancel out unwanted inductance with capacitance and vice versa both in circuits and in antennas. Understanding resistance, reactance, capacitance, and inductance will get you more than half way through both circuitry and antennas--and all the way through transmission lines.

+

Fourth, the account will help us talk some of the same language as we explore antennas. Part of the problem of reading magazines articles about great new antennas is that each author tends to use antenna and transmission line words a little differently. Understanding an author requires that we catch on to how he is using the words. This little introductory picture of how antennas, transmission lines, and circuits interrelate will help you catch on to how I use various antenna concepts. And that will help you understand the next few installments when we really get down to business.

+

Although I shall keep the math of these articles to a minimum, you should be willing to do some of it. Unless you just love hand calculation, I recommend that you get a copy of HAMCALC. This collection of ham calculation programs uses GW BASIC (supplied with the structured array) so that you can look at the equations behind the calculations just by listing any of the programs. And you can also run through a string of input values and get a feel for the pattern of the results. This will help build your intuitions about what is sensible and what is problematical about some antenna or feedline problem you are having. Any similar collection of calculation programs will do equally well, but I know of none that are both so comprehensive and so open to inspection.

+

Get a copy of the latest HAMCALC from George Murphy, VE3ERP, 77 McKenzie Street, Orillia, Ontaria, Canada L3V 6A6. Include a $5 donation, which George uses to pay for disks and postage from Canada and then donates the excess to the Canadian National Institute for the Blind to support its ham radio work.

+

Finally, to understand antennas and get a good feel for them, you have to change your way of looking at and thinking about them--unless you already think about them in something like the way we have started here. We shall not stick to the transmission line analogy for antennas, but we shall in every installment always think of antennas as integrated parts of our communications systems.
+

+
+ +
+

Updated 4-27-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Transmission Line


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+

ANTENNAS FROM THE GROUND UP

+
+
+

10. Up, Up, and Away
+ or Harmonic Operation of OCFs

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In our last episode, we looked at the operation of the off-center-fed dipole (OCF) and discovered no magic--only something like a þregularþ center-fed dipole. However, many of the claims made for the OCF have to do with the convenience or the power of using the antenna on its harmonics. To be thorough, we must look in a little more detail at this aspect of the OCF. Perhaps there is magic left in the antenna yet. +

To review, our OCF looks like this:

+
+ +
+

I am taking this long on the OCF for a couple of reasons. First, the antenna has been the subject of considerable speculation, not to mention overzealous claims. These have obscured or ignored many of the basic facts about OCF operation. Second, antenna modeling is growing more popular. For newcomers to this higly educational activity, there is a temptation to accept what the machine says without checking the basic adequacy of the model fed to the machine. Hence, some added notes about modeling the OCF might prove useful to new owners of NEC and MININEC.

+

How the Harmonic Stuff Got Started: When the OCF first appeared on the ham scene, vacuum tube output stages were in vogue. Initially, these stages used parallel-tuned high-impedance output circuits with tuned link coupling to transform the tube's 1200 to 3000 ohm impedance to something closer to feedline impedances. Later, PI networks came into popularity for their ability to permit bandswitching, but wide ranging adjustment of the circuit remained possible.

+

Either type of adjustable circuit would match the tube impedance to a wide range of output impedance requirements. A range of 20 to 200 ohms was not uncommon. Without an ATU, one might directly match lines presenting up to 4:1 SWR levels with good efficiency of power transfer. The OCF was popular as a directly matched antenna on its fundamental and most of its even harmonics.

+

Even before the advent of fixed tuned solid state output stages, manufacturers began removing the "load" control from the new SSB transceivers. Thus was born the 2:1 SWR limit of ham transmitter output stages. Suddenly, OCF users began to have troubles effecting a direct match from the feedline to the transmitter. Since the dang system put RF into the shack anyway, many simply chose other types of antennas. From the 1960s to the 1980s, the OCF went into decline. Then came some US and Canadian hams with new antenna kits and new claims for the antenna. These resulted largely from the ease of making matching transformers using the more readily available iron and ferrite cores. We thought we could hit that magic 300-ohm or equally magic 100-ohm point and match our way to a mutliband antenna.

+

Some purveyors of OCF kits said "Put them up at 35' in a field free and clear of ground clutter." When buyers complained that the antenna seemed not to work on one or another band, the sellers simply blamed the operator's site (and gave no refund). Some have suspected that other kit makers have intentionally or unwittingly used a fairly lossy matching device at the antenna-feedline junction to make a match on all advertised bands "at any cost."

+

So we have two questions to answer: a. What happens to the impedance of an OCF on the even harmonics? And b. Are the patterns on these harmonics as good as they are claimed to be? Once more, we shall use our friendly old center-fed half wavelength dipole as the standard of comparison.

+

Impedance: First, the resonant lengths of an OCF are not directly harmonically related. The following four tables show the resonant frequencies of the fundamental and even harmonics for a 7.15 MHz OCF at 70' and at 35' for fundamental impedances in the 100-ohm and the 300-ohm vicinities. Resonance is defined for this exercise as a feedpoint impedance with less than 1 ohm reactance. Dimensions are listed as minus and plus either side of the feedpoint.

+ 
1.  Length:  -10.4'/+57.35'
+Height: 70'    Material: #14 copper
+Frequency      Impedance
+ 7.15 MHz      302 ohms
+14.34 MHz      138 ohms
+28.77 MHz      130 ohms
+
+2.  Length:  -11.71'/+55.15'
+Height: 35'    Material: #14 copper
+Frequency      Impedance
+ 7.15 MHz      298 ohms
+14.56 MHz      117 ohms
+29.13 MHz      173 ohms
+
+3.  Length:  -20.21'/+47.15'
+Height: 70'    Material: #14 copper
+Frequency      Impedance
+ 7.15 MHz      102 ohms
+14.38 MHz      107 ohms
+29.0 MHz       312 ohms
+
+4.  Length:  -24.89'/+41.48'
+Height: 35'    Material: #14 copper
+Frequency      Impedance
+ 7.15 MHz        98 phms
+14.63 MHz      191 ohms
+29.37 MHz      115 ohms
+

The resonant frequencies of the harmonics of the fundamental frequency to which the antenna is originally cut depart more radically from true harmonics the closer the antenna is to the ground in terms of fractions of a wavelength. Note that since the model used in this exercise is for 40 meters, an 80-meter OCF at 35' and 70' would be only 1/8 and 1/4 of a wavelength in height, respectively.

+

At true harmonics within the ham bands, the feedpoint impedance of the antenna on 20 and 10 meters would contain a large reactive component. Although this situation is not significant for a system consisting of parallel feedline and an antenna tuning unit, it presents major problems for systems using a balun and coaxial cable. Transmission-line transformer baluns of the type designed and investigated by W2FMI require resistive loads.

+

The impedances at the feedpoint for ham bands which are not even harmonics of the antenna's fundamental frequency are not suited for balun operation. If the antenna is to be used on any of these amateur bands, parallel feedline and an ATU is a must.

+

Patterns: The azimuth patterns for a center-fed half wavelength dipole operated on harmonic frequencies are quite different from those of the harmonics of an OCF. Interestingly, with or without feedline radiation, the elevation angles of maximum radiation are the same for either antenna, making pattern comparison relatively uncomplicated. For comparison, here are the azimuth patterns for the center-fed antenna:

+

1. 7.15 MHz; elevation angle 27 degrees

+
+ +
+

This pattern is not significantly different from that of an OCF when the antenna element alone is presumed to radiate. The side rejection of is about 11 dB.

+

2. 14.15 MHz; elevation angle 14 degrees

+
+ +
+

The second harmonic of a center-fed half wavelength dipole yields a full wavelength antenna with a high feedpoint impedance, along with higher maximum gain in a narrower beamwidth.

+

3. 28.5 MHz; elevation angle 7 degrees

+
+ +
+

To get a feel for how the OCF differs in harmonic performance, let's look at azimuth patterns for the same frequencies and elevation angles for OCFs in which only the antenna element is presumed to radiate. These antennas are modeled for a 300-ohm feedpoint impedance.

+

1. 7.15 MHz; elevation angle 27 degrees

+
+ +
+

This pattern is indistinguishable from the pattern of the center-fed dipole shown above. Wherever patterns are identical, antenna performance will also be identical. Harmonic patterns, however, will differ considerably.

+

2. 14.15 MHz; elevation angle 14 degrees

+
+ +
+

This cloverleaf most resembles the 10-meter pattern of the center-fed dipole. The pattern may be more useful for general communications than the bi-directional pattern of the center-fed dipole, although the dipole pattern can reduce QRM from the sides more effectively.

+

3. 28.5 MHz; elevation angle 7 degrees

+
+ +
+

The 8-lobe pattern of the OCF operated on 10 meters is distinctly canted toward the longer end of the antenna. However, do not confuse the relatively high gain with that of a beam. Even a simple 2-element Yagi at a half wavelength height will have slightly more gain and at least 2 S- units of front-to-back ratio.

+

Claims have been made to the effect that allowing the feedline to radiate provides benefits in the signal pattern. To test this claim, let's look at azimuth patterns for 7.15 MHz, 14.15 MHz, and 28.5 MHz for an OCF at 70' height and designed for the 300-ohm feedpoint. The radiating feedline is presumed to be restricted to 10' by use of a line isolator or W2DU choke.

+

1. 7.15 MHz; elevation angle 27 degrees

+
+ +
+

2. 14.15 MHz; elevation angle 14 degrees

+
+ +
+

3. 28.5 MHz; elevation angle 7 degrees

+
+ +
+

In all cases, the antenna gain is down slightly. Only in 10-meter operation does the antenna show any marked effects from the vertical radiator, as four of its lobes disappear into one broad and modest lobe. For operational purposes, the likely effect of using the short section of feedline to supplement radiation from the antenna element is negligible.

+

To be fair, let's also look at the case of using 35' of the feedline as a supplemental radiator. Compare each of the azimuth patterns (all of which have the same elevation angle of maximum radiation as the preceding patterns on each band) with its corresponding patterns above.

+

1. 7.15 MHz; elevation angle 27 degrees

+
+ +
+

2. 14.15 MHz; elevation angle 14 degrees

+
+ +
+

3. 28.5 MHz; elevation angle 7 degrees

+
+ +
+

A comparison of the patterns using 10' of feedline radiator and 35' of feedline radiator demonstrates the variability of the effect of supplementing the antenna element's radiation. The 10-meter pattern has returned to its shape with no feedline radiation, while the 20-meter pattern shows more cant toward the long end of the antenna and the 40-meter pattern shows a measurable decrease in gain with only a slight widening of the pattern off the antenna element ends.

+

In the final analysis, it is doubtful that feedline radiation will either significantly help or significantly harm the performance of an OCF antenna. Feedline radiation will affect the presumed impedance of the antenna, making it less predictable. Consequently, the use of an ATU is always a wise procedure.

+

However, if one is going to use an ATU, then maximizing the use of parallel feedline is the surest way to reduce losses. As noted in the initial installment on this antenna, conversion to coaxial cable at the shack entrance may be necessary to prevent RF on equipment cases. This precaution is wise even at QRP, since RF in the shack is lost to propagation.

+

We have one more question to ask: how does the OCF perform as an "all-band" antenna? But we shall save that question for next time.
+

+
+ +
+

Updated 1-25-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Off Center Fed Dipole


+ + diff --git a/content/gup/gup11-1.gif b/content/gup/gup11-1.gif new file mode 100644 index 0000000..c86b182 Binary files /dev/null and b/content/gup/gup11-1.gif differ diff --git a/content/gup/gup11-10.gif b/content/gup/gup11-10.gif new file mode 100644 index 0000000..5a2f6c5 Binary files /dev/null and b/content/gup/gup11-10.gif differ diff --git a/content/gup/gup11-11.gif b/content/gup/gup11-11.gif new file mode 100644 index 0000000..766bd7d Binary files /dev/null and b/content/gup/gup11-11.gif differ diff --git a/content/gup/gup11-12.gif b/content/gup/gup11-12.gif new file mode 100644 index 0000000..68ddbb6 Binary files /dev/null and b/content/gup/gup11-12.gif differ diff --git a/content/gup/gup11-13.gif b/content/gup/gup11-13.gif new file mode 100644 index 0000000..dc60359 Binary files /dev/null and b/content/gup/gup11-13.gif differ diff --git a/content/gup/gup11-14.gif b/content/gup/gup11-14.gif new file mode 100644 index 0000000..c33fc28 Binary files /dev/null and b/content/gup/gup11-14.gif differ diff --git a/content/gup/gup11-15.gif b/content/gup/gup11-15.gif new file mode 100644 index 0000000..c61fb0f Binary files /dev/null and b/content/gup/gup11-15.gif differ diff --git a/content/gup/gup11-16.gif b/content/gup/gup11-16.gif new file mode 100644 index 0000000..0252e35 Binary files /dev/null and b/content/gup/gup11-16.gif differ diff --git a/content/gup/gup11-17.gif b/content/gup/gup11-17.gif new file mode 100644 index 0000000..2531ba0 Binary files /dev/null and b/content/gup/gup11-17.gif differ diff --git a/content/gup/gup11-2.gif b/content/gup/gup11-2.gif new file mode 100644 index 0000000..5a415f8 Binary files /dev/null and b/content/gup/gup11-2.gif differ diff --git a/content/gup/gup11-3.gif b/content/gup/gup11-3.gif new file mode 100644 index 0000000..0735aca Binary files /dev/null and b/content/gup/gup11-3.gif differ diff --git a/content/gup/gup11-4.gif b/content/gup/gup11-4.gif new file mode 100644 index 0000000..f391e3e Binary files /dev/null and b/content/gup/gup11-4.gif differ diff --git a/content/gup/gup11-5.gif b/content/gup/gup11-5.gif new file mode 100644 index 0000000..1cdf097 Binary files /dev/null and b/content/gup/gup11-5.gif differ diff --git a/content/gup/gup11-6.gif b/content/gup/gup11-6.gif new file mode 100644 index 0000000..ac9b0c1 Binary files /dev/null and b/content/gup/gup11-6.gif differ diff --git a/content/gup/gup11-7.gif b/content/gup/gup11-7.gif new file mode 100644 index 0000000..17b11ee Binary files /dev/null and b/content/gup/gup11-7.gif differ diff --git a/content/gup/gup11-8.gif b/content/gup/gup11-8.gif new file mode 100644 index 0000000..0391657 Binary files /dev/null and b/content/gup/gup11-8.gif differ diff --git a/content/gup/gup11-9.gif b/content/gup/gup11-9.gif new file mode 100644 index 0000000..a7d88e3 Binary files /dev/null and b/content/gup/gup11-9.gif differ diff --git a/content/gup/gup11.html b/content/gup/gup11.html new file mode 100644 index 0000000..1f00171 --- /dev/null +++ b/content/gup/gup11.html @@ -0,0 +1,135 @@ + + + + + + A 135' Off-Center-Fed Multi-Band Dipole Data Compendium + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

11. Unbalanced But Sane
+ or a 135' Off-Center-Fed Multi-Band Dipole Data Compendium

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The fundamental concepts and realities of Off-Center-fed (OCF) wire antennas developed in terms of 40-meter models apply to any other fundamental band with adjustments of height in terms of fractions of a wavelength. However, several folks have asked for more specifics for an 80-meter-based OCF in order to have reasonable expectations of performance. +
+ +
+

For an 80-meter fundamental OCF , L will equal about 135' if the antenna is resonant. If the antenna is fed with parallel transmission line to an ATU, the exact length is not critical. However, for the sample patterns, it has been made resonant.

+

We shall sample an 80-meter OCF at 35' height, a typical amateur installation. The frequency of basic resonance is 3.5 MHz to ensure that harmonics fall within the amateur bands. However, pattern samples will cover all 8 amateur bands between 80 and 10 meters.

+

We shall also sample two points of antenna element-to-feeder junction: the 100-ohm and the 300-ohm points. The antenna dimensions for these two antennas are as follows:

+
    +
  • +

    100-ohm Connection: L = 135.25' D1 = 34.7' D2 = 100.55'

    +
    • +
  • +

    300-ohm connection: L = 135.67' D1 = 18.2' D2 = 117.47'

    +
    • +
+

Interestingly, this same antenna raised to a height of 70' shows the following resonant characteristics:

+
    +
  • +

    100-ohm Connection: L = 135.7' D1 = 50.5' D2 = 85.2'

    +
    • +
  • +

    300-ohm Connection: L = 136.55' D1 = 24.1' D2 = 112.45'

    +
    • +
+

35' and 70' are 1/8 and 1/4 wavelength heights, respectively, a region where we can expect large changes of antenna characteristics with small changes in height. The patterns and numbers associated with the antennas should thus be used with due caution. They are indicators, not absolutes.

+

For each pattern, a feedpoint impedance figure, Zi, is given. Zi is the impedance assuming that the radiation is confined to the antenna element. Since this assumption will be violated in most installations using parallel feedline directly connected to the antenna, the impedance figures are best treated as indicators of moderate or high impedances, not as numbers to be expected in reality. The actual impedance presented to the ATU will be a complex combination of the degree to which the feedline contributes to radiation and the transformation of the antenna impedance along the line.

+

80 Meters: 3.6 MHz

100-ohm Connection: Zi = 120 + j100 ohms -- Elevation angle = 45 degrees +
+ +
+

Note: Since the actual elevation angle of maximum radiation is greater than 45 degrees for 80 and 40 meters, the azimuth patterns are taken at an elevation angle of 45 degrees.

+

300-ohm Connection: Zi = 455 + j310 ohms -- Elevation angle = 45 degrees

+
+ +
+

40 Meters: 7.15 MHz

100-ohm Connection: Zi = 105 + j15 ohms -- Elevation angle = 45 degrees +
+ +
+

Note: For a different slant on OCF antennas, see Chapter 3 of Bill Orr, W6SAI, HF Antenna Handbook. He presents some interesting variations on the versions studied here.

+

300-ohm Connection: Zi = 185 + j20 ohms -- Elevation angle = 45 degrees

+
+ +
+

30 Meters: 10.1 MHz

100-ohm Connection: Zi = 690 - j890 ohms -- Elevation angle = 37 degrees +
+ +
+

Note that differences between the 100-ohm and the 300-ohm patterns are beginnig to appear with respect to both azimuth and elevation.

+

300-ohm Connection: Zi = 90 - j295 ohms -- Elevation angle = 36 degrees

+
+ +
+

20 Meters: 14.15 MHz

100-ohm Connection: Zi = 3145 - j1355 ohms -- Elevation angle = 28 degrees +
+ +
+

At 20 meters, there is a wide divergence between 100-ohm and 300-ohm patterns, with the 100-ohm pattern more closely resembling the pattern of a center-fed antenna.

+

300-ohm Connection: Zi = 120 - j105 ohms -- Elevation angle = 25 degrees

+
+ +
+

17 Meters: 18.1 MHz

100-ohm Connection: Zi = 205 + j15 ohms -- Elevation angle = 20 degrees +
+ +
+

Note that the 100-ohm and 300-ohm patterns are again similar, with difference confined to the minor lobes.

+

300-ohm Connection: Zi = 170 + j65 ohms -- Elevation angle = 19 degrees

+
+ +
+

15 Meters: 21.15 MHz

100-ohm Connection: Zi = 135 + j240 ohms -- Elevation angle = 17 degrees +
+ +
+

On 15 meters, the 300-ohm version of the antenna shows considerably less gain to the short side of the antenna element.

+

300-ohm Connection: Zi = 920 - j600 ohms -- Elevation angle = 17 degrees

+
+ +
+

12 Meters: 24.95 MHz

100-ohm Connection: Zi = 545 - j420 ohms -- Elevation angle = 15 degrees +
+ +
+

Note that, although the number of lobes are the same, the 300-ohm version puts more energy into high lobes and less into lobes off the ends of the antenna.

+

300-ohm Connection: Zi = 2930 + j350 ohms -- Elevation angle = 15 degrees

+
+ +
+

10 Meters: 28.5 MHz

100-ohm Connection: Zi = 1755 - j905 ohms -- Elevation angle = 14 degrees +
+ +
+

Note the deep nulls broadside to the 100-ohm version of the antenna, compared to the smoother lobe structure of the 300-ohm version.

+

300-ohm Connection: Zi = 875 - j925 ohms -- Elevation angle = 15 degrees

+
+ +

+
+
+ +
+

Updated 1-20-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Off Center Fed Dipole


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+

ANTENNAS FROM THE GROUND UP

+
+
+

12. A Tiger by the Tail
+ or a 135' End-Fed Multi-band Dipole Data Compendium

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ A 1/2 wavelength wire antenna, fed at one end with parallel transmission line is also known as the end-fed Zepp. Figure 1 shows the general outlines of a Zepp cut for the 80-meter band. +
+ +
+

The Zepp can be cut for other bands, but a 135' length of #14 wire at a height of about 35' is one of the most common ham installations. 35' is only about 1/8 wavelength at 80 meters and about 1 wavelength at 10 meters. Therefore, the Zepp will exhibit all the variability and sensitivity to terrain of any low horizontal antenna.

+

The distinguishing feature of the Zepp is that it is fed at a high-voltage low-current point. Hence, its impedance is very high. More significantly, the impedance will usually have a large reactive component: capacitive if a tad longer than a multiple of a half wavelength, inductive if a tad short of a half wavelength. At the center point of an odd multiple of a half wavelength, the impedance of an antenna will be low with slow changes in reactance. At even multiples of a half wavelength, the impedance will be high. The reactance climbs to a very high value of inductive reactance and with only a tiny lengthening of the antenna (or increase in frequency) swings suddenly to a very high value of capacitive reactance that will gradually drop as the antenna is further lengthened (or the frequency climbs higher). 135' will prove a smidgeon long at all test frequencies.

+

Because the antenna is fed at a high-voltage point, the current along the feedline is not nearly so unbalanced as some have believed, especially on the fundamental frequency. End-fed Zepps rarely create problems of RF in the shack. One side of the line goes to the very high antenna impedance, the other side to the almost indefinitely large impedance of the missing antenna connection. Hence, the lines are fairly well in balance. However, balance is not perfect, especially as the frequency is increased. If balance were perfect, the line would show very low values of impedance for most of each half wavelength, making a match to the ATU very difficult.

+

Imbalance between the wires of the feedline does create some radiation from the feedlines. However, its consequences on the overall radiation pattern depend on the length of the feeder, the frequency of operation, and the angle at which the feeder leaves the antenna. We shall show patterns for the Zepp assuming a. that all radiation is in the antenna and b. also with a 34' 410-ohm feeder. The pattern you achieve with your Zepp will depend on your layout.

+

80 Meters: 3.6 MHz

Without feedline: Z = 3000 - j60000 ohms -- Elevation angle = 45 degrees +
+ +
+

Note: Since the actual elevation angle of maximum radiation is greater than 45 degrees, the azimuth patterns are taken at an elevation angle of 45 degrees.

+

With feedline: Z = 15 - j420 ohms -- Elevation angle = 45 degrees

+
+ +
+

40 Meters: 7.15 MHz

Without feedline: Z = 2700 - j30000 ohms -- Elevation angle = 45 degrees +
+ +
+

All impedance figures are very rough approximations to indicate the range of values. They are in no case the actual figures individual layouts will achieve.

+

With feedline: Z = 17 + j5 ohms -- Elevation angle = 45 degrees

+
+ +
+

30 Meters: 10.125 MHz

Without feedline: Z = 300 - j21000 ohms -- Elevation angle = 36 degrees +
+ +
+

Note that at this frequency, the feedline radiation actually lowers the elevation angle of maximum radiation, a fairly rare occurrence with shorter lengths of feedline.

+

With feedline: Z = 30 + j280 ohms -- Elevation angle = 32 degrees

+
+ +
+

20 Meters: 14.15 MHz

Without feedline: Z = 920 - j14000 ohms -- Elevation angle = 25 degrees +
+ +
+

The feedline radiation below significantly rounds all the lobes of the azimuth pattern and reduces maximum gain while increasing overall broadside radiation.

+

With feedline: Z = 7500 + j2000 ohms -- Elevation angle = 26 degrees

+
+ +
+

17 Meters: 18.1 MHz

Without feedline: Z = 2200 - j12000 ohms -- Elevation angle = 19 degrees +
+ +
+

On 17, the two patterns return to close coincidence. Whether patterns are similar or different will vary with feedline length and dress, as well as frequency.

+

With feedline: Z = 55 - j400 ohms -- Elevation angle = 20 degrees

+
+ +
+

15 Meters: 21.15 MHz

Without feedline: Z = 410 - j10000 -- Elevation angle = 17 degrees +
+ +
+

Note that even though the pattern differences appear very minor, they are enough to reduce maximum gain below by a full dB.

+

With feedline: Z = 50 - j90 ohms -- Elevation angle = 17 degrees

+
+ +
+

12 Meters: 24.95 MHz

Without feedline: Z = 620 - j8000 ohms -- Elevation angle = 14 degrees +
+ +
+

Note how slight thickening of the elevation lobes produces a significant decrease in the maximum gain of the main lobes of the pattern.

+

With feedline: Z = 45 + j370 ohms -- Elevation angle = 14 degrees

+
+ +
+

10 Meters: 28.5 MHz

Without feedline: Z = 470 - j7000 ohms -- Elevation angle = 13 degrees +
+ +
+

Although your situation is unlikely to copy this one, studying the upper and lower patterns for each band may give you a better idea of how to compare the details of antenna patterns.

+

With feedline: Z = 4750 + j720 ohms -- Elevation angle = 13 degrees

+
+ +

+
+
+ +
+

Updated 1-21-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: EDZ / Zepp, HF Multi Band


+ + diff --git a/content/gup/gup13-1.gif b/content/gup/gup13-1.gif new file mode 100644 index 0000000..ddca498 Binary files /dev/null and b/content/gup/gup13-1.gif differ diff --git a/content/gup/gup13.html b/content/gup/gup13.html new file mode 100644 index 0000000..7c3ce16 --- /dev/null +++ b/content/gup/gup13.html @@ -0,0 +1,237 @@ + + + + + + What Happens Along a Length of Feedline + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

13. Great Expectations
+ or What Happens Along a Length of Feedline

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

We have looked (and will continue to look) at antennas that present complex feedpoint impedances, that is, impedances composed of both resistive and reactive components. In the shorthand that we use for calculations, Z = R ± jX.

+

We have previously noted that a transmission line is (among other things) an impedance transformer. An impedance presented to the line as a load will appear as a different impedance at every point along the line. We can calculate precisely the value of impedance for any point along the line, as illustrated in Figure 1.

+
+ +
+

Knowing the values of impedance along a transmission is very handy. For a monoband antenna, we can select the point along a line where R is 50 Ohms and insert a compensating reactance so that we can then run coax the rest of the way to the shack. For multiband antennas fed with parallel line, we can estimate how much line to add or subtract in order to let the values fall within the range of adjustment of our ATU.

+

To calculate the value of impedance anywhere along a transmission line, we need only know the following: the load impedance, the characteristic impedance and velocity factor of our feedline, the line length in any units, and the frequency of operation. For ultraprecision, we can improve the result by knowing the line loss figures for the feedline type and the frequency of operation. However, for many purposes, assuming lossless lines will provide all the accuracy needed.

+

Now some good news and some bad news. The bad news is that, even though the necessary equation looks straightforward, the use of complex numbers (a ± jb) results in a tedious job for hand calculation. However, we have good news: we can resort either to Smith charts or to computer programs to do the heavy work for us. HAMCALC has a program called "Transmission Line Performance" that will calculate both single values and tables of values of voltage, current, and impedance (and their phases), as well as resistance and reactance along a lossless transmission line.

+

Actually, for impedance, we only need to look at ½ wavelength of line, since in lossless lines, the values repeat themselves at that interval. In real lines with some loss, the values will change slightly as the line length is increased in multiples of ½ wl.

+

Note, however, that values of voltage and current only change once per full wavelength. Although this fact will not affect the work we shall do in this installment, failure to appreciate it has led to some interesting errors in analyzing antennas. For example, most accounts of the ZL Special, a phased 2- element array, have viewed it as a 135° phased impedance antenna. However, antenna phasing is a product of antenna currents, not impedance. When this fact is appreciated, the antenna is more properly analyzed as a -45° phased current array.

+

For most low-HF wire antenna matching problems, we can focus on the impedance. The question that faces users of multiband antennas is whether the length of line in use will present to the ATU a set of values for resistance and reactance that fall within the tuning range of the ATU. The actual range of permissible values varies with the ATU network type and components. But let's arbitrarily adopt these limits: R should range from about 20-25 Ohms to several hundred Ohms while jX should run no higher than ± a few hundred Ohms. These limits would place almost all the common ATU types within their high-efficiency matching zones.

+

Line Length and Degrees: The first step in analyzing our situation is finding the line length we have. Actually, we need only know where along the last ½ wl the line ends. We can calculate this length by plugging the following equations into a hand calculator:

+

1. Divide the total length of line by the length of ½ wl of line, adjusted for the velocity factor (VF) of the line in use. Common 450-Ohm line has a VF of 0.95, while common 300-Ohm line has a VF of 0.80. The tables below list line lengths for various increments and frequencies. Use the figure for 180° for the nearest frequency to the one in which you are interested.

+

2. Throw away the integer (the part left of the decimal, if any) and save the decimal part. Multiply this number times 180 to get the number of degrees along a half wavelength of transmission line that represents the termination point of your line.

+

Virtually all transmission line work is done in degrees relative to a full 360° circle. 180° represents the half-circle in which we are interested. The tables below list the lengths of transmission line for various degrees along the line for selected HF frequencies that are useful for estimating your line length. Line lengths are in feet for 450-Ohm and for 300-Ohm lines.

+ 
+    80-meters  3.6 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        21.63     18.21
+ 60        43.26     36.43
+ 90        64.89     57.68
+120        86.52     72.86
+150       108.15     85.00
+180       129.78    109.29
+
+    40-meters  7.15 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        10.89     9.17
+ 60        21.78     18.34
+ 90        32.67     27.51
+120        43.56     36.68
+150        56.27     45.85
+180        65.34     55.02
+
+    30-meters  10.125 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        7.69      6.48
+ 60        5.38     12.95
+ 90       20.51     19.43
+120       30.76     25.90
+150       38.45     32.38
+180       46.14     38.86
+
+    20-meters  14.15 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30         5.50     4.63
+ 60       11.01      9.27
+ 90       16.51     13.90
+120       22.01     18.54
+150       27.51     23.17
+180       33.02     27.80
+
+    17-meters  18.1 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        4.30      3.62
+ 60        8.60      7.25
+ 90       12.91     10.87
+120       17.21     14.49
+150       21.51     18.11
+180       25.81     21.74
+
+    15-meters  21.15 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        3.68      3.10
+ 60        7.36      6.20
+ 90       11.04      9.30
+120       14.73     12.40
+150       18.41     15.50
+180       22.09     18.60
+
+    12-meters  24.95 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        3.12      2.63
+ 60        6.24      5.26
+ 90        9.36      7.88
+120       12.48     10.51
+150       15.60     13.14
+180       18.73     15.77
+
+    10-meters  28.5 MHz
+L(°) L(ft): 450-Ohm 300-Ohm
+ 30        2.73      2.30
+ 60        5.46      4.60
+ 90        8.20      6.90
+120       10.93      9.20
+150       13.66     11.50
+180       16.39     13.80
+

Sample Cases: Since impedance transformations are a function of the number of degrees along a line we take a reading, regardless of frequency, we can look at some transformations that are interesting and list them in terms of degrees. You can then translate them into actual line lengths for your situation, depending on the line you are using and the frequency at which you encounter something similar to the example.

+

1. Mismatch with no load reactance:

+ 
Load Z = 150 ± j0 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       193 + j223     185 + j120
+ 60       450 + j520     343 + j223
+ 90       1350 + j0      600 + j0
+120       450 - j520     343 - j223
+150       193 - j223     185 - j120
+180       150 + j0       150 + j0
+

Note the symmetry of the variations of values for this line with no reactance. Still, none of the values seems to exceed what a good ATU might handle. Line length is thus not at all critical.

+

2. Mismatch with small inductive reactance.

+ 
Load Z = 150 + j30 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       208 + j260     206 + j153
+ 60       538 + j564     419 + j226
+ 90       1298 - j259    577 - j115
+120       380 - j475     282 - j209
+150       179 - j188     166 - j90
+180       150 + j30      150 + j30
+

Note the disruption to the symmetry due to the presence of reactance. Although the values appear reasonable, I would avoid a 90° length, if possible.

+

3. Mismatch with small capacitive reactance.

+ 
Load Z = 150 - j30 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       179 + j188     166 + j90
+ 60       380 + j475     282 + j209
+ 90       1298 + j259    577 + j115
+120       538 - j564     419 - j226
+150       208 - j260     206 - j153
+180       150 - j30      150 - j30
+

Notice the pattern of values and signs in the comparison of this case and the preceding one, where the only change is the type of reactance in the load.

+

4. Mismatch with larger inductive reactance.

+ 
Load Z = 150 + j150 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       290 + j438     339 + j316
+ 60       1172 + j598    781 - j52
+ 90       675 - j675     300 - j300
+120       213 - j321     142 - j132
+150       137 - j69      115 - j8
+180       150 + j150     150 + j150
+

This plot reveals that as the reactance goes up, part of the curve of values along the line grows quite steep. In this case, it is the first 90° of each half wavelength. The second 90° provides the best region for connection to an ATU.

+

5. Mismatch with larger resistance and inductive reactance.

+ 
Load Z = 600 + j150 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       643 - j105     435 - j252
+ 60       435 -j180      200 - j165
+ 90       318 - j79      141 - j35
+120       307 + j50      155 + j90
+150       397 + j164     267 + j221
+180       600 + j150     600 + j150
+

As the resistive component of the antenna feedpoint impedance goes considerably higher than the characteristic impedance of the feedline, (also making the ratio of resistance to reactance greater), the best matching region becomes the mid-region of the half wavelength line section, where the rate of change of resistance and reactance values is also the lowest. However, none of the values shown should present most ATUs with any problems.

+

6. Mismatch with the larger resistance and a high capacitive reactance.

+ 
Load Z = 600 - j1000 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       138 - j371     81 - j314
+ 60       83 -j85        41 - j92
+ 90       89 + j149      40 + j66
+120       89 + j149      69 + j268
+150       1189 +j1216    365 + j812
+180       600 - j1000    600 - j1000
+

As the reactance grows larger than a resistance which is already larger than the characteristic impedance of the line, the region of easiest match to an ATU shifts. For this capacitive reactance, 30° to 120° becomes the best region; for an equivalent inductive reactance, 60° to 150° would be the best region.

+

7. Mismatch with very large resistance and inductive reactance.

+ 
Load Z = 2000 + j2000 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       295 - j960     116 - j606
+ 60       77 - j327       33 - j203
+ 90       51 - j51       23 - j23
+120       59 + j192      28 + j143
+150       138 + j587     70 + j432
+180       2000 +j2000    2000 + j2000
+

As the resistance and inductive reactance reach the 2K level, as is common when 80-meter and 40-meter antennas are used on WARC bands, line lengths near 90° become more favorable for easy matches. Note that 300-Ohm line becomes less favorable for use, since at 90° it present a very low impedance to the ATU.

+

8. Mismatch with very large resistance and capacitive reactance.

+ 
Load Z = 2000 - j2000 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       138 - j587     70 - j432
+ 60       59 - j193      28 - j143
+ 90       51 + j51       23 + j23
+120       77 + j327      33 + j203
+150       295 + j960     116 + j606
+180       2000 - 2000    2000 - j2000
+

Notice the reversal of the progression of values, but not signs attached to the reactance, compared to the previous case. Also compare cases 7. and 8. to cases 2. and 3.

+

Cases 7. and 8. also show why the use of the 4:1 balun built into many ATUs should be avoided. With higher feedpoint impedances, the region of best match along the line encounters low impedance values. Assuming a perfect 4:1 ratio and no loss (actually, a rather poor assumption when there is significant reactance), the values seen by the ATU would be very low, either beyond the range of the ATU or subject to further losses in the network.

+

9. Mismatch with very large resistance and extremely large inductive reactance.

+ 
Load Z = 2000 + j10000 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       18 - j863      8 - j556
+ 60       5 - j286       2 - j185
+ 90       4 - j19        2 - j8
+120       5 + j234       2 + j162
+150       13 + j707      6 + j487
+180       2000 +j 10K    2000 + j10K
+

Note that the transformer effect of the feedlines, as their characteristic impedances become very small compared to the magnitude of the feedpoint impedance (especially the reactance), confines the high impedance values to a small region near 0 and 180°. The remainder of the line section shows very low values of resistance.

+

10. Mismatch with very large resistance and extremely large capacitive reactance.

+ 
Load Z = 2000 - j10000 Ohms
+Line Length        R ± jX
+(degrees)  450-Ohms       300-Ohms
+ 30       13 - j707      6 - j486
+ 60       5 - j234       2 - j162
+ 90       4 + j19        2 + j9
+120       5 + j286       2 + j185
+150       18 + j863      8 + j556
+180       2000 - 10K     2000 - j10K
+

These final two cases demonstrate why half wavelength loops and similar antennas are unusable with standard lines and ATUs. Indeed, with the end- fed Zepp, if the feedlines were not at least slightly out of balance, effecting a match with common forms of ATUs would not be possible, since the impedances presented to the feedline would be even higher.

+

Exploring the behavior of impedances along a feedline can be very instructive in estimating the most favorable line lengths for presenting the ATU with not only a load it can match, but one which it can match efficiently. The samples presented here only scratch the surface of the subject. However, they do show some of the emergent patterns of how the values change with different ranges of antenna feedpoint impedances. I heartily recommend that you get a copy of HAMCALC and run the values presented with some of the antennas we have already explored and will yet explore in future episodes. What you learn just might increase your antenna system efficiency a notch or two.
+

+
+ +
+

Updated 11-11-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Transmission Line


+ + diff --git a/content/gup/gup14-1.gif b/content/gup/gup14-1.gif new file mode 100644 index 0000000..d7d5cbd Binary files /dev/null and b/content/gup/gup14-1.gif differ diff --git a/content/gup/gup14-2.gif b/content/gup/gup14-2.gif new file mode 100644 index 0000000..e815a69 Binary files /dev/null and b/content/gup/gup14-2.gif differ diff --git a/content/gup/gup14-3.gif b/content/gup/gup14-3.gif new file mode 100644 index 0000000..fcfa320 Binary files /dev/null and b/content/gup/gup14-3.gif differ diff --git a/content/gup/gup14.html b/content/gup/gup14.html new file mode 100644 index 0000000..ce4c1e6 --- /dev/null +++ b/content/gup/gup14.html @@ -0,0 +1,142 @@ + + + + + + ATUs, Delta, and Tuner Losses + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

14. A Good Match
+ or ATUs, Delta, and Tuner Losses

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Losses from the insertion of antenna tuning units or transmatches between transmitters and transmission lines have bothered numerous folks for some time. There are two questions: how much loss can I expect? and how do I minimize the loss? Both are good questions with good answers. Unfortunately, they are not super simple answers. But some old material combined with some new material can make the answers easier to come by. Those who like the math involved can focus on the equations, while those interested in operational matters can concentrate on the tables and the resulting rules of thumb to minimize losses.

+

Most of this installment and the next appeared originally in QRP Quarterly for January, 1996. I have added some material, especially about 2-element L-C ATUs, and rearranged some of the ideas. This review of the estimate of losses in ATUs is also a good review of the most common types of network ATUs in use in amateur circles these days.

+

Most ATUs used today are L-C networks. The most common configuration is the C-L-C Tee network. However, L-C-L Tees and C-L-C PIs are in use, as are SPC and Ultimate Transmatch designs. Loss figures can be calculated for all such networks.

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The old material that contributes to determining ATU losses appears in Terman's Radio Engineers' Handbook (McGraw-Hill, 1943), pages 210-215. Based predominantly on work done in the 1930s by W.I. Everitt, Terman's analysis of classic impedance-matching networks is still referenced by current handbooks. The relevant part for considering ATU losses is the term, delta, which is a justifiably simplified measure of power dissipation in networks. For any impedance matching network, the primary power dissipation culprit is the inductance, and inductor losses can be calculated.

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The efficiency of L-C networks is dependent upon the impedance transformation ratio and the phase shift. PI networks and L-C-L Tees generally exhibit a large angle of phase retardation, while the C-L-C Tee circuit shows a large angle of phase advance. In contrast, simple L-networks show small angles of phase advance or retardation. Losses increase with increasing transformation ratios and tend to be larger when the phase shift is either very large or very small. The delta figure takes both into account. (Note, in some explanations of networks, but not in all, Terman's delta goes under the name of "working Q," "circuit Q," or "network Q.")

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The concept of delta has certain limitations. First, it ignores capacitor losses. This is justified for well- designed capacitors at HF and below, but capacitor losses may become significant at the boundary between HF and VHF (about 30 MHz). Second, the loss figure ignores the effects of strays, both capacitive and inductive, within a real ATU, especially one cramped inside a metal case. At 10 meters, the principal L and C in a matching circuit may be composed more of strays than of component values. Third, the technique will assume we know the coil Q in figuring ultimate efficiency and losses. On this score, we mostly guess, but a figure of 100 for good air wound coils is a conservative guess. Good powdered iron core toroids may yield more. Of course, the "suck out" effect of shorted coil turns is also ignored. Moreover, only networks, and not inductively coupled ATUs, are covered.

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The developer of the mathematical analysis used here, ZL1LE, recently ran a comparison between delta calculations and a more complex analysis published in QEX. The results showed an exceptionally high degree of correlation above load impedances in the 20-25 Ohms range, with the delta calculations being the more pessimistic below that level.

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Within these limits, the Terman-Everitt delta yields a fair estimate of loss and efficiency. As Terman notes,

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In other, equally approximate terms, network efficiency = 1 - delta/Q. (Multiply this figure times 100 for a percentage value of efficiency).

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Now if we only knew how to calculate delta, the rest would be simple. Terman provides graphs for estimating delta. Each type of network requires its own calculation, and it can be a bit tedious to calculate delta for several combinations of component settings. However, Brian Egan, ZL1LE, has derived equations for delta-calculations and added them to his program TUNER.BAS. This versatile program is now included in the collection of programs called HAMCALC, made available by George Murphy.

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Among the networks for which ZL1LE includes calculations are PIs, C-L-C Tees, SPCs, Ultimates, and L-C-L Tees. By running the program through a selection of values, one can learn the trends of tuning that will minimize losses. Operationally, that is the best we can hope for with a fixed set of impedance conditions presented by the transmission line from the antenna. From the general relationship of power lost to power delivered, it is clear that we always want to tune for minimum delta.

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For almost any loed presented to the tuner, there is usually more than one set of values for the ATU components that will effect a match so that the SWR meter shows a 1:1 SWR ratio. Not every combination is of equal quality in terms of losses within the ATU. Any limitations we encounter on the range of component variability-- such as switched coil taps or switched fixed capacitors--can also limit our ability to achieve the lowest possible loss setting.

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I ran TUNER.BAS through a number of exercises, and here are some results for some configurations. I chose 10.1 MHz, because I was working on a network problem for that band. To standardize the tests, I chose the following load conditions for each network: 150 +/- j0 Ohms, 150 + 100 Ohms, and 150 - j100 Ohms. Looking at a straight 3:1 SWR purely resistive load is a good beginning point, while exploring the network with both capacitive and inductive reactances indicates limitations of the network with certain types of loads. This test is limited, since a higher delta at a 3:1 impedance transformation ratio is not indicative of the network's overall capability. Some networks are more efficient with lower transformation ratios, while others grow more efficient as the transformation ratio increases.

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PIs: This familiar low-pass network configuration appears in Figure 1.

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For those interested, the Egan equation for delta for a PI network (where omega = 2piF wherever it occurs) is the following:

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Here is a small table of results for 10.1 MHz:

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Input = 50 Ohms; Output = 150 =/- j0 Ohms;
+                           Maximum permitted L = 1.365 µH
+L   1.364       C1  172         C2    179       delta   2.2
+or  1.364           192               185               2.5
+L   1.2         C1   36         C2    150       delta   1.5
+L   1.15        C1   15         C2    149       delta   1.5
+
+Input = 50 Ohms; Output = 150 + j100 Ohms
+                           Maximum permitted L = 1.640 µH
+L   1.639       C1  140         C2    197       delta   2.5
+L   1.6         C1   84         C2    187       delta   2.2
+L   1.5         C1   26         C2    182       delta   1.9
+
+Input = 50 Ohms; Output = 150 - j100 Ohms
+                           Maximum permitted L = 1.640 µH
+L   1.639       C1  140         C2    100       delta   2.5
+L   1.6         C1   84         C2     90       delta   2.2
+L   1.5         C1   26         C2     85       delta   1.9
+

In all three cases, the lists stop where one of the values approaches the minimum usually obtainable with ordinary components. In this case, a value for C1 lower than about 20 pF is not normal for most ATUs. In many instances, as illustrated by the very first entry, two solutions to the matching problem are possible. After the first entry, only the more promising set of values is shown. PI networks are, within limits, equally capable of handling capacitive and inductive reactances in the load, with the limits of both being related to the range of C2. Notice that efficiencies of 98% are possible within the limits of the method. As Terman notes, increasing the ratio of the impedances to be matched increases the value of delta and decreases efficiency. For example, when the resistive component of the output impedance is 300 Ohms, with or without a reactive load, the lowest value of delta is about 2.3. To achieve the highest efficiency possible for any given matching situation, we must use the following rule of thumb:

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PI networks: Use the lowest value of L that still permits C1 to be effective.

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C-L-C Tees: This most common ATU network configuration appears in Figure 2.

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Whereas the PI network is a natural low-pass filter, the C-L-C network is a natural high-pass filter. However, this fact does not hamper its ability to match a wide range of complex load impedances.

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To determine delta, use the Egan equation

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+ +
+ 
Input = 50 Ohms; Output = 150 +/- j0 Ohms
+                          Maximum permitted C1 = 222.9 pF
+C1  222.8       C2 6027         L    1.65       delta   1.4
+C1  222         C2 1468         L    1.59       delta   1.5
+C1  220         C2  992         L    1.56       delta   1.5
+C1  210         C2  362         L    1.43       delta   1.8
+C1  200         C2  262         L    1.39       delta   2.0
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Although a very low value of delta is theoretically possible, a realistic value of 2.0 or higher is to be expected with common components used in ATUs. As with a PI network, the C-L-C Tee yields higher values of delta as the output impedance is increased. At 6:1 ratio of output-to-input impedance, delta does not go below 2.1 with normal ATU components.

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Input = 50 Ohms;  Output = 150 + j100 Ohms
+                          Maximum permitted C1 = 222.9 pF
+C1  222.8       C2  154         L    1.65       delta   1.4
+C1  220         C2  132         L    1.54       delta   1.6
+or  220             196              1.85               1.3
+C1  210         C2  110         L    1.43       delta   1.8
+or  210             279              2.12               1.2
+C1  200         C2   98         L    1.39       delta   2.0
+or  200             396              2.34               1.2
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In this table, two sets of matching values are possible, even within the range of normal ATU components. One set drives toward maximal efficiency as C1 is decreased, while the other set moves away from the highest efficiency under the same condition. The primary setting to watch, therefore, is that of C2.

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Input = 50 Ohms;  Output = 150 - j100 Ohms
+                          Maximum permitted C1 = 172.6 pF
+C1  172.5       C2  91080       L    1.37       delta   2.5
+C1  150         C2    456       L    1.42       delta   3.0
+C1  130         C2    223       L    1.52       delta   3.6
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With respect to efficiency, the C-L-C Tee is less effective with capacitively reactive loads than with inductively reactive loads. With some load conditions, here a capacitive reactance of 100 Ohms combined with our standard 150-Ohm resistive component, a very low delta will not be possible with normal components. The best we can do is to keep delta as low as possible by following the common advice for C-L-C Tee tuners:

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C-L-C Tees: Use the maximum capacitance possible, especially for C2, for a given matching situation.

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However, even with a delta of 3.6 to 4, efficiency with a coil Q of 100 will be in the neighborhood of 96%.

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SPC: The SPC (series-parallel capacitance) network is the more general case of which the C-L-C Tee is a specific instance. Note that the C-L-C results from the SPC if we lower the value of the capacitor in parallel with L to zero.

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Ordinarily, the parallel capacitor is ganged as a dual unit with either C1 or C2. The requirement for a high-voltage dual-section capacitor has limited commercial production of SPC tuners. Figure 3 shows the more common configuration, with Cp and C2 ganged as equal-value units.

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The SPC departs from the C-L-C Tee in two significant operational characteristics. First, the actual values required for a given impedance transformation will differ. Second, the SPC tends to tune much more sharply. I recommend the use of verniers on the capacitors for ease of tuning. However, the equation for determining delta for the SPC is the same as that given for the C-L-C Tee.

+ 
Input = 50 Ohms;  Output = 150 +/- j0 Ohms
+                          Maximum permitted C1 = 222.9 pF
+C1  222.8       C2 6027         L    0.04       delta  58.8
+C1  210         C2  362         L    0.64       delta   4.7
+C1  180         C2  176         L    0.69       delta   4.6
+C1  170         C2  152         L    0.75       delta   4.7
+
+Input = 50 Ohms;  Output = 150 + j100 Ohms
+                          Maximum permitted C1 = 222.9 pF
+C1  222.8       C2  154         L    0.82       delta   2.9
+C1  220         C2  137         L    0.85       delta   2.8
+C1  215         C2  118         L    0.87       delta   2.9
+
+Input = 50 Ohms;  Output = 150 - j100 Ohms
+                          Maximum permitted C1 = 172.6 pF
+C1  172.5       C2 91080        L    <0.01      delta  1256
+C1  140         C2   305        l     0.52      delta   9.1
+C1  120         C2   172        l     0.76      delta   8.2
+C1  110         C2   136        l     0.88      delta   8.3
+

The SPC tuner improves the harmonic rejection characteristics of the C-L-C Tee (which is inherently a high-pass filter), but apparently at the cost of lower efficiency. All three tables show the values surrounding the lowest value for delta obtainable under the given load conditions. The SPC appears to do better with inductive loads than with purely resistive transformations or capacitive loads. The value of delta increases for resistive and inductive loads as the ratio of output-to-input impedance increases, but shows a slight decrease for capacitive loads at higher ratios. Because tuning points are quite specific, no general rule of thumb is possible for the SPC.

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The C-L-C PI, the C-L-C Tee, and the SPC are perhaps the most common networks in use at amateur stations these days. Of these, the C-L-C is the most common because it is the cheapest to produce commercially. PIs are less common at QRO levels because at least one of the capacitors must ordinarily have very high values of capacitance, which makes the component expensive.

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At QRP levels, receiving capacitors from older BC receivers have more than enough power-handling capability to make any of these or other networks feasible for the station ATU. Indeed, the entire concept of using one ATU for all possible bands can give way at QRP levels to ATUs that are optimized for a small collection of bands. For example, large value capacitors needed for the lower HF bands often have minimum capacitance values that are too high for maximum ATU efficiency at the upper HF bands. For these bands, it is possible to use lower value capacitors having very low minimum capacitance values. Likewise, the smaller coils needed for these bands may avoid the so-called suckout effect by reducing the number of turns shorted out for a given band. Monoband QRP transceivers are common practice, especially with kits. It is feasible to optimize ATUs for each band and to include them in the same case (thus also eliminating connector losses as well). More next time.

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Updated 1-31-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Matching


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ANTENNAS FROM THE GROUND UP

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15. One Good Match Deserves Another
+ or More on ATUs, Delta, and Losses

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L. B. Cebik, W4RNL

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In our last episode, we explored the nature and losses of some common ATU networks, namely, the C-L-C PI, the C-L-C Tee, and the SPC. This time, we shall look at L-C-L Tees, McCoyþs Ultimate Transmatch, and simple 2-element L-C networks. The tables showing the trends in ë continue to be for 10.1 MHz. Values of capacitance and inductance will vary for the frequency in use, but the values of delta will remain the same for the same input and output values of resistance and reactance at any HF frequency.

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We are restricting ourselves here to networks, and we have set aside inductively coupled matching circuits. In some future installment, we shall examine these circuits, which are capable of excellent efficiency but suffer in many cases from some mechanical inconveniences for multiband use. Among commonly used wide-band inductively coupled ATUs on todayþs market, perhaps only the Z- match overcomes, at least for QRP operation, most of the mechanical problems. But let's, for the moment. return to our network programming.

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L-C-L Tees: The L-C-L Tee, shown in Figure 1, has suffered from neglect until recent years. It is a natural low- pass filter, like the C-L-C PI shown earlier. However, whereas the intermediate impedance of the PI is lower than either the input or output impedances, the intermediate impedance of the L-C-L Tee is higher than either the input or output impedances. This results in higher voltages and lower currents at the junction of the three components.

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Determining delta for the L-C-L Tee requires attention to both inductors, which for simplicity are assumed to have the same Q in the following Egan equation:

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+ 
Input = 50 Ohms;        Output = 150 +/- j0 Ohms
+                          Minimum permitted L1 = 1.114 µH
+L1  1.115       L2   0.07       C   152         Delta   1.4
+L1  1.12        L2   0.20       C   157         Delta   1.5
+L1  1.20        L2   0.77       C   176         Delta   1.8
+
+Input = 50 Ohms;        Output = 150 + j100 Ohms
+                          Minimum permitted L1 = 1.438 µH
+L1  1.439       L2   0.01       C   181         Delta   1.8
+L1  1.50        L2   0.16       C   180         Delta   2.0
+L1  2.00        L2   1.30       C   159         Delta   3.1
+
+Input = 50 Ohms;        Output = 150 - j100 Ohms
+                          Minimum permitted L1 = 1.114 µH
+L1  1.115       L2   1.51       C   145         Delta   2.1
+L1  1.12        L2   1.38       C   140         Delta   2.0
+L1  1.14        L2   1.16       C   129         Delta   1.9
+L1  1.43        L2   0.02       C    85         Delta   1.8
+

Despite the use of two theoretically lossy inductances in the L-C-L Tee, it maintains low values of ë over a wide range of load conditions and transformation settings. Delta climbs more rapidly with inductive loads than with capacitive loads away from optimal settings. The operative rule of thumb for maximum efficiency is this:

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L-C-L Tees: Choose the lowest value of L2 that permits a match.

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This operative rule holds true at higher ratios of output-to-input impedance, even though values of delta increase at those ratios. L-C-L Tees are subject to losses from circulating currents in the shorted turns of either switched or rotary solenoid or toroid coils, losses that the value of ë cannot take into account. Therefore, construction of this network requires special care.

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Ultimate Transmatch: Lew McCoy's Ultimate Transmatch (UT) is an interesting variation on the C-L-C Tee. It places a dual capacitor at the input of the network, one section in series with the signal path, the other section to ground. Figure 2 shows the general outline of the network.

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Calculating delta for the UT design requires the following Egan equation:

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+ +
+ 
Input = 50 Ohms;  Output = 150 +/- j0 Ohms
+                Maximum permitted C1 = 750 pF per section
+C1   749   C2   168   L   0.57   Delta    5.8
+C1   600   C2   161   L   0.68   Delta    5.0
+C1   400   C2   143   L   0.90   Delta    4.1
+C1   250   C2   113   L   1.17   Delta    3.8
+
+Input = 50 Ohms;  Output = 150 + j100 Ohms
+                Maximum permitted C1 = 750 pF per section
+C1   749   C2    81   L   0.57   Delta    5.8
+C1   400   C2    75   L   0.90   Delta    4.1
+C1   250   C2    66   L   1.17   Delta    3.8
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+Input = 50 Ohms;  Output = 150 - j100 Ohms
+                Maximum permitted C1 = 546 pF per section
+C1   545   C2   >350K   L   0.73  Delta   4.7
+C1   300   C2     615   L   1.06  Delta   3.8
+C1   250   C2     400   L   1.17  Delta   3.8
+C1   200   C2     256   L   1.30  Delta   3.9
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Like other series-capacitance designs, the UT appears most effective with purely resistive and inductive loads: Required values for a match fall easily within the ranges of normal components just as the network approaches maximum efficiency. (If C1 is lowered further in these cases, delta increases.) However, with capacitively reactive loads, maximum efficiency has passed by the time C2 enters the range most normal for ATUs.

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Although the values for delta are higher than with some other designs, efficiency remains in the 96% ballpark. In fact, the efficiency of the Ultimate Transmatch appears to increase (at least to some limit) with increases in the ratio of output-to-input impedance. Using a 300-Ohm output resistance with either no reactance or 100 Ohms of inductive reactance, the UT achieved values of delta in the neighborhood of 2.8, while with 100 Ohms of capacitive reactance, delta was about 3.5. The rule of thumb for the UT design is not as simple as with some other designs:

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UT: With normal ATU components (Cmax less than 400 pF), choose the highest value of C2 that permits a match within the range of C1.

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Remember that, for any of the network designs, as the frequency decreases, some of the efficiencies achieved in these 10.1 MHz tables may not be reached, since proportionately greater values of C and L may be needed for the same load conditions. Moreover, switched inductors may not provide the values necessary for highest efficiencies. This limitation is rarely a problem, since the value of delta in most cases "bottoms out" over a fairly wide range. Nonetheless, the rules of thumb continue to apply.

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Moreover, remember that these figures are based solely on losses in the inductor, one assumed to have a Q in the range of 100. Additional losses due to poor components, bad wiring and switching, stray inductances and capacitances, and coil "suck-out" are not accounted for by the calculations. If components get warm or arc under matched conditions at 100 watts, even though the calculations indicate less than 5% losses, believe your senses. Then analyze the components and construction of your ATU. Something other than network choice is very wrong.

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2-Element L-Circuits: Although less versatile than 3-element networks, 2- element networks (L-circuits) are more fundamental. Each circuit consists of a series reactance and a parallel (shunt) reactance. The shunt reactance goes at either the input or the output side of the circuit depending upon whether one is transforming an impedance downward or upward, respectively. The reactances are normally of opposite types.

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Thought of in terms of reactance, rather than components, the reactances can be swapped with respect to type for the same impedance transformation. This will, of course, change the component values.

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Figure 3 shows two L-circuits, one for transformation upward, the other for transformation downward. As given, L is the series reactance and C is the shunt reactance. The result is a low pass filter. Had we placed L in the shunt position and C in the series position, we would have a high pass filter.

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Figure 4 redraws the L-circuits in their high-pass configurations. The top circuit, transforming downward, is the basis for the Beta-match, where the capacitance is actually a function of shortening the antenna element rather than being a separate lumped component.

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It is possible to treat the input and output impedances as purely resistive, as done in Figure 3, and then to add on any capacitive or inductive reactance necessary to cancel out load reactances. If we follow this procedure, the delta figure for the L-circuit simplifies to the follow expression:

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Then, the required series and shunt reactances (Xs and Xp) can be calulated from simple equations:

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Convert these figures to a capacitance and an inductance by use of the usual equations involving 2piF.

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When the load presented to an L-circuit is complex, that is, when it contains both resistance and reactance, the calculation of delta becomes somewhat more complex. However, we can show the trends by looking at our test case at 10.1 MHz. With L-circuits, with some exceptions in small regions where designs overlap under certain reactive loads, only one set of values provides a desired impedance transformation.

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In each test case, we shall be transforming an impedance of 50 Ohms upward, so the Rlo-to-Rhi versions of the L-circuits will apply. The interesting data will concern what happens to delta as we add either inductive or capacitive reactance. (LP = low-pass configuration; HP = high-pass configuration.)

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Input = 50 Ohms;  Output = 150 Ohms
+LP:     Ls 1.114 µH     Cp 148.6 pF     Delta 1.41
+HP:     Cs 222.9 pF     Lp 1.671 µH     Delta 1.41
+
+Input = 50 Ohms;  Output = 150 + 100 Ohms
+LP:     Ls 1.438 µH     Cp 181.3 pF     Delta 1.83
+HP:     Cs 172.6 pF     Lp 2.946 µH     Delta 1.16
+
+Input = 50 Ohms;  Output = 150 - 100 Ohms
+LP:     Ls 1.438 µH     Cp  84.3 pF     Delta 1.83
+HP:     Cs 172.6 pf     Lp 1.370 µH     Delta 2.49
+

Note that when the load is purely resistive, the high-pass and the low- pass configurations are equally efficient, that is, they have the same value of delta. When the load is inductively reactive, the high-pass configuration has the lower value of delta and thus has lower losses. When the load is capacitively reactive, the low- pass configuration has the advantage.

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Traditionally, we have built L-circuit tuners in the low-pass configuration for mechanical ease, not for the added filtering of transmitted signals. The attenuation of harmonics in a single L- circuit is somewhat minimal at best. However, most variable capacitors with any power-handling capability have ground rotator plates, and traditional construction has called for a metal chassis or case.

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Now add to this situation the fact that few hams have bothered to calculate the network efficiency of even the simple L-circuit (let alone other networks). Hence, they knew only that they either did or did not have a match. At power levels from 50 watts upward, the additional tuner losses seem to make little difference to the average operator. As a consequence, the high- pass L-circuit configuration has been neglected in all but Beta matches to Yagis and other low-impedance antennas.

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At QRP, where every avoidable loss is to be eliminated, the high-pass configuration for inductively reactive loads should be considered, especially in cases where the inductive reactance is high. Switches and jumpers can adapt the same coil and capacitor to use in high-pass, low-pass, high-to-low impedance, and low-to-high impedance combinations. Since the ATU network, whatever its configuration, is composed of passive components, no shielding is necessary. Non-metallic cases are not only satisfactory, they in fact reduce many stray capacitances that lower the overall component Q within the network.

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Single-Ended Networks: All of the networks we have examined for efficiency (or losses, to look at the other side of the coin) are single-ended or unbalanced. Many of the uses to which they are put involve parallel or balanced transmission line. From early days, we have been taught not to use a single-ended network on balanced lines. ATU manufacturers who use unbalanced networks often install a 4:1 balun or transmission-line transformer between the network and a pair of so- called balanced output terminals.

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As we saw in a past installment, high impedance loads with large reactive components on balanced transmission lines do not present high impedances to the ATU terminals for most of each half wavelength of transmission line. Just the opposite prevails: the load the ATU sees is a very low impedance that needs no division by 4. Moreover, transmission-line transformers are efficient only with nearly pure resistive loads, and the best expert recommendations consistently tell us to compensate for reactance at the antenna terminals. We can effect a match that achieves a low SWR for the transmitter-to-line junction, but at indeterminate loss levels.

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So what can we do? Two answers have emerged from amateur experience.

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1. Some amateurs have found that, at least for their situations, the seemingly unbalanced network introduces no serious imbalance in currents and voltages along the transmission line. By floating the case, that is, leaving it ungrounded, the network performs normally and yields a perfectly or nearly perfectly balanced output. If a 1:1 balun or a line isolator (a W2DU- type balun choke or a series of split ferrite cores) is placed on the transmitter side of the ATU, any currents that remain on the outside of the coax are effectively blocked from the transmitter and other equipment cases.

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2. Other amateurs have had good success by transitioning to unbalanced line either at the ATU-to-transmission line junction or within a few feet of the ATU--perhaps at a window sill. Again, a line isolator prevents RF currents from flowing on the outside of the ATU case or the short section of coaxial line from the ATU to the window sill. The series section of coxial line introduces an altered impedance transformation and does impart some loss. Even the line isolator is not completely lossless, as W2FMI found some heating of the core material nearest the load in testing the W2DU balun under high power. However, the losses may be less than those accompanying alternative techniques of feeding power to the antenna. In such cases, this method may prove attractive.

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In the end, decisions fall into the domain of the practical. What is the most efficient and least lossy method of feeding my antenna among the practical alternatives I have? However, the more we know about networks, the greater the number of our alternatives.

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Updated 3-11-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

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Topics: Matching


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ANTENNAS FROM THE GROUND UP

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16. Quiet, Please!
+ or Noise, Antennas, and Receiving Systems

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L. B. Cebik, W4RNL

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We often hear reference to "noise" in antenna work, but often we are not sure what kind of noise is being talked about. So let's talk about noise and antennas. "Noise" comes in a wide variety of styles, and here is one way to divide the group into usefully smaller chunks.

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Noise generally refers to any signal components at the point of demodulation except the intelligence of the desired signal. Noise may come from outside the receiver or be generated within it. In fact, all active devices in a receiver generate some noise, creating a so-called noise floor that determines the absolute minimum noise level for the receiver. Receiver designers constantly seek to improve the noise floor, but at the lower HF bands, other noise sources generally make the noise floor a hypothetical idea. Only at the upper HF regions can the receiverþs noise floor be perceived with an antenna connected.

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1. Man-made noise: This category includes the usual machinery sparking, faulty signs, auto engine sparking, etc. As you can see from thinking about the sources, it largely derives from spark generation and hence produces useless RF over a wide frequency range. Most human-made noise is vertically polarized and of ground wave propagation. Hence, ground-mounted verticals are most susceptible to this category of noise. A horizontal antenna generally shows an immediate 3 dB reduction. Additionally, antenna elevation also helps reduce the noise level. Finally, a narrow-band antenna also reduces the total amount of noise energy in this category from reaching the receiver. A parallel feedline-ATU arrangement sometimes shows improvement over the same antenna fed with coax by filtration action, i.e., narrowing the bandwidth of the energy allowed to reach the receiver.

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One technique that has been the subject of recent articles is the use of a short vertical noise sensing antenna (long enough to pick up local noise but too short for effective reception of propagated signals), inverting its signal, and combining the result with the regular antenna signal. With proper adjustment, local human-made noise can be canceled quite effectively, with only slight reductions in received signal strength. The benefit lies in the large improvement in signal-to-noise ratio, the truer mark of effective reception.

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Except for very near by sources, such as an arcing pole pig, man-made noises create the most problems on the lower HF bands. Near by sources include any number of household devices, such as touch control lamps, dimmer switches, and similar devices. The noise from these devices often enters the receiver not only though the antenna terminals, but as well through the power lines and the grounded case and chassis. Remember that the receiver does not care if a signal varies around some preset bias level on the main signal line or if it alters the level of the common bus while the bias remains constant. The cure for these noise sources lies at the sources themselves.

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2. Atmospherics: Atmospheric noise refers to radio frequency energy generated by natural phenomena and carrying no man-made communications intelligence. There are two main sources of "atmospheric" noise and energy coupling to antennas:

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a. Sparks: Nature also generates wide-band sparks in the form of lightning. There are other atmospheric noise sources, but especially on the lower HF bands, QRN is largely propagated lightning signals. Lightning energy is generally AM modulated, and the difference between lightning modulation and some forms of rock music played by AM stations has been disputed. As with all spark energy, the energy decreases as the frequency increases, hence, the quieter high bands. There is little difference in the reception of propagated spark energy between vertical and horizontal energy, since the polarization is lost in the skip refraction.

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Narrow-banding the pre-receiver reception system can reduce the total energy from such signals that reaches the receiver front end. One way to achieve a narrower bandwidth for signals entering the receiver is to place a narrow band, tunable filter at the antenna terminals. Except for pure receiving systems, this technique is not in wide-spread use by amateurs because it tends to attenuate outgoing signal power as well. The alternative is an equally undesired complex switching system to remove the filter during transmit cycles.

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An alternative is to use high impedance antennas that require sharp adjustment, usually of an ATU, as the frequency is changed. Even though the bandwidth of filters and sharply tuned antennas is wider than the IF passband of the receiver, the effects of noise reception are reduced. Receivers respond to signals and noise over a wide range, and this response can activate the AGC system, create thumps and other unwanted outputs, and otherwise disrupt reception of the desired signal. The narrower the bandwidth of the receiving system at the antenna terminals, the less noise is a problem.

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Since the perceived level of spark energy is the sum of energy received from all angles accepted by the antenna, narrowing the overall beamwidth of the antenna is one way to reduce noise levels. One might think that Yagis and other unidirectional antennas might achieve this, since they reduce radiation to and reception from the rear. However, their higher gains often offset this quieting for an overall tie with a dipole at the same height.

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On the lower HF bands, one can feed certain vertically oriented loop antennas so that the horizontal radiation pattern is largely self-canceled. The horizontal portion of the antennas pattern is largely responsible for higher angle radiation in a broad vertical and horizontal beamwidth. By eliminating this portion of the pattern, as shown in Figure 1, the overall gain and receptivity to noise and signals is lowered. However, the remaining portion of the pattern is at low elevation angles that favor dx. Although the signals are usually weaker, their signal-to-noise ratio is much higher, resulting in higher quality reception. This technique, championed by ON4UN and other low-band DXers, proves that antenna gain is not everything, especially if that gain increases noise levels faster than it increases desired signal strengths.

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b. Charges: The more that air molecules strike each other, the more they lose electrons and become charged. The thinner the atmosphere, as at high altitudes, the longer molecules can stay charged before recombining with lost electrons. It is from phenomena such as these that we get the static charge build-up on antennas. For most home antenna systems, charge build- up was no real problem with tube grids, but a real problem with solid-state front ends. The longer the antenna wire, the windier the location, and the drier the air, the more likely that static charge can build to damaging proportions. At the very least, static charge collection on an antenna is an additional noise source and problem.

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For some antennas mounted very high, the energies involved could not be drained effectively before damage occurred to antenna elements. At the extreme, antennas can display St. Elmoþs fire. The development of the quad loop was to solve HCJB's end coupling problem with its Yagis: at the high altitude of Quito, Ecuador, the energy coupling did not produce a mere glow; it was burning the ends off the antenna elements.

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Loop antennas have no ends: hence, for a portion of the incoming energy, there is a reduction in the amount of energy coupled to the antenna from wire-end capacitance. Where the high voltage region is distributed across a wire length, whether vertical or horizontal, capacitive coupling is minimized. For this reason, some operators find quads and other loop antennas quieter than Yagis and dipoles.

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Regardless of antenna type, static charge is simple to drain away. One technique is to have the antenna at DC ground. Some antenna designs are naturally at DC ground. Loops go from the coax center to coax braid, and if the braid is well grounded, the charge does not build up. Placing an RF choke across the antenna terminals or from the hot terminal to a ground line can continuously drain charge build-up. In some multi-band antenna systems, parallel feed lines can carelessly omit this protection, but a pair of RF chokes, one from each line to ground where the feedline enters the house, can protect equipment. However, remember that the impedance level at that point can be high, requiring a very high value of RF choke to ensure that significant signal energy does not go through the choke.

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Modern receivers usually employ noise blankers to eliminate as much noise as possible. Older receivers employed noise limiters. A noise limiter simply clips a signal as it exceeds a preset level. This level was set somewhat above the level of the strongest anticipated intelligent signal so that what was clipped had to be noise energy. Unfortunately, clipping often introduced distortion and mixing products (see next entry) into the remaining stages of the receiver chain.

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Noise blankers involve sending part of the signal energy to a separate amplifier. This amplifier is designed to detect energies of durations shorter than most forms of intelligence. Each energy pulse so detected is used to trigger a circuit that turns off a designated amplifier, usually in the IF chain. Hence, the amplifier is þblankedþ for a period too short for the human ear to tell. Gone is the noise pulse. Unfortunately, noise blanker circuits are imperfect devices: the sudden on-off square wave cycling can create distortion of the desired signal, as well as some mixing products.

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3. Mixing products: Two signals, neither of which is on the frequency to which we are tuned, can be mixed and produce a third signal (or a bunch of signals) that may fall on a frequency we want to use. The cure for mixing products begins by locating where the mixing occurs. If the mixing occurs in the receiver, then filtration of the unwanted frequency (or frequency range) is the best solution. If the mixing occurs externally to anything one's receiving and antenna system can control, then there is no cure immediately at hand. However, such problems often involve violations of technical standards by one or both of the signal generators involved as the sources of the mix, and patient bureaucratic pressure can sometimes alleviate the problem.

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If the mixing occurs within one's antenna system, then there is usually something wrong with the system--bad connections, unwanted couplings, less than optimal tuning set-ups: all of these are correctable and should be part of one's routine periodic maintenance on the antenna system. Some mixing problems occur from þfront-end overload;þ that is, signals are so strong that, regardless of frequency, they enter into the mixing and amplifying chain of the receiver. Very often for low-HF operators, these signals are AM broadcast band signals. The cure usually involves a trap or narrow bandpass filter at the antenna terminals.

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Along the way, we have mentioned ATUs, bandpass or trap filters, and other circuits external to a receiver's antenna terminals as possible aids in noise reduction. It is possible to end up with a string of small boxes, each containing a certain kind of filter, and each connected in series with cables and connectors. Although this situation is typical ham, it is better suited to the test bench than to a communication system. Cables and connectors are invitations to new ways of noise pickup. A better system would be to build all of the necessary external noise reduction tuning and filter devices into a single case with direct (or switched) connections between them.

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We have not covered all the noise sources. Power company equipment problems, such as arcing pole pigs, require a simple procedure: locate the problem transformer, keep on reporting the situation until you get action, and hope there is a ham on the technical staff that handles such complaints. RFI from light dimmers and other home products that use AC waveform chopping to control a voltage level has been noted in many articles and requires that we locate the source and cure it individually. Likewise with noise from computer timing circuits. ARRL maintains a bibliography of articles on RFI and related matters for use by interested amateurs.

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A series of articles on antennas is hardly the place for political comment, but it is a sad though hardly surprising fact of life that commercial interests constantly pressure legislatures and regulatory agencies for relaxation of standards for interference and noise production. Counter- pressure from amateurs and others adversely affected by eliminable noise and interference is necessary to at least hold the line on the ever-noisier RF environment. Although there are no guarantees of success, especially since amateurs can rarely marshal the monetary resources for high-pressure lobbying, constant goading and enlightenment of regulators can at least minimize the rate of noise increase.

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Although every amateur operator has a vested interest in identifying, controlling, and eliminating man-made sources of noise, we should all remember that noise is a reciprocal issue. We should also go to great lengths to ensure that our stations and test benches are not noise sources relative to any other devices able to pick up RF energy. This includes such non-RF devices as modern telephones, along with their portable RF cousins. The less we tolerate noise and interference that might emerge from our own equipment, the more justified we are in insisting that other interests do likewise.

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The final defense against noise is ultimately the same as the final defense against both willful and unwitting QRM. That defense is to perfect our abilities as operators. When our equipment is state-of-the-art relative to noise elimination and reduction, we have nothing left to use in the war on noise but our well-honed skills as operators.

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Operators skills involve three areas of effort: equipment adjustment, reception, and transmission. We need to perfect our abilities to get the most out of the equipment at hand. This includes experiential knowledge of where to point pointable antennas for the best signal-to-noise ratio; how to integrate bandpass, bandwidth, and blanker adjustments for maximum effectiveness; and a myriad of other subtle receiver settings. In addition, we need to constantly practice receiving signals in order to tune our ears more finely than any electronic decoding device can match. Lastly, we need to transmit not only with the precision that makes code or voice reception Q5, but as well with the intuition that alters code or voice speed and patterns to fit the operator at the other end of the line.

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In the end, however, some folks are condemned to live in areas where noise is beyond control and even beyond the ability of the best noise blanker (in the receiver or between the ears) to handle. The solution, short of illegally de-powering these sources, is to save money and move to a quiet location--or to concentrate on portable operation. Short of those drastic remedies, however, antenna choice, feed system choice, filtration, noise cancellers, noise blankers, and operator skills can go a long way toward reducing currently unlivable noise to a mere constant irritation.

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Updated 7-11-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Lower, Noise / Receive, Quad, Vertical, Yagi


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+

ANTENNAS FROM THE GROUND UP

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+

17. At Cross Purposes
+ or Vertically-Oriented, Horizontally Polarized 1 wl Loops

+
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L. B. Cebik, W4RNL

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There are many ways to make a 1 wl loop: a triangle, a square, a diamond, a hexagon, a circle. . .. What these loop antennas have in common is that they are resonant on a chosen fundamental frequency.

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Physically, we can set the antennas in three positions: horizontal (parallel to the ground), sloping (at some chosen angle), or vertical (at right angles to the earth. Horizontal and vertical orientation are the most fundamental. We have already presented some notes on horizontally oriented loops, so let's focus on vertically oriented loops.

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Before we dig into these loops, let's set up another distinction: horizontal vs. Vertical polarization. First, all low antennas (under 1/2 wl in height) have both horizontally and vertically polarized fields. So the question is not about exclusive polarization, as it might be if we were talking about a 2-meter Yagi at a height of 10 wl. Instead, the question is one of dominance.

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Second, the polarization of a loop's transmissions (and receptions) only indirectly affects the far end of the communications circuit. For the most part, the ionosphere randomizes the polarization of signals. Polarization of the antenna's pattern plays a major role in the shape of the radiation and reception pattern, and it is this shape that affects signal strength, signal-to-noise ratio, and whether the antenna favors high or low angle radiation.

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We shall look at vertically-oriented, vertically-polarized loops (VOVPLs) in a future installment, but for now, let's concentrate on vertically-oriented, horizontally-polarized loops (VOHPLs).

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Some folks like to think of VOHPLs as folded dipoles opened up into sundry geometric loops. That is fine, if you remember to stress the dipole aspect of the matter. We can expect virtually any VOHPL to act like a pair of dipoles, one above the other. The resulting patterns will usually be a compromise between the pattern of the higher dipole and the pattern of the lower dipole.

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The graph below (Fig. 1) charts the angles of maximum radiation for a 40-meter dipole, a 2-element wire Yagi, and three typical VOHPLs, the right-angle delta, a square loop, and a horizontal rectangle. The chart is based on practical considerations of lower HF-band wire antennas. Foremost is the fact that amateurs will install a wire antenna as high as possible, given the many constraints of backyard construction. Thus, the heights listed are for the top wire of each antenna. The premise is that if one can get a wire up to a given height, then whatever the wire antenna choice, its topmost wire will be at that height.

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In all cases, the dipole and the wire Yagi have lower angles of maximum radiation than any loop. The explanation is simple: half of the loop's power is being distributed to a wire well below the peak of the antenna.

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One can thus expect a dipole to outperform a vertically-oriented loop with respect to low-angle gain. The natural question is this: why install a loop? There are three very significant positive reasons why one might choose a loop:

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1. The space between supports is too short for a dipole, but the supports are high enough to support the loop.

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2. There is only a single high support, thus favoring one of the Delta loops.

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3. The loop is inherently more immune to noise pick-up than an antenna with free ends, and the improvement in signal-to-noise ratio is worth the loss in other performance factors.

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The pattern of the VOHPL on its fundamental frequency is essentially the same, whatever the precise shape of the loop. Figure 2 overlays azimuth patterns for a dipole, a rectangle, and a delta loop, all at top-wire height of 40' and with a 45° elevation angle. Patterns for increased height begin to show the peanut shape we associate with dipoles. Operationally, the rectangle most closely approaches the performance of the dipole, since its lower wire is highest among the loops.

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Let's tabulate some of the properties of the various VOHPLs we might choose as an antenna. All dimensions are for 40 meters (7.15 MHz), and are approximate, since actual resonant length will vary with height above ground. Likewise, feedpoint impedance figures are ballpark to guide initial feedline thoughts.

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All antennas were modeled on EZNEC-Pro over medium ground with #14 copper wire. All models have been stabilized by increasing the number of segments per half wavelength until further increases showed no significant changes. For new modelers, this technique is standard practice in the generation of reliable NEC models. Although dipoles may be stable with the minimum number of segments per half wavelength, antennas with more complex geometry, such as loops, may require more segments per half wavelength.

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Right-Angle Delta: This antenna, as shown in Figure 3, uses a right triangle to hold down its height. Fed in the center, the impedance is 170-220 Ohms, depending upon height. The circumference is about 141', with a 58.4' base and a 29.2' height. Resonant dimensions will vary with antenna height.

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+ 
Height          T-O Angle   Gain
+Min.    Max.    (Degrees)  (dBi)
+10.8    40      90         4.3
+20.8    50      64         5.3
+30.8    60      46         5.6
+40.8    70      37         6.1
+50.8    80      31         6.9
+

Equilateral Delta: This antenna, as shown in Figure 4, is taller than the right-angle triangle. Fed in the center, the impedance is 105-135 Ohms, depending upon height. The circumference is about 144', with a 48' base and a 41.5' height. As with the right-angle delta, resonant dimensions will vary with antenna height.

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Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+1       42.5    79         -1.6
+8.5     50      67         3.4
+18.5    60      53         5.0
+28.5    70      42         5.6
+38.5    80      35         6.2
+

Square Quad Loop: The square loop, as shown in Figure 5, is often used as the standard for loops, although there is nothing electronically significant about its shape over and against other loop shapes. Fed in the center, the impedance is 115-145 Ohms, depending upon height. The circumference is about 145', with about 36.2' per side, with the exact resonant dimensions varying with antenna height.

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Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+3.8     40      55         3.5
+13.8    50      46         5.3
+23.8    60      38         5.9
+33.8    70      33         6.6
+43.8    80      28         7.3
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Diamond Quad Loop: The diamond loop, as shown in Figure 6, is usually too large both vertically and horizontally for lower-HF use. However, the builder can shrink the diamond vertically and stretch it horizontally. Fed in the center, the impedance is 120-140 Ohms, depending upon height. The circumference is about 144', with about 36.1' per side, with variations in resonant length owing to antenna height.

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+ +
+ 
Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+(A maximum height of 40' is not feasible
+with this configuration of the diamond
+loop.  Note that the lowest maximum height
+is about 52'.)
+1       52      53         4.8
+9       60      45         5.5
+19      70      37         6.1
+29      80      32         6.8
+

Rectangular Loop: The rectangular loop, as shown in Figure 7, is among the most practical of VOHPLs, since one can tailor its precise dimensions to the space available. The model used here, fed in the center, has an impedance of 200-270 Ohms, depending upon height. The circumference is about 138', with 49' horizontal wires and 20' vertical wires. However, exact resonant dimensions will vary with antenna height.

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Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+20      40      63         5.5
+30      50      46         5.7
+40      60      37         6.2
+50      70      31         6.9
+60      80      27         7.7
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Dipole: As a standard for reference, here are the numbers on the half wavelength center-fed dipole, as shown in Figure 8. The model used here, fed in the center, has an impedance of 50-80 Ohms, depending upon height. The approximate resonant length is 67', but will also vary with height. A folded dipole will yield just about the same figures, with a higher feedpoint impedance.

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+ +
+ 
Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+40      40      50         5.9
+50      50      39         6.2
+60      60      32         6.8
+70      70      27         7.6
+80      80      24         8.0
+

2-Element Wire Yagi: For reference, here are the numbers on a 2-element wire Yagi, shown in Fig. 9. I note it here because it uses only about the same amount of wire as a full wavelength loop The driven element is 66' long, while the reflector is 70' long. The element spacing is 20'. The feedpoint impedance is between 50 and 60 Ohms, depending upon height.

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+ +
+ 
Height          T-O Angle  Gain
+Min.    Max.    (Degrees)  (dBi)
+40      40      41          8.8
+50      50      35          9.5
+60      60      30         10.0
+70      70      26         10.5
+80      80      23         10.8
+
+ +
Figure 10 provides the azimuth and elevation patterns for the wire beam at a height of 50'. Although the antenna will not outperform a rotatable Quad or Yagi at 200', it will show significant gain and front-to-back ratio in its fixed position--hopefully aimed at DX. +

Throwing the 2-element wire Yagi into the mix has a purpose: to force you to think in three dimensions about the space available for antennas and about all the options that may be available. There are other directional wire designs, such as the Moxon rectangle, which we shall review in another installment.

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Loop performance does not significantly change if fed at the center of the top rather than the center of the bottom. Inverting the delta designs so that the long horizontal wire is on top will improve performance, since a longer horizontal wire is now at maximum height. However, figures will still not outperform the basic dipole at the same maximum height. With the inverted delta, half the power still radiates from a lower conductor.

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Most of the loop designs will require matching at the antenna feedpoint, along the line, or at the equipment position (an ATU). Therefore, parallel feedline has been the transmission line of choice, especially if multiband operation is contemplated. For single-band operation, networks, X:1 baluns, and line sections have all been successfully used to match any of the loops to a 50-Ohm coaxial feedline.

+

However, many antenna builders choose the VOHPL because it permits multiband operation with an ATU (or dual band operation with simpler matching means). So let's look next time at multiband loops.

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+ +
+

Updated 9-8-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

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Topics: Delta Loop, Dipole, HF Lower, Quad Loop, Rectangle, Yagi


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ANTENNAS FROM THE GROUND UP

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18. Plain Plane Geometry
+ or Multiband Use of VOHPLs

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L. B. Cebik, W4RNL

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Last time, we examined the performance of vertically oriented, horizontally polarized 1-wl loops (VOHPLs) on their fundamental frequency. We chose 40-meter loops to study, since they are generally the most practical. As with almost everything we have noted about antennas, the information applies to other bands with appropriate scaling, especially of heights above ground in terms of fractions of a wavelength.

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However, many would-be loop builders want to use VOHPLs on frequencies above their fundamental. With parallel transmission line and an ATU, multiband operation is certainly possible. The key question is this: what do we get for our trouble? And how does it stack up against other possible multiband antennas. We have already examined the 135' center-fed antenna, the 102' center-fed antenna, the 135' end-fed Zepp, and the 135' off- center-fed antenna. The compendiums of patterns for these antennas will make excellent comparative references for you as you try to decide which multiband wire to build. Developing this reference library of patterns and data is one of the reasons for this series.

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For the VOHPLs, we shall vary the procedure used for the other antennas. There are simply too many variants to analyze one pattern at a time. Therefore, we shall begin with a collection of types of patterns that occur on various bands with the VOHPLs, labeling each with a letter. Then, we shall tabulate the modeling results for each type of VOHPL on each band, referring to a pattern by letter (if one exists in our collection). We shall also list other data, such as maximum gain, elevation angle of maximum radiation, and approximate feedpoint impedance. All antennas (except the equilateral delta) will have a maximum top wire height of 40' as representative of a typical backyard ham installation. All the modeled data emerge from EZNEC with models constructed of #14 copper wire over medium ground.

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A1: Rounded Oval

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The width of the azimuth oval may vary widely, depending upon frequency and antenna configuration. When the side rejection increases sufficiently, the pattern takes on the look of the next pattern, A2.

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A2: Peanut

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The side rejection does not exceed the amount shown here for any of the models given below.

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B: High Oval

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The width of the azimuth oval is a product of using an elevation angle of 45 degrees. High ovals have maximum radiation angles of 65 degrees to 90 degrees and the base bulges may vary in shape.

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C1: Very Small Wings

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This patterns shows the beginnings of side wings due to radiation from the vertical wire segments.

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C2: Large Smooth Wings

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The radiation is now predominantly off the edges of the antenna. The structure of the elevation patternþs lower angle lobes may vary from one band to another.

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C3: High-Angle Wings

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The lowest elevation angle pattern details may vary. The wing structure, however, ranges from about 35 degrees to 60 degrees from one instance to another.

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Virtually all of the radiation patterns of 1 wl VOHPLs will fit one of these general patterns, although gain and precise elevation angle of maximum radiation will vary widely. The following tables for two deltas and two rectangles provide data on take-off angle, maximum gain, approximate feedpoint impedance, and pattern type. The diamond is omitted due to its size.

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1. Right-Angle Delta

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Freq.     TO     Gain    Impedance      Ptn
+MHz       Ang    dBi     R ñ jX
+10.1      55     5.2     2000+j2500     A1
+14.15     90     6.3     150-j90        B
+18.1      67     8.0     1100-j850      A1
+21.15     49     7.2     200-j10        C1
+24.95     90     8.4     1800-j1900     B
+28.5      72     6.4     400+j20        C3
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2. Equilateral Delta

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+ 
Freq.     TO     Gain    Impedance      Ptn
+MHz       Ang    dBi     R ñ jX
+10.1      37     4.6     1400+j3900     A2
+14.15     90     5.2     350+j50        B
+18.1      52     7.3     1100-j1400     A1
+21.15     90     5.5     150+j150       C2
+24.95     69     8.8     1000-j800      B
+28.5      50     5.9     350+j400       C3
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3. Square Quad Loop

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+ 
Freq.     TO     Gain    Impedance      Ptn
+MHz       Ang    dBi     R ñ jX
+10.1      36     4.6     4000+j1900     A2
+14.15     90     0.8     300+j160       B
+18.1      90     4.3     900-j1500      B
+21.15     32     4.7     350+j50        C2
+24.95     90     2.9     1000-j1500     B*
+28.5      45     7.0     400+j220       C3
+

*This pattern is stretched to the side so that maximum radiation is off the antenna edges.

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4. Rectangular Quad Loop

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+ 
Freq.     TO     Gain    Impedance      Ptn
+MHz       Ang    dBi     R ñ jX
+10.1      42     5.9     2500+j1100     A1
+14.15     90     2.8     150-j210       B
+18.1      43     7.2     3600-j1000     A2
+21.15     19     7.7     130-j350       C2
+24.95     39     5.7     2100+j950      A1
+28.5      37     7.0     330-j170       C3
+

All of the antennas modeled had peak top-wire heights of 40' except the equilateral delta. Because of its vertical size, its bottom wire was placed 8.4' above ground with an apex height of 50'. The square quad loop's bottom wire is an unnaturally low 3.85' above ground to set the top wire at 40'.

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In order to evaluate the overall pattern of the data, we need a reference standard. Since we have not presented the data for the 40-meter dipole at 40', let's use it for reference. Patterns will resemble those of half their frequency in the set for the center-fed 135' wire.

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Freq.     TO     Gain    Impedance      Ptn
+MHz       Ang    dBi     R ñ jX
+7.15      50     5.9     90+j9          A1
+10.1      34     7.0     300+j750       A2
+14.15     24     9.5     6000-j600      A2*
+18.1      19     10.0    180-j900       D
+21.15     16     7.8     100-j130       E
+24.95     14     8.8     390+j750       F
+28.5      12     9.4     3400+j700      F
+

Pattern A2, flagged for 14.15 MHz, is a peanut with a narrow bandwidth. Pattern D is the typical extended double Zepp pattern, which resembles a peanut with ears. Pattern E has six major lobes, while pattern F has four major lobes.

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Pattern D

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Pattern E (elevation pattern not shown)

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Pattern F (elevation pattern not shown; this is the 28.5 MHz pattern.)

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The high feedpoint impedances presented at 14.15 MHz and 28.5 MHz result from the fact that the antenna is an even number of 1/2 wavelengths long at these frequencies. Nonetheless, the antenna is notable for the smooth drop in the angle of maximum radiation as the frequency increases. With few exceptions, the 40-meter dipole at 40' has a lower take-off angle and more gain at any frequency than any of the loops.

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All of the loops show high oval patterns on several bands. The high oval pattern indicates that maximum power is being radiated directly or nearly directly upward, as if the loop wires formed a beam antenna in that direction. In fact, that is just what is happening. Wherever the tables indicate a high oval pattern, the ground is acting as an additional reflector element, and radiation is concentrated upward. Reflections alter the phase angles of the top and bottom wires so that they act as a driven element and a director to enhance--in an inefficient manner--the skyward directivity of the antenna.

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If we rotated the axis of the antenna to make it a horizontally oriented horizontally polarized loop, we could cut the wire in the middle of each side and insert a small insulator. VK2ABQ used a button for his antenna of this sort. Without further adjustment of wire length or spacing, the antenna becomes directional on its fundamental frequency. It is the forerunner of the Moxon rectangle.

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The 1 wl loop, then, is sensitive to certain changes that can alter its overall pattern of radiation. In use on lower HF bands, a VOHPL is necessarily close to the ground, which affects the radiation pattern, directing it nearly straight up on many frequencies. Elevated by 10 wl, in models and actual VHF antennas, the antenna loses much of the near ground effect and radiates more nearly broadside to the loop. Unfortunately, lower HF band users do not normally have the ability to elevate an antenna 10 wl above the ground.

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A 40-meter 1-wl loop will make contacts and be a quiet antenna on all bands. However, its performance leaves much to be desired on frequencies above the fundamental. In most configurations on most bands, it is far from a DXer's dream. But the loop can be transformed into a decent DX antenna with only one small change--which we shall make next time.

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Updated 11-1-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

+

Return to Amateur Radio Page

+

Topics: Delta Loop, Dipole, HF Multi Band, Quad Loop, Rectangle


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+

ANTENNAS FROM THE GROUND UP

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19. DXing Can Be Loopy
+ or Vertically Oriented, Vertically Polarized 1 wl Loops

+
+
+

L. B. Cebik, W4RNL

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+

When we began our study of vertically oriented 1 wl loops, we restricted ourselves to feeding the loop so that it acted like a variant of a dipole, with predominantly horizontal radiation. In that radiation, there is a vertical component that many low-band DXers find extremely useful. However, we shall have to give up something to get the DX advantage: gain. But, as we shall see, gain is not everything in this world.

+

Interestingly, we shall make only one significant change in the loop antennas we have studied: the position of the feedpoint. We shall also alter the size of the antenna slightly to bring it to resonance (for reasons to be told as we go along). We then have a vertically oriented, vertically polarized loop (VOVPL). It will look the same as a VOHPL to any outsider, but it will be electrically different. Instead of a spread (folded) dipole, we shall have a pair of phased quarter wavelength verticals. In fact, these loops become close kin to the half-square, a fact that one can prove to oneself with either modeling software or an actual antenna.

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As verticals, the loops and the half square share a fascinating advantage: they require no ground plane, counterpoise, or other massive and messy wire structure other than the antenna/phase-line itself. In another episode, we shall look more closely at what ground planes really amount to at HF. For now, it suffices that the loops and half-square free us from the dirt-digging, wire stringing part of vertical antennas.

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We buy this advantage by accepting a disadvantage: many of these antennas must be fed part or all the way up a vertical or sloping leg. And the antenna is essentially a one-band affair, since its performance on bands above the fundamental is too poor to be worth mentioning (unless one moves the feedpoint and converts the antenna back into a VOHPL).

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Anyone wishing seriously to understand large loops for the lower HF bands should study Chapter 10 of Low-Band Dxing by John Devoldere, ON4UN. He was among the first to understand the VOVPL as two quarter wavelength (nearly) vertical antennas connected by a half wavelength nonradiating phasing line.

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Figure 1 shows a collection of antennas having something in common. In each case (except for the 1/2 wl vertical dipole, shown for size reference), part of the antenna can be viewed as a nonradiating phase line, and part as a pair of vertical radiators connected together at the their tops. However, if 1/2 wl provides the optimum spacing between radiators, then all but the half-squares are less than optimum. As we shall see, the other designs will have less gain than the half-squares, just as one might suspect from spacing them too closely. The half-squares have another unique feature: the verticals are not top-connected.

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Top-connection is actually unnecessary. (It is, however, very convenient mechanically, since it permits a single length of wire to form a loop.) Using NEC models or VHF antennas, you can verify this fact with a little experiment: build a loop (for example, the right-angle delta) that is resonant on a desired frequency. Then snip the top connection and separate the wires by a tiny amount. Antenna properties will not change. This includes the currents and their phases along the wire lengths. As you widen the gap, changes will occur in light of the changing geometry created by further separation. Eventually, you will arrive at the half square configuration.

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The quad configurations are not usually thought of in these terms, due to the complexities of their lower structures marked by the 1/2-wl indicators in Figure 1. However, these complexities are not different in principle than those created by the bends in the delta phase line. The chief result of bending the phase line is incomplete cancellation of radiation from the line and less than optimum spacing of the verticals for maximum gain.

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Let's look more closely at a few samples of 40-meter (7.15 MHz) VOVPLs.

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The Equilateral Delta

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Compared to VOHPLs, VOVPLs will be slightly larger for resonance, and resonance will be important for some VOVPL designs, since they will be fit for direct coax feed. Here are some numbers for the equilateral delta, fed 25% up one side (or, 1/4 wl from the apex). Note the low elevation angles of maximum radiation, but at the cost of most of the horizontally polarized radiation at higher angles for the equilateral delta of Figure 2.

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Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      51.9'   1.1      21°      160 - j8
+20       61.9    1.4      18       130 - j24
+30       71.9    1.5      16       115 - j20
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It is also possible to feed the equilateral delta at a lower corner, with a somewhat different pattern, as shown in Figure 3.

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When fed in the corner, the figures for the equilateral delta look like this:

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Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      51.9'   1.0      29°      150 + j2
+20       61.9    1.6      25       135 - j15
+30       71.9    1.8      22       125 - j20
+

The equilateral delta is slightly directional away from the feedpoint, with a bit of rejection to the feedpoint side. It is the only loop among those reviewed here that shows this pattern; in all other cases, displacement is negligible.

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The Right-Angle Delta

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Although it has a longer baseline, the right-angle delta in Figure 4 is more compact vertically. It is fed about 12-15% up one sloping leg, or about 1/4 wl from the apex of the triangle and has a half dB more gain than the equilateral delta.

+ 
Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      40.4'   1.6      23°       80 + j15
+20       50,4    1.9      20        61 + j0
+30       60.4    2.0      17        52 + j0
+

With most VOVPLs, figures for the angle of maximum radiation and for gain begin to increase only slowly once the baseline is 20' up. Figure 5 compares the elevation patterns for the right-angle delta with 10' and 30' baseline heights. The patterns are typical of almost all the VOVPLs.

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The right-angle delta can also be fed at its corner, with only slight decreases in gain and no practical change in take-off angle. This feature is a convenience to antenna builders, since the coaxial cable--extremely relevant to this antenna as a direct-feed system--can be handled more simply. It can be dropped to the ground, and buried, if necessary.

+ 
Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      40.4'   1.3      24°       90 + j12
+20       50,4    1.7      20        70 - j3
+30       60.4    1.8      17        60 - j3
+

The Rectangle

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The rectangle (Figure 6) is more practical than the square quad loop, so let's focus on this shape. There is nothing magical about the 20' vertical height, and other heights can be used. Like the other VOVPLs, the rectangle is larger at resonance than when fed bottom center. It also has more gain than either of the delta loops, largely due, I suspect, to the fact that the high-current portions of the vertical radiators are parallel.

+ 
Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      30'     2.2      24°       61 + j12
+20       50      2.6      20        45 - j2
+30       60      2.8      18        40 - j3
+

With only a slight drop in gain, the rectangle may be fed at a lower corner for ease of feedline handling.

+ 
Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+10'      30'     2.0      25°       75 + j10
+20       50      2.4      21        60 - j8
+30       60      2.6      18        50 - j11
+

One of the differences in the pattern of the rectangle and the half-square (whose details follow almost instantly) is side rejection. Although the gains are similar, the half-square has more side rejection, while the rectangle shows the more classic oval, as shown in Figure 7. Whether side rejection is an advantage or a disadvantage may have something to do with your choice between these antennas.

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The Half-Square

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The half-square, shown in Figure 8 and brought back to current ham attention by N4PC some years back (although it is much older), is the most optimally spaced phased vertical array among wire antennas. Conventional ham construction inverts the configuration, relative to the deltas. In free space or at a height of several wavelengths above ground, the antenna can be used pointing up or pointing down with no dimensional changes. In fact, I built a version of this antenna, pointing up, for 146 MHz, where it provides the highest gain and deepest side nulls of any vertically polarized antenna I have examined.

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At 40 meters, the antennaþs proximity to the ground compels the inverted arrangement. Since the vertical tips are high voltage-low current points, changes in height will dictate changes in element length. The dimensions shown in Figure 7 are optimized for a minimum height of 5 to 10' above the ground.

+ 
Height           Gain     TO       Impedance
+Min      Max     dBi      Ang      R +/- jX
+ 5'      40'     3.1      21°       60 -  j0
+10       45      3.15     20        55 - j8
+15       50      3.0      18        50 - j12
+20       55      2.9      17        50 - j14
+

As the height is further increased, the elevation of the high current points on the vertical radiators will also begin to result in a higher angle radiation lobe, which takes power from the lowest lobe. Therefore, it is best for lower HF use to keep the half-square fairly close to the ground.

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Using a VOVPL

For DXing, wire VOVPLs provide an effective low angle antenna that is simple to erect, compared to other verticals. It is free of ground plane needs, either in-ground or elevated. It is shorter than a true vertical dipole, but has none of the losses associated with various forms of loading. +

Which version of the VOVPL you choose to build will depend as much upon the physical features of your available space as upon the characteristics of the various versions we have examined. If you have only one high support, one of the deltas may be your only choice. If you have more lateral than vertical space, the rectangle or the half-square may fit your needs. Just keep the antennaþs broadside toward the DX you want to work.

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Using a VOVPL also requires that you change your way of thinking about reception. The absence of high-angle sensitivity automatically reduces the total volume of noise you will pick up. This increase in quieting is additional to the normal reduction of noise of a loop over an antenna with free ends.

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However, the VOVPL will not increase the signal strength of incoming DX signals. Some versions, like the half-square, may show very slight increases in very low angle signal strength relative to a dipole at the same maximum height, but the differences will be small.

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The advantage of the VOVPL lies in signal-to-noise ratio. Since receivers have excess gain that we seldom use, audio levels are easily increased to whatever you prefer. With a VOVPL, the faint DX signal will stand out against the noise. It takes some getting used to and practice to use a VOVPL effectively. If you use shorter skip signals to test the effectiveness of the antenna, you will likely be disappointed.

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Since noise is not a consideration with transmitted signals, do not expect your signal to increase dramatically at the other end of the DX path. However, unless you can place a dipole very high, your transmitted signal will not suffer any decrease in the ears of the DX.

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If you like to work a combination of short and long skip stations, you should consider having two antennas--perhaps a multiband dipole and a VOVPL. Of course, when you win the sweepstakes, you can replace both with a single, 200' high 80-40-30 meter beam.

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Updated 04-04-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to series index page

+

Return to Amateur Radio Page

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Topics: Delta Loop, Dipole, HF Lower, Half Square, Quad Loop, Rectangle, SCV


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ANTENNAS FROM THE GROUND UP

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2. The Incredible Inedible Dipole
+ or The Resonant Half-Wavelength Center-Fed Antenna

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L. B. Cebik, W4RNL

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+ We call it a "dipole," but that is only shorthand. It's real name is "the resonant half wavelength center-fed dipole." No wonder we shorten the name. Unfortunately, by forgetting the full name, we also end up forgetting the basic properties of amateur radio's most basic antenna. +

So let's start again, looking at each of the elements in the antennaþs name and seeing what we can discover about the dipole. Often maligned as too simple to be much good, the dipole turns out to be a rather fantastic antenna.

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Everyone knows that a basic dipole looks like Figure 1. Now here is how the full name works:

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1. Dipole: the antenna is a dipole because it has two "poles," that is, regions of the antenna where the current goes from maximum to minimum.

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2. Center fed: The antenna is fed at its exact center.

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3. Half wavelength: the antenna is approximately 1/2 wavelength long.

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4. Resonant: the feedpoint impedance, Z, which is ordinarily composed of resistive and reactive components (R ± jX), is purely resistive.

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In addition, everyone knows how to calculate the length of our resonant half wavelength center-fed dipole: L (in feet) is the length figured according to a simple recipe:

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And everyone also knows that the feedpoint impedance of a resonant dipole is about 70 to 72 ohms. All we have to do to put up a dipole for 7.15 MHz is to apply the formula and cut our wire to a length of 65' 5.5" and hang it up.

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First, the formula is only a ball park generalization, and not very accurate at that. Even in free space (a presumed volume in which the antenna is centered with absolutely nothing reflective in any direction), the formula does not match up well with NEC-2 models. Using #14 copper wire, the length of a free space dipole for 7.15 MHz is 66.95' and its feedpoint impedance is 73.6 ohms.

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Second, the formula is shorthand for a more accurate equation:

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where K is a shortening factor due to what some treat as capacitance off the ends of the wire elements. The standard formula assumes a value for K of 0.95.

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Values of K appear in handbooks as graphs, the origin of which no one currently remembers. These graphs and the presumed figure of 0.95 are once more ball park numbers. For a more correct readout of values of K, see "Calibrating K to NEC," QEX, March, 1996, pp. 3-8, or HAMCALC.

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K varies with the wire size: the larger the diameter, the lower the value of K. It also varies in a minor way according to antenna material, with higher loss material showing a lower value of K. No single value can capture every wire size used by antenna builders. We can construct with spreads of wires effective diameters up to a foot or more. By comparison, #12 AWG wire is 0.0808" in diameter.

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While we are focused on wire diameter, we might also note that fatter wires also increase the bandwidth of a dipole. We tend to define bandwidth in terms of SWR. An antennaþs bandwidth might be said to be the frequency spread between those frequencies at which the antenna shows a 2:1 SWR relative to its natural resonant impedance. Changing wire size from #34 at the thinnest end of the line to about 2" at the upper end results in an increase in bandwidth of over 2 to 1. For other comparisons, see the Bandwidth program in HAMCALC

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Real Dipoles

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None of us (non-astronauts) gets to put up an antenna in free space. But, just for the record, here is the azimuth pattern for our 40-meter dipole in free space. +
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You may think that the gain in dBi of this NEC-2 model is too low, for we have all ben told that a dipole's gain in free space is about 2.15 dBi. However, #14 copper wire has some (small) loss, which the model incorporates.

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Unfortunately, from 160 meters to 30 meters, our antennas are usually less than 1/2 wavelength in height. Therefore, the real dipoles with which we operate show considerably different traits from our free space model. The Sommerfeld-Norton ground calculation system permits accurate models of low antennas, with the limitation that the antenna is modeled over level ground free of the ground clutter of real ham installations.

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At heights below 1/2 wavelength, the resonant length of an antenna will vary considerably from the free space length. (By way of contrast, the fluctuations of all properties of antennas above 1/2 wl grow much smaller, reaching relatively insignificant proportions for most, but not all, types of antennas above 2 wavelengths. See "The Effects of Height on Other Antenna Properties," Communications Quarterly, Fall, 1992, pp. 57-79.). See Magazines Page.

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Figure 3 graphs the changes in the resonant length of the dipole in 1/8 wl increments from 1 wl down for a 7.15 MHz dipole. The same pattern, with only insignificant variations due to such factors as the wire diameter-to-length ration, ground penetration of RF energy, etc, will hold true for all dipole in the 160-meter to 30-meter range, so long as height is measured in percentages of a wavelength.

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The traditional way of presenting this information has been to show the variation in feedpoint resistance and reactance with height, but this graph gives the builder a better idea of just how long the dipole must be.

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From the second graph, we can see that the resonant feedpoint impedance (a pure resistance) also varies considerably as the height changes. Contrary to some accounts, the impedance goes above 70 ohms as well as below it as the antenna height changes. The curves are actually smooth, but many more data points would have been needed to establish that fact.

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In order to translate the graphs into feet above ground, here are some figures for the low ham bands:

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160 meters: 1.9 MHz: 1 wl = 517.7' or 157.8 meters.

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80 meters: 3.5 MHz: 1 wl = 281.0' or 85.65 meters.

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75 meters: 4.0 MHz: 1 wl = 245.89' or 74.95 meters.

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40 meters: 7.0 MHz: 1 wl = 140.5' or 42.8 meters.

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30 meters: 10.1 MHz: 1 wl = 97.4' or 29.7 meters.

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Figures for the gain of a dipole are even trickier to handle. At very low heights, such as 1/8 wl, almost all of the radiation of a dipole is straight upward. Even at twice the height, the angle of maximum radiation is about 60° and drops to the 28-30° range at 1/2 wl in height. Consequently, it makes little sense to compare gain at maximum angles of radiation for dipoles below 1/2 wl in height.

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However, it is possible and practical to choose an semi-arbitrary low angle of radiation and make comparisons. I have chosen 20° elevation as the comparison point, using either it or the maximum radiation angle, if the latter is lower than 20° elevation. This comparison gives a measure of long-distance performance capability of the antenna as its height changes up to 1 wl.

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The chart has several interesting features. First, it shows a negative gain figure for the lowest height. This figure does not mean that the antenna will not work, but merely that its gain is less than an isotropic radiator. (Mathematical systems, such as NEC, use a theoretic isotropic radiator for calculations, but Brian Beezley, K6STI, has shown that a good approximation of one can be built.)

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Second, the gain at 20° elevation increases rapidly as the antenna is raised, reaching a peak at about 5/8 wl. The angle of maximum radiation for this height is 22° while the angles for the remaining heights are 19°, 16°, and 14° respectively. Note especially the dip in gain in the 7/8 wl region.

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The explanation for this dip lies in the way in which secondary lobes develop as the antenna is raised. The phase relationships of the direct "ray" and the ray reflected off the ground (with some loss) changes as the antenna goes up, resulting in complex collections of lobes and nulls vertically around the antenna.

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At 1/2 wl, almost the entire radiated energy is concentrated in two broad lobes, one opposite in direction from the other. The elevation pattern of Figure 6, for a 40- meter dipole at a height of 1/2 wl, clearly shows the concentration of energy.

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In contrast, Figure 7, shows the same antenna at 7/8 wl. A second lobe, virtually straight up and with considerable energy content has made its appearance. Except for some very special purpose, the nearly vertical lobe represents a waste of communications energy. Hence, antenna heights in the 3/4 wl to 7/8 wl should be avoided, even with upper HF frequency antennas. One other factors bears noting in our saga of the dipole: the front-to-side ratio. One reason for using a dipole (other than just to make contacts, although that is a good one) is to take advantage of the antenna's bidirectionality. By broadsiding it to the stations or areas we want to work, we also gain nulls in directions from which we do not want to hear.

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However, the front-to-side ratio of a dipole increases dramatically as the antenna height is raised. The following graph tells the story. Once more, I have used the 20° angle until the antenna was high enough to have a main lobe below that angle.

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The information on the graph can be illuminated by a pair of azimuth patterns for dipoles: one at 1/8 wl and the other at 5.8 wl. In the first case, Figure 9, the pattern is a broad oval, with almost no rejection off the sides. In the second, Figure 10, the pattern shows that it is growing toward the figure-8 of free-space fame. It would take several wavelengths of height (achievable only at VHF and up) for the nulls to reach 30 dB deep.

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This exercise has not been aimed at giving you advice on where and how to install your dipole. Instead, it has tried to make you better informed about how and how well low-altitude dipoles work. Remember that even at 50 feet up, a dipole has more gain at 20° than any of the Delta Loops, although those antennas quiet the high angle incoming QRM, QRN, and noise. Nonetheless, a dipole is a good antenna, and gets better the higher we install it. For its simplicity, it is nothing short of incredible.
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Updated 4-27-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

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Topics: Dipole


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ANTENNAS FROM THE GROUND UP

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20. SWeaRing
+ or Some Facts and Fantasies About Standing Wave Ratios

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L. B. Cebik, W4RNL

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We have all read dozens of articles about SWR. So we all know that the Voltage Standing Wave Ratio is a complex function of the relationship between the feedpoint impedance of our antenna and the characteristic impedance of our transmission line. When the antenna feedpoint impedance is a pure resistance, the relationship is simple: SWR equals the larger of the two divided by the smaller of the two. If the antenna feedpoint exhibits reactance in addition to resistance, then the SWR is usually higher by a somewhat more complex calculation.

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We also all know that generally, the better the match between the load, the transmission line, and the source (our transmitter outputs), the more power is consumed by the load. Hence, it is generally wise to strive for a well- matched antenna-feedline-transmitter system. So we place an SWR meter in the line at or near the transmitter and monitor the SWR at that point.

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And, unfortunately, that is where most of us stop in our efforts to understand SWR and its place in antenna work. The first thing we want to notice is that we can measure SWR. More correctly, we measure Voltage Standing Wave Ratio (VSWR), because we are measuring the ratio of the maximum voltage along a transmission line to the minimum voltage along the line. Since the ratio of maximum current to minimum current along that same line (ISWR) has the same value, we have gotten in the habit of referring simply to SWR.

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SWR is directly related to the impedance of the load and the impedance of the feedline connected to it. It has become, because we can measure it, the standard measure of a match or mismatch between the load (usually an antenna, for our purposes) and the feedline. Transmission lines are almost (but not quite) purely resistive, which simplifies the arithmetic a lot. We can call their characteristic impedance Zo and treat it as a resistance. However, the relationship is still not absolutely simple, since the load impedance may have both resistive (RL) and reactive (XL) components.

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To calculate SWR, let's define two arbitrary terms, A and B.

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The only difference (although it is a big difference) is the + vs. - at the resistive ends of the expressions.

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From these expressions, we can already figure a lot of things. Here is a quick sampling of a few.

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1. When we have a load that matches the transmission line, it will first of all have to have XL = 0, since the line is presumed to be resistive. Second, RL and Zo will have to be equal. These two facts make the B-equation equal zero, and A/A=1 for our SWR value. So a perfect match has an SWR value of 1.

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2. It does not matter if the load resistance is higher or lower than the transmission line Zo. Whether the difference comes out positive or negative, its square will be positive. Hence, all SWR values will be positive values.

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3. There is no direct connection between the overall load impedance and the SWR. The only time SWR equals ZL/Zo or Zo/ZL is the very special case where the load has no reactance. Never assume your antenna feedpoint presents no reactance to your transmission line. Even as you change frequency within a band, your antenna can be resonant at only one specific frequency and at all others presents at least some reactance to the feedline. So even if your antenna's resistive component remained unchanged (which it does not, but may only change by a very little bit), you would still encounter increases in SWR as you move away from the specific frequency of resonance. (And that assumes a perfect match at resonance, which might not be the case.)

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4. We traditionally express SWR as a ratio rather than as a single value. Do not be fooled by that practice into thinking that the ratio is telling you something more than the output of the calculation. Every calculated number can be expressed as a ratio to 1, and that adds nothing to our knowledge.

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5. From the form of the expressions, you can tell that even though we can calculate SWR from a knowledge of the transmission line Zo and the feedpoint impedance values of RL and XL, we cannot go the other way around. There are innumerable combinations of RL and XL that will give the same SWR value.

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Where do you find all these other values of R and X that yield the same SWR? Right along your transmission line. As we have noted in past installments, a transmission line is an impedance transformer. If the value of SWR at the load end is higher than 1, then everywhere along the line there are different values of R and X that yield the same SWR. (This, of course, assumes a lossless line, which is not quite precise. Every line has at least a little loss. But the assumption is no more a problem for this discussion than our other assumption that feedlines are purely resistive.)

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Fortunately, the values of R and X along a transmission line, where the load is a mismatch to the line (another way of saying that the load impedance is not identical to the line impedance), transition smoothly through the range of values that yield the same SWR all along the line. In fact, from a knowledge of the load RL and XL and the line impedance Zo, we can calculate those values all along the line.

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Before you wear out your hand calculator, remember that virtually all of these equations have been placed into one or more of the programs of HAMCALC, that handy collection made available by VE3ERP.

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So what can the SWR value tell me that is useful. First, it tells you in very broad terms how closely your load is matched to your transmission line. That is useful information if in advance you know that by some simple adjustment you can bring the load (which is changeable) into alignment with the Zo of the transmission line (which is not changeable by any simple adjustment). For example, when you prune a dipole for lowest SWR, you are assuming from statements made by authorities that the impedance at resonance is close to the impedance of your coaxial feedline.

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For many other situations, knowing broadly that you have a big or small degree of mismatch is fairly useless. Knowing the degree of mismatch between the 135' antenna feedpoint and the transmission line on 30 meters gives us no useful instructions for making antenna changes.

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But that leads us to the second thing that knowing the SWR can do for us. It provides a means of calculating what happens all along the line so that we can introduce other methods of matching. But, again, most of them have already been put to use in HAMCALC. And, if you know how to use a Smith Chart, you are using mechanical geometrics to do the algebra for you. Either way, you can calculate where to place matching components along the line, how much to trim a line to let the ATU find more efficient settings, and numerous other jobs.

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I shall not pretend that this is a particularly complete story about SWR. In fact, most books start with a related concept called reflection coefficient and then define SWR in terms of it, which helps keep SWR a little more of a mystery for those not inclined to do all the algebra involved in bringing the ideas together. Here, we started with SWR simply because most hams own SWR meters and almost no one has a well-calibrated reflection coefficient meter. (It is possible to make a scale face for an SWR meter for this factor.)

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Some Misconceptions About SWR

Despite all this available knowledge, I still encounter some interesting misunderstandings about SWR. Of course, they come from "outside," so each of you can claim, "Well, I knew better than that." Even so, it may be useful to review a few of them. +

1. "My SWR is low, so my transmitter is safe." In olden days when tube-type rigs had adjustable output circuits, folks worried about burning out tubes and other components "because" of SWR. Actually, the combination of resistance and reactance seen by the transmitter output circuit would sometimes permit only a small RF transferral. However, operators continued to load their finals to full DC plate input power. What is not RF in a final is heat, and that excess conversion of DC power to heat is what destroyed tubes and stuff around the tubes.

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Today's transistor rigs have feedback circuits that sample the reverse voltage at the output and automatically reduce drive to the finals in the event of a high SWR. Thus, it is pretty difficult to hurt a rig by connecting it to a high SWR output load. SWR is NOT the modern way to hurt a rig. Overdrive, with or without SSB compression, is a source of major stresses on a rig's circuitry. However, the chief modern rig killer seems to be voltage surges coming from the antenna, the power line, or the ground. And that is a matter of safety that calls for measures outside the rig-- like disconnecting the antenna, power cord, and system ground to totally isolate the rig when not in use.

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2. "My antenna system is fine, because the SWR is better today than when I put it up three years ago." The fact of a lower SWR over time is often true. However, the conclusion drawn is false. If the SWR is lower than it used to be, the chief reason is an increase in losses in the system. Losses represent that portion of energy converted to heat along the line and at the antenna terminals, energy that is no longer available as energy to radiate. As systems age, cables become "lossier," terminals become corroded, and a variety of other things contribute to the problem.

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Yes, a lowering of SWR can indicate problems, not improvements. It is not impossible, but it is exceedingly rare for an antenna system to change its feedpoint impedance to match the transmission line. It is so rare that the lowering of SWR with time should always be taken as a sign that it is time for antenna system maintenance. Clean, deoxidize, tighten, and seal, as appropriate. If things do not improve, replace the outdoor coax with new stock (but save the old stuff for noncritical uses, if it has any life left in it).

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3. "My antenna is operating very well because my SWR is a perfect 1:1 match." Unfortunately, my dummy load gives a nearly perfect 1:1 match, and I cannot hear anyone when it is in the line. SWR is one measure of impedance match, but it is not an indicator of the quality of antenna performance as an antenna. Antennas convert radio frequency energy--a form of AC voltage and current--into electro- magnetic radiation (and also the reverse for reception); and they also manage to focus that radiation in various patterns. How well an antenna does this job is only indirectly connected with the impedance match to the transmission line carrying the energy to be converted and directed.

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The practical consequences of this fact are pretty basic. First, before committing to an antenna, try to determine what kind of operating you want to do and select an antenna that will enhance that operation--within the limits of what you can handle in terms of finances, maintenance, and home site restrictions. Second, maintain your antenna regularly--even more regularly than most folks change automobile oil. Preventive maintenance will keep your antenna operating to its maximum ability. Third, if you build your own antenna for a long-term installation, use sensible quality materials. Stainless steel hardware is a must. Tubing and wire made for antennas or equally strong and conductive materials are necessary. Applying No-Ox or similar antioxidation conductive materials at connections of dissimilar metals is always a good idea.

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4. "My antenna has a feedpoint impedance of 100 ohms. Surely 50- ohm coax will give me lower losses than the more highly mismatched 450-ohm parallel feedline." This misconceptions stems from the belief that SWR is a direct measure of the ability of an antenna to "absorb" energy and convert it into radiation. SWR is only part of the story.

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Every transmission line displays two kinds of losses: first is a basic loss based on two significant factors: the ability of the wires to handle RF currents and the leakage between wires through the insulation. Because any coax we can afford compromises cost vs. effectiveness, all common coaxial cables have a higher basic loss per 100 feet than parallel feedline, whether 300- ohm or 450-ohm. In fact, for the HF bands, most parallel feedline has a minuscule loss compared to coax.

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The second loss source is a result of SWR--or rather the mismatch that SWR indicates. Since peak voltages climb, leakage increases. Since peak currents climb, heat conversion losses are higher. In effect, SWR puts a multiplier on the transmission line's basic loss. Since coax begins with significant basic losses, additional losses due to SWR are that much more significant. Parallel transmission lines begin with almost insignificant losses, and the same or higher multipliers usually mean that losses are still insignificant. Under some common conditions, a parallel transmission line with a 10:1 SWR may have lower power losses than a coax cable with a 3:1 SWR. Parallel transmission line is almost always the best bet for multiband wire antennas that require an antenna tuner.

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But remember that even at 3:1 SWR on the lower bands, like 80 meters, coax losses may still be too low to worry about. If your 80 meter dipole shows an SWR at the high end of 75 within the limits of your rig's built-in antenna tuner to handle and you would like to work a little SSB, go for it.

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5. "My meter shows the reflected power to be 25 watts. I'm worried about losing that power at the antenna and what it must be doing to my rig." Most folks who see these kinds of readings have never looked seriously at their forward power under the same conditions. Suppose you set your rig to exactly 100 watts output. Your reflect power reads 25 watts on a decent meter. Your forward power will read at least 125 watts--perhaps a couple of watts more to account for the cable losses just described (and your rig will be putting out about 102 watts). The difference is 100 watts. Where is it--and where did the extra forward power come from?

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The reflected power simply returns to the forward direction and adds to the rig's power along the line. No need to worry about the rig, since it is not affected by the reflected power (except as the reverse voltage may activate a power reduction circuit). The antenna is receiving and converting 100 watts of power (less only the very small amount changed to heat due to cable losses). A receiving station cannot tell the difference in signal strength between an exactly matched dipole and one running a 10:1 SWR to a parallel feedline and ATU system. The received signal strengths will be the same, assuming the antennas occupied the same transmitting positions with the same propagation conditions. Both antennas converted just about 100 watts of RF energy into radiation. It may take about a dozen cycles for the high SWR system to build to full power and an equal number to return to zero, but when you have millions of cycles per second to use, those few make no difference to the signal intelligence.

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I hope these notes help all those "other" folks approach SWR and antennas a little more intelligently. WorldRadio's Kurt N. Sterba occasionally runs into SWR misconceptions, and I assure you that his treatment is far more entertaining than mine--except to the sources of those misconceptions, who are technical writers who ought to know better. He is a good incentive for writers to keep things right and sensible. The best extended treatment of SWR and medicine for SWR misconceptions is still Walt Maxwell's book, Reflections. Unfortunately, it appears to be out of print. You may want to petition ARRL to reprint it. Hopefully your library has a copy. Mine is too dog-eared to be borrowed. Anything right in these notes belongs to Walt. Anything wrong is likely to be noted by Kurt.

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Updated 05-15-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

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Topics: Matching


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+

ANTENNAS FROM THE GROUND UP

+
+
+

21. Pointing the Way
+ or A Short Look at Wire Beams

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Folks often forget that we do not need aluminum tubing to make a beam antenna. Wire will do, if we are content to point it in only one direction. For the lower HF bands, wire beams can be particularly useful for folks desiring more gain in front and less behind.

+

We shall look at two types of wire beams that operate fairly well at how antenna heights-- say 35' up at 40 meters. First is the standard parasitic reflector-driven element combination we call the 2-element Yagi. Second will be a somewhat more compact wire beam called the Moxon rectangle. Both use only about 1 wavelength of wire and may be worth considering.

+

The 2-Element Yagi

The basic 2-element Yagi looks like Figure 1. +
+ +
+
+ Figure 1. Basic outline of a 2-element Yagi. +
+

The reflector is parasitic because it is not directly fed power. Rather, because of its length and distance from the driven element, the current on the wire is of a magnitude and phase to augment the radiation in the forward direction and to diminish it to the rear. Because the two elements are electrically interlocked, the elevation angle of maximum radiation tends to be lower than for a single wire antenna, such as a center-fed dipole.

+

Figure 2 shows the free-space azimuth pattern of a typical wire 2-element Yagi for 40 meters.

+
+ +
+
+ Figure 2. Free space azimuth for a typical 2-element Yagi. +
+

The Yagi gain can run up to about 6 dBi in free space, about 4 dB higher than a dipole in the same position. The front-to-back ratio for a 2-element Yagi will typically run 10 to 12 dB, about 2 S-units reduction in signal strength to the rear. Designing for an easy match will lower the above numbers a bit. Still, the forward lobe is relatively wide, and side rejection can be good.

+

For 40 and 30 meters, typical wire dimensions are the following:

+ 
Dimension               40 Meters   30 Meters
+
+El. #1 (DE)             66'         46.6'
+El #2 (Refl)            70'         49.4'
+Spacing                 20'         14.1'
+

With these dimensions, the feedpoint impedance will be close to 50 Ohms and the 2:1 SWR bandwidth should cover most of the band. (Wire antennas will have somewhat narrower SWR bandwidths than antennas made from fatter tubing.).

+

One of the advantages of a wire Yagi is that it requires no more wire than a full-wave loop. Unlike vertically-oriented loops, both wires of the Yagi are at the maximum height available. Therefore, standard wire antenna construction can be used throughout. The 2- element Yagi is thus a very useful step on the road to even more complex antennas in the future.

+

Figure 3 and Figure 4 show the anticipated azimuth patterns of wire Yagis at antenna heights of 1/2 wl and 1/4 wl, respectively. In each case, although some of the side rejection is diminished, the antenna retains useful gain and front-to-back ratio. In addition, the elevation angle of maximum radiation is lower than a dipole at the same height.

+
+ +
+
+ Figure 3. Typical azimuth pattern of a 2-element wire Yagi at 1/2 wl height (elevation angle = 26° ). +
+
+ +
+
+ Figure 4. Azimuth pattern of a tyoical wire Yagi at a height of 1/4 wl (elevation angle = 42°). +
+

Of course, wire Yagis are fixed-direction antennas. Hence, the builder must orient them in the direction most desired. In exchange for this limitations, the builder can save large amounts of money required for towers, rotators, and self-supporting aluminum antennas for the lower bands. Structural engineers may find the challenge of designing, erecting, and maintaining a rotatable beam for 40 and/or 30 meters a wonderful project. However, the average home builder will be able to build multiple Yagis for less than the cost of the rotator alone.

+

It is possible to build 3-element Yagis by adding directors to the assemblies noted here. However, at low heights typical of most backyards, the added complexities rarely add significant performance. The feedpoint impedance of 3-element beams tends to drop rapidly, making antenna matching more of a problem.

+

In the end, the 2-element Yagi is perhaps the most practical wire beam for most builders. Feeding it with parallel transmission line is feasible and may make the antenna usable as a single wire on higher HF bands.

+

The Moxon Rectangle

The Moxon rectangle is a variant on the Yagi. The basic outline appears in Figure 5. Behind a driven element is a parasitical reflector. Both elements, however, are bent towards each other. Maximum front-to-back ratio occurs when two conditions are met: a. The spacing between the driven element and the reflector is correct, and b. The spacing of the element tips is correct. At that point, the reflector current is of the correct magnitude and phasing for a very high front-to-back ratio. +
+ +
+
+ Figure 5: Layout of the Moxon Rectangle. +
+

A full analysis of the Moxon Rectangle appears in the Spring, 1995, issue of Communications Quarterly. The dimension given here, reproduced from an article I originally wrote for QRPp, have been adjusted to provide a match closer to 50 Ohm coax.

+

The Moxon rectangle is a wire antenna that can be fix-mounted or rotated. It is directional with almost the gain of a 2-element Yagi (5.8 dBi in free space) and has an outstanding front-to-back ratio (greater than 40 dB in free space), with a very broad frontal lobe (-3dB beamwidth = 70 degrees, usable beamwidth = nearly 180 degrees forward). The basic free space pattern of the Moxon is in Figure 6.

+
+ +
+
+ Figure 6. Typical free space azimuth pattern for a Moxon rectangle. +
+

Table 1 provides dimensions for Moxon rectangles for 40 through 10 meters. The dimensions are not perfect simple scalings, because the length-to-wire-diameter ratio changes for each ham band.

+ 
Moxon Rectangle Dimensions for 40-10 Meters
+Band        Freq.       A           B           C           D           E
+10          28.50       12.44       1.94        0.41        2.41        4.76
+12          24.94       14.22       2.22        0.46        2.76        5.44
+15          21.20       16.72       2.63        0.52        3.25        6.40
+17          18.12       19.56       3.10        0.59        3.80        7.49
+20          14.17       25.00       4.00        0.72        4.85        9.57
+30          10.12       35.00       5.60        1.00        6.80        13.40
+40          7.15        49.56       8.01        1.33        9.63        18.97
+
+Table 1.  Dimensions for Moxon Rectangles for 40 through 10 meters.  All models #14 copper
+wire.  Dimensions are in feet, and frequencies are in MHz.
+

All of the antennas exhibit feedpoint impedances between about 56 and 58 Ohms, a close match to the standard amateur 50-Ohm coaxial cable. Free space gain and front-to-back ratio are consistent for all the models, averaging 5.8 dBi and greater than 32 dB in free space, respectively.

+

All of the models use #14 copper wire, although the various factors that contribute to the Moxon pattern tend to cancel out as wire size increases. Hence, tubing models will have dimensions close to those for the thin wire models. However, they will exhibit a broader SWR bandwidth.

+

At heights below 1/2 wavelength, the front-to-back ratio will deteriorate somewhat, but usable values can be obtained. Figure 7 and Figure 8 respectively show the azimuth pattern of a Moxon rectangle at the elevation of maximum radiation, with a height of a half wave length and a quarter wave length above real, medium ground.

+
+ +
+
+ Figure 7. Typical Moxon azimuth pattern with the antenna 1/2 wl up (elevation angle = 25°). +
+
+ +
+
+ Figure 8. Typical Moxon azimuth pattern with the antenna 1/4 wl up (elevation angle = 44°). +
+

The bandwidth for 2:1 SWR is about 100 kHz on 40 meters, using #14 wire. Above 40 meters, the 2:1 SWR bandwidth covers the entire amateur band. For 30 and up, the front-to-back ratio is better than 15 dB across the band at heights of 35 feet and up. Many construction methods are possible, whether the material is wire or aluminum tubing. I shall leave the exact methods to the reader's ingenuity. For 40 and 30 meters, installation would likely be similar to the construction of any other fixed wire array. As with 2-element Yagis, it is possible to build separate antennas oriented in different directions. The only costs are for wire, insulators, rope, and feedline.

+

For 20 meters and up, it is possible to erect lightweight platforms of stressed PVC tubing and possible to rotate the entire antenna with a small TV rotator. Although I have not built concentric Moxon rectangles, a "Christmas-Tree" of Moxons is likely to be easier to tune. Separate feedlines for each band are desirable, as a common feed is likely to run into detuning effects, especially between 20 and 10 meters.

+

The standard of comparison for the Moxon is the 2-element Yagi. While a Yagi has marginally more gain, the Moxon's front-to-back ratio is very much superior. It will likely improve your ears much more than it will diminish your voice or yur key. And, as the old but true saying goes, if you can't hear 'em, you can't work 'em.

+

The basics of the Moxon rectangle appear in G6XN's HF Antennas for All Locations. The necessary information is scattered throughout the volume, which, unfortunately, is written in a somewhat difficult style. However, wading through the somewhat dense prose can be rewarding for the wealth of information there, along with some very strong opinions--not all of which are equally well founded. Moxonþs own antenna is a fixed rectangle with equal element lengths. He remotely loads them as needed to make a reversible beam. The design is derived from the VK2ABQ "button" beam, formed by splitting a horizontally oriented 1 wl loop on each side and inserting a small insulator or coat button. One element is fed; the other forms a modest reflector. From this humble beginning was born the more refined and optimized rectangle described in this installment.

+

Some Other Wire Beam Possibilities

Once you begin thinking of a wire beam, the possibilities become endless. Here are two other arrays of interest: +

The ZL Special: Two elements spaced approximately 1/8 wl and connected with a parallel transmission line about 45° (with a half twist) long form the classic ZL Special antenna, popular in the early days of post World War II beams. In those days, Yagi design among amateurs was a hit or miss affair, mostly miss, and performance was usually disappointing. The ZP Special seemed to rival 3-element beams of the time.

+

However, the ZL Special is a 2-element beam and cannot exceed in gain the limits for 2 elements. Original models with standard dipoles used 72 Ohm parallel transmitting transmission line for the phasing line. This line is almost impossible to come by these days (although a lighter lab signal line is available on occasion).

+

Roy Lewallen's Field Day Special is a version of the ZL Special using 300 Ohm feedline for both the elements and the phasing line. It makes a dandy Field Day antenna that rolls up in a compact ball for transport.

+

Quad Beams: Delta, square, and rectangular loops, vertically oriented but horizontally polarized, are popular antennas. Adding a second element, tuned to a frequency about 5% lower than the driven element, can transform any of these loops into a beam with performance capabilities similar to a 2-element wire Yagi. (These antennas for the lower HF bands are low in height and excess claims for gain and front-to-back ratio should be avoided.)

+

With loading stubs for the reflector and a switchable driven element, it should be possible to create a bidirectional beam. These antennas will not likely match coax, but parallel feedline for a beamþs driven element is perfectly good. You may even be able to use the array as a non-beam on other bands.

+
+ +
+

Updated 07-01-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Lower, HF Upper, Moxon, Yagi


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+

ANTENNAS FROM THE GROUND UP

+
+
+

22. Ho-Ho-HOHPLs
+ or a Horizontal 80-Meter Multi-Band Loop Data Compendium

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The horizontally oriented, horizontally polarized 1 wavelength loop (at the lowest frequency of operation) (HOHPL) has become a fairly popular multi-band antenna. It has an advantage over the single wire that is 1/2 wavelength long at its lowest frequency of operation. Each side of the loop is only half as long as the doublet. But the loop also has a disadvantage: it requires 4 supports rather than 2. Which works better for a given ham location is something that only a careful survey of available land and supports will tell for certain. What can be done is to provide a compendium of patterns for a multi-band loop, similar to those provided in past episode for the 135' doublet, the 102' doublet, the OCF, and the 135' end-fed wire. Therefore, I modeled an 80-meter HOHPL, 70' on a side, using #12 copper wire. This length, when elevated 35' off the ground, was approximately resonant at 3.5 MHz.

+
+ +
+

The next question was where to feed the square. There are two reasonable locations: at a corner or midway along one side. Since the resulting patterns can be very different on some bands, there was no choice but to model the antenna both ways.

+

Also modeled is a corner-fed (no phase line) N4PC loop at 50.7' per side. The N4PC loop is to the 102' G5RV what the 80-meter loops is to the 135' doublet. It has different patterns and somewhat higher elevation angles of maximum radiation than the larger loop.

+

Although the HOHPL is a cloud-burner on 80 meters--like almost all low-level horizontal antennas--the performance on bands above the fundamental makes it very competitive among multi-band wires. An especially interesting feature is that the feedpoint impedance for either configuration is quite manageable on all bands. The resistive part of the impedance tops out at about 400 ohms, while only on 30 meters does the reactance exceed 200 ohms. With either 300-ohm or 450-ohm parallel transmission line, the antenna tuning unit (ATU) should have little difficulty establishing a match. The N4PC is only a little more of a matching challenge for the ATU.

+

As always, the patterns are typical, but not precise, since modeling cannot reproduce the terrain and ground clutter of any given station. Feedpoint impedances are likewise ballpark numbers.

+

80 Meters: 3.6 MHz

+
+ +
Corner-Fed: Z = 70 + j25 Ohms +
+ +
Side-Fed: Z = 65 + j25 Ohms +
+ +
N4PC Corner-Fed: Z = 40 - j1215 Ohms +

40 Meters: 7.1 MHz

+
+ +
Corner-Fed: Z = 85 - j100 Ohms +
+ +
Side-Fed: Z = 260 + j80 Ohms +
+ +
N4PC Corner-Fed: Z = 4060 + j1640 Ohms +

30 Meters: 10.1 MHz

+
+ +
Corner-Fed: Z = 360 - j560 Ohms +
+ +
Side-Fed: Z = 280 - j535 Ohms +
+ +
N4PC Corner-Fed: Z = 105 + j25 Ohms +

20 Meters: 14.1 MHz

+
+ +
Corner-Fed: Z = 285 - j120 Ohms +
+ +
Side-Fed: Z = 265 - j165 Ohms +
+ +
N4PC Corner-Fed: Z = 270 - j570 Ohms +

17 Meters: 18.1 MHz

+
+ +
Corner-Fed: Z = 370 + j205 Ohms +
+ +
Side-Fed: Z = 405 + j175 Ohms +
+ +
N4PC Corner-Fed: Z = 780 - j1165 Ohms +

15 Meters: 21.1 MHz

+
+ +
Corner-Fed: Z = 240 - j105 Ohms +
+ +
Side-Fed: Z = 405 - j125 Ohms +
+ +
N4PC Corner-Fed: Z = 575 + j810 Ohms +

12 Meters: 24.95 MHz

+
+ +
Corner-Fed: Z = 325 + j100 Ohms +
+ +
Side-Fed: Z = 370 + j35 Ohms +
+ +
N4PC Corner-Fed: Z = 345 + j180 Ohms +

10 Meters: 28.1 MHz

+
+ +
Corner-Fed: Z = 215 - j145 Ohms +
+ +
Side-Fed: Z = 245 - j180 Ohms +
+ +
N4PC Corner-Fed: Z = 450 - j725 Ohms +
+ +
+

Updated 10-01-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Horizontal Loop


+ + diff --git a/content/gup/gup23-1.gif b/content/gup/gup23-1.gif new file mode 100644 index 0000000..4c91f5a Binary files /dev/null and b/content/gup/gup23-1.gif differ diff --git a/content/gup/gup23.html b/content/gup/gup23.html new file mode 100644 index 0000000..954d1b1 --- /dev/null +++ b/content/gup/gup23.html @@ -0,0 +1,68 @@ + + + + + + Where to Place Your Impedance Matching Efforts + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

23. Three on a Match
+ or Where to Place Your Impedance Matching Efforts

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The array of combinations of antennas and feedlines can be bewildering. There are so many combinations and options for matching that tracking them all seems an impossible task. A few combinations-- like the standard dipole of Vee plus a 50-ohm coaxial feedline--seem to be inherently well matched to the transceiverþs 50-ohm input/output.

+

Most combinations, however, require some form of impedance matching network somewhere in the system. And so, once more, we must go back to basics and begin again. Where can we effect a good match for SWR and an efficient match for maximum power transfer and minimum power loss?

+

The system that needs the match: Ultimately, the system consists of three parts: the transceiver, the transmission line, and the antenna. The transceiver is normally a fixed part of the system, with a given input/output impedance that has been designed into the unit by the manufacturer.

+

At the other end of the line is the antenna. First, unless feedlines are unbalanced and act as part of the antenna, the antenna itself will radiate in just the same way, whatever feed and matching system is in use. Moreover, an antenna (and here we are talking mostly of center-fed horizontal wires) will convert to radiation all the rf electrical energy at its feedpoint after a few cycles (out of the millions per second). Third, resonance in an antenna is simply the condition of having no reactance, either inductive or capacitive. Resonance is a very narrow frequency phenomena, but one which occurs repetitively as one scans up the frequency spectrum. Note that resonance does not specify any particular resistive impedance, only zero reactance. Hence, feedpoint resistance can be higher or lower than the characteristic impedance of a proposed transmission line.

+

Between the antenna and the transceiver is the transmission line or lines. The characteristic impedance of a transmission line is always considered resistive. However, no feedline is perfect, and there is always a small amount of reactance. Moreover, although the characteristic impedance does not itself dissipate power as heat or some other form of energy, transmission lines do have small loss factors which do dissipate a bit of the energy.

+

Parallel transmission lines have the lowest losses, almost insignificant in the HF bands. Even with a fairly high SWR along the line, total losses may still be insignificant. Well-made coaxial cables have more significant losses. Transmission line losses increase with frequency. At 160 through 40 meters, cable losses may be low enough that the increase in loss due to SWR along the line may result in total losses that are still insignificant. However, on the upper HF bands, the same level of SWR may yield unacceptably high losses. For any installation, when losses reach the point of being unacceptably high is a judgment call.

+
+ +
+

Where to effect a match: Against the background of these system elements we can pose our basic question. If the impedance at the antenna feedpoint does not match the characteristic impedance of a transmission line, where can we effect a match? The answer is simple: anywhere between the antenna terminals and the transceiver terminals (output/input connector).

+

At the antenna terminals: If the resistive part of the antenna's impedance is close to that of our feedline, we can introduce for a given frequency reactances of equal magnitude but opposite type and present the feedline with a resistive impedance. We can also place a network at these terminals, not different in priciple from ATU networks, to achieve both a compensation for reactance and a transformation of resistance to the desired level. In fact, with some ingenuity, we might place the final amp of a rig at the antenna terminals, with remote signal and power feed, and eliminate all feedline losses.

+

Much more common are a variety of matching networks used to transform the antenna feedpoint impedance, whatever its value, to the characteristic impedance of the transmission line. Essentially, these networks consist of two varieties: transformers and L-C networks.

+

Transformers come in three general types. First is the broad-band inductively coupled transformer. Although not widely used today, such transformers are capable of 98-99% efficiency if the load is resistive and the turns ratio is correct. Second are the transmission-line transformers (which may also function as UNUNs or BALUNs). Transmission line transformers can be better than 99% efficient, if the load is resistive and the required transformation ratio matches the transformer design. No one has done as much work on these devices as Jerry Sevick, W2FMI. Any one of his books is a good starting point for understanding these devices. Both of these methods of impedance transformation are generally used with coaxial cable feedlines and with antenna impedances that are not too distant (say, 4:1) from the feedline characteristic impedance, although some larger transformation ratios (say, up to 9:1) are possible.

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Transformers may also be in the form of transmission line lengths that vary their characteristic impedance continuously to change from one impedance to another. The delta and Tee matches (when used without capacitors) are versions of this type of transformation.

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LC networks consist of Pis, Tees, and Ls, the same array of networks that we often use in ATUs. When used at the antenna terminals, they most commonly transform low antenna impedances up to the characteristic impedance of a coaxial cable. The well-known beta match is actually a form of L-circuit used to transform a lower antenna impedance to a higher value of transmission line impedance. L-circuits require both a series reactance and a shunt or parallel reactance. In most cases, the shunt reactance is inductive, either in the form of a coil or in the form of a shorted transmission line stub (or hairpin). The invisible series capacitive reactance is a part of the antenna feedpoint impedance and thus does away with the need for a second physical component.

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The gamma and similar matches use another principle: intercepting the antenna element at a point where a match may be made and the reactance tuned out by a series capacitor. A Tee with a series capacitor becomes a matching network of this form.

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Although none of the matching systems is perfectly efficient, system losses are often least when the match is effected at the antenna. However, LC matching networks placed at the antenna terminals often apply only to monoband antennas. On the other hand, transformers are wide-band devices; however, they are not without limits.

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At the station (transmitter/receiver location): This location is generally chosen for convenience, not for best efficiency. And this is where ATU networks and inductively coupled circuits come into play. They have losses, but when well designed with high-Q components and adjusted for maximum efficiency settings, losses can be quite low--a few percent for most loads presented by incoming feedlines. When ATUs use low Q (lossy) components, are set to inefficient settings (sometimes by poor designs that only permit inefficient settings), use poor physical layouts that create stray inductances and capacitances, etc., losses can be considerable.

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Between the ATU and the antenna terminals, standard practice is to use feedline with the lowest loss, which usually means 300- 450- or 600-ohm parallel feedline. Losses multiply with SWR on the line; hence a low starting loss figure provides the most efficient power transfer. With any load.

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The ATU-parallel feedline system of matching the load to the transceiver is most used with multiband antennas, such as the 135 doublet. It is also used where the width of the band is a high percentage of the operating frequency, such as 160 meters. On such bands, different ATU settings may be required across the band.

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Network ATUs, such as C-L-C Tees, L-C-L Tees, and Pis, are ordinarily designed as single-ended or unbalanced networks. Most are designed for use with coaxial cables, with balanced transmission line use an afterthought. The afterthought is a 4:1 balun, often of dubious design. The efficiency of such a balun in the presence of highly reactive loads presented by the feedline is often questionable. Moreover, the use of a 4:! Impedance transformation presumes that the load will be much higher than 50 ohms. With a random length of parallel transmission line to the antenna, it is very likely that the load will be less than 100 ohms, which the balun than transforms downward to something far less than 50 ohms. Although network ATUs may sometimes effect an efficient match with parallel transmission lines, just as often they are far from maximally efficient.

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More suited to parallel transmission lines are inductively-coupled antenna tuners, such as the Johnson Match Box series. Perhaps in the not-to-distant future, both finished and kit models will once more become available. In the interim, home brewing will have to do. A basic tutorial on these designs is available in a 5-part series published in QRP Quarterly.

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Anywhere along the line: Technically, although the ATU is installed near the transceiver--or even inside the same case--it is never quite at the exact input-output point of the transceiver. Thus, it ordinarily qualifies as a matching unit that is installed somewhere along the transmission line. Actually, every ATU is an impedance conversion device to permit changing from one value of transmission line characteristic impedance to another value of transmission line characteristic impedance. Of course, we can effect that conversion anywhere along the transmission line we choose, so long as the impedance at that point is suited to both the amount of conversion and the technique of conversion we try to use.

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When we choose to place the impedance transformation somewhere along the transmission line, we have to pay attention to losses from the point of match back to the antenna. Most of the techniques apply to coaxial cable installations, where basic cable losses, multiplied by significant SWR levels, may create unacceptably large total losses, especially on upper HF bands. Hence, a technique useful for 160-40 meters may not be acceptable on 20-10 meters. Of the many techniques and rationales, we can cite only a few examples to illustrate this idea.

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Stub matching: For any frequency and antenna feedpoint antenna impedance and feedline characteristic impedance, there will usually be points where one may introduce series or parallel reactances to achieve a resistive impedance of some desired level. This technique is widely useful, especially for high-impedance antennas, such as the extended double Zepp. However, the technique is not absolutely universal, since certain lines and antenna impedances will not together reach a resistive value matching a desired line. When the reactance component is a parallel-connected device, it is usually called stub matching, since common practice in pre-WW II days was to use a shorted or open length of feedline as the reactance rather than using a lumped component (capacitor or inductor). HAMCALC has a program for calculating stubs for any feedpoint impedance and proposed feedline.

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Series matching: The math of series matching, that is, using feedline lengths as series sections, was worked out by Regier and appears in the IEEE proceeding for 1970 and Electronic Engineering for 1973, as well as QST for July 1978 (and subsequent editions of the Antenna Book). As with stubs, there are antenna impedance-feedline characteristic impedance combinations that do not permit a match, but most cases will work. These techniques are--from the perspective of convenience--best suited to monoband antennas, although one might develop switching or clipping techniques for multiband use of an antenna.

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Delayed series matching: When the antenna feedpoint impedance is higher than the characteristic impedance of the proposed feedline, we often insert a quarter wavelength section of an intermediate impedance to effect a match. Thus, for impedances in the 100-ohm range, a 75- ohm quarter wavelength section will often transform the impedance to a very good match for 50-ohm coaxial cable.

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However, we may insert between the antenna and the quarter wavelength section a length of 50-ohm coax that is either « wavelength or a multiple of « wavelength long. At the design frequency, the impedance is the same at each end of the 50-ohm line. Below the design frequency, the 50-ohm length is a bit short, resulting in a higher impedance at the matching section end than at the antenna terminals for the low end of the band. Above the design frequency, the 50-ohm line length is long, again resulting in an impedance higher than that at the antenna terminals for that end of the band.

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The result is a set of impedances across the band which the 75-ohm quarter wavelength section can transform into values closer to 50 ohms. The effect is to provide a wider operating bandwidth. Remember, however, that the antenna feedpoint impedance has not changed; hence, the SWR relative to the antenna-to-matching section run of 50-ohm coax has not changed. Hence, this technique is usually confined to the lower HF bands where the SWR loss multiplier for the antenna-to-matching section 50-ohm cable does not yield unacceptable total losses along the line.

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50-75-50-Ohm systems: It is not necessary to restrict our systems to a single impedance transformation. The strongest and lowest-loss coaxial cables available at reasonable cost are often 75-ohm hardlines. When towers and antennas are distant from the station, these cables can cut losses. However, commercially-made antennas and transceivers are 50-ohm devices. Many operators insert high- efficiency transmission-line transformers at each end of the line to go from 50 to 75 and back to 50 ohms again.

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So, what have we accomplished? In many high power applications, especially where radiated power from the antenna is the user's critical question, efficiency of the matching network may not be considered significant, since lost power (so long as it does not harm the components) can be made up by adding power to the system. For QRPers, there is no such luxury. Hence, it is very useful to learn all we can of ways to improve the efficiency of our matches--wherever along the line we place them.

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This survey of possibilities is not to provide any absolute rules (or even rules of thumb). Instead, it is intended to put some of the chief methods and placements of impedance-matching techniques into some perspective.

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But this survey is just a start. Some future episodes in this series may be devoted to individual matching techniques mentioned along the way in this brief account. However, excellent information is available from many sources--especially from antenna handbooks. Although it is very useful to work hard at understanding the math involved in impedance transformation techniques, most of the drudgery of making complex calculations can be side-stepped with simple BASIC utility programs, such as those in HAMCALC. We can never learn too much.

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Updated 03-17-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

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Topics: Matching


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ANTENNAS FROM THE GROUND UP

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24.Two Zs for a Quarter
+ or The 75-Ohm 1/4 Wavelength Matching Section

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L. B. Cebik, W4RNL

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In numerous projects, writers will specify the use of a 1/4 wavelength matching section of 70-to 75-ohm coax between the antenna feedpoint and the 50-ohm coax run to the shack. A typical installation is illustrated in Fig. 1.

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Let's see how these matching sections do their work. These types of matching sections are handy and easy to make, so you may find them useful in future antenna projects.

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The Raw vs. the Matched Antenna: Let's start by comparing the feedpoint impedance of a 10-meter quad, both with and without the matching section. The figures are based on a quad beam that is self-resonant just below 28.25 MHz. The 1/4 wavelength section of 75-ohm, 0.66 velocity factor coax was cut for 28.5 MHz and turned out to be 68.3" long. All SWR figures are relative to 50 ohms.

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+Frequency        Without matching section              With matching section
+  in MHz         Feed Z           SWR                  Feed Z           SWR
+                 (R+/-jX)                              R+/-jX)
+28.00            70.6 - j29.2     1.81                 66.6 + j27.4     1.73
+28.25            96.8 + j 3.4     1.94                 58.1 - j 2.5     1.17
+28.50            125.1 + j25.9    2.63                 43.1 - j 9.0     1.28
+28.75            150.1 + j39.4    3.23                 35.0 - j 8.5     1.51
+29.00            168.6 + j47.7    3.67                 30.7 - j 7.1     1.68
+29.25            180.8 + j54.8    3.97                 28.3 - j 6.0     1.81
+29.50            188.2 + j63.1    4.22                 26.6 - j 5.4     1.91
+29.75            192.6 + j73.6    4.45                 25.1 - j 5.2     2.02
+............................................................................
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Without the matching section, the SWR for the quad is high enough so that the automatic shut down feature of most current solid state rigs would reduce rig output to almost nothing. With the matching section, the SWR within 10 meters permits normal operation.

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As the unmatched impedances go up, the matched impedances go down. This gives us a clue as to how the matching section operates. Every length of coax of any characteristic impedance (ZO) is an impedance transformer. For odd lengths, the transformation is complex.

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However, when a length of coax is exactly 1/4 wavelength long at a given frequency, the transformation is simple, especially if the impedance to be transformed is wholly resistive. We can use a calculator to handle this equation:

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where Zin is the impedance at the junction of the matching section and the main 50-ohm line, ZO is the characteristic impedance of the matching section line, and Zant is the feedpoint impedance of the antenna.

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The Approximate and the Exact: This little formula is only approximate in the real world. For example, with the quad, there is a reactive part of the antenna feedpoint impedance in every line of the table. The equation presumes a purely resistive impedance. If we want to calculate the actual impedance transformation for complex antenna feedpoint impedances, we would have to use something like this equation:

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where ZO, Zin, and Zant have the same meanings as in the simple equation, and L is the electrical length of the matching section in degrees. A quarter wavelength line is exactly 90 degrees long, since a full wavelength is 360 electrical degrees. Additionally, the quarter wavelength line will be shorter than a full quarter wavelength in free space because every transmission line has a shortening effect called velocity factor (VF), which is always 1.0 or less. In our table, the VF of the 75-ohm matching section is 0.66.

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Because this equation for Zin requires that we separate the "real" and the "imaginary" (j) terms and perform other operations to obtain the desired values, we sometimes use a pair of equations that will directly calculate the input impedance in terms of R and jX, the resistance and reactance respectively. These are handy, since we usually are given the antenna feedpoint impedance in terms of R and jX.

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where Rant and Xant replace Zant and Rin and Xin replaces Zin. Although these equations look formidable, they easily separate into parts for placement in a BASIC language computer program. However, that work has already been done in a program called "Transmission Line Performance" in the HAMCALC collection, available from VE3ERP.

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These equations are for lossless lines, and no line is ever completely lossless. However, the losses in quarter wavelength matching sections are negligible in practice and can be bypassed. In theory, we ought also to use the full formulas for all calculations, because the matching section is only an exact 1/4 wavelength at 28.5 MHz and nowhere else. However, if the reactances are not too high and the frequency span is not too great, the simple equation makes a good approximation. As we look at the table, for a single ham band and for reactance values less than half the resistive values, the simple equation works well enough for antenna building.

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We can illustrate the effects of accounting for the reactance and for the fact that our matching section is only 1/4 wavelength long at one frequency with the following graph (Fig. 2).

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Using the impedance values from the quad table, we can look at the situation in 3 steps. Step 1 uses only the resistive component of the feedpoint impedance and true 1/4 wavelength matching lines for each frequency checked. This line yields over-optimistically low SWR values across 10 meters. Step 2 includes the reactance at the antenna feedpoint, but again uses true 1/4 wavelength matching section lines for each frquency check point. This is the top line.

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Step three uses both the resistive and reactive components of the feedpoint impedance, but restricts the matching section to a line that is 1/4 wavelength long at 28.5 MHz. Below this frequency, the line is a bit short (about 88 degrees at 28 MHz). The antenna impedance is not transformed a full 90 degrees worth, and the resulting impedance presents a slightly lower SWR to the 50-ohm feedline at the low end of the band. Likewise, at the upper end of the band, the matching section is a bit long (nearly 94 degrees at 29.75 MHz) which yields an impedance transformation that is more than from a 90-degree line. The SWR at the 50-ohm line junction is slightly lower than with a true 1/4 wavelength line. The effect is slight but definite, as the middle line of the graph clearly shows.

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Remember that for purely resistive impedances, a 2:1 50-ohm SWR accommodates an impedance range of 25 to 100 ohms. This resistive range shrinks when we combine reactances with resistance. However, note the 4:1 range of impedance that these SWR limits can handle. (Also remember that the 2:1 ratio is somewhat arbitrary as a set of limits. It's chief effect is noted by automated power reduction circuits in transceivers. Apart from this, there would be little difference in radiated power between, say, SWRs of 1.8 and 2.5.)

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With a 1/4 wavelength 75-ohm matching section, again in purely resistive terms, we can take antenna feedpoint impedances between just above 56 ohms up to 225 ohms and transform them to values that fit the 50-ohm 2:1 SWR limits--again, a 4:1 range. Notice that our quad does not reach 225 ohms when the matched SWR exceeds 2:1, but notice also that there is considerable reactance that accompanies the resistive value at 29.75 MHz.

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Likewise, at 28 MHz, we would expect the antenna impedance of 70.6 ohms to yield about an 80-ohm figure instead of the 66.9-ohm figure that actually emerges. However, not only do we have reactance at the antenna feedpoint, but as well the matching section is shorter than 1/4 wavelength at this frequency. Hence, the impedance does not undergo a full quarter wavelength transformation. (Likewise, above 28.5 MHz, the impedance undergoes more than a 1/4 wavelength transformation.)

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These are the finer points of using a 1/4 wavelength matching section that affect the matching range by just a little bit and throw the actual impedances somewhat off the calculated results from the simple formula. But the simple formula works well enough for most ham antennas. To be on the safe side, let's express the limits conservatively: if you have a range of antenna feedpoint impedances from about 80 to 200 ohms, then a 1/4 wavelength section of 75-ohm coax will transform them to values appropriate to a 50-ohm feedline and transceiver system.

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Cutting the Matching Section: A question many folks ask is how precisely the matching section line must be cut. Does the length of the pin in the connector make a difference? Should I try to be precise to a quarter, eighth, or sixteenth of an inch?

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Actually, if you are within an inch or two of the correct length at 10 meters (with appropriate expansions as the frequency goes down and contractions as the frequency goes up), you will not notice the difference.

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For the quad example, I calculated the impedances and SWR figures for matching sections based on design frequencies of 28, 28.5, and 29 MHz, hoping to make another graph. However, the graph lines could not be separated. The maximum difference in SWR anywhere across the band was 0.06, a truly insignificant difference. Yet the matching section length varied by 2.5 inches, and we can all be more precise than 2.5" of length.

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As a guide to cutting, we might note the following: most antennas show a steeper rise in feedpoint impedance on one side of resonance than on the other. Cut your line to a frequency on the shallow-rise side of resonance. Better yet, obtain a calculation program or a version of NEC-2 or better (which permit modeling of lossless transmission lines) and experiment with lengths until you obtain the desired or best SWR curve for your operating.

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Other Applications: 50-ohm and 75-ohm coax cables are the ones most easily obtained by hams, even though other values are available from manufacturers. However, this fact does not limit us to matching only values above 50-ohms to our 50-ohm system. If you cut 2 lengths of 75-ohm cable to 1/4 wavelength and connect them in parallel (center conductor to center conductor and braid to braid at both ends), you have a 37.5-ohm cable. If we plug this value into the simple equation, we find that we can match impedances values below 50- ohms up to values within the 2:1 50-ohm SWR limits. This is useful for Yagis and other antennas that often have feedpoint impedances in the 20-35 ohm range. The double line can be a bit bulky, but that is about its only significant disadvantage over other matching methods.

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Consider another situation illustrated in Fig. 3: At certain wire antenna heights below 1/2 wavelength, the feedpoint impedance of a dipole is not 70 ohms, but more like 80-95 ohms. The 75-ohm matching section would transform these values to a 70-60 ohm range. However, we can broaden the range over which these values apply by first running a section of 50-ohm cable that is 1/2 wavelength long or a multiple of 1/2 wavelength (allowing, of course, for the cableþs velocity factor). Cut the 50-ohm cable for a frequency at the band center, such as 7.15 MHz for a 40-meter dipole. Since the cable is short at the low end of the band, the impedance will be higher than at the antenna at the same frequency. Equally, since the cable is long at the high end of the band, the impedance will also be higher than at the antenna terminals. The result will be band edge values closer to 100-120 ohms.

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Now, if we plug in our 1/4 wavelength 75-ohm matching section, we have lower SWR values across the band than we would have by placing the 75-ohm matching section at the antenna terminals. In fact, such a system can, with some dipole heights on 80 meters, cover more than 4/5 of the band with under 2:1 SWR.

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Flexibility and Limitations: 75-ohm quarter wavelength matching sections (and derivatives) make up a quite flexible array of methods for adapting 50-ohm transmission line to antennas that do not present 50-ohms at their feedpoint terminals. However, they do have some major limitations. Because a length of coax is 1/4 wavelength long at only one frequency, this technique is for monoband antennas only. If you have a multiband antenna, you will have to use some other method of matching your 50-ohm coax/transceiver system to the antenna.

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Likewise, the transformations become far more complex the higher the reactance at the antenna feedpoint. Hence, the quarter wavelength matching system is also only for low- reactance matching situations, such as the one shown in the table for the quad. If you have higher reactances, you may need a different matching system.

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But where the 1/4 wavelength matching section is suited to the task, it is simple, inexpensive, low-loss, and effective. Those are pretty good credentials for any matching scheme.

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Updated 05-02-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

+

Topics: Matching


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+

ANTENNAS FROM THE GROUND UP

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25. Turning the Corner
+ or a 1/2 Wavelength Inverted-L Multi-Band Antenna Data Compendium

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L. B. Cebik, W4RNL

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An often-neglected multi-band wire antenna is the 1/2þ inverted-L. The antenna consists of a half wavelength of wire at the lowest frequency of interest and can be fed either at the upper corner with parallel feedline or at the base of the vertical arm, usually via an L-network to a coaxial feedline to the transceiver. Fig. 1 shows the options.

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An 80-meter 1/2wl inverted-L requires about 65.5' horizontally and the same amount of vertical space. For a full size antenna, the height needs to be slightly more to ensure that the bottom of the vertical arm--a high-voltage point--is out of reach from anyone. If the fundamental frequency is on 40 meters, the antenna will be half the size.

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For odd installation situations, the antenna can be distorted in either the vertical or horizontal dimension. Adding more horizontal and less vertical length tends to make the horizontal arm more dominant, with a reduction in lower-frequency, lower-angle radiation. Lengthening the vertical arm and shortening the horizontal arm does the opposite, with slight reductions in gain on the upper HF bands.

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Top-corner feed usually requires parallel transmission line to a wide-range balanced antenna tuner. Often, however, hams feed the antenna through an L-network placed right at the base of the vertical arm and well-grounded for RF. Although a good RF ground is essential, a ground plane immediately beneath the antenna is unnecessary and in fact does little if any good.

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Installation variations, if moderate, also create few problems for operation of the antenna on all bands. The horizontal arm can be modestly sloped downward or bent downward at its outer end. Likewise, a center-fed version of the antenna might have the lowest part of the vertical arm bent to one side to maintain a safe height above peopleswl heads.

+

The following pages present azimuth and elevation plots of a 1/2wl inverted-L cut for the middle of 80 meters and used on all the HF bands. The patterns and data are representative and will vary with the specifics of your situation. However, notice the absence of very high- angle radiation on any band. Moreover, even though the gain is almost always less than that of a 135' doublet, the patterns are smoother, with fewer and shallower nulls. That feature alone makes the antenna a good general operating aerial.

+
+ 80 Meters +
+
+ +
+

Center-Fed
+ Gain: 1.98 dBi
+ T-O Angle: 44°
+ Feed Z: 65 + j4 Ohms

+
+ +
+

Base-Fed
+ Gain: 2.03 dBi T-O Angle: 46°
+ Feed Z: 4800 - 1060 Ohms

+
+ 40 Meters +
+
+ +
+

Center-Fed
+ Gain: 4.08 dBi
+ T-O Angle: 26°
+ Feed Z: 6500 + j710 Ohms

+
+ +
+

Base-Fed
+ Gain: 5.12 dBi
+ T-O Angle: 28°
+ Feed Z: 920 + 825 Ohms

+
+ 30 Meters +
+
+ +
+

Center-Fed
+ Gain: 4.05 dBi
+ T-O Angle: 20°
+ Feed Z: 150 - j495 Ohms

+
+ +
+

Base-Fed
+ Gain: 4.36 dBi
+ T-O Angle: 24°
+ Feed Z: 190 + j280 Ohms

+
+ 20 Meters +
+
+ +
+

Center-Fed
+ Gain: 5.38 dBi
+ T-O Angle: 14°
+ Feed Z: 1850 - j2330 Ohms

+
+ +
+

Base-Fed
+ Gain: 5.28dBi
+ T-O Angle: 15°
+ Feed Z: 360 + j325 Ohms

+
+ 17 Meters +
+
+ +
+

Center-Fed
+ Gain: 7.02 dBi
+ T-O Angle: 36°
+ Feed Z: 170 - j255 Ohms

+
+ +
+

Base-Fed
+ Gain: 7.16 dBi
+ T-O Angle: 41°
+ Feed Z: 475 + j440 Ohms

+
+ 15 Meters +
+
+ +
+

Center-Fed
+ Gain: 6.74 dBi
+ T-O Angle: 9°
+ Feed Z: 700 + j1375 Ohms

+
+ +
+

Base-Fed
+ Gain: 6.22 dBi
+ T-O Angle: 10°
+ Feed Z: 230 + j165 Ohms

+
+ 12 Meters +
+
+ +
+

Center-Fed
+ Gain: 6.62 dBi
+ T-O Angle: 8°
+ Feed Z: 215 - j525 Ohms

+
+ +
+

Base-Fed
+ Gain: 6.64 dBi
+ T-O Angle: 8°
+ Feed Z: 200 + j175 Ohms

+
+ 10 Meters +
+
+ +
+

Center-Fed
+ Gain: 7.54 dBi
+ T-O Angle: 7°
+ Feed Z: 535 + j1055 Ohms

+
+ +
+

Base-Fed
+ Gain: 7.63 dBi
+ T-O Angle: 7°
+ Feed Z: 195 + j90 Ohms

+
+ +
+

Updated 07-18-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Inverted L


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+

ANTENNAS FROM THE GROUND UP

+
+
+

26. Small Corners
+ or a 3/8 Wavelength Inverted-L Multi-Band Antenna Data Compendium

+
+
+

L. B. Cebik, W4RNL

+
+

Suppose that you just cannot manage the 1/2 wl inverted-L for 80 meters that we featured in the preceding data compendium. However, you would like to do some 80-meter work. So a 40-meter version of the inverted-L seems a bit small. Is there a better answer?

+

One (but not the only) better answer is the 3/8 wl inverted-L. See the sketch.

+
+ +
+

The 3/8 wl inverted-L for 80 meters is about 47.6' (14.5 m) for each leg, taking up much less altitude and horizontal space than the 1/2 wl version with its 65.5' arms. Both feeding options are still open to us: we may feed the antenna with parallel transmission line at the top corner or we may bring the antenna near to ground and feed it at the base with a standard L-network tuner.

+

In either configuration, the antenna competes quite well against its big brother. The chief gain losses are on 80 meters, where the effects of the shorter arms show up most vividly. On the higher bands, performance differences are less noticeable.

+

In fact, there are wider variations in performance between the two versions of the 3/8 wl inverted-L than with the 2 versions of the 1/2 wl antenna. These differences result from the non- resonant length of the antenna wire. Feeding it at different points results in different current distributions along the wire on different bands.

+

Top-corner feed requires parallel transmission line to a wide- range balanced antenna tuner. Often, however, hams feed the antenna through an L-network placed right at the base of the vertical arm and well-grounded for RF. Although a good RF ground is essential, a ground plane immediately beneath the antenna is unnecessary and in fact does little if any good. As was the case with the 1/2 wl, moderate installation variations create few problems for operation of the antenna on all bands.

+

The following pages present azimuth and elevation plots of a 3/8 wl inverted-L cut for the middle of 80 meters and used on all the HF bands. The patterns and data are representative and will vary with the specifics of your situation. However, notice the absence of very high-angle radiation on any band. Moreover, even though the gain is almost always less than that of a 135' doublet, the patterns are smoother, with fewer and shallower nulls. For limited spaces, the 3/8 wl inverted-L may be a good choice for an all-band general operating antenna.

+
+ 80 Meters +
+
+ +
Center-Fed
+ Gain: 1.31 dBi
+ T-O Angle: 52 degrees
+ Feed Z: 25 - j400 Ohms
+
+ +
Base-Fed
+ Gain: -0.15 dBi
+ T-O Angle: 31 degrees
+ Feed Z: 125 + 480 Ohms
+
+ 40 Meters +
+
+ +
Center-Fed
+ Gain: 3.14 dBi
+ T-O Angle: 32 degrees
+ Feed Z: 220 + j795 Ohms
+
+ +
Base-Fed
+ Gain: 5.99 dBi
+ T-O Angle: 40 degrees
+ Feed Z: 70 - 220 Ohms
+
+ 30 Meters +
+
+ +
Center-Fed
+ Gain: 4.87 dBi
+ T-O Angle: 24 degrees
+ Feed Z: 5680 - j2540 Ohms
+
+ +
Base-Fed
+ Gain: 5.27 dBi
+ T-O Angle: 27 degrees
+ Feed Z: 1440 + j625 Ohms
+
+ 20 Meters +
+
+ +
Center-Fed
+ Gain: 4.32 dBi
+ T-O Angle: 23 degrees
+ Feed Z: 130 - j400 Ohms
+
+ +
Base-Fed
+ Gain: 4.28dBi
+ T-O Angle: 24 degrees
+ Feed Z: 235 + j350 Ohms
+
+ 17 Meters +
+
+ +
Center-Fed
+ Gain: 5.62 dBi
+ T-O Angle: 14 degrees
+ Feed Z: 360 + j990 Ohms
+
+ +
Base-Fed
+ Gain: 6.38 dBi
+ T-O Angle: 16 degrees
+ Feed Z: 145 - j35 Ohms
+
+ 15 Meters +
+
+ +
Center-Fed
+ Gain: 5.31 dBi
+ T-O Angle: 12 degrees
+ Feed Z: 1550 - j2330 Ohms
+
+ +
Base-Fed
+ Gain: 6.16 dBi
+ T-O Angle: 44 degrees
+ Feed Z: 785 - j480 Ohms
+
+ 12 Meters +
+
+ +
Center-Fed
+ Gain: 6.96 dBi
+ T-O Angle: 33 degrees
+ Feed Z: 150 - j245 Ohms
+
+ +
Base-Fed
+ Gain: 7.17 dBi
+ T-O Angle: 41 degrees
+ Feed Z: 450 + j405 Ohms
+
+ 10 Meters +
+
+ +
Center-Fed
+ Gain: 6.91 dBi
+ T-O Angle: 9 degrees
+ Feed Z: 390 + j920 Ohms
+
+ +
Base-Fed
+ Gain: 6.88 dBi
+ T-O Angle: 10 degrees
+ Feed Z: 165 - j5 Ohms
+

Updated 10-15-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Lower, HF Multi Band


+ + diff --git a/content/gup/gup27-1.gif b/content/gup/gup27-1.gif new file mode 100644 index 0000000..a6b7d38 Binary files /dev/null and b/content/gup/gup27-1.gif differ diff --git a/content/gup/gup27-2.gif b/content/gup/gup27-2.gif new file mode 100644 index 0000000..03b1069 Binary files /dev/null and b/content/gup/gup27-2.gif differ diff --git a/content/gup/gup27-3.gif b/content/gup/gup27-3.gif new file mode 100644 index 0000000..479cdd6 Binary files /dev/null and b/content/gup/gup27-3.gif differ diff --git a/content/gup/gup27-4.gif b/content/gup/gup27-4.gif new file mode 100644 index 0000000..24eb2b9 Binary files /dev/null and b/content/gup/gup27-4.gif differ diff --git a/content/gup/gup27.html b/content/gup/gup27.html new file mode 100644 index 0000000..d742c6a --- /dev/null +++ b/content/gup/gup27.html @@ -0,0 +1,86 @@ + + + + + + Differentiating Among Many Types of Grounds + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

27. On the Ground
+ or Differentiating Among Many Types of Grounds

+
+
+

L. B. Cebik, W4RNL

+
+

For a series with the title, Antennas from the Ground Up, we have said very little about the ground itself. That is close to heresy, and something that we shall begin to correct with this general note about grounds and grounding.

+

We are very careless with the ground. We tend to treat it as a single homogenous entity. In simplest terms, that means that we think about the ground in the same way, no matter in what radio context it appears. That habit can lead to trouble, since a satisfactory ground in one context may be no ground at all in another. Such thinking often leads to confusion-- including the use of confusing terms--replete with terms like "counterpoise," "ground plane," and others.

+

So let's go back to the beginning and begin sorting out some grounds and ground systems. First, a fundamental distinction. The very term "ground" has a built in confusion, since it is commonly used in the context where "common" or "common bus" should be used.

+

For example, we refer to a "chassis ground" (and this is accepted practice). However, the chassis ground is only the circuit common against which measurements are made. It also offers us a connection point for placing the chassis in common with the earth (often called an "earth ground"). As the figure shows, we use separate schematic symbols in the U.S. to differentiate chassis ground from earth ground.

+
+ +
+

Without some connection external to the chassis, the entire circuit might be--relative to the earth--floating or ungrounded.

+

Here are some rough and ready distinctions among grounds of relevance to HF radio work.

+

G1. The DC and static discharge ground: This is the ground of long ground rods by which we ensure that DC, small static charge build-ups, and power line AC are shunted to ground. Our station ground strap gets into the act here, because we make a common ground for all cases, keeping them at the same potential, hopefully ground potential if our distance from the rod into the earth is not too long.

+

For many purposes, the DC and static discharge ground rod is also an AC power safety ground. Hence, we often use the power company ground rod as a reference, connecting the station ground bus to it either directly or indirectly (via the "third" wire of the house wiring or a copper cold water pipe). For maximum safety relative to house power, a ground rod as near to the station equipment as feasible is always in order.

+

G2. Circuitry common bus (ground): There is a very important difference between a circuitry common and an earth ground. Sometimes we have learned this the hard way with shocks and tingles. As we initially noted, a circuitry common--or chassis ground--does not ensure an earth ground. In some kinds of cases, we may in fact need to keep some circuitry commons isolated from others. For example, many low-voltage power supplies intentionally leave the DC side of the circuit (relative to the power transformer) floating so that the supply, with suitable external contacts, can be used to provide either positive or negative voltages.

+

G3. Lightning ground: Lightning strokes and other sudden high voltage and high current impulses require more attention than G1-type grounds. The details of a satisfactory, equipment-protecting grounding system for lightning is more complex than that required for simply preventing the wind from building a static charge on our dipoles.

+

Truly safe operation during an electrical storm--or even safe conditions for inactive equipment--is itself a complex subject requiring extensive study and application of principles, techniques, and devices to each given station situation. In general, we can note two key ideas. First is the use of heavy, very low resistance interconnecting wiring to ensure that everything within the protective system remains at the same common potential as everything else, even in the face of sudden surges. Second is the use of devices to cut off or bypass spikes and surges, thus protecting our equipment. Essential to this process is bypassing the unwanted energy to the earth as efficiently as possible. This requires many regularly spaced long ground rods and heavy interconnecting cable or strap. The complex nature of lightning itself makes the design of an adequate lightning protection system a very specialized field of study.

+
+ +
+

G4. RF ground: Effective RF ground also requires attention to many details. Deep rods, while useful, may be less effective as RF grounds than we previously thought, and the U.S. Army developed a system of perimeter straps and a sequence of shorter rods to effect a satisfactory overall station RF ground, as sketched (with many missing elements) above. RF paths to and from ground via transmission lines, circuitry-to-case connections, common mode paths, and numerous other sources are receiving increased attention both by those who build equipment and by those who assemble operating stations.

+

There are many elements of a good RF ground system that are compatible with the elements of a good lightning-protection ground system. The use of long rods and a perimeter bus might serve both purposes. However, we should not assume without adequate planning that one system is doing the work of two.

+

We might extend this list--not to mention subdivide it. But let's turn to a couple of new categories created out of one old one. Both have to do with antennas.

+

We tend to think of the ground relative to an antenna as a single ground. Hence, we tend to lump together the ground from which signals reflect to contribute to antenna far field patterns and the ground directly under a monopole antenna. The "only" difference is their relative distance from the antenna itself. However, let's see where separating the two ideas leads.

+

G5. Far-field reflective ground: The ground quality is usually specified in terms of conductivity (given in Siemens or millisiemens per meter) and a dielectric constant (permittivity). ON4UN did some modeling with some vertical radiators that suggests the ground kicks in as a reflective medium somewhere around 2 and a half wavelengths from the antenna--possibly more for highly elevated antennas. Although the ground immediately under the antenna has some effect on antenna effectiveness relative to far field patterns, the effect is small (unless the ground is needed to complete the antenna). Dipoles, for example, exhibit only small gain changes as the quality of soil is ranged from very poor through very good.

+

Do not confuse ground quality with terrain considerations. The quality of ground at varying distances from an antenna is only one factor among many with which terrain evaluation is concerned. Slope and interfering objects are samples of other factors that go into terrain evaluation for determining the ultimate elevation pattern for a given antenna and site.

+

Self-contained vertically polarized antennas, running from the vertical dipole to complex arrays like the bobtail curtain, exhibit far field radiation properties with respect to ground similar to those of dipoles and other horizontally polarized antennas at HF. The surface wave of an HF antenna is small, relative to the sky wave. Losses may be slightly higher than with a high horizontal antenna, but generally are not significant.

+
+ +
+

G6. Antenna-completion ground: Monopole antennas are generally analyzed as having their missing pole (relative to a dipole) within the ground. This is often pictorially presented as an "image" antenna sticking straight into the earth. While this portrayal allows the solution to certain basic equations, it is actually a very poor picture of what is going on.

+

It is the surface volume of the ground that provides the completion of the antenna. Signals penetrate the ground to depths that vary directly with wavelength and inversely with frequency. However, even with a monopole, the penetration does not act like a spear into the ground.

+

A more correct picture is a surface area (with some depth) around the monopole. The conventional radius of this surface is about 1/4 wl. Since even the best soil is lossy compared to conductors, we lay screens and radials under the soil to improve its conductivity. Somewhere between 60 and 120 radials approaches the conductor saturation point of most soils. This is the most traditional ground plane.

+

Of course, we can also elevate the ground plane. A number of investigators (nicely referenced by ON4UN) have discovered that even a few feet of elevation can improve the performance of a monopole over that obtainable with buried radials.

+

Another interesting phenomenon is that rooftop monopole vertical antennas do not seem to benefit from littering the roof with 60 to 120 radials. 4 to 8 seems to be enough to achieve all the performance of which the antenna design is capable. Experimenters have also discovered that the best length for radials is slightly less than 1/4 wl. Of course, these were elevated radials. Moreover, if we model a monopole with radials in free space, it does not care what its orientation is.

+

What Kind of Ground are We Talking About? This is a key question to ask whenever you encounter talk of ground. Very often, terms are confused, and the speaker may misinterpret a visible structure for a function. A perimeter RF ground system might look from the surface like a lightning protection ground but be wholly inadequate to the task.

+

Let's take a closer look at another kind of example. In the past two episodes, we examined 1/2 WL and 3/8 WL inverted-L antennas. The base-fed design, with the associated L-network tuner, is most interesting to us here.

+
+ +
+ 
         No Ground Plane                  10-Radial Ground Plane
+Freq.   T-O Ang   Gain    Feed Z        T-O Ang    Gain      Feed Z
+ MHz    degrees   dBi     R+/-jX        degrees    dBi       R+/-jX
+3.7     31        -0.15    125+480      31         0.52       100+480
+7.15    40        5.99      70-220      40         3.33       150-260
+10.1    27        5.27    1440+625      27         5.19      1400+660
+14.15   24        4.28     235+350      25         3.87       325+420
+18.1    16        6.38     145-35       16         5.80       160-40
+21.2    44        6.16     785-480      43         5.96       880-570
+24.9    41        7.17     450+405      41         7.10       480+395
+28.5    10        6.88     165-5        10         6.02       205-5
+
+ 3/8 WL Base-Fed Inverted-L With and Without a Ground Plane: Modeled Values
+

The table lists modeled values for the antenna system over all of the HF ham bands. In one case, the antenna uses no ground plane, but the ground beneath it is average (conductivity = 0.005 S/n; dielectric constant = 13). In the other case, a modest ground plane of 10 radials has been added, with the same soil quality. The ground plane chosen is for many hams larger than one that might be installed, since the average is 4-6 radials. Still, it is far smaller than many vertical antenna experts recommend (60-120 radials).

+

Except for the lowest band, the ground-plane system, consisting of 1/4 WL radials, actual decreases performance on almost all of the bands. At the same time, for antennas that are equally self-complete, one often hears claims to the effect that the antenna operated poorly until some radials were added. Such claims are often accompanied by further reports that performance did not improve with the addition of further radials. Moreover, the addition of the radial system did not affect antenna resonance. Such claims are not consistent with either good theory or good practice associated with ground plane systems used with 1/4 WL monopole systems.

+

What's going on here? The answer is quite straightforward. What the L-network for this inverted-L requires--as do many other types of self-complete antennas mounted near the ground and base-fed--is a good RF ground relative to the source. A single ground rod may or may not provide the necessary RF ground. However, a few radials might do the job in some instances. In such cases, their length and position is likely to be highly non-critical.

+

Our bad habits lead us to refer to these radials as a ground plane, when in fact they provide no antenna-completion function at all. Instead, they provide the rudimentary conditions of an adequate RF ground to ensure antenna operation, especially when receiving.

+

The table shows representative figures for the subject antenna with just a good ground and with a radial system. The good RF ground is sufficient for good antenna performance. Without the good RF ground system, voltages across the antenna side of the L-network tuner may float and not vary with reference to a standard value, namely, earth ground. Voltage swings, upon which reception is based at the other end of the coaxial cable, will likewise not be as large and signals will be weak.

+

There are many other important reasons for having a good RF ground systems for an amateur station--too many to list here. As well, it is important that all of the other types of grounds be studied and improved to the highest degree possible. The listing has only scratched the surface--and not very deeply--of this fundamental subject.

+

However, in the process of evaluating our ground systems, it is equally important that we distinguish among the grounds that we are investigating. The history of radio (including amateur radio) is full of reports of techniques that seemed to fulfill a purpose, with the later discovery that how it did the job was not fully understood at the time. The result has been the adoption of terms that later proved inapt but continued in common usage.

+

The lesson then is not to get lost in short-cut talk and inexact terms. Think through every aspect of your ground systems and be certain each is the best that you can implement.

+

Updated 11-15-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Inverted L, Vertical


+ + diff --git a/content/gup/gup28-1.gif b/content/gup/gup28-1.gif new file mode 100644 index 0000000..96afa6e Binary files /dev/null and b/content/gup/gup28-1.gif differ diff --git a/content/gup/gup28-2.gif b/content/gup/gup28-2.gif new file mode 100644 index 0000000..ffa83d3 Binary files /dev/null and b/content/gup/gup28-2.gif differ diff --git a/content/gup/gup28-3.gif b/content/gup/gup28-3.gif new file mode 100644 index 0000000..4bb19f2 Binary files /dev/null and b/content/gup/gup28-3.gif differ diff --git a/content/gup/gup28-4.gif b/content/gup/gup28-4.gif new file mode 100644 index 0000000..d2248a9 Binary files /dev/null and b/content/gup/gup28-4.gif differ diff --git a/content/gup/gup28-5.gif b/content/gup/gup28-5.gif new file mode 100644 index 0000000..5620737 Binary files /dev/null and b/content/gup/gup28-5.gif differ diff --git a/content/gup/gup28.html b/content/gup/gup28.html new file mode 100644 index 0000000..b8329a2 --- /dev/null +++ b/content/gup/gup28.html @@ -0,0 +1,79 @@ + + + + + + Why Parasitic Beams Work + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

28. Coupling
+ or Why Parasitic Beams Work

+
+
+

L. B. Cebik, W4RNL

+
+

We know that Yagi-types antennas work well. But most of us do not have a basic understanding of how or why they work like they do. We buy them and trust the manufacturer. Or we build one from an article and trust the writer to have done his design work well. We make contacts with them and marvel at their gain and front-to-back ratios. But we still have only a fuzzy idea of how they do what they do.

+

Let's break with tradition and get to know the parasitic beam a little better. To get well-acquainted with these antennas, we shall have to use some terms that pop up only rarely in basic antenna discussions. (They should appear more often than they do.) We shall discuss near and far fields. We shall see some of the effects of mutual coupling. And finally, we shall look at one more aspect of antennas besides the usual parameters of gain, front-to-back ratio, and feedpoint impedance: we shall pay close attention to current magnitude and phase on the elements.

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Finally, we shall discover that all of these terms are closely inter-related.

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Let's begin with the simple dipole, the left-hand sketch in Fig. 1. The dipole we shall use as our example is set for 14.175 Mhz and uses 1" diameter aluminum tubing. All the rest of the antennas we shall look at use the same frequency and the same material. However, the principles apply to any dipole of any material on any band. Since we are working on general principles, we shall place our antennas in free space as an environment.

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The dipole in question is 397.4" long and is resonant at 14.175 Mhz. The feedpoint impedance is 71.9 Ohms with no reactance.

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The antenna produces electric and magnetic fields that we usually divide into three kinds. The far field, a function of the electric lines of force, produces the energy that we receive in our own systems. The near field is a bit more complex. There is a radiating near field that extends a little ways from the antenna. This is the field with which we are environmentally concerned for our own safety and the safety of others. Finally, there is the reactive near field, sometimes called the induction field, because it is the product of the antenna's magnetic field or lines of force. Although the radiation fields are never excluded from the workings of a parasitic beam, the induction field is crucial to beam operation.

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If you examine the right-hand sketch of Fig. 1, you find two dipoles identical to the one we just examined. We have spaced them apart, but not too far apart. Notice that we feed both antennas. Now the question is what their feedpoint impedances might be.

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The answer is this: it depends on how far apart we space them. Here is a table of feedpoint impedances for each of the two dipoles (without changing their length relative to the single dipole) when we place them at different spacings, expressed as fractions of a wavelength. For ease of reading, I have rounded the values of the impedance to integers.

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Space      Feedpoint Impedance
+ wl         R +/- jX Ohms
+1/16        147  + j  7
+1/8         135  - j 10
+3/16        122  - j 23
+1/4         108  - j 32
+5/16         93  - j 37
+3/8          79  - j 37
+7/16         67  - j 34
+1/2          57  - j 28
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Notice that each dipole affects the feedpoint impedance of the other, and the effect is more radical as the spacing between antennas decreases. We call the phenomenon mutual coupling. Each antenna has its own energy to radiate plus some of the energy received from the other antenna. Some of that energy is from the radiation as we usually think of it, but at these close spacings, much is from the coupling of magnetic fields associated with the reactive near field.

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Now, let's go to Fig. 2, where we feed only one of the two elements. We shall once more begin with the left-most antenna design, which again uses our two original dipoles. However, only one of them is now fed. What happens in this case?

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First of all, we get an antenna pattern that looks like Fig. 3. With a front-to-back ratio of only 1.3 dB, there is not much beam action. However, notice the gain value: nearly 6.3 dBi. The gain comes from the fact that part of the energy of the driven element is coupled to the undriven element, which then radiates that energy. Part of that energy contributes to the combined radiation that gives us the gain.

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Another part of that energy is coupled to the driven element to be radiated along with the energy from the source. In other words, we have mutual coupling, even though only one element is driven. How do we know? One indicator is that the feedpoint impedance of the driven element is 17 + j 8 Ohms. This value is nothing like the value associated with a single dipole.

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The next question is why we get such a poor beam pattern with almost no front-to-back ratio. For the answer to this question, we must look at the current at the center of the two elements. If we arbitrarily set the current on the driven element to a value of 1 with a phase angle of 0 degrees, then we shall discover that when the two element are 1/8 wl apart, the current magnitude at the center of the rear element is about 0.88 with a phase angle of 176 degrees.

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When elements are 1/8 wl apart, we can achieve a very high front-to-back ratio (and still have good gain) when the rear element has a magnitude of almost exactly 1.00 (relative to the current on the driven element) and a phase angle of just about 135 degrees. As we get further away from these figures, the front-to-back ratio deteriorates, just as in Fig. 3.

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Every change in element spacing will require a different rear element current phase angle for maximum front-to-back ratio. We shall look more closely at those requirements in a future column. For the moment, let's retain our 1/8 wl spacing (about 208.2" for our test frequency of 14.175 Mhz). Is there anything that we can do to improve the front-to-back ratio apart from changing the spacing?

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We can change the length of the elements. As we change element lengths, the relative current magnitude and phase angle on the undriven element will change. Even here, we have two directions in which we can move.

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First, look at the middle diagram in Fig. 2. This is a classic driver-reflector Yagi design. With a reflector that is about 419" long and a driver that is about 386.4" long, we can maximize the front-to-back ratio for the fixed spacing we have chosen. The azimuth pattern for this arrangement appears in Fig. 4.

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The 11 dB front-to-back ratio is a big improvement over initial parasitic design. Notice that to achieve this value, we had to lengthen the reflector considerably. At the same time, we shortened the driven element to restore it to resonance. The feedpoint impedance of this model is 34 Ohms with no reactance'a typical figure for antennas of this general design.

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Now let's look at the rear element current (always taken at the element center, which corresponds to the centered feedpoint of the driven element). The relative current on the rear element is 0.67 with a phase angle of 143 degrees. Although the magnitude is lower than for the first parasitic design, the phase angle is much closer to the ideal.

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However, we have all seen designs of multi-element Yagis and other antenna types with higher front-to-back ratios. Unfortunately, we have done just about all we can do with this design to maximize the front-to-back design while keeping the spacing at the 1/8-wl mark. Lengthening or shortening the reflector from the given mark will decrease the front-to-back ratio, and changing the length of the driver will have far more effect on the feedpoint impedance' especially the reactance'than it will have on the other performance factors. In fact, for a driver-reflector design, 1/8 wl spacing yields about the best front-to-back values we can obtain from a 2-element parasitic beam of this configuration.

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Alternatively, we can let the driven element be longer than the undriven element, as in the right-most sketch in Fig. 2. In this case, the antenna becomes a 2-element driver-director type of Yagi. The listed dimensions (again, with a constant 1/8 wl spacing) were chosen for maximum performance. With a driver that is 406.8" long and a director that is 377" long, we end up with a resonant antenna. The feedpoint impedance is just about 36 Ohms, with no reactance.

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Note that the two elements in this configuration are shorter than those used in the driver- reflector design. To make a driver-director design, we cannot simply swap the element we drive. We have to redesign the antenna completely.

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At the spacing we have selected, the performance of the antenna is almost identical to the performance of the driver-reflector design at 14.175 Mhz, asshown in Fig. 5. The relative current on the director is 0.75 with a phase angle of -146 degrees. That is equivalent to having a phase angle of 0 degrees on the forward element and an angle of 146 degrees on the rear element.

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Unlike the driver-reflector design, for which 1/8 wl is close to the ideal spacing for a maximum front-to-back ratio, the driver-director design benefits from closer spacing. Free-space gain can approach 7 dBi, and the front-to-back ratio can exceed 20 dB, but at a cost. The resonant feedpoint impedance drops very rapidly to low values that may be difficult to match to 50-Ohm coax. More significantly, the operating bandwidth of the antenna becomes narrower as we decrease the spacing. Hence, the high values for gain and front-to-back ratio are good only over a very narrow portion of any band. For general operation, the reflector-driver version of the Yagi is usually the design of choice.

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With only two straight elements, we are limited in our ability to improve the front-to-back ratio. There are some techniques we can apply to achieve a more ideal current magnitude and phase angle on the rear element. One of them is to feed both elements, usually using a phasing line to achieve nearly ideal relative current conditions on the two elements. Alternatively, we can bend the ends of each element toward its counterpart and introduce additional coupling between element ends. This latter technique is the basis of the Moxon rectangle, an antenna that achieves nearly ideal rear-element current magnitude and phasing and which has a very high front-to-back ratio'at only a small cost in gain.

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However, for this installment, it is sufficient for us to get a feel for how relatively close-spaced elements mutually couple when at least one of them is driven. One very significant consequence of the coupling is the presence of a relative current magnitude and phase angle on the undriven element. For any given spacing, the closer the current values to the ideal, the higher the front-to-back ratio.

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Updated 04-30-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

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Topics: Yagi


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ANTENNAS FROM THE GROUND UP

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29. Phased In and Out
+ or Interesting Alternatives to the Yagi

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L. B. Cebik, W4RNL

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In our last episode, we looked (all too briefly) at some of the basic concepts underlying the operation of parasitic or Yagi beams. We noted the importance of near and far fields, as well as examining what mutual coupling was all about. Finally, we peeked at the idea of relative current magnitude and phase between 2 elements, one fed with a signal, and the other energized by mutual coupling. Although very far from the whole story of Yagi antennas, it is a start from comparatively basic ideas.

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Let's continue our look at the relative current magnitude and phasing among elements. By keeping an eye on these quantities, we can get an insight into some alternative antenna designs and perhaps also see how the whole family of 2-element beams is interrelated. The kinship may remove some of the mystery surrounding antenna names like "ZL-Special," "HB9CV," and "Moxon Rectangle."

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Fig. 1 will be one key to keeping track of current magnitudes and phase angles. In the typical 2-element array in which one element is fed and the other is energized via mutual coupling, we track the current magnitude and phase at the center of each element (the circles in the figure). Even if we fed both elements separately or if we energized the 2 elements from a third source, we would normally use the element center as our point of reference. For this little excursion, we shall not worry about the exceptions to our rule of thumb.

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Last time, we saw that, for any given spacing, there was a limit as to how much we could change the relative current magnitude and phase just by adjusting the 2 element lengths. This action alone would not yield much more than 11 dB of front-to-back ratio with the elements 1/8 wl apart.

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There is a technique we can use to obtain a better front-to-back ratio. We can feed both elements. In fact, we can by a number of means feed each element with a specific value for either the magnitude or the phase or both. To see how this might work, let's perform a small experiment.

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Fig. 2 shows two 10-meter arrays. We shall not be concerned with how well they perform. Our interest in them begins with the fact that if we feed only one element, each array is resonant. What is also interesting to us is the fact that one array uses equal-length elements, while the other uses unequal- length elements. This difference gives us two (of an endless number of) possibilities for arrangements.

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Now let's feed both elements. We shall arbitrarily set the current magnitude on the forward (upper) element in each case to a magnitude of 1.0 and a phase angle of 0.0 degrees. Then, we shall feed the rear (lower) element of each array with a current that is variable in both magnitude and phase angle.

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The goal of the experiment is to find the exact current and magnitude that produces the maximum front-to-back ratio for each array. Actually, we can perform each maneuver with greater and greater precision at least in theory so that we end up with an indefinitely large ratio. When I performed this task on antenna modeling software, I stopped when the front-to-back ratio exceeded 50 dB. This is well beyond what we would need in practice, but it helped me create some interesting graphs.

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Now let's add one more variable into the mix. We shall vary the spacing between the elements for each array. Since most 2-element arrays or beams are well under « wl from front to back, I chose to vary the spacing in 0.05 wl increments from 0.05 wl up to 0.40 wl.

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What I wanted to find out for these two slightly different arrays is how the current magnitude and phase angle on the rear element (relative to the preset value on the forward element) might vary as we changed the spacing. These (and a number of similar) exercises proved to be very instructive.

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One discovery is that for any combination of element lengths and spacings, there will be a specific value of relative current magnitude and phase angle on the rear element that will produce the deep rear null. That set of values will vary if we change the spacing or if we change the length of one or both elements. In other words, there is no general magic number for either how much current, or at what phase angle it is, on the rear element, relative to the forward element.

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Each antenna configuration will have a specific pair of values that yields the maximum front-to-back ratio. If we look at Fig. 3, we can see how the values vary with spacing for our two sample antenna arrays. Let's start on the right axis with the current phase. Notice that as we change spacing, the required phase of the rear element current changes. Since both of our antennas are near resonance, the two phase curves overlap each other. Had one of them been well off resonance, the lines would have been further apart.

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Since the two arrays have different element lengths, we should expect at least the current magnitude required for a maximum front-to-back ratio to be different and we can see the difference. The two curves track each other as we change the spacing, but at quite different current magnitudes.

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Very often, phased arrays are set up to produce the maximum front-to-back ratio. This applies often to phased arrays of vertical antennas. But it also applies to some horizontal designs, such as the ZL-Special. This antenna uses a length of transmission line between elements. Among its other properties, a transmission line is a continuous transformer of voltage, current, and impedance. When we construct "phased" arrays, we are most interested in the transformation of the current magnitude and phase, relative to the forward element, where the phase line, the forward element, and the feedline join.

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By choosing the right kind of line considering its characteristic impedance and its velocity factor and by choosing the right length, we can often get close to the best level of transformation to feed the rear element with the right current magnitude and phase angle. Here "right" means the best values to maximize front-to-back ratio, given the element spacing and lengths. Transmission lines come in only a small range of characteristic impedances. So if a certain element arrangement will not yield the deep rear null, we can change element lengths or the spacing until some useable line length does the job.

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Of course, the absolute maximum front- to-back ratio occurs over only a tiny frequency range, and away from the test frequency, the value drops into the ordinary range say about 20 dB. In addition, maximum front-to-back ratios do not tend to coincide with maximum gain that the antenna might give. Some antenna designers look for a balance of properties.

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Before we can look for the balance, we should find out how the rear element current magnitude and phase angle affect the maximum antenna gain for our small arrays So let's do a second experiment: find the rear element current and phase angle that will give us the highest gain from the element lengths we originally set up, but let's vary the spacing along the way.

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Fig. 4 gives us an initial look at how the current magnitudes and phase angles change as we increase the spacing from 0.05 wl up to 0.40 wl. Once more, the phase angle changes considerably as we change the amount of spacing between the two elements. Yet, because the two antennas are near resonance, the curves for the required phase angle closely match each other.

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In contrast to the phasing situation, the relative current magnitude required by the rear elements on each of the antennas for maximum gain differs for the two configurations. There is an average of more than 10% difference between the two levels.

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However, what is interesting is that both magnitude curves are almost flat. Changing the spacing of either array does not change the ideal current magnitude by much, but the required phase angle will change.

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There is no need to memorize any of this. Instead, simply develop an appreciation for the fact that the relative current magnitude and phase on the elements of a beam largely account for its performance. These values are affected by element lengths and spacing, and every configuration requires a careful study to find the values that give the best results.

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Sometimes, those results are a compromise between maximum gain and maximum front-to-back. The HB9CV is an phased array that purposely uses intermediate values to obtain good 2-element gain with a good front-to-back ratio across most of any ham band for which it is designed. Like the ZL-Special, it uses a phasing system , but it consists of separate lines to the forward and rear elements, joined in the center.

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Last time, we noted that there is a limit to how closely we can approach our ideal front-to-back phasing requirements just by adjusting antenna element lengths while avoiding the use of a phasing system. There is an antenna design that can do much better in the front-to-back department than the common Yagi with its linear elements.

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In Fig. 5 we find the general outline of the Moxon rectangle. It is capable of better than 30 dB front-to-back ratio at its design frequency, whether we are talking about a wire version for 80 meters, a tubing version for 20 or 10, or one made from rods for 2 meters or higher. Let's see how the Moxon is able to improve on the Yagi without losing more than a couple of tenths of a dB in gain.

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Like our Yagis, the Moxon has parallel wires, one forming the driver and the other forming a reflector. We would take our current magnitude readings at the centers of these element sections. Like any other antenna where wires are parallel (or nearly so), there is a great deal of mutual coupling. Hence, a good part of the radiation from the Moxon is produced by standard parastic means (meaning just like a Yagi).

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However, the Moxon's parallel wires are only about 3/4ths full Yagi length, with the ends bent around. The driver ends point at the corresponding reflector ends. The driver length consists of length A plus twice the length of B, and usually, we choose the length to be resonant. The reflector overall length is length A plus twice length D. We choose this length to place maximum front-to-back ratio on the desired frequency.

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"C" is the critical dimension. It sets the amount of the second kind of coupling involved in the antenna. The "tip" coupling (sometimes called "capacitive" to distinguish it from the mutual or "inductive" coupling between parallel wires) is set to get maximum front-to- back ratio. We then juggle the various dimensions to get a rectangle with the desired feedpoint impedance.

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The combination of couplings allows the rear element to reach a set of current magnitude and phase angle values that comes close to the ideal for maximum front-to-back ratio. It does so without using a second (or phased) feed to the rear element. Magnitude values near to 1.0, phased at about 140 degrees, are common. If you look back at Fig. 3, you will see that these are close to ideal front-to-back values for a resonant array of element that differ in length. A most interesting array, indeed!

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Updated 06-21-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

+

Return to Amateur Radio Page

+

Topics: Moxon, Phased Array, Yagi


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ANTENNAS FROM THE GROUND UP

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3. Playing the Angles
+ or Azimuth, Elevation, and Antenna Modeling

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L. B. Cebik, W4RNL

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+ One of the goals of this series is to help you answer your own antenna questions. There are many tools available to help you do this. For new antennas you construct, there are antenna analyzers, SWR meters, and the like. For theory and construction ideas, there are books galore (not to mention articles like these). Finally, but very importantly, there is antenna modeling software. +

First, you have to like your computer. Second, although there are some basic modeling cores for MAC, modeling is a PC business, especially if you want to use one of the commercial versions. Third, you have to learn how to ask the modeling program good questions and read its answer intelligently. Although I cannot make you like your computer, I can tell you where to find software and how to get started in using it wisely.

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Even if you do not intend to buy or download a modeling program, you should continue reading. When you are done, you will at least have a better grasp of what all those antenna plots and graphs in the magazine articles are trying to tell you.

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What's Available and Where

There are many types of antenna modeling programs. Modeling an antenna is simply calculating some of the antenna properties. There are BASIC programs in HAMCALC for designing a number of different antennas. (Some are more accurate than others.) There are special purpose programs, like YAGIMAX, that can help you optimize certain kinds of antennas. +

However, when most folks speak of antenna modeling these days, they are referring to the Numerical Electromagnetics Code, either in its FORTRAN version (NEC) or its offshoot BASIC version (MININEC). These programs are very powerful "method of moments" calculation machines that, within limits, can produce a lot of accurate information about antennas.

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Both NEC-2 and MININEC are public domain programs, so you can download them for free. However, you have to design your own user interface to get information about your antenna in and get calculation results out. Like this:

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+ Figure 1: An SWR curve of a model. +
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Figure 1 told me that I cut the 40-meter dipole model too long, so I pruned a number rather than a piece of wire.

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Both NEC and MININEC have limitations. NEC-2 cannot handle wires of dissimilar diameters well, but it can deal with antennas close to ground. MININEC is limited to antennas above 0.2 wavelengths above ground and requires special techniques to handle wires that meet at angles. Both have their place, but for wire antennas in the 160-30 meter region, I recommend NEC.

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There are three commercial versions of NEC-2 available to hams for under $90. These are

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EZNEC, by Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007. This DOS program ($89) has a "friendly" user interface by most reports and a 500-segment limit for antenna size.

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NEC/Wires by Brian Beezley, K6STI, 3532 Kinda Vista, San Marcos, CA 92069. This DOS program ($70) uses a different input interface that allows formulas; also with a similar segment limit.

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NEC-Win Basic by Paragon Technologies, 3006 Research Drive, State College, PA 16803. This is the only Windows version of NEC ($75) and uses a spreadsheet style input system.

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Both EZNEC and NEC-Win have "big brothers" for virtually unlimited antenna sizes, and NEC-Win Pro has added graphics capabilities. However, prices are considerably higher.

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All three programs have been designed or tested by hams. I use versions of all three from time to time, along with the MININEC versions of each (ELNEC from W7EL and AO from K6STI, along with NEC4WIN from Orion in Canada and MININEC for Windows from MININEC creators Rockway and Logan).

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What Can I Learn From Models?

Lots! Many purchasers simply try to model the antenna(s) they have and then never use them again. Bad approach. Making good models takes a good bit of experience in playing with the program, and the programs can teach you a lot about different types of antennas in different circumstances. +

First, you create a physical model of the antenna of interest, laying out wires on an X, Y, Z coordinate system, and specifying wire size and material, ground conditions, and other information needed for the analysis. Then the program provides you with (as a start) complete far field information (available graphically or in tables), feedpoint impedance and related data, antenna current levels, and more.

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The numerical data, such as feedpoint impedance and SWR relative to 50 ohms, is easy to interpret. Antenna patterns require a little more effort.

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Let's start in free space, that spherical volume in þouter spaceþ free of all conductive obstructions. Let's place a dipole there and look at its 3-D pattern. It looks like Figure 2, where the wire-line is a highly magnified orienting guide to the antenna position. Since this is a "far-field" pattern, the actual antenna would be too minuscule to see.

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+ Fig. 2. +
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An azimuth pattern is one tracing a horizontal circle around the antenna pattern. We take azimuth patterns at some specified elevation angle. For free space, the angle is typically (but not absolutely always) 0° elevation. Mentally cutting Figure 2 on the flat, which is almost from the bottom left corner to the top right corner, we get the following azimuth pattern:

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+ Fig. 3. Free space azimuth pattern of a dipole. +
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You will recognize the side nulls as corresponding to the side-pucker of the 3-D view. In free space, for a dipole, every slice through the donut would present the same view of the antenna pattern.

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The elevation view of the pattern is a slice vertically through the 3-D pattern. It can be at any specified azimuth angle, but typically we choose the azimuth angle of strongest radiation. Here the angle is either 90° or 270°.

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What determines the 90-270° orientation in part results from how the model was constructed. For a horizontal dipole, you can put the length of the antenna in the X dimension--which gives the pattern in Figure 3--or in the Y dimension--which would change the antenna orientation by 90 degrees. A Y-dimensioned dipole would show maximum radiation in azimuth directions 0° and 180°. (My preference for speed of making alterations is to put the longest or most changeable length in the X dimension. Hence, all broadside patterns will be oriented as in Figure 3.)

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The vertical slice through the donut, of course, would yield a simple circle indicating equal power at all elevation angles. All NEC models presume the principle of reciprocity; that is, the pattern of power radiation equals the pattern of receiving sensitivity.

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Antennas mounted over the ground are more complex, because the portion of the free space pattern representing downward radiation is reflected by the ground back upward in accord with basic optical principles, adjusted by the program for ground losses. The actual amount of ground loss for horizontal antennas does not differ greatly from great soil to very poor soil, so for most purposes, models are taken over average ground. The values of conductivity and the dielectric constant are usual built into the program as defaults.

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Let's put a 40-meter dipole up 70' and look at its 3-D pattern:

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+ +
+
+ Fig. 4. +
+

The exaggerated line represents the antenna wire. Here it passes at the base of the pattern through the bottom-most side puckers. Maximum radiation is broadside to the wire, but at upward angles.

+

The next step is to take an elevation pattern, a vertical slice through the direction of maximum radiation (from lower left to upper right). For this antenna, the angle will again be either 90° or 270° on the azimuth circle.

+
+ +
+
+ Fig.5. Elevation pattern of a 40-meter dipole at 70' height along the azimuth of maximum radiation. +
+

You can likely recognize the center "hump" from the 3-D plot and the upturned ends. Note that there is no radiation at 0° elevation angle because far-field plots are assumed to be so far distant that point-to- point and ground wave radiation are no longer factors that determine the pattern.

+

Creating an azimuth pattern involves choosing an elevation angle above 0°. We may use any number of bases for our selection, but two are most common. One is the angle of maximum radiation to see just what the maximum gain of the antenna may be and how the pattern at that angle looks. The model told me that the angle of maximum radiation (also called the "take-off" angle) is 27°.

+

Figure 6 displays the azimuth pattern of the dipole at its take-off angle. Remember that the pattern is actually a sort of cone, with the center of the pattern circle at the antenna height. The cone slopes upward all around the circle at an angle of 27° above the horizon. You can also see from Figure 6 that the maximum gain is 7.6 dBi.

+
+ +
+
+ Fig. 6. Azimuth pattern of a 40-meter dipole at 70' height at an elevation angle of 27°, the angle of maximum radiation. +
+

A second route to creating an azimuth pattern is to begin with an independent interest in some skip path angle. Suppose, for instance, that you have good reason to believe that the best path to Europe requires a skip angle of 17°. What would the antennaþs pattern look like at that angle?

+
+ +
+
+ Fig. 7. Azimuth pattern of a 40-meter dipole at 70' height at an elevation angle of 17°, the angle of special interest. +
+

From Figure 7, it is clear that the shape of the pattern has not significantly changed relative to the pattern shape at the 27° elevation angle. However, the gain is down considerably. Looking at the 3-D pattern and the elevation pattern, we can see that this new cone slice is taken at an angle of lesser radiation.

+

The lobes and nulls of an antenna over real ground are functions of the phases of the direct or incident waves and the reflected waves as they occur at the same angles away from the antenna. Sometimes they are in phase and add, resulting in gain numbers far higher than the free space gain. We call this a lobe. In other parts of the overall pattern, they are out of phase with each other, partially or wholly canceling the radiation. We call this a pattern null.

+

Is That All There Is?

Individual patterns are very instructive, but they only provide spot data. There are numerous ways to increase the amount of information from models of antennas. +

One way to increase the amount of information in a pattern is to combine several elevation or several azimuth patterns into one graph. For example, if we had combined Figures 6 and 7, the lesser strength of the radiation at the lower angle would have been evident.

+

We can also combine elevation patterns. For example, place a dipole, a 2- element Yagi, and a 3-element Yagi at the same height and combine their elevation patterns in the azimuth of greatest radiation. You will see the evolution of the bidirectional dipole into a pattern with high forward gain and a high front-to-back ratio.

+
+ +
+
+ Fig.8. 10-meter dipole, 2-element Yagi, and 3-element Yagi elevation patterns +
+

A second way to derive more antenna information from a modeling program is to frequency-sweep an antenna. Specify upper and lower frequency limits and the increments for spot checks between these limits. You can produce data on pattern changes, such as where the gain reaches maximum and where the front-to-back ratio (if relevant) reaches maximum. You can also watch the feedpoint impedance, both resistance and reactance, change across the sweep range. Some antenna designs are quite narrow, and one or more of their properties may change drastically even within a ham band. Others are broad and do not radically change any characteristics over wide frequency ranges.

+

Another instructive exercise is to watch the properties of an antenna change with height as you step the model height at regular intervals. Although most programs have frequency sweep capabilities, you will have to increase the model height manually. However, you may discover interesting changes of patterns or the feedpoint impedance along the way.

+

There are innumerable systematic questions you can pose to a modeling program, and the answers you glean can teach you much about antennas. Unfortunately, most antenna modeling program users make a few spot checks of their own antennas and then never open the program again. These folks lose fully 90% of the benefits of the program.

+

I have dwelled on the basics of antenna modeling because much in this series will be derived from them or illustrated by them. In fact, you can make a whole handbook of expectations from them.
+

+
+ +
+

Updated 4-29-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Modeling


+ + diff --git a/content/gup/gup30-1.gif b/content/gup/gup30-1.gif new file mode 100644 index 0000000..9004a9b Binary files /dev/null and b/content/gup/gup30-1.gif differ diff --git a/content/gup/gup30-2.gif b/content/gup/gup30-2.gif new file mode 100644 index 0000000..37fd3e6 Binary files /dev/null and b/content/gup/gup30-2.gif differ diff --git a/content/gup/gup30-3.gif b/content/gup/gup30-3.gif new file mode 100644 index 0000000..69013eb Binary files /dev/null and b/content/gup/gup30-3.gif differ diff --git a/content/gup/gup30-4.gif b/content/gup/gup30-4.gif new file mode 100644 index 0000000..10b638a Binary files /dev/null and b/content/gup/gup30-4.gif differ diff --git a/content/gup/gup30-5.gif b/content/gup/gup30-5.gif new file mode 100644 index 0000000..d690e1e Binary files /dev/null and b/content/gup/gup30-5.gif differ diff --git a/content/gup/gup30.html b/content/gup/gup30.html new file mode 100644 index 0000000..1dcc3cb --- /dev/null +++ b/content/gup/gup30.html @@ -0,0 +1,55 @@ + + + + + + A Collection of Inverted-Vee Patterns + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

30. Victory or Villainy
+ or A Collection of Inverted-Vee Patterns

+
+
+

L. B. Cebik, W4RNL

+
+

A common all-band doublet for smaller ham properties is the inverted-Vee, usually cut to either 135' or to 67' (or thereaboutsþsince the exact dimensions are not critical for an antenna fed with parallel line and an antenna tuner). The question that recurs is whether the Vee þworks as wellþ as the level or flat-top doublet of the same length.

+

The answer depends on 2 factors. One factor is the frequency of use. The other factor is the angle of the Vee wires relative to the level doublet. To see what difference each of these factors make, letþs look at the doublets in Fig. 1.

+

The basic length of the doublet will be 67' for a fundamental frequency of 40 meters. We shall look at both azimuth and elevation patterns for 40, 20, 15, and 10 meters, on frequencies about mid-band in each case. However, the patterns will not change from one end of a band to the other.

+
+ +
+

We shall look at patterns for the level doublet as a sort of basline against which to measure the patterns of the 2 Vee versions. One version will be a moderate Vee that slopes downward only 30 degrees relative to the level doublet. The other Vee version will slope downward 45 degrees. Together, the two Vees will give us a picture of the trend in pattern change for intermediateþor even more radicalþslopes.

+

In some cases, Vee patterns will be weaker, that is, have no lobes as strong as the strongest lobes of the doublet. Does that make the Vee a poorer antenna? Not necessarily. In each case, look also at the shape of the pattern and the strength of the lower angle elevation lobes. It will be the evaluation of all of the pattern features that will tell you which version of the doublet is best for your operation. This assumes, of course, that some kind of doublet is best in the first place. On 40 meters, there is really very little to choose between a flat doublet and a Vee. The elevation angle of maximum radiation climbs upward as we make the Vee slope more radically. It changes from 38 degrees for the flat-top to 46 degrees for the 45-degree Vee. However, in all three cases, the elevation lobe is so vertically broad that the differences are unlikely to make a detectable difference in performance.

+
+ +
+

Likewise, there is a slight difference in the strength of the main lobe broadside to the antenna, which is 50' up at the center in these patterns. A difference of 1-2 dB is not likely to be detected by the user without high-cost lab equipment. (That is why we rarely detect reduced performance due to the lack of antenna maintenance until the antenna falls down.) So on 40 meters, A Vee and a flat-top are about equal.

+
+ +
+

On 20 meters, where the doublet is about 1 wavelength long, we begin to see significant differences. The elevation angles of maximum radiation climb from 19 degrees for the flat-top to 25 degrees for the 45-degree Vee. As well, the gain drops by over 3.5 dB as we increase the slope of the Vee, although most of that drop occurs in the move from 30 degrees of slope to 45 degrees.

+

However, notice the shape of the azimuth patterns. The flat-top shows extremely deep side nulls (off the ends of the wire. The user can look at these nulls as QRM fighters or as directions in which almost no QSOs are possible even under the best propagation conditions. The lesser nulls of the two Vees offer some hope of contacts, although condition might have to be very good to get them.

+
+ +
+

On 15 meters, the situation becomes a good bit more complex, perhaps even more complex than the maze of lobes and nulls in the combined sets of patterns. The flat-top has the strongest lobes by far, although the four best are fairly narrow in width. If these lobes happen to go exactly where you want them to go, then all is well. If not, then they may radiate where no one lives. Antenna orientation is important.

+

The broader patterns of the Vee antennas offer slightly weaker but more uniform propagation in most directions. However, nothing is perfect. Note the elevation patterns, which show almost all radiation to be at higher angles in the 23 to 30-degree range on a dx band that does best when radiation is at much lower angles. The flat-top take-off angle is 13 degrees, just about right if the lobe points at a target.

+
+ +
+

On 10 meters, we have a similar situation to the one on 15 meters. Everything is just a bit more extreme. The flat-top lobes are narrower, but at a nice low 10-degree elevation angle for DX. Unfortunately, the two Vee antennas have lost virtually all of their low- angle radiation: their lowest elevation lobes correspond to the secondary lobe from the flat-top. Hence, the DX potential of the Vees on 10 meters is somewhat dismal.

+

Indeed, it might be better for 10 meters to erect a simple dipole, even one that can rotate. At a 16' length, it can be hidden if need be. It pattern is likely to be superior to either the narrow flat-top lobes of the high-angle Vee radiation. In other words, the idea of 1 antenna for everything may not be best for everyone.

+

Updated 09-28-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Inverted V


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+

ANTENNAS FROM THE GROUND UP

+
+
+

31. Caring for Twins
+ or Handling Parallel Feedlines

+
+
+

L. B. Cebik, W4RNL

+
+

Call it twinlead, open-wire line, or parallel transmission line, the concept is the same: two wires with a constant spacing make up a very useful form of transmission line to convey power from the transceiver or antenna tuner to the antenna (and back) with minimal loss. We use parallel line whenever coax will not do the job, for example, with multi-band doublets and loops where the impedance at the antenna terminals may range from very high to very low.

+

We have all seen the handbook accounts of how to figure parallel line--at least when we have air as the dielectric between the wires. See Fig. 1.

+
+ +
+

The characteristic impedance (Zo) of the line depends on the wire diameter (d) and the center-to-center spacing (S) between wires:

+
+ +
+

But what does this mean in practical terms involving the range of wire to which we have access? In terms of AWG wire sizes and spacing between wires in inches, the table below gives a good sense of what impedance results from what wires and gaps.

+ 
           Parallel Wire Transmission Lines
+
+Wire Size (AWG)         #8      #10     #12     #14     #16
+Wire dia. (in.)         0.128   0.102   0.081   0.064   0.051
+Spacing (inches)        Characteristic Impedance (Zo) in Ohms
+0.5                     246.0   273.7   301.5   329.3   357.1
+1.0                     329.0   356.8   384.6   412.4   440.2
+1.5                     377.6   405.4   433.2   461.0   488.8
+2.0                     412.1   439.9   467.7   495.5   523.3
+2.5                     438.9   466.7   494.5   522.3   550.0
+3.0                     460.9   488.5   516.3   544.1   571.9
+3.5                     479.2   507.0   534.8   562.6   590.4
+4.0                     495.2   523.0   550.8   578.6   606.4
+4.5                     509.3   537.1   564.9   592.7   620.5
+5.0                     522.0   549.7   577.5   605.3   633.1
+5.5                     533.4   561.2   589.0   616.8   644.6
+6.0                     543.8   571.6   599.4   627.2   655.0
+

Fig. 2 provides a graphic view of the same information. Note that the impedance increases rapidly as we move from 0.5" to 1.0" spacing, but then tapers off. By the time we reach a 3" spacing, the impedance climbs slowly, and we are within the most common region of parallel line Zo values: 400 to 600 Ohms.

+
+ +
+

These values apply only to wire pairs when air is the dielectric (insulation) between them. A few spacers along the way do not materially change the Zo. However, the impedance will undergo significant change if we place a different dielectric between the wires, as in the case of the flat twinlead shown in Fig. 3. The special vinyl has a dielectric constant higher than that of air (1.0) which modifies the calculation of the Zo. As well, the line acquires a Velocity Factor (VF) of less than 1.0 (which open-wire lines closely approximate) with a special consequence. An electrical wavelength of line is now shorter than a physical wavelength of line. To figure a precise electrical wavelength of line, we multiply the physical length of a wave by the VF. Common twinlead has a VF of about 0.8, although it varies with manufacturing quality. To raise the VF, makers invented tubular line, with more air between the conductors.

+
+ +
+

Remember that a transmission line operates by virtue of the very close coupling of fields in each wire that result from current in the line. The currents at any point in an ideal line are equal in magnitude but opposite in phase. Hence, we get no radiation, since the fields cancel, and the energy is simply guided to something, like an antenna or a receiver input, where it can be used.

+

In a parallel transmission line, the strongest field exists between the two wires, but field components surround the wires and the wire pair. In tubular twinlead, the strongest portion of the field has mostly an air dielectric, compared to flat twinleadþs vinyl. Hence, a difference in VF, and a slight differences in losses. If you use twinlead for your parallel transmission line, use the very best quality that you can obtain.

+
+ +
+

If you prefer open-wire or ladder line, you can purchase good quality line, or you can make it yourself. Fig. 4 and Fig. 5 show two common construction methods.

+

When using tubes, rods, or dowels, holes or slots, with a means of locking wires in position, create the most durable line. Almost any non-conductor can be pressed into service, from wood boiled in paraffin to polycarbonate rods (the best material). One can use rods cut from plastic coat hangers, CPVC tubing, and similar materials that are easy to obtain, but at a cost: the ladder-line rungs do create a slight loss, so the better the material, the better the line.

+

One key point is to ensure that the material used is UV resistant, or the separators may grow brittle and break up over time. For this reason, and for its high RF insulation properties, polycarbonate (trade name Lexan) may be among the very best materials to use.

+
+ +
+

You can press other UV resistant materials into service, for example, remnants of vinyl siding. By cutting slats and using the technique in Fig. 5, a very durable line can be formed. However, the more material between lines, the lower the VF.

+

We have been discussing ladder line (open-wire parallel transmission line, to put in all of the words) from the construction perspective. Our goal is to construct the most durable, low loss line that we possibly can. However, unless we exercise good installation practices, we can undo all of the low-loss promised by such transmission lines.

+

We have noted the key factor that governs the installation of any parallel line, whether twinlead or open-wire. Although the fields between the wires are very tightly coupled, they are not confined to just the area between the wires. The fields extended for a considerable distance around the wire pair, perhaps up to several times the space between wires. These fields must not be disturbed, lest we create an imbalance in the current magnitudes and phases between the wires. When the current balance is upset, the differential in current becomes a field that expands without limit, which happens to be the definition of an antenna. Any energy radiated from the line is energy not available to the antenna itself.

+

There are a series of common practices that we need to avoid when using parallel lines. Most of the bad practices arise from hasty or careless installation, and the users often claim that they work--often because they have not compared the results with a proper installation. Sometimes, you cannot know that bad is bad until you have something good with which to compare it.

+
+ +
+

Fig. 6 illustrates some of the worst of the common practices. Placing parallel lines across or along metal, such as gutters, downspouts, aluminum window frames, interior house-wiring or ductwork is an open invitation to couple valuable energy into objects that not only will leave less to be radiated by the antenna, but as well may create RF hazards or irritations in the home or shack. The RF can get into telephones or into the radio gear itself. It only requires a few millivolts to disrupt the operation of keying, VOX, and similar circuits. As well, the RF feedback can add an FM component to a usually clean VFO signal or show up as hum on an audio line.

+

The remaining bad practices are mostly loss sources. Paralleling a line too close to a tree or other support can create line imbalances of lost energy that may vary with the weather. Trees and posts are variable conductors, depending on dampness.

+

Running lines along the ground or under a house in the crawl space may not show up in RF problems in the shack. However, coupling of energy to the ground increases line losses, even if the line is run through a PVC pipe or a similar means of isolating the line from direct ground contact. A through-wall entry may be needed, but it should be as short as possible.

+

Let's finish up on a positive note by listing a number of good amateur practices associated with parallel feedlines. These practices apply to both twinlead and open-wire lines and are sumarized by Fig. 7.

+
+ +
+

First, keep line runs as straight and in the clear as possible. Straight, clear runs are as important indoors as outdoors. Straight is self-evident. Clear means as far from other objects as possible, and in no case less than several times the line spacing away from anything.

+

Of course, we must bring the line indoors. We can use a short through-wall pipe, perhaps with caps that have cuts to keep the line centered. Or we can use a wood or plastic plate with feed-through insulators. The difference in spacing and bolt size of the board relative to the line is not important: it may create a small impedance bump but will minimize losses.

+

Outdoor supports can be of two general types: rings or clamps. We can suspend non-conductive rings (slices of PVC or similar) from limbs and posts to support the line on its way to the antenna. As well, we can create non-conductive guides or clamps that extend outward from tree trunks, posts, or walls to route the transmission line. Be sure to use enough supports.

+

Wherever possible, keep direction changes shallow. Never let the line fold back upon itself or roll it in a coil.

+

At the junction with the antenna, use a strain-relief fixture. A simple insulator may keep the line from being pulled by the antenna wire. However, over a relative short time, the line wires will flex back and forth until they break. A fixture that minimizes the flexing at the junction itself will make the connections much more durable.

+

These general guidelines will tend to give you the most efficient parallel line installation possible. Combined with good line construction, they will provide an effective and durable feed system for most antennas, and especially for multi-band wires.

+

Updated 11-05-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Transmission Line


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+

ANTENNAS FROM THE GROUND UP

+
+
+

32. Pair-ental Problems
+ or When and Which Parallel Feedline to Use

+
+
+

L. B. Cebik, W4RNL

+
+

We have in a past episode looked at how to construct and install parallel transmission lines. However, we have not yet looked at the questions of when we might profitably use such a line in preference to a coaxial cable. Nor have we asked which line to use among those available to be bought or built. Letþs remedy those gaps.

+

Here is an incomplete list of occasions on which you might want to use twinlead or open-wire parallel lines.

+
+ +
+

1. When the antenna presents an impedance that is a close match to such lines. Many terminatedd antennas, such as the rhombic or the T2FD use terminating resistors, as shown, for example, in Fig. 1. Usually, the feedpoint impedance will be a close match to the value of the resistor. Then, you have two choices for feeding the antenna. You can install impedance transformation components at the antenna terminals and run coax to the equipment. Or, you can use an open wire line that matches the antenna to a matching unit in the shack. The rhombic (8 wl long) in the figure with a 600-Ohm resistor shows under 1.3:1 SWR at 600 Ohms from 14 to 28 Mhz, a candidate for use with a 600-Ohm open-wire feedline.

+

2. When the losses need to be minimized on a budget. Hardline coaxial cables rival parallel lines for low losses, but they are expensive and often hard to handle. If the cable run is very long, one might wish to use a parallel line for most of it. I have heard of 50-Ohm beam installations at a long distance from the equipment that use impedance transformers at each end of the line and an open-wire feeder between. The open-wire line goes from the shack entry point to the base of the tower, with coax at either end.

+

3. When the impedances at the antenna terminals may show a wide range of values. This case is perhaps the most common, since it is true of almost all multi-band doublets. The typical doublet may show both resistance and reactance values running from well under 100 Ohms to well over 1000 Ohms. Because any coaxial cable would see a very high SWR on at least some of the bands, losses may well be unacceptably high on those bands. A parallel transmission line with its very low matched loss value will show much lower losses under the same conditions.

+

There are other reasons for using parallel lines, such as handling power levels in the 100 kW to 5 MW range, that apply to commercial operations. We can pass over them. However, we should not pass over the fact that parallel lines require special installation care to ensure that they deliver the promised low losses. Having looked at when we should use parallel lines, we can now turn to the question of which line to use. Let us use as a jumping off point a typical 135' multi-band doublet with a line to an ATU, as in Fig. 2. Which line should we use in this system.

+
+ +
+

Before we can answer this question, we must know what lines are available. The commercially available lines come in 3 general types, each with a different characteristic impedance, construction, velocity factor, and loss value.

+

1. 300-Ohm transmitting twinlead, sometimes flat and sometimes tubular, has a velocity factor of about 0.80 and a loss of about 0.17 dB per 100' at 3.5 Mhz. Remember that line losses increase with frequency. But RG-213 half-inch coax has double the loss of the best 300-Ohm twinlead.

+

2. 450-Ohm window line, a form of flat twinlead with cut-outs to minimize the vinyl between the wires, has a velocity factor of about 0.95 and a 0.1 dB loss per 100' at 3.5 Mhz, down to almost half the loss of 300-Ohm line.

+

3. 600-Ohm open-wire ladder line typically has a velocity factor of about 0.97 or higher and a loss of only about 0.03 dB per 100' at 3.5 Mhz. There are also commercially available ladder lines in the 400-500 Ohm range, and their VF and loss values would resemble those of the 600-Ohm line.

+

In looking at the loss values associated with various kinds of lines, remember that they are figures for a matched conditions, that is, a 300-Ohm resistive load with a 300-Ohm line, etc. Additional losses that result from a mismatch between the load and the line (that is, a high SWR) represent a multiplier on the basic loss value. Let's suppose that a certain SWR value creates 3 times the loss of a matched condition. The coax (RG-213) at 3.5 Mhz with a .35 dB loss per 100' will now show a loss of over 1 dB. The 600-Ohm line will show a loss of under 0.1 dB for the same SWR value.

+

However, there are other reasons besides line losses for selecting among the available parallel lines. Effecting a good match with the ATU in the shack requires that we have values of resistance and reactance that fall within the range of the tuner to match. Our selection of line may have a bearing on the ease and efficiency with which we can get that match.

+

One rough initial guide to the selection of a parallel line impedance for a muti- band antenna (or any other for which the feedpoint impedance may vary over a wide range) is the choose a line characteristic impedance (Zo) that is the geometric mean between the maximum and minimum impedances at the antenna terminals. To get a geometric mean, we simply multiply the minimum value times the maximum value and then take the square root of the result. All we need to know now is the range of values we might encounter.

+

Here is a list of values taken from a model of a 135' #12 AWG copper wire doublet at a height of 50' above average soil. We can use this antenna as an example.

+ 
Freq. (Mhz)                            Feedpoint R +/- jX
+ 3.6                                        75 + j 55
+ 7.15                                     4760 - j1270
+10.1                                        95 - j 330
+14.15                                     4270 - j1005
+18.1                                       125 + j   5
+21.15                                     2330 + j1435
+24.95                                      130 - j 180
+28.5                                      2070 + j1225
+

The list is representative, but not necessarily exactly what any given installation would discover. The 40-meter and 20-meter values are very high, because the antenna is very close to 1 and 2 wavelengths long at those frequencies, respectively.

+

The highest impedance in the table is over 4900 Ohms, while the lowest is about 93 Ohms. The geometric mean is about 677 Ohms, suggesting that a 600-Ohm parallel line would be the transmission line of initial choice.

+

The simple selection guide does not take into account what happens to the impedance along the line and how long the line will be for a given installation. As we have seen in past episodes, the impedance along a line undergoes continuous transformation, with changing values of both resistance and reactance. What emerges at the equipment end of the line is therefore very dependent upon the line length as well as on the impedance at the antenna terminals.

+

Each of the three sample lines that we looked at has a different characteristic impedance. Therefore, for any antenna terminal impedance, the transformations of impedance will be somewhat different for each of the lines. In addition, each line has a different velocity factor. Hence, for any given physical length of line, each of the three lines will be a different electrical length. The transformation of impedance is dependent on the electrical length of the line. There are programs from which we can quickly get an idea of what the equipment end conditions will be for any antenna terminal conditions. TLW, the N6BV program that comes with The ARRL Antenna Book, is one good source, and HAMCALC also has a program (Transmission Line Performance) to do the calculating task.

+ 
Representative Line Lengths and Impedances for the 135' Doublet
+
+Freq.                   Line Values (Zo/VF)
+(Mhz)       300/0.80          450/0.95          600/0.97
+
+A.  50' Feedline
+ 3.6        1175 - j 270       810 + j1190       765 + j1680
+ 7.15        235 + j1030        92 + j 510       145 + j 620
+10.1          40 + j 10         70 - j 180        81 - j 200
+14.15         60 + j 415        45 + j 30         80 - j 10
+18.1         280 + j 265       130 - j 80        140 - j 185
+21.15         35 + j 175       135 - j 470       360 - j 845
+24.95         90 - j 20       1460 - j 705      2800 - j 785
+28.5          35 + j 100      2480 - j 905      1740 + j1335
+
+B.  75' Feedline
+ 3.6         140 - j 270       480 - j 960       735 - j1645
+ 7.15         20 - j 130       175 - j 820       395 - j1235
+10.1         185 - j 525       710 + j1300      1070 + j1970
+14.15         30 + j 220        75 - j 370       175 - j 635
+18.1         665 + j 175       135 - j 120       155 - j 295
+21.15       2680 - j1200        75 - j 195       175 - j 445
+24.95        710 - j 410       130 - j 170       160 - j 345
+28.5          35 - j 85         75 + j 60        130 - j 110
+
+C.  100' Feedline
+ 3.6           75 - j 20       115 - j 325       120 - j 470
+ 7.15         60 + j 475        40 + j 53         71 + j 15
+10.1         110 + j380         60 - j 60         74 - j 85
+14.15         20 + j 100      1975 - j2210      3460 + j1886
+18.1         475 - j 295       145 - j165        190 - j 415
+21.15         35 - j 145        65 - j   0       125 - j 200
+24.95        115 + j 135       170 + j 320       140 + j 225
+28.5          75 - j 345      1015 - j1305      1455 + j1355
+

Even though the table presents us with only a few of the nearly infinite number of values we might encounter with our own 135' doublet, it nevertheless reveals many important facts about the use of parallel feedlines. First and foremost, we can see clearly the differences that line length makes to the impedance at the equipment end of the feedline.

+

Second, let us consider the antenna tuner or ATU. Every tuner has limitations in both the range of resistance values that it can efficiently match--or match at all--to a 50-Ohm input. Equally, every ATU has limits to the range of reactances which it can compensate for--and the ranges may differ for capacitive and inductive reactance depending upon the tuner design. Therefore, for a wide-ranging antenna like the doublet in our example, we would be wise in arriving at equipment-end values that least tax the ATU.

+

We can achieve our goal in one of two ways. One way is to select a line length for our pre-chosen type of parallel line that gives us the fewest þhighþ values of resistance and reactance. We might loosely define "high" as exceeding 1500 Ohms or 1000 Ohms, but the goal would be the same. As we scan the chart under any one of the lines, we select the length that gives us the fewest high values. Where this is not possible and we already have a line in place, we still use the technique. We insert an extra length of feedline for "troublesome" bands to get an easy match there.

+

Of course, to arrive at an optimal line length for a particular characteristic impedance and velocity factor, we would need to calculate equipment-end impedances for numerous other line lengths. Just for this job, programs like TLW and Transmission Line Performance in HAMCALC come in handy to make short work of the task. Smith Charts can also be used for this purpose.

+

Wherever the line length is relatively fixed in advance, but where one has a chance to choose the characteristic impedance of the line, there is another way to minimize resistance and reactance excursions at the ATU terminals. We simply select the line impedance and velocity factor combination that gives us the smallest range of resistance and reactance at the equipment end of the line. In vinyl lines, which are commercial products, we have a limited choice. However, in open-wire or ladder lines--all of which would have velocity factors similar to the 600-Ohm line used in the example--we can construct our own lines to meet the need. Ladder lines from about 400 Ohms to 600 Ohms are available commercially, but if we need an even higher values, we can roll our own.

+

Remember that the doublet used in this example is only one possible multi-band antenna out of many. Changing the length of the doublet by even a foot or two might change some of the upper band impedance values considerably. Moving to a 102' or 67' doublet or to a horizontal loop would create a whole new ball game of values with which to work. However, the tools of analysis do exist in the form of antenna modeling programs and feedline calculation programs. So the task need not be merely a guessing game.

+

Before we close the door on the selection of parallel feedlines, let's note one final fact from the table. In each column for each line length and Zo, notice how many of the resistance values are less than 100 Ohms. In most commercial ATUs that use a network design (like the common C-L-C Tee network), it is nearly standard practice to install some sort of 4:1 transmission line transformer (often called a balun) to provide a means of converting the single-ended network into a balanced output. The "4:1" reference is to the impedance transformation in the device.

+

The result of having such an impedance transformer--on the dubious assumption that it performs correctly while a considerable reactive component is part of the impedance--is to transform already low impedances into still lower ones. While a match to the new very low impedances might be made by the tuner, efficiency under these conditions is very suspect. Indeed, it might be better if such units came with 1:1 broadband toroidal transformers of standard design with cores large enough not to saturate. Efficiency might well show improvement.

+

Updated 11-05-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Transmission Line


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+

ANTENNAS FROM THE GROUND UP

+
+
+

33. Common or Unbalanced
+ or Unwanted Currents and Their Suppression

+
+
+

L. B. Cebik, W4RNL

+
+

Unwanted or misplaced currents within the antenna system represent wasted power. In addition, they can often disrupt some of the more sensitive circuits in a transceiver, such as the keying or VOX control circuits. Sometimes, RF can show up as a hum on audio lines. With higher than QRP power, the final indignity is a tingle or shock hazard on cabinet corners and case screw heads. Often, these phenomena occur even when the operator is satisfied that there is a good and effective common ground for all of the equipment.

+

The only way to remove these currents is to block them from the shack. There are tried and true means of accomplishing this preventive measure. In fact, there are enough means that sometimes we use the wrong one in the wrong place. Therefore, it seems useful to briefly look at the sources of unwanted currents from the antenna system and the means to rid ourselves of them.

+

Unwanted currents have two general sources, both of which can be analyzed as disruptions to the standard transmission line currents. Transmission line currents, whether on the outer surface of the center conductor and the inner surface of the braid of coax or on the two wires of a parallel transmission line, have under ideal conditions equal magnitude and opposite polarity at any position along the line. Anything that changes this condition may be trouble.

+
+ +
+

Fig. 1 shows the ideal condition at the top. Remember that we are dealing with alternating currents, so the arrows represent an instant in time. They would all reverse at some other instant, and they will continuously change size as a representation of magnitude.

+

Common mode currents are shown at the bottom. In general, they travel at any instant in the same direction on both conductors of the transmission line. (However, on coaxial cables, skin effect forces all common mode currents to the surface, that is, to the outside of the braid.) The termination for these currents is an earth ground (or a reasonable substitute). If one side of the line is connected to the same ground line as the equipment case(s), then common mode currents travel on the case(s). From the case, the currents can affect the circuit common of any section of the equipment, and what affects the circuit common can be just as disruptive as introducing a current into the "hot" side of the circuit. Our strategy should not just be to eliminate such currents, but to eliminate their possibility.

+
+ +
+

Fig. 2 shows two common sources of common mode currents. When we feed a balanced antenna, like a dipole, loop, or beam, directly with coaxial cable, we are inviting trouble. Although the currents inside the coax are presumed to be balanced, the current on the braid has a potential double path: on the inner and on the outer surfaces. The current on the outer surface becomes a common mode current.

+

Alternatively, if the feedline--either coax or parallel--is long enough, radiation can couple directly to it and also produce common mode currents. In fact, such currents do not have to be from one's own antenna, but might come from a nearby high power source, such as a broadcast transmitter or a noise source. These external sources often create problems in receivers ranging from front-end overload to mixer products and resulting spurious signals.

+

Before we look at cures for common mode currents, let's look at a second source of unwanted RF currents in the station equipment. These currents arise from unbalanced conditions in the feedline. Sometimes, the unbalanced condition is natural to the type of antenna that we may be using.

+

End fed and off-center fed doublets are the most common examples of antennas that produce unbalanced currents in the transmission line. However, there are many more possible cases. We can feed verticals off center--sometimes without knowing that the feed is not at a true voltage-minimum point. Some stations use non-symmetrical triangles, with a resulting imbalance in currents on the line. Poor parallel line installation is another source.

+
+ +
+

Fig. 3 simply illustrates the condition. One of the difficulties that current imbalance presents is that we often cannot distinguish it from a common mode current condition. Both situations can result in RF in the shack, with consequences for equipment operation. Both can result in power radiated from the transmission line instead of from the antenna. The amount of power does not have to be great to create interference with home devices or with station equipment. A few millivolts is often enough to create interference or circuit disruption.

+

The are some antenna vendors who imply or even boldly state that feedline radiation can make a positive difference in the operation of some antennas. Most of these claims are more hype than fact. Getting significant radiation from a feedline requires the use of certain line lengths for any frequency and lines that are free and clear of potential coupling into unwanted wires or metallic surfaces. Good design practices strongly suggest that we let the antenna itself do the radiating in a predictable manner and let the feedline do its work of conveying power from the source to the load without radiation.

+

A problem facing the QRP operator is knowing when there are unwanted currents from the antenna system. QRO operators can often detect them by touching the equipment cases and getting a small shock. Another symptom for the QRO operator is keying circuit lock-up or VOX lock-up, as the currents are rectified and change the bias level on the trigger circuits. At QRP levels, the current level may be insufficient to create these problems.

+

One good indicator for coax systems is to have a good external SWR-power meter designed for QRP power levels. The first test is to make up two coax cables, a very short one and a longer one--perhaps at least 3 times longer. First, place the meter close to the gear and then farther from the gear. The forward and reverse power levels should not change at all in a system with no unwanted currents. If there is a difference, then unwanted currents exist and beg for treatment.

+

Actually, we should always think in terms of preventing such currents from occurring in the shack as a basic part of antenna system design. In short, a few ounces of prevention can save a lot of work later on trying to diagnose and treat problems. The prevention and the treatment measures are the same.

+

The name of the cure is choking. An RF choke is any device that presents to an unwanted current a sufficiently high impedance that the current is reduced to an acceptable level. Some choking occurs by virtue of neutralizing the unwanted current. Let's look at the three most common means of choking or neutralizing unwanted currents in coaxial cable systems.

+

1. The coil of coax: By making a tight coil of several turns of coaxial cable, we can create a considerable inductive reactance on the outer surface of the braid without disturbing the transmission line currents between the center conductor and the inner braid surface. This form of choke is perhaps the cheapest and most convenient of all, but it does suffer some limitations. First, such chokes are heavy, consisting of between 8 to 20 feet of cable wound into 8 or more turns. From the current ARRL Antenna Book (page 26-21), here are some recommended single and multi-band sizes for RG-58:

+ 
Single-Band (very effective)
+      80/75 20'; 6-8 turns
+      40    15'; 6 turns
+      30    10'; 7 turns
+      20    8'; 8 turns
+      15    6'; 8 turns
+      10    4'; 6-8 turns
+Multi-Band (less effective)
+      80-10 10'; 7 turns
+      80-30 18'; 8-10 turns
+      20-10 8'; 6-7 turns
+

The chokes are considered most effective when placed closest to the antenna, which can be a weight problem at the center of a dipole or other wire antenna.

+

2. W2DU-type ferrite bead "baluns": A series of ferrite beads placed over a piece of coaxial cable can provide a high impedance over a broad frequency range. For 80-10 meters, about 50 cores will provide the desired impedance of about 1000 Ohms, while about a dozen adequate for VHF. Type 73, 77, and 43 ferrite materials are most used at HF, with type 43 and 61 considered the best choices for VHF. Type 77-2401 cores fit well over RG-58A, but may not slip over RG-8X. Walt Maxwell used a foot of RG-142 and smaller beads for his original: the coax has high power capability despite small size due to the use of a silver coated center conductor and teflon insulation.

+

You can build your own ferrite bead balun, but be certain to make it water proof. Inexpensive commercial bead baluns (in kit or complete versions) are available from such sources as the Wireman of South Carolina. Incidentally, the device is a balun because eliminating the unwanted currents from the coax effectively transforms the balanced feedpoint of a dipole into the condition needed for single ended coax to function properly.

+

3. A 1:1 current balun: A current balun can also effectively suppress common mode currents. The most common types of current baluns on the market are transmission line transformers. Jerry Sevick has two books available on the design and construction of these transformer types. The transmission line transformer can be used for both common mode current suppression and for impedance transformation. Most of the designs from commercial vendors are wound over toroidal or linear ferrite cores. Hence, the units tend to be somewhat heavy, although some types are specifically designed as dipole center devices.

+

A true transmission line transformer operates best with minimal SWR on the line. Hence, the best use of such baluns is with antenna terminal impedances having a very low reactive component. Mono-band dipoles, beams, trap antennas, and others having the a low reactance source impedance are the best candidates for most types of current baluns.

+

The transmission line transformer effectively suppresses common mode currents by neutralizing them within the turns of the device. We shall look at this action in a moment. First, let's see where we should place our common mode current suppressors. For this purpose, Fig. 4 can be useful to our planning.

+
+ +
+

The sketch shows two chokes instead of the usual one-choke system. Most folks place a choke at the antenna terminals, and in many cases that is enough. It solves to a large degree the problem of the balanced-to-unbalanced condition at the junction of the antenna and feedline. However, it does not always resolve the problem of radiation pick-up by the feedline itself.

+

At the shack entry, a ground lead to a good earth ground can go part of the way in suppressing common mode currents. However, a second choke, with the shack common (ground) lead brought to the choke and then to the earth ground, can often suppress remnant and random common mode currents that a line might pick up. A bead balun for the second choke is a good choice. The use of bulkhead connectors at both ends can provide the necessary connection points for the earth ground leads.

+
+ +
+

So far, we have noted suppression means for coax systems, but not for parallel line systems. Fig. 5 may help us out here. For parallel lines, the most effective suppression means is a transformer of some sort. Note that transmission line currents create a proper set of currents in the turns for normal transformer action. However, common mode currents create equal magnitude but opposite polarity currents in the transformer turns, thus canceling themselves out relative to transformer action. In effect, this neutralization of common mode currents is what occurs in a transmission line transformer and in transformers of standard design.

+

A transformer can also be used to convert a balanced output side to an unbalanced input side--or we can let the input side also be balanced. Therefore, although not common on the amateur market, there are broadband RF transformers available that are designed to do the same work as most baluns. The cost is a percent or 2 less efficiency than a properly matched transmission line transformer. The benefit is that a standard transformer handles complex impedances as a matter of course, so long as we do not let the core of a toroidal version reach saturation.

+

The transformer does not have to be toroidal or use a core of any kind. Air-core transformers work fine, although they tend to be frequency limited. However, the most promising place to find such a transformer is in a link-coupled antenna tuner. However, for both older and younger tuners, we have to make a revision to common tuner building practice. The secondary of the tuner that connects directly to the feedline terminals must "float" relative to the system ground or common. The common would allow a path for unbalanced or common mode currents through the equipment cases. A floating secondary isolates the offending currents.

+

Our little exercise has shown that we can overcome unbalanced currents and suppress common mode currents, if we plan them into our antenna systems.

+

Updated 11-05-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Balun


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+

ANTENNAS FROM THE GROUND UP

+
+
+

34. 1 Wire, 7 Bands, 2 Directions
+ or The 44' Doublet as a 40-10 Meter

+
+
+

L. B. Cebik, W4RNL

+
+

The average operator is as concerned over where his or her signal is going as well as how well it is getting there. That is the premise for the following notes. Letþs also set up a scenario where the longest possible wire antenna an operator might set up in his or her back yard is a 40-meter doublet. Unfortunately, the 40-meter doublet, while being a very effective wire antenna, does not meet the requirements of the "where" part of our initial problem.

+
+ +
+

Fig. 1 shows in the simplest possible sketch the dimensions of a 40-meter doublet. The length can be varied by plus or minus a few feet without affecting performance. In fact, in the following performance table, only the impedances would change noticeably.

+

Let's assume that the yard has some high old trees and that we can get the antenna about 66' up, a half wavelength high on 40, where horizontals become very competitive with verticals.

+

The figures in the table represent some important operating parameters that are worth noticing. The gain, in dBi, is obvious. The TO angle is the elevation angle of maximum radiation, an indication of the most potent skip angle. The vertical beamwidth (VBW) and horizontal beamwidth (HBW) are indicators of the general departure from the line of maximum gain where we can still get good performance. The feedpoint impedance is at the antenna terminals. Since we would normally feed the antenna with parallel feedline to an antenna tuner, the impedance at the tuner terminals will vary with the line length and characteristic impedance.

+

The figures are not to be viewed as exact, but only as a general guide to what we can expect from the 67' long, 66' high doublet.

+ 
      General Performance of a 67' 40-10 Meter Doublet
+
+      Freq. Max. Gain   TO    VBW   HBW   Feedpoint Z
+      Mhz    dBi        Deg   Deg   Deg   R +/- jX Ohms
+       7.15  7.3        28    35    86      70 - j  10
+      10.1   8.1        20    23    70     275 + j 800
+      14.15  9.0        15    16    51    4670 - j 345
+      18.1  10.5        11    12    33     175 - j 860
+      21.2   8.4        10    10    33     100 - j 115
+      24.95  9.3         8     9    33     375 + j 730
+      28.5   9.5         7     8    28    3265 + j 375
The 40-meter doublet has some good signal strength in its main lobes. However, the antenna will only be bi-directional broadside to the wire up to about the 17-meter band. For higher frequency bands, the lobes will begin to break up so that we can get 4-petal and 6-petal patterns, where maximum radiation is at some angle to the wire. See Fig. 2 for some representative overlaid azimuth patterns (40, 15, and 10 meters). If the antenna is broadside to Europe on 20 meters, then 15- and 10-meter signal may miss Europe altogether. +
+ +
+

A solution to the problem of knowing where oneþs signal is going on all bands lies in a key fact: a doublet reaches a maximum length for a truly bi-directional pattern when it is about 1.25 wl long, that is, when it is about EDZ length. There is nothing absolutely precise in the length, but it must be well under 1.5 wl long, since at that length, we get 6 lobes. In contrast, the EDZ or 1.25 wl doublet has a main bi-directional lobe and some ears that are 10 dB down or more.

+
+ +
+

Fig. 3 shows a doublet that meets the condition of having bi-directional patterns on all bands from 40 through 10 meters. There is nothing magical about the 44' length. It might easily be 2' shorter or longer without noticeable change in performanceþexcept for the impedance at the feedpoint. Like any doublet, the antenna is designed for parallel feedlines and an ATU.

+ 
      General Performance of a 44' 40-10 Meter Doublet
+
+      Freq. Max. Gain   TO    VBW   HBW   Feedpoint Z
+      MHz    dBi        Deg   Deg   Deg   R +/- jX Ohms
+       7.15  7.0        29    35    94      25 - j 580
+      10.1   7.6        20    23    83      55 - j 100
+      14.15  7.7        15    16    72     195 + j 485
+      18.1   8.6        12    12    60     920 + j1565
+      21.2   9.0        10    10    51    4160 + j 155
+      24.95 10.4         8     9    40     520 - j1545
+      28.5  10.4         7     8    31     140 - j 650
+

The table shows that the range of impedances is well within the capabilities of most tuners if we select a good line length. The gain column shows that the antenna has slightly less gain on 40 through 10 meters than the longer doublet. However, a glimpse at Fig. 4 shows that all of our patterns are broadside to the wire itself. The EDZ-type patterns show up on 12 and 10 meters, while 17 and 15 meters show patterns typical of a 1-wl long doublet. At 40 meters, the antenna is about 1/3 wl long, about the minimum length from which we can get good performance and a feedpoint impedance whose resistance is not exceedingly low and whose reactance is not exceedingly high at the same time.

+
+ +
+

Because the antenna has relatively narrow horizontal beamwidths at the highest bands, we cannot get coverage of the entire horizon from placing two such antennas at right angles to each other. However, such a system would require at least three supports for wire ends (assuming that there is a common support for the ends of two wires). Why not rearrange the supports so that the three together support 3 44' doublets, as in Fig. 5.

+
+ +
+

The ends of such an array of 3 doublets need only a small amount of clearance from each other. A 6' wire-end-to-support distance is shown. Models of the situation show that there is no significant interaction among the doublets. This is true whether the feed points of the unused doublets are open or shorted.

+

In addition, the triangle can be considerably distorted before any interaction occurs among the active and unused doublets. Therefore, in planning such a system, you can alter the broadside vector to place signals more directly at desired target areas.

+

It is possible to use the system by running three lengths of feedlineþone from each antennaþto the shack and switching among the doublets at the operating position. This scheme has one major disadvantage. The individual feedlines are likely to have different lengths. Therefore, when switching among the antennas, trying to find the one with the strongest signal, one may well have to retune the ATU. Apart from the extra time involved, the switch-and-retune routine may obscure which of two doublets indeed provides the strongest signal.

+

A more convenient arrangement, although one requiring more work during the installation of the array, is to set up a central support for a remote switching box consisting of 3 double throw-double pole relays. Even for QRP power levels, the contacts should be sturdy and well spaced to simulate the feedline spacing. 12-volt relays are generally the safest, since the control voltages are low, but almost any coil voltage will do. From the shack to the relay box, you will need two lines: a common feedline and a control voltage line. Fig. 6 provides a general sketch of the system.

+
+ +
+

Of course, as with any remote system, you would need to take special precautions. First, be sure that the relay box is water-protected. This does not mean totally water tight, since a þweepþ hole is necessary to carry away any condensation. With open-wire feeders, a non-conductive (plastic) box tends to reduce the number of problems with unwanted couplings.

+

Second, be sure that you account for safety. The common feedline should be well elevated. The 12-volt (or more generally, the control voltage) line may be buried, if it is made from materials that are recommended for such use. The control voltage line should not closely parallel the feedline, lest it become a means of disrupting the balance of the feedline. Burying the voltage line works well.

+

For world-wide coverage, the only alternative to the 3-doublet system would be a single rotatable doublet. However, such a scheme would require a considerable investment in aluminum, a sturdy tower and concrete base, an expensive rotator, and some ingenuity in setting up the parallel feedline so that it does not couple disruptively to the tower or rotator, especially as you turn the doublet. In addition, a 44' element would likely require a mast extension and tension ropes from the peak to the mid-points of the element in order to reduce the sag stress on the element.

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+

Nevertheless, such an arrangement is possible for advanced antenna builders. One element arrangement is shown in Fig. 7. The element-diameter taper schedule shown is likely only satisfactory up to about 60 mph winds. However, many other taper schedules can be used.

+

All of these ideas are icing on the original cake. Basically, the antenna concept is a broadside 44' doublet for 40-10 meters. It works.

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Doublet, EDZ / Zepp, HF Multi Band


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+

ANTENNAS FROM THE GROUND UP

+
+
+

35. That Phased Look
+ or Sorting Out Bi-Directional Phased Arrays

+
+
+

L. B. Cebik, W4RNL

+
+

The bi-directional phased array is a venerable antenna type that we should not overlook in our quest for a good wire antenna. In this episode, we shall review a pair of old-timers: the 8JK "flat-top" array and the expanded Lazy- H. But first, a little nomenclature. Fig. 1 shows three common terms used in phased-array work. An antenna element is collinear whenever it is two or more half wavelengths long, since it can always be analyzed as a series of half wavelength elements. In multi-element arrays using long elements relative to a given frequency, we often drop the term to emphasize other features of the array. However, the 8JK and the Lazy-H that we shall examine will consist of collinear elements on many frequencies on which we operate them.

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An array is an end-fire antenna whenever the main direction of radiation is in a plane with the elements. Yagis are end-fire arrays, and so is the 8JK. An array is called broadside when the main direction of radiation is at right angles to the plane of the elements. The 1 wl quad loop and the Lazy-H are broadside arrays. In phased array work, the difference tells us something about the array. For example, end-fire phased arrays generally reverse the phase-line with a half twist between elements, not only in the 8JK, but in the LPDA as well. Broadside arrays are generally fed in phase.

+

Let's begin with an 8JK, named after its developer, W8JK. It consists of two elements, normally about a wavelength long each spaced from 1/8 to 1/2 wl apart. The elements are fed 180 degrees out of phase by a simple means: run two parallel feedlines to the center point between elements and give one side a half twist. The lines can actually be any length so liong as they are equal. See Fig. 2 for a sketch of the basic 8JK. In the last episode, we looked at a 44' wire antenna for 40-10 meters. On 10, it was an EDZ. The 8JK that we shall look at here consists of two 44' elements spaced 22' apart. Like the single wire, we shall place them at a height of 66' so that you can make comparisons between the single and double wire arrays.

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+

The following table provides modeled performance data on the 8JK for 40-10 meters. The azimuth patterns for the array, each at its own TO (take-off or maximum radiation elevation) angle, appear in Fig. 3.

+
+ +
+ 
        General Performance of a 44' 40-10 Meter 8JK
+
+      Freq. Max. Gain   TO    VBW   HBW   Feedpoint Z
+      MHz    dBi        Deg   Deg   Deg   R +/- jX Ohms
+       7.15  9.0        26    30    66      1 - j 92
+      10.1  10.5        19    22    64     15 + j 138
+      14.15 10.8        14    15    60    132 - j 463
+      18.1  11.3        11    12    54     26 - j 98
+      21.2  11.4        10    10    47     23 + j   3
+      24.95 11.9         8     9    40     30 + j 131
+      28.5  11.6         7     8    32    142 + j 441
+

The 8JK, in the form shown here, gives significant gain improvement over the single wire 44' antenna. The spacing used here, 22', provides peak gain on 12 meters, with over 11 dBi gain on 17-10 meters, and over 10.5 dBi on 30 and 20 meters. The key limitation of the array appears on the lowest 2 bands: a very low resistive component to the composite feedpoint impedance at the junction of the two phasing wires. Some change in the values can be obtained by changing the line lengths (together to keep them the same), but the element length on 40 and 30 meters is falling below 1/2 wl. Hence, the composite impedance will be low, with a consequential tendency for higher losses. The losses result from the fact that any connection and wire losses will claim a higher percentage of the power supplied to the array assembly. Hence, the array might best be used from 20 meters on upward.

+

Note that there is an upper limit to the use of the array. On 10 meters, the pattern shows the typical EDZ ears, indicating the formation of a new lobe set. Extending the wire length to 1.5 wl on 10 meters would yield a 6-lobe pattern. As a result, the 8JK is best considered to have a 2:1 frequency range for best operation. Nevertheless, over this range, the array provides very even gain from band to band, with the low TO angles that result from both wires being at the top height of the array.

+

Unlike single-wire 44' element in 40-10-meter use, the 8JK is not as easily placed into a triangle for full horizon coverage. Hence, its best use is where there are main target communications regions both fore and aft of the array. In my location (Tennessee), setting the array for Europe on one side would yield good results with VKs and ZLs in the other direction.

+

The end-fire 8JK we have just examined has a broadside counterpart: the Lazy-H. Conventionally, a Lazy-H consists of two 1-wl wires placed a half wavelength apart vertically. The wires are fed in phase by running equal-length parallel feedlines to the center point between them, with a main feeder to the station. However, the version that we shall explore will be set up as an expanded Lazy-H. For 10 meters, the wires will be 1.25 wavelengths long or about 44'. The spacing will be 5/8 wl or 22'. Fig. 4 gives an outline sketch of the array. Again, the phase-line feeders can be any equal lengths. In both this case and the 8JK, the phase line feeders are 450-Ohm, 0.95 VF line, such as might be found in vinyl "window" line. If we use a different line having either a different Zo or a different VF, then the charted composite feed impedances will differ from those given. However, the principles of operation will not change.

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+ +
+

The two wires of the array are stacked vertically,. Since we have arbitrarily set the top wire height at 66', the bottom wire of the Lazy-H will be at 44'. Relative to the 8JK and to the single 44' wire explored in the last episode, the Lazy-H will have slightly lower TO angles. The lower angles result from the fact that the TO angle is a composite of the angles that result from the two wires, with the lower wire contributing a higher angle. Hence, the net of the two is slightly higher than for an array with all wires at the 66' level.

+

The Lazy-H will also show considerably more range in the gain levels, unlike the even gain of the 8JK across the bands we wish to use. The following table gives performance numbers, with Fig. 5 showing azimuth patterns.

+
+ +
+ 
    General Performance of a 44' 40-10 Meter Expanded Lazy-H
+
+      Freq. Max. Gain   TO    VBW   HBW   Feedpoint Z
+      MHz    dBi        Deg   Deg   Deg   R +/- jX Ohms
+       7.15  6.4        33    44    99     10 - j 97
+      10.1   8.1        24    27    85     48 + j 103
+      14.15  9.0        17    18    73    385 - j 395
+      18.1  10.9        13    14    61     43 - j 126
+      21.2  12.5        11    12    52     22 - j 17
+      24.95 14.6        10    10    41     18 + j 115
+      28.5  15.1         8     9    31     64 + j 425
+

Like the 8JK, the Lazy-H shows no very large extremes in reactance. Hence, most ATUs can accommodate these values. However, the impedance values that appear at the tuner terminals may vary widely from those shown in the chart, depending on the length of feedline from the antenna assembly to the shack. Only 40 meters shows a quite low impedance, although it may be high enough to be usable without undue loss. However, careful construction to minimize wire-junction losses is advisable.

+

Because the lower wire presents such a high TO angle on 40 meters, the gain on that band is actually lower than the gain using a single 44'. However, the reduction is only a little over a half dB, which some may find acceptable to acquire the improved gain on the higher bands. (A full-size dipole for 40 meters would have a gain of about 7.5 dBi if placed at a height of 66'.) Perhaps the most interesting question is how the Lazy-H achieves such fine gain values, especially from 15 meters upward.

+
+ +
+

Fig. 6 provides part of the answer by comparing the elevation patterns of the single-wire 44' element and the Lazy-H on 10 meters. Both the single wire and the Lazy-H have horizontal beamwidth that are virtually identical. Therefore, looking only at the vertical pattern will give a good idea of where the Lazy-H gets its added (5 dB) gain. The single wire--and the 8JK, for that matter--show a series of lobes all the way to a vertical angle, and the lobes are of nearly equal strength. In contrast, the Lazy-H, with its vertical stack of wires, tends to suppress upward radiation, leaving more power within the lowest lobe.

+
+ +
+

This same phenomena occurs at least down through 20 meters. Fig. 7 compares the elevation patterns for the single-wire antenna and for the Lazy-H. Again, since the horizontal beamwidths of the two antennas are so nearly equal, the elevation pattern can tell an accurate story. In this case, we can estimate the area under the two upper lobes of the single wire and compare it to an estimate of the area under the corresponding part of the Lazy-H pattern. The differential shows up as stronger lobes in the Lazy-H. As well, the vertical beamwidth of the Lazy-H array is larger, giving a bit more coverage to the possible angles of arriving signals.

+

As we did for the single 44' wire antenna, we can design a triangle to hold 3 of the 44'-element Lazy-Hs. The antennas will show minimal interaction, and we can offset one or more of them to obtain the best headings for our desired target areas. The same structure and feed-switching system that we showed in the last column can be used with the Lazy-H with no changes.

+

If we had the room, both vertically and horizontally, an array of 88' Lazy-Hs would provide similar coverage for the bands from 80 to 20 meters. Unless we could also double the height, performance will be down just a bit. However, even with a top height of 75', the array will give outstanding performance, with 13-14 dBi gain on 20 meters. If we have to reduce the spacing from the optimal 44' between wires down to say 35' (« wl on 20 meters), we would still have an exceptional bi-directional array.

+

The 8JK and the Lazy-H are extremely simple examples of phased arrays, but they are also very effective antennas. And they are relatively inexpensive!

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Lazy H, Phased Array, W8JK


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+

ANTENNAS FROM THE GROUND UP

+
+
+

36. Phased and Phased Again
+ or The Dual Expanded Lazy-H for 80-10 Meters

+
+
+

L. B. Cebik, W4RNL

+
+

In the last episode, we examined the expanded Lazy-H as a multi-band antenna. There are actually 2 versions for HF use. With 44' elements spaced vertically by 22', we have a good multi-band antenna for 10 meters through 40 meters. With 88' elements spaced 40 to 46 feet apart, we have an antenna that will cover 80 through 20 meters. The 4:1 frequency ratio represents the limits for ensuring that our pattern is always broadside to the wire. As well, we need to get that antenna as high as possible so that on the lower bands in the covered range, the elevation angle is as low as feasible.

+

I have received correspondence with an interesting question: Can I combine the two versions of the expanded Lazy-H and cover all of the HF region from 3.5 ro 29.7 Mhz? The answer is a qualified "yes." You can combine the antennas with the smaller centered inside the area occupied by the larger. Because the Lazy-H has so little vertical radiation, the two antennas will not interfere with each other significantly.

+

However, there is a right way and a wrong way to feed the combined array. If you feed the system correctly, you will lose little or nothing from the individual phased pairs of elements. If you feed the system incorrectly, you will lose the broadside radiation on virtually all of the upper bands. It is often as important to understand why something does not work as it is to understand why something else does work. Therefore, let's take a look at both the right and the wrong way to set up the Lazy-H array. And letþs begin with the tempting wrong way.

+

Getting it Wrong: Fig. 1 shows a tempting way to connect the parallel feedline to a combined large and small array.

+
+ +
+

The sketch shows the basic wire spacing. For the test case, I modeled the antenna with the long wires at 32' and 78' up and the short wires at 44' and 66' up.

+

The shortcut that tempted us was to connect the 450-Ohm phasing line from the top long wires to the top short wire and then to the center point between wires. We also connected a feeder from the bottom long wire to the bottom short wire and then to the center junction. Unfortunately, this configuration lets the longer wires dominate the radiation patterns on all bands, not just those from 80 through 20 meters. In fact, we might just as well have set a single 88' wire at the top wire height of 78' and fed it like any other doublet.

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+ +
+

Fig. 2 shows us why the patterns go to pot on the upper bands. In 17 meters, the band selected to illustrate the point, we can see that the longer wires have a higher current level (magnitude) than the shorter wires. Yet. It is the shorter wires that we wanted to do the work of providing a pattern that is broadside to the array wires.

+

The following table summarizes the potential performance of the mis-connected array.

+ 
Freq  Gain  TO    Feed Z
+Mhz   dBi   Deg.  R+/-jX
+3.6   5.64  67      8 - j  75
+7.15  8.28  27     15 - j 125
+10.1  7.10  25     20 + j 125
+14.1  11.97 15     55 + j 445
+18.1  10.22 13    115 + j 540
+21.1  11.55 11    1700-j1005
+24.95 10.75 10     40 - j 45
+28.5  12.58  8    445 - j 580
+

At first glance, the table seems to say that the antenna performs quite well. However, tabular data can be misleading if we do not have all of the labeling information that helps us make sense of the information. For example, in the table of modeled performance, we no where saw an indication of the azimuth angle at which the antenna provides its maximum gain. In fact, that angle is broadside only up through 20 meters.

+

At 17 meters and higher, the antenna creates clover-leaf patterns. For 17 and 15 meters, the patterns are essentially 4-leaf clovers, with the main lobes about 40 degrees off of the broadside direction. In the desired broadside direction, the signal strength is down from the maximum value by 7 to 12 dB. Hence, the entire reason for having the dual Lazy-H is completely defeated.

+

On 12 and 10 meters, we end up with 6-petal azimuth patterns (with a few extra weaker lobes thrown in). The strongest lobes happen to be those which are broadside to the wire, but they are very narrow--perhaps 20 degrees wide or less. The broadest lobes are those pointed in directions far off the broadside headings.

+

Not only does the azimuth pattern go to pot compared to what we want, but as well, the elevation pattern also suffers significantly. On the upper bands, the combined effects of having current on both the short and long wires yields considerable high angle radiation. On the upper HF bands, we want as much radiation as possible at lower angles to catch the DX skip.

+
+ +
+

Fig. 3 shows the 10-meter azimuth and elevation patterns for the dual Lazy-H with a combined feeding and phasing line. The narrow lobes broadside to the wire would make aiming very difficult. As well, the antenna wastes considerable power at high elevation angles, where it does not do much to aid communications. In short, our tempting simple feed system has ended up defeating our ultimate goal of having broadside radiation throughout the HF range.

+

The Right Way: If we are willing to overcome temptation and rethink the way we feed the dual expanded Lazy-H, we can achieve our objectives with pretty fair ease. The trick is to use separate phasing line pairs for each of the two Lazy-Hs, as shown in Fig. 4. Note that nothing has changed with respect to the wires. The only change is to the feed system by which we get power to the 2 antennas. The two feed lines must be separated by a couple of feet at their center junctions. A length of CPVC or similar light weight material will do this job well. Somewhere down the line, in the shack or remotely, we can add a switch to shift between the two arrays.

+
+ +
+

The key question is simply this: will separating the phase-line pairs improve array performance? The answer is a solid yes, as the modeled performance table below indicates. All gain figures are for major lobes broadside to the wires of the array.

+ 
Freq  Gain  TO    Feed Z
+Mhz   dBi   Deg.  R+/-jX
+88' Array
+3.6   5.58  65     9 - j 90
+7.15  7.53  29    250 - j 355
+10.1  10.84 20     20 - j  20
+14.1  12.76 15     80 + j 505
+44' Array
+7.15  6.39  32      8 - j 91
+10.1  8.33  23     55 + j 110
+14.1  9.26  17    395 - j 375
+18.1  11.25 13    435 - j 125
+21.1  12.35 11     23 - j 15
+24.95 14.65 10     20 +  j 115
+28.5  14.97  8     70 + j 425
+

I have shown the performance for all bands on each antenna. From the table, you can see that the array of choice for 20 meters and below is usually the 88' H. However, on some occasions, the wider beamwidth of the 20-meter azimuth pattern of the 44' array might come in handy. Having an A-B switch to try each antenna on a desired path is a wise practice.

+
+ +
+

You may also wish to compare the performance figures with those for the independent 44' array we discussed in the last episode. The slight differences in numbers will reveal that we have not eliminated all interactions, but we have reduced them to a very low level. As an example, I fed the short array on 18.1 Mhz, just as I did for the combined feed system. However, this time, as Fig. 5 reveals, the long wires did not directly receive energy from the feed system. The vary shallow current level lines on the longer wires reveals how very low the level of interaction is on 17 meters--barely detectable. In contrast, the shorter carry virtually all of the current that yields radiation. A similar picture emerges on all of the upper bands. Hence, we can expect the array to provide broadside patterns on all bands if we feed the two arrays with separate pairs of phase lines.

+
+ +
+

If we examine the azimuth and elevation patterns for 10 meters, we can confirm what the current distribution graphic has told us. In Fig. 6, we see the typical 10-meter EDZ pattern. The main lobes are both stronger and wider than those for the simple-feed version of the array. The elevation pattern is virtually indistinguishable from the one for a single 10-40-meter Lazy-H. The high lobes of Fig. 3 are totally missing. Instead, we have two low angle lobes, and the weaker, higher one may prove useful for sporadic E skip. In short, we have a successful array.

+

For someone with the tall pines or firs to get the longer array up high enough, a dual expanded Lazy-H may prove useful. The triangle array of arrays can also be used effectively with these antennas in order to cover as much of the horizon as possible with the least investment of antenna materials. Perhaps the only complexity will be to the suggested switching scheme that we explored 2 episodes back in connection with a simple 44' or 88' doublet.

+

Nevertheless, a triangle of dual Lazy-Hs will turn out to be far less expensive than a beam, rotator, and tower that covers only 20-10 meters. On many bands, the gain will be significantly higher than for all but the longest-boom beams on the market. Never sell wire short.

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Lazy H


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+

ANTENNAS FROM THE GROUND UP

+
+
+

37. All the Right Angles
+ or A Potpourri of Bent Dipoles

+
+
+

L. B. Cebik, W4RNL

+
+

The basic 1/2 wavelength dipole, shown for scale at the left of Fig. 1, has been the subject of many past episodes, and we have looked at it in both straight and zig-zag forms. We have also devoted columns to the inverted-V and the inverted-L, which are the most common bent versions of the dipole. Perhaps it is time to look both backward and forward to examine the entire family of dipoles bent at a right angle. We shall look at 40-meter versions, since we are assuming a backyard with limited space.

+
+ +
+

In Fig. 1, we have almost all of the family members, both common and rare. The inverted-V is perhaps the most-used version of a dipole with a right-angle bend, since it suits the backyard with only one tall support. The upright-V has similar properties to its inverted brother, but needs two supports. However, those supports can be closer together than the ones needed for a straight dipole. At 40 meters, if a dipole needs 70' between supports, the upright-V needs only 50'. If we set all of the antennas with a maximum top height of 50', the two V antennas will have their lowest points at just under 25' above ground, a safe distance over the heads of family members and visitors. Since all dipoles have high voltages at their ends, safety must be a significant concern.

+

The upright-L is rarely used as a low-band bent dipole. However, it is useful as a utility antenna at 10 meters and up. Made from tubing, rod, wire, or a combination and set above a roof top, it can serve to capture the signals from both horizontal and vertical antennas, covering point-to-point and repeater communications.

+

More common is the inverted-L. Many operators feed this antenna at its base, close to ground. However, fed at the upper corner, the antenna can be set a safe height above ground, about 16' at its lowest point, and still meet the 50' top height limit of this exercise. The supports can be about 35-40 feet apart.

+

Less commonly used is the quadrant antenna, shown in a top view. It is an antenna for the yard with more supports than space. Both legs are at 50', but form a V, with bidirectional radiation. A space about 25' by 50' will hold the quadrant. What can we expect from the various members of the right-angle family of dipoles? To answer that question, the following pages present azimuth and elevation patterns for each antenna, cut to be nearly resonant at 7.15 Mhz. All of the models for the antennas use AWG #12 copper wire. The top-most height for the wires is 50'. Hence, we can expect the upright-L to have poorer performance than the other antennas, since half the antenna is at a low height. When raised (in a 6-meter or 10-meter version) to 20' up or so, the performance improves dramatically.

+

The following table give you the length of each of the two legs, plus the approximate feedpoint impedances.

+ 
  The Right-Angle Family
+Ant.            Leg-Length  Feedpoint Z
+                (Feet)      (Ohms)
+Dipole          33.55       88
+Inv.-V          34          55
+Upr.-V          34          46
+Inv.-L          34.2        52
+Upr.-L          34.2        42
+Quadr.          34.2        51
+

Feedpoint impedance will vary somewhat with height, although the Vs and Ls will be less sensitive to height changes than the straight dipole, especially at top heights from .25 wavelength to 1.0 wavelength. For the Vs and Ls, the closer to ground, the lower the feedpoint impedance.

+

Of course, since every yard has its collection of objects that affect antenna operation, be prepared to prune the lengths slightly to bring them to a satisfactorily low SWR, if you feed them with 50-Ohm coax. For the antennas that place one end beyond reach, you may prune only the end in reach without disturbing the performance noticeably.

+

The azimuth and elevation patterns that follow aim to give you a set of reasonable expectations about the relative performance of the antennas. You may adjust your personal expectations by taking into account the likely affects of your trees, metal cables, buildings, tin roofs, and the like. Also account for any height changes from the 50' top height used here. A lower top height will generally reduce gain, raise the elevation angle of maximum radiation (TO angle), and further circularize the oval patterns. At 1/4 wavelength and below, all of the patterns are nearly circular.

+

The dipole has the highest broadside gain and lowest gain off the ends. The upright-V has good gain, but at a higher TO angle, while the quadrant has pretty good gain at the same TO angle as the dipole. The center-fed inverted-L has somewhat less gain, but at an overall lower TO angle, due to the radiation from the vertical leg of the antenna.

+

The quadrant antenna is less well-known in the U.S. than elsewhere in the world, but unfortunately, some claims for it just do not hold up. Some folks have claimed that it has a circular pattern, but in fact, at the 50' height (about 3/8 wavelength at 40 meters), the pattern is an oval with the strongest directions along the line that bisects the V of the layout. Nonetheless, it is a highly usable pattern for general communications.

+

The dipole takes the most space between supports. The invert-L takes the least, although the vertical leg should be well spaced from its support. The quadrant takes an intermediate amount of space and may still fit a small backyard with more supports than area. A further advantage of the quadrant is that you can bring the feedline down vertically from the antenna and minimize coupled common mode currents. For some installations, this feature may be very useful.

+

The Straight Dipole

+

Note not only the gain and the elevation angle of maximum radiation, but also the 6.6 dB reduction in signal strength off the ends of the wires. The antenna is oriented as if it were a vertical line in the middle of the azimuth pattern. The elevation pattern results if we look straight into the end of the wire and see how the pattern emerges broadside to the wire.

+
+ +
+

The Inverted-V

+

The azimuth pattern results from placing the wire so that the vertical peak is centered in the diagram and the two drooping leg make a vertical line on the page. To capture the elevation pattern, picture yourself as looking at the edge of the drooping wire pair so that the pattern shows what emerges broadside from the antenna. Note the reduced gain relative to the dipole and the greater radiation in the direction of the wire ends, giving a rounder azimuth pattern overall.

+
+ +
+

The Upright-V

+

Although this version of the V seems to have a higher gain than its inverted brother, note that the maximum radiation is at a considerably higher angle--almost too high for most skip path communications. Since the elevation pattern is still very broad, communications will still be good, but at a lesser strength than for the inverted-V for most skip paths. However, this antenna is a good candidate for NVIS use.

+
+ +
+

The Upright-L

+

The patterns for this antenna are mostly for reference to show what happens when the horizontal wire is too low for effective radiation. The pattern is something like that of a distorted 1/4 wavelength vertical. However, this antenna shows very much improved performance when the height of the bottom wire is raised to 1/2 wavelength or more above ground. Thus, it tends to work best on 10 meters and above, where it would make a small roof-top antennas or even an antenna to place outside the window of a high-rise apartment building.

+
+ +
+

The Inverted-L

+

With its horizontal wire at the top, the center-fed inverted-L shows a nice combination of vertical and horizontal radiation. The overall gain is not as high as some other bent dipoles, but the elevation angle of maximum radiation is the lowest of the group. Picture the vertical wire at the center of the azimuth pattern, with the open end of the horizontal wire pointing downward on the page. Hence, the kidney-bean shape of the azimuth pattern. Positioning the feedline to minimize coupling to the antenna legs can be a challenge.

+
+ +
+

The Quadrant V

+

Picture the quadrant in the azimuth pattern as forming a V with the open end to the right and the closed end to the left. Note that there is a very tiny difference in radiation, favoring the open end. However, the difference is so far below the level of being detectable as to make no difference in performance: the azimuth pattern is bi-directional. It has the same elevation angle of maximum radiation as the dipole, but the pattern is slightly rounder and the gain is slightly less. However, if this antenna fits your backyard, use it.

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+ +
+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, HF Lower, Inverted L, Inverted V


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+

ANTENNAS FROM THE GROUND UP

+
+
+

38. Angling to Work All Bands
+ or A Collection of Quadrant Antenna Patterns

+
+
+

L. B. Cebik, W4RNL

+
+

In the last episode, we examined a collection of right-angle dipoles. Among the collection was the so-called "quadrant" antenna, a flat-top V-shaped version of the dipole. Like all of the other antennas in the collection, inverted and upright Vs and Ls, the quadrant was resonant at 7.15 MHz. Fig. 1 shows the basic elements of the quadrant, using a top-down (or bottom-up) perspective. Since we shall be looking at some more azimuth patterns, the sketch indicates the heading that correspond to those on the patterns. 0 degrees will always indicate the direction away from the open face of the V-shaped antenna.

+
+ +
+

The basic antenna will be a 40-meter version constructed from AWG #12 copper wire, which is typical of backyard antenna materials. #10 through #14 wires would not perform differently in any significant way.

+

The chief application of the antenna is for the small yard with more supports than ground area. The antenna occupies an area of only 25 by 50 feet. Gently sloping the wires downward from the presumed 50' height for this exercise would not create large changes of performance. However, if that slope approaches a 45-degree downward angle, then the patterns might well look like compromises between the ones we shall see here and the ones in the inverted-V collection in episode 30.

+

Our aim in this installment is to see what kind of an antenna the quadrant might become in all-band use from 40 through 10 meters. There are two reference points for you to use in looking at the patterns.

+

1. Examine the patterns for the 44' doublet in episode 34 of this series. The 44' wire is essentially 1.25 wavelength at 10 meters and progressively shorter as we move downward in frequency toward 40 meters. At 7 MHz, the antenna is only about 3/8 wavelength long. Still, the antenna is a relatively good performer as wire antennas go. It produces bi-directional patterns on all frequencies from 7 through 28 MHz. The advantage of using this scheme is that you always know in what direction your signal is going.

+

2. Examine also the patterns in installment 3, which dealt with the 135' center-fed doublet. You will need to make an adjustment in your thinking if you want to apply these patterns as comparators to the ones in this exercise. What applies to an 80-meter doublet on 80 meters also applies to a 40-meter doublet on 40 meters. Each antenna is about 1/2 wavelength long and thus develops the same kind of pattern. Make some adjustment for the height of the wire above ground in terms of a wavelength. A 40 meter wire at 50' up is like an 80-meter wire 100' above ground. As the height of the antenna increases, as measured in terms of a wavelength, the elevation angle of maximum radiation, the take-off or TO angle gets lower.

+

The chief adjustment, however, has to do with making frequency changes. An 80-meter (135') doublet is about 2 wavelengths long on 20 meters. A 40-meter (70') doublet is about 2 wavelengths long on 10 meters. What determines the number of lobes in an azimuth pattern is the antenna length as measured in terms of wavelengths. So a 1.5 wavelength wire (an 80-meter doublet on 30 meters or a 40-meter doublet on 15 meters) will have 6 lobes. A 2 wavelength wire will have 4 lobes, each nearly 45 degrees off broadside to the wire.

+

I am calling your attention to these patterns because a 40-meter straight doublet (about 67-70 feet long) has patterns that begin to break into lobes that are no longer broadside to the wire as the wire length exceeds about 1.25 wavelength. Hence, from 15 through 10 meters, the standard 40-meter doublet will display lobes at somewhat odd angles to the wire. Unlike the 44' wire, where the direction of the main lobes is well-known, the 40-meter doublet will have lobes that point in slightly different directions from 15 through 10 meters. The quadrant antenna, even though at 40-meter wire length, has nothing but bi- directional patterns. On 10 meters, side lobes become quite evident, but not to the demise of the main lobes down the apex of the V. Now the open end of the V is about 48', quite close to our 44' straight wire that produced similar results. Hence, the pattern comparisons grow ever more interesting.

+
+ +
+

40-Meter Feedpoint Z: 50 + j1 Ohms

+
+ +
+

30-Meter Feedpoint Z: 180 + j 810 Ohms

+
+ +
+

20-Meter Feedpoint Z: 4200 - 2900 Ohms

+
+ +
+

17-Meter Feedpoint Z: 210 - j 750 Ohms

+
+ +
+

15-Meter Feedpoint Z: 115 - j 75 Ohms

+
+ +
+

12-Meter Feedpoint Z: 275 + j 820 Ohms

+
+ +
+

10-Meter Feedpoint Z: 4470 - j 760 Ohms

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, HF Lower


+ + diff --git a/content/gup/gup39-1.gif b/content/gup/gup39-1.gif new file mode 100644 index 0000000..f82f4af Binary files /dev/null and b/content/gup/gup39-1.gif differ diff --git a/content/gup/gup39-2.gif b/content/gup/gup39-2.gif new file mode 100644 index 0000000..85840d3 Binary files /dev/null and b/content/gup/gup39-2.gif differ diff --git a/content/gup/gup39-3.gif b/content/gup/gup39-3.gif new file mode 100644 index 0000000..b130cc8 Binary files /dev/null and b/content/gup/gup39-3.gif differ diff --git a/content/gup/gup39-4.gif b/content/gup/gup39-4.gif new file mode 100644 index 0000000..91ea78a Binary files /dev/null and b/content/gup/gup39-4.gif differ diff --git a/content/gup/gup39-5.gif b/content/gup/gup39-5.gif new file mode 100644 index 0000000..91d6530 Binary files /dev/null and b/content/gup/gup39-5.gif differ diff --git a/content/gup/gup39-6.gif b/content/gup/gup39-6.gif new file mode 100644 index 0000000..8f533f3 Binary files /dev/null and b/content/gup/gup39-6.gif differ diff --git a/content/gup/gup39-7.gif b/content/gup/gup39-7.gif new file mode 100644 index 0000000..7c9e5c3 Binary files /dev/null and b/content/gup/gup39-7.gif differ diff --git a/content/gup/gup39-8.gif b/content/gup/gup39-8.gif new file mode 100644 index 0000000..a63a5a3 Binary files /dev/null and b/content/gup/gup39-8.gif differ diff --git a/content/gup/gup39.html b/content/gup/gup39.html new file mode 100644 index 0000000..b93bd4d --- /dev/null +++ b/content/gup/gup39.html @@ -0,0 +1,66 @@ + + + + + + A Nearly All-Band Vertical Doublet + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

39. The Skinny Mini Antenna
+ or A Nearly All-Band Vertical Doublet

+
+
+

L. B. Cebik, W4RNL

+
+

Perhaps the ultimate crisis for a radio amateur who is used to stringing horizontal wires is to move into a home or apartment where horizontal wires are not possible. Of course, no ham ever gives up and continually looks for ways around the problem. However, let's suppose there is no escape: we must use a vertical antenna. Our question is this: how can we get the most performance from the least antenna on the most bands?

+

At the risk of sounding repetitious of episode #34, the answer is 44' of wire--but strung vertically and fed in the middle. With this antenna, we can work 40 through 10 meters with fairly low-angle signals, which is one of the reasons for using a vertical at all. The gain will not equal that of a Yagi or even of a horizontal wire 1/2 wavelength high or more, but we will make contacts.

+

The first question is why I cut off the wire at 44'. The antenna that we shall construct is going to be about 1.25 wavelengths at 10 meters. A 1.25 wavelength vertical doublet will have a very similar pattern to a 5/8 wavelength vertical monopole: both are at the dividing region between low angle patterns and high angle patterns that go over the skip angles of propagation.

+
+ +
+

Fig. 1 gives us some idea of how radical the change is in the elevation angle of the lower lobe. The vertical dipole at 28.5 MHz is 3' off the ground at the base. Hence the top wire is 3' above the listed wire length. There are several notable features about the patterns. First, note the increase in gain as the antenna becomes longer. The first pattern is for a 1/2 wavelength wire, while the second is for a 1 wavelength vertical. The third pattern is for the 44' wire, while the last is for a 1.5 wavelength wire doublet.

+

Second, note the appearance and growth of the second lobe as the wire gets longer. When the wire is about 1.25 wavelengths long, the lowest lobe has reached its strongest level. If the wire reaches 1.5 wavelengths long, the lowest lobe almost disappears and the second lobe becomes the strongest. For most amateur radio communications, its angle is too high for regular success.

+

We would have obtained a similar set of patterns had we replaced the wire doublets with 1/4 wavelength monopoles and ground-plane radials. When elevated, the ground-plane radials are simply the lower half of the doublet, but arranged in a manner so that their radiation self-cancels.

+

The following pages present elevation patterns for all of the HF ham bands from 40 through 10 meters. Since we are dealing with a vertical antenna, the azimuth patterns will all be circular. Thus, elevation patterns will provide us with the most necessary data. You can always picture a circle at the elevation angle of maximum radiation, as well as at any other elevation angle of interest to you.

+

Do not evaluate the antenna patterns solely by reference to the maximum gain values. A vertical has more to offer.

+

Although the gain levels will seem low, remember that the elevation angles of maximum radiation are also low. As well, your signal will only be down only by about an S-unit relative to a horizontal 44' wire at about 50' in the air. Under some circumstances, you may actually be stronger than a horizontal wire antenna.

+

Remember also that we are--according to our hypothesis--trying to operate from a location that might not have room for any other kind of antenna. Our goal is not to compete with long-boom Yagis and mutli-wire horizontal phased arrays. Instead, our goal is to develop the best possible signal that we can at the best possible communications angles in the least amount of space.

+

For the task at hand, then, a vertical doublet has much to offer and may well outdo many of the so-called mini-antennas, some of which offer gains that are less than 0 dBi by a considerable amount. So the vertical doublet does have a place among ham antennas.

+
+ +
+
+ +
+
+ +
+

At 20 meter, we just begin to detect the formation of the second higher lobe, which appears as a high-angle bulge in the elevation pattern. The absence of high-angle radiation also means a lack of receiving sensitivity to high-angle radiation. The result is a reduction in overall QRN, since most atmospheric noise that results from electrical discharges occurs at closer range and hence has a higher skip angle to the antenna. Above 20 meters, the second lobe meters grows, but noise tends to diminish.

+
+ +
+
+ +
+

The feedpoint impedances on the various bands tend to be quite moderate, well within the capabilities of most antenna tuners. The exception is 15 meters, where the antenna is close to 1 wavelength long, resulting in a high resistive component to the impedance. On the adjacent 17 and 12 meter bands, we find more moderate resistive values, but high reactive components. The parallel feedline for this antenna should depart the wire at right angles if possible for as long as possible to reduce direct coupling into the line.

+
+ +
+
+ +
+

Hanging the 44' wire is subject to many situational variables. Hence, there is very little useful general comment. However, if a 44' height--plus a little extra to clear the ground and ideally some further height to place the hot wire-end out of reach--is not quite possible, you may zig-zag the vertical wire as necessary. Two guide ropes might make the zig-zag more stable. Expect a slight reduction in performance, but no radical degradation. The 44' vertical can be an effective 40-10-meter antenna for the space-starved amateur.

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Doublet, HF Multi Band, Vertical


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+

ANTENNAS FROM THE GROUND UP

+
+
+

4. Fold, Bend, and Mutilate
+ or Making a Dipole Fit the Space Available

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ We have taken a look at the basic resonant half wavelength center-fed dipole antenna constructed at low heights (relative to a wavelength). However, the antenna was too perfect: we stretched it out full length horizontally. This is its most desirable form. +

But what do we do if we cannot quite fit a dipole into the space we have. Before we jump into the box marked "loading coils," let's consider some less lossy alternatives. In general, unless we turn the antenna into a piece of origami, the losses will be less than those of a helical dipole.

+

Option 1: Bend the ends. If you cannot fit the full dipole in your space, bend the ends, usually at right angles, and usually down. The "right angle and down" technique results from the absence of additional high supports; hence, the ends just drop.

+

First, do not just drop the ends near and parallel to a metal end support pole. The close coupling will likely detune the antenna severely. Second, consider angling the excess length in a slope to a house top, tree, or other support that is lower.

+

Since we cannot cover all the possibilities, letþs look at the drooping-end version, pictured in Figure 1. Do I lose anything? If so, what? How far can I shorten the horizontal part of the antenna before I lose too much? What happens to the overall wire length?

+
+ +
+
+ Fig. 1. Full and bent dipoles. +
+

Here is a table of what happens to the resonant length of an 80-meter dipole at 35' when the ends are bent downward:

+ 
     Size      L(h)      L(v)      L(total)
+     Full      131.4'    --        131.4'
+     92%       121'      5.55'     132.1'
+     84%       111'      10.9'     132.8'
+     77%       101'      16.1'     133.2'
+     69%       91'       21.3'     133.6'
+

As you can readily see, the coupling of the vertical and horizontal lengths at the corners requires a gradual lengthening overall. The wire grows longer with the shortening of the horizontal section because the current, fields, and coupling all grow stronger.

+

Not only does the antenna get longer, its gain in dBi at a fixed elevation angle decreases. For an elevation angle of 45°, the decrease in broadside gain and in front-to-side ratio in dB look like this:

+ 
     Size      45°       F-S       Feedpoint
+               Gain      Ratio     Impedance
+     Full      3.93      3.85      54.7 ohms
+     92%       3.88      3.74      54.4
+     84%       3.75      3.45      53.7
+     77%       3.51      3.03      52.4
+     69%       3.16      2.52      50.9
+

As the horizontal portion of the antenna is shortened and more hangs down at a lower height, the gain of the antenna drops. The drop is more precipitous as the antenna grows shorter horizontally. Also decreased is the antennaþs directivity. The front-to-side ratio drops ever more rapidly as the horizontal section grows shorter. These properties are functions of antenna shape and would apply proportionately to bent dipoles for any HF band.

+

There are alternative ways to bend dipole ends, shown in Figure 2.

+
+ +
+
+ Fig. 2. Horizontally bent dipoles. +
+

Simply bend the ends of the dipole horizontally, either in the same direction of in a zig-zag form. Gain and front-to-side ratio hold up much better, although when the ends of the zig-zag version exceed 20' each, the pattern takes a tilt away from the bent ends.

+

Here are the tables corresponding to those of the vertically bent dipole, carried one increment of shortening further. Separate figures are given only where significantly different.

+ 
     Size      L(h)      L(b)      L(total)
+     Full      131.4'    --        131.4'
+     92%       121'      5.55'     132.1'
+     84%       111'      11.0'     133.0'
+     77%       101'      16.3'     133.6'
+     69%       91'       21.65'    134.3'
+     62%       81'       27.0'     135.0'
+ 
     Size      45°       F-S       Feedpoint
+               Gain      Ratio     Impedance
+     Full      3.93      3.85      54.7 ohms
+     92%       3.92      3.82      54.0
+     84%       3.87      3.75      52.3
+     77%       3.80      3.63      49.3
+     69%       3.72      3.45      45.1 *
+                         3.56      45.6 **
+     62%       3.56      3.22      40.9 *
+               3.65      3.46      41.5 **
+     * = horizontally bent dipole
+     ** = zig-zag dipole
+

All of the dipoles have maximum gain broad side to the main horizontal wire except for the last two models. The 69% zig-zag model (134.3' total) is 7ø off broadside, while the 62% zig-zag model (135' overall) is 11ø off broadside, both away from the inside bend. Elevation patterns are unaffected by the bends.

+
+ +
+
+ Fig. 3. 45° azimuth pattern of the 62% zig-zag dipole. +
+

In many ways, horizontally bending or zig-zagging a dipole is superior to vertically bending the antenna. At any height, horizontal bends tend to preserve both gain and directivity. The cost is a more rapid decrease in the feedpoint impedance.

+

In the end, decreasing the main wire run below about 60% of full size decreases gain ever-more rapidly, especially for versions of the antenna with the ends bent in the same direction. The zig-zag bend is more immune to this effect because its bends produce less field cancelling.

+

Bending or zig-zagging a dipole at angles that are neither purely horizontal or purely vertical will produce intermediate values of both feedpoint impedance and gain. Moreover, the ends do not have to be bent in precisely equal amounts or angles. And, you may have more than one bend per leg. The antenna will still perform reasonably well as a dipole.

+

As with the vertically bent dipole, the results of these 3.6 MHz models can be extrapolated for dipoles on any HF band. When performaing any extrapolation, remember to adjust for height differences in terms of fractions of a wavelength, using the graphs in an earlier installment as a guide.

+

Although we shall look at center-fed multiband dipoles in another installment, we should note here that any of these 80-meter dipoles may be fed with 300-ohm or 450-ohm parallel feedline and an antenna tuner (ATU). Expect azimuth patterns to vary from the norm for straight wires as the frequency goes up and the bent portions become more significant portions of a half wavelength.

+

Option 2: Make an inverted Vee. Although many folks think of the inverted Vee antenna as relevant just to situations where there is only one hanging point in the yard, the Vee is also a space-saving antenna. Drooping the wires 30° produces a horizontal dimension only 87% that of a full length dipole, while drooping the wires down to 45° shortens the length along the ground to about 70% of that required by the truly horizontal dipole.

+
+ +
+
+ Fig.4. 30° and 45° Inverted Vees +
+

Some purists claim that an inverted Vee is not an inverted Vee unless the element slope is 45°. Actually, the inverted Vee is any antenna whose elements have appreciable downslope. Whatever the actual angle, the Vee has all its length below the feedpoint. Therefore, it is important to mount the Vee as high as possible.

+

One way to equate the height of antennas of roughly comparable polarization but different geometries is to find the heights that give equal angles of maximum radiation. So how do the Vee and the standard dipole compare?

+
+ +
+
+ Fig. 5. 20° azimuth patterns of a standard dipole, a 30° Vee and a 45° Vee, all resonant at 7.15 MHz. +
+

Figure 5 can be either informative or confusing, depending upon how carefully we read it. It summarizes the performance at a 20° elevation angle of comparable dipoles and Vees. The following tables specify the antennas and why they are considered comparable.

+ 
     Ant.           Dipole         V-30°          V-45°
+     Height         51'            40-57'         35-59'
+     L (wire)       67.25'         67.9'          68.4'
+     L (horiz)      67.25'         58.6'          48.7'
+     Feed Z         86.6 ohms      71.5 ohms      53.3 ohms
+     Gain at
+      20° el.       4.09 dBi       3.75 dBi       3.32 dBi
+     Front-to-side
+      Ratio         12.4 dB        9.2 dB         7.5 dB
+     Angle of Max.
+     Rad.           38°            38°            38°
+

In this table, I have chosen equal angles of maximum radiation as the basis of comparison. To obtain the angle of a dipole at 51', the 30° Vee must have a peak height of about 57', about 11% higher than the dipole. The 45° Vee must be about 16% higher it is apex, with a peak height of 59'. As one might expect, the 30° Vee more closely approaches the dipole in all performance characteristics than does the 45° Vee.

+

With low wire antennas, the gain at the angle of maximum radiation is seldom a good measure of the antennaþs working performance. Hence, Figure 5 displays the patterns at 20° elevation, closer to the angle needed for long distance communications.

+

Reading the gain figures from the table might leave the impression that the Vee is quite deficient compared to the dipole. However, the azimuth patterns demonstrate that there is less operational difference among the antennas. The dipole gain is only slightly higher than that of the Vee with a comparable take-off angle. Where the dipole shines is in its directivity, which will be a boon to some, the bane of others who desire all-direction communications.

+

Evaluating the Vee vs. the dipole at other heights requires that one adjust all three antennas by roughly equivalent amounts. Likewise, extrapolating these modeling results for other bands will require adjustment in terms of fractions of a wavelength above ground. The dipole at 51' height is about 3/8 wavelength above ground.

+

If we were to use a certain maximum antenna support height as the basis for our comparison, the Vee would appear to be an inferior performer. For the exercise, letþs compare a 45° Vee and a dipole, each with a maximum height of 35' and resonant at 7.15 MHz. The data table would look like this:

+ 
          Antenna        Dipole         V-45°
+          Height (max.)  35'            11.2-35'
+          L (wire)       66.35'         67.36'
+          L (horiz)      66.35'         47.7'
+          Feed Z         83.9 ohms      51.4 ohms
+          Gain at
+           20° el.       1.61 dBi       -1.22 dBi
+          Front-to-side
+           Ratio         10.5 dB        2.6 dB
+          Angle of Max.
+           Radiation     60°            90°
+

First, do not be put off by the negative gain figure for the Vee. At a 20° elevation angle, it will be about 3 dB or half an S-unit less sensitive (or powerful from the transmitting point of view). Compared to many successfully used mobile antennas, the Vee will be a superior performer-- just not superior to a dipole with the same peak height.

+

Second, notice that the Vee takes up less than 48' of linear space in the yard, compared to the dipole's 66+ feet. And, of course, a Vee needs only a single high support, with 2 end supports.

+
+ +
+
+ Fig. 6. Elevation patterns of a dipole and a 45° Vee, both with a maximum height of 35'. +
+

Figure 6 shows the elevation patterns for the two antennas along the axis of maximum gain for each (broadside to the wires). This graphic shows the Vee with the same maximum height as a dipole to be the lesser performer at all elevation angles. The question is this: when does it make sense to live by this pattern plot?

+

The simple answer is this: if you have two supports more than 67' apart and each 35' tall or taller, then by all means, go for the dipole. (Of course, you can also opt for some other antennas that need two supports 67' apart and that we have not looked at yet.) On the other hand, if you have only one support, centered in the antenna area, then the Vee is for you.

+

Option 3: Slope your dipole. There is no rule that says you cannot slope a dipole as needed to meet the levels of available supports. Nothing significantly bad happens if a dipole is closer to the ground at one end than the other. The imbalance created by having one end higher than the other is little more than the imbalance created because we cannot measure long pieces of wire accurately when they are stretched out on the grass. We already know that if we have a certain maximum height for wire support, the sloping antenna will have less gain that the flat-top version, But what happens if we align their center feedpoints and tilt them? Let's compare a flattop with a 30ø and a 45ø tilted antenna. And letþs use a 30-meter dipole at 35' for the comparison.

+ 
     Ant.      Flattop        Tilt-30°       Tilt-45°
+     Height    35'            23-46'         18-52'
+     L (wire)  47.45'         47.45'         47.45'
+     L (horiz) 47.45'         41.09'         33.55'
+     Feed Z    87.2 ohms      82.5 ohms      78.9 ohms
+     Gain at
+      20° el.  3.78 dBi       3.29 dBi       2.65 dBi
+     Angle of Max.
+      Rad.     39°            37°            34°
+

There is not much difference among the three antennas. Figure 7 shows that tilting the antenna puts an odd pinch in one side, but the main lobes are reliably broadside. The flattop does have higher gain at higher angles, and would thus be superior for shorter range communications by about a half S-unit.

+
+ +
+
+ Fig. 7. 20° elevation azimuth plots of flat and tilted dipoles. +
+

The bent, folded, and mutilated dipole is still a dipole and still the heart and soul of amateur radio. If it will not fit straight, bend it. The only way it won't work is rolled up in a tight ball.
+

+
+ +
+

Updated 5-1-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole


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+

ANTENNAS FROM THE GROUND UP

+
+
+

40. Power-House and SWL
+ or the Terminated Wide-Band Folded Dipole Antenna

+
+
+

L. B. Cebik, W4RNL

+
+

There is an antenna that has tempted many a ham, even many a low-power operator. It offers all-HF-band performance using a single 50-Ohm coaxial cable, with no need for an antenna tuner, no need for adjustments after installation, and no need for expensive test equipment to determine if it is working correctly. The antenna is the terminated wide-band folded dipole or TWBFD for short. The one item omitted from this appealing description is the fact that transmitted levels are down a minimum of 5-6 dB relative to a center- fed doublet of the same length, when we feed it with open-wire transmission line and a tuner in the shack.

+
+ +
+

Fig. 1 shows the general layout of the TWBFD. It resembles a standard folded dipole, except for two features. First, we have a resistor of 800-900 Ohms positioned opposite the normal feedpoint. Second, we find an RF transformer at the feedpoint. The natural feedpoint impedance of the antenna itself is roughly equal to the value of the terminating resistor. For a 50-Ohm coaxial cable we shall need either a wide-band standard toroidal transformer or a 16:1 balun (which might consist of 2 4:1 baluns in series).

+

For receiving-only purposes, we can construct the terminating resistor from a series-parallel combination of carbon composition resistors, and almost any power level resistor will do. For transmitting purposes, the resistor must be able to dissipate considerable power. Commercial versions of the antenna often specify reduced power limits for the antenna below certain frequencies, since the power dissipation may climb very rapidly below a frequency that we can call the "knee" frequency.

+

The wire spacing is wholly non-critical. Hence, we can construct our own TWBFD from any good wire from AWG #18 to #12 or so, spaced from 1" to 20" apart. For the moment, we shall not specify the antenna length, although the wire length will be important to one aspect of antenna operation. However, one commonly used length is about 90' or 27 meters. This length is about 1/2 wavelength between 5 and 6 MHz.

+
+ +
+

Fig. 2 gives us some vital information on the anticipated performance of the 27.2-m (90') TWBFD. The bottom line shows the modeled gain of the antenna in question. The top line shows the modeled gain of a plain, single wire doublet that is the same length as the TWBFD. If we ignore the portion of the lower curve that descends rapidly, the doublet shows at least 5 dB more gain everywhere across the operating spectrum.

+

However, the TWBFD does have that region of rapidly decreasing gain. In that region, the SWR on the coaxial feedline smooths out, compared to the ripples in the curve above the 5-6-Mhz knee frequency. The reason is very straightforward: below the knee frequency, more and more of the power fed to the antenna dissipates in the terminating resistor. That power is not available for radiation. However, the smooth near-50-Ohm impedance that produces the low SWR can give us the impression of good antenna operation. Actually, the antenna performs better at higher frequencies, where the SWR shows considerable variation between 1.0:1 and 2.0:1.

+

Because the terminating resistor determines the antenna's characteristic feedpoint impedance, the resistor must be non-inductive, that is, not wire-wound. It should be capable of dissipating half or more of the power fed to the antenna. Since 800-900-Ohm non-inductive resistors are difficult to find, some builders use a 16:1 balun at the resistor point and install a 50-Ohm resistor. Other schemes are also possible.

+

The reason why many builders favor an 800-Ohm terminating resistor is that the higher the value of the terminating resistor, the smoother the SWR curve above the knee frequency. For a receive-only antenna, where SWR may be less critical, values from 200 to 400 Ohms have been used successfully. Higher values are rarely used because of the difficulty of transforming the high feedpoint impedance to 50 Ohm coaxial cable.

+
+ +
+

One poorly understood feature of the TWBFD is that its patterns are exactly the same shape as those produced by a single-wire doublet of the same length. Fig. 3 provides a random sample at 10 Mhz, comparing the patterns of the TWBFD and a doublet. As the figure makes plain, the doublet pattern is about 6 dB stronger. Depending upon the calibration of the S-meter in your rig, the difference is at least 1 S-unit. For those running very low power, where signals may be at the threshold of readability under the best of conditions, losing an S-unit from the transmitted signal may mean the difference between a contact and no contact.

+

Reception, however, is rarely a major problem, since most receivers have excess gain. Seldom do we move the volume control more than 20 to 30 degrees above the lowest level. Many transceivers also have receiving pre-amps to increase signal strength by 10 to 20 dB. Hence, the 6 dB loss of the TWBFD is not a significant receiving problem. In some cases, such as reception in the night-time 40-meter band, the inherent loss can reduce receiver front-end overload from short-wave broadcasting stations.

+
+ +
+

Fig. 4 compares the doublet performance with the TWBFD at a higher frequency, 25 Mhz. Once more, the two patterns are virtually identical except for signal strength. Again, the TWBFD signal is about 6 dB weaker than the signal from a single-wire doublet. However, the pattern bears another message besides relative signal strength.

+

When we set up horizontal doublets, we expect that the pattern will begin to show multiple lobes as we increase frequency to the point where the antenna is more than about 1.25 wavelengths long. At a length of 1.5 wavelengths, a doublet will show a pattern with 6 lobes. As Fig. 4 shows, the TWBFD antenna will follow suit.

+

The TWBFD is often used in a vertical position, sometimes as an adjunct receiving antenna appended to a large tower supporting the main antenna. In such installations, the antenna should be no more than 1.25 wavelengths long at the highest frequency used. Otherwise, the lobe structure will favor only high angle radiation at just those higher frequencies where propagation yields low angle radiation. (You can visualize the lobe angle by drawing a vertical line at the center of Fig. 4. Then turn the page 90 degrees so that the line simulates ground. Although not a perfect picture of the pattern shape, it does show that the main lobes will be at high elevation angles.) For very broad frequency coverage, some installations use two TWBFD antennas--a long one for the lower portion of the HF spectrum, and a shorter one for the upper regions.

+

Thus, we have two frequencies of concern for any TWBFD: the frequency at which the antenna is more than 1.25 wavelengths long (if installed vertically) and the knee frequency.

+
+ +
+

Fig. 5 compares the modeled performance curves of 3 different length TWBFDs. The shortest is 15-m long (49+'). The middle-length is our 27.2-m (90') version. The longest TWBFD is 50-m long (164').

+

As the curves reveal, the longer the antenna, the lower the frequency of the knee, below which, performance rapidly decreases. In fact, the knee frequency is a function of the antenna length in wavelengths. The longest antenna is about a half wavelength long at 3 Mhz. The middle antenna is 1/2 wavelength long at about 5.3 Mhz, while the shortest antenna is 1/2 wavelength long at 10 Mhz. The knee frequencies on the graph correspond neatly to these lengths. However, if you return to Fig. 2, you will discover that the simple single-wire doublet shows only a slow decline in gain as it shrinks below a half- wavelength long.

+

The TWBFD and many other variants on the terminated doublet theme are most favored by two groups of people. First are European short-wave listeners. The decreasing performance of the antenna at lower frequencies is actually a blessing where short-wave broadcasts routinely overload receivers so that a station appears everywhere on the dial. The second group of users tend to be military and government installations where transmitted power is no problem. What they need is quick installation and no-adjustment operation.

+

Whether the antenna is suitable for radio amateur use is a user judgment. There are trade-offs to be measured, and only the user can measure them.

+

Updated 11-06-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, HF Multi Band


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+

ANTENNAS FROM THE GROUND UP

+
+
+

41. Traveling Man
+ or The Terminated (Very) Longwire Antenna

+
+
+

L. B. Cebik, W4RNL

+
+

One of the themes of this series has been how we can get the most antenna into the lest space. That theme makes sense in light of the shrinking yards of modern urban and suburban life. However, there are amateurs who have room to spare. There are a number of interesting wire antennas suited to such hams. Perhaps the most interesting a simply a piece of wire that is many wavelengths long at some operating frequency.

+
+ +
+

Consider the simple antenna in Fig. 1. It consists of a relatively short vertical wire that is just long enough to reach from the ground to the much longer horizontal wire. We feed the antenna at the ground. However, this antenna is not an inverted-L--although if the horizontal wire were considerably shorter, it might become one. (We are for the moment ignoring that third wire with the resistor in it.) Instead, the wire--considering only the fed vertical section and the horizontal section--is a classical longwire antenna. As we make a wire many wavelengths long, the number of lobes increases, with the strongest lobes approaching the line of the wire (in contrast to the broadside pattern of a 1/2 wavelength dipole). Because the wire has finite conductivity, the pattern is not truly bidirectional, using the wire ends as a reference. Instead, the pattern leans toward the open end of the wire. This unterminated longwire antenna is highly usable. especially if we have two target communications areas that are 180 degrees apart and one is somewhat more important than the other.

+

The 2-legged version of this antenna is, like almost (but not quite all) of the antennas that we have explored, a standing wave antenna. The open end of the wire presents an open circuit, so the electrical energy arriving at the end is virtually totally reflected. The combination of incident and reflected waves creates a standing wave on the antenna.

+

Let's now add the final leg of the antenna in Fig. 1. In that leg, we place a large resistor. If we let the resistor equal the feedpoint impedance, there will be no reflected wave and hence no standing wave on the wire. Traditionally, we call such antennas traveling wave antennas.

+
+ +
+

One consequence of placing the resistor in the third leg is to change the shape of the pattern. Instead of a slightly unbalanced bi-directional pattern, we arrive at a very directional pattern. Fig. 2 shows the difference for wires that are 5 wavelengths long and 1 wavelength above ground. We lose about 1 dB gain for the termination, but gain 15 dB of front-to-back ratio. In both cases, note the presence of significant sidelobes. Since a wire antenna that is multiple wavelengths long has many lobes, they remain part of the pattern. Terminating the wire can suppress them to some degree, but it cannot eliminate them.

+

There are techniques for calculating the termination resistor for antennas, especially when the height is low--the Beverage antenna. However, for upper HF use, we generally place a 600-800-Ohm resistor and allow the feedpoint impedance to make gradual swings as we change operating frequency.

+

We can make a rudimentary comparison between a standing-wave and a traveling-wave antenna by examining the current magnitude swings down the long horizontal wire. In the case of the 5 wavelength version, we obtain the current patterns in Fig. 3. The left end of the graph represents the part of the long wire that is closest to the feedpoint.

+
+ +
+

For a standing-wave antenna, the current makes very large magnitude swings that approximate (but do not equal) a sine wave. In the traveling-wave antenna, the current magnitude is relatively constant. It would be even flatter if the wire itself had no loss and if the terminating resistor exactly equaled the feedpoint impedance. We can see another difference when we examine the swings in the current phase angle, as shown in Fig. 4.

+
+ +
+

The current goes through one complete phase-angle cycle with each wavelength. At "junctions" between wavelengths, the phase angle will swing very quickly from negative to positive. However, between those junctions, the terminated antenna shows a virtually linear rate of change from the most positive to the most negative phase angle. In contrast, the unterminated version shows variations in the rate of change that are associated with the near-sine wave behavior of the current magnitude.

+

The bottom line is that a terminated longwire antenna becomes a highly effective directional array. The pattern does not have the clean forward look of a Yagi array. However, unless the various sidelobes present a problem in terms of potential interfering segnals, the antenna will perform very well.

+

The longwire also has a couple of other advantages worth noting. First, it will operate over a 4:1 frequency range. Fig. 5 shows the 600-Ohm SWR curve for the 5 wavelength version of the antenna. The low SWR values across the range suggest that a single wide-band transformer (conventional or transmission-line) might provide a good match between the target 600-Ohm feedpoint impedance and a 50-Ohm feedline. (Although transmission line transformers have become very wide-spread for matching impedances, we only lose a couple per cent of efficiency with a well-designed conventional transformer.)

+
+ +
+

The gain and horizontal beamwidth of the antenna will, of course, vary with the operating frequency. At 1/2 of the design frequency, the sample antenna is 1/2 the length and 1/2 the height. So we can expect a lower gain and a wider beamwidth. In contrast, at twice the frequency, the antenna is twice the length (10 wavelengths instead of 5) and twice the height (2 wavelengths rather than 1). The result is a higher gain, a narrower beamwidth, and a lower elevation angle of maximum radiation.

+

For maximum gain and the narrowest beamwidth, try for the longest wire that you can support. To get an idea of the differences that length can make to the longwire, see Fig. 6.

+
+ +
+

As may be clear from the patterns, the longwire just gets started toward high levels of directivity as it passes the 5 wavelength mark. If we wished to use a longwire antenna for the 40- through 10-meter bands, we might make it about 5 wavelengths at 40 meters or about 700'. Such a length will be 20 wavelengths on 10 meters. One of the secondary advantages of the longwire is that we do not need to be very precise in cutting the wire length. We shall not likely notice any operational differences between a 10 wavelength antenna that requires the erection of a new support post or a 9.5 wavelength longwire that ends near the limb of an existing tree.

+

At 10 wavelengths, the beamwidth of the array is about 30 degrees. Assuming that we have supports and a good supply of wire to go along with our acrage, we can place a longwire antenna in the direction of each of our target communications areas. Then, a simple switch will allow us to change antennas to the one pointed at a particular target. We need no rotator. As well, we do not have to make the wire and support investment all at once. We can add new target areas as the supports and wire become available.

+

There are two disadvantages to the terminated long wire antenna. First is the terminating resistor. If we only desire to receive, we can make up the resistor from low-wattage carbon resistors, strung in series-parallel combinations to approximate the target value. However, transmitting changes the problem. We need a non-inductive resistor capable of dissipating about 1/2 the power supplied to the antenna. Such resistors tend to be very expensive, although some occasionally appear on the surplus market.

+

A second challenge presented by the terminated longwire antenna is the matching for the feedpoint. If we only need a single band, we can use a standard L-network. Since the antenna feedpoint is inherently unbalanced, an automatic tuner would work for multi-band operation. However, this option would be expensive if we decide to put into place several of these antennas in order to have more communications targets. The most general solution is to build or buy a wide-range transformer capable of matching 600 to 50 Ohms (a 12:1 impedance transformation). For the design of transmission line transformers that would fit the need (either singly or in a combination of 2 of them), see the writings of Jerry Sevick, W2FMI.

+

The longwire antenna is attractive due to its seeming simplicity. However, the challenge of supports, terminating resistor, and impedance transformation make it an antenna that requires a good bit of pre-decision thought before committing the family farm to a system of them. In addition, the antenna has relatively low gain that depends upon the wire length as measured in wavelengths. Between lengths of 5 and 10 wavelengths, the forward gain over average ground varies between 7.5 and 9.5 dBi. Hence, the chief reason for using the terminated longwire is directivity. To obtain more gain and good directivity from a wire array, we shall have to examine some other designs.

+

Updated 11-07-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Multi Band, Longwire


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+

ANTENNAS FROM THE GROUND UP

+
+
+

42. Diamonds are Forever
+ or The Terminated Vee-Beam and Rhombic

+
+
+

L. B. Cebik, W4RNL

+
+

The terminated longwire antenna that we explored in the last episode is perhaps the simplest of the large terminated wire arrays, but its is not the best performer. In this follow-up session, we shall look at two other arrays. The long, terminated Vee-beam provides considerably more gain for the same length legs, but does not have the longwire's ease of feeding over a large frequency spread. The rhombic, in contrast, provides gain even over the Vee-beam and allows multi-band coverage. However, it is perhaps the most complex of the terminated arrays.

+

Designing either type of array for maximum performance is not simply a matter of stringing hundreds of feet of wire. Behind each type of array are a number of design equations that take into account the length of the legs, the angles formed by the wires, and the antenna height (or desired elevation angle of maximum radiation). These notes only survey some of the potential of these wire antennas, but are not sufficient for designing an effective array for your own farm. Our goal is to provide enough information so that you may decide whether further study into the designs is a worthwhile project.

+

The Vee-Beam: Do not confuse the Vee-Beam with some of the small Vee-shaped antennas whose total wire length is only about 1/2 wavelength. We do not arrive in Vee-beam territory until each leg is several wavelengths long. Like the longwire antenna, the Vee-beam depends upon the fact that as we make a wire longer and longer in wavelengths, the main radiation lobe moves from broadside to the wire to a position nearly in line with the wire.

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+ +
+

Fig. 1 shows two ways of designing a terminated Vee-beam. One uses terminating resistors that operate like those in the simple longwire. The other uses a cross wire that includes the terminating resistor. Just as in the last episode, the terminating resistor must be a non-inductive element with the ability to dissipate about half of the power supplied to the antenna. Both versions of the Vee-beam use the same principle of operation.

+

To design a Vee-beam, we must know the planned length of the element legs in wavelengths. Since the length of the leg determines the angle of the main lobes relative to the plane of the leg, the length of the legs also determines the angle that we must use between the two legs for maximum forward gain. The goal is to align the two legs so that a main lobe from each wire combine to form a single large forward lobe. See Fig. 2.

+
+ +
+

The plots show the patterns for the left and right legs of a planned Vee-beam with 7 wavelength legs. The height of the array is 1 wavelength above average ground. When we combine the two legs, we obtain the pattern at the right. For the leg-lengths that we chose, the main lobes are about 15 degrees off the plane of the wire. By making a Vee with a 30-degree total apex angle, we approach the maximum gain of which the antenna is capable. Obviously, had we selected longer legs, we would have used a narrower apex angle, while shorter legs would have called for a wider angle. If we do not match the angles and the length of the legs, we shall obtain inferior performance.

+

With 7 wavelength legs, the Vee-beam yields a maximum forward gain over average ground of about 13.5 dBi. This value is considerably higher (by about 5 dB) than the simple longwire antenna. However, the Vee-beam is not capable of achiving the high front-to-back ratio that the terminated longware gave us. If you examine the two left patterns in Fig. 2, you will see that each has a rearward lobe that is less than 10 dB down from the favored lobe. In the Vee configuration, these lobes also add, giving the Vee-beam a significant rearward lobe that remains only about 10 dB down from the forward lobe. Like all all arrays composed of wires that are several wavelengths long, the patterns will be filled with sidelobes.

+

Like the longwire antenna, the Vee-beam is capable of good use with or without its terminating resistors. Fig. 3 gives us comparative patterns for the two versions, using the same legs. Only the presence or absence of the terminating resistors marks the pattern differences. Note that the unterminated Vee-beam has (like the unterminated longwire) about 2 dB more gain. However, it is more truly bi-directional (than the longwire), since the rearward radiation is down by only about 2.5 dB.

+
+ +
+

The unterminated Vee-beam is also a useful antenna. It does not require that we obtain suitable terminating resistors (400 Ohms each in the sample antenna). Therefore, only land, wire, and supports stand between us and an array of Vee-beams that can cover the horizon. Fig. 4 shows the required number of Vee-beam legs needed, if we use the 7 wavelength legs and a 30-degree apex angle between legs.

+
+ +
+

We need outer-end (and perhaps intermediate) wire supports for each leg. However, we need only a single inner-end support for all of the legs. By a suitable means of switching--either at the antenna or near the shack, to which we bring a circular array of feedline wires--we select the adjoining pair of legs that gives us radiation in the two directions that we want.

+

The Vee-beam has some limitations. It is essentially a 1-band antenna, although we can press it into service on other bands. However, as we move away from the design frequency, the legs change their length as measured in terms of a wavelength. That change moves the angle of the main lobe on each leg relative to the plane of the wire. Hence, on these distant frequencies, the lobes will not match to form as strong a main lobe. To sustain the higher gain and re-acquire the broadband characteristics, we need to use a different shape.

+

The Rhombic: The terminated Rhombic antenna employs two sets of Vee-beams joined at the outer ends so that the second one forms a distant apex angle at which we install a terminating resistor. Fig. 5 shows the general outlines of a rhombic. Each leg has a pair of main lobes, and the combination of the 4 legs produces a very strong forward lobe.

+
+ +
+

The figure also shows in the lower half two ways of building a rhombic using either single-wire legs or tripple-wire legs. Builders have reported improved performance with the three wires, although the 1-wire version is satisfactory for most amateur installations.

+

The rhombic is a venerable directional array for which design equations had been developed in the 1930s. The design equations take into account the elevation angle of radiation, as well as the proper combination of angles and leg lengths to produce a strong forward lobe and a good front-to-back ratio. Indeed, there are alternative equations for developing various compromise designs that combine antenna height, leg length, and angles in various ways. See John Kraus, Antennas, 2nd Ed., pp. 503-508, if you are truly interested in designing a rhombic that will fit your yard.

+

For many year, The ARRL Antenna Book has featured an interesting rhombic design suitable for use on the amateur bands from 20 through 10 meters. It employs a 600-Ohm terminating resistor and is a good match for a 600-Ohm transmission line. Hence, all matching can be done at the shack with a system of impedance-matching transformers or baluns or with an antenna tuner. Fig. 6 provides a 600-Ohm SWR curve across the operating span to show the relatively good match between the terminating resistor and the feedpoint impedance.

+
+ +
+

The rhombic is 377.5' long and 184' wide, with a 52-degree angle at both the feedpoint and the termination end. Of course, we shall require longer wire, since each side of the array requires about 420' of wire. If we set the rhombic at 70' above average ground--1 wavelength at 20 meters--we can anticipate the following performance figures.

+ 
Sample Rhombic Modeled Performance
+
+Freq.   Length  Height  Gain    TO Angle        Front-Back      B/W             Feed Z          600-Ohm
+MHz     WL      WL      dBi     degrees         Ratio dB        degrees         R+/-jX Ohms     SWR
+14.2    5.5     1       16.2    14              17.1            17               810 + j 60     1.4
+18.12   7       1.25    17.8    10              15.3            13              1010 - j200     1.8
+21.2    8.1     1.5     18.4     9              19.2            11               830 + j 60     1.4
+24.95   9.5     1.75    18.3     7              15.2             9               990 - j 80     1.7
+28.3    11      2       17.2     6              20.2             7               900 + j 40     1.5
+

Note that the array is optimized for 15 meters, where it shows the highest gain. However, performance is high on all of the bands. However, the array is not without some important limitations.

+

First, the array is fixed in position. We cannot re-aim it easily, if at all. We may combine this restriction with the second limiting factor: the beamwidth of the rhombic is very narrow compared to most wire arrays. The horizontal beamwidth, as measured to the half-power or -3-dB point is narrower than almost any other array. Fig. 7 provides a band-by-band view of the azimuth patterns of the array to provide a sense of how narrow the beamwidth really is.

+
+ +
+

The earliest uses of the rhombic involved point-to-point communications circuits and well-defined broadcast target areas. Contemporary use of the array should have some of these elements as part of the communications goals before deciding to erect a rhombic.

+

Rhombics have also seen use in the VHF range as outdoor television receiving antennas. More recent improvements in design techniques have produce double-loop versions that further suppress the side lobes that naturally occur with multi wavelength element legs. Some amateurs have used these principles on bands as high as 1296 MHz.

+

The rhombic represents perhaps the pinnacle of refinement of large wire arrays. More recent developments in steerable arrays have largely supplanted the rhombic. However, the design still has adherents and users. It is likely to survive as an antenna option for generations to come.

+

Updated 11-08-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: HF Upper, Rhombic


+ + diff --git a/content/gup/gup5-1.gif b/content/gup/gup5-1.gif new file mode 100644 index 0000000..4b18490 Binary files /dev/null and b/content/gup/gup5-1.gif differ diff --git a/content/gup/gup5-2.gif b/content/gup/gup5-2.gif new file mode 100644 index 0000000..679fb47 Binary files /dev/null and b/content/gup/gup5-2.gif differ diff --git a/content/gup/gup5-3.gif b/content/gup/gup5-3.gif new file mode 100644 index 0000000..6754bc6 Binary files /dev/null and b/content/gup/gup5-3.gif differ diff --git a/content/gup/gup5-4.gif b/content/gup/gup5-4.gif new file mode 100644 index 0000000..d56fe28 Binary files /dev/null and b/content/gup/gup5-4.gif differ diff --git a/content/gup/gup5-5.gif b/content/gup/gup5-5.gif new file mode 100644 index 0000000..1ea090c Binary files /dev/null and b/content/gup/gup5-5.gif differ diff --git a/content/gup/gup5-6.gif b/content/gup/gup5-6.gif new file mode 100644 index 0000000..2d5e994 Binary files /dev/null and b/content/gup/gup5-6.gif differ diff --git a/content/gup/gup5-7.gif b/content/gup/gup5-7.gif new file mode 100644 index 0000000..434ef93 Binary files /dev/null and b/content/gup/gup5-7.gif differ diff --git a/content/gup/gup5-8.gif b/content/gup/gup5-8.gif new file mode 100644 index 0000000..868360d Binary files /dev/null and b/content/gup/gup5-8.gif differ diff --git a/content/gup/gup5-9.gif b/content/gup/gup5-9.gif new file mode 100644 index 0000000..ce94e6f Binary files /dev/null and b/content/gup/gup5-9.gif differ diff --git a/content/gup/gup5.html b/content/gup/gup5.html new file mode 100644 index 0000000..1e4bc28 --- /dev/null +++ b/content/gup/gup5.html @@ -0,0 +1,331 @@ + + + + + + A 135' Center-Fed Multi-band Dipole Data Compendium + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

5. 8-to-1 Odds
+ or a 135' Center-Fed Multi-band Dipole Data Compendium

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The most popular multiband wire antenna is the 80-meter dipole fed with parallel transmission line and an antenna tuning unit (ATU). It goes under many names. Likewise, it has many recommended lengths. We shall somewhat arbitrarily use 135' as our length. The models will assume #14 copper wire over average earth. Figure 1 illustrates the antenna. +
+ +
+

It is important to understand that the pattern of lobes and nulls varies with each band. This information is useful for orienting the antenna and for properly anticipating performance. The precise length of the antenna between 130' and 140' will have little effect on the individual band patterns.

+

Changes of length will have a more profound effect upon the feedpoint impedance, as will changes of height. In contrast, changes of wire diameter between AWG #18 and #10 will have little noticeable effect.

+

The pages to follow are designed to allow the antenna builder to have some reasonable expectations both for antenna patterns and for impedances presented to the ATU by the antenna and its feedline. Each column in the following pages is devoted to the performance of the antenna on one of the HF bands from 80 to 10 meters. For each band there is a composite pattern plot and a pair of tables.

+

The patterns show NEC-2 plots of the antenna at heights of 35' and 50'. The 35' pattern is always the inner or weaker of the two patterns. If the angle of maximum radiation is greater than 45°, then the azimuth pattern is taken at an elevation angle of 45°. If the angle of maximum radiation is less than 45°, then the take-off angle is used. The elevation patterns are taken at the azimuth angle of the strongest lobe. Therefore, interpreting the patterns requires that you consider azimuth and elevation together.

+

The tables list, in highly rounded numbers, the impedance presented along parallel transmission lines every 20° (electrical) for a half wavelength. Standard 450-ohm (Velocity Factor = 0.95) and 300-ohm (VF = 0.80) lines are given. Note that each electrical degree represents a different length in feet and meters for each band and line type. Values are for lossless lines from the 50' high antenna.

+

Since impedance values repeat themselves every 180° along a feedline, you may estimate (very broadly at best) the impedance presented to your ATU. Divide the length in feet or meters of your transmission line by the length of a half wavelength (180°) of the same line. Ignore the integer and multiply the fraction of a half wavelength by 180 to arrive at the value in degrees to check against the applicable table.

+
+ +
+ 
80 meters: 3.6 MHz
+AZ plots:   Elevation angles = 45°
+EL plots:   Azimuth angles = 90°
+
+Feedpoint Z (R ± jX): 75 + 55 ohms
+
+TL = 450 ohm; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       75 + 55
+20   14.4       4.4     95 + 220
+40   28.8       8.8     155 + 455
+60   43.3       13.2    420 + 890
+80   57.7       17.6    2450 + 770
+100  72.1       22.0    680 - 1107
+120  86.5       26.4    200 - 555
+140  101.0      30.8    105- 280
+160  115.4      35.2    80 - 100
+180  129.8      39.6    75 + 55
+
+TL = 300 ohm; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       75 + 55
+20   12.1       3.7     95 + 165
+40   24.3       7.4     170 + 315
+60   36.4       11.1    450 + 540
+80   48.6       14.8    1220 - 55
+100  60.7       18.5    415 - 525
+120  72.9       22.2    160 - 305
+140  85.0       25.9    95 - 155
+160  97.1       29.6    75 - 45
+180  109.3      33.3    75 + 55
+
+ +
+ 
40 meters: 7.15 MHz
+AZ plots: El. Angle = 45° @ 35';
+                      39° @ 50'
+EL plots: Az. Angles = 90°
+
+Feedpoint Z (R ± jX): 4760 - 1270 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       4760 - 1270
+20   7.3        2.2     285 - 1085
+40   14.5       4.4     90 - 500
+60   21.8       6.6     50 - 245
+80   29.0       8.9     40 - 70
+100  36.3       11.1    40 + 90
+120  43.6       13.3    55 + 270
+140  50.8       15.5    100 + 550
+160  58.1       17.7    365 + 1240
+180  65.3       19.9    4760 - 1270
+
+TL = 300 ohms; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       4760 - 1270
+20   6.1        1.9     135 - 765
+40   12.2       3.7     40 - 345
+60   18.3       5.6     25 - 165
+80   24.5       7.5     20 - 50
+100  30.6       9.3     18.3 + 60
+120  36.7       11.2    25 + 180
+140  42.8       13.0    45 + 365
+160  48.9       14.9    160 + 840
+180  55.0       16.8    4760 - 1270
+
+ +
+ 
30 meters: 10.125 MHz
+AZ plots: El. Angle = 39° @ 35';
+                      27° @ 50'
+EL plots: Az. Angles = 90°
+
+Feedpoint Z (R ± jX): 95 - 330 ohms
+
+TL = 450 ohm; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       95 - 330
+20   5.1        1.6     65 - 135
+40   10.3       3.1     60 + 20
+60   15.4       4.7     70 + 185
+80   20.5       6.3     110 + 405
+100  25.6       7.8     270 + 805
+120  30.8       9.4     1805 + 1645
+140  35.9       10.9    910 - 1445
+160  41.0       12.5    195 - 655
+180  46.1       14.1    95 - 330
+
+TL = 300 ohms; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       95 - 330
+20   4.3        1.3     55 - 165
+40   8.6        2.6     40 - 45
+60   13.0       4.0     40 + 55
+80   17.3       5.3     55 + 175
+100  21.6       6.6     100 + 350
+120  25.9       7.9     330 + 730
+140  30.2       9.2     2160 - 230
+160  34.5       10.5    290 - 685
+180  38.9       11.8    95 - 330
+
+ +
+ 
20 meters: 14.15 MHz
+AZ plots: El. Angle = 27° @ 35';
+                      19° @ 50'
+EL plots: Az. Angles = 52° @ 35'
+                       55° @ 50'
+
+Feedpoint Z (R ± jX): 4270 - 1005 ohms
+
+TL = 450 ohm; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       4270 - 1005
+20   3.8        1.1     405 - 1215
+40   7.3        2.2     115 - 550
+60   11.0       3.4     60 - 270
+80   14.7       4.5     45 - 90
+100  18.3       5.6     45 + 70
+120  22.0       6.7     60 + 240
+140  25.7       7.8     100 + 500
+160  29.4       9.0     320 + 1070
+180  33.0       10.1    4270 + 1005
+
+TL = 300 ohm; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       4270 - 1005
+20   3.1        0.9     180 - 830
+40   6.2        1.9     50 - 365
+60   9.3        2.8     25 - 180
+80   12.4       3.8     20 - 60
+100  15.5       4.7     20 + 50
+120  18.5       5.7     25 + 165
+140  21.6       6.6     45 + 345
+160  24.7       7.5     150 + 760
+180  27.8       8.5     4270 - 1005
+
+ +
+ 
17 meters: 18.1 MHz
+AZ plots: El. Angle = 19° @ 35';
+                      14° @ 50'
+EL plots: Az. Angles = 29° @ 35'
+                       30° @ 50'
+
+Feedpoint Z (R ± jX): 125 + 5 ohms
+
+TL = 450 ohm; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       125 + 5
+20   2.9        0.9     145 + 155
+40   5.7        1.8     205 + 335
+60   8.6        2.6     420 + 585
+80   11.5       3.5     1210 + 645
+100  14.3       4.4     1155 - 670
+120  17.2       5.2     400 - 575
+140  20.1       6.1     205 - 325
+160  22.9       7.0     140 - 145
+180  25.8       7.9     125 + 5
+
+TL = 300 ohm; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       125 + 5
+20   2.4        0.7     140 + 90
+40   4.8        1.5     195 + 185
+60   7.3        2.2     340 + 280
+80   9.7        2.9     635 + 195
+100  12.1       3.7     610 - 215
+120  14.5       4.4     320 - 275
+140  16.9       5.2     190 - 180
+160  19.3       5.9     140 - 85
+180  21.7       6.6     125 + 5
+
+ +
+ 
15 meters: 21.15 MHz
+AZ plots: El. Angle = 18° @ 35';
+                      13° @ 50'
+EL plots: Az. Angles = 41° @ 35'
+                       43° @ 50'
+
+Feedpoint Z (R ± jX): 2330 + 1435 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0         0       2330 + 1435
+20   2.5        0.8     735 - 1300
+40   4.9        1.5     185 - 605
+60   7.4        2.2     90 - 305
+80   9.8        3.0     65 - 120
+100  12.3       3.7     65 + 40
+120  14.7       4.5     75 + 205
+140  17.2       5.2     125 + 435
+160  19.6       6.0     320 + 870
+180  22.1       6.7     2330 + 1435
+
+TL = 300 ohm; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0          0      2330 + 1435
+20   2.1        0.6     310 - 905
+40   4.1        1.3     75 - 395
+60   6.2        1.9     40 - 195
+80   8.3        2.5     30 - 70
+100  10.3       3.2     30 + 35
+120  12.4       3.8     35 + 150
+140  14.5       4.4     60 + 310
+160  16.5       5.0     170 + 660
+180  18.6       5.7     2330 + 1435
+
+ +
+ 
12 meters: 24.95 MHz
+AZ plots: El. Angle = 14° @ 35';
+                      10° @ 50'
+EL plots: Az. Angles = 23° @ 35'
+                       24° @ 50'
+
+Feedpoint Z (R ± jX): 130 - 180 ohms
+
+TL = 450 ohm; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0          0      130 - 180
+20   2.1        0.6     110 - 25
+40   4.2        1.3     120 + 130
+60   6.2        1.9     170 + 305
+80   8.3        2.5     325 + 565
+100  10.4       3.2     1020 + 855
+120  12.5       3.8     1490 - 675
+140  14.6       4.4     440 - 670
+160  16.6       5.1     200 - 375
+180  18.7       5.7     130 - 180
+
+TL = 300 ohm; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0          0      130 - 180
+20   1.8        0.5     100 - 70
+40   3.5        1.1     95 + 25
+60   5.3        1.6     110 + 125
+80   7.0        2.1     170 + 250
+100  8.8        2.7     370 + 410
+120  10.5       3.2     920 + 205
+140  12.3       3.7     575 - 440
+160  14.0       4.3     230 - 320
+180  15.8       4.8     130 - 180
+
+ +
+ 
10 meters: 28.5 MHz
+AZ plots: El. Angle = 13° @ 35';
+                      10° @ 50'
+EL plots: Az. Angles = 36° @ 35'
+                       37° @ 50'
+
+Feedpoint Z (R ± jX): 2070 + 1225 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0          0      2070 + 1225
+20   1.8        0.6     835 - 1230
+40   3.6        1.1     215 - 605
+60   5.5        1.7     105 - 310
+80   7.3        2.2     75 - 120
+100  9.1        2.8     70 + 35
+120  10.9       3.3     85 + 200
+140  12.8       3.9     135 + 420
+160  14.6       4.4     345 + 825
+180  16.4       5.0     2070 + 1225
+
+TL = 300 ohms; VF = .80
+Deg  Feet       Meters  R ± jX (ohms)
+ 0    0          0      2070 + 1225
+20   1.5        0.5     360 - 895
+40   3.1        0.9     90 - 395
+60   4.6        1.4     45 - 195
+80   6.1        1.9     35 - 70
+100  7.7        2.3     30 + 35
+120  9.2        2.8     40 + 145
+140  10.7       3.3     65 + 305
+160  12.3       3.7     190 + 640
+180  13.8       4.2     2070 + 1225

+
+
+ +
+

Updated 7-1-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, Doublet, HF Lower, HF Upper


+ + diff --git a/content/gup/gup6-1.gif b/content/gup/gup6-1.gif new file mode 100644 index 0000000..7c72c75 Binary files /dev/null and b/content/gup/gup6-1.gif differ diff --git a/content/gup/gup6-2.gif b/content/gup/gup6-2.gif new file mode 100644 index 0000000..206d48c Binary files /dev/null and b/content/gup/gup6-2.gif differ diff --git a/content/gup/gup6-3.gif b/content/gup/gup6-3.gif new file mode 100644 index 0000000..ba52b7b Binary files /dev/null and b/content/gup/gup6-3.gif differ diff --git a/content/gup/gup6-4.gif b/content/gup/gup6-4.gif new file mode 100644 index 0000000..0ed01db Binary files /dev/null and b/content/gup/gup6-4.gif differ diff --git a/content/gup/gup6-5.gif b/content/gup/gup6-5.gif new file mode 100644 index 0000000..1043a2e Binary files /dev/null and b/content/gup/gup6-5.gif differ diff --git a/content/gup/gup6-6.gif b/content/gup/gup6-6.gif new file mode 100644 index 0000000..c75e06a Binary files /dev/null and b/content/gup/gup6-6.gif differ diff --git a/content/gup/gup6-7.gif b/content/gup/gup6-7.gif new file mode 100644 index 0000000..db997e4 Binary files /dev/null and b/content/gup/gup6-7.gif differ diff --git a/content/gup/gup6-8.gif b/content/gup/gup6-8.gif new file mode 100644 index 0000000..37663f5 Binary files /dev/null and b/content/gup/gup6-8.gif differ diff --git a/content/gup/gup6.html b/content/gup/gup6.html new file mode 100644 index 0000000..9723a11 --- /dev/null +++ b/content/gup/gup6.html @@ -0,0 +1,324 @@ + + + + + + A 102' Center-Fed Multi-Band Dipole Data Compendium + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

6. But My Yard's Too Small
+ or a 102' Center-Fed Multi-Band Dipole Data Compendium

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ If you cannot fit a 135' dipole in your yard, perhaps an antenna about 102' long will fit. 102' is about 3/8 wl at 80 meters, which is about as short as you dare go for decent feedpoint impedances and minimal gain. (In dire circumstances, of course use what you have, even if shorter. It will work, but just not as well as something longer.) +

We shall feed the 102' wire with parallel transmission line all the way to the ATU. With this feed system, the exact length is not critical ±5' or so. The patterns will be mostly unaffected, but variations in length and height will change the feedpoint resistance and reactance more significantly.

+

100' flattops or doublets have been used as long as any old timer remembers. The precise 102' length became famous when G5RV developed a feed system that he hoped would allow hams to use the antenna on harmonically related bands with about 33' of 450-ohms line or 29' of 300- ohms line, and the rest 50-ohms coax. Two problems changed fame into controversy. First, the WARC bands opened, adding nonharmonically related frequencies to the multiband antenna wish list. Second, on the low bands, small changes of length and height alter the feedpoint impedance, thus disrupting the low SWR match effected by the parallel line lengths.

+

But the 102' doublet (= any center-fed wire) does work well with parallel line all the way to the ATU. However, its patterns and impedances along parallel transmission line differ from those of the 135' dipole. Therefore, the 102' antenna deserves a data compendium of its own.

+

See the preceding installment of this series for instructions on interpreting the patterns and the feedline impedance tables, along with the method for calculating the ballpark impedance presented to your own ATU.

+

The line impedances are calculated from the feedpoint impedance of the NEC- 2 model of the antenna at a 50' height. For intermediate values at 5 deg. intervals, see the transmission line performance program in HAMCALC. If you need values that account for line loss, ARRL's N6BV has written a fine program, but it calculates one value at a time.

+

The impedance values are intended only as indicators of the magnitude of resistance and reactance and the rising or falling direction of those magnitudes along the line. The accuracy of the values for any given ham installation, with its typical domestic "clutter," is no more than about 20%, considering variations in height and antenna length. At most, they can tell you that a longer or a shorter line might be better for a given band. In other words, they can suggest why your tuner may be having difficulties in matching the antenna on a given band. It is usually cheaper to add a little line length than to add a new tuner to the system.

+
+ +
+ 
80 meters: 3.6 MHz
+AZ plots:   Elevation angles = 45 deg.
+EL plots:   Azimuth angles = 90 deg.
+
+Feedpoint Z (R ± jX): 35 - 420 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0        0         35 - 420
+20   14.4      4.4       20 - 190
+40   28.8      8.8       20 - 25
+60   43.3      13.2      20 + 135
+80   57.7      17.6      30 + 335
+100  72.1      22.0      60 + 685
+120  86.5      26.4      350 + 1870
+140  101.0     30.8      1165 - 3330
+160  115.4     35.2      90 - 880
+180  129.8     39.6      35 - 420
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        35 - 420
+20   12.1      3.7       15 - 205
+40   24.3      7.4       15 - 80
+60   36.4      11.1      10 + 30
+80   48.6      14.8      15 + 140
+100  60.7      18.5      25 + 305
+120  72.9      22.2      70 + 650
+140  85.0      25.9      1475 + 3010
+160  97.1      29.6      165 - 1065
+180  109.3     33.3      35 - 420
+
+
+ +
+ 
40 meters: 7.15 MHz
+AZ plots: El. Angle = 45 deg. @ 35';
+                      39 deg. @ 50'
+EL plots: Az. Angles = 90 deg.
+Feedpoint Z (R ± jX): 450 + 1045 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        450 + 1045
+20   7.3       2.2       3260 + 150
+40   14.5      4.4       480 - 1075
+60   21.8      6.6       150 - 520
+80   29.0      8.9       85 - 255
+100  36.3      11.1      65 - 80
+120  43.6      13.3      65 + 75
+140  50.8      15.5      80 + 250
+160  58.1      17.7      145 + 505
+180  65.3      19.9      450 + 1045
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        450 + 1045
+20   6.1       1.9       1380 - 1500
+40   12.2      3.7       145 - 580
+60   18.3      5.6       55 - 280
+80   24.5      7.5       35 - 130
+100  30.6      9.3       30 - 20
+120  36.7      11.2      30 + 85
+140  42.8      13.0      45 + 215
+160  48.9      14.9      95 + 435
+180  55.0      16.8      450 + 1045
+
+
+ +
+ 
30 meters: 10.125 MHz
+AZ plots: El. Angle = 39 deg. @ 35';
+                      27 deg. @ 50'
+EL plots: Az. Angles = 90 deg.
+Feedpoint Z (R ± jX): 2220 - 3200 ohms
+
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        2220 - 3200
+20   5.1       1.6       155 - 925
+40   10.3      3.1       60 - 440
+60   15.4      4.7       35 - 205
+80   20.5      6.3       30 - 35
+100  25.6      7.8       30 + 125
+120  30.8      9.4       45 + 320
+140  35.9      10.9      90 + 645
+160  41.0      12.5      435 + 1625
+180  46.1      14.1      2220 - 3200
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        2220 - 3200
+20   4.3       1.3       80 - 680
+40   8.6       2.6       30 - 315
+60   13.0      4.0       15 - 150
+80   17.3      5.3       15 - 35
+100  21.6      6.6       15 + 75
+120  25.9      7.9       20 + 200
+140  30.2      9.2       35 + 405
+160  34.5      10.5      160 + 995
+180  38.9      11.8      2220 - 3200
+
+
+ +
+ 
20 meters: 14.15 MHz
+AZ plots: El. Angle = 26 deg. @ 35';
+                      19 deg. @ 50'
+EL plots: Az. Angles = 37 deg. @ 35'
+                       40 deg. @ 50'
+Feedpoint Z (R ± jX): 100 - 50 ohms
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        100 - 50
+20   3.8       1.1       105 + 100
+40   7.3       2.2       140 + 275
+60   11.0      3.4       60 - 270
+80   14.7      4.5       780 + 930
+100  18.3      5.6       1920 - 485
+120  22.0      6.7       500 - 790
+140  25.7      7.8       200 - 430
+160  29.4      9.0       120 - 215
+180  33.0      10.1      100 - 50
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        100 - 50
+20   3.1       0.9       100 + 45
+40   6.2       1.9       125 + 145
+60   9.3       2.8       200 + 275
+80   12.4      3.8       450 + 410
+100  15.5      4.7       925 + 25
+120  18.5      5.7       475 - 40
+140  21.6      6.6       210 - 285
+160  24.7      7.5       125 - 155
+180  27.8      8.5       100 - 50
+
+
+ +
+ 
17 meters: 18.1 MHz
+AZ plots: El. Angle = 21 deg. @ 35';
+                      15 deg. @ 50'
+EL plots: Az. Angles = 54 deg. @ 35'
+                       54 deg. @ 50'
+Feedpoint Z (R ± jX): 2040 + 1640 ohms
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        2040 + 1640
+20   2.9       0.9       815 - 1400
+40   5.7       1.8       185 - 635
+60   8.6       2.6       90 - 320
+80   11.5      3.5       65 - 130
+100  14.3      4.4       60 + 30
+120  17.2      5.2       70 + 195
+140  20.1      6.1       110 + 415
+160  22.9      7.0       285 + 835
+180  25.8      7.9       2040 + 1640
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        2040 + 1640
+20   2.4       0.7       325 - 955
+40   4.8       1.5       75 - 405
+60   7.3       2.2       40 - 200
+80   9.7       2.9       30 - 75
+100  12.1      3.7       25 + 30
+120  14.5      4.4       30 + 145
+140  16.9      5.2       55 + 305
+160  19.3      5.9       155 + 640
+180  21.7      6.6       2040 + 1640
+
+
+ +
+ 
15 meters: 21.15 MHz
+AZ plots: El. Angle = 18 deg. @ 35';
+                      13 deg. @ 50'
+EL plots: Az. Angles = 60 deg. @ 35'
+                       61 deg. @ 50'
+Feedpoint Z (R ± jX): 375 - 1135 ohms
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        375 - 1135
+20   2.5       0.8       115 - 525
+40   4.9       1.5       65 - 255
+60   7.4       2.2       50 - 80
+80   9.8       3.0       50 + 80
+100  12.3      3.7       65 + 255
+120  14.7      4.5       110 + 520
+140  17.2      5.2       370 + 1125
+160  19.6      6.0       4300 + 75
+180  22.1      6.7       375 - 1135
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        375 - 1135
+20   2.1       0.6       75 - 445
+40   4.1       1.3       35 - 220
+60   6.2       1.9       25 - 90
+80   8.3       2.5       20 + 20
+100  10.3      3.2       25 + 130
+120  12.4      3.8       40 + 280
+140  14.5      4.4       110 + 585
+160  16.5      5.0       1215 + 1830
+180  18.6      5.7       375 - 1135
+
+
+ +
+ 
12 meters: 24.95 MHz
+AZ plots: El. Angle = 15 deg. @ 35';
+                      11 deg. @ 50'
+EL plots: Az. Angles = 34 deg. @ 35'
+                       35 deg. @ 50'
+Feedpoint Z (R ± jX): 205 + 335 ohms
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        205 + 335
+20   2.1       0.6       415 + 590
+40   4.2       1.3       1215 + 660
+60   6.2       1.9       1160 - 685
+80   8.3       2.5       400 - 575
+100  10.4      3.2       200 - 325
+120  12.5      3.8       140 - 145
+140  14.6      4.4       125 + 5
+160  16.6      5.1       140 + 155
+180  18.7      5.7       205 + 335
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        205 + 335
+20   1.8       0.5       560 + 515
+40   3.5       1.1       1050 - 240
+60   5.3       1.6       360 - 460
+80   7.0       2.1       155 - 270
+100  8.8       2.7       100 - 135
+120  10.5      3.2       80 - 30
+140  12.3      3.7       85 + 70
+160  14.0      4.3       115 + 180
+180  15.8      4.8       205 + 335
+
+
+ +
+ 
10 meters: 28.5 MHz
+AZ plots: El. Angle = 14 deg. @ 35';
+                      10 deg. @ 50'
+EL plots: Az. Angles = 44 deg. @ 35'
+                       44 deg. @ 50'
+Feedpoint Z (R ± jX): 3235 - 65 ohms
+TL = 450 ohms; VF = .95
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        3235 - 65
+20   1.8       0.6       460 - 1050
+40   3.6       1.1       145 - 510
+60   5.5       1.7       80 - 250
+80   7.3       2.2       65 - 75
+100  9.1       2.8       65 + 80
+120  10.9      3.3       85 + 255
+140  12.8      3.9       150 + 515
+160  14.6      4.4       475 + 1065
+180  16.4      5.0       3235 - 65
+
+TL = 300 ohms; VF = .80
+Deg  Feet      Meters    R ± jX (ohms)
+ 0    0         0        3235 - 65
+20   1.5       0.5       220 - 765
+40   3.1       0.9       65 - 350
+60   4.6       1.4       35 - 170
+80   6.1       1.9       30 - 50
+100  7.7       2.3       30 + 55
+120  9.2       2.8       35 + 170
+140  10.7      3.3       65 + 350
+160  12.3      3.7       225 + 770
+180  13.8      4.2       3235 - 65
+

+
+
+ +
+

Updated 9-1-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, Doublet, HF Lower, HF Upper


+ + diff --git a/content/gup/gup7-1.gif b/content/gup/gup7-1.gif new file mode 100644 index 0000000..71acdd2 Binary files /dev/null and b/content/gup/gup7-1.gif differ diff --git a/content/gup/gup7-2.gif b/content/gup/gup7-2.gif new file mode 100644 index 0000000..6da0bc5 Binary files /dev/null and b/content/gup/gup7-2.gif differ diff --git a/content/gup/gup7-3.gif b/content/gup/gup7-3.gif new file mode 100644 index 0000000..cac2400 Binary files /dev/null and b/content/gup/gup7-3.gif differ diff --git a/content/gup/gup7-4.gif b/content/gup/gup7-4.gif new file mode 100644 index 0000000..cf4852e Binary files /dev/null and b/content/gup/gup7-4.gif differ diff --git a/content/gup/gup7-5.gif b/content/gup/gup7-5.gif new file mode 100644 index 0000000..268e814 Binary files /dev/null and b/content/gup/gup7-5.gif differ diff --git a/content/gup/gup7.html b/content/gup/gup7.html new file mode 100644 index 0000000..06a9fe1 --- /dev/null +++ b/content/gup/gup7.html @@ -0,0 +1,90 @@ + + + + + + How to Make Your Tuner Work on Every Band + + + +
+

ANTENNAS FROM THE GROUND UP

+
+
+

7. My ATU Is No Darn Good
+ or How to Make Your Tuner Work on Every Band

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Once in a while, every multiband antenna user finds him- or herself in this situation: the tuner will just not make a match on one or more bands. So we first check inside the tuner. Then we check all the antenna connections. Finally we check the manufacturerþs address so we can write a letter telling him what a rotten product he makes. +

Actually, the situation is most likely just as it should be--and all because you are not one of the three hams in the country who measured the parallel feedline up to the 135' or 102' multiband antenna.

+

To understand why matters are as they should be--and how we can make them better for us--we need to understand 3 things: 1. What is antenna is doing; 2. What the feedline is doing; and 3. What the ATU is doing.

+

What the Antenna Does: With resepect to the antenna-feedline-ATU system, the antenna presents the feedline with a (normally) complex impedance. This impedance varies from one type of antenna to another and from one band to another, with lesser changes caused by height and wire size differences. Check the feedpoint impedances in the last two installments to see typical variations.

+

What the Feedline Does: Every transmission line is also an impedance transformer. Unless there is a perfect match between the antenna feedpoint impedance and the characteristic impedance (Zo) of the feedline, the complex impedance (R ± jX) will vary all along the line, with values repeating only at 1/2wl or 180° increments.

+

Many hams expect the impedance to vary in nice smooth curves. In fact, the curves are far from sinusoidal.

+
+ +
+

The graph above plots the resistive and reactive components of the impedance along a line that begins at the antenna with a feedpoint impedance of 100 -j50 ohms. These modest values yield a resistance rise near the midpoint of the line and a very rapid shift from inductive to capacitive reactance. This latter shift is characteristic of every line, although the position of the shift and the magnitude of the peak values are functions of the feedpoint impedance and the line Zo.

+
+ +
+

The second graph plots impedances values for another antenna that presents a feedpoint impedance of 2220 - j3200 ohms. Note the differences in the magnitude of peak values and the different placement of the peaks.

+

You can plot graphs of this nature for any antenna feedpoint impedance and feedline type using the transmission line performance program in HAMCALC, which will give you tables of values every 5° along the lossless line. For our purposes here, line losses are not significant to the exercise.

+

To find out about where along your own plot your feedline comes out (at the ATU terminals), divide the total feedline length by the length of 180° (a half wavelength). Toss out the integers and multiply the remaining fraction or decimal by 180. The result is the number of degrees along the line your ATU sees.

+

Remember that these will be ball park figures. But for bands where your ATU has trouble, you should see either very high or very low values for R and/or very high values of X, either capacitive or inductive.

+

What the ATU Does: Right now, I could give you the solution to the dilemma of getting the ATU to match the feedline-antenna system. However, let's go slowly enough to understand how antenna tuners work and why some--even most--have troubles with some combinations of R and jX on at least some bands.

+

ATUs come in two general types: inductively coupled tuners, like the Z- match, and networks, which are the bulk of commercial tuner designs. Both are subject to similar restrictions, but the networks make the problem a little clearer. Networks include all those letter combinations, like CLC, CL, LC, LCL, SPC, and the McCoy Ultimate Transmatch. HAMCALC has a program of great utility, written by ZL1LE, that will let you calculate the values of components for all these networks for matching almost any impedance from the feedline to almost any ATU input impedance. Of course, 50-ohm resistive (meaning no reactance) is the most common impedance to which we match.

+
+ +
+

Let's consider the CLC network that so many manufacturers place on the market. Figure 3 presents the basic components of the network: a series input capacitor, a shunt inductor, and a series output capacitor. Nothing could be simpler. Or is this complete schematic hiding something beneath its bland features?

+

What the simple schematic is hiding is its relationship to its load, the antenna feedpoint impedance. The antenna is in series with the network, so let's draw the load as in Figure 4.

+
+ +
+

We can look at a network from two perspectives. One way, the one used in ZL1LE's transmatch program, is to treat the antenna impedance as the complex quantity to be matched to the ATU input impedance. The other way-- the one we may find it useful to use here--is to split the work into two parts. One part is the resistive part of the antenna impedance: that is the part the ATU matches to the input. The second part is the antenna reactance: that part the ATU output component must compensate for with an equal but opposite type of reactance.

+

If the antenna reactance is inductive, then it seems reasonable that the output capacitor should be able to find a matching setting so that the net reactance is 0. But what about capacitive reactance? There is no inductance in the output. How we do this job requires that we go back to the resistive load matching situation.

+

Every matching situation between the input impedance and the output impedance requires a set of values for Xc-in, Xl, and Xc-out. These values translate into values of Cin, L, and Cout for some specific frequency. But let's think in terms of X (reactance) for a moment.

+

Now let's set up a realistic matching problem at 14.15 MHz. The input impedance is 50 ohms resistive. Initially, the output impedance from the feedline is 100 ohms resistive. There are many settings of a CLC tuner that will provide a match, but for a loss factor under 2%, we need the value of Cin to be at least 175 pF. With an inductance at L of 0.8 µH, the output capacitance should be about 197 pF or (in terms of reactance) -j57 ohms.

+

Now make the impedance at the feedline terminals of the ATU complex: 100 + j50 ohms. The values of Cin and L remain the same, but the value of Cout changes to 105 pF, for a capacitive reactance of -j107 ohms. Notice that this value is exactly -50 ohms different from the value needed to match the pure resistive load. Moreover, it is equal and opposite the reactance in the load, effectively canceling it.

+

With a CLC ATU, the values of inductive reactance that the network can cancel is limited only be the lowest value of the variable capacitor at Cout. Values of 10 to 20 pF are typical for large capacitors. However, there is a 2:1 variance in this lower limit, and that can make a difference in the reactance obtainable. At 14.15 MHz, our frequency in the example, 10 pf = 1125 ohms, while 20 pF = 562 ohms. That difference can make a big difference in the limits of inductive reactance for which the ATU can compensate.

+

Now let's turn the problem around and let the ATU feedline impedance be 100 - j50 ohms. Since the feedline reactance supplies all but 7 ohms of the 57 ohms needed to match the 100 ohms resistive part of the load, the capacitor must be set to a reactance of 7 ohms. However, at 14.15 MHz, this value of reactance corresponds to a capacitance of over 1580 pF, well beyond the range of most capacitors used in ATUs. 250 pF is a practical limit in higher power units, while 350 to 500 pF is about the maximum for QRP units using receiving capacitors.

+

In short, the requirements for a match are beyond the limits of the components. In every network, there are always a range of values that will effect a match. However, in this case, all of them are less efficient (or have greater losses) by a factor of 3 or more.

+

The test case used values which are low enough that we might think there is no problem with them. Operationally, of course, all ATUs would handle them with ease and we would not readily be aware of the greater losses of the less than optimum settings used. However, it is also clear that we can, with extreme values of R and high values of jX, reach the point where no value of the output capacitor will satisfy the conditions of even a lossy match.

+

For example, the first graph at 10.125 MHz shows an input impedance of 2220 - j3200 ohms. Although there are mathematical solutions for matching this load to 50 ohms, they require values of Cout less than 7 pF, a value tuners are not likely to achieve.

+

LCL networks have similar limits in the opposite direction of reactance. In fact, there is no such thing as a perfect tuner. Is there another way to attack the problem of getting a match--and even making it an efficient one?

+

Scissors and Tape Measure: Since buying a new tuner is unlikely to add much tuning capability and is expensive, let's look for a cheaper way to solve the problem. The first step is to measure the length of the parallel feedline. Next, find or develop models of your multiband antenna, similar to those in the last two installments. These models will provide you with ballpark feedpoint impedances.

+

Third, calculate where along a span of 180° your line hits the tuner terminals, as described earlier. Note that throughout this exercise, we are assuming that you are NOT using the 4:1 balun built into many tuners. If necessary to effect connections, use a line isolator choke. Better yet, install terminals suited to parallel feedline that connect directly to the network.

+

Use HAMCALC or another similar program to find the ballpark impedance for each band at the ATU terminals. It is best to run a table of values, because we shall need to refer to other points along the line.

+

Review the graphs at the beginning of this exercise. Notice that along any 180° length of line, there are considerable stretches where the resistance and reactance are both fairly low. Those are values we want the ATU to see. For a CLC tuner, inductive (+jX) reactance is preferable, while LCL tuners prefer capacitive (-jX) reactance.

+

Using the information at hand, calculate a length of line which, if added to the present line, will place your ATU terminals in the proper position to see the desired impedance.

+

Because models and calculations yield only ballpark values that cannot take into account ground clutter, terrain, and construction techniques that place slight deformations into the real antenna, perfecting the results may require some cut and try methods. However, parallel line is cheap, and a failed experiment on one band may leave a line length long enough to trim for another band.

+
+ +
+

Figure 5 illustrates the mechanical elements involved in line lengthening. You will need to find a place to insert line so that it is free and clear, in accord with the principles of good parallel feedline installation. Since it does not matter where along the line you make the addition, you may wish to consider an outdoor insertion point, one that may add a bit of droop to the system when lengthened but which can still be reconnected with ease. Avoid coils and tight hairpins of feedline.

+

If one end of the junction is at the house or shack wall, you can also make this the bad-weather disconnect for the antenna system. Add the special sections here and also connect the line to a ground rod in the event of approaching electrical storms.

+

Once installed, you may discover that the antenna tunes very well on many of the other bands that were not originally part of the problem. If so, make a list to keep at hand so that you only change the line length when necessary. Also copy down for each band the new settings of the ATU required by the new line length. You may even wish to experiment with different lengths of added line, seeking one that works on all your favorite bands.

+

Connectors are largely a matter of choice, since rarely are they critical on parallel feedline systems. If the line does not experience violent pulls, paired banana plugs and jacks used for test instruments can be handy. A myriad of other usable connectors are available, and are most likely already in your junk box.

+

You can, of course, create a monster switching system, remotely controlled from the operating position.

+

Ten years ago, you would have had to develop your "added-line" system solely by cut-and-try methods. Some folks are still satisfied with this shot-in-the-dark technique: they do not want to know whether their additions have improved or worsened the efficiency of their matching network, just so long as they get some kind of match. The tools we have today can upgrade our guesses into reasonable estimates and better understanding. That always helps.
+

+
+ +
+

Updated 11-1-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to series index page

+

Return to Amateur Radio Page

+

Topics: Matching


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+

ANTENNAS FROM THE GROUND UP

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+

8. Crossword Puzzles
+ or Horizontal vs. Vertical Antennas on the Low HF Bands

+
+
+

L. B. Cebik, W4RNL

+

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+ +

+
+ Even on the low bands (160-30 meters), there is a controversy over which is better: a horizontal or a vertical antenna. And of course, the inevitable answer is this: it all depends. . . +

I do not intend to resolve the controversy. Instead, let's try to understand some of what makes the controversy a hamfest favorite. First of all, the polarization of signals is only indirectly related to the dispute. The ionosphere skews most polarized signals most of the time, so that everyone receives a mixed bag--most of the time.

+

Polarization does influence the far field antenna pattern. And that does make a difference. So that is what we shall probe here. We shall confine ourselves to elevation patterns of various antennas, because that will give us a good picture of how far we can throw a signal and catch one coming back.

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Second, since our space is limited, I shall put all of our antennas on 7.15 MHz. However, everything said applies to each of our low bands if you translate all heights into fractions of a wavelength.

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The Horizontal Tradition: Let's start with the 1/2 wl dipole and use it as a standard for comparisons. For the most part, we are interested in various angles of radiation: a. the elevation angle of maximum radiation (take-off angle) and b. certain specific elevation angles for comparing long-distance performance. We can chart the take-off angle at several heights with intervals of 1/8 wl, (which is about 17.2' at 7.15 MHz).

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Ht wl       Ht feet        T-O Angle (deg)
+0.125       17.2           90
+0.25        34.4           61
+0.375       51.6           38
+0.5         68.8           28
+0.625       86.0           22
+0.75        103.2          19
+0.875       120.4          16
+1.0         137.6          14
+
+

Most ham antennas are 1/2 wl or lower on 160-30 meters. Hence, the dipole has a high angle of radiation. The elevation pattern for the dipole at 1/4 wl up looks like Figure 1.

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Although the antenna is quite satisfactory for high-angle, shorter skip paths, the gain at an elevation angle of 20° is about 1.5 dBi. Obviously, the received signals and noise will be dominated by sources closer in.

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We can improve on this situation by building horizontal antennas with lower take-off angles. One such antenna is the wire Yagi. Using #14 wire, a driven element about 66' long and a reflector about 70' long, with about 20' spacing, will give us some improvement in both take-off angle and in gain in the desire direction.

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Ht wl                   Ht feet                 T-O Angle (deg)
+0.125                   17.2                    58
+0.25                    34.4                    45
+0.375                   51.6                    34
+0.5                     68.8                    27
+0.625                   86.0                    22
+0.75                    103.2                   18
+0.875                   120.4                   16
+1.0                     137.6                   14
+

Note that the improvement in elevation angle is mostly at the lowest heights. Above a half wavelength, the take-off angle closely matches that of the dipole. The 2-element Yagi elevation pattern at a 1/4 wl height looks like Figure 2.

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The Yagi exhibits about 3 dB more gain than the dipole at the angle of maximum radiation. At an elevation angle of 20°, the gain is about 5.3 dBi, nearly 4 dB better than the simple dipole. Nevertheless, like the dipole, the received signal and noise is dominated by high angle radiation.

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A unidirectional beam is not the only way to achieve better performance at lower angles. Consider a single, vertically oriented, quad loop about 36' on a side. We shall feed our model at the bottom for a horizontally polarized pattern. This antenna will require high support, but that high wire also provides the antenna with a lower overall elevation angle of radiation at every height. Indeed, with respect to take-off angles, the dipole-equivalent height of a quad is about 2/3rds the way up a quad. Here is the table of take-off angles for the quad loop.

+ 
Ht wl                   Ht feet                 T-O Angle (deg)
+0.125                   17.2                    43
+0.25                    34.4                    32
+0.375                   51.6                    26
+0.5                     68.8                    21
+0.625                   86.0                    18
+0.75                    103.2                   15
+0.875                   120.4                   14
+1.0                     137.6                   12
+

The elevation pattern for the loop with the bottom wire 1/4 wl up appears in Figure 3.

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Although the quad loop cannot match the gain of the Yagi at their respective angles of maximum radiation, the quad has a gain of 5.3 dBi at an elevation angle of 20°. Moreover, if you inspect the pattern of the quad loop, you will see that it devotes less pattern space to the highest angles of radiation found in the dipole or Yagi patterns. The result is that lower angle signals will be proportionally stronger relative to higher angle signals, making reception easier for the operator.

+

There are some very good reasons to avoid horizontally oriented 1 wl loops of any shape (triangle, square, hexagon, etc.) All such loops are designed for radiation broadside to the flat of the antenna. When laid out horizontally, they try their best to radiate upward. At very low heights (up to 1/4 wl), they display take-off angles well above those of a dipole. Between 5/8 wl and 1 wl, they display a center bulge straight upward that is stronger than the low angle radiation lobes. In the table, the main lobe is shown, followed by a secondary lobe angle if the main lobe is straight up.

+ 
Ht wl           Ht feet         T-O Angle (deg)
+0.125           17.2            89
+0.25            34.4            86
+0.375           51.6            44
+0.5             68.8            30
+0.625           86.0            23
+0.75            103.2           84 (19)
+0.875           120.4           59 (17)
+1.0             137.6           48 (15)
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+ +
+

Figure 4 shows the elevation plot of a hex 1 wl loop at 1/4 wl height for comparison with the other antennas.

+

Because it sometimes difficult to grasp the full import of antenna plots when each is set to touch the outer ring, Figure 5 compares in scale the elevation patterns of the dipole, the Yagi, and the vertically oriented quad loop, all at 1/4 wl height, with the quad's lower wire at that height. The figure is larger to make the comparison easier.

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Note especially the very comparable low angle radiation gains for both the quad and the Yagi. However, notice the amount of high-angle radiation in the Yagi pattern.

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The Vertical Mystique: Low-band DXers claim that they can work more DX on a vertical than a horizontal antenna. This assumes, of course, that the DXer in question does not have access to 200' towers and unlimited funds for quads, Yagis, and log periodics. Does the claim make any sense, and if so, why?

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First, let's understand what we mean by a vertical antenna. They come in three general types. First is the quarter-wave ground plane vertical, either ground-mounted or elevated. Related to this antenna are phased arrays of verticals and the 5/8 wl vertical. Second comes the vertical dipole and any antenna that we might derive from a dipole, such as a Yagi. These antennas require no ground plane, since both poles of the antenna are physically included in the design. Third is a class of wire antennas that include the equilateral delta (fed 25% up one leg), the right-angle delta (fed 12% up one leg), and the half square. All of these antennas are closed loop antennas (with the half-square being harmlessly opened at what would have been the high voltage apex). This last antenna is usually mounted with its horizontal wire a the top and the vertical elements hanging downward, while the usual arrangement for the deltas is to run the horizontal wire at the bottom and let the apex be at the top.

+

A more correct way to view the feedpoints of these three antennas is to see them as being 1/4 wl from the apex or open end. All require a full wavelength of wire, with the centermost 1/2 wl of wire constituting a phasing section whose radiation cancels itself, leaving only the radiation from the most vertical quarter wavelength sections. The result is predominantly vertical polarization; more importantly, the patterns take on many of the characteristics of the other classes of vertical antennas. Note, however, that moving the feedpoint to other parts of the antenna radically changes the antenna's pattern and performance. Fed at the center, they are not verticals.

+

Because the ground plane vertical has so many variables that affect its efficiency, let's use the vertical dipole as our standard. Even bypassing the ground-plane antenna, it is difficult to draw exact comparisons among vertically polarized antennas. Verticals do not share a common horizontal plane that we can call the antenna height. However, Figure 6 shows the elevation plot of a vertical dipole 10' off the ground at its lower end. Its feedpoint is about 44' up and the highest end is about 78' up.

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The angle of maximum radiation is 16° and the gain is only 0.24 dBi. However, notice the relative absence of high angle radiation. We shall say more about this before we are finished.

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The right-angle delta is perhaps the more effective of the two deltas, with a feedpoint impedance near 50 ohms. It takes more horizontal space, but less vertical space than the equilateral delta. And it has more gain off the broadside of the antenna. Figure 7 shows the elevation patterns of a right-angle delta with the base at 30' At this height, the take-off angle is 17° and the gain is 2.0 dBi. Lowering the base of the antenna to 20' decreases the gain to 1.9 dBi and raises the take-off angle to 20°.

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+ +
+

Among the wire verticals, the half square has the highest gain, in part because its normal low-band orientation places the high current feedpoint at the uppermost part of the antenna structure. Like the right-angle delta, the corner-fed half square has a feedpoint impedance that closely matches coax. Figure 8 shows the elevation pattern of a half square whose lowest point is 20'. I recommend you keep the half square at this level (slightly lower does not harm performance significantly). The pattern shows a slight bulge at the 60° elevation point, and this bulge grows into a significant lobe as the antenna is further elevated.

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Notice that the gain of the half square is about 3.3 dBi, a significant improvement over both the dipole and the right-angle delta. The cost is a somewhat narrower oval azimuth pattern at the take-off angle of 16° (the lowest of the three verticals modeled here).

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+ +
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To get a better grasp of how much the high angle radiation is reduced by these verticals, Figure 9 shows a composite of the horizontal dipole, the vertical dipole, and the half square, all at the heights specified earlier. Since there is no planar standard, the comparison is only suggestive and not authoritative.

+

Notice that the dipole has the highest gain, but at very high radiation angles. At the lowest angles, the verticals have higher gain, plus a very dramatic reduction of high-angle radiation.

+

Consider the high angle radiation pattern in terms of reception. For the dipole, all of the QRM, QRN, and background noise of the closer skip distances dominates reception, lowering the signal-to-noise ratio of any low angle DX that might otherwise be heard. The verticals, despite their lower maximum gains, act as natural filters, being less sensitive by at least 2 S-units to high-angle radiation. At the lowest (DX) elevation angles, the verticals are competitive in strength with the dipole. Little wonder that low-budget Dxers like them.

+

So What's A Poor Ham To Do? First, think about what kind of operating you like to do and choose the class of antenna that is likely to perform best for that purpose. Second, figure out the limits of what you can erect and maintain. Then go to work on your antenna. Ideally, of course, it is nice to have two antennas, one for shorter skip, one for DX--and a switch. With proper planning and a lot of work, dreams can come true.
+

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Updated 12-15-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

+

Return to Amateur Radio Page

+

Topics: Dipole, HF Lower, Vertical


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+

ANTENNAS FROM THE GROUND UP

+
+
+

9. The Old Gray Mare Ain't What She Used to Be
+ or the Fundamentals of Off-Center-Fed Dipoles (Windoms)

+
+
+

L. B. Cebik, W4RNL

+

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+ +

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+ Off-center-fed dipoles (OCFs) are 1/2 wavelength wire antennas fed at neither the center nor the end, but somewhere between--off-center. They look like Figure 1. +
+ +
+

OCFs are derived from the Windom antenna, a 1929 concoction using a single- wire feed attached to the antenna element at what was believed to be the 600-ohm point. The single wire feedline was presumed to have an impedance of 600 ohms against ground. See Notes of Mr. Windom's "Ethereal Adornments".

+

The magic dimensions of the OCF vary from writer to writer. The dimension L is almost universally given as the ballpark dipole formula

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Windom gives the offset by the formula

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Later developments that replaced the single-wire feedline with a normal two-wire feedline preferred somewhat different dimensions. The ARRL Antenna Book uses the formula

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Carr gives the figure as 0.174 (Practical Antenna Handbook). What these numbers have in common is the belief that the feedpoint is the 300-ohm point along the antenna element. Some builders wish to insert a 4:1 or a 6:1 balun at this point and feed the antenna with 50-ohm coaxial cable.

+

The antenna is claimed to provide a good match under these conditions to coax on the fundamental and most even harmonics. An 80-meter antenna would thus match well on 40, 20, and 10, while a 40-meter antenna would match well on 20 and 10 meters.

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A more recent version of the antenna cut for 40 meters uses a different ratio:

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This placement is believed to hit the 100-ohm point on the antenna wire, where a 2:1 balun will reduce the impedance to 50 ohms for coaxial feed on the fundamental and even harmonics. This version of the OCF assumes that there is RF on the outside of the coax forming a supplemental vertical radiator of about 10' length on the 40-meter model. The claims made for this technique are (1) an increase in gain off the ends of the antenna and (2) a lower angle of maximum radiation.

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We could go on reciting claims about the OCF, but these are enough to give a flavor of the reported benefits of the design. I have even seen claims that it outperforms a beam. On the down side are experiences by many QRO users of RF in the shack. In addition, many builders have seemed unable to achieve the nice clean 50-ohm matches claimed by some Windom kit sellers.

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So we have a pair of questions: a. How does an OCF work? And b. Are any of the claims about OCFs true enough to be reliable?

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The OCF does work! Before we tackle the claims made about the OCF antenna, let's start by saying that it will work, but not significantly better than a dipole of the same length. Hence, the best installation for an OCF is a matter of convenience. If feeding the antenna up to a ratio of D1/D2 of 1/3 is more convenient to the shack, then do so. However, use parallel feedline and an ATU for all-band matching purposes, omitting all baluns (even the one inside the tuner.)

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To prevent RF from affecting other shack equipment, do one of the following things: a. At the entry to the house or shack, install a W2DU choke and convert to coax to the ATU; or b. Between the ATU and the transceiver, install a line isolator (another name for the W2DU choke) at the ATU end of the cable.

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By the time we complete our analysis of the claims made for the OCF, you will understand why the antenna is not much different than a center-fed dipole, and certainly not significantly better.

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How long to make it and where to feed it: As you move the feedpoint of a 1/2 wavelength wire from the center toward the end, the impedance increases while remaining essentially resistive with no reactive component. Hence, somewhere along the wire, there is a 100-ohm feedpoint, a 300-ohm feedpoint, and a 450-ohm feedpoint. However, we have learned that the feedpoint impedance of a resonant center-fed dipole changes with the height of the antenna. Moreover, the resonant length of the antenna changes with the height. Hence, the various desirable feedpoints are not at the same place on antennas of different heights.

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The first graph shows the length of two 40-meter OCFs, one at 35' and the other at 70' (1/4 and 1/2 wavelength up, respectively). The percentages are the ratio of D3 to 1/2L, in other words, the percentage of the distance outward from the center for the feedpoint. Not only are the lengths of the two antennas different, but as well, the resonant length of the antenna grows longer as the feedpoint is moved outward, especially after the 25% to 30% mark. In no case does the antenna correspond to the overall length given in equation (1).

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The second graph gives an overview of what happens to the feedpoint impedance of the antenna as that point is moved outward from center. Note that as the impedance passes through 300 ohms, the curve grows steeper rapidly, making the process of setting a 300-ohm feedpoint tricky at best. It is much easier to hit the 100-ohm feedpoint, but not quite as easy as this compressed graph suggests.

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The third graph decompresses the second by cutting off the steepest part of the curve. It reveals the quite different feedpoint impedances for the two antennas as the feedpoint moves away from center.

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Remember that the NEC models from which these graphs are derived presume level, uncluttered terrain. Messy, uneven terrain will throw additional variables into the mix. Finding the exact feedpoint positions to match any given feedline will be challenging at best.

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Moreover, the feedpoint positions are fairly narrow-banded. The illusion of broadband performance is usually achieved by the use of lossy balun designs. Although QRO may have power to spare for such purposes, QRP operations rarely have that luxury.

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What About the Radiation Pattern? An OCF at its fundamental frequency performs similarly to a center-fed dipole of the same length. A center-fed half wavelength wire antenna cut for 7.15 MHz (about 67.3' long) has a maximum gain of about 7.6 dBi at 70' up, with an elevation angle of maximum radiation of 27 degrees above the flat, uncluttered terrain assumed by NEC programs. This is the standard against which to measure the performance of OCF antennas.

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If we first assume that all radiation occurs in the antenna element and none in the feedline, then we discover that the gain of an OCF for the same frequency at the same height is 7.6 dBi with a take-off angle of 27 degrees. Figure 5 shows the azimuth pattern.

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This pattern is taken from the 300-ohm feedpoint position, which (at this height) indicates a length of 10.4' on the short side of the feedloint and 57.35' on the long side. In this configuration, the asymmetry is barely noticeable, as the angle of maximum radiation bends by a mere 2 degrees from that of a dipole and the long end of the antenna shows about 2 dBi less indentation than the short side.

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We might assume that this pattern holds for the version of the OCF antenna that uses a 4:1 or a 6:1 balun at the antenna feedpoint. Of course, we must also assume that the balun is lossless and that it effects a very high degree of isolation between the antenna wire and the feedline. If the balun alone does not achieve the isolation, we might also insert a W2DU choke on the coax side of the balun.

+

Next, let's assume that the feedline radiates. Most treatments of feedline radiation in modeling have been oversimplified to the point of presenting highly misleading results. The key mistake has been to assume that there is a lossless division of current at the junction of the antenna and the radiating vertical wire. The second assumption is that the feedpoint impedance remains essentially the same as when the antenna alone does the radiating. Neither assumption is necessarily true.

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Moreover, modeling transmission line physically also presents problems that lead many modelers to improperly oversimplify their models. 450-ohm line is easier to model, since it uses wider spacing. 300-ohm line requires closer spacing. Since NEC-2 is most accurate when all wires are of the same diameter, and since physical models of transmission lines will have a velocity factor of 1, the physical model will always be only an approximation of the use of actual feedlines.

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Nonetheless, modeled feedlines checked for accuracy against a center-fed dipole can determine certain facts and trends that apply to the OCF. First among those facts is that when the feedline radiates, the impedance at the junction of the antenna element and the feedline is no longer what is was for a nonradiating feedline. The feedline is part of the antenna. If we use a parallel feedline from the antenna element to some point below it, the radiation that results from this line is not due to the entire current on the line, but only from that part of it which is not balanced. Failure to note this situation has resulted in significant overestimates of the degree to which feedlines radiate and to the contribution of the feedline to the overall antenna pattern.

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Figure 6 shows the azimuth pattern of our 7.15 MHz OCF with 35' of 300-ohm parallel feedline. With this length of radiating parallel feedline, the gain of the maximum lobes drops to about 5.9 dBi. The lost gain goes into the radiation off the ends, which is increased a few dB on each side of the pattern. The overall performance in this mode is essentially that of a basic dipole.

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Terrain unevenness and ground clutter will likely make a much larger difference in the performance of individual OCFs than the radiation from the feedline.

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Let us assume that instead of a length of parallel feedline, a single wire runs from one side of the antenna straight down for 35' or so. This is the assumption made by many modelers for the situation of radiating coaxial cable shields. Although this assumption may be closer to correct for center-fed antennas where there is a direct connection between the cable shield and one side of the antenna, the assumption is dubious in the case of OCFs because builders ordinarily insert baluns or ununs at the antenna element junction to effect an impedance transformation.

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Figure 7 shows the azimuth pattern of an antenna meeting our assumptions. The gain of the main lobes is up to 7.3 dBi, but the radiation off the ends is down compared to the radiating parallel feedline. However, the differential among all three of our antennas is operationally insignificant.

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Even lengthening the feedline to a half wavelength does not alter the pattern very significantly. Under these same conditions, again assuming a perfect connection to the antenna element, one might achieve a one-sided puckered peanut pattern, but with a maximum gain of only 5.7 dBi and with only a 1 degree reduction in the angle of maximum radiation.

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Figure 8 shows what happens if we increase the radiating parallel feedline to a full half wavelength. The gain drops to about 3.7 dBi, with a take- off angle of 24 degrees. The pattern is a significant oval (instead of a peanut): it yields a somewhat stronger signal off the ends--but no more than for an inverted Vee of moderate slope at the same peak height.

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At the fundamental frequency of an OCF antenna, performance is thus at best similar to that of a center-fed 1/2 wavelength dipole and at worst about that of an inverted Vee. Intentionally striving for a radiating feedline achieves very little, while accepting a feedline that radiates harms little (if adequately isolated from equipment in the shack). Stay tuned; there's more to come.
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Updated 1-25-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to series index page

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Return to Amateur Radio Page

+

Topics: HF Multi Band, Off Center Fed Dipole


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+

+ 		+
+

Antennas

+

Service and Education

+ Version 10, December 2008
+
+ L. B. Cebik, W4RNL (SK)
+ 1939-2008 +
+
+


+

Tales and Technicals

+

At present, this portion of the site contains the complete set of selections from my notebooks, called Tales and Technicals. Besides a few notes on the history of radio work and some other semi-technical oddities, the collection contains information of interest to radio amateurs and professionals interested in antennas, antenna modeling, and related subjects, such as antenna tuners and impedance matching. My notebooks are geared to helping other radio amateurs and antenna enthusiasts discover what I have managed to uncover over the years and then to go well beyond.

+

Antenna Modeling Aids

+

Until now, there has been no systematic introduction to antenna modeling. To correct this lack I have prepared a book, Basic Antenna Modeling: A Hands-On Tutorial, for Nittany-Scientific's NEC-Win Plus NEC-2 antenna modeling software. The volume can be used as a college text, a seminar manual, or as a self-study guide. The book contains models in .NEC format for over 150 exercises. Since the principles in the book apply to any modeling software, I have also created the same exercise models in the EZNEC format as a separate product. The book and the .nec models are available on the Antenna Modeling Aids page.

+

In addition, to answer the needs of those wishing to have a significant collection of models to study or to use as the foundation for further design or analysis work, I have prepared sets of models in both .EZ and .NEC formats. These models, comprising 7 sets of over 100 models each.

+

For more advanced modelers using either NEC-2 or NEC-4, I have prepared an additional volume, Intermediate Antenna Modeling: A Hands-On Tutorial, based on Nittany-Scientific's NEC-Win Pro and GNEC. The volume includes hundreds of antenna models used in the text to demonstrate virtually the complete command set (along with similarities and differences) used by both cores. An analytical table of contents and a sample chapter are available at the NSI site, found on the "Books" page.

+

The books and its models, and information about antenna modeling programs are available on the Antenna Modeling Aids page.

+

Antenna Books

+

I have written a few books for amateur radio operators and for antenna enthusiasts. They are listed on the linked page, with further links to their sources.


+

See you later.......

+

+
+ + + + + +
L. B. Cebik, W4RNL (SK)
+ Knoxville, TN
+
+
+

+

To Learn. To Teach. To Serve.

+

+

Pages by The House of Two Lions


+ + diff --git a/content/link/annecke1.jpg b/content/link/annecke1.jpg new file mode 100644 index 0000000..d9ec38f Binary files /dev/null and b/content/link/annecke1.jpg differ diff --git a/content/link/annecke2.jpg b/content/link/annecke2.jpg new file mode 100644 index 0000000..774d0d1 Binary files /dev/null and b/content/link/annecke2.jpg differ diff --git a/content/link/annecke3.jpg b/content/link/annecke3.jpg new file mode 100644 index 0000000..b5ebe90 Binary files /dev/null and b/content/link/annecke3.jpg differ diff --git a/content/link/annesch1.jpg b/content/link/annesch1.jpg new file mode 100644 index 0000000..c126deb Binary files /dev/null and b/content/link/annesch1.jpg differ diff --git a/content/link/l-bal-1.gif b/content/link/l-bal-1.gif new file mode 100644 index 0000000..b65efea Binary files /dev/null and b/content/link/l-bal-1.gif differ diff --git a/content/link/l-bal-2.gif b/content/link/l-bal-2.gif new file mode 100644 index 0000000..6a05526 Binary files /dev/null and b/content/link/l-bal-2.gif differ diff --git a/content/link/l-bal-3.gif b/content/link/l-bal-3.gif new file mode 100644 index 0000000..c71f499 Binary files /dev/null and b/content/link/l-bal-3.gif differ diff --git a/content/link/l-bal-4.gif b/content/link/l-bal-4.gif new file mode 100644 index 0000000..c98d2bc Binary files /dev/null and b/content/link/l-bal-4.gif differ diff --git a/content/link/l-bal.html b/content/link/l-bal.html new file mode 100644 index 0000000..fa6fa39 --- /dev/null +++ b/content/link/l-bal.html @@ -0,0 +1,127 @@ + + + + + + The Balanced-L Network + + + +
+

The Balanced-L Network

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The demise of the link-coupled antenna tuner has left a hole in the array of available antenna tuners. The link-coupled tuner had been the mainstay among tuners for handling antennas that present a wide range of impedance values to parallel transmission line and required--ideally--a balanced coupler to coincide with the transmission line balance. The multi-band doublet, the horizontal or vertical multi-band loop, and a host of phased arrays come to mind as antennas that achieve the greatest efficiency with a balanced antenna tuner. However, as of this writing (12-2002), despite some initial hope, no maker has come forward with a commercial link coupled tuner to replace the long-gone U.S. Johnson MatchBox or the German Annecke ATU.

+

The single-ended network--including the PI, T, and L--is inherently unsuited to matching the impedances of such antennas, as presented to the ATU terminals, to the standard 50-Ohm unbalanced outputs of current transmitting and receiving equipment. Placing a 4:1 balun at the output terminals of such tuners has always been a source of concern, since the impedance at the terminals may be highly reactive, a condition unsuited to many balun designs. As well, the terminal impedance may also be low as the line transforms the impedance continuously along each half wavelength, and a 4:1 balun only succeeds in making it lower.

+
+ +
+

A 1:1 choke balun has been used with some success. As Fig. 1 shows, placing this choke-balun at the shack-entry point can serve two purposes. A. It converts the balanced line input to an unbalanced condition by essentially suppressing currents that would otherwise flow on the outside of the coax braid. B. It permits the installation of a good earth ground at the shack-entry point, which has some advantages for safety and for further isolation of equipment from common-mode currents.

+

However, the advantages come at a price. The SWR on the coax inside the shack remains in many cases very high. The losses in this line due to SWR increase with both frequency and the length of the line and function as a multiplier on the basic loss per unit length of the coax line selected. The keys to minimal inside line loss are then to use as short as feasible a length of coax from the entry-point to the tuner and to use the lowest-loss coax that one can obtain. Even at QRP power levels, using a large diameter, low-loss length of coax for this run is extremely advisable.

+

The Balanced L-Network

+
+ +
+

Recent times have seen the development of balanced network tuners. Fig. 2 shows a comparison between the single-ended L-network and its balanced counterpart, set up here for up conversion and in a low pass configuration. (A down conversion L-network would place the capacitor at the input side of the network. A high- pass configuration would use series capacitors and shunt or a parallel inductor.) The values required for converting a single-ended network to a balanced network are in the aggregate the same as those for the single-ended network. However, the inductors in the lower part of the figure are in series, so each has 1/2 the value of the required single-ended inductor.

+

The capacitor, as shown, represents the total capacitance required across the network output to effect a match for a given impedance condition. With a single capacitor, we cannot place an earth ground at the line center as an aid to effecting balance between the two legs of the transmission line. In most, but not all, practical applications, this ground is not necessary. However, should we wish to implement such a line-centered ground, we may change the capacitor to a split-stator type and ground its common. Since the two halves of the capacitor must in series yield the required total capacitance for a match under given output terminal conditions, each half of the capacitor must have twice the capacitance of the single unit shown in the figure. This requirement result in large capacitors, especially where high power and high voltage across the plates might be anticipated. The vastly increased space requirements (or cost requirements for one who purchases such a component) generally has led designers to use single-section capacitors.

+

The 1:1 balun in the balanced L-network appears at the input side of the network, between the balanced L and the line connector for the transceiving equipment. Except for brief periods during initial tune-up, the balun operates under ideal or close to ideal conditions, that is, with 50 Ohms resistive at its output terminals. Hence, most standard trifilar or bead-choke 1:1 balun designs operate at very high efficiency levels.

+
+ +
+

Fig. 3 shows the balanced L-network--and its single-ended counterpart--set up as a down converter using a low-pass configuration. If we had used a high-pass configuration, with series capacitors and a parallel or shunt inductor, we would achieve a circuit identical to that of the beta or hairpin match. The hairpin match achieves its shunt inductive reactance with a shorted transmission line stub instead of a "lumped" inductor. Otherwise, all of the principles applicable to the up-converting L also apply to the down-converting L, whether single-ended or balanced.

+

Balanced L-Networks vs. 3-Component Networks

Commercial implementations of the balanced L-network are beginning to appear. In general, they are offered in preference to balanced PI-networks and balanced T-networks. Fig. 4 shows the general outlines of both of these 3-component networks in single-ended configurations. The PI is a low-pass configuration, while the T is a high-pass configuration. +
+ +
+

The 3-component network offers a distinct advantage over the L-network. One may effect a match on a given frequency for any "in-range" impedance without switching a component from the output to the input side of the network (or vice versa). As well, one may even effect a match for a 50-Ohm resistive load at the antenna terminals of the tuner. In most cases, the user does not know what the load impedance is, and the ability to tune any load within the overall tuner range is a convenience.

+

However, we pay a price for the convenience. For virtually any load impedance, the L-network has lower losses than the T or PI. We may define a factor for any of the networks and call it (following Terman) delta. In recent times, we have come to refer to the factor as the network Q or the working Q of the network. For the L-network,

+
+ Delta = SQRT ((Ri/Ro)-1) +
+

where Ri is the network input impedance and Ro is the network output impedance.

+

By itself, delta is simply a number. However, the network losses are directly related to the ratio of delta to the unloaded Q of the network components. In most--but not all-cases, the limiting component Q is that of the inductor. Maintaining a low loss network of any type requires that we uses network components with the highest possible unload values of Q.

+

The calculations of delta for PI and T tuner networks are more complex. In the series "Antennas From the Ground Up, see the article ATUs, Delta, and Tuner Losses for further information on 3-component network losses, and the following item as well. The general outcome is this: for any matching conditions within the range of both an L-network and a PI or a T network, the L-network sill show lower losses (assuming that the components in all cases have the same unloaded Q values).

+

However, the L-network, whether single-ended or balanced has a second inconvenience besides the requirement for switching the shunt component when going from up-conversion to down-conversion and back. The component values required to effect a match for impedances within a ratio of about 1.5:1 (or .67:1 for down conversion) relative to the input impedance tend to be impractical in a wide-band antenna tuner. Hence, for matching impedance above 35 Ohms but below about 75 Ohms, one must simply omit the L-network and feed the antenna directly (accounting for the shift from unbalanced coax to a balanced line, of course).

+

Commercial implementations of the balanced network tuners tend to opt for the L- network because it achieves economy. Anyone who has priced high-voltage variable capacitors of either standard or vacuum design will easily note the saving accrued by eliminating one from the circuit. A patch panel, switch, or relay tends to be far less expensive. While this economy also affects ATU home- builders, the lower losses of the 2-component network may also be appealing, while the inconvenience of switching network ends with the shunt component may be accepted as the appropriate trade-off.

+

Balanced L-Network Component Values

The next question concerning a balanced L-network concerns the components that we must use to effect a match with various loads. Using calculation methods developed by Brian Egan, ZL1LE, and available on recent version of HAMCALC from VE3ERP, we can survey those values from 160 to 10 meters. Table 1 provides calculated data for some up- and down-conversion loads that are purely resistive. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 1.  Calculated Values for L-Network matching to various Resistive loads
+from 15 to 2500 Ohms.  All inductance values (L) in uH, all capacitance values
+(C) in pF.  Loads are in Ohms.
+
+Up-Conversion     Load = 100  Load = 250  Load = 500  Load = 1000 Load = 2500
+Freq.             L     C     L     C     L     C     L     C     L     C
+1.8               4.4   884   8.8   707   13.3  531   19.3  385   30.9  248
+3.75              2.1   424   4.2   340   6.4   255   9.3   185   14.9  119
+7.15              1.1   223   2.2   178   3.3   134   4.9   97    7.8   62
+10.125            .79   157   1.6   126   2.4   94    3.4   69    5.5   44
+14.175            .56   112   1.1   90    1.7   67    2.4   49    3.9   31
+18.118            .44   88    .88   70    1.3   53    1.9   38    3.1   25
+21.225            .38   75    .75   60    1.1   45    1.6   33    2.6   21
+24.94             .32   64    .64   51    .96   38    1.4   28    2.2   18
+29.0              .27   55    .55   44    .82   33    1.2   24    1.9   15
+
+Down-Conversion         Load = 35   Load = 25   Load = 15
+Freq.                   L     C     L     C     L     C
+1.8                     2.0   1158  2.2   1768  2.0   2701
+3.75                    .97   556   1.1   849   .97   1296
+7.15                    .51   291   .56   445   .51   680
+10.125                  .36   206   .39   314   .36   480
+14.175                  .36   147   .28   225   .26   343
+18.118                  .20   115   .22   176   .20   268
+21.225                  .17   98    .19   150   .17   229
+24.94                   .15   84    .16   128   .15   195
+29.0                    .13   72    .14   110   .13   168
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table uses amateur-band center frequencies for all but the limiting bands, where we use a low frequency for 160 meters and a high (but not the highest) frequency on 10 meters.

+

Maximum and Minimum Component Values

For up-conversion, the maximum component values are all feasible, even on 160 meters. However, for down-conversion, the lower the impedance, the greater the chances for requiring a capacitance value that exceeds practical implementation as a standard-construction high-voltage air-variable capacitor. A 3000-pF, 5-kV or higher air-variable is a very large unit, indeed. +

The inductor--with respect to maximum required component values--is not a problem. The table lists the total for the 2 series inductors, so each inductor requires only half the total. A pair of inductors, each with a 20 uH maximum value, would easily handle the required load.

+

The troublesome part of the patterns of required component values concerns minimums. The values given are--in a practical circuit--the sum of the component values and any stray capacitances and inductances within the overall ATU unit. The minimum capacitance available is partly a consequence of capacitor construction. Many capacitors--especially military surplus units found at hamfests--use heavy frames with full size end plates and even bottom plates that cover most of the bottom of the capacitor. Such units may have a minimum capacitance of up to 30 pF for a maximum capacitance of 150-200 pF. In contrast stand the E. F.Johnson (later, Cardwell) high-voltage units that have small trapezoidal end plates and a bar running the length of the unit to connect the end plates and permit mounting. For the same maximum capacitance, the minim is only 12-15 pF. Even better are some current designs that use non-conductive end plates and front-to-rear bracing bars. Their minimum value may be as low as 8-9 pF. Some capacitors also use plate-shaving techniques to further lower the minimum capacitance.

+

However, minimum capacitance is not solely a function of the capacitor structure. The plates and other components of the network may be at a different potential from each other, from nearby leads, and from the metal ATU case. In all of these instance, we have a level of capacitance that we cannot eliminate with redesign of the circuit and the overall unit. The simplest way to tell if a case is introducing stray capacitance is to remove it and check the ATU settings under very low power and otherwise controlled test conditions.

+

As the basic table shows, minimum inductance can be a major limitation in down conversion. All is not lost in this regard, even if the minimum inductance that we can obtain is higher than the required component value. Down conversion tends to be very broad-band, and one can obtain usually a match to within less than 1.5:1 50-Ohm SWR, a useful if not perfect value.

+

Adding to the series combination (additive) of the two inductors in a balanced L-network is the inductance of the leads. The more complicated the switching-- whether we are switching in a fixed capacitor to achieve a high value or switching the capacitor from the output to the input end of the network--the more likely we are to find stray inductance that raises the minimum value that we may obtain. A secondary problem associated with stray inductance within an ATU is the fact that is usually has a low unloaded Q. Hence, the loss level of the circuit rises.

+

The appropriate countermeasures, of course, include a detailed inspection of the circuit to see if one can redesign component placement to keep leads as short as feasible. With large components designed for high power duty, we can do only so much in this arena. We can also try replacing the case with a non-conductive case. To a large measure, any radiation from an ATU is a function of linear leads that do nothing to confine the fields that surround them. Hence, it is a bit of a gamble to move to a non-conductive case. However, it is worth a try. If the radiation is too high and eludes efforts to reduce it, then one can simply use a larger case within which we try to center the network components, that is, we try to keep the network components well-spaced from the case walls.

+

Reactive Loads

We have based our initial survey of the conditions under which a balanced L- network must operate on resistive loads. As a general guide, let's look at some sample cases of reactive loads. In Table 2, we shall examine some high- and low- impedance loads, each impedance having a 45-degree phase angle. Hence, we shall match 100 Ohms resistance with +j100 Ohms and with -j100 Ohms. In addition, we shall only look at 160, 80, and 10 meters, the HF frequencies likely to represent the limits of an ATU that we might construct. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Table 2.  Calculated Values for L-Network matching to various Resistive +/-
+Reactive loads from 100 to 2500 Ohms.  All inductance values (L) in uH, all
+capacitance values (C) in pF.  Loads are in Ohms.
+
+Up-Conversion           R = 100     R = 100     R = 2500    R = 2500
+                        X = j100    X = -j100   X = j2500   X = -j2500
+Freq.                   L     C     L     C     L     C     L     C
+1.8                     7.7   1208  7.7   324   44.0  194   44.0  158
+3.75                    3.7   580   3.7   155   21.1  93    21.1  76
+29.0                    .48   75    .48   20    2.7   12    2.7   10
+
+Down-Conversion         R = 35      R = 35      R = 15      R = 15
+                        X = j35     X = -j35    X = j15     X = -j15
+Freq.                   L     C     L     C     L     C
+1.8                     2.8   2062* 5.1   1158  0.7   2701  3.4   2701
+3.75                    1.3   990*  2.5   556   .34   1297  1.6   1297
+29.0                    .17   128*  .32   72    .04   168   .21   168
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The starred entries in the down-conversion portion of the table indicate that the required configuration of the balanced L-network is for up-conversion, that is, with a shunt output capacitor. Note the high values of capacitance required for both 160 and 80 meters. such values will likely fall outside the range of what we build into either a 160-10-meter or an 80-10-meter ATU.

+

At the highest frequency for which I calculated values, down conversion requires the smallest inductance values. 0.2 uH will be difficult enough to attain with the best components; 0.04 uH is outside of practical reality in a multi-band tuner.

+

For an interesting home-brew balanced-L tuner using tapped coils, see the website of Adam, N4EKV: www.n4ekv.com/tuners.asp.

+

Why 160 or 80 Meters Through 10 Meters?

I once designed an SPC single-ended network tuner for 20-10 meters due to the relatively poor performance on my C-L-C single-ended T-network tune on the highest bands (12, 10). No single cause attended the weakness in the 80-10-meter ATU, but the component minimum values and a tight-fitting metal case all contributed to 10-meter problems with a 100' doublet. The SPC unit used Johnson 4.5 kV air variables (a 50 pg single unit and a 50-50 pF split stator), and the rotary inductor had a maximum inductance of 6 uH. The case was no deeper than the original, although the components were considerably shorter. My case was both wider and higher than the commercial case. These measures doubled--at least--the range of matchable impedances, and the component Q was sustained at least through 30 MHz. +

Similar thinking is applicable to a balanced L-network. Although we tend to think of an 80-10-meter ATU as some sort of standard, only our demand for convenience has created that standard. Neither commercial nor handbook designs covering those bands tend to address either the range of matchable impedances as it changes with frequency or the loss of component Q with increasing frequency due to strays.

+

Consequently, it is up to the individual ATU builder to design a unit to meet his or her needs and having the highest component Q available. If attaining a wide tuning range on the upper HF bands requires one to reduce the coverage to 20-10 meters to achieve this goal, then perhaps this is the route to go. In many cases, we shall have to suffer with the shortcomings of a wide-band unit, since it is difficult to carry individual ATUs for each band to a DXpedition on a remote island. Nevertheless, we are not under such restrictions at the home station. As well, it is often easier to find rotary coils with low values at good prices, since they are in far less demand then units with a maximum inductance ranging from 10 to 30 uH.

+

These notes certainly do not cover every aspect of balanced L-networks. However, they may serve to alert you to both the potentials and the limitations of these substitutes for the link-coupled tuner.

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+ +

+
+

Updated 12-13-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: Matching


+ + diff --git a/content/link/link.html b/content/link/link.html new file mode 100644 index 0000000..ce11bc4 --- /dev/null +++ b/content/link/link.html @@ -0,0 +1,133 @@ + + + + + + Link-Coupled Antenna Tuners + + + +
+

Link-Coupled Antenna Tuners

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+

L. B. Cebik, W4RNL

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We have gone to great lengths to adapt unbalanced antenna tuners (ATUs or transmatches) to service with balanced lines. Among the schemes used are the following most common ones:

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1. Float the tuner from ground and install a balun at the input end;

+

2. Install a balun, usually 4:1, at the antenna side of the tuner, to convert the balanced line to an unbalanced line;

+

Either system is subject to limitations. Floating the tuner does not guarantee freedom from common-mode currents that defeat balance. A 4:1 balun often reduces the already low impedance at the antenna terminals to a still lower one, and high reactances are normally unfriendly to the cores used in such baluns.

+

It is possible to build perfectly usable balanced network tuners. However, the parts count goes up, and ganging the components often presents further building and size difficulties. However, in the search for an ATU design that will handle balanced lines naturally, balanced PIs and Tees should not be overlooked by adventuresome home builders. A simple 1:1 balun on the transmitter side converts the resistive balanced input load to the unbalanced line for which the transceiver is designed.

+

To make a balanced network, chose a good unbalanced network as a model. Look at the series elements. Put one in each line in corresponding positions, but use half the reactance. For a coil, that is half the inductance; for a capacitor, that is twice the capacitance. Now look at the shunt component(s), those from the series line to ground in the unbalanced network. Use the same value across the two lines of the balanced network. This simple conversion leaves the system center floating, but that is rarely a problem. Do not forget to add the balun (1:1, 50 ohms) at the input. And remember that there is no safe place to put your finger when the system is hot.

+

A more classic alternative is the link-coupled or inductively coupled ATU. The figure shows the basic circuitry. The unbalanced input is inductively coupled to the main inductor. Since the mutual inductance between the coils is critical for maximum efficiency, the coupling is varied either by a movable link or by a series input capacitor.

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The output is shown in a typical parallel configuration. To effect the best match, clips are provided to connect the line to the proper turns on the main inductor, as determined by maximum feedline currents. The split- stator capacitor or dual ganged capacitors can be connected to ground so that the system is balance with respect to system ground, as shown at *. However, the tuner will remain balanced if the ground is lifted.

+

The ** point indicates that the rotators of the capacitors may be separated and lifted from ground. In this case, they can be connected to the output terminals instead of using a coil tap. For further flexibility, the stators can be connected to various taps on the coil for maximum output. This configuration, often called the series connection, permits efficient matching to low impedances presented at the output terminals of the ATU.

+

To the best of my knowledge, no one in the U.S.A. is currently producing such a tuner commercially. Chapter 25 of recent ARRL Antenna Books has a simple tuner with some limitations in link-main coil coupling efficiency, but not a bad start. The only commercial unit I know of was made in Germany until a few years ago.

+

Despite their relative scarcity, link-coupled tuners have certain advantages over all other tuners. First, they are inherently designed for use with balanced feedlines. Second, they exhibit very low losses, even at high power levels with reasonable care of construction. Third, they can be configured to almost any balanced line condition that might face the operator.

+

However, they also have certain disadvantages. First, they do not lend themselves to automated or rapid changes in setting and configurations as one changes bands. Second, they work best when equipped with plug-in coil sets that permit the most optimal coil-link size ratios.

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A network tuner provides the most efficient match when its variable components are truly variable rather than switched. This principle applies especially to the inductor. A switched inductor may provide a 1:1 match at one or more settings, but it does not necessarily permit the use of the most efficient (lowest loss) setting of the coil. Likewise, a single coil and link for all HF bands does not provide the best coupling ratios for all possible conditions. Without provision for coil tapping and series connections, the most efficient operating mode may be inaccessible, despite a 1:1 match.

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For a "hurry-up" operator, these inconveniences may be worse than the losses inherent in current systems pressed into balanced-line duty. However, for operators seeking the most efficient transfer of power to balanced lines, nothing beats a properly designed and constructed link- coupled ATU.

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Will we ever see link-coupled tuners on the market--or even the components necessary for us to roll our own? These include reasonably priced capacitors or capacitor sets, along with plug-in coil systems similar in concept to some of the old Millen sets. (I doubt that, even under the best of conditions, that we shall see reasonably priced swinging link sets.)

+

Here is a wide-open field for the entrepreneur who understands both the concepts of link coupled tuners and has the know-how to develop well constructed plug-in coil assemblies and allied components. If parts and designs were available, I'll bet there is a customer base that would make the venture mildly profitable at the 100-200 watt level and at least break- even at the 1500 watt level. (For QRP work, I would use nothing less than a 100-200 watt ATU to minimize losses associated with tiny layouts and components. I would reserve the super-tiny--for example, compact Z- matches--for field work, where size and weight reductions may overshadow potential losses.)

+

To this moment, I have received no direct word of a return of the Annecke tuner to the marketplace or of a modern replacement for the Johnson Matchbox. Parts, especially coil stock for the inductor and link, may have become prohibitively expensive. As well, there is a fiercely competitive market for single-ended network tuners equipped with various types of toroidal baluns (transmission-line transformers) to handle balanced lines. However, interest in inherently balanced tuner designs, such as the link coupled tuner and some balanced network tuners with 1:1 choke baluns on the 50-Ohm side of the system remains quite high. Interestingly, the latest and most competent of the single-ended network tuners seem to be priced in the range one might expect for a link tuner of the same power-handling capability. Balanced network tuners are even more costly. Indeed, the manufacturing economies inherent in network tuners may likely have removed the possibility of any return to commercially-made link-coupled tuners.

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+

The Johnson Matchbox and the Annecke Parallel-Line Tuners

+
I have heard the Johnson Matchbox described as a modified Z match, which is not quite right. Having obtained one, I thought I might describe the circuit, which appears to be very similar to the link coupler offered by Annecke in Germany. +

The circuit is a straightforward link-coupled circuit. The input with the relay and associated circuitry includes taps for a 50-ohm transmitter connection and a 300-ohm receiver connection, since receivers continued to used balanced input strips long after transmitters had gone to shielding, pi networks, and 50-ohm outputs.

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The Johnson Matchbox uses a single link for all bands with no variability. The Annecke design does away with the relay, receiver tap, and other pre-50-ohm transceiver features. Instead, it uses a larger (overcoupled) link with taps for the various bands (80, 40, 30-20, 17-15, and 12-10) mechanically linked to the secondary coil tap switches. In addition, it employs a series variable capacitor to adjust coupling (or input impedance, which amounts to the same thing). The Annecke design is superior in this regard.

+

The secondary systems of both the Matchbox and the Annecke are almost identical, differing only in output connection options. The secondary coil is tapped at reasonable positions for 80/40/20/15/10 meters, shorting out the unused turns toward the outer ends. Although the Annecke is marked with the preferred settings for the WARC bands, Matchbox users will have to experiment on these bands. Across the outer limits of the coil is a split stator capacitor, center grounded, which is used to set the tank at resonance. The required value of capacitance will vary somewhat as the reactance and resistance at the antenna terminals is varied.

+

The terminals are not connected directly to the outer limits of the tank. Each side of ground passes to a differential capacitor. The center of each differential goes to the antenna terminal. A differential capacitor is a split stator variable arranged so that as capacitance on one side goes up, it decreases on the other. The antenna terminal on each side of ground is thus set at a certain reactance from ground and certain series reactance from the tank. This arrangement is said to form a voltage divider. It also forms a means of compensating for reactance at the antenna terminal of the tuner, allowing it to match a wide range of R+/-jX combinations that might be present at the antenna terminals and still present the requisite high impedance to the tank circuit ends. Because the entire series combination of capacitance (and capacitive reactance) appears across the tank circuit and the load, the function of the differential capacitors is not so simple as this brief note might lead one to believe.

+

The design goes back to AM days, so the 275 watt rating is likely not only conservative, but conservative to the power of the carrier plus side bands of a 100% modulated AM signal. Capacitors appear to be spaced for at least 3 kV or better. The KW matchbox uses the same circuit with beefed up components and only some slight connection changes. The Annecke unit is rated at 200 watts and appears (from the photo of the case and the control arrangement) to use slightly lighter components than the Johnson, even though the 200 watt rating is also conservative.

+

Perhaps the only thing I would do to improve the design is not mechanically feasible: to have a rotary coil with contra-rotating sections (in line) to permit the full span of taps in order to eliminate the switch. The goal is to make available the most efficient coil settings for every possible set of R+/-jX presented, but I have no idea of how to make that work mechanically and preserve the center link and main coil center efficiency.

+

I thought those who have never seen a Matchbox might be interested in the basic design. (Love those elegant Johnson panel colors used after about 1960, similar to the colors on my own QSL, but not intended that way.) I have come across two photos, one of the 275 watt unit without meter for SWR through the external directional coupler, and the other with the available couplers on top and the meter in place. The difference in the panel lettering is a clue as to which is older and which is younger.

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The rearside detail is also interesting for those who might wish to home brew a link tuner or for those wishing to know what to expect from the unit. Jan Axing, SM5GNN, provided photos of the rear of his unit, which does not have the coupler. My thanks for his thoughtfulness. The 275-watt Match Box is about 10" wide, 10" deep, and 7.5" high.

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Phil Grill, KA2IWR, sent me photos of the Nye-Viking version of the Matchbox. Nye obtained rights to the Matchbox when Johnson ceased production. The Nye version omits the relays from the start, since the transceiver had already become the main type of amateur rig. However, Nye either used surplus Johnson cases or the dies for punching cases, since the relay terminal strip cut-out is evident. Due either to increased difficulties in obtaining parts or the prevalent hype about single-ended network tuners, Nye ceased making the Matchbox clone and turned to a single-ended design. So Nye Viking Matchboxes are not common. +
+ +
+
+ +
+

The circuitry of the KW version of the Match Box is virtually identical to that of the smaller 275 watt version, although considerably beefier. Instead of a ceramic terminal for single-ended antennas, there is a coax connector. For identificatioin purposes, here are photos, front and back, of the KW Match Box, but they appear to be of different units. The front shows the later paint scheme, while the back shows the earlier logo without the "J" behind the Viking. You can gauge the relative size difference between the 275 watt and KW versions from the directional couplers on top of the respective units. My thanks to Peter, SM5HUA, for the photos.

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A copy of the Johnson Manual--used for both sizes of the Match Box--can be obtained from K4XL's BoatAnchor Manual Archive. Incidentally, the 1963 prices for the Johnson Matchbox were $64.95 for the 275 W unit less the indicator, $94.94 for the same unit with the SWR indicator, and $154.50 for the 1 KW Matchbox.

+

At some point in the production of Matchboxes, Johnson added an extended range tuner covering about 2 to 30 MHz, with obvious applications to the 160-meter amateur band. Harry MacLean, VE3GRO, sent me the following panel close-up of the extended range version that he has. It is a 275-watt model, and I do not know if there was an extended-range KW version of this design.

+
+ +
Note the "auxiliary" control at the top left corner of the main panel. As Harry describes the interior, "The coils--both main and link--are the same as in the 5-band ham matchbox, but the variable capacitors all have double the number of plates. The auxilary capacitors are switched in on only the three lower ranges. Ranges are 2-3.5, 3.5-5, 5-7 7-9, 9-14, 14-21.6, and 21.6-30 Mhz." Harry has used the unit on 160 meters be adding a couple of turns to the ends of the main coil. +

My photocopies of the Annecke case are black and white, so I do not know the color scheme (although it appears to be black and white). The outer case thickness gives the impression of battleship construction. Catalog price (now out of date) was 495 DM. I have since learned (Jan. 4, 1999) that the Annecke company is no longer in business due to the severe illness of its owner. So far as I know, the designs have not been bought or otherwise picked up by any other company. It is indeed regretable that the only surviving major commercially-made link-coupled antenna tuner is no longer available. Now European hams can feel the loss of these units as keenly as we U.S. hams feel the loss of the old faithful Match Box. However, any entrepreneur will tell me that now the market is clear for the first manufacturer who presents us with a new match box. (Late note: Annecke may have been purchased by a Dutch ham. Will post more as it is learned.)

+

Courtesy of Jan Anker, ON4CAF/PA0LBN, I can show something of the inside of the Annecke unit. The first photo is of the inside from the bottom rear, showing the split-stator tuning capacitor to the left. The input tuning capacitor is to the right.

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The second photo is of the interior from the top rear, showing the differential capacitor to the right (with the input capacitor nbow to the left). Since the two large capacitors are vertically aligned, a single photo cannot show both.

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The last photo is of the coil assembly, which is remarkably similar to the scheme used in the Johnson Match Box. For maintenance of circuit balance, symmetry is essential.

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The 200-watt Annecke unit is about 5" high, 10" deep, and 12" wide. Personally, I would have left a bit more room in the cabinet to reduce stray capacitance, but I certainly would not refuse to use the Annecke unit.

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Again, courtesy of ON4CAF/PA0LBN, here is a photo of the schematic on the back of the Annecke unit. In case the cvalues are hard to read, the split stator os 155 pF per section, the differential is 100 pF per section, and the input capacitor is 270 pF.

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One bad habit of all antenna tuner makers is to list a simple impedance range for the antenna matching capabilities, for example, 50-3000 ohms for the Annecke. Actually, the ability of any tuner to effect a match is determined by the combination of R and jX at the antenna terminals. Whatever the reactance-compensating scheme, it will have some limitations, usually being more effective with large values of either jX or -jX, but not both. Moreover, the range of impedances for which any given tuner design can achieve maximum efficiency is ordinarily quite a bit narrower than for achieving a mere 1:1 SWR on the transmitter side. However, bringing the impedance presented to the antenna terminals within the range of the tuner's maximum efficiency potential is usually only a transmission-line length change away.

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In early 2004, Anthony (Tony) Brent, WD7G, sent me some useful notes on the availability of components for anyone wishing to replicate either of the classic link tuner designs. With his permission, I shall simply quote what he wrote.

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I thought I would pass along some information to you that I have found that will be of interest to anyone who wants to build such a tuner.

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I recently ordered new manufacture Johnson variable capacitors which are duplicates of those used in the Johnson Matchbox. Cardwell Condensers in New Jersey is manufacturing these units, and also Hammarlund variable capacitors under the original Johnson and Hammarlund part numbers, so these nice variables are indeed available again brand new in the box.

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www.cardwellcondenser.com

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I spoke with Paul Meyer, who was very helpful. He informed me that Cardwell can also manufacture custom variable capacitors to customer's specifications.

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I ordered two Johnson 154 series capacitors, a single section 450 pF 2000 volt for $75, and a dual section 330pF 2000 volt for $150. See the attached photo. Not exactly ham fest prices, but not that outrageous either. A builder ought to be able to come up with a finished Matchbox for somewhere in the neighborhood of $250 to $300, I would think, and that isn't bad given the price of most of the mid- to high-power T-network tuners on the market today.

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Cardwell also has various fixed and variable inductors, and the old stand-by Velvet Vernier drives.

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Jackson Brothers in England also have variable capacitors available at their web site: www.mainlinegroup.co.uk/jacksonbrothers/ (web.archive.org)

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They also have the nice Jackson Brothers vernier drives and other parts that may be useful.

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The remaining hurdle is the coils. B and W are still in the coil stock business, but they are quite expensive, and some times out of stock. I have experimented with a method of coil winding that the British and Australian amateurs have been using that works very well, and is quite easy to do.

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Their trick is to use an acrylic or polycarbonate sheet laid out and drilled for the proper coil diameter and spacing. One set of holes is offset by half the coil spacing from the other so the coil will advance at the proper pitch when wound through the holes. One extra hole is added at each end of one line of holes for the start and finish of the winding. The other row has the same number of holes as the number of turns in the coil.

+

The wire is wound on a former a little smaller than the finished diameter, and then is threaded through the holes in the acrylic, which hold the coil to its proper dimensions and keeps everything in place while only touching the wire at two points along the coil. It also provides a secure means of mounting the coil by using brackets fastened to the acrylic. It works very well.

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I imagine other materials could also be used. I happened to have some acrylic on hand so I gave it a try. I was very pleased with how well it worked.

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See the attached photo, which is my attempt at a single coil Z match tuner following the design work of Lloyd Butler, VK5BR (www.qsl.net/vk5br) Interesting circuit that I am still playing with, but I think I still prefer the Matchbox circuit.

+

The same type of coil former ought to work well for winding a Matchbox style coil and link, and perhaps with some extra holes to hold the wires for the coil taps, so they don't depend only on the solder joint.

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Updated 5-23-1999, 12-30-2000, 08-16-2002, 09-01-2003, 03-01-2004, 09-12-2004, 08-04-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Matching


+ + diff --git a/content/link/link0.html b/content/link/link0.html new file mode 100644 index 0000000..9a49cb7 --- /dev/null +++ b/content/link/link0.html @@ -0,0 +1,45 @@ + + + + + + Link-Coupled Antenna Tuners Index + + + +
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Link-Coupled Antenna Tuners: A Tutorial

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L. B. Cebik, W4RNL

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+ In recent editions of various amateur radio handbooks in English, information on inductively coupled (link-coupled) antenna tuners has decreased just to the degree that data on unbalanced network tuners has increased. We may be passing a certain critical threshold below which the information is insufficient for a good understanding of inductively coupled circuits. In response to a number of requests, I have pulled together materials from some older sources (from the 1940s through the 1970s) to make available a more complete and hopefully more cohesive account of link- coupling. The account might be made even more complete, but at the risk of making it excessively obscure. As with every tutorial, one draws a line and takes a risk that enough has been shown to aid understanding without breeding misunderstanding from what has not been said. +
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Updated 11-25-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
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+

Topics: Matching


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Part I: Inductive Coupling

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L. B. Cebik, W4RNL

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+ Link-coupled--or inductively-coupled--antenna tuners virtually disappeared from the amateur market almost a quarter century ago. In their place came network tuners, most notably the C-L-C Tee network and its variants: the Universal Transmatch of Lew McCoy, and the SPC brought to our attention by Doug DeMaw. Although these networks perform admirably with unbalanced (coaxial) cables, they require special accommodations for balanced (parallel) transmission lines. As a result, there is a growing new interest in link-coupled tuners, along with a continuing interest on the part of many wire antenna users. +

Just as interest grows, the number of available link-coupled tuners continues to dwindle. Moreover, parts for such tuners grow scarcer. Along with the depletion in tuners and parts, there is also a scarcity in available information on the operating and construction principles underlying the link-coupled tuner. This series of articles is designed at least to correct the information part of the problem. Restoration of the parts supply and the inventory of complete units is another problem entirely.

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The Need

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Although numerous hams have found ways of adapting single ended antenna tuners to service with balanced lines, perfectionists see many remaining problems. Some tuners use baluns at their outputs, and these units may be (depending upon design) subject to losses when faced with highly reactive loads. Many of these baluns use a 4:1 ratio, which can give the tuner added problems when it is presented with very low load impedances. A few operators have gone so far as to carefully measure their parallel transmission lines so as to present a 200-ohm load with a mild capacitive reactance that is tuned out with an external capacitor across the line. +

Some hams have attempted to avoid balun losses by placing a 1:1 balun at the source side of the tuner and floating the unit to provide a nearly balanced output to the load. Common- mode currents continue to be a problem in many installations.

+

Rarely have hams attempted to build balanced networks for their tuners. Balanced Ls, Tees, and PIs are certainly feasible, but at a cost. In some schemes, component values double; in others, mechanical linkages present construction complexities. Such units remain rare.

+

For many hams, the tuner of choice for parallel transmission line systems is the inductively-coupled tuner. It yieldss efficient power transfer to a naturally balanced output. Moreover, it provides a degree of isolation from the line due to the inductive or magnetic coupling. This latter feature often suffices to attenuate out-of-band RF from strong local sources.

+

However, not just any old tank and link will make a satisfactory tuner. We have largely forgotten the fundamental principles behind good tuners of this type. Perhaps the high point of available information was in the 1960s. In my own collection of old ARRL Antenna Books, the 9th Edition of 1960 contains an account that is both mathematically and practically superior to the account of my next older edition, the 7th of 1955. By the 13th edition of 1974, much of the material had been digested to make room for the single ended network and baluns and has remained essentially unchanged since that time. The link coupled transmatch still in the 18th edition of the ARRL Antenna Book of 1997 is the same as that in my 1982 ARRL Handbook (although few have noticed that the front panel photo has changed appearance over the years, while the top view shows the original unit).

+

These notes on the evolutionary ups and downs in available link tuner information are not at all a criticism of ARRL publications. Quite to the contrary, other handbooks in English present considerably less information on these tuners and their principles. Yet the information is available from a combination of sources. The 1960 ARRL Antenna Book account is, of course, crucial. One source especially useful on inductive coupling is George Grammer's A Course in Radio Fundamentals which ARRL published as a full text in 1972. The source behind this treatment--as it is for so many other matters relating to radio fundamentals--is Terman's Radio Engineers' Handbook. They all make good reading for those interested in going beyond the treatment presented here.

+

So perhaps it is time to go back to the beginning and reintroduce the link coupler from the ground up. Nothing in these notes will be new, but only a restatement of principles and practices gleaned from the sources. At most, I shall be adding some tables and examples to the account in order to give the applicable equations some real meaning. The tables may also allow those who do their math intuitively a chance to see the trends of values to permit more accurate ballpark extrapolations. Moreover, I shall not try to give a fully integrated mathematical account, but simply present certain of the most useful equations that either explain tuner operation or permit calculations useful to constructing such tuners. Since most will be practical simplifications, there will be gaps in mathematical progressions of derivation. But then, our aim is to provide--so far as possible--a practical grounding in inductive tuner principles.

+
+

What's in a Name

+
+
+ +
We call the line-to-transmitter matching device a link-coupled tuner, which it is and isn't. The name arose in the days before PI network outputs. As shown in Figure 1A, older transmitters used a parallel-tuned output circuit, with energy coupled to a low-impedance secondary. Often, the secondary coil was connected to another such coil, which in turn was coupled to a high-impedance parallel-tuned circuit used to match the high impedance of the antenna. The link, as such low-impedance-to-low-impedance coils were called, might be something as simple as a twisted line. Such circuits were equivalent (assuming zero losses in the link) to a direct coupling between the two tank coils, as shown in Figure 1B, with theoretically calculable adjustments of values. Few hams made the calculations because it was simply easier to adjust the number of turns in the link coils to achieve maximum power transfer. +
+ +
+

In isolation, the antenna tuning unit (ATU) shown in Figure 2, is an inductively coupled impedance matching network. Even though networks dominate the output circuits of modern transmitters, the concept of coefficient of coupling may still be applied to the inductively coupled circuit, and to that degree it is still correct to call these ATUs link-coupled tuners.

+

However, the old name often carries with it an attitude: the small coil is merely the link and as such is not of great importance. Calling the unit an inductively coupled impedance matching network gives equal importance to both the primary and secondary inductors. That is crucial for understanding this class of ATUs.

+

We shall keep the old name, since that is only a war of words, but we shall lose the old attitude. That way, the link coupler and the inductively coupled impedance matching network will become one and the same. Now if we only knew what is going on with inductive coupling, we would be in good shape to understand the link coupler.

+
+

Inductive Coupling: Back to Basics

+
When any two coils are positioned such that the magnetic lines of force of the one which is connected to a source of RF energy cut across the turns of the other coil (assumed to be connected to a load), energy is coupled to the second coil. The expanding and collapsing field of the first coil provides the changing magnetic field necessary to induce a voltage across the second coil, with a consequential current flow through the load. +

Two key concepts arise in this connection. The first is mutual inductance (M), that is, the voltage induced in the second coil by the rate of current change in the first. M is measured in Henrys, just as is the inductance of the coils. Often neglected is the fact that mutual inductance can be measured. First measure the inductance of the two coils individually and well apart from each other. Second, fix the positions of the coils with respect to each other, connect the coils in series, and measure the total inductance. Finally, reverse the series connections and remeasure the inductance. Note that inductance-measuring devices ordinarily use an internal alternating current signal source to make their measurements.

+
+ +
+

If the two coils as positioned have any mutual inductance, as illustrated in Figure 3, then the two readings will differ, one being larger than the sum of the inductances of the coils as measured independently, the second smaller than that sum. The larger reading (LTA) records the coils connected so that the fields are said to aid each other; the smaller (LTO) records the connections that oppose each other. In fact, the readings express some precise relationships:

+
+ +
and +
+ +
where all values are in Henrys or in fractions thereof. By some easy combination of the equations, we get +
+ +
again, in Henrys. +

The importance of reviewing this very basic idea is to establish the significance of mutual inductance in the coupling of energy in a magnetic circuit. Because M is a real inductance, it also has a reactance (XM) associated with it for any given frequency, which we calculate in the ordinary way:

+
+ +
where XM is in ohms, M in Henrys, and f is the frequency in Hertz. +

Mutual coupling increases as the coils are brought closer together or positioned so that more lines of force from the source or primary coil cut across the turns of the load or secondary coil. If we use magnetic materials, such as iron cores as power line frequencies, the value of M can reach close to the square root of the product of the two individual inductors. In fact, the square root of the product of the inductances of the two coils defines the highest possible value for M. Under these ideal conditions, the coupling is as high as it can possible go and is said to be 1. All other situations will have a coefficient of coupling (k) of less than 1.

+
+ +
Air wound coils, no matter how closely coupled, will have a coefficient of coupling well below 1. For most cases, values of k from 0.3 to 0.6 are common with air wound coils. Table 1 provides a sampling of some variations in k and M with different values for L1 and L2. + 
   Sample Values of M and k With Sundry Values of L1 and L2
+
+L1          L2          LTA         LTB         M           k
+Values yielding k = 1
+5           5           20          0           5           1.0
+8           4           23.32       0.68        5.66        1.0
+10          1           17.32       4.68        3.16        1.0
+Values yielding M = 2.5
+5           5           15          5           2.5         0.5
+8           4           17          7           2.5         0.44
+10          1           16          6           2.5         0.79
+Values yielding M = 1.0
+5           5           12          8           1.0         0.2
+8           4           14          10          1.0         0.18
+10          1           13          9           1.0         0.32
+
+Note:  Values of L1, L2, and M are inductances and may be read as Henrys,
+milli-Henrys, or micro-Henrys, so long as the unit of measure is the same
+for L1, L2, and M.
+
+Table 1.  Sample values of M and k with sundry values of L1 and L2.
+

One misconception is that a lower coefficient of coupling implies that less than full power is being coupled from the primary to the secondary circuit. This is incorrect. The value of k is simply a very convenient way of helping to calculate various factors involved in the transfer of energy or in impedance matching. What is correct is this: the rules we learn to use with power and other transformers with high coefficients of coupling do not apply to air wound coil pairs with lower coefficients of coupling. Hence, the technique of using the turns ratio to calculate voltage, current, and impedance ratios must be set aside for inductive coupling with air wound coils.

+

Transformers with strong magnetic core materials not only achieve high coefficients of coupling, but tend also to be frequency insensitive within the working range of the core material. Thus, we can build wide-band transformers for radio work by employing either ferrite or powdered iron materials in a toroidal core. Like the laminated iron cores of power transformers, these cores concentrate the magnetic lines of force within a very tight area surrounding all the turns of the primary and secondary coils. Air-wound coils have more widely spread magnetic fields. They tend to retain their energy transfer characteristics over a much narrower frequency range in ways related to the reactance of the coils.

+
+

Simple (Untuned) Inductive Circuits

+
+
+ +
Figure 4A shows the simplest inductively coupled circuit, with a resistive source and a resistive load. The inductors are designated LP and LS, as primary and secondary coils for the circuit. Because the circuits are coupled, the coupled impedance from the secondary appears in the primary in the form of series components. The values for the series resistance (RA) and reactance (XA) can be approximated from the following equations: +
+ +
and +
+ +
where XM is the reactance of the mutual inductance, RS is the secondary circuit resistance, and XS is the secondary circuit reactance. Figure 4B shows the coupled impedance factors in place. +

For example, suppose we use an inductor pair (taken from a table of recommended values) where LP is 1.2 micro-H and LS is 12 micro-H. XS will be 528 ohms at 7 MHz. Add a load resistance of 1500 ohms. We shall assume a coefficient of coupling (k) of 0.6. From equation (5) transformed, M = 2.3 micro-H, and the value of XM is 100 ohms. Under these conditions, using the equations above, the coupled values in the primary will be RA = 5.9 ohms and XA = 2.1 ohms.

+

Note that the reactance of the secondary which is coupled back to the primary is numerically equal to the transformed secondary reactance, but of the opposite sign or type. Hence, the reactances cancel in part. Ideally, selection of the right values for the two inductors and the right coefficient of coupling would provide a resistive load for the source.

+

In order to effect a match between the load and the source, both the mutual inductance and the reactance of one of the inductors must be varied, a highly impractical situation. I have passed along these equations only to demonstrate the reversal of reactance sign in the mutually coupled reactance, a factor that will be of importance in practical link-coupled circuits of only slightly more complex design.

+
+

Coupling With a Tuned Secondary

+
+
+ +
Figure 5A shows the more commonly used inductively coupled circuit: an untuned primary circuit with a resonated secondary circuit. For resonate circuits, the Q is determined almost wholly by the load resistance relative to the reactance of either the coil or the capacitor (which are equal) at resonance. The resistive impedance of a resonant parallel tuned circuit is very high, and the lower load resistance in parallel with the tuned circuit largely determines the coupled resistance into the primary. +

The loaded Q (QL) of the secondary of Figure 5A is given by

+
+ +
where X is the reactance of either the coil or the capacitor at resonance. For example, if the resistive load is 2500 ohms and the reactance of the coil and capacitor are each 250 ohms at resonance (a common value), the loaded Q is 10. +

For loaded Qs of 10 and better, simplified equations are possible with little error. With lower values of QL, some error will results, but not outside the range of the variable components. One way to show the resistance coupled back to the primary (RA)--shown as a series resistance in Figure 5B--is with this expression:

+
+ +
where XM is the reactance of the mutual inductance, RL is the resistive load on the secondary, and XL is the reactance of the coil at resonance. +

If we use the same coil values as earlier, 1.2 micro-H and 12 micro-H, for the primary and secondary coils, along with the presumed coefficient of coupling, 0.6, we may obtain values of 100 ohms for XM and 528 ohms for XL at 7 MHz. The requisite capacitor to resonate the circuit at this frequency is 43 pF. With a load resistance of RL = 1500 ohms, QL = 2.8. Since the loaded Q of the circuit is well under 10, the calculations from this point onward will provide ballpark guidance, not accuracy, since the equations employed are intended for use with circuits with loaded Qs of 10 or more. However, employing equation (9), we derive a value for RA of about 54 ohms.

+

Notice that in figure 5B we have a primary impedance consisting of a resistance (desired) and a reactance (not desired in matching circuits). The reactance of the primary inductance remains uncompensated because the tuned secondary is wholly resistive. To make the primary impedance wholly resistive, we must alter the component values of the tuned circuit to permit it to show a small inductive reactance. From equation 7, we know that the transformed and coupled value of this inductive reactance will be capacitive, thus cancelling the inductive reactance. What is left will be a pure resistance.

+

The procedure employed is normally derived empirically rather than calculated. We tune the secondary circuit to a higher frequency than the operating frequency, normally by reducing the value of capacitance and thereby increasing the value of capacitive reactance to the increased value of the fixed inductor at this higher frequency. The parallel resonant secondary circuit at the original (slightly lower) frequency will show inductive reactance, just what we need to couple back to the primary, where it appears as a capacitive reactance in series with the reactance of the primary inductor. With the correct selection of secondary values, the primary reactances will cancel, leaving a purely resistive impedance for the primary circuit. In the process, the value of the resistance coupled back to the primary will not change by very much at all.

+

Because we are now using ballpark equations at low operating or loaded Qs, any calculation of this phenomenon will not be precise. However, if we walk through the process a couple of times, we can get a view of the trends and understand how things work. The standard equation for determining the reactance of a parallel combination of L and C, when transformed into reactances XL and XC for the frequency in question, is

+
+ +
where XP is the resultant reactance that is in parallel with the load resistance, RL. +

Using the same example we have been tracking, we can plug simplified series transforms of these parallel values into equations (6) and (7) and obtain something like the values in Table 2. Although these values are not precise by any means, they do show that as we increase the resonant frequency of the parallel resonant secondary circuit, the capacitive reactance coupled back to the primary increases steadily, while the resistance decreases very slowly. The right combination of values will eventually yield a purely resistive input impedance, although the coefficient of coupling might have to be altered to keep the value of RA close to 50 ohms. Remember that in equations (6) and (7), the numerator is XM2, and raising its value will raise the values of both the RA and XA. However, the example employs a value of k of 0.6, already close to the limit of what is feasible with air-wound inductors.

+ 
Sample Values of RA and XA as the Secondary is Resonated at Higher Frequencies
+
+Resonant    Parallel    Parallel    Series      Series      Coupled     Coupled
+Frequency   Resistance  Reactance   Resistance  Reactance   Resistance  Reactance
+FMHz        RL (ohms)   XP (ohms)   RS (ohms)   XS (ohms)   RA (ohms)   XA (ohms)
+
+7.0         1500        --          186         --          54          --
+7.3         1500        6590        186         42          51          -12
+7.5         1500        4090        186         68          47          -18
+
+Note 1.  Resonant Frequency refers to the resonant frequency of the parallel tuned
+secondary circuit and is altered by reductions in the capacitance, while maintaining a
+fixed value for the inductor.
+
+Note 2.  Because simplified calculations have been used, the table is useful only for
+noting the trends in values.  Actual values will vary considerably due both to the the
+low loaded Q of the circuit and the variables of actual coupler construction.
+
+Table 2.  Sample values of RA and XA as the secondary is resonated at higher frequencies.
+
+

The purpose of this exercise in equation-mongering is to provide you with an understanding of some of the basic principles of link-coupled tuners. More exacting forms of the equations applicable to the low values of loaded Q often encountered in ATUs are available. We have restricted ourselves to these convenient approximations because the evolution of practical coupler circuits has largely proceeded by workbench experience. If this brief account simply makes you a little more comfortable dealing with inductively coupled circuits and convinces you that they operate in accord with principles that do allow us to calculate necessary values, it will have served its purpose.

+

The next step is to begin wending our way through typical inductively coupled circuits in order to see how some of the enhancements work. Unlike many other accounts of tuners, we shall start where the transmitted signal starts: on the input side of the tuner.
+

+
+ +

+
+

Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 2: The Input Story
+
+ Return to Index
+
+
+

Topics: Matching


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+

Part II: The Input Story

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Having digested the fundamentals of inductive coupling, we can next turn to a step-by- step investigation of inductively coupled antenna tuning units (ATUs). We already know that the tuner will consist of an input inductor (LP) plus any other refinements we eventually choose to add. It will also consist of an inductor (LS) and capacitor (CS) in the secondary, where the components for a parallel resonant or near resonant (tank) circuit, with the load (RL) connected in parallel to the tank. Figure 1 shows the most basic schematic once more. +
+ +
+

The input resistance in series with LP is designated RA and is the resistive impedance coupled back to the primary. As we have noted, the secondary tuned circuit at resonance has no series-equivalent reactance and therefore does not couple a reactance back to the primary or input side of the circuit. To couple a compensating capacitive reactance back to the primary, one must resonate the secondary at a frequency somewhat higher than the operating frequency. In this case, there is both a resistive and reactive component to the secondary impedance, and hence, resistive and reactive components to the impedance coupled back to the primary.

+

Since the offset adjustment has little effect on the value of the coupled resistive component, but chiefly provides the capacitive reactance needed to cancel the inductive reactance of the primary inductor, we shall normally not mention (except where necessary) this offset adjustment. However, tuner designers and users should remember that this offset is a normal part of most antenna tuner adjustments. When we use an SWR meter between the ATU and the transmitter, we are making this adjustment automatically in seeking a 1:1 SWR. If we leave the reactance of the primary inductor uncompensated, the SWR will be above 1:1 for the case where RA is 50 ohms.

+
+

A Little Orientation

+
In the account of inductive coupling fundamentals, we gave the following equation as the most basic approximation of the input resistance to the remaining conditions in the coupling circuit: +
+ +
where RA is the resistive impedance coupled back to the primary, XM is the reactance of the mutual inductance between coils, and XLS is the reactance of the secondary inductor (or capacitor) at secondary resonance on the operating frequency. +

In editions of the ARRL Antenna Book since at least 1960, a different equation is given, presenting the initial appearance that the account there may differ from this one. However, let's do a little work on equation (1) above.

+

First, we know that the coefficient of coupling (k) and the mutual inductance (M) are related by the square root of the product of the two coupled inductances. Since converting an inductance to its reactance at any given frequency is a matter of multiply the inductance by 2pif, which cancel out in the relationship, we can also express how k relates to M this way:

+
+ +
where XM is the reactance of the mutual inductance, and XLP and XLS are the reactances of the primary and secondary inductances, respectively. +

Squaring both sides of equation (2), we can replace the term XM2 in equation (1), cancel out an XLS above and below the line, and reach this step:

+
+ +
where all terms have the definitions given in the equations so far. +

For a parallel loaded circuit where the load resistance is small compared to the resistive impedance of the resonant circuit, the loaded circuit Q is approximately the following:

+
+ +
If we replace RL over XLS with Q, we obtain the very equation shown in the ARRL Antenna Book: +
+ +
The only differences lie in the choice of subscripts, and I have selected mine to be consistent with those in Part I. +

Equations (3) and (5) give us important information about the design of inductively coupled ATUs. First, the resonant secondary ATU is most efficient when the numerical values of RA and XLP are the same. (Note that we only approximate this condition when we detune the secondary in order to cancel the reactance in the primary.) Under these conditions, a relationship emerges between k and Q:

+
+ +
+

The upshot is this: we can optimize our ATU design by varying the relationship between the load resistance and the reactance of the secondary inductor, or we can optimize our design by varying the coefficient of coupling--or we can do both. That gives us a good bit of flexibility in designing the ATU.

+

We shall look at both sides of the circuit for ways to optimize our design. As we did in Part I, we shall stick to purely resistive loads and leave the question of reactance on the line for later consideration. Likewise, we shall retain the parallel configuration of the secondary circuit and devote some attention later on to low impedance loads and the series-counterpart of the circuit. Let's master one thing at a time.

+
+

The Big Little k and XLP

+
Let's reset the parameters of our initial ongoing problem that we initiated in Part 1. We wanted a tuner for 7 MHz and chose a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) along with a primary inductor of 1.2 micro-H (53 ohms reactance). The resonant capacitance was 43 pF. We chose as our load (RL) 1500 ohms (resistive). +

With the chosen values and an assumed k of 0.6, the mutual reactance was 100 ohms. The secondary loaded Q was 2.8 or so (which tells us that everything we are doing here is an approximation, since the equations are truly accurate only for Qs above 10). Whichever equation we use to obtain the coupled resistance to the primary, we obtain about 54 ohms. However, this value of RA applies only to a load of 1500 ohms resistive.

+

What happens if we have a different load to match with the same components? The following table tells us a story.

+ 
                      Some Values of RA for Various Loads
+                  RL (ohms)            Loaded Q       RA (ohms)
+                   500              0.95         18
+                  1000              1.89         36
+                  1500              2.84         54
+                  2000              3.79         72
+                  2500              4.73         90
+
+Table 1.  Some values of RA for various loads (RL) in the standardized circuit.
+

In order to effect a 50-ohms match, we might consider altering the value of XLP. This would entail altering the size of the primary inductor, which would inevitably alter the values of M and k. However, assuming we could retain a k of 0.6, the following table gives us the trend of value changes needed for the 50-ohms match.

+ 
                    Some Values of XLP for a 50-ohms Match
+                  RL (ohms)            Loaded Q       XLP (ohms)
+                   500              0.95         146
+                  1000              1.89          73
+                  1500              2.84          53
+                  2000              3.79          37
+                  2500              4.73          29
+
+Table 2  Some values of XLP for various loads (RL) to achieve a 50-ohms match.
+

For most inductively coupled tuners, this is not a practical alternative. The primary inductor is normally fixed within or immediately over the secondary inductor. Tapping it precisely would require closely spaced taps. Mechanically, the switch leads or the manual tapping wires would introduce variations in the impedance seen at the input terminals of the tuner. But the exercise does give us a feel for what happens at the primary with changes in antenna feedline loads.

+
+

Swinging Links

+
We mentioned that our changes in the reactance of the primary inductor would occasion changes in the coefficient of coupling. We can use that idea in another way. Suppose that we could change the coefficient of coupling without disturbing (too much) the reactance of the primary inductor. Figure 2 shows how this has been done traditionally. +
+ +
+

The swinging or movable link or primary inductor, moving within a space at the center of the secondary coil, effectively changes the coefficient of coupling and hence the mutual impedance of the coupled inductors. The value of k increases as coupling is increased, that is, as the link is moved into the secondary field. Notice that the value of k changes continuously with changes in the primary inductor position, in effect giving us a variable k-control. We cannot say in the abstract what the value of k might be with each possible position. However, we can look at the values of k necessary to effect a 50-ohms match in our standard circuit.

+ 
                     Some Values of k for a 50-ohms Match
+                  RL (ohms)            Loaded Q         k
+                   500              0.95         0.99
+                  1000              1.89         0.71
+                  1500              2.84         0.57
+                  2000              3.79         0.50
+                  2500              4.73         0.45
+
+Table 3  Some values of k for various loads (RL) to achieve a 50-ohms match.
+
+

Since values of above about 0.6 are normally not achievable with air-wound inductors, the standardized 7 MHz tuner circuit would not be able to match loads less than about 1500 ohms. However, we might select a larger primary inductor value, which would reduce the required values of k. Unfortunately, this move would also increase the value of XLP so that it no longer match the desired value of RA, thus setting a less than optimum ratio between the two figures.

+

A second alternative results from equation (6), which suggests that we might redesign the coupler secondary, tailoring its Q to provide a more usable range of values for k. We shall retain a target values for RA and XLP of 50 ohms each. Let's also set a limit: at a load impedance (RL) of 300 ohms, the value of the coefficient of coupling (k) will be 0.6. From Table 3, we can see that at lower impedance values, k will need to reach values not likely to be achieved, but at load values above this value, required values of k will be lower. By swinging the link further out from the main inductor, these values of k can be achieved.

+

Since k, XLS, and RL are related, we can rewrite equation (6) as

+
+ +
Having set the limits as k=0.6 and RL=300, we can calculate that XLS=108 ohms. At 7 MHz, this translates into an inductor of 2.45 micro-H and a capacitor of 210 pF for the tuned secondary. With these values, we obtain the following table of values of k vs. the various load resistances. + 
               Some Alternative Values of k for a 50-ohms Match
+                  RL (ohms)            Loaded Q         k
+                   500               4.63        0.46
+                  1000               9.26        0.32
+                  1500              13.89        0.27
+                  2000              18.52        0.23
+                  2500              23.15        0.21
+
+Table 4  Some values of k for various loads (RL) to achieve a 50-ohms match
+with the revised swinging link coupler.
+

Although this redesign achieves the immediate goal of providing values of k within the range of a swinging link for a span of realistic load values, all is not well. When the Q exceeds a value of about 10, the tuning becomes very sharp, requiring one to reset the tuner variables more than once across a single amateur band.

+

Although the swinging link might be combined with some techniques applied to the tuner secondary that we shall explore a bit further on, they are no longer the input circuit of choice. Swinging links were once popular, but have essentially gone out of style because they are mechanically large and complex. Moreover, there is a much simpler means of achieving the same goal.

+
+

The Series Capacitor

+
+

The most common way to adjust the input circuit of an inductively coupled ATU is with a series capacitor. See Figure 3 for a revision of our standard circuit to incorporate the unit.

+
+ +
+

The first task that the new series capacitor, CP, can perform is to cancel the reactance of LP. This frees us from having to retune the secondary circuit to achieve this effect. Essentially, CP and LP form a resonant series circuit, leaving only RA as the input impedance of the overall impedance matching circuit.

+

We choose the value of CP to resonate with LP at the lowest frequency in the band to be covered. In our running example, at 7 MHz the reactance XLP is 53 ohms; hence, the reactance of the capacitor must be the same at resonance. The corresponding capacitance is 430 pF. However, we show the capacitor as a variable for a set of good reasons.

+

The values just calculated apply for the case where the overall circuit load is 1500 ohms resistive. However, not all loads faced by the ATU will be exactly 1500 ohms. Other load values will not be converted by the circuit constants to the values of RA and XA in the example (where XA has had a value of zero).

+

In the first episode, we showed how to cancel the value of XLP by tuning the secondary circuit to a higher frequency, so that at the operating frequency, XLP and XCP did not have the same values at the operating frequency. As we increased the frequency at which XLP and XCP were equal, a value of XA was coupled back into the primary circuit, and the value was capacitive. At the same time, the value of RA slowly lowered.

+

Had we begun with a secondary load, RL, that was higher than 1500 ohms, the value of RA would also have been initially higher. To a limited degree, we may use the same technique of making XLP and XCP equal at a higher frequency to produce something closer to 50 ohms for RA. However, when we do this, we also couple a capacitive reactance, XA, into the primary circuit. Since this coupled reactance provides part of the reactance needed to cancel the reactance of the primary inductor, the new series capacitor, CP, must now be set at a lower reactance--just enough lower so that the sum of its reactance and the coupled reactance together cancel the coil reactance. A lower reactance in CP means a higher capacitance. Therefore, the series capacitor used in the primary should have a value sufficiently greater than the target value to handle such cases.

+

Lower values of RL would have yielded lower values of RA. To raise them, within limits, we may set XLP and XCP to be equal at a frequency below the operating frequency. This will simultaneously raise the value of RA coupled back to the primary and also introduce a value of inductive reactance XA. The series capacitor must now be set at a higher value of reactance (and a lower value of capacitance) to cancel the sum of the introduced and the primary inductor reactances.

+

The series capacitor in the ATU primary circuit may be thought of as a "fine tuning" device, capable of allowing a given fixed secondary circuit inductor and its associated variable capacitor to handle a wider range of loads without directly altering the coefficient of coupling. Still, the range of variation that the primary capacitor, CP, can handle is limited. For wide ranges of RL, other means of coupling the load to the primary are necessary. The chief function of the series primary capacitor is always to cancel the primary inductor reactance, thus presenting the input source with a resistive load.

+
+

A Note on Resonance

+
To this point, we have referred to resetting the value of the tank capacitor as an offset tuning. Relative to our ordinary understanding of resonance, where the values of XLS and XCS are equal, the retuning of the tank amounts to an offset. However, let's remember that we are dealing with circuits whose operating Q is often well under 10. And here the single definition of resonance breaks down into several definitions, each with a proper context of use. +
+ +
+

Figure 4 shows a conventional parallel tuned circuit. Note that the series resistance in the coil leg (RS) is in addition to the load resistance (RL), but the two are not in either direct series or parallel with each other. When the operating Q of the circuit is above 10, the presence of RS makes little or no difference to the notion of resonance. When the operating Q is below 10, differences begin to appear.

+

When a series or parallel tuned circuit is just off resonance, we expect several differences from performance at resonance. First, XL is not equal to XC. Second, the current through the parallel circuit (in contrast to current within the circuit load) is greater than minimum. Third, the current through the circuit is not in phase with the voltage. In a high loaded-Q circuit, XL and XC are equal, current though the circuit is minimum, and current is in phase with the voltage all at just about the same frequency. However, in low-QL circuits, these three phenomena occur at somewhat different frequencies.

+

The goal in tuning a parallel resonant circuit in an impedance matching circuit is to achieve minimum current within the parallel circuit and maximum current to the load at the operating frequency. With respect to this goal, successful tuning of the circuit produces resonance. It is not the goal to have the current and voltage in perfect phase within the tank circuit or to have XL and XC be equal. These latter phenomena may occur at nearby frequencies, and they become resonant frequencies relative to each phenomenon. (In 1995, the ARRL Handbook expanded the coverage of low-Q parallel resonant circuits to cover these points more thoroughly: see pages 6.37-6.42 of any edition since then.)

+

Hence, for the aims of the inductively coupled tuner, the definition of resonance that is relevant is to maximize current in the load of the secondary (equivalent to minimizing current through the paralleled inductor and capacitor). Hence, when we retune the secondary to achieve maximum power output from the tuner, we are resonating the circuit, no matter what values of XL and XC may be required to do this.

+

We have also ignored the values of resistance and reactance coupled from the primary into the secondary. Given the disparity of coil sizes, the amounts are quite small in most matching situations and hardly call for any change of control settings to maximize current in the secondary. However, the effect is real and the control settings are not quite the same as they would be without the mutual coupling. In some cases, these further adjustment requirements add to those just mentioned; in other cases, they may partially cancel each other out. Nonetheless, the overall readjustment of the tank circuit to account of all factors affecting maximum current flow within the tank circuit are part of the effort to achieve resonance.

+

The most certain way to assure that proper resonance has been achieved is some form of output power measurement.

+

We have only begun to see the flexibility of the inductively coupled impedance matching circuit by surveying the most common variations we impose on the input side of the circuit. In the next installment, we shall look at some useful variations of the output side of the circuit.
+

+
+ +

+
+

Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 3: The Output Story
+
+ Return to Index
+
+
+

Topics: Matching


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+

Part III: The Output Story

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In the preceding installment, we look closely at the most common circuit variations on the input side of the inductively coupled ATU. The adjustments available to the coefficient of coupling and the series L-C combination provide limited flexibility. However, in conjunction with some techniques we can apply to the output side of the coupler, they add the refinement needed for very precise tuning that provides a 50-ohm resistive load for the source and maximum power output to the feedline. +

First, before we jump into these output side circuit variations, let's again reset the parameters of our initial ongoing problem that we initiated in Part 1 and continued in Part II. We wanted a tuner for 7 MHz and chose from a list of recommended values a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) along with a primary inductor of 1.2 micro-H (53 ohms reactance). The resonant capacitance was 43 pF. We chose as our load (RL) 1500 ohms (resistive). As in the earlier sections, we shall continue to work with resistive loads and save reactance for later.

+

With the chosen values and an assumed k of 0.6, the mutual reactance was 100 ohms. The secondary loaded Q was 2.8 or so (which tells us that everything we are doing here is an approximation, since the equations are accurate for Qs above 10). We obtain about 54 ohms for RA, given the resistive load of 1500 ohms.

+

Second, let's take another look at the basic equation that will aid our overall understanding of inductively coupled tuners, expressed both in terms of working Q and in terms of the relationship in the secondary parallel tuned circuit of the load resistance and the reactance of the tank components.

+
+ +
where RA is the primary resistive impedance (coupled back from the secondary), k is the coefficient of coupling, XLP is the reactance of the primary inductor, RL is the load resistance, XLS is the reactance of the secondary inductor (and of the capacitor at resonance), and Q is the loaded or working Q of the circuit. +

The ratio of the load resistance to the reactance of the inductor (or Q) is critical to obtaining a desired value of RA. If we alter that ratio, then we must alter one of the other components of the equation in order to obtain the same value of input impedance. For a fixed parallel-tuned secondary and a fixed value for the input inductor, if Q increases as the load resistance increases, then the coefficient of coupling must decrease. Under the same circumstances, if the load resistance decreases, thus decreasing Q, we must increase k. However, we are already close to or at a practical limit for coefficients of coupling for air-wound inductors.

+

In addition, many of the coupled loads we shall face will be well below 1500 ohms. The range from 200 to 1000 ohms is perhaps the most common with parallel feedlines. Clearly, we need some flexibility in the secondary values.

+
+

Changing the L-C Ratio

+
As the load resistance decreases, we can simply decrease the inductor reactance accordingly and preserve the original value of Q. This move would seem to allow us to retain the same input inductor and coefficient of coupling to arrive at the same desired value of RA. There is a catch in this plan which we shall take up shortly. However, let's begin with the assumption that we can maintain the coefficient of coupling and input inductor value. Then we might imagine a modification to our basic tuner as in Figure 1. +
+ +
+

Figure 1 shows a series input capacitor, but for now, let us only use it to cancel out the reactance of the input inductor so that the source has a purely resistive load. The secondary shows a set of coil taps to which the capacitor is connected, so that the result is a tuned circuit of differing L-C ratio as one moves from one tap to another. Since each tap represents a different value of inductance, the inductive reactance also changes accordingly. This requires a new value of capacitive reactance for resonance, and hence a new value of capacitance. Since we are lowering the inductance and the inductive reactance of the secondary, new lower values of the load resistance will be needed to re-establish Q at its former value.

+

For the exercise, here is a table of values we might derive from this situation, using our initial tuner design as a basic starting point:

+ 
           Tuner Component Values for a Constant Q and Varying Loads
+
+            RL (ohms)   XLS=XCS (ohms)    L (micro-H)       C (pF)
+            1500        528               12.0               43
+            1350        475               10.8               48
+             750        265                6.0               86
+             300        105                2.4              215
+
+Table 1.  Tuner component values for a constant Q and varying loads.
+

The table presents us with usable values down to at least a 750-ohms load. Below that point, the required value of capacitance to resonate with the tapped inductor increases to a much more difficult level. If we install a 250 pF capacitor, the rate of change of capacitance grows higher, while if we install only a 100 pF capacitor, the range is insufficient for lower values of RL. This is a limitation of changing the L-C ratio of the secondary tuned circuit, but it is not the catch we mentioned.

+

The catch is simply this: in order to reduce the value of the secondary inductor reactance, we have to reduce the inductance of the coil. In practice, simply eliminating some turns in the secondary coil will alter the relationship of the primary to the secondary, changing the mutual inductance and hence the coefficient of coupling. Restoring the coefficient of coupling will therefore require some physical alteration of the coil positions.

+
+ +
The equation relating k to XM gives an indication of the required change. If k is to remain constant, then the mutual inductance must decrease as the square root of the decrease in secondary coil inductance and inductive reactance. Restoring or retaining the coefficient of coupling will therefore require some physical alteration of the coil positions. +

Although this system of tailoring the inductor reactance to the load resistance for a constant Q is feasible for a single band of operation, it has additional drawbacks when applied to link couplers designed to cover most of the HF bands. First, the number of taps grows well beyond the range of a switching system, and manual tapping becomes necessary. Second, on the higher frequency bands, most of the coil is unused. Since inductors have inter-turn capacity, it is possible for the large unused portion of the coil to have a self-resonant frequency at the operating frequency or a harmonic of it.

+
+

Load Impedance Transformation

+
A number of the potential problems associated with changing the L-C ratio of the secondary tuned circuit can be avoided by leaving the L-C ratio constant. To handle load resistances lower than the natural value of RL that--with the given size of LP and value of k-- transforms to a primary impedance of about 50 ohms, we first transform the load resistance to the natural value of RL. In the running example, this value is 1500 ohms. +
+ +
+

Figure 2 shows one way of effecting the transformation. We simply create a second inductively coupled circuit between the original secondary and the load. We may call this new inductor LL, the load winding. We could even add optional series capacitors, CL, which would provide us with the ability to resonate LL at the operating frequency.

+

The impedance transformation between LS and LL operates according to the same equations that govern the relationship between LS and LP. Since we are interested here in the ratio of primary to secondary impedance, let's rewrite equation (1) in general primary-secondary terms:

+
+ +
where RP is the primary resistive impedance, RS is the secondary resistive impedance, XLP is the primary inductor reactance, XLS is the secondary inductor reactance, and k is the coefficient of coupling. The value of k, of course, indicates the function of XM, the mutual inductance between the inductors. Unless k=1, the ratio of primary to secondary impedance will always be less than the ratio of the inductor reactances. Since the individual inductor reactances are directly proportional to coil size--or, for a given inductor diameter and turns per inch, the number of turns--the ratio of primary to secondary impedance will always be less than the ratio of primary to secondary coil turns. +

Where the secondary of the coupled load circuit is not resonant, the ratio will vary further due to the presence of a coupled value dependent on XLL, the reactance of the load winding, and an additional reactance will be coupled to the tuned parallel circuit. The reactance is normally compensated for by a revised setting for the variable capacitor.

+

The circuit of Figure 2 is not often used in amateur work, although it is an efficient way in which to transform lower load resistances to the higher value required by the parallel tuned inductive circuit. The use of a further inductor complicates mechanical arrangements, especially if the arrangements involve switch leads. However, the circuit is applicable to special situations that call for the matching of a single load value with small variations around the target value.

+
+ +
+

Equivalent to the coupled circuit in figure 3 is the arrangement shown in Figure 3. Instead of a separate winding, we use coil taps on LS to create an autotransformer. Nothing changes relative to the principles of operation that we have just surveyed, except that we lose control over the value of k. However, normal practice is to tap the inductor LS every turn or two, depending upon its construction. The result is the ability to handle a wide range of specific values of RL lower than the value required by the full inductor for a given desired primary impedance.

+

Although subject to variations by virtue of the value of k (or the mutual inductance) necessary to effect maximum power transfer between windings, the impedance transformation may be crudely estimated by taking the ratio of the squares of the individual inductor values (or the squares of the inductor reactances). In the following representative table, we have further simplified the calculation to one comparing numbers of turns, beginning with a coil of 20 turns. Since the coil is tapped inward one turn from each end with each step, the net reduction is 2 turns per step.

+ 
                   Values of RL vs. Approximate Turns Ratios
+
+Number      Ratio to          Ratio Squared     Approximate Ideal RL
+of Turns    Full Coil
+  20          1.0                   1.00              1500 ohms
+  18          0.9                   0.81              1215
+  16          0.8                   0.64               960
+  14          0.7                   0.49               735
+  12          0.6                   0.36               540
+  10          0.5                   0.25               375
+
+Table 2.  Values of RL vs. approximate turns ratios.
+

The values in Table 2 are not be construed as accurate for any particular coil. Their function is to show the trend in values as an inductor is tapped further toward its center. Note that it is possible to obtain a good match with load resistances in the neighborhood of 300 ohms by this method. Indeed, loads as low as 25 to 50 ohms may be accommodated by this arrangement, although when loads are less than about 100 ohms, a series circuit is generally recommended for maximum efficiency and convenience. We shall discuss series secondary circuits in a future installment.

+

The values of RL which transform to the higher value occur in step-fashion. However, the values of RL between those steps are ordinarily easily accommodated by the variable capacitors in the tuned circuit and in the primary. Therefore, the optional series capacitors in the output circuit, which we noted were optional, are usually not required in order to effect a match.

+

One operating inconvenience of the tapping arrangement is that the effective Q of the circuit increases as the coil is tapped closer to its center. The lower the load resistance, the higher the Q. The result throws off the values in Table 2, but this is rarely a problem, given the number of available taps and the variable capacitors in the primary and in the tuned circuit. The inconvenience arises from the sharpness of the resultant tuning. The higher the load resistance and the lower the Q, the more easily a single setting of controls and taps may cover an entire amateur band. With lower load resistances, settings may have to be changed several times to cover the same band. For very low load resistances, a series tuned secondary circuit may provide a lower-Q alternative and more convenient operation.

+

A second inconvenience associated with the tapped-secondary form of the inductive coupler is the need to change taps. On multi-band tuners, the number of available taps can easily outgrow the ability of good RF-rated switches to handle. Manual tapping with band changes is possible, but it is often inconvenient in high speed operations, such as contests. Therefore, the tapped-secondary type inductive coupler is often used mostly for casual operation or for single-band units, such as couplers for 160 meters, where a set of taps may suffice for a given antenna, with only capacitor adjustments required as the operator moves across the band.

+
+

Capacitor-Divider Impedance Transformers

+
The inconvenience of tapped secondary inductors can be largely overcome by changing the method of transforming the load resistance to the desired higher value. Instead of changing the impedance by inductive methods, one can use a capacitor divider circuit, as illustrated in Figure 4. +
+ +
+

Except for the input-side capacitor, the schematic is similar to the Johnson Match Box design. With the capacitor, it resembles the Annecke link coupler. To see how the capacitor diver system accomplishes the same goal as the tapped inductor, lets break the circuit down into useful chunks. First, we can note that the circuit is balanced around the ground point, so let's work with a single-ended (or unbalanced) circuit. It might make the principles somewhat clearer.

+
+ +
+

In Figure 5, we take a single-ended tuned circuit through several stages of development. In 5B, we simply divide the tuning capacitor shown in 5A into two paralleled capacitors: CT, which will be the main tuning capacitor, and CD, the "divider" capacitor. Of course, no dividing is yet going on.

+

In our running example, we needed 43 pF of capacitance. We might have selected a 75 pF capacitor to provide plenty of range on either side of the projected ideal setting. If we divide the capacitor into 2 sections, we might let CT be 65 pF and CD be 12 pF. (We are here working with some convenient hypothetical values that ignore the balanced nature of the full circuit. We shall restore that circuit and more nearly correct values at the end of this exercise.)

+

In 5C, we replace the simple capacitor CD with a differential capacitor. A differential capacitor is a split stator capacitor with the plates arranged so that as one set meshes, the other set separates. If the plates are cut for straight-line capacitance, the sum of the two capacitances is approximately equal.

+

However, the two capacitors are arranged in series, so that the net capacitance will range from a very low value (depending on the minimum capacitance of each unit) to a maximum when each unit is meshed 50%. We might select a capacitor with a maximum capacitance per section of 50 pF, which would yield a maximum total capacitance across the unit of 12.5 pF with the plates meshed half way. If the minimum capacitance is 10 pF, then the minimum capacitance for a 10 pF and a 50 pF capacitor in series is a little over 8 pF. The differential would require very little readjustment of the tuning capacitor, CT, across the range of our new CD.

+

Of greater interest here is the fact that the differential capacitors form a capacitor-divider, with the load resistor connected at the center junction of the differential. Since capacitive reactance is inversely proportional to capacitance, the lower capacitance side of the differential has the greater reactance, and vice versa. The reactances that apply to 5C are XT (total reactance across the differential), XU (upper side reactance), and XL (lower side reactance). since the reactances are in series, XT = XU + XL.

+

A load of 1500 ohms (our ideal load resistance that couples back to the primary as just about 50 ohms) would require that the XU be minimum and XL be maximum. Since the minimum value of reactance is set by the maximum value of the capacitor section, there may still be some division and the load may appear as a higher value across the tuned circuit than the actual 1500 ohms value.

+

For load values less than 1500 ohms, the differential is set at an intermediate value such that the load appears across the tuned circuit as close to the ideal value as feasible. As a crude approximation that ignores some of the variables involved in the actual circuit, the load resistances to be matched vary as the ratio of the square of the reactance across the load to ground to square of the total reactance across the capacitor divider. The following table will illustrate the trend.

+ 
           Values of RL vs. Approximate Capacitor Reactance Ratios
+
+            CU    XCU   CL    XCL         XT          XCL/XT      RL
+                                                             (ideal = 1500 ohms)
+            10    2273  50     455        2728        .17           43
+            25     909  25     909        1818        .50          375
+            40     455  10    2273        2728        .83         1041
+
+Table 2.  Values of RL vs. approximate capacitor reactance ratios.
+

Once more, the values in the table are not meant to be accurate, but to indicate the trends. Obviously, some circuit adjustments to the secondary L-C ratio would have to be made to handle higher loads, since a load of a little over a thousand ohms appears as 1500 ohms across the tuned circuit. However, it is evident that the capacitor-divider system is capable of handling a very wide range of load resistances with components of limited range.

+

There is no reason why the sections of the differential capacitor must have the same maximum capacitance. The capacitance per section can be tailored for a desired range of XCL to XT. However, in multi-band tuners, expected perhaps to cover 80 thorugh 10 meters, the component selection will be a compromise. Hence, the range of load resistances that the tuner can accommodate may differ from one part of the spectrum to the another.

+

In order to restore our circuit to a fully balanced version, as shown in Figure 4, we need to use a split stator tuning capacitor. Since the total capacitance across the series connected capacitor sections is to be about 75 ohms, we need to choose a 150-150 pF unit (although a 100-100 pF unit will provide the basic 43 pF required by the running example). Likewise, for a 12.5 pF total series capacitance maximum for the dual differential unit (when it is set for 50% mesh of both differential units), we shall need a maximum capacitance of about 100 pF per section at full mesh.

+

One final advantage attaches to the dual differential capacitance divider: tuning is continuous, with none of the stepping required by the tapped inductor. Thus, a precise setting is possible for any load resistance within the divider range. In principle, this ability within the secondary does away with the need for a series variable capacitor in the primary circuit, and the Johnson Match Box indeed omitted this component. However, Annecke has restored it in order to provide the operator with an added measure of flexibility. The flexibility does mean that more than one set of control positions will provide a 1:1 SWR for the input. The best set of control positions is the one providing maximum output to the line, which requires a measurement not usually provided in any ATU.

+
+

A Final Note on Approximations

+
It is necessary to add to the running warnings a final warning that all of the tables shown in this episode are based on approximations that presumed that certain other variables remained constant. In practice, these other variables would change, thus giving figures different from those in the tables. Thus, the tables show trends in values, but not actual values. +

Although it is possible for any particular case to calculate quite accurate values, doing so would require the specification of all applicable variables. Where those variables can be fully specified, one might adapt the full algebraic procedures spelled out in detail in an old Rider publication called Impedance Matching, one small volume in the "Electronic Technology Series" from the late 1950s (edited by Alexander Schure). The relevant section is called "Transformer as Impedance Matching Device."

+

For our purposes in this brief tutorial, not only would the full specifications obscure the general principles being presented, they would also be of limited, if any, use in designing a working link-coupled ATU. Because real ATUs operate over a wide range of load resistances and Qs, their actual design is largely a combination of approximation and experimental experience. Later, we shall present some tables of recommended values based on experience, and hopefully, these principles will be evident in their selection.

+

At the same time, a good link-coupled ATU must also provide maximum flexibility to achieve a good match and maximum output together. So far, the circuit in Figure 4 comes closest to that ideal.
+

+
+ +

+
+

Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 4: Series Circuits and Reactance
+
+ Return to Index
+
+
+

Topics: Matching


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+

Part IV: Series Circuits and Reactance

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Every ATU circuit--network or link-coupled--has limitations. No circuit can match every possible load to the typical 50-ohms transmitter line. Two of the limitations are reactance in the load and very low values of load resistance. In this episode, we shall look at both of these problems and typical routes of solution. There is a third limitation associated with trying to design a tuner to cover all of the amateur bands. We shall deal with that one in the next installment, when we pass along some notes on components, construction, and measurement. +
+

The Effects of Reactance

+
So far, we have dealt exclusively with resistive loads. Our purpose has been to keep the calculations--however approximate they may be--within reason. But inevitably, one has to admit that typical loads have both resistive and reactive components. +

Arithmetically, we have two ways of handling reactance as part of the load. For some purposes, it is better to treat the two components together as a complex number typically shown as R +/- jX, where both R and X are given in ohms. In other applications, we can separate the two. When it comes to ATUs, reactance can usually be treated separately at the load end of the design.

+
+ +
+

Figure 1 shows once more out basic link-coupled tuner circuit. We have opted initially to use a simplified tapped inductor scheme for matching lower resistive loads to the full tuned circuit. As a first step, let's consider once more a 1500 ohms resistive load connected in parallel with the resonant parallel L-C circuit. At 7 MHz, with a secondary inductor of 12 micro-H (with a reactance of 528 ohms at that frequency) and a primary inductor of 1.2 micro-H (53 ohms reactance), the resonant capacitance in the secondary was 43 pF. We chose our 1500 ohms resistive load (RL) to go with an assumed k of 0.6 for a mutual reactance (XM) of 100 ohms. The secondary loaded Q was 2.8 or so to obtain about 54 ohms for RA.

+

However, Figure 1 shows a complex load impedance with the series values RL +/- jXL. normally, complex antenna feedpoint impedances and impedances to be found along the length of a given feedline are specified in series terms. In order to evaluate the situation, we need to convert the complex load into parallel equivalents, using the standard conversion equations:

+
+ +
and +
+ +
where RP and XP are the parallel equivalents to the series values RS and XS, shown as RL and XL in Figure 1. Figure 2 shows the equivalent circuits, using for the moment only the secondary of the ATU circuit. +
+ +
+

Note that XP is in parallel with XLS and XCS, the reactances of the secondary coil and capacitor, respectively. If the equivalent parallel load reactance, XP, is inductive, then the total inductive reactance is the parallel combination of XLS and XP. Likewise, if the equivalent parallel load reactance is capacitive, then the total capacitive reactance is the parallel combination of XCS and XP.

+

Since calculators have a convenient inverse (1/X) key, it is normally much more convenient to convert parallel reactances to parallel susceptances, which simply add, in order to obtain the value of the parallel combination. In other words,

+
+ +
where XT is the total parallel reactance, XP is the parallel equivalent of the series load reactance, and XXS is either XLS or XCS, as is appropriate to the combination being evaluated. +

The following table illustrates what happens to the parallel combinations for our standard 1500-ohms resistive load when there are various series reactive loads, XL, of moderate proportions.

+ 
 Parallel Inductive and Capacitive Reactances with Load Reactances
+RL=RS         XL=XS         RP            XP            XLT           XCT
+1500          -500          1667          - 5000        528           -477
+1500          -200          1527          -11450        528           -505
+1500           200          1527           11450        505           -528
+1500           500          1667            5000        477           -528
+
+Note:  all values in ohms.
+
+Table 1.  Total parallel inductive (XLT) and capacitive (XCT) reactances with load
+reactances.
+

With modest (XL < 1/3 RL) reactive components to the load, the parallel equivalent resistive load across the tuned circuit does not change very much. The values of reactance that now compose the tuned circuit are sufficiently different to require adjustment of the variable capacitor to restore resonance. Where the reactive load is capacitive, the capacitor must show less capacitance and more capacitive reactance to make up for the loss occasioned by the parallel equivalent capacitive load reactance.

+

Where the reactive load is inductive, the capacitor must show more capacitance and less reactance to resonate with the reduced inductive reactance occasioned by the parallel equivalent inductive load reactance. However, these values are not the optimum to effect a transformation to 50 ohms in the primary. Hence, other adjustments of the tuner components may be needed to effect a good match, including moving to a different tap of the coil.

+

When the load is transformed from a lower value to a higher value needed by the secondary tuned circuit to effect a transformation to a desired primary impedance, not only is the resistive component increased in value, but so too is the reactive component. For most cases, the chief effect of this transformation is to reduce the effects of the secondary variable capacitor in compensating for the changes in total parallel reactance. This effect is especially pronounced with inductively reactive loads which, when treated in parallel equivalent form, move the inductive reactance of the tuned circuit components well off their optimum values. The capacitor setting required may result in a considerable offset, resulting in a resonant frequency (in terms of XLS = XCS) significantly removed from the operating frequency. The result will often be higher circulating currents within the tuned secondary circuit and lower efficiency of power transfer to the load. However, these losses are ordinarily very small if a high Q coil is used and the loaded Q of the circuit is held low.

+

The conditions of maximum efficiency cannot always be achieved, especially if the ratio of reactance to resistance in the load becomes great. Moreover, the higher the Q of the secondary circuit, the smaller the frequency range over which a single set of adjustments are usable. These conditions hold true whether one is using a tapped inductor or a capacitor divider as the means of effecting a match with a wide range of load values.

+
+

Advanced Compensation for Reactance

+
As we earlier noted, we can separate the resistive and reactive components of the load impedance presented to the ATU terminals. In doing so, we can think about compensating for the reactance before it becomes part of the secondary tuned circuit values. Figure 3 shows several ways of handling the situation. +
+ +
+

In 3A and 3B, we treat the reactance at the terminals in its series form. If the reactance is inductive, we insert a mechanically linked pair of capacitors--one in each side of the line--to provide an equal but opposite value of capacitive reactance. If the reactance at the terminals is capacitive, we insert a pair of series inductors in the line to provide equal but opposite reactance. The net reactance is zero, and the tuner sees a resistive load.

+

Series compensation is normally mechanically difficult, especially with the use of variable components. First, each side of the line must be broken to insert the proper compensating component. Dual components are necessary to preserve line balance. Second, mechanically linked components are bulky--inductors even more so than capacitors. Series compensation is rarely used.

+

In 3C and 3D, we treat the reactance in its parallel equivalent form. This conversion permits us to place either a coil or a capacitor across the line to provide an equal but opposite reactance value to cancel the parallel equivalent reactance presented by the load. Very usually, single ended components are employed in this function. Because of slight imbalances in the structure of such components, the line balance may be slightly disturbed, but ordinarily not enough to hinder circuit or transmission line operation. The switching or tapping methods should remove both sides of the compensating component when it is not in use.

+

The use of advance reactance compensation is necessarily reserved for very high load reactances that challenge the ability of the variable capacitor in the secondary circuit to effect a match or which unduly raise the Q of line or the coupler circuit. Series reactances in this range normally convert to parallel-equivalent low to moderate reactance values which are within the range of reactance compensation by good quality everyday components. When series reactances are themselves low to moderate, most coupler designs can easily accommodate them. In addition, their parallel equivalent values may be beyond the range of compensating components.

+

For example, in Table 1, a series reactance of 200 ohms, is easily handled by the coupler design used in our running example. However, compensation by parallel components is another matter. If the load reactance is capacitive, it would require a compensating inductance of 260 micro-H, and if the load reactance is inductive, it would require a compensating capacitor of 2 pF at the 7 MHz operating frequency. Needless to say, neither of these are practical values to find in variable components.

+
+

Feedline Length

+
An alternative means of reducing the reactance at the terminals of any coupler is to change the length of feedline from the antenna to the coupler output terminals. +

Every feedline is also an impedance transformer all along every 180 degrees of its length. If the antenna feedpoint impedance exactly matches the characteristic impedance (ZO) of the feedline, then the impedance along the line is constant at the value of line ZO. If the antenna feedpoint impedance differs from the ZO of the line, then the value of impedance, in terms of R +/- jX, varies all along each 180-degree length of line. This is true, whether the antenna feedpoint impedance is purely resistive or a combination of resistance and reactance.

+

With a complex feedpoint impedance that does not match the ZO of the feedline, there may be some line lengths that present easy combinations of R +/- jX for a given coupler design to handle and other lengths that present values that may exceed the coupler design limits. Hence, selecting something close to an optimum line length may enhance the ability of the tuner to compensate for the reactance and maximize power transfer to the feedline.

+

Let's use a challenging antenna case to see how this works. A certain antenna presents a feedpoint impedance at 7 MHz of 1828 + j1826 ohms. Assuming that we are using 450-ohms parallel feedline with a velocity factor of 0.95, we can obtain the following table of impedance values along a 180-degree length of line. (Similar tables at 5-degree intervals can be obtained from a program included with the VE3ERP HAMCALC collection. The values assume lossless line, but for planning use with antenna tuners, the accuracy will be more than adequate.)

+ 
                     Resistance and Reactance Along a 450-ohms Feedline
+
+                     Line Length                 Impedance
+              Degrees       Feet          Resistance (ohms)    Reactance (ohms)
+                0            0              1828                 1826
+               10            3.7            3173                -1291
+               20            7.4             857                -1513
+               30           11.1             334                - 970
+               40           14.8             179                - 662
+               50           18.5             116                - 469
+               60           22.3              85                - 333
+               70           26.0              69                - 226
+               80           29.7              60                - 136
+               90           33.4              55                -  55
+              100           37.1              55                   22
+              110           40.8              57                  101
+              120           44.5              64                  187
+              130           48.2              77                  285
+              140           51.9             100                  407
+              150           55.6             146                  571
+              160           59.3             249                  820
+              170           63.0             545                 1245
+              180           66.7            1828                 1826
+
+Table 2.  Resistance and reactance along a 450-ohms feedline for a typical antenna.
+

If the line length must be more than 1/2 wavelength, just add increments of 66.7' to the lengths listed to get just about the same values. But now that we have the table, what do we look for?

+

We are seeking a length of line where the reactance values are low. Achieving a zero level of reactance is unnecessary, but values under 200 ohms would be well within the range of virtually any coupler. Notice that the reactance passes through zero in two places. However, reactance curves are not orderly sine waves. Between 0 and 10 degrees, the reactance rapidly changes from a high inductive value to a high capacitive value. Since this makes finding the right length difficult, we shall avoid this transition. Between 90 and 100 degrees, the reactance passes slowly through 0. Hence, the exact line length becomes far less critical. In feet at 7 MHz, the ideal length is close to 36 feet long, but plus or minus 7-10 feet either way would not challenge the coupler.

+

Since almost any multi-band antenna can be modeled with reliable ballpark accuracy on all intended bands of use, it is possible to develop a full set of feedline charts plotting the excursions of resistance and reactance. Simply plug the modeled feedpoint impedance for each band into the impedance transformation program and print out a chart. By examining the reactance progressions for each band, it may be possible to find a minimal number of line lengths that will permit an easy match for the coupler.

+

Under very fortunate circumstances, you may find a single line length that will physically work with the antenna in question and also provide reasonable reactance levels for the tuner. If two or more lengths are requires, then switching or manually adding in the required line lengths for the band or bands which need them becomes the next order of business. Of course, all of the rules for treating parallel line carefully apply to this system. Hence, the actual switching system becomes a challenge for the creativity of the individual station operator. Line switching is often very much cheaper and less complex than installing and switching pre-coupler compensating inductors and capacitors.

+
+

Low Impedances and Series Connections

+
Because parallel-tuned secondary capacitor-divider load input ATUs are capable of matching loads from less than 50 ohms up to several thousands of ohms, we have focused primarily on parallel connection of the load to the secondary of the coupler. However, there are antennas which present loads in the 5 to 100 ohms range which can often benefit from a series secondary in the coupler. Figure 4 shows a typical arrangement. +
+ +
+

Typical inductor and capacitor values are so similar to those for parallel tuners that we can retain our chosen values in the running example: 12 micro-H for the secondary and 1.2 micro-H for the primary. Their respective reactances are 528 and 53 ohms. The series reactance of the capacitor will likewise be 528 ohms at ideal resonance, and hence, each section must be able to provide half this value, just as in the parallel tuner. For a total capacitance of 43 pF, each section must be able to reach 86 pF. However, the capacitor cannot be a simple split stator-common rotor model, but must be a pair of independent units mechanically driven as a unit. Some apparent split stator models are actually of this design and use a jumper for achieving a common rotor, which is then grounded for balance across the line. With the series connection, the capacitor sections must each float (that is, be well insulated from a common ground).

+

From one perspective, the equations that drive a series circuit look quite different from those that drive the parallel circuits we have been examining. Yet, as an exercise in "what goes around comes around," let's look at these equations.

+

For a series tuned inductively coupled tuner, where the secondary is presumed to be resonant, the input or primary impedance is a function of the reactance of the mutual inductance and the load resistance:

+
+ +
where RA is the coupled primary impedance, XM is the reactance of the mutual inductance, and RL is the value of the resistive load, with all values in ohms. +

Once more, XM is related to the coefficient of coupling (k) in this way:

+
+ +
where XLP is the reactance of the primary inductor and XLS is the reactance of the secondary inductor, both in ohms. This equivalence allows us to replace the term XM2 in equation (4) with its counterpart: +
+ +
where all terms have the same meanings as previously noted. +

Unlike a parallel tuned circuit, the loaded or working Q of a series-tuned circuit is

+
+ +
If we replace the terms XLS and RL with Q, we obtain +
+ +
which is the same equation we used for analyzing parallel-tuned circuits in the last two episodes. +

Series-tuned couplers are normally used with low coefficients of coupling to effect matches of low impedances to the coupler input impedance. If we let the desired value of RA be the same as the value of the primary inductor reactance (about 50 ohms),

+
+ +
where all values are as previously defined. +

Using equation (9) with our running example circuit values, we can develop a small table of reasonable values of k to effect a 50-ohms match with various load resistances.

+ 
                     Values of k for a 50-ohms Match with Various Loads
+
+                     Load Resistance      Loaded Q      Required k
+                          (RL)            (XLS/RL)      for 50-ohms match
+                          100                5.3          0.44
+                           50               10.6          0.31
+                           25               21.1          0.22
+                           10               52.8          0.14
+
+Table 3.  Values of k for a 50-ohms match with various loads where XLS = 528 ohms.
+

The table clearly shows the progression of values, but also shows a rapidly increasing Q as the load resistance to be matched goes down. High Q has the same effect with series- tuned circuits as with parallel-tuned circuits: the required settings become very narrow and must be changed with small excursions of the operating frequency.

+

Additionally, the presence of reactance in the load has the effect of requiring the tuning capacitor to be reset to restore resonance. Where the load reactance is capacitive, the overall component reactance at resonance can be maintained, because shifting the capacitor to a higher capacitance setting reduces its reactance to compensated for the line reactance: the net capacitive reactance is the same as the inductor's reactance at resonance. However, if the load reactance is inductive, it adds to the reactance of the secondary coil. This situation requires a change in the capacitor setting to a smaller value to match the combined inductive reactance to restore resonance. The effective reactance at resonance is higher, thus increasing the circuit Q and increasing the inconveniences (and possible problems) associated with high Q.

+

The most convenient way in most typical amateur circumstances to rid the load of its high reactance with a series tuned coupler is to alter the line length. However, in doing so, we can usually find a line length with a higher load resistance as well as a lower load reactance. Since parallel tuned coupler designs are available for loads of 50 ohms or even slightly less, the end result has been a gradual decline in the use of series-tuned coupler circuits.

+

In the end, the parallel-tuned link coupler, with either a tapped secondary or a capacitor- divider for handling a wide range of load impedances, is the circuit of choice for inductive couplers. The tapped secondary version, while useful for manual operation in multi-band units, is often used with single-band couplers, say, for 160 meters. Once the right settings are found, no further manual changes in taps are normally needed during operation. Such tuners are also cheaper to build, since soldering taps to coil turns is normally less expensive and easier to accomplish than finding a suitable differential capacitor for the alternative load network.

+

For multi-band couplers, the capacitor divider provides continuous front panel adjustment for changes of load impedance. With a multi-section ceramic wafer switch to set the inductor size for each band, along with the tuned circuit variable capacitor and the optional series input capacitor, this design can be reset from band to band quickly as one changes operating frequencies.

+

We have now looked into the basic theory and fundamental circuitry of inductively coupled ATUs. The remaining questions we need to examine concern component values and ratings, construction practices, and measurements to assure best results. Perhaps we can do all this in just one more session.
+

+
+ +

+
+

Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 5: Components, Construction, and Measurement
+
+ Return to Index
+
+
+

Topics: Matching


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+


+ Part V: Components, Construction,
+ and Measurement

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The remaining questions we need to examine with respect to inductively coupled ATUs are component values and ratings, construction practices, and measurements to assure best results. Let's look at these questions, one at a time. We shall be focusing upon parallel-tuned secondaries, with either taps on the inductor secondary or a capacitor-divider to accommodate a wide range of load impedances. Figure 1 provides an abbreviated schematic diagram of both types of circuits. We shall use CP, CS, and CD to sort out the capacitors in the primary, secondary, and (if used) divider circuit. LP and LS will designated the inductor primary and secondary windings. +
+ +
+
+

Component Values

+
There is no magic set of values for the components in an inductively coupled tuner. Instead, there are a few situations we want to avoid and then a set of reasonable compromises to make. The situation to avoid is having too high a value of CS relative to LS. Lower values of inductance carry with them lower values of inductive reactance. This, in turn, lowers the Q of the coil for resonant combinations on the ham bands, resulting in greater power losses in the coil. +

The 1960 ARRL Antenna Book recommends a secondary component reactance value of about 500 ohms as a reasonable compromise. This value tends to yield higher Q inductors whose physical size is not too much different than the physical size of variable capacitors having the desired characteristics. Here is a table of the resulting values, not only for the secondary components, but for the primary components as well (assuming a 50-ohms matching with the transmitter). I have extended the list to include the WARC bands.

+ 
              Recommended Component Values for a Link-Coupled Tuner
+       Band           LS             CS             LP             CP
+       160            42 micro-H     170 pF         4.2 micro-H    1700 pF
+       80-75          22              90            2.2             900
+       40             12              45            1.2             450
+       30              8              32            0.8             320
+       20              6              23            0.6             225
+       17              4.5            18            0.45            180
+       15              4              15            0.4             150
+       12              3.2            13            0.32            130
+       10              2.9            12            0.29            120
+
+Table 1.  Recommended component values for a link-coupled tuner.
+

These recommended values tell us several very practical things. First on the list is the reason why commercial ATU manufacturers rarely try to cover 160 meters with an all-band tuner. The 160-meter coil will be roughly twice as large--for any given power level--as he 80-10-meter coil. Likewise, the tuning capacitor will be large. In the primary circuit, the series capacitor may require either ganging two variables or adding fixed capacitors in parallel with a 1000 pF unit.

+

In general, the component size question for 160-meter tuners also inclines builders to using a tapped coil secondary circuit (instead of the capacitor-divider system). Taps every 2 or 3 turns down to a coil size of 50% of the full length should suffice for most loads encountered. For a specific antenna system, once the correct taps are found, they should not need to be changed. Indeed, it may be possible to use a good ceramic wafer rotary switch to move between taps.

+

Second on our list of lessons from the recommended values is the practicality of an 80-10 meter link coupled tuner. For a very simple design, coil taps may be used, but the capacitor divider system may prove far superior in terms of its continuous range of adjustment. A dual differential capacitor of about 100 pF per section will generally suffice for the capacitor divider.

+

If we use the primary series capacitor, we may be able to combine the 12 and 10 meter positions to save one band switch position. Likewise, the 17 and the 15 meter position may be combined. A 3 section, 6 position ceramic rotary switch should suffice to cover all the bands.

+

Notice that the primary coil should also be tapped for band changing purposes. Depending on the coil construction, some builders may wish to cover more than 2 bands with a single tap, since tapping at partial turns may be physically inconvenient. Tapping the primary is normally done on only one end of the coil. Hence, the position of the primary coil may not be perfectly centered for all bands. This slight imbalance does not produce any significant negative effects.

+

The series circuit may be altered to use lower values of series capacitance by increasing the size of the primary inductor. Values up to double or triple the recommended value may be used on 80 meters to make use of series capacitors in the 350-500 pF range. As the frequency is increased, the coil taps may be brought closer to their optimum recommended values, since the required resonating capacitance would fall within the range of the smaller unit selected.

+

As one increases frequency toward the high end of the HF spectrum, the range of the capacitors is not optimum for smooth tuning. Even though circuit Q may be satisfactorily low, control positions may be very sharp. Ideally, one should consider separate tuners for 80-20 meters and for 20-10 meters. The latter unit may use smaller capacitors and more widely spaced inductor turns. However, for all-band doublets and similar wide-ranging antennas, the 80-10 meter ATU is usually the design of choice.

+

In principle, if space is available, paralleling a high value and a low value variable capacitor can provide more optimal control of capacitance. Both capacitors should have the same voltage rating. At 14 MHz and above, the larger capacitor is switched out of the circuit. Below 20 meters, the smaller capacitor is set at mid-range, with main tuning done with the larger capacitor. The smaller capacitor may then be used as a "fine tuning" control. Since this system requires extra space, an alternative is to use a reduction drive with the main tuning capacitor.

+

The capacitance values given in the chart are the total capacitance across the parallel- tuned secondary circuit. Split-stator or ganged capacitors are normally used to preserve balance across the circuit. Each section should have a capacitance of twice the listed value so that the series combination equals the recommended value.

+

Varying the circuit values does little harm to coupling efficiency so long as sufficient flexibility is maintained in the primary series resonant circuit and in the secondary load impedance transformation circuit. Limitations show up chiefly in the range of load impedances that the coupler can effectively handle, and careful line-length adjustment can usually provide load values within the capabilities of the coupler.

+
+

Component Specifications

+
The best way to look at the components, is one at a time. +

Inductors: For moderate power levels up to 200 watts or so, air-wound inductors with a diameter of 2 to 2.5" and 8 turns per inch (tpi) are very practical. They provide reasonably sized inductors with good Q across the HF range. Inductor Q will normally decrease at the highest frequencies in the range. For 160 meters, a coil of larger diameter may be required to hold its length within reason.

+

Placement of the link at the center of the secondary usually follows one of two physical designs. In simpler designs, the link may be several turns of the main coil stock. The turns adjacent to the limit of the link are tied together to provide continuity in the secondary. Although this system will work, it limits the range of coefficients of coupling. Tighter coupling can be obtained by placing the primary inductor over the secondary. For fixed links using typical air- wound inductor stock, a nonconductive adhesive can bind together the support bars of the coils.

+

The current which the parallel-tuned secondary coil must handle can be estimated from the following simple equation:

+
+ +
where IC is the estimated maximum circulating current in amps, QL is the loaded or working Q of the coupler, P is the power level in watts, and RL is the load resistance in ohms at resonance. For a maximum Q of about 10, a power level of 100 watts, and load resistance of 5000 ohms, the maximum current will about 1.4 A. If we use the ideal case in our running example of a load resistance of 1500 ohms and a Q of 2.8, the current is only 0.7 A. +

Increasing the power to 1500 watts from 100 watts increases the circulating current by the square root of the power ratio. For the two sample cases, the maximum current will be 5.4 A and 2.7 A, respectively. For high power applications, #12 wire is generally satisfactory for these levels, while #14 wire may be used at mid-level powers.

+

For very low power levels, such as those encountered in QRP work (5 watts or less), it is theoretically possible to use wire as fine as #20 or #22. However, at very low power levels, every effort should be made to minimize power loss. The high power wire sizes do not guarantee minimum loss, but only that power losses in the inductor wire are not problematical. Minimum loss wire sizes would be larger, and at QRP levels #18 wire or larger is always in order for inductors with minimal losses.

+

The current in the primary winding is a function of the coil reactance and the power level. For example, if we use a coil with a reactance of about 50 ohms, the current at 100 watts power will be about 1.4 A. Viewed another way, the current will be about the same as the maximum circulating current in the secondary tank circuit. Hence, wire size recommendations applicable to the secondary are also applicable to the primary.

+

Capacitors: The chief problem facing inductors is heat from the conversion of RF currents. This problem has a time domain, and brief periods of excessive current are often without harm. With capacitors, the chief problem is arc-over, which may result from virtually instantaneous peak voltages across the capacitor plates.

+

The voltage across the primary series capacitor will be a function of the capacitor reactance and the power level. If a 50-ohms capacitive reactance is used, then at 100 watts, the voltage peak will be 1.4 times the r.m.s. voltage across the capacitor or about 100 volts. At 1500 watts, this peak voltage will increase by the square root of the power increase to about 385 volts. These levels are within the abilities of various sizes of receiving capacitors, which are often employed to achieve the high values of capacitance needed at 80 meters.

+

If the 80 meter capacitance is reduced to 1/3 of the recommended 1000 pF, the capacitive reactance will increase by a factor of 3. In this case, the peak voltage at the 100 watt power level will be about 170 volts. At 1500 watts, the peak voltage reaches about 665 volts. More widely spaced capacitor plates will be required.

+

In the parallel-tuned secondary circuit, the peak voltage is simply 1.4 times the r.m.s. voltage across the tuned circuit. The line voltage is a function of power level and load resistance, where

+
+ +
For the example using a load of 5000 ohms at 100 watts, the peak voltage is about 1000 volts. Where the load is 1500 ohms at the same power level, the peak voltage drops to 540 volts. At the 1500 watt power level, these peak voltages increase to 3870 and 2100 volts, respectively. However, off-resonance voltage peaks may be considerably higher. +

The actual arc-over voltage for a capacitor depends on many factors, including the sharpness of the edge of the capacitor plates and the air quality and humidity around the capacitor. In general, capacitors are chosen with a good reserve. 1500-volt units are common at 100 watts, 3 kV units at 250 watts, and 7 kV of higher units for the legal amateur power limit. These values provide about a 2:1 safety margin in balanced circuits using split stator or ganged capacitors, where each unit of the whole capacitor sees only half the total peak voltage across the line.

+

An often overlooked aspect of capacitor construction is the size of the capacitor frame and its materials. Large, closely space metallic frames can restrict the minimum value of capacitance obtained by a variable capacitor. E. F. Johnson units used in their Match Box series of link tuners employed the minimum metal frame to support the capacitor and permitted very low values of minimum capacitance. These or similar units are desirable in tuners designed to cover the entire 80 to 10 meter range of amateur bands, especially in the parallel tuned secondary of the coupler.

+

Capacitor construction is equally important in maintaining circuit balance with respect to ground. Split-stator capacitors provide an inherently balanced structure, with roughly equal influences on both sides of the circuit from stray capacitance to a metal case or other metallic objects in the circuit. Single-section capacitors, while usable, tend to unbalance the circuit by coupling more capacitance through the larger structure of the frame than through the set of plates not connected to the frame.

+

For capacitor-divider circuits, the capacitors form a series chain of 4 units across the line. Each unit sees about a fourth of the total line voltage. However, with considerable reactance on the line, the voltage across each unit may be somewhat higher. Therefore, the voltage rating of the dual differential capacitor is usually set to be the same as for the split-stator tuning capacitor.

+

When an inductive coupler is undergoing initial tuning, the control combinations may result in very high voltages across capacitors in the circuit. Therefore, initial tune-up should always be done at the lowest power possible to prevent component arc-over.

+

Rotary Switches: Rotary switches used to change bands or coil taps should have large, well-spaced contacts. The material should be ceramic, rated for RF service. For medium power levels, standard 1.25" wafers are normally satisfactory. For high power, use larger switching wafers with more widely spaced and large contacts.

+

Shorting switches--that is, switches that connect together all preceding switch positions-- are preferable to simple switches that leave preceding switch positions open. Shorting out the unused turns in the secondary coil normally results in fewer problems with power losses from circulating currents in those turns. However, only experiment can usually determine whether the interturn capacitance in combination with the inductance of the unused turns may result in a resonance at some harmonic of the operating frequency. For this reason, some designers add an additional coil position on multi-band tuners, roughly tuned to 5 to 5.5 MHz. Although this tap might prove useful on some occasion with particularly troublesome 80 or 40 meter loads, its chief function is to reduce the size of shorted inductor sections when operating above 40 meters.

+

Terminals: The input terminal for most ATUs will a standard coaxial cable fitting. Output terminals should be ceramic feed-through types. Ring or U terminals are normally used for both inside and outside connections to the threaded shaft that runs through the dual ceramic pillars. Steatite, developed three quarters of a century ago, is still the usual ceramic of choice for RF service in the HF bands.

+
+

Construction and Operation

+
The inductively coupled tuner is essentially a combination of passive circuits and produces no power of its own. Therefore, the shielding practices normally used for power producing equipment are to a large measure optional with antenna tuners. Perfectly operational tuners may be laid out on breadboards or placed within attractive wooden or clear acrylic cabinets. Perhaps the only operational caution with unshielded layouts is to insulate control shafts in order to prevent shock haxards and hand-capacitance effects. Safety to shack visitors (or to the operator) is a strong reason for enclosing the tuner. +

If a metal case is used, it should be large enough to permit all components to be well spaced from metallic surfaces. This precaution reduces the introduction of stray capacitance, which can reduce the flexibility of the variable controls, especially at higher frequencies. With metal cabinets, long, sturdy ceramic stand-off insulating posts must be used for components that require isolation from ground.

+

Component layout should follow good RF practice, with attention to maintaining secondary circuit balance. Hence, leads to and from comparable points on either side of the center of the secondary should be as short as possible and of roughly equal length and proximity to adjacent components. Leads in the secondary should use wire of the same size as the coil winding. It is possible to space switch wafers to achieve this physical balance, and the rest is largely a matter of component placement.

+

The primary side should use short heavy leads. If the coil primary assembly is at some distance from the coax fitting, a length of coaxial cable may be used to connect the two.

+

A common ground of the smallest spread provides the least potential for excessive current circulating in this path. Even when metal cases are used and form the ground bus, care should be taken to use contact points in closest proximity to each other, commensurate with the use of short leads.

+

Input and output measurement circuits, if internal to the tuner, should be isolated from the fields surrounding the main components of the tuner. The DC and meter portions of the measuring circuits are best isolated by placing them in grounded metal boxes as far as possible from the main coil and capacitors.

+

The input side of the coupler is normally an unbalanced circuit. It requires a common ground. Ideally, this ground should be common with the other station equipment ground as well as the station earth ground.

+

The balanced secondary of the tuner presents the user with some options. Ordinarily, the center of the coil is left ungrounded (or "floating"), largely due to difficulties presented by the centering of the link over the center of the secondary inductor. The center of the split-stator tuning capacitor and the junction of capacitor-divider differential units are often grounded as a matter of construction convenience when using metal cases or chassis. This connection is, however, optional. (However, it is good practice to connect the junction of the differential capacitors to the common rotor of the main tuning capacitor.)

+

Grounding the center of the of the secondary circuit provides a common reference for the two sides of the feedline and the secondary circuit. However, it also provides a point of direct coupling for out-of-band signals. Such coupling is significantly reduced if all secondary components are left floating. Home constructors may wish to experiment to determine the better system for their individual situations. A floating secondary may be especially useful with 160- meter tuners, where strong AM broadcast band stations require all the filtering possible.

+

Tuning up the coupler is a matter of finding the correct control settings for maximum output and a 1:1 SWR at the input. Initial tuning is largely trial and error in the absence of definitive knowledge of the load resistance and reactance. For a tuner using a tapped secondary inductor, a trial balanced pair of taps is the starting point (at low power, of course). The secondary capacitor is resonated, as indicated by a dip in the SWR metering circuit that is in the primary line either inside or outside the tuner. The series capacitor is then adjust to the lowest SWR, followed by a series of alternate tweakings" of the primary and secondary capacitors. If the initial taps do not result in a 1:1 SWR, the next adjacent set should be tried--and so on until the match is obtained.

+

The goal is to use the set of taps closest to the outer limits of the secondary inductor that permit a perfect match. These taps represent the lowest working Q for the circuit and thus provide the largest bandwidth for satisfactory operation without further control adjustment. Ordinarily, they also provide maximum power output. However, as noted along the way, it is possible--although unusual--to find a perfect match while most of the current is circulating within the components rather than going to the line.

+

For the capacitor-divider coupler, the coil tap is usually fixed by a band switch. Adjustment involves alternate changes to the series primary capacitor, the secondary resonating capacitor, and the differential capacitor. However, the aim is the same: the lowest Q (and broadest tuning) that still permits a perfect input SWR reading. Since an opaque case and simple reference marks tend to obscure what is happening with the capacitor-divider, the bandwidth of an adjustment set may be the only indication that the most satisfactory match has been obtained.

+

All final setting should be logged and attached to the tuner case. Not only do they ease the adjustment when changing frequencies, they also provide a reference for antenna system diagnosis. If the required settings drift with time, vary radically with certain weather changes, or change suddenly to a new permanent set, antenna and feedline maintenance is indicated.

+
+

Measurement

+
Two measurements are important to any coupler: the match of the input circuit with the line to the transmitter (and receiver) and the relative power output. Ordinarily, we make the first of these measurements and simply presume that the second needs no measurement. The ordinary is simply not good radio practice. +

The input monitor usually consists of an SWR metering circuit mounted within the tuner cabinet or placed in the line between the tuner and the transmitter. Either system works well. Since SWR circuits are legion, no further comment on them is required, except perhaps for the reminder that the DC metering portion of the circuit should be well shielded from the fields of the tuner components.

+

Output measuring has long been unnecessarily difficult, since standard recommendation call for RF ammeters, which are difficult to find, especially in the ranges useful for the wide variety of amateur power levels. For higher power, light sources coupled to high-voltage positions along the line have provided an alternative power output indication.

+

Since the coupler may encounter a wide range of load impedances whose actual values are not easily determined, true power output is not the measurement of choice. Rather, efficient operation of the coupler is a matter of achieving the highest possible power output for any given input. Hence, a relative power output indicator is sufficient for most non-laboratory applications.

+

For any given load impedance, both the current and the voltage will rise as power is increased. Both rise as the square root of the power increase. Therefore, a simple voltage sampler may be connected to the output terminals of the coupler and left in the line permanently. The sample voltage can be rectified, filtered, and then measured with a voltmeter. For relative readings, where we wish to track the rise and fall of the voltage as we adjust tuning controls, an analog meter is preferable.

+
+ +
+

Figure 2 shows the basic schematic diagram of a relative output meter. High value voltage dividers go from each terminal to ground. The resistors should be in the Megohms, but the exact values should be determined experimentally relative to the range of impedances and power levels used by a particular station. Diodes provide full-wave rectification of the sampled RF. At levels higher than QRP, use high-voltage diodes as a protection from reverse voltage breakdown. The potentially high impedance of the output circuit dictates a higher level of filtering than usually applied to low impedance circuits.

+

In this basic circuit, a simple potentiometer may act as a sensitivity control and thus be the only element within the "Amp. & Control" box in Figure 2. An FET op amp in a voltage follower circuit provides the voltage and current the voltmeter. It is wise to add zener diode or other protection to prevent meter damage from excessive voltage levels.

+

The circuit is open to innumerable improvements in the "Amp. & Control" section, especially for automating the meter range for the wide variety of sample voltage levels that the tuner may provide. A second voltage divider might be used as a reference to one of the bargraph LED driver chips to obtain up to ten decades of control. The chip output would not only light an LED telling the operator which decade was in use, but as well trigger a control chip that inserted the correct voltage reducing resistor for each step rise in power level. Of course, such improvements require a modicum of power, and all such circuitry requires excellent shielding.

+

The point of this exercise is to move us into contemporary means available for monitoring coupler output without disturbing the balance of the tuner at any power level. By tracking relative power output from the tuner, we can assure that we not only have achieve a correct input-side match, but as well have achieved maximum power output. It is the output that does the work of communicating, not the match.

+

This small tutorial has drawn on a large number of sources in an effort to bring together the principles and practices of inductively coupled tuners. If such tuners are better understood, they may once more take their proper place beside network tuners, each doing the job for which it is best fitted and not being forcefully adapted to a task which it is not well-fit to perform. Despite nearly a half century's effort to make coaxial cable the only ham cable, amateurs are discovering that parallel transmission line has an important place in the array of antenna- transmission line combinations. And wherever parallel transmission line is used, the inductively coupled tuner has a natural home.
+

+
+ +

+
+

Updated 11-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Return to Index
+
+
+

Topics: Matching


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+

Antenna Books

+
+
+
+ 
+Antenna Books of Interest to QRP Enthusiasts               Version 1.3
+                                                         April 3, 1997
+Compiled by L. B. Cebik, W4RNL
+
+Contents:  This file contains basic information on antenna books of
+especial interest to QRP enthusiasts, but also of interest to all antenna
+builders and users.  The listing contains books on Basic Antenna
+References and Texts; Wire Antennas; Beam and Yagi Antennas; Quads;
+Vertical Antennas; Miscellaneous Antenna Projects; Antenna Testing and
+Experimenting; and Transmission Lines and Matching
+
+This list is restricted to books on antennas, because there are so
+many of them.  Books on more general aspects of electronics and
+operating for QRP enthusiasts  and periodicals of interest to QRP
+enthusiasts will be found in separate listings.
+
+Each entry in this book list provides the following information:
+author, title, publisher, year of publication, cost, ISBN #, numbers
+of pages, and a brief description of the contents.
+
+The individual items in this list are believed to be reasonably
+complete and accurate as of the date of this notice.  Corrections and
+additions may be e-mailed to me at the listed address.  I shall be
+pleased to add to the list any publication omitted if it is of high
+interest to QRP operators and builders.  And, of course, I shall be
+pleased to correct any errors and update the information listed.
+
+Permission to reproduce this list is hereby granted on condition that
+a full reference to its source is included.
+
+Good reading, good building, and good operating to you.
+
+                                                    L. B. Cebik, W4RNL
+
+======================================================================
+                        ==========================================
+                           Books of Interest to QRP Enthusiasts
+                        ==========================================
+
+                                        ==========
+                            Basic Antenna References and Texts
+                                        ==========
+
+Author:            R. Dean Straw, N6BV, Ed.
+Title:             The ARRL Antenna Book
+Publisher:         ARRL
+Year:              1994
+Cost:              $30.00
+ISBN #:            0-87259-473-4
+Pages:             736 plus diskette
+Contents:          The largest amateur antenna reference book, covering
+                   basic theory, many antenna types, transmission lines,
+                   and allied information, with many practical designs to
+                   construct.
+
+Author:            Richard C. Johnson
+Title:             Antenna Engineering Handbook, 3rd Ed.
+Publisher:         McGraw-Hill
+Year:              1993
+Cost:              $110.00
+ISBN #:            0-07-032381-X
+Pages:             1000+
+Contents:          A comprehensive engineering reference on antenna types
+                   and design methods, applications from low frequencies
+                   to radio-telescopes, and associated topics, including
+                   transmission lines, radomes, and materials.
+
+Author:            John D. Krauss
+Title:             Antennas, 2nd Ed.
+Publisher:         McGraw-Hill
+Year:              1988
+Cost:              $90.00
+ISBN #:            0-07-032xxx-x
+Pages:             892
+Contents:          A classic engineering reference on antenna theory and
+                   design, including a wide range of applications, with
+                   extensive bibliographical references.
+
+Author:            George J. Monsur
+Title:             Antenna Design:  A Practical Guide
+Publisher:         McGraw-Hill
+Year:              1996
+Cost:              $60.00
+ISBN #:            0-07-032xxx-x
+Pages:             192
+Contents:          A primer for antenna engineers: designing prototypes
+                   producing, testing, and analyzing antennas.
+
+Author:            John A. Kuecken
+Title:             Antennas and Transmission Lines
+Publisher:         MFJ
+Year:              1996 (rerelease)
+Cost:              $19.95
+ISBN #:            
+Pages:             320
+Contents:          Theory of antennas and transmission lines midway
+                   between mathematical and nonmathematical treatments.
+                   Each of the 37 chapters covers an individual topic for
+                   easy digestion.
+
+Author:            Joseph J. Carr
+Title:             Practical Antenna Handbook, 2nd Ed.
+Publisher:         McGraw-Hill: TAB
+Year:              1994
+Cost:              $35.00
+ISBN #:            0-07-011104-9
+Pages:             560
+Contents:          A handbook of fundamental concepts, formulas, and
+                   practical antenna designs, including muti-band wires,
+                   hidden and limited space antennas, VHF/UHF/microwave
+                   designs, and mobile/maritime/emergency antennas
+
+Author:            William I. Orr, W6SAI, and Stuart D. Cowan, W2LX
+Title:             Antenna Handbook
+Publisher:         Radio Amateur Callbook
+Year:              ---
+Cost:              $11.95
+ISBN #:            0-8230-870x-x
+Pages:             ---
+Contents:          An overview with dimensions of many antenna types,
+                   including verticals, horizontals, quads, deltas,
+                   slopers, quagis, and log-periodics, with information on
+                   transmission lines, SWR meters, wind loading and
+                   hazards.
+
+Author:            L. A. Moxon, G6XN
+Title:             HF Antennas for All Locations, 2nd Ed.
+Publisher:         RSGB
+Year:              1993
+Cost:              $20.00
+ISBN #:            1-872309-15-1
+Pages:             322
+Contents:          Basic ideas and detailed construction data on many
+                   antenna types, especially for small "gardens" (yards),
+                   with evaluations of both recommended and disrecommended
+                   types; includes the "Moxon rectangle."
+
+Author:            R. Dean Straw, N6BV
+Title:             All the right Angles
+Publisher:         LTA
+Year:              1992
+Cost:              $65.00 (with software)
+ISBN #:            
+Pages:             500
+Contents:          The basics of ionospheric propagation and the use of
+                   IONCAP software to model propagation paths, with
+                   applications to antenna system design.
+
+Author:            J. M. Haerle, WB5IIR
+Title:             The Easy Way:  HF Antenna Systems
+Publisher:         Overtones, Inc.
+Year:              1984
+Cost:              $12.00
+ISBN #:            ---
+Pages:             109
+Contents:          No-nonsense information on antenna fundamentals, basic
+                   wire antennas, special antennas--such as the sloper,
+                   DSRR, Beverage, and folded unipole--beam antennas, and
+                   160-meter antennas.
+                   tuners and SWR bridges.
+
+Author:            Lew McCoy, W1ICP
+Title:             Lew McCoy on Antennas
+Publisher:         CQ
+Year:              1994
+Cost:              $15.95
+ISBN #:            0-943016-08-8
+Pages:             111
+Contents:          Basic concepts of antennas and matching written in the
+                   style of an experienced writer for beginners, but
+                   includes numerous recent designs and advances.
+
+Author:            Bill Orr, W6SAI
+Title:             HF Antenna Handbook
+Publisher:         CQ
+Year:              1996
+Cost:              $19.95
+ISBN #:            0-943xxx-xx-x
+Pages:             200
+Contents:          A compendium of wire, loop, Yagi, and vertical antennas
+                   along with other information on resources and tools to
+                   start or improve antenna installations.
+
+                                        ==========
+                                       Wire Antennas
+                                        ==========
+
+Author:            William I. Orr, W6SAI, and Stuart D. Cowan, W2LX
+Title:             Simple, Low-Cost Wire Antennas for Radio Amateurs
+Publisher:         Radio Amateur Callbook
+Year:              1990
+Cost:              $11.95
+ISBN #:            0-8230-8707-7
+Pages:             188
+Contents:          Instructions for building tested wire antennas for 2
+                   through 160 meters, including horizontal, vertical,
+                   multi-band trap, and beam antennas, with information on
+                   matching systems, and ground systems.
+
+Author:            John D. Heys, G3BDQ
+Title:             Practical Wire Antennas
+Publisher:         RSGB
+Year:              1989
+Cost:              $14.00
+ISBN #:            0-900612-87-8
+Pages:             100
+Contents:          Practical aspects of wire antennas, from theory to
+                   buying or building them, including Marconis, Windoms,
+                   loops, dipoles, with a chapter on matching systems.
+
+Author:            Erwin David, G4LQI, Ed.
+Title:             HF Antenna Collection
+Publisher:         RSGB
+Year:              1991
+Cost:              $18.00
+ISBN #:            1-872309-08-9
+Pages:             233
+Contents:          Articles from RSGB's Radio Communication, covering
+                   single and multi-element horizontal and vertical
+                   antennas, including some very small types, as well as
+                   feed systems and antenna tuners.
+
+Author:            Edward M. Noll, W3FQJ
+Title:             73 Dipole and Long-Wire Antennas
+Publisher:         MFJ
+Year:              ---
+Cost:              $12.95
+ISBN #:            ---
+Pages:             ---
+Contents:          A collection of tested wire antennas needing a minimum
+                   of tools for building and testing, ranging from the
+                   dipole to the rhombic.
+
+Author:            Dick Pascoe, G0BPS
+Title:             Pascoe's Penny Pinchers
+Publisher:         R. A. Pascoe
+Year:              ---
+Cost:              4.95 L stirling
+ISBN #:            ---
+Pages:             ---
+Contents:          A collection of simple wire antennas that can be built
+                   "for pence, not pounds."  Includes building guidance
+
+                   and ideas for hidden antennas.
+
+                                        ==========
+                                  Beam and Yagi Antennas
+                                        ==========
+
+Author:            James L. Lawson, W2PV
+Title:             Yagi Antenna Design
+Publisher:         ARRL
+Year:              1986
+Cost:              $15.00
+ISBN #:            0-87259-041-0
+Pages:             210
+Contents:          Yagi performance calculations and optimization, ground
+                   effects, stacking, and practical designs from simple to
+                   very long.
+
+Author:            William I. Orr, W6SAI, and Stuart D. Cowan, W2LX
+Title:             Beam Antenna Handbook
+Publisher:         Radio Amateur Callbook
+Year:              1990
+Cost:              $11.95
+ISBN #:            0-8230-8704-2
+Pages:             268
+Contents:          Comprehensive look at HF and VHF Yagis, including
+                   matching, building, antenna erection, and antenna
+                   system evaluation.
+
+Author:            David B. Leeson, W6QHS
+Title:             Physical Design of Yagi Antennas
+Publisher:         ARRL
+Year:              1992
+Cost:              $20.00
+ISBN #:            0-87259-381-9
+Pages:             325
+Contents:          Designing and reinforcing Yagi antennas to survive 120
+                   mph winds, including structural design of elements,
+                   booms, and masts.
+
+                                        ==========
+                                           Quads
+                                        ==========
+
+Author:            Bob Haviland, W4MB
+Title:             The Quad Antenna:  A Comprehensive Guide to the
+                   Construction, Design, and Performance of Quad Antennas
+Publisher:         CQ
+Year:              1993
+Cost:              $15.95
+ISBN #:            0-943016-05-3
+Pages:             159
+Contents:          A comprehensive look at the concepts of the design and
+                   construction of quad and other loop antennas, including
+                   tips on optimizing quad designs.
+
+Author:            William I. Orr, W6SAI, and Stuart D. Cowan, W2LX
+Title:             Cubical Quad Antennas, 3rd Ed.
+Publisher:         Radio Amateur Callbook
+Year:              1993
+Cost:              $11.95
+ISBN #:            0-8230-8703-4
+Pages:             109
+Contents:          History, characteristics, design demension,
+                   construction, and tuning of multi-element quads, with
+                   chapters on feed systems and quad variants.
+
+Author:            John Koszeghy, K2OB
+Title:             High Performance Cubical Quad Antennas, 2nd Ed.
+Publisher:         self-published
+Year:              1996
+Cost:              $29.95
+ISBN #:            
+Pages:             205
+Contents:          A study of quad antennas of all types, from 2 to many
+                   elements, including test and measurement data for
+                   comparing Quads with Yagis.
+
+Author:            George McCarthy, W6SUN
+Title:             More About Cubical Quads
+Publisher:         WorldRadio
+Year:              1994
+Cost:              $9.95
+ISBN #:            
+Pages:             60
+Contents:          A guide to the practical side of building quads,
+                   on many years of experience, including where to
+                   find parts and accessories.
+
+
+                                        ==========
+                                     Vertical Antennas
+                                        ==========
+
+Author:            Robert Schetgen, KU7G, Editor
+Title:             Vertical Antenna Classics
+Publisher:         ARRL
+Year:              1995
+Cost:              $12.00
+ISBN #:            0-87259-521-8
+Pages:             123
+Contents:          Reprints of vertical antenna theory, design, and
+                   applications from QST, and the Antenna Compendium
+                   series, gathered in one place for convenience.
+
+Author:            Paul H. Lee, N6PL
+Title:             The Vertical Antenna Handbook
+Publisher:         CQ
+Year:              ---
+Cost:              $9.95
+ISBN #:            0-943016-xx-x
+Pages:             ---
+Contents:          Basic theory, design, and practice of vertical
+                   antennas, including grounds and construction of both
+                   simple and multi-element arrays; a classic.
+
+Author:            William I. Orr, W6SAI, and Stuart D. Cowan, W2LX
+Title:             All About Vertical Antennas
+Publisher:         Radio Amateur Callbook
+Year:              ---
+Cost:              $11.95
+ISBN #:            0-8230-870x-x
+Pages:             ---
+Contents:          A compendium of 52 vertical antenna designs, including
+                   Marconis, multi-band verticals, phased arrays, shunt-
+                   fed towers, and vertical loops, with information on
+                   ground, matching systems, loading coils, and TVI.
+
+Author:            Edward M. Noll, W3FQJ
+Title:             73 Vertical, Beam, and Triangle Antennas
+Publisher:         MFJ
+Year:              ---
+Cost:              $12.95
+ISBN #:            ---
+Pages:             ---
+Contents:          A collection of vertical antennas and phased and
+                   parasitic arrays, including end-fire, broadside, and
+                   colinear arrays.
+
+                                        ==========
+                              Miscellaneous Antenna Projects
+                                        ==========
+
+Author:            Dick Ganderton, G8VFH, Ed.
+Title:             More Out of Thin Air
+Publisher:         PW Publishing Ltd  (Practical Wireless)
+Year:              1995
+Cost:              $12.00
+ISBN #:            1-874110-05-0
+Pages:             111
+Contents:          A collection of antenna construction articles covering
+                   all aspects of amateur operation, from low bands to
+                   VHF, from wires to beams, with workshop information
+                   and lots of construction detail.
+
+Author:            George Dobbs, G3RJV, Ed.
+Title:             The G-QRP Club Antenna Handbook
+Publisher:         (available from N8ET, Kanga USA, 3521 Spring Lake Dr.,
+                   Findlay, OH 45840)
+Year:              ---
+Cost:              $12.00
+ISBN #:            ---
+Pages:             155
+Contents:          A collection of all the antenna articles in SPRAT's
+                   first 68 issues, including ATUs and test equipment, HF
+                   beam, wire, and vertical antennas, loop and restricted
+                   site antennas, and VHF antennas, with additonal
+                   information in appendices.
+
+Author:            Jerry Hall or Dean Straw
+Title:             Antenna Compendium, Vol. 1, 2, 3, 4, and 5
+Publisher:         ARRL
+Year:              1990-96
+Cost:              $10-20
+ISBN #:            0-87259-xxx-x
+Pages:             varies according to volume number
+Contents:          Collections of articles on antenna types, designs,
+                   modeling, construction, impedance matching, and other
+                   aspects of HF, VHF, and UHF antennas.
+
+Author:            Doug DeMaw, W1FB
+Title:             W1FB's Antenna Notebook
+Publisher:         ARRL
+Year:              1987
+Cost:              $10.00
+ISBN #:            0-87259-xxx-x
+Pages:             136
+Contents:          How to get the best performance from unobtrusive wire
+                   and vertical antennas, and how to build simple antenna.
+
+Author:            John Devoldere, ON4UN
+Title:             Antennas and Techniques for Low Band DXing, 2nd Ed.
+Publisher:         ARRL
+Year:              1994
+Cost:              $20.00
+ISBN #:            0-87259-xxx-x
+Pages:             400
+Contents:          Antenna designs and software for DXing on 40, 80, and
+                   160 meters, with operating tips and strategies.
+
+Author:            Frank Hughes, VE3DQB
+Title:             Hidden Ham Antennas
+Publisher:         ---
+Year:              ---
+Cost:              $12.95
+ISBN #:            ---
+Pages:             ---
+Contents:          A collection of ideas for small and hidden antennas for
+                   HF, VHF, and UHF.
+
+Author:            Larry Luchi, W7KZE
+Title:             The Technician Antenna Handbook
+Publisher:         MFJ
+Year:              ---
+Cost:              $12.95
+ISBN #:            ---
+Pages:             ---
+Contents:          Beginners book of antennas using easily available
+                   materials.
+
+                                        ==========
+                             Antenna Testing and Experimenting
+                                        ==========
+
+Author:            Peter Dodd, G3LDO
+Title:             The Antenna Experimenter's Guide
+Publisher:         (available from N8ET, Kanga USA, 3521 Spring Lake Dr.,
+                   Findlay, OH 45840)
+Year:              ---
+Cost:              $15.00
+ISBN #:            ---
+Pages:             200
+Contents:          Focuses on antenna measurements, including resonance,
+                   impedance, field strength, and antenna performance, wit
+                   information on antenna modeling, masts and materials,
+                   and experimental antennas.
+
+Author:            Ralph Tyrrell, W1TF
+Title:             MFJ Troubleshooting Antennas
+Publisher:         MFJ
+Year:              ---
+Cost:              $12.95
+ISBN #:            ---
+Pages:             ---
+Contents:          An overview of tests to evaluate antenna performance.
+
+                                        ==========
+                              Transmission Lines and Matching
+                                        ==========
+
+Author:            Walt Maxwell, W2DU
+Title:             Reflections:  Transmission Lines and Antennas
+Publisher:         Formerly, ARRL:  put of print, but may be reissued
+Year:              1990
+Cost:              $20.00
+ISBN #:            0-87259-299-5
+Pages:             388
+Contents:          Information on transmission lines, matching networks,
+                   and Smith chart use mixed with the correction of myths
+                   in amateur circles about SWR, reflected power, and
+                   antenna tuners.
+
+Author:            Wilfred Caron
+Title:             Antenna Impedance Matching
+Publisher:         ARRL
+Year:              1989
+Cost:              $20.00
+ISBN #:            0-87259-220-0
+Pages:             200+
+Contents:          How to use Smith charts to develop both simple and
+                   complex matching networks, with detailed examples to
+                   guide the new Smith chart user.
+
+Author:            Wes Hayward, W7ZOI
+Title:             ARRL MicroSmith, V. 2.00  (Software)
+Publisher:         ARRL
+Year:              1992
+Cost:              $39.00
+ISBN #:            0-87259-407-6
+Pages:             48 (Instruction Booklet)
+Contents:          Smith chart simulation program for PCs to design
+                   networks with fixed or variable L-C components, with
+                   graphic screen outputs.
+
+Author:            Jerry Sevick, W2FMI
+Title:             Transmission Line Transformers, 2nd Ed.
+Publisher:         ARRL
+Year:              1990
+Cost:              $20.00
+ISBN #:            0-87259-296-0
+Pages:             247
+Contents:          The fundamental textbook on the theory, design, and
+                   construction of transmission line transformers.
+
+Author:            Jerry Sevick, W2FMI
+Title:             Building and Using Baluns and Ununs
+Publisher:         CQ Communications
+Year:              1994
+Cost:              $19.95
+ISBN #:            ---
+Pages:             ---
+Contents:          Construction and application of practical transmission
+                   line transformers based on a series of articles in CQ.
+
+Author:            Roger R. Block
+Title:             The Grounds for Lightning and EMP Protection, 2nd Ed.
+Publisher:         PolyPhaser Corporation
+Year:              1993
+Cost:              $21.95
+ISBN #:            ---
+Pages:             95
+Contents:          Basic concepts of grounding and lightning protection
+                   from a leading manufacturer of protection materials and
+                   equipment.
+

+
+
+ Go to Amateur Radio Page
+ Return to Home Page
+
+
+

Topics: Books


+ + diff --git a/content/links/ac6la.gif b/content/links/ac6la.gif new file mode 100644 index 0000000..df3439e Binary files /dev/null and b/content/links/ac6la.gif differ diff --git a/content/links/ant2.gif b/content/links/ant2.gif new file mode 100644 index 0000000..0a2b223 Binary files /dev/null and b/content/links/ant2.gif differ diff --git a/content/links/antcom.html b/content/links/antcom.html new file mode 100644 index 0000000..8e40bf4 --- /dev/null +++ b/content/links/antcom.html @@ -0,0 +1,168 @@ + + + + + + + Manufacturers and Dealers + + + +
+ + + + + +
L. B. Cebik, W4RNL (SK)
+ Knoxville, TN
+
+
+
+ +
+
+

Links to Manufacturers and Vendors

+
+
+ +
+

Note (2023): Links table on this page is currently commented out, many of the links are broken or the domain expired and has since been re-registered for other uses. At some point I'll go through them all and update the table.

+
+ +
+

Updated 01-01-2008

+

Return to Main Index

+

Topics: Links


+ + diff --git a/content/links/antdish.gif b/content/links/antdish.gif new file mode 100644 index 0000000..fb6fa43 Binary files /dev/null and b/content/links/antdish.gif differ diff --git a/content/links/antelmr.gif b/content/links/antelmr.gif new file mode 100644 index 0000000..eb7e2b5 Binary files /dev/null and b/content/links/antelmr.gif differ diff --git a/content/links/antennex.gif b/content/links/antennex.gif new file mode 100644 index 0000000..4132b5a Binary files /dev/null and b/content/links/antennex.gif differ diff --git a/content/links/antsite.html b/content/links/antsite.html new file mode 100644 index 0000000..45441c8 --- /dev/null +++ b/content/links/antsite.html @@ -0,0 +1,188 @@ + + + + + + Antenna Sites + + + +
+ + + + + +
L. B. Cebik, W4RNL (SK)
+ Knoxville, TN
+
+
+
+

Links to Some Other Notable Antenna Sites

+
+
+ +
+


+
+ These links carry a lot of valuable information and ideas, ranging from antenna fundamentals to advanced topics in antenna design, modeling, feeding, and building. In addition, some provide links to other sites, including manufacturers and dealers. Because URLs change without notification to those linking to them, not all of these links may work at any given time. I shall update links as soon as I receive the appropriate information.
+

+
+ +
+

(web.archive.org) For those interested in antenna experimentation, the magazine AntenneX is now an on-line monthly subscription publication. It appeals to both new and experienced antenna experimenters and builders.
+
+

+
+
+

Cemtach (web.archive.org - no images captured) has obtained a very large collection (over 500) models and provided information and patterns at their web site. The information may be useful to those wishing an overview of the patterns produced by various types of antennas. In addition, the simulations make extensive use of color in their pattern images, which the browser can download in .PNG format
+
+
+
+
+

+
+
+

Rudy Severns, N6LF, has a site set up in blog style with a considerable number of papers and presentations on antennas and related antenna system elements. The articles contain the results of Rudy's extensive research conducted in a professional manner, but with results especially useful to radio amateurs. The site also contains a comparison of VNA-type instruments that are supplanting simpler type SWR meters to provide more complete analyses of antenna systems
+
+

+
+
+

David Robbins, K1TTT, has developed a most useful collection of technical notes that include important items on antenna and related antenna system elements. These notes include his own analyses as well as hard-to-find items drawn from internet sources. (The partial photo is just the tip of one tree in his antenna farm.) Among other items, you will find W3LPL's long Yagi designs (until Frank establishes his own web site).
+
+

+
+
+

Tom Rauch, W8JI, provides a multi-faceted site with a strong component devoted to antenna topics, including adjunct devices and measurements. Low-band activity, techniques, and technology is one of his specialties. The site is also one of the best sources of detailed information on the popular MFJ-259 anatenna analyzer.
+
+
+

+
+
+

George Fremins, III, K5TR, maintains a selection of pages describing his own developing antenna farm and as well has a fairly nice collection of Yagi models--including the W3LPL designs and some Hy-Gain and Cushcraft models--in YO form for use with this popular Yagi optimizing program.
+
+
+

+
+
+

David Jefferies, (web.archive.org) has placed on line a large number of very useful papers on fundamental aspects of antennas, ranging from Maxwell's Laws to Yagi-Uda antennas to transmission lines to radiation impedance to the basics of arrays. . .. This is just a sampling of the topics covered. The items appear aimed toward his E.E. students, but the papers are useful to all who wish another look at some of the basics ideas behind antennas.
+
+
+
+

+
+
+

Ian White, G3SEK, maintains an excellent "Technical Notebook" site. Information focuses on VHF/UHF and contains important antenna, filter, moonbounce, and circuitry data. The information on Yagi stacking and construction is especially interesting to me, but you may find his other notes to be just what you need. Ian writes the highly respected monthly RadCom "In Practice" column.
+
+
+

+
+
+

R. J. (Reg) Edwards (web.archive.org) maintains a site with free calculation software of considerable interest and utility to radio amateurs. With about 100 utility programs (with some of the Pascal coding also available), the site covers many calculations needed for antennas, transmission lines, loading coils, and other related topics. All programs are open--that is not zipped--and are ready for use upon downloading.

+
+
+

Go to Part 2

John Reynolds, G3PTO, provides another fine British antenna web site. Actually, antennas are only one portion (but an important portion) of John's collection of useful information for QRPers and other operators.
+
+

+
+
+

Dan Maguire, AC6LA, provides amateurs and others interested in system feeding and Smith Charts with an interesting program (XLZIZL) and explanations of how it works. The program can be downloaded from Dan's site. The site also contains some very useful information on Smith charts and their alternatives, as well as some interactive features for those who access the pages.
+
+
+
+

+
+
+

Kevin Schmidt, W9CF, has placed at his site a consider number of papers on tuners, baluns, networks, antennas, and related topics, along with some interesting and instructive applets for users to download. The material is advanced, with a strong mathematical element throughout.
+
+
+

+
+
+

Roger Cox, WB0DGF / W8IO, author of LPCAD and a veteran antenna engineer and designer, provides considerable information on and links to sites devoted top both antenna modeling and stealth antennas.
+
+
+

+
+
+

Aaron Schmitz, KB0YKI, maintains several pages of good basic construction information on some useful antennas for VHF/FM work.
+
+
+

+
+
+

Phil Karras, KE3FL, maintains a diverse set of web pages which include some very useful, downloadable software on power output, SWR bandwidth, J-poles, and other subjects.
+
+

+
+
+

Mike Banz, AA3RL, has some interesting studies of dipoles, both vertical and and horizontal, at his site, along with the results of tests with a commercial multi-band vertical antenna. Also featured is a spreadsheet transmission line calculator that you can down load without cost.
+
+

+
+
+

Cecil Moore, W6RCA (W5DXP), (web.archive.org) has produceded an interesting page that focuses on techniques of matching parallel line fed antennas to station equipment, the G5RV antenna, and a variety of loop antennas.
+
+

+
+
+

John Tait, EI7BA gives excellent detail about the construction of his multi-band quad (exact number of bands keeps growing). Also included are details of the feed system and its rationale, along with many photos, drawings, and tables.
+
+
+

+
+
+

VK1BRH Ralph Holland, VK1BRH, shares my interest in antenna modeling. He specializes in low band short or compact vertical antennas, but his work covers a wide range of antenna simulation experiments.
+

+
+
+

Dan Warren (web.archive.org) Dan Warren, an Air Force antenna engineer, has developed (and continues to develop) one of the very best compact treatments of antenna fundamentals under the title "How to Become an Antenna Guru." Besides providing a technically sound introduction to an array of arrays (and basic antennas, too), Dan illustrates the long web entry with excellent color 3-D antenna patterns.
+
+

+
+
+

Prof. Natalia Georgieva (web.archive.org) of McMaster University in Ontario has made available her lectures in two subjects. The link is to her course in Modern Antennas in Wireless Telecommunications, which is an excellent survey of many antenna principles and practices. Also available from another link at her site is Theory and Applications in Electromagnetics on the fundamental principles underlying electromagnetic radiation. These courses are designed to be used with texts and lab exercises, but the lectures themselves make a very useful and compact survey of the field. They are heavy in relevant equations that are useful for reference.

+

The lectures themselves are in .PDF format, so an Adobe reader is necessary.
+
+
+

+
+
+

Prof. Miguel Ferrando Bataller (web.archive.org) of Universidad Politecnica de Valencia has made his university course lecture notes and other helpful aids available on his website. These notes are in Spanish and may be extremely helpful to those for whom English is not the native language. The site includes pages of equations of fundamental importance in addition to extensive notes.

+

The site also has some very useful links to advanced antenna tutorials, especially for those working in the area of microwave and wireless antenna technology. See, for example, the tutorials provided by IEC (broken link http://www.iec.org/online/tutorials).
+

+
+
+

The G3YCC QRP site (web.archive.org) contains a wealth of information on a large number of topics of interest to QRP operator, including a variety of articles on antenna and related system items for both home and portable use. The site is related to (but not directly sponsored by) the GQRP club, a long-standing organization of QRP operators world-wide and publisher of SPRAT, a highly respected journal of QRP techjnical information and ideas. Only the antenna index page is linked here, but you can back up to the home page for the array of other QRP topics that George has provided.
+
+
+

+
+
+

A good site for learning antenna basics and designing basic antennas.
+
+

+
+
+

Ken Harker (web.archive.org) is developing new ways to present visualizations of antenna patterns. Although in the early development stages, this project bears watching and may one day find its way into commercial antenna modeling software.
+
+

+
+
+ Commercial Antenna Manufacturers and Vendors: A collection on known sources, offered because these pages often contain educational as well as commercial information.
+
+
+
+
+

Other Amateur Radio Links: A collection of links to organizations and linkage sites to help you find other good sources of information.
+
+
+

+
+ +
+

Updated 10-02-2007.

+

Return to Home Page

+

Topics: Links


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+ + + + + +
L. B. Cebik, W4RNL (SK)
+ Knoxville, TN
+
+
+
+ +
+
+

Ham Links

+
+
+ +
+

With some half-million licensed operators in the United States, the interests of individuals in the overall opportunities offered by amateur radio vary widely. As a result, there are numerous organizations dedicated to fostering interests and skills in various aspects of the service. Below are links to a few of the ones in which I am a life or long-term member.

+

ARRL

+

The American Radio Relay League is the largest membership organization of amateur radio operators in the United States and is viewed informally as the U.S. national amateur organization. It conducts an extensive program of services for members and for the amateur community as a whole, including a wide range of educational activities. The ARRL WWW site contains a wealth of amateur radio and membership information.
+

+
+
+

RSGB

+

The Radio Society of Great Britain is the UK national amateur radio organization, with information and links to information that are useful world-wide.

+


+
+
+

QCWA

+

The Quarter Century Wireless Association serves the "old timers" of amateur radio in numerous ways. QCWA celebrated its own 50th anniversay in 1997. If you have been a ham for 25 years or more, consider joining.

+
+
+

10-10 International

+

10-10 International is devoted to the responsible and active use of the 10-meter amateur band world-wide. There are over 100 local chapters throughout the United States and the world.
+

+
+
+

QRP-ARCI

+

QRP ARCI is the oldest U.S.-based organization devoted exclusively to encouraging the use of low power (5 watts CW, 10 watts P.E.P SSB or lower) on the amateur bands. Its programs include educational and operating activities for all interested amateurs, from the very new to the oldest old timer. QRP operators do perhaps more home brewing (building) of station equipment than almost any other segment of the amateur radio population.

+
+
+

FISTS

+

FISTS is an international organization of radio amateurs dedicated to preserving and encouraging radio communications via CW (Morse Code).

+
+

Very Special Amateur Radio Sites


+

The Courage Handi-Ham System

Handi-Hams is devoted making amateur radio accessible to those with physical disabilities and sensory impairment.
+
+
+

Morse 2000 (web.archive.org)

The Morse 2000 group is dedicated to exchanging information on the use of Morse code as an interface between handicapped individuals and such items as computers. Its work involves both experts on code and experts on enabling the disabled.
+
+
+

Other Amateur Radio Sites with Many Links


+

The AC6V Link Site

A general Amateur Radio site, with many links to all facets of hamming.
+
+
+
+
+
+

The eHam Net

A very large site with search facilities for almost everything an amateur radio operator might be interest in. The site has over 2500 links to related sites, as well as equipment review, opinions, and a store of useful information. +
+
+
+ +

Exploring Amateur Radio by N9AVG (web.archive.org)

This Amateur Radio site has over 500 links to all aspects of hamming, along with many articles of interest.
+
+
+

Books and Periodicals

As an educational service to amateurs--especially those interested in QRP--I maintain lists of periodicals and books ranging from beginner volumes to engineering texts. The lists are updated as new materials become available. +

Periodicals

+

Books on Electronics Projects and Operating

+

Books on Antennas

+
+
+ +


+

-73-

+

LB, W4RNL
+
+

+
+
+
+
+
+ Updated 12-21-2007.
+
+ +
+

Return to Home Page

+

Topics: Links


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+

Notes on Reactive Antenna Loads and Their NEC Models

+

L. B. Cebik, W4RNL

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+ +

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+ Although the basics of changing the electrical length of an antenna wire by adding a reactive load to it are seemingly well-known, the precise relationship between real loads provided to real antennas and modeled loads provided to modeled antennas is not so certain as one might think. Therefore, this series of notes will try to look at some of the ins and outs of the matter--all without pretending either to authoritativeness or completeness. It will be enough if we can get a better handhold on the subject. +

In the first note, I focus on the means for implementing loads in modes as complex impedances, that is, as resistance and reactances, and as series R-L-C loads. The effort will be to translate a reactance into an inductance as might be found in a solenoid inductor of standard single layer winding. Moreover, we shall also focus only on center or source- point loading, whether the math of the effects of loading is simple addition. Eventually, however, we shall have to return to R+/-jX and translate this into the other major means of implementation: the shorted transmission line stub of under 1/4 wl. That means of load implementation has another name: the linear load.

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Center or source-point loads are not the only reactive loading we can use to electrically lengthen an antenna. With dipoles and similarly balanced antennas, we can place loading reactances almost anywhere along the element, with the proviso that they be symmetrical in placement and value with respect to the element center. Actually, such loads do not have to be symmetrical, but symmetry does simplify most design and analysis problems. So we shall remain symmetrical to a fault.

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Next, we shall address both solenoid inductors and transmission line stubs placed well away from center on antenna elements. They will show some interesting patterns of which we should be aware before taking the next more difficult modeling step.

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NEC offers us short-cut methods of modeling both the solenoid and the stub reactive load via purely mathematical models. Before we conclude this sequence of notes, we shall investigate modeling both types of reactive loads--linear or transmission line loads and solenoid loads--as physical wire assemblies. One reason for taking pains to develop the models used in the preliminary investigation of using the LD and TL functions of NEC for antenna loads is that physically modeling both transmission line loads and single layer solenoid (or helical) loads requires care lest one exceed one or another limitation of the NEC modeling calculation system. The early models are developed with the later physical models in mind.

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The results of physically modeling linear or transmission line loads and of physically modeling coils (helices) may hold a few surprises relative to some commonly held beliefs about load models. For one example, not all apparent mid-element linear loads are in fact mid-element loads. For another example, loading coils turn out not to be simple inductances (or inductive reactances), but are instead a complex combination of inductance and radiating antenna wire.

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Although these notes may be useful in demonstrating a few principles, their numerical results cannot be automatically transferred to some existent antenna making use of loads. The final note will suggest some of the possible transfer errors that might be made, as well as some of the modeling challenges yet to be met when working with existing antennas.

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Updated 2-6-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Amateur Radio Page +

Topics: Loading, Modeling


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Notes on Reactive Antenna Loads and Their NEC Models
+ Part 1: Some Center Loading Basics

+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Although the basics of changing the electrical length of an antenna wire by adding a reactive load to it are seemingly well-known, the precise relationship between real loads provided to real antennas and modeled loads provided to modeled antennas is not so certain as one might think. Therefore, this series of notes will try to look at some of the ins and outs of the matter--all without pretending either to authoritativeness or completeness. It will be enough if we can get a better handhold on the subject. +

For antennas up to (but not including) 1/2 wl long, the source impedance is capacitive. To bring the antenna to resonance, we electrically lengthen it by adding an inductive reactance. We can add the reactance at the element center, or we may split the load into two equal parts and place them farther out on the element. The require inductive reactance needed to bring an element to resonance increases the farther out along the element we place the reactances.

+

Since every method of implementing an inductive reactance has some resistive loss, the reactive device has a Q, a ratio of inductive reactance to resistance. The higher the Q, the lower the losses. The most common two means of providing an antenna in the HF region with an inductive reactance are the air-wound solenoid inductor and the shorted transmission line stub less than 1/4 wl long. Both are physical entities having both basic and functional loss mechanisms. For example, solenoid wire for any given RF frequency has an AC resistance that is a function of skin effect. In addition, the interaction of the individual turns of the coil may yield other losses. Whatever the source of the loss, the solenoids Q or figure of merit expresses them all within the resistive denominator of the ratio.

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Modeling Resistance-Reactance Loads

NEC (either -2 or -4) provides several means of modeling inductively reactive loads. The most common type is the following: +
+ +
+

Type 4: Complex loads consisting of a resistance and a reactance. This is the native type of load for NEC. All loads are eventually translated into values of resistance and reactance. However, this type of load remains constant. That is to say, for the frequency sweep specified in the simple model in the figure, the values of resistance and of reactance remain the same for each frequency checked.

+

Type 4 loads are therefore not useful for frequency sweeps, since real solenoid components do not have the same reactance on every frequency. Reactance changes with frequency in relationship to a solenoid inductance. For most purposes in antenna work, the inductance and the resistance of the coil are treated as constants in simple inductive reactance loading problems.

+

Type 4 loads, however, are especially useful for initial design work. For example, if one has a short center-fed antenna, the reactive component of the source impedance will specify the absolute value of center reactive load necessary to eliminate it. The type of reactance introduced will, of course, be the opposite of the reactive component of the source impedance. since antenna wires shorter than 1/2 wl show a capacitive reactance at the source, a center reactive load must be inductive.

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Type 4 loads are also very useful for setting up or exploring the effects of the load Q on antenna performance. The results will apply only at the frequency for which the values hold good. However, one can easily obtain a family of value curves for comparing various antenna parameters.

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Let's set up a test dipole to see the type 4 load at work.

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The test dipole is exactly 1/4 wl long at 7.15 MHz, which makes it far short of resonant. We shall introduce a reactive load at the center, in the same position as the source or feedpoint. In NEC models, the source and the load are in series when the modeler specified the same position or segment for both the source and the load. The effect is comparable to splitting the center-loading solenoid at the center to insert the source (normally a transmission line for operational amateur radio stations).

+

The test model antenna uses lossless or perfect wire so that the only losses that appear will be from the load or loads we add. It uses 91 segments for reasons that will appear in later episodes. If this little test is replicated, be sure to use the same number of segments as in the example to obtain the same results. Antenna resonance in the modeling exercise is defined as a source impedance of less than +/-1.0 Ohm, and in most cases, the reactance will be less than +/-0.1 Ohm. Since there will be a slight drift in the source impedance as the segmentation of a given wire is changed, even for well-converged models, replication of results requires detailed replication of all of the model parameters.

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We may determine the required load for the antenna simply by reading the source impedance before inserting a load. We shall use two diameters of wires for this example: #8 and #12 AWG (with diameters of 0.1285" and 0.0808", respectively). To cancel out the capacitive reactance, the #8 antenna requires a center inductive reactance of 833.3 Ohms, while the #12 wire antenna of identical length requires 889.4 Ohms. For any value of Q, the resistance is simply the reactance divided by the selected Q value. Thus, we can select a range of Q-values to check. In this case, let us check a perfect inductively reactive load (R = 0), along with finite Q-values of 1000, 750, 500, 250, and 100. For the two antennas--which differ only in wire diameter--we get two families of values, which the following graph artificially connects with an identifying line just to keep the two antennas differentiated from each other.

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First, let's remember that the two antennas required two different reactive load values solely as a function of the source impedance. Both antennas use lossless wire, so the source impedance difference is a function of wire diameter. Now, if we look at the left-most line, where Q is infinite because the load resistance is zero, the antenna gain is the same for both wires. The fact that the value (1.85 dBi) is less than the traditional values for a resonant dipole (2.14-2.15 dBi) results from the length of the wire. It is much shorter than a resonant dipole. The wire shows the same gain without a load in place. Part of the gain of an antenna is a direct function of its length. In fact, you wish to obtain more gain from a dipole, make it longer--up to about 1.25 wl long. You may not like the resulting source impedance, but the antenna will have more gain simply by being longer--until it reaches a length where the pattern begins to degenerate into multiple lobes.

+

Second, the divisions from left to right following no special pattern. Hence, the actual curve of the values is not apparent. The drop in gain from a perfect load to one with a high Q-value of 1000 is noticeable. The region between a Q of 1000 and a Q of 500 strongly suggests that the curve of gain does not track arithmetically. Indeed, the curve is much straighter if each selected Q-value is of a constant ratio with the immediately preceding value throughout the chart.

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Third, the two families of values track each other, with lower gain values for the #12 wire antenna. If we remember that the necessary inductive reactance for the #12 wire antenna was higher than for the #8 antenna, then it follows that for any given Q, the resistance will also be higher. The higher the resistance of a center load, the lower the gain.

+

The type 4 load from which we derived the modeled data is a mathematical entity only. Whereas the wire is modeled as a physical entity, the load is only a mathematical modification of the results. Hence, any physical properties that the load may have will not play a role in its modeled performance. The length and diameter of the loading mechanism are never modeled in Type 4 loads, even if in reality they may play some kind of role in the performance of the antenna.

+

Modeling Series Resistance-Inductance-Capacitance Loads

Equally mathematical are loads of the following type: +

Type 0: Loads consisting of the following is series: resistance, inductance, and capacitance. Missing elements are entered as values of zero (which the program automatically interprets as a missing value, not a zero value). to specify an inductor of 6 microH with a series resistance of 2 Ohms, one enters this: 2, 6E-6, 0. The final zero indicates that there is no capacitor.

+
+ +
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The LD line in the input file shows the load type and values for resistance and inductance, again with a missing capacitor. Another load type (Type 1) is available for parallel combinations of resistance, inductance, and capacitance. We shall not need it for this particular set of notes.

+

The advantage of using R-L-C loads is that NEC translates them into appropriate values of reactance for each frequency checked in a file request. Hence, with R-L-C loads, one may run a frequency sweep and have the correct reactance at each frequency is the sweep.

+

However, there is an accompanying limitation. The value of R remains constant. Therefore, the Q of the reactive device changes slightly with each frequency checked, since the ratio of reactance to resistance changes across the range of the frequency sweep. For limited-range frequency sweeps, such as across one of the HF amateur bands, the possible error is too small to be significant.

+

Of course, one needs to be able to translate reactance to inductance (or, in other cases, capacitance) and back again to set the proper values. If one begins with a value of inductance, one must find the value of reactance for the frequency in question in order to use a value of Q to set the resistance or to find the value of Q from an assigned or measured value of resistance. The standard relationship of reactance to inductance, where inductive reactance is 2 PI times frequency times inductance in basic units, is an essential utility tool for using R-L-C loads.

+

A set of frequency sweeps between 7.0 and 7.3 MHz in 0.05 MHz steps for the #8 perfect wire dipole, center-loaded at the design frequency of 7.15 MHz for resonance with an inductance of 18.549 microH will yield a family of SWR curves. For each curve, the source impedance against which the antenna impedance is compared is the resistive impedance of the antenna at resonance on the design frequency. Hence, each curve shows a 1:1 VSWR at design center.

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+ +
+

The graph shows a family of such curves for a perfect inductor (zero Ohms resistance) and for inductors with Qs of 1000, 750, 500, 250, and 100. The requisite values of series resistance for the inductor are 0.8333, 1.1111, 1.6666, 3.3332, and 8.333 Ohms from 1000 down to 100. Once more, as we suspected from the gain curves earlier, the results of altering Q are more geometric than arithmetic, varying more linearly as Q forms a constant ratio from one value to the next.

+

Apparent in the graph is the fact that as we lower the Q of the loading coil, the operating bandwidth--set by any arbitrary selection of a VSWR ratio--become wider in terms of frequency. Often, we simply summarize the effect by saying that the increased losses broaden the operating bandwidth, as if the summary were an explanation. It is not.

+

In fact, what occurs, as modeled, is interesting in itself--and somewhat obvious if we stop to think about it. Consider the following two tables of values of source impedance for the #8 and the #12 dipoles, each center- loaded. The #12 wire antenna requires a 19.798 microH inductor with suitable adjustments in the values of the series resistor for the Q-values indicated earlier.

+ 
#8 Wire Dipole           Source Impedance (R +/- jX Ohms)
+Freq.     Q=Inf.         1000           750            500              250            100
+7.00      12.58-46.28    13.41-46.29    13.69-46.28    14.24-46.29      15.91-46.29    20.91-46.29
+7.05      12.78-30.76    13.61-30.76    13.89-30.76    14.45-30.76      16.11-30.76    21.11-30.76
+7.10      12.98-15.30    13.82-15.30    14.09-15.30    14.65-15.30      16.32-15.30    21.32-15.30
+7.15      13.19-0.02     14.02-0.02     14.30-0.02     14.86-0.02       16.52-0.02     21.52-0.02
+7.20      13.40+15.26    14.23+15.26    14.51+15.26    15.06+15.26      16.73+15.26    21.73+15.25
+7.25      13.61+30.25    14.44+30.25    14.72+30.25    15.27+30.25      16.94+30.25    21.94+30.25
+7.30      13.82+45.29    14.65+45.29    14.93+45.29    15.49+45.30      17.15+45.29    22.15+45.30
+Delta R    1.24          1.24           1.24           1.25             1.24           1.24
+Delta X   91.57          91.58          91.57          91.59            91.57          91.59
+
+#12 Wire Dipole          Source Impedance (R +/- jX Ohms)
+Freq.     Q=Inf.         1000           750            500              250            100
+7.00      12.61-49.30    13.50-49.29    13.79-49.29    14.39-49.29      16.16-49.29    21.51-49.30
+7.05      12.81-32.78    13.70-32.78    13.99-32.78    14.59-32.78      16.37-32.78    21.70-32.78
+7.10      13.01-16.29    13.90-16.30    14.20-16.30    14.79-16.29      16.57-16.29    21.91-16.29
+7.15      13.22-0.00     14.11-0.00     14.40-0.00     15.00-0.00       16.78-0.01     22.11-0.00
+7.20      13.43+16.31    14.32+16.31    14.61+16.31    15.21+16.31      16.98+16.31    22.32+16.31
+7.25      13.64+32.29    14.53+32.29    14.82+32.29    15.42+32.28      17.19+32.28    22.53+32.28
+7.30      13.85+48.35    14.74+48.34    15.04+48.34    15.63+48.34      17.41+48.34    22.74+48.35
+Delta R    1.24          1.24           1.25           1.24             1.25           1.24
+Delta X   97.65          97.63          97.63          97.63            97.63          97.65
+

The limits of accuracy are set by the last digit in each number, plus or minus 1, as a function of the sum of rounding conventions within the program. Within those limits, which vary only the value in the hundredths column, for each antenna, the range of variation of both resistance and reactance is invariant, regardless of the value of Q. Since Q is a function of changing R, the values for source reactance do not change at all. The values of source resistance is simply the values at infinite Q plus the series resistance of the inductive load.

+

In other words, the presence of a center load of finite Q does not alter the VSWR operating bandwidth curve by changing the source impedance other than adding the load resistance to the natural source resistance of the antenna without any load at all.

+

What the addition of the load series resistance does is to change the ratio of resistance to reactance at any of the frequencies swept, essentially raising the ratio of resistance to reactance. For the test antennas, the amount of change ranges from a fraction of an Ohm to under 10 Ohms. However, in each case, the result is a change in the impedance phase angle toward the resistive and away from the reactive.

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+ +
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The basic SWR equation shows the importance of this simple adjustment in terms of a lowering of the SWR at any frequency within the sweep range, when the value of Zo is the same as the value of Rin at the design center frequency. With values of Xin constant, higher values for Rin and Zo will together lower the VSWR relative to a design center frequency value of 1:1.

+

Transmission Line Stub Loads

Before we turn away from the modeling of center loads with the mathematical models available in NEC, let's look at the alternative method of creating an inductively reactive load: the transmission line stub. These stubs present us with an immediate modeling problem. Modeled transmission lines appear in parallel with sources. So we must move them. Moreover, a single stub would be very long (over 20' long for a 600-Ohm line). Common practice is to split the stub into two equal parts, installing one on either side of the line at the main element feed point. Our simple modeling counterpart would be to place TL entries in NEC on each of the adjoining segments to the source segment. +

However, we cannot simply use the value of the center-loading reactance and split it into two pieces. If the reactance is split and moved away from the source point, the sum of the pieces will be greater than the value of the exactly centered single reactance. The center loading reactance required for the #8 perfect wire dipole that is exactly 1/4 wl long overall in free space was 833.3 Ohms. Two reactances placed about 9" apart center- to-center, one on either side of the source, require 426.3 Ohms each (or 852.6 Ohms total)

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+ +
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With a type 4 reactive load, we can move in two loading directions. One of them is a Type 0 series R-L-C load, which requires an inductance at 7.15 MHz of 9.4892E-6 H on each side of the source. The other direction is a pair of transmission line stubs each side of center. Since the models of the stubs are mathematical only and a form of a NEC network, they will not show any interaction, loss, or other factors other than reactance.

+

The reactance of a shorted stub is equal to the characteristic impedance of the transmission line times the tangent of the electrical length of the stub in degrees or radians. Since we know that the stubs will each show 426.3 Ohms reactance, we can work backwards through the relationship to obtain the electrical length for a variety of common lines. Then we can obtain the physical length, since we know that a wavelength at the design frequency is 137.5624' long. For this exercise, we shall look at several common transmission lines with characteristic impedances of 50, 75, 300, 450, and 600 Ohms. We shall let the velocity factor be 1.00, since many of the lines offer options and variability. We have cut off the characteristic impedance at an upper limit of 600 Ohms, since with #8 wire, even 700-Ohm line requires over 22" of spacing without significantly altering the 600-Ohm values across the band.

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Let's first determine the VSWR for a pair of perfect solenoid coils and then for lines of 300, 450, and 600 Ohms across the 40 meter band. Each lossless coil will have a 9.4892 microH inductance. The line lengths required by each of the lines (including the ungraphed 50 and 75 Ohm lines) will be as follows:

+ 
Line Zo             50        75        300       450       600
+L (degrees)         83.31     80.02     54.86     43.45     35.39
+L (feet)            31.83     30.58     20.96     16.60     13.52
+
+

We create on the segments on each side of the source a TL or transmission line entry. Depending on the program we use, we might have to create a distant wire to terminate the stub or the program might do this for us and simply let us specify that we desire a short at end 2. Do not enter the length in electrical degrees, or a frequency sweep will not be accurate. That same electrical length, with a different physical length, will appear at each frequency checked by the sweep. Instead, enter the design center physical length of the stub, along with the characteristic impedance of the line. We shall explain in a moment why the 50- and 75-Ohm lines are not included in the graph below

+
+ +
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With all practical characteristic impedance lines, the SWR bandwidth is significantly narrower for a transmission line stub load than for a coil of indefinitely high Q. Note that the SWR bandwidth decreases as the characteristic impedance of the line decreases. The low impedance lines were omitted because their end values of SWR exceeded 100 and would have obscured the detail of the graph.

+

The reason for the narrower bandwidth is not Q as ordinarily understood in terms of resistive losses within the reactive loading device. Neither loading means has any resistive losses in the models. Rather, the stubs have reduced bandwidth because the value of reactance is a tangential function of their electrical length as the frequency changes, which yields a curve quite unlike the curve of solenoid coil reactance vs. frequency. The difference shows up vividly in these examples, since the required reactance is so high. For small-value line-vs-coil applications, such as the values associated with beta matches, the curves across a ham band will not be significantly different if the stub uses a high characteristic impedance.

+

To reinforce the differences between single-layer solenoids and transmission lines stubs as sources of reactance in antenna loading, let's look at tables of values for the perfect coil and the bank of transmission lines used.

+ 
             Source Impedance (R +/- jX Ohms)  (Values rounded)
+Frequency      Coil                          Line Zo
+MHz                      50         75         300        450        600
+7.00      13.1-47.3      13.0-207   13.0-154   13.1-64.8  13.1-56.3  13.1-52.7
+7.05      13.3-31.5      13.2-147   13.3-107   13.3-43.3  13.3-37.5  13.3-35.0
+7.10      13.5-15.6      13.5-78.5  13.5-55.9  13.5-21.7  13.5-18.7  13.5-17.5
+7.15      13.8-0.0       13.8-0.2   13.8-0.1   13.8+0.0   13.9-0.0   13.8+0.0
+7.20      14.0+15.7      14.0+91.5  14.0+61.2  14.0+22.0  14.0+18.8  14.0+17.6
+7.25      14.2+31.1      14.3+201   14.3+122   14.2+43.9  14.2+37.4  14.2+33.9
+7.30      14.4+46.6      14.7+334   14.6+205   14.5+66.1  14.5+56.2  14.4+52.3
+

The table shows several features of using transmission line stubs as loading elements at or near the center of the antenna element. First, the range of reactance variation is higher in all cases than for the perfect inductor. Second, although the phenomenon is smaller by far, the range of source resistance values is also greater for transmission line stubs than for perfect (and, by reference to earlier data, for finite-Q) inductors.

+

Since all of the loading devices used here have no resistive losses, their Qs as determined by the usual ratio of reactance to resistance are identical. However, their operating bandwidths are not at all equal due to the manner in which the reactance changes with frequency for the two types of reactive loads. Although there are ways around the problem for special cases, there is no direct way to introduce losses into the transmission line model used by NEC. Hence, one cannot by this means explore the effects of accounting for losses in the stubs.

+

Despite this shortcoming, TL models of transmission lines stubs do reveal some properties of their use as reactive loads. The fundamental differences in behavior relative to inductors across a band of frequencies should be clear. Second, for single frequency use, stubs are equivalent in all ways to inductors. Finally, we may note in passing that inductively reactive stub loads have an alternative name: linear loads. That name has, unfortunately, led to a number of persistent misunderstandings about their basic nature. We shall have to return to that name later.

+

However, lest a small matter go unnoticed, let me set it out in relief. In splitting and moving the loading reactance only about 9" each side of the source, we found an increase in the required value of loading reactance. At the same time, the 7.15 MHz resonant source impedance for the antenna increase in the perfect reactance models from 13.19 Ohms to 13.76 Ohms. Although two cases alone do not constitute a trend, I shall bet that one is afoot. And with this, we have a prelude to looking at inductively reactive loads installed at a distance from the centered source of our very short dipole.
+

+
+ +

+
+

Updated 12-11-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Mid-Element Loading Basics +

Return to Loading Index

+

Return to Amateur Radio Page

+

Topics: Loading, Modeling


+ + diff --git a/content/load/load1e1.gif b/content/load/load1e1.gif new file mode 100644 index 0000000..a3480ae Binary files /dev/null and b/content/load/load1e1.gif differ diff --git a/content/load/load2-1.gif b/content/load/load2-1.gif new file mode 100644 index 0000000..1628749 Binary files /dev/null and b/content/load/load2-1.gif differ diff --git a/content/load/load2-10.gif b/content/load/load2-10.gif new file mode 100644 index 0000000..b8dd48f Binary files /dev/null and b/content/load/load2-10.gif differ diff --git a/content/load/load2-2.gif b/content/load/load2-2.gif new file mode 100644 index 0000000..84bc1a6 Binary files /dev/null and b/content/load/load2-2.gif differ diff --git a/content/load/load2-3.gif b/content/load/load2-3.gif new file mode 100644 index 0000000..6e6e826 Binary files /dev/null and b/content/load/load2-3.gif differ diff --git a/content/load/load2-4.gif b/content/load/load2-4.gif new file mode 100644 index 0000000..587c487 Binary files /dev/null and b/content/load/load2-4.gif differ diff --git a/content/load/load2-5.gif b/content/load/load2-5.gif new file mode 100644 index 0000000..6790515 Binary files /dev/null and b/content/load/load2-5.gif differ diff --git a/content/load/load2-6.gif b/content/load/load2-6.gif new file mode 100644 index 0000000..f001c4e Binary files /dev/null and b/content/load/load2-6.gif differ diff --git a/content/load/load2-7.gif b/content/load/load2-7.gif new file mode 100644 index 0000000..db415eb Binary files /dev/null and b/content/load/load2-7.gif differ diff --git a/content/load/load2-8.gif b/content/load/load2-8.gif new file mode 100644 index 0000000..a909a5f Binary files /dev/null and b/content/load/load2-8.gif differ diff --git a/content/load/load2-9.gif b/content/load/load2-9.gif new file mode 100644 index 0000000..68f2ee2 Binary files /dev/null and b/content/load/load2-9.gif differ diff --git a/content/load/load2.html b/content/load/load2.html new file mode 100644 index 0000000..dd61e23 --- /dev/null +++ b/content/load/load2.html @@ -0,0 +1,153 @@ + + + + + + Reactive Antenna Loads and Their NEC Models Part 2: Some Mid-Element Loading Basics + + + +
+

Notes on Reactive Antenna Loads and Their NEC Models
+ Part 2: Some Mid-Element Loading Basics

+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In the first installment of these notes, we looked almost solely at short, center-loaded dipoles. Our test dipole is exactly 1/4 wl long (34.39') at 7.15 MHz and uses perfect or lossless wire of various sizes between AWG #8 and AWG #12. For reasons that will become apparent in still later episodes, the test model has 91 segments, each about 4.53" long. For Type 4 (complex R +/- jX) loads or for Type 0 (series R-L-C) loads, we placed the load on the center segment (#46). +

The one exception to this procedure arose when we substituted shorted transmission line stubs for the series R-L-C load, using the TL function of NEC. Since transmission lines appear in parallel with loads, we were forced to split the load and move the stubs to the segments immediately adjacent to the center segment (Segments #45 and #47). Two phenomena appeared:

+

1. Even with such a small spacing between loads, the source impedance of the dipole increased by a measurable amount. Using the #8 AWG wire model, the resonant source resistance climbed from 13.2 Ohms to 13.8 Ohms.

+

2. Likewise, the required reactance for loading the wire to resonance also increased. For the #8 wire model, the required reactance each side of center climbed from 416.65 Ohms to 426.3 Ohms just by moving the loads to a spacing of about 9" apart.

+

These two phenomena form part of a set of trends with which all designers of loaded elements must be familiar. We shall look at them initially by using the same load-creation facilities of NEC that we used in looking at centered loads. Before we are finished with these basics, however, we shall formulate some questions about the reliability of models to tell us the entire story using only the "regular" means of load creation: Type 4, Type 0, and transmission line (TL) shorted stubs.

+

Load Position Trends

In theory, it is possible to split a center inductively reactive load and to place the halves symmetrically anywhere along the wire of our short dipole. As we move the load halves outward, we must increase the value of reactance of each half in order to bring the dipole to resonance. The following exercise is designed to generate an appreciation of how much reactance must be pressed into service for the purpose of re-resonating the dipole as we push the loads further outward. +
+ +
+

Let us take the #8 model and place the loads successively 10% further outward from center. In terms of total antenna length, this amounts to placing the load at the 45%-55% positions, the 40%-60% positions, etc. For a 91-segment dipole, we can only approximate these positions, but the results are certainly close enough to reveal the trends involved. The exercise can use simple R +/- jX loads. At each position, we increase the value of inductive reactance to bring the dipole to within +/- 1 Ohm reactance of resonance at 7.15 MHz.

+

Initially, we can let the Q of the load be indefinitely high (or infinite, meaning resistively lossless) by setting the value of the load resistance to zero. We obtain the following table of results.

+ 
Position  Position       Reactance in   Source Impedance    Free Space
+Approx %  Actual %       Ohms per Side  R +/- jX Ohms       Gain dBi
+ 5/95      4.95/95.05    3948           37.7 + j 0.3        1.91
+10/90     10.44/89.56    1939           34.4 - j 0.5        1.90
+15/85     14.84/85.16    1369           32.0 + j 0.4        1.89
+20/80     20/33/79.67     996           28.9 + j 0.8        1.88
+25/75     24.73/75.27     817           26.5 + j 0.8        1.87
+30/70     30.22/69.78     668           23.6 - j 0.6        1.87
+35/65     44.62/65.38     586           21.3 + j 0.7        1.86
+40/60     40.11/59.89     510           18.4 - j 0.5        1.86
+45/55     44.51/55.49     465           16.2 + j 0.7        1.86
+50/50     50/50           416.65        13.2 - j 0.0        1.85
+

The most significant trend to note is the steady rise in the required reactance to bring the dipole to resonance as the load is moved progressively outward from center. The following graph shows the trend with some clarity.

+
+ +
+

The source resistance and gain figures are predicated on the unlikely event of obtaining a perfect (lossless) inductively reactive load. A more realistic value would be a Q of about 300. This requires that for each load, we divide the reactance by 300 to obtain a series resistance for the total load. If we insert the required values of resistance into our R +/- jX loads, we obtain the following values at 7.15 MHz with our #8 lossless wire model. (Reactance values do not change and are not shown below.)

+ 
Position  Series R  Source Impedance    Free Space     Inductance
+Approx %  Ohms      R +/- jX Ohms       Gain dBi       microH
+ 5/95     13.16     57.4 - j 0.9        0.08           87.9
+10/90      6.46     44.7 - j 0.9        0.77           43.2
+15/85      4.56     39.6 + j 0.2        0.96           30.5
+20/80      3.32     34.9 + j 0.6        1.07           22.2
+25/75      2.72     31.6 + j 0.7        1.11           18.2
+30/70      2.23     27.9 - j 0.7        1.13           14.9
+35/65      1.95     25.2 + j 0.6        1.13           13.0
+40/60      1.70     21.9 - j 0.5        1.12           11.4
+45/55      1.55     19.6 + j 0.7        1.02           10.4
+50/50      1.39     16.0 - j 0.2        1.02            9.3
+

The inductance that yields the required reactance is shown in the right- most column for convenience, and we shall return to it in a moment. First, however, let us look at the values from left to right. The series resistance values can be compared to the reactance values in the preceding table to confirm a Q of 300. The other values may benefit from a bit of graphing.

+
+ +
+

The source resistance increases approximately, but not exactly, as the loss resistance increases for each pair of loads. The small differential between the reported source resistance and the sum of the source resistance with an infinite Q and the total of resistive losses results from placing the loads ever farther from the center or source point of the dipole. Nonetheless, the trend is abundantly clear.

+
+ +
+

The graph that compares the free space gain of the dipole without load losses and with losses of a Q=300 load is perhaps more interesting. The lossless loads show a wholly insignificant variation of gain, regardless of load position. However, with a Q=300 load, the gain of the dipole shows a rise of 0.1 dB when the loads are place 20% to 60% of the total element length each side of center outward from the center--relative to the gain with the load centered. Beyond the 60% mark (20/80%, in terms of total dipole length), the gain decreases severely and rapidly as a result of the equal rapid increase in resistive loss that goes along with the steep rise in required loading reactance.

+

The 0.1 dB gain differential between center and mid-element loading is of questionable operational benefit. In a horizontal dipole, the use of mid-element loading in preference to center-loading is for other reasons, most often the higher source resistance of the dipole with mid-element loading. There remains a persistent myth that mid-element loading shows significantly higher gain than center loading. This myth derives from short mobile antenna experience using loaded monopoles. Field strength differences resulting from the environment within which such antennas work and from the very short lengths they use have become unwarrantedly generalized to cover all antennas making use of inductively reactive loads.

+
+ +
+

A second source of the myth is an uncritical examination of current magnitude curves along loaded elements. The graph above displays the current magnitude for the R-L-C center-loaded element, the TL near-center-loaded element, and the mid-element R-L-C loaded element. Seemingly, the current magnitude (relative to a source value of 1.0) indicates a stronger far field based on the assumption that the field is roughly proportional to the current. However, that assumption needs considerable modification with loaded elements.

+
+ +
+

One modification is occasioned by the current phase change along the element. For the mid-element loaded model, the rate of phase change along the element is much higher than for either center-loaded model. Moreover, the current magnitude curve is not a direct measure of the undissipated power in the element.

+

Using the strictly mathematical models of loads of all sorts, we may replace the Type 4 loads with either series R-L-C loads or with transmission lines (TL networks). The right-most column of the table shows the equivalent inductance values for the reactance loads used in this exercise. Although the weight and gain drop associated with such large inductance values is reason enough not to place loading inductors at the far ends of antenna elements, there is another reason as well. In at least the most extreme case (87.9 microH), for any practical single-layer solenoid coil-winding technique, we would not reach the required inductance before the antenna had passed resonance and had begun to show an inductive reactance at the source. We shall return to this point in a later episode.

+

Alternative Means of Placing Loads

Although certainly precise enough to show the important trends associated with mid-element placement of loads, the technique of choosing segments on which to place loads was only approximate. Except at the very center of the dipole, the loads were a bit off their desired marks. +

We could so segment the dipole that the loads would appear (as centered on their segments) in the desired places--but only for this exercise. If we chose other percentage values for load placement, further revisions of segmentation would be required. There is an alternative.

+

Consider the following problem (which, for the moment is academic only): suppose we wish to find the places along the dipole element where each of two mid-element loads are identical in required reactance to a single center load. For our 1/4 wl #8 perfect wire dipole, the required reactance of a center load is 833.3 Ohms to achieve resonance at 7.15 MHz. The question then is where along the wire to place two 833.3-Ohm loads also to achieve resonance.

+

The model has 91 segments. If we place the loads on segments 23 and 69, the source impedance reports as 27.11 + j 31.7 Ohms, which indicates the loads are too far inboard. If we place the loads one segment further outward--on segments 22 and 70--the source impedance reports as 26.34 - j 39.04 Ohms, which indicates that the loads are too far outboard. Within the limits of the model, neither placement satisfies the requirement of achieving resonance within +/-1 Ohm.

+
+ +
+

These unsatisfactory situations are indicated in parts A. and B of the figure above. The figure also indicates an alternative modeling method that permits precise load location without sacrificing model accuracy. The model in C. is a 5-wire model, all composed of the same type of wire. Two outer sections and a center section are long wires having many segments. Two special wires have 3 segments each, with the load placed on the center segment.

+

The use of 3 segments on the load wires serves to ensure that the segments immediately adjacent to the load segment are equal in length to the load segment. The center wire and the outer wires are segmented so that each segment length is as close as possible--within the limits of the total segmentation of the antenna--to the length of the load wire segments.

+
+ +
+

The .NEC model above shows the dimensions of the final model in terms of the wire geometry for the dipole with Type 4 reactive loads. For the #8 wire model, a center wire 199" long (+/- 99.5") used 45 segments, each 4.42" long. The outer wires are each 94.24" long and use 20 segments, each 4.71" long. The 3-segment load wires are 13.6" long, with segments 4.53" long. The total number of segments for the antenna remains 91.

+

The loads are centered 106.3" each side of the source. With this configuration, the reported source impedance is 26.78 + 0.53 Ohms, well within the limits set for resonance. The figures are for a pure reactance, with no series resistance.

+

The technique used here is subject to many variations, including re-segmentation to achieve even closer segment length equality along the antenna. Even more precise placement is possible to achieve resonance within narrower limits (for example, +/- 0.1 Ohm). However, for the purposes of this demonstration, the techniques used are sufficiently precise for both placement and resonance.

+

Center vs. Mid-Element Loading

Having placed the 833.3-Ohm load correctly at mid-element positions, it useful to take a preliminary look at the performance curves that result from applying the equivalent Type 0 (series R-L-C) load at both center and mid-element positions. The inductive equivalent of 833.3 Ohms at 7.15 MHz is 1.8549E-5 H. We can look at the curves both for infinite Q and for some representative Q, say, 300. The series resistance required for a Q of 300 at the design frequency is 2.778 Ohms. +

Once more, we shall use our #8 lossless wire 34.39' dipole.

+ 
#8 Wire Dipole           Source Impedance (R +/- jX Ohms)
+Freq.     Center Load    Center load    Mid-El. Load   Mid-El. Load
+MHz       Q=inf.         Q=300          Q=inf.         Q=300
+7.00      12.58-46.28    15.35-46.29    24.33-82.17    29.07-82.25
+7.05      12.78-30.76    15.56-30.76    25.11-55.15    29.98-55.23
+7.10      12.98-15.30    15.76-15.31    25.93-27.54    30.94-27.64
+7.15      13.19-0.02     15.97-0.02     26.78+0.53     31.93+0.40
+7.20      13.40+15.26    16.18+15.26    27.67+29.19    32.98+29.08
+7.25      13.61+30.25    16.39+30.25    28.60+58.35    34.07+58.54
+7.30      13.82+45.29    16.60+45.29    29.58+87.98    35.21+87.84
+Delta R    1.24          1.25           5.25           6.14
+Delta X   91.57          91.58          170.15         170.09
+

Mid-element loading results in a larger swing of both source resistance and source reactance across the span of frequencies swept in this exercise. The result for resistance is larger not only in terms of Ohms, but also when taking the swing as a percentage of the design center frequency value. The result for reactance, however, is the opposite: as a percentage of the design center frequency resistance, the reactance swing is smaller for the mid-element load case than for the center loading case. Moreover, for the mid-element loads, there is not the virtual identity of swings for either resistance or reactance that holds over the frequency span swept by the models with center loads.

+

The smaller change of reactance relative to the resonant source resistance also suggests that the SWR curves for the mid-element loading cases might be broader than for their center-load counterparts. Of course, SWR is plotted relative to the design center frequency resistance value, where the antenna is resonant within the prescribed limits for this exercise.

+
+ +
+

The graph confirms our suspicions. The upper two curves are for the test runs at an indefinitely high Q, while the lower curves are for the value Q=300. In both pairs, the curve for the mid-element loaded dipole is broader than its center-load counterpart. Two cautions attend these curves. First, the effect of wire losses are not accounted within the overall curve, since we are using perfect wire in order to isolate, as best we can within the model, the phenomena that may ascribed directly to the load itself. Second, the conditions of modeling must be remembered: the model is a free space model that, of course, does not take any ground effects into account. The modeled loads assign both the series resistance and reactance and do not take into account any further effects that might accompany a real single-layer solenoid inductor placed in center or mid-element loading service. Although specified in a Type 0 load in terms of a series combination of resistance and reactance, the loads are strictly mathematical entities whose physical properties are not calculated in the overall antenna evaluation.

+

The antenna free space gain for the various cases corresponds well to the curves earlier presented. The infinite-Q antenna shows a gain of 1.85 dBi for the center-loaded case and 1.87 dBi when mid-element loaded. When each loading inductor is set at a Q of 300, the gains are 1.02 dBi and 1.11 dBi, respectively. Again, these gain figures do not include any wire loss associated with the main element.

+

While we are exploring these modeling curves, we might as well compare transmission line loading when placed at the same mid-element point with the case developed in Part 1. In that instance, we placed a split load in the segments immediately adjacent to the source segment, because placement exactly on the source segment would not have yielded valid series load results. Even that small move of the load position required that we use two 426.3-Ohm loads, rather than a pair of 416.65-Ohm loads (833.3/2). The resultant 600-Ohm (velocity factor = 1.0) transmission line stubs were each 13.52' long. To replace the mid-element 833.3-Ohm loads with transmission line stubs with the same characteristic impedance requires lengths of 20.73' each. Once more, remember that transmission lines used in NEC models are lossless and mathematical. Within those constraints, the results are as follows:

+ 
#8 Wire   Source Impedance (R +/- jX Ohms)
+Freq.     Near-Center    Mid-Element
+MHz       Placement      Placement
+7.00      13.09-52.66    23.84-110.0
+7.05      13.31-35.04    24.76-74.67
+7.10      13.53-17.46    25.74-37.85
+7.15      13.76-0.03     26.78+0.42
+7.20      13.98+17.57    27.90+40.47
+7.25      14.21+34.88    29.09+82.25
+7.30      14.44+52.30    30.38+126.0
+Delta R    1.35          6.54
+Delta X   104.96         236.0
+

The mid-element transmission line load source impedance value verifies that the transmission line stub is the correct replacement for the reactance load of 833.3 Ohms. However, even with a 600-Ohm transmission line, the variance of reactance across the band is very large. As we have noted, with transmission lines of lower impedance, the variance will be larger still.

+
+ +
+

Comparing the SWR curves (relative to an SWR of 1:1 at resonance) for the near-center and the mid-element transmission line loads shows an interesting result that is opposite to results from using series R-L-C loads. The mid-element loading stub system yields a narrower SWR curve than the near-center loading system. This consequence follows from the much high values of reactance required of the stub. Since the reactance of the stub is a tangent function of the electrical length of the stub, stubs over 45 degrees long change their reactance values rapidly. The required stub length in this case is 54.2 degrees.

+

Concerns About Modeled Loads

Commonly, series R-L-C loads are considered to be adequate models of single-layer solenoid inductor performance in a loaded dipole or similar element. Despite their strictly mathematical nature, that is, the fact that their physical structure does not play a role in the calculation of predicted antenna performance, the resulting antenna performance figures are considered accurate enough for most practical design and analysis purposes. The key loss factor in a solenoid inductor is the series resistive loss, and other losses and factors that might cause variations from the predicted outcomes are considered too small to be of significance. Consequently, only in the most critical cases are solenoid loading coils physically modeled--and usually only where such coils are very simple. An example of such a case is the solenoid in the middle of many automobile UHF antennas for cellular telephone service. +

Transmission line loads, on the other hand, are widely distrusted as models of linear loads used in HF antennas. Most obviously, they do not permit the accurate introduction of resistive losses in the transmission line. Nor do they permit, except as an external calculation, the introduction of the line's velocity factor. (Some programs permit velocity factor information to be introduced into the interface between the user and the core calculation, subsequently converting it to the values needed by the core's network calculations.)

+

Most antenna's employing linear loads use load wire having a diameter different from that of the main element. Although MININEC can directly handle these types of models, the required model often presses the segmentation limit of the program. (Some recent MININEC developments, such as NEC4WIN, have broken the 256-segment barrier, and one version permits virtually unlimited numbers of segments, but at the cost of slow calculation speeds.) MININEC has additional requirements in order to reduce errors at sharp corners, NEC (in either version 2 or version 4) is inaccurate when faced with angular junctions of wires having dissimilar diameters. Consequently, physically modeling existent antennas with linear loads is not normally attempted.

+

However, it is possible to physically model linear loads using a uniform wire diameter throughout the model. While the technique does not yield an accurate model of a particular antenna, it does produce quite accurate results that can reveal some interesting properties of linear loads. The technique may also permit some preliminary sorting of different functions performed by a linear load and the conditions under which it performs them. Physically modeling some linear load configurations will therefore be our next task.
+

+
+ +

+
+

Updated 12-29-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Linear Loading Basics +

Return to Loading Index

+

Return to Amateur Radio Page

+

Topics: Loading, Modeling


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+

Notes on Reactive Antenna Loads and Their NEC Models
+ Part 3: Some Linear Loading Basics

+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Linear loads do not model accurately using the TL facility of NEC. There are two major factors (and a number of minor ones) that contribute to the inaccuracy. First, the currents on the wires of the linear load are rarely, if ever, exactly equal in magnitude and opposite in phase. Consequently, the linear load does not as a pure transmission line. Second, most applications of linear loading snug the parallel load wires close to and parallel to the main radiating element. This placement creates complex interactions between the linear load wires and the antenna wire. often to the point that the contributions of each wire to the total far field and to the total element length cannot easily be distinguished. +

Nevertheless, NEC is able to physically model linear loads with a good level of accuracy, where "good" might be provisionally defined as providing reasonable guidance for building or providing reasonable calculations for analysis. Good accuracy, however, is subject to certain restrictions. For example, for best accuracy, the wires comprising the antenna element and the wires comprising the linear load must be the same diameter to avoid both closely spaced wires of differing diameters and wires of different diameters meeting at an angular junction. In both cases, NEC results can be quite inaccurate. One consequence of this restriction is that NEC cannot directly model most of the existing commercial antennas employing linear loading, since these antennas generally use element and load wires of radically different diameters.

+

MININEC is subject to neither of these restrictions. With due attention to the need for very short segment lengths at angular junctions and to the overall segment limitation of many versions of MININEC, the program is capable of directly modeling virtually any linear loaded element. MININEC was the program of choice in my 10-meter study of linear loaded dipoles and Yagis in "Modeling and Understanding Small Beams: Part 4: Linear-Loaded Yagis." Communications Quarterly, (Summer, 1996), pages 85-106. These antennas used 0.75" aluminum elements and #12 copper wire linear loads, and MININEC provided excellent building guidance. Despite the different materials used, no construction correctives could be directly attributed to the program limitation of specifying a single material for the entire modeled structure. For conservative predicted results, the higher loss material (aluminum) was used throughout the modeling.

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Nonetheless, NEC (either -2 or -4) can model linear loaded elements where all wires are of the same diameter. This much capability is sufficient to reveal a number of linear load properties that are fundamental to this loading technique. Consequently, we may for this exercise employ some of the models already developed for other parts of this series and simply add to them various linear load configurations. Central to the work in this episode will be the 34.39' (412.68") short dipole that we have loaded in several ways. We shall principally use the #8 wire version. Throughout, we shall retain the use of 91 segments for the overall antenna main element, with an average segment length of about 4.53". This segment length will determine several other parameters in the course of physically modeling transmission lines or linear loads.

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In previous exercises, we have used perfect or zero-loss wire for the dipole element. So long as we could specify load losses in Type 0 or Type 4 loads (series R-L-C and series R-X loads, respectively), we could isolate losses directly attributable to the load. In this exercise, we shall physically model linear loads as wires in the antenna structure. In order to leave the "main" element perfect and register the material losses of the load wires, we shall have to use either NEC-Win Pro or GNEC (NEC-2 and NEC- 4 programs from Nittany Scientific), as these are the only commercial versions of NEC commonly available that permit specification of different materials for each wire in the antenna.

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Also see the Antenna Modeling Programs page for more information.

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Physically Modeling Transmission Lines

Modeled transmission lines must be parallel wire assemblies, since there is no practical way to model coaxial cables. (It is possible to simulate the cable braid with several wires of the same diameter as the center wires, but the cost in wire segment total makes the technique impractical here.) However, since a parallel wire line with significant spacing between wires represents the most common form of linear loading, this restriction will impose no problems. +

The linear loads we shall use will have a spacing of 4.53" center-to-center between wires. The diameter of a #8 AWG wire is about 0.1285". We can calculate the anticipated characteristic impedance of the resulting parallel line from this standard equation:

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where Zo is the characteristic impedance in Ohms, S is the center-to-center spacing of the wires, and d is the wire diameter, with both S and d in the same units. For the #8 line, the Zo is 510.1 Ohms.

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The standard equation presumes an indefinitely long line without connection wires to either a source or load. Moreover, it is invariant for any wire type and thus does not account for variations in the materials one might use for an open line. (In addition, it does not account for spacers, insulation, and other line variables that are not a part of this exercise.) In fact, wires physically arranged as parallel transmission lines do not model with precisely the same characteristic impedance as those yielded by the standard equation.

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We can model transmission lines to determine their characteristic impedance using the figure above as guidance. The "top" and "bottom" wires are single segments, each 4.53" long. The parallel wires will be an odd multiple of a quarter wavelength for the frequency tested. In our case, the frequency is 7.15 MHz, and we shall check the line using lengths of 1/4, 3/4, and 5/4 wl.

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By adjusting the line to a length that yields resonance at the source for a given load, we can find the characteristic impedance of the line from the standard equation,

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where Zo is the characteristic impedance of the line, ZL is the load impedance, and ZS is the source impedance. If we use a purely resistive load and bring the line length to resonance (defined as usual as less than +/- 1 Ohm reactance), the calculation is simplified. Let us initially specify a load of 5,000 Ohms resistance with a zero-loss (perfect) #8 wire line and see what we get.

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Test Length    Resonant     ZS           Zo       Segs/Length    Delta L"
+ in WL         Length "  R +/- jX       Ohms
+1/4             409.9    59.2 - j 0.1   544.1      91 / 4.50"    2.75"
+3/4            1236.6    59.3 - j 0.0   544.6     271 / 4.56"    1.45"
+5/4            2063.0    59.5 + j 0.0   545.3     451 / 4.57"    0.40"
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The "Delta L" figure is the departure of the resonant length from a perfect odd multiple of a quarter wavelength. The model has two wires at top and bottom which contribute to the overall line length and become error sources with respect to having a perfect parallel transmission line. However, the error they introduce decreases as the test line length increases.

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The selection of 5000 Ohms as the resistive load for this construction was arbitrary. For any given test length for the line, selection of a different load value will give slightly different results. Let's look at a 3/4 wl (1236.6") line and examine the characteristic impedance yielded by various load values.

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ZL                ZS                Zo
+Ohms           R +/- jX            Ohms
+    50         5920.0 - j 40       544.1
+   100         2961.0 - j 10       544.2
+   250         1185.0 - j 2.0      544.3
+ 1,000          296.3 - j 0.0      544.3
+ 2,500          118.6 - j 0.0      544.5
+ 5,000           59.3 - j 0.0      544.6
+10,000           29.7 - j 0.1      544.6
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With perfect wire, the range of variation in this second test of the characteristic impedance derived from the test model is not especially significant, with a maximum variance of about 0.5 Ohm for the range tested. The key variance in this exercise is between the modeled-derived Zo and the value calculated by the standard equation: about 33 Ohms--or a 6% variance, with the modeled impedance higher than the calculated value.

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If we specify the #8 wire to be copper (Resistivity = 1.72E-08), we end up with slightly different tables relative to those for perfect wire:

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Test Length    Resonant     ZS           Zo       Segs/Length    Delta L"
+ in WL         Length "  R +/- jX       Ohms
+1/4             409.7    60.1 + j 0.1   548.1      91 / 4.50"    2.98"
+3/4            1235.6    61.7 - j 0.0   555.4     271 / 4.56"    2.44"
+5/4            2061.0    63.4 - j 0.1   563.1     451 / 4.57"    2.40"
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The range of variation in derived Zo for the different test lengths, using the arbitrary 5000-Ohm load, is almost 15 Ohms. This represents a range of change of around 3%, which is well within the range of variation in real lines, especially those with insulation and a consequential velocity factor. However, the question remains as to whether the test yields accurate results. The second test provides the clue we need.

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ZL                ZS                Zo
+Ohms           R +/- jX            Ohms
+    50         5669.0 - j 80       532.4
+   100         2901.0 - j 22       538.6
+   250         1179.0 - j 5.3      542.9
+ 1,000          298.5 - j 0.5      546.3
+ 2,500          121.0 - j 0.1      550.0
+ 5,000           61.7 - j 0.0      555.4
+10,000           32.0 - j 0.0      565.9
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Note: when using low values of load impedance, it may not be possible to remove all of the reactance to the arbitrary standard of resonance that we have been using (+/- 1 Ohm reactance). However, if the reactance value is less than about 2% of the resistive value and slight line length changes to achieve resonance do not change the resistive value significantly, then the resulting resistive value will be usable.

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The test using different load values shows a wide range of values both above and below the values yielded by the perfect wire test. Since the approximate value of the characteristic impedance is also approximately the geometric mean between the adjacent load values (250 and 1000 Ohms), we can zero in on the actual line impedance by using that mean as a new load. If the first try does not yield a source impedance equal to the load we chose, we can adjust the load slightly until the results are equal within about 0.1 Ohms (to allow for rounding conventions in the software).

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Using this method, the final value for the perfect wire Zo is a little over 544.3 Ohms, while the final value for the copper wire is a little over 544.8 Ohms: very close indeed. In fact, we have extended the number of significant digits with respect to the characteristic impedance of the line too far for practical purposes in order to ensure clarity of the mathematical progressions. A value of 544 or 545 Ohms would suffice for all practical enterprises. This conclusion means that running the characteristic impedance modeling test with perfect wire with any reasonable load would have produced an acceptable result with a single test run.

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Modeling Transmission-Line Loads

We have lingered over the transmission line modeling test not only to show that transmission line characteristic impedance may differ in modeling software from values derived from standard equations, but as well to ensure that when modeling transmission line loads, we do not draw the wrong conclusions from the results we encounter. In order to get a handle on drawing the right conclusions, the next step is to model some transmission line loads using our #8 parallel transmission line. Because the principles do not change whether or not we account for wire losses and because the models are for demonstration purposes and do not represent structures anyone would actually build, we may use perfect wire transmission lines for these tests. +
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The models we shall construct use the basic 34.39' #8 perfect wire dipole. We shall insert transmission line loads at the segments adjacent to the feedpoint or source segment in the center and later at the points in the lines calling for 833.3-Ohm mid-element loads. From previous episodes of this exercise, we determined that loads placed immediately adjacent to the source for the 91-segment model required a reactance of 426.3 Ohms. We also used the 5-wire model to arrive at the positions of loads requiring 833.3 Ohms (the value of a single center load for this antenna).

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For our model, we may place the transmission lines parallel to each other or at 180 degrees apart. I have chosen the latter type of model to minimize interactions between the transmission lines, especially in the close-spaced model. Whichever model we choose, there will be a significant radiation component at right angles to the radiation from the main element.

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Let us take the Zo of the transmission line as 544 Ohms. Using the equations shown in earlier episodes, the 426.3-Ohm load requires a transmission line length of 174.6" while the 833.3-Ohm load is 260.7" long. Modeling these lines via the TL facility, in which the lines are mathematically but not physically modeled, would require these calculated values.

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Physically modeling the lines tells a quite different story, one that reveals why using the TL facility of NEC yields inaccurate results. To achieve resonance with the closely-spaced transmission line loads required a length of 155.3" for each line, almost 20" shorter than called for by the equation. The mid-element model required loads that were 157" long, more than 100" shorter than called for by the standard equations. (For alternate models using lines that parallel each other, the values were 151.2" and 156.5" respectively.) Each loading transmission line replaced one segment of the main element and the spacing was set at 4.53" between transmission line wires.

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A transmission line acts as a pure transmission line if and only if the currents everywhere along the line are equal in magnitude and opposite in phase on the two wires. An examination of the current tables produced by the NEC core reveals the degree to which this condition is not met by physical lines used as loads. In constructing models to perform this test, it is essential that the segments on each wire align perfectly.

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The current phase differential along the transmission line wires does not exceed 0.4 degrees in either case, so current magnitude comparisons are sufficiently accurate for the level of analysis required here.

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The graph shows the current magnitude differential between the transmission line wires for both cases tested. Current differential is greatest where the transmission line joins the main element. It does not reach zero at the far end of the line. The level of current differentials is far less along the closely-spaced or "center" load lines than along the mid-element load lines. Note, however, that there is nothing like a linear relationship between the degree of current magnitude differential and the degree of shortening of the lines.

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The current differential is an indicator of--but not a measure of--the fact that the lines have significant radiation. As radiating lines, they contribute linearly to the length of the antenna. To the degree that the wires in the load contribute to the linear length of the antenna wire, less reactive loading is required, and the lines required will be shorter than called for in standard equations. The higher the current magnitude differential, the greater the contribution to the antennas linear length and the higher the level of load shortening relative to equation-derived values. By mid-element, the contribution to the wires to the antennas linear length is so great that the load lines may be over a third shorter than their calculated value.

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In designing this overall exercise, I specifically chose a very short dipole (about 1/2 normal length) in order to set the effects we have noted in bold relief. Antennas only mildly shortened will show lesser current differentials in each of the models, and the degree of load shortening will be correspondingly less. Nonetheless, I know of no way of eliminating the fact that transmission line loads act as both reactive loads and as part of the linear antenna length--short of eliminating transmission lines as loads.

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The placement of the loads in this drill is far from optimal for maximum performance for the antenna. The gain of the close-spaced or center load model is 1.67 dBi, while the gain of the mid-element model is 1.88 dBi. The latter value is comparable to the values for zero-loss center and mid- element R-L-C loads (1.85 and 1.87 dBi, respectively), but there is considerable cross-polarized radiation that reduces the normal side nulls of a free space dipole model.

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Before we leave these informative but impractical models, we should briefly examine the SWR curves (relative to the source impedance at resonance for each model). The close-spaced or center loaded model shows a curve consistent with those we examined earlier in connection with transmission line loads generated with the TL facility. The mid-element line, in contrast, shows a very shallow curve, indicating a much wider operating bandwidth. This curve is in stark contrast to curves associated with TL- generated loads.

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The source of the broader SWR curve for the mid-element transmission line load lies mostly in the fact that the load lines act to a much higher degree as part of the linear or radiating length of the antenna. Consequently, the SWR curve approaches that of a standard full-size dipole. The major difference is that the shortened dipole has a resonant impedance of about 20 Ohms. (The resonant impedance of the close-spaced model is under 10 Ohms. The impedance of a perfect center-loaded dipole in this series of models is about 13 Ohms, while a perfect mid-element loaded version shows a resonant impedance of about 27 Ohms.)

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Linear Loads

The transmission line loads that we have just explored place the load lines at right angles to the main element in order to minimize interactions. Conventional linear loads tend to place the loading lines parallel to and close by the main element. +
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The sketch shows three typical linear load line assemblies. Actual antennas tend to fall into one of the three categories, although details may vary. The triangular load at the top feeds the center junction point of the linear load shorted lines, which then attach to the main element. Although we cannot accurately model actual structures in this exercise, the main element of most antennas of this type will be much larger in diameter than the load lines. For many purposes, the load lines may be placed in a plane with the main element, as shown in the middle sketch. Once more, the main or upper element will be larger in diameter than the load lines.

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A third popular assembly is shown at the bottom as a mid-element linear load. In this case, a "main" or larger diameter element is the feedpoint. The apparent load lines begin at mid-element and return toward the center, terminating and returning to the completion of the main element. Ordinarily, the apparent load lines are placed symmetrically about the main element, forming a triangle or a single plane. Why the sketch refers to this schema as a "pseudo-mid-element linear load" will become apparent as we proceed.

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The models for the tests were carefully constructed to achieve several goals. The segments throughout are all close to 4.53" long, and the spacing between lines is exactly that figure. Hence, the triangular models form equilateral triangles so that the influence of the main element is as equal upon both load lines as possible. The center separation between load ends (shorting segments) is also 4.53" or one segment's length. This procedure permitted alignment of all segments both between the load wires and on the main segment as well. All of the models are #8 AWG wire.

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In this sequence of test, however, we shall look both at load lines that use perfect wire and lines that use other materials. The figure below shows an in-plane model in which only the load lines (wires 2 through 8) are copper. In this way, we may isolate the losses due to the load from the losses due to the main element wire, which remains a perfect or zero- loss wire like the ones used in earlier R-X and R-L-C load models.

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The table below presents the load line lengths, measured from the source point for each of the three types of loads modeled. The "triangular mid- element" load line is measured from the source point both to the start and to the finish of the line outward. For the center triangular and in-plane models, line lengths for perfect, copper, and aluminum load lines are recorded, while the mid-element line is recorded only for the perfect wire version.

+ 
Antenna             Load Material       Load-Line Length (")
+Triangular Center   Perfect             175.2"
+                    Copper              174.5"
+                    Aluminum            174.35"
+In-Plane Center     Perfect             188.0"
+                    Copper              187.3"
+                    Aluminum            187.15"
+Mid-Element         Perfect             176.43" (outer)
+                                        171.90" (inner)
+

The decrement in length for the loads with the use of materials having a reduced conductivity is identical for both the triangular and the in-plane models. The load length for the in-plane model is longer than for the triangular or the mid-element model. However, the mid-element model load structure is virtually identical in length to the equally triangular center loaded model. Note that the triangular model load lengths correspond very closely to lengths for a split center load reactance when calculated from standard equations using the 544-Ohm Zo of the load line. For the required 416.7-Ohm load, the required load line calculates to 171.7" or within 2% of the actual modeled line lengths.

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Although the triangular models are physically set to minimize unequal influence from the main element, the current differential on the load wires is not zero. The graph shows the two values of current differential to be almost precisely the same for the zero-loss wire models, with closely corresponding phase differences as well. With the exception of a 4.53" change of wire alignment, the two models are the same model in every operational respect. In the mid-element model, the so-called fed main element is actually one leg of the loading line, and the apparent second leg of the loading line corresponds to the main element in the triangular center-loaded model.

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In contrast, the current differential between the load wires of the in- plane model is much higher. The higher differential is due to the differential interaction between the main element and the individual wires which are at different distances from the main element.

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A further insight into the difference between the triangular and the in- plane models can be gather from examining the currents on the main element outward from center. Note once more the close coincidence between the triangular models. In contrast, the current magnitudes along the outbound wire for the in-plane model are lower everywhere. Part of this reduction is due to the increased length of the in-plane linear load, which results in an electrical shift in the position of the beginning of the main element at the antenna's center.

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As might be expected, the current distribution on the in-plane model results in a lower gain than for either triangular model. With perfect wire, both triangular models report an anticipated gain of 1.86 dBi, while the in-plane model gain is 1.79 dBi--not a big reduction, but noticeable. With copper loads, the triangular model gain is 1.35 dBi, while the in- plane gain is 1.30. An aluminum (6061-T6) loading wire set yields a gain of 1.11 dBi for the triangular models and 1.06 dBi for the in-plana model. The values for aluminum wire load lines (with perfect wire main elements) correspond closely to the values for center and mid-element load dipoles using R-L-C loads with a Q of 300 (1.02 and 1.11 dBi, respectively).

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Equally revealing about the behavior of linear loads are SWR curves for the three models, each predicated on the source impedance at resonance at the design center frequency of 7.15 MHz. The resonant source impedances are 12.0, 12.1, and 12.2 Ohms for the triangular center, in-plane center, and triangular mid-element models. The coincidence of the mid-element linear load model source impedance with the center loaded models and not with the mid-element transmission line load model examined earlier is further confirmation that the mid-element model is simply a minor variation of the triangular center loaded model. The SWR curves confirm this further by overlaying each other, while the in-plane curve is slightly broader, as one might expect of a very slightly lossier structure. The mid-element linear load model no where approaches the broadness of the mid-element transmission line load we explored earlier.

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The SWR curves for the triangular model for the three load line materials show the expected broadening of the curve with the use of materials with a lower conductivity. Similar results accrue to the in-plane model.

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Conclusion

The linear load is essentially a shorted transmission line stub placed in line with the main element of the antenna it loads. As an antenna load, the stub cannot act as a pure transmission line; the current can never be equal in magnitude and exactly opposite in phase on the two wires making up the load line, since the current magnitude and phase on the antenna element into which it is inserted is not the same at any two points along a path from the antenna center outward. However, the condition is most closely approximated when loads are as exactly at center as possible and symmetrically placed about the main element to equalize its influence on each load wire. +

Since linear loads are transmission lines and answer in part to the equations for calculating length from required loading reactance-- especially when placed at the center of the antenna structure--their operating bandwidth curves, as reflected in the SWR curves shown, are narrower than for corresponding R-L-C loads.

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The graph above plots curves for center and mid-element loads using perfect loads and loads with a Q of 300. Additionally, the graph records the SWR curves for the triangular linear load model using perfect and copper wire. note that the curve for the copper wire linear load is sharper than any of the R-L-C loads except the center load with infinite Q. The broadest lines in the curve are for R-L-C curves with a Q of 300.

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Because the operating bandwidth of a linear load rests in large part on transmission line stub behavior and not on solenoid inductor behavior, losses cannot be directly correlated with operating bandwidth. Within each type of load, increases in bandwidth might point to increasing losses in the loads. However, cross-load type correlations are far less certain.

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To the degree that the currents on the linear load transmission line stubs are unequal, the wires also contribute to the linear length of the antenna. If placed at right angles to the main element wire, the radiation appears as a cross polarized field relative to the radiation from the main element. Moreover, the larger the current magnitude differential between load line wires, the more the wires act as linear contributions to the overall antenna length and the shorter the required stub.

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As with any complex electrical structure inserted into an antenna and modeled physically, the modeling calculations cannot directly account for all phenomena. For example, some theory exists to suggest that transmission line wires have greater losses for a given wire size and frequency of RF current than that same wires in an electrical circuit, due to the effects of the intense field between the wires. However, these effects turn out to be small, even for the long linear loads used in the very short modeled dipole. MININEC tests and other marginally valid tests within NEC suggests additional total field antenna gain losses between 0.1 and 0.2 dB. These losses, if present, have no noticeable effect on the operating bandwidth of the linear-loaded antenna models.

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While the bulk of the transmission-line view of linear loads has been previously established, presenting it here is useful if--for no other reason--than because it raises an interesting question. Just as linear loads have unequal current magnitudes at their junction with the main antenna element as a function of the current distribution along an antenna element, it would appear that solenoid inductors used as loads would share the same behavior. If this turns out to be the case, then the mathematical specification of loads within NEC would be equally incomplete, despite the high trust antenna designers and analyzers place in R-L-C loads of Type 0 and Type 1.

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It may be worth one more episode just to test the hypothesis and confirm (or disconfirm) the trust we place in Type 0 and Type 1 R-L-C loads.
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Updated 1-2-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to Solenoid Loading Basics

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Return to Loading Index

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Return to Amateur Radio Page

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Topics: Loading, Modeling


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Notes on Reactive Antenna Loads and Their NEC Models
+ Part 4: Some Solenoid Loading Basics

+

L. B. Cebik, W4RNL

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The final question in our inquiry is whether Type 0, 1, or 4 mathematical loads (each within their application limitations) fully or adequately specify inductively reactive loads used in a shortened antenna. Answering this question via antenna construction would seem natural, were it not for our customary building practices and presumptions. When we install a loading coil and it proves too large relative to the wire length, we simply shorten the wire to match the coil. Then we fail to interrogate the situation further to discover why the coil was too large. Most of the time, we assume that we miscalculated or that the usual coil equations are not sufficiently accurate to yield a coil that requires no subsequent wire pruning.

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As a consequence, few modelers have explored the behavior of helically wound single layer solenoid inductors in their models--simply because winding a coil is too laborious a task relative to using the loading facilities built into NEC. We have presumed that the loads--especially Type 0 series R-L-C loads--adequate specify the loads we need.

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Yet nagging suspicions remain about such loads. The current differential that is present at each end of the load suggests that--like their linear load counterparts--these loads do not act like pure inductances, but may also function as simple current bearing wires. Models of helical dipole elements show very usable gain, which parallels the experience of those who have constructed such antennas. I guess we shall not know whether mathematical models of loads accurately reflect the operation of single layer solenoid inductances unless we actually wind some model coils and replace the Type 0 loads with them.

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Winding a Helix and Making a Model

The basic model for the half-size (1/4 wl) 7.15 MHz dipole uses #8 (0.125" diameter) zero-loss wire that is 412.68" (34.39') long and divided into 91 segments. Each segment is about 4.53" long. For least error, the segments within the helix will be as close to this value as helix construction permits. +

The required center loading reactance for the antenna is 833.3 Ohms or 18.549 microH. We may let the coil be 3 segments long or 13.6" overall. Using the standard Wheeler equations (either the common 1928 version or the 1982 version), a circular single layer solenoid inductor of this length will require 10 turns and an 11.852" diameter.

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The most reasonable approximation of a circular solenoid is an octagonal structure. Fig. 1 shows the resultant structure and the basic relationships that determine the coordinates of the points around each loop. For this exercise, let's adopt the convention of extending the turns along the X-axis and using the Y-axis and the Z-axis for the radial points of each loop. Under this convention, the point references in the lower part of the drawing refer to Y and Z coordinates. Beginning, perhaps, with half the diameter as the value of R (5.926"), we might place the first entry at 0, 5.296, 0 (assuming a free space modeling environment). Intermediate points between the horizontal and the vertical will require values of 0.707 R (3.744"). (Note: rounding to one less decimal place will make no significant difference in the long run.)

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Each point progresses along the X-axis by the total length (13.6") divided by the number of turns (10) divided by the number of points in each turn (8), for a value of 0.17" in this case. Hence, the second point of the turn will be located at 0.17, 3.744, 3.744. We can then proceed to complete the first turn. Then, using whatever copy function may be present, we add progressively more turns, increasing the value for the X- coordinate by 1.36 with each turn.

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The resulting solenoid will be about 2.5% short in overall wire length used compared to a truly circular solenoid, suggesting a slightly lower inductance than provided by the Wheeler calculation. Since the wire is small compared to the turns spacing, a slight additional variance may also be encountered. Of greater significance for the model, each wire in the helix is about 4.56" long, a close match to the length of the segments in the remaining portions of the dipole wires.

+

Once the coil is complete, it should be saved as a file, since we may use it later. For the initial test of center-loaded short dipole, we may replace the center 3 segments of the basic wire with the helix. The best coordinates for the coil may be -6.8 to + 6.8 on the X-axis to obtain a useful symmetry in the now enlarged geometry sheet--useful for visual error trapping. The formerly single wire is now two wires extending to + and to - 206.343" respectively, and each with 44 segments.

+

Part of the extended exercise in looking at NEC loads, both mathematical and physical, has involved sorting out the losses attributable to the load from those which may be associated with the linear wire portion of the antenna. For this purpose, we shall need to make the linear wire lossless and the coil wire of a suitable material, namely, copper. At present, only GNEC (Nittany-Scientific) permits a wire-by-wire material selection. Fig. 2 shows a partial .NEC file from GNEC, with the dimensions in meters.

+
+ +
+

The portion of the model shown shows the last few turns of the helix, wire by wire. The last wire (82) is the linear dipole wire in the +X direction. Skipping down to the Type 5 load lines (material loading), we see that wire 1 (and also 82) is skipped, being lossless, while the conductivity value for copper appears for each wire in the helix.

+

Finally, because the turns of the helix have an equal number of wires per turn, a split feed is used at the wires forming the very center of the inductor.

+

The Center-Loaded Half-Length Dipole

The model just constructed in a free space environment yielded an inductive reactance of over 86 Ohms, indicating not that our octagonal coil was slightly small, but rather that it was considerably too large. Achieving resonance required a significantly smaller helix. In order to preserve the length of the coil that was equal to 3 segments of the linear wire, the coil was reduced in diameter. With a diameter of 11.12" the loaded antenna achieved resonance (as defined in this study as less than +/- 1 Ohm source reactance). Wheeler calculations for a circular coil of this diameter, length, and number of turns yielded an inductance value of about 16.6 microH, roughly 10% less than the value called for by the mathematical load systems provided in NEC. The length of the coil wires reduces to about 4.25" each, which is unlikely to induce any significant error in the model. +

The following table provides some basis for making comparisons between the physically modeled load and the Type 0 loads used in earlier parts of this exercise. In all cases, the linear portion of the antenna is composed of lossless wire.

+ 
Load                Free Space          Source Impedance
+                    Gain dBi            R +/- jX Ohms
+Lossless Type 0     1.85                13.19 - j 0.02
+Q=300 Type 0        1.02                15.97 - j 0.01
+Copper Helix        1.35                10.61 + j 0.64
+

The higher gain provided by the physically modeled center load should not be surprising, considering that the helix contains wire that radiates. See Fig. 3.

+
+ +
+

The small but definite vertically polarized radiation field results from radiation from the portions of the helix that are vertically oriented. This field along would not suffice to provide the added gain over the Q=300 center loaded model, but the entire 13.6" length of the inductor would. More precisely, that portion of the overall inductor wire beyond the 13.6" it replaces in the overall antenna length would suffice to provide additional gain.

+

The actual Q of the inductor cannot be ascertained with accuracy. Some calculations estimate the Q at over 400, but only under the conditions that the wires be closer to half the spacing between turns. The modeled helix uses much smaller diameter wire, resulting in a decrease in Q, perhaps to the 200-300 range at best.

+
+ +
+

Despite the lower Q estimate, the source impedance of the physically modeled helical loaded dipole is lower than even the Type 0 model at zero load loss. As Fig. 4 shows, the SWR curve is slightly steeper than even the R-L-C lossless load model--and a lossless helix yields a steeper curve yet.

+

The actions of the physically modeled helix load are in part a function of the current magnitude and phase profile along the coil. Fig. 5 shows the two curves from the center point outward toward the end.

+
+ +
+

The current magnitude differential between the source and the coil end is approximately 20% of the maximum value. Since the inductance of a helix is in theory predicated upon equal current magnitudes at both ends of the coil, the differential currents dictate that in part the indictor does not act solely as an inductor. The physical model of the center load provides indications that the helix also radiates in the manner of any length of wire included within the total length of the dipole--in terms of gain over the Type 0 load, the vertical radiation field, and the reduction in the required inductance to effect loading to resonance.

+

There are potential error sources within the model. First, the octagonal inductor with less then optimal wire diameter relative to runs spacing casts some doubt on the precision of the calculations relating inductance to turns, diameter, and length. However, most of these factors suggest that the octagonal coil's inductance would be low, when in fact, the model showed it to be very much higher required for resonance.

+

Second, the helix design, although apt to the modeling task, is very large and open compared to coils one might ordinarily apply as center loads in a shortened dipole. However, as an error source, the helix configuration would be a matter of degree and not of fundamental principle of operation. What the dimensionless load of a Type 0 load does not show is the relatively large early drop of current magnitude along the total length of the dipole. Fig. 5 shows the more dramatic drop occasioned by the physically modeled coil. Although different coil configuration may alter the amount of drop somewhat, the current magnitude curve is unlikely to resemble that for the Type 0 load.

+

The plausibility of the physical model might be put to still another test. The original short dipole model was designed to permit one to place load values equal to the center load value at specific mid-element points. If the center load helix as modified to achieve resonance acts like a Type 0 load, then placing the same coils at the specified points should also result in resonance.

+

The Mid-Element-Loaded Half-Length Dipole

The original model was modified into a 5-wire model having the same operational characteristics as the original. The inserted 3-segment wires were placed at points between 99.5" and 113.1" from the center so that the Type 0 load was positioned 106.3" from the center. At these positions either side of center, a load of 833.3 Ohms (18.549 microH) resonated the antenna. The value of these two loads was the same as the value of the single center loading reactance. +
+ +
+

As shown in Fig. 7, the helix developed for the center load may directly replace the inserted 3-segment wires in the 5-wire model. By copying the original helix and changing the values for all of the X coordinates by the same amount, each coil may be placed in the correct position. The connection points to the coils are very slightly displaced relative to the axis line, but not by an amount to show up in a movement of the antennas resonant frequency. The 11.12" diameter (R = 5.56") helix was copied and transferred to these points and the model run.

+

The result was a source impedance of about 29 + j 229 Ohms, indicating that the inductor size (16.6 microH) was much too large for resonance. This result was consistent with but considerably larger than expected. To create helices that allowed the overall antenna to achieve resonance required a reduction in the coil diameter to 10.2" (R = 5.10"). By Wheeler calculations, the inductance was reduced to about 14.3 microH for a truly circular coil. The wire length from coil point to coil point diminished to 3.90" compared to linear wire segment lengths of 4.53" each.

+

The amount of reduction in coil size was about 14% relative to the final center loading coil and almost 23% relative to the inductance required by a Type 0 load. This reduction is consistent with several factors involved in inductive loading, including the fact that the further out along an element one places the inductor, the less it acts as an inductor and the more it acts as a compact form of wire length to increase the overall wire length to resonance. By the outer ends of a shortened dipole, helices and others forms of element extension cannot be viewed as inductances almost at all.

+
+ +
+

The current magnitude and phase profile within the helix may be of some surprise to some. Along the mid-element loading helix, after size adjustment to resonance, the current does not show a steady progression lower in magnitude. Instead, there is a current peak about a fourth of the way outward from the inboard end of the coil. From that point onward, the current magnitude descends rapidly. The phase transition, although not linear, generally follows the progression along the entire antenna element.

+

Compared to the center loading coil, the current magnitude excursion within the inductor is about 34% of the maximum value, and the end to end difference is about 30% of maximum current magnitude. This compares to the 20% differential from center to end for the center loading coil. The greater differential of current magnitude along the mid-element inductor wire is another indicator that it is functioning to a greater extent than the center loading coil as part of the element length and hence requires less inductance and inductive reactance to effect loading to resonance.

+

Like the physically modeled center load, the physically modeled mid-element load shows a much larger drop in current at its outer end than does a corresponding Type 0 load. The dramatic decrease in current immediately outside the loading helix appears vividly in Fig. 9, with the Type 0 load curve shown for comparison.

+
+ +
+

Despite the close correspondence of current up to the load position and the dramatically lower current beyond that point for the physically modeled helix, the model shows a significantly higher gain than either the corresponding Type 0 load model or even the physically modeled center load. The following table summarizes the gain situation for various models.

+ 
Antenna                            Free Space          Gain Relative to a
+                                   Gain dBi            Full Length Dipole
+Full-Length                          2.14                   ---
+Half-Length Lossless Wire            1.85                   -0.29 dB
+Type 0 Center Load, Q=300            1.02                   -1.12 dB
+Helical Center Load, Copper          1.35                   -0.79 dB
+Type 0 Mid-Element loads, Q=300      1.11                   -1.03 dB
+Helical mid-Element Loads, copper    1.71                   -0.43 dB
+

The gain figures strongly suggest that the current within the turns of the helix is not going wholly to waste within a tightly coupled inductive field. That part of the current not devoted to the field, as indicated by the current differential at the coil ends and among the turns is contributing to the total field of the antenna.

+

The use of Type 0 loads to characterize both center and mid-element loading strongly suggests that there is little difference between the gain potential of two antennas of equal length loaded in each manner. however, physically modeled loading helixes tell a quite different story. Not only do both types of loaded antennas potentially perform better than mathematically inserted loads would indicate, but as well the empirical experience giving the nod in gain to mid-element loading gains some support from the physically modeled loading coils.

+
+ +
+

Although the physically modeled center loaded antenna showed a steeper SWR curve than its Type 0 counterpart, the mid-element loaded antennas show a good correspondence between mathematical and physical loads. In fact, as shown in Fig. 10, the mid-element physical helices correspond nicely to mathematical loads with a Q of 300. This curve corresponds reasonable well with estimates for the Q of the coil at or just below 300, based upon reductions from the calculated Q of over 400 that presumed an ideal wire diameter to spacing ratio. The resonant source impedance of about 24.6 Ohms is a bit lower than the Type 0 model at Q=300, where the source impedance was about 31.9 Ohms.

+

It should be noted for accuracy and completeness that the actual resonant frequency for the model using physically modeled mid-element coils with a 10.2" diameter was 7.16 MHz, and that the curves for this antenna actually run from 7.01 to 7.31 MHz. This 10 kHz displacement did not seem great enough to warrant reconstruction of the coils through the iterations necessary to move the resonant frequency. The estimated diameter would have been something of the order of 10.205" +/- 0.002" for resonance at 7.15".

+

Potential Errors and Conclusions

The potential error sources for the mid-element load model remain the same as for the center loading coil. The octagonal helices may in fact show a lower inductance than the values calculated by the Wheeler equations. Moreover, the widely spaced open helix may prove a better radiator than some more tightly wound loading coils. Unique to the modified mid-element loading coils is the shortening of the wires and a somewhat greater differential to the lengths of the segments in the linear wire portions of the antenna. +

Some of these possible error sources work in the wrong direction relative to the results, for example, the reduced inductance of octagonal helices relative to truly circular ones. The sum of the remaining error sources appears to be far short of what would be required to account for the radical reduction in required inductance for the loading coils. Indeed, the most telling part of the demonstration is the further reduction in coil size required in moving the center-loading inductor out to the position where the same value should have served as a mid-element loading inductor. Although absolute values of the inductors involved may be off the mark by some small amount, the trends are in al probability accurate reflections of anticipated antenna performance.

+

As a consequence of these data and considerations, the bottom line seems inevitable: Type 0 (and by extension, Type 1 and Type 4) loads do not fully characterize the performance of inductively reactive loads in the form of single layer solenoids. For many purposes, that characterization may be adequate to a design task. For example, where design criteria permit adjustment of the antenna outer section length, designing to the Type 0 load value may cause not harm.

+

However, using mathematical loads alone can give a potentially misleading impression of the gain of the loaded antenna. The gain for physically modeled loads is considerably higher than the gain for mathematical loads. Where multi-element arrays--such as Yagis--may employ center or mid-element loads in all elements, Type 0 load models may seriously underestimate the overall array gain.

+

This exercise, along with the previous portions of this study, should be viewed as only a beginning to the investigations into modeling loaded shortened antennas. Further work might yield additional insights into the behavior of linear loads examined in the last episode. Likewise, for helical inductive loads, much remains to be done with respect to the use of more compact forms of inductance. Even using these models, additional data can be gathered for the use of linear wires with non-zero losses and for the use of other helix materials, such as aluminum.

+

Nonetheless, if the present demonstration holds up as reasonably valid, then the suspicion raised at the outset has been established. In several important respects, the mathematical loading features provided within NEC do not fully characterize the action of these loads when physically modeled. Nevertheless, modeling actual loading inductors that form junctions with elements of radically different diameter from the coil wire and modeling small-diameter coils without violating adjacent segment length restrictions may prove to set major challenges for the amateur and the professional modeler. This study was carefully designed to use models that stayed well within all NEC restrictions. Most real antennas that use inductive reactance to electrically lengthen a physically short element will press those restrictions or result in quite large models.

+

In other words, what we can establish in principle in a straightforward manner might prove to be an exceptional modeling challenge when real antennas and their parts are involved. Loads are not quite as simple as casual modeling might lead us to believe.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +
+

Updated 2-4-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Some Unfinished Business

+

Return to Loading Index

+

Return to Amateur Radio Page

+

Topics: Loading, Modeling


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+

Notes on Reactive Antenna Loads and Their NEC Models
+ Part 5: Some Unfinished Business

+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In the first four sections of this series on inductively reactive loads used to electrically lengthen physically shortened antennas, we uncovered some interesting disparities between the standard mathematical models of loads and loads which are physically modeled. If the demonstration models are valid, then the following summary points are true in principle.

+

1. Because the current magnitude and phase in a transmission line used to load a short antenna do not show a true transmission line relationship in a physical antenna, the use of the TL facility in NEC is not a reliable model of the real line and should be confirmed with a physically modeled transmission line load.

+

2. Linear loads are a variety of transmission line stub load, but their behavior should be physically modeled for greatest reliability, especially when folded back from a mid-point along the so-called main element. Within the length of the linear load, which wire comprises the "main" element is ambiguous, since the radiation from that portion of the antenna is a function of the closely coupled fields from the element and the load wires in the stub.

+

3. To a lesser but still significant degree, physical models of single layer solenoids, when modeled as helices, depart from the Type 0, 1, and 4 NEC mathematical models of them when placed as loads along an antenna element. In general, such loads show composite properties as inductances and as added wire length, the latter of which properties contributes to the radiation field of the antenna. The effect increases as the inductors are moved outward from the center of a dipole, with less inductance being required for the load than for a center loading coil. Even a center loading coil requires less inductance in physical models than called for by the NEC mathematical load.

+

Although the exercises have demonstrated the effects, they fall far short of establishing a set of universal principles, mostly due to the limitations of NEC. Some of the potential error sources in NEC-4.1 have been reviewed in "NEC-4.1: Limitations of Importance to Hams," QEX (May/June, 1998), pages 3-16.

+

Throughout the exercises, NEC-4.1 was used in the EZNEC Pro and the Nittany-Scientific GNEC implementations. In all models, unless otherwise specified, the linear wire was modeled as lossless in order to sort out losses and performance curves due to the load from those attributable to the linear wire. Hence, all gain figures in previous exercises will be higher than with any real antenna using copper or aluminum elements. All models were constructed in free space.

+

The model short dipole for 7.15 MHz was 1/2 full size at 34.39' (412.7") long and used #8 AWG (0.1285" diameter) wire. All physically modeled load structures used the same wire in order to avoid possible errors resulting from angular junctions of wires having dissimilar diameters. The original antenna was assigned 91 segments, each about 4.53" long. The selection of segment length served a number of purposes. First, it set the spacing of linear load wires from each other at a reasonable distance for accurate modeling. Second, it permitted the construction of octagonal single layer solenoid inductors that were exactly 3 segments long and whose wire lengths for each portion of each turn were close in length to the adjacent segments of the linear wire.

+

The original model was revised for mid-element loading exercises into a 5- wire model. 3-segment wires were placed on each side of the center wire so that the center segment of the insert was positioned exactly where a mid- element load was equal in size (reactance and inductance) to a corresponding center load such that either system brought the antenna to resonance with no change in the overall length of the dipole. The overall segmentation was not changed, so that segment length among models remained close to equal. A 3-segment long (13.6") physical inductor model replaced the center 3 segments of the model for center loading and replaced the two inserts for mid-element loading tests.

+

Subject to continuing review, it is believed that these models fall well within the limitations of NEC-4.1's ability to provide accurate results. It should be unnecessary to add that the relationship of the NEC-4.1 modeling system to real antennas is not like the relationship of a child's plastic toy to a real automobile. Rather, NEC-4.1 (and other version of NEC and MININEC) are complex mathematical systems based upon both fundamental antenna theory and fundamental mathematical principles for calculating the various performance parameters of many types antennas. Those who dismiss antenna modeling in general largely reveal only a general lack appreciation of the role of mathematics in both antenna theory and antenna practice.

+

Those who develop, implement, and work with any version of NEC are also conscious of its limitations. All version of NEC have been extensively tested against experimental results for many fundamental antenna types. However, it is possible to create antenna geometries that exceed the limitations of the calculation system. In such cases, NEC yields results that do not tally with either theory or practice. Since no program developer or development team can fully predict all of the antenna geometries (or environmental circumstances) that users will model, they can only enumerate some of the program limitations. Users will discover other limitations in the course of their work, and these limitations set the challenges for further development.

+

This note is about some of the limitations that apply to the extension of the models used in this exercise set to various real antenna designs.

+

Linear Load Limitations

The difficulty of extending the models used for linear loads in these notes to real antennas can best be illustrated by taking up a few concrete examples of extant antennas. +
+ +
+

Fig. 1 shows a sketch that outlines the basic design features of one commercially manufactured antenna element using a linear load. To this point, I have been unable to construct a model of this element that falls within NEC limitations.

+

The element uses a series of tubes of decreasing diameter as one moves from the center point outward. The NEC-2 limitation with tapered diameter elements is largely, but not completely, overcome in the NEC-4.1 algorithms. Modeling this element in NEC-2 with Leeson corrections (or, more properly, conversion of the element into its equivalent uniform diameter equivalent) is not possible, since the linear load junctions would block correction implementation (and the implementation of the correction would be inaccurate, since the element is not continuous).

+

In this particular design, the linear load wires are very thin compared to the center element, and they are very closely spaced to the center element. All versions of NEC yield erroneous results when wires of different diameter are closely spaced. Moreover, there is a right-angle junction of wires of different diameter, another case in which NEC yields erroneous results.

+
+ +
+

A second design of commercial origin appears in Fig. 2. In this case, the previously noted limitation involving angular junctions of wires having dissimilar diameters also applies to this design, since the load wires are very much thinner than the center element tubing. The tubing also uses a diameter tapering schedule, adding a definite limitation to modeling with NEC-2 and a minor limitation for NEC-4.1.

+

The wires of the load are not parallel to each other. This feature would make the correlation of the load to transmission line stubs more complex, although for general purposes, the averaged characteristic impedance of the line might be used with fair accuracy. However, to the degree that physical models of parallel transmission lines yield results at variance form standard calculations, determining the characteristic impedance of the physically modeled line will prove more difficult.

+

A third feature of this design is the placement of the long shorting bar near the center of the element. Physical models of shorted transmission line stubs take into account the current magnitude and phase of the shorting bar. In this instance of a long bar, the bar itself becomes an integral part of the line, one having a rapidly decreasing spacing between opposing segments. The design also may place the shorting bar at a distance from the element center point than used in the exercise models. Hence, the correlation drawn in the exercise between mid-element loads folded back to the center and loads properly called center linear loads may be less certain for this case.

+
+ +
+

We can illustrate the difficulties of modeling a real linear load in NEC by looking once more, in Fig. 3, at the model of the in-plane center linear load, discussed in part 3. In that model, using #8 wire uniformly throughout the model, several facets of real antenna construction were simplified. The spacing between the three wires was set at 4.53" center-to-center. This spacing produced identical surface-to-surface spacings that were 0.1285" less than the center-to-center spacing.

+

If we increase the "main" element to a 1" diameter, center-to-center spacings no longer correlate to surface-to-surface spacings, changing the relationship among the elements. In addition, we encounter the potential problem in NEC of closely spaced wires with different diameters.

+

Fortunately, this model just barely fits within the MININEC segmentation limit and can be evaluation on that system. MININEC does not show a limitation with respect to closely spaced wires with different diameters. However, MININEC models tend to clip corners with angular connections, and we should expect (without invoking length tapering) some required change in the length of the loading wires if we hold the overall length constant.

+

The following table shows the results of modeling the in-plane antenna in both NEC-4.1 and in MININEC. Load line lengths (from center to short) are given to indicate the require modifications to achieve a value close to resonance (in this demonstration, loosely defined as under +/- 5 Ohms). In addition, values are shown for models using lossless, copper, and aluminum wire throughout.

+ 
                         MININEC                       NEC-4.1
+Main                Free Space     Feed Z         Free Space     Feed Z
+Element             Gain dBi       R+/-jX         Gain dBi       R+/-jX
+
+#8 AWG                   (Load = 194.5")               (Load = 188")
+  Lossless wire     1.85           11.9-j1.2      1.79           12.1-j0.0
+  Copper            1.30           13.5-j1.2      1.25           13.7+j1.5
+  Aluminum          1.04           14.3-j1.2      0.99           14.5+j2.4
+
+1"                       (Load = 158")                 (Load = 165.3")
+  Lossless wire     1.85           11.9+j4.5      1.25           13.7-j0.5
+  Copper            1.39           13.2+j4.5      0.83           15.1+j0.9
+  Aluminum          1.17           13.9+j4.5      0.62           15.9+j1.6
+

In the table, gain figures are shown to 2 decimal places in order to show numerical trends that would have been erased by excessive rounding. (For operational purposes, figures to a single decimal place would suffice for many comparative cases, and the decimals might be dropped from certain generalized discussions. However, those who believe that showing gain to multiple decimal places should be dropped in all cases simply lack an appreciation for all of the purposes for which the antenna modeling programs can be put to effective use. Each degree of precision in reportage has its proper context. My own preference would be to see modeling reports overly precisely reported and then to do my own rounding than to see such figures prefiltered.)

+

The gain and impedance figures for the #8 model show excellent correlation between the modeling systems, with a maximum gain variance of 0.05 dB and a maximum resistive variance of 0.2 Ohms. If we look at the MININEC column and read downward, then the reported performance of the 1" main element version of the modeled antenna shows very sensible results. The lossless version of the model shows minuscule differences from the #8 version (actually none in the truncated decimals used here). The copper and aluminum versions of the 1" version show increases in gain over the #8 version as the material becomes more lossy. This is a function of the increased surface area of the larger element, and a similar trend shows up in full size dipoles. Likewise, the feedpoint impedance of the 1" antenna decreases more rapidly from the #8 version as the material loss increases, again for the same reason of lower overall losses. Once more, this trend also shows itself in unloaded antennas.

+

Regardless of the absolute accuracy of the MININEC figures, the trends in numbers are not only intuitively sensible, they correlate with the behavior of models of unloaded antennas. In contrast, the NEC-4.1 figures for the 1" diameter main element model report decreases in gain and increases in feedpoint impedance for each material assignment. These numbers indicate either that the wire spacing for the element sizes involved and the frequency of test (7.15 MHz) has crossed the threshold at which NEC-4.1 no longer delivers accurate results or that the angular junction of the #8 wire with the 1" wire is yielding less than accurate results--or both. It is common in either error mode for NEC to report a gain that is too high/low while reporting an source impedance that is too low/high.

+

Allowing for corner junction errors, MININEC remains the program of choice for modeling complex geometries that involve junctions of wires having dissimilar diameters and/or closely spaced wires of differing diameters. Recent developments in MININEC to break the segment limit, such as in NEC4WIN, will go far to make more complex MININEC models possible. However, not until the other MININEC limits are overcome--namely, raising the speed of matrix execution and grafting on the Sommerfeld-Norton ground calculation system--will the program be fully competent for all purposes.

+

Solenoid Coil Limitations

+

In the physical models of single-layer solenoid inductances used as loads, the constraints imposed on the exercise dictated the use of helices with a relatively large diameter (11.85") and a long length (13.6"). The wire size (0.1285") was relatively thin compared to the turns spacing (1.36"), which yielded a coil Q somewhat less than the theoretical maximum for the overall configuration.

+
+ +
+

Fig. 4 shows some of the key parameters of coil construction that play a role in physical determination of coil inductance. Length, diameter and turns spacing are parts of the classic 1928 Wheeler approximation for single-layer solenoids (as found in ARRL Handbooks since almost time immemorial):

+
+ +
+

where L is the inductance in microHenries, d is the diameter, l is the length, and n is the number of turns, and where d and l are in the same units. The number of turns can be determined from the length and turns spacing (or vice versa). For coils used at upper HF and higher, the lead length becomes a significant factor in the coil's inductance. In antenna modeling, the lead length is generally absorbed by the linear element length.

+
+ +
+

In Fig. 5, we find some variations on the coils used in the physical models. If we let A represent the coil configuration used, we might obtains the same inductance (and reactance) using a coil like that in B, which uses the same spacing, but a smaller diameter and more turns. C spreads the turns over a longer length, while D uses a shorter length, closer spacing, and a larger diameter, perhaps to effect the highest Q configuration that might be practical. E employs fatter wire to achieve a high Q by optimizing the wire-diameter-to-turn-spacing ratio. Each of the preceding variants on the original coil was based on theoretical factors. However, in practical antenna design, one might also accept a somewhat lower Q in order to achieve a design that slipped wind by virtue of its small diameter, as suggested in F.

+

Each coil configuration is likely to affect antenna performance slightly, due to different radiation field additions that depend on diameter and turn spacing. Some of the variants are more easily modeled than others. With proper attention to segment lengths, coils that use the same size wire as the main or linear element can be modeled with fair ease. However, length tapering of the linear element as it approaches the helix may be necessary for coils with small diameters. Where coils use wire diameters that differ from that of the main element, NEC (in any version) will exhibit a tendency toward erroneous results.

+

The consequence is that modeling solenoids as physical loading elements in an antenna may not in cases be practical, although the task itself may become design-specific, especially in view of all of the variations possible. Thus, it may be some time before there is a more general profile of the affects of coil design on the performance of shortened antenna elements that use them. However, whatever differential there is between a physical coil and a mathematical load will apply equally to both NEC and MININEC, since both use essentially the same mathematical loading schemes, allowing for the fact that NEC places the load on a segment and MININEC places a load on a pulse or junction of segments.

+

It is perhaps a curiosity (since multiple types of coils have not been checked) that the loading coil used as the center load in part 4 of this series--and also used as the mid-element load--can be trebled to yield a 30-turn helical dipole only 40.8" long by less than 12" diameter. The resonant frequency of this experimental design was 7.105 MHz, only slightly lower than the standard design frequency used throughout the demonstration. If the exercise has any utility at all, it lies in the confirming the soundness of the advice to model solenoids using the material that will actually form the coil.

+ 
Material            Free Space          Feedpoint Impedance
+                    Gain dBi            R +/- jX Ohms
+Lossless wire        1.76               0.3 + j 0.5
+Copper              -5.46               1.3 + j 1.6
+Aluminum            -6.99               1.9 + j 2.2
+

The impracticality of the design, as indicated by the source impedance, is less important than a comparison of the anticipated gain of the antenna from the lossless wire to normal materials. Lossless wire makes the antenna look like a promising performer, while the gain figures for real materials tell the true story. There is no magic in this system. Indeed, it packs over 93' of wire into the helix, more than required for a standard 40-meter dipole. Yet, at 7-9 dB below the performance of a full size dipole, signals would be down by only about 1.5 S-units. Such performance would be usable under certain kinds of operating conditions, although the losses associated with feeding the antenna might attenuate signals even more than the basic design itself.

+

Obviously, those interested in helical antennas will always benefit from making them as long and open as possible. an adequate model of a helical monopole or dipole will always take the form of a physical model.

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+ +
+

One final note on solenoids seems necessary, based on Fig. 6 above. A common practice, especially in commercial antenna manufacture is placing a solenoid within a shield, and the shield may be connected (or not) to either of the linear wires extending from it. At present, I am unaware of any technique of modeling this situation which has been correlated to experimental results. On can surround the solenoid with a series of wires or even a wire grid--with one end connected to an antenna wire if desired. To what degree antenna fields arising from the solenoid will interact with the shield and what the consequences for the overall antenna field will be remains an area yet to be fully explored. It, too, is likely to remain a project-specific task for antenna designers. If we add in the variables of coil construction that might be present within the shielding structure, the task is no small one. Note that the term "shield" is here used by convention. To whatever degree that casing plays a role in radiation field production, it shielding effects may be only mechanical. Its electrical role may turn out to be either simple or complex.

+

Conclusion

These notes are intended to provide a reasonably fair view of the limitations of the modeling studies undertaken in the first 4 parts of this series. They provide some cautions against taking the results of the work as numerically general principles, which they are not. They also caution against hasty modeling that might unwittingly cross the boundaries of NEC capabilities. Finally, they also outline a host of work that might be done to extend the study and to make its conclusions both more general and more precise. +

Some of the further work can be done with some modeling ingenuity. Other parts of the work might be undertaken in alternative programs, such as MININEC. However, there may be a residue of the effort that may have to await the next generation of modeling cores.

+

Also see the Antenna Modeling Programs page for more information.

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Updated 2-7-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Loading Index

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Return to Amateur Radio Page

+

Topics: Loading, Modeling


+ + diff --git a/content/load/load5e1.gif b/content/load/load5e1.gif new file mode 100644 index 0000000..f20ec8d Binary files /dev/null and b/content/load/load5e1.gif differ diff --git a/content/load/loadtl.html b/content/load/loadtl.html new file mode 100644 index 0000000..fb127f3 --- /dev/null +++ b/content/load/loadtl.html @@ -0,0 +1,44 @@ + + + + + + Modeling Loads and Transmission Lines Index + + + +
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Modeling Loads and Transmission Lines

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L. B. Cebik, W4RNL

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+ Questions often arise about how properly to model loads and transmission lines within various versions of NEC and its commercial implementations. So I thought a brief primer might be useful. The utility of a primer is unquestionable, but that it can be brief quickly proved false. +

Although the information is covered in both the NEC manuals and the instruction manuals that accompany commercial implementations, something more systematic seems needed--something with examples carried from one level to another so that users can see the transitions and get a sense of what is and is not possible--and how to get around what is not possible. I also discovered that we cannot begin in the middle, assuming that readers know the basics. When it comes to antenna modeling, modelers come at the enterprise from many different backgrounds, enter it with different interests, and get into modeling loads and transmission lines with different goals and interests. Hence, everybody knows the basics in a slightly different way.

+

So we shall begin at the beginning--with simple antennas and simple loads-- and work our way to more interesting examples. Along the way, we shall have occasion to mention some useful adjunct calculation programs and some equations for use on calculators. Modeling programs just do not do everything we need to do to make good models. But there are some utility programs that can take most of the drudge work out of modeling.

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In the end, we shall quit far short of exhausting the subject, but a little ways beyond exhausting the writer. However, incomplete, I hope the information is useful to you.

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Updated 12-29-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
+

Topics: Loading, Modeling, Transmission Line


+ + diff --git a/content/load/loadtl1.html b/content/load/loadtl1.html new file mode 100644 index 0000000..27a8928 --- /dev/null +++ b/content/load/loadtl1.html @@ -0,0 +1,133 @@ + + + + + + Modeling Loads and Transmission Lines Part 1: Getting Oriented: Basic Loads and Simple Antennas + + + +
+

Modeling Loads and Transmission Lines
+ Part 1: Getting Oriented: Basic Loads and Simple Antennas

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+
+

L. B. Cebik, W4RNL

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+ NEC models antennas as collections of straight wire segments. Within NEC programs, we specify the antenna structure as one or more wires and then subdivide each wire into one or more segments. One way in which we can modify one or many segments of an antenna is to load them. +

A load is simply a combination of resistance or reactance assigned to a segment. NEC is capable of assigning load as series R-L-C circuits (load type 0), parallel R-L-C circuits (load type 1), or as complex series R +/- jX impedance loads (load type 4). (NEC may also assign loads as series or parallel R-L-C values per unit of length (load types 2 and 3), but we shall not have occasion to deal with this option in this series.) Figure 1 surveys some of the options.

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In this part of the series, we shall deal only with series R +/- jX impedance loads. They are among the simplest to implement and manipulate, although they do have some limitations. We shall also mention the load that many users do not think of as a load: wire conductivity (load type 5). (NEC-4 is also able to handle wire relative permeability.)

+

For many modelers, this first part is a review of the most basic sort. However, within the review there might be a detail or two that will make a more advanced procedure a little bit clearer.

+

A. The Load Entries: Material Loading

NEC input consists of a series of lines of entry in a model description. Each line corresponds to a "card" in older FORTRAN input systems. It has a label and a sequence of entries that the program interprets as values and instructions. CM entries are comments; GW entries are straight wire specifications; etc. Load entries carry the designation LD. +

Unless we wish to use lossless wire in our model, we ordinarily specify a material or materials for the antenna elements. With commercial implementations of NEC, this specification may occur as a special entry apart from program means of introducing other types of loads. Nevertheless, the specification results in LD entries of type 5. Here is a typical entry:

+ 
  LD  5    1     1       101     5.8001E7
+     Type Tag 1st-Seg Last-Seg Conductivity
+

The entry spacing has been widened to permit labeling the parts. A Type 5 load is a round wire internal impedance specification. The Tag indicates the wire number, here the only wire of a simple dipole antenna. The first and last segment designators set the limits of application of the value. Finally, the conductivity figure is in Siemens(mhos)/meter. The 1-wire antenna has 101 segments, all with the conductivity of copper.

+

Various implementations of NEC may handle the conductivity figure differently. Some provide named entries (for example, "copper"). Others provide conductivity figures or provisions for conductivity entry so that users can specify exact material properties. Still others provide custom entry in terms of resistance per unit of length, the inverse of conductivity. However entered, the entry is translated to an input of the type shown or its programmatic equivalent.

+

Unless an antenna uses materials of very specialized sorts, performance will not be altered to a significant degree by specifying either copper of aluminum (in its own various types). EZNEC permits only a single wire material specification, and users may use with confidence in the results either the conductivity of the "worst" material or the conductivity of the most dominant material in the antenna. However, NEC itself permit all manner of combinations of materials to be specified. NEC-Win Pro permits all the element load entries permitted by NEC itself, if modeling changes of material is an important consideration. With access to individual line entries, one may also within NEC-Win Pro load all segments or all wires to the same value in a single line by specifying the tag and the first and last segment entries as 0.

+

B. The Load Entries: Spot Loads

All spot or specifically placed loads within NEC consist of mathematical objects that do not themselves radiate, whatever the size of their physical implementations. However, the segment(s) on which they are placed do enter into the calculations for mutual impedance and current and are thus a part of the calculations for antenna pattern and other properties. Consequently, the error introduced by treating the loads themselves as non- radiating is normally insignificant. Spot loads do affect the current magnitude and phase along the antenna wire in mathematically correct ways to replicate reality very closely. Hence, they are normally a very accurate way to model loading coils and capacitors, traps, and resistances. +

Entering spot loads differs according to the implementation of NEC. Since we shall restrict ourselves in this part of the series to complex impedances composed of resistance and reactance only, we shall speak only in terms of type 4 loads for the moment. A basic NEC entry cord for such a load might look like the following:

+ 
  LD  4    1     77       77       0         870.4
+     Type Tag 1st-Seg Last-Seg Resistance Reactance
+

At wire (tag) 1, on segment number 77 (first and last segment), we introduced a load of type R +/- jX with a resistance of 0 ohms and an inductive reactance of 870.4 ohms. (R and jX are always entered in ohms.) Although a 0-ohm resistance is does not coincide with reality, introducing pure reactances as a step in the modeling process can be useful, as we shall see down the line.

+

Specifying spot loads within commercial implementations of NEC may take a number of forms. In EZNEC, there is a separate load screen, a sample of which is replicated in Figure 2.

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Making an entry consists of adding the desired number of loads and then specifying their positions and values. In EZNEC, the user specifies a position in terms of a percentage along the wire. The program places the load on the segment closest to the specified percentage and lists the segment number and the actual percentage along the wire. R and X entries are self-explanatory.

+

NEC-Win Pro permits three modes of load entry. One is to create a load line of the type shown by typing it into the antenna description. One may also access a "Place Load" box from the description and enter the requisite data, as shown in Figure 3 (which replicates load #1 in the EZNEC figure).

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An alternative exists within the NEC-Win Basic module, which is provided for rapid entry of basic antenna information. The user may "drag and drop" loads (and sources) and then access a data box for numerical entries and load-type specification. Although the first two methods refer only to tags, this system also provides a percentage along the wire, which is useful for calculating the precise linear position of loads. Figure 4 shows an example.

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Virtually all other implementations of load placement in commercial implementations of NEC will be a variant on these systems.

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C. Simple Loads and Simple Antennas

The Type-4 loads we place on an antenna consist of series R-jX circuits. These circuits are also in series with other features of the wire, including the source. Figure 5 presents a simple dipole, modeled in 11 segments, with possible loads. One position is at the source, simulating a series loading inductor (or capacitor). Other loading positions are indicated by the outer 2 loads, usually spaced equidistant from the center on symmetrical antennas like the dipole. +
+ +
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1. Loading Short Dipoles: X Only

To illustrate the utility of modeling loads, let us consider a 20-meter wire dipole of #14 copper wire. (I shall not show the LD line for the type-5 element loading information.) A full (1/2 wavelength) resonant dipole in free space would be just about 33.736' long (404.84" or 10.282 meters) at 14.15 MHz. The free space gain for reference is 2.08 dBi. The numerical precision outstrips real building conditions, but is here used as also a measure of resonance. Resonance in an antenna is the condition of having a feedpoint impedance that is purely resistive, that is, with 0 reactance. For modeling purposes, depending upon one's goal, resonance may be approximated for any design frequency with greater or lesser limits. In most pure modeling exercises, I tend to use +/- j1 ohm as the limits of resonance. In this example, the feedpoint impedance happens to calculate to 73.06 - j0.01 ohms. This particular model was done in NEC-4 using 101 segments. (If not pressing the limits of either program, NEC-2 results might still vary from those of NEC-4 by an amount that has no practical significance. Moreover, results from different implementations of NEC may also vary, according to input and output processing--but, again, only by amounts that have no practical significance.) +

Like loads, sources are distributed along a segment, although it is often convenient to think of them as appearing in the center of a segment. Hence, for a single-wire element, we need an odd number of segments in order to truly center a single source. (We shall take up split sources in just a little bit.)

+

This 20-meter full-size dipole will be our reference point. Let us now cut the wire in half, for a length of 16.868' (2.571 m). We shall retain the 101 segments, since each segment turns out to be just about 2" long (about 5.1 cm). At 14.15 MHz, gain is 1.73 dBi, and the feedpoint impedance registers as 12.67 - j870.4 ohms.

+

Let us introduce a complex or R +/- jX load at the center of the antenna (the 50% mark or segment 51). Let it be a pure inductive reactance of 870.4 ohms (R=0; jX=870.4). Loads are considered by NEC to be in series with sources. Therefore, it should be no surprise that rerunning the model produces feed point impedance of 12.67 - j0.04 ohms. The effect is equivalent to introducing a perfect center loading inductor having the require reactance. If the inductor could be perfect, the gain of the antenna would not change: 1.73 dBi.

+

As an interesting exercise, let us replace the center load with two other loads spaced away from the center. In fact, let us place them at the points where equal inductive reactances of 870.4 ohms (with no resistance) also produce resonance. These positions happen to be at segments 25 and 77 of our 101 segment model, a little over 24% inward from the ends. In other words, the positions are just beyond the midpoints of each half of the dipole. Interestingly, the antenna gain is 1.76 dBi, an insignificant amount greater than with center loading. (Mid-element loading of dipoles and dipole-based antennas is done not for added gain, but for other antenna properties, some related to the feedpoint impedance on the prime and other frequencies, some related to mechanical considerations).

+

The feedpoint impedance climbs to 26.08 + j1.65 ohms. (This value is as close to resonance as one may come in the model without changing the value of the loads.) The higher feedpoint impedance is one of those good reasons for using mid-element loading in preference to center-loading.

+

As an initial exercise, try moving these mid-element loads, without changing the reactance, one segment closer to center and then one segment farther from center. Notice that a 2" change in placement per load results in over 60-ohms reactance at the feedpoint. You may also replicate this entire sequence using other element wire diameters. Expect to find a different resonant length for the basic reference antenna, as well as changes in the requisite loading to restore resonance using either a center or mid-element loading technique. The patterns will familiarize you with trends that may be useful in the design of more advanced antennas.

+

As a further exercise, the modeler may also wish to check all of the points along the antenna length between center loading and the point at which mid- element loads reach the value of the center load. One will discover a curve of ever-more rapidly increasing reactance values. In fact, if one continues the exercise beyond the point used in this exercise, there will come a point where adding reactance to achieve resonance is no longer effective in terms of practical inductors. Yet helical structures placed at the ends of short inductors can resonate the antenna. Are they not inductors, that is vehicles of inductive reactance?

+

In fact, although the structures exhibit inductive reactance, at the ends of antennas they function primarily as lengths of wire necessary to achieve the current distribution along the entire wire to produce a feedpoint impedance that is wholly resistive. Many non-helical structures, including so-called capacitive hats, may achieve similar results. The inductive reactance of end coils is largely incidental to most amateur designs. However, it may be used for other purposes, such as in a trap. (Models suggest that the trap is not an appendage to the antenna length that it terminates, but is indeed a part of that length.)

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2. Split Sources and Loads (and Alternatives)

The procedures noted so far for applying loads to antennas, especially at sources, are applicable only to linear elements. When elements meet at angles and the apex of the angle is the source, we must use another procedure. The procedure is also applicable to linear elements, although hardly ever used except in exercises like this one. +

Our original dipole consisted of a single wire, divided into 101 segments. Let us replace that wire with two wires, each half the length of the original. We shall assign 50 segments to each and let them join in the middle. Unless we use a different feed system, the source will not be centered.

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NEC is able to use a split source. If we specify either a split voltage or a split current source, we should place the source on the last (right-most) segment of the first wire--the segment joining the second wire. It pays to use any graphical antenna viewing system to ensure that the source is properly place. On some systems, the source will show up as two sources, one on the last segment of the first wire and the other on the first segment of the next wire.

+

NEC treats these two sources as being in series, and the total impedance is simply the sum of the individual impedances of the source. Normally, only the composite values is shown in the outputs of commercial implementations. For our reconfigured dipole (with no change in total length, the split feed system returns a gain of 1.73 dBi (identical to that of the center, single source model) and a feedpoint impedance of 12.93 - j879.4 ohms. The source impedance is within a percent or so of the earlier model.

+

Loading the antenna mid-element requires no change except for the precise value of the load assigned to each of the two med-element loads. Moreover, because the segmentation varies very slightly from the single-source model, moving the loads inward or outward by one segment may surround true resonance, rather than hitting it with precision. (Obviously, other models may reverse the effect.)

+

Loading at the antenna center, however, calls for a change in procedure. Instead of assigning a single load to a single segment, we create two loads, each half the total load. We assign these loads to the segments containing the sources. Hence, the last segment of wire 1 (Seg 50) receives a load of R=0, X=j439.7, and the first segment of the next wire (Seg 1) receives an identical load. In our example, the source impedance returned a value of 12.93 + j0.04 ohms.

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The figure shows a schematic representation of the principle of split sources and loads applied to an inverted Vee. For simplicity, I simply rotated the dipole elements downward (still in free space) by 45 degrees. This actually made the elements a bit shorter than half size. But since we are going to load the elements, the difference make no big difference.

+

Using a split source, the model returned an impedance of 6.84 - j900.9 ohms. Adding purely reactive loads of -j450.45 ohms to each segment containing a source produced a source impedance of 6.843 + j0.05 ohms, showing that the technique indeed works.

+

There is an alternative to using split sources and loads. At the junction of the wires where we desire to place either a source or a load (or both), we may do a little substitute modeling. At the center point of the antenna element, create a short wire that is horizontal. To this very short wire, connect the angled wires at their normal lengths or their lengths minus half the length of the new wire.

+

Recommendations concerning the minimum length of this wire vary. However, if the wire has the same diameter (or radius, in pure NEC terms) as the connecting wires and if the segments are about the same length as the segments in the joining wires, it will make little difference whether the new center wire has 1 or 3 segments or what its precise length is. Place a single source on the center segment of the new wire.

+

For the inverted Vee with 100 segments, I created first a 3 segment wire 6" long. This preserved the approximate 2" length of all segments. I made no direct changes in the angled-wire lengths, but simply connected them to the new wire. This did alter the overall length of the antenna very slightly. The source was placed at the center of this new wire (Wire 2, Seg 2). The source impedance returned a value of 6.72 - j855.6 ohms. A single purely inductive load of the same absolute value placed on the same segment (in series with the source) eliminated the reactance.

+

I also use a single 2" long horizontal segment as the center wire. This changed the antenna length slightly less than the 6" center wire. The source was placed on the only segment of this Wire (Wire 2). The source impedance returned was 6.687 - j875.7, which a suitable inductive load placed on the same segment also eliminated.

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With angled wires, expect minor variations in the values returned between the split source/load technique and the center section technique. In these examples, the values are well within the range of adjustments one normally expects to make with real antennas on site. However, the models with the longer horizontal center sections consistently showed a slightly higher gain than the split source model, and this effect showed up over real ground as well. The effect results from a portion of the antenna at the high current region being immune from the partial canceling of fields that results from the Vee configuration. Expect up to a 0.1 dB difference in gain, depending on the length of the center section.

+

These notes apply to heavily segmented models, such as the ones used in these examples. Ordinarily, NEC yields accurate results with linear elements with as few as 11 segments per half wavelength. Moreover, the fewer the segments, the faster the run-time for a model. However, where geometries grow complex even to the slightest degree--as in the case of the Vee--attention to segment length is advisable for the most accurate results. For a given configuration, the modeler should always achieve convergence to the degree required by the practical application. Convergence is simply raising the number of segments per wire (usually as a percentage) until further increases yield output figures that do not significantly vary from those produced by the next lower number of segments. These exercises, of course, are unduly segment and precision laden in order to familiarize you with the numbers and movements of numbers you may expect from the program.

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D. Reactance, Resistance, and Q

Unfortunately, I know of no way of implementing an inductive (or capacitive) reactance as an antenna load without also having a series resistance. The ratio of the reactance to the series resistance defines the Q of the component used as the loading device. +

Knowing or being able to estimate the Q of a loading capacitive or inductive reactance allows us to calculate the resistance needed to complete a realistic load. Most commercial inductors I have encountered have had a Q between 150 and 300. As an exercise, let's go back to the shortened dipole with 101 segments and see what these particular Qs do to antenna performance. The following input line shows a typical entry:

+ 
  LD  4    1     77       77       2.9       870.4
+     Type Tag 1st-Seg Last-Seg Resistance Reactance
+

With a center load of j870.4 and infinite Q (or zero resistance), the antenna gain was 1.73 dBi, with a source impedance of 12.67 - j0.04 ohms. If we let Q=300, then the resistance in series with the reactance is about 2.9 ohms. Under these conditions, the antenna model returns a gain of 0.83 dBi and a source impedance of 15.57 - j0.04 ohms. The source impedance is clearly the sum of the load loss resistance and the source impedance without a loss. If we let Q=150, the load resistance is 5.8 ohms, returning a gain value of 0.09 and a source impedance of 18.47 - j0.02.

+

Using the model with two mid-element loads of the same value as the center load and positioned to provide resonance, we come up with comparable figures. With no resistance, the model showed a gain of 1.76 dBi and a source impedance of 26.08 + j1.65 ohms. With a Q of 300, each load has a series resistance of 2.9 ohms. This model shows a gain of 0.93 dBi and a source impedance of 31.55 + j1.52 ohms. Lowering the Q to 150 requires a series resistance of 5.8 ohms, with a consequential gain of 0.24 dBi and a source impedance of 37.01 + j1.37 ohms.

+

Notice that resistive component of the source impedance is close to but not quite the sum of the load resistors and the source resistance of the unloaded antenna. This difference exists because the current magnitude at the load is not the source current, but a slightly less value of about 97% source current. The loads, of course, are positioned only a little over 1/16 of a wavelength away from the source.

+

NEC also returns data on the loads, which is accessible in the outputs of most implementations. Among the direct or calculable data is the power consumed in the loads. With a Q of 300, the center-loaded model consumes nearly 19% of the power in the load, while the mid-element loaded model consumes about 17% of the power between the two loading inductors. Hence, there is about a 0.1 dB difference in the gain of the two models.

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At a Q of 150, the center-loaded model consumes over 37% of the power in the load, while the mid-element loads together consume a little under 30% of the power. Hence, there is a greater (0.15) difference in the gain levels of the two models. If mid-element loading begins to show a distinct advantage over center loading (apart from source impedance and mechanical considerations), it is with low Q loads.

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As with models using pure reactances, the numbers yielded by your specific implementation of NEC may vary slightly from these. However, you should notice the same trends. As an exercise, you may wish to run load Qs ranging from 100 to 1000 for various load positions and values in order to familiarize yourself with the trends involved. Be sure to make use of all relevant outputs from NEC, including load data and current distribution along the antenna.

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E. Capacitive Reactance as a Load

So far, we have dealt only with inductive reactance as a load. This feature of the exercise has been a product of our initial model: a heavily shortened dipole and some angular cousins. However, capacitive loading is also possible and often useful. +

Consider a 20-meter dipole of #14 copper wire, which for free space resonance was 33.7' long. The source impedance was just about 73 ohms. Suppose, as an exercise, we make the antenna 36' long. The source impedance now registers as 90.9 + j102.8 ohms: highly nonresonant.

+

However, using the same techniques as shown earlier, let us insert in the model a load in the same segment as the source. The load will be R=0, jX=- 102.8 ohms.

+ 
  LD  4    1     51       51       0        -102.8
+     Type Tag 1st-Seg Last-Seg Resistance Reactance
+

Now the model will show a source impedance of 90 - j0.05 ohms. The lengthening of the element increased the gain by 0.06 dB, but we ignore that small amount.

+

Although we may divide an inductor into two parts, we must use separate capacitors to place equal amounts of capacitive reactance on each side of the source. Let's revise the load to place a reactance of -j51.4 ohms on each side of the load, by using the segments just before and after the source segment.

+ 
  LD  4    1     50       50       0         870.4
+  LD  4    1     52       52       0         870.4
+     Type Tag 1st-Seg Last-Seg Resistance Reactance
+

Now the source impedance is 89.25 - j0.32 ohms.

+

Although the movement of the loading was small, the trend is evident. Just as placing inductive reactance farther outward on an element moved the source impedance closer to that of a standard dipole (relative to center loading), so too, placing a capacitive reactance farther outward on an element will also move the impedance closer to that of a standard dipole (again, relative to center loading). You can continue to move the capacitive reactance load outward to familiarize yourself with the trends in effects.

+

Here, the exercise is largely academic. However, the scheme of lengthening a driven element to raise the resistive component of its source impedance and then using capacitive loading to compensate for the resulting inductive reactance at the source has been used by at least one Yagi manufacturer in the past. The case involved a Yagi, whose driven element showed an impedance below 50 ohms. Lengthening and loading it provided the desired source impedance to match a 50-ohm coaxial cable feedline system.

+

Other applications of intentional capacitive loading include the controlled current distribution antenna, described by WB9RQR and W9WQ in the ARRL Antenna Compendium, Vol. 2 (pp. 132-135). A less load-laden antenna using capacitive loading to control antenna characteristics is the modified extended double Zepp (also called the double extended Zepp) described by N6LF in the ARRL Antenna Compendium, Vol. 4 (pp. 78-80).

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Most capacitors whose ratings are not exceeded by an antenna application have Qs well in excess of 1000. Consequently, it is much safer to model capacitive loads without adding in a series R value than it is inductive loads. However, in some instances, capacitor leakage cannot be ignored. In such cases, estimates of Q will result in series resistance values calculated just as for inductive reactances. However, in most cases, the values will be much smaller, since the Qs will still be quite high.
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+ +

+
+ These exercises take us just about to the limit of resistance-reactance (Type 4) loads. Although easy to use--and often the first step in placing loads into amateur antennas--they suffer an important limitation. Real capacitors and inductors show a change of reactance as we change frequency, even slightly. Specified reactances maintain the value assigned. Consequently, they do not accurately represent element loading across a span of frequencies, even as narrow a span as a single amateur band. +

In order to more accurately model the behavior of loads, we shall have to learn how to place series and parallel combinations of resistors, capacitors, and inductors as loads. In the process, we shall not only be able to model inductors and capacitors individually, but as well we shall be able to model traps and other tuned circuits placed within antennas. However, all that is for another segment of this series.
+

+
+ +

+
+

Updated 12-18-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 2: From Place to Laplace
+
+ Return to Index
+

Topics: Loading, Modeling, Transmission Line


+ + diff --git a/content/load/loadtl2.html b/content/load/loadtl2.html new file mode 100644 index 0000000..057338e --- /dev/null +++ b/content/load/loadtl2.html @@ -0,0 +1,213 @@ + + + + + + Modeling Loads and Transmission Lines Part 2: From Place to Laplace: Converting X and R to C, L, and R + + + +
+

Modeling Loads and Transmission Lines
+ Part 2: From Place to Laplace: Converting X and R to C, L, and R

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Although complex resistance-reactance loads are handy for rapid antenna development, they are limited in application. NEC does not change the value of reactance as the frequency changes. However, real-world components with which we implement reactances do change their reactance value with frequency. If we intend to evaluate an antenna over a range of frequencies, we shall have to employ different kinds of loads that use actual capacitance and inductance values. We have two choices: series R- L-C circuits (type 0) and parallel R-L-C circuits (type 1). Since the series circuit most closely coincides with the complex R +/- jX loads we have been using, let's begin there. +

A. Series (Type 0) R-L-C loads: Finding and Entering the Numbers

If we know a set of values for R, L, and C (or any one of them), we can go straight to the data entering process. However, if we have begun our design process with R +/- jX, then we must convert the reactance to a value of inductance or capacitance. +

Although the equations for conversion are common handbook material, let's repeat them here for reference (in case you have a calculator handy):

+
+ +
+

where Xl is in Ohms, L is in Henries, and F is in Herz. Incidentally, NEC works almost exclusively in basic units for inductance and capacitance, so using the most basic equations is apt.

+
+ +
+

where Xc is in Ohms, C is in Farads, and F is in Herz.

+

Now we may turn to a definite example. We shall resurrect the 1/2-size #14 copper wire dipole in free space, with its 2 mid-element loads. For the moment, we shall let the resistance be zero and worry only about the load reactance, which was 870.4 Ohms.

+

Using the appropriate equation, we discover that this reactance, at the target frequency of 14.15 MHz, yields a required inductance of 9.79 microH. However, for modeling purposes, we should get used to specifying this and similar inductances in the computer form of engineering notation, hence 9.79e-06 H. (Likewise, although most HF capacitance values are in pF, for example, 23 pF, we need also to express them in a similar way, that is, as 23e-12 F. Notice that we insert no spaces in any part of the number.)

+

The following figure shows the antenna description in NEC input file format for the 20-meter dipole with the loads expressed in type 0 format:

+
+ +
+

Each of the load lines (ignoring the type 5 wire loading) follows the conventions just noted:

+ 
  LD  0    1     77       77       0       9.79e-6       0
+  LD  0    1     25       25       0       9.79e-6       0
+     Type Tag 1st-Seg Last-Seg Resistance Inductance Capacitance
+

For type 0 loads, some of the entries have changed their meanings, specifically, the entries after resistance. Note that the order in which we enter the loads makes no difference to the calculation, although--except for examples like this one--I tend to enter all loads in some logical order. That practice makes modification easier, since I can more easily find the load I wish to modify and less easily select the wrong one. following the order of the elements in the antenna and working from left to right or from End 1 to End 2 for each element generally works in most cases.

+

The inductance entry is in the notation we described. In some cases, exponents with leading zeroes will be truncated to a single digit; in others, the leading zero will appear. Where values are missing (we had no resistance and no capacitance in this example, enter zero. NEC knows to treat these as missing values, whether we are dealing with series or parallel loading circuits. NEC does not create inappropriate short circuits for missing values. The user has to do that by specifying very small values other than zero.

+

Besides allowing the user to enter a load line in the antenna description, NEC-Win Pro provides two other means for entering load data. One is the load screen accessed from the load line.

+
+ +
+

On this screen, we specified a Series RLC load and entered zeroes for the missing values and the inductance value. This screen produces the entry line for the load at segment 77.

+

Within the NEC-Win Basic model, calling up the drag-and-drop screen produces the following screens:

+
+ +
+

Although the data is the same, this screen set permits us to specify the load position as a percentage of element wire length.

+

Within EZNEC, entering R-L-C loads is a 3-screen sequence, as shown in the following partial replication of EZNEC screens.

+
+ +
+

Since EZNEC defaults to R+/-jX values, we changed the load type. If we had been working from a previous model that had R+/-jX loads, these loads would have been deleted. Therefore, we had to enter two new loads in the exact positions occupied by the old loads, as seen on Screen 1.

+

We begin the process of providing values for these loads on Screen 2, by selecting either a series or parallel type load.

+

On screen 3, we enter the values for the R, L, and C components of the load, using the engineering-computer notation, as shown.

+

Once we enter the values, they appear at the bottom of the screen as Laplace coefficients for the equations in the program that supply the NEC core with its input data. I have treated this example as if I were modifying existing values. Had there been no previous entry, all numerator (Num) values would have been 0.000E+00. However, note that the inductance value appears as the numerator for S^1.

+

For simple series loads, the Laplace coefficient for resistance will appear as the numerator for S^0 and the inductance will appear as the numerator for S^1. In some complex loads, some of the coefficients will not be the same as the values entered. Therefore, it is a good practice to keep a record of the actual R, L, and C values entered for each model.

+

Now that we have our model, we might as well run it. EZNEC Pro, using NEC- 4 returned a gain of 1.76 dBi and a source impedance of 26.08 + j1.65 Ohms. NEC-Win Pro, running NEC-2 return values of 1.76 dBi and 26.09 + j2.13 Ohms. In short, no difference.

+

B. The Significance of R-L-C Loads

Placing loads as series R-L-C circuits results within EZNEC in a number of cases that may initially mystify the user, since these loads are transformed and displayed in the load menu as Laplace coefficients. For the case of the "inductance only load" of 9.79e-6 H, the coefficient lines looked like this (to S^2 only, since everything beyond that point is zero): + 
     Load 1:   S^0            S^1            S^2
+     Num       0.000E+00      9.790E-06      0.000E+00
+     Den       1.000E+00      0.000E+00      0.000E+00
+

If we add an arbitrary 2 Ohms resistance in series with the inductor, we see the following table:

+ 
     Load 1:   S^0            S^1            S^2
+     Num       2.000E+00      9.790E-06      0.000E+00
+     Den       1.000E+00      0.000E+00      0.000E+00
+

For inductors and resistors in series, we now know where to look for the values we inserted.

+

With capacitive loads, the table takes on a different look. Consider once more our slightly long dipole that we center loaded with a capacitor having a reactance of -j102.8 Ohms. If we convert the reactance to a capacitance at 14.15 MHz, the value required is 109.4 pF or 109.4e-12 F. If we now plug this value into the EZNEC load screen, we see a table like this one:

+ 
     Load 1:   S^0            S^1            S^2
+     Num       1.000E+00      0.000E+00      0.000E+00
+     Den       0.000E+00      1.094E-10      0.000E+00
+

The capacitive value shows itself in the denominator line at S^1. Complex loads having resistance and capacitance are a bit more complex in appearance. Let us place an arbitrary 2 Ohm resistor in series with the capacitor. The coefficients now look like this:

+ 
     Load 1:   S^0            S^1            S^2
+     Num       2.000E+00      2.188E-10      0.000E+00
+     Den       0.000E+00      1.094E-10      0.000E+00
+

The resistance is in the numerator line at S^0, while the capacitance value remains where it was. The new number in the numerator line at S^1 is the product of the two values. Incidentally, note that all values are transformed to the form x.xxx, with whatever exponent is needed to make the figure equal to the number entered.

+

The long dipole with capacitive loading is also interesting because it seems (and only seems) to suggest that it makes little difference whether we use a complex R +/- jX or an R-L-C load when evaluating an antenna across a ham band. A frequency sweep of the capacitively loaded dipole from 14.0 to 14.3 MHz produces the following table of source impedance values for each type of load:

+ 
     Frequency      Load=R+/-jX         Load=R-L-C
+                    Source Impedance    Source Impedance
+     14.00          86.88-j17.46 Ohms   86.87-j18.58 Ohms
+     14.05          87.90-j11.64        87.90-j12.37
+     14.10          88.94-j 5.85        88.94-j 6.23
+     14.15          90.00+j 0.05        90.00+j 0.04
+     14.20          91.05+j 5.78        91.05+j 6.13
+     14.25          92.13+j11.70        92.13+j12.42
+     14.30          93.22+j17.48        93.22+j18.55
+
+ +
+

The SWR curves are hardly distinguishable, as one might expect from the table of source impedance values. However notice the steeper rise in reactance with the series R-L-C load, which provides the correct reactance of the loading capacitor for each frequency checked.

+

When the characteristics of an antenna vary more extremely across a band of frequencies, the trend becomes more noticeable and important. Consider our short, mid-element-loaded dipole once more. Just as an example, we shall use the model that does not introduce the series resistance that represent losses due to having a finite Q. The table below provides the source impedance values reported by each type of load, while the graph supplies comparable SWR data.

+ 
     Frequency      Load=R+/-jX         Load=R-L-C
+                    Source Impedance    Source Impedance
+     14.00          25.13-j25.45 Ohms   24.84-j42.26 Ohms
+     14.05          25.44-j16.46        25.24-j27.82
+     14.10          25.76-j 7.44        25.66-j13.14
+     14.15          26.08+j 1.65        26.08+j 1.65
+     14.20          26.41+j10.62        26.52+j16.47
+     14.25          26.74+j19.93        26.96+j31.77
+     14.30          27.08+j29.07        27.42+j47.06
+
+ +
+

Clearly, the R+/-jX loaded model provides an excessively optimistic report of the antenna operating bandwidth--by nearly a factor of 2. Once more, just to be repetitive, accurate modeling of a loaded antenna across a band of frequencies requires the use of R-L-C loads.

+

C. Parallel (Type 1) R-L-C Loads and Traps

Any series load having a series resistance as well as reactance can be converted into a corresponding parallel load (type 1). If we begin with series values of R and C or L, we must convert the C or L into a value of +/-jX. For the record, the conversion equations are the following. For series to parallel conversions: +
+ +
+

where Rs and Xs are the series values of resistance and reactance and Rp and Xp are the corresponding parallel values of resistance and reactance.

+

For parallel to series conversions:

+
+ +
+

with the same designations.

+

Parallel R-L or R-C circuits do not have much utility, since they are only the converted counterparts of series R-L and R-C circuits. However, for the exercise, you can convert the mid-element loads with a Q of 300 into their parallel counterparts, arriving at values of Rp=261243 and Xp=870.41 Ohms from the series values of Rs=2.9 and Xs=870.4 Ohms. The reactance, of course, yields a required inductance of 9.79e-6 H

+

For NEC-Win Pro, we would simply select a parallel RLC circuit and enter the calculated values of R and L, with zero for the missing C. In EZNEC, we would similarly select a parallel RLC load and enter "261243,9.79e-6,0." In the coefficients table, we would see

+ 
     Load 1:   S^0            S^1            S^2
+     Num       0.000E+00      2.558E+00      0.000E+00
+     Den       2.612E+05      9.790E-06      0.000E+00
+
+

We recognize the values of R and L in the S^0 and S^1 positions of the denominator line, while the value in the S^1 position of the numerator is simply the product of the two.

+

To further establish the equivalence of appropriately converted series and parallel loads, here are sample results for the mid-element loaded short dipole run with both types of loads in NEC-4 within EZNEC Pro:

+ 
Frequency           Series RLC Model              Parallel RLC Model
+             Gain (dBi)  Source R+/-jX     Gain (dBi)  Source R+/-jX
+14.00 MHz      0.92      30.07-j42.36        0.94      29.96-j42.38
+14.15          0.93      31.55+j 1.52        0.93      31.55+j 1.52
+14.30          0.94      33.13+j46.95        0.92      33.26+j46.95
+

The most useful application of parallel loads is with traps and similar RLC circuits. A trap is a resonant L-C circuit used to provide multiband service from a single element. There are several studies devoted to traps listed in the main index to these articles. Here we shall only cover certain essentials related to traps as computer modeling loads.

+
+ +
+

The figure shows a typical dual-band trap dipole for 20 and 10 meters, resonant on 28.5 and 14.175 MHz. The element material is 0.5" diameter aluminum. The traps are resonant on 27.75 MHz to equalize performance on the two bands.

+

The models for this consist of three wires. The first is 6.41' (76.9" or 1.95 m) long with 12 segments. The last wire is identical to the first. Between them is a wire 16.36' (196.3" or 4.99 m) long, with 31 segments. The first and last segments are loaded by parallel R-L-C circuits representing the traps.

+

The figure also shows trap circuit-equivalents. The upper schematic provides the basis for modeling a trap. The main losses in a trap are normally in the coil, given its finite Q. For this model, a Q of 200 was selected as being slightly more conservative than some commercial traps available. However, Qs from 100-400 have been successfully constructed.

+

The trap values are 1.2 microH and 27.4 pf to achieve resonance at 27.75 MHz. The reactance of each component is about 210 Ohms at resonance. With a Q of 200, the coil series resistance is about 1.05 Ohms. To create a true parallel circuit, we must convert the series inductive leg to its parallel equivalent. The inductance remains almost identical to its series value, but the equivalent parallel resistor becomes quite large.

+

However, we must do the conversions at other than the trap resonant frequency. At 28.5 MHz, the net reactance of the circuit is capacitive, and the required parallel resistance is nearly 43 kOhms. At 14.175 MHz, the net reactance is inductive and the required parallel resistance is about 21.3 kOhms. There is a program within HAMCALC and also within another trap article in this collection that will perform the requisite calculations, as well as explain the procedure in detail.

+

In effect, we have two sets of parallel R-L-C loads, one for 10 meters, on for 20 meters. (The amount that the parallel resistance changes within a band the size of 20 meters is too small to be significant, especially in view of the rounded figures used in most cases for coil Q, although one may calculate the resistor's value for each frequency of interest.)

+

Entering the parallel R-L-C circuit for which ever band interests us is done in the same way as for series loads, except that we select the parallel option and enter figures for all three types of components. The following figure shows a typical NEC-Win Pro entry screen for one of the loads for the 10-meter model.

+
+ +
+

With EZNEC, entry procedures are also the same as with a series load. The Laplace coefficient lines that result may seem mysterious at first sight:

+ 
     Load 1:   S^0            S^1            S^2
+     Num       0.000E+00      5.155E-02      0.000E+00
+     Den       4.296E+04      1.200E-06      1.413E-12
+

S^0 in the denominator line is the resistance, while S^1 in the same line is the inductance. S^1 in the numerator line is the product of the two numbers. It would appear that S^2 in the denominator line must have something to do with the capacitance, but the value seems to have no relationship to the 27.4 pF entered. However, if we divide S^2(d) by S^1(n), we arrive at our original capacitance. This is handy to keep in mind if you forget to record the capacitance you entered.

+

At 28.5 MHz, the model (in NEC-4) returns a gain of 2.08 dBi, with a source impedance of 85.69 + j0.02 Ohms. The same model using NEC-2 returns the same gain and a source impedance of 85.57 - j0.33 Ohms, establishing equal reliability in both programs for handling parallel R-L-C loads. At 14.175 MHz, the model with the appropriate parallel resistor yields a gain of 1.97 dBi with a source impedance of 63.16 - j0.63 Ohms. (Once more, these figures are excessively precise for practice, but are given to illustrate the numbers provided by the programs.)

+

As with all loads, the parallel R-L-C load is placed in series with sources and transmission lines. There is no direct provision for placing a load in parallel with sources or transmission lines within NEC.

+

D. R-X and R-L-C Loads in Parallel with the Source

Not all loads that we might use at the same segment as the source go in series with the source. One good example is the beta or hairpin match. Ultimately, this matching system places an inductance or inductive reactance in parallel with the source. The question is this: can we effectively model a beta match as part of the antenna? The answer is a qualified "yes." +

The beta match is a modified L-network for transforming a higher (feedline) impedance to a lower (antenna) impedance. An L-network consists, when transforming to a lower impedance, of a shunt or parallel reactance on the high impedance side and a series reactance of the opposite type on the low impedance side.

+
+ +
+

As the figure shows, the modification consists in letting the antenna feedpoint impedance supply the series reactance and then installing only the shunt reactance. Normally, we make the antenna a bit shorter than resonant to provide a capacitive series reactance and then add a shunt inductive reactance. The inductive reactance may be in the form of an inductor or a shorted transmission line length (the hairpin). However, for special cases, we might also make the antenna long, providing a series inductive reactance and then install a shunt capacitive reactance.

+

Beta values are easily calculated, either from the following equations or from a program such as found in the HAMCALC collection. Let's sample the normal case, letting the series reactance be capacitive and the shunt reactance be inductive.

+

The common factor in L-networks is delta, which may be called the working Q or measure of efficiency of the network.

+
+ +
+

From delta, we can calculate the requisite values of Xa (the series reactance at the antenna feedpoint) and Xl (the shunt inductor).

+
+ +
+

Now let's return to one of the antennas in the first episode of this series. Consider the half-length 20-meter dipole with mid-element loading. This model used a single wire of 101 segments 16.868' long. The mid- element loads were on segments 25 and 77 and had values of 870.4 Ohms. The source impedance of this antenna was 26.08 + j1.65 Ohms.

+

The transformation from 26 Ohms to 50 Ohms for coax feed is a good job for the beta match. Using the equations above, we find a delta of about 0.95, resulting in an Xa of 24.97 and an Xl of 52.7. Now, let's model this antenna, working toward the beta match.

+
+ +
+

The figure indicates several steps we need to take in order to ensure an adequate model of the antenna and its beta match. Step 1 we have already taken in modeling the original antenna. The gain, using lossless mid- element loads in this exercise, is 1.76 dBi.

+

Step 2 consist of preparing the model for a parallel load. Break the single antenna wire into 3 parts, the two outer parts having 50 segments each, with the loads installed where they physically had been in the original model. This would place them on segment 25 (49%) of the left wire and segment 26 (51%) of the right. At the center is a single segment wire the length of the segment that it replaced (about 2" in this example). When we run this model, we obtain a feedpoint impedance of 26.08 +j1.68 Ohms and a gain of 1.76 dBi, establishing that we have not made anything but a cosmetic change in the model.

+

Step 3 will establish the antenna shortening in order to provide the desired series source capacitive reactance. Here, we have two choices. We may physically shorten the outer wires, or we may simply reduce the mid- element loads a bit. Let's do the latter. Lowering the mid-element load reactances to 857 Ohms each produces a feedpoint impedance of 25.63 - j23.20 Ohms.

+

Step 4 requires that we add to the physical structure of the antenna. We add 3 1-segment wires to form a box around the center source wire. On the wire parallel to the source wire, we initially install a resistive load of 10 MOhms. This resistive load produces what is essentially an open circuit in the new structure so that we may check the effects, if any, of the structure on the antenna performance. Under these conditions, we obtain a feedpoint impedance of 25.97 -j23.55 Ohms, and an antenna gain of 1.70 dBi.

+

Although these changes are small, they do indicate that the structure is not insignificant. Had we used fewer segments, each would have been longer, and the box wires would have had greater effects on performance of the model. Reversing the positions of the source and the resistive load provide another indication that the structure is not insignificant: the feedpoint impedance and the gain change by very noticeable amounts. In practice, we tend to ignore small lumps and bumps in linear antenna element structure, but careful modeling suggests that their cumulative effects on performance may be more than trivial.

+

Step 5 consists in replacing the resistive load with the reactive load indicated by our work with the equations. Placing a purely inductive reactance of 52.7 at the parallel load point yields a source impedance of 53.28 - j0.10 Ohms. Using a very small structure to model the parallel load produced results very close to predictions from the equations.

+

Step 6 takes into account the Q of the beta coil. Let us assume a small inductor with a Q of 300 and hence a series resistance of 0.18 Ohms. This small move produces a source impedance of 53.13 + j0.12 Ohms, all the while making no change in the antenna gain of 1.70 dBi in free space.

+

If we wish to check the performance of the beta matched antenna away from the design frequency (14.15 MHz), we must make one further move: change the load type from a Type 4 (R +/- jX) load to a type 0 (series R-L-C) load. The resistance remains at 0.18 Ohm, while the requisite inductance is 0.59 microH. At the target frequency, the source impedance is reported by NEC as 52.91 + 0.13 Ohms.

+

The importance changing to a series R-L-C load becomes apparent the moment we frequency sweep the completed antenna model from 14.0 to 14.3 MHz.

+
+ +
+

As the graph shows, assuming that the reactance of the coil will remain "close enough" to the value at the design frequency produces an overly optimistic curve of SWR. Using a series R-L-C load for which NEC provides the correct reactance at each frequency checked shows a much narrower (and more correct) operating bandwidth for the antenna. The difference is more than slight.

+

As the exercise demonstrates, it is possible to model loads in parallel to a source using the smallest feasible structures and paying close attention to details along the way. Among those details are deviations from the modeled performance without the added structure and an evaluation of the degree to which those deviations also apply to the real-world antenna. Equally important is using the right load type to model antenna performance across the relevant band of frequencies.
+

+
+ +

+
+ Although we have not fully covered all of the possibilities for using loads in NEC antenna models, perhaps we have gone far enough to let you continue on your own. If that is true, then we can turn our attention to a related subject, the entry and use of transmission lines in NEC models.
+
+
+ +

+
+

Updated 12-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 3. Transmission Lines as Lines
+
+ Return to Index
+
+
+

Topics: Loading, Modeling, Transmission Line


+ + diff --git a/content/load/loadtl3.html b/content/load/loadtl3.html new file mode 100644 index 0000000..a5393c9 --- /dev/null +++ b/content/load/loadtl3.html @@ -0,0 +1,154 @@ + + + + + + Modeling Loads and Transmission Lines Part 3: Transmission Lines as Lines + + + +
+

Modeling Loads and Transmission Lines
+ Part 3: Transmission Lines as Lines

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Modeling transmission lines between the source and the antenna can take two forms. We can physically model parallel transmission lines. And we can model them as TL inputs. Each method has its advantages and limitations. +

A. Physical Models of Parallel Transmission Lines

Consider a simple antenna fed at the center. The source is in series with the antenna wire. Any transmission line we use to feed the antenna thus forms a series circuit with the antenna wire. At the base of the transmission line, the actual source is now in series with the two wires making up the line. +
+ +
+

These simple facts determine the basic rules for modeling a parallel transmission line as a parallel set of wires. First, we break the single antenna wire element into two segments, with the centermost ends spaced the same distance apart as the spacing of the wires in the transmission line.

+

In the figure are a set of arrows indicating ends 1 and 2 of each wire, using a left-to-right convention for this example. Note that we keep the series of wires continuous so that End 2 of Wire 1 connects to End 1 of Wire 2, etc. This is crucial to ensure that the transmission line has equal and opposite currents at every point. (For many placements of transmission lines, the "equal and opposite currents" situation will not fully materialize in reality. However, we always model the transmission line in the manner shown.)

+

The source wire may simply be a one-segment wire from one side of the transmission line to the other. This wire will only be as long as the spacing between transmission line wires, and its segment length sets some specifications for the transmission line segmentation.

+

Segments that meet at angular junctions should be about the same length and in any event within about a 2:1 length ratio. Closely spaced transmission lines require much shorter segments due to the close spacing of their wires. The similar junction at the top of the assembly, where transmission lines wires and antenna wires meet, dictates short antenna wire segments lengths. Even for simple antennas, the entire assembly can quickly grow past the overall segment limit (usually abut 500) for modestly priced commercial NEC packages.

+

One possible solution is to taper the segments lengths along the transmission line, especially at the end closest to the source. EZNEC provides for element length tapering. However, the shortest segment length selected should not be the standard value (0.0025 wavelength), but should match the element spacing. However, NEC-2 recommends that no segment be shorter than 0.001 wavelength long, which the spacing of a 300-ohm line will violate at many HF frequencies. Errors for lines in the 450-ohm to 600-ohm range run about 5 ohms difference from full segmentation (at the test frequency of 14.15 MHz and save from 30 to 130 segments per 1/4 wavelength of each side of the transmission line.

+

Physical transmission lines are usually calculated according to one of two equations:

+
+ +
+

where Zo is the characteristic impedance of the resulting air-insulated parallel feedline, S is the center-to-center wire spacing, and d is the wire diameter in the same units as S. The first form is handiest for calculators, while the second form is somewhat more accurate for closely spaced lines.

+

Program suites such as HAMCALC have modules for calculating the Zo from the wire size and spacing of air-insulated lines--or for calculating any third factor from the other two. Note that these equations do not account for insulation other than air, and the velocity factor is either 1.0 or very close to it. Therefore, any models of physical transmission lines should be based on a velocity factor of 1.0 and the results later readjusted for the actual velocity factor of the line used. Likewise, any losses due to the dielectric must also be accounted for after modeling.

+

Interestingly, an extensive series of models using NEC-4 reveals that transmission lines between 300 and 600 ohms show a higher impedance than that calculated for them with the equations. The figure immediately below shows the test modeling arrangement. Instead of an antenna structure at the top of the transmission line, the lines were bridged with a resistive load.

+
+ +
+

The following table shows the results of using the arrangement with a carefully adjusted 1/4 wavelength line of #14 AWG copper wire at 14.15 MHz (210"). Theoretically, the source impedance should be the same as the load resistance only when both are equal to the line impedance, according to the standard 1/4 wavelength line equation:

+
+ +
+

where Zo is the characteristic impedance of the line, Rl is the load resistance, and Zs is the reported source impedance, all in Ohms.

+

First, there is a small and uneliminable reactance at the source from the test model. Second, the wires are very close together, approaching the limits of NEC-4 to handle, even when segments are carefully paralleled. In all cases, the modeled impedance is higher than the calculated impedance by from 5% to 7%.

+ 
Line Zo        Wire      Spacing   Modeled Zo     New Wire
+Calculated     Dia.      (inches)  in Ohms        Size for Zo
+600            0.064"    4.78"     635            0.086"
+450            0.064"    1.37"     483            0.084"
+300            0.064"    0.39"     316            0.075"
+

All results used segments lengths equal to the wire spacing. As the segment lengths were lengthened, the 600-ohm line was least affected, but the 300-ohm and 450-ohm lines changed values for each new segment length tried--without a definitive pattern. As the segment lengths increased, the far field from the test model increased from nearly -40 dBi to values in the low 30s.

+

Increasing the wire size brought the line impedance close to the calculated value. Equally, one might widen the spacing.

+

NEC-2 results with the same models correlated well with NEC-4 results with segment lengths greater than 0.005 wavelength. With shorter segments, the two programs apparently respond somewhat differently to closely spaced wires. Tapered-length transmission line models correlated well between the two programs, especially in the 450-ohm to 600-ohm Zo range.

+

For many applications, the exact line impedance may be unimportant. However, when physically modeling lines where their impedance does make a difference, running a test model to determine the line Zo is recommended. Physical models of transmission lines are at best somewhat cumbersome. However, they are important to any application where the lines may experience unequal currents and therefore radiate. Typical of such applications is the off-center-fed wire antenna. Comparing the far fields (including both vertical and horizontal components) of the antenna alone and the antenna with its parallel feedline will provide an estimate of such things as the field shape modification occasioned by the feedline, any change of elevation angle of maximum radiation, and any far-field gain changes. An examination of the currents along the transmission line may also be useful in determining the degree of unbalance occasioned by the off-center feed point. Similar exercises may prove useful with other antenna types.

+

Within their limitations, physically modeled parallel transmission lines can provide useful information, even if in some cases exactitude is sacrificed. To date, I have found no useful technique to model physically a coaxial cable such that the cable model fits within the segmentation limitations of versions of NEC aimed at radio amateurs.

+

B. The NEC TL Card

NEC-2 and up provide an alternative (TL input) means of modeling transmission lines of any type. However, the models are mathematical and not physical. By physical, I mean any portion of the antenna structure for which mutual impedances, currents, and fields are calculated. Although the terminals of transmission lines are real and interact with other parts of the model in regular ways, the line itself is not treated as a physical element. Hence, radiation from transmission lines that are handled by this alternative TL input means is not accounted for by the model. +

In exchange for this limitation, the modeler acquires the ability to place one or more transmission lines into the model. The lines may have any Zo and any velocity factor. Moreover, the transmissions lines do not add to the total wire and segment count. For a given antenna structure, core runs will be faster. Alternatively, where there is a limit to the number of segments allowed by a program, more segments are available for detailing the antenna structure itself.

+

Transmission lines inserted via the TL input will be treated as lossless. Consequently, if line losses are significant to the analysis, they will have to be separately calculated via a program such as Dean Straw's TL.

+
+ +
+

The figure shows the NEC input file for a simple 20-meter dipole with a transmission line running from the antenna's normal feedpoint to another point used as the source. The terminating point of a transmission (as well as the starting point) must be a wire. When dealing with transmission lines used to feed an antenna, the "other wire" may be a very short single segment wire. Wire 2 in the sample is the terminating wire for the transmission line. It is only 0.003 wavelength long. The reason for keeping such wires very short is to ensure that they are minimally affected by the main antenna field and likewise minimally affect that field. For most amateur purposes, keeping the current on the secondary wire to 0.1% of the highest level of current on the antenna structure is sufficient to safeguard the accuracy of the reported antenna performance results.

+

The actual transmission line is specified on the line marked TL. The significance of the entries is as follows:

+ 
     TL    1     8      2     1    50   10.6   0    0     0    0
+        1st End Seg. 2nd End Seg.  Zo  Length Real Imag. Real Imag.
+         Wire #  #    Wire #  #   Ohms meters Adm. Adm.  Adm. Adm.
+                                               W1 shunt   W2 shunt
+

The input entry tells us that the transmission line runs from segment 8 (the center) of wire 1 to segment 1 of wire 2. The Zo is 50 ohms. If the entry had been -50, the negative sign would indicate to the program to cross or reverse the terminals at the far end. The length is 10.6 meters, about 1/2 wavelength at the test frequency of 14.15 MHz. Note that there is no provision on the input line for a velocity factor. Any input system that permits entry of a velocity factor pre-calculates the length of an equivalent line with a velocity factor of 1.0 and enters that figure in the length place.

+

The last four places are for shunt admittances containing conductivity and susceptibility factors for ends 1 and 2 of the transmission line. We shall not use them in this exercise.

+

Note also that the distance between the two wires specified in the GW, or wires, entries is 69 feet. However, the length of the transmission line used in calculations will be the one specified in the TL card unless a zero is entered for length. In that case, the program will use the straight-line distance between the two terminating points of the transmission line as the line length. This latter entry capability is useful for placing straight line phasing lines between fixed elements and similar applications.

+

C. Entering Transmission Line Data

Commercial implementations of NEC use a variety of methods for entering transmission line data. Of course, the TL input may be entered in the editor by directly typing in the requisite information. +

NEC-Win Basic and the Basic module of NEC-Win Pro use a special window to simplify data entry:

+
+ +
+

Although the label says, "No Transmission Lines Defined, this window shows one in the process of being defined. The terminating points are defined in the upper left, while the Zo and Length are immediately below. Note again that there is no provision for a velocity factor: the line length for a VF of 1.0 must be pre-calculated by the user. In the lower left is an entry to specify phase reversal or normal connections, with the unused shunt entries immediately above.

+
+ +
+

NEC-Win Pro also accesses a similar window from the TL line of the antenna description. Although styled slightly differently, the data entry scheme is identical to the one just described.

+
+ +
+

EZNEC enters transmission lines on a separate page, somewhat similar to the one used for loads. The partial replications in the figure take you through the transitions as you move from one item to the next in creating a transmission line. The top section shows the complete data entry, ready for revision, if one chooses to do so. The remaining partial screen section change as the user highlights one item after the other.

+

The second screen appears when either end of the transmission line is illuminated. The next screen highlights the length, which in EZNEC is entered in the same units as the wire dimensions. In this case, it is feet. If the user specified the length with a "d" suffix, the entry is interpreted as electrical degrees, which is then calculated into meters for the NEC core. Be careful not to use electrical degrees for a frequency sweep designed to show the properties of a fixed length of transmission line over an amateur band. An entry of "a" for the length will use the straight-line distance between the specified wire segments as the line length.

+

When either the Zo or the velocity factor are illuminated, the user has the option of selecting a transmission line from a table of both coaxial cables and parallel lines. Alternatively, the user can enter the required values. Finally, the user can construct an air-insulated parallel line by supplying the wire diameter (in measured units or as an AWG value) and the wire spacing.

+

The normal-reverse flag is activated in EZNEC by specifying N or R as the final line entry.

+

D. Basic Transmission Line Applications

The most basic transmission line application is as a feedline from a power source to the antenna, as shown in the figure. +
+ +
+

Although the figure shows 11 segments, the antenna wire can have any (odd) number of segments (if a true center connection is desired). The second wire is very short and has one segment. The transmission line goes from the center of one wire to the next.

+

Consider a 20-meter dipole similar to the one in the figure, but with 101 segments of #14 copper wire. The total length is 33.696' (5.141 m). The second wire is 0.02' (0.006 m) long and has 1 segment. (This length at the test frequency of 14.15 MHz is about 0.0003 wavelength long, while the recommended NEC-4 minimum wire length for such applications is about 0.0001. For NEC-2, the wire should be at least 0.001 wavelength long.)

+

The NEC-4 source impedance of the antenna alone is 73.06 - j0.01 ohms. Now let's do a familiarization exercise based on the fact that a lossless feedline repeats the antenna source impedance every multiple of 1/2 wavelength. First, we move the source from the long antenna wire to the short second wire. Then, we specify a 50-ohm, VF=1.0 transmission line between the center of the antenna (the former feedpoint or segment 51) to the center of the second wire.

+

Since TL-type transmission lines are in parallel with sources, the effect of placing both the source and the transmission line on the second wire is to place a source in series with each wire of the transmission line, just as we would model the system physically. Except for the fact that the TL- type transmission line will not even show copper wire loss, the results will be identical for physical and TL transmission lines.

+

For example, let us assign to the transmission line a length that is exactly 180 electrical degrees. The resulting reported source impedance will be 73.06 - 0.08 ohms in NEC-4. (As with all models in the exercises in this series, minor adjustments will have to be made for NEC-2, adjustments that are only apt to yielding the excessively precise outputs used for numerical comparison, but which have little or no practical application to real-world antennas.)

+

EZNEC permits the specification of transmission line lengths in electrical degrees (and automatically specifies a velocity factor of 1.0). For other programs, we may have to calculate precisely the length of the transmission line that is exactly 180 electrical degrees long at the test frequency. At 14.15 MHz, this length is 34.7552' or 10.593 m. Using either of these values, the source impedance reported is the same as just noted.

+

Now let us substitute a truer 50-ohm coaxial cable, perhaps RG-213, with a velocity factor of 0.66. The requisite length of the cable is simply 0.66 times the value used with the assumed velocity factor of 1.0, or 22.9384' (6.9914 m). Using this transmission line, the reported source impedance is 73.06 - j0.00 ohms.

+

A real coaxial cable, even brand new, will not deliver lossless performance. If we use a program like TL, we shall discover that RG-213 at the specified length of nearly 23' (nearly 7 m) with an antenna impedance of 73.06 - j0.01 ohms will show that the source end an impedance of 71.91 - 0.03 ohms. This value represents the apparent SWR decrease (from 1.46 to 1.42) due to line loss with which most antenna users are familiar. The line also creates a 0.195 dB power loss, which amounts to 4.4%. The loss is a combination of basic line loss plus the additional loss due to the SWR level.

+

There is no convenient way to incorporate this loss into the antenna wire at either end of the model. Nor should we want to. Whatever the power delivered to the antenna, its gain and other characteristics remain constant (assuming that material junction losses can be neglected). If the losses and gains within an overall antenna-plus-transmission line-plus- source system are important, they can easily be calculated externally to modeling the antenna itself.

+

This exercise has little practical value other than familiarizing the modeler with the placement of TL transmission lines within a model. The model used here can be extended by changing the length of the transmission line in increments of 10 electrical degrees and observing the change in source impedance across a full half wavelength. One might also use 300-ohm and 450-ohm transmission lines in order to observe the greater excursions of resistance and reactance with each 10 degrees of electrical length. All of these are familiarization exercises, designed to develop a set of reasonable expectations for models employing TL transmission lines.

+

In each case, we must remember that the values given are for a lossless line. The TL transmission line will return the same value of source impedance for 0, 180, 360, and 540 electrical degrees, or multiples of 34.7552' (10.593 m) for velocity factors of 1.0. For comparison, run each length through a program such as TL to determine the losses for each length and the anticipated impedance presented at the source end of the line.

+

E. Sample Practical Applications

There are many practical combinations of antenna elements plus feedline(s) for which modeling is very apt. The figure below illustrates only three of them. +
+ +
+

At the upper right is a pair of horizontal antenna elements spaced some distance apart. The spacing might be anything from 1/8 to 1/2 wavelength. We may feed the antennas either in phase or out of phase. To explore the various situations, we need only create a third wire. Then we create transmission lines from wire 1 and from wire 2 to wire 3, where we also locate the source. In order the reverse the phase of feeding, we simply specify one of the two transmission lines as "reversed" or "180-degree phase reversal," which enters a minus sign in front of the Zo we specify for the two lines. We can even experiment with different Zos for the transmission lines and different lengths. The models, even though subject to slight inexactitudes due to the lossless nature of the transmission lines, will teach much about phasing lines with a common feed point.

+

At the bottom is the KB8I phasing system for feeding two 1/4 wavelength verticals that are spaced 1/8 wavelength apart. TL1 and TL2 are 50-ohm coaxial cables 157 degrees long, each terminating with a wire in the model. Between the wires is another cable, TL3, which is 29 degrees long. To create this model, we might place the verticals over perfect ground. If we wish to model over real ground, we would elevate the verticals and their ground planes for NEC-2. In either event, wires 3 and 4 should be elevated. There are methods for calculating the phasing lines to achieve a desired current phasing of -135 degrees for one of the verticals with the other at zero degrees, giving a broad, nearly cardioidal pattern to the array. Of course, we can replicate Al Christman's dual directional array switch simply by moving the source from wire 3 to wire 4 and back again. For this array, which permits a direct 50-ohm coaxial cable feed from the model source to the shack, it is wise to look at the current magnitude and phase at the based of each antenna as well as the overall current and source impedance. You might even wish to experiment by replacing the 50- ohm cable with 75-ohm cable, just to see what happens. Be sure to remember to calculate for the velocity factor when translating the cable lengths in electrical degrees into feet or meters.

+

At the upper left is an interesting system for improving the operating 2:1 SWR bandwidth of an antenna-feedline system for dipoles. This can be operationally important to amateurs using gear with sensitive SWR shut-down systems with certain antenna situations. Consider a half wavelength center-fed dipole for 40 meters, which we might model as #14 copper wire 67.2' long with 101 segments. Let us place this antenna at a height of 50' above medium earth. We would obtain the following values of source impedance and 50-ohm SWR from NEC-4:

+ 
Freq.    7.0     7.05    7.10    7.15    7.2     7.25    7.3
+R        83.28   84.88   86.44   88.07   89.72   91.38   93.06
+X        -32.5   -21.3   -10.1   - 0.9    12.0    23.0    34.0
+SWR      2.03    1.85    1.76    1.76    1.84    1.99    2.19
+

Even allowing for the lower SWR that appears at the shack end of the line due to line losses, the band edge values may activate power reduction circuitry in some gear. As a step toward resolving the problem, let us create a short wire spaced well away from the dipole. From the antenna, run a 50-ohm coaxial line exactly 1/2 wavelength long at the band center, 7.15 MHz. RG-213, with a velocity factor of 0.66, would be 45.40' long for this application. Be sure to move the source to the new wire (wire 2 in the diagram). Because the transmission line is less than 1/2 wavelength long at 7.0 MHz and longer than 1/2 wavelength long at 7.3 MHz, we obtain the original feedpoint impedance only at the band center, 7.15 MHz. At other frequencies across the band, we obtain the following values for the lossless line:

+ 
Freq.    7.0     7.05    7.10    7.15    7.2     7.25    7.3
+R        90.09   87.80   87.13   88.07   90.58   94.75   100.8
+X        -27.1   -17.3   - 8.0     0.9     9.5    17.9    26.0
+SWR      2.03    1.85    1.76    1.76    1.84    1.99    2.19
+

Note that the SWR has not changed, but the impedance values have, except for mid-band. The resistive component has gone up, and the reactive component has gone down. In fact, the values are sufficiently higher than 50-ohms to make a 1/4 wavelength 75-ohm matching section useful to transform them to lower values. So let's add a new short wire (wire 3) and move the source to it. Then let's create a 75-ohm, 0.66 velocity factor transmission line from wire 2 to wire 3. The line will be 22.70' long. From it--again allowing for the fact that the model uses lossless line--we obtain the follow source values:

+ 
Freq.    7.0     7.05    7.10    7.15    7.2     7.25    7.3
+R        56.45   61.26   63.92   63.86   61.31   56.96   51.72
+X         16.0    11.5     5.6   - 0.7   - 6.2   -10.1   -12.2
+SWR      1.38    1.34    1.30    1.28    1.26    1.26    1.27
+

The result is a set of SWR values across 40-meters that should satisfy any piece of amateur equipment. The line losses at any point in the band may be calculated from TL and compared to the use of a single 50-ohm cable or to the use of a single 75-ohm cable with impedance transformation (and network losses) at the shack. There is not likely to be a significant difference.

+

For developing the general picture of what occurs all across the band with this system of matching, modeling both the antenna and the transmission lines provides one of the most efficient methods. I am indebted to Dave Leeson, N6NL, for bringing the matching system to my attention. Dave attributes it to Frank Witt, AI1H and other sources. All in all, it provides a good exercise in seeing the modeling capabilities of NEC in handling multiple lengths of transmission line on the way from the source to the antenna.

+

Not all transmission lines must have a short wire at one end. Consider the following sketch of a ZL Special. Pioneered, although apparently not invented, by George Prichard, ZL3MH (later ZL2OQ), the antenna consists of two elements spaced about 1/8 wavelength apart. The feedpoint is the junction of the forward element and the phase line (transmission line) to the rear element.

+
+ +
+

Let's build one of these antennas as a model. For 28.5 MHz, we might choose 3/4" diameter aluminum tubing and make two identical elements, each 16' long with 51 segments. We shall space them 3.46' apart, which is just about 0.1 wavelength. We shall set one element as the forward element and place the source at its center. We create the phasing line by placing a transmission line between segments 26 of each of the two elements. Let us follow Prichard's lead and use 71- ohm parallel line, which had a reported velocity factor of 0.67. Let's be sure to place the traditional half twist in the line by reversing the phase. If we place the antenna at 35' above medium earth, NEC will return a gain of about 11.8 dBi, a front-to-back ratio of about 25.7 dB, and a source impedance of about 7.2 + j8.8 ohms. (The low source impedance did not bother Prichard, since he fed his arrays with parallel feeders and an antenna tuning unit.) These facts are perhaps the least interesting in connection with the ZL Special.

+

Now let's examine the current tables available as an output from NEC. If we used a current source of 1 for the antenna, we shall find the current at the center of the forward element to be about 0.455 at -16.69 degrees. At the center of the rear element, we find the current to be about 0.462 at 159.78 degrees. The rear element has a magnitude of 1.015 and phase of 143.09 degrees relative to the forward element. Yet, the phase line length was only 0.1 wavelength long physically and 0.15 wavelength long electrically. How is this possible?

+

To find out, let's make a slight change in the model. If the forward element was modeled from left to right (-8.0' to +8.0'), then let's make the rear element in the reverse direction (+8.0' to -8.0'). Next, let's change the transmission line back to its normal or non-reversed orientation.

+

When we run this model, we obtain identical performance figures to those cited above. However, the current tables show another story. The forward element remains as it was, but the rear element shows a center current of 0.462 at -20.22 degrees. The rear element is -36.91 degrees relative to the forward element, which is equivalent to a phase angle of 323.15 degrees. Of course, subtracting 180 degrees from this figure yields 143.15 degrees, which we obtained from the first version of the model.

+

The current phase change of (-)36.91 degrees along the 71-ohm, 0.67 VF phase line of 3.46' from the rear element to the forward element is precisely what we need to provide the two elements with the relative current magnitude and phase angles so that the array achieves a front-to-back performance far in excess of what a similar driven element-reflector Yagi might obtain with the same spacing. The details of the analysis of ZL Specials go way beyond our purpose here, but the ZL Special is an excellent example of modeling transmission lines between two elements.

+

There are numerous other feedline uses of feedlines, but these examples should get you started. We may also use feedlines for other things, for example, as substitutes for lumped components. However, that set of applications will require that we search for shorted and open lines, and they can only be found in the next part of this series.
+

+
+ +

+
+

Updated 12-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 4. Transmission Lines as Lumped Constants
+
+ Return to Index
+

Topics: Loading, Modeling, Transmission Line


+ + diff --git a/content/load/loadtl4.html b/content/load/loadtl4.html new file mode 100644 index 0000000..7ad706f --- /dev/null +++ b/content/load/loadtl4.html @@ -0,0 +1,182 @@ + + + + + + Modeling Loads and Transmission Lines Part 4: Transmission Lines as Lumped Constants + + + +
+

Modeling Loads and Transmission Lines
+ Part 4: Transmission Lines as Lumped Constants

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Lengths of transmission line can be used as "lumped constants," that is as inductive or capacitive reactances. In many cases, the use of a transmission line to provide a desired reactance is preferable to or at least as equally good as the use of a capacitor or inductor. The reasons are many and depend on the particular circumstances of the application. For some purposes, transmission line lengths have a higher Q; in others, they are more durable or better shaped. In antenna work, transmission line lengths--or stubs--are very useful, and therefore worth modeling in place. +

A. Stub Principles

The general principles of creating reactances from transmission line stubs is well known. The figure shows the general technique. +
+ +
+

Shorted stubs less than 1/4 wavelength long provide inductive reactance. At exactly 1/4 wavelength long, the stub becomes the equivalent of a very high impedance parallel resonant circuit, creating a virtual open circuit between the terminals. Longer than 1/4 wavelength, the shorted stub becomes a capacitive reactance.

+

Open stubs follow an opposing path. Shorter than 1/4 wavelength, they provide capacitive reactance. At exactly 1/4 wavelength, they are the equivalent of a very low impedance series resonant circuit, creating a virtual short circuit between the terminals. Longer than 1/4 wavelength, the open stub becomes an inductive reactance.

+

We can easily calculate the reactance of a length of shorted transmission line if we know the characteristic impedance (Zo)--along with the velocity factor of the line. For shorted stubs, the equation is as follows:

+
+ +
+

where Zo is the characteristic impedance of the line, X is the reactance, and "beta l" is simply the line length in electrical degrees or radians. Of course, you must pre-calculate how many electrical degrees or radians there are in the physical length of line with which you start. Likewise, if you turn the equation around to determine the length of line required for a certain reactance, you will have to translate the result from electrical degrees or radians in the units of measure of length you are using.

+

For open stubs, we use the equation

+
+ +
+

where the terms have the same meaning. The value of X will be either positive or negative, indicating inductive or capacitive reactance. At exactly 90 degrees, the tangent of the angle climbs without limit, resulting in a value of reactance that is zero for open stubs and that is indefinitely high (some folks like to say infinite) for shorted stubs.

+

At zero degree lengths and at multiples of 180 degree lengths, the value of the tangent of the angle is zero. The stubs reverse their roles with their 1/4 wavelength counterparts.

+

There are a number of applications of shorted and open stubs in antennas, and we can model most of them. However, we must always remember that transmission lines (TL entries) in NEC represent lossless lines. For all but short lines, we should externally calculate line losses in the final evaluation of any antenna design where the line or stub is a part of the antenna.

+

B. Entering Stub (TL) Data

Every transmission line or TL entry in NEC requires two wire segments to act as terminations for the line. In effect, the TL entry opens the wire segment and inserts the transmission line segment in series with it at that point. Without wire segments at either end, the transmission line cannot be formed. +

This process is invisible with EZNEC.

+
+ +
+

As the screen replica shows, we have inserted 2 stubs in Wire 1. The first is a shorted stub, which we specified simply by keying "s" for end 2 of the transmission line. The remainder of the entry of length, Zo, and velocity factor are normal. We use a similar procedure for the second open stub by specifying "o" for end 2 of the line.

+

What the entry does not show you is a second wire created by the program to act as the other termination of the line specified. The line is created about 100 wavelengths away from the antenna in all 3 axes, X, Y, and Z. Additionally, the line is about 0.002 wavelengths long and divided into two segments, one to act as the terminal point of each of the two loads. The wire has a radius of about 0.0001 wavelength, the smallest permissible under NEC. Each of these measures ensures that the wire will interact minimally with the other wire segments, thus not disturbing the accuracy of the impedance, current, and field calculations.

+

You can easily recreate this situation with programs, such as NEC-Win, where you may have to create your own stub conditions.

+
+ +
+

The TL window in NEC-Win presumes that you have created the second wire. In this case, we are creating a shorted stub at wire 1, segment 25, and it goes to wire 2, segment 2. We are using 450-ohm transmission line with a length of 3.687 meters (12.09'). Note, however, one final necessary element of the stub. End 2 must specify the conditions for a short circuit across the terminals, which means an indefinitely high value of "shunt admittance" (the inverse of a shunt impedance). Since the boxes are small, I have move the "real" (conductance) component to the right to show the exponent value, while the "imaginary" (susceptance) component remains shifted left. Values of 1E+10 are so high as to be indistinguishable from a true short circuit.

+

The corresponding input line in the text editor would appear as follows:

+ 
     TL    1     25     2     2    450  3.687  0    0    1E+10 1E+10
+        1st End Seg. 2nd End Seg.  Zo  Length Real Imag. Real  Imag.
+         Wire #  #    Wire #  #   Ohms meters Adm. Adm.  Adm.  Adm.
+                                               W1 shunt    W2 shunt
+

For an open circuit, we would use the same procedure, but place values of 1E-10 in each of the boxes. This low a value of admittance corresponds to a value of 1E+10 for impedance, indistinguishable from an open circuit. Although such values are manually placed in this NEC-Win example, EZNEC places them automatically and invisibly to the user.

+

Now that we can create transmission line stubs, we can litter our antennas with them. Unlike physically modeled transmission lines and stubs, these TL entries occupy no wire segments, speeding core calculation runs and allowing greater antenna detailing. They appear in series with loads on the same segments they occupy, but in parallel with sources on the same segment.

+

C. A Basic Stub Use

One basic use of transmission stubs is to replace inductors as loads along antenna elements. To understand their use within models, let us return to our running model: the 101 segment #14 copper wire model in free space of a dipole shortened to about half-normal length. In past exercises, we loaded this dipole at segments 25 and 77, first with a reactance of 870.4 ohms, and then with an inductor of 9.79e-6 H, at 14.15 MHz. For a lossless inductor, we obtained a gain of 1.76 dBi in free space, with a feedpoint (source) impedance of 26.08 + j1.65 ohms. +

Now let's replace the R-X and R-L-C type loads with a transmission line stub. In fact, let's try a couple of different stubs.

+
+ +
+

First, we can replace the loads with TL entries at the same segments using 450-ohm, 0.95 VF transmission line. The standard equation tells us that the line needs to be 11.494' (3.503 m). This will show up in the TL line in the text editor as 3.687 m, the equivalent length of line with a VF of 1.0. (The second wire is assumed to have been placed either manually or automatically by the program.)

+

At our test frequency, the model returns (in NEC-4) a source impedance of 26.09 + j1.72 ohms, and a gain of 1.76 dBi in free space. The slight numerical differences from the R-x and R-L-C load models, of course, make no difference at all.

+

Now let's replace the 450-ohm line with 50-ohm coaxial cable with a VF of 0.66 (RG-213). The required line length will be 11.05' (3.369 m), which will translate to 5.104 m of 1.0 VF line in the TL entry.

+

Using this line in the model, it returns a source impedance value of 26.09 + j2.147 ohms and a free space gain of 1.76 dBi. Again, no difference.

+

Although we recognize that these lines are lossless in the model, losses in transmission line lengths--when used within their recommended limits--tend to be negligible for such short lengths. We would expect no changes in the real antenna that are attributable to line loss adjustments, in contrast to those occasioned by wire and line cutting and assembly precision. However, transmission lines have at least wire losses which given them finite Qs in applications such as these. Although the Qs may be higher than those of inductors, we may not expect true lossless performance.

+

An exercise such as this one can mislead as well as instruct. At first sight, it would appear that we might easily replace our loading inductor with transmission line stubs and have the same antenna. This would be true if and only if we operated the antenna only at 14.15 MHz.

+

D. Frequency Sweeping Inductive and Stub Loads

Let us take the trouble to run frequency sweeps of our half size dipole using all three loads: the inductor, the 450-ohm stub, and the 50-ohm stub. Across 20 meters from 14.0 to 14.3 MHz, we would obtain the following sets of values. The values are grouped according to source resistance, source reactance, and SWR relative to 26.08 Ohms (the value at resonance). + 
Source Resistance (in Ohms):
+Type Load  FQ: 14.0    14.05  14.1    14.15   14.2    14.25   14.3
+Inductive      24.84   22.24  25.66   26.08   26.52   26.96   27.42
+450-ohm Stub   24.38   24.92  25.49   26.09   26.70   27.36   28.04
+50-ohm Stub    20.25   21.65  23.50   26.09   29.98   36.50   49.50
+
+Source Reactance (in Ohms):
+Type Load  FQ: 14.0    14.05  14.1    14.15   14.2    14.25   14.3
+Inductive      -42.3   -27.8  -13.1    1.65   16.47   31.77   47.06
+450-ohm Stub   -68.9   -46.1  -22.5    1.72   26.59   52.64   79.38
+50-ohm Stub    -320.   -240.  -136.    2.15   198.8   502.9   1038.
+
+SWR relative to 26.08 Ohms:
+Type Load  FQ: 14.0    14.05  14.1    14.15   14.2    14.25   14.3
+Inductive       4.54    2.82   1.65    1.07    1.85    3.12    4.90
+450-ohm Stub    9.35    5.07   2.34    1.07    2.65    5.71   10.50
+50-ohm Stub    >100.   >100.   32.3    1.08    52.5   >100.   >100.
+

Clearly, something is different about the stubs relative to the inductor-- and between the stubs themselves. Although the rate of change in source resistance is moderate as we move from one load to the next, the rate of change in the source reactance is much higher for the stubs--and extremely high for the low-impedance transmission line. The 2:1 SWR operating bandwidth for the inductive load is less than 200 kHz, for the 450-ohm stub less than 100 kHz, and for the 50-ohm stub less than 20 kHz.

+

Stubs change reactance according to changes in the TAN function of the electrical length in degrees or radians and relative to the characteristic impedance of the transmission line. Inductors, however, change reactance according to changes in frequency. The differences in the way each changes reactance do not show up if the required inductive reactance of a shorted stub is low--in the 0 to 100 ohm range.

+
+ +
+

The graph compares change in reactance at 14.0 and at 14.3 MHz for an inductor (inner lines) and 50-ohm transmission stubs (outer lines) when the load at 14.15 MHz is assigned values between 0 and 100 ohms. Even at the upper end of the graph, the differential between 50-ohm stubs and an inductor is a matter of a few ohms. However, when the required inductive reactance is greater--between 100 and 800 ohms--a more radical divergence appears.

+
+ +
+

As the graph shows, the inductor changes its reactance by only small amounts all the way up to 800 ohms. However, the 50-ohm transmission line stub changes its value more rapidly as the frequency departs from the design center as the load value increases. The result is that for antennas requiring high values of inductive reactance as loads, the 50-ohm stub permits only a very narrow operating bandwidth.

+

The 50-ohm stub is a very extreme case, used here to dramatize the differences in the rate of change of value between transmission line stubs and inductors with frequency movement from the design center. Fortunately, the higher the impedance of the transmission line stub, the smaller the difference between its change of reactance and the change of reactance of an inductor over the same frequency deviation from design center.

+
+ +
+

The graph above is developed on a different premise. Let us use the change of reactance of the inductor as a base line. If the design center is 14.15 MHz, then at a frequency of 14.3 MHz, the percent of change in reactance will be constant over the entire range of reactances. In contrast, the percent of change of transmission line stubs will very, increasing with the reactance required, and so too will the ratio of the change in reactance in stubs to the change in inductors.

+

The graph shows the ratios for 50, 100, 300, and 600 ohm lines, relative to the inductor's baseline. The lesson is clear: for the widest bandwidth when using transmission line stubs, use the highest feasible characteristic-impednace transmission line. Even so, a lossless inductor will always show a wider operating band width than an equally lossless transmission line stub.

+

For inductors, Qs of 150 to 300 are common in antenna loading service. These Qs generally further increase the operating bandwidth at the cost of slight losses in antenna gain due to the resistive losses. In contrast, transmission line stubs less than 1/4 wavelength long rarely have Qs less than 300, and often they can reach 1000 to 1500. Hence, stubs offer slightly higher gain at the expense of operating bandwidth for any given antenna design that is inductively loaded.

+

For the antenna modeler, this exercise should reinforce the importance of making frequency sweeps across every the range of frequencies for which the antenna is designed. The sweep must be run using the correctly modeled load for the application. Even if losses are not apparent from the modeling exercise itself, they can be separately calculated and factored into the design.

+

E. Other Applications of Stubs

Element loading is not the only possible application for modeled transmission line stubs. We can also combine stubs with normally terminated transmission lines to explore the properties of the combined array. A common application in this vein is the matching-section-and-stub system used to match an antenna's odd source impedance to a standard feedline. +
+ +
+

Consider the following example, corresponding to the sketch. We have an extended double Zepp antenna with a design center frequency of 28.5 MHz which we wish to feed with 50-ohm coax. Can we design a match and stub system to do the job? If we can design the system, what will be the 2:1 SWR operating bandwidth of the resulting antenna and match system?

+

The antenna model consists of one wire, 44.2' (13.48 m) long, with 31 segments. We shall place this antenna at a height of 35' (1 wavelength) above medium ground conditions. The program returns a gain of 10.76 dBi and a source impedance of 135.3 -j680.1 ohms. The source impedance becomes the starting point for our match-and-stub system. We shall use 450-ohm, 0.95 VF parallel line for the transition to our 50-ohm coax.

+

Because transmission lines are impedance transformers, we can find 2 points along each half wavelength of the initial 450-ohm line at which a properly sized stub (either open or shorted) will yield an impedance of 50 +/- j0 ohms. (The limiting case is where the impedance along the line never reaches 50 ohms, in which case, we must select a different Zo line for the match and stub system.) We can use either a Smith Chart or a utility program, such as the one included in the HAMCALC collection, to simplify the calculation process.

+

For the case in hand, we find that lengths of A. 4.983' and B. 5.441' are able to support stubs for the transformation. At point A., a shorted stub 1.176' long or an open stub 9.373' long will do the job. At point B., a shorted stub 12.216' long or an open stub 7.020' long will also do the job.

+

Ordinarily, we select the combination of matching section and stub that is shortest. In this example, the 4.983' + 1.176' stub combination is the most compact.

+

To place these lines in the model, we create a second wire, 0.02' long at a height of about 30' up. The exact height is not critical, since we shall control the length of the match line with the TL entry. If we must manually create the distant wire for the termination of the shorted stub, we do so at this time.

+

Then we enter two transmission lines, both 450 ohms and 0.95 VF. The first goes between wire 1, segment 16 and wire 2, segment 1. The length is 4.983 feet. The second is a shorted stub from wire 2 segment 1, with a length of 1.176 feet. (Adjust lengths for a VF of 1.0 if directly entering values into the TL line: 1.599 m for the match line and 0.378 m for the stub.) Be certain to move the source from the center of wire 1 to wire 2, segment 1.

+

Running this revised model yields at 28.5 MHz a source impedance of 49.97 - j0.01 ohms, showing the coincidence between the external calculations and our modeling. The gain, of course, does not change. However, once we have established the fact that our external calculations and our modeling work coincide, is there any use to installing the transmission lines in our model?

+

The answer is affirmative, for we can use this installation to determine the anticipated 2:1 SWR operating bandwidth of the antenna. If we perform a frequency sweep across the first MHz of 10 meters, we obtain the following data:

+ 
     Frequency         Source Impedance       50-Ohm SWR
+       in MHz            R +/- jX Ohms
+     28.0              111.0 - j26.13         2.37
+     28.1              93.43 - j22.74         2.02
+     28.2              79.03 - j17.74         1.71
+     28.3              67.30 - j11.98         1.43
+     28.4              57.75 - j 5.97         1.20
+     28.5              49.97 - j 0.01         1.00
+     28.6              43.57 + j 5.74         1.20
+     28.7              38.29 + j11.21         1.45
+     28.8              33.89 + j16.36         1.73
+     28.9              30.22 + j21.18         2.07
+     29.0              27.12 + j25.70         2.47
+
+

The data tell us that we are likely to be able to operate the antenna without equipment indisposition over at least 0.8 MHz bandwidth. Moreover, using the curve as a guide, we are likely to be able to make field adjustments of the actual match and stub system to bring it into line with the portion of the band we most wish to use. Since we are using a mere 6' (2 m) of line for the match and stub system, line losses will be negligible within it. In any event, the losses will be far less than had we designed an inductor at the feedpoint to compensate for the capacitive reactance, followed by a 2:1 transformer to bring the resistive component of the source impedance closer to 50 ohms.

+

This example, I hope, illustrates the utility of judiciously employing stubs in antenna models beyond their function to load antenna wires. I recommend that you rebuild the model using each of the other three combinations of match line and stub just for the practice in using TL entries in models (if not out of curiosity over whether those values "work").

+

E. Physically Modeling Stubs

Like regular transmission lines, we can also model stubs as physical elements within the antenna design. The advantage is that any interactions of the stubs with other parts of the antenna structure will show up in the model's output data. The disadvantage is that modeling the stubs will occupy wires and segments, thus slowing the core calculations. For complex designs, modeling all stubs can drive the model size to the program limits. +

In addition, we must always be aware of basic NEC limitations. Primary among these limits is the possible unreliability of results where wires of different radii (diameters) meet, especially at angular junctions. If possible, one should model such geometries using the same wire size throughout, and this may require the development of several different models to obtain all of the desired output data, such as element lengths, stub lengths, gain, and source impedance. In addition, segments at and near angular junctions should be consistent in length and short.

+

Let's sample the process by replacing the loads and transmission lines in the half-length dipole with physically modeled transmission line stubs. To do this, we must restructure the entire model. Instead of one wire, we shall need 9, in accord with the upper diagram of the following figure.

+
+ +
+

The wires follow the following table:

+ 
Wire  Conn.  End 1 (x,y,z : in)     Conn.  End 2 (x,y,z : in)
+
+1          -101.21,  0.000,  0.000  W2E1 -54.000,  0.000,  0.000
+2     W1E2 -54.000,  0.000,  0.000  W3E1 -54.000,  0.000, 76.300
+3     W2E2 -54.000,  0.000, 76.300  W4E1 -50.000,  0.000, 76.300
+4     W3E2 -50.000,  0.000, 76.300  W5E1 -50.000,  0.000,  0.000
+5     W4E2 -50.000,  0.000,  0.000  W6E1  50.000,  0.000,  0.000
+6     W5E2  50.000,  0.000,  0.000  W7E1  50.000,  0.000, 76.300
+7     W6E2  50.000,  0.000, 76.300  W8E1  54.000,  0.000, 76.300
+8     W7E2  54.000,  0.000, 76.300  W9E1  54.000,  0.000,  0.000
+9     W8E2  54.000,  0.000,  0.000       101.210,  0.000,  0.000
+

The source is at the center of wire 5. Dimensions have been translated into inches for ease of seeing the modeled structure. The stubs are composed of the same #14 copper wire as the antenna element and are 4" wide by 76.3" long. The stubs are centered at the approximate points where the loads and transmissions lines had been assigned in previous models.

+

The model returns a gain of 1.47 dBi and a source impedance of 18.02 - j0.55 ohms. The gain figure is less than the 1.76 dBi returned by the earlier models. However, remember that the stub now accounts for wire resistance losses. In fact, if we add a resistance of 0.93 ohms to the reactive load of 870.4 ohms in previous models, we find that the R-X model returns the same gain figure of 1.47 dBi. 0.93 ohms resistance in series with a reactance of 870.4 ohms represents a Q of about 936, well higher than what we can achieve with real inductors.

+

The model is also instructive with respect to the length of the stub, which is considerably shorter than what a standard calculation of a shorted stub would yield. #14 wire with 4 inch spacing has an approximate Zo of 580 ohms, which would call for a length of about 130" for the stub. The actual stub is 76.3" long. However, the theoretical stub presumes equal but opposite currents in each leg. Examining the current table returned for this model will show the currents for any given position across the stub lines to be significantly different.

+

(Note: Modelers should be very cautious at this point with respect to the accuracy of the stub length as modeled in NEC-2 or NEC-4. Even 4" apart at 14.15 MHz, the stub wires are very close. NEC may become inaccurate with very closely spaced wires, even when the modeler has observed all cautions regarding using the same wire diameter at angular junctions and regarding the alignment of segments in the parallel wires. This same antenna was modeled in MININEC 3.13 (which has limitations of its own, but not in this area) via ELNEC, and the requisite stub lengths were 1.3 to 1.6 inches longer, depending upon the precise technique used to construct the model. Since the stub length differential approaches 2%, the variance must be considered significant.)

+

Stubs close to the feed point, where the current changes slowly as one moves along the antenna wire, will model physically in close accord with standard parallel transmission line calculations. However, for closest equality of current magnitude on the wires, they must be positioned symmetrically relative to the antenna wire, as shown in the lower left of the figure. If they are positioned linearly, the currents will be unequal due to the unequal distances from the main antenna element. Likewise, stubs positioned further out along the antenna wire, even if positioned symmetrically relative to the antenna wire, will show considerable differences of current on the two parallel wires. At a certain indefinite point along the wire, stubs act less like transmission line sections and more like simple wire extensions necessary to lengthen an antenna element to resonance.

+

The differences in currents along the two stub wires tend to be somewhat less if the stub wires are folded back or folded outward, parallel to the antenna wire and equally spaced from it. When positioned straight down, the unequal currents in the stubs yield a small vertically polarized field that in one plane is down from the main lobe by only -18 dB. It is largely the interaction of this field with the main element field that reduces the source impedance to 18 ohms from the 26 ohms found in the other models.

+

A physical model of the stub-loaded half-length dipole also provides an interesting lesson in operating band width. Relative to the resonant source impedance of 18 ohms, the SWR at 14.0 MHz is 2.50 and at 14.3 MHz is 2.30, well below the modeled figures for lossless transmission lines and lossless inductors. However, the physical model includes its losses, which increase the operating bandwidth.

+

The point of generating this sample physical model of transmission line stubs--usually called "linear loads" among antenna designers--is to illustrate some, but by no means all, of the differences between using lossless and non-interacting mathematical antenna parts and physical lossy and fully interactive antenna parts. Each provide valuable information about anticipated antenna performance and each withholds valuable information. Physical modeling is limited by certain program limitations that force the modeler to depend in part on the use of mathematical substitutes. However, only by thorough modeling in both modes can one develop a good sense for what to expect by way of field adjustment in real antennas.
+

+
+ +

+
+ This last point is as good as any for bringing to a close this inexhaustive but hopefully useful set of exercises in modeling with loads and transmission lines. One could multiply the examples almost endlessly to draw out innumerable subtleties regarding both antennas and models of them. However, I hope that the examples and notes in this series allow you to carry on the process on your own. There is much we can learn about antennas, and antenna modeling can go a little way toward instructing us-- even about its own limitations.
+
+
+ +

+
+

Updated 1-3-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Index
+

Topics: Loading, Modeling, Transmission Line


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The Monoband Log-Cell Yagi Revisited

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+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Although the design had been known earlier, the monoband log-cell Yagi array was briefly popular in amateur literature in the late 1970s and early 1980s, largely through the work of Rhodes, K4EWG, Painter, W4BBP, and Zimmer, K4JZB. The purpose of this series is to contribute a little toward the re-evaluation of the log-cell Yagi, using NEC-4 as a means of analyzing various aspects of the design.

+

In Part 1, I shall look briefly at a superior log-cell Yagi design, and then look at the performance characteristics of some pure Yagi designs that we might use as standards of comparison. In this way, we can begin to see more clearly where the log-cell Yagi fits into the amateur arsenal of antennas.

+

In Part 2, we shall examine some basic principles behind the log cell itself, with especial attention to element phasing. One might also use LPDA principles to show how a log-cell works, but the basics of element phasing can make a number of facets of both Yagi and log-cell Yagi design somewhat clearer.

+

In Part 3, we shall look at several (at least 4) practical 10-meter log-cell Yagi designs. I shall claim no great originality for any of the designs, although each has required considerable effort to optimize all of the operating characteristics, including gain, front-to-back ratio, and SWR bandwidth. All of the antenna designs will feature direct 50-Ohm feedpoint impedances.

+

In the final section, Part 4, we shall examine the V-element question. Does bending half wavelength elements forward contribute anything useful to the performance of the log-cell Yagi? This question, of course, will involve us in a broader question of V-ing any half wavelength element.

+
+ +
+

Part 1: An Introduction to the Log-Cell Yagi and Some Standards of Comparison

+

Part 2: Element Phasing and Log-Cell Design

+

Part 3: Some Practical Log-Cell Yagi Designs

+

Part 4: Vee-ing the Log-Cell Yagi Elements

+
+ +
+

Updated 7-14-2000. © L. B. Cebik, W4RNL. A version of these items appeared in The National Contest Journal. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Index

+

Topics: HF Upper, LPDA, Yagi


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+

The Monoband Log-Cell Yagi Revisited
+ Part 1: An Introduction to the Log-Cell Yagi and
+ Some Standards of Comparison

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Although the design had been known earlier, the monoband log-cell Yagi array was briefly popular in amateur literature in the late 1970s and early 1980s, largely through the work of Rhodes, K4EWG, Painter, W4BBP, and Zimmer, K4JZB.1 Versions can be found in Orr and Cowan's Beam Antenna Handbook, and in the ARRL Antenna Book. In recent times, interest in the design has renewed.

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+ +
+

Fig. 1 shows the outline of a typical monoband log-cell Yagi. It consists of a log-cell driver consisting of 2 or more elements driven with a phasing line that reverses as it connects each element. The element set is fed at the forward-most position, much like a log-periodic dipole array (LPDA). To the driver cell are added a reflector (usually) and one or more directors.

+
+ +
+

In Fig. 2, we see a common variant of the basic log-cell Yagi. In this case, favored especially by K4JZB, the elements are bent forward by about 40 degrees from linear each side of center.

+

Since most of the articles on the log-cell Yagi appear before the advent of computer antenna modeling via MININEC and NEC, the claims for their performance are highly optimistic. One source reports a 6 element log-cell Yagi to have a gain of 16 dB, but it conveniently gives no reference standard. Most sources report gain to be greater than for Yagis of equivalent boom length, but these reports compare the log-cell Yagi with antennas deeveloped before computerized optimization of the Yagi design became commonplace. Perhaps only Rhodes and Painter stress operating bandwidth as a major advantage of the antenna design.

+

With the renewed interest in the antenna, many potential users read the older claims as if they would stand up to modern scrutiny. However, to date, I have seen no re-evaluation of the log-cell Yagi design. Modern analytical tools, such as computer modeling, offer us a chance to better understand the antenna and to assess its place among monoband antennas used by amateurs.

+

The purpose of this series is to contribute a little toward the re-evaluation of the log-cell Yagi, using NEC-4 as a means of analyzing various aspects of the design. Throughout, I shall uses 10-meters as a focal point, since this band is the widest of the upper HF amateur bands. In this introduction, I shall look briefly at a superior log-cell Yagi design, and then look at the performance characteristics of some pure Yagi designs that we might use as standards of comparison. In this way, we can begin to see more clearly where the log-cell Yagi fits into the amateur arsenal of antennas.

+

In Part 2, we shall examine some basic principles behind the log cell itself, with especial attention to element phasing. One might also use LPDA principles to show how a log-cell works, but the basics of element phasing can make a number of facets of both Yagi and log-cell Yagi design somewhat clearer.

+

In Part 3, we shall look at several (at least 4) practical 10-meter log-cell Yagi designs. I shall claim no great originality for any of the designs, although each has required considerable effort to optimize all of the operating characteristics, including gain, front-to-back ratio, and SWR bandwidth. All of the antenna designs will feature direct 50-Ohm feedpoint impedances.

+

In the final section, Part 4, we shall examine the V-element question. Does bending half wavelength elements forward contribute anything useful to the performance of the log-cell Yagi? This question, of course, will involve us in a broader question of V-ing any half wavelength element.

+

A Real Log-Cell Yagi of Considerable Potential

Let's begin with an advanced log-cell Yagi design using a 5-element log-cell plus a reflector and director. This 7-element array was extensively revised from a CB design sent to me by Alan Hughes, ZL3KR. The original had a free-space gain of about 9 dBi, but poor front-to-back ratio. In addition, the SWR and operating characteristics remained usable over only a very narrow portion of the spectrum. +
+ +
+

The basic dimensions of the refined model appear in Fig. 3. The material for the model is 1" diameter aluminum, although similar performance can be achieved with elements as small as 0.5" in diameter.

+

The log-cell is designed as a true LPDA, with elements tapering in length and spacing as one moves forward toward the feedpoint. As one might expect, the reflector is the longest element of the entire set. However, the director is longer than the forward-most element of the log cell. Directors for log-cell Yagis must be cut for the operating frequency, while the forward element of the log cell will be resonant well above the highest operating frequency. The overall length of the antenna is about 14.6' or so, which would fit the antenna easily on a 15' boom.

+
+ +
+

Fig. 4 provides a snapshot of antenna performance across all of 10 meters from 28.0 to 29.7 MHz. The highest free-space gain is at the upper end of the band, with the free- space gain at 28 MHz being just above 8 dBi. The first MHz of the band also shows a very high and stable front-to-back ratio of 30 dB or more, with the figure at 28.5 MHz exceeding 40 dB. The 50-Ohm SWR of this antenna remains well below 2:1 across the entire 10-meter band.

+

Actually building this antenna would require element length adjustment if an element diameter tapering schedule is used. However, nothing in the design would require special construction except perhaps the 100-Ohm phasing line for the log cell. We shall return to this and other practical designs later in the series. First, let's consider whether the antenna is worth building. For that evaluation, we need some standards of comparison.

+

Some Standards of Comparison

Since the days in which log-cell Yagis were claimed as higher gain, more compact beam designs than pure Yagis, the understanding of Yagi design has improved considerably. Lawson's Yagi Antenna Design2 has become the basic volume for modern Yagi design. In addition, there are several Yagi optimizing programs whose results correlate well with NEC models, assuring the builder of predictable results. Consequently, monoband Yagi designs as we approach the end of the century are quite different from those of 15 to 20 years ago. +

Because the most common comparator for a log-cell Yagi is a pure monoband Yagi, perhaps it may be useful to examine some of the operating characteristics of several good Yagi designs. Let's begin with designs I refer to as medium-bandwidth arrays, because they hold their operating characteristics from 28 MHz up to 29 MHz--or close to it. We shall look at three designs in particular.

+

First is a 3-element Yagi on an 8' boom (3-8). The actual overall length of the antenna is about 7.5'. The design is adapted from one of Dean Straw's (N6BV) design in the collection of antennas accompanying the program YA.3 Table 1 provides the modeled dimensions for this and the other two antennas in the medium bandwidth group.

+ 
               Medium-Bandwidth 3- and 4-Element 10-Meter Yagi Dimensions
+
+1.  3-Element, Short-Boom (< 8') Yagi:  0.5" diameter aluminum elements
+Element             Length (")          distance from reflector (")
+Reflector            211.9                     ------
+Driver               193.8                      36.0
+Director             184.9                      90.0
+
+2.  3-Element, Long-Boom (<12') Yagi:  0.5" diameter aluminum elements
+Element             Length (")          distance from reflector (")
+Reflector            206.3                     ------
+Driver               197.0                      62.4
+Director             185.3                     134.5
+
+3.  4-Element, 13'-Boom Yagi:  0.5" diameter aluminum elements
+element             length (")          Distance from Reflector (")
+reflector            207.5                     ------
+driver               195.9                      35.8
+director 1           194.4                      65.5
+director 2           182.2                     152.2
+
+Table 1:  Dimensions of medium-bandwidth Yagis used as standards of comparison
+

The second design is adapted from Brian Beezley's (K6STI) design in the samples accompanying AO.4 This longer-boom design (3-12) is actually about 11.2' long and fits easily on a 12' boom. The third design (4-13), again adapted from an N6BV design, uses 4 elements in under 12.7' of length for an easy fit in a 13' boom.

+

For this exercise, all designs use uniform diameter elements. All are modeled on NEC-4 in free space for the purposes of direct comparison.5 The driven elements of the 3-element beams have been resonated so that SWR figures can be taken relative to the resonant impedance. Because the 4-element beam had a somewhat lower impedance, it has been equipped with a beta match, that is, a shorted transmission-line stub to effect a match compatible with 50Ω coax. The 3-element beams can be matched with a quarter wavelength matching section, or their drivers can be shortened for use with a beta match.

+
+ +
+

Fig. 5 provides a sweep of the free-space gain of each beam design from 28.0 to 29.0 MHz. As one might expect, the 3-element, 8' boom model shows the lowest gain--just above 7 dBi. However, the gain is fairly constant across the selected portion of the band.

+

The long-boom 3-element Yagi shows considerably higher gain, averaging nearly a full dB above the short-boom model. Because the boom length is close to the limit of stable operation for a considerable bandwidth, the curve shows greater changes with increasing frequency.

+

In contrast, the 4-element Yagi shows only slightly higher gain than the 3-element long-boom model. However, the boom length is only about a foot greater than the long-boom 3-element Yagi. What the fourth element provides is more even gain across the selected bandwidth.

+
+ +
+

In Fig. 6, we get a picture of the 180-degree front-to-back ratio of the antennas. Interestingly, the short-boom 3-element Yagi shows the highest peak front-to-back ratio and the highest average front-to-back ratio across the band, never falling below 20 dB. Comparatively, the long-boom 3-element Yagi shows a good peak front-to-back ratio, but the value falls below 20 dB between 28.7 and 28.8 MHz. The 4-element Yagi shows a much lower value of peak front-to-back ratio, but the overall curve is smooth and falls below 20 dB only at the lower edge of the band.

+

From these two parameters alone, we can obtain an impression of the designs. The short-boom 3-element and the 4-element designs are conservative. However, the long-boom 3-element design is pressing the limits of what is possible for that number of elements and boom length. One might obtain even higher gain, but at the expense of an even narrower bandwidth for the operating characteristics.

+
+ +
+

The impression is further deepened in the SWR curves in Fig. 7. The long-boom model shows under 2:1 SWR relative to the resonant impedance through 28.9 MHz. The short-boom 3-element Yagi easily achieves a 2:1 SWR bandwidth relative to the resonant impedance that is wider than the selected band portion. Despite the slight narrowing of the long-boom SWR bandwidth, the use of a beta match would likely permit a wider operating bandwidth at the 50-Ohm matched value. This is illustrated by the 4-element Yagi 50-Ohm bandwidth, which shows under 2:1 SWR across the band. The native bandwidth relative to the antenna's resonant impedance would be about 800 kHz. (However, there may be slight losses associated with operating a beta match well off its optimal values, despite the resulting good impedance match.)

+

These three antennas are good designs of their types, despite the limitations of each. However, they are not adequate to cover the entirety of 10-meters. For that, we must turn to wide-band designs. The dimensions of two wide-band Yagi designs appear in Table 2.

+ 
               Wide-Bandwidth 3- and 4-Element 10-Meter Yagi Dimensions
+
+1.  3-Element, Long-Boom (<12') Yagi:  1.0" diameter aluminum elements
+Element             Length (")          distance from reflector (")
+Reflector            214.0                     ------
+Driver               195.6                      74.5
+Director             176.0                     134.5
+
+2.  4-Element, Short-Boom (8') Yagi:  0.5" diameter aluminum elements
+element             length (")          Distance from Reflector (")
+reflector            212.0                     ------
+driver               205.0                      40.5
+slaved driver        189.0                      44.0
+director             181.0                      96.0
+
+table 2:  dimensions of wide-bandwidth Yagis used as standards of comparison
+

One design is a 3-element Yagi. This version was developed by Joe Reisert, W1JR, and is similar to a design published by Bill Orr, W6SAI, in Ham Radio many years ago.6 The boom would be 12' long to hold an antenna whose inherent length is about 11.2' or so. The other design is my own, which fits on a 8' boom and uses 4 elements. The extra element is a second driver open-sleeve coupled to the first such that the two together cover all of 10-meters.

+
+ +
+

As shown in Fig. 8, the gain curves of the two antennas are very similar, with the 4-element model having a slight edge at the lower end of the band, a function of the dual driver system. It is notable that in a 3-element design, wide-banding the gain requires a boom length similar to that of the higher-gain medium-bandwidth long-boom model--about 12'.

+
+ +
+

The front-to-back curves in Fig. 9 once more do not give one design a major edge over the other. The dip in value below 20 dB occurs at opposite ends of the band for the two designs--but might be made more coincident with slight redesign of element lengths and spacings. The 4-element model shows a very high front-to-back ratio peak around 29 MHz, where all 4 elements show the highest activity in terms of current magnitude.

+
+ +
+

The SWR curves for both wide-band antennas in Fig. 10 are referenced to 50 Ohm without need for a matching system. The 3-element antenna easily achieves a 2:1 operating bandwidth that covers the entire band. The open-sleeve coupled drivers of the 4-element model allow superior performance in this department, with an SWR that never rises to 1.2:1 across the entire band.

+

Relevant Comparisons

The standards of comparison we have just established will be used throughout this series in various ways. To illustrate how we may sensibly use them, we may return to the 7-element log-cell Yagi that we briefly described. The 4-element medium-bandwidth Yagi matches the log-cell Yagi in gain on a boom that is 1-2 feet shorter. However, that antenna is limited to only about 1 MHz of the band, while the log-cell Yagi provides coverage of the entire band. The gain of the log-cell Yagi is from 1 to 1.5 dB greater than either of the 2 wide-band beams discussed. +

In front-to-back ratio, the log-cell Yagi is superior to all of the standard designs, with better than 30 dB until well past 29 MHz and better than 22 dB across all of the band. One of the areas in which well-designed log-cell Yagis excel is in front-to-back ratio. The log-cell Yagi also has a 50-Ohm SWR well under 2:1 across the entirety of the 10-meter band, matching both wide-band Yagis in that performance category.

+

For a given boom length, then, a log-cell Yagi does not make its claim to fame at the end of the 20th century in the gain department. Advances in pure monoband Yagi design give the edge to the pure Yagi. What may have been true of 1980 Yagi designs is no longer true today.

+

However, well-designed log-cell Yagis can achieve very wide operating bandwidths, not only with respect to SWR, but as well with respect to operating characteristics. In particular, the log-cell Yagi has the potential for very smooth front-to-back ratio curves at very high levels across a band as wide as 10 meters.

+

There is, of course, a cost involved in achieving these goals: extra elements and their associated weight. In addition, the log cell requires careful design with considerable attention to the phasing line that interconnects the phased driven elements. To the subject of element phasing we shall turn in Part 2.

+

Notes

+

1. For information on various log-cell Yagi designs see the following items on this incomplete literature list:

+

P. D. Rhodes, K4EWG, and J. R. Painter, W4BBP, "The Log-Yagi Array," QST, Dec, 1976. The main elements of this article are reprinted in The ARRL Antenna Book, 18th Ed., pp. 10-25 to 10-27.

+

Robert F. Zimmer, K4JZB, "Development and Construction of 'V' Beam Antennas," CQ, Aug., 1983, pp. 28-32; and "Three Experimental Antennas for 15 Meters," CQ, Jan., 1983, pp. 44-45.

+

W. I. Orr, W6SAI, and S. D. Cowan, W2LX, Beam Antenna Handbook, pp. 251-253. John J. Meyer, N5JM, "A Simple Log-Yag Array for 50 MHz," Antenna Compendium, Vol. 1, pp 62-63.

+

Reference to log-cell Yagis is also made by L. A. Moxon, HF Antennas for All Locations, 2nd Ed., pp. 199-200, but the design shown is the Rhodes-Painter version in The ARRL Antenna Book.

+

2. James L. Lawson, W2PV, Yagi Antenna Design (ARRL, 1986).

+

3. YA is a Yagi Analysis program developed by Brian Beezley, K6STI, and accompanies recent editions of The ARRL Antenna Book.

+

4. AO is a MININEC analysis and antenna optimizer program by K6STI that is no longer available.

+

5. Two commercial implementations of NEC-4 are available: EZNEC Pro by Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007; and GNEC by Nittany Scientific, 1733 West 12600 South, Suite 420, Riverton, UT 84065. Use of NEC-4 requires licensure from the University of California. Fortunately, most of the analysis in this series can be replicated using more easily obtained versions of NEC-2.

+

6. Joe, Reisert, W1JR, "Yagi/Uda Antenna Design: Part 1: A Different Approach," Communications Quarterly, Winter, 1998, pp. 49-59. Orr's version of the antenna appeared in his regular column for Ham Radio, May, 1990.

+

Also see the Antenna Modeling Programs page for more information about modeling software.

+
+ +
+

Updated 1-15-2000. © L. B. Cebik, W4RNL. A version of this item appeared in The National Contest Journal, Jan-Feb, 2000, 19-22. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 2 +

Go to Log-Cell Yagi Index

+

Topics: HF Upper, LPDA, Yagi


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+

The Monoband Log-Cell Yagi Revisited
+ Part 2: Element Phasing and Log-Cell Design

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Monoband log-cell Yagis have been designed using anywhere from 2 to 5 elements in the log cell itself. They may or may not use a reflector, and the number of directors has ranged from 1 to 3 in the designs I have encountered. Some log-cell designs have been very casual, while others (such as the Rhodes-Painter array1) have adhered to rigorous LPDA design procedures. Since the key to a log-cell Yagi is the log cell itself, it may be useful for us to spend some time exploring some facets of its design.

+

When the log cell has only 2 elements, one cannot distinguish it from a 2-element phased array. Indeed, one can build a successful beam by adding a director to a 2-element phased array--if the phased elements are properly designed. So let's begin with this simplified case and then proceed to more complex log cells.

+
+

The Phasing of 2 Elements

+
+

Element phasing refers to the relative current magnitude and phase of each element in an array of elements. The current magnitude and phase are ordinarily read at the center of elements in symmetrical arrays in which each element length is in the vicinity of 1/2 wavelength.

+

By this accounting, a 2-element Yagi is a phased array, even though only the driven element is fed. The current magnitude and phase on the parasitic reflector is a function of coupled energy from the driver. We alter the current magnitude and phase on the rear element by varying the lengths of the elements and the spacing between them. For a simple 2-element driver-reflector Yagi, we have limited abilities to adjust the rear element relative current magnitude and phasing through modifying the antenna geometry itself. For example, the rear lobe gain of such arrays is rarely more than 12 dB below the main forward lobe.

+

By some judicious alterations of geometry, we can change the rear element current magnitude and phase to improve the depth of the rear null. One of the most remarkable designs in this regard is the Moxon rectangle. Folding the elements toward each other at the ends results in a rear element current magnitude and phase for the element spacing that yields a very deep rear null--often better than 35 dB below the main forward lobe at the design frequency.

+

As an alternative to the limitations of geometric means of altering the rear element relative current magnitude and phase, we can directly feed both elements of the array. Let's adopt the convention that the forward element will be set at a relative current value of 1.0 at a phase angle of zero degrees. With this constant, we may then focus on the current magnitude and phase angle of the rear element (always relative to the constant values of the forward element).

+

The required current magnitude and phase on the rear element will depend upon several variables. First are the lengths of the elements. We may make them equal or unequal. Moreover, we may set the lengths close to resonance or distant from resonance. Each variation will show changes in either or both the magnitude and the phase on the rear element for a desired operating characteristic of the array. For example, if the elements, whether equal in length or unequal, show a feedpoint impedance close to resonance when only the forward element is fed, then the phase angles of equal length and unequal length element sets will be very close in value, although the current magnitudes will vary for a given spacing and operating condition.

+

Second, element spacing will have a major affect on the required rear element current magnitude and phase for a desired operating characteristic. Third, the desired operating characteristic will also alter the current magnitude and phase for any set element lengths and spacing.

+
+ +
+

As a little experiment, let's look at what happens when we phase both elements of two different array pairs, shown in Fig. 1. At a spacing of about 0.125 wavelength, the unequal element pair makes up a very workable 2-element Yagi for 28.5 MHz, when only the forward element is fed. At the same spacing, the equal-length pair is close to resonant, but with a typical dipole pattern.

+

Now let's set as our operating goal achieving a maximum rear null 180 degrees from the peak of the forward lobe. We can define the null as adequate if it exceeds -50 dB relative to the forward lobe. This value would exist only over a tiny bandwidth, but for study purposes, it is a goal that modeling programs, such as NEC-4, can easily show. We shall vary the distance between the elements in 0.05 wl increments. For each distance, we shall change the current magnitude and phase on the rear element until the desired null is achieved.

+ 
                        Phasing 2 Elements for Maximum Rear Null
+                            Equal vs. Unequal Element Lengths
+
+                           Rear Element Current
+Spacing      Spacing       Magnitude    Phase         Free-Space   Front-to-Back
+ wl          inches        (relative)   degrees       Gain dBi     Ratio dB
+
+Designed for Maximum Rear Null:
+Equal-Length Elements (196.8" x2 at 28.5 MHz)
+ 0.05         20.7         1.035        163           6.55         >50
+ 0.1          41.4         1.07         145           6.46         >50
+ 0.15         62.1         1.09         125.5         6.18         >50
+ 0.2          82.8         1.09         106           5.76         >50
+ 0.25        103.5         1.07          87           5.14         >50
+ 0.3         124.2         1.045         69           4.26         >50
+ 0.35        144.9         1.02          51           2.72         >50
+ 0.4         165.7         1.00          34           0.31         >50
+
+Unequal-Length Elements (192" forward, 208.1" rear at 28.5 MHz)
+ 0.05         20.7         0.925        163.3         6.57         >50
+ 0.1          41.4         0.945        145           6.45         >50
+ 0.15         62.1         0.955        126.0         6.19         >50
+ 0.2          82.8         0.95         106.7         5.77         >50
+ 0.25        103.5         0.94          88           5.16         >50
+ 0.3         124.2         0.92          69.5         4.21         >50
+ 0.35        144.9         0.90          51.8         2.73         >50
+ 0.4         165.7         0.88          34.5         0.28         >50
+
+Note 1:  All forward element currents set at a relative magnitude of 1.0 at 0° phase angle.
+
+Note 2:  All values of rear current relative magnitude and phase angle taken when the rear
+null passed -50 dB relative to the forward lobe.
+
+Note 3:  Elements are 1" diameter aluminum.
+
+Table 1:  Phasing 2 elements for maximum rear null using equal and unequal element
+lengths.
+

Table 1 shows the results for both element pairs. As predicted, the current phase for each step is virtually the same for both arrays, but the required current magnitude on the rear element is different according to whether the elements have the same or different lengths. Other element lengths we might have chosen would have resulted in other values.

+

For each increase in spacing, the current magnitude changes very little with each array, but the required phase angle on the rear element shows a continuous decrease. In short, there is no single ideal spacing for achieving a deep rear null. Instead, for any spacing, there is a current magnitude and phase angle that will achieve the null.

+ 
                       Phasing 2 Elements for Maximum Forward Gain
+                            Equal vs. Unequal Element Lengths
+
+                           Rear Element Current
+Spacing      Spacing       Magnitude    Phase         Free-Space   Front-to-Back
+ wl          inches        (relative)   degrees       Gain dBi     Ratio dB
+
+Designed for Maximum Rear Null:
+Equal-Length Elements (196.8" x2 at 28.5 MHz)
+ 0.05         20.7         1.02         173           7.32         7.64
+ 0.1          41.4         1.03         165           7.35         7.19
+ 0.15         62.1         1.02         158           7.23         6.90
+ 0.2          82.8         1.03         152           7.03         6.00
+ 0.25        103.5         1.03         147           6.76         5.03
+
+Unequal-Length Elements (192" forward, 208.1" rear at 28.5 MHz)
+ 0.05         20.7         0.91         173           7.33         7.70
+ 0.1          41.4         0.92         166           7.36         7.22
+ 0.15         62.1         0.92         159           7.24         7.03
+ 0.2          82.8         0.92         150           7.04         6.59
+ 0.25        103.5         0.93         147           6.77         5.13
+
+Note 1:  All forward element currents set at a relative magnitude of 1.0 at 0° phase angle.
+
+Note 2:  All values of rear current relative magnitude and phase angle taken when the
+forward lobe reached a peak gain, beyond which gain fell off.
+
+Note 3:  Elements are 1" diameter aluminum.
+
+Table 2:  Phasing 2 elements for maximum forward gain using equal and unequal element
+lengths.
+

Much of antenna element phasing theory is devoted to the achievement of rearward nulls. Little attention has been given to achieving maximum gain from the array. Let's look at Table 2 to see what the effects of changing space might have on the required rear element relative current magnitude and phase for this goal. For spacing from 0.05 through 0.25 wavelengths, the required current magnitude for each array remains relatively constant. However, the required phase angle decreases with increased spacing, but at far less than the rate for achieving a maximum rearward null. Maximum gain does not occur with the closest spacing, but in the vicinity of 0.1 wl. As one might expect, the front-to-back ratio of two elements becomes mediocre (at best) when the goal is maximum gain.

+

The reason I have presented the table of values for maximum forward gain is simple: when designing an array with a pair of phased elements plus some further element--such as a director--the proper design procedure is to set the phased pair of elements for maximum forward gain. It will be the added element (or elements) that shapes the antenna's operating pattern to the desired specifications.

+
+ +
+

Let's examine a test array consisting of a phased pair plus a director, as shown in Fig. 2. The phased portion of the array consists of unequal-length elements. In this design, a 50-Ohm phase line about 69.3" (for 0.66 VF line) provides the requisite current magnitude and phase transformation. (Although 50-Ohm parallel line is not possible using round conductors, parallel strips can be used, with the velocity factor adjusted back to 1.0. If the boom is RF transparent, then coaxial cable can also be used.) The design frequency for this test array is 28.5 MHz.

+
+ +
+

Fig. 3 shows two things at once. One azimuth pattern show what happens if we omit the director. The phased pair is set for maximum gain--or very close to it. Adding the director increases gain, but even more significantly, the director increases the front-to-back ratio to a very respectable level. (Even in pure Yagi design, reflectors do not control the front-to-back ratio nearly so much as do the directors.)

+
+ +
+

Let's look more closely at the performance of this antenna across the first MHz of 10 meters. Fig. 4 graphs the gain across the band, with the 4-element Yagi presented as a comparator in Part 1 as a standard for comparison. Both antennas are about the same overall length--a bit over 12.5' long. The 3-element array (labeled "3-L 2-cell" on the graphs) shows a very steep gain curve, especially when compared to the stable 4-element Yagi curve. At the design center frequency (28.5 MHz), the 3-element array actually show slightly better gain.

+
+ +
+

The front-to-back curves appear in Fig. 5. The 3-element array shows a very high peak value at the design frequency, but exceeds 20 dB for less than half of the bandwidth in the graph. The stability of the 4-element Yagi front-to-back ratio across the band is self- evident.

+
+ +
+

The native feedpoint impedance of the 3-element array is about 15 + j23 Ohms. This value is amenable to a beta match using an open stub (instead of the usual shorted stub used when the reactance is capacitive). 2:1 SWR operation across all of the first MHz of 10 meters is not possible, as shown in Fig. 6.

+

The narrow-band characteristics of this array illustrate in part what happens when 2- element phased pairs are operated too close to maximum gain. Nevertheless, scaled for any of the WARC band, this array might provide quite good performance with a minimum of elements.

+
+

More Complex Log Cells

+
+

Larger log cells are often designed exactly as one might design a full LPDA, except that the design will be for a single band and also be considerably shorter that an independent LPDA, as illustrated in Fig. 7. The design principles for LPDAs are fully described in The ARRL Antenna Book and in standard professional antenna compendia, so I shall not review them in detail here.2 Most of the math can be passed through a computer design program, such as LPCAD by Roger Cox, WB0DGF.3 To these resources, we can add only a few practical notes.

+
+ +
+

First, many LPDA and log-cell designers select too high a phase-line impedance to achieve maximum gain from the array. My experiences designing a monoband LPDA suggest strongly that the lowest practical phase-line impedance yields the highest gain and overall operating characteristics. This procedure may require careful rethinking of the mechanical aspects of the design, especially implementing a low impedance phase line with double-boom construction or other means.

+

Second, the fatter the elements, the higher the cell gain and the wider the bandwidth for the desired operating characteristics. For monoband cells and LPDAs at 10 meters, elements should be at least 0.5" in diameter, with diameters up to 1" desirable.

+

Third, the closer one attends to making the cell in accord with the LPDA principles in which both element lengths and spacings decrease together, the wider-band the resulting cell and array. One test of a good log cell--as we shall illustrate in more detail in Part 3--is that the feedpoint impedance of the log cell without added parasitic elements should not radically change from the feedpoint impedance with those elements in place.

+

Even with these practical notes in mind, a good modeling program is a major aid to log-cell Yagi and LPDA design. Every cell design requires Tw2 (Twisting and Tweaking), that is, final adjustment of element lengths and spacings, along with phase-line impedance value settings, to produce the desired operating characteristics of the antenna.

+
+ +
+

To illustrate this point, let's look briefly at an LPDA--a log cell without additional parasitic elements--for 10 meters. Fig. 8 shows the outlines of the antenna, which is given in two versions, one with a 217" rear element, the other with a longer 218.9" element. The 75- Ohm phase line can be achieved with twin square booms or with facing aluminum strips. Although the basic dimensions emerged from LPDA calculations, the final dimensions are the result of considerable tweaking.

+

Because this antenna sought to combine smooth curves of both acceptable gain and an adequate adequate front-to-back ratio, a ratio of about 0.90 was selected. That is, each element forward of the one to its rear is about 0.90 of its length. Moreover, the element spacing moving forward is also 0.90 of the spacing between the next elements rearward. As we shall see in Part 3, practical log cell design for log-cell Yagis employs a ratio closer to about 0.95.

+
+ +
+

The gain across the entire span of 10-meters appears in Fig. 9, with the curve for the 4-element wide-band Yagi from Part 1 added for comparison. The LPDAs and the wide-band 4-element Yagi are both 8' long. Version 2 of the LPDA provides slightly higher gain than version 1. Both curves are more stable across the band than is the Yagi curve.

+
+ +
+

Although version 1 of the LPDA has slightly less gain than version 2, the first version shows an overall better front-to-back profile across the band, with a very high peak at 28.5 MHz, as shown in Fig. 10. Both version of the LPDA exceed the Yagi in average front-to- back ratio across the band.

+
+ +
+

In Fig. 11, we have the 50-Ohm SWR curves for all three antennas, none of which requires a matching network. With a peak SWR value of 1.35:1, there is little to choose among the antennas in this department.

+

A 4-element log-cell designed for 10-meters without parasitic elements is capable of better than 7 dBi free-space gain all across the band with excellent front-to-back ratio values and an easy direct coax match--all on an 8' boom. This becomes another standard of comparison for log-cell designs by giving us a new question for our list: what advantages do parasitic elements give us?

+

A partial answer to that question showed up in the narrow-band, high-gain, high-front- to-back design we discussed earlier. We can add some gain and possibly improve the front- to-back ratio. We shall do that by designing our log cells to enhance gain rather than striving for a balance of operating characteristics. Parasitic elements will finish the job of tailoring the pattern.

+

We shall encounter some practical designs that casually design the cell and some that design it very carefully. The results of each practice will show themselves in the resulting antenna performance. But all of that is for Part 3.

+
+

Notes

+
+

1. P. D. Rhodes, K4EWG, and J. R. Painter, W4BBP, "The Log-Yagi Array," QST, Dec, 1976. The main elements of this article are reprinted in The ARRL Antenna Book, 18th Ed., pp. 10-25 to 10-27.

+

2. See The ARRL Antenna Book, 18th Ed., pp. 10-1 to 10-6, plus such professional references as Johnson and Jasik.

+

3. LPCAD has been available at many world wide web archives, but availability may vary in this fast-changing medium. LPCAD 2.8 appeared in 2000.

+
+ +
+

Updated 3-5-2000. © L. B. Cebik, W4RNL. A version of this item appeared in The National Contest Journal, Mar-Apr, 2000, 10-13. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 3 +

Go to Log-Cell Yagi Index

+

Topics: HF Upper, LPDA, Yagi


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+

The Monoband Log-Cell Yagi Revisited
+ Part 3: Some Practical Log-Cell Yagi Designs

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

In this part of our visit to the log-cell Yagi, we shall look at some practical designs. The first two versions--using log cells of 2 and 3 elements, respectively--will involve casual designs, typical of those in some of the past literature. Then, we shall examine more complex designs using log cells with 4 and 5 elements, each carefully constructed on LPDA principles. In the process, we shall also look at a test we can perform to estimate the chances for a log cell Yagi performing to its fullest potential.

+

Each of our design examples will use a reflector and a director in addition to the log-cell driver. Hence, the total element count will be two greater than the number of elements in the cell. As with all of the models in this series, the designs will be for 10 meters. Scaling to 20 meters in one direction and to 6 meters in the other direction are straightforward tasks.

+

All models will use uniform diameter elements. Actual element lengths will have to be lengthened if a builder chooses a tapered diameter schedule. Additionally, the builder will have to devise a plan for implementing the phase line associated with each log cell. High impedance lines can be fabricated from round wires. Low impedance lines may require the use of flat aluminum strap or of a double square boom to effect a satisfactory phase line.

+
+

Casual 4- and 5-Element Log-Cell Yagis

+
+

Our initial models employ either 2 or 3 elements in the log cell, as illustrated in Fig. 1. Both models use 200-Ohm phase lines, with driver elements spaced a standard 2' apart. This spacing accords with a number of articles from the past, although the magic in its selection eludes me. The resulting 4-element log-cell Yagi is 96" (8') long, while the 5-element log-cell Yagi is 138" long (11.5'). Coincidentally, these two lengths coincide closely with the lengths of the medium-bandwidth Yagis introduced in Part 1 as comparators for log-cell Yagis. You should keep the graphs for those antennas handy as we examine the 2 new designs. Both of the antennas in Fig. 1 use 1" diameter elements.

+
+ +
+

Both log-cell Yagis exhibit very smooth gain curves over the first MHz of 10 meters, as demonstrated in the frequency sweep graph in Fig. 2. The 4-element antenna with only 2 elements in the cell has the lower gain level, as one might expect. It coincides roughly with the gain curve for the 8' 3-element Yagi of Part 1. The 5-element antenna provides only about a half dB of additional gain. In contrast, the 3-element Yagi of the same boom length in Part 1 provides an average free-space gain of about 8 dBi, another half dB greater than the log-cell Yagi with the same boom length.

+
+ +
+

Fig. 3 shows that the two log-cell Yagi designs provide fairly mediocre front-to-back ratios. No where in the specified bandwidth does the front-to-back ratio of either antenna reach 18 dB. (In contrast, both Yagi designs exceed 20 dB front-to-back ratio for most of the first MHz of 10 meters.) Where the log-cell Yagis have an advantage is in the feedpoint impedance. Both designs, as illustrated in Fig. 4, provide less than 2:1 50-Ohm SWR from 28 to 29 MHz. By way of contrast, the two Yagi designs require a beta match or comparable network to yield similar results.

+
+ +
+
+ +
+

The two log-cell Yagis, then, require extra elements to provide performance that fails to equal the performance of well-designed 3-element Yagis. One only skirts the issue by saying that the failure results from casual design, since that statement gives no clue of how to distinguish casual from careful design. However, there is a fairly simple modeling test we can perform as a measure of a log-cell Yagi's performance.

+

If we extract the log-cell driver elements from the overall antenna, we may model them independently. In a well-designed log-cell driver, the array will show fairly high gain and a feedpoint impedance that does not depart radically from the values obtained when the driver is part of the total log-cell Yagi.

+

Table 1 provides values for the 2- and 3-element log cells extracted from the antennas we have been examining. The check points at 28, 28.5, and 29 MHz for both cells show fairly low gain, with the 2-element cell especially low. (Although registered for reference, the low front-to-back ratios are of no concern in this test.) The feedpoint impedances of the cells are roughly one-fourth the values obtained for the complete antennas. We shall want to keep these figures in mind as we check more complex and more carefully designed log-cell drivers.

+ 
                   2- and 3-Element Log Cell Independent Performance
+
+Frequency (MHz)                   28.0                28.5                29.0
+
+2-Element Log Cell:
+
+Free-Space Gain (dBi)             4.58                4.70                4.83
+
+Front-to-Back Ratio (dB)          6.88                7.21                7.48
+
+Feedpoint Impedance
+       (R +/- jX Ohms)            13 + j 0            12 + j 5            11 + j11
+
+3-Element Log Cell:
+
+Free-Space Gain (dBi)             7.09                6.93                6.74
+
+Front-to-Back Ratio (dB)          11.6                11.9                12.0
+
+Feedpoint Impedance
+       (R +/- jX Ohms)            11 - j22             9 - j 8             8 + j 3
+
+
+Table 1:  2- and 3-element log cell independent performance.
+
+

A 6-Element Log-Cell Yagi

+
The 6-element log-cell Yagi, with a 4-element log cell, shown in Fig. 5, is adapted and scaled from the Rhodes and Painter log-cell Yagi for 20 meters in The ARRL Antenna Book.1 The log cell has been designed according to LPDA principles, using an element length and spacing ratio of approximately 0.95. This ratio, when applied to a pure LPDA, tends to produce more gain but a lesser front-to-back ratio than lower numbers, for example, the value of 0.90 used in the LPDA design examined in Part 2. The higher ratio value also produces a shorter cell for the same number of elements. The entire antenna, including the reflector and director, requires a 12.2' boom, nearly as long as the 4-element medium-bandwidth Yagi presented in Part 1 as a potential comparator. +
+ +
+

If we extract the log cell from the antenna, we obtain the check-point values recorded in Table 2. Note the relatively uniform gain across the entirety of 10 meters, as well as the 50-Ohm SWR values. According to our test, this log cell promises to form the basis of a good antenna that may be useful across all of 10 meters.

+ 
                       4-Element Log Cell Independent Performance
+
+Frequency (MHz)                   28.0         28.5          29.0         29.5
+
+Free-Space Gain (dBi)             7.24         7.47          7.47         7.29
+
+Front-to-Back Ratio (dB)          17.7         14.0          12.8         13.1
+
+Feedpoint Impedance
+       (R +/- jX Ohms)            95 - j 2     39 - j11      39 + j12     75 + j 4
+
+50-Ohm SWR                        1.90         1.41          1.42         1.51
+
+
+Table 2:  4-element log cell independent performance.
+

Before we look at the modeled performance figures, we should note an additional dimension of this antenna. The phase line impedance is low (75 Ohms). In addition, if we use different element diameters, we obtain results that change to a degree that is greater than the changes we might expect in a Yagi using the same two element diameters. The effects of element diameter on the log cell driver (or on LPDAs) are significant. Therefore, the performance graphs for this antenna will record values for both 1/2" and 1" diameter elements.

+
+ +
+

Free-space gain figures appear in Fig. 6. The fatter element model not only shows a gain peak that is lower in frequency than the thinner version, but as well its peak gain values are higher. Moreover, the curve is flatter. The gain values rival those of the 3-element medium-bandwidth Yagi on a 12' boom, but do not match the values for the 4-element medium bandwidth Yagi on the 13' boom. Both of the Yagis, of course, only covered the first MHz of 10 meters.

+
+ +
+

The front-to-back values are less radically different, as illustrated in Fig. 7. Essentially, the thinner version is capable of a higher peak front-to-back ration. However, both versions of the antenna exhibit better than 20 dB front-to-back ratio across the 28 to 29.7 MHz span.

+
+ +
Both versions of the antenna exhibit acceptable SWR curves across all of 10-meters, as shown in Fig. 8. +
+

A 7-Element Log-Cell Yagi

+
The bandwidth of 10 meters presses the 4-element log cell to its limits, although the 6-element log-cell Yagi does manage to cover the band with good gain, good front-to-back values, and a direct 50-Ohm feed system. We can improve upon the design by adding one more element to the log-cell to obtain the design shown in Fig. 9. The 5-element log cell for this antenna uses the same tapering ratio for elements in the log cell. However, using an additional element allows the longest element to be a bit longer and the shortest element to be a bit shorter. The cost is a longer boom, about 14.6' long in this case. The phase line is 100 Ohms. +
+ +
+

Table 3 provides a look at the performance of the log cell independently of the entire antenna. Gain is even more uniform across the band than for the 4-element log cell, with acceptable 50-Ohm SWR figures. Once more, the front-to-back figures are unimportant in this context, since the parasitic elements will establish those values in the final antenna. In fact, the log cells used in these antennas are designed for gain rather than for a balance of operating characteristics, just as was the case for the 2-element cell in the 3-element array examined in Part 2.) We should expect the overall antenna to reflect the potentials of the log cell.

+ 
                       5-Element Log Cell Independent Performance
+
+Frequency (MHz)                   28.0         28.5          29.0         29.5
+
+Free-Space Gain (dBi)             7.31         7.38          7.42         7.43
+
+Front-to-Back Ratio (dB)          12.0         12.4          13.4         15.2
+
+Feedpoint Impedance
+       (R +/- jX Ohms)            34 - j 6     46 + j14      80 - j 1     46 - j27
+
+50-Ohm SWR                        1.51         1.37          1.60         1.77
+
+
+Table 3:  5-element log cell independent performance.
+

Fig. 10 shows the free-space gain of two versions of the resulting log-cell Yagi, one using 1/2" diameter elements, the other using 1" diameter elements. For contrast, values are also shown for the 4-element wide-band Yagi, introduced in Part 1. We should expect lesser performance from this 8' boom Yagi. If you desire, you may substitute the values for the 8'-boom LPDA.

+
+ +
+

The differences between the half-inch and 1-inch versions of the log-cell Yagi are even more dramatic than for the preceding model, with nearly 0.25 dB differential in gain in places across the band. Values for the half-inch model are similar to those for the 3-element 12-foot boom medium-bandwidth Yagi, but the log-cell Yagi covers the entire 10-meter band. The one-inch model shows only slightly less gain than the 4-element medium-bandwidth Yagi. For either model, the gain curve is very smooth, illustrating the benefit of the extra element in the log-cell.

+
+ +
+

One reason for adding the wide-band 4-element Yagi to the graphs is that it demonstrates the incremental improvement in front-to-back ratio provided by the 7-element log-cell Yagi all across the band, as shown in Fig. 11. Because no element length adjustments were made when changing element diameters, the half-inch model exhibits the superior curve, with a front-to-back ratio better than 30 dB up to 29.5 MHz. The 1" model, with a few added adjustments, can replicate the half-inch model curve, but with a slightly lower peak value. If you refer to the azimuth "snapshot" in Part 1 of this series, you will also learn that the rear quadrants show a very well-behaved rear lobe with no major quartering side lobes to falsify the impression left by the 180-degree front-to-back values.

+
+ +
+

The 50-Ohm SWR curves, shown in Fig. 12, demonstrate that the 7-element log-cell Yagi has a smoother curve than its 6-element counterpart. The curve for the version using 1" diameter elements is flatter, but does not dip quite so low as the curve for the half-inch version. However, adjustments to the exact phase-line characteristic impedance would likely permit either curve to bottom at close to 1:1 SWR. The phase-line characteristic impedance selected for the models represent a standard number, but actual construction would permit refinements.

+
+

Summing Up So Far

+
The development of a log-cell Yagi requires careful attention to the design of the log-cell driver to obtain optimal results. Well-designed log-cell Yagis are capable of good gain, but their chief operating characteristics that fall into the range of excellence (when compared to other available designs) are the front-to-back ratio and the operating bandwidth. As the 6- and 7-element log-cell Yagis demonstrate, the antenna type is capable of well over 6% frequency coverage in a monoband design. +

Designing a log-cell Yagi for gain as we cross into Y2K appears to be an exercise in futility. Although Yagi design in the late 1970s and early 1980s had yet to reap the benefits of computerized optimization, current Yagi design can provide as much or more gain for a given boom length than log-cell designs. The Yagis have the additional advantage of mechanical simplicity, since they do not require the precision construction of a phase line to interconnect the elements in the log cell driver.

+

An interesting example of this point can be found by modeling the 5-element log-cell driven Yagi in Orr and Cowan.2 The antenna uses a 2-element log-cell with a reflector and 2 more directors. This design on a 21' boom is capable of a peak free-space gain of about 9.5 dBi, with a very sharp peak in both the operating characteristics and the SWR curve. The rear lobes were acceptable but the front-to-back ratio exceeded 20 dB for only a narrow bandwidth.

+

I had occasion to study 5- and 6-element 20-meter Yagis of existing design.3 The boom lengths ranges from 45 to 55 feet, corresponding to 22- to 27-foot booms on 10 meters. All of the designs were capable of a free space gain of 10 dBi across all of 20 meters, with better than a 20 dB front-to-back ratio. Some, such as the NW3Z/WA3FET OWA 6-element design, were capable of exceptionally low 50-Ohm SWR values all across the band. In fact, the OWA design can be scaled readily for 10 meters and provide 1 MHz coverage on a 24' boom.4

+

As a gain enhancement, the log-cell driver technique has very limited utility amid current Yagi technology. Its chief merits involve operating bandwidth and front-to-back ratio. However, even here, its utility may be limited when the complexity and weight of the array are factored into antenna design and construction decisions. The medium-bandwidth Yagis described in Part 1 as comparators are fully adequate to provide full coverage of all of the upper HF bands except 10 meters. Only if weight is no concern and if extra front-to-back performance is a necessity on 20 or 15 meters would a log-cell Yagi such as the 6- and 7- element designs seem justified.

+

The natural home of the log-cell Yagi in Y2K is at 10 meters and above, where the bandwidths are more than 3% or so of their center frequencies. However, as we increase frequency, the materials we use for antenna elements increase in diameter relative to a wavelength. So even at VHF, the fat elements of Yagis can provide a wider operating bandwidth that often precludes the need for log-cell technology.

+

These notes are far from exhaustive, and my summary is based only on a few hundred models, the best of which have appeared in this series. Since antenna enthusiasts have an endless appetite for experimentation, it would not surprise me to see these analyses supplanted in the future by better and more ingenious log-cell Yagi designs.

+

One perennial direction of experimentation that we have not examined is the effect of setting the antenna elements into a forward swept Vee. Perhaps we can overstay our welcome for one more part in this series, devoted to this one topic in order to discover whether "V" means "victory" or only half of a "virtual reality."

+
+

Notes

+
+

1. P. D. Rhodes, K4EWG, and J. R. Painter, W4BBP, "The Log-Yagi Array," QST, Dec, 1976. The main elements of this article are reprinted in The ARRL Antenna Book, 18th Ed., pp. 10-25 to 10-27.

+

2. W. I. Orr, W6SAI, and S. D. Cowan, W2LX, Beam Antenna Handbook, pp. 251-253. For a 6-meter adaptation, see John J. Meyer, N5JM, "A Simple Log-Yag Array for 50 MHz," Antenna Compendium, Vol. 1, pp 62-63.

+

3. See "Modeling 6 Long-Boom Yagis" at my web site, ...

+

4. An model of a 10-meter version of the NW3Z/WA3FET OWA is reported in Cebik, "The OWA for 10, 6, and 2 Meters," AntenneX, August, 1999.

+
+ +
+

Updated 5-7-2000. © L. B. Cebik, W4RNL. A version of this item appeared in The National Contest Journal, May-Jun, 2000, 10-13. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 4 +

Go to Log-Cell Yagi Index

+

Topics: HF Upper, LPDA, Yagi


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+

The Monoband Log-Cell Yagi Revisited
+ Part 4: Vee-ing the Log-Cell Yagi Elements

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

One perennial design feature of log-cell Yagis has been the use of elements that form a forward Vee. Perhaps the chief proponent of this design features has been Zimmer, K4JZB, in his 1983 CQ articles on log-cell Yagis, although the idea reappears from time to time in related contexts.1 For one 5-element version of the antenna, the text claims a 16 dB gain, although the frame of reference for the gain figure is not given.

+

All of the designs we have explored in the first three parts of this series have used linear elements. Given the wide-spread repute of Vee-ed elements to improve gain, directivity, or other aspects of beam performance, it may be useful to explore the matter further. Since Vee-ed elements present no challenges to the limits of NEC, we may use this modeling software to develop some appropriate comparisons between various types of antennas using linear and Vee-ed elements.

+
+

The Vee-ed Dipole

+
In order to understand the performance of Vee-ed beams, we should begin with the Vee-ed dipole, that is a dipole that is bent forward from linear by a certain number of degrees on each side of center. Fig. 1 shows the general outline of the models used in this exercise. A standard 200" dipole length is used throughout, with 1" aluminum tubing as the material. The model uses a short, 3-segment, linear wire at the center of the antenna in order to provide the feedpoint segment with equal length segments on either side. +
+ +
+
+ Fig. 1 General outlines of linear and horizontally-Vee-ed dipoles. +
+

The degree of Vee-ing refers to the angle made on each side of the antenna relative to a line that would represent a linear element. Hence, 10 degrees of Vee-ing would bend each side of the dipole 10 degrees forward of the linear line. None of the angles used in this test presses any NEC limitation for accuracy of results.

+ 
                        Gain, Front-to-Side Ratio, and Impedance
+                        of Dipoles at Various Degrees of Vee-ing
+
+Forward Angle       Free-Space          Front-to-Side        Feedpoint Impedance
+Relative to a       Gain (dBi)          Ratio (dB)           (R +/- jX Ohms)
+Linear Dipole
+(Degrees)
+
+  0 (linear)        2.15                > 30                 77 + j18
+ 10                 2.12                  21                 76 + j17
+ 20                 2.02                  15                 70 + j15
+ 30                 1.85                  12                 62 + j10
+ 40                 1.62                   9                 50 + j 2
+ 50                 1.37                   7                 37 - j 8
+
+Note 1:  The total length of the 1" diameter aluminum dipole element is 200" to yield a
+feedpoint impedance close to resonance at 28.5 MHz when each side is bent forward 40
+degrees from linear.  See Fig. 1 for the general outline of the test model.
Table 1: Gain, front-to-side ratio, and impedance of dipoles at various degrees of Vee-ing. +

Table 1 provides an indication of what occurs when a dipole element is vee-ed forward. The free-space gain of the antenna decreases for each level of Vee-ing. As well, the feedpoint impedance decreases. Perhaps most significantly, the front-to-side ratio also decreases. Fig. 2 compares the free-space azimuth patterns of a linear and a 40-degree Vee-ed dipole and graphically illustrates the reduction in side rejection for the Vee-ed version.

+
+ +
+
+

Fig. 2 Free-space azimuth patterns for linear and Vee-ed dipoles at 28.5 MHz.

+
+

When used as an inverted Vee antenna with the legs angled downward, the reduced side rejection is sometimes listed as an advantage, despite the reduction in broadside gain. However, when the dipole is Vee-ed horizontally, nothing is gained by way of directivity or other effect that might be useful in a multi-element beam antenna. Since all of the designs that we shall consider use the 1/2 wl dipole as their starting point, we should not have any expectations that Vee-ing the elements will yield added performance in any particular area.

+

Perhaps what lies behind the idea that Vee-ing elements may yield added performance is the concept of the Vee-beam, a very old and simple antenna design. However, the Vee-beam is always many wavelengths long and produces many lobes and nulls. When the designer chooses the proper angle between the elements, the main lobes combine to form a single very strong bi-directional lobe set along the line bisecting the angle between wires. There will almost always be lesser lobes and nulls to the sides, that is, roughly broadside to the wires. If one terminates each of the far ends of the Vee with resistors to ground, then the Vee-beam develops a unidirectional pattern.

+

However, the 1/2 wl dipole develops only a single lobe ar right angles to the wire, resulting in a bi-directional pattern. There are no lobes at angles away from broadside that may combine into a single stronger lobe. The dipole lobes can only be distorted from their shape when produced by a linear wire.

+
+

2-Element Vee-ed Beams

+
+
+ +
+
+

Fig. 3 General outlines of linear and horizontally-Vee-ed 2-element Yagis.

+
+

Rather than leave the subject with only the dipole as an indicator of the performance of Vee-ed antenna arrays, let's look at a few beam designs, beginning with 2 elements. Throughout, we shall bend the elements forward 40 degrees as a standard level of Vee-ing. Fig. 3 shows the general outline of linear and Vee Yagis using a driver and reflector in each case. The driver length is 196" for both antennas, and the reflector is 210" long. Element spacing is 48". The Vee-ed version of the antenna shows a feedpoint impedance of 23 + j 4 Ohms at 28.5 MHz, close to resonance. When stretched to linear shape, the impedance rises to 36 + j30 Ohms.

+
+ +
+
+

Fig. 4 Free-space azimuth patterns for linear and Vee-ed 2-element Yagis at 28.5 MHz.

+
+

Fig. 4 provides comparative free-space azimuth patterns for the two versions of the Yagi. The Vee-ed version has a free-space gain of only 5.45 dBi. compared to the linear version gain of 6.09 dBi. Both antennas have front-to-back ratios of about 10.8 dB, but the Vee shows far less side rejection than the linear antenna. This result is, of course, consistent with the results of our dipole test.

+

Since our ultimate goals is to evaluate Vee-ed element use in log-cell Yagis, we may revise the outline in Fig. 3 to provide each element with a separate feed point. In this manner, we may directly control the relative current magnitude and phasing on each element. Let's try this experiment to see if Vee-elements promise any improved performance when independently phased.

+
+ +
+
+

Fig. 5 Free-space azimuth patterns for linear and Vee-ed 2-element phased arrays at 28.5 MHz, using separate feeds for each element.

+
+

When independently phased for a maximum rear null, the Vee-ed version shows a free-space forward gain just below 5.9 dBi when the rear element is set at a relative current magnitude of 0.94 and a phase of 141 degrees (with the forward element set to a magnitude of 1.0 at a phase angle of zero degrees). For a maximum null to the rear, the comparable linear rear element must be set at a current magnitude of 0.98 with a phase angle of 139 degrees. Under these conditions, the linear phased array shows a forward gain of nearly 6.4 dBi. Fig. 5 shows free-space azimuth patterns that illustrate the pattern differences. Besides the half-dB gain differential, the low side rejection of the Vee version is clearly evident.

+
+ +
+
+

Fig. 6 Free-space azimuth patterns for a Vee-ed 2-element phased array at 28.5 MHz, using a phasing line between elements.

+
+

There are no simple means of obtaining the optimal phasing conditions for the Vee-ed phased array. The closest that I have come is the use of a 35-Ohm phasing line from one element to the next. Higher values of phase-line characteristic impedance yield lower performance figures. However, unlike available lines, the modeled line required a velocity factor of 1.0, with lesser values producing poorer results. Fig. 6 shows the resulting free-space azimuth pattern, which has a forward gain of just over 5.6 dBi and a front-to-back ratio of just under 17 dB.

+

All-in-all, we must account the results of our attempt to Vee 2-element arrays a disappointment. However, the results should not be surprising, since such arrays depend for their performance directly upon the dipoles that compose them.

+
+

The Vee-ed Log-Cell Yagi

+
The results of our experiments with 2-element parasitic and phased arrays unfortunately do not bode well for the performance of Vee-ed log-cell Yagis. However, with a multi-element cell and additional parasitic elements, we cannot dismiss the possibility of superior Vee performance without suitable testing. Therefore, I have taken one of Zimmer's designs--a 5-element log-cell Yagi--and developed both linear and Vee-ed models. The general outline of the Vee-ed version appears in Fig. 7. +
+ +
+
+

Fig. 7 General outline of a 5-element Vee-ed log-cell Yagi.

+
+

The reflector for each model is 211.5" long and placed 48" behind the 3-element log-cell. Working from the rear forward, the cell elements are 201', 198.8", and 196.6", each spaced 24" from the next. The director is placed 48" forward of the cell and is 187.6" long. The phase-line characteristic impedance producing the most usable results was 200 Ohms.

+
+ +
+
+

Fig. 8 Free-space azimuth patterns for linear and Vee-ed 5-element log-cell Yagis at 28.5 MHz, using 200-Ohm phase lines between driver cell elements.

+
+

Fig. 8 shows free-space azimuth patterns for the linear and the Vee-ed versions of this antenna. The linear version is virtually identical to the 5-element log-cell Yagi examined in Part 3 of this series. Once more, the Vee-ed version of the antenna shows lower gain with a reduced front-to-side ratio.

+

For the Vee-ed log-cell Yagi, the relative current magnitude and phasing on the three driven elements at 28.5 MHz with the 200-Ohm phasing line--from front to rear--was 0.87 at 15.9 degrees, 0.52 at 147.2 degrees, and 0.32 at 171.4 degrees. These values offer us one more experimental possibility. Suppose we separately feed each element of the log cell and optimize the current magnitude and phasing on each element. For example, if we set the forward element at a magnitude of 0.7 and a phase angle of 20 degrees, the middle element at 0.67 at 145 degrees, and the rear element at 0.4 at 169 degrees, we can increase both the gain and the front-to-back ratio of the array. The resulting free-space azimuth pattern appears in Fig. 9.

+
+ +
+
+

Fig. 9 Free-space azimuth patterns for a Vee-ed 5-element log-cell Yagi at 28.5 MHz, using separate feeds for each element.

+
+

For a further comparison across the first MHz of 10 meters, we can plot the free- space gain values of the linear and 200-Ohm phase-line Vee array against the Vee array with separately fed driver elements. Fig. 10 shows the results. The linear array exceeds the gain of the phase-line-fed Vee array by an average half dB. The hypothetical separately fed array has slightly more gain than the linear array.

+
+ +
+
+

Fig. 10 Free-space gain from 28-29 MHz of log-cell Yagis: linear, Vee-ed with a phase line, and Vee-ed with separate feeds.

+
+

In Fig. 11, we can see the potential front-to-back values for each antenna, with the linear and phase-line-fed Vee-ed array having quite similar values. The hypothetical array using separately fed driver elements is potentially capable of considerably better front-to-back performance.

+
+ +
+
+

Fig. 11 Front-to-back ratio from 28-29 MHz of log-cell Yagis: linear, Vee-ed with a phase line, and Vee-ed with separate feeds.

+
+

The difficulty with both the phase-line-fed Vee array and the alternative with separately fed drivers is feeding the system. The Vee-ed array with a phase line shows a tendency toward rapid feedpoint impedance changes, ranging from 50 Ohms at 28 MHz down to about 10 Ohms at 29 MHz. Indeed, experiments that varied the spacing of the reflector and the director failed to come up with a relatively constant feedpoint impedance for the first MHz of 10 meters. The smooth 50-Ohm direct feed obtained by the linear model (which was far from the best of the log-cell Yagis examined in Part 3) is wholly absent from the Vee-ed model. Hence, the Vee-ed model with a phasing line would be useful for only a narrow operating bandwidth.

+

With separate feed for each driver element, the problem becomes insurmountable for the average amateur construction project. I know of no practical way to effect separate feeds for each element short of phasing networks for each element. The builder would also need the ability to measure currents and phase angles to a degree of precision beyond most ham shops.

+
+

The Bottom Line

+
In the entire set of experiments reported here--plus a considerable number of other models--Vee-ing elements of 1/2 wl-based arrays has proven to be an exercise in futility. Throughout, the Vee-ed versions always exhibited lower gain and reduced side rejection relative to comparable arrays using linear elements. The comparative azimuth patterns shown in this final part of the series are truly representative of the total collection of Vee-ed models run. +

Since each Vee-ed model shows its heritage in the Vee-ed dipole, we may take the performance of that basic antenna in comparison to a linear dipole as correctly indicative of the performance reduction likely to occur in any vee-ed array when set over and against a comparable array of linear elements. This note, of course, applies only to arrays based upon the 1/2 wl dipole. As we noted at the very beginning, multi wavelength Vee-beams are another matter entirely.

+

The myth of the Vee-ed element array of 1/2 wl elements has perhaps persisted too long in amateur circles. I hope these notes help dispel it to some degree. More to the point, if a monoband log-cell Yagi is the design of choice to meet a given set of operating needs, then the best of the linear element log-cell Yagis examined in Part 3 will likely always be a better selection than a Vee-ed counterpart.

+
+

Notes

+
+

1. Robert F. Zimmer, K4JZB, "Development and Construction of 'V' Beam Antennas," CQ, Aug., 1983, pp. 28-32; and "Three Experimental Antennas for 15 Meters," CQ, Jan., 1983, pp. 44-45.

+
+ +
+

Updated 7-14-2000. © L. B. Cebik, W4RNL. A version of this item appeared in The National Contest Journal, Jul-Aug, 2000, 11-14. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Log-Cell Yagi Index +

Topics: HF Upper, LPDA, Yagi


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+

4-30 MHz LPDA Design Concepts

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Government, military, and some commercial enterprises have employed wide-range LPDAs for coverage of the HF region from about 4 to 30 MHz. The appeal of using a single antenna for the entire frequency range is multi-faceted. A single antenna permits frequency scanning and rapid changes of frequency without the need for antenna retuning or switching. The directional pattern of the LPDA offers gain in the desired direction at all frequencies, as well as QRM and QRN reduction from other directions.

+

A Review of single LPDA Design Potential

+

However, the single LPDA designed to cover the entire HF spectrum from about 4 to 30 MHz suffers some serious limitations. In a pair of articles in QEX ("Notes on Standard Design HF LPDAs," May-August, 2000), I explored some of the problems and pitfalls of designing LPDAs with a wide passband--something of the order of a 10:1 frequency range. It may be useful to review some of the outcomes of the study.

+
+ +
+

Fig 1 provides outlines of three different LPDAs, each the best of its boom length used in the earlier study. The following table provides some of the basic data about each antenna model.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Boom        No. of      Phase Stub? Element
+      Length      Elements    Line                    Treatment
+      feet                    Impedance
+1.     65'        20          200         No          Tau-tapered diameter
+2.    100'        23          200         Yes         Tau-tapered diameter
+3.    164'        26          150         Yes         Tau-tapered diameter
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The reference to Tau-tapering of the element diameter refers to increasing the diameter of each element--referenced to the most forward elements--by the inverse of the value of Tau used to establish the basic design. In general, element diameters ranged from 0.5" for the forward element to about 6.5" for the rear-most element. This practice maintains a relatively constant length-to-diameter ratio for the design.

+

The shortest LPDA in the lot was specifically designed for 4-30 MHz and has a 132.1' rear element. The longer boom designs set the low frequency cut-off at 3 MHz and have a 167.3' rear element.

+

The following graphs explore the performance potential of the resulting LPDAs in 0.25 MHz increments. To make the graphs readable, I have divided each parameter into 2 charts, one covering 3.5-17 MHz, the other covering 17.25-30 MHz. Vertical axis scales have been matched so that the two graphs for each parameter will join seamlessly.

+
+ +
+
+ +
+

Fig. 2 and Fig. 3 provide the gain potential of the LPDA designs. The shortest- boom model is obviously gain deficient until it reaches 5 MHz or higher. As well, it exhibits an obvious weakness at about 7.75 MHz. Above 10 MHz, the average free-space gain fluctuates around the 6 dBi mark.

+

The 100' boom model has no obvious weaknesses in gain across the spectrum, but the added 35' of boom and 3 additional elements only raises the average gain to about 6.3 dBi (free-space). However, the 100' boom length is already a major mechanical challenge for support and rotation.

+

The longest model averages just above 7 dBi free-space gain, with one odd peak at 8.5 MHz. To achieve this gain, we need at least 26 elements and a boom of nearly 165'.

+
+ +
+
+ +
+

Fig. 4 and Fig. 5 present the potential 180-degree front-to-back ratio performance potential of the big LPDAs. Only the longest LPDA model sustains a front-to-back ratio of better than 20 dB. The mid-size model achieves that level of performance above about 8 MHz, while the shortest model slowly approaches the 20-dB level in the 12-14 MHz range. Below 5 MHz, the front-to-back ratio of the 65' model drops below 10 dB.

+
+ +
+
+ +
+

The VSWR curves of Fig. 6 and Fig. 7 use different reference impedances. Each reference value was chosen to provide the flattest possible SWR curve. Of the three wide-range LPDA models, only the longest maintains an SWR of less than 2:1 across the design range (with a 75-Ohm reference). The mid-size model, using a 95-Ohm reference, shows significant peaks above 2:1 in the upper frequency region--where SWR in the HF region becomes a more important factor in terms of line losses. The shortest model, using an 85-Ohm reference, shows similar upper HF peaks as well as some narrow peaks at the low end of the spectrum.

+

Not evident in these graphs is the very high variability in the behavior of the antenna patterns. The shorter the boom length, the wider the frequency range over which we encounter pattern distortion. The forward lobe may be shaped like a garden spade or even develop a minor double lobe. Rear patterns tend to broaden so that the 180-degree front-to-back ratio is no longer a reasonable guide to rear lobe behavior. Rear side lobes down by only 15 dB are common. These expanded rear lobes are marks of incipient harmonic activity in lobes to the rear of those most active at a given frequency. Hence, the problems increase with frequency.

+

If we take these models as typical of LPDA performance for the boom lengths indicated--and well-engineered exceptions certainly are possible--we are faced with a dilemma. The shortest boom is most easily maintained at operating height but has marginal performance at best. However, to attain performance roughly on a par with a 2-element quad--but across the wide passband--we need boom lengths that present very major mechanical challenges. The challenges do not merely include erecting the array, but also involve wind, snow, and ice load factors.

+

The single LPDA for the entire HF range concept arose over 20 years ago. At that time, the basic idea was a single antenna for a single receiver or transceiver, with a single feedline coming to the equipment's single antenna connection. In the intervening years, a number of technical advances have appeared that seem not yet to have affect HF LPDA use for complete spectrum coverage. Perhaps it is time to rethink the LPDA for 4-30 MHz.

+

Not 1, But 3

+

In the intervening years, a number of techniques for antenna selection or "polling" have appeared, and the technology is widely applied to cell and related services wherever higher gain and narrower beamwidth antennas are required. Such techniques might easily be applied to wide-range HF service as well.

+

In addition, for most applications requiring the coverage or scanning of the entire HF range, neither resources nor real estate are a major problem. Hence, one might well erect multiple towers, each one holding an LPDA optimized to the degree possible for a portion of the total frequency range. The feedlines can be brought to a central location for polling and then routed to the equipment.

+

The entire 4-30 MHz range is nearly 3 octaves in bandwidth. We may easily subdivide the design problem into 3 roughly 2:1 frequency-range models. 2:1 bandwidth LPDAs are significantly easier to design than a single antenna with nearly a 10:1 frequency range. To make the design challenge more difficult but the mechanical and maintenance problem less daunting, let's set a 50-56 foot limit to the boom in each case.

+

It might be tempting to suggest placing all three antennas on a single rotating tower. Such a system might well be made to work in some cases. However, it presents another dilemma. Mechanically, the antenna for the lowest portion of the range wants to rest at the lowest of the 3 levels, where mechanical support is greatest. However, electronically, it needs to be at the highest level for transmitting and receiving effectiveness in terms of lower elevation angles of radiation.

+

For the moment, we can set aside the problem of support systems and look in a more focused way at the electrical design of the individual LPDAs. For convenience, we shall divide the spectrum into 3 sections. The Low Range will run from 4 to 7 MHz. The Middle Range will cover 7 to 14 MHz. The High Range will complete the picture with 14 to 30 MHz coverage. The ratio of highest to lowest frequencies for each antenna increase with frequency, since we have limited the boom length. It is easier to reach beyond the 2:1 target ratio at the upper HF region than it is even to reach that ratio at the low end of the spectrum.

+

As well, the system of LPDAs in this design exercise has considerable overlap, as shown in the following table:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Range       Boundary    Low Freq.         High Freq.        Overlap as a
+            Frequency   Limit for         Limit for         Percentage of
+                        <2:1 vswr         <2:1 vswr         boundary frequency
+low         7           3.75 MHz          7.70 MHz          12%
+middle      14          6.85              15.4              16%
+high        --          13.1              30+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The overlapping coverage of the arrays points to a further advantage of a triple LPDA antenna farm for covering the HF spectrum: if one antenna suffers damage, the other two remain in operation. As well, some of the gap in coverage is filled by the remaining antennas.

+

The three antennas forming the array for this exercise have the following basic properties.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Range       No. El.,    Element     Tau         Sigma       Phase       Stub?
+            Boom Len.   Size/Type                           Line Zo
+Low         13          Tau-taper   0.9245      0.0250      200 Ohms    Yes
+            53.0'       2.5-6.4"
+Middle      16          1.0"        0.9300      0.0400      150         Yes
+            56.17'      alum.
+High        22          0.5"        0.9500      0.056       100         No
+            55.83'      alum.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In all three designs, the value of Tau was kept high to maintain a relatively high element density for better low-end performance. As well, the highest frequency of use was set well above the highest frequency to be used to sustain gain at the upper spectrum end. However, each antenna in the set presented unique design challenges, so each deserves an individual examination.

+

The Low-Range LPDA

+
+ +
+

Fig. 8 provides an outline of the low-range antenna designed to cover 4 to 7 MHz. Clearly apparent is the relatively close spacing of the elements that results from the selection of a low Sigma value. Indeed, the value of Sigma is below that recommended in design calculations. Hence, the design was developed by a good bit of trial-and-error modeling. The values of Tau and Sigma, suited to the design length of the boom, also dictated the narrower frequency coverage for this array (1.75:1).

+

The low-range model has some interesting features. First, it is the only model of the set to require Tau-tapered elements to achieve the design goals. The elements range from 2.5 to 6.4 inches in diameter, as shown in the following partial model table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+13 el 53' 3.8-7.5 MHz                Frequency = 4.35  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1            0.000,-64.729,  0.000         0.000, 64.729,  0.000 6.41E+00  29
+2            6.559,-60.750,  0.000         6.559, 60.750,  0.000 5.93E+00  27
+3           12.622,-56.435,  0.000        12.622, 56.435,  0.000 5.48E+00  25
+4           18.228,-52.173,  0.000        18.228, 52.173,  0.000 5.07E+00  23
+5           23.410,-48.233,  0.000        23.410, 48.233,  0.000 4.69E+00  21
+6           28.201,-44.591,  0.000        28.201, 44.591,  0.000 4.33E+00  19
+7           32.630,-41.223,  0.000        32.630, 41.223,  0.000 4.00E+00  17
+8           36.724,-38.110,  0.000        36.724, 38.110,  0.000 3.70E+00  17
+9           40.509,-35.417,  0.000        40.509, 35.417,  0.000 3.42E+00  15
+10          44.009,-32.667,  0.000        44.009, 32.667,  0.000 3.16E+00  13
+11          47.244,-30.167,  0.000        47.244, 30.167,  0.000 2.93E+00  13
+12          50.235,-28.750,  0.000        50.235, 28.750,  0.000 2.70E+00  11
+13          53.000,-26.583,  0.000        53.000, 26.583,  0.000 2.50E+00  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The stub used in the model is 1.5' of 600-Ohm shorted line.

+
+ +
+

The free-space gain of the array from 4 to 7.5 MHz appears in Fig. 9. Only above 7 MHz does the gain drop below 6 dBi. (Do not let the steep curve mislead you into thinking that gain varies by a wide margin. The Y-axis spreads a relatively small range--0.5 dB--over a large linear distance.) The gain in this frequency region is similar to that of the 100' wide-range model, but with half the boom length. For the remainder of the frequency span, gain will be higher. Indeed, part of the design conception was to limit lower gain performance to the smallest possible portion of the entire passband. No other combination of Tau and Sigma within the general limit of the boom length approached these gain figures for the entire 4-7 MHz range.

+
+ +
+

The 180-degree front-to-back ratio shows, in Fig. 10, generally increasing values as the frequency increases. Although low by upper HF standards, the values are in keeping with the general gain levels shown in Fig. 9.

+
+ +
+

Fig. 11 provides a 60-Ohm referenced VSWR curve for the array. It surpasses 2:1 at two points: at 6.5 and 7.25 MHz. In general, VSWR values above 2:1 but below 2.5:1 may be considered acceptable in the lowest portion of the spectrum where even coaxial cable losses are close to negligible at these levels. If equipment is sensitive to the reflected voltage taken from a line sample, one might well add one of the newer automatic antenna tuners to the line to ensure full power output.

+

Short-boom LPDAs for the lower HF range press LPDA design not only up to its limits, but beyond. However, by judicious experimental modeling, it is possible to design an acceptable LPDA for the lowest frequency range without limiting the remainder of the HF spectrum to the same level of performance. Even a 53' boom length will present mechanical challenges, since the elements will be very long. The longest element is nearly 130'. The design element diameter can be approximated either through the use of open-frame triangular structures or by multiple strands of widely spaced wire.

+

The Mid-Range LPDA

+
+ +
+

As shown in Fig. 12, the mid-range LPDA in the set is quite standard in appearance. The 16-element design using 1.0" diameter aluminum elements requires a 56.17' boom and a 150-Ohm phase-line. The following wire table provides element details.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+.93/.04 6.88-15 MHz                      Frequency = 13  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-36.200,  0.000         0.000, 36.200,  0.000 1.00E+00  27
+2            5.904,-34.150,  0.000         5.904, 34.150,  0.000 1.00E+00  27
+3           11.395,-31.915,  0.000        11.395, 31.915,  0.000 1.00E+00  25
+4           16.501,-29.681,  0.000        16.501, 29.681,  0.000 1.00E+00  23
+5           21.250,-27.603,  0.000        21.250, 27.603,  0.000 1.00E+00  21
+6           25.667,-25.671,  0.000        25.667, 25.671,  0.000 1.00E+00  21
+7           29.774,-23.874,  0.000        29.774, 23.874,  0.000 1.00E+00  19
+8           33.594,-22.203,  0.000        33.594, 22.203,  0.000 1.00E+00  19
+9           37.146,-20.649,  0.000        37.146, 20.649,  0.000 1.00E+00  17
+10          40.450,-19.203,  0.000        40.450, 19.203,  0.000 1.00E+00  15
+11          43.522,-17.859,  0.000        43.522, 17.859,  0.000 1.00E+00  15
+12          46.380,-16.609,  0.000        46.380, 16.609,  0.000 1.00E+00  15
+13          49.037,-15.525,  0.000        49.037, 15.525,  0.000 1.00E+00  13
+14          51.520,-14.654,  0.000        51.520, 14.654,  0.000 1.00E+00  13
+15          53.892,-14.042,  0.000        53.892, 14.042,  0.000 1.00E+00  11
+16          56.167,-13.692,  0.000        56.167, 13.692,  0.000 1.00E+00  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 72.4' longest element will likely require an equivalent diameter considerably in excess of 1 inch, while the 27' shortest element might well have an equivalent uniform diameter closer to a half inch. Tau-tapering the elements in this array had no significant effect upon the performance. However, a shorted stub consisting of 2' of 600-Ohm line proved useful.

+

Although the bulk of the elements adhere to the 0.93 Tau and 0.04 Sigma values, the rear-most and forward-most elements were subjected to Tau-circularization to optimize performance. A close look at Fig. 12 will reveal that the element tips do not form a straight line, but a small ogee curve.

+
+ +
+

As shown in Fig. 13, the average free-space gain of the array is between 7.1 and 7.15 dB, about the same as the gain of a 2-element quad. Note that this performance was achieved only by the 164' full-spectrum LPDA model--about 3 times longer than our mid-range LPDA. Because the boom length has been limited, resulting in a fairly low value of Sigma, the upper end of the spectrum shows increasing fluctuations, for a total gain variance of about 0.35 dB from 7 to 14 MHz. The gain drops below 6.9 dBi only within the overlap region with the high- range LPDA.

+
+ +
+

Fig. 14 shows the 180-degree front-to-back ratio across the passband. The ratio remains above 20 dB, with well-control rear lobes, up to 14 MHz.

+
+ +
+

The 50-Ohm SWR curve in Fig. 15 shows the mid-range LPDA to maintain under 2:1 across the pass band. The curve would be slightly better using a reference impedance of 55 Ohms.

+

The mid-range LPDA is in every way conventional, including the circularized Tau factor used to modify the original design that emerged from initial calculations. It provides good performance for the boom length and number of elements.

+

The High-Range LPDA

+

The high-range LPDA requires only scant comment, since it has appeared before in these pages.

+
+ +
+

As the outline in Fig. 16 reveals, the design is the same 14-30 MHz design on a 55.83' boom developed in detail in the past few months. The design uses a parasitic director to enhance upper range performance more than circularizing Tau alone can do. The following wire table will review the dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21+dir 55.8            Frequency = 28  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-18.025,  0.000         0.000, 18.025,  0.000 5.00E-01  25
+2            4.015,-17.083,  0.000         4.015, 17.083,  0.000 5.00E-01  23
+3            7.829,-16.167,  0.000         7.829, 16.167,  0.000 5.00E-01  23
+4           11.452,-15.367,  0.000        11.452, 15.367,  0.000 5.00E-01  21
+5           14.894,-14.598,  0.000        14.894, 14.598,  0.000 5.00E-01  21
+6           18.164,-13.868,  0.000        18.164, 13.868,  0.000 5.00E-01  19
+7           21.271,-13.175,  0.000        21.271, 13.175,  0.000 5.00E-01  19
+8           24.222,-12.516,  0.000        24.222, 12.516,  0.000 5.00E-01  17
+9           27.025,-11.890,  0.000        27.025, 11.890,  0.000 5.00E-01  17
+10          29.689,-11.296,  0.000        29.689, 11.296,  0.000 5.00E-01  15
+11          32.219,-10.731,  0.000        32.219, 10.731,  0.000 5.00E-01  15
+12          34.623,-10.195,  0.000        34.623, 10.195,  0.000 5.00E-01  15
+13          36.907, -9.685,  0.000        36.907,  9.685,  0.000 5.00E-01  13
+14          39.076, -9.201,  0.000        39.076,  9.201,  0.000 5.00E-01  13
+15          41.137, -8.741,  0.000        41.137,  8.741,  0.000 5.00E-01  13
+16          43.095, -8.304,  0.000        43.095,  8.304,  0.000 5.00E-01  11
+17          44.955, -7.888,  0.000        44.955,  7.888,  0.000 5.00E-01  11
+18          46.722, -7.494,  0.000        46.722,  7.494,  0.000 5.00E-01  11
+19          48.400, -7.119,  0.000        48.400,  7.119,  0.000 5.00E-01   9
+20          49.995, -6.763,  0.000        49.995,  6.763,  0.000 5.00E-01   9
+21          51.510, -6.425,  0.000        51.510,  6.425,  0.000 5.00E-01   9
+22          55.833, -7.392,  0.000        55.833,  7.392,  0.000 5.00E-01  11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The feedpoint is on wire 21, and the phase line for this model is 100 Ohms. (The 250-Ohm phase line model uses a 14.2' element for wire 22.) The following graphs are presented to show performance below 14 MHz as wel as within the design passband.

+
+ +
+

Fig. 17 shows the gain curve at 0.25 MHz intervals. Note that this close spacing of check point reveals two relatively weak region: at 19.75 and 26.5 MHz. One or both of these regions can be virtually eliminated by adding a shorted stub to the rear of the assembly. Neither is so serious as to reverse the antenna pattern, but both show that even with relatively high values of Tau and Sigma, harmonic operation of elements to the rear of the most active element may still occur.

+

The free-space gain drops off rapidly below 14 MHz, but remains above 8.2 dBi at 13.25 MHz. The parasitic director permits a free-space gain above 9.0 dBi at 28.25 MHz and higher.

+
+ +
+

The 180-degree front-to-back ratio, shown in Fig. 18, reaches 20 dB by 13.75 MHz and remains above that value until 29.5 MHz. The exceptions are the two weak regions previously noted. The weaknesses can be removed by using a 250-Ohm phase line. Using this line will lower the gain slightly across the passband and result in a feedpoint impedance best referenced to about 110 Ohms. A 2:1 wide-band transmission-line transformer balun would provide a satisfactory match to a 50-Ohm cable.

+
+ +
+

Fig. 19 provides the VSWR curve relative to a directly fed 50-Ohm feedline. The SWR drops to under 2:1 by 13.1 MHz. Only in the upper region of the passband--largely as a result of adding the parasitic director--does the SWR approach 2:1.

+

With high-range LPDA performance that is superior to the mid-range LPDA down to 13.1 MHz, the crossover point between the mid-range and the high-range LPDAs is a matter of choice at installation. The overall free-space gain of the high-range array averages about 8.8 dBi, with a superior front-to-back ratio.

+

Conclusion

+

Three 55' booms just about equal the total boom length of the 164' wide-range LPDA. However, each of the individual LPDAs with an approximate 2:1 frequency span manages patterns that are better behaved. The use of three separate arrays confines lesser performance to the frequency region where it may be necessary, with increasingly better performance as we move up in the frequency regions. As well, the use of separate arrays and electronic selection and/or polling offers at least partial system operation should one antenna be down for maintenance.

+

The triple LPDA array is an expensive proposition, best fit for military, governmental, or commercial applications calling for relatively complete coverage of the HF spectrum. The present design exercise has attempted to see if there might be an alternative to the use of single arrays with somewhat marginal performance in such applications. Using 3 LPDAs, each optimized to a portion of the spectrum, provides increasingly better performance within the 55' boom limitation.

+

It is possible, in principle, to build an unconditionally stable LPDA to cover the range from 3 to 30 MHz. The free-space gain will range from a low of 10.25 dBi to a high of about 11.35 dBi, using a Tau of 0.955 and a Sigma of 0.18. Unfortunately, this 60-element antenna will be just short of 1250' long.

+

Perhaps three relatively short LPDAs are not so bad after all as a substitute.

+
+ +
+

Updated 03-01-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for February, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
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Go to Main Index

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Topics: HF Multi Band, LPDA


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+

3 More 14-30 MHz LPDA Designs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In an earlier article ("Long-Boom LPDAs for 14-30 MHz"), I described the basic design of an idealized log-periodic dipole array (LPDA) for the 20-10 meter range. It had a free-space gain range of 8.7 to 9.0 dBi, with correspondingly high front-to-back figures. The 56' boom was not considered a hindrance for this "dream beam." The array used a Tau of 0.9500 and a Sigma of 0.0560 along with 22 elements to achieve its performance.

+

The design had some interesting features, designed to overcome some of the weaknesses of finite-length LPDAs. First, the value of Tau was circularized in the elements at each end of the array, resulting in a shortening of the very longest elements and a lengthening of the shortest elements. The result is an LPDA whose element ends describe a slight ogee curve. The "Tau-circularizing" technique tends to equalize gain at the passband ends relative to mid-band performance. However, it must be used with care so as not to unduly disturb the feedpoint impedance across the pass band.

+

Since the circularizing technique is most effective at the lower end of the passband, gain still tends to fall off at the upper end of the passband unless the shortest element is calculated as if the highest operating frequency was about 1.6 times its actual value. Such a high upper-end frequency limit adds a number of elements to the design, along with considerable boom length. Interestingly, early work on LPDAs in the 1960s recognized a "high frequency truncation coefficient," but failed to associate the idea with a clear notion of which elements in an LPDA are active. Early thinking led to the misconception that only the immediately adjacent elements to the one nearest resonance were active. In fact, virtually all elements forward of the most active element are themselves active and contribute to the pattern formation for a given frequency.

+

To effect the desired performance gain with fewer elements, the forward-most element was made parasitic and lengthened to form a director for the highest band (10 meters). The length and spacing for this element are selected to achieve the desired gain with least effect on the feedpoint impedance of the array at all other frequencies. The further away from the closest LPDA element, the higher the gain, but the lower the front-to-back ratio and the greater the disturbance to feedpoint impedance values.

+

These same design techniques can be applied to shorter-boom LPDAs with relatively equal success--subject only to limitations imposed by using fewer elements on a shorter boom. In this article, in addition to a quick review of the ideal LPDA for 20-10 meters, we shall examine designs using 16, 12, and 9 elements on 42, 32, and 21 foot booms respectively. The ideal design replicates 4-element monoband Yagi performance assuming a moderately long boom. The 16-element design provides close to long-boom 3-element monoband Yagi performance across the pass band--about 8 dBi free-space gain. The 12-element model gives us about 2-element quad or short-boom 3-element monoband Yagi performance--about 7 dBi across the passband. Finally, the shortest member of the family comes close to 2-element monoband reflector-driver Yagi performance--something close to 6 dBi free-space gain. When comparing the performance numbers to those of other types of arrays, remember that the LPDA provides performance both within and between the ham bands.

+
+ +
+

Fig. 1 provides some comparative outline sketches of the 4 members of this LPDA family. There is little difference in the longest and shortest elements for each set, but considerable difference in total boom length, total weight, and performance. Note also that the position of the parasitic director has been selected by hand to optimize each design within the overall objectives for each.

+
+ +
+

In Fig. 2, we have the free-space azimuth patterns for the family members for the middle of the 20-meter band (14.175 MHz). The stepped gain differential is clearly apparent. The larger step downward in gain for the smallest LPDA is a function of the fact that the shorter the LPDA, the lower both Tau and Sigma go, mutually reducing gain potential for the array.

+

The rear lobes of an LPDA pattern in a very general way are the reciprocal of the forward lobes. The higher the forward gain, the higher the 180-degree front-to-back ratio. Once that ratio passes about 30 dB, we find variations in the rear pattern, even in the best controlled arrays. The rear may look like a single lobe, a three-lobe pattern with either the central or side lobes emphasized, or a small ripply blob. Although gain and front-to-rear performance are closely correlated, the natural variations in each over the full passband do not directly coincide.

+
+ +
+

Fig. 3 shows the corresponding free-space azimuth patterns for 28.85 MHz. Here, we do not see the even stair-stepping of forward gain due to the variable treatment of the parasitic director. The highest gain model (9556) has a widely spaced director which reduces the front-to-back ratio to barely 20 dB. In contrast, the 16-element model (9306) shows considerably better rearward performance, but less relative forward gain--due to the close spacing of the director (see Fig. 1). The smallest two LPDAs in the collection (9105 and 8705) have relatively wide-spaced directors, although 9105 manages a higher gain than perhaps it needed for balance across the entire passband. However, as we shall see, it also shows the widest gain range across 10 meters.

+

In designing the members of this LPDA family, I set as a goal the equalization of high-end gain with mid-band gain (about 21 MHz) with acceptable feedpoint impedances and a 180-degree front-to-back ratio of 20 dB. Only in a couple of instances does the front-to-back ratio dip slightly below the target value.

+

The feedpoint impedance was selected to match either a 50-Ohm or a 75-Ohm system. In some designs, the use of 75-Ohm coaxial cable or a 75-to-50 Ohm balun transformer may yield lower SWR values than a direct 50-Ohm feed. The practical concern is not so much line losses, but the sensitivity of some equipment to SWR values above 1.5:1: some gear tends to reduce power or shut down at SWR values well below the traditional limit of 2:1. In all cases, for the low impedance feed system, the phase lines were set at a characteristic impedance (Zo) of 100 Ohms.

+

The designs were also tested--and modified, if necessary--for a phase line Zo of 250 Ohms. As we shall see, the higher phase-line impedance reduces gain performance slightly (0.1 to 0.15 dB on average), but results in an unconditionally stable array across the passband. The mid-point feed impedance ranges from 100 to 120 Ohms, and the arrays may be fed using a 2:1 broad-band transmission line transformer, such as one of those designed by W2FMI, Jerry Sevick, and available from Amidon. In general, the higher phase-line Zo results in a smoother SWR curve across the passband and a total absence of "spikes."

+

All of the family members use an idealized element diameter of 0.5". In general, the dimensions shown for each family member are satisfactory for all but the longest and shortest elements (including the parasitic director) in the arrays. Elements whose lengths have been adjusted for a parasitic function or in the course of circularizing Tau should be remodeled using the exact element diameter taper to be used the version constructed. In practical terms, this means remodeling the entire array with each element using its diameter taper. However, this necessary procedure may limit those who model LPDAs in NEC-2. The Leeson-correction system for linear elements using a tapered diameter schedule will only function on elements that are within about 15% of resonant length for the frequency being tested. Elements outside that range will not be corrected, and subtle errors in the modeled performance may result. Hence, NEC-4 would be the software of choice for final design modeling for the LPDAs in our family.

+

A Review of 9556

+

9556 is the ideal 56' long LPDA which we have examined in the past. The following table gives the overall element length and cumulative spacing for the design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.05                 -----
+ 2               34.17                  4.02
+ 3               32.33                  7.83
+ 4               30.73                 11.45
+ 5               29.20                 14.89
+ 6               27.74                 18.16
+ 7               26.35                 21.27
+ 8               25.03                 24.22
+ 9               23.78                 27.03
+10               22.59                 29.69
+11               21.46                 32.22
+12               20.39                 34.62
+13               19.37                 36.91
+14               18.40                 39.08
+15               17.48                 41.14
+16               16.61                 43.10
+17               15.78                 44.96
+18               14.99                 46.72
+19               14.24                 48.40
+20               13.53                 50.00
+21               12.85                 51.51
+22               14.78/14.60           55.83  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The two lengths listed for the director apply to the different values of phase-line Zo: the longer director applies to the 100-Ohm line, while the shorter applies to the 250-Ohm line. The change in length was necessitated to optimize--so far as possible--the gain and SWR curves on 10 meters.

+
+ +
+

Fig. 4 shows the SWR curves for the entire passband, taken at 0.25 MHz intervals. The interval is sufficiently small to show signs of performance instability, and none appear with either choice of phase line Zo. In fact, the design does not require the use of a shorted transmission line stub behind the longest element, although one may be added to set all of the elements at the same DC value. Something of about 450-600 Ohms characteristic impedance and a length of about a foot should do the job with minimal disturbance to the performance curves. When both Tau and Sigma together reach a certain level--obtained in this design--a stub is not necessary to control or remove impedance and performance spikes.

+

The anticipated performance of the array for each value of phase line Zo is listed in the following tables.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9556143X:  22 elements (21 LPDA + 1 par):  55.83' boom: 0.5" dia.
+Tau = 0.9500; Sigma = 0.0560:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      8.85      24.84     75.6 + j 0.2        1.51      1.01
+14.175    8.85      30.28     74.2 - j 3.5        1.49      1.05
+14.35     8.81      39.01     71.9 - j 6.5        1.46      1.10
+17
+18.118    8.83      38.18     67.2 - j 7.0        1.38      1.16
+15
+21.0      8.72      42.61     64.7 + j 0.1        1.29      1.16
+21.225    8.71      41.67     66.9 - j 0.5        1.34      1.12
+21.45     8.72      41.04     67.2 - j 1.8        1.35      1.12
+12
+24.94     8.81      32.04     73.2 - j 2.2        1.47      1.04
+10
+28.0      8.92      24.94     72.3 + j16.5        1.58      1.26
+28.85     9.04      21.29     47.3 - j30.7        1.87      1.98
+29.7      9.05      19.57     50.2 + j20.9        1.51      1.69
+
+Delta Gain:  0.34 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9556143Y:  22 elements (21 LPDA + 1 par):  55.83' boom: 0.5" dia.
+Tau = 0.9500; Sigma = 0.0560:  ogee'd:  TL = 250 Ohms
+(Parasitic length revised for 250-Ohm TL:  from +/-7.392 to +/-7.3)
+
+Freq.     Gain      F-B       Feed Impedance      100-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      8.68      26.48     131.1 - j 5.5       1.32
+14.175    8.68      30.95     134.1 - j 3.9       1.34
+14.35     8.69      34.01     137.6 - j 8.2       1.39
+17
+18.118    8.71      47.27     130.3 - j 9.4       1.32
+15
+21.0      8.79      36.30     130.3 - j11.9       1.33
+21.225    8.81      34.27     132.2 - j18.4       1.38
+21.45     8.80      33.29     127.4 - j26.1       1.40
+12
+24.94     8.63      32.78      98.7 - j21.6       1.24
+10
+28.0      8.76      25.63      82.1 - j39.7       1.61
+28.85     8.66      25.92     102.0 - j 7.5       1.08
+29.7      8.83      22.34      70.1 - j40.9       1.82
+
+Delta Gain:  0.20 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Since both models are stable across the entire passband, the choice of phase line Zo value is optional with the builder. Note that the average gain of the model with the higher Zo is about 0.15 dB lower than for the model using a 100-Ohm line. However, the 250-Ohm line model shows a lower variation in gain across the pass band.

+

9306: 16 Elements on a 42' Boom

+

If 9556 is unrealistic for all but a hand full of builders, 9306 might appeal to perhaps a double handful of antenna constructors. The 42' boom is somewhat less daunting, but should not be underestimated for its support complexity. As well, the 16 elements carry considerable raw weight and wind load. Nonetheless, the array comes close to providing full 3-element monoband performance from 14 to 30 MHz.

+

The following table provides dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               35.80                 -----
+ 2               33.80                  4.43
+ 3               31.70                  8.55
+ 4               29.60                 12.38
+ 5               27.60                 15.94
+ 6               25.67                 19.25
+ 7               23.87                 22.33
+ 8               22.20                 25.20
+ 9               20.65                 27.86
+10               19.20                 30.34
+11               17.86                 32.64
+12               16.61                 34.79
+13               15.45                 36.78
+14               14.36                 38.63
+15               13.36                 40.36
+16               14.70/14.20           41.96  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Regardless of the choice of phase line Zo, the design uses a 0.5' long shorted stub with a 600-Ohm characteristic impedance. Fig. 5 will show why the stub--optional on the big brother of this LPDA--is necessary here.

+
+ +
+

The SWR curves for two versions of the LPDA appear in Fig. 5. The 100- Ohm phase line curve uses the 75-Ohm SWR because it shows smaller excursions than the corresponding 50-Ohm line. However, either feedline would be quite usable.

+

The 250-Ohm phase line model is completely stable. However, the 100-Ohm line model shows a spike at about 23 MHz. The impedance spike actually peaks narrowly at 22.95 MHz with an SWR that is greater than 4:1 and a reduction in gain to under 6 dBi. The front-to-back ratio is less than 10 dB. Such a narrow spike, well outside of the amateur bands, may be acceptable for some builders, not for others, depending upon the design specifications one sets for the array.

+

Within the ham bands, the performance of the array in both versions can be summarized in two tables.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9306Q16:  16 elements (15 LPDA + 1 par):  41.96' boom: 0.5" dia.
+Tau = 0.9300; Sigma = 0.0600:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      8.08      28.78     61.5 + j 3.3        1.24      1.23
+14.175    8.07      33.97     67.2 + j 5.1        1.36      1.14
+14.35     8.05      39.35     72.3 + j 1.4        1.45      1.04
+17
+18.118    8.06      33.96     74.0 - j 5.2        1.49      1.07
+15
+21.0      8.02      37.06     70.9 - j 1.0        1.42      1.06
+21.225    8.03      36.56     72.8 - j 4.3        1.47      1.07
+21.45     8.03      36.38     71.8 - j 8.6        1.47      1.13
+12
+24.94     8.00      40.49     71.5 + j 1.3        1.43      1.05
+10
+28.0      7.77      27.28     72.1 + j 0.4        1.44      1.04
+28.85     7.93      25.88     47.7 - j11.1        1.26      1.63
+29.7      8.15      20.55     56.0 + j33.3        1.88      1.79
+
+Delta Gain:  0.38 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+9306P16:  16 elements (15 LPDA + 1 par):  41.96' boom: 0.5" dia.
+Tau = 0.9300; Sigma = 0.0600:  ogee'd:  TL = 250 Ohms
+(Parasitic length revised for 250-Ohm TL:  from +/-7.35 to +/-7.1)
+
+Freq.     Gain      F-B       Feed Impedance      120-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      7.95      31.96     126.2 - j15.3       1.14
+14.175    7.97      34.68     126.4 - j 7.5       1.08
+14.35     7.99      38.02     133.4 - j 2.5       1.11
+17
+18.118    7.90      335980    119.7 - j 9.1       1.08
+15
+21.0      7.91      38.50     116.2 - j26.3       1.25
+21.225    7.86      39.66     112.2 - j20.9       1.21
+21.45     7.82      40.10     111.6 - j14.8       1.16
+12
+24.94     7.83      32.41     112.4 - j41.0       1.43
+10
+28.0      7.70      31.41     104.5 - j15.5       1.22
+28.85     7.85      27.78     126.6 + j 5.1       1.07
+29.7      7.81      23.33     137.3 - j82.3       1.90
+
+Delta Gain:  0.29 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 250-Ohm phase line version of the 16-element LPDA shows a gain deficit of about 0.15 dB on average relative to the 100-Ohm phase line version. In exchange for the reduced gain, the builder obtains a completely stable array, with no weaknesses. In general, the lower the phase-line Zo, the greater the tendency to have one or more weaknesses in the overall performance curve, and these are generally signaled by a spike in the SWR curve. However, the SWR spike maximum and the greatest disturbance to performance may not occur at precisely the same frequency. However, they will be overlapping phenomena within 100 kHz or so.

+

The higher the values of both Tau and Sigma--resulting in a higher number of elements and a longer boom--the narrower that a spike will be. The use of the stub can reduce either the number or severity of a spike, as well as control its frequency. In this case, the spike was moved to a frequency that is generally harmless in terms of amateur operations. As the values of Tau and/or Sigma are reduced, the chief protection from spikes becomes a higher phase line Zo.

+

9105: 12 Elements on a 32' Boom

+

The next step down the ladder in our family of LPDAs is a 12-element model on a 32' boom. The dimensions of the array appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.00                 -----
+ 2               34.00                  4.15
+ 3               31.30                  7.93
+ 4               28.47                 11.36
+ 5               25.90                 14.48
+ 6               23.55                 17.33
+ 7               21.42                 19.93
+ 8               19.47                 22.28
+ 9               17.70                 24.43
+10               16.10                 26.38
+11               14.63                 28.15
+12               15.17                 32.00  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For this design, it was unnecessary to alter the length of the director to obtain acceptable results with both the 100-Ohm and 250-Ohm phase lines. The design does use a 1' 450-Ohm Zo shorted stub on the rear of the boom. However, as we shall see, this stub can reduce and/or move weaknesses that appear in the 100-Ohm phase line model, but it cannot eliminate "spikes" altogether.

+
+ +
+

Fig.6 shows the 50-Ohm SWR with the 100-Ohm phase line and the 110-Ohm SWR with the 250-Ohm phase line. As we reduce the number of elements and boom length--with a correspondingly reduced value of Tau--we should note larger excursions of SWR, regardless of the phase line value. The excursions are interesting, if we also track the changes of resistance and reactance along the way. Maximum values of capacitive and inductive reactance tend to occur when the resistance value is near its mean, while reactance tends to go to zero when the resistive component of the feedpoint impedance is at a high or low. Excursions of reactance are smaller with higher values of Tau and Sigma (together): hence, the SWR changes are smaller. As we shorten the boom and reduce Tau, the reactance undergoes a wider range of values.

+

The spike in the 50-Ohm curve in Fig. 6 is also more extreme than the one in Fig. 5. It is both higher--exceeding an SWR of 10:1--and wider, covering nearly a half MHz. Fig. 7 shows the worst-case azimuth pattern, in which the pattern technically reverses direction.

+
+ +
+

Fig. 8 shows why. Virtually all of the elements to the rear of the active one are also active, but in a harmonic mode, as indicated by the "double-hump" curves that register the current magnitude. This example is especially interesting, since in most cases, not all of the rear elements will be so active.

+
+ +
+

The following two tables provide the anticipated performance of the 12- element array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+91051431:  12 elements (11 LPDA + 1 par):  32.000' boom: 0.5" dia.
+Tau = 0.9099; Sigma = 0.0550:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      7.33      32.93     94.6 - j 1.8        1.89      1.26
+14.175    7.30      27.52     84.5 + j 5.7        1.78      1.26
+14.35     7.25      24.91     71.0 - j16.0        1.55      1.25
+17
+18.118    7.19      26.48     62.7 - j 0.2        1.25      1.20
+15
+21.0      7.24      24.86     82.5 - j 5.4        1.66      1.12
+21.225    7.26      25.85     78.2 - j11.9        1.62      1.17
+21.45     7.28      27.19     71.8 - j14.3        1.54      1.22
+12
+24.94     7.19      24.57     47.7 + j 1.1        1.05      1.57
+10
+28.0      7.57      27.68     41.4 - j18.6        1.56      1.97
+28.85     7.69      24.26     35.6 + j 1.6        1.41      2.11
+29.7      8.01      19.95     70.6 + j25.9        1.73      1.43
+
+Delta Gain:  0.82 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+91051431:  12 elements (11 LPDA + 1 par):  32.000' boom: 0.5" dia.
+Tau = 0.9099; Sigma = 0.0550:  ogee'd:  TL = 250 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      110-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      7.12      26.83     106.2 - j 0.8       1.04
+14.175    7.07      25.63     117.2 + j11.7       1.13
+14.35     7.03      24.90     134.2 + j14.2       1.26
+17
+18.118    7.02      25.95     131.3 - j15.8       1.25
+15
+21.0      7.20      27.91     107.7 - j28.8       1.30
+21.225    7.18      28.71     105.2 - j21.9       1.23
+21.45     7.15      29.10     106.2 - j16.4       1.17
+12
+24.94     7.20      27.34     138.9 + j 6.0       1.26
+10
+28.0      7.38      28.70      70.4 - j22.4       1.66
+28.85     7.52      26.51      84.3 - j 6.0       1.31
+29.7      7.89      20.33     113.4 - j63.3       1.75
+
+Delta Gain:  0.88 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Performance of the 250-Ohm phase line model is down about 0.14 dB from the 100-Ohm phase line model. However, the 250-Ohm version is stable across the entire passband.

+

8705: 9 Elements on a 21' Boom

+

The final member of the LPDA family is the shortest--only 21' in boom length (plus a little excess for element mounting fixtures). As well it has the least number of elements--9--and the lowest value of Tau--0.8688. Indeed, these values are about the least that I would recommend for satisfactory performance, if we define that term as being close to the performance of a 2-element reflector-driver monoband Yagi. Even so, we shall discover that the low values used in the design of the LPDA yield the highest fluctuations in performance.

+

The dimensions for the 9-element array are as follows.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Element #        Length (feet)         Spacing from
+                                       Reflector (feet)
+ 1               36.00                 -----
+ 2               32.30                  3.89
+ 3               28.06                  7.26
+ 4               24.38                 10.19
+ 5               21.18                 12.74
+ 6               18.40                 14.96
+ 7               15.98                 16.88
+ 8               13.89                 18.55
+ 9               13.60                 21.00  Director:  See text.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Both designs employ a stub. In both cases, a 1.9' shorted length of 450-Ohm transmission line or its equivalent is sufficient to tame the design.

+

As with the 12-element model, the 9-element design requires no change in the length of the director as we move from a 100-Ohm phase line to a 250-Ohm version. However, the spike which we might anticipate in the 100-Ohm phase line model shows itself vividly in Fig. 9, the SWR curves for both phase lines across the entire passband. The spike is higher and wider (with respect to frequency) than any other so far encountered. SWR values higher than 2:1 extend from abut 26.25 to 27.5 MHz.

+
+ +
+

Although the spike in the 100-Ohm phase line model is located well outside the amateur bands, it does interfere with operation of the array on the Citizen's Band. In contrast, the 250-Ohm phase line model permits operation throughout the passband.

+

Amateur band performance of both models appears in the following tables.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+8705B:  8 elements (7 LPDA + 1 par):  21.000' boom: 0.5" dia.
+Tau = 0.8688; Sigma = 0.0523:  ogee'd:  TL = 100 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      50-Ohm    75-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR      VSWR
+20
+14.0      5.63      11.20     82.3 - j27.4        1.91      1.43
+14.175    5.74      11.88     67.4 - j29.4        1.79      1.53
+14.35     5.83      12.43     55.4 - j26.0        1.65      1.65
+17
+18.118    6.03      14.13     66.3 + j25.1        1.67      1.46
+15
+21.0      6.33      15.06     61.5 + j19.2        1.49      1.41
+21.225    6.30      15.10     69.5 + j17.6        1.56      1.29
+21.45     6.26      15.18     76.1 + j11.8        1.58      1.17
+12
+24.94     6.13      18.10     67.2 + j29.5        1.79      1.53
+10
+28.0      6.03      18.21     61.4 - j19.0        1.49      1.41
+28.85     6.17      17.05     64.6 - j10.4        1.37      1.23
+29.7      6.24      17.36     61.1 - j14.7        1.39      1.35
+
+Delta Gain:  0.70 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+8705C:  8 elements (7 LPDA + 1 par):  21.000' boom: 0.5" dia.
+Tau = 0.8688; Sigma = 0.0523:  ogee'd:  TL = 250 Ohms
+
+Freq.     Gain      F-B       Feed Impedance      120-Ohm
+MHz       dBi       dB        R +/- jX Ohms       VSWR
+20
+14.0      5.55      10.69      93.6 - j18.8       1.36
+14.175    5.61      11.07      91.7 - j 3.0       1.31
+14.35     5.66      11.38      94.6 + j12.5       1.30
+17
+18.118    6.09      13.58     168.3 - j48.3       1.61
+15
+21.0      6.14      15.48     150.5 - j29.6       1.37
+21.225    6.13      15.46     136.8 - j41.6       1.42
+21.45     6.12      15.44     120.8 - j45.3       1.45
+12
+24.94     6.26      17.22     159.2 - j47.0       1.55
+10
+28.0      6.27      19.07     104.5 - j13.6       1.20
+28.85     6.27      19.74     100.4 - j29.4       1.38
+29.7      6.39      22.64      80.6 - j31.2       1.66
+
+Delta Gain:  0.84 dB
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The average gain of the two arrays across the entire passband is about the same. However, the 250-Ohm phase line version begins with lower gain on 20 meters and ends with higher gain on 10 meters. As well, relative to longer members of the array family, the 20-meter gain is in both cases below the array average--a result of decreasing the value of Tau below about 0.9. Most LPDAs with Tau values below about 0.9 and with Sigma values in the 0.04 to 0.06 range tend to show decreasing gain at the low end of the spectrum.

+

Nonetheless, the array provides serviceable performance a cross the design passband--about as good as a 20' long LPDA can do with elements that average 0.5" in diameter. Increasing the average element diameter can improve gain somewhat, with the most needed increase on 20 meters. Since most implementations of this or similar designs would have equivalent element diameters larger than 0.5" for the longest elements, we can expect some natural improvement to 20 meter performance as a matter of course.

+

Conclusion

+

The goal of this design exercise was to produce a family of LPDAs with relatively smooth performance across the entire design passband from 14 to 30 MHz. By the judicious use of standard LPDA modification techniques, the goal has been achieved, although before construction can begin, the designs would need to be customized to the element diameter taper schedule actually used.

+

Since small changes of construction may move the spike frequencies that occur on the smaller members of the family, the use of the 250-Ohm phase line--or something similar, may be the surest route to a successful building project. The average loss of 0.15 dB forward gain is unlikely to be noticed in operation. Because low-loss wide-band 2:1 transmission line transformer baluns are available, the higher feedpoint impedance natural to the high impedance phase line should present no problems. In fact, with the smaller version of the array, the higher natural feedpoint impedance may reduce SWR excursions.

+

Further LPDA construction details can be found in various handbooks, most notably, Chapter 10 of the latest ARRL Antenna Book. Since this is a basic design study, I shall forego construction details altogether. The object has been to show what is possible. The 4 LPDA family members do that well enough to encourage those interested to perfect the designs for particular building circumstances.

+
+ +
+

Note: The purpose of this article is to disseminate information and ideas. The author retains all design rights associated with the subject arrays, including modifications for improved performance over standard arrays of a similar type and including all reasonable variations upon them both stated or implied by the text or the designs themselves.

+
+ +
+

Updated 11-1-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: HF Upper, LPDA


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+

An 80-Meter LPMA: A Design Idea and a Modeling Dilemma
+ Part 1. Designing the LPMA With a MININEC Ground

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Although many amateurs are familiar with the log periodic dipole array (LPDA), fewer are familiar with the log periodic monopole array (LPMA). The LPMA has been around almost as long as its bigger brother, but not many amateur applications have emerged from the basic design. These notes will focus on a 3.5-4.0 MHz limited passband LPMA in a design exercise that will highlight some of the main electrical and physical characteristics of the antenna type. As well, we shall look at some of the stumbling blocks to the design of an LPMA that might actually be implemented with confidence.

+

In principle, the LPMA is a series of ground-mounted monopoles (although other arrangements have been used) with a phasing line running from the base feedpoint of one monopole to the next--complete with the line reversal as it connects to each succeeding vertical element. The elements can be designed using standard LPDA design equations and then using only one side of the dipole. As well, the LPMA is amenable to the same kinds of performance-enhancing modifications as the LPDA.

+

These are the design principles of the LPMA. Most LPMAs are designed by equation and then checked on software something like MININEC. Such software might be MININEC itself or a version of NEC with access to a MININEC ground. The elements are set with their bases touching ground, without the use of an actual ground plane. For many purposes, a MININEC ground is an adequate substitute--at least in preliminary design work--for a NEC-4 buried radial field of considerable size--more than 32 or so radials. However, as I have shown in the series I did on 160-meter vertical arrays, MININEC has some limitations that make its ground system inadequate for accurately modeling the performance of some antenna types. In the end, the question that will face us is whether the MININEC ground is adequate for the modeling of an LPMA, and if so, under what conditions.

+

A Single LPMA

+

The basic design used in this exercise is the 8-element version of the horizontal LPDA for 3.5 to 4.0 MHz described near the end of "80-Meter Wire LPDAs" in last month's issue of AntenneX. Since the elements are wholly vertical and a large ground radial field is assumed, the initial design effort can use a MININEC ground for efficiency. It is well to note that the array gain will vary with the ground quality in the Fresnel zone of the antenna well beyond the radial system. Therefore, the cited gain figures should be compared to a reference. A 1/4 wavelength resonant monopole over good ground using a MININEC ground system with NEC-4 registers a gain between 0.4 and 0.5 dBi. Although the LPMA gain will vary with the quality of the radial system and the surrounding ground quality, its advantage over a monopole with a similar radial system and surrounding ground quality will be close to the difference between the gain figures to be cited and the reference monopole.

+

The initial modeling of the 8-element array--86' long overall--yielded the following performance figures across 80/75 meters:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+                           8-Element LPMA Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         4.36        22          18.34       133         50.8 - j 3.0      1.06
+3.75        4.04        22          14.94       137         54.2 + j 4.6      1.13
+4.0         4.32        22          19.53       129         45.1 - j 7.0      1.20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

The test model specified #12 AWG copper wire, and for this reason, the model has a defect. It has no support. Therefore, except as a reference point, it is not a feasible antenna, although one might build the end elements from tower sections. However, even though the elements have been Tau-tapered to increase performance, the catenary arc of the non-conductive support cable would not likely be above all of the element tips.

+
+ +
+

As a consequence of these considerations, the LPMA was further modified by the addition of two parasitic elements, each composed of tower sections. A 79' tower reflector was added to the rear of the 8 phased elements, and a 50' tower director was added ahead of the same element set. Fig. 1 shows the general layout of the LPMA. The overall length was increased to 123' to accommodate these support towers. The following model description shows the dimensions of the design, along with the specified 100-Ohm phase line.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+80-m t=.92 s=.05 3.3-4.5                    Frequency = 3.75  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1            0.000,  0.000, 79.000     G   0.000,  0.000,  0.000 6.00E+00  29
+2           18.000,  0.000, 75.500     G  18.000,  0.000,  0.000    # 12   27
+3           33.494,  0.000, 69.500     G  33.494,  0.000,  0.000    # 12   25
+4           47.771,  0.000, 64.563     G  47.771,  0.000,  0.000    # 12   23
+5           60.928,  0.000, 60.000     G  60.928,  0.000,  0.000    # 12   21
+6           73.050,  0.000, 55.500     G  73.050,  0.000,  0.000    # 12   19
+7           84.221,  0.000, 51.500     G  84.221,  0.000,  0.000    # 12   17
+8           94.515,  0.000, 48.000     G  94.515,  0.000,  0.000    # 12   17
+9          104.000,  0.000, 44.500     G 104.000,  0.000,  0.000    # 12   15
+10         123.000,  0.000, 50.000     G 123.000,  0.000,  0.000 6.00E+00  17
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          15     9 / 96.67   (  9 /100.00)      0.707       0.000       V
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      2/98.1  (  2/100.)    3/98.0  (  3/100.)  Actual dist  100.0  1.00  R
+2      3/98.0  (  3/100.)    4/97.8  (  4/100.)  Actual dist  100.0  1.00  R
+3      4/97.8  (  4/100.)    5/97.6  (  5/100.)  Actual dist  100.0  1.00  R
+4      5/97.6  (  5/100.)    6/97.4  (  6/100.)  Actual dist  100.0  1.00  R
+5      6/97.4  (  6/100.)    7/97.1  (  7/100.)  Actual dist  100.0  1.00  R
+6      7/97.1  (  7/100.)    8/97.1  (  8/100.)  Actual dist  100.0  1.00  R
+7      8/97.1  (  8/100.)    9/96.7  (  9/100.)  Actual dist  100.0  1.00  R
+Ground type is Real, MININEC-type analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

The double-duty towers not only are capable of supporting the non-conductive cable to hold the elements in place, but as well add considerably to the performance of the LPMA. The following table can be legitimately compared to the preceding one, since the 8 phased elements were not altered.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+               8-Element LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.04        22          20.35       115         48.8 + j 5.5      1.12
+3.75        4.99        22          18.46       113         42.4 + j 4.7      1.21
+4.0         5.28        22          20.33       106         38.4 - j21.9      1.75
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

The addition of the parasitic elements added about 0.85 dB to the average array gain across the band. However, higher gain brings with it a somewhat narrower beamwidth. The performance is very stable, as demonstrated by the 50-Ohm SWR graph in Fig. 2.

+
+ +
+

Fig. 3 overlays azimuth patterns for the 3 80-meter checkpoints to demonstrate that the array holds a fairly consistent pattern throughout the operating passband, with under 0.3 dB variation across the band.

+
+ +
+

The array design and its performance potential as compared to a simple monopole over the same ground system is somewhat self-explanatory. Therefore, let's focus on a limitation of the array as presented. It is anchored to the ground at every element and hence is fixed. If we wish to cover more than the stated -3 dB beamwidth, we must add more such arrays.

+

A Bi-LPMA

+

The parasitic reflector has a third function besides being an anchor tower and a reflector: it also serves to isolate arrays placed in opposing directions. When one array is active, the other shows no negative effects on its operation. Fig. 4 shows the outline of the bi-LPMA with a common parasitic reflector.

+
+ +
+

Each array is identical to its mate, and both are designed to be mechanically anchored at the high end by the central tower-reflector. In the model description, simply create a directional mirror image of the single array shown. The following table shows the reported performance potential for each of the two arrays.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+              8-Element Bi-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.28        22          19.61       110         48.8 + j 6.2      1.14
+3.75        5.15        22          21.93       113         42.4 + j 5.1      1.22
+4.0         5.31        22          25.43       108         38.4 - j21.7      1.74
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

The operational predictions have scarcely changed any numbers, and the reported feedpoint impedance values are a measure of the degree to which the two LPMAs are isolated. The only change worthy of notice is the slight increase in average gain for the array. It has climbed another 0.15 dB and is now a full dB higher than the 8-element model without parasitic elements.

+
+ +
+

The SWR curve in Fig. 5 shows its close kinship to the one for the single array. There are slight changes in the pattern shapes, especially to the rear, as demonstrated by the overlaid patterns in Fig. 6. For most situations, the differences from the single LPMA would be considered operationally insignificant.

+
+ +
+

More significant for anyone contemplating the implementation of a dual LPMA is the coverage provided. Fig. 7 overlays sample patterns to show both the covered area and the gaps in coverage at right angles to the dual LPMA.

+
+ +
+

Although the double array might be suitable for a station on a great arc between Europe and Australia, the gaps remain troublesome for anyone wishing full horizon coverage.

+

A Tri-LPMA

+

It is possible to redesign the dual array into a triple array by placing LPMAs at 120-degree angles around the central reflector tower. Since the bandwidth of the array is somewhat less than 120 degrees, it is possible that the central reflector would provide sufficient isolation to permit the individual arrays to operate without pattern distortion from elements of the inactive arrays.

+
+ +
+

Fig. 8 shows the general outline of the tri-LPMA system. Each array is operated independently of the other two, with only the reflector serving as a common element. The degree of isolation maintained by the system is demonstrated in the potential performance table that follows.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+             8-Element Tri-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         5.38        21          14.24       102         48.0 + j 7.7      1.18
+3.75        5.52        21          19.02       101         41.6 + j 5.7      1.25
+4.0         5.67        21          23.94        97         37.9 - j21.7      1.76
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

The triple array is perfectly usable, with another 0.3 dB increase in average gain. The increase suggests that the 3 arrays are not completely independent, and the reduction in 3.5-MHz front-to-back ratio confirms the suggestion. As well, the slight reduction in array independence and the small increase in gain also appear as a further reduction on -3 dB beamwidth.

+
+ +
+

As Fig. 9 shows, however, the changes in the feedpoint impedance across the band are relatively insignificant. The 50-Ohm SWR curve is not materially different from the two we have already seen.

+
+ +
+

The degree to which the rearward arrays effect changes in the azimuth patterns of the active LPMA becomes apparent in Fig. 10, where checkpoint patterns are overlaid once more. More crucial to the desire for full horizon coverage from the triple array is Fig. 11, which set forth the worst case coverage on 4.0 MHz, where the beamwidth is narrowest. Whether the coverage is adequate is, of course, a potential user judgment.

+
+ +
+

The desire for relatively equal signal strength across the entire horizon raises the possibility of making an array of 4 LPMAs at 90-degree angles to each other. The outline of such an array appears in Fig. 12.

+
+ +
+

Although such an array is tempting, especially within the paper-design phase, it will turn out to be impractical. The interaction among arrays that began to appear at 3.5 MHz in the triple array will become major interaction across the band. The modeled performance report for a square of LPMAs appears in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. . . . . .
+            8-Element Square-LPMA Plus Parasitic Elements Performance Potential
+Freq.       Gain        TO Angle    F-B Ratio   Beamwidth   Feedoint Z        50-Ohm
+ MHz        dBi         degrees      dB         degrees     R +/- jX          VSWR
+3.5         3.59        21           7.52       171         44.4 + j11.1      1.30
+3.75        5.46        21          16.59        96         40.1 + j 6.7      1.31
+4.0         5.98        21          25.61        86         37.2 - j21.9      1.78
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+. .
+

Although the SWR curve has remained relatively stable, other operating categories shows major fluctuations relative to the previously examined versions of the LPMA.

+
+ +
+

Fig. 13 overlays 3.5 and 4.0 MHz patterns for a quadruple LPMA. Not only has the gain and front-to-back ratio diminished at 3.5 MHz, the beamwidth at that frequency has widened extremely. At the other end of the band, we see some pattern distortion that contributes to a narrowing of the beamwidth to 86 degrees. In fact, the narrowest beamwidths occur in the region from 3.55 to 3.65 MHz, with the beamwidth shrinking to about 78 degrees.

+

The highly variable set of patterns in the 4-square LPMA arrangement result from the natural operation of an LPDA or and LPMA. As we change frequencies, different elements become highly active, that is, carry higher levels of current. This phenomenon applies not only to the active array, but as well to the inactive arrays to which the near field of the active array may be coupled. At the lowest frequencies, the elements closest to the reflector will be active. The effect of parasitic inactive long elements on the pattern will be quite different than the effect at higher frequencies of shorter elements spaced further from the reflector. As well, the degree of coupling will also be variable as we change frequency and involve different elements, thus changing the current magnitude and phase on the inactive parasitic side elements. On this narrow-band LPMA, the range of effects is small, although two distinct types of pattern distortion emerge. On a wider-range LPMA, the range of potential pattern distortion is considerably greater.

+

The square LPMA composed of 4 arrays places the side arrays well within the stronger portions of the active LPMA. Consequently the interactions are high--high enough to dis-recommend this arrangement. By way of contrast, the tri-LPMA places the two inactive arrays well to the rear and generally in the weakest portions of the active array's pattern. Consequently, a much higher degree of isolation exists. The isolation is not perfect, as shown by the rise in gain and by the reduction in the 3.5 MHz front-to-back ratio. However, the tri-LPMA remains perfectly serviceable for full horizon coverage with a gain variation of just about 4-5 dB.

+

The Adequacy of the Design and the Design Technique

+

When I began this design exercise, I had confidence in the use of a MININEC ground system for the initial work. In general, where a MININEC ground goes astray is when one or more of the elements in a vertical array at or close to ground level is not perfectly vertical. A horizontal component to any element--driven or parasitic--in a MININEC model invokes to one degree or another the errors inherent in the system with horizontal wires below about 0.2 wavelength. Since the elements of an LPMA are vertical throughout, the MININEC ground should be reliable as a guide to design.

+

However, in attempting to translate the final designs into NEC-4 models employing buried radials, a number of difficulties were encountered, especially in attempts to develop either simplified or composite buried radial systems. Eventually, I discovered that the most successful route to a buried radial model was also the most straightforward, if not the easiest from a modeling perspective. The result is the conclusion that the LPMA design explored here is usable as a physical antenna, but only if certain conditions are met. Since these conditions are not quite simple or easy to implement--and since the temptations to alternative ground treatment systems are many--perhaps we should devote some time to the subject in Part 2.

+
+ +
+

Updated 05-01-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for April, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Go to Main Index

+

Topics: HF Lower, LPDA, Vertical


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+

An 80-Meter LPMA: A Design Idea and a Modeling Dilemma
+ Part 2. The Adequacy of the LPMA Design

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Everything that has been said so far about the 10-element 3.5-4.0 MHz LPMA design, whether using 1, 2, or 3 arrays, is based upon models in NEC-4 using a MININEC ground. The use of NEC-4 is not essential, since the same results appear using NEC-2. Unfortunately, the requirement to use a mathematical phase line precludes modeling the array wholly in MININEC 3.13, since public domain MININEC does not have the TL facility. Physically modeling the transmission line would require an exceptional number of segments, since the number of right-angle junctions would be very high.

+

However, the real question that we must raise is whether the MININEC ground is adequate to provide an accurate model whose performance can be transferred to a physical antenna. On the surface, the LPMA has none of the features previously identified as invalidating the use of a MININEC ground. (A study of such invalidating factors appeared in the National Contest Journal series on "Some facts of Life About Modeling 160-Meter Vertical Arrays" during 2000 and 2001.) All of those array types that resulted in faulty MININEC-ground models used elements that were not completely vertical. They had to one or another degree a horizontal component to their radiated fields, and at close proximity to ground, the performance reports were erroneous.

+

In contrast to the faulty models, the 80/75-meter LPMA consists of entirely vertical elements. Since the phase line is a mathematical and not a modeled physical entity, it does not modify the radiation patterns except by current magnitude and phase variations of predictable sorts. Consequently, the model based on the use of a MININEC ground should be reliable.

+

Whatever we may expect at first sight, there is a test that we can make to determine whether or not the MININEC-ground model provides enough confidence for us to build the LPMA (assuming that we have the resources to build it). For every adequate MININEC ground model, there is a purely NEC-4 model that uses a buried ground plane/radial/grid system that achieves results that are very closely akin to those reported by the MININEC-ground model. For example, consider monopole that is 1/4 wavelength long at 2 MHz and intended for use until it is about 5/8 wavelength long at 5 MHz.

+
+ +
+

Fig. 1 shows the outline of a monopole for 2-5 MHz (where its height varies from 1/4 wavelength to 5/8 wavelength). The monopole is 118' tall and 6" in diameter to simulate a tower structure. The monopole was run on NEC-4 over a MININEC ground and over a Sommerfeld-Norton ground with radials buried 0.5' beneath the ground surface using recommended modeling techniques. Radial systems of 30 and 60 125'-radials of 0.1" diameter were tested. Throughout, the ground quality was set at "good" (cond.: 0.005 S/m; D.C.: 13). Since take-off angles did not vary at any given frequency by more than 1 degree between the two ground systems, they are omitted from the following table of results. As the table shows, when compared to the MININEC-ground results, the results for the NEC-4 buried radial systems are very sensible--and vice versa.

+ 
                                   Monopole Performance
+Freq. Gain  Source Z          Gain  Source Z                Gain  Source Z
+                                 1.  2-7 MHz 118' monopole
+a.  MININEC ground            b.  S-N Ground, 30 radials    c.  S-N Ground, 60 radials
+2     1.31    36 + j  2       0.94    41 + j 10             1.25    37 + j  8
+3     0.66   175 + j287       0.75   245 + j319             1.04   232 + j325
+4     0.44  1064 - j 85       0.70   672 - j489             0.93   658 - j493
+5     1.00   118 - j318       0.68    78 - j251             0.77    79 - j252
+

The progression shows a few notable variations from a fully adequate correlation of MININEC and buried-radial models. The S-N radial systems show a consistent increase in gain and a consistent reduction of the resistive component of the feedpoint impedance with the increase in the size of the radial system. In short, the S-N buried radial model is capable of showing the decreasing ground losses with increases in the field size, in contrast to the single value returned by the MININEC-ground model. Moreover, the changes in gain with changes in frequency are not completely consistent between the MININEC ground and the S-N radial systems. For the test monopole, the gain progression is steadily downward from the low frequency to the high. The MININEC system is variable.

+

It appears that the MININEC ground system is based throughout on image calculations whenever the lower end of an element has a Z-axis value of zero, that is, touches the ground. Impedance with a MININEC ground is always calculated for a perfect ground. It appears that with a MININEC ground, gain and other performance figures are also calculated for a perfect ground--which uses image techniques--and then adjusted for wire and ground quality losses. In contrast, when not using a perfect ground but instead using the Sommerfeld-Norton system, NEC-4 calculates the actual ground losses entering into the antenna performance. Hence, although the MININEC ground system and calculating technique provides a ballpark estimate of values for a highly refined radial field (more than about 70 radials), its performance calculating technique falls short of perfection relative to modeling a full buried radial system. However, the MININEC values are sufficiently close to those emerging from the large radial systems to account the simplified model adequate for many purposes.

+

When I started work on the 80-meter LPMA, I was also working on designs for larger LPMAs, larger in terms of the number of elements (17-24), larger in terms of frequency range (2 to 7 MHz), and larger in terms of overall size (boom length: 220'). Arrays of this size almost defy efforts to provide buried ground radial, grid, or treatment systems, since the number of segments required can easily run to 10,000 or more. Consequently, the search for a simplified system to serve the entire array was a natural direction of effort.

+
+ +
+

Fig. 2 shows some of the configurations explored. The results of none of the systems were anywhere close to satisfactory. No buried radial model in the sequence has approached closely the performance predictions supplied by the MININEC-ground model of an LPMA. Depending upon the buried ground system design, gain has ranged from 2 to 10 dB below values reported with a MININEC ground. In fact, the monopole model shown earlier as an example of good coincidence between MININEC-ground and buried radial results provides more gain in the 3.5-4.0 MHz region than do any of the buried-radial LPMA models that I tried.

+

The following table summarizes only some of the trial models. It will be useful to help isolate a few of the temptations that proved simply not to work.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Reference Table of Gain Ranges with Types of Ground Systems
+
+No.          System Type                                               Gain Range dBi
+                                                                       1.8 MHz 7.3 MHz
+ 1    No radials, S-N ground                                            2.88    1.02
+ 2    Pair of radials, same length as elements, 2 per element
+      (called SW for "side-wires" in further entries), 1' deep         -6.20  -15.55
+ 3    Revised SW system, with 1' feed segment per element              -6.06  -15.48
+ 4    System 3 with tapered segment length elements                    -6.40  -15.84
+ 5    System 4 with 4' spaced longitudinal grid lines at 1.5'          -2.03  -17.73
+ 6    System 4 with a connecting line between SW junctions             -0.40  - 5.49
+      (Note: variations of this system with extensions beyond towers
+      yielded no better results.)
+ 7    Single buried wire connecting elements 1' below ground           -5.12  -11.98
+ 8    System 6 with a centered radial system at -1.5' of 30 140'
+      radials                                                           0.27  - 5.43
+ 9    System 6 with 2 sets of 30 radials:  140' set at 82' mark, 47'
+      set at 214' mark (most active elements at 1.8 and 7.3 MHz,
+      respectively)                                                     0.32  - 4.13
+10    System 9 radial sets connected to nearest SW junction             0.96  - 4.52
+11    SW system only, all wires elevated 1' above ground                0.58    0.53
+12    SW system only, towers touch ground, phased elements elevated 1'  1.21  - 0.35
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The attempt to provide "side-wires" for each element is a natural temptation. The spacing of wires in the array does not permit full radial systems at the same level without a multitude of intersections. Indeed, it is difficult to provide any given element in the array with more than one radial without intersections among the radials that are not at perfect right angles to the boom line. None of these systems yielded worthy results. One temptation that seemed to improve results slightly was running a buried model wires between the intersections of the side-wires along the boom line. In fact, this line would ultimately prove more problematical as the correct solution to the problem emerged.

+

Combining side-wires with spot radial systems had some ameliorative affect on the array gain. However, the array gain appeared to peak in certain frequency regions and to decline rapidly in others. System 10 proved the most promising, although better results would be needed.

+

To achieve better results, it would be necessary to initially work with a smaller model. The 24-element LPMA that defied simplified buried radial systems was replaced with a version of the 80/75-meter LMPA in Part 1. The model used had only the 8 0.1" diameter elements and omitted the 2 parasitic support towers. For the validation work at hand, it was considered legitimate to presume that the 0.1" wires could be self-supporting. The following model description provides the essential physical and electrical details.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80-m t=.92 s=.05 3.3-4.5                    Frequency = 3.5-4.0  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1            0.000,  0.000, 75.500     G   0.000,  0.000,  0.000 1.00E-01  27
+2           15.494,  0.000, 69.500     G  15.494,  0.000,  0.000 1.00E-01  25
+3           29.771,  0.000, 64.563     G  29.771,  0.000,  0.000 1.00E-01  23
+4           42.928,  0.000, 60.000     G  42.928,  0.000,  0.000 1.00E-01  21
+5           55.050,  0.000, 55.500     G  55.050,  0.000,  0.000 1.00E-01  19
+6           66.221,  0.000, 51.500     G  66.221,  0.000,  0.000 1.00E-01  17
+7           76.515,  0.000, 48.000     G  76.515,  0.000,  0.000 1.00E-01  17
+8           86.000,  0.000, 44.500     G  86.000,  0.000,  0.000 1.00E-01  15
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          15     8 / 96.67   (  8 /100.00)      0.707       0.000       V
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      1/98.1  (  1/100.)    2/98.0  (  2/100.)  Actual dist   75.0  1.00  R
+2      2/98.0  (  2/100.)    3/97.8  (  3/100.)  Actual dist   75.0  1.00  R
+3      3/97.8  (  3/100.)    4/97.6  (  4/100.)  Actual dist   75.0  1.00  R
+4      4/97.6  (  4/100.)    5/97.4  (  5/100.)  Actual dist   75.0  1.00  R
+5      5/97.4  (  5/100.)    6/97.1  (  6/100.)  Actual dist   75.0  1.00  R
+6      6/97.1  (  6/100.)    7/97.1  (  7/100.)  Actual dist   75.0  1.00  R
+7      7/97.1  (  7/100.)    8/96.7  (  8/100.)  Actual dist   75.0  1.00  R
+
+Ground type is Real, MININEC-type analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance of the array with a MININEC ground can be summarized by using 3.5, 3.75, and 4.0 MHz checkpoints. In the following table, TO angle is the elevation angle of maximum radiation. The front-to-rear ratio is the worst case ratio of gain forward to rear taken from an elevation plot. The 180-degree front-to-back ratio is taken from an azimuth plot at the TO angle. The beamwidth refers to the angle between -3 dB points on the azimuth pattern. The 75-Ohm phase line yield a reasonable match for 50-Ohm coaxial cable and the 50-Ohm SWR is given in the last column.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    8-Element 80/75 MHz LPMA with MININEC Ground
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          4.44  22     16.11        18.97        132   50.3-j 3.5   1.07
+3.75         4.12  22     13.80        15.32        136   54.7+j 4.4   1.13
+4.0          4.39  22     16.59        19.94        128   44.7-j 6.5   1.20
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In attempting to validate this model, it is not necessary to produce the exact figures. However, the patterns and general levels should be consistent with the values given. For example, the model shows a small gain decline mid-band, accompanied by a similar small decline in the F-R and F-B values. The mid-band region also shows a rise in the resistive component of the feedpoint impedance.

+

Providing this model with sundry simplified ground-treatment systems all failed to yield acceptable results. For example, placing a single 60-radial buried system beneath the array, using 140' radials and a connection to the center element of the LPMA yielded no better gain -1.84 dBi and that only at one frequency. The key move was proving 3 radial systems of differential lengths connected to the end and the middle elements. Gain rose to a peak of 1.34 dBi, but again, only at one frequency.

+

The key to a satisfactory radial system for the array did not arise from the differential radial lengths used in the last trial, but from the connections to elements. The more elements that had a radial system directly and independently tied to them, the better the response. Hence, the final system provided an independent radial system for each element in the array.

+
+ +
+

Fig. 3 shows the outline sketch of the largest model in the final test group, with 976 wires and 2690 segments. However, it only achieves 23 radials per element. In fact, the radial systems themselves are interesting in terms of the techniques used to ensure their independence, where independence means that no wire from one system touches a wire from another system. The 8 individual radial systems are at different levels, separated by 3". This technique held the lowest level, used for the rear element, at the 2' level below ground. Other test models have shown that in the lower HF region, there is insignificant difference among models with buried radials in the 6" to 24" range below ground.

+

Since each radial system has a connecting wire to the element that it serves, it was necessary to ensure that no radial passed though a connecting wire. Therefore, I chose to use an odd number of radials, beginning with a set of 7 per element, as shown in Fig. 4.

+
+ +
+

By setting the initial radial at right angles to the boom line, all of the subsequent radials would take angles so that none would be parallel to the boom. By increasing the sequence in 8-radial steps (7-15-23-31-etc.), the same condition would exist and avoid model crashes.

+
+ +
+

Modeling a buried radial system requires adherence to several NEC guidelines which will explain the modeling structure shown in Fig. 5. A segment junction--usually a wire end-- must be a Z=0, that is, at ground level. Since the connector wires to the radials would be short, and since angular junctions are best served by segment lengths that are equal, a form of segment length tapering for the radials was in order. As well, the segments on either side of the source segment should equal the length of the source segment. For a vertical element, the source (or phase line connection for an LPMA) should be on the lowest segment. To achieve this and to have the first segment above the source segment be of the same length, a separate "source wire" was constructed, with the vertical element above that point also tapered in terms of segment length.

+

The resulting model results in wire junctions quite different from those of the MININEC model. Therefore, a second MININEC-ground model was constructed with the elements tapered exactly as they would be in the buried-radial model. The results are extremely close to the version using standard segmentation techniques.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+       8-Element 80/75 MHz LPMA with MININEC Ground (Segment Tapered Elements)
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          4.48  22     16.10        18.98        132   49.7-j 3.7   1.08
+3.75         4.17  22     13.79        15.30        136   54.2+j 3.9   1.12
+4.0          4.44  22     16.59        19.96        128   44.2-j 6.6   1.21
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The only differences occur in the last decimal column for any entry, indicating a very tight correlation with the original model.

+

The buried radial model was run using 7, 15, and 23 radials per element. These runs produced interesting results, and further runs with higher numbers of radials per element would be useful. However, the run time increases exponentially with increases in wires and segments, so tests were limited to data gathering that required less than 1.5 hours per check point. (We shall see an indirect validation technique shortly.) The results for the runs are in the following table.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             8-Element 80/75 MHz LPMA with 7 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          0.87  22     13.75        15.07        135   48.5-j 1.4   1.04
+3.75         0.99  22     15.80        18.26        130   54.8-j 4.7   1.14
+4.0          1.34  23     14.91        15.95        129   45.3-j 2.5   1.12
+
+             8-Element 80/75 MHz LPMA with 15 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          2.81  22     13.38        14.51        138   50.5-j 2.7   1.06
+3.75         2.98  22     13.98        15.49        135   59.2-j 4.7   1.21
+4.0          3.30  23     14.44        15.56        133   45.3-j 1.6   1.11
+
+             8-Element 80/75 MHz LPMA with 23 Buried Radials per Element
+Freq.        Gain  TO     F-R Ratio    F-B Ratio    B/W   Feed Z       50-Ohm
+MHz          dBi   deg    dB           dB           deg   R+/-jX       SWR
+3.5          3.53  23     12.99        14.03        140   51.1-j 4.2   1.09
+3.75         3.61  23     13.25        14.41        137   60.4-j 1.6   1.21
+4.0          3.85  23     14.42        15.59        133   45.8-j 1.5   1.10
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The progression of values with increasing numbers of radials per element is promising, and the impedance values are especially attractive, since even with the lowest number of radials per element, they track the MININEC model very closely. Performance has smoothed out across the passband of the array to a level that is not only higher, but is as well more equal at every checkpoint than in any of the simplified ground treatments. The question that remains is whether there is a radial count level per element that will likely yield array results equal to or better than those predicted by the MININEC model.

+

By fiat, I declared the 23-radial system to be the largest that I would run with the full 8-element array. This foreclosed direct determination of an answer to the remaining quandary. However, there is an indirect route to an answer. I modeled a simple monopole for 3.75 MHz using radial systems in increments of 8 but starting with 7. Fig. 6 shows the smallest (7 radials) and the largest (63 radials) of the sequence. Each monopole and radial system used the same structure as an individual element in the LPMA model.

+
+ +
+

The following table summarizes the results of the test model.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              3.75 MHz Monopole Performance with Various Radial Systems
+No. of       Gain         TO Angle           Feed Impedance            50-Ohm
+Radials      dBi          degrees            R +/- jX Ohms             SWR
+ 7           -1.08        24                 54.8 + j 16.2             1.38
+15           -0.25        25                 46.5 + j 13.1             1.33
+23            0.13        25                 43.1 + j 11.9             1.34
+31            0.36        25                 41.1 + j 11.2             1.37
+39            0.51        25                 39.7 + j 10.6             1.39
+47            0.61        25                 38.7 + j 10.2             1.41
+55            0.69        25                 37.9 + j  9.8             1.43
+63            0.74        25                 37.3 + j  9.4             1.44
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model surpasses a MININEC-ground version of the monopole in gain at the 39-radial level and equals it in impedance at the 63-radial level.

+

By examining the rate of change of the monopole figures throughout its range of radial systems, we can project similar rates of change to the progression of LPMA values, using average gain values for the entire array passband. The result is a projection of values above the level of radial systems explored directly.

+
+ +
+

Fig. 7 provides a graph of the monopole values, the combined LPMA direct and indirect values, and reference lines for the predicted MININEC-ground models for both antennas. The LPMA projection values should be read with caution, since a number of real antenna variables may intervene to deny the array its ultimate performance levels. Obtaining the highly complex field of radials for the LMPA is a construction challenge several orders of magnitude greater than that associated with layout radials for a single monopole.

+

Nevertheless, the modeling and derivation techniques do establish some useful points. First is the fact that the MININEC-ground LPMA can be realized with a buried radial system. However, that system may be more extensive and of a nature not fully appreciated before this exercise. Each element needs to be supplied with a radial system of its own, independent of the radial system serving other elements. At this point, it is not certain whether one can use an interlocking grid where the radial wires make good electrical contact, although the model suggests that electrical independence is the best method so far obtained.

+

Second, the radial system for each element will have to be fairly extensive to obtain more than mediocre performance from the LPMA. About 39 radials per element seems called for by the model for average to good soil (conductivity: 0.005 S/m; dielectric constant: 13). Worse soils will call for more extensive radial systems per element. A full field, as defined by the AM broadcast industry, would not be out of place for a serious installation of the LPMA. It is likely that poor performance from any lower-HF LPMA can be traced primarily to a poor ground treatment system (with room for poor-design causes as an additional factor).

+

The use of a MININEC ground in a model, then, is legitimate and the general performance predicted by such a model can be obtained. However, the cost in terms of modeling and especially in terms of required construction is very high. Consider the following alternatives. We examined a fixed-position horizontal LPDA of the same general design as the LPMA. To arrive at roughly equivalent performance levels, The LPDA would need to by 90-100 feet high, requiring 4 support towers, appropriate non-conductive support cables, and sundry materials. The comparable LPMA would require only 2 towers, but complex and extensive treatment of the ground at the element bases. Which option might be best for a given installation makes an interesting thought project.

+
+ +
+

Updated 06-01-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: HF Lower, LPDA, Vertical


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+

80-Meter Wire LPDAs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

For many years, the ARRL Antenna Book has contained an LPDA for 80 meters that uses 4 elements and is arranged as both a forward-sloping Vee and an inverted Vee, with its ends close to the ground. It was carefully designed from basic LPDA design equations with a Tau of 0.845 and a Sigma of 0.06, resulting in a #14 copper wire array close to 50' from front to rear (ignoring the forward Vee extension).

+

Unfortunately, this array has a number of properties that reduce its potential performance:

+
    +
  • 1. The elements are Vee'd forward, reducing gain and decreasing the front-to-side ratio.
    • +
  • 2. The elements are modified inverted Vees, again reducing gain and decreasing the front-to-side ratio.
    • +
  • 3. The array uses thin wire, reducing gain relative to elements of an optimal diameter.
    • +
  • 4. The combination of Tau (0.845) and Sigma (0.06) alone yield a maximum free-space gain potential to well under 6 dBi.
    • +
+

The combination of performance-degrading factors in this array strongly suggest that a redesign is in order. In these notes, I shall explore more adequate arrays for 80 meters. However, each will presume standard linear elements at right angles to the main array axis. In the course of these notes, we shall look at the question of optimal element size and how to simulate it with a wire array. We shall also examine some limits (and the reasons for those limits) of improving thin wire lower HF arrays with simulated fatter elements.

+

An Improved 6-Element Wire LPDA for 80 Meters

+
+ +
+

Fig. 1 shows the outline of an LPDA using 6 elements, with a Tau of 0.8918 and a Sigma of 0.0702. The Tau and Sigma values are the initial values of the design. However, the element lengths have been optimized for the best performance across the 80-meter band (3.5-4.0 MHz) using standard circularized-Tau techniques. The final design--which might still be improved further with judicious experimentation--retains the original spacing, but 4 of the 6 elements have modified lengths.

+

Key to array performance is the element diameter, specified in the original design as 2". The elements are modeled as copper, although there is less than 0.02 dB difference between copper and aluminum when the elements are as fat as specified here.

+

The following table provides the wire specifications in the form of a NEC wire table. The phase line has a characteristic impedance of 100 Ohms.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3.3-4.5 MHz t=.89 s=.07                  Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-76.000,  0.000         0.000, 76.000,  0.000 2.00E+00  91
+2           21.346,-67.800,  0.000        21.346, 67.800,  0.000 2.00E+00  81
+3           40.382,-60.500,  0.000        40.382, 60.500,  0.000 2.00E+00  73
+4           57.358,-55.500,  0.000        57.358, 55.500,  0.000 2.00E+00  65
+5           72.498,-51.000,  0.000        72.498, 51.000,  0.000 2.00E+00  59
+6           86.000,-47.500,  0.000        86.000, 47.500,  0.000 2.00E+00  53
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          27     6 / 50.00   (  6 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance of this array is quite good for an 86' long LPDA on 80 meters, with an average free-space gain of about 6.9 dBi across the band. Whether the performance can be maintained in practice depends, of course, on the ability of the builder to raise the antenna to a height where horizontally polarized antennas perform well over desired propagation paths. The front-to-back ratio is above 20 dB across the band.

+

The use of 2" diameter elements on 80 meters is exceptionally rare, given the need for elements that are at their longest 152'. As an experiment, I took the same array and tested it in model form using #12 AWG wire (0.0808" diameter). Interestingly, the average free-space gain dropped to about 5.9 dBi with an average front-to-back ratio of about 13.5 dB. The loss of a full dB of gain in the move from 2" to 0.0808" element diameters seemed less than desirable.

+

Therefore, I reconstructed the elements from 2 parallel wires in accord with the sketch in Fig. 2.

+
+ +
+

The principle, as I have elsewhere noted, consists in taking a representative element in the array and finding its self-resonant frequency. Then, I constructed a model of a two-wire element of the same length and varied the spacing between the wires until it was resonant at the same frequency. In the present exercise, a spacing of between 10 and 12 inches proved to be close to precise, with a remnant reactance of under 10 Ohms at the widest spacing used.

+

For modeling simplicity, I used the 12" spacing, which translates into 1 foot (or a shortest segment length of 0.5'). See Fig. 3.

+
+ +
+

Fig. 3 shows the element model. The center portion is (for this model) 1.5' long and consists of 3 segments to ensure that the source segment is equal in length to the segments adjacent to it. The single wire is also necessary within the LPDA array, since the phase-line must meet a single wire segment at each element in the array. On each side of center, single segment wires, each 0.5' long, connect the center wire to the parallel wires that constitute the bulk of the elements. These wires, which have the same number of segments to sustain parallel segment junctions throughout, are connected together at the outer ends with 2-segment wires. The 11-wire element constitutes a reasonably fair model of the 2-wire element.

+

The attention to segment lengths at the center-most part of the element allowed me to reduce the number of segments in the long wires. Ideally, the segment length should be 0.5' throughout the model, which would have resulted in about 150 segments per long wire in the longest element. However, reducing the number to about 50 yielded a change of reactance in the test element of under 5 Ohms. So reduced segmentation--but still with parallel segment junctions--was used in the final array model. For reference, the following partial table shows just 2 elements of the modified array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80, t=.89 s=.07                              Frequency = 3.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W2E1   0.000,-76.000, -0.500  W3E1   0.000,-76.000,  0.500    # 12    2
+2     W1E1   0.000,-76.000, -0.500  W4E1   0.000, -0.750, -0.500    # 12   51
+3     W1E2   0.000,-76.000,  0.500  W5E1   0.000, -0.750,  0.500    # 12   51
+4     W2E2   0.000, -0.750, -0.500  W5E2   0.000, -0.750,  0.000    # 12    1
+5     W3E2   0.000, -0.750,  0.500  W6E1   0.000, -0.750,  0.000    # 12    1
+6     W4E2   0.000, -0.750,  0.000  W7E1   0.000,  0.750,  0.000    # 12    3
+7     W8E1   0.000,  0.750,  0.000  W9E1   0.000,  0.750, -0.500    # 12    1
+8     W6E2   0.000,  0.750,  0.000 W10E1   0.000,  0.750,  0.500    # 12    1
+9     W7E2   0.000,  0.750, -0.500 W11E1   0.000, 76.000, -0.500    # 12   51
+10    W8E2   0.000,  0.750,  0.500 W11E2   0.000, 76.000,  0.500    # 12   51
+11    W9E2   0.000, 76.000, -0.500 W10E2   0.000, 76.000,  0.500    # 12    2
+12   W13E1  21.346,-67.800, -0.500 W14E1  21.346,-67.800,  0.500    # 12    2
+13   W12E1  21.346,-67.800, -0.500 W15E1  21.346, -0.750, -0.500    # 12   46
+14   W12E2  21.346,-67.800,  0.500 W16E1  21.346, -0.750,  0.500    # 12   46
+15   W13E2  21.346, -0.750, -0.500 W16E2  21.346, -0.750,  0.000    # 12    1
+16   W14E2  21.346, -0.750,  0.500 W17E1  21.346, -0.750,  0.000    # 12    1
+17   W15E2  21.346, -0.750,  0.000 W18E1  21.346,  0.750,  0.000    # 12    3
+18   W19E1  21.346,  0.750,  0.000 W20E1  21.346,  0.750, -0.500    # 12    1
+19   W17E2  21.346,  0.750,  0.000 W21E1  21.346,  0.750,  0.500    # 12    1
+20   W18E2  21.346,  0.750, -0.500 W22E1  21.346, 67.800, -0.500    # 12   46
+21   W19E2  21.346,  0.750,  0.500 W22E2  21.346, 67.800,  0.500    # 12   46
+22   W20E2  21.346, 67.800, -0.500 W21E2  21.346, 67.800,  0.500    # 12    2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The use of the twin-wire (#12 AWG) elements restored much of the performance to the array--on average about 80% of the performance lost in going from a 2" element to a #12 single wire element. The average free-space gain rose to over 6.6 dBi, with an average front-to-back ratio of over 20 dB.

+

However, a better measure of appreciating how well the double-wire elements simulate the tubular elements can be gleaned from some graphs.

+
+ +
+

Fig. 4 shows the free-space gain across 80 meters a 0.05 MHz intervals. Not only is the double-wire curve much higher on average than the single wire curve; as well, it parallels the 2" element curve very closely. The single-wire curve peaks at a quite different frequency from the peak for the upper two curves.

+
+ +
+

In Fig. 5, for the front-to-back ratio, we find a similar pattern, with the 2" element and the double-wire curves not only higher, but also more parallel than the curves for the single thin-wire version of the antenna.

+
+ +
+

Perhaps the least significant set of differences can be found in the 50-Ohm VSWR curve for the three versions of the array shown in Fig. 6. All would be acceptable 80-meter SWR curves. I shall note in passing that these curves are easy to obtain with experimental modeling shifts in the phase-line characteristic impedance. However, the original design equations called for a phase-line impedance of closer to 200 Ohms, with the illusion of needing a matching device for a coaxial feedline for the array.

+

The ability of a simple 2-wire element to restore most of the performance to the array arises from the fact that an LPDA--like any multi-element array--derives its performance not only from driving the elements, but as well from the mutual coupling between elements. The simulated fat elements, composed of wide-spaced wires, indeed has close to the same mutual coupling between array elements as the fat-wire model.

+

What differs between the 2-wire model and the fatter single-element version is the overall efficiency of the antenna. With 2" elements, the array is about 99.7% efficient, with losses due to material resistance that are a small fraction of 1%. The single #12 wire version is about 95.9% efficient, with over 4% material losses. The double-wire version reaches an efficiency of about 97.1%, which is only about a third of the way above the efficiency of the single-wire version toward the fat-element version. In short, the double-wire version of the antenna cannot restore all of the performance of the fat-wire version because it cannot decrease wire losses to the level of a single fat element. However, it can restore a large portion of the mutual coupling lost by using a single then wire for each element.

+

The process of restoring performance has a limit, and another LPDA design can illustrate this limit.

+

A 14-Element Wire LPDA for 80 Meters

+

By judiciously changing the values of Tau and Sigma, it is possible to arrive at an LPDA design with even better performance than we have so far attained. Fig. 7 shows the outline of a 14-element 88.5' long array, again, initially using 2" elements.

+
+ +
+

The new array uses a Tau of 0.96 and a Sigma of 0.03 to pack the large number of elements into the prescribed space. Again, the phase-line characteristic impedance is 100 Ohms to arrive at a 50-Ohm feedpoint impedance. The following table shows the dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+80m t=.96 s=.03                              Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-72.500,  0.000         0.000, 72.500,  0.000 2.00E+00  25
+2            8.603,-69.000,  0.000         8.603, 69.000,  0.000 2.00E+00  25
+3           16.862,-66.071,  0.000        16.862, 66.071,  0.000 2.00E+00  23
+4           24.790,-63.428,  0.000        24.790, 63.428,  0.000 2.00E+00  23
+5           32.402,-60.891,  0.000        32.402, 60.891,  0.000 2.00E+00  21
+6           39.709,-58.455,  0.000        39.709, 58.455,  0.000 2.00E+00  21
+7           46.723,-56.117,  0.000        46.723, 56.117,  0.000 2.00E+00  19
+8           53.457,-53.872,  0.000        53.457, 53.872,  0.000 2.00E+00  19
+9           59.922,-51.717,  0.000        59.922, 51.717,  0.000 2.00E+00  19
+10          66.128,-49.649,  0.000        66.128, 49.649,  0.000 2.00E+00  17
+11          72.086,-47.663,  0.000        72.086, 47.663,  0.000 2.00E+00  17
+12          77.805,-46.000,  0.000        77.805, 46.000,  0.000 2.00E+00  17
+13          83.296,-45.000,  0.000        83.296, 45.000,  0.000 2.00E+00  15
+14          88.567,-43.500,  0.000        88.567, 43.500,  0.000 2.00E+00  15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    14 / 50.00   ( 14 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Like the smaller array, this design employs a measure of circularized Tau to obtain better performance than provided by the initial design taken from LPDA equations. The rear-most 2 and the forward-most 3 elements have been modified, and further refinement may be possible.

+

With 2" elements, the array has an average free-space gain across 80 meters of nearly 7.6 dBi, with an average front-to-back ratio of about 20 dB. A single #12 wire version of the antenna achieves an average free-space gain of about 6.75 dBi, about 0.8 dB lower than the fat-element version. Interestingly, the single-wire version of the antenna has an average front-to-back ratio of about 25 dB, about 5 dB higher than that of the fat-element version.

+

The same techniques used with the smaller array were applied to the 14-element LPDA to produce a double wire version. The resulting array model had over 2300 segments, even using the reduced levels of segmentation in the long parallel sections of each double-wire element. The resulting array showed an average free-space gain of about 7.1 dBi, less than half way toward the fat-element version from the single-wire model. The average front-to-back ratio was about 21 dB, close to the value of the fat-element version.

+
+ +
+

Fig. 8 shows the gain curves for the three models. The double-wire and fat-wire versions are very synchronous, while the single-wire model curve shows divergent frequencies for its peaks and valleys.

+
+ +
+

In Fig. 9, we see much the same results. The fat-wire and double-wire curves are closely matched, while the single-wire takes a direction of its own--and at a higher average level of front-to-back ratio.

+
+ +
+

In keeping with the front-to-back curves, Fig. 10 shows 50-Ohm VSWR curves that are very similar for the fat-wire and double wire models. In contrast, although still a very flat curve, the single-wire SWR curve shows a progression of its own.

+

Initially, one might have expected a relatively uniform performance upgrade relative to that shown for the 6-element LPDA. However, 2 factors count against that expectation.

+

First, the efficiency of the larger array is inherently lower than that of the small LPDA. The fat-element version has an efficiency of about 99.2%, against a single #12 wire version efficiency of 88.5%. Doubling the wires for each element only raises the efficiency to 90.8%, a gain of 2.3% but still 8.4% shy of the fat wire model. From an efficiency perspective alone, the ability of the double-wire version to restore most of the performance of the fat-wire version is limited.

+

However, we should have also noted the fact that the LPDA front-to-back ratio decreased as we moved from the thin-wire to the fat-wire model. This fact suggests that the most closely spaced elements of the 14-element array are already over-coupled when using fat elements. Gain increases with wire size are largely functions of increased efficiency rather than superior mutual coupling between elements. The following table provides the key performance reports of NEC for the same 14-element array using a variety of element diameters ranging from the single-wire #12 AWG version up to and including the 2: element version. The progression may prove interesting for data taken at 3.75 Hz.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+El. Dia.    Gain        F-B Ratio         Feed Impedance          50-Ohm
+ inches     dBi         dB                R+/-jX Ohms             VSWR
+0.0808      6.80        26.25             62.9 - j 4.4            1.28
+0.25        7.24        23.57             60.2 - j 6.9            1.25
+0.5         7.37        21.91             55.0 - j 9.2            1.22
+1.0         7.45        20.65             46.8 + j 8.2            1.20
+1.5         7.48        20.03             42.3 - j 4.9            1.22
+2.0         7.50        19.68             40.1 - j 1.5            1.25
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The largest increment of gain occurs with the first move that increases the element diameter by a factor of 3. As well, the front-to-back ratio also shows its steepest decrease. Above that level, performance stabilizes within a quite narrow range.

+

The result for this particular model is a set of alternative building strategies. One might go to the trouble of constructing 14 sets of double-wire elements. However, one can get as much performance improvement of the single-thin-wire model by simply using 0.25" wire, either copper or aluminum--the latter being lighter.

+

An Alternative Method of Modeling 2-Wire LPDA Elements

+

The method used in these notes to model the 2-wire substitute elements for an LPDA results in a very large model. The model of the 14-element array used 154 wires and 2334 segments. Even the smaller 6-element LPDA required 66 wires and 1010 segments for the 2-wire substitute.

+

There is a technique that results in smaller models with respect to the number of wires and segments, although the number of TL-transmission lines does increase. An increase in TL entries does not materially increase the run time of a model. Nor does it press any program limitations for the number of allowable segments. Consequently, the alternative method does have some advantages for the LPDA modeler. Therefore, consider Fig. 11.

+
+ +
+

The sketch shows the modeling structure--reduced to the forward 2 elements of a full array. The sketch presumes that the modeler creates a single 4-wire loop for each element, proceeding in a counter-clockwise direction as he adds wires to make the loop. With only 4 wires, the modeler has already saved 7 wires per element in the process. Moreover, each wire can use longer segment lengths, thus reducing the number of segments per element by as much as half to two-thirds.

+

The presumption that the element loop was created by going "around the horn" with wires creates an interesting situation with respect to the TL (transmission line) entries for the phase line. With a single wire assembly per element (or the single-wire central sections to the earlier technique for creating double-wire elements), each TL entry would be set to "Reverse" rather than to "Normal" in order to simulate the phase reversal between elements. In the new technique, using the presumed method of forming elements, we want to have both wires of each element connected in parallel, with a phase reversal between elements.

+

To achieve this goal, we must remember that our method of forming elements has reversed the direction of current. Therefore, to simulate a direct parallel connection between the two closely spaced wires, we must use a reverse connection of the tiny TL line between them. We can make the line that creates the parallel connection as short as we wish, since the line is mathematical only--and the physical distance between wires makes no difference. A TL entry for a length as short is 0.001 foot (since the model is in feet) will do fine.

+

Between elements, we wish to have a phase reversal. However, the current directions of the two wires we connect are already opposite in phase. Therefore, we use a "Normal" TL line entry for the "actual" distance between wires. The following extracts from an LPDA model using this technique will demonstrate the process further.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3.3-4.5 MHz t=.89 s=.07                         Frequency = 4  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W4E2   0.000,-72.500,  0.000  W2E1   0.000, 72.500,  0.000    # 12   57
+2     W1E2   0.000, 72.500,  0.000  W3E1   0.000, 72.500,  1.000    # 12    1
+3     W2E2   0.000, 72.500,  1.000  W4E1   0.000,-72.500,  1.000    # 12   57
+4     W3E2   0.000,-72.500,  1.000  W1E1   0.000,-72.500,  0.000    # 12    1
+5     W8E2   8.603,-69.000,  0.000  W6E1   8.603, 69.000,  0.000    # 12   53
+6     W5E2   8.603, 69.000,  0.000  W7E1   8.603, 69.000,  1.000    # 12    1
+7     W6E2   8.603, 69.000,  1.000  W8E1   8.603,-69.000,  1.000    # 12   53
+8     W7E2   8.603,-69.000,  1.000  W5E1   8.603,-69.000,  0.000    # 12    1
+9    W12E2  16.862,-66.071,  0.000 W10E1  16.862, 66.071,  0.000    # 12   51
+10    W9E2  16.862, 66.071,  0.000 W11E1  16.862, 66.071,  1.000    # 12    1
+11   W10E2  16.862, 66.071,  1.000 W12E1  16.862,-66.071,  1.000    # 12   51
+12   W11E2  16.862,-66.071,  1.000  W9E1  16.862,-66.071,  0.000    # 12    1
+. . .
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          17    55 / 50.00   ( 55 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    3/50.0  (  3/50.0)    0.001 ft   100.0  1.00  R
+2      3/50.0  (  3/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  N
+3      5/50.0  (  5/50.0)    7/50.0  (  7/50.0)    0.001 ft   100.0  1.00  R
+4      7/50.0  (  7/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  N
+5      9/50.0  (  9/50.0)   11/50.0  ( 11/50.0)    0.001 ft   100.0  1.00  R
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The "wires" portion of the table shows the rear 3 elements of an LPDA composed of 2-wire elements. The 4 "Transmission Line" entries show the portions of the phase line connecting these elements. TLs 1, 3, and 5 are clearly the connections within each element, while lines 2 and 4 interconnect elements.

+

Some modelers run all long wires either left-to-right or right-to-left. Had we used this convention, the short TL within an element would require a "Normal" connection and the inter-element phase lines would require a "Reverse" connection. Either system will yield accurate results in terms of antenna performance, but mixed systems will result in bewildering outputs.

+

The alternative modeling system for LPDA double-wire elements may in fact produce more accurate results. At least the results are a bit more coincident with those for the single fat elements that the double-wire versions replace. The following short tables summarize for each of the two different LPDA designs the key parameters for 3.5, 3.75, and 4 MHz.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6-element LPDA Model Performance
+Frequency     Gain     Front-to     Feedpoint Impedance     50-Ohm
+   MHz        dBi      Back Ratio     R +/- jX Ohms          VSWR
+2" Elements
+  3.5         7.04      23.91         59.9 - j 16.5          1.418
+  3.75        6.78      22.51         52.8 + j 11.1          1.248
+  4.0         6.78      27.13         92.2 + j 10.3          1.875
+Double-Wire Model: Initial Method
+  3.5         6.83      23.84         58.3 - j 13.3          1.336
+  3.75        6.49      19.99         55.8 + j 14.6          1.346
+  4.0         6.59      26.65         90.8 + j  4.6          1.822
+Double-Wire Model: Revised Method
+  3.5         6.87      23.18         60.4 - j 15.5          1.402
+  3.75        6.58      20.82         54.7 + j 12.6          1.291
+  4.0         6.57      25.46         90.8 + j 12.4          1.864
+
+14-element LPDA Model Performance
+Frequency     Gain     Front-to     Feedpoint Impedance     50-Ohm
+   MHz        dBi      Back Ratio     R +/- jX Ohms          VSWR
+2" Elements
+  3.5         7.67      18.84         61.5 + j  3.1          1.239
+  3.75        7.50      19.68         40.1 - j  1.5          1.250
+  4.0         7.49      21.52         58.4 - j  5.3          1.202
+Double-Wire Model: Initial Method
+  3.5         7.21      22.11         60.3 - j  3.8          1.220
+  3.75        7.06      20.54         44.3 + j  5.2          1.178
+  4.0         7.03      20.64         50.3 - j 15.2          1.352
+Double-Wire Model: Revised Method
+  3.5         7.27      20.33         60.7 + j  2.7          1.221
+  3.75        7.10      20.02         42.9 - j  0.0          1.165
+  4.0         7.10      21.33         58.7 - j  9.0          1.259
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Operationally, the differences between the two double-wire substitutes for 2" tubular elements are insignificant. However, in terms of finding the most adequate model of the 2-wire substitute, both alternatively modeled 2-wire arrays show a slightly greater coincidence with the fat-wire model in terms of the parallel of changes of values. Note, for example, the dip in the gain curve of the original substitute element model, compared to the way in which the new model changes values. As well, the impedance values--in terms both of values and of the type of reactance--of the new method more closely match those of the basic model. In short, the alternate method of modeling double-wire LPDAs may result in both smaller and slightly more accurate models.

+

Alternative Designs

+

Between 6 and 14 elements, there is a great design space for the individual who wishes to eventually build an LPDA for 80 meters. To save some initial effort in evaluating what different designs might do within the space allocated for the array, I have calculated and then modified for relatively (but not perfectly) optimized performance a collection of LPDA designs ranging from 6 to 14 elements. All except the 14-element version are limited to 86' in length, with the longest one being about 88.5' in total length. All use 100-Ohm phase lines. Other values can be used but would require an impedance matching network or device at the array feedpoint. As well, higher phase line values may slightly alter the performance curves--in places showing slight gain reductions.

+

As we have seen from the graphs presented earlier, every LPDA exhibits peaks and valleys of gain, front-to-back ratio, feedpoint impedance, and SWR. However, for initial evaluations, we can use average values, since the gain changes are under 0.3 dB in the worst case. Only the longest LPDA in the collection shows front- to-back values under 20 dB. The average value of the 50-Ohm SWR is a reasonably good indicator of the impedance swing range. The "Model" label indicates the approximate values of Tau and Sigma. All models use 2" copper elements, and further on, we shall note the potential of these models for conversion to double- wire substitutes.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Average Performance Values of 80-Meter LPDAs
+Model       Gain        F-B         SWR
+8907-6      6.86        24.33       1.517
+9205-8      7.10        26.74       1.420
+9404-10     7.18        25.91       1.378
+9503-12     7.26        25.40       1.186
+9603-14     7.55        19.95       1.230
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As we would expect, the gain increases steadily as we increase the number of elements. However, the front-to-back ratio peaks with the 8-element design. This peak is a rough indication that, with respect to the front-to-back ratio, optimal inter-element coupling occurs with the spacings of this array. We may also note that the average SWR decreases steadily until at the 1.25:1 region, differences no longer make a difference. As well, impedance swings decrease in step with the average SWR.

+

Selecting an array to replicate is always a composite judgment based on many factors. The more elements, the higher the gain, but not necessarily a higher the front-to-back ratio. If we translate the designs into double wire elements, then we must also consider the fact that as we increase the number of elements, the lower the return rate to full 2"-element performance due to a decreasing efficiency (added material losses) as we add more double-wire elements.

+

In broadest terms, perhaps the 8- and 10-element arrays show the most promise. They provide a useful increment of gain above the 6-element LPDA and provide peak front-to-back performance. Using double-wire elements will allow the wire array to more closely approximate the performance of the fat-element model with these smaller arrays than with the longest versions in the set. The prospective builder can interpolate from the 6-element and the 14-element figures the likely performance figures for double-wire versions of these intermediate arrays. The overall array weight of the 8- and 10-element LPDAs is also likely to be more manageable than the weight of larger models.

+

For reference, the following wire-tables of the models will provide enough guidance to replicate as models or in wire any of the designs discussed.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8907-6 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-76.000,  0.000         0.000, 76.000,  0.000 2.00E+00
+2           21.346,-67.800,  0.000        21.346, 67.800,  0.000 2.00E+00
+3           40.382,-60.500,  0.000        40.382, 60.500,  0.000 2.00E+00
+4           57.358,-55.500,  0.000        57.358, 55.500,  0.000 2.00E+00
+5           72.498,-51.000,  0.000        72.498, 51.000,  0.000 2.00E+00
+6           86.000,-47.500,  0.000        86.000, 47.500,  0.000 2.00E+00
+
+9205-8 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           15.494,-69.500,  0.000        15.494, 69.500,  0.000 2.00E+00
+3           29.771,-64.563,  0.000        29.771, 64.563,  0.000 2.00E+00
+4           42.928,-60.000,  0.000        42.928, 60.000,  0.000 2.00E+00
+5           55.050,-55.500,  0.000        55.050, 55.500,  0.000 2.00E+00
+6           66.221,-51.500,  0.000        66.221, 51.500,  0.000 2.00E+00
+7           76.515,-48.000,  0.000        76.515, 48.000,  0.000 2.00E+00
+8           86.000,-44.500,  0.000        86.000, 44.500,  0.000 2.00E+00
+
+9404-10 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           12.160,-71.000,  0.000        12.160, 71.000,  0.000 2.00E+00
+3           23.570,-66.953,  0.000        23.570, 66.953,  0.000 2.00E+00
+4           34.277,-62.826,  0.000        34.277, 62.826,  0.000 2.00E+00
+5           44.324,-58.700,  0.000        44.324, 58.700,  0.000 2.00E+00
+6           53.752,-55.800,  0.000        53.752, 55.800,  0.000 2.00E+00
+7           62.599,-53.000,  0.000        62.599, 53.000,  0.000 2.00E+00
+8           70.900,-49.500,  0.000        70.900, 49.500,  0.000 2.00E+00
+9           78.690,-47.500,  0.000        78.690, 47.500,  0.000 2.00E+00
+10          86.000,-45.000,  0.000        86.000, 45.000,  0.000 2.00E+00
+
+9503-12 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-75.500,  0.000         0.000, 75.500,  0.000 2.00E+00
+2           10.006,-71.800,  0.000        10.006, 71.800,  0.000 2.00E+00
+3           19.504,-68.519,  0.000        19.504, 68.519,  0.000 2.00E+00
+4           28.521,-65.044,  0.000        28.521, 65.044,  0.000 2.00E+00
+5           37.081,-61.746,  0.000        37.081, 61.746,  0.000 2.00E+00
+6           45.206,-58.614,  0.000        45.206, 58.614,  0.000 2.00E+00
+7           52.919,-55.641,  0.000        52.919, 55.641,  0.000 2.00E+00
+8           60.241,-53.000,  0.000        60.241, 53.000,  0.000 2.00E+00
+9           67.192,-52.000,  0.000        67.192, 52.000,  0.000 2.00E+00
+10          73.790,-48.500,  0.000        73.790, 48.500,  0.000 2.00E+00
+11          80.054,-46.500,  0.000        80.054, 46.500,  0.000 2.00E+00
+12          86.000,-44.500,  0.000        86.000, 44.500,  0.000 2.00E+00
+
+
+9603-14 elements
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+
+1            0.000,-72.500,  0.000         0.000, 72.500,  0.000 2.00E+00
+2            8.603,-69.000,  0.000         8.603, 69.000,  0.000 2.00E+00
+3           16.862,-66.071,  0.000        16.862, 66.071,  0.000 2.00E+00
+4           24.790,-63.428,  0.000        24.790, 63.428,  0.000 2.00E+00
+5           32.402,-60.891,  0.000        32.402, 60.891,  0.000 2.00E+00
+6           39.709,-58.455,  0.000        39.709, 58.455,  0.000 2.00E+00
+7           46.723,-56.117,  0.000        46.723, 56.117,  0.000 2.00E+00
+8           53.457,-53.872,  0.000        53.457, 53.872,  0.000 2.00E+00
+9           59.922,-51.717,  0.000        59.922, 51.717,  0.000 2.00E+00
+10          66.128,-49.649,  0.000        66.128, 49.649,  0.000 2.00E+00
+11          72.086,-47.663,  0.000        72.086, 47.663,  0.000 2.00E+00
+12          77.805,-46.000,  0.000        77.805, 46.000,  0.000 2.00E+00
+13          83.296,-45.000,  0.000        83.296, 45.000,  0.000 2.00E+00
+14          88.567,-43.500,  0.000        88.567, 43.500,  0.000 2.00E+00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Conclusion

+

80-meter wire LPDAs can be effective horizontally polarized antennas for the entire band if they are better designed than past versions. Minimally, I would recommend the 6-element 86' long model as an array whose effort at construction and mounting would be rewarded by decent performance. The double-wire version is apt for fixed installations, while--for certain builders with abilities matching the mass--the use of large tubular elements might well permit rotation of the antenna.

+

Further increments of performance will require larger arrays, such as the 14-element 88' LPDA noted in the design exercise. However, because the elements have already reached the limits of their inter-element coupling, the double-wire version may be more work than is worth the effort. The use of a larger wire size--0.25" or greater--may be the best way to improve performance above the level one can obtain from a single #12 wire.

+

Along the way, we have seen that the double-wire simulation of fat elements has a limit. The more elements to the array, the less the double-wire element can effectively restore performance lost when using single thin wires. Mutual coupling varies with several variables, including element spacing, element diameter, and frequency. The peaks and valleys evident in both gain and front-to-back curves for LPDAs arise largely because the mutual coupling among the most active elements does vary with frequency--variations which also yield changes in the current magnitude on each element in the array. The peaks and valleys in the performance curves are not coincident for both gain and the front-to-back ratio, suggesting that the optimal mutual coupling conditions for one parameter are not necessarily optimum for the other. However, since many elements are simultaneously active to a significant, if not controlling, degree, exacting formulations of the relationships lie beyond the realm of modeling. Nevertheless, in revealing the coincidence and displacement of curves as we vary the element diameter of the elements, modeling can show the effects of changes in coupling among elements.

+

The upshot of these exercises is this: it pays to explore a given design in many different kinds of models before deciding on the best method of construction.

+
+ +
+

Updated 04-01-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for March, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: HF Lower, LPDA


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+

Long-Boom LPDAs for 14-30 MHz

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In this note, I want to discuss a pair of long-boom LPDA designs to cover all of the amateur bands from 20 through 10 meters. Long-boom means (for our purposes) anything over 45' or so. We know that 5-6-element monoband Yagis can achieve a little over 10.1 dBi free-space gain with better than 20 dB front-to-back ratios across 20 meters with boom lengths between 45 and 53 feet. The question before us is this: what can we achieve using a similar boom length in a multi-band antenna?

+

Standards of Comparison

+

In the tri-band category, Force 12 has a 49-foot model with excellent performance on 20, 15, and 10 meters. However, the standard for comparison for an LPDA would need to cover all 5 upper HF bands.

+

The only single-boom design with high performance on all 5 amateur bands is the ON4ANT forward-stagger design, which has recently appeared in journals and also appears at my web site. Fig. 1 shows the general outline of the "final" 14-element, 60'-boom model designed by Johan Van de Velde.

+
+ +
+

For each band below 10 meters, the director also serves as the reflector for the next higher band. As well, for all bands above 20 meters, the director serves as the reflector for the next higher band. Additional directors have been added to improve 10-meter performance.

+

For reference, the following EZNEC-4 model description will provide the dimensions (in meters):

+ 
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+ON4ANT 5-b Yagi:  14-28 Final              Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 3.20E+01  37
+2           -5.200,  2.000,  0.000         5.200,  2.000,  0.000 3.20E+01  35
+3           -4.900,  3.600,  0.000         4.900,  3.600,  0.000 3.20E+01  34
+4           -4.150,  5.250,  0.000         4.150,  5.250,  0.000 2.50E+01  28
+5           -4.020,  6.400,  0.000         4.020,  6.400,  0.000 2.50E+01  27
+6           -3.800,  7.200,  0.000         3.800,  7.200,  0.000 2.50E+01  25
+7           -3.395,  8.400,  0.000         3.395,  8.400,  0.000 2.50E+01  23
+8           -3.020,  9.500,  0.000         3.020,  9.500,  0.000 2.50E+01  21
+9           -2.910, 10.800,  0.000         2.910, 10.800,  0.000 2.50E+01  21
+10          -2.680, 12.000,  0.000         2.680, 12.000,  0.000 2.30E+01  19
+11          -2.550, 13.014,  0.000         2.550, 13.014,  0.000 2.30E+01  19
+12          -2.470, 13.816,  0.000         2.470, 13.816,  0.000 2.30E+01  17
+13          -2.440, 15.775,  0.000         2.440, 15.775,  0.000 2.30E+01  16
+14          -2.310, 18.250,  0.000         2.310, 18.250,  0.000 2.30E+01  16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+

More important is the performance potential, which the following table reveals:

+ 
+Freq.     Gain      F-B       Feed Impedance
+MHz       dBi       dB        R +/- jX Ohms
+20
+14.0      8.30      36.74     28.8 - j 0.4
+14.175    8.41      27.35     24.7 + j 7.9
+14.35     8.55      20.57     19.0 + j18.8
+17
+18.118    8.35      23.06     31.7 - j 4.9
+15
+21.0      8.73      23.12     34.1 + j 2.0
+21.225    8.86      23.15     35.9 + j10.3
+21.45     8.99      23.04     37.4 + j18.6
+12
+24.94     9.70      37.50     23.4 + j14.6
+10
+28.0      9.92      26.58     30.0 - j 8.8
+28.35     9.99      39.15     33.5 - j 4.7
+28.7      9.69      34.30     20.3 - j12.2
+
+

Because elements must do double duty, performance improves with frequency. Even the 20-meter performance improves as one moves up the band, since the 20-meter director must be cut and positioned also to serve as the 17-meter reflector. 15 meters shows a similar pattern. The 180-degree front-to-back value exceeds 20 dB throughout the passband.

+

No SWR figures appear since the antenna's 5 feedpoints (one for each band) are designed for use with a gamma match. The significant limitation (from the perspective of broadband design, but not from the perspective of some kinds of operating interests) is the "cut-off" of 10-meter coverage somewhere between 28.7 and 28.8 MHz, as gain continues to decrease and the feedpoint resistive component of the impedances continues to decrease.

+

The ON4ANT design makes a good standard against which to compare a high-performance LPDA.

+

Version 1: Circular-Tau-Modified Standard LPDA Design

+

The initial version of the LPDA uses a Tau of 0.95 and a Sigma of 0.056. Ideally, one should use a Tau of 0.96 and an optimized Sigma somewhat higher than 0.18. However, the boom length for such an antenna becomes well over 3 times the length of the present design. With the Tau and Sigma values given, the boom length is about 51.5' with 21 elements, all of which are uniformly 0.5" in diameter. Fig. 2 shows the general outline of the array.

+
+ +
+

For reference and element dimensions (in inches), the EZNEC model description follows:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21 el 51.5'             Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-216.30,  0.000         0.000,216.300,  0.000 5.00E-01  25
+2           48.177,-205.00,  0.000        48.177,205.000,  0.000 5.00E-01  23
+3           93.944,-194.00,  0.000        93.944,194.000,  0.000 5.00E-01  23
+4          137.424,-184.40,  0.000       137.424,184.399,  0.000 5.00E-01  21
+5          178.729,-175.18,  0.000       178.729,175.179,  0.000 5.00E-01  21
+6          217.969,-166.42,  0.000       217.969,166.420,  0.000 5.00E-01  19
+7          255.248,-158.10,  0.000       255.248,158.099,  0.000 5.00E-01  19
+8          290.662,-150.19,  0.000       290.662,150.194,  0.000 5.00E-01  17
+9          324.306,-142.68,  0.000       324.306,142.685,  0.000 5.00E-01  17
+10         356.267,-135.55,  0.000       356.267,135.550,  0.000 5.00E-01  15
+11         386.630,-128.77,  0.000       386.630,128.773,  0.000 5.00E-01  15
+12         415.475,-122.33,  0.000       415.475,122.334,  0.000 5.00E-01  15
+13         442.878,-116.22,  0.000       442.878,116.217,  0.000 5.00E-01  13
+14         468.911,-110.41,  0.000       468.911,110.407,  0.000 5.00E-01  13
+15         493.642,-104.89,  0.000       493.642,104.886,  0.000 5.00E-01  13
+16         517.136,-99.642,  0.000       517.136, 99.642,  0.000 5.00E-01  11
+17         539.456,-94.660,  0.000       539.456, 94.660,  0.000 5.00E-01  11
+18         560.660,-89.927,  0.000       560.660, 89.927,  0.000 5.00E-01  11
+19         580.804,-85.431,  0.000       580.804, 85.431,  0.000 5.00E-01   9
+20         599.940,-81.159,  0.000       599.940, 81.159,  0.000 5.00E-01   9
+21         618.120,-77.101,  0.000       618.120, 77.101,  0.000 5.00E-01   9
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    21 / 50.00   ( 21 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As one decreases the characteristic impedance of the phasing line from 200 Ohms downward, the array draws closer to having an acceptable 50-Ohm or 75-Ohm SWR throughout its passband (14-30 MHz). However, these same reductions often reveal frequencies at which an LPDA will show a weakness. A weakness means that the elements to the rear of the element with the highest current magnitude begin to operate in a harmonic mode. The result is a reduction in forward gain and a very significant reduction in front-to-back ratio. In short, rearward radiation becomes quite large at frequencies of weakness. The design uses a 100-Ohm phase line, which is physically practical for either double boom construction or for a separate phase line structure. The array shows potential weaknesses at about 19.75 MHz and again at 26.5 MHz. Since these frequencies lie between amateur bands, no compensatory treatments were applied.

+

To enhance performance in the upper HF region, the forward elements were subjected to circularization, a process of decreasing the value of Tau with respect to be element length and spacing for the affected elements. The result was a small increase in upper HF gain, but a more useful improvement in the feedpoint SWR curve.

+

The following table provides the potential performance figures for the NEC-4 model:

+ 
+Freq.     Gain      F-B       Feed Impedance    50-Ohm      75-Ohm
+MHz       dBi       dB        R +/- jX Ohms     VSWR        VSWR
+20
+14.0      8.82      25.45     75.0 + j 0.1      1.50        1.00
+14.175    8.82      31.25     73.9 - j 2.9      1.48        1.04
+14.35     8.78      42.54     72.5 - j 6.3      1.47        1.10
+17
+18.118    8.74      40.48     69.1 - j 7.6      1.42        1.14
+15
+21.0      8.52      34.31     60.6 + j 1.3      1.21        1.24
+21.225    8.50      34.54     65.9 + j 4.2      1.33        1.15
+21.45     8.50      34.73     71.3 + j 1.4      1.43        1.06
+12
+24.94     8.39      32.03     61.7 - j 8.9      1.28        1.25
+10
+28.0      8.00      25.31     66.6 - j16.8      1.50        1.30
+28.5      8.05      26.38     54.1 - j 3.3      1.11        1.39
+29.0      7.97      25.35     73.6 - j 0.8      1.47        1.02
+29.5      7.79      23.27     63.6 - j30.7      1.80        1.60
+
+

As the frequency approaches 30 MHz, the 75-Ohm VSWR exceed 2:1 by a small amount, although the 50-Ohm SWR remains at about 1.8:1. The feedpoint resistance begins to sink rapidly above 29.5 MHz.

+

Below 15 meters, the gain performance of the LPDA exceeds the ON4ANT forward-stagger Yagi. More generally, the LPDA front-to-back ratio is more stable, as it tracks the gain of the antenna at each frequency. 10-meter performance is down considerably relative to the Yagi. This phenomenon is quite normal for an LPDA where the upper design frequency is less than 1.6 times the highest frequency used. Adding further elements (to a self-resonant frequency of about 50 MHz) would have significantly lengthened the boom. At least 5 further elements would have been required.

+

The reduction in gain (and front-to-back) at higher frequencies stems in large measure from the fact that in a wide-band LPDA array, all of the elements forward of the one with the highest current magnitude at a given frequency are active, essentially adding many "directors" to the array. As we increase frequency, the element with the highest current magnitude moves forward, leaving fewer elements to serve as "directors." Circularizing the value of Tau for the forward-most elements can improve the upper-end gain, but it cannot fully compensate for all of the reduction.

+

As a consequence of the gain fall-off, further design was undertaken.

+

Version 2: Circular-Tau-Modified Standard LPDA Design With a Parasitic Director

+

I added a director to the array, as shown in Fig. 3. The director adds only 4.3' to the boom length, but equalizes performance at both ends of the passband.

+
+ +
+

The resulting array is described in EZNEC-4 terms:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21+dir 55.8'              Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-216.30,  0.000         0.000,216.300,  0.000 5.00E-01  25
+2           48.177,-205.00,  0.000        48.177,205.000,  0.000 5.00E-01  23
+3           93.944,-194.00,  0.000        93.944,194.000,  0.000 5.00E-01  23
+4          137.424,-184.40,  0.000       137.424,184.399,  0.000 5.00E-01  21
+5          178.729,-175.18,  0.000       178.729,175.179,  0.000 5.00E-01  21
+6          217.969,-166.42,  0.000       217.969,166.420,  0.000 5.00E-01  19
+7          255.248,-158.10,  0.000       255.248,158.099,  0.000 5.00E-01  19
+8          290.662,-150.19,  0.000       290.662,150.194,  0.000 5.00E-01  17
+9          324.306,-142.68,  0.000       324.306,142.685,  0.000 5.00E-01  17
+10         356.267,-135.55,  0.000       356.267,135.550,  0.000 5.00E-01  15
+11         386.630,-128.77,  0.000       386.630,128.773,  0.000 5.00E-01  15
+12         415.475,-122.33,  0.000       415.475,122.334,  0.000 5.00E-01  15
+13         442.878,-116.22,  0.000       442.878,116.217,  0.000 5.00E-01  13
+14         468.911,-110.41,  0.000       468.911,110.407,  0.000 5.00E-01  13
+15         493.642,-104.89,  0.000       493.642,104.886,  0.000 5.00E-01  13
+16         517.136,-99.642,  0.000       517.136, 99.642,  0.000 5.00E-01  11
+17         539.456,-94.660,  0.000       539.456, 94.660,  0.000 5.00E-01  11
+18         560.660,-89.927,  0.000       560.660, 89.927,  0.000 5.00E-01  11
+19         580.804,-85.431,  0.000       580.804, 85.431,  0.000 5.00E-01   9
+20         599.940,-81.159,  0.000       599.940, 81.159,  0.000 5.00E-01   9
+21         618.120,-77.101,  0.000       618.120, 77.101,  0.000 5.00E-01   9
+22         670.000,-88.700,  0.000       670.000, 88.700,  0.000 5.00E-01  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    21 / 50.00   ( 21 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The parasitic director length and position represent a design compromise. Further gain is achievable, but at the cost of unacceptable 10-meter SWR values. A parasitic element also decreases the front-to-back ratio at upper frequencies of the passband. The design goals included a front-to-back ratio at 29.5 MHz of at least 20 dB plus a 50-Ohm SWR no higher than 2:1 across 10 meters. The following performance table reveals that both objectives were met.

+ 
+Freq.     Gain      F-B       Feed Impedance    50-Ohm      75-Ohm
+MHz       dBi       dB        R +/- jX Ohms     VSWR        VSWR
+20
+14.0      8.85      24.83     75.6 + j 0.2      1.51        1.01
+14.175    8.85      30.27     74.2 - j 3.5      1.49        1.05
+14.35     8.81      38.97     71.9 - j 6.5      1.46        1.10
+17
+18.118    8.83      38.07     67.2 - j 6.9      1.38        1.16
+15
+21.0      8.72      42.38     64.8 + j 0.1      1.30        1.16
+21.225    8.71      41.41     66.9 - j 0.6      1.34        1.12
+21.45     8.72      40.76     67.1 - j 1.8      1.34        1.12
+12
+24.94     8.81      32.04     73.6 - j 2.4      1.48        1.04
+10
+28.0      8.92      24.94     72.3 + j16.5      1.58        1.26
+28.5      9.02      22.35     82.3 - j31.3      1.99        1.50
+29.0      9.04      20.97     39.6 - j22.4      1.73        2.12
+29.5      9.04      20.03     38.7 + j 8.8      1.38        1.97
+
+

Although the LPDA does not achieve all of the upper-end gain of the ON4ANT Yagi, it does achieve a remarkably smooth free-space gain curve with only about 0.3 dB variation across the entire passband of the array.

+

Some Comparisons

+

In order to assess the full potential of the LPDA arrays, I performed frequency sweeps of them in 0.25 MHz increments from 13 through 31 MHz. The following graphics are very nearly self-explanatory. Except where values on the tables above coincide with frequency markers in the graphs below, expect to find very slight differences in values, since all properties of an LPDA undulate across the passband.

+
+ +
+

Fig. 4 shows the free-space gain curve of the arrays in dBi. Note the frequencies (19.75 MHz and 26.5 MHz) at which the gain shows an abnormal decrease. If one wishes to eliminate these dips, then the weakness can be suppressed with a single stub on the lower frequency element that shows the highest harmonic mode operation.

+

The graph also shows performance deterioration at both upper and lower ends of the band, except for the gain on the version with the director. However, that increasing high frequency gain will be offset by decreases in the front-to-back ratio.

+

The most significant feature of the gain curve is a revelation of the effects of the parasitic director. The director improves gain (although insignificantly so) even at the lowest design frequency of the array. Given the current magnitude on it, the director must be considered an active element through the design spectrum.

+
+ +
+

The 180-degree front-to-back curve, shown in Fig. 5, shows far more variation than the gain curve relative to the two array designs. However, the "unnatural" dips in the front-to-back ratio reach their lowest values at same frequencies as the gain dip minima: 19.75 MHz and 26.5 MHz. In actuality, the minima occur at very slightly different frequencies. The peaks and nulls in the undulating gain and front-to-back curves do not exactly coincide.

+

Above 20 MHz, the presence of the director most significantly alters the front-to-back performance of the array, shifting the overall curve so that the peaks are lower in frequency relative to the version without the director. As well, above 28 MHz, the array with the director shows a much more rapid drop in front-to-back ratio. The overall front-to-back curve can be altered further with changes in director length and spacing. However, balancing goals for gain, front-to-back ratio, feedpoint impedance, and overall boom length require a design compromise. The closer the spacing of the director to the forward LPDA element, the more radical its effect upon performance at the upper end of the passband.

+
+ +
+

Fig. 6 shows 2 pairs of SWR curves, with 50-Ohm curves and 75-Ohm curves shown for each version of the array. To distinguish the designs, in the legend, "ND" means "no director," and "D" means "director." Despite the fact the impedance values seem to track a 75-Ohm impedance center across most of the passband, a 50-Ohm feedline appears to be the better choice at the passband edges. Both versions of the LPDA show a 50-Ohm 2:1 SWR or better from 14 through 29.7 MHz.

+

Conclusion

+

The Director-LPDA offers somewhat better low-end performance but slightly inferior high-end performance relative to the ON4ANT Yagi. However, the LPDA 10-meter performance extends across the entire band. The LPDA has the advantage of requiring only a single feedline. However, it does require the construction of a phasing line and element-to-boom insulating plates for all elements. Of course, the LPDA is usable at all frequencies between 14 and 30 MHz (with a corrective for the weaknesses noted). Even with a director, the array is 4' shorter than the "final" forward-stagger Yagi.

+

Although the design employs a value for Tau (0.95) close to the maximum recommended value, the array does not achieve all of its potential gain. With the use of an optimized value for Sigma (rather than the 0.056 value actually used in the design), free-space gain would increase to a maximum close to 11.5 dBi, with some front-to-back (and averaged front-to-rear) figures exceeding 50 dB. As noted initially, however, such an array would require 3 to 4 times the boom length.

+

The LPDA with no director is not so inferior to the director array that it should be ignored. At a height of 70' or so, the gain of the array across the entire passband is remarkably equal, allowing for the lowering of the take-off angle with increasing frequency. There is under 0.4 dB difference in maximum among 14, 21, and 28 MHz values.

+

At present, these LPDA arrays are design exercises, since I lack the facilities to construct and the robust tower and rotator to support a long-boom LPDA. Therefore, I shall not include potential mechanical design considerations in these notes. However, the arrays are samples of what an LPDA can do within the limitations of what amateurs consider to be long-boom antennas. Although the long-boom LPDA presents mechanical challenges, it achieves performance competitive with stacks of 2 ordinary multi-band Yagis without the extended mast. In short, it is one more option within the amateur arsenal of high performance multi-band arrays.

+
+ +
+

Note: The purpose of this article is to disseminate information and ideas. The author retains all design rights associated with the subject arrays, including modifications for improved performance over standard arrays of a similar type and including all reasonable variations upon them both stated or implied by the text or the designs themselves.

+
+ +
+

Updated 07-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for June, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: HF Upper, LPDA


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+

LPCAD Designs and NEC Models of LPDAs

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

The log-periodic dipole array (LPDA) arouses amateur interest every so often. Based on a series of mathematical relationships, the LPDA design is amenable to computerized calculations for all element lengths and spacings. One program that has found wide use is LPCAD by Roger Cox, WB0DGF.

+

The point of this note is not to discuss basic LPDA design. This information can be found in the ARRL Antenna Book, Chapter 10, and in many standard antenna texts and references, for example, Kraus or Johnson and Jasik.

+

This note is devoted to a number of precautions we should take when moving from a page of design calculations, such as those produced by LPCAD, to a NEC model of the antenna design. To ease the transition, LPCAD provides a save function to capture the antenna design in standard NEC format (as well as in other formats). This model description will run on almost any version of NEC, -2 and above. Those having a version of EZNEC that translates from the .NEC format can import the file to that program.

+

The save function is undoubtedly offered as a convenience to designers. However, the designer who models the antenna in NEC must take responsibility for ensuring that the model meets all of the requirements for being a good NEC model. Let's use an example: a 20-element 100' long 3-30 MHz LPDA of standard design. The value of Tau for this example is about 0.8737 and the value of Sigma is about 0.0409. Fig. 1 provides an outline of the general antenna design.

+
+ +
+

The LPCAD NEC file provides both a wires table and a TL transmission line table. The most accurate way to model LPDA designs that do not have unusual mechanical features, such as overlapping element ends, is to create each element at the correct spacing. Then use the TL facility of NEC-2 and higher to create the phasing line between each element pair, being sure to reverse connections of the line at each element. LPCAD adheres to this procedure in creating its NEC file.

+

The LPCAD NEC-file does not specify any wire loss, since material specifications are not used in the element calculations. Therefore, the first step for the modeler is to specify the wire material for the elements. Second, modeler should check the output azimuth plot specification. LPCAD uses a standard 10-degree step in the pattern, and the user may wish to reduce the step to 1 or 2 degrees to obtain smoother patterns with more detail.

+

With just these steps, an EZNEC description of the resulting file will look like the following listing.

+ 
20 el 100' 3-30 MHz                      Frequency = 3  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 3.50E+00  15
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 3.50E+00  15
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 3.50E+00  15
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 3.50E+00  15
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.50E+00  15
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.50E+00  15
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 3.50E+00  15
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 3.50E+00  15
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 3.50E+00  15
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 3.50E+00  15
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 3.50E+00  15
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 3.50E+00  15
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 3.50E+00  15
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 3.50E+00  15
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 3.50E+00  15
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 3.50E+00  15
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 3.50E+00  15
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 3.50E+00  15
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 3.50E+00  15
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 3.50E+00  15
+
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    20 / 50.00   ( 20 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13  13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14  14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15  15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16  16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17  17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18  18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19  19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+

Judging from some correspondence, many modelers would accept this model at face value as a proper model and proceed to check the performance at frequencies of interest. In fact, this model would show up as acceptable of better on the Average Gain Test, since this test does not pick up segmentation flaws unless they are wildly flagrant. However, there are two important modifications that one should make to this model before trusting any outputs.

+

First, the model is uniformly specified with 15 segments per wire throughout the 20 elements. However, every element is a different length. Hence, segmentation should vary from one element to the next. How many segments each element should have is a function of the length of the longest element and the highest frequency at which the antenna will operate. The longest element is a little over 2000" and the highest frequency is 30 MHz. We need conservatively about 10 segments per half wavelength, but because we shall place a transmission line along the exact center line of the antenna, we need for each element an odd number of segments. The requirement for an odd number of elements will limit the precision of our segmentation.

+

Since the longest element is a bit over 5 wl long at 30 MHz, let's assign 107 segments to the longest element. For each shorter element, in order, we simply multiply by Tau, using the preceding element answer as the basis for the next element. We shall have to round upward or downward to the closest odd number to obtain the segment number for the element in question. For the example in question, the shortest two elements each receive 9 segments, since their 1/2 wl resonant frequencies are above 30 MHz.

+

Second, consider the element diameter. The value in the diameter column is the average element diameter that the user specified as an input to the calculations. However, this value is very often not an accurate reflection of the intended element diameter for the actual antenna. Hence, we should replace the average diameter with value as close to reality as possible.

+

For the model in question, I specified a range of diameters from 0.5" for the shortest element to 6.5" for the longest. The design required that each element change according to Tau in the descent from 6.5" to 0.5". Once more, this is a simply matter of successive multiplication of preceding values by Tau to obtain the next smaller diameter. (The design purpose in this case was to have a constant element length-to-diameter ratio for the entire model. In any event, you should use element diameter values as close to reality as the stage of design will allow.)

+

The modified antenna model then took on this appearance.

+ 
20 el 100' 3-30 MHz                       Frequency = 3  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 6.50E+00 107
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 5.68E+00  93
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 4.96E+00  81
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 4.34E+00  71
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.79E+00  63
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.31E+00  55
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 2.89E+00  47
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 2.53E+00  41
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 2.21E+00  37
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 1.93E+00  31
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 1.69E+00  27
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 1.47E+00  25
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 1.29E+00  21
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 1.12E+00  19
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 9.80E-01  17
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 8.60E-01  15
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 7.50E-01  13
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 6.50E-01  11
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 5.70E-01   9
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 5.00E-01   9
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    20 / 50.00   ( 20 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13  13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14  14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15  15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16  16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17  17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18  18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19  19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20   1/50.0  (  1/50.0)  Short ckt (Short ck)   90.000 in   200.0  1.00
+
+Ground type is Free Space
+

Besides the changes to the element segments and element diameter columns, one other addition to the model is evident. I added a shorted transmission line stub to the phasing line at the rearmost element. Actually, I ran this model with and without the stub to see the difference in performance at selected frequencies.

+

Notice that the stub has a specific length and is not the oft-used 1/4 wl (or the length of 1/2 the longest element). The stub was chosen to improve low frequency performance while having the least effect on upper frequency performance.

+

The modification significantly increase the segment count for the entire model (with or without the stub). The example above uses 792 segments, which may be beyond the common 500-segment limit of many entry-level NEC programs. However, it is the minimal satisfactory model of the LPDA design in question. In fact, convergence testing should check the model up to at least 1.5 times the segmentation density used here. (See the end of this note for the convergence test.)

+

Is all this really necessary? To find out, let's run frequency sweeps of the original model (with the aluminum elements and smaller plot step level in place) and of the two modified models (without and with a stub). If the original model formulation is satisfactory, then its curves should track the curves of the modified models except for any stub effects. As a preliminary set of checks, let's plot the following parameters: free-space gain in dBi, 180-degree front-to-back ratio in dB, source resistance in Ohms, source reactance in Ohms, and VSWR relative to some standard.

+

For a real design, we would run detailed frequency sweeps across each intended band of operation. For this general profile, we can use a sweep that checks the values of interest at 1 MHz intervals from 3 through 30 MHz, the design range of the model. In the following graphs, "20100" refers to the unmodified model, "20100A" refers to the stubless modified model, and "20100ATL" refers to the modified model with a shorted stub.

+
+ +
+

Fig. 2 provides graphs of the gain values for the three models. Except for the 6 MHz region, the stub and no-stub modified models track each other very well, with the stub model having the highest gain at 3 MHz. The original model using a constant 15-segments per element erroneously predicts a gain peak at 6 MHz. More significantly, above about 12 MHz, the original model provides significantly over-optimistic values for the gain of the antenna, a typical result of inadequate segmentation. However, note that the values occur in the frequency region in which we might think that the segmentation is adequate. This is a lesson to the effect that all of the elements of an LPDA design play a role at all frequencies.

+
+ +
+

In Fig. 3, we see the generally coincident curves for all three models with respect to front-to-back ratio. The original model is once more a bit over-optimistic at the highest frequencies, but these high reports are confined to the 25 to 29 MHz region. The most serious anomaly is at 6 MHz, where the original model predicts a very low front-to-back ratio (the same frequency on which it predicted an unusually high gain value). The stubless model that corresponds to the initial model (which is also without a shorted stub) predicts exactly the opposite--an unusually high front-to- back ratio. Addition of the stub smoothes the curve considerably.

+
+ +
+

When we turn to the resistance and reactance components (Fig. 4 and Fig. 5) of the source impedance, the odd performance of the original model shows itself most vividly. The curves for the stub and stubless models are so close together above the lowest region of the passband that one curve obscures the other. This phenomenon makes all the more evident that fact that the initial model tends to dip and peak in a rhythm directly opposite that of the more adequately segmented model. The resistance values reported by the 15- segment per element model would have to be accounted wholly unreliable.

+
+ +
+

The graph of reactance values tells a very similar story. Again, the stubbed and stubless models coincide above the lowest frequencies, but the initial model fails to track these curves. In fact, it tends to take just the opposite turn. It is well to remember that the larger model more closely approaches convergence than the smaller model and hence must be accounted a more proper model of the antenna than the smaller model.

+
+ +
+

Because the resistance and reactance values were at such odds, it was necessary to track VSWR against different reference values in Fig. 6. The initial model used a 75-Ohm standard, suggesting that it might be directly fed with a coaxial cable. However, both larger models are referenced to 95 Ohms, a value taken as close to the mean between the extremes of the resistive components of the source impedance. Incidentally, the LPCAD prediction for a source impedance is 103 Ohms.

+

The importance of the difference in VSWR reference standards lies in the consequences for designing the impedance matching required for connecting a main feedline to the antenna. The initial model's prediction that a 75-Ohm cable would be sufficient is unlikely to be fulfilled. More likely is the potential for using a wide-band 2:1 impedance matching device to connect the antenna to a 50-Ohm cable.

+

The inadequacies of uncritically adopting the transfer model as a proper NEC model are all too evident from the comparative graphs. This is not a criticism of LPCAD, since the main function of saving the LPDA design as a NEC model is to release the designer from the tedium of entering every element length, space, and transmission line without omission, slippage, or transposition of numbers. However, it remains the responsibility of the modeler to use sufficient care to ensure that the resulting model meets all applicable NEC standards for being a proper model within the guidelines for the core. If a model turns out to be too big for the limits of a software package, it is dangerous to trust the results of a model squeezed down in segmentation to fit those limits. Instead, the model needs to be whatever size is required for it to yield reliable results--and sometimes, that calls for a software package with larger limits. Most especially, models should never be shrunken just to reduce the time it takes to make a set of runs.

+

Programs like LPCAD are exceptionally useful design tools. However, like NEC itself, they have limitations. When using them, it pays to find and understand those limitations so that they do not impede design progress. Translating LPCAD designs into NEC models is a fascinating case in point.

+

A Note on the Convergence of Large Models

It is always useful to perform a convergence test on a model to determine its reliability. The convergence test is a necessary but not sufficient test of reliability: a model that fails to converge should be considered unreliable, but one that does converge might have problems that the convergence test cannot detect. +

In the present case, we are dealing with relatively large models--relative, that is, to normal amateur radio modeling practices, although these models would be small in the confines of some engineering projects. The modified models--with and without a stub--have 792 segments overall, distributed in 20 elements. A reasonable convergence test might add 50% to that number as a basic convergence check.

+

However, the segmentation of the model must meet special requirements. The number of segments per element is determined by a rolling Tau calculation starting from the longest element. The calculation is then rounded to the nearest odd-number of segments. To avoid double rounding errors, I performed the Tau-based calculations, beginning with 161 segments on the rear element, up from 107 on the models considered above. The result appears in the partial model description below:

+ 
              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-1003.7,  0.000         0.000,1003.68,  0.000 6.50E+00 161
+2        164.166,-876.93,  0.000       164.166,876.934,  0.000 5.68E+00 141
+3        307.601,-766.19,  0.000       307.601,766.193,  0.000 4.96E+00 123
+4        432.923,-669.44,  0.000       432.923,669.437,  0.000 4.34E+00 107
+5        542.419,-584.90,  0.000       542.419,584.899,  0.000 3.79E+00  93
+6        638.087,-511.04,  0.000       638.087,511.037,  0.000 3.31E+00  81
+7        721.675,-446.50,  0.000       721.675,446.503,  0.000 2.89E+00  71
+8        794.707,-390.12,  0.000       794.707,390.118,  0.000 2.53E+00  63
+9        858.516,-340.85,  0.000       858.516,340.853,  0.000 2.21E+00  55
+10       914.267,-297.81,  0.000       914.267,297.810,  0.000 1.93E+00  47
+11       962.978,-260.20,  0.000       962.978,260.202,  0.000 1.69E+00  41
+12       1005.54,-227.34,  0.000       1005.54,227.343,  0.000 1.47E+00  37
+13       1042.72,-198.63,  0.000       1042.72,198.634,  0.000 1.29E+00  31
+14       1075.21,-173.55,  0.000       1075.21,173.550,  0.000 1.12E+00  27
+15       1103.60,-151.63,  0.000       1103.60,151.634,  0.000 9.80E-01  25
+16       1128.40,-132.49,  0.000       1128.40,132.485,  0.000 8.60E-01  21
+17       1150.07,-115.75,  0.000       1150.07,115.755,  0.000 7.50E-01  19
+18       1169.00,-101.14,  0.000       1169.00,101.137,  0.000 6.50E-01  17
+19       1185.55,-88.365,  0.000       1185.55, 88.365,  0.000 5.70E-01  15
+20       1200.00,-77.206,  0.000       1200.00, 77.206,  0.000 5.00E-01  13
+

I then took a long walk while I frequency swept the enlarged model from 3 to 30 MHz in 1 MHz steps. The results were then entered into a spreadsheet. Differentials between the values for the smaller and the larger model covered gain and front-to-back ratio (in dB), source resistance and reactance (in Ohms), and 95-Ohm VSWR. The results form the basis for a judgment of whether the smaller model is sufficiently converged with the larger to be considered reliable.

+
+ +
+

Fig. 7 shows the differentials for gain and front-to-back ratio. The maximum gain difference is under 0.15 dB or less than 3% of the average gain. The maximum front-to-back differential is 0.49 dB, again, less than 3% of the average front-to-back level.

+

Whether these numbers represent significant differences is a question of judgment related to the purposes for which one is doing the modeling. A gain difference of 0.15 dB is certainly not operationally detectable. Nor is a front-to-back differential of 0.49 dB. Since these maximum figures do not represent a general trend in the curves, they are unlikely to be meaningful for any design work one might do on an antenna of this sort. In fact, the most notable fact about the two curves in Fig. 7 is how closely they coincide, that is, how much of the curves remains within +/-.05 dB of zero.

+
+ +
+

The resistance and reactance curves appear in Fig. 8. The maximum resistance and reactance deviations are about 6 Ohms each, within 5% of the total range of values for each parameter. What the graph of differences cannot show is that differences are largest where the values compared are large. The resistance ranges from about 49 Ohms to over 170 Ohms, and the 6-Ohm peaks occur with the largest values. Likewise, reactance ranges from about -55 Ohms to nearly +70 Ohms, and once more, peak differences attach to the highest values. We may have noticed that in the progression of source impedance values for an LPDA, most instances of high reactance occur when the resistance is most distant from its mean value. Hence, the resistance and reactance peak values appear at different points on the basic graphs.

+
+ +
+

The result is a 95-Ohm VSWR graph of differences (Fig. 9) that peaks at values less than 0.025, a truly insignificant differential for any operational antenna consideration with which I am acquainted.

+

The general conclusion one might reach here is that the smaller model converges well with the larger and may be considered reliable for most purposes. This kind of test--and the results--give confidence that the graphed results for the modified models are far more usable than those for the unmodified model using a standard 15 elements per element.

+

Nevertheless, the general conclusion represents a "smoothed" judgment. There are still a few values on the difference graphs that call attention to themselves. In such cases, we may usefully do two things: 1. We can keep our eye out in further modeling for significant anomalies that occur at the same frequencies. 2. Should we implement the design used for discussion here, we might make a few special checks at these frequencies during the field testing and adjustment to ensure that operational values do not exceed whatever limits might be specified in the final design.

+

A Note on Design Method in LPCAD

When designing LPDAs in LPCAD, you have a choice: to use values of Tau and Sigma or to use specifications of the number of elements desired and the total length of the array. Now, suppose you initially design an LPDA using Tau and Sigma. Then, suppose you use the number of elements and the length given in that design report to design a new LPDA. You might expect to get a design whose element lengths and spacings were identical to the first design, with precisely the same values for Tau and Sigma. +

You will not. There will be slight differences in the two designs. As an example, here are the element descriptions for two LPDAs, the first designed by entering a Tau of 0.85 and a Sigma of 0.04. The second design was derived by entering 7 elements and 294.185" as the length, both figures taken from the first design. The frequency range for the design is 6.8 to 15 MHz.

+ 
1.  Designed with Tau = 0.85; Sigma = 0.04
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           70.848,-376.38,  0.000        70.848,376.380,  0.000 1.00E+00  25
+3          131.069,-319.92,  0.000       131.069,319.923,  0.000 1.00E+00  21
+4          182.257,-271.93,  0.000       182.257,271.935,  0.000 1.00E+00  17
+5          225.766,-231.14,  0.000       225.766,231.144,  0.000 1.00E+00  15
+6          262.749,-196.47,  0.000       262.749,196.473,  0.000 1.00E+00  13
+7          294.185,-167.00,  0.000       294.185,167.002,  0.000 1.00E+00  11
+
+2.  Designed with 7 Elements and 294.185" Length
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           72.738,-371.50,  0.000        72.738,371.495,  0.000 1.00E+00  25
+3          133.763,-311.67,  0.000       133.763,311.673,  0.000 1.00E+00  21
+4          184.961,-261.48,  0.000       184.961,261.484,  0.000 1.00E+00  17
+5          227.915,-219.38,  0.000       227.915,219.377,  0.000 1.00E+00  15
+6          263.951,-184.05,  0.000       263.951,184.050,  0.000 1.00E+00  13
+7          294.185,-154.41,  0.000       294.185,154.413,  0.000 1.00E+00  11
+

The calculated values for the second design are Tau = 0.840 and Sigma = 0.041. These small changes result in a 10" shortening of the second element (the prime current carraier at the low end of the passband) and a 26" shortening of the 7th element. These changes are not minor, as Fig. 10 demonstrates.

+
+ +
+

Lowering the value of Tau shortens every element in the array except the rear one. One consequence is to lower gain everywhere in the passband. Whether the amount is significant is a user judgment based on design goals. However, it is sufficient to be noticeable and designers should be alerted to this facet of LPCAD operation.

+
+ +
+

Updated 09-26-99; 10-7-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Main Index

+

Topics: HF Multi Band, LPDA


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Notes on the Extended Aperture Log-Periodic Array

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Part 1: The Extended Element and the Standard LPDA

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Part 2: The Extended Aperture LPDA

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This page exists to include the PDF in the topic index

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Topics: HF Multi Band, LPDA, Vertical


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Notes on HF General Coverage LPDAs Using 30-35' Booms

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L. B. Cebik, W4RNL

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The most popular range for LPDAs among radio amateurs is 14-30 MHz. Within that range, boom lengths of 30-35' hold considerable interest, since these booms are similar to the ones used for advanced multi-element, multi-band Yagis. In fact, it is quite possible to construct an LPDA with a 30' boom that provides better than 7 dBi free-space gain and better than 20 dB front-to-back ratio across all of the amateur bands included in the passband.

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Fig. 1 shows the outline of one such design. Because the design is proprietary, I cannot provide exact dimensions. However, the outline shows--if you look carefully--signs of Tau circularization on the longest and shortest elements. To maximize gain on the amateur bands, the designs employs a 100-Ohm phase line, for direct connection to either a 50-Ohm or 70-Ohm feedline.

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A quick survey of amateur-band performance, as modeled on NEC-4 will show the potential of the design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+         Amateur-Band Performance Potential of a 12-Element LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   50-Ohm    70-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR       SWR
+14.175     7.33       27.66      84.9 + j 10.7    1.74      1.27
+18.118     7.17       25.41      62.8 - j  5.0    1.28      1.14
+21.225     7.04       27.39      65.4 - j  9.7    1.37      1.17
+24.94      7.37       23.18      47.6 - j 11.9    1.28      1.55
+28.0       6.88       22.98      66.1 - j  3.2    1.33      1.08
+28.85      7.32       25.22      43.4 - j 10.0    1.29      1.67
+29.7       7.67       20.62      94.0 - j  8.1    1.90      1.37
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Because 10 meters is such a wide band, I have given 3 check points. Changes in performances are very small for the other bands. Although 50-Ohm SWR is generally acceptable, the 70-Ohm SWR performance is superior. Only at the low end of 10 meters does the gain drop below 7 dBi, but not by much.

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Suppose, however, that the design goals for our 30-35' long LPDA go beyond simple amateur-band performance. Suppose that we wish to develop a general coverage LPDA from 14-30 MHz. We might set up the criteria in the following manner:

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  • 1. Gain: >7 dBi everywhere across the passband
    • +
  • 2. Gain Differential: <0.5 dB across the passband
    • +
  • 3. Front-to-Back (Worst-Case): >20 dB
    • +
  • 4. SWR: <1.5:1 relative to an impedance standard across the passband
    • +
+

The significance of these design criteria stem from the needs of some services to use frequency-nimble communications techniques. Wide divergence of performance from one frequency to the next may jeopardize communications, especially with marginal signal levels. Hence, we may legitimately set these goals and then see if we can meet them.

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Our outstanding 12-element LPDA ham-band performer unfortunately does not meet these more stringent criteria.

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Fig. 2 shows the free-space gain and both the 180-degree and the worst- case front-to-back ratios at intervals of 0.25 MHz from 14-30 MHz. Since the LPDA has no secondary forward lobes, the front/sidelobe ratio curve reliably tracks the strongest rear lobe and thus presents a picture of the worst-case front-to-back performance of the array.

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Immediately apparent is the anomaly in the curves in the region of 24.5 MHz. The array employs a shorted stub on the rear element. The length of the stub can move the frequency of the anomaly, but cannot eliminate it. Even if we ignore the anomaly, the gain range runs from 6.75 dBi to 7.67 dBi, a 0.92 dB range. The front-to-back performance is also subject to the anomaly. In addition, the worst-case value drops below 20 dB from 26.75 to 28.0 MHz and again above 29.75 MHz.

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Fig. 3 shows both the 50-Ohm and the 70-Ohm SWR curves for the array across the entire passband. The 70-Ohm curve is superior--relative to the 1.5:1 standard--below the anomalous frequency region, while the 50-Ohm curve is superior from the anomaly up to 29.5 MHz. Above 29.5 MHz, the SWR climbs rapidly, and it goes completely to pot in the region of 24.5 MHz.

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Relative to the general coverage standards, the 12-element, 30' LPDA does not fill the bill, despite its high utility as an amateur band array. Indeed, if we re-examine the design, we can see several reasons for the failure. The 100-Ohm phase line value is too low to ensure stable performance across the entire passband: hence, the anomaly. Of equal importance is the gain curve in general--apart from the anomaly. Element length changes on the shortest elements improve high-end performance. However, they also occasion wider gain swings than we see in the lower portions of the passband. We also detect a gradual lowering of the average gain and worst-case front-to-back ratio as we increase frequency until the high-end compensation kicks into action--and the compensation improves the gain more than the worst-case front-to-back ratio.

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To achieve a general-coverage LPDA with a boom length in the 30-35' region, we shall have to look at other design options.

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A 12-Element Hybrid LPDA

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In volume 1 of LPDA Notes on the Books Page, I presented a family of basic LPDA designs--at the proof-of-principle level--and included a 12-element, 32' long array that used 11 LPDA elements plus a parasitic director. The original design used 0.5" diameter elements. I have adjusted the element diameters to 0.8" for the longest elements down to 0.5" for the shortest, since this range of element diameters reflects the uniform-diameter element equivalents for common element structures that might survive 120 mph winds. The potential users who might insist upon the high performance criteria would likely also insist upon high wind survival values for the elements.

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Fig. 4 shows the general outline of the array. A careful scrutiny of the outline created by the LPDA element ends will show that some degree of tau-circularization has been employed--along with a shorted stub--to tailor the low and high frequency performance of the array. The array uses a 250-Ohm phase line, the lowest value of impedance that will ensure stable performance across the entire passband. The SWR reference impedance therefore becomes 100 Ohms, with the presumed use of a 2:1 balun device for a 50-Ohm feedline.

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Within the amateur bands, the array is a solid performer.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     Amateur-Band Performance Potential of a 12-Element Hybrid LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.11       27.28      132.8 + j 21.9   1.41
+18.118     7.04       25.56      123.5 - j 22.5   1.34
+21.225     7.19       28.75      106.3 - j 17.2   1.20
+24.94      7.21       27.01      152.3 + j  3.2   1.52
+28.0       7.45       30.76       71.8 - j 22.4   1.53
+28.85      7.51       27.03       84.6 - j  5.9   1.20
+29.7       7.89       20.56      114.0 - j 63.6   1.82
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The range of SWR values suggests that a 250-Ohm phase line is not ideal for a 100-Ohm feedpoint impedance. In the bands through 12 meters, the reference impedance--roughly, the median value of feedpoint resistance values--is closer to 110-120 Ohms. When the parasitic director begins to show its influence on performance--above 28 MHz--the median feedpoint resistance drops considerably, a natural phenomenon with the use of parasitic elements ahead of LPDA arrays. Already, we can see that the design, even as improved, will not meet all of the more stringent standards set of a general coverage array with a 30-35' boom length.

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+ +
+

Fig. 5 shows the free-space gain and the front-to-back curves across the entire passband of the array. The gain curve has a total range of 6.95 to 8.09 dBi, for a 1.14 dB differential. More significantly, we can see that the curve shows increasing swings from gain maxima to gain minima as we increase frequency, with a radical upswing above 28.0 MHz. The notch in the curve just below 28 MHz does not indicate an anomaly, but it does indicate where one occurs (with the length of shorted stub used in the design) if we decrease the phase line impedance down to 200 Ohms or lower.

+

The 180-degree front-to-back curve also shows the notch below 28 MHz, although the worst-case curve does not show any deviation from a smooth curve in this region of the operating spectrum. However, both front-to-back curves drop below 20 dB as we approach 30 MHz.

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+ +
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The feedpoint performance curves in Fig. 6 show no notches and serve to confirm that the array has no anomalous frequencies. However, they do show other weaknesses of the design. As we increase frequency, the average feedpoint resistance decreases, and the average feedpoint reactance becomes increasingly capacitive. (In an ideal LPDA using a very high value for Tau and its corresponding ideal Sigma, the reactance will remain capacitive throughout the operating range, although it will vary over a very small range.) In the region where the parasitic director is most effective, the slope of the resistance and reactance curves combine to yield relatively high SWR values as we near 30 MHz. As already noted, the use of a 250-Ohm phase line alone is sufficient to yield SWR values in excess of 1.5:1 in several regions throughout the operating passband.

+

Why the Hybrid Design is Unlikely to be Successful at the 30-35' Boom Length

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Before we look at any alternative designs, let's pause to understand why this design--and similar ones--are unlikely to meet the rigorous design specifications. The exercise gains some importance because if we increase the boom length to greater than 40', we can obtain a satisfactory array. Such arrays typically average from 7.5 to 8.0 dBi free-space gain using either pure or hybrid LPDA techniques. Since LPDA front-to-back ratios increase with increases in gain, meeting that standard is no major problem. However, careful design is required to meet the narrow gain differential limit and the SWR limit. Nonetheless, boom lengths in the 42' range are sufficient to meet the goal.

+

If we shorten the boom by about 10', our design tendency is also to reduce the element population. With 16 elements, a 42' boom has about 3.8 elements per 10' of boom length. At a similar element rate, we obtain about 12 elements for a 32' boom. However, the frequency span remains the same--14 to 30 MHz--and the value of Tau must therefore be lowered. With lower values of Tau, we tend to find reduced low-end performance prior to compensation and slightly higher upper-end performance, relative to similar values of Sigma.

+

The design that we just examined used a Tau of 0.909 and a Sigma of 0.055 prior to compensation. If we try to smooth the upper end performance prior to compensation by increasing the upper frequency limit, we end up with a lower value of Tau, with decreases in the low-end performance. Even though circularization of Tau and a well-designed stub can restore the performance in the 14-18 MHz range, there will be a decrease in performance in the 20-23 MHz range. On the other hand, if we increase Tau and reduce the upper-end frequency limit, then the influence of the parasitic director more radically affects the feedpoint impedance, and the SWR curve exceeds limits at a lower frequency.

+

Although there may be a workable compromise among the design values that go into a hybrid LPDA that will achieve the desired goals, I have yet to find it in several dozen designs for hybrid LPDAs with 30-35' boom lengths. Each design has been subjected to a considerable number of compensatory variations. If there is a hybrid LPDA design in the 30-35' boom length range that will meet all specifications, I should like to be enlightened. In the mean time, meeting the desired specifications may require other design directions.

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A 16-Element Pure LPDA on a 35' Boom

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My experiences with LPDA designs strongly suggests that the original design calculations must be modified for arrays using far less than the ideal Sigma value for a given value of Tau. Ordinarily, computations set the shortest element to be resonant at a frequency of about 1.3 times the highest operating frequency. For a 30 MHz upper operating limit, the shortest element will be self-resonant at about 39 MHz.

+

Even with high values of Tau and close-to-ideal values of Sigma, pure LPDAs will show a performance decrease with increasing frequency using the traditional multiplier. The decrease in performance becomes more pronounced with shorter boom lengths and sparse element populations. For the region of LPDAs most commonly used in the upper HF region, a multiplier of 1.6 times the highest operating is closer to optimal for the shortest element in an array. This multiplier sets the self-resonant frequency of the shortest element at about 48 MHz for a 14-30 MHz array. There is no magic in this value: it may range from 46 to 50 MHz, depending upon the particular values of Tau and Sigma used in a given design.

+

Based upon this re-formulation of the upper design limit, I reconstructed the original 11-element LPDA design (omitting the parasitic director) that used a Tau of 0.909 and a Sigma of 0.055, adding elements until the performance met specifications. Interestingly, 16 elements fit on a boom under 35' long, since the new elements required fairly close spacing. The elements used a modification of the usual circularization of Tau procedures to arrive at their final lengths. Fig. 7 shows the outline of the array. The array uses a 200-Ohm phase line with a 100-Ohm reference feedpoint impedance for the SWR values.

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+ +
+

The amateur band performance of the resulting array is remarkable smooth, as the following table shows.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 16-Element Pure LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.27       23.88      130.2 + j  1.4   1.30
+18.118     7.27       25.82       91.1 - j 13.8   1.19
+21.225     7.32       26.63      115.8 - j 13.7   1.21
+24.94      7.28       28.74       94.6 - j  5.6   1.08
+28.0       7.27       29.41       90.2 - j 16.2   1.22
+28.85      7.18       27.62       83.8 - j  7.9   1.22
+29.7       7.19       26.67       87.7 + j  2.6   1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The gain range across the entire operating spectrum reflects the smooth performance shown in the ham-band table. The minimum free-space gain is 7.15 dBi, while the maximum is 7.45 dBi, for a differential of only 0.3 dB. Fig. 8 provides the relevant curves. With adjustments to the element-length compensation used at both the long and the short ends of the array, we might narrow that range even more. However, the array meets both the minimum gain and gain differential criteria that we set earlier for general coverage LPDAs.

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+

The array also meets the front-to-back standards with ease. The bump in the gain curve and the notch in the front-to-back curves indicate that if we reduce the phase line impedance too much below 200 Ohms, we may encounter an anomaly. The overall worst-case front-to-back ratio curve (indicated by the front/sidelobe ratio line) is remarkable smooth.

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Fig. 9 shows the feedpoint values across the operating passband of the array. The maximum 100-Ohm SWR value is 1.318:1, with the average SWR only 1.16:1. Although the average feedpoint resistance decreases slowly with increasing frequency, the reactance tends to fall within an ever-narrowing range as we increase the operating frequency. Hence, we obtain a very well-behaved SWR curve, despite the small notch that corresponds to notches in the gain and front-to-back curves.

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Like the hybrid LPDA examined earlier, the element diameters taper from 0.8" for the longest element to 0.5" for the shortest. In any final design, we would replace these elements with fully structured stepped diameter elements reflecting the physical design of an intended array. Because we find a slight rise in performance, we might even experiment with removing the 16th element and shortening the boom by about a foot. For now, the present design meets the general-coverage performance criteria that we established earlier. The following table provides the element dimensions in EZNEC model-description format for the 16-element array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+16 el LPDA 14-30 200tl
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,   -213,      0                  0,    213,      0       0.8   33
+2                   49.8, -205.5,      0               49.8,  205.5,      0       0.8   31
+3                   95.1,   -188,      0               95.1,    188,      0       0.8   29
+4                  136.3, -170.8,      0              136.3,  170.8,      0       0.8   27
+5                  173.8, -155.4,      0              173.8,  155.4,      0       0.7   25
+6                    208, -141.3,      0                208,  141.3,      0       0.7   23
+7                  239.1, -128.5,      0              239.1,  128.5,      0       0.7   21
+8                  267.4, -116.8,      0              267.4,  116.8,      0       0.7   19
+9                  293.1, -106.2,      0              293.1,  106.2,      0       0.6   17
+10                 316.5,    -97,      0              316.5,     97,      0       0.6   15
+11                 337.8,    -89,      0              337.8,     89,      0       0.6   13
+12                 357.2,  -81.7,      0              357.2,   81.7,      0       0.6   11
+13                 374.8,    -78,      0              374.8,     78,      0       0.5   11
+14                 390.8,  -71.7,      0              390.8,   71.7,      0       0.5   9
+15                 405.3,    -66,      0              405.3,     66,      0       0.5   9
+16                 418.5,  -60.7,      0              418.5,   60.7,      0       0.5   9
+
+Total Segments: 302
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The high number of elements on a shorter (but not short) boom likely will disturb some LPDA designers and home builders. However, the population density assures performance well within the design specifications. We might wish to look toward the borderline to try to find the minimal configuration that meets the standards that we set early in this exploration.

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A 14-Element 32' Pure LPDA for 7-dBi General Coveragee

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I have tested a number of designs using NEC-4 and have found some candidates for a borderline general coverage LPDA with at least 7.0 dBi free-space gain, less than 0.5 dB gain differential across the passband, better than 20 dB front-to-back ratio, and less than 1.5:1 SWR within the operating spectrum. The model selected is truly a borderline case. Its outline appears in Fig. 10.

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+ +
+

The array consists of 14 elements on a 32' boom. The shortest element is resonant in the region of 46-48 MHz for smooth upper frequency performance. I modified the longest two elements to bring the low end performance above minimal levels, and placed a 12" stub on the longest element. The phase line is 200 Ohms for a feedpoint reference impedance of 100 Ohms. For comparison with the other models, let's show the ham-band performance.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 14-Element Pure LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     7.12       27.91      106.8 + j  7.5   1.10
+18.118     7.26       25.73      118.9 + j  2.9   1.19
+21.225     7.10       26.45      107.4 - j 15.1   1.18
+24.94      7.06       27.38      109.3 - j 12.9   1.16
+28.0       7.07       23.60      122.4 - j  9.3   1.25
+28.85      7.15       25.13      106.5 - j 25.2   1.29
+29.7       7.09       25.78       97.7 - j 14.4   1.16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The average free-space gain is 7.14 dBi (compared to 7.26 for the larger array), with a gain range that runs from 6.93 to 7.28, a differential of 0.35 dB. The gain drops below the 7.0 dBi minimum from 25.5 to 27.25 MHz, but hovers within 0.05 dB of the standard throughout the range. As Fig. 11 shows, there is a notch in performance in the 28.5-MHz region, with a minimum gain value of 6.93 dBi at 28.55 MHz. Adjustment of the stub length can move the notch and even prevent it from showing the lowest gain by placing it at a frequency where the gain is well above 7 dBi. The gain curve itself shows the most rapid and wide variation above 25 MHz, with a rapid drop to 7.05 dBi at 30 MHz. From a gain perspective, this design and variations on it represent a true borderline array.

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+ +
+

The front-to-back curves are quite well behaved. The worst-case front-to-back value ranges only between 20.72 and 22.89 dB, for an average value of 21.95 dB. As is typical of LPDA designs with extended upper frequency elements, the 180-degree front-to-back shows fewer sharp peaks and lesser valleys than typical designs, with only a 4-dB difference between maximum and minimum values.

+
+ +
+

The feedpoint conditions appear in Fig. 12. The 100-Ohm SWR exceeds 1.4:1 only from 15 to 15.25 MHz and is well below 1.45:1 in that region. All of the remaining values are less than 1.35:1. In general, both the resistance and reactance values make only small excursions all the way across the passband.

+

For reference, the following table shows the elements used in this borderline model--using the EZNEC model description format.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-37 14el t=0.909 s=0.057
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,   -210,      0                  0,    210,      0       0.8   37
+2                49.0591,   -194,      0            49.0591,    194,      0       0.8   35
+3                93.6748,-177.88,      0            93.6748,177.879,      0       0.8   31
+4                134.249,-161.77,      0            134.249,161.768,      0       0.7   29
+5                171.149,-147.12,      0            171.149,147.116,      0       0.7   25
+6                204.707,-133.79,      0            204.707,133.792,      0       0.7   23
+7                235.225,-121.67,      0            235.225,121.674,      0       0.6   21
+8                262.979,-110.65,      0            262.979,110.653,      0       0.6   19
+9                 288.22,-100.63,      0             288.22,100.631,      0       0.6   17
+10               311.174,-91.517,      0            311.174,91.5167,      0       0.5   17
+11               332.049,-83.228,      0            332.049,83.2278,      0       0.5   15
+12               351.034, -75.69,      0            351.034,75.6896,      0       0.5   13
+13               368.299,-68.834,      0            368.299,68.8342,      0       0.5   13
+14                   384,  -62.6,      0                384,62.5997,      0       0.5   11
+
+Total Segments: 306
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I have left the excessively long decimal values for element coordinate entries to show clearly which elements (1 and 2) have received modifications.

+

Model 143714 represents a truly borderline design relative to the standard set for general coverage LPDAs in the 30-35' boom length category. Fewer elements or a shorter boom appears to inevitably yield lower performance levels for more significant portions of the operating passband. Even this model has shown small dips below the minimum gain levels. On the other hand, extending the boom by a foot or so or increasing the number of elements by 1 would likely ensure performance above the minimum gain level everywhere in the passband.

+

The notch in performance can be moved, but I left it to warn against lowering the phase line impedance below the 200-Ohm level. A 100-Ohm phase line will show an uneliminable anomaly in performance. At the other end of the phase-line possibility range, we might consider raising the phase-line impedance for unconditional stability. However, this move is subject to several cautions. First, the gain and front-to-back performance will decrease with significant increases in phase-line impedance. Second, the average gain may change in different parts of the operating spectrum. Hence, for high-impedance phase lines, one should design an LPDA from scratch, with enough iterations to ensure not only stable performance, but smooth performance across the operating passband.

+

Conclusion

+

We may design both pure and hybrid LPDAs in the 40-45' boom-length range for smooth general coverage--using the standards suggested here, but with an increase in gain. However, reducing the boom length to the 30-35' range, with a reduction also in the number of elements, tends to reduce our design options. The most promising designs for shorter-boom arrays involve extending the upper frequency limit of the basic design, and they inevitably result in a higher number of elements than we require for ham-band-only operation of an LPDA.

+

The designs presented for study are by no means final. They require adaptation to the element taper schedule to be used in any physical implementation. As well, they are subject to further optimization procedures. Nevertheless, they do serve to illustrate the design principles and procedures in attempting to develop a 14-30 MHz LPDA that meets rigorous general coverage performance criteria.

+
+ +
+

Updated 09-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for August, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: HF Upper, LPDA


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+

Notes on a Long-Boom General Coverage LPDA

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In a recent article, "Notes on HF General Coverage LPDAs Using 30-35' Booms," I explored the design factors involved in obtaining smooth general coverage from 14-30 MHz from a relatively short-boom array. In this exercise, I should like to explore the same goal, but to employ a much longer boom to obtain a gain level average at least 1.5 dB higher than we could get from the shorter boom. The boom lengths involved in the new exercise fall in the 55-60 foot range. As one might expect, we shall increase the number of elements accordingly.

+

In the preceding exploration, I defined--not without reason, but somewhat arbitrarily--the concept of general LPDA coverage in terms of a set of operational standards:

+
    +
  • 1. Gain: >7 dBi everywhere across the passband
    • +
  • 2. Gain Differential: <0.5 dB across the passband
    • +
  • 3. Front-to-Back (Worst-Case): >20 dB
    • +
  • 4. SWR: <1.5:1 relative to an impedance standard across the passband
    • +
+

Obtaining these goals might seem easier with so much boom length and so many elements at our disposal, but, as we shall see, the task is not as simple as it may seem.

+

Model 9556143X: a Hybrid LPDA Using 21 LPDA Elements and 1 Director

+

In Vol. 1 of LPDA Notes on the Books Page, I presented a hybrid high-performance LPDA using 21 LPDA elements and a parasitic director on a 55.8' boom. The array used a Tau of 0.95 and a Sigma of 0.056. The design (and all of the others in this exercise) will use no shorted stub. The overall appearance of the array follows the outline sketch in Fig. 1.

+
+ +
+

Although the dimensions appear in the book, the following partial EZNEC wire table will serve as a reminder of the array dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 21+dir 55.8
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (ft)              End 2     Coord. (ft)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,-18.025,      0                  0, 18.025,      0       0.8   25
+2                4.01472,-17.083,      0            4.01472,17.0833,      0       0.8   23
+3                 7.8287,-16.167,      0             7.8287,16.1667,      0       0.8   23
+4                 11.452,-15.367,      0             11.452,15.3666,      0       0.8   21
+5                14.8941,-14.598,      0            14.8941,14.5983,      0       0.7   21
+6                18.1641,-13.868,      0            18.1641,13.8684,      0       0.7   19
+7                21.2706,-13.175,      0            21.2706,13.1749,      0       0.7   19
+8                24.2218,-12.516,      0            24.2218,12.5162,      0       0.7   17
+9                27.0255, -11.89,      0            27.0255,11.8904,      0       0.7   17
+10               29.6889,-11.296,      0            29.6889,11.2959,      0       0.6   15
+11               32.2192,-10.731,      0            32.2192,10.7311,      0       0.6   15
+12               34.6229,-10.195,      0            34.6229,10.1945,      0       0.6   15
+13               36.9065,-9.6848,      0            36.9065,9.68479,      0       0.6   13
+14               39.0759,-9.2006,      0            39.0759,9.20056,      0       0.6   13
+15               41.1368,-8.7405,      0            41.1368,8.74052,      0       0.5   13
+16               43.0947,-8.3035,      0            43.0947, 8.3035,      0       0.5   11
+17               44.9547,-7.8883,      0            44.9547,7.88833,      0       0.5   11
+18               46.7217,-7.4939,      0            46.7217,7.49391,      0       0.5   11
+19               48.4003,-7.1192,      0            48.4003,7.11922,      0       0.5   9
+20                49.995,-6.7633,      0             49.995,6.76325,      0       0.5   9
+21                 51.51,-6.4251,      0              51.51,6.42509,      0       0.5   9
+22               55.8333,-7.3917,      0            55.8333,7.39167,      0       0.5   11
+
+Total Segments: 340
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The dimensions above are in feet. The array employs a 100-Ohm phase line for use with either 50-Ohm or 75-Ohm feedlines. Note that for this exercise, I have modified the proof-of-principle design from a uniform element diameter of 0.5" to graduated diameters running from 0.8" for the longest element to 0.5" for the shortest. This adjustment represents one step toward more adequately modeling a full array and including the stepped-diameter elements in detail.

+

The amateur-band performance of the array shows a significant gain improvement over the 30-35 foot boom arrays in the preceding exercise.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     Amateur-Band Performance Potential of a 22-Element Hybrid LPDA
+
+Freq.      Gain       180-Deg.   Feed Impedance   50-Ohm    75-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR       SWR
+14.175     8.89       29.93      74.8 - j  6.3    1.51      1.09
+18.118     8.83       37.14      66.5 - j  6.2    1.36      1.16
+21.225     8.70       41.54      65.6 - j  3.2    1.32      1.15
+24.94      8.79       31.08      71.8 + j  2.5    1.44      1.06
+28.0       8.92       25.02      72.5 + j 16.6    1.58      1.25
+28.85      9.04       21.33      47.3 - j 30.7    1.87      1.98
+29.7       9.05       19.63      50.2 + j 20.9    1.51      1.67
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The free-space forward gain averages about 1.5 dB more than for the shorter-boom models. Many--but not all--of the front-to-back ratios exhibit a parallel improvement. Below 10 meters, the design favors the use of a 70-75-Ohm feedline, but above 28 MHz, a 50-Ohm line shows the better SWR curve. Although the array provides good amateur band performance, we can already see that we have not met the more stringent standards set for a general coverage array. We obtain a more complete picture of these failings from a general graph of free-space gain and front-to-back ratios, as shown in Fig. 2.

+
+ +
+

The gain varies from 8.42 to 9.05 dBi, a 0.68 dB differential. More significantly, the use of the low impedance phase line results in two suspect frequencies: 20.0 MHz and 26.75 MHz. Here we have potentially anomalous array operation. Moreover, the front-to-back ratio (both 180-degree and worst-case) drops below 20 dB at 20.0 MHz and above 29.5 MHz. (Note: the front/sidelobe ratio indicates the worst-case front-to-back ratio, since the array nowhere exhibits any secondary forward lobes.)

+
+ +
+

The addition of a parasitic director almost always adversely affects the SWR curve at the upper end of the operating spectrum. Above 28 MHz, the SWR--shown in Fig. 3--exceeds 1.5:1, and the 70-Ohm SWR actually exceeds 2:1 from 29.0 to 29.25 MHz. The source of these swings is apparent in the wide variations in both the resistance and reactance curves at the high end of the operating spectrum.

+

Rather than modifying this array as a hybrid to see if a higher phase line impedance and readjustments to the parasitic director would stabilize performance within the desired limits, I decided to see if a pure LPDA might fulfill the need in a more straightforward way.

+

Model 9556Z: a 26-Element Pure LPDA with a 100-Ohm Phase Line

+

For maximum gain, I initially retained the 100-Ohm phase line. I added elements up to a total of 26 in order to set the self-resonant frequency of the shortest element in the 46-48 MHz region. I retained the same values of Tau and Sigma (0.95 and 0.056) throughout. The general outline of the new array appears in Fig. 4.

+
+ +
+

The boom length of the array grew to 58', which is long, but not too much longer than the nearly 56' boom of the hybrid array. For reference, the following model description shows the element dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 26 el
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 30 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0, -216.3,      0                  0,  216.3,      0       0.8   29
+2                48.1766,   -205,      0            48.1766,    205,      0       0.8   27
+3                93.9445,   -194,      0            93.9445,    194,      0       0.8   27
+4                137.424, -184.4,      0            137.424,184.399,      0       0.8   25
+5                178.729,-175.18,      0            178.729,175.179,      0       0.7   23
+6                217.969,-166.42,      0            217.969, 166.42,      0       0.7   23
+7                255.248, -158.1,      0            255.248,158.099,      0       0.7   21
+8                290.662,-150.19,      0            290.662,150.194,      0       0.7   21
+9                324.306,-142.68,      0            324.306,142.685,      0       0.7   19
+10               356.267,-135.55,      0            356.267, 135.55,      0       0.6   19
+11                386.63,-128.77,      0             386.63,128.773,      0       0.6   17
+12               415.475,-122.33,      0            415.475,122.334,      0       0.6   17
+13               442.878,-116.22,      0            442.878,116.217,      0       0.6   15
+14               468.911,-110.41,      0            468.911,110.407,      0       0.6   15
+15               493.642,-104.89,      0            493.642,104.886,      0       0.5   15
+16               517.136,-99.642,      0            517.136, 99.642,      0       0.5   13
+17               539.456, -94.66,      0            539.456,94.6599,      0       0.5   13
+18                560.66,-89.927,      0             560.66,89.9269,      0       0.5   13
+19               580.804,-85.431,      0            580.804,85.4306,      0       0.5   11
+20                599.94,-81.159,      0             599.94, 81.159,      0       0.5   11
+21                618.12,-77.101,      0             618.12,77.1011,      0       0.5   11
+22                635.39,-73.246,      0             635.39, 73.246,      0       0.5   9
+23                 651.8,-69.584,      0              651.8, 69.584,      0       0.5   9
+24                667.39,-66.105,      0             667.39, 66.105,      0       0.5   9
+25                 682.2,  -62.8,      0              682.2,   62.8,      0       0.5   9
+26                696.27, -59.66,      0             696.27,  59.66,      0       0.5   9
+
+Total Segments: 430
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Dimensions are in inches. All of the new elements use a 0.5" diameter, since this is likely to be close to the equivalent uniform diameter of a stepped-diameter physical element with the smallest diameter being 0.5". A presumed wind survival of 120 mph guides my thinking here.

+

The amateur-band performance of the array remains very high for an LPDA.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 26-Element Pure LPDA
+                           100-Ohm Phase Line
+
+Freq.      Gain       180-Deg.   Feed Impedance   50-Ohm    75-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR       SWR
+14.175     8.88       31.34      67.2 - j  6.3    1.37      1.15
+18.118     8.87       37.80      68.5 - j  2.3    1.37      1.10
+21.225     8.77       33.34      64.1 - j  0.1    1.28      1.17
+24.94      8.68       44.15      68.8 - j 10.9    1.45      1.19
+28.0       8.57       35.28      68.8 - j  5.9    1.40      1.13
+28.85      8.64       37.30      66.9 - j  2.4    1.34      1.13
+29.7       8.49       30.12      60.7 - j 13.2    1.36      1.33
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The ham-band table shows that a pure LPDA with the shortest element self-resonant in the region of 1.6 times the highest operating frequency results in a remarkably stable set of feedpoint impedances, even with the low 100-Ohm phase line. The values favor a 75-Ohm line, but the 50-Ohm performance is completely acceptable relative to our standards. As well, the gain exhibits only modest excursions and the front-to-back ratio is everywhere above 30 dB. The remaining question is whether this performance holds up across the entire operating spectrum.

+
+ +
+

Fig. 5 shows the gain and front-to-back curves. The gain variation is exactly 0.5 dB. However, just as we did with the hybrid array, we find suspect frequencies: 20.0 MHz and 26.75 MHz. At 20 MHz, the front-to-back ratio drops to under 17.5 dB. Whether or not we have a true anomaly at either suspect frequency, we can see performance drops below the standards.

+
+ +
+

The feedpoint conditions in Fig. 6 show reasonably good stability. The 50-Ohm SWR rises above 1.5:1 in the 24.5-24.75 MHz region. Otherwise, the spectrum is clean.

+

Overall, then, the array very nearly meets all standards almost everywhere in the operating spectrum. However, "almost" and "nearly" need not be "good enough" in an exercise like this one.

+

Model 9556Z200: a 26-Element Pure LPDA with a 200-Ohm Phase Line

+

For improved stability, I raised the phase-line impedance to 200 Ohms. The feedpoint reference impedance thus becomes 100 Ohms, with a presumed 2:1 balun device for use with a 50-Ohm supply cable. The element dimensions otherwise remained the same. This modest revision yielded the following amateur-band performance table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 26-Element Pure LPDA
+                           200-Ohm Phase Line
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     8.81       28.53      121.9 - j 12.8   1.26
+18.118     8.77       34.99      103.1 - j  2.6   1.04
+21.225     8.74       41.77      112.7 - j 12.3   1.18
+24.94      8.72       34.88      112.6 - j  9.1   1.16
+28.0       8.64       35.77      110.2 - j 14.3   1.18
+28.85      8.46       30.97       88.8 - j 20.7   1.28
+29.7       8.31       29.39       96.2 + j  5.5   1.07
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In the process of raising the phase line impedance, we lost little performance at the lower end of the operating spectrum. However, we have lost performance in the upper range. The free-space gain and front-to-back curves for the entire operating spectrum more vividly portray these losses.

+
+ +
+

In Fig. 7, we can observe the increasing acceleration in the reduction of gain with increases in frequency. The gain differential has actually increased to 0.55 dB across the range, even though there are no suspect frequencies. Except for the region near 14 MHz, the front-to-back ratios remain above 30 dB.

+
+ +
+

The feedpoint conditions appear in Fig. 8. The 100-Ohm SWR never reaches 1.3:1, and the small variations in the resistance and reactance provide the basis for the stable SWR conditions.

+

Increasing the phase line impedance thus had two effects. It stabilize the array, but it also changed the gain curve. At 100-Ohms, the gain remained nearly constant, with only a small drop-off at the higher frequencies of operation. Doubling the line impedance produced a gain curve whose average value shows a nearly linear drop with increasing frequency. This is one of the phenomena that LPDA designers should bear in mind, one that often requires some redesign of an entire array to smooth performance.

+

Of course, we have not done any modifications to the calculated design. Hence, circularizing Tau for the forward-most elements still remains an option. We have spare SWR with which to maneuver, since our limit is 1.5:1, and adjusting the lengths of the forward elements very often produces somewhat less optimal SWR values.

+

Model 9556Z201: a 26-Element Pure LPDA with a 200-Ohm Phase Line and Modified Forward Elements

+

Since the basic array with the extended frequency coverage has so many elements whose self-resonant frequencies are above 30 MHz, I circularized the Tau of the forward-most 7 elements. The results show up in the outline sketch in Fig. 9. As with the other models in the exercise, the array uses no shorted stub on the longest element.

+
+ +
+

The following wire table from EZNEC shows more clearly how much revision occurred.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+14-30 MHz .95/.056 26 el:  200-Ohm phase line; modified
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 14 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0, -216.3,      0                  0,  216.3,      0       0.8   29
+2                48.1766,   -205,      0            48.1766,    205,      0       0.8   27
+3                93.9445,   -194,      0            93.9445,    194,      0       0.8   27
+4                137.424, -184.4,      0            137.424,184.399,      0       0.8   25
+5                178.729,-175.18,      0            178.729,175.179,      0       0.7   23
+6                217.969,-166.42,      0            217.969, 166.42,      0       0.7   23
+7                255.248, -158.1,      0            255.248,158.099,      0       0.7   21
+8                290.662,-150.19,      0            290.662,150.194,      0       0.7   21
+9                324.306,-142.68,      0            324.306,142.685,      0       0.7   19
+10               356.267,-135.55,      0            356.267, 135.55,      0       0.6   19
+11                386.63,-128.77,      0             386.63,128.773,      0       0.6   17
+12               415.475,-122.33,      0            415.475,122.334,      0       0.6   17
+13               442.878,-116.22,      0            442.878,116.217,      0       0.6   15
+14               468.911,-110.41,      0            468.911,110.407,      0       0.6   15
+15               493.642,-104.89,      0            493.642,104.886,      0       0.5   15
+16               517.136,-99.642,      0            517.136, 99.642,      0       0.5   13
+17               539.456, -94.66,      0            539.456,94.6599,      0       0.5   13
+18                560.66,-89.927,      0             560.66,89.9269,      0       0.5   13
+19               580.804,-85.431,      0            580.804,85.4306,      0       0.5   11
+20                599.94,  -81.5,      0             599.94,   81.5,      0       0.5   11
+21                618.12,    -78,      0             618.12,     78,      0       0.5   11
+22                635.39,  -74.7,      0             635.39,   74.7,      0       0.5   9
+23                 651.8,  -70.5,      0              651.8,   70.5,      0       0.5   9
+24                667.39,  -68.5,      0             667.39,   68.5,      0       0.5   9
+25                 682.2,  -65.8,      0              682.2,   65.8,      0       0.5   9
+26                696.27,  -63.1,      0             696.27,   63.1,      0       0.5   9
+
+Total Segments: 430
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The object of the exercise was not to radically alter array performance, but only to bring it within the initial specifications and limits. The following table of potential amateur-band performance gives an indication of the degree of performance change.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      Amateur-Band Performance Potential of a 26-Element Pure LPDA
+              200-Ohm Phase Line; Modified Forward Elements
+
+Freq.      Gain       180-Deg.   Feed Impedance   100-Ohm
+ MHz       dBi        F-B dB     R +/- jX Ohms     SWR
+14.175     8.82       28.23      119.1 - j 15.0   1.25
+18.118     8.78       34.01      100.2 - j  3.1   1.03
+21.225     8.77       40.78      109.2 - j 13.7   1.17
+24.94      8.79       32.16      110.2 - j 14.4   1.18
+28.0       8.75       31.74      109.8 - j 21.3   1.25
+28.85      8.56       28.14       77.4 - j 19.3   1.40
+29.7       8.43       27.59      102.2 + j 10.0   1.11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The most noticeable effect is the slight hitch in the impedance at 28.85 MHz, although the SWR remains well below the 1.5:1 limit. The array produced usable SWR values--at reduced performance levels down to 13.5 MHz and well above 35 MHz, although the SWR rises above the 1.5:1 level around 32 MHz.

+
+ +
+

Fig. 10 shows the overall gain and front-to-back curves. As is evident, the decreasing gain curve did not come close to flattening. However, free-space gain now ranges from 8.43 dBi to 8.88 dBi, a differential of 0.45 dB. The average gain is 8.74 dBi, the same value as for the 100-Ohm phase-line version and 0.05 dB higher than for the initial 200-Ohm phase-line version. Due to element length modifications, the average worst-case front-to-back ratio drops by about 1 dB, from 34.86 dB to 33.88 dB. Although numerically interesting, these differences are not operationally significant.

+
+ +
+

In Fig. 11, we have the feedpoint conditions. As noted in connection with ham-band performance, there is on region where the SWR exceeds 1.4:1--28.5 to 28.75 MHz), but the average 100-Ohm SWR is 1.16:1. The upshot is that the revised array now meets all of the general coverage criteria set forth at the beginning of the exercise.

+

Conclusion

+

It is not at all clear that the final stage of array revision is necessary to achieve an adequate general coverage LPDA on a boom between 55 and 60'. However, the move to a 200-Ohm phase line and the extension of the upper design frequency appear to be advisable steps to achieve the general goals. The initial array, however, would be quite suitable for amateur band and SWL use, as well as any other use imposing less stringent standards of performance smoothness.

+

Perhaps the easiest way to design LPDAs with extended upper frequency limits, especially when the calculation program presumes a design limit of 1.3 times the upper operating frequency, is simply to trick the system. Multiply the upper operating frequency by 1.6. Then divide the new frequency by 1.3 to obtain the upper operating frequency you will plug into a design program, such as LPCAD. For an operating limit of 30 MHz, the highest self-resonant frequency will be 48 MHz. Hence, the virtual upper operating frequency will be about 37 MHz.

+

How much above or below the virtual upper operating frequency you should go depends on the values of Tau and Sigma used in the design. For reasonably high values of Tau, the higher the value of Sigma, the better the inherent upper range performance. Hence, the designer may not need to raise the upper limit so high. For reasonable values of Sigma, the higher the value of Tau, the better the low end performance, and the greater the performance fall-off with increasing frequency. Such design may need a higher upper limit. Since the phase-line impedance will alter these rules-of-thumb somewhat, the final design may require some trial and error.

+

Nonetheless, the exercise does demonstrate that it is possible--without excessive additions to the weight of an array--to achieve smooth general coverage performance within rigorous standards.

+
+ +
+

Updated 11-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: HF Upper, LPDA


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+


+ Notes on Standard Design HF LPDAs (for 3-30 MHz) Design and Modeling Data

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The following items originally appeared in QEX in May/Jun, 2000 and Jul/Aug, 2000. They are copyright by ARRL (2000), all rights reserved. Reproduced with permission. +
+
+
+ +

+
+ Go to Amateur Radio Page +

Topics: HF Multi Band, LPDA


+ + diff --git a/content/lpda/lp60.html b/content/lpda/lp60.html new file mode 100644 index 0000000..146bc33 --- /dev/null +++ b/content/lpda/lp60.html @@ -0,0 +1,405 @@ + + + + + + A 3.5 Octave LPDA of High Potential Performance Part 1: No One Will Build + + + +
+

A 3.5 Octave LPDA of High Potential Performance
+ Part 1: But an Antenna that No One Will Build

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

In my two part series in QEX (May and July, 2000) of relatively short boom 3.5 octave LPDAs (60 to 160 feet), I had occasion to note the shortcomings of such antennas. Lest anyone think that a good LPDA that covers 3 to 30 MHz is not possible, I employed LPCAD 2.7 by Roger Cox to begin design of a high performance LPDA for the entire HF range. This note presents a kind of picture show of the antenna performance as modeled on NEC-4. Since the graphics tell the story, commentary will be limited.

+

An Almost Adequate Design

The first design was a 60-element LPDA array of standard design with little or no modification. The normal modeling care went into element segmentation to ensure adequate numbers of segments on all elements on all frequencies within the passband. As well, element diameters were staggered from 6" for the longest elements to 0.5" for the shortest ones. Since most designs show a fall-off in gain at the higher end of the frequency range, I designed the first model for an upper limit of 35 MHz, and the software automatically calculated elements for up to 1.3 times this frequency. As we shall see, even this buffer was not fully sufficient for even performance across the entire working passband. +

Modeling tests were done using transmission line characteristic impedances from 75 to 200 Ohms, with the last value being set as the standard. For an antenna with this much frequency coverage, pattern instabilities appeared whenever the phase line Zo was lowered to the 100-Ohm region or below. As a result, the feedpoint SWR values for selected frequencies checked are referenced to 160 Ohms, and a balun (transmission line transformer) would be required for use with a 50-Ohm feedline.

+

For reference, the EZNEC-4 model description of the first design follows.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-35 MHz Tau=.955 Sigma=.18                   Frequency = 3.5  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-83.640,  0.000         0.000, 83.640,  0.000 6.00E+00 111
+2           60.221,-79.876,  0.000        60.221, 79.876,  0.000 5.88E+00 107
+3          117.732,-76.282,  0.000       117.732, 76.282,  0.000 5.75E+00 101
+4          172.654,-72.849,  0.000       172.654, 72.849,  0.000 5.62E+00  97
+5          225.106,-69.571,  0.000       225.106, 69.571,  0.000 5.50E+00  93
+6          275.197,-66.440,  0.000       275.197, 66.440,  0.000 5.38E+00  89
+7          323.034,-63.450,  0.000       323.034, 63.450,  0.000 5.25E+00  85
+8          368.718,-60.595,  0.000       368.718, 60.595,  0.000 5.12E+00  81
+9          412.347,-57.868,  0.000       412.347, 57.868,  0.000 5.00E+00  77
+10         454.012,-55.264,  0.000       454.012, 55.264,  0.000 4.88E+00  73
+11         493.802,-52.777,  0.000       493.802, 52.777,  0.000 4.75E+00  71
+12         531.802,-50.402,  0.000       531.802, 50.402,  0.000 4.62E+00  67
+13         568.091,-48.134,  0.000       568.091, 48.134,  0.000 4.50E+00  63
+14         602.748,-45.968,  0.000       602.748, 45.968,  0.000 4.38E+00  61
+15         635.845,-43.900,  0.000       635.845, 43.900,  0.000 4.25E+00  59
+16         667.453,-41.924,  0.000       667.453, 41.924,  0.000 4.12E+00  57
+17         697.638,-40.038,  0.000       697.638, 40.038,  0.000 4.00E+00  53
+18         726.465,-38.236,  0.000       726.465, 38.236,  0.000 3.88E+00  51
+19         753.995,-36.515,  0.000       753.995, 36.515,  0.000 3.75E+00  49
+20         780.286,-34.872,  0.000       780.286, 34.872,  0.000 3.62E+00  47
+21         805.394,-33.303,  0.000       805.394, 33.303,  0.000 3.50E+00  45
+22         829.372,-31.804,  0.000       829.372, 31.804,  0.000 3.38E+00  43
+23         852.271,-30.373,  0.000       852.271, 30.373,  0.000 3.25E+00  41
+24         874.140,-29.006,  0.000       874.140, 29.006,  0.000 3.12E+00  39
+25         895.024,-27.701,  0.000       895.024, 27.701,  0.000 3.00E+00  37
+26         914.969,-26.454,  0.000       914.969, 26.454,  0.000 2.88E+00  35
+27         934.016,-25.264,  0.000       934.016, 25.264,  0.000 2.75E+00  33
+28         952.206,-24.127,  0.000       952.206, 24.127,  0.000 2.75E+00  33
+29         969.578,-23.041,  0.000       969.578, 23.041,  0.000 2.62E+00  31
+30         986.167,-22.004,  0.000       986.167, 22.004,  0.000 2.50E+00  29
+31         1002.01,-21.014,  0.000       1002.01, 21.014,  0.000 2.38E+00  27
+32         1017.14,-20.069,  0.000       1017.14, 20.069,  0.000 2.25E+00  27
+33         1031.59,-19.166,  0.000       1031.59, 19.166,  0.000 2.12E+00  25
+34         1045.39,-18.303,  0.000       1045.39, 18.303,  0.000 2.12E+00  25
+35         1058.57,-17.479,  0.000       1058.57, 17.479,  0.000 2.00E+00  23
+36         1071.15,-16.693,  0.000       1071.15, 16.693,  0.000 2.00E+00  23
+37         1083.17,-15.942,  0.000       1083.17, 15.942,  0.000 1.87E+00  21
+38         1094.65,-15.224,  0.000       1094.65, 15.224,  0.000 1.87E+00  21
+39         1105.61,-14.539,  0.000       1105.61, 14.539,  0.000 1.75E+00  19
+40         1116.08,-13.885,  0.000       1116.08, 13.885,  0.000 1.75E+00  19
+41         1126.08,-13.260,  0.000       1126.08, 13.260,  0.000 1.62E+00  17
+42         1135.62,-12.663,  0.000       1135.62, 12.663,  0.000 1.62E+00  17
+43         1144.74,-12.094,  0.000       1144.74, 12.094,  0.000 1.50E+00  17
+44         1153.45,-11.549,  0.000       1153.45, 11.549,  0.000 1.50E+00  15
+45         1161.77,-11.030,  0.000       1161.77, 11.030,  0.000 1.38E+00  15
+46         1169.71,-10.533,  0.000       1169.71, 10.533,  0.000 1.38E+00  13
+47         1177.29,-10.059,  0.000       1177.29, 10.059,  0.000 1.25E+00  13
+48         1184.53, -9.607,  0.000       1184.53,  9.607,  0.000 1.25E+00  13
+49         1191.45, -9.174,  0.000       1191.45,  9.174,  0.000 1.12E+00  13
+50         1198.06, -8.762,  0.000       1198.06,  8.762,  0.000 1.12E+00  11
+51         1204.36, -8.367,  0.000       1204.36,  8.367,  0.000 1.00E+00  11
+52         1210.39, -7.991,  0.000       1210.39,  7.991,  0.000 1.00E+00  11
+53         1216.14, -7.631,  0.000       1216.14,  7.631,  0.000 8.75E-01  11
+54         1221.64, -7.288,  0.000       1221.64,  7.288,  0.000 8.75E-01   9
+55         1226.88, -6.960,  0.000       1226.88,  6.960,  0.000 7.50E-01   9
+56         1231.89, -6.647,  0.000       1231.89,  6.647,  0.000 7.50E-01   9
+57         1236.68, -6.347,  0.000       1236.68,  6.347,  0.000 6.25E-01   9
+58         1241.25, -6.062,  0.000       1241.25,  6.062,  0.000 6.25E-01   9
+59         1245.61, -5.789,  0.000       1245.61,  5.789,  0.000 5.00E-01   9
+60         1249.78, -5.529,  0.000       1249.78,  5.529,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4    60 / 50.00   ( 60 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  200.0  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  200.0  1.00  R
+22    22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist  200.0  1.00  R
+23    23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist  200.0  1.00  R
+24    24/50.0  ( 24/50.0)   25/50.0  ( 25/50.0)  Actual dist  200.0  1.00  R
+25    25/50.0  ( 25/50.0)   26/50.0  ( 26/50.0)  Actual dist  200.0  1.00  R
+26    26/50.0  ( 26/50.0)   27/50.0  ( 27/50.0)  Actual dist  200.0  1.00  R
+27    27/50.0  ( 27/50.0)   28/50.0  ( 28/50.0)  Actual dist  200.0  1.00  R
+28    28/50.0  ( 28/50.0)   29/50.0  ( 29/50.0)  Actual dist  200.0  1.00  R
+29    29/50.0  ( 29/50.0)   30/50.0  ( 30/50.0)  Actual dist  200.0  1.00  R
+30    30/50.0  ( 30/50.0)   31/50.0  ( 31/50.0)  Actual dist  200.0  1.00  R
+31    31/50.0  ( 31/50.0)   32/50.0  ( 32/50.0)  Actual dist  200.0  1.00  R
+32    32/50.0  ( 32/50.0)   33/50.0  ( 33/50.0)  Actual dist  200.0  1.00  R
+33    33/50.0  ( 33/50.0)   34/50.0  ( 34/50.0)  Actual dist  200.0  1.00  R
+34    34/50.0  ( 34/50.0)   35/50.0  ( 35/50.0)  Actual dist  200.0  1.00  R
+35    35/50.0  ( 35/50.0)   36/50.0  ( 36/50.0)  Actual dist  200.0  1.00  R
+36    36/50.0  ( 36/50.0)   37/50.0  ( 37/50.0)  Actual dist  200.0  1.00  R
+37    37/50.0  ( 37/50.0)   38/50.0  ( 38/50.0)  Actual dist  200.0  1.00  R
+38    38/50.0  ( 38/50.0)   39/50.0  ( 39/50.0)  Actual dist  200.0  1.00  R
+39    39/50.0  ( 39/50.0)   40/50.0  ( 40/50.0)  Actual dist  200.0  1.00  R
+40    40/50.0  ( 40/50.0)   41/50.0  ( 41/50.0)  Actual dist  200.0  1.00  R
+41    41/50.0  ( 41/50.0)   42/50.0  ( 42/50.0)  Actual dist  200.0  1.00  R
+42    42/50.0  ( 42/50.0)   43/50.0  ( 43/50.0)  Actual dist  200.0  1.00  R
+43    43/50.0  ( 43/50.0)   44/50.0  ( 44/50.0)  Actual dist  200.0  1.00  R
+44    44/50.0  ( 44/50.0)   45/50.0  ( 45/50.0)  Actual dist  200.0  1.00  R
+45    45/50.0  ( 45/50.0)   46/50.0  ( 46/50.0)  Actual dist  200.0  1.00  R
+46    46/50.0  ( 46/50.0)   47/50.0  ( 47/50.0)  Actual dist  200.0  1.00  R
+47    47/50.0  ( 47/50.0)   48/50.0  ( 48/50.0)  Actual dist  200.0  1.00  R
+48    48/50.0  ( 48/50.0)   49/50.0  ( 49/50.0)  Actual dist  200.0  1.00  R
+49    49/50.0  ( 49/50.0)   50/50.0  ( 50/50.0)  Actual dist  200.0  1.00  R
+50    50/50.0  ( 50/50.0)   51/50.0  ( 51/50.0)  Actual dist  200.0  1.00  R
+51    51/50.0  ( 51/50.0)   52/50.0  ( 52/50.0)  Actual dist  200.0  1.00  R
+52    52/50.0  ( 52/50.0)   53/50.0  ( 53/50.0)  Actual dist  200.0  1.00  R
+53    53/50.0  ( 53/50.0)   54/50.0  ( 54/50.0)  Actual dist  200.0  1.00  R
+54    54/50.0  ( 54/50.0)   55/50.0  ( 55/50.0)  Actual dist  200.0  1.00  R
+55    55/50.0  ( 55/50.0)   56/50.0  ( 56/50.0)  Actual dist  200.0  1.00  R
+56    56/50.0  ( 56/50.0)   57/50.0  ( 57/50.0)  Actual dist  200.0  1.00  R
+57    57/50.0  ( 57/50.0)   58/50.0  ( 58/50.0)  Actual dist  200.0  1.00  R
+58    58/50.0  ( 58/50.0)   59/50.0  ( 59/50.0)  Actual dist  200.0  1.00  R
+59    59/50.0  ( 59/50.0)   60/50.0  ( 60/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model was spot-checked at the HF region limits (3.0 and 30.0 MHz) and within each amateur band. The following table summarizes the results, with gain being the free space value.

+ 
Frequency         Gain        Front-to-Back     Source Impedance        160-Ohm
+  Mhz             dBi           dB              R +/- jX Ohms            VSWR
+ 3.0              11.27       53.01             162.1 - j 0.8           1.014
+ 3.5              11.28       55.40             163.2 - j 0.0           1.020
+ 4.0              11.30       64.09             163.6 - j 2.3           1.027
+ 7.15             11.31       59.19             164.6 - j 3.4           1.036
+10.125            11.34       53.86             167.5 - j 6.4           1.062
+14.175            11.32       50.29             161.8 - j 6.0           1.039
+18.118            11.21       47.28             159.1 - j15.7           1.104
+21.225            11.16       45.26             158.1 - j21.5           1.145
+24.94             10.99       43.31             161.4 - j31.3           1.215
+28.0              10.25       31.80             142.0 - j 8.7           1.142
+28.5              10.25       32.59             156.6 - j 4.4           1.036
+29.0              10.30       34.20             172.3 - j11.7           1.107
+29.5              10.44       37.65             179.5 - j27.1           1.218
+30.0              10.56       42.41             178.1 - j40.7           1.301
+

First, we shall display on this page only the 3 MHz and 30 MHz free-space azimuth patterns and the relative magnitudes of currents on the LPDA elements. However, you may examine similar graphics for each of the frequencies sampled by the "Gallery" link at the end of this note.

+

3 MHz:

+
+ +
+
+ +
+

30 MHz:

+
+ +
+
+ +
+

Let's just note two principle facts that you can derive from the table. First, above 12 meters, the gain and front-to-back ratios begin to drop relative to the lower HF values. Second, from 28 MHz up, the impedance values lose their systematic progression and begin to vary erratically. Now add in the relative current magnitude graphic for 30 MHz and see how many (or how few) elements are active at 30 MHz, compared to the 3 MHz graphic of the same data. At the upper end of the spectrum, there are still too few elements to achieve full performance from the LPDA, despite the 0.955 Tau and 0.18 Sigma values.

+

A More Nearly Adequate Design

Some redesign was certainly in order. I have elsewhere outline many of the techniques by which one can raise the performance of an LPDA at the higher frequency range. Due to the tediousness of some, I opted simply to add 4 more elements to the front end of the LPDA. The highest frequency (shortest) element is now independently resonant at approximately 50 MHz, and the array is now 64 elements long. Here is the model description. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-35 MHz Tau=.955 Sigma=.18                             Frequency = 3  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1            0.000,-83.640,  0.000         0.000, 83.640,  0.000 6.00E+00 111
+2           60.221,-79.876,  0.000        60.221, 79.876,  0.000 5.88E+00 107
+3          117.732,-76.282,  0.000       117.732, 76.282,  0.000 5.75E+00 101
+4          172.654,-72.849,  0.000       172.654, 72.849,  0.000 5.62E+00  97
+5          225.106,-69.571,  0.000       225.106, 69.571,  0.000 5.50E+00  93
+6          275.197,-66.440,  0.000       275.197, 66.440,  0.000 5.38E+00  89
+7          323.034,-63.450,  0.000       323.034, 63.450,  0.000 5.25E+00  85
+8          368.718,-60.595,  0.000       368.718, 60.595,  0.000 5.12E+00  81
+9          412.347,-57.868,  0.000       412.347, 57.868,  0.000 5.00E+00  77
+10         454.012,-55.264,  0.000       454.012, 55.264,  0.000 4.88E+00  73
+11         493.802,-52.777,  0.000       493.802, 52.777,  0.000 4.75E+00  71
+12         531.802,-50.402,  0.000       531.802, 50.402,  0.000 4.62E+00  67
+13         568.091,-48.134,  0.000       568.091, 48.134,  0.000 4.50E+00  63
+14         602.748,-45.968,  0.000       602.748, 45.968,  0.000 4.38E+00  61
+15         635.845,-43.900,  0.000       635.845, 43.900,  0.000 4.25E+00  59
+16         667.453,-41.924,  0.000       667.453, 41.924,  0.000 4.12E+00  57
+17         697.638,-40.038,  0.000       697.638, 40.038,  0.000 4.00E+00  53
+18         726.465,-38.236,  0.000       726.465, 38.236,  0.000 3.88E+00  51
+19         753.995,-36.515,  0.000       753.995, 36.515,  0.000 3.75E+00  49
+20         780.286,-34.872,  0.000       780.286, 34.872,  0.000 3.62E+00  47
+21         805.394,-33.303,  0.000       805.394, 33.303,  0.000 3.50E+00  45
+22         829.372,-31.804,  0.000       829.372, 31.804,  0.000 3.38E+00  43
+23         852.271,-30.373,  0.000       852.271, 30.373,  0.000 3.25E+00  41
+24         874.140,-29.006,  0.000       874.140, 29.006,  0.000 3.12E+00  39
+25         895.024,-27.701,  0.000       895.024, 27.701,  0.000 3.00E+00  37
+26         914.969,-26.454,  0.000       914.969, 26.454,  0.000 2.88E+00  35
+27         934.016,-25.264,  0.000       934.016, 25.264,  0.000 2.75E+00  33
+28         952.206,-24.127,  0.000       952.206, 24.127,  0.000 2.75E+00  33
+29         969.578,-23.041,  0.000       969.578, 23.041,  0.000 2.62E+00  31
+30         986.167,-22.004,  0.000       986.167, 22.004,  0.000 2.50E+00  29
+31         1002.01,-21.014,  0.000       1002.01, 21.014,  0.000 2.38E+00  27
+32         1017.14,-20.069,  0.000       1017.14, 20.069,  0.000 2.25E+00  27
+33         1031.59,-19.166,  0.000       1031.59, 19.166,  0.000 2.12E+00  25
+34         1045.39,-18.303,  0.000       1045.39, 18.303,  0.000 2.12E+00  25
+35         1058.57,-17.479,  0.000       1058.57, 17.479,  0.000 2.00E+00  23
+36         1071.15,-16.693,  0.000       1071.15, 16.693,  0.000 2.00E+00  23
+37         1083.17,-15.942,  0.000       1083.17, 15.942,  0.000 1.87E+00  21
+38         1094.65,-15.224,  0.000       1094.65, 15.224,  0.000 1.87E+00  21
+39         1105.61,-14.539,  0.000       1105.61, 14.539,  0.000 1.75E+00  19
+40         1116.08,-13.885,  0.000       1116.08, 13.885,  0.000 1.75E+00  19
+41         1126.08,-13.260,  0.000       1126.08, 13.260,  0.000 1.62E+00  17
+42         1135.62,-12.663,  0.000       1135.62, 12.663,  0.000 1.62E+00  17
+43         1144.74,-12.094,  0.000       1144.74, 12.094,  0.000 1.50E+00  17
+44         1153.45,-11.549,  0.000       1153.45, 11.549,  0.000 1.50E+00  15
+45         1161.77,-11.030,  0.000       1161.77, 11.030,  0.000 1.38E+00  15
+46         1169.71,-10.533,  0.000       1169.71, 10.533,  0.000 1.38E+00  13
+47         1177.29,-10.059,  0.000       1177.29, 10.059,  0.000 1.25E+00  13
+48         1184.53, -9.607,  0.000       1184.53,  9.607,  0.000 1.25E+00  13
+49         1191.45, -9.174,  0.000       1191.45,  9.174,  0.000 1.12E+00  13
+50         1198.06, -8.762,  0.000       1198.06,  8.762,  0.000 1.12E+00  11
+51         1204.36, -8.367,  0.000       1204.36,  8.367,  0.000 1.00E+00  11
+52         1210.39, -7.991,  0.000       1210.39,  7.991,  0.000 1.00E+00  11
+53         1216.14, -7.631,  0.000       1216.14,  7.631,  0.000 8.75E-01  11
+54         1221.64, -7.288,  0.000       1221.64,  7.288,  0.000 8.75E-01   9
+55         1226.88, -6.960,  0.000       1226.88,  6.960,  0.000 7.50E-01   9
+56         1231.89, -6.647,  0.000       1231.89,  6.647,  0.000 7.50E-01   9
+57         1236.68, -6.347,  0.000       1236.68,  6.347,  0.000 6.25E-01   9
+58         1241.25, -6.062,  0.000       1241.25,  6.062,  0.000 6.25E-01   9
+59         1245.61, -5.789,  0.000       1245.61,  5.789,  0.000 5.00E-01   9
+60         1249.78, -5.529,  0.000       1249.78,  5.529,  0.000 5.00E-01   7
+61         1253.76, -5.280,  0.000       1253.76,  5.280,  0.000 5.00E-01   7
+62         1257.57, -5.042,  0.000       1257.57,  5.042,  0.000 5.00E-01   7
+63         1261.20, -4.815,  0.000       1261.20,  4.815,  0.000 5.00E-01   7
+64         1264.67, -4.599,  0.000       1264.67,  4.599,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4    64 / 50.00   ( 64 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  200.0  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  200.0  1.00  R
+22    22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist  200.0  1.00  R
+23    23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist  200.0  1.00  R
+24    24/50.0  ( 24/50.0)   25/50.0  ( 25/50.0)  Actual dist  200.0  1.00  R
+25    25/50.0  ( 25/50.0)   26/50.0  ( 26/50.0)  Actual dist  200.0  1.00  R
+26    26/50.0  ( 26/50.0)   27/50.0  ( 27/50.0)  Actual dist  200.0  1.00  R
+27    27/50.0  ( 27/50.0)   28/50.0  ( 28/50.0)  Actual dist  200.0  1.00  R
+28    28/50.0  ( 28/50.0)   29/50.0  ( 29/50.0)  Actual dist  200.0  1.00  R
+29    29/50.0  ( 29/50.0)   30/50.0  ( 30/50.0)  Actual dist  200.0  1.00  R
+30    30/50.0  ( 30/50.0)   31/50.0  ( 31/50.0)  Actual dist  200.0  1.00  R
+31    31/50.0  ( 31/50.0)   32/50.0  ( 32/50.0)  Actual dist  200.0  1.00  R
+32    32/50.0  ( 32/50.0)   33/50.0  ( 33/50.0)  Actual dist  200.0  1.00  R
+33    33/50.0  ( 33/50.0)   34/50.0  ( 34/50.0)  Actual dist  200.0  1.00  R
+34    34/50.0  ( 34/50.0)   35/50.0  ( 35/50.0)  Actual dist  200.0  1.00  R
+35    35/50.0  ( 35/50.0)   36/50.0  ( 36/50.0)  Actual dist  200.0  1.00  R
+36    36/50.0  ( 36/50.0)   37/50.0  ( 37/50.0)  Actual dist  200.0  1.00  R
+37    37/50.0  ( 37/50.0)   38/50.0  ( 38/50.0)  Actual dist  200.0  1.00  R
+38    38/50.0  ( 38/50.0)   39/50.0  ( 39/50.0)  Actual dist  200.0  1.00  R
+39    39/50.0  ( 39/50.0)   40/50.0  ( 40/50.0)  Actual dist  200.0  1.00  R
+40    40/50.0  ( 40/50.0)   41/50.0  ( 41/50.0)  Actual dist  200.0  1.00  R
+41    41/50.0  ( 41/50.0)   42/50.0  ( 42/50.0)  Actual dist  200.0  1.00  R
+42    42/50.0  ( 42/50.0)   43/50.0  ( 43/50.0)  Actual dist  200.0  1.00  R
+43    43/50.0  ( 43/50.0)   44/50.0  ( 44/50.0)  Actual dist  200.0  1.00  R
+44    44/50.0  ( 44/50.0)   45/50.0  ( 45/50.0)  Actual dist  200.0  1.00  R
+45    45/50.0  ( 45/50.0)   46/50.0  ( 46/50.0)  Actual dist  200.0  1.00  R
+46    46/50.0  ( 46/50.0)   47/50.0  ( 47/50.0)  Actual dist  200.0  1.00  R
+47    47/50.0  ( 47/50.0)   48/50.0  ( 48/50.0)  Actual dist  200.0  1.00  R
+48    48/50.0  ( 48/50.0)   49/50.0  ( 49/50.0)  Actual dist  200.0  1.00  R
+49    49/50.0  ( 49/50.0)   50/50.0  ( 50/50.0)  Actual dist  200.0  1.00  R
+50    50/50.0  ( 50/50.0)   51/50.0  ( 51/50.0)  Actual dist  200.0  1.00  R
+51    51/50.0  ( 51/50.0)   52/50.0  ( 52/50.0)  Actual dist  200.0  1.00  R
+52    52/50.0  ( 52/50.0)   53/50.0  ( 53/50.0)  Actual dist  200.0  1.00  R
+53    53/50.0  ( 53/50.0)   54/50.0  ( 54/50.0)  Actual dist  200.0  1.00  R
+54    54/50.0  ( 54/50.0)   55/50.0  ( 55/50.0)  Actual dist  200.0  1.00  R
+55    55/50.0  ( 55/50.0)   56/50.0  ( 56/50.0)  Actual dist  200.0  1.00  R
+56    56/50.0  ( 56/50.0)   57/50.0  ( 57/50.0)  Actual dist  200.0  1.00  R
+57    57/50.0  ( 57/50.0)   58/50.0  ( 58/50.0)  Actual dist  200.0  1.00  R
+58    58/50.0  ( 58/50.0)   59/50.0  ( 59/50.0)  Actual dist  200.0  1.00  R
+59    59/50.0  ( 59/50.0)   60/50.0  ( 60/50.0)  Actual dist  200.0  1.00  R
+60    60/50.0  ( 60/50.0)   61/50.0  ( 61/50.0)  Actual dist  200.0  1.00  R
+61    61/50.0  ( 61/50.0)   62/50.0  ( 62/50.0)  Actual dist  200.0  1.00  R
+62    62/50.0  ( 62/50.0)   63/50.0  ( 63/50.0)  Actual dist  200.0  1.00  R
+63    63/50.0  ( 63/50.0)   64/50.0  ( 64/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance table tells most of the story.

+ 
Frequency         Gain        Front-to-Back     Source Impedance        160-Ohm
+  Mhz             dBi           dB              R +/- jX Ohms            VSWR
+ 3.0              11.27       52.92             163.5 - j 0.3           1.022
+ 3.5              11.29       55.73             165.4 - j 0.1           1.034
+ 4.0              11.30       64.98             164.4 - j 2.6           1.031
+ 7.15             11.31       60.12             165.8 - j 6.3           1.054
+10.125            11.31       54.81             161.4 - j11.8           1.077
+14.175            11.29       50.03             161.3 - j16.9           1.111
+18.118            11.21       46.71             161.1 - j16.9           1.111
+21.225            11.10       44.48             158.8 - j19.0           1.127
+24.94             11.00       43.87             159.2 - j22.9           1.154
+28.0              10.75       37.12             158.0 - j16.8           1.112
+28.5              10.73       37.90             163.7 - j18.6           1.124
+29.0              10.77       39.74             166.8 - j25.9           1.178
+29.5              10.85       43.39             163.6 - j33.4           1.230
+30.0              10.93       46.74             157.8 - j36.2           1.256
+

The upper HF gain increase averages about a half dB, with about an average of 8 dB high front-to-back ratio. The original model resistive impedance varied by 37.5 Ohms: that value is down to 11 Ohms. In short, the LPDA is now better behaved (but not perfectly behaved) across its passband. 30 MHz:

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+ +
+
+ +
+

The 30 MHz graphics demonstrate the improvement. (The 3.0 MHz through 18.118 MHz graphics are virtual replicas of those for the original model. The entire set of graphics for 21.225 MHz and up appear on the Gallery page for comparison with those for the first model.)

+

Conclusion

Needless to say, no ham will ever build either of these LPDAs, despite their high performance potential from 80 through 10 meters. Arrays between 1250' and 1265' long, with elements up to 167' long at the rear are too big for the average ham back yard. Although the array can be lightened by the use of multiple wires for elements rather than simple heavy tubular elements, it would still take an old railroad roundhouse turntable with several support towers at least 135' tall to handle and rotate the array. +

However, the figures here and on the Gallery page make a few interesting points. First, the exceptional front-to-back ratio and the overall rear pattern gives us an understanding of one of the LPDA advantages: almost no power radiated to the rear. I have yet to model an antenna design with anything near to these rear patterns.

+

Second, we can see that the LPDA gain and front-to-back ratio are intimately connected. Although both values undulate and their peaks do not coincide relative to frequency, the general trend holds: the higher the gain, the higher the front-to-back ratio.

+

Third, the LPDA acquires its performance from the elements ahead of the element with the highest relative current. Every element in the array is active at 3.0 MHz, with only a few acting as the correlates to reflectors in parasitic beams. At the high end of the design spectrum, the rear elements are largely inert. Hence, to achieve high performance at the upper frequencies, one must ensure an adequate supply of "director-correlate" elements. (Otherwise, one must resort to one or more of the techniques of design revision that depart from standard LPDA design.)

+

Fourth, from 20 meters on up, notice how few of the elements are active. More than half of the array is active only at the lowest frequencies and above 14 MHz, only about 20% of the array is active. Therefore, a 14-30 MHz high performance LPDA might require perhaps 200-220' feet of boom--a considerably more manageable length. A rotating 1 acre plot might easily handle the array for just the 5 upper-end bands.

+

From a construction point of view, this has been an idle exercise. However, from a study perspective, the design illustrates the degree to which amateur-size LPDAs are deficient in performance relative to what an LPDA can do.

+
+ +
+

A Gallery of LPDA Graphics for 3-30 MHz

+
+ +
+

Updated 04-14-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Index

+

Topics: HF Multi Band, LPDA


+ + diff --git a/content/lpda/lp60g.html b/content/lpda/lp60g.html new file mode 100644 index 0000000..f55e712 --- /dev/null +++ b/content/lpda/lp60g.html @@ -0,0 +1,187 @@ + + + + + + A 3.5 Octave LPDA of High Potential Performance Part 2: Performance Graphics + + + +
+

A 3.5 Octave LPDA of High Potential Performance
+ Part 2: But an Antenna that No One Will Build

+
+
+ A Gallery of Performance Graphics +
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

The following graphics show the free-space azimuth patterns and the relative current magnitudes for the two designs discussed in the linked note. The "60-Element" design provides patterns for all bands, while the "64-Element" design shows patterns only for the uppermost bands--where the graphics differ from those of the 60-Element design.

+

Among other things, one might well note the rear azimuth patterns for all of the frequencies checked. Perhaps more important, note the number of active elements for each band and the relationship (on the uppermost bands) of the antenna performance to the number of active elements forward of the one with the highest relative current magnitude.

+

60-Element LPDA

+

3 MHz:

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3.5 MHz:

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4 MHz:

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7.15 MHz:

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10.125 MHz:

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14.175 MHz:

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18.118 MHz:

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21.225 MHz:

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24.94 MHz:

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28 MHz:

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28.5 MHz:

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29 MHz:

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29.5 MHz:

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30 MHz:

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+

64-Element LPDA

+

21.225 MHz:

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+ +
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+ +
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24.94 MHz:

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+ +
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+ +
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28 MHz:

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28.5 MHz:

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29 MHz:

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29.5 MHz:

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+ +
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30 MHz:

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+ +
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+ +
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+ +
+

Updated 04-14-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to LPDA Discussion Page

+

Go to Index

+

Topics: HF Multi Band, LPDA


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+


+ Split or Continuous LPDAs for Personal Communications?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

A split-band LPDA is simply 2 LPDAs for different frequency ranges that have been placed on the same boom and designed for the same phase-line characteristic impedance. Of course, the lower frequency section with its longer elements goes behind the higher frequency, short-element section. A single feedline handles the duties for the pair of frequency ranges covered by the array. Fig. 1 sketches the general arrangement.

+
+ +
+

One of the motivating factors behind the development of such arrays is to save space and possibly money (in commercial antenna construction) by omitting the unnecessary elements. The question that confronts the LPDA designer is at what point a split-frequency LPDA makes good sense relative to one designed for continuous coverage of the desired pair of bands. Older conceptions of LPDA design placed the highest frequency element at about 1.3 times the highest frequency used. However, to avoid significant decreases in performance at the highest operating frequencies, the resonant length of the shortest element turns out to be closer to 1.6 times the highest operating frequency. This value is somewhat variable and depends upon the choices made for tau and sigma in the basic design

+

The concept of split-frequency LPDAs is most generally applicable to VHF and UHF services other than amateur radio. Amateur bands are generally narrow enough so that for the ranges of free-space gain attained by LPDAs (generally below 11 dBi), wide-band Yagis that cover entire amateur bands are feasible. However, there are a pair of commercial service bands, one in the 800-1000 MHz region, the other in the 1800-2000 MHz region.

+

To make the investigation significant, we must set some specification for the performance that we expect of the LPDA. Let's set a free-space gain value of 9.5 dBi as the minimum gain for our arrays. This gain assures about 30 dB or better front-to-back ratio. Because it would be anticipated that construction might involve twin U-channel booms, we may use phase-line characteristic impedance values from 75 to 100 Ohms in the designs. With these simple parameters as our design goals, we may begin our work.

+

The problems posed by the new bands to be covered by an LPDA are multiple. First, for standard construction, the sizes of the materials--for example, the twin boom pieces--begin to interact with the very short element lengths. Consequently, designing for a very precise frequency range may prove self-defeating should the materials shift the frequency range as a whole. Therefore, we shall adopt the procedure of setting the two design bands as 800 to 1000 MHz and 1800 to 2000 MHz.

+

Second, many antenna types can be developed for each of these bands. For example, wide-band Yagis are possible. As well, corner reflector arrays become quite feasible with respect to both size and performance. The appeal of the LPDA lies in its ability to be designed to cover both bands.

+

Before beginning detailed design work, let's go through a few basic calculations.

+

1. The upper limit of the low band is 1000 MHz. The older resonant frequency for the shortest element would be 1300 MHz, while the newer recommendation would yield 1600 MHz as the resonant frequency of the shortest element.

+

2. The lower limit of the upper band is 1800 MHz, with the longest element resonated about 2.5% lower, or about 1755 MHz.

+

The two elements of concern are at a border line. They are close enough together to suggest that a continuous frequency LPDA design might be applicable. However, they are far enough apart to make the process of designing separate LPDAs and combining them sensible as a preliminary investigation. In the days before computer antenna modeling, such a process would call for extensive construction and range testing. Today, mathematical simulation shortens the work considerably.

+
+ +
+

I used the same values of tau (0.9045) and sigma (0.1879) for the individual LPDAs and for the single design. The low-band and the high-band LPDAs each required 8 elements. Fig. 2 provides the outlines for the two arrays. Table 1 supplies the dimensions. The designs used an 80-Ohm phase line and 0.118" (3 mm) elements.

+
+ +
+

Each of the two individual LPDAs offers adequate performance relative to the standards with which we began: a minimum free-space gain of 9.5 dBi (with its associated high front-to-back ratio) and a 50-Ohm SWR well under 2:1. Table 2 provides the modeled performance data at 20 MHz intervals in each of the two bands.

+
+ +
+

If we combine the two arrays into a single array, using the same phase line value, we obtain an LPDA that is about 23.5" (597 mm) long. The performance does not vary by much from the values produced by the individual arrays that comprise it. Unfortunately, this performance also includes the weakness at 860 MHz, as shown in Fig. 3.

+
+ +
+

Combining arrays did not remove this weakness, and the addition of a shorted stub manages to move its frequency upward, but not out of the desired operating range of the low band. Indeed, the relatively weak front-to-back performance of the individual and combined arrays results from using a value of sigma that is slightly above the optimum value. The arrays yield more gain, but at the cost of the front-to-back ratio. As well, the element diameters may be somewhat large for the frequency range in use.

+
+ +
+

We may create a single LPDA using the very same values of tau and sigma. Fig. 4 shows the outline of such an array. Note that the length is a mere 3 mm greater than the combined array. What differs, however, is the fact that the space between elements 8 and 9 adheres to the specifications for the array and is not based on an arbitrary or experimental adjustment. For comparison with the individual arrays, Table 3 lists the total array dimensions.

+
+ +
+

From some of the rounded numbers in the millimeters column for element lengths, it should be clear that the four rear-most and the last forward elements have been modified to improve performance. Moreover, the phase-line has a continuously variable characteristic impedance ranging from 78 Ohms at the feedpoint to 120 Ohms at the array rear. In addition, a 2" (50 mm) 120-Ohm stub has been added to the rear of the array. This combination of ingredients removes weakness from the coverage and smoothes the SWR values across the passband. The benefit includes a modicum of gain, but an even greater improvement in the front-to-back ratio. Table 4 provides the modeled performance values.

+
+ +
+

All three parts of the table are useful. The specific performance potentials within the two operating regions show about a 0.3 dB differential, which indicates a good match. As well, the single array shows a very high improvement in the front-to-back ratio over the separate or combined separate arrays. As well, within each operating range, there are no signs of any weaknesses in terms of tendencies toward pattern reversals created by harmonic operation of rearward elements.

+
+ +
+

Fig. 5 shows a mid-range (900 MHz) free-space azimuth patterns for the single array. Although the basic numbers for gain and front-to-back ratio, as well as the overall shape of the pattern, appear to be excellent, the rear lobes show a small amount of excess lobing. The extra lobes are operationally insignificant by any standard, but should be noted.

+
+ +
+

Fig. 6 shows a mid-range (1900 MHz) free-space pattern for the same array. At this higher frequency, the rearward lobes are considerably more fragmented, even though the magnitude remain below operational significance. As well, careful examination of the forward lobe reveals that it is on the verge of slight deformation. Essentially, this array is close to the limit for using an excessive value of sigma for the value of tau chosen in the design phase. The selected tau has an optimum sigma of 0.1688, whereas the value used in the array is 0.1879, over 10% high. A smaller value of sigma would have increased the element count.

+
+ +
+

The SWR curves, shown in Fig. 7, show no significant problems, either within the operating ranges or overall. In fact, they do not show the indications of any weakness, although the data table tells a different story. The combination of correctives applied to this LPDA design has moved the weakness in the individual arrays outside the operating range. In fact, the SWR curve is accurate in the sense that there is no SWR value above about 1.34:1 in the frequency region of the low value of front-to-back ratio. In addition, the value shown in the overall chart of performance is close to the minimum value encountered in more specific sweeps of the frequency area (15.13 dB at 1102 MHz). Hence, unless the reduction of front-to-back ratio at about 1100 MHz is a problem for some other use of this array, the correctives can be viewed as having eliminated weaknesses in a standard design.

+

Application of correctives is most usually done with greatest ease and without unexpected surprises when the subject antenna is a single array of unified design. The breach in the normal progression of elements created by combining two independently designed arrays often gives the designer more problems when the goal is multi-faceted, as in the case of this split-range array. In this case, we sought to provide relatively equal gain across each range and to match the gain levels of the two ranges. As well, we wished to have a usable 50-Ohm SWR across each operating range, with no weaknesses in coverage anywhere within them. The use of a unified single design considerably shortened the necessary design process in reaching these goals--at least in models.

+

As an aside, the element lengths for this array strongly suggest its adaptation to circuit-board fabrication rather than construction using standard twin-boom U-channel methods. When elements are under 1" each side of the centerline, even 1/2" U-channel stock may prove troublesome as a phase line.

+

Whatever the method of construction, the test case with which we have been working strongly suggests that unified single LPDA design has significant advantages over combining independent designs for split-range operation. If initial array calculation was all that we needed to do in order to create a satisfactory array, then combined independently designed arrays might be useful. However, so long as LPDA designs depart from the use of optimal values for tau and sigma, it is likely that correctives will be needed to reach satisfactory performance. A unified single array facilitates experimenting successfully with these modifications.

+
+ +
+

Updated 10-22-2002, 11-12-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: LPDA, VHF / UHF


+ + diff --git a/content/lpda/lp96.pdf b/content/lpda/lp96.pdf new file mode 100644 index 0000000..0dfc4d8 Binary files /dev/null and b/content/lpda/lp96.pdf differ diff --git a/content/lpda/lpd.html b/content/lpda/lpd.html new file mode 100644 index 0000000..872358d --- /dev/null +++ b/content/lpda/lpd.html @@ -0,0 +1,60 @@ + + + + + + LPDA Design and Modeling Data + + + +
+


+ LPDA Design and Modeling Data

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

I have drawn together all the the notes concerning general log periodic dipole array (LPDA) design and modeling into this single index. I hope some of the items are useful to those who are interesting in this intriguing class of (within design limits) frequency-independent antennas.

+ +
+ +
+
+ +
+
+ +
+

Updated 10-22-99, 03-18-00. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


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+

A 10-Meter LPDA
+ Notes on a Work in Progress

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

The search for a compact directional antenna that provides coverage of the entire 10-meter band has gone on since 10 meters was opened to amateur operations. So I wondered if I could design one, using some of the more recent concepts and tools available for antenna work. Among the tools are antenna modeling software, such as NEC and MININEC, and some antenna calculating utilities, like LPCAD. One of the more promising antenna concepts for covering all of 10 meters is the Log Periodic Dipole Array, or LPDA for short. Most LPDAs cover a wide frequency range and they require some careful selection and adaptation for monoband use. Although the LPDA is the primary focus of this collection of notes, some wide-band Yagi ideas are also worth investigating, for example, the use of open-sleeve coupled drivers.

+

To make the project more interesting, I set some goals for myself in the form of design objectives. Since we can design a short-boom (8") 3-element Yagi to cover half the band with 7 dBi free space gain and a 20 dB front-to-back ratio, these same boom length, gain, and front-to-back figures became criteria for successful design. Of course, the antenna--either directly or via a matching system--must provide less than 2:1 SWR to the system's 50-Ohm main feedline across the entire band.

+

The notes in this collection record as much the process of thinking I went through in finding a satisfactory design as they present antenna designs. Along the way, questions about LPDA dimensions and performance kept arising to compound the design process--and to make more difficult the selection of a final LPDA design to build and test. In fact, some of the questions led to at least one non-LPDA alternative: a wide-band Yagi noted in Phase 6 of the process and further analyzed in Phase 7.

+

The job is not yet done, but I am in no hurry. What I am learning while designing and deciding may turn out to be more important than the final product. As a matter of fact, a fairly satisfactory design emerges in Phase 1. Then again, I never was one to leave well enough alone.

+
+
+
+ +

+
+

Updated 11-21-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

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+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda1.html b/content/lpda/lpda1.html new file mode 100644 index 0000000..6909c62 --- /dev/null +++ b/content/lpda/lpda1.html @@ -0,0 +1,178 @@ + + + + + + A 10-Meter LPDA Phase 1: From Calcuations to Models + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 1: From Calcuations to Models

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The search for a compact directional antenna that provides coverage of the entire 10-meter band has gone on since 10 meters was opened to amateur operations. Here is a brief rundown of what I have so far found. +

1. A full-size 2-element Yagi, with just over 6 dBi free space gain requires a boom at least 5' long if it is to cover most of the 28 to 29.7 MHz span. However, front-to-back ratio will be quite low, average between 10 and 11 dB.

+

2. Small 2-element beams with better front-to-back ratios, such as the Moxon rectangle (15-30 dB across much of the band), have slight lower gain figures and rarely cover the entire band with consistent gain and front-to- back ratios.

+

3. ZL-Special/HB9CV antennas can raise the free space gain to about 6.5 dBi peak, with a peak front-to-back ratio of about 20 dB. However, they cover a little more than 1 MHz of the band.

+

4. 3-element Yagis, while providing more gain, are limited in a number of ways. For high gain (8 dBi), one needs a 12' boom. With an 8' boom, the gain peaks at just over 7 dBi, and the bandwidth is less than 1 MHz. Orr and Reisert designs can cover the band at the 7 dBi peak gain figure, but require something close to a 12' boom.

+

5. 2-element quads are capable of about 7 dBi peak gain and about 20 dB front-to-back ratio, but lose most of their gain and front-to-back ratio when pressed beyond about 1 MHz of 10-meter coverage.

+

One can dream up other contenders in the contest for adequate gain, good front-to-back ratio, and full-band coverage, but almost all tend to show severe roll-offs in gain and front-to-back when pressed beyond about 1 MHz of 10 meters. All but one, that is.

+

It is possible to design--at least in principle--a 10-meter array on an 8' boom that will provide very consistent 7 dBi free space gain and 20+ dB coverage across 10-meters with a flat SWR well below 1.5:1. The design is a monoband log-periodic dipole array (LPDA). The ARRL Antenna Book has carried a K1TD monoband 2-meter design for a number of years (pages 10-17 to 10-19 in the 18th Edition). Jerry Hall's design had to cover a 2.75% frequency range, while a 10 meter LPDA would have to cover a 6.9% frequency range. But the project seemed feasible on paper.

+

Requirements for the antenna are a free space gain at or close to 7 dBi across the band with a 20 dB or better front-to-back ratio. The design would have to fit on an 8' boom to meet my preconception of compactness. Here are some practical notes on what I have encountered so far in this unfinished business. (The theory and design notes in The ARRL Antenna Book and other basic references, such as Johnson and Jasik, are essential background reading in Log Periodic Dipole Arrays (LPDAs). I shall not go into that material here.)

+

Developing a Basic Design

Design software for developing a basic LPDA configuration is readily available. Among the best is Roger Cox's LPCAD, now in version 2.7 and available as freeware. The software offers options for designing from preselected values for tau and sigma or from physical constraints placed on the proposed design. I began with a 4-element design on an 8' (96") boom as the maximum. +

The designs were cross checked on NEC-4, using linear elements and the TL function to simulate the element-to-element reversing antenna transmission line. I believe that LPDA models using this technique are reasonably accurate when they have elements with a uniform diameter. LPCAD provides a source impedance estimate that holds up quite well in NEC-4 models. All models were designed for a 200-Ohm antenna transmission line. Although the software recommends a 4:1 balun at the feedpoint, the recommendation is not wholly consistent with the projected (and modeled) source impedances for various versions of the antenna. For various models, I achieved a relatively flat SWR curve for a 50-Ohm system feedline cable by employing matching sections of 75-Ohm and 93-Ohm cable for source impedances in the 100 to 145-Ohm range. The basic design of these sections is the quarter wavelength, but the actual lengths were adjusted to compensated for remnant reactance. This matching system, of course, would not be apt to a wide-band LPDA, such as a 20-10-meter antenna. However, it suits the needs of the monoband design.

+

Initial models based on software generated designs showed that if I specified a frequency range of 28 to 30 MHz, most of the higher gain and front-to-back figures occurred at the uppermost portion of the range and beyond. For 0.5" linear elements, satisfactory NEC-4 modeling results were achieved by specifying a range of 27.5 to 29.5 MHz, about 2% low at both ends. The software uses an upper-end frequency buffer to ensure high frequency performance. At the lowest frequency selected, the element length is calculated according one of three element length-to-diameter ratios, the highest value limit being equal to or greater than 105. The longest element in this example has a ratio of over 400:1. (My thanks to Roger Cox, the software author, for providing the lower frequency calculation numbers.) Hence, it is reasonable that the rear element length would show up as short in the initial calculations.

+

Once a satisfactory model had emerged using uniform-diameter 0.5" elements, the model was converted to 108" center sections of 0.5" diameter aluminum with 0.375" diameter outer sections--in prospect of building an actual antenna one day. The conversion resulted in a degradation of modeled performance until the ends of the rearmost element were shortened by about 3.5" each. The following, with an exception to be noted, is the EZNEC-4 model description of the semi-frozen design.

+ 
lpda10m:  tapered element design   Frequency = 28 (to 30) MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-106.00,  0.000  W2E1   0.000,-54.000,  0.000 3.75E-01  10
+2  W1E2   0.000,-54.000,  0.000  W3E1   0.000, 54.000,  0.000 5.00E-01  23
+3  W2E2   0.000, 54.000,  0.000         0.000,106.000,  0.000 3.75E-01  10
+4        35.605,-98.003,  0.000  W5E1  35.605,-54.000,  0.000 3.75E-01   8
+5  W4E2  35.605,-54.000,  0.000  W6E1  35.605, 54.000,  0.000 5.00E-01  23
+6  W5E2  35.605, 54.000,  0.000        35.605, 98.003,  0.000 3.75E-01   8
+7        67.475,-87.720,  0.000  W8E1  67.475,-54.000,  0.000 3.75E-01   6
+8  W7E2  67.475,-54.000,  0.000  W9E1  67.475, 54.000,  0.000 5.00E-01  23
+9  W8E2  67.475, 54.000,  0.000        67.475, 87.720,  0.000 3.75E-01   6
+10       96.000,-78.515,  0.000 W11E1  96.000,-54.000,  0.000 3.75E-01   4
+11W10E2  96.000,-54.000,  0.000 W12E1  96.000, 54.000,  0.000 5.00E-01  23
+12W11E2  96.000, 54.000,  0.000        96.000, 78.515,  0.000 3.75E-01   4
+13      150.000, -0.200,  0.000       150.000,  0.200,  0.000    # 14    1
+             -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1    13 / 50.00   ( 13 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1  Length      Z0    Vel Rev/
+      Actual  (Specified)   Actual  (Specified)             Ohms  Fact Norm
+
+1    2/50.0  (  2/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+2    5/50.0  (  5/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+3    8/50.0  (  8/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+4   11/50.0  ( 11/50.0)   13/50.0  ( 13/50.0)   80.000 in    75.0  1.00  N
+5    2/50.0  (  2/50.0)  Short ckt (Short ck)   36.000 in   200.0  1.00
+Ground type is Free Space
+

Wires 1-12 are the 4 elements, while wire 13 is a short segment used as a source point for the far end of the 80" (VF=1) section of 75-Ohm cable (TL #4). TL #5 is not part of the original design, but is part of a modified model to be discussed later. I include it here, since there are few change made to the original model, and reproducing the entire wire table further down seems unnecessary.

+
+ +
+

The figure shows graphically what the table reveals in detail. LPCAD had specified end lengths of +/- 109.448" (nearly 219" overall) for the rear element, which was reduced to +/- 106" (212") in the model for enhanced modeled performance.

+
+ +
+

The free space azimuth patterns give a reasonably clear picture of anticipated performance from the antenna. Gain is remarkable consistent across the band, and the front-to-back ratio meets the goal of 20 dB or better across the band. Hence, the basic goal of the exercise (apart from the question of whether the antenna can be reasonably home-brewed) has been met.

+

The Rear Stub Question

TL #5 in the model description represents a shorted rear stub, the use of which has been debated but remains a bit murky in the literature. Besides the safety factor of providing DC continuity throughout the antenna structure, the stub has also been claimed to improve performance, especially with respect to front-to-back ratio, although some experimenters claim satisfactory performance without it. Most of the reports appear to come from very wide-band applications of the LPDA, and hence, their relevance to the narrow-band 10-meter design is uncertain. A 1/8 wl limit is the standard for the stub, but the exact length seems to elude at least the Antenna Book account. +

So I tried several lengths of stubs, ranging from 1" (simulating a practical short across the rear of the antenna transmission line) to 52". Here is a quick table of modeled performance figures for 28.5 MHz with various stub lengths:

+ 
Stub Length    Gain dBi  F-B dBi   Source Z       Notes
+(inches)                           (R+/-jX)
+  1            7.18      21.14     43.1 - j 9.7
+  6            7.16      27.11     43.6 - j 6.4
+ 12            7.13      34.78     43.9 - j 4.3   Max F-B at 28.0 MHz
+ 18            7.11      45.47     44.2 - j 3.2
+ 24            7.09      40.92     44.4 - j 2.4
+ 30            7.08      36.13     44.5 - j 1.8
+ 36            7.07      33.57     44.6 - j 1.4   Max F-B at 28.7 MHz
+ 42            7.07      31.94     44.7 - j 1.1
+

The chief effect of using stubs of different lengths is to move the frequencies of maximum gain and of maximum front-to-back ratio, with shorter lengths moving those frequencies lower. There is a general increase in both the gain and the front-to-back ratio at the test frequency, although it may be somewhat marginal in actual operation.

+

With exceedingly short stubs (1 to 12"), the gain at 28 MHz increases--up to 7.5 dBi for the shortest stub that simulates a near direct short circuit. However, three factors suffer. First, the gain across the band becomes quite unequal, with the gain at 30 MHz no higher than for any of the stub lengths. Second, the front-to-back ratio at 28 MHz drops below 20 dB. Third, the source impedance at 28 MHz falls outside the matching range of the matching section, with an increase in SWR to about 2:1 with a 1" stub.

+
+ +
+

The figure shows the free space azimuth patterns of the array across the 28-30 MHz span with a 36" stub added to the original model. The improved front-to-back ratios are apparent.

+

The following figures graph performance for the model using a 212" rear element and having either no stub (open) or a 36" stub. These figures use the red and green lines; ignore the blue line in each chart for the moment.

+
+ +
+

The gain values and peak positions appear best in graphs like the one above. Clearly apparent is the displacement of the gain curve lower in frequency relative to the open-ended model. Since this model uses tapered- diameter elements, the gain figure is likely about 0.05 dB high everywhere on the graph. This over-report of gain is an estimate based on the modeled performance with uniform 0.5" diameter elements. It is not possible to model this antenna with the tapered-diameter correction factor active for every element, since the shortest element falls outside the +/-15% natural resonance limitation. Hence, models with the feature activated will only correct a maximum of 3 of the 4 elements.

+
+ +
+

The increase in overall front-to-back ratio, plus the displacement of the curve lower in frequency, also appears most clearly in a graph like the one above. Relative to a MININEC model, it is likely that both curves may suffer about a 50 kHz displacement higher in frequency due to the tapered- element diameters.

+
+ +
+

Adding the 36" stub has virtually no effect on the post-matching section 50-Ohm SWR curve. Either version of the modeled antenna provides among the flattest curves obtainable over a 2 MHz span. However, as noted, the use of a very short stub will displace the SWR curve at the lower end of the band covered.

+

The advisability of the termination for the antenna transmission line is a mixed bag. The improvements in performance are desirable. However, an additional 3' of transmission line extending from the rear of the antenna might physically defeat the antenna's claim to compactness.

+

Let us remember, however, that the open-end model had its rear element optimized for this application. It might be possible to change the rear element length to a value optimized for the use of the 1" (simulated short) at the rear. I finally settled on a value of 215" (+/- 107.5") for the rear element--longer than the open-rear model and shorter than the LPCAD recommended length.

+

The blue lines on the three graphs above show the results of using this longer element with a 1" stub. The length of the matching line (TL #4) was increased to 90" to center the SWR curve across the band.

+

Adding a direct short or a very short stub to the rear of the antenna transmission line changes the gain curve of the antenna. Although the peak value at 28 MHz exceeds either of the other models, the gain rapidly decreases (relative to LPDA design, but not necessarily to other phased arrays or to Yagis) so that the 30-MHz end value is noticably lower than the other LPDA models. The front-to-back curve, on the other hand, is almost without peak compared to other LPDA models, with a smoother curve across the band and always above the 20 dB design goal value. The SWR curve, while steeper than those of the other LPDA models, is still very good, with no point reaching 1.5:1.

+
+ +
+

The revised ("blue-line") model, whose free space azimuth patterns appear in the figure above, overcomes the need for a long stub. However, the gain and SWR curves are not so well behaved as those of the open-end model. Hence, the ultimate decision of which design to use still rests on a judgment of which characteristics are most important to the builder. At this point in the design work, I suspect--but do not know for certain--that judicious element length or spacing changes might smooth out the gain curve without jeopardizing other factors, but obviously, the first order design techniques lose their ability to guide these efforts.

+

Why Not Use Wire?

In principle, one may develop a light weight frame and use wire elements for the compact 10-meter LPDA. However, wisdom dictates approaching this option with caution. First, the optimum element length to diameter ratio for the calculations used in LPCAD is 125:1. The 0.5" elements used in the initial models in NEC-4 have ratios in the 315:1 to 440:1 range, depending on frequency. Likewise, for this short-boom model, sigma is not optimum. Hence, although it is possible to make minor adjustments in the model to optimize front-to-back ratio, the maximum gain for the tau value of 0.9 used in these models does not approach the theoretical maximum of 8-9 dBi. Rather, the actual gain of about 6.8-6.9 dBi falls near the lower end of the scale. +

Using #12 AWG copper wire as the material of choice, the length-to-diameter ratio of the elements exceeds 2000:1. Nonetheless, let's look at a preliminary model of a wire LPDA for the 10-meter band.

+ 
lpda10m:  #12 AWG wire   Frequency = 28 (to 30)  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-111.52,  0.000         0.000,111.520,  0.000    # 12   43
+2        35.619,-99.776,  0.000        35.619, 99.776,  0.000    # 12   41
+3        67.488,-89.269,  0.000        67.488, 89.269,  0.000    # 12   39
+4        96.000,-79.869,  0.000        96.000, 79.869,  0.000    # 12   37
+5       150.000, -0.200,  0.000       150.000,  0.200,  0.000    # 14    1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1   Length     Z0    Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)   80.000 in    93.0  1.00  N
+Ground type is Free Space
+

In order to center the operating characteristics of this antenna within the 28-30 MHz spran, it was necessary to lower the lower and upper design limit frequencies fed to LPCAD to 27 and 29 MHz, respectively. Hence, all elements are longer than for the tubing model version.

+

The source impedance for this version of the LPDA increased from the 120- Ohm region to the 140-Ohm region. Hence, the 75-Ohm matching section was replaced with a 93-Ohm section, simulating RG-62, but without the velocity factor being taken into account (an easy calculation during construction). The matching section used here provides SWR curves very much like those for the model using aluminum tubing.

+

For a general picture of the anticipated antenna performance, we may look at the free space azimuth patterns below.

+
+ +
+

Clearly apparent are the overall reduce gain of the wire antenna in this configuration, as well as the well-controlled but lower values of front-to- back ratio.

+
+ +
+

How the gain curve compares to the tapered-diameter tubing version of the antenna is clearest on a graph that separates each frequency.

+
+ +
+

Comparable front-to-back curves appear in the graph above.

+

The overall gain and front-to-back curves, although covering the entire 10- meter band, are closer to what an HB9CV antenna might achieve with fewer elements and a shorter boom (but with a narrower operating bandwidth for both the SWR and the antenna characteristics). They are shy of short-boom 3-element Yagi performance by a good bit.

+

These results do not condemn wire LPDAs. However, they do show that the methods of calculating elements optimized for much lower length-to-diameter element ratios do not yield the same results when translated to wire elements. In short, further research into the calculation methods--or plain old modeling cut and try--will be needed to arrive at a higher performance model--if one is possible for the given boom length.

+

Summary (So Far. . .)

This is an unfinished project. However, I thought that a report of what I have encountered in translating LPDA design calculations, as implemented in LPCAD, into NEC-4 models might be useful to others working in this area, especially if for the first time. +

Programs like LPCAD are valuable tools in the design process. They automate most of the initial calculation work, as well as a good portion of the re-calculation work. However, one must supplement them with as good a set of models as the current cores will permit. NEC-2 is entirely adequate for uniform-taper elements, but even NEC-4 must be used with caution when moving to tapered-diameter elements.

+

The original goals of the project were met early on. The open-rear tubing version of the antenna yields a consistent gain close enough to that of a short-boom 3-element Yagi to serve the purpose, and the front-to-back ratio exceeds 20 dB across all of 10 meters. The operating bandwidth--including both the SWR and the antenna characteristics--is clearly superior to anything else I have seen on the same length of boom.

+

However, every project raises as many questions as it answers. So besides leaving some unsettled matters concerning construction methods that might be replicated in the average home workshop, there are a number of questions regarding LPDA calculations for thin elements to be researched, a number of rear stub versions to be optimized, and a number of other questions that likely will not be known until they crop up in the supplemental work.

+

When I learn more, I'll add to these notes. I hope what is here is useful.
+

+
+ +

+
+

Updated 11-08-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Part 2: Notes on a Low-Impedance LPDA for 10 Meters

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda2.html b/content/lpda/lpda2.html new file mode 100644 index 0000000..ecb7a29 --- /dev/null +++ b/content/lpda/lpda2.html @@ -0,0 +1,162 @@ + + + + + + A 10-Meter LPDA Phase 2: A Low Impedance Version + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 2: A Low Impedance Version

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ My initial modeling trials for a compact (8' boom) LPDA to cover all of 10 meters with short-boom 3-element Yagi performance used the recommended higher-impedance antenna transmission line. These notes look at some low- impedance models derived from calculations from LPCAD. +

200-Ohm vs. 75-Ohm Antenna Transmission Line

General recommendations for LPDAs include a warning about the use of low impedance antenna transmission lines. For wide-band LPDAs, unwanted resonances can occur with low impedance lines. As N7CL, Eric Gustafson, reminded me, these problems usually do not occur with monoband LPDAs. +

The models so far cited have used a 200-Ohm antenna transmission line, which permits the use of a double boom for antenna construction (similar in principle to the type used by Tennadyne LPDAs). A matching section is required to provide a 50-Ohm match, since the source impedance of an LPDA in the element length-to-diameter ratio range used by this model is about 0.6 to 0.7 the antenna transmission line characteristic impedance. For a direct 50-Ohm match, a transmission line in the neighborhood of 72-75 Ohms can work well, although it will require alternative construction methods.

+

One of the interesting features of the LPDA using a low impedance transmission line is that the velocity factor (VF) of the line makes very little difference to the actual performance of the antenna. Since I have done the initial modeling using a VF of 1.0, I went back and checked VFs of 0.79 and 0.66 as representative numbers that we might call mid-range and low. The 75-Ohm models use open-rear construction (no stub) and also extend the rear element to the initially calculated value of nearly 219". The results are reported in the following table. (I use a table because of the illegible overlap of lines on a standard graph.)

+ 
Freq MHz      28            28.5          29            29.5          30
+
+Antenna Transmission Line:  72-Ohm; VF = 1.00
+Gain          6.82          7.04          7.18          7.21          7.16
+F-B           20.15         26.72         31.27         24.75         21.07
+R             66.54         56.88         50.84         49.29         51.52
+X             -2.536        -6.026        -4.532        -1.792        -0.8594
+SWR-50        1.335         1.187         1.096         1.04          1.035
+
+Antenna Transmission Line:  72-Ohm; VF = 0.79
+Gain          6.84          7.04          7.15          7.16          7.09
+F-B           19.47         25.32         29.68         24.41         20.69
+R             66.48         59.32         56.93         58.36         61.66
+X             -9.031        -5.494        -1.561        0.478         -1.601
+SWR-50        1.383         1.219         1.142         1.168         1.236
+
+Antenna Transmission Line:  72-Ohm; VF = 0.66
+Gain          6.84          7.02          7.11          7.11          7.03
+F-B           19.22         24.71         28.22         23.62         20.03
+R             65.41         63.6          65.16         68.6          70.85
+X             -11.02        -5.16         -1.666        -2.093        -7.4
+SWR-50        1.391         1.293         1.305         1.375         1.447
+
+Antenna Transmission Line:  75-Ohm; VF = 1.00
+Gain          6.81          7.04          7.17          7.21          7.15
+F-B           20.07         26.63         31.74         25            21.21
+R             69.26         59.15         53.07         51.68         54.1
+X             -3.87         -6.84         -4.99         -2.124        -1.353
+SWR-50        1.394         1.233         1.12          1.055         1.087
+
+Antenna Transmission Line:  75-Ohm; VF = 0.79
+Gain          6.83          7.04          7.14          7.16          7.09
+F-B           19.42         25.3          30.04         24.64         20.83
+R             68.36         61.44         59.36         61.08         64.44
+X             -10.54        -6.493        -2.383        -0.4839       -2.994
+SWR-50        1.434         1.267         1.194         1.222         1.296
+
+Antenna Transmission Line:  75-Ohm; VF = 0.66
+Gain          6.83          7.01          7.1           7.1           7.02
+F-B           19.21         24.77         28.57         23.83         20.15
+R             66.95         65.65         67.61         71.2          73.17
+X             -12.12        -6.196        -2.904        -3.788        -9.612
+SWR-50        1.431         1.34          1.358         1.432         1.51
+

Since the 75-Ohm, 0.66 VF line represents the worst case of the group (showing the lowest 28-MHz front-to-back ratio and the highest SWR), we may fairly use it in comparison with the 200-Ohm line open-rear model. The curve trends are so consistent within the groups above that the chosen comparison will stand for all the tabular entries.

+
+ +
+

The gain comparison shows the displacement of the 75-Ohm gain peak upward in frequency relative to the 200-Ohm peak at mid-band. The 75-Ohm curve also shows a much wider variation in gain across the band, so that the 75-Ohm gain at 28 MHz, while entirely acceptable for this project, is noticeably lower than the 200-Ohm gain at the same frequency.

+
+ +
+

The front-to-back curves of the 75-Ohm and 200-Ohm models are congruent, although the 75-Ohm curve is several dB lower. At 28 MHz, the 75-Ohm front-to-back ratio marginally approaches the 20- dB level set as the project goal.

+
+ +
+

The 50-Ohm SWR curve of the 75-Ohm model reaches a value of 1.5 only at the upper end of the band. However, it is consistently higher than the comparable 200-Ohm model curve. Of course, the 200-Ohm curve is based on the use of a custom 75-Ohm matching section, adjusted in length downward from 1/4 wl to compensate for the capacitive reactance at the antenna feedpoint. Although some builders do not favor the use of matching sections, their use can save losses in long lines from the antenna to the shack by providing the main 50-Ohm line with a lower SWR across a wider operating bandwidth. The losses due to higher SWR levels--even marginally higher--are confined to the short length of matching section line. In the present case, however, the direct match values of the low impedance transmission line model LPDA are low enough to be of little concern.

+

A Redesign Exercise

Because the gain curve peak was pushed upward in frequency with the change to a low-impedance antenna transmission line, it seemed useful to try to redesign the antenna using a slightly different set of upper and lower frequencies. The original set that yielded a well centered curve with the 200- Ohm antenna transmission line used 27.5 MHz as the low frequency and 29.5 as the upper frequency. I tried (among others) two tactics: 1. simply shifting the frequency range down by 25 kHz, and 2. shifting the low end down but widening the overall frequency range by leaving the upper frequency at its original level. The calculations were based on 0.5" elements, but the models used a combination of 0.5" and 0.375" aluminum elements (with the half inch sections a constant +/- 54" from the center line and the smaller tips of variable length). +

Just for the record, here are the calculated element lengths and spacings for the three models in question.

+ 
Frequency Range:  27.5--29.5
+Element Length (")          Cumulative Spacing (")      L/D Ratio
+218.985                     00.000                      438.0
+196.006                     35.605
+175.439                     67.475
+157.030                     96.000                      314.1
+
+Frequency Range:  27.25--29.25
+Element Length (")          Cumulative Spacing (")
+220.994                     00.000                      442.0
+197.763                     35.612
+176.975                     67.481
+158.372                     96.000                      316.7
+
+Frequency Range:  27.25--29.5
+Element Length (")          Cumulative Spacing (")
+220.994                     00.000                      442.0
+197.203                     35.706
+175.974                     67.568
+157.030                     96.000                      314.1
+

The first notable fact is that the amount of adjustment is small, especially when thought of in terms of physical construction. The spacing of the intermediate elements changes by about 0.1" overall throughout the range. This fact places some limitations on the final antenna being able to hit the desired performance curves in a precise manner. Nonetheless, the resulting model performance changes are interesting (at least to me). Let's look at some comparative curves for 75-Ohm, VF 0.66 antenna transmission line models. First, the gain.

+
+ +
+

The red line is the gain curve for the 27.5-29.5 model, while the green line is the gain curve for the 27.25-29.25 model. The latter (green) is better centered in the frequency span covered, although the extrapolated peak value is a bit less than for the former (red). It is not yet clear if this reduction in gain peak is a function of the greater length-to-diameter ratio of the elements for the lower frequency span.

+

The blue line represents the gain curve of the expanded frequency span model. While generally centered in the frequency span, its end values are as low as the worst case for each of the other two curves. Moreover, its peak value is noticeably below that of the other two curves. both these phenomena are likely functions of the wider frequency span covered by the model.

+

Value differences are visually and mathematically noticeable. However, the differences would make little operational difference, amounting in the worst case to under 0.1 dB. Their chief use for me is in helping me understand the consequences of various changes that might be made in the selection of variables for the monoband LPDA.

+
+ +
+

The front-to-back curves are equally interesting in principle, although not very significant operationally. Before making an descriptive interpretations, we should note that the 5-point curves are incomplete pictures of the actual front-to-back value changes. However, if you understand that the front-to-back ratio peaks somewhat symmetrically, then you can adjust the curves accordingly. For example, the 27.5-29.5 curve (red) actually peaks a bit below 29.0 MHz and a bit above the 28+ dB value shown. The 27.25-29.25 curve (green) peaks between 28.5 and 28.75 MHz. The 27.25-29.5 curve (blue) peaks just above 28.75 MHz.

+

The wider frequency range curve has the highest peak value, while the other two have similar peaks. The peak value numbers are actually the least interesting on the graph. The more interesting values are at the band edges, indicating the minimal level of performance across the band. Both of the revised models have a front-to-back ratio greater than 20 dB at the low end of the band. Although they dip below 20 dB at 30 MHz, at 29.7 MHz, both are greater than 20 dB. Hence, with respect to front-to-back ratio, there is virtually nothing to choose between the two revised models.

+
+ +
+

For a 75-Ohm antenna transmission line using a material with a 0.66 velocity factor, the 50-Ohm SWR curves tell a story of passing interest. The two revised models show improvements in SWR at the low end of the band, most likely a direct result of the lower low-frequency limit in both cases. At the upper end of the band, the original and the wide-band models, with identical upper frequency limits, have virtually identical values. However, the model with limits of 27.25 and 29.25 MHz shows an increase in 50-Ohm SWR at the upper end of the band. In short, the changes in 50-Ohm SWR corresponding directly to the changes in the frequency range limits used for the element calculations. Although, once more, the changes are not too significant operationally, they are instructive in terms of understanding the consequences of design changes one might make.

+

An alternative way of viewing the same data (minus the SWR values) is to examine the collection of free space azimuth patterns that might accumulate from gathering the information in the graphs. Two features are of special note. First is the amount of gain variation across the band, remembering that the actual peak gain value may elude the collection of patterns. Second is the variation in the rear lobes across the band, with an eye toward not only the direct 180-degree front-to-back ratio, but as well the entire front-to-rear performance.

+
+ +
+

As this figure for the 27.5-29.5 MHz model shows (along with the ones to follow), gain variation will make virtually no operational difference in antenna performance. However, the centered front-to- back curve is evident in the pattern of rear lobes.

+
+ +
+

The 27.25-29.25 MHz model shows the shift in rear lobes which leaves the weakest rear performance at the upper end of the frequency span. The 30 MHz curve, of course, will be worse than the upper 10-meter value at 29.7 MHz.

+
+ +
+

The wide-band (27.25-29.5 MHz) model reveals some further shifting of values, but no very significant changes from the previous model.

+

The utility of the azimuth curves is to reinforce the reminder that value changes that are important in understanding design principles do not always result in changes of actual performance that one might even be able to measure using practical devices available to hams. Actually, all three antenna versions would be acceptable as practical antennas, as would be the 200-Ohm antenna transmission line model. Low impedance LPDA design provides one more alternative in the collection of decisions to be made about which antenna to construct.

+

Why A 75-Ohm Antenna Transmission Line

In the process of looking at low impedance LPDA models, none has yet proven satisfactory with a stub. However, the process of looking is far from over. +

The calculating and modeling I did in connection with low-impedance antenna transmission lines employed a 72-75-Ohm transmission line. Part of the reason for using the 75-Ohm line in the graphs is that, with a 0.66 VF, it provides a worst case analysis. The other reason for the use of lines in this range is the fact that I have some Belden 72-Ohm transmitting cable left over from another project. However, its use may be a bit marginal.

+
+ +
+

The graph of the source resistance values for the three low-impedance line models shows that, with 72-75 Ohm lines, the resistance varies between about 66 and 73 Ohms. Once more, the high frequency end shows a closer correspondence between the antenna transmission line and the source resistance. It is at this end of the antenna that the L/D ratio of the elements is lower as well.

+

These facts present a conflict in directions in which to take the investigation. First, I have seen some design reports using a variety of techniques for achieving lines of lower impedance. It would be tempting to investigate first the use of lower impedance lines.

+

However, the question of the effect of the L/D ratio of the elements seems to arise at almost every turn. Will a lower L/D ratio a. increase gain, b. smooth out performance curves, c. flatten the source resistance curves? As well, I can ask the same questions of an element diameter schedule that preserves a relatively constant L/D ratio from one end of the antenna to the other (within the limits of eventually using tapered-diameter elements.

+

Since doing everything at once is out of the question, I think I might next tackle the L/D questions-- trying to see what happens when we turn calculations into models. Then I shall return to the direct- feed question.

+

My notes are not designed to be a finished product. Instead, they are a record of how one question leads to another in the design process I am using. It would have been easy to quit as soon as an acceptable model arose. However, I might then have built an antenna and understood far less about it. An antenna that I build is mostly an exercise in testing my understanding of its principles, since, if it fails to work properly, there must be something I have misunderstood. (That fact does not preclude misunderstandings even if it does work as predicted.) If the result is something that someone else can replicate in the garage, so much the better. Still, I tend not to build until I believe I can predict the outcome of every adjustment I might make to the actual physical structure. That is where modeling and calculation software come in handy--by aiding the process of understanding. If nothing else, they shorten the time I need to stand in the wind, rain, and cold wondering what will happen if I change something by a little bit.

+

So if these notes get a little tedious at times, by all means read something more exciting. This record is, after all, more an account of a process than it is a report of a product.
+

+
+ +

+
+

Updated 11-12-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Part 3: Notes on Length/Diameter Ratios for an LPDA for 10 Meters

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda3.html b/content/lpda/lpda3.html new file mode 100644 index 0000000..c812973 --- /dev/null +++ b/content/lpda/lpda3.html @@ -0,0 +1,158 @@ + + + + + + A 10-Meter LPDA Phase 3: Element Length and Diameter + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 3: Element Length and Diameter

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ During the earliest part of this pre-design investigation, we encountered hints that element diameter may affect monoband LPDA gain, as well as other properties. In addition, we learned that the calculation software was set up for rather low values of element length-to-diameter ratios, relative to common light building practices. Before committing to a design--even though we found some that met the original design criteria--it seemed prudent to look into these questions with some systematic modeling. +

Note: the original design criteria required that we develop an LPDA for 10 meters that would cover the band with a. roughly equivalent gain to a short boom (8') Yagi, b. have at least 20 dB front-to-back ratio across the band, and c. have a low 50-Ohm SWR across all of 10 meters, d. all on an 8' boom. The basic monoband LPDA design uses 4 elements.

+

To investigate the questions relating to element diameter and the length- to-diameter ratio, I used LPCAD to design an antenna with input frequency limits of 28 and 30 MHz. I chose this design frequency span knowing that it was not the optimum for thinner elements, but that it would grow more optimal as the element diameter increased. Regardless of element diameter, the program yields the same set of element specifications:

+ 
Element Length (")       Cumulative Spacing (")
+     215.074                  00.000
+     192.584                  35.592
+     172.445                  67.462
+     154.412                  96.000
+

For element diameters of 0.5" through 1", the dimensions yielded the following length-to-diameter ratios for the longest and shortest elements:

+ 
Diameter (")        0.5       0.625     0.75      0.875     1.0
+L/D (longest)       430.1     344.1     286.8     245.8     215.1
+L/D (shortest)      308.8     247.1     205.9     176.5     154.4
+

Element Diameter and Antenna Transmission Line Impedance

The results of the runs were a large collection of frequency sweep data collection sheets, of which I can record only a sampling. However, the sample is revelatory. Essentially, I ran each model using a different element diameter (but the same diameter throughout the model) with a. a 200-Ohm, VF=1.0 antenna transmission line, b. a 75-Ohm, VF=1.0 antenna transmission line, and c. a 75-Ohm, VF=0.66 antenna transmission line. +
+ +
+

The gain graph compares 3 diameters of elements for the 200 and the 75 Ohm lines, both with VFs of 1.0. For any given diameter of element, the low- impedance antenna transmission line provides higher gain by a significant amount. The 200-Ohm line models all peak low in the band and decrease in value at the upper end, except for the 0.5" diameter model, whose curve is fairly symmetrical. The 75-Ohm line models show that, for thinner diameters, the gain peaks are in the upper portion of the band, with a rough symmetry being achieved with the largest (1") element. The superiority of the low-impedance antenna transmission line with respect to gain is a clear result.

+
+ +
+

The front-to-back results, using the same sampling of models, present a somewhat more confusing graph that must be tracked almost a line at a time. However, two of the three lines showing high peaks at 29 MHz represent 200- Ohm line models, with the thinnest element (0.5") showing the highest peak. The largest element (1.0": blue line)) shows almost no peak, but reaches it highest value just above 28.5 MHz. The thin-element lines show their lowest values at 28 MHz.

+

In contrast, the three 75-Ohm line models display much "tamer" curves with no sharp peak, except for the 0.5" diameter element, which also shows a value of less than 20 dB at 28 MHz. Larger elements with a low impedance line provide higher front-to-back ratios at the low end of the band and lower values at the upper end of the band. The 1" element barely sustains a 20 dB figure at the 29.7 MHz upper limit of 10 meters.

+

The higher gains associated with a low impedance line come at the cost of lower average front-to-back ratios. However, the front-to-back curve for the low-impedance line is much more nearly constant across the band.

+
+ +
+

The direct-feed 50-Ohm SWR curves for the low impedance line, with a VF of 1.0, form a well-behaved group of curves. As the element diameter increases, the lowest SWR frequency become lower, falling in the center of the band at an element diameter of 1". This placement is a fairly clear indication that the element diameter is approaching a value for which the calculation software has been optimized.

+

The curve appears to be much steeper at the low end of the band. However, be certain to read the Y-axis values, which only peak at an SWR of 1.4:1.

+

To this point, I have recorded none of the values associated with a low- impedance line with a VF of 0.66. In general, the gain and front-to-back values are lower than those for the same line with a VF of 1.0.

+
+ +
+

If you pair elements with the same diameter but different values of VF and trace the corresponding lines (red to gray, green to brown, and blue to black), you can see that the gain of the VF=0.66 line tapers off rapidly as the frequency increases. However, the gain at the lower end of the band is higher for the VF=0.66 line than for the VF=1.0 line in each pair.

+
+ +
+

The gain curves for the two values of velocity factor show different curves. In contrast, the front-to-back curves are congruent for each pair of maodels having the same element diameter. The VF=0.66 lines show a consistently lower value for the front-to-back ratio throughout the sequency of models.

+
+ +
+

The figure above records the SWR values using the 0.66 VF line, all of which climb above 28.5 MHz. Although the upper limit is not disastrous, being still below 2:1, the curve does show an increasing upper band limit SWR as the element diameter increases.

+

The conclusion reached earlier in these investigations was that a VF of 0.66 had no great impact on antenna performance. This conclusion, it now appears, holds true only for thinner elements, including the 0.5" diameter element used in that phase of the study. As the element diameter is increased, the velocity factor has an increasing affect--mostly adverse--on the monoband LPDA performance.

+
+ +
+

To get some understanding of why the velocity factor of the low impedance line almost reverse the SWR curves when going from 1.0 to 0.66, it may be useful to look at curves for the source resistance. The graph above records the results for a VF of 1.0. As the element diameter increases, the lowest value of source resistance moves downward in frequency. At a size of 1", the resistance curve is nearly perfectly symmetrical, with end values just above 60 Ohms at both ends of the band. The reactance values at the band edges are both under 10 Ohms (capacitive).

+
+ +
+

With an antenna transmission line of 75 Ohm, but with a VF of 0.66, the source resistance shows values in the 60s only for 28 and 28.5 MHz. All frequencies above these show higher source resistance values. Thinner elements show their peak value at 30 MHz, while the three largest diameters show a peak at 29.5 MHz. Although the capacitive reactance at the low end of the band is under 10 Ohms or so, the capacitive reactance at the upper end of the band can exceed 25 Ohms.

+

As noted with the SWR curves, the increase in both resistance and reactance at the upper end of the band for this monoband LPDA are not specifically prohibitive. However, if an alternative to common lines have a VF in the 0.66 range can be found, its use is advisable, especially since the poorer SWR performance is also reflected in poorer gain and front-to-back performance as well.

+

The initial conclusion that seems inherent in these modeling exercises is that fat elements and a low impedance, high VF antenna transmission line are preferable to thin elements and a high impedance antenna transmission line. Each factor adds about 0.25 dB to the antenna gain potential, as well a promising a flatter SWR curve.

+

Of course, with the higher impedance line, a matching section can be devised to provide a very flat SWR curve. However, that line will not change the lower gain of the array relative to the same array with a low impedance line. Fat (1.0") elements elevate the gain of both types of arrays by about the same amount. However, the upper band-end gain of the low-impedance line model is better sustained than with the high-impedance line model. Hence, fat elements and a low impedance, high VF line seem the optimal conditions for the monoband LPDA.

+

A Constant L/D Ratio

Wide-band LPDAs often use elements whose diameters decrease with their lengths, so that something like a roughly constant length-to-diameter ratio is maintained. to test the advisability of using elements of different diameter on the monoband LPDA, I created some further models using different orders of antenna element diameters. The initial model used a 1" rear element, 2 0.875" middle elements, and a front element of 0.75" diameter. I subsequently revised this stepping so that the rear 2 elements used 1" material, with the third 0.875" and the front element 0.75" in diameter. A final model used 1.125, 1.0, 0.875, and 0.75 inch elements from rear to front. +
+ +
+

The gain figures for the three tapered element models-with the constant 1" diameter model used for comparison show why I ended the progression. All models are for a 75-Ohm, VF=1.0 antenna transmission line. The three tapered diameter element models show virtually the same gain at all frequencies--and all three are below the values obtained with the 1" diameter element model.

+
+ +
+

With respect to front-to-back ratio, the tapered element models show a peak at 28.5 MHz, with the two more highly tapered models showing the highest peak. However, all of the curves, including that of the 1" diameter element model, become coincident at about 29.5 MHz. Whether the region of higher peak front-to-back compensates for an overall lower gain is a question with no immediate answer.

+
+ +
+

With tapered elements, one might well expect a shallower SWR curve at the upper end of the band, and the graph above fulfills that expectation. However, the amount by which any of the tapered element model curves is superior is too small to constitute a reason, in and of itself, for opting to taper the diameter of elements.

+
+ +
+

The source resistance curve for the tapered diameter models also shows a very slight improvement over the 1" constant diameter model. Once more, the degree of improvement is so small that the loss of gain in the process may count against moving in this direction.

+

The upshot of the exercise is the conclusion that the electrical performance of a monoband LPDA is not significantly affected by the use of element that have different diameters from front to rear. Unless there are mechanical reasons for developing a monoband design in this direction, a constant-diameter model will provide essentially the same overall performance and is at least conceptually simpler.

+

This conclusion, of course, applies only to a monoband LPDA. The results obtained with wide-band LPDAs may differ.

+

From Where Does the Gain Come?

At first sight, the prospect of having more gain with less front-to-back ratio--as is the case with the fattest elements--seems odd. However, the oddity is strictly a function of confining ourselves to linear thinking, that is, visualizing the forward gain of an array as coming solely out of the rear gain along the 180-degree line through the array. In such linear terms, what makes the 1"-element LPDA seem odd is that the forward and rear gain simultaneously increase. +

In fact, our thinking must be spherically 3-dimensional, and once we make that shift, the answer to the question of where the gain comes from becomes straightforward. It comes from everywhere else on the sphere except the 180-degree line running through the array.

+

One of the indicators is the -3 dB beamwidth figure, when taken in both the E-plane and the H-plane of the antenna in free space. If we cannot get more gain from the rear, then we would normally have to have narrower beamwidths in one or both directions--in short, a more focused forward lobe.

+

In our models, we have optimized a wire LPDA using 27 and 29 MHz as the input frequency limits. The result is a gain peak at 29 MHz. A similar peak resulted when we optimized an LPDA with 0.5" elements, using 27.5 and 29.5 MHz as the input limits. Finally, we obtained a third 29 MHz gain peak with 1" diameter elements using 28 and 30 MHz as the input limits. (The last example shows a gain peak variance when using a 200-Ohm antenna transmission line, but is otherwise consistent with the other models.)

+

The following table provides some comparative data for these antennas at 29 MHz using both 200-Ohm and 75-Ohm antenna transmission lines with VFs of 1.0.

+ 
Antenna/       Gain dBi       F-B dB         E-plane   H-plane
+ ATL                                         BW-deg    BW-deg
+
+#12/200-Ohm    6.45           19.45          68.4      131.8
+#12/75-Ohm     6.62           19.71          67.4      127.6
+
+0.5/200-Ohm    6.88           30.37          67.8      125.0
+0.5/75-Ohm     7.15           26.24          66.4      119.0
+
+1.0/200-Ohm    7.04           24.56          67.6      122.2
+1.0/75-Ohm     7.36           22.01          65.8      115.4
+

Clearly, the gain does not come solely from one plane, but from the overall beamwidth on a spherical surface. (For example, the #12/75 model has the second lowest gain of the group, but its E-plane beamwidth is only 4th widest.) As a rough gauge (but certainly not a definitive one), the rank order of gain figures is also the inverse rank order of the products of the E-plane and H-plane beamwidths.

+

Although indicative of the source of the LPDA gains, the analysis is quite incomplete, since all points on the sphere would have to be considered for a complete analysis. The rear lobe patterns show considerable variety, so that the 180-degree front-to-back figures can be equally useful or misleading in figuring the gain sources. Nonetheless, for the case at hand, the -3 dB beamwidths are sufficient indicators of how the LPDA models can simultaneously increase their forward and rear gain levels.

+

Why is the Peak Forward Gain So Different as the Element Diameter Changes?

The three antennas use quite different element diameters and end up with significantly different forward gain values. With an array in which every element is fed, one almost expects to find less disparity of peak gain. However, a glance at the element current tables can be revealing. The following table samples the element center current magnitude and phase for each element in each of the three 75-Ohm line arrays, where element numbers are from the rear to the front: + 
El. Dia.       El. #                    Current
+inches                        Magnitude                Phase
+                              (relative to 1.0)
+1.0"           1              0.53                       10.6
+               2              0.89                     - 79.1
+Efficiency     3              0.94                     -168.1
+99.7%          4              0.55                      109.6
+
+0.5"           1              0.48                       10.6
+               2              0.85                     - 81.3
+Efficiency     3              0.88                     -168.4
+99.5%          4              0.47                      110.4
+
+0.08"          1              0.44                       12.6
+               2              0.80                     - 86.2
+Efficiency     3              0.75                     -165.6
+98.4%          4              0.32                      110.4
+

Although there is a fairly tight correlation among the current phase values for corresponding elements, the decrease in magnitude across the span of models with decreasing wire sizes is clearly apparent. Since the phase line is identical in all three cases, the slight spacing difference among the models (of the order of 0.1") is not sufficient to account for the differentials of current magnitude on the basis of different amounts fed to each element.

+

Mutual coupling is the second source of element current. In the case of these models, the mutual coupling is directly dependent upon the wire size as well as spacing, and--given the relatively constant spacing between corresponding elements among the models--the wire size difference is sufficient to increase or reduce quite noticeably the level of current induced by and in the wires of the array. For corresponding wires, elements 1 and 2 show a magnitude difference across the span of models of about 0.1, while wires 3 and 4 show total differences in the 0.2 range. Given the wire sizes (which are all quite large in terms of basic wire loss), the differential is mostly a matter of basic element diameter and surface area and not of material losses in the elements. The forward gain differential among the arrays does not indicate power gained or lost by the antenna as a whole, but--as noted in the preceding section--power spread narrowly or less narrowly in the forward beam of the array.

+

Like the analysis of gain source, this account is indicative, but by no means complete. Looking at the current magnitudes and phase changes all along the elements would be necessary for a complete picture of the role of each element in each array. Nonetheless, even a cursory glance at model current tables can provide a wealth of information about an antenna's operation.

+

To Where Has All This Brought Us?

The modeling analysis of the effects of element diameter and the element length-to-diameter ratio has changed one earlier conclusion. Whereas the small-diameter-element analysis suggested that the velocity factor of a low impedance line had little effect on performance, we have found that for larger diameter elements, the effect is fairly profound. A low-impedance antenna transmission line should have as high a velocity factor as possible to sustain gain and SWR bandwidth across the 28 to 30 MHz span. +

For elements that are large enough--for example, 1" diameter as a practical limit--element diameter improves both spot and overall LPDA performance more than tapering the element diameters to achieve a constant L/D ratio. (Note especially that this conclusion is true of the monoband LPDA and may not hold for wide-band LPDAs.) Although the original small-diameter element model provides acceptable performance in terms of the original conditions of this exercise, the 1" element model provides the highest gain level and the flattest SWR curve. The front-to-back ratio is reduced on average, but remains above 20 dB across the 10-meter band in a curve without a sharp peak.

+

The fat-element model is most effective with the low-impedance antenna transmission line having the highest possible velocity factor. The gain of the 1" element model is about 0.25 dB higher than the 0.5" element model, using uniform-diameter element models.

+

The question that remains is whether the quarter dB added gain is a seduction or an asset. It is an asset if it can be implemented in a mechanically sound design that can be replicated in the average garage. The result should not be very much heavier than a 0.5" diameter element model and should be able to slip or withstand about the same wind forces. Half-inch diameter elements offer a light but sturdy structure of proven durability.

+

Likewise, the low-impedance antenna transmission line offers higher gain and a direct 50-Ohm feed. However, those advantages are offset a bit by the possibility of a steeper SWR curve across the band compared to the use of a carefully cut matching section applied to a 200-Ohm antenna transmission line. The latter is capable of providing a very flat SWR curve, even though the higher impedance antenna transmission line shows reduced gain.

+

Note also that the fat-element and low-impedance line effects are cumulative--up to nearly a half dB in the gain column, when comparing 0.5" and 1" diameter elements. Consequently, it seems desirable to achieve, if not both, then at least one out of the two goals.

+

So the questions facing this design project, if it is to achieve the highest possible monoband LPDA performance, are two: 1. Can a 1" diameter element version of the antenna be practically implemented? 2. Can a high- VF 75-Ohm antenna transmission line be fabricated so that it is light and sturdy?

+

Of the two questions, perhaps the second is the more interesting, since it requires the most investigation. However, at this stage, I need to use special care to ensure that I am not simply succumbing to a predilection for thin-element construction. The antenna diameter question also needs careful weighing.
+

+
+ +

+
+

Updated 11-14-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

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+ +

+
+

Go to Part 4: 3 vs. 4 Elements in an LPDA for 10 Meters

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda4.html b/content/lpda/lpda4.html new file mode 100644 index 0000000..34a6b5c --- /dev/null +++ b/content/lpda/lpda4.html @@ -0,0 +1,154 @@ + + + + + + A 10-Meter LPDA Phase 4: 3 vs. 4 Elements in an LPDA for 10 Meters + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 4: 3 vs. 4 Elements in an LPDA for 10 Meters

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Here is a rule of thumb for antenna design: just when you think you have covered all of the bases and are ready to start planning the physical implementation of an antenna design, something comes along to make you rethink the project. Actually, if you are lucky, the source of new directions emerges before you start cutting and drilling aluminum. If not, you have some material to support bird feeders, to recut for 6 and 2 meter antennas, or to use as strengthen stress points on the final design. +

The N7CL Design and Its Modification

Eric Gustafson, N7CL, who has worked with LPDAs, sent me a model he scaled and modified from some military work he once did. His original handled 30 KW, but the scaled model was appropriate for ham work and centered in the 10-meter band. The key feature of Eric's design was that he captured most of the requirements I had originally set up for the project in 3 elements, rather than 4. +

Here is an EZNEC description of Eric's design:

+ 
3 el. Log Cell (S=0.12, K=1.1)     Frequency = 28.8  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-84.400,  0.000         0.000, 84.400,  0.000 3.75E-01  27
+2       -47.700,-94.300,  0.000       -47.700, 94.300,  0.000 3.75E-01  31
+3       -105.25,-105.25,  0.000       -105.25,105.250,  0.000 3.75E-01  35
+               -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          14     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length    Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)             Ohms Fact Norm
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist   50.0  0.95  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist   50.0  0.95  R
+3    3/50.0  (  3/50.0)  Short ckt (Short ck)    5.000 in   200.0  0.95
+4    1/50.0  (  1/50.0)  Short ckt (Short ck)   14.000 in   200.0  0.95
+Ground type is Free Space
+

Eric used 3/8" diameter elements with a 50-Ohm, VF-0.95 antenna transmission line. (The function of the 0.95 VF is largely to be conservative for construction methods using pairs of wires, bars, or booms with periodic spacers.) TL #3 is a shorted stub at the rear of the antenna, while TL #4 is a beta match shorted transmission line stub. The natural source impedance of the antenna is in the 20s, with a considerable capacitive reactance, and the beta match becomes a natural form of matching to a 50-Ohm line.

+

The one feature about Eric's design that troubled me was its extra 9.4" of boom length. Everything else in this exercise had been designed for 8' booms (that might be obtained from hardware depots rather than special sources, since the ultimate goal is a garage-built antenna). Hence, I wondered what the consequences might be of shortening the boom. To provide some initial element length and spacing numbers to compare with Eric's, I resorted to LPCAD once more. LPCAD is intentionally limited to 4 elements as the minimum number for any design. So I simply increased the upper frequency limit so that the third element fell at about the 8' mark, and deleted the shorted element when transferring the model to EZNEC. Only a little adjustment was necessary to derive a 3-element monoband LPDA on an 8' boom.

+ 
lpda10m                  Frequency = 28-30  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-106.00,  0.000         0.000,106.000,  0.000 3.75E-01  43
+2        50.559,-95.400,  0.000        50.559, 95.400,  0.000 3.75E-01  41
+3        95.339,-86.000,  0.000        95.339, 86.000,  0.000 3.75E-01  39
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          20     3 / 50.00   (  3 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist   50.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist   50.0  1.00  R
+3    1/50.0  (  1/50.0)  Short ckt (Short ck)   19.000 in    50.0  1.00
+4    3/50.0  (  3/50.0)  Short ckt (Short ck)   15.000 in   200.0  1.00
+Ground type is Free Space
+

In this final design using 3/8" elements, I used a 50-Ohm line for the antenna transmission line stub, along with a VF of 1.0. Stubs can be adjusted in length for the materials used during construction, so long as the inductive reactance is the same.

+
+ +
+

The sketch may place some perspective on the numbers in the tables.

+
+ +
+

The overlaid patterns of the modified N7CL LPDA--using a version with 0.5" elements and a VF of 0.95, show a generally promising pattern across 10 meters, with only the 30 MHz front-to-back value falling below 20 dB. How this model stacks up against Eric's original will emerge later on in this phase of the design process.

+

Optimizing the Elements

Before settling on the best design on an 8' boom in the 3-element version of the LPDA, I wanted to check the consequences of using different size elements. So I created models using 0.5" and 0.375" elements. Then I mixed them to yield something like a tapered element size and a constant length-to-diameter ratio. One version used 2 half-inch elements and 1 3/8- inch element; a second version reversed the mix. Looking at the data for all four versions at once can help us decide if element tapering is worth the effort and also provide an overall picture of the 3-element LPDA. +
+ +
+

The antenna free space gain across 10 meters shows a decreasing set of values from above 7 dBi to about 6.6 dBi. The half-inch model is marginally superior, but the constant 3/8" element version is never worse than the mixed size models. Hence, from the perspective of gain, changing element size to achieve a constant length-to-diameter ratio is an exercise in futility.

+
+ +
+

The front-to-back curves tell essentially the same tale. The constant element diameter curves bracket the mixed-size models. Interestingly, a pattern picked up earlier replicates itself here: the higher the gain, as yielded by a fatter element, the lower the front-to-back ratio for any given set of element lengths and spacings on a given frequency. Here the thinner (3/8") element passes through 20 dB at about 29.7 MHz, while the larger (0.5") element drops to about 18.5 dB at 30 MHz.

+
+ +
+

For the type of design in question, the SWR increases more rapidly above the design center frequency than below it. Using 2 or 3 3/8" elements provides the shallowest curve, while using 2 or 3 1/2" elements provides steeper curves on one or the other end of the band of operation.

+

Although a successful version of the short-boom 3-element LPDA might well be built using half-inch or 3/8-inch elements, the thinner elements actually provide a modicum of advantage over the thicker ones. In no category did the tapered element diameter schedule provide any advantage over using elements of one diameter throughout the design.

+

The descending gain pattern is a function of the design using an inductive stub to close the rear of the antenna transmission line and to tailor the antenna operating characteristics. Removing the stub from the rear provides an antenna with more gain on every frequency, but far less front- to-back ratio. One way to view the stub is as a load that electrically lengthen elements acting as a reflector. This view is at best partial, since every element is active at every frequency in the narrow span of a monoband LPDA. However, like reflector loads in parasitical beams, the increased front-to-back ratio also has the consequence of reducing gain by a small amount and of changing the source impedance. What Eric did in his design was to balance these effects to yield a 3-element LPDA having the characteristics he wanted. These characteristics are general enough to carry over into modified versions of his work.

+

8' vs. 8.8' Booms

A natural question is how well the shortened boom version of the antenna stacks up against the slightly longer one, using the same modeling machinery on both. Actually, the shorter boom requires a few compromises relative to the N7CL original--for example, a sacrifice of a smooth SWR curve for gain. +
+ +
+

A comparative gain curve for the N7CL original and the shortened version shows excellent coincidence. In fact, in the shorter version, other characteristics were sacrificed to provide as high an upper band limit gain as possible, since the shorter model tended toward a more rapid gain drop off in its original set of dimensions.

+
+ +
+

As noted, squeezing gain from a monoband LPDA tends to lower the front-to- back ratio in the area of squeeze. Although the front-to-back curve for the 8' boom model might have its curve moved slightly to equalize low-end of the band values, it would still show a deficit relative to the 8.8' boom model at the upper end of the band. In short, for the monoband LPDA, gain and front-to-back ratio are trade-offs. When there is a surplus, as in 4- element models, the trade-off appears mostly as a minor adjustment of the operating characteristic curves. When the values are at the limits of a preset specification sheet, the trade-off process become serious.

+
+ +
+

What was traded to achieve as shallow as possible as gain curve with acceptable front-to-back ratio was source reactance. The unmatched variance in reactance across the band for the 8' boom model is much greater than for the 8.8' model. The result when beta matched for 50-Ohms is a flatter SWR curve for the 8.8' boom model than for the 8' boom model. Both versions of the monoband LPDA maintain an SWR of less than 1.5:1 across the band, but the long boom model is clearly superior.

+

For the average builder, using the long boom will result in slightly superior overall performance. As well, it will likely be somewhat more forgiving of the normal range of variances that occur using home shop construction methods. However, the exercise in modifying the design has revealed something of the limits of the 3-element design and the trade-offs necessary to achieve a design close to the specifications set up at the beginning of the project.

+

3 vs. 4 Elements

How well does the 3-element 8' boom design stack up against the best of the 4-element designs so far considered? In other words, does the 3-element design provide a replacement for the heavier models developed in earlier phases of this project? To answer the question, I compared the 0.5" element 8' boom design to the best of the 4-element designs (performance- wise), which used 1" diameter elements and a 75-Ohm, VF=1.0 antenna transmission line. +
+ +
+

The gain curve of the 4-element design is clearly superior to that of the 3-element design. For designs so far investigated, it appears that a 3- element LPDA cannot sustain a gain near 7 dB over all of the 2 MHz bandwidth. At the upper end of the band, the 3-element design shows about 0.6 dB less gain than its 4-element counterpart. Moreover, the 3-element design begins to fall short of the desired goal of having 3-element 8' boom Yagi gain all across the band. (Remember that one of the specifications set was not merely that the antenna achieve a match across the 10-meter band, but that it also sustain certain operating characteristic levels throughout.)

+
+ +
+

Although the 4-element front-to-back curve is superior to that of the 3- element LPDA, the difference is not so great as to be decisive--at least not to the degree that the gain curve differentials appear to be decisive. Although the upper band edge front-to-back for the 3-element model drops below 20 dB, the amount is operationally slight.

+
+ +
+

The SWR curve for the half-inch 3-element model using a 0.95 VF line is steeper than some of the others for more perfected models of the smaller antenna. However, in this context, it demonstrates somewhat vividly the SWR curve advantage of the 4-element model using fat elements. Although the small antenna SWR curve cannot be considered unacceptable, the 4-element model curve is especially attractive for rigs having ultra-sensitive power-reduction circuits. (Note that the original N7CL design has an SWR curve more closely akin to the 4-element design.)

+

To conclude that the 4-element design is superior to the 3-element design on the same length of boom (or slightly longer) is not to classify the lighter antenna as unacceptable. If the reduced upper band-end gain is acceptable and the marginalness of the front-to-back ratio in the same region is not obstacle, then the simpler design might well be the design of choice.

+

How Might We Implement the 3-Element Design

A 50-Ohm antenna transmission line with a high velocity factor cannot be achieved with normal round conductors. In fact, many transmission line calculating programs have an automated cut-off of about 80 Ohms, since round conductors would begin to overlap, using standard transmission line calculation means and formulas. +

Although seldom used for ordinary transmission line purposes, flat-face conductors can be brought to much closer center-to-center distances than round conductors. In addition, they present a higher equivalent "diameter" than round conductors in this application.

+
+ +
+

The sketch shows some possibilities for the construction of low impedance antenna transmission lines for the monoband LPDA. Flat plates might present the most problems for home constructors without welding equipment for making connections. Jerry Hall, K1TD, used a modification of the L- stock configuration with his 2-meter LPDA. Square stock promises the possibility of combining both boom and transmission line functions in one assembly.

+
+ +
+

Perhaps the chief problem facing the user of square stock is the element attachment problem. The figure shows two types of element locking mechanism. However, what is not shown can create more mechanical problems than what is shown (since elements can be tapped). First, the element is suspended from a very small region at its end. Either the square stock should be thick or it should be reinforced so that the element does not rest on a metal edge. The holes in the element should be as precise as possible. For the "top" set crew model, inserting a length of stiffening rod or tubing inside the main element may also distribute the load.

+

The elements are non-symmetrical relative to each boom and tend to place twisting forces on the boom pieces. In the sketch, there is compression on the right side and separation on the left. Hence, near each element, the booms should be locked, possibly using an insulating plate with screws into each boom piece. The plates should be attached on both side of the boom assembly to counter both the compression and separation forces. Such plates might well eliminate the need for periodic spacers to maintain boom spacing.

+
+ +
+

L-stock requires a separate boom, as well a some system for keeping the antenna transmission line parts far enough away from the boom to negate any interaction. The spacing is convenient, since it also provides enough room for crossing wires (for at least one element in the 3-element designs and 2 in the 4-element designs). The L-stock flanges are convenient for making attachments to the connecting wires without disturbing the facing surfaces of the transmission line. If the orientation shown in the sketch yields problematic interactions with the boom, the co-planar parts of the stock can be moved to the top edge. Of course, the element mounting plates must be insulators.

+

For initial prototypes, something like the L-stock version of the antenna transmission line seems advisable. Revisions to the design that emerge during or after initial construction may leave some holes in the flange, but these will likely not affect the performance or mechanical soundness of the antenna. The open structure permits many test-bed practices that might well be revised in final versions. For example, the spacers might be held in place with cable tie-wraps until testing and final positioning has been set. Likewise, simple copper wire might be used as the connecting wires to the element, even if the final version might call for aluminum strips to minimize bi-metal effects.

+

These preliminary thoughts on constructing a prototype suggest that I am getting closer to actually committing to one--at least one to try out. I have reduced the materials needs to those I can obtain locally for the most part--or obtain easily from ham vendors. Some of the mechanical parts may require some ingenuity, remembering that this is a garage project and not a manufacturing prototype. So I am expecting a good bit of trial and error, as well a setting some dimensions (like the antenna transmission line spacing) through both pre-element and post-element assembly testing.

+

Now if I could only decide whether the 3-element version is good enough or whether I should try the 4-element version for more assured performance across the band. My thanks to Eric Gustafson, N7CL, for sharing his design, even if it has resulted in a bad case of indecision.
+

+
+ +

+
+

Updated 11-14-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Part 5: Preconstruction Decisions

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda5.html b/content/lpda/lpda5.html new file mode 100644 index 0000000..281a619 --- /dev/null +++ b/content/lpda/lpda5.html @@ -0,0 +1,148 @@ + + + + + + A 10-Meter LPDA Phase 5: Preconstruction Decisions + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 5: Preconstruction Decisions

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Decision and construction time are approaching. So let's review the project so far: +

1. Specifications: since the overall project goal was to see if 3-element short-boom Yagi performance could be extended across the entire 10-meter band with an LPDA, I set the following specifications:

+
    +
  • a. Frequency coverage: 28-29.7 MHz
    • +
  • b. Boom length: 8' maximum
    • +
  • c. Free space gain: 7 dBi minimum
    • +
  • d. Front-to-back ratio: 20 dB minimum
    • +
  • e. 50-Ohm SWR: 1.5:1 maximum
    • +
+

These specifications are apt to the project goal, but not necessarily to some set of specific operator needs for such an antenna. The specs presume equal interest in all parts of the band, which would be a rare phenomena. For just the CW end of the 10-meter band, for example, a 2-element driver- director Yagi would come close to meeting the specifications other than frequency coverage. However, the original questions driving this design and exploration exercise are "Can it all be done, and can a monoband LPDA do it all?"

+

2. Candidates: Phase 1 eliminated almost all of the common types of antenna used at 10 meters, mostly for want of a wide-band enough combination of performance and SWR coverage. In the course of developing an LPDA design, some other variants were checked and abandoned. For example, the Log-Yagi combination never seemed to approach either of the final candidates in performance across the band. Note, however, that my inability to find the right combination to make the Log-Yagi do the job does not mean that it cannot do the job in principle. It only means that I did not uncover a combination of element length and spacing to make the Log-Yagi work in this context.

+

The final candidates are represented by models of 3-element and 4-element LPDAs. Since some slight variations of the version presented earlier have emerged since the preceding phases of work were closed (but not necessarily completed), I shall present the models as EZNEC descriptions.

+

a. 3-element LPDA

+ 
LPDA3          Frequency = 28-30  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-106.00,  0.000         0.000,106.000,  0.000 3.75E-01  43
+2        50.559,-95.300,  0.000        50.559, 95.300,  0.000 3.75E-01  41
+3        95.339,-86.000,  0.000        95.339, 86.000,  0.000 3.75E-01  39
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          20     3 / 50.00   (  3 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist   50.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist   50.0  1.00  R
+3    1/50.0  (  1/50.0)  Short ckt (Short ck)    2.200 in   450.0  1.00
+4    3/50.0  (  3/50.0)  Short ckt (Short ck)    7.000 in   450.0  1.00
+Ground type is Free Space
+
+ +
+

The figure summarizes the element length and spacing data from the model description. This model, now called LPDA3, is essentially the same as the modified N7CL model reviewed in Phase 4. For convenience, 2 small changes have been made, and both involve the modeling of the antenna transmission line and beta match stubs. In this model, the stubs are composed of 450- Ohm parallel line. Actually, any type of line will do. The required antenna transmission line stub reactance is 15.3 Ohms at 29 MHz, while the beta match required reactance is 48.8 Ohms at 29 MHz. Any stub arrangement providing these values of inductive reactance will work as well as any other within the limits of physical feasibility.

+

b. 4-element LPDA

+ 
LPDA4               Frequency = 28-30  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1         0.000,-108.50,  0.000         0.000,108.500,  0.000 5.00E-01  43
+2        35.605,-98.003,  0.000        35.605, 98.003,  0.000 5.00E-01  41
+3        67.475,-87.720,  0.000        67.475, 87.720,  0.000 5.00E-01  39
+4        96.000,-78.515,  0.000        96.000, 78.515,  0.000 5.00E-01  37
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          19     4 / 50.00   (  4 / 50.00)      1.000       0.000       I
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist   75.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist   75.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist   75.0  1.00  R
+Ground type is Free Space
+
+ +
+

The sketch provides a summary of element length, diameter, and spacing information from the chart. With the 4-element model, elements have undergone a final tweaking, and the 0.5" model was selected as the best compromise between the higher performance offered by the same antenna with very large elements and the desire to hold weight as low as practicable.

+

3. The Final (?) Decision: selecting the final candidate essentially boiled down to forcing myself to adhere rigidly to my initial specifications, even if one of the candidates offered some advantages in terms of weight.

+
+ +
+

The gain curves show that only the 4-element LPDA meets the gain specification originally set. The 3-element LPDA is a fine antenna for those with more intense interests in the low end of the band and more casual interests in the upper portion. Indeed, where the 8' boom length limit is not a requirement, the N7CL model is to be recommended as providing smoother operation and somewhat more forgiving construction.

+
+ +
+

The front-to-back graph reveals the 3-element LPDA to have a smoother curve. Nevertheless, the curve for the 4-element version shows that it meets the front-to-back specification, with the ratio passing through 20 dB at almost precisely 29.7 MHz. Whether this can be preserved in a physical version of this modeled beam is another matter.

+
+ +
+
+ +
+

The pair of SWR curves show that both beams would meet the 50-Ohm SWR specification. However, the 4-element version has the shallower curve, which promises a bit more room for the normal prototype construction variables.

+

In addition to the performance specifications, one also should note the methods by which performance is obtained. The 3-element version requires carefully cut antenna transmission line and beta matching stubs (or coils). Both techniques are well-documented and implementation would be straightforward. However, they do add further variables to the design and construction mix. In contrast, the 4-element model can be fed directly (with a feedline choke) and requires no stub at the other end of the antenna transmission line. Since these items were not included in the original specifications, selection of one or the other method would be largely a matter of preference.

+

In the end, I have decided to pursue the 4-element monoband LPDA, because it promises, by virtue of the design model, to meet all of the original specifications.

+

4. Construction Planning: in the preceding phase, I looked into several options for constructing the antenna transmission line. Because it offers more flexibility in revising the prototype easily, L-stock lines seem to be the best option. This choice of basic construction methods entails a number of other considerations, ranging from weight to nuts and bolts.

+

a. Weight: My initial list of weight increments included the following estimates:

+

1. Boom: an 8' 1.25" boom of standard 0.58" wall thickness stock weighs about 0.26 pounds per foot, or about 2.1 pounds. However, the boom will require judicious reinforcement at least at the boom-to-mast point and possibly where the elements join the boom on insulated plates. Using internal 1.125" diameter stock might yield anywhere from 1 to 8 feet of additional boom weight. For initial estimates, I used 4' or 0.9 pounds, at about 0.23 pounds per foot, for an anticipated total boom weight of about 3 pounds.

+

2. Antenna transmission line: the L-stock eventually used might range from 0.5" per side to 1" per side. The middle size (0.75" per side) weights about 0.1 pounds per foot, for 0.8 pounds per 8' length. Since we need 2 lengths, we can add 1.6 pounds to the boom weight.

+

3. Boom-to-mast mounting: my initial plans are to use an unusual mounting system composed of Schedule 40 PVC pieces in order to keep the antenna transmission line well-spaced from the mast. The necessary parts weigh about 0.5 pounds

+

4. Elements: the 4 elements require a total of a little over 62' of 0.5" diameter aluminum tubing. At nearly 0.1 pound per foot, the elements weigh in at about 6 pounds total. However, initial construction ideas also call for element stiffening with 0.375" tubing, requiring about 16' total of the material. At about 0.05 pounds per foot, we can add 0.8 pounds, for a total element weight of 6.8 pounds. Element plates will likely weight about 4 to 6 ounces each or another 1.5 pounds, for a total of 8.3 pounds.

+

5. Support hardware and pieces: the antenna transmission line support pieces, coax connector, and the stainless steel hardware necessary to connect and secure the various parts of this prototype will likely add another pound to the total weight.

+

The total projected weight of the prototype is about 14.5 pounds. A 3- element version of the LPDA would weight about 2.1 pounds less. A production antenna might weight considerably less (perhaps 10 pounds), but the prototype has to be rugged enough to withstand the typical abuse involved in testing, rebuilding, and readjusting. I find it interesting to compare my projections with the weight of the final working unit. Experience has divided my antennas into 3 equal groups: those that weighed significantly less, those that weighed about as projected, and those that weight considerably more. Hence, I have no experiential "fudge factor" to throw into the mix.

+

b. The antenna transmission line: before adding any elements to the antenna, I want to experiment with various types of hardware depot L-stock, ranging from 0.5" per side to 1" per side (all .0625" thick) for the line.

+
+ +
+

The general scheme shown in the sketch will support the lines. However, it will require revision to suit the actual line used. 0.5" L-stock will fit between the support pillars and require a cross piece. 1" stock might use screws that pass through the stock flange into a threaded tap in the pillar. The exact length of the pillars may also require some testing to see how close the lines can be to the boom before interaction is harmful.

+

I know of no figures or equations exactly applicable to L-stock in the proposed configuration. Hence, determining when the line has a characteristic impedance of about 75 Ohms will be experimental, although straightforward. For 80-Ohm lines of square stock, the calculated separations from facing surfaces are 0.23" for 0.5" material, 0.34" for 0.75" material, and 0.45" for 1" stock. Another 5 Ohms decrease in Zo, along with somewhat different requirements for L-stock relative to square stock, still holds the potential for a light-weight half-inch L-stock line. Whether this line, if feasible, is also convenient for element and pillar attachment, only testing will tell.

+

c. Insulated plates: the elements require insulated plates for isolation from the boom. For half-inch diameter elements, plates that are 2" wide by about 12" long (side-to-side relative to the boom) should suffice. 3/8" spar varnished plywood will do in a pinch, but Lexan or some other sturdy structural plastic would be better. U-bolts are the standard fasteners for plate-to-boom and plate-to-element mounting. However, for this light structure, equally light hardware is desirable.

+
+ +
+

The line support pillars can be true pillars or plates through-fastened to the boom. Since their exact positions are non-critical, drilling the boom is a satisfactory option for mounting. The top assembly will be determined by transmission line construction experiments. Quarter-inch plexiglass or better will serve for the side pillars/plates and allow tapping for either direct fastening of the line stock or of a top plate to support the line.

+

d. Boom-to-mast mount: proper testing of a prototype suggests strongly that possibly disturbing influences on the antenna structure be minimized. A standard plate for side-mounting the boom to the mast would require spacers to keep the mast from touching or coming in very close proximity to the line. Although this close approach might not affect the line, initial testing can be done with a more isolated mounting system.

+
+ +
+

Using Schedule 40 PVC pieces cemented together, one can use the system sketch above to provide an isolated boom to mast mount. Once the center of gravity of the antenna array is determined, set screws can be replaced by bolts passing through both the PVC and the boom. (The mast will be equipped with a shorting strap to the boom to test the effects of grounding the boom or leaving it floating.) Because the 4-element version of the monoband LPDA has no center element, the system has adequate room for adjustment to the actual center of weight with all elements and lines connected.

+

Initially, the feedline will be taped beneath the boom. A finished version might consider running the feedline through the boom.

+

This is what I plan to do, even with all of the uncertainties which will take shape in the course of construction and testing. The next phase is gathering parts for the prototype--and that will take a bit of time. Then come the various stages of building, testing, and rebuilding. So there is not likely to be a Phase 6 to this report of a project in progress until Spring (I hope, Spring of 1999).

+

Nonetheless, the design exercise has produced a very promising antenna within the scope of the original specifications. I am assuming, based on past experience, that the 4-element monoband LPDA will work pretty much as modeled. But sometimes there are surprises--both good and bad--which is why we turn the models into physical antennas, no matter how carefully we have structured the models within the software.

+

Of course, while pursuing the prototype, I just may learn a little more about both the design of this antenna and other possibilities. I have already turned a number of unanticipated corners in the process of getting this far. So the phase of gathering and assembling materials will proceed without foreclosing other options.

+

Practical goals, like antennas for specific operational purposes, can lead to great satisfaction when the job is accomplished. On the other hand, sometimes it is sheer pleasure to work on a project with no other goal than to see if it will work.
+

+
+ +

+
+

Updated 11-16-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Part 6: A Yagi Standard and Alternative

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda6.html b/content/lpda/lpda6.html new file mode 100644 index 0000000..e87687b --- /dev/null +++ b/content/lpda/lpda6.html @@ -0,0 +1,214 @@ + + + + + + A 10-Meter LPDA Phase 6: A Yagi Standard and Alternative + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 6: A Yagi Standard and Alternative

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Sometimes reviewing the standard against which a design project has set its specifications can yield some new ideas. So I thought it useful to look at the basic short-boom 3-element Yagi that prompted me to formulate the project goals. +

A 3-element 10-Meter Yagi on an 8' Boom

The 3-element Yagi that I have been using as a standard is derived from a K6STI design that is available on the YA program that accompanies The ARRL Antenna Book. The YA program uses a tapered-diameter element version, but for comparative modeling purposes, I tend to use a version with uniform 0.5" diameter elements. The EZNEC model description pretty much tells the entire design story. + 
3el Yagi K6STI 310-08 no taper     Frequency = 28-29  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1        -105.93,  0.000,  0.000       105.926,  0.000,  0.000 5.00E-01  21
+2        -96.892, 36.000,  0.000        96.892, 36.000,  0.000 5.00E-01  21
+3        -92.443, 90.000,  0.000        92.443, 90.000,  0.000 5.00E-01  21
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+No loads specified
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1      2/50.0  (  2/50.0)  Short ckt (Short ck)   55.000 in    50.0  1.00
+Ground type is Free Space
+
+ +
+

The antenna outline sketch summarizes the overall dimension of the model.

+

The shorted transmission line stub is a beta match at the feedpoint, simply registered with 50 Ohm cable, although it would be much shorter with high impedance line. However, for modeling convenience, low impedance stubs are often handy. A 1" change at 50 Ohm represents a 9" change for 450-Ohm line, so incremental length changes are less sensitive with low-impedance cable. The actual characteristic impedance of the beta match shorted stub (or hairpin) can be inserted just prior to construction.

+

The native impedance of the antenna prior to matching is 27 Ohms resistance with a capacitive reactance of about -j25 Ohms. Hence, the antenna is a good candidate for a beta match. However, the driven element can be extended to resonance and matching accomplished with a 1/4 wl 37.5-Ohm section (paralleled 72-Ohm cables). Performance differential is negligible.

+
+ +
+

The combined free space azimuth patterns, taken from NEC-4, show the degree to which the antenna is extremely well-behaved across the first MHz of 10 meters. Indeed, the antenna has been tweaked so that the front-to-back patterns at 28 and at 29 MHz are about the same along the 180-degree line. Maximum 180-degree front-to-back ratio occurs just about at 28.5 MHz. The curves for the rear quadrant show that the worst-case front-to-back ratio is about the same all across the band.

+

Because the differences between MININEC and NEC will become important in this set of notes a little later, it seemed useful to compare the two programs with respect to the major operating parameters of the standard antenna. NEC-4 figures come from EZNEC Pro, while MININEC figures come from AO.

+
+ +
+

The gain curves for the antenna under the two programs are very closely coincident. Even with laboratory conditions, it would be difficult to determine which is closer to reality, and the minuscule numeric differences make no operational difference at all. As with most Yagi designs using one or more directors, the gain increases with frequency. It continues to climb above 29 MHz, but becomes largely unusable for reasons having to do both with the front-to-back ratio and with the source impedance.

+
+ +
+

The front-to-back curves have insufficient data points to show their congruity in detail. However, the peak front-to-back ratio of the NEC-4 model is actually just below 28.5 MHz, while the AO max occurs right at 28.5 MHz. There is less than 50 kHz difference in the front-to-back peak, another numeric difference that makes no difference at all operationally. Note that the front-to-back ratio deteriorates rapidly above 29 MHz, limiting the utility of the antenna above that frequency.

+
+ +
+

The 2:1 50-Ohm operating bandwidth for the antenna models come from two different bases. The NEC-4 line is a true 50-Ohm SWR line based on the beta match stub placed in the model itself. The match stub length was adjusted to yield the relatively coincident end points on the curve. The AO line is based on a match at the center frequency and is useful in noting the more rapid climb in SWR above center frequency than below it. In fact, the source resistance of the antenna prior to match begins to drop very rapidly above 29 MHz, making it difficult to achieve any kind of match at all and still cover the first MHz of the band.

+

As short-boom (8' and under at 10 meters) Yagis go, this is an excellent design. It sustains a free space gain of at least 7 dBi across the band, with better than 20 dB 180-degree front-to-back ratio across the same span. The source impedance is stable enough to permit common matching schemes to provide a very reasonable set of values for 50-Ohm coax, and the basic impedance is high enough to permit high efficiency without too much concern for resistive losses at connections (although this source of loss is very often overlooked by builders). So, for the record, these are the reasons I tend to use this design as a short-boom 3-element standard against which to measure other antenna designs.

+

The Possibility of a Wide-Band Yagi Design

While looking at the 3-element short-boom standard Yagi, I began to wonder about various techniques for creating wider band Yagis without increasing the boom length. One possibility was to use the "extra" element employed by the NW3Z long-boom Yagi design (6 elements in 48' for a 20-meter model). However, going to a 4-element design by this method required that the second or forward director be much farther out from the driven element than the 8' boom permitted. +

A second design direction was to employ open-sleeve coupled drivers, one tuned low in the band and the other high. The ARRL Antenna Book, in Chapter 7, has an excellent introduction to open-sleeve coupling written by Roger Cox, WB0DGF. However, most of the design work has been applied to widely separated frequencies. An 80/75-meter dipole appeared in QST sometime back (meaning that I do not remember just when and have not yet found the article). This method seemed promising--if the reflector-to-director spacing could be held to 96" or so.

+

A design emerged from NEC-4 modeling, using open-sleeve coupling, a reflector, and a director. The reflector-to-driver spacing--as well as the master-to-slave driven element spacing--was set to provide a direct 50-Ohm match across the entire 10-meter band. The director was placed at the maximum forward position allowed by the original specifications--and turned out to be in just about the right position. Forward and rearward changes of position--even with small changes of element length--do not alter the performance in any significant way.

+

The final NEC-4 model appears in this EZNEC description:

+ 
4-el WB             Frequency = 28-29.7  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.---End 1 (x,y,z : in)  Conn.---End 2 (x,y,z : in)   Dia(in) Segs
+1        -106.00,  0.000,  0.000       106.000,  0.000,  0.000 5.00E-01  27
+2        -102.50, 40.500,  0.000       102.500, 40.500,  0.000 5.00E-01  27
+3        -94.500, 44.000,  0.000        94.500, 44.000,  0.000 5.00E-01  25
+4        -90.500, 96.000,  0.000        90.500, 96.000,  0.000 5.00E-01  23
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          14     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+
+ +
+

The outline sketch summarizes the dimensions of the antenna. The two drivers are segmented so that their segment junctions are as parallel as the elements permit, a necessity due to the close proximity of the two wires. Essentially, the reflector and rear driver control the low end of the band, while the forward driver and director control the upper end of the band. The relative control can be loosely demonstrated by recording the current magnitude (relative to 1.0) and phase at element centers for frequencies of 28, 28.8, and 29.7 MHz.

+ 
Frequency           28.0           28.8           29.7
+Reflector           0.69/ 95.5     0.43/ 71.3     0.33/ 52.7
+Driver 1            1.00/  0.0     1.0/   0.0     1.0/   0.0
+Driver 2            0.74/-98.0     0.97/-111.1    1.67/-120.1
+Director            0.55/-135.4    0.71/-171.2    1.14/136.8
+

First, notice the relatively balanced current magnitudes on the 2 drivers at the mid-band frequency, and compare these values to those for each band edge. Second, note the relatively smooth decrease in relative current magnitude on the reflector with increasing frequency. Third, note both the increase in relative current magnitude and the wide phase shift across the 10-meter band. In no case does the current on an element decrease to a wholly ineffectual level (say, less than 0.1); however, which elements dominate performance is clearly evident.

+
+ +
+

The overall composite free space azimuth patterns for the antenna from 28- 30 MHz in 0.5 MHz steps give a hint at potential performance. The 30 MHz pattern can be discounted as outside the band of interest, although it shows the trend for the antenna at its upper frequency limit. The free space gain of 7.82 dBi also applies to 30 MHz, showing that the antenna, like any Yagi with a director, increases gain as the frequency increases. Within the 10-meter band, performance is promising, if not perfect-- relative to the specifications for the original project.

+

The possibility of turning to a Yagi design offers a saving in both overall weight and in construction complexity. Each element can be mounted in one of the standard ways, and the feedline will by more nearly in line with the mast than with the LPDA design. Indeed, a standard boom-to-mast plate can be employed without concern for harmful interaction between the mast and the elements. In all, the omitted LPDA antenna transmission line and supporting hardware and brackets might amount to over 2.5 pounds in weight saved, reducing the final antenna weight to the 12 to 12.5 pound region.

+

Performance Potential

The wide-band Yagi will not achieve all of the design goals of the project, but it will come close. However, before looking at the performance potential graphs, we must note a limitation in the NEC-4 model of the antenna. NEC (whether -2 or -4) does not yield wholly accurate results when wires are too closely spaced. The degree of inaccuracy is a combined function of wire diameter, closeness of spacing, and frequency. The 3.5" spacing of the master and slave drivers falls just within the region of sensitivity. When wires are too close, NEC tends to over-report the gain and under-report the source impedance. The gain figure, however, is the most sensitive when wires are at the fringe of the sensitivity area, as they are in this example. +

Therefore, it was necessary to also model the antenna in MININEC (AO, in this case) as a cross-check on the figures produced by NEC-4. We have already seen that for models that do not press program limitations, the two programs yield highly comparable figures. When NEC limits are pressed, MININEC provides a reasonable counterweight.

+
+ +
+

The gain graphs graphically illustrate NEC-4's likely over-reportage. The two curves are almost perfectly congruent, but NEC-4 reports about 0.16 dB more gain than MININEC, giving the illusion that the antenna free space gain never falls below 7 dBi. The 6.9 dBi minimum figure of MININEC is likely more accurate. Whether or not the difference is operationally significant, it is difficult to sustain a gain of 7 dBi for the antenna when the director is less than fully active--which the current tables show it not to be at the low end of the band.

+
+ +
+

The 180-degree front-to-back curves are quite comparable, even though there is a very slight frequency offset between the two programs with respect to the frequency of maximum front-to-back ratio. NEC-4 report that maximum to occur just above 29 MHz. That the two peak figures should coincide despite differences in gain reporting is natural: NEC-4 tends to over-report all gain values in the plane of the antenna, and those reports include both forward and rearward gain. Thus, the difference tends to remain approximately the same as the MININEC report.

+

The design--as reported in either program--only meets the 20 dB front-to-back ratio criterion for the span between 28.25 and 29.50 MHz. The front-to-back performance falls off to roughly 17.5 dB at the band edges. At these extremes, the director and reflector cannot both be fully effective at the same time. At mid-band, where both are fully effective, front-to-back performance is impressive.

+
+ +
+

The SWR curve reported by NEC-4 is outstanding, never exceeding 1.2:1 across the entire 10-meter ham band. However, NEC-4 tends to under-report the source resistance in this type of case. MININEC reports highly acceptable figures that never exceed 1.3:1, based on higher values of both source resistance and capacitive reactance.

+

The final evaluation of the design is that it comes exceptionally close to meeting the original design goals, even by MININEC reckoning. The low end gain only misses the 7 dBi figure by a small margin. The band-edge front- to-back ratio deficits relative to the criteria are not so great as to disable use of the antenna for most purposes. The SWR performance exceeds even reasonable expectations. When weight reduction and simplified construction are added to the mix, the design becomes very attractive.

+

Perfecting the MININEC Model

If MININEC figures are more accurate than NEC-4 figures, it stands to reason that the design should be optimized for the MININEC system. Actually, the required changes in dimensions and spacing are quire small. The drivers required a bit of respacing from each other as well as from the reflector--and these moves set the director closer to the reflector--but only by a half inch. Changes in element lengths were equally small. +

The following tables, derived from AO, illustrate the changes and their consequences in modeled performance.

+ 
4-Element Wide-Band Yagi
+Free Space Symmetric       28.75 MHz              4 6060-T6 wires
+
+Parameter (Inches)       Revised Model            Original Model
+Reflector length              212.50                   212.00
+Driver 1 length               205.50                   205.00
+Driver 2 length               189.50                   189.00
+Director length               180.80                   181.00
+Spacing from Reflector
+Driver 1                       39.50                    40.50
+Driver 2                       43.50                    44.00
+Director                       95.50                    96.00
+
+28.000 MHz:   Impedance        52.7 - j 8.0            51.0 - j9.4
+              SWR              1.18                    1.20
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.4%                   99.4%
+              Forward Gain     6.90 dBi                6.93 dBi
+              F/B              18.53 dB                18.23 dB
+
+28.250 MHz:   Impedance        53.0 - j 8.9            51.7 - j 10.2
+              SWR              1.20                    1.22
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.4%                   99.4%
+              Forward Gain     6.87 dBi                6.90 dBi
+              F/B              20.69 dB                20.61 dB
+
+28.500 MHz:   Impedance        52.1 - j 8.3            51.2 - j 9.4
+              SWR              1.18                    1.21
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.3%                   99.3%
+              Forward Gain     6.88 dBi                6.91 dBi
+              F/B              23.09 dB                23.30 dB
+
+28.750 MHz:   Impedance        50.9 - j 6.3            50.5 - j 7.3
+              SWR              1.13                    1.16
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.3%                   99.3%
+              Forward Gain     6.93 dBi                6.96 dBi
+              F/B              26.06 dB                26.75 dB
+
+29.000 MHz:   Impedance        50.4 - j 3.6            50.8 - j 4.5
+              SWR              1.07                    1.10
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.2%                   99.2%
+              Forward Gain     7.02 dBi                7.04 dBi
+              F/B              28.49 dB                29.39 dB
+
+29.250 MHz:   Impedance        51.2 - j 1.4            52.7 - j2.4
+              SWR              1.04                    1.07
+              Wire Losses      0.04 dB                 0.04 dB
+              Efficiency       99.1%                   99.1%
+              Forward Gain     7.14 dBi                7.17 dBi
+              F/B              25.74 dB                25.60 dB
+
+29.500 MHz:   Impedance        52.9 - j 2.1            56.2 - j 3.5
+              SWR              1.07                    1.14
+              Wire Losses      0.05 dB                 0.05 dB
+              Efficiency       98.9%                   99.0%
+              Forward Gain     7.28 dBi                7.32 dBi
+              F/B              21.03 dB                20.57 dB
+
+29.750 MHz:   Impedance        51.4 - j 9.0            56.8 - j 12.8
+              SWR              1.20                    1.31
+              Wire Losses      0.06 dB                 0.06 dB
+              Efficiency       98.6%                   98.6%
+              Forward Gain     7.44 dBi                7.48 dBi
+              F/B              17.10 dB                16.57 dB
+
+30.000 MHz:   Impedance          36.5 - j 16.6         41.0 - j 24.5
+              SWR                 1.64                 1.76
+              Wire Losses         0.10 dB              0.10 dB
+              Efficiency         97.7%                 97.8%
+              Forward Gain        7.59 dBi             7.64 dBi
+              F/B                13.87 dB              13.29 dB
+

The revised model provides a more balanced SWR across the 10-meter amateur band with 9 Ohms or less capacitive reactance at the source and a variation of only 2.6 Ohms in the source resistance. The front-to-back ratios at the band edges are numerically better balanced at a maximum cost of 0.05 dB gain.

+

Will the differences actually make a difference? Not likely. However, the comparative figures may act as a guide to construction, giving some hint as to which element may need lengthening or shortening and which spacing may need slight adjustment.

+

Nevertheless, even though it falls short of the absolute design criteria, the wide band Yagi with open-sleeve coupled drivers is highly competitive with the 4-element LPDA. Both designs give us a short-boom (8') antenna that covers all of 10 meters with performance that is consistent with the performance of 3-element, 8'-boom Yagis over only half the band.

+

It seems that the design exercise, which I suspected might not be complete, really is not done after all. Even this work leaves some open questions. For example, can I save some weight by tapering the element diameters, using 0.5" and 0.375" tubing and not lose anything in performance? I'll bet that question alone will lead me to some others before I buy aluminum, plastic, and hardware.

+

Remember that I am not on a deadline. The inquiry is not driven by an upcoming contest or DXpedition. So I can take my time and explore all the nooks and crannies that show themselves along the way. The only major problem is that the paper output from gathering models and data already weighs as much as the proposed Yagi and is fast approaching the weight of the LPDA.
+

+
+ +

+
+

Updated 11-18-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Phase 7: Wide-Band Yagis: Element Diameter Questions

+

Go to LPDA Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpda7.html b/content/lpda/lpda7.html new file mode 100644 index 0000000..b0a19a5 --- /dev/null +++ b/content/lpda/lpda7.html @@ -0,0 +1,263 @@ + + + + + + A 10-Meter LPDA Phase 7: Wide-Band Yagis: Element Diameter Questions + + + +
+

A 10-Meter LPDA
+ Notes on a Work in Progress
+ Phase 7: Wide-Band Yagis: Element Diameter Questions

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

To leave behind the wide-band Yagi using open-sleeve coupled drivers with only a basic design would be incomplete. The antenna deserves to be interrogated with respect to some of the same questions we posed of the LPDA. Most of the relevant questions have to do with element diameter, and the answers may bring us full circle in a special way.

+
+ +
+

As a reference, the sketch above designates the parts of our wide-band Yagi design. Driver 1 is directly fed, while Driver 2 is open-sleeve coupled to Driver 1. The result is a wide band Yagi capable of covering all of 10 meters with performance that approaches the earlier 4-element 75-Ohm line LPDA. With respect to our initial specifications, free space gain is a tiny bit lower than 7 dBi at the lower end of the band and the front-to- back ratio does not quite reach 20 dB at the band edges. However, the savings in weight and construction complexity might well offset these minor deficiencies.

+

The Element Diameter Question

When exploring a monoband LPDA for 10 meters, I noticed that the diameter of the elements had a relatively large effect upon some of the performance predictions offered by modeling software. The effect was especially noticeable with respect to the free space gain curves of several antenna models. The next question is natural: does antenna element diameter have a significant effect on a wide-band Yagi designed to cover all of 10 meters? +

To check the degree to which element diameter might alter the Yagi performance, I changed from the initial 0.5" elements to 1" elements. This required changing virtually all of the element lengths and positions to achieve a model with essentially the same coverage and flat SWR curve. The results appear in the table below, which sets the 0.5" and 1.0" element models side by side. Once more, the modeling is done in MININEC (AO), because the close spacing of the 0.5" diameter drivers yields slightly erroneous reports in NEC-4.

+ 
4-Element Wide-Band Yagi
+Free Space Symmetric       28.75 MHz              4 6060-T6 wires
+
+Element Diameter (Inches)      0.5                      1.0
+Reflector length              212.50                   212.50
+Driver 1 length               205.50                   209.00
+Driver 2 length               189.50                   188.00
+Director length               180.80                   178.00
+Spacing from Reflector
+Driver 1                       39.50                    37.75
+Driver 2                       43.50                    44.75
+Director                       95.50                    95.75
+
+28.000 MHz:   Impedance        52.7 - j 8.0            48.4 - j 5.1
+              SWR              1.18                    1.11
+              Wire Losses      0.03 dB                 0.01 dB
+              Efficiency       99.4%                   99.7%
+              Forward Gain     6.90 dBi                6.99 dBi
+              F/B              18.53 dB                19.86 dB
+
+28.250 MHz:   Impedance        53.0 - j 8.9            47.7 - j 4.5
+              SWR              1.20                    1.11
+              Wire Losses      0.03 dB                 0.01 dB
+              Efficiency       99.4%                   99.7%
+              Forward Gain     6.87 dBi                6.99 dBi
+              F/B              20.69 dB                22.63 dB
+
+28.500 MHz:   Impedance        52.1 - j 8.3            46.4 - j 2.6
+              SWR              1.18                    1.10
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.3%                   99.6%
+              Forward Gain     6.88 dBi                7.02 dBi
+              F/B              23.09 dB                26.44 dB
+
+28.750 MHz:   Impedance        50.9 - j 6.3            45.2 + j 0.4
+              SWR              1.13                    1.11
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.3%                   99.6%
+              Forward Gain     6.93 dBi                7.08 dBi
+              F/B              26.06 dB                33.24 dB
+
+29.000 MHz:   Impedance        50.4 - j 3.6            44.8 + j 3.8
+              SWR              1.07                    1.15
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.2%                   99.6%
+              Forward Gain     7.02 dBi                7.17 dBi
+              F/B              28.49 dB                35.24 dB
+
+29.250 MHz:   Impedance        51.2 - j 1.4            45.5 + j6.8
+              SWR              1.04                    1.19
+              Wire Losses      0.04 dB                 0.02 dB
+              Efficiency       99.1%                   99.5%
+              Forward Gain     7.14 dBi                7.27 dBi
+              F/B              25.74 dB                26.27 dB
+
+29.500 MHz:   Impedance        52.9 - j 2.1            47.1 + j 7.6
+              SWR              1.07                    1.18
+              Wire Losses      0.05 dB                 0.02 dB
+              Efficiency       98.9%                   99.4%
+              Forward Gain     7.28 dBi                7.40 dBi
+              F/B              21.03 dB                21.23 dB
+
+29.750 MHz:   Impedance        51.4 - j 9.0            47.2 + j 3.6
+              SWR              1.20                    1.10
+              Wire Losses      0.06 dB                 0.03 dB
+              Efficiency       98.6%                   99.3%
+              Forward Gain     7.44 dBi                7.53 dBi
+              F/B              17.10 dB                17.73 dB
+
+30.000 MHz:   Impedance          36.5 - j 16.6         37.7 - j 3.5
+              SWR                 1.64                 1.34
+              Wire Losses         0.10 dB              0.05 dB
+              Efficiency         97.7%                 98.9%
+              Forward Gain        7.59 dBi             7.65 dBi
+              F/B                13.87 dB              15.07 dB
+

Although the element lengths do not require very large changes, the spacing of the drivers between the limits set by the 8' boom does change significantly. Driver 1 is 1.75" close to the reflector, while Driver 2 is 1.25" closer to the director in the 1.0" diameter model. The net spacing between driven elements increases by 3.0", which nearly doubles the spacing relative to the half-inch model. The most notable element length change is the increase in Driver 1, which was necessary to accommodate the spacing changes and still yield a satisfactory SWR curve and curves that parallel those for the smaller diameter model.

+

Although the essential data appears in the table, separating each category of information may provide further insight into the two models.

+
+ +
+

The gain curves for the two models show a small increase for the 1.0" model relative to the 0.5" model. The average increase across the band is about 0.11 dB, which is numerically noticeable, but not very significant operationally. Even this size increase may not be typical for all increments of difference one might choose for making the comparison. We shall return to this point when we later look at tapered-diameter elements.

+
+ +
+

For comparison, we may plot the gain curves of optimized 75-Ohm antenna transmission line 4-element LPDAs, using the 0.5" and the 1.0" element sizes. The curve above shows the results. Between the two element sizes, the average gain differential is about 0.18 dB, about one and two-thirds the difference for the Yagi (and, as we shall see, the Yagi figures may be artificially high). Although one case does not prove a general point, the results are indeed suggestive for monoband LPDAs: element diameter does have a noticeable impact on overall antenna gain across the limited passband of a monoband antenna.

+
+ +
+

With respect to the front-to-back ratio of a wide-band Yagi of the design we are exploring, the difference in element diameter has less of an impact at the band edges than it does on the peak front-to-back ratio (recorded here as the 180-degree ratio). The peak in the front-to-back ratio of the model using fatter elements, which occurs at about 29.85 MHz, would not in itself be a sufficient reason for selecting that model over the one using smaller elements.

+
+ +
+

The comparative 50-Ohm SWR curves for the two antennas permits us to put some factors into perspective. Within the 10 meter band from 28 to 29.7 MHz, both antennas provide SWR values no greater than 1.2:1, with climbing values above the upper band edge. In practical terms, neither antenna outperforms the other.

+

However, notice the differences in the undulations of the curves across the band. They reflect some of the less precise points of designing a wide-band Yagi using open-sleeve coupled drivers. Slightly different lengths and spacing chosen for the drivers, in their interactions with the reflector and director can produce differently shaped SWR curves for essentially the same gain and front-to-back figures. Since there is only one reflector and one director, each will favor a frequency region (at the low end for the reflector and at the upper end for the director), with some territory resting upon the balance of the two drivers together. Slight changes to any element can change the favored region of lowest SWR. These changes also tend to move the gain and front-to-back curves up and down the band, and usually the designer will compensate by changing the dimension of a different element to bring the curve back into the desired full-band coverage. The result will be some variance in the undulations of the SWR curve from one design to another, designs that achieve just about the same gain and front- to-back figures.

+

The upshot is that for the wide-band Yagi, element diameter has far less an impact on overall performance than it does for the monoband LPDA. While the LPDA seemed to benefit from the use of larger diameter elements, the Yagi shows only such marginal improvements as may be offset by the increase in weight of the larger elements.

+

Tapered-Diameter Elements

The use of tapered-diameter elements is a fairly standard feature of Yagi design. We know that tapered diameter elements will be longer than uniform diameter elements. That change alone might also require redesign of the antenna with respect to element spacing. Hence, it seemed wise to sample a reasonable diameter taper for the antenna. +

I selected 0.625" inner element sections, 72" long (or 36" either side of center). The ends are 0.5" diameter tubes. As expected, the shift to tapered-diameter elements required a total redesign of the antenna dimensions. The results, as modeled in MININEC (AO), appear in the table below.

+ 
4-Element Wide-Band Yagi
+Free Space Symmetric       28.75 MHz              4 6060-T6 wires
+
+Element Type                  Uniform             Tapered-Diameter*
+Element Diameter (Inches)      0.5                     0.625/0.5
+Reflector length              212.50                   215.50
+Driver 1 length               205.50                   207.20
+Driver 2 length               189.50                   191.80
+Director length               180.80                   182.60
+Spacing from Reflector
+Driver 1                       39.50                    37.75
+Driver 2                       43.50                    45.00
+Director                       95.50                    96.00
+(*Note:  0.625" portion = 72" centered)
+
+
+28.000 MHz:   Impedance        52.7 - j 8.0            52.3 - j 8.4
+              SWR              1.18                    1.19
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.4%                   99.5%
+              Forward Gain     6.90 dBi                6.95 dBi
+              F/B              18.53 dB                19.08 dB
+
+28.250 MHz:   Impedance        53.0 - j 8.9            52.4 - j 8.0
+              SWR              1.20                    1.18
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.4%                   99.5%
+              Forward Gain     6.87 dBi                6.94 dBi
+              F/B              20.69 dB                21.63 dB
+
+28.500 MHz:   Impedance        52.1 - j 8.3            51.3 - j 6.1
+              SWR              1.18                    1.13
+              Wire Losses      0.03 dB                 0.02 dB
+              Efficiency       99.3%                   99.4%
+              Forward Gain     6.88 dBi                6.96 dBi
+              F/B              23.09 dB                24.80 dB
+
+28.750 MHz:   Impedance        50.9 - j 6.3            49.9 - j 2.7
+              SWR              1.13                    1.06
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.3%                   99.4%
+              Forward Gain     6.93 dBi                7.02 dBi
+              F/B              26.06 dB                29.54 dB
+
+29.000 MHz:   Impedance        50.4 - j 3.6            49.1 + j 1.6
+              SWR              1.07                    1.04
+              Wire Losses      0.03 dB                 0.03 dB
+              Efficiency       99.2%                   99.4%
+              Forward Gain     7.02 dBi                7.11 dBi
+              F/B              28.49 dB                32.97 dB
+
+29.250 MHz:   Impedance        51.2 - j 1.4            49.5 + j6.1
+              SWR              1.04                    1.13
+              Wire Losses      0.04 dB                 0.03 dB
+              Efficiency       99.1%                   99.3%
+              Forward Gain     7.14 dBi                7.22 dBi
+              F/B              25.74 dB                26.59 dB
+
+29.500 MHz:   Impedance        52.9 - j 2.1            51.6 + j 9.2
+              SWR              1.07                    1.20
+              Wire Losses      0.05 dB                 0.04 dB
+              Efficiency       98.9%                   99.2%
+              Forward Gain     7.28 dBi                7.36 dBi
+              F/B              21.03 dB                21.38 dB
+
+29.750 MHz:   Impedance        51.4 - j 9.0            54.5 + j 7.2
+              SWR              1.20                    1.18
+              Wire Losses      0.06 dB                 0.05 dB
+              Efficiency       98.6%                   99.0%
+              Forward Gain     7.44 dBi                7.50 dBi
+              F/B              17.10 dB                17.69 dB
+
+30.000 MHz:   Impedance          36.5 - j 16.6         49.5 - j 3.0
+              SWR                 1.64                 1.06
+              Wire Losses         0.10 dB              0.07 dB
+              Efficiency         97.7%                 98.5%
+              Forward Gain        7.59 dBi             7.63 dBi
+              F/B                13.87 dB              14.86 dB
+

The increase in element lengths is about as expected. More noticeable is the change in driver spacing relative to the uniform 0.5" model, with Driver 1 moved toward the reflector and Driver 2 moved toward the director. In fact, the spacing (and to some degree, the element lengths) are closer to those required by the uniform 1.0" model. Once more, we can look at the data more closely by separating it into categories.

+
+ +
+

The gain curves are congruent, with the tapered model showing a slight increase in gain over the untapered model. The amount of the increase is operationally insignificant. However, the gain of the tapered-element model is also insignificantly different from the gain of the uniform 1.0" diameter model. Given the similarities of driver spacing between the tapered and fat element design, it is likely that the lower gain of the 0.5" is the more abberant result, stemming from the required closer spacing of drivers. (See the notes near the end on the SWR curve for NEC-4 for related findings.)

+
+ +
+

The front-to-back ratio curve of the tapered-diameter model has a more distinct peak than that of the uniform-diameter model. Because the net increase in element size is so small, the more likely source of the front- to-back peak is the alteration of the driver spacing. With spacing that is close to that used for the 1" model, the tapered-diameter model shows a peak that also resembles the one obtained for the larger diameter element model. As expected, band-edge performance is not greatly affected by the presence of the peak.

+
+ +
+

For the tapered-diameter element model, the SWR curve shows a value of 1.2:1 or less not only across the 10-meter band, but above 30 MHz as well. I described the design situation that yields undulations of various types. The new model has simply compressed the undulations for two peaks within the passband of the model. The other models used so far have had a single peak, with the second one trailing off beyond the band edge.

+
+ +
+

Regardless of slight peaks and valleys in the SWR curve, the tapered- diameter design appears to be a complete success within the overall limitations of the antenna configuration. The representative free space azimuth patterns (shown within the AO limit of two patterns overlaid) reveal well-behaved forward and rearward lobes that meet our standard expectations of Yagi designs.

+

Back to NEC-4

We began this design exercise in NEC-4 and transferred to MININEC because the very close-spaced drivers of the uniform-diameter 0.5" element model pressed the NEC-4 limits for yielding accurate results. However, in the process of redesigning the wide-band Yagi for both large element diameters and for tapered-diameter elements, the spacing between the drivers increased. In fact, it increased by almost double that of the original model and passed to the other side of the sensitive region in which NEC-4 over-reports gain. +

It seemed reasonable to transport the MININEC model back to NEC-4 (using EZNEC Pro) and see what might result by way of reports. The following graphs compare the MININEC numbers with those of NEC-4. Since NEC-4 is sensitive to tapered diameter elements to a small degree (but no where to the degree of NEC-2), I ran the model first with no Leeson correction factor. Then I reran the model invoking the Leeson corrections that transform tapered-diameter elements into substitute uniform-diameter elements with the same electrical properties. The results of invoking the correction factor will be coincide with those of using the same correction factors in NEC-2, since uniform-diameter elements yield the same results in both levels of NEC.

+
+ +
+

The gain curves are instructive. If the close spacing of the elements had any remnant affect on the gain report, it would show up in the corrected curve, since the Leeson correctives do not affect the close-spacing sensitivity of the program. However, the corrected curve for NEC-4 and the MININEC curve are coincident from one end of the passband to the other. The uncorrected NEC-4 curve shows slightly higher gain figures as a result of the still imperfect handling of tapered-diameter elements.

+

(This account is incomplete. It is possible, but unlikely, that the thinner uniform-diameter elements used in the Leeson corrections, which range from 0.538" to 0.55", might have a very slight positive affect in reducing the close-spacing sensitivity of uncorrected NEC-4 beyond the wider spacing used in the model. The net diameter difference of about 0.07" has a very low probability of showing any gain over-reportage on its own. However, to decisively establish this as fact would require one to separate the effects of element spacing completely from the effects of element diameter changes, which is not practical in this context.)

+
+ +
+

The front-to-back curves are insignificantly different. Although there might be a slight difference in the ultimate peak value, the curve indicates that most of the difference is due to a slight difference in reported frequency of the peak (as indicated by the changing slope of the lines leading to the reported peak value in the sampling). Nothing in these curves can suggest that any one modeling system is more authoritative than any other.

+
+ +
+

The 50-Ohm SWR curves for the three model runs are most interesting. The uncorrected NEC-4 curve most closely coincides with the MININEC curve. This raises the question of why the corrected NEC-4 curve departs from the others by a noticeable amount--even if the amount still yields a report of outstanding wide-band performance in this category of concern.

+

Part of the answer lies in the Leeson correctives themselves as they are applied to open-sleeve coupling models. The substitute elements produced by the corrective range in diameter from 0.538" to 0.55", with the Driver 1 having a diameter of 0.541" and Driver 2 having a diameter of 0.55". These diameters are smaller than the center 0.625" diameter of the 2 drivers. Although the Leeson correctives can capture the relatively correct source impedance at the low end of the band, when the directly-fed driver dominates, the source impedances reports by the corrective at the upper end of the band indicate a drop in source resistance, as we might well expect of thinner elements with the prescribed spacing. Although the amount of difference in coupling between the master and slave drivers is too small to materially affect the gain and front-to-back ratio figures, the impedances at element centers differ enough to show up in the source resistance and 50-Ohm SWR numbers. This is not fault of the Leeson correctives, since they were never designed to cover open-sleeve coupling situations.

+

One of the motivations for checking the performance of NEC-4 on the tapered-diameter model grew from a desire to check a large number of free space azimuth pattern simultaneously (AO is limited to 2).

+
+ +
+

Since we have established the general reliability of corrected NEC-4 with respect to gain and front-to-back ratio, the azimuth patterns collected in the above figure can be considered reliable guides to expectations you may have from the wide-band open-sleeve coupled Yagi.

+

So What Do You Get From All That Graphing?

First, you get a buildable model of a wide-band Yagi that will satisfactorily cover 10 meters with just about true 3-element 8' boom Yagi performance. The tapered-diameter model can be implemented in a straightforward manner with no great surprises. All of these models will not ease the need to tweak both the driver lengths and spacings, but they do provide some good guidance in what to expect from various moves you might make during field adjustment. +

Second, we have had a chance to compare Yagis and LPDAs with respect to the question of the influence of element diameter. Unless some contrary evidence emerges, the results tell me to expect much less difference in performance from Yagis using elements of different diameter than from LPDAs with the same range of variation. What we suspected early in this inquiry has received some further (but far from final) confirmation.

+

Third, we learned that the original 0.5" wide-band model of a Yagi for 10 meters was no fluke--that it can be replicated in a large range of material diameters and tapers with due attention to element length and spacing. The optimizing process may be a bit slower than for simple Yagis (which are amenable to automated processes), but results are assured. That factor alone is worth the time of investigation, because it converts question into confidence. One can now listen to the voice that whispers, "Build it. It will work."

+

However, that was the same voice I heard when I reached a similar point in looking at the monoband 4-element LPDA. Both appear to be highly promising designs that come as close as possible, each in its own way, to meeting the criteria set for this project.
+

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+ +

+
+

Updated 11-18-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to LPDA Index

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Go to Amateur Radio Page

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Topics: HF Upper, LPDA


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+

So You Want to Build Your Own LPDA
+ 2. 5 Strategies for Doctoring the Basic Design

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

In Part 1 of this series, we looked at the effects of varying Tau and Sigma (over a limited range of samples) and at some short-boom LPDAs. All of the designs used standard calculation techniques. In addition, each was assigned a 200-Ohm inter-element phasing line, according to general recommendations. Since our frequency range for the exercise is 7 to 15 MHz, we selected a standard 1" uniform diameter for every element of every design. The only concession we made to improvement was to decrease the lower design frequency from the 7 MHz operational limit to 6.8 MHz to ensure a reasonable gain at the low end of the passband.

+

In this part of the exercise, let's explore some of the means that might be used to improve the performance of a basic LPDA design. We shall explore each technique individually, rather than try from the start to develop an optimized design. Our goal will be to understand the likely amount and type of improvement that each technique offers. In practice, optimizing an LPDA design with all of the factors involves many iterations, each making a small adjustment in one or more of the possible improvement factors until one reaches a peak performance level or ends the process in exhaustion.

+

We should make each effort comparable, so that we can distinguish major advances from minor ones. One step in this direction is to select from the models in Part 1 a single design that might benefit from the efforts. My choice is model 8904, a 10-element LPDA that is 34.87' long with a Tau of 0.89 and a Sigma of 0.04. Fig. 1 provides the general outline.

+
+ +
+

For most of the efforts, the dimensions of this design will not change. It will retain throughout the same lengths with the same elements spacing (with one or two clearly announced exceptions). Hence, the following description will suffice for almost all of our work.

+ 
8904C                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .89/.04                           10-08-1999     09:18:15
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-442.80,  0.000         0.000,442.800,  0.000 2.85E+00  31
+2         70.848,-394.09,  0.000        70.848,394.092,  0.000 2.54E+00  27
+3        133.903,-350.74,  0.000       133.903,350.742,  0.000 2.26E+00  25
+4        190.021,-312.16,  0.000       190.021,312.160,  0.000 2.01E+00  23
+5        239.967,-277.82,  0.000       239.967,277.823,  0.000 1.79E+00  19
+6        284.419,-247.26,  0.000       284.419,247.262,  0.000 1.59E+00  17
+7        323.981,-220.06,  0.000       323.981,220.063,  0.000 1.42E+00  15
+8        359.191,-195.86,  0.000       359.191,195.856,  0.000 1.26E+00  13
+9        390.528,-174.31,  0.000       390.528,174.312,  0.000 1.12E+00  13
+10       418.418,-155.14,  0.000       418.418,155.138,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    10 / 50.00   ( 10 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+

You may note that the element diameters are not uniform. That will be one of our exercises. However, it is easy enough to substitute any desired element diameter for any element in the set (including our standard 1" diameter) All models use aluminum elements.

+

Element Diameter

Since standard LPDA design uses a very low element length-to-diameter ratio as an assumption underlying the calculation of elements lengths, increasing the diameter of the elements should effect some improvement in performance. And it does. +

One strategy for increasing element diameter is simply to increase all element diameters by the same amount. Since our original designs specified 1" diameter elements, we might check performance with 2" diameter elements. We are here more interested in the degree of improvement we might obtain than with the question of how easily we might implement the change. Elements with an average diameter of 2" at 7 MHz are heavy under any design, and they present stress loads to the central boom of the design.

+

A second strategy we might try is to taper the element diameters. Although we could start with an arbitrary scheme, one effective way to ensure that elements have the same length-to-diameter ratio throughout the design is to use the value of Tau. If we set a diameter for the shortest elements, we may simply increase the diameter of each longer element by the inverse of Tau (sometimes called k or Kappa). The inverse of 0.89 is 1.1235955. . .. If we limit the precision to 2 decimal places, the tapered elements have the diameters shown in the model description above. The length-to-diameter ratio is a little over 310:1.

+

These are enough changes to make at one time, so let's explore the results.

+
+ +
+

Fig. 2 shows the free-space gain in dBi of the three models with 1", 2", and tapered-diameter elements, respectively. Note that the curves generally track each other, coming together in the 12-12.5 MHz region of the passband. In general, the fatter elements add between 0.25 and 0.5 dB gain to the array. Except for the top two MHz of the passband, the tapered-element design general tracks the constant 2" design in gain performance.

+
+ +
+

The front-to-back performance of the three models appears in Fig. 3. Once more, the 3 curves track each other with one major exception. In the 12 to 13.5 MHz range, the 1" diameter model shows a continuous decrease in front- to-back ratio, while the two designs with larger elements show a single sharp dip. Both of the larger-diameter models add about 1.5 dB to the front-to-back ratio at the low end of the passband, where it is naturally the lowest.

+
+ +
The VSWR curves in Fig. 4 tell us that each of these designs is capable of achieving an SWR level of below 2:1 throughout the passband of the antenna. The 2" diameter model uses a 75-Ohm reference, while the 1" and tapered diameter models use a 90-Ohm reference. Hence, among the designs, there may be differences in the way in which we match the arrays to 50-Ohm feedlines. Otherwise, in this performance category, there is nothing to choose among the arrays. +

One of the reasons for selecting model 8904 as our subject was the existence of the gain and front-to-back ratio dip. The dip is not fatal to array operation, as the SWR curves remain within limits in the 13-14 MHz region of the passband. Moreover, the decrease in value does not extend below the lowest values for the entire passband. But it is still a problem if one of the design goals is the most even performance we can attain across the entire passband.

+

Once More, The Stub

We noted briefly in Part 1 that a transmission line stub connected to the center of the longest element in the array can often eliminate performance aberrations in some 1-octave LPDA designs. Let's explore this concept a little further. However, first, we must select a single design from the three we have so far examined, lest our graphs become excessively cluttered. My choice is the tapered-element diameter model matching the description given earlier. I could make up a set of reasons, but since we have no specific operational goals (other than smooth performance across the passband at the highest levels we can achieve), none of them would be superior to reasons we might use to select one of the other models. At this stage of design improvement, it is simply as good as either of the other models. +

All three models are subject to harmonic operation of the rear-most elements within a critical frequency region of the passband. Where that mode of operation occurs most drastically is indicated by the frequency difference between the lowest gain and the lowest front-to-back ratio. We should look in the vicinity of about 13.25 MHz.

+
+ +
+

Fig. 5 shows the current distribution (and relative magnitudes) for the stubless tapered-diameter array at 13.25 MHz. Note that only the forward 5 elements show a single gain peak. The rear 5 elements all show the double hump of harmonic operation. (If the words were not so long, we could label the difference as that between dromedary and bactrian operation.) In LPDA operation, suppression of harmonic operation of elements is normally desired as a means to smooth the performance across the passband. So let's suppress it.

+

For the 1-octave LPDA, a simple shorted transmission line stub is sufficient to alter the impedances of the longest elements in the critical frequency region so that harmonic operation of the element does not occur. With a stub, element currents remain too low for the pattern of the array to be altered from its norm at the critical frequency region. Almost any stub length of moderate proportions will do the job. Generally, higher impedance stubs are preferred to lower impedance stubs, since they can be shorter for the same reactance level. However, some lengths are better than others.

+

To find the right stub length in a model simply means trying various lengths and watching the performance figures over the critical region of the passband. In my trials for 8904 with the tapered diameter elements, I examined lengths ranging from 36" down to 3" while checking performance at half-MHz intervals from 12.5 to 15 MHz. Here, in tabular form, is a portion of the survey. The figures shown are free-space gain in dBi and the front-to-back ratio in dB.

+ 
Freq                     8904C Stub length in inches
+(MHz)          36"                 18"                 6"
+12.5      6.09 / 15.54        6.08 / 15.65        6.08 / 15.75
+13.0      5.99 / 15.44        6.00 / 15.35        6.00 / 15.27
+13.5      5.95 / 15.53        5.97 / 15.35        5.99 / 15.11
+14.0      5.97 / 15.57        6.00 / 15.45        6.01 / 15.11
+14.5      6.01 / 15.16        6.03 / 15.75        6.03 / 15.95
+15.0      6.02 / 13.63        6.01 / 15.89        6.00 / 16.33
+

There is nothing dramatic in the differences among stub lengths, although the shortest stub length shown does, on average, promise to outperform longer lengths. Nevertheless, field trimming the stub, however it might be implemented, is far from a tedious job, since any approximation would be indistinguishable in operation from any other.

+

The dramatic changes in performance come from comparing the same model, both with and without the stub.

+
+ +
+

Fig. 6 provides the free-space gain curves for the stubless and stubbed models of 8904. If we say that the gain from 13 to 15 MHz now makes a smooth curve, we have only begun to notice significant differences in the curves. The addition of the stub has also altered the number and frequency placement of gain peaks across the passband. With the stub, we find peaks at 9, 11, and 14.5 MHz. Without the stub, we noticed peaks at 7.5, 9.5, 11.5, and 13.5 MHz. The 2 MHz interval between peaks in the stubless model has been replaced with peaks showing far less of an obvious pattern.

+

In exchange for the smoothness of the curve, we lost some interesting gain peaks. In a 1/2-scale version of the antenna, gain would be less at both 21 and 28 MHz. Nevertheless, given the variables of construction, we might find that the gain nulls might just move from the modeled positions to less desirable ones. Hence, a smooth curve is a major goal wherever it can be achieved.

+
+ +
+

The front-to-back ratio curves in Fig. 7 also show the same curve displacement that we saw in the gain curves. However, note that gain and front-to-back ratio do not peak for most designs at the same frequencies. When we spot unnaturally large peaks on the same or adjacent check frequencies, we should examine the design for harmonic operation of some elements.

+

The stubbed model has peaks at 8, 9.5, and 12 MHz, with a possible peak at 15 MHz. The placement is about a half MHz higher than the corresponding gain peaks. In the unstubbed model, peaks occur at 7.5, 9, 11, 13, and 15 MHz, in almost all cases, about a half-MHz below the gain-peak frequencies. There are further refinements to the development of these curves that the profile intervals cannot display, but this much should suffice to show the power of a stub to move performance peaks and valleys around, while smoothing the curve overall. I suppose we should note in passing that the deep front-to-back dip at 13.5 MHz is missing from the stubbed curve.

+
+ +
+

The SWR curves, shown in Fig. 8, provide evidence that an optimized stub for an LPDA array has minimal effect on the overall SWR performance of the antenna. As we might expect, the stub does alter the source resistance and reactance at the lowest frequencies, where peak current magnitudes involve the longest elements--where the stub is attached. A second region of source impedance change is in the critical frequency region. Outside of these two regions, the SWR curves for the stubbed and unstubbed models track each other closely.

+
+ +
+

For the record, we might record what is now happening at 13.25 MHz, the frequency at which we examined the current distribution and magnitude on the elements of the 8904C LPDA array. As Fig. 9 shows, the addition of the 6" stub brings the rear 5 elements into relative quiescence so that the forward 5 elements take almost complete control of the antenna pattern. And while we are recording for the record, Fig. 10 shows the azimuth pattern of the stubbed array at 13.25 MHz. The pattern is perfectly ordinary for an array of this size and all of the patterns at all of the frequencies look almost identical. That is why we added the stub.

+
+ +
+

The Inter-Element Phasing Line Characteristic Impedance

Another way in which designers improve the performance of standard LPDA designs is to reduce the inter-element phase line characteristic impedance. The recommended standard design value is 200 Ohms. This high value tends to reduce the erratic behavior occasioned by the harmonic operation of rearward elements, although in shorter-boom designs it does not always succeed--as we just saw with our stub exercise. +

Many LPDA designs--for example, those intended for use on the amateur band only--do not care about having smooth performance curves across a given pass band. Instead, they wish to optimize performance within specific passband segments. Since we can control wayward performance in critical frequency regions with a stub, we can often obtain good ham band performance, but at the expense of performance outside those primary frequencies.

+

Lowering the inter-element phase line characteristic impedance can increase the harmonic operation of the rearward elements. Therefore, there is a certain "danger" in designing with a lower phase line impedance. Nonetheless, the appeal of more gain and possibly a higher front-to-back ratio makes this strategy appeal to designers.

+

Our prime model, 8904, is actually not a good candidate for this use. The performance increase, while notable on a graph, will not be very operationally significant. LPDAs with higher values of Tau tend to show better results. Nonetheless, rather than confuse matters by introducing wholly new designs, let's see what happens with old 8904.

+

We shall begin with the initial model that used 1" elements throughout.

+
+ +
+

See Fig. 11. If we reduce the phase line impedance to 150 Ohms, the 1" model acquires a little free-space gain at most frequencies, along with a gain peak at 13 MHz, rather than the original dip. There are a few places in the spectrum where the original 200-Ohm model surpasses the 150-Ohm model in gain, such as 8.5, 10.5, and above 13.5 MHz. In fact, for all of the comparisons in this section, we shall discover that with standard design element lengths and spacings, the lower the phase line impedance, the lower the upper-end gain.

+
+ +
+

Before we cheer too loudly over the gain peaks in Fig. 11, we should examine Fig. 12, the graph of front-to-back ratios for the 200-Ohm and 150- Ohm versions of 8904. Although we can see some peak values for the 150-Ohm version marginally above those for the 200-Ohm version, we can hardly miss the deep depression in the front-to-back ratio from 12 to 14 MHz. Not only is the reduction of the ratio much deeper with our lower impedance line, it is also displaced to a lower frequency. The situation illustrates graphically the possibility in LPDA design of exacerbating undesirable conditions by lowering the phase line impedance.

+

Other measures that we take to improve performance may also contribute to problems in obtaining smooth performance across the passband when we add in the reduction in phase line impedance. Let's look at what happens when we taper the element diameters, as we did in version C of 8904.

+
+ +
+

The free-space gain curves of Fig. 13 compare 200-Ohm and 150-Ohm versions of the tapered-element-diameter version of our basic LPDA design. What we find in these graphs is--at the gain levels appropriate to the design change--essentially the same as with the basic 8904 model. Higher gain peaks are accompanied by deeper valleys. Moreover, pay especial attention to the frequency region between 12.5 and 13 MHz. One might get the impression that only a mild dip in gain occurs at 12.5 MHz, followed by a rise on the way to 13 MHz. In fact, as a detailed (0.1 MHz) sweep might show, the dip goes much deeper before it starts back upward toward the mark it reaches at 13 MHz.

+
+ +
+

The front-to-back curves in Fig. 14 tend to replicate the results we obtained earlier. 13 MHz in this profile is a disaster of harmonic operation of the rearward elements. For the remainder of the curve, the lower impedance phase line does yield on average a slightly higher front-to- back ratio.

+

These notes are, of course, predicated on the design goal of the exercise to obtain smooth performance of the highest attainable levels across the passband. Therefore, the gain and front-to-back ratio problems in the critical frequency region for this design have great weight. If one only wished to operate on 40, 30, and 20 meters, performance in the critical frequency region would likely be of little or no concern.

+

In this section we are bypassing concern for the VSWR curves, basically because for each model, there is a reference impedance that will yield values under 2:1 throughout to pass band. For 8904-200, the reference value is 90 Ohms, while for 8904-150, the value is 65 Ohms. For 8904C-200, the reference value is 90 Ohms, while for 8904C-150, the value is 75 Ohms. The trend is obvious: as we lower the phaseline impedance, the reference source impedance decreases.

+

What we have not shown--basically because graphing the phenomenon clearly is difficult--is the relative behavior of resistance and reactance as they compose the impedance. For the most part within the design passband, when the resistance reaches either its uppermost value or lowermost value, the reactance tends to be very low. At the median value of resistance, the reactance tends to be the highest. Hence, for a given reference impedance taken at about the median resistance value, the SWR level tends to be stable.

+

With very high values of Tau and optimum Sigma, the resistance value may change only by a few Ohms across the best operating range of the array. Likewise, the reactance will also vary little, yielding a very low SWR relative to a reference impedance. But even the longest LPDAs are not immune to changes in impedance, especially at the upper end of the passband.

+

Short-boom LPDAs tend to show the widest variation in both resistance and reactance. For example, the basic 8904 model with 1" diameter elements showed a resistance as high as 149 Ohms and as low as 51 Ohms. These are not the absolute peak values, but only the high and low that appeared within the boundaries of our limited profiles. In fact, the two values appeared at 14 and 15 MHz, with highs and lows hitting 120 and 60 Ohms, respectively, at lower frequencies in the passband.

+

The reactance range for 8904, as recorded in the profile, was +36 Ohms inductive and -52 Ohms capacitive. Capacitive reactance entries outnumbered inductive reactance entries, suggesting that this particular design has a median value that is inherently capacitively reactive.

+

To serve as a contrast, let me note once more the 434' LPDA design that covers 7 to 15 MHz with a Tau of .96 and a Sigma of 0.18 (optimal by calculation). The resistance rises above 69 Ohms only once, at 14.5 MHz, where it reaches 74 Ohms. The lowest profiled values is 57 Ohms, for a maximum range of 17 Ohms. If we exclude the 15 MHz reactance value of -33 Ohms, then the range of values across the rest of the passband runs from a low of j-4 Ohms to a high of j-17 Ohms, a mere 13 Ohms. And the reactance was capacitive throughout the profiled range. Such performance is largely unavailable to the short-boom LPDA designer.

+

Before we depart the strategy of reducing phase line impedance to improve performance of a design with a set value of Tau and Sigma, let's look briefly at the model 8904C with a stub. This time, we shall compare three phase line impedances: 200, 150, and 100 Ohms. As with the other exercises in reducing phase line impedance, the reference impedance for the 2:1 SWR curve also goes down. The 200-Ohm model uses a reference impedance of 90 Ohms. The 150-Ohm version uses 75 Ohms, while the 100-Ohm model uses 55 Ohms (but might have used 50 Ohms as well).

+
+ +
+

Fig. 15 presents the free-space gain curves of the three variant models. The 100-Ohm model has the highest average gain of the group, although its gain falls at the upper end of the passband. The front-to-back ratio curves in Fig. 16 also show the general, but slight, superiority of the 100-Ohm model.

+
+ +
+

The general equality of values from an operational standpoint raises the question of why one would move to the 100-Ohm phase line value. There is more than one reason. First, the 100-Ohm model can be fed directly with 50-Ohm feedline, without a matching device. Second, phase lines in the vicinity of 100 Ohms can be fabricated from square metal stock, thus allowing the phase line also to serve as the boom to support the antenna elements. From a structural perspective, then, there are good reasons for lowering the phase line impedance even when the performance improvements are marginal or non-existent.

+

However, a lower phase line value requires a shorter stub than a higher phase line value if we are to control the critical frequency region of the passband. The 200-Ohm model used a 6" stub, while the 150-Ohm version used a 3" stub, both 600 Ohm lines. The 100-Ohm model used a 1" stub, essentially a short circuit jumper at the rear of the double boom phase line. Despite tailoring the stub length to the phase line impedance value, the stub proved less effective in reducing harmonic operation of the rear elements as the phase line impedance decreased. Fig. 17 shows the remnant harmonic current distribution and magnitude for the 100-Ohm model at 13.25 MHz.

+
+ +
+

The design goal with lower impedance phase lines is rarely to wholly eliminate harmonic operation of the rear elements. Rather, the aim is to reduce such currents to levels that permit relatively normal performance levels relative to the overall curves, as well as azimuth patterns that can be called "well-behaved." The current distribution and magnitude on the rear elements of Fig. 17, while higher than for the 200-Ohm model at the same frequency, still do not significantly distort the main pattern.

+

Nevertheless, the overall gain pattern of Fig. 15 might be considered a bit distressing from the design perspective. The gain falls off at both ends of the passband, with the lower end of the band a special concern. Is there a way to elevate the gain at the band edges without losing significant amounts of gain in the mid-passband region?

+

Extending the Curves: Circular Tau

One seemingly obvious route toward extending the gain and front-to-back curves for better performance at the passband edges is simply to redesign the LPDA. We may choose the same Tau and Sigma values (in our examples, 0.89 and 0.04), and then select lower and higher frequency limits. The graphic curves we have seen so far might suggest that 6.4 and 17 MHz might make better limiting frequencies. +

The resulting LPDA appears in the following description.

+ 
8904EX.EZ                      EZNEC/4  ver. 2.5
+
+6.4-17 MHz .89/.04                           10-09-1999     07:41:09
+
+Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-470.47,  0.000         0.000,470.475,  0.000 1.00E+00  39
+2         75.276,-418.72,  0.000        75.276,418.723,  0.000 1.00E+00  35
+3        142.272,-372.66,  0.000       142.272,372.663,  0.000 1.00E+00  31
+4        201.898,-331.67,  0.000       201.898,331.670,  0.000 1.00E+00  27
+5        254.965,-295.19,  0.000       254.965,295.187,  0.000 1.00E+00  25
+6        302.195,-262.72,  0.000       302.195,262.716,  0.000 1.00E+00  23
+7        344.229,-233.82,  0.000       344.229,233.817,  0.000 1.00E+00  19
+8        381.640,-208.10,  0.000       381.640,208.097,  0.000 1.00E+00  17
+9        414.936,-185.21,  0.000       414.936,185.207,  0.000 1.00E+00  15
+10       444.569,-164.83,  0.000       444.569,164.834,  0.000 1.00E+00  13
+11       470.942,-146.70,  0.000       470.942,146.702,  0.000 1.00E+00  13
+12       494.415,-130.56,  0.000       494.415,130.565,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    12 / 50.00   ( 12 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12   1/50.0  (  1/50.0)  Short ckt (Short ck)    6.000 in   600.0  1.00
+
+Ground type is Free Space
+

Immediately apparent is the fact that the new LPDA design with which we hope to achieve performance extensions is about 6.3' longer than our standard model (41.2' vs. 34.9'), and it has two more elements. It is in every way a larger antenna. Now we can ask what we gain for our trouble.

+

To set the comparison on fair ground, both model will use our original 1" diameter elements and the standard 200-Ohm inter-element phase line. Hence, the standard of comparison will be the antenna described at the beginning of this part. To smooth the curves, a 6" 600-Ohm stub has been installed at the center of the longest element of each antenna. Since we have established that virtually all of the models with which we are dealing have decent SWR profiles across the 7 to 15 MHz passband, we shall omit these curves. The original 10-element model is referenced to 90 Ohms, while the new extended model is referenced to 100 Ohms. With this in mind, we can look at the free-space gain and front-to-back curves in search on improvements.

+
+ +
+

Fig. 18 shows us what we gained in the battle for gain: only a little. The extended LPDA improves the low-end gain by under 0.2 dB. There are higher gain peaks along the curve, especially in the 12.5 to 14 MHz region, but the gain is actually lower than that of the original model at the upper passband limit.

+
+ +
+

Our most consistent gain is in front-to-back ratio, as shown in Fig. 19. Except for the significant improvement in the 13 to 14.5 MHz region, the increase tends to average about 1 dB. It is dubious whether this improvement would be operationally significant--and whether it would justify the added complexity of the resulting design.

+

If we recall that out goal was to improve performance at the passband edges rather than seeking an overall improvement, we have gained very little from the first effort to improve performance. We need a different strategy.

+

One commercial strategy appears to be varying the Tau used for element lengths while preserving a constant Tau for element spacing. There are proprietary algorithms used for such designs which may go under the name of "circular" design. I have also seen an interesting spot application of the principle by Eric Gustafson, N7CL. The general principle is sound, and might even be applied also to element spacing, although I have not tried it there.

+

I have redesigned the original 8904 model (with stub) according to the circular-Tau principle, so let's examine the new element lengths as a basis for explaining the procedure and discovering why it might be called circular.

+ 
8906CIR.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .89/.04                           10-09-1999     10:43:05
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-424.00,  0.000         0.000,424.000,  0.000 1.00E+00  31
+2         70.848,-386.30,  0.000        70.848,386.300,  0.000 1.00E+00  27
+3        133.903,-349.00,  0.000       133.903,349.000,  0.000 1.00E+00  25
+4        190.021,-312.16,  0.000       190.021,312.160,  0.000 1.00E+00  23
+5        239.967,-277.82,  0.000       239.967,277.823,  0.000 1.00E+00  19
+6        284.419,-247.26,  0.000       284.419,247.262,  0.000 1.00E+00  17
+7        323.981,-221.00,  0.000       323.981,221.000,  0.000 1.00E+00  15
+8        359.191,-198.00,  0.000       359.191,198.000,  0.000 1.00E+00  13
+9        390.528,-181.00,  0.000       390.528,181.000,  0.000 1.00E+00  13
+10       418.418,-170.00,  0.000       418.418,170.000,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    10 / 50.00   ( 10 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10   1/50.0  (  1/50.0)  Short ckt (Short ck)    6.000 in   600.0  1.00
+
+Ground type is Free Space
+

In this sample application, I chose to preserve the lengths of elements 4, 5, and 6. These element lengths are related by a Tau of 0.89. The rear three elements and forward 4 elements use a variable Tau that might roughly approximate a curve described by a circle.

+

Elements 3 and 7 increase the value of Tau by about 0.05% (multiply 0.89 by 1.005). The 7th element length is thus about 0.894 times the 6th element length. For the rearward elements, we use the inverse of Tau, or about 1.118 to obtain the new length of element 3 from element 4. Then, we increase Tau once more, this time by a slightly greater amount, say 1%. Hence, we take our new value of Tau and multiply by 1.01 to get about 0.903. The 8th element length is about 0.903 the length of the new 7th element, while the 2nd element is about 1.107 times the length of the new 3rd element. The next Tau value can be about 1.5% or so the values just established, or about 0.917, and so on until we run out of elements in either direction, or until we reach about 0.96 for Tau.

+

The elements shown use rounded lengths for our experiment, since we are only testing the principle of circular Tau. Moreover, the shortening of the rearmost element was halted just at the point where the SWR curve (referenced to 95 Ohms) remained within the 2:1 limit without changing the 6" stub. This called for a longer than ideal length for the rear element. You may experiment with changing the stub to effect further improvements while retaining a usable SWR profile. In fact, you may also wish to apply any of the other strategies we have so far discussed to our circular Tau model. Remember that we are illustrating techniques only. We are not striving for a final design to build.

+
+ +
+

However, circularizing Tau brings us dramatically toward that goal, as witnessed by Fig. 20. The gain at both passband edges shows a dramatic upturn: about 0.5 dB at the low end and 0.3 dB at the upper end. The overall curve is slightly stronger than that of the original model, but the chief improvement is more consistent gain across the entire spectrum.

+
+ +
+

The improved front-to-back curve, shown in Fig. 21, would also be a marginal improvement were it not for passband edge improvements. At 7 MHz, the improvement is nearly 3 dB, an amount that approaches operational notice. Unlike the extended range LPDA design, these improvements add nothing to the length of the array, the number of elements, or the weight. Hence, pursuit of this strategy--perhaps in conjunction with larger element diameters, stub refinements, and a lower inter-element phaseline characteristic impedance to obtain a direct 50-Ohm match across the passband--might be a useful exercise for anyone wishing to perfect old 8904.

+

The Variable Impedance Phase Line

One of the phenomena attached to standard LPDA design is the drift in source resistance as we approach the upper frequency limit of the array. The profiles do not all show this phenomenon clearly because we are taking spot checks at 0.5 MHz points. Hence, the 15 MHz source impedance may or may not fall nicely within the general curves. Nonetheless, the gradual skewing of source impedance is a general tendency. +

There is a technique that will overcome this tendency. Let's specify that the design will use the standard 200-Ohm inter-element phase line as a basic factor. This impedance may not offer the highest gain at every point in the passband, but it helps to suppress any instabilities in pattern shape occasioned by harmonic operation of longer elements.

+

Instead of bringing the 200-Ohm line all the way to the shortest element, let's taper the characteristic impedance until it reaches a lower value at the feedline junction. The exact lower limit of the tapered Zo will depend on the natural reference impedance for the antenna, but something between 80 and 150 Ohms will do for most designs. We need not taper the impedance for the entire length of the LPDA, but only for about the forward-most 15% of the elements. Since this value amounts to about 1.5 elements for our standard demonstration model, it is inconvenient to demonstrate the technique on a small LPDA without introducing some modeling techniques that would obscure the point.

+

However, I have mentioned, in this part and the last, a long LPDA (434') that uses 27 elements with a Tau of 0.96 (maximum recommended value) and a Sigma of 0.18 (optimum value). This is a convenient model to use for the demonstration for several reasons. First, it has many elements, and the tapered phaseline can be implemented in small steps that simulate the taper. Second, the design, created by standard calculations, has some other features of interest.

+
+ +
+

Fig. 22 shows the outline of the antenna. Remember that the elements are within the same length range used by those of the short LPDA we have been studying. Thus, the scaled sketch gives a true picture of the antenna's overall length.

+

Of great interest is the current distribution and relative magnitude shown in the graphic. Of first note is the element showing the highest current in this 7 MHz view. As we increase Tau, we increase the number of elements and, with it, the inter-element coupling. Hence, we should for any high- Tau design also see the low-frequency high-current element move forward in the array. In this array, we might remove the rear-most element with little ill effect.

+

Of second note is the number of very active elements that affect the pattern formation of the array at even the lowest frequency. For all but one element, the current levels are non-negligible. We should expect from this array a good gain, but more especially, an astounding front-to-back ratio, regardless of whether we are concerned with 180-degree, worst-case, or front-to-rear ratios.

+
+ +
+

Fig. 23 confirms our suspicions. More dramatic than the 11.5 dBi free- space gain of the array is the truly insignificant radiation to the rear. It should be no mystery why many commercial and government shortwave stations have gone to sizable LPDA arrays and given up many of the older wire arrays that once covered hillsides.

+

In case you wish to operate a (duly-licensed) multi-frequency shortwave station between 7 and 15 MHz, here is the model description, using 1" diameter elements and requiring no stub.

+ 
9618.EZ                      EZNEC/4  ver. 2.5
+
+.96/.18 6.8-15 MHz 27 el                     10-09-1999     15:57:49
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  31
+2        318.816,-425.09,  0.000       318.816,425.088,  0.000 1.00E+00  31
+3        624.879,-408.08,  0.000       624.879,408.084,  0.000 1.00E+00  29
+4        918.700,-391.76,  0.000       918.700,391.761,  0.000 1.00E+00  29
+5        1200.77,-376.09,  0.000       1200.77,376.091,  0.000 1.00E+00  27
+6        1471.55,-361.05,  0.000       1471.55,361.047,  0.000 1.00E+00  25
+7        1731.51,-346.61,  0.000       1731.51,346.605,  0.000 1.00E+00  25
+8        1981.06,-332.74,  0.000       1981.06,332.741,  0.000 1.00E+00  23
+9        2220.64,-319.43,  0.000       2220.64,319.431,  0.000 1.00E+00  23
+10       2450.63,-306.65,  0.000       2450.63,306.654,  0.000 1.00E+00  23
+11       2671.42,-294.39,  0.000       2671.42,294.388,  0.000 1.00E+00  21
+12       2883.38,-282.61,  0.000       2883.38,282.612,  0.000 1.00E+00  21
+13       3086.86,-271.31,  0.000       3086.86,271.308,  0.000 1.00E+00  19
+14       3282.20,-260.46,  0.000       3282.20,260.456,  0.000 1.00E+00  19
+15       3469.73,-250.04,  0.000       3469.73,250.037,  0.000 1.00E+00  17
+16       3649.75,-240.04,  0.000       3649.75,240.036,  0.000 1.00E+00  17
+17       3822.58,-230.43,  0.000       3822.58,230.434,  0.000 1.00E+00  17
+18       3988.49,-221.22,  0.000       3988.49,221.217,  0.000 1.00E+00  15
+19       4147.77,-212.37,  0.000       4147.77,212.368,  0.000 1.00E+00  15
+20       4300.67,-203.87,  0.000       4300.67,203.874,  0.000 1.00E+00  15
+21       4447.46,-195.72,  0.000       4447.46,195.719,  0.000 1.00E+00  15
+22       4588.38,-187.89,  0.000       4588.38,187.890,  0.000 1.00E+00  13
+23       4723.66,-180.37,  0.000       4723.66,180.374,  0.000 1.00E+00  13
+24       4853.53,-173.16,  0.000       4853.53,173.159,  0.000 1.00E+00  13
+25       4978.21,-166.23,  0.000       4978.21,166.233,  0.000 1.00E+00  11
+26       5097.89,-159.58,  0.000       5097.89,159.584,  0.000 1.00E+00  11
+27       5212.79,-153.20,  0.000       5212.79,153.200,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    27 / 50.00   ( 27 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13  13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14  14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15  15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16  16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17  17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18  18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19  19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20  20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  200.0  1.00  R
+21  21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  200.0  1.00  R
+22  22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist  175.0  1.00  R
+23  23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist  150.0  1.00  R
+24  24/50.0  ( 24/50.0)   25/50.0  ( 25/50.0)  Actual dist  125.0  1.00  R
+25  25/50.0  ( 25/50.0)   26/50.0  ( 26/50.0)  Actual dist  100.0  1.00  R
+26  26/50.0  ( 26/50.0)   27/50.0  ( 27/50.0)  Actual dist   80.0  1.00  R
+
+Ground type is Free Space
+

The model description actually shows the modifications in transmission lines 22-26 for the tapered impedance technique. Returning all of the lines to 200 Ohms would show the basic model. Note that the impedance increases in 20-25 Ohm steps from a feedpoint junction value of 80 Ohms up to the standard value for the remainder of the line. The impedance- tapering technique does have some useful effects on the performance of the array at the upper end of the passband.

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In Fig. 24, we can see the smoothing of the gain curve above 12.5 MHz. What we lose in the 13.5 MHz peak of the original we more than make up in the improved gain at 14.5 and 15 MHz. The front-to-back curve in Fig. 25 shows improvements for the tapered-impedance line model, although there are sharper peaks. Only at 13 MHz does the original model show a higher front- to-back ratio, but I suspect that adding a stub to the original might smooth its curve in this region. However, I did not add a 6" stub to the 434' array. Nor did I apply a circular Tau correction to the forward elements, although such a trial might show whether the value of Tau can be usefully raised above 0.96 to improve upper frequency performance. Implementing this last possible strategy might have obscured the effects of the tapered-impedance phaseline.

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+ +
+

We noted earlier that this high-Tau array has extended low-frequency capability. In fact, the array performance does not decrease significantly until below 6.5 MHz, and it is still usable at 6 MHz, where the gain is above 10 dBi and the front-to-back ratio above 20 dB. Therefore, the following SWR curves encompass the range of 6 to 16 MHz.

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+ +
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The upper portion of Fig. 26 shows the 150-Ohm SWR curve for the model with a uniform 200-Ohm phase line. For a very large portion of the passband, the 150-Ohm reference is clearly the natural impedance of the antenna. However, at the upper end of the spectrum, the resistive component of the impedance descends toward 80 Ohms, while the reactance climbs to exceed 100 Ohms at the passband limit.

+

The lower curve uses a 50-Ohm reference. The entire curve is well below the 2:1 limit we set somewhat arbitrarily as the goal. By the use of the tapered-impedance phase line, we electrically simplify the array by eliminating the need for a wide-band matching device at the feedpoint, should we choose to feed the array with standard 50-Ohm coaxial cable.

+

Conclusion--For Now

We have surveyed 5 different strategies for improving LPDA performance. These may not be all of the ways, but they are the main ones. Remember that our goals in this exercise were not directly ham-band related. We did not strive to achieve peak performance at specific frequencies. Instead, we strove for the smoothest performance across the passband at the highest levels we could obtain. +

Moreover, we have only demonstrated the techniques. We did not seek to arrive at a final design that we might build. The techniques can be combined to yield a final design, but just which combination and to what degree each technique might be used would form a set of design decisions based on having a clear set of operational goals. Without such goals, but only our general guideline, any claim that one of the design results within the demonstration was "best" would be foolish.

+

Moreover, we chose a basic model that clearly could stand improvement. Old 8904 is a modest LPDA design, not necessarily the best, even for its boom length. Other combinations of Tau and Sigma that yield the same boom length might prove initially superior--or more amenable to some of the improvement techniques. 8904 was simply handy because it permitted the techniques to be demonstrated.

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Likewise, the frequency range was semi-arbitrary, since it avoided any possible controversy that might surround comparing LPDAs that have been built for the upper HF region. Nevertheless, the models used are easily scaled by a factor of 2 (including element diameter) for the 14 to 30 MHz range. Only the losses of the aluminum elements will shift any of the modeled results--and any shift will be slight.

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With all of these qualifications, I still hope that sorting out the various techniques available to improve the performance of basic LPDA designs is useful. The exercise may go some distance toward improving our understanding of LPDAs in all their major variations.

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Updated 10-11-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to LPDA Index

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Topics: HF Upper, LPDA


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So You Want to Build Your Own LPDA
+ 1. 11.5 Models To Start You Off

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+
+

L. B. Cebik, W4RNL

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This note starts in the middle of things. It assumes you know what a log periodic dipole array (LPDA) is. It also assumes that you have a handbook of some sort to provide you with background on the equations one uses to design an LPDA--or that you have a copy of some software with which to design LPDAs, such as LPCAD by Roger Cox, WB0DGF.

+

We shall use only two LPDA terms, but we shall use them continuously. So here are a couple of basic statements (spelling out the Greek letters for ease of encoding this in HTML):

+

1. Tau: the ratio of an element to the next longer one, and the ratio of a space between two elements and the next wider space. For standard LPDA designs, Tau is not varied, so any two or three elements can be used to find it.

+

2. Sigma: the initial spacing constant, equal to the distance between two elements divided by twice the length of the longer element.

+

Tau is sometimes thought of as the basic determiner of array gain: the higher the value of Tau, the higher the array gain. For any value of Tau applied to a given frequency range, calculations will yield a certain number of elements and their lengths. Large values of Tau (0.93-0.96) will yield large numbers of elements, while low values of Tau produce arrays with relatively fewer elements.

+

For a given value of Tau, Sigma determines how long the array will be. The higher the value of Sigma, the longer the array. There is an ideal value of Sigma for any value of Tau, but that value is normally 2-3 times any value hams might use, since the resulting array can easily be over 100' long at mid-HF range. So hams use lesser values to get shorter arrays.

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In this exercise, I want to look at three questions:

+

1. How precisely does the value of Tau affect the performance of an LPDA? There are some graphic curves in the literature, but they apply to a generalized gain value calculated for an entire array. Some judicious modeling in NEC might reveal how the array performance is affected across the entire passband assigned to a design.

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2. What precisely is the effect of Sigma on LPDA performance? Suppose we keep a constant value of Tau and then see--with reasonably well-constructed models--what the resulting effect will be on gain, front-to-back ratio, and feedpoint impedance as we vary Sigma. There are notices in the literature that tell us that the gain will decrease if we reduce Sigma and that we should not use values below 0.03. But hams do use values down to 0.02. How much do we lose (or gain, if we move in the other direction) for each increment of Sigma in a typical case?

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3. Hams love short-boom antennas, hoping to gain the world with 1-pound antennas. What performance expectations should we have of short-boom LPDAs? How do Tau and Sigma interrelate to yield array sizes that are practical and that we can term "good performers?" Although this exercise will not an exhaustive study, it will start a process by which some combinations can be recommended as promising and others excluded as excessively deficient.

+

How shall I proceed? Most hams who use (or discuss) LPDAs work with designs that cover 14 to 30 MHz--or thereabouts. Because of the number of commercial and handbook designs available, working with that frequency range can be distracting. So I chose to work with the range of 7 to 15 MHz and to design independently a collection of models with which to work. In this way, I could focus on the questions of what Tau and Sigma are doing to the array and its performance without worrying about whether I was treading on the toes of another designer or a manufacturer.

+

Of course, one can always scale the models by a factor of two--including the element diameter--to come up with a 14-30 MHz model that does exactly the same thing in free-space modeling. My outputs for this exercise consist of profiles of performance across the 7-15 MHz range at 0.5 MHz intervals. My object is to look at overall performance. Anyone interested in the models for more serious purposes would have to examine more closely the frequency bands of interest. Nonetheless, the 7 and 7.5 MHz results will give clues to 40 meter operation, while 10 MHz is close to 30 meters. 14 and 14.5 MHz give an overview of probable 20 meter performance. But, again, a design of interest needs a frequency sweep in small intervals across each ham band.

+

Likewise, anyone contemplating scaling the model can get a usable impression by looking at 7 MHz for 20 meters, 9 MHz for 17, 10.5 MHz for 15, 12.5 MHz for 12, and 14-14.5 MHz for 10 meters. It pays in such cases to look at the values on either side of the target frequency to see trends that may be hopeful or worrisome.

+

All of the LPDAs in this initial exercise use element diameters of 1" for all elements. This value corresponds roughly to the equivalent uniform diameter that would emerge from common tapered element practice in this frequency range. Moreover, it scales to 0.5" in the next frequency range upward, which is also roughly the uniform element diameter emergent from tapered element schedules used from 20-10 meters. For consistency in this initial exercise, all LPDA designs use a 200-Ohm inter-element phasing line. An appendix to this item lists the 11 (plus one modified extra) models used in this very basic study.

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I have bypassed picturing each LPDA model, since they are all alike, varying only in the number of elements and the spacing between them. Instead, prepare yourself for some colorful graphs, a few having some confusing zigzags.

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What Does Tau Do for My LPDA?

For a given value of Sigma--which sets the initial spacing between the rear two elements--the array length and number of elements will vary with the value of Tau. The recommended values of Tau are usually given as extending from 0.80 to 0.96. Suppose we survey values between 0.87 and 0.95 in intervals of 0.02. +

A complete survey at fair increments would also develop a cross matrix of values of Sigma between 0.03 and about 0.05, the most common range for amateur LPDAs. However, in this short exercise, we can only sample a single value. So let's arbitrarily pick 0.04 as falling in the middle of the range. With these selections of values, we obtain the follow array of arrays.

+ 
Tau       No.       Array length        Scaled length       Model name
+          of El.     (feet)              for 14-30
+0.85       7          24.52'                 12.3'               8504
+0.87       9          30.51'                 15.3'               8704
+0.89      10          34.87'                 17.5'               8904
+0.91      12          42.35'                 21.2'               9104
+0.93      16          55.94'                 28.0'               9304
+0.95      22          77.87'                 39.0'               9504
+

As you can see, there is a code in the model filenames, with the value of Tau appearing first, followed by the value of Sigma. This practice will be followed throughout the exercise for ease of correlating the models in the appendix to the work at hand. Because calculations must work to an integral number of elements, the taper of the elements and the precise spacing between the first two elements will vary slightly from model to model.

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Fig. 2 shows the modeled gain values. The first thing to notice is that the higher the value of Tau, the higher the average gain of the array. However, some incremental increases appear to have greater affects on gain than others. Once Tau is greater than about 0.90, the gain difference per 0.02 change in Tau is about the same: about 0.5 dB on average. Moreover, the curves for values of Tau above 0.90 are quite well behaved.

+

Values of Tau below 0.90 (for a Sigma of 0.04) show two significant phenomena. First, the gain values at the lower end of the passband are more significantly lower than the peak value for the curve. Second, values at the upper end of the passband are subject to sudden erratic changes that become worse as the value of Tau decreases. We shall have further notes on both these phenomena at various places along the way in this exercise. For now, let us note that the degree of erratic change at both ends of the gain curve does correlate roughly to the number of elements in the array.

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For all the curves, the gain tends to decrease toward the upper end of the passband relative to the peak value along the curve. What these 1-octave curves cannot show--in part because of the large interval between readings- -is that the gain and other properties tend to move in waves with peaks and nulls. The topmost curves for the highest values of Tau tend to indicate this wave-like movement most clearly.

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In Fig. 3, we have the 180-degree front-to-back curves for the 6 arrays. In a general way, the level of front-to-back ratio is a function of the gain at any particular place along the curves. Gain values below 5 dBi (free-space) rarely achieve a 10 dB ratio, while gain values above or close to 8 dBi are capable of front-to-back ratios of 30+ dB. In general, these high front-to-back ratios are not simply dimples in a broader front-to-rear lobe set. Rather, they represent reductions in the entire radiation pattern to the rear quadrants, as shown in Fig. 2A.

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As you progress to the right in Fig. 3, you will note the same sort of erratic behavior of models with lower values of Tau. It is important to distinguish this behavior from the general trend toward reduced value in front-to-back ratios that accompanies similar gain trends for the models with the highest values of Tau. We may also note that with a Sigma of 0.04, we do not achieve a consistent front-to-back ratio in excess of 20 dB until a Tau value of .93.

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The curves for SWR in Fig. 4 form a confusing medley that requires good patience to sort. With increasing frequency, both the resistive and reactive components of the feedpoint impedance become more erratic, relative to general trends lower in the passband. Both resistance and reactance excursions show much wider limits. Hence, the selection of a reference impedance for taking the curve becomes tricky at best.

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The lower values of Tau tend to show impedance excursions throughout the passband that require a higher reference impedance to derive curves in which the values surpass 2:1 at as few places as possible. In contrast, the higher values of Tau tend to yield flatter curves at the 75-Ohm reference level--again, with a 0.04 Sigma value. These curves are of greatest importance if one is interested in using the entire antenna passband. However, the SWR problem for lower values of Tau (or for shorter arrays with fewer elements) can be overcome if one is interested in only selected portions of the passband--as would be the case for purely amateur radio applications.

+

Before we depart these curves for a constant Sigma and variable Tau, let's look once more at the gain curves in Fig. 2. Why do the band edges tend to show lower gain values (and usually lower front-to-back ratios) than the mid-region of the passband? Part of the answer appears in Fig. 5.

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At 10 MHz for model 9304 (16 elements), there are at least 5 elements with high current levels, with several elements forward of this group having moderate current levels. Elements to the rear have lower and descending values. In essence, every element in an LPDA contributes to the pattern formation, and the number of elements with a significant current level is far higher than general LPDA gossip usually allows.

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At 7 MHz, there are once more 5 elements with the highest current levels, as well as elements with some current forward of that group. However, there is no element with significant current behind the group of 5. In a large array, such as 9304, the drop of gain at the low end of the passband is small. But, in arrays with only a small number of elements, the problem of low-end gain becomes much greater. The problem of "low-end" gain would be even worse had all of the models in this exercise not been designed with a lower frequency limit of 6.8 MHz, about 3% below the operational lowest frequency. Even though standard LPDA design set the longest element at a frequency below the operationally selected low frequency, additional margins are necessary for adequate performance unless the design uses a relatively high number of elements.

+

At the high end of the passband, normal design procedure calculates the shortest element for a frequency 1.3 times the upper operating frequency. However, even this margin cannot fully compensate for the number of elements with moderate current levels at 10 MHz. The 15 MHz current distribution shows 6 elements with high levels, with elements to the rear having only at modest current levels. Three of the 6 high-current elements have current levels that we might associate with Yagi directors--although the function of the elements of the two antenna types differs. Missing are elements forward of the group that have moderate current levels--gradually reducing the gain at the upper frequencies of the passband.

+

For each of the problems we have so far noted, there are compensating techniques. However, we shall reserve mention of them for a future exercise.

+

What Does Sigma Do for My LPDA?

For a given Tau, the array length will vary in direct proportion to the value of Sigma. Hence, an array with a Sigma of 0.035 will be half as long as one with a Sigma of 0.07, if the value of Tau is the same. However, the array will have the same number of elements. +

To see what Sigma values might mean for performance, I chose an arbitrary value of Tau: 0.93. Actually, this value is not totally arbitrary. It is in the upper range of values. Hence, the value of Sigma is likely to have a significant effect on antenna parameters, if it has any effect at all. For the design range of 6.8 to 15 MHz, the resulting LPDAs all have 16 elements.

+

As noted earlier, I chose to set the lower frequency limit of the array design at 6.8 MHz rather than at the lowest operating frequency of 7.0 MHz. The result is an antenna whose performance comes nearly "up to speed" by the 7 MHz mark--unless the design has an inherently slow rise due to overall design factors.

+

Likewise, the antenna lengths produced by a Tau of 0.93 are not wholly outside of construction range, even in the 7-15 MHz range. Here are the array lengths for LPDA with a Tau of 0.93 and values of Sigma between 0.6 and 0.2:

+ 
Sigma          Array length (feet)      Scaled length for 14-30  Model name
+0.06                83.92'                   42'                 9306
+0.05                69.93'                   35'                 9305
+0.04                55.94'                   28'                 9304
+0.03                41.92'                   21'                 9303
+0.02                27.97'                   14'                 9302
+

Although 84' is somewhat long for amateur construction, its scaled counterpart for 14-30 MHz is well within ham capabilities.

+
+ +
+

In Fig. 6, we can clearly see the "wave" motion of free-space gain values across the passband, especially for Sigma values from 0.04 upward. With a Tau as high as 0.93, the curves show much less tendency toward erratic values. Moreover, except for the lowest value of Sigma, the average gain increase for every Sigma increase of 0.01 is about 0.5 dB. The relative evenness of the gain increase with increase in the value of Sigma stands in contrast to the curve in Fig. 2. There, the gain increase itself appears to become larger as we increase Tau arithmetically. Because the curves are functions of complex geometric properties of the antenna structure-- including the individual elements lengths and spacings--a more precise quantification of the relationship would involve many other variables.

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As a point of reference, model 9304 appears in the graphs for both the constant-Tau and the constant-Sigma graphs. Using this reference, we might note that the curve for model 9306 in the constant-Tau graph is roughly comparable to the curve for model 9504 in the constant-Sigma graph. The "2-point" differential in both models relative to 9304 should not go unnoticed. However, 9504 has 22 elements on a 77' boom, while 9304 has 16 elements on an 84' boom. Additional elements can go some ways toward smoothing curves and reducing the rate of higher-frequency gain decrease. Model 9505--not shown here--with a Tau of .95 and a Sigma of 0.05 shows higher gain yet than either of the two high-end models noted here.

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At the other end of the scale, model 9302 is interesting, despite the fact that the Sigma value falls below recommended levels. This 14' long array shows a relatively smooth gain curve, with little sign of erratic behavior, owing to the relative high value of Tau involved. The front-to-back curve in Fig. 7 shows those values to be equally well-behaved. However, 16 elements is normally more than short-boom LPDA designers desire.

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+ +
+

Like the gain curve, the front-to-back curve for the highest performing models in Fig. 7 shows a rapid decrease at the upper end of the passband. Arrays with a Sigma of 0.04 or higher (for a Tau of 0.93) show an average front-to-back ratio of better than 20 dB.

+

Interestingly, the highest performing antenna models show the most variability in front-to-back ratio. This fact stems from the shapes taken by the rearward lobes as we change frequency and other antenna characteristics. At some frequencies, the rear lobes will look like the "bowtie" of Fig. 2A. At other frequencies, the lobe will be a small "bell," which decreases the front-to-back ratio without changing the amount of energy radiated rearward. In general, one may mentally smooth all front-to-back ratio curves in excess of 30 dB without significant distortion to actual antenna performance.

+

Some designers believe that the second element length at the lowest operating frequency should be near resonance. This theory is incomplete, since all of the elements--place for place--in this series of models are the same length. Yet the transition from 7 to 7.5 MHz in the gain curve is upward in 4 models and downward in 2. Much more consistent is the front- to-back pattern, which shows a downward turn in all models from 7 to 7.5 MHz, with a subsequent upward turn. Only the spacing of the elements has changed in this sequence.

+
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The SWR curves in Fig. 8 for the collection of LPDA designs show the usual morass of twists. All are referenced to 75 Ohms in this case for a number of reasons. Most important is the fact that as one increases the value of Sigma, using a 200-Ohm inter-element phase line, the "natural" reference impedance as we increase the value of Tau should be higher--something closer to 100 Ohms. The higher level would reduce the SWR values of these curves and better suit the arrays to the use of a wide-band 2:1 matching device for a 50-Ohm coax main feedline.

+

Nonetheless, all of the higher-Tau curves fall tamely within a 1.8:1 75-Ohm SWR level. Only the lower two values of Sigma result in values that exceed 2:1, and for model 9303, only at 15 MHz. In contrast is Fig. 4, the SWR curve for the constant-Sigma, variable-Tau exercise, where a number of models show values in excess of 1.8:1 when referenced to an optimized level. All of those models have Tau values of 0.91 or less, suggesting that perhaps higher Tau values tend to level SWR excursions.

+

Once more, model 9304, with a boom length of 56' for the 7-15 MHz range, marks a certain breaking point. LPDA arrays with Tau values of at least 0.93 AND Sigma values of at least 0.3 tend to be the most stable in almost all performance categories without any need for compensatory actions to improve the performance of the design. However, 56' (or 28' in the 20-10 meters version) is a fairly sizable array. Many hams are looking for short-booms and high performance.

+

What Should I Expect From My Short-Boom LPDA?

It is not possible to answer our third question exhaustively, but some sort of suggestive answer may be possible. I have gathered together the models we have so-far explored with lengths of 35' or less. I added to it another "stray design" with a 37' length. (Translated by a factor of 2, the upper HF boom length would be under 20' for all of these models.) Here are the particulars for the short-boom LPDA designs. + 
Model     Length    No. of Elements     Tau       Sigma
+8504      24.52'          7             0.85      0.06
+9302      27.97'         16             0.93      0.02
+8904      34.87'         10             0.89      0.04
+8506      36.77'          7             0.89      0.06
+

In the graphs to follow, there is also a variant of model 8504 that we shall discuss after some more general notes on these models.

+
+ +
+

In Fig. 9 are the free-space gain curves for the models in this group. Note that they fall into two general groups. 9302, 8904, and 8506 all have very comparable gain curves, with a maximum variation of about 0.25 dB. Hence, there is little to choose among them. 9302 has the shortest boom of the lot, but also requires a higher number of elements than any other model.

+

The two versions of model 8504 have lesser gain, although the curves in the main are congruent with those of the higher-gain group. The precipitous drop in gain of the basic 8504 model at 14 MHz is corrected in the model called 8504s. 8504 is noteworthy for having the shortest length of all of the models.

+
+ +
+

Boom length makes a difference to the front-to-back ratio as well as to gain. In Fig. 10, we can identify a 14 MHz drop in front-to-back ratio for 8504. Note, however, that the drop is preceded by an erratic rise in front-to-back ratio at 13.5 MHz. This phenomenon is not unusual: erratic performance is often forecast by an unnatural rise in performance at a slightly lower frequency.

+

The same generic type of forecast is offered to model 8506 by the drop in front-to-back ratio at 12 MHz, followed by a notable, but only slightly better value at 12.5 MHz. The anomaly in the performance of model 8506 is at 12.5 MHz with the sudden peak in gain--not a very large peak, but noticeable in relationship to the general trend in the curve. A similar glitch in the smooth curves occurs with model 8904 with a front-to-back warning at 13 MHz and further drop at 13.5 MHz: watch the gain curve for this model from 12.5 to 13.5 MHz.

+

These exceptions to smooth curves are common for short-boom LPDAs. Otherwise, the curves for front-to-back ratios again divide themselves between those for 8504 and for the longer-boom designs.

+
+ +
+

The SWR curves, set out in Fig. 11, will also show some of the same anomalies, even though they are each matched to an optimized reference impedance. With a 200-Ohm inter-element phase line, it is almost impossible to achieve a curve with values under 2:1 at the antenna feedpoint for the entirety of the passband--without using some compensatory measures or using only selected portions of the passband.

+
+ +
+

One of the models in the group is a "sleeper." That is, it has a reasonable 90-Ohm SWR curve with no value higher than 1.9. The SWR curve for model 8904 appears in Fig. 12 with the curve for 9302 as a contrast. These two antennas exhibit the best gain and front-to-back curves of the group, but 9302--with its very low value for Sigma and its 16 elements-- would still be a more difficult antenna to match to a coaxial cable. It is more likely that 8904 would work well into 50-Ohm coax with an intervening 2:1 broadband impedance matching device.

+

However, let's not give up on the shortest boom model, 8504, before trying to fix the anomalies in all of its curves. The critical frequency for this antenna is 14 MHz.

+
+ +
+

In Fig. 13, we can see the problematical azimuth pattern, as well as its source. In every other well-behaved current distribution curve, we saw only one current peak per wire, whatever the frequency within the passband and whatever the wire length. However, with 8504, the rearmost wires are operating in a true harmonic mode, with double peaks of current. These double peaks radiate both forward and rearward, widening the forward lobe and producing very significant rearward radiation. In this short-boom design with only 7 elements, the inter-element phase line is not terminated properly to prevent this mode of operation. Note also that forward-most element carries the highest current level.

+

The solution to the problem, known almost as long as LPDAs have been designed, is to change the termination of the rear-most element by adding a shorted stub. In model 8504s, a 36", 600-Ohm stub has been added to the rear of the model. The exact value is not critical, and further tweaking is certainly possible. The results of adding this stub are visible in all of the short-boom graphs and in Fig. 14.

+
+ +
+

The array's gain and front-to-back ratio have been returned to normal, relative to curves for LPDAs with Tau and Sigma values in the ballpark of those for model 8504. Why this happens appears in the current distribution curve. The stub prevents the rear-most elements from operating in a harmonic mode by changing the element source impedances. In fact, the SWR for the array goes down between 13.5 and 14.5 MHz, relative to the uncorrected version. Moreover, the second most forward element now shows the highest current level, just where the peak should be for an array of this size. The array has been saved for valuable use--if operating needs call for an LPDA of this small size and for the modest gain and front-to- back characteristics it offers.

+

More?

The use of a stub to change the operating characteristics of an LPDA over part of its frequency range is but one of a number of ways in which LPDA designers find higher performance than the levels offered by the basic models. Among other techniques we might try are the following: +

1. Changing some of the design criteria.

+

2. Changing the inter-element phase line impedance.

+

3. Varying Tau and/or Sigma along the array length.

+

4. Changing the element diameters.

+

Some of these measure are easy to implement, but others require a good bit of fundamental redesign. Since this note is already too long, we shall likely have to work up another to cover them--as soon as I finish the complete cross-matrix of models with Tau values from 0.85 to 0.95 (interval 0.02) and Sigma values from 0.02 to 0.06 (interval 0.01). Remember that we have only sampled the field, and hence, any conclusions can only be very tentative so far.

+

Incidentally, there is a model LPDA for the 7-15 MHz range with a gain at 7 MHz of 11.5 dBi and a gain at 14.5 of 10.3 dBi, all with a feedpoint impedance across the range that will match either 50 or 75 Ohms with smoothness and ease. Unfortunately, the antenna's 27 elements require 434 feet.

+
+

Appendix: Some LPDA Model Descriptions

+
+ 
9504.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .95/.04                           10-06-1999     09:10:48
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  33
+2           70.848,-420.66,  0.000        70.848,420.660,  0.000 1.00E+00  31
+3          138.154,-399.63,  0.000       138.154,399.627,  0.000 1.00E+00  29
+4          202.094,-379.65,  0.000       202.094,379.646,  0.000 1.00E+00  27
+5          262.837,-360.66,  0.000       262.837,360.663,  0.000 1.00E+00  27
+6          320.543,-342.63,  0.000       320.543,342.630,  0.000 1.00E+00  25
+7          375.364,-325.50,  0.000       375.364,325.499,  0.000 1.00E+00  23
+8          427.444,-309.22,  0.000       427.444,309.224,  0.000 1.00E+00  23
+9          476.920,-293.76,  0.000       476.920,293.763,  0.000 1.00E+00  21
+10         523.922,-279.07,  0.000       523.922,279.074,  0.000 1.00E+00  21
+11         568.574,-265.12,  0.000       568.574,265.121,  0.000 1.00E+00  19
+12         610.993,-251.86,  0.000       610.993,251.865,  0.000 1.00E+00  19
+13         651.291,-239.27,  0.000       651.291,239.271,  0.000 1.00E+00  17
+14         689.575,-227.31,  0.000       689.575,227.308,  0.000 1.00E+00  17
+15         725.944,-215.94,  0.000       725.944,215.942,  0.000 1.00E+00  15
+16         760.495,-205.15,  0.000       760.495,205.145,  0.000 1.00E+00  15
+17         793.318,-194.89,  0.000       793.318,194.888,  0.000 1.00E+00  15
+18         824.500,-185.14,  0.000       824.500,185.144,  0.000 1.00E+00  13
+19         854.123,-175.89,  0.000       854.123,175.887,  0.000 1.00E+00  13
+20         882.265,-167.09,  0.000       882.265,167.092,  0.000 1.00E+00  13
+21         909.000,-158.74,  0.000       909.000,158.738,  0.000 1.00E+00  11
+22         934.398,-150.80,  0.000       934.398,150.801,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    22 / 50.00   ( 22 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  200.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  200.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  200.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  200.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  200.0  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9104.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .91/.04                           10-06-1999     09:06:32
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  31
+2           70.848,-402.95,  0.000        70.848,402.948,  0.000 1.00E+00  29
+3          135.320,-366.68,  0.000       135.320,366.683,  0.000 1.00E+00  25
+4          193.989,-333.68,  0.000       193.989,333.681,  0.000 1.00E+00  23
+5          247.378,-303.65,  0.000       247.378,303.650,  0.000 1.00E+00  21
+6          295.962,-276.32,  0.000       295.962,276.321,  0.000 1.00E+00  19
+7          340.173,-251.45,  0.000       340.173,251.452,  0.000 1.00E+00  17
+8          380.406,-228.82,  0.000       380.406,228.822,  0.000 1.00E+00  17
+9          417.017,-208.23,  0.000       417.017,208.228,  0.000 1.00E+00  15
+10         450.334,-189.49,  0.000       450.334,189.487,  0.000 1.00E+00  13
+11         480.652,-172.43,  0.000       480.652,172.434,  0.000 1.00E+00  13
+12         508.241,-156.91,  0.000       508.241,156.915,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    12 / 50.00   ( 12 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8704.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 .87/.04\                              10-06-1999     09:05:47
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  33
+2           70.848,-385.24,  0.000        70.848,385.236,  0.000 1.00E+00  29
+3          132.486,-335.16,  0.000       132.486,335.155,  0.000 1.00E+00  25
+4          186.111,-291.59,  0.000       186.111,291.585,  0.000 1.00E+00  23
+5          232.764,-253.68,  0.000       232.764,253.679,  0.000 1.00E+00  19
+6          273.353,-220.70,  0.000       273.353,220.701,  0.000 1.00E+00  17
+7          308.665,-192.01,  0.000       308.665,192.010,  0.000 1.00E+00  15
+8          339.387,-167.05,  0.000       339.387,167.048,  0.000 1.00E+00  13
+9          366.114,-145.33,  0.000       366.114,145.332,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     9 / 50.00   (  9 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9306.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz 16 el .93/.06                     10-05-1999     11:28:11
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  27
+2          106.272,-411.80,  0.000       106.272,411.804,  0.000 1.00E+00  27
+3          205.105,-382.98,  0.000       205.105,382.978,  0.000 1.00E+00  25
+4          297.020,-356.17,  0.000       297.020,356.169,  0.000 1.00E+00  23
+5          382.500,-331.24,  0.000       382.500,331.237,  0.000 1.00E+00  21
+6          461.997,-308.05,  0.000       461.997,308.051,  0.000 1.00E+00  21
+7          535.929,-286.49,  0.000       535.929,286.487,  0.000 1.00E+00  19
+8          604.686,-266.43,  0.000       604.686,266.433,  0.000 1.00E+00  19
+9          668.630,-247.78,  0.000       668.630,247.783,  0.000 1.00E+00  17
+10         728.098,-230.44,  0.000       728.098,230.438,  0.000 1.00E+00  15
+11         783.403,-214.31,  0.000       783.403,214.307,  0.000 1.00E+00  15
+12         834.837,-199.31,  0.000       834.837,199.306,  0.000 1.00E+00  15
+13         882.670,-185.35,  0.000       882.670,185.354,  0.000 1.00E+00  13
+14         927.156,-172.38,  0.000       927.156,172.380,  0.000 1.00E+00  13
+15         968.527,-160.31,  0.000       968.527,160.313,  0.000 1.00E+00  11
+16         1007.00,-149.09,  0.000       1007.00,149.091,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    16 / 50.00   ( 16 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9305.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz 16 el .93/.05                     10-05-1999     11:27:38
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  27
+2           88.560,-411.80,  0.000        88.560,411.804,  0.000 1.00E+00  27
+3          170.921,-382.98,  0.000       170.921,382.978,  0.000 1.00E+00  25
+4          247.516,-356.17,  0.000       247.516,356.169,  0.000 1.00E+00  23
+5          318.750,-331.24,  0.000       318.750,331.237,  0.000 1.00E+00  21
+6          384.998,-308.05,  0.000       384.998,308.051,  0.000 1.00E+00  21
+7          446.608,-286.49,  0.000       446.608,286.487,  0.000 1.00E+00  19
+8          503.905,-266.43,  0.000       503.905,266.433,  0.000 1.00E+00  19
+9          557.192,-247.78,  0.000       557.192,247.783,  0.000 1.00E+00  17
+10         606.748,-230.44,  0.000       606.748,230.438,  0.000 1.00E+00  15
+11         652.836,-214.31,  0.000       652.836,214.307,  0.000 1.00E+00  15
+12         695.698,-199.31,  0.000       695.698,199.306,  0.000 1.00E+00  15
+13         735.559,-185.35,  0.000       735.559,185.354,  0.000 1.00E+00  13
+14         772.630,-172.38,  0.000       772.630,172.380,  0.000 1.00E+00  13
+15         807.106,-160.31,  0.000       807.106,160.313,  0.000 1.00E+00  11
+16         839.168,-149.09,  0.000       839.168,149.091,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    16 / 50.00   ( 16 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9304.EZ                      EZNEC/4  ver. 2.5
+
+.93/.04 6.88-15 MHz                          10-05-1999     11:27:02
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  27
+2           70.848,-411.80,  0.000        70.848,411.804,  0.000 1.00E+00  27
+3          136.737,-382.98,  0.000       136.737,382.978,  0.000 1.00E+00  25
+4          198.013,-356.17,  0.000       198.013,356.169,  0.000 1.00E+00  23
+5          255.000,-331.24,  0.000       255.000,331.237,  0.000 1.00E+00  21
+6          307.998,-308.05,  0.000       307.998,308.051,  0.000 1.00E+00  21
+7          357.286,-286.49,  0.000       357.286,286.487,  0.000 1.00E+00  19
+8          403.124,-266.43,  0.000       403.124,266.433,  0.000 1.00E+00  19
+9          445.754,-247.78,  0.000       445.754,247.783,  0.000 1.00E+00  17
+10         485.399,-230.44,  0.000       485.399,230.438,  0.000 1.00E+00  15
+11         522.269,-214.31,  0.000       522.269,214.307,  0.000 1.00E+00  15
+12         556.558,-199.31,  0.000       556.558,199.306,  0.000 1.00E+00  15
+13         588.447,-185.35,  0.000       588.447,185.354,  0.000 1.00E+00  13
+14         618.104,-172.38,  0.000       618.104,172.380,  0.000 1.00E+00  13
+15         645.684,-160.31,  0.000       645.684,160.313,  0.000 1.00E+00  11
+16         671.334,-149.09,  0.000       671.334,149.091,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    16 / 50.00   ( 16 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9303.EZ                      EZNEC/4  ver. 2.5
+
+.98/.03 6.8-15 MHz                           10-05-1999     11:26:29
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  27
+2           53.136,-411.80,  0.000        53.136,411.804,  0.000 1.00E+00  27
+3          102.552,-382.98,  0.000       102.552,382.978,  0.000 1.00E+00  25
+4          148.510,-356.17,  0.000       148.510,356.169,  0.000 1.00E+00  23
+5          191.250,-331.24,  0.000       191.250,331.237,  0.000 1.00E+00  21
+6          230.999,-308.05,  0.000       230.999,308.051,  0.000 1.00E+00  21
+7          267.965,-286.49,  0.000       267.965,286.487,  0.000 1.00E+00  19
+8          302.343,-266.43,  0.000       302.343,266.433,  0.000 1.00E+00  19
+9          334.315,-247.78,  0.000       334.315,247.783,  0.000 1.00E+00  17
+10         364.049,-230.44,  0.000       364.049,230.438,  0.000 1.00E+00  15
+11         391.702,-214.31,  0.000       391.702,214.307,  0.000 1.00E+00  15
+12         417.418,-199.31,  0.000       417.418,199.306,  0.000 1.00E+00  15
+13         441.335,-185.35,  0.000       441.335,185.354,  0.000 1.00E+00  13
+14         463.578,-172.38,  0.000       463.578,172.380,  0.000 1.00E+00  13
+15         484.263,-160.31,  0.000       484.263,160.313,  0.000 1.00E+00  11
+16         503.501,-149.09,  0.000       503.501,149.091,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    16 / 50.00   ( 16 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9302.EZ                      EZNEC/4  ver. 2.5
+
+.93/.02 6.88-15 MHz                          10-05-1999     11:24:47
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  27
+2           35.424,-411.80,  0.000        35.424,411.804,  0.000 1.00E+00  27
+3           68.369,-382.98,  0.000        68.369,382.978,  0.000 1.00E+00  25
+4           99.007,-356.17,  0.000        99.007,356.169,  0.000 1.00E+00  23
+5          127.500,-331.24,  0.000       127.500,331.237,  0.000 1.00E+00  21
+6          153.999,-308.05,  0.000       153.999,308.051,  0.000 1.00E+00  21
+7          178.643,-286.49,  0.000       178.643,286.487,  0.000 1.00E+00  19
+8          201.562,-266.43,  0.000       201.562,266.433,  0.000 1.00E+00  19
+9          222.877,-247.78,  0.000       222.877,247.783,  0.000 1.00E+00  17
+10         242.700,-230.44,  0.000       242.700,230.438,  0.000 1.00E+00  15
+11         261.135,-214.31,  0.000       261.135,214.307,  0.000 1.00E+00  15
+12         278.279,-199.31,  0.000       278.279,199.306,  0.000 1.00E+00  15
+13         294.224,-185.35,  0.000       294.224,185.354,  0.000 1.00E+00  13
+14         309.052,-172.38,  0.000       309.052,172.380,  0.000 1.00E+00  13
+15         322.842,-160.31,  0.000       322.842,160.313,  0.000 1.00E+00  11
+16         335.668,-149.09,  0.000       335.668,149.091,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    16 / 50.00   ( 16 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  200.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  200.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8506.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .85/.06                           10-05-1999     11:26:03
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2          106.272,-376.38,  0.000       106.272,376.380,  0.000 1.00E+00  25
+3          196.603,-319.92,  0.000       196.603,319.923,  0.000 1.00E+00  21
+4          273.385,-271.93,  0.000       273.385,271.935,  0.000 1.00E+00  17
+5          338.649,-231.14,  0.000       338.649,231.144,  0.000 1.00E+00  15
+6          394.124,-196.47,  0.000       394.124,196.473,  0.000 1.00E+00  13
+7          441.277,-167.00,  0.000       441.277,167.002,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     7 / 50.00   (  7 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8904.EZ                      EZNEC/4  ver. 2.5
+
+6.8-15 MHz .89/.04                           10-05-1999     11:25:12
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  31
+2           70.848,-394.09,  0.000        70.848,394.092,  0.000 1.00E+00  27
+3          133.903,-350.74,  0.000       133.903,350.742,  0.000 1.00E+00  25
+4          190.021,-312.16,  0.000       190.021,312.160,  0.000 1.00E+00  23
+5          239.967,-277.82,  0.000       239.967,277.823,  0.000 1.00E+00  19
+6          284.419,-247.26,  0.000       284.419,247.262,  0.000 1.00E+00  17
+7          323.981,-220.06,  0.000       323.981,220.063,  0.000 1.00E+00  15
+8          359.191,-195.86,  0.000       359.191,195.856,  0.000 1.00E+00  13
+9          390.528,-174.31,  0.000       390.528,174.312,  0.000 1.00E+00  13
+10         418.418,-155.14,  0.000       418.418,155.138,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    10 / 50.00   ( 10 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8504S (Stub)                      EZNEC/4  ver. 2.5
+
+6.8-15 .85/.04                               10-05-1999     11:23:35
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           70.848,-376.38,  0.000        70.848,376.380,  0.000 1.00E+00  25
+3          131.069,-319.92,  0.000       131.069,319.923,  0.000 1.00E+00  21
+4          182.257,-271.93,  0.000       182.257,271.935,  0.000 1.00E+00  17
+5          225.766,-231.14,  0.000       225.766,231.144,  0.000 1.00E+00  15
+6          262.749,-196.47,  0.000       262.749,196.473,  0.000 1.00E+00  13
+7          294.185,-167.00,  0.000       294.185,167.002,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     7 / 50.00   (  7 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7      1/50.0  (  1/50.0)  Short ckt (Short ck)   36.000 in   600.0  1.00
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8504 (No Stub)                      EZNEC/4  ver. 2.5
+
+6.8-15 .85/.04                               10-05-1999     11:22:21
+
+Frequency = 7  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,-442.80,  0.000         0.000,442.800,  0.000 1.00E+00  29
+2           70.848,-376.38,  0.000        70.848,376.380,  0.000 1.00E+00  25
+3          131.069,-319.92,  0.000       131.069,319.923,  0.000 1.00E+00  21
+4          182.257,-271.93,  0.000       182.257,271.935,  0.000 1.00E+00  17
+5          225.766,-231.14,  0.000       225.766,231.144,  0.000 1.00E+00  15
+6          262.749,-196.47,  0.000       262.749,196.473,  0.000 1.00E+00  13
+7          294.185,-167.00,  0.000       294.185,167.002,  0.000 1.00E+00  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     7 / 50.00   (  7 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Updated 10-07-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to LPDA Index

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/lpnec-1.gif b/content/lpda/lpnec-1.gif new file mode 100644 index 0000000..1a4bb2d Binary files /dev/null and b/content/lpda/lpnec-1.gif differ diff --git a/content/lpda/lpnec.html b/content/lpda/lpnec.html new file mode 100644 index 0000000..4748bb0 --- /dev/null +++ b/content/lpda/lpnec.html @@ -0,0 +1,193 @@ + + + + + + NEC-2 Models of LPDAs Some Special Considerations + + + +
+

NEC-2 Models of LPDAs
+ Some Special Considerations

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

The most common software used to model log periodic dipole arrays (LPDAs) is probably NEC-2. NEC-2 allows us to use the TL facility to construct the phasing line from mathematical lines that suffer no problems with the fact that they must be reversed ass they connect with each set of elements. In its most common implementations, NEC-2 is cheaper than NEC-4 but has a high segment limit than MININEC.

+

If the models we generate have uniform diameters, then we encounter few problems with NEC-2 other than ensuring an adequate number of segments for each element on all the frequencies covered by the LPDA. However, suppose we encounter an antenna design with tapered element diameters, that is, with several sizes of tubing use to make up each element. Fig. 1 shows a 7-element LPDA and allows you to distinguish the segment junction dots from the dots indicating a new tubing diameter.

+
+ +
+

The model description for this 14 to 30 MHz LPDA shows the element-diameter tapering complexity.

+ 
7 el lpda 20-10m                       Frequency = 29  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -216.50,  0.000,  0.000  W2E1 -140.00,  0.000,  0.000 7.50E-01   8
+2   W1E2 -140.00,  0.000,  0.000  W3E1 -80.000,  0.000,  0.000 8.75E-01   6
+3   W2E2 -80.000,  0.000,  0.000  W4E1 -16.000,  0.000,  0.000 1.00E+00   6
+4   W3E2 -16.000,  0.000,  0.000  W5E1  16.000,  0.000,  0.000 1.12E+00   3
+5   W4E2  16.000,  0.000,  0.000  W6E1  80.000,  0.000,  0.000 1.00E+00   6
+6   W5E2  80.000,  0.000,  0.000  W7E1 140.000,  0.000,  0.000 8.75E-01   6
+7   W6E2 140.000,  0.000,  0.000       216.500,  0.000,  0.000 7.50E-01   8
+8        -183.88, 57.360,  0.000  W9E1 -140.00, 57.360,  0.000 7.50E-01   4
+9   W8E2 -140.00, 57.360,  0.000 W10E1 -80.000, 57.360,  0.000 8.75E-01   6
+10  W9E2 -80.000, 57.360,  0.000 W11E1 -16.000, 57.360,  0.000 1.00E+00   6
+11 W10E2 -16.000, 57.360,  0.000 W12E1  16.000, 57.360,  0.000 1.12E+00   3
+12 W11E2  16.000, 57.360,  0.000 W13E1  80.000, 57.360,  0.000 1.00E+00   6
+13 W12E2  80.000, 57.360,  0.000 W14E1 140.000, 57.360,  0.000 8.75E-01   6
+14 W13E2 140.000, 57.360,  0.000       183.875, 57.360,  0.000 7.50E-01   4
+15       -155.62,106.270,  0.000 W16E1 -140.00,106.270,  0.000 7.50E-01   2
+16 W15E2 -140.00,106.270,  0.000 W17E1 -80.000,106.270,  0.000 8.75E-01   6
+17 W16E2 -80.000,106.270,  0.000 W18E1 -16.000,106.270,  0.000 1.00E+00   6
+18 W17E2 -16.000,106.270,  0.000 W19E1  16.000,106.270,  0.000 1.12E+00   3
+19 W18E2  16.000,106.270,  0.000 W20E1  80.000,106.270,  0.000 1.00E+00   6
+20 W19E2  80.000,106.270,  0.000 W21E1 140.000,106.270,  0.000 8.75E-01   6
+21 W20E2 140.000,106.270,  0.000       155.625,106.270,  0.000 7.50E-01   2
+22       -132.50,147.980,  0.000 W23E1 -80.000,147.980,  0.000 8.75E-01   5
+23 W22E2 -80.000,147.980,  0.000 W24E1 -16.000,147.980,  0.000 1.00E+00   6
+24 W23E2 -16.000,147.980,  0.000 W25E1  16.000,147.980,  0.000 1.12E+00   3
+25 W24E2  16.000,147.980,  0.000 W26E1  80.000,147.980,  0.000 1.00E+00   6
+26 W25E2  80.000,147.980,  0.000       132.500,147.980,  0.000 8.75E-01   5
+27       -113.06,183.540,  0.000 W28E1 -80.000,183.540,  0.000 8.75E-01   3
+28 W27E2 -80.000,183.540,  0.000 W29E1 -16.000,183.540,  0.000 1.00E+00   6
+29 W28E2 -16.000,183.540,  0.000 W30E1  16.000,183.540,  0.000 1.12E+00   3
+30 W29E2  16.000,183.540,  0.000 W31E1  80.000,183.540,  0.000 1.00E+00   6
+31 W30E2  80.000,183.540,  0.000       113.060,183.540,  0.000 8.75E-01   3
+32       -95.940,213.870,  0.000 W33E1 -80.000,213.870,  0.000 8.75E-01   2
+33 W32E2 -80.000,213.870,  0.000 W34E1 -16.000,213.870,  0.000 1.00E+00   6
+34 W33E2 -16.000,213.870,  0.000 W35E1  16.000,213.870,  0.000 1.12E+00   3
+35 W34E2  16.000,213.870,  0.000 W36E1  80.000,213.870,  0.000 1.00E+00   6
+36 W35E2  80.000,213.870,  0.000        95.940,213.870,  0.000 8.75E-01   2
+37       -82.500,239.730,  0.000 W38E1 -48.000,239.730,  0.000 8.75E-01   3
+38 W37E2 -48.000,239.730,  0.000 W39E1 -16.000,239.730,  0.000 1.00E+00   3
+39 W38E2 -16.000,239.730,  0.000 W40E1  16.000,239.730,  0.000 1.12E+00   3
+40 W39E2  16.000,239.730,  0.000 W41E1  48.000,239.730,  0.000 1.00E+00   3
+41 W40E2  48.000,239.730,  0.000        82.500,239.730,  0.000 8.75E-01   3
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           2    39 / 50.00   ( 39 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    4/50.0  (  4/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+2   11/50.0  ( 11/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+3   18/50.0  ( 18/50.0)   24/50.0  ( 24/50.0)  Actual dist  100.0  1.00  R
+4   24/50.0  ( 24/50.0)   29/50.0  ( 29/50.0)  Actual dist  100.0  1.00  R
+5   29/50.0  ( 29/50.0)   34/50.0  ( 34/50.0)  Actual dist  100.0  1.00  R
+6   34/50.0  ( 34/50.0)   39/50.0  ( 39/50.0)  Actual dist  100.0  1.00  R
+7    4/50.0  (  4/50.0)  Short ckt (Short ck)   90.000 in    75.0  0.66
+
+Ground type is Free Space
+

The design is an adaptation of a 20' LPDA designed by K4EWG for The ARRL Antenna Compendium, Vol. 3 (pp. 118-123). However, a few things have been changed, such as the length of the stub. Moreover, some of the construction features of the original--such as the overlapping elements and the large brackets--have not been captured in this model. Hence, it cannot be considered in any way an evaluation of the original antenna.

+

The model has several interesting features in addition to the tapered element diameter schedules, which parallel the original design. The 90" stub, composed of 75-Ohm, 0.66 velocity factor line moves the depression of feedpoint impedances outside the 14-30 MHz passband of the antenna. The 100-Ohm phasing line was selected for best modeled performance.

+

The use I want to make of the model is to revert to my old classroom days and give you a pop quiz. The question is this: What is the most accurate way to model this LPDA?

+

As a hint, let me provide you with a series of representative figures taken from different ways of modeling the antenna. For each of the mid-band frequencies, there are 3 sets of performance numbers. The "NEC-4" entry gives the reports of NEC-4. The "NEC-2-C" entry provides the output data for NEC-2 with Leeson corrections in operation. Leeson corrections correct the inherent tendency of NEC-2 to give incorrect results for tapered diameter linear elements. Finally, the NEC-2-N" entry gives the NEC-2 data reports without the correction factors activated.

+

Here is the table of reported values. Frequency is in MHz, Gain is the free-space value in dBi, F-B is in dB, Feed Z is R +/- jX in Ohms, and the 50/75 Ohms SWR is self-explanatory.

+ 
Freq      Core      Gain      F-B       Feed Z         50/75 Ohm SWR
+14.175    NEC-4     5.36       9.53     83.0 + j 8.8   1.69 / 1.16
+          NEC-2-C   5.30       9.48     77.9 + j10.8   1.61 / 1.16
+          NEC-2-N   5.49       9.73     82.5 + j 5.5   1.66 / 1.13
+
+18.12     NEC-4     6.26      13.61     67.4 - j10.3   1.42 / 1.20
+          NEC-2-C   6.24      13.58     69.0 - j 5.8   1.40 / 1.12
+          NEC-2-N   5.31      13.59     63.8 - j 9.3   1.34 / 1.24
+
+21.225    NEC-4     6.44      16.70     67.7 - j 1.5   1.36 / 1.11
+          NEC-2-C   6.46      16.70     66.8 - j 3.9   1.35 / 1.14
+          NEC-2-N   6.55      15.96     66.8 - j 0.3   1.30 / 1.16
+
+24.94     NEC-4     6.34      15.33     71.2 - j33.2   1.91 / 1.57
+          NEC-2-C   6.35      15.43     66.5 - j30.2   1.80 / 1.55
+          NEC-2-N   6.44      15.11     67.9 - j34.2   1.92 / 1.62
+
+29.0      NEC-4     6.17      19.36     65.5 - j26.5   1.70 / 1.49
+          NEC-2-C   6.17      19.69     59.5 - j28.1   1.71 / 1.61
+          NEC-2-N   6.20      19.38     61.4 - j28.6   1.73 / 1.59
+

If all we wish to receive from the data reports is a general impression of how well the antenna might work within the ham bands covered by the design, then the answer to our question is simple. Any of the modeling techniques is sufficient to provide the general impression. Nothing fatal seems to be reported by any of the techniques, despite some variance among the numbers.

+

Uncorrected NEC-2, of course, is considered least accurate when modeling elements with a diameter-tapering schedule. We can note that the reports for this option tend to yield slightly higher gains than either of the other two options. NEC-4 is considered to be a very significant improvement on NEC-2 in the handling of tapered-diameter linear elements, and the values it yields are somewhat closer to the values offered by NEC-2 with the element diameter correction activated (using EZNEC Pro, for this exercise).

+

For precision work, in which numerical progressions might be important (in contrast to the simple operational significance of the data), NEC-4 results do not tally exactly with corrected NEC-2 (or with the application of the corrections to NEC-4 models). There is still some variance.

+

Moreover, in an LPDA model, the correction factor does not affect every element. It has a limit, being activated for wire groups composing an element within about 15% of 1/2 wl resonance. Hence, the figures for the corrected NEC-2 entries are misleading. On 20, only element 1 and 2 were corrected. 17, 15, 12, and 10 activated only one wire each: numbers 3, 4, 5, and 6, respectively. Wire 7 was not corrected in length for its taper within any model run. Hence, to call the modeling run "corrected" was a misnomer; at best, each run was only partly corrected.

+

NEC-2 is most accurate when the linear elements of a model have a uniform diameter. Under those conditions, a NEC-2 and a NEC-4 run on the same LPDA model will show virtually indistinguishable results. Hence, for the most accurate modeling results, it is advisable to convert each tapered diameter element into its equivalent uniform diameter element, using Leeson or similar equations. Utility programs are available for this task.

+

However, users of EZNEC and other NEC-2 software having the correction factor available (such as NEC-Win Plus) can do the work for us. Each program allows us to see the corrected uniform diameter element length and diameter. We may have to make several software runs, changing frequency each time, in order to compile a complete list of the equivalent elements, but that process is usually faster than entering all of the tapered diameter element lengths and sizes into a utility program.

+

For our little sample case, here is the resulting model.

+ 
7 el lpda 20-10m                       Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -212.91,  0.000,  0.000       212.910,  0.000,  0.000 8.93E-01  31
+2        -180.94, 57.360,  0.000       180.940, 57.360,  0.000 9.21E-01  27
+3        -153.52,106.270,  0.000       153.520,106.270,  0.000 9.49E-01  23
+4        -131.05,147.980,  0.000       131.050,147.980,  0.000 9.71E-01  19
+5        -111.88,183.540,  0.000       111.880,183.540,  0.000 9.88E-01  15
+6        -95.106,213.870,  0.000        95.106,213.870,  0.000 1.00E+00  15
+7        -81.342,239.730,  0.000        81.342,239.730,  0.000 9.74E-01  15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8     7 / 50.00   (  7 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7    1/50.0  (  1/50.0)  Short ckt (Short ck)   90.000 in    75.0  0.66
+
+Ground type is Free Space
+

The results offered by this equivalent model are as follows.

+ 
Freq      Core      Gain      F-B       Feed Z         50/75 Ohm SWR
+14.175    NEC-2     5.26       9.27     81.4 + j 9.6   1.66 / 1.16
+
+18.12     NEC-2     6.18      13.40     68.7 - j10.9   1.44 / 1.19
+
+21.225    NEC-2     6.37      16.96     69.0 - j 1.3   1.38 / 1.09
+
+24.94     NEC-2     6.28      15.30     72.7 - j33.4   1.93 / 1.57
+
+29.0      NEC-2     6.12      19.20     66.8 - j25.3   1.68 / 1.44
+

For generalized work, nothing startling emerges from the report. Impedance reports are closest to the NEC-4 reports. The gain reports are lower overall--by about 0.2 dB on the lower bands and by abut 0.1 dB on the upper bands. The greater effect on the lower frequencies of the LPDA passband is most likely due to the fact that the element taper schedule used tends to make the longest elements have the smallest equivalent uniform diameter. Normally in an LPDA design, we tend to expect the opposite trend.

+

Had the element tapering schedule been significantly more complex, we would have seen a wider variation among values between the equivalent model and the original. If the original had modeled mounting brackets, using substitute short large-diameter segments at the element centers, the differences between the equivalent and original models would likely have been as striking as they can be with many Yagi models. However, had I created such a model for our example, I might be open to the charge of melodrama.

+

Nonetheless, the amount of difference in the outputs from the various options strongly suggests that it is good modeling practice in NEC-2 always to develop and use the equivalent uniform diameter element model as the basis for design and analysis of LPDAs.

+
+ +
+

Updated 09-29-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to LPDA Index

+

Topics: HF Upper, LPDA, Modeling


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+

Some Notes on LPDA Stubs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Log Periodic Dipole Arrays (LPDAs) very often employ shorted transmission line stubs connected across the phase line at the rear-most element terminals. The function and operation of these stubs is not as well understood as one might hope. Therefore, I am offering the following notes to clarify the situation somewhat.

+

From the earliest accounts of LPDAs, the use of a terminating stub has been recommended. The ARRL Antenna Book design procedure for stubs recommended until recently that the designer short out the longest elements on an HF array with a 6" jumper, but that VHF arrays should use a 1/8 wavelength stub as calculated from the longest wavelength used. There is a (lost) reason for this odd recommendation. At HF, where early amateur experience focused its attention, experimenters discovered that LPDAs seemed somewhat insensitive to the stub length. However, the initial recommendation remained in effect for VHF arrays.

+

For an LPDA with a 2:1 frequency range, a 1/8 wavelength stub at the lowest operating frequency represents a 1/4 wavelength stub at the arithmetic mean frequency. For a 14-30 MHz LPDA, the mean is about 22 MHz. We shall see the significance of this value as we move a little further into our exploration.

+

Some LPDA Phase-Line Basics

+

Ideally, every LPDA design carries with it a recommended value for the characteristic impedance of the phase line interconnecting the elements. (For the most fundamental aspects of LPDA design, see LPDA Notes, Vol. 1 and 2 on the Books Page). For the range of Tau and Sigma values most often used by the relatively short and sparsely populated arrays in amateur service, the most commonly calculated value is about 200 Ohms. However, this general value sits upon a fence between better gain (and front-to-back ratio, since these two values tend to follow each other in LPDAs) on one side and performance stability on the other.

+

The higher the phase-line characteristic impedance, the more stable the operation of the LPDA. We can define stable operation as the absence at any operating frequency of anomalous behavior. Fig. 1 shows the undesired anomalous behavior.

+
+ +
+

Ordinarily, for any given frequency of operation within the passband of an LPDA, there will be a most active element, as indicated by the current magnitude at its center. All elements forward of the most active element will also be active to varying degrees. To the rear of the most active element, 1 element (and normally not more than 2 elements) will be significantly active. The current levels on the remaining rearward elements will be relatively insignificant.

+

At one or more frequencies in the operating spectrum of an LPDA, the rearward elements relative to the most active element may show high current levels, with each element operating in a harmonic mode. For a 2:1 frequency range, an LPDA will usually show no more than one anomalous frequency. Wider frequency specifications may result in multiple anomalous frequencies. The anomalous operation results in strong rearward radiation, effectively destroying the well-behaved LPDA pattern.

+

If we select a phase-line impedance well above the recommended value, such anomalies do not appear. However, the cost of increasing the phase-line characteristic impedance is a reduction in gain across the operating spectrum relative to the full potential of a given set of elements. (If the relative smoothness of the array gain across the operating passband is a design concern, then we may also have to redesign some elements when changing the phase-line characteristic impedance to restore that smoothness. The initial properties of an array are relative to using the phase-line value that emerges from calculations.)

+

For a variety of reasons, we may wish to use a phase-line characteristic impedance that is lower than the calculated value. For the range of Tau and Sigma values used in amateur arrays, a phase-line impedance of about 100 Ohms often permits a direct match to a 50-Ohm coaxial feed cable using only a simple 1:1 balun. As well, lowering the phase-line impedance also tends to yield higher gain (and better front-to-back ratios). However, accompanying these practical improvements is a tendency for the array to reveal an anomaly.

+

Whether or not the decrease in phase-line characteristic impedance reveals an anomaly depends on a number of design values. The higher the values of both Tau and Sigma, the lower the tendency of an array to show an anomaly. In the 14-30 MHz operating range, LPDAs with Taus above 0.95 and Sigmas above 0.055 may show no anomaly with a 100-Ohm phase line. Such a design has appeared in antenneX. Unfortunately for the average builder, the array is well over 50' long. At the opposite end of the scale, when we drop the value of Tau below 0.90 and the value of Sigma below 0.050, we may find anomalies even with a 250-Ohm phase line. For stability, very small arrays should likely use relatively high impedance phase-line values, perhaps 400 Ohms or more, even if the already small performance is further reduced slightly.

+

Let's look at the operating characteristics of a representative LPDA design using a Tau near 0.91 and a Sigma of about 0.055. We shall equip the design with a 100-Ohm phase line. Arbitrarily, we shall add a 25" shorted stub, using the same 100-Ohm phase line.

+
+ +
+

Fig. 2 shows the free-space forward gain, the 180-degree front-to-back ratio, and the worst-case front-to-back ratio, as plotted on EZPLOT. The legend designation "front/sidelobe" represents the worst case front-to-back ratio, since there are no secondary forward lobes to corrupt this value. In a broadband array, where the rear lobes may change their shapes periodically, the worst-case front-to-back ratio is often a better predictor of overall array performance to the rear. In a well designed LPDA, the graphed line is relatively smooth, in contrast to the many peaks in the 180-degree front-to-back line. The graph employs 0.25 MHz intervals.

+

In the region of 25.5 to 25.75 MHz, we note a sudden decrease in gain and an equally sudden decrease in front-to-back ratio. Note that the frequencies are not identical for gain and front-to-back ratio. The actual worst-case gain and front-to-back ratio will coincide at the precise anomalous frequency, but the curves approaching that frequency tend to differ for gain and front-to-back ratio.

+
+ +
+

In Fig. 3, we can track the effects of anomalous operation on the feedpoint values: resistance, reactance, and SWR (here referenced to 50 Ohms). In this particular instance, not only does the SWR climb to a very high value (and much higher, since the precise anomalous frequency is slightly higher than 25.25 MHz), but as well, the resistance climbs to a high value and the reactance becomes very inductive. In other instances of anomalies, the feedpoint resistance might become very low instead.

+

The Role of A Shorted or Terminating Stub

+

There are two general practices in placing shorted stubs across the terminals of the longest element. One practice is to use the same characteristic impedance as the phase line itself. In the graphed sample, the line was 100 Ohms and 25" long. The alternative practice is to use a higher value of characteristic impedance. For short stubs, the result is a shorter stub than when using a lower characteristic impedance.

+

We may track the effect of using different stub impedances and lengths. The only preparation that we need is a simple warning. For the present design, we cannot eliminate the anomaly. We may only push its frequency up and down the LPDA's passband.

+
+ +
+

Fig. 4 tracks the anomalous frequency of the sample LPDA using 100-Ohm and 600 Ohm stubs at lengths ranging from virtually nothing to 450". The actual length of the so-called zero-length line was 0.1" in order to make the TL facility in NEC functional. 450" is slightly over 1/2 wavelength at the lowest operating frequency (14 MHz: 1 wavelength = 843").

+

The 100-Ohm stub curve is interesting for its nearly linear shape. Slight irregularities in the curve result from sampling at 0.25 MHz intervals. The 600-Ohm curve changes the anomalous frequency very rapidly initially, but the curve flattens considerably at middle lengths, and resumes a more rapid decrease rate in the anomalous frequency at long stub lengths.

+

Of first note is the fact that we may actually push the anomalous frequency below the lower end of the operating passband. However, as the final entry shows, we do not rid ourselves of the anomaly in this way. Instead, the anomaly reappears at the upper end of the passband as the stub approaches and passes a length of 1/2 wavelength at the lowest operating frequency. At best, we may select a stub length that places the anomaly in an unused portion of the operating spectrum.

+

Of second note is the line length at which the two curves cross: about 137" or so. Close to this length, both stubs are 1/4 wavelength near the crossing frequency, 22 MHz. This fact represents the significance of the original specification for this line at 1/8 wavelength relative to the lowest frequency used. The simple calculation works reasonably for LPDAs having a 2:1 frequency range. The difficulty is that the line length has no magic. It does not eliminate anomalies and it does not necessarily move the anomalous frequency to a desirable frequency. The length does have one further significance. The frequency of the anomaly does replicate the frequency at which an anomaly occurs if we use no stub at all.

+

Lest we think that anomalies are simply regions of reduced performance, let's take a closer look at a different sample. In this case--which uses the same array with a longer stub line--I expanded the coverage by using 0.1 MHz intervals. Fig. 5 is the result.

+
+ +
+

The circled point on the graph is an artifact. The gain value shown is actually the gain of the array in the opposite direction, a result of the very high currents on the rear elements, as displayed in Fig. 1. The very worst effects occur just above 20.9 MHz. From the perspective of the expanded sweep, we can see that the gain and front-to-back ratio tend to drop precipitously, only to rise at a slower rate than they fell--if we use rising frequency as our reference. The SWR tends to rise more slowly and then suddenly drop back into the normal range. Hence, the SWR curve alone is not a sufficient guide to setting the anomaly's frequency through adjustments to the stub length.

+
+ +
+

Fig. 6 contrasts two patterns from the same array at 19.5 MHz and 20.9 MHz. The well-behaved upper pattern turns into a reverse-direction lower pattern of very low gain, given its dipole-like shape. I have used this sample to show also that incorrect selection of the stub length can move an anomaly too close to a desired operating range, in this case, the 21 MHz amateur band.

+

It is unwise to use Fig. 4 as a general guide to stub lengths and anomaly frequencies. It is design specific. Those who design LPDAs via modeling techniques can estimate the required stub length for any value of characteristic impedance in order to place an anomaly where it will do the least harm. The lines in the samples shown use a velocity factor of 1.0, and so any actual line will have to use a shorter length in accord with the velocity factor of the line used.

+

Besides moving an anomaly from one frequency to another, stubs also function to place both sides of each element at the same static charge potential. There appears to be no good reason why the center point of the shorting bar across the stub may not be grounded to the mast. However, the use of a balun at the feedpoint may make this move unnecessary, since one line of the balun on the unbalanced side may already be at boom potential. Unless one is using a normal transformer instead of a transmission-line transformer in the balun device, static charge continuity should be present.

+

Borderline Phase-Line Impedances

+

Although phase-line impedances values above 200 Ohms should result in stable operation, we cannot simply assume that no anomalies will appear. Most contemporary LPDA designs use a series of modifications to calculated values in order to enhance performance. Practical construction considerations do not permit the use of a single--let alone ideal--element length-to-diameter ratio. The longest and shortest elements may be varied to improve passband-edge performance. As well, one may add a parasitic director to an array to improve high-end performance in lieu of adding a series of LPDA elements. The result of these and other design modifications is to alter the anticipated smooth curves of a stable LPDA. The examples that we used above all employed a parasitic director and some circularization of Tau.

+

Let's simply change the phase-line impedance of our initial model, this time using 250 Ohms. We shall retain the 25" stub, but let it also have a 250-Ohm impedance. The stub in this instance functions to slightly alter the characteristics at the lowest operating frequency in order to obtain the best combination of gain, front-to-back ratio, and 100-Ohm SWR.

+
+ +
+

As the circled element in Fig. 7 shows, we have an apparent warning signal of a possible anomaly at 27.5 MHz. The free-space forward gain suddenly drops by nearly 0.15 dB to 7.07 dBi. Interestingly, the 2 front-to-back curves show no symptoms of an anomaly.

+
+ +
+

Fig. 8 shows that there are no sudden changes in any of the feedpoint values, thus confirming that fact that we may have a false alarm. (The SWR values would be lower overall had we used a reference standard of 120 Ohms, but this value is generally inconvenient for transformation to 50 Ohms by most standard methods.) In fact, detailed frequency sweeps of the frequencies around 27.5 MHz reveal no anomaly, but only the sudden drop in gain. The drop is not serious in terms of the overall gain curve of the array (which requires further optimization to smooth the upper half of the passband). Indeed, we may wish to correlate the two figures and note that the gain drop occurs in the region where the SWR curve changes from its regular undulations into a slowly dropping value. Undoubtedly, the two performance factors are under the influence of the parasitic director.

+
+ +
+

Just as we may move the frequency of an anomaly downward by lengthening a shorted stub, so too can we move the frequency of false alarm. Fig. 9 shows the curve for the same array, but with a 225" stub. The upper portion of the curve--above 27 MHz--now has the smoothness that we expected to see. However, we find sudden value changes around 23.5 MHz: sudden shifts upward in both gain and the 180-degree front-to-back ratio. Once more, neither the feedpoint value curves nor a detailed frequency sweep uncover a true anomaly.

+

Let's push the phase-line impedance borderline somewhat closer to the limit: from 250 Ohms down to 200 Ohms. The advantage of the move is that the 100-Ohm SWR curve improves considerably, while the gain increases by a small but numerically noticeable amount.

+
+ +
+

If we model an array similar to the one we have been using as a sample, but omit the stub altogether, we obtain a peak in gain and a slight null in front-to-back ratio at about 22.5 MHz, as shown in the expanded graph in Fig. 10. The 0.25 dB rise in gain over a small frequency spread is a function of the parasitic director in concert with the other LPDA elements for this particular design. At most, it is an oddity, unless we are striving for the smoothest possible gain curve across the entire passband.

+

Now let's add an arbitrary 25" 200-Ohm shorted stub across the rear element. This action tends to coincide with the older advice simply to use a short stub of some arbitrary length--and the 25" stub at 200 Ohms has about the same effect as a 6" 600-Ohm stub.

+
+ +
+

Fig. 11 shows that the short stub will increase the frequency of an oddity (even if not an anomaly) relative to using no stub at all. However, our former gain peak has turned into a 0.8 dB drop in gain and a drop in front-to-back ratio of about 10 dB. Although these values--confirmed as the lowest in the curves by an even more detailed frequency sweep--are not technically anomalous, they do represent a serious--and unnecessary--decrease in performance.

+
+ +
+

Fig. 12 provides one solution. By using a longer stub--125" in this case--we return the curves to very nearly their former positions.

+

The upshot of the exercise is that a short stub is not necessarily the answer to every ill or near-ill that may befall an LPDA design. In cases where the phase-line impedance is lowered to marginal stability, a simple shorted stub may cause more harm than good. In such cases, if we need a stub at all, then we must experiment with lengths until we have satisfied all the design goals of a particular LPDA. As noted earlier, the more modifications that we make upon a given calculated design in order to improve performance, the more likely it will be that finding a satisfactory stub length will be a matter of trial and error.

+

Summary

+

The reasons for using a shorted stub in an LPDA include the following items.

+

1. A stub provides DC continuity between the halves of each element in an LPDA. The result may be a reduced noise level and a degree of safety if there is a path to ground for any static charge.

+

2. A stub permits us to slightly tailor the performance characteristics of an LPDA at the lowest operating frequencies, as we aim for the best combination of gain, front-to-back ratio, and feedpoint impedance.

+

3. A stub permits us to move anomalous and other "odd-performance" frequencies to the most desirable frequency--often an unused portion of the operating spectrum.

+

However, a stub does not permit us to remove an anomaly that results from using a very low phase-line impedance. Indeed, in cases of phase-line impedances that provide only marginal stability, selecting the wrong stub length relative to its characteristic impedance can create more problems than it solves. Most cases in which we have reports that a stub eliminates an anomaly are actually cases of changing a poor line length into a better line length.

+

The longer the stub, the lower the frequency of an anomaly until a stub approaches 1/2 wavelength, at which point, anomalous behavior repeats itself. A stub that is about 1/8 wavelength long at the lowest operating frequency yields performance very close to the performance of an array with no stub at all--assuming an LPDA frequency range of about 2:1.

+

In wider-range LPDAs, we may encounter multiple anomalous frequencies. A single stub usually is insufficient to move all of them to desirable frequencies.

+

A stub may be unnecessary if the performance of an array meets design specifications without a stub and if alternative means are used to obtain DC continuity between array element halves.

+

The sample cases used in this exercise are subject to almost an indefinitely large number of variations, given the large number of variables involved both basic LPDA calculations and in subsequent modifications to improve performance. Hence, the only way to determine the correct length for a stub remains trial and error. NEC models of arrays and their stubs can shorten the design work, but all such models are subject to stub-length modification on the physical antennas that they represent.

+
+ +
+

Updated 08-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for July, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
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+

Go to Main Index

+

Topics: HF Upper, LPDA


+ + diff --git a/content/lpda/teler-1.gif b/content/lpda/teler-1.gif new file mode 100644 index 0000000..c913c0a Binary files /dev/null and b/content/lpda/teler-1.gif differ diff --git a/content/lpda/teler-2.gif b/content/lpda/teler-2.gif new file mode 100644 index 0000000..b322de4 Binary files /dev/null and b/content/lpda/teler-2.gif differ diff --git a/content/lpda/teler-3.gif b/content/lpda/teler-3.gif new file mode 100644 index 0000000..9f06205 Binary files /dev/null and b/content/lpda/teler-3.gif differ diff --git a/content/lpda/teler-4.gif b/content/lpda/teler-4.gif new file mode 100644 index 0000000..9cf9dfb Binary files /dev/null and b/content/lpda/teler-4.gif differ diff --git a/content/lpda/teler-5.gif b/content/lpda/teler-5.gif new file mode 100644 index 0000000..789ced8 Binary files /dev/null and b/content/lpda/teler-5.gif differ diff --git a/content/lpda/teler-6.gif b/content/lpda/teler-6.gif new file mode 100644 index 0000000..31aad49 Binary files /dev/null and b/content/lpda/teler-6.gif differ diff --git a/content/lpda/teler-7.gif b/content/lpda/teler-7.gif new file mode 100644 index 0000000..475c93c Binary files /dev/null and b/content/lpda/teler-7.gif differ diff --git a/content/lpda/teler-8.gif b/content/lpda/teler-8.gif new file mode 100644 index 0000000..7b3e7e2 Binary files /dev/null and b/content/lpda/teler-8.gif differ diff --git a/content/lpda/teler-9.gif b/content/lpda/teler-9.gif new file mode 100644 index 0000000..b37772e Binary files /dev/null and b/content/lpda/teler-9.gif differ diff --git a/content/lpda/teler.html b/content/lpda/teler.html new file mode 100644 index 0000000..03b476c --- /dev/null +++ b/content/lpda/teler.html @@ -0,0 +1,485 @@ + + + + + + Build Your Own LPDA 3. Wire and Vee-Element LPDAs: The Telerana + + + +
+

So You Want to Build Your Own LPDA
+ 3. Wire and Vee-Element LPDAs: The Telerana

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Considerable interest persists in the Telerana, a very light-weight wire LPDA with elements bent forward into Vees. The original design emerged from work by George Smith, W4AEO, and Ansyl Eckols, YV5DLT. The design first appeared in QST for July, 1981 and has been in most editions of The ARRL Antenna Book since that time (pp. 10-13 to 10-16 in the 18th Edition). A modified hybrid, consisting of the basic Telerana with parasitic reflectors, by Markus Hansen, VE7CA, appeared on Volume 4 of The ARRL Antenna Compendium (pp. 112-117).

+

The Telerana begins as a standard-design 13-element LPDA with a Tau of 0.9 and a Sigma of 0.05. It presents us with the opportunity to analyze two facets of LPDA design: 1. the advantages or disadvantages of using Vee-shape elements and 2. the advantages or disadvantages of using small diameter wire in contrast to large tubular elements. We shall look only at the original design in what follows, since the topic of LPDA-parasitic hybrids is a subject all its own. By sticking to the pure LPDA design, the results will be comparable to those drawn out of models in Parts 1 and 2 of this sequence.

+

Straight vs. Vee-Element Models

Modeling the Telerana design, with its Vee elements, presents some challenges. I began with a straight element model using the element lengths and spacings provided by the designers. The overall length of the straight-line model is just over 29 feet and uses #14 AWG copper wire for modeling purposes--about 0.064" in diameter. The outline of this model appears in Fig. 1. +
+ +
+

The design specifies a 400-Ohm inter-element phasing line, with a 200-Ohm design feedpoint impedance. In the model, each element is assigned an odd number of segments so that the TL-facility transmission line will be centered on each element. Segment numbers were assigned by giving the shortest element 11 segments and increasing that number for longer elements by the inverse of Tau (1.11) and rounding to the nearest odd number. This technique ensures that the longest element will have a sufficient number of segments at the highest frequency (30 MHz) used by the antenna.

+

For reference, here is the antenna model description.

+ 
Telerana-Ant Bk 10-13: Straight Elements          Frequency = 14  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1          0.000,-20.330,  0.000         0.000, 20.330,  0.000    # 14   39
+2          4.060,-18.300,  0.000         4.060, 18.300,  0.000    # 14   35
+3          7.710,-16.460,  0.000         7.710, 16.460,  0.000    # 14   31
+4         11.020,-14.820,  0.000        11.020, 14.820,  0.000    # 14   29
+5         13.970,-13.310,  0.000        13.970, 13.310,  0.000    # 14   25
+6         16.630,-12.000,  0.000        16.630, 12.000,  0.000    # 14   23
+7         19.050,-10.790,  0.000        19.050, 10.790,  0.000    # 14   21
+8         21.140, -9.710,  0.000        21.140,  9.710,  0.000    # 14   19
+9         23.150, -8.720,  0.000        23.150,  8.720,  0.000    # 14   17
+10        24.890, -7.870,  0.000        24.890,  7.870,  0.000    # 14   15
+11        26.470, -7.080,  0.000        26.460,  7.080,  0.000    # 14   13
+12        27.890, -6.360,  0.000        27.890,  6.360,  0.000    # 14   13
+13        29.160, -5.740,  0.000        29.160,  5.740,  0.000    # 14   11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    13 / 50.00   ( 13 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  400.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  400.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  400.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  400.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  400.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  400.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  400.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  400.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  400.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  400.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  400.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  400.0  1.00  R
+
+Ground type is Free Space
+

Note that no stub is used with this design, and none of the compensation techniques noted in Part 2 of this sequence has been applied. No stub is needed because the high characteristic impedance of the phasing line tends to suppress harmonic operation of rear elements on the upper frequencies. The absence of compensation techniques was a design choice by the originators of the Telerana.

+

Transforming the antenna into one with elements that form forward Vees requires considerable care. The outline of the model appears in Fig. 2.

+
+ +
+

The segmentation of the straight-element model yielded a segment length of just about 1 foot. To ensure that the TL transmission line in NEC would be centered on each element, I created a 1-segment, 1-foot wire at each element position. The outer portions of each element were segmented in approximate 1-foot lengths and then bent forward at the appropriate angle. Let's count elements from the longest (#1) to the shortest (#13).

+

Elements #2 through #11 are bent forward about 30 degrees on each side, relative to an equivalent straight element. Element #1 is bent forward by about 45 degrees, while elements #12 and #12 are bent forward about 22 degrees and 12 degrees, respectively. The angle changes for these elements is a function of fitting the elements within the framework specifically design for the antenna. The resulting antenna is longer (30.3') but narrower than the straight-element model.

+

For reference, here is the model description.

+ 
Telerana-Ant Bk 10-13: Vee                Frequency = 14  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1         12.746,-15.691,  0.000  W2E1   0.000, -0.500,  0.000    # 14   20
+2   W1E2   0.000, -0.500,  0.000  W3E1   0.000,  0.500,  0.000    # 14    1
+3   W2E2   0.000,  0.500,  0.000        12.746, 15.691,  0.000    # 14   20
+4         14.270,-15.081,  0.000  W5E1   4.060, -0.500,  0.000    # 14   17
+5   W4E2   4.060, -0.500,  0.000  W6E1   4.060,  0.500,  0.000    # 14    1
+6   W5E2   4.060,  0.500,  0.000        14.270, 15.081,  0.000    # 14   17
+7         15.690,-14.322,  0.000  W8E1   7.710, -0.500,  0.000    # 14   15
+8   W7E2   7.710, -0.500,  0.000  W9E1   7.710,  0.500,  0.000    # 14    1
+9   W8E2   7.710,  0.500,  0.000        15.690, 14.322,  0.000    # 14   15
+10        18.180,-12.901,  0.000 W11E1  11.020, -0.500,  0.000    # 14   14
+11 W10E2  11.020, -0.500,  0.000 W12E1  11.020,  0.500,  0.000    # 14    1
+12 W11E2  11.020,  0.500,  0.000        18.180, 12.901,  0.000    # 14   14
+13        20.375,-11.594,  0.000 W14E1  13.970, -0.500,  0.000    # 14   12
+14 W13E2  13.970, -0.500,  0.000 W15E1  13.970,  0.500,  0.000    # 14    1
+15 W14E2  13.970,  0.500,  0.000        20.375, 11.594,  0.000    # 14   12
+16        22.380,-10.459,  0.000 W17E1  16.630, -0.500,  0.000    # 14   11
+17 W16E2  16.630, -0.500,  0.000 W18E1  16.630,  0.500,  0.000    # 14    1
+18 W17E2  16.630,  0.500,  0.000        22.380, 10.459,  0.000    # 14   11
+19        24.195, -9.411,  0.000 W20E1  19.050, -0.500,  0.000    # 14   10
+20 W19E2  19.050, -0.500,  0.000 W21E1  19.050,  0.500,  0.000    # 14    1
+21 W20E2  19.050,  0.500,  0.000        24.195,  9.411,  0.000    # 14   10
+22        25.745, -8.476,  0.000 W23E1  21.140, -0.500,  0.000    # 14    9
+23 W22E2  21.140, -0.500,  0.000 W24E1  21.140,  0.500,  0.000    # 14    1
+24 W23E2  21.140,  0.500,  0.000        25.745,  8.476,  0.000    # 14    9
+25        27.260, -7.619,  0.000 W26E1  23.150, -0.500,  0.000    # 14    8
+26 W25E2  23.150, -0.500,  0.000 W27E1  23.150,  0.500,  0.000    # 14    1
+27 W26E2  23.150,  0.500,  0.000        27.260,  7.619,  0.000    # 14    8
+28        28.575, -6.883,  0.000 W29E1  24.890, -0.500,  0.000    # 14    7
+29 W28E2  24.890, -0.500,  0.000 W30E1  24.890,  0.500,  0.000    # 14    1
+30 W29E2  24.890,  0.500,  0.000        28.575,  6.883,  0.000    # 14    7
+31        29.760, -6.198,  0.000 W32E1  26.470, -0.500,  0.000    # 14    6
+32 W31E2  26.470, -0.500,  0.000 W33E1  26.470,  0.500,  0.000    # 14    1
+33 W32E2  26.470,  0.500,  0.000        29.751,  6.203,  0.000    # 14    6
+34        30.085, -5.933,  0.000 W35E1  27.890, -0.500,  0.000    # 14    6
+35 W34E2  27.890, -0.500,  0.000 W36E1  27.890,  0.500,  0.000    # 14    1
+36 W35E2  27.890,  0.500,  0.000        30.085,  5.933,  0.000    # 14    6
+37        30.249, -5.625,  0.000 W38E1  29.160, -0.500,  0.000    # 14    5
+38 W37E2  29.160, -0.500,  0.000 W39E1  29.160,  0.500,  0.000    # 14    1
+39 W38E2  29.160,  0.500,  0.000        30.249,  5.625,  0.000    # 14    5
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1    38 / 50.00   ( 38 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    2/50.0  (  2/50.0)    5/50.0  (  5/50.0)  Actual dist  400.0  1.00  R
+2    5/50.0  (  5/50.0)    8/50.0  (  8/50.0)  Actual dist  400.0  1.00  R
+3    8/50.0  (  8/50.0)   11/50.0  ( 11/50.0)  Actual dist  400.0  1.00  R
+4   11/50.0  ( 11/50.0)   14/50.0  ( 14/50.0)  Actual dist  400.0  1.00  R
+5   14/50.0  ( 14/50.0)   17/50.0  ( 17/50.0)  Actual dist  400.0  1.00  R
+6   17/50.0  ( 17/50.0)   20/50.0  ( 20/50.0)  Actual dist  400.0  1.00  R
+7   20/50.0  ( 20/50.0)   23/50.0  ( 23/50.0)  Actual dist  400.0  1.00  R
+8   23/50.0  ( 23/50.0)   26/50.0  ( 26/50.0)  Actual dist  400.0  1.00  R
+9   26/50.0  ( 26/50.0)   29/50.0  ( 29/50.0)  Actual dist  400.0  1.00  R
+10  29/50.0  ( 29/50.0)   32/50.0  ( 32/50.0)  Actual dist  400.0  1.00  R
+11  32/50.0  ( 32/50.0)   35/50.0  ( 35/50.0)  Actual dist  400.0  1.00  R
+12  35/50.0  ( 35/50.0)   38/50.0  ( 38/50.0)  Actual dist  400.0  1.00  R
+
+Ground type is Free Space
+

The number of wires increases, but the total number of segments remains about the same as with the straight-line model. The phasing line remains the same as in the other model.

+

Both models were checked within each of the 5 ham bands between the 14 to 30 MHz design passband for the antenna. Modeling was done on NEC-4, but NEC-2 would be entirely satisfactory, since neither model presses any limitation in either program. The only limitation applies to both programs and both models: the mathematical phasing line does not show wire losses, although these would be minimal. Be intention, the velocity factor of the phasing line has been set at 1.0.

+

Both antennas have feedpoint impedance that fall generally within the design figures for a 2:1 SWR relative to 200 Ohms. The simplest way to show the relative performance between the Vee and straight element models is a simple table of gain and front-to-back ratios. A single frequency was used for 17 and 12 meters, but on 20 and 15 meters, band-edge and band-center values are shown. For 10 meters, the values cover 0.5 MHz intervals from 28 to 30 MHz.

+ 
Frequency           Free-Space Gain (dBi)         Front-to-Back Ratio (dB)
+   MHz              Straight       Vee            Straight       Vee
+14.0                5.71           4.50           11.63           7.53
+14.175              5.71           4.54           11.69           7.73
+14.35               5.72           4.58           11.79           7.92
+
+18.12               6.08           5.21           15.85          11.16
+
+21.0                6.26           5.40           16.70          12.17
+21.225              6.24           5.38           16.70          12.16
+21.45               6.21           5.36           16.92          12.13
+
+24.95               6.13           5.18           18.16          12.75
+
+28.0                5.93           5.14           18.23          13.06
+28.5                5.86           5.11           17.77          12.74
+29.0                5.81           5.08           17.31          12.39
+29.5                5.79           5.05           16.87          12.04
+30.0                5.80           5.03           16.48          11.75
+

If we select the center-point of each band and average the gain values and the front-to-back values, we obtain 5.99 dBi and 15.94 dB for the straight-element model and 5.08 dBi and 11.24 dB for the true Telerana with Vee elements. The straight line model is almost a full dB higher in gain and over 3.5 dB better in front-to-back ratio. These values are not unusual for arrays using elements near 1/2 wl long, whether LPDA or parasitic in design.

+
+ +
+

Fig. 3 overlays the free-space azimuth patterns for the straight-element and the Vee model at 14 MHz. It demonstrates some of the reasons why Vee-ed elements have a lower forward gain. Not only does the Vee-model radiate more strongly to the rear, it also radiates to the sides, reducing the front-to-side ratio that some designers count on to reduce QRM levels in unidirectional arrays.

+
+ +
+

Fig. 4 shows the same two free-space azimuth patterns at 21 MHz. The same phenomena apply, as they do at 28 MHz, as shown in Fig. 5.

+
+ +
+

I have shown several comparative azimuth patterns to establish that the pattern shapes for each antenna are not isolated or frequency-specific phenomena. The once-prevalent notion that Vee-ing elements increased gain has proven to have no foundation in any modeling that I have done with arrays based on 1/2 wl elements. In all cases, Vee-ing elements reduces gain, front-to-back ratio, and front-to-side ratio. Anyone who desires to examine the basis for these reductions should begin first by comparing a 1/2 wl dipole with a Vee of the same element length. What happens to the pattern for a single element simply accumulates for arrays of similar elements.

+
+ +
+

Although Vee-ing the elements in the Telerana yields an acceptable 200-Ohm SWR profile across the passband of the antenna, the equivalent profile for the straight-element design is somewhat superior, with smaller excursions in both the resistive and reactive components of the feedpoint impedance. Fig. 6 shows the two profiles for comparison. The Vee model would show an acceptable feedpoint impedance only up to about 29 MHz, but at the end of a 4:1 balun-plus-coaxial feedline, the SWR might appear to be somewhat lower.

+

Lest the Vee model be open to question, I performed a convergence test on it. To ensure that there were equal segments lengths on either side of the source/phase-line segment at the element centers, I increased the number of segments to 3. This required an increase by a factor of 3 for the number of segments on each wire making up the outer sections of the elements. For comparison, here are some values for the smaller and larger models of the Vee-d Telerana.

+ 
Freq.          F-S Gain       Front-Back     Feedpoint Impedance
+MHz            dBi            dB             (R +/- jX Ohms)
+
+14.0
+Smaller        4.50            7.53          195.0 - j 19.5
+Larger         4.48            7.53          190.6 - j 19.9
+
+18.12
+Smaller        5.21           11.16          213.6 - j 91.5
+Larger         5.17           11.15          203.7 - j 92.2
+
+21.0
+Smaller        5.21           12.17          195.0 - j 19.5
+Larger         5.36           12.14          190.6 - j 19.9
+
+24.95
+Smaller        5.18           12.75          256.7 + j 22.5
+Larger         5.14           12.76          258.7 + j 12.3
+
+28.0
+Smaller        5.14           13.06          173.8 - j  3.5
+Larger         5.06           13.04          172.9 - j  7.1
+

Nothing in the differences in the values returned by NEC-4 suggests that anything is amiss in the general accuracy of the analysis.

+

Element Diameter

Whether one chooses the Telerana as originally designed for its light-weight structure or selects the straight-element version for its higher performance is a design decision that goes beyond the present analysis. We are here only concerned with the electrical performance of the antenna design, and structural matters would add a dimension to the analysis to which modeling cannot contribute. +

A similar set of considerations applies to the decision on whether to use wire or tubular elements. Wire is lighter than tubing. However, tubing may be obtained in much larger diameters than wire. The only question to which modeling can contribute an answer is whether larger diameter tubing offers any advantages in antenna performance over the same design in wire.

+

To answer this question, I changed diameter of the elements in the straight-element model from #14 AWG to 0.5". The increase factor is nearly 8. Since the elements in the model are of uniform diameter, the choice of 0.5" as the new diameter reflects the effective diameter of heavily stepped diameter elements that might begin with diameters of nearly 1" and descend to about 3/8" at the element tips. Therefore, as a modeling exercise, the comparison might well be representative of building practice.

+

For reference, here is the revised straight-element model description.

+ 
Telerana-Ant Bk 10-13: Straight: 0.5" elements     Frequency = 14  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1          0.000,-20.330,  0.000         0.000, 20.330,  0.000 5.00E-01  39
+2          4.060,-18.300,  0.000         4.060, 18.300,  0.000 5.00E-01  35
+3          7.710,-16.460,  0.000         7.710, 16.460,  0.000 5.00E-01  31
+4         11.020,-14.820,  0.000        11.020, 14.820,  0.000 5.00E-01  29
+5         13.970,-13.310,  0.000        13.970, 13.310,  0.000 5.00E-01  25
+6         16.630,-12.000,  0.000        16.630, 12.000,  0.000 5.00E-01  23
+7         19.050,-10.790,  0.000        19.050, 10.790,  0.000 5.00E-01  21
+8         21.140, -9.710,  0.000        21.140,  9.710,  0.000 5.00E-01  19
+9         23.150, -8.720,  0.000        23.150,  8.720,  0.000 5.00E-01  17
+10        24.890, -7.870,  0.000        24.890,  7.870,  0.000 5.00E-01  15
+11        26.470, -7.080,  0.000        26.460,  7.080,  0.000 5.00E-01  13
+12        27.890, -6.360,  0.000        27.890,  6.360,  0.000 5.00E-01  13
+13        29.160, -5.740,  0.000        29.160,  5.740,  0.000 5.00E-01  11
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6    13 / 50.00   ( 13 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  200.0  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  200.0  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  200.0  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  200.0  1.00  R
+5    5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  200.0  1.00  R
+6    6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  200.0  1.00  R
+7    7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  200.0  1.00  R
+8    8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  200.0  1.00  R
+9    9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  200.0  1.00  R
+10  10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  200.0  1.00  R
+11  11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  200.0  1.00  R
+12  12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  200.0  1.00  R
+
+Ground type is Free Space
+

The other change occasioned by the altered element diameter was the choice of the optimal inter-element phasing line characteristic impedance. Although higher gain levels are possible with lower phase line impedances, evidences of harmonic operation of longer wires shows up especially in the 15 meter band. These would have required compensating treatment, such as the addition of a stub. The result would have altered overall performance enough to cast doubt on the fairness of the comparison. Therefore, I selected a 200-Ohm line with no further "doctoring" of the design.

+

I also left the material as copper: The difference in performance values by using aluminum will be 0.01 dB of gain and 0.01 dB of front-to-back ratio. Once the diameter of an element reaches a certain level, changes of conductivity in the range between copper and aluminum no longer make a significant difference in the radiation efficiency of otherwise equivalent elements. In the upper HF region, that diameter is about a half inch.

+

However, diameter differences between #14 wire and 0.5" tubing can make a significant difference in performance. This difference shows up not only in LPDA designs, but as well in other arrays. One reason that multi-element quads fail to achieve their theoretically possible improvement over Yagis with an equal number of elements is not a function of basic design. Instead, it involves the habitual use of small-diameter wire in quad elements. Increasing the element diameters to a half-inch or more shows a much higher potential for quad designs, whatever the mechanical difficulties of implementing such designs.

+

Similar differences show up in LPDA designs, as the following table will attest.

+ 
Frequency           Free-Space Gain (dBi)         Front-to-Back Ratio (dB)
+   MHz              #14            0.5"           #14            0.5"
+14.0                5.71           6.39           11.63          15.59
+14.175              5.71           6.37           11.69          15.63
+14.35               5.72           6.36           11.79          15.81
+
+18.12               6.08           6.59           15.85          21.01
+
+21.0                6.26           6.90           16.70          17.90
+21.225              6.24           6.92           16.70          17.72
+21.45               6.21           6.99           16.92          16.49
+
+24.95               6.13           6.66           18.16          21.31
+
+28.0                5.93           6.45           18.23          20.79
+28.5                5.86           6.39           17.77          20.30
+29.0                5.81           6.36           17.31          19.65
+29.5                5.79           6.35           16.87          18.89
+30.0                5.80           6.38           16.48          18.09
+

At the 21.45 MHz marker, one can see evidence of the onset of harmonic operation with the peak gain that opposes the curve for the wire model. The lowering of the front-to-back ratio below expected norms is also a clue to this phenomenon. Reducing the phase line impedance to 100 or 150 Ohms allows the harmonic operation to become graphic. Indeed, even for the 200-Ohm phase-line model, I would recommend stub treatment to suppress this phenomenon or to move it well outside the ham bands. There is some literature that suggests the operation of LPDAs in harmonic mode for added gain. However, combined fundamental and harmonic operation of elements is generally to be avoided in LPDAs operating over an octave or more range. Smooth performance figures over the frequency bands or interest become more difficult to obtain where both fundamental and harmonic operation are combined.

+

The average gain for the wire model is 5.99 dBi and the front-to-back ratio average to 15.94 dB. The 0.5" model shows 6.58 dBi and 19.06 dB as the comparable averages. Although the gain figure is only about 0.6 dB more, the 3 dB advantage in front-to-back ratio may well be worthy. Fig. 7 shows one representative comparison: the overlaid free-space azimuth patterns of the wire and tube models at 21 MHz.

+
+ +
+

The lower phase-line characteristic impedance yields a lower design feedpoint impedance. Although it might well be refined further, 75 Ohms provides a reasonable reference for an SWR profile. As Fig. 8 shows, the 0.5" model has a well-behaved SWR curves relative to the reference.

+
+ +
+

Additional design refinements are certainly possible. We have already noted the utility of adding a stub to this model. The element might also be increased in size, working from the shortest element and increasing the diameter by the inverse of Tau. Likewise, circularization of Tau, especially at the lower end of the spectrum, would tend to equalize the gain and front-to-back ratio across the passband at the highest level obtained near mid-band.

+

I shall not try to implement such revisions in this exercise. The goal of this study has been to compare straight-wire LPDA design to designs using Vee-ed elements and to compare thin-wire and fat-wire elements within the same design. Having done that much, it is time to set the Telerana at rest.

+

Nothing in this analysis has tried to be critical of the Telerana design. It is a mechanical marvel of stressed fiberglass support of a complex wire assembly. This analysis has looked at some electrical properties of LPDAs without regard for the ease or difficulty of implementation. Only the Telerana electrical design has been brought to the modeling table. The mechanical aspect of the Telerana remains a classic in amateur antenna design.

+

Wire Substitutes for Tubular Elements

It is possible to obtain the performance of a "fat" tubular element with a wire substitute. Two parallel wires can be shorted at their far ends and shorted again on each side of the feedpoint or phaseline connection point in the center. If the wires are properly spaced apart, they will simulate very closely the behavior of a single fat wire. +

In this space, we cannot develop a complete data base of wire equivalents to tubes. First of all, too many tube sizes are used to make this feasible. Second, the wire spacing will depend on the wire size used, and that multiplies the number of possibilities. However, we can make a small demonstration and show the modeling procedures one might use to develop a specific substitution.

+

Let's begin with the longest element of the Telerana in its 0.5" implementation. If we separate that element from the LPDA of which it is a part, we can find its resonant frequency. The 487.92" (40.66') element resonates at 11.63 MHz with a source impedance of 72.0 - j 0.1 Ohms. I generally set a reactance of +/-j1 Ohm as the criterion of resonance for most investigations--a figure somewhat more precise than we would need for an operational situation.

+

Now let's take 2 #14 AWG wires and make them parallel. Now we must figure out how to feed the wires without creating a folded dipole. Fig. 9 shows the general technique.

+
+ +
+

We create a short single center section of 1 segment (C). Then, we create short wires from the center section to each long wire of the pairs (B). This will make 2 wires, which we recreates with a single 2-segment wire at the far ends of the assembly (A). Each horizontal wire (D) is appropriately segmented.

+

The ideal situation would require that all wire segments be of approximately equal length. Hence, the lengths, of segments in A, B, C, and D would be the same. Equalizing the segment (wire) lengths of B and C is especially important. The far-end wires (A) can be of 1 or 2 segments: the difference makes little difference to the result. The segments of the parallel wires (D) should be no more than about 1.5 to 2.0 times the length of B or C. Working outside these dimensions generally yields poor results from the wire model.

+

A parallel-wire (#14 AWG) model of the 0.5" element yielded resonance at 11.60 MHz when the wires were 2" apart. With 120 segments each side of center along wire D, the feedpoint impedance was 72.81 + j0.3 Ohms, which was satisfactorily close to the value for the 0.5" tube. One might have nudged the spacing more precisely to place the resonance at 11.63 MHz, but the convenient 2" spacing number would have been lost.

+

So far, we have created a single element out of wire, one that has the same length as the original tube. One reason we wanted to preserve the length is to also preserve the current distribution along the length of the element. This function is just as important to LPDA operation as the phase line, since mutual coupling works together with phased element feed to yield the LPDA performance.

+

Will these substitution elements produce the same performance as the tubular original elements in an LPDA design? To create a little demonstration, let's look at a simpler design than the one with which we have been working. The reasons for this will become self-evident in a bit. The design we shall use is one that appears in The ARRL Antenna Book as a little exercise. It is not an especially good LPDA, but its merit is that it is small and designed for 17-10 meters. The model description of the test version follows.

+ 
17-10m Log Per - ARRL Ant Book              Frequency = 18.12  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1          0.000,-163.46,  0.000         0.000,163.460,  0.000 5.00E-01  37
+2         39.230,-130.76,  0.000        39.230,130.760,  0.000 5.00E-01  29
+3         70.620,-104.62,  0.000        70.620,104.620,  0.000 5.00E-01  23
+4         95.720,-83.690,  0.000        95.720, 83.690,  0.000 5.00E-01  19
+5        115.810,-66.950,  0.000       115.810, 66.950,  0.000 5.00E-01  15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  490.1  1.00  R
+2    2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  490.1  1.00  R
+3    3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  490.1  1.00  R
+4    4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  490.1  1.00  R
+5    1/50.0  (  1/50.0)  Short ckt (Short ck)    6.000 in   490.1  1.00
+
+Ground type is Free Space
+

This model also appears as an example in the EZNEC software.

+

Now let's present the substitute wire-element model.

+ 
17-10m Log Per Ant Bk Wire Sub              Frequency = 18.12  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1   W3E1 -163.46, -1.000,  0.000  W2E1  -1.000, -1.000,  0.000    # 14   60
+2   W1E2  -1.000, -1.000,  0.000  W5E2  -1.000,  0.000,  0.000    # 14    1
+3   W1E1 -163.46, -1.000,  0.000  W4E1 -163.46,  1.000,  0.000    # 14    2
+4   W3E2 -163.46,  1.000,  0.000  W5E1  -1.000,  1.000,  0.000    # 14   60
+5   W4E2  -1.000,  1.000,  0.000  W6E1  -1.000,  0.000,  0.000    # 14    1
+6   W2E2  -1.000,  0.000,  0.000  W7E1   1.000,  0.000,  0.000    # 14    1
+7  W10E1   1.000,  0.000,  0.000  W8E1   1.000,  1.000,  0.000    # 14    1
+8   W7E2   1.000,  1.000,  0.000  W9E1 163.460,  1.000,  0.000    # 14   60
+9   W8E2 163.460,  1.000,  0.000 W11E2 163.460, -1.000,  0.000    # 14    2
+10  W6E2   1.000,  0.000,  0.000 W11E1   1.000, -1.000,  0.000    # 14    1
+11 W10E2   1.000, -1.000,  0.000  W9E2 163.460, -1.000,  0.000    # 14   60
+12 W14E1 -130.76, 38.230,  0.000 W13E1  -1.000, 38.230,  0.000    # 14   50
+13 W12E2  -1.000, 38.230,  0.000 W16E2  -1.000, 39.230,  0.000    # 14    1
+14 W12E1 -130.76, 38.230,  0.000 W15E1 -130.76, 40.230,  0.000    # 14    2
+15 W14E2 -130.76, 40.230,  0.000 W16E1  -1.000, 40.230,  0.000    # 14   50
+16 W15E2  -1.000, 40.230,  0.000 W17E1  -1.000, 39.230,  0.000    # 14    1
+17 W13E2  -1.000, 39.230,  0.000 W18E1   1.000, 39.230,  0.000    # 14    1
+18 W21E1   1.000, 39.230,  0.000 W19E1   1.000, 40.230,  0.000    # 14    1
+19 W18E2   1.000, 40.230,  0.000 W20E1 130.760, 40.230,  0.000    # 14   50
+20 W19E2 130.760, 40.230,  0.000 W22E2 130.760, 38.230,  0.000    # 14    2
+21 W17E2   1.000, 39.230,  0.000 W22E1   1.000, 38.230,  0.000    # 14    1
+22 W21E2   1.000, 38.230,  0.000 W20E2 130.760, 38.230,  0.000    # 14   50
+23 W25E1 -104.62, 69.620,  0.000 W24E1  -1.000, 69.620,  0.000    # 14   40
+24 W23E2  -1.000, 69.620,  0.000 W27E2  -1.000, 70.620,  0.000    # 14    1
+25 W23E1 -104.62, 69.620,  0.000 W26E1 -104.62, 71.620,  0.000    # 14    2
+26 W25E2 -104.62, 71.620,  0.000 W27E1  -1.000, 71.620,  0.000    # 14   40
+27 W26E2  -1.000, 71.620,  0.000 W28E1  -1.000, 70.620,  0.000    # 14    1
+28 W24E2  -1.000, 70.620,  0.000 W29E1   1.000, 70.620,  0.000    # 14    1
+29 W32E1   1.000, 70.620,  0.000 W30E1   1.000, 71.620,  0.000    # 14    1
+30 W29E2   1.000, 71.620,  0.000 W31E1 104.620, 71.620,  0.000    # 14   40
+31 W30E2 104.620, 71.620,  0.000 W33E2 104.620, 69.620,  0.000    # 14    2
+32 W28E2   1.000, 70.620,  0.000 W33E1   1.000, 69.620,  0.000    # 14    1
+33 W32E2   1.000, 69.620,  0.000 W31E2 104.620, 69.620,  0.000    # 14   40
+34 W36E1 -83.690, 94.720,  0.000 W35E1  -1.000, 94.720,  0.000    # 14   30
+35 W34E2  -1.000, 94.720,  0.000 W38E2  -1.000, 95.720,  0.000    # 14    1
+36 W34E1 -83.690, 94.720,  0.000 W37E1 -83.690, 96.720,  0.000    # 14    2
+37 W36E2 -83.690, 96.720,  0.000 W38E1  -1.000, 96.720,  0.000    # 14   30
+38 W37E2  -1.000, 96.720,  0.000 W39E1  -1.000, 95.720,  0.000    # 14    1
+39 W35E2  -1.000, 95.720,  0.000 W40E1   1.000, 95.720,  0.000    # 14    1
+40 W43E1   1.000, 95.720,  0.000 W41E1   1.000, 96.720,  0.000    # 14    1
+41 W40E2   1.000, 96.720,  0.000 W42E1  83.690, 96.720,  0.000    # 14   30
+42 W41E2  83.690, 96.720,  0.000 W44E2  83.690, 94.720,  0.000    # 14    2
+43 W39E2   1.000, 95.720,  0.000 W44E1   1.000, 94.720,  0.000    # 14    1
+44 W43E2   1.000, 94.720,  0.000 W42E2  83.690, 94.720,  0.000    # 14   30
+45 W47E1 -66.950,114.810,  0.000 W46E1  -1.000,114.810,  0.000    # 14   25
+46 W45E2  -1.000,114.810,  0.000 W49E2  -1.000,115.810,  0.000    # 14    1
+47 W45E1 -66.950,114.810,  0.000 W48E1 -66.950,116.810,  0.000    # 14    2
+48 W47E2 -66.950,116.810,  0.000 W49E1  -1.000,116.810,  0.000    # 14   25
+49 W48E2  -1.000,116.810,  0.000 W50E1  -1.000,115.810,  0.000    # 14    1
+50 W46E2  -1.000,115.810,  0.000 W51E1   1.000,115.810,  0.000    # 14    1
+51 W54E1   1.000,115.810,  0.000 W52E1   1.000,116.810,  0.000    # 14    1
+52 W51E2   1.000,116.810,  0.000 W53E1  66.950,116.810,  0.000    # 14   25
+53 W52E2  66.950,116.810,  0.000 W55E2  66.950,114.810,  0.000    # 14    2
+54 W50E2   1.000,115.810,  0.000 W55E1   1.000,114.810,  0.000    # 14    1
+55 W54E2   1.000,114.810,  0.000 W53E2  66.950,114.810,  0.000    # 14   25
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1    50 / 50.00   ( 50 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+
+1    6/50.0  (  6/50.0)   17/50.0  ( 17/50.0)  Actual dist  490.1  1.00  R
+2   17/50.0  ( 17/50.0)   28/50.0  ( 28/50.0)  Actual dist  490.1  1.00  R
+3   28/50.0  ( 28/50.0)   39/50.0  ( 39/50.0)  Actual dist  490.1  1.00  R
+4   39/50.0  ( 39/50.0)   50/50.0  ( 50/50.0)  Actual dist  490.1  1.00  R
+5    6/50.0  (  6/50.0)  Short ckt (Short ck)    6.000 in   490.1  1.00
+
+Ground type is Free Space
+

This 55-wire, 865-segment model is sizable and slow running. However, it is considerably shorter and faster than had we presented the wire substitute for the Telerana with its 13 elements replaced by 143 wires and well over double the total number of segments as the small model. The smaller model is also a good test of the substitution, since it does not have especially good performance. If the substitute were a poor one, we could expect results that significantly diverge from the original.

+

The following table shows how the original and the substitute fared in modeling tests at sample frequencies.

+ 
Frequency           Free-Space Gain     Front-Back Ratio    Feed Impedance
+  MHz                    dBi                 dB             R +/- jX Ohms
+18.12
+Original                 4.44                6.42            60.2 + j 95.8
+Substitute               4.35                6.29            72.3 + j112.5
+
+21.0
+Original                 4.47                6.15           142.9 - j 87.0
+Substitute               4.43                6.10           127.6 - j 70.5
+
+24.95
+Original                 5.09                7.94           382.8 - j 82.3
+Substitute               5.07                8.02           330.0 - j141.6
+
+28.0
+Original                 5.36                9.81           105.3 - j 54.8
+Substitute               5.32                9.81           102.7 - j 36.9
+

The maximum gain differential is 0.09 dB and the maximum front-to-back differential is 0.13 dB. The very small gain degradation stems in part from the smaller area available on the two wire surfaces compared to the surface of the larger tube. The original tube from which we derived the substitute 2-wire spacing had a dipole gain of 2.13 dBi, while the substitute had a gain of 2.07 dBi in free space.

+

Although the impedance differences are greater, they are in part attributable to the slight difference we selected for resonant frequencies for the elements in order to preserve round numbers for with wire spacing. However, the impedance differences are not great enough to disturb the general trends of an SWR profile.

+

The demonstration shows that it is possible to develop 2-wire equivalents of larger elements. The technique used to develop the #14 wire substitute for 0.5" elements can be replicated to make substitutes out of almost any wire size for any size original element. The demonstration also shows that the performance of the 2-wire substitute can be effectively modeled with due attention to the constraints of NEC segmentation--and if one is willing to work with larger models that require considerable run time.

+

Whether the 2-wire substitute element would be satisfactory in an actual LPDA antenna involves mechanical considerations beyond the scope of this modeling exercise. Nonetheless, it is an option that the LPDA designer- builder should not overlook in the quest for an adequate LPDA.

+

Needless to say, the 5-element demonstration model would be hardly worth the effort of building. There are far better designs with which to work.

+
+ +
+

Updated 10-22-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to LPDA Index

+

Topics: HF Upper, LPDA


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+


+ Periodicals

+

+
+
+ 
+======================================================================
+
+Periodicals of Interest to QRP Enthusiasts                 Version 2.0
+                                                          July 1, 1999
+Compiled by L. B. Cebik, W4RNL
+
+Contents:  This file contains basic information on periodicals of
+especial interest to QRP enthusiasts.  It lists club-sponsored and
+subscription periodicals that are of wide interest to QRPers
+world-wide and that are readily available.
+
+NOT included are standard, general interest amateur radio journals,
+such as QST, CQ, Communications Quarterly, 73, RADCOM, and others from
+all over the world.  Although these journals often contain articles of
+interest to QRP enthusiasts, they are too well known to require space
+here.  World Radio and FISTs have regular QRP columns.
+
+Electronics books and antenna books of interest to QRP enthusiasts
+will be found in two separate listings.
+
+Each entry in this list providess the following information:  journal
+name, issues per year, source, cost per year, basis of subscription,
+average pages per issue, subscription or membership address, a brief
+description of the usual contents, and special notes.
+
+This list is believed to be reasonably complete and accurate as of the
+date of this notice.  Corrections and additions may be e-mailed to me
+at the listed address.  I shall be pleased to add to the list any
+publication omitted if it is of high interest to QRP operators and
+builders.  And, of course, I shall be pleased to correct any errors
+and update the information listed.
+
+Permission to reproduce this list is hereby granted on condition that
+a full reference to its source is included.
+
+Good reading, good building, and good operating to you.
+
+                                                    L. B. Cebik, W4RNL
+
+======================================================================
+                        ==========================================
+                        Periodicals of Interest to QRP Enthusiasts
+                        ==========================================
+
+1.    Name:        QRP Quarterly                    Issues per year:   4
+      Source:      QRP ARCI                         Cost:        $15.00 US*
+      Basis:       Membership                       Pages:        60+/issue
+      Address:     Ken Evans, W4DU (Treasurer)
+                   848 Valbrook Court
+                   Lilburn, GA 30047  USA
+      Contents:    Construction (circuits, antennas, modifications,
+                   test equipment, etc.), equipment and accessories
+                   reviews, shop and building tips ("Idea Exchange,"
+                   WA8MCQ), operating, award, editorial views and QRP
+                   philosophy, contest dates and results, and member
+                   news (KI6SN); Editor Ron Stark, KU7Y
+      Notes:       *$18/yr VE; $20/yr DX; 8.5x11 format
+
+2.    Name:        SPRAT                            Issues per year:   4
+      Source:      G-QRP Club                       Cost:        $14.00 US*
+      Basis:       Membership                       Pages:         44/issue
+      Address:     *Bill Kelsey, N8ET; Kanga US
+                   3521 Spring Lake Drive
+                   Findlay, OH 45840  USA
+      Contents:    Ed. George Dobbs, G3RJV; 60% construction each issue
+                   (circuits, antennas, test equipment, etc., both basic
+                   and advanced, with some pcb layouts) from many
+                   different countries; award, operating, contest, G-
+                   novice, SSB, VHF, and member columns and news
+      Notes:       *Membership/subscription dues to be sent according
+                   to country of residence; see list of clubs for
+                   information on non-US costs and addresses; SPRAT =
+                   "Small Powered Radio Amateur Transmitter", 5.75x8.5
+
+3.    Name:        QRPp                             Issues per year:   4
+      Source:      NORCAL                           Cost:         $15.00 US
+      Basis:       Membership                       Pages:      64-84/issue
+      Address:     The QRP Club of Northern California
+                   Jim Cates, WA6GER
+                   3241 Eastwood Road
+                   Sacramento, CA 95821  USA
+      Contents:    Ed. Doug Hendricks, KI6DS; over 20 articles per issue,
+                   mostly devoted to technical and construction topics
+                   including new designs, conversions, improvements, and
+                   modifications, featuring NORCAL club projects, with a
+                   member profile and some operating features.
+      Notes:       $15/yr US and VE; $20/yr DX (air mail delivery);
+                   mailing schedule:  March, June, Sept, Dec.; Make
+                   subscription checks payable to Jim Cates, not NORCAL;
+                   5.75x8.5; bound past volumes available.
+
+4.    Name:        Low Down                         Issues per year:  6
+      Source:      Colorado QRP Club                Cost:        $15.00 US
+      Basis:       Membership*                      Pages:     32-36/issue
+      Address:     Rich High, W0HEP (Editor)*
+                   740 Galena Street
+                   Aurora, CO 80010-3922  USA
+                   FAX: 303-344-0741   e-mail: CQC@aol.com
+      Contents:    Technical articles; rig profiles and other
+                   equipment reviews; overseas QRP operating features;
+                   club member profiles ("Check-Ins"); CQC contest news,
+                   rules, and forms; QRP philosophy and views; regular
+                   antenna column (Antennas From the Ground Up)
+      Notes:       $20/yr DX; 5.75x8.5
+                   *Send memberships and renewals to this address:
+                     Colorado QRP Club
+                     P.O. Box 371883
+                     Denver, CO 80237-1883
+
+5.    Name:        The Five-Watter (T5W)            Issues per year:   4
+      Source:      Michigan QRP Club                Cost:        $ 7.00 US*
+      Basis:       Membership                       Pages:         20/issue
+      Address:     Editor: Tom Arvo, WA8DXD
+                   P.O. Box 2550
+                   Goldenrod, FL  32733-2550
+      Contents:    A mix of club, operating, building, and antenna
+                   information
+      Notes:       *New memberships:  $7.00 US/VE, $12 DX; renewal dues
+                   $5.00 US/VE, $10 DX; Size 5.75x8.5
+                   Membership and renewal address:
+                     654 Georgia Avenue
+                     Marysville, MI  48040
+
+6.    Name:        Lo-Key                           Issues per year:  4
+      Source:      CW Operators QRP Club (VK)  Cost              $14.00 A*
+      Basis:       Mem/Subscription                 Pages:        32/issue
+      Address:     Kevin Zietz, VK5AKZ
+                   41 Tobruk Avenue
+                   St. Marys, SA 5042
+                   Australia
+      Contents:    Ed. Don Callow, VK5AIL; Two to three construction
+                   articles/issue, including advanced ideas,
+                   equipment modifications, keyers, etc. (some with parts
+                   kits available); awards, contest, and net program news.
+      Notes:       *VK price $10/yr; ZL $12/yr; dx S14/yr:  N8ET will
+                   accept subscription money at Dayton and forward in
+                   order to assist with currency conversion.  5.75x8.5
+
+7.    Name:        QRP Report                       Issues per year:   4
+      Source:      DL-QRP-AG                        Cost:        $20.00 US*
+      Basis:       Membership/Subscription          Pages:      32-48/issue
+      Address:     Peter Zenker, DL2FI
+                   Saarstrasse13
+                   12161 Berlin
+                   Germany
+      Contents:    Numerous construction articles, equipment reviews, and
+                   other technical topics of interest to QRPers.  Many short
+                   articles and small projects, plus a complete transceiver
+                   in almost every issue.  Most projects are available as kits
+                   from DL-QRP-AG.  Edited by Matthias Rauhut, DF2OF
+      Notes:       Format:  7.75x8.25".  *Yearly subscription 20 DM in Germany
+
+8.    Name:        OK QRP INFO                      Issues per year:   4
+      Source:      OK (Czech) QRP Club              Cost:        $10.00 US*
+      Basis:       Membership                       Pages:         35/issue
+      Address:     Petr Doudra OK1CZ  (IN: HRUSKA@ig.cas.cz)
+                   U 1. baterie 1
+                   16200 Praha (Prague)
+                   Czech Republic
+      Contents:    Several construction articles (up to 8 brief ones),
+                   most with English translations; also general interest
+                   reports on QRP activities
+      Notes:       *Cost/yr:  15 IRCs; GBP 5.00; US$ 10.00; DM 15;
+                   5.75x8.5
+

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Go to Amateur Radio Page

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Topics: Books


+ + diff --git a/content/model/boomeff.html b/content/model/boomeff.html new file mode 100644 index 0000000..c4bdd2d --- /dev/null +++ b/content/model/boomeff.html @@ -0,0 +1,144 @@ + + + + + + Boom Effects with Short 3-Element 146-MHz Yagis + + + +
+

Notes on Boom Effects with Short 3-Element 146-MHz Yagis

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+

L. B. Cebik, W4RNL

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+
+ +
+

There is a long-standing question concerning the effects of directly connecting Yagi elements to a boom vs. having them well insulated and isolated from the boom. The empirical evidence shows that the boom connection requires an adjustment to element lengths relative to the use of insulated elements (or a non-conductive boom). However, at least two questions remain. 1. Can NEC show the difference? 2. What are the currents along the boom relative to those on the active elements?

+

As a preliminary investigation, I used 2 of a series of 3-element optimized utility Yagis and remodeled them to show element-to-boom connections. NEC (-2/-4) is limited in its ability to model such situations, since it develops errors if there are angular junctions of dissimilar-diameter materials. However, since I had optimized the designs for a number of element diameters, I selected the models using 0.5"-diameter elements. This selection permitted the use of a 0.5"-diameter boom for the NEC-4 modeling tests.

+

Each modeling test proceeded in 4 steps:

+

1. The initial model using no boom

+

2. Pre-boom model adjustments: The adjustments included a. moving the driver 1" above the plane of the antenna to maintain its insulation from the boom, b. dividing the elements into wires joining along the array centerline, and finally c. optimizing the segmentation at a value of about 0.85 segments per inch of wire element.

+

3. Adding a boom extending from the reflector junction to the director junction, using the same segmentation as in step 2.

+

4. Adding 1.7" extensions from the reflector back and from the director forward, with 2 segments each.

+

The following notes provide the modeling data for the tests.

+

1. 23FB-50: A 2-meter, 3-element Yagi optimized for maximum front-to-back ratio at 146 MHz

+

Step 1. The following dimensions apply to the initial (no-boom) model of the max FB design. Element lengths are in half-length units to simplify replication of the model. All element diameter values will be 0.5" (radius = 0.25"). Each element used 31 segments. The material is aluminum. The environment is free-space.

+ 
Element           Length            Distance from Reflector
+Reflector         +/- 20.06"        -----
+Driver            +/- 18.16"        13.39"
+Director          +/- 17.21"        25.10"  (11.71" from driver)
+

Performance report:

+ 
                  144 MHz           146 MHz           148 MHz
+Gain              7.66 dBi          7.81              8.02
+Front-back        23.34 dB          56.80             22.82
+Source Z          65.90 + j 8.24    50.17 - j 0.60    33.41 - j 1.76
+50-Ohm SWR        1.364             1.012             1.500
+

The reverse curve of source reactance stems from the use of a beta match consisting of a transmission-line stub across the source after shortening the driver to show the requisite capacitive reactance.

+

Step 2. The model was revised to use 2 wires for the reflector and director elements, with 17 segments per half reflector and 15 segments per half director. The driver was elevated 1" with 31 segments. The following performance figures resulted from the revisions.

+

Performance report:

+ 
                  144 MHz           146 MHz           148 MHz
+Gain              7.65 dBi          7.79              8.00
+Front-back        23.57 dB          56.50             22.57
+Source Z          65.56 + j 8.24    49.86 - j 0.46    33.21 - j 1.52
+50-Ohm SWR        1.358             1.010             1.508
+

I consider the performance differences between the initial and the Step-2 model insignificant, but the latter forms the baseline for the following steps.

+

Step 3. The model added a 0.5"-diameter aluminum boom from the reflector to the director, using 21 segments. The resulting performance report was identical to that shown for Step 2, with no changes even in the last decimal place.

+

The currents are interesting. The driver was given a current source of relative magnitude 1.0 and phase angle 0 degrees. Because the source has a transmission line stub across it to effect a match to a 50-Ohm feedline, the driver current value will be other than 1.0 at 0 degrees, as shown in the following short table of values for 146 MHz. The element currents are identical to those that appear for Step 2.

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
Reflector:        4.17E-1//172.31 deg     Boom junction:    6.5E-7//105.83 deg
+Driver:           1.37E+0//42.48
+Director:         9.25E-1//-93.54         Boom junction:    4.6E-7//-54.68
+

Step 4. The Step-3 model added 1.7"-long 0.5"-diameter boom extensions to simulate construction realities, but permit the use of 2 segments, each the same length as others in the model. The performance report did not change. However, the boom-to-element junction current changed somewhat.

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
Reflector:        4.17E-1//172.31 deg     Boom junction:    4.97E-7//96.27 deg
+Driver:           1.37E+0//42.48
+Director:         9.25E-1//-93.54         Boom junction:    6.6E-7//-69.82
+

Nowhere along the booms in Steps 3 and 4 did the relative current magnitude exceed 6.6E-7, about 6 orders of magnitude below the current peaks recorded on the parasitic elements.

+

2. 23WB-50: A 2-meter, 3-element Yagi for wide-band operation from 144-148 MHz

+

Step 1. The following dimensions apply to the initial (no-boom) model of the wide-band design. Element lengths are in half-length units to simplify replication of the model. All element diameter values will be 0.5" (radius = 0.25"). Each element used 31 segments. The material is aluminum. The environment is free-space.

+ 
Element           Length            Distance from Reflector
+Reflector         +/- 20.46"        -----
+Driver            +/- 19.15"        18.10"
+Director          +/- 16.80"        28.60"  (10.50" from driver)
+

Performance report:

+ 
                  144 MHz           146 MHz           148 MHz
+Gain              7.04 dBi          7.14              7.30
+Front-back        19.78 dB          23.20             26.42
+Source Z          52.58 - j 7.78    49.95 - j 0.76    46.30 + j 7.58
+50-Ohm SWR        1.173             1.015             1.191
+

The driver source impedance shows a normal curve because the antenna was designed for direct feed by a 50-Ohm coaxial cable.

+

Step 2. The model was revised to use 2 wires for the reflector and director elements, with 17 segments per half reflector and 14 segments per half director. The driver was elevated 1" with 33 segments. The following performance figures resulted from the revisions.

+

Performance report:

+ 
                  144 MHz           146 MHz           148 MHz
+Gain              7.04 dBi          7.14              7.30
+Front-back        19.85 dB          23.26             26.33
+Source Z          52.56 - j 7.68    49.94 - j 0.61    46.31 + j 7.78
+50-Ohm SWR        1.171             1.012             1.196
+

I consider the performance differences between the initial and the Step-2 model insignificant, but the latter forms the baseline for the following steps.

+

Step 3. The model added a 0.5"-diameter aluminum boom from the reflector to the director, using 21 segments. The resulting performance report was again identical to that shown for Step 2, with no changes even in the last decimal place.

+

The currents reflect the situation with the first Yagi design. The driver was given a current source of relative magnitude 1.0 and phase angle 0 degrees, as shown in the following short table of values for 146 MHz. The element currents are identical to those that appear for Step 2.

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
Reflector:        2.72E-1//98.38 deg      Boom junction:    2.1E-7//50.20 deg
+Driver:           1.00E+0//0.0
+Director:         7.24E-1//-132.3         Boom junction:    7.1E-7//120.46
+

Step 4. The Step-3 model added 1.7"-long 0.5"-diameter boom extensions to simulate construction realities, but permit the use of 2 segments, each the same length as others in the model. The performance report did not change. However, the boom-to-element junction current changed somewhat.

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
Reflector:        2.72E-1//98.38 deg      Boom junction:    4.0E-7//62.84 deg
+Driver:           1.00E+0//0.0
+Director:         7.24E-1//-132.3         Boom junction:    5.0E-7//122.32
+

Nowhere along the booms in Steps 3 and 4 did the relative current magnitude exceed 7.1E-7, about 6 orders of magnitude below the current peaks recorded on the parasitic elements. However, we may note that the boom-to-director current phase differs on the wide-band model relative to the max F-B model. It does not reflect the phase angle of the director (a negative value on the max F-B design), but has a high positive value in a progression running from the reflector forward.

+

Special note: On the wide-band design, I pressed the segmentation limit by increasing the number of segments uniformly by a factor of about 1.5. Hence, the reflector halves used 25 segments, the director halves used 21, while the driver used 49. The main boom used 37 segments, with the end extensions using 3 each. In the pre-boom adjusted model (Step 2), the results varied by no more than a digit or two in the last decimal column, relative to the model with conservative segmentation. The highly segmented version of the design achieved an AGT of 1.000, although pressing further to double the original segmentation yielded core and program based warnings.

+

The pre-boom (Step 2) model and the boom + extensions (Step 4) model of the highly segmented design produced identical performance reports to the last decimal place. The following table of current reports reflects that fact that the element and boom junction currents are closer to the actual junction than in the conservatively segmented model.

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
Reflector:        2.73E-1//98.10 deg      Boom junction:    1.4E-6//-132.1 deg
+Driver:           1.00E+0//0.0
+Director:         7.23E-1//-132.4         Boom junction:    1.1E-6//50.75
+

The table appears anomalous, because the current phases for the boom junctions appears to be reversed from what one might expect. However, in the region of the boom below the driver--with its current at 1.0 and 0.0 degrees--the boom current is about 1.1E-7 at 180 degrees.

+

The current magnitudes reported for the boom junctions--actually the segment centers for the segment forming the junction--is nearly an order of magnitude higher than for the conservatively segmented model.

+

The next step was to question whether the exact centering of the boom--and its identify in diameter to the elements--might be a reason for the identity of results between the boomless and boomed models. So I moved the boom to a position 0.51" below the parasitic elements. This situation provided a clearance of 0.01" (0.00012 wavelength) between the boom and element surfaces. The performance reports remained unchanged.

+

I then transported this model with higher segmentation density to MININEC, and included a pre-boom adjusted model for comparison. The implementation of MININEC was Antenna Model. It is necessary to specify the implementation of MININEC, since the core is quite variably modified by each available implementation. Antenna Model has passed numerous benchmark tests involving areas where raw MININEC shows deficiencies. It has passed more tests than any other implementation.

+

The MININEC version of the model differs from the NEC version only by having 48 segments on the driver in order to place the source at the exact center on a pulse (segment junction).

+

Performance report--both pre-boom and full boom + extension models:

+ 
                  144 MHz           146 MHz           148 MHz
+Gain              6.97 dBi          7.04              7.20
+Front-back        19.06 dB          22.11             25.35
+Source Z          53.94 - j 9.05    51.76 - j 2.11    48.49 + j 6.13
+50-Ohm SWR        1.209             1.055             1.137
+

Since MININEC does not suffer the NEC weakness with angular junctions with dissimilar diameter wires, I increased the boom diameter to 1", reducing the segmentation in the extension to avoid segment-length/diameter warnings. Increasing the boom diameter created no change in the performance reports

+

The current at element junctions with the boom in MININEC is the current in the junction itself, since MININEC places pulses of current maximums at segment ends. For the 0.5" and the 1" booms, the current reports are as follows:

+

Relative current magnitude and phase at 146 MHz at element centers and boom junctions:

+ 
0.5" boom:
+Reflector:        2.81E-1//97.11 deg      Boom junction:    5.2E-6//10.88 deg
+Driver:           1.00E+0//0.0
+Director:         7.08E-1//-131.2         Boom junction:    5.0E-6//167.0
+
+
+1.0" boom:
+Reflector:        2.81E-1//97.11 deg      Boom junction:    5.7E-6//8.94 deg
+Driver:           1.00E+0//0.0
+Director:         7.08E-1//-131.2         Boom junction:    6.3E-6//166.3
+

As expected, the element center current magnitude and phase do not change as we change to boom diameter. However, the boom currents do change slightly. Nevertheless, the boom current magnitudes are generally in accord with NEC results for the more highly segmented model, although the phase angles do not coincide.

+

3. Ruminations on the results

+

1. The models were all given an average gain test (AGT) and returned values of 1.000, an unusually perfect score that likely resulted from the careful segmentation of the elements and boom parts. Hence, within the terms internal to NEC-4 and a highly corrected version of MININEC, the models are fully adequate, with no detectable defects.

+

2. The segment lengths are 1.17" (with very small variations from one model wire to another). The NEC current report for each segment is centered within the middle 1/3 of the segment. Junction surface penetration along a segment length is 0.25" maximum or about 21% into the segment length. This value is well short of the penetration needed to disturb segment currents during calculation, as evidenced by the AGT values. The segment lengths are restricted to the lengths shown to ensure a segment-length-to-radius ratio of over 4:1 (actual, about 4.7:1) in order to preserve model adequacy as registered in the AGT score. MININEC models are not limited by exactly the same set of phenomena, but the segment length should be at least 1.25 times the wire diameter for maximum reliability. The more highly segmented versions of the models press both NEC and MININEC to the limit of reliable performance with respect to element-length/element-diameter, but both programs return results considered reliable.

+

3. Nothing in the model itself exceeds any limitations of the programs, and there is a variance between modeled results and building experience for element-to-boom connections. Hence, one must look elsewhere for the reason why there is no difference in performance reports with or without a conductive boom connected between the parasitic elements. In the NEC-2 Manual, we find the following:

+

"In the thin-wire kernel, the current on the surface of a segment is reduced to a filament of current on the segment axis. In the extended thin-wire kernel, a current uniformly distributed around the surface is assumed. . . In either of these approximations [used in the kernel of the electric field integral equations], only currents in the axial direction on a segment are considered, and there is no allowance for variation of the current around the wire circumference." (pp. 3-4)

+

The axial current (along the element axis) does not yield a detectable interaction with the conductive boom. The only unaccounted current remaining as the source of that interaction is the current around the circumference of the wire, which is caused to vary by the presence of the boom from the level normally accompanying an element not connected to a conductive boom. IF this inference is correct, then several likely facts follow:

+

a. The region of interaction in terms of the total length of the boom is likely to be quite small, since the axial and the circumferential currents are inter-related and controlled largely by the axial currents, which are controlled, in turn, by the driver (or in larger arrays, the adjacent elements). If the current on the boom (except at the junction) were large, then current division would occur, and the general operation of a parasitic array would be thrown off by an amount that simple element-length adjustments could not overcome. In a 3-element Yagi, the source impedance due to significant current division (even of a 10:1 element-to-boom current division ratio) would not return to normal with an element-length adjustment. However, empirical evidence from building and testing Yagis suggests that element length adjustments are satisfactory to compensate for direct element-boom connections.

+

b. The most likely effect of circumferential current interaction with the boom would be to enlarge the current region at the point and very near to the connection, thus creating the effect of a stepped-diameter element. The requisite adjusted element length would be longer than for an independent element. Hence, it is likely that the technique of empirically deriving larger-diameter element insert corrections for boom-to-element assemblies and connections is a generally correct one.

+

c. An alternative interpretation based upon axial current occurs in the Guy Fletcher, "Effects of Boom and Element Diameters on Yagi Element Lengths at 144, 432, and 1296 MHz," QEX (Jan/Feb, 2001, pp. 16-22. In this account, as interpreted by the journal editor, the axial currents set up around the element circumferential magnetic field lines that intercept the boom. Although the mechanisms are speculative, the results "can be represented as a pure negative reactance, the value of which depends also to a lesser extent on the element diameter. [The effect is to require an] increase in [element] length to compensate for this reactance" (p. 20). Nevertheless, if the speculative mechanism is an accurate account and in fact controlled by axial currents, then it should produce results within NEC and/or MININEC. However, as the modeling evidence shows, no such effects appear. Although field influence is undoubtedly involved--especially in cases where the boom and elements are close but not touching--it seems more likely to be a function of circumferential currents, since NEC already accounts for variations in axial current. See also the work of Lief Asbrink, SM5BSZ, much of which is at the commercial web site, www.antennspecialisten.com (web.archive.org).

+

d. Until or unless NEC or MININEC adopts algorithms for integral equations that include circumferential currents as well as axial currents, there will be no straightforward way of actually calculating directly the exact boom-to-element interaction. Hence, these notes are speculative and deserve discarding to the degree that the process of elimination and the subsequent inferences can be shown to be faulty.

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+ +
+

Updated 10-22-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: Boom Effects, VHF / UHF, Yagi


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+

The Coaxial Folded Monopole:
+ A Modeling Adventure

+
+
+

L. B. Cebik, W4RNL

+

+
+ +
+

The coaxial folded monopole lies at the base of the coaxial collinear array and a number of other antennas. The difficulty that designers and analysts have with the antenna lies partly in our inability to effectively model the relatively simple device. However, in principle, the antenna is as easy to understand as a simple folded monopole. Fig. 1 outlines the basic considerations.

+
+ +
+

The antenna has two "legs." One extends from the ground upward to the top of the structure and bridges to a second conductor running back to the ground. Here, the term "ground" may mean a ground-plane assembly of radials, a perfect ground in models, or a mirror of the upper structure to form a coaxial dipole. In our efforts to model the coaxial monopole, we shall use perfect ground for simplicity. Any changes that we make in length to set the antenna at resonance will not depend upon the radius of a radial set. Hence, we may easily compare one model to the next.

+

What differentiates the coaxial monopole from a standard folded monopole is the fact that the conductors have a concentric arrangement, with one conductor wholly inside the larger one. Like any folded monopole, the coaxial monopole has two sets of currents. One set is the transmission-line current, where at any given point along the length, the currents on the two conductors are equal in magnitude and opposite in polarity. These currents exist on the outer surface of the inner conductor and the inner surface of the outer conductor. As well, the coaxial monopole should exhibit radiation currents, which in principle have the same polarity on both conductors. However, skin effect places the radiation current on the outer surface of the outer conductor. In principle, the coaxial monopole should have the same gain as a simple single-wire monopole.

+

Fig. 1 shows the source terminals in series with the bottom edge of the two coaxial conductors. Efforts to model the coaxial monopole cannot proceed with the actual layout of the final product because neither MININEC nor NEC can handle coaxial structures effectively. Rather than using an outer solid-wall tube as the outer conductor, most models employ a number of wires that are parallel to the inner or center wire, each equally spaced from the center conductor and from each other. Fig. 2 shows the general layout used in most models.

+
+ +
+

The sketch shows the outline of the type of model that has proven most successful and that also has numerous implementations in actual practice. The source connects to each of the outer wires in parallel. The perimeter wire at the base of the monopole only suggests the parallel connection, but does not show the best method for achieving as close to a true parallel connection as possible in a model. At the top, bridge wires connect each outer wire to the center wire that returns to the ground. Theoretically, we may reverse the source connection. We may place it on the base of the center wire, with each of the outer wires returned to ground. Herein lies a problem.

+

Casual models of the center-fed coaxial dipole appear to produce very disheartening results. If we believe such models, the center-fed coaxial monopole should not be worth the effort of building. Nevertheless, many coaxial collinear vertical arrays are in service and appear to perform to specification. In the past, a number of large arrays of coaxial dipoles were built for narrow-beam radar use. (The patents for the coaxial collinear array go back to Germany in the 1930s.) Either something is wrong with the casual models or something is wrong with the antenna design.

+

The plan for these notes is to examine the basic modeling requirements that affect models of coaxial monopoles and then to review some data drawn from the version of the antenna that has proven relatively reliable. Only after looking in some detail at the outer-wire-fed coaxial dipole will we be positioned to approach the center-fed version with some idea of what may count as successful modeling.

+

Some Basic Constraints and Specifications

+

The models in this exercise will use a test frequency of 299.7025 MHz, where 1 meter = 1 wavelength. All dimensions will be in millimeters to allow for an easy conversion of element lengths to a fraction of a wavelength. All models will use a perfect ground in NEC to allow for ready comparisons among models.

+

All wires in the assemblies will be 5-mm in diameter, using both perfect or lossless wire and copper wire in tabulated results. (At the test frequency and element diameter selected, we normally find only minuscule differences in the reported performance numbers, so that departures from that condition may prove instructive.) The center-to-center spacing between the fed wire(s) and the return wire(s) will be 20-mm, about 0.8". If the outer wires are numerous enough to form a rough approximation of a circle, the diameter will be about 40-mm. As we shall discover, 6 wires is enough to approach but not quite reach the status of a full circle enclosing the center wire.

+

Wherever relevant, we shall adjust the length of the center and outer wires together to reach a resonant length with no more than +/-j1 Ohm of reactance at the feedpoint. The values that we obtain in the first series of tests will provide a guide for what sort of feedpoint impedance emerges from a sensible model that uses a center-fed wire.

+

Besides this condition, we shall be very interested in several model properties. The Average Gain Test (AGT) is critical to testing the models and to adjusting reported values of both gain and feedpoint resistance. We shall use the AGT score to correct the feedpoint resistance value, and we shall use the AGT converted to dB to provide a corrected gain report. Some appearances of both superior and inferior performance will disappear once we make the corrections. However, we must also be aware that the AGT score is also a measure of a model's reliability or adequacy as a model. Some suggested interpretations of AGT scores supply the following meanings to attach to the numbers.

+
+ 
+AGT Value                 Meaning
+0.95 to 1.05              Highly reliable model
+0.90-0.95 and 1.05-1.10   Good model, adequate for most purposes
+0.85-0.90 and 1.10-1.15   Fair model, broadly adequate but may be refined
+<0.85 or >1.15            Poor model, inadequate for most purposes
+
+
+

We shall also be interested in the current magnitude distribution along the wires of the model. Some erroneous models of coaxial dipoles reveal their deficiency by showing both aberrant feedpoint impedance vales and an inappropriate set of current magnitude curves.

+

Outer-Wire-Fed Multi-Wire Folded Dipoles

+

The folded monopole need not consist simply of two vertical wires with a bridge wire at the top. Because the most familiar form of folded monopole performs an upward impedance transformation to a value that many user do not wish, some designers have increased the number of wires to form 3-, 4-, 5-, and 6-feed-wire assemblies. Rarely do we need to go beyond three outer fed wires to obtain a source impedance compatible with common coaxial cables (50 Ohms). Nevertheless, I extended this exercise to 6 outer fed wires to prepare the way for later models.

+

In fact, the exercise begins with a single-wire monopole as a reference point. Then it proceeds to models with 2 through 6 outer fed wires, all using the same spacing from the center return wire and all forming a regular polygon around the center wire. Each vertical wire uses 25 segments, for a segment length between 9 and 10 mm, depending upon the particular model. Each top bridge wire is the same diameter as the outer wires and the center wire to eliminate errors due to NEC angular junctions of wires having dissimilar diameters.

+
+ +
+

Fig. M-1 shows the EZNEC wire table for one of the models in the series. It uses 4 outer fed wires with a center return wire. The segmentation of the wires is clear, along with the equal spacing of the outer wires. At the bottom of the list is a very short (5-mm long) 1-mm diameter wire. Its function is to serve as the source wire.

+
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A single perimeter wire with a single feedpoint does not normally produce equal current magnitudes at the bases of all of the conductors. Even with lossless wire, the length of the wire between the source segment and the bottom of each outer wire differs enough to produce unequal current magnitudes at each corresponding segment among the 4 wires. To ensure parallel feeding of all four outer wires, I use a short wire separated physically from the antenna by an amount sufficient to prevent significant interaction between the antenna structure and the new wire. Between the source wire and each vertical leg to be fed, I run a transmission line, using the NEC TL facility. Fig. M-2 shows the lines relevant to the model in Fig. M-1. The significant aspect of the lines is our ability to select a length independent of the actual physical distance between the new wire and the outer wires. Hence, each line has the same length. Moreover, each line is exceptionally short: 0.001-mm in this case. Such a line length is too short to exhibit any impedance transformation relative to the specified source magnitude and phase angle. Hence, the characteristic impedance (Zo) is arbitrary within very broad limits. The 20-Ohm value shows no differences when changed to 50 Ohms, for example. The net effect is to create a virtual short circuit between the source wire and the base segment of each fed leg. Therefore, for a source current magnitude of 1.0, the current magnitude on each base segment is 1/n, where n is the number of fed legs. At the same time, the reported source impedance, within the limits of the AGT value, is the parallel combination of all outer legs.

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The short-TL method of deriving parallel feedpoints is not strictly necessary. You can place a source in the lowest segment of each out wire, take the average value of all 6 sources and then divide by 6 for a net feedpoint source. The result will be the same. For example, I converted the 7-wire/6-feed model into separate sources and obtained a reported feedpoint impedance of 41.0 Ohms, the same value that appears in the tabulated values below. The short-TL technique simply saves some post-modeling calculations by letting the program do the work.

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The exercise using models of multi-wire folded dipoles fed on the outer wires produced both reliable models and interesting numbers. Table 1 provides the relevant tabular data.

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Perhaps the most important columns in the table are the ones devoted to the AGT. The single-wire monopole and the 2-wire folded monopole achieve AGT values of 1.000. As we add more fed wires, the AGT values depart from the ideal value, but the more outer and bridge wires that we add, the closer to ideal the AGT becomes. No AGT value is any worse than good, which gives us confidence in applying the correctives. The gain corrective consists of subtracting the converted AGT score (10*log(10)AGT) from the reported gain. The corrected feedpoint resistance results from multiplying the AGT times the reported source resistance value.

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Although the raw NEC reports might suggest that there are small but noticeable differences in the far-field performance of the various models, the correct gain values show a remarkable equality of gain. The absence of differences between the zero-loss wire models and the copper models gives us greater confidence in this result. The corrected feedpoint impedance values show numerical differences but no operationally significant differences relative to the raw values. The impedance ratio between the single-wire monopole and the 2-wire folded monopole is 3.92:1, where a theoretically perfect value would be 4:1. However, the theoretical calculation does not take into account the 20-mm bridge wire.

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Fig. 3 shows two different facets of the series of folded monopoles from 2 to 7 wires total (1 to 6 fed outer wires). First, the required length of the monopole does not change more than about 1% over the sampled range. Second, the resonant source resistance values--both raw and adjusted--undergo an interesting progression downward as we add more fed outer wires. Moving from a 2-wire to a 3-wire model results in a 50% reduction in the feedpoint impedance. However, the impedance ratio for additional fed wires does not keep pace with the increase in the number of fed wires that gradually enclose the center return wire. We might innocently expect the 6-fed-wire model (7 total wires) to show 1/6 the impedance of the 2-wire folded monopole. However, the impedance is about 29% of the 2-wire model value at 41 Ohm reported and 41.9 Ohms corrected.

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It is likely that the feedpoint impedance of the multi-wire folded dipole could not go below the 36-Ohm value for a single wire monopole. The 6-outer-wire/7-total-wire model does not approach that value largely because it does not provide complete virtual coverage of the center return wire. (If the models had provided complete coverage, the resulting coaxial cable would have a Zo of approximately 115 to 125 Ohms, depending on the exact virtual position of the inner surface of the outer ring of wires.) Nevertheless, the 41-Ohm source impedance of the 7-wire model represents a good benchmark value for use when evaluating other kinds of models of this antenna structure. Part of this status results from its emergence from a model that we may rate as highly reliable by reference to the AGT score.

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As we increase the number of outer wires, we may also note a change in the current magnitude distribution along the wires, with special attention to the difference between the curves for the fed wires and for the center return wire. Fig. 4 shows the progression of relative current magnitudes on each of the sampled models. The single wire monopole provides a standard current distribution that runs from 1.0 at the base to about 0.1 at the top. The reported current does not go to zero in a NEC model, since the virtual sampling point is in the middle of the topmost segment, not at the wire tip. In contrast and easily expected are the current magnitude curves for the 2-wire folded monopole. The curves do not approach zero due to the fact that the assembly yields both radiating and transmission-line currents. The latter reach a peak value at the antenna top end, as the radiating current goes toward zero.

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As we add more outer fed wires to the assembly, we may note changes in the overall current magnitude distribution of the center wire. The 2-wire model shows maximum current on the return wire at the antenna base. The 3-wire model shows nearly equal overall current magnitudes at both ends. By the time we reach 4 wires, the center return wire shows maximum current at the top and minimum current at the base. Additional coverage with outer fed wires simply increases the ratio of top current magnitude to bottom current magnitude. Table 3 shows some of the differences as numerical values of the current magnitudes for 2-wire, 3-wire, 4-wire, and 7-wire models. The progression skips a few steps since the rate of change shows dramatically after the assembly consists of at least 4 wires. The table shows the top 6 segments and the bottom 6 segments of each sampled wire or wire set. Note that "top" and "bottom" reverse positions in this extraction from the NEC current tables.

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The sum of the fed wires results simply from multiplying the current magnitude on 1 of the outer wires by the number of fed wires. The procedure is accurate within the limits of the table. As we increase the number of fed wires, we may note that maximum current does not occur on the lowest segment of the fed-wire set. Rather, it occurs 1 to 2 segments higher. This condition results from the fact that the transmission-line component of the current does not change magnitude or phase angle at the same rate as the radiating current. Therefore, the highest vector sum of these current may not always occur on the source segment.

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As we move up the fed-wire set of current values, we find that the composite current on the topmost segment (1) systematically decreases as we add more outer fed wires. The same situation occurs at the top of the return wire at the other end of the bridge wires. As we move down the return wire, the 3-wire system's return-wire currents barely manage parity between the top and bottom segments. However, from the 4-wire system upward, the bottom segment of the turn wire shows less current magnitude than the top, and the reduction increases with the number of outer wires.

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The situation suggests that the behavior of the assembly changes with respect at least to transmission-line currents as we more completely surround the return wire, that is, as we approach a coaxial situation. One way to view the difference quantitatively is to sort the radiating and the transmission-line currents from at least two examples. The first sample uses the 2-wire folded monopole, the current patterns for which should be reasonably familiar. Table 3 separates the radiating and transmission-line currents for all 25 segments of the 2-wire folded monopole.

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The radiating-current column shows a pattern that exactly parallels the current distribution on the single-wire monopole. The only significant difference is that the folded monopole radiating currents change phase angle more than do the single-wire monopole currents (about 13 degrees for the folded monopole and 9 degrees for the single-wire monopole). The transmission-line current on this model shows its highest value at the top end of the structure and the lowest value at the ground plane. The phase angle is nearly a constant 90 degrees with respect to the phase angle of the source current in the model.

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To apply the same sorting process to the 7-wire model requires that we again multiply the current magnitudes (but not phase angles) of a sample fed wire by 6 to obtain a very close approximation of the total current in the fed wires. We may use the return wire without change. The results appear in Table 4.

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If we examine the radiating-current column, we find a progression that is almost the same as for the 2-wire folded monopole. Of course, we might wish to increase the maximum value to 1.0, but on a strictly relative scale, we may simply use the values shown and trace the curve from bottom to top. The curve is essentially a typical monopole curve of current magnitude along the wire assembly. The phase angle for the radiating current changes somewhat more radically as we added outer fed wires and reaches about 24 degrees for the 7-wire model.

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The greatest difference between a standard 2-wire folded monopole and the 7-wire model appears in the transmission-line columns. The 2-wire model showed large changes in magnitude but almost no change in phase angle. The model that approaches (but does not reach) the status of a coaxial assembly reverses the trends. The transmission-line current magnitude shows only a very small change (about 0.15), while the phase angle undergoes nearly a 75-degree change. It is likely that a perfect coaxial system (assuming a velocity factor of 1.0) would show slightly over 80 degrees of phase shift for a structure that is just under 90% of a quarter wavelength. (The bridge wires, at 20-mm each, are more than trivially long.) Although we must be cautious in evaluating the level of success in the model capturing a coaxial system, the small difference between the theoretical limit of phase change and the level achieved in the model is one preliminary measure of success.

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Hypothetically, we might continue the modeling process by adding further outer wires. However, practical systems that I have encountered have not risen to a 6-fed-outer-wire system. Moreover, such systems generally use thin wires around a large-diameter center return structure (such as a tower), which would present a massive difficulty for NEC. Finally, the use of 6 outer wires results in a spacing between each pair of outer wires that is the same as the spacing between the center wire and each outer wire. The sense of symmetry adds an aesthetic reason for closing the book (at least temporarily) on outer-fed quasi-coaxial systems.

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Center-Wire-Fed Multi-Wire Folded Monopoles

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In theory, we need only shift the position of the source within the 7-wire model to obtain a model of the coaxial monopole with a source on the inner wire so that the outer wires become the returns to the perfect ground. Since all outer wires terminate at the ground, we likely need not retain the TL-based parallel short-circuit among the lowest segments on the outer wires. I shall presume that some such arrangement underlies the models of a coaxial monopole that I have heard about from time to time. Accompanying reports of such models have been commentaries to the effect that the arrangement tends to have a low performance level, almost as if the outer return wires were trapping the energy within the structure. Admittedly, such comments have a casual basis, and the models are not available to me. So at most, we can only see if we can find a reason (not necessarily the reason) why one might reach such a conclusion.

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Therefore, I constructed a series of models, of which we shall sample two that I classify as potential casual models of a center-wire-fed coaxial monopole with 6 outer wires. The wires and model environment are identical to the conditions set for the outer-feed structures that we have explored. The first sample appears in the EZNEC wire table shown in Fig. M-3. The model uses no transmission lines. The bridge wires at the top of the structure are 20-mm long with the same diameter wire as the vertical legs of the structure. The segmentation is also the same as in earlier models.

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The outline of the structure appears on the left in Fig. 5. The figure also shows an alternative version of the structure. In order to ensure that the return wires electrically terminate at the end of the segment containing the source, I ended the vertical outer wires 5 mm above ground. From each "loose" end, I ran a 2-segment wire to the bottom of the center wire at the ground-plane level (Z=0). The right-hand outline in Fig. 5 should make the plan clear. The wire table in Fig. M-4 will confirm the wire structure.

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Each of these models uses the vertical leg-length assigned to the 2-wire folded dipole. I did not proceed further in length adjustment because each of these models mis-performs beyond the limits of reliability of the AGT score. The top entries in Table 5 show the situation. The model designated M-3 or Top Only has an AGT score of 0.538, when a sensible limit to even a poor but usable model is a score of about 0.85. The model reports an exceptionally low far-field gain value and perhaps underlies the sense that the outer wires somehow trap the energy in the center wire. The problem does not lie in the antenna, but rather in its model. If we use the AGT score as a correction on the gain value, we obtain a quite normal value for a monopole over perfect ground. We obtain further evidence of complete model inadequacy from the gain difference between the version using lossless wire and the version using copper wire. Ordinarily we expect a gain change no greater than about 0.01 dB. Any larger difference indicates significant trouble in the model, which the AGT score confirms.

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The model called M-4 or Top/Bot suffers an inverse but equal difficulty. The reported AGT score is 2.466, when the limits of a poor but usable model might be about 1.15. The raw gain report seems to promise nearly magical performance in the 9-dBi range. However, if we correct that gain value by reference to the AGT value, the gain drops to a more normal monopole level. Once more, we find an inordinate decrease in the gain of the model version using copper wire relative to the version using lossless wire, another indication of the model's inadequacy.

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In both casual models, the reported source data falls well outside of what we might expect, if we use our experience with outer-fed 7-wire models as a reference. Moreover, adding a corrected source resistance column would only exacerbate the difficulty. The low AGT value for M-3 would reduce the already low raw impedance value even further. Likewise, the high AGT value for M-4 would raise an already high value of source impedance. Moreover, the high value of reactance in the reported source impedance does not decrease to zero until the model height shrinks to the 80-85-mm region, and even then, the impedance is unstable. Very small changes in height create very large changes in the reactance value.

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The casual models, then, prove to be wholly inadequate to capture the performance of a center-wire-fed 7-wire monopole structure. Table 5 also contains performance reports on three models (out of many that I constructed along the way) that may prove more useful. I modeled them to yield reasonable gain values, good AGT scores, and source impedance values that seem to be relatively typical for 7-wire folded structures. Hence, I call them careful models, but not necessarily ideal models. Each model records an AGT of 1.000, since nothing in the structure comes close to pressing any NEC limit. All of the wires use a simple straight uniform diameter geometry. Fig. 6 shows some suggestive outlines.

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Model Top-Bot forms the baseline for the series. At the top, it eliminates the bridge wires and replaces them with TL short circuits of the same type used for the feed system of the outer-fed monopoles. However, each top TL runs between the top segment of the outer wire and the top segment of the center wire. At the base of the model, I also used TL short circuits to connect together the lowest segments of the outer wires. The only difference between these TL entries and those of Fig. M-2 is that the source is not on the external junction wire, but on the lowest segment of the center wire. This model forms perhaps the key comparator with the performance of the 7-wire outer-fed monopole.

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The data in Table 5 shows very normal gain performance. The slightly high gain value (by 0.03 dB) results from the fact that the overall height of the model is taller than the models for the corresponding outer-fed monopole. In fact, the length is about as much longer than the single-wire monopole as the outer-fed systems are shorter than the single wire monopole. The extra length stems from replacing the bridge wires--which do affect current distribution--with TL shorts that have no practical length. The correlation cannot be precise because the TL connections extend from the virtual centers of the segments to which they are attached, and each segment is between 9 and 10 mm long.

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The reported feedpoint impedance is about 45.2 Ohms, only slightly higher than the value yielded by our final outer-fed model. As a consequence, we may account this model to be a reasonable facsimile of an actual center-fed 7-wire folded monopole. For functional analyses, the model may prove sufficient. However, it is not perfect, since the replacement of bridge wires at the top with TL shorts modifies the current distribution relative to a physical structure. The modification becomes more evident if we sort out the radiating and transmission-line currents, using the same method employed for the corresponding outer-fed 7-wire model. Compare Table 4 with the data in Table 6.

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The radiating current column shows a progression of magnitude values not very different from the ones in the earlier table. Indeed, one might account any magnitude differences to the slight height differences between the two models. The change in radiating current phase angle is somewhat greater than in the outer-fed model, but does not reach suspicious or doubtful levels. The key difference lies in the transmission-line current columns, especially in the range of phase angles from bottom to top. The outer-fed system showed a considerable (74-degree) shift in phase angle, while the center-fed model shows slightly less than 45 degrees. It is likely that the bridge-wire replacement with TL shorts is the major source of the difference, but the degree of error attributable to each model remains unknown in the present context.

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Both the center-fed and the outer-wire-fed models show impedances in the 40-45-Ohm region. The curves shown by Fig. 3 suggest that a truer coaxial structure would gradually approach the source impedance of the single-wire monopole. Therefore, I performed a 2-step experiment, adding TL shorting structures around the outer wires of the center-fed model. The first step added a set of shorts half way up the structure. The final step added two more encircling shorts at the one-quarter and three-quarter length points. Fig. 6 shows the outlines of these models, while the final lines of Table 5 provide the resulting data. Since the TLs add nothing to the actual geometry, they do not affect the AGT score.

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As we add the TLs, the resonant height of the structure decreases somewhat. As a consequence, the reported maximum far-field gain also decreases slightly. Perhaps more significant within this context is the continued decrease in the source impedance value. The final figure in the table is almost identical to the value for a single-wire monopole. However, we should not too quickly equate the two, since the effective diameter of the 70-wire model is many time the diameter of the single-wire monopole.

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The final models are an attempt (but not necessarily a fully successful one) at capturing the performance of a true coaxial monopole composed of a center wire and a virtually solid outer shell. The model suggests that the idea of a coaxial monopole is sound. The radiating (or common-mode) currents yield normal operation for a monopole. At the same time, the transmission-line currents remain within the structure, that is, between the outer surface of the inner conductor and the inner surface of the outer conductor. The short circuit at the monopole top ensures that the impedance at the bottom will be a parallel combination of a very high impedance value 1/4 wavelength from the short and the resonant monopole impedance. The result, under ideal conditions, would simply be the monopole impedance.

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The simplified impedance analysis presumes a velocity factor of 1.0 and no further geometric disturbances to the structure. However, bridge wires at the top of the structure modify the current distribution. If we add the normal material found within real coaxial cables, the current distribution may show further non-ideal conditions. Therefore, cutting a real coaxial monopole to length and still having a usable impedance value may prove to be a somewhat finicky task. Nevertheless, the existence of successful coaxial collinear monopoles and dipoles attest to that fact that the task is feasible.

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Conclusion

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Our goal has been to explore the possibility of modeling the coaxial monopole. To that end, we set up a test environment over perfect ground and created a series of models at 299.7925 MHz. The first series used well-established techniques for parallel feeding the outer wires of such systems while adhering to tight NEC guidelines for equality of diameter throughout the model. These models showed that we can model structures using up to 6 relatively fat outer wires and obtain results that both are reasonable and show a progression of feedpoint values and other transitions toward a true coaxial situation.

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We next turned to center-fed models and had to modify the antenna geometry and the method of connecting wires to avoid wholly unreasonable AGT values. One result was a model that replicated very closely the performance of the corresponding outer-fed model, while preserving an ideal AGT score. We further pressed the center-fed model toward true coaxial conditions, but remained cognizant of limitations other than the AGT score they may reduce the accuracy of the model relative to a physical implementation of a coaxial monopole.

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Since there is a theoretical (tight) and practical (rough) equality between the outer-fed and the center-fed 7-wire models, the choice of which to use within a more complex structure remains a modeler option. In some ways, the 7-wire outer-fed model may be simpler and more direct to use when modeling such arrays as the coaxial monopole or dipole. Notwithstanding, the exercise has demonstrated that there are ways to model both feedpoint positions with multi-wire folded monopoles.

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Updated 03-01-2007. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for February, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: VHF / UHF, Vertical


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Notes on Modeling and Convergence Testing

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L. B. Cebik, W4RNL

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+ Every commercial method of moments antenna modeling software manual warns the user to perform convergence testing to validate to the extent possible the reliability of the model. Many such packages also offer automatic wire segmentation, using algorithms developed from the basic NEC criteria for recommended minimum segment lengths. Unfortunately, for many users, the two facilities come into conflict, and convergence testing loses out. In fact, convergence testing should always take priority over the modeling speed made possible by automatic segmentation of wires. +

Convergence testing is the process of increasing the number of segments in each wire of a model until the program output values change by only insignificant amounts relative to the purpose of modeling. Notice that what counts as satisfactory convergence may vary according to what the modeler wants to get out of the exercise. Among the most used outputs are gain, front-to-back ratio, feedpoint impedance, and antenna current magnitudes and phases.

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Every antenna model should be tested for convergence of results. Otherwise a model cannot be counted as a reliable indicator of antenna performance, with resultant uncertainties about construction, adjustment, or evaluation. However, convergence testing should only occur after certain basic good modeling practices have been employed. To the degree permitted by the antenna structure, antenna segments in parallel and almost parallel wires should be aligned. The wire containing the feedpoint should be examined to ensure the correct source type--single or split--according to the segmentation and desired source position. Segment length minimums should be checked at the highest frequency of interest. For greatest utility of all program outputs, segmentation should begin at one consistent end of each element and progress in the same direction until reaching the other end of the element. For some types of antennas with linear elements, the only difficulty posed by violating this practice may be reading the current levels and phases on each wire of the model. For antennas with phasing networks built into the model or with certain orders of complex geometry, almost all outputs may become erroneous if consistent wire construction practices are not followed.

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Once the model is in good order, convergence testing can begin. Some models may show convergence with the first increase in segmentation. Some may require only 2 or 3 test steps. Others may require many steps. Finally, some models may never converge. A model that fails to converge over critical performance outputs cannot be considered reliable at any segmentation without some external standard.

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Here are some examples of convergence results taken on EZNEC, which permits automatic segmentation at two levels: a level of absolute minimum numbers of segments per half wavelength (Smin) and a level of recommended or conservative numbers of segments per half wavelength (Scon). It is always tempting to model at the least possible number of segments, since every extra segments adds to the time required for NEC to make its matrix calculations. So we shall begin each sample model with the absolute minimum segmentation to see what happens. Besides Smin and Scon, we shall use the following abbreviations: Saligned = segments equalized in length and aligned with those of parallel elements; Sx## = the segmentation of Scon multiplied by the number ##.

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1. A dipole element for 20 meters with many steps in diameter. Note: many versions of NEC-2 contain a stepped-element diameter correction algorithm, since NEC-2 produces unreliable results without it. NEC-4 handles stepped diameters directly. In this example, NEC-2 results are used. We shall look only at the feedpoint impedance of this free space model

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Model     Total Segmentation       Feedpoint Z (R +/- jX) in ohms
+Smin            9                       81.5 + 39.3
+Scon           15                       81.1 + 39.5
+S aligned      21                       81.3 + 40.2
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Clearly, for most purposes, such as building the antenna element in question, data produced by the minimal model is quite reliable. This is generally true of one-element linear antennas, although for multi- wavelength antennas, higher levels of segmentation may be needed.

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2. To the element of example 1., we might install a center section 2 or more times the diameter of the adjacent sections to simulate boom mounting hardware.

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Model     Total Segmentation       Feedpoint Z (R +/- jX) in ohms
+Smin           11                       78.5 + 29.6
+Scon           15                       79.7 + 31.8
+S aligned      21                       80.0 + 32.5
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Although the model seems sufficiently reliable for most purposes at all level of segmentation, note the differentials in values for each step of increase. The decrease of difference between the Scon and S aligned levels is precisely the definition of convergence. Here, the difference may make no practical difference, but it might for an antenna of which this element is but one of many.

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3. Let's look at a 5-element Yagi using the element in example 1 as the driven element.

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Model     Total               Gain      F-B Ratio      Feedpoint Z
+          Segmentation        in dBi    in dB          (R +/- jX) in ohms
+Smin            45            10.1      24.3           38.9 + 23.5
+Scon            69            10.2      23.9           38.4 + 22.8
+S aligned      102            10.2      23.7           38.4 + 22.6
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Since the Yagi elements are linear and gently tapered, the results achieve almost instant convergence at a practical level.

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4. Lest we grow overconfident that convergence is an easy thing to achieve, consider the following 2-element beam using an extended double Zepp driven element and a pair of reflectors, one at each extremity of the driven element. The elements are quite closely spaced. These figures are for a height over medium ground of 50 feet on 20 meters. Elements are #12 copper wire and begin well aligned.

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Model     Total               Gain      F-B Ratio      Feedpoint Z
+          Segmentation        in dBi    in dB          (R +/- jX) in ohms
+Smin            24            12.9      12.1           93.6 - 1297
+Scon            46            12.8      12.5           80.3 - 1120
+S x 1.5         70            12.8      12.5           68.9 - 1016
+S x 2           92            12.8      12.4           66.6 -  992
+S x 2.5        114            12.8      12.4           64.9 -  976
+S x 3          138            12.8      12.4           62.5 -  956
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In this exercise, checking only the gain and front-to-back ratio would have misled us into thinking that the model had achieve convergence at an early stage--perhaps between the Scon and S x 1.5 levels. However, suppose we plan to stub-tune the antenna. Stub construction requires a reasonably accurate measurement or forecast of feedpoint impedance. This particular model achieves convergence at the 1.5-2% level only as we increase segmentation considerably. Had we used the feed impedance provided by the conservative auto-segmented model, our initial stub would have been way off the mark. In short, before ended a convergence test, be sure to check all of the relevant output data.

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5. Let's try a single quad loop. To make matters interesting, we shall make it square, with the horizontal members made from 0.5" diameter tubing and the vertical members from #12 wire. We shall feed the center of the bottom horizontal section and place the whole thing in free space. Here is what we get within the limits of most ham versions of NEC-2.

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Model     Total               Gain      Feedpoint Z
+          Segmentation        in dBi    (R +/- jX) in ohms
+Scon            28            3.61      154 +  81
+S x 1.5         44            3.60      158 +  91
+S x 3           84            3.59      164 + 108
+S x 4.5        124            3.58      168 + 119
+S x 9          244            3.57      175 + 140
+S x 16         444            3.56      183 + 161
+[MININEC       240            3.61      137 -   6]
+[MININEC        56 (tapered lengths)
+                              3.61      137 -   2]
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In this example, convergence is never achieved with respect to feedpoint impedance, even though the gain stabilizes from the beginning. Consequently, there is no internal evidence produced by NEC-2 that any of the output data is reliable.

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By importing an external standard, we can judge that the smallest segmentation produces outputs closest to reality for cases in which NEC-2 encounters angularly joined wires of different diameters. MININEC is the standard used here, and by its internally correlated figures it suggests that at any level, the feedpoint impedance figures of NEC-2 are unreliable for this type of case.

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Knowing in what cases a modeling program yields unreliable data is just as important as making good use of reliable data. Convergence testing is one method of establishing the reliability of some data and the unreliability of other outputs.

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The examples, may be multiplied, and perhaps from time to time, I shall add others. In the meantime, I hope this little survey clarifies the principles of convergence testing and helps make it a part of every modeling exercise.
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Return to Amateur Radio Page

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Topics: Modeling


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Notes on Fat-Wire Dipole Convergence:
+ MININEC, NEC-2, NEC-4

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L. B. Cebik, W4RNL

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A standard dipole at HF made from commonly used materials can be accurately modeled in any of the NEC-based programs using minimally recommended segmentation. Convergence testing (increasing the segmentation density) confirms the accuracy of the model for virtually any purpose the model might be used.

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Similar behavior is often expected from dipoles of increasing diameter, for example up to 1' at 14 MHz. 2 * PI * radius (circumference) / wavelength must be much less than 1, a condition easily met by this large dipole. MININEC prefers the largest minimum segment length to diameter ratio: 1.25:1. This condition is easily met if the segmentation density is about 40 per half wavelength or less.

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Even within program limitations, however, the modeler encounters some interesting program-to-program variations that are worth noting. They may not be operationally significant in terms of model reliability. Still, they will increase our awareness of program tendencies and trends, thus enabling the modeler to view a certain set of progressions as either expected or unusual.

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To see what happens with fat dipoles, I systematically modeled a sequence of resonant dipoles at 14.0 MHz. Since I was interested in the numerical progressions (rather than operationally-relevant limitations), I defined resonance as a source reactance of less than +/-0.01 Ohm. This permitted very small variations in resonant length to show up with normal graphing means. To encompass the widest range of diameters in the smallest span of runs, I used a semi-logarithmic progression of diameters: 0.0843, 0.2666, 0.8431, 2.6660, and 8.4306 inches. Remember that the point of this exercise is numeric: therefore, outputs will be recorded to more decimal laces than within a practical modeling exercise.

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MININEC 3.13

The MININEC graph of results for free space dipoles of zero-loss wire demonstrates an unexceptional progression of lengths through convergence from 10 to 40 segments per half wavelength. The following table shows the segment length related to a median dipole length of 400" and the resultant length-to-diameter ratios for the graph. + 
Segments  Length/        Ratio of Segment Length to Wire Diameter
+          Segment"  0.0843    0.2666    0.8431    2.6660    8.4306
+10        40.00     474.50    150.04    47.45     15.00     4.75
+20        20.00     237.25     75.02    23.73      7.50     2.37
+30        13.33     158.17     50.01    15.82      5.00     1.58
+40        10.00     118.62     37.51    11.86      3.75     1.19
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As is evident, segment lengths and wire diameters were selected based on a wavelength at 14.0 MHz, 843.0611 inches. The smallest wire diameter is close to the diameter of #12 AWG copper wire (0.0808").

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MININEC results are entirely unexceptional. As the dipole diameter increases, the rate of decrease in resonant length with increasing segmentation is greater. However, the largest single change in value occurs between segmentation densities of 10 and 20 per half wavelength. For the thinnest wire, the difference between the least and most segmented wires is a little over 0.3" in length, while for the fattest wire, the difference is a bit over 3.5" in length.

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The line for the 0.84306" diameter wire is virtually linear between segmentation densities of 10 and 40. Lines for thinner wires show an upward trend between densities of 10 and 20, while lines for fatter wires show a downward trend in the same region. Nonetheless, the variation from linearity for the 100:1 range of diameters is quite small. Moreover, the curve for the fattest wire, even though it exceeds the limitation of MININEC for diameter to segment length, shows no radical departure from the general trends.

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For this and NEC tests, similar runs were made using wires with some material loss (aluminum). No detectable difference in the trends was noted, so no further reference to them is needed here.

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The version of MININEC used (3.13) is uncorrected for the 0.5% frequency shift relative to NEC-2 and NEC-4. Frequency correction would have changed the absolute values of resonant dipole length, but not the trends recorded on the graph.

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So far, our investigation has made a colorful graph, but otherwise has been seemingly devoid of interest. It acquires interest only as we compare it with NEC.

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NEC-4

The corresponding graph for NEC-4 adhered as closely as possible to the same standards as the one for MININEC. However, segmentation was increased by 1 to ensure that the source placement would be centered. This altered the table of segment lengths and the ratios of segment length-to-diameter in the following way: + 
Segments  Length/        Ratio of Segment Length to Wire Diameter
+          Segment"  0.0843    0.2666    0.8431    2.6660    8.4306
+11        36.36     431.29    136.38    43.13     13.64     4.31
+21        19.05     225.96     71.46    22.60      7.15     2.26
+31        12.90     153.01     48.39    15.30      4.84     1.53
+41         9.76     115.77     36.61    11.58      3.66     1.16
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The corresponding graph of NEC-4 runs with a free space dipole of lossless wire at 14.0 MHz yields some interest results, if we look closely.

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For all but the fattest wire, the curves are very well behaved. There is only 0.2" difference between the shortest and longest resonant dipoles for the thinnest wire and less than 0.8" difference for a wire over 2.5" in diameter. These figures are more tightly grouped than the corresponding figures for MININEC.

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However, if we examine the curve for the fattest wire, its behavior should arouse some curiosity. The curve is at every point the opposite of the curves for the other wire diameters. This behavior is not a function of having passed a certain program limit, since only the highest level of segmentation density surpasses the limit we set for MININEC. Moreover, the rate of change for the fattest wire is nearly three times the rate for the next size lower.

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Somewhere between the two largest diameters explored in this general test, the NEC-4 curves changed direction. The nature of the change called for more detailed modeling of intermediate values. So I checked wire diamters between 3.0" and 7.5" in diameter. Some key results for the x.5" values are shown below.

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The graph of intermediate values of wire diameter shows how the curvature changes. The curves show that for any wire diameter, the downward trend typifying thin wire dipoles is only temporary. With increasing segmentation such that the wire diameter grows closer to the segment length. there is a relationship that yields the lowest resonant dipole length. This value is in the vicinity of 0.3 for the ratio of diameter to segment length. For both higher and lower values of the ratio, the resonant length tends to increase.

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The results of this sequence of models can be replicated at any frequency by scaling both the length and the diameter of the wire along with the frequency. Runs made at 28 MHz with wires of half the diameters resonated within limits with exactly half the length of those used in the 14 MHz test. The ratio of segment length to diameter remained the same. The behavior of the curves is endemic to NEC-4.

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The result has some implications for convergence testing with relatively fat wires. The fatter the wire, the less applicable the convergence test. First, increasing the number of segments per half wavelength more quickly approaches the implicit length-to-diameter limit of the program. Second, the rate of rise in resonant length for the fattest wires suggests that convergence will not be obtained in some cases.

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Despite these results, nothing peculiar arises with respect to either reported gain (2.12-2.14 dBi free space gain throughout) or source impedance (total range: 71.82 to 73.16 Ohms resistive). Hence, although the behavior of the NEC-4 curves is quite interesting, little of operational significance emerges from it beyond the realm of convergence testing.

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NEC-2

The curves for NEC-2 are singularly uninteresting for all diameters except the fattest (8.43"). In fact, they overlay the NEC-4 curves better than most gloves do hands. Hence, for all values up to about 2.5" diameter wires, the NEC-4 curves may also be called the NEC-2 curves. +

However, for the fattest wire, there is a notable difference in the behavior, as shown in the following graph:

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The NEC-4 curve is identical to the one on the general graph, but expanded by the graphing system. The NEC-2 curve, however, resembles most the NEC-4 curve for a wire of 5.5" diameter. In short, with respect to dipoles, NEC- 2 is somewhat better behaved when it comes to fat wires in isolation, possibly by a factor of 1.5. The shortest resonant dipole length appears to occur when the diameter is about 0.4 to 0.5 the segment length.

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Conclusion

No significant conclusions emerge from this inquiry other than those to be found in the graphs. MININEC, NEC-2, and NEC-4 each respond differently to increases in segmentation density when wires of very large diameter (relative to frequency) are involved. Understanding these differences will at most reduce the number of surprises we encounter while modeling, and thus let us devote more time to the design exercise and less to wondering if we have done something wrong. This exercise in systematic modeling has at least satisfied a curiosity.
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Updated 3-11-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Amateur Radio Page
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Topics: Modeling


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Some Pitfalls of Careless dBd-ing

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L. B. Cebik, W4RNL

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In an earlier note on why I use dBi--mostly, written over 2 years ago, I distinguished several possible meaning for dBd, each of which was distinct.

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dBd-I (Ideal): Since a free space lossless infinitely thin-wire dipole has a gain of 2.15 dBi (Isotropic), this interpretation of dBd simply subtracts 2.15 from the gain in dBi and presents a gain number. It has no application except in free space.

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dBd-RM (Real Model): A dipole constructed of the same material as an antenna used for comparison and placed in a model at the same height over the same ground type may make a meaningful comparison. Many antennas with directional patterns (Yagis, for example) do not experience the same gain fluctuations as a dipole does at varying heights below 2 wl, so the comparison must be used with caution. By judicious selection of heights without revealing those numbers, one can make a given antenna look up to 0.5 dB better than itself.

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dBd-RR (Real Range): A range test will use a relevantly similar dipole as a comparator for horizontally polarized gain antennas under carefully controlled test circumstances and procedures. Since the range test cannot use an isotropic radiator as the baseline comparator, translation of range tests into dBi is only dome with caution and often may be dispensed with altogether.

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One of the difficulties of dealing with live claims of antenna (especially Yagi) gain given in dBd is that the sources rarely tell us which--if either--sensible meaning of dBd is being used. So we are left to our own devices in evaluating these claims. One major exception has been the independent comparative studies of N0AX and K7LXC (HF Tribander Performance, now in its 2nd expanded edition), which has used a thoroughly discussed and consistent methodology throughout. Even if one should disagree with any of the results obtained, one has at least a firm foundation for resolving outstanding issues.

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Trying to Have Reasonable Expectations

Having a set of expectations for what is sensible by way of gain claims, whatever the baseline for the claimed gain, is a challenge. There are some guideposts that can assist us. +

1. Jim Lawson, W2PV, established in his classic, Yagi Antenna Design, that gain is a function of boom length and that for any given number of elements, there is a maximum gain length, after which gain tends to level of fall off. The maximum gain figures obtainable are accompanied by a quite narrow operational bandwidth over which they obtain and also by mediocre front-to-back (or front-to-rear) figures. More realistic gain expectations run at least 1 dB below maximums when accompanied by a satisfactorily broad operating bandwidth and a reasonable front-to-back ratio--usually expressed in terms of a 20 dB standard.

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However, if we are not careful, we can misuse Lawson's work by putting into out minds a single figure for a given boom length and forgetting the bandwidth aspect of the situation.

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2. Programs like YA (the K6STI variant of his full featured YO Yagi Optimizing program) can develop a good sense of what is sensible with Yagi design, using the N6BV optimized designs plus some others of local origin. The key is to use the graphical outputs to supplement number sets in order to understand the performance of Yagis across a desired bandwidth.

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Fig. 1 shows the gain and front-to-rear performance of a 3-element Yagi on a 0.22 wl boom (about 8') for the 10-meter band. Note that the gain climbs steadily across the band from below 7.2 dBi to nearly 7.5 dBi. I this design, the front-to-rear ratio creates a plateau, with a rapid fall-off at either end of the band covered.

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In Fig. 2, we have essentially a scaled version of the same antenna (0.22 wl boom, about 16') for the 20-meter band. The gain progression yields quite similar numbers, and the front-to-rear plateau is simply displaced in the band slightly, relative to the 10-meter curve.

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If we lengthen the boom to about 0.33 wl (about 24'), we can obtain additional gain, as shown in Fig. 3. As with most 3-element deigns, the gain increases across the band from about 7.95 dBi to 8.4 dBi. In this design, the front-to-rear ratio peaks at a very high value, but at the upper end of the band it drops to about 18 dB.

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If we compare antenna gains in terms of dBd-I--since these are free space models--then the 0.22 wl beam provides a gain range of 5.0 to 5.3 dBd-I, while the longer boom model runs from 5.8 to 6.2 dBd-I. Note that these numbers apply to aluminum elements that are full length. On 20 meters the maximum reflector length is about 34.5', while on 10, the same element is over 17' long.

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In general, these are quite good numbers considering the composite specification requirements for gain, front-to-rear ratio, and operating bandwidth. (It should be clear that I am ignoring matching considerations in this discussion.)

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Triband Yagis of boom lengths similar to those used in the examples can approach the monoband figures, but only through the use of added elements--which may take a number of forms. Out-of-band elements may contribute to gain on a given band if their positions provide some "forward stagger" effect. Negative effects of an out-of-band element can be (sometimes) overcome by the careful placement of a compensating in-band element. In evaluating tribanders, we should look at the boom length as a fraction of a wavelength for each band covered and develop gain standards accordingly.

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Using Our Expectations

I recently ran into some interesting gain claims for a pair of triband Yagis, each with 3 elements. The gain numbers looked like the following: + 
Antenna                       A                   B
+Gain:  10 m                   4.5 dBd             5.5 dBd
+Gain:  15 m                   3.9 dBd             4.5 dBd
+Gain:  20 m                   3.2 dBd             4.0 dBd
+Boom length                   6.0'                9.8'
+Longest element               16.8'               12.3'
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Nowhere did I find any basis for these numbers, so my only recourse was to assess the claims against what I have learned about Yagis from modeling several hundred of them and building a number of the models in to functioning antennas.

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Let's look at the higher claims for antenna B first. The 10-meter gain claim exceeds that obtained for the 0.22 wl boom monobander, even at its peak. However, the boomlength of B is 0.27 wl on 10 meters, so the gain claim has some initial plausibility. However, the elements are only 3/4s full size. Shortening elements of any dipole-based antenna array, such as the Yagi, will result in some slight gain reduction per element, which is cumulative. These numbers do not specify how the elements are electrically lengthened to full size--or even if the entire element is functional on 10 meters.

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On 15 and 20 meters, the elements diminish to a maximum of one-half and one-third full size. The boom length reduces to 0.22 wl and 0.14 wl for 15 and 20, respectively. The gain of a 2-element Yagi (driver and reflector) using full size elements will be about 6.2 dBi or 4.0 dBd-I in free space for a spacing of 0.12 to 0.15 wl. That gain will vary across the band, and since it lacks a director, the gain will fall with increasing frequency. Yet antenna B, with element only 1/3 full size and no specification of the means of electrical lengthening claims the same gain.

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The claims of antenna A are more modest. On 10 meters, the claimed gain is about the peak gain of a decent 2-element monoband beam using the same boom length--6 feet. This antenna uses elements that are full length on 10 meters, but once more does not in these numbers specify how much of the element is active on each band.

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On 15 and 20, the elements shrink to 3/4 and 1/2 full size, but once more, without specification of electrical lengthening methods or the amount active on each band. The boom length shrink to 0.135 wl and 0.085 wl on 15 and 10, respectively.

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What's a Poor Consumer to Conclude?

Note that I have not claimed anywhere that these antennas do not achieve their claimed figures. If dBd-I is the operative notion of gain involved and if applied in free space, then it is possible that the designs might achieve these numbers as a peak figure. That they achieve such gains as a band average is dubious, because shortened elements and shortened booms tend to reduce operating bandwidth (regardless of SWR bandwidth) very significantly. Moreover, element placement for a given monoband design is a function of placement on the boom in terms of fractions of a wavelength, and using a fixed physical dimension placement tends to result in lesser performance of the bands for which placement is not optimal. +

Of course, if dBd does not mean dBd-I, then this entire exercise is meaningless. However, so too are the gain numbers claimed, since they have no reference. Even should someone to claim, "This is what I measured on the range," (that is, used dBd-RR), we would have to have a complete description of the test methodology and the dipole used as a comparator before we could begin to assess the numbers.

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If the numbers refer to dBd-RM, then--of course--one wants to see the models used and to assess them for oneself. That would require the revelation of far more technical detail than is usually made available to potential buyers. We may note again in these numbers the absence of data regarding the active length of each element on each band and the method of electrically lengthening elements to full size.

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Hence, for the case study used here, one must regretfully conclude that in the absence of much more extensive data, the numbers are meaningless. Of course, one set of meaningless numbers compared to another set of meaningless numbers yields a meaningless comparison. From the claimed figures we learn nothing about the respective antennas--except the length of their longest elements and their boom lengths. Unspecified used of dBd for gain claims too often leads to just this result.

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However, even had the numbers been given in dBi, one still would have had to know a great deal more before those numbers would have been in any way informative. Spot numbers--even based on published models or tests--are potentially misleading. Curves across a desired operational bandwidth are far more informative.

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Updated 6-3-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: Modeling


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Why I use dBi - Mostly

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L. B. Cebik, W4RNL

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Although current commercial practice is to specify antenna gain in dBd, I tend in my modeling work to use dBi. It is reasonable to ask why, if for no other reason than to understand better the other entries in this collection of notes. So I shall explain why. My object is not to get anyone to change their preferred ways, but only to make a little clearer my preference for specifying gain in dBi.

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dBi

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Every measure in decibels, or dB, is ultimately a relative power measurement (with some defined relative voltage and current measures having been derived from the basic power measure). Decibels are defined this way: +
+ Relative power in dB = 10 log (base 10) P1 / P2, +
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where P1 and P2 are two power levels measured in the same units (e.g., watts).

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Since we may pick any two powers for P1 and P2, power gain or loss is strictly relative.

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However, we have found it useful to select--for specific purposes--certain baseline power levels. One such level is whatever power there might be in the radiation far field of an isotropic radiator. An isotropic radiator is a lossless dimensionless point in free space that radiates equally well in all directions. Although some say this is a absolutely theoretic concept only, Brian Beezley, K6STI, has established that a pretty good approximation of an isotropic radiator can actually be constructed.

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Using this radiator as the baseline and taking measurements at the same far field distance from the antenna, the power received from the antenna will have a certain relative level in comparison to what would have been received from the isotropic radiator. What that level is depends on the characteristics of the test antenna and the direction in which we choose to take the readings, using a full 3-dimensional sphere as the possible directions for readings. In some directions we may get more power; in others we may receive less.

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One of the chief advantages of the isotropic radiator is that its field never changes, so that it functions as an agreed upon constant against which every antenna may be measured in every direction.

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Every antenna measurement referenced to a P2 that is the far field power from an isotropic radiator has a positive or negative gain in dBi.

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Gain

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When we casually refer to antenna gain, we do not normally mean the gain in any haphazard direction from the test antenna. Nor do we mean all the possible gain numbers we might gather from a systematic tour around the surface of our far field globe surrounding the antenna. Gain in every direction is important, for it defines the antenna pattern and tells us where the far field is strongest and weakest and in the middle--and by how much. +

However, when we casually mention gain, we are usually interested in the direction(s) of maximum gain from a given test antenna. Then we rotate the antenna to present that antenna direction to the receiving station. For satellites, we may rotate in 3 dimensions, but for HF, 2-dimensional rotation usually suffices (unless we must somehow compensate for a bit of tricky terrain and have the wherewithal to do so).

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We can specify maximum antenna gain in terms of dBi. Then we can compare maximum antenna gains from 2 or more antennas by citing their gains in dBi and merely comparing numbers.

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This practice is perfectly reasonable so long as we do not make it a fetish; that is, so long as we do not use this number exclusively in our gain considerations. Horizontal beamwidth is also important and is usually defined in terms of the number of degrees between half-power or -3 dB points where the direction of maximum gain is the center. Vertical beamwidth is also important in estimating the success of a potential path. We also want to know, in conjunction with vertical beamwidth, the elevation angle of maximum radiation. Together, these numbers give a more complete picture of antenna performance in a desired direction than raw gain alone.

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I have modeled an array with a 21 dBi gain figure. However, the horizontal beamwidth is only about 17 or 18 degrees wide, making it unsuited for general amateur operation. However, we often assume that competing antennas have the same beamwidth and that all we need to know in making our selection is the maximum gain. Good practice calls for making no such assumption. Rather, before we focus on maximum gain, we should establish that all other factors are equal.

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dBd: a warm but fuzzy concept

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The concept of dBd was formed to capture the gain of an antenna relative to a dipole. A dipole is considered the standard basic horizontal antenna, and comparisons to it seemed to some folks to be more meaningful than comparisons to the isotropic radiator. +

Unfortunately, the concept of dBd has become a cluster of concepts. Here are some of them. The notation is my own, since few folks are anxious to distinguish the individuals in the cluster.

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1. dBd-I: dBd ideal compares the gain of an antenna to an ideal dipole in free space. An ideal dipole uses infinitely thin lossless wire and is resonant at the frequency of interest. In this application, the ideal dipole has a gain of about 2.15 dBi, that is, 2.15 dB over an isotropic radiator. All measurements are thus arithmetically transportable between dBi and dBd-I by adding or subtracting 2.15, as appropriate.

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dBd-I is of limited utility, since my backyard dipole may have a gain of 7.15 dBi and 5 dBd. Some folks become confused by the idea that a dipole has gain over a dipole. We then have to explain that the real wire dipole has gain over the perfect dipole in free space. That rarely helps a lot. And it does not tell us until we do some arithmetic how much gain some other antenna has over a real dipole.

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2. dBd-RM: dBd can be expressed as the gain over a real dipole modeled at the same height as the test antenna. For studies that are strictly modeling investigations, this measure is sometimes useful. However, it requires that we further specify the construction of the dipole in terms of element diameter and element material. Using the same material, dipole gain will vary with element diameter. It will also vary inversely with the loss of the material used for the dipole.

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Both these constraints apply within the further rule of keeping the dipole resonant. If we make measurements across a ham band, we shall find that the dipole gain varies with frequency unless we re-resonate it for each readout frequency. Actually, we are usually more careless than this and take one resonant reading and apply it across the band without checking. And we tend to use fairly loose standards of resonance rather than converging the results. We may more precisely say that an antenna is resonant when the reduction of feedpoint reactance results in no further changes in gain to the number of significant digits that apply to the test.

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As one more qualification, we should note that dipoles and other antennas may have different elevation angles of maximum radiation over the same type of ground. When we cite dBd-RM, we must also say whether we are giving the figure for the dipole at its angle of maximum radiation or at the angle chosen for the test antenna. To avoid confusion, it is usually better to give details about the differing elevation patterns.

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3. dBd-RR: dBd can be expressed as the gain over a real dipole set in the same position as the test antenna, where both antennas are oriented for maximum gain relative to the far field receiving site of the test range. For fairness, one should specify the construction of the dipole to ensure that the materials are comparable to those of the test antenna.

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However, there are a number of variables that occur within this way of handling dBd. First, range conditions vary considerably from one site to another. Second, some testers take the average of a number of readings in various directions, while others take readings along a single line defined as the best test line. Third, different ranges may use different test heights. The importance of this factor stems from the fact that many antennas that might be tested have different elevation angles of maximum radiation than a dipole, and this variance may introduce differences in readings as we change test antennas and as we move from range to range with different test antenna heights.

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Good testing and modeling protocols would specify all of the relevant factors applying to the comparisons involved. We sometimes do find these specifications. Unfortunately, we often don't. Without the specifications, comparisons in dBd-R (either M or R) are quite difficult to make. If we could only bring all antennas to a single test range with a single (large) set of dipoles and standardized conditions, we could likely establish the gain of each antenna over its standard dipole and then have truly precise comparisons among antennas. Someone has noted to me that the odds of the earth being struck by a meteor like the one which ended the reign of the dinosaurs are higher than the odds of the emergence of a universal test range. I really wish I could have disagreed with this individual.

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For additional pitfalls of careless dBd-ing, see the next item on the Index.

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Why I tend to stick to dBi

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My antenna work includes the building of test models of antennas that are feasible to construct, but is devoted predominantly to modeling all sorts of antennas for all sorts of purposes. This factor alone suggests the use of a single standard for all comparisons, such as dBi. However, there are a number of reasons I tend not to use dBd except in special circumstances. +

1. The relevant comparisons are not with a dipole. Very often, antenna comparisons are among antennas that do not include dipoles. In such cases, simply comparing gain figures in dBi tells us all we need to know and can know about the relative maximum gains of the antennas. For example, in comparing the gains of self-contained 1 wl wire-loop antennas, the best designs for a given purpose are the ones that are best within the group, and the group does not include a horizontal dipole.

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Likewise, when contemplating whether it is worthwhile to increase the size of a Yagi for 20 meters from 3 to 4 elements, the dipole is not relevant. Rather, the relevant gain comparison is between both models and real antennas of 3 and 4 element design. The gain advantage is derived as easily from dBi as from any other system of gain numbers.

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2. The relevant comparisons have only passing reference to maximum gain. Additional factors, such as elevation angle, beamwidth, etc., may be far more important than gain itself. For some applications, good antennas do not need gain relative to a dipole. But they may require close specification of other antenna properties. Gain becomes a secondary specification for which dBi suffices nicely.

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Range tests are another matter

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If my work were primarily with real antennas, then dBi would become a problematical term. A test range approximation of an isotropic radiator is an unlikely event anytime soon. Hence, antennas on test ranges must be compared to some standard, and the dipole is the most likely simple horizontally polarized candidate. If we accept this premise, then it is unreasonable to expect range testers to then correlate their results to a scheme of modeling in which the gain is converted to a value in dBi. +

However, this situation makes it imperative that range testers specify a test protocol and comparison antenna for the evaluation of the procedure against good engineering practice. In many instances, the comparison antenna will not be a dipole (although amateurs often think only in terms of Yagi tests). Verticals require specification of a vertical standard of the appropriate class. Nothing substitutes for the revelation of detailed test protocols where range testing is at stake.

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Conversion of the test situation to models--like any other case of modeling--is at best the most reasonable approximation we can develop. Absolute precision is unlikely in most instances. Hence, the conversion of range test results to modeling results--with the accompanying conversion of dBd-RR (with a clear specification of the standard dipole used) to dBi--is not an automatic process and is subject to varying degrees of adequacy.

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Modeling of detailed test protocols, on the other hand, can yield some correlation factors among different test protocols. A model may substitute one standard dipole for another, may insert or remove test range objects affecting results, may change antenna heights with ease, etc. As a simple example, if Smith tests his antenna at 60' up and Jones tests his at 85' up, the differences in test results (all other factors being equal or equalized) can be at least tentatively resolved with effective modeling.

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Whatever the prospects for such work in the future (for we have just begun to scratch the surface of effective modeling in antenna work), those who predominantly model will likely stick to dBi as the basic measure of maximum gain. Range testers will likely stick to dBd-RR, where the range test is a comparison to a dipole or other relevant standard.

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Since I am mostly a modeler, I use dBi---mostly.

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Updated 6-23-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: Modeling


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Multi-Diameter Dipoles: MININEC vs. NEC-4

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L. B. Cebik, W4RNL

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+ While examining some Yagi models developed by K6STI, I encountered an anomaly. The models employed a large-diameter, short-length center section for each element to simulate boom mounting plates, a technique that has proven sound relative to real-world construction. +

When modeled in MININEC, no problems with convergence were encountered with reasonable numbers of segments per half wavelength. However, when modeled with NEC-4, convergence only occurred with very large numbers of segments per half wavelength. Reducing the diameter of these center sections to that of the immediately adjacent sections eliminated the problem of convergence--that is, convergence occurred with reasonable numbers of segments per half wavelength.

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To explore this anomaly, I set up a small test of systematically modeling dipoles with larger center sections. The test frequency was 14 MHz. The initial material was 0.5" diameter aluminum. In increments of 2 feet each side of center, I increased the length of a larger diameter center section in progressive steps for total lengths of 4, 8, 12, etc. feet up to an including the total antenna length.

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Each antenna was resonated to less than 1 ohm reactance. Thus, the length of each model differs. In the graphs that follow, the far right entry labeled "36" is a place holder for the actual total length of the antenna at the increased diameter. Thus, that column alone violates the linear progression of the other enlarged center sections.

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Each model was tested using ratios of 2:1, 3:1, and 4:1 relative to the original dipole diameter of 0.5 inches, for center section diameters of 1, 1.5, and 2 inches. All models are free space.

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The models were first run in MININEC 3.13 via ELNEC 3. Segmentation was set at 34 segments overall, using 1 segment per foot of enlarged center section, with the remaining segments split between the smaller diameter end sections. This yielded segment lengths that are well within all MININEC boundaries for accurate results, as well as very reasonably close in length between the antenna wires.

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The following graphs shows the progression of gain figures for the MININEC runs. Interestingly, the gain of the models peak when the enlarged center section is just under half the total length of the antenna. As the larger center section is further lengthened, MININEC shows a decrease in gain. The curves for the 3 ratios are nicely congruent.

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The length of the resonant antenna also changes with the length of the larger-diameter center section. Overall antenna length actually peaks with center-section lengths slightly longer than those for maximum gain, as the following graph demonstrates. MININEC models do not reach a final shortened length associated with fatter elements until the entire antenna is at the larger diameter.

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The same antennas were run with NEC-4, initially with EZNEC Pro and later with a beta version of GNEC. Segmentation was virtually the same as with the MININEC models with a single additional segment in the center section to permit the required mid-segment feedpoint. As with the MININEC models, each antenna was resonated within +/- 1 ohm of zero reactance for models using 2:1, 3:1, and 4:1 ratios of the center segment to the end sections.

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The pattern of gain produced by the NEC-4 models, shown in the following graph, is quite unlike that yielded by MININEC. Maximum gain occurs with the shortest possible larger-diameter center section and progressively decreases as the center section is lengthened. The curves for NEC-4 are less smooth than for MININEC because the former, in the commercial versions noted, yield gain figures to 2 decimal places, while the latter yields figures to 3 decimal places. Hence, NEC-4 rounding yields somewhat stair- step curves. within those limits, the curves for the three different diameter ratios are congruent.

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Equally congruent are the overall antenna length curves (shown in terms of lengths each side of the feedpoint in the graphs).

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Interestingly, despite the vastly different gain curves, the overall antenna length curves for MININEC and NEC are exceedingly comparable. MININEC yields slightly longer resonant lengths for each modeled case, a phenomenon long noted (and corrected for in some commercial versions of MININEC). Nonetheless, MININEC and NEC-4 show the longest resonant length at just about the same length of larger-diameter center section, as shown in the following graph. This graph uses the 4:1 ratio curves because they produce the sharpest length peaks and would be most sensitive to significant differences in the peak point for each modeling system with these models.

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The question that remains is which of the two gain curves is the more reliable. The MININEC gain curves with a 2:1 diameter ratio of center section to end sections were rerun with double the number of sections. Gain figures were convergent within a maximum divergences of 0.003 dB. The comparable NEC-4 models, when segments were doubled (minus 1 to retain an odd number of segments in the wire containing the feedpoint), showed an order of magnitude less convergence with short center sections of 4 and 8 feet. Convergence within the two decimal places occurred only when the center section reached 24 feet long. This result is consistent with the difficulty of converging Yagi models employing short, large-diameter center sections for each element.

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Moreover, the NEC-4 curve totally envelopes the MININEC curve, as shown in the following graph for diameter ratios of 2:1. Within the limits of NEC-4 rounding, nowhere does the MININEC curve exceed the NEC-4 curve in gain value. In contrast, for shorter center sections, the reported gain of the NEC-4 model is significantly higher.

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The anomalous results yielded by NEC-4 with shorter, large-diameter center sections of multi-diameter dipoles gains importance as these figures accumulate in multi-element antenna arrays. Since these gains are usually cumulative in most antennas designed for maximum or close to maximum gain, the reported gain may be significantly higher than reality.

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The convergence test and the fact that the NEC-4 curve envelopes the MININEC curve are strong indicators that NEC-4 may be simply inaccurate when antenna elements consist of multi-diameter sections such that the center section is short and significantly larger in diameter than succeeding sections of the element. The degree to which such an inaccuracy becomes significant operationally to an antenna design depends on many variables of both design and engineering goal and cannot be independently estimated. Unless independently confirmed as in fact accurate (with MININEC's curves consequently invalidated), the phenomenon will at least be disconcerting to antenna modelers.

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Attributing an anomaly to NEC-4 in this case does not itself certify the accuracy of the MININEC result. Even if correct, the increase of gain is of more mathematical interest than operational significance. At a diameter ratio of 4:1, the maximum gain is only about 0.06 dB relative to a dipole of the thinner size.

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For those who model antennas, the disparity between the two modeling programs should at least be noted and accounted for wherever it emerges.
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Updated 9-19-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to Amateur Radio Page

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Topics: Modeling, Stepped Diameter


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Notes on Two Limitations of NEC-4

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L. B. Cebik, W4RNL

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+ NEC-4 is an advance on NEC-2. Among its advantages is the ability to handle linear elements of stepped diameter directly with accurate results. NEC-4 has not proven wholly unlimited in this regard, since segmentation must be very extensive in proportion to the largest step-size within an element. +
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Closely Spaced Parallel Wires of Different Diameters

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NEC-4 has also proven to be limited in its ability to handle closely spaced wires of different diameters. Although it produces more reasonable results than NEC-2, it remains significantly off the mark. The following notes are a demonstration of that limitation. +
Dipoles
The baseline for the demonstration is the dipole. Since dipoles of 0.5" and 0.0808" (#12) wire at 28.5 MHz are used in further steps, here is the data for MININEC (public domain version), NEC-2, and NEC-4 (as modeled in free space on ELNEC 3 and EZNEC Pro 2). Gain is in dBi and Feed Z is the feedpoint impedance recorded as R +/- jX in ohms. Segmentation is drawn from MININEC; add 1 segment for NEC. + 
Antenna        Output    MININEC        NEC-2          NEC-4
+0.5" dipole    Gain      2.13           2.13           2.13
+16.52'; 66 seg Feed Z    72.08 + j0.29  72.88 + j3.69  72.90 + j3.75
+0.0808" dipole Gain      2.11           2.11           2.11
+16.72'; 66 seg Feed Z    72.64 + j0.21  73.06 + j3.09  73.06 + j3.13
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The antenna models were initially resonated within MININEC, where resonance was considered to be a feedpoint impedance with under 1-ohm reactance. Both NEC-2 and NEC-4 show a slight difference from MININEC. The difference is of no practical importance, but is only of numerical significance for exercises like the present one. For open-ended elements, such as those of a dipole, NEC-4 (single precision mode) shows a regular numerically more positive reactance than NEC-2.

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Equal Diameter Folded Dipoles
The actual test consists of modeling a folded dipole. A folded dipole, where the long parallel wires have the same diameter, effects an impedance transformation of 4:1 for any spacing within reason. Thus, the anticipated feedpoint impedance should be in the region of 288 ohms (72 x 4). Since folded dipoles also act like fat wires and are thus shorter at resonance than single wire dipoles, the anticipated modeled feedpoint impedance was slightly lower than the theoretical calculation. The modeled folded dipoles used 0.5" diameter elements spaced 0.25' (3"). +

MININEC tends to chop corners and give erroneous results unless one of two procedures is followed. A. One may use as many segments as the program allows to minimize the size of the corner chopped. B. One may taper the segment lengths approaching the corner so that corner segments are small while the overall segment count is held to a practical minimum.

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The basic MININEC folded dipole used 66 segments longitudinally and 2 segments at the ends. NEC models added one segment to each longitudinal wire to maintain parallel segmentation. Tapered MININEC models used the internal segmentation values of the ELNEC program. Since these produced 8- segment mid-length wires, the NEC models added one segment to this section to satisfy the need for an off number of segments for center feeding. Finally, a more highly segmented model, using 120 segments per longitudinal wire was created to equalize the segment lengths with those of the 2- segment end wires. This last model was not adjusted for resonance.

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Antenna        Output    MININEC        NEC-2          NEC-4
+FD: equal seg  Gain      2.22           2.22           2.22
+16.1'; 66/2 x2 Feed Z    285.7 + j0.90  285.9 + j4.10  285.8 + j3.99
+FD: tapered    Gain      2.21           2.21           2.21
+16.06'         Feed Z    281.0 - j0.68  284.2 + j9.87  284.0 + j8.66
+FD: equal seg  Gain      2.22           2.22           2.22
+16.1'; 120/2x2 Feed Z    285.8 - j1.80  286.0 + j2.27  285.8 + j0.51
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In practical terms, all programs do a satisfactory job of modeling a simple folded dipole when both wires have the same diameter. When sufficient segments are used in MININEC, tapering proves less accurate, assuming that the balance of results represents a consensus close to reality.

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Systematically, NEC-4 shows a slightly lower feedpoint impedance for these closed models than NEC-2. Nonetheless, when all wires have the same diameter and other modeling geometry guidelines are met, all modeling programs give equally usable results.

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Unequal Diameter Folded Dipoles
When the wires of a folded dipole differ in diameter, they effect (relative to a single-wire dipole) a different feedpoint impedance transformation ratio than do folded dipoles with equal diameter wires. The theoretical impedance transformation ratio is given by +
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where R is the impedance transformation ratio, s is the wire spacing, center-to-center, d1 is the diameter of the fed wire, and d2 is the diameter of the second wire, and where s, d1, and d2 are given in the same units. +

If we use a wire 0.0808" in diameter (#12 AWG) for the fed wire and a wire 0.5" in diameter for the second wire, maintaining the 3" spacing, then the impedance transformation ratio will be approximately 7.47. A folded dipole of this construction would have a calculated feedpoint impedance of about 533 ohms. In practice, due to "fat wire" effect, we might expect a feedpoint impedance slightly lower than this.

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It should be noted that the impedance transformation equation does not account for the end wires. In this test, the end wires were also 0.0808" in diameter.

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If either version of NEC can handle parallel wires of differential diameters, then the results should coincide reasonably with those of MININEC, which takes such cases in stride. The test used models of similar construction to those used with equal diameter folded dipoles. A basic model used 66 segments per longitudinal wire and 2 segments per end wire; and a tapered-segment version of the antenna was created using internal tapering values. Here are the results:

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Antenna        Output    MININEC        NEC-2          NEC-4
+FD: equal seg  Gain      2.21           0.69           1.59
+16.2'; 66/2 x2 Feed Z    530.5 + j1.47  375.2 + j25.8  462.6 + j17.4
+FD: tapered    Gain      2.21           0.37           1.22
+16.2'          Feed Z    526.5 + j10.8  347.2 + j38.5  423.4 + j37.5
+FD: equal seg  Gain      2.21           0.56           1.53
+16.2'; 122/2x2 Feed Z    527.6 - j2.99  364.1 + j25.1  456.0 + j15.43
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The MININEC models clearly come very close to expectations. Since the tapered model was not re-resonated, its values are lower, but the large equal-segmented model is likely the more accurate.

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NEC-2 models of parallel wires of different diameters, as has been well- established, produce highly erroneous values. Tapering throws the values even farther off the mark. Although somewhat better, NEC-4 values are also highly unreliable. Moreover, reducing segmentation of the NEC-4 models produced nothing reliable. An auto-segmented model at conservative minimums of 11 segments for the longitudinal wires and 1 segment each for the ends yielded a gain of 1.82 dBi and a feedpoint impedance of 443.8 + j39.6 ohms. Further reducing segmentation to the absolute minimums of 5 segments per long wire and 1 segment per short calculated a gain of 2.64 dBi and a feedpoint impedance of 371.3 + j26.07 ohms.

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Conclusions and Implications
Because the behavior of a folded dipole is well-established and easily predicted, the antenna forms a very good test of the present modeling question: the adequacy of the program to deal with parallel wires of unequal diameters. The conclusion is that NEC-4 remains deficient in this regard, and antenna modelers are duly cautioned. +

The inadequacy of NEC-4 to model this situation adequately casts doubts on a number of possible modeling challenges. For example, modeling gamma and Tee matching sections as physical elements contributing to the radiation pattern as well as to effecting an impedance transformation is now dubious. Other cases are too numerous to mention. For situations calling for parallel wires of unequal diameter, MININEC remains the modeling program of choice, despite its other limitations.

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Wires of Different Diameters Joined at Sharp Angles

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A second problem in the NEC-2 calculation engine is the unreliability of results when wires of unequal diameter join at right or acute angles. Although NEC-4 improves upon this situation, its results are not wholly reliable. +
Single Quad Loops of a Single Wire Diameter
The foundation for testing the reliability of NEC-4 outputs when wires of different diameter join at right angles is the single quad loop. The test employed loop materials of 0.5" and 0.0808" diameters. When only a single diameter wire is used, all programs perform credibly, so long as models adhere to the antenna geometry criteria of the specific program. All loops were again modeled at 28.5 MHz, with copper wire in free space. All loops are square. Dimensions and segmentation are given for one side of the loop. The tapered-segment MININEC model employs the internal values of the ELNEC program. + 
Antenna             Output    MININEC        NEC-2          NEC-4
+0.0808" wire        Gain                     3.26           3.26
+9.146'; 31 segs     Feed Z                   126.9 + j 0.02 126.9 - j 0.13
+0.0808" wire        Gain      3.25           3.26           3.26
+9.146'; 61 segs     Feed Z    126.3 - j 7.93 127.0 - j 0.27 127.0 - j 0.69
+0.0808" wire        Gain      3.26
+9.146'; tapered     Feed Z    126.0 - j 3.38
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+0.5" wire           Gain                     3.37           3.37
+9.364'; 31 segs     Feed Z                   129.7 + j 0.21 129.7 - j 0.10
+0.5" wire           Gain      3.36           3.36           3.26
+9.364'; 61 segs     Feed Z    129.5 - j 4.07 130.0 + j 0.49 129.8 - j 0.41
+0.5" wire           Gain      3.36
+9.364'; tapered     Feed Z    129.1 - j 0.42
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The initial models were created in NEC-4 and tested on NEC-2 and MININEC. A tapered-segment length model was created in MININEC for comparison with the equal-segment models. Convergence of the two MININEC models is good for practical purposes, although a slight numerical difference shows.

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For the NEC models, there is no significant numerical, let alone practical difference between NEC-2 and NEC-4 models. Moreover, and especially significant for this test, there is no significant difference between the values achieved at 31 segments per side and 61 segments per side. Practical convergence of results is achieved at much lower levels of segmentation.

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Single Quad Loops of a Different Wire Diameters
To test the ability of the programs to handle wires of different diameter joining at right angles, I modeled a single square quad loop. The top and bottom wires were 0.5" diameter, while the vertical wires were 0.0808" diameter. This might be a model of a portable quad loop using tubing for the horizontal members and wire for the vertical pieces, thus allowing the assembly to be collapsed for transportation. +

The initial model was constructed in MININEC and then re-tested in NEC-2 and NEC-4, using 61 segments per side. The MININEC model required 10.15' side lengths to approach modeled resonance.

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Antenna             Output    MININEC        NEC-2          NEC-4
+10.15' sides        Gain      3.61           3.57           3.60
+61 segs/side        Feed Z    137.2 - j 5.71 175.4 + j 140  150.3 +j 44.3
+10.15' sides        Gain      3.61
+tapered segs        Feed Z    136.7 - j 2.30
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The MININEC model converges well with its tapered alternative model. However, the NEC models diverge in values. Although the gain values are plausible, the feedpoint impedance values indicated a condition far from resonance. The divergence from MININEC is worse for NEC-2 than for NEC-4, suggesting that the NEC-2 figures are least reliable. Since there is no simple theoretical calculation with which to compare the overall results, one cannot claim that the MININEC qualifies as a standard against which to measure the other programs. However, given MININEC's abilities to handle wires of different diameters in other contexts and the general trend of NEC-4 results with such conditions to be closer than NEC-2 results to the MININEC figures, it seems likely that MININEC may yield outputs that are closest among the three to reality.

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The NEC-4 model with 61 segments per side can be brought closer to resonance by shortening each side to 9.94' in length. This figure might seem equally reliable with the MININEC lengths of 10.15' per side, except for one significant factor: the MININEC figures achieve convergence, while the NEC figures do not, especially with respect to feedpoint impedance. I ran the revised NEC-4 model through various segmentations ranging from 21 to 121 segments per side. In the following table, "delta R" and "delta X" indicate changes in the feedpoint impedance values from the preceding level of segmentation.

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Segments/Side  Gain      Feedpoint Impedance      Delta R   Delta X
+      21       3.54      133.4 - j 13.280
+      31       3.54      134.5 - j  9.375         1.1       3.905
+      41       3.53      135.5 _ j  5.589         1.0       3.786
+      51       3.53      136.4 - j  1.943         0.9       3.646
+      61       3.53      137.3 + j  1.616         0.9       3.559
+      71       3.53      138.3 + j  5.119         1.0       3.503
+      81       3.53      139.2 + j  8.663         0.9       3.544
+      91       3.53      140.0 + j 11.880         0.8       3.217
+     101       3.52      140.9 + j 15.36          0.9       3.48
+     111       3.52      141.7 + j 18.57          0.8       3.21
+     121       3.52      142.4 + j 21.60          0.7       3.03
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The values for gain are well converged. However, those for feedpoint impedance are not. Compare, for example, the differences among figures for 31 and 61 segments per side for the equal-diameter wire loops, using either the 0.0808" or 0.5" models. NEC-4 varies by only 0.1 ohm resistance and under 0.5 ohm reactance across that spread. With the present multi-wire diameter loop, the same difference in segmentation yields a difference of 2.8 ohms resistance and 10.991 ohms reactance, a 200+% difference for each output figure.

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Moreover, the progression of values shows no signs of closure within the limits of practical modeling. Although there is a trend downward in the delta numbers, where it will occur remains unclear. Without convergence, the figures cannot be regarded as reliable.

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Conclusions and Implications
Because there is no independent standard at hand against which to measure the modeled results, the MININEC figures for the single quad loop cannot be certified as in fact closer to reality than those yielded by NEC-4 for antennas constructed of different-diameter wires joining at right angles. However, MININEC's achievement of reasonable convergence of results and NEC-4's inability to achieve converged results suggests that the NEC-4 results are less trustworthy than those of MININEC. NEC-2 figures are most divergent and least reliable of the three modeling calculation engines. +

It is clear that, for a loop of a given size, NEC-4 will yield lower gain numbers and higher feedpoint values than MININEC. Otherwise expressed, NEC-4 will call for a loop of smaller dimensions to approach resonance.

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These trends also apply to other antennas using wires of different diameters joining at right and sharper angles. Models of folded X-beams show lesser gain and higher feedpoint values on NEC-4 than on MININEC.

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Given the limitation of NEC-4 with respect to parallel wires of different diameters, it is probable that the present limitation of NEC-4 is an extension of the same root mechanism. Therefore, it is likely that MININEC remains the modeling engine of choice for antennas employing angular junctions of different-diameter wires.
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Updated 4-10-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
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Topics: Modeling


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Notes on Modeling Antenna Elements

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L. B. Cebik, W4RNL

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Having examined numerous antenna models from a wide variety of sources, I am struck by the diversity of ways in which antenna elements, subdivided into wires and segments, are created. The variety of ways in which wires are placed into the antenna geometry description makes it difficult for another modeler to read the wires page. Moreover, many of the models will produce correct far-field data and feedpoint information, but most will skew the antenna currents. This latter information can become quite important in analyzing why a complex antenna yields its particular set of performance outcomes.

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The usual reasons given for the odd collections of wires making up an antenna model are convenience and speed. Many antenna specifications are for half elements, where the other half is presumed to be a mirror image. So we begin in the middle and work outward. Dimensions are given with positive numbers, and it is faster to do the positive side and then replicate it with minus signs. We go directly from whatever sketch or data sheet we have to the screen entries. I've been there, done that, and learned the hard way that slowing down at the beginning saves me a bucket of time later on when I try to troubleshoot my model.

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So let me make some suggestions, scratched with chalk, not etched in stone. I'll also say why along the way.

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First, do the model on a piece of paper before touching the keyboard of your favorite modeling program. That way, you can organize your keyboarding before you begin the computer work. Second, adopt a convention, like working from the far left to the far right (since so many of our American conventions are left-to-right in direction). Avoid working from the middle outward, however initially convenient that seems.

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Now consider the simple dipole 8.25' long, 3/4" in diameter, and fed in the middle, shown in Figure 1. Even following our conventions, there are a couple of ways of setting down the X, Y, Z coordinates. My own preference is to center the antenna at 0,0,Z, where Z is an unspecified antenna height. That way, if I add elements projecting equally beyond the first element limits, I can place their coordinates as the same number but with a different sign. So my one wire antenna description looks like this (in free space):

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Wire End 1     x         y    z    End 2     x         y    z    Diameter
+ 1             -4.125    0    0              4.125     0    0     .75
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You may choose to place the wire ends in the Y dimension just by reversing X and Y entries. My feedpoint is now Wire 1 at the 50 percent mark, which exactly centers it. For MININEC, use an even number of segments; for NEC use an odd number of segments.

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Now consider an element of a beam using many shorter sections of tubing that decreases in diameter as you progress outward. Let's assume an element that from center outward has these dimensions: 22" at 1.125" diameter; 36" at 1"; 24" at 0.825"; 24" at 0.75"; 24" at 0.625"; and 40.5" at 0.5". The first step is to obtain running totals: 22"; 58"; 82"; 106"; 130"; and 170.5".

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I we follow our conventions, the full element will look like this on paper and in the geometry entry spread sheet:

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Wire End 1     x         y    z    End 2     x         y    z    Diameter
+ 1             -170.5    0    0              -130      0    0     .5
+ 2             -130      0    0              -106      0    0     .625
+ 3             -106      0    0              -82       0    0     .75
+ 4             -82       0    0              -58       0    0     .825
+ 5             -58       0    0              -22       0    0     1
+ 6             -22       0    0              22        0    0     1.125
+ 7             22        0    0              58        0    0     1
+ 8             58        0    0              82        0    0     .825
+ 9             82        0    0              106       0    0     .75
+10             106       0    0              130       0    0     .625
+11             130       0    0              170.5     0    0     .5
+
+

This may seem like a long way to go, but for an accurate model, all these wires will have to be in the chart anyway. This left-to-right scheme just keeps them well-ordered. Note that wire 6 is the center section and can have the feedpoint specified at its center, with correct segmentation. For NEC, I might assign it 5 segments; for MININEC, 4. The sections with dimensions in the 20s might get 2 segments each, with the 36" section getting 3 segments, and the end sections 4 segments. This keeps segments lengths as close to equalized as this structure permits, while keeping the segments lengths well below maximum recommended length.

+

A rule of thumb: do not wed yourself to the minimum segments per half wavelength rule. The more complex the antenna, the more segments per half wavelength needed to arrive at convergence, the condition where adding further segments does not alter output values significantly. Closed 1 wavelength loops may require 40-60 segments total to achieve convergence. If you are working with a multiband beam, be sure to raise the number of segments per wire in the chart in proportion as you raise frequency.

+

For complex antennas with closely space elements, it is wise to align the segments as closely as possible from one element to another, especially with NEC. To keep myself in the habit, I try to do this with every antenna having parallel elements.

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+ +
+

Now let's consider one final example, a shortened dipole with wire hats on each end. The hats consist of 4 radial wires and a perimeter wire. Where does the antenna start and end. Some quick modelers use the horizontal dipole ends and then separately model the wire structures outward and around. However, the wire hat assemblies are part of the antenna. An equally quick second answer is to treat the peaks where the radial wires end as the antenna beginning and ending. Both answers are wrong. The antenna begins and ends where the current goes to zero. MININEC gives a true zero reading, because it takes current nodes to be at the ends of segments. NEC takes current nodes to be at the center of segments, and so the lowest value will never be zero. However, you can get equally low values either side of a correctly chosen wire junction.

+

For this example, the antenna begins in four places: at the center of each of the four perimeter lengths. It ends in the comparable places at the other end assembly. Hence, a fully modeled version of this antenna will have, starting on the left end, 8 perimeter wires, each starting mid-length and ending at a radial wire peak. The 4 radial wires come next, working from peak to center, which happens to be the horizontal wire end point. Then we have the horizontal wire, center fed, followed by 4 radial wires working outward from the hub, and finally the 8 perimeter wires, 2 from each peak to common centers.

+

I tend to collect these wires by type so that I can adjust all the radials as a group, adjust perimeter wire lengths as a group, etc.

+

Once more, you can take shortcuts, but only if a. you can decide in advance that you will never need or want to know the correct current magnitudes and phases on each wire, or b. you are willing to reconstruct the model if you should ever become interested in such matters.

+

One more note: In each case, I ran the wire containing the feedpoint as a single wire fed in the center with either a voltage or current source. I could have ended each wire in the center and used a split feed (split voltage or split current). However, use care here. Some versions of NEC will return incorrect values of feedpoint impedance using split feed if you adopt the center-outward style of geometry construction. You may even get impossibly high negative resistances. (Note that some instances of negative feed resistances are correct values, but not in this particular instance.)

+

I hope these notes are useful toward the goal of achieving more reliable models that play correctly on the first run.

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Return to Amateur Radio Page

+

Topics: Modeling


+ + diff --git a/content/model/modelform.html b/content/model/modelform.html new file mode 100644 index 0000000..1548cef --- /dev/null +++ b/content/model/modelform.html @@ -0,0 +1,35 @@ + + + + + + Model Planning Form + + + +
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Model Planning Form

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L. B. Cebik, W4RNL

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I have received numerous requests for the model planning form that I put together many years ago when first getting involved in antenna modeling. It is a convenient form that has proven useful over time for basic modeling activities that involve wires, loads, and sources as the primary elements. It allowed me to keep track of the ingredients that I placed in models, and also helped me troubleshoot models that did not seem to work as expected.

+

As a service to newer modelers, I am making the forms available in two modes: as a Word document and as a PDF document. You may view the PDF version on the screen to ensure that it is something you can use. However,, I suspect that ultimately, you may develop an impreoved version that best suits you individual needs. Each form has a front and back side, although many models will require only the first page.

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To access the PDF version go to planning-form.pdf.

+

To download the Word version, go to planning-form.doc.

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Good luck in your modeling ventures.

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+

Updated 10-17-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

+

Topics: Modeling


+ + diff --git a/content/model/nec.html b/content/model/nec.html new file mode 100644 index 0000000..de207ce --- /dev/null +++ b/content/model/nec.html @@ -0,0 +1,103 @@ + + + + + + Antenna Modeling Programs + + + +
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Antenna Modeling Programs

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L. B. Cebik, W4RNL

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2024 Update

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Most of the software listed here is old, or no longer exists. Where possible internet web archive copies of websites have been found and linked for sites that no longer exist. Currently the most commonly used modeling software in amateur radio circles is EZNEC, 4NEC2, and MMANA-GAL.

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+

NEC-4 / NEC-5

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As of 2024 the current version of NEC is NEC-5 (EZNEC 7 supports NEC-5), which overcomes most of the shortcomings with earlier codes. It permits the modeling of underground radial systems, elements of varying diameter sections, carefully-constructed close-spaced parallel wires, as well as all the modeling capabilities of earlier versions of the code. NEC-4 and NEC-5 is a proprietary code of the Lawrence Livermore National Laboratory and the University of California, from whom a user-license must be obtained. Export restrictions may apply. You may obtain the license materials on line at the LLNL site.

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Nittany Scientific NEC-Win Plus+ and NEC-Win Synth

+
+

Cebik created and made available a number of models throughout the site using NEC-Win Plus+. Version 1.2 download: NWPlus-Setup12.zip.

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    +
  • + Note: v1.2 (2003) predates Windows Vista, but installs and runs ok on Windows 7 - 11, except the polar plots function which returns a run time error. Later versions likely fixed this, appears the last version was v1.6 from 2008. +
    • +
+

NEC-Win Synth is used to generate typical models and provides a set of building blocks to build more complex models. Version 1 download: NWSynth.zip.

+

Windows Help: Opening the help on Windows Vista or later may result in an "Feature not included" error. KB917607 for Windows Vista, 7, and 8 can be downloaded from archive.org/download/kb917607 which will enable the help file feature.

+

The installers have been scanned with Virustotal, no security vendors and no sandboxes flagged the files as malicious.

+

The Nitany Scientific site also has a number of example model files which can be downloaded from www.nittany-scientific.com/examples/examples.htm (web.archive.org).

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+ +
+

Much of my antenna research work is based on systematic antenna modeling in one or another version of the Numerical Electromagnetics Code (NEC). The following brief notes will provide links to known antenna modeling software providers.

+

At present, I know of only two sources of commercial software for NEC-4:

+

Roy Lewallen, W7EL produces EZNEC Pro, which has an option for NEC-4, if the purchaser has a confirmed license for NEC-4. EZNEC Pro and EZNEC Plus are also available for NEC-2 (see below). W7EL also makes available EZNEC (v. 4.0), a segment-restricted version of NEC-2. The latest W7EL NEC software packages are Windows-based and employ similar user interfaces which have earned praise in DOS versions for their user-friendliness. New versions of EZNEC contain a 3-D plot graphic that can be "sliced" for select 2-D patterns, direct entry for trap as well as for series and parallel R-L-C loads, and the average gain test. EZNEC also implements the NEC2/NEC-4 ground wave (RP1) output. Wire construction freatures are limited to GW commands, but include special facilities for creating rectangular wire grids, radial systems, circles, and helices. EZNEC Pro will import or export files in .NEC format. Special processing has increased the segment limit to 20,000.

+

Nittany Scientific (web.archive.org) produces a 32-bit Windows version of NEC-4 called GNEC. This program implements all all of the input cards of the complete NEC-4 input deck, thus permitting the use of catenary wires, helices, networks, rotational and linear structure movement, and coordinate and rotational based symmetry options. Control commands include the insulated sheath, near fields in both coordinate and axial form, the upper medium, as well as far-field and ground wave analysis. Output capabilities include 3-D, polar plots, and many rectangular (X-Y) graphs, as well a a large array of tabular reports and the Average Gain Test. A special insert using the NEC-Win Plus interface allows modeling by equation. The basic ASCII interface uses assist screen to formulate each command entry and is similar to the one used in NEC-Win Pro, described below under NEC-2.

+
+

NEC-2

+
NEC-2 is a highly capable version of the code which is in the public domain. It is restricted to antenna elements of a single diameter (although some software providers have introduced corrections for linear elements whose diameters varies). It cannot handle buried radial systems, although above ground systems close to the earth can be handled. However, it is equipped with the Sommerfeld-Norton high accuracy ground model for accurate modeling of horizontal wires close to the earth. +

Nittany Scientific (web.archive.org) produces a Windows version of NEC-2 called NECWin Plus, which features a true spreadsheet geometry construction page set with design-by-equation capabilities. The program also offers stepped-diameter corrections, Gain Averaging Test, CAD (.DXF) file input, 2-D and 3-D plots and antenna views, and graphical outputs. NSI considers this to be an entry level program and offers a companion volume with exercise models called Basic Antenna Modeling: A Hands-On tutorial.

+

The company also offers a research NEC-2 program: NECWin Pro (NWP). NWP employs a user-selected choice between a spreadsheet geometry construction page (adapted from NEC-Win Plus, or the normal ASCII model input page with help screen/windows for all antenna model input parameters. In addition, NWP provides direct entry or importation of NEC model inputs and provides a large assortment of available rectangular output graphics, along with other advanced NEC capabilities. NSI views NEC-Win Pro as a profession-level program.

+

Recently added to NSI offerings is NEC-Win Synth, a program to synthsize wire-grid structures for use in any NEC (-2/-4) program. The user may select a preset shape and enter critical dimensions or synthsize a structure with the spreadsheet entry facility. NEC-Win Synth can be directly linked to NEC-Win Plus or save its output in a standard .NEC file.

+

EZNEC for Windows, both in basic and professional versions, is available from Roy Lewallen. See the general description of EZNEC/ELNEC products under NEC-4 above. EZNEC 4.0, the basic version of the NEC-2 programs, offers 3-D plots with 2-D slicing, ground-wave output, stepped diameter correction, and numerous short-cuts to antenna geometry modification. As well, there are new facilities for entering traps and considerable annotation capabilities. Standard EZNEC is restricted to 500 segments. EZNEC Plus offers additional wire construction and movement capabilities, along with a 1500-segment limit. EZNEC Pro M offers all of the features of EZNEC Pro/4, with the exception of being limited to the use of NEC-2.

+

NEC2GO, a general purpose Nec-2d interface to Windows, is available from Nova Plus Software. It provides "Modeling by Equation," sweeping of variables, and support for Coax and Ladder Line feedlines to show impedance transformation and loss. Features include unlimited segments, sources, and loads, shifting and rotating wire definitions, automatic segment generation and Tapering, Auto Gain Test and Average gain, quick convergence testing, automatic creation of plots at max gain angles, LAPACK routines, all NEC ground options, and NT-based feedpoint matching networks. The program is fully Windows compliant with no DOS executables. A free Demo Version is available.

+

4NEC2 is a no-cost experimental version of NEC-2, with continuous development of its facilities and interface by its programmer, Arie Voors. Since the program changes with regularity as Arie introduces new features, such as improvements to the user interface and an optimizer, a detailed description is not feasible here. The program can be downloaded freely from the unofficial NEC Archives (see below).

+

Antenna Solver is a product of Grating Solver Development Co. that uses NEC-2 as rewritten into C++ using dynamic array allocation. The user interface, graphical editing features, and data display capabilities allow analysis of antenna patterns, of near, far, and ground-wave fields, as well as currents and charge densities. A full-featured version of the program can be downloaded in the "DEMO" mode for 30-day use, after which the purchase of a password will be needed to permanently enable the program.

+

Poynting Software (web.archive.org) is making available version 2.5 of its hybrid NEC-2/UTD program "SuperNEC," which is implemented in C++. The program has a parallel execution option. It makes use of MatLab 5.2 to run the program and avails itself of MatLab's many input and output facilities, such as the use of MatLab language assemblies that users may add to or modify. A version (SuperNEC Lite) which is restricted to 300 segments and 3 GTD objects is available at a student price, and a demo is available at the web site.

+

EM Software and Systems (http://www.emss.co.za/wiregrid/default.htm not found in web.archive.org) produces a specialized user interface for NEC called "WireGrid." The program is a graphical user interface that automates the process of creating surfaces via wire meshes, while providing visual feedback on the structure, sources, networks, and field points. A demonstration version of the program can be down loaded from the EMSS web site.

+
+

Expert MININEC

+
Before recent advances in speed and memory, it was not feasible to run NEC on a PC. Rockway and Logan developed MININEC, a Basic language adaptation of NEC for PCs. More recently, they have advanced the MININEC algorithms and code to overcome many of its initial limitations. The "new" MININEC can handle sharp angles in antenna geometry directly (without segment length tapering) and handles antennas close to ground with much better accuracy. However, the MININEC Professional code (as well as the input/output interfaces) is a proprietary product. +

EM Scientific (web.archive.org) offers several levels of Expert MININEC Professional, ranging from the basic level MININEC for Windows to MININEC Broadcast Professional. The product-level distinctions include the number of segments and unknowns available; advanced features of geometry, electrical, and solution description; and auxiliary calculations. These are all Windows products.

+
+

MININEC

+
The public domain MININEC code (version 3.13) is available with several commercial user interfaces, as indicated in these notes. For general antenna analysis that does not press its limitations, MININEC is a highly competent code. It handles elements of changing diameter directly, and with segment-length tapering, can accurately model a wide range of antenna geometries. However, horizontal antennas must be at least 0.2 wavelengths above ground for accurate results. Moreover, specification of ground conditions affects only antenna far field results, but not feedpoint conditions. +

Antenna Model (web.archive.org), (from Teri Software) which first appeared in a DOS version in 1992, has returned with an advanced Windows version of MININEC based on 3.13. Wholly reprogrammed, the core has virtually unlimited segment capacity for models and uses revised (and sometimes alternate) algorithms to overcome MININEC difficulties with errors with increasing frequency, angular junctions, wire junctions less than 28 degrees, and wires spaced closer than 0.23 wavelengths. The program offers both 2-D and 3-D patterns, and a variety of supplemental calculating features, for example, inductor calculations that include leads and distributed capacitance and matching networks including gamma, Tee, and beta (or hairpin). The program also permits for each wire separate values of conductivity and permeability, and it is able to import successfully a wide range of model files in .nec format.

+

Orion (web.archive.org) of Canada offers a Windows95/98/NT 32-bit version of MININEC, NEC4WIN, using a spreadsheet geometry input page, pull down boxes for other antenna parameters, and a pattern plotting output that includes lobe identification and bandwidth. In addition, the user can vary the height of the antenna without invoking a complete recalculation of the matrix for faster results. Recent upgrades include 3-D patterns, and optimization routines. The VM (virtual memory) version of the program permits almost unlimited numbers of segments in a model.

+

MMANA, version 0.5E (English language), is available as freeware from VK5KC's "MMHamsoft" website. Based upon public domain MININEC, the program offers a large segment (pulse) capacity because the author, JE3HHT, Makoto Mori, has placed the program in a Windows framework using C++. The program offers advanced features such as segment length tapering, optimizing, and network calculation, but lacks some basic features, such as assigning a user-specified material conductivity or resistivity to the model wires, frequency compensation, or close-wire compensation. However, the price (no-cost) is excellent, although there is no customer support for the package.

+
+

Other MOM and Antenna Software

+
MultiNEC by Dan Maguire, is an Excel application that can make multiple simulation runs of an antenna model while automatically changing one or more aspects of the model between runs. The program requires that the user have one of the commercial implementations of NEC-2, a generic NEC-2 core, a NEC-4 program, or the Antenna Model implementation of MININEC. The program is now available in a new upgrade for a very low cost. However, AC6LA has ended support for this application. +

NEC-BSC (web.archive.org), the NEC-Basic Scattering Code (and its "workbench") and other MoM-related software (including EM Surface Patch Code, Reflector Antenna Code, and Aircraft Code) are available (at about $300 per package) from the Ohio State ElectroScience Laboratory.

+

Ansoft Ensemble (web.archive.org) offers planar EM simulation software for RF and wireless design, providing s-parameters and full wave fields using MoM methods. The software is applicable to microstrip and planar microwave structures, including antennas and transmission line applications. A limited-function student version is available as a free download.

+

EMMCAP (web.archive.org) is a user-oriented 3D "Curved" MoM software for the modeling of arbitrarily shaped wire structures and for the computation of their electromagnetic behavior, including radiation and scattering problems. The code is based in a Method of Moments formulation with curved segments. It is intended for solving problems in the areas of antenna analysis and design, EMC applications, transmission lines and nonradiating networks. The modeling of the structure can be performed by means of the EMMCAP specific 3D-tools. System responses can be computed in a frequency sweep and plotted in 2D and 3D graphical representations.

+

ASAP, Antenna Scatterers Analysis Program--originally developed by J. W. McCormack and made available as free downloadable software in the FORTRAN source code and PC executables by R. L. Cross--is a method-of-moment antenna analysis program with a "more English-like" input system.

+

MOMIC, made available without cost by Professor Andrzej Karwowski of the Silesian Technical University in Gliwice, Poland. MOMIC is a Method of Moments Interactive Code for numerical modeling of arbitrary thin-wire radiating and scattering structures in free space.

+

Polar Plot (web.archive.org) is a program for the Windows 95/98 environment that uses the audio capabilities of the PC and a receiver to allow the user to generate a polar plot of his antenna. The program was developed for Windows by Bob Freeth, G4HFQ.

+

Arbitrary Transmission Line Calculator is a suite of programs in C developed for the analysis and design of electrical transmission lines and directional couplers of totally arbitrary cross section. By analysis, it is assumed one requires to find the electrical properties of a transmission line or coupler, where the physical dimensions of the device are known. By design, it is assumed one requires a transmission line or coupler to have certain electrical properties and one wishes to find how to physically realise such a structure. The software is under general public license.

+

ASL Antenna Software Ltd (web.archive.org) of Great Britain offers a range of specialized antenna software.

+

CEMTACH (web.archive.org) offer specialized computational EM simulation services and software.

+

The sources listed above have web pages for further information on the relevant software. Brian Beezley, K6STI, also has until recently offered a wide range of NEC-related software, as well as a Yagi optimization program, a terrain analysis program, and DSP software. Contact the author via mail, since the most recent e-mail address (k6sti@n2.net) may no longer be active.

+

These listings do not include a considerable array of hybrid modeling programs (with the exception of Ensemble) that make use of multiple techniques--many, but not all, MoM based--to model circuitry (usually derived from PSpice lists or outputs), transmission lines, and antennas (including flat surfaces and substrates). Some are compatible with AutoCAD outputs for direct graphic-to-model links. Virtually all of the advanced versions of these programs are proprietary and expensive compared to NEC offerings. However, for many aspects of UHF and EHF design, they be the proper programs of choice.

+
+

Additional Resources

+
The Applied Computational Electromagnetics Society (ACES) is perhaps the professional focal point of advances in all forms of electromagnetics codes and related mathematical models. It holds an annual meeting on the west coast in March with a very full and varied program. +

The (Unofficial) NEC Archives (web.archive.org) are maintained by Ray Anderson, WB6TPU. Formerly, this collection of NEC-related software has been available only via FTP. However, the entire contents are now accessible via the web. They include many source codes for NEC and for pre- and post-processing of NEC, along with some sample input files. Another valuable website of NEC-2 information (web.archive.org) was originated by Peter Richeson and is now maintained by Nittany-Scientific.

+

There are several self-study modeling courses available. ARRL offers Antenna Modeling in its Continuing Education Series. The 30-lesson course uses EZNEC and NEC-Win Plus to introduce basic modeling concepts, techniques, and limitations related to NEC-2. The volume and the exercise models are available independently of the tutored educational program for self-study purposes. An alternative tutorial geared to NEC-Win Plus is Basic Antenna Modeling: A Hands-On Tutorial.

+

For more advanced users of NEC-2 and NEC-4, NSI is releasing Intermediate Antenna Modeling: A Hands-On Tutorial. This self-study volume encompasses virtually the entire command sets for both cores, including details of command revisions in the transition between NEC-2 and NEC-4. The 450-page volume includes about 300 exercise models in .NEC format. Although geared to the cores used by NSI (NEC-Won Pro and GNEC), the volume is useful with almost any version of NEC-2 or NEC-4.

+

To examine some of the differences among the NEC and MININEC offerings, see QEX, for Sep/Oct, 2005, and Nov/Dec, 2005. The 2-part series text and graphics provide an overview of significant user differences among programs, many of which appear in the above listing. It can be interesting to compare this overview to an earlier version that appeared in QEX, Mar/Apr, 1998. The differences will show the rate of change and of development in the field of antenna modeling software.

+

There are--for many reasons--no instructional manuals for MININEC of the scope and independence of the self-study course for NEC. Software instruction manuals or "help" compendiums may be the best source of instruction. However, you may wish to get started by looking back to "A Beginner's Guide to Using Computer Antenna Modeling Programs," from The ARRL Antenna Compendium, Volume 3, reprinted in Vertical Antenna Classics.

+

For more details on the use of commands, the limitations of various NEC and MININEC programs, and numerous work-arounds, see the Antenna Modeling series that appears monthly in antenneX. You can freely view past columns (at this site in the Antenna Modeling series).

+

This listing is necessarily limited. However, the indicated web pages will lead you to other information on details, specifications, related developments, and a more complete understanding of the rapidly expanding field of electromagnetic modeling. However, as with all software information, development efforts quickly outrun written accounts.

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+ +
+

Updated 03-10-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

Return to Main Index

+

Topics: Modeling


+ + diff --git a/content/model/nec4.html b/content/model/nec4.html new file mode 100644 index 0000000..eece27e --- /dev/null +++ b/content/model/nec4.html @@ -0,0 +1,596 @@ + + + + + + NEC-4 vs. NEC-2 Stepped-Diameter Correction and Auto-Segmentation + + + + +
+

NEC-4 vs. NEC-2 With Stepped-Diameter Correction
+ and Auto-Segmentation

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

NEC-4 is supposed to overcome several limitations of NEC-2, notable among which is the ability to handle with computational accuracy stepped-diameter elements. Implementations of NEC-2, such as EZNEC, employ a correction factor, substituting a single wire for the linear stepped-diameter group, the single wire diameter being calculated according to a formula. In the case of EZNEC, the technique follows that of Leeson.

+

One might be tempted to simply transfer a NEC-2 model--designed for use with a stepped-diameter correction equivalency--directly to NEC-4 in order to check the accuracy of the equivalency output. However, NEC-4 is subject to its own limitations, and model adjustment is necessary.

+

Initial comparative tests of models, performed on EZNEC Pro for ease of comparing NEC-2 corrected, NEC-2 uncorrected, and NEC-4 models, have turned up a number of interesting factors involved in transferring models. Tests were performed on Yagi antenna models developed by K6STI and presented on disk with the ARRL Antenna Compendium, Volume 4. One notable feature of K6STI's models is the use of short, fat element-center sections to account for mounting plates and other boom-related phenomena. This factor alone presents all versions of NEC with a challenge insofar as the diameter jump is great between the center and the immediately adjacent segments.

+

To facilitate examination of the variances among models, I have set forth notes on the tables that immediate follow. The tables show gain, front-to- back ratio, and feedpoint impedance of models using various segmentations. "Auto S Min" = auto-segmentation, using recommended absolute minimal numbers of segments. "Auto S Con"" = auto-segmentation using recommended conservative minimal numbers of segments. The following entries represent manual segmentation designed to equalized segment lengths and, to the degree possible within the limits of the structure, to align the segments for greatest accuracy.

+

Following each set of notes and tables are sample models used in this study, given in the form of NEC decks, with all units in meters.

+
+

1. 240-20

+
The first model is a 2-element 40-meter Yagi for 7.1 MHz. The K6STI segmentation and antenna performance date are shown for reference. The entry called "Space" represents the distance rear to front of the elements. In this case, the reflector and driven element are separate by 234." All dimensions are in inches. K6STI's rearward performance figure is not directly comparable to front-to-back ratio, since it is actually a front- to-rear ratio that averages rear quadrant performance. For a 2-element Yagi, this figure will normally exceed a direct front-to-back ratio. +

Notes:

+

1. Because the centermost element section is very short, neither mode of auto-segmentation is adequate to produce a center segment anywhere close to the length of the adjacent segments. NEC-4 is sensitive to this factor, especially where there is considerable current on the unequal adjoining segments. When the center segment is very short (even though passing NEC-4 criteria checks), the gain is generally too optimistic. The last entry, which purposely makes the center segment significantly longer than adjacent segments, typically yields a pessimistic gain.

+

2. The 58 segment manually segmented model approaches adequacy, as verified by the 116 segment model, which again was manually segmented to equalize segment length and alignment. The two models may be considered as having achieved convergence. What these models have in common is equalized segment lengths and segment alignment within structural limits, NEC-4 modeling factors that cannot be overstressed.

+

3. NEC-2 models that do not employ a stepped-diameter correction are wholly inadequate to this task. Since convergence is not possible, model accuracy is in no way self-identifying.

+

4. NEC-2 models employing stepped-diameter correction appear closest to NEC-4 converged models when using the minimum number of segments consistent with NEC conservative guidelines for element length and length-to-diameter ratio. Note that the NEC-2 corrected model that is auto-segmented by conservative standards most closely coincides with the values accepted above as reasonable for NEC-4.

+

5. To check the sensitivity of NEC-4 and NEC-2 corrected to the large jump in element diameter close to the high current section of the antenna, an alternate model was constructed. The only change was to reduce the center section diameter from 4.7" to 2.5." Since this antenna now differs from the K6STI model, output figure comparisons must be confined within the model group. Once more, NEC-4 shows its sensitivity to segment length equalization at the center of the elements. Auto-segmentation is inadequate to achieve segment equalization for this particular model. However, NEC-2 with a stepped-diameter correction produces a model that coincides with the converged NEC-4 model only with manual segmentation to equalize segment lengths. This raises the question of whether the note in item 4 above is a rule or an accident. If an accident, then confidence in models using a stepped-diameter correction is compromised, even if the results are not as far afield as the results from NEC-2 when no stepped-diameter correction is used.

+ 
K6STI Model 240-20:  2-element Yagi; 7.1 MHz
+
+Element tapered dimensions from center outward in inches:
+El.       Space     4.7"      2.25"     2"   1"   .75" 0.5"      Total
+Refl        0        12       108       120   66   66   85         457"
+D.E.      234        12       108       120   66   66   25.5       397.5"
+
+K6STI Reference (YO)     6.12      11.08     34.0  - 34.5
+
+NEC-4          Segs      Gain dBi  F-B dB    Feed Z R +/- jX
+Auto S Min      22       7.37      10.60     29.68 - 22.26
+Auto S Con      32       6.75      10.54     34.32 - 25.31
+20A-1 ctr       58       6.23      10.44     38.92 - 27.05
+20B-2 ctr      116       6.23      10.30     39.42 - 24.52
+20B-1 ctr      114       5.86      10.30     42.88 - 26.88
+
+NEC-2 with stepped-diameter correction
+Auto S Min      22       6.69      10.75     33.14 - 30.60
+Auto S Con      32       6.21      10.68     37.03 - 33.82
+20A-1 ctr       58       5.85      10.66     40.31 - 36.78
+20B-2 ctr      116       7.13      10.45     34.48 +  4.097
+20B-1 ctr      114       5.58      10.62     43.02 - 38.43
+
+NEC-2 without stepped-diameter correction
+Auto S Min      22       7.32       9.43     31.97 -  9.381
+Auto S Con      32       6.80       9.15     36.38 -  8.086
+20A-1 ctr       58       6.35       8.67     41.02 -  3.797
+20B-2 ctr      116       6.47       8.20     40.59 +  1.733
+20B-1 ctr      114       6.04       8.21     44.81 +  1.611
+
+Revised Taper:  First Segment 2.5"
+
+NEC-4          Segs      Gain dBi  F-B dB    Feed Z R +/- jX
+Auto S Min      22
+Auto S Con      32       6.33      10.38     38.00 - 25.30
+20A-1 ctr       58       5.89      10.27     42.30 - 26.35
+20B-2 ctr      116       5.84      10.12     43.34 - 24.09
+20B-1 ctr      114       5.55      10.12     46.21 - 25.79
+
+NEC-2 with stepped-diameter correction
+Auto S Min      22
+Auto S Con      32       6.14      10.46     38.21 - 30.29
+20A-1 ctr       58       5.78      10.44     41.59 - 32.95
+20B-2 ctr      116       6.04      10.25     44.48 +  5.403
+20B-1 ctr      114       5.51      10.40     44.37 - 34.37
+
+NEC-2 without stepped-diameter correction
+Auto S Min      22
+Auto S Con      32       6.01       9.02     43.58 -  8.877
+20A-1 ctr       58       5.52       8.56     49.62 -  3.890
+20B-2 ctr      116       5.43       8.12     51.51 +  2.456
+20B-1 ctr      114       5.14       8.12     55.08 +  2.538
+
+ 
CM 2el Yagi 240-20:  32 segments
+CM Auto-segmented
+CE
+GW 1,2,-11.607,0.,0.,-9.4488,0.,0.,.00635
+GW 2,1,-9.4488,0.,0.,-7.7724,0.,0.,.00953
+GW 3,1,-7.7724,0.,0.,-6.096,0.,0.,.0127
+GW 4,2,-6.096,0.,0.,-3.048,0.,0.,.0254
+GW 5,2,-3.048,0.,0.,-.3048,0.,0.,.0286
+GW 6,1,-.3048,0.,0.,.3048,0.,0.,.0597
+GW 7,2,.3048,0.,0.,3.048,0.,0.,.0286
+GW 8,2,3.048,0.,0.,6.096,0.,0.,.0254
+GW 9,1,6.096,0.,0.,7.7724,0.,0.,.0127
+GW 10,1,7.7724,0.,0.,9.4488,0.,0.,.00953
+GW 11,2,9.4488,0.,0.,11.6078,0.,0.,.00635
+GW 12,1,-10.096,5.9436,0.,-9.4488,5.9436,0.,.00635
+GW 13,1,-9.4488,5.9436,0.,-7.7724,5.9436,0.,.00953
+GW 14,1,-7.7724,5.9436,0.,-6.096,5.9436,0.,.0127
+GW 15,2,-6.096,5.9436,0.,-3.048,5.9436,0.,.0254
+GW 16,2,-3.048,5.9436,0.,-.3048,5.9436,0.,.0286
+GW 17,1,-.3048,5.9436,0.,.3048,5.9436,0.,.0597
+GW 18,2,.3048,5.9436,0.,3.048,5.9436,0.,.0286
+GW 19,2,3.048,5.9436,0.,6.096,5.9436,0.,.0254
+GW 20,1,6.096,5.9436,0.,7.7724,5.9436,0.,.0127
+GW 21,1,7.7724,5.9436,0.,9.4488,5.9436,0.,.00953
+GW 22,1,9.4488,5.9436,0.,10.0965,5.9436,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+LD 5,16,0,0,2.5E+07,1.
+LD 5,17,0,0,2.5E+07,1.
+LD 5,18,0,0,2.5E+07,1.
+LD 5,19,0,0,2.5E+07,1.
+LD 5,20,0,0,2.5E+07,1.
+LD 5,21,0,0,2.5E+07,1.
+LD 5,22,0,0,2.5E+07,1.
+FR 0,1,0,0,7.1
+GN -1
+EX 0,17,1,0,1.414214,-1.883E-7
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+ 
CM 2el Yagi 240-20:  116 segments
+CM Manually segmented for equal lengths
+CE
+GW 1,6,-11.607,0.,0.,-9.4488,0.,0.,.00635
+GW 2,4,-9.4488,0.,0.,-7.7724,0.,0.,.00953
+GW 3,4,-7.7724,0.,0.,-6.096,0.,0.,.0127
+GW 4,8,-6.096,0.,0.,-3.048,0.,0.,.0254
+GW 5,8,-3.048,0.,0.,-.3048,0.,0.,.0286
+GW 6,2,-.3048,0.,0.,.3048,0.,0.,.0597
+GW 7,8,.3048,0.,0.,3.048,0.,0.,.0286
+GW 8,8,3.048,0.,0.,6.096,0.,0.,.0254
+GW 9,4,6.096,0.,0.,7.7724,0.,0.,.0127
+GW 10,4,7.7724,0.,0.,9.4488,0.,0.,.00953
+GW 11,6,9.4488,0.,0.,11.6078,0.,0.,.00635
+GW 12,2,-10.096,5.9436,0.,-9.4488,5.9436,0.,.00635
+GW 13,4,-9.4488,5.9436,0.,-7.7724,5.9436,0.,.00953
+GW 14,4,-7.7724,5.9436,0.,-6.096,5.9436,0.,.0127
+GW 15,8,-6.096,5.9436,0.,-3.048,5.9436,0.,.0254
+GW 16,8,-3.048,5.9436,0.,-.3048,5.9436,0.,.0286
+GW 17,2,-.3048,5.9436,0.,.3048,5.9436,0.,.0597
+GW 18,8,.3048,5.9436,0.,3.048,5.9436,0.,.0286
+GW 19,8,3.048,5.9436,0.,6.096,5.9436,0.,.0254
+GW 20,4,6.096,5.9436,0.,7.7724,5.9436,0.,.0127
+GW 21,4,7.7724,5.9436,0.,9.4488,5.9436,0.,.00953
+GW 22,2,9.4488,5.9436,0.,10.0965,5.9436,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+LD 5,16,0,0,2.5E+07,1.
+LD 5,17,0,0,2.5E+07,1.
+LD 5,18,0,0,2.5E+07,1.
+LD 5,19,0,0,2.5E+07,1.
+LD 5,20,0,0,2.5E+07,1.
+LD 5,21,0,0,2.5E+07,1.
+LD 5,22,0,0,2.5E+07,1.
+FR 0,1,0,0,7.1
+GN -1
+EX 0,17,2,0,.707107,-9.416E-8
+EX 0,17,1,0,.707107,-9.416E-8
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+
+

2. 310-08

+
The second example is a 3-element Yagi designed for 28.4 MHz. For the most part, front-to-back ratios can be ignored, since they reflect only the depth of the pucker in the rear lobe(s) and do not give a clear picture of the rearward radiation. Indeed, no single number can do this job. The clearest non-graphical portrait of rearward radiation comes from a combination of the front-to-back ratio, the front-to-rear average ratio, and the "worst case" rearward ratio. This example is most notable for its exceptionally short element center section (4"). The alternative model simply eliminates this section and continues the 0.75" tubing across the center. Boom lengths total 90" with the element spacing shown. +

Notes:

+

1. As noted for the 2-element, 40-meter Yagi, NEC-2 without a stepped- diameter correction overestimates gain in both the original and the alternate model. However, in accord with generally received wisdom, the alternate model is closest to converged models with somewhat minimal segmentation. However, there is no convergence to self-identify the most reliable result.

+

2. For the original design, NEC-4 models only approach convergence at 283 segments. Even that large model suffers from the large center-section to adjacent-section diameter jump insofar as the center section is longer than desired. However, breaking it into 2 segments exceeds the recommended diameter-to-length ratio.

+

3. For the alternate model, NEC-4 results converge reasonably between the conservative auto-segmentation version and the manually segmented and equalized version. The 48" center section of each element provides a foundation for more reliable outputs with a far smaller model than needed for the original design.

+

4. With this antenna design, NEC-2 results for stepped-diameter correction tend to approach NEC-4 convergence within the range of the smallest reliable NEC-4 model. However, even stepped-diameter correction results tend to progress through the NEC-4 convergence point, indicating an absence of a reliable convergence region and hence lesser confidence in the chosen model size without a cross-reference to NEC-4.

+ 
K6STI Model 310-08:  3-element Yagi; 28.4 MHz
+
+Element tapered dimensions from center outward in inches:
+El.       Space     2.5"      .75"      .625"     .5"       Total
+Refl        0         2        22        18       66.75       108.75"
+D.E.       36         2        22        18       57.625       99.625"
+Dir        90         2        22        18       53.125       95.125
+
+K6STI Reference (YO)     7.21      22.91     25.1 - 24.4
+
+NEC-4          Segs      Gain dBi  F-B dB    Feed Z R +/- jX
+Auto S Min      27       10.15     38.92     12.93 - 14.32
+Auto S Con      42        9.34     25.28     15.72 - 16.78
+08A-1 ctr       73        8.88     36.54     17.32 - 17.86
+08B-1 ctr      143        8.14     35.63     20.33 - 20.41
+08C-1 ctr      213        7.68     35.21     22.57 - 22.45
+08D-1 ctr      283        7.32     35.22     24.50 - 24.49
+
+NEC-2 with stepped-diameter correction
+Auto S Min      27        8.33     31.30     20.19 - 21.84
+Auto S Con      42        7.80     37.49     23.12 - 24.08
+08A-1 ctr       73        7.52     42.85     24.55 - 24.94
+08B-1 ctr      143        7.11     50.08     26.87 - 26.84
+08C-1 ctr      213        6.92     55.47     28.02 - 27.82
+08D-1 ctr      283        6.81     59.46     28.76 - 28.43
+
+NEC-2 without stepped-diameter correction
+Auto S Min      27       11 22     28.91      9.46 -  8.74
+Auto S Con      42       10.81     24.99     10.34 -  8.81
+08A-1 ctr       73       10.68     21.84     10.18 -  7.63
+08B-1 ctr      143       10.59     19.39      9.91 -  6.25
+08C-1 ctr      213       10.61     18.26      9.57 -  5.34
+08D-1 ctr      283       10.65     17.57      9.30 -  4.70
+
+NEC-4
+Auto S Min      21        6.96     37.69     27.29 - 27.44
+Auto S Con      35        7.26     37.34     25.16 - 24.73
+081X eq         68        7.30     33.06     24.69 - 23.23
+
+NEC-2 with stepped-diameter correction
+Auto S Min      21        6.88     48.93     28.25 - 27.66
+Auto S Con      35        7.17     41.08     26.23 - 25.04
+081X eq         68        7.32     41.99     26.56 - 13.47
+
+NEC-2 without stepped-diameter correction
+Auto S Min      21        7.08     29.59     25.35 - 22.42
+Auto S Con      35        7.42     25.38     22.85 - 18.83
+081X eq         68        7.51     21.93     21.42 - 15.35
+
+ 
CM 3el Yagi 310-08  42 segments
+CM Conservative autosegmentation
+CE
+GW 1,5,-2.7622,0.,0.,-1.0668,0.,0.,.00635
+GW 2,1,-1.0668,0.,0.,-.6096,0.,0.,.00794
+GW 3,2,-.6096,0.,0.,-.0508,0.,0.,.00953
+GW 4,1,-.0508,0.,0.,.0508,0.,0.,.0318
+GW 5,2,.0508,0.,0.,.6096,0.,0.,.00953
+GW 6,1,.6096,0.,0.,1.0668,0.,0.,.00794
+GW 7,4,1.0668,0.,0.,2.76225,0.,0.,.00635
+GW 8,3,-2.5304,.9144,0.,-1.0668,.9144,0.,.00635
+GW 9,1,-1.0668,.9144,0.,-.6096,.9144,0.,.00794
+GW 10,2,-.6096,.9144,0.,-.0508,.9144,0.,.00953
+GW 11,1,-.0508,.9144,0.,.0508,.9144,0.,.0318
+GW 12,2,.0508,.9144,0.,.6096,.9144,0.,.00953
+GW 13,1,.6096,.9144,0.,1.0668,.9144,0.,.00794
+GW 14,3,1.0668,.9144,0.,2.53047,.9144,0.,.00635
+GW 15,3,-2.4161,2.286,0.,-1.0668,2.286,0.,.00635
+GW 16,1,-1.0668,2.286,0.,-.6096,2.286,0.,.00794
+GW 17,2,-.6096,2.286,0.,-.0508,2.286,0.,.00953
+GW 18,1,-.0508,2.286,0.,.0508,2.286,0.,.0318
+GW 19,2,.0508,2.286,0.,.6096,2.286,0.,.00953
+GW 20,1,.6096,2.286,0.,1.0668,2.286,0.,.00794
+GW 21,3,1.0668,2.286,0.,2.41617,2.286,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+LD 5,16,0,0,2.5E+07,1.
+LD 5,17,0,0,2.5E+07,1.
+LD 5,18,0,0,2.5E+07,1.
+LD 5,19,0,0,2.5E+07,1.
+LD 5,20,0,0,2.5E+07,1.
+LD 5,21,0,0,2.5E+07,1.
+FR 0,1,0,0,28.4
+GN -1
+EX 0,11,1,0,1.414214,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+ 
CM 3el Yagi 310-081X  68 segment alternate
+CM Manually segmented for equalized segments
+CE
+GW 1,7,-2.7622,0.,0.,-1.0668,0.,0.,.00635
+GW 2,2,-1.0668,0.,0.,-.6096,0.,0.,.00794
+GW 3,6,-.6096,0.,0.,.6096,0.,0.,.00953
+GW 4,2,.6096,0.,0.,1.0668,0.,0.,.00794
+GW 5,7,1.0668,0.,0.,2.76225,0.,0.,.00635
+GW 6,6,-2.5304,.9144,0.,-1.0668,.9144,0.,.00635
+GW 7,2,-1.0668,.9144,0.,-.6096,.9144,0.,.00794
+GW 8,6,-.6096,.9144,0.,.6096,.9144,0.,.00953
+GW 9,2,.6096,.9144,0.,1.0668,.9144,0.,.00794
+GW 10,6,1.0668,.9144,0.,2.53047,.9144,0.,.00635
+GW 11,6,-2.4161,2.286,0.,-1.0668,2.286,0.,.00635
+GW 12,2,-1.0668,2.286,0.,-.6096,2.286,0.,.00794
+GW 13,6,-.6096,2.286,0.,.6096,2.286,0.,.00953
+GW 14,2,.6096,2.286,0.,1.0668,2.286,0.,.00794
+GW 15,6,1.0668,2.286,0.,2.41617,2.286,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+FR 0,1,0,0,28.4
+GN -1
+EX 0,8,4,0,.707107,0.
+EX 0,8,3,0,.707107,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+

3. 320-16

+
The third example is a 3-element Yagi designed for 14.175 MHz. Cautions similar to those given for the 10-meter beam apply to the front-to-back ratios. Also, like the 10-meter design, this example has a short element center section (8"). Because the properties of this antenna design when modeled replicate so closely those of the 10-meter model, no alternate version is shown. +

Notes:

+

1. NEC-2 without a stepped correction factor displaces the beam relative to frequency and overestimates gain while underestimating front-to-back ratio and feedpoint impedance. Because the number of steps per half- element is 50% greater than the steps used for the 10-meter beam, the offset is even worse.

+

2. The center element diameter is about 3 times the adjacent section diameter. However, the number of diameter steps is large. These factors combine to set a practical limit to achieving convergence in NEC-4. Although the final doubling of segments between 16B and 16C shows an approach to convergence, the model has grown to 442 segments. The reasonableness of convergence and use of the output numbers at this level will depend upon the purposes of the modeling.

+

3. As with the 10-meter model, the NEC-2 with stepped-diameter correction numbers approach those of a converged NEC-4 model somewhere between the conservative auto-segmented version and the smallest manually segmented and equalized version. However, again, this point is not self-identifying within NEC-2, since the model continues to vary in value with changes in the number of segments. Notable in this progression is a clear indication that too many segments defeats the stepped-diameter correction and produces results little better than NEC-2 without the stepped-diameter correction.

+ 
K6STI Model 320-16:  3-element Yagi; 14.175 MHz
+
+Element tapered dimensions from center outward in inches:
+El.  Space     3.75 1.25 1.0  .875 .75  .625"     .5"       Total
+Refl    0        4   44   24   20   42   20       69.625    223.625"
+D.E.   80        4   44   24   20   42   20       51.25     205.25"
+Dir   186        4   44   24   20   42   20       46.625    196.625"
+
+K6STI Reference (YO)     7.25      23.32     26.7 - 25.3
+
+NEC-4          Segs      Gain dBi  F-B dB    Feed Z R +/- jX
+Auto S Min      39        9.84     33.04     14.66 - 15.32
+Auto S Con      57        9.08     33.24     17.44 - 17.73
+16A-1 ctr      112        8.40     31.39     20.08 - 19.58
+16B-1 ctr      221        7.83     29.04     22.54 - 21.02
+16C-2 ctr      442        7.74     27.80     22.74 - 20.73
+
+NEC-2 with stepped-diameter correction
+Auto S Min      39        8.25     36.90     22.16 - 22.75
+Auto S Con      57        7.77     48.71     24.77 - 24.48
+16A-1 ctr      112        7.35     45.51     27.19 - 26.40
+16B-1 ctr      221        7.02     41.97     29.17 - 28.02
+16C-2 ctr      442       10.23     43.00     16.05 +  4.83
+
+NEC-2 without stepped diamter correction
+Auto S Min      39       10 87     19.04      9.37 -  5.82
+Auto S Con      57       10.48     16.74      9.69 -  4.33
+16A-1 ctr      112       10.30     13.80      8.97 -  0.60
+16B-1 ctr      221       10.28     11.40      7.89 +  3.67
+16C-2 ctr      442       10.94      9.31      5.85 +  7.02
+ 
CM 3el Yagi 320-16 57 segments
+CM Conservative autosegmentation
+CE
+GW 1,2,-5.68,0.,0.,-3.9116,0.,0.,.00635
+GW 2,1,-3.9116,0.,0.,-3.4036,0.,0.,.00794
+GW 3,2,-3.4036,0.,0.,-2.3368,0.,0.,.00953
+GW 4,1,-2.3368,0.,0.,-1.8288,0.,0.,.0111
+GW 5,1,-1.8288,0.,0.,-1.2192,0.,0.,.0127
+GW 6,2,-1.2192,0.,0.,-.1016,0.,0.,.0159
+GW 7,1,-.1016,0.,0.,.1016,0.,0.,.0476
+GW 8,2,.1016,0.,0.,1.2192,0.,0.,.0159
+GW 9,1,1.2192,0.,0.,1.8288,0.,0.,.0127
+GW 10,1,1.8288,0.,0.,2.3368,0.,0.,.0111
+GW 11,2,2.3368,0.,0.,3.4036,0.,0.,.00953
+GW 12,1,3.4036,0.,0.,3.9116,0.,0.,.00794
+GW 13,2,3.9116,0.,0.,5.68008,0.,0.,.00635
+GW 14,2,-5.2133,2.032,0.,-3.9116,2.032,0.,.00635
+GW 15,1,-3.9116,2.032,0.,-3.4036,2.032,0.,.00794
+GW 16,2,-3.4036,2.032,0.,-2.3368,2.032,0.,.00953
+GW 17,1,-2.3368,2.032,0.,-1.8288,2.032,0.,.0111
+GW 18,1,-1.8288,2.032,0.,-1.2192,2.032,0.,.0127
+GW 19,2,-1.2192,2.032,0.,-.1016,2.032,0.,.0159
+GW 20,1,-.1016,2.032,0.,.1016,2.032,0.,.0476
+GW 21,2,.1016,2.032,0.,1.2192,2.032,0.,.0159
+GW 22,1,1.2192,2.032,0.,1.8288,2.032,0.,.0127
+GW 23,1,1.8288,2.032,0.,2.3368,2.032,0.,.0111
+GW 24,2,2.3368,2.032,0.,3.4036,2.032,0.,.00953
+GW 25,1,3.4036,2.032,0.,3.9116,2.032,0.,.00794
+GW 26,2,3.9116,2.032,0.,5.21335,2.032,0.,.00635
+GW 27,2,-4.9942,4.7244,0.,-3.9116,4.7244,0.,.00635
+GW 28,1,-3.9116,4.7244,0.,-3.4036,4.7244,0.,.00794
+GW 29,2,-3.4036,4.7244,0.,-2.3368,4.7244,0.,.00953
+GW 30,1,-2.3368,4.7244,0.,-1.8288,4.7244,0.,.0111
+GW 31,1,-1.8288,4.7244,0.,-1.2192,4.7244,0.,.0127
+GW 32,2,-1.2192,4.7244,0.,-.1016,4.7244,0.,.0159
+GW 33,1,-.1016,4.7244,0.,.1016,4.7244,0.,.0476
+GW 34,2,.1016,4.7244,0.,1.2192,4.7244,0.,.0159
+GW 35,1,1.2192,4.7244,0.,1.8288,4.7244,0.,.0127
+GW 36,1,1.8288,4.7244,0.,2.3368,4.7244,0.,.0111
+GW 37,2,2.3368,4.7244,0.,3.4036,4.7244,0.,.00953
+GW 38,1,3.4036,4.7244,0.,3.9116,4.7244,0.,.00794
+GW 39,2,3.9116,4.7244,0.,4.99428,4.7244,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+LD 5,16,0,0,2.5E+07,1.
+LD 5,17,0,0,2.5E+07,1.
+LD 5,18,0,0,2.5E+07,1.
+LD 5,19,0,0,2.5E+07,1.
+LD 5,20,0,0,2.5E+07,1.
+LD 5,21,0,0,2.5E+07,1.
+LD 5,22,0,0,2.5E+07,1.
+LD 5,23,0,0,2.5E+07,1.
+LD 5,24,0,0,2.5E+07,1.
+LD 5,25,0,0,2.5E+07,1.
+LD 5,26,0,0,2.5E+07,1.
+LD 5,27,0,0,2.5E+07,1.
+LD 5,28,0,0,2.5E+07,1.
+LD 5,29,0,0,2.5E+07,1.
+LD 5,30,0,0,2.5E+07,1.
+LD 5,31,0,0,2.5E+07,1.
+LD 5,32,0,0,2.5E+07,1.
+LD 5,33,0,0,2.5E+07,1.
+LD 5,34,0,0,2.5E+07,1.
+LD 5,35,0,0,2.5E+07,1.
+LD 5,36,0,0,2.5E+07,1.
+LD 5,37,0,0,2.5E+07,1.
+LD 5,38,0,0,2.5E+07,1.
+LD 5,39,0,0,2.5E+07,1.
+FR 0,1,0,0,14.175
+GN -1
+EX 0,20,1,0,1.414214,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+ 
CM 3el Yagi 320-16 442 segments
+CM Manually segmented and equalized
+CE
+GW 1,20,-5.68,0.,0.,-3.9116,0.,0.,.00635
+GW 2,8,-3.9116,0.,0.,-3.4036,0.,0.,.00794
+GW 3,12,-3.4036,0.,0.,-2.3368,0.,0.,.00953
+GW 4,8,-2.3368,0.,0.,-1.8288,0.,0.,.0111
+GW 5,8,-1.8288,0.,0.,-1.2192,0.,0.,.0127
+GW 6,16,-1.2192,0.,0.,-.1016,0.,0.,.0159
+GW 7,2,-.1016,0.,0.,.1016,0.,0.,.0476
+GW 8,16,.1016,0.,0.,1.2192,0.,0.,.0159
+GW 9,8,1.2192,0.,0.,1.8288,0.,0.,.0127
+GW 10,8,1.8288,0.,0.,2.3368,0.,0.,.0111
+GW 11,16,2.3368,0.,0.,3.4036,0.,0.,.00953
+GW 12,8,3.4036,0.,0.,3.9116,0.,0.,.00794
+GW 13,20,3.9116,0.,0.,5.68008,0.,0.,.00635
+GW 14,16,-5.2133,2.032,0.,-3.9116,2.032,0.,.00635
+GW 15,8,-3.9116,2.032,0.,-3.4036,2.032,0.,.00794
+GW 16,16,-3.4036,2.032,0.,-2.3368,2.032,0.,.00953
+GW 17,8,-2.3368,2.032,0.,-1.8288,2.032,0.,.0111
+GW 18,8,-1.8288,2.032,0.,-1.2192,2.032,0.,.0127
+GW 19,16,-1.2192,2.032,0.,-.1016,2.032,0.,.0159
+GW 20,2,-.1016,2.032,0.,.1016,2.032,0.,.0476
+GW 21,16,.1016,2.032,0.,1.2192,2.032,0.,.0159
+GW 22,8,1.2192,2.032,0.,1.8288,2.032,0.,.0127
+GW 23,8,1.8288,2.032,0.,2.3368,2.032,0.,.0111
+GW 24,16,2.3368,2.032,0.,3.4036,2.032,0.,.00953
+GW 25,8,3.4036,2.032,0.,3.9116,2.032,0.,.00794
+GW 26,16,3.9116,2.032,0.,5.21335,2.032,0.,.00635
+GW 27,16,-4.9942,4.7244,0.,-3.9116,4.7244,0.,.00635
+GW 28,8,-3.9116,4.7244,0.,-3.4036,4.7244,0.,.00794
+GW 29,16,-3.4036,4.7244,0.,-2.3368,4.7244,0.,.00953
+GW 30,8,-2.3368,4.7244,0.,-1.8288,4.7244,0.,.0111
+GW 31,8,-1.8288,4.7244,0.,-1.2192,4.7244,0.,.0127
+GW 32,16,-1.2192,4.7244,0.,-.1016,4.7244,0.,.0159
+GW 33,2,-.1016,4.7244,0.,.1016,4.7244,0.,.0476
+GW 34,16,.1016,4.7244,0.,1.2192,4.7244,0.,.0159
+GW 35,8,1.2192,4.7244,0.,1.8288,4.7244,0.,.0127
+GW 36,8,1.8288,4.7244,0.,2.3368,4.7244,0.,.0111
+GW 37,16,2.3368,4.7244,0.,3.4036,4.7244,0.,.00953
+GW 38,8,3.4036,4.7244,0.,3.9116,4.7244,0.,.00794
+GW 39,16,3.9116,4.7244,0.,4.99428,4.7244,0.,.00635
+GE 0
+LD 5,1,0,0,2.5E+07,1.
+LD 5,2,0,0,2.5E+07,1.
+LD 5,3,0,0,2.5E+07,1.
+LD 5,4,0,0,2.5E+07,1.
+LD 5,5,0,0,2.5E+07,1.
+LD 5,6,0,0,2.5E+07,1.
+LD 5,7,0,0,2.5E+07,1.
+LD 5,8,0,0,2.5E+07,1.
+LD 5,9,0,0,2.5E+07,1.
+LD 5,10,0,0,2.5E+07,1.
+LD 5,11,0,0,2.5E+07,1.
+LD 5,12,0,0,2.5E+07,1.
+LD 5,13,0,0,2.5E+07,1.
+LD 5,14,0,0,2.5E+07,1.
+LD 5,15,0,0,2.5E+07,1.
+LD 5,16,0,0,2.5E+07,1.
+LD 5,17,0,0,2.5E+07,1.
+LD 5,18,0,0,2.5E+07,1.
+LD 5,19,0,0,2.5E+07,1.
+LD 5,20,0,0,2.5E+07,1.
+LD 5,21,0,0,2.5E+07,1.
+LD 5,22,0,0,2.5E+07,1.
+LD 5,23,0,0,2.5E+07,1.
+LD 5,24,0,0,2.5E+07,1.
+LD 5,25,0,0,2.5E+07,1.
+LD 5,26,0,0,2.5E+07,1.
+LD 5,27,0,0,2.5E+07,1.
+LD 5,28,0,0,2.5E+07,1.
+LD 5,29,0,0,2.5E+07,1.
+LD 5,30,0,0,2.5E+07,1.
+LD 5,31,0,0,2.5E+07,1.
+LD 5,32,0,0,2.5E+07,1.
+LD 5,33,0,0,2.5E+07,1.
+LD 5,34,0,0,2.5E+07,1.
+LD 5,35,0,0,2.5E+07,1.
+LD 5,36,0,0,2.5E+07,1.
+LD 5,37,0,0,2.5E+07,1.
+LD 5,38,0,0,2.5E+07,1.
+LD 5,39,0,0,2.5E+07,1.
+FR 0,1,0,0,14.175
+GN -1
+EX 0,20,2,0,.707107,0.
+EX 0,20,1,0,.707107,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+

Conclusions:

+
+

1. NEC-4 has limits in dealing with stepped-diameter elements, especially under the following circumstances:

+
    +
  • a. Where the step in diameters between adjacent elements is large, and
    • +
  • b. Where the large step occurs in the region of maximum element current.
    • +
Achieving convergence under these circumstances may require quite large models relative to the number of antenna elements involved. These models grow larger for every diameter step involved in the structure of the element. +

2. Inadequate segmentation in stepped-diameter elements in NEC-4 may result in unrealistically high values for forward gain and low values for feedpoint impedance. Adequacy of segmentation includes the following:

+
    +
  • a. Number of segments,
    • +
  • b. Equalization of segment lengths within the element structural limits, and
    • +
  • c. Alignment of segments among the elements.
    • +
+

3. NEC-2 with stepped-diameter corrections can yield reasonable figures on antenna performance. However, the best segmentation to achieve those results is not self-identifying within NEC-2 due to the absence of a convergence trend. In general, the best modeling region for achieving reasonable results from NEC-2 with stepped-diameter corrections involves the following constraints:

+
    +
  • a. Use the fewest segments possible within the limits of conservative NEC guidelines; and
    • +
  • b. Adjust segment lengths and alignment for equalization for the major element section lengths, but not for very short lengths.
    • +
The result will be a model somewhat larger in segment numbers than the conservative minimum, but smaller than a converged NEC-4 model. +

4. NEC-2 without a stepped-diameter correction is highly unreliable. The larger the diameter jump between adjacent section of the element, the more unreliable the output figures. With small increments of diameter change and long constant-diameter sections, the results may be tentatively usable if the total number of segments is small. However, precision antenna analysis is not possible.

+

Given the trends in the values of forward gain and front-to-back ratio (or front-to-rear calculations) for the test Yagis with stepped-diameter elements, it is entirely possible to generate misleading models in either NEC-2 or NEC-4. Good practice calls for extreme care in developing models and in reporting results. Not only should one present modeling results, but as well one should reveal all the relevant details of the model used to generate them. Likewise, those with modeling programs should check reported figures for themselves.

+

Indeed, modeling is not in itself the solution to resolving issues of reported antenna performance figures. Without adequate descriptions of the models used (and the good engineering reasons for using those models), the output of NEC programs can be as misleading as any other antenna performance report. Properly used within their limitations and fairly reported, NEC models can be a source of important and useful information not otherwise easily obtained.
+

+
+ +

+
+

Updated 4-6-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Amateur Radio Page

+

Topics: Modeling, Stepped Diameter


+ + diff --git a/content/model/necdeck.html b/content/model/necdeck.html new file mode 100644 index 0000000..aa7e4c3 --- /dev/null +++ b/content/model/necdeck.html @@ -0,0 +1,162 @@ + + + + + + Reading a NEC Deck + + + +
+

So You Want to Read a NEC Deck

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Many users of ELNEC and EZNEC are unfamiliar with the basic elements of a standard .NEC input file. There may be some users of NEC-Win who are unfamiliar with the terms and layout of an EZNEC antenna description file (called a PD file for the abbreviated keystrokes used to generate it). So let's do a correlation between the two in order to show the basic terms of the NEC deck.

+

In most implementations, NEC uses a card-deck input file whose format goes back to the early days of FORTRAN, when punch cards provided computational inputs. For brevity, each card contain a labeled sequence of information, the individual parts separated by a delimiter. Since we Americans use "." as our decimal indicator, we use commas or spaces to separate information. European formats may vary.

+

To get us started, let's compare the antenna description file for a simple 2-element Yagi with the corresponding card deck. Then we can explain each type of card we encounter. If you wish, you can try your hand at correlating each element in the NEC deck to elements in the EZNEC antenna description file before reading beyond them.

+
+ +

+
+ 
                      EZNEC Antenna Description File
+2el Yagi 12M
+Frequency = 24.95  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 Ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.-- End 1 (x,y,z : ft)  Conn.-- End 2 (x,y,z : ft)   Dia(in)  Segs
+1         -9.100,  0.000, 40.000       9.100,  0.000, 40.000  1.00E+00   11
+2         -8.800, -4.800, 40.000       8.800, -4.800, 40.000  1.00E+00   11
+3         -0.200,  0.000,  1.000       0.200,  0.000,  1.000     # 14     1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     3 / 50.00   (  3 / 50.00)      1.000       0.000       V
+
+              --------------- LOADS ---------------
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           6     2 / 50.00   (  2 / 50.00)       1.000       100.000
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1      1/50.0  (  1/50.0)    3/50.0  (  3/50.0)  Actual dist  50.0  0.66  N
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+
+              --------------- MEDIA ---------------
+Medium       Conductivity(S/m)   Dielectric Const.    Ht(ft)   R Coord(ft)
+
+1                5.000E-03            13.00           0 (def)     0 (def)
+

+
+
+ +

+
+ 
                              .NEC Input File
+
+CM 2el Yagi 12M
+CE
+GW 1 11 -9.1 0 40 9.1 0 40 .04165
+GW 2 11 -8.8 -4.8 40 8.8 -4.8 40 .04165
+GW 3 1 -.2 0 1 .2 0 1 2.6706E-03
+GS 0 0 .3048
+GE 1
+GN 2 0 0 0 13 .005 0 0 0 0
+EX 0 3 1 0 1 0
+LD 4 2 6 6 1 100 0
+LD 5 1 1 11 2.4938E7
+LD 5 2 1 11 2.4938E7
+LD 5 3 1 1 2.4938E7
+TL 1 6 3 1 50 18.01 0 0 0 0
+FR 0 1 0 0 24.95 0
+RP 0 1 361 1000 76 0 1 1
+EN
+
+ +
+

The antenna described by these two files is shown in Figure 1. It is a simple 2-element Yagi of relatively poor performance: Gain: 11.1 dBi; front-to-back: 11.1 dB; feedpoint impedance: 42 + j4 Ohms. I have purposely altered the antenna to include an inductive load in the reflector, thus making it physically shorter than the driven element. I have also run a 50-Ohm transmission line straight down to within 1' of the ground and created a source wire there. Otherwise, our NEC deck would be pretty skimpy.

+
+ +
+

Let's look at each card in the deck and read out the information, cross checking it against the EZNEC file. In most cases, I have spread the data units out and labeled them beneath.

+ 
1.  CM 2el Yagi 12M
+

This is a comment card for storing information about the file in ASCII text. It does not enter into the calculations. You may have any number of comment cards, although some implementations limit them. In EZNEC, you may have only one CM card, called the "title."

+ 
2.  CE
+

This card is the "comment end" card, signaling that data for calculation follows.

+ 
3.  GW    1    11   -9.1     0    40     9.1    0    40    .04165
+    GW    2    11   -8.8   -4.8   40     8.8  -4.8   40    .04165
+    GW    3     1    -.2     0     1      .2    0     1    2.6706E-03
+   Type  Tag  Segs  E1 X   E1 Y  E1 Z   E2 X  E2 Y  E2 Z    Radius
+

Type GW cards describe the antenna geometry. Each antenna wire, or "Tag," has a separate numbered card or line (1, 2, and 3). The Segs (segmentation) entry tells how many segments the wire is divided into (11 each for Tags 1 and 2, 1 segment for Tag 3). Then come the Cartesian coordinates for End 1 and End 2 of each straight wire. Here, as in the EZNEC file, they are given in feet. Finally, the wire size is given as a radius (1/2 the diameter given in the EZNEC file. However, the EZNEC file lists the radius in inches. The NEC deck must use the same units throughout the GW cards, so a 1" diameter become a 0.04165' radius. The wire size figure for Tag 3 is the radius of #14 wire, in feet.)

+ 
4.  GS    0    0    .3048
+   Type            Multiplier
+

Although most implementations of NEC, such as NEC-Win and EZNEC, give the user a choice of common units of measure for setting up the antenna geometry, NEC itself calculates only in meters. In the last of its 4 columns, the "geometry scaling" card gives the multiplier needed to convert to meters.

+ 
5.  GE    1
+   Type  End
+

The "geometry end" type card signals the end of the wire set-up and prepares the way for other data that enter into the calculations.

+ 
6.  GN    2      0    0    0    13    .005    0    0    0    0
+   Type  G-type               Die-C.  Cond.
+

The ground parameter card specifies the type of ground calculation system and the necessary parameters to make the calculation. Here, we show a single medium, although a second medium can be set.

+

There are 4 types of ground systems used with NEC: -1 = free space; 0 = a finite ground with a reflection coefficient approximation (the "fast" ground in EZNEC); 1 = a perfectly conducting ground; and 2 (used here) specifies a finite ground using the Sommerfeld-Norton method of calculation for greatest accuracy. (In addition, EZNEC implements the MININEC ground calculation system.)

+

Finite ground conditions (cases 0 - 2) require two numbers to implement calculations. The first is a relative dielectric constant, usually given as an integer. Second is the conductivity in Siemens/meter (mhos/meter in older terminology). Both are generally derived from tables. The values shown represent a default presumption of medium earth conditions. Both numbers are omitted for perfect ground.

+

As with many cards in the NEC deck, there are unlabled "0" fields. Some of these represent fields simply left blank; others represent input positions for more specialized conditions not relevant to most common ham HF antennas. (Some may be relevant to VHF and UHF antennas.)

+ 
7.   EX     0     3     1     0                1     0
+    Type  S-type Tag   Seg        Voltage:   Real  Imaginary
+

The "exitation" or source information card allows for many types of exitation, of which only voltage sourcing is usually of HF ham use. Hence, the source-type is "0". The next two columns specify the placement of the source in terms of tag number and segment number in that wire. Here, the remote wire has only one segment, and the source is placed at its center. Many programs allow specification of the source at some distance from End-1 of the designated wire, and will then place the source as close to that point as segmentation permits.

+

For most ham uses, sources are either voltage or current. The latter is useful for scanning current levels along a wire, since a voltage source of "1" yields small fractions of an amp current, making scanning more difficult. Current sources may also be necessary for some advanced applications.

+

Nonetheless, both types of sources are voltage sources ultimately. The current source is generated by a voltage source set on a remote wire and transformed into a current source by a transmission line. The NEC deck will show the wire and line, while EZNEC stores this information internally.

+

Voltages are given in terms of X and Y ("real" and "imaginary") coordinates derived from inputs that can be given as a voltage and its phase angle. User current magnitude and phase angle inputs are converted to appropriate voltage values at the remote source wire.

+

In general, when converting among programs (for example, between EZNEC Pro and NEC-Win Pro), it is best to use a voltage source to avoid the possibility that one program cannot read the other's remote wire current source technique. Changing back to a current source can be done after file conversion is complete.

+ 
8.    LD      4      2      6           6      1      100      0
+     Type  L-type   Tag   Start Seg   End Seg  R     L or X    C
+

There are two types of loads to consider: concentrated element loading quantities and distributed element material loads. This card illustrates an inductive load added to the center of the reflector. Load types 0 through 3 represent categories of R-L-C combinations that can make up a load. This card shows a type 4 load, which is specified in terms of a series resistance and reactance in Ohms.

+

The "tag" and "segment" items locate the load at the midpoint of wire 2. Since there are start and end segment numbers, some loads may be distributed for more than a single section, but most ham antennas employ concentrated loading located within a single segment.

+

The final two values (1 and 100) specify the resistance and reactance of the load in Ohms. Capacitive reactance, of course, would be entered as a negative number.

+ 
9.    LD       5      1      1         11        2.4938E7
+      LD       5      2      1         11        2.4938E7
+      LD       5      3      1          1        2.4938E7
+     Type   L-type   Tag  Start Seg End Seg    Conductivity
+

Material losses are type-5 loads. As with other loads, the wire (tag) must be identified, along with the first and last segments to which the load applies. Note that these loads apply in addition to any lumped-constant loading of types 0 through 4.

+

To avoid confusion by newer modelers, EZNEC only refers to lumped constants as loads, preferring instead to call material loads "wire losses." EZNEC also expresses these losses as a function of resistivity and relative permitivity. However, the value of resistivity in this case, 4.0E-08 Ohms, is simply the reciprocal of the NEC deck conductivity value of 2.4938E7 mhos or Siemens. Additionally, EZNEC restricts antennas to one type of material per model, although the NEC deck permits a specification of a different conductivity value for each wire.

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10.    TL        1    6       3    1    50    18.01    0    0    0    0
+      Type Start tag/seg  End tag/seg   Zo    Length
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Transmission lines are not physical models in NEC, but mathematical constructs. Hence, they can have any length, regardless of the actual distance between their start and end points on wires. Special techniques are used for shorted and open stubs, but the example here runs a common coax line from the antenna proper to a short segment used a. to terminate the transmission line and b. to serve as the overall source point for the antenna system.

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By now, the start and end wire and segment numbers are obvious. As in the EZNEC PD file, the next two columns specify the characteristic impedance of the line and its length. In EZNEC, this can be done in several ways, all of which translate into a final characteristic impedance and definite length in meters. In the PD file, the length was given as the actual distance between wires, 39', modified by the velocity factor of the line, .66. This results in an electrical length of 59.1' or 18.01 meters.

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11.    FR     0         1         0     0     24.95     0
+      Type  Stepping   No. of FQs            Start FQ  Increment
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Antennas are modeled at one or more frequencies. If a single frequency is used, as in this example, the information needed is limited. "Frequency sweeping" requires more information.

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Stepping can be non-linear (stepping = 1), but normal ham frequency sweeps are linear, changing frequency by the same amount each time. For sweeps, the user specifies the number of frequency steps, the start frequency, and the increment by which to step. For this single frequency model, the number of frequency steps is 1, and the increment is 0, while the modeled frequency is 24.95 MHz.

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12.  RP     0     1           361     1000     76     0     1       1
+   Type   Mode  No. Theta   No. Phi  Special  Theta  Phi  Th Inc  Ph Inc
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The report card specifies what output data is desired from the calculations. Mode "0" is the normal mode.

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Horizontal angular changes are measured as "phi" degrees. Elevation angular changes are measured as "theta" degrees. Although most hams are used to counting elevation from the ground up, NEC counts theta angles from the zenith down.

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This example specifies a report for one theta (elevation) angle, but a full circle of azimuth (phi) angles. Skipping the "Special" column for a moment, the theta angle is 76° (or 90° - 76° for a 14° elevation angle). The figure is a start figure, although only one theta angle has been specified. The azimuth or phi start angle is 0°, but will pass through 361° (to ensure a complete circle with a common value at each end of the progression). Both theta and phi are specified for increments of 1° for good resolution.

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The "Special" column contains 4 values that direct the calculations to produce certain types of outputs. 1000 is normally used for vertical, horizontal, and total non-normalized power gains with no averaging. Other outputs are available, and the user is usually interrogated in plain language for the desired output data and form by each program.

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Users of NEC will sometimes be surprised to find that a symmetrical antenna, such as a Yagi, produces a main lobe identified by as much as 2° to 3° less than the expected bearing. Apparently, NEC identifies the first instance of the maximum power gain as the main lobe. Increasing the phi increment will often return the main lobe to its expected position.

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13.    EN
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EN signals the end of the .NEC file.

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Hopefully, this brief trip through a short NEC deck will orient you to how the input files are constructed for use with NEC. Remember that the card explanations have not covered all the ways in which one may place data on a card of a given type. Only the most common kinds of data inputs for typical ham antenna installations have been illustrated.

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Some programs, like EZNEC, do not generate a NEC deck, but instead communicates with the NEC-2 calculating engine via a number of binary files. (A NEC deck is available in EZNEC Pro with the NEC-4 calculating engine.) Some programs, like NEC-Win Plus, use alternative formatting methods--a spreadsheet file in this case, but also make available the option of saving the mode as a .NEC file. Others, like NEC-Win Pro or GNEC, make the deck an integral part of the modeling process. Getting used to the NEC deck can increase your ability to glean more from whatever program you choose as your basic modeling vehicle. Familiarity may also aid you in interpreting articles that present antenna modeling data in .NEC input file format. Patches, Green's functions, networks, and wire grids are beyond the scope of this introduction, but may be found in NOSC Technical Document 116, Volume 2, Numerical Electromagnetics Code (NEC)--Method of Moments, Part III: User's Guide (1981), which is the source of most of this data.

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Updated 3-30-1997, 04-21-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Modeling


+ + diff --git a/content/model/necdeck1.gif b/content/model/necdeck1.gif new file mode 100644 index 0000000..152a5ec Binary files /dev/null and b/content/model/necdeck1.gif differ diff --git a/content/model/p.html b/content/model/p.html new file mode 100644 index 0000000..200dda4 --- /dev/null +++ b/content/model/p.html @@ -0,0 +1,286 @@ + + + + + + Getting the Most Out of Antenna Patterns + + + +
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Getting the Most Out of Antenna Patterns

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L. B. Cebik, W4RNL

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Ham journals are filled these days with antenna pattern graphics, like the pair shown in Figure 1.1 The patterns are supposed to be highly informative about antenna performance. Unfortunately, to the new ham, they can be somewhat bewildering. Even the experienced ham may not be getting from them all the information that is compactly presented in the patterns. So let's start from scratch, seeing how these patterns represent antenna data that is useful to us, whether we plan to buy an antenna or build our own.

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+ Figure 1: Free space azimuth (E-plane) and elevation (H-plane) far field patterns for the common dipole. +
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Although modern antenna modeling software produces data that can yield many different kinds of antenna patterns, the most common ones are called total far field patterns. They combine all calculated radiation from an antenna in every direction and produce a pattern that is related to a constant strength. In Figure 1, we can see that the pattern bulges and indents. Incidentally, the bulges are called lobes and the indentations are called nulls.

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Hypothetically, if we stand on a line proportional to the pattern line distance from the center point (where the antenna is located), we shall receive a radiated signal of constant strength, no matter where on the line we stand. Likewise, if someone moves a transmitter along the line, then the antenna we are using will receive a signal of constant strength, no matter where along the line we place the transmitter. In short, antenna patterns reflect both transmission and reception characteristics of the antenna being patterned, where the lobes indicate stronger signals and the nulls indicate weaker ones.

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Mastering the art of reading antenna patterns intelligently requires that we learn a number of ideas and conventions. Some relate to antenna theory itself. Some emerge from antenna modeling. Still others come from actually building and testing antennas on carefully constructed ranges. So our short story cannot end here. However, if we learn to sort out the key factors that are relevant to a particular antenna pattern we encounter, we can read them as easily as the words on this page.

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Free Space: A Starting Point for E and H Planes

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Let us begin in free space. Unlike the reflective surface of the earth, free space is a region in which there is nothing but the antenna. In fact, the patterns in Figure 1 are free space patterns of a common horizontal resonant half wavelength dipole fed at the center. Figure 2 shows a complete 3-dimensional view of the antenna pattern. The antenna is grossly exaggerated in size to clarify its position through the center of the pattern. In reality, it would be too small to be seen.

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+ Figure 2: The common dipole (greatly exaggerated in length) with its 3-dimensional far field pattern in free space. +
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The first thing to notice is that the pattern is symmetrically even all around the wire when viewed from the wire end. That symmetry shows up in Figure 1B. However, the radiation is not so even when viewed as a slice through the pattern in the plane of the wire. That is the view shown in Figure 1A.

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The difference between the two patterns reflects a fundamental property of antennas. They emit (and receive) radiation in two planes, conventionally called the E and H planes. The radiation in the E-plane is parallel with the wire. An antenna pattern taken parallel to the wire is also called an E-plane pattern. If we slice the 3-D pattern at any angle, but always barely include the antenna wire's total length, we shall in free space obtain the pattern of Figure 1A. Every plane will show the same indentations in field strength off the ends of the dipole wires.

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There is also radiation at right angles to the wire. By convention, if we take a slice, normally through the center of the antenna element, but at right angles to the wire, we have an H-plane pattern. This is the pattern of Figure 1B.

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However, the two patterns in the figure are not marked E- and H-plane. Instead, they carry a more conventional designation used these day: azimuth and elevation. We use these terms because most of our actual antennas are place above the earth, and the planet gives us a nearly flat reference plane to give meaning to the ideas of horizontal and vertical, and also to azimuth and elevation.

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+ Figure 3: Free space E-plane and H-plane views of a 3-element Yagi. +
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When we have more complex antenna arrays, the E-plane and H-plane patterns become even more rigorous. See Figure 3. Here we have a 3-element Yagi. The E-plane not only parallels the length of the main element, but as well passes through the plane formed by the 3 elements. The H-plane is at right angles and is normally centered on the driven element, to which is connected the signal source. The elements of this antenna form a horizontal line across the H-plane.

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E-plane and H-plane patterns for antennas are convenient is free space. In a region of space, we do not have any reflecting surfaces, so it does not matter in what orientation we place an antenna. We can always derive E-plane and H-plane patterns. The patterns are significant in just this way: when we place an antenna horizontally relative to the earth, the E-plane pattern will dominate the azimuth pattern we derive. When we place the antenna at right angles to the earth at any height, that is, when we make it vertical, the H-plane pattern will dominate the azimuth pattern we derive.

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In Figure 1, I could have set up the antenna vertically instead of horizontally in the software frame of reference. Had I done that, then the same two patterns would have emerged, but in reverse order. The elevation pattern would now correspond to the E-plane and the azimuth pattern would be the H-plane. In free space, that is the only difference of note. However, once we return to earth, the difference in orientation will make a big difference in how the antennas work.

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Just to make life a little more complicated, we should note in passing that in NEC, the most used antenna modeling core, the native orientation to antenna positions is not azimuth and elevation. NEC refers to ? (phi) and ? (theta) angles. Phi corresponds to azimuth, referenced to a zero point. However, theta is a "zenith" angle. That is, instead of counting in degrees up from the ground (or whatever is designated as the horizontal plane in free space), it counts down from directly overhead. If you see the "theta" notation, you can obtain the elevation angle just by subtracting the theta angle from 90 degrees.

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Variations on a Theme

Let's dwell a bit on the hypothetical Yagi in Figure 3. For the moment, we shall consider only the free space E-plane pattern, which is the azimuth pattern in most pattern-generating software. One of the key dimensions you must track is the progression of angles around the perimeter of the outer circle. To illustrate this point, consider Figure 4, Figure 5, and Figure 6. All three patterns show the same antenna model with their lengths plotted along one axis (call it the X-axis) and their distance apart plotted along a second axis (call it the Y-axis). The Z-axis would represent height, either measured from the ground or--in free space--measured above and below the plane made by the X and Y axes. We can call this last dimension the Z-axis. +
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+ Figure 4: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in AO 6.5. +
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+ Figure 5: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in EZNEC 2. +
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+ Figure 6: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC-Win Pro. +
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I plotted these antennas in this way to illustrate that you may see different conventions used by different software in the production of antenna patterns. The Figure 4 pattern orients zero degrees at the top of the graph, with 90 degrees to the right. In Figure 5, zero degrees is to the right, with 90 degrees at the top. Figure 6 places zero degrees at the top with 90 degrees to the left. Yet, they all present the same pattern information.

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Pattern-producing software may place varying amounts of supplemental data about the antenna on the pattern graphic. Very often, the pattern-maker has options on whether to include the data in the graphic or separately. Figure 4 present basic pattern-identifying information in the corners. Figure 5 provides an optional chart of data overlaid on an unused portion of the graph. Figure 6 is bare in the presented version, but might have had other information added.

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+ Figure 7: Free space azimuth (E-plane) far field pattern of the 3-element Yagi in NEC4WIN. +
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Figure 7 represents a pattern of the same antenna with a chart of fairly complete antenna data to the side. Notice that its data, as well as the data in the other graphics, tend to show small variations. Different modeling software--even when using the same calculation core--tends to show operationally insignificant variations in data output. Maximum gain figures that vary under 0.1 dB and front-to-back ratios that vary by under 1 dB are normally insignificant.

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Free Space and Signal Strength

Before we come down to earth, let's consider how we determine how good an antenna may be. There are very many dimensions to this question, but the relevant one here is how we measure the antenna pattern. The patterns we have looked at contain both lobes and nulls, points showing gain maxima and minima. Figure 7 provided a list of all the lobes of the 3-element Yagi, giving their angular direction. Figure 5 gave us information on the main lobe (the strongest) and the side-lobe (or secondary lobe--the second strongest). Conveniently for our exercise, this lobe was directly to the rear of the main lobe. +

One of the key figures of antenna merit is gain. We measure the gain of an antenna by looking at the point in the 3-D pattern that shows the highest level of radiation field strength. We compare that with a arbitrary but standard field and register in decibels (dB) how much stronger or weaker the antenna field is.

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In free space, the most common standard is the isotropic source, a hypothetical antenna point that radiates equally well in all directions. So the unit of maximum gain for our test antenna is measured in dBi, decibels stronger or weaker than an isotropic source that might be placed in the same position.

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There are alternative measures you may encounter. Of these, the most prevalent is dBd, decibels gain relative to a dipole. In free space, the standard hypothetical lossless dipole of immeasurably thin wire has a gain of 2.15 dBi. Hence, the translation from dBi to dBd and back again is simple arithmetic. Consequently, in antenna modeling--from which most antenna patterns emerge--dBi has become the de facto standard.

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In range testing antennas, measurement using dBd still have an important place. However, the reference is not to a hypothetical lossless thin wire dipole, but to a dipole that has real dimensions and material losses. Signals transmitted from it or received by it are carefully measured. Then test antennas are likewise measured and compared to the standard dipole. The gain of the test antenna may then be specified in dBd. However, the dipole used as the standard for the test must be completely described, since dipole characteristics can vary slightly according to the material used as well as the antenna height in terms of wavelengths or fractions of a wavelength.

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The measurements just noted apply mostly to horizontal antennas. Dipoles are less universally used as standards in the testing of vertical antennas.

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With the increasing use of antenna modeling software--especially NEC and MININEC--as vehicles of comparison of antenna designs, dBi is becoming the most common measure of maximum antenna gain in the most favored direction.

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Front-to-. . .: Back? Rear?

As shown in the Yagi patterns, many antennas exhibit unidirectional patterns, that is, patterns with maximum gain in only one direction. Unlike the bi-directional pattern of the common dipole in Figure 1, the Yagi beam (and many other antennas) has a much higher gain in one (forward) direction that in the other (reverse) direction. How much difference there is between the two directions is a measure of how well the antenna may suppress signals from the rear relative to signals from the forward direction. +

There are several ways of measuring the difference. Perhaps the most common is the 180-degree front-to-back ratio, sometimes simply called the front-to-back ratio. To obtain this value, we simply subtract the gain to the rear from the gain forward along a straight line running from the point on the pattern of maximum gain through the pattern center where the antenna is and out the rear of the pattern. Using the data presented in Figure 5, if the forward gain is +8.11 dBi and the rear gain is -19.15 dBi, then the front-to-back ratio is 27.26 dB. (In dBd, for our free space model, the forward gain would be 5.96 dBd, while the rear gain would be -21.30 dBd, for a net front-to-back ratio of the same 27.26 dB. Note that the 0.01 difference in the numbers here and those in the figure is a function of rounding in the software; the difference is insignificant.)

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However, note the rear portion of the antenna pattern. The 180-degree direction represents a special portion of the pattern where signal rejection is greatest. However, gain to the rear off to the sides of the "dimple" is higher, meaning less rejection of signals. For this reason, alternatives to the 180-degree front-to-back ratio are often used.

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One system, sometimes called the averaged front-to-rear ratio, averages the gain for a rear quadrant of the antenna. This figure of merit gives an average front-to-rear ratio that many believe is a better measure of actual antenna performance in signal rejection. A further alternative is the worst-case front-to-rear ratio, which simply compares the forward gain with the highest gain found in the rear quadrants of the antenna.

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When interpreting statements about antenna performance, you can examine the antenna pattern and often determine what standard of rear performance is being used, even if an author does not tell you.

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Polar Plots and Linear Graphs

The antenna patterns display so far use the most common format: the polar logarithmic plot. The antenna is at the center of the graph, and far field strengths are plotted in a circle for all relevant directions. In free space, the plots for azimuth and for elevation both encompass 360 degrees. Although the outer circle can be specified at any level, most patterns use the antenna's maximum signal in the favored direction as the graph edge. Inner circles, as shown in Figure 4 through Figure 7, represent lesser signal levels, measured in dB lower than the level of the outer ring. +

However, note that the inner circles are not equally spaced, but represent a logarithmic progression. The higher the negative number toward the center, the more compressed the circles become. This most common log plot is often said to show with greatest clarity the high gain features of the pattern.

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+ Figure 8: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a polar plot with linear divisions. +
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Figure 8 shows a common alternative: the polar linear plot. Here, the circles of decreasing gain are equally spaced, which tends to clarify the details of the low gain portions of the pattern. When looking at an antenna pattern, it is always necessary to note whether a log or linear plot is being used, especially when assessing matters like front-to-back ratio. The rear pattern lobes appear very different in the two figures, even though exactly the same data is being displayed by both.

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+ Figure 9: Free space azimuth (E-plane) far field pattern of the 3-element Yagi using a linear graph. +
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A third way to present antenna pattern data is with a standard linear graph. Figure 9 shows the same antenna plot on a graph where the X-axis is linearly divided into 360 degrees and the Y-axis represents the antenna's gain. When made large enough, linear graphs can show very fine pattern detail. However, they are to this date fairly rare in amateur literature.

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So where are we so far? Actually, we have come a fairly good distance. Although we are still in free space, we have distinguished the common antenna pattern azimuth and elevation orientations from E-plane and H-plane representations of the pattern. We have also compared the various gain measures (dBi, dBd), with dBi becoming perhaps the most used measure. We have also seen how to measure front-to-back ratio, with reference to features on the antenna pattern. Then, we looked at three ways to present antenna patterns, with the polar log plot being the most common.

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Having looked at all these options, we shall standardize the rest of our work. We shall use azimuth and elevation polar plots with log scaling, and when we refer to front-to-back ratio, we shall employ the 180-degree ratio as our general standard. We select these options not because they are always the best ones, but because they are the ones you will encounter most often in amateur radio antenna literature. Now we can come back to earth.

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Down-to-Earth Reflections

An antenna over real ground changes the way in which we use antenna patterns. Let's consider the elevation pattern first. A typical horizontally oriented Yagi pattern is shown in Figure 10, the same one as used in the free-space patterns of Figures 4-7. Notice that half of the free space pattern is missing, the part that would be below ground if the earth did not reflect antenna signals. +
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+ Figure 10: Elevation pattern of a 3-element Yagi 1 wavelength over average ground. +
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Second, notice that the pattern is elevated. Due to signal reflections, the elevation angle of maximum radiation (also called the Take-Off angle) is not at zero degrees. Since we are dealing with far field patterns instead of ground waves, there is essentially no signal at zero degrees, and antenna modeling patterns will not show line of sight radiation in its far field patterns.

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Third, notice that the forward lobe is not a line, but a lobe having a certain vertical thickness. The common way to designate this thickness is by measuring the number of degrees between points where the signal is reduced in strength by 3 dB relative to its maximum strength. This figure is called the vertical beamwidth of the antenna pattern.

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For horizontally polarized antennas, such as our Yagi, the pattern of lobes, the take-off angle of the lowest (and usually strongest) lobe, and the vertical beamwidth will vary with the antenna height, as measured in fractions of a wavelength. Suppose we have 2 3-element Yagis, one for 10 meters and one for 20 meters. We place the 20-meter Yagi at a height of 70 feet and the 10 meter Yagi at a height of 35 feet. Since each antenna is at 1 wavelength height, we would expect very similar elevation patterns from them--in fact, just the pattern shown if Figure 10.

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We shall take another look at polarization of the antenna in a while, since it make a considerable difference in antenna performance over real ground. But first, let's get acquainted with what happens to the azimuth pattern when we place our Yagi over real ground.

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An azimuth pattern at zero degrees elevation--the horizontal plane--will show nothing. In fact, most NEC-based programs will disallow your attempt to take that pattern. Instead, we take azimuth patterns at some higher angle of interest. The question now is what is interesting.

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+ Figure 11: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 14 degrees (elevation angle of maximum radiation). +
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In the absence of any other considerations, most folks who present azimuth patterns over real ground do so at the take-off angle. Figure 11 is an illustration, using our handy Yagi. The pattern shape is quite similar to the free space azimuth pattern in Figures 4-7. However, there are some important differences.

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The free space azimuth pattern was a true horizontal pattern. The pattern over ground is a cone elevated from the horizontal by the specified elevation angle. Since the take-off angle of this antenna is 14 degrees, the azimuth pattern is a cone 14 degrees above the horizon. You can picture this best by drawing a line straight across the elevation pattern at point 14 degrees up from the horizontal on each side of the graph.

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The pattern shows a front-to-back line. This ratio is not necessarily the maximum front-to-back ratio for the antenna (although it often is). Rather, it is the front-to-back ratio for the chosen angle (14 degrees). Maximum front-to-back ratio (or front-to-rear) may be at some other angle. To get an idea of where it may be--or whether it might be different enough to be notable--simply look at the elevation pattern in the rearward direction. Or, specify some other elevation angles for the azimuth plot.

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+ Figure 12: Azimuth pattern of a 3-element Yagi 1 wavelength over average ground, at an elevation angle of 5 degrees. +
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Although the take-off angle is a handy reference point in many cases, it may not be the most important one. Antenna builders may be more interested in particular paths to the stations they wish to work. If we work a lot of DX, then lower angles--perhaps in the 5 to 10 degree range--might interest us for some paths. In these cases, the antenna modeler and builder might show a lower angle for his or her chosen azimuth pattern. Figure 12 shows the azimuth pattern for our 1 wavelength high Yagi at a 5 degree elevation angle. Note the reduced gain and slight change of pattern shape. In contrast, near-vertical incidence skip is of interest to a number of amateurs, and very high angle radiation may dictate what azimuth pattern they choose. Hence, it pays always to 1. compare both elevation and azimuth patterns and 2. read any accompanying text to find out why the pattern variables were chosen.

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Finally, note that the maximum gain in both our patterns over ground is considerably greater (when taken at the take-off angle) than the same antenna in free space. The signal reflected off the earth is not lost. Rather, it combines with the unreflected signal. At some elevation angles, the two are in phase and add up to a stronger signal--between 5 and 6 dB stronger. At other angles, they are out of phase and cancel, resulting in nulls rather than lobes. In general, for horizontal antennas, the number of lobes counting from the ground up to a point overhead (90 degrees up) is about 1 more than the number of wavelengths in height of the antenna. Remembering this fact will help you both to understand antenna patterns and to anticipate them as you read specifications in the text.

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As a rule of thumb, the lobes and nulls above the horizon can be calculated by a simple equation:

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where Ae is the angle of the lobe or null, N is the lobe or null number counting from the ground up, and h is the antenna height in wavelengths or a fraction of a wavelength. For lobes, the value of N will be an odd integer (1, 3, 5, 7, etc.), while for nulls, the value of N will be even (0, 2, 4, 6, etc.). Our Yagi at a 1 wavelength height has lobes at about 14 degrees (the main lobe) and at 49 degrees. This calculation is only a rough guide, since the exact structure of the antenna and the terrain may alter the angles by small amounts.

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Does the Good Earth Make a Difference?

Most antenna patterns derived from antenna modeling software presume a flat, uncluttered terrain for the antenna. Because we live in spaces that may be littered with building, objects, and vegetation, and also because our terrain, both near and far, may be anything from flat to mountainous, model patterns only approximate the actual antenna performance we can achieve. +

In general, the ground immediately beneath and around an antenna affects antenna efficiency and the feedpoint impedance. The far field pattern is most affected by the quality of earth several wavelengths from the antenna and beyond.

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The quality of the ground beneath an antenna can vary from exceptionally poor to salt-water good. Modeling software records the quality of the earth in a composite of two figures: conductivity, which is measured in Siemens per meter, and a dielectric constant, which has no unit of measure. For the most part, the larger either of these figures, the better the quality of ground. The range of possible ground conditions is very wide. Average soil has a conductivity of 0.005 S/m with a dielectric constant of 13. Salt water values are 5.0 S/m and 81. At the other end of the scale, extremely poor soil found in heavy inductrial areas may show values of 0.001 S/m and 3. Antenna handbooks usually have tables and even maps to help to determine the quality of ground in your area.

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The effect of terrain upon horizontally polarized antennas, such as our model Yagi, tends to be slight. To see this point in action, look at Table 1, which lists the gain and take-off angles for our model Yagi at various heights above 3 types of ground: "Very Poor" (0.001 S/m; 5), "Average" (0.005 S/m; 13), and "Very Good" (0.0303 S/m; 20). Note that the take-off angles are very stable, while the gain figure increase only a little as the ground quality increases.

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                               Table 1
+Gain and Take-Off Angle of a 3-Element Yagi Over Various Soil Conditions
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+                                 Ground Type
+                    Very Poor      Average        Very Good
+                 (C=0.001/DC=5) (C=0.005/DC=13) (C=0.0303/DC=20)
+
+Antenna Height    Gain (dBi)/    Gain (dBi)/    Gain (dBi)/
+(Wavelengths)         TO angle       TO angle       TO angle
+
+0.50 wl             11.7 / 24      12.3 / 25      12.8 / 26
+
+0.75 wl             12.6 / 17      13.1 / 18      13.4 / 18
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+1.00 wl             13.0 / 13      13.4 / 14      13.7 / 14
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+1.25 wl             13.2 / 11      13.6 / 11      13.8 / 11
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+1.50 wl             13.4 /  9      13.7 /  9      13.9 /  9
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+1.75 wl             13.5 /  8      13.7 /  8      13.9 /  8
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+2.00 wl             13.6 /  7      13.8 /  7      14.0 /  7
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+Note:  The model used for these representative values is aluminum and the
+check frequency is 14.175.  As always, modeling is done over flat terrain
+and does not account for terrain variations.  C is conductivity as measured
+in S/m; DC is a dielectric constant and has no units.  TO angle is the
+elevation angle of maximum radiation and is in degrees above the horizon.
+
+Table 1:  Representative values for gain and take-off angle of a 3-element
+Yagi over various soil conditions.
+

We can make the same point by noting that when the E-plane of an antenna is parallel to the earth, the effects of ground quality are relatively small. However, if the E-plane is at right angles to the earth, the situation changes considerably. Of course, this situation corresponds to having a vertical antenna.

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+ Figure 13: Vertical dipole for 40 meters place 10' above ground at the antenna base. +
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Using the same three soil types, we can take a simple vertical dipole and illustrate the difference. In this case, I modeled a full-length vertical dipole with the bottom 10' off the ground, as shown in Figure 13. The resulting patterns for the three ground qualities can be combined in a single graphic of the multiple polar plots, as shown in Figure 14. Note that the best ground quality produces the lowest take-off angle and the greatest signal strength, while the worst produces a weaker field strength at a higher angle.

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+ Figure 14: Elevation patterns for the 40-meter vertical dipole over three different soil types. +
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At the same time, notice the absence of strong higher angle lobes in any of the three patterns in Figure 14. You will begin to see why many operators prefer vertical antennas for DX work, especially on the lower HF bands, where getting a horizontal antenna high enough to have a low-angle lobe of maximum radiation is often not feasible.

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These sample patterns should do more than acquaint you with the terminology and geometry of antenna patterns. They should be the beginning of the development of your expectations when seeing antenna plots of either horizontal or vertical antennas. Polarization: the Simple and the Complex

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Most modeling programs from which antenna patterns emerge can show not only the total far field of the antenna, but as well show both the vertically polarized and horizontally polarized components of that field. Linear antennas, such as the vertical dipole or the Yagi, tend to have negligible radiation cross polarized to the general orientation of the antenna. However, Many antenna types yield both types of radiation.

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+ Figure 15: Azimuth pattern of a half-square antenna at a 16-degree elevation angle over average soil showing the total field and its horizontally and vertically polarized components. +
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Figure 15 shows the azimuth pattern at 19 degrees elevation of a half square, the general outlines of which have been superimposed on the plot. Although the maximum gain of the antenna's total field is a function of the vertically polarized radiation, the width of the field is considerably enlarged by the presence of horizontally polarized radiation, which shows itself in the cloverleaf pattern.

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+ Figure 16: Elevation patterns of a right-angle delta loop, taken broadside to the loop, for side-feed (for maximum vertically polarized radiation) and for bottom-center-feed. +
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At HF, polarization becomes skewed in the ionosphere, and we normally think of the total field as making up the effective far field. However, for many types of loop antennas (quads, deltas, rectangles, etc.), where we feed the antenna can make a difference in the ratio of horizontally to vertically polarized radiation, and this, in turn can have an effect on the overall total field of the antenna. Consider Figure 16, which shows elevation patterns of the same delta loop. On the right, it is fed at the center of the horizontal wire, while on the left, it is fed 1/4 wavelength down from the triangle's apex. The patterns are significantly different, to say the least.

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+ Figure 17: Azimuth patterns for a 3-element 2-meter Yagi 30' above average soil for both horizontal and vertical orientations of the beam. The outer ring represents the same field strength in both patterns. +
+

Even where antennas are linear, we should expect pattern differences according to whether they are set up for horizontal or vertical polarization. Consider a small Yagi for 2 meters, elevated about 30' up. Figure 17 shows the azimuth pattern at the take-off angle for the antenna when it is horizontal and when it is vertical. Vertically, it shows less gain and a much wider beam width than when horizontal. If we want to achieve a vertically polarized pattern whose shape resembles that of the horizontal Yagi, we have to turn to a different antenna design. Despite its higher gain, we cannot simple press the horizontal Yagi into service, because in line-of-sight, we shall likely lose more to cross-polarization losses than the extra gain will give us.

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Comparisons, Both Educational and Practical

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Now that we know how to read antenna patterns with reasonable accuracy, let's look at some ways in which comparing antenna patterns can assist us in understanding antennas. The following examples are only starters, chosen for their variety. Getting a comprehensive look at antennas is a lifetime's vocation.

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1. The Center-Fed Doublet: One of the most common antennas is still one of the most misunderstood. Because the center-fed doublet yields a dipole-like pattern at its lowest frequency of operation, many hams believe that it provides a dipole-like azimuth pattern at all its frequencies of operation. Generating some azimuth patterns can tell us very quickly whether this belief is true or false.

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+ Figure 18: Azimuth patterns for a 135' doublet 50' above average soil when used on 80, 40, 20, and 10 meters. In each case, the doublet is oriented left-to-right in the pattern graphic. +
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Let's make our doublet 135' long and use it from 80 meters through 10 meters. We shall make it of #14 copper wire and place it at 50' in the air. Ignoring ground clutter and terrain variables, we would get the patterns of Figure 18 on 80, 40, 20, and 10 meters. Notice that the elevation angle of maximum radiation is different for each band. In fact, on 80 meters, because the take-off angle is so high, an arbitrary angle of 45 degrees was selected for the azimuth pattern.

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The antenna is 1/2 wavelength long at 80 meters, 1 wavelength long at 40 meters, etc. For your reference file, you can count the number of lobes and relate them to the antenna length in terms of wavelengths. Also note that as the antenna becomes longer relative to the frequency of operation, the direction of the strongest lobes moves from a broadside direction toward the ends of the antenna.

+

Besides acquainting you with the antenna patterns on various bands, the azimuth patterns are also useful for practical antenna planning. First, decide which bands are your favorites and, as well, which directions from your station are best for making your most desired contacts. If you have a choice of directions in which to string up the doublet, you can to some measure erect the antenna for maximum signal strength on your favorite bands in your most desired directions. The azimuth patterns can be a useful planning tool.

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2. Directional Beams and Elevation Patterns: In the maze of antenna materials, we often find it difficult to see how antennas are related. For example, in a number of talks I have given to beginners in ham radio, questions have arisen about how dipoles and various size Yagis may be kin to each other. The questioners are often surprised by how close the relationship is.

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+ Figure 19: Composite elevation patterns for a dipole, a 2-element Yagi, and a 3-element Yagi, each placed 1 wavelength above average soil. +
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One simple demonstration I have used is to combine the elevation patterns of a dipole, a 2-element Yagi, and a 3-element Yagi, all at the same height. A representative version of this pattern combination appears in Figure 19. I have added labels to the portions of the curves that might get confusing.

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From the figure, two significant features appear. First, all three antennas have the same lobes and nulls at almost identical angles. Second, the symmetry of the dipole pattern fore and aft of the vertical center line disappears steadily as the parasitical elements direct the main lobe in one direction. Hence, both kinship and differences appear at once.

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Combining curves is something that an antenna modeler can do with ease. The casual reader of amateur magazines may see only individual patterns. However, by examining either the graphic or the text for further information on gain, front-to-back ratio, and other features of the antennas, one can get a pretty good view of two or more antennas in combination. In fact, one can transpose the pattern of one antenna upon the other for greater clarity. However, be sure that the transposed patterns are truly comparable before transposing them.

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3. Directional Beams and Azimuth Patterns: There is a myth that pervades amateur radio: for every operating purpose whatsoever, always choose the highest gain, highest front-to-back antenna you can afford. Like all myths, this one has some truth, but not all truth.

+

To sort out what is true and what is false in the myth, let's combine in one graphic the azimuth patterns for a good 2-element Yagi and a good 3-element Yagi. We shall place both at 1 wavelength in height so that the elevation angles for the patterns will be the same. The result appears in Figure 20.

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+ Figure 20: Composite azimuth patterns at 14 degrees elevation of a 2-element Yagi and a 3-element Yagi, each 1 wavelength above average soil. +
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Obviously, the 3-element Yagi has superior gain and front-to-back ratio. As such, it may indeed be the better antenna for serious DXing, where we wish to maximize our signal to the distant receiving station and suppress as much as possible all the potential QRM from the sides and rear of our station. However, serious DXing is not the only important type of amateur operating activity.

+

Many contesters and net operators do not want to suppress completely signals from the sides and rear. They wish to know that someone worth working is present, but not so loud as to interfere with the current station being worked. Hence, they tend to prefer antennas with some front-to-back ratio and some gain, but not the ultimate in each. For their type of operation, the 2-element Yagi may in fact be the preferred antenna.

+

In this example, I have given a choice of only two antennas. However, the basic principle can be applied to a host of antenna types. A comparison of antenna patterns, when placed against a list of operating goals and the needs one has to achieve those goals, can be a valuable tool in antenna selection.

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4. Truth--Pattern Shape and Pattern Detail: The shape of an antenna pattern is not the whole story, and one can easily fall into traps of hasty interpretation. To illustrate the point, let's look at Figure 21 and fall into one kind of trap together.

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+ Figure 21: Azimuth patterns for two 2-element Yagis (A and B) along with a composite pattern graphic of the two (C), with each antenna 1 wavelength above average soil. +
+

Part A of the figure shows the free space azimuth pattern of a 2-element Yagi. The main lobe is, as expected, quite round with a good beam width. The rear quadrant shows a very high 180-degree front-to-back ratio. In most respect, this pattern appears to be superior to the free space pattern shown in Part B, where the 180-degree front-to-back ratio is under 20 dB.

+

Part C of the figure springs the trap. The patterns in parts A and B are overlaid, demonstrating the far lower gain of the initial pattern. In fact, the gain for A is only 3.8 dBi, while the gain for B is nearly 6.6 dBi. In addition, the 180-degree front-to-back ratio for B is a little under 19 dB and is the worst case of the entire rear quadrant. By contrast, the 29 dB 180-degree front-to-back ratio of A covers only a small part of the rear quadrant and drops to a worst-case value of just over 16 dB.

+

Without the added data, we might not have realized that the performance of the two antennas was so radically different. Even without the pattern overlay, the data for both the forward and rear quadrants of the antenna pattern make those differences clear. In fact, A is based on a model of a highly loaded and shortened 10 meter beam, while B is based on a model of a full-size 10-meter beam with phasing line connecting the two elements.

+

When comparing antenna patterns, be certain that you have a complete data set before you start the work of comparison. As we have seen, free space patterns are not directly comparable, even though similar, to patterns over ground. When comparing patterns taken over ground, be certain that the heights are comparable and that the ground types are similar. Wherever antennas are of different types, examine both the azimuth and elevation patterns of each.

+

These considerations become very important when trying to make purchase decisions among commercial beams. The manufacturers do not present their information with a common format, and therefore, comparisons are very difficult, even where patterns are offered. If a significant number of manufacturers do submit antenna models to ARRL in conjunction with its new advertising policy, then it will be much easier to comparatively examine models of competing antennas. However, even then, we shall have plenty of other evaluative work to do.

+

Antenna patterns do not tell anything like the whole story with antennas. We have already seen the need to place the performance figures in juxtaposition with our operating goals and needs. In addition, we shall have to factor in such considerations as cost, weight, available space, installation complexity, and maintenance, not to mention the legalities which are becoming an increasing burden to antenna installation.

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In the End, There is No End

We have barely scratched the surface of the things we can learn from antenna patterns, when we learn to read them accurately and carefully. By examining the azimuth and elevation patterns for single antennas, we can gauge their performance in terms of gain, front-to-back specifications, lobes and nulls, beam width, and polarization composition. We can also compare antennas, both within a single type and among types, analyzing high and low angle lobes, lobe direction and shape, and numerous other properties. +

In the end, the information you can gain from antenna patterns will help you make intelligent decisions about the best antenna for your station location. When combined with all of the other types of information you can and should gather, the more information you draw from antenna patterns, the more satisfying your ultimate decision is likely to be.

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Notes

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1. The antenna patterns used to illustrate the ideas in this article are taken from several commercial implementations of either MININEC or NEC-2, the most frequently used antenna modeling calculation cores. The most familiar implementations of these cores come from the following sources (listed in alphabetical order):

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  • AO (MININEC) and NEC-Wires (NEC-2): Brian Beezley, K6STI
    • +
  • EZNEC (NEC-2) and ELNEC (MININEC): Roy Lewallen, W7EL
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  • NEC-Win (NEC-2): Nittany Scientific
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  • NEC4WIN95 (MININEC): Madjid Boukri, VE3GMI, Orion Microsystems
    • +
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Nothing in these notes should be interpreted either as an endorsement or as a criticism of any particular software.

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In addition to the commercial implementations noted above, there are other antenna modeling software packages available, some based on the most used cores and some based on individual or proprietary cores. Also obtainable are some specialized output packages for specific graphical purposes.

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Also see the Antenna Modeling Programs page for more information.

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Updated 7-18-99, 02-06-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. An earlier version of this items appeared in CQ (Jan. and Feb, 1999).

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Go to Main Index
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Topics: Modeling


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NEC and Reciprocity

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L. B. Cebik, W4RNL

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In these notes, we shall examine a relatively simple-sounding question: Does NEC honor the reciprocity theorem as applied to antennas? We shall look at two demonstrations that we might use to satisfy ourselves that the popular wire-antenna modeling program does honor the theorem. One method of demonstation will not be accessible to those using some entry-level NEC implementations, such as EZNEC or NEC-Win Plus. Therefore, we shall add a second demonstation that, although less graphically complete, should satisfy any user that reciprocity applies to NEC models. In the process of setting up these demonstrations, I have striven to keep to an absolute minimum any software user calculations that are external to the NEC program. In fact, we shall need only one simple equation, letting NEC's calculations do the reminder of the work. Indeed, these notes are less about the foundations and validity of the reciprocity theorem and more about NEC itself.

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What is Reciprocity?

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The ARRL Antenna Book (20th Ed., p. 2-1) contains a beginner's discursive explanation of reciprocity. "In the same fashion that a loudspeaker can act as a microphone, a radio antenna also follows the principle of reciprocity. In other words, an antenna can transmit as well as receive signals." This brief extract follows on an explanation of an antenna as a "special transducer" capable of converting RF current into propagating electromagnetic waves and converting intercepted waves into electrical current. The context is the very beginning of a chapter called "Antenna Fundamentals." Hence, we should not expect mathematical sophistication. Indeed, at this stage of the volume's exposition, the discussion is unprepared to answer many questions that arise within a radio operator's experience. For example, in 2-way HF communication, we very often find that there are differences in the received strengths of an outgoing signal and an incoming signal. From the initial description of reciprocity, we cannot tell if the differences are a function of how the antenna works in transmit and receive modes or a function of what happens to the electromagnetic waves between the transmitting and receiving sites, that is, a function of HF radio wave propagation.

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More mathematically inclined readers may wish to consult various college-level antenna texts. I keep a small number on my shelf as references, for example, Stutzman and Thiele, Antenna Theory and Design (2nd Ed., pp. 404-409), and Balanis, Antenna Theory: Analysis and Design (2nd Ed., pp. 127-132). I have listed the most relevant pages of each text for a reason. Balanis discusses reciprocity early in the text's development, but Stutzman and Thiele defer the treatment until late in the text. We shall have occasion to note the Stutzman and Thiele treatment later.

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Both treatments share a common kernel, the development of antenna reciprocity from the the Lorentz reciprocity theorem, which itself derives from Maxwell's equations. (Those comfortable with calculs may wish to compare the Stutzman and Thiele equation 9-36 with Balanis' equation 3-66. Because my goal is to minimize necessary reader math in these notes, I shall not reproduce the equation here, especially since it is so readily available elsewhere.)

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A better-known text among amateur radio operators is Kraus, Antennas (2nd Ed., pp. 410-413). One interesting aspect of the Kraus treatment is that he uses a different starting point for his development of reciprocity. He begins with the Rayleigh-Helmholtz reciprocity theorem as generalized in the 1920s by J. R. Carson. (Rayleigh's initial context of sound is not unrelated to the ARRL basic analogy between antennas and loudspeakers.) Without ado, Kraus expresses the theorem in the following terms: "If an emf is applied to the terminals of an antenna A and the current measured at the trerminals of another antenna B, then an equal current (in both amplitude amd phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B." (p.411) Krause goes on to note some of the limiting conditions in which the theorem applies. Of course, the frequency of the applied emf (or voltage) must by the same, and the media must be "linear, passive and also isotropic." For our purposes in evaluating whether NEC honors reciprocity, the following note is critical: "An important consequence of this theorem is the fact that under these conditions the transmitting and receiving patterns of an antenna are the same."

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The last note that I cited from Kraus gives us something that we can test in various ways within the context of NEC software solely by examining the NEC output report. Sometimes, we shall even be able to use graphical representations of selected output data to illustrate the results.

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NEC Transmit and Receive Patterns

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We may use NEC itself to establish the transmit and receive patterns are the same. However, the entry-level software used by most modelers gives no clue to a proper answer to the question. Most entry-level software restricts the user to only one of the excitation possibilities, the direct voltage source (EX0) (or an indirect current source). For example, we might encounter a 6-element Yagi modeled in free space. The following lines define the model in ASCII format.

+ 
+CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0 1 0 0 146. 0
+GN -1
+EX 0 2 11 0 1 0.
+RP 0 1 361 1500 90. 0. 1.00000 1.00000 0.
+EN
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The EX command line specifies that we apply a voltage source to the center segment of wire 2. In most entry-level programs, we then request a radiation pattern (RP0). Since the antenna is in free space, we request an azimuth pattern, which is technically an E-plane pattern. The result appears in Fig. 1. Note that the wire entries place the element spacing values in the Y columns, while the elements extend in the +X and -X directions. The conventions of the software used here (NSI's GNEC) place 0 degrees at the top of the polar plot. The pattern is a phi pattern (where a true azimuth pattern would increase the degree values clockwise). Hence, the main lobe of the antenna points to the left at 90 degrees phi.

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The side panel in the figure provides the analytical data to accompany the normalized plot on a logarithmic scale. One reason that I selected this antenna was its free-space gain value of just over 10 dBi. For data-gathering purposes, the XNDA specification in the RP0 command is 1500. When N=5, the radiation pattern portion of the NEC output file produces an additional table. It lists for each value of phi and theta the antenna gain normalized to the peak gain of the antenna. The bearing of peak gain will read 0 dB, and all other gain values will be negative, indicating how much below the peak gain they are, as recording in dB. However, even a pattern like this one does not show why the antenna is or is not reciprocal, or even what reciprocity might mean.

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An antenna is reciprocal if its receiving pattern and its transmitting pattern are the same. We ordinarily record the transmitting pattern in dBi, or dB relative to an isotropic source. Normalized, the gain appears relative to a peak value of 0 dB. The counterpart to transmitting gain would be receiving sensitivity. More advanced versions of NEC offer a number of options for deriving receiving patterns. They involve the EX1 command for linear antennas, that is, providing the antenna with external excitation in the form of linear plane waves. We systematically rotate the excitation around the antenna in a series of steps. Then we invoke the PT command to record the relative current at a selected point--our former feedpoint. Fig. 2 shows in simplified form with only 8 positions for the EX1 command how the development of receiving patterns differs from the development of transmit patterns.

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EX1 is only one of three types of excitation that are external to the antenna geometry.

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EX 1: incident plane wave, linear polarization

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EX 2: incident plane wave, right hand (thumb along the incident vector) elliptic polarization

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EX 3: incident plane wave, left hand (thumb along the incident vector) elliptic polarization

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Both of the elliptical polarization options are useful when simulating signal sources from helical and similar antennas. Linear polarization simulates from antennas that we normally classify over ground as either vertically or gorizontally polarized, both of which are forms of linear polarization. For reference, the following line shows the meaning of the entries within an EX1 command. Note that as we change the type of excitation from EX0 through EX5, the leanings for the integer and floating decimals will change. See the NEC-4 manual for other forms of excitation.

+ 
+Com  I1   I2     I3     I4   F1        F2        F3         F4    F5   F6    F7
+ID   Type # Thta # Phi  Not  Th angle  Ph angle  Eta        Theta Phi  Axis  El. field
+          angles angles used to vector to vector pol. angle step  step ratio V/m
+EX   1    1      8      0    90        0         90         0     45   0     0
+
+

The sample entry is for a linear plane wave. Hence, F6 is 0 by non-relevance. F7 also has a 0, but that value indicates a default value of 1 V/m. In some problems designed to ferret out coupling potentials among wires, you may use a specific value that closely approximates the value from the source signal at the structure being examined in model form.

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Most of the remaining entries define incident plane waves as a calculation loop within NEC (with some properties resembling the loop operation of frequency sweeps using the FR command). In the sample, for the sake of clarity, there is only one theta angle: 90 degrees. This angle is parallel to the plane of the antenna elements. The sample specifies 8 phi-angle (azimuth-angle) steps at 45-degree increments, thus providing samples evenly spaced in the element plane. The entry corresponds to the simplified situation shown in Fig. 2.

+

The F3 entry, called Eta, under linear polarization is easy to memorize. With a value of 0, the polarization is in the +/-Z direction--vertically polarized for antennas over ground. If F3 is 90, the polarization is in the X-Y plane--horizontally polarized for antennas over ground. The sample in free space uses horizontal polarization for simplicity, but there is no restriction against checking results when cross-polarized or with the polarization set to intermediate angles. When using EX 2 or EX 3, elliptical polarization, the entry changes its meaning and defines the major ellipse axis. (Remember that true circular polarization is simply a special case of elliptical polarization having equal axes.)

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[Special Note for NEC-2 Users: The structure of the NEC-2 plane-wave excitation entry is slightly different than the NEC 4 entry. It has the following structure:

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+Com  I1   I2     I3     I4   F1        F2        F3         F4    F5   F6
+ID   Type # Thta # Phi  Not  Th angle  Ph angle  Eta        Theta Phi  Axis
+          angles angles used to vector to vector pol. angle step  step ratio
+EX   1    1      8      0    90        0         90         0     45   0
+
+

Note that the NEC-2 version lacks the F7 floating point entry for the electrical field strength, and the default value of 1 V/m always applies. Only 1 incident plane wave is allowed at a time (that is, before a succeeding execution step). If excitation types are mixed before a succeeding execution step, then the program will use only the last excitation type encountered.]

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The second command necessary to produce a receiving pattern is PT (technically, Printing Options for Currents on Wires). The options of interest are the following ones: +
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PT 1: Currents printed in a format designed for a receiving pattern.

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PT 2: Currents printed in a format designed for a receiving pattern, plus a normalized value for the last segment's current.

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PT 3: Only the normalized current is printed.

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Our present interest lies in the PT entries followed by positive integers. The general format is as follows.

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+Com  I1    I2     I3       I4
+ID   Type  Tag #  1st Seg  Last Seg
+PT   2     2      1        11
+
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The I2 through I4 entries are necessary only for PT 0 through PT 3. In this instance, the sample request asks both for the data on Tag 2, Segments 1 - 11, and for the normalized value of the data on segment 11. To make sense of this entry, refer to the initial model. Tag 2 represents the Yagi driver, and segment 11 is the segment connected to the feedline--a source segment in the transmitting mode and the focal segment in the receiving mode.

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From the EX1 and PT3 commands, we can construct a model that will provide us with the receiving counterpart of the transmitted radiation pattern for our 6-element Yagi. The following lines show the model in .NEC format. Note that NEC has a limitation in how large a receiving matrix may be. Therefore, the data generation has two parts, one from -90 to +90 degrees, the other from 90 to 270 degrees. Fig. 1 tells us why we selected the division of the work, since peak gain occurs at a phi heading of 90 degrees. Since we shall request normalized data, each section of data must contain a peak gain/current point, which occurs at 90 degrees phi. The program then normalizes the data against this value. The PT3 command allows us to capture only the normalized current in dB at a selected segment, in this case, the same segment that we formerly used as the transmit source or feedpoint.

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+CM 6-el 2M Yagi
+CE
+GW 1 21 -.514604 0. 0. .514604 0. 0. .0024
+GW 2 21 -.5075174 .257302 0. .5075174 .257302 0. .0024
+GW 3 21 -.4746752 .3637788 0. .4746752 .3637788 0. .0024
+GW 4 21 -.461137 .6585204 0. .461137 .6585204 0. .0024
+GW 5 21 -.461137 .9469628 0. .461137 .9469628 0. .0024
+GW 6 21 -.443992 1.377137 0. .443992 1.377137 0. .0024
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+PT 3 2 11 11
+EX 1 1 181 0 90 0 90 0 1 0 0
+XQ
+PT 3 2 11 11
+EX 1 1 181 0 -90 180 90 0 1 0 0
+XQ
+EN
+
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The data for both the transmitting pattern and the receiving pattern can be transferred to a spreadsheet for graphing. For both sets of data, we have 361 data points (from 0 to 360 degrees phi). Table 1 provides a glimpse of the data from 0 to 120 degrees for the 6-element Yagi in free space at 146 MHz. Three data points call for attention: 0, 180, and 360 degrees. Each of these points represents a free-space side null. Values for these nulls have two properties that are problematical for graphing. First, they may have very large negative values. Graphing such values may result is severe compression of the upper part of the graph. Second, the values are subject to large variations with very small differences in the rounded values of numbers that go into their development. For the sake of graphing, I have set these numbers to an artificially high value of -100 dB.

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If we conjoined the two graphs--one for the transmitting pattern and one for the receiving pattern--we obtain a result like Fig. 3.

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Computer-generated graphs "write" the curve for one color and then overwrite it with the second color line. The result for our test case is the nearly complete disappearance of the red line beneath the green. A few red "dots" appear as verification that the line is present. However, as both the graph and the table suggest, the normalized pattern graphs are as identical as one might find in any data generation system. In short, within the limits of our ability to calculate and present the results, the patterns for transmitting gain and for receiving sensitivity are the same. From the perspective of NEC, the antenna performance is reciprocal with respect to transmitting and receiving.

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An Alternative Procedure Using only EX0 and RP0

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Early in the notes, I mentioned that the Stutzman and Thiele text reserves treatment of recprocity until late in their work, specifically the chapter devoted to antenna measurements. In this context, the identity or radiated and received patterns becomes significant insofar as it allows us to set up four equivalent test procedures for determining the pattern of a linear antenna. Fig. 4 shows the possibilities.

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Let us suppose that we have a reasnably complex antenna with an equally complex radiation pattern. Our 6-element, 146-MHz Yagi will do well in this regard. In order to obtain the pattern, we shall need not only the test antenna, but as well a second antenna that we may use to transmit a standard unvarying signal or to receive a signal from the test antenna. We may place the test antenna in a fixed position and rotate the second antenna around it, as suggested by the upper two parts of Fig. 4. This arrangement tends to be mechanically complex, costly, and inconvenient for all but the crudest measurements, such as in a walk-around. However, periodic checks made of fixed broadcast antennas tend to use this system with checks at selected points around the compass. If we use the second antenna in the transmit mode, then we replicate the receive model that we have just concluded. For models, the techniques is equally applicable in both NEC-2 and NEC-4.

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The lower two options in Fig. 4 represent procedures that a more common to HF and VHF antenna range testing by manufacturers. We may let the test antenna transmit while rotating it, and receive the signal of varying strength at the second antenna. Alternatively, we may let the test antenna receiving while rotating, using the second antenna as a transmitted signal source.

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For horizontally polarized antennas over ground, the second antenna is normally a dipole. A dipole that is resonant at the test frequency has known properties and performs very close to an ideal dipole, despite the use of common cxonductive materials and the shortening that accompanies a non-infinitesimal diameter. Since the early days of antenna experimentation, it has served as both a reference antenna and as a signal source or recpetion aerial.

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For reliable pattern data, the two antennas need to be well separated. At lower frequencies, one needs to be concerns about Rayleigh limits for the far field. In a VHF model, we can simply set the two antennas apart by a wide distance. In the model that we shall use, the separation will be 1 mile (5280' or 63360"). Since a wavelength at 146 MHz is between 80" and 81", the antennas will be over 750 wavelengths apart. In order to assure that we have enough current on the receive antenna elements to register, we may set the transmit power at an arbitrary 1000 W.

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To further simplify the set-up, we shall set the two antennas in a free-space environment. Our goal is to demonstrate a reciprocity between transmitted and received patterns, so we need not be concerned by introducing an intervening variable, such as the ground.

+ 
+CM 6-el 2M Yagi and dipole
+CE
+GW 1,21,-.6885686,.514604,0.,-.6885686,-.514604,0.,.0023813
+GW 2,21,-.4312666,.5075174,0.,-.4312666,-.5075174,0.,.0023813
+GW 3,21,-.3247898,.4746752,0.,-.3247898,-.4746752,0.,.0023813
+GW 4,21,-.0300482,.461137,0.,-.0300482,-.461137,0.,.0023813
+GW 5,21,.2583942,.461137,0.,.2583942,-.461137,0.,.0023813
+GW 6,21,.6885684,.443992,0.,.6885684,-.443992,0.,.0023813
+GW 7,21,1609.344,-.48641,0.,1609.344,.48641,0.,.0023813
+GE 0
+LD 5 0 0 0 2.5E+07 1.
+FR 0,1,0,0,146.
+GN -1
+EX 0,7,11,0,1.,0.
+RP 0,1,361,1000,90.,0.,0.,1.,0.
+EN
+
+

The model that we require, in .NEC format, looks very much like the initial model for the the original 6-eleent Yagi, with only a few changes. First, we have added the dipole that is 1 mile away from the Yagi. Second, we have provided the dipole with the source (Wire 7, Segment 11). To reverse the transmit and receive functions, we need only place the source on Wire 2, Segment 11.

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For the sake of the doemnstation, we shall need some data about the Yagi in free space. Fig. 5 provides a free-sapace radiation pattern and performance data from an EZNEC model. The only differences between the pattern shown and Fig. 1 are that fact that the new pattern derives from EZNEC software, the main lobe extends along the X-axis, and the EZNEC graphic convention is to place 0 degrees phi horizontally to the right.

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Thge figure includes some data that we shall later use, including the maximum forward gain in dBi, the 180-degree front-to-back ratio, the front-to-sidelone ratio, and phi angles for the half-power points. (The sidelobes for this model are actually the rear quartering lobes, but they will serve our needs quite well.) We shall use all of this data to establish a coincidence between tra smit and receive patterns using only the standard entry-level RP0 request for a radiation pattern.

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Although I have shown the model in .NEC format, it will run on EZNEC, which simplifies the process of rotating the 6 wires that form the Yagi. In EZNEC, we shall be rotating the antenna in 10-degree increments from 0 degrees phi to 180 degrees phi. In addfition, EZNEC has a provision for setting the power level of the transmitting antenna, a facility that relieves us of the need to calculate the correct voltage to achieve that power level. We shall make two sets of model runs, one with the Yagi transmitting and one with the dipole transmitting. Fig. 6 shows the outline of the model set-up, although only a few Yagi positions appear for clarity. The figure also includes the free-space patterns of the two antennas, derived when each in in a transmit mode.

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Except as a check to see that we have in fact rotated the Yagi by 10 degrees for each run of the model, we shall not initially examine the output data. The radiation pattern will show essentially the same values wherever we point it when we use it in the transmit mode. Instead, we shall use some data that is readily available even in entry-level software, although too few modelers ever even look at it. We shall look at the current magnitude and phase angle on a certain wire and segment. The relevant segment is the one that would have the source in the transmit mode, but which does not have a source in the receive mode. Many modeler would place a load on this segment, one that corresponds to the segment's impedance when in the transmit mode. Because our initial tests will seek only a clear indication of the pattern shape, we may overlook the load, but we shall add one eventually.

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The required current magnitrude and phase data appear in the NEC output report. Entry-level software, such as EZNEC and NEC-Win Plus, provide this data in special tables extracted from the output file. NEC itself uses peak values of voltage and current. EZNEC is somewhat unique in converting these values to RMS values. Hence, the numbers in the EZNEC current table will be related to the values in the NEC output table by a constant factor (1.414), which will not affect our ultimate evaluation of the pattern shape. One limitation of the current table is that for values that require engineering notation (for example, 1.2E-5), the table limits the entry to two significant digits. We shall keep that fact in mind when we perform a few simple external calculations on the data that we obtain.

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Table 2 provides the data that we gather from our experiment. For each row in the table, we rotate the Yagi by 10 degrees counterclockwise (in the phi direction). The middle columns record the current on the second antenna "feedpoint" segment when we provide the Yagi feedpoint with a voltage source equivalent to a supply power level of 1 kW. The right-hand columns record the current on the Yagi "feedpoint" segment when we provide the second antenna feedpoint with a voltage source equivalent to a supply power level of 1 kW. We only need to gather data between 0 and 180 degrees since the pattern is symmetrical. In certain other cases, we may wish to extend the survey for a full 360 degrees.

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Although the phase angles for the two situations tightly coincide, the current magnitude entries do not. However, we would find an invariant adjustment factor between the two sets of current magnitudes. The difference results from the fact that each feedpoint requires a different source voltage to obtain the requisite 1-kW power level. The Yagi impedance is about 50+j9 Ohms, but the second antenna, a resonant dipole, has a feedpoint impedance of 72+j1 Ohms. This difference will make no difference to our evaluation of the patterns as we swap positions for the transmitted and received signals.

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We might try to create a semblance of a polar plot using the data in the table, although it would have likely not be a pretty affair. Instead, we may evaluate the patterns against the radiation plot for the Yagi that appears in Fig. 4. The critical data in that plot use gain values in dB, for example, for the 180-degree front-to-back ratio and for the front-to-sidelobe ratio. We only have current magnitudes with which to work. However, we may obtain usable values in dB by reference to the common equation:

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+ +
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Our only question will be what values to use for I1 and for I2. For I1, lets use the current for zero degrees. To obtain a value for the 180-degree front-to-back ratio, we use the current for 180 degrees. In passing, we may not the the pattern in Fig. 5 shows a higher gain at 180 degrees than on either side of that heading, and the Table 2 record of data shows the same small increase in terms of the current magnitude. Compare the values for 170 and 180 degrees.

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+ +
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Table 3 shows the calculated front-to-back ratios from erach data set along with the NEC data for the radiation pattern. Since the current value for 180 degrees uses only 2 significant digits, the values coincide closely with the NEC report. Moreover, the values for the two test situations are very close to each other.

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With caution, we may apply the same technique to obtain a front-to-sidelobe value from the test data in Table 2. If we check Fig. 4, we find that the peak sidelobe gain occurs at 126 degrees. Our data only includes values for 120 and 130 degrees. However, these values are the dame in both sets of columns and the pattern does not show much change across the 10-degree span. Hence, we may plug the tabular datas as I2 values into our simple equation and obtain the next set of calculated data in Table 3. Remembering that the current data is only good to 2 significant digits, the result coincide remarkable well.

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Without resorting to any sort of plotting exercise, we may perform one further test. The data for Fig. 4 show that the half-power beamwidth limit is 26.3 degrees from the heading of the main forward lobe. We have data only for 20 degrees and 30 degrees. If we use the 20-degree values for I2, we should obtain a value less than 3 dB. The result using the data for 30 degrees should be greater than 3 dB. Table 3 confirms this anticipated result. More significantly for this test, the values derived from the reversal of transmit and receive antennas tighly coincides.

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The sum of these tests is that NEC produces within very close limits equivalent patterns in the test situation when the test Yagi transmits and when it receives. Even though we may be limited within entry-level software in the commands to which we have access, we can still confirm reciprocity of transmit and receive pattern shapes using the tools available.

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We have not tried to determine the forward gain of the Yagi in the test situation. To obtain this data, we shall require a modified test situation. Fig. 7 shows its general outlines.

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At the top, we see our familiar test situation, except that this further test will require no rotation. We point the Yagi direcly at the second antenna. The lower portion of the figure shows that we have replaced the Yagi with a resonant dipole. For this test, we shall let the test antenna serve as a transmitter. We shall fit the second antenna with a 72-Ohm load resistor at its feedpoint segment. Now let's take current readings at the second antenna's feedpoint in both situations. When the Yagi transmits 1kW, the current is 1.57E-3 A at -13.98 degrees. When we replace the Yagi with the dipole, we obtain 6.2E-4 A at -10.24 degrees. Since we are working with such a limited number of significant digits we may ignore the slight difference in phase angle and use the two current values as I1 and I2 in our conversion equation. We obtain a value of about 8.1 dBd(r), that is gain over a dipole in a modeled range situation. Since we know that the dipole (with a significant diameter and made from real materials) has a free-space gain of 2.1 dBi, we may add this value to the calculated values to obtain a free-space gain of 10.2 dBi for the Yagi. The value reported by NEC for the transmit pattern in Fig. 4 is 10.23 dBi.

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We would have obtained very similar results had we omitted the load resistor in the receiving antenna (that is, a gain of 8.1 dBd(r)). Whichever way we set up the problem, we need to be consistent with the remote antenna's load resistor. With this result, we may declare--at least for the moment--that the case is closed.

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Conclusion

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We have examined a certain question, namely, whether or not NEC calcuations honor reciprocity between transmit and receive patterns. We used two basic techniques of modeling to arrive at an answer. The first technique required access to all NEC commands so that we could produce normalized receiving patterns. The second technique used only commands that are available within the most rudimentary entry-level software. In both cases, we obtained results that confirm reciprocity within a free-space environment, that is, an environment that does not introduce intervening variables.

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Although the demonstrations should be sufficient to establish a confidence in NEC's adherence to reciprocity in its calculations, we have not exhausted all the the tests that we might perform. There are more complex tests (or demonstrations) involving the use of ground and numerous other variables that we might throw into the model set-up. Those cases each hold an interest. However, for the moment and within the scope of these notes, we have shown some easily replicated modeling experiments that demonstrate reciprocity within NEC.

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Updated 06-14-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Modeling


+ + diff --git a/content/model/sp.html b/content/model/sp.html new file mode 100644 index 0000000..82619cd --- /dev/null +++ b/content/model/sp.html @@ -0,0 +1,137 @@ + + + + + + Close-Spaced Wires + + + +
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Close-Spaced Wires: MININEC vs. NEC-4

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L. B. Cebik, W4RNL

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+ In another note, I established that there is a strong possibility of a systematic error in NEC-4 with respect to linear antenna elements composed of wires having significantly different diameters, especially when the center section is larger than the end sections of the element and when the larger center section is short compared to the total element length. This potential error is in addition to an earlier discovery of limitations of NEC-4 in accurately modeling closed geometry antenna elements, such as folded dipoles and quad loops, when the wires have different diameters. +

Certain problems encountered with modeling Tee matches and open sleeve coupled elements led me to explore more systematically the possibility of a further systematic error. Apparent anomalous results occurred when antenna wires in NEC-4 were placed in close proximity, despite following recommended guidelines of aligning the segments of the wires to the degree possible.

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Therefore, I performed a simple modeling test of modeling a 1" diameter aluminum dipole for 14 MHz. I then created 3 different models of resonant 21 MHz dipoles, all aluminum, but having diameters of 0.5, 1.0, and 1.5 inches.

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In separate tests, I placed each of these 21 MHz dipoles in proximity to the 14 MHz dipole at distances of 2 through 12 inches in 2" increments. The 2" spacing was deemed the least permissible that would prevent the wire surfaces from touching. For each test, the 14 MHz fed dipole was reresonated and the gain figure recorded. As in past tests, resonance is defined as a feedpoint reactance of under 1 ohm. Since the test was designed to see the effect of the shorter wire on the longer, the original lengths of the 21 MHz antennas were preserved for each size throughout the test runs.

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The tests were performed on both MININEC 3.13 within ELNEC 3.0 and on NEC-4 within EZNEC Pro. Likewise, the lengths of the 21 MHz elements differed from a half-inch for the smallest diameter element to about 1" for the largest.

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The 14 MHz antenna used 34 segments in MININEC and 35 segments in NEC-4. The 21 MHz element was assigned 22 segments in MININEC and 23 in NEC-4. This segmentation aligned the segments quite reasonably. Since this segmentation already exceeds common practice in linear antenna design, convergence testing was not systematically undertaken, although the same performance curves appear with both fewer and more segments per half- wavelength.

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All gain figures were recorded as free space gain in dBi. With respect to closely spaced elements, there are two gain figures of note: the in-plane gain and the out-of-plane gain. The former is the maximum gain of the dipole and extra wire with the wires in line with each other. The latter is the gain in a direction broadside to a plane through the two wires. Out-of-plane gain will ordinarily be less than in-plane gain, although in- plane gain will show a front-to-back ratio approximately double the difference of the two gain figures.

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The tests were first run with MININEC. The following graph shows the in- plane gain for each diameter of extra wire as the distance between elements is decreased from 12 to 2 inches. Most notable in the graph is the flattening of the curves as the spacing reaches 2 inches, despite a reasonably linear progression to that point.

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Some of the reason for the flattening appears in the follow graph, which records the out-of-plane gains for the wire pairs over the same range of spacings. As the distance reaches 2 inches, the gain begins a steep increase. To all appearances, the two wires begin at this close proximity to act as a single fat wire. Whatever the true accuracy of the MININEC results, they do at least accord with normal expectations for closely spaced wires.

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The MININEC results acquire a further degree of confidence when one examines the range of variation. The total in-plane gain variation is less than 0.06 dB, while the out-of-plane gain variation is less than 0.02 dB.

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The gain figures encountered with NEC-4 show a quite different pattern. For example, the in-plane figures, shown in the following graph, show an overall increase through the same range of distances separating the two wires. The range of variation between 12 and 6 inch spacing is about 0.04 dB, but over the entire span of separations, the range increases to more than 1 dB.

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Equally notable is the fact that NEC-4 shows the highest gain when the two wires have the same diameter. How exact this equality is cannot be determined by this test, since the secondary wire diameters are widely separated.

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A similar curve accompanies the figures for out-of-plane gain. There is a larger spread of gains in the 12 to 6 inch range (0.06 dB), but the overall gain increase with closing separation is greater than 1 dB.

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At least for case at hand, which uses a secondary wire about 2/3rds the lengths of the fed wire, there appears to be a critical distance at which anomalous results begin to emerge. The following two graphs compare the in-plane and out-of-plane gains for MININEC and NEC-4 when the elements have the same diameter.

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Careful examination of the graphs shows that the curves overlap for spacing of 12 inches and 10 inches. However, between the 10" and 8" marks, the curves begin to diverge ever more radically.

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It is also interesting to contrast MININEC and NEC with respect to the required length of the 14 MHz element for resonance with the 21 MHz wire in close proximity. As the following graph shows, once we allow for the slight length variation of the 2 systems, the MININEC curve is much steeper than the NEC-4 curve at the closest spacings. However, the curve is in fact smoother than the NEC-4 curve, as the break in the NEC-4 curve at 6" is real and not a function of rounding.

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Moreover, there are also interesting differences in the feedpoint resistance curves. As noted, the 14 MHz elements were resonated to less than 1 ohm reactance. In the graph below, the MININEC feed resistance curve shows a small dip at the 8" spacing and then a smooth progression upward. In contrast, the NEC-4 curve shows a rapid progression downward past the 6" point. These same phenomena occurred with scaled VHF antenna models.

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These tests are only the beginning of a systematic exploration of the differential in gain and other figures from the MININEC and NEC-4 modeling systems. Here are a few further developments of these tests.

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Scaling: Scaling all the dimensions of the situation by a factor of 10 upward--including frequency, lengths, and wire diameters--produces curves that tightly fit those produced so far. This applies to both the MININEC and NEC-4 curves. The resonant 140 MHz 0.1" diameter aluminum wire spaced from 1.2 to 0.2 inches offsets are so slight, relative to the resonant 14 MHz 1.0" diameter aluminum wire spaced from 12 to 2 inches, that they would not appear in any form of graphing.

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Wire Length Ratios: The 20-meter antenna with a 15 meter wire forms a length ratio of 3:2. A series of NEC-4 runs was made to compare this ratio of wire lengths to wires with a 2:1 ratio and with a 4:3 ratio, focusing on wires of the same diameter (1" aluminum). The results appear in the following graph.

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Interestingly, the departure of the gain from a typical MININEC curve is greatest when the fed wire is about 50% longer than the closely spaced unfed wire, at least when the wires have the same diameter. Once more, the widely separated selection of test ratios does not lend precision to this conclusion. Since wires having a 1:1 diameter ratio appear to have a greater departure from typical MININEC curves than other wire diameter ratios, it would appear that by chance, my initial tests have fallen into at least the ball park of greatest deviation.

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Close Spacing and Multi-Element Arrays: The effects of a close-spaced wire on a dipole model are only indicators, but not predictors of the effect of a close-spaced wire on a parasitical beam model. Indeed, the disparity of gain and other performance figures between MININEC and NEC-4 might well be either quite profound or quite trivial.

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I quickly created a 3-element Yagi model to check the potential for divergent readouts. An extra wire was placed ahead of the driven element at the spacing indicated in the tables. The results were as follows:

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               MININEC                       NEC-4
+Space     Gain   F-B     Z           Gain    F-B       Z
+No wire   8.03   24.97   26.9+j2.1   8.08    27.94  26.6+j4.8
+2:1 Ratio
+ 4"       8.02   24.86   26.9+j1.1   8.68    27.81  23.4+j3.4
+ 7"       8.03   24.87   27.0+j1.3   8.26    27.84  25.7+j3.9
+10"       8.03   24.88   27.0+j1.4   8.14    27.85  26.4+j4.1
+13"       8.03   24.88   27.0+j1.5   8.10    27.86  26.6+j4.2
+16"       8.03   24.89   27.0+j1.5   8.09    27.88  26.7+j4.2
+3:2 Ratio
+ 4"       7.88   24.77   28.0+j0.0   9.35    27.68  20.3+j1.8
+ 7"       7.96   24.79   27.6+j0.4   8.61    27.76  24.1+j2.6
+10"       8.00   24.82   27.5+j0.6   8.33    27.81  25.6+j3.0
+13"       8.01   24.84   27.4+j0.7   8.21    27.86  26.4+j3.2
+16"       8.02   24.87   27.3+j0.7   8.15    27.91  26.7+j3.3
+4:3 Ratio
+ 4"       8.20   24.74   26.2-j1.0   6.81    27.93  37.7+j3.3
+ 7"       8.12   24.78   27.0-j0.5   7.34    27.91  33.1+j3.6
+10"       8.08   24.82   27.4-j0.3   7.67    27.93  30.6+j3.4
+13"       8.06   24.87   27.5-j0.2   7.85    27.98  29.2+j3.1
+16"       8.05   24.91   27.6-j0.1   7.94    28.04  28.5+j3.0
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The tables hold some surprises. First, the NEC-4 gain values diverge more radically than the MININEC numbers, especially for the 2:1 ratio of driven element to extra wire. Second, for the 3:2 and 4:3 ratios, MININEC and NEC-4 gain numbers diverge in opposite directions. Nonetheless, the NEC-4 figures are still farther from the "no-wire" baseline than those of MININEC. Third, unlike the simple dipole examples, the gain of some models may decrease in the presence of the extra wire.

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Before you draw any conclusions, let me reveal that the above table is erroneous. It is based on a defective model that is nevertheless all too common in amateur modeling practice. All 4 elements, the 3 20-meter elements plus the added wire, whatever its length, were assigned 10 segments in MININEC and 11 segments in NEC-4. The segments do not align, which is especially important in NEC, but not insignificant in MININEC with some models. Moreover, neither model converges well with models having twice as many elements. These practices cast doubt on the reliability of the results.

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So I reset the models, using 34 segments per 20 meter element (35 in NEC), and a proportionate number for the shorter extra elements. Convergence with models of twice the segmentation was excellent, with a gain difference of about 0.01 dB. Running these models resulted in a change of extra- element spacing to begin at closest with 3" rather than 4." Despite the closer spacing, the following results developed.

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               MININEC                       NEC-4
+Space     Gain   F-B     Z           Gain    F-B       Z
+No wire   8.01   26.66   28.4+j5.4   8.12    26.86  26.3+j6.6
+2:1 Ratio
+ 3"       8.01   26.64   28.9+j4.1   8.40    26.72  25.0+j5.2
+ 6"       8.01   26.65   28.7+j4.5   8.15    26.74  26.4+j5.8
+ 9"       8.01   26.66   28.7+j4.7   8.12    26.75  26.5+j6.0
+12"       8.01   26.67   28.6+j4.8   8.12    26.77  26.5+j6.0
+15"       8.01   24.68   28.6+j4.8   8.12    26.78  26.5+j5.2
+3:2 Ratio
+ 3"       8.00   26.52   29.3+j3.7   8.33    26.62  26.0+j4.1
+ 6"       8.00   26.57   29.2+j3.7   8.14    26.66  27.0+j4.9
+ 9"       8.00   26.61   29.1+j3.6   8.12    26.69  27.0+j5.2
+12"       8.00   26.65   29.1+j3.3   8.12    26.73  26.9+j5.3
+15"       8.00   26.70   29.1+j2.6   8.12    26.76  26.9+j5.3
+4:3 Ratio
+ 3"       8.01   26.73   30.0+j1.6   7.40    26.69  33.3+j3.9
+ 6"       8.01   26.80   29.8+j2.6   8.03    26.66  28.3+j4.4
+ 9"       8.01   26.87   29.7+j2.9   8.10    26.70  27.7+j4.5
+12"       8.01   26.95   29.6+j3.1   8.11    26.76  27.5+j4.6
+15"       8.01   27.02   29.6+j3.1   8.12    26.82  27.4+j4.7
+

A comparison of the tables shows two very significant facts. First, when models are developed carefully, rather than casually, any tendencies for any program to deliver potentially erroneous results is lessened. All figures for each length of extra element are far more tightly grouped.

+

Second, despite the tighter grouping, the same types of curves develop as with the casual model. To two decimal places, MININEC results are totally stable, although the third decimal place shows the mathematical progressions that appeared in the earlier model. Likewise, NEC-4 progressions show increasing gain with closer spacing for the two shorter lengths of extra elements and reduced gain with closer spacing for the longest extra element. In general, the instability with the figures occurs when spacing are closer than 6 to 9 inches at 14 MHz. Maximum deviations from the norm run from 0.2 dB to 0.5 dB for the example used. While less than with the casual model, the amounts of deviation from the normal can be significant, especially when compared to the extremely stable MININEC figures.

+

Conclusion: Each of these directions of research will require many more runs of wire combinations at many different frequencies before precise conclusions and systemmatic formulations of the MININEC/NEC-4 differentials can be drawn. I presume such work exists within appropriate research institutions and has simply not yet reached the community of modeling program users. At least, none has yet crossed my admittedly limited path.

+

Nonetheless, the simple test performed here is sufficient to suggest strongly that users of NEC-4 model closely spaced wires with great caution. If NEC-4 proves to be the anomalous case, then it may not be possible to routinely model closely spaced antenna structures with any presumption of accuracy with respect to resulting gain figures.

+

On the other hand, if MININEC proves to be more accurate in such cases, then perhaps it is time that an enterprising programmer undertook an effort to reprogram MININEC to a. release it from its 256-segment limitation and b. to enable the matrices to execute far more rapidly than in the current version.

+

(It would be useful to be able to compare these results with the Rockway- Logan revised MININEC, but the copy I purchased is apparently flawed so that some key modules will not work after 1 or 2 runs and must be reinstalled, even then with no assurance of working results. Moreover, the interface lacks the degree of user convenience associated with such diversely styled programs as AO and ELNEC, thus lengthening the time required for setting up even simple antenna models. However, the new MININEC calculating engine within an AO, ELNEC, or NEC-Win interface would be interesting to test thoroughly.)

+

As with all such tests, reasonableness of the appearance of results is not a sufficient validation of a modeling system. Nonetheless, it appears safe to note that closely spaced wires modeled in NEC-4 should always be approached with more caution than confidence.
+

+
+ +

+
+

Updated 9-24-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: Modeling


+ + diff --git a/content/model/sp1.gif b/content/model/sp1.gif new file mode 100644 index 0000000..c06ddcc Binary files /dev/null and b/content/model/sp1.gif differ diff --git a/content/model/sp2.gif b/content/model/sp2.gif new file mode 100644 index 0000000..700fd6a Binary files /dev/null and b/content/model/sp2.gif differ diff --git a/content/model/sp3.gif b/content/model/sp3.gif new file mode 100644 index 0000000..923d19d Binary files /dev/null and b/content/model/sp3.gif differ diff --git a/content/model/sp4.gif b/content/model/sp4.gif new file mode 100644 index 0000000..fa770bf Binary files /dev/null and b/content/model/sp4.gif differ diff --git a/content/model/sp5.gif b/content/model/sp5.gif new file mode 100644 index 0000000..d1ea7f7 Binary files /dev/null and b/content/model/sp5.gif differ diff --git a/content/model/sp6.gif b/content/model/sp6.gif new file mode 100644 index 0000000..6f229f8 Binary files /dev/null and b/content/model/sp6.gif differ diff --git a/content/model/sp7.gif b/content/model/sp7.gif new file mode 100644 index 0000000..e7f8927 Binary files /dev/null and b/content/model/sp7.gif differ diff --git a/content/model/sp8.gif b/content/model/sp8.gif new file mode 100644 index 0000000..978bab7 Binary files /dev/null and b/content/model/sp8.gif differ diff --git a/content/model/sp9.gif b/content/model/sp9.gif new file mode 100644 index 0000000..e22fafb Binary files /dev/null and b/content/model/sp9.gif differ diff --git a/content/model/tee1.gif b/content/model/tee1.gif new file mode 100644 index 0000000..8c983c3 Binary files /dev/null and b/content/model/tee1.gif differ diff --git a/content/model/tee2.gif b/content/model/tee2.gif new file mode 100644 index 0000000..dda10ff Binary files /dev/null and b/content/model/tee2.gif differ diff --git a/content/model/tee3.gif b/content/model/tee3.gif new file mode 100644 index 0000000..78a9af4 Binary files /dev/null and b/content/model/tee3.gif differ diff --git a/content/model/tee4.gif b/content/model/tee4.gif new file mode 100644 index 0000000..57c4014 Binary files /dev/null and b/content/model/tee4.gif differ diff --git a/content/model/teea.html b/content/model/teea.html new file mode 100644 index 0000000..c523d8d --- /dev/null +++ b/content/model/teea.html @@ -0,0 +1,172 @@ + + + + + + The Tee-Match + + + +
+

The Tee-Match:
+ NEC Illusions and MININEC Realities

+
+


+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Prior investigations of the Tee-Match left the impression that perhaps fat Tee bars may be more effective that thin Tee bars by yielding slightly, if not significantly, greater antenna gain in large Yagi antennas. The present modeling investigation, which shifted the modeling engine from NEC to MININEC, strongly suggests that there is no significant difference in performance in antennas using a Tee match with bars ranging from 0.5 to 1.5 times the driven element diameter. +

The Original T-Match Problem

Many months ago, I attempted to apply NEC-4 to the modeling of a Tee-match system. The original system modeled was based on a 5-element 48'-boom Yagi design by W3LPL. The modeling was done at a height of 195' over medium earth. The Tee match elements are shown in the figure. +
+ +
+

Of all the variables investigated, the relative diameters of the Tee-match bar to the main driven element had the greatest effect on the reported antenna gain.

+ 
Antenna without Tee-match:
+Gain:  16.1 dBi @ 5 degrees
+Beamwidth:  52 degrees (does not change)
+F-B:   23.0 dB
+Feedpoint Z:  36.3 + 16.1 ohms
+
+Antenna with 0.5" diameter 48" Tee match rod, spaced 6":
+Gain:  15.31 dBi
+F-B: 23.13
+Feedpoint Z: 262 + 87.9 ohms
+
+Antenna with 0.5" diameter 48" Tee match rod, spaced 7.5":
+Gain: 15.5 dBi
+F-B: 22.8 dB
+Feedpoint Z:  215.7 + 87.55 ohms
+
+Antenna with 2.0" diameter 48" Tee match rod, spaced 7.5":
+Gain:  16.2 dBi
+F-B: 23.0 dB
+Feedpoint Z:  196.2 + 29.9 ohms
+

The variability of results, including the increases in gain with increasing diameters of Tee-match rod, raised many questions about the adequacy of the model and limitations of even NEC-4 to correctly model the T-match situation. As subsequent investigation established, at 14 MHz, spacings of elements under about 9" (with variation for changes in element diameters) yield unreliable results in NEC-4. (Matters are worse in NEC-2.). Therefore, the notes were withdrawn from circulation.

+

However, many questions remained. One was a nagging feeling that perhaps the ratio of the diameter of the Tee rod to the main driven element might have some effect on antenna gain, although perhaps not to the extent suggested by the NEC-4 models. The second question concerned how to model the Tee match adequately on MININEC.

+

Modeling in NEC and MININEC

The original model of the W3LPL 5-element Yagi with a Tee-match is not suitable for MININEC. First, the antenna is too complexly structured, as the wire table shows: + 
5-element Yagi with Tee match (2" diameter Tee rod): Freq. = 14.2  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z :in)  Conn.--- End 2 (x,y,z :in)  Dia(in) Segs
+
+1          0.000,-217.00,2340.00  W2E1   0.000,-150.00,2340.00 7.50E-01  12
+2   W1E2   0.000,-150.00,2340.00  W3E1   0.000,-117.00,2340.00 8.75E-01   9
+3   W2E2   0.000,-117.00,2340.00  W4E1   0.000,-84.000,2340.00 1.00E+00   9
+4   W3E2   0.000,-84.000,2340.00  W5E1   0.000,-33.750,2340.00 1.12E+00   9
+5   W4E2   0.000,-33.750,2340.00  W6E1   0.000, 33.750,2340.00 1.25E+00  12
+6   W5E2   0.000, 33.750,2340.00  W7E1   0.000, 84.000,2340.00 1.12E+00   9
+7   W6E2   0.000, 84.000,2340.00  W8E1   0.000,117.000,2340.00 1.00E+00   9
+8   W7E2   0.000,117.000,2340.00  W9E1   0.000,150.000,2340.00 8.75E-01   9
+9   W8E2   0.000,150.000,2340.00         0.000,217.000,2340.00 7.50E-01  12
+10        86.000,-214.00,2340.00 W11E1  86.000,-150.00,2340.00 7.50E-01  12
+11 W10E2  86.000,-150.00,2340.00 W12E1  86.000,-117.00,2340.00 8.75E-01   9
+12 W11E2  86.000,-117.00,2340.00 W13E1  86.000,-84.000,2340.00 1.00E+00   9
+13 W12E2  86.000,-84.000,2340.00 W14E1  86.000,-48.000,2340.00 1.12E+00   9
+14 W48E1  86.000,-48.000,2340.00 W15E1  86.000,-33.750,2340.00 1.12E+00   3
+15 W14E2  86.000,-33.750,2340.00 W16E1  86.000, 33.750,2340.00 1.25E+00  15
+16 W15E2  86.000, 33.750,2340.00 W17E1  86.000, 48.000,2340.00 1.12E+00   3
+17 W50E2  86.000, 48.000,2340.00 W18E1  86.000, 84.000,2340.00 1.12E+00   9
+18 W17E2  86.000, 84.000,2340.00 W19E1  86.000,117.000,2340.00 1.00E+00   9
+19 W18E2  86.000,117.000,2340.00 W20E1  86.000,150.000,2340.00 8.75E-01   9
+20 W19E2  86.000,150.000,2340.00        86.000,214.000,2340.00 7.50E-01  12
+21       171.000,-199.38,2340.00 W22E1 171.000,-135.88,2340.00 7.50E-01  12
+22 W21E2 171.000,-135.88,2340.00 W23E1 171.000,-102.88,2340.00 8.75E-01   9
+23 W22E2 171.000,-102.88,2340.00 W24E1 171.000,-69.875,2340.00 1.00E+00   9
+24 W23E2 171.000,-69.875,2340.00 W25E1 171.000,-22.000,2340.00 1.12E+00   9
+25 W24E2 171.000,-22.000,2340.00 W26E1 171.000, 22.000,2340.00 1.25E+00   9
+26 W25E2 171.000, 22.000,2340.00 W27E1 171.000, 69.875,2340.00 1.12E+00   9
+27 W26E2 171.000, 69.875,2340.00 W28E1 171.000,102.875,2340.00 1.00E+00   9
+28 W27E2 171.000,102.875,2340.00 W29E1 171.000,135.875,2340.00 8.75E-01   9
+29 W28E2 171.000,135.875,2340.00       171.000,199.375,2340.00 7.50E-01  12
+30       349.000,-196.25,2340.00 W31E1 349.000,-119.25,2340.00 7.50E-01  15
+31 W30E2 349.000,-119.25,2340.00 W32E1 349.000,-86.250,2340.00 8.75E-01   9
+32 W31E2 349.000,-86.250,2340.00 W33E1 349.000,-53.250,2340.00 1.00E+00   9
+33 W32E2 349.000,-53.250,2340.00 W34E1 349.000,-22.000,2340.00 1.12E+00   9
+34 W33E2 349.000,-22.000,2340.00 W35E1 349.000, 22.000,2340.00 1.25E+00   9
+35 W34E2 349.000, 22.000,2340.00 W36E1 349.000, 53.250,2340.00 1.12E+00   9
+36 W35E2 349.000, 53.250,2340.00 W37E1 349.000, 86.250,2340.00 1.00E+00   9
+37 W36E2 349.000, 86.250,2340.00 W38E1 349.000,119.250,2340.00 8.75E-01   9
+38 W37E2 349.000,119.250,2340.00       349.000,196.250,2340.00 7.50E-01  15
+39       570.000,-183.75,2340.00 W40E1 570.000,-131.75,2340.00 7.50E-01  12
+40 W39E2 570.000,-131.75,2340.00 W41E1 570.000,-98.750,2340.00 8.75E-01   9
+41 W40E2 570.000,-98.750,2340.00 W42E1 570.000,-65.750,2340.00 1.00E+00   9
+42 W41E2 570.000,-65.750,2340.00 W43E1 570.000,-22.000,2340.00 1.12E+00   9
+43 W42E2 570.000,-22.000,2340.00 W44E1 570.000, 22.000,2340.00 1.25E+00   9
+44 W43E2 570.000, 22.000,2340.00 W45E1 570.000, 65.750,2340.00 1.12E+00   9
+45 W44E2 570.000, 65.750,2340.00 W46E1 570.000, 98.750,2340.00 1.00E+00   9
+46 W45E2 570.000, 98.750,2340.00 W47E1 570.000,131.750,2340.00 8.75E-01   9
+47 W46E2 570.000,131.750,2340.00       570.000,183.750,2340.00 7.50E-01  12
+48 W13E2  86.000,-48.000,2340.00 W49E1  86.000,-48.000,2332.50 1.25E-01   2
+49 W48E2  86.000,-48.000,2332.50 W50E1  86.000, 48.000,2332.50 2.00E+00  21
+50 W49E2  86.000, 48.000,2332.50 W16E2  86.000, 48.000,2340.00 1.25E-01   2
+
+ +
+

The antenna has 481 segments, organized to align corresponding segments on the elements while preserving the specified lengths of each diameter of material. All modeling was done using a 48" rod and varying only the length of the driven element end sections to restore the desired 200-ohm feedpoint impedance.

+

MININEC is limited to 256 segment antennas. Moreover, it was anticipated that the length of the Tee-bar and the parallel section of antenna element would have to be varied, in order to achieve the desired 200-ohm feedpoint impedance. With the W3LPL model, re-segmentation would become burdensome.

+

I chose a different model, based on a design (520-40 in YA) by K6STI, using constant diameter (1") elements. The 5-element, 40'-boom model employed 30 segments per element. This permitted adjustments to both the main element and the Tee bar with only local re-segmentation for some models to keep segments about the same length throughout the sequence of models.

+

In addition, MININEC 3.13 has its own limitations. I have established that within normal spacings of a couple of inches and up at 14 MHz, MININEC exhibits none of the problem characteristics of NEC with respect to close- spaced wires. However, MININEC has difficulties with corners: it cuts them off, thus providing results of limited reliability. These difficulties can be overcome by a. using enough segments in the model to make the corner cut-off insignificant, or b. by tapering element lengths so that corner segments are small and of equal length.

+

I chose the former procedure, since any change of Tee bar length or driven element length would require re-tapering the entire model. A final segmentation of 30 segments per complete element, however, made the segments adjoining the Tee-bar-to-Driven-Element connectors about twice as long as the connectors themselves. This limited the intrinsic accuracy of the reported lengths, relative to what might be found in adjusting a real Tee-match. However, the internal consistencies in the modeling sequence ensured that the results would be equally self-consistent.

+

A further modeling issue surrounds the different implementations of MININEC. AO, by K6STI, provides a correction factor by which AO's MININEC model results coincide with those from NEC-2 without change in modeling dimensions. ELNEC, by W7EL, does not contain this factor, but it does provide a parallel-wire corrector that provides better results with close- spaced wires. Since close-spaced elements form the subject of the study, ELNEC was the program of choice. However, this forced slight changes in the model dimensions relative to a corresponding model used for NEC and AO. Nonetheless, these changes do not affect the consistency of the results reported by MININEC.

+

The final model, shown for only one of the Tee-match situations, is shown in the following wire table. For this model, dimensions are in feet, except for wire diameter, which is in inches.

+
+ +
+ 
5-element Yagi with Tee match (1" diameter Tee rod): Freq. = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1        -17.600,  0.000,  0.000        17.600,  0.000,  0.000 1.00E+00  30
+2        -16.900,  6.000,  0.000  W3E1  -3.500,  6.000,  0.000 1.00E+00  12
+3   W8E1  -3.500,  6.000,  0.000  W4E1   3.500,  6.000,  0.000 1.00E+00   6
+4  W10E2   3.500,  6.000,  0.000        16.900,  6.000,  0.000 1.00E+00  12
+5        -15.900, 12.000,  0.000        15.900, 12.000,  0.000 1.00E+00  30
+6        -16.100, 23.580,  0.000        16.100, 23.580,  0.000 1.00E+00  30
+7        -15.250, 39.500,  0.000        15.250, 39.500,  0.000 1.00E+00  30
+8   W2E2  -3.500,  6.000,  0.000  W9E1  -3.500,  6.000,  0.500 1.00E+00   1
+9   W8E2  -3.500,  6.000,  0.500 W10E1   3.500,  6.000,  0.500 1.00E+00   7
+10  W9E2   3.500,  6.000,  0.500  W3E2   3.500,  6.000,  0.000 1.00E+00   1
+

This 159-segment model proved well-suited to MININEC's capabilities. A representative free space azimuth pattern is shown for reference.

+
+ +
+

I have given these modeling details for the inspection of other modelers. Like antennas themselves, antenna models must be open to critical inspection if the reported results are to be trusted.

+

The Results: Fat and Thin Tees are of Equal Value

The only changes among models in the following sequence are alterations of the driven element length, the Tee bar length and diameter, and the segmentation of the driven element to maintain a constant segment length to the degree possible. Therefore, a tabular presentation of the data seems most efficient. All models are in free space. Length dimensions are in feet. Except for the reference model, all models are distinguished by the diameter of the Tee bar. + 
Model          D.E.      Tee       Gain      F-B       Feed Z
+               Length    Length    dBi       dB        R+/-jX
+Reference      33.20'    ----      9.827     22.15      25.5 - j0.96
+T-0.5          34.10'    8.40'     9.855     21.71     209.7 + j0.85
+T-0.75         33.90'    7.50'     9.789     21.81     210.7 + j1.36
+T-1.0          33.80'    7.00'     9.817     21.86     209.7 + j2.49
+T-1.25         33.80'    6.80'     9.832     21.86     198.6 - j1.27
+T-1.50         33.70'    6.50'     9.853     21.92     205.2 + j1.41
+

In compiling these results, the reference antenna had its driven element divided into three wires, corresponding to those used in models having the Tee bar. The results are insignificantly different from a model that used a continuous driven element.

+

The gain reports are given to 3 decimal places to demonstrate how truly insignificant the differences are among the models. Re-segmenting Tee bar and the driven element at borderline cases (around 7') creates a higher degree of change in reported gain than changing the Tee bar diameter--at the extremes no more than 0.066 dB in the above table. Compare this to the full dB of difference in the NEC models. Likewise, front-to-back ratio changes by a maximum of 0.44 dB among the models.

+

The Tee bar length undergoes a different set of changes than with the W3LPL model (used for the original NEC studies), which had a pre-match feedpoint impedance in the vicinity of 40 ohms. Driven element lengths correctly show the requisite lengthening to provide the necessary inductive reactance for the Tee-match system.

+

Increasing the segmentation does alter all of the figures shown. The progression from 10 to 20 to 30 segments per element shows no abatement in the changes, which suggests that final convergence of the models has not been achieved and is unlikely to be achieved within MININEC's limits. However, operationally, the gain varies by less than 0.05 dB and the front- to-back ratio varies by less than 0.6 dB across this range of segmentation for any particular model. Only the feedpoint impedance changes by amounts calling for adjustment of the model. Therefore, the models shown are considered to be reliable indicators of gain and front-to-back ratio for the range of Tee bar diameters covered.

+

There is some small indication that further increases in the diameter of the Tee bar may indeed increase gain, but only in very small amounts. If the Tee bar is raised to twice the diameter of the main driven element, the gain reports as 9.882, which forms a progression of sorts on the high side of the chart. However, for an amount that is truly undetectable in operation, one acquires an ungainly mechanical construction problem.

+

At the other end of the scale, reducing the Tee-bar to 1/4 the diameter of the main element appears to approach an area where the lengths of both the bar and of the main element become critical, which translates into highly finicky adjustment. It is possible that the modeling may be trickier than the actual antenna. However, the following general proposition applies: the greater the diameter of the Tee bar, the broader and easier the adjustment.

+

Conclusion

NEC-4 models of the Tee-match system, when applied to a high gain antenna like the 5-element Yagi, are quite erroneous in their gain reports. Despite its limitations, MININEC gives every appearance of producing more reliable modeling results for this close-spaced structure. +

For the range of ratios of Tee bar to driven element (0.5 to 1.5), MININEC gives no indication that any particular ratio is better or worse than any other. Variations in the reported figures are insignificantly different in all respects, especially given the limitations of the models and the program.

+

The net result is this: within reason (+/- 50% of the main element diameter), any size Tee bar may be used with any size element with no change in antenna performance.
+

+
+ +

+
+

Updated 1-7-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Return to Amateur Radio Page
+

Topics: Modeling


+ + diff --git a/content/model/trap.html b/content/model/trap.html new file mode 100644 index 0000000..1b4a101 --- /dev/null +++ b/content/model/trap.html @@ -0,0 +1,206 @@ + + + + + + Modeling Trap Antennas + + + +
+

Modeling Trap Antennas

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ A number of excellent multi-element antennas exist, and many use traps. Those without traps can be modeled in a direct manner, even if the exercise is tedious with stepped-diameter elements. However, modeling element with traps still eludes some folks. +
+

Modeling Traps in NEC

+
The procedure for modeling an element with traps is actually quite straightforward. Consider a dipole cut for 20 meters with a 15 meter trap in each leg. Figure 1 illustrates the situation. The element diameter has been made constant to simplify that aspect of the modeling so that we may concentrate on the trap. +
+ +
+

A trap consists of an inductance and a capacitance, normally resonated just at or below the lowest frequency of the higher antenna frequency range. The limiting factor in a trap is the resistive loss of the coil, since the losses in capacitors at HF are very small. A trap effectively consists of a series combination of resistance and inductive reactance in parallel with capacitive reactance. See Figure 2a.

+
+ +
+

Unfortunately, we cannot directly model the situation in Figure 2 as a lumped constant load. NEC loads permit series R-L-C combinations, parallel R-L-C combinations, or series R-X combinations. It is necessary therefore, to convert the complex series-parallel circuit into an equivalent parallel R-L-C circuit, as illustrated in Figure 2b. However, since this procedure requires the transformation of component values into reactances, the conversion is frequency specific. Therefore, modeling a trap requires separate calculations and models for each frequency band of interest.

+

To do an actual calculation, we require some one of the following combinations of data:

+

a. The inductance and Q of the coil, the capacitance, and the frequency of interest;

+

b. The inductive and capacitive reactances, the resistance, and the frequency of interest; or

+

c. The inductive and capacitive reactances, the coil Q, and the frequency of interest.

+

Using measurements made by Roger Cox, WB0DGF, of commercial traps, we can consider a 15-meter trap that consists of a 3.3 uH coil with a Q in the range of 235. For resonance at 21 MHz, the coil requires a capacitance of about 17.4 pF.

+
+ +
+

With the given Q, the series resistance of the coil requires that we find the reactance of the coil at 21 MHz. By the standard formula, the reactance is about 436 ohms.

+
+ +
+

Dividing the reactance by Q, we get a resistance of about 1.9 ohms.

+

To convert the series R-L into a parallel R-L combination, we use the standard conversion equations:

+
+ +
+

The equations give these values: XL = 436 ohms; R = 100,000 ohms. The corresponding value of L comes from the reverse of equation (2):

+
+ +
+

The parallel inductance value will be 3.3 uH. We now have our parallel R- L-C trap load for operation at 15 meters.

+

At 20 meters, we may also calculate the requisite values of parallel R and L. The 3.3 uH inductance has a reactance of about 292 ohms. Dividing this reactance by the Q, which we assume to remain fairly constant, the series resistance is 1.25 ohms. The parallel equivalents are these: XL = 292 ohms; R = 67,300 ohms. The inductance of this parallel combination is 3.3 uH. The capacitance remains at 17.4 pF.

+

To model the trap dipole at 21.2 MHz and 14.1 MHz (as sample frequencies), we can create a model using a 1" diameter aluminum element with the following wire limits of the X coordinate (where both the Y and Z coordinates remain "0" for a free space model):

+ 
          Wire      End 1          End 2          Segments
+          1         -13.67         -11.3             8
+          2         -11.3          -10.8             1
+          3         -10.8           10.8            41
+          4          10.8           11.3             1
+          5          11.3           13.67            8
+

We place a parallel R-L-C load in elements 2 and 4. These short wires, no longer than a single segment of adjacent wire, permit independent adjustment of the antenna length for the two bands in question. For 21.1 MHz, the R-L-C values are expressed in the form most used by implementations of NEC: 1E05, 3.3E-06, 17.4E-12. For 14.1 MHz, the R-L-C values are 6.73E4, 3.3E- 06, 17.4E-12. The overall antenna element length absorbs the length of the trap. Slight differences in diameter for the short trap lengths at the current levels in the region of the traps are not significant variables, relative to real installations: ground clutter will create larger variations than trap diameters. A possible exception are dual-trap assemblies, which may be directly modeled as a larger wire diameter between traps. Use of shorted stubs as inductors also make no difference since, in principle, these radiate even less than solenoid inductors.

+

For comparison purposes, model dipoles were constructed of the same 1" diameter aluminum tubing, but without traps. The 14 MHz dipole was 33.3' long at resonance, while the 21.2 MHz dipole was resonant when 22' long. Both dipoles showed a free space gain of 2.13 dBi with a feedpoint impedance of 72 ohms.

+

The 21.2 MHz trap-loaded dipole showed a free space gain of 2.06 dBi, a mere 0.07 dB less than the trapless dipole. The feedpoint impedance was 73.9 ohms. The trap showed an impedance of 5175 - j22155 ohms, effectively terminating the antenna. Current levels beyond the traps were not significant, never rising above 2.5% of the source current.

+

In contrast, the 14.1 MHz trap-loaded dipole (trap resonant at 21.0 MHz) showed a free space gain of 1.87 dBi, 0.26 dB less than its trapless counterpart, with a feedpoint impedance of 66.2 ohms. The reduction in gain is partly due to the shortening of the overall dipole length.

+

However, the parallel R-L-C equivalent of the trap also plays a role in the gain reduction. We may derive a value for the trap's Q by reversing our calculations and deriving a set of series values for R and XL. The net parallel reactance of the trap at 14.1 MHz is given by the equation:

+
+ +
+

Using the resultant value of parallel reactance, 532 ohms, and the 63.7 kohms parallel resistance, we may calculate equivalent series values of resistance and reactance from standard equations:

+
+ +
+

The calculated series values are these: R = 4.2 ohms; XL = 532 ohms. (These values are automatically calculated by NEC and appear as part of its output data.) Dividing XL by R, we derive a Q of approximately 126 at 14.1 MHz. Note that this value varies from the expectation of those who wish to discount the capacitor and reduce the trap to a simple series combination of resistance and inductive reactance. NEC data suggests that the losses in the trap at 14.1 MHz are approximately double the losses at 21.2 MHz.

+

An equally shortened 14.1 MHz dipole with a center loading coil requires an inductive reactance of 174 ohms to be resonant. A lossless center coil yields a dipole free space gain of 2.00 dBi. Only by adding a series resistance of 1.2 ohms can the free space gain of the dipole with 15-meter traps (1.87 dBi) be replicated. The Q of the equivalent center loading coil thus becomes about 145.

+

The lower the frequency below the resonant frequency of the trap, the higher the Q of a given trap. At some very low frequency, lower than 1/10th the resonant trap frequency, the trap Q very closely approaches the initial Q of the coil (assuming that the initial Q is valid at that distant a frequency, which is dubious). Q of the trap assembly is lowest at resonant frequency. Hence, a 10-meter trap may show a higher Q at 20 meters than at 15 meters.

+
+

The Effects of Traps on Beams

+
+

Experience has shown that the losses in gain of center loaded elements are additive, at least in 2-element Yagis. If this experience holds true of the 14.1 MHz elements with 15-meter traps, then one might expect about 0.5 dB loss of forward gain relative to a full size Yagi of the same design but unloaded.

+

To test this hypothesis, I scaled a 10-meter beam with a 50-ohm feedpoint impedance for 14.1 MHz. The new full-size beam spaced the elements by 12.12', again using 1" aluminum tubing for modeling simplicity, as shown in Figure 3. With a driven element 32.2' long and a reflector 34.94' long, the beam achieved its maximum front-to-back ratio (10.68 dB), a figure almost exactly that of its 10-meter counterpart. The resonant feedpoint impedance was 50.7 ohms. The forward gain under these condition was 6.13 dBi.

+
+ +
+

If a beam using two trapped elements could be constructed with a comparable maximum front-to-back ratio and a comparable feedpoint impedance, then the gain difference between it and the full size beam would be a good measure of gain reduction due to the shortening and other losses imposed the traps. In fact, such a beam was modeled, using the same element spacing. The driven element was 27.06' long, and the reflector was 27.7' long. The 15-meter traps were left in their original positions. It is possible that positioning the traps as they might be in a 2-band trap beam could alter the 20-meters values slightly, but the alteration was judged unlikely to be significant.

+

The maximum front-to-back ratio of the 14.1 MHz beam with 15-meter traps was 10.68 dB, while the feedpoint impedance was 50.5 ohms. Under these control parameters, the forward gain was 5.64 dBi. (Note: for all the 2- element beams modeled here, higher forward gains are certainly possible, but at reduced front-to-back ratios.) The gain difference between the full size Yagi and the version with 15-meter traps is 0.49 dB.

+
+ +
+

Models of tri-band beams with 3 or more elements and/or more than 2 traps per element will follow the same procedure used here for these simplified models. Data for each trap will be needed for calculations of appropriate parallel R-L-C values. Also need will be a precise element diameter schedule, along with the exact location of the traps. Although time-consuming, such modeling projects should be quite straightforward.

+
+

Conclusion

+
+

If the technique of modeling traps is sound, then their presence does occasion some loss in forward gain relative to trapless antennas of comparable design, at least for frequencies lower than the resonant trap frequency. How significant this loss may be is a judgment requiring the examination of factors in addition to those included in the modeling exercise. Models also suggest that at frequencies for which the traps represent resonant terminations, gain will be very similar to that of trapless versions of the antenna.

+

Whatever the gain situation, the exercise does demonstrate that traps can be modeled effectively as parallel R-L-C loads for each frequency of interest.
+

+
+ +

+
+

In order to ease the calculator work, I have thrown together the following GW BASIC program to calculate the properties of traps at various frequencies, based on an initial input of measured or estimated trap resonant frequency and either a. coil inductance and Q or b. coil reactance and resistance, whichever pair is known or more easily estimated. The user may refine the program as desired.

+ 
10 'trap.bas:  L. B. Cebik, W4RNL  April 1, 1997
+20 CLS:PRINT "Estimating Trap Properties"
+30 PRINT "L. B. Cebik, W4RNL":PRINT
+40 PRINT "To estimate the properties of a trap at various frequencies, you
+will need to   know or be able to estimate the following information:"
+50 PRINT "  a.  The resonant frequency of the trap (normally, just below or
+at the lowest       frequency of the frequency band for which it is a
+trap); and either"
+60 PRINT "  b.  The inductance and Q of the trap coil, or"
+70 PRINT "  c.  The inductive reactance and resistance of the coil.":PRINT
+100 PRINT:INPUT "Resonant frequency of trap in MHz  ";FR
+110 PRINT "Coil Data:  Select the letter of the data pair you know or can
+estimate.":PRINT "A.  Inductance and Q;  B.  Inductive Reactance and
+Resistance"
+120 A$=INKEY$:IF A$="A" OR A$="a" THEN 130 ELSE IF A$="B" OR A$="b" THEN
+160 ELSE 120
+130 PRINT:INPUT "Inductance in microhenries         ";L
+140 INPUT "Inductor Q                         ";Q
+150 XL=(6.28*FR)*L:R=XL/Q:GOTO 190
+160 PRINT:INPUT "Inductive reactance in ohms        ";XL
+170 INPUT "Coil resistance in ohms            ";R
+180 L=XL/(6.28*FR):Q=XL/R:GOTO 190
+190 C=25330/(L*(FR^2)):CB=C/1E+12
+200 CLS:PRINT "Estimating Trap Properties"
+210 PRINT "L. B. Cebik, W4RNL":PRINT
+220 PRINT "Basic Trap Properties at Trap Resonance"
+230 PRINT "Resonant Frequency ";FR;" MHz"
+240 PRINT "Coil Q ";Q
+250 PRINT "Coil inductance ";L;" microH"
+260 PRINT "Coil reactance ";XL;" ohms"
+270 PRINT "Capacitor ";C;" pF":PRINT
+300 PRINT "Output Data:  Select the letter of the data type your would
+like.":PRINT "A.  3 selected frequencies;  B.  Several frequencies in one
+band"
+310 A$=INKEY$:IF A$="A" OR A$="a" THEN 320 ELSE IF A$="B" OR A$="b" THEN
+500 ELSE 310
+320 INPUT "Frequency #1 in MHz               ";F1
+330 INPUT "Frequency #2 in MHz               ";F2
+340 INPUT "Frequency #3 in MHz               ";F3
+400
+XL1=6.28*(F1*L):R1=XL1/Q:N1=R1^2+XL1^2:R1P=N1/R1:XL1P=N1/XL1:FC1=F1*1000000
+!:XC1=1/(6.28*(FC1*CB)):D1=XL1-XC1:IF D1=0 THEN D1=.000001
+410
+XN1=-(XL1*XC1)/D1:DP1=R1P^2+XN1^2:RS1=(R1P*(XN1^2))/DP1:XLS1=((R1P^2)*XN1)/
+DP1:Q1=ABS(XLS1/RS1)
+420
+XL2=6.28*(F2*L):R2=XL2/Q:N2=R2^2+XL2^2:R2P=N2/R2:XL2P=N2/XL2:FC2=F2*1000000
+!:XC2=1/(6.28*(FC2*CB)):D2=XL2-XC2:IF D2=0 THEN D2=.000001
+430
+XN2=-(XL2*XC2)/D2:DP2=R2P^2+XN2^2:RS2=(R2P*(XN2^2))/DP2:XLS2=((R2P^2)*XN2)/
+DP2:Q2=ABS(XLS2/RS2)
+440
+XL3=6.28*(F3*L):R3=XL3/Q:N3=R3^2+XL3^2:R3P=N3/R3:XL3P=N3/XL3:FC3=F3*1000000
+!:XC3=1/(6.28*(FC3*CB)):D3=XL3-XC3:IF D3=0 THEN D3=.000001
+450
+XN3=-(XL3*XC3)/D3:DP3=R3P^2+XN3^2:RS3=(R3P*(XN3^2))/DP3:XLS3=((R3P^2)*XN3)/
+DP3:Q3=ABS(XLS3/RS3)
+460 PRINT:PRINT"Frequency","Reactance","Resistance","Q","Para. Res."
+470 PRINT F1,XLS1,RS1,Q1,R1P
+480 PRINT F2,XLS2,RS2,Q2,R2P
+490 PRINT F3,XLS3,RS3,Q3,R3P
+495 GOTO 640
+500 CLS:PRINT "Estimating Trap Properties"
+510 PRINT "L. B. Cebik, W4RNL":PRINT
+520 PRINT "Basic Trap Properties at Trap Resonance"
+530 PRINT "Resonant Frequency ";FR;" MHz"
+540 PRINT "Coil Q ";Q
+550 PRINT "Coil inductance ";L;" microH"
+560 PRINT "Coil reactance ";XL;" ohms"
+570 PRINT "Capacitor ";C;" pF":PRINT
+580 INPUT "Lowest frequency for band scan in MHz    ";FL
+585 PRINT:PRINT"Frequency","Reactance","Resistance","Q","Para. Res."
+590 FOR J=FL TO (FL+.5) STEP .1
+600
+F1=J:XL1=6.28*(F1*L):R1=XL1/Q:N1=R1^2+XL1^2:R1P=N1/R1:XL1P=N1/XL1:FC1=F1*10
+00000!:XC1=1/(6.28*(FC1*CB)):D1=XL1-XC1:IF D1=0 THEN D1=.000001
+610
+XN1=-(XL1*XC1)/D1:DP1=R1P^2+XN1^2:RS1=(R1P*(XN1^2))/DP1:XLS1=((R1P^2)*XN1)/
+DP1:Q1=ABS(XLS1/RS1)
+620 PRINT F1, XLS1, RS1, Q1,R1P
+630 NEXT
+640 PRINT:PRINT "Press (a) for a new trap; (f) for a new frequency run; or
+(q) to quit"
+650 A$=INKEY$:IF A$="A" OR A$="a" THEN 10 ELSE IF A$="F" OR A$="f" THEN 200
+ELSE IF A$="Q" OR A$="q" THEN 19000 ELSE 650
+19000 PRINT:PRINT "To return to Main Menu, press (m)."
+19001 REM c:\basic\autoend.bas
+19005 M$=INKEY$:IF M$="m" OR M$="M" THEN RUN "C:\basic\menu.bas" ELSE 19005
+

+
+
+ +

+
+

Updated 4-2-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: Modeling, Traps


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+

Systematic Trap Modeling

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Some previous notes I developed on traps left me with some unanswered questions. For example, low Q traps appeared to unduly affect antenna gain. Traps using certain forms of linear or transmission-line stub inductors appeared to yield dipole gains above standard full size models. The only way to settle some of these questions is to do some systematic modeling and watch the curves develop. +

This brief report is the first step in the process. It models a 10-20 meter dipole using traps that consist of 1.2 microH inductors and 26.92 pF capacitors, resonant at 28 MHz, consistent with common trap practice. As previously noted, the traps are treated as loads on the ends of the 10 meter sections of the antennas. Modeling the traps consisted of calculating the requisite value of the equivalent parallel resistance for each trap Q level for each of the two bands and then inserting the trap as a parallel R-L-C load in the last segment of the outer ends of the 10-meter wire, with 20-meter wire extensions added. The antennas used approximate 3" segments throughout. Hence, trap length is considered for these models to be 3" per trap.

+

The total antenna assembly was resonated within +/-1 Ohm of reactance on each band for each wire size and level of Q. Selected frequencies were 28.5 MHz and 14.175 MHz, which were considered fair samples of antenna performance with the traps selected.

+

For the test, trap Qs began at 25 and were doubled up to 1600. The lowest end of the scale represents a well-worn or badly designed unit. The upper end (800 and 1600) represents what might be expected from transmission-line stub inductances. The midrange values from 100 to 400 represent a typical range of trap Q values for inductors of various types. Although inductor Q tends to vary with frequency, it was held constant for both 20 and 10 meters for this modeling exercise.

+
+

Copper Wire Models

+
+

The initial exercise modeled trap dipoles constructed from copper wire of AWG sizes 18 through 8. The following table lists the wire diameters for reference.

+ 
AWG Size       Diameter in inches       AWG size       Diameter in inches
+     18             0.0403                   12             0.0808
+     16             0.0508                   10             0.1019
+     14             0.0641                    8             0.1285
+

This size range carries the project up to about 1/8" in diameter. A later portion of the study will systematically chart performance for aluminum wire from 0.50" to about 2.00" in diameter.

+
+

10-meter Performance

+
The initial 2 charts tracking performance cover the free-space gain in dBi of the test antenna for 28.5 MHz. The data appear in two charts, one using separate lines for each wire size, the other using separate lines for each Q level evaluated. (In the latter, the Q=25 model is omitted due to limitations of the graphing program.) +

Note that there is very little difference in performance when Qs reach 800 and above, that is, when well-designed transmission-line stub inductors are used. However, the gain levels reached with such Q levels exceed the gain of a standard full-size 10-meter wire dipole of the same material, indicating that the gains of earlier models employing transmission-line inductors as physically modeled entities are not aberrations, but consistent with modeling high-Q traps as loads. One advantage of transmission-line stub inductors (besides their inherent high Q) is the ability to design them for light weight and relative freedom from concerns about voltage breakdown or current burn-up.

+

The chart showing each Q-level as a separate line across the wire-size values has the advantage of more dramatically showing the effects of trap Q on antenna gain. Little is gained using fatter copper wires than #12 or #14, but much is gained with each doubling of Q up to the Q=800 level.

+
+ +
+
+ +
+
+

20-Meter Performance

+
20-meter performance is presented in the same manner as 10-meter performance. However, on 20 meters, the range of performance improvement with wire size and with trap Q increases covers a narrower range: approximately 0.6 dB. Again, the charts present the data 2 ways to permit maximum clarity. Due to the limited range of values, any variation from smooth curves is due to rounding of gain values to 2 decimal figures by the modeling program. +

The total length variation in the outer length of the antenna to achieve resonance was only 7.2" across the entire span of wire sizes and Q values modeled. Changes required for the 10-meter segment of the antenna covered a maximum range of 3" for the same spread of wires and Qs. Feedpoint impedances showed a greater range of variation and will be graphed at a later date. Throughout the exercise, the feedpoint impedance of the antenna on 10 meters exceeded 80 Ohms, while on 20, the feedpoint impedance reached up to 75 Ohms only for the lowest Q and smallest wire size. These values can be changed to some extent by judicious selection of trap L and C.

+
+ +
+
+ +
+
+

Aluminum Tubing Models

+
The exercise of modeling copper wire trap dipoles produced curves that are open-ended upward. They do not appear to have reached peak values, even with Q=1600 and wire size AWG #8. Therefore, I undertook a second exercise using larger diameter elements. For reasonable applicability to real antenna situations, I used aluminum wires from 0.50" to 2.00" in diameter. The trap values and Q-range are the same, as is the segmentation of the antenna models. +
+

10-Meter Performance

+
As the following 2 graphs show, in two different ways, 10-meter performance peaks with Qs of 800 and above for all wire diameters. In fact, tubing diameter makes little difference in gain for Qs above 200. Qs above 800 are those one might expect with transmission-line stub inductors, as reflected in the models of perpendicular and folded inductors in an earlier note on traps. (Transmission-line inductors are always hybrids, combining properties of the antenna element and an inductor, since there will always be an imbalance of currents in the parallel wires in this type of application. Therefore, their optimum position will not be that of a lumped-constant inductor, but will be further inboard in the assembly. Likewise, their remnant reactance on 20 meters will be less than that of a lumped-constant inductor, requiring a longer wire for the 20-meter extension.) +

The feedpoint impedance on 10-meters for this collection of antennas ranges from a high of nearly 120 Ohms for the lowest value of Q and the thinnest tubing to values near 80 Ohms for higher Qs and fatter tubing. Although the progression of feedpoint impedances is generally inversely proportional to both Q and wire diameter, for Qs from 200 upward, the feedpoint impedance actually shows a very slight increase with the largest tube diameters. The increase is only about 1 Ohm for 2" tubing, but the progression is distinct and would likely continue with even larger diameter tubing. Operationally, the increase is insignificant.

+
+ +
+
+ +
+
+

20-Meter Performance

+
As with the copper wire models, 20-meter performance for the aluminum models shows a far narrower range of variation than does 10-meter performance. The two graphs below demonstrate this clearly. Little is gained, if anything, with trap Qs above 400. Feedpoint impedance is also more stable, ranging from 72 Ohms with the lowest Q and thinnest tubing to a low of about 60 Ohms with the highest Qs and fattest tubing. Values in the low to mid 60-Ohm range are typical across most of the range. +

The gain values for 20 meters show an interesting negative curve for all the aluminum models, although the phenomenon is minimal at the highest Qs. Gain decreases with increases in tubing diameter. This phenomenon is due largely to the shortening of the overall length of the antenna at 20 meters, a shortening that exceeds the shortening of the 10-meter section by a factor of over 5:1 as the tubing diameter at any Q is increased from 0.5" to 2" and up.

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+
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SWR Bandwidth

+
As demonstrated in the next three graphs, the SWR bandwidth on 10 meters is affected normally by increasing the diameter of the antenna element. Each graph includes #14 copper wire (0.0641"), #8 copper wire (0.1285"), 1" diameter aluminum, and 2" diameter aluminum. Each graph covers a different representative Q-level: 50, 200, and 800. In all cases, the SWR is relative to the resonant feedpoint impedance of the antenna, and all antennas were resonated within +/-1 Ohm of reactance at 28.5 MHz. +
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The SWR bandwidth is inversely proportional to the trap Q on 10 meters, as demonstrated in the following graph of #14 wire at Q-levels of 50, 200, and 800. Although the Q=50 model shows SWR values under 2:1 for the entire first MHz of 10 meters, the Q=800 model reduces that bandwidth to about 600 kHz. However, with antenna elements at least 0.5" in diameter, a full MHz of 2:1 SWR bandwidth is available at virtually any realizeable value of Q.

+
+ +
+

20-meter 2:1 SWR bandwidth is not a problem for any of the models at any value of Q. The following graph shows the SWR bandwidth of the best and worst cases: 2" diameter aluminum at Q=50 and #14 copper wire at Q=800, respectively. All other models tested fit within these limits.

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+
+

The Effects of L/C Ratio

+
To this point in the study, all traps for the 10-20 meter dipole have used a 1.2 microH inductor and a 26.92 pF capacitor. To investigate the effects of various L/C ratios on antenna performance, I reformulated the traps in 4 steps, using the following L and C values: +
+ Inductance Capacitance in microH in picoF 0.8 40.39 1.2 26.92 1.6 20.19 2.0 16.15 +
+

Each traps resonates at 28.0 MHz and has a Q of 200. Q=200 was selected because it is a realistic value for lumped-constant traps and because it has an intermediate value in the range explored above. The antenna model uses 0.5" diameter aluminum wires in free space at frequencies of 28.5 MHz (10 meters) and 14.175 MHz (20 meters). The results of the systematic modeling are summarized in the following graphs.

+

1. Antenna Length: The first graph plots the required lengths of 10 and 20 meter wires ("Inner" = 10 and "Outer" = 20). The L/C ratio makes a greater difference in element length than any other factor explored so far. The result is not surprising for 20 meters, where the L/C ratio makes a large difference in the trap reactance on the lower frequency. On 10 meters, the moderate increases in capacitive reactance at the element ends/traps (about -2000 Ohms per inductance step) may be sufficient to explain the moderate increases in resonant length.

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2. Antenna Gain: With increases in inductance and decreases in capacitance in the traps, the gain of the antenna follows opposing paths on 10 and 20 meters. The gain at 28.5 MHz increases as both a function of length and as a function of decreasing trap losses. In contrast, the gain at 14.175 MHz decreases as the L/C ratio grows larger mostly due to the rapid shortening of the 20 meter element extensions, but as well because of increasing (although modest) trap losses.

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+ +
+

3. Trap Losses: With an increasing L/C ratio, trap power losses decrease rapidly at 28.5 MHz from 8% with the 0.8 microH inductor to 3.7% with the 2 microH inductor. As the gain chart suggests, this phenomenon is less a concern for raw element gain than it is for the construction of traps to handle the voltages and currents involved. Actual trap losses may vary from the charted figures to the degree that the capacitor in the trap has a finite Q. In the models, Q is a function of assumed coil losses. As L increases for a trap resonant at a constant frequency below the operating frequency, the parallel L-C circuit returns a capacitive reactance that also increases. As a consequence (given the constant Q), the parallel equivalent resistance also increases, resulting in lower current through the power-dissipating branch of the circuit. The increase in equivalent parallel resistance in the trap is proportional to the increase in inductance. Since capacitor losses at HF are generally presumed to be in parallel with the capacitor, any capacitor losses will also be in parallel with the equivalent parallel resistance for the coil, resulting in a lower overall parallel resistance and greater power dissipation. In a large coil with considerable inter-turn capacitance, the losses in the capacitive branch of the trap may become significant, and in extreme cases, may nullify the decreased losses shown in the graph by assigning losses only to the coil.

+

At 14.175 MHz, the trap losses rise from a low of about 1.1% with an inductor of 0.8 micoH to 3.1% with an inductor of 2 microH. The rise is nearly linear. Although the losses in these traps are low on 20 meters (twice the trap frequency), they promise to become significantly large, especially when the inductors reach proportions such that the resonating C consists of the stray capacitances within the coil. (This condition also promises to lower the Q of the virtual capacitor from its presumed high value as a lumped-constant component. To what degree this note pertains to the Q of the capacitance of trap assemblies employing the C along the length of coaxial cables, which are also wound to provide inductance is unknown.)

+
+ +
+

4. Feedpoint Impedance: With an increasing L/C ratio, the feedpoint impedance of the antenna tends to decrease on both the upper and lower test frequencies. However, the decreases are moderate, with the 10-meter impedance remaining largely in the 80s, and the 20 meter impedance holding in the 60s. (Throughout this exercise, the coaxial feedline of choice for the free space models would be a 70-Ohm cable rather than a 50-Ohm cable.)

+
+ +
+

5. SWR Bandwidth: On 10 meters the SWR bandwidth increases with an increasing L/C ratio, as shown in the graph below. All SWR figures are relative to the resonant feedpoint impedance of the element at 28.5 MHz. Only with the lowest values of inductance does the test 0.5" aluminum element fail to achieve at least a full MHz of less than 2:1 SWR.

+

20-meter SWR performance is not shown, since it fits entirely within the limits of the 20 meter "best-case-worst-case graph shown earlier.

+
+ +
+

By judiciously comparing the results obtained with these models at a Q of 200 and with 0.5" diameter wires with the array of models using other Q-values and other wires sizes, one may interpolate reasonable expectations for almost any size trap in a 2:1 frequency situation. However, when in doubt, the best procedure is to model the exact situation with which one is confronted.

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+

The Effect of Trap Resonant Frequency on Performance

+
All of the antenna models used so far have had a trap resonated at the lower edge of the higher band of operation, that is, 28.0 MHz. Many trap antenna builders prefer to use traps whose resonant frequency is below the lowest frequency of the higher band. To test the wisdom of this procedure, I calculated a series of Q=200 traps as follows. + 
+Trap Resonant           L in            C in
+Frequency in MHz        microH          picoF
+        27.75             1.2           27.41
+        28.00             1.2           26.92
+        28.25             1.2           26.45
+        28.50             1.2           25.99
+        28.75             1.2           25.54
+
+

As a representative case, these traps were modeled at 10 and 20 meters using 0.50" diameter aluminum wire in free space.

+

The effects of variations in trap resonant frequency were minimal on the 20 meter band. 20-meter gain increased with increasing trap resonant frequencies, but by only about 0.02 dB across the span of trap frequencies tested. Feedpoint impedance changed by less than 2 Ohms across the same span. Changes in the variation of feedpoint resistance across the band and in the total variation in feedpoint reactance across the band were also minimal from one end of the trap frequency spectrum to the other.

+

Perhaps the only significant change required to re-resonate the antennas on 20 meters as trap frequency was changed occurred with respect to the length of the wire extensions beyond the traps. The following graph shows the changes in resonant 10-meter and overall 20-meter lengths for the spread of traps modeled. Note the lowest line, which indicates the sum of the two 20-meter extensions. It diminishes significantly as trap frequency increases, even though the reactance of the traps at 14.175 MHz is stable.

+
+ +
+

The major variations in performance occur on 10 meters. Since most folks are concerned about gain, the changes are graphed below. The total decrease in gain with increasing trap frequency averages about 0.25 dB across the span of models. It is quite likely that further gain increases would occur as the trap resonant frequency is further lowered. Note, however, that gain increases are accompanied by reductions in the 10-meter dimensions of the antenna, setting some lower size limit below the graph edge at which the effects of antenna shortening would meet to cancel the effects of lowering the trap frequency.

+
+ +
+

The effects of lowering the trap frequency are equally profound on the feedpoint impedance. The following chart catalogs the free space figures across the range tested.

+ 
+Trap Frequency          Feedpoint Impedance at Test Frequencies (R+/-jX)
+in MHz                      28.0            28.5             29.0
+   27.75                71.00 - j49.68  85.69 + j0.02   102.1 + j47.96
+   28.00                68.96 - j50.81  83.63 - j0.33   100.1 + j48.33
+   28.25                67.06 - j51.58  81.76 - j0.29   98.24 + j49.13
+   28.50                65.20 - j52.42  79.91 - j0.26   96.43 + j49.93
+   28.75                63.37 - j53.28  87.11 - j0.24   94.69 + j50.78
+ Change in Feed R           -7.63                   -7.58                   -7.41
+
+

The impedance change is approximately 10% of the center value. Although the changes in gain and feedpoint impedance appear small when viewed in isolation, their effects on a multi-trap, multi-element antenna are cumulative. The achievment of maximum performance will therefore be a compromise between lowering the trap frequency still further and seeing the effects created by the altered geometry of the 10-meter antenna element.

+

How low in frequency can the resonant trap frequency go before the gain begins once more to decrease? The answer is this: a lot farther than one might initially think. I calculated Q=200 traps at every MHz marker from 22 to 28 MHz and then re-resonated the resultant 10-20 meter dipole (0.5" diameter aluminum) at each step, using 28.5 MHz and 14.175 MHz as the test frequencies. The following graph records the free space gain in dBi at 28.5 MHz.

+
+ +
+

The cross-over point is around 23 MHz or just slightly lower. (Remember that because trap variables interlock, this frequency may vary with trap Q, wire size, and a number of other factors.) The antenna length varies regularly at about 1.32'/MHz for the 10-meter section and 0.88'/MHz for the outer or 20-meter dimension. (The slower decrease for the 20-meter section actually represents a lengthening of the 20-meter extensions.) As the following graph shows, the 28.5 MHz resonant feedpoint impedance also climbs as the resonant trap frequency decreases.

+
+ +
+

Although the gain increase at 10 meters is real, several factor mitigate against resonating a 10-meter trap as low as 23 MHz. First, the interaction between the 10- and 20-meter segments of the antenna grows touchy from about 24 MHz down so that small changes in one area require changes in the other. Second, the 20-meter gain continues to drop at an increasing rate so that with a 22 MHz trap, the free space gain is only 1.68 dBi. Third, the 14.175 MHz resonant feedpoint impedance decreases as the resonant trap frequency decreases, driving the 10-meter and 20-meter impedances further apart. Consequently, even for straightforward dipole operation, the final selection of a trap frequency will be a compromise offering the best combination of gain figures and usable impedances for both antenna sections.

+
+

Other Two-Band Trap Antenna Ratios

+
All test models in this investigation have used 10 and 20 meters as the focus of attention. Trap antennas, of course, are often made using target frequencies having different ratios from the 2:1 ratio used so far. Therefore, I used the standard Q=200 trap with a 1.2 microH coil and 26.92 pF capacitor (resonant at 28.0 MHz) to take a brief look at both 10-15 meter and 10-40 meter combinations. The standard 0.5" aluminum wire in free space was once more pressed into service. Physically, the only notable effect of changing the dual-band frequency ratio was that effect on the 10-meter section. As the frequency ratio decreases, the required length of the 10-meter section increases. This phenomenon suggests strongly that not only does the trap itself form a load on the end of the 10-meter antenna section, but as well the extensions for the lower frequency also form part of that load. +

The results (along with the 10-20 meter combination for comparison) appear in the following table.

+ 
+Combo   Frequency       Gain    Feedpoint Z     % Power dissipated
+        in MHz          in dBi  (R +/- jX Ohms)  in trap
+
+10/15   28.5            1.94    76.16 - j0.79    4.53
+        21.225          1.97    70.04 + j0.06    2.69
+
+10/20   28.5            2.03    83.63 - j0.33    5.83
+        14.175          1.98    63.56 - j0.72    1.76
+
+10/40   28.5            1.21*   79.61 - j0.73    5.92
+         7.15           2.03    62.79 + j0.50    0.87
+
+

The progression of figures appears regular and reasonable in every category except one: the 10-meter gain figure in the 10/40 meter combination. As the following free space azimuth pattern shows, the anticipated figure-8 pattern is distorted into a pair of opposing molars, with an overall lower gain.

+
+ +
+

The reason for the pattern distortion becomes plain from an examination of the 10-meter antenna current levels, especially in the 40-meter extensions.

+
+ +
+

Each extension is longer than 1/2 wl so that current may form a nearly sinusoidal curve with peaks about 10% of the overall antenna peak current. These peaks are sufficient to distort the anticipated radiation pattern, with some field cancellation in the areas where radiation normally peaks. Virtually any trap element with a frequency ratio approaching 4:1 will share this property. Therefore, every proposed trap antenna design requires individualized modeling and testing to ensure desired results.

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+

Not a Conclusion

+
The notes and charts presented here are not a finished work. But perhaps these explorations into systemmatic modeling are sufficient for the moment to provide a somewhat broadened understanding of trap antenna behavior. +

Much work awaits in the wings. The effects of traps on multi-element antennas and the use of multiple traps in each element have not been explored here. There is also another entire class of trap antennas wherein the trap is not resonant near any of the intended ham bands. On the use of traps that are not resonant near or within any band of antenna use, Al Buxton, W8NX, has likely done the most work.

+

If anything, investigations like this one should go some way toward correcting over-simplified views of traps. Traps and their effects on antennas using them form a fascinating complex landscape of their own.
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Updated 7-12-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
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Topics: Modeling, Traps


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Preliminary Notes on Trap Placement

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L. B. Cebik, W4RNL

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Part 1: Conventional Trap Designs

+
Many claims have been made about trap losses in dipoles and more complex antennas made from dipoles, such as multi-band Yagis. These claims led to an interest in discovering to what degree these losses might be verified through modeling trap antennas. Other notes in this series establish that it is possible to model traps for each band of operation with quite reasonable accuracy. So a preliminary analysis was undertaken. +

At the same time, alternatives to the use of a standard solenoid inductor came to my attention. Sometimes called "linear" inductors, all the alternatives consisted of the use of a shorted transmission line stub to achieve the level of inductive reactance need to resonate with the selected capacitor at the trap frequency. Since the reactance of a shorted stub does not vary with frequency in the same manner as it does in a solenoid inductor, at least some properties of the resultant trap dipole were expected to change.

+

The process of optimizing NEC-4 models of trap dipoles for 10 and 20 meters in free space yielded some surprising results. Conventional wisdom, for example, suggests that one place a trap at the end of a resonant antenna at the higher frequency and then extend the element for resonance at the lower frequency. This conventional wisdom is called into serious question by models, especially when the trap inductor is some form of a shorted stub.

+

Modeling traps is most accurate on NEC-4 with standard lumped components. Models of "linear" inductors as physical elements required the use of physically modeled lines of the same diameter (0.5") as the antenna wire in order to ensure that results would not exceed the NEC-4 limitation with parallel and right angle wires of different diameters. (See notes on limitations of NEC-4 in another entry in this series.) Moreover, physical modeling of the transmission line stub required placing it across a single segment wire loaded with the appropriate capacitive reactance. Since modeling is most accurate when segments lengths are as equal as possible, a minimum spacing of the transmission line wires was established, roughly 0.5 feet for reasonably sized models. As will be noted in appropriate places, the resultant unorthodox construction of the "linear" inductors sets limits on the direct applicability of the results of this study to real antennas. However, the results are sufficiently suggestive to call for further studies and extensive field experimentation by hams thinking of building their own trap antennas.

+

The phantom second study: In order to provide a check on the work done with fat aluminum elements, I also undertook a study of trap wire dipoles using #14 copper wire for all segments, including those that are a part of linear inductors. To separate the wire results from the aluminum results, I am setting forth the wire notes within as addenda to any relevant segment of the study.

+

The copper wire antennas will be given in inches, while aluminum dimensions will be in feet. This will distinguish the two in the intermix of the text. Additionally, the copper wire antennas are more heavily segmented than the aluminum ones, at about 4" per segment.

+
+

The Basic Antennas

+
The basic models of 10- and 20-meter dipoles used for all comparative purposes in this study have aluminum elements 0.5" in diameter. The 10 meter (28.5 MHz) model used 31 segments for an approximate length of 0.5' per segment. The 20 meter (14.175 MHz) model used 61 segments for an equivalent segment length. 0.5' per segment is well within both upper and lower limits of recommended segment lengths for accurate NEC-4 modeling. These independent models had the following properties. All gain figures are for free space. + 
Antenna        Length (ft)    Gain (dBi)          Feed Z (R+/-jX)
+10 meter       16.46'         2.13                71.92 - j0.28
+20 meter       33.32'         2.13                72.22 + j0.54
+

Obviously, there is nothing surprising in these models. The combination of element diameter and material losses result in a net loss of 0.02 dBi relative to the ideal free space dipole of infinitely thin, but lossless wire.

+

It should be noted that throughout this study, antennas are resonated, where resonance is defined as a feedpoint reactance of less than +/-1 ohm. Further accuracy of resonance was deemed unnecessary, given other limitations of the modeling exercise.

+

In order to make comparisons as reasonable as possible, antenna wire of 0.5" diameter aluminum is used throughout the study.

+

Basic #14 copper wire dipoles differ from fat aluminum dipoles in gain, with only minor differences in feedpoint impedance. Although copper is more conductive than aluminum, the losses due to the small diameter of the wire more than offset the conductivity to yield noticeably lower gains (although nothing is operationally noticeable for full-size standard dipoles).

+

The basic dipoles in copper wire are as follows:

+ 
Antenna        Length (in)    Gain (dBi)          Feed Z (R+/-jX)
+10 meter       200.4"         2.10                72.68 - j0.05
+20 meter       404.0"         2.08                72.99 - j0.38
+

As noted, all dimensions for wire antennas will be in inches to provide for additional segmentation in a convenient manner--and to allow you to easily know when we are working with aluminum and when with copper.

+
+

Conventional Dipole Traps

+
A conventional trap consists of a parallel combination of capacitance and inductance resonated (usually) at the lower limit of the higher frequency band to be covered by the trap dipole. Past conventions suggest that a component reactance near 200 ohms (at resonance) is useful, and some measurements suggest that coil Qs of 200 and upward are possible. +

Therefore, a trap was designed using a 1.2 microH inductor and a 26.92 pF capacitor in parallel. The reactance of each component at resonance (28.0 MHz) was 211 ohms. A Q of 200 was arbitrarily assigned to the coil.

+

At 28.5, the 10 meter target frequency, the capacitor reactance is about 207 ohms, while the inductor reactance is about 215 ohms. At 14.175 MHz, the 20 meter target frequency, the reactance of the capacitor climbs to about 417 ohms, while the inductor reactance decreases to about 107 ohms. However, in analyzing the trap at any frequency, one cannot simply use any of these figures. Calculations of the reactance and Q at the target frequencies yielded the following results:

+ 
Frequency           Reactance           Q
+28.5 MHz            -6019 ohms            7
+14.175 MHz            144 ohms          149
+

Although the 20 meter reactance figure does not seem too far off the reactance of the inductor alone, it is in fact nearly 40% different, an amount that results in a considerable difference in the required additional linear element length needed to resonate the trap dipole at 20 meters.

+

Since the parallel equivalent resistance for a circuit with a coil Q of 200 differs from band to band, separate models were required for each band. In each model, a parallel R-L-C load was placed in the last segment of the 10 meter inner wire. Reiterative modeling was done until the models resonated at both target frequencies with the same inner and outer wire lengths with their appropriate loads. Figure 1 illustrates the models, with standard 20-meter and 10-meter dipoles for comparison.

+
+ +
+

The dimensions of the model in Figure 1 should draw some attention. compared to a 10 meter dipole with a length of 16.46, the 10 meter inner wire's length of only 16.66' indicates that the load is mostly within the standard 10 meter length. The segments of the antenna are roughly 0.5' each, and the loaded segment is on each end. A load is distributed throughout the segment, although often thought of as centered in the segment. In either way of thinking, the load is within the 16.46' limits of the standard unloaded dipole for all but 0.1' per end.

+

The following "explanation" is a tempting one: If we look at the antenna from a different perspective, the dimension become much clearer. The load is a part of the antenna at 10 meters. Except at 28 MHz precisely, the trap offers a heavily capacitive load (more than 6000 ohms at 28.5 MHz) to each end of the antenna, thus demanding some slight lengthening--namely about 0.1' per end. (Note: although it requires only small inductive or capacitive loads at the center of a dipole to effect significant changes in the dipole's electrical length, it requires massive loads at or near the element ends to create relatively minuscule changes in electrical length. Hence, the 0.1' change of length for 6000 ohms of loading is normal.) As experience with the wire version of the trap antenna suggests, we cannot wholly accept this account.

+

At 20 meters, the overall length of the antenna is only 29.3' or about 4' shorter than a full size dipole. This shortening is fully expected due to the inductive loading provided by the trap at 14.175 MHz. (Note: a dipole loaded only by the 107 ohm reactance of the coils, without consideration of the full trap circuit, would have required about a 30.2' length, nearly a foot longer than the trap dipole at 20 meters.) For reference, we may note that the extensions beyond the traps are 6.32' long each.

+

The dimensions of the #14 copper wire trap antenna partially adhere to the account for the aluminum version and partially deviate from it. The overall length of the wire trap dipole with identical traps is 366.4" with a 196.4" 10-meter section (including two 4" trap segments) and 85" 20 meter extensions. The reduction in 20 meter length from the standard dipole 404" is evident, due to the loading by the remnant reactance of the trap. However, the 10-meter section is 4" shorter than a standard 10-meter dipole of the same material. Although it remains true that the trap lies within the 10-meter antenna an acts as a load on it, the effects of wholly capacitive reactance on the end does not wholly account for the element length.

+

Part of the explanation consists of noting that the wire diameter and the resonant frequency of the trap are not independent variables. As the resonant frequency of a trap is lowered relative to the operating frequency, the required length of the trapped section grows shorter. The resonant frequency effect is larger for smaller diameter wires than for large diameter wires, thus shortening the wire antenna more than the capacitive reactance at its end would lengthen it.

+

Performance of the Q=200 trap dipole on each band is as follows:

+ 
Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.03                83.63 - j0.33
+14.175 MHz     1.98                63.56 - j0.72
+

Note that the high band feed impedance rises and the low band feed impedance falls relative to a standard dipole. The 10 meter dipole gain is down from the standard by 0.1 dB, while the 20 meter dipole gain is down by 0.15. The decrease in gain on 20 meters is due mostly to a combination of the shortening of the dipole from its standard length and to trap losses. We can roughly sort these losses. An unloaded dipole at 14.175 MHz with a length of 29.3' has a gain of about 2.03 dBi, about 0.1 dB down from a standard dipole. The remaining 0.05 dB loss stems from power losses within the Q=200 trap itself.

+

Similar trends show themselves with the copper wire antenna. Its performance figures are as follows:

+ 
Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       1.83                90.40 + j0.18
+14.175 MHz     1.94                66.33 - j0.96
+

The gain and feedpoint impedance differences between the 20 meter aluminum and copper trap models are fully consistent with the differences between the standard dipoles for that band. However, the losses at 10 meters are unexpectedly high. The 10-meter model was, of course, double checked for error. The figures are consistent for a variety of wire models using NEC models of R-L-C loads for the traps. The program shows nearly a 0.5 dB power loss within the loads of the wire antenna, far above the loss of less than 0.1 dB for the same traps in the aluminum dipole. The notion that "traps are traps" may be called into question, since it appears that the losses of identical traps may differ according to other factors of antenna design.

+
+

Currents and Losses

+
It is also useful to examine the current distribution in a trap antenna. Figure 2 compares the current distribution for a standard dipole, the 10-20 meter trap dipole at 10 meters and the 10-20 meter trap dipole at 20 meters. Current maxima are not to scale to save drawing space and to clarify a few matters. The standard dipole shows are decrease in current away from the feedpoint in a curve that is close to sinusoidal. +
+ +
+

The trap dipole at 10 meters also shows a roughly sinusoidal curve outward to the traps. The feedpoint current maximum is exaggerated to reveal the small but real current magnitude curves on the outer parts of the elements. The curve on each extension is not a sine curve, but reaches a maximum about 1/4th the way outward on the extension. Depending on trap design, current levels can reach 8 to 10% of the feedpoint current. Although this current is small, it is not negligible. It does contribute to the overall radiation of the antenna at its higher frequency.

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The 20-meter curve is also exaggerated, this time to reveal the slight "hip" in the current curve at the trap point. If we think of the antenna as divided into segments, each about 0.5' long, we may note that the segment of the trap antenna just inside the trap has a current level (relative to 1) of .79. The corresponding current in the standard dipole is about .77. In the segments just beyond the trap, the current levels for the trap and standard dipoles are both .71. However, the current decreases to zero in 15 segments for the standard dipole, while the curve is steeper for the shorter trap dipole--only 12 segments.

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The more rapid decrease in current in the trap dipole results in a slightly weaker radiation field than for the standard dipole, as reflected in the slightly lower gain figure. The Q=200 trap at roughly one-half its resonant frequency has regained 3/4ths of its Q (about 148), and hence its losses are low. Had the models used here been for 10-15 meters or for 15- 20 meters, trap Q at the lower frequency would have been lower, with a somewhat higher loss. However, for relatively high-Q traps, design losses are low, as reflected in the earlier division of loss calculation.

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This modeling exercise cannot, of course, address construction losses that may be present in poorly designed traps. Connection losses, inadequate sizing of coil wire, coil wire material losses, and container/shield- induced losses may all contribute to trap losses not included in these models. However, with a frequency separation of at least 2:1, a well- design trap appears to reduce gain on the lower frequency mostly by shortening the resonant length of the antenna.

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As a comparison, the same values for trap inductance and capacitance were run for 28 MHz traps with a Q of 75. The result was an antenna of almost the same dimensions as the Q=200 trap dipole for 10 and 20 meters. The 10- meter element was lengthened by 0.2' and the overall length increased by the same amount. (The performance table for the Q=200 trap is repeated to make the contrast more evident.)

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Trap Coil Q=200
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.03                83.63 - j0.33
+14.175 MHz     1.98                63.56 - j0.72
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+Trap Coil Q=75
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       1.63                91.81 - j0.70
+14.175 MHz     1.85                65.49 - j0.65
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The performance difference at 20 meters is most readily explicable. Reduced length has already been shown to contribute approximately 0.1 dB loss of gain relative to a full size standard dipole of the same materials, the gain loss due to the trap design and construction is 0.05 dB in the Q=200 model and 0.18 dB in the Q=75 model. Power losses in traps are inversely proportional to relative Qs for any two proposed designs. Although these figures do not translate directly into accurate assessments of gain loss, they are indicative of those losses.

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The losses at 28.5 MHz are more dramatic: 0.4 dB. These are losses of power wholly within the trap assemblies themselves.

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In multi-element antennas, losses due to loading and shortening of elements tend to be additive. Therefore, one might expect about three times the gain reduction of a single dipole in an optimized 3-element trap Yagi relative to a similarly optimized 3-element Yagi with full-length elements. This feature holds apart from any other design factors that may also affect antenna performance.

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The same comparison with Q=200 models was run with the #14 copper wire antenna, again using the same trap design at Q=75. Like the aluminum antenna, slight dimensional adjustments were made to achieve resonance. However, for this table, the dimensions were left identical to those for the Q=200 model to show the amount of frequency shift at both 10 and 20 meters, as indicated by the remnant feedpoint reactance. The comparison is as follows:

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Trap Coil Q=200
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       1.83                90.40 - j0.18
+14.175 MHz     1.94                66.33 - j0.97
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+Trap Coil Q=75
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       1.15                105.3 - j3.52
+14.175 MHz     1.83                68.15 - j1.18
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At 20 meters, where the trap acts as an inductive load, the decrease in gain due to the lower Q trap is 0.11 dB, comparable to the drop in the aluminum antenna. The same inverse relationship between Q and power loss in the trap applies to the wire antenna model as well.

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The drop in gain at 10 meters for the Q=75 model is 0.68 dB relative to the Q=200 model, with the power loss in the trap also inversely proportional to the ratio of Qs. However, the drop is less than double the drop in the aluminum antenna. It would appear that the rate of drop depends in part upon the relative Qs of the antenna and the traps. The aluminum antenna is fairly low-Q, with something like 10 times the circumference and surface area of the wire antenna. Not until the descending trap Q reaches a certain value relative to the antenna Q does the power loss in it increase at an initially rapid but then a tapering rate. For the higher-Q wire antenna, this relative value is reached at trap Qs higher than 200; for the aluminum antenna, the critical value region may lie between trap Qs of 75 and 200.

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A test of this perspective on the relationship of antenna Q to trap Q would require the use of traps of very high Q relative even to the wire antenna. It is possible to artificially specify impossibly low-loss coils for conventional traps. However, a more realistic alternative is also open to us. We may physically model the trap inductor as a parallel transmission line shorted stub. Such stubs would have Qs in the high hundreds, if not higher yet, and are also one of the construction alternatives used in practical antennas. If the proposed perspective on 10-meter trap losses is correct, then there ought to be no significant gain difference on 10 meters between comparable fat aluminum model and thin copper models.

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Since we wish to examine alternative trap designs and their proper placement in a trap dipole anyway, we might as well test the perspective in Part 2.
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Updated 7-11-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Part 2
+ Go to Amateur Radio Page
+

Topics: Modeling, Traps


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Preliminary Notes on Trap Placement

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L. B. Cebik, W4RNL

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Part 2: Modeling Alternative Trap Designs

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A trap consists of a parallel L-C circuit, resonant at a design frequency. In conventional traps, the inductance and the capacitance are lumped components, with the coil most usually a solenoid inductor (although toroidal core inductors have also been used). Alternative capacitor designs include the use of lengths of coaxial cable (used as capacitors rather than as open-end transmission line stubs) and of concentric overlapping lengths of insulated antenna element tubing. Most of these designs have been chosen either for mechanical reasons or to obtain non- standard values of capacitance. Since the Q of these alternative capacitor designs far outstrips the Q of a conventional coil, they have presented few problems in understanding the fundamental properties of trap elements. +

To achieve even higher inductor Qs, some builders have employed so-called linear inductors. A linear inductor is nothing more or less than a shorted transmission line stub. The stub may use either an existent commercial parallel transmission line or be constructed especially for a particular antenna design. The stub may be run perpendicular to the antenna element. For mechanical reasons, the stub is often folded back or outward along the antenna element. Samples of such lines are shown in Figure 3.

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For small values of inductive reactance, the required length will adhere closely to standard stub calculations. If the folded stub lines are equidistant from the main element, the stub length will by slightly shorter than if the lines are run in a plane with the element. When the lines are placed in a plane, the induced currents from the element field are unequal in the two lines and therefore do not fully cancel.

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Of special note is the so-called "coat-hanger" inductor. To calculate this line requires that we treat it as two inductive reactances in series, one for each half of the inductor. Otherwise, its properties are essentially similar to the folded inductors. As we shall see, folding the inductor toward the feedpoint or toward the element end makes no significant difference in performance.

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Investigating stub inductors via NEC-4 models calls for attention to program limitations. The models used in this preliminary investigation adhere to the general outline shown in Figure 4. The higher frequency element is terminated one segment shy of its true end (remembering that the trap is part of the element). A single segment, 0.5' long is added. This segment is loaded with the capacitive reactance of the trap capacitor. Since the alternative inductor trap designs adhered to the values of the conventional traps, the target capacitance is 26.92 pF, which yields reactances of 207.4 ohms at 28.5 MHz and 417.1 ohms at 14.175 MHz. The capacitor is not assigned any resistive losses. To the end of the loaded segment, the 20 meter extension is added to complete the linear portion of the assembly.

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The stub is a physically modeled wire assembly. Each parallel line connects to the junction at either end of the loaded 1-segment wire, with a shorting bar (wire) at the far end of the parallel wires. Two precautions must be met. The direction of the wire assembly is significant, since the current direction in the two wires is roughly opposite. Exact opposition is not the case with these assemblies, since the current magnitude and phase are not identical at the two terminals. As well, the segmentation should be as close to identical in the two wires as possible to permit each segment to align with its counterpart in the other parallel wire.

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NEC-4 presents some accuracy concerns for wires of different diameters that are parallel or which meet at angles. To minimize these errors, the shorted transmission line stub was constructed of the same materials as the main element: 0.5" diameter aluminum spaced 0.5' apart. Folded models space the inner wire 0.5' from the main element, with the outer wire 1.0' from the main element. These constraints permit NEC-4 to operate well within its design limitations. Independent calculations of stubs of this design yielded a required length of 2.83' for the 28 MHz inductive reactance of 211 ohms. (A 450-ohm parallel line with a velocity factor of 0.95 would require 2.33' of shorted stub.)

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Relative to real-world construction practices, the stubs are too fat and too widely spaced. The fold-back models will show excess gain that is a function of the fat inductor wires, as well as a small but significant vertically polarized radiation component. Actual antenna elements using thinner wires more closely spaced to the main element will likely fail to realize the excess gain and lose much of the vertically polarized radiation. Relative to standard stub calculations, which presume that the shorting bar has no significant dimension, the widely spaced stubs will be slightly shorter than calculated lengths, with some of the length occupied by the shorting bar's approach to center-point.

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Despite these constraints--which limit the direct application of the models to a test antenna--modeling alternative trap inductors provides some data that is extremely useful, even if only in marking trends.

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The copper wire antenna of #14 wire with dimensions in inches makes it convenient to add segments and to produce somewhat more realistic transmission line stubs. The average segment in wire antenna models is between 3" and 4" and therefore, a segment of 4" was selected as the loaded segment. This set the stub construction of 4" spaced wires of #14 copper. The pre-calculated stub length was 23.472" (1.956'). In all other respects, the wire antenna models follow the rules set forth for the aluminum models.

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Perpendicular Stub Traps

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Initial tests of the model were run by placing the trap assembly directly in the position formerly occupied by the conventional trap--that is, between 7.83' and 8.33' outward from the feedpoint on either side of the dipole. The stub lengths were adjusted until 10-meter resonance was obtained. Then, the stub values were transferred to the 20-meter model (with a different capacitive reactance in the loaded segment) and the extensions adjusted for resonance. With only a few iterations, the antenna showed resonance on both bands with stubs 2.313' long, with a total 20 meter length of 28.10' (5.72' extensions from each trap). +

The performance of the antenna was as follows (with the Q=200 model shown for comparison):

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Trap Coil Q=200
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.03                83.63 - j0.33
+14.175 MHz     1.98                63.56 - j0.72
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+Perpendicular Stub 2.313'
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       1.53                63.29 - j0.76
+14.175 MHz     2.02                52.99 + j0.91
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Two data discrepancies should call themselves to immediate attention. First, the 10-meter gain has suffered a very serious drop (0.5 dB). Second the 10-meter feedpoint impedance is 20 ohms less than the Q=200 conventional trap model. In addition, the stub length is very seriously shorter than predicted.

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The error in this model might be difficult to assess in practice, since this is an antenna that can be made to operate and to show resonance on both bands. What the error is becomes immediately apparent when we remember that the trap assembly, treated as a load, is a part of the 10- meter antenna. Although the antenna shows a resonance at 28.5 MHz, it is not configured for maximum radiation effectiveness.

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A correct model requires that the 10-meter section of the antenna be shortened. A useful target for this shortening is maximum 10-meter gain. Figure 5 contrasts the dimensions of the initial and the final model (which might be tweaked even further). The stub is now across a capacitively loaded wire running from 5.9 to 6.4' from the feedpoint. To the trap ends are added 6.99' 20-meter extensions for an overall 26.78' length. The required stub increased to 2.723' long, a figure much closer to the calculated 2.83' once the shorting bar is considered. Evidence of being close to optimum for this antenna design is the fact that the current phases of the loaded element and the stub shorting bar are almost exactly 180 degrees apart, with allowance for the slightly different current magnitudes occasioned by aluminum losses in the modeled stub lines. In this configuration, the performance figures are these:

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Perpendicular Stub 2.723'
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.00                73.82 - j0.96
+14.175 MHz     1.99                45.09 + j0.44
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Evidence that the stub lines play a role in determining the overall length of the 10-meter segment comes not only from the gain and feedpoint figures, but as well from the vertically polarized radiation component in the antenna's free space azimuth pattern. The vertically polarized component is only about 18 dB down from the main antenna lobe. Figure 6 is a free space 10-meter pattern for the antenna with both vertical and horizontal components shown.

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Copper wire models corresponding to the aluminum models were constructed. The overall length of the wire antenna was 348.8" with 145.6" between the stub sections and 153.6" including the stubs. The distance including the traps is identical to that of the aluminum model. Given the thinner copper wire and the trend toward higher gain figures, we would expect to see a gain value at or just slightly higher than the figure for the aluminum model. This expectation is predicated on the view that the effective Q of the stubs is much higher than the Qs of either antenna model, as outlined in Part 1 of this study. If the relationship of antenna Q to trap Q does not obtain, then 10-meter performance should merely track conventional trap performance, and the gain of the antenna on 10 meters would likely be significantly less than 2.0 dBi.

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At 20 meters. the 95" (7.92') extensions confirm the lower remnant reactance value of stubs relative coils. Since the chief effect of the stubs at 20 meters is inductive loading, we would expect the 20 meter gain to be slightly lower than that of the aluminum model, given the greater losses in the thinner wire.

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The performance figures for the copper wire antenna are as follows:

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Perpendicular Stub 21.59"
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.08                90.83 + j0.41
+14.175 MHz     1.86                52.81 - j0.05
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The feedpoint impedance of the 10 meter model reflects very well the feedpoint impedance of the conventional trap model, suggesting that the stub placement is fairly well optimized. (The aluminum model might stand a bit more tweaking in this respect.) The gain is above that of the aluminum model by an insignificant amount, given the methods used here. However, the similarity of the values for comparably placed stubs is significant, as is the 0.25 dB gain improvement over the conventional trap with a Q of 200.

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The suggested rule of thumb for antenna segments at the trap frequency is this: For maximum gain, the trap Q must exceed the antenna element Q by some significant amount. Once that value is reached, resorting to higher Q traps leads to little gain improvement (although there may be mechanical reasons for selecting a higher Q design). We have provided no clear definition of antenna Q in this context. Such a definition and the development of gain expectation curves is a detailed investigation beyond the scope of available time.

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At 20 meters, the gain of the antenna is lower than with a conventional trap, largely due to the further shortening of the overall antenna length. The stub trap antenna is about 1' shorter than the conventional trap model, with a consequential further erosion of gain as it is related to antenna length. This reduction overrides the advantages of longer 20-meter extensions and trap Q at 20 meters. Trap Q does play a role, since lower Q traps at this length would further reduce 20 meter gain. The stub trap antenna at 20 has a gain intermediate between the gain of the longer conventional trap antenna with traps of Q=75 and Q=200.

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There are additional factors at work in the increased gain shown by the placement of stubs inward from their anticipated positions. The resonant frequency of a physically modeled stub and a load capacitance (or capacitive reactance) is difficult to determine in the course of modeling. Hence, the search for the maximum gain point does not ensure that the stub is indeed resonant at the same frequency as a pre-calculated load consisting of R-L-C components. As the resonant frequency of a trap is lowered further below the operating frequency, two phenomena occur: 1. The gain of the antenna increases and 2. the length of the trapped section decreases. Consequently, the use of a maximum gain criterion as the marker of correct trap placement most likely indicates that the trap is resonant on a frequency well below the operating frequency. That the 20-meter gain decreased slightly is a further indication of a lowered trap resonance frequency.

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Since one major goal of a dipole is gain (with the other being a usable feedpoint impedance), the seemingly radical shortening of the element poses no significant problems. However, in multi-element antennas, geometric relationships of the elements also play a role in overall antenna performance, trap placement and consequential gain may be subject to compromise to achieve the best possible physical relationship among the elements for the desire performance.

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Current levels in the parallel circuit made up by the stub and the capacitive loading wire are interesting. NEC-4 calculates only the losses of the capacitance load, not of the entire trap. However, physically modeling the trap assembly provides data on the current in the assembly. Current magnitude just prior to the trap is .52 (relative to 1.0) and just after the stub is .09. Within the trap, current varies from 1.15 to 1.57, indicating considerable circulating current within the assembly. (In the initial model, with its higher losses at 10 meters, the current peaked at 2.29 with much lower currents on either side of the trap.)

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We may note in passing that current levels in the wire antenna models corresponded quite reasonably with those of the aluminum model, again suggesting that the very high trap Q relative to the Q of either antenna model is the dominant factor in circulating current magnitude.

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For optimized 10-meter performance, the alternative trap assembly using a shorted stub inductor must be considered a part of the 10-meter segment of the antenna, and the linear portion of the assembly shortened accordingly. For 20-meters, the length of the extensions is a function of the net trap reactance at 14.175 MHz. Since a stub's reactance is a function of the tangent of its length, the remnant reactance of the stub is only about 70 ohms at 20 meters (in contrast to the 107 ohms remnant from the conventional trap coil). Hence, we should expect longer extensions for 20 meters with the stub design--and we get them: 6.99' in contrast to the 6.33' extensions for the conventional trap model.

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Folded Stubs

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Since perpendicular stubs are mechanically inconvenient for most real antenna designs, the stubs were folded, first inward toward the feedpoint and then outward toward the antenna ends. Using the 0.5' spacing noted earlier, the designs required no adjustment of the 10-meter length. Figuring the exact contribution made by each wire of the assembly would be inexact at best, but they approximate close to the prediction. The longest dimensions horizontally are 2.337' for the fold-back model and 2.285' for the fold-out model. +

The major difference among models was the required length for the extensions to bring the antenna to resonance on 20 meters. The fold-back model required extensions of 7.37' for a total antenna length of 27.54' overall. Extensions for the fold-out model were 7.47' for a 27.74' overall length.

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Performance figures for the two models are these:

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Fold-Back model:
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.34                79.23 + j0.79
+14.175 MHz     1.94                47.37 - j0.36
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+Fold-Out Model
+Frequency      Gain (dBi)          Feed Z (R+/-jX)
+28.5 MHz       2.30                83.76 - j0.20
+14.175 MHz     1.98                50.72 - j0.24
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There is little to choose between the two models, given the limitations of the modeling technique which precludes assigning precision to the numbers. Performance is comparable to 0.04 dB and about 4 ohms for each antenna version. And, further tweaking of the designs is likely possible using either models or test antennas. It is quite unlikely that the excess 10- meter gain would be realized using smaller more closely spaced wires for the trap inductors.

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10-meter circulating currents in the trap assemblies are quite comparable to those in the perpendicular trap version, reaching peaks of about 1.62 (relative to one). Interestingly, peak currents in the 20-meter wire extensions with an operating frequency of 28.5 MHz are almost twice as high in the fold-back model (where stub wires are parallel to the 10-meter element segments) than they are in the fold-out model (where stub wires are parallel to the extensions).

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The use of folded stubs as trap elements provides some mechanical advantage in the construction of trap antennas. Their performance is at least as good as the use of conventional coils, if appropriate adjustments are made to the length of the 10-meter portion of the antenna to achieve maximum gain. If those adjustments are not made and the trap treated, as in the past, as an appendage to (rather than a part of) the 10-meter antenna, stub inductors are likely to give very disappointing 10-meter service.

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There is an alternative trap procedure, suggested to me by ZL1ANJ and attributed to EA7BA, of using concentric but insulated antenna tubing as the entire trap. Presumably, the concentric length from the point at which the tubes are shorted (at an inward point) to some unspecified point along the way constitutes a coaxial stub. The remaining length of concentric tubing (until the inner tube emerges) provides the capacitance across the stub that is necessary for resonance. Although mechanically promising, this technique cannot be directly addressed by reasonably simple models. Hence, comparative performance remains unknown and will require field models for determination.

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This study has been of a preliminary nature. Much work to tweak the designs can be done. Too, much needs to be done to check the applicability of the fat wide stub designs against stubs of more normal dimensions. However, the investigation has fairly well established the need to treat traps as parts of the antenna segment which they limit and to suggest directions for the builder to take in constructing the most effective trap antennas possible.
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Updated 7-11-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Return to Part 1
+ Go to Amateur Radio Page
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Topics: Modeling, Traps


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VOACAP Type-13 Files for Amateur Band Antennas

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L. B. Cebik, W4RNL

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Amateur interest in the use of propagation software is growing, especially as VOACAP becomes more readily available. The best way to obtain the most accurate propagation forecasts and analyses for a given amateur installation is to use within VOACAP an antenna that closely resembles the actual station antenna at each frequency of operation. The resemblance need not be physical, but needs only to have a radiation pattern that closely fits the performance of the station antenna.

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VOACAP has a provision for using a special file type, type-13, which is a file of the radiation pattern in all azimuth direction and for all elevation angles in 1-degree increments. Each antenna at each frequency of operation requires an ASCII file about 260 KB long to include all elements of the pattern in the proper format. The file uses the compass rose (clockwise) convention and counts elevation from the horizon. In addition, each antenna must be over ground, and for many types of antennas, performance may vary with the ground quality. All antennas that can be rotated and are directional are oriented to place the main lobe due North (0 degrees azimuth). Use VOACAP controls to re-aim the antenna at a desired target communications region. Fixed antennas present different challenges for the user, and individual description sheets that accompany each collection will make suggestions on how to best use the files.

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Amateurs versed in the use of NEC or MININEC can create custom models of their actual antennas. Since NEC and MININEC generally use phi and theta conventions to produce the radiation pattern report, radiation-pattern data conversion is tedious at best. The latest version of EZNEC at its Plus and Pro levels can produce the desired type-13 files by use of the 3-dimension plot option.

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Amateurs who are not familiar with antenna modeling may not have access to radiation patterns of typical amateur station antennas. Therefore, I have begun a process of producing type-13 files of monoband antennas to cover most of the HF amateur bands. The files come in collections as the download list below indicates. Each file is zipped and contains a considerable number of files internally. Each collection contains models of the same antenna for each band. Where relevant--for horizontal rotatable antennas especially--there are variations of files at each frequency for different heights above ground. For vertical antennas, especially those using a ground or near ground mounting, there are variations for ground qualities known as very good, average, and very poor. Where relevant, there are also variations for different sizes of radial fields, namely, 4, 16, and 64 buried radials.

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Each file collection contains a 1-page document describing the specific file-name coding used for that group. VOACAP restricts type-13 files to 8 characters, requiring a careful coding to provide key file data. Since all antennas are monoband antennas, the group document also specifies any key features. For example, the collections for Yagis include the free-space gain (dBi) and boom length (wavelengths) of the model to allow the user to select an antenna whose performance most closely matches the station antenna, even if the station antenna is a multi-band array. A number of directional antenna types can be omitted for similar reasons. For example, those who use quagis, log-periodic dipole arrays, and similar antennas may select the Yagi or the quad pattern shape and gain that most closely match the performance of the actual station antenna.

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The collection does not attempt to model commercially built (or even home built) multi-band antennas. With the facilities available to most antenna makers, developing type-13 files for each antenna in their line at each operating frequency should be standard practice and would allow the maker to classify the file as authorized. Until makers take this step, most amateurs will have to estimate the performance of their antennas and select from the collections (as they slowly emerge) the model that is closest in performance and other variables to the station antenna.

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Despite the relative ease of constructing an individual type-13 file using the latest modeling software, the development of generally usable collections of files is a long-term task. For example, each zipped Yagi file contains 28 separate type-13 files for 80 through 10 meters. Zipped file collections include from 15 to 45 individual type-13 files. The basic collection is now as complete as I can effectively make it. Since each zipped file is itself very large, I recommend that you only download those files that are potentially useful to your station.

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The following list is what is presently available for download. For sample azimuth patterns, see the link at the bottom of this page.

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Horizontal Rotatable Arrays

All rotatable arrays in the following list have separate versions for each HF band from 80 through 10 meters so that the free-space E-plane (azimuth) pattern and performance level are the same within a collection to very small limits of variation. Each antenna has a type-13 file for each band at a specific height above average ground. (Horizontal antennas are generally less sensitive to ground quality variations than ground-mounted vertical antennas.) The heights for the upper HF region (20 through 10 meters) are 35', 55', 75', and 95', corresponding generally to typical amateur tower heights. For the lower HF bands from 80 through 30 meters, different files exist for heights of 75' and 100'. Selecting a file for use within VOACAP is a matter of determining the installation height and the performance level that most closely matches an available file. Some multi-band Yagi and quad designs might require selections from different collections on different amateur bands. The goal is to match performance levels and height, not to match the exact number of elements and boom length. +

All horizontal rotatable arrays use elements oriented east-to-west so that the file main lobe points toward 0 degrees azimuth. Use VOACAP controls to change the direction of the main lobe. One might change the orientation of the main lobe of a truly rotatable array to different sections of the world. If the directional array in use is fixed, then a single orientation setting is required to reflect the actual orientation of the array.

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1. Monoband Yagi Antennas: The Yagi collection consists of versions using 2 through 8 elements, with a long-boom and a short-boom version of the 3-element Yagi.

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2-element driver-reflector Yagis (6.2 dBi free-space gain)

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3-element short-boom Yagis (7.1 dBi free-space gain)

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3-element long-boom Yagis (8.2 dBi free-space gain)

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4-element Yagis (8.8 dBi free-space gain)

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5-element Yagis (10.1 dBi free-space gain)

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6-element Yagis (11.5 dBi free-space gain)

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7-element Yagis (12.4 dBi free-space gain)

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8-element Yagis (13.3 dBi free-space gain)

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2. Monoband Quad Beams: The quad collection consists of versions using 2 through 6 elements, with a wider-band and a higher-gain version of the 3-element quad. (Heights refer to the hub or center points of the square quad elements.)

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2-element quads (7.0 dBi free-space gain)

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3-element wider-band quads (8.6 dBi free-space gain)

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3-element higher-gain quads (9.2 dBi free-space gain)

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4-element quads (10.4 dBi free-space gain)

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5-element quads (11.1 dBi free-space gain)

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6-element quads (11.7 dBi free-space gain)

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3. Other Rotatable Horizontal Arrays

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2-element Moxon rectangles (6.0 dBi free-space gain)

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2-element phased array (or 2-element driver-director Yagi) (6.7 dBi free-space gain)

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2-element bi-directional W8JK flat-top with 1 wavelength elements and 1/2 wavelength spacing

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2-element bi-directional W8JK flat-top with 1 wavelength elements and 1/4 wavelength spacing

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Collinear, 2 wavelengths with phasing sections

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Bi-Square with 1/2 wavelength legs

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Fixed Horizontal Multi-Band Wire Antennas

Many amateur stations employ fixed wire antennas, such as a center-fed doublet or a large horizontal loop, for all HF amateur bands. The following lists of available type-13 file collections provide samples of popular configurations, but by no means all configurations. All linear wire antennas are oriented east-to-west so that one of the two main lobes on the lowest band will project due north (0 degrees azimuth). The user must within VOACAP re-orient the antenna to reflect the actual station installation. Horizontal loops come in too many variations to sample adequately. The small collection provided here are square loops with the feedpoint located at the center of the south side. Using these files requires reorientation so that the file feedpoint is on the opposite side of the loop from the aiming direction. End-fed wires have their feedpoint on the west end (270 degrees) of the array. Using the end-fed files requires careful re-orientation within VOACAP to ensure both wire alignment and feedpoint position relative to the actual installation. +

All fixed wire antennas and arrays are evaluated at heights of 35', 55', 75', and 95' on all bands within the normal coverage range of the antenna. For example, the 135' doublet has files for 80 through 10 meters, but the 44' doublet has files only from 40 through 10 meters. There are no sample free-space azimuth-equivalent patterns for this group of antennas, since the patterns will change with each band change. All models underlying the type-13 files use AWG #12 wire. The type-13 files show only the performance and patterns data; they do not include limitations and possible losses relative to various methods of feeding them. Note that the file-name coding system for these antennas differs from the one used for rotatable horizontal beams. See the individual information sheets that accompany each collection for details.

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1. Linear Center-Fed Doublets: The doublet collection contains center-fed doublets with lengths from 270' (lowest band = 160 meters) down to 44' (lowest band = 40 meters).

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270' doublet for 160-10 meters

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135' doublet for 80-10 meters

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102' doublet for 80-10 meters

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88' doublet for 80-10 meters

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67' doublet for 40-10 meters

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44' doublet for 40-10 meters

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2. End-Fed Linear Wire Antennas: The end-fed collections include unterminated wires that are 270' and 135' long. (Note: above the band on which an end-fed unterminated wire is 1/2 wavelength long, its pattern will differ from patterns for a center-fed wire of the same physical length.)

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270' doublet for 160-10 meters

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135' doublet for 80-10 meters

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3. 30-Degree Inverted Vs: The inverted-V collection consists of center-fed wires that slope 30 degrees from the horizontal on each side of the center point. The heights listed in the files represent the feedpoint heights. Due to the 30° angle of the wires, some versions are not available at the lowest heights.

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270' inverted-V

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135' inverted-V

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102' inverted-V

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67' inverted-V

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4. Horizontal Square Mid-Side-Fed Loops: Horizontal loops range from a circumference of 288' (about 1 wavelength at 80 meters) to 1152' (about 2 wavelengths at 160 meters). (Note: due to variations in the feedpoint locations and the shapes of actual installations, the samples are less certain guides to actual lobe formation and strength.)

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1152' circumference for 160-10m

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576' circumference for 160-10m

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288' circumference for 80-10m

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5. Terminated Folded Dipoles: Each antenna is terminated with a 900-Ohm resistance at the point opposite the center feedpoint.

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165' terminated folded dipole for 160-10 meter

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90' terminated folded dipole for 80-10 meters

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6. Multi-Band Wire Arrays: Bi-directional wire arrays for either 20-10 meters or 40-20 meters

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W8JK with 88' elements spaced 44' apart (40-20 meters)

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W8JK with 44' elements spaced 22' apart (20-10 meters)

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Lazy-H with 88' elements spaced 44' apart (40-20 meters)

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Lazy-H with 44' elements spaced 22' apart (20-10 meters)

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Vertically Polarized Antennas: General Note

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The collections of type-13 files for vertically polarized HF antennas have several distinctive features relative to the collections of files for horizontally polarized HF antennas. 1. They are generally used on the lower amateur bands from 160 through 30 meters. With some exceptions, file collections will be restricted to these bands. 2. Vertically polarized antennas are more sensitive in performance to differences in the ground quality beneath the antenna. Therefore, models will use samples over three different soil qualities: very good (0.0303 S/m, 20), average (0.005 S/m, 13), and very poor (0.001 S/m, 5). Over the bands covered, performance differentials due to ground quality tend to be larger at lower frequencies. Other differences may be specific to the type of antenna in question. Although amateur antennas employ a wide variety of materials, all files rest on the use of AWG #12 copper wire.

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Basic Vertical Monopoles and Dipoles

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Basic vertical antennas include ground-mounted vertical monopoles with buried radials, elevated vertical monopoles with attached radials, vertical dipoles, and multi-band vertical doublets. The ground-mounted vertical monopoles include 1/4 wavelength and 1/2 wavelength versions using models with buried radials in field sizes of 4, 16, and 64 total radials. The other antennas in this group do not use buried radials. All antennas in the group use AWG #12 copper wire as conductors. Unless otherwise indicated, patterns are available for 160-30 meters. Patterns are available for very good, average, and very poor ground.

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Ground-mounted 1/4-wl monopoles

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Ground-mounted 1/2-wl monopoles

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Elevated monopoles with 4 attached radials at 20' (80-10 meters)

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Vertical dipoles with 0.05-wl base heights (160-10 meters)

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Multi-band vertical doublet, center-fed, 44', 5' above ground (30-10 meters)

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Self-Contained Vertically Polarized Phased Arrays (SCVs)

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SCVs are 2- or 3-element vertical broadside arrays with in-phase feeding of each vertical using a single feedpoint. They do not require ground radial systems. Feedpoint placement determines the polarization of these antennas. All arrays align a main lobe (or the main lobe) due North (0° azimuth). Reorient patterns within VOACAP to coincide with the actual installation. Patterns are available for very good, average, and very poor ground.

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Half-squares

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Bobtail curtains

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Equilateral delta loops

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Right-angle delta loops

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Side-fed rectangular loops

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5-element Bruce array

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Phased Vertical-Element Arrays

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The collection of representative basic phased arrays contains both monopole and dipole versions of many types. Because of the complexity of the arrays and because any array in the collection will only approximate an actual installation, the monopole models in NEC-4 employ a MININEC ground, which is roughly equivalent to a radial field of between 32 and 64 elements. All dipole arrays set the base of the dipole at 0.05 wavelength above a high-accuracy ground system with no radial system. The collection includes monopole and dipole versions of triangular arrays that use a fed driver vertical element and two parasitic reflector elements. All arrays are situated so that a main lobe (or the main lobe) points due North (0 degrees azimuth). Hence, broadside arrays have elements on an East-West line, while in-line phased arrays have elements on a North-South line. The 4-square array forms a diamond with the elements at 0, 90, 180, and 270 degrees. In all cases, reorient the patterns within VOACAP to coincide with the actual installation. Patterns are available for very good, average, and very poor ground.

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2 In-Phase Monopoles, Broadside Pattern

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3 In-Phase Monopoles, Broadside Pattern

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2 Phased In-Line Monopoles

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2 In-Phase Dipoles, Broadside Pattern

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3 In-Phase Dipoles, Broadside Pattern

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2 Phased In-Line Dipoles

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Triangle of 3 Monopoles with 2 Parasitic Reflectors

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Triangle of 3 Dipoles with 2 Parasitic Reflectors

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4-Square Array

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The total collection has many omissions relative to antennas and systems used by radio amateurs. Some omissions, such as the inverted-L, have too many variations for any one version to capture its specific behavior. Other omissions, such as stacks of Yagi antennas, are too variable from one installation to another for inclusion. However, despite the present size of the type-13 file collections (61 zipped files, with over 1500 individual type-13 files), future additions are always possible.

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When selecting a type-13 file, remember that the pattern shape, the forward gain, and the elevation angle are more important factors to consider than the name applied to the array. The goal is to match the type-13 file to your best estimate of the performance of your own array or antenna. The sample patterns in the linked gallery of model plots can go a long way in assisting in the selection. If a closer approximation is required by a specific application, then you should consider modeling your actual antenna or array.

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One way to simplify the file structure within your version of VOACAP is to download only the collection (or collections) that have the most promise of closely matching your station antenna (or antennas). Unzip the files into a separate hard-drive directory. Then copy only the relevant files to your directory within the VOACAP program. You may rename the files within the 8-character limit, retaining the extension. As well, you may open the files within Notepad or Wordpad and revise the top line description to suit your needs. However, do not disturb the format of the remaining lines of the file.

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These notes are no substitute for mastering your particular VOACAP software. Moreover, the collections are made available without charge and without warranty. Use of the files is the sole responsibility of the user.

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Book Radio Wave Propagation Volume 4 (VOCAP Explained) - ON5AU.

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Updated 08-4-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Sample Azimuth Patterns

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Return to Index

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Topics: Modeling, VOACAP


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VOACAP Type-13 Files for Amateur Band Antennas
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L. B. Cebik, W4RNL

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To provide some idea of the anticipated azimuth pattern shape for the antennas included in the type-13 collections, the following plots may be useful. Elevation patterns vary for each combination of height, frequency, and other variables and are therefore impractical to present. These azimuth patterns are simply an aid to matching your antenna type to the nearest monoband antenna collection. All beam patterns within a collection have the same shape, with some small variations in the rearward patterns due to differences in height above ground as measured in wavelengths.

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Horizontal Arrays

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Monoband Yagis

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Monoband Quads

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Moxon Rectangle

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2-Element Phased Array (or 2-Element Driver-Director Yagi)

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2-Element Bi-Directional W8JK Flat-Top with 1 wavelength elements and 1/2 wavelength spacing

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2-Element Bi-Directional W8JK Flat-Top with 1 wavelength elements and 1/4 wavelength spacing

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Collinear Array with 2 wavelength total length (4 1/2 wavelength sections with phasing sections)

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Bi-Square Array with 4 1/2 wavelength legs

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Multi-Band W8JK Array with 1.25-wl elements and 0.625-wl spacing at highest frequency

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Multi-Band Lazy-H Array with 1.25-wl elements and 0.625-wl spacing at highest frequency

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Vertical Arrays

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(images for this section are missing)

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Basic Vertical Monopoles and Dipoles (All azimuth patterns are omni-directional.)

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Ground-mounted 1/4-wl monopoles

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type13-53.gif

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type13-54.gif

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Ground-mounted 1/2-wl monopoles

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type13-55.gif

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type13-56.gif

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Elevated monopoles with 4 attached radials at 20' (80-10 meters)

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type13-59.gif

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Vertical dipoles with 0.05-wl base heights (160-10 meters)

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type13-57.gif

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type13-58.gif

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Multi-band vertical doublet 44' center-fed, 5' above ground (30-10 meters)

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type13-60.gif

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Self-Contained Vertically Polarized Arrays

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Note: SCV patterns include sample elevation and azimuth patterns, but use with caution. Gain and elevation values change with the frequency, the base height above ground, and the quality of ground below the antenna.

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Half Square

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Bobtail Curtain

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Equilateral Delta Loop

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Right-Angle Delta Loop

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Side-Fed Rectangular Loop

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5-Element Bruce Array

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Phased Vertical-Element Arrays

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2 In-Phase Monopoles, Broadside Pattern

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3 In-Phase Monopoles, Broadside Pattern

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2 Phased In-Line Monopoles

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2 In-Phase Dipoles, Broadside Pattern

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3 In-Phase Dipoles, Broadside Pattern

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2 Phased In-Line Dipoles

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Triangle of 3 Monopoles with 2 Parasitic Reflectors

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Triangle of 3 Dipoles with 2 Parasitic Reflectors

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4-Square Array

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Updated 08-4-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Type-13 document

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Topics: Modeling, VOACAP


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Using Moxon Rectangles for WARC-Band Antennas
+ Part 1: Some 17-12 Meter Ideas

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+
+

L. B. Cebik, W4RNL

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+

Many hams who wish to work the WARC bands also wish to have a compact directional antenna for the job. In the past, I have designed a number of 17 and 12 meter combinations using Yagis. Because the WARC bands have narrow bandwidths, combinations of director-driver and driver-reflector Yagis work well. A number of design possibilities appear at my web site (..) in the "upper HF" portion of the main index.

+

In this note, I wish to explore the possible use of the Moxon rectangle as a potential replacement for the standard driver-reflector Yagi in such combinations. The Moxon rectangle is often thought of as a wide-band antenna. However, it offers some advantages for WARC-band use. First, its side-to-side width is about 70% that of a full-size Yagi, which is a space saver. A 17-meter Yagi that would be between 25' and 26' wide becomes less than 20' wide in the Moxon configuration.

+

The Moxon also provides for a direct 50-Ohm feed. Although Yagis can also be set for this feed impedance, they must be about 20% wider in the front-to-back dimension than a Moxon. In addition, the Moxon is only about 0.2 dB lower in forward gain than a comparable driver-reflector Yagi, but the Moxon front-to-back ratio will be well over 20 dB--and may peak in the 30 dB range.

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The end result is that a Moxon has a number of characteristics that some operators may find desirable for WARC band use, even if the wide operating bandwidth is not one of them. Hence, it is worthwhile to see if there are multi-band designs that might use the Moxon rectangle at their core. Fig. A shows some conventions for describing the dimensions of a standard Moxon rectangle. Dimension A is the side-to-side length, while E is the overall front-to-back dimension, subdivided into the driver and reflector arms (B and D) and the element tip-to-tip spacing (C).

+

The simplest way to combine two or more bands in one array whose performance can be certified on each band is to use open-sleeve coupling. In this system (made popular by the Force 12 C-3), only the driver for the lowest band is connected to the feedline. The driver for a supplemental (higher-frequency) band is positioned so that it achieves two goals. First, it is coupled close enough to the lower-band driver that the upper band elements receive sufficient energy to provide relatively standard performance. Second, the length and position of the driver for the upper band is set so that the feedpoint connection on the lower band driver registers a desired impedance on the new band. In the case of the Moxon + supplement array, 50 Ohms for both bands is the goal.

+

For simplicity, I shall confine design efforts to open sleeve coupling. In this episode, we shall explore a couple of options for covering 12 and 17 meters. In Part 2, we shall explore some possibilities that include 30 meters. All of the designs will use aluminum tubing in prospect of developing a rotatable beam.

+

The Possibility of a Dual-Band Moxon

+

Since I began investigating the Moxon rectangle design, I have received numerous inquires about whether it is feasible to nest 2 or more of these antenna in the same plane. It is certainly possible to create a "Christmas tree" of Moxon rectangles, each with its own feedline. However, nesting 2 or more Moxons in the same plane presents some difficulties. G6XN did so with his wire multi-band array. However, this array used remote (antenna tuner) tuning for each element, as well as some decoupling arrangements. Although this system can be quite effective, it adds complexity to the operation of the antenna. The design goal for this effort is an antenna that requires no tuning and that can be fed with a single 50-Ohm coax transmission line.

+

For the harmonically related ham bands, I have modeled pairs nested Moxons using open-sleeve coupling. However, I have never recommended the designs. The high-band antenna within the lower band array displays very narrow bandwidth, both with respect to the resulting feedpoint impedance and with respect to the gain and front-to-back ratio characteristics. Hence, the designs would not have been satisfactory for these wider ham bands.

+

However, the WARC bands are inherently narrow, covering no more than 100 kHz maximum. Thus, the possibility for a dual-band WARC Moxon became a live possibility. Fig. 1 shows the outlines of the final model.

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The following table shows the dimensions (in feet) for the dual Moxon with open-sleeve coupling, using the conventions of Fig. A to designate parts of the antenna.

+ 
Band              Dimension         Length (feet)
+17 meters   (all elements use 0.75" diameter aluminum tubing)
+                  A                 19.46'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12 meters   (all elements use 0.5" diameter aluminum tubing)
+                  A                 15.08'
+                  B                  1.99'
+                  C                  0.455'
+                  D                  2.13'
+                  E                  4.58'
+

Dimension E may not be exactly the sum of B, C, and D due to rounding, but the numbers are in principle close enough for construction. The 12-meter driver is set 1.15' behind the 17-meter driver, which places the 12-meter reflector 1.77' ahead of the 17-meter reflector.

+

A caution applies here and to any other tubular Moxon rectangle. The model uses uniform diameter elements of a specified size for each band. Changing the element diameter will result in slight changes for the required spacing of the element tips. Different size tubing changes the coupling between the tips. More than slight changes in element diameter may require juggling all of the dimensions to maintain performance and still have a near-50-Ohm feedpoint impedance. Using elements with different sized tubing along the length ("stepped-diameter" elements) may also require adjustments in the dimensions, just as it does with a Yagi.

+

The projected performance of the array can be summarized in the following table, where gain is shown as free-space gain.

+ 
Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+18.068            6.11          24.9                  58.8 + j 0.8      1.18
+18.118            6.02          29.5                  62.9 + j 2.7      1.26
+18.168            5.94          31.8                  66.8 + j 4.3      1.35
+
+24.89             6.13          18.9                  34.6 - j11.5      1.58
+24.94             5.81          34.1                  34.1 + j 2.6      1.48
+24.99             5.47          18.5                  33.9 + j15.9      1.72
+
+ +
+

Fig. 2 shows the mid-band 17-meter free-space azimuth pattern for the array, while Fig. 3 shows the same pattern for 12 meters.

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+ +
+

At first sight, it would appear that the dual Moxon is a distinct possibility for home construction. With a boom just over 7' long, it would seem to make a nearly ideal compact antenna for 17 and 12. Unfortunately, I cannot recommend the array.

+

The main reason for not recommending the array is the exceptional finickiness of the required adjustments. The performance table gives one set of clues to this fact. Compare the rate of change for both the gain and front-to-back ratio for the two bands. On 12 meters, the rate of change is over twice as fast as on 17. The consequence of this fact is that any slight variation in construction from the model could result in very large changes in performance.

+

Remember, too, that any open-sleeve coupled element pair requires careful adjustment on its own. When combined with rapidly changing performance characteristics for tiny changes in dimensions, arriving at a usable match and having good performance may prove to be beyond reasonable construction methods.

+

An additional aspect of the difficulty is the fact that the two Moxons force on each other changes in dimensions relative to the dimensions needed for independent use. In short, the two Moxons are essentially too tightly coupled throughout their structure to make the task of finding exactly the right configuration feasible, let alone easy.

+

However, since the antenna is just under 20' wide (slightly narrower than a 15-meter Yagi, even though the frequency is lower), we might be willing to try a 10' boom. At this length, we may be able to develop a 17-12 combination far more easy to adjust.

+

A Moxon-Yagi Combination

+

It is much more convenient to combine the Moxon for 17 meters with a 12-meter Yagi. Unfortunately, placing a driver-reflector Yagi inside the Moxon does not work, since the required length of the reflector would overrun the side arms of the 17-meter Moxon. However, we can place a director-driver combination ahead of the Moxon.

+

In commercial antennas, like the Force 12 C3, the highest band (10 meters) requires several elements to achieve a combination of good operating bandwidth and gain. The WARC bands do not have significant bandwidth requirements. Hence, we can use a simple director-driver combination to achieve results that are compatible with the basic performance of the Moxon for 17 meters. Fig. 4 shows the outline of the resulting design.

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+

Once more, the basic design uses 0.75" elements for 17 meters and 0.5" elements for 12 meters. Changes in element diameter will require adjustment relative to the following table of dimensions. For the Yagi portion of the design, "Space" refers to the distance from the Moxon driver to the 12-meter element in question.

+ 
Band              Dimension         Length (feet)
+17-meter Moxon    (all elements use 0.75" diameter aluminum tubing)
+Moxon             A                 19.56'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12-meter Yagi     (all elements use 0.5" diameter aluminum tubing)
+Driver            Length            19.40'
+                  Space              0.35'
+Director          Length            18.50'
+                  Space              3.08'
+

Perhaps the first thing to notice is the set of dimensions for the 17-meter Moxon. These dimensions are unchanged from those for a design optimized for independent use. The presence of the Yagi elements ahead of the Moxon does not affect the Moxon itself to any significant degree--that is, to a degree requiring redesign. The following performance table provides the data to show this fact even more clearly.

+ 
Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+18.068            6.41          20.0                  62.9 - j 7.9      1.31
+18.118            6.34          22.6                  67.2 - j 7.3      1.38
+18.168            6.27          25.8                  71.4 - j 7.1      1.46
+
+24.89             6.78          29.2                  58.7 + j 9.3      1.26
+24.94             6.86          30.2                  52.1 + j 7.4      1.16
+24.99             6.94          28.2                  44.4 + j 7.0      1.21
+

The performance of the Moxon is altered by a small amount, as shown in Fig. 5.

+
+ +
+

The presence of the 12-meter elements creates a slight "director" effect on the Moxon, which lowers the front-to-back ratio a small amount and which raises the feedpoint impedance somewhat from the 50-Ohm design specification for the antenna when used independently. The amount was considered too small to require design revision. In exchange for the slightly reduced front-to-back ratio--still at least 20 dB across the 17-meter band--the director effect gives a small boost to gain--about 0.3 dB. This increase in gain will be too small to notice operationally.

+

On 12 meters, the director-driver combination exhibits a standard Yagi pattern, as shown in Fig. 6.

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+ +
+

The gain of the array on 12 meters is greater than the two 12-meter elements would normally provide. The "forward-stagger" effect provides a small gain increase, since the Moxon elements provide a bit of a reflector effect. The 180-degree front-to-back ratio for 12 meters can mislead the user a bit, as Fig. 6 also shows. Although the pattern has a fine dimple directly to the rear, the rear quartering lobes are down by only about 18 dB, for an average front-to-rear ratio in the 22 dB neighborhood. In fact, the 17 meter front-to-rear performance is superior overall, despite the lower 180-degree front-to-back ratio.

+

The feedpoint impedance figures for 17 meters might be improved by a very small shortening of the side-to-side length (dimension A)--perhaps an inch or so. However, the reflector arms (D) should be lengthened by an equally small amount to restore and possibly center the front-to-back peak value within the operating passband on 17 meters. Indeed, it would be wise to make the reflector adjustment first to see the effect on the feedpoint impedance before adjusting the Moxon driver.

+

The key adjustment will be the placement and length of the 12-meter driver. Models of open-sleeve coupled elements always require subsequent field adjustment (a sophisticated way of saying "cut and try"). If the change of spacing relative to the given design is very small, then no further movement of the director will be required. If the change is more than a couple of inches, then readjust the director spacing closer to the value specified in the dimensional table in order to ensure that the array gives a satisfactory pattern. The juggling for 12-meters will have no significant effect on the 17-meter portion of the array.

+

The Simplest Dual Moxon Rectangle?

+

As an addendum to this set of design notes, I cannot overlook a deceptively simple design for a dual 17-12 m Moxon. In fact, as Fig. 7 reveals, it is actually only 1.5 Moxon rectangles, having a single driven element and two reflector elements.

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+ +
+

The dimensions for the antenna as modeled are these:

+ 
Band              Dimension         Length (feet)
+17 meters   (all elements use 0.5" diameter aluminum tubing)
+                  A                 19.46'
+                  B                  2.74'
+                  C                  0.625'
+                  D                  3.68'
+                  E                  7.04'
+12 meters   (all elements use 0.5" diameter aluminum tubing)
+                  C                  1.07'
+                  D                  2.43'
+                  E                  3.50'
+

Of course, dimension C, which is normally the gap between element tails, is in this design the distance of the reflector tail from the driven element itself.

+

The drawback of this simplified design is the need to use parallel feedline and an ATU, since the 12-meter feedpoint impedances are not compatible with a coax feed. As well, 12-meter performance is down somewhat, as the following table shows.

+ 
Frequency         Gain        Front-to-Back           Feedpoint Z
+  MHz              dBi         Ratio  dB              R+/-jX Ohms
+
+18.068            6.28          19.1                  40.8 - j 9.8
+18.118            6.19          22.2                  44.0 - j 6.9
+18.168            6.10          26.6                  47.2 - j 4.1
+
+24.89             5.96          14.7                  65.7 + j 425
+24.94             5.91          14.5                  69.9 + j 431
+24.99             5.85          14.2                  74.2 + j 437
+

The pattern for 17 meters holds up quite well, despite the proximity of the 12-meter reflector to the driven element, as evidenced in Fig. 8.

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+ +
+

Although the gain is slightly down and the front-to-back ratio considerably down, the pattern shape remains quite well-behaved and well within the norms for a "typical" Moxon pattern. Fig. 9 tells the tale for the entire 12-meter band.

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+ +
I would not necessarily recommend construction of this version of the dual Moxon. Supporting the "free-floating" reflector might be a bit of a structural challenge. Nevertheless, the design does show some of the flexibility of the Moxon rectangle design. +

As noted earlier, changes in element diameter relative to the given design will require element length (and possibly spacing) changes to account for them. For those who may wish to experiment with the designs we have looked at in model form, the following model descriptions may ease some of the entry work in modeling programs like EZNEC, NEC-Win Plus, AO, or NEC4WIN.

+ 
17-12 m dual Moxon                        Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.730, -2.738,  0.000  W2E1  -9.730,  0.000,  0.000 7.50E-01   7
+2     W1E2  -9.730,  0.000,  0.000  W3E1   9.730,  0.000,  0.000 7.50E-01  45
+3     W2E2   9.730,  0.000,  0.000         9.730, -2.738,  0.000 7.50E-01   7
+4           -9.730, -3.364,  0.000  W5E1  -9.730, -7.040,  0.000 7.50E-01   9
+5     W4E2  -9.730, -7.040,  0.000  W6E1   9.730, -7.040,  0.000 7.50E-01  45
+6     W5E2   9.730, -7.040,  0.000         9.730, -3.364,  0.000 7.50E-01   9
+7           -7.540, -3.139,  0.000  W8E1  -7.540, -1.150,  0.000 5.00E-01   5
+8     W7E2  -7.540, -1.150,  0.000  W9E1   7.540, -1.150,  0.000 5.00E-01  33
+9     W8E2   7.540, -1.150,  0.000         7.540, -3.139,  0.000 5.00E-01   5
+10          -7.540, -3.594,  0.000 W11E1  -7.540, -5.720,  0.000 5.00E-01   7
+11   W10E2  -7.540, -5.720,  0.000 W12E1   7.540, -5.720,  0.000 5.00E-01  33
+12   W11E2   7.540, -5.720,  0.000         7.540, -3.594,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+
+ 
+
+17-12 m Moxon + Yagi                         Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.779, -2.738,  0.000  W2E1  -9.779,  0.000,  0.000 7.50E-01   7
+2     W1E2  -9.779,  0.000,  0.000  W3E1   9.779,  0.000,  0.000 7.50E-01  45
+3     W2E2   9.779,  0.000,  0.000         9.779, -2.738,  0.000 7.50E-01   7
+4           -9.779, -3.364,  0.000  W5E1  -9.779, -7.040,  0.000 7.50E-01   9
+5     W4E2  -9.779, -7.040,  0.000  W6E1   9.779, -7.040,  0.000 7.50E-01  45
+6     W5E2   9.779, -7.040,  0.000         9.779, -3.364,  0.000 7.50E-01   9
+7           -9.700,  0.350,  0.000         9.700,  0.350,  0.000 5.00E-01  45
+8           -9.250,  3.080,  0.000         9.250,  3.080,  0.000 5.00E-01  45
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+
+ 
+
+17-12 m dual Moxon                            Frequency = 18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1           -9.730, -2.738,  0.000  W2E1  -9.730,  0.000,  0.000 5.00E-01   7
+2     W1E2  -9.730,  0.000,  0.000  W3E1   9.730,  0.000,  0.000 5.00E-01  45
+3     W2E2   9.730,  0.000,  0.000         9.730, -2.738,  0.000 5.00E-01   7
+4           -9.730, -3.364,  0.000  W5E1  -9.730, -7.040,  0.000 5.00E-01   9
+5     W4E2  -9.730, -7.040,  0.000  W6E1   9.730, -7.040,  0.000 5.00E-01  45
+6     W5E2   9.730, -7.040,  0.000         9.730, -3.364,  0.000 5.00E-01   9
+7           -7.530, -1.070,  0.000  W8E1  -7.530, -3.500,  0.000 5.00E-01   7
+8     W7E2  -7.530, -3.500,  0.000  W9E1   7.530, -3.500,  0.000 5.00E-01  33
+9     W8E2   7.530, -3.500,  0.000         7.530, -1.070,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

Of the three designs, the Moxon-Yagi offers the greater potential for being replicated in the average home shop. One Moxon construction technique (for 10 meters) appears in a piece I did for the ARRL Antenna Compendium, Vol. 6. Other techniques are also possible. It is wise to insulate all of the elements from a metal boom. Whatever the construction, the open-sleeve coupled Moxon-Yagi combination should acquit itself quite well during the present (and future) sunspot cycles.

+

The only WARC-related question left is whether there is any way to get 30 meters into the array. The answer to that question will be the subject of Part 2 of this mini-series.

+
+ +
+

Updated 5-1-2000, 8-4-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for April, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Upper, Moxon


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A Truly Portable Moxon Rectangle for Nearly No-Tool Field Assembly

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L. B. Cebik, W4RNL

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Since I began development of the Moxon Rectangle as a 2-element monoband directional beam with a superior front-to-back ratio and a direct 50-Ohm feed, I have had numerous exchanges with various hams on making the antenna truly portable. Various ideas have filtered through discussions, including the use of a fiberglass support frame--alternatively stressed and unstressed--with wire elements. However, tubular elements offer a wider bandwidth for all of the main operating characteristics. So I have focused in this direction.

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Basic Moxon Rectangle Dimensions and Performance

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We may calculate the dimensions for any Moxon rectangle from a convenient online calculator on the Moxon Rectangles and Online Calculator page. The figure below gives us a set of references that will make sense of the following table of dimensions.

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The tubing that I selected for the series of portable rectangles is 5/8" (0.625") diameter 6063-T832 aluminum, available from such sources as Texas Towers (http://www.texastowers.com) in convenient 6' lengths. Based on the use of this material, we may plug the element diameter and the design frequency into the program to derive dimensions. For 20 and 15 meters, a design frequency about 40% up from the bottom of the band provides whole band coverage. Therefore, 14.150 and 21.200 MHz are the design frequencies. On 10 meters, a frequency of 28.350 seems best for covering the entire first MHz of the band. The following chart provides the dimensions in feet.

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                       Moxon Rectangle Dimensions
+Dimension        20 Meters       15 Meters        10 Meters
+      A          25.12'          16.73'           12.49'
+      B           3.54'           2.31'            1.69'
+      C           0.95'           0.69'            0.55'
+      D           4.77'           3.19'            2.39'
+      E           9.26'           6.19             4.63'
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E, of course, is the simple sum of B, C, and D to give the overall front-to-back dimension. The constant diameter material means that the diameter as a fraction of a wavelength increases with frequency. Hence, the gap (C) at 10 meters is more than half the gap at 20 meters.

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In the note that follow, I shall focus on the most difficult of the versions to make truly portable--the 20-meter rectangle. You may adapt the idea for construction with greater ease to smaller versions than you can try to scale up constructions. Fig. 1 shows the 20-meter rectangle with dimensions and several kinds of markings that will be of significance in construction.

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The decision to attempt construction of a truly portable Moxon depends in part on the antenna performance. Fig. 2 shows free-space azimuth patterns for the 20-meter band edges and center for the array. The very high front-to-back ratio diminishes to about 18 dB at the band edges, while the gain decreases in a typical 2-element reflector-driver parasitic array curve.

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The anticipated performance figures--which will be similar for all 3 wide upper HF bands--appear in the following table.

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                20-Meter Moxon Performance in Free Space
+Frequency        Gain       Front-to-Back   Feed Impedance        50-Ohm
+  MHz            dBi        Ratio dB        R +/- jX Ohms         VSWR
+14.0             6.36       18.0            39.3 - j 18.0         1.60
+14.05            6.25       21.7            43.1 - j 13.7         1.39
+14.10            6.14       27.6            46.9 - j  9.9         1.24
+14.15            6.02       38.0            50.6 - j  6.5         1.14
+14.20            5.91       29.0            54.1 - j  3.5         1.11
+14.25            5.80       23.5            57.4 - j  0.7         1.15
+14.30            5.69       20.3            60.5 + j  1.9         1.21
+14.35            5.59       18.1            63.3 + j  4.4         1.28
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The gain drops about 3/4 dB across the 20 meter band. As Fig. 3 shows, the SWR curve is steeper below the design frequency than above it. This curve parallels the front-to-back ratio curve, and together, the two curves dictate a design frequency of maximum front-to-back ratio that is a bit below the mid-band point.

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For the average radio amateur without high towers and the finances to put a high performance set of beams into the air, the Moxon performance offers a chance for effective communications. The azimuth patterns suggest that the beam has two principle offerings. First, it is very quiet to the rear, enhancing signals from the forward direction. Second, the forward lobe is very wide, which requires less precision in aiming the antenna.

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For Field Day and similar operations, the antenna can be very effective, whether constructed of wire or tubing. Wire Field-Day versions of the Moxon--including a reversible version--appear in May, 2000, QST. In this set of notes, we shall concentrate on making the tubular Moxon truly portable.

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The Requirements for Portable Operation

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A truly portable beam must meet several requirements:

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  • The array must form a compact package for storage and transport.
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  • The array must go together using the minimum number of tools.
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  • The array must come apart in a simple reversal of the assembly order.
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  • The pieces must go together and come apart many times.
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  • The array must be reasonably sturdy in light winds.
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The ideas that following meet all of the criteria. However, the structure must not be used for either permanent installation or for winds that are brisk or better. 15 knots represents the highest recommended wind load for the antenna.

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The key to the ideas sketch in these notes is to assemble in the shop those pieces that form permanent subassemblies or pieces. Shop construction will require stainless steel hardware (bolts, sheet-metal screws, or clamps) for any junction of metals. In the field, a freshly made junction will provide electrical continuity for the duration of an operating session. Therefore, the only task for hardware will be to securely hold in place the junctions created in the field. Screws, clamps, and bolts are unnecessary for this purpose.

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The only hardware needed for field junctions appears in the figure above: the hitch pin clip (otherwise knows as the hitch pin, the hairpin cotter pin, or the spring retainer). When properly sized, these pins will more than suffice to keep the pieces of a portable Moxon in place. Hitch pins are available in many sizes. Although stainless steel pins are the most durable, they cost twice as much for half the number of zinc-plated steel version, according to McMaster-Carr catalog pages (page 2971 of the on- line catalog at http://www.mcmaster.com.

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Effective use of the hitch pin requires careful shop work. Drill the junction pieces of tubing together with the junction tightly in place. Use a hole size just barely large enough for the straight side of the pin. The tighter the fit, the more durable the junction. However, if a pin hole becomes loose and sloppy after a few uses, then a redrill at a nearby location with fix the problem.

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Hitch pins come in many sizes. For 5/8" diameter tubing, the pin rated from 1/2" to 3/4" service is suitable. The pin wire diameter is 1/8" (0.125"), which dictates the shop drill bit size. Unless you have a precision shop, it is unlikely that similar pieces will be interchangeable at junctions. Therefore, it is wise to use tape on both side of a junction with a coding that allows you to join the correct pieces in the field.

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Hitch pins are one of those items most likely to become lost in the grass. Therefore, be sure to obtain and store with the antenna parts a sufficient over-supply. As well, you might obtain brightly colored tape and add a tab through the top ring of each pin. These cautions fall under the basic principle that the more worst-case thinking you do in the shop, the fewer worst-case events will occur in the field.

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Designing the Portable Moxon

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Making a portable Moxon rectangle for 20-meters is our goal. The design effort begins by breaking the antenna into many sub-assemblies. The dimensions for these assemblies emerged from the dimensional requirements, shown in Fig. 1 and the available materials. Tubing comes in 6' lengths from many mail-order sources in order to fit with the UPS limits above which special shipping charges apply. Since the 20-meter version of the antenna is 12.56' (150.7") each side of the center line, we can use two sections between 5' 9" (69") and 6.0' (72") for each element's long portion. (A 10-meter version would require only one section per element per side of center line, and a 15-meter version might use two shorter sections.) The corner assembly will make up the remaining few inches. The tail pieces are well under 6', so they can be independent parts. The junctions consist of 0.5" tubing inside the main 0.625" tubes.

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The array for 20 meters will need about 70' of tubing, which weighs less than 7.5 pounds in the 0.58" wall size. The boom and other hardware, if carefully chosen and constructed will about double to total weight, for a 15-pound package. Because the hardware needs--including the boom, boom-to-element mounts, and boom-to-mast mount--will not substantially change for the smaller versions of the antenna, expect a 10-pound 10-meter Moxon and a 12-pound 15-meter version.

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The first stop along our examination of details consists of the corner assemblies. The 9" lengths of tubing will be variable according to the exact lengths of the tubing from the center-line (boom) to the element end. A 6" 0.5" diameter tube is permanently attached with stainless steel hardware to the linear section of the element--both to the long element and to the tail piece. Hitch pins position the junctions and also hold down a length of non-conductive strap or bar that holds the corner square during use. Two small plates make up the corner hinge that allows the piece to fold for storage and transport. The folding corner's chief advantage is storage compactness.

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The drawback of the folding corner is the need for tools to tighten the corner. You might well replace the type of corner shown with a section of bent 0.5" diameter aluminum. If you choose this route, be certain that the straight and curve sections of each element add up to the correct overall element length shown in the chart of dimensions. The total driver length is A + (2 x B), while the total reflector length is A + (2 x D). Bending aluminum tubing to 90 degrees requires some care. Fill a piece longer than the final dimensions with play sand, the finer the better. Many benders warm the aluminum and sand to the point where they can just handle the piece with gloves. Make up a form (or use a suitable solid circular piece among the "found-objects" in the shop). Pin down one end of the tube. Bend slowly in small increments until the piece reaches a slightly tighter angle than the 90 degrees. It is easier to slightly unbend the cooled piece than to add to the curve later on.

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The bent corner requires no brace. Hitch pine holes aligned with the inserted junction pieces are the final step in shop work--except for the labeling. Four corners with hitch pin holes of slightly different alignments can become a frustrating field exercise if not labeled for easy selection.

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Detail 2 shows the general junction scheme used throughout the portable design. 0.5" diameter tubing forms each junction piece. The inward section of the long element portions and that tail pieces use appropriate hardware for permanent connection. The more outward tubing or the corner section gets a hitch pin hole. Create the hitch pin holes by first ensuring a tight butt joint at the ends of the 5/8" tubing section to be joined. Then drill carefully through both the inner and outer tubing all the way through the "top" and "bottom" of the junction. If the drill bit will pass though both holes, the hitch pin straight side will also fit.

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Detail 3 shows the tail assemble, although not to scale. For the 20-meter Moxon, obtain about 36" of rigid or nearly rigid tubing with a true outside diameter of 0.5". (Measure any tubing that lists its dimensions as "nominal," since such materials tend to use pipe dimensions and only a measuring device will show the true outside diameter.) 18" per tail will hold the ends of the 20-meter Moxon tails the correct distance apart while maintaining alignment. Since the driver tail will be shorter, the permanent hardware goes on that side, with the hitch pin applied to the reflector tail portion. Since you need a similar assembly on each side of the array, good labeling is important.

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Detail 4 reveals that the Moxon requires a split feed mount that insulates and isolates the elements from the boom. A 1/4" thick polycarbonate plate provides the strongest plate for this service. It can be any length and width that will fit the need. For the feedpoint plate, be sure there is room for a small aluminum bent piece to hold a coax connector and leads to the tubing on each side of the plate.

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Since the plate shown uses U-bolts, obtain a polycarbonate or fiberglass rod to fit within the tubes. Such a rod keeps the tubes aligned, thus reducing the number of U-bolts required. It also prevents the tubing from collapsing under the pressure of tightened U-bolts.

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For storage, the system shown in Detail 4 and repeated in the alternative figure has a disadvantage. It requires tools to loosen at least one side of the assemble so that you can disassemble one of the 69" element sections. (Remember that 69" is approximate and depends on how you apportion the subsections of the parallel element portions.) The alternative construction shown in the lower portion of the figure uses a shorter length of non-conductive rod. Its function is to align the tubing ends and to provide a base for hardware that allows connection to the coax receptacle.

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The alternative center mount uses portions of the first long-element section with a cut-off just beyond the feedpoint plate. To strengthen the inner portion of the 20 meter elements, a full 6' length of 0.5" tubing runs the entire length of the element and forms the junction inside the feedpoint assemble as well as the junction with the next outward section of tubing. The long tube holds the permanent hardware, with hitch pins on the other side of each junctions. The sketch shows the positions of the pins, but not their orientation. The hitch pin at the feedpoint plate should be parallel to the face of the plate.

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Although somewhat more complex to construct, the alternative feedpoint plate assembly can now remain fully constructed with no need for tools at the field site. Hitch pins do the work.

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Detail 5 shows the corresponding reflector plate. As shown, the plate will require tools to loosen one of the element U-bolts. For a no-tool assembly job at the field site, revise the sketch to resemble the alternative feedpoint plate, but with a 0.5" junction tube instead of the fiberglass or polycarbonate rod. Of course, the coax connector is irrelevant to the reflector.

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The final detail (6) concerns the boom and the boom-to-mast mount. I recommend nested sections of 1.25" and 1.125" aluminum if the wall is 0.58" thick. Single thickness tubing might work, but is subject to distortion under the pressure of U-bolts. For 20 meters, we need 9.5 to 10 feet of boom. To create such a boom, use a 6' length of each size tubing and a shorter (3.5' to 4') length. Alternate their placement and position with hitch pins. The pins allow disassembly for storage as lengths no more than 6' long--roughly that same as the longest element pieces. The boom-to-mast plate can be either 1/8" thick aluminum or 1/4" polycarbonate. U-bolts should be stainless steel. Saddles are useful in preventing slippage and tubing distortion.

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Storage, Transport, and Use

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There is nothing magic in the suggested construction of the portable Moxon rectangle. Feel free to adapt and revise as you wish--and you may well have ideas to improve the techniques suggested here. The two key goals are these:

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1. Keep to an absolute minimum the number of tools needed at the field site to assemble and disassemble the antenna. Murphy's Law dictates that you will forget to bring the one key tool you need to complete the assembly. Keep Murphy at bay by developing the antenna so that it needs no tools at all--or only a small steel rod (sometimes called a screwdriver) to free the hitch pins after use.

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2. Keep the storage package as short and small of girth as possible. The 6' tubing lengths, plus fixed extensions for junctions, dictates one dimension. The stack of well-labeled tubes has a certain girth when bound together. The folding corners add least to the girth of a round stack, but bent tubes might well be accommodated with a flatter storage scheme.

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Develop some sort of storage container. Canvass or similar material works well. Be certain that the hardware fits in a well-marked and hard-to-lose bag or box--with extra pins. If your assembly needs a few tools, purchase a few inexpensive tools especially for the antenna and store them with the aluminum and hitch pins.

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I have made no comments on the mast assembly, since the options are too many and often are site-specific. However, try to raise the Moxon rectangle as high as safely feasible. For 20 meters, the approximate minimum recommended height is about 3/8 wavelength or 26' above ground. At this height and above, the SWR curve will be very stable.

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Fig. 10 shows the band-edge and band-center azimuth pattern at the take-off angle for the array at a height of 26' on 20 meters. At 3/8 wavelength, the TO angle is 35 degrees, but drops to about 26 degrees when the antenna is 1/2 wavelength up. The lower height, however, is often satisfactory for field use, since the vertical lobe of the far-field pattern is very broad, with usable radiation down to 10 to 15 degrees elevation. As well, at 3/8 wavelength height, as the figure shows, the front-to-back ratio is excellent for a two-element array.

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These notes are only a set of ideas on the construction of a truly portable Moxon array for 20 through 10 meters. The hitch pin is a much overlooked fastener that can simplify field assembly and disassembly. However, it requires the tubing itself to make the electrical contact at the junctions. If you clean the tubing (with a plastic abrasive pad, not steel wool or other scarring materials) before each use, electrical contact should pose no problems.

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For permanent installations involving long term exposure to weather and the chemical soup called the atmosphere, use other connection methods and a stronger basic design.

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However, for short-term field operations, the construction ideas shown here and supplemented by your own knowledge of materials and hardware can produce a truly portable Moxon rectangle--or almost any other type of array you wish to carry into the field.

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Updated 02-01-2003. © L. B. Cebik, W4RNL. This item appeared in AntenneX, January, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: HF Upper, Moxon, Portable


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Using Moxon Rectangles for WARC-Band Antennas
+ Part 2: Some 30-17-12 Meter Ideas

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L. B. Cebik, W4RNL

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Last month we looked at the Moxon rectangle, cut for 17 meters, as the basis for a very compact dual-band Moxon-Yagi for 17 and 12 meters. The design used open-sleeve coupling between the physically driven 17-meter driver and the slaved 12-meter driver. The Yagi portion was a standard driver-director design with about 0.07 wavelength spacing. The result was a two-band array about 10' long and 20' wide that provided over 6 dBi free-space gain, better than 20 dB front-to-back ratio, and a direct feed with 50-Ohm coax (with, as always, a recommended choke or 1:1 balun to attenuate common-mode currents).

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Compactness: this goal was one of the good reasons for using a Moxon as the basis for the dual band beam. The width of a Moxon is only about 70% that of a full size Yagi with a driver and reflector, and the Moxon uses no loading to achieve the shortening. Instead, it bends the elements around to point toward each other. By selecting the correct proportions and tip-to-tip spacing, one can obtain a parasitic driver-reflector array with nearly the gain of the full size Yagi and considerably improved front-to-back ratio over the Yagi. Part of the reason for the excellent front-to-back performance lies in the current magnitude and phasing on the rear element relative to the front element: they are close to what one might obtain with each element driven to perfection for maximum rearward rejection.

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Fig. A provides an outline sketch of a basic Moxon, a refresher. As well, the portions of the Moxon structure are identified, since we shall once more provide some design ideas involving this antenna. However, this month, we shall include 30 meters.

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A 30-meter Yagi with unloaded elements would be about 48' to 49' side-to-side. A Moxon rectangle for 30 meters requires only 35' of side-to-side space, and about 13' front-to- back. These dimensions are close to those for a common 20-meter beam. The structure of a 30-meter Moxon might have to be a bit beefier than that of a 20-meter Yagi, since the parallel element must support the "tails" (B and D in Fig. A). Nonetheless, for those with space limitations, 35' elements are usually easier to sustain than 48' elements.

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A 30-17 m Combination

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When we examined the possibilities for 17 and 12 meters, we reached two practical conclusions. First, a dual Moxon array may be too sensitive to minor variations to be truly practical for home building. Second, placing a full size 12-meter Yagi of driver- reflector design inside the 17-meter Moxon was not feasible due to the length of the 12- meter elements--especially the reflector.

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Therefore, we shall bypass a dual Moxon for 30 and 17 meters. However, we shall not forego the possibility of a full-size 17-meter Yagi placed within the frame of a 30-meter Moxon. The longest element of a driver-reflector Yagi for 17 meters is 27' and that should be no problem within the 35' dimension of the 30-meter Moxon. Fig. 1 shows the general outline of the combination.

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The following table of dimensions uses the designators of Fig. A for the Moxon. The Yagi element spacing entries are distances from the Moxon driver. All dimensions are in feet. The Moxon elements are 1.25" aluminum tubing, while the Yagi elements are 1" diameter aluminum tubing.

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Band              Dimension         Length (feet)
+30-meter Moxon    (all elements use 1.25" diameter aluminum tubing)
+Moxon             A                 34.91'
+                  B                  4.89'
+                  C                  1.12'
+                  D                  6.56'
+                  E                 12.57'
+17-meter Yagi     (all elements use 1.0" diameter aluminum tubing)
+Driver            Length            25.80'
+                  Space              1.30'
+Reflector         Length            27.00'
+                  Space              8.00'
+

The spacing between the Yagi elements is 6.7' or about 1/8 wavelength. The spacing of the Moxon elements is about 0.13 wavelength. The Moxon dimensions are unchanged from those optimized for maximum front-to-back and a 50-Ohm feed when used independently. Of course, changes in material dimensions or the use of stepped-diameter elements will require readjustment of the design to yield satisfactory performance. As I did last month, I shall place model descriptions at the end of these notes for those who wish to experiment with other material combinations.

+

However, once the basics are established, the only post-construction adjustment will be to the slaved 17-meter driver. Its exact length and spacing from the Moxon driver will determine the feedpoint impedance on 17 meters at the physical feedpoint.

+

The Moxon-Yagi combination is a very well-behaved. The following performance table, listing the gain in terms of free-space gain, gives a good general picture.

+ 
Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+10.100            6.21          22.9                  47.6 - j 3.6      1.09
+10.125            6.13          27.0                  50.7 - j 1.4      1.03
+10.150            6.05          33.4                  53.7 + j 0.6      1.07
+
+18.068            6.37          10.8                  52.4 - j22.5      1.55
+18.118            6.26          10.9                  49.9 - j 5.4      1.11
+18.168            6.16          10.9                  47.5 + j10.9      1.26
+

As we saw last month, the addition of a closely-spaced parasitic beam slightly detunes the Moxon in terms of moving the peak front-to-back ratio upward in frequency. However, the gain and the source impedance are mostly unaffected. Fig. 2 provides a free-space azimuth pattern of the 30-meter Moxon performance at mid-band. One of the side-benefits of the Moxon rectangle design is that it tends to hold its high front-to-back ratio even down to a height of 3/8 wavelength--about 36' on 30 meters. Of course, the old rule that higher is better still applies. Nevertheless, even a modest installation can expect quite reasonable results on 30 meters.

+
+ +
+

On 17 meters, we must expect the lesser front-to-back ratio associated with the driver- reflector Yagi design. Fig. 3 shows the mid-band free-space azimuth pattern for the array at 18.118 MHz.

+
+ +
+

Because the upper band Yagi is behind and within the Moxon rectangle, there is no significant forward-stagger effect. Hence, the Yagi gain and front-to-back ratios are virtually identical to those one might obtain from an independent driver-reflector Yagi for 17 meters. However, with 1/8 wavelength spacing, the feedpoint impedance of an independent Yagi would be closer to 35 Ohms. The near-50-Ohm match is obtained by virtue of the open-sleeve coupling, which can be set for virtually any desired impedance by changes in the length and/or spacing of the driver relative to the physically fed element. As we saw last month, the impedance changes more rapidly on a slaved element than on a directly fed element. In the case of the 17-meter Yagi, it is the reactance that undergoes the most rapid change, while the resistance remain quite stable.

+

Although the 17-meter Yagi does not gain anything from being inside the Moxon, it does not lose anything either. Moreover, it does not take up an additional space on a supporting tower. The two-band array has identically the same outside dimensions as the 30-meter Moxon itself. Except for the additional weight and wind load of the 17-meter elements, there seems little reason not to add the upper band if one seriously plans a 30-meter Moxon.

+

A 30-17-12 m Combination

+

Suppose we might be willing to extend the boom of the Moxon-Yagi from 12.6' to about 16 feet. For the additional 3.4' of boom length, we add one more band to the array--with virtually no change in the design work done so far. A driver-director Yagi with an element spacing of about 0.07 wavelength can be added ahead of the Moxon driver to arrive at a WARC 3-band array of considerable compactness. Fig. 4 shows the general outline of the arrangement.

+
+ +
+

For the lower bands, the design once more uses 1.25" diameter elements for 30 and 1" diameter elements for 17. The 12-meter elements are 0.5" in diameter, and everything is aluminum. With these materials we can uses the dimensions in the table below. For the 17-meter elements, the spacing entry indicates the distance behind the Moxon driver. For 12 meters, the spacing entry indicates the element spacing forward from the Moxon driver.

+ 
Band              Dimension         Length (feet)
+30-meter Moxon    (all elements use 1.25" diameter aluminum tubing)
+Moxon             A                 34.91'
+                  B                  4.89'
+                  C                  1.12'
+                  D                  6.56'
+                  E                 12.57'
+17-meter Yagi     (all elements use 1.0" diameter aluminum tubing)
+Driver            Length            25.80'
+                  Space              1.30'
+Reflector         Length            27.00'
+                  Space              8.00'
+12-meter Yagi     (all elements use 0.5" diameter aluminum tubing)
+Driver            Length            19.46'
+                  Space              0.70'
+Director          Length            18.70'
+                  Space              3.43'
+

For the Moxon and the 17-meter Yagi, nothing has changed. The dimensions of the 12-meter Yagi are very slightly different from those used with the 17-meter Moxon last month. However, that Moxon used elements with a smaller diameter than the 30-meter Moxon in this design. The major change is in the spacing from the Moxon to the 12-meter slaved driver--somewhat wider than in the 12-17 design.

+

If we see little difference in dimensions, we should also expect little difference in performance. The following performance table provides the numbers.

+ 
Frequency         Gain        Front-to-Back           Feedpoint Z       50-Ohm
+  MHz              dBi         Ratio  dB              R+/-jX Ohms       VSWR
+
+10.100            6.23          22.5                  48.5 - j 4.9      1.11
+10.125            6.15          26.3                  51.7 - j 2.8      1.07
+10.150            6.07          32.1                  54.9 + j 0.9      1.10
+
+18.068            6.40          11.3                  53.3 - j16.3      1.38
+18.118            6.31          11.4                  51.3 - j 1.2      1.04
+18.168            6.21          11.4                  49.4 + j13.6      1.31
+
+24.89             6.57          25.3                  59.4 - j 9.9      1.28
+24.94             6.67          22.1                  48.7 + j 3.4      1.08
+24.99             6.76          19.2                  38.9 + j18.5      1.62
+

On 30 meters, performance only shows insignificant changes in the last decimal places of the performance figures. On 17 meters, the performance values are numerically up, but again, not in a way that makes a difference that one could detect in use. The numeric increase is due in part to the forward stagger effect that gives the 12-meter elements a slight director effect during 17-meter operation.

+

On 12 meters, the 2-element driver-director array performs normally for an antenna of this type, although the independent feedpoint impedance of about 20 Ohms is overcome by slaving the driver to the 30-meter Moxon driver. Last month we saw higher gains on 12 meters. However, the 30-meter driver is farther removed from the 12-meter elements and provides some isolation of them from the interior 17-meter elements. Hence, forward stagger effects are minimal.

+

Nonetheless, for a beam with a 16' boom length, the tri-band Moxon-Yagi offers excellent potential. Fig. 5 shows the free-space azimuth pattern at 10.125 MHz.

+
+ +
+
+ +
+

In Fig. 6, we see essentially the same pattern as in Fig. 3 for the middle of 17 meters. The 12-meter free-space azimuth pattern for 24.94 MHz (Fig. 7) is similar to the one shown for 12 meters last month. The same rear quartering lobes are present to moderate the 180-degree front-to-back ratio.

+
+ +
+

The exact spacing and length of the slaved drivers will require field adjustment to arrive at a final setting to achieve a good 50-Ohm match on each band. However, those adjustments are about the only critical matters related to construction--once you decide on and design for the precise set of materials you will use. Essentially, you can design an independent Moxon for 30 meters and adjust it to perfection. Then, you can add the 17-meter elements and perform driver adjustments until you are satisfied. Rechecking the 30-meter impedance should show no significant change. Finally, add the 12-meter elements and adjust its driver for a good match on that band. Because element spacing is a bit more critical for driver-director arrays than for driver-reflector Yagis, recheck the element spacing for 12 meters before concluding the adjustment procedure. Once more, the impedances for 30 meters and 12 meters should not have significantly changed by adding the 12-meter elements.

+

I have good luck in adjusting Moxons and simple Yagis close to the ground by pointing the array as close to straight up as possible, with the reflector anywhere from 4 to 12 feet off tghe ground. The adjustments have held true at heights from 20 to 35 feet up. This technique is not applicable for all beams, but it is worth a try for those who do not relish adjusting beam elements from the top of a tower.

+

In 2006, Charles Johnson, K4ZRJ, built a version of the 3-band antenna. Fig. 8 shows the antenna mounted above his tribander. Charles used parts originally designed for the Hy-Gain 203BA for his version of the antenna. He reports good results with the antenna, and his workmanship is very evident from the photo that I have included with his permission.

+
+ +
+

Charles used a taper schedule for the aluminum tubing that required him to modify the design somewhat. The EZNEC listings show his model for the design that he produced. If you use different materials, you may have to redesign the element sections to suit those materials.

+

For those who wish to do further design work on models of the two basic antenna designs, here are model descriptions that should ease wire coordinate entries for most NEC modeling software.

+ 
30-17 m Moxon-Yagi                           Frequency = 10.125/18.118  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1          -17.457, -4.888,  0.000  W2E1 -17.457,  0.000,  0.000 1.25E+00   7
+2     W1E2 -17.457,  0.000,  0.000  W3E1  17.457,  0.000,  0.000 1.25E+00  45
+3     W2E2  17.457,  0.000,  0.000        17.457, -4.888,  0.000 1.25E+00   7
+4          -17.457, -6.005,  0.000  W5E1 -17.457,-12.569,  0.000 1.25E+00   9
+5     W4E2 -17.457,-12.569,  0.000  W6E1  17.457,-12.569,  0.000 1.25E+00  45
+6     W5E2  17.457,-12.569,  0.000        17.457, -6.005,  0.000 1.25E+00   9
+7          -12.900, -1.300,  0.000        12.900, -1.300,  0.000 1.00E+00  33
+8          -13.500, -8.000,  0.000        13.500, -8.000,  0.000 1.00E+00  33
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+
+30-17-12 m Moxon-Yagi                        Frequency = 10.125/18.118/24.94  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1          -17.457, -4.888,  0.000  W2E1 -17.457,  0.000,  0.000 1.25E+00   7
+2     W1E2 -17.457,  0.000,  0.000  W3E1  17.457,  0.000,  0.000 1.25E+00  45
+3     W2E2  17.457,  0.000,  0.000        17.457, -4.888,  0.000 1.25E+00   7
+4          -17.457, -6.005,  0.000  W5E1 -17.457,-12.569,  0.000 1.25E+00   9
+5     W4E2 -17.457,-12.569,  0.000  W6E1  17.457,-12.569,  0.000 1.25E+00  45
+6     W5E2  17.457,-12.569,  0.000        17.457, -6.005,  0.000 1.25E+00   9
+7          -12.900, -1.300,  0.000        12.900, -1.300,  0.000 1.00E+00  33
+8          -13.500, -8.000,  0.000        13.500, -8.000,  0.000 1.00E+00  33
+9           -9.730,  0.700,  0.000         9.730,  0.700,  0.000 5.00E-01  25
+10          -9.350,  3.430,  0.000         9.350,  3.430,  0.000 5.00E-01  25
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+Version designed and built by Charles Johnson, K4ZRJ:
+
+                      EZNEC/4 ver. 4.0
+
+30,17,12 M Moxon Yagi Combo                   Frequency = 10.125/18.118/24.94  MHz.
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs       Insulation
+          Conn.      X       Y       Z       Conn.      X       Y       Z                   Diel C  Thk(in) Loss Tan
+1          W8E1     -222,  196.9,    816      W2E1     -189,  196.9,    816     0.438   7       1        0        0
+2          W1E2     -189,  196.9,    816      W3E1     -109,  196.9,    816     0.875   13      1        0        0
+3          W2E2     -109,  196.9,    816      W4E1   -2.925,  196.9,    816      1.25   17      1        0        0
+4          W3E2   -2.925,  196.9,    816      W5E1    2.925,  196.9,    816      2.14   3       1        0        0
+5          W4E2    2.925,  196.9,    816      W6E1      109,  196.9,    816      1.25   17      1        0        0
+6          W5E2      109,  196.9,    816      W7E1      189,  196.9,    816     0.875   13      1        0        0
+7          W6E2      189,  196.9,    816      W9E1      222,  196.9,    816     0.438   7       1        0        0
+8          W1E1     -222,  196.9,    816               -222,  117.1,    816     0.438   13      1        0        0
+9          W7E2      222,  196.9,    816                222,  117.1,    816     0.438   13      1        0        0
+10                -173.5,  138.5,    816     W11E1     -106,  138.5,    816     0.438   13      1        0        0
+11        W10E2     -106,  138.5,    816     W12E1      -49,  138.5,    816     0.875   13      1        0        0
+12        W11E2      -49,  138.5,    816     W13E1   -2.925,  138.5,    816         1   9       1        0        0
+13        W12E2   -2.925,  138.5,    816     W14E1    2.925,  138.5,    816      2.14   3       1        0        0
+14        W13E2    2.925,  138.5,    816     W15E1       49,  138.5,    816         1   9       1        0        0
+15        W14E2       49,  138.5,    816     W16E1      106,  138.5,    816     0.875   13      1        0        0
+16        W15E2      106,  138.5,    816              173.5,  138.5,    816     0.438   13      1        0        0
+17                  -162,   57.1,    816     W18E1     -106,   57.1,    816     0.438   13      1        0        0
+18        W17E2     -106,   57.1,    816     W19E1      -49,   57.1,    816     0.875   13      1        0        0
+19        W18E2      -49,   57.1,    816     W20E1   -2.925,   57.1,    816         1   9       1        0        0
+20        W19E2   -2.925,   57.1,    816     W21E1    2.925,   57.1,    816      2.14   3       1        0        0
+21        W20E2    2.925,   57.1,    816     W22E1       49,   57.1,    816         1   9       1        0        0
+22        W21E2       49,   57.1,    816     W23E1      106,   57.1,    816     0.875   13      1        0        0
+23        W22E2      106,   57.1,    816                162,   57.1,    816     0.438   13      1        0        0
+24        W31E1     -222,   41.5,    816     W25E1     -189,   41.5,    816     0.438   7       1        0        0
+25        W24E2     -189,   41.5,    816     W26E1     -109,   41.5,    816     0.875   13      1        0        0
+26        W25E2     -109,   41.5,    816     W27E1   -2.925,   41.5,    816      1.25   17      1        0        0
+27        W26E2   -2.925,   41.5,    816     W28E1    2.925,   41.5,    816      2.14   3       1        0        0
+28        W27E2    2.925,   41.5,    816     W29E1      109,   41.5,    816      1.25   17      1        0        0
+29        W28E2      109,   41.5,    816     W30E1      189,   41.5,    816     0.875   13      1        0        0
+30        W29E2      189,   41.5,    816     W32E1      222,   41.5,    816     0.438   7       1        0        0
+31        W24E1     -222,   41.5,    816               -222, 103.25,    816     0.438   13      1        0        0
+32        W30E2      222,   41.5,    816                222, 103.25,    816     0.438   13      1        0        0
+33                  -122,   33.1,    816     W34E1      -73,   33.1,    816     0.438   9       1        0        0
+34        W33E2      -73,   33.1,    816     W35E1   -2.925,   33.1,    816     0.875   13      1        0        0
+35        W34E2   -2.925,   33.1,    816     W36E1    2.925,   33.1,    816      2.14   3       1        0        0
+36        W35E2    2.925,   33.1,    816     W37E1       73,   33.1,    816     0.875   13      1        0        0
+37        W36E2       73,   33.1,    816                122,   33.1,    816     0.438   9       1        0        0
+38                  -117,      0,    816     W39E1      -73,      0,    816     0.438   9       1        0        0
+39        W38E2      -73,      0,    816     W40E1   -2.925,      0,    816     0.875   13      1        0        0
+40        W39E2   -2.925,      0,    816     W41E1    2.925,      0,    816      2.14   3       1        0        0
+41        W40E2    2.925,      0,    816     W42E1       73,      0,    816     0.875   13      1        0        0
+42        W41E2       73,      0,    816                117,      0,    816     0.438   9       1        0        0
+
+Total Segments: 446
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       27       50.00      50.00    2        1           0         V
+
+

The 30-17 or the 30-17-12 combination arrays offer some interesting potentials for small WARC band beams. These design notes aim to whet your appetite for further and improved designs. However, you will have to go some to improve performance on all bands while shrinking the size of these arrays. However, if you do manage the trick, I'd be first in line to find out how.

+
+ +
+

Updated 06-01-2000, 07-04-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Moxon Index

+

Go to Main Index

+

Topics: HF Lower, HF Upper, Moxon, Yagi


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+

40 + 30 = 50 (Not 70)
+ The Rudiments of a Design Idea

+

+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

A number of requests over the years have taken this direction: can you design a combination 40 meter and 30 meter beam on a single boom--making everything give full-size performance but still be compact--relative to the bands involved?

+

That request is a tall order. Full size Yagi elements for 40 meters run over 70' in length. Most commercial Yagis for 40 meters use various methods of element shortening to reduce the raw physical load created by full size elements. Linear and inductive loading are the two most popular approaches. However, there are a number of 3 and 4 element full size Yagis on the job. (Very often, the 4th Yagi element functions less to increase gain and more to permit a wide operating bandwidth.)

+

30-meter elements are more modest at lengths approaching 45-50'. As well, the band is narrow enough (50 kHz) to permit the use of narrow-band, high performance driver-director Yagis. A beta match usually suffices to bring the low feedpoint impedance up to standard coax levels. (Of course, we should not overlook the relatively compact phased array for 30 meters developed by N7CL.)

+

It would be nice if a combined 40 and 30 array could have elements that extended no further outward than the +/-25' required for 30-meter elements. There is a way of achieving this goal, but it is not likely to be an easy one to implement in a physical design. There are some adjustments that require field implementation, and they can be a bit daunting. As well, supporting the number of elements in the final array, along with their peculiarities, will also require engineering beyond the scope of this design exercise. However, for whatever it may be worth, here is a design that will cover all of both bands with only a 50' side-to-side width.

+

These note can only be the rudiments of a design and not a finished product. Because I do not have the facilities or tower to build and test the array, I cannot complete all of the mechanical details that will also have an impact on the electrical design. At best, I can only locate some of the many points where the individual designer and builder will have to make decisions and refine the outlines given here.

+

The basic design consists of a Moxon rectangle for 40 meters with a 2-element driver-director Yagi for 30 meters. The 30-meter driver is slaved to the 40-meter Moxon fed element. Fig. 1 shows a general outline sketch of the array.

+
+ +
+

The maximum side-to-side width of the array is 50'. The boom length is 26' (plus whatever excess is necessary for proper element support). There are a total of 4 elements, with the Moxon elements having end tails that point toward each other. The Moxon element arrangement will present physical problems that we shall take up later.

+

Fig. 1 labels each dimension, and the following table provides numbers that go with the labels. However, the dimensions are based on NEC-4 models of the array using 1" diameter aluminum elements throughout. I chose the modeling diameter based upon the equivalent uniform diameter of elements from a number of 40-meter arrays on file. Although such arrays begin with large diameter tubing--sometimes up to 3"--they step downward rapidly and end up with 0.5" and even 0.375" element diameters at the outer ends. We shall go into the meaning of this situation for practical antenna construction before we are done. First, some basic dimensions.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 40-30-Meter Moxon-Yagi Combination Dimensions
+
+Note: all dimensions are in feet and correspond to designations shown in Fig. 1.
+
+            Dimension         Length in Feet
+                  A           50.00'
+                  B            7.21'
+                  C            1.73'
+                  D            9.47'
+                  E           18.41'
+                  F            0.64'
+                  G            6.95'
+                  H           26.00'
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Before we look into the dimensions and their implications for refinement and construction, let's first see if this is a design in which you would be interested by virtue of its performance. The 40-meter performance is strictly Moxon-rectangle standard. One of the reasons for using fatter elements (instead of wire) is to increase the operating passband width, not just in terms of SWR, but as well, to include a spreading of the gain and front-to-back profiles.

+
+ +
+

Fig. 2 provides azimuth and elevation plots for the 40-meter array at the edges and middle of the band. The antenna height is 70' or about 1/2 wavelength on 40. I would not recommend using the array below 70' or else you will have to make some adjustments to center the SWR curve. Like every Moxon rectangle, the beamwidth tends to be wider than that of most Yagis.

+
+ +
+

Fig. 3 provides band edge and center patterns for 30 meters, which are mostly a function of the forward two elements. However, the 40-meter elements also function in a minor way as reflectors to increase the overall performance. (We determine this in part by the current levels on the Moxon elements and also by the increase in performance over a stand-alone 2-element driver-director Yagi of the same spacing.) A 2-element driver director Yagi with closely spaced elements (less than 0.08 wavelength) yields quite high gain and a good front-to-back ratio, but only over a narrow bandwidth. Being "slaved" to the Moxon rectangle (or any other fed array) tends to further reduce the operating bandwidth. Only the narrowness of 30 meters permits good performance (for an array of this type) across the entire band.

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To translate the patterns into more definite numbers, the following table gives the principal operating predictions from the model.

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+                  40-30-MHz Array Operating Potential at 70'
+
+Freq.       Gain        180-Deg/Worst-Case      Feedpoint Z       50-Ohm
+ MHz        dBi         Front-to-Back dB        R +/- jX Ohms     SWR
+40 Meters:  TO/Elevation Angle of Maximum Radiation:  26 degrees
+ 7.0        11.29       13.32--13.32            41.3 - j22.1      1.68
+ 7.1        11.14       20.37--20.37            67.3 - j12.9      1.49
+ 7.2        10.90       15.99--15.73            85.3 - j16.8      1.80
+ 7.3        10.66       12.17--12.17            91.7 - j21.2      1.97
+30 Meters:  TO/Elevation Angle of Maximum Radiation:  19 degrees
+10.0        11.50       16.35--14.25            84.0 + j10.4      1.72
+10.125      12.05       24.76--18.18            42.9 + j 3.1      1.18
+10.15       12.17       22.47--19.43            32.3 + j 8.7      1.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The take-off angles for the two bands, of course, are functions of the fact that, with respect to a wavelength, the antenna is higher on 30 meters than on 40 meters. Only part of the extra 30-meter gain is attributable to the increased height. Most of it stems from the fact that a closely spaced driver-director Yagi in fact has more gain than the Moxon rectangle or a comparably spaced driver-reflector Yagi.

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The key influences of the arrays on each other show up in the impedance reports. The slaved 30-meter driver keeps the Moxon feedpoint reactance capacitive in this array, when an independent Moxon might well show a shift from capacitive to inductive reactance across the band. The slaved 30-meter driver also affects the feedpoint impedance on the 40-meter element during 10-MHz operation, creating a dip in the inductive reactance at mid-band, but not going into the capacitive region. Expect impedance curves in an actual antenna that may even vary from these, according to the finally selected dimensions used in the array.

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Fig. 4 provides both 50-Ohm SWR curves on one graph. It is unlikely that one can change the 30-meter curve much, except to move it a bit up and down the narrow band. The Moxon 40-meter curve might well show improvement with careful adjustment of some of the dimensions.

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One cannot simply buy a batch of 1" diameter tubing and construct this array. The first task for any builder is to determine the stepped-diameter schedule to be used. For the 4 elements, the first portions up to 25' from center can all be identical, assuming that the smallest diameter tubing used allows sufficient strength to support the tails.

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Once you have selected a mechanically sound element taper schedule, the best procedure is then to convert the uniform 1" diameter element lengths into lengths suitable for the stepping schedule. It is very likely that you will have to lengthen all side-to-side dimensions with the tubing that you use. Elements that taper downward from center to outer end usually require greater length than uniform diameter elements. The differential may amount only to a few inches, but it will be enough to detune both portions of the array considerably if not taken into account.

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There are handbook formulas for making the transformation of element lengths. However, one of the most convenient methods is to create a model on a NEC program and adjust the element tip lengths until you arrive at uniform-diameter equivalents that match the initial design. If the equivalent uniform element diameter is between 0.8 and 1.2 inches, the original dimensions will not require much adjustment. However, feel free to customize the design to your own desires. Both EZNEC and NEC-Win Plus have provisions for creating uniform-diameter substitute elements for unloaded symmetrical elements using a tapering schedule.

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In the Moxon portion of the array, perhaps the most critical dimension is the gap between element tails. The Moxon makes use of 2 forms of elements coupling to achieve its patterns and impedance: mutual coupling between the element portions parallel to each other and end coupling between the tails. The degree of end coupling depends upon 2 factors: the space between the tail ends and the diameter of the elements at that point. The initial design makes use of 1" diameter tail ends, but a tapered-element schedule is likely to use smaller diameter tubing for the tail ends. Therefore, to achieve the same coupling with smaller tubing, the tails will need to be brought closer together--without significantly changing the overall final design length of the reflector element (including the parallel and tail sections). Incidentally, one cannot use the tapered-diameter correction facility in NEC-2 programs with the Moxon rectangle, since the elements are not linear. However, one can use sundry work arounds to arrive at adequate construction guidance (including obtaining a NEC-4 program).

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To keep the tails aligned, it is very useful to use a section of non-conductive tubing that just fits inside the two tail end tubes. Since the goal is alignment rather than mechanical support, the tubing can be relatively light, such a CPVC or similar. We shall turn to mechanical support soon.

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The slaved 30-meter driver must be very close (0.64' in the model) to the 40-meter Moxon driver to achieve the desired feedpoint impedance. Several factors suggest that the element spacing will not be identical to the initial model used here. First, using a tapered diameter schedule will alter the coupling slightly along the length of both elements. Second, the model is reaching the limits for giving accurate reports with closely spaced elements of different lengths, even though the segment ends are closely aligned throughout the mode. This is a NEC limitation. Therefore, expect to make adjustments to the spacing of the slaved driver and to its length as well. At 30 meters, one can make several inches worth of adjustment without having to restore the director to the initial design spacing from the driver. However, finding the right combination of element spacing and length to achieve an acceptable 50-Ohm SWR curve on the main driver from 10.0 to 10.015 MHz can be laborious. Adjustments work best when the initial setting is somewhere close to ideal. When the elements are spaced too far apart, the progression of results for small adjustments seems to move in the opposite direction than when inside the ballpark. Hence, once can work for hours, being led all of the time in the wrong direction. When adjustments only seem to make matters worse, return to the starting point and begin again, but in the opposite direction as used during the first run.

+

Elements as large as those used in the array will tend to oscillate in the wind. Because the Moxon elements, with their tails, are constrained by the non-conductive tail links, the 40-meter assembly will have wind-motion characteristics quite unlike the 30-meter elements, with their free ends. Collisions between the 30-meter slaved driver and the 40-meter fed driver will be inevitable. Therefore, some means of holding the 30-meter slaved driver and the 40-meter Moxon driver in alignment is likely more a necessity than something merely desirable.

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Besides holding the drivers in alignment, we also need a means of supporting the 40-meter tails. The tail assemblies on a large Moxon rectangle place significant strain on the two elements supporting them. One method of support is to use tubing sizes large enough that the weight of the tails is no especial problem. Alternatively, one might develop a supplemental support system for the entire array that can reduce element stress and keep the elements aligned.

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Fig. 5 shows the basic outline of such a scheme. Somewhere (sensible, from a mechanical perspective) above the main boom, install a shorter stiff boom on the mast. This boom will be used to hold one end of a series of stays, that is, non-conductive support lines for the elements.

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At a mechanically sensible point outward on each side of center, place a non-conductive support arm (tube?) so that it is beneath each element. By a series of notches and/or ties, fastened to each element to the arm. Because there will still be differences in the way elements react to the wind, the tie system should be set to fix the spacing but to let the individual elements slide a bit. On one or more elements, fix the arm in both directions so that the stay-system does not pull the arm inward.

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At points near the out ends of the arms, connect and fasten the stays. If the arm material is too flexible, you may add a third set of stays perpendicular to the mast. The support system then depends on the equalization of tension on the stays.

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Without a set of specific load figures, derived from a program like YagiStress and customized to the particular element diameter schedule chosen for the array, it is impossible to recommend any particular set of dimensions for the support-arm-and-stay system. Indeed, there are many variations on this theme that one might apply to the array. However, the basic message is that this is a major collection of aluminum tubing that has considerable weight and wind area. Adequate support is a necessity if the design and construction effort goes for naught during the first stiff breeze.

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As we noted at the beginning, these notes only begin the design process; they do not complete it. I have tried to locate many of the areas that will need detailed attention before one can begin to gather materials, let along start actual construction.

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Nonetheless, the design principle is sound, having been applied to light arrays for the upper HF region. It does show that a combination 40-30-Meter array is possible with quite decent full-band performance for a 26' boom. Until I have facilities and space to try out the design with an actual set of elements on a tower that will give me the minimal height for adequate performance, these notes will have to do. Unfortunately, I do not have time at present to customize the design for specific taper schedules, but you can do the job yourself with any of the low-end NEC-2 programs with a facility for providing uniform-diameter equivalents. Even when the customizing has been completed within the design system, expect to do considerable adjustment on the physical product of this work.

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For those who wish to model the array, the following EZNEC model description should suffice to create a model in any of the leading programs.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+40-30-M Moxon-Yagi Array                     Frequency = 7.1  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+(40-meter elements)
+1          -25.000, 11.200, 70.000  W2E1 -25.000, 18.406, 70.000 1.00E+00   7
+2     W1E2 -25.000, 18.406, 70.000  W3E1  25.000, 18.406, 70.000 1.00E+00  45
+3     W2E2  25.000, 18.406, 70.000        25.000, 11.200, 70.000 1.00E+00   7
+4          -25.000,  9.472, 70.000  W5E1 -25.000,  0.000, 70.000 1.00E+00   9
+5     W4E2 -25.000,  0.000, 70.000  W6E1  25.000,  0.000, 70.000 1.00E+00  45
+6     W5E2  25.000,  0.000, 70.000        25.000,  9.472, 70.000 1.00E+00   9
+(30-meter elements)
+7          -24.000, 19.050, 70.000        24.000, 19.050, 70.000 1.00E+00  43
+8          -22.900, 26.000, 70.000        22.900, 26.000, 70.000 1.00E+00  41
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          23     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Real, high-accuracy analysis
+Conductivity = .005 S/m    Diel. Const. = 13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Updated 10-20-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: HF Lower, Moxon, Yagi


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Moxon Rectangles for 6 Meters

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L. B. Cebik, W4RNL

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I have had numerous requests over the last few years for the dimensions and construction plans for Moxon rectangles designed for the 6-meter band. The Moxon rectangle is a quite broad-band antenna, but it is not quite broad enough to cover the entire band. As well, the lower end of the band is the major arena for horizontal polarization using CW or SSB. The upper portion of the band sees most of the FM activity, with vertical polarization being standard.

+

Hence, for full band coverage--or for selected use of one or the other mode of activity--we really need 2 Moxons. The first will be a horizontally oriented beam designed for 50.5 MHz with coverage of the first MHz of the band. The second will be a vertically oriented version designed for 53 MHz, with coverage from 52 to 54 MHz. After looking at the characteristics of these two versions of the same basic design, we shall make a few construction suggestions. Finally, we shall show how to combine them into a single array--but with separate feedlines.

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Fig. 1 shows the general outlines of the two types of Moxons. The Moxon is a driver-reflector type of parasitic array. Unlike standard Yagi designs that employ only the coupling between parallel lengths of element conductor, the Moxon folds back its elements to provide a second form of coupling. The coupling of the driver and reflector tails that face each other provides a second form of coupling, and the combination of the two gives us an array that we can design for very good front-to-back performance, about as much forward gain as a 2-element Yagi, and a 50-Ohm feedpoint impedance for direct connection of a standard coaxial cable feedline.

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Since we need a way to refer to the parts of a Moxon when giving dimensions, Fig. 2 supplies what has become a set of default designations. Dimension A is the total side-to-side dimension of the array. B is the driver tail or fold-back portion, and D is the reflector fold-forward portion or tail. C is the most critical dimension, the gap, and tends to vary as a direct function of the element diameter. E is simply the sum of B, C, and D, and gives us the total front-to-back dimension of the array.

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All 6-meter Moxons will be about 7' wide or about 3.5' each side of the center line. The front-to-back dimension with be about 2.5', plus or minus a little. Hence, the Moxon makes a very compact array, suitable for enhancing repeater communications or for SSB operation in local nets.

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In fact, the precise dimensions for a 50-Ohm Moxon for any frequency and element diameter have been developed into several computer programs, ranging from a GW Basic utility in the HAMCALC suite to a NEC-Win Plus model to a stand-alone Windows program developed by AC6LA and available for free download from his site (www.ac6la.com/moxgen1.html). Since all of them are based on the same modeling and regression analysis that I performed some time back, all will give the same dimensions for the same design frequency and element diameter.

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Let's start our foray into 6-meter Moxons with the low-end horizontal version.

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A Horizontal Moxon Rectangle for 50.5 MHz.

The materials that folks have access to will vary from region to region. Therefore, let's make a chart of dimensions. All of the dimensions will presume that we are using some form of aluminum tubing, ranging from 1.0" down to 0.25" in diameter. As we shall see in the construction section, aluminum tubing is an optimal choice for a 6-meter Moxon. +

In the following table, all dimensions refer to Fig. 2 and are in inches.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 50.5-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+      1.0             83.61      10.40      4.58       16.22      31.20
+      0.875           83.68      10.53      4.46       16.21      31.20
+      0.75            83.76      10.69      4.32       16.19      31.20
+      0.625           83.86      10.86      4.16       16.18      31.20
+      0.5             83.97      11.07      3.97       16.15      31.19
+      0.375           84.12      11.32      3.74       16.12      31.19
+      0.25            84.31      11.65      3.44       16.08      31.18
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that the dimensions change only a small amount from one tube diameter to the next. Moreover, the front-to-back dimension (E) changes almost not at all. However, the differences are important to centering the performance curve of the Moxon on the design frequency, which then has consequences for performance at the band edges. So using the dimensions that apply to the element diameter that you will use does have significance.

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Let's set the antenna 25' above ground, which is just over 1.34 wavelengths up. The forward gain will be about 11.4 dBi at 50.5 MHz, with a 180-degree front-to-back ratio of about 30 dB and a 78-degree beamwidth between -3-dB points. The feedpoint impedance of 50 Ohms, plus or minus 1 to 2 Ohms reactance.

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Fig. 3 overlays the design frequency and the passband edge azimuth patterns of the Moxon rectangle when oriented horizontally. As you can see from the patterns, taken for a version using a 0.5" diameter element set, as we move lower in frequency, the gain increases very slightly (too slightly to ever be measured in operation), and the rearward radiation begins to increase. Above the design frequency, the gain decreases by an equally slight amount, and, again, the rearward radiation pattern shows growth.

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The performance of the antenna is virtually unchanged at the design frequency for any tubing size. However, the band-edge performance does change (in this case, using a 1-MHz passband). The fatter the tubing, the slower the rate of forward gain change. More significantly, the fatter the tubing, the slower the growth of rearward radiation lobes both above and below the design frequency. However, those changes are not so great as to override considerations such as the most convenient tubing size for constructing a Moxon rectangle.

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Tubing size also makes a difference in the 50-Ohm SWR for the final antenna, as measured at the antenna terminals, as shown in Fig. 4. For a 1-MHz passband, almost any size tubing will do, and the SWR at the shack end of the coax is likely to be too low to get a definite frequency for the lowest value.

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A Vertical Moxon Rectangle for 53.0 MHz.

The design principles do not change at all when we flip the Moxon rectangle for upper 6-meter service. However, the dimensions will change, since we are now using a design frequency of 53.0 MHz in order to cover the 52-54-MHz range. The following table provides dimensions, again in inches and again using Fig. 2 as a reference. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 53.0-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+      1.0             79.64       9.86      4.41       15.46      29.73
+      0.875           79.71       9.99      4.29       15.45      29.73
+      0.75            79.79      10.14      4.16       15.44      29.73
+      0.625           79.88      10.31      4.00       15.42      29.73
+      0.5             79.99      10.50      3.82       15.40      29.72
+      0.375           80.13      10.75      3.60       15.37      29.72
+      0.25            80.31      11.07      3.31       15.33      29.71
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The last decimal place in column E, the overall front-to-back dimension, may be a digit or two off the sum of B, C, and D due to rounding of the individual values. However, I doubt that any builder will be constructing the elements to a hundredth of an inch tolerances. In fact, in the construction section, we shall be slightly altering the dimensions to take account of the fact that we shall bend the tubing at the corners.

+

Once more, let's place a 0.5" diameter version of the antenna at a height of 25' above ground. At the design frequency, we shall obtain a 50-Ohm feedpoint impedance accompanied by a front-to-back ratio well above 30 dB. (Vertical orientation affects the front-to-back ratio less than horizontal orientation for an antenna within about 2 wavelengths of ground.) However, unlike the horizontal version of the array, the peak gain is only about 7.6 dBi. Let's see why.

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Fig. 5 overlays the azimuth patterns of the antenna at the design frequency and at 52 and 54 MHz. In all cases, we see a very wide beamwidth, over 142 degrees between -3-dB points. That increased beamwidth--about twice the value for the horizontal version--spreads the radiated power over a much wider area and thus reduces the peak gain. This is inherent in any parasitic array with all of the elements in a single plane. Nevertheless, both the horizontal and the vertical versions of the array have almost 4 dB gain over their counterpart dipoles at the same height.

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As the patterns show, the increased bandwidth that we require of a vertical Moxon increases the rearward radiation at the band edges. Once more, the fatter the elements, the less growth to the rearward radiation for any change in frequency relative to the design frequency.

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In Fig. 6, we have the 50-Ohm SWR curves for the array at selected element diameters. The SWR increases more rapidly below the design frequency than above it. The antenna feedpoint impedance for the thinnest tubing actually is above 2:1, although at the shack end of the coax, where we usually measure SWR, it may seem lower than that value. Hence, one might well think in terms of at least an intermediate tubing size for the vertical Moxon.

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The SWR climbs more slowly above the design frequency, suggesting that we might choose a lower design frequency and extend the coverage from 51 to 54 MHz. This tactic is possible, but at a cost. The forward gain and the front-to-back ratio degrade continuously as we move above the design frequency. Hence, with a design frequency of, say, 52 MHz, the array performance would not be very good at 54 MHz.

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Building a Moxon Rectangle for 6 Meters

There is an unfortunate tendency among newer antenna builders to see a design they like and then to grab almost any materials close at hand and slap together a version that almost works. Many a good antenna design has gotten a bad name in some regions because builders did not exercise the same care in construction as the original builder. To obtain performance that agrees with the design notes above, acquire the right materials and then build the antenna with all the care possible. +

A good tubing size for a 6-meter Moxon--whether horizontal or vertical--is 0.5". This size is useful, since we can use #8 or #10 hardware for fastenings. Of course, the hardware will all be stainless steel, both for rust prevention and to avoid bi-metallic contact problems.

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For a 6-meter Moxon rectangle, we shall need 4 6' lengths of 1/2" diameter tubing. This size tubing can be shipped from suppliers like Texas Towers by UPS. (Yes, we shall have some scrap left over for use as garden stakes.) Use 6061-T6 or 6063-T832. Hardware depot tubing has an unknown vintage, so good quality antenna tubing is highly desirable. Do not use aluminum electrical conduit or copper tubing. The conduit is too heavy, and so is the copper in any form rigid enough not to gradually fold over on its own accord.

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We shall also require a short (under 6") length of 3/8" aluminum tubing and a similar length of 3/8" diameter fiberglass or similar rod. We shall be constructing the elements in halves, so we need to join and align them. The short length of 3/8" aluminum tubing will join the two halves of the reflector, making them electrically one. The fiberglass or equivalent rod will align the driver halves, but allow a gap for connecting the feedline. Finally, we shall require some 3/8" outer-diameter fairly rigid tubing, something light but straight. These tubes will fit inside the ends of the driver and reflector tails to hold the spacing constant under all conditions.

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For hardware, we shall require some #8 nuts and bolts, along with some locking washers. We can use sheet metal screws to fasten the tail junction tubes in place. However, all hardware must be stainless steel, including the washers. Since some of this falls outside what home warehouse hardware bins contain, consider locating a hardware supplier or use an on-line ordering source like McMasters-Carr. From such sources, you can also obtain a small sheet of 1/4" thick UV-protected polycarbonate (trade-name Lexan) to use as boom-to-element plates. Polycarbonate cuts nicely with woodworking saws and drills cleanly with standard bits.

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The needs for a single Moxon rectangle are small, so you may wish to combine orders with others interested in the antenna in order to make up the minimum order requirements for a given supplier. Since we have vowed to be careful, we need not rush to get parts, but can go slowly and get everything we need.

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For a boom, you can use either metal or Schedule 40 PVC (if the PVC in your area is adequately UV protected--this varies around the U.S.). In the southeastern US, white PVC gives me about 10 years of service before becoming brittle.

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Fig. 7 shows some of the suggested construction methods that I use. you may have better ones, in which case, use them. There are 4 keys areas of construction concern.

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1. The reflector junction: A 3/8" section of tubing a little longer than the boom-to-element plate joins the two halves. If we use polycarbonate plates about 4" long and 3" wide, we have plenty of room for the elements and the nuts/bolts for boom fastening. A 1" nominal PVC pipe is actually about an inch and a quarter in diameter and is very rigid for a boom that is less than 3' long. For the plate-to-boom bolts, #10 hardware is very secure, using only 2 bolts per plate. However, use a compression lock washer against the plate or obtain self-locking nuts (with a nylon insert).

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Since a #10 bolt requires a larger hole, you may wish to fasten the elements to the plate with #8 hardware, again with compression lock washers against the plate. (Toothed lock-washers may gradually loosen by gouging the polycarbonate.) For all drilling of the boom and the elements, make up a jig from scrap wood to pin the material in place while you drill. If you can gain access to a drill press--even a small device designed to hold an electric hand drill--by all means use it. Align all holes before drilling instead of widening holes later to bring parts into alignment.

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2. The driver gap: By using a 3/8" fiberglass rod to align the driver halves, we can fasten the driver and the rod to the plate using #8 hardware. Note that there are two sets of hardware at the driver: an outer set to pins the element to the plate and an inner set to which we shall connect the feedline. If you prefer, you can set the connection hardware at right angles to the element-to-plate hardware to keep the coax more in line with the boom.

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The sketch shows direct connections between the element and the coax, with no connector. I have found that from 6 meters on upward, connectors and their associated leads contribute reactance to the feedpoint impedance. A direct connection and a short length of coax taped to the boom for strain relief simplifies feedpoint construction. Once everything is complete, seal the connections, especially since solder terminals may not be available in stainless steel. Plasti-Dip or similar materials provide a weather-secure coating.

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A note on the gap: The gap at the feedpoint is part of the overall element length (or dimension A), NOT an addition to it. Whether you start with a 1/4" gap or a much wider one, let the driver side-to-side dimension remain constant. In effect, the coax leads make up the seemingly missing tubing. The driver gap is not critical from 1/4" to over 3/4", but closer is always better in this type of antenna.

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3. The tail separation: Because we must keep the tail ends at a specified distance and aligned, we need a short piece of non-conductive tubing to lock their relative positions. Almost anything will do here, if it is 3/8" in outside diameter and relatively rigid. We shall need only about 4-4.5 inches exposed, so even flexible nylon tubing will work, although rigid plumbing CPVC is superior. You may use sheet metal screws to fasten the tube inside the tail pieces--after careful measurement, of course.

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4. The element bends: Bending aluminum tubing requires care to prevent crimping that will eventually result in a metal crack and break. The radius of the corner bends will depend on the tubing size used. A plumber's tubing bender is applicable only up to about 1/4" diameter tubing. Larger tubing requires larger bend radii, and that means a home-made jig.

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Fig. 8 shows a simple jig: a circle mounted on a base plate. The circle can be cut from plywood or be a pulley wheel. For larger radius bends, I have used such materials as a worn-out power mower wheel.

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Mark a point on the 6' length of tubing that marks the center of the bent corner and leaves excess on both the tail and the parallel sections. Try to keep this mark at the center of the bend. As well, mark the tubing to indicate the parallel length (1/2 of dimension A) and the tail (B or D, as applicable). Fill the tube with the finest sand available and tape the end shut. If you prefer, warm the tube until it can just barely be handled with gloves. Pin one end of the tube (a nail in the base board will do) and slowly bend the tubing. The fatter the tubing, the more important it is to bend a few degrees and pause. Continue the bend until it is at least a 90-degree bend. A little more will not hurt, since a slight unbending of the tube does no harm.

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Bend the tubing before you drill any mounting holes to make sure that all such holes are at right angles to the mounting plates. In fact, let's delay any drilling and do some work on the floor.

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From the dimensions that apply to your tubing size, draw out the Moxon on the floor (or on paper taped to the floor). Be sure to mark the center or boom line as well as the points where the tails end. Next, lay the untrimmed bent pieces on the drawing. Because the corners are "clipped" by the bending, the pieces will just exceed the lines on the floor.

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NOTE: For the adjustment of positions, be sure that the gap is constant and does not change!

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With a constant gap distance as specified for the tubing size and measured against the marks made on the tubing, adjust the tube position to equalize the amount by which the tubes fall outside the original lines. At the same time, align the tubes. Now trim the tubes. Remember to trim a bit (1/8" or so per tube) off the driver to leave a gap for the coax connection. Smooth all cuts. Aluminum oxide sandpaper is best so that you do not leave residues of other metals on the aluminum. Clean the outer and inner edges of the tubes, since you will be inserting rods or tubes inside the main elements.

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Now return to the assembly process and complete the Moxon rectangle. If you have used sufficient care, it should be right on target on the first try. However, you can always trim a bit more from the reflector and driver tubes at their centers--and a little expansion that leaves a little inner reflector tube showing and widens the driver gap a small amount should do not harm.

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I assume that you have a boom-to-mast plate and stainless steel U-bolt hardware. As well, I assume that the coax from the feedpoint has a connector and a double-female in-line connector. If those assumptions are correct, you are ready to put the Moxon rectangle into service.

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Crossed Moxons

Suppose that you have both SSB and FM operations on 6 meters and that you decide that the Moxon has characteristics that are suitable for each job. Then you may wish to think about Fig. 9. +
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The outline sketches crossed Moxon rectangles. Since the low-end horizontal version is a bit larger than the vertical high-end version, let's place the horizontal reflector slightly ahead of the vertical reflector. Actually, it will make no difference if the two reflector join at the center. However, we shall need physically separate feedpoints--and separate feedlines as well. However, the assembly will fit on a single boom.

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Crossing Moxons and operating them separately makes no difference at all to the performance of either one.

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One precaution applies to either a single vertical Moxon or to crossed Moxons: we shall need a non-conductive boom if we attach the mast at the center of the boom. (6-meter arrays are heavy enough where I do not recommend extending the boom rearward for attachment to a mast without a further extension and counterweight.) Schedule 40 PVC has two sizes that nest reasonably well for stiffening the material for mast use: 1" inside 1-1/4" nominal (closer to 1.25" and 1.5" actual outside diameters). You will need about 3.5' to go from the boom to the edge of the vertical Moxon and perhaps another 2' above any metal structure (like a tower), plus a few more feet to reach a rotator. (An old TV rotator is more than sufficient to handle even the crossed Moxons). However, do not use more PVC mast than you need to do the job.

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A Wire Moxon for 6 Meters?

As a final note, we should address the question of making a wire Moxon. A #12 or #14 copper wire Moxon is feasible for the horizontal version only. However, the thin wire will narrow the passband severely. If you operate within a very narrow spread of frequencies at the low end of the band, then you may consult one of the design aids and set up a wire version. It will perform well--as well a the tube version. As well, it may be easier to make sharp corners and trim to length. +

However, a wire version of the vertical Moxon is likely to prove unsatisfactory for repeater hopping. It will work well for monitoring a single repeater--or a couple that are within a half-MHz of each other (allowing for the frequency split). However, for general coverage of the FM region of 6 meters, a version with fatter elements is strongly advised.

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We can illustrate the opportunities and the limitations of a wire Moxon for 6 meters with a simple example. Let's design a wire Moxon for horizontal use around the design frequency of 50.5 MHz. The dimensions will be as follows:

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Dimensions for a 50.5-MHz Moxon Rectangle
+
+      El. Dia.        A          B          C          D          E
+  AWG #14 (0.0641")   84.86      12.53      2.61       15.95      31.09
+      0.25            84.31      11.65      3.44       16.08      31.18
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I left the figures of the quarter-inch version for comparison. As shown in Fig. 10, the wire Moxon has a steeper gain curve and a sharper front-to-back curve than the tube version of the same antenna. However, for local and net operations, these figures may be very adequate.

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The SWR curve, while steeper than the ones for the tube versions of the antenna, guarantees coverage of the first MHz of the band. See Fig. 11. You may note in the two graphs that the front-to-back ratio peaks just below the design frequency, as does the 50-Ohm SWR curve.

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You can make the frame from 1/2" or 3/4" CPVC. By passing the frame through carefully aligned holes in a central Schedule 40 PVC mast, you can cement the structure together. Each cross arm will need to be just over 7.5' long (3.75' each side of the mast). As well, you will have to plan your angles for the holes carefully to get the correct shape between corners. However, if you are only a little off, you can stress the arms with Nylon line (1/8" to 3/16") to perfect the shape of the ultimate support structure. If you adjust the holes in the mast, then add through bolts to finalize the positions of the support arms. The details of a suggested construction for the frame, line, and wires appears in Fig. 12.

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Even if you get the angles between supports correct, you may still run a length of nylon or similar line from the corners along the line of the tails. Then, tape the tails to this line, and the ends (raw cut and not looped) will stay in alignment and maintain their spacing. (I tend to prefer to use a full perimeter line to pre-stress the frame so that it maintains its shape under all conditions.) The resulting wire Moxon very likely will be considerably cheaper then any of the tube versions, since we can make it from PVC and household wire, along with a little hardware at the feedpoint.

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Whether the Moxon is the right antenna--and which version is the one to build--depends on your own analysis of operating needs. Do not build one unless it will do the job that you need. But if you do build one, build it carefully, and it will work correctly without further field adjustment.

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Updated 02-03-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: Moxon, VHF / UHF


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Moxon-Modifying the C3-Type Tri-bander

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L. B. Cebik, W4RNL

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The Force 12 C3 tri-band Yagi has become a very popular compact beam for the general operator. Nevertheless, its 35' wing-spread has prevented some would-be owners from purchasing the antenna because their available space is not sufficient for full-size 20-meter elements. I have over the years received a number of inquiries as to whether the 20-meter elements could be shortened by various types of loading.

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In general, but not absolutely, the answer has been negative. Most forms of loading--except element-end loading--disrupt the current phase relationships between the fed driver and the slaved drivers, destroying the feed system.

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However, the 2-element 20-meter portion of the array can in principle be replaced by a Moxon rectangle without disturbing the other elements of the array. The result is not only a beam with only a 25' side-to-side spread, but as well a boom length nearly 2' shorter than the original.

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The following notes are designed only as a feasibility study to validate the replacement in principle. I developed the foundations for these notes in late 1999, but have not had the opportunity to implement them with an actual beam. Hence, I can only provide the information suggested by extensive modeling in NEC-4. However, as we shall see at the end of the article, reality has caught up with design theory.

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Our first step is to understand something of how the C3-type array is designed. For that purpose, I shall not present a detailed model of the Force 12 C3. To obtain an authorized computer model of the antenna, one should contact the company directly. My model makes use of uniform-diameter elements and hence represents only a C3-type antenna, not the actual commercial version.

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As well, many facets of the actual C3 are protected by patents and other proprietary considerations, for example, the open-sleeve feed system. Therefore, these notes are intended only as a design study for individual use and not for any commercial purpose whatsoever.

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The C3-Type Tri-Band Antenna

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The C3-type tribander consists of three antennas: a 20-meter 2-element driver-reflector Yagi, a 15-meter 2-element driver-reflector Yagi, and a 3-element driver-director Yagi. The general arrangement is sketched in outline in Fig. 1.

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The following model description from EZNEC provides details of the element lengths and spacings.

+ 
C-3-Type 20-10-m tribander                   Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -138.50, 34.000,  0.000       138.500, 34.000,  0.000 7.50E-01  43
+2          -132.35,119.000,  0.000       132.350,119.000,  0.000 7.50E-01  43
+3          -101.00,134.500,  0.000       101.000,134.500,  0.000 5.00E-01  33
+4          -97.000,146.500,  0.000        97.000,146.500,  0.000 5.00E-01  33
+5          -89.000,212.500,  0.000        89.000,212.500,  0.000 5.00E-01  33
+6          -195.00,130.250,  0.000       195.000,130.250,  0.000 1.00E+00  61
+7          -209.00,  0.000,  0.000       209.000,  0.000,  0.000 1.00E+00  61
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          31     6 / 50.00   (  6 / 50.00)      1.000       0.000       I
+

The elements are organized in the order 15 meters, 10 meters, 20 meters. My placement of the 20-meter elements at the end results from the fact that we shall eventually replace them with a Moxon rectangle. Note also that I have used 1" diameter elements for 20 meters, 0.75" for 15, and 0.5" for 10 meters.

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The most central feature of the C3-type multi-band Yagi is the drive system. It makes use of open-sleeve coupling such that only the 20-meter element is driven, whatever the band in use. The 15-meter driver is slaved to the 20-meter element on the side of the fed-driver closer to the corresponding reflector. Likewise, the 10-meter slaved driver is on the side of the fed driver closer to the 10-meter directors.

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I should note that the spacing and lengths of the slaved drivers relative to the fed driver may differ from the actual spacings used in a C3. Both NEC-2 and NEC-4 have some limitations when wires of different lengths and diameters are brought into close proximity. Even with great care in aligning segment junctions among the elements, the closer the spacing, the more the potential error in the model. Hence, the actual required slaved driver lengths and spacings may be different from those used in the model. However, the model is sufficiently accurate to establish the principles involved in the operation of a C3-type antenna.

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The 20-meters driver and reflector together form a 2-element beam of relatively standard design and performance. Fig. 2 shows the free-space azimuth patterns of the NEC-4 model at the ends and center of 20 meters. The following table summarizes 20-meter modeled performance.

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Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+14.0        6.44        10.48       68.8        44.7 - j 4.4      1.16
+14.175      6.13        10.90       69.6        55.4 + j 6.8      1.18
+14.35       5.84        10.51       70.2        65.9 + j16.6      1.49
+

As the table shows, the performance is everywhere normal for a 2-element Yagi. The gain descends with frequency increases. The element spacing to achieve a 50-Ohm match reduces the front-to-back ratio slightly relative to that obtainable with closer spacing and a lower feedpoint impedance. However, the SWR curve for a direct feed system is outstanding.

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Placing the 15-meter driver and reflector between the corresponding 20-meter elements results in close to optimal coupling, something that is more difficult to obtain had the 15-meter slaved driver been placed forward of the fed driver. However, a slaved driver generally has a narrower operating passband with respect to impedance than a directly driven element. The narrowing tends not to show up in terms of pattern shape, as evidenced by Fig. 3. However, the <2:1 SWR passband on 15 meters is only about 360 kHz, somewhat less than the whole band. However, the peak SWR of about 2.8:1 is well within the range of antenna tuners built into modern transceivers. As well, the SWR curve will be noticeably shallower at the shack end of any common coaxial cable if the cable is over a wavelength long. The following table shows the modeled performance of the subject antenna on 15 meters.

+ 
Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+21.0        6.55        10.78       67.2        52.9 - j36.0      1.99
+21.225      6.20        11.19       68.6        44.1 + j 4.9      1.18
+21.36       5.99        10.92       69.6        39.3 + j28.5      1.96
+21.45       5.84        10.59       70.4        36.2 + j44.2      2.83
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The band-edge patterns of the 20-meter and 15-meter sections of the antenna are quite similar, as is the front-to-back level. Only the SWR curve reveals the presence of the open-sleeve coupling system, and it is still a highly workable set of values.

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The 10-meter section of the antenna differs considerably from the 20-meter and 15 meter sections. Beginning with a slaved driver forward of the fed driver, there are two directors. Although there is no tuned 10-meter reflector, the 15-meter elements (especially) fulfill part of that function in a system known as forward-stagger design.

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Note that the first director is quite closely spaced to the slaved driver. Although this director does not lose all of its gain-enhancing function, its chief role is in setting the impedance and the operating passband of the 10-meter section. It bears more than a small resemblance to the spacing that would be used in OWA designs. The result is a 900 kHz SWR passband with usable patterns above 29 MHz. Fig. 4 shows the 28, 28.5, and 29 MHz free-space azimuth patterns for the modeled array.

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The following tables shows the reported properties of the 10-meter section across the first MHz of the 10-meter band.

+ 
Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+28.0        6.34        15.12       66.8        55.7 - j35.1      1.94
+28.5        6.55        16.65       68.8        45.0 + j 0.2      1.09
+28.9        6.80        17.68       70.4        36.0 + j26.6      2.00
+29.0        6.87        17.86       70.8        32.7 + j33.0      2.44
+

Once more, the SWR curve at the shack end of a coaxial cable will likely be shallower than the one at the feedpoint terminals, and any remnant SWR in excess of 2:1 is easily handled by a built-in ATU in the transceiver. More significantly, the performance curve reflects a typical Yagi with directors, as the gain increases with increasing frequency. The use of two directors provides a bit higher gain across the operating passband than the driver-reflector sections used on 20 and 15 meters.

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Replacing the 20-Meter Section with a Moxon Rectangle

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If we replace the 20-meter elements with a Moxon Rectangle, we obtain an array with a smaller footprint: 10' narrower and almost 2' shorter. Fig. 5 shows the outlines of such an array.

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The following model description permits a direct comparison of element length and spacing between the Moxon-ized version of the C3-type antenna and the basic model just examined.

+ 
Moxon-C3-type tribander                      Frequency = 14  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -138.50, 34.000,  0.000       138.500, 34.000,  0.000 7.50E-01  43
+2          -131.90,119.000,  0.000       131.900,119.000,  0.000 7.50E-01  43
+3          -101.00,134.500,  0.000       101.000,134.500,  0.000 5.00E-01  33
+4          -97.000,146.500,  0.000        97.000,146.500,  0.000 5.00E-01  33
+5          -89.000,212.500,  0.000        89.000,212.500,  0.000 5.00E-01  33
+6          -150.00, 88.250,  0.000  W7E1 -150.00,130.250,  0.000 1.00E+00   7
+7     W6E2 -150.00,130.250,  0.000  W8E1 150.000,130.250,  0.000 1.00E+00  51
+8     W7E2 150.000,130.250,  0.000       150.000, 88.250,  0.000 1.00E+00   7
+9          -150.00, 78.650,  0.000 W10E1 -150.00, 22.250,  0.000 1.00E+00  10
+10    W9E2 -150.00, 22.250,  0.000 W11E1 150.000, 22.250,  0.000 1.00E+00  51
+11   W10E2 150.000, 22.250,  0.000       150.000, 78.650,  0.000 1.00E+00  10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          26     7 / 50.00   (  7 / 50.00)      1.000       0.000       I
+

If you examine wires 1-5, you will notice that the only change is to the 15-meter driver length--a slight adjustment needed to bring all of the SWR passbands back into alignment. I have left these elements at there original marks to facilitate the comparison. However, the Moxon reflector is 22.25" forward of the position of the former Yagi reflector.

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Perhaps the most significant change in performance occurs on 20 meters, as the typical Moxon pattern replaces the 2-element driver-reflector pattern of the original array. Fig. 6 shows the increased beamwidth, increased front-to-back ratio, and slight decrease in forward gain. The numbers associated with these patterns appear in the following table.

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Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+14.0        6.40        16.56       77.2        43.0 - j11.4      1.33
+14.175      6.03        31.51       77.8        60.9 - j 3.3      1.23
+14.35       5.67        19.94       78.4        75.6 - j 1.1      1.51
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While the gain differential is unlikely to be detectable in operation, the increased front-to-back ratio will be readily noticed. The 10-degree wider beamwidth may or may not be useful, depending upon the type of operation. In a contest, it reduces the need for re-aiming the beam so often.

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However, the key benefit of using the Moxon is the reduction in the side-to-side dimension of the array. However, every benefit is usually accompanied by a challenge. In this case, the difficulty lies in building element corners and a means of keeping the element ends in alignment. As well, unless good construction is used, the forward and rear elements may react to winds in differing rhythms, thus stressing the element tail assemblies. In short, Moxon rectangle construction for 20 meters may require a bit more careful planning than the usual 2-element Yagi.

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On 15 meters, the chief feature to notice is that there is no significant change in performance compared to the basic array from which this one is derived. The Fig. 7 free-space azimuth patterns are virtually identical to those for the basic array, and the following table of modeled values confirms the appear of the patterns.

+ 
Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+21.0        6.63        11.08       67.0        61.9 - j37.3      1.99
+21.225      6.22        11.75       67.8        50.1 + j 8.4      1.18
+21.36       5.99        11.25       68.2        44.0 + j33.2      2.01
+21.45       5.84        10.74       68.4        40.3 + j49.4      2.91
+

Gain values, where they differ at all, do so only in the meaningless hundredths column. All of the other values a mere smidgens apart from the numbers reported for the basic array. In short, confining the 15-meter elements within the Moxon rectangle results in no significant interactions in addition to those one might find when the elements are between Yagi elements for 20 meters.

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In similar fashion, the 10-meter performance--as sampled in the free-space azimuth patterns of Fig. 8--also replicates closely the performance on 10 meters by the original array. The following table, when compared with the corresponding table for the original antenna, confirms how closely the two perform.

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Freq.       F-S Gain    F-B Ratio   Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          Degrees     R +/- jX Ohms     SWR
+28.0        6.32        15.14       67.0        57.4 - j34.7      1.92
+28.5        6.61        16.51       67.4        46.8 + j 0.7      1.07
+28.9        6.90        17.38       68.0        36.5 + j26.8      1.99
+29.0        6.99        17.51       68.2        33.0 + j33.2      2.43
+

In principle, then, it is possible to replace the 20-meter elements in a C3-type antenna with Moxon Rectangle elements with no loss of performance and only a change in the nature of the 20-meter patterns that reflect the differences between a 2-element Yagi and a Moxon Rectangle. In principle, one obtains a smaller array that might fit in spaces in which a full-size C3-type antenna might not fit.

+

The Differences Between Principles and Practice

+

The design exercise has established a principle, but there may be numerous problems to overcome in translating the principle into practice. Although I have mentioned a few along the way, let's review what they might be in one place.

+

1. Modeling limitations: I have called attention to the fact that NEC-2 and NEC-4 have limitations associated with closely spaced wires having different lengths and diameters, even when one is careful to set up those wires so that the segment junctions align as closely as possible. The closeness of the slaved drivers to the fed driver, especially on 10 meters, suggests that the element dimensions and spacing are only suggestive. They will require considerable adjustment in practice. For the 10-meter slaved driver forward of the fed driver, here is the guideline.

+
+

A. Increasing the element length decreases the feedpoint resistance and makes the reactance more inductive (or less capacitive). Decreasing the element length does just the opposite, increasing the feedpoint resistance and making the reactance more capacitive (or less inductive).

+

B. Closing the spacing decreases the feedpoint resistance and makes the reactance more capacitive (or less inductive. Opening the spacing increases the resistance and makes the reactance more inductive (or less capacitive).

+
+

If this is your first open-sleeve coupled beam, be extra patient. It is easy to forget the guidelines and adjust the wrong parameter. If that happens and the feedpoint values appear to be going awry, return the slaved element to its original length and spacing and start the procedure again. Make very small changes between feedpoint measurements until you get a good feel for how much each increment of change affect the feedpoint impedance.

+

2. Element diameter taper and other construction points: the models use uniform-diameter elements, which is normally impractical on the HF bands. For a practical antenna, one must first reconstruct the model using the element taper schedule that reflects proposed construction. The linear elements can be re-sized using Leeson correction factors. However, these corrections only apply to linear elements. Hence, the Moxon elements may require either the use of NEC-4 to obtain a reasonably reliable model or considerable experimentation during construction.

+

However, all is not thrown into a murky bog by this limitation. The Moxon elements can be built and tested independently. Once established, the remaining elements have almost no effect upon them. (Similarly, the 20-meter elements of the original array are almost wholly unaffected by the addition of the elements for 15 and 10 meters.)

+

There have been many techniques used for the construction of Moxon corners. One can bend aluminum around various forms by first filling the tubing with sand and then--if possible--warming it. However, numerous Moxon builders have found pre-bent sections of aluminum in many places. Among the most original was the use of leg-sections from lawn chairs that had been placed on a pile of discarded items. CPVC (thin-wall PVC) makes a cheap and reasonably rigid separator for the element ends. Polycarbonate tubing would be superior from a UV and RF perspective, but CPVC is quite serviceable.

+

Finally, it is wise to develop a simple bracket to keep the fed driver and the two slave drivers well aligned. Sheets of acrylic, Plexiglas, or polycarbonate placed about 6-7 feet outward from the boom and "trapping" all three drivers will reduce SWR excursions created by winds that wave the elements out of step with each other.

+

This design exercise is, in the end, only a proof of principle and an invitation to those who wish to experiment further. I have no wish to reduce sales of the original C3 antenna. However, for those with too little space for the original, the Moxon version may--with considerable construction care--prove to be a feasible alternative.

+

The OptiBeam OB6-3M

+

Since developing the models for the modified C-3-type antenna, I have encountered a new beam that resembles on the surface the C-3. OptiBeam of Germany makes a line of multiband Yagis that differs from the Force 12 line in 2 respects: the OptiBeams use a method of directly feeding all drivers and the beams themselves are somewhat heavier in construction.

+

I suggested to the makers indirectly that they might consider Moxon-izing their smallest model, and they have done so. Below is a photo of the OB6-3M, a 6 element, 3-band beam using a Moxon rectangle for 20 meters. Relative to the C3-type antenna, the OptiBeam small model uses only 2 elements on 10 meters, placing the driver behind the 20-meter element with only 1 director. The makers claim a wider operating bandwidth for this arrangement.

+
+ +
+

For those who do not wish to experiment but instead directly purchase a finished version of the beam, the OB6-3M and the other beams in the OptiBeam line are available from OptiBeam. Since I do not have a version of the antenna on hand, I cannot vouchsafe for the claimed specifications, but they are quite similar to those noted in the study above.

+

Reality sometimes does catch up with antenna modeling.

+
+ +

+
+

Updated 06-08-2002. © L. B. Cebik, W4RNL. This item first appeared in antenneX for June, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Moxon Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, Moxon, Yagi


+ + diff --git a/content/moxon/dd.html b/content/moxon/dd.html new file mode 100644 index 0000000..bd98c69 --- /dev/null +++ b/content/moxon/dd.html @@ -0,0 +1,69 @@ + + + + + + The Double-D Antenna + + + + +
+

The Double-D Antenna

+

+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+ Peter Dodd, G3LDO, developed the Double-D antenna as an improvement on the VK2ABQ square. Between 1980 and 1990, he evolved several versions of the antenna, as described in his book, The Antenna Experimenter's Guide (Chapter 8 of the first edition). Actually, the antenna is a slightly revised version of the Moxon rectangle, with "tails that either go up or down and inward toward the mast for easier assembly. +

As a reference point, Figure 1 reviews the structure of a Moxon rectangle, while Figure 2 provides a free space pattern for a 20-meter Moxon rectangle. No dimensions are given here for the Moxon, but there are other notes at this site for wire Moxons from 10-40 meters. The sketch is from that note. Also note that the parts of the sketch with letter labels do not coincide with the parts of the Double D shown below.

+
+ +
+
+ +
+

The Double-D has a somewhat more complex geometry due to its elevated tails. Figure 3 illustrates the basic structure, with identification of the arms. The antenna forms a horizontal square, 28' from corner-to-corner for 20 meters. Dodd has preferred to make both Ds equal in overall length, although he reports one version with a very small difference in tail length between the driven element and the reflector.

+
+ +
+

The best modeled performance I have been able to derive from a 20-meter version of the Double-D has required that the reflector tails be significantly longer than the driven element tails. Here are the dimensions of the best modeled version:

+ 
Table 1.  Dimensions for a bare-copper wire Double-D.
+
+Designator     Item                     Length
+A, B           Length/Width             19.8'
+C              Arm length (from mast)   14.0'
+D              Junction elevation        2.3'
+E              Tail length, DE           7.9'
+F              Tail length, Ref          8.2'
+
+All element #14 copper wire.
+

Notice that these dimensions use a very conservative elevation of the tails. More radical elevation changes, as well as shorter dimensions for the length and width, yield lower performance figures. Even so, the best free space gain obtained from the antenna has been about 4.1 dBi, with a front-to-back ratio just over 15 dB. As Figure 4 shows, the beamwidth is nearly 90 degrees, and the rear quadrant is well-behaved, that is, the rear quadrant shows a smooth pattern of rejection.

+
+ +
+

The Double-D is designed for compact yards or gardens and modest installations. The arms are nonconductors. The wires and cords from the arm ends to the mast serve double duty: as tails and as supports for the arm ends. A perimeter cord is recommended to keep the arms properly positioned laterally.

+

Over level average terrain, at a height of 1/2 wl (about 35' on 20 meters), the antenna exhibits a broad forward lobe and an equally broad rear lobe. The front-to-back ratio increases to about 22 dB, while the forward gain is in the neighborhood of 9.5 dBi. Figure 5 overlays a Moxon and a Double-D pattern for relevant comparison.

+
+ +
+

Although the two patterns look similar, there is a major difference: the elevation angle of maximum radiation for the Moxon is 26°, while the Double-D's take-off angle is 4° higher. The double-D falls considerably short of Moxon rectangle performance. However, it lends itself to somewhat easier construction, especially if one contemplates rotating the antenna by hand or rotor. For some types of operation, the front-to-back ratio may be of more utility than raw forward gain. A convenience is the fact that the feedpoint impedance is in the neighborhood of 50-55 ohms, a good match for coaxial feed systems.

+

In the end, however, Dodd's claims of 3-4 dB gain over a dipole do not fully materialize. At best, I have been able to model about 2 dB over a similarly situated dipole, and my models have been optimized. The end result is an antenna with somewhat less gain than a properly tuned X-beam, but with a superior rear pattern. It also has less gain than a 2-element Yagi shortened to about 2/3rds full size using linear or inductive loading at the feedpoint, although shortened Yagis are capable of quite good front- to-back ratios. These comparisons are intended neither to compliment nor condemn the Double-D, but only to place it relevantly within the cluster of antennas to which it belongs.

+

The dimensions have been altered by Dodd for the 2nd Edition of his excellent book, The Antenna Experimenter's Guide (RSGB), with some improvements in performance. However, compared to a standard Moxon Rectangle, which takes up very little more room for any given band, the high performance region occurs over a very narrow portion of the band. The newer version has a peak gain a little more than 3 dB better than a dipole. Because Peter's book is such a good reference volume for the antenna experimenter, I shall leave further details of the improvements "as an exercise for the reader."

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+ +

+
+

Updated 3-18-97, 5-4-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +

+
+

Return to Moxon Index

+

Go to Amateur Radio Page

+

Topics: HF Upper, Moxon


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+

Multi-Banding the Moxon Rectangle

+

+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

I have had a number of inquiries into multi-banding the Moxon rectangle. The compact antenna seems to beg for nesting. However, to the present time, I have had no success in developing a workable model of the antenna for any HF band combination in the nested configuration.

+

In Moxon's book, HF Antennas for All Locations, G6XN notes a detuning system that he uses with his wire version. However, the wire spacing required by the system makes for a bad model. Consequently, I cannot say whether or not the system would work with aluminum rectangles, each of which has been optimized for its band.

+

One solution is to create a "Christmas Tree" of rectangles, each well spaced from the one below it. Such systems have been used with ZL-Specials and HB9CVs, both of which are phased arrays. 10-12 feet of spacing should provide ample separation. The system would require separate feedlines, with switching done either at the mast or on the ground.

+

Most inquiries have indicated a preference for a single array boom on which to mount all elements. Within this constraint, a solution of sorts may be possible--in fact, two solutions. Let's examine them one at a time.

+

Back-to-Back Moxons

For some potential Moxon users, the pattern is the most important aspect of the antenna. The near cardioidal pattern with a very high front-to-back ratio in a 2-element beam has a niche in the operating needs of hams. We can obtain that pattern on two bands by placing a pair of rectangles back- to-back. +

To see how well this would work, I modeled 10-meter and 15-meter rectangles in a back-to-back configuration, drawing the two reflectors as close together as possible without severely damaging the overall pattern. A practical limit of about 2' of separation emerged for the 10-15 combination. Fig. 1 shows the general outlines of the array.

+
+ +
+

The overall boom length is about 12.7' with a little extra needed for element-to-boom mounting. The following table shows the values used in constructing the model:

+ 
10-15-meter Moxons back-to-back             Frequency = 21.225  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+1         -8.417, -4.930,  0.000  W2E1  -8.417, -7.007,  0.000 1.01E+00   7
+2   W1E2  -8.417, -7.007,  0.000  W3E1  -8.249, -7.175,  0.000 1.17E+00   1
+3   W2E2  -8.249, -7.175,  0.000  W4E1  -2.685, -7.175,  0.000 1.01E+00  15
+4   W3E2  -2.685, -7.175,  0.000  W5E1   2.685, -7.175,  0.000 1.17E+00  15
+5   W4E2   2.685, -7.175,  0.000  W6E1   8.249, -7.175,  0.000 1.01E+00  15
+6   W5E2   8.249, -7.175,  0.000  W7E1   8.417, -7.007,  0.000 1.17E+00   1
+7   W6E2   8.417, -7.007,  0.000         8.417, -4.920,  0.000 1.01E+00   7
+8         -8.417, -4.222,  0.000  W9E1  -8.417, -1.168,  0.000 1.01E+00   9
+9   W8E2  -8.417, -1.168,  0.000 W10E1  -8.249, -1.000,  0.000 1.17E+00   1
+10  W9E2  -8.249, -1.000,  0.000 W11E1  -2.685, -1.000,  0.000 1.01E+00  15
+11 W10E2  -2.685, -1.000,  0.000 W12E1   2.685, -1.000,  0.000 1.17E+00  15
+12 W11E2   2.685, -1.000,  0.000 W13E1   8.249, -1.000,  0.000 1.01E+00  15
+13 W12E2   8.249, -1.000,  0.000 W14E1   8.417, -1.168,  0.000 1.17E+00   1
+14 W13E2   8.417, -1.168,  0.000         8.417, -4.222,  0.000 1.01E+00   9
+15        -6.270,  3.920,  0.000 W16E1  -6.270,  5.575,  0.000 7.50E-01   5
+16 W15E2  -6.270,  5.575,  0.000 W17E1  -6.145,  5.700,  0.000 8.75E-01   1
+17 W16E2  -6.145,  5.700,  0.000 W18E1  -2.000,  5.700,  0.000 7.50E-01  11
+18 W17E2  -2.000,  5.700,  0.000 W19E1   2.000,  5.700,  0.000 8.75E-01  11
+19 W18E2   2.000,  5.700,  0.000 W20E1   6.145,  5.700,  0.000 7.50E-01  11
+20 W19E2   6.145,  5.700,  0.000 W21E1   6.270,  5.475,  0.000 8.75E-01   1
+21 W20E2   6.270,  5.475,  0.000         6.270,  3.920,  0.000 7.50E-01   5
+22        -6.270,  3.400,  0.000 W23E1  -6.270,  1.125,  0.000 7.50E-01   6
+23 W22E2  -6.270,  1.125,  0.000 W24E1  -6.145,  1.000,  0.000 8.75E-01   1
+24 W23E2  -6.145,  1.000,  0.000 W25E1  -2.000,  1.000,  0.000 7.50E-01  11
+25 W24E2  -2.000,  1.000,  0.000 W26E1   2.000,  1.000,  0.000 8.75E-01  11
+26 W25E2   2.000,  1.000,  0.000 W27E1   6.145,  1.000,  0.000 7.50E-01  11
+27 W26E2   6.145,  1.000,  0.000 W28E1   6.270,  1.125,  0.000 8.75E-01   1
+28 W27E2   6.270,  1.125,  0.000         6.270,  3.400,  0.000 7.50E-01   6
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1 (15 M)    8     4 / 50.00   (  4 / 50.00)      1.000       0.000       I
+or
+1 (10 M)    6    18 / 50.00   ( 18 / 50.00)      1.000       0.000       I
+
+Ground type is Free Space
+

One slight peculiarity of this model is that the corners use a sloping wire to simulate tubing bends. However, in actual construction practice, this nicety of modeling has proven unnecessary: results with or without the corner sloping wire are well within the normal home shop construction variables.

+
+ +
+

Performance on each band is quite normal. Fig. 2 shows the 50-Ohm VSWR curve for 15 meters, while Fig. 3 shows the 10-meter 50-Ohm VSWR curve. The slightly higher values of SWR across the band on 10 meters suggest that the 15-meter rectangle influences the 10-meter rectangle more than the other way around. As with monoband Moxon rectangles, forward gain varies from about 6.2 dBi at the low end of the band to about 5.7 dBi at the upper end in free space models. Relative to other 2-element designs, the front-to-back ratio is superior across the band.

+
+ +
+

A Hybrid Tri-Band Moxon-Yagi

One of the features of the Moxon rectangle that appeals to many builders is the reduction in side-to-side width of the antenna relative to linear elements. On 20 meters, the normal 36' elements are reduced to 25' side-to-side--a value not much greater than the width of a 15-meter beam. Since small tri-banders tend to use short booms, the reduction in the side-to- side dimension also means a significant reduction in the antenna turning radius. +

I have received a number of notes wondering if parasitic elements might be added to a 20-meter Moxon to produce a tri-band beam. The addition of a 10- meter director and a 15-meter reflector yields some forward gain, but the feedpoint impedance makes large excursions, forbidding the use of coax.

+

These initial steps into developing a tri-band antenna around a 20-meter Moxon tend to stop short of something truly satisfactory. What is required for easy use is a system that permits a 50-Ohm feed for each band. The result will be more elements, but not a major increase in the footprint over and above the initial addition of a reflector and director.

+

To develop a beam of this order, one might well adapt some of the principles underlying the Force 12 C3. This popular antenna uses a 2-element 20 meter driver-reflector Yagi at its core. It also places a 15-meter driver-reflector combination behind the 20-meter driver. The two drivers are close enough to permit open-sleeve coupling. Ahead of the 20-meter driver are 3 10-meter elements--a driver (also open-sleeve coupled to the 20-meter driver) and two directors. The furthest director provides the essential pattern shaping function, while the closely-spaced first director functions much like the added director on the NW3Z/WA3FET OWA designs: it helps form a wider band feedpoint impedance than a single director could provide. Performance remains essentially the same as a 2-element driver-director Yagi, but over a larger portion of the band.

+

It is possible to replace the 20-meter elements with a Moxon rectangle and obtain tri-band performance on a 16' boom. Fig. 4 shows the general outline.

+
+ +
+

The following table presents some element data used in the models testing this idea. The elements are of uniform diameter for each band. Consequently, adjustments would be required for any element diameter tapering schedule used in an actual antenna. Likewise, none of the dimensions should be taken to be those of an actual C3.

+ 
Hybrid Moxon-Yagi                                 Frequency = 29  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -138.50, 11.750,  0.000       138.500, 11.750,  0.000 7.50E-01  21
+2        -132.00, 96.750,  0.000       132.000, 96.750,  0.000 7.50E-01  21
+3        -101.00,112.250,  0.000       101.000,112.250,  0.000 5.00E-01  15
+4        -97.000,124.250,  0.000        97.000,124.250,  0.000 5.00E-01  15
+5        -89.000,190.250,  0.000        89.000,190.250,  0.000 5.00E-01  15
+6        -150.00, 66.000,  0.000  W7E1 -150.00,108.000,  0.000 1.00E+00   3
+7   W6E2 -150.00,108.000,  0.000  W8E1 150.000,108.000,  0.000 1.00E+00  25
+8   W7E2 150.000,108.000,  0.000       150.000, 66.000,  0.000 1.00E+00   3
+9        -150.00, 56.400,  0.000 W10E1 -150.00,  0.000,  0.000 1.00E+00   4
+10  W9E2 -150.00,  0.000,  0.000 W11E1 150.000,  0.000,  0.000 1.00E+00  25
+11 W10E2 150.000,  0.000,  0.000       150.000, 56.400,  0.000 1.00E+00   4
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          13     7 / 50.00   (  7 / 50.00)      1.000       0.000       I
+
+Ground type is Free Space
+

For this exercise, the 20-meter elements were set at 1" diameter, the 15- meter elements at 0.75" diameter, and the 10-meter elements at 0.5" diameter. Since the design uses open-sleeve coupling, a single feedpoint suffices for all bands.

+

Here is a band-by-band run-down of potential performance. These figures are generated on MININEC (AO 6.5), since the close spacing of the drivers produces excess gain estimates in NEC-2. The error is an especially large overestimation of gain on 10 meters. Hence, MININEC is the core of choice for this exercise.

+

20 Meters: On 20 meters, the Moxon rectangle performs normally, with a typical Moxon pattern, as shown in the free-space azimuth pattern in Fig. 5.

+
+ +
+

The following table summarizes the performance across the band.

+ 
Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+14.0      6.46            15.6          38-15          1.55
+14.175    6.09            32.4          55- 6          1.15
+14.35     5.72            21.0          69- 1          1.38
+

Fig. 6 demonstrates the anticipated SWR curve on 20 meters.

+
+ +
+

Relative to a Yagi driver-reflector combination, the Moxon shows a gain decrease of about 0.25 dB, but an increase in front-to-back ratio that exceeds 10 dB on average.

+

15 Meters: On 15, the pattern is that of a 2-element driver-reflector, as illustrated in the free-space azimuth pattern in Fig. 7.

+
+ +
+

The modeled free space performance figures across 15 meters are these:

+ 
Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+21.0      6.63           10.8           61-40          2.01
+21.225    6.21           11.6           50+ 6          1.13
+21.35     5.99           11.2           44+29          1.87
+21.45     5.82           10.7           40+47          2.82
+

Note that the effective 2:1 SWR bandwidth is about 350 kHz or just a little bit more on 15 meters. One consequence of a simple open-sleeve coupling feed system is a more rapid rise in reactance as one moves away from resonance. At the upper end of the band, the reactance controls the SWR figure. One may, of course, reset the driver length to favor the upper end of the band. In addition, a broader operating bandwidth may exist at the ground end of a standard 50-Ohm coaxial cable--the exact width depending upon the line's length and losses.

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Fig. 8 shows in graphic form the SWR curve on 15 meters, as modeled in free space.

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10-Meters: Fig. 9 shows a free-space azimuth pattern for the hybrid antenna at 28.5 MHz. Again, it is a typical 2-element Yagi pattern, with a slightly better front-to-back ratio due to the use of directors.

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In tabular form, here are the AO predictions of performance, as referenced to free space.

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Freq.     F-S Gain        F-B           Feed Z         50-Ohm
+MHz       dBi             dB            R+/-jX         VSWR
+28.0      6.31           15.0           57-37          2.00
+28.5      6.59           16.4           46- 0          1.08
+28.9      6.89           17.4           36+26          1.98
+29.0      6.98           17.5           33+32          2.42
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The gain and front-to-back ratio are typical for a 2-element driver- director design with one exception. The standard driver-director design has a narrow operating bandwidth for both the performance and the impedance characteristics. Something as narrow as 100 to 150 kHz is not unusual. The first director that is close to the driver provides the builder with the ability to tailor characteristics in a couple of ways. First, it forces the second director to a considerable distance from the driver so that characteristics change more slowly across the band. Second, it allows the builder to achieve a stable feedpoint impedance over much of the band--in this case, about 900 kHz between 2:1 SWR points, as illustrated in Fig. 10.

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Undoubtedly, one can improve on this hybrid design. Indeed, the requirement for adjusting element lengths and spacings to account for element diameter taper schedules would enforce an exploration of possible improvements. As with all models of open-sleeve coupling, considerable adjustment may be needed in the slaved drivers to achieve the correct impedance and bandwidth. Moreover, although home construction of single antennas for personal use requires no special attention to any legalities, any other use of the non-Moxon-rectangle techniques noted in the design should involve consultation with Force 12 to ensure compliance with any proprietary or patent rights held by that company.

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Conclusion

The two designs shown here are simple illustrations that multi-band designs involving Moxon rectangles are possible. The back-to-back design is "pure rectangle" and makes use of the very high front-to-back ratio in order to closely space two independent antennas. The hybrid design makes use of a number of techniques to maximize performance within each element group of a multi-band antenna with a single feed system. +

In both cases, the antennas use no loading devices, but instead employ full size elements. Any compacting of the overall size relative an antenna with only linear elements is a function of geometry. If I discover additional multi-banding techniques, I shall certainly add them to this note.

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Updated 8-12-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Return to Amateur Radio Page

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Topics: HF Upper, Moxon


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An Aluminum 2-Element Moxon Rectangle 10m

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L. B. Cebik, W4RNL

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+ I often receive inquiries from folks who cannot quite support the width of a 10-meter Yagi (either 2 or 3 elements) because obstructions give them less than the 16.5' needed. Is there an antenna with decent performance that will fit in a space about 12-13' wide? If it can be home built to save money and require no fancy tuning or matching system, so much the better. +

In fact, there is an antenna that fits this category almost perfectly. Imagine an antenna with the gain (over real ground) of a 2-element Yagi (11+ dBi), the front-to-back ratio of a 3-element Yagi (>20 dB from 28.3 to 28.5 MHz), and an SWR of below 2:1 from one end of 10 to the other. In fact, imagine that the antenna has better than 15 dB front-to-back ratio all the way down to 28 MHz and still has about 12 dB front-to-back ratio at 29.7 MHz. (All figures are free space modeling estimates, except gain.) Imagine also that the antenna can be directly connected to 50-ohm coax with no matching system whatsoever (even though I always recommend a 1:1 choke balun). Imagine also that you can make it yourself from hardware store materials, that it will weigh about 10 pounds including the boom (under 5 pounds without the boom), and that you can make it in your garage with no special tools. Imagine also that when it is done, you will still have change from a $50 bill.

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The antenna is the Moxon rectangle. Past versions that I built using wire elements required lots of PVC to support them. See "Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and Moxon Rectangles," Communications Quarterly (Spring, 1995), 55-70. Those versions were to prove the principles of the Moxon rectangle, not to produce an easy-to-build antenna.

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However, if we translate the antenna into hardware store aluminum tubing, we can easily build a 1-boom version. Now peak at the sketch of the pieces. (Note: to get the detail into the figure, I had to make it a bit too large for 640-wide screens. Hence, it may not print well unless you download it and print it out landscape.)

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Some 7/8" and 3/4" diameter aluminum tubing form the main elements, with 3/4" tubing for the side elements. The corners can use radius-bent tubing or be squared by making some corner supports from L-stock. Cut the straight tubing at 45-degree end angles and use 1/16" thick L-stick to fashion over and under supports. About 1-2" length each way with stainless steel sheet metal screws or pop rivets will solidify the corners with minimal weight. I even tried 1/2 inside conduit Ls, but had to ream out the ends to accept the 3/4" tubing.

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The corners I used were 7/8 aluminum radius-bent sections sent to me by N6BT (of Force 12) to speed up the experimentation. You can bend your own by filling the aluminum tube with sand (or cat litter in a pinch) and bending around a 6" or larger wheel or pulley. Work slowly. Keep the sand well packed in the tube to prevent pinch bends.

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The combination of 7/8" and 3/4" aluminum tubing lets you telescope the ends into the center for a precise fit or a center frequency adjustment. A similar advantage accrues from using 1" and 7/8" hardware store aluminum tubing.

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The side-to-side length is the key to centering the SWR curve for lowest reading at about 28.4 to 28.5 MHz. The center frequency changes about 150 kHz for every 1" of length adjustment. Hence, using the U-shaped outer ends as trombone slides will let you center the antenna anywhere in the 10 meter band. If you use slightly larger stock, say 1" and 7/8" hardware store aluminum tubing, performance will change very little. With 7/8" tubing for the outer main elements and the sides, you can weld or otherwise fasten (with Penetrox or another bi-metal conductor/protector between metals) 3/8" copper plumbing pipe Ls as the corners.

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Since the end spacing and alignment is critical to make the antenna give its full performance, you can slide a piece of CPVC or similar lightweight, durable tubing either inside the ends or over the ends and lock them in place with sheet metal screws. The rigid spacer is also a good idea to limit the twisting force placed on the curved or right-angle corners. Sheet metal screws also connect the 3/4" and 7/8" tubing together. Be sure that all hardware screws are stainless steel. "Pop" rivets will also do well, if you use the sturdiest kind.

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The feedpoint assembly is not shown in the sketch. I used a very simple system. I cut one side of the driven element tubing 1" short at the feedpoint. I then cut a 2" section of 1/16" thick L-stock, and cut a 5/8" diameter hole at one end. A chassis-mounting female coax connector (with a lock washer) fits into the hole, with the plug-side pointed at the mast. stainless steel sheet metal screws attach the "extra-inch" side of the L-stock to the cut-off tube. A #14 copper wire (tinned the entire length) goes from the center pin to the other side of the feedpoint, where it is fastened under another sheet metal screw. You can devise your own more durable set of feedpoint connections. After testing but before committing the antenna to permanent installation, be sure to waterproof the rear of the coax connector as well as the coax plugs.

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For element-to-boom plates, you can use any durable material. Spar varnished 3/8" plywood or LE plastic make good plates. About 3" by 9" (or longer) plates give ample room to U-bolt the elements to the plate and have room for U-bolts that go over the mast. My test model used 1/2" PVC electrical conduit U-straps fastened in place with #8 stainless steel hardware. Since 7/8" tubing stresses these straps a bit too much, I placed an extra washer between the U-strap and the plywood plate. The object is a very firm grip, but not a broken strap. Two straps hold the reflector center tube in place, but the driven element requires two on each side of the feedpoint.

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As with all good antenna structure, let the elements hang under the boom. What boom? Well, almost anything, from 1-1/4" nominal diameter PVC (which I had on hand) to a good grade of aluminum tubing (thicker-wall than the usual 0.55" hardware store variety--or two pieces nested) to a 5' length of spar varnished 1.25" diameter closet rod. Make up a boom-to-mast plate similar to the boom-to-element plates, only a bit more square, and you are in business. PVC is the heaviest; aluminum the lightest, but at 5', the boom weight is not a significant issue.

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The dimensions of the antenna in the drawing are too fussy, being direct translations of the computer model used to generate the antenna. Just try to keep the dimensions within about 1/4" of the drawing, and no one will be able to tell any difference in performance. Squaring the corners or missing the dimensions by a half inch will shift the performance centers by about 100 kHz at most. In most cases, you will not be aware of any difference at all. To assure that the assembly is neatly squared and close to the prescribed dimensions, you can draw the outer dimensions and center line on the shop/garage/basement floor with a marker pen and then assemble the pieces within those boundaries. As "they" always say, measure twice, cut and assemble once.

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Note that the antenna is just about 12.7' wide and under 5' front-to-back, for a turning radius of about 6'8" or so. Strapped up on the side of the house, the antenna is unlikely to overhang the neighbor's yard line. The antenna is light enough for hand rotating, but an old TV rotator might come in handy. Because of the antenna's characteristics, you may not need to rotate it much.

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The free-space azimuth patterns for 28.1, 28.5, and 28.9 MHz show the possibilities for the Moxon rectangle. Note the very broad forward lobe that is almost a cardioid, giving reception and transmission as wide as your peripheral vision. Behind you is silence--or at least a large dose of silencing. Les Moxon, G6XN, uses a wire version of the antenna with both elements remotely tuned: that way he works the world just by electrically reversing front and rear elements with a fixed mounting. Note also that the performance characteristics promise to hold up well across the most active part of 10-meters.

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But what about performance at real heights above ground?

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At 35' up, about 1 wavelength, the antenna provides most of its free space performance across the band. At higher mounting levels, the performance moves closer to free-space patterning. The elevation angle at 35' for maximum gain is 13-14 degrees.

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Even at 20' up, a typical portable antenna height at 10 meters, the antenna continues to display excellent front-to-back characteristics with the gain of a 2-element Yagi (which does not have good front-to-back characteristics at this height--perhaps 9-10 dB or so). The elevation angle of maximum radiation is about 23 degrees at the 5/8 wavelength height.

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The Moxon rectangle is quite stable with respect to feedpoint characteristics as the antenna is raised and lowered. The curves actually flatten some over real ground. Therefore, setting up the antenna for operation is simple.

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My own initial procedure was to fasten the antenna to a 20' mast propped up by a sturdy tripod. The reflector was no more than 5' above ground. I then adjusted the side-to-side length to minimize SWR at 28.45 MHz, sing the trombone-slide end sections. After fastening down the sections and raising the antenna, there was no detectable difference in SWR performance from the adjustment position pointing at the sky.

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A view of the completed all-aluminum (and a little PVC) Moxon for 10 meters atop its test mast. The CPVC element-end separators and corner pieces should be visible with reasonable clarity for comparison with the sketch.

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A close-up view of the test model feedpoint assembly and element mounting scheme. The PVC half-clamps should be replaced every 2-3 years before they grow brittle (about 4-5 years average in my climate in East Tennessee). The rear of the female coax connector and the coax junction should be weather sealed if the antenna is to be used for a permanent installation.

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Contrary to claims made for the VK2ABQ, these antennas do not like to be nested for a multiband array. Even stacking requires a minimum of 10' or more between 10 and 15 meter models. However, you might consider back-to-back 10 and 15 meter antennas. A 13' boom would hold both antennas, reflector-to-reflector with minimal interaction.

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It is unlikely that anyone will ever produce this beam commercially, since it is a monobander without the super gain that avid DXers and contesters crave. You can only get that kind of performance from many Yagi elements. However, you can build your own compact antenna with a pretty good chance of success on the first try. It will beat a fixed wire dipole or a dry-land vertical hands down at 20 meters and up. It also makes a dandy Field Day antenna. So if you need a compact 10-meter beam for your compact home site, then you might roll your own version of the aluminum Moxon rectangle.

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So why am I placing this item at the web site rather than sending it off to a magazine? My usual outlets have a backlog of items, and the article would not appear for over a year. Sunspots are approaching for 10 meters, and a year would perhaps force some folks to wait too long. Antenna-building season is upon us. In short, this seemed the best way to disseminate the information in the shortest time. If you have a friend who needs a shortened, but full performance 2-element antenna, and who does not have web access, pass along a copy.

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Updated 4-6-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Return to Amateur Radio Page

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Topics: HF Upper, Moxon


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The Elusive Moxon Nest

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L. B. Cebik, W4RNL

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For the last decade or so, since the Moxon Rectangle emerged as a compact full-size 2-element array of considerable utility, folks have searched for a means of nesting Moxons for more than one band. Despite G6XN's reported successful use of wave traps to isolate elements within a multi-band array, there has been little success in nesting rectangles that have been optimized for maximum gain, maximum front-to-back ratio, and a direct-feed 50-Ohm impedance.

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This report will examine some of the reasons why nesting Moxons is difficult. It will also describe a successful design that combines 17 and 12 meter Moxons in a nested pair with a common feedpoint.

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Background

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Moxon derived his rectangular tri-band array from the VK2ABQ square. Both designs used the coupling of parallel portions of a driver and a reflector element and the element-end coupling from the tails of the elements bent toward each other. The rectangle proved to have a higher gain than the square, while preserving a near cardioidal pattern with a very high front-to-back ratio.

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Since the early 1990s, I have refined the design of monoband Moxon rectangles to yield beams with about as much forward gain as a standard 2-element Yagi, but with only about 70% of the side-to-side width. The designs are quite broadband and are compatible with a 50-Ohm feedline. The result is an effective beam for the spatially challenged ham.

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However, the further stretching of the rectangle that produced these results presented a new challenge: nesting at least 2 Moxons on the same plane. Moxon "Christmas Trees" that provide vertical separation among antennas have been common, but trying to nest two Moxons proved detrimental to the performance of one or both antennas.

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As a sample of such a nest, let's put together fairly standard Moxons and see what happens. The following table lists the dimensions for the two bands, using what has become standard notation. In this and all of the design models for this report, the 17-meter elements average 0.75" in diameter, while the 12-meter elements average about 0.5" in diameter.

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A is the total side-to-side dimension. B is the length of the fold-back driver tail. C is the gap between tails. D is the length of the fold-forward reflector tail, and E is the length of the entire array from the driver back to the reflector--the sum of B, C, and D. Because we have nested the Moxons, I have added the dimension DR for the distance between the two drivers and the dimension RE for the distance between the two reflectors. I have also appended as a reference a guide to dimensions (Fig. 15) at the end of this report.

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Moxon Rectangles and Calculator page has a ready-to-use calculator for entering the design frequency and the proposed element diameter to arrive at monoband Moxon dimensions. As well, a number of stand-alone programs and equation-based models also exist for this purpose.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     Independently Fed Nested Moxon Rectangles for 17 and 12 Meters
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+All dimensions in feet
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+Dimension             18.118 MHz            24.94 MHz
+      A               19.46                 15.08
+      B                2.74                  1.99
+      C                0.63                  0.46
+      D                3.68                  2.13
+      E                7.05                  4.58
+      DR                         1.15
+      RE                         1.32
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Free-space E-plane or azimuth plots of the band-center performance of each array may give the illusion that we have a successful nesting. See Fig. 1.

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The patterns give the impression that we have an operable array with only a modest reduction in front-to-back ratio on the upper band. However, seeing the same data in tabular form, supplemented by feedpoint information, may give another impression altogether.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     Independently Fed Nested Moxon Rectangles for 17 and 12 Meters
+                        Modeled Performance Data
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+Category                    18.118 MHz            24.94 MHz
+Free Space Gain (dBi)       6.02                  5.88
+180-Deg Front-Back (dB)     29.50                 17.75
+Feedpoint Z (R+/-jX Ohms)   62.9 + j 2.7          6.8 - j 0.6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Although the performance promise is high, feeding the 12-meter rectangle poses a totally unsatisfactory problem. Let's see why.

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As shown in Fig. 2, the relative current magnitude distribution on 17 meters is virtually normal. Although there is measurable current on the 12-meter driver, it is sufficiently low that one can arrive at a 50-Ohm 17-meter feedpoint impedance by very small element adjustments that do not disrupt performance.

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However, on 12 meters, the situation is quite different. From its interior position, the 12-meter rectangle excites the 17-meter elements--both fore and aft--to very significant levels. The current levels are high enough to prevent the array from achieving anything close to a 50-Ohm feed impedance until the performance pattern is wholly unacceptable. The proximity of the parallel portions of the elements for each band prevents us from effectively isolating them on the upper band.

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An Intermediate Design

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The is a technique for ameliorating some of the effects of the close proximity of the Moxon elements. Fig. 3 shows the method in the form of an outline sketch.

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In the sketch, we have the same two rectangles, with only slight modifications to the dimensions, as shown in the following table.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Commonly Fed Nested Moxon Rectangles for 17 and 12 Meters
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+All dimensions in feet
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+Dimension             18.118 MHz            24.94 MHz
+      A               19.46                 15.08
+      B                2.74                  1.97
+      C                0.63                  0.38
+      D                3.68                  2.22
+      E                7.05                  4.57
+      DR                         1.15
+      RE                         1.32
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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We have adjusted the tails and the gap of the 12-meter antenna to suit the new feed conditions. As shown in the outline sketch, we use a common feedpoint on the 12-meter driven element. Between that point and the 17-meter feedpoint, we run a length (1.15') of 70-Ohm, 0.8 VF transmission line. The impedance and velocity factor values reflect foam versions of either RG-11 or RG-59.

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The phase line must be "normal," that is, the center conductor and the braid attach to the left or right sides, as applicable, of the drivers for both bands. Reversing the line at only one end disrupts its ameliorative action.

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Interestingly, the use of the common feedpoint and phase line does not significantly alter the current magnitude distribution on the array elements. However, it does make a significant alteration in some of the current phase values, and this change makes all the difference. The following table shows the modeled relative current magnitude and phase at the element centers for the independently fed and common-feed arrays.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+    Current Magnitude and Phase At Element Centers for a Moxon Array
+
+All values at 24.94 MHz
+
+Element                          Ind. Feed             Common Feed
+12-M Driver                      1.00/0.0 deg          1.00/-8.7 deg
+12-M Reflector                   0.80/152              0.86/119
+17-M Driver                      0.44/177              0.44/173
+17-M Reflector                   0.21/-81              0.20/-40
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

There is not much difference in the relative driver current magnitudes or phase angles. However, the reflector phase angles have changed significantly. This change is reflected in the performance figures for the array, shown in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Commonly Fed Nested Moxon Rectangles for 17 and 12 Meters
+                        Modeled Performance Data
+
+Category                    18.118 MHz            24.94 MHz
+Free Space Gain (dBi)       6.06                  5.47
+180-Deg Front-Back (dB)     27.24                 12.54
+Feedpoint Z (R+/-jX Ohms)   52.0 + j10.5          50.7 - j 3.6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although we have now obtained satisfactory feedpoint impedances on both bands, we have sacrificed performance. We have lost a half-dB of gain and about 5 dB of front-to-back performance at 12 meters, relative to the independently-fed but unfeedable version of the nested array. However, if these performance losses are not considered severe, then this version of nested Moxons is suitable for building.

+

To test whether or not these dimensions are excessively finicky, I ran a 400-kHz frequency sweep of the array on both bands.

+
+ +
+

Fig. 4 shows the gain and the relevant front-to-back ratios (180 degrees and worst-case) on 17 meters. The gain curve is completely normal for a 2-element parasitic array with a driver and reflector. It is also normal relative to monoband Moxon rectangles. The front-to-back ratios peak on the upper band edge but have more shallow curves than most monoband Moxons.

+
+ +
+

In Fig. 5, we find the corresponding curves for the 12-meter performance. The close coupling of the two array reduces gain and makes its curve sharper than normal Moxon gain curves. The peak is below the lower end of 12 meters but within the sweep passband. Because the front-to-back region shows only a single bulge and is fairly low, the 180-degree front-to-back curve is coincident with the front-to-sidelobe curve that indicates the worst-case front-to-back ratio. As well, the weaker values yield a quite shallow curve across the sweep passband.

+
+ +
The 17-meter (Fig. 6) and the 12-meter (Fig. 7) graphs of the feedpoint resistance and reactance are both very well-behaved--a key benefit of using the common feedpoint and phase line system. The 17-meter 50-Ohm SWR curve never rises above 1.45:1. However, the 12-meter curve is considerably steeper. Nevertheless, since the sweep passband is 4 times the width of the actual 12-meter amateur band, there is considerable leeway for construction variables without jeopardizing the ability to effectively feed the array with a 50-Ohm coaxial cable. +
+ +
+

An Alternative Nesting Strategy

+

To improve the performance of the 2-band array would require a design revision that further separates the parallel portions of the drivers and the reflectors. Most strategies applied to nested Moxons have concentrated on modifying the inner or high-band Moxon, since it shows the greatest departure from monoband performance. However, we might begin to focus on modifying the low-band or outer Moxon instead.

+

If we maintain a standard design for the Moxon, effecting increased separation between drivers and reflector involves returning the rectangle toward its squared origins. Widening the space between the driver and the reflector of a Moxon rectangle has two major effects. First, it reduces gain. A fully square VK2ABQ array loses about a full dB of gain relative to the Moxon. As well, the feedpoint impedance increases. So this direct of effort will only lose us the gain that we lost in our first successful nest and a little bit more. As well, we shall lose our 50-Ohm impedance match.

+

Now a side-note to prove that one sort of misunderstanding can lead to a different sort of understanding. I was reviewing the model of a recent OptiBeam commercial antenna which used a Moxon rectangle on 20 meters and a loaded Moxon for 40 meters. The main decoupling devices are stubs past each mid-element load, for which the designers have made patent application. The design also called for wider separation between element tails. (Since a loaded antenna normally results in a reduced feedpoint impedance, the wider gaps were required to raise the impedance back to 50 Ohms.) Between the tails, for mechanical support reasons, they introduced metallic tubes with insulators at each end.

+

My initial reaction was to interpret the new tubes as element end coupling wires to distribute the capacitive coupling of element ends in a series manner. However, Tom Schmenger, DF2BO, of Optibeam assured me that they were not part of the decoupling system. My secondary reaction was this: the tubes could be part of the decoupling system.

+

Suppose that we increased the spacing between elements just far enough to minimize the interaction between the drivers and reflectors for the two bands. To assure adequate element end coupling, we would introduce short elements--which we can call end-coupling wires--to sustain the element end coupling. What we would lose is some of the front-to-back ratio, which is dependent upon both the end coupling and the coupling between parallel portions of the elements for a given band. However, what we might gain is more satisfactory performance for the array's gain and for the feedpoint resistance and reactance.

+

The Modified Moxon Nest for 17 and 12 Meters

+

We can see the elements of the resulting array in the outlines of Fig. 8. The array is about 4' wider (front-to-rear) than our original nest. Note that we have retained the common feedpoint and the 70-Ohm, 0.8 VF line between the driver feedpoints, and feed the 12-meter element. Again, reversing the phase line harms performance. The line length is now 3.15'.

+
+ +
+

To provide dimensions (see the appended Fig. 15), we must introduce 2 new dimension terms. We now have gaps C1 (driver-to-coupling wire) and C2 (coupling wire to reflector). Of course, we also must specify the length of CW, the coupling wire itself. The coupling wire is the same diameter as the element tails.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+   Commonly Fed Nested Modified Moxon Rectangles for 17 and 12 Meters
+
+All dimensions in feet
+
+Dimension             18.118 MHz                  24.94 MHz
+      A               20.00            A          15.00
+      B                2.73            B           1.90
+      C1               0.11            C           0.45
+      CW               4.57
+      C2               0.10
+      D                3.54            D           2.22
+      E               11.04            E           4.57
+      DR                               3.15
+      RE                               3.32
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

That the system does isolate the high- and low-band elements becomes apparent from the relative current magnitude curves in Fig. 9. Indeed, the current ib the inactive elements due to coupling to the active elements is nearly equal for operation on both bands.

+
+ +
+

The general properties of the antenna patterns appear in the free-space E-plane or azimuth patterns for the centers of the two bands. As shown in Fig. 10, the 12-meter curve is completely normal for a monoband Moxon rectangle. However, as we surmised from pre-design analysis, the rear lobe of the 17-meter Moxon is significantly larger than that for the 12-meter rectangle.

+
+ +
+

Nonetheless, mid-band performance--especially on the less-active 12- and 17-meter bands seems to be quite adequate for a 2-element array. The following table of performance values derived from the models will bear out this conclusion.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+   Commonly Fed Nested Modified Moxon Rectangles for 17 and 12 Meters
+                        Modeled Performance Data
+
+Category                    18.118 MHz            24.94 MHz
+Free Space Gain (dBi)       5.95                  6.19
+180-Deg Front-Back (dB)     14.32                 30.32
+Feedpoint Z (R+/-jX Ohms)   69.7 - j 0.9          58.4 + j 1.9
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 12-meter performance is Moxon-normal. The 17-meter performance has restored virtually all of the rectangle's gain, while its front-to-back ratio is over 2 dB better than the 12-meter value for our initial common-feed nested Moxon pair. The feedpoint impedances are well within acceptable levels.

+

To test whether the array is buildable or simply too finicky for practical basement construction, let's sweep the array on both frequencies. We shall use the same 400-kHz sweep range that we applied to the initial nested pair.

+
+ +
+

Fig. 11 gives us the gain and front-to-back information for 17 meters. The gain curve is once more normal for a parasitic 2-element driver-reflector array. The 180-degree and worst-case front-to-back curves coincide in a very shallow and stable value set that reflects the wider element spacing. We might classify these curves as "well-behaved."

+
+ +
+

The corresponding 12-meter curves in Fig. 12 are equally well-behaved, although the front-to-back curves are more Moxon-esque, with a peak just below the lower end of the amateur 12-meter band. Even the worst-case curve is greater than 20 dB at both sweep passband edges. The gain curve is also completely normal.

+
+ +
+

Since the 50-Ohm SWR curve for 17 meters is shallow, as shown in Fig. 13, I thought it unnecessary to further modify the outer array to seek a perfect 1:1 value within the amateur band. Some slight tweaking may be possible, but it will involve juggling not only a driven element overall length, but as well, the length of the coupling wire. It is likely that under any modification, the very small gaps at each end of this wire will remain fairly constant at around 0.1' (between 1.2" and 1.4"). Nonetheless, the rates of change for both the resistance and reactance are quite tame.

+
+ +
+

The SWR curve for 12 meters, shown in Fig. 14, is a bit steeper, although it bottoms out just below the low end of the amateur band. The chief source of the steeper--but entirely acceptable--curve is the rate of change of resistance. This higher rate of change is a function of the closer spacing between the driver and reflector on this band.

+

I am placing the dimensional guide to the main variations on nested Moxon arrays (Fig. 15) at this point, since it functions more as a reference than as array information.

+
+ +
+

A Third Alternative: 1/8-Wavelength Stubs

+

There is a third alternative for a nested pair of Moxon rectangles--using our designated 17-meter and 12-meter pair. This alternative employs 1/8 wavelength stubs somewhat after the fashion of the OptiBeam 40-meter-20-meter combination. However, unlike the Optibeam 40-meter antenna, our 17-meter Moxon is not loaded. As a result, we can place the stubs close to the feedpoint of the antenna, as shown in the tilted-image sketch in Fig. 16.

+
+ +
+

Ideally, the stubs should be as close as feasible to the feedpoint. However, to ensure that the feedpoint of the driver has equal length segments on either side of the source segment, the stubs begin about 0.7' each side of element center. As well the 17-meter feedpoint is an indirect one, being the termination of a 70-Ohm, 0.8-velocity factor line from the combined feedpoint on the 12-meter driver. The line length in this case is 1.23'. The following table provides complete dimensions for the new nested array, including the distances between drivers and reflectors and the stub lengh.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+   Commonly Fed Nested/Stubbed Moxon Rectangles for 17 and 12 Meters
+
+All dimensions in feet
+
+Dimension             18.118 MHz            24.94 MHz
+      A               19.46                 15.22
+      B                2.54                  1.91
+      C                0.80                  0.50
+      D                3.70                  2.13
+      E                7.04                  4.54
+      DR                         1.23
+      RE                         1.27
+      Each Stub                  4.93
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The stubs are almost exactly 1/8 wavelength long at 24.94 MHz. The initial model used 0.1" diameter stub elements. However, varying the diameter up to 0.25" yielded virtually no change in the required length for optimal performance on each band. You may also note that this array requires modification of the dimensions used for the stub-less nested Moxon array. The stubs alter the pattern of coupled current magnitude and phasing on the 17-meter elements when the antenna is operated at 24.94 MHz. See Fig. 17. As the 12-meter current magnitude distribution curves show, even stubs do not effect complete isolation from significant coupling. Instead, they tend to render the coupling less troublesome to effective operation.

+
+ +
The net result is reasonably good performance on both bands, although--as shown in the following performance table--the front-to-back ratio at 12 meters does not quite match that on 17 meters. Nonetheless, it is superior to the front-to-back ratio for either of the preceding alternatives when reference to the non-optimal band. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+   Commonly Fed Nested/Stubbed Moxon Rectangles for 17 and 12 Meters
+                        Modeled Performance Data
+
+Category                    18.118 MHz            24.94 MHz
+Free Space Gain (dBi)       6.19 (6.05)           5.84 (5.95)
+180-Deg Front-Back (dB)     34.62                 17.95
+Feedpoint Z (R+/-jX Ohms)   43.3 - j 2.1          36.6 + j10.1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The values of maximum forward free-space gain in parentheses are adjusted figures based upon the AGT value for the model at each design frequency. Despite the use of a stub element that differs in diameter from the main elements, the NEC-4 AGT at 18.118 MHz was 1.034 (gain high by 0.14 dB) and at 24.94 was 0.974 (gain low by 0.11 dB). +
+ +
+

Fig. 18 provides us with free-space E-plane or azimuth patterns for the array at each design frequency. In all of the non-optimal azimuth patterns, one may notice that with lowered front-to-back values, the beamwidth and overall cardioidal pattern shape diminished relative to the pattern under optimal Moxon conditions. As we did for the other major nests of 17-meter and 12-meter Moxons, we ran a frequency sweep of 400 kHz, with the relevant amateur band roughly centered in the sweep.

+
+ +
The 17-meter gain and front-to-back data are in every way normal for a Moxon rectangle, despite the presence of the stubs, as shown if Fig. 19. The rates of change of gain and of both the 180-degree and the worst-case front-to-back ratios are comparable to those of a monoband version. However, it is easier to center the peak front-to-back ratio and the SWR at the same frequency in a monoband version of the antenna. +
+ +
+

The comparable gain and front-to-back data for the 12-meter elements, as they appear in Fig. 20, show reductions in bandwidth, despite the shallower front-to-back curves which overlie each other. The highest gain occurs very close to the lower edge of the sweep passband and peaks well below the value of a typical monoband rectangle or of a rectangle with better isolation between the lower- and higher-frequency elements.

+
+ +
+

The resistance, reactance, and 50-Ohm SWR curves in Fig. 21 show that the close coupling of elements--despite the isolation effected by the stubs--still presents a fairly steep SWR curve on 17 meters, although the value remains below 2:1 across the swept passband. The culprit is the resistance, which does not reach 50 Ohms at the design frequency. Nonetheless, a good SWR value within the 17-meter band is easily obtained.

+
+ +
+

On 12 meters, as shown in Fig. 22, the situation differs, but in a manner parallel to the gain values in Fig. 20. Like the rapidly changing gain, the resistance changes value more rapidly with frequency than for a monoband 12-meter Moxon. As well, it also does not rise to 50 Ohms until well-above the 12-meter amateur band. Hence, the 50-Ohm SWR curve is quite steep below the design frequency. Under these conditions, the 12-meter portion of the array has a narrower operating passband than does the 17-meter portion.

+

The stubbed and nested pair of Moxon rectangles offers a more compact arrangement than the modified array, but remains under the influence of mutual element coupling based on element proximity. However, it offers better 12-meter performance than the un-stubbed version of the compact arrangement. The trade-off is a somewhat narrower operating range.

+

Conclusion

+

Any of the variations on the nested Moxon pair is likely to serve quite well on 17 and 12 meters for the space-starved modern amateur. The modified outer Moxon version has slightly better performance figures than the unstubbed common-feed array but not as good as the stubbed array. The cost to the modified design is two lengths of tubing and 4' of front-to-rear width. The stubbed array, however, has a narrower operating bandwidth, which translates into somewhat more finicky construction and adjustment than the other two versions. In all three cases, the common feed with a phase line is not merely a convenience. It is a necessity to drive the arrays to their performance potential.

+

Translating these designs to available materials will likely require considerable design effort and a reliable modeling program. NEC-2 does not provide accurate results if one uses several diameters of tubing for the elements, since the corner bends will prevent the Leeson correctives from activating in either EZNEC or NEC-Win Plus. These correctives only activate with symmetrical linear elements. Perhaps the most effective work-around is to re-design the array using the average value of diameter with uniform-diameter modeling elements. The results will be accurate for that diameter, but not exact for the actual tubing sizes used. Nonetheless, our analyses suggest that the design is not so finicky as to prevent fully adequate performance. Perhaps--as in all Moxons--the most critical dimension is the gap (or the gaps).

+

I would also not recommend nesting Moxons in any of these systems for adjacent bands, such as 12 and 10 or 15 and 17 meters. The drivers and the reflectors for each band are that much closer together, with stronger interactions. However, skipping a band makes a 20-15 or a 15-10 version of the array entirely within the realm of practical feasibility.

+

We have not seen the last word on nesting Moxon rectangles. The techniques used in these designs simply contravene my earlier experience in which the nesting problem seemed insurmountable. However, I always expressed my frustration in terms of not "yet" finding a way to effectively nest Moxons. I now have three ways to do that, even if none of them is absolutely optimal. But, then, the future offers plenty of time to more closely approach the ideal of nested Moxons such that each rectangle in the nest performs like a monoband version.

+
+ +
+

Updated 06-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: HF Upper, Moxon


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The Moxon Rectangle: A Review

+

+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+ The Moxon rectangle is a fascinating antenna on several scores. Although I have written about this design before, questions still pop up regularly. So perhaps a review of the antenna can put a few things into the right perspective. +

The Moxon rectangle is a 2-element parasitical beam or unidirectional antenna about 70% the length of a full size 2-element Yagi of standard driver-reflector design. The rectangle, however, far exceeds other 2-element beams in front-to-back ratio, while almost equalling them in gain. This combination of properties is prized by those who adhere to the "good ears" theory of hamming.

+

Origins

The Moxon rectangle is a derivative of the VK2ABQ square. Some folks still call Moxon's design a version of the square. Fred Caton, VK2ABQ, discovered that if you take a quad loop and lay it horizontally, you can get some directivity and gain in the direction of the feedpoint by a simple action. Cut the loop at each side in the center and insulate the two resulting half wavelength wires from each other. Fred used close spacing by inserting large buttons as insulators. The basic outline of the VK2ABQ square is in part A of Figure 1. +
+ +
+

Les Moxon, G6XN, whose book HF Antennas for All Locations is now in its second edition, made two very significant discoveries about the Caton squares. First, a rectangular shape would improve gain. Second, the spacing between the ends of the wires is critical to proper antenna operation, and that spacing had to be greater than that provided by even the largest coat button. These significant improvements are noted in part B of Figure 1.

+

G6XN used a rectangle composed of two equal lengths of wire. However, he tuned each wire remotely from the shack, thus giving himself a fixed position reversible beam. He also developed a detuning addition to the elements to allow him to nest several bands' worth of rectangles.

+

My own work, aided considerably by the emergence of modeling software, has been devoted to refining and understanding the characteristics of the Moxon rectangle. To those ends, I developed the antenna as a uni-directional beam, allowing the elements to have their own native dimensions instead of electrically tuning them. This tack, shown in part C of Figure 1, led in turn to an understanding of why the antenna does what it does so well.

+

What Does a Moxon Rectangle Do?

+
+ +
+

Figure 2 shows the free space azimuth pattern of a 20-meter all aluminum Moxon rectangle that we shall describe later on. At its design frequency, the antenna provides a forward lobe with a beamwidth so wide that it is nearly cardioidal. The forward gain is down from a full size 2-element Yagi only by about 0.2 dB. At the same time, the rear lobe is minuscule (compared to a front-to-back ratio of about 10- 12 dB as typical of a full size 2-element Yagi). The Moxon achieves this pattern without the use of a phasing line.

+

The combination of parasitical coupling from the parallel portions of the elements and the end coupling of the wires produces a current magnitude and phasing on the reflector element that is superior to that of many phased arrays in terms of effecting a rear null. Even the best ZL Specials and HB9CVs also leave quartering rear lobes that are often down by well under 20 dB. The Moxon geometry, which includes the side wires or tails, tends to suppress those rear lobes, resulting in a very quiet rear quadrant.

+
+ +
+

Although the most suppressed rearward pattern is frequency specific, the Moxon pattern holds up quite well across a ham band. Figure 3 shows the combined patterns for 14.05, 14.175, and 14.3 MHz for the example at hand. The gain changes by about 0.6 dB across the band, while the front-to-back ratio is still around 20 dB near the band edges.

+
+ +
+

Not only does the pattern hold up well, so too does the feedpoint impedance. The 20-meter model at hand was designed for a 50-Ohm feed-- which is a natural for the rectangle--and Figure 4 shows the 50-Ohm SWR curve across 20 meters. Coax feed--with a choke, of course--is the order of the day.

+

Building an Aluminum Moxon

Construction techniques vary with individual builders. For 10-meters, I tend to use PVC booms, which keep the elements well insulated and distant from detuning effects. However, the Moxon can be built using an aluminum boom with suitable insulating plates. +

For tubing models, the Moxon corners can be a challenge. You can bend corner section of the next size larger or smaller tubing than the 1" size used in the 20-meter model. Or, you can try various fittings designed for other purposes, such as electrical conduit corners and the like.

+

The one critical factor is keeping the element ends in a fixed position relative to each other. I tend to use light-weight CPVC sections inserted into each aluminum tubing end, with sheet metal screws as simple position holders.

+
+ +
+

Figure 5 shows the operative dimensional parts of any Moxon rectangle. For the aluminum 20-meter Moxon, the length (A) is 25' and the overall width (E) is 9'. This yields a beam not much different than the size of a 2-element 15 meter antenna, but resonant on 20 meters.

+

The driver tail (B) is 3.5' long, while the reflector tail (D) is 4.7' long. The spacing between tail ends (C) is 0.8'. If you use tapered diameter elements or change the element diameters altogether, you should refigure the antenna with one of the antenna modeling programs.

+

For an interesting case study on the construction of a 20-meter Moxon rectangle, see "The Moxon Rectangle," by Morrison Hoyle, VK3BCY, in Radio and Communications (Australia), July, 1999, pp. 52-53.

+

Wire Moxons

Setting up wire versions of the Moxon has proven popular for coastal Field Day systems. The methods of construction can range from a center hub and light rods to support a rotatable wire antenna to a 4-corner support arrangement for a fixed-position version. +

Although I have published some numbers for wire Moxons before, here is a list of dimensions, using Figure 5 as a guide. {Later Note: These dimensions are based upon models crated prior to the development of the "MoxGen" algorithms. Using the later development allows you to select your element diameter as part of the design process.]

+ 
                  Table 1.  Moxon Dimensions for 40 - 10 Meters
+
+Band     Design                      Dimension  (feet)
+       Frequency (MHz)   A              B         C         D        E
+
+10      28.50          12.44          1.94      0.41      2.41     4.76
+
+12      24.94          14.22          2.22      0.46      2.76     5.44
+
+15      21.20          16.72          2.63      0.52      3.25     6.40
+
+17      18.12          19.56          3.10      0.59      3.80     7.49
+
+20      14.17          25.00          4.00      0.72      4.85     9.57
+
+30      10.12          35.00          5.60      1.00      6.80    13.40
+
+40       7.15          49.56          8.01      1.33      9.63    18.97
+
+Note:  all wire models composed of #14 copper wire.
+
+

All of the antennas exhibit feedpoint impedances between about 56 and 58 ohms at the design frequencies, a close match to the standard amateur 50-ohm coaxial cable. Free space gain and front-to-back ratio are consistent for all the models, averaging 5.8 dBi and greater than 32 dB in free space, respectively.

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For a reversible direction wire Moxon rectangle with a stub-tuned reflector, see "Two-Element 40-Meter Switched Beam," by Carroll Allen, AA2NN, in The ARRL Antenna Compendium, Volume 6, pp. 23-25. The same volume also contains an expended treatment of the all-aluminum 10-meter Moxon that appears elsewhere in these pages.

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Performance Over Real Ground

Free space patterns are one thing, and performance over real ground at various heights quite another. To provide an idea of how well the Moxon patterns hold up, the following three figures give azimuth patterns at three different heights at 14.05, 14.175, and 14.3 MHz for the aluminum 20-meter version of the antenna. +
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The pattern group at 35' up (1/2 wl) in Figure 6 shows that the antenna maintains quite usable forward gain and front-to-back ratio, although the rear patterns do not quite match the free space nulls.

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At 55' up (about 3/4 wl on 20 meters), Figure 7 shows that the rear lobes are almost non-existent at center band--and very good at the band edges.

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At 70' up (1 wl), the antenna shows a still different rear aspect, as revealed in Figure 8. At all three heights, the SWR curve does not depart significantly from the free space curve shown in Figure 4.

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Tuning up a Moxon rectangle--or adjusting the dimensions for other materials--is straightforward. The length (A) tends to control the overall impedance. However, adjusting the driver tail (B) has the most immediate affect on feedpoint reactance. Adjusting the reflector tail (D) affects most the resistance at the feedpoint. The spacing (C) has the greatest affect upon the place of the deepest null within the ham band of choice. These guides assume that the antenna has been initially adjusted within some sort of ballpark specification set.

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The wire dimensions use slightly longer tails and slightly closer spacing between tail ends than the tubing models to achieve roughly the same results and feedpoint impedances. Tubing models tend to show slightly (operationally insignificantly) higher gains (about 0.15 dB), as well as shallower SWR curves. However, a wire model for 20 meters would easily cover the band.

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Other Moxon-Rectangle-Related Developments

The Moxon rectangle principle shows up in a number of designs, some of which make clear reference to G6XN's work and others of which seem unaware of the roots of the antenna. The Double-D of Peter Dodd is an interesting design for a very compact "garden" and has recently been redesigned for the 2nd edition of G3LDO's well-known book, Antenna Experimenter's Guide. At the other extreme, a recently introduced 80- meter 2-element beam on the US west coast uses the Moxon design (with a slight Vee to the parallel portions of the elements) with no reference to G6XN. +
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The principle also has application to 3-element design. The optimized 40-meter "V-Yagi, " (superficially resembling an older G4ZU design) by Nathan Miller, NW3Z, and Jim Breakall, WA3FET, in QST for May, 1998, has an azimuth pattern quite similar to those shown for the Moxon rectangle, but with the higher gain associated with three elements. See Figure 9. The wire director and reflector angle back toward the driven element, effecting some degree of end coupling while retaining parasitic characteristics. More recently (about 2003), some German hams have developed multi-band upper HF beams for field use made from wire and employing the same general principles. See www.spiderbeam.com for more details, including the availability of a manual for building your own.

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Whether you call the antenna a VK2ABQ square, a Moxon rectangle or something else, the design is well worth considering if you want a compact beam about 0.35 wl long by 0.13 wl wide with a direct coax match. For those who desire more QRM rejection than raw gain, the design has much to offer.

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For further reading, see the following:

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"Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and Moxon Rectangles," Communications Quarterly (Spring, 1995), 55-70.

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"Moxon Rectangles for 40-10 Meters," QRPp (December, 1995), 25-27.

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Updated 12-18-1999, 02-28-2005 . © L. B. Cebik, W4RNL. A version of this item first appeared in AntenneX, Oct., 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Return to Amateur Radio Page

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Topics: Moxon


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Further Notes on 40-Meter Wire Moxon Rectangles

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L. B. Cebik, W4RNL

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The growing interest in the Moxon Rectangle as a wire beam for 40-meter use has prompted me to collect some of my casual notes on the subject and place them here. The aim is to provide a few extra ideas for those wishing to experiment with the antenna.

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We can divide the notes into two parts. The first will look at some alternative "wires" that we might use to build the 40-meter Moxon rectangle. We shall discover that the choice of materials has some consequences worth noting.

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The second part will discuss the potential of the Moxon Rectangle as a bi- directional wire beam, using a simple "switching" mechanism.

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What Size Wire Shall I Use?

The standard sketch of the Moxon Rectangle used in all of the notes on this antenna appears in Fig. 1. +
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For convenience, I shall refer to dimension A as the "side-to-side length" and to dimension E as the "front-to-back width."

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In another note in this series, I provided dimensions for a 40-meter Moxon Rectangle made from #14 wire and design to provide a reasonable match to 50-Ohm coaxial cable. That design was centered on the band center (in the U.S.) of 7.15 MHz. One consequence was that the design did not provide a 2:1 VSWR curve that covered the entire band.

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By lowering the center frequency just a little, the VSWR objective can be attained without undue loss of operating properties at the upper end of the US 40-meter band.

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#14      Design                      Dimension  (feet)
+Cu     Frequency (MHz)   A              B         C         D        E
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+40       7.08          50.05          8.09      1.34      9.73    19.16
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This revision was part of a larger group of models, the differences of which are summarized in Fig. 2.

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I also experimented with a model of the antenna made from 2" diameter aluminum, again striving for a 50-Ohm feedpoint impedance with under 2:1 VSWR across the band. The resulting dimensions are as follows:

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2.0"     Design                      Dimension  (feet)
+Al     Frequency (MHz)   A              B         C         D        E
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+40       7.10          49.91          6.99      1.60      9.38    17.97
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Note the shortening of dimension A, with the increase in element diameter. However, the major changes occur in dimensions B and C. The tail length of the driver is nearly 1' shorter than for the #14 version, and the required spacing for the element ends (dimension C) is about 2" greater. Remember that the most critical building dimension for the Moxon rectangle is the spacing of the element tails, so the 2-inch change may be more important than the larger tail length change. In all modes of construction, strive to make sure the element end spacing remains constant as the antenna moves in the wind.

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The aluminum Moxon rectangle was a thought experiment, although a similar antenna, composed of a wire and tubing combination, is made commercially. A more practical version of the antenna might consist of simulated large diameter wire. The simulation consisted--for my modeling experiment--of two #14 wires spaced 3" (0.25') apart--a reasonable set-up for shop-made parallel transmission line and hence a possibility for the antenna structure. The wires come together at their ends. for the reflector, that means junctions at the element ends only. For the driver, junctions occur at the element ends and at the feedpoint. The dimensions that modeled within our design goals are these:

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2x#14    Design                      Dimension  (feet)
+Cu     Frequency (MHz)   A              B         C         D        E
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+40       7.10          49.59          6.28      2.26      9.68    18.22
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Because two parallel wires do not act in exactly the same way as a single fat wire, changes occurred in all dimensions. With respect to the front- to-back width, the driver tails grew shorter and the spacing larger. However, the reflector tails also grew, relative to the aluminum model.

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Now for some interesting results, which I have graphed from frequency sweeps of the three antennas across the US 40-meter band. The figures are for free space, but the Moxon rectangle translates these very reliably into performance at any chosen height above the ground. See some of the other notes in this collection for changes of pattern that occur as we move from free space to realistic antenna placement heights.

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Fig. 3 provides comparative gain curves for the three versions of the antenna. Note that the single #14 wire version has the steepest curve. The 2" aluminum model has the shallowest curve, even shallower than the higher gain double #14 version. This further shows that while a double wire is a useful simulation of a single fat wire, it is not an exact replacement.

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The gain progression from the single #14 wire to the 3"-spaced pair is clear. Whether the gain increase is worth the added complexity or weight of construction is a builder option.

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More significant are some interesting facts about the rectangle. Although the geometry is not closed, the Moxon shares a property in common with the single quad loop (and beams composed of multiple quad loops). Wire versions are relatively inefficient. Almost any antenna design has a minimum diameter (and consequential surface area) for the efficiency to approach or surpass 99%. #14 wire is too small to achieve this figure in the Moxon rectangle, since the single wire model reports a 95.3% efficiency. The 2" elements of the aluminum are more efficient, despite the increased resistivity of aluminum compared to copper. The NEC report was 99.7% efficiency. Part of the improved gain of the aluminum model undoubtedly comes from the improved efficiency.

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Part--but not all. Remember that the design goal was to retain something close to a 50-Ohm feedpoint impedance. The dimensions changed in every respect, and those changes also play a role in spacing the parallel portions of the elements and in spacing the element ends to yield better gain. The evidence for this comes from the reported figures for the double-wire #14 version of the antenna: the gain is systematically higher, but the efficiency is only 96.8%, well under that of the aluminum beam and not much higher than that of the single-wire #14 model.

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The 180-degree front-to-back curves in Fig. 4 show a tight coincidence between the two "fat-wire" version of the antenna. The single-wire #14 version also has a peak front-to-back value that comes close to those of the other two models. However, it occurs at about 7.07 MHz. If we arbitrarily place a point at that frequency in the neighborhood of 32 dB, we would immediately see that the "thin-wire" version of the antenna has a much steeper curve than the other two models.

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In this case, effective wire thickness has a direct bearing on the broadness of the front-to-back characteristic of the rectangle. The double wire does not quite match the values across that band that are achieved by the aluminum model, but the differences are relatively insignificant. Compared to either "fat-wire" model, the single-wire #14 version is extremely thin--and that takes it toll on the front-to-back ratio-- especially at the upper end of the band. For those with narrower 40-meter windows, the difference might not make any difference at all.

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The VSWR curves in Fig. 5 show that any of the antennas would provide a 2:1 operating bandwidth that covers the entire band. Since the single wire center design frequency is below 7.1 MHz, its lowest SWR value does not show. The double-wire version of the antenna was optimized only to the point of providing a 50-Ohm SWR under 2:1 at the band edges. Further tweaking would drop its curve lower, but at no essential gain in any other operating parameter.

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Greater dimensional changes are likely to occur as a result of adopting one of the recommendations often made for double-wire or cage construction. To keep the current the same in each wire at any length along the antenna, some builder use periodic shorting wires across the two wires. The effects on the dimensions of this practice have not yet been modeled.

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An additional builder option may also occasion a change in the listed dimensions, especially in the spacing of the element ends. The model developed for this exercise used "blunt" ends, that is, wires brought to parallel points with a shorting wire across them. If the builder brings the element tails to a point, the coupling between the driver and reflector element ends will be reduced, very likely requiring that the space between ends be closed somewhat.

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Whatever, the variables, these three versions of the 40-meter Moxon rectangle provide some insight into the operation of the antenna. They also offer some challenges to the builder in getting the most out of the array.

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A Bi-Directional Moxon

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In other notes on lower HF wire beams, I introduced two designs by AA2NN--one for a bi-directional Yagi, the other for a bi-directional Moxon. These notes deserve some repetition and embellishment here, since fixed wire beams often earn their space by working in two directions.

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Fig. 6 notes the basic features of a bi-directional Moxon. Each element is cut as a driver and hence are identical. The feedline chosen as the driver line acts as simply another section of the main feedline. The feedline section selected as the reflector line is a stub that electrically loads the element to proper reflector length. Like all of the rectangles in this note, the design frequency was low in the band to provide operating coverage over the full 300 kHz spread. The dimensions of the design considered here are as follows:

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#14      Design                      Dimension  (feet)
+Cu     Frequency (MHz)   A              B         C         D        E
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+40       7.08          50.05          8.09      1.34      8.09    17.52
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If you compare the design to the single-wire #14 copper rectangle, you will see that the driver has not changed, but the reflector has been shrunk to match the driver. The spacing between element remains as before.

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The result is a design centered on the CW end of 40 meters. The AA2NN design uses different dimensions to center the design in the U.S. phone portion of the band. Interestingly, despite seemingly significant differences in the dimensions, the required stub lengths to load the reflector are within 1 degree of each other.

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The inductive loading reactance required to restore the array to peak performance at the design frequency is about 73 Ohms (subject to variations according to the circumstances of installation). An equivalent shorted stub of 50 Ohm coax is 55.6 degrees long--or 21.45' if the velocity factor (VF) were 1.00. (Simply multiply this length times the velocity factor of your own coax to get the final length.) If a much longer line is needed to reach a ground-mounted central remote switch, you can add 180 degrees (1/2 wl) to this figure. If an intermediate length is required, you can use an open-ended stub that is 145.6 degrees long--or 56.18 feet at a VF of 1.00. Techniques for calculating the length of stub lines from the required reactance appear in most antenna manuals.

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Expect losses from the stubs. The longer the stub the higher the loss. For most parasitic arrays, reflector stub losses result in slightly reduced gain, but may actually increase the front-to-back figures relative to modeled ideals. The switch or relay converting the stub from and to part of the transmission line system should be DPDT. In stub use, the center conductor and the braid of the stub should be independent of the center conductor and braid of the main feedline, whether used in a shorted or open configuration.

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Let's compare the performance of the bi-directional #14 copper Moxon with the one-way counterpart.

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In Fig. 7, we can see that the gain curve of the bi-directional model is slightly steeper than the curve of the one-way model. Loading the reflector yields slightly different relative current magnitudes and phases on the elements at all but one frequency. However, the differential is not operationally significant.

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In Fig. 8, we can see the effects of using a loaded reflector. The front- to-back curves of the two antennas are almost perfectly parallel. However, the bi-directional model shows a lower front-to-back ratio, partly due to the closer spacing of the horizontal wires that results from loading and element that is only as long as the normal driven element. To this front-to-back figure, one must add the effects of stub losses, which are not accounted for in the model. The operational difference from the model will be insignificant compared to differences created by the circumstances of installation.

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Fig. 9 shows comparative 50-Ohm VSWR curves. With a bit of further dimensional juggling, the curve for the bi-directional model can be brought within 2:1 values for both band edges. However, the curve given is sufficient to note that the bi-directional model displays somewhat sharper tuning than the one-way version. With a load in the reflector element, the reactance tends to increase more rapidly across the band.

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Nonetheless, the bi-directional Moxon rectangle can be designed to provide full band coverage of 40 meters--or to be focused in one favorite segment of the band. There is no significant performance degradation except for a little of the front-to-back ratio. I have not carried out any bi- directional modeling exercises using the double-wire model, but it should perform within similar limits relative to its one-way version.

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As a monoband array, the Moxon rectangle remains one of the most flexible compact wire beams around. I hope these notes encourage further experimentation with the design. Many untouched possibilities remain to be discovered.

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Updated 5-4-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Return to Amateur Radio Page

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Topics: HF Lower, Moxon


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Building a 2-Meter Moxon

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L. B. Cebik, W4RNL

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In a past issue of AntenneX, I described the properties of a 2-meter Moxon rectangle and surveyed some potential uses for the antenna. There are almost innumerable ways to build the antenna--that is, ways to support the elements. However, it may be useful to go through the process of building a Moxon rectangle at least once as an exercise that may trigger further creative construction thoughts of your own.

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What the Moxon Can Do

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The basic azimuth pattern of a Moxon shows, at its design frequency, a deep null, with some forward gain. For most VHF uses, it is the pattern shape, with its very high front-to-rear ratio, that holds more interest than the antenna's gain.

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Fig. A shows the azimuth pattern of a 2-meter Moxon when the antenna is vertically oriented and, hence, vertically polarized. Patterns are shown across the 2-meter band for a model designed for 146 MHz. Even though the deepest null occurs only in the vicinity of the design frequency, the front-to-rear ratio--accounting for the full rear quadrant--is very good anywhere in the band.

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Moreover, as Fig. B shows, the antenna has a very broad operating bandwidth. The SWR curve never reaches 1.4:1 anywhere in the band. For reference, here are band edge and center numbers for a modeled 3/16" element diameter Moxon placed at a height of 30', with readings taken at an elevation angle of 3 degrees:

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Freq.     Gain      F-B       Feed Z
+ MHz       dBi       dB       R +/- jX
+144       10.7      18.6      40 - j 10
+146       10.4      40.0      52 + j  1
+148       10.1      19.7      63 + j 10
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A 3-element Yagi might exceed the gain by about 2.5 dB, but would not equal the Moxon's front-to-rear pattern.

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Vertically polarized, the Moxon can be useful in preventing interference when two repeaters use the same channel and can be accessed from some particular location. The fact that access is already possible suggests that gain is not an important consideration. However, reducing one's signal to the repeater not desired is a very significant goal. Likewise, at a repeater site itself, being able to direct one's signal away from a co-channel repeater may also be necessary on occasion.

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The advantage of the Moxon over the standard vertical antenna shows clearly in Fig. C. The model uses a vertical dipole, but patterns for a monopole with ground-plane radials or a J-pole would be very similar to those for the dipole. The most important portion of the graphic to examine is where the Moxon pattern does not go. Since my area has a number of very strong repeaters in many directions, I decided to test the Moxon by building one.

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The Basic Antenna Configuration

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Fig. 1 shows the basic outline of a Moxon rectangle for 146 MHz using 3/16" aluminum rod elements.

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Essentially, I settled in on the Moxon dimensions from 2 directions. I scaled a 1/8" element diameter model upward, and I scaled a 1/4" element diameter model downward. In this way, I arrived at 2 sets of dimensions, both of which promise to perform equally well. The dimension sets-- versions A and (B) in the sketch--represent limits within which to build a real antenna. The most critical dimension is the gap between the driver and the reflector, with a required limit to variations of less than 1/4". Notice that, despite slight changes in the side-to-side and the front-to- back dimensions, the driver and reflector overall lengths remain relatively constant. Hence, it is desirable to set the element pieces to the correct length as the first act in building.

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I selected 3/16" aluminum rod initially because I had some on hand from another project. However, for full band coverage with maximal front-to- back values, 3/16" rod (about 4 mm) is necessary.

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The antenna and support details appear in Fig. 2. Looking at details B-B and C-C, we can see the plan of assembly and feeding. The antenna will consist of 4 rods, each threaded to 10-24 on one end. The driver will have pairs of 10-24 stainless or aluminum nuts to hold terminal rings from the feedline. The reflector half-elements will join in a stainless steel coupling nut (a short piece threaded all the way through). You can purchase these or make one from a small piece of 1/2" by 1/2" aluminum stock. Simply drill though the piece from end to end and tap the required 10-24 threading.

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My favorite antenna support material is Schedule 40 PVC. As frequency increases, I like to minimize contact with the material. It would appear that Schedule 40 PVC varies in exact composition from one part of the US to another. In some places, UV retardants are effective, while in others, they are either ineffective or non-existent. Likewise, RF characteristics may vary from one manufacturer to another. By minimizing contact with the elements, any RF deficiencies in the PVC have little or no effect on the antenna.

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In Fig. 2, you can see the scheme I used. 1/2" nominal PVC is glues into a T, with elbows pointing upward in the sketch. The elements pass through end caps. These caps and the pipe stubs necessary to cement them to the elbows permit the use of set screws that pass through threaded holes in the double thickness of PVC. With threading that deep, setscrews work well, although other methods can be used to ensure that the element do not move. One system that also works is to use short pieces of plastic tubing over the rods between the PVC supports and the nuts.

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Fig. 2 also shows a center Tee fitting for connection to a mast. This fitting is optional and would be suited more to the horizontal use of the antenna. Lets look at the alternative I actually used in Fig. 3.

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When vertically orienting the Moxon, a rear support system is very useful. We can make one up out of more PVC fittings and pipe. For my test antenna, I used a single PVC pipe section between elements, with the reflector center point holding a 4-way cross fitting. Another pipe stub proceeds rearward and friction fits into the Tee in the support. I drilled two sets of holes through the stub so that I could change the antenna's orientation from vertical to horizontal and back by removing only a single bolt.

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The support consists of a straight section and an angular section, forming a strong triangle. The terminating sections are 1.25" to 1/2" adapters sections. The antenna support pipes fit into the 1/2" side ports, while the 1.25" through sections receive piping of the same size to fit over a standard TV mast. Clamps mounts are shown, although one might also use set screws. The space between the upper and lower adapters can consist of the short clamps pipe sections shown, or the space can be filled with a single section of 1.25" nominal PVC. The resulting structure has a bit of flexibility, but stands up to abuse very well.

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One of the keys to building a good PVC structure is to be prepared in advance for aligning portions of the structure that must be at right angles or parallel to each other. PVC cement may give you as little as 15 seconds before glued parts become immovable. I have cataloged a number of right- angle junctions in the shop suitable for aligning PVC pieces. Among them are legs and other supports for the work bench. If a Tee or an elbow requires fitting, I usually put a scrap of pipe dry into the open end. The longer section makes alignment much easier than a junction stub. I simply glue the junction in question and then press it against my sturdy preformed angle.

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For the element mountings in their caps, I first cemented the junction pipe stubs in the caps. (These stubs will be glued into the elbows later.) Then I drilled the caps and stubs together. A drill press makes easy work of centering the holes on both sides of each cap. Next, I pushed each pair of caps over a scrap of 3/16" diameter rod to keep them aligned while cementing each one into its corresponding elbow joint. These and similar techniques simplify making almost any conceivable structure from PVC parts.

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Bending rod elements is most simply done with a copper tubing bender, a small device that can be found at most hardware depots. The bender will make a 1" radius bend. 3/16" rod and smaller will easily handle bends of this radius with no noticeable weakening or visible cracks. I first cut each element section to length and mark the point (away from the threaded end) that corresponds to one half the side-to-side width. I place this point in the middle of the 90-degree bend. This technique has yielded results identical to those predicted by models using sharp corners.

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Some Alternative Mounting Structures

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The cradle shown in Fig. 2 and Fig. 3 can be modified for other materials. For example, the Moxon can be made from aluminum strap or flat stock easily obtained from hardware depots. The only change required in the construction techniques shown so far is to replace the cap holes through which the rods pass. In their place, cut slots in each cap to a depth of at least 2/3 the width of the aluminum flat stock used. 1" wide by 1/16" thick stock makes a good assembly, and set screws will hold the pieces in place, especially if the flat stock is tapped for the set screw thread. In addition, flat stock can be bent into tighter radius corners. (However, be sure there is at least a small radius--perhaps 1/8"--to prevent the stock from cracking.)

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For this version of the antenna, the overall side-to-side width should be about 28.2" or a bit shorter than the rod model. The front-to-back overall width should be about 13.2" with a 2" gap to separate 4.4" driver tails and 6.8" reflector tails. The wider gap emerges from the greater surface area between ends. However, widening the gap requires alteration to the other dimensions to achieve a 50-Ohm feedpoint impedance. The strap alternative shows a marginally higher gain (about 0.1 to 0.2 dB) due to the slightly squarer rectangle that emerges. In addition, it also shows a lower reactance swing across the band (+/- 6 Ohms, compared to +/- 10 Ohms for the round elements), resulting in a slightly shallower SWR curve.

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Rod elements can be used in a simplified structure composed of 3/4" nominal Schedule 40 PVC, as shown in Fig. 4.

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A single boom holds this version of the Moxon together. The sketch shows both a Tee for balanced horizontal mounting and a coupler for rear mounting suitable for vertical or horizontal orientations. The front cap is simply a brace to prevent the slow distortion of the boom from the weight of the driver, which passes through the tube. Note the hole in the boom for passing the feedline from inside the boom to the external world.

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Fig. 5 shows some of the mounting details. As in the initial version of the antenna, the 4 rod element sections are threaded (10-24) on one end. The driver is pinned to the walls of the boom tube by inside and outside nuts, while another set of nuts secures the ring terminals from the feed line. A coupling nut holds the reflector ends together. Be sure these are screwed in place before securing the open ends of the tails in thjeir final alignment, since turning the coupling nut will simply loosen one end while the other one tightens.

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Once the tail gaps are adjusted, they can be secured by a length of tight- fitting tubing and a spacer, as shown in Fig. 5. To keep an air gap between the ends, you can omit the spacer and use heat shrink tubing. I usually use a double thickness of tubing, shrinking them one at a time. The outer piece is a bit longer than the inner piece, to cover the inner piece ends. Of course, a rigid piece of plastic tubing with set screws that set into dimples in the tail ends would work as well.

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However, be certain that spacer material you use is RF-inert at 2-meters. Some plastics may conduct sufficiently to change the coupling at the ends. If sufficiently conductive, the tubing or other spacer can seriously affect antenna performance.

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The variations on these techniques are without end. However, these few will provide a basis for some creative use of adapted materials that you may have available.

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Adjustments and Tests

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The first task after placing all of the Moxon element pieces in their PVC holders and attaching the feedline is to adjust and temporarily lock the gaps between element ends. The first rod Moxon showed a 50-Ohm resonance at about 145.5 MHz, just about where the design placed it. The SWR curve over the 2-meter band was too close to the modeled curve to need retracing.

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It is usually dangerous to assume that, because an antenna is tuned to provide a good match for the feedline, it will also show the modeled gain and front-to-back ratio. However, in this case, the antenna geometry that determines the source impedance also determines the pattern shape. Since the elements were uniform in diameter, there was no reason to expect any performance surprises. Therefore, I locked the assembly tight and moved on to performance tests.

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The Knoxville, TN, area has repeaters from close to 145 MHz up to nearly 148 MHz. All of them are easily accessed and heard at full quieting from my location with only a low elevation ground-plane vertical. In fact, a telescoping whip on my hand-helds will access all of our main repeaters. On a 15' mast, the Moxon made telephone copy of all of the repeaters when the antenna pointed anywhere near the forward direction to them. A distant repeater that I hear poorly on a vertical was now full quieting. The Moxon's gain can make a difference for signals at the FM threshold.

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When the antenna faced away from the repeaters, only 1 of 6 that I checked could still be heard, and then at far less than full quieting. I could not access any of the repeaters with 5 watts of power--the limit of my gear.

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I repeated the test using two hand-helds on simplex across the FM portion of the band. Differences in the patterns at the band edges and at the design frequency were not especially detectable at distances of a quarter mile. Face forward, communications was easy and full quieting. With the antenna pointed in the other direction, communications was virtually impossible. More power at one or the other end of the line might have broken through, but that can be said for almost any system.

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The proto-type vertical rod Moxon has proven a very effective antenna at blocking unwanted signals from the rear. I fully suspect that it would be effective in limiting reflected signals from rearward objects because so little signal is radiated in that direction.

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There are many ways to construct the Moxon for VHF use. The sample shown here is only one of them. For an alternative construction method, with many useful additional notes on the design, see "A Compact Two-Element, 2-Meter Beam" by Lee Lumpkin, KB8WEV, and Bob Cerrito, WA1FXT. The article appeared in the January, 2000, QST, pp. 60-63. Their version used #10 AWG wire, which is just over 0.1" in diameter.

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The Moxon can be scaled for 220 or 440 MHz use--so long as one remembers also to rescale the element diameter or to make appropriate adjustments in dimensions if a scaled element cannot be used. The thinner the wire relative to the original, the smaller the gap; the fatter the element, the wide the gap. And other dimensions will also alter slightly to obtain the maximum null at the new design frequency, with the resonant point slightly lower to obtain full operational coverage of a band or the subsection of interest.

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Updated 10-22-99, 11-1-99, 12-18-99. © L. B. Cebik, W4RNL. A version of this item originally appeared in AntenneX, September, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: Moxon, VHF / UHF


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Designing Moxon Rectangles by Equation and by Model

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L. B. Cebik, W4RNL

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There is an urge among antenna builders to discover "magic formulas" for determining the element lengths of various antenna types. In most cases, tradition sets the form of these formulas in the following terms:

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We seek the length in customary dimensional units (and "dim" may equal feet, inches, meters or millimeters) using some constant, K, and the frequency, f, in MHz.

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Except for the simplest of antennas, we should wean ourselves from this urge. Antenna dimensions do not tend to scale in such simplistic terms. Even the simple 1/2 wl dipole resonant length varies with wire size and height above ground. Hence, using a cutting formula becomes a matter more of luck than of antenna knowledge.

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More complex antennas tend to be less prone to performance variations created by antenna height, if the antenna is at least 1/2 wl high. The more closed the structure of the antenna, the more immune it becomes to variations in resonant element length by virtue of height above ground. However, nearly all common types of antennas will vary according to the diameter of the element size.

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In most cases, dimensional differences will be negligible between antennas built of materials with perfect conductivity and those using ordinary materials such as copper and aluminum. A difference is negligible if it falls within the margins of error that are inherent in standard construction practices. For home shop construction practices, a 1 to 2 percent dimensional error range is normal. Of course, the more elaborate the shop and the more experienced the builder, the smaller the potential error range.

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In the end, then, we are left with the diameter of the element wire (or rod or tubing) as the key to determining the element length. One common warning that we give with respect to scaling antennas for other than the design frequency is also to scale the wire diameter. Only under this condition will the scaling play true. In addition, we must also attend to element length differences between uniform-diameter elements and those which are tapered in steps, normally from a large diameter at the element center to a small diameter at the tip. Likewise, different tapering schedules may result in different element lengths for the same frequency and materials.

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A Procedure for Developing Sensible Design Equations

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If we work initially with uniform-diameter elements, it is possible to develop design equations for many antenna types. The starting point will normally be the element diameter. Again, the equations should begin using perfectly conductive material, with any necessary adjustments for real materials made later. The question then becomes how we may develop such equations. To answer the question, we may turn to an example.

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Fig. 1 is the outline of a Moxon Rectangle, a two element array that combines mutual coupling between elements and coupling between the element tips to yield a broad forward lobe with nearly the strength of a 2-element driver-reflector Yagi. The pattern is almost cardioidal so that minimum radiation does not occur 90 degrees off the main lobe, but closer to 120 degrees away. The antenna at its design frequency is capable of better than 30 dB front-to-back ratio, with better than 20 dB front-to-back ratio across most HF amateur bands. Because the side-to-side dimension of the antenna is only about 70% of the width of a full-size 2-element Yagi, the antenna has found interest among those with limited space. Further interest has arisen among those who can put the antenna pattern to good use. An additional advantage of the design is the 50-Ohm feedpoint impedance, which simplifies matching requirements. A considerable bibliography on the antenna is available from British, American, and Australian sources, as well as at my web-site (..).

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Our interest in the antenna stems from the designations of the element dimensions, listed as A through E in Fig. 1. By judicious modeling in NEC (version 2, 3, or 4), one can develop fairly precise models to create a base-line data set for the development of some design equations. However, the data set must meet standards for use as the basis for this development. For the Moxon Rectangle, I set these standards for each model in the data set.

+ 
Free-Space Gain Range:              5.95-6.05 dBi
+180-Degree Front-to-Back Ratio:     >35 dB
+Source Impedance: Resistance:       50-54 Ohms
+                  Reactance:        <+/-1 ohm
+

The next step is to decide upon the wire diameters to use for development purposes. Several factors enter into this decision.

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Common antenna building materials include AWG wire sizes (in the U.S.) and aluminum tubing and rods ranging from 1/8" to over 1" in diameter. For reference, the following table lists commonly used AWG wires sizes and their diameters in various units of measure.

+ 
AWG Size          Dia. Inches             Dia. Feet               Dia. mm
+18                .0403                   0.003358                1.0236
+16                .0508                   0.004233                1.2903
+14                .0641                   0.005342                1.6281
+12                .0808                   0.006733                2.0523
+10                .1019                   0.008492                2.5883
+

As useful as these conversions may be, they will not satisfy the needs of developing design equations. The wire size used must be given in terms of a fraction of a wavelength, and this number will vary with frequency for any given physical wire size. To provide a sense of the range of wire sizes, when given in terms of wavelengths, the following table presents some materials that have been used in published antenna projects, with the element diameter given in wavelengths for various frequencies.

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      Wire                                Frequency (MHz)
+Size        Dia.(")           1.8         7           28          50          144
+AWG #18     0.0403            6.146E-6    2.390E-5    9.560E-5    1.707E-4    4.917E-4
+AWG #14     0.0641            9.775E-6    3.802E-5    1.521E-4    2.715E-4    7.820E-4
+AWG #10     0.1019            1.554E-5    6.043E-5    2.417E-4    4.317E-4    1.243E-3
+1/4"        0.25              3.813E-5    1.483E-4    5.931E-4    1.159E-3    3.050E-3
+1/2"        0.50              7.625E-5    2.965E-4    1.186E-3    2.118E-3    6.100E-3
+1"          1.00              1.523E-4    5.931E-4    2.372E-3    4.236E-3    1.220E-2
+

In practical terms, the range of wire sizes--given in terms of a fraction of a wavelength- -runs between about 1E-5 and 1E-2. Extending the range to thinner wires presents no problems, although it is not especially useful. However, at the upper limit, there is a potential modeling problem. The Moxon "tails" (dimensions B and D in Fig. 1) require proportional segmentation to the parallel wires (dimension A). For good convergence, I chose to set B at 5 segments and D at 7 segments, with A using 35 segments. As the wire diameter approaches 0.01 wl, the wire diameter begins to exceed the segment length. Ideally, the segment length should be considerably greater than the wire diameter. Hence, the modeled results become less reliable with the fattest wires in the set. (A model with only linear elements would not present this difficulty, and a lower level of segmentation might well be used with excellent reliability.)

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The next step is to decide what wire-size steps to use in developing the base-line data set. In most cases, antenna dimensions tend to show changes that relate to the logarithm of the wire size rather than to linear steps in wire size. For the range of wire sizes shown, we can conveniently take the common log of wires sizes from 1E-5 through 1E-2 to get a progression of logarithms from -5 to -2 in integral steps. However, the data set would be very small. To keep the log steps linear, we may take intermediate wire sizes from 3.162E-5 through 3.162E-3 to obtain values for the common logs -4.5 through -2.5. How much finer one might wish to go depends very much on the rate of variation of values and the anticipated complexity of the resultant curves. For this project, the seven data sets provided a sufficiently large basis for the development of design equations.

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The following table lists the results of the modeling exercise, showing the free-space gain, 180-degree front-to-back ratio, feedpoint impedance, and dimensions A-E (in wavelengths) for the models.

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1.  Performance Parameters
+Wire Size   Log         Gain        Front-to-Back     Feedpoint Z
+(wl)        (base 10)   (dBi)       Ratio (dB)        (R+/-jX Ohms)
+1E-5        -5          6.04        48.1              52.5 + j 0.4
+3.162E-5    -4.5        6.06        39.2              51.5 + j 1.0
+1E-4        -4          6.03        41.8              52.5 - j 0.8
+3.162E-4    -3.5        6.01        36.1              52.5 + j 0.6
+1E-3        -3          6.00        41.7              53.0 - j 0.7
+3.162E-3    -2.5        5.95        35.4              53.3 - j 0.8
+1E-2        -2          5.95        35.0              53.9 + j 0.8
+
+2.  Dimensions (See Fig. 1)
+Wire Size               Dimensions in Wavelengths
+                  A           B           C           D           E
+1E-5              0.366       0.057       0.007       0.067       0.131
+3.162E-5          0.366       0.056       0.009       0.067       0.132
+1E-4              0.364       0.055       0.010       0.068       0.133
+3.162E-4          0.364       0.053       0.012       0.068       0.133
+1E-3              0.360       0.051       0.013       0.069       0.133
+3.162E-3          0.358       0.046       0.018       0.069       0.133
+1E-2              0.356       0.040       0.024       0.070       0.134
+

The front-to-back ratios of the base-line models seem to vary considerably. However, the peak 180-degree front-to-back ratio--which may reach 50 dB in models--is a very narrow band phenomenon. Hence, values between 35 dB and 45 dB may be only a few kHz apart.

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In order to maintain a feedpoint impedance close to 50 Ohms, the side-to-side dimension (A) must decrease as the wire size increases. One expected result would be an increase in the driver tail length (B). However, the increasing wire diameter overrides this increase and results in a shortening of the tails as well as the side-to-side dimension. The reflector is less affected by the changes in wire diameter and shows an increase in tail length (D) with the shortening of A.

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Most evident and rapid is the increase in dimension C, the gap between the tips of the driver and reflector tails. As the wire size increases, the degree of coupling between tips also increases. To sustain roughly equivalent performance across the base-line set of models, the gap must be increased in an ascending curve. The greatest increases in the table do occur where the models begin to show reduced reliability. However, the general trend holds true. Note that the overall front-to-back dimension (E) does not change much over the entire range of wire sizes.

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Step-wise (rather than smooth) variations occur in the tabulated results because the increments of dimensional change were limited to 0.001 wl. For almost identical performance, there is a small range of values for the gap. (If there were not, the antenna would be difficult to reproduce.) Centering the gap value within its range would have yielded smoother curves for all of the dimensions. However, this degree of precision would have been superfluous to the effort.

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From Data to Equations

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The data set generated by the base-line models is sufficient to develop design equations. The easiest way to develop usable equations is to subject the data to regression analysis, which is available in many mathematical software packages, either in stand-alone form (such as DataFit) or in larger suites of functions. Although a significant description of regression techniques is well beyond the scope of these notes, we can indicate the process and its output.

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For any data set--especially where the plotted data has a linear X axis scale--regression analysis can develop polynomial equations that best fit the data. The routines can produce any order of polynomial. For example, the form most used in the following discussion is a 2nd order polynomial of the form

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where a, b, and c are coefficients generated by the regression analysis, (for our case) x is the common log of the wire diameter, and y is the dimension under analysis. Dimensions A, B, and C require second-order polynomials, while dimension D can be satisfied with a first order equation.

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In any such exercise in regression analysis, it is important to understand that the equations developed have no inherent physical meaning relative to antenna theory or practice. The results are simple curve-fitting exercises within the upper and lower limits of the values for X and the data supplied. However, the results are usable in practice with some care. Foremost is the need to determine when a generated equation is adequate to a given task. Although in complex cases, the test routines report important information by which to evaluate the equations, simply plotting the equations against the data points can--in simpler cases--provide enough information to decide which level of polynomial will satisfy the needs of a project. For the present data set, one significant factor is that the equations should not result in extreme departures from the modeled data at the limits of the values for x. For A through C, 2nd-order equations sufficed, and for D, a first order equation (ax + b) proved sufficient. (In other cases, I have used up to 4th-order polynomials.)

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To establish the fits, the following graphs of dimensions A though D may be useful.

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Fig. 2 shows a comparison of modeled and calculated values for dimension A. Within any normal building tolerances, this curve is a very tight fit.

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A comparison of modeled and calculated values for dimension B (the driver tail) appears in Fig. 3. This curve is an even tighter fit than for dimension A.

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Fig. 4 shows a comparison of modeled and calculated values for dimension C, the gap between element tips. The modeled values do not have enough significant digits for a smooth curve.

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A comparison of modeled and calculated values for dimension D (the reflector tail) appears in Fig. 5. The sharpness of turns in both curves is due to the very small change overall on dimension D.

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I have not yet shown the values for the coefficients, because they will appear shortly within each of the two methods I have selected for packaging the results. However, it should be apparent that all of the curves fit the data reasonably well, given the increment of change within which the models were developed. It cannot be stressed enough that a. the equations have no direct theoretical meaning within antenna theory and b. care must be used to ensure that the equations are neither more complex than they need to be for a task nor too simple to capture the essential data within the limits of the defined range of values.

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Packaging the Design Equations

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There are innumerable ways to package the design equations in order to make them usable and convenient. We shall look at only two here.

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1. A Basic (or other language) utility program: The following listing provides a small utility program for calculating Moxon dimensions from an input of the wire diameter and the design frequency. The wire diameter may be input in inches, millimeters, or wavelengths. The output is given in wavelengths, feet, and inches. The simple addition of a few lines converting the English output into metric units (0.3048 * feet) would complete the program.

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10 CLS:PRINT "Program to calculate the dimensions of a Moxon Rectangle."
+20 PRINT "All equations correlated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 1E-5 to 1E-2 wavelengths."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:DW=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:DW=WD/WLI
+120 IF U=3 THEN DW=WD
+130 PRINT "Wire Diameter in Wavelengths:";DW
+140 D1=.4342945*LOG(DW)
+150 IF D1<-6 then 160 else 170
+160 print "Wire diameter less than 1E-6 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AA=-.0008571428571#:AB=-.009571428571#:AC=.3398571429#
+200 A=(AA*(D1^2))+(AB*D1)+AC
+210 BA=-.002142857143#:BB=-.02035714286#:BC=.008285714286#
+220 B=(BA*(D1^2))+(BB*D1)+BC
+230 CA=.001809523381#:CB=.01780952381#:CC=.05164285714#
+240 C=(CA*(D1^2))+(CB*D1)+CC
+241 DA=.001:DB=.07178571429#
+242 D=(DA*D1)+DB
+243 E=(B+C)+D
+250 PRINT "Moxon Dimensions in Wavelengths:"
+260 PRINT "A = ";A
+270 PRINT "B = ";B
+280 PRINT "C = ";C
+290 PRINT "D = ";D
+295 PRINT "E = ";E
+299 WF=983.5592/F:WFI=WF*12:PRINT "Wavelength: =";WF;"Feet or ";WFI;"Inches
+300 PRINT "Dimensions in Feet and Inches"
+301 PRINT "A = ";A*WF;"Feet or ";A*WFI;"Inches"
+302 PRINT "B = ";B*WF;"Feet or ";B*WFI;"Inches"
+303 PRINT "C = ";C*WF;"Feet or ";C*WFI;"Inches"
+304 PRINT "D = ";D*WF;"Feet or ";D*WFI;"Inches"
+305 PRINT "E = ";E*WF;"Feet or ";E*WFI;"Inches"
+350 INPUT "Another Value = 1, Stop = 2: ";P
+360 IF P=1 THEN 10 ELSE 370
+370 END
+

Lines 190 through 243 contain the design equations and coefficients derived from the regression analysis. The variable names AA through DB should be self-explanatory. Note that the calculations use the log of the wire diameter in wavelengths, and not the wire diameter itself. Dimension E is the simple sum of B, C, and D. It serves as a check on the fittingness of the other calculated dimensions by comparing it with the corresponding modeled value. Additionally, I have expressed the coefficients and other constants to full calculated values, rather than using truncated values based on the least significant digits of any entry. The resulting output values can easily be trimmed by the user at any sensible level.

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With the calculated dimensions in hand, one can create a model of the Moxon as a check, as a basis for optimization in models, or as a guide to building. The side-to-side dimension with require halving in order to place the front-to-back axis along the center-line of the antenna in any NEC model.

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2. Development of a model by equation: The equations can also be entered directly into a NEC program that has the facility to accept design-by-equation. As an example, Fig. 6 shows the equations screen for a NEC-Win Plus model.

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Only one of the equations appears fully in the upper entry line, but it suffices to show the parallel to the Basic program. The spreadsheet does know the difference between natural and common logarithms, so the calculation of the log of the wire diameter in wavelengths (variable I) has a different meaning of "LOG" from its meaning in Basic. (Common GW Basic uses only natural logs and hence requires a conversion factor to yield common logs.)

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The list of coefficients is entered in column D. As the sample equation for box B4 indicates, the equations of the dimension variables call upon the locations of the coefficients to employ their values in the calculation. Column E contains the identification of each coefficient, using the same labels as in the Basic listing.

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The advantage of entering the equations directly into a modeling program is that one can then design a Moxon for any reasonable frequency with any reasonable wire diameter and evaluate the model--all in one operation. One of the variable entries equates the design frequency with the current frequency. However, you can lock in a set of dimensions by simply entering a design frequency. This is useful for frequency sweeps and other activities that will optimize the design.

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How Good Are the Results?

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The easiest way to find out how adequate the equations are is to design a few Moxon Rectangles and then test their modeled performance. So that you can correlate the dimensions to the model description, Fig. 7 provides the variables entry version of the wires page. Note the calculated values for all X entries and the calculated values for the driver tails. In the examples, I shall show only the values version of the wires page, and you can extrapolate back to the equations page values for A through E. All dimensional values will be in inches. I have also adopted the convention of placing the reflector at Y=0.

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1. A 7.15 MHz #12 wire version: The wires page for this antenna appears in Fig. 8

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The following table gives the modeled performance for both perfect wire and for copper wire.

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Frequency   Version           Gain        Front-to-Back     Feedpoint Z
+MHz                           dBi         Ratio dB          R+/-jX Ohms
+7.15        Perfect           6.01        39.07             53.9 + j 4.6
+            Copper            5.80        31.29             55.9 + j 4.4
+

For reference, Fig. 9 shows the typical free-space azimuth pattern for a Moxon Rectangle, based on this particular model.

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+ +
+

Because AWG #12 wire is only 0.0808" in diameter, the efficiency of this antenna drops to 96.1% as we move from perfect wire to copper wire. The losses not only show up in the additional 2 Ohms in the feedpoint impedance, but as well in decreased gain and front-to- back ratio.

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Despite these facts about the wire Moxon Rectangle, the calculations yield a design that is within original modeling limits set for this exercise, with a remnant reactance of only about 4.6 Ohms.

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2. A 28.5 MHz 1" tubing version: Fig. 10 contains the wires page dimensional values for the calculated model.

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+ +
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The following table lists the performance using perfect wire and aluminum tubing:

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Frequency   Version           Gain        Front-to-Back     Feedpoint Z
+MHz                           dBi         Ratio dB          R+/-jX Ohms
+28.5        Perfect           5.97        36.89             52.9 - j 2.5
+            Aluminum          5.96        36.43             53.0 - j 2.5
+

Despite the greater losses of aluminum relative to copper, the larger surface area of the 1" material and the higher frequency (which makes the diameter a larger fraction of a wavelength) yield a very high efficiency: 99.97%. Hence, the differential between perfect wire and large aluminum tubing is negligible. Once more, the calculated dimensions of the antenna come very close to matching the modeling limits, with only a 2.5-Ohm remnant reactance.

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3. A 146 MHz 0.125" rod version: Fig. 11 shows the relevant wires page for this model.

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+ +
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The following table lists the performance using perfect wire and aluminum rod:

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Frequency   Version           Gain        Front-to-Back     Feedpoint Z
+MHz                           dBi         Ratio dB          R+/-jX Ohms
+146         Perfect           6.01        43.50             51.8 - j 3.4
+            Aluminum          5.96        39.68             52.3 - j 3.5
+

The aluminum version of the antenna has a 99.1% efficiency. Although the frequency is roughly 5 times higher than the 10-meter model, the rod is only 1/8 the diameter of the 10-meter material: hence, the slightly lower efficiency. Once more, the calculated model falls well within the requirements for the goal of producing a design that can be translated directly into a constructed antenna.

+

Conclusion

+

The goal of the exercise was to develop a series of equations that one might use to design Moxon Rectangles for any reasonable frequency using any reasonable wire diameter. The equations make use of the common log of the wire diameter and the design frequency to determine the dimensions for the antenna, based upon a base-line data set of models optimized for maximum front-to-back ratio and about 50 Ohms feedpoint impedance at the design frequency. However, the equations apply only to uniform-diameter elements. The use of stepped diameter elements would require optimization within NEC-4. Since the elements are not linear, the Leeson corrections built into some commercial implementations of NEC-2 will not operate. A version of MININEC might also be used if (for the public domain version) the elements are length-tapered toward the 4 corners of the array.

+

Regression analysis proves a very usable technique of developing working equations for the design exercise, although the equations themselves have no theoretical significance other than fitting curves to a data set within the limits of that set. The equations can be packaged in utility programs--such as the little exercise in Basic--or they can be applied directly to a NEC model within a program capable of modeling by equation.

+

For those interested in modeling by equation, the model shown here is available in .NWP format at the Nittany Scientific (web.archive.org) website, along with some other models using equations featured in the monthly Antenna Modeling column. Also see the Antenna Modeling Programs page.

+

A stand-alone Windows program that calculates the dimensions of a Moxon rectangle for a near-50-Ohm feedpoint impedance, as described in "Designing Moxon Rectangles by Equation and by Model," has been developed by Dan Maguire, AC6LA. You may obtain a free copy from his web site: www.ac6la.com/moxgen1.html. The program will also create a model in .EZ format for use with EZNEC or in .NEC format for use with NEC-Win software or with generic NEC programs. The only required input entries are the design frequency and the diameter of the wire or tubing to be used. Dan's site also contains a number of other very useful programs for modelers and others interested in antenna design and analysis.

+

An online Moxon Rectangle Calculator is also available on this site.

+

The quest for magic formulas for cutting antennas only futilely chases after super-simple equations using only a constant and the operating frequency. Most antenna types answer better to collections of equations based on both wire size and operating frequency. Although the equations themselves may not be simple, one can put them into packages that are simple to use. However, easy generation of building dimensions is no substitute for understanding the fundamentals of how such antennas work.

+

Note: I am indebted to the work of Lee Lumpkin, WB8WEV, and Barbara Craig, KC8KJA, whose initial regression analysis work on some of my #14 copper wire Moxon models convinced me that a more general solution to Moxon Rectangle design was possible. Dan Hendelsman, N2DT, also deserves thanks for leading me to shareware regression analysis software.

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Updated 06-12-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for September, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

+

Go to Amateur Radio Page

+

Topics: Moxon


+ + diff --git a/content/moxon/moxgene1.gif b/content/moxon/moxgene1.gif new file mode 100644 index 0000000..19c02b5 Binary files /dev/null and b/content/moxon/moxgene1.gif differ diff --git a/content/moxon/moxgene2.gif b/content/moxon/moxgene2.gif new file mode 100644 index 0000000..3b9e92d Binary files /dev/null and b/content/moxon/moxgene2.gif differ diff --git a/content/moxon/moxon.html b/content/moxon/moxon.html new file mode 100644 index 0000000..a5015c9 --- /dev/null +++ b/content/moxon/moxon.html @@ -0,0 +1,84 @@ + + + + + + Wire Moxon Rectangles for 40-10 Meters + + + + +
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Wire Moxon Rectangles for 40-10 Meters

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L. B. Cebik, W4RNL

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+ Since a posting on QRP-L, the Moxon rectangle has drawn considerable attention. A full analysis of the antenna appears in the Spring, 1995, issue of Communications Quarterly. Basically, the Moxon rectangle is a wire antenna that can be fix-mounted or rotated. It is directional with about the gain of a 2-element Yagi (6 dBi in free space) and has an outstanding front-to-back ratio (greater than 30 dB in free space), with a very broad frontal lobe (-3dB beamwidth = 70 degrees, usable beamwidth = nearly 180 degrees forward). The basic outline of the antenna appears in Figure 1. +
+ +
+

Since the article and the posting appeared, I have heard of successful constructions of Moxons, one for a Field Day Novice station. I have also had two types of requests. One has asked for dimensions for other bands. The other inquiry wondered if the feedpoint impedance might be brought closer to 50 ohms. The original design showed a feedpoint impedance close to 80 ohms.

+

I remodeled the antenna with good results on both counts. Table 1 provides dimensions for the Moxon rectangle for 40 through 10 meters. The dimensions are not perfect simple scalings, because the length-to-wire- diameter ratio changes for each ham band. {Later Note: These dimensions are perfectly usable. However, they emerge from separate models of the Moxon Rectangle, prior to the development of the "MoxGen" algorithms. By using the later development, you may enter the wire size and desired design frequency into one of the several design program formats and arrive at custom dimensions.]

+ 
                  Table 1.  Moxon Dimensions for 40 - 10 Meters
+
+Band     Design                      Dimension  (feet)
+       Frequency (MHz)   A              B         C         D        E
+
+10        28.50          12.44          1.94      0.41      2.41     4.76
+
+12        24.94          14.22          2.22      0.46      2.76     5.44
+
+15        21.20          16.72          2.63      0.52      3.25     6.40
+
+17        18.12          19.56          3.10      0.59      3.80     7.49
+
+20        14.17          25.00          4.00      0.72      4.85     9.57
+
+30        10.12          35.00          5.60      1.00      6.80    13.40
+
+40         7.15          49.56          8.01      1.33      9.63    18.97
+
+Note:  all models composed of #14 copper wire.
+
All of the antennas exhibit feedpoint impedances between about 56 and 58 ohms, a close match to the standard amateur 50-ohm coaxial cable. Free space gain and front-to-back ratio are consistent for all the models, averaging 5.8 dBi and greater than 32 dB in free space, respectively, at the design frequency, centered in each band. Figure 2 shows a typical free space azimuth pattern for the antenna. +
+ +
+

All of the models use #14 copper wire, although the various factors that contribute to the Moxon pattern tend to cancel out as wire size increases. Hence, a tubing model will have dimensions close to those for a thin wire model. However, it will exhibit a broader SWR bandwidth. The models were constructed on EZNEC Pro, a NEC-4 implementation by W7EL.

+

At heights below 1/2 wavelength, the front-to-back ratio will deteriorate somewhat, but usable values can be obtained. Figure 3 shows the azimuth pattern of a Moxon Rectangle at the elevation of maximum radiation, with a height of a half wavelength above real, medium ground. The pattern (especially front-to-back ratio) improves toward free space values as the antenna is further elevated. Elevation angle of maximum radiation is the same as a 2-element Yagi at the same height, for example 25° at 1/2 wl up, 14° at 1 wl up, etc.

+

The bandwidth for 2:1 SWR is only about 100 kHz on 40 with #14 wire. Above 40, the 2:1 SWR bandwidth covers the entire amateur band. For 30 and up, the front-to-back ratio is better than 15 dB across the band.

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+

The original article showed one construction technique for 10 meters. Many others are possible, whether the material is wire or aluminum tubing. I shall leave the exact methods to the reader's ingenuity.

+

A Hybrid Wire Moxon-Yagi for 20-10 Meters

Although the Moxon rectangle does not lend itself readily to nesting in a single plane without careful trapping (as described in Moxon's account in his classic HF Antennas for All Locations), ingenuity has produced some interesting variants for multi-band use. Dennis Schaefer, W5RZ, has designed a hybrid Moxon based on the 20-meter wire dimensions shown above. Inside the rectangle, he added elements for 10 and 15 meter operation. The 15-meter element is a reflector, but the 10-meter element turns out to be a director, reversing the antenna pattern. The dimensions are sketched in Figure 4. +
+ +
+

The design frequency performance for each band is summarized in Table 2. All values are based on free-space models.

+ 
     Table 2.  Modeled Tri-band Performance of the W5RZ Hybrid
+Frequency       Gain (dBi)      F-B (dB)        Feedpoint Impedance
+  14.15           5.8            34.0             60 - j   2
+  21.2            6.4             9.7            180 + j 935
+  28.4            5.8 (rev)      16.9           2100 + j3060
+

The antenna is designed to be fed with parallel transmission line and to be matched by a balanced antenna tuning unit. Free-space modeling of the antenna design shows that on 15 meters, the drive provides a double-humped current distribution, with a high reflector current on the 15-meter element. Current on the 10-meter element and the 20-meter reflector is low. On 10-meters, the current distribution is typical of a 1-wl element, with high director current on the 10-meter element.

+

This is just one possible direction of expanding the capabilities of the Moxon Rectangle, and the future is likely to see additional examples of antenna design ingenuity, using the rectangle as the foundation.

+

Conclusion

The standard of comparison for the Moxon is the 2-element Yagi. While a Yagi has marginally more gain, the Moxon's front-to-back ratio is very much superior. It will likely improve your ears much more than it will diminish your voice. And, as the old but true saying goes, if you can't hear 'em, you can't work 'em. +
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First printed in QRPp, December, 1995. Updated and enlarged 6-10-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

+

Return to Main Index

+

Topics: HF Lower, HF Upper, Moxon


+ + diff --git a/content/moxon/moxon1.gif b/content/moxon/moxon1.gif new file mode 100644 index 0000000..8285cac Binary files /dev/null and b/content/moxon/moxon1.gif differ diff --git a/content/moxon/moxon2.gif b/content/moxon/moxon2.gif new file mode 100644 index 0000000..9cdc8b0 Binary files /dev/null and b/content/moxon/moxon2.gif differ diff --git a/content/moxon/moxpage-1.gif b/content/moxon/moxpage-1.gif new file mode 100644 index 0000000..379385d Binary files /dev/null and b/content/moxon/moxpage-1.gif differ diff --git a/content/moxon/moxpage.html b/content/moxon/moxpage.html new file mode 100644 index 0000000..f930ed2 --- /dev/null +++ b/content/moxon/moxpage.html @@ -0,0 +1,358 @@ + + + + + + + Moxon Rectangles and Online Calculator + + + + + + + + + +
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Moxon Rectangles and Online Calculator

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L. B. Cebik, W4RNL

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Moxon Rectangle Dimension Calculator

Moxon calculator dimensions diagram +
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Frequency : MHz
Wire Diam :
Impedance :
Output Units :
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Results:

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A
B
C
D
E
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Online Moxon Calculator: Above is a version of the Moxon dimension calculator that you may use right on this page, thanks to Joe Faber, KG4UHP, who created the JAVAScript and gave me permission to place it here. Remember that the dimensions apply to Moxon rectangles that use the same diameter material throughout. Decide on the design frequency and the diameter of the elements. You may use inches or millimeters for the diameter--or you may select an AWG wire gauge. Be certain to select the unit of measure for the output. Then, click on any of the output boxes if the calculations have not already appeared.

+

2024 Update: Added 93 ohm option used in Simplifying the Turnstile Moxon Rectangle Fixed-Position Satellite Antennas, removed dependence on body tag.

+

MOXGEN: A stand-alone Windows program that calculates the dimensions of a Moxon rectangle for a near-50-Ohm feedpoint impedance, as described in "Designing Moxon Rectangles by Equation and by Model," has been developed by Dan Maguire, AC6LA. You may obtain a free copy from his website: www.ac6la.com/moxgen1.html. The program will also create a model in .EZ format for use with EZNEC or in .NEC format for use with NEC-Win software or with generic NEC programs. The only required input entries are the design frequency and the diameter of the wire or tubing to be used. Dan's site also contains a number of other very useful programs for modelers and others interested in antenna design and analysis.

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+

Moxon Rectangle Notes

+

The Moxon Rectangle is growing in popularity as a compact 2-element array that approaches a full-size 2-element Yagi in gain but with a far superior front-to-back ratio and a direct match for the standard 50-Ohm coaxial cable. The antenna can be built as a wire array--especialy for the lower HF regions--or as a rotateable aluminum beam. For convenience, I have pulled together the growing selection of Moxon Rectangle notes into this single subdirectory and organized them in the order of recommended reading--unless you already know what you are looking for.

+ +

Additonal information on building wire and tubing versions of Moxon rectangles for a direct 50-Ohm feed is available in Simple and Fun Antennas for Hams, ed. Hutchinson and Straw (ARRL, 2002), pp. 12-19 to 12-28.

+

The KD6WD Moxon Antenna Project is another good source of information on various construction techniques, especially for the operator needing a light-weight or a semi-stealthy antenna.

+

Moxon Rectangle Notes is also available in PDF book format with model sets on the Books Page.

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Updated 07-04-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

+

Topics: Moxon


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Notes on the Moxon Rectangle Pattern

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+

L. B. Cebik, W4RNL

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+

There are some interesting differences in the azimuth pattern between a Moxon Rectangle and a Yagi. Here, Yagi means a reflector-driver 2-element parasitic beam, which is comparable to the reflector-driver structure of the Moxon Rectangle.

+

As a comparison between the structures of the two antennas, Fig. 1 shows the dimensions and relative sizes of #14 AWG copper wire antennas cut for 14.175 MHz. The frequency is somewhat arbitrary, but the choice of wire construction is not. Much of what follows will be applicable to lower HF versions of these antennas, where wire construction is the norm.

+
+ +
+

In simplicity, the Yagi has the advantage, since laying out a 2-element wire Yagi requires only the we support the wire ends at about the right spacing. The Moxon is structurally more complex, because the dimensions include a fairly critical gap distance between the driver and reflector tails. Hence, maintaining the tail lengths and gap space become important.

+

In size, the Moxon has the advantage, since it fits in a space about 70% as large as the Yagi. Hence, it is suited for more cramped quarters or smaller back yards for any given frequency. For example, a 40-meter version would be only about 50' from side to side, in contrast to the 67' width of a Yagi.

+

Most 2-element driver-reflector Yagis with a spacing of about 1/8 wl will have a feedpoint impedance between 30 and 35 Ohms. Although for narrow frequency spans, we may directly feed them with 50-Ohm coax, the operating bandwidth benefits from the use of a matching network, such as the gamma or beta. To achieve a Yagi feedpoint impedance close to 50 Ohms, the spacing should be increased to about 0.15 wl. This move, however, will result in slightly reduced gain and front-to-back figures. In contrast, the Moxon Rectangle can be designed for a direct 50-Ohm feedpoint match and will exhibit good operating bandwidth. Even in wire, the 20-meter Moxon will cover all of the band.

+

There are also differences in the azimuth patterns of the two antennas. The Moxon tails produce radiation to the sides, since the current in these portions of the antenna is not negligible. The tip-to-tip coupling, when combined with the mutual coupling of the parallel parts of the elements, yields a current magnitude and phase on the rear element that is nearly ideal for maximum front-to-back ratio. When we model these antennas in free space, we see comparative patterns like the ones in Fig. 2.

+
+ +
+

The Moxon will always have slightly less gain than a comparable 2-element Yagi. However, the front-to-back ratio will also always be very high in comparison--up to 20 dB better at the design frequency. In addition, the Moxon pattern is faintly cardioidal, meaning that the maximum front-to-side ratio points do not occur at 90 degrees from the maximum forward gain direction. Instead, they occur 15 to 20 degrees further back in the pattern. Hence, there is a potential for reception and transmission to the antenna sides. Even the -3 dB horizontal beamwidth of the Moxon is about 10 degrees wider than that of the Yagi.

+

The combination of factors that make up the Moxon and Yagi patterns present the user with choices. Which antenna may be considered superior depends in great measure (and apart from structural considerations) on the operating specifications set for a given station. For example, some operations may call for a single direction fixed beam with one direction favored, but not exclusively, over the opposite direction. The 2-element Yagi permits operation off the rear of the beam at a deficit of about 2 S-units.

+

In contrast, some operations may call for the maximum rejection of signals to the rear, with the widest forward beamwidth obtainable. In such cases, the Moxon Rectangle would be the option (of the 2 listed here). Indeed, the antenna can be designed for switching directions. See "Two-Element 40-Meter Switched Beam" by Carrol Allen, AA2NN, in The ARRL Antenna Compendium, Vol. 6, pp. 23-25, for an example of the techniques involved.

+

The final decision in the selection of any antenna requires that the station designer develop a set of operating specifications regarding antenna performance. Only by placing the specifications next to a set of antenna potentials can the operator designate one antenna type as superior to another type. The specifications and potentials lists may include both structural and performance considerations. And, of course, the final decision may involve one or more compromises.

+

The Wire Antenna at Height

We hardly ever get to operate antennas in free space, especially lower HF wire constructs. Hence, a free-space azimuth pattern is only the start of evaluating the patterns of antennas under comparison. In the present case, which compares a Yagi with a Moxon Rectangle intended for use on one of the bands from 80 through 20 meters, we can anticipate some antenna heights as low as 3/8 wl. We know in general that as we lower the height of an antenna from above 1 wl to something that hugs the ground, some of the pattern properties will change. Hence, in comparing the Yagi with the Moxon, we cannot stop in free space. +

Although NEC models cannot evaluate performance over irregular terrain, they can give some comparative guidance for performance over ground at various heights. Let's look at patterns for the two antennas at various heights below 1 wl.

+

I shall present information for each height in two ways. First, comparative azimuth patterns will show the outlines that indicate relative antenna performance. Second, some tabular data will allow us to zero in on some similarities and differences. The data will include the maximum gain in dBi, the 180-degree front-to-back ratio, antenna gain to the rear (listed as 180-degree gain) in dBi, and the antenna gain at right angles to the maximum forward power direction (listed as +/-90-degree gain) in dBi. As well, the tabulated data will include the elevation angle of maximum radiation (TO angle) in degrees and the -3 dB horizontal beam width in degrees. For pattern analysis, we may ignore some other data, such as the feedpoint impedance, especially since that value does not change radically from the free space value. The difference line in the tables will always subtract the Yagi values from the Moxon values. Note that the TO angles at the same throughout for both antennas.

+

1. 0.375 WL: We can begin with a 3/8 wl height, since many lower HF horizontal beams are used in this vicinity. Moreover, as Fig. 3 shows, the high Yagi front-to-side ratio almost disappears.

+
+ +
+

For the Yagi and Moxon at a 3/8 wl height, the tabular data is as follows:

+ 
Antenna   TO Angle  Max. Gain F-B       +/-90 Gain     180 Gain  Hor. B/W
+Yagi      33        9.9       13.0      -4.7           - 3.1     75
+Moxon     33        9.5       28.3      -2.8           -19.8     85
+Mox-Yag             -.4       15.3       1.9           -16.7     10
+

At a height of 3/8 wl, the Yagi has nearly a half dB more gain. However, the front-to-back ratio at 180 degrees is over 2 S-units lower. The Moxon beamwidth is about 10 degrees wider, but at the 90-degree points, there is less than 2 dB difference.

+

2. 0.5 WL: As we elevate the antenna by an eighth of a wavelength, both patterns begin to develop trends that lead eventually to the free-space pattern back in Fig. 2. We can detect the trends in Fig. 4.

+
+ +
+

For the Yagi and Moxon at a 1/2 wl height, the tabular data is as follows:

+ 
Antenna   TO Angle  Max. Gain F-B       +/-90 Gain     180 Gain  Hor. B/W
+Yagi      26        10.9      13.5      -6.0           - 2.7     73
+Moxon     26        10.5      20.0      -3.8           - 9.4     82
+Mox-Yag             - .4       6.5       2.2            -6.7      9
+

At a height of 1/2 wl, the Yagi shows the same gain advantage as at the lower height. Its front-to-back ratio improves, while the Moxon value decreases, resulting in a net difference of about 1 S-unit. The front-to-side ratio shows a slow growth in the Yagi, so that the Moxon is a little over 2 dB stronger at the 90-degree points. The beamwidth differential remains essentially the same.

+

3. 0.75 WL: At a 3/4-wl height, both antennas continue the emergence of their characteristics, with the Yagi developing distinct side nulls. The Moxon, on the other hand, shows a better front-to-back pattern, as seen in Fig. 5.

+
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+

For the Yagi and Moxon at a 3/4 wl height, the tabular data is as follows:

+ 
Antenna   TO Angle  Max. Gain F-B       +/-90 Gain     180 Gain  Hor. B/W
+Yagi      18        11.3       9.7      -11.0            1.6     70
+Moxon     18        10.9      22.2      - 6.2          -11.3     79
+Mox-Yag             - .4      12.5        4.8          -12.9      9
+

The Yagi gain advantage remains constant at 0.4 dB, while the 180-degree Moxon front-to-back advantage has re-grown to over 11 dB (nearly 2 S-units). Note the difference between the front-to-back ratio, which gives a measure of relative signal strength from the front and rear, and the 180-degree gain, which compares "absolute" signal strength from the rear. These values will differ by the differential in the forward gain of the arrays. The 90-degree gain value differential has grown to nearly 5 dB, approaching an S-unit of difference.

+

4. 1.0 WL: At 1 wl up, both antenna azimuth patterns continue to look more and more like their corresponding free-space patterns--but not completely. As shown in Fig. 6, the Moxon does not achieve its free-space front-to-back ratio, and the Yagi does not achieve its free-space front-to-side ratio.

+
+ +
+

For the Yagi and Moxon at a 1.0 wl height, the tabular data is as follows:

+ 
Antenna   TO Angle  Max. Gain F-B       +/-90 Gain     180 Gain  Hor. B/W
+Yagi      14        11.6      12.1      -13.9           -0.5     68
+Moxon     14        11.2      27.6      - 6.9          -16.4     78
+Mox-Yag             - .4      15.5        5.0          -15.9     10
+

The Yagi has the same 0.4 dB gain advantage, but the Moxon front-to-back ratio advantage has grown to over 15 dB--approaching 3 S-units. The ability of the Moxon to hear at a 90-degree angle to the main lobe is now at the 5 dB better mark relative to a Yagi, and something approaching an S-unit can make a considerable difference in weak signal operation.

+

Overall, except for the 1/2 wl height, the Moxon has by far the stronger front-to-back pattern, while the Yagi has a consistent small edge in gain. The Moxon shows an ability to utilize its wide beam width to some advantage when used as a fixed beam, especially as the antenna height is increased--something likely in the upper HF region but less likely in the lower HF realm. There is no difference in TO angles.

+

In the end, one can read out the numbers for any proposed height of operation between the Yagi and the Moxon (or between any other pair of possible antennas). By placing these numbers against the initial operating specifications, one can select the antenna that will best fulfill the purposes of the station. This exercise is simply a sample of what every station should ultimately do in the process of selecting antennas. Of course, one cannot neglect structural and financial considerations in the final evaluation. Nonetheless, comparing azimuth patterns at the intended height of operation can go a long way toward translating free-space abstractions into real planning tools.

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Updated 2-22-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Index

+

Return to Amateur Radio Page

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Topics: Moxon


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Stacking Moxon Rectangles
+ Part 2: Vertically Stacking Vertically Oriented Rectangles

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L. B. Cebik, W4RNL

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In Part 1, we reviewed the situation surrounding the vertical stacking of horizontally oriented Moxon rectangles. Mechanically, this practice is applicable to almost any HF or VHF frequency. However, we discovered that there was a very wide difference between the separation that yields maximum gain (0.61-0.67 wavelength) and the separation that yields a maximum front-to-back ratio (1.0-1.1 wavelength). The maximum gain separation shows a low front-to-back ratio (about 13 dB compared to a maximum 180-degree front-to-back ratio of 50 dB for a single antenna). Conversely, the maximum front-to-back separation showed about 1 dB less forward gain than the maximum gain separation.

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The end result is simply an inability to recommend or dis-recommend a stack of horizontally oriented Moxons. To reach a conclusion in either direction would require a set of operational specifications against which to measure the extremes of either maximum gain or maximum front-to-back ratio--or some intermediate separation yielding the best compromise between the two extremes.

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When we turn to vertically oriented Moxon rectangles, we find a much simplified situation. First, a vertical stack of vertically oriented Moxons is normally applicable only at VHF and UHF ranges, where the physical size of each antenna is small and the separation as a function of a wavelength is also reasonable. Second, as we shall see, we do not encounter a quite so radically disparate set of extremes with respect to maximum gain and maximum front-to-back ratio. The simplified conditions, however, do offer us more options, including 2-, 3-, and 4-stack possibilities.

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The Vertically Oriented Moxon and Its Stacking Potentials

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Fig. 1 shows the range of possibilities that we shall explore. If the performance of one or more of the vertical stacks of Moxons has the right performance characteristics, then a stack may be the order of the day for numerous communications tasks. The Moxon's high front-to-back ratio allow close mounting to a conductive mast or tower behind the reflector. Hence, one may set up a stack of Moxons without undue concern for wind resistance and loading of the support boom.

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The first step in our progression is to examine the performance potential of a single Moxon rectangle when vertically oriented. The following table lists the free-space performance figures, along with figures for heights of 2, 3.3, 4.6, and 5.9 wavelength above average ground. We shall reveal the reasons for using those special heights above 2 wavelengths as we proceed. However, the 2 wavelength height represents the baseline height for our work, on the presumption of a 2-meter (146-MHz) Moxon rectangle.

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+2-Meter Vertically Oriented Moxon Rectangle:  146 MHz
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+Single Antenna    Gain        Front-Back  TO Angle    H-B/W       Feed Z
+                  dBi         Ratio dB    degrees     degrees     R+/-jX Ohms
+Free-Space         5.95       32.88       ----        143         54 - j  1
+2-WL   13.47'      8.77       32.62        5.9        143         54 + j  1
+3.3-WL 22.23'      9.86       32.76        3.9        143         54 + j  1
+4.6-WL 30.99'     10.39       33.03        2.9        143         54 + j  1
+5.9-WL 39.75'     10.72       32.76        2.3        143         54 + j  1
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Over the same range of heights, a horizontally oriented Moxon would have shown gain values between 11.5 and 12.5 dBi. However, vertically oriented antennas are more sensitive to ground losses and thus show lower gain values at lower heights. However, the gain values increases more rapidly with height than would a corresponding horizontally oriented Moxon. Eventually, the gain values coincide closely, but the height exceeds 10 wavelengths.

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Remarkably constant is the beamwidth and the front-to-back ratio. Fig. 2 shows the E-plane (corresponding to an elevation pattern over ground) and the H-plane (corresponding to an azimuth pattern over ground) patterns for the vertically oriented Moxon in free-space. The H-plane pattern shows the deep rear null and cardioidal pattern typical of a vertical Moxon. The E-plane pattern shows significant radiation beyond 90 degrees distant from the forward bearing, but not as strong to the rear as in the H-plane. Hence, we shall anticipate antenna interactions within a stack that yield less disparate performance differences with changing separation than when we stacked horizontal Moxons.

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Except for the forward gain value, the azimuth patterns for the single Moxon do not vary when we take each pattern at its take-off (TO) angle--or elevation angle of maximum radiation. The beamwidths and the 180-degree front-to-back ratios are virtually the same for every new height at which we place the antenna.

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However, we do find significant differences in the elevation patterns. Fig. 3 shows 2 samples, one at a height of 2 wavelengths, the other at a height of 5.9 wavelengths. As we might expect, the number of elevation lobes increases with increasing height. Unlike single horizontally oriented arrays, however, the vertically oriented antenna shows a variability in the strength of some of the lower elevation lobes. Hence, connecting the lobe points of maximum strength does not yield a smooth curve. Still, if we were to overlay the upper half of the E-plane pattern on top of either elevation pattern, the lobes would fit wholly within the idealized shell.

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Stacking 2 Vertically Oriented Moxon Rectangles

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The next step in our progression is to stack 2 Moxons, with the lower antenna at 2 wavelengths above ground. We shall gradually increase the height of the upper antenna in 0.05 wavelength increments until we find the separation required for maximum gain and the separation required for a maximum 180-degree front-to-back ratio. That work yields the following table of values. Separation (and height) represent the values for the centerline of each antenna structure. Hence, parts of the antenna extend above and below the listed value. To find the separation of the element tails for any situation, subtract about 0.35 wavelength from the listed separation value.

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+Vertically Oriented Moxon 2-Stack: 146 MHz:  Base Height:  2 wl
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+Separation  Gain        Front-Back  TO Angle    Top Z       Bottom Z
+WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+0.85        12.16       22.87        4.9        57 - j  0   57 - j  1
+0.90        12.17 +     23.62        4.8        57 - j  2   57 - j  1
+0.95        12.16       24.58        4.8        56 - j  2   56 - j  1
+1.00        12.13       25.81        4.7        55 - j  3   55 - j  3
+1.05        12.09       27.34        4.7        55 - j  3   55 - j  3
+1.10        12.04       29.28        4.6        54 - j  3   54 - j  3
+1.15        11.99       31.77        4.5        54 - j  2   54 - j  2
+1.20        11.95       35.16        4.5        53 - j  2   53 - j  2
+1.25        11.92       40.40        4.5        53 - j  2   53 - j  2
+1.30        11.90       51.18 +      4.5        53 - j  1   53 - j  1
+1.35        11.88       45.08        4.4        53 - j  1   53 - j  1
+1.40        11.87       38.69        4.3        53 - j  1   53 - j  1
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Maximum gain occurs with a separation of 0.9 wavelength between antenna centerlines. Maximum front-to-back occurs with a separation of 1.3 wavelengths. Fig. 4 shows the azimuth and elevation pattern differences for those two conditions.

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One of the main features of a vertically oriented Moxon rectangle that gives it a nearly unique place among parasitic arrays is the extreme rear null that we can obtain. I shall assume--in the absence of task-driven specifications--that we wish to retain that deep null in any stack that we create. Therefore, the separation value of 1.30 wavelengths will become a key to further developments. That value is also the one used in choosing increments of height above the base height for successive performance reports of a single Moxon.

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Fig. 5 graphs both the forward gain and the 180-degree front-to-back ratio for the Moxon stack at the 0.05 increments of increasing separation. The graph clearly shows the separate peaks for the two phenomena. However, unless we examine the Y-axis labels carefully, we may make too much of the relative sharp peaks.

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The gain differential between the maximum gain and maximum front-to-back conditions is only 0.27 dB, or about 1/4 of the difference we obtained for a 2-stack of horizontal Moxons. As well, the front-to-back ratio at maximum gain is nearly 24 dB, a very respectable figure for most types of operation. The conclusion that we must reach from these numbers is that stacking separation for a pair of vertically oriented Moxons is far less critical than for a pair of horizontal rectangles. Mechanically, the beneficial consequence is that in an actual structure, we may move an antenna in a stack a few inches either way for mounting convenience without jeopardizing the stack performance. The stability of the feedpoint impedance values adds a further vote of confidence to such maneuvers that are typical of real construction projects.

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Recognizing our freedom to alter optimal settings without unduly reducing array performance, we shall nonetheless use the 1.3 wavelength separation as our marker for creating taller stacks and evaluation their performance.

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Taller and Higher Stacks of Vertically Oriented Moxon Rectangles

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All stacks in our progressions presume standard techniques of in-phase feeding. However, the performance figures that we use do not take into account any power losses in the feed system. Since vertically oriented antennas in a stack tend to place the antennas further apart, the lengths of cable in the feed distribution system will be longer than in many, if not most, stacks of horizontally oriented antennas. The stack designer must take these losses into account when designing and evaluating an overall system.

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Nothing in principle prevents us from creating a stack of as many vertical Moxons as we desire. However, for brevity, we shall examine only 2 more steps in the progression--the 3-stack and the 4-stack. The following table compares the performance of all of the configurations in Fig. 1, each with a base height of 2 wavelengths. In each stack, the separation used is the maximum front-to-back ratio spacing: 1.3 wavelengths.

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+Vertically Oriented Moxon Stacks: 146 MHz:  Base Height:  2 wl
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+Stack       Gain        Front-Back  TO Angle    Bot Z/3 Z   2 Z/4 Z
+Size        dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+1            8.77       32.88        5.9        54 - j  1
+      Gain over 1:  3.13 dB
+2           11.90       51.18        4.5        53 - j  1   53 - j  1
+      Gain over 1:  4.95 dB   Gain over 2:  1.82 dB
+3           13.72       47.26        3.5        53 - j  1   52 - j  2
+                                                53 -1
+      Gain over 1:  6.24 dB   Gain over 2:  3.11 dB   Gain over 3:  1.29 dB
+4           15.01       43.69        2.9        53 - j  1   51 - j  1
+                                                51 - j  1   53 - j  1
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For each added antenna in the stack, we obtain a smaller increase in gain. However, the added gain of a 4-stack over a 2-stack is about 3.1 dB, just about what we should expect in theory for a doubling of the stack height. Obviously, to add another 3 dB to the array, we would need to go to an 8-stack. Since the 4-stack is already 26.28' between the bottom and top antennas, an 8-stack is likely not feasible physically. As well, the feeding complexity would be considerable. However, at UHF, the physical size of the array would be no hindrance to its use.

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Fig. 6 shows the elevation patterns of the 2-, 3-, and 4-stack arrays. Because the overall height of the dull arrays differs for each case, the exact number and angle of the secondary lobes also suffers. However, it is interesting to compare these patterns with the free-space E-plane pattern for a single Moxon rectangle. In each of our elevation patterns, all of the forward lobes fits within the envelope created by the upper half of the free-space patterns. As well, the strongest forward secondary elevation lobe is about 4 dB weaker than the lowest main lobe. To the rear, the strongest lobe is about 30 dB down from the main forward lobe.

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We can obtain some of the improvement in gain simply by using a 2-stack at a top height equal to the third or fourth antennas. The following table compares potential performance from 2-stacks with the top height of each of the stacks in the table just listed.

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+Vertically Oriented Moxon 2-Stacks: 146 MHz:  Variable Base Heights
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+Top Height  Gain        Front-Back  TO Angle    Top Z       Bottom Z
+WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+3.3         11.90       51.18        4.5        53 - j  1   53 - j  1
+4.6         12.88       50.42        3.2        53 - j  1   53 - j  1
+5.9         13.38       52.86        4.8        56 - j  2   56 - j  1
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Relative to the 3-stack, the 2-stack with the same top height (4.6 wavelengths) is about 0.85 dB down. Relative to a 4-stack, the 2-stack with the same top height (5.9 wavelengths) is over 1.6 dB down. The conclusion we might reach is that for a given top height, reducing the stack size by 1 antenna and removing it from the bottom creates a loss that we might live with in some operating circumstances. However, removing 2 from the bottom yields losses that may be less acceptable. The decisions to be made, of course, require reference to a set of operational specifications related to the communications goals. Nevertheless, the technique of redoing this exercise from the top down (in contrast to our basic procedure of working from the bottom up) will yield a different set of comparative numbers and in some design situations may be the more applicable procedure.

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Tentative Conclusions

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The vertical stack of vertically oriented Moxon rectangles represents a viable way of increasing total array gain while preserving the most desired aspects of the Moxon performance figures. These figures include the deep rear null and the very wide beamwidth in the azimuth pattern. We have not mentioned the beam width because it has changed by no more than 0.2 degrees in any of the stacks that appear in the examples. All of the examples exhibit -3 dB beamwidths between 143.2 and 143.4 degrees.

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The rear null combined with the wide beam width result in an array that covers fully 1/3 of the horizon. Hence, we would require only 3 such stacks, aimed at 120-degree intervals, to create a polling array for any of the VHF/UHF bands. (A polling array is one in which we measure the signal strengths from each of the 3 receiving array directions and automatically select the one having the strongest signal. A polling array can consists of however many antenna we need to provide full horizon coverage, relative to the beamwidth of the individual antennas or sub-arrays.)

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For repeater operations on the border between 2 different coverage areas, the very high front-to-back ratio and the pattern shape of the Moxon, when vertically oriented, can eliminate keying up the wrong repeater. Indeed, a pair of arrays situation to place each unwanted repeater in the null, can be switched to use only one with high confidence that the other will be unaffected by the operation.

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Additionally, the high rear null of the vertically oriented Moxon permits relatively close mounting to a vertical supporting conductive mast or tower. The closer the antenna to its support tower, the less problems we shall suffer relative to the durability of the supporting boom during high wind or ice loading. A UHF polling array set might well be covered totally by a single shell composed of RF-transparent material that also sheds wind and ice effectively.

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Horizontal Stacking of Vertically Oriented Moxon Rectangles

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To complete our survey of stacking possibilities with the Moxon rectangle, we should deal with a final possibility for stacking vertically oriented antennas: the horizontal stack. Also called the side-by-side stack, this possibility has the general appearance of the antennas in Fig. 7.

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For our purposes, we may use the same base height that we have used throughout this exercise: 2 wavelengths. The base height uses the antenna centerline as a reference, so the rectangle extends above and below this line by equal amounts.

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When we stacked horizontally oriented Moxons vertically, we found that the maximum front-to-back separation was 1.1 to 1.15 wavelength. However, when we tip the resulting array on its side to obtain a horizontally stacked pair of vertically oriented antennas, we obtain the azimuth pattern that appears in Fig. 8.

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The gain of the array in this configuration is about 11.6 dBi at a TO angle of 5.9 degrees. The front-to-back ratio approaches 21 dB. However, we can hardly miss the forward side lobes. When we set the array for horizontal polarization, these side lobes combined (due to ground reflection) to produce a relatively harmless secondary high-angle elevation lobe. However, in the present configuration, the lobes are free to extend at angles to the main lobe and at a strength only a bit over 2 dB less than the main lobe. The presence of these side lobes also narrows the Moxon forward lobe to a very small beamwidth.

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For almost all purposes, the maximum front-to-back spacing yields a wholly unsatisfactory pattern. To overcome the side-lobe problem, we must narrow the separation between the arrays. The following table shows the results for separation starting at a high of 0.65 wavelength and extending to a low of 0.35 wavelength. The table lists only one feedpoint impedance, since that value applies to each antenna in the array. The added data, relative to past tables, lists the front-to-side ratio, that is, the ratio in dB of the main forward lobe to the side lobe.

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+Vertically Oriented Horizontal Moxon 2-Stacks: 146 MHz:  Base Height: 2 WL
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+Separation  Gain        Front-Back  TO Angle    Front-Side  Bottom Z
+WL          dBi         Ratio dB    degrees     Ratio dB    R+/-jX Ohms
+0.65        12.62  +    13.06        5.9        10.47       67 - j 15
+0.60        12.47       12.80        6.0        14.30       72 - j  9
+0.55        12.19       12.77        6.0        20.10       73 - j  2
+0.50        11.84       12.92        6.0        ----        71 - j  3
+0.45        11.46       13.17        6.0        ----        69 + j  6
+0.40        11.08       13.49        6.0        ----        69 + j  6
+0.35        10.71       13.84 +      5.9        ----        69 + j  6
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From the table, we can see that any selection of a separation for the horizontal 2-stack is a compromise. The highest gain in the list occurs in conjunction with the worst front-to-sidelobe ratio. Conversely, the gain continuously decreases as we shrink the separation, although the front-to-back ratio continues to climb.

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As we might expect, the sidelobes disappear whenever the separation is 0.5 wavelength or less. However, the azimuth patterns of array are not identical once the sidelobes diminish. Fig. 9 gives us a view of the azimuth patterns of the array at spacings of 0.65, 0.5, and 0.35 wavelength.

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Although the 0.65 wavelength configuration provides the most gain--about 4 dB more than a single vertically oriented Moxon, the array has a narrow beamwidth, large sidelobes, and a modest front-to-back ratio. In contrast, the 0.5 wavelength configuration eliminates the sidelobes altogether. However, we have lost about 0.8 dB gain and have a worse front-to-back ratio. We can notice a trend: the closer the spacing, the broader the beamwidth. With the 0.35 wavelength configuration, we obtain a front-to-back ratio of nearly 14 dB with a broader beamwidth still, but the gain has dropped by nearly 2 dB relative to the 0.65 wavelength version of the stack. Moreover, we are no where near to the 140-degree beamwidth we obtained with a single Moxon or with the vertical stacks.

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Close spacing produces another effect of note: interaction that modifies the feedpoint impedances of the arrays. The single Moxon used as the basis for these stacks has a feedpoint impedance of 54 - j 1 Ohms. The impedances of our stacks show resistances in the high 60s and low 70s, with a variable reactance. to make an effective array of the sort that we are examining here, we likely would have to further modify the basic Moxon rectangle for a lower single-antenna feedpoint impedance in order to achieve values near to 50 Ohms in the stack.

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For the sake of completion, let's perform one more experiment: creating a 4-stack composed of 2 pairs of horizontally separated Moxons with a vertical separation between the pairs. Fig. 10 shows the outline of our square, although the dimensions do not actually form a square. From our table, the best horizontal spacing for a reasonable front-to-back ratio and the best beamwidth is 0.35 wavelength. The best front-to-back vertical separation for a strictly vertical stack was about 1.3 wavelengths. However, for the square of pairs arrangement, a vertical spacing of 1.15 wavelengths proved the best in terms of achieving the maximum front-to-back ratio possible from the stack.

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+Square Moxon 4-Stack: 146 MHz:  Base Height: 2 WL
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+Separation  Gain        Front-Back  TO Angle    Top Pair Z  Bottom Pair Z
+WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+0.35x1.15   13.93       15.47        4.7        68 + j  7   68 + j  7
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The 4-stack square achieves over 5 dB more gain than a single Moxon at a 2 wavelength base height. However, the front-to-back ratio is mediocre compared to the levels achieved by the strictly vertical stacks. As well we continue to have feedpoint impedances calling for further design efforts to effect in-phase feeding of the entire set of antennas in the array.

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Fig. 11 shows, especially in the azimuth pattern, that we have not improved upon the beamwidth situation. The end result seems to be that if this form of stacking has a place, it is for applications unlike those we suggested as fitting the strictly vertical stack. At UHF, this stack is likely to be useful for point-to-point circuits, for example, wireless relays. With overall dimensions of 0.35 by 1.5 wavelengths, the array is smaller than many competitive corner reflector and similar designs. The 3-sided reflector, with higher gain, becomes effective with reflector panels about 2 wavelengths per side. For broad beamwidth applications, vertical stacks are likely to prove themselves to be the most versatile array designs.

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Conclusion?

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This exercise is by no means a complete survey of possibilities or an authoritative set of design dictates. Instead, it is an exploration of some opening possibilities in stacking Moxon rectangles. Because the antenna has some relative unique pattern features relative to standard 2-element Yagis, it requires an exploration of stacking potentials on its own ground. These notes have only opened the door to further exploration.

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As well, the techniques used here to examine the stacking potentials of antennas by use of antenna modeling software are also applicable to a systematic treatment of other antenna types. The amateur literature is full of arrangements that builders have experimentally found to be relatively optimal. However, we can well benefit from a set of more complete surveys for each antenna type.

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So our conclusion is simply a beginning. . .

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Updated 12-04-2003. © L. B. Cebik, W4RNL. This item originally appeared in antenneX, Dec., 2003). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Upper, Moxon, Stacking, VHF / UHF


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Stacking Moxon Rectangles
+ Part 1: Vertically Stacking Horizontally Oriented Rectangles

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L. B. Cebik, W4RNL

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The Moxon rectangle is a 2-element array using dual coupling between elements to produce its nearly cardioidal pattern. Because it depends upon both the mutual coupling between parallel portions of the elements and the coupling between element ends, it is not amenable to the addition of further elements for increased gain. In other words, a Moxon rectangle is not expandable by the addition of director in the manner of a standard Yagi.

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An alternative route to increased gain is the stacking of like antennas and feeding the antennas in phase. At HF, operators employ stacks for a number of tasks. Combined, the antennas deliver the highest gain available. However, separately, the two antennas in the stack exhibit different take-off (TO) angles--or elevation angles of maximum radiation. Having a choice among the potentials allows the operator to elect an elevation most suited to a given propagation path. At VHF, additional gain is normally used solely for the purpose of increased gain.

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Stacking Moxon rectangles is certainly possible. However, implementing that possibility requires that we answer several questions:

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1. What performance can we obtain from a stack of at least 2 Moxon rectangles--and is it sufficient to justify the added mechanical and electrical requirements of such a system?

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2. Just how does stacking work?

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To answer these questions, we shall divide the stacking question into two parts: the vertical stacking of horizontally oriented rectangles and the vertical stacking of vertically oriented rectangles. Since the latter type of stack is normally used only at VHF and above, we shall begin with the more general case.

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A VHF Stack of 2 Horizontal Moxon Rectangles

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Fig. 1 shows the general outline of a 2-stack of (or stack of 2) Moxon rectangles. We normally begin for convenience with two identical antennas, although it is not at necessary that we do this. With sufficient patience, we might customize each antenna for its position in the stack. However, the added benefits of such tedious work rarely outweigh the design and construction effort.

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We must decide upon a base height for the array. Normally, we decide the base height of the lower antenna in the stack based upon task specifications and constraints. Since this discussion aims for some general ideas rather than a task-specific design, we shall arbitrarily select base heights of about 1 wavelength and about 2 wavelengths for the exercise. These heights translate at 146 MHz--the center of the 2-meter amateur band--into about 80" (6.67') and 160" (13.33'), respectively. Above a base height of 2 wavelengths, about the only parameter of operation that will change is the TO angle. Hence, the selection gives us a fair representation of performance.

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The next decision involves the distance between the lower and the upper antennas in the array. We shall have more to say about this variable at the end of our Moxon discussion. However, in general terms, arrays with low element counts tend to show that the separation required for maximum gain from the array and the separation required for retention of the high front-to-back ratio that is a hallmark of the Moxon rectangle are not the same distances. In fact, they are so far apart that we obtain very different patterns for the two conditions.

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With a base height of 1 wavelength, as shown in the patterns in Fig. 2, the maximum gain pattern shows a considerable vertical elevation lobe that results from spacing that is just above a half wavelength. The maximum front-to-back patterns result from a separation of just over 1 wavelength. The azimuth patterns, taken at the TO angle, show the differential of front-to-back ratio, but do not reveal the forward gain differential of just over 1 dB. The elevation angle for the maximum gain configuration appears normal, that is, similar to the pattern of a single array at a height that is about 2/3 the way between the two physical antennas. However, the maximum front-to-back stack shows oddities that do not appear with a single antenna, including a high variability in the strength of secondary elevation lobes. The number of lobes is a function of the added height of the top antenna and the fact the that elevation structure is a function of the lobes produced by both antennas. Since the radiation combines at a distance from the pair of antennas and since it also includes ground reflections as well as direct radiation, the pattern of radiation lobes and nulls can be erratic to the eye, even if predictable and calculable in straightforward ways.

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Fig. 3 repeats the same modeling exercise using a 2 wavelength base height. Between the azimuth patterns in this set and the one for a 1 wavelength height, there is little to choose except for a slight addition to the forward gain for the higher pair. However, the elevation patterns, even for the maximum gain condition, begin to show some of the variations in lobe strength that we saw only in the maximum front-to-back pattern at a 1 wavelength base height. We find more elevation lobes as a simple function of the greater overall height of the antennas. However, on either side of the most vertical lobe, we see some "suppressed" lobes, that is lobes that are weaker than we might expect from a single antenna. These are functions of the complex combinations of direct and reflected radiation from each of the antennas composing the stack.

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The maximum front-to-back elevation pattern is especially interesting. It breaks the single large forward secondary lobe into 2 lobes, with additional strong and weak lobes, relative to the comparable pattern in Fig. 2 for a 1 wavelength base height. We can see that the stacked array offers strong radiation either at very low or very high elevation angles.

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Now let's overlay the patterns in our minds and note the similarities of corresponding elevation patterns for both base-height levels. In the maximum front-to-back elevation pattern, we note a low angle main lobe, at least one strong lobe at mid-elevation angles, and a moderate strength vertical lobe--or perhaps "bubble." The maximum gain patterns for each base-height level show increasing radiation strength below about 35 degrees, with a single vertical lobe of considerable strength. These pattern similarities are more than accidental.

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As we increase the height of an antenna or a complex array, such as our stacks, we find that elevation pattern properties tend to repeat themselves every 1/2 wavelength, allowing for the addition of new lobes with every significant height increase. Since the pattern pairs in Fig. 3 are almost exactly 1 wavelength higher than those in Fig. 2, we should expect to see the overall outline of the pattern repeated. The phenomenon is perfectly general. Hence, you may begin with an antenna at any height above about 1/2 wavelength and then check the patterns at half wavelength intervals above that. A single antenna will do for such a modeling exercise, but the principle applies as well to complex arrays.

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A More Detailed Analysis of the VHF Arrays

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The azimuth and elevation patterns sample the stack performance at only two points of separation for each base height. It is useful to examine data for the entire span of possible separations for the two antennas in the stack. Therefore, I modeled each stack at 5" intervals of separation, always leaving the lower antenna at its base height. 5" at 146 MHz is just a little under 1/16 wavelength, so the accumulated data gives us picture of array performance for regular intervals. The following tables summarize the data recorded for each new amount of separation.

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+2-Meter Moxon 2-Stack:  146 MHz:  Base Height:  80" (Approx. 1 wl)
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+Single Antenna    Gain        Front-Back  TO Angle    Feed Z
+                  dBi         Ratio dB    degrees     R+/-jX Ohms
+                  11.29       26.15       13.7        56 + j  3
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+Separation        Gain        Front-Back  TO Angle    Top Z       Bottom Z
+In.   WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+35    0.4277      13.68       13.63       11.1        65 + j 10   69 + j 10
+40    0.4888      14.08       13.22       10.7        69 + j  6   70 + j  7
+45    0.5498      14.44       13.08 -     10.4        71 - j  1   72 + j  2
+50    0.6109      14.65 +     13.42       10.1        68 - j 10   71 - j  5
+55    0.6720      14.62       14.41        9.6        60 - j 14   65 - j 11
+60    0.7331      14.41       16.05        9.3        52 - j 12   57 - j 11
+65    0.7942      14.14       18.20        9.0        48 - j  9   52 - j  9
+70    0.8553      13.89       20.62        8.9        46 - j  5   49 - j  5
+75    0.9164      13.67       23.06        8.7        46 - j  2   48 - j  2
+80    0.9775      13.48       25.06        8.4        47 + j  1   48 + j  1
+85    1.0386      13.32       26.05 +      8.1        48 + j  2   49 + j  3
+90    1.0997      13.18       25.88        7.8        49 + j  3   50 + j  5
+95    1.1608      13.08       24.95        7.7        50 + j  4   51 + j  7
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+2-Meter Moxon 2-Stack:  146 MHz:  Base Height:  160" (Approx. 2 wl)
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+Single Antenna    Gain        Front-Back  TO Angle    Feed Z
+                  dBi         Ratio dB    degrees     R+/-jX Ohms
+                  11.66       30.23        7.1        54 + j  2
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+Separation        Gain        Front-Back  TO Angle    Top Z       Bottom Z
+In.   WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+35    0.4277      14.16       13.51        6.3        66 + j 10   68 + j 10
+40    0.4888      14.60       13.21        6.2        69 + j  7   70 + j  7
+45    0.5498      15.00       13.11 -      6.1        72 - j  0   72 + j  1
+50    0.6109      15.26       13.38        5.9        70 - j  9   70 - j  7
+55    0.6720      15.30 +     14.14        5.9        61 - j 15   64 - j 12
+60    0.7331      15.14       15.44        5.8        53 - j 14   56 - j 13
+65    0.7942      14.90       17.15        5.7        48 - j 10   50 - j 10
+70    0.8553      14.67       19.02        5.7        46 - j  6   47 - j  6
+75    0.9164      14.47       20.79        5.6        45 - j  2   46 - j  2
+80    0.9775      14.30       22.18        5.4        46 + j  0   46 + j  1
+85    1.0386      14.17       23.01        5.4        47 + j  2   47 + j  3
+90    1.0997      14.06       23.21 +      5.2        48 + j  4   48 + j  5
+95    1.1608      13.98       22.94        5.1        49 + j  5   50 + j  7
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For each base height, I have listed the corresponding properties of a single Moxon rectangle. The forward gain improves with added height, but not by a major amount. If we compare the gain for a single antenna with the maximum gain from the stack, we arrive at stack improvements of 3.33 and 3.64 dB, respectively for the lower and the higher stack. There is a generalization that the maximum gain theoretically obtainable by stacking arrays is 3 dB, and the reality of material losses dictates that the actual realized gain advantage will be slightly less than 3 dB in an optimized stack. The excess gain for our calculations in not erroneous, but rather stems from comparing a stack with an antenna at the lower of the two stack levels. Since the stack has a composite height advantage of about 2/3 the distance between antennas in the stack, the excess is natural as a function of the greater effective stack height.

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Fig. 4 graphs the forward gain curves of the 2 array sets in order to note a special fact. The closer the array to the ground, the smaller the separation needed for achieving a maximum gain configuration. With a 2 wavelength base height, the array achieves maximum gain at about 1/16 wavelength greater separation between the antennas. Above about 2 wavelengths base height, the curves show an ever-decreasing differential so that the difference becomes virtually unnoticeable.

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Fig. 5 shows the front-to-back ratio of each stack with increasing separation. Once more, the stack with the greater base height requires slightly more separation to achieve its maximum.

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There is one more interesting facet of the separation between arrays: the effect of separation upon the TO angle. For the VHF series of beams, I used a pattern increment of 0.1 degree to achieve relatively fine differentiations in TO angles, especially with the 1 wavelength base-height array. As shown in Fig. 6, the change in TO angle does not form a linear or other simple curve. With a separation close to 7/8 wavelength, the change in TO angle per increment of separation slows very noticeably, only to speed up again to a more normal rate of about 0.3 degrees per increment.

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The TO-angle exercise simply illustrates that fact that the interaction of arrays in a stack is far from a simple matter. You may survey the feedpoint data--comparing it to the values for a single antenna--for the various amounts of separation. Note that there is very little difference between the sets of each base height. However, within each set, both the resistance and reactance vary considerably when we stack Moxon rectangles. The maximum gain separation tends to yield feedpoint values that are close to maximally divergent from the single antenna. In fact, the feedpoint values most distant from those of a single antenna occur with a separation that marks the front-to-back minimum level.

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Repeating the Experiment on 20 Meters

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To ensure that the stacking phenomena that we observed at 2-meters are not unique to VHF stacks, I repeated the experiment. This time I used a frequency of 14.175 MHz, where 1 wavelength is just under 70'. I examined the data for baselines of 70' and 140', corresponding roughly to 1 and 2 wavelengths, respectively. The interval for the data scan is 5', with each increment being just over 0.07 wavelength. The 20-meter data appears in the following tables.

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+20-Meter Moxon 2-Stack:  14.175 MHz:  Base Height:  70' (Approx. 1 wl)
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+Single Antenna    Gain        Front-Back  TO Angle    Feed Z
+                  dBi         Ratio dB    degrees     R+/-jX Ohms
+                  11.47       24.79       14          54 + j  6
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+Separation        Gain        Front-Back  TO Angle    Top Z       Bottom Z
+Ft.   WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+30    0.4324      13.78       13.33       11          62 + j 14   64 + j 13
+35    0.5044      14.24       12.98 -     11          66 + j 10   67 + j 11
+40    0.5765      14.63       13.13       10          68 + j  2   69 + j  5
+45    0.6485      14.77 +     14.03       10          63 - j  6   66 - j  3
+50    0.7206      14.61       15.80       10          54 - j  9   59 - j  6
+55    0.7926      14.35       18.43        9          48 - j  6   53 - j  5
+60    0.8647      14.07       21.44        9          46 - j  2   49 - j  2
+65    0.9368      13.81       24.52        9          45 + j  1   47 + j  1
+70    1.0088      13.60       26.53 +      8          46 + j  3   47 + j  4
+75    1.0809      13.43       26.47        8          46 + j  5   48 + j  7
+80    1.1529      13.25       24.90        8          46 + j  6   49 + j  9
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+20-Meter Moxon 2-Stack:  14.175 MHz:  Base Height:  140' (Approx. 2 wl)
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+Single Antenna    Gain        Front-Back  TO Angle    Feed Z
+                  dBi         Ratio dB    degrees     R+/-jX Ohms
+                  11.79       28.49        7          52 + j  5
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+Separation        Gain        Front-Back  TO Angle    Top Z       Bottom Z
+Ft.   WL          dBi         Ratio dB    degrees     R+/-jX Ohms R+/-jX Ohms
+30    0.4324      14.21       13.21        6          63 + j 14   66 + j 13
+35    0.5044      14.74       13.00 -      6          66 + j 10   66 + j 10
+40    0.5765      15.18       13.16        6          68 + j  3   69 + j  4
+45    0.6485      15.39 +     13.93        6          64 - j  6   65 - j  5
+50    0.7206      15.31       15.44        6          55 - j  9   58 - j  8
+55    0.7926      15.06       17.51        6          48 - j  7   51 - j  7
+60    0.8647      14.78       19.83        6          45 - j  3   47 - j  3
+65    0.9368      14.53       21.93        6          44 + j  1   45 + j  0
+70    1.0088      14.37       23.14        5          44 + j  3   45 + j  4
+75    1.0809      14.23       23.28 +      5          44 + j  5   46 + j  6
+80    1.1529      14.12       22.64        5          46 + j  7   47 + j  9
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Within the limits of correspondence between the increments (in terms of a wavelength) of separation between the 2 exercises, the 20-meter data very precisely parallels the 2-meter data. The maximum gain configuration requires a separation of about 0.65 wavelength. This value applies to both base heights, but the curves in Fig. 7 show a tilt to the curve of the greater base height that corresponds to the same tilt in the 2-meter curves.

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Likewise, the maximum front-to-back configuration requires a slightly wider separation (about 1/16 wavelength) when the base height is 2 wavelengths relative to a base height of 1 wavelength. Moreover, the separation requirements are virtually identical for the 2-meter and the 20-meter stacks. Fig. 8 shows the 20-meter front-to-back curves relative to the separation distance.

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Since the 20-meter exercise utilized pattern increments of 1.0 degree, the TO data is insufficiently refined to graph the rate of change. However, allowing for a slight difference in the feedpoint impedances of the 20-meter and the 2-meter single antennas, the feedpoint impedance data describe the same curves in both the resistance and the reactance columns.

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Should We Stack Moxon Rectangles?

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Achieving a maximum gain configuration for a vertical stack of horizontally oriented Moxon rectangles requires a moderate amount of separation--about 0.65 wavelength. However, the available front-to-back ratio of the stack is very low compared to the front-to-back ratio of a single antenna.

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Maximizing the front-to-back ratio in the stack requires a far wider separation, something close to 1 wavelength. This separation is not likely to be feasible at HF in modest antenna installations, but may be possible in the VHF and upward regions. However, the cost of that achievement is 1 dB less gain than we can obtain from the maximum gain configuration. Indeed, the gain improvement over a single antenna at the base height is down to 2 dB.

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The situation that applies to stacking Moxon rectangles applies to a considerable degree to standard Yagis using only 2 elements. to a lesser but significant extent, it also applies to larger Yagis up to 4-5 elements. For some data on Yagi stacks of 2 using various length arrays, see the notes titled "Supplementary Notes on Stacking" at Supplementary Notes on Stacking.

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A 3-stack of Moxons fares even worse. Besides the differential between the required separation for maximum gain and maximum front-to-back ratio, we encounter another problem. The very wide vertical (H-plane) beamwidth of the moxon results in extreme interaction between the arrays. The middle beam takes the brunt of the interaction. Its feedpoint impedance in a stack of three with the sources all in phase is almost 50% higher than the impedance of a single antenna and well-above the feedpoint impedances of the outer 2 antennas. Hence, equal power distribution to the antennas approaches a problematical level.

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A Few General Notes on Stacking Horizontal Antennas

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The interaction of any two antennas in a vertical stack is more complex than may appear at first sight. Perhaps the most common observation about the proper stacking height to achieve maximum gain concerns its relationship to the gain of an individual array in the stack. The higher the gain of the individual antenna in the stack, the farther apart the arrays must be to achieve maximum gain. For standard Yagis ranging from about 3 to 7 elements or so, we may even develop a rule of thumb:

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where S(lambda) is the required separation in wavelengths and G(dBi) is the free-space gain of the individual antenna in the stack.

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We know that this is a mere rule of thumb by virtue of the fact that we do not obtain a cancellation of units of measure. However, the quasi-equation does yield a first-order approximation of the required separation for maximum gain. However, it tends to go inaccurate when we deal with 2-element Yagis and other small arrays. There are reason for this--other than the rough-and-ready nature of the rule.

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Fig. 9 shows the free-space E-plane patterns of 3 different arrays superimposed in a single plot. The longest array is a 7-element Yagi, which shows the narrow beamwidth associated with longer arrays. The 4-element Yagi shows a very wide beamwidth, but without any secondary lobes, such as those associated with the 7-element Yagi. The least strong pattern belongs to the 2-element Moxon rectangle. Although it has the lowest forward gain, it shows the greatest beamwidth at over 140 degrees between -3 dB points. As well a good bit of the side-energy lies behind the points that are 90 degrees each side of the main forward lobe bearing.

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What the plots illustrate is that the interaction of two antennas in a stack is more dependent upon the shape and strength of the E-plane structure of the antenna's pattern than upon gain alone. In fact, we can begin by creating a rule of thumb for maximum gain configuration separation in terms of the antenna's vertical beamwidth.

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where S(lambda) is the required separation between stacked antennas in wavelengths and VBW is the free-space vertical beamwidth of an individual antenna in the stack. This approximation is also only apt between about 3 and 7 elements. It may be useful for longer arrays but lacks testing for larger Yagis.

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The approximation cannot be fully precise because it does not account for antenna radiation close to the 90-degree points of the array. The 4-element antenna E-plane shows radiation at the 90-degree points, but the 7-element Yagi has lower level sporadic lobes in these regions. If we change the strength of these lobes, then we also change the level of interaction between antennas and hence possibly change to a small degree the required separation for maximum gain from a stack.

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The Moxon has radiation to the vertical side regions that extends smoothly well to the rear of the 90-degree points. So, too, do 2-element reflector-driver Yagis and similar small arrays. This phenomenon changes the nature of the interaction, widening the required spacing relative to the rules of thumb. Indeed, two dipoles in a stack present intersecting circles and require about a 5/8 wavelength spacing for maximum stack gain. The required separation figure remains in this region--0.6 to 0.65 wavelength--until we start working with long-boom 3 element Yagis.

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The reason why we increase spacing with additional gain and its associated forward lobe shape is--in part--the greater distance between the antenna and the intersection of the forward lobes. Fig. 10 provides some guidance here, with plots of 2-stacks of each of our antennas in Fig. 9, each stack set for maximum gain in free space.

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The 7-element Yagi requires a spacing of about 1.45-1.48 wavelengths for maximum gain. Maximum gain in the forward lobe requires a convergence of the main forward energy from the individual antennas in the stack. The wide separation needed for maximum gain does not place the antennas in the right position for convergence of the strongest forward secondary lobes from each antenna. Hence, you will find an additional forward lobe compared to the single antenna pattern in Fig. 9. The rearward lobes are wide enough and weak enough to be unchanged in shape. However, the lobes at 90 degrees from the forward bearing are weakened by cancellation that occurs in the regions that are multiples of 1/2 wavelength separation. The antennas in the 7-element Yagi stack are nearly 1.5 wavelength apart.

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Pattern convergence also appears with some clarity in the patterns for the 4-element Yagi stack--with a separation of 0.76 wavelength--and the Moxon stack--with a separation of 0.63 wavelength. Note that the 4-element Yagi, which had no sidelobes as a single antenna, now has major sidelobes in the E-plane. The pattern of addition and cancellation of radiation bends these sidelobes forward of the 90-degree points, which coincides with the fact that the single 4-element Yagi had most of its side-ward energy forward of the 90-degree points. However, the Moxon sidelobes are almost aligned with the 90-degree points, because so much of the side-ward energy was to the rear of the 90-degree points. In fact, the rearward energy from the individual antennas combines to give the stack a very considerable rear lobe, reducing the front-to-back ratio relative to the performance on an individual Moxon rectangle.

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If we need a further reason why simple rules of thumb break down with certain individual arrays and with arrays beyond the limits of the rule, we need only consider that another set of radiation combinations occur when we stack antennas over real ground. At a distance from the antenna stack, reflected and direct radiation combine to yield patterns like those in Fig. 2 and Fig. 3. The greater distance of the upper antenna from the ground than the lower antenna yields a slightly different phase angle to any pair of rays that we wish to combine to produce the strongest forward lobe. We have already seen that the elevation angle of the main forward lobe is roughly equal to that of a single antenna placed about 2/3 of the way upward between the actual antennas in the stack. Indeed, there will be small differences in the required separation for maximum gain as we move the base height from 1 wavelength to 2 wavelengths. The rules of thumb for maximum gain separation are most accurate applied to arrays with a base height of 2 wavelengths or more, even though the error for lower heights is small.

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Not only does the forward lobe receive some modification from ground reflections; so, too, do the remaining lobes. Fig. 11 shows elevation patterns for our 3 stacks, each with a base height of 1 wavelength (about 70') above average ground. Notable are the additional lobes and nulls in the individual patterns that result from ground reflections combining with direct radiation. However, in general terms--and except for the elevated main forward and rearward lobes, the total lobe structure fits within the "shell" of the simpler free-space pattern. Fig. 12 gives an example using the 7-element Yagi.

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Calculating the total effects of both the stacked-antenna interactions and the interaction of reflected and direct radiation might seem a daunting task. However, the calculations are routine within antenna modeling programs such as NEC, from which all of the patterns shown have emerged. Indeed, the surest way of finding the appropriate separation for two individual antennas in a stack is the use of such software. In this arena, modeling can turn rules of thumb into nimble fingers on the computerized abacus.

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"Appropriate separation" does not necessarily mean the use of the maximum gain separation. If we recall the tables for the Moxon rectangles, we may achieve a front-to-back ratio of at least 20 dB at a separation of about 0.85 wavelengths, about halfway between the maximum gain and maximum front-to-back separations. At this height, rather than losing a full dB relative to maximum gain, we lose only about a half dB. In addition, the feedpoint resistance and reactance values are quite manageable for an in-phase feed system. Hence, for some operations, this compromise setting might constitute the optimal separation between rectangles in a stack. For other antennas, we can only find comparable appropriate separations by careful analysis in small separation increments. Once more, the swift calculations of modeling software earn their keep.

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Our voyage through the world of stacked arrays, with attention to the Moxon rectangle, is only half a story. We can also stack the rectangles when they are positioned vertically--as we might wish to do for improved gain for VHF/UHF FM service. That is a story for another episode.

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Updated 12-04-2003. © L. B. Cebik, W4RNL. This item originally appeared in antenneX, Dec., 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Return to Moxon Index

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Go to Amateur Radio Page

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Topics: Moxon, Stacking, VHF / UHF


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Stepped-Diameter Moxon Rectangles for 20 through 10 Meters

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L. B. Cebik, W4RNL

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The Moxon rectangle has proven itself to be an effective 2-element parasitic beam of good performance and compact size. The forward gain is slightly lower (by about 0.2 dB) than a standard reflector-driver Yagi, but the beamwidth is wider (by about 10 degrees) and the front-to-back ratio is very much improved (by an average of over 10 dB). The side-to-side dimension is about 70% of the comparable dimension in a Yagi, while the space between elements is about 0.13 to 0.14 wavelength.

+

We may design the Moxon rectangle for almost any feedpoint impedance from about 35 Ohms to about 100 Ohms. The lower the feedpoint impedance, the wider and narrower the beam becomes physically. Wider rectangles with lower feedpoint impedances tend to show slightly higher gain than higher impedance versions with squarer shapes.

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The Moxon combines 2 forms of coupling to achieve its performance. First, we have the coupling between parallel elements, just as we find in a Yagi. However, Moxon beams bend the element ends toward each other, resulting in fairly close spacing of the tips. Hence, we have additional coupling. The gap between the element tips is fairly critical and varies depending upon the diameter of the element. Thinner elements require considerably closer spacing than thicker elements. Since there is some current in the side portions or tails of the elements, the beamwidth increases relative to a standard Yagi. As well, the side nulls move from the standard Yagi position of 90 degrees away from the main forward heading to between 110 and 120 degrees away from that heading.

+

Some years ago, I develop a set of algorithms for calculating the dimensions of any Moxon rectangle that uses a uniform-diameter element set. The initial algorithms focused on beams with a 50-Ohm feedpoint impedance, although I later added a different set for feedpoint impedances closer to 100 Ohms. The latter Moxon type has particular application in turnstile antennas used for fixed satellite operation. The main algorithms for 50-Ohm arrays allow a direct feedpoint connection with the usual coaxial cable, although a common-mode suppression (1:1) balun or ferrite-bead choke is a standard precaution at the feedpoint. Fig. 1 shows the general outline of a Moxon rectangle, along with the conventional designations of the element dimensions used in design algorithms. A is the total side-to-side dimension of the antenna. B is the driver tail and D is the reflector tail. The most critical dimension is C, the gap between carefully aligned tails. E is the total front-to-back dimension of the beam and is the simple sum of B, C, and D.

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The algorithms for uniform-diameter elements are highly useful at VHF and above, since virtually all arrays above the HF region use single tubes or rods for elements. However, over the years, I have received numerous requests to design for HF use some Moxons that use a tapered-diameter element schedule. The design of such Moxons has two challenges. First, an element with a stepped or tapered diameter that decreases as we move away from the element center will be physically longer than a comparable element with a uniform diameter. This fact changes the current distribution and results in a rectangle that is longer (side-to-side) and narrower (front-to-back) than an array that uses elements with a uniform diameter. Moreover, changing the diameter steps also changes the ultimate outer dimensions of the Moxon, including the required gap. The changes that may alter rectangle dimensions include not only the set of element diameters used, but also the length of each section of tubing along the element. The result of the stepped-diameter effect is that we can no longer rely on the Moxon calculator as a guide to design, although it may still provide a starting point for the necessary re-design work. The remainder of the work proceeds on a case-by-case basis.

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Second, we must find a set of tubing steps that can withstand significant wind loads. Therefore, not all stepped diameter progressions are usable. With linear elements, we may use a program such as YagiStress to calculate the wind load for a given element design. However, these programs are set for linear elements, and the Moxon rectangle has a set of tails. The tails not only add weight to the end of the long portion of the element, but they introduce additional forms of loading. For example, the rectangle will show some stresses associated with wind-induced racking forces.

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Despite the challenges, I have designed a series of HF Moxon rectangles using stepped-diameter element construction. The element structures should be able to withstand winds up to about 70-75 mph. U.S. antenna builders have an advantage due to the availability of 6063-T832 aluminum tubes. These tubes come in outside diameters that step in 1/8" increments from 3/8" upward. The wall thickness for readily available tubes (from sources such as Texas Towers) allows for close nesting of one tube size inside the next larger tube. The wall thickness is just under 1/16" (actually, 0.058") for a snug and strong fit with simple fasteners. For all of the designs in the set, the tail pieces use 3/8" tubes for their light weight. The center-most section of the 10-meter beam uses 3/4" stock. The diameter increases to 1" at 20 meters. For strength, the center-most element sections are doubled.

+

Each beam in the set of 5 is a separate design for the HF bands from 20 through 10 meters based on NEC-4 models. To provide nearly equal front-to-back and 50-Ohm SWR values at the band edges, the design frequency for the wider amateur bands is about 1/3 the way up from the lowest frequency in the band. Since the gain of any 2-element parasitic array decreases with rising frequency across a defined passband, the designs tend to favor the lower end of the band with respect to gain. The amount of gain decrease depends upon the overall width of the band as measured in percentage. (The bandwidth of a passband as a percentage is determined by dividing the total width of the band by the center frequency--using the same units for both--and multiplying by 100.) For the smaller WARC bands, designing for the band center works very well. Because the progression of tube sizes and lengths varies from one band to the next, the beams are not direct scalings of those for any other band. However, all will show the same narrowing and widening relative to calculated models using elements with a uniform diameter.

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The design notes that follow consist of tables, sketches, and graphs to show the design details and the performance potential of the beam on each band. The tables will include a comparison of the dimensions (A through E) of a calculated rectangle using a 1/2" element and the dimensions of the present design using stepped-diameter elements. Figures and tabulated data will provide a more detailed look at the element construction for each band. The potential performance--as modeled in free space--will appear in graphs, with a table sampling the numerical values at the band edges and at the design frequency. Finally, a set of free-space E-plane (azimuth) patterns will conclude the data collection for each band. I use free-space data because the patterns will vary slightly depending upon the antenna mounting height. Free-space patterns are generally almost identical to those obtained at the take-off angle for any antenna mounted at least 1 wavelength above ground. Of course, to all free-space gain values, you must add the ground reflection component, which usually runs between 5 and 6 dB, depending upon mounting height.

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20 Meters

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The 20-meter Moxon rectangle is the largest and beefiest of the entire set. It uses tubing sizes from 1" down to 3/8". Note in Fig. 2 that the 7/8" tube runs from the its outer end back to the centerline, effectively doubling the tube wall thickness for the portion inside the 30" section of 1" diameter tube. The table compares the outer dimensions of the tapered model with a calculated 1/2" model. The side-to-side widening and front-to-back narrowing are evident. However, also note the reduction in the gap distance, which is a consequence of the other dimension changes based on the need to bring the array to its performance curves and a 50-Ohm feedpoint impedance.

+
+ +
+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+20 Meters (14.15 MHz)  See text for element diameter tapering schedule.  Uniform diameter = 0.5"
+Dimension     Tapered Model     Uniform Model
+A             317"              301.78"
+B              42.5"             43.07"
+C               7.5"             10.88"
+D              58"               57.19"
+E             108"              111.14"
+
+Half-Element Diameter Taper Schedule
+The difference between the exposed length and the total length is the amount of the smaller
+diameter tube inserted into the larger tube.  Trim about 1/4" from the largest diameter tube
+at the centerline of the driver element for the gap required for feedline connections.  All
+dimensions are in inches.
+Diameter       Exposed Length       Total Length          Element Length
+1"             30                   30                     30
+0.875"         36                   66                     66
+0.75"          30                   33                     96
+0.625"         24                   27                    120
+0.5"           32                   35                    152
+0.375"          6.5 *                9.5 *                158.5 *
+* Add length of either driver or reflector tail to the length of the 0.375" diameter tube.
+
+

The half-element table correlates directly with the sketch in Fig. 2. The second column lists the length of tube needed for both the exposed section and for insertion into the next larger tube size. Except for the doubled second section, the normal insertion length is about 3" as a compromise between strength and weight minimization. The 3/8" section length represents only the portions in the parallel element section. The tube will be bent at 90 degrees so that it includes the driver or reflector tail length, as applicable.

+

Fig. 3 graphs the free-space performance of the beam across 20 meters in terms of gain and front-to-back ratio. The front-to-back data includes the 180-degree ratio (labeled front-to-back) and the worst-case ratio (labeled front-to-side).

+
+ +
+

To translate the curves into representative numbers, the following table samples the data at 14, 14.15, and 14.35 MHz. The design frequency is 14.15 MHz.

+ 
+Moxon Rectangle 20-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+14.0          6.46           18.11          38.1 - j11.7            1.46
+14.15         6.13           28.42          48.5 - j 0.2            1.03
+14.35         5.73           18.09          60.6 + j11.6            1.33
+
+

The table shows a slightly higher SWR at 14 MHz than at 14.35 MHz, since the design frequency is slightly greater than 1/3 the way up the passband. Fig. 4 shows the resistance, reactance, and 50-Ohm SWR curves for the design across the entire band. It is possible to raise the impedance slightly at the design frequency and therefore to equalize the band-edge SWR values. However, for this exercise, I wanted to hold all dimension changes to increments of 1/2". As we move upward in frequency for the smaller Moxons in this series, it will be necessary to reduce the increment to 1/4". However, the easy dimension markers may ease the problem of replicating the design with physical element materials.

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+ +
+

The 20-meter band is fairly wide (about 2.5%), and so the patterns in Fig. 5 show a fair amount of evolution. However, they are superior in front-to-back ratio and equal in gain to the patterns for any standard 2-element reflector-driver Yagi design. The blue line in the rear lobe shows the heading for the worst-case front-to-back reading that appears in the curve in Fig. 3. The red lines show the beamwidth of the forward lobe. As well, draw a virtual vertical line through the pattern rings to see how far the side nulls are from 90 degrees relative to the forward lobe line.

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+ +
+

17 Meters

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On 17 meters, we may design the Moxon rectangle for the center of the 100-kHz band, since the band is only about 0.5% wide. In terms of proportion, the dimension that differs most between the uniform-diameter and the tapered-diameter versions is the gap. Fig. 6 and the following table provide the dimensions for the array. Because the side-to-side dimension is about 70" shorter than the 20-meter Moxon, we may use 7/8" tubes at the center.

+
+ +
+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+17 Meters (18.118 MHz)  See text for element diameter tapering schedule.  Uniform diameter = 0.5"
+Dimension     Tapered Model     Uniform Model
+A             245"              235.40"
+B              33.5"             33.16"
+C               6.5"              8.94"
+D              46"               44.73"
+E              86"               86.89"
+
+Half-Element Diameter Taper Schedule
+The difference between the exposed length and the total length is the amount of the smaller
+diameter tube inserted into the larger tube.  Trim about 1/4" from the largest diameter tube
+at the centerline of the driver element for the gap required for feedline connections.  All
+dimensions are in inches.
+Diameter       Exposed Length       Total Length          Element Length
+0.875"         30                   30                     30
+0.75"          36                   66                     66
+0.625"         18                   21                     84
+0.5"           32                   35                    116
+0.375"          6.5 *                9.5 *                122.5 *
+* Add length of either driver or reflector tail to the length of the 0.375" diameter tube.
+
+

As shown in Fig. 7, the gain and front-to-back ratio vary only a small amount across the 17-meter band. The gain curve is steep only because the total range is well under 0.2 dB. As well, the gain records only to 2 decimal places, giving the curve a somewhat stair-step quality. The actual change is smooth.

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+

The following table translates the curves into spot values at the band edges and center. Fig. 8 provides a graphic view of the very small changes in resistance, reactance, and 50-Ohm SWR.

+ 
+Moxon Rectangle 17-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.17           28.24          48.0 - j 2.7            1.07
+18.118        6.09           30.01          50.6 - j 0.2            1.01
+18.168        6.01           27.40          53.1 + j 2.1            1.08
+
+
+ +
+

Although the front-to-back curves in Fig. 7 suggest a growing divergence between 180-degree and worst-case values, the patterns in Fig. 9 show that the spreading curves are a function of the very small actual change in front-to-back values. Had the curves extended well above the upper end of the 17-meter band, the 180-degree front-to-back ratio would decrease, while the worst case value would almost hold steady. The result would be a return to an overlapping curve, as shown in the comparable 20-meter curve.

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+ +
+

15 Meters

+

15 Meters returns us to a fairly wide amateur band (2.1%). As a result, we may bring to the Moxon rectangle for this band similar expectations to those developed from the 20-meter results. The decreasing size of the Moxon rectangle, shown in the element taper sketch in Fig. 10, allows us to use the same center tube size that we used in the 17-meter array. In fact, the structure is the same until the beam nears the end of the rectangle's long dimension.

+
+ +
+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+15 Meters (21.15 MHz)  See text for element diameter tapering schedule.  Uniform diameter = 0.5"
+Dimension     Tapered Model     Uniform Model
+A             210.5"            201.49"
+B              28.5"             28.14"
+C               6"                7.91"
+D              39.5"             38.36"
+E              74"               74.41"
+
+Half-Element Diameter Taper Schedule
+The difference between the exposed length and the total length is the amount of the smaller
+diameter tube inserted into the larger tube.  Trim about 1/4" from the largest diameter tube
+at the centerline of the driver element for the gap required for feedline connections.  All
+dimensions are in inches.
+Diameter       Exposed Length       Total Length          Element Length
+0.875"         30                   30                     30
+0.75"          36                   66                     66
+0.625"         18                   21                     84
+0.5"           16                   19                    100
+0.375"          5 *                  8 *                  105 *
+* Add length of either driver or reflector tail to the length of the 0.375" diameter tube.
+
+

Because the 15-meter band is slightly smaller than 20 meters in terms of bandwidth recorded as a percentage (2.1% vs. 2.5%), we can expect slightly shallower curves on 15 meters than on 20 meters. As shown in the gain and front-to-back curves in Fig. 11, the gain range is under 0.6 dB (compared to more than 0.7 dB on 20 meters). Both band-edge front-to-back ratio values are higher on 15 than on 20.

+
+ +
+

The table provides selected performance values at the band edges and at the design frequency. 21.15 MHz is exactly 1/3 the way up the total passband for the array. Fig. 12 converts the spot values for the feedpoint impedance components and the 50-Ohm SWR into smooth curves across the band. A comparison of corresponding curves for 20 and 15 meters tells us that the Moxon rectangle performance is consistent from band to band once we find the right dimensions for the selected element-diameter taper schedule. The rate of gain decrease and the rates of resistance and reactance increase across the band are very nearly linear.

+ 
+Moxon Rectangle 15-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+21.0          6.32           21.41          42.9 - j 6.6            1.23
+21.15         6.12           28.38          49.5 + j 0.1            1.01
+21.45         5.74           18.93          61.0 + j10.9            1.32
+
+
+ +
+

Further evidence of band-to-band consistency of performance appears in the free-space E-plane (azimuth) patterns shown in Fig. 13. The patterns virtually replicate those for 20 meters. Note that we obtain this performance by re-optimizing the design for each band after selecting the desired element-diameter taper schedule.

+
+ +
+

12 Meters

+

12 meters returns us to a band only 100 kHz wide. However, as a percentage, the band has shrunk to only 0.4%. Hence, we should expect flatter curves than those we obtained for 17 meters. As well, the beam size has shrunk so that we may use 3/4" tubes at the very center, as shown in the tables and in Fig. 14. The total side-to-side dimension of a 12-meter Moxon rectangle is just over 14.5', with a width just over 5'.

+
+ +
+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+12 Meters (24.94 MHz)  See text for element diameter tapering schedule.  Uniform diameter = 0.5"
+Dimension     Tapered Model     Uniform Model
+A             175"              170.72"
+B              24.5"             23.61"
+C               4.25"             6.94"
+D              33.75"            32.56"
+E              62.5"             63.12"
+
+Half-Element Diameter Taper Schedule
+The difference between the exposed length and the total length is the amount of the smaller
+diameter tube inserted into the larger tube.  Trim about 1/4" from the largest diameter tube
+at the centerline of the driver element for the gap required for feedline connections.  All
+dimensions are in inches.
+Diameter       Exposed Length       Total Length          Element Length
+0.75"          30                   30                     30
+0.625"         24                   54                     54
+0.5"           27                   30                     81
+0.375"          6.5 *                9.5 *                 87.5 *
+* Add length of either driver or reflector tail to the length of the 0.375" diameter tube.
+
+

The performance of the beam is almost invariant across the band with a 0.1-dB change in gain, as shown by the gain values in Fig. 15. Once more, the limitations in the decimal places of the gain reports provides the stair-steps in the graph. Because the worst-case front-to-back ratio remains almost constant across the band, it makes little difference that the peak 180-degree front-to-back ratio occurs at the upper band edge. To move that peak to the band's center frequency would have required a number of dimensions that used smaller fractions of an inch than the quarter-inch limit that I set.

+
+ +
+ 
+Moxon Rectangle 12-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+24.89         6.17           28.17          48.5 - j 2.5            1.06
+24.94         6.12           33.72          50.4 - j 0.7            1.02
+24.99         6.06           42.14          52.4 + j 1.0            1.05
+
+

I have included Fig. 16 solely to make the record complete. All values of resistance, reactance, and 50-Ohm SWR are as close to flat lines as we are likely to find in such graphs.

+
+ +
+

The very small changes in the patterns in Fig. 17 show how truly narrow the 12-meter band is. The rear lobe changes are visually noticeable, but operationally, it is unlikely that even the best ears could tell the difference in the suppression of rearward QRM across the band. Indeed, normal construction variations are likely to move the peak front-to-back ratio to a slightly different frequency than the one shown in the graphs and tables.

+
+ +
+

10 Meters

+

If we define 10 meters in terms of the first MHz of the total band, we still obtain the widest of the upper HF amateur bands at 3.5%. Many Yagis (especially the 10-meter sections of tri-band designs) manage to cover only the first 800 kHz with under 2:1 50-Ohm SWR. However, the Moxon rectangle easily covers the entire first MHz if we can accept the normal gain reduction across the passband. As the smallest of our rectangles (12.8' by 4.6'), the array has plenty of strength with 3/4" tubing at the center and 3/8" tail sections. Fig. 18 shows the element taper schedule corresponding to the tabular values below the figure.

+
+ +
+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+10 Meters (28.35 MHz)  See text for element diameter tapering schedule.  Uniform diameter = 0.5"
+Dimension     Tapered Model     Uniform Model
+A             154"              150.08"
+B              21.25"            20.59"
+C               4"                6.27"
+D              29.75"            28.67"
+E              55"               55.53"
+
+Half-Element Diameter Taper Schedule
+The difference between the exposed length and the total length is the amount of the smaller
+diameter tube inserted into the larger tube.  Trim about 1/4" from the largest diameter tube
+at the centerline of the driver element for the gap required for feedline connections.  All
+dimensions are in inches.
+Diameter       Exposed Length       Total Length          Element Length
+0.75"          24                   24                     24
+0.625"         24                   28                     48
+0.5"           24                   27                     72
+0.375"          5 *                  8 *                   77 *
+* Add length of either driver or reflector tail to the length of the 0.375" diameter tube.
+
+

Because the 10-meter band is so wide, the gain decreases by about 0.9 dB from one end of the band to the other, as shown in Fig. 19. As well the front-to-back values at the band edges are between 16 and 17 dB. Still, these values a 5 to 6 dB higher than we might obtain with a wide-band 2-element reflector-driver Yagi, and a wide-band Yagi would have larger dimensions in both directions (side-to-side and front-to-back).

+
+ +
+ 
+Moxon Rectangle 10-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+28.0          6.44           17.18          38.6 - j13.6            1.49
+28.35         6.10           36.07          50.6 + j 1.7            1.04
+29.0          5.53           16.18          68.6 + j13.4            1.47
+
+

As shown by the performance table and the curve in Fig. 20, the Moxon rectangle with the selected element taper schedule still manages to show less than 1.5:1 50-Ohm SWR across the band. Of course, cable losses at 10 meters begin to show themselves, so the SWR values recorded at the transmitter end of the feedline will be slightly less.

+
+ +
+

Even under wide-band conditions, such as those on 10 meters, the rearward lobes remain well behaved. Except for the peak value of 180-degree front-to-back ratio, where we find two lobes symmetrically arranged on each side of the centerline, the rearward radiation forms a single lobe. As shown in the patterns in Fig. 21, the rearward pattern is relatively straight-sided below the design frequency. Above the design frequency, the pattern shows a a single bulbous lobe.

+
+ +
+

I have provided complete design data and performance projections for each version of the Moxon rectangle. A complete record of design and performance data across each band of operation is perhaps the only fair way to allow a potential builder or user to evaluate the design to determine if it is one to implement. I could have cited spot values only or, more extremely, peak values. Such data would have given a distorted picture of the true performance potential of the array. For example, citing the peak gain values for each band would have given the impression that performance changes from band to band. As well, citing only peak gain and peak front-to-back values would distort the portrait even further, since these values do not occur at the same frequency. With regard to feedpoint impedance issues, only the curves give the potential user a clear picture of the rates of change of SWR both above and below the design frequency. In these designs, I have no vested interest. Hence, I have no reason not to show all of the data for each band's design, including any performance facts that might count against the use of the Moxon rectangle. (For example, someone interested only in phone operation might wish to redesign one or more of the wide-band designs to favor that portion of the band.)

+

Since I brought attention to the Moxon rectangle back in the early 1990s, numerous versions have been built by various enthusiasts. The arrays range from fixed wire versions for the lower HF range to lightweight wire versions for upper HF to vertically and horizontally polarized versions for a variety of special VHF and UHF applications. More recently, commercially built stepped-diameter rectangles for the upper HF region have appeared. AerialActs of Silver Spring, MD (web.archive.org) (Craig Roberts, W3CRR) markets a series of Moxon rectangles (called the MaxiMoxon) that employ different taper schedules than the models shown here. The differences in the taper schedule result in a different set of overall dimensions, although they are likely not too far from the values shown in the tables. In addition, there are differences in the preferred construction methods.

+

Re-design of a Moxon rectangle that employs a stepped-diameter taper schedule is not a task for NEC-2. Because the stepped-diameter correction of NEC-2 implementations does not operate for non-linear elements, the program will not correctly handle the bent Moxon elements. Re-design should use either NEC-4 or a highly corrected version of MININEC 3.13, such as the one sold as Antenna Model. A MININEC implementation must have at least the frequency-drift correctives if it is to handle the 12 and 10- meter designs adequately.

+

A Few Construction Notes

+

Constructing a beam for long-term station use is not a casual task. Building a durable beam does not require a massive shop. Rather, it involves taking pains to ensure that the result is the best possible combination of strength and relatively light weight. Careful planning, careful measurement, and careful fabrication go hand-in-hand-in-hand. Indeed, having a third hand in the shop (in the form of someone willing to help and equally committed to a quality finished product) is extremely helpful. If you work alone, take the trouble to construct jigs from scrap wood around the shop to assist in the drilling and other assembly processes.

+

The Moxon rectangle uses a direct 50-Ohm feedpoint, which calls for a split driver to make connections at the element center. At HF, the size of the gap is generally not critical, although the actual gap is in principle simply the distance between the two conductors of the feedline cable. The leads from the cable or from the cable connector are part of the driven element. The element dimensions from end-to-end do not change, so we subtract half the gap size from each half-element in the driver.

+
+ +
+

Modeled designs also presume that all elements are well insulated and isolated from any conductive boom that might provide physical support. A section of 1.25" outside diameter aluminum tubing is probably the most common boom material. Although the assembly is fairly light, a 1/8" wall tube or a nest of 1.25" and 1.125" tubing is necessary to support the wind-induced twisting loads on the entire assembly. The double-tube boom is wise, even for the short 10-meter boom, since it will resist crushing at the boom-to-mast junction. Fig. 22 shows one method (out of several) for constructing the feedpoint. A polycarbonate or similar plate provides the element isolation and supports the boom U-bolts. Size the plate according to the weight of the elements, using a larger plate for 20 meters and a smaller one for 10. UV protected polycarbonate sheets in 1/4" and 3/8" thicknesses are available from local plastic supply houses in medium to large cities and via the web (for example, McMasters-Carr). If we insert a non-conductive tube or rod into the ends of each element half, we assure element alignment with only 2 U-bolts and also establish an anchor point for the gap and the feedpoint connections. If we also run the inner tube to the gap, then it also provides support that will keep the aluminum elements from crushing as we tighten the U-bolts. The outside diameter of the gap-setting tube should just fit inside the center tube section of the element. For the doubled Moxon element sections, the required rod or tube size would have an outside diameter 1/4" less than the outside diameter of the largest tube in the taper schedule. All hardware is stainless steel to prevent corrosion and to avoid bimetallic electrolysis.

+

As shown in Fig. 23, we may treat the reflector of any Moxon design in a similar manner. In this case, we bring the ends of the tubes together to form a continuous element or we use a single piece of tube to form the center element section. The advantage of using a split section at the reflector center is that we may use an interior piece of aluminum tubing to form the physical and electrical junction of the 2 element halves. Extending the inner tube to the center provides the same insurance against U-bolt crushing that we obtained from the non-conductive tube in the driver elements. The inner tubing should have the same diameter as the non-conductive tube in the driver. If we use a continuous center tube for the largest diameter in the reflector, we may also use separate tubes for the next size, bringing them together at the center of the largest tube. The doubled section should provide sufficient strength to resist U-bolt crushing. U-bolts with solid aluminum saddles are available from sources such as DX Engineering. These U-bolts provide the most secure mounting and also resist element crushing better than U-bolts styled like muffler clamps.

+
+ +
+

The Moxon rectangle 3/8" tail sections must meet several criteria. First, they must turn a corner. Second, they must maintain the gap size, even in the face of winds. Third, they must keep the tail ends aligned. For 3/8" diameter tubing, turning a corner is not difficult. Starting with a tube section that is longer than needed, we can bend one end in the same tubing bender used for small copper tubing. Filling the tube with very fine play sand will further reduce the tendency for crushing during the bending operation, and many builders like to heat the tubing as a further precaution. We can insert the short end into the 0.5" diameter section with the standard 3" insertion overlap. The small curve at the corner will not alter the overall element length enough to cause any noticeable change of performance if we keep the total element length equal to the sum of all of the exposed portions of the sections. Fig. 24 shows the general scheme.

+
+ +
+

The figure also shows a simple way to maintain the gap and to keep the ends aligned. We simply insert a 1/4" non-conductive tube or rod into the tail ends and fasten it with stainless steel sheet metal screws. The tube or rod should be light and should also be UV protected. The result is a physically closed rectangle. Unlike beams with linear elements, the rectangle will not whistle, although you may wish to cap the boom ends. Because the Moxon rectangle in this configuration is subject to racking forces, we likely should reduce the wind load capacity of the elements by a small amount. The structures shown in the taper schedule sketches should handle winds up to about 75 mph.

+

There are as many variations on physical construction as there are potential element-diameter taper schedules. Therefore, consider these notes as simply a starting point for your own ingenuity.

+

Conclusion

+

These notes present usable designs for home built Moxon rectangles for the upper HF range. The Moxon rectangle is--for full performance--essentially a monoband 2-element array with close to the gain of a full size 2-element Yagi but superior front-to-back performance. For wide-band use, the Moxon is shorter than most Yagis and offers a 50-Ohm feedpoint impedance. The Moxon may also be used for yards that do not permit full-length linear elements that a standard Yagi requires.

+

The Moxon designs shown here employ element-diameter taper schedules that should suffice for winds up to about 75 mph, a condition for long-term home-station use. Due to the effects of the decreasing element diameter, the dimensions for each band differ from those for a uniform-diameter Moxon, and each design requires a custom fit to the selected taper schedule. Hence, each version in the series requires individual design optimizing and individual data graphs and tables. However, the construction of each version differs only in the size of the tubes and the boom-to-element plates. The construction techniques shown are but one set out of many that you might devise.

+

In the end, the exercise has satisfied my curiosity as to whether a complete line of Moxons might evolve, each with an element taper schedule suited to the beam size for the operating frequency. The answer is yes.

+
+ +

+
+

Updated 04-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Moxon Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Moxon


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+

HF Vertically-Oriented Moxon Rectangles
+ A 40-Meter Example

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Over the years, readers have sent me questions concerning the possibility for setting up an HF Moxon Rectangle that is vertically oriented for a lower HF band. The desires have ranged from simply reducing QRM in a specific quadrant to needing a fixed-position wide beamwidth array for various operating conditions: contests, field day, and some types of nets.

+

A Vertically Oriented Wire Moxon Rectangle

+

A vertically oriented Moxon rectangle is not feasible for every HF band. 160 and 80 meters would require such tall supporting structures that the physical result would be nearly impossible to handle. Perhaps the lowest band for which a vertically oriented Moxon rectangle might be built is 40 meters, and even on this band, the support requirements are severe. The Moxon rectangle is based on 1/2 wavelength elements, although the ends are bent toward each other. The result is still about 70% the length of a linear dipole, which is considerably longer than a typical full-size monopole on 40. In fact, a 40-meter Moxon rectangle is about 50' from one tail set to the other, and if we vertically orient the array, then that is the top to bottom dimension. We also require some spacing between the bottom of the beam and the ground. We shall discuss the exact amount in the course of describing the antenna.

+

Supposing that we have the tall redwoods and Douglas firs to use as support posts--or some towers on an otherwise well-equipped antenna farm--a 40-meter vertically oriented Moxon rectangle is feasible within some restrictions. Let's create one by using the calculator on the Moxon rectangle index page. We shall use AWG #12 copper wire and set the design frequency at 7.1 MHz so that the beam will cover the band. Fig. 1 shows the detailed dimensions.

+
+ +
+

Since the Moxon rectangle consists of a driver and a reflector, the main forward lobe is outward from the feedpoint. Like all 2-element driver-reflector beams, the gain is highest at the low end of the band and tapers off as we increase frequency. The design program places the highest front-to-back ratio at the design frequency so that the ratio is about the same at the band edges. As well, placing the 50-Ohm resonant impedance (or something very close to it) at the design frequency yields similar SWR values at the band edges. Both the front-to-back ratio and the SWR depart from optimal values more rapidly below the design frequency than above it. Hence, the design frequency is normally about 1/3 the way up the overall operating passband.

+
+ +
+

Fig. 2 illustrates the gain and front-to-back performance across the band by overlaying free-space H-plane patterns for 7.0, 7.1, 7.2, and 7.3 MHz. These patterns correspond to azimuth patterns for a vertically oriented Moxon rectangle placed over ground. Note what happens to the pattern as we move below and above 7.1 MHz, where the front-to-back ratio is highest. The cardioidal pattern deteriorates in different ways as we change frequency in different directions. The following small table summarizes the free-space performance of the array.

+ 
+Free-Space Performance of a Vertically Oriented AWG #12 Wire Moxon Rectangle in Free-Space
+Frequency      Gain        Front-to-Back Ratio    E-Plane Beamwidth
+7.0 MHz        6.34 dBi         12.3 dB              123 degrees
+7.1            5.80             31.4                 144
+7.2            5.22             14.2                 163
+7.3            4.77             10.1                 179
+
+

The impedance is very close to a resonant 50 Ohms at 7.1 MHz. We can gauge the impedance performance across 40 meters from Fig. 3. The graph shows the 50-Ohm SWR performance across the band. The thin-element (wire) version of the array on 40 meters just manages about 2:1 SWR at the band edges. Of course, if you only plan to use a portion of 40 meters, you are free to design the antenna around the frequency you most often use.

+
+ +
+

When we place the antenna over ground, we obtain about the same beamwidth as in a free-space model. The gain progression, with values adjusted for the presence of ground, follows the same progression across the band. However, perhaps the most important facet of behavior over ground involves the elevation pattern of the array. As we move the antenna farther above ground without disturbing the dimensions of the array itself, we obtain different elevation patterns. There is a lowest main lobe. However, even at a modest height above ground, the antenna shows the emergence of a second higher-angle lobe. The higher the antenna, the stronger the higher-angle lobe until as a certain height, it dominates over the lower lobe. Let's consider raising the antenna in approximate 0.05 wavelength increments from 0.15 wavelength up to 0.35 wavelength. At 40 meters, we obtain heights of 21, 28, 35, 42, and 48 feet for the bottom wire, with resulting top heights of 72, 79, 86, 93, and 99 feet. Fig. 4 shows what happens to the elevation pattern. The table below the figure provides numerical details of the modeled performance.

+
+ +
+ 
+Modeled Performance at 7.1 MHz of a Vertically Oriented Moxon Rectangle Over Average Ground
+Height        Height     Gain     TO Angle     Vertical Beamwidth     Front-to-Back Ratio     Horizontal Beamwidth
+Wavelengths   Feet       dBi      degrees      degrees                dB                      degrees
+0.15          21         4.08     16           23                     33.5                    142
+0.2           28         4.03     15           22                     30.0                    145
+0.25          35         3.92     14           21                     27.0                    147
+0.3           42         3.81     13           20                     26.0                    147
+0.35          48         3.74     12           22                     27.0                    146
+                         4.13     47           37                     19.0                    152
+
+

First, let's notice that the maximum gain at the TO angle is considerably less than we are used to seeing for the Moxon rectangle when we orient the antenna horizontally. Part of the gain reduction is a function of the much wider beamwidth, and part is a function of placing a vertically polarized antenna close to the ground. For this exercise, a proper comparison antenna is a vertical monopole or a 1/2-wavlength vertical dipole. Its gain would be in the vicinity of 0.3 dB, so the vertically oriented Moxon shows the gain improvement of any 2-element parasitic array with a driver and reflector: almost 4 dB.

+

Second, let's also notice that the main lobe gain decreases slightly as we elevated the antenna above ground, despite the slowly dropping value for the TO angle, the elevation angle of maximum radiation. The reason for the slow decrease in maximum forward gain is the relatively rapid growth of the higher-angle second lobe. It uses energy that, for each new height increase, would have gone into the main lobe. At the highest level for the antenna bottom wire, the higher-angle lobe becomes stronger than the lower lobe, as shown in the table by the double entry.

+

For maximum reduction of high-angle QRN and other noise, a lower installation height is indicated by the modeled performance. The smaller the upper lobe, the less sensitive the antenna will be to RF from high-angle skip--which includes most of the lightning noise from beyond ground-wave distances. Since the vertical beamwidth is so wide, there would be no noticeable difference in DX signal strength for any of the listed installation heights. However, the lower level antenna would often produce a better signal-to-noise ratio.

+

However, DX communications is not the only operating mode. Many operators are interested in more general communications and in net operations. Many contacts have a range of 1000 miles or less. For such operators, the growth of the higher angle lobe can enhance the higher skip angle of signals from closer sources, despite the higher noise levels. Indeed, for some net operations, the highest installation level shown might well be the best of the lot. In effect, the double lobe forms a wall of radiation or receiver sensitivity with less than a half S-unit difference for any angle from below 12 degrees to well above 47 degrees.

+

Installation height, then, becomes a compromise between what is desirable relative to the signal sources involved in the communications and what is physically feasible for supporting and maintaining the antenna.

+

Like most vertical antennas, the Moxon rectangle, when vertically oriented, does not change its impedance very much over a wide range of heights above ground. The sample 50-Ohm SWR graphs in Fig. 5 cover the lowest, highest, and middle heights of the ones used to produce the elevation patterns, and they show too little variation to need comment.

+
+ +
+

A Reversible-Direction Vertically Oriented Moxon Rectangle

+

I took a long look at horizontally oriented Moxon Rectangles in "Having a Field Day with the Moxon Rectangle," QST (June, 2000, pages 38-42). The article was reprinted in Simple and Fun Antennas for Hams, pp. 12-19 to 12-24. I note this reprint, because the entire volume is a potpourri of interesting ideas that may be useful to newer antenna builders. However, in the present context, the key element in the article is the possibility of using the Moxon rectangle as a reversible-direction beam. That use was feasible when the antenna was horizontal, and it is equally feasible when the antenna is vertically oriented.

+

The key is to use 2 identical elements, each with the dimensions of a driver in the original design. When we wish to convert one of those elements into a reflector, we can load the reflector to make it electrically longer. The load will consist of a length of transmission line set up to form a shorted stub. Since the transmission line will be the same kind of stock that we use for the main feedline, we can set up a switching system for a stub from each element. In one switch position, line 1 becomes simply part of the feedline to the driver and line 2 to the other element is shorted to provide inductive loading. In the other switch position, the line from element 2 becomes part of the feedline, and the line from element 1 becomes a stub.

+
+ +
+

Fig. 6 shows the dimensions for the reversible direction vertically oriented Moxon rectangle. If you compare these dimensions with the one in Fig. 1, you will see that we have two drivers and a gap that has not changed its size. However, we do have a load in the form of a shorted transmission line stub. The required reactance to load the reflector is about +j65 Ohms. If 50-Ohm coaxial cable had a velocity factor of 1.0, the required length at 7.1 MHz to produce the desired Moxon pattern and a near-resonant impedance would be just about 20.4'. The most common velocity factors that we find are 0.66-0.67 for solid dielectric coax versions and about 0.78-0.80 for foam and other special dielectrics. Multiply the velocity factor for the line you actually use times the calculated line length to obtain the physical line length for each stub. Since the velocity factor may vary from one batch of coax to the next, it may pay to actually measure the velocity factor of the line you have. However, the line length is not overly finicky, and you can trim it to the level of perfection you desire.

+

One effect of compressing the overall width or E-dimension of the Moxon rectangle is to lower the feedpoint impedance from about 52 Ohms down to about 45 Ohms at resonance. The actual value may vary between 40 and 46 Ohms, depending on the precise length of the stub. One consequence is a slight compression of the 50-Ohm SWR curve, as shown in Fig. 7. We lose about 35 kHz of the 40-meter band, if we wish to keep the SWR below 2:1. This fact may lead you to re-design the array more closely to one or the other end of the band, depending upon the type of operating that you do. However, except for a number of linear amplifiers, an SWR slightly above 2:1 is not fatal to either your signal or your rig.

+
+ +
+

With an ability to reverse the beam direction, the vertically oriented Moxon rectangle provides excellent overall coverage, with small decreases (less than 1 S-unit) at right angles to the beam headings. Fig. 8 overlays patterns for the beam when set for use in each direction to show both the main lobes and the nulls in coverage. While the antenna is not designed to directly complete with a rotatable beam, the coverage is not bad for a fixed set of wires.

+
+ +
+

The reversible-direction vertically oriented Moxon is just one of many possibilities. If you happen to have more real estate and tall supports than money, you might even consider a Y formed from 3 different Moxon rectangles. With the backs or reflectors separated by perhaps 1/4 wavelength, the antennas will show almost no interaction due to the high front-to-back ratios. The beamwidth of the vertically oriented Moxon rectangle is wide enough to allow full horizon coverage with just 3 beams.

+

At the design frequency, the Moxon rectangle has good gain. However, its true benefit to operation lies in the exceptional front-to-back ratio. It achieves in a parasitic array front-to-back ratios that are rarely seen outside the realm of phased arrays. A single Moxon rectangle requires no attention to interconnecting line phase angles, since the arrays geometry provides the current magnitude and phase angle on the rear element to achieve the high level of silence from the rear.

+

Installation

+

In the beginning, I noted that a vertically oriented Moxon rectangle is feasible within a set of restrictions. One of those restrictions is the height of the array overall and above ground, and we have examined the effects of various heights on performance. For many operators, the antenna is simply not physically feasible. However, antennas designed for 30 or 20 meters are more feasible. The elevation pattern effects are a function of the bottom height of the array as measured in fractions of a wavelength, so when scaling the antenna for other bands, be certain to scale the bottom height as well in order to tailor the performance to your needs.

+

Most of the supports for a vertically oriented Moxon rectangle will be vertical, and that fact presents us with another restriction. Keep any conductive or even semi-conductive vertical support (or other object) as far away as possible from the antenna. The goal is to avoid to the degree possible any unwanted coupling that would alter the antenna's performance. Fig. 9 shows one sort (out of many) of support system that meets this need. The support posts are well-spaced from the array itself, and there is no vertical structure directly ahead of the antenna. If the antenna is a reversible direction version, then the free-area requirement includes both directions from the antenna. However, a single direction array has less critical requirements behind the reflector.

+
+ +
+

The system shown in the sketch uses ropes that perform two functions. First, they support the wire structure at both the top and bottom. Second, they provide a degree of tension to hold the array in place. The exact tension will be a function of the wire and rope used. Since the gap between the 2 sets of tails needs support, it is usually wise to use a rope or sizable twine and to tape the wires to the rope that goes from front-to-back. In that way, the wire is only slightly stressed, but the front-to-back ropes take up the major stress in the system.

+

Another restriction is common to many forms of vertically oriented antennas based upon the dipole. The feedline should depart from the feedpoint at right angles to the driver for as far as feasible before changing directions. The goal is once more to prevent unwanted coupling. For horizontal versions of the antenna, we can achieve this goal by bringing the feedline straight back until we reach a centered mast. Then the feedline can proceed downward, supported by the mast.

+

The vertically oriented array cannot use a vertical mast. In many instances, the feedline must go at right angles to the driver until reaching a suitable support outside the antenna vicinity. Alternatively, for a single direction rectangle, the coax may proceed directly to the rear until it pass the reflector--and then proceed downward. Supporting the coax along its path becomes a major challenge to ingenuity. For all but the highest power levels, RG-8X is a preferred cable for this application because of its lighter weight and its relatively low loss at 40 meters. However, even this cable will load the support structures for the array.

+

A reversible direction version of the array presents even more challenges. The two lines from the twin drivers must come together at a remote switching box. That box needs support, but in a manner that does not disturb the antenna pattern. We can obtain greater distance from the elements by adding 1/2 wavelength of cable to each line, but at a cost of somewhat higher losses in the stubs. At 40 meters, the losses are small enough to perhaps be acceptable in exchange for placing the switch box beyond the limits of adverse affect on the antenna patterns.

+
+ +
+

Fig. 10 shows the general principles of the remote switching. The system requires that when one of the lines is used as a shorted stub, both the coax center conductor and braid must be isolated from the other line and from the incoming feedline cable. Hence, the figure shows a 4-pole, 2-throw switch or relay system. Of course, the remote portion of the system must be weather protected, and the remote system requires some form of control voltage line.

+

The vertically oriented Moxon rectangle is certainly not an array for everyone, and perhaps in the end, not for anyone. However, it does show the performance of the Moxon rectangle when vertically oriented and set up for one of the lower HF bands. Hence, if it serves no other purpose, it provides a comparator for various other types of directional vertical systems, both simple and complex. So even if no one ever builds a vertically oriented Moxon rectangle on 40 through 20 meters, the design exercise will have some use.

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Updated 12-28-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Moxon Rectangle Index

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Return to Amateur Radio Page

+

Topics: HF Lower, Moxon, Reversible, Vertical


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The Moxon Rectangle on 2 Meters

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L. B. Cebik, W4RNL

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We often think of the Moxon rectangle as strictly an HF antenna. However, its small size and special far field pattern lend themselves to some VHF applications. So let's see how to adapt the design to 2 meters (as a popular band choice) and also see a few of the uses to which we may effectively put the design.

+

Basic Moxon 2-Meter Properties

+

The Moxon rectangle is a parasitic 2-element array with the ends of each element folded back towards each other for additional coupling. The result is a beam with a very broad beamwidth and a very high front-to-back ratio, with a gain similar to that of a standard 2-element Yagi. Fig. 1 sketches the general outline of the antenna with the crucial dimensions designated by letters.

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+ +
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When scaling the Moxon rectangle to VHF, the typical materials we use to make antennas will have a much greater diameter as a percentage of a wavelength than do the materials we use at HF. Hence, to obtain the same performance as at HF, VHF versions of the antenna will have proportionately larger gaps between element ends. The larger gap then forces some changes in other dimensions to achieve the desired gain, front-to-back, and feedpoint impedance characteristics. In Table 1 are modeled dimensions for three rectangles using different diameter materials. All dimensions are in inches.

+ 
  Dimension                        Material
+               1/4" dia.           1/2" dia.           1" dia.
+     A         29.2"               28.8"               28.2"
+     B          3.65"               3.42"               3.17"
+     C (gap)    1.70"               2.04"               2.12"
+     D          5.45"               5.58"               5.76"
+     E         10.80"              11.04"              11.05"
+

From these examples, the average builder can interpolate dimensions for materials with intermediate diameters. Note that as the material diameter increases, everything gets a little shorter except for the gap and the reflector tails. The larger diameter materials provide closer coupling between element ends and thus must be widened to restore performance. The driven element gets shorter overall, with a smaller side-to-side dimension as well as shorter tails to provide the 50-Ohm feedpoint impedance. As the driver grows shorter, the reflector grows shorter by a smaller amount (about 0.4" from the smallest to the largest diameter material in the table). Since we keep the side-to-side dimension the same for both driver and reflector and since that dimension is growing shorter with fatter elements, we must lengthen the tails of the larger diameter models. With a wider gap and longer reflector tails, 50-Ohm rectangles will be wider from front-to-back as we increase the element diameter.

+

There is no significant difference in the performance of copper or aluminum, since the diameter of all of the elements is great enough to make the material losses very low. Table 2 lists the predicted performance of the 3 antenna versions at 144, 146, and 148 MHz. All numbers are free space modeled values.

+ 
Parameter      1/4" dia.           1/2" dia.           1" dia.
+               144  146  148       144  146  148       144  146  148
+Gain dBi       6.4  6.0  5.7       6.2  6.0  5.7       6.2  6.0  5.8
+F-B dB         18   33   21        22   35   21        22   33   25
+Feed Z:
+  R            39   50   60        44   53   61        45   54   61
+  jX           -11  0    +8        -8   0    +6        -6   0    +4
+50-Ohm SWR     1.4  1.0  1.3       1.2  1.0  1.3       1.2  1.0  1.2
+

The fatter the elements, the broader the characteristics of the antenna across the band. Clearly, however, all three element diameters will perform quite well across the 2-meter band. Hence, the choice of materials will be whatever you find easiest to work with and most desirable for a given application.

+

One would not normally select the Moxon rectangle for gain. Simple Yagis with 3 or more elements can provide higher gain without the complexity of bending the elements and maintaining the critical gap between element ends. The Moxon rectangle recommends itself wherever one needs any one or more of the following properties:

+
    +
  • Broad bandwidth for operating parameters
    • +
  • Broad beamwidth
    • +
  • Very high front-to-back ratio
    • +
  • Broad 50-Ohm VSWR bandwidth
    • +
+

Most of the positive properties of the rectangle appear in Table 2. To supplement the numbers there, we can look at some overlaid free space patterns.

+
+ +
+

Fig. 2 show free space azimuth patterns of the 1/2" diameter model across the 2-meter band. The design center frequency is 146 MHz, and both the front-to-back ratio and the feedpoint impedance were optimized for that frequency. The gain differential from 144 to 148 MHz is well under 1 dB. Although the ideal front-to-back ratio holds good only around the design frequency, the front-to-back ratio of this model is nowhere under 20 dB, even at the band edges. The -3 dB beamwidth across the band is between 75 and 80 degrees. The maximum front-to-side ratio does not occur at the usual 90-degree points relative to the direction of maximum forward gain. The maximum front-to-side ratio angles are close to 30 degrees further back in the pattern.

+

Horizontally and Vertically Polarized Patterns over Ground

+

At heights above 1/2 wl, the Moxon rectangle feedpoint impedance is very stable and is thus of little concern once established during construction. Elevation angles of maximum radiation accord well with standard dipole based antennas. Therefore, the rectangle might be classed as a "very well behaved" antenna. We can move it from one height to another without worrying about adjustments beyond a secure mounting.

+

Perhaps the only significant construction worries are these two.

+

1. Element corners: Bending tubing into the sharp 90-degree angles used in the models is often not feasible. We can manage the trick with 1/4" diameter aluminum rod to form continuous elements. If we use copper tubing, we can solder 90-degree elbows to straight pieces to form sharp angles. If we bend aluminum or copper tubing, the radius of the corner will likely require that we lengthen the side-to-side dimensions a bit to restore the performance curve.

+

2. Gap-fixing: Aligning the element ends and maintaining both the alignment and the gap distance is critical to long-term use of the rectangle. Wire versions used at HF often stretch the rectangle at the four corners and use a non-stretch section of rope or twine to maintain both alignment and spacing. For larger diameter aluminum tubing, one may place a section of CPVC in the ends of both elements and fasten it with sheet metal screws. The stresses are low enough to give the fixed light-weight spacer good durability.

+

For rods or smaller diameter tubing used at VHF, we can use a small length of fiberglass rod. The weight of a 2" length should not pose a problem. Heat shrink tubing placed over the rod and element ends will hold everything aligned for a considerable period.

+

The right applications for a horizontally polarized rectangle are dictated by the pattern, shown in Fig. 3, taken at a typical 2-meter installation height of 30' above the ground.

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+ +
+

The high-front-to-back ratio suggests that the antenna is most at home in a fixed installation where interference from the rear is more troublesome than signal strength from the forward direction. The wide coverage from the forward direction requires minimal redirection of the antenna under these conditions. Even if the desired station is off the center line, we might best orient the array so that we achieve a maximum null for the source of interference.

+

Often neglected is the fact that a Moxon rectangle will perform as well when vertically oriented and hence vertically polarized. Fig. 4 shows the azimuth pattern of the rectangle, once more at a 30' height.

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+ +
+

The gain of the vertical rectangle is slightly less than for the horizontal rectangle, but the -3 dB beamwidth is much larger: about 144 degrees, or just shy of a full half compass. There are many repeater applications for such a wide-band and wide-beamwidth antenna, especially in installations where mutual repeater interference is common. One can null out the interfering repeater to a high degree--or one can reduce one's interference to that other repeater.

+

In multiple antenna installations, the rectangle can be used in conjunction with other rectangles or other types of antennas to achieve full coverage over a desired area. Indeed, proper antenna choice can ease the problem of dead spots and antenna polling indecision.

+

There are a number of repeater users who live along ridges and in other areas where two repeaters may both be accessed simultaneously. The Moxon rectangle--actually a pair of rectangles--vertically oriented, may present a simple solution.

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+ +
+

Fig. 5 shows the alternate azimuth patterns of two rectangles back-to-back and separated by about 30 inches. Each antenna is built to the dimensions shown early in this note. The interaction of the active antenna with the inactive reflector is minimal--just enough to reduce the front-to-back ratio to about 20 dB. Interestingly, this front-to-back level and the "flat-back" pattern remains fairly constant across the entire band.

+

The feedpoint impedance is unaffected by the presence of the inactive antenna to the rear. It should be possible to arrange up to three such rectangles to provide coverage of virtually the entire horizon, one section at a time. The key is to remember to use only one antenna at a time, letting the feedpoint of the other(s) be shorted when inactive. Shorting the unused feedpoints can be accomplished by either electrical or mechanical means.

+

The Moxon and Satellites

+

The current generation of amateur satellites do not generally require high gain for either transmission of reception. Indeed, power control is the constant plea of those folks who try to keep the birds active for the benefit of amateur everywhere. For some satellites, a much simpler antenna system may be useful, if not as the station's primary system, then as a back-up when the main array is down for maintenance or improvement.

+

Can the Moxon rectangle play a role here? See Fig. 6.

+
+ +
+

Fig. 6 shows the elevation pattern broadside to a 2-meter Moxon rectangle that is 1 wl off the ground. Although each side of the pattern shows a null, the remaining curve is remarkably smooth and with roughly equal gain from one side to the other.

+

Elevating the antenna too high will produce a series of lobes and nulls, with consequential ups and downs in signal level. Hence, the use of the rectangle depends on keeping it at a fairly low height. The feasibility of using the antenna in this application therefore depends in part on the collection of ground clutter objects that might adversely affect the pattern.

+
+ +
+

Fig. 7 shows the general outlines of the elevation patterns of the rectangle both broadside to the antenna and in-line with the wires. The 3-dimensional pattern makes a kind of tunnel across the sky from one horizon to the other (or from above the ground clutter to just above it reentry into the picture). Consider the antenna to be mounted so that its plane is at right angles to the usual satellite path across the sky. For overhead paths, a fixed antenna appears capable of providing nearly maximum time for contacts during each pass of the satellite. One limitation of the system is that paths that are lower to the horizon may not be as easily accessed.

+

One possible cure is to use a pair of fixed rectangles--again switched so that one is active at a time. Each antenna will be tipped in the plane of the wires to make a shallow angle with the ground. Thus, each will be slightly better than the other for lower angle paths, without jeopardizing gain for the overhead paths. The lowest levels will be subject to some pattern skewing, since tilting an antenna does not produce patterns exactly like the overheard pattern. However, the system should handle at least 80% of the fullest possible range of satellite captures.

+

If polarization becomes an issue, then 2 Moxons can be placed at right angles, crossing (without touching) at their centers. Feeding the two drivers 90 degrees out of phase will equalize the pattern in all directions, and the vertical and horizontal components of their combined fields will be roughly equal. Since each antenna is a good 50-Ohm match at its design frequency, we can use a 50-Ohm, 90-degree phasing line between the two feedpoints. The resultant combined feedpoint impedance will be 25 Ohms. A 35-37-Ohm ¼ wavelength section will restore the 50-Ohm main line feed impedance.

+

Elevating the 2-meter Moxon (and possibly a 440 MHz companion) would require the use of a sizable ground screen. Because ground reflection involves a Fresnel zone at some distance to the antenna, small screens are of limited use in overcoming the series of lobes and nulls that appear in the pattern of a highly elevated rectangle. However, providing a screen as a substitute ground is one direction of experimentation that might permit the rectangles to clear most of the ground clutter.

+

Conclusion and Beginning

+

We have looked briefly at the Moxon rectangle on 2-meters in all three directions: horizontal, vertical, and straight up. However, we likely have only scratched the surface of possible applications. Indeed, there may be both amateur and commercial applications from 50 MHz up to a GHz. For example, in urban communications--whether via amateur or commercial links--few antennas radiate to the rear as little as the rectangle, and few are likewise as insensitive to radiation from the rear. Hence, the rectangle may be useful in overcoming at least part of the reflection and re-radiation problem common to antennas in the vicinity of building with acres of steel and copper.

+

By the same token, the Moxon rectangle is not a cure-all for every antenna need. Where gain is the name of the game, long Yagis and arrays of Yagis still rule the roost in the VHF range, while parabolic reflectors command the frequencies from UHF on up. These notes are designed only to show some of what a rectangle can do well. Use it where it fits the need.

+
+ +

+

Updated 10-01-99, 10-21-99. © L. B. Cebik, W4RNL. This item originally appeared in AntenneX, September, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

Return to Moxon Index

+

Go to Amateur Radio Page

+

Topics: Moxon, VHF / UHF


+ + diff --git a/content/mu/mu0.html b/content/mu/mu0.html new file mode 100644 index 0000000..55f1a19 --- /dev/null +++ b/content/mu/mu0.html @@ -0,0 +1,68 @@ + + + + + + Modeling and Understanding Small Beams Index + + + + + + + + + +
+

Articles from Communications Quarterly
+ Modeling and Understanding Small Beams

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+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Because I have received numerous requests for reprints, I am placing at the site revised versions of the most substantial articles (listed below) that have been printed in Communications Quarterly at least 2 years past (1997 and before). Because of limitations in the reproduction process, the scanned figures may be less than optimal. However, the main text and equations have been converted into HTML and .GIF from my manuscripts. A few characters that do not readily convert from one program to another may turn up missing, and I shall reinsert them as I discover them.

+

I have taken the occasion to add to the texts references to notes at this site that carry on discussions and investigations begun in these studies. Hence, everything is incomplete. Despite these limitations, I hope some of the articles are useful to you. (* items have not yet been converted and appear in page .GIF form.)

+

"The Effects of Antenna Height on Other Antenna Properties: A Computer Study," Communications Quarterly (Fall, 1992), 57-79. See Magazines Page.

+

"Modeling and Understanding Small Beams:"

+ +

A number of the ideas in these articles have been updated with further information that appears in other notes at this site. For example, there are updates on the Moxon Rectangle, EDZ antennas, ZL Specials and other phased 2-element beams, and quad beams. Therefore, the articles above should be read as initial studies, not as finished, final, or authoritative treatises.

+

You may also note some changes along the way. When I began my modeling efforts, MININEC was the only readily available software. It was followed by NEC-2 and finally NEC-4. Likewise, my initial TurboCAD-for-DOS sketches have slowly evolved into drawings that used a more advanced Windows version of the program. Graphs started in Quattro-Pro-for-DOS have also evolved through version 7 for Windows. However, if you can bear the evolution of computer tools as well as antenna information, there may still be a useful item or two in the collection.

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+ +
+

Updated 7-25-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to Amateur Radio Page

+

Topics: Small Beams


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+

Modeling and Understanding Small Beams

+

Part 1: The X-Beam

+

L. B. Cebik, W4RNL

+
+
+ +
+

Between miniature loop antennas and full size arrays exists a special class of antennas: the small beams. Small beam antennas are intriguing and misunderstood. To some, they represent the search to achieve something for nothing. Like lotteries and sweepstakes, they receive as much moral disapproval as technical discrediting. To others, they are a necessity, since something is at least better than nothing. Space and money are the chief motivations to build a mini-beam of one or another design.

+

Quite frankly, for me, small beams are fun. Many types of small beams have received only casual empirical development. What their performance limits may be remains a mystery in the literature. Here, computer modeling can offer a service by estimating with buildable accuracy antenna gain, front-to-back ratio, overall azimuth and elevation patterns, and feedpoint conditions. For under $30 per antenna, with hardware store parts, I can test what modeling tells me ought to be the case.

+

In this series, we shall look at several contemporary small beams, including the folded X-beam, the modified Moxon rectangle, the linear-loaded Yagi, fan-element Yagis, shrunken quads, capacity-hat Yagis, ZL-Specials, and the parasitic EDZ. The last is admittedly not small in element length, but it is short and cheap. Our purpose is not to recommend any of the designs. Rather, the goal is to understand what each design can and cannot do. Only then can one assess what each beam's place may be in the scheme of amateur antennas.

+
+ Standards of Comparison +
+

Small beams appeal to the builder because they are manageable. They are "hands-on" devices, not set and forget store items. On 10 meters, where all the beams in this series were modeled and tested, dimensions are reasonable as one-person projects. Moreover, the results are generally scalable down to at least 20 meters with little adjustment. Moreover, since 10 meters is closed part of the day, even during sun spot maxima, one can test the antennas without causing QRM. A temporary mast about 20-feet long, a method to prop it securely but not permanently, some feedline, a small rig (like the HTX-100 I use), a good noise bridge and SWR meter, and a reliable helper (like N4TZP, my XYL) are all one needs to try out a few 10-meter mini-beams.

+

However, a good modeling program makes an even better beginning. It permits one not only to reject numerous ideas that simply are not worth the effort of building, but as well it puts dimensions close enough to reality so that adjustments go in the right direction the first time. Most of all, a modeling program allows a relatively rapid investigation of the most significant antenna properties, which produces an understanding of the antenna to be tested. This series will contain extensive notes on the modeling aspect of these investigations to show the evolution of various designs. These notes may also prompt kindred spirits to try some directions not taken here and to uncover some possibilities that have eluded me. Modeling data in this series will often be given for free space (to permit ready general comparisons), at 20 feet (a common height for portable antennas), and for 35 feet (a common permanent installation height).

+

There are several general propositions about small beams that underlie both our knowledge and our mythology:

+

1. Small beams generally have narrower bandwidths than full size beams. This proposition is true, but it is not always the limiting factor that we may think it is.

+

2. Small beams present complex construction problems. The truth of this proposition depends upon the sort of antenna construction with which you are comfortable. If you have only slipped tubing in and out of other tubing in normal Yagi construction fashion, then some closed geometry beams will seem ungainly at first sight. However, if you look at plumbing and electrical supplies and see antenna possibilities, then small beams offer a pleasant challenge. But, admittedly, a few require careful construction.

+

3. Small beams give reduced performance. In its absolute form, this proposition may be the most mythical of all. At design center, some small beams can outperform their full size brethren in one or another specification, with only a small sacrifice in other areas. For example, some of the beams in this series--all two-element parasitic types--will outperform the standard two-element Yagi in front-to-back ratio with little loss of forward gain over a small bandwidth. And, for certain operators, this property may be just the one desired. This fact does not mean that the small beams are superior, for many have other deficiencies. Rather, every beam must be measured against a particular set of applications.

+
+ +
+
+ Fig. 1. Composite free space azimuth patterns of a wide-band 2-element Yagi from 28 to 29 MHz. +
+

As a standard of comparison, let's present a well-known 2-element Yagi with a driven element and a reflector. Using 1-inch aluminum tubing, the driven element is 16-feet long, the reflector is 17.5 feet long, and the spacing is 4.25 feet.(1) The resonant feedpoint impedance is about 32 ohms at 28.5 MHz. What makes this antenna a good standard of comparison for understanding the mini-beams in this series is that it is well-behaved. As Fig. 1 and Table 1 demonstrate, the beam maintains its characteristics across a 1 MHz span of 10 meters with excellent consistency. Free space forward gain varies by about 0.76 dBi, while the front-to-back ratio varies by less than 1 dB. Variations over real ground at 20 feet and 35 feet are somewhat greater, but still quite minor.

+ 
                                      Wide-Band 2-Element Yagi Performance
+
+Frequency (MHz)                       28.00          28.25          28.50          28.75          29.00
+
+Free Space
+        Gain (dBi)                    6.7            6.5            6.3            6.1            5.9
+        F-B ratio (dB)                10.3           11.0           11.2           11.0           10.6
+        Impedance (R jX)              24 - 17        28 - 8         32 + 1         36 + 9         40 + 18
+
+20' high
+        Gain (dBi)                    11.7           11.5           11.3           11.2           11.1
+        F-B ratio (dB)                13.3           12.2           10.9           9.7            8.8
+        Impedance (R jX)              27 - 21        30 - 13        34 - 5         37 + 2         39 + 10
+
+35' high
+        Gain (dBi)                    12.0           11.9           11.7           11.5           11.4
+        F-B ratio (dB)                12.7           13.7           13.5           12.6           11.5
+        Impedance (R jX)              27 - 17        31 - 8         35 + 0         40 + 8         43 + 15
+
+Note:  Performance figures for 20 and 35 foot heights were taken over average ground (also called medium
+earth:  dialectric constant = 13, conductivity = 5 milliSiemens/meter).  See text for antenna dimensions and
+material.
+
+Table 1.  Performance characteristics in free space, at 20 feet, and at 35 feet of a wide-band 2-element Yagi
+using a driven element and a reflector.
+

The antenna's performance in terms of raw gain and front-to-back ratio at design center is modest. However, 6.3 dBi forward gain (free space) and 11.2 dB front-to-back ratio are quite serviceable figures compared to the free space gain of a wire dipole (about 2.15 dBi). You can design Yagis for another dB of forward gain and alternatively for a somewhat greater front-to-back ratio, but only at the expense of bandwidth. Thus, the given design seems well suited to its role as a standard of comparison. With it in mind, we can turn to the first of our small beams.

+
+ The Folded X-Beam +
+

In Volume 1 of The Antenna Compendium, Brice Anderson presented dimensions for a folded X-beam for the upper HF bands.(2) His empirically derived antennas have received both praise and censure within amateur circles.(3) Unfortunately, much of the criticism has stemmed from one remark born of enthusiasm: the X-beam rivals a 3-element beam in performance. I have known some 3-element tribanders of older design which might fit the remark, but newer designs likely reduce the claim to approaching the performance of a full-size 2-element beam.

+

Anderson built his X-beams using a driven element and a director element to match as closely as possible a 50-Ohm line without additional components. His aim was a design that home builders could replicate and use reliably across a chosen band. In achieving this goal, he produced a 2-element parasitical beam with less than its full potential for gain and front-to-back ratio. Nevertheless, the X-beam as Anderson presented it may well serve hams operating in very limited space. With dimensions approximately a quarter wavelength on a side, the X-beam is a compact way to achieve some gain and some front-to-back ratio in a compact arrangement. Indeed, those who build X-beams generally do not seek to equal the performance of a 3-element Yagi, but only to achieve an improvement both in gain and in signal rejection relative to fixed-position dipoles. The X-beam will certainly do that.

+
+ Modelling the X-Beam +
+

Computer modelling via MININEC offers us a chance to understand better some of the characteristics of the X-beam. Due to its complex geometry, full of acute angles, it is not the simplest beam to model. However, the auto-tapering feature of ELNEC 3.02 permits some reliable looks at X-beam performance under various conditions.(4) Similar work can be done using the bent-wire correction feature of AO 6.0, if one uses enough wire segments.(5) The X-beam is worth the effort to examine, especially if one wants to get more than minimal results from it.

+
+ +
+
+

Fig. 2. TRU-X beam configuration and azimuth pattern at 35' above average earth.

+
+

Where Does the X-Beam Come From? Any two wires, one of which is fed, will show some degree of parasitic element properties if they are not too dissimilar in length, not too far apart, and not at right angles to each other. Paralleling elements is efficient, but not necessary. One can construct a true X-beam (or TRU-X), as shown in Fig. 2, and alter the dipole pattern to show a bit of gain in a favored direction. With over 3 dB gain above a dipole in the same setting (35' in Fig. 2), the TRU-X might be a useful beam were it not so large and were the pattern something less than a 3-leaf clover. The side lobes are only 4 dB down from the main lobe, inviting confusing QRM.(6)

+
+ +
+
+

Fig. 3. Roman-X beam configuration and azimuth pattern at 35' above average earth.

+
+

Now, let us bend back the ends of the X-elements to form a Roman X, as shown in Fig. 3. This simple act pushes the side lobes toward the back, reduces them, and increases forward gain. A comparison of the patterns in Fig. 2 and Fig. 3 reveals the differences. Forward gain can improve by up to 1 dB over the TRU-X, while the side lobes are down 7 dB from the main lobe. However, as Table 2 shows, the Roman-X is a big antenna relative to these marginal improvements. Both the TRU-X and the Roman-X produce beams are, in general, about the same breadth as, but unequal in performance to, a standard 2-element Yagi. Table 2 compares the dimensions for the X configurations and for the Yagis.

+ 
                          Performance and Dimensions of the Tru-X and Roman-X Antennas
+
+Performance (in free space):
+
+Antenna                Gain           Front-to-Back         Band width             Source Impedance
+                       (dBi)          (dB)                  (degrees)              R +/- X
+
+Tru-X
+  Max. Gain            5.5            16.4                  58                     42.8 +  3.1
+  Max. F-B             5.2            29.5                  62                     51.8 + 2.5
+
+Roman-X
+  Max. Gain            6.3            12.1                  58                     41.2 + 27.3
+  Max. F-B             5.7            23.1                  62                     59.8 + 25.3
+
+
+Dimensions:
+
+Antenna                  DE                    Dir                  Total Side-side       Total Front-back
+                       Length                Length                     Length                Length
+
+Tru-X                   20.6'                 20.4'                     14.5'                 14.5'
+                       DE = 2 x Arm          Dir = 2 x Arm
+Roman-X                 21.4'                 20.4'                     17.4'                  9.8'
+               DE = 2 x (Arm + Tail)         Dir = 2 x (Arm + Tail)
+
+Typical 2-element Yagis
+  DE + Dir              17.0'                 15.6'                     17.0'                  4.0'
+  DE + Ref              16.0'                 17.5'                     17.5'                  4.3'
+
+X-Beam                  6.9' + 3.8'           6.9' + 3.3'                9.8'                  9.8'
+               DE = 2 x (Arm + Tail)         Dir = 2 x (Arm + Tail)
+
+Table 2.  Dimensions of Tru-X, Roman-X, DE + Dir Yagi, DE + Refl Yagi, and X-beam antennas.
+

If we bend the ends of the Roman-X wires still further back until the director ends and driven element ends point at each other, we can retain the performance of the Roman-X in a square only slightly greater than a quarter wavelength on a side, as shown in Fig. 4. This is the X-beam Anderson presented in Volume 1 of Antenna Compendium, and Fig. 4 shows the dimensions he recommended for 10 meters.(7) The question is whether it is worth building such an antenna, on the assumption that a 3-element Yagi is out of the question at one's location.

+
+ +
+
+

Fig. 4. Configuration and terminology of the X-beam.

+
+

Basic Anderson Performance: In order to answer the question, I constructed numerous computer models of Anderson's design and variations upon it. In the process, I discovered some general patterns of theoretic interest, as well as some other patterns and progressions that pointed to performance improvements. The end result was a better understanding of what X-beams could and could not do and a better sense of what I should and should not do in playing with them. Throughout, I shall presume construction methods similar to those used by Anderson and retain his terminology, calling the angular tubing the arms and the bent-back wire ends the tails.

+
+ +
+
+

Fig. 5. Representative azimuth pattern of the X-beam, configured for best match to 50-Ohm coaxial cable.

+
+

The initial stage in the work was to see what MININEC might tell about Anderson's beam. I modeled his dimensions for 10 meters (28.5 MHz), using 0.5" diameter aluminum tubing and #18 wire. The result was a beam with modest gain over a real dipole in free space, at 20 feet (a common height for portable beams on 10), and at 35 feet (a common 10-meter fixed installation height). The results appear in Table 3, with Fig. 5 showing a representative azimuth pattern for the "best match" configuration at 35 feet above average earth (dielectric constant 13, conductivity 5 mS/m). Three aspects of the figure are especially notable. First, the gain over a dipole in the same position is less than 3.5 dB and not up to average 2-element Yagi figures. The front-to-back ratio is also modest, but odd. The side lobes quartering to the rear are less than 10 dB down from the main lobe, which limits signal rejection in these directions. These rearward lobes will remain, no matter how much front-to-back ratio is achieved in the 180-degree direction. Third, the input impedance is in the mid-30-Ohm range, which permits a direct coax connection with an SWR ratio of under 2:1. One can either live with or cancel the remnant reactance at the feedpoint with not too much trouble.

+ 
                                         Properties of a 10-Meter X-beam
+
+Antenna A:  Basic Anderson design:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29'.
+
+Environment            Gain           Take-Off       F-B Ratio      Beam width     Source Impedance
+                       (dBi)          Angle          (dB)           (degrees)      R ± X
+
+Free Space             5.5            --             20.9           66             36.3 - 19.2
+20', ave. gnd.         10.7           24             11.8           74             38.6 - 12.1
+35', ave. gnd.         10.9           14             17.1           68             34.3 - 16.1
+
+Antenna B:  +0.2' to Tails:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.49'.
+
+Free Space              6.6           --             13.0           62             20.3 +  0.4
+20', ave. gnd.         11.6           23             24.2           66             22.9 +  1.9*
+35', ave. gnd.         11.9           14             15.4           62             20.3 +  1.9
+
+Antenna C:  +0.3' to Tails:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 4.09', Dir = 3.59'.
+
+Free Space              6.9           --              7.0           58             14.1 + 15.1
+20', ave. gnd.         11.9           23             10.6           62             15.3 + 15.1
+35', ave. gnd.         12.1           14              7.9           60             14.3 + 15.6
+
+* Dimensions of antenna B were optimized for a 20' height above average earth.  Free space models require
+adjustment for low heights and require real earth models.
+
+Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
+dialectric constant = 13, conductivity = 5 milliSiemens/meter).
+
+Table 3.  Properties of a 10-meter X-beam in free space and at 20 and 35 feet over medium earth.
+

Attempts to improve performance led to some alteration of the element dimensions, while adhering to Anderson's advice to keep the tail lengths a certain amount different--on 10 meters, 6 inches. This procedure lent consistency to all my models, which allowed the patterns and progressions to appear more easily. My first attempts lengthened all the elements by 0.2 feet per end. As Table 3 shows, the resulting antenna increased in gain by a small but useful amount. However, the front-to-back ratio increased by much more. Nonetheless, the rearward side lobes did not materially shrink. Fig. 6, a representative azimuth pattern, displays the side lobes quite well. Finally, the input impedance decreased into the mid-20-ohm range. This antenna promised improved performance at the cost of requiring a 2:1 matching system.

+
+ +
+
+

Fig. 6. Representative azimuth pattern of the X-beam, configured for maximum front-to-back ratio.

+
+

Increasing the tail lengths by 0.3 feet over the original Anderson dimensions produced further changes in X-beam characteristics. Gain increased to equal or surpass average 2-element Yagis. However, as Table 3 shows, the front-to-back ratio decreases dramatically. Yagis with 2 elements show a similar phenomenon when optimized for maximum gain. Fig. 7 shows a representative "max gain" X-beam azimuth pattern. Finally, the source impedance dropped into the mid-teens range.

+
+ +
+
+

Fig. 7. Representative azimuth pattern of the X-beam, configured for maximum gain.

+
+

None of these models represents the absolute peak of coax match, front-to-back ratio, or gain that might be obtained with an X-beam. Rather, they are models designed to find out about where various parameters end up with changes of element length. Initial observations of the data in Table 3 suggested that with the X-beam, one cannot wholly rely on a free-space model. Modeling over the anticipated real terrain of the antenna is a must. Since MININEC calculates the source impedance over perfect ground, not the modeled ground, slight differences between the models and reality are the order of the day.

+

Constructing an X-beam without loading requires a tuning process that opposes what we normally do. If we wish to move from best 50-Ohm match to maximum front-to-back ratio, we must lengthen the element tails, a process that requires more forethought than merely snipping dipole wires.

+

Loading the X-Beam: If we could achieve some desirable improvements in X-beam performance by changing element lengths, the next question was whether similar results might be obtained by loading the director. This idea came from W2EEY's X-beam that I encountered in Antenna Roundup, Vol. 2.(8) Table 4 shows some initial results. Using the original Anderson dimensions, we can achieve the performance of the maximum front-to-back ratio model and the maximum gain model by placing a series inductor of the proper reactance at the center point of the director. Although the models use a lossless inductor as the loading element, reasonably high-quality coils should not reduce the performance figures significantly.

+ 
            Properties of a 10-Meter X-beam with an Inductively Loaded Director
+
+Antenna:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29'.
+
+Environment    Dir Xl         Gain           Take-Off       F-B Ratio      Beam width     Source Impedance
+               (Ohms)         (dBi)          Angle          (dB)           (degrees)      R ± X
+
+Antenna A:  Anderson best 50-Ohm match design
+
+Free Space         0          5.5            --             20.9           66             36.3 - 19.2
+20', ave. gnd.     0          10.7           24             11.8           74             38.6 - 12.1
+35', ave. gnd.     0          10.9           14             17.1           68             34.3 - 16.1
+
+Antenna B:  Maximum front-to-back ratio design
+
+Free Space      + 6            5.9           --             27.6           64             29.7 - 19.6
+20', ave. gnd.  +12           11.4           24             24.0           68             26.1 - 15.7
+35', ave. gnd.  +10           11.5           14             27.2           64             24.9 - 16.6
+
+Antenna C:  Maximum gain design
+
+Free Space     +23             6.8           --              6.9           58             13.1 -  9.9
+20', ave. gnd.  +23           11.7           24             10.3           62             14.3 - 10.2
+35', ave. gnd.  +20           12.1           14             10.3           60             15.5 - 11.8
+
+Note:  Loading permits each antenna to be optimized for each environment.
+
+Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
+dialectric constant = 13, conductivity = 5 milliSiemens/meter).
+
+Table 4.  Properties of a 10-meter X-beam with an inductively loaded director in free space and at 20 and 35
+feet over medium earth.
+

There is no need to display further azimuth patterns from this point onward, since one of the progressions began to show itself at this point. Best match, maximum front-to-back, and maximum gain patterns each look alike, whatever means are used to arrive at them. Moreover, the resistive component of the source impedance remains in the same ball park for each category: the mid-30s for best match, the mid-20s for maximum front-to-back ratio, and the mid-teens for maximum gain.

+

Inductive loading is usually less preferable than capacitive loading, wherever a choice is available. Therefore, following W2EEY's lead, the next set of models lengthened the director tails to require a capacitive load for each X-beam category. By increasing the capacitive loading, one can move from best match through maximum front-to-back ratio to the maximum gain level. At the same time, one passes smoothly through the three source impedance ranges. The result is an X-beam that permits adjustment with the turn of a knob.

+

Anderson recommended a constant length difference between driven element and director tails. However, since a variable capacitor is capable of tuning the system to the desired characteristics and since the driven element reactance remains stable across the span of adjustments, we may depart from Anderson's empirically-derived constraint and resonate the capacitively loaded X-beam. Table 5 shows in finer detail the result of returning the driven element to an approximately resonant length while leaving the director long for capacitive tuning. The results are precisely comparable to those for all other models.

+ 
Properties of a Resonant 10-Meter X-beam with a Capacitively Loaded Director
+
+Antenna:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.79'.
+
+Dir Load       Gain           F-B Ratio      Band Width     Source Impedance       Side Lobe      Side Lobe
+ -Xc           (dBi)            (dB)          (degrees)         R ± X              Angle (deg)    Ratio (dB)
+
+Environment 1:  Free Space
+ -15            6.9            6.9             58             13.7 + 8.1            100 (est)      -9.0 (est)n. 1
+ -20            6.8           10.1             60             17.0 + 4.4            101            -9.1
+ -25            6.5           14.4             62             21.1 + 1.5            105            -9.4
+ -30            6.2           21.1             64             26.2 - 0.3            108            -9.4
+ -35            5.9           51.5             66             31.4 - 0.9            112            -9.4      n. 2
+ -40            5.6           22.2             68             35.6 - 0.4            115            -9.2
+ -45            5.3           16.8             68             39.7 + 0.8            118            -9.0
+ -50            5.0           13.9             70             43.1 + 2.3            121            -8.7      n. 3
+
+Environment 2:  20' above average earth, takeoff angle 23 degrees
+ -15           11.8           10.4             62             14.9 + 8.2            101            -9.2      n. 1
+ -20           11.8           16.3             66             19.1 + 5.1            105            -9.4
+ -25           11.5           33.0             68             23.9 + 3.5            109            -9.4      n. 2
+ -30           11.3           21.2             70             28.9 + 3.4            114            -9.2
+ -35           11.0           15.2             72             33.3 + 4.5            118            -8.8
+ -40           10.8           12.2             74             37.0 + 6.5            123            -8.4
+ -45           10.5           10.2             74             39.7 + 8.9            127            -8.0       n.3
+
+Environment 3:  35' above average earth, takeoff angle 14 degrees
+ -15           12.2            7.8             60             13.9 + 8.7            100            -9.0      n. 1
+ -20           12.1           11.6             62             17.2 + 5.4            102            -9.2
+ -25           11.8           16.8             64             21.3 + 3.1            106            -9.5
+ -30           11.5           24.3             66             25.5 + 1.8            110            -9.5      n. 2
+ -35           11.2           22.1             68             29.7 + 1.6            113            -9.3
+ -40           10.9           16.9             68             33.4 + 2.2            117            -9.1
+ -45           10.6           13.8             70             36.6 + 3.5            120            -8.8
+ -50           10.5           11.8             72             39.2 + 5.0            124            -8.5      n. 3
+
+Note 1:  maximum gain         Note 2:  maximum front-to-back ratio         Note 3:  best coax match
+
+Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
+dialectric constant = 13, conductivity = 5 milliSiemens/meter).
+
+Table 5.  Properties of a resonant 10-meter X-beam with a capacitively loaded director in free space and at 20
+and 35 feet over medium earth.
+

In fact, the representative azimuth patterns shown in earlier figures are taken from the 35' model of this X-beam. Moreover, rearward side-lobe angles shown in Table 5 apply to all the models within a few degrees and with close matching of their level below the main lobe. Additionally, the X-beam does not lend itself to close stacking or interlacing. W9PNE confirmed my own modeling failures in correspondence: no one he knew had had any luck trying to create a compact multi-band X-beam assembly.

+

Changing Materials and Frequencies: Since not everyone has access to the same materials, I checked the sensitivity of the X-beam in Table 6 to variations in arm diameter and tail thickness. Increasing the arm diameter to 1" and the tail wires to #12, while preserving the dimensions of the antenna in Table 5, produced the results shown in Table 6. Those who are only used to working with linear elements, where fat equals electrically long, may be surprised to find that both the driven element and the director play short. Both require lengthening to match the antenna in Table 5. (Those who have modeled quads with wires and tubing of varying diameters will not find the phenomenon strange at all.) The requisite lengthening--on the order of 0.2' to 0.3' per tail--approaches the point of requiring slightly longer arms to keep the tails from nearly touching. In the end, varying the materials of an X-beam by any significant amount requires either a new model for a blueprint or some empirical experimentation.

+ 
Properties of a 10-Meter X-beam with Thicker Arms and Tails and with a Capacitively Loaded Director
+
+Antenna:  Arms 1.0" dia., 6.92' long, Tails #12, DE = 4.29', Dir = 3.79'.
+
+Environment    Dir Xl         Gain           Take-Off       F-B Ratio      Beam width     Source Impedance
+               (Ohms)         (dBi)          Angle          (dB)           (degrees)      R ± X
+
+Antenna A:  Best 50-Ohm match design
+
+Free Space      -25            5.3           --             15.7           70             39.9 -  2.9
+20', ave. gnd.  -25           10.5           24              9.6           76             39.5 +  5.3
+35', ave. gnd.  -25           10.7           14             13.0           70             36.7 -  0.4
+
+Antenna B:  Maximum front-to-back ratio design
+
+Free Space      -15            5.9           --             33.0           66             31.4 -  4.8
+20', ave. gnd.  - 5           11.6           24             53.0           68             24.0 -  0.4
+35', ave. gnd.  -10           11.5           14             24.2           66             26.5 -  2.3
+
+Antenna C:  Maximum gain design
+
+Free Space      + 5            7.0           --             6.9            58             13.4 -  4.4
+20', ave. gnd.  + 5           11.9           24             10.5           64             14.5 +  4.3
+35', ave. gnd.  + 5           12.3           14              7.7           60             13.6 +  4.8
+
+Performance figures for 20 and 35 foot heights were taken over average ground (also called medium earth:
+dialectric constant = 13, conductivity = 5 milliSiemens/meter).
+
+Table 6.  Properties of a 10-meter X-beam with thicker arms and tails and with a capacitively loaded director in
+free space and at 20 and 35 feet over medium earth.
+

SWR Bandwidth: Developing 2:1 SWR bandwidth curves does help us determine which of the design variations will best serve a specific application. The bandwidth of the X-beam appears to be little better or worse than most antennas. Table 7 charts two models of the X-beam at 35', the first of which is the original Anderson specifications. Referenced either to the center frequency resistive component of the source impedance or to a 50-ohm cable, the Anderson design provides a broad curve within the usual 2:1 SWR limits. The curves are graphed in Fig. 8. Note that as the frequency increases, the design transitions from a "best match" condition to a "max gain" condition, with the "max front-to-back" condition occurring about three-fourths of the way through the 1 MHz spread. Although the gain and front-to-back ratio drop off seriously at the lowest end of the band, performance is quite adequate throughout most of the range. Anderson's empirical findings once more vindicate themselves, especially for the individual with limited space who needs a monoband beam for full-band use.

+
+ +
+
+

Fig. 8. 2:1 SWR bandwidth graph for the Anderson 10-meter X-beam in Table 2.

+
+ 
                                        X-Beam Bandwidth Characteristics
+
+Antenna:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.79', Dir = 3.29' @ 35'
+               Design center:  28.5 MHz (original Anderson design)
+
+Frequency
+ (MHz)                        28.00          28.25          28.50          28.75          29.00
+Gain (dBi)                     9.9           10.3           10.9           11.5           12.0
+Front-to-back
+ ratio (dB)                    8.9           11.6           17.1           33.8           13.1
+Beam width
+ degrees                      72             70             68             66             62
+Source Impedance
+ R +/- X                      42.1 - 26.1    39.4 - 21.5    34.3 - 16.1    27.2 - 8.4     19.5 + 3.1
+SWR (50)1                     1.797          1.706          1.710          1.913          2.569
+SWR (Ctr)2                    2.020          1.808          1.594          1.433          1.766
+
+
+Antenna:  Arms 0.5" dia., 6.92' long, Tails #18, DE = 3.99', Dir = 3.79' @ 35'
+               Director load (Xc) = -30; Load = 1.86þ10-10F (186 pF) @ design center:  28.5 MHz
+
+Frequency
+ (MHz)                        28.00          28.25          28.50          28.75          29.00
+Gain (dBi)                    10.3           10.9           11.5           12.1           12.1
+Front-to-back
+ ratio (dB)                   11.6           16.9           24.3           12.0            5.5
+Beam width
+ degrees                      72             68             66             62             58
+Source Impedance
+ R +/- X                      37.0 - 12.9    32.3 - 6.7     25.5 + 1.8     18.4 + 14.0    13.3 + 29.5
+SWR (50)1                     1.524          1.596          1.961          2.959          5.141
+SWR (Ctr)2                    1.744          1.390          1.074          2.030          4.800
+
+1 SWR (50) gives the calculated SWR relative to a 50-Ohm feedline.
+
+2 SWR (Ctr) gives the calculated SWR relative to the approximate center design frequency impedance (25.5
+Ohms).
+
+Table 7.  Frequency-related properties of the original Anderson design and of an X-beam optimized at 28.5 MHz
+for maximum front-to-back ratio.
+

Using the capacitively loaded antenna at 35' of Table 5, I converted the load reactance at 28.5 MHz into a capacitance for insertion into the model as a LaPlace figure. The results of a selective frequency sweep appear in Table 7 and are graphed in Fig. 9. Again, the lower line references the SWR to the center frequency, while the upper line references it to 50 ohms. The figures suggest that the 2:1 SWR bandwidth exceeds 750 kHz on 10 meters. However, most of the bandspread lies below the design center. Therefore, when planning an antenna for a specific bandspread, the designer should center the model about two-thirds to three-fourths the way up the spectrum. Like the Anderson design, this X-beam changes its characteristics from a "best match design" through a "max F-B" design to a "max gain" design. If a particular characteristic is especially needed at a specific frequency, one must design for that frequency and live with the results at other frequencies.

+
+ +
+
+

Fig. 9. 2:1 SWR bandwidth graph for the director-loaded 10-meter X-beam in Table 5.

+
+
+ Building an X-Beam +
+

Because a folded X-beam for 10 meters is under 10 feet on a side, garage construction is easy. A 10-pound package is easy to achieve, which means that a simple mast will hold the antenna, and antenna raising is a simple matter. At the risk of repeating some of what Brice Anderson has said about building an X-beam, let's look at some possibilities.

+

Basic Structure: For a number of reasons relating to the bandwidth of the antenna, "permanent" X-beam installations should consider using Anderson's original recommendations for dimensions. Although the rear lobe of the antenna will be wide and gain will not be maximum, matching the antenna to a 50-ohm cable and transmitter is vastly simplified. In fact, a simple sleeve balun (such as the W2DU model or those available through Radio Works) may be the only device between the coaxial feedline and the antenna terminals or connector.

+

Refer to Fig. 10 for some construction details. Although this figure shows elements relevant only to a hilltopper version of the X-beam, it also reveals the basic construction technique for all X-beams. For 10 meters, a plywood plate 18 inches on a side supports the X members. Scrap plywood 3/8 to 1/2 inch thick will easily bear the antenna load. My technique for attaching the antenna to the mast is to cut a circular hole in the plywood at the exact center to admit an 18-inch length of 1-inch nominal diameter Schedule 40 PVC. Two 2-inch L-brackets support the plate. Stainless steel bolts (#10 x 2") run through the pipe to clamp the L-brackets, while 1-inch #10 bolts hold the plate. This method has proven superior to butting the pipe against the plate in terms of getting a true 90-degree angle.

+
+ +
+
+

Fig. 10. Construction details of a collapsible hilltopper X-beam with beta match and remote director tuning.

+
+

Drill the plywood for the X-members, using 2-inch #10 bolts for the fasteners closest to the mast stub and 1 1/2-inch #10 bolts about a half inch from the plate corners. (All hardware is stainless steel, now more readily available in hardware stores.) I used a drill press to drill the tubing, keeping the two holes per piece aligned by dropping a long nail through the first hole and matching it to a reference vertical. The only other holes needed are at the X-member far ends, about 1/4-inch in for attaching the perimeter line and the tails.

+

Disassemble the basic X and weather treat the plywood. Spar varnish has been a standard, but scrap plywood often admits moisture through gaps in the edge. A more weather-proof alternative is to fiberglass epoxy the board, using epoxy-soaked glass cloth strips to cover the edges. A simple boat repair kit will serve several beams. Before coating the board, enlarge all holes slightly. Then heavily coat their edges. When everything is set, use the correct drill bit to reestablish bolt holes and some sandpaper to refit the mast stub. An orbital sander (or heavier) with course paper will make quick work of smoothing and leveling the surface. The result is weather-proof nearly forever.

+

When the hub and X members are reassembled, run a perimeter line of 1/8-inch nylon rope or cord, using the end bolts as attachment points. Solder ring connectors on the tails and place them on the end bolts with an additional nut. Add very short leads (with ring connectors) to a coax connector and attach the ring connectors to the underside bolt extensions for the driven element, using additional #10 nuts. Add a shorting bar across the bolt extensions of the director.

+

My model bolts the mast stub inside a 3-foot length of 1 1/4-inch PVC, which then slips over the main mast. A pair of heavy sheet metal screws locks the larger diameter stub to the mast. Alternatively, the larger diameter stub can be cut to match the length of the inner stub and the pair locked in a rotator.

+

Although the result is light, it is mechanically sound. My test beams have survived winds in excess of 45 miles per hour without damage. The perimeter line dampens vibrations and reduces metal fatigue. Rain cannot reach the coax connections on the underside of the plate. The end result is simple and long-lived.

+

Adjustment: Since the lowest obtainable SWR does not coincide with the antenna's best performance, careful adjustment is required. Adjusting the tail lengths of the director will affect the resistive component of the driven element impedance, while changing the tail length of the driven element will alter its reactive component. If the center frequency is to be in the lower portion of the 10-meter phone band, alter the tail lengths so that the lowest SWR (whatever its value) is just about at the 28.0 MHz point. Then alter the driven element tail lengths to reduce the SWR at the center frequency further by bringing the driven element to resonance. Since initial adjustments may require lengthening elements, do not install ring connectors until the tail length is set.

+

A Hilltopper Version of the X-Beam: The ability to capacitively load the director for optimum performance suggested that the folded X-Beam would make a compact collapsible antenna for portable hilltop operations. Fig. 11 shows the theoretic coincidence of five patterns across the first MHz of 10-meters with the antenna director adjusted in each case for maximum front-to-back ratio at a 20-foot height level over medium ground, the average conditions for my portable operations.

+
+ +
+
+

Fig. 11. Azimuth patterns of the hilltopper X-beam at 20' from 28.0 to 29.0 MHz.

+
+

Since local hardware stores carried only 3/4-inch, 0.050-inch wall thickness aluminum tubing, I remodeled the antenna for this material. With 6' 11" arms, the director and driven element tails became functions of the tuning and matching system. Since a beta match requires driven element shortening, its tails worked out to be 3' 11" long to provide a requisite 25 ohms of capacitive reactance. The director element had to be lengthened so that the tuning capacitor could electrically shorten it; 4' 1" tails provided for this factor. (Note: despite that fact that the physical length of the driven element is shorter than the parasitic element, the electrical lengths are reverse and the beam remains a driven element-director arrangement.)

+

Beta matches are easily calculated from information in the ARRL Antenna Book.(9) I set 25 ohms as the desired feedpoint impedance, since this is close to optimum for maximum front-to-back performance from the antenna. A beta match was then calculated for a 2:1 reduction in impedance. Coil construction utilizes data from recent editions of the ARRL Handbook(10). The coil required a 50 ohm inductive reactance, which works out to about 0.28 uH, or 6 turns spaced over 3/4 inch with a 1/2 inch diameter, using #12 wire.

+

Antenna construction is identical to that described for the "permanent" model, with only a few changes to accommodate collapsing the antenna and adding the tuning and matching elements. First, the beta-match coil has ring connectors on its very short leads and connects across the driven element inner bolt extensions. Second, a half wavelength (adjusted for velocity factor, about 16') of 450-ohm ladder line attaches to the director bolt extensions in place of the shorting bar. At the other end of line, which is within easy operator reach, are two pin jacks. The tuning capacitor has pin terminals to mate with the jacks. The line is spaced from the mast by plastic spray can tops with four punched holes. Cable ties hold the tops to the mast every few feet, and smaller cable ties hold the line to the tops.

+

Every use of the antenna sacrifices a few cable ties during disassembly. However, the process of putting up and taking down the remote tuning system is quick. The capacitor goes into a protective box when not in use, and the line (with caps attached) rolls up semi-neatly.

+

The bolts marked "P" on Fig. 10 are pivot bolts; they are loosened for antenna transport and storage. The others are removed to free the arms to pivot and then replaced in their plate holes for storage. The perimeter line is looped over the arm point marked "L" and removed when the antenna is not in use. The entire assembly is then pivoted so that all arms point the same way. Use care not to distort the beta match inductor. Fold the tail lines neatly along the lengths of the nestled arms. The resulting compact mass fits in my hatchback, with a tape-wrapped bundle of four 5-foot sections of TV mast and a small box for the capacitor and line. Guy rope (and tent pegs for use when no trees are handy) completes the collection of antenna materials.

+

Adjustment: Using the antenna is simply a matter of putting it up and tuning the remote director capacitor for minimum SWR. More accurately, SWR minimum is optimum at the design center frequency only. Below center frequency, use slightly less capacitance than for absolute minimum SWR (within the usual 2:1 transmitter limits) and above center frequency, use slightly more. These guidelines are a function of the complex resistance-reactance combinations that occur off center frequency and the desire to hold the antenna at the maximum front-to-back ratio point.

+

Initial adjustment is similar to the procedure used for the permanent model. Tune the capacitor for the lowest SWR at the center frequency and then trim the driven element tails for a further drop.

+

Variations in materials can create significant differences from modeling figures. For example, the hilltopper model used plastic covered speaker wire as a convenience in cutting identical tails. However, this material yielded tails that were electrically long for both elements. (Only a very small part of this excess can be attributed to the modeling limitations of MININEC, since the segment lengths at the apex are very short when properly tapered.) I anticipated a need for a capacitor covering a range of 10 to 45 ohms capacitive reactance (about 125 to 570 pF) to tune the range from 28 to 29 MHz. With the wire used, a 100 pF variable capacitor covered the resultant 80 to 220 ohm range (25 to 70 pF).

+

The tails also required 6 inches of pruning each to place the SWR curve well within the desired band. However, the result was a curve that went below 1.15:1 at 28.300 MHz and rose to 1.5:1 at 28 MHz and to 1.9:1 at 29 MHz. Local point-to-point contacts verify the pattern as generally in accord with the shape shown in Fig. 11. Performance is detectably better than with a reference dipole placed on the same mast, with the reasonably sharp null to the rear being more pronounced than the forward gain.

+
+ Overall Evaluation +
+

This goals of this edxercise have been, first, to model the X-beam in order to understand its performance characteristics, and, second, to build test models to cross check theory and to enjoy some contacts. The effort does not aim either to praise or to bury the X-beam. The X-beam is a parasitic 2-element beam, but not a 2-element Yagi in either appearance or performance. However, for those with restricted budgets and space, it may provide significant improvements in performance over a dipole or other simple antenna. The X-beam lends itself to home construction, since hardware store aluminum tubing and fastenings combine with scrap wire and a few other parts to make a sturdy antenna.

+

One ingredient in making the decision to build an X-beam should be the pattern of usual QRM that one finds exasperating. If that QRM comes directly off the rear of a dipole, then a "max F-B" X-beam set-up may be quite helpful. However, if the QRM angles in off the rear (for example, QRM in St. Louis from New England and Florida when the beam points due west), then it may be wise to hold out for a small Yagi. Otherwise, the operator can expect similar results from the two designs.

+

The Yagi has long been the standard against which we compare beams. In that comparison, the X-beam has some deficiencies. First, X-beam gain only approaches the 2-element Yagi as the pattern deteriorates. Moreover, the X-beam has rearward lobes that are not eliminable and that are only about 1.5 S-units down from the main lobe.

+

However, the Yagi standard rests upon some operating assumptions that may not hold true for all hams. The standard presumes a desire to work one station in a favored direction, with all other signals reduced, if not eliminated. Hence, maximum forward gain and front-to-back ratio are assumed to be desirable in all cases. Of course, 5 to 7 element Yagis approach this standard well. Some amateur radio operations may not benefit from this standard. For example, local and even wide area nets may suffer from an inability to hear stations in "off" directions. Casual band sweeping in search of a rag chew may benefit from a less directive antenna while still profiting from a little gain and front-to-back ratio. In short, an antenna must be judged by reference to an application as well as to certain performance specifications.

+

The X-beam is flat and compact. As a cheap ($25 to $35 dollars, depending on local hardware store prices), easily built antenna that fits on a mast (instead of a tower) with a TV rotator (or simply an "Armstrong" rotator), the antenna lends itself to some home applications. Its turn radius is a little less than that of a rotatable dipole. But, for me, it comes into its own as a collasible, tunable hilltopper.

+

In sum, the X-beam is not a magic antenna, but neither should it be automatically discarded from the list of potentially useful ham antennas. Instead, it is an antenna with both possibilities and limitations. If its possibilities fit a particular set of needs and its limitations do not hinder operation more than those of other antennas, then it could be the right choice for some hams.

+

However, it is only one of several small beams that one might choose to build. Before putting an X-beam in the attic, you may want to compare it with another interesting beam that uses a closed geometry: the modified Moxon rectangle. We shall look at this unjustly neglected mini-beam next time.

+
+ Notes +

+
+

1. This beam is quite obviously a minor variation of the Yagi presented by Bill Orr, W6SAI, in CQ (December, 1990, pp. 83-84). For modeling purposes, the driven element has been lengthened to resonance.

+

2. Brice Anderson, W9PNE, "Designing X-Beams," Antenna Compendium, Vol. 1 (Newington: A.R.R.L., 1985), pp. 64-66.

+

3. For some words of praise, see Michael Harris, KM4UL, "Ten for 10," 73 (April, 1991), pp. 52-56. This builder concludes that he is "confident that you'll find this to be a compact, high performance beam which is easy to build and won't lighten your pocket book. Enjoy it!" For a contrasting viewpoint, see the remark by Brian Beezley that he built into the X-Beam antenna description in AO 5.0: "By no means does this antenna live up to the claims made for it, which include performance comparable to that of a 3-element Yagi!" It is not clear whether Beezley based his conclusion on the analysis of this one model.

+

4. ELNEC, an enhanced version of MININEC, is available from Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007.

+

5. AO 6.0 is also an enhancement of MININEC (with an additional antenna optimizing feature) available (until recently) from Brian Beezley, K6STI.

+

6. Incidentally, it is this configuration--and not the Anderson configuration--against which Moxon recommends in his study of small antennas. Indeed, Moxon might appreciate the folded model of the X, given the many folds in some of his recommended antennas, such as the VK2ABQ square, an interesting antenna in its own right. See L. A. Moxon, HF Antennas for All Locations (R.S.G.B., 1982), pp. 81-83 and 172-175. However, he might object to the quartering rear lobes of the X-beam.

+

7. For those wishing to scale the X-beam to other bands, Anderson provides the following formulas. Arm length (ft) = 195/f (MHz); Total driven element length (ft) = 603/f (MHz); Driven element tail (ft) = 106.5/f (MHz); Total director element (ft) 575/f (MHz); and Director tail (ft) = 92.5/f (MHz). (Anderson, p. 64) Although the choice of materials--tubing diameter for the arms and wire size for the tails--will alter the required dimensions, #18 wire and tubing with a length-to-diameter of about 200:1 will make these dimensions a good starting point for modeling.

+

8. W2EEY, "The X Beam on 20," in Antenna Roundup, Tom Kneitel, K2AES, ed. (Port Washington: Cowan Publishing Corp., 1966), pp. 60-62; originally published in CQ (June, 1965). Incidentally, W2EEY's X-beam has different proportions than Anderson's design. Modeled without the all-metal support spider, from which the arms are insulated by plastic hose, the beam shows a free space gain of 6.0 dBi and a front-to-back ratio of about 26 dB in a "max F-B" model. The input impedance is low and capacitively reactive: not a good direct match to 50-ohm coax. Moreover, the director required considerable inductive loading, not the capacitive loading specified by the author. The differences between the model and the actual antenna are likely due to W2EEY's construction method.

+

9. Beta matching is described in detail in the 16th edition of The ARRL Antenna Book (Newington, 1992), pp. 26-21 to 26-23.

+

10. The ARRL Handbook (Newington, 1992), p. 2-18.

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+ +
+

Return to Article Index Page

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Topics: HF Upper, Small Beams, X Beam


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+

Modeling and Understanding Small Beams

+

Part 2: VK2ABQ Squares and The Modified Moxon Rectangle

+

L. B. Cebik, W4RNL

+
+
+ +
+

Miniature directive antennas appeal to hams with little space. Commercially, the Butternut HF5B has enjoyed good success. However, its price tag has led numerous hams to look for home brew antennas. The folded X-Beam, examined in Part 1 of this series, was brought to ham attention by W2EEY as a simplified birdcage and empirically perfected by W9PNE. It has some proponents as well as a few critics. In the U.S., little else seems available to the home brewer.

+

The VKs and Gs, however, have long been familiar with a square antenna about the same size as the folded-X. The basic idea for the antenna is simple: take a single quad loop and tip it 90 degrees to put the wire in the horizontal plane. At the midpoints of the sides (calling the feedpoint wire the front and the parallel wire to it the rear), cut the loop and insulate the cut ends from each other while preserving the loop. It is reported that VK2ABQ, the antenna's sire, used coat buttons for insulators. The antenna now looks like a 2-element parasitic beam with a driven element and a reflector. It provides gain and front-to-back differential. Folding the ends inward, relative to a Yagi in normal linear configuration improves the front-to-back ratio at the loss of some theoretically possible forward gain. Moreover, loops for several bands (typically, 10, 15, and 20) can be laid out concentrically and fed from a single coaxial cable. Fig. 1 shows the general layout.

+
+ +
+
+ Fig.1. General outline of a VK2ABQ "square" beam. +
+

There is an older history to the square, which you can read in Everything Old Is New Again.

+

One problem the potential square-builder faces in trying to replicate the VK2ABQ antenna is finding the right dimensions. The problem is not a lack of dimensions, but too many sets. Table 1 and its notes list several sets taken from a couple of British sources.(1) Apparently, the antenna is somewhat sensitive both to the wires for the bands not in operation and to the method of construction. Different builders have used different amounts of metal in the hub and support spokes, leaving the new builder to play endlessly with wire lengths with not much clue as to what the goal should be. Although I have only scanned the literature, it appears that American builders have largely ignored the design. In fact, no one seems to have modeled the antenna to find out what it can theoretically do for amateur operation.

+ 
                      A Sampling of Recommended Dimensions for the VK2ABQ "Square" Beam
+
+Source*       Moxon, p. 168; Hawker p. 334                       Hawker, pp. 315-316
+
+Arm length                    6' 2"                        6'  0"        5' 9"         5' 11"
+
+Perimeter length             34' 9"                       33' 11"       32' 6"        33'  5"
+
+Side length                   8' 9"                        8'  6"        8' 2"         8'  4"
+
+Formula/side                 248/f (MHz)                  242/f (MHz)   232/f (MHz)   238/f (MHz)
+
+*See Note 1 at end of text for references cited here.  All dimension in feet and nearest inches:
+
+Table 1.  A sampling of recommended dimensions for the VK2ABQ "square" beam.
+

L. A. Moxon, in his HF Antennas for All Locations, provides the essential clue: "the main benefit [of a beam] accrues from the reduction of interference during reception, though the 4 to 6 dB gain provided by typical amateur beams is an important bonus and probably the reason which carries the most weight with the majority of amateurs."(2) Here is a theory of beam operation quite unAmerican is style: instead of gain, Moxon strives for front-to-back ratio as the most crucial aid to ham operation. His statement is an affirmation of the "good ears" theory of operation. Even more, it forms the basis for his rectangular improvement upon the VK2ABQ square.

+

Moxon's revelation of the operative notions behind his compact beam-building efforts provided the clue that made possible a venture into modeling these beams with MININEC. The goals were to ascertain their general performance capabilities and to find patterns of development toward optimum performance. By judiciously loading the reflector, one can fairly quickly find the maximum front-to-back ratio. Then, by adjusting dimensions, the modeler can create a pure loop, that is, one with little or no reactance at the driven element source and with little or no requirement for reflector loading.

+

Finally, there was the task of discovering whether the model dimensions play out in practice. For this exercise, I chose a single band antenna, a 10-meter version of an optimized Moxon rectangle to be precise. Construction minimized metal throughout. The results brought together several interrelated questions. First, given the complex geometry of this antenna, would MININEC reliably model reality? Second, was the antenna too sensitive to any metal in its plane to reflect its idealized MININEC model? Third, would the antenna live up to its theoretical promise? Finally, where does the VK2ABQ/Moxon antenna fit in the world of miniature or small or simple antennas?

+

This report tries to provide some tentative answers to a few of these questions by taking a systematic look at this "fallen-quad" beam. We shall examine a progression of models that begins with the VK2ABQ and ends up with an optimized Moxon rectangle. Then we shall look at the construction and performance of a real model. The report has some limitations, however. First, it does not model multiband versions of the antenna. Second, the use of metallic masts and hub spiders has not been explored. Nonetheless, the results are both promising and useful. They provide an understanding of the VK2ABQ/Moxon beam potential, and they form a basis for constructing some interesting real antennas for both limited space and portable operation.

+
+ The VK2ABQ Square +
+

Moxon's search for a little gain and a lot of front-to-back ratio excludes the folded X-Beam from consideration here. Fig. 2 shows why. Although the front-to-back ratio of an X-Beam can be very considerable in the narrow path directly opposing maximum gain, there are quartering rear sidelobes that never decrease far below about 10 dB less than maximum gain. On 10 meters in the U.S., such a pattern, which can yield a forward gain slightly higher than either of the designs we shall explore here, may satisfy the ham with limited space. Elsewhere in the world--on 20 and 15 especially--those rearward lobes would increase QRM levels excessively. One can sacrifice gain if the overall front-to-rear-area ratio can be improved. Precisely here lies the inspiration behind Fred Caton's invention, the VK2ABQ square.

+
+ +
+
+ Fig. 2. Free space azimuth pattern of a folded X-Beam per Anderson. +
+

Using the original design, optimized for least reflector loading and least reactance at the feedpoint, but retaining the close-spaced element ends, early models achieved respectable performance. Fig. 3 shows the performance of an optimized model, while Table 2 supplies the dimensions and analysis figures of the models that led up to this performance. For those unused to trying to capture an antenna with a model, the process may prove instructive.

+
+ +
+
+ Fig. 3. Free space azimuth pattern of VK2ABQ model #6 (Table 1). +
+ 
                       A Sampling from the Series of VK2ABQ "Square" Antennas Modeled
+
+Antenna              Dimensions (feet)            Reflector      Gain   Front-to-Back         Source Z
+              X      Y       Space  El. Length    Load (±X)      (dBi)       (dB)              (R ± X)
+
+ 1.           8.8    8.8     0.2    17.4             0            4.2        16.3             133 + 23
+
+ 2.           9.0    8.8     0.8    17.0           +45            4.5        22.4             103 - 14
+
+ 3.           9.1    8.8     1.0    16.9           +60            4.3        22.2              94 - 28
+
+ 4.           9.2    8.8     1.2    16.8           +60            4.6        30.6              94 - 19
+
+ 5.           9.4    8.8     1.4    16.8           +60            4.7        34.2              88 - 24
+
+ 6.           9.8    8.8     1.6    17.0           +47            4.7        26.6              88 - 8.0
+
+Note:  All performance values are calculated free space figures.
+
+Table 2.  A sampling from the series of VK2ABQ "square" antennas modeled.
+

Beginning with a model only slightly smaller than the largest encountered in British sources, I modeled antenna 1. Since all sources on the VK2ABQ recommended extremely close spacing of the driven element and reflector ends, I held this spacing at 0.2' or less. The resulting inductive reactance at the feedpoint showed that driven element was long. Moreover, the front-to-back ratio, while slightly better than a typical 2-element Yagi, was not up to expectations.

+

Tackling the second problem first, I began to increase the spacing between element ends. This move shortened the element lengths, since I held the front-to-back (Y) dimension constant. The front-to-back ratio began to improve dramatically, as models 2, 3, and 4 demonstrate. However, to achieve this calculated performance, it was necessary to insert an inductive load into the center of the reflector element, suggesting that the reflector was short for optimum performance. Note that in all models of the VK2ABQ, the elements are the same length, a design that is counterintuitive for someone familiar with Yagi configurations.

+

Model 5 achieves the best front-to-back performance, but at the cost of considerable inductive reactance at the feedpoint and the need for sizable reflector loading. Model 6 lengthened the element to bring down the feedpoint reactance successfully. However, it widens the gap between element ends beyond optimum and still requires reflector loading.

+

Modeling ceased at this point because of several factors. First, the forward gain of the beam was not improving significantly. The best VK2ABQ, while providing exceptional front-to-back ratio, produced a forward gain only bit higher than that of a single quad loop mounted in the normal plane. Second, the model was departing from square to a degree that made the Moxon rectangle the next logical step in the work.

+

However, before departing the VK2ABQ, we should notice the general pattern in Fig. 3 once more. Unlike the X-Beam (Fig. 2), the VK2ABQ puts all its power in the forward lobe, with a beam width that settles in around 88 to 90 degrees between -3 dB points. The main lobe extends around to the sides so that direct side rejection is only half the front-to-back ratio. In comparison, the X-Beam has good front-to-side ratio (at the expense of the rearward lobes), and the dipole, single quad loop, and 2-element Yagi antennas have excellent front-to-side ratios. None of these antennas, however, can even approximate the VK2ABQ for the clean and empty wide rear quadrants. This feature may be useful in more than one application.

+
+ The Moxon Rectangle +
+

To achieve better performance, Moxon lengthened the front and rear elements and shortened the side tails. The resulting rectangle requires very little more turning radius than the square, but improves the gain of the antenna considerably. Modeling Moxon's beam required some initial guesses at the actual 10-meter dimensions, since the builder created u-shaped insets at the corners to handle excess wire needed to make up the perimeter.(3) Nonetheless, only two steps yielded a pretty good Moxon beam model. Fig. 4 shows the general outline of the Moxon rectangle, while Table 3 shows the progression of models and their results.

+
+ +
+
+ Fig. 4. General outline of a Moxon "rectangle" beam. +
+ 
                     A Sampling from the Series of Moxon "Rectangular" Antennas Modeled
+
+Antenna              Dimensions (feet)            Reflector      Gain   Front-to-Back         Source Z
+              X      Y       Space  El. Length    Load (±X)      (dBi)       (dB)              (R ± X)
+
+ 1.           11.2   6.6     0.2    17.6           -20            5.3        22.5             115 + 86
+
+ 2.           11.0   6.6     0.2    17.4           - 5            5.2        21.3             114 + 69
+
+ 3.*          10.4   6.6     0.2    16.6 DE        +30            5.3        18.7             103 + 5.1
+                                    17.0 Re
+
+ 4.           11.0   6.6     0.8    16.6 DE        +35            5.5        37.0              80 - 3.6
+                                    17.0 Re
+
+ 5.           11.0   6.7     0.8    16.6 DE        +20            5.5        35.0              81 - 4.2
+                                    17.0 Re
+
+ 6.           11.2   6.6     0.8    16.6 DE        + 5            5.5        33.6              79 - 2.7
+                                    17.4 Re
+
+*Models from this point onward use unequal lengths for the driven element and the reflector.
+
+Note:  All performance values are calculated free space figures.
+
+Table 3.  A sampling from the series of Moxon "rectangular" antennas modeled.
+

The initial models preserved the VK2ABQ close end spacing (although Moxon widened the gap). Model 2 is especially interesting, since it shows excessive driven element length in the inductively reactive source impedance. The reflector is about right for this configuration. However, the front-to-back ratio is not up to VK2ABQ standards. The next moves were a simultaneous increase of the gap between ends and an unbalancing of the forward and rear elements. Moxon prefers matched elements, tuning each of them to optimum performance remotely. That way, he can reverse the beam and do away with expensive and maintenance-intensive rotators. However, rotators are a way of life in the U.S. (a TV rotator will likely handle a 3-band Moxon beam), and there are many uses for portable beams that are hand-rotated or fixed in the field. Thus, I decided to continue the exercise in unequal element lengths.

+

In models 3, 4, and 5, we can see the approach to a model that would have a roughly resonant feedpoint and require no loading of the reflector. The last model, number 6, is considered optimum for these reasons. Fig. 5 provides a free space azimuth pattern for comparison to other antennas. The modified Moxon rectangle is a close match to RG-11 or RG-59 coax for direct feed. The differentials of front-to-back ratio in models 4, 5, and 6 make little difference in practice, and the forward gains of the three models are the same.

+
+ +
+
+ Fig. 5. Free space azimuth pattern of Moxon rectangle #6 (Table 3). +
+ 
              A Performance Comparison Among the VK2ABQ, the Moxon, and Some Reference Antennas
+
+              Antenna                      Conditions     Refl. Load    Gain   Front-to-Back          Source-Z
+                                                          (±X ohms)     (dBi)       (dB)             (R ± X)
+
+VK2ABQ #6 (Table 2)                        Free Space      +47           4.7          26.6           88 -  8
+                                           35' Ave Gnd*    +47          10.3          30.8           98 - 13
+
+Moxon #6 (Table 3)                         Free Space      + 5           5.5          33.6           80 -  3
+                                                             0           5.6          24.1           76 +  1
+                                           20' Ave Gnd     - 5          11.1          20.4           81 -  6
+                                                             0          11.0          18.9           85 - 10
+                                           35' Ave Gnd     + 5          11.0          25.5           88 -  3
+                                                             0          11.1          21.9           83 +  1
+
+2-element Yagi (DE + Refl.)                Free Space      --            6.3          11.2           32 +  1
+(16.0'/17.5'/4.25' space)                  35' Ave Gnd     --           11.7          13.5           35 ±  0
+
+Single loop quad, #18 copper wire          Free Space      --            3.2          --             127 + 4
+(L=1040/f(MHz) or 9.12' per side)          35' Ave Gnd     --            8.5          --             125 - 6
+
+Wire dipole, #18 copper wire               Free Space      --            2.1          --              72 ± 0
+(L= 468/f(MHz) or 16.42'                   35' Ave Gnd     --            7.7          --              86 - 8
+
+*Average ground or earth:  dielectric constant = 13, conductivity 5 mS/m
+
+Note:  Compare free space figures only to other free space figures and over-ground figures only to other over-
+       ground figures.
+
+Table 4.  A performance comparison among the VK2ABQ, the Moxon, and some reference antennas.
+

Free space is not a fully adequate indicator of these quasi-loop beams over real ground. The potential for needing reflector loading was too great simply to build the free space model and hope it would work. Table 4 presents some comparative figures. Without any reflector load at all, the Moxon 6 model promised adequate performance at both 20 feet (a typical portable height) and 35 feet (a typical home-installation height) above medium earth. The 20' Moxon exhibits a small wide swell in rear coverage (Fig. 6), while the 35' Moxon demonstrates a more stepped appearance (Fig. 7). Both front-to-back ratios are reasonable for the heights, although neither reaches the level of the tiny free space rear lobes.

+
+ +
+
+ Fig. 6. Azimuth pattern of Moxon rectangle #6 20' above average earth. +
+
+ +
+
+ Fig. 7. Azimuth pattern of Moxon rectangle #6 35' above average earth. +
+
+ +
+
+ Fig. 8. Free space azimuth pattern of a reference 2-element Yagi. +
+

The Moxon beam shows a gain midway between the VK2ABQ and the typical 2-element Yagi. Fig. 8 provides a free space azimuth pattern for a typical 2-element Yagi as a reference standard against which to compare the Moxon rectangle. Why the Moxon rectangle's gain is less than that of a linear 2-element Yagi, despite the absence of power in the rear lobe, may raise some questions. However, such questions reveal 2-dimensional thinking. Antennas are three dimensional devices. Besides forward and back, power may radiate up and down and anywhere between. Both the VK2ABQ and the Moxon rectangle radiate considerably more power to the sides and at high radiation angles relative to the horizontal than 2-element Yagis. Fig. 9 demonstrates the difference in free space high angle radiation between the VK2ABQ and the Yagi, while a comparison of Fig. 3 and Fig. 8 reveals the 18-degree beamwidth difference. Although these properties hold down forward gain, they may prove useful in other applications.

+
+ +
+
+ Fig. 9. Free space elevation patterns of the Yagi in Fig. 8 and the VK2ABQ square in Fig. 3. +
+

Of concern to every small beam builder are bandwidth considerations for both the pattern and the feedpoint impedance. Fig. 10 and 11 display the pattern bandwidth in sets of azimuth patterns taken at five points between 28 and 29 MHz. At 28 MHz and a 20-foot height, the front-to-back ratio of the rectangle drops to about 11 dB. At 29 MHz, the figure is also about 11 dB. These figures approximate a 2-element Yagi, but the Moxon exceeds the Yagi between 28.25 and 28.75. A similar pattern of reduced front-to-back ratio at band edges appears with the antenna at 35 feet, but the effect is smaller. Except for the lowest edge of the 10-meter band, the front-to-back ratio remains above 15 dB and above 25 dB at design center. At both heights, the forward gain, while less than that of a 2-element Yagi, remains fairly constant across the band.

+
+ +
+
+ Fig. 10. Pattern bandwidth of the Moxon rectangle at 20' using composite azimuth patterns at a 24-degree take-off angle. +
+
+ +
+
+ Fig. 11. Pattern bandwidth of the Moxon rectangle at 35' using composite azimuth patterns at a 24-degree take-off angle. +
+

With respect to feedpoint impedance, the Moxon rectangle is well-behaved across the entire first MHz of 10 meters. Since the design center frequency impedance is about 80 ohms at all heights, 75-ohm coax provides the best match, as shown in Fig. 12 and 13. However, the SWR relative to a 50-ohm transmitter output and cable never exceeds 2:1 from 28 to 29 MHz, thus simplifying matching requirements. As the test model verified, these anticipated values are close to reality, despite the limitation of MININEC in calculating impedance and SWR for perfect grounds only.

+
+ +
+
+ Fig. 12. SWR bandwidth of the Moxon rectangle at 20' for 50 and 75 ohm cables. +
+
+ +
+
+ Fig. 13. SWR bandwidth of the Moxon rectangle at 35' for 50 and 75 ohm cables. +
+

The Moxon rectangle's 3 dB gain over a dipole at the same elevation is useful, but the most significant Moxon feature is the reduction in all rear directions of potential QRM. At 6 dB per S-unit, the Moxon beam promises (at least, in model form) to reduce QRM by more than a full S-unit and perhaps as much as 2 S-units compared to a 2-element Yagi. Whether the beam could deliver on its model's promise required an exercise in building.

+
+ Building a Moxon Rectangle +
+

Since the diversity of VK2ABQ dimensions in the literature suggests a sensitivity to the conductivity of the antenna structure, the portable Moxon beam requires a minimum of metal to test the model dimensions. Therefore, the beam I built was an exercise in plywood, PVC, and nylon cord. See Fig. 14. A center platform of well-varnished or fiber-glassed 3/8" plywood measured 22.4" by 13.2". These dimensions assured that the rectangular X-frame would have the proper angles. A pair of #10 1 1/2" stainless steel bolts (with washers and nuts) secures each of the four half-inch nominal thin-wall PVC arms. In place of the bolts nearest the corners of the platform, one may use 1/2" nominal PVC conduit clamps with #8 stainless steel hardware. Fifth and sixth arms project from the platform to the center of the driven element to support the feedline and to the center of the reflector element.

+
+ +
+
+ Fig. 14. Construction sketch of the 10-meter test Moxon rectangle. +
+

The platform has a center hole to pass a 3-foot length of 1" nominal schedule 40 PVC pipe. Two 2" corner brackets secure the platform to the pipe 18" down from the top. The brackets use bolts that pass through a bracket, the pipe, and the opposing bracket. Short #10 stainless steel hardware secures the brackets to the platform. Note that the brackets are above the platform, since it will rest on the 1 1/4" nominal PVC mast pipe, with a pair of bolts through the nested pipes to lock them together.

+

At the upper end of the platform pipe, an X-cut--enlarged and smoothed--provides a channel for eighth-inch nylon support cord. The cord ends pass through holes in opposing arms about 2/3rds the way out to the corner. Several wrappings of the cord before knotting reduce stress on this light guy. Fig. 15 provides guidance for setting up the support guys.

+
+ +
+
+ Fig. 15. Sketch of the support guy system used with the test Moxon rectangle. +
+

Each arm is 6'6" long. Mounted on the plate about 1" from the center point (to allow room for the pipe hole), the arms extend about an inch beyond the precise corner points. Quarter-inch holes through the arm in the plane of the wire permit the insertion of plastic tubing to reduce stress on the element wires that pass through them.

+

Measure each element with some excess. Thread each element through the plastic corner tubes. To the ends of each element, attach about a foot of nylon cord to tie the element ends together and maintain spacing between them. Add the guys running across the X-cut in the vertical pipe. The result will be a well-braced Moxon rectangle for use in up to moderate winds.

+

Use part of the driven element's excess wire to provide whatever is needed to attach a simple dipole center insulator and coax fitting. When you are satisfied that the dimensions are correct enough for initial testing, snug up all the tie-off points. Do not solder the element ends wires yet, since some length adjustment may be needed to put the beam on target. (In fact, after completing all length adjustments, remove the cord from the element end. Solder the wrapped wire to secure it and make a loop. After cooling, reinsert the cords and resnug the assembly. This caution is needed, since nylon cord melts well before solder does.) Attach 75-ohm coax to the dipole center insulator, taping it to the extra PVC arm. One can also insert a choke or sleeve balun here to reduce chances of RF traveling down the outside of the coax braid. Alternatively, one can insert a 75-to-50 ohm balun or unun and use 50-ohm coax to the rig.

+

It is not necessary to make any of the initial adjustments and tests with the beam in the air. Lay the beam over a wooden prop so that the reflector is a few feet off the ground and the driven element points to the sky. With a low power signal, adjust the driven element lengths for the lowest SWR at the frequency of choice. Now erect the antenna in the normal plane at least 15 feet high. With a small signal source and a receiver, adjust the reflector for minimum signal off the rear. Try to keep the element ends about 9 to 10 inches apart. The SWR of the driven element should not be adversely affected. However, you may wish to lower the antenna and redo the driven element length one more time to finish the adjustment task. Only the most finicky operator should need to make further adjustments at height.

+

With minimal metallic mass in the mounting, the Moxon rectangle adjusts quite closely to the model dimensions. Although my test set-up does not permit test range figures, the antenna performs to expectations at a height of 20 feet. For signal strength, it does not quite match my 2-element beam at 35 feet, but the front-to-back ratio is much better, despite the height disadvantage. If you feed the antenna with 50-ohm coax cable, expect an SWR that varies from 1.5:1 to 1.9:1 in a rippling fashion across the first MHz of 10-meters. The normal dip in the resonance curve only appears with 75-ohm cable.

+

Point-to-point tests with local operators located 10 to 15 miles from the station confirmed the modeling exercises quite well. Using both received signals and reports of transmitted signals, the front-to-back ratio of the antenna averaged better than 4 S-units on a variety of transceivers, compared to a little over 2 S-units for my HF5B at 35 feet. The front-to-side ratio averaged a between 1 and 2 S-units, but signals fell off rapidly as the beam was rotated past the side point to the rear. These results cannot be translated into the 20-foot azimuth pattern figures (Fig. 6), since that pattern is taken at an elevation angle of greater than 20 degrees and assumes no ground clutter. Moreover, the relationship of S-units on a transceiver meter to dB of front-to-back ratio is too uncertain for quantitative comparison. However, for practical operation, the basic characteristics of the Moxon rectangle appear satisfactorily confirmed. Nonetheless, other construction methods using a greater metal mass in the support structure may require more extensive adjustment.

+

The wood-wire-PVC model of the modified Moxon rectangle has withstood stormy wind gusts of about 45 m.p.h., far above the design goal for the portable antenna. However, in continuous use, the wood platform is bound to age, and the thin nylon rope will fray. For permanent installations, a more robust construction method may be in order. Models of the rectangle using 3/4" aluminum tubing suggest that only the driven element needs adjustment to compensate for the fatter element diameter. Shortening the driven element tails by about 0.2' each, while maintaining the spacing from the ends of the reflector tails, brings the beam's operating characteristics into line with the wire model.

+
+ Some Applications of the Moxon Rectangle +
+

The Moxon rectangle offers the ham with limited space the chance for a compact directional beam. Adding elements concentrically for other bands is possible. Moxon reported interaction between elements 15 and 10 meters and offers some hints on curing the problem. Of course, the multiband builder will have to experiment with element lengths for peak performance, as will the builder who uses more metal to support the arms.

+

If the builder does not make Gordian knots in the nylon guys and stays, the beam should disassemble in 15 minutes for transportation. The broad main lobe of the Moxon rectangle may serve Field Day and other operations well. It rivals W7EL's Field Day Special, but may be erected where there are no trees for end supports.(4) On either coast, a single fixed position would cover most of the U.S., while inland, a TV rotator or an Armstrong assistant will rotate the beam with ease. For many contests and other applications, front-to-back ratio may serve the operation better than raw gain.

+

The antenna offers a further potential. Given the wide beam angle both horizontally and vertically, plus the exceptional front-to-back ratio, the Moxon rectangle provides a very smooth curve in both X and Y planes when pointed straight up. See Fig. 16 and Fig. 17. Off the flat of the reoriented beam, models show almost horizon to horizon coverage with minimal dips in the pattern at a wavelength height. Side-to-side, the coverage is very smooth, although it may require a pair of rectangles, each tipped 30 degrees or more to extend coverage to near the horizon. The patterns exhibit none of the vertical holes of vertical dipoles nor any of the pattern irregularities of simple horizontal antennas. Since satellite operations have reached the point for many birds of not requiring steerable arrays, the Moxon rectangle may be serviceable as a simple fixed antenna. Hybrid construction using aluminum tubes or rods for what are now the horizontal elements, with wire and cord for the ends, may simplify the building process, but preconstruction modeling is recommended to check the effects of larger element diameters.

+
+ +
+
+ Fig. 16. Elevation pattern of a vertically-oriented Moxon rectangle beam (#6) off the flat plane of the antenna. +
+
+ +
+
+ Fig. 17. Elevation pattern of a vertically-oriented Moxon rectangle beam (#6) off the edge plane of the antenna. +
+

Modeling the modified Moxon rectangle at 144.5 MHz with #14 copper wire for the elements produced the following dimensions: a rectangle 2.36' long by 1.32' wide, with a driven element 3.40' total length and a reflector 3.62' total length. These lengths translate into 0.52' end pieces for the driven element and 0.63' end pieces for the reflector, with a 0.17' space separating the end pieces. The 2-meter model showed all the properties of the 10-meter version at 1 wavelength above ground or ground plane. Elevated to several wavelengths above ground and pointed straight up, the patterns develop deep nulls between adjacent nulls lobes that multiply with height. Therefore, VHF and UHF scalings of the rectangle might use an artificial ground plane (a wire screen) below the reflector to tailor the pattern even further.(5) The driven element impedance drops to about 65 ohms due to the larger element diameter relative to the wavelength of the signal. This suggests that tubing models might approach a good match to 50-ohm coax. (A 10-meter model using 0.75 aluminum tubing produced a calculated 72-ohm source impedance, a 9 percent reduction relative to the #14 wire version.)

+
+ Overall Evaluation +
+

In our quest for gain, we may have overlooked the important "good ears" principle of effective amateur operations. The modified Moxon rectangle presented here, as an improvement of the VK2ABQ square, offers exceptional front-to-back ratio with only two elements. Moreover, its pattern offers other potentials usable by field operators and possibly even by satellite operators. The beam lends itself to home construction with components easily accessed from hardware and home improvement outlets. As the "loose ends" in this report suggest, the modified Moxon rectangle offers a fertile field for experimentation with other materials. All in all, it is an antenna worth further study; even more, it is an antenna worth further use.

+

Some of the further experimentation is reported on in the notes at this site. See the Moxon Rectangles and Online Calculator page, where you will find a growing number of items on wire and tubing Moxons for HF and VHF.

+

However, if tubing and wire are more to your building taste than PVC and plywood, there are small beams for you. For example, linear-loaded Yagis can be 25% shorter than full-size Yagis with little loss in performance. But that is for next time.

+
+ Notes +
+

1. See L. A. Moxon, HF Antennas for All Locations (R.S.G.B., 1982), p. 168; see also Pat Hawker, Amateur Radio Techniques (R.S.G.B., 1980), pp.315-316, p. 320, and p. 334. For a summary of work on the VK2ABQ square and the Moxon rectangle, see Erwin David, G4LQI, Ed., HF Antenna Collection (RSGB, 1991), pp. 23-28.

+

2. Moxon, p. 67.

+

3. Moxon, pp. 172-175.

+

4. See Roy Lewallen, W7EL, "Try the 'FD Special' Antenna," QST (June, 1984), pp. 21-24.

+

5. See A.R.R.L. Antenna Book, 16th Ed. (Newington: A.R.R.L., 1991), pp. 19-7-19-9 for ideas in this vein.

+
+ +
+

Return to Article Index Page

+

Topics: HF Upper, Moxon, Small Beams


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+

Modeling and Understanding Small Beams

+

Part 3: The EDZ Family of Antennas

+

L. B. Cebik, W4RNL

+
+
+ +
+

The Extended Double Zepp (EDZ) has been a lonely antenna for most of its life, since Hugo Romander, W2NB, introduced its potential to the amateur community in 1938. Even its vertical cousin, the Extended Single Zepp, seems to have changed its name to the 5/8 wavelength ground plane to avoid identification with the EDZ.1 By contrast, everyone knows about the family of antennas related to the half wavelength dipole: the quarter wavelength ground plane, the 2-, 3-, and more-element Yagis, the ZL-Special. The EDZ also spawns a family of antennas that include parasitic and phase-fed beams. This report tries to fill in some of the family tree without necessarily recommending everything that the computer modeling says is theoretically possible with the EDZ. What looks good on the computer may not work out in backyard practice. However, the ideas we shall consider may spur someone else to realize some of the potential shown by EDZ beams.

+

Here is a sample: A good 2-element dipole-based Yagi shows about 3 1/2 dB gain over a similarly placed wire dipole. To achieve 6 dB gain over that same piece of wire requires 4 to 5 elements. Suppose one could make an 2-element antenna with the same 6 dB gain over the original wire. That fact would qualify the EDZ beam as a small beam in boom length, although not in element length. Both parasitic and "135-degree" phase-fed versions of the EDZ promise the computer to give the indicated performance. However, achieving that performance will impose severe restrictions that mark the antennas for special purposes under narrowly defined circumstances.

+

For this study, all antennas are referenced to 10-meters, with any exceptions clearly noted. Within limits, the results can be scaled, at least within the upper HF region of the spectrum.

+
+ The Basic EDZ +
+

Before turning to the more distant cousins of the EDZ, let's begin at home with the basic horizontal EDZ. It is a wire antenna, about 1 1/4 wavelengths long, fed in the center. It presents a high, complex impedance at the feedpoint, ordinarily necessitating the use of parallel feeders and an antenna tuner. Fig. 1 suggests the basic set-up.

+
+ +
+
+ Fig. 1. The basic structure of a horizontal single-wire EDZ antenna. +
+

The chief advantage of the EDZ over a resonant half wavelength dipole is bidirectional gain. See Fig. 2, which provides patterns for free space half wavelength and EDZ dipoles. Relative to a wire dipole, whether in free space or over real ground, the EDZ provides about 2.9 dB gain over the resonant dipole, with a bandwidth in the main lobe some 45 degrees narrower. For the cost of wire, the EDZ provides some significant advantages.

+
+ +
+
+ Fig. 2. Free space azimuth patterns of a 1/2 wl dipole and a single-wire EDZ antenna. +
+

Some authors have provided formulas for cutting the EDZ. The most common is based on the long wire length formula:

+

L (in feet) = 984 (N - 0.025)/ f (in MHz), where N = number of wavelengths, or

+

L (in feet) = 1205/f (MHz).

+

Beers prefers a constant of 1218, while recent editions of The ARRL Antenna Book call for 0.64 per side, which yields a numerator of 1258.2

+

Most wire models using #12 to #18 show their maximum gain in 10-meter models with a length closer to 1225/f (MHz). However, such number-crunching devices are misleading. They obscure the fact that selecting the length of an EDZ is always a compromise between gain and another factor that dipole builders do not have to confront: side lobes. Fig. 3 overlays three EDZ patterns for wires of different lengths. The pattern with the greatest gain also has large side lobes and a narrow beam width. The other patterns show slightly less gain (less than -0.1 dB), but the shortest model (L= 1180/f (MHz)) also has the least off-axis gain. The cost of smaller sidelobes is a higher capacitive reactance at the feedpoint. In the end, selecting a length for an EDZ may be determined less by absolute gain potential than by the amount of off-axis QRM to be tolerated. Table 1 summarizes the modeled variations of gain and front-to-sidelobe ratio for 10 meter antenna lengths from 41.4' to 44.6' in free space.

+
+ +
+
+ 3. Three free space azimuth patterns for short (41.4'), medium (43.0') and long (44.6') EDZ antennas. +
+ 
                   EDZ Antenna Length vs. Gain and Sidelobes
+
+Length      #12 Copper Wire               #18 Copper Wire
+(Feet)      Gain (dBi)  Front-to-Side     Gain (dBi)  Front-to-Side
+                        Lobe Ratio (dB)               Lobe Ratio (dB)
+
+41.4        4.94        -15               4.90        -16
+
+41.8        4.98        -13               4.94        -14
+
+42.2        5.01        -11               4.96        -11
+
+42.6        5.02        -10               4.98        -10
+
+43.0        5.03        - 9               4.98        - 9
+
+43.4        5.02        - 8.5             4.97        - 8.5
+
+43.8        5.00        - 8               4.95        - 8
+
+44.2        4.96        - 7               4.91        - 7
+
+44.6        4.90        - 6.5             4.85        - 6.5
+
+  delta G=0.13 dB  delta F-S=8.5 dB  delta G=0.13 dB  delta F-S=9.5 dB
+
+Notes:
+1.  Antenna model is for 28.5 MHz in free space.
+2.  Gain figures are recorded to 2 decimal places for comparison purposes only.  Single digit
+differences in the first decimal column are unlikely to be significant to performance.
+3.  Front-to-side lobe ratios are estimated from antenna plots.  Higher accuracy is not required
+to show the trend in sidelobe growth with antenna length.
+
+Table 1.  EDZ antenna length vs. gain and front-to-side lobe ratio.
+

Had Fig. 3 showed further shortening of the antenna wire, eventually the side lobes would have disappeared--just as the antenna length approached a single full wavelength. Moving in the other (longer) direction, the main lobe gain quickly falls off to yield the traditional 6-petal pattern of a 1 1/2 wavelength antenna. Fig. 4 illustrates these extremes.

+
+ +
+
+ Fig. 4. Comparative free space azimuth patterns for 1 wl, 1.25 wl, and 1.5 wl wire antennas. +
+

With the EDZ, there are also subtleties occasioned by antenna height. Within the usual amateur backyard building limits (20 to 70 feet antenna height), antenna gain will vary, with peaks at the 5/8, 1 1/8, and 1 5/8 wavelength heights and minima at the 7/8, 1 3/8, and 1 7/8 wavelength heights. Unfortunately, the 7/8 wavelength height, about 30 feet on 10 meters and 35 feet on 12 meters, is often a tempting and convenient amateur construction height. However, moving up a quarter wavelength in height (to about 39 feet on 10 meters) can increase gain by 1.6 dB over the 7/8 wavelength point and decrease the main lobe take-off angle by 4 degrees, with a consequent increase in radiation at the lower angles most favorable to DX. Above a height of 1 1/2 to 2 wavelengths, the gain fluctuations with height become insignificant, but the radiation at low radiation angles continues to increase. Half wavelength dipoles also show such fluctuations at about the same heights, but to a much lesser degree. Gain variations with height result from reflected antenna currents being reinduced into the wire at phase angles that vary according to antenna height. The same phenomenon also creates a varying feed point impedance.3

+

The EDZ is a nonresonant antenna, displaying great capacitive reactance. Within the range of reasonable lengths (about 41.5' to 44.5' on 10 meters), the antenna shows a feedpoint impedance ranging from 175-j930 at the short end to 110-j640 at the long end. The impedance--both the resistive and reactive components--falls off more rapidly as the length passes the midpoint (43'), where the impedance is about 150-j840 .

+

Most commonly, hams feed the EDZ with open-wire or similar parallel transmission lines and an antenna tuner. This style of operation permits the operator to use the antenna on other bands in a way similar to the use of center-fed (double) Zepps in the 1930s. (I suspect that this fact contributed much to the name "extended double Zepp.") More recently, Yardley Beers reminded us that impedance matching need not be done at a distance from a highly reactive antenna. He developed a system of transformer matching between the antenna and a coaxial feedline. The secondary of the transformer not only provided the step-up ratio for the resistive component of the impedance, but as well provided the inductive reactance to compensate for the antennas natural capacitive reactance.4

+

Stub matching to a 50- coaxial feedline is also possible by selecting a line (for example, 450-Ohm parallel line) and, by calculation or experiment, choosing a length that results in a 50-Ohm resistive impedance when a suitable stub is connected in parallel across the junction of the matching section and the main feedline. A 44-foot long #14 wire 10-meter EDZ at about 35 feet above average ground would require a 450- (.95 VF) matching section just over 5-feet long and a parallel shorted stub of the same material just over 1.2 feet to provide a perfect match to 50- coax. Setting more precise dimensions than these would require information on the antenna's feedpoint impedance over the actual terrain of the site. Stub matching should result in a very reasonable 2:1 SWR bandwidth of over 800 kHz on 10 meters. See the Appendix to review the characteristics of stub matching and a method of calculating the elements of such a system.5

+
+ The 180-Degree Phased 2-Element EDZ +
+

John Reh, K7KGP, was perhaps the first in recent times to experiment with 2-element arrangements of the EDZ, developing a 180-degree phased array of identical elements spaced 1/8 wavelength apart. The antenna is an extension of one version of the "two-section W8JK," which used 1 wavelength elements. Fig. 5 provides free space patterns of the 8JK and the phased EDZ antennas, both bidirectional arrays, along with a single element EDZ. The phased EDZ provides about 1.1 dB gain over the 8JK and about 2.9 dB gain over a single EDZ. This is equivalent to about 5.8 dB gain over a 1/2 wavelength wire dipole equally situated.

+
+ +
+
+ Fig.5. Comparative free space azimuth patterns for the 8JK, the single-wire EDZ, and the 2-element 180° phase-fed EDZ array. +
+

One advantage of the 180-degree phased EDZ array, like all other 180-degree phased arrays of any length, is the immunity of the antenna to variations in gain and impedance with changes in height. From 0.5 to about 2 , the gain of the array climbs quickly and then more slowly to essentially flat-top above 1.2 . The impedance remains quite constant, with the reactance varying by less than ± 1 . The difference in these characteristics from their counterparts in a single-wire antenna is due to the cancellation of radiation vertically (both incident and reflected), thus reducing the complexity of radiation interactions with the elements with changes in height. Fig. 6 compares the elevation patterns of a single wire EDZ with its 180-degree phased counterpart over medium earth at a height of 35 feet, about 1 at 10 meters.

+
+ +
+
+ Fig. 6. Elevation patterns over real ground for the single-wire and the 2-element 180° phase-fed EDZ antennas. +
+

Fig. 7 shows the general outline of the phased array, along with two feed systems. Dimensions of the elements are not critical. Neither is the exact spacing. Construction can consist of two #18 copperweld or #12-14 copper wires with spreaders every 5 to 8 feet. For 10 meters, 4.5' lengths of thin wall PVC thin-wall conduit serve well. Hack saw slots into the ends to point 4.3' to 4.4' apart. Drill the ends of the cuts to pass the wire with friction. Leaving the burrs on the holes increases friction and holds the wires in place. Press the wires into the slots until they reach the holes. A 2-year test of this system showed no tendencies for the spreaders to slip from their initial positions, even without any adhesives or additional wire ties. Single end supports (towers, trees, guyed masts, etc.) are adequate for the antenna if the element ends, extended by 3/16 to 1/4 inch diameter sun-resistant synthetic rope, are attached to a longer and studier PVC length. Schedule 40 material is strong enough to permit the installation of eye-bolts. The end ropes pass through the eye-bolts and down to a tie off point for raising and lowering the antenna.

+
+ +
+
+ Fig. 7. General construction outline of a 2-element 180° phase-fed EDZ array with two different methods of feed. +
+

Feed systems are numerous, but only two are shown here. Section A. in Fig. 7 shows individual feedlines brought together with a reactance-cancelling stub, while Section B. shows a taut section of feedline between the elements, with a section dropped vertically to the coaxial cable junction. Either system will work over a narrow frequency range. It is possible to model feedline sections and correlate the results with feedline calculations using standard formulas.6 Calculations used standard 450-ohm line with a velocity factor of 0.95, while MININEC models used #18 wire spaced 0.083' (1") apart and NEC models specified transmission line lengths, impedances, and velocity factors. Of course, MININEC models do not treat feedline as feedline, but as part of the radiating structure where the fields tend to cancel each other. Nevertheless, the resulting figures came within construction variations of each other.

+

For an array consisting of two 44' #14 elements spaced between 4.3' and 4.4' at 28.5 MHz, the feedpoint impedances of the elements are each approximately 20-j650 . For reasonable variations in these dimensions (up to a half foot shorter and wire as thin as #18 copperweld), the resistive component will vary by an Ohm or 2, while the reactive component may range between -600 and -800 .

+

To achieve a Vee-shaped junction of two feedlines that in parallel produce a resistive impedance of 50 when a compensating parallel stub is added, requires a pair of lines, each nearly 5 feet long. Remember, one of the two lines has a half-twist to place the elements 180 out-of-phase. Where they join at the point of the Vee, a shorted stub only about an inch to an inch and a half long provides the proper compensation. Is the stub essential? Without the stub, the antennas feed impedance at the junction of the Vee is about 3 resistive and 12 reactive.

+

Only general figures are given here, because exact numbers depend upon knowledge of all the antenna and feedline variables for a given installation. In the area of line length required for a 50-Ohm match, the impedance shows a rapid change per unit length. Hence, a very fractions of an inch of line length may separate the impedance values generated by slight variations on a given version of the antenna. Trimming must be done in small increments. Series or parallel capacitors of a capacitive stub will compensate for the remnant reactance.

+

Using a taut 4.4' line between elements, with a further feedline centered at the 2.2' mark yields a different situation. Each line--a bit under 25 in length--shows an impedance of about 8.5-j300 at the junction point of the two, for a parallel combination of 4.25-j150 . Various models of this structure gave values of 3.9 to 4.3 resistive, with a reactive component of 140 to 175 . Connecting a single length of 450 feedline vertically from this junction a usable stub-main feed junction about 1.5 feet down the line. A very short shorted stub (about 2 inches long) in parallel across the junction will provide the 50- match to a coaxial feeder. Due to the very low resistive component of the junction, special care should be taken to ensure as lossless and weatherproof a set of connections as possible. Moreover, the very high reactance-to-resistance ratio indicates that the match will have a quite narrow bandwidth.

+

Models also suggest an untried scheme as a variant on Fig. 7B. Without a twist in the line, divide the antenna structure down the middle of the taut feedline, with each half fed in the center of its side of the line. Cross-connect the two resulting feedpoints in a parallel connection (essentially putting the twist at the connection), and the feedpoint impedance will be about 4.5-j150 , ready for the same connecting line as above.

+

Of course, the use of coax may be set aside and the parallel feeders run all the way to the station antenna tuner. Several factors recommend this method in preference to a stub match. First is the criticalness of the system tuning. Matching sections require lengths over which both resistance and reactance are changing by great amounts per unit of line length. With either the Vee or the flat-top stub-feed systems shown, the 2:1 SWR bandwidth is just over 100 kHz wide at 10 meters.

+

Second, the dimensions just given apply to a single height for the experimental antenna; alterations of antenna height from the 35' model height will require total recalculation. Indeed, the more critical the dimensions of a matching line and stub, the more ease of adjustment a good antenna tuner will provide.

+

The resulting array produces a pair of opposing narrow main lobes (28 to 32) with sidelobes about 50 off-axis and down about 12 to 14 dB, depending upon the exact choice of element lengths, spacing, and wire size. At a wavelength in height (35' at 10 meters), the take-off angle is about 13 with a -3 dB point at 7 above ground. Models also suggest that interaction between the antenna elements and the feeding-phasing structure may reduce gain by up to a dB from the theoretical optimum. The missing power reappears in the 90 off-axis directions, reducing the front-to-side ratio by a small but determinant amount. Nonetheless, for a fixed array where both forward and reverse directions may be useful but do not usually result in QRM, this antenna may be worth the work it takes to pruning it to a particular frequency and to a match with the transceiver.

+
+ Parasitic EDZ Beams +
+

If one could make the 2-element EDZ unidirectional, one might achieve a little more gain, plus have the advantage of reduced QRM from the rear. Theoretically, there are two ways of achieving this goal: a. create a parasitical beam, and b. phase-feed the rear element in a manner similar to the ZL Special. Table 2 shows a comparison of the free space gains of models of the full EDZ family, along with a standard half wavelength wire dipole and the 2-element Yagi that has been used as a reference in earlier installments of these reports.

+ 
        Relative Free-Space Gains of Various Antennas in the EDZ Family
+
+      Antenna                    Gain (dBi)
+
+1/2 wl  Dipole                   2.07
+
+1-el. EDZ                        4.85
+
+2-el. reference Yagi             6.30
+
+2-el. EDZ, 180-degree phase fed  7.85-8.10
+
+2-el. EDZ, parasitic             8.70-9.25
+
+2-el. EDZ, 135-degree phase fed  8.95-9.30
+
+Notes:
+1.  The "2-el. reference Yagi" refers to the modified W6SAI 10-meter beam used as a standard of
+broadband 2-element design throughout this series.
+2.  All values are derived from computer models and, except for the reference Yagi, average
+several designs using, as relevant, different element lengths, spacings, and wire sizes.
+
+Table 2.  The relative free-space gains of various antennas in the EDZ family, along with a
+reference dipole and Yagi.
+

The idea for a two-element beam based on the double extended Zepp was first presented to me in 1991 by Brian Egan, ZL1LE, who proposed for his computer studies of a 15-meter model element spacing of 100 inches, with one element fed and the other a loaded reflector. My concern for keeping the wires properly spaced led me to consider closer spacing, something in the neighborhood of 1/8 wavelength spacing, as used in the ZL Special. The result was the development of two different, but related antenna concepts. One is a double extended Zepp version of the ZL Special, with phased feed. The other, following ZL1LE's lead, uses two elements of the same length, with one fed and the other loaded as a reflector. The computer says both should work quite similarly. The ZL Special version (referred to as the 5/4ZLS hereafter) offers the potential for eliminating loading coils. The symmetrical antenna (referred to as the ZL1LE hereafter) offers the potential for reversibility, allowing me to orient it toward Europe and toward down-under just by moving an accessible feedline.

+
+ +
+
+ Fig. 8. General construction outline of a ZL1LE 2-element EDZ parasitic beam. +
+

The original ZL1LE antenna used wide spaced elements. The modified version shown in Fig. 8, uses 1/8 wavelength spacing (4.39 feet) between two equal length elements. The forward element is fed, while the rear element is parasitic. However, to achieve any forward gain and significant front-to-back ratios, the rear element must be loaded inductively. With a carefully selected load, and minimizing losses in the load inductor, the antenna is capable of potentially superior performance. The gain at most heights averages across the design bandpass better than 14.5 dBi, or about 6.5 dB better than a dipole of equal height and orientation. The front-to-back ratio for various models runs from just under 20 dB to more than 30 dB.

+
+ +
+
+ Fig. 9. Azimuth patterns for two versions of the ZL1LE parasitic EDZ beam at 35' above real ground. +
+

Fig. 9 shows the azimuth patterns for two model beams at a 35' height. The patterns with smaller sidelobes and a smaller front-to-back ratio (about 23 dB) uses #12 copper elements 41.67' long, spaced 4.39' apart and requires a reflector load of 1035 . The version with larger sidelobes and a higher front-to-back ratio uses 44' elements at the same spacing, with the same wire and a 685 reflector load reactance. As with any member of the EDZ family, balancing various characteristics determines the final choice of design. In any event, one must model the parasitic EDZ beam over real ground, as in Fig. 9, to gain a perspective on the actual characteristics. The free space pattern yields a pattern whose rear lobes look like miniatures of the forward lobes, a picture that does not hold over real ground.

+

Table 3 compares the modeled performance of the ZL1LE antenna in two versions to the performance of a single element EDZ and of a 2-element 180-degree phase-fed array. Also noted are the necessary changes in loading inductor for the parasitic element to achieve maximum front-to-back ratio at each height. Below a height of about 2 , the parasitic EDZ beam in almost any form is height sensitive with respect to gain, front-to-back ratio, and the required loading inductance to achieve maximum front-to-back ratio. A height of about 1 provides the best combination of gain and front-to-back ratio. In fact, experimental models of the antenna appear to lose much of their dx potential if not at least 1 above ground.7

+ 
         Comparisons of Antenna Models Based on the Extended Double Zepp
+
+HeightGain  Front-to-   Front-to    S/L   Beam  Source      Source      Load
+(Feet)(dBi) Back Ratio  Side Ratio  Gain  Width Resistance  Reactance   Z=10+jXL
+            (dB)        (dB)        (dBi) (°)   R (Ohms)    -XC (Ohms)  XL (Ohms)
+
+                  Single Wire EDZ (42.8' Elements, #18 Copper)
+F.S.   4.9              10          -5    32    162         840
+20    11.3              10           1    36    128         860
+25    10.0              10          -1    34    150         810
+30     9.6              10          -1    34    193         830
+35    11.0              10           1    34    159         870
+40    11.0              10           1    32    137         830
+45    10.0              10           0    32    173         820
+
+        2-Element EDZ, 180° Phase-Fed Array (42.8' Elements, #18 Copper)
+F.S.   7.8              15          -7    30    26.4 (x2)   820
+20    12.2              17          -5    32    26.3        822
+25    12.8              16          -3    32    25.2        820
+30    12.7              15          -2    32    26.8        819
+35    12.9              15          -3    32    27.0        820
+40    13.2              15          -3    32    25.9        820
+45    13.2              15          -3    32    26.1        819
+
+            2-Element Parasitic EDZ Beam (42.8' Elements, #18 Copper)
+F.S.   8.7  16.4        11.8        -3.1  32    89.8        775         950
+20    14.3  18.0        13.5         0.8  34    80.7        792         905
+25    13.6  11.9        13.0         0.5  34    76.6        777         945
+30    13.1  18.1        12.3         0.7  32    97.1        760         980
+35    14.4  25.3        12.8         1.6  32    96.0        775         935
+40    14.4  13.2        12.0         2.4  32    79.1        785         930
+45    13.8  14.3        11.9         1.9  32    88.3        768         970
+
+           2-Element Parasitic EDZ Beam (41.67' Elements, #12 Copper)
+F.S.   8.8  15.4        14.0        -5.0  34    102.0       830         1055
+20    14.5  16.9        15.8        -1.3  36     94.8       852         1000
+25    13.7  11.1        14.0        -0.3  36     86.2       832         1050
+30    13.5  16.9        14.7        -1.2  34    109.3       813         1095
+35    14.5  23.4        15.1        -0.6  34    110.0       830         1035
+40    14.6  12.5        14.0         0.6  34     89.2       843         1025
+45    13.9  13.4        14.0        -0.1  34     99.1       822         1080
+
+Notes:
+1.  F.S. = free space   2.  Sidelobe figures estimated from graph for bidirectional antennas.
+3.  Loading coil assumed to have an approximate Q of 100
+
+Table 3.  Comparisons of antennas based on the Extended Double Zepp as modeled at typical
+amateur construction heights and optimized (where necessary) for maximum front-to-back ratio.
+

The source impedance for the antenna shows a large capacitive reactance which requires compensation. Assuming the use of a suitable inductance to eliminate the reactance, the feedline impedance, now only resistive, is roughly twice that of the normally used 50-ohm coaxial cable. A 2:1 quarter-wave matching section of 75 ohm cable cut to design center frequency would likely yield an acceptable match. A linear choke, such as the W2DU ferrite choke balun, would be apt between the feedline and the matching section.

+

Since this antenna requires inductors in both elements, one to cancel the series capacitive component of the source impedance and the other to load the reflector, the system holds potential for being used as a fixed beam whose direction is reversible. However, if the components are mounted at the antenna, it is unlikely that anyone would climb a structure to readjust the inductor values. However, the inductors need not be mounted at the antenna.

+

Low loss parallel feedline--450-ohm is recommended for its ability to withstand power and weather--permits both matching inductors to be mounted closer to the ground. A wavelength (assuming .95 velocity factor) at 28.5 MHz is about 32.8 feet, and a half wavelength is 16.4 feet. For 10-meter antennas at 20 or 35 feet, feedline runs to a platform near the ground are feasible with a length of line that permits the impedance conditions at the element centers to replicate. Using rotary or tapped inductors, one can adjust the loading and the compensating inductors with comfort and ease. A chart of settings would ensure quick adjustment. Installing a coaxial connector near each coil would permit shifting the feedline from one element to the other, thus permitting the direction of the beam to be reversed.

+

The reason for employing this scheme is to achieve a reversible fixed beam. A 44'-element beam was constructed for reversible parasitic operation. I mounted a rotatable 5' plank on the end of a 4-by-4 sunk in the ground. One end of the plank held the reflector inductor, the other held the driven element matching system. Rotating the plank and reconnecting the feedlines reversed the antenna. A modified version of the Beers matching system converted the driven element impedance to 50-ohm coax values. Fig. 10 shows two systems tried with equal success. One uses a rotary coil with a fixed 3-turn link of #18 solid hook-up wire. The other uses a fixed 2-turn link over a fixed coil of 8 turns of 1.5" diameter, 10 turns per inch stock, with a 50 pF variable capacitor in series with the link to control the degree of coupling. Either system amounts to installing an antenna tuner at the antenna, a multiple of a half wavelength below it.

+
+ +
+
+ Fig. 10. Two feed systems for the ZL1LE parasitic EDZ beam. +
+

Tuning the inductor to maximum front-to-back ratio requires a variable inductor and a signal source several wavelengths behind the antenna. Coil variability should range of 4.0 to 6.5 uH to cover a 10-meter reactance range of 770 to 1100 . A 10 uH variable inductor picked up at a hamfest provided sufficiently sharp tuning for tests. Of course, weather-proofing the tuning components is essential for this scheme.

+

Test results showed that the parasitic EDZ beam has excellent gain and reasonably good front-to-back ratio for the frequency to which everything is tuned. However, without retuning--especially the reflector inductor--everything goes to pot very quickly as one tunes off frequency, especially downward. SWR curves do not necessarily provide significant information in this connection. After adjustment of all the variables for 28.5 MHz, an SWR meter in the coaxial feedline showed under 2:1 between 28.1 and 28.9 MHz. However, below the design frequency, the beam had lost its unidirectional characteristic.

+

Table 4 models the effects of off-frequency use of the parasitic EDZ. If the value of XL is low by 10%, the reflector becomes a director, and the beam reverses its direction. Using values of XL optimal for a frequency 0.5 MHz higher in the 10-meter band results in performance similar to that of the bidirectional array. A higher XL value, optimal for a lower frequency, results in a gradual drop in gain and a more rapid drop in front-to-back ratio. If one must choose a single inductor value for the reflector coil, the best choice is the optimum value for the lowest operating frequency in the band. However, the large variation in optimum inductance required across a wide band like 10 meters suggested that the parasitic EDZ beam is best used as a fixed-direction, fixed-frequency or narrow band antenna. For that use, however, it is inexpensive compared to a Yagi with similar gain and front-to-back ratio.

+ 
   Performance of a 2-Element Parasitic EDZ with Nonoptimum Reflector Loading
+
+Measurement Optimum Frequency Optimum Load      Reactance   Gain        Front-to
+Frequency   for XL Used       Reactance (XL)    Used (XL)   (dBi)       Ratio (dB)
+
+28.0 MHz    28.0 MHz          1030 Ohms         1030 Ohms    14.6       22.3
+28.5                           905              1030         13.7        8.0
+29.0                           795              1030         13.0        5.2
+
+28.0 MHz    28.5 MHz          1030 Ohms          905 Ohms   -12.4       -0.9
+28.5                           905               905         14.6       22.3
+29.0                           795               905         13.6        8.0
+
+28.0 MHz    29.0 MHz          1030 Ohms          795 Ohms   -12.9       -3.4
+28.5                           905               795        -12.5       -0.9
+29.0                           795               795         14.6       22.0
+
+Note:  Modeled antenna used 2 42.8' elements, #18 copper wire space 4.39' apart at a height of 20'
+over medium earth.  Similar results were obtained with other "equal-element" parasitic models at
+various heights above ground.
+
+Table 4.  Performance of a representative 2-element parasitic EDZ with nonoptimum reflector loading.
+

One untested potential for the ZL1LE antenna is at 2 meters, where materials and dimensions make the antenna self-supporting. Using 0.75" diameter aluminum tubing, one can construct a beam with a driven element 8.2' long and a reflector 8.6' long, spaced just over 10" apart. Models indicate a reflector load between 250 and 305 ohms at 144.5 MHz. The source impedance is about 50-j290 , which simplifies the process of matching the antenna to coaxial cable to the elimination of the reactance alone. Due to the increase in element diameter to element length ratio, bandwidth increases over HF wire models and may cover a full megahertz of the band without undue loss of gain or front-to-back ratio if the antenna is optimized near the low end of the desired frequency range.

+

Such antennas almost exist. One commercial advertisement includes a double 5/8 wavelength vertical, that is, two such antennas end to end. The same ads indicate that some directionality will result if the antenna is mounted on the side of a tower, which apparently forms an untuned reflector. Perhaps some day a manufacturer who can control the reflector loading reactance within tight specifications may produce a true 2-meter ZL1LE.

+
+ +
+
+ Fig. 11. Azimuth pattern for a 2-meter version of the parasitic EDZ beam mounted vertically with the center 35' above real ground. +
+

The horizontal advantages of the 2-meter antenna for low-end CW and SSB operations, despite bandwidth restrictions, are the same as for HF models. However, Fig. 11 shows an azimuth pattern of the antenna mounted vertically, with the center 35' above ground. The bandwidth to half-power points is about 135 and the gain is over 13 dBi. The utility of such an antenna at a ham station for both repeater and Packet work seems obvious, and three of these antennas arrayed around a tower might well increase the range of any repeater. The lack of suitable VHF test equipment must leave the development of a working model of the 2-meter ZL1LE to others.

+
+ Phase-Fed EDZ Beams +
+

The phase-fed version of the two element EDZ beam consists of two unequal length elements spaced 4.31' apart for 28.5 MHz. The directly-fed forward element is 42.3 feet long, while the phase-fed rear element is 44.7 feet long. Configured as a wire beam, this assembly is unidirectional. Computer models show a peak gain of 14.7 dBi across the 1 MHz design bandwidth, with an average front-to-back ratio of about 20 to 23 dB, peaking at about 30 dB. The beamwidth is a narrow 34 degrees. All of these figures apply to a 35-foot height for the antenna. Fig. 12 shows the pattern of the antenna as optimized for 28.5 MHz.

+
+ +
+
+ Fig. 12. Azimuth pattern of a phase-fed EDZ beam (54ZLS) 35' above real ground. +
+

Experience with ZL-Special would suggest that with 1/8th wavelength spacing, the rear element should be fed 135 out-of-phase with the forward element. Modeling suggests otherwise. The model whose pattern appears in Fig. 12 is current phase fed at 143 to achieve maximum front-to-back ratio. Since the proposed method of feed is a twisted parallel feedline section, the modeling technique was altered. The rear element is modeled in the opposite direction from the forward element, and the phasing directly applied as -37 to the rear element source point. This technique yields identical pattern figures, but provides correct information on current and voltage amplitudes and phases for use in calculating phasing lines.

+

The chief difficulty in implementing the 5/4ZLS version of the 2-element EDZ is feeding two elements with highly reactive components in such a way as to ensure that equal power flows to both elements and that the rear element is about 143 out of phase with respect to the forward element. The source impedances for the model under discussion are 100-j830 and 5-j660 for the forward and rear elements respectively. I have been unable to discover any cable of any length that will provide the proper phasing in the manner of the traditional ZL Special. Moreover, the demands of this antenna may exceed even the flexibility of a phasing network. The high reactances at the feedpoint place any network in a region which is experiencing very rapid changes in current phase and in impedance per unit length. Regretfully, the 54ZLS has had to be consigned to the realm of antennas with theoretical potential but no present feasibility.

+

Nevertheless, models do suggest that the dimensions of this antenna, when fed as a Yagi, will produce excellent unidirectional gain and a good front-to-back ratio with a reflector load of 675 . In essence, the ability to adjust the reflector loading substitutes for a phasing line in bringing the reflector current to the correct magnitude and phase to achieve a deep rear null. However, no unidirectional EDZ array will do much better than about 20 dB front-to-rear ratio when including all parts of the rear lobes.

+

It is worth noting, however, that what we call "phasing" lines in antennas like the ZL Special are actually impedance transformers, with or without the half twist. Explorations of models using approximately 1/8th half-twist parallel transmission lines between two identical elements produced an alternative means of matching an EDZ to 50- coaxial cable. A two-element version of the 10-meter EDZ with such a connecting section made up from 600- (.95 VF) parallel line shows an almost perfect impedance for coaxial-cable feed. The gain of the antenna is about the same as a single element EDZ (about 11 dBi at 35 feet over medium earth), with a slight (less than 0.9 dB) difference between the two main lobes. The SWR is less than 2.5:1 over the first MHz of 10-meters. For the cost of an additional element and some separators, the builder can produce a coax-fed adjustment-free EDZ.

+
+ Summary +
+

Understanding the possibilities for EDZ arrays and beams depends, as we have seen, on understanding the basic properties of the single element EDZ antenna. Two-element arrays, either bidirectional or unidirectional are possible and feasible--if they fit the operating needs and circumstances of a particular station. As wire beams, they are fixed and thus fit for point-to-point communications. Their narrow bandwidths and beamwidths reinforce this type of use. Moreover, they are not forgiving of casual building and tune-up practices.

+

There remains much to be learned about the behavior and the possibilities of EDZ beams. A bit of that data appears in other notes at this site, for example, EDZ Beam Update; Feeding the EDZ; and Phased Yagis, EDZ Beams, and Landstorfer-Sacher Yagis.

+

If thelimiting factors factors are not deterrents to building one of the EDZ family of beams, but part of the needs of a station, then the operator can expect considerable gain over many other types of wire antennas. Moreover, the cost of these antennas, including wire elements and feedlines, is well below the cost of Yagis with equal gain (and equal front-to-back ratio for the ZL1LE). EDZ beams may have a small but not insignificant niche in the spectrum of amateur antennas. I do not recommend them, since recommendation would require a detailed knowledge of too many variables directly related to the communications situation in which the antenna might play a part. However, I do recommend further experimentation, modeling, calculation, and ingenuity in pursuit of getting the most out of this interesting family of antennas. EDZs and other nonresonant arrays may have gone unjustly neglected in our dipole-and-coax age.8

+
+ Notes +
+

1. This tongue-in-cheek introduction does have a serious point. The Jones handbook mentions the 5/8 wavelength vertical, especially as a broadcast antenna, as early as 1936, if not before. See Frank C. Jones, Jones Radio Handbook, 3rd Ed. (San Francisco: Pacific Radio Publishing Co., 1936), pp. 73-74. However, see Hugo Romander, W2NB, "The Extended Double-Zepp Antenna," QST, June, 1938. The antenna remained much neglected after this initial introduction to the ham community.

+

2. Yardley Beers, "The 5/4-Wavelength Dipole: A Revival," Communications Quarterly (November, 1990), pp. 40-41. Jerry Hall, Ed., The ARRL Antenna Book (Newington, ARRL, 1991), p. 8-34.

+

3. See L. B. Cebik, "The Effects of Height on Other Antenna Properties," Communications Quarterly (Fall, 1992), pp. 57-79.

+

4. Beers, "The 5/4-Wavelength Dipole: A Revival," pp. 41-44.

+

5. K7KGP's 12-meter EDZ, shown in recent ARRL Handbooks, can mislead builders, since his stubless match applies only to the antenna feedpoint impedance figures he lists. See The ARRL Handbook (Newington: ARRL, 1992), p. 33-11. The matchline he specifies leaves an Ohm or 2 of remnant reactance, much too little to be of concern. Except in very rare cases, other feedpoint impedance figures will require a stub to compensate for reactance at the junction of the matchline and the main feedline. The Appendix to this article provides a method of directly calculating both the matchline and stub elements of a stub-matching system.

+

6. See Terman, Radio Engineer's Handbook (New York: McGraw-Hill, 1943), pp. 185-186, among other sources (for example, Johnson's Antenna Engineering Handbook, 3rd Ed.), for the basic formulas for calculating the impedance, current, and voltage along a lossless transmission line for any length from the load. Fortunately, these formulas are amenable to simple basic programming that, in addition to figures for specific line lengths, will produce charts of results for any desired interval. Such charts permit estimation of desirable line lengths within trimming range. As previously noted, it is also possible to use these formulas to calculate required stub-matching systems; see the Appendix.

+

7. A 2-element Yagi at 35' provided stronger signals on 10 meters on the eastern U.S. to VK/ZL path than an initial experimental model of the EDZ beam at 25', despite the fact that models estimated roughly equal radiation in the 5 to 10 elevation region. Raising the wire antenna resolved the problem. However, the experience impressed upon me the importance of choosing antenna heights such that the lowest required path angle clears fields of obstructions, such as nearby woods with 70' trees and the like. The effect can be dramatic.

+

8. All patterns shown in this discussion were plotted on ELNEC 3.02, but figures cited have been cross-checked on various programs and by various means of calculation (including versions of NEC-2 and NEC-4).

+
+ +
+
+ Appendix +
+
+ Stub Matching: A Review +
+

As long as hams wish to use or experiment with antennas like the Extended Double Zepp and others that present complex feedpoint impedances, stub matching will remain one alternative method of matching the antenna to a 50- feedline. Most discussions of stub matching, however, appear almost wholly in qualitative terms. The purpose of this discussion it to convert that discussion into quantitative terms. We shall proceed by reviewing the basic concept of stub matching, presenting the basic equations for calculating the elements of a stub-matching network, and finally using a simple BASIC implementation of those equations to solve a couple of exemplary problems.

+
+ The Stub-Matching System +
+

Most antenna manuals give the simple equations for calculating the reactance of both shorted and open transmission line stubs. However, these treatments regularly omit similar equations for calculating the length of the line between the antenna and the stub-feedline junction. So let's begin again.

+

Fig. 13 shows the basic structure of a typical stub-matching system. It consists of the antenna with its complex feedpoint impedance, a length of matching-feedline (the Line) leading to the critical junction, a reactive Stub, and the main feedline (the Feed) leading to the power source, ordinarily a transmitter or transceiver. The functions of the antenna and the main feedline are well-known, but the functions of the other two elements require brief comment.

+
+ +
+
+ Fig. 13. Basic elements of a stub-matching network +
+

The matching-feedline operates as an impedance transformer. When there is a complex antenna feedpoint impedance or a mismatch between the antenna impedance and the matching-feedline impedance, the overall impedance, as well as the resistive and reactive components of that impedance, will vary along the line. These values are normally given as series values. If the line type (that is, its characteristic impedance) is properly chosen, at some point along the line, the resistive component of the impedance will be of such a value that its corresponding parallel value will equal the characteristic impedance of the main feedline. This point defines the correct length of matching feedline to use.

+

Ordinarily, at the junction of the matching-feedline and the main feedline, there will also be a reactive component to the overall impedance. Although usually given as a series value, it too has a corresponding parallel value. A reactance of the opposite type but of the same magnitude will compensate for the junction reactance. In this exercise, the compensating reactance will be composed of a feedline stub, even though lumped components (capacitors or inductors) are also usable with somewhat greater losses in some instances. Compensating for the parallel reactance will leave a parallel resistance equal to the main feedline. With the reactance compensated, the resulting series resistance value will be the same value, thus effecting a match to the main feedline.

+
+ Calculating the Matching-Feedline and Stub Lengths +
+

Often left to graphical analysis along with some miscellaneous calculations, the calculation of match-line and stub systems can be direct. With the advent of home computers and BASIC, the reputed tediousness of the calculations is no longer a hindrance. Indeed, a simple computer program is faster than most graphical methods (some of which have been computerized).

+

The process begins by understanding that along a match-line, we are seeking the point at which the parallel-equivalent value of the series resistance is equal to the characteristic impedance of the main feedline. Associated with these values is a value of series reactance and its parallel equivalent. If we call the series resistance and reactance the target values, then we define RT and XT. Let ZF be the characteristic impedance of the main feedline. Then, using the series-to-parallel resistance conversion equation,

+
+ +
+

Solving for XT2, we get

+
+ +
+

Before using equation (2), we must calculate the reflection coefficient, rho, (actually its square) of the antenna-to-match-line system. Let the match-line characteristic impedance by ZM. Then, using the antenna feedpoint impedance, RL ± jXL, we can calculate.

+
+ +
+

Using this figure for rho, we can then calculate the value of series resistance at the point in the line defined by equation 2, using that equation to remove reactance values from the calculation of RT:

+
+ +
+

The target value of reactance is, of course, the square root of equation 2.

+

The equation, in various forms, for calculating the impedance, Zin, anywhere along a transmission line back from a load, ZL, is well known.1 That equation can be rewritten as separate equations for Rin and Xin, which will be more useful for present purposes. We shall use equations for lossless lines for three reasons. First, the lengths of line involve--all well under a wavelength, have losses far less significant than other potential error factors that enter the use of matching stubs. Second, for most types of transmission line, the most imprecise figure is the velocity factor of the line to be used, and most ham do not have access to laboratory grade measuring equipment to bring experimental determination of that figure under 5%. Third, physically replicating a calculated antenna, especially one with a significant reactive component at the feedpoint, usually results in departures from calculated values. Nevertheless, a calculation of the anticipated matching line and stub lengths will do much better than put one in the ball park: it will allow one to make a close play at the plate.

+

Since we wish the matching line to yield a resistive impedance component that correlates with the characteristic impedance of the main feedline, we may begin with the formula that has appeared in the ARRL Handbook in the 80s and early 90s.2

+
+ +
+

where RL is the resistive component of the antenna impedance, XL is the reactive component of the antenna impedance, ZO is the characteristic impedance of the matching section transmission line, and Rin is the resistive component of the impedance at a distance lr from the antenna along the line. In this exercise, Rin is precisely our target value of resistance, RT. For our purposes, we shall assume that lr is in radians, although in general, it might also be in degrees relative to a wavelength at the frequency of interest for the antenna.

+

The matching line length calculation simply requires us to solve equation (1) for lr and to convert that length in radians into degrees and feet. A rewrite of equation (1) yields a quadratic:

+
+ +
+

Solving for lr, we obtain

+
+ +
+

Note that there are two solutions, since for every 180 of line length (under mismatch conditions), there will be two points at which the resistive component of the impedance has the same value.

+

The limiting case is where the value under the radical in equation (7) goes to less than zero. This condition indicates that, with the combination of line values chosen for the antenna impedance values measured or derived from a modeling program, the resistive component never reaches the chosen main feed line characteristic impedance. The solution to this problem is usually to select a different transmission line for the matching line section.

+

Equation (7) returns two lengths in terms of radians along a wavelength. We can convert these lengths to a more familiar measurement in degrees by the equation

+
+ +
+

where lr is the length in radians and ld is the length in degrees. Transformation of these lengths into feet involves the equation

+
+ +
+

where Lf is the required length in feet, fMHz is the frequency of interest in MHz for the antenna, and VF is the velocity factor of the matching section transmission line.

+

Using the value of lr, we may calculate the remnant reactance by using the Handbook formula for Xin:

+
+ +
+

where all of the variables have the same meaning as in equation (7). Applying equation (10) to the two lengths resulting from equation (7) will yield opposing values of reactance. We may choose to match either with a stub. Alternatively, we may calculate the reactance values directly from the square root of equation (2), assigning the signs this way: the reactance associated with the shorter line length will have the sign of the reactance at the antenna feedpoint.

+

For the stub calculations, we shall first convert the reactance into a parallel value to facilitate mechanical connections for the stub.

+
+ +
+

where Rs is the main feedline characteristic impedance, Xs is the calculated input remnant reactance, and Xp is the equivalent parallel reactance which the stub is to compensate.

+

Reversing the signs of the reactances gives the values that must be returned by appropriate compensating stubs. The length of a shorted stub, when the desired reactance is known, is given by

+
+ +
+

and the length of a corresponding open stub is given by

+
+ +
+

where Xin is the desired reactance, ZO is the characteristic impedance of the transmission line used for the stub, and lS and lO are the lengths of shorted and open stubs, respectively. Since the values of lS and lO are in radians, they can be converted into feet by the same means used to convert the length of the matching line.

+

The final step is to select the best combination of matching line and stub for the proposed antenna. Ordinarily--for least loss and mechanical simplicity--the combination with the shortest matching line and stub is most desirable.

+
+ A Simple Utility BASIC Program for Stub Matching +
+

The calculations for a stub-matching system lend themselves to a simple utility program in BASIC or almost any other language. Fig. 14 gives the listing for my own program, replete with my personal programming quirks. Lines 10-130 set up the input values for the calculation. Lines 140 through 170 calculate the target resistance value along the match-line. Lines 180-440 calculate the length of the matching-line section and the series resistance and reactance values at that point. The equations is broken down into components to precalculate repetitive parts. Line 200 catches the case where the value under the radical is less than zero. Lines 360-410 calculate the reactance for each of the solutions to equation (7), once more with the relevant equation broken down into segments or normalized. (These lines also recalculate the input resistance of the matching line; I put this in while setting up the program as a check and never took it out, since it involves only a few extra lines. The technique is useful for error catching during the program writing process. However, using RT and XT and bypassing these steps would shorten the program somewhat.)

+ 
+10 'file STUB.BAS
+20 CLS:COLOR 11,1,3:CLS
+30 PRINT"                    General Solutions for Stub Matching,": PRINT"               given Antenna R & X plus
+Line, Stub, & Feed Zo":PRINT"                             L. B. Cebik, W4RNL":PRINT
+40 PRINT"For any antenna load R and X, this program finds the Line and Stub length neededto match any
+feedline Zo, if a match is possible with the proposed Line, Stub,  and Feed Zo values.":PRINT
+50 INPUT "Enter Antenna Load Resistance in Ohms         ",RL
+60 INPUT "Enter Antenna Load Reactance in Ohms          ",XL
+70 INPUT "Enter Frequency (in MHz)                      ",FQ
+80 INPUT "Enter Zo of Line (from antenna to stub)       ",ZL
+90 INPUT "Enter Velocity Factor of Line (as decimal)    ",VFL
+100 INPUT "Enter Zo of Feed (from stub junction to rig)  ",ZF
+110 INPUT "Enter Velocity Factor of Feed                 ",VFF
+120 INPUT "Enter Zo of Stub (from line-feed junction)    ",ZS
+130 INPUT "Enter Velocity Factor of Stub                 ",VFS
+140 RLS=(RL*RL):XLS=(XL*XL):ZLS=(ZL*ZL):RIS=(RI*RI)
+150 RHOS=(((RL-ZL)*(RL-ZL))+XLS)/(((RL+ZL)*(RL+ZL))+XLS)
+160 RT=((ZL*ZL)*(1-RHOS))/((ZF*(RHOS-1))+((2*ZL)*(RHOS+1))):RI=RT
+170 'IF (ZF*RT)-(RT*RT)<0 THEN 350 ELSE XT=SQR((ZF*RT)-(RT*RT))
+180 A=(XLS/ZLS)+(RLS/ZLS)-(RL/RI):B=2*(XL/ZL):C=1-(RL/RI)
+190 IF A=0 THEN A=1E-08
+200 NUM=((B*B)-(4*(A*C))):IF NUM<0 THEN 350
+210 TLP=(B+SQR((B*B)-(4*(A*C))))/(2*A)
+220 TLM=(B-SQR((B*B)-(4*(A*C))))/(2*A)
+230 LP=ATN(TLP):LM=ATN(TLM)
+240 PI=3.141592654#
+250 LPD=(LP*180)/PI:LMD=LM*180/PI
+260 IF LPD<0 THEN LPD=180+LPD
+270 IF LMD<0 THEN LMD=180+LMD
+280 LPF=(LPD*VFL)/(.3660131*FQ):LMF=(LMD*VFL)/(.3660131*FQ)
+290 PRINT"Possible line lengths are A. ";LPF;"feet and B. ";LMF;"feet."
+300 LR=LP:GOTO 360
+310 RIA=RI:XIA=XI:PRINT"For Line length A., Rs=  ";RI;"Ohms and Xs=  ";XI;"Ohms."
+320 LR=LM:GOTO 360
+330 RIB=RI:XIB=XI:PRINT"For Line length B., Rs=  ";RI;"Ohms and Xs=  ";XI;"Ohms."
+340 GOTO 440
+350 IF NUM<0 THEN PRINT"There are no possible solutions with this combination of of antenna
+impedance   and line impedance.":GOTO 710
+360 IF RL=0 THEN RL=1E-08
+370 RA=RL/ZL:XA=XL/ZL:T=TAN(LR):TS=T*T
+380 DA=(1-(XA*T))*(1-(XA*T)):DB=(RA*T)*(RA*T):DN=DA+DB
+390 RS=RA*RA:XS=XA*XA
+400 RN=RA*(1+TS):XK=XA*(1-TS)
+410 XM=((1-RS)-XS)*T:XN=XK+XM:RZ=RN/DN:XZ=XN/DN:RI=ZL*RZ:XI=ZL*XZ
+420 IF LR=LP THEN GOTO 310
+430 IF LR=LM THEN GOTO 330
+440 PRINT"For a record of these calculations, press <Print Screen>."
+450 PRINT:PRINT"Press <C> to continue."
+460 I$=INKEY$:IF I$="c" OR I$="C" THEN GOTO 470 ELSE 460
+470 CLS:PRINT:PRINT"Stub Calculations:":PRINT
+480 PRINT"Option A: Rs= ";RIA;" and Xs= ";XIA;" Ohms
+490 XPA=((RIA*RIA)+(XIA*XIA))/XIA:XCOMPA=(-1*XPA)
+500 PRINT"The required parallel stub reactance to compensate is ";XCOMPA;"Ohms."
+510 LRL=ATN(XCOMPA/ZS):LDL=(ABS(LRL)*180)/PI
+520 IF XCOMPA<0 THEN LDL=180-LDL
+530 LFL=(LDL*VFS)/(.3660131*FQ)
+540 LRC=ATN(ZS/XCOMPA):LDC=(ABS(LRC)*180)/PI
+550 IF XCOMPA>0 THEN LDC=180-LDC
+560 LFC=(LDC*VFS)/(.3660131*FQ)
+570 PRINT:PRINT"The required SHORTED STUB length is ";LDL;"degrees or ";LFL;"feet.
+580 PRINT"The required OPEN STUB length is ";LDC;"degrees or ";LFC;"feet.
+590 PRINT:PRINT:PRINT"Option B: Rs= ";RIB;" and Xs= ";XIB;" Ohms
+600 XPB=((RIB*RIB)+(XIB*XIB))/XIB:XCOMPB=(-1*XPB)
+610 PRINT"The required parallel stub reactance to compensate is ";XCOMPB;"Ohms."
+620 LRL=ATN(XCOMPB/ZS):LDL=(ABS(LRL)*180)/PI
+630 IF XCOMPB<0 THEN LDL=180-LDL
+640 LFL=(LDL*VFS)/(.3660131*FQ)
+650 LRC=ATN(ZS/XCOMPB):LDC=(ABS(LRC)*180)/PI
+660 IF XCOMPB>0 THEN LDC=180-LDC
+670 LFC=(LDC*VFS)/(.3660131*FQ)
+680 PRINT:PRINT"The required SHORTED STUB length is ";LDL;"degrees or ";LFL;"feet.
+690 PRINT"The required OPEN STUB length is ";LDC;"degrees or ";LFC;"feet.
+700 PRINT:PRINT"Press <Print Screen> to complete the record of calculations."
+710 PRINT:PRINT"For another run, press <A>; to quit, press <Q>."
+720 I$=INKEY$:IF I$="a" OR I$="A" THEN 10 ELSE IF I$="Q" OR I$="q" THEN 730 ELSE 720
+730 END
+
+Fig. 14.  Program listing for STUB.BAS
+
+

The results of the calculations so far can be recorded on paper by a program pause and a <Print Screen> command. Since two screens of material will fit on one piece of paper, do not <Form Feed> at this time. Lines 450-710 calculate the required parallel reactive components and the stub values that will compensate for them, two values for each line length. A second <Print Screen> will combine this information with the input values for a complete record. A sample double screen printout appears in Fig. 15. The antenna is a 10-meter (28.5 MHz) Extended Double Zepp with a 450- stub match system for a 50- feedline where the EDZ models a feedpoint impedance of 141-j694 . Option A is 5.0' with a shorted stub of 1.2' or an open stub of 9.4', and option B is 5.5' with a shorted stub of 15.2' or an open stub of 7.0'. Option A and a shorted stub provide the mechanically simplest system to implement. You can truncate the decimals in the results almost anywhere, since in most cases, results to the nearest ohm and tenth of a foot will be close enough to permit antenna system adjustment.

+
+ General Solutions for Stub Matching, +
+
+ given Antenna R & X plus Line, Stub, and Feed Zo +
+
+ L. B. Cebik, W4RNL +
+

For any antenna load R and X, this program finds the Line and Stub length needed to match any feedline Zo, if a match is possible with the proposed Line, Stub, and Feed Zo values.

+

Enter Antenna Load Resistance in Ohms 141.36

+

Enter Antenna Load Reactance in Ohms -693.56

+

Enter Frequency (in Mhz) 28.5

+

Enter Zo of Line (from antenna to stub) 450

+

Enter Velocity Factor of Line (as decimal) .95

+

Enter Zo of Feed (from stub junction to rig) 50

+

Enter Velocity Factor of Feed .66

+

Enter Zo of Stub (from line-feed junction) 450

+

Enter Velocity Factor of Stub .95

+

Possible lines lengths are A. 5.038553 feet and B. 5.485493 feet.

+

For line length A., Rs= 41.10245 Ohms and Xs= -19.12316 Ohms.

+

For line length B., Rs= 41.10246 Ohms and Xs= 19.12327 Ohms.

+

For a record of these calculations, press <Print Screen>.

+

Press <c> to continue.

+

Stub Calculations

+

Option A: Rs= 41.10245 Ohms and Xs= -19.12316 Ohms.

+

The required parallel stub reactance to compensate is 107.4669 Ohms.

+

The required SHORTED STUB length is 13.43154 degrees or 1.223229 feet.

+

The required OPEN STUB length is 103.4315 degrees or 9.419658 feet.

+

Option B: Rs= 41.10246 Ohms and Xs= 19.12327 Ohms.

+

The required SHORTED STUB length is 166.5685 degrees or 15.16963 feet.

+

The required OPEN STUB length is 76.56851 degrees or 6.973203 feet.

+

Press <Print Screen> to complete the record of calculations.

+

For another run, press <A>; to quit, press <Q>.

+
+ Fig. 15. Typical output sheet from STUB.BAS +
+

One caution is necessary with the use of calculating programs. Unlike graphical solutions, calculating programs give no feel for the sharpness or broadness of the results, that is, how small physical variations from the calculations will affect the adjustments. In general, the higher the ratio of reactance to resistance at the antenna feedpoint, the sharper the curve. In these cases, small physical variations may require extensive adjustment of the calculated lengths.

+

Recent ARRL Handbooks have presented an interesting 12-meter EDZ cut to a length that provides a feedpoint impedance of 142-j555 .3 With 450- transmission line (VF=.95), both options yield 5'5" of matching line with negligible reactance, obviating the need for a stub. The impedance presented by the matching line to the coax is 55 . In fact, using the program with a feedline impedance of 50 produces a "no possible solution message." The lesson is that before giving up on a combination, try raising or lowering the feedline impedance by 10% to see if a solution emerges. The resulting SWR on the coax will be well within limits. However, K7KGP's antenna is quite unusual, and exact reproduction or scaling for other bands may require extensive on-site adjustment.

+

These examples only sample the use of a utility BASIC program in making matching-section calculations. The limits of stub matching are far wider than these examples. Of course, modeling the results on NEC with transmission-line capabilities permits all calculations to be verified.

+
+ Notes +
+

1 See, for example, Terman, Radio Engineer's Handbook, p. 186, or Kuecken, Exploring Antennas and Transmission Lines by Personal Computer, pp. 180-181.

+

2 See, for example, p. 16-2 of the 1987 Handbook for a normalized version of the equation or p. 16-3 of the 1992 Handbook for a non-normalized version.

+

3 See, for example, the 1992 Handbook, p. 33-11.

+
+ +
+

Return to Article Index Page

+

Topics: EDZ / Zepp, HF Upper, Small Beams, W8JK


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+

Modeling and Understanding Small Beams

+

Part 4: Linear-Loaded Yagis

+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The most common reason for designing and building a small, 2-element beam or array is the size. Whether for home or portable field use, small antennas have a niche in the ham world.

+

There is a second, often overlooked reason for building antennas with reduced dimensions relative to a standard 2-element Yagi: increased front-to-back ratio. Standard, closed spaced (approximately 1/8) Yagis are not capable of large front-to-back ratios because the parasitic reflector will not be positioned or sized to have the correct current level and phase angle for maximum rejection off the rear. Most notably, the Moxon rectangle achieves close to optimal reflector conditions. Its altered geometry attains a very high front-to-back ratio for a 2-element array. The cost is about a half dB of forward gain.

+

A second strategy that will also improve the front-to-back ratio is to shorten the Yagi elements while maintaining the close spacing. With center- or linear-loading of both the driven element and the reflector of a 2-element Yagi with about 1/8 spacing, the front-to-back ratio increases from about 12 dB to about 18 dB, a full S-unit of improvement. Models of the beam show that the current amplitude and phase more closely approach values necessary for a complete rearward null than those for a full size 2-element Yagi. As with the Moxon rectangle, the short beam's forward gain drops about a half dB in the process. Additionally, the bandwidth of the beam decreases.

+

The result of modeling and testing these ideas was a 2-element 10-meter Yagi with 12' elements, which is a 25% savings in size, turning radius, and weight. In addition, the antenna uses 6' lengths of hardware store aluminum tubing for the elements, making parts acquisition easier. (Note, however, that the aluminum tubing usually available at hardware centers does not have the strength and durability of tubing used by commercial antenna manufacturers. This factor has little affect on small, weight-balanced 2-element beams for 10 meters, but may be very significant in tapered-element 20-meter models.1)

+
+ Linear-loading Vs. Inductive Loading +
+

The principle of center loading is very old and well-understood. A coil at the center of a shortened inductor compensates for the capacitive reactance that results from shortening the element from its naturally resonant length (approximately 1/2), thus restoring resonance. A parasitic element, such as a reflector may be similarly shortened and use an inductor to compensate for the resultant capacitive reactance until its relationship to the driven element is as optimal as possible. Center-loaded dipoles and Yagis have appeared in numerous antenna books over the decades.

+

The performance of a center-load dipole or Yagi depends largely upon the Q of the inductor. A shortened antenna, solely by virtue of its shortening, will show a reduction in gain relative to an unshortened antenna used as the reference. We might let a center-loaded dipole or Yagi use theoretic inductors with infinite Q (that is, with no resistance) to form a base line for comparisons. Then, by selectively establishing values of Q for the inductors and modeling the result (via a program such as MININEC), some rough comparisons become possible.

+ 
                        A Comparison of Gain and Other Properties of Center-Loaded
+                                    and Linear-Loaded Dipoles and Yagis
+
+1/2 wl Dipole: 12' 0.75" diameter aluminum
+
+Type           QLoad           Gain             Impedance
+                                dBi              R±jX
+C-L             Inf.            1.93            28 + 0.4
+C-L              50             1.24            33 + 0.5
+C-L             100             1.57            31 + 0.5
+C-L             200             1.75            30 + 0.5
+C-L             300             1.81            29 + 0.5
+L-L             ---             1.82            29 + 0.3
+
+2-Element Yagi:  DE = 11.6' 0.75" diameter aluminum; RE = 12' 0.75" diameter aluminum
+
+Type           QLoad           Gain             Front-to-Back                   Impedance
+                                dBi              Ratio dB                         R±jX
+C-L             Inf.            6.20             20.0                           17 - 0.7
+C-L              50             4.21             13.2                           22 - 3.9
+C-L             100             5.14             15.8                           19 - 2.4
+C-L             200             5.65             17.6                           18 - 1.6
+C-L             300             5.83             18.3                           18 - 1.3
+L-L             ---             5.82             18.4                           17 - 2.8
+C-L            DE=200           5.02             13.2                           19 - 3.9
+               RE= 50
+C-L            DE= 50           4.84             17.6                           22 - 1.6
+               RE=200
+
+Notes:  C-L = center-loaded; L-L = linear-loaded.  All values taken from models in free space and
+include materials losses (aluminum).  As an indicator of loading coil losses, QLoad=XL/RL.  XL for
+DE=250 Ohms; for RE=257 Ohms.  Antennas L-L are linear-load with a 4' loading element of #12 wire in a
+vertical plane, with the upper wire 1.2" below the main element and the lower wire 1.2" below the upper
+wire.
+
+Table 1.  A comparison of gain and other properties of center-load and liner-loaded dipoles and Yagis.
+

Table 1 summarizes two such exercises, one for 12' aluminum dipoles at 28.5 MHz, the other for a 2-element Yagi of similar element length at the same frequency. The table shows Qs of 300, 200, 100, and 50 as typically realizable values, although sustaining an inductor at a Q of 200 or more in outdoor conditions is unlikely. A Q of 100 is more likely. Note the decrease in performance with the decrease in Q for both the dipole and the Yagi.

+
+ +
+
+ Fig.1 A schematic diagram of a dipole element with linear loading. +
+

A linear load is simply a folded continuation of the main element, usually (but not necessarily) of a lighter (hence, thinner) material, as shown in the dipole sketch in Fig. 1. Linear loading can be introduced anywhere along an antenna element, including current and voltage maxima points, but we shall restrict our focus here to current nodes, that is, to the center point of 1/2 elements. Although there are numerous reports of empirically generated antennas using linear loading, little has been quantified in amateur literature.2 As a start toward this goal one may juxtapose linear-loaded dipoles and Yagis with their center-loaded counterparts. For comparison with the center-load models of both dipoles and Yagis in Table 1, I added a linear-load model with #12 wire extending 2' either side of the element center in a vertical plane below the main element. The upper wire is 1.2" below the main element, and the lower wire is 1.2" below the upper wire.

+

A model of the linear-loading element is only approximately comparable to the model of the center-loaded element because of differences in modeling conventions. A loading inductor (or capacitor) is treated in both NEC and MININEC as a nonradiating item inserted into the structure. By contrast, the linear-loading structure is part of the overall radiating structure of the antenna. Moreover, since most versions of MININEC permit but one material, the models are all-aluminum, even though in practice the linear-load element will usually be copper. Nevertheless, figures for the linear-loaded model given in Table 1 are roughly comparable with the center-loaded results and indicative of relative performance. In both cases, the material losses of the main aluminum element are included in the model.

+

Whether a dipole or a Yagi, the gain of linear-loaded elements tends to surpass that of the corresponding center-loaded elements by a significant amount. So, too, does the front-to-back ratio of the Yagi model. If we assume that a Q of 100 is a reasonable and sustainable figure for a center-loading inductor, then linear loading becomes a very attractive alternative in shortened horizontal antennas. It generally requires a center-loading coil Q of 300 or better to reach the performance of a linear-loaded Yagi.

+

The last two entries under the Yagis in Table 1 are included to demonstrate the effects of losses should only one of the Yagi's two elements exhibit more than design losses, perhaps due to weathering. Reduction of reflector Q results in a lower front-to-back ratio and a higher reactive component to the feedpoint impedance. In contrast, reduction of the driven element Q results in a lower antenna gain and a higher resistive component of the antenna feedpoint impedance. Understanding these differences can be an aid to trouble shooting antenna problems.

+
+ A Preliminary Method of Calculating Linear Loads +
+

The resemblance of a centered linear-loading element to a transmission line is no accident. In fact, each half of the linear-loading element can be viewed as a shorted, inductive transmission line stub, and this view provides a basis for approximate calculations of the element length. Each half of the element represent a reactance, and the two halves are in series.

+

The designer can derive the required total reactance of a shortened dipole by simply using MININEC or NEC to model the short element at the desired frequency. Alternatively, one can measure the feedpoint impedance of an actual main element without loading. The capacitive reactance at the feedpoint requires exact compensation by an equal inductive reactance provided by either a center loading coil or, as here, a shorted length of transmission line.

+

Materials for a linear-loading element are a matter of designer preference within the limits of good structure. Given the selection of wire, rod, or tubing for the linear load, the process of calculating the linear load begins by determining the characteristic impedance, Zo, of the proposed load line, using the standard approximation,

+
+ +
+

where S is the spacing between the wire centers and d is the wire diameter, both in the same units.3

+

From the value of Zo and the desired reactance, determine the line length in electrical degrees, LE, from the equation,

+
+ +
+

where XL is the total desired reactance. The doubling of Zo in the denominator provides for the length of each half of the linear loading element. Converting the length into feet requires the design frequency, FR, the assumption of a velocity factor of 1, and the equation

+
+ +
+

Remember to double the length for the full element.

+

The utility of this calculation procedure is limited. There are two generally popular geometries for constructing linear-loaded center elements. Fig. 2 compares the "end-on" appearance of vertical-plane geometry with triangular geometry. Because the load lines of the triangular arrangement are usually equi-spaced from the main element, the transmission-line calculation produces useable results as a first approximation for building. However, the vertical-plane geometry places one "side" of the transmission line closer to the main element, thus disrupting the presumed equal currents and voltages essential to the calculation's accuracy.

+
+ +
+
+ Fig. 2. Vertical-plane and triangular geometries for linear-loading sections. +
+

Calculations of triangular linear load elements correspond in the main with models of fully structured antennas within about 2 to 3 percent. Because of limitations in modeling linear-loaded antenna structures, the calculations are as good as the model as a guide to building.4 However, transmission-line calculations vary from modeling results for vertical-plane antennas by 15 to 30 percent, depending upon the particular line size and spacing. The calculations tend to call for radically shorter linear load elements than actually needed. To get a handle on vertical-plane linear loading arrangements requires a different technique.

+
+ Calibrating Vertical-Plane Linear Loads +
+

A standard Yagi element or a dipole antenna shows a set of currents that decrease continuously but not linearly from the feedpoint, since the elements are roughly resonant. An element with a linear-loading element has an overall wire length (counting both the element tube and the load wire) that is longer than a half wavelength. Hence, the current rises as one moves away from the feedpoint, reaching a secondary maximum over halfway out the loading element and reaching a primary maximum on the way back in toward the junction with the tube. The inequality of currents in the outgoing and incoming wires of a vertical-plane linear-loading element verifies that the loading element is not acting as a pure transmission-line element. The current along the element does not rise much and the tube-to-load element junction shows over 99% of the current. Essentially, the radiation produced by the currents in the loading element cancel, leaving the tube element radiation to dominate the far field pattern. Cancellation is not perfect, thus leaving a high current level over a greater length of the antenna element than with lower-Q center loading schemes.

+

Correlating models of linear-loaded dipoles with center-loaded counterparts permits a rudimentary calibration of linear-loaded dipole of both vertical-plane and triangular geometries. Free space models of fixed-length main elements with variable linear loads were checked for resonant frequency as indicated by a near-zero reactance. Then, using the same frequency, an equivalently long dipole of the same material was center loaded to resonance by the same test. The requisite reactance became the center-load lossless-inductor reactance for the linear load. Flipping between copper and aluminum elements (both tubing and linear-load wire) produced no change in the resonant point. As noted above, the modeling process is subject to certain limitations of both MININEC and NEC.

+ 
             Sample table of linear-loaded dipoles listing gain, feedpoint impedance, resonant
+                      frequency, equivalent center-load reactance, and approximate Q
+
+                               Antenna element = 12' 0.75" diameter aluminum
+       Linear load = #12 wires spaced 2" (0.167') from antenna element; 2" (0.167') from each other
+                             Antenna-to-linear load geometry:  vertical plane
+
+Linear load    Gain            Z (R±jX)       Resonant        Equivalent            Approximate
+length - ft     dBi             Ohms          Frequency      Center-load             equivalent
+                                                 MHz          Reactance                  Q
+                                                                 Ohms
+
+0 (self-        2.13       72.2 + 0.01         38.94           -----                  -----
+resonance)
+1               2.01       49.4 + 0.00         35.04            85.4                   225
+2               1.94       37.4 - 0.02         31.84           157.7                   303
+3               1.85       29.6 - 0.00         29.34           217.4                   294
+4               1.78       24.4 - 0.01         27.12           273.9                   326
+5               1.69       20.7 - 0.00         25.20           327.2                   327
+6               1.60       18.0 - 0.02         23.58           375.8                   334
+
+Notes:
+1.  Antennas were considered resonant if the remnant reactance was less than 0.05 Ohm.  Figures are
+rounded from 3- and 4-place decimal results.
+2.  Equivalent Q is determined by finding a value of resistance for the center load inductance at the
+given reactance that produces an antenna gain equal to that of the corresponding linear-loaded model.
+Q results are subject to variables of the modeling process and are likely no more reliable than 10 to
+15 percent.
+
+Table 2.  Sample table of linear-loaded dipoles listing gain, feedpoint impedance, resonant
+        frequency, equivalent center-load reactance, and approximate Q.
+

Table 2 provides a sample of the data developed for just one linear-load configuration: a vertical-plane arrangement with a #12 wire spaced about 2" from the main element and 2" apart for a 12' element. The table clearly shows the decrease of gain as the linear element is lengthened, along with the increase in equivalent reactance and the decrease in resonant frequency. Since the goal was to develop dimension figures adequate to the start of home construction, resonance was defined as a remnant feedpoint reactance of less than 0.05.

+
+ +
+
+ Fig. 3. Linear load line equivalent reactances (to a lossless center loading inductor) between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations. +
+

Fig. 3a and 3b show the results of six dual runs on linear elements (1/2 dipoles) of different lengths, materials, and spacing. Each type of element shows a reasonably linear increase in equivalent reactance with increases in length. (Note that the element length is for the folded element; the actual wire length is twice that amount plus connecting leads.) Extrapolation to intermediate lengths and similar but deviant linear-load configurations is possible for other required values of reactance.

+
+ +
+
+ Fig. 4. Equivalent Qs of linear load lines (relative to a center loading inductor) between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations. +
+

Although the equivalent reactance was derived using zero-loss center-loading inductors, an indication of equivalent Q was derived by adding resistance to the inductor until the antenna gain was the same as the linear-loaded model. Table 3 provides the data on equivalent Q-ranges for the linear-load geometries shown in the graphs in Fig. 4a and 4b, with specific data on gain and Q for one typical linear section length. Fig. 5a and 5b provide gain profiles for 6 variations each using 12' and 24' 0.75" diameter aluminum main elements.

+
+ +
+
+ Fig. 5. The gain of dipoles with varying lengths of linear loading between ratios of 1:12 to 1:2 for (a.) a 12' 0.75" diameter aluminum main antenna element and for (b.) a 24' 0.75" diameter aluminum main antenna element for 6 linear-load configurations. +
+ 
                    A comparison of linear-loaded dipoles listing geometry, materials,
+               Q range (for all load lengths), and gain and Q (with a 4' or 8' load length)
+
+Antenna        Geometry &              Range of Q               Gain with               Q with
+   #            Materials             (1-6' length)          4' linear section      4' linear section
+
+                      Antenna element = 12' 0.75" diameter aluminum; load length = 4'
+
+   1           VP, 0.25" rod            1075-355                  1.90                   812
+               sp: 0.25'/0.25'
+   2           VP, 0.125" rod            532-328                  1.82                   487
+               sp: 0.25'/0.25'
+   3           VP, #12 wire              355-267                  1.74                   343
+               sp: 0.25'/0.25'
+   4           VP, #12 wire              334-224                  1.78                   326
+               sp: 0.167'/0.167'
+   5           VP, #12 wire              293-183                  1.82                   293
+               sp: 0.1'/0.1'
+   6           Tri, #12 wire             411-233                  1.80                   411
+               sp: 0.1'/0.1'
+
+Antenna        Geometry &              Range of Q               Gain with               Q with
+   #            Materials             (1-12' length)         8' linear section      8' linear section
+
+                      Antenna element = 24' 0.75" diameter aluminum; load length = 8'
+
+   1           VP, 0.25" rod             739-600                  1.91                   632
+               sp: 0.25'/0.25'
+   2           VP, 0.125" rod            375-229                  1.81                   352
+               sp: 0.25'/0.25'
+   3           VP, #12 wire              256-225                  1.72                   256
+               sp: 0.25'/0.25'
+   4           VP, #12 wire              238-168                  1.75                   232
+               sp: 0.167'/0.167'
+   5           VP, #12 wire              213-138                  1.77                   196
+               sp: 0.1'/0.1'
+   6           Tri, #12 wire             313-185                  1.76                   266
+               sp: 0.1'/0.1'
+
+Note:  VP = linear load elements in vertical plane with antenna element; Tri = linear elements in triangular
+        configuration with antenna element.
+
+Table 3.  A comparison of linear-loaded dipoles listing geometry, materials, Q range (for all load lengths), and
+        gain and Q (with a 4' or 8' load length).
+

Triangular geometry loads do not fully overlap their vertical-plane counterparts. As shown in Fig. 3a and 3b, the close-spaced triangular arrangement of #12 wire turns out to parallel closely the reactance progression of vertically planed #12 wire spaced more widely (0.167' vs. 0.1') or 1/8" rod spaced at 0.125'. However, the equivalent Q of the triangular configuration shows a clear peak at midlength load element sizes, as shown in Fig. 4a and 4b. In common with the vertical plane #12 linear-load configuration, the #12 triangular configuration shows a more rapid fall-off in gain after the 4' point with 12' main elements and after the 6' point with 24' main elements. See Fig. 5a and 5b. The rapid reduction in gain for close-spaced #12 linear-load elements suggests that the break points on the graph represent the limit of their effective use compared to other configurations.

+

Besides the linear relationship between element length and equivalent center-loaded lossless-inductor reactance, certain other trends in Fig. 3, 4, and 5 are noteworthy:

+

1. Spacing: For a given geometry, load-length, and wire size, antenna element gain decreases and Q increases as spacing increases.

+

2. Wire size: For a given geometry, load-length, and spacing, antenna element gain and Q increase as the wire size increases.

+

3. Geometry: For a given load-length, spacing, and wire size, a triangular geometry yields a higher Q than the vertical-plane geometry, but provides less antenna element gain.

+

4. Diameter: As main element and linear section wire diameters decrease relative to a wavelength at the signal frequency, reactance increases slowly and Q decreases.

+

5. Long linear elements: As the ratio of linear-load length to main element length exceeds 5:12, both the equivalent center-load reactance and Q tend to depart from a relatively linear curve. Note that, although the Q curves for 0.125" and 0.25" diameter linear-load elements seem to depart radically from the #12 vertical-plane models, a closer examination of the curves show that they are topographically similar, with a fairly complex magnitude adjustment factor.

+

6. Short linear elements: As the ratio of linear-load length to main element length falls below 1:6, both the equivalent center-load reactance and Q tend to depart from a linear curve, with the Q falling off rapidly.

+

7. Recommended linear element lengths: Between ratios of 1:6 and 5:12 of the linear-load element to the main element, equivalent reactance and Q curves are nearly linear, as is the rate of decrease in antenna element gain with increased linear-load length. As noted, close-spaced #12 linear-load elements depart from this near-linearity of gain and Q beyond certain "break" points, which limit their applicability.

+

One further trend also deserves notice: the longer the loading element (or the higher the reactance of any center-loading means), the lower the resistive feedpoint impedance. Linear-loading elements in the vicinity of one-third the total length of the main element show a resistive component between 20 and 30 , depending upon design. A direct match to 50- coaxial cable is accordingly not feasible, although simple beta, gamma, balun, and transformer matching systems are available. For anyone concerned about the small mismatch that exists between a full size dipole (72 nominal) and 50- coax, a short linear load of 1/12 the main element length is a solution. The result is, in almost any construction mode, a feedpoint impedance within ±5 of the coaxial cable's Zo. Of course, the main element will have to be shortened from full size, but the decreased size produces negligible gain loss (less than 0.1 dB).

+

For shortened Yagi designs or portable field dipoles, a close-spaced linear element approximately 1/3rd the length of the main element represents a good compromise among a number of factors to consider when designing a shortened antenna. It maintains element gain at a high level, while effecting a significant shortening of the overall element length. Specific design objectives, of course, may require a departure from these very general recommendations.

+

The linear-loading section curves developed for 12' and 24' main elements can be used directly for 10- and 20-meter beams by extrapolation. Extrapolations for other bands will be less precise, but sufficient for reasonable construction estimates. A recommended alternative is to create a set of curves for the specific materials to be used in a given project. With almost any antenna modeling program, the task is an evening's work. In the end, no matter how extensive the modeling, home construction techniques will rarely be exact enough with respect to replicating the modeled spacing among the parts of a linear-loaded element to permit building without adjustment. However, the tables and graphs do provide some initial quantitative guidance. For those who prefer to use the transmission-line stub calculations as a foundation for building, Table 4 provides a set of generalized deviance factors for correcting the calculations to correspond with each of the types of linear loads described here. The averaged factor holds for linear-load lengths between about 15 and 40 percent of the main element length. The progressions of correction factors may also serve as a guide to builders using load dimensions outside the range of those analyzed here.

+ 
                        Correction Factors for Using Transmission Line Calculations
+                       With Some Lengths of Vertical-Plane Linear-Loading Elements.
+
+12' Aluminum Main Element Models
+
+        Linear-Load Characteristics:                   Multiply Transmission-Line
+Diameter       Spacing from    Spacing Between         Calculations by This Value
+               Main Element     L-L Elements           to Agree with Modeling Results
+
+#12 (.0808")    0.1' (1.2")     0.1' (1.2")                  1.30
+#12             0.167' (2")     0.167' (2")                  1.23
+#12             0.25'  (3")     0.25'  (3")                  1.15
+0.125           0.25'           0.25'                        1.18
+0.25            0.25'           0.25'                        1.24
+#12             0.1'            0.1' (triangular)            1.05
+
+24' Aluminum Main Element Models
+
+        Linear-Load Characteristics:                   Multiply Transmission-Line
+Diameter       Spacing from    Spacing Between         Calculations by This Value
+               Main Element     L-L Elements           to Agree with Modeling Results
+
+#12 (.0808")    0.1' (1.2")     0.1' (1.2")                  1.27
+#12             0.167' (2")     0.167' (2")                  1.23
+#12             0.25'  (3")     0.25'  (3")                  1.18
+0.125           0.25'           0.25'                        1.21
+0.25            0.25'           0.25'                        1.27
+#12             0.1'            0.1' (triangular)            1.03
+
+Note:  Because MININEC models return slightly long dimensions, coreection factors may be reduced by up to 3%.
+
+Table 4.  Correction factors for using transmission line calculations with some lengths of vertical-plane linear-
+        loading elements.
+
+ Designing a 2-Element Linear-Loaded Yagi +
+

The technique of using center-load reactance as a substitute for a linear-loaded element for dipole modeling carries over into the design of 2-element Yagis. Choosing a set of main element lengths, center-loading them for the desired antenna performance (within the limits imposed by shortening the elements), and replacing the center loads with their equivalent linear-loading elements can produce buildable models. Since changing the magnitude of a center-load inductive reactance is far quicker in all antenna modeling programs than changing the complex dimensions of a linear loading element, the design process is significantly shortened.

+

As a design example, let us select 12' main elements of 3/4" diameter aluminum as the main elements for a 2-element shortened Yagi for a center frequency of 28.5 MHz. A little element juggling, along with the addition of center loads for the elements of about 250 each produced a reasonable design with the following properties: Driven element: 11.6'; reflector: 12.16'; spacing: 4.25'. The extension of the reflector did not violate my intention to use 6' lengths of hardware store aluminum tubing, since construction would place the two lengths about 2" (0.167') apart. The anticipated gain of the array (using a Q of 300 for both loading coils) was 5.8 dBi, with a front-to-back ratio of about 18 dB. The feedpoint impedance of the center-loaded beam calculated by the modeling program was about 17.

+
+ +
+
+ Fig. 6. Free space azimuth pattern for a linear-loaded 2-element beam with close-spaced elements. +
+

The chart for 12' aluminum elements shows a linear-loading element of #12 wire, spaced 0.1' (about 1.2") and 4' long corresponds closely to the 250- center-loading inductors. Substituting the required linear sections into the model yielded a 2-element beam with the same gain, front-to-back ratio, and feedpoint impedance as the center loaded model. Fig. 6 shows the free space azimuth pattern of the beam design. Since modeling an antenna with linear-loading sections requires extensive and careful element segment tapering techniques with MININEC programs, the resultant antenna description is quite large. Those with slower computers or restricted RAM may wish to skip this step and go directly from the graphs to the shop. However, it pays to check an extrapolated design to ensure against errors.

+
+ +
+
+ Fig. 7. Azimuth pattern at 23° elevation for the 2-element linear-loaded beam at a height of 20' above medium real ground. +
+

A 2-element beam, like every other array, will tend to vary in gain and front-to-back ratio at heights above real ground below about 2. As a check on the design, patterns were run at the angle of maximum radiation for heights of 20' and 35', with the results shown in Fig. 7 and Fig. 8. However, as usable as these performance expectations are, this step did not end the design process.

+
+ +
+
+ Fig. 8. Azimuth pattern at 14° elevation for the 2-element linear-loaded beam at a height of 35' above medium real ground. +
+

Because one of the main uses for shortened antennas is for portable field operations, I anticipated building the linear-loaded Yagi so as to make it transportable. Under these conditions, it is possible to add to the reflector a tuning capacitor remotely placed some multiple of a half wavelength from the antenna and connected by a suitable length of parallel feeder (450-, in this case). This required lengthening the linear element of the reflector purposely to make it inductive. Lengthening the linear section of the reflector to 5' (2.5' either side of center) permitted the use of loading capacitance between about 50 and 95 pF to retune the reflector back to maximum front-to-back ratio.

+

A second design modification was required by the use of a beta-match to convert the 17- feedpoint impedance to the 50- coax value. Shortening the driven element linear section to 3.7' (1.85' either side of center) yielded the requisite 23 ohms of capacitive reactance in the driven element to go with the 32.7- inductive reactance across the feedpoint terminals (0.18 uH or about 4 turns of #12 copper wire, 1/2" in diameter and 1/2" long at 8 turns per inch).5 Fig. 9 shows the general scheme of the beta match applied to the linear-loaded antenna.

+
+ +
+
+ Fig. 9. General scheme of the beta match used with the 2-element linear-loaded beam. +
+

These modifications for portable use actually improve one aspect of the antenna's performance: the SWR bandwidth. Fig. 10 is a graph of the SWR bandwidth of several antennas, all of which use the same main element dimensions: center-loaded Yagis with Qs of 300 and 100, the unmodified linear-loaded antenna, and the modified version for portable use. That the linear-loaded antenna is equivalent to a center-loaded beam with a Q well over 300 is obvious from the steepness of the SWR curve below the design frequency. The curve for the remotely tuned portable version shows a greater symmetry, with about 700 kHz of usable (<2:1) SWR bandwidth at optimum front-to-back ratio.

+
+ +
+
+ Fig. 10. Calculated SWR bandwidth for center- and linear-loaded Yagis. +
+

Actually, the antenna will tune within a 2:1 SWR across the entire first MHz of 10 meters. However, the front-to-back ratio will degrade at the band edges. Fig. 11 is a composite pattern of a fixed-reflector model between 28 and 29 MHz. Fig. 12 shows the composite free space azimuth pattern of the remotely tuned version over the same spectrum. The minor retuning required for bringing the SWR into the 2:1 range at the band edges does not reduce the front-to-back ratio very much.

+
+ +
+
+ Fig. 11. Composite free space azimuth pattern for a fixed-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz. +
+
+ +
+
+ Fig. 12. Composite free space azimuth pattern for a remotely-tuned-reflector linear-loaded 2- element Yagi from 28.0 to 29.0 MHz. +
+

Tuning the reflector actually improves the front-to-back ratio over real ground relative to a fixed-reflector free-space-derived model. Fig. 13 and 14 show composite patterns for the first MHz of 10 for 20' and 35' elevations respectively, with the reflector in each case tuned for maximum front-to-back ratio. These patterns and numbers, of course, are anticipations bred from models. The final question is whether they can be realized.

+
+ +
+
+ Fig. 13. Composite 20'-height azimuth pattern for a remotely-tuned-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz. +
+
+ +
+
+ Fig. 14. Composite 35'-height azimuth pattern for a remotely-tuned-reflector linear-loaded 2-element Yagi from 28.0 to 29.0 MHz. +
+
+ Constructing and Testing a Test Model +
+

Building a linear-loaded beam for portable field use (10-meter hilltopping) is not difficult, because the elements are light. The basic dimensions are these: Driven element: 11.6'; reflector: 12.16'; spacing: 4.25'. Four 6' lengths of 0.75" diameter tubing from the local hardware outlet provided the main elements. With a 2" center spacing, the reflector lengths are correct as purchased, but the driven elements were cut to 5'8" each.

+
+ +
+
+ Fig. 15. The basic element-to-boom assembly of the test 2-element linear-loaded Yagi with details of the linear load support plate at the main element center point. +
+

The element-to-boom plates are 1/2" plywood, about 6" to 7" wide and 2' long. As shown in Fig. 15, excess wood was removed from the corners for minimum weight. Each plate was coated with car-repair epoxy for fiberglass patching. This material is more weather-resistant than any other I have found. #10 stainless steel nuts, bolts, and lock washers fasten the element to the plate. (Small U-bolts are recommended for larger antennas.) Since the boom is a 5' section of 1 1/4" nominal diameter Schedule 40 PVC, 1 1/2" U-bolts make the plate-to-boom connection.

+

The plate-to-boom U-bolts also hold another fixture: the center supports for the linear-loading wire. The test antenna uses #12 solid copper wire linear sections in two pairs: two 2'6" sections for the reflector and two 1'5" sections for the driven element. Each section attaches to a thick plastic plate angled from the outer U-bolt inward, as shown in Fig. 15. A heavy plastic freezer box a little over 4" square and 1" high provided two plates that had the correct angle to place the linear-load wires directly under the main element when mounted to the outer U-bolts. The composition of the plastic ensures good weathering characteristics, and no RF problems have surfaced.

+

Wires a little over twice each section length were straightened and then bent over a piece of 1 1/4" mast to establish the spacing. Before mounting, I slipped mid-length and end supports over each wire loop. I cut eight 4" by 4" squares from the corners of a squared-off half-gallon plastic jug. On each side of each corner I used a hole-saw to cut 3/4" circles for the main elements and then drilled 1/8" holes for the linear-load wires. Squeezing the corners allows the wire and the main element to pass through each pair of holes. Releasing the corners places the assembly under tension, which keeps the main element and the linear-loading wires aligned. Local storm winds have not moved this assembly, but something stronger is recommended for larger or more permanently mounted antennas.

+

Solder rings on the ends of the linear-load wires attach the section to bolts (#10 stainless steel) on the center plastic plate. Short #12 wires, also with solder rings provide a junction between the wire assembly and the main aluminum element. Before attaching solder rings to wires, I usually let solder flow all over the ring, since many types will rust in the weather.

+

The driven element linear section terminates its lower center in a coaxial chassis connector mounted on the plastic plate with the threads facing the mast. A ferrite bead or shield 1:1 balun taped to the boom allows the coax to be run inside or outside the mast, in my case, sections of TV mast. The beta match coil mounts across the plate-to-linear-wire bolts with solder rings. The reflector section center terminates in two pin jacks. For initial testing, a capacitor with mating pins connects at the element. For field use, a half wavelength of 450 parallel feeder terminated at one end with pins and at the other with pin jacks places the capacitor within easy reach for remote adjustment with 20' of mast. A series of plastic spray can tops, each punched with 4 holes for cable ties that clamp the mast and the feeder, space the feeder from the mast.

+

For testing, solder rings can be omitted from the linear section wires until the correct length is determined. Clamping the wires under washers at the plate will suffice for initial tests. The object is to obtain the lowest possible SWR at the center design frequency by first tuning the reflector capacitor for a minimum reading and then spreading or compressing the beta match turns for a final null. Adjust the length of the wire section to bring the null frequency to the design center. If initial test are close, then minor adjustments can be made by squeezing or spreading the linear wire sections (using the bottom wire only): squeezing lowers reactance and raises the frequency, while spreading increases reactance and lowers the frequency. If significant wire deforming is required, adjust the length instead.

+

Off center frequency, do not adjust the reflector capacitor for absolutely the lowest SWR. Instead, find the lowest SWR point and then slight off-tune the capacitor (within a 2:1 SWR ratio) in the direction of the setting for the antenna's design center frequency. That will establish a point closer to maximum front-to-back ratio in the absence of a reference signal. Refer to the SWR bandwidth graph for guidance.

+

The test antenna built to the specifications provided by the graphs and models performed to expectations. As indicated, the linear-loading element on the driven element was somewhat long, partly because the models yield slightly long dimensions and partly because the spacing used was slightly wider than the model for horizontal plane #12 wire elements at 0.1' spacing. Removing 3' of load wire on each side of center brought the antenna to resonance. The reflector element was also somewhat long, requiring a less capacitance than specified. At the design center frequency of 28.5 MHz, 27 pF brought the antenna to maximum front-to-back ratio. Matching required only a small adjustment of the beta-match coil, a matter of squeezing the turns slightly.

+

With a fixed reflector loading capacitor, the 2:1 SWR bandwidth of the antenna was slightly over 300 kHz, confirming its high Q. A variable capacitor in the reflector increased the bandwidth to nearly 1 MHz, with over 750 kHz of that bandwidth at maximum front-to-back ratio. Performance tests at a 20' height with local line-of-sight signals confirmed about 3 S-units of front-to-back ratio, although these rough tests cannot be equated with the elevated patterns shown in various figures. Nonetheless, they strongly suggest that the antenna performs close to its modeled specifications.

+

The 2-element linear-loaded Yagi has proven to be a most satisfactory field antenna. Although the linear load assembly on the elements requires some care, once assembled, it is almost as carefree as a full size 2-element Yagi. The added front-to-back ratio shows up in practice, while the half-dB reduction in gain does not. In a fixed-tuned model, the chief drawback is the narrower usable bandwidth: that configuration is most useful where the operator tends to use a small portion of the band. The field version with a tunable reflector overcomes this limitation in large measure, making this antenna a good competitor with a full-size 2-element Yagi.

+

In addition to yielding a buildable antenna, the modeling that has gone into the development of the linear-loaded Yagi demonstrates something else. Antenna modeling programs are not restricted to providing pattern-pictures of existing antennas. With proper care, they can be used to generate a considerable body of adjunct data of use to antennas builders. The calibration of linear-loading elements is but one example of techniques that can expand the utility of such programs. The more we can interconnect the direct data produced by such programs with other collections of data that are important to antenna design, the better we can understand the antennas we use. Whether this result or the development of linear-loaded Yagis is the more important result of the investigation is a question for fireside, coffee-cup debate on cold evenings when the bands are closed.

+
+ Notes +
+

1 For more expert information on the construction of full size Yagis, see Leeson, Physical Design of Yagi Antennas (Newington: ARRL, 1992).

+

2 For example, see pages 6-7 and 6-8 of either the 16th or 17th Edition of the ARRL Antenna Book. See also pp. 11-22 and 11-23 of the 16th Edition for W0YNF's linear-loaded 14-MHz driven-element-director Yagi, which uses triangular geometry. A linear-loaded 40-meter dipole also appears in Orr and Cowan, Beam Antenna Handbook (Radio Publications, 1990), pp. 58-59. It uses vertical-plane geometry.

+

3 For somewhat greater accuracy, especially with large wires and close spacing, substitute for the given equation, the following:

+
+ +
+

4 Both MININEC 3.13 and NEC 2 are subject to systematic errors when combining elements of differential radii in complex geometries. The models used in this study are fully-tapered MININEC models. By extensive comparisons with various modeling techniques, including the use of single-wire-size substitutes for various parameters, the utility and general validity of the MININEC models was established. However, the linear-loads called for by those models may be up to 2 to 4 percent long, which closes the apparent gap between transmission-line calculations and the models. Nevertheless, extensive modeling, including modeling the antennas listed in note 2 above, establishes that triangular and vertical-plane geometries are not interchangeable without lengthening the linear-load element. Elements modeled in free space on W0YNF's dimensions and triangular geometry show a feedpoint reactance at 14.2 MHz of less than -10 , although a similar close-space vertical geometry model with the same dimensions show nearly -60 reactance (indicating a need to be longer to achieve resonance). Similarly, the vertical-plane geometry of the Orr dipole for 40 meters required a #12 wire linear load almost 8 feet longer than a #12 wire triangular linear load to achieve resonance with a 44.2-foot 1-inch diameter aluminum main element. The calculated triangular linear load modeled within 3- reactance of resonance.

+

5 A beta match is a form of L-section match in which the series capacitor is created by shortening the antenna element. A shunt coil completes the section that matches an antenna impedance of less than 50 to the higher impedance of the coaxial cable. Formulas for L-sections appear in almost any handbook. Designing an antenna for resonance on a modeling program and then shortening the driven element by an amount that yields the required value of capacitive reactance provides guidance for building the driven element, usually within limits that permit final adjustment by spreading or compressing turns in the shunt coil. A "hairpin" section of shorted transmission line can also make up the shunt inductor, usually with smaller losses, although the coil's lower Q permits a wider bandwidth. See the ARRL Antenna Book, 16th or 17th Edition, pp. 26-21 to 26-23, for further details, and be sure to read Thomas Cefalo, Jr., WA1SPI, "The Hairpin Match: A Review," Communications Quarterly (Summer, 1994), 49-54, and Gooch, Gardiner, and Roberts, "The Hairpin Match," QST (April, 1962), 11-14, 146, 156.

+
+ +
+
+ Appendix: How Short Can We Go? +
+

After developing the data and model antenna for linear loading, I ran across an article on a 10-meter 2-element Yagi that used 8' elements on a 4' boom with center-loading and a beta hairpin match.1 That led me to wonder how short we might make a Yagi, given that shortening elements permits an increase in front-to-back ratio at the expense of some gain. The results are interesting and worth passing on.

+ 
Modeled Performance of Shortened 10-Meter Dipoles
+
+
+Antenna         Load            Feed                            Gain in dBi
+
+Length (ft)      XL          Z               ------------------------ Q= -----------------
+                (Ohms)          (Ohms)          ---     500     400     300     200     100
+
+16.54
+(full size)       0             70.9            2.12
+
+14'             131             43.0            2.02    1.98    1.97    1.96    1.94    1.83
+
+12'             247             28.4            1.93    1.86    1.84    1.81    1.75    1.57
+
+10'             366             18.1            1.87    1.70    1.66    1.59    1.46    1.07
+
+8'              510             10.7            1.83    1.43    1.34    1.19    0.90    0.14
+
+6'              697              5.7            1.79    0.83    0.62    0.29    -0.29   -1.70
+
+Table 1.  A comparison of the modeled performance characteristics of shortened center-loaded dipoles on 10-meters.
+

Beginning with center-loaded dipole performance, I modeled 0.75" aluminum elements ranging from full size (16.54') down to the point where gain in dBi fell below zero (6'). Table 1 summarizes the data, while Fig. 1 displays it in graphical form. The dipoles were initially modeled using infinite Q (0.0 Ohms resistance) and then rechecked at Qs of 500 down to 100. The infinite-Q reading provides a measure of the natural drop in basic gain as the antenna element becomes shorter. The finite Qs provide a measure of the losses incurred by center-loading the element to resonance with an inductor (or even a linear-loading element). Note the shape of the curve as the Q decreases linearly.

+
+ +
+
+ Fig. 1 A comparison of the gain and the Q of a center-loading inductor for shortened 0.75" aluminum dipoles at 10 meters. +
+

Although conventional, registering comparisons in terms of one gain figure as a percentage of another may not be greatly informative in making comparisons. Negative gains relative to an isotropic source are possible and do represent radiation by the antenna. The real question is whether the gain of any configuration is adequate to the job to which the antenna is assigned or whether something better may be available. The graph may give a better sense of the manner in which an antenna with decreasing length and centerload-Q may likely disappoint the builder if a full-size dipole is the standard of comparison.

+

Applying the dipole data selectively to full-size and shortened center-loaded 2-element Yagis produced the data in Table 2. The full-size Yagi used the 4' boom specified for the 8' model and is only a slight variation on the standard used throughout these tests. Models with 8' elements and with 12' elements were run at Qs from infinity to 100 to gauge the performance possibilities of half- and three-quarter-size antennas. With both shortened antennas, the front-to-back ratio is superior to a full-size 2-element Yagi at a cost in gain and SWR bandwidth. However, the 12' model shows a decrease in front-to-back ratio as the Q decreases, while the 8' model increases the front-to-back ratio with Q decreases down to 200.

+ 
Modeled Performance of Shortened 2-Element Yagis
+
+Antenna                         Gain            Front-to-Back           Feedpoint
+  and                           (dBi)            Ratio (dB)             Impedance
+ Load Q                                                                   (Ohms)
+
+Full-size Yagi1                      6.63             11.27                  29.9
+
+12' Elements
+ ---                            6.24             21.22                  16.7
+ 500                            6.01             19.98                  17.2
+ 400                            5.95             19.70                  17.3
+ 300                            5.86             19.25                  17.6
+ 200                            5.68             18.43                  18.0
+ 100                            5.17             16.38                  19.3
+
+8' Elements
+ ---                            5.76             13.69                  11.0
+ 500                            4.88             16.93                  12.1
+ 400                            4.68             17.92                  12.4
+ 300                            4.36             19.80                  12.8
+ 200                            3.78             24.96                  13.7
+ 100                            2.34             21.83                  16.2
+
+Note 1:  All antennas modeled with 0.75" aluminum elements and a 4' boom.  Full size antenna:
+DE = 16.08'; Refl = 17.49'.  All driven elements resonated, although in practice, the matching
+system may require a different length or load.
+
+Table 2.  A comparison of modeled performance characteristics of center-loaded shortened 2-element Yagis.
+

Fig. 2, 3, and 4 provide frequency-swept azimuth patterns in free space for the full-size, the 12' and the 8' models respectively. The full-size model, as expected, shows a consistent rear pattern throughout the 28 to 29 MHz range. In contrast, the rear pattern of the 12' model shows the narrow bandwidth of the maximum front-to-back ratio point, with usable front-to-rear ratios from 28.25 to 29 MHz, as compared to the full-size model. The rear pattern of the 8' model deteriorates much more quickly as the frequency departs from the 28.5 MHz design center. At 28.0 MHz, the antenna is essentially a lossy dipole.

+
+ +
+
+ Fig. 2 Free-space azimuth patterns for a full-size 2-element Yagi from 28 to 29 MHz. +
+
+ +
+
+ Fig. 3 Free-space azimuth patterns for a shortened 2-element Yagi with 12' elements and inductive center loading having a Q of 300. The largest rearward lobe occurs at 28 MHz, with the smallest rearward lobe occurring at 28.5 MHz. +
+
+ +
+
+ Fig. 4 Free-space azimuth patterns for a shortened 2-element Yagi with 8' elements and inductive center loading having a Q of 300. The largest rearward lobe, along with the diminished forward lobe, occurs at 28 MHz, with the smallest rearward lobe occurring at 28.5 MHz. +
+

That the patterns of the shortened Yagis degrade more quickly below design center is also reflected in the SWR bandwidth curves shown in Fig. 5. Even the full size Yagi shows a steeper SWR curve below design center than above. The 12' model is well off match at 28 MHz, while the 8' model reaches a similar departure from match only 250 kHz below design center. The curves suggest that the antennas are best designed for a lower center-frequency, since the SWR increases slowly above that frequency. However sound that conclusion may be with respect to the full-size Yagi, it tells only part of the story with respect to the shortened models: one must also account for the degrading front-to-back ratio as the frequency departs upward from center.

+
+ +
+
+ Fig. 5 A comparison of the SWR bandwidths of full-size and shortened Yagis with 12' and 8' elements. The shortened Yagi loading coils are assigned a Q of 300. +
+

Do the numbers condemn the shortest model? Not necessarily. Whether a particular antenna is right to build depends upon a collection of factors that perhaps only the user can balance. A full-size 2-element Yagi exhibits good gain within its class, about 2 S-units of front-to-back ratio, and a broad bandwidth, all at the expense of a larger physical structure. The 12' model shows a decreased bandwidth with respect to front-to-back ratio and SWR, but it maintains reasonably good gain and up to 3 S-units of front-to-back ratio with a size only three-fourths that of the full-size Yagi. The 8' model holds the appeal of a truly portable Yagi with some gain and 3 S-units of front-to-back ratio at its design center frequency. However, its gain is significantly reduced and its bandwidth is quite narrow. Moreover, with a feedpoint resistance in the neighborhood of 12 Ohms, the ratio of loss resistance to radiation resistance is much increased. Nevertheless, a small antenna with some gain over a dipole and a good front-to-back ratio over a narrow bandwidth can have many uses.

+

Both shortened antennas were modeled for patterns and SWR bandwidth curves at a centerload Q of 300, that obtainable on the 12' model with a linear-loading element. It is dubious whether such a Q could be sustained for either the 12' or the 8' model with inductive loading. Connection losses, weathering losses, and other factors are likely to reduce the Q of even the most elegant loading coil assemblies to levels below 100 unless the antenna is often cleaned or is operated within a protected environment. Unfortunately, as Table 2's data would suggest, these further reductions in gain might make the antenna less attractive as it weathers. However, for portable use--where assembly and disassembly provide reminders to clean all connections--the antenna may have its niche in the array of antennas in amateur use.

+

Like almost every other final evaluation question we have encountered, the inquiry, "How short can we go?" has no single reply. User needs, competing designs, parts availability, and building skills all contribute to the final answer for each ham.

+
+ Notes +
+

1. Glenn Blackwell, K4HJJ, "A Half-size Two Element Beam with a Full Size Punch," 10-10 International News, 33 (Spring, 1995), 6.

+
+ +
+

Return to Article Index Page

+

Topics: HF Upper, Loading, Small Beams, Yagi


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+

Modeling and Understanding Small Beams

+

Part 5: The ZL Special

+

L. B. Cebik, W4RNL

+
+
+ +

+
+

When George Prichard (ZL3MH, later ZL2OQ and unfortunately recently deceased) introduced the amateur population in 1949 to 2-element horizontal phased arrays, they promised to overcome all the shortcomings of early home brew Yagis.1 Early experimental results by F. C. Judd, G2BCX, who dubbed the antenna the "ZL Special" in honor of Prichard's work, seemed to indicate gains as high as 7 dBd and front-to-back ratios as high as 40 dB.2 Moreover, the antenna was relatively simple to construct: 2 half-wave elements separated by about 45 degrees relative to the frequency of choice and connected by a phasing transmission line with a half twist would produce an array phased 135 degrees with maximum gain and a deep null to the rear. Fig. 1 shows the general outline of the antenna, which may use either straight dipoles or folded dipoles.

+
+ +
+
+ Fig. 1. The basic construction of a ZL Special horizontal 2-element phased array. +
+

The variability of success in replicating the claimed results has been exceeded only by the variability of explanations of what happens to make a ZL Special work. Moxon and Lewallen have pointed out that the success of any phased array depends not upon shifting the impedance of an element, but upon establishing correct current magnitude and phase angle relationships between the two elements. Indeed, Moxon found that successful ZL Specials were more likely the result of accident than engineering, although Lewallen succeeded in designing replicable and reliable equal-length element models using "twinlead" for use as "Field Day Specials."3

+

It would be easy to lose ourselves in the fascinating history of misconceptions of the ZL Special within the amateur community. However, let's look instead at a (not THE) conception of the ZL Special that in fact permits one to design an antenna that will work as predicted. The design technique will combine data supplied by antenna modeling programs, such as NEC and MININEC, with some further algebraic analysis to produce an accurate model of both the geometric and phasing dimensions of the ZL Special problem.

+
+ The Background for ZL Special Analysis +
+

We can reduce the ZL Special problem to an orderly series of propositions and explanations. The following notes are an outline of that process.

+ 
+                     Wide-Band 2-Element Yagi Performance
+       
+Antenna                Driven Element   Reflector     Element       Material
+Dimensions                Length         Length       Spacing       Aluminum
+DE + Ref                   16.0'          17.5'         4.3'         1" dia.
+       
+Free Space:
+       
+Frequency (MHz)            28.00         28.25         28.50         28.75         29.00
+Gain (dBi)                 6.7           6.5           6.3           6.1           5.9
+F-B ratio (dB)             10.3          11.0          11.2          11.0          10.6
+Impedance (R±jX)           24 - 17       28 - 8        32 + 1        36 + 9        40 + 18
+       
+35' over real medium earth:
+       
+Frequency (MHz)            28.00         28.25         28.50         28.75         29.00
+Gain (dBi)                 12.1          11.9          11.7          11.5          11.4
+F-B ratio (dB)             11.7          12.5          12.5          11.9          11.1
+Impedance (R±jX)           26 - 18       30 - 9        34 + 0        38 + 8        42 + 16
+
+Table 1.      Performance characteristics in free space and at 35' over real medium earth of a
+              wide-band 2-element Yagi using a driven element and a reflector.
+
+

1. The significant reason for phasing 2 horizontal half wavelength elements is front-to-back ratio, not gain. Two phased half wavelength horizontal elements will not significantly exceed the gain of a 2-element Yagi. For reference, the performance figures of the modified W6SAI beam, used as our stand throughout this series, appear in Table 1. Although 2-element Yagis with higher gain are possible, they sacrifice even the modest front-to-back ratio of the Orr beam.

+

The rational for designing a phased array is to improve the front-to-back ratio of the antenna for QRM reduction. Phasing promises, in the abstract, to produce a deep rear null, while preserving the gain obtainable with a 2-element Yagi. Fig. 2 compares the plots (35' above real ground) of the reference Yagi and a modestly well-designed ZL Special.

+
+ +
+
+ Fig. 2. Comparison of azimuth plots for the reference Yagi and a ZL Special at 28.5 MHz, 35' above real medium earth. +
+

2. We may think of the ZL Special as a "-45 degree" antenna. Traditionally, we have conceived of the ZL Special as two parallel horizontal elements connected by a short (about 45 degrees) phaseline with a half twist. Thinking in impedance terms, where all values reappear every half wavelength, we subtracted the half-twist line from 180 degrees to obtain 135 degrees phasing. However, we can make two modifications to this traditional view.

+

First, we may think of the antenna in terms of current phase shifts rather than impedance phase shifts. Current magnitude-phase combinations occur only once per wavelength along a transmission line. Although full length 135° lines will achieve the desired phasing for well-designed models, a 45° length of phaseline with a half twist is not the equivalent of a 135° line with respect to current.

+

Second we may for modeling purposes move the half twist of the phase line anywhere along the line, including at the point of junction with the rear element. In modeling terms, this move means twisting the element. In practical terms, if the front element is modeled in increasing length values (for example, from -8' to +8'), then the rear element is modeled in decreasing values (for example, from +8' to -8'). The two elements are 180° out of phase, and connected by an untwisted 45 length of phaseline.

+

With respect to the front element, the rear element is ideally current phased -45° (or 315°). The model will now return correct values for calculating voltage and current along the phaseline, with no change in the impedance transformation. However, as we shall see, impedance transformation is largely incidental to understanding the ZL Special.

+

3. For any two close-spaced near-resonant elements, there is a value of current magnitude and phase for each element that will yield a deep null to the rear. The values of current phase relative to the front element are roughly proportional to the spacing between elements. Fig. 3 shows in graphic form the results of modeling half wavelength elements for maximum front-to-back ratio. The precise angles required by the front and rear current will depend to some degree on the antenna geometry and thus may vary slightly from those graphed.

+
+ +
+
+ Fig. 3. Graphic representation of the relationship between ZL Special element spacing and the phase angle required for maximum front-to-back ratio. +
+

The first consequence of the graph is to dispel the idea that the 2-element horizontal phased array is in any sense either a 135° or a -45° antenna. Within reason, there is a continuum of usable spacings and phasings. Consequently, the rationale for using wide-spaced planar folded dipoles for elements is lacking, and computer models can detect no advantage for that geometry.

+
+ +
+
+ Fig. 4. Front-to-back ratio vs. phase angle for two-element arrays. +
+
+ +
+
+ Fig. 5. Front-to-back ratio vs. current ratio at element feedpoints for two-element arrays. +
+

The second consequence of the graph is to indicate why many hams obtain usable results from casually designed ZL Specials, even if somewhat off the critical marks. Fig. 4 and Fig. 5 graph the results of modeling phased arrays at increasing departures from the optimal current phasing and the optimal current magnitude (relative to a front element current value of 1 at 0). If we arbitrarily set 20 dB front-to-back ratio as the minimum mark of an improved 2-element array relative to the standard Yagi, then ZL Specials may depart considerably from optimal values and still meet the criterion.

+

4. NEC and MININEC models using separate front and rear element sources are "forced" and may not be amenable to phaseline construction. By judiciously arranging the antenna geometry (element length, diameter, and spacing) and the relative current magnitudes and phase angles, we may obtain a deep rear null in many antenna models. In general, such antennas rarely translate into arrays that work with phasing lines of the ZL Special sort.

+

Virtually any forced or 2-source model can be built successfully under that condition that each element can be supplied with the correct magnitude and phase angle of current. Perhaps the only practical way to achieve this goal is through a lumped-constant network. ZL1LE has provided the analysis that underlies the design of such networks.

+

5. Horizontal 2-element phased arrays with phaselines are heavily interactive at all points of measurement. The basic antenna geometry consists of the element diameters and their lengths (both absolute and relative to each other) and the spacing between elements. Slight variations in any parameter will yield different values (magnitude and phase angle) of voltage, current, and impedance at the element feedpoints. The rear element values undergo transformation along the phaseline, depending upon the characteristic impedance and the velocity factor of the transmission line used. The phaseline front terminal values combine with the front-element values to produce a feedline matching situation.

+

NEC and MININEC 2-source models calculate the feedpoint values of magnitude and phase angle for voltage, current, and impedance for each element. Moreover, for available transmission lines--and for those one might build--we know the characteristic impedance and the velocity factor. Therefore, it is possible to analyze proposed ZL Special designs, to evaluate their feasibility and likely performance, and to adjust the design to a level of satisfactory performance. The following procedure will permit some precision in the process of design.

+
+ Analyzing ZL Special Designs +
+

The analysis of 2-element phased arrays with phaselines is a stepped procedure that uses the values of voltage and current magnitude and phase provided by a 2-source model derived from NEC or MININEC analysis.4 Table 2 lists the meanings of the terms of the following equations as a handy reference. Most 2-source models used to obtain values for the following analysis will normally designate the element 1 current as 1 at a phase angle of 0° and the element 2 current as a set of values optimized by trial. The magnitude of the rear element current will be close to 1 and the phase angle will be close to the value corresponding to the element spacing, as found in Fig. 1. Alternatively, one may use a front element current value of 0.5 and a correspondingly adjusted rear element current close to 0.5. The utility of the alternative will be explained later in the discussion.

+ 
+Equation Terms
+
+Efr    Voltage at the front element; appears as Element 1 voltage in modeling program outputs;
+       corresponds to Ein in general equations for transmission lines
+Ifr    Current at the front element; appears as Element 1 current in modeling program outputs
+Err    Voltage at the rear element; appears as Element 2 voltage in modeling program outputs;
+       corresponds to EL in general equations for transmission lines
+Irr    Current at the rear element; appears as Element 2 current in modeling program outputs;
+       corresponds to IL in general equations for transmission lines
+Zrr    Impedance at the rear element feedpoint
+Iin    Current at the input end of the phasing transmission line; corresponds to Iin in general
+       equations for transmission lines
+Efp    Feedpoint voltage, equals Efr in "perfect" models of ZL Specials
+Ifp    Total current at the antenna system feedpoint
+Zfp    Impedance at the antenna system feedpoint
+Rfp    Resistive component of the feedpoint impedance, Zfp
+Xfp    Reactive component of the feedpoint impedance, Zfp
+Ir2    Recalculated rear element current
+lf    Length in feet
+lm     Length in meters
+ld     Length in electrical degrees
+lr     Length in radians
+ZO     Characteristic impedance of the phaseline
+VF     Velocity factor of the phaseline
+
+Note:  Each term for E, I, and Z will have an associated phase angle, theta.
+
+Table 2.      Terms of equations used in the analysis of horizontal 2-element phased arrays
+              using phaselines.
+       
+
+

1. For any antenna geometry that yields a "perfect" ZL Special, the voltage at the front element feedpoint will be identical to the voltage at the input end of the phaseline connected to the rear element. We may use this fact as a starting point in our analysis of the antenna design, since it provides the necessary third term (in addition to the values of voltage and current at the rear element feedpoint) for calculating either the characteristic impedance of the phaseline or its length, where the other is given. The basic formula for calculating the voltage along a lossless transmission line is given by the equation,

+
+ +
+

where EL and IL are the rear element feedpoint values, Ein is the front element feedpoint voltage value, and the parenthetical expressions represent the phaseline length. We may simplify calculations by precalculating the line length into radians to obtain lr.5

+

Since we cannot calculate the line length and ZO simultaneously, we must assume one or the other. Letting the line length equal the element spacing is most convenient. We can always set up a small utility program in BASIC to step the calculation through several plausible values of line length, each of which will require a different ZO. We must also make a judicious guess as to the likely velocity factor of the line. In general, if the proposed ZL Special design uses straight dipoles, use a figure in the 0.67 to 0.7 range, since the phaseline will likely have a low ZO. If the design uses folded dipoles, then an initial velocity factor of 0.8 will serve, since the range of the phaseline ZO will be from about 150 to 350 .

+

If we select lr and VF, rewrite the terms for front and rear element values, and solve for ZO, we obtain the following equation:

+
+ +
+

If the array design is "perfect," it will require a phaseline with line length lr and the characteristic impedance, ZO to provide the correct phase and magnitude shift of current to the rear element.

+

2. To understand the conditions at the antenna feedpoint, we must also know the current at the input end of the phaseline. We may obtain this value from the standard equation for calculating the current along a transmission line (written here in terms of front and rear elements):

+
+ +
+

The value of current obtained, along with its phase angle, will also be crucial in evaluating the proposed array design.

+

3. For the array, if perfect, the total current at the feedpoint is the sum of currents in the two branches, namely, the front element and the phasing line input end, or

+
+ +
+

This equation, of course, is for a vector sum.

+

The phase angle of the total feedpoint current represents in "perfect" models the appropriate source current phase angle to obtain a forward element current phase angle of 0° and a rear element current phase angle of the value obtained from the original model. If fed with a current at 0 phase angle, the antenna forward element will show a phase angle shifted in the positive direction by the amount of the phase angle of Ifp, with the rear element current shifted positive by the same amount. The net difference between forward and rear element current phases will remain the same.

+

4. From the front element voltage and the feedpoint current, we may obtain the feedpoint impedance, along with values for the resistive and reactive components:

+
+ +
+

The calculation of Zfp, of course, is again a matter of vector division involving the subtraction of Ifp's phase angle from the phase angle of Efr. Rfp and Xfp provide the values of resistance and reactance to be matched to the feedline for the system.

+

5. The preceding steps provide the crucial data for a "perfect" phased array. To test the feasibility of the design, simply recalculate the rear element current, Ir2, using the calculated value of Iin and ZO, along with Efr. Use the standard equation (with terms rewritten for the present problem).

+
+ +
+

If the model's chosen geometry is perfect, then this calculation will simply return the current magnitude and phase angle of Irr. Anything less than perfect will show a divergence between Ir2 and Irr, especially with respect to the phase angle.

+
+ Evaluating ZL Special Designs +
+ 
+                                 Test Models of ZL Specials
+       
+Name          El. Type      Front El. Lft        Rear El. Lft         El. Spacing Lft
+
+Folded Dipole Models
+
+Short         1" Cu         15.36'               15.68'               3.86'
+
+Off Z         1" Cu         16.06'               16.80'               4.31'
+
+1"            1" Cu         16.16'               16.16'               4.27'
+
+3/8"          3/8" Cu       16.26'               16.26'               4.27'
+
+Straight Dipole Models
+
+#12           #12 Cu        16.42'               16.42'               3.46'
+
+5/8"          0.625" Al     16.04'               16.04'               3.46'
+
+3/4"          0.75" Al      16.00'               16.00'               3.46'
+
+Notes:  Cu = copper; Al = aluminum.  Folded dipole element type dimension = width of the
+folded dipole; straight dipole element type dimension = element diameter.  The 1" folded dipole
+approximates the use of 450-Ohm ladder line as the element, while the 3/8" folded dipole
+approximates the use of 300-Ohm twinlead as the element.
+
+Table 3.      Test models of ZL Specials discussed in text.
+
+

Performing the calculations just noted provides a significant body of data by which to evaluate the feasibility of a proposed ZL Special design. Table 3 describes 7 models (from among the dozens in my files) for which Table 4 provides selected results. The results appear in three groups. The first data group comes from 2-source models and provides the current magnitude and phase relationship between the elements, along with the models projected front-to-back ratio. The second data group comes from calculations in accord with the equation just described, listing the output ZO, the return current phase (and its difference from the design value), and the calculated feedpoint impedance. The last data group comes from applying the basic antenna model to a version of NEC capable of handling transmission lines within the model.6 Using one or more values for the phaseline ZO, the data group provides the projected front-to-back ratio and the feedpoint impedance. All the antennas were modeled over real medium earth using NEC's more accurate ground modeling capabilities.

+ 
+                                          Modeling and Calculation Results with Test Models
+       
+Model         <      two-source data          >   <      calculations                       >   <      test model results     >
+Name          I @ El. 1  I @ El. 2     F-B (dB)    Zo Ohms Rtn I El. 2  Ph. Dif.    R      jX    Zo     F-B (dB)     R      jX
+
+Folded Dipole Models
+
+Short         0.5/0°     0.49/-38.7°   41.89       268.9  -63.61°       24.91°    55.8   -48.9  268.9     12.80    29.5   -18.1
+                                                                                                300       12.46    35.3   -12.8
+Off Z         0.5/0°     0.49/-42.7    44.95       194.4  -42.63°        0.07°    52.3    36.3  194.4     45.38    52.4    36.3
+                                                                                                300       17.95    74.9    56.2
+1"            0.5/0°     0.5/-42.9°    39.52       330.2  -41.16°        1.74°    40.8    53.4  330       30.12    43.3    51.3
+                                                                                                300       25.64    37.8    44.9
+3/8"          0.5/0°     0.49/-42.7°   44.16       330.1  -42.69°        0.01°    42.0    42.7  330       44.19    42.0    42.6
+                                                                                                300       27.60    36.6    36.4
+Straight Dipole Models
+
+#12           0.5/0°     0.5/-34.75°   29.61        66.9  -35.44°        0.69°     6.7     6.6   71       27.17     7.1     5.8
+5/8"          0.5/0°     0.5/-34.75    26.06        67.0  -36.19°        1.44°     7.1     7.7   71       26.63     7.2     8.8
+3/4"          0.5/0°     0.5/-34.75    25.66        66.7  -36.57°        1.82°     7.2     7.5   71       25.46     7.2     8.8
+
+See Notes, Table 3.
+
+Table 4.      Some modeling and calculation results using test models described in Table 3.
+
+
+

The model called "Short" represents a casual design I found in the literature. Although the model calculates a promising phaseline ZO of about 269 Ohms, thus suggesting the use of 300- twinlead for both the elements and the phaseline, notice the phase differential between the design figure and the return calculation. In general, any difference greater than ±4 degrees or so is likely to bring disappointment. Moreover, as the phase differential between the design value and the return calculation increases, the feedpoint impedance values grow more inaccurate. Compare the calculated value with either of the test models to the right, noticing the subpar front-to-back figures along the way.

+

Perhaps what made this model attractive was the wide-band low SWR of the antenna. Frequency sweeping the 300-Ohm phaseline model showed that the antenna would show an SWR below 2:1 for over a MHz of 10 meters. Unfortunately, horizontal 2-element phased arrays cannot be adequately designed by reference to SWR. Feeding the assembly must be the last design step, not the first.

+

The model named "Off Z" demonstrates another problematic situation. The 2-source model and the calculations show that the design is in principle quite feasible and capable of good performance, as indicated by the tiny 0.07 phase differential. However, the 194-Ohm characteristic impedance of the recommended phaseline is uncommon, to say the least. Attempting to execute this model using the nearest common transmission line as the phaseline, 300-Ohm twinlead, results in a serious degradation of performance. See the test model figures to the right. Phaseline ZO should be within about 10% of the calculated value for reasonably successful performance of the array. Unless you can build a short length of your own transmission line, which is quite feasible in many instances, many good models of ZL Specials must be set aside as impractical.

+

The two models we have so far evaluated used elements based upon Yagi theory: the rear element should--in a driven element-reflector design--be somewhat longer than the forward element. This mode of thinking is detrimental to ZL Special design. The remaining models in the group all use equal element lengths as a starting point. There are good reasons on occasion to alter the length of either (or both) the forward or the rear element, but those reasons have virtually nothing to do with the considerations crucial to Yagi design. We shall look at some design alterations after examining the better models on the list.

+

The 1" and 3/8" folded dipole models used good care in selecting the current magnitude and phase angle for the rear element, while the straight dipole models were more quickly settled by letting the current ratio between elements be 1:1. The use of 0.5 A as the current value permits a more rapid correlation of values with those of the NEC transmission line models using a source current value of 1 A. In actuality, the total antenna current for the antenna system is slightly higher than 1 A, since the phaseline transforms not only the current phase angle, but its value as well.

+

Both folded dipole models show similar results, despite their different lengths. Although the figures varies slightly as the length-to-diameter ratio changes, the folded dipole elements for a ZL Special should be about 2.44% shorter than a single self-resonant folded dipole at the frequency of interest. The #12 straight dipole model used elements only about 2% shorter than a self-resonant single dipole, while the tubular elements required a little under 2.9% shortening.

+

The 1" folded dipole model is interesting because it demonstrates the fall-off in performance (front-to-back ratio) as the phase differential between the design value and return calculation value increases. Although 30 dB is a respectable ratio, it is down nearly 10 dB from the 2-source model with only a 1.74° phase differential. Attending more closely to the rear element current phase angle would likely have resolved the difference, but also resulted in a different value of phaseline ZO. Compare this model to the 3/8" model for a closer correlation of all relevant values.

+

In practical terms, the differential is moot, since 330-Ohm twinlead is not common. Both antennas promise very good performance with a 300-Ohm phaseline, if a figure of 25 to 27 dB for the front-to-back ratio can be considered very good. Compared to the reference Yagi, the figure certainly represent an improvement that may be both detectable and desirable. Note that the phaseline meets the ±10% criterion noted earlier.

+

Feeding a ZL Special that uses folded dipoles and equal-length elements is little problem. The resistive component of the feedpoint impedance presents a reasonable match to 50-Ohm coax, while the remnant inductive reactance can be canceled by the use of either a capacitive stub or a pair of capacitors, each with half the reactance value, in series with the two sides of the feedline at the feedpoint junction.7 Indeed, it is characteristic of well-designed ZL Specials using equal length elements to have similar numerical values for the resistive and reactive components of the feedpoint impedance, in other words, for the feedpoint impedance to have a phase angle approaching 45° inductive.

+

Similar results can be obtained from straight dipoles and 72- nominal twinlead. The three models differ only in the wire size used, with consequential differences in element length. The calculated phaseline ZO of 66.7 to 67 Ohms departs from the twinlead impedance by only about 6%, and the transmission-line models of the antennas verify antenna performance. Unfortunately, the very low feedpoint impedances, require careful attention to both design and construction to minimizes losses. A 71-Ohm twinlead or a 75-Ohm coax stub, something over 4' long will provide the required match to 50-Ohm coax, with either a capacitive stub or a parallel capacitor used to cancel the remaining reactance, which will be in the range of 150-200 Ohms.

+
+ Improving ZL Special Performance +
+

One straightforward means of improving ZL Special performance is to construct a phaseline with a characteristic impedance and velocity factor that accords with calculations, after fully optimizing a 2-source model of the desired antenna. However, most builders will be limited to altering the antenna geometry to accord with the available transmission lines. In general, there are only two methods of achieving this goal.

+

First, you may change the spacing between elements. Unfortunately, element spacing is insensitive to change. Raising the required characteristic impedance of the phaseline for the straight dipole models demanded shortening the spacing to something around 2.5 feet. Lowering the required line impedance of the folded dipole models demanded an increase in spacing to around 7 feet. Neither move seems attractive mechanically.

+

Second, you may change the ratio of element lengths. Each model with equal-length elements was initially optimized with respect to element length for maximum front-to-back ratio. Only the ratio of element lengths remains to be changed in pursuit of a geometry that requires a phasing line of the desired characteristic impedance. The rule of thumb is this: to decrease the required ZO, make the front element shorter than the rear element. To increase the required phasing line ZO, make the front element longer than the rear element. The adjustments will be small if the original antenna requires a phaseline ZO within 10% of the desired value. In addition, either or both elements may require adjustment.

+ 
+                                                  Some Improved Test Models
+       
+Name   Type   Front El.   Rear El.  El. Spacing   <      calculations                           >  < test model results >
+       Wire      Lft         Lft       (feet)     Zo Ohms Rtn I El. 2 Ph. Dif.    R      jX    Zo  F-B (dB)    R      jX
+
+Folded Dipole Models
+1"     Cu     16.06'      16.16'      4.27'       300.2  -42.79°     0.01°      41.3   39.8  300    47.54    41.2   39.8
+3/8"   Cu     16.23'      16.34'      4.27'       299.8  -42.53°     0.07°      41.4   38.0  300    43.20    41.5   38.0
+
+Straight Dipole Models
+5/8"   Al     16.10'      15.98'      3.46'        71.0  -34.69°     0.31°       6.4    9.0   71    38.39     6.5    8.9
+3/4"   Al     15.98'      15.78'      3.46'        71.2  -33.95°     0.80°       5.7    7.3   71    34.17     5.9    7.1
+See Notes, Table 3.
+
+Table 5.      Modeling and calculation results using improved test models.
+
+
+

Table 5 catalogs four improved models. The folded dipole models have front elements slightly more than 1" shorter than the rear. Not shown on the table are the new design values of rear element current magnitude and phase, which will change as the element-to-element ratio changes.

+

The straight dipole models show the reverse effect: to raise the required ZO from 67 to 71 Ohms, the rear element must be slightly shorter than the front element, with a consequential change in rear current magnitude and phase relative to the front element current. Because the curves approaching the maximum possible front-to-back ratio are steepest above 30 dB or so, very small changes in element dimensions produce large changes in front-to-back ratio.

+

Having shown that and how it is possible to refine ZL Special performance by adjustment of the antenna geometry, we must note the very proper question of whether such measure a worth while for the average home builder. Fig. 6 superimposes two of the straight dipole antenna patterns, one for equal-length elements. the other improved. Although there is some improvement in the overall front-to-rear pattern (taking into account the entire region from 180° to 360°), the improvement is not large compared to the initial improvement over the reference 2-element Yagi.

+
+ +
+
+ Fig. 6. Comparative azimuth patterns for equal-length element and "improved" versions of the 5/8" straight dipole ZL Special (35' above real medium earth). +
+

Moreover, achieving the absolute maximum rear null in fixed construction may be beyond the building and measurement capabilities of most hams. Indeed, phased arrays with equal-length elements may have advantages that offset their slightly reduced front-to-back performance. Such an array is reversible if we attach to both elements ladder line feeders that are a multiple of a half wavelength (adjusted for the velocity factor). One feeder is attached to the line to the transceiver, the other left open as an indefinitely large impedance that does not significantly affect antenna operation.

+

However, carefully pruning a ZL Special for maximum null at the design frequency does center the front-to-rear pattern within a desired frequency span. For a front-to-back null of over 40 dB, the front-to-back ratio degrades uniformly above and below the center frequency. On 10 meters, the front-to-back ratio is better than 25 dB 25 kHz each side of the design center and about 20 dB 50 kHz each side of the design center. Less careful pruning will likely improve the front-to-back ratio in one direction from the center frequency, but degrade it in the other down to about 15 dB.

+
+ Construction and Placement Notes +
+

All of the antennas noted in this analysis have been modeled at 35' above medium or average ground for consistency. More than many antennas, ZL Specials require modeling over real ground, rather than the construction of free space models, because they are somewhat sensitive to ground effects. This applies most especially to the array's front-to-back ratio.

+
+ +
+
+ Fig. 7. Yagi and ZL Special gain vs. height above ground from 20' to 40' over real medium earth. +
+

Fig. 7 and Fig. 8 graph the gain and front-to-back ratio, respectively, of the ZL Special (the 5/8" diameter straight dipole model), with the comparable values for the reference Yagi provided as a standard. The gain curves are quite parallel. Their spacing is a graphing convenience; the difference in values makes little, if any, operational difference. However, the excursions in front-to-back ratio for the ZL Special are many times those for the Yagi. The curves are based on a single configuration for each antenna. While the Yagi shows a relative constancy of performance, the variability of the ZL Special's front-to-back ratio suggests that optimizing it for the anticipated height of use is certainly in order.

+
+ +
+
+ Fig. 8. Yagi and ZL Special front-to-back ratio vs. height above ground from 20' to 40' over real medium earth. +
+

As a further indication of the fact that Yagis and ZL Special operate according to quite different principles once we move beyond the mutual coupling of elements, the correlation of feedpoint impedance and other parameters differs for the two antennas. ZL Special front-to-back peaks and nulls tend to correspond with peaks and nulls in the reactive component of the feedpoint impedance. For driven-element-reflector Yagis, the front-to-back peaks and nulls correspond with their counterparts in the resistive component of the feedpoint impedance. By way of contrast, to the degree they are detectable, gain peaks and nulls show a reverse correspondence.

+

There is little that anyone can add to the construction of ZL Special, whether using straight dipoles or folded dipoles. Straight dipoles lend themselves to the use of rotary beam techniques. One caution is required: do not permit metal antenna structural elements (such as a boom or mast) to disturb the balance of the currents in the phaseline. Moreover, the sum of 45 years of ZL Special construction wisdom dictates the following rule: use parallel feedline, not coax, for the phaseline. A mixture of wood, PVC, and similar construction materials for the structural assembly can leave your twinlead phaseline unaffected. Unfortunately, the demise of 70-ohm twinlead as an easily obtained commodity has made the straight-dipole version of the ZL Special an endangered--if not an extinct--species of the antenna. What remains to build are twinlead folded dipole versions.

+

However, use caution when buying materials for a folded dipole ZL Special. Belden 8230, the standard 300-Ohm twinlead for many amateur applications has #20 stranded conductors and a nominal velocity factor of 0.80. It is the basis for the models and the test antenna studied in this article. Many common local sources of supply for twinlead no longer carry equivalents of this transmission line. The foam lines they do carry often have no listed velocity factory, and it is unlikely that the figure will be 0.80. Velocity factor is important chiefly in the physical length of the phasing line, which is perhaps the most critical factor in building a ZL Special.

+

Decades ago, when bamboo was cheap, taping 300- twinlead to support elements permitted folded dipole versions of the ZL Special to approximate rotary beam configurations. More recently, the idea of fixed beam installations, whether in an attic or in the field, has regained popularity, if for no other reason than necessity in today's tighter ham quarters. A twinlead ZL Special, following W7EL's lead, makes a good Field Day Special, since it rolls up into a small ball for transportation. Elevated at the ends and pointed roughly toward the main body of hams to be worked, the antenna outperforms dipoles by a good measure. Coastal hams can use a single feedline version, while midwestern operators may wish to opt for a reversible version.

+
+ +
+
+ Fig. 9. General sketch of a single-mast support structure for testing wire ZL Specials. +
+

As a test bed for validating modeling figures, I built the single-mast support system shown in Fig. 9, 10, and 11. With inner arms of Schedule 40 PVC and outer triangular sections of lighter PR 315 PVC, the assembly permitted me to place practically no metal in the vicinity of the antenna elements or the phase line. Support arms for the center connections to each folded dipole are optional. If you use them, light-weight half-inch nominal CPVC is recommended. All junctions are glued.

+
+ +
+
+ Fig. 10. Detail A of the support structure, showing the combination of PVC materials used in its construction. +
+

Although the assembly is a good bit more rigid than it appears at first sight, I do not recommend it for a permanent installation. The guys do not stabilize the structure in all axes and certain twisting motions are possible in high winds. In lighter winds, the structure is quite stable. Thus, it is adaptable to short-term portable operations if some of the junctions are only press-fitted into the couplings.

+
+ +
+
+ Fig. 11. Detail B of the support structure, showing the center plate and mast connection. +
+

Those who wish to hang the elements from their ends might use the 17' length, since a 10-meter 2-element phased array is just over 16' long. My own final version of the support system was about 15'9" long. The ends of each front-to-back arm were slit, with the twinlead pressed in place. A pair of holes punched in the insulation of the twinlead permitted the use of a cable tie to hold the element in place. The short ends sticking out beyond the limits of the structure were self-supporting and easily accessed for pruning.

+

The antenna tested was the improved 3/8" model in Table 5. The insulation on twinlead elements requires about 1-2% shortening (relative to the models) of the elements for resonance at 10 meters. (Note: the velocity factor of a transmission line used as a radiating antenna element is not the same as the velocity factor of the material used as a transmission line. As a radiator, twinlead is just another type of insulated wire.) The final lengths for the test frequency of 28.5 MHz and a height of slightly more than 20' were 16' and 16'1" using Belden 8230. Feedpoint series capacitors are 300 pF in each leg of the feedline on the antenna side of a choke balun. Since the impedance at resonance is in the neighborhood of 40 Ohms resistive, the lowest SWR does not necessarily indicate the frequency of the null, which will be at a slightly lower frequency. If heights other than 20' to 35' are used, these test numbers may be somewhat different.

+

Once pruned, the antenna worked as predicted, within the coarse methods available for tests. Point-to-point contacts established a front-to-back ratio at the design frequency that rivaled the Moxon rectangle, described earlier in this series. Performance held up across the first MHz of 10-meters, both in terms of anticipated front-to-back ratio and in terms of an SWR bandwidth within 2:1 limits. Unless one has a very special operating need, the extra work of obtaining a "perfect" null would not likely show up, since it is frequency specific and rapidly flattens with excursions away from the design frequency.

+
+ +
+
+ Fig. 12. General configuration of the 'BRD Zapper ZL Special. +
+

One variant of the ZL Special is especially apt for attic use (assuming that the broad surface faces the best QSOs). W9BRD bent the ends of straight dipoles toward each other and phase fed the resultant assembly.8 Fig. 12 shows the general outline of the antenna. The original antenna used equal length elements and a system of voltage feeding a transmission line segment between the element ends on one side. The dimensions shown are for a modified version using #18 wire unequal length elements and a 71- phasing line. The resulting feedpoint impedance is 33 + j45 Ohms, a tolerable match for coax once the inductive reactance is cancelled.

+
+ +
+
+ Fig. 13. Azimuth patterns of the 'BRD Zapper at 28.5 MHz, 20' and 35' over real medium earth. +
+

Fig. 13 shows the pattern at both 20' and 35' above real medium earth for the 'BRD Zapper. Relative to a model with linear elements, the closed geometry of the 'BRD Zapper costs a little under 0.5 dB of gain. At the higher elevation, the worst rear lobe is down over 25 dB. At 20' (perhaps an average attic height), the front-to-back ratio drops to about 20 dB, although further refinement of the geometry may restore much of the dimple in the most rearward direction. Perhaps the only competitive small parasitical antenna in this respect is the Moxon rectangle, reported on earlier in this series. In fact, either antenna would make a good fixed beam for attic use, and the Moxon would be easier to build, since it requires no phase line. The best reason for noting the 'BRD Zapper here is to demonstrate that the geometry of horizontal 2-element phased arrays is not exhausted by straight and folded dipoles.

+

In fact, this analysis of ZL Specials has not even come close to exhausting the possibilities for horizontal 2-element phased arrays. The lure of indefinitely deep rear nulls is likely to keep the creative juices flowing in many a ham builder. Hopefully, this exploration into modeling and analyzing ZL Specials has added a modicum of better understanding to the process. The operation of ZL Specials can be understood in terms of the voltages and currents at the terminals of each element and along the transmission line used to establish correct phasing. A combination of modeling and calculation makes the performance of a proposed version of the ZL Special far more predictable than we have thought in the past. My hat is off to all those past experimenters who made workable ZL Specials while laboring under a limiting set of assumptions. That is a testimony to persistence of trial and error efforts.

+

This study has limited itself to those versions of the 2-element horizontal phased array in which the common feedpoint is identical with the forward element feedpoint. This focus stems from my basic interest in resolving the nature of transmission-line phasing in these antennas. The common feedpoint can be placed anywhere between the elements, with transmission line current magnitude and phase conversion along two lengths of transmission line. This is the operative nature of the HB9CV antenna, some notes on which appear at this site: The HB9CV Phased Array and Gain Comparisons. The use of gamma match line to the elements has often obscurred the nature of this antenna's feed and phase system. For an example of a phased horizontal array feed neither at the phase line center nor at the junction with an element, see my article in Antenna Compendium, Vol. 6 (ARRL), on "Two Hilltoppers for 10-Meters."

+
+ Notes +
+

1. Prichard, "A New Driven Array," Break-In (May, 1949), 13-14; "Two Beams for the Price of One," Break-In (Jul., 1949), 15-17; "Some Notes on the Driven Arrays," Break-In (Sep., 1949), 5-7; and "Further Experimentation with the '3MH' Beam," Break-In (Dec., 1949), 13. ZL3MH credits two U.S. hams, W5LHI and W0GZR, for supplying him with the basic idea for the array, which was apparently developed commercially just prior to World War II. I have been unable to uncover the identities of the two hams who inspired Prichard. However, see the appended bibliography for some fascinating reading on the history of the ZL Special and its workings.

+

2. Judd, "The ZL Special," Short Wave Magazine (Jul., 1950), 337-339.

+

3. Moxon, HF Antennas for All Locations (RSGB, 1982), pp. 77, 222.

+

4. Similar results might be obtained by using any two of the three value sets, since E, I, and Z are interrelated. However, the use of E and I provides a very straightforward set of calculations. Too, concern for graphical outputs from NEC and MININEC often obscures the fact that these programs are precise calculational programs. The limits on the accuracy of the models produced relative to "real" antennas is a separate issue (or set of issues).

+

5. Supplementary equations for calculating line lengths, along with expansions of the equations in the text for use with complex E and I values are given in an appendix to this discussion.

+

6. The modeling programs used for this analysis were ELNEC 3 and EZNEC 1.

+

7. I owe this idea to Roy Lewallen, W7EL, who has implemented it with success. See Lewallen, "Try the 'FD Special' Antenna," QST (Jun., 1984), 21-24.

+

8. Newkirk, "The 'BRD Zapper: A Quick, Cheap, and Easy 'ZL Special' Antenna," QST (Jun., 1990), 28-29.

+
+ +
+
+ Appendix 1: Using the ZL Special Equations +
+

Using the equations given in the main text for the ZL Special requires that we expand them to account for the fact that each voltage, current, and impedance may be a complex number, that is, a magnitude with a phase angle. As a convenience to anyone who might wish to put these calculations into a utility computer program, the following expansions are provided, along with some convenient additional calculations of casual interest in the analysis of horizontal 2-element phased arrays.

+

First, the rear element values of Err and Irr, along with their associated phase angles, yield the impedance at the rear element, Zrr:

+
+ +
+

where Zrr is the rear element feedpoint impedance and thetaZrr is its associated phase angle. Obtaining this figure allows one to determine the impedance phase change along the phaseline as a matter of interest.

+

The use of Equation 2 in the text requires that we first convert the physical length of the phaseline, initially identical to the spacing between elements, into radians. This is a standard two-step process that begins by converting the physical length into an electrical length in degrees:

+
+ +
+

where ld is the length of the line in degrees, f is the frequency in MHz, VF is the velocity factor of the line, and lm and lf are the initial lengths in meters and feet, respectively.

+

Converting degrees into and out of radians requires the familiar equations,

+
+ +
+

where lr is the electrical length in radians.

+

Equation 2 in the text yields a value of ZO that produces the desired change of current phase with an incidental change of magnitude:

+
+ +
+

Expanded to account for the complex numbers involved, it becomes

+
+ +
+

Gathering real and imaginary terms in the numerator allows one to split the equation into its parts. However, since the denominator is also complex, inverting the parts allows further subdivision. Each real and imaginary subdivision pair may be recombined by vector addition. Reinverting and using vector addition once more produces the final result, the ZO of the phaseline.

+

Calculating the current at the input end of the phaseline, given the phaseline ZO, is straightforward:

+
+ +
+

This equation expands into the following form:

+
+ +
+

where the real and imaginary parts of the equation are recombined by vector addition.

+

Zin, the impedance at the input end of the phaseline, can be obtained from Efr and Iin by the same calculation method used to obtain Zrr. The difference in the phase angle for the two impedances is the total impedance phase angle change for the phaseline.

+

Since the total feedpoint current is a vector sum, that is,

+
+ +
+

the magnitude and phase angle of Ifp are determined from

+
+ +
+

Precalculation of various recurrent terms, of course, can simplify programming of such equations.

+

Determination of the feedpoint impedance, resistance, and reactance are self-explanatory from the equations in the main text, with the addition of one item:

+
+ +
+

The recalculation of Ir2, the rear element current magnitude and phase angle, via the standard formula,

+
+ +
+

requires an expansion similar to that for calculating input current from load current, with some appropriate sign changes along the way. Expanded, the equation is

+
+ +
+

The equation requires completion in the same manner as the calculation of Iin.

+

Undoubtedly, this appendix provides superfluous detail for many readers and insufficient detail for others. If it assists a few readers, it will have served its purpose. Those who wish precision beyond the capabilities of average home construction may replace the lossless transmission line formulas with those for lossy lines. Terman's Radio Engineer's Handbook and Johnson's Antenna Engineering Handbook provide ready references.

+
+ +
+
+ ZL Special Bibliography +
+

Bluhm, "The Penny-Pincher's Dream," QST (Dec., 1965), 63-64.

+

Bradley, "The 'Half ZL Special'--a Beam for the City Dweller," Break-In (Jul., 1989), 9-10.

+

Bradley, "The 'Half ZL Special' Revisited," Break-In (Sep, 1991), 4-5.

+

Glover, "ZL Special for 2m," Break-In (Apr, 1985), 12.

+

Judd, "ZL Special 2m Beam," Out of Thin Air, pp. 56-59.

+

Judd, "The ZL Special," Short Wave Magazine (Jul., 1950), 337-339.

+

Kear, "'Five for Five:' (Five Decibels for Five Bucks)," QST (Jan., 1971), 40-42.

+

Lewallen, "Try the 'FD Special' Antenna," QST (Jun., 1984), 21-24.

+

McCoy, "The Scotsman's Delight," QST (Jun., 1963),24-26.

+

Moxon, "Two-Element Driven Arrays," QST (Jul., 1952), 28.

+

Moxon, HF Antennas for All Locations (RSGB, 1982), pp. 77, 222.

+

Newkirk, "The 'BRD Zapper: A Quick, Cheap, and Easy 'ZL Special' Antenna," QST (Jun., 1990), 28-29.

+

Prichard, "A New Driven Array," Break-In (May, 1949), 13-14.

+

Prichard, "Two Beams for the Price of One," Break-In (Jul., 1949), 15-17.

+

Prichard, "Some Notes on the Driven Arrays," Break-In (Sep., 1949), 5-7.

+

Prichard, "Further Experimentation with the '3MH' Beam," Break-In (Dec., 1949), 13.

+

Prichard, "Two Element Rotary: The '3MH Special,'" Short Wave Magazine (Dec., 1950), 666-667.

+

Prichard, "The 'ZL Special' Beams, Break-In (May, 1961), 129-130.

+

Prichard, "ZL Specials in 1985," Break-In (Oct., 1985), 11.

+

Schick, "A Shortened ZL-Special Beam," CQ (Jul., 1959).

+

---, "Modified 'ZL' Special, Antenna Roundup, Vol. 2 (Cowan Publishing, 1966), pp. 65-66.

+

Note: Special thanks go to Elaine Richards, News and Features Editor for PW Publishing Ltd., publishers of Shortwave Magazine and Practical Wireless for her kindness in supplying me with copies of articles on the ZL Special appearing in those journals. My thanks also go to Brian Egan, ZL1LE, for providing copies of ZL Special articles appearing in Break-In, and to Bridget DiCosimo of A.R.R.L. for finding similar materials that have appeared in QST.

+
+ +
+

Return to Article Index Page

+

Topics: HB9CV / ZL Special, HF Upper, Phased Array, Small Beams


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+

Modeling and Understanding Small Beams

+

Part 6: Fans, Bowties, Butterflies, and Dragonflies

+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Except for the EDZ and the ZL Special, all of the antennas we have look at in this series of small beams have averaged about 3/4ths normal side-to-side length, about 12' on 10 meters. To achieve this size, we had to either adopt a nonlinear geometry (the X-beam and the Moxon rectangle) or load the linear element (the linear-loaded Yagi). The nonlinear geometries were both in the horizontal plane, adding nothing to the height of the antenna structure.

+

A different alternative, driven by a different goal, is to increase the thickness of the beam's dipoles, thereby automatically shortening them. The goal has been to increase the SWR bandwidth of the basic half wavelength dipole. A "fat" wire such as a large diameter conduit will achieve this, within the limits of the added weight. However, a virtual fat wire works just as well. A virtual fat wire is a structure of multiple thin wires that simulates by outlining the overall wire size desired. Enter the fan and the bowtie.

+

The terms "fan" and "bowtie" have a checkered history in amateur antenna lore. Some writers have treated any set of spread multiple dipoles as a fan antenna. The most common use of the term in this way is for 2 or 3 dipoles--with each end independent--cut for various portions of the 3.5 to 4 MHz band. This multiple antenna exhibits separate SWR minima for each dipole. The spread multiple dipole is not what we shall mean by a fan. To be a "true" fan (for our purposes), the structure must electrically connect the element members at the end. The "true" fan is a single virtual fat element that exhibits a single resonant point. Unlike the folded dipole, the wires of each side of the fanned element are also joined that the feedpoint.

+

Moreover, almost any version of the spread single element (except for the multiwire cage) has been called either a fan or a bowtie, with no distinction between the two terms. Perhaps the use of the antenna in television reception occasioned the double reference, or perhaps it has been around since the antenna achieved some notice in the late 30s and 40s, evolving into the "Wonderbar" of the 50s. However, there are two distinct ways of widening an antenna element. The first way involves a linear fanning of two wires and bringing them back together vertically at the end (with or without a conductive center tube for support): this element we shall call the fan. The second way involves spreading the wires to a maximum separation somewhere along each half of the dipole--usually the midpoint--and bringing them back together angularly toward the end: for obvious visual reasons, we shall call this the bowtie. Fan and bowtie elements have similar, but not identical, properties.

+

Looking at models of these antenna configurations can lead to the construction of a very practical small beam. Since the center support-conductor of certain fan and bowtie antennas required a large-diameter tube, while the remaining structure was either wire or small tubing, MININEC was the modeling program of choice.1

+
+ The Fan +
+

Center-mounted antennas, like a half wavelength dipole of aluminum tubing, permit simple mountings. Therefore, the classic fat-wire geometry is the fan, as sketched in Fig. 1. Ignoring the horizontal member for a moment, the basic fan consists of a triangular loop of wire or tubing on either side of the center point. Some have been made from a continuous piece of 0.25" to 0.5" diameter tubing, bent to shape, flattened at the center junction, and mounted to a center insulator-support. After a violent thunderstorm, these wind-grabbers often took on shapes only seen in abstract art.

+
+ +
+
+ Fig. 1 General outline of a fan-element half-wave dipole, with dimensions for 10 meters. The horizontal center member is optional. +
+

Using a horizontal center support made the structure more durable. Sturdier aluminum tubing of standard Yagi diameters could support a thinner vertical tube at the end. In turn, the vertical tube supported wires forming the slanting members of the fan. The resulting fan slipped the wind well, stressed the tubing for strength, and reduced the element's weight.

+
+ +
+
+ Fig. 2 The azimuth far field pattern (in free space) of a fan or bowtie dipole is virtually identical to its linear counterpart. +
+

A fan dipole is still a dipole, in fact, a slightly shortened dipole. Therefore, it displays the typical dipole pattern, as shown in Fig. 2, but at with a slight reduction in gain relative to a standard thin-wire dipole. The reduction is insignificantly fractional (about 0.1 dB) and cannot be detected in operation, but it is determinate.2

+

Adding the conductive center member to the fan structure tends to increase the resonant frequency of a fan dipole relative to a similarly sized fan without the member. The amount of change is not insignificant. A 10-meter fan without the center member with the dimensions shown in Fig. 1 is resonant at about 28.25 MHz, while adding a center member raises the resonant frequency to about 28.75 MHz. The increase in resonant frequency results from changes in the current distribution, some of which is now flowing on the shorter center member. Conversely, fattening the vertical members at the outer ends of each element lowers the resonant frequency.

+
+ +
+
+ Fig. 3 SWR bandwidth curves for two linear dipoles (#14 copper wire and 1" diameter aluminum tubing) and for a fan dipole. +
+

How broad-banded is the fan? The somewhat disillusioning answer appears in the graph in Fig. 3. While the fan with a 3:1 ratio of overall length to vertical height shows an SWR bandwidth that is significantly better than that of a #14 wire dipole, it approximates the bandwidth of a simple horizontal half wavelength dipole constructed from 1" diameter aluminum tubing. With most rigs, all three antennas would operate satisfactorily across the wide reaches of 10 meters.3 However, the bandwidth advantages of fans will begin to appear when we construct a 2-element Yagi from them.

+

The fan dipole, using the dimensions of Fig. 1, does have one small additional advantage. The resonant frequency of the structure is close to 50 Ohms, a closer match for the standard ham coaxial feedline than the linear dipole.

+
+ The Bowtie +
+

An alternative to the fan is the bowtie, another form of the vertically fattened dipole. The bowtie stretches the vertical dimension in the middle of each half of the dipole, as shown in Fig. 4. The vertical supports for the wire perimeter are normally nonconductive. As with the fan, the bowtie may use or omit a conductive horizontal center member.

+
+ +
+
+ Fig. 4 General outline of a bowtie-element half-wave dipole, with dimensions for 10 meters. The horizontal center member is optional. +
+

The dimensions shown for the bow tie will produce a resonant dipole at 10 meters. Without a center member, the assembly will resonate at about 28.5 MHz; with the center member, the resonant point moves to 29.25 MHz.

+

The bowtie shows a resonant feedpoint impedance a bit lower than a fan, but still close to 50 Ohms. Likewise, its SWR bandwidth is quite similar to the fan, as shown in the 4 curves of Fig. 5. Despite the offset in resonant points, the curves are all congruent to a high degree.

+
+ +
+
+ Fig. 5 SWR bandwidth curves for both fan and bowtie dipoles, with and without horizontal center members. The displacement of the resonant points of these congruent curves permits the display of values at greater distances from resonance. +
+

The bowtie requires a larger structure to achieve resonance at the same frequency as a comparable fan, about a foot longer and several inches higher. Largely for that reason, plus the fact that the element is fatter in the region of higher current, the antenna shows a slight gain advantage over the fan (but still marginally less than a linear dipole). However, Fig. 6 demonstrates that the advantage is nowhere greater than 0.1 dB across the band, an increase that could make no difference in practical amateur operation.

+
+ +
+
+ Fig. 6 The gain properties of both fan and bowtie dipoles, with and without horizontal center members. +
+

Fans and bowties have no magic formulas for determining the ratio of overall length to height. With the exception of the 12' length of the fan, the dimensions are somewhat arbitrary, although the 3:1 length-to-height ratio appears to be a practical limit for home construction. The two antenna configurations do lend themselves to comparisons relative to how fat we make them. The amount of current carried in the fat part of the wire assembly begins to show up in terms of several different factors.

+
+ +
+
+ Fig. 7. The resonant frequency variation of both fan and bowtie dipoles as the vertical dimension is varied. +
+

If we reduce the height of the assemblies to 75%, 50%, and 25% of their 10-meter resonant height and then find the resulting resonant frequency, we obtain the two curves in Fig. 7. Note that the curve for the fan dipole is relatively linear, while the curve for the bowtie tapers toward its value for a 7.05' linear element. A similar difference occurs with respect to the gradual increase of the feedpoint impedance as the antenna approaches the condition of being a linear half wavelength dipole: as shown in Fig. 8, the fan dipole impedance increases almost linearly, while the bowtie impedance tapers toward the dipole value.

+
+ +
+
+ Fig. 8. The feedpoint resistance variation of both fan and bowtie dipoles as the vertical dimension is varied. +
+

The effects of increasing the height of the bowtie closer to the high-current portion of the antenna structure also show up in a comparison of gain figures. Interestingly, as shown in Fig. 9, the fan's gain increases as it approaches a resonant linear element, but the bowtie's gain decreases under the same condition.

+
+ +
+
+ Fig. 9. The gain variation of both fan and bowtie dipoles as the vertical dimension is varied. +
+

If one wishes to build a half wavelength dipole to cover all of 10 meters and wishes to have a reasonably good match to 50-Ohm coax, then the fan dipole may be a good choice. Six-foot lengths of aluminum tubing are standard hardware outlet items, and the 4' vertical members may be 0.25" or 0.375" diameter rods from the same source: a single 8' section will suffice for both ends. The wire pieces can be #14 stranded, which is widely available. Construction details will appear later when we look at a practical 10-meter 2-element Yagi.

+
+ Butterflies and Dragonflies +
+

Since fans and bowties are fat dipoles, rather than loaded or geometrically altered dipoles, we would expect the performance of comparably spaced 2-element Yagis to be similar. For this exercise, we used as a standard the 2-element broadband Orr Yagi, with a driven element 16.1' long, a reflector 17.6' long, and 4.25' element spacing. Centered at 28.5 MHz, this antenna exhibits moderate gain and front-to-back ratio, while holding its characteristics across most of the 10-meter band.

+

For comparison, we modeled Yagis made up of both fan and bowtie elements. A commercial version of a Yagi using fan elements has enjoyed considerable success: the Butternut HF5B Butterfly beam.4 If a fan Yagi is a butterfly, then perhaps a bowtie Yagi must be a dragonfly.

+

The bowtie and fan models in this study use 1/8th wavelength spacing. It is easier to retain the basic geometry of the fan and bowtie dipole elements and to load them for parasitic operation than it is to reshape each element for optimal performance without loading. (The Butternut beam also uses this method, since its two basic element structures are identical.) Therefore, the elements in the models have dimensions the same as those in Fig. 1 and Fig. 4. The models explored used horizontal center members, since it is difficult to build a sturdy element without the center tube.

+

A resonant dragonfly beam requires about 35 load on the reflector for maximum front-to-back ratio. A small inductor or inductive (shorted) transmission line stub across an insulated split in the reflector would provide the required loading.5 The resulting feedpoint impedance at the design center frequency of 28.5 MHz is close to 20 Ohms, with a reactance of +j12. If the inductive reactance is compensated with a pair of series capacitors (about 930 pF each), a 2.5:1 impedance ratio (1.6:1 turns ratio) broadband transformer might provide a good matching system, as would one of W2FMI's baluns. However, one might also consider using a modified beta match, with a capacitor (about 140 pF) across the terminals as the shunt element.6 The actual values requiring compensation may vary with the exact materials used for the elements.

+

A resonant fan-element Yagi using 12' by 4' with a 1" diameter horizontal center member requires similar treatment. A 1/8th wavelength spaced Yagi using fan elements as described earlier requires reflector loading with either an inductor or a shorted transmission line stub. The driven element shows a resistive feedpoint component of about 17 to 25 Ohms, with an inductive reactive component that varies with the size of the members of the element. One may either use a pair of capacitors on each side of the feedpoint to compensate for the reactance and then insert a 2:1 balun, or one might use a beta match with a capacitor as the parallel element.

+
+ +
+
+ Fig. 10. The gain across 10 meters of a fan, a bowtie, and a linear element Yagi. +
+

Among the three 2-element Yagi model antennas--the linear, the dragonfly and the fan-element version--there is nothing to choose with respect to pattern, gain, or front-to-back ratio. Fig. 10 records the modeled gains of the antennas across the 10-meter band. The maximum difference of 0.2 dB would be undetectable. The dragonfly and the fan Yagi do exhibit something over 2 dB additional front-to-back gain at design center (as shown in Fig. 11), but this is less than half an S-unit improvement, and that figure deteriorates as one moves to the high end of the band. Moreover, if the reflector is loaded to achieve its gain and front-to-back ratio, the load losses, although quite small, will have an impact on the figures to reduce them very slightly.

+
+ +
+
+ Fig. 11. The front-to-back ratio across 10 meters of a fan, a bowtie, and a linear element Yagi. +
+

Fig. 12 shows the composite patterns of any of the three antennas across the band. The innermost rear lobe (almost inverted-bell shaped) represents the 28 MHz pattern, as does the highest forward gain circle. The other gain rings decrease sequentially as the frequency increases. Likewise, using an angle of 330 as a reference line, the rear lobe patterns are sequential outward on that line as frequency increases. The innermost lobe line at 270 (directly to the rear of the forward lobe) represents the maximum front-to-back ratio, which is at 28.5 MHz, the design center for all three antennas.

+
+ +
+
+ Fig. 12. Azimuth patterns (in free space) of a fan, a bowtie, or a linear element Yagi across 10 meters at 0.25 MHz intervals. +
+

All three antennas have the same gain and front-to-back characteristics. Moreover, the dragonfly and the fan Yagi are more complex structures. Why build anything but a full size Yagi? There are two potential reasons for doing so. First, the full size Yagi is over 17' wide, while the dragonfly is a little over 14' wide and the fan Yagi is 12' wide. If space is at a premium, then fan and bowtie elements may be very useful for giving full-size performance by trading some vertical space for some horizontal space.

+
+ +
+
+ Fig. 13. The SWR bandwidth across 10 meters of a fan, a bowtie, and a linear element Yagi. +
+

Second, the fan Yagi and the dragonfly have a broader 2:1 SWR bandwidth than a linear 2-element Yagi. Fig. 13 traces those curves. The linear Yagi can cover 28.1 to 29.2 at a 2:1 SWR. However, by moving the design center of the dragonfly and the fan Yagi to about 28.75 MHz, either would likely cover the entire 10-meter band. The fan Yagi is slightly superior in this regard to the dragonfly.

+

For many--if not most--hams, these reasons may not be significant enough to prompt a construction project. Moreover, the remaining bands from 14 MHz upward are narrower and do not require element fanning for whole band coverage. Nonetheless, it is worth the effort to build a trial antenna to test the values suggested by the models.

+
+ Building a Fan-Element Yagi +
+

Of the two element types--the fan and the bowtie--the fan promises to save the most room with full-size performance. Moreover, it appears easier to build. Therefore, I decided to try a fan-element Yagi, even though I already had a Butternut Butterfly on my tower. The commercial antenna is multiband, has numerous matching pieces attached, and is somewhat larger than the 10-meter model developed here for single-band use. (The Butternut elements are about 12.5' long, with 6' vertical end spreaders on a 6' boom. An individual fan element, minus the added metal of the matching system, is resonant above 25 MHz, with the antenna loaded to Yagi performance on each band.)

+
+ +
+
+ Fig. 14. General outline of a 2-fan-element Yagi, showing the names used in the text for the various mechanical components. +
+

A Yagi using fan dipole elements presents interesting construction challenges. Fig. 14 shows the general outline of a 2-element fan Yagi. Its function is to associate the component names with the physical structures of the antenna. Each element has three major conductive components: the center member, the vertical member, and the fan wire. Everything else, including the boom and mast, are supports. The wire portions of each element come together at the feedpoint or the center of the reflector. The center connection and the boom-to-element support must not interfere with each other. The vertical end pieces must fasten to the center member of the element without slipping. The wires must connect to the vertical member ends with enough stress to stiffen the structure but not enough to deform or break it. A simple system of epoxy-coated plywood plates would not do here.

+

Since my standard test boom is a 5' length of 1.25" diameter nominal Schedule 40 PVC, I decided to put the drill press to use to mount a 0.5" diameter nominal Schedule 40 PVC through the boom. The real outside diameter of the half-inch material is closer to 0.875" for a good fit with 1" outside diameter aluminum (0.55 thickness) center members, with a little tape at two points on each side of center for a tight fit. If the sag of the Schedule 40 PVC, which allows about a 3-degree droop in the fans, causes concern, you can stiffen the center insulated piece. One technique is to thread thin strips of fiberglass cloth through the center of the half-inch PVC. Then seal one end, stand the piece vertically, and fill it with car-repair epoxy resin. Allow extra setting time, since the tube is closed. The resulting rod is easily machined with wood bits and will outlast any other part of the antenna.

+

Aluminum rods, either 0.25" or 0.375" in diameter form the end members and fit through holes in the center member. Although I initially had some fears of weakening the center member tubing by drilling out holes, the results has stood the test of time and wind--so far. If you have access to 0.5" diameter aluminum tubing for the end members, you can save a significant bit of downward force at the ends of the center members. The rods used in the test antenna have created no problems and were used owing to their easy access at hardware depots.

+

Actual construction may take any electrically and mechanically sound form. The construction method used in the test antenna began with a 5' length of 1.25" (nominal) Schedule 40 PVC. At a distance of 4.31' apart, I used a 7/8" diameter hole cutter (for wood) to form the openings for the center-member supports, two 3' lengths of 0.5" (nominal) Schedule 40 PVC. Aligning the first hole for the center of the tubing in a drill press or other jig is the first careful task. A little sanding prepares the opening for the center member support, which is bolted in place with a 2" long #10 stainless steel (SS) bolt and nut. The first support acts as an alignment tool for setting up the second hole in the boom. The half-element fans will slide over the center-member support during final assembly, as shown in Fig. 15. For now, remove the supports from the boom.

+
+ +
+
+ Fig. 15. Construction details of the element-to-boom mounting for the fan elements of the test antenna. +
+

To prepare the 1" diameter 6' long aluminum center members, use a drill press or other alignment jig to drill 0.25" (or 0.375" for 3/8" rod) holes within a half inch of the outer end of each tube. Slide the 4' sections of aluminum rod through the holes with their centers in the middle of the tubes. Several clamping systems are possible. The simplest might be a pair of the smallest size stainless steel hose clamps available placed above and below the center member. A #6 or #8 SS bolt and nut assembly can act as an electrical contact to a small flat spot filed on the rod. Alternatively, the U clamp shown in Fig. 16 can be inserted while passing the rod through the tube. The U should be just large enough to press into the tube. Again, a separate bolt and nut system should be used to ensure good electrical contact between the two elements.

+
+ +
+
+ Fig. 16. Construction details relating to the vertical member of the fan elements. +
+

Drill a hole in each end of each vertical member for a bolt and nut to secure a clamp to be soldered to the fan wire, as suggested in Fig. 16. The sketch shows separate wire clamp and wire elements, but wrapping the wire around the nut and using a sufficiently large washer to provide good electrical and mechanical contact should also suffice. Wrap the wire back around itself for mechanical strain relief and solder the wire with a large iron or small torch. (Be certain that the #14 fan wire is long enough--about 12.65' plus wrap-around stubs--to make both fan wires on each side from one wire length. See below.)

+

Prepare the hole in the center member at the antenna element center. At this stage, it is easiest to insert the PVC center-element support to ensure total system alignment. If the fit is too loose, wrap electrical tape around the support at a minimum of two points to create a snug but nonbinding fit. If you fit both halves of the element to the support and lay them on a floor surface, you can assure your self that the fan wire bolt holes at the center (see Fig. 15) will be aligned.

+

The bolts closest to the boom that secure the center member to the PVC support should be about 2" long, since they will go through the center member and support, secure the feed and loading elements, and clamp the fan wire. Extra nuts and washers are useful to isolate these functions. You can place the fan wire on the "outside" of the overall structure, using large washers to clamp the midpoint of the wire and secure the assembly (to this point, without matching or loading elements) with a lockwasher and nut. Later, you can add leads for the antenna feed and for the reflector load.

+

The fan wire for each half element can be a continuous piece running from the upper tip of a vertical member to its lower tip (12.65' plus stubs). Prepare one tip-end as earlier described and run the wire around the bolt at the center. Stress the vertical member slightly and clamp the center bolt. Then run the wire to the other tip, choosing a length that will stress that end of the rod by an equal amount. Now you can cut and finish the wire according to your choice of tip clamps. Finally, loosen the clamping washers and nut at the element center. Equalized the stress on the vertical member and reclamp.

+

While the element is flat on the floor, you may add a second bolt through the center member and its support near the end of the support within the tube, about 15 to 17" from the element center. Choose a point that does not go through the tape shim.

+

Once both antenna elements are ready, insert the center-member support PVC through the boom hole and lock it in place with its bolt. (The boom will likely be vertical if the antenna element is on the floor during this phase of assembly. I taped mine to a plumb house support post to assure correct element alignment during this step of construction.) Reassemble the other half element to the support, remembering to clamp the fan wire center with equal stress on the vertical member tips. Using a prop to support the completed element, add the second element to complete the basic assembly. Place a boom-to-mast plate at the center of the boom and install a short section of mast. These additions will permit you to balance the assembly in a fixture while installing the feedpoint match components and the reflector load. I use an old "dish-pack" box with a 1.25" hole in the top as my favorite prop for light antennas.

+
+ +
+
+ Fig. 17. Construction details for a quick assembly version of the fan elements. +
+

After experimenting with several construction techniques for long-term installation, the final test antenna opted for the most rapid assembly and disassembly techniques. Fig. 17 shows some of the variant details of this option. Vertical members were locked in place with stainless steel hose clamps. The wires passed over grooves in the ends of the vertical rods and were clamped with similar hose camps. The resultant structure requires about 15 minutes for field assembly and a like time for disassembly. The antenna pieces and the 4 sections of 5' 1.25" diameter masting require a space about 1' by 1' by 6' in the back of a pickup truck for transport.

+
+ Test Results +
+

The antenna is almost ready for testing. The study of the general properties of fan and bowtie elements and their Yagi counterparts employed simplified models using #14 copper wire for all members. The trends and curves that result from these models are accurate, but changes in materials will alter the test results and expectations of performance, especially with respect to matching and feeding the array. The actual antenna is predominantly aluminum, and element sizes are variable, with #14 wire, 0.375" diameter vertical members, and 1" diameter center members. Therefore, the antenna was remodeled using these figures to ascertain how close to reality the model would be. Additionally, the model was run at a height of 20' above real medium earth, as MININEC defines it (remembering that MININEC calculates feedpoint impedances as if over perfect ground).

+

A detailed model of a single fan element dipole showed resonance at about 28.7 MHz, with a feedpoint impedance near 50 Ohms. Raising the antenna assembly with only the driven element mounted on the boom, I found a resonance closer to 28.5 MHz. The differences stem partly from limitations of the modeling program, since very small corners of the fans are cut off, despite extensive element tapering. The greatest part of the variance stems from the inevitable differences between the model and the constructed element. The 1.75" diameter boom adds that much to the overall element length, minus part of the 0.5" inset at the ends for the vertical members. Additionally, the vertical members are stressed, creating slight bows rather than truly straight vertical members.

+

Remodeling the Yagi version of the antenna suggested reflector loading of about 18 for maximum front-to-back ratio, which translates into a 0.5" inside diameter coil with 3 turns space to just under a half inch in length. Alternatively, a 2.5" wide stub between 3" and 4" long, with a shorting bar, matched the terminal spacing of the reflector element of the test antenna. (See the appendix for a utility program for calculating stubs.) The revised model also reported a feedpoint impedance of about 26 + j24 , values close to optimum for a beta match with a capacitor of about 110 pF as the parallel reactance. Both the reflector coil and beta-match capacitor would be subject to experimental variation to see how close to reality the model came.

+

As with most Yagis, the fan-element beam can be initially tuned near the ground by pointing it as straight up as possible, with the reflector toward the ground.7 Adjusting the reflector load for minimum SWR should place the antenna at its maximum front-to-back ratio operating point. The predicted beta-match capacitor--110 pF--can be varied to further reduce the SWR. The value may be less than predicted if the series inductance in the driven element is less than 25 Ohms.

+

Tune-up of the test antenna began with a 2.5" wide stub a bit over 4" long, with a shorting bar and a 100 pF beta-match capacitor. Reducing the stub to almost exactly 4" and reducing the capacitor to 75 pF produced a broad 2:1 SWR bandwidth between 28 and 30 MHz, with lowest readings (1.1:1) for 100 kHz around 28.75 MHz. Part of the below-predicted capacitance for the beta match stems from stray capacitance across the feedpoint assembly, part from a deficit of inductive reactance in the driven element as the frequency was lowered. At a 20-foot height, the best stub length was 3.5" with the same beta-match capacitor, and the region of lowest SWR was narrower. In addition, the center frequency shifted upward by 250 kHz. Although a coil across the reflector produced similar feedpoint readings, the stub proved more rugged and simple and is recommended for similar antennas.

+

Because the driven element's inductive reactance is marginal for a beta match at the lower end of 10 meters, the SWR curve is much steeper at those frequencies than the curves graphed in Fig. 13. There are at least two solutions to this problem. One is to use a different matching system. Another is to enlarge the elements by a couple of inches, either horizontally or vertically, in order to lower slightly their natural resonant points in the Yagi configuration. This latter measure would also reduce the amount of reflector loading required.

+

One interesting characteristic of the fan-element Yagi is its apparent greater susceptibility to coupling effects from surround objects than other linear antennas tested at precisely the same location. SWR variations as the antenna was rotated were greater than those experienced with any other test antenna. Since the antenna is not a closed loop (as is the quad), but instead a pair of dipoles with broad vertical end surfaces, its tendency toward unwanted end coupling is no surprise. A fan-element beam should be used in as clear an area as possible.

+

Operationally, the antenna appears to be a typical 2-element beam, similar in gain and front-to-back ratio as any other. It remains reasonably matched as one moves up 10 meters well past the point where gain and front-to-back ratio have diminished noticeably. In short, the fan-element beam behaves close to the predictions of the model, despite limitations on exact correspondence imposed by both MININEC constraints and construction deviance. Indeed, without a computer model with which to begin, I would not have known just where to begin the process of shortening the elements as I spread their ends. The ham antenna builder does not require lab-grade predictions, but reasonable expectations for construction and testing.

+
+ Summary +
+

A fan-element Yagi may be the most practical way to obtain full 2-element Yagi gain from a 12'-wide antenna without sacrificing SWR bandwidth. In fact, the bandwidth is improved, which is a plus for a band as wide as 10 meters. The 2-S-unit front-to-back ratio does not equal that of the narrower-bandwidth linear-loaded Yagi or the superb figure of the Moxon rectangle, both comparably sized antennas. However, as has been noted along the way, the final selection of antenna features and specifications requires attention to the major operating goals for a given station. For some operators, a high front-to-back ratio is the key element to success (if the gain among eligible antennas varies by only a dB or so), while for others, excessive front-to-back ratio can actually hinder operations.

+

The fan-element Yagi has its best home on 10-meters (and perhaps on 6 and 2, for some styles of operating). The smaller frequency range of the lower bands from 20 through 12 meters permits successful use of linear elements, even linear-loaded elements, with their simplified construction. However, for 10-meter operators whose interests require spanning the band from end-to-end, fan elements are worth serious consideration.

+

The vertical dimension of the fan-element Yagi, especially the commercial Butternut HF5B Butterfly, approaches that of a small quad. A 2-element quad has the further space-saving benefit of reducing the horizontal dimension to about half that of a linear Yagi. Some experimenters have tried to reduce the quad dimensions even further. This series would be incomplete if we did not take a good look next time at shrunken quads.

+
+ Notes +
+

1. NEC-2, while having advantages over MININEC in many respects, has difficulty in dealing with complex geometries involving wires of significantly different diameters. The models of fans, bowties, and their 2-element Yagi counterparts do not tax the limits of MININEC. All patterns and figures graphed were derived from ELNEC 3.02. Initial models used all #14 wire, while subsequent models, especially of antennas based on the fan, replaced the center member with a 1" diameter tube in order to model the practical antenna actually built. Because the antenna elements have many right and acute angles, elements were extensively segment-tapered. The resulting Yagi models required 198 segments for fan versions and 190 segments for bowtie versions.

+

2. I have discovered that some hams believe that a half wavelength dipole shows maximum gain at its resonant frequency. This belief likely represents a confusion between the gain of the main lobe and our ability to get the antenna to perform due to the increasing SWR off its resonant frequency. The bidirectional lobes of a dipole show reduced gain (in dBi) as they are shortened below resonance at a frequency of interest and more gain as they are lengthened. The gain increases with wire length until the antenna is about 1.25 wavelengths long (the EDZ), after which the main pattern lobes begin to decrease as the formerly minor lobes increase.

+

3. For this reason, fans have not found widespread use on the lower bands. On 80 meters, a better choice may be dual dipoles, one cut for the CW end of the band, the other for the phone end. The dipoles may be connected at the feedpoint or you can use close-coupled spacing for similar broadband results.

+

4. Although not an insignificant task to assemble and tune, the HF5B performs to specifications supplied by the maker. My 12-year-old model has survived a local area house move (thanks to a very careful mover) and continues to perform as specified. Although its dimensions are a bit larger than the fan Yagi given here in order to accommodate multiband operation, the principles remain the same. Butternut records in their instruction manual that "BUTTERFLY" is a trademark, although the status of the lower-case version of the word is uncertain. (In any event, we shall not have to revert to the original term "flutterby" when referring to certain showy insects.)

+

5. See the Appendix for a short utility program to calculate transmission line stubs from required capacitive or inductive reactances. The program also permits use of capacitor or inductor value inputs and allows for commercial or home-constructed transmission lines.

+

6. See Thomas Cefalo, Jr., WA1SPI, "The Hairpin Match: A Review," Communications Quarterly, Summer, 1994, pp. 49-54; L. B. Cebik, W4RNL, "Technical Conversations: Further Notes on the Beta Match," Communications Quarterly, Winter, 1995, pp. 51-54; Gooch, Gardiner, and Roberts, "The Hairpin Match," QST (April, 1962), 11-14, 146, 156; and Jerry Hall, K1TD, ed., The ARRL Antenna Book, 16th Ed., pp. 26-21-26-23.

+

7. See Brian Beezley, W6STI, "Adjusting HF Yagi Matches." "Technical Correspondence," QST, April, 1995, p. 74.

+
+ +
+
+ Appendix +
+
+ Calculation of Inductive and Capacitive Stubs +
+

Inductive (shorted) and capacitive (open) transmission line stubs less than 1/4 wavelength long are very useful for introducing frequency-sensitive amounts of inductance (or inductive reactance) or capacitance (or capacitive reactance) into circuits. Their main use is in antenna work, where they serve to load antenna elements (electrically lengthen or shorten them). They also serve as inductors or capacitors in matching networks.

+

The simple GW Basic utility program that follows allows you to calculate the length of either an inductive (shorted) or capacitive (open) stub by entering the frequency of interest and either a reactance value or a capacitance or inductance. Then you may enter either the known line impedance (Zo) or the physical dimensions (wire size and spacing in inches) of a feedline (along with its velocity factor). The program will then provide the stub length. The program likely replicates similar utilities written by large numbers of folks, but since I found none among my freeware stock, I wrote this one. I list it on the assumption that some few others might also need such a program. A visually enhanced version of the program appears in the latest version of HAMCALC by George Murphy, VE3ERP.1

+

Even number wire sizes that are greater than 3 and less than 19 (for example, 10, 14, 18) will be automatically recognized as AWG sizes. Decimals (e.g., .25) and whole numbers less than 3 are wire diameters in inches.

+

For somewhat greater accuracy, especially with large wires and close spacing, substitute the following for line 250:

+

250 SD=SP/DIA:ZO=120*LOG(SD+SQR((SD*SD)-1))

+

The chief error trapping is for division by zero whenever a potential denominator is accidentally entered as a zero. An arbitrary minuscule number substitution avoids the program break, but the results will be meaningless, and a retry is necessary.

+
+ Program +
+ 
+10 'file XMSNSTUB.BAS
+20 CLS:COLOR 11,1,3
+30 CLS:PRINT"Calculation of Inductive and Capacitive Stubs":PRINT"L. B. Cebik, W4RNL"
+40 PRINT:PRINT"For any value of Lx, Cx, L, or C, calculates the length of a transmission line   stub for a given frequency."
+50 PRINT:INPUT " Enter frequency of interest in MHz",F:FB=F*(1000000!)
+60 PRINT:PRINT" Select desired starting point:":PRINT"A. Inductive Reactance    B.
+Capacitive      Reactance":PRINT"C. Inductance    D. Capacitance"
+70 PI=3.141592654#:T=0
+80 A$=INKEY$:IF A$="A" OR A$="a" THEN 110 ELSE IF A$="C" OR A$="c" THEN 90 ELSE IF A$="B" OR A$="b" THEN 140 ELSE IF A$="D" OR A$="d" THEN 120 ELSE 80
+90 'Inductance to inductive reactance
+100 INPUT" Enter Inductance in microHenries",L:LB=L*.000001: LX=((2*PI)*(FB*LB)):       T=1:GOTO 150
+110 INPUT" Enter Inductive reactance in ohms",LX:T=1:GOTO 150
+120 'Capacitance to capacitive reactance
+130 INPUT" Enter Capacitance in picoFarads",C:CB=C*(1E-12):CX=1/((2*PI)*(FB*CB)):       T=0:GOTO 150
+140 INPUT" Enter Capacitive reactance in ohms",CX:T=0:GOTO 150
+150 'Stub construction
+160 PRINT:PRINT" Select desired starting point for stub construction":PRINT"1. Feedline Zo
+        2. Line structure"
+170 B$=INKEY$:IF B$="1" THEN 180 ELSE IF B$="2" THEN 200 ELSE 170
+180 INPUT" Enter Zo of transmission line",ZO
+190 INPUT" Enter Velocity Factor of transmission line",VF:IF T>0 THEN 280 ELSE 370
+200 INPUT" Enter Line spacing in inches",SP
+210 INPUT" Enter Wire diameter in inches or in even AWG",DIA
+220 IF DIA>3 THEN IF DIA=4 THEN DIA=.257 ELSE IF DIA=6 THEN DIA=.186 ELSE IF DIA=8 THEN DIA=.144 ELSE IF DIA=10 THEN DIA=.1019 ELSE IF DIA=12 THEN DIA=.0808 ELSE IF DIA=14 THEN DIA=.0641 ELSE IF DIA=16 THEN DIA=.0508 ELSE IF DIA=18 THEN DIA=.0403
+230 IF DIA>3 THEN 210
+240 IF DIA=0 THEN DIA=.0000001
+250 ZO=(276*.43429)*(LOG((2*SP)/DIA))
+260 INPUT" Enter Velocity Factor of transmission line",VF
+270 IF T>0 THEN 280 ELSE 370
+280 'Inductive stub
+290 PRINT:PRINT" Inductive stub for a reactance of";LX;"ohms and a Zo of";ZO;"ohms"
+300 IF ZO=0 THEN ZO=.0000001
+310 LR=ATN(LX/ZO):LDG=(180*LR)/PI
+320 IF F=0 THEN F=.0000001
+330 LFT=(VF*LDG)/(.366*F)
+340 PRINT"Length of Inductive stub =";LFT;"feet"
+350 PRINT:PRINT" <A>nother run or <Q>uit?
+360 C$=INKEY$:IF C$="A" OR C$="a" THEN 30 ELSE IF C$="Q" OR C$="q" THEN END     ELSE 360
+370 'Capacitive stub
+380 PRINT:PRINT" Capacitive stub for a reactance of";CX;"ohms and a Zo of";ZO;"ohms"
+390 IF CX=0 THEN CX=.0000001
+400 LR=ATN(ZO/CX):LDG=(180*LR)/PI
+410 LFT=(VF*LDG)/(.366*F)
+420 PRINT"Length of Capacitive stub =";LFT;"feet"
+430 PRINT:PRINT" <A>nother run or <Q>uit?
+440 C$=INKEY$:IF C$="A" OR C$="a" THEN 30 ELSE IF C$="Q" OR C$="q" THEN END     ELSE 440
+
+
+ Notes +
+

1. HAMCALC (Version 38 as of this writing, but undoubtedly higher by now) is available from VE3ERP, 77 McKenzie Street, Orillia, Ontario L3V 6A6. Murph requests a $5 donation to cover disks, mailers, and postage, and he donates the excess of donations over costs to a Canadian institute for the blind which offers amateur radio services. The program includes a structured menu system, its own copy of GW Basic, and nearly 100 handy calculation programs of interest to hams. They range from basic ohms law computations to more complex antenna, transmission line, inductor, and basic matching system calculations, with tables of wire, cable, and other construction materials, as well as many more features.

+
+ +
+

Return to Article Index Page

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Topics: Bowtie / Fan, Dipole, HF Upper, Small Beams


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Modeling and Understanding Small Beams

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Part 7: Shrunken Quads

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L. B. Cebik, W4RNL

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Quad beams remain one of the most controversial antennas around, simply because we inevitably want to compare them to linear Yagis of similar element numbers. Entire books have been written on the quad, the two most notable of which are the Orr and Cowan classic and the more recent detailed study by Haviland.1 The foundation of the quad is the full wavelength loop, which builders have constructed in squares, rectangles, diamonds, and even circles.2 Whatever the shape of this structure, it is mechanically ungainly, requiring a nonconductive support structure (or at least one in which the conductive portions are broken into nonresonant or non-detuning lengths) for a wire loop. Putting two or more such elements together has been a challenge for both commercial and home builders. If high winds mangle Yagis and quads equally, ice has shown a distinct preference for the destruction of quads.

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Reducing the dimensions of the quad loop has been an enterprise almost as old as the quad itself. If the quad loop can be shrunk considerably, then the mechanical problems diminish almost as the square of the percentage of shrinkage. The ingenuity of home builders in trying schemes for shortening the quad has produced diverse techniques. In his own "corner-inductor" version of the shortened quad, KA2OIG/TI2 noted that "in the literature on reduced quads there are examples of top-hat or capacitive loading, linear loading, stub loading, trap and coil loading, a folded-mini, and finally coil loading."3 Almost all of these systems add one or another physical complexity to quad construction as repayment for the reduction in overall antenna loop size.

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More recently, N4PC has experimented with a diamond-shaped "squished quad" using linear loading at the voltage maxima, which are located half way up the vertical sides in a quare design and at the horizontal apexes of the diamond design. The object was to leave as much as possible of the high-current portion of the antenna unaffected by loading, thereby maximizing gain. The added wire at the voltage maxima could be a continuation of the overall wire loop, thereby simplifying mechanical construction.4 Except for the copper wire losses, the mid-side or voltage-maximum loading scheme avoids losses associated with the use of coils and capacitors as loading elements. In addition, voltage-maximum loading is usable with both diamond and square quad loops.

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N4PC's success with the "Squad" left some question as to what sort of performance we might expect of such an antenna in advance of building one. If, as he noted, 85% of the antenna current occurs in the center-most 65% of the antenna wire, what would this mean for overall antenna performance? The availability of NEC-2, which can handle complex geometries with some ease (as long as the wire diameter does not change) suggested that modeling both the squad and the loops that compose its elements might be an instructive exercise. The result was my own version of a shrunken diamond-form 2-element quad for 10 meters with dimensions less than 7' per side.

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+ Full-Size and Shrunken Quad Loops +
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Despite the plethora of articles on quads, data on the proper dimensions for a simple quad loop are hard to come by. The traditional formula, L (in feet) = 1005/f (in MHz) is simply wrong for bare copper wire. Additionally, the diameter of the wire will have an influence on the total length of the quad loop. Thus, any formula given must be specified for the wire size as well. On 10 meters (28.5 MHz design center), the proper length (in feet) for a resonant quad loop of #14 bare copper wire is approximately 1045/f (in MHz). At 28.5 MHz, this yields a circumference of about 36.5' or about 9.13' per side. These dimensions apply to both the square and diamond configurations shown in Fig. 1.

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+ Fig. 1 Simplified outlines of full square and diamond quad loops. +
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Whether square or diamond, the loop provides a free space gain of about 3.25 dBi (about 1.1 dB greater than a free space dipole of similar materials). The pattern shown in Fig. 2 displays both the horizontal and vertical components of the total far field pattern: the vertical component is insignificantly larger for the square loop. The feedpoint impedance is between 125 and 130 Ohms resistive for both configurations.5 Free space gain and feedpoint impedance figures can be used with confidence for the comparisons that follow, since none of the models exhibited any surprising changes in characteristics when modeled over real ground. If a shrunken model exhibits a reduced gain relative to a full size model of 1 dB in free space, an equivalent reduction will be found in models over real ground.

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+ Fig. 2 Free-space azimuth pattern of a full-size quad loop. +
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Three types of shrunken quad loops, shown in Fig. 3, were modeled for performance comparisons. All use #14 copper wire. The diamond loop (referred to as "Diamond loop: 1LL" on graphs) has a circumference (in feet) of 725/f (in MHz), about 25.5' or about 6.36' per side. The diamond is thus about 70% full size. One advantage of the diamond is that it allows the most room for the voltage-maximum linear load, shown as the side insets on the diagram. The model uses a short horizontal feed wire to reflect usual diamond quad loop construction. Using a perfect diamond with a split feed yielded linear load lengths only 3/4" longer than those indicated by the single feed model at 28.5 MHz, with no change in feedpoint impedance.

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+ Fig. 3 General outline of three test models used to establish shrunken quad loop performance potentials. +
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A comparable square requires a larger circumference to permit resonance at the design center frequency of 28.5 MHz, since the maximum inset linear load is shorter. The model used here (designated "Square Loop: 1LL" on graphs) answers to the formula 789/f (in MHz), which is about 27.7' overall and 6.92' per side. The resulting quad loop is about 76% full size. Its advantage mechanically is that the X-members or spreaders supporting the wire can be 10' long, a convenient hardware store supply dimension.

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N4PC used a double inset linear load on his Squad. Therefore, a third version seemed appropriate for modeling, a square with a double inset (designated "Square Loop: 2LL" on graphs). The double inset permits a reduction of the circumference to about 689/f (in MHz) or 66% of full size. The 24' circumferences is distributed at 6' per side.

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Initially, all voltage-maximum loads were identically constructed (except for length). Composed of #14 copper wire, they are 3" (0.25') wide and extend inward from the side wires horizontally toward the center of the element assembly, as shown in Fig. 3.

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+ +
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+ Fig. 4 Load-line length vs. resonant frequency for test antenna models. +
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For each type of loop, the resonant frequency is close to a linear function of the load length, as Fig. 4 demonstrates. Each loop size was chosen to resonate at 28.5 MHz with the load length at or near its practical maximum length to achieve the smallest loop size possible. The diamond loop allowed 4' load-lines on each side of center, while the single-load square allows 3' load lines. The double-load square is 3' on a side by fiat, which yielded a load-length on each side of 2.595' for resonance at 28.5 MHz. With an even 2.5' of load length per side, the resonant frequency rises to 29.05 MHz as the starting point of the graph.

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The single-load diamond and square loops show nearly parallel linear rises in frequency as the load length on each side is reduced toward zero. In contrast, the double-load square loop increases in frequency at almost twice the rate of either single-load loop. Thus, the double-load line is much more frequency-sensitive to adjustments.

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As one might expect, the longer the load-line at resonance of the loop, the lower the gain of the loop. Because the load lines are of the same material as the element, the only losses are those of the copper wire in the line, which are too small to account for the reduction of gain in all loaded quad loops. The gain of a quad loop is in part dependent upon its physical size. Hence, any shrinkage of the loop relative to a full-size loop at resonance will reduce its gain. In turn, reduction of loop gain will limit the gain obtainable from a multielement quad beam using these shrunken loops.

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+ Fig. 5 Load-line length vs. free-space gain for test antenna models. +
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Fig. 5 displays the gain of loops using voltage-maximum loading, with each length of linear load corresponding to a resonant frequency for the assembly (see Fig. 4). Comparisons are possible only where corresponding loops have the same length of load line. For all practical purposes, the gains of the single-load elements, diamond and square, are the same (under 0.05 dB difference). However, the gain of the double-load-line square is significantly less than that of either single-load configuration, reaching more than 0.25 dB difference at a 2.5' load length. At that load length, the single-load elements have lost about half the advantage of a full size quad over a dipole; the double-load element is only slightly better than a dipole.

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+ Fig. 6 Load-line length vs. feedpoint impedance gain for test antenna models. +
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Both of the single-load loops show a resonant feedpoint impedance just above 50 Ohms, as shown in Fig. 6. The square element progresses in near linear fashion toward the impedance value of an unloaded resonant quad as the load line is shortened. However, the diamond loop reaches a peak value with load lines of 0.5' each. Like the single-load square, the double-load line square displays a near-linear rise in impedance value. Near the design center frequency, its feedpoint impedance is in the 35-Ohm region.

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Of the three configurations, the double-load-line element shows the least promise, despite its great compactness. Its low feedpoint impedance and noticeably reduced gain relative to the other shrunken loops suggest inferior beam performance. Add to these factors the frequency-sensitivity of the assembly to adjustments, and the configuration loses more appeal. A 6' wide and high 10 meter quad would not likely be worth the effort to build; however, a 7' wide and high quad beam may be well worth the effort, especially at about 58% of the volume required by a full size beam.6

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Before attempting a 2-element antenna, we should note that changing the spacing of the wires in the linear loads also changes the characteristics of a single element quad loop slightly. Although gain and feedpoint impedance do not change enough to alter design considerations, the resonant frequency for a given length of load on each side of the loop will create design concerns. Fig. 7 shows part of the curve of load length and resonant frequency for three different load widths. Narrowing the spacing between load lines for a given load length raises the resonant frequency of the loop. The amount of resonant frequency increase is proportional to the percentage of decrease. The decrease from 2" to 1" yields a larger increase in resonant frequency than the decrease from 3" to 2" of load width.

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+ Fig. 7 Single load-line width vs. resonant frequency for test square-loop model. +
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Looking at the assembly from a different perspective, the narrower the line width, the longer the load line needs to be for a desired resonant frequency. Resonating a 1" wide load line at 28.5 MHz would have required a line longer than the 3.46' from the side wire to the center of the quad element. At the far right end of the scale, of course, all three curves on the graph converge as the load line reach zero length.

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Wider spacing between the load lines reduces the necessary line length for a given resonant frequency. However, increasing the spacing beyond 3" (say, to 6, 9 or 12") produces only marginal shortening. Lines spaced 1' apart are only half a foot shorter for the single-line square and the diamond than lines spaced 3" apart for resonance at 28.5 MHz. Since maintaining the larger spacing would add weight to the small 10-meter structure, the 3" line spacing represents a good compromise between mechanical and electrical efficiency. wider spacing might be used in a pinch if a given load-line length does not quite reach down to the desired resonant frequency: increasing the spacing by an inch or two is equal to adding a few inches to the line length at its narrower spacing.

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Because a quad loop, loaded or unloaded, has gain over a dipole, it qualifies as an array of sorts. However, it is barely an array (two bent dipoles touching ends). If one goes to the trouble to construct a full wavelength loop, one might as well construct two and have a classic 2-element quad beam.

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+ Full-Size and Shrunken Quad Beams +
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A full-size 2-element quad beam consists of two quad loops cut to optimal dimensions and spaced for the closest conjunction of gain and front-to-back ratio. Many formula sets are available, for example in Orr and Cowan, the ARRL Antenna Book, and Haviland. Fig. 8 outlines the parasitic quad beam and provides formulas for a close-spaced version (1/8th wl). Using #14 wire at a design center frequency of 28.5 MHz, the beam shows a free space gain of over 7 dBi with a front-to-back ratio over 23 dB. With a feedpoint impedance of about 100 , the antenna falls in the middle of the 75 to 125 feedpoint impedance range common with quad designs.

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+ Fig. 8 Outline of a full-size 2-element quad beam model. +
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The sample quad beam is neither the best performer nor the broadest-banded of possible quads, since its spacing is somewhat close by quad standards. However, it demonstrates the performance characteristics that lead many to choose quads over 2-element Yagis or 3-element trap-Yagis: it has higher gain and a very respectable front-to-back ratio (in fact, a good front-to-rear ratio, if we look at everything to the rear of the main lobe). Fig. 9 shows the free space azimuth pattern of the antenna.

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+ Fig. 9 Free space azimuth pattern of a full-size 2-element quad beam model. +
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Full-size quads tend to perform well at modest heights. Fig. 10 and Fig. 11 show the beam azimuth pattern at the angle of maximum radiation for the antenna at heights of about 5/8 wavelength and about a full wavelength above medium ground. Although the pattern of ground reflections tends to degrade the rearward performance at the lower height, at a wavelength, the antenna recovers close to full free-space front-to-back ratio. The broad beamwidth provides good forward coverage for general operation.

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+ Fig. 10 Full-size 2-element quad beam model azimuth pattern at the angle of maximum radiation for a height of 20' over medium earth. +
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+ Fig. 11 Full-size 2-element quad beam model azimuth pattern at the angle of maximum radiation for a height of 35' over medium earth. +
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These notes on full-size quads are not a recommendation of the antenna. For further data on modeled quads of all sizes, see Some Model Quads Parts 1-7, at this site, as well as standard quad references. Instead, the notes here provide a set of standards against which to compare shrunken quads with side (voltage-maximum) loading. Whereas the full-size quad requires either that the reflector be physically larger than the driven element or that an inductive stub be added to electrically lengthen the reflector, any model of a side-loaded shrunken quad can be adjusted solely by lengthening or shortening the linear load elements. In fact, for most models, the driven element will require a shorter load and the reflector a longer one than a resonant single quad element.

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         Table 1.  Construction Values for Three Models of Side-Loaded Shrunken Quads
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+Type               Formula           Total L      L / side    DE load L    RE load L   L-Support
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+Diamond            725/f (MHz)       25.44'       6.36'       3.64'        4.07'       9.0'
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+Square: 1LL        789/f (MHz)       27.68'       6.92'       2.62'        2.98'       9.8'
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+Square: 2LL        684/f (MHz)       24.00'       6.00'       2.42'        2.58'       8.5'
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+Notes:
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+1.  DE and RE load lengths refer to the length of each of two identical load lines at the center of each vertical
+wire on the square models and at the horizontal apexes of the diamond model.  See Fig. 3 for reference.
+
+2.  L = length of wire or wire assembly, including the total circumference of each loop, the length per side, the
+length of each load assembly consisting of two wires and a junction, and the length of the support element
+reaching across the antenna from apex to apex.
+
+3.  All three models use #14 copper wire.
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+Table 1.  Construction values for three 1/8 wl spaced shrunken quad beams, using side-loading for both the
+driven element and the reflector.
+

Table 1 provides initial dimensions for test model shrunken quads for each of the three types of loops investigated. Spacing is a constant 4.31' (1/8 at 28.5 MHz). Each driven element was resonated and each reflector adjusted for maximum front-to-back ratio at approximately 28.5 MHz. Although reflector adjustment affects primarily the antenna feedpoint resistance and driven element adjustment affects primarily the feedpoint reactance, the two adjustments are sufficiently interactive to require a few iterations before optimal values appear.

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All three types of loaded quad loops can be molded into a reasonable parasitic beam. To assess how well we might expect them to perform requires that we look at some of the parameters that can be modeled and compare those values with numbers for a full size quad. Using the entire 10-meter band as a baseline, we can better appreciate what some of those numbers may mean.

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+ Fig. 12 Comparative free space gains of full-size and shrunken quad beam models across 10-meters. +
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Fig. 12 provides a snapshot of the gain performance of the three shrunken beams in comparison with two full size quads, one using #18 wire, the other using #14 wire. Because quad gain does not peak at the same point as the front-to-back ratio, the two full size quads show a decreasing gain across the band. The #14 full-size quad peaks outside the lower end of the band. However, both beams maintain above 6.5 dBi gain for the first MHz of the band, peaking above 7.15 dBi. For comparison, the broadband 2-element Yagi used as a standard in other parts of this series has a maximum gain of about 6.1 dBi.

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The two single-load-per-element quads show a considerable peak in gain--above 6.7 dBi--but only over a smaller segment of the band. Like any shortened antenna, the gain cannot approach that of a full size model. Like any loaded antenna, the bandwidth for most characteristics will be smaller than that of a full size model. The square double-load-line model provides the lowest gain and the narrowest gain bandwidth of all three. At the upper end of the band, its gain drops to that of a full-size single quad loop.

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+ Fig. 13 Comparative free space front-to-back ratios of full-size and shrunken quad beam models across 10-meters. +
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Similar comments apply to the front-to-back ratios of the quad beams, as displayed in Fig. 13. The two full size beams have front-to-back ratios that peak above 25 dB (but at frequencies between the check points that form the graph). The ratio falls off fairly rapidly below design center frequency and more slowly above that frequency.

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There is little to distinguish the front-to-back performance of the single-load-line shrunken quads. The front-to-back ratio peaks at about 13 dB, falling off rapidly at the low end of the band and more slowly at the higher end. The standard broadband Yagi, by contrast, holds its front-to-back ratio at about 10 dB or better across the first MHz of 10 meters. The double-load-line model not only has a lower peak front-to-back ratio (less than 10.5 dB), but as well its band-edge values fall well below 5 dB. Except for a 200 kHz window, its ability to reject QRM is marginal or worse.

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+ Fig. 14 Comparative free space 50-Ohm SWR-bandwidths of full-size and shrunken quad beam models across 10-meters. +
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The SWR curves relative to 50 Ohms and to 75 Ohms, respectively, shown in Fig. 14 and Fig. 15, provide a lesson in some of the illusions of a low SWR. For the full-size quads, a quarter-wave 75-Ohm matching section or a 2:1 transformer would provide a good match between the antenna and a 50-Ohm coaxial cable. At the high end of the band, the SWR performance appears worse than that of the shrunken quads, which exhibit a good match to 75-Ohm cable from the design center frequency to the upper edge of the band.

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+ Fig. 15 Comparative free space 75-Ohm SWR-bandwidths of full-size and shrunken quad beam models across 10-meters. +
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However, one cannot take these numbers in isolation. The steep portion of the shrunken quad SWR curves at the lower end of the band overlaps the antenna's gain peak: the input impedance is most variable where the antenna performs best. In contrast, the curve is flattest in the region where the antenna barely shows beam characteristics. The SWR bandwidth curves of the shrunken quads are essentially more exaggerated versions of the curves for full-size quads, but those exaggerations have more pronounced negative affects upon antenna performance across 10 meters.

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In essence, all three shrunken quads are narrow-band performers when gain, front-to-back ratio, and SWR (or feedpoint impedance) are taken together. Optimal performance covers about 200 kHz of 10 meters, with reasonable performance for about another 100 kHz each way.

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The single load-line models, whether diamond or square, clearly outperform the double-line model. Moreover, in optimizing models of the double load-line model for maximum performance, adjustments as small as 0.001' made a somewhat significant difference. In adjusting the single-line models, change minimums of 0.01' sufficed to optimize the model. (An inch is 0.0833.')

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+ Fig. 16 Free space azimuth pattern of the shrunken diamond-shaped 2-element quad beam model. +
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Between the diamond and the square there is little to choose in performance. Fig. 16 shows the azimuth pattern of the diamond in free space; the pattern of the square is too similar to need reproduction. In evaluating either or both these small beams, investigate the patterns over real ground at the planned height. The azimuth pattern of the diamond (taken at the angle of maximum radiation in Fig. 17) at 5/8 wl height shows a considerable rear lobe that is unlikely to provide much rejection. (The equivalent rear pattern of the standard broadband Yagi is smaller.) At a full wavelength up (Fig. 18), matters improve, especially with respect to side-rejection, but not to the level of a full size quad.

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+ Fig. 17 Shrunken diamond-shaped 2-element quad beam model azimuth pattern at the angle of maximum radiation for a height of 20' over medium earth. +
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+ Fig. 18 Shrunken diamond-shaped 2-element quad beam model azimuth pattern at the angle of maximum radiation for a height of 35' over medium earth. +
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Because these initials models used close spacing and identical loops, with their electrical sizes adjusted by changing the length of the loading lines, they do not achieve all of the gain and front-to-back ratio possible from a shrunken quad beam. Just how much more you can obtain from side-loaded elements depends to a great extent on how much you are willing to unshrink the loops and spread them apart.

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+ Unshrinking the Shrunken Quad for Better Performance +
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In an attempt to improve the anticipated performance of a shrunken quad, I explored several models that alternately increased the spacing between elements and gradually enlarged the physical size of the reflector. The basic dimensional properties of these models are listed in Table 2. Model 1 is the same square quad with a single load line per element used above. Model 2 increases the spacing to 5' (about .14 ), close to the optimum value recommended by Orr and Cowan for a full size 2-element quad. Model 3 returns to the 1/8 wavelength spacing, but enlarges the reflector about 4.5%. Using the new reflector size, Model 4 increase spacing to 4.65' and model 5 further increases spacing to the 5' mark. With this new spacing, model 6 further increases the reflector size to 7% over the original. All models were optimized for maximum front-to-back ratio at a design center frequency of 28.5 MHz.

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+           Table 2.  Some Variations on the Single Load-Line Square Quad
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+Model       Length of Driven Element       Length of Reflector      Spacing
+            per side in feet               per side in feet         in feet
+
+11                6.92'                          6.92'                4.31'
+LL                2.62'                          2.98'2
+
+2                 6.92'                          6.92'                5.00'
+LL                2.72                           3.01
+
+3                 6.92'                          7.24'                4.31'
+LL                2.64'                          2.69'
+
+4                 6.92'                          7.24'                4.65'
+LL                2.68'                          2.71'
+
+5                 6.92'                          7.24'                5.00'
+LL                2.72'                          2.73'
+
+6                 6.92'                          7.40'                5.00'
+LL                2.72'                          2.56'
+
+
+Notes:
+
+1.  Model 1 is the same as the single-load line model used in the comparison with other loaded
+configurations above.  Models 2 through 6 vary the size of the reflector or the spacing or both.
+
+2.  LL=length of load-line assembly on each side of the element.  All load lines are #14 copper
+wire (same as the antenna element) with a spacing of 3" between lines.
+
+Table 2.  Some variations on the single load-line square quad to improve performance.
+

Fig. 19, 20, and 21 graph the results of these modeling experiments. Because performance falls below usable values above 29 MHz, the graphs are limited to data for the first MHz of 10 meters.

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+ +
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+ Fig. 19 Comparative free-space gains of shrunken 2-element quad beams with increased spacing and/or enlarged reflectors. +
+

In general, gain increases with spacing, as Fig. 19 demonstrates. All three models with 5' spacing show the highest gain peak (at 28.25 MHz). However, the smaller the reflector, the more quickly the gain decreases as the frequency departs from the gain center. In fact, model 6, with the largest reflector in the sequence, actually shows a slight increase in gain toward 28 MHz. Merely enlarging the reflector will not increase peak gain, as a comparison of model 3 and 1 at 28.25 MHz will establish. However, enlarging the reflector will increase the gain-bandwidth. Model 3's gain falls off more slowly than that of model 1.

+
+ +
+
+ Fig. 20 Comparative free-space front-to-back ratios of shrunken 2-element quad beams with increased spacing and/or enlarged reflectors. +
+

The front-to-back ratio of the antenna, shown in Fig. 20, also increases most dramatically with increased spacing between the two loaded elements. Model 2, with equal size elements but 5' spacing, rivals the largest reflector for peak front-to-back ratio. The models with the largest reflector dimensions show the slowest decrease in front-to-back ratio as the frequency departs from the design center. However, none of the models is a stellar performer at the low end of 10 meters.

+
+ +
+
+ Fig. 21 Comparative free-space 75-ohm SWR-bandwidths of shrunken 2-element quad beams with increased spacing and/or enlarged reflectors. +
+

The SWR bandwidth relative to 75 is shown in Fig. 21. All of the models show a fairly flat line and a good 75-Ohm match above the design center frequency. Below design center, greater spacing more dramatically flattens the SWR curve than does a larger reflector. Notice model 2 (equal size squares at 5'), whose SWR curve largely overlaps the curve of model 4 (an intermediate size reflector at an intermediate spacing). However, the combination of the two factors, as in models 5 and 6, produces an antenna that is a direct match for 75-Ohm coax from 28.25 MHz to 29 MHz.

+

Summing up the three sets of characteristics, wide spacing and a physically larger reflector produce the maximum gain, highest front-to-back ratio, and the flattest SWR curve. However, the antenna remains superior to a standard 2-element Yagi only over about 500 kHz, with usable directional characteristics for about another 250 kHz. For effective use at the low end of 10 meters, the design center should be set another 250 kHz lower to bring the front-to-back ratio up to productive levels and to bring the feedpoint impedance to levels easily matched in a 75- system. However, the practical upper limit of the antenna as something better than a single full-size quad loop would then be about 28.75 MHz.

+

If the narrower bandwidth for full performance is acceptable and there is a need for compactness, then a shrunken quad can be a good choice. If hardware store supplies are the source of the antenna parts (except for the #14 wire, a Radio Shack staple), then perhaps the model having equal-size loops and 5' spacing may be the best choice. Larger reflectors would require supports longer than standard 10' lengths of thin-wall PVC. The diamond tends to shed ice and water better than the square. However, the square requires less horizontal space.

+
+ A Test Model of a Shrunken Quad +
+

The test antenna was a diamond single-load-line quad with equal size loops spaced 5' apart. This configuration permitted an all-PVC support system on a 5' boom of 1.25" nominal Schedule 40 PVC. The spreaders are 9.1' lengths of PR 315 0.5" nominal PVC. Each piece fits through a 0.875" hole through the boom, adjacent holes for spreaders at each end. #10 stainless steel (SS) hardware fixes each spreader in place. As shown in Fig. 22, spreaders are mounted about 9" to 10" from the ends of the boom. To the end of each spreader, I glued a half-inch Tee to carry the wire. At the sides, I glued extra 2" lengths of half-inch PVC, drilled at 3" spacing, to establish the load-line separation. (Of course, at the center of the boom is the plate and U-bolts for the boom-to-mast mounting.)

+
+ +
+
+ Fig. 22 Overall structural features of a PVC-supported 10-meter shrunken quad. +
+

The total circumference of the diamond loop is about 25.4' long. With expendable twine, create a loop through the tees, stressing the spreaders outward towards the end of the boom. The twine loop should be just about the right circumference as the spreaders bend in a plane with the end of the boom. Stressing the spreaders prevents them from waving front-to-back in the wind and strengthens the overall structure.

+

I drilled the end of the boom for an additional short piece of half-inch diameters CPVC about 5" long. (Tan CPVC is closer than white PVC to its listed diameter: 0.5" nominal diameter CPVC has an outside diameter just enough larger than a 5/8" hole-cutter to require a small amount of filing for a fit.) Drilled at a 3" spacing, this piece acts as the anchor for the load lines. A pair of short sections of 1/8" nylon rope will attach to the final spacer of the lines each side of center.

+

Models of the test antenna in free space, as well as at 20' and at 35' over real medium ground suggest driven element load line lengths of 3.6' to 3.8' each for the driven element and 4.0' to 4.1' for the reflector. I chose to install driven element lines (without a shorted end) of 4' and reflector lines of 4.25' to allow for variables of building. Although there is a slight mismatch with the model, since the Tees round the quad corners, the most significant variable concerns the stressing of the spreaders. I found that I tended to overstress the assembly, loosing a half inch or so of wire length per side. The longer load lines permit on-site adjustments before final soldering.

+

I used a single piece of wire for the top two sides and the top wire of each load line. Install at least 2 spacers (4" pieces of half-inch CPVC, drilled at a 3" spacing) on each load wire and tie off the load wire to a third spacer. Tie this last spacer to the one on the boom with the end of the nylon rope. Fig. 23 shows some of the details of the load-line arrangement. A single wire for the reflector lower half and load-line bottom wire replicated the top half, including load-line spacing and termination. Separate wires for the remaining sides and their associated bottom wire for the loads of the driven element completed basic assembly. Add thin position-locking wires, soldered to the main wire at each major corner, including the top spreader. A coax connector on an L-shaped piece of plastic completes assembly.

+
+ +
+
+ Fig. 23 Loadline assembly details for the PVC-supported 10-meter shrunken quad. +
+

The resulting structure, with outward-curved spreaders at each end of the boom has its own aesthetic appeal. More significantly, it is sufficiently rigid to hold its shape in a gale, but flexible enough to wiggle through the breezes, transferring spot stress throughout the structure.

+

Initial testing can be done with the beam pointed skyward. Temporary shorting bars permit easy adjustment. I used short lengths of #12 copper wire terminated with ring connectors. Around the load-line wires I crimped half-inch L-brackets, passing a #6 bolt through the two holes and the ring connector on one end of the #12 wire.

+

If not off the mark by more than a half MHz, you can initially adjust the driven element for lowest SWR as a marker of resonance. Adjusting the reflector will either be a matter of guess work or of in-place adjustment. A low-level signal source at a distance of at least 10 wavelengths (about 350' on 10 meters) will help you find and adjust the minimum signal off the rear of the beam. On my test model, my initial guess-work settings, based on the computer models and upon my estimates of how much I shortened the beam during construction, allowed the reflector adjustment to be made in one trial, with no further work needed on the driven element. (I am not always--or even usually--this lucky, even with computer guidance.)

+

I added about 2.5" of length to each load line initially to compensate for loop compression during building (about half an inch short on each of the diamond's four sides). With a 50-Ohm coax line connected directly to the feedpoint, the final settings placed a minimum SWR window of 1.6:1 from about 28.3 to 28.7 MHz, with under 2:1 SWR from 28.1 to over 29 MHz. At a 25' height, these frequencies climbed about 0.2 MHz.

+

Reflector adjustment was also close to the compensated mark, requiring about a half-inch of load-line lengthening to place the maximum null at 28.5 MHz. Rechecks of the driven-element SWR proved unworthy of further adjustment. The reflector null was fairly sharp, with noticeable drops as little as 50 kHz off maximum. However, within the limits of simple S-meter readings of uncalibrated test signals, the curve tracked the model's predictions quite well. Once set, the difference between maximum null and the rearward signal at the band edges of 10 meters was about 2 S-units.

+

Although the shrunken quad can be operated as-is over a fair portion of 10 meters, its impedance is a better match for 75-Ohm cable than for the 50-Ohm test cable. A quarter-wave section of 75-Ohm cable might well improve the SWR bandwidth, although a 1.5:1 broadband transformer or transmission-line transformer might produce a more accurate match. The basic narrow bandwidth of the antenna's gain and front-to-back ratio will not be affected by these measures.

+
+ Summary +
+

Because the shrunken quad can be built from wire and PVC, it is among the cheapest of the beams so far tested, even requiring the least hardware. N4PC's sturdier all-Schedule 40 construction for 17 meters is a model for lower band use.7 In fact, on the WARC bands, the narrow bandwidth of the shrunken quad's peak performance figures is no hindrance. Indeed, the antenna may have its best home on those bands. It is also at home wherever one requires a small footprint but can tolerate some offsetting vertical dimensions.

+

Alternatives to the use of linear load lines are unlikely to improve performance in any especially noticeable way. R. G. D. Stone, G3YDW, reported the same narrowness of performance and SWR bandwidth on his capacitively loaded miniquad for 20 meters.8 Indeed, voltage-maximum loading, whether by load-lines or linear capacitive "hats," is likely to yield the fewest loss sources of the many schemes used to shrink quads.

+

Capacitive hats, of course, are not limited to quads, nor to verticals. I wonder what they might do for a shortened Yagi.

+
+ Notes +
+

1. See William Orr, W6SAI, and Stuart Cowan, W2LX, Cubical Quad Antennas, 3rd Ed. (Lakewood, NJ: Radio Amateur Callbook, 1993); and Bob Haviland, W4MB, The Quad Antenna (Hicksville, NY: CQ Communications, 1993). The number of articles on quads is legion--and this piece makes legion + 1.

+

2. For a circular quad, see Howard Hawkins, WB8IGU, "12-Meter Quad" in The ARRL Antenna Compendium, Vol. 3 (Newington, ARRL, 1992), p. 114.

+

3. Kris Merschrod, KA2OIG/TI2, "Coil Shortened Quads - A Half-Size Example on 40 Meters" in The ARRL Antenna Compendium, Vol. 2 (Newington, ARRL, 1989), p. 90. See this article for references in the literature to each of these loading schemes.

+

4. Paul Carr, N4PC, "The N4PC SQUAD (Squished Quad)" in Lew McCoy, W1ICP, Lew McCoy on Antennas (Hicksville, NY: CQ Communications, 1994), pp. 83-85. See this article for references to earlier work on the mid-side loaded quad.

+

5. All patterns and figures in this study are derived from NEC-2 in the EZNEC 1.0 package available from W7EL. It should be noted that tapered models in MININEC tend to show resonance with a length formula between 1044 and 1045 divided by the frequency in MHz, all other factors held constant. Since NEC-2 does not "cut" corners, it is used as a basis for discussion here. This preference applies only where the wire diameter is constant throughout the model. NEC-2 has difficulty with changes in wire diameter, especially in models with some degree of geometric complexity. The diameter change difficulty can be minimized by adding separate wires for the last portion of each corner. Using this technique for quads with tubing for the horizontal members and wire for the sides brings the gain figures into close coincidence with MININEC models, although the feedpoint impedance in the two modeling systems continues to diverge significantly.

+

The diamond models used here generally have a short horizontal 3-segment wire at the lower apex as the feedpoint. Compared to a pure diamond, fed at the apex under a combined split feed modeling system, the diamond models with the flattened bottoms tend to require a slightly smaller circumference (about 0.5%), which would make no significant difference in actual construction.

+

6. With each dimension about 75% of full size, the area is less than 58% of that of a full size quad loop. However, element spacing would remain unchanged from a full size model, yielding 58% as the volume gain as well.

+

7. See Carr, N4PC, "The N4PC SQUAD (Squished Quad)" in Lew McCoy, W1ICP, Lew McCoy on Antennas, pp. 83-85.

+

8. R. G. D. Stone, "Practical Design for a Top-hat Loaded 14 MHz Miniquad," Radio Communications, October, 1976, as quoted in Moxon, HF Antennas for All Locations, 2nd Ed. (RSGB, 1993), pp. 207-208.

+
+ +
+
+ Appendix +
+
+ Capacity Loading vs. End-Stub Loading a Shrunken Quad +
+

Long after I completed my foray into shrunken quads, my perceptive YL, N4TZP, noticed my brief remarks on capacity-loaded quads. These versions of shortened quads use a single wire from the side points instead of the parallel lines that I used, following Paul Carr's lead. She asked a simple question: is there any advantage to one system of loading over the other?

+

The answer comes in two parts: 1. There is no electrical advantage to one system over the other. 2. There may be a mechanical advantage to one over the other, depending upon your quad construction technique.

+
+ +
+
+ Fig. 24 General outlines of a capacity-loaded shrunken quad, with driven element dimensions to the left and reflector dimensions to the right. The missing parts of the diagram are mirror images of the parts shown. +
+

Fig. 24 shows the physical layout of a 2-element diamond quad beam using a capacity "side" hat (the electrical equivalent of a vertical's top hat) to permit tuning the elements to resonance or other points. The diamond's dimensions are the same as the model built and tested from Fig. 22 and Fig. 23. Capacity hat dimensions are shown on one side for the driven element and on the other for the reflector. Element spacing remains the same at 5 feet.

+

I derived the dimensions by a simple modeling technique. From the final model of the quad I built, I erased one of the elements in each of two separate models and determined the resonant frequency of each element. Then I eliminated the parallel stubs and joined the side peaks. Finally, I created a capacity hat with a wire inset plus two wires parallelling the main element, adjusting their lengths until the loop was resonant on the same frequency as its stub-predecessor. I then rejoined the two separate elements in one model.

+

You can adapt this technique to the actual construction of antennas. Construct one element at a time and tune it to the resonant frequency given by a model that you have previously broken down into separate elements. Combining the elements should assure that you are close to optimal performance without concern for interpreting element interactions during tune-up.

+

The technique of replacing the stub by a capacity hat is justified on the basis of the fact that the two point originally separated by the parallel stub have the same current and can therefore be connected together. However, a capacity hat in one dimension (ignoring wire thickness) requires a greater length than a two-dimensional flat disk-type hat. The dimensions shown are applicable to #14 copper wire and to the separation wire length (0.5' in this model). As with the parallel wire stub, careful pruning is necessary.

+
+ +
+
+ Fig. 25 Free space azimuth pattern for a 2-element capacity-hat-loaded shrunken quad of the dimensions shown in Fig. 24. +
+

Fig. 25 shows the free space pattern that resulted from the exercise. Forward gain (nearly 6.2 dBi) and front-to-back ratio (about 18 dB) are too close to the corresponding numbers for the stub-quad to make any difference in performance. SWR, gain, and front-to-back figures over 10 meters correlate well with those for the stub-quad.

+

Which shortening technique you use likely will depend upon your construction method. The stubs in the shrunken quad I built are preferable with the stressed support arms, since each stub rides free, with no nearby metallic masses to detune it. Scaling up the antenna for lower bands, however, may call for the capacity hat technique. If you use flat-face Xs to support the quad wires and if there is any metal in them, then the capacity hat technique may be better suited to your needs. It would reduce coupling to the support framework.

+

End loading antenna elements is a technique that deserves some further study. Although capacity hats are somewhat out of vogue in amateur antenna-making, except for vertical mobile antennas, they do offer somewhat higher efficiencies than other forms of loading. They load where the current is least, rather than adding coil losses at high current points or otherwise distorting the radiation pattern near the feedpoint. Although near-circular hats are considered somewhat ungainly, they may still have a place in at least monoband horizontal antennas.

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Return to Article Index Page

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Topics: HF Upper, Quad, Small Beams


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Modeling and Understanding Small Beams

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Part 8: Capacity Hats

+

L. B. Cebik, W4RNL

+
+
+ +

+
+

For horizontal antennas, capacity hats seem to have gone out of style. However, we may be overlooking a useful means of shortening Yagi antennas by neglecting what some call "capacity loading." In fact, by using hats, we can construct a quite useful 2-element Yagi and gain something over inductive loading.

+

The elements for the proposed Yagi were just under 75% of full size, so I calculated the anticipated hat size using the usual means for antennas down to about 2/3rds normal length. The results were far off the dimensions modeled on NEC-2. The shortened capacity-hat 2-element Yagi for 10-meters built as a test prototype answered closely to the NEC results. The success of the antenna suggested that the traditional methods for calculating hats might need some revision to calibrate them to NEC models. Both the calibration and the antenna are worth noting, if for no other reason than to restore capacity hats to the repertoire of techniques for building shortened Yagi beams.

+
+ Modeled Antennas with Hats +
+

A hat is a "loading" assembly attached to the end(s) of an antenna element. It has two very significant properties. First, it is used to bring a shortened antenna to resonance or some other specific set of characteristics. An example of the use of a hat for other than feedpoint resonance is the shortening of a parasitic element in a Yagi. Second, the hat does not contribute to the radiation of the overall antenna element.

+

In these two characteristics, the hat performs like a lumped constant load inserted at the feedpoint (center-loading for a dipole, base-loading for a vertical) or along the antenna element (mid-loading for a dipole, center-loading for a vertical). For a given antenna length down to about 60 degrees (for a vertical or for each side of a dipole), a hat generally provides greater efficiency than other forms of loading.

+

A hat performs its function as a significant physical structure rather than as a lumped component. To programs like NEC and MININEC, an antenna is just a physical structure along which currents flow. Inductive and capacitive loads are treated as lumped constants. Hats, however, are parts of the structure and modeled as such. Models may thus provide some insight into hat operation.

+
+ +
+
+ Fig. 1 The current flow along a "bent" vertical antenna. +
+

Related to the hat is the bent antenna, one with the element beginning in one direction and, at a certain point, taking off in a direction 90 different. The bent vertical over perfect ground, modeled in Figure 1, illustrates the current flow along the antenna. Notice that the current in the bent portion contributes significantly to the overall antenna pattern, as illustrated in the far field pattern modeled in Figure 2.

+
+ +
+
+ Fig. 2 The far-field pattern of the bent vertical, showing both vertical and horizontally polarized components. +
+

By way of contrast, a hat is a symmetrical structure. Although Figure 3 shows a Tee configuration, any number of symmetrical structures achieve the same goal. Among the more common forms are spokes, circular disks, and other open-frame structures with perimeters, including squares, hexagons, and octagons. Even triangles or simple opposed wires will work well, so long as symmetry is maintained. Figure 4 shows a few examples of hat structures.

+
+ +
+
+ Fig. 3 The current flow along the elements of a hat structure. +
+
+ +
+
+ Fig. 4 Some examples of hat structures. +
+

At corresponding points outward from the element end to which the hat is attached, currents are equal but flowing in opposite directions. The result is (if perfect) no resultant field or (within construction limits) a negligible field. Figure 5 models the far field for an antenna of the same vertical dimension as the antenna in Figure 2, but with a hat instead of a bent top. There is no horizontal far field component to the antenna's radiation pattern.

+
+ +
+
+ Fig. 5 The far-field pattern of a hatted vertical. Note the absence of a horizontal component. +
+

The antenna's current distributes itself at the hub of the hat and flows equally, but at decreasing values, along the hat spokes. If the structure has a perimeter wire, the current then proceeds from the spoke tip in two directions, reaching minimum value at the mid-perimeter points of the framework. Assuming a vertical antenna portion of fixed length, the current level at the hat hub will be somewhat higher than the current level at the bend of an antenna like that if Figure 1. The lower level for the bent vertical is occasioned by the interaction of fields at and near the bend point.

+

Well-modeled antennas with hats provide a close correlation to constructed antennas. The models I have used generally provide enough wire segments in the main element so that each segment length is similar to the segment lengths in the hat. The results have been as accurate as my modest shop equipment will allow me to reproduce.

+

However, hat models tend to drive both NEC-2 and MININEC toward their limits of accuracy, but in different ways. Some hat models in NEC can easily exceed recommended limits for multi-wire junctions and for minimum angles between adjoining wires. If the hat material is of a different diameter than the main antenna element, NEC-2 can respond to some combinations with scarcely credible values for gain and source impedance. Although MININEC handles such junctions as a matter of course, it is sensitive to the acute angles between hat spokes. Moreover, complex hat structures can quickly exceed the allowable number of segments permitted by the program. Both programs are sensitive to other limitations as well. Nonetheless, models of closed hats structures (with spokes and a perimeter wire) showed a close correlation between programs, while the deviation between the programs with hats composed of spokes alone was usually within 2% or so. I suspect that the antenna current cancellation within the hat assemblies has much to do with the better than anticipated modeling results.

+
+ +
+
+ Fig. 6 Moving from very casual to more precise methods of modeling. The arrows indicate directions of wires from End 1 to End 2 in NEC wire table conventions. The sample dipole consists of a 10.6' 1" aluminum element with 1" material also used in the hat, which has 0.8' spokes. +
+

Modeling capacity hats also requires careful attention to detail, depending upon the data one seeks from the model. As Figure 6 suggests in part A, the most casual technique in modeling would be to create a dipole and then add outward pointing spokes at each end. Finally, connect the spoke tips with a perimeter wire. Although this model will return correct values for gain and feedpoint impedance, the currents along the spokes will be incorrect with respect to phase at the left (or starting) end of the model. For example, in one 10-meter model, the current phase along the spoke is approximately -4.6° instead of the figure of 175.3° that the casual model returns.

+

Reversing the spokes at the initial end to model them from point to hub (main element) will correct this error, as shown in part B. However, using single wires to connect the spokes will return an erroneous phase reversal at the midpoints of the wires on both ends. Current is least at the midpoints of the perimeter wires: this is the point at which the model should begin on one end and end on the other. For most accurate modeling of antenna current, each perimeter segment should be split in the middle into two wires, as shown in part C. On the initial end, begin from the midpoint and extend the wire to the spoke point. On the finishing end, model the last wires from the spoke points to the perimeter midpoints.

+

If you only require a little data from your model of a capacity-hat vertical, dipole, or Yagi, quicker casual models will do. However, if you wish to derive the maximum understanding of antenna performance and properties, model with great care. Even with the greatest care in model construction, there remain limits to what method-of-moment models can calculate, especially within the boundaries of nonengineering versions of the programs. For further notes on the placement of hats at other than antenna element ends, see Where Do I Hang My Hat? at this site.

+

So far, we have a shortened antenna with a symmetrical physical end structure called a hat. However, looking at the antenna this way alone does not yet justify calling the assembly a capacity hat.

+
+ Capacity Hats +
+

According to the classical transmission-line analogy for antennas, we may view an antenna as a single open-wire transmission line. The usual sorts of antennas investigated from this perspective are either equal to or shorter than quarter wavelength verticals or half wavelength dipoles. If not resonant, these antennas will exhibit capacitive reactance. Hence, lumped component inductive loads may be used to increase their electrical length.

+

Alternatively, one may calculate the amount by which an antenna is shorter than resonant in electrical degrees. If we know the characteristic impedance of the antenna-transmission line, we can use this figure in the same way we do for parallel line capacitive stubs to calculate the necessary size of a corresponding single-wire "stub" for the end of the antenna.

+

A stub for a single wire transmission line will have a different construction from parallel line stubs. It will appear as a symmetrical surface or framework of a size providing the necessary capacitive reactance called for by the calculation of the missing antenna segment. This is the capacity hat.

+

Thinking of the hat as a capacitor "plate" can lead to many misleading conceptions about hats. Although real-world antennas capacitively couple to many conductive objects and surfaces, the capacity of a capacity hat is not a function of coupling to anything. For example, the capacitance between capacity hat "plates" for a free space dipole at 3 MHz and 2/3rds resonant length is under 0.05 pF. Hat "capacity" is a function of the capacitive reactance necessary to bring a shortened antenna to resonance (or some other specification) under the transmission-line analogy calculation. The value of calculating it is to convert the electrical property of reactance into a physical property: area. The standard model surface for a hat has long been the circular disk with no thickness in isolated free space. Standard references correlate its diameter to a certain capacitance.

+
+ +
+

where C is the capacitance in pF and d is the diameter of the disk in inches.1

+

The capacitance of open-frame capacity hats made up of spokes and (optionally) a perimeter wire is not the same as that of a flat disk. Open-frame capacity hats have a finite thickness. Moreover, the capacity of the hat will vary with the number of spokes in a complex manner. Therefore, the simple correlation between disk diameter and capacitance will not work for these types of hats.

+

As an exercise, I constructed models of hats at 3 MHz for a 60 long, 1"-diameter antenna using increasing numbers of spokes for both spoke-only and perimeter-wire configurations. The hats in the models used #28 wire to approach a condition where the thickness was insignificant relative to the surface area. The exercise ceased at 32 spokes, which approaches or exceeds the NEC-2 recommended number of wire junctions at any given point on an antenna. The data points included 3, 4, 6, 8, 12, 16, 24, and 32 spokes, which were then resolved into curves fitting the following equations:

+
+ +
+

where LT is the spoke length, LS is the shortest spoke length (at 32 spokes), LL is the longest spoke length (at 3 spokes), NH is the highest number of spokes considered (32), and NX is the number of spokes presently in question. The exponent, EE, is given by

+
+ +
+

where NL is the lowest number of spokes considered (3). This simple curve-fitting exercise made it possible to generate graphs on a linear baseline, as shown in Figure 7.

+
+ +
+
+ Fig. 7 The required length of spokes vs. the number of spokes in spoke-only and in spoke-plus-perimeter-wire capacity hats (from 3 to 32 spokes) at 3 MHz for a 60 long 1" diameter aluminum antenna. +
+

The significance of the curves is that they indicate a convergence in the vicinity of about 60 inches. This value would approximate a solid disk, since adding further spokes would not significantly further reduce the length of each spoke. A disk with a diameter of 120 inches would have a capacitance of approximately 108 pF. This value is from 30% to 60% distant from values generated by any of the transmission-line analogy equations. Nonetheless, one can correlate open-frame hats to antenna element loading requirements and to modeled hats in a rough but systematic manner. See the Appendix for further notes on calibrating transmission-analogy calculations to NEC-modeled hats.

+

Whatever the correlation between capacity hats and loading requirements, it will work equally well for a vertical over perfect ground and for each end of a dipole in free space with no ground reference of any sort. The same holds true of open-frame hat structures. In short, the hat should be thought of in the same way we think of parallel transmission-line capacitive stubs: both provide requisite amounts of reactance where needed. Like stubs, capacitive hats are thrown off their prescribed task by being too closely coupled to external objects.

+

For some further studies of capacity-hat verticals--along with variations on strict "hat" top loading--see Half-Length 80-Meter Vertical Monopoles: the Best Method of Loading Parts 1-5.

+
+ Calculating Capacity Hats +
+

Modeling a capacity hat is a matter of trial and error without some guiding approximation of the proper hat size. However, without extensive modification, classical VLF calculations of hat size provides confusing guidance, if any at all. See the Appendix for further notes on this subject. Here we shall briefly look at the traditional transmission-line analogy.

+
+ +
+
+ Fig. 8 A bi-conical antenna-transmission line and a thin-wire antenna. +
+

Figure 8 shows the essential elements of two antennas: a conical dipole and a wire dipole. For the conical dipole or bi-conical transmission line, the ratio of voltage to current will be everywhere the same along the length of the dipole (ignoring the ends). Hence, the antenna-transmission line has a constant or characteristic impedance, ZO. Thin wire antennas only approximate this condition: the impedance varies along the wire and is greatest at the ends. However, it is useful to derive the average impedance of the antenna and to use that figure as if it were the characteristic impedance.

+

As Belrose has noted in his review of resolutions to the integrals that describe the average characteristic impedance (Zo) of antennas, there are at least four different formulations: Shelkunoff, Laport, Howe, and Labus (as modified by Jordan and Balmain). All were developed for low frequency applications.2 The methods all give different values for Zo and consequently for the requisite loading capacitive reactance and its associated capacitance at the frequency of interest. Figure 9 demonstrates the differences at 30 MHz, using capacitive reactance as the comparative figure for a 30 compensating hat. None closely approaches the reference curve of reactances derived from NEC models of 30-long antennas, which most closely approximate the values of capacitance indicated by exercises illustrated earlier in Figure 7.

+
+ +
+
+ Fig. 9 A comparison of calculated "loading" (compensating) reactances derived from several formulations of the characteristic impedance equation. The line labeled "NEC" is the curve of values derived from the feedpoint reactance of 30-long verticals over perfect ground and 60-long dipoles in free space. +
+

Belrose adopts Howe's equation as yielding results for feedpoint impedances that agree most closely with measured results. For purposes explained in the Appendix, I shall note the Shelkunoff equation to illustrate the calculation technique. This is also the version used by Schulz and which appears in ARRL publications.3 For dipole antennas less than a half wavelength long,

+
+ +
+

where Z0(av) is the "average" characteristic impedance of the antenna, h is the overall height or length of the antenna element, and a is its radius (with h and a in the same units and where h is much greater than a). For a vertical antenna, a quarter wavelength or less in height, the multiplier is halved:

+
+ +
+

For clarity, the following discussion will be limited to shortened vertical antennas at least 60 electrical degrees long, that is, at least two-thirds full size. To apply the discussion to dipoles in free space, think of the dipole as two verticals base-to-base.

+

Neither equation 5 nor any of the other versions notes above provides a basis for correlating open-frame capacity hats to antenna element lengths of varying diameter throughout the HF frequency range (3 to 30 MHz). Since the antenna diameter is a significant percentage of antenna length at HF, and a varying one as the frequency increases, one must introduce a corrective based upon the ratio of diameter (or radius) to length. The diameter corrective will yield consistent results as the main element is varied in diameter at any given frequency, but the correlation varies as the frequency is raised. Hence, an additional frequency corrective is needed.

+

The remainder of the required calculation is provided by most recent editions of The ARRL Antenna Book. The difference (in electrical degrees) between the shortened antenna and the full-size antenna represents the number of degrees of capacitive reactance to be supplied by the capacity hat. The required capacitive loading can be found in two simple equations:

+
+ +
+

where ZO is the average characteristic impedance just calculated, XC is the required capacitive loading reactance in ohms, and is the required loading length in electrical degrees, that is, the missing part of a quarter wavelength. From the capacitive reactance, we move to the required capacitance

+
+ +
+

where f is the frequency in MHz and C is the capacitance in pF. Ostensibly, we need only move to equation 1 to convert this value into the diameter of a capacity hat. However, we have already seen that complex open-frame hat structures do not answer readily to this simple maneuver.

+
+ Capacity Hat Dipoles and Yagis +
+

To construct a capacity hat dipole, simply construct two vertical antennas, base-to-base, and feed at the base junction. The capacity hat sizes for any given frequency and choice of materials will be virtually identical to those calculated for a vertical. Expect the feedpoint impedance of a 120° dipole to be about double that of a corresponding 60° vertical: about 59 Ohms compared to 28 Ohms.

+

Horizontal capacity-hat dipoles do not suffer the same type of ground loss as ground-mounted verticals. Assuming similar structural losses as a vertical due to the choice of antenna and hat materials, as well as construction methods, a capacity-hat dipole is subject to standard ground reflection losses that depend upon ground quality. Capacity-hat dipoles do not radically change their feedpoint impedance when modeled over ground, which makes them reasonably close matches for 50- coax feedlines. Moreover, they do not suffer nearly the degree of narrowed SWR bandwidth experienced with center-loaded dipoles.

+

The comparative gains of 120° dipoles (twice the length of a 60° vertical) when center loaded with a 300-Q inductor (a generous value out of doors) and when capacity-hat loaded are approximately 1.85 dBi and 2.05 dBi, respectively. Figure 10 demonstrates the reason for the difference: the capacity hat dipole maintains close to the same current levels--increment for increment--as a full-size dipole, whereas the center-loaded dipole shows lower current levels everywhere along the element. The gain differential for a dipole is small, perhaps small enough to be ignored in operation. However, when such dipoles are placed in a 2-element Yagi configuration, they suffice to alter performance more significantly.

+
+ +
+
+ Fig. 10 Simplified portrait of current levels along a full-size, center-loaded, midelement-loaded, and capacity-hat loaded dipole. +
+

The center-loaded Yagi can attain a higher front-to-back ratio, which can be tailored to some degree by changing the reflector inductor Q. However, the increase comes at the expense of forward gain. The capacity-hat Yagi exhibits higher gain that approaches the value for a full-size Yagi of the same spacing. At the same time, its front-to-back ratio is limited essentially to the levels achieved by a full-size 2-element Yagi. Figure 11 provides comparative free-space azimuth patterns for the two types of Yagis using identical element lengths, diameters, and spacings. Figure 12 shows in graphical form the gain across the 10-meter band of center-loaded and capacity-hat-loaded Yagis with elements of identical length, diameter, and spacing. Figure 13 shows the front-to-back ratio across the band for the same antennas.

+
+ +
+
+ Fig. 11 Free space azimuth patterns for 2-element center-loaded and capacity-hat loaded Yagis using identical element lengths. +
+
+ +
+
+ Fig. 12 Comparative gain from 28 to 29.5 MHz of center-loaded and capacity-hat loaded 2-element Yagis. +
+
+ +
+
+ Fig. 13 Comparative front-to-back ratios from 28 to 29.5 MHz of center-loaded and capacity-hat loaded 2-element Yagis. +
+

The weight one gives to the relative advantages of center-loaded and capacity-hat Yagis depends upon the requirements of the application. For general amateur work, the greatest advantage of the capacity-hat Yagi may lie in its broader SWR-bandwidth curve. Figure 14 compares 10-meter 2-element Yagis of comparable spacing. The capacity-hat model more closely approximates the performance of a full-size antenna than does the center-loaded model (set for a load Q of 300). Moreover, the capacity hat Yagi also maintains its other characteristics--gain and front-to-back ratio--over a wider bandwidth. The capacity-hat Yagi is at least a candidate for a small mono-band Yagi--if one can build it.

+
+ +
+
+ Fig. 14 SWR bandwidth curves for full-size, center-loaded, and capacity- hat loaded 2-element Yagis, referenced to the feedpoint impedance. +
+
+ Building a Capacity-Hat Yagi +
+

The test antenna was a 10-meter 2-element Yagi with the following dimensions: driven element: 11' 7"; reflector: 12'2"; spacing 4'3"; elements: 0.75" diameter hardware store aluminum (0.05" wall thickness). These dimensions are the same as those for the linear-loaded antenna used as a test model. In fact, the capacity-hat antenna was created by removing the linear loads and adding capacity hats to the element ends. Figure 15 reviews the general construction methods used for the PVC boom and half-inch plywood element plates.

+
+ +
+
+ Fig. 15 General construction of a 2-element 10-meter capacity-hat loaded Yagi. +
+

Since the linear loads (or corresponding inductive loads) were of equal value for the driven element and for the reflector, I anticipated needing capacity hats of equal size for these elements. Models indicated that a #12 square hat with a perimeter wire would require spoke between 10.6" and 10.8" long for both elements. I constructed four "identical" hats from #12 house wire with the insulation removed. Using a scrap of plywood about 2' square, I drilled a 3/4" hole in the center and laid out the spoke and perimeter wire runs in pencil. I placed a short scrap of 3/4" diameter aluminum tubing in the hole. The spoke wires were cut long with a 1.5" "U" at one end, bent 90 to the spoke. The four spoke Us were placed against the aluminum tube and clamped with a stainless steel hose clamp. The Us spaced the spokes evenly around the outside of the tube. The excess of the U at the curved end was bent outward slightly to prevent the clamp from falling off when loosened. The spokes were temporarily stapled to the base-board along their inscribed paths. Each was about a half inch longer than the correct spoke length.

+

The assembly of the hat was a task for a heavy (100 watt) soldering iron or gun. Starting at one corner, I bent the spoke end around the perimeter wire and soldered the junction. Bending the perimeter wire 90, I proceeded to the next corner and repeated the process, finally ending back where I began. Figure 16 shows the outlines of the hat on the jig. After construction, each hat was removed from the jig tube by loosening the hose clamp and moved to its element. since copper met aluminum at the junction, both metals were coated with contact "butter" during assembly. For long-term outdoor installation, the junction should be sealed as much as possible to slow weathering and other bi-metal problems.

+
+ +
+
+ Fig. 16 Simple hat construction for the 10-meter beam. +
+

Models indicated that the individual elements of the Yagi, if fed as dipoles, should resonate at 28.25 MHz for the driven element and 27.3 MHz for the reflector. I pretuned each element by resonating it independently. The maximum hat placement adjustment required was about a quarter inch down the element length, a move likely created by either the inexactness of my simple shop technique or by the flaring structure at the hat-element junction--or by both. The models proved quite accurate, and each dipole resonated with a feedpoint impedance close to 60 Ohms.

+

Combining elements into a Yagi required two steps beyond mounting the dipoles on the boom. First, the reflector-element feedpoint space was closed with a half-section of tubing across the former feedpoint opening. Second, the driven element feedpoint reactance was compensated by two 300 pF series capacitors, one from each side of the element center. This compensation provided a modeled SWR under 2:1 from 28 to 29.5 MHz without compromising antenna performance.

+
+ +
+
+ Fig. 17 Free-space azimuth patterns for the 10-meter capacity-hat Yagi across the band. +
+

Figure 17 shows the modeled antenna performance across the 10-meter band. Although the figure does not permit one to sort the lines, the overall consistency of performance in terms of gain and front-to-back ratio is clear. Figure 18 shows the modeled SWR across the band. Although both figures are for models in free space, at 20 feet above medium ground, the antenna showed no significant variations.

+
+ +
+
+ Fig. 18 Calculated SWR of the compensated 2-element capacity-hat Yagi across 10-meters. +
+

Pretuning the elements individually resulted in a Yagi requiring no further adjustments after final assembly. Band-edge SWR figures were slightly higher than those modeled, rising to about 2.2:1. Local point-to-point test confirmed performance similar to my full-size 2-element Yagi, allowing for a 15' height differential. Several months of use has also confirmed the ability of the simple hats to slip the wind and remain well-positioned, since no change of performance of SWR have been noted. However, the dissimilar metal junction should be inspected and renewed at least yearly.

+

Like its linear-loaded predecessor, the capacity-hat Yagi can be partially disassembled for transport to portable operating sites. A six-foot long truck bed or van handles the 10-meter antenna with ease.

+
+ Conclusion +
+

This exercise began with a simple question: are capacity hats an apt candidate for short 2-element Yagis. The initial model for the 10-meter beam was discovered by a trial-and-error process after handbook calculation procedures missed the mark by a good bit. That failure led to a more detailed investigation of the applicability of classical transmission-line analogy calculation procedures to HF antennas.

+

The capacity hat is a very reasonable way to obtain most closely full-size performance from a shortened-element Yagi. Although the hat structure is somewhat more ungainly than a feedpoint linear or inductive load, the capacity-hat Yagi exhibits a broader bandwidth for the essential performance properties of gain, front-to-back ratio, and feedpoint impedance. If these factors are important to a particular operational set-up, then building a capacity-hat Yagi is worth serious consideration.

+

The other artifact of the exercise, the simple GW Basic program attached to this article, in conjunction with one of the MININEC or NEC-2 modeling programs, may get you started.4

+
+ Notes +
+

1. F. E. Terman, Radio Engineers' Handbook (New York: McGraw-Hill, 1943), p. 113.

+

2. See John S. Belrose, "VLF, LF, and MF Antennas," in Rudge, et al., Ed., The Handbook of Antenna Design, Volume 2 (London: Peregrinus, 1983), pp. 562-565, 598-599. See also E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems, 2nd Ed. (Englewood Cliffs: Prentice-Hall, 1968), pp. 390-96, for a treatment of the work of Siegel and Labus. Also recommended is E. A. Laport, Radio Antenna Engineering (New York: McGraw-Hill, 1952), Chapter 1 ("Low Frequency Antennas"). Laport notes that even at these low frequencies, we must be "contented" with approximations (p. 28). Finally, see S. A. Schelkunoff, Electromagnetic Waves (New York: Van Nostrand, 1943), p. 290, as well as Jordan and Balmain, pp. 384-88.

+

3. Walter Schulz, K3OQF, "Designing a Vertical Antenna," QST (September, 1978), 19-21. Schulz's graphs have been replaced by equations in recent editions of The ARRL Antenna Book, 17th Ed. (Newington: ARRL, 1994), p. 2-40.

+

4. All NEC-2 models were done on EZNEC 1.06, available from Roy Lewallen, W7EL.

+
+ +
+
+ Appendix A +
+
+ CALIBRATING TRANSMISSION-LINE-ANALOGY CALCULATIONS TO NEC MODELS +
+

The classic process of calculating the required size of a capacity hat to load a shortened vertical antenna to resonance presents a model of apparent simplicity in 4 steps. Using the height and radius of the main antenna element, one calculates the average characteristic impedance, treating the antenna as a one-wire transmission line. From the characteristic impedance and the "missing" length of antenna relative to a resonant quarter wavelength antenna, one calculates the required capacitive reactance to achieve resonance. That reactance, in turn, converts to a capacitance for the frequency in question. Finally, using a solid disk without thickness as a model, one calculates the diameter of final capacitive hat.

+

Unfortunately, for amateur antennas in the HF range, the calculations and the theory underlying them are fraught with problems at every step. However, it seemed possible to at least correlate this independent means of calculating capacity hat size to modeled antenna-hat combinations in the HF frequency range. The attempt is summarized in the accompanying BASIC program. The goal was not to add anything significant to the fundamental theory underlying the transmission-line analogy on which the calculation scheme is based. Briefly looking at a number of the hurdles encountered along the way may be useful in the understanding of the application of that method to HF antennas in the 60 length range, whether verticals over perfect ground or dipoles in free space.

+

For the project at hand--correlating hat calculations to NEC-2 and MININEC models--the exact values of average characteristic impedance, reactance, and capacitance are unimportant except in the most derivative sense, because the feedpoint reactance can be determined by modeling. What the calculations required were values of Zo, Xc, and C amenable to simple correlation to the spoke lengths of various configurations of open-frame capacity hats. The Shelkunoff equation proved to be best suited to serve as the basis of these correlations. The final form of the modified Schelkunoff equation for the calculation of Zo for the HF range became

+
+ +
+

where h is the antenna height, M is the inverse of K (the antenna end effect shortening factor), d is the main element diameter, F is the frequency of interest in MHz (and 30 is the highest frequency of interest in MHz), and N is a calculation constant. Since the correctives are only approximate, the selection of N will bias the equation for certain types of capacity hats in preference to others. Using N = 0.583 biases the equation toward square spoke-plus-perimeter-wire closed hats of small hat-wire diameters. The result will be errors up to 5% for some types of hats.

+

There are two separate modifications of the basic Schelkunoff equation to account for varying antenna element diameters and for variations of frequency in the HF range. First, of all the various techniques tried, placing the antenna shortening factor (K, or M in equation 1) into the fundamental formulation for antenna height yielded the most correct curve for the effect of antenna element diameter on the spread of open-frame capacity hats considered. The same goal might have been achieved using an external correction equation, but it would have added considerable complexity to the calculation.

+

The first step in the process finding a usable figure for K is to derive from NEC models an adequate approximation. Resonating models of full-length quarter-wave verticals at the highest and lowest frequencies of interest--here 3 MHz and 30 MHz--over perfect ground allows calculation of intermediate values for K. (Throughout, resonance of a model is defined as a feedpoint reactance of less than ±0.01 Ohm.) One very good approximation is

+
+ +
+

where K is the antenna shortening factor, Khf is the K of a resonant quarter wavelength antenna of a given diameter at its highest frequency, Klf is the K of a resonant quarter wavelength antenna of a given diameter at its lowest frequency, FH is the highest frequency (for Khf), and F is any frequency in the range of interest. The exponent, KV, also varies with frequency,

+
+ +
+

for the frequency range 3 to 30 MHz.1 The resulting values are those implicit in NEC-2 models and therefore most apt to the goal of correlating independent calculations to modeled structures.

+

The frequency correction factor was applied to the logarithm adjustment factor in equation 1 by decreasing the reduction in the logarithm of height vs. radius from the standard value of 1. Again, this correction could have been introduced externally to the basic calculation of Zo, but would have required a more complex formulation, the form of which would have resembled that of the calculation of K, but with a different progression of the exponent. Even the given form of the adjustment is an oversimplification, since letting N = 0.583 is accurate within 1% only for small diameter square hats with a perimeter wire of the same diameter as the spokes. Focusing on other parts of the matrix of hat configurations considered could vary the value of N by as much as 10%.

+

The value of C, the requisite capacitance that translates into a set of physical dimensions for a capacitive hat, is somewhat arbitrary, even if useful in this exercise. The capacitance value given in the accompanying program is for calculational reference only and not to be construed as a reliable figure. The calculation of a value of C required for a hat provides a convenient number which, when multiplied by a constant for a common hat configuration, results in an approximation of the spoke length required for the hat. Low order hats commonly consist of 4, 6, or 8 open-ended spokes. Alternatively they may consist of 4, 6, or 8 spokes connected by a perimeter wire. Both modeling and calculations here assume the perimeter wire is the same diameter as the spokes. This assumption may not be true in reality and result in further deviations from calculated sizes. Squares, hexagons, and octagons are perhaps the most common hat geometries hams will use at HF, and Figure 19 illustrates the three. The key dimension is the spoke length, from which everything else can be hand calculated or laid out on the shop bench. Hams use a variety of element sizes ranging ordinarily from 0.5" to 2" in diameters. Hat material is likely to range from #12 wire (0.0808" in diameter) up to about 1" tubing.

+
+ +
+
+ Fig. 19 Outlines of square, hexagon, and octagon hats. +
+

Determining the final constant of correlation between the previously calculated value of capacitance and the spoke length for the various configurations requires modeled hats at the four corners of the matrix: 3 MHz and 0.5" antenna element, 3 MHz and 2.0" element, 30 MHz and 0.5" element, and 30 MHz and 2.0" element. For any size spoke material, the modeled length is divided by the capacitance to produce a constant. The four constants are averaged. The process is repeated for each hat configuration and for each size of spoke material.

+

With the selection of the value of N given above, deviations from modeled antenna-hat combinations increases with the number of spokes and the increasing size of the hat spoke material. However, the method is accurate to within about 5% of the modeled hat size at the extremes of the matrix marked by the frequency range and the hat material range. Over much of the matrix, deviations from modeled antennas is in the 1% range.

+

Accuracy of the calculations can be improved by introducing further "curve-fitting" correctives to the final determination of spoke lengths. They are omitted here, since my purpose has been to provide only initial guidance toward the development of detailed capacity-hat models.

+

Choice of NEC modeling parameters will, of course, vary the baseline of calibration. The models I used placed 25 segments in the main element so that their length was reasonably close the length of segments in the spokes and perimeter. Spokes used 3 segments each. Square perimeter sides used 5 segments, while hexagon and octagon perimeter sides used 3 segments.

+

The hat size calculations are only as accurate as the models, plus or minus the inherent error factors in the equations and the care of calibration. The methods we have looked at are not so much designed for lab precision as they are a convenient starting point for other tasks. One of those tasks is modeling a capacity hat antenna at a new frequency. Another is constructing a hat in the home ham shop. When used with due caution, the calculation technique used here may be adequate to both tasks.

+

The attached GW Basic listing provides a convenient utility program for starter calculations toward the construction of capacity hats of square, hexagon, and octagon configurations. Given the modifications of fundamental transmission-line analogy equations to produce the calibration, the values for characteristic impedance, capacitive reactance, capacitance, and standard disc size should be considered only as artifacts of the calculations, not as accurate values.

+

These investigations suggest that classic transmission-line analogy theory faces serious challenges if extended into the HF range, where the diameter of an antenna element is virtually always a quite significant percentage of the antenna height and the departure of the antenna shape from conical reduces the reliability of what careful theorists have always called an approximation, even at very low frequencies. The difficulty of calibrating classic calculations to method-of-moments models is a double hurdle, since neither method to this point provides a definitive baseline for the other. At best, the modifications to basic equations, gathered into the simple GW BASIC program accompanying these notes, can provide a rough guide to modeling efforts for capacity hat antennas in the 60° or longer range. The program returns results that are less than precise, but perhaps much better than a blind guess.2

+
+ +
+ 
+                                             Appendix B
+
+                                               Program
+
+10 '           file "CAPHAT.BAS"  --  Compensated calculation of capcity-hat Zo equation with
+        averaged results used to calculate hat spoke lengths
+20 COLOR 11,1,3
+30 CLS:LOCATE 1,12:PRINT"Calculation of Capacitive Hats for Vertical Antennas":LOCATE
+        2,28:PRINT"L. B. Cebik, W4RNL"
+40 PRINT:PRINT" The information requested yields approximations for spokes of open-frame hats
+         with 4, 6, and 8 sides for common materials used by hams in the HF bands from"
+50 PRINT" 3 to 30 MHz.  Spoke lengths are within about 5% of NEC-2 Models.":PRINT
+60 '          Frequency selection
+70 LOCATE 8,1:X$=STRING$(79,32):PRINT X$:LOCATE 8,1:INPUT" Enter the frequency of
+        interest in MHz        ",F
+80 FL=3:FH=30:IF F<FL OR F>FH THEN 70 ELSE 90
+90 LOCATE 8,1:X$=STRING$(79,32):PRINT X$:LOCATE 8,1:PRINT" Selected frequency in MHz
+                          ";F
+100 '          Antenna element diameter selection
+110 LOCATE 9,1:PRINT" Select the letter by the main element diameter (in inches) closest to
+        yours.":PRINT"  a.  0.50   b.  0.75   c.  1.00   d.  1.25   e.  1.50   f.  1.75   g.  2.00"
+120 A$=INKEY$:IF A$="a" THEN 130 ELSE IF A$="b" THEN 140 ELSE IF A$="c" THEN 150
+        ELSE IF A$="d" THEN 160 ELSE IF A$="e" THEN 170 ELSE IF A$="f" THEN 180 ELSE
+        IF A$="g" THEN 190 ELSE 120
+130 KL=.9688:KH=.953:D=.5:GOTO 200
+140 KL=.9669:KH=.9483:D=.75:GOTO 200
+150 KL=.9654:KH=.9445:D=1:GOTO 200
+160 KL=.9641:KH=.9412:D=1.25:GOTO 200
+170 KL=.963:KH=.9383:D=1.5:GOTO 200
+180 KL=.962:KH=.9358:D=1.75:GOTO 200
+190 KL=.9611:KH=.9335:D=2:GOTO 200
+200 KV=(((F/3)-1)*.0333333)+.61:KQ=KH+((.4342945*LOG(FH/F))^KV)*(KL-KH):
+        LK=KQ*245.8928:MQ=1/KQ
+210 LOCATE 9,1:X$=STRING$(79,32):PRINT X$:LOCATE 9,1:PRINT" Selected main element
+        diameter in inches     ";D
+220 '          Open-frame hat wire or tubing diameter selection:  perimeter wire               assumed
+        to have same diameter as spoke wire.
+230 LOCATE 10,1:X$=STRING$(79,32):PRINT X$:LOCATE 10,1:PRINT" Select the letter by the
+        material you plan to use for the capacity hat.":PRINT"  a. #12=.0808  b.#10=.1019  c.
+        #8=.1285  d. .25   e. .50   f. .75   g. 1.00"
+240 A$=INKEY$:IF A$="a" THEN 260 ELSE IF A$="b" THEN 290 ELSE IF A$="c" THEN 320
+        ELSE IF A$="d" THEN 350 ELSE IF A$="e" THEN 380 ELSE IF A$="f" THEN 410 ELSE
+        IF A$="g" THEN 440 ELSE 240
+250 '          Calibration constants derived from models
+260 KCL=1.2397:HKCL=1.1042:OKCL=1.0359
+270 KCLS=2.1124:HKCLS=1.7032:OKCLS=1.483:KLC=.9745:KHC=.9664
+280 DCAP=.0808:GOTO 470
+290 KCL=1.2272:HKCL=1.0913:OKCL=1.0234
+300 KCLS=2.0761:HKCLS=1.6726:OKCLS=1.4542:KLC=.974:KHC=.9652
+310 DCAP=.1019:GOTO 470
+320 KCL=1.2143:HKCL=1.078:OKCL=1.0106
+330 KCLS=2.0385:HKCLS=1.6416:OKCLS=1.4312:KLC=.9732:KHC=.9639
+340 DCAP=.1285:GOTO 470
+350 KCL=1.1747:HKCL=1.0376:OKCL=.9723
+360 KCLS=1.9122:HKCLS=1.5441:OKCLS=1.3508:KLC=.9713:KHC=.9593
+370 DCAP=.25:GOTO 470
+380 KCL=1.1276:HKCL=1.0037:OKCL=.9293
+390 KCLS=1.7822:HKCLS=1.449:OKCLS=1.2625:KLC=.9688:KHC=.953
+400 DCAP=.5:GOTO 470
+410 KCL=1.096:HKCL=.9678:OKCL=.9028
+420 KCLS=1.6889:HKCLS=1.3598:OKCLS=1.2007:KLC=.9669:KHC=.9483
+430 DCAP=.75:GOTO 470
+440 KCL=1.0707:HKCL=.9372:OKCL=.8831
+450 KCLS=1.6244:HKCLS=1.3067:OKCLS=1.1576:KLC=.9654:KHC=.9445
+460 DCAP=1!:GOTO 470
+470 LOCATE 10,1:PRINT X$
+480 LOCATE 10,1:PRINT" Selected hat material diameter in inches     ";DCAP
+490 '          Antenna length selection between 60 and 85 electrical degrees
+500 KV=(((F/3)-1)*.0333333)+.61:KR=KHC+((.4342945*LOG(FH/F))^KV)*(KLC-KHC)
+510 KF=LK*12:KA=KF/90
+520 HS=(KA*60)/F:HL=(KA*85)/F:HSF=HS/12:HLF=HL/12
+530 LOCATE 11,1:PRINT X$:LOCATE 11,1:PRINT" For a frequency of";F;"MHz, a capacitive hat
+        vertical should be between    ":PRINT"     ";HSF;"feet long and";HLF;"feet long."
+540 INPUT" Enter the desired antenna length in feet      ",HF:IF HF>HLF OR HF<HSF, THEN 550
+        ELSE 560
+550 PRINT" Length must be between";HSF;"and";HLF;"feet":GOTO 540
+560 LOCATE 11,1:PRINT X$:LOCATE 12,1:PRINT X$:LOCATE 11,1:PRINT" The desired antenna
+        length in feet           ";HF
+570 '          Required hat capacitance calculation
+580 HR=LK/F:H=HF*12
+590 ZO=60*(LOG((4*(H*MQ))/D)-(1-((F/30)*.583)))
+600 LA=(HF/HR)*90:LC=90-LA:LCR=(3.14159*LC)/180:X=ZO/TAN(LCR)
+610 C=1000000!/((2*3.14159)*(F*X)):CHD=1.1121*C
+620 PRINT:PRINT" The antenna length in degrees is              ";LA
+630 PRINT" The loading length in degrees is              ";LC
+640 PRINT" The required capacitive reactance in Ohms is  ";X
+650 PRINT" The required capacitance in pF is             ";C
+660 PRINT" Solid disc radius in inches is                ";CHD/2
+670 PRINT " Spoke Length (inches)           Spoke only            Spoke & Perimeter"
+680 '          Square spoke calculation and calibration
+690 SPT=(KCL*C)
+700 SPTS=(KCLS*C)*KR
+710 PRINT"     Square":LOCATE 19,34:PRINT SPTS:LOCATE 19,58:PRINT SPT
+720 '          Hexagon spoke calculation and calibration
+730 HSPT=(HKCL*C)
+740 HSPTS=(HKCLS*C)*KR
+750 PRINT"     Hexagon":LOCATE 20,34:PRINT HSPTS:LOCATE 20,58:PRINT HSPT
+760 '          Octagon spoke calculation and calibration
+770 OSPT=(OKCL*C)
+780 OSPTS=(OKCLS*C)*KR
+790 PRINT"     Octagon":LOCATE 21,34:PRINT OSPTS:LOCATE 21,58:PRINT OSPT
+800 '          Closeout
+810 PRINT:PRINT" <A>nother run or <Q>uit?"
+820 A$=INKEY$:IF A$="A" OR A$="a" THEN 30 ELSE IF A$="Q" OR A$="q" THEN END ELSE 820
+
+ Notes +
+

1. For further notes on correlating the antenna shortening factor to NEC-2 models, see "Calibrating K to NEC," QEX, 170 (March, 1996), 3-8.

+

2. A more accurate (and longer) version of the program included here is part of the HAMCALC collection compiled by George Murphy, VE3ERP.

+
+ +
+

Return to Article Index Page

+

Topics: HF Upper, Loading, Small Beams, Yagi


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+
+ The HB9CV Phased Array and Gain Comparisons

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+ The HB9CV version of the 2-element phased array appeared in 1961. In Europe, some writers refer to almost any 2-element horizontal phased array as an HB9CV, while the English-speaking world tends to refer to the ZL- Special to mark the genre of antenna. The HB9CV version of the antenna and many variants are widely used in Europe, with Christmas tree stacks for 20- 15-10 meters. Users swear by them, claiming near to, and sometimes better than, 3-element Yagi performance. +

These facts set up a small cluster of interesting questions. What is the HB9CV phased array, and how does it differ from the "ordinary" ZL-Special? The antenna has been so successfully built by so many European hams that it deserves more attention by US hams.

+

But before we look at the HB9CV, let's first look at what a claim for 3- element performance by a 2-element antenna might mean. Then we can make some intelligent evaluations of the performance claims.

+
+

3-Element Yagis

+
We can roughly divide well-designed monoband 3-element Yagis into two classes: high-performance, narrow band models and moderate performance, wide-band models. +

A high-performance, narrow band 3-element Yagi aims for the highest levels of gain and front-to-back ratio (in some form of a design balance) at the expense of a wide operating bandwidth--normally defined in terms of a 2:1 SWR ratio. The narrower bandwidth does not necessarily mean that the antenna will not operate with a 2:1 SWR ratio across any of the upper HF bands (or the first MHz of 10 meters). The following model antenna shows a gain of 8.1 dBi free space gain and a front-to-back ratio of over 27 dB at 28.5 MHz with better than 900 kHz of operating bandwidth. This performance is typical of what is possible with moderate boom-length 3-element Yagis.

+ 
                        3-Element Yagi:  High Gain
+Element        Length in Feet      Spacing from Driven Element in Feet
+Reflector           17.19                    5.2
+Driven Element      16.41                    ---
+Director            15.44                    6.0
+
+ +
+
+ +
+
+ +
+

For wide bands, say from 10 meters on up, some 3-element monoband Yagi designers sacrifice some gain and front-to-back ratio for operating bandwidth. The following model shows an operating bandwidth that exceeds all of the 10-meter band (with a direct 50-ohm feed impedance). The design frequency of 28.5 MHz shows a gain of 7.0 dBi free space with a front-to- back ratio of about 21 dB. The gain is stable across the band, varying by about 0.25 dB, while the equally stable front-to-back ratio varies by only a little over 2 dB. A scaled version of the antenna covers all of 6 meters with ease.

+ 
                        3-Element Yagi:  Wide Band
+Element        Length in Feet      Spacing from Driven Element in Feet
+Reflector           17.83                    6.2
+Driven Element      16.50                    ---
+Director            14.67                    5.0
+
+ +
+
+ +
+
+ +
+

We can get more than 8.1 dBi free space gain from a narrow-band 3-element Yagi either by using a longer boom or by resizing and spacing elements--or both. In the process, we generally sacrifice front-to-back ratio. However, if we need a standard for 3-element monoband Yagis, the 8.1 dBi free space gain figure will do nicely, especially if we keep in mind the other properties of the antenna that make it desirable. The wide-band Yagi becomes, by comparison, somewhat of a special purpose antenna.

+
+

2-Element Yagis

+
Well-designed 2-element Yagis that seek the best blend of gain and front- to-back ratio tend to be spaced about 1/8 wavelength as a compromise between those figures and an adequate operating band width. Under these conditions, we can expect to show at the design target frequency (28.5 MHz) about 6.25 dBi free space gain and between 11 and 12 dB front-to-back ratio. The 30-35-ohm feedpoint impedance is amenable to beta, gamma, or Tee matches. + 
                      2-Element Yagi:  Typical Design
+Element        Length in Feet      Spacing from Driven Element in Feet
+Reflector           17.50                    4.3
+Driven Element      16.00                    ---
+
+ +
+
+ +
+
+ +
+

Unlike the stable 3-element Yagis, 2-element models show much greater variations of gain across the band. Gain varies by over 0.7 dB across the first MHz of 10-meters with this model, which is typical of the genre. The gain for this particular antenna peaks outside the 10-meter band at 27.3 MHz, with a figure of 7.04 dBi free space gain (with a front-to-back ratio of only 6.0 dB and a feedpoint impedance of about 16 ohms).

+

The 2-element Yagi is thus capable of better than 7 dBi free space gain--if we are willing to sacrifice other desirable antenna properties. More efficient at producing raw gain are 2-element Yagis using a director closely spaced to the driven element. With a spacing of 2.5', one such model shows (at 28.5 MHz) 6.73 dBi free space gain with a front-to-back ratio of over 22 dB and a feed point impedance of about 18 ohms. However, such beams have very narrow operating bandwidths. The subject model at 28 MHz shows only 5.9 dBi free space gain and a 2.7 SWR relative to the target frequency impedance. At 29 MHz, the gain reaches a peak of 7.38 dBi (free space), but the front-to-back ratio has dropped to 8 dB and the SWR is above 6:1 relative to the target frequency feedpoint impedance.

+ 
                2-Element Yagi:  Driven Element + Director
+Element        Length in Feet      Spacing from Driven Element in Feet
+Driven Element      17.10                    ---
+Director            16.00                    2.5
+
+ +
+
+ +
+
+ +
+

There are uses for such 2-element Yagis, if front-to-back ratio is of no concern and if feedpoint and matching losses can be accommodated or overcome. It is clear that, in terms of raw gain, it is possible to exceed the wide-band 3-element Yagi, although figures are still short of well- designed high performance 3-element Yagis.

+
+

The ZL-Special 2-Element Phased Array

+
The 2-element phased array has been around in ham circles since the 1950s. Originally thought to be a 135-degree impedance phase-shifted array, we have come to understand the antenna as a -45-degree current shifted array with a reversed rear element (created by half-twisting the phasing line). Actually, depending on a number of variables--such as element size, spacing, natural feedpoint impedance, etc.--the magnitude and phase of the current required on the rear element relative to the forward element for desired operation can vary quite widely from about 0.75 to 1.1 and from about 20 to 65 degrees. +

The classic ZL and G manner of constructing such arrays is to use two dipoles--either equal in length or with the forward element shorter--spaced about 0.125 wavelengths apart with a length of standard parallel feedline between the two (with the half-twist, of course). For a phasing line, single-wire dipoles have usually used 70-ohm parallel line (almost impossible to come by today in power handling versions), while folded dipole models tend to use 300-ohm parallel line.

+

Phased arrays are usually designed to optimize front-to-back ratio as a mark of perfect phasing. The mathematics of the requisite current phasing were shown in "Modeling and Understanding Small Beams: Part 5: The ZL Special," Communications Quarterly, (Winter, 1997), pages 72-90. One interesting result was that standard Yagi dimensioning that shortens forward elements and lengthens rear elements must be set aside. At least one model required a rear element shorter than its forward partner to achieve so-called perfect phasing.

+

The number of design options using standard parallel transmission lines as the phasing element are not very many. Such designs tend to perform with respect to gain about on a par with well-designed 2-element Yagis with average forward gains of about 6.3 dBi free space. One would tend to prefer such an array only if the high front-to-back ratio (which can approach 50 dB at a target frequency) is needed. However, the rear null is quite frequency specific, and most such antennas will drop to a front-to- back ratio of under 20 dB within a half MHz of the target design frequency on 10 meters.

+
+

The HB9CV

+
The HB9CV version of the 2-element horizontal phased array seeks greater gain as well as freedom from the restrictions of existing parallel feedlines as phasing elements. The technique involves a careful selection of element lengths and an interesting combined phasing and matching system. +

The following data is taken from 10th edition of Y21BK, Karl Rothammmel's Antennenbuch (Berlin: 1984) (graciously provided to me by Siegfried Rambaum, KB2YVC/DE8FGO). There are two versions of the antenna, one for balanced lines; the other for unbalanced lines. What the two antennas have in common is the basic dimensions of the elements. The forward element is 0.46 wavelengths long, while the rear element is 0.50 wavelengths long, with a spacing of 0.125 wavelengths. Y21BK reports that elements should be 0.47 and 0.51 wavelengths for antennas made from wire. For tubing (copper or aluminum), the recommended diameter is about 0.0025 wavelength.

+

Before examining the phasing and matching system, we can discover some interesting data about the potential of the antenna from the element recommendations. For 28.5 MHz, the dimensions call for 1" tubing spaced 51.77" (4.31') apart. The forward element is 190.5" (15.875') long, while the rear element is 210.31" (17.526') long.

+

Plugging these dimensions into a NEC or MININEC model and using separate sources for the front and rear elements, we can determine a number of things. First is the current magnitude and phase for the reversed rear element, relative to the forward element, to achieve maximum gain. A maximum free space gain of 7.32 dBi was achieved with a rear current magnitude of 0.90 of the forward element at a relative phase angle of -18 degrees (equivalent to 162 degrees standard rear element phasing). At this gain, the front-to-back ratio is 7.2 dB. These figures are quite similar to those of a similarly sized Yagi set for maximum gain.

+

Second, we can also determine the rear element relative current magnitude and phase to achieve maximum front-to-back ratio. With the model, a front- to-back figure of over 50 dB was achieved. However, as with all 2-element horizontal phased arrays, this figure represents the ratio in a direct line with the maximum forward gain lobe. It amounts to a deep dimple in the overall rearward lobe, which has a worst-case figure of about 20 dB down from the forward gain lobe. The requisite rear element relative current magnitude was 0.92 at a relative phase of -44 degrees (equivalent to 136 degrees standard rear element phasing). Antenna gain for this situation was about 6.37 dBi free space, or about 0.9 dB down from maximum gain.

+

Performance tapers gradually as the phase angle increases above -44 degrees and more rapidly as the current departs from the target magnitude. With lower relative current magnitudes and higher current phase numbers it is possible to achieve figures similar to those one might obtain with a constant 0.9 current magnitude and phase figures between -18 and -44 degrees.

+

The figure below outlines the complete HB9CV antenna, including the two versions of the matching network. The sketches are not to scale in order to permit the addition of the necessary dimensional annotations.

+
+ +
+

The dimensions in the sketches are for a feedpoint impedance for the balanced system of 150 ohms and for the unbalanced system of 75 ohms. Adjustment is essentially a matter of lengthening or shortening the length of the Tee or Gamma section (or the element length) until the proper feedpoint impedance is achieved.

+

Modeling a complete HB9CV system is not a simple task, because the antenna parts press the limits of both MININEC and NEC (2 or 4). The number of right angles in the system calls for complex wire length segment tapering or extremely small segment lengths, both of which exceed the maximum allowable number of segments within public domain MININEC. NEC produces inaccurate results with angular junctions of wires having dissimilar diameters or with closely spaced parallel wires of dissimilar diameters.

+

One potential solution is the use of a modeled transmission line between the forward and rear element matching "bars," a potential open only to NEC. The balanced system yielded quite plausible models when the Tee bars and connectors were increased to 1" diameter to match the main elements.

+

To reduce the effects of closely spaced element, which can introduce errors, the Tee bar was set at a 4" distance from the main element, both front and rear. Using check models with no feedline between the front and rear elements and with 2 sources (one on each of the Tee bars), NEC models showed a systematic variance of about 0.13 to 0.15 dB difference in gain and a difference of up to 1 dB in front-to-back ratio (between 20 and 30 dB ratios) from equivalent MININEC models, each fed with identical current magnitudes and phase angles. For the present exercises, these differences were considered not significant.

+

However, it is possible to construct models that give wholly unrealistic results. The HB9CV design is limited by the maximum gain and maximum front-to-back figures inherent in the element size and spacing relationships when dual sources are optimized for both magnitude and phase angle. Every matching system can only match: it cannot increase either maximum gain or maximum front-to-back ratio beyond the limits. Models that suggest higher gains are suspect, and turn out to commit one or more violations of NEC limitations. I have produced models showing up to 8.2 dBi free space gain with almost 28 dB front-to-back ratios: as appealing as these numbers are, they will not stand tests of convergence and independent source substitution.

+

Using most of common line impedances from 50 to 450 ohms along with sundry velocity factors, HB9CV models with Tee matching ranged in gain from 6.2 to 6.54 dBi free space. Front-to-back ratios ranged from 19.5 to 26.1 dB at the design center frequency, with lower values generally corresponding to higher gain figures.

+

The most stable nonsymmetrical model was a gamma-match system that used 1" elements throughout, even for the gamma bars and connectors, with a spacing of 4" between the element and gamma bars. The connecting transmission line was 75 ohm, 0.66 VF line. This model produced a very stable model between 28 and 29 MHz with a center point source impedance of 53 ohms. However, the gain was only about 6.2 dBi, with a front-to-back ratio of 20 dB (+/-3 dB across the frequency span). The gain is only that of a normal 2-element Yagi, while the front-to-back ratio is about an S-unit better. This model falls well within the range of models using a Tee-match system.

+

These models, of course, have limitations, since the Tee-bars and gamma-bars are not as specified within the HB9CV instruction set. However, nothing in a matching system, when physically modeled within the limits of any of the NEC programs, alters gain by more than 0.1 dB and front-to-back by more than about 0.5 dB. (See notes on the Tee match elsewhere in this collection.) The correspondence between the Tee-bar models with and without a connecting phasing line (using dual sources in the latter case) suggests that within broad limits, the models correctly report performances that one may obtain from the HB9CV.

+

A gain in the range of 6.4 to 6.5 dBi free space is an improvement over the standard 2-element Yagi. Front-to-back ratios between 20 and 26 dB represent improvement factors of 1.5 to 2.0 over the standard 2-element Yagi. Indeed, operators will likely interpret the QRM-killing ability of the HB9CV over the 2-element Yagi as additional gain, given improvements in signal-to-noise ratio.

+

An additional advantage of the HB9CV is the flexibility of its matching design. Using almost any phasing line design, the Tee or gamma can be adjusted with respect to length and spacing from the main element to achieve a desired match, either with or without a transformer or balun. The antenna models showed good stability over a minimum of 750 kHz on 10 meters, and most covered more than the first MHz with under 2:1 SWR and very reasonable gain and front-to-back ratios at the operating band ends.

+

The following graphs show the free space gain, front-to-back ratio, and Matched SWR curves for two models: one a relatively high-gain model with a 300-ohm phase line, the other a relatively high SWR model with a 150-ohm phase line. The rates of change for both gain and front-to-back are less steep than those of standard 2-element Yagis. The feedpoint impedances are not 50-ohms, so matching was employed. The medium-gain, high-F-B model used a 1/4 wl 75-ohm match section, while the high-gain, medium F-B model used 3.3' of 75-ohm (VF=0.66) line to achieve a 50-ohm match. (The use of other than 1/4 wl sections of 75-ohm lines as matching sections to 50-ohm lines for reactive impedances in the 70-90 ohm range is a subject needing more widespread understanding, since it is a cheap and effective matching technique.)

+
+ +
+
+ +
+
+ +
+

The graphs show that it is relatively easy to develop a fine-performing HB9CV without too much concern for the exact phasing line impedance--and to match it to a 50-ohm feedline.

+

Despite these laudable properties, extensive modeling and model testing shows that the claims of gains above 7 dBi free space are supported only by faulty models to this point in the testing process. With a front-to-back (or front-to-rear) ratio of about 20 dB as a cut-off point for minimal rearward performance, gains have only approached 6.6 dBi maximum in all models tested. However, within the "normal" range of HB9CV figures, characteristics are stable across a wide operating bandwidth.

+

In the end, the HB9CV uses element phasing to excellent effect in yielding the most productive combinations of gain and front-to-back ratio achievable from the basic geometry, combinations that cannot be achieved from parasitical operation alone. Moreover, it does so within a basic boom length of 1/8th wavelength. When well designed, it offers stable operating characteristics over a considerable bandwidth. Nonetheless, it remains an antenna subject to the physical limitations of its basic geometry.

+
+

An Alternative Phasing System

+
It is possible to increase the design target frequency gain to in excess of 7.0 dBi free space and to increase the front-to-back ratio to better than 20 dB in a 2-element horizontal phased array--and to achieve at the same time a relatively wide (1 MHz at 10 meters) operating bandwidth with a direct 50-ohm feed. +

One overlooked factor that the ZL-Special and the HB9CV have in common is the use of elements approximately 0.5 wl long. When the elements are fed by any phasing method that achieves high gain or maximum front-to-back ratio, the rear element shows an impedance of R - jX, while the forward element shows an impedance of R + jX. This condition sets limitations on direct phase-line interconnection of the two elements or--as with the HB9CV--requires special matching circuitry.

+

If both elements could be made to show inductive reactance at system resonance, then the element impedances could be tailored to simpler phase- line interconnection. The resistive component can be altered by varying the element length, while the reactance can be set by placing series capacitance at the element feedpoint.

+

In order to achieve this goal, both elements must be lengthened. Elements in the 0.7 region suffice to provide a direct 50-ohm feed using a phasing line between 75 and 150 ohms (with a velocity factor of 1.0). For the test model using 1" diameter elements, the forward element was 23.4' long (0.678 wl), while the rear element was 24.2' long (0.701 wl) with a spacing of 4.31' (0.125 wl). A 150-ohm open wire transmission line connects the two elements. The figure shows the antenna schematically.

+
+ +
+

Because the elements are longer than 0.5 wl, they exhibit inherently more gain, which also translates into greater gain of the phased system. When the elements are separately fed, the array shows a maximum free space gain of 7.7 dBi when the rear element shows a current magnitude of 1.07 of the forward element at a relative phase angle of -18 degrees. (This figure is under 0.5 dB down from the narrow-band 3-element Yagi gain figure used as our standard.) The front-to-back ratio in this condition is only about 7.6 dB. Maximum front-to-back is better than 50 dB (with a free space forward gain of 6.8 dBi) when the rear element current is 1.27 of the forward element current with a phase angle of -44 degrees.

+

The actual array is designed for reasonable wide-band 50-ohm operation with a compromise between gain and front-to-back ratio. The following graphs display the anticipated performance across the first MHz of 10 meters.

+
+ +
+
+ +
+
+ +
+

A 150-ohm phasing line can be constructed from almost any wire from #14 to #10. #12 AWG copper wire requires 0.14" center-to-center spacing or 0.06" edge-to-edge spacing. Placing a piece of #14 AWG wire between 2 lengths of #12 wire achieves the correct spacing. Tape the wires and withdraw the center wire, replacing the center wire with a small insulated spacer at each tape point. The result is a 150-ohm parallel line. Keep the line taut to prevent shorts. Using #12 AWG enamel wire will not likely adversely affect the velocity factor by much. However, for 100-Ohm and 150-Ohm lines, it may be simpler to construct lines using series connected 50-Ohm and 75-Ohm coaxial cables. The shielding permits the builder to place the lines inside a metal boom used to support the elements with no interaction. However, one must account for the velocity factor of the chosen line to ensure that the physical length will reach the elements and the electrical length will meet the phasing requirements.

+

The series capacitors can be standard value lumped components. However, one can also use lengths of smaller tubing, insulated by a tube (or rolled sheet) of Teflon or other material for a tight but movable fit. Because of the number of variables involved in the tubing and insulating materials available, you will have to experiment to check the capacitance per inch of overlapping tubing to determine the correct amount for each elements.

+

One advantage of lumped components is that they can be brought out at right angles to the element. In this manner, if you are concerned that your phasing line has a velocity factor less than 1.0, you can use a slightly shorter length. However, slight changes in element spacing are less problematical than most experimenters are usually led to believe. Hence, you can adjust spacing and phase line length in small amounts for the best compromise.

+

The following figure shows the free space azimuth pattern of the suggested alternative phased array at 28, 28.5, and 29 MHz.

+
+ +
+
+

Conclusion

+
The alternative phased array is a design exercise to see if one can do with 2 elements what others do with 3. Although the HB9CV array surpasses the performance of a 2-element Yagi, it fails to match the performance of even a wide-band lower-gain 3-element Yagi. In contrast, the alternative design meets or exceeds the goal in most respects--even to having a 50-ohm feedpoint impedance. However, because hams tend to be conservative and prefer common half wavelength elements, I doubt that anyone will actually build the design. +

Hence, the alternative is largely a design exercise. The exercise demonstrates that understanding all aspects of each element, plus what occurs along a transmission line current transformer, provides a wealth of design opportunity for improving antenna performance. It is not enough to rely on a few broad antenna ideas. The goal should be to grow familiar with every possible aspect of both element and array condition and performance.

+

Has the limit been reached for maximizing gain while retaining a good front-to-back ratio and a workable feedpoint impedance in a 2-element array? I doubt it. The alternative design is simply a step in a certain direction. It exists because I asked why I should restrict myself to half- wavelength elements when longer elements offered some interesting advantages. The next design will come when I discover the right question to ask about another antenna.

+
+ +

+
+

Updated 2-10-98, 09-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
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Return to Amateur Radio Page

+

Topics: HB9CV / ZL Special, HF Upper, Phased Array


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+

Some Notes on Two-Element Horizontal Phased Arrays

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

The directional 2-element phased array achieved notoriety in the 1950s with builder claims that one or another variation on the basic design outperformed 3- and even 4-element Yagis. Although we now know that the appearance of high performance owed much to Yagi deficiencies of the period, horizontal phased arrays have retained much of their mid-century aura of magic. Since magic and an understanding of antennas are mutually exclusive, perhaps we should begin again.

+

The notes in this series will begin with some basic modeling data that tends to set limits to the performance expectations that we may logically have of 2-element phased arrays. In the second part, we shall explore the degree to which the geometry of the parasitic array can capture the potential of phased element performance. Part 3 will examine one of the two classic methods of array phasing: the ZL-Special with its single phase line. In Part 4, we shall look at two different ways of phasing a pair of elements using element-matching techniques, one by R. Baumgartner, HB9CV, the other by Eric Gustafson, N7CL. Throughout. we shall try to integrate specific design strategies into an overall picture of the performance of which 2-element phased arrays are capable.

+

This series of items has appeared in The National Contest Journal in 2001-2002. All items will appear at the site after their appearance in NCJ

+

1. The Limits of Performance (Nov/Dec, 2001)

+

2. The Limits of Geometric Phasing (Jan/Feb, 2002)

+

3. The Limits of a Single Phase Line: The ZL-Special (Mar/Apr, 2002)

+

4. Removing the Limits of a Single Phase Line by Element Matching (May/Jun, 2002)

+
+ +
+

Updated 05-10-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Phased Array


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+

Some Notes on Two-Element Horizontal Phased Arrays
+ Part 1: The Limits of Performance

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

The directional 2-element phased array achieved notoriety in the 1950s with builder claims that one or another variation on the basic design outperformed 3- and even 4-element Yagis. Although we now know that the appearance of high performance owed much to Yagi deficiencies of the period, horizontal phased arrays have retained much of their mid-century aura of magic. Since magic and an understanding of antennas are mutually exclusive, perhaps we should begin again.

+

The notes in this series will begin with some basic modeling data that tends to set limits to the performance expectations that we may logically have of 2-element phased arrays. In the second part, we shall explore the degree to which the geometry of the parasitic array can capture the potential of phased element performance. Part 3 will examine one of the two classic methods of array phasing: the ZL-Special with its single phase line. In Part 4, we shall look at two different ways of phasing a pair of elements using element-matching techniques, one by R. Baumgartner, HB9CV, the other by Eric Gustafson, N7CL. Throughout. we shall try to integrate specific design strategies into an overall picture of the performance of which 2-element phased arrays are capable.

+

A Few Preliminaries

The idea of a 2-element phased array contains an ambiguity. At the most general level, the notion can refer to the relative phasing of the elements in any 2-element array. Under this heading, we may include arrays with a single driven element as well as two driven elements. The perspective offered by this most general idea of a phased array will be useful in seeing where some antennas fit into a larger picture. +

Alternatively, the concept of a 2-element phased array often refers specifically to an "all-driven" antenna, that is, to an array in which both elements receive power directly from the source. The key question that immediately arises within this view of phased arrays is how we may get energy to the individual elements in the correct magnitude and phase to effect a desired set of performance characteristics. The most common means is via a "phasing line" composed of a length or lengths of transmission line. Indeed, this means of conveying energy from the array source to the individual elements has been the source of numerous misconceptions about how phased arrays operate.

+

The phasing-line system of energy transfer, of course, is quite unnecessary. As Brian Egan, ZL1LE, demonstrated with a 15-meter phased array in the 1990s, one may create a phasing network of lumped components and then use separate lines to each element so long as they preserve the relative values of current magnitude and phase created by the network.

+

The key to understanding 2-element horizontal phased arrays is the fact--stressed by Roy Lewallen, W7EL, in many writings--that the relative current magnitude and phase between the two elements determines the operating characteristics of the antenna. In the early days of phased-array popularity, most builders thought in terms of the impedance transformation along a transmission line linking the elements. However, the impedance along a mismatched line does not track with the current magnitude and phase transformations along the line. Impedance values repeat on a lossless line twice for each wavelength of line. However, current magnitude and phased values appear only once per wavelength.

+

From this misunderstanding others emerged. Although the most popular line lengths interconnecting elements were in the vicinity of 1/8 wavelength, most folks thought in terms of a 135-degree phase shift. However, with or without a half twist in the short line, the current can only make an approximate 45-degree phase shift. (The number is a crude marker, since we have already noted that the current phase may change more or less than 45-degree in a line that is 45-degree long.) If a straight line yields a 45-degree phase shift in current, then a line with a half twist yields a -45-degree phase shift. Antenna patterns may be identical to those produced by feeding the elements 135 degrees out of phase, but the current behavior and the consequences for evaluating means of obtaining the correct phasing of the elements will depend upon the -45-degree perspective. Because we shall be looking at close-spaced element systems, we shall adopt this orientation throughout these notes.

+

A further constraint upon our understanding of 2-element horizontal arrays has been the magic associated with 1/8 wavelength spacing. In fact, no particular spacing between elements holds any theoretically superior place in the scheme of 2-element arrays. We shall discover that in some respects, almost any spacing will do, although specific spacings between elements can result in arrays that are easier to implement.

+

A Modeling Project

In a number of past articles, I have presented a partial portrait of phased array performance potentials, for example, in the series in NCJ on log-cell Yagis. In the remainder of this first set of notes, I want to expand our appreciation of phased array performance parameters, although space will not allow an absolutely complete account. +
+ +
+
+ Fig.1-1 The basic parts and structural variables of a 2-element horizontal phased array. +
+

Fig. 1-1 presents the basic parts of a 2-element phased array as we shall model it in NEC-4. We shall assign to each element a current source, specifying both the magnitude and phase angle. By convention, the designated forward element will have a current magnitude of 1.0 and a phase angle of 0.0 degrees. The designated rear element will then be assigned the values of current magnitude and phase that yield a desired performance limit. Since we are working with directional arrays with a single main forward lobe, the forward element will always be the element in the direction of that lobe. Assigning separate values of current magnitude and phase angle to each element is an analog of what we accomplish with a phasing network. Such networks cannot yield performance that exceeds the limits of separate sources for each element, no matter the ingenuity of the system.

+

For the notes in this section, we shall reduce the total number of variables to a manageable number. We shall vary the spacing between elements systematically. We shall also examine some variations in element length, using both equal-length and unequal-length elements in the study. However, these results will change if we alter the diameter of the elements. For convenience, we shall employ 10-meter (28.5-MHz) elements made from 0.5" diameter aluminum. These elements give us a reasonably realistic model that scales easily to other amateur bands. With a fixed element diameter, we shall not explore variations that result from selecting other diameter materials.

+

When exploring sources with a relative phase angle between 0 and -90-degree, we must simulate the line half twist by setting up the model elements in opposite directions. That is, if the forward elements extends from a - value to a + value, then the rear element extends from a + value to a minus value. Adhering to this modeling scheme keeps the instantaneous current directions correct.

+

The basic element for our exploration is a resonant dipole of the specified material. In a NEC-4 model, such a dipole is 197.6" long or about 0.4771 wavelength long at 28.5 MHz. (The half-inch diameter element is 0.001207 wavelength across.) The subject dipole has a resonant impedance of 72.1 + j 0.5 Ohms. Now we are finally ready to examine a 2-element phased array.

+

Maximum Front-to-Back Ratio Configurations

The basic model consisted of two self-resonant dipoles of the type just described set at various distances apart. The spacing ranged from 0.05 wavelength to 0.2 wavelength in 0.025 wavelength increments. This range covers--with some interesting but practically useless excess--the element spacing used in virtually all recorded directional phased array construction. +

In addition to using equal-length self-resonant elements, I also made up pairs that are 10% shorter and 10% longer than the basic model. The short elements are 177.84" long (0.4294 wavelength), while the long elements are 217.36" long (0.5249 wavelength). As we shall see, resonance is not a requisite for a phased pair of elements. (We shall look at unequal-length elements soon.)

+

The first exercise attempted to arrive at the rear element relative current magnitude and phase angle necessary top achieve a maximum 180-degree front to back ratio. Although the pursuit of a perfect null can go on indefinitely, it proved fairly easy to obtain a rear null greater than 60 dB lower than the forward lobe maximum value. Since the maximum null is a very narrow-bandwidth phenomenon, -60 dB seemed deep enough to show general trends when we set 2-element phased arrays for a maximum front-to-back ratio.

+
+ +
+
+ Fig. 1-2 Comparative free-space azimuth patterns of a 2-element horizontal phased array configured for maximum 180-degree front-to-back ratio with close-spaced and wide-spaced elements. +
+

Fig. 1-2 shows typical patterns for the narrowest element spacing and the widest element spacing used. Although only one set of patterns appear in the figure, the general properties apply to all three of the subject models. As element spacing increases beyond 0.1 wavelength, gain drops off. More notable are the rear lobes. The deep null occurs within a rearward lobe, leaving angle side lobes. The lobes are weakest at the most narrow spacing levels and increase with wide spacing. To some degree, then, aiming at the maximum 180-degree front-to-back ratio may be operationally misdirected, although it serves to set operational limits for the 2-element array.

+ 
                       Equal-Length 2-Element Phased Array Performance
+                       Maximum 180-Degree Front-to-Back Configuration
+
+Model SHT-E                                Element Length (Front and Rear):  0.2147 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wavelength (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Foprward)      Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      6.41    65.58           3.9 - j110.3       3.2 - j 78.8      1.024          -17.4
+0.075     6.42    66.13           7.9 - j117.1       7.5 - j 71.8      1.035          -26.4
+0.1       6.36    73.68          11.9 - j120.7      14.7 - j 64.0      1.045          -35.6
+0.125     6.25    61.40          15.7 - j122.8      24.4 - j 57.6      1.051          -44.9
+0.15      6.11    65.41          19.1 - j123.8      35.7 - j 53.7      1.056          -54.3
+0.175     5.92    68.86          22.3 - j124.3      47.7 - j 53.0      1.057          -63.8
+0.2       5.69    65.46          25.7 - j124.2      59.1 - j 55.8      1.057          -73.2
+
+Model RES-E                                Element Length (Front and Rear):  0.2386 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wavelength (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      6.50    63.70          10.7 - j 35.5      -1.6 + j  7.0      1.033          -17.0
+0.075     6.50    88.97          15.9 - j 37.5       4.6 + j 24.2      1.049          -26.0
+0.1       6.44    60.36          20.7 - j 38.4      15.3 + j 39.4      1.063          -35.2
+0.125     6.33    64.42          25.1 - j 38.8      29.8 + j 51.2      1.074          -44.7
+0.15      6.18    66.73          29.1 - j 38.6      46.8 + j 58.2      1.080          -54.3
+0.175     5.99    61.47          32.8 - j 38.2      64.6 + j 60.1      1.083          -64.0
+0.2       5.76    63.34          36.0 - j 37.6      81.3 + j 56.7      1.080          -73.6
+
+Model LNG-E                                Element Length (Front and Rear):  0.2624 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wavelength (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magitude       Phase
+0.05      6.59    66.90          18.9 + j 39.0      - 7.3 + j 95 5     1.045          -16.6
+0.075     6.59    74.73          25.9 + j 41.8        1.0 + j125.3     1.067          -25.5
+0.1       6.52    63.87          32.0 + j 43.8       16.4 + j150.6     1.087          -34.9
+0.125     6.41    65.07          37.4 + j 45.5       37.7 + j169.4     1.101          -44.5
+0.15      6.26    66.57          42.3 + j 47.0       62.8 + j180.7     1.110          -54.4
+0.175     6.08    72.84          46.7 + j 48.6       88.8 + j183.6     1.113          -64.3
+0.2       5.85    67.24          50.7 + j 50.0      113.3 + j178.5     1.110          -74.3
+
+Note:  All gain values are for free-space.  Rear current (I) magnitude and phase
+values are relative to forward element values of 1.0 and 0.0 degrees.  Model RES-
+E uses elements of equal length to an independent resonant dipole at the test
+frequency.  Models SHT-E and LNG-E uses elements that are 10% shorter and 10%
+longer, respectively.
+
+
+Table 1.  Performance and operating conditions of 3 equal-length element 2-
+element phased arrays in a maximum 180-degree front-to-back ratio configuration.
+

Table 1 provides full data for the short, resonant, and long element pairs. As we might expect, the maximum gain for any spacing is partly dependent upon the element lengths. consistent among the three test models is the occurrence of maximum gain at the closest spacing levels: 0.05 and 0.075 wavelength. Thereafter, gain decreases steadily. The front-to-back values are simply for the record to verify that the model obtained the requisite depth of rear null.

+

At a spacing of 0.125 wavelength, a popular element separation for 2-element Yagis and phased arrays, the forward gain of the maximum-null phased arrays do not differ significantly from the gain of a well-designed Yagi. In the maximum front-to-back configuration, then, the phased array's claim to fame is only its rearward null and not its gain.

+
+ +
+
+ Fig. 1-3 The rear element relative current magnitude and phase angle for short, resonant, and long element lengths in arrays having equal- length forward and rear elements, and set for maximum front-to-back ratio. "I-M" means rear element relative current magnitude. "I-P" means rear element relative current phase. "Sht" refers to model SHT-E; "Res" refers to model RES-E; and "Lng" refers to model LNG-E. See Table 1 for model specifications. +
+

Of primary interest to us are the rear element relative values of current magnitude and phase angle necessary to yield the deep null. Fig. 3 graphically portrays the tabulated data of Table 1. Of immediate notice is that the change in element lengths between models has almost no effect on the requisite phase angles. The graphs of the three lines overlap and proceed in a virtually linear curve from about -17 degrees at 0.05 wavelength spacing to about -73 degrees at 0.2 wavelength spacing. Equally notable is the fact that we may obtain a rearward null for any spacing in this range.

+

What does change with the length of the elements is the relative current magnitude required on the rear element. The longer the element pair, the higher the required value of relative rear element current to achieve. The differentials for 10% changes in element length are between 2% and 3%.

+

Not all element spacings will be easy to implement with standard means of element phasing. The tabulated data shows negative resistance values in some entries for very close-spaced elements. These values are correct and simply mean that the mutual coupling between elements is providing more energy to the affected element than the source itself.

+

A Test of Equal vs. Unequal Element Lengths

There are three possible element arrangements for a 2-element horizontal phased array. As we have just examined, both elements may be equal in length. However, Fig. 1-4 shows two more configurations. The forward elements may be shorter than the rear element, and the forward element may be longer than the rear element. Our familiarity with the requirements for parasitic beams makes one of the arrangements natural and the other almost unthinkable. +
+ +
+
+ Fig. 1-4 Three options for element length relationships between the forward and rear elements of a 2-element phased array. +
+

Nevertheless, both types of unequal-length element arrays are fully functional in a phased array. all that we need to do is provide the two elements with the correct relative current magnitudes and phase angles. Table 2 provides the complete modeling data on the test runs. The equal-length model is the same as used for the earlier runs. Each of the unequal-length arrays has one element that is the same as our original self-resonant dipole and a second element that is 5% longer: 207.48" or 0.5010 wavelength. As the table shows, there is no significant difference in the maximum forward free-space gain. Once more, at the closest element spacing modeled, a negative resistive component on the forward element is possible.

+ 
                      Unequal-Length 2-Element Phased Array Performance
+                       Maximum 180-Degree Front-to-Back Configuration
+
+Model RES-UF                        Element Length: Front: 0.2505 wl; Rear: 0.2386 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      6.52    62.19          12.1 - j 38.7      -3.6 + j 53.5      1.114          -16.9
+0.075     6.52    69.26          17.3 - j 39.5       3.5 + j 75.7      1.139          -25.9
+0.1       6.45    63.68          22.0 - j 39.7      16.4 + j 95.2      1.160          -35.3
+0.125     6.34    65.22          26.2 - j 39.5      34.0 + j109.8      1.175          -44.9
+0.15      6.20    63.14          30.1 - j 39.0      54.6 + j118.6      1.185          -54.6
+0.175     6.02    67.19          33.5 - j 38.4      76.1 + j120.6      1.186          -64.4
+0.2       5.79    68.90          36.6 - j 37.6      96.3 + j116.4      1.184          -74.2
+
+Model RES-UR                        Element Length: Front: 0.2386 wl; Rear: 0.2505 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      6.52    63.77          13.3 + j  4.5      -2.4 + j  3.7      0.962          -16.9
+0.075     6.52    61.79          19.3 + j  3.7       3.7 + j 22.1      0.974          -25.9
+0.1       6.45    67.19          24.8 + j  3.6      14.5 + j 38.0      0.985          -35.1
+0.125     6.35    62.79          29.7 + j  3.7      29.2 + j 50.1      0.992          -44.5
+0.15      6.20    65.18          34.2 + j  4.2      46.2 + j 57.4      0.997          -54.1
+0.175     6.01    65.28          38.4 + j  4.9      64.0 + j 59.3      0.998          -63.7
+0.2       5.78    63.36          42.1 + j  5.9      80.8 + j 56.3      0.998          -73.3
+
+For comparative data on Model RES-E, see Table 1.
+
+Note:  All gain values are for free-space.  Rear current (I) magnitude and phase
+values are relative to forward element values of 1.0 and 0.0 degrees.  Model
+RES-E uses elements of equal length to an independent resonant dipole at the test
+frequency.  Models RES-UF and RES-UR uses elements that are 5% longer than those
+in RES-E at the forward and at the rear elements, respectively.
+
+
+Table 2.  Performance and operating conditions of 2 unequal-length element
+2-element phased arrays in a maximum 180-degree front-to-back ratio configuration.
+

Fig. 1-5 shows the relative current magnitude on the rear element, along with the relative phase angle. As with the three equal-element-length arrays, the phase angles required to achieve a 180-degree front-to-back ratio in excess of 60 dB overlap with considerable precision. The differences are almost solely in the realm of the required relative current magnitude for the rear element. In this figure and in Fig. 1-3, you will note a slight decrease in the rear element current magnitude at the maximum spacing used (0.2 wavelength). The reversal of direction in current magnitude is consistent for all models in the series, both the ones used here and others in my collection.

+
+ +
+
+ Fig. 1-5 The rear element relative current magnitude and phase angle for various element-length relationships in 2-element horizontal phased arrays that are set for maximum front-to-back ratio. "Equal" refers to model RES-E; "F=Lng" refers to model RES-UF; and "R=Lng" refers to model RES-UR, according to whether the elements are equal in length, the forward element is 5% longer, or the rear element is 5% longer. See Table 2 for the specifications of models RES-UF and RES-UR. +
+

These models cannot guarantee that any particular element arrangement will provide an adequate basis for a practical array. However, when experimenting with phased arrays and various phasing schemes, it pays not to overlook the potential of a longer forward element.

+

Maximum Gain Configurations

The maximum front-to-back ratio configuration of a phased array represents one limit of performance, one marked by moderate gain and a deep rearward null. We may also set the relative current magnitudes and phase angles to achieve maximum forward gain, letting the front-to-back ratio become whatever it will be. In general, the conditions for maximum forward gain in a 2-element horizontal phased array do not favor high front-to-back ratios. Fig. 1-6 shows a typical maximum gain pattern, with a front-to-back ratio well below 10 dB. +
+ +
+
+ Fig. 1-6 A typical free-space azimuth pattern for a 2-element phased array set for maximum forward gain. +
+

For the 5 models that we previously examined, Table 3 provides the necessary data. Maximum gain does not occur at the very closest spacing tested, but appears in the 0.75 to 0.1 wavelength region of element spacing. Front-to-back ratios show a steady decrease with increasing element spacing. The maximum gain phenomenon has a wider bandwidth than the maximum front-to-back null. Therefore, each registered data set comprises a centered set of values in the middle of the range or phase angles and the range of current magnitudes that yield the highest gain. Over this region, the front-to-back ratio may change by as much as 2 dB, and the table shows only the center value.

+ 
             Equal-Length and Unequal-Length 2-Element Phased Array Performance
+                                 Maximum Gain Configuration
+
+Model SHT-E                                Element Length (Front and Rear):  0.2147 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      7.10     8.57           1.8 - j102.1       1.5 - j 87.4      1.010          - 8.0
+0.075     7.23     7.57           3.5 - j104.5       3.2 - j 85.1      1.015          -11.0
+0.1       7.24     7.42           5.4 - j105.0       6.2 - j 80.1      1.020          -14.8
+0.125     7.21     7.01           7.0 - j103.8      10.5 - j 75.5      1.020          -18.0
+0.15      7.15     6.67           8.8 - j101.9      15.5 - j 70.4      1.025          -21.3
+0.175     7.06     6.33          10.6 - j 99.7      21.4 - j 66.5      1.025          -24.5
+0.2       6.96     5.95          12.6 - j 97.2      27.7 - j 63.4      1.030          -27.5
+
+Model RES-E                                Element Length (Front and Rear):  0.2386 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      7.19     8.17           4.9 - j 24.6      -0.7 - j  5.7      1.015          - 7.5
+0.075     7.31     7.72           7.0 - j 21.8       2.0 + j  5.1      1.020          -11.0
+0.1       7.31     7.38           9.5 - j 18.1       6.2 + j 15.9      1.030          -14.5
+0.125     7.28     7.08          11.8 - j 14.2      12.3 + j 25.5      1.038          -18.0
+0.15      7.21     6.75          13.7 - j 10.2      20.3 + j 33.7      1.035          -21.5
+0.175     7.13     6.46          16.1 - j  6.3      28.9 + j 40.6      1.040          -25.0
+0.2       7.02     5.97          18.3 - j  1.7      37.9 + j 45.1      1.040          -27.8
+
+Model LNG-E                                Element Length (Front and Rear):  0.2624 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      7.28     8.48           9.3 + j 52.5      - 3.8 + j 78 0     1.025          - 7.5
+0.075     7.39     7.71          11.8 + j 62.1        0.3 + j 98.1     1.030          -10.8
+0.1       7.39     7.47          14.5 + j 69.9        7.0 + j116.4     1.035          -14.5
+0.125     7.35     7.11          17.5 + j 77.5       15.6 + j132.1     1.045          -18.0
+0.15      7.29     6.77          20.3 + j 84.5       26.6 + j145.2     1.050          -21.5
+0.175     7.20     6.43          23.4 + j 91.1       39.2 + j155.7     1.055          -25.0
+0.2       7.10     6.03          26.1 + j 97.6       53.0 + j162.6     1.050          -28.3
+
+Model RES-UF                        Element Length: Front: 0.2505 wl; Rear: 0.2386 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      7.21     8.19           5.2 - j 28.3      -1.1 + j 38.7      1.085          - 7.5
+0.075     7.33     7.74           7.6 - j 24.2       1.7 + j 53.1      1.100          -11.0
+0.1       7.33     7.36           9.7 - j 19.8       7.1 + j 66.5      1.110          -14.5
+0.125     7.30     7.04          11.9 - j 15.3      14.3 + j 78.6      1.120          -18.0
+0.15      7.23     6.70          13.7 - j 11.0      23.7 + j 88.6      1.120          -21.5
+0.175     7.15     6.40          16.0 - j  6.7      34.1 + j 96.9      1.125          -25.0
+0.2       7.04     6.02          18.5 - j  2.4      45.1 + j102.8      1.130          -28.3
+
+Model RES-UR                        Element Length: Front: 0.2386 wl; Rear: 0.2505 wl
+Frequency:  28.5 MHz                       Diameter:  0.001207 wl (0.5")
+
+Space     Gain    Front-to-Back     Z1 (Rear)       Z2 (Forward)       Rear I         Rear I
+  wl      dBi     Ratio dB          R +/- jX Ohms   R +/- jX Ohms      Magnitude      Phase
+0.05      7.21     8.60           6.6 + j 16.5      -1.4 - j  8.8      0.950          - 7.8
+0.075     7.33     7.80           8.8 + j 21.8       1.5 + j  2.8      0.950          -11.0
+0.1       7.33     7.44          11.5 + j 27.0       5.9 + j 14.2      0.955          -14.5
+0.125     7.30     7.13          14.1 + j 32.2      12.0 + j 24.4      0.960          -18.0
+0.15      7.23     6.82          16.9 + j 37.3      19.6 + j 33.3      0.965          -21.5
+0.175     7.15     6.36          19.0 + j 42.6      28.5 + j 39.7      0.960          -24.5
+0.2       7.04     6.01          21.7 + j 47.6      37.9 + j 44.7      0.960          -27.8
+
+Note:  All gain values are for free-space.  Rear current (I) magnitude and phase
+values are relative to forward element values of 1.0 and 0.0 degrees.  Model
+RES-E uses elements of equal length to an independent resonant dipole at the test
+frequency.  Models SHT-E and LNG-E uses elements that are 10% shorter and 10%
+longer, respectively.  Models RES-UF and RES-UR uses elements that are 5% longer
+than those in RES-E at the forward and at the rear elements, respectively.
+
+
+Table 3.  Performance and operating conditions of 5 2-element phased arrays in
+a maximum-gain configuration.
+

Fig. 1-7 graphs the current magnitude and phase angle data for the 3 equal-element-length models. Once more the phase angle curves form an overlapping trio. Irregularities in the current magnitude curves arise from the simple averaging and centering procedure used to produce the curves. However, the general trend is both clear and consistent with the maximum front-to-back curves: the longer the elements, the higher the required relative current magnitude level on the rear element to achieve the desired performance curve.

+
+ +
+
+ Fig. 1-7 The rear element relative current magnitude and phase angle for short, resonant, and long element lengths in arrays having equal- length forward and rear elements, and are set for maximum forward gain. "I-M" means rear element relative current magnitude. "I-P" means rear element relative current phase. "Sht" refers to model SHT-E; "Res" refers to model RES-E; and "Lng" refers to model LNG-E. See Table 3 for model specifications. +
+

The maximum gain curves represent the highest gain level that we may achieve with 2 elements of the sizes in the models. In general, the highest gain levels coincide with those for a quite short boom 3-element Yagi or a 2-element quad, both of which are designed for adequate 10-meter band coverage. The Yagi boom length would be about 8' for this gain level, with 12' boom 3-element Yagis capable of 8 dBi free-space gain across the first MHz of 10 meters. However, the phased-array data, taken at a single frequency, do not necessarily hold over an equivalent operating bandwidth.

+

Conclusions and Compromise

The exercise that we have presented is at most a demonstration of phased array properties and not a proof of them. What it shows is two sets of limits between which most horizontal phased arrays operate. In general, designers either consciously select or discover through experimentation phasing arrangements that yield acceptable performance with respect to gain, front-to-back ratio, and operating bandwidth. + 
        Performance Shifts With Changes in Relative Current Magnitude and Phase Angle
+                              Model RES-E at 3 Element Spacings
+
+Element Spacing: 0.05 wavelength
+1.  Rear Element Relative Current Phase Angle:  -17.0 degrees
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Magnitude         dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+0.933             6.34      15.23                    3.7 - j 38.9       5.9 + j  6.1
+0.983             6.47      21.48                    7.4 - j 37.0       2.2 + j  6.6
+1.033             6.50      63.70                   10.7 - j 35.3      -1.6 + j  7.0
+1.183             6.42      21.95                   13.7 - j 33.8      -5.3 + j  7.5
+1.133             6.28      16.30                   16.4 - j 32.4      -9.0 + j  7.9
+
+2.  Rear Element Relative Current Magnitude: 1.033
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Phase Angle       dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+-13.0             6.88      17.45                    8.5 - j 30.7      -2.0 + j  1.6
+-15.0             6.69      23.97                    9.6 - j 33.1      -1.8 + j  4.3
+-17.0             6.50      63.70                   10.7 - j 35.3      -1.6 + j  7.0
+-19.0             6.30      25.07                   11.9 - j 37.6      -1.2 + j  9.7
+-21.0             6.11      19.47                   13.2 - j 39.8      -0.7 + j 12.4
+
+Element Spacing: 0.125 wavelength
+1.  Rear Element Relative Current Phase Angle:  -44.7 degrees
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Magnitude         dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+0.974             6.31      23.22                   20.3 - j 42.5      33.8 + j 46.2
+1.024             6.33      29.53                   22.8 - j 40.5      31.8 + j 48.7
+1.074             6.33      64.42                   25.1 - j 38.8      29.8 + j 51.2
+1.124             6.31      29.77                   27.2 - j 37.1      27.9 + j 53.7
+1.174             6.28      24.03                   29.1 - j 35.7      25.9 + j 56.2
+
+2.  Rear Element Relative Current Magnitude: 1.074
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Phase Angle       dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+-40.7             6.52      25.75                   22.7 - j 35.4      26.2 + j 48.1
+-42.7             6.42      31.85                   23.9 - j 37.1      28.0 + j 49.7
+-44.7             6.33      64.42                   25.1 - j 38.8      29.8 + j 51.2
+-46.7             6.23      32.45                   26.4 - j 40.4      31.7 + j 52.7
+-48.7             6.14      26.50                   27.8 - j 41.9      33.7 + j 54.0
+
+Element Spacing: 0.2 wavelength
+1.  Rear Element Relative Current Phase Angle:  -73.6 degrees
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Magnitude         dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+0.980             5.76      26.01                   32.5 - j 41.3      80.3 + j 51.3
+1.030             5.76      32.36                   34.3 - j 39.4      80.8 + j 54.0
+1.080             5.76      63.34                   36.0 - j 37.6      81.3 + j 56.7
+1.130             5.76      32.38                   37.5 - j 36.0      81.8 + j 59.3
+1.180             5.75      26.68                   38.9 - j 34.5      82.3 + j 62.0
+
+2.  Rear Element Relative Current Magnitude: 1.080
+Rear I            Gain      Front-to-Back           Z1 (Rear)          Z2 (Forward)
+Phase Angle       dBi       Ratio dB                R +/- jX Ohms      R +/- jX Ohms
+-69.6             5.92      28.63                   33.6 - j 35.1      77.3 + j 57.3
+-71.6             5.84      34.61                   34.8 - j 36.4      79.3 + j 57.0
+-73.6             5.76      63.34                   36.0 - j 37.6      81.3 + j 56.7
+-75.6             5.69      35.05                   37.3 - j 38.8      83.3 + j 56.3
+-77.6             5.61      28.98                   38.7 - j 39.9      85.3 + j 55.8
+
+Note:  Total rear element relative current magnitude shift:  +/- 10%; total rear
+element relative current phase angle shift:  +/- 2 degrees
+
+Table 4.  Performance shifts in model RES-E at 0.05, 0.125, and 0.2 wavelength
+element spacing with a constant rear element relative phase angle and a variable
+relative current magnitude and with a constant rear element current magnitude and
+a variable relative current phase angle.
+

Table 4 gives us a partial view of what happens to the performance characteristics of a 2-element array as we drift away from the conditions that yield maximum front-to-back ratio. Varying the rear element relative current magnitude alone (with a fixed relative current phase angle) by about +/- 10% shows a gradual decline in gain and a more rapid decrease in front-to-back ratio whether the current magnitude goes too high or too low. However, as we fix the current magnitude on the rear element and vary the phase angle, we obtain a different progression. The front-to-back ratio decreases on both sides of the optimal values. However, the change in phase angle shows a single low-to-high progression in the +/-2 degree variation in the example.

+

The table shows clearly that the operating bandwidth for a set of conditions varies directly with the spacing between elements. The cost of obtaining the wider operating bandwidth is, of course, a decrease in the forward gain. However, the rate of gain decrease itself increases with spacings above about 0.125 wavelength. Indeed, one of the sensible reasons for selecting an element spacing in the 0.1 to 0.15 wavelength region is that we acquire reasonable operating bandwidth while maintaining higher gain levels.

+
+ +
+
+ Fig. 1-8 Typical "desirable" free-space azimuth pattern for a 2-element horizontal phased array set for acceptable amateur operation. +
+

Designers of phased arrays rarely survey the potentials for practical beams by extending the systematic model variation exemplified by Table 4. There are too many variables involved in the design work for one to fix upon a set of relative current magnitudes and phase angles and then design means for obtaining them. Instead, they tend to discover configurations that meet our usual amateur standards for what counts as a "good" beam. Fig. 1-8 shows a typical and desirable phased array pattern for an array using equal length (self-resonant) elements and spaced 0.125 wavelength. Gain does not appear on the pattern, but the triple rear lobe everywhere exceeds -20 dB relative to the forward lobe.

+ 
        Performance Shifts With Changes in Relative Current Magnitude and Phase Angle
+        Model RES-E at 0.125 wavelength Element Spacing Stepped Between Front-to-Back
+and Gain Settings
+
+Setting   Rear I    Rear I  Gain    Front-to-Back   Z1 (Rear)          Z2 (Forward)
+No.       Mag.    Phase     dBi     Ratio dB        R +/- jX Ohms      R +/- jX Ohms
+1         1.074   -44.7     6.33    64.42           25.1 - j 38.8      29.8 + j 51.2
+2         1.065   -38.0     6.64    21.05           20.8 - j 33.3      24.2 + j 45.5
+3         1.056   -31.4     6.94    14.53           17.1 - j 27.4      19.5 + j 39.3
+4         1.047   -24.7     7.17    10.32           14.1 - j 21.0      15.4 + j 32.6
+5         1.038   -18.0     7.28     7.08           11.8 - j 14.2      12.3 + j 25.5
+
+Table 5.  Performance shifts as the relative rear element current magnitude and
+phase angles are shifted in proportional steps between maximum front-to-back
+ratio and maximum gain settings.
+

There is no single set of values for relative current magnitude and relative phase angle that will yield patterns of this sort. Table 5 lists data for a set of compromise values developed simply by taking proportional parts of the differentials between the magnitude and phase angle values for the two extreme or limiting cases. Fig. 1-9 graphs the free-space gain and front-to-back ratio. The setting numbers correspond to the combinations shown in the table.

+
+ +
+
+ Fig. 1-9 Free-space gain and front-to-back ratio of 2-element horizontal phased arrays at compromise settings of rear element relative current magnitude and phase angles between the limits of maximum forward gain settings and maximum front-to-back ratio settings. See Table 5 for details of the compromise settings. +
+

As noted earlier, the very high 180-degree front-to-back ratio decreases quickly, so that a phase angle of -38 degrees on the rear element with a 1% decrease in current magnitude results in a front-to-back ratio just over 20 dB. However, in this increment, gain only rises by about 0.1 dB, with the steeper gain increase curve appearing between settings 2 and 3. As a result, one must accept a front-to-back ratio of less than 20 dB to achieve gain levels higher than 6.5 dBi.

+

The strategy used for these models can well be altered with possibly different results. We have sampled only two of many strategies in the effort to find a satisfactory set of operating conditions, and we have not explored the question of operating bandwidth--the frequency range over which the performance characteristics sustain themselves at acceptable levels. One reason for this void in our discussion is that the means by which we effect the current magnitudes and phase angles on each element play a significant role in setting the operating bandwidth. The exploration of such means is yet to come. We can only note at this stage that the number of variables involved in phased array design is high enough to preclude anything like a complete treatment.

+

So far, we have only scratched the surface of horizontal array understanding. The exercise has set performance limits. The data in Tables 1 and 2, however, are more than interesting numbers: they provide insight into the conditions that yield individual element impedances in paired combinations. The pattern of impedances will take on considerable importance in Parts 3 and 4 of this series.

+

As well, we have identified some of the factors affecting operating bandwidth, such as element spacing and where we set the rear element relative current magnitude and phase angle between the maximum gain and the maximum front-to-back values. Of course, we have not mentioned a third significant factor that affects operating bandwidth, namely, the diameter of the elements that we use. However, element diameter as a fraction of a wavelength will play a role in operating bandwidth, especially as one examines wire and tubular implementations of 2-element phased arrays.

+

So far, we have not explored how close we may come to a nearly perfect array with the ordinary design means available to us. One of those ordinary means that we usually overlook is antenna geometry. We shall explore the nature and limitations of that design route in the next episode.

+
+ +
+

Updated 01-12-2002. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Nov./Dec., 2001). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Return to Series Index

+

Go to Main Index

+

Topics: HF Upper, Phased Array


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+

Some Notes on Two-Element Horizontal Phased Arrays
+ Part 2: The Limits of Geometric Phasing

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

In Part 1, we noted that there are two ways of looking at the idea of a phased array. One perspective views the phased array as a combination of elements, all of which are fed. The other perspective is more general: it examines the relative current magnitude and phase angle of element combinations, regardless of which one or more of them may be fed. From this latter perspective, a 2-element parasitic array is phased in the sense that the unfed element will display a relative current magnitude and phase angle.

+

The parasitic array, of course, has a more common name: the Yagi-Uda beam. The Yagi (for short) may have as many parasitic elements as a designer can put to good use. Our interest will be in the smallest of such arrays: 2-element models. Fig. 2-1 shows the options that we have for creating 2-element Yagis. We may either use a director or forward parasitic elements with a driven element, or we may use a reflector or rear parasitic element with a driven element.

+
+ +
+
+ Fig. 2-1. Options for the element arrangement of a 2-element Yagi. +
+

The names "director" and "reflector" are simply conventional tags by which we identify a given parasitic element. The names do not themselves indicate how a parasitic array operates. Indeed, among those new to antennas, we find numerous misconceptions concerning reflectors, including the idea that they function similarly to the mirrored surface behind the light source in a flashlight. Directors, by the same analogy, appear to function in the manner of optical lenses by focusing the beam of RF.

+

Let's approach 2-element Yagis from a different point-of-view. The close proximity of the 2 elements provides significant inter-element coupling such that the unfed element will show at its center a relative current magnitude and phase angle. By adjusting the element diameters, spacing, and lengths, we may alter the unfed element relative current magnitude and phase angle. However, this process is limited by the basic geometry of the array. It is composed of parallel linear elements. Hence, the three variables of length, diameter and spacing can only go so far in yielding on the unfed element a relative current magnitude and phase angle that corresponds with those identified in Part 1 as able to produce a desired radiation pattern.

+

In this episode, we shall look more closely at the basic properties of 2-element Yagis in both the reflector-driver and the driver-director configuration. Our efforts will be to understand what limitations that geometry alone, as a set of design variables, places on the performance of 2-element arrays, especially compared to independently feeding both elements. When we are done, we should be able to correlate typical Yagi patterns with the relative phasing conditions for the two elements. At the end, we shall look at some alternative 2-element geometries designed to improve those conditions.

+

The Reflector-Driver and Driver-Director 2-Element Arrays

The earliest detailed study of 2-element Yagis using method-of-moments modeling software is the work of Jerry Hall, K1TD, whose results appear in the 15th and 16th editions of The ARRL Antenna Book (pp. 11-2 through 11-8). I shall replicate his work in part, using the modeling constraints applied in Part 1. The test frequency will be 28.5 MHz. The array elements will use 0.5" (0.001207 wl) diameter elements. Throughout our simplified examination of 2-element Yagis, I shall aim for two simultaneous goals: maximum front-to-back ratio and driver resonance. A driver will be considered resonant when the source reactance is +/-1 Ohm or less. Using these twin goals will not yield the absolute maximum 180-degree front-to-back ratio possible with two elements, but it will be close. As well, the results will permit easier graphing of the source impedances of corresponding reflector-driver and driver-director arrays. +

We shall also limit our samples to the same increments of element spacing that we used in Part 1: from 0.05 wl to 0.2 wl in 0.025-wl increments. Where our interest will depart from the earlier study is in the recording of the relative current magnitude and phase angle on the parasitic element when the driver has a current magnitude of 1.0 and a phase angle of 0.0 degrees.

+ 
                           2-Element Reflector-Driver Performance
+                Set for Maximum 180-Degree Front-to-Back Ratio and Resonance
+
+Element       Reflector     Driver         Gain          Front-to-Back        Feedpoint Z
+Spacing wl    Length wl     Length wl      dBi           Ratio dB             R +/- jX Ohms
+0.05          0.2505        0.2387         6.24          11.36                 8.1 + j 0.1
+0.075         0.2507        0.2356         6.36          11.40                15.4 - j 0.2
+0.1           0.2511        0.2334         6.32          11.33                24.3 - j 0.1
+0.125         0.2514        0.2310         6.25          11.18                33.8 + j 0.0
+0.15          0.2513        0.2312         6.18          10.96                42.9 - j 0.1
+0.175         0.2513        0.2310         6.06          10.69                52.1 + j 0.0
+0.2           0.2511        0.2312         5.91          10.36                60.2 - j 0.0
+
+Note:  All elements 0.5" (0.001207 wl) aluminum
+
+Table 1.  2-element reflector-driver Yagi performance when set for maximum 180-degree
+front-to-back ratio and driver resonance.
+

Table 1 provides the basic performance data for the models of a reflector-driver parasitic array meeting the conditions we have just specified. In addition to the usual performance data (free-space gain in dBi, 180-degree front-to-back ratio in dB, and the source impedance in Ohms), the table provides element lengths as a function of a wavelength at the test frequency. Unlike the models in Part 1, which used a relatively arbitrary but consistent dimensions for each model, the parasitic array must have different element lengths at each increment of spacing to achieve the maximum front-to-back ratio at a resonant driver impedance.

+

The dimensions themselves hold some interest. As you scan the table, note that the reflector length required to meet the twin modeling objectives reaches a peak length at a spacing of 0.125 wl and then decreases. In contrast, the required driver length decreases until the element spacing is 0.175 wl and then increases.

+
+ +
+
+ Fig. 2-2. Gain and 180-degree front-to-back ratio of reflector-driver 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.05 wl to 0.2 wl. +
+

Fig. 2-2 graphs the gain and front-to-back ratio data as a convenient way to examine the trends. Within the limitations of the increments of element spacing used here, the gain and the front-to-back ratio reach their peak values with an element spacing of 0.075 wl. As we shall see, there are two good reasons why we rarely, if ever, design 2-element reflector-driver Yagis with this particular spacing. One of those reason is the low source impedance: just above 15 Ohms. The other reason is the narrowness of the operating bandwidth at this spacing, a facet of 2-element Yagi design that we shall examine more thoroughly in a moment.

+

The low level of the front-to-back ratio of the reflector-driver design has struck many antenna enthusiasts and has occasioned two responses. One is the design of 3-element and larger Yagis. The second is the design of arrays that feed both elements. The front-to-back ratio with an element spacing of 0.125 wl is about 11.18 dB. We can increase this level to about 11.50 dB largely by shortening the driver and thereby changing the mutual coupling between the elements. However, in the process, the gain begins to decrease, and the source impedance reaches a value of about 30 - j 52 Ohms. Hence, draining the reflector-driver design of the last modicum of front-to-back ratio tends to result in relatively impractical source impedance values.

+ 
          Actual vs. Ideal Rear Element Relative Current Magnitude and Phase Angle
+                              2-Element Reflector-Driver Yagis
+
+                            Actual                                     Ideal
+Element              Relative       Relative      Relative      Relative      Gain
+Spacing wl           I Mag.         I Phase       I Mag.        I Phase       dBi
+0.05                 0.833          165.1         0.963         163.1         6.51
+0.75                 0.774          158.1         0.953         154.1         6.51
+0.1                  0.719          150.7         0.944         144.9         6.44
+0.125                0.670          143.1         0.938         135.6         6.33
+0.15                 0.636          136.5         0.938         126.1         6.18
+0.175                0.603          129.3         0.936         116.6         6.00
+0.2                  0.576          122.4         0.937         107.1         5.77
+
+Note:  all phase angles adjusted for positive values.  For negative angle values
+corresponding to those in Part 1, subtract 180 from the listed value.  All "ideal
+models" set to a 180-degree front-to-back ratio greater than 60 dB.
+
+
+Table 2.  Actual vs. ideal rear element relative current magnitude and phase
+angle values for maximum 180-degree front-to-back ratios for 2-element reflector-
+driver Yagis in Table 1.
+ 
               Bandwidth Characteristics for 2-Element Reflector-Driver Yagis
+                         At 0.1, 0.125, and 0.15 WL Element Spacing
+
+Element Spacing:  0.1 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 24.3 Ohms
+28.0          6.84           9.53                 16.3 - j 23.1               3.20
+28.25         6.58          10.94                 20.2 - j 11.3               1.71
+28.5          6.32          11.33                 24.3 - j  0.1               1.01
+28.75         6.07          11.01                 28.4 + j 10.4               1.53
+29.0          5.86          10.41                 20.5 + j 20.5               2.16
+
+Element Spacing:  0.125 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 33.8 Ohms
+28.0          6.72           9.92                 24.7 - j 21.4               2.19
+28.25         6.48          10.91                 29.3 - j 10.3               1.43
+28.5          6.25          11.18                 33.8 + j  0.0               1.00
+28.75         6.04          10.94                 38.1 + j  9.8               1.35
+29.0          5.85          10.45                 42.3 + j 19.2               1.73
+
+Element Spacing:  0.15 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 33.8 Ohms
+28.0          6.61           9.89                 33.3 - j 20.0               1.78
+28.25         6.39          10.71                 38.1 - j  9.7               1.31
+28.5          6.18          10.96                 42.9 - j  0.1               1.00
+28.75         5.98          10.80                 47.4 + j  9.0               1.25
+29.0          5.80          10.41                 51.7 + j 17.7               1.52
+
+
+Table 3.  Bandwidth characteristics for 2-element reflector-driver Yagis at 0.1,
+0.125, and 0.15 wl element spacing.
+

Table 2 reveals the reason for the low levels of front-to-back ratio associated with reflector-driver Yagi designs. The table lists the modeled rear-element relative current magnitude and phase angle values, along with the values needed for the same set of elements to achieve more than 60 dB front-to-back ratio. (The ideal front-to-back ratio models show the same deep 180-degree null as those in Part 1, along with the rearward side lobes that result in worst-cast front-to-back ratios between 17 and 22 dB.) The gain of the models using two sources appear in the right-most column. The ideal phase angles have been converted from the negative angles typical of models in Part 1 to values that correspond to those yielded by models of Yagis. To convert either value to more suited to phasing networks, simply subtract 180 degrees from the listed value.

+

In concert with the curves that we saw in Fig. 2-2, the relative current magnitude and the phase angle of the optimized Yagi both depart more radically from the ideal numbers with the widening of the spacing between elements. Coincidence is closest at the narrowest spacings. However, the narrower the spacing between elements, the more exact the coincidence must be to yield the ideal maximum front-to-back value of more than 60 dB. Hence, the closeness of the values at a spacing of 0.05 wl is still not close enough to yield the highest front-to-back ratio. As well, the ideal model shows its highest gain at the narrowest spacing, although the Yagi does reach maximum gain until the spacing is 0.075 wl. Interestingly, the ideal models have a higher gain potential only until the spacing reaches 0.15 wl, after which the Yagi shows slightly higher gain.

+ 
                            2-Element Driver-Director Performance
+                Set for Maximum 180-Degree Front-to-Back Ratio and Resonance
+
+Element       Driver        Director       Gain          Front-to-Back        Feedpoint Z
+Spacing wl    Length wl     Length wl      dBi           Ratio dB             R +/- jX Ohms
+0.05          0.2498        0.2378         6.48          26.03                11.0 - j 0.0
+0.075         0.2486        0.2335         6.52          23.60                21.1 + j 0.2
+0.1           0.2465        0.2298         6.44          14.85                29.7 + j 0.2
+0.125         0.2443        0.2263         6.22          10.66                36.6 + j 0.1
+0.15          0.2423        0.2234         5.98           7.94                41.2 + j 0.2
+0.175         0.2407        0.2202         5.62           5.96                45.9 + j 0.1
+0.2           0.2395        0.2170         5.23           4.45                50.0 + j 0.2
+
+Note:  All elements 0.5" (0.001207 wl) aluminum
+
+Table 4.  2-element driver-director Yagi performance when set for maximum 180-
+degree front-to-back ratio and driver resonance.
+

If we shift to driver-director models of parasitic arrays, we do not get the same picture of results. Table 4 lists the element lengths and the basic performance figures for the driver-director configuration. Unlike the reflector-driver dimensions, the driver-director element lengths continuously decrease with increased spacing between elements.

+
+ +
+
+ Fig. 2-3. Gain and 180-degree front-to-back ratio of driver-director 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.05 wl to 0.2 wl. +
+

The table also confirms the general proposition that a driver-director array develops a significant gain and front-to-back superiority over the reflector-driver array when the spacing is fairly narrow--under 0.1 wl. Fig. 2-3 tracks the gain and front-to-back ratio values. Above 0.1 wl element spacing, the front-to-back ratio drops rapidly to the reflector model values and below. The gain values start their drop above 0.75-wl spacing. Since the 21-Ohms impedance of the 0.075-wl model is manageable with a matching network, this element spacing region is among the most popular for driver-director arrays.

+

The flatted curve between 0.05-wl and 0.075-wl element spacing hides a surprise for those not familiar with Jerry Hall's study. The slope of the curve beyond the 0.075-wl mark suggests that in the lowest region of spacing, there is a peak in the front-to-back value. In fact, at a spacing of 0.0625 wl, the front-to-back ratio can reach nearly 47 dB with a free-space gain of 6.52 dBi and a source impedance of about 16.5 + j 7.9 Ohms. Such an array also comes closest to meeting the ideal conditions for maximum front-to-back ratio, with a relative magnitude of 0.964 and a phase angle (adjusted) of 158.6 degrees (or -21.4 degrees). For single-frequency use, such an array might well fill a need.

+ 
          Actual vs. Ideal Rear Element Relative Current Magnitude and Phase Angle
+                               2-Element Driver-Director Yagis
+
+                            Actual                                     Ideal
+Element              Relative       Relative      Relative      Relative      Gain
+Spacing wl           I Mag.         I Phase       I Mag.        I Phase       dBi
+0.05                 0.934          162.8         0.961         163.1         6.51
+0.75                 1.006          149.5         0.951         154.1         6.51
+0.1                  1.140          149.7         0.948         144.9         6.43
+0.125                1.333          146.1         0.943         135.5         6.31
+0.15                 1.555          145.6         0.939         126.1         6.16
+0.175                1.845          145.8         0.926         116.7         5.96
+0.2                  2.188          147.3         0.910         107.3         5.72
+
+Note:  all phase angles adjusted for positive values.  For negative angle values
+corresponding to those in Part 1, subtract 180 from the listed value.  In
+addition, actual angles are taken from the director and appear as negative angles
+relative to the driver to the rear.  The relative current magnitude values have
+been adjusted to reflect the values on the rear element if the forward element
+is set at 1.0.  All "ideal models" set to a 180-degree front-to-back ratio
+greater than 60 dB.
+
+
+Table 5.  Actual vs. ideal rear element relative current magnitude and phase
+angle values for maximum 180-degree front-to-back ratios for 2-element driver-
+director Yagis in Table 3.
+ 
                Bandwidth Characteristics for 2-Element Driver-Director Yagis
+                         At 0.075, 0.1, and 0.125 WL Element Spacing
+
+Element Spacing:  0.075 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 21.1 Ohms
+28.0          5.59          12.31                 33.0 - j 21.6               2.47
+28.25         6.03          16.75                 27.0 - j 11.6               1.72
+28.5          6.52          23.60                 21.1 + j  0.2               1.01
+28.75         7.00          15.47                 15.7 + j 13.9               2.22
+29.0          7.30           8.87                 11.6 + j 29.2               5.66
+
+Element Spacing:  0.1 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 29.7 Ohms
+28.0          5.64          11.39                 39.2 - j 19.5               1.87
+28.25         6.03          13.54                 34.7 - j 10.3               1.43
+28.5          6.44          14.85                 29.7 + j  0.2               1.01
+28.75         6.84          12.96                 24.6 + j 12.4               1.63
+29.0          7.15           9.28                 20.1 + j 26.4               2.98
+
+Element Spacing:  0.125 wl
+Frequency     Gain          Front-to-Back         Feedpoint Z                 SWR Relative
+MHz           dBi           Ratio dB              R +/- j X Ohms              to 36.6 Ohms
+28.0          5.55           9.35                 43.2 - j 18.7               1.64
+28.25         5.87          10.24                 40.2 - j  9.8               1.31
+28.5          6.22          10.66                 36.6 - j  0.1               1.00
+28.75         6.56          10.05                 32.7 + j 11.1               1.40
+29.0          6.84           8.36                 28.8 + j 23.7               2.11
+
+
+Table 6.  Bandwidth characteristics for 2-element driver-director Yagis at 0.075,
+0.1, and 0.125 wl element spacing.
+

Table 5 provides data comparing the modeled relative current magnitude and phase angle for the unfed element. The data has been adjusted to coincide in form with other data that we have examined. The negative phase angles of the director have been made positive, as if the forward element had a value of 0.0 degrees. As well, the current magnitude has been adjusted as if the director had a value of 1.0. This set of adjustments allows the ideal data to correspond with all other dual-source models we have so far examined, where all forward elements are set to a magnitude of 1.0 and a phase angle of 0.0 degrees, and the rear element values are presented for comparison. In concert with the curves of Fig. 2-3, Table 5 makes evident the rapid departure from ideal phasing conditions for maximum front-to-back ratio above 0.075-wl element spacing. Equally evident, in comparison with the data for the reflector-driver Yagi, is the relative uselessness of the driver-director array as a directional beam able about 0.1-wl element spacing.

+
+ +
+
+ Fig. 2-4. Resonance impedance of reflector-driver and driver-director 2-element Yagis at element spacings from 0.05 wl to 0.2 wl. +
+

Despite the radical differences in gain and front-to-back behavior between reflector-driver and driver-director Yagis, the resonant impedances of the two arrays do not differ greatly for any given element spacing. Fig. 2-4 tracks the source resistance of the two array designs as optimized for each element spacing increments. An interesting property of reflector-driver designs is that the impedance curve is nearly linear, in contrast to the curve for the driver-director array.

+
+ +
+
+ Fig. 2-5. SWR curves of reflector-driver 2-element Yagis set for maximum front-to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.1 wl to 0.15 wl. +
+

In our exploration of the two types of parasitic arrays, we overlooked Table 3 and Table 6. These tables present modeled performance figures for each array at 3 increments of element spacing from 28.0 to 29.0 MHz. For each array, the most common element spacings are listed: 0.1 through 0.15 wl for the reflector-driver array and 0.75 through 0.125 wl for the driver-director Yagi. As expected, operating bandwidth increases with increased element spacing. The reflector-driver Yagi, shown in Fig. 2-5, can be adjusted to cover the entire 1-MHz bandwidth by selecting a design frequency of about 28.35 rather than the 28.5-MHz figure used in this study. At a slightly wider element spacing of 0.15 wl, the 2-element reflector-driver design can be designed to cover all of the 10-meter band. At each level of element spacing, the gain and the front-to-back values tend to show the same sort of curve broadening with each increase in spacing, although the peak values decrease along the way.

+
+ +
+
+ Fig. 2-6. SWR curves of driver-director 2-element Yagis set for maximum front- to-back ratio and resonance at the design frequency (28.5 MHz) at element spacings from 0.075 wl to 0.125 wl. +
+

The driver-director Yagi SWR curves, shown in Fig. 2-6, are naturally steeper, given the narrower element spacings involved. The most notable feature of the SWR graph is it reversal from the one for the reflector-driver array: here, more rapid increases occur above the design frequency rather than below it. Likewise, gain increases with rising frequency (rather than with decreasing frequency in the case of the reflector-driver array). The source impedance of the driver-director array shows an increasing reactance with frequency in accord with the relative shortening of the element. However, the resistive component of the impedance decreases with rising frequency (in contrast to the resistance curve of the reflector-driver Yagi). At the spacing increments generally used in driver-director designs, narrow bandwidth is a condition of maximizing performance.

+

Understanding basic 2-element Yagi-Uda performance is a necessary condition of understanding the urge to design phased arrays in which both elements are fed. In principle, the dual source phased array is capable of higher gain and better front-to-back performance than all but the most closely spaced parasitic arrays. The reason is simple: the wider the spacing of a parasitic array, the further the elements get from relatively ideal conditions of element current magnitude and phase angle.

+

Alternative Geometries

Although we have omitted many details of 2-element Yagi behavior (relative to the more complete data in some areas on interest that appear in Jerry Hall's study), we would be remiss if we did not acknowledge design efforts to overcome some of the phasing failings of 2-element parasitic arrays using linear parallel elements. Let's look in detail at only one of those efforts to use an alternative geometry: the Moxon rectangle. Fig. 2-7 shows the basic outline of this antenna that owes its origin largely due to the initial efforts of G6XN. +
+ +
+
+ Fig. 2-7. An alternative geometry array with parallel and end coupling: the Moxon rectangle. +
+

The Moxon rectangle owes its operating characteristics to not one, but two forms of inter-element coupling. Between the parallel portions of the elements, we encounter the same sort of mutual coupling that is almost the sole source of coupling within a standard Yagi design. However, by bending the elements toward each other, we obtain an added form of coupling, often called capacitive coupling between the element ends. The result is a broader beamwidth and an increase in the front-to-back ratio. By judicious control of the element diameter, the gap between element tails, and the other dimensions of the array, we may obtain a broad-band reflector-driver array.

+
+ +
+
+ Fig. 2-8. Gain and 180-degree front-to-back ratio of a Moxon rectangle from 28.0 to 29.0 MHz (design frequency: 28.35 MHz). +
+

Fig. 2-8 shows the free-space gain and front-to-back curve for a typical Moxon rectangle designed for 28.35 MHz using 0.5" aluminum elements. The design frequency is necessary, since reflector-driver arrays decrease their front-to-back ratio and increase their SWR more slowly above the design frequency than below it. The resulting array covers the first MHz of 10 meters. The gain decreases nearly linearly across the passband, while the front-to-back ratio peaks just below the 28.4-MHz mark on the graph. Fig. 2-9 shows the 50-Ohm SWR curve for the design.

+
+ +
+
+ Fig. 2-9. 50-Ohm SWR curve of a Moxon rectangle from 28.0 to 29.0 MHz (design frequency: 28.35 MHz). +
+

Since Moxon rectangle designs using a variety of element materials and design frequencies are now common in antenna literature, we may turn our attention to Table 7. This table summarizes the performance data shown in the graph. In addition, it provides values for the rear element relative current magnitude and phase angle. At the design frequency, the parallel portions of the elements are about 0.133 wl apart. At that spacing, an ideal phase angle would be about 132.5 degrees (or -47.5 degrees). The rear element relative current magnitude would be close to 0.94. Compare these values to the ones in the table for 28.2 (0.967 and 134.1 degrees) and 28.4 MHz (0.943 and 128.0 degrees). Little wonder that the Moxon rectangle achieves a maximum front-to-back ratio of well over 30 dB at its design frequency.

+ 
                   Bandwidth Characteristics for 2-Element Moxon Rectangle
+
+Frequency     Gain   Front-Back     Feedpoint Z          50-Ohm        Refl.          Refl.
+MHz           dBi    Ratio dB       R +/- j X Ohms       SWR           I Mag.         I Phase
+28.0          6.36   17.79          39.2 - j 15.7        1.53          0.980          140.1
+28.2          6.16   25.95          46.3 - j  8.3        1.21          0.967          134.1
+28.4          5.95   34.12          53.2 - j  2.2        1.08          0.943          128.0
+28.6          5.75   22.21          59.3 + j  2.9        1.20          0.911          122.5
+28.8          5.57   17.81          64.6 + j  7.3        1.33          0.874          117.6
+29.0          5.40   15.20          69.2 + j 11.4        1.46          0.835          113.2
+
+Note:  Aluminum element diameter:  0.5"  (0.001207 wl)
+
+Table 7.  Bandwidth characteristics for 2-element Moxon rectangle, with modeled
+rear element relative current magnitudes and phase angles.
+

The cost for this improved front-to-back figure is a decrease in gain, partly resulting from the increased beamwidth relative to a standard Yagi design. Since the bent portions of the elements still have significant current levels near the array corners, their contribution to gain becomes a contribution to beamwidth. Hence, the Moxon rectangle has an average free-space gain of about 6.0 dBi, somewhat below the levels of the optimized Yagis and of the idealized phased arrays that we examined in Part 1.

+
+ +
+
+ Fig. 2-10. Some alternative 2-element parasitic array geometries. +
+

The Moxon rectangle is not the only attempt to alter geometry to improve performance over parallel-element Yagis. Fig. 2-10 shows some of the other arrangements tried with greater or lesser success. The VK2ABQ square was a forerunner of the Moxon rectangle. The diamond lends itself to inexpensive construction with a single non-conductive support for wire element ends. The hex and folded-X have been popular from time to time as near-ultimate compact but full size designs. An interesting study, but beyond the scope of these notes, would be to investigate the relative current magnitude and phase on the unfed element in each design, noting that the most common implementation of the folded X-beam is as a driver-director array. The others are all reflector-driver arrays.

+

Conclusions

Our goal has been to track the performance potential of parasitic arrays with only a single fed element with an eye toward understanding the limitations of using geometry alone to set the relative current magnitude and phase angle conditions between the elements. Both reflector-driver and driver-director Yagis show very serious limitations in this regard, except for very closely spaced driver-director models that are impractical for most (but not all) amateur applications. Alternative geometries, such as the Moxon rectangle, are able to overcome the problem of achieving high front-to-back ratio values by using multiple element coupling methods. However, they cannot achieve the higher gain levels (by about 0.5 dB or so) attained in principle by some ideal and compromise phased array designs. +

The key to 2-element Yagi design shortcomings is also the key to 2-element horizontal phased array success. Can we find a practical way to implement a 2-element phased array with both elements fed to arrive at desired gain, front-to-back ratio, and bandwidth values? In the next episode, we shall begin our exploration by reviewing the ZL-Special and its variants, all of which make use of what seems in principle to be the simplest phasing mechanism possible: a single phasing line that connects the two elements. More complex systems, such as the HB9CV and the N7CL systems do exist, but basic principles of phasing are often best explored by keeping the number of design variables to a minimum. The more complex systems will have their turn in Part 4.

+
+ +
+

Updated 01-12-2002. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Jan/Feb, 2002). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

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+

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+

Topics: HF Upper, Phased Array


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Some Notes on Two-Element Horizontal Phased Arrays
+ Part 3: The Limits of a Single Phase Line: The ZL-Special

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+

L. B. Cebik, W4RNL

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When George Pritchard (ZL3MH, later ZL2OQ) introduced the amateur community to the 2-element phased array, it seemed to offer magic in the form of performance up to 7 dBd (9+ dBi free-space equivalent) and up to 40 dB front-to-back ratio. Unfortunately, the comparators of the day were relatively primitive 2- and 3-element Yagis that rarely performed up to their theoretical possibility. Nonetheless, the antenna type acquired the name "ZL-Special" and has been the subject of performance debate ever since. For a reasonably complete bibliography of ZL-Special articles in English, see my "Modeling and Understanding Small Beams: Part 5: The ZL Special," Communications Quarterly, (Winter, 1997), 72-90.

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+ Fig. 3-1. Outline sketches of several classic ZL-Special designs. +
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Fig. 1 shows several of the variations on the ZL-Special theme. Some of them work; others do not--or at least not very well. Virtually all early work on horizontal phased arrays presumed that we needed only attend to the impedance transformation along a transmission line. Hence, with 1/8 WL spacing and a similar transmission line, a half twist would yield a 135° phase shift with the accompanying high gain forward lobe and a deep rear null. Fig. 1 shows both linear and folded elements, along with the most popular phase line characteristic impedances. The trombone attempted to overcome the velocity factor of the common TV twinlead line (about 0.8) by making wide-spaced folded elements that were physically 1/8 WL at their outer edges but electrically 1/8 WL apart relative to the phase line. Although the trombone works quite well, the structure is completely unnecessary: simple folded dipoles would work as well.

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Not until Roy Lewallen, W7EL, pointed out the fundamental error in amateur conceptions of the ZL-Special did we begin to re-analyze the 2-element horizontal phased array with some precision. (See Lewallen, "Try the 'FD Special' Antenna," QST (June, 1984), 21-24.) What controls the performance of the ZL-Special phase line is not so much the impedance transformation, but the current transformation (in terms of both current magnitude and phase angle). The current and the impedance do not change at the same rate except when the line is exactly matched to the element that forms its load. Hence, we had to take a wholly new approach to the single-line phased array. In these notes, we shall follow this lead.

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ZL-Special Basics

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Fig. 2 shows the deceptively simple elements of a ZL-Special. The two elements bear "forward" and "rear" element labels, where the forward element indicates two things. First, the main forward lobe is in the direction of the forward lobe. Second, the standard ZL-Special feedpoint is at the junction of the phase line and the forward element. +
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+ Fig. 3-2. The basic elements of a ZL-Special 2-element horizontal phased array. +
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Most radio amateurs do not fully appreciate how many variables are at work in this seemingly simple arrangement. First, the individual elements exhibit center-point impedances that are functions of the mutual coupling between them. The mutual coupling depends upon the element diameters, lengths, and spacing between them. Second, the feedline meets a parallel current division at the forward junction, which requires that all other variables result in the same voltage at the junction. The requisite voltage is a function of the source impedance of the forward element and the "share" of current received by that element.

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Third, the rear element impedance at its center sets both a current magnitude and phase angle and a voltage magnitude and phase angle, both of which undergo transformation down the selected length of phase line. From Terman, Radio Engineers' Handbook (McGraw-Hill: 1943), p. 185, we have equations for the current and the voltage at any point down a transmission line from a load or antenna element. The following equations are for lossless lines, which is satisfactory for the short phasing lines used in 2-element horizontal phased arrays and which also coincides with the calculations within the TL facility of NEC-2 and NEC-4:

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The meaning of the terms is as follows:

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  • Er is the voltage at the load or antenna end of the line,
    • +
  • Es is the voltage at the source end of the line,
    • +
  • Ir is the current at the load or antenna end of the line,
    • +
  • Is is the current at the source end of the line,
    • +
  • Zo is the characteristic impedance of the line, and
    • +
  • (2PI (l/WL)) is an expression for the electrical length of the line of the line in degrees for the frequency of interest.
    • +
+

Because both the voltage and the current have an associated phase angle and resolve into real and imaginary components, the use of these equations in calculations is more complex that the initial appearance of them. Some of the math involved appears in the earlier note Communications Quarterly article. However, such calculations are available within NEC in the TL facility and are also available in the HAMCALC suite of GW Basic utility programs from VE3ERP.

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Critical to our understanding of is the fact that the resultant values of voltage and current (magnitude and phase) at the forward end of the phase line are interactive, as the basic equations make evident. Achieving a current level that balances with the portion of source current used by the forward element at a common voltage such that the rear element then has a current magnitude and phase angle to yield a desirable pattern requires juggling all of the variables into a usable collection.

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Even if we arrive at a usable collection of values, we have several other variables to consider. First, the calculated characteristic impedance of the phase line must be one that we can acquire or build. Second, the requisite physical length of the phase line (accounting for the line's velocity factor) for the current transformation must be at least the space between the elements. As well, it should not be too much longer than that spacing in light of practical considerations for supporting the line. Since the line will be open--whether we use coax or parallel line for the task--we must isolate it from disturbances that a metallic boom might create. Designing a ZL-Special, then, requires either careful analysis or some very lucky guesses.

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A Design Example

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Let's analyze a single design for 28.5 MHz to see if we can make the picture clearer. We shall begin with 2 elements. Both will be our standard 0.5" (0.001207 WL) aluminum elements. The forward element will be 0.465 WL long, while the rear element is 0.506 WL long. The spacing will be 0.125 WL. However, from Part 1 of this series, we should now understand that the selected spacing is somewhat arbitrary, since for any element spacing, we may find element lengths that result in a desired phased array pattern. +
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+ Fig. 3-3. Design steps for a ZL-Special used for array analysis. +
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Fig. 3 shows the 4 steps in our analysis, and the results appear in Table 1. If we arrange the elements individually in a NEC model and feed them independently with current sources, then the feed values in the table's step 1 under the relative current columns will result in the relative voltage and the individual element impedances. The models follow the system used in Part 1 of reversing the direction of the rear element relative to the forward element so that any phase line that we add can be in normal orientation. Notable is the similarity of the element impedances, a useful condition (but not the only such condition) for successful ZL- Special design. The tables in Part 1 show in a general way what conditions must exist for us to achieve such similar impedances: the relative longer length of the rear element when both elements are longer than a self-resonant dipole at the frequency of interest is a promising combination at the 1/8-WL spacing. As Fig. 4 shows, we have not striven for the highest gain or front-to-back value, but simply for highly usable values.

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+ Fig. 3-4. Free-space azimuth pattern of the sample ZL-Special at 28.5 MHz. +
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The second step in our analysis creates a model with a transmission line attached to the rear element, but with its forward end brought to a source wire independent of the forward element. The selected line--from calculations, is RG-83, 35-Ohms coax with a velocity factor of 0.66. The required length is 0.13 WL physically or 0.197 WL electrically. This length of the chosen line yields the correct relative rear element current magnitude and phase angle. At the same time, it yields the required forward-end voltage magnitude and phase angle to match the value for the forward element. Note that the required forward line end current is 0.664 (relative to a forward element value of 1.0) with a phase angle of 44.25°.

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Step 3 in the analysis requires that we connect the forward end of the phase line and the forward element center to create a single feedpoint for the array. Under these conditions, supplying the feedpoint with a current of 1.0 at 0.0° phase angle, we obtain the relative element current levels and phase angles shown. The forward element phase angle is a function of the reactance at its center. However, the net phase angle difference between elements is still - 44.18°. At this stage, we have a complete array that we can frequency sweep from 28.0 to 29.0 MHz. Fig. 5 shows the results. The gain shows a nearly linear curve upward, with a total change of about 0.9 dB. The front-to-back ratio remains above 20 dB from the lower band edge to above 28.8 MHz and is at all points superior to the front-to-back ratio of a common reflector- driver Yagi by 5 dB minimum. However, as Table 1 shows, the source impedance is just above 20 Ohms.

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+ Fig.3-5. Gain and 180° front-to-back ratio of the sample ZL-Special from 28.0 to 29.0 MHz. +
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The final step in our design is to add a matching system to raise the impedance to something compatible with common 50-Ohms coaxial cable. The low source impedance reactance suggest a matching section. A 0.13-WL section of the same 35-Ohms cable (RG-83) used for the phase line functions as a near-1/4-WL section to achieve the goal. With this section in place, we achieve the 50-Ohms SWR curve shown in Fig. 6. One might select other lengths for the matching line to better center the SWR curve, but the values shown would be in most cases quite satisfactory. For reference, Fig. 7 shows the array patterns at 28.1 and 28.9 MHz to confirm that the patterns are usable and to show the evolution of the rear lobes as we increase frequency.

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+ Fig. 3-6. 50-Ohm SWR curve of the sample ZL-Special from 28.0 to 29.0 MHz. +
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+ Fig. 3-7. Free-space azimuth patterns of the sample ZL-Special at 28.1 and 28.9 MHz. +
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The design explored here has attempted to show the required alignment of the many variables involved in ZL-Special design. It is not the only design that will work, but it shares many characteristic with successful ZL-Specials. Most significant is the required low characteristic impedance of the phase line, calling for a coaxial cable. Such lines are vulnerable to external disruption from near-metallic contact, so a non-conductive boom is desirable without resorting to complex phase line support construction.

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                               Sample ZL-Special Analysis Data
+
+The following data come from NEC-2/NEC-4 models of a 2-element horizontal phased array for
+28.5 MHz using 0.5" aluminum elements.  The rear element is 0.506 WL long, while the forward
+element is 0.465 WL long.  The modeling environment is free space.  In all cases, the free-space
+gain is 6.34 dBi, and the 180° front-to-back ratio is 30.15 dB.
+
+Step 1.  Independent elements, independent sources:
+Element       Rel. I        Rel. I         Rel. V        Rel. V        Impedance
+              magnitude     phase angle    magnitude     phase angle   R +/- J X Ohms
+Rear          0.8935        -44.18°        26.24         -23.58°       27.49 + j 10.34
+Forward       1.0             0.0°         33.53          31.94°       28.46 + j 17.76
+
+Step 2.  Independent elements, independent sources, phase line installed:
+Element       Rel. I        Rel. I         Rel. V        Rel. V        Impedance
+              Magnitude     phase angle    Magnitude     phase angle   R +/- J X Ohms
+Rear          0.8935        -44.15°        ---           ---           27.49 + j 10.34
+Phaseline     0.664          44.25         33.56         32.02°        49.74 - j  8.98
+Forward       1.0             0.0°         33.51         31.96°        28.43 + j 17.73
+
+Step 3.  Phase line connected to forward element, single source
+Element       Rel. I        Rel. I         Rel. V        Rel. V        Impedance
+              Magnitude     phase angle    Magnitude     phase angle   R +/- J X Ohms
+Rear          0.5734        -60.80°        ---           ---
+Forward       0.6418        -16.62°        ---           ---
+Feedpoint     1.0             0.0°         21.53          15.34°       20.76 + j  5.70
+
+Step 4.  Matching section added:
+Element       Rel. I        Rel. I         Rel. V        Rel. V        Impedance
+              Magnitude     phase angle    Magnitude     phase angle   R +/- J X Ohms
+Rear          0.9774        -133.7°        ---           ---
+Forward       1.0939        -89.48°        ---           ---
+Feedpoint     1.0             0.0°         60.67           6.14°       60.32 + j  6.49
+
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+Table 1.  Sample ZL-Special analysis data from NEC models in the 4 steps of antenna analysis
+demonstrated in the text.
+
+

Folded-Dipole ZL-Specials

+
The use of folded dipoles as ZL-Special elements arose to overcome to problems: cost and the need for low-impedance phasing lines. Early versions of such designs taped the elements to bamboo horizontal supports. In general, most of these designs simply set two TV- twinlead elements 1/8 WL apart with a section of TV twinlead as the phasing line. Element lengths were a matter of trial and error experimentation. +
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+ Fig. 3-8. Basic outline of a W7EL Field-Day Special for 28.5 MHz. +
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W7EL's "Field-Day Special" rests on a different approach--an attempt to calculate the mutual impedance consequences of the elements, with the selection of element length, spacing, and line length designed to achieve the required current magnitude and phase angle transformation. Fig. 8 shows the outline of a 10-meter version of the antenna that I have built. The line lengths indicated are for modeled versions using #18 wire at a 1" spacing (about 450 Ohms impedance as a transmission line and for #20 wire spaced 0.375" (about 300 Ohms as a transmission line. The longer length for the thinner wire, when taken individually and as a spaced 2-wire pair) is natural. The following notes are based on the 1"-spaced model. In both cases, using vinyl-covered wire shortens the physical element by 1-2% to account for the velocity factor of the insulation in antenna use.

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+ 3-9. Free-space azimuth patterns of the Field-Day Special at 28.1, 28.5, and 28.9 MHz. +
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Although the element spacing is 4.27' (0.1237 WL), the phase line is 4.9' (0.1420 WL) long, despite the 0.8 velocity factor of high-quality twinlead. Indeed, calculations suggest that a higher front-to-back ratio results from the use of 340-Ohms line. However, as Fig. 9 shows in the free-space azimuth patterns across the first MHz of 10 meters, performance with a 300- Ohms line achieves similar levels to the first design that we explored. As well, with a 300-Ohms line, slightly better performance is possible by lengthening the forward element slightly, although the difference is unlikely to be noted in practical operation.

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+ Fig. 3-10. Gain and 180° front-to-back ratio of the Field-Day Special from 28.0 to 29.0 MHz. +
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Fig. 10 shows the gain and 180° front-to-back curves for the model across the 28.0 to 29.0 MHz span. Typical of ZL-Special designs of any sort, the gain rises almost linearly, while the front-to-back ratio shows a broad peak centered a bit below the center of the design passband. Fig. 11 provides figures on the resistance and reactance within the design passband. The resistance range is only about 7.5 Ohms. The reactance changes by a total of 56 Ohms. As Fig. 8 indicated, a pair of series capacitors, each with a reactance of -110 Ohms (about 50 pf at 28.5 MHz) would provide a very reasonable SWR curve across the passband.

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+ Fig. 3-11. Source resistance and reactance of the Field-Day Special from 28.0 to 29.0 MHz. +
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The need for a compact portable antenna inspired the original design of the Field-Day Special. However, for our purposes, it serves additional functions. One is to illustrate that equal- length elements (each about 0.468 WL long) result in wide-band performance that is not significantly different from the use of unequal length elements in the first example. A second function is to show that folded dipole elements have no advantage or disadvantage relative to single elements in performance--although there may be differences in the physical convenience of one or another element type. Third, the elements have widely divergent impedances: forward Z 124 + j 84 Ohms; rear 80 - j 256 Ohms. Nevertheless, the right length of the right impedance phase line effects the correct current division at the feedpoint junction so that we arrive ar the correct current magnitude and phase angle on the rear element to achieve proper or acceptable phased performance.

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A Dual-Line ZL-Special

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Before we leave the ZL-Special, let's examine a further variation on the general theme of phasing with a single transmission line section between the element. There is no rule that says that one must feed the system precisely at the junction with the forward element, even if tradition has imbedded this view in our minds. Fig. 12 shows the general outline of a variant of our first ZL-Special study model. +
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+ Fig. 3-12. Basic outline of the dual-line ZL-Special for 28.5 MHz. +
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The design uses the same element lengths as our initial model. The forward element is 0.465 WL long and the rear element is 0.506 WL long. Both are 0.5" (0.001207 WL) diameter aluminum. The original design used a single phase line length of 0.13 WL of 35-Ohms 0.66 velocity factor line. Suppose that one cannot obtain the required RG-83, but has some RG-8X with a 50-Ohms impedance and a velocity factor of 0.78. The higher-impedance line at any length will not achieve in a single line the desired phasing for reasonable ZL-Special performance.

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However, we may effect transformations of current magnitude and phase angle on both the forward and the rear elements by bringing lengths of transmission line from each element to a middle point. The length of line from the rear element is 0.13 WL. Although this length is physically similar to our original design, electrically, it is only 0.167 WL electrically, since the velocity factor of our new line is higher. A 0.015-WL line from the forward element is 0.192 WL electrically or about 0.52'. At the junction, given a source current of 1.0 at 0.0°, we arrive at a relative current split of this dimensions: forward 0.950 at 4.35° and rearward 0.458 at -2.1°. The resulting current ratio of rear to forward elements is 0.811 at -44.8°, close to the values for the original design.

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+ Fig. 3-13. Free-space azimuth pattern of the dual-line ZL-Special at 28.1, 28.5, and 28.9 MHz. +
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Fig. 13 shows the azimuth patterns across the 28-29 MHz span of the design passband. Only the front-to-back ratio suffers a bit relative to the more ideally phased original example, as shown in the gain and front-to-back curves in Fig. 14. A bit of element length adjustment might well have improved the numbers a bit, but would have altered the demonstration.

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+ Fig. 3-14. Gain and 180° front-to-back ratio of the dual-line ZL-Special from 28.0 to 29.0 MHz. +
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The natural impedance at 28.5 MHz for the new phase line arrangement is about 23.5 + j 13.1 Ohms. The low reactance suggests that a modified 1/4-WL line section might effect a match. 0.167 WL (electrical) of 35 to 37 Ohms line provides the broad 50-Ohms SWR curve shown in Fig. 15. The line might consist of either RG-83, or in the absence of such line, a parallel section of RG-59. In each case, the line velocity factor will determine the physical length.

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+ Fig. 3-15. 50-Ohm SWR curve of the dual-line ZL-Special from 28.0 to 29.0 MHz. +
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The design shown here is similar in principle to the one used to improve front-to-back performance of a 10-meter hilltopper 2-element Yagi. (See "Two Hilltoppers for 10 Meters," The ARRL Antenna Compendium, Vol. 6, pp. 1-9.) Like the single-line ZL-Special, the antenna requires a non-conductive boom to ensure that the phase-line remains clear of unwanted interactions.

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Tentative Conclusions

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We have examined the numerous variables that go into the design of a ZL-Special. The somewhat simplistic view of 2-element horizontal phased array design taken in the early years of ZL-Special building has given way to a more complete appreciation of the number of interactive variables involved, including the antenna dimensions and consequential mutual coupling. As well, the phasing work became more complex in terms of the current magnitude and phase angle transitions down a length of line having a given characteristic impedance so as simultaneously to provide each element with the correct relative current magnitude and phase angle and to effect a current division as the line junction or feedpoint that would result in those values. +

Many possible ZL-Special designs prove to be unfeasible. The requisite characteristic impedance of the phasing line may not exist and cannot be constructed. The required line length may be shorter than the distance between the elements, or it may be excessively long.

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The key to successful ZL-Special design is to find a set of element lengths and a spacing that meets two conditions. First, the relative current magnitude and phase angle on the individual elements must provide a satisfactory pattern in terms of gain and front-to-back ratio. Second, the impedances of the elements under the first condition must permit the design of a phasing line (or pair of lines) that employs an available or achievable characteristic impedance and that allows the requisite current division and transformation. As we saw in Part 1, there is in principle not restriction upon element spacing within the range of 0.05 to 0.2 WL, although element spacing in the 0.1 to 0.13 WL range tends to yield the most easily achieved gain and operating bandwidth levels.

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There is, in principle, no restriction upon the element lengths relative to the length of a resonant dipole at the design frequency. As well, there is no restriction upon the relative lengths of the elements: the forward element may be in principle shorter than, equal to, or longer than the rear element. Some combinations may be more favorable than others, although to date, there is no complete survey of all combinations.

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Perhaps the major disadvantage of the ZL-Special phasing system lies in the need to use folded dipole elements with high-impedance phase lines or to use with single tubular elements a low-impedance line. Many, if not most, builders wish to use a metallic boom and hence to have a phase line that is not susceptible to unwanted interactions. The quest for a stable phasing system has led to some interesting variants of phasing schemes for the 2-element horizontal array. The early HB9CV system--still in use today--and the recent N7CL system are two approaches to the same end. If the elements and the desired phase line do not match, let's add matching networks. As we shall see in the next episode, a slight increase in electrical complexity can lead to significant simplifications in the physical design of 2-element horizontal phased arrays.

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Updated 03-14-2002. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (Mar/Apr, 2002). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 4

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Topics: HB9CV / ZL Special, HF Upper, Phased Array


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+

Some Notes on Two-Element Horizontal Phased Arrays
+ Part 4: Removing the Limits of a Single Phase Line
+ by Element Matching

+

+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

The chief limitation of the ZL-Special form of a 2-element horizontal phased array has been mechanical: how to use single tubular elements with phase lines that are not susceptible to interaction with a metallic boom supporting the elements. Successful tubular-element ZL-Specials require low-impedance phase lines, while higher-impedance phase lines are more suited to folded-dipole elements.

+

Solutions to this problem have been available since R. Baumgartner, HB9CV, developed the array bearing his call in 1954. Interestingly, the HB9CV array has been exceptionally popular on the continent of Europe, but has met mostly silence in the English-speaking realm of amateur radio. Indeed, Rothammels Antennenbuch (now produced by DARC) devotes several sections to HB9CVs for various frequency ranges, and 1984 saw the production of a book devoted to the antenna (Fuchs-Collins, HB9CV: Richtantenne mit allen Variationen [Frech-Verlag, 1984]). This later book still insisted on favorably comparing the phased 2-element array to a 4-element Yagi.

+

Since the HB9CV's appearance, several other systems of overcoming the shortcomings of the ZL-Special have appeared. We shall sample only two of them: the recent N7CL phased array and a system of capacitively matching elements to the phase line. All three systems have a common thread. If the natural impedance of the rear element does not match well with a higher impedance phase line, we may alter the impedance of the element through the use of a matching system. The techniques that we shall examine vary chiefly in the means used to effect the match.

+

All of the variables that we examined in the case of the ZL-Special remain in effect. Element diameter and length, and the relative lengths of the two elements, determine the required relative current magnitudes and phase angles on the individual elements for a desired level of performance within the limits set in Part 1. However, instead of selecting the physical dimensions that will match the phase line we opt to use, we shall select dimensions that are appropriate for the application of a matching network to create the desired impedance on the rear element. We shall not ignore the forward element, since its dimensions must not only provide the desired rear element impedance when combined with that element, but as well, its impedance must allow the desired current division at the feedline junction and yield a feedpoint impedance that we can match to our most common feedlines.

+
+

The HB9CV

+
The original HB9CV design, shown at the top of Fig. 4-1, attempted to permit the use of 300-Ohm (or other parallel line available in the 1950s) with single tubular elements by the use of Tee or double gamma-match sections. A later version, shown in the lower part of the figure, varied the feedline system for use with 75-Ohm coaxial cable. By setting the gamma match in opposite directions on the two elements, the coax shield could connect to the element centers and to the boom. In fact, later versions of the HB9CV employed the boom as in of a pair of lines, with a small diameter line forming the partner. Since the smaller wire in a parallel line with different diameter wires general determines the line impedance, a single line could run from the rear element connection to the forward element connection and serve both as half the phase line and as the gamma section. Although the feedpoint is shown at the forward element of the illustrated versions of the HB9CV, various feedpoints between that point and the mid-point between elements are used. +
+ +
+
+ Fig. 4-1. General outlines of 2 versions of the HB9CV array. +
+

HB9CV specified certain dimensions for the antenna. The rear element should be 0.5 wavelength long, and the forward element should be 0.46 wavelength long, if the element diameter is between 0.004 and 0.007 wavelength in diameter. At ten meters, 0.004 wavelength is well over 1.5", which is larger than most builders would use. Therefore, adjustments are natural to HB9CV design. As well, HB9CV also specified the lengths and spacing of the gamma sections for both the Tee and gamma versions. Once more, these dimensions will vary with the actual materials used in construction.

+

Although not fully appreciated by some antenna modelers, the HB9CV antenna is somewhat difficult to model physically. Since the gamma sections will have a different diameter than the elements, we encounter angular junctions of dissimilar diameter wires in NEC-2 and NEC-4 models, and this situation tends to yield inaccurate results. MININEC models do not suffer this problem, but require very high segmentation densities, since the wires of the antenna structure create so many sharp angles. As well, the gamma match section are closely spaced to the elements and may need a version of MININEC having a close-wire correction factor. I have created models of the HB9CV with unreasonably high gain reports (>8.1 dBi free-space gain) by violating some of the limitations of the modeling system.

+

However, the HB9CV antenna can be modeled in principle within NEC-2 or NEC-4 by using a constant diameter wire size for both the elements and the gamma sections, adequate segmentation, and a TL phase line. In these notes, I shall examine the modeled results of both Tee and gamma versions of the HB9CV that use 1" diameter materials throughout. The forward element is 0.46 wavelength long, while the rear element is 0.508 wavelength long, with an element spacing of 0.125 wavelength. The gamma sections are spaced 0.0096 wavelength from the main element with lengths adjusted as follows: The Tees are 0.125 wavelength long, while the one-sided gammas are 0.053 wavelength long. The results do not report directly on the performance of the original designs or any specific variation of them, but they do indicate a set of reasonable expectations for performance.

+

These modeled dimensions vary from the original design chiefly in the spacing and length of the Tee and gamma sections. The revised model spacing is to avoid potential NEC inaccuracies of closely spaced wires of different lengths. However, the sections are only crucial to performance in setting the impedance of the elements, as seen by the phase line, at a desired level. As long as the element obtain the required relative current magnitudes and phase angles for a desired performance level, one may use any gamma diameter and length that will produce it.

+
+ +
+
+ Fig. 4-2. Gain and 180-degree front-to-back ratio of the sample HB9CV arrays from 28.0 to 29.0 MHz. +
+

Fig. 4-2 shows the modeled free-space gain and front-to-back performance of the Tee and gamma models. The Tee uses a 300-Ohm phase line, while the gamma uses a 75-Ohms line. As with all of the models in this series, these models do not necessarily indicate the peak performance of which an array is capable. They only serve to illustrate the principles of the array designs. Hence, the relatively low gain figures for the gamma-HB9CV might well increase with further optimization.

+

More interesting than the precise numbers for the reported gain is the difference in the gain curves for the two types of HB9CVs. The gamma version shows the nearly linear increase in gain with frequency to which we have grown accustomed from our ZL-Special efforts. However, the balanced Tee-HB9CV shows an almost perfectly flat gain across the first MHz of 10 meters. Independent element versions of the modeled design show the rear element, with its matching section, to have an impedance of about 250 Ohms with almost no reactance, a good match for the phase line. The single-sided gamma version does not show the same closeness of match with its 75-Ohms line. Indeed, measurements on an HB9CV 2-meter antenna that uses a single-wire for the phase line and gamma sections indicates a line in the 200-Ohm range for a direct 50-Ohm coax feed.

+
+ +
+
+ Fig. 4-3. SWR curves of the sample HB9CV arrays from 28.0 to 29.0 MHz. +
+

The cost of the Tee-version's relatively even performance across the first MHz of 10 meters is the feedpoint impedance. As shown in Fig. 4-3, the HB9CV has an SWR curve referenced to 100 Ohms. A 2:1 matching network or device is required for standard coax feed. In contrast, the gamma version shows a well-behaved 50-Ohm SWR curve. Fig. 4-4 samples the free-space azimuth patterns of the Tee-version of the HB9CV at 28.0, 28.5, and 29.0 MHz to indicate the evolution of the pattern across the operating passband.

+
+ +
+
+ Fig. 4-4. Free-space azimuth patterns of the Tee-version of the HB9CV array at 28.0, 28.5, and 29.0 MHz. +
+

In the 1950s, the 1/8 wavelength spacing of elements and the use of element lengths similar to those of 2-element Yagis held a mystique among phased array designers. From our work with both ideal phased arrays in Part 1 and optimized Yagis in Part 2, we now understand the appeal of the 1/8 wavelength spacing. It represents a reasonable balance between operating bandwidth and gain. Beyond the 1/8 wavelength mark, gain tends to decrease ever more rapidly for elements near the 1/2 wavelength or self-resonant length. Below a spacing of 1/8 wavelength, the operating bandwidth decreases ever more rapidly.

+

However, for the proper phasing of an array to produce good performance--relative to having only 2 elements--there is no magic spacing. So long as we achieve the correct confluence of all of the variables in a phased 2-element horizontal array, we may use any spacing between 0.05 and 0.2 wavelength. The gamma and Tee matching system to bring the rear element into reasonable alignment with the impedance of a chosen phase line and the forward element to an impedance that yields the proper current division and feedpoint impedance might well be adaptable to other element lengths and spacings. However, the success builders have had with the original HB9CV designs has tended to suppress both experimentation and calculation that would yield new variants.

+
+

The N7CL Beta-Matching System

+
In the search for less complex mechanical designs of 2-element horizontal phased arrays, Eric Gustafson, N7CL, has developed within the past few years a different approach to the same end. N7CL wanted to do away with virtually all of the visible superstructure of the HB9CV while achieving similar performance capabilities. To this end, he turned to the shorted-stub form of the beta or hairpin stub, although he used coaxial cable sections for his stubs. +
+ +
+
+ Fig. 4-5. General outlines of the N7CL phased array. +
+

Fig. 4-5 shows the schematic outline of the N7CL phased array. It consists of 2 elements, a phase line, and two stubs. For the Phase line, N7CL selected a 100-Ohm line created from side-by-side (series) sections of standard coaxial cable. The shielding provided by the cable braids permit the line to ride inside the metal mast supporting the elements with no ill effects.

+

However, single tubular elements do not match well to 100-Ohms phase lines. The key to effecting a match is to change the element impedance from its natural value to something very close to 100 Ohms. A beta match will do the job, but under the condition that the element impedance exhibits a sufficient capacitive reactance to form the series reactance to go with the shunt or parallel inductive reactance of the stub in classic L-network terms.

+

We cannot simply apply a beta match to any element and expect good results. We must begin with an acceptable 2-element design using separate feedpoints. Since the rear element must show a capacitive reactance, it must be shorter than a self-resonant half wavelength, if we are to believe the indications of the tables in Part 1. We shall want a net reactance on the feedline-phase line junction that is also capacitive, which indicates a forward element that is shorter still.

+

For this 10-meter design example, using 0.5" aluminum elements, I selected a forward element length of 0.4446 wavelength and a rear element of 0.0.4772 wavelength. The element spacing is 0.1112 wavelength. With this combination and a rear element relative current magnitude of 0.8762 at -38.53 degrees, we obtain a performance potential of 6.39 dBi free-space gain and 23.88 dB front-to-back ratio. One might further vary these values for higher performance, but for the design example, I declared them satisfactory.

+

The forward element impedance is 20.9 - j 32.7 Ohms. The rear element impedance is 16.4 - j 39.7 Ohms. I selected a 100-Ohm phase line. To raise the impedance of the rear element to about 100 Ohms, I added a shorted stub, the shunt component of a beta or L-network. The required value from network calculations was about j 44 Ohms. Since the length of a shorted stub will vary with both the desired reactance and the characteristic impedance of the line used, I arbitrarily created a 50-Ohms stub with an electrical length of 0.1116 wavelength.

+

I then created a phase line with the specifications of 100 Ohms and a velocity factor of 0.78 to simulate RG-8X or similar cable. The physical length is 0.1314 wavelength to ensure that there is enough cable to reach from the center of the boom tube to the elements at each end. The line has an electrical length of 0.1684 wavelength, the length necessary to transform the current magnitude and phase for the desire conditions on each element. With the rear stub and the 100-Ohms phase line added to the model, we obtain the desired performance indicated from the initial model with independently fed elements. However, the feedpoint impedance at the junction of the forward element and the phase line is 21.33 - j 22.45 Ohms.

+

The capacitive reactance and low resistance at the feedpoint are ripe for a second beta match, this time a 50-Ohm shorted stub with an electrical length of about 0.126 Ohms. The result is a feedpoint impedance of 43.8 - j 7.0 Ohms at the design frequency.

+
+ +
+
+ Fig. 4-6. Gain and 180-degree front-to-back ratio of the N7CL phased array from 28.0 to 29.0 MHz. +
+

Fig. 4-6 shows the free-space gain and front-to-back curves for this sample design across the first MHz of 10 meters. Because the rear-element beta match reverses the impedance progression with changing frequency relative to an element with no matching system, the gain curve shows a reverse direction relative to other phased arrays with which we have worked. The front-to-back curve peaks at about 28.3 MHz. Both progressions of values can be altered with further design refinements.

+
+ +
+
+ Fig. 4-7. SWR curve of the N7CL phased array from 28.0 to 29.0 MHz. +
+

In the design example, the elements were not sufficiently optimized to yield both an SWR under 2:1 across the passband and a minimum value close to 1:1, as shown in Fig. 4-7. The feat may be more difficult than might appear at first sight, since any adjustment to the length of the forward element to move the SWR curve will also affect the natural--and hence, the transformed--impedance of the rear element. Moreover, the element spacing--just over 0.11 wavelength--also works to narrow the operating passband of the array. Fig. 4-8 shows sample free-space azimuth patterns at both the band edges and mid-band.

+
+ +
+
+ Fig. 4-8. Free-space azimuth patterns of the N7CL phased array at 28.0, 28.5, and 29.0 MHz. +
+

The N7CL phasing system is currently in use in 30-meter and 40- meter arrays under the Cal-Av label. I am grateful to Eric for permission to describe his patented matching system, although he is in no way responsible for the slant given to the explanation or for my simple design example. As I have noted, design examples do not necessarily equal production designs in performance.

+
+

Capacitive Element Loading

+
+

A few years ago (1998-99), I took a different tack in trying to overcome the problem of designing a phased array that could use a higher impedance or twin-coax phasing line. (See "The HB9CV Phased Array and Gain Comparisons".) As we increase the length of a dipole, the impedance increases. If we lengthen the dipole sufficiently, the impedance approaches 100 Ohms resistive, but with a considerable inductive reactive component. We may compensate for this reactance by inserting capacitors at the element feedpoint in series with the element.

+
+ +
+
+ Fig. 4-9. General outlines of the capacitive-element-matching phased array. +
+

When we deal with 2 elements, the problem becomes only slightly more complex due to the interaction of the elements. The result will be elements considerably longer than a self-resonant dipole. The final design result was the array pictured in Fig. 4-9. The forward element is 0.602 wavelength long, while the rear element is 0.622 wavelength long. Because the gain of a dipole tends to increases modestly with increases in length, I used a relatively wide spacing of 0.145 wavelength to achieve satisfactory performance. The elements are 1" diameter aluminum.

+

We need not bring each element to zero reactance in order to have a satisfactory array. The rear element uses a total capacitance of 25.4 pF (two 50-pF capacitors in series on each side of the feed junction). The forward element uses 15 pF (two 30-pF capacitors). When modeled as independent element separately fed, the rear element impedance is 82.9 - j 11.4 Ohms, while the forward element is 102.6 + j 35.7 Ohms. We may now add a 100-Ohms phase line using the same 0.78 velocity factor twin 50-Ohms coax construction used in the preceding example. The physical length for the design example is 0.145 wavelength, although in practice, some extra line may be useful for making connections. A 0.150 wavelength line will not significantly change performance due to the initial good match between the line and the rear element. The feedpoint junction requires no additional matching network, because the forward-element capacitors were adjusted to provide a low 50-Ohms SWR.

+
+ +
+
+ Fig. 4-10. Gain and 180-degree front-to-back ratio of the capacitive-element- matching phased array from 28.0 to 29.0 MHz. +
+

Fig. 4-10 shows the free-space gain and front-to-back ratio potential performance across the 28.0 to 29.0 MHz spread. The system is not at all finicky, as revealed by the values obtained simply by replacing the 100-Ohm line with a 150-Ohm, as might be obtained by employing 75-Ohm coax lengths as shielded twinlead. However, the system is relatively optimized for the 100-Ohm line. The 150-Ohm line shows superior band-edge front-to-back performance, although the 100-Ohm line version shows a higher peak value. Since the matching capacitors only compensate for the element inductive reactance and do not transform the impedance, the gain curve shows its normal upward trend with frequency.

+
+ +
+
+ Fig. 4-11. SWR curve of the capacitive-element-matching phased array from 28.0 to 29.0 MHz. +
+

In Fig. 4-11, we find the SWR curves for both the 100-Ohm and the 150-Ohm line versions. Both are satisfactory. However, we might classify the 100-Ohm line version as somewhat "tamer." Fig. 4-12 provides the standard 28.0, 28.5, and 29.0 MHz free-space azimuth patterns for performance reference. The array with capacitively loaded elements is an experiment and not a finished product. The elements are long by most array standards--about 20% longer than those of a standard array. However, the reward for heavier elements is a somewhat simplified structure for matching the rear element impedance to the phase line and the array feedpoint impedance to standard coaxial cable feedlines.

+
+ +
+
+ Fig.4-12. Free-space azimuth patterns of the capacitive-element-matching phased array at 28.0, 28.5, and 29.0 MHz. +
+
+

Conclusions

+
The three systems we have explored in this part of the series illustrate ways in which we may achieve 2-element phased arrays using normal beam constructions with a metallic boom supporting the elements. In each case, the designer has matched the element impedances to a desired phase line, using a varied assortment of techniques. Once more, our goal has not been to produce paradigm production designs, but only design examples sufficient to illustrate the principles involved. If we have gained some appreciation of the techniques of matching the rear element to the phase line and changing everything else to align the other variables involved in a 2-element horizontal phased array, then we have gotten out of them everything intended. +

Indeed, some may wish to emphasize the performance differences among the examples, but this would be a mistake. Many designs can undergo further optimization. What should strike us is the basic similarity in performance among the ZL-Special and the matched-element designs. One cannot be absolute on the basis of a sampling, but it is likely that the performance range among the models explored so far represents the main arena for 2-element horizontal phased array performance.

+

Free-space makes an ideal environment for comparing the potential performance of antennas of essentially the same type. However, over the years, some folks have questioned whether or not there might be a difference between the performance of phased horizontal arrays and of parasitic arrays over ground. The only free-space evidence a potential difference in performance would be a significant dissimilarity between the elevation or H-plane patterns of Yagis and phased arrays. None exists.

+ 
            Comparative Performance Figures of Sample 2-Element Arrays
+                   All Arrays 1 Wavelength Above Good Ground at 28.5 MHz
+
+1.  Reflector-Driver Yagi
+Dimensions:
+Reflector  Driver          Element    Element
+Length wl  Length wl       Spacing wl Diameter wl
+0.5028     0.4620          0.1250     0.001207 (0.5")
+Performance:
+Gain       TO Angle   Second Lobe     Angle      Main-Second           Front-Back
+dBi        degrees    Gain dBi        degrees    Lobe Ratio dB         Ratio dB
+11.61      14         9.35            46         -2.26                 12.52
+
+2.  Driver-Director Yagi
+Dimensions:
+Driver     Director        Element    Element
+Length wl  Length wl       Spacing wl Diameter wl
+0.4972     0.4670          0.0750     0.001207 (0.5")
+Performance:
+Gain       TO Angle   Second Lobe     Angle      Main-Second           Front-Back
+dBi        degrees    Gain dBi        degrees    Lobe Ratio dB         Ratio dB
+11.83      14         9.49            46         -2.34                 19.58
+
+3.  ZL-Special
+Dimensions:
+Rear El.   Forward El.     Element    Element          Phaseline--Note 1
+Length wl  Length wl       Spacing wl Diameter wl      Length    Zo    VF
+0.5060     0.4650          0.1250     0.001207 (0.5")  0.1300    35    0.66
+Performance:
+Gain       TO Angle   Second Lobe     Angle      Main-Second           Front-Back
+dBi        degrees    Gain dBi        degrees    Lobe Ratio dB         Ratio dB
+11.68      14         9.51            47         -2.17                 31.62
+
+2.  N7CL Phased-Array with Rear-Element-Matching
+Dimensions:
+Rear El.   Forward El.     Element    Element          Phaseline--Note 2
+Length wl  Length wl       Spacing wl Diameter wl      Length    Zo    VF
+0.4972     0.4670          0.0750     0.001207 (0.5")  0.1314    100   0.78
+Performance:
+Gain       TO Angle   Second Lobe     Angle      Main-Second           Front-Back
+dBi        degrees    Gain dBi        degrees    Lobe Ratio dB         Ratio dB
+11.74      14         9.49            46         -2.25                 31.44
+
+Note 1:  ZL-Special uses a feedpoint impedance matching section.
+Note 2:  N7CL array uses shorted stubs for rear-element matching and for
+feedpoint matching.
+
+Table 1.  Comparative performance figures of sample 2-element arrays with all
+arrays 1 wavelength above good ground at 28.5 MHz.
+

However, we may use a more direct demonstration by modeling sample parasitic and phased arrays over real ground. Table 1 lists the critical performance parameters of two Yagis, a reflector-driver array with an element spacing of 0.125 wavelength and a driver-director array with a 0.075 wavelength element spacing. These arrays come from part 2 of the series. The sample phased arrays are the 35-Ohms phase line model from Part 3 and the N7CL array from our work in this section. All arrays are 1 wavelength above ground. At 1 wavelength, a parasitic array elevation pattern shows both a lower main lobe at about 14 degrees elevation along with a secondary lobe above. The differential in the secondary lobe is a good indicator of performance similarity or difference.

+
+ +
+
+ Fig. 4-13. Elevation patterns of two types of parasitic arrays 1 wavelength above good ground. +
+
+ +
+
+ Fig. 4-14. Elevation patterns of two types of phased arrays 1 wavelength above good ground. +
As the figures in the table show--backed up by the elevation patterns in Fig. 4-13 and Fig. 4-13--the differentials are too small to support a claim of performance differential. The differentials that do exist lie in the realm of gain and front-to-back ratio. The 2-element horizontal phased array is capable of slightly higher gain than a 2-element Yagi of similar operating bandwidth. The gain advantage runs between 0.2 to 0.7 dB. However, with a reasonable front-to-back ratio, the gain of a 2-element horizontal phased array never reaches the level of a well-designed 2-element quad or a short-boom 3 element Yagi. +

If the gain advantage of the horizontal phased array is marginal relative to parasitic arrays of similar operating bandwidth, the front-to-back advantage is significant and operationally noticeable. A reflector-driver Yagi with coverage of the first MHz of 10 meters will have a peak front-to-back ratio of about 12 dB. A similarly sized phased array with equal or greater gain is capable--when optimally designed--of nearly 20 dB across the full passband, with peak values in the 30 dB region. Whether one wishes the additional quietness from the rear of the phased array or wants to be able to hear what may be happening in directional to which the beam is not aimed depends on the type and style of operation. In short, the desirability of one type of array over another is a user judgment.

+

These comparative notes relate only to full-size models of both parasitic and phased arrays. Shortened, loaded elements yield lesser gain in virtually all circumstances, although loaded reflectors may increase the front-to-back ratio of a reflector-driver Yagi. A shorter-element phased array may be capable of the full gain that its elements permit with inherently good front-to-back ratio as well. In the end, the variables involved in antenna selection--where 2 elements form the common baseline among candidates--may outnumber the variables involved in properly phasing 2-element horizontal arrays.

+
+ +
+

Updated 05-10-2002. © L. B. Cebik, W4RNL. This item originally appeared in The National Contest Journal (May/Jun, 2002). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

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+

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+

Topics: HF Upper, Phased Array


+ + diff --git a/content/phase/phagi.html b/content/phase/phagi.html new file mode 100644 index 0000000..8f9ffa7 --- /dev/null +++ b/content/phase/phagi.html @@ -0,0 +1,75 @@ + + + + + + Horizontal Phased Arrays with Parasitic Directors + + + +
+

Horizontal Phased Arrays with Parasitic Directors

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Although well-known in other parts of the world, combined horizontal phased arrays with parasitic directors are relatively obscure in the U.S. To remove some of that obscurity, I went through the process of capturing a design procedure appropriate to this type of antenna. The result is an experimental 3-element beam with the gain of a 4-element short-boom Yagi and the front-to-back ratio of a saint. +

Background

Consider the 2-element phased horizontal array, which is often called the ZL-Special, with HB9CV variations. Both elements are fed. A phasing line between the two elements is designed to set the relative magnitude and phase angle of the currents at the two feed points. The phase line is often brought to the forward element, but need not be that way. In many instances, achieving the correct phasing will require a central current dividing point with different length lines running to each of the two elements. +

2-element phased arrays can be set up for maximum gain or for maximum 180- degree front-to-back ratio. The latter set-up is the norm for phased verticals, but does not yield maximum gain. Indeed, for most horizontal 2- element arrays, maximizing the rear null results in gain that equals or is less than that of a 2-element Yagi (which has only a modest front-to-back ratio).

+

Maximizing gain results in about an extra dB of gain relative to the maximum rear null configuration. However, the front-to-back ratio goes to pot, dropping easily to under 10 dB.

+

Note that all of this is done without changing the antenna dimensions. Although Yagis require a certain geometry to achieve either maximum gain or maximum rear null, phased arrays achieve the same results by setting the relative current magnitude and phase on the two elements. If we use networks to set the individual current magnitudes and phases, we may use equal element lengths of approximately 1/2 wl.

+

The norm is to use transmission line lengths to set the relative current magnitudes and phases, and this practice sets limits to what is possible. Since we have only a few types of available commercially made transmission lines, using them restricts design variations. We may also make our own lines, but in most cases, they will have too high a characteristic impedance to handle linear dipole-style elements and are better suited for use with folded dipoles.

+

To compensate for restrictions in the feasible limits of setting current magnitudes and phases with transmission lines, we often alter the geometry of the elements to achieve a given result. For maximum rear null configurations, the rear element may actually be shorter by a small amount than the forward element in some cases.

+

However, practical design rarely chooses either the maximum gain (too little front-to-back ratio) or the maximum rear null (too little gain) configurations. Intermediate values are the general rule and result in gains up to about 1/2 dB greater than with a 2-element Yagi of equal spacing while keeping the front-to-back ratio in the 18-20 dB ballpark. Such phased arrays tend to have the appearance of a 2-element Yagi with a low impedance connecting cable between the two elements.

+

For further work on the fundamentals of 2-element horizontal phased arrays, see "Modeling and Understanding Small Beams: Part 5: The ZL Special," Communications Quarterly (Winter, 1997), pp. 72-90

+

Adding a Director

The design we shall explore is not new to the world, although it may be new to many folks. The configuration of the antenna is shown in Figure 1. +
+ +
+

The sketch makes the antenna appear to be a 2-element phased array with a director ahead. Appearances do not deceive. This experimental antenna for 24.95 MHz uses a 14' boom (roughly comparable to 12' at 10 meters or 24' at 20 meters). This is considered a long boom for a 3-element Yagi but a short boom for a 4-element Yagi. Dimensions appear in the figure. Models of the antenna use 3/4" diameter aluminum. The phasing line is a 6.6' length of RG-8 (velocity factor 0.66) or equivalent. Connections are reversed, since the required current phasing is that of a -45-degree line, not that of a +135-degree line. (Although impedance goes through two cycles per 360 degrees of transmission line, voltage and current go through but 1 cycle in the same length. A short half-twist line thus cannot effect a 135-degree current transition directly, but accomplishes the equivalent by a reversal of both voltage and current phase, but must always count backwards from zero in accounting for the current magnitude and phase in the line.)

+

Using coax as the phase line calls for special precautions due to the reversal. Proximity to metal booms can disrupt the characteristic impedance of the line due to external couplings. Hence, spacing the line from the boom is necessary. (Early ZL-Special builders often forgot this and taped the phased line to the metal boom, resulting in disappointing performance.)

+
+ +
+

The antenna performance is quite remarkable and quite even across narrow bands like 12 meters. As Figure 2 notes, the maximum free-space gain is over 8.6 dBi, with a 180-degree front-to-back ratio approaching 34 dB.

+

Feeding the antenna is a bit of a challenge, since the feedpoint impedance is about 15.5 + j23.0 Ohms. However, we can use a little appreciated version of the beta match. The beta match is simply an L-network, where the series reactance is part of the antenna feedpoint impedance in series with the resistive component. If the reactance is correct, we can simply add a shunt reactance of the opposite type across the terminals to effect an impedance transformation to 50 Ohms. See Figure 3.

+
+ +
+

Since the series reactance of the antenna feedpoint is inductive, the shunt reactance must be capacitive. The required reactance value is about 35 Ohms, which translates into a capacitance of about 180 pF for 12 meters. Since there will be construction variables in every antenna, a variable capacitor should be used to establish the exact value required for a good coax match. Replace the variable with an equivalent fixed capacitor of the nearest value. Be certain that it has substantial internal and external lead size to handle the high currents at the feedpoint. Because of the low antenna source impedance, ensure that all connections are very tight electrically. Weather seal the capacitor and its connections. Use a choke balun between the matching section and the main coax cable. The director essentially controls both the gain and the front-to-back ratio of the array. (In Yagi design of greater than 2 elements, the reflector largely controls the driver impedance, with the director having the greater effect upon both gain and front-to-back ratio.) We can easily glimpse this fact by stripping away the director and checking the performance of the 2 phased elements.

+
+ +
+

As Figure 4 shows, the correct design of the 2-element phased array portion of the total antenna is to set it for maximum gain, in this case, a native free-space value approaching 7.2 dBi. The front-to-ratio is about 10 dB, mediocre at best.

+

Adding the director yields an additional gain of about 1.4 dB. Moreover, the front-to-back ratio improves by over 20 dB. Had the original phased 2- element section been set for maximum rear null, the final performance figures would not have been obtained.

+

Comparative Performance

How does the phased array with director stack up against other antennas with similar boom lengths. To check this, I went into my files and chose the best 3-element and 4-element designs with similar boom lengths. +

The 3-element design uses a boom length less than a foot shorter than our array. However, its gain is limited to about 8.1 to 8.15 dBi in free space if it is to sustain a front-to-back ratio above 20 dB. The feedpoint impedance is just about 25 Ohms when resonant.

+

The 4-element Yagi uses a boom less than a foot longer than our array. Its gain approaches that of the array, being about 0.2 dB less. The front-to- back ratio is in the same ball park. The feedpoint impedance is midway between our array and the 3-element Yagi. However, this performance is purchased at the cost of an added element.

+
+ +
+

Figure 5 tells the same story graphically. Phased arrays with parasitical directors can yield exceptional performance relative to wholly parasitical antenna designs with the same boom length and number of elements.

+

Not all designs calling themselves phased arrays with directors are true 3- element designs. Some multiband designs use "log" cells for drivers on multiple bands or multiple parts of bands. The crossed lines work, but not as either contributors to gain or to rear nulling.

+

Conclusion: Just the Beginning

For monoband beam use, the combination of a phased 2-element array replacing the normal reflector and driven element of a Yagi can add up to 0.5 dB added gain--at least in three element versions--for a given boom length over conventional Yagis. It also is capable of excellent front-to- back performance. +

However, these brief notes only hint of work to be done. The phased array portion of the antenna has not been optimized for the source impedance. Whether the performance of this design can be sustained at a higher and more desirable source impedance is not known to me at this time. Whether the added gain of the 3-element array carries over into 4 and 5 element versions is also not known to me at this time.

+

This very preliminary work was done without reference to any commercial antenna. Unfortunately, I do not have on file any detailed design plans of antennas claiming to use or actually using these principles. In the end, these unknowns suggest that the phased array plus director(s) is a design worth further investigation as time permits.
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8-27-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to Amateur Radio Page

+

Topics: HF Upper, Phased Array


+ + diff --git a/content/phase/phagi1.gif b/content/phase/phagi1.gif new file mode 100644 index 0000000..2ce4282 Binary files /dev/null and b/content/phase/phagi1.gif differ diff --git a/content/phase/phagi2.gif b/content/phase/phagi2.gif new file mode 100644 index 0000000..f12bb92 Binary files /dev/null and b/content/phase/phagi2.gif differ diff --git a/content/phase/phagi3.gif b/content/phase/phagi3.gif new file mode 100644 index 0000000..fdd5e45 Binary files /dev/null and b/content/phase/phagi3.gif differ diff --git a/content/phase/phagi4.gif b/content/phase/phagi4.gif new file mode 100644 index 0000000..05a7c2d Binary files /dev/null and b/content/phase/phagi4.gif differ diff --git a/content/phase/phagi5.gif b/content/phase/phagi5.gif new file mode 100644 index 0000000..218b279 Binary files /dev/null and b/content/phase/phagi5.gif differ diff --git a/content/phase/phase-1.gif b/content/phase/phase-1.gif new file mode 100644 index 0000000..c2fd853 Binary files /dev/null and b/content/phase/phase-1.gif differ diff --git a/content/phase/phase-2.gif b/content/phase/phase-2.gif new file mode 100644 index 0000000..3a7b238 Binary files /dev/null and b/content/phase/phase-2.gif differ diff --git a/content/phase/phase.html b/content/phase/phase.html new file mode 100644 index 0000000..be47315 --- /dev/null +++ b/content/phase/phase.html @@ -0,0 +1,70 @@ + + + + + + Don't Be Phased By Phasing + + + +
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Don't Be Phased By Phasing

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+
+

L. B. Cebik, W4RNL

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+ +

+
+ Many antenna builders cringe at the mention of a certain word: phasing. Unless you are using a simple antenna, like a resonant 1/2 wavelength wire (commonly called a dipole), your antenna consists of phased elements. If it is a Yagi, it is phased. If it is a 135' doublet used on 10 meters, it is phased. If it is a 4-element system of collinear extended double Zepps spaced 5/8 wavelengths vertically with all elements fed, it is phased. (I have modeled this little system for about 22 dBi forward gain and a beam width of under 17 degrees--or better than most flashlights in directivity.) +

What Phasing Is: It may be useful to understand a little better what phasing is all about. Any time we have more than a half- wavelength of wire (or more than a quarter wavelength with verticals), we have phasing. Phasing is simply a readout of the current on a designated secondary part of the antenna or antenna system relative to the designated primary part. We are not interested in those currents for their own sake, but for what they do to the resulting radiation pattern of the antenna. The patterns that result are a function of the current magnitudes, the current phases, the length of the primary and secondary parts, and their separation.

+

Geometric and Electronic Phasing Control: If we understand phasing well enough, we can not only see what the interaction of these 4 phasing factors yields, but we can also control the radiation pattern by juggling the factors. Consider a 2-element Yagi: a driven element and a reflector.

+

Just the relative lengths of elements and their spacing can determine the current magnitude and phase on the reflector relative to the driven element. There are good combinations and bad combinations--those with more gain and/or front-to-back ratio and those with less. But we quickly learn that with two elements, there is a limit to both gain and front-to-back ratio.

+
+ +
+

Figure 1 will show some of the limits we encounter, if we supplement it with a small table. The curve marked "normal" is a typical 2-element Yagi design. Let us for the sake of the example freeze a couple of dimensions: spacing is set at 51" and the aluminum elements are 0.75" in diameter. Moreover, in all cases, the current on the front element is given an arbitrary magnitude of 1.0 at 0.00 degrees phase.

+ 
Antenna   DE L.     Ref. L.   Gain      F-B       Feed Z    Ref. Current
+          inches    inches    FS dBi    dB        R+/-jX    Mag/Phase
+Normal    191.0     210.0     6.06      11.0      36+j2     0.64/140.5
+Max Gain  191.8     200.0     7.02       5.6      19-j6     0.82/164.1
+Max F-B    38.1     204.4     6.22      14.6      0.8-j1100 0.12/145.8
+Phased    191.0     210.0     6.35      52.0      -------   0.93/136.4
+

First, let's explore what some simple changes of geometry can do for and to our antenna. We can alter the lengths of the two elements to achieve the maximum gain from the elements, but at a cost of most of the front-to-back ratio and with a feedpoint impedance that is quite low. To achieve a nearly 5 dB greater front-to-back ratio, we must radically alter the length of the driven element until the feedpoint impedance become wholly unusable. In short, there are limits to what we can achieve simply by altering the physical geometry of the antenna.

+

Suppose we could control the current magnitude and phase on the rear element without changing the original dimensions of our modest "normal" antenna. One thing we discover is that we cannot squeeze out significantly more gain, but we can improve the front-to-back ratio--at least for a small frequency range. Using the original elements, we find that we can dramatically increase the front-to-back ratio by controlling the current magnitude and phase to the rear element. (The very sharp null in the rear holds good for only a very narrow frequency range.)

+

One way to achieve the required phasing for a maximum front-to-back ratio is to construct a ZL Special, a 2-element phased array. It uses a precisely calculated set of element lengths, spacings, and an equally precisely calculated length of transmission line between them. The current splits at the feedpoint, part going to the forward element, and part being transformed along the phasing line so that, at the rear element, the current has the magnitude and phase to maximize front-to-back ratio at the target frequency. An alternative is the HB9CV, which aims for a combination of gain (approaching 7 dB) and reasonable front-to-back ratio (about 20 dB) with a specially formulated phase line and matching system. In principle, the HB9CV is a variation of the ZL Special, and both antennas employ the same basic principles.

+

Of all 2-element configurations that I have encountered, the Moxon rectangle comes closest to achieving the rear element phasing necessary for maximum front-to-back ratio with purely geometric means--that is, without the use of phasing networks or phasing lines. Moxon rectangles are explored in other notes in this collection. Essentially, bending the elements inward toward each other at the ends--in precise lengths and end spacings--alters the element coupling from the standard Yagi straight element design. The cost is a little gain, but the benefit is a highly enhanced front-to-back (and front-to-rear) ratio. The result is also amenable to direct 50-ohm feed and has a very wide operating bandwidth.

+

Let's look again at the difference between geometric and electronic control of the current on a second element, this time using 1/4 wavelength verticals. We shall set two of verticals exactly 1/4 wavelength apart. First, we shall make both antenna elements the same length and feed only one. That yields the "spaced" pattern in Figure 2. It is a nice pattern, but we can improve the front-to-back ratio. Next, we shall increase the rear (reflector) element length and shorten the driven element back to resonance so that the two elements have about a 4% length difference. The performance peaks out on the curve called "parasitic" in Figure 2. In short, altering geometry can do only so much to establish the conditions for maximum front-to-back ratio. (For many operating situations, the improvement in front-to-back ratio may be sufficient; for others, it will need improvement.)

+
+ +
+

The curve marked "phased" is the pattern of two elements of the same length 1/4 wavelength apart when both are fed in a certain way. The forward element has a current of 1 and a phase angle of zero; the rear element has a current of 1.03 and phase angle of 96 degrees. What the pattern shows is over 42 dB of front-to-back ratio.

+

The patterns also show other important things. First, the maximum gain set-up differs from the maximum front-to-back set-up. The "spaced" array of two identical elements with only one fed yields the most gain. Both attempts to improve front-to-back ratio show less gain. Second, we always have to evaluate whether the gain or the front-to-back ratio will do us the most good for our operating needs.

+

More Elements: To improve gain, we shall need more elements, that is, more 1/2 wavelength sections for antenna. Yagis with 3 or more elements alter the relative current phase and magnitude on all unfed elements by the proper spacing and sizing of directors in addition to a reflector. We can also create collinear arrays, that is, antennas with the elements end-to-end. The patterns will add or subtract according to their placement. Think of an extended double Zepp (a 1 1/4 wavelength wire, center-fed) as two half- wavelength wires separated by a quarter wavelength. This spacing lets the dipole patterns add up and narrow for more gain and a narrower beamwidth. The center section establishes the pattern of current distribution along the wire to permit the addition of patterns from the two half wavelength sections.

+

Phasing Methods: There are only a few basic methods of altering the current magnitude and phasing of the secondary antenna parts.

+

1. Element length and spacing: We have seen with both the Yagi and vertical examples how element length and spacing alter current distribution. If we need or want a current distribution that geometry will not give us, then we must use other means.

+

2. Transmission lines as phasing transformers: Every transmission line is a transformer of voltage, current, and impedance along its length. For antenna work (and contrary to what we think about when considering the feedline to the shack), it is the current phase and magnitude that is most important. How this transformation occurs is a function of the characteristic impedance of the feedline (and its velocity factor). The ZL Special transformation is a very precise thing if one wants more than mediocre results. Not just any line will do, nor will just any length of line (relative to the antenna element lengths and spacing) do. For certain simple cases, like phasing 2 verticals 90 degrees, lengths of line can do the job, but those cases are somewhat limited.

+

Many collinear arrays make use of phasing lines between element ends. Most are simple cases of reversing the end-to-end phasing. The 1/2 wavelength wire that runs between the two drooping ends of a half-square antenna is such a line. It does not radiate (much), but presents the "far end" vertical with the same magnitude of current as the fed end, but 180 degrees out of phase. The vertical patterns then add to give the peanut- shaped pattern useful to low band DXers. More complex arrays may need precise electrical lengths of phasing lines to effect a specific change of current phase to an adjacent wire, as in collinear EDZs.

+

3. "Brute force": For precisely tuned phased arrays, nothing beats L- networks (along with PIs and Tees) for establishing the exact phase change needed to make an array work. Every such network changes the phase of the entire voltage-current magnitude set relative to the input (although the voltage and current retain their initial phasing relative to each other). Hence, we can achieve any desired relative current settings. If we then use multiples of a half wavelength of transmission line from the network to the element, we can set each element where we want to set it. Sounds simple, doesn't it.

+

In some ways it is, but. . .let's not forget that the network also creates an impedance transformation. When we take these matters into account, the calculations can get a little more complex. We have to make certain that the element gets the correct current level and phase under a matched condition. Phasing 3, 4, and more wire systems is an exercise for someone who loves his calculator.

+

Vertical Phasing: So far we have been thinking in 2-dimensional terms. Now lets add a third--the vertical. We can stack antennas vertically for more gain. The principle is to place the two patterns in a proper phase relationship so that the forward patterns add--a vertical version of collinear pattern adding. The principle works with almost any type of antenna. Vertically spaced EDZs are common. Most vertically spaced arrays feed each antenna in phase--that is, each driven element has the same current magnitude and phase. A number of notes in this collection sample a fair array of different phasing situations.

+

In another note in this series, we have shown with models that the proper spacing for maximum gain increases for a pair of Yagis increases as the gain of the original Yagis increases. While 5/8 wavelength spacing works well for 3-element Yagis of good gain, we need a lot more space between 5- or 6-element Yagis to get the maximum gain possible from the pair. To make matters a bit hairier, the front-to-back maxima do not occur in the same spacing places as gain maxima. However, the antennas can be redesigned slightly to bring the maximum stacked gain and the maximum stacked front-to-back ratio into alignment.

+

This small note is not a how-to-do-it manual. We would need a book for that, and handbooks already abound. Instead, the point is only to ensure that we understand that phasing is a significant concept even when there are no phasing networks or phasing lines in sight. If we have convinced you that phasing is everything in antenna work, then you may not be phased by all the references to phasing in what you read about antennas. Phasing can never be phased out of antenna work.
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Updated 02-04-98. © L. B. Cebik, W4RNL. A briefer version of this item appeared in QRP Quarterly, January, 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Return to Amateur Radio Page

+

Topics: Phased Array


+ + diff --git a/content/pvc/pvc-1.gif b/content/pvc/pvc-1.gif new file mode 100644 index 0000000..fea67e3 Binary files /dev/null and b/content/pvc/pvc-1.gif differ diff --git a/content/pvc/pvc-10.gif b/content/pvc/pvc-10.gif new file mode 100644 index 0000000..4da64c7 Binary files /dev/null and b/content/pvc/pvc-10.gif differ diff --git a/content/pvc/pvc-11.gif b/content/pvc/pvc-11.gif new file mode 100644 index 0000000..ccf0310 Binary files /dev/null and b/content/pvc/pvc-11.gif differ diff --git a/content/pvc/pvc-12.gif b/content/pvc/pvc-12.gif new file mode 100644 index 0000000..b372e28 Binary files /dev/null and b/content/pvc/pvc-12.gif differ diff --git a/content/pvc/pvc-13.gif b/content/pvc/pvc-13.gif new file mode 100644 index 0000000..dc853c8 Binary files /dev/null and b/content/pvc/pvc-13.gif differ diff --git a/content/pvc/pvc-14.gif b/content/pvc/pvc-14.gif new file mode 100644 index 0000000..b0b6c4d Binary files /dev/null and b/content/pvc/pvc-14.gif differ diff --git a/content/pvc/pvc-15.gif b/content/pvc/pvc-15.gif new file mode 100644 index 0000000..2f5056a Binary files /dev/null and b/content/pvc/pvc-15.gif differ diff --git a/content/pvc/pvc-16.gif b/content/pvc/pvc-16.gif new file mode 100644 index 0000000..e534e0e Binary files /dev/null and b/content/pvc/pvc-16.gif differ diff --git a/content/pvc/pvc-17.gif b/content/pvc/pvc-17.gif new file mode 100644 index 0000000..71d113e Binary files /dev/null and b/content/pvc/pvc-17.gif differ diff --git a/content/pvc/pvc-2.gif b/content/pvc/pvc-2.gif new file mode 100644 index 0000000..7ee0385 Binary files /dev/null and b/content/pvc/pvc-2.gif differ diff --git a/content/pvc/pvc-3.gif b/content/pvc/pvc-3.gif new file mode 100644 index 0000000..28cfa82 Binary files /dev/null and b/content/pvc/pvc-3.gif differ diff --git a/content/pvc/pvc-4.gif b/content/pvc/pvc-4.gif new file mode 100644 index 0000000..32378a3 Binary files /dev/null and b/content/pvc/pvc-4.gif differ diff --git a/content/pvc/pvc-5.gif b/content/pvc/pvc-5.gif new file mode 100644 index 0000000..1a40caf Binary files /dev/null and b/content/pvc/pvc-5.gif differ diff --git a/content/pvc/pvc-6.gif b/content/pvc/pvc-6.gif new file mode 100644 index 0000000..f783c48 Binary files /dev/null and b/content/pvc/pvc-6.gif differ diff --git a/content/pvc/pvc-7.gif b/content/pvc/pvc-7.gif new file mode 100644 index 0000000..e5f809d Binary files /dev/null and b/content/pvc/pvc-7.gif differ diff --git a/content/pvc/pvc-8.gif b/content/pvc/pvc-8.gif new file mode 100644 index 0000000..c76addf Binary files /dev/null and b/content/pvc/pvc-8.gif differ diff --git a/content/pvc/pvc-9.gif b/content/pvc/pvc-9.gif new file mode 100644 index 0000000..bf9dd58 Binary files /dev/null and b/content/pvc/pvc-9.gif differ diff --git a/content/pvc/pvc.html b/content/pvc/pvc.html new file mode 100644 index 0000000..d12e7ca --- /dev/null +++ b/content/pvc/pvc.html @@ -0,0 +1,193 @@ + + + + + + PVC for Antenna Applications + + + + +
+

Tinker Toys for Adults
+ Some Notes and Ideas on PVC for Antenna Applications

+

+
+

L. B. Cebik, W4RNL

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Part 1: General Notes on Working with PVC

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Every since I called PVC "tinker toys for adults," the phrase has gained popularity (except among the erector set and "lego" generations). The material is extremely versatile for amateur radio applications ranging from operating furniture to antenna supports. It cuts with a simple saw, glues eternally, and may last a long, long time. However, it also has some pitfalls and inconveniences. Only experience and creativity limit the ways we can put it together to form useful ham items. My interest is chiefly in antenna applications, but other uses abound.

+

The following notes are taken from several dozens of projects in which I have used the material in various ways. They do not form a comprehensive list of uses, Instead they are one of many possible starter collections to whet your appetite and your get your own creative juices flowing.

+

What is PVC?

PVC (poly-vinyl chloride) is a plastic material most usually formed into tubes and associated junctions. It is used extensively in plumbing in its white form and in electrical conduits in its gray form. The difference between colors can be important, depending on where you live. Apparently, there is no clear nationwide uniformity in the exact formulation of the material, so long as it meets certain specifications. The gray form seems everywhere to include a healthy dose of UV-protectant material, while the white form is more variable. In the Southeast, the white form tends to contain more UV-protectants and lasts a long time in outdoor use. In the Northwest, the white form tends to contain less UV-protectants and becomes brittle more rapidly in sunlight. (The white form available in Tennessee is quite durable in continuous sunlight, as some 10-year-old yard benches, arbors, and birdhouse supports all attest.) Hence, before choosing a PVC form to use, check with local experience. +

For most uses that are continuously exposed to daily sunlight, about 10 years is a maximum lifetime, even for UV-resistant forms of PVC. Assuming that you perform annual preventive maintenance on your exposed structures, you can detect increased brittleness from the sound made when a tube is tapped. The dull thud of new PVC becomes a sharper rapping sound. When in doubt, replace the length: PVC is amongst the cheapest material available for construction. If your interests include gardening, then 1 1/4" to 1 1/2" nominal PVC can be used to make up the framework of a greenhouse and its integrated work benches.

+

The primary family of PVC tubing and fittings used for most projects is likely to be Schedule 40. This family consists of tubes that are listed in nominal diameters, where "nominal" means that the inside diameter is at least the size listed. Typically, Schedule 40 tubes have walls that are roughly 5/32" thick. The following table lists some common sizes and their inside and outside diameters--as measured informally.

+ 
                      Schedule 40 Dimensions (in Inches)
+Nominal Size            Inside Diameter               Outside Diameter
+        1/2                     9/16                          7/8-
+        3/4                     3/4+                        1 1/16
+      1                       1                             1 5/16
+      1 1/4                   1 5/16+                       1 5/8+
+      1 1/2                   1 9/16                        1 15/16
+Note:  + and - correspond roughly to woodworker measurements called "strong" (a bit over, but
+not enough to call for the next increment) and "weak" (a bit under).
+
+

The are other diameters of Schedule 40 PVC tubing, roughly in half-inch increments (nominal). Above a certain diameter, we may tend to call these "pipes." Many can be used for in-ground supports for masts and pipes. Our interest, though, is mainly in joining sections into assemblies, so we shall let the big sizes be an exercise in your own creativity.

+

From the table, we can immediately see one of the inconveniences of Schedule 40 PVC: it does not nest, one size inside the other. The one exception is 1" and 1 1/4" tubing, which will loosely nest. However, the gap is such that a glue connection will not be secure. Nuts and bolts make the best link.

+

In place of nesting sizes, there are fitting galore, some of which are intended to link tubing of the same size and others of which are intended for permit joining two different sizes of tubing. So all is not lost.

+

Before we move on to junctions of tubing, let's note that within the PVC umbrella are a number of other types and sizes. For example, CPVC is available. It is a thin wall (about 1/32") tubing whose dimensions are closer to copper piping. 1/2" nominal CPVC has an inside diameter of about 1/2"- with an outside diameter of about 9/16". I have successfully used this material in relatively unstressed or very low load conditions. For example, I have used it as 4.5' spacers for a 10-meter wire beam and as spacers to separate the ends of tubular Moxon rectangle elements to keep them aligned.

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Also available are other families of white PVC. Schedule 80 PVC is sometimes available, but usually not in the common home center. A thinner-wall white PVC is more readily available. One common designation is SDR 21, although you may encounter other notations. It has the same outside diameter as Schedule 40 for the same nominal size. However, the wall is only about 3/32" thick. Hence, 1/2" nominal SDR 21 has an inside diameter of 11/16" and 3/4" nominal has an inside diameter of about 15/16". For many VHF projects, this thinner PVC may be adequate to support an antenna, although it is weaker and more flexible in longer lengths. For example, some aluminum rods shipped to me inside a 5' long 1 1/2" nominal SDR 21 tube arrived intact, but the tube had been cracked somewhere along the route. Schedule 40 would not have cracked, but would have cost considerably more in shipping charges. Do not underestimate the weight of Schedule 40 PVC.

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Connecting Lengths of PVC

As we earlier noted, only the 1" and 1 1/4" nominal sizes of Schedule 40 PVC nest, and they tend to require nuts and bolts to secure the junction. I have built portable masts with up to three 5' sections by alternating the two sizes, with stove bolts securing the assembly. However, there are better ways. +

The two chief forms of junctions pieces are the glue and the screw joints. Since every joint requires at least some gluing, let's begin with them. Gluing is more properly called cementing, and the process requires two steps. There is a joint cleaner, usually blue or purple, that prepares the surface for mating with a junction fitting. Many hams skip this step, since the joint need not be as water-tight as a plumbing joint. However, it is always recommended.

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PVC cement actually fuses the two surfaces of the pieces to be mated. Depending on the amount of cement used, you have between 15 and 30 second to fit and align a joint before the two surfaces become a single solid. Hence, it pays to have pre-prepared jigs for aligning multiple joint structure, such as a U-shaped assembly. Often, simply locating good straight surfaces is sufficient for the job of alignment. For example, I use my shop floor and workbench legs to align right angles with enough precision for most applications.

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Once glued, the connection is permanent. If it is not right, cut off the junction and use other junctions and tube pieces to replace the cut-out section. Be sure to wipe off each junction immediately after gluing to keep the exposed surfaces clean and smooth.

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+ 1 A collection of PVC junctions from my junk box. +
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Glue junction pieces come in many types: in-line, 90-degree Ls (or elbows), 45-degree elbows, Tees, Ys (with a side 45-degree piece), (4-arm) crosses, and caps. Fig. 1 is a casual photograph of some of the junction types from my junk box. Some combination of these fitting will let you create triangles, squares, and octagons suitable for yard furniture.

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+ 2 A bottom view of a yard bench illustrating some PVC assembly techniques. +
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See the photos of an inverted yard bench (Fig. 2) and a gurney (Fig. 3) used for my YL's wild bird rehabilitation cages.

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+ 3 A wild bird rehabilitation cage gurney showing additional PCV construction techniques. +
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The photos also reveal another secret of PVC. We can install junctions--usually 90- degree Ls and Tees--wherever we need to change direction. Since each fitting is limited in the number of junctions available, our designs must offset each junction that changes the direction of the tubing. Between each junction, we must use a link piece of tubing. The link tubing between two adjacent junction fittings may not be visible in the finished product, because it is cut to exactly twice the inset depth of the fitting. However, it is a necessary element in the structure: it serves as a glue surface for the junction pieces, and it doubles the total thickness of PVC at these junction stress points.

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Screw joints are handy for joining sections of tubing that you may wish to take apart later or which may serve multiple functions. Each screw joint consists of a male and female section, and each of these is glued to their respective lengths of tubing. Then, the two assemblies are simply screwed together.

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Screw sections are available for changing tubing sizes. In fact, there are Tees with a side screw section in smaller sizes. Hence, you can have a vertical support with a removable "handle" for turning. One note of caution. The gray PVC screw fittings, designed to connect sections of electrical conduit, may not be as substantial as the white equivalents. For example, the locally available male gray screw section has a thinner wall than its white counterpart. In the 1 1/4 nominal size. the white version fits over the swaged end of common 1.25" steel masting, and wedges nicely onto the full diameter section. The thinner-wall gray equivalent simply slides over the full diameter of the mast. Once more, check your local supplies and test fit everything before buying, since there may be regional variations on the available stock.

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Every glue job usually requires some tube cutting to a specification. PVC cuts well with a simple hack saw. You should take time to deburr the edges, including a good rub of the corners with medium sandpaper. Dry-fitting joints is not only unnecessary; it sometimes is disastrous. I have a few dry-fit junctions around that act as if they were glued. Just be sure the junction areas are clean and evenly cut for a good fit with cement applied.

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If you have a motorized shop, then a "chop" saw is very good for cutting PVC--with a couple of precautions. First, clean the blade after every use for PVC is you wish to get clean wood cuts later. Second, be sure to use hold-downs of some sort for each side of the cut. The saw can spit out the shorter cut end at a very damaging rate. I tend to make my cut and let the blade brake to a stop before raising the saw. Of course, safety glasses are mandatory, and gloves are recommended. Also, beware of cutting well-aged and more brittle PVC tubes: the shrapnel can be painful. Hand tools are slower, but rarely create the danger levels of power tools.

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PVC also drills easily. A starter hole created by an awl helps to prevent drill-bit skidding. a drill press is useful here, but rarely mandatory. However, a jig or vise to hold the tube is often the key to a neat job. You can also cut slots in the end of PVC. In fact, some applications may involve a combination of slots and drilled holes at their inner ends. For very large diameters of tubes, you can use a saber saw (which are now called jig saws, and the old jig saw is now called a scrolling saw, even though saber saws may have scrolling features.) See Fig. 4 the photo of the outdoor electrical outlet post for an example of this technique.

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+ 4 One way to add an outdoor outlet in your yard using a PVC post. +
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Although we shall focus on PVC alone, do not hesitate to look throughout your home center for metal fittings that you can join with sheet metal screws or with nuts and bolts to a PVC framework. You can solder or braze other metal to a copper plumbing pipe cap and add a solder lug or other connector. Some metal parts may require a bit of work to make a good mechanical junction with PVC, but the possibilities are almost as endless as the hardware supplies in home centers.

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You may wish to compare these general notes with the materials available in your area. Modify the notes to reflect what is true of PVC to which you have access. Now let's look at some distinctly ham applications of PVC.

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+

Part 2: Some Ham Applications of PVC

+
Let's divide our applications into several categories: masts, booms, element supports, and storage. We shall omit other uses of PVC--for example, as a coil form or as a chair frame-- for another time. +

1. Masts: My best general recommendation: don't. There is a temptation to use 10' lengths of PVC for masting. My personal experience suggests that even Schedule 40 PVC sags and sways too much compared to other available materials. 5' lengths can be coupled with less sag and more convenient transport. However, they tend to be heavier than common 5' 1.25" TV masting of the same length--and the TV masting shows less sag and instability when raising it from the horizontal to the vertical position.

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+ 5 A beam mounted on a PVC mast mounted in my shop antenna assembly jig. +
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However, using a 1 1/4" 5' section with a screw coupling at the top is convenient for workshop use. In fact, I tend to keep all PVC lengths at 5' and under, since they bundle and fit both my pick-up and may more easily. The photo in Fig. 5 shows part of a small beam under construction outside my shop. The short mast lets me assemble the antenna parts comfortably.

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2. Booms: The photo (Fig. 6) of the boom structure of the Moxon rectangle shows one way to use 1 1/4" PVC as a boom. Beyond the 5' length, PVC tends to sag too much for effective boom use. However, in the shorter lengths, it hands very much like an aluminum boom--with one advantage: the elements are automatically insulated (or, more properly, isolated) from metal structures.

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+ 6 A Moxon rectangle using a PVC boom with element and boom plates. +
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I have not detected any RF conductivity in Schedule 40 PVC in the HF range. Hence, its use to support elements can be easily recommended. Whether or not PVC has any conductivity at VHF is a question for which I have not seen any definitive data. As we shall see, there are ways of using PVC to support VHF elements that will tend to minimize any possible interaction, just in case at least some formulations are RF conductive above the HF range.

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+ 7 A portable dipole with a PVC hub and screw fitting, mounted on a steel mast. +
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A second form of boom is used with my dipole in a tube and my beam in a boom, both of which have been published in the ARRL Antenna Compendium, Vol. 6. The center hub of the dipole and the boom of the beam terminate in a screw fitting. A short section of tubing with a male fitting permits the short mast to fit over the end of a standard section of TV mast and to wedge in place for portable use, as shown in the photo in Fig. 7. You can wrap the TV mast with a few layers of electrical tape where the short PVC stub just fits on top. This move will keep the antenna-and-PVC portion stable. No additional clamping is necessary for the usual short- term portable operating session, but for longer periods at height, you may wish to add a stove bolt through the joined sections to keep the wind from turning the assembly without turning the mast.

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+ 8 A close-up of a PVC dipole element hub for aluminum rod elements. +
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The elements for there two antennas represent two (of many) different ways of mounting elements. The rod elements are threaded, as shown in one close-up photo (Fig. 8), and simply bolt in place in the end of a section of 1 1/4" nominal tubing, using nuts both inside and outside the tube. The 10-meter rod elements can be replaced with eye-screws and a large solder lug for attaching wires for ant band. As shown in Fig. 9, the tubular beam elements fit over a 3/8" diameter fiberglass rod and are held in place with #8 stainless steel nuts and bolts. In both cases, I dry fit a PVC cap over the end of the tubing. The cap functions mainly to remove stresses from the elements that might eventually deform the PVC. (As a plastic, PVC retains some fluid properties and may be deformed over time by a continuous set of pressures.) We shall look at another cap function a bit later.

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+ +

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+ 9 A close-up of a PVC boom with details of the aluminum tubing element assembly. +
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3. Element supports: Technically, booms and masts support antenna elements, but in this category, I include more complex structures. The first three examples happen to be associated with 2-meter antennas.

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+ 10 A #12 AWG wire 2-meter half square on a PVC test frame. +
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The first example, shown in the photograph in Fig. 10, is a wire half-square vertically polarized bi-directional antenna. The antenna itself provides a very sharp figure-8 pattern, similar to that of a horizontal dipole, but vertically polarized--and stronger than that of a quad loop. The structure is a custom arrangement of PVC. The horizontal piece is SDR 21, since the only weight it supports is itself. Its function is simply to hold the #12 AWG copper house wire in position. The vertical piece nearest the coax is Schedule 40, since this is the main support. The remaining short pieces are SDR 21. Everything is 1/2" nominal. This fixture is solely for the purpose of testing the antenna design, although it has serve for several years without injury to the antenna.

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+ 11 A more complex PVC mounting frame for a 2-element 2-meter half-square beam. +
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The next photograph (Fig. 11) shows a 2-element half-square parasitic beam. The 1/2 nominal pieces are Schedule 40, arranged to provide even alignment for the two element sets. An array of Tees and elbows spaces the elements from the PVC to minimize potential interaction. The horizontal tubing (3/4" diameter) passes through the 1/2" nominal Tees and is fixed in position by single sheet metal screws at each Tee. This support system is designed for a centered support mast.

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+ 12 A vertically oriented 2-meter Moxon end-mounted on a braced PVC support. +
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Similar to the half-square beam mounting is the element support system for the 2-meter Moxon rectangle, shown in the photo (Fig. 12) oriented for vertical polarization. A single bolt on the support arm behind the reflector permits me to rotate the antenna to the horizontal position. The unique part of this assembly is the remainder of the support arm, which extends to a mast stub well behind the antenna elements. To brace the support arm, Tees plus Ys are arranged to form a triangular brace. Also evident is a repair in the angular tube: I cut the bad portion out and added an in-line junction and the short piece to the Y junction. Once more, everything here is 1/2" nominal.

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+ 13 A sketch of a stressed-PVC quad spreader and boom assembly. +
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For either HF or VHF quad antennas (likely no larger than a 15-meter version), we can use a stressed-PVC spreader and boom structure. A sample is shown in Fig. 13. For miniature quads for 10 meters, a single 10' length of 1/2" nominal SDR 21 (or similar thin-wall PVC) can pass through holes in a 1 1/4" nominal Schedule 40 boom. Pin the tubing in place with #10 stainless steel hardware. Offset the two lengths of tubing required to obtain 4 spreaders. Add 1/2" Tee fittings to the ends of the spreaders as a smooth surface for the quad element wires at the corners. Stress the tubing to create a square of the right size for the quad loop. I initially use twine to secure the square and then add the wire. I add bridge wire at each tee, which prevents slippage and a wind-forced reversal of the arms.

+

If you need longer arms, you can use a short piece of Schedule 40 PVC through the boom holes, with in-line junction glued in place. Then you can make arms up to 10' long in each of the 4 directions. However, there is a limit to the durability of stressed arms based on a. the amount of stress and b. the UV resistance of the tubing used.

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+ +

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+ 14 A sketch of one way to use PVC spreaders or spacers. +
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Thin-wall PVC and CPVC are highly usable as wire spacers. Among the possible applications are home-made parallel transmission line, double-wire dipole elements (for wide operating bandwidth), and wire beams for 10 meters and up. Fig. 14 shows one good technique for preparing the spacers. Hack saw a slot, and then drill a hole as closely as possible to the exact diameter of the wire. I prefer not to deburr the holes. When I press the wire through the slot into the hole, the burrs create a good friction fit that prevents slippage. However, the spacer can still be moved without much force.

+

These examples are just five of endless ways to arrange PVC as useful element support structures. Perhaps they are enough to give you a start on your own project.

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4. Storage: We may store in a PVC tube, plus caps, almost anything long and thin--like antenna elements. Earlier we saw the dipole in a tube element junction mounted on a mast. In the photo in Fig. 15, we can see the rod elements stored inside a capped tube, where the top of the tube holds a female screw junction to mate with the capped element junction piece. The rods are split into two pieces (5/16" inner sections, 3/16" outer sections), joined by a 1/2" x 1/2" x 1 1/4" aluminum block, tapped for the threaded ends of the rods. Disassembled, everything pits inside the tube with room to spare.

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+ 15 Dipole elements stored in a PVC tube. +
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Slightly more complex is the boom of the beam in a boom. The elements are 1/2" and 3/8" diameters tube sections on each side. The tubing nests for each element side. The four tube pairs and the two 2' section of 3/8" fiberglass rod all fit inside the boom itself, a 5' section of 1 1/4" nominal Schedule 40 PVC. As Fig. 16 shows, the mast stub makes a good grip for carrying the entire antenna to and from the car trunk. Although the assembly may look a bit complex, I have in demonstration talks managed to assemble and disassemble both the dipole and the beam within a 40 minute period, all the while trying to describe the antennas to an audience. On a hilltop, everything goes faster, since I can keep my eyes on the work, only occasionally glancing around for East Tennessee black bears.

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+ 16 Aluminum Yagi elements stored inside a PVC boom. +
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My last photo (Fig. 17) is an obvious one. A short length of 1 1/2" nominal tubing, with one end capped permanently by a glue joint, becomes a tool carrier for the two antennas. Inexpensive screw drivers, nut-drivers, and wrenches, along with a sack of small hardware, easily store in the tube.

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+ 17 A simple tool storage tube to carry with portable antennas to hilltops. +
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These are not by any means the only things we can do with PVC. For example, the four- legged oak support frame, which I used both in my shop and for traveling demonstrations, could also have been made from PVC. I just happen to like wood as well as plastic. In fact, about the only antenna parts that I cannot make from PVC are the conductive elements themselves. At present, the price of aluminum tubing and wire is too low to make PVC elements very practical.

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One final note for the ham homestead: If you sand the surface of PVC to give it a "tooth," it will accept a primer for enamel followed by a color coat of good outdoor paint. Hence, it is possible to decorate your yard with your call sign constructed from PVC (including legs to support it). Alternatively, you can create both 2-D and 3-D sculptures from PVC. Combining this idea with others, you can make very non-standard trellises for your decorative vines. You may also construct fences around ground-mounted verticals for safety, using them also as morning glory trellises. With a little ingenuity, a little paint, and a few flowering vines, you can make neighbors forget that 70' tower and maze of wire antennas in the backyard.

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Updated 8-29-00. © L. B. Cebik, W4RNL. This item first appeared in QRP Homebrewer, Spring, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: PVC


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Calibrating K to NEC

+ hr +

Calibrating K to NEC

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Topics: Modeling


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Some Aspects of Long-Boom, Monoband Log-Cell Yagi Design

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Some Aspects of Long-Boom, Monoband Log-Cell Yagi Design

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+ hr
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Topics: HF Upper, LPDA


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Notes on the OWA Yagi

+ hr +

Notes on the OWA Yagi

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+ hr
+

Topics: VHF / UHF, Yagi


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Notes on Designing Large 5-Band Quads

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Notes on Designing Large 5-Band Quads

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+ hr
+

Topics: HF Upper, Quad


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The Quest for the Elusive TBWB4EQ
+ (The Tri-Band Wide-Band 4-Element Quad)

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The Quest for the Elusive TBWB4EQ (The Tri-Band Wide-Band 4-Element Quad)

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This page exists to include the PDF in the topic index

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Topics: HF Upper, Quad


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Some Notes on Turnstile Antenna Properties

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Some Notes on Turnstile Antenna Properties

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Topics: Turnstile, VHF / UHF


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+

+ In Pursuit of Better VHF Quad Beams
+ A Work in Progress

+

L. B. Cebik, W4RNL

+

+
+ +
+

In both commercial and home-brew circles, quad beams have long vied with Yagis as the means to a high performance antenna array. Indeed, that very competition has very likely robbed the quad of the independent study necessary to establish its properties well-enough to capitalize effectively on them. In contrast, the development of antenna modeling and optimizing software has contributed to whole new generations of Yagis that effectively utilize parasitic relationships to develop both better patterns and wider operating bandwidth in virtually of all of critical categories.

+

With the exception of only a few investigators, such as Bob Haviland, W4MB, Dan Handelsman, N2DT, and David Jefferies, most quad designers have relied upon one of two methods to develop new antennas. The first method is the set of antique equations, long printed in The ARRL Antenna Book. This design method--which pays absolutely no attention to the diameter of the element wires--yields reasonably accurate thin-wire HF quads that are exceptionally narrow-banded. Neither their SWR curves nor their front-to-back curves will hold up to modern standards across even the HF wide ham bands. Yagis have set a standard of less than 2:1 SWR across a band like 20 or 15 meters, with a front-to-back ratio of at least 20 dB across those bands. Equation-designed quads using the old formulas simply cannot yield antennas that meet such performance standards.

+

The second method of development is trial and error, with emphasis upon error. Chief among the errors is the attempt to keep the boom length for any given number of elements as short as possible. If this initial temptation is overcome, there seems reticence to extend the quad boom longer than necessary for a Yagi with the same number of elements. The results have been narrow-banded quad beams, often with performance deficiencies, especially in the front-to-back category.

+

So I think that we must return to the starting line and redevelop our thinking about quads from scratch. In this work-in-progress, I shall take a long look at 2- and 3-element quad beams, with some observations about 4-element beams. Although I have some 5- and 6-element designs in my collection of models, they are not sufficiently well-developed to admit of systematic discussion. Hence, these notes represent the first part of yet-to-be finished business.

+

However, along the way, you will note some recurrent themes that I might as well summarize at the outset.

+

1. Quad antennas, whether single loops or arrays, are narrow-band arrays by nature--contrary to the long standing myth about them. Because quads often offer a very wide SWR curve in some configurations, the entire set of antennas has received the unwarranted categorization as "low-Q" devices. Unfortunately, this has misled many builders into believing that the quad is a non-critical antenna so that careful construction is not really necessary.

+

In effect, compared to properly design Yagis, the quad array with the same number of elements is a narrow-band antenna. Its front-to-back performance falls off more than 2.5 times as fast as the SWR curve deteriorates. Although some users claim they only care about the gain, the design challenge for me is to discover what it takes to obtain superior performance in all major categories across a given band.

+

2. The physical specifications for a quad array are critically dependent upon the diameter of the elements that compose them. I shall show along the way just how much the quad is dependent in raw performance (such as gain) upon element diameter as much as it is dependent upon the loop circumference for each of the elements and upon the element spacing. The element-diameter factor is elusive in trial-and-error design exercises, but can become clear when optimizing basic quad designs becomes a systematic enterprise. In fact, we shall show that monoband 2-, 3-, and 4-element quad design is amenable to computerized calculations requiring only the element diameter and the design frequency as inputs.

+

3. For optimal performance, the parasitic coupling of quad elements requires considerably more spacing than equivalent coupling of linear elements in Yagi design. Indeed, beyond a certain point, the boom length of an optimized quad with reasonably wide-band performance characteristics may be the limiting factor in comparisons with Yagis of similar performance capabilities. At this point, I might estimate the break-even point to be somewhere between 4 and 5 elements. However, this estimate is very tentative, as the work is nowhere near complete.

+

4. The theoretical gain of a quad over a Yagi with a similar number of elements cannot be attained if the quad elements are significantly smaller in diameter than the Yagi elements. HF quads suffer most in the regard, since the #12 to #16 AWG wire we generally use is often less than 0.1 the diameter of typical Yagi elements for the same frequencies. However, VHF quads suffer similarly when they use thin wire, while the Yagis with which they compete employ aluminum rod or tubing. In many cases, the wire quad will lose up to half of the theoretic advantage over a single linear element solely in terms of wire losses. If we wish a quad to achieve its full theoretical potential relative to Yagis, we shall have to use "Yagi-size" elements.

+

The themes I have just enumerated are more fully developed in a series of articles appearing in AntenneX starting in October, 2000. However, we shall see significant confirming evidence as we look at VHF quad design. For the purposes of keeping everything coherent, all of the quads examined here have a design frequency of 146 MHz. In terms of properties, I have set the 2-meter band in the U.S. (144-148 MHz) as the design bandwidth for both the SWR bandwidth curve and the front-to-back bandwidth curve. Front-to-back figures will be given as the 180-degree front-to-back value, although we shall examine the rear quadrant performance in more detail in the text.

+

2-Element Quad Beam Design

+
+ +
+

To fully appreciate a 2-element quad beam, sketched in Fig. 1 for reference, it may be useful to make a few comparisons to comparable 2-element Yagi behavior. In a 2-element driver-reflector configuration, a Yagi exhibits maximum front-to-back ratio in the region of about 0.1 to 0.12 wavelengths spacing, with element lengths optimized. The peak front-to-back ratio is low--about 12 dB--and the curve is shallow as we increase the spacing.

+

The behavior of the Yagi represents a limit for parasitic operation of two 1/2 wavelength linear elements. It is possible to derive much higher front-to-back ratios for any pair of such elements by any one of many methods of phase-feeding both center-points. In fact, for any spacing and set of near-1/2 wavelength element lengths, we can find a set of relative current magnitudes and phases for the two elements to achieve at least 50 dB of 180-degree front-to-back ratio. However, parasitically, the mutual coupling between elements is not sufficient to achieve more than the approximate 12 dB figure at the optimal spacing.

+

A quad loop may--for this exercise--be thought of as two dipoles bent so that the ends meet each other. In this configuration, the current distribution along each of the two dipoles is different from that of a linear dipole. The current at the square loop corners--which approximates the distance from the center to the mid-points of a linear element--is about 14% higher with double the phase shift of the current on the corresponding points of a linear element. The net result is a high level of mutual coupling between elements. Since the optimal distance for achieving maximum front-to-back ratio is a function of coupling, we should expect that the element spacing for a quad would have to be greater than for a driver-reflector Yagi. It is: in the neighborhood of 0.17 wavelengths.

+

For both the Yagi and the quad, the exact spacing required for maximum front-to-back ratio is a function of two other variables: the element lengths and the element diameter. As the element diameter increases, the quad loop lengths (for maximum front-to-back ratio combined with driver resonance) increase and the required spacing between elements increases. It is possible to derive a series of antenna models using NEC--which is highly accurate in this kind of exercise--that track the array dimensions for any element diameter ("wire size") from 3.16E-5 up to 1E-2 wavelengths. Subjecting the results to regression analysis results in a series of equations suitable for automated design of a 2-element quad beam having maximum front-to-back ratios of more than 50 dB. Such a program, in GW Basic format for structural transparency, appears in Appendix 1 of this study. One need only enter the element diameter and the design frequency to derive 2-element quad dimensions and some basic performance data.

+

At VHF, few will be tempted to build a quad using wire in the 3.16E-5 range--somewhere in the #80 AWG range. However, the program is calibrated for 3 to 300 MHz, and quads in the 1300 kHz range have been developed from the automated process. There are a few cautions to observe. The program lists a design frequency gain that is correct for about 30 MHz. Since skin effect and its resultant losses do not change linearly with the change in element diameter, the actual gain of an array will be higher than predicted for frequencies significantly lower than 30 MHz and be lower than predicted for frequencies higher than the median. As well, changing antenna materials will result in small deviations from the predictions, especially for very thin element quads. The result of these material changes will be minimal with elements larger than 1E-3 wavelengths in diameter.

+

Table 1 lists the wires sizes that we shall sample in this study, arranged in an overall 8:1 total ratio in 2:1 increments. The smallest size is just barely thinner than #14 AWG (0.0641"). The largest size (0.5") represent a practical limit to modeling accuracy for the exercise, as the diameter approaches 1E-2 wavelengths. The common logs for the wire diameters (in wavelengths) are also listed, since the properties of antennas tend to vary more directly with the common log of wire size than with the size itself.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Table 1:  Wire Sizes Used in This Study
+
+Wire Size in Inches      Wire Size in             Common Log
+                         Wavelengths              of Wire Size
+     0.0625              0.0007731                -3.1118
+     0.125               0.0015462                -2.8107
+     0.25                0.0030925                -2.5097
+     0.5                 0.0061849                -2.2087
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
My concern to develop the automated program for maximum front-to-back 2-element quads stems from the fact that the maximum front-to-back configuration also yields the widest operating bandwidth for this array type, where bandwidth includes both 2:1 SWR and >20 dB front-to-back ratio. Table 2 lists the resultant quad designs based on this analysis. + 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 2:  Calculated Data for 2-Element Quads Modeled
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.                                 2.
+Wire Diameter:           0.0625"        Wire Diameter:           0.125"
+Reflector Circumference: 88.480"        Reflector Circumference: 89.672"
+Driver Circumference:    82.304"        Driver Circumference:    82.584"
+Refl-Driver Spacing:     13.140"        Refl-Driver Spacing:     13.324"
+Feedpoint Impedance:     141.1 Ohms        Feedpoint Impedance:     142.3 Ohms
+Free-Space Gain:         7.06 dBi       Free-Space Gain:         7.11 dBi
+< 2:1 swr bandwidth:     18.17 mhz      < 2:1 swr bandwidth:     20.78 mhz
+>20 dB F-B Bandwidth:    3.45 MHz       >20 dB F-B Bandwidth:    4.19 MHz
+
+3.                                 4.
+Wire Diameter:           0.25"          Wire Diameter:           0.5"
+Reflector Circumference: 91.304"        Reflector Circumference: 93.608"
+Driver Circumference:    83.064"        Driver Circumference:    83.936"
+Refl-Driver Spacing:     13.493"        Refl-DriverSpacing:      13.718"
+Feedpoint Impedance:     145.0 Ohms        Feedpoint Impedance:     150.4 Ohms
+Free-Space Gain:         7.14 dBi       Free-Space Gain:         7.17 dBi
+< 2:1 swr bandwidth:     24.63 mhz      < 2:1 swr bandwidth:     31.11 mhz
+>20 dB F-B Bandwidth:    5.29 MHz       >20 dB F-B Bandwidth:    6.87 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The dimensional growth of the array with increasing element diameter is clear in the table. The feedpoint impedances are resonant at the design frequency within +/-1 Ohm reactance. We can summarize a number of the other features of the table better in a selection of graphs that capture frequency sweeps of each design across the 2-meter band. For example, Fig. 2 records not only the free-space gain of the array at the design frequency at the design frequency, but as well the rate of change of gain across the band. As one might expect, the fatter the element, the lower the rate of gain change, thus ensuring more equal gain at both band edges. While commenting on element diameter, one should not that, contrary to experience with linear elements, closed loops tend to grow larger with increasing diameter elements and to have higher feedpoint impedances.

+
+ +
+

Fig. 3 extracts the 180-degree front-to-back data, which reflect also the > 20 dB bandwidth entry in the Table 2. Note that the front-to-back bandwidth--when held to this standard--does not exceed 4 MHz until the element diameter reaches 0.125", and with a mid-band design frequency, does not exceed 20 dB at the low end of the band until we use a 0.25" diameter element. We shall shortly explore why it is best to design quad arrays for a position about 1/3rd up from the bottom of the desired operating passband.

+
+ +
+

The SWR curves (relative to the resonant impedance of each array) for these 2-element optimized arrays, as shown in Fig. 4, present little concern to the builder. They are the reason so many builders classify the quad as a "low-Q" antenna, although the front-to-back curves--even for these fat-element arrays--show the inaccuracy of that claim.

+
+ +
+

The use of 180-degree front-to-back values was necessary to achieve maximum operating bandwidth for the antenna. However, these values should not be mistaken for the overall performance in the rear quadrants of a 2-element quad. Fig. 5 shows free-space azimuth patterns for the low end of the band for the thinnest and thickest elements used in this study. Note that in each case, the worst-case front-to-back ratio just approaches 18 dB--which tends to hold for all models used across the band. What does not appear as rearward gain in one direction tends to show up as gain in another direction within the rear quadrants. Thus, there is an overall limit to rear quadrant performance for any 2-element single-feed quad array.

+
+ +
+

While we are comparing the thinnest and thickest elements in our collection of models, let's look more closely at the wider-band performance of the array--especially at the front-to-back ratio and at the SWR curves. Fig. 6 presents the data for each parameter from 140 through 175 MHz, with each array having a design frequency of 146 MHz. Note that the front-to-back curves fall off much more rapidly below design frequency than above it, although the two curves parallel each other closely. With respect to SWR, we would correctly anticipate a steeper curve for the thinner element model. However, for both the 0.625" and 0.5" model, the curves are both more shallow above design frequency than below. The lesson of these curves is simple: for a given desired operational passband, design the quad array for a frequency about 1/3rd the way up from the lower end of that passband in order to achieve roughly equal values of SWR and front-to-back ratio at both ends of the passband. The loss of gain from using this procedure will be rather slight.

+
+ +
+

The actual resonant frequency of the driver is, for small changes in loop diameters, relatively independent of changes in front-to-back ratio--which is largely controlled by the spacing and loop diameter of the reflector. Hence, for special purposes, one may place the resonant frequency of the driver almost anywhere within a passband without moving the frequency of maximum front-to-back ratio significantly. In short, the 2-element quad array can be customized within reason to the builder's desires.

+

Although 2-element quads for 2-meters are "small potatoes" by most array standards, it is necessary to understand the properties of these basic arrays in order to better understand the properties of larger quads. Therefore, let's add a director and see what happens.

+

3-Element Quad Beam Design

The addition of a director to a quad array introduces a plethora of new variables into beam design. Not only must we account for the spacing between individual elements, we must also account for the relative spacing between driver-director and driver-reflector. Consequently, the number of design variables increases exponentially as we add elements to the array. Little wonder that many builders seek out a simple standard by which to build these antennas. +

In my own efforts to optimize 3-element quad arrays, I selected two criteria initially: gain and operating bandwidth. Initially, I gave precedence to operating bandwidth, using the >20 dB front-to-back standard. Later, I turned to gain as the paramount criterion, with reasonably-wide bandwidth as the secondary standard. The results proved interesting. For the wire sizes we have selected as most relevant to 2-meter arrays, the arrays ranged between 32" and 36" long. This value is nearly 30% longer than most 3-element 2-meter quads, but the results turn out to be very consistent in each category for operating properties. Table 3 lists the resultant arrays for both wide-band and for high-gain applications.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 3:  Calculated Data for 3-Element Quads Modeled
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.  Wire Diameter:                           0.0625"
+                              Wide-Band                High-Gain
+Reflector Circumference:      87.088"                  86.736"
+Driver Circumference:         82.320"                  83.040"
+Director Circumference:       75.92"                   79.336"
+Refl-Driver Spacing:          13.155"                  14.244"
+Driver-Dir Spacing:           22.759"                  18.033"
+Total Boom Length:            35.914"                  32.277"
+Feedpoint Impedance:          74.3 Ohms                54.5 Ohms
+Free-Space Gain:              8.87 dBi                 9.36 dBi
+<2:1 swr bandwidth:           5.72 mhz                 3.91 mhz
+>20 dB F-B Bandwidth:         2.77 MHz                 2.41 MHz
+
+2.  Wire Diameter:                           0.125"
+                              Wide-Band                High-Gain
+Reflector Circumference:      88.008"                  87.512"
+Driver Circumference:         82.632"                  83.352"
+Director Circumference:       75.824"                  79.296
+Refl-Driver Spacing:          13.323"                  14.193"
+Driver-Dir Spacing:           22.234"                  18.050"
+Total Boom Length:            35.557"                  32.243"
+Feedpoint Impedance:          72.4 Ohms                52.1 Ohms
+Free-Space Gain:              8.99 dBi                 9.48 dBi
+<2:1 swr bandwidth:           6.44 mhz                 4.31 mhz
+>20 dB F-B Bandwidth:         3.27 MHz                 2.77 MHz
+
+3.  Wire Diameter:                           0.25"
+                              Wide-Band                High-Gain
+Reflector Circumference:      89.256"                  88.552"
+Driver Circumference:         83.056"                  83.752"
+Director Circumference:       75.568"                  79.240"
+Refl-Driver Spacing:          13.521"                  14.150"
+Driver-Dir Spacing:           21.760"                  18.024"
+Total Boom Length:            35.281"                  32.174"
+Feedpoint Impedance:          71.7 Ohms                50.2 Ohms
+Free-Space Gain:              9.07 dBi                 9.57 dBi
+<2:1 swr bandwidth:           7.43 mhz                 4.84 mhz
+>20 dB F-B Bandwidth:         3.96 MHz                 3.28 MHz
+
+4.  Wire Diameter:                           0.5"
+                              Wide-Band                High-Gain
+Reflector Circumference:      90.960"                  90.032"
+Driver Circumference:         83.624"                  84.272"
+Director Circumference:       75.040"                  79.104"
+Refl-Driver Spacing:          13.693"                  14.133"
+Driver-Dir Spacing:           21.194"                  17.869"
+Total Boom Length:            34.887"                  32.002"
+Feedpoint Impedance:          71.5 Ohms                49.0 Ohms
+Free-Space Gain:              9.13 dBi                 9.63 dBi
+<2:1 swr bandwidth:           8.72 mhz                 5.63 mhz
+>20 dB F-B Bandwidth:         4.95 MHz                 4.03 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Let's begin with the wide-band arrays. Fig. 7 shows the frequency sweep of gain across the 2-meter band for each array in the left column of Table 3. For wide-band operation, the peak gain occurs below the lower limit of the operating passband. Hence, gain decreases across the band. However, the decrease is significantly lessened as we increase the element diameter, with the 0.5" element model showing just over a 0.05 dB change. When maximum operating bandwidth is the primary consideration, increasing the element diameter draws the point of maximum gain closer to being within the operating passband so that the gain curve is at its shallowest.

+
+ +
+

The 180-degree front-to-back curve in Fig. 8 reveals that the operative design technique--as used with the 2-element quad--was to place maximum front-to-back at or very near to the design frequency. However, the addition of the 3rd element limits the maximum value of front-to-back ratio as well as the bandwidth over which the value exceeds 20 dB. Although any of the curves might well be usable for many purposes, in terms of the design standards of this exercise, only the 0.5" element version of the antenna achieves 20 dB across the entire band.

+
+ +
+

As with the 2-element quads, the SWR bandwidth of the arrays is considerably wider than the front-to-back bandwidth, as shown in Fig. 9. The more rapid rise in SWR below the design frequency is evident for all versions of the array. However, all of the curves would be acceptable. In fact, referring to Table 3, any of these antennas would be matchable directly to a 75-Ohm main feedline.

+
+ +
+

Fig. 10 provides--among the models given in Table 3--a worst-case look at the patterns of the 0.0625" element diameter model for the entire 2-meter band. In practical terms, the gain would be accounted as reasonably stable, even if not as good as that of the 0.5" model. As well, the rear quadrants--although not up to the 20 dB standard at the band edges--remain quite well controlled and predictable. The nearly 9 dBi free-space gain is rarely achieved in common short-boom 4-element Yagis.

+
+ +
+

If we turn to the high-gain versions of the antenna, we should expect more gain and a narrower operating bandwidth. In fact, the design of these arrays turned out to be something of a surprise for the designer. As shown in Fig. 11, the peak gain appears within the operating passband, although it gradually shifts toward the high end of the band with the fattest- element version of the array. For the 0.5" diameter model, the gain is about a half dB higher than for the wide-band version, with excellent gain stability across the band.

+
+ +
+

In terms of front-to-back ratio, graphed in Fig. 12, the peak front-to-back ratio approaches that of the wide-band array and almost achieves the 20-dB standard with 0.5" diameter elements. Since peak gain was the primary criterion, the exact placement of the front-to-back peak was left a bit more variable, but it occurs in all cases between 145.5 and 146.0 MHz.

+
+ +
+

The limiting factor in the high-gain arrays is the SWR curve. shown in Fig. 13. The second surprise of the design exercise was that fact that these arrays all yielded impedance values close to 50 Ohms. The 0.0625" element model fails to achieve a 2:1 50-Ohm SWR curve for the entire 2-meter band. However, the larger-diameter models fit safely within the limits, although with higher band-edge SWR values than for the wide-band models.

+
+ +
+

Fig. 14 provides a set of free-space azimuth patterns across the band for the 0.0625" model--allowing a comparison with the wide-band version of the array shown in Fig. 10. Whether these patterns are suitable for particular applications is a user judgment.

+
+ +
+

The maximum design-frequency gain of the high-gain models is about 9.6 dBi (free-space), which approaches the gain of a standard 5-element Yagi (about 10 dBi). The wide-band version achieves about 9.1 dBi for the same 0.5" element diameter, with a proportionally wider operating bandwidth. The most interesting aspect of this seemingly small set of differentials is that they require very different dimensional profiles to maximize each set of design goals. Fig. 15 shows the side profiles of the two arrays, while Table 3 shows in detail the differences in actual dimensions.

+
+ +
+

Nonetheless, each type of array follows a natural progression similar to that of the 2-element arrays. It is possible to optimize a series of each type of array using wire sizes ranging from 3.16E-5 through 1E-2 wavelengths and then to subject the results to regression analysis. The regression equations can than be programmed into any setting for calculations of array dimensions and properties that hold good for 3 to 300 MHz. The same limitations regarding skin effect and array gain that applied to 2-element quads also apply to these arrays. Appendix 2 provides a GW Basic listing for the wide-band array design, while Appendix 3 supplies a similar listing for the high-gain version. Note that GW Basic recognizes only natural logs so that a multiplier must be added to convert the value to a common log--which is used by the regression analysis. If the program is translated to a spreadsheet that already knows the difference between common and natural logs, the multiplier can be omitted.

+

As with the 2-element arrays, the designs are resonated within +/-1 Ohm reactance at the design frequency. However, the driven element can be adjusted to place resonance within a MHz of the design frequency with minimal effect on the other antenna properties. Alterations to the director and reflector loop sizes have greater consequences for performance. Thus, to move the center point for the peak front-to-back ratio or SWR curve lower in the band, it is recommended that one choose a slightly lower design frequency.

+

Very-High-Gain 3-Element Quad Beams

I must confess at this point to having arrived at the limit of completely systematic work on 3-element quad designs. The remainder of these notes will address more suggestive conclusions that are insufficiently confirmed to be completely reliable. Nonetheless, they will indicate some directions of development for further design work. In many ways, this is the most interesting arena of quad design, since once quad dimensions are reduced to a set of usable equations for automated design, they become rather dull. +
+ +
+

The first interesting anomaly we might address is the possibility of a 3-element quad having even more gain than the standardized model--and on a short boom. The design is based on a high-gain Yagi which has a design frequency free-space gain of about 8.1 dBi, with about 24 dB front-to-back ratio and a resonant feedpoint impedance of about 25 Ohms. By optimizing the loop sizes of the comparable quad, I was able to achieve with 3/16" diameter elements and a 27" boom length nearly 9.9 dBi gain with over 32 dB of 180-degree front-to-back ratio. Fig. 16 shows the free-space azimuth patterns for the array over the 2-meter band. With a worst-case front-to-back value of better than 15 dB, this array looks promising.

+
+ +
+

Fig. 17 shows the gain curve and front-to-back curve across the 2- meter band for this array. The front-to-back rate of change is not unusual, but the rate of gain change across the band is very steep, ranging from 9.57 dBi at 144 MHz to 9.94 dBi at 147 MHz. However, for most of the band, the forward gain exceeds the best gain of the 0.5" high-gain model in the series just examined.

+
+ +
+

The limiting factor of this design appears in the SWR curve, shown in Fig. 18. The 2:1 SWR curve is under 2 MHz wide, less than half the band. Moreover, the resonant impedance is about 22.7 Ohms. Interestingly, the resistive component of the impedance changes by less than 0.5 Ohms across 2 meters. However, the reactance varies by nearly 67 Ohms from one end of the band to the other. The array is thus most useful for narrow band applications, since achieving a match over such a wide range of reactance would present a very significant challenge. Table 4 lists the properties of the array that we have been discussing.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Table 4:  Design Data for a High-Gain Short 3-Element Quad
+
+Element Diameter:             0.1875"
+Reflector Circumference:      86.688"
+Driver Circumference:         86.064"
+Director Circumference:       81.888"
+Refl-Driver Spacing:          12.388"
+Driver-Dir Spacing:           14.275"
+Total Boom Length:            26.663"
+Feedpoint Impedance:          22.7 Ohms
+Free-Space Gain:              9.89 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

One reason for working with this array--besides its narrow-band potentials for some applications--was to test the possibility of applying to quads certain Yagi techniques to broaden the operating bandwidth and to control the feedpoint impedance. Called "Optimized Wide-Band Antennas" (OWA) by their developer, Jim Breakall, WA3FET (with preceding work by Tom Schiller, N6BT, and even further back, incipient OWA properties in DL6WU long Yagis), the techniques have proven highly effective with Yagis of almost any size over 2 elements. The key is the addition of a new first director that, in conjunction with reflector spacing, sets the feedpoint impedance stably over a wide operating passband, while the remaining elements set the pattern characteristics of the array. I have designed a number of such arrays ranging from 4 to 7 elements, each of which has a flat 50-Ohm feedpoint impedance that is under 1.3:1 SWR across the wider ham bands in both HF and VHF versions. For each array, the essential operating characteristics of 3-6 element Yagis of the same boom length have been replicated, but with the desired feedpoint characteristics.

+

The question thus arose as to whether these techniques might be applied to quad designs using parameters initially derived from Yagis. The answer is a highly qualified affirmative, but with a very strong reservation--at least so far. Table 5 lists the 4-element OWA quad trial design dimensions and properties.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Table 5:  Design Data for an "OWA" 4-Element Quad
+
+Element Diameter:                  0.25"
+Reflector Circumference:           87.952"
+Driver Circumference:              84.136"
+Director 1 Circumference:          76.960"
+Director 2 Circumference:          76.640"
+Refl-Driver Spacing:               11.965"
+Driver-Dir 1 Spacing:              12.287"
+Dir 1-Dir 2 Spacing:                8.085"
+Total Boom Length:                 32.337"
+Feedpoint Impedance:               42.7 Ohms
+Free-Space Gain:                   9.60 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Fig. 19 shows the set of free-space azimuth patterns for the array across 2 meters. As is evident, the rear quadrants are well controlled, although the forward gain has not yet been restored to the peak value attained from the model before "OWA" treatment. Fig. 20 affirms this failure to achieve peak gain as well as showing that the rate of gain change across the band is consistent with the untreated model. The front- to-back curve is similar to the original.

+
+ +
+

The gain in performance appears in the SWR curve of Fig. 21, which shows the 50-Ohm SWR performance of the array. However, both the gain and the SWR curves are similar to those of 0.25" diameter 3-element high-gain model shown earlier--with the earlier model having a more stable gain across the band.

+
+ +
+

If the present attempt at applying OWA techniques to a 3-element Yagi-Spaced quad is indicative (and perhaps design evidence is not yet sufficient to assert this with confidence), attempting to apply OWA techniques runs into a conflict that is endemic to quads. The optimal coupling between quad elements requires greater spacing than for Yagis. Hence, the spacing of the new "OWA" element is forced a greater distance from the driver to obtain impedance control. In the end, the resultant spacing yields a quad that would obtain similar results in terms of both gain and feedpoint impedance without the OWA element. In essence, the director of the high-gain 3-element quad performs both pattern control and impedance control duties--as well as it can. Although too soon to be said with authority, it is likely the case that obtaining further wide-band performance from a quad simply requires the addition of properly spaced directors.

+

4-Element Quad Array Design

The foray into 4-element quad array design is fraught with further complications. The additional director multiplies the number of variables. However, we may be able to indicate some useful directions for design effort--and possibly some limitations that may be inherent in long quads. +

A useful place to begin would be with a sample or two of existing design. I have selected two widely disseminated design, although they appear in disguise. Models of each of them required that I frequency scale the design in order to produce any usable results. Hence, one is redesigned 1.5 MHz below its original design frequency, while the other is 2 MHz below its original design frequency. Table 6 summarizes the design and performance data for the two designs.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            Table 6:  Design Data for Two 4-Element Quad Arrays
+
+                              Version A:          Version B:
+Element Diameter:             #14 AWG             #18 AWG
+Reflector Circumference:      87.696"             85.264"
+Driver Circumference:         83.448"             83.136"
+Director 1 Circumference:     80.960"             80.712"
+Director 2 Circumference:     78.554"             78.272"
+Refl-Driver Spacing:          15.152"             16.320"
+Driver-Dir 1 Spacing:         12.460"             13.187"
+Dir 1-Dir 2 Spacing:          12.452"             11.192"
+Total Boom Length:            40.064"             40.699"
+Feedpoint Impedance:          42.4 Ohms           42.4 Ohms
+Free-Space Gain:              10.18 dBi           10.05 dBi
+
+                      Performance Data:  144-148 MHz
+
+Version A:
+Frequency Free-Space     Front-to-      Feed Impedance 50-Ohm SWR
+  MHz     Gain dBi       Ratio dB       R +/- jX Ohms
+ 144       9.68           7.99          31.6 - j 32.9       2.50
+ 145       9.99          10.25          34.9 - j 12.8       1.60
+ 146      10.18          12.81          39.0 + j  6.4       1.33
+ 147      10.27          15.61          43.5 + j 24.3       1.71
+ 148      10.30          18.43          47.7 + j 40.4       2.24
+
+Version B:
+Frequency Free-Space     Front-to-      Feed Impedance 50-Ohm SWR
+  MHz     Gain dBi       Ratio dB       R +/- jX Ohms
+ 144       9.55           7.89          35.6 - j 39.0       2.50
+ 145       9.86          10.04          38.6 - j 17.3       1.60
+ 146      10.05          12.42          42.4 + j  3.7       1.20
+ 147      10.14          14.85          46.7 + j 23.7       1.63
+ 148      10.17          16.86          50.8 + j 42.4       2.27
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The similarity of the final designs is a function of their design premises: to use thin wire and a short boom. There should be little wonder that the performance is similar for each array, since there is so little difference in the design, despite their independent sources.

+

The two designs have boom lengths about 6" longer than the average 3-element quad, and their design frequency gain level is only about 0.4 dB higher than the best of the high-gain series of 3-element quads. The point of maximum front-to-back ratio is well above the passband of the array (that is, above 148 MHz). Finally, the neither antenna manages to provide less than 2:1 SWR across 2-meters.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 7:  Design Data for a Wide-Band 4-Element Quad
+
+Unless otherwise specified, all antennas are designed for a center
+frequency of 146 MHz.  Also, all models use aluminum wire and hence will
+show slightly less gain than predicted by the GW BAsic program, which is
+calibrated for perfect (lossless) wire.  Models are calibrated for
+resonance in NEC-2.  NEC-4 will show a very slight (operationally
+insignificant) frequency shift for resonance.
+
+1.                                 2.
+Wire Diameter:           0.0625"        Wire Diameter:           0.125"
+Reflector Circumference: 86.658"        Reflector Circumference: 87.360"
+Driver Circumference:    82.448"        Driver Circumference:    82.728"
+Refl-Driver Spacing:     13.218"        Refl-Driver Spacing:     13.218"
+Dir 1 Circumference:     78.024"        Dir 1 Circumference:     77.952"
+Refl-Dir 1 Spacing:      38.885"        Refl-Dir 1 Spacing:      38.885"
+Dir 2 Circumference:     75.264"        Dir 2 Circumference:     75.192"
+Refl-Dir-2 Spacing:      68.338"        Refl-Dir-2 Spacing:      67.947"
+Feedpoint Impedance:     60.6 Ohms         Feedpoint Impedance:     58.5 Ohms
+Free-Space Gain:         10.23 dBi      Free-Space Gain:         10.40 dBi
+< 2:1 swr bandwidth:     4.11 mhz       < 2:1 swr bandwidth:     4.50 mhz
+>20 dB F-B Bandwidth:    2.53 MHz       >20 dB F-B Bandwidth:    2.90 MHz
+
+3.                                 4.
+Wire Diameter:           0.25"          Wire Diameter:           0.5"
+Reflector Circumference: 88.448"        Reflector Circumference: 89.976"
+Driver Circumference:    83.072"        Driver Circumference:    83.424"
+Refl-Driver Spacing:     13.218"        Refl-Driver Spacing:     13.218"
+Dir 1 Circumference:     77.782"        Dir 1 Circumference:     77.760"
+Refl-Dir 1 Spacing:      38.885"        Refl-Dir 1 Spacing:      38.885"
+Dir 2 Circumference:     74.992"        Dir 2 Circumference:     74.352"
+Refl-Dir-2 Spacing:      67.446"        Refl-Dir-2 Spacing:      66.953"
+Feedpoint Impedance:     57.3 Ohms         Feedpoint Impedance:     55.0 Ohms
+Free-Space Gain:         10.52 dBi      Free-Space Gain:         10.61 dBi
+< 2:1 swr bandwidth:     5.06 mhz       < 2:1 swr bandwidth:     5.59 mhz
+>20 dB F-B Bandwidth:    3.39 MHz       >20 dB F-B Bandwidth:    4.01 MHz
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

However, it is possible to design 4-element quads with better than 10 dB free-space gain across the entirety of 2-meters. Table 7 provides the specifications for 4 such quads with our standard range of element diameters. As shown in Fig. 22, even the thinnest element provides good gain across the band, although the 0.5" diameter version supplies an additional 0.4 or more dB gain.

+
+ +
+

These wide-band 4-element quads are only relatively wide--that is, for the class of 4-element quads. In Fig. 23, we can see that only the 0.5" version of this design provides better than 20 dB 180-degree front-to-back ratio for the entirety of 2 meters, although the thinnest element version provides better than 15 dB front-to-back ratio across the band. The SWR curves in Fig. 24 reveal that 3 of the 4 arrays meet the 2:1 SWR standard. Since (as shown in Table 7) the resonant impedances are all close to 50 Ohms, these curves will reflect performance with a standard 50-Ohm cable as well.

+
+ +
+

Very often gain and 180-degree front-to-back ratios come at the expense of general pattern shape. However, the designs we are presently discussing have well controlled patterns. The free-space azimuth patterns for the 0.5" diameter element version of the array appear in Fig. 25 to verify this claim. The forward lobe is especially consistent from one end of the band to the other, while the rear lobes remain quite well controlled.

+
+ +
+

The arrays that we have sampled emerged from a small GW Basic program, which is listed in Appendix 4. The optimized samples that provided the basis for the regression analysis are extensions of the 2- and 3-element wide-band quads that we earlier discussed.

+
+ +
+

The collection of quad designs with which we have been working reveals some interesting trends. Fig. 26 graphs the design-frequency gains of all four programmed quad designs for each of the sample 2-meter element diameters. Although the relative gain figures for 2-, 3-, and 4-element quads are interesting, the relative slope of the curves is the key attention-getter. Note that the more elements we add to the quad design, the more dependent the quad becomes on the element diameter. Making multi- element quads of thin wire at VHF and up is one way to lose a significant part of any design's potential.

+
+ +
+

Fig. 27 reveals another fact of life about quads: the greater the number of elements, the narrower the SWR bandwidth of the array. Above a certain number of elements (I do not yet know the exact number), the only way to achieve a wide SWR bandwidth may be to stagger parasitic elements. However, in every case of stagger-tuned elements, the gain falls below maximum. Hence, the multi-element quad may be self-limiting relative to competeing designs wherever operating bandwidth is a significant consideration.

+

If we permit a narrower operating bandwidth, then we can derive considerably more gain from a 4-element quad. For significantly higher gain from a 4-element quad, we must turn to a design with fat elements and wide spacing. Table 8 lists the structural parameters of one such design.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Table 8:  Design Data for a High-Gain 4-Element Quad
+
+Element Diameter:             0.5"
+Reflector Circumference:      89.120"
+Driver Circumference:         83.760"
+Director 1 Circumference:     77.760"
+Director 2 Circumference:     74.080"
+Refl-Driver Spacing:          13.200"
+Driver-Dir 1 Spacing:         25.937"
+Dir 1-Dir 2 Spacing:          30.715"
+Total Boom Length:            69.840"
+Feedpoint Impedance:          43.1 Ohms
+Free-Space Gain:              10.98 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Three items should be immediately apparent from Table 8. First, the design uses large-diameter elements: 1/2" in this case. Second, the boom is quite long--about 2" shy of 6'. Third, the design frequency gain is nearly a full dB higher than for the short-boom models with which we began our foray into 4-element quads. The question remaining is whether we have made sufficient improvements to justify the added mechanical requirements of a quad over a Yagi.

+

To partially answer this question, I shall present the design data for 3 OWA Yagis for 2 meters: a 6-element design using 3/16" elements, a 7-element design using 0.1" elements, and another 7-element design using 1/4" elements. Comparative physical and performance data may prove instructive--at least provisionally.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   Table 9:  Design Data for 3 OWA Yagis
+
+Antenna                  6 0.1875" El        7 0.1" El      7 0.25" El
+Reflector Length              40.520"        41.180"        41.200"
+Driver Length                 39.962"        39.634"        39.400"
+Director 1 Length             37.376"        37.338"        36.800"
+Director 2 Length             36.310"        36.660"        36.100"
+Director 3 Length             36.310"        36.730"        36.100"
+Director 4 Length             34.960"        36.542"        35.900"
+Director 5 Length              ----          34.856"        34.200"
+Refl-Driver Spacing:          10.130"         8.570"         8.942"
+Driver-Dir 1 Spacing:          4.192"         4.923"         4.658"
+Dir 1-Dir 2 Spacing:          10.974"        12.016"        12.030"
+Dir 2-Dir 3 Spacing:          11.356"        15.484"        15.253"
+Dir 3-Dir 4 Spacing:          16.936"        20.848"        20.538"
+Dir 4-Dir 5 Spacing:           ----          22.488"        22.079"
+Total Boom Length:            54.218"        84.329"        83.500"
+Feedpoint Impedance:          50.0 Ohms      45.7 Ohms      44.3 Ohms
+Free-Space Gain:              10.23 dBi      11.47 dBi      11.55 dBi
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
As shown in Table 9, the boom lengths of the Yagis bracket our improved 4-element quad array. The 70" quad boom lies roughly evenly between the 54" 6-element Yagi boom and the 84" 7-element Yagi booms. As well, the 4-element quad gain also lies between the Yagi numbers. However, before we make judgments using date from just the design frequency, let's survey the entirety of the 2-meter band for all 4 antenna designs. +
+ +
+

Fig. 28 shows the free-space gain figures for the 4 antennas--3 Yagis and a quad. Apparent is the greater stability of the Yagi gain, as the quad changes gain by over 0.4 dB across the band. By way of contrast, the Yagis show a maximum gain change of about 0.2 dB. How significant this factor is will be a user judgment.

+
+ +
+

The 180-degree front-to-back figures appear in Fig. 29. Although the 6-element OWA Yagi shows the highest peak front-to-back ratio, the band-edge values for all three Yagis are very similar and are above 20 dB. In contrast, the 4-element quad achieves a 20 dB front-to-back ratio for only about 3/4 of the passband. Once more, the relatively narrow-band operating characteristic of the quad emerges.

+
+ +
+

All of the antennas achieve 50-Ohm SWR values of under 2:1 across 2 meters, as shown in Fig. 30. All three OWAs have values of under 1.25:1 across the band, with the 7-element 0.25" element version achieving under 1.2:1 across 2 meters. All three Yagis can be tweaked for this performance. The quad comes nowhere near this performance, although it does stay within the <2:1 standard. Whether the OWA curves are significantly preferable to the quad curve may rest on a user judgment of the significance of line losses within the total antenna-feedline system.

+
+ +
+

It is interesting also to investigate pattern shape for various antennas that one might consider using. Fig. 31 compares the free-space azimuth patterns for the quad with those for the 0.25" element 7-element OWA Yagi. The Yagi displays better control of rear quadrant radiation across the band. However, the long Yagi also shows some "neck bulges," that is, emergent secondary lobes. Similar lobes are just appearing within the quad pattern, but are far less prominent. To an antenna designer who is not under the press of commercial deadlines, the existence of all such pattern bulges is a sign that further development work is in order. Such emergent lobes are not always eliminable, but the purist tries anyway. This last note is a way of saying that the work is still in progress and far from complete.

+

Some Very Tentative Conclusions

The conclusions to be drawn from this investigation may be obvious, but are perhaps worth noting anyway. +

1. For quad design at VHF, using large-diameter elements can be beneficial in achieving close to the full theoretical gain of a quad over a Yagi with a similar number of elements. Thin-wire elements narrow the operating bandwidth and reduce gain by significant amounts.

+

2. Traditional short-boom monoband quad designs fail to realize full quad gain and bandwidth by overlooking the naturally higher mutual coupling of quad elements--a factor that dictates longer boom lengths for optimal performance (relative to arrays with linear elements).

+

3. Quads up through 3 elements are certainly capable of performance that is superior to that of Yagis with the same number of elements and relevantly similar boom lengths. However, above 3 elements, the need for added boom length to achieve optimum inter-element coupling may set a limit on the utility of quads wherever operating bandwidth is an equal concern with gain.

+

4. Quads--even short-boom quads--may still excel for narrow-band applications. However, achieving full performance from a narrow-band quad requires the use of sizable element diameters. Otherwise, the simplicity of VHF Yagi construction may prevail, especially with the availability and simplicity of OWA designs.

+

5. When it comes down to simple and cheap utility antennas with some gain and directivity, the Yagi-quad decision becomes more a matter of what materials are available and less upon the purist considerations that have gone into these notes. Coat hangers, scrap wire, wood, and PVC have yielded generations of utility antennas of either the Yagi or the quad type.

+

6. The work is far from done.

+ 
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 1:
+    A GW Basic Program to Calculate Dimensions of a 2-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 2-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00336#:BD=.04966518519#:CD=.2731955556#:DD=.6716364021#:ED=1.644147937#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.003173333333#:BR=.0508237037#:CR=.3081977778#:DR=.8663851852#:ER=2.040064444#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AS=-.003#:BS=-.03551851852#:CS=-.1553055556#:DS=-.2902116402#:ES=-.02540079365#
+240 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+250 AZ=1.976333333#:BZ=30.84751852#:CZ=172.4909722#:DZ=419.5162831#:EZ=519.8747579#
+260 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+270 AG=-.06333333333#:BG=-.7203703704#:CG=-3.010277778#:DG=-5.381375661#:EG=3.738769841#
+280 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+290 AW=1.688666667#:BW=23.76837037#:CW=124.9339444#:DW=295.8872328#:EW=281.2755159#
+300 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+310 AF=-.00266666667#:BF=.388#:CF=4.790666667#:DF=19.55485714#:EF=28.76628571#
+320 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+330 AN=-.08333333333#:BN=-.9462962963#:CN=-3.943055556#:DN=-7.582671958#:EN=-5.23234127#
+340 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+350 WL=299.7925/F:PRINT "Wavelength in Meters =";WL
+360 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+370 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+380 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+390 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+400 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+410 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+420 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+430 PRINT "Approximate Resonant Feedpoint Impedance =";ZR;"Ohms"
+440 PRINT "Approximate Free-Space Gain =";GN;"dBi"
+450 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+460 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+470 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+480 INPUT "Another Value = 1, Stop = 2: ";P
+490 IF P=1 THEN 10 ELSE 500
+500 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 2:
+A GW Basic Program to Calculate Dimensions of a Wide-Band 3-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00064:BD=.01044148148#:CD=.06484444444#:DD=.1886626455#:ED=1.232080635#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0009333333333#:BR=.01915555556#:CR=.13983333333#:DR=.4587492063#:ER=1.64042381#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.0012#:BI=-.0209037037#:CI=-.13021111111#:DI=-.3498137566#:EI=.5941126984#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=-.0033#:BS=-.03927777778#:CS=-.1724583333#:DS=-.3239603175#:ES=-.04951547619#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.004866666667#:BP=-.06262962963#:CP=-.29347222222#:DP=-.6174457672#:EP=-.2289269841#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=-2.227066667#:BZ=-26.75247407#:CZ=-115.9142556#:DZ=-217.8183323#:EZ=-79.59203175#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.07#:BG=-.7877777778#:CG=-3.350833333#:DG=-6.143888889#:EG=5.104166667#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=-.05847333333#:BW=-.5028392593#:CW=-.4586494444#:DW=6.080227037#:EW=17.61091389#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11695666667#:BF=1.717985556#:CF=9.6510925#:DF=25.23848992#:EF=27.78167988#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 AN=-.04666666667#:BN=-.5414814815#:CN=-2.302777778#:DN=-4.364074074#:EN=-3.092777778#
+380 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+390 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+400 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+410 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+420 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+430 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+440 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+450 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+460 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+470 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+480 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+490 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+500 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+510 PRINT "Free-Space Gain =";GN;"dBi"
+520 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+530 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+540 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+550 INPUT "Another Value = 1, Stop = 2: ";P
+560 IF P=1 THEN 10 ELSE 570
+570 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 3:
+A GW Basic Program to Calculate Dimensions of a High-Gain 3-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "Alternate Design",,,"L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.000266666667#:BD=.00506666667#:CD=.03633333333#:DD=.1221904762#:ED=1.183285714#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0037333333333#:BR=.05362962963#:CR=.29275555556#:DR=.7424529101#:ER=1.814412698#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.00266666667#:BI=-.033244444444#:CI=-.1550666667#:DI=-.3222793651#:EI=.7283809524#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=.00033333333#:BS=.004837037037#:CS=.02552777778#:DS=.05643756614#:ES=.2191230159#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.002333333333#:BP=-.03128148148#:CP=-.15586111111#:DP=-.3417669312#:EP=-.05499206349#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=4.4029#:BZ=53.43954444#:CZ=239.2408583#:DZ=462.3614437#:EZ=373.3035655#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.15#:BG=-1.768518519#:CG=-7.763055556#:DG=-14.78592593#:EG=-.609722222#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=.16666666667#:BW=2.265925926#:CW=11.706111111#:DW=27.93058201#:EW=28.88753968#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11933333333#:BF=1.671777778#:CF=8.9885#:DF=22.45931746#:EF=23.68797619#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+380 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+390 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+400 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+410 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+420 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+430 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+440 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+450 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+460 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+470 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+480 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+490 PRINT "Free-Space Gain =";GN;"dBi"
+500 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+510 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+520 INPUT "Another Value = 1, Stop = 2: ";P
+530 IF P=1 THEN 10 ELSE 540
+540 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                                Appendix 4:
+A GW Basic Program to Calculate Dimensions of a Wide-Band 4-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 4-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=-.00018:BD=-.002359259259#:CD=-.01090277778#:DD=-.01971296296#:ED=.1174938889#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED:DE=DE*8
+210 AR=.0002666666667#:BR=.004237037037#:CR=.02554444444#:DR=.07158756614#:ER=.2119230159#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER:RE=RE*8
+230 AI=-.0002#:BI=-.002525925926#:CI=-.01182777778#:DI=-.02473915344#:EI=.1008246032#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI:IR=IR*8
+250 AT=-.0006#:BT=-.009059259259#:CT=-.04912777778#:DT=-.1152343915#:ET=.01678174603#
+260 TT=(AT*(D1^4))+(BT*(D1^3))+(CT*(D1^2))+(DT*D1)+ET:TT=TT*8
+270 SP=.1635:IP=.481
+280 ATT=.0026666666667#:BTT=.036888888889#:CTT=.177#:DTT=.3386587302#:ETT=1.046738095#
+290 TTP=(ATT*(D1^4))+(BTT*(D1^3))+(CTT*(D1^2))+(DTT*D1)+ETT
+300 AZ=1.2#:BZ=13.92592593#:CZ=60.777777778#:DZ=113.9177249#:EZ=132.618254#
+310 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+320 AG=-.1#:BG=-1.184444444#:CG=-5.228333333#:DG=-9.831507937#:EG=4.045238095#
+330 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+340 AW=-.06663333333:BW=-.6539148148:CW=-1.677836111:DW=1.361137831:EW=9.502790079
+350 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+360 AF=-.03#:BF=-.27666667#:CF=-.4475#:DF=2.348809524#:EF=7.853214286#
+370 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+380 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+390 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+400 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+410 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+420 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+430 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+440 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+450 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+460 PRINT "Director 1 Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+470 PRINT "Director 1 Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+480 PRINT "Director 1-Reflector Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+490 PRINT "Director 2 Side =";(TT/4);" WL or";(TT/4)*WF;"Feet or";(TT/4)*WL;"Meters"
+500 PRINT "Director 2 Circumference =";TT;" WL or";TT*WF;"Feet or";TT*WL;"Meters"
+510 PRINT "Director 2-Reflector Space =";TTP;" WL or";TTP*WF;"Feet or";TTP*WL;"Meters"
+520 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+530 PRINT "Free-Space Gain =";GN;"dBi"
+540 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+550 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+560 INPUT "Another Value = 1, Stop = 2: ";P
+570 IF P=1 THEN 10 ELSE 580
+580 END
+
+Note:  "LOG" in GW Basic always mean the natural logarithm.  Hence, a conversion factor is necessary
+to convert the natural log to the common log required by the program.  If the medium to which this
+program may be transferred already knows the difference between "LOG" and "LN," the conversion factor
+can be dropped.
+. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Updated 04-21-2001. © L. B. Cebik, W4RNL. This article first appeared in Proceedings of the 2001 Southeastern VHF Society Conference (ARRL, 2001), pp. 116-156. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Quad List

+

Go to Main Index

+

Topics: Quad, VHF / UHF


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+

A 3-Band, 2-Element Spider-Supported Quad Beam

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

One of the most difficult tasks in designing a multi-band 2-element quad beam is obtaining full band coverage. This problem has two dimensions. One dimension involves obtaining at the antenna an SWR that is less than 2:1 relative to the impedance of the main feedline all across each of the bands covered by the beam. The second dimension covers other important operating parameters, such as adequate gain and front-to-back ratio across each band.

+

The design that we shall show covers only the widest amateur upper-HF bands: 20, 15, and 10 meters. For the narrower bands, 17 and 12 meters, one may use a dual-band quad with a common feedpoint, as shown in Part 3 of the recent series of articles analyzing the element interactions and the use of a common feedpoint. The present beam uses separate feedpoints and restricts coverage to only 3 bands in order to obtain between adjacent bands the largest feasible frequency ratios. The result is relevantly similar band-to-band performance and a set of manageable feedpoint resistance and reactance values. By judicious use of a 75-Ohm matching line on each band, the 50-Ohm SWR values will be under 2:1 across all passbands.

+

The design specifically excludes the narrow bands, even though we might have thrown in loops for them. In the latter portion of our discussion, we shall examine a pair of 5-band designs previously analyzed in Volume 1 of Cubical Quad Notes. The exercise will clearly indicate why a 3-band limit within the upper HF range is desirable for a 2-element quad.

+

The Physical Design

+

The tri-band quad sketched in Fig. 1 derives from the same set of monoband 2-element quads that we have used as the basis for dual-band quad behavior. In fact, it is simply a refined version of the sample tri-band, 2-element quad shown in Part 2 of "Sneaking Up on 2-Element Common-Feed Quads." The design frequencies for the 3 bands are 14.14, 21.19, and 28.4 MHz. At these frequencies, the monoband quads are set for resonance (within +/-j 1 Ohm) and for peak 180-degree front-to-back ratio. At the design frequency, the free-space forward gain is 7.04 dBi on all frequencies. The designs derive from calculations based on a large collection of models and regression analysis. The programs appear in Volume 2 of Cubical Quad Notes and require the designer only to input the element diameter and the design frequency. The model outline sketch on the left shows the positions of the 3 separated feedpoints, but not the match-line needed to feed the array with a 50-Ohm main cable. Of course, only one feedpoint would be active at any one time, so the array requires a remote switch on the mast or 3 separate feedlines to the shack.

+
+ +
+

In adapting these monoband designs for a tri-band quad, I am using spider construction. It requires non-conductive support arms that "lean" forward and backward about 31 degrees relative to a vertical line created by the mast is it reaches the hub (and virtually passes through to continue that line). This angle is the average of the angles for each of the 3 bands. Since AWG #14 copper wire has a different diameter on each band if we measure it in wavelengths, the angle varies slightly from band to band. However, the small discrepancy in driver-to-reflector spacing will make no practical difference in the performance. The loop lengths are much more sensitive to changes. If a builder wishes to use the specified spacing between elements, he or she may attach a fiberglass or similar rod between the forward and rearward support arms near to the elements for each band.

+

Table 1 provides the required dimensions for the tri-band 2-element quad. All dimensions are in inches. The side lengths are for full sides. Modelers may need to divide those numbers by 2 in order to center a NEC or MININEC model at the center of the coordinate system. Later, all performance numbers will use free-space values. The gain of the array over ground will increase by about 5 or more dB (depending upon the actual height), but the front-to-back ratio will remain unchanged. If the array is at least 1 wavelength above ground, the impedance will be virtually unchanged from the free-space value. Even at lower heights, the quad is less prone to ground-induced impedance changes than a beam using linear elements. The quad loop is actually two dipoles spaced about 1/4 wavelength vertically, with the ends brought together at the zero-current points. When measured as a function of the elevation angle of the main lobe and the same angle for a dipole or 2-element Yagi, the working height of a quad is about 2/3 of the distance from the bottom to the top horizontal wires. For non-critical purposes, the centerline or the hub height will do as the conventional marker of antenna height.

+
+ +
+

The dimensional table lists the sizes of the foundational monoband quads as well as the dimensions used in the tri-band version. For each band, the driver-to-reflector spacing remains unchanged. On 20 meters, the tri-band driver is longer than the monoband driver, but the tri-band reflector is shorter. On 10 meters--the innermost set of loops--the tri-band driver is shorter than the monoband driver, but the tri-band reflector is longer. In the recent study of dual-band interactions ("Adjacent-Band Quad Behavior"), I noted that when an element set undergoes interactions with both an inner and an outer set of elements, the middle set is not influenced equally. Hence, the effects on both the middle driver and reflector are not simply canceled out. In the case of the present tri-band design, the 15-meter driver and reflector are both shorter than in the monoband design on which they rest.

+

Each driver requires a match-line consisting of a length of 75-Ohm cable. The 20-meter quad uses a relatively precise 1/4 wavelength. On 15 meters, 1/4 wavelength is about 139", while on 10 meters, 1/4 wavelength or close to 104". The prescribed lengths for 15 and 20 are both shorter. When we examine the modeled performance data for the quad, we shall better understand why the lines use less than a full quarter wavelength of impedance transformation. Since the quad uses square rather than diamond construction, the match-lines (or even directly connected main feed lines) require support. I recommend the use of a UV-protected rope running from the hub through each feedpoint. You may then tape or otherwise clamp the match-lines to the rope, since coaxial cable is not designed to support loads--not even its own weight for very far. Of course, there is no rule that requires a coaxial match-line. Parallel 75-Ohm transmission line--if available or if you can fabricate it--will work as well. However, at the remote switch or the transition to a 50-Ohm coaxial feed line, you will need a 1:1 balun or ferrite-bead choke to suppress (or, more correctly, attenuate) common-mode currents. Such a device is good practice at the remote switch even if you use coaxial cables for the match-lines.

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The dimensions for the tri-band quad are more finicky than those for a monoband quad (but less finicky than the dimensions for a 5-band quad). Therefore, you will wish to use careful construction methods to avoid the need for nearly endless field adjustments. The support arms should be non-conductive. As well, the method for attaching the elements to the arms at the element corners should make use of non-conductive materials or hardware. Metal clamps or loops can create 1-turn inductors at the element corners. The 4 required for each element may be enough to significantly detune the element. There are methods of compensating for such methods of fastening, but they tend to be long and tedious. If you are constructing quads commercially, going through the compensation process once for each new design may well be worth the effort to obtain a desired set of corner fixtures. However, for a one-of-a-kind antenna that grows out of one's workshop, giving some extensive forethought to designing an effective means of arm-to-element attachment that involves only non-conductive materials may actually shorten the construction time considerably.

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TriBand Performance

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The goal of the design was to obtain--to the degree possible--all of the performance potential offered by the monoband quads that form the basis for each element set. Studies in element interaction suggest that we may not be able to succeed completely. However, we may be able to develop a very good tri-band quad. As a yardstick, a short-boom Yagi will show about 7+ dBi free-space gain. Here, a short boom is about 8' on 10 meters and 16' on 20 meters. (A long-boom 3-element Yagi might develop just over 8-dBi free-space gain, where a long-boom on 20 is about 24' and on 10 is about 12'.) A 2-element driver-reflector Yagi may be able to manage about 6 dBi free-space gain. The 2-element Yagi front-to-back ratio will run between 10 and 12 dB across any of the wider amateur upper HF bands. However, a well-designed short-boom 3-element Yagi may achieve 20 dB across 20 and 15 meters and at least 17-18 dB across 10 meters. Although it is possible to design a 2-element driver-reflector Yagi for direct connection with a 50-Ohm cable, most higher-performance Yagis below 6 elements require a matching network to raise a lower feedpoint impedance to the usual 50-Ohm cable impedance. In general, a 2-element quad can match the gain of a short-boom (but not a long-boom) 3-element Yagi, but the quad suffers fairly narrow bandwidth for its front-to-back performance. Under the best conditions, a monoband quad will show band-edge front-to-back ratio values somewhere between 12 and 18 dB, depending on the passband width. For this reason, I have used an initial monoband quad design with the broadest possible bandwidth for both the front-to-back and impedance performance.

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Element interactions in a multi-band beam will limit our ability to achieve full monoband performance. However, Gain is not one of those limitations. As shown by the graph in Fig. 2, the gain curves are normal or above normal for 2-element monoband quads. The design frequency is at the 40% marker on the steps up each of the bands. At that point, the monoband gain is about 7.04 dBi, and even the 20 meters elements achieve this level. The more inward loop sets manage slightly higher gain levels. However, the difference in not sufficient to be operationally noticeable. We may note in passing that the closer a set of elements is to the outer position, the steeper is the slope of gain decrease with rising frequency.

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Like all 2-element driver-reflector parasitic structures, the gain decreases as the frequency increases. The rate of descent of even the steepest curve is not far from the monoband curve. (Any parasitic array with at least one well-designed director will show a reverse curve, that is, one that increases in gain with rising frequency. For example a typical short-boom Yagi would show a curve that is virtually the reverse of the quad gain curves, but with very similar band-edge gain values.)

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One reason for tweaking the dimensions of the tri-band beam elements was to place the front-to-back peak as close as feasible to the design frequency on each band. The curves in Fig. 3 measure the success of that move. I wanted to find out if centering the front-to-back peak at the design frequency would yield relatively equal band-edge values, as the process did for the monoband quads. The band-edge front-to-back values are only slightly less equal than for the monoband beams on which this design rests.

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For comparative purposes, the monoband 20 meter quad achieves about 16-dB front-to-back values at the band edges. The tri-band 20 meter elements fall from 1 to 2 dB below that value. The 15-meter monoband quad shows about 18-dB at the band limits. The 15-meter elements of the tri-bander are again about 1-2 dB lower. On 10 meters, the monoband quad reached a very high peak level, with about a 14-dB front-to-back ratio at 28 and 29 MHz. The inward position of the 10-meter elements in the triband quad prevents us from achieving the very high peak front-to-back value, but the band-edge values are 2 to 3 dB higher than for the monoband model.

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We must add two notes to these reports of modeled performance. First, the actual peak front-to-back ratio--as a 180-degree value--will not be as operationally significant as it is dramatic in the graphs. Not only is the peak a narrow-bandwidth phenomenon, it is also a dimple in the overall rearward gain levels of the array. Second, the values appear in the graphs due to simple changes in the modeled array geometry. It is also unlikely that one will be able to precisely place the peak value with respect to frequency. (The best way to tell is to perform tests with a nearby patient friend, with the quad pointed directly away from that station.) The final construction-ending test is the adequacy of the front-to-rear overall performance, especially at the band edges.

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The band-edge patterns are quite unlike those at the design frequency or at the nearby band center. To show the range of likely patterns, Fig. 4 presents a gallery of free-space E-plane (azimuth) patterns for each of the bands, using the band limits and the band center as snapshot frequencies.

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The patterns show both good and not quite so good things about 2-element quad performance in a tri-band array. The very good aspect of the gallery views is the fact that the patterns for each band are very similar for corresponding positions in each band. The design constraints brought to the project have resulted in a quad that performs in a very similar manner on each of the included bands. Less than very good is a fundamental limitation in the rearward lobes of a quad when used on a wider amateur band. Note that the lines that indicate the strongest rearward gain have similar values at the lower band edge and at mid-band: very roughly 15 dB below the main forward lobe. However, at the upper band edge, the worst-case front-to-back ratio is down to about 12 dB or so, even though the 180-degree value is somewhat higher. We would find the same pattern of rearward lobes, even using monoband quads.

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The next step in our review of tri-band quad performance takes us into the region of the feedpoint impedance. The monoband quads showed design-frequency resonant impedance values between 130 Ohms at 20 meters to 136 Ohms at 10 meters. Those values allow us to use a standard 1/4 wavelength 75-Ohm match-line on any of the monoband quads to obtain a good match to a 50-Ohm main feed cable and still have an acceptable SWR across each of the bands.

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Fig. 5 shows what happens to the feedpoint impedances in terms of resistance and reactance before we add any matching devices or networks. Again, the 40% marker represents the approximate design frequency for each band. At this point, we can see the crossing reactance lines at about j0 Ohms. As we learned in the study of adjacent-band quad behavior, it does not matter whether a multi-band loop set occupies an outer or an inner position. The feedpoint resistance will decrease. The 20-meter value is about 123 Ohms. Perhaps the new information offered by the tri-band quad is that as we add set of loops, the resistance decreases further as we move toward the innermost set. On 15 meters, the resonant impedance is only about 106 Ohms, and on 10 meters, it has decreased to 94 Ohms. We shall look at these values once more in the last part of these notes when we compare tri-band performance to 5-band performance.

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The reactance curves are rather modest for 20 and 15 meters, partly as a function of having other element sets inward from them and partly because the bands are between 2.1% and 2.5% wide. In contrast, the 10-meter reactance curve undergoes the greatest excursion and virtually in a linear progression. The size of the excursion of reactance is a joint function of the added bandwidth (3.5% wide) and the fact that the 10-meter elements are the most inward of the bands included in this array.

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Fig. 6 shows the resistance and reactance at the shack-end of the match-line prescribed for each band. On 20-meters, we can employ a 1/4 wavelength 75-Ohm line, which is about 209" at the design frequency. A corresponding 15-meter line would be about 139" long. However, a transmission line effects an impedance transformation at any length. By judicious line length selection, we can often achieve a more desirable set of resistance and reactance values across a given band. Note that the use of a 130" line on 15 yields band-edge resistance values that are very similar to those we obtain on 20 meters with the full 1/4 wavelength line. At the same time, the reactance curve for 15 meters is actually flatter than the one for 20 meters.

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Important Note: The line lengths noted here are electrical lengths translated into inches. Multiply the listed electrical length by the velocity factor of the line actually used to arrive at the necessary physical line length. For most purposes, you may use 0.66 as the velocity factor for 75-Ohm lines with a solid dielectric and 0.8 for lines with a foam dielectric. However, for best precision, it may be useful to measure the velocity factor of the line used.

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On 10 meters, we have less than an ideal situation. A quarter wavelength line does not yield an acceptable range of impedances, largely due to the wider range of reactance values that we encounter on this band. However, an electrical length of 95" will yield acceptable SWR values. As shown in Fig. 6, the resistance range is very similar to the range resulting from the 20- and 15-meter match-lines. However, the reactance curve is considerably wider than those for 15 and 20.

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For most operators, the final measurement is simply the 50-Ohm SWR at the junction of the matchline and the main feed cable. (I am avoiding all temptation to show values that might result from taking measurements 50, 75, 100 or more feet down an actual cable with its loss factors included. These shack-end SWR values will always be lower than the values at the point where the 50-Ohm cable is closest to the antenna.) Fig. 7 shows the modeled SWR curves. The match-lines use the NEC-provided lossless cable for the match-line. However, since each match-line is 1/4 wavelength or less, the lossless values are a very good approximation of reality.

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The 50-Ohm SWR curves 20 and 15 meters are very satisfactory, with the peak value just over 1.4:1. The 15-meter curve shows a lowest value that is higher than the lowest 20-meter value because the 15-meter match-line is a bit shorter than 1/4 wavelength. Had we used a perfect 1/4 wavelength line, the curve would have still been acceptable, but one end of the band would have shown a much higher value than the other.

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On 10 meters, we departed the farthest from 1/4 wavelength, and the resulting SWR curve has a low value of about 1.2:1, At the band edges, the SWR is 1.8:1 or slightly higher. The result is an acceptable, but certainly not an outstanding 50-Ohm SWR curve. However, in the world of multi-band 2-element quads, covering the entire first MHz of 10 meters with under 2:1 50-Ohm SWR is itself a bit rare, especially if we wish to achieve any performance across this wide band.

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The tri-band spider quad based on wide-band monoband quad designs achieves its goals of providing close to monoband performance across all three included bands. Gain is standard. The front-to-back curves are what we might expect from a 2-element quad, and the band-edge values hold up better than in most designs. The use of match-lines for the separate feedpoints on each band allows us to obtain very good 50-Ohm SWR curves on 20 and 15, with an acceptable curve on 10 meters.

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We have a left over question that is more than trivial. Why not include all 5 upper HF amateur bands in the array? There is a very straightforward answer, but it may not be completely believable without a demonstration. Therefore, let's spend a little time exploring the performance of some typical 5-band spider quads.

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3 Bands or 5 Bands

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In Volume 1 of Cubical Quad Notes, I reviewed the performance of two different but related 5-band 2-element quad beams. Both used spider construction and thus had the general layout shown in Fig. 8. The figure shows the positions of all of the feedpoints, but only 1 would be active at a time. The difference between the two beams rested on the spacing between elements. The narrow version used an element spacing of 0.125 wavelength. The wide version used a spacing of 0.174 wavelength or 6' at 10 meters.

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Both quad beams differed from the present design not only in spacing, but as well in the design frequency used for the wider amateur bands. The design frequency for all bands was the mid-band frequency: 14.175, 18.118, 21.225, 24.94, and 28.5 MHz. If I were interested in redesigning these arrays using the prescribed spacing today, I likely would lower the design frequency on each wider band to ensure equalized front-to-back ratios at the band edges.

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However, our use of these older designs is not to produce a buildable design. The narrow version is attractive in some building circles because it results in a more compact array with arm supports that require less of an angle relative to a vertical line drawn from the mast upward. The required angle is about 25.5 degrees or about 51 degrees between the driver and reflector support arms. The wide version is actually slightly wider than the 3-band quad that we have reviewed in these notes. Relative to a vertical line, the arm angle is a bit over 33 degrees, or 66 degrees total between driver and reflector support arms. Indeed, the wide version will be useful in showing differences between 3- and 5-band quads without having to replicate the newer design in a 5-band version.

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Table 2 provides the dimensions for the 2 older 5-band designs. The chart shows both the side length and the circumference of the loops--as well as element spacing--so that you may directly compare the numbers to the corresponding dimensions for the 3-band quad in Table 1. Let's examine the basic free-space performance of these arrays as background for the critical conclusions that we shall draw from them.

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A 5-Band 2-Element Quad Using 0.125-Wavelength Element Spacing

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The use of narrow spacing allows the quad array to achieve slightly higher gain levels than the 3-band version. The differentials average about 0.15 dB, which may not be operationally significant. The gain curves for the 3-wide bands of the array appear in Fig. 9. I have omitted the narrow bands from the performance review. More complete data appear in the original discussion.

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Although the front-to-back peaks do not occur precisely at mid-band, as shown in Fig. 10, we can glean something about band-edge performance from the curves. Across the upper HF range, the band-edge front-to-back performance averages from 10 dB at 20 meters to about 15 dB at 10 meters. The corresponding values for the tri-band design at 14 and 17 dB, respectively. The difference is a joint function of the narrower element spacing and the proximity of the loop sets in a 5-band quad beam.

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One temptation that accompanies a 5-band quad design is to use direct feeding. The impedances suggest that a 75-Ohm feedlines might be satisfactory for the array. Fig. 10 shows the 75-Ohm SWR curves of the array for each of the wider bands.

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The results are not satisfactory from the perspective of full band coverage. On 20 meters, we manage to cover about 90% of the band, and with some juggling of the 20-meter driver, we likely would obtain full band coverage. The SWR curve for 15 meters with resonance at mid-band yields only about 75% coverage. However, the low SWR at the upper end of the band suggests that judicious redesign of the 15-meter driver might extend that coverage. However, 10 meters provides only about 30% band coverage. We shall see the reasons for this difficulty after examining the wide 5-band quad array.

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A 5-Band 2-Element Quad Using 0.174-Wavelength Element Spacing

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Wider element spacing provides some improvement in the performance values. The wide 5-band array emerged before the development of idealized 2-element monoband models and hence uses a spacing just wider than optimum. However, as the curves in Fig. 12 reveal, the gain values do not differ greatly from those of the tri-band model. The 5-band 20-meter curve is steeper than in the tri-band case, while the 5-band 10-meter gain curves is somewhat flatter. Both results stem from the closer proximity of loop sets in the 5-band model.

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As shown by Fig. 13, the front-to-back performance again fails to place peaks precisely at the mid-band design frequencies. However, band-edge performance is fairly balanced. The 10-meter band-edge values average 19 dB--higher than for the tri-band version. However, the 20-meter band-edge values remain low, averaging about 11 dB. Thus, at the band edges, the band-to-band range of 180-degree front-to-back ratios is about 8 dB, compared to about 3 dB for the tri-band model. The results suggest (but do not definitively prove) that it may be more difficult to obtain even band-to-band 2-element quad performance when covering 5 bands with a lower frequency ratio between adjacent loop sets.

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Direct 75-Ohm feeding of the wide 5-band quad is tempting. In fact, Fig. 14 shows that we obtain quite satisfactory 75-Ohm SWR curves on both 20 and 15 meters. 10 meters remains the most difficult case, with only about 75% band coverage with less than a 2:1 75-Ohm SWR ratio.

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The wider 5-band quad achieves satisfactory gain values. Within general limitations of 2-element quad design, we might also rate the front-to-back performance as adequate at the band edges. However, the feedpoint impedances remain problematical. To see why, let's compare in a simple table (Table 3) the minimum and maximum resistance values for all three 2-element quad designs. For good measure, we shall also show the range of reactance values that accompany the resistance values across each of the wide upper HF amateur bands.

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The first step is to compare the narrow and the wide 5-band quads. Since the frequency ratio between adjacent loops is the same for both beams, any differences are functions of the element spacing. The average differential in the feedpoint resistance between these two beams is 15 to 20 Ohms, with the higher average on 10 meters. Accompanying the lower feedpoint resistances for the narrow beam is a higher range of reactance values across each of the bands. Narrow element spacing therefore has an obvious negative impact on the ability of the array to cover all of each band. The 5-band arrays also show a systematic lowering of the feedpoint resistance as we increase the frequency band. The inner loops show a systematic lowering of the feedpoint resistance relative to more outward loops. Hence, when we combine this effect with the larger reactance excursion for the inner loops, we obtain large difficulties in covering 10 meters with narrow spacing.

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The table allows us to make a second comparison, this time between the wide 5-band quad array and the tri-band design that we featured earlier. Note the descending values of feedpoint resistance for the 3-band model: about 90, 80, and 70 Ohms for 20, 15, and 10 meters, respectively. Every multi-band quad shows a reduction in the feedpoint resistance regardless of loop position in the presence of loops for other bands. The lower the frequency ratio between loops, the greater the reduction in feedpoint resistance. The tri-band quad uses frequency ratios between 1.34:1 and 1.5:1.

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In contrast, the 5-band wide quad uses frequency ratios between bands that average about 1.2:1. As a result, even the 20-meter minimum feedpoint resistance is lower than for the tri-band beam: about 80 Ohms compared to the tri-band value of 90 Ohms. The impedance value declines more rapidly as we move up in the HF region. On 10 meters, the differential between tri-band and 5-band minimum feedpoint resistance values is double that of 20 meters: about 70 Ohms vs. abut 50 Ohms for the 5-band model. For reference, the reactance ranges for the wide 5-band model and the tri-band model are comparable. You may repeat the exercises that we just ran using the maximum resistance values, although the minimum values are perhaps more critical.

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The net result is that, as we move up the bands of a 5-band 2-element quad array, the feedpoint resistance drops much more rapidly than it does for a tri-band array that omits 17 and 12 meters. On 10 meters, the low resistance accompanied by a wide reactance range results in matching difficulties that are difficult to overcome. In most cases, we must de-rate the 10 meter coverage and even then rely on line losses of the main feedline to achieve a 2:1 SWR across the smaller portion of 10 meters. The comparisons provided by the numbers in Table 3 provide a demonstration of a quite general phenomenon. Given pre-set upper and lower frequency limits, the more bands that we pack into a multi-band 2-element quad array, the lower the frequency ratio between adjacent loop sets. As we lower the frequency ratio, the feedpoint resistance drops more rapidly, even though the reactance range may not change very much. The higher the ratio between reactance and resistance, the more difficulties we encounter in effecting a match to a main feedline of a specified characteristic impedance, with or without matching devices or networks.

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The tri-band quad begins with higher feedpoint resistance values on all band. Hence, we require some form of matching. A 75-Ohm (or similar) match-line that is 1/4 wavelength--or shorter as necessary--allows us to match the quad on each band to a 50-Ohm main feedline. As well, we may achieve full band coverage on all 3 bands with an SWR value of less than 2:1 (without relying upon losses in the main feedline). In a nutshell, this small demonstration shows why I chose to design a tri-band 2-element quad beam rather than stretch for a 5-band model that would fail to provide full-band coverage on 20 through 10 meters.

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Conclusion

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These notes have described and analyzed the structure and performance of a tri-band 2-element quad beam for the wider upper-HF amateur bands of 20 through 10 meters. The design rests upon wide-band monoband quad beams and adjusts the dimensions to obtain as close to monoband performance on each band as feasible. In fact, the beam comes very close to replicating monoband performance. The array allows us to match the individual feedpoints to a 50-Ohm main feedline by the use of 75-Ohm lines of prescribed lengths, some of which are less than the usual 1/4 wavelength. The array presumes the use of a remote switch or separate feedlines for each band. The structure uses spider construction to sustain the required spacing between the driver and the reflector on each band.

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My choice of a tri-band quad array rather than a 5-band beam results from previous studies of what happens to the feedpoint resistance as we add bands and consequently reduce the frequency ratio between adjacent loops sets. The more bands that we add to a multi-band quad, the lower the ratio becomes. The result is both a general lowering of all feedpoint resistance values and a greater differential between the feedpoint resistance values for 20 and 10 meters. Since the reactance ranges tend not to change by any great amount, the high ratio of reactance to resistance tends to reduce matched coverage of 10 meters, regardless of whether or not we use a matching device or network. By sustaining a higher frequency ratio between adjacent loop sets in a tri-band model, we may overcome the matching issue.

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All of these notes presume that the general parameters of quad operation over the wide amateur bands are acceptable. A 2-element quad shows good gain with the typical driver-reflector parasitic-assembly decrease in gain with increasing frequency. However, the 180-degree front-to-back ratio shows considerable variability, with a relatively high mid-band peak but band-edge values that are only somewhat higher than the ones that we obtain from a 2-element driver-reflector Yagi. Finally, full-band matching is achievable with an appropriate matching line, but only if we begin with a basic design optimized for wide band coverage.

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Cubical Quad Notes Vol 1 - 3 available in PDF book format on the Books Page.

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Updated 04-01-2007. © L. B. Cebik, W4RNL. This item appeared in AntenneX, March, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Upper, Quad


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Why Not Use a 3-Band, 3-Element Quad?

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L. B. Cebik, W4RNL

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Although we can find a number of designs for 3-element monoband quad beams, we would have a difficult time uncovering tri-band or 5-band versions of them. There are both physical and electrical reasons for this lacuna in the range of available quad multi-band designs. We should spend at least a brief time discovering what the reasons are.

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Monoband 3-Element Quads

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Among 3-element quad beams, we can find both good and mediocre designs. In Volume 2 of Cubical Quad Notes, I offered computer programs for two types of 3-element monoband quads. One version stressed the widest obtainable bandwidth for both the front-to-back ratio and the SWR curve. The other version gave up bandwidth (but not altogether) in exchange for the maximum gain that we might obtain from 3 quad loops, commensurate with a reasonable front-to-back ratio at the design frequency. Both programs (along with a NEC-Win Plus NEC model that incorporated the equations) required only two input variables: the element (wire) diameter in the units in use and the design frequency. Fig.1 shows the outlines of the two beam types to provide an idea of their proportions.

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The wide-band version is about 19% longer than the high gain model. Despite the greater length, the wide-band driver is closer to the reflector than the corresponding element on the high-gain version. The wide-band director is also considerably smaller in circumference than the high-gain director.

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The wide-band version may be the easier antenna to mount. If you draw a centerline through the elements to represent a boom, then the mid-point of the boom will fall just beyond the "r" in the word "driver." However, since there would be two elements and their support arms left of the midpoint, the actual position for the boom-to-mast plate would fall somewhere within the word "driver." Alternatively, some builders have placed additional weights inside the director end of the boom to provide a mast position closer to the boom mid-point.

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The situation is a bit more precarious with the high-gain version of the antenna. Here, the mid-point of the imaginary boom line falls close to the "d" in "driver." Since support arms tend to be flexible and an element wire extends across the face of the support mast or tower, builders tend to use counter weights inside the director boom end to arrive at a balance point that maximizes the flexing space for the driver support arms and wire.

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Because the data will be significant when we explore the electrical properties of attempted tri-band 3-element quads, let's quickly review the potential performance of both types of monoband quads. Since all bands provide similar performance, except for bandwidth issues, we can illustrate performance by reference to the widest of the upper HF bands, 10 meters. Table 1 provides the dimensions for both antennas. All dimensions are in inches, and the table lists full side lengths and loop circumferences. The spacing dimension is referenced to the reflector.

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The modeled performance in free space for both beams represents close to the best obtainable for 3-element quads of each type. Table 3 samples the performance at the band edges and at the design frequency. Note that the worst-case and the 180-degree front-to-back ratios are the same at the band edges and differ only in the middle portion of the band, where the rear lobe shows a characteristic "dimple." Also notable is the difference in beamwidth between the two designs. As gain increases, beamwidth decreases.

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We may correlate the main performance data in the table to the gain and 180-degree front-to-back curves for both models in Fig. 2. The high-gain version of the 3-element quad allows one to structure the design so that the maximum forward gain occurs at the design frequency, with lesser values at the band edges. Obtaining a high-gain curve of this shape with a Yagi is not normally possible. The high-gain quad model obtains in its 3 elements about the same gain as a long-boom 4-element Yagi. However, unlike Yagis that usually manage close to a minimum front-to-back ratio of 20 dB across the band, the quad shows the typically narrow-band nature of its front-to-back curve. The high-gain model manages 20-dB front-to-back ratio for only about 35% of the 10-meter band.

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The wide-band version of the 3-element quad trades gain for a more acceptable feedpoint impedance range. The trade-off results in a gain level that is about 0.55-dB lower than the high gain model at the design frequency. The design frequency free-space gain level is close to the value obtained from a short-boom 4-element Yagi. In addition, the wide-band model shows peak gain at the low end of the band, with a decreasing gain curve toward the high end. However, the minimum gain value is about 8.2 dBi, about 1.5-dB higher than the minimum value for a 2-element monoband quad on 10 meters. Interestingly, the front-to-back curves for both the wide-band and the high-gain versions of the antenna are very similar. Differences would fall below the operationally noticeable level.

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The graph also contains a pair of marks at each end--along the upper edge. Since the curves for all 3-element quads derived from the equation models would be very similar, the marks show the curve limits for the 20-meter and the 15-meter amateur bands. You may extrapolate the likely gain and front-to-back values for each band by using these limiting marks. The impedance data in Fig. 3 contains the same marks for similar extrapolations.

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The wide-band resistance curve centers at about 75 Ohms. Although the resistance change across the band is higher than the corresponding change for the high-gain model, the reactance shows a much lower total change from 28 to 29 MHz. Hence, the wide-band models shows a 75-Ohm SWR curve that covers about 900 kHz of the band with less than a 2:1 value. The same curve on 20 and 15 meters would show band-edge values well below 2:1.

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The resonant impedance for the high-gain model is closer to 50 Ohms, allowing within the limits of the antenna a direct connection to the typical main feedline (with a common-mode current attenuator, of course). However, the total range of reactance across the band limits the 2:1 50-Ohm SWR operating bandwidth to about 600 kHz or about 60% band coverage. Since 20 meters is about 70% of the bandwidth of 10 meters, the curve would not quite allow 2:1 SWR use of that band. However, the curve would just about fit 15 meters, since it is about 60% of the bandwidth of 10 meters.

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The monoband data will prove useful in evaluating the potential performance of any attempted tri-band 3-element quad. Tri-band 2-element quads managed to produce performance levels on each band that are similar to monoband values for each band. The key electrical question will be whether or not we can expect similar results from a tri-band 3-element quad.

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Tri-Band 3-Element Quads: the Physical Questions

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Typically, there are two ways of constructing a multi-band quad: the spider and the planar methods. The spider method uses the distance between elements as measured in wavelengths as a constant. Therefore, the physical spacing between elements varies from one band to the next. Fig. 4 shows a possible arrangement of elements for a tri-band quad in which the drivers form a plane and the reflectors and directors vary their distance in inches, feet, or meters as we change frequency band. The model uses the wide-band version of the monoband quad as the basis for the elements shown.

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The alternative construction method uses planar support arms for each elements. Fig. 5 shows the general outline for such a quad in terms of the element placement. Since the element spacing would be optimal for only one of the 3 bands--at most--the element spacing values will vary according to the design compromises used to create the structure.

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At this juncture, we shall overlook performance questions to concentrate on the physical challenges presented by each design direction with constructing a tri-band 3-element quad. If we add support arms to the spider quad in Fig. 4, we obtain a sketch resembling the side view shown in Fig. 6.

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The optimal angles for the parasitic support arms exceed what is wise (or perhaps, even what is possible) using the wide-band quad as a model. Quad support arms must be relatively light and strong, a combination that gives the arms considerable flexibility. When we exceed certain angles (that vary with the arm structure), flexibility turns into sag that tension rods between pairs of forward and rearward arms cannot overcome. We can modify the structure somewhat, perhaps be using the high-gain design with its shorter overall front-to-back dimension. However, even this design would show support-arm angles that threaten serious sag, especially if we add an ice load to the array. The next strategy might be seriously to reduce the spacing between elements. However, this tactic will either reduce the operating bandwidth or reduce the performance level below 3-element expectations.

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Fig. 7 shows the fundamental difficulty with all planar 3-element quads. The compromises called for in the electrical performance of this type of multi-band array tend to place the driver very close to the support mast. Typical reflector-to-driver spacing values for upper HF multi-band quads are from 8' to 10'. However, driver-to-director spacing values use the same range. Support arm structures are lightweight and flexible. However, they still have some weight. Hence, even if we use different spacing values for the forward and rearward elements, we must adjust the mast-to-boom connection to compensate for the double X-structure on one side of the mast. The net effect is to put the driver elements in jeopardy of contacting the mast or tower during normal wind loads.

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For the reasons outlined, we find few 3-element tri-band quad designs available. Most builders prefer to move from 2 to 4 elements. Virtually all 4-element quad designs use planar construction. Hence, the load on each end of the boom, relative to the mast or tower, is equal. The reflector and driver elements go to the rear, while the directors ride in front. It is still important to mount the quad at its center of mass rather than using the boom-length center point. However, even that adjustment leaves several feet of space between the mast and the nearest set of element wires.

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Tri-Band 3-Element Quads: the Electrical Questions

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There is more to dis-recommend a multi-band 3-element quad than just the mechanical details. Someone might well be able to overcome the physical constraints if the 3-element quad offered near-monoband performance on all bands, even if only in a 3-band version. However, we are unlikely to see such an antenna because the 3-element design--when multi-banded--presents some electrical problems.

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To test the tri-band 3-element quad, I created a number of models using both planar and spider construction. All of the planar models failed to have either the gain or the bandwidth of the wide-band monoband 3-element quad. Since it is not possible in a finite lifetime to exhaust all of the possibilities, I cannot claim the survey to be exhaustive, although it has so far proven both exhausting and futile. Among spider models, the version of the antenna shown in Fig. 4 and in Fig. 6 proved to provide the best performance. Table 3 samples that performance at the design frequencies. The table also lists the design-frequency monoband performance on all 3 bands to ease the task of making comparisons.

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The table clearly shows that we encounter a lower feedpoint resistance as we increase the frequency. However, the rate of decrease is lower than for 2-element tri-band quads. The reduced rate rests on a combination of factors, including the planar arrangement of the drivers and the fact that each driver has two elements that exert influence on the feedpoint impedance. Were it not for other factors, we might use this beam without further adjustment to the driver lengths.

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Unfortunately, as we increase frequency, we also see a decline in the array gain. In fact, the 10-meter gain falls within the range that we can achieve with only 2 elements in a tri-band quad. As well, we also find a decrease in the front-to-back ratio. These numbers are not simply the product of a front-to-back peak that is on a different frequency. Rather, the decrease in front-to-back ratio is part of the same set of effects that yields the lower gain on each band above 20 meters. In fact, 20 meters is the only band on which we see near-normal (monoband) gain, and this fact provides a clue to what is happening.

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We can visualize the problem by examining Fig. 8, which shows the relative current magnitudes when we operate the array on 15 meters and on 10 meters. On the left, we find fairly high peak currents on the 15-meter elements, since the operating frequency is 21.2 MHz. There is one additional active element: the 20-meter director. Its current magnitude is over 1/3 the value of the 15-meter director current magnitude. Likewise, on 10 meters or 28.42 MHz, we find fairly high values of current magnitude on the 10-meter elements. As well, the 15-meter director is active at a current magnitude that is more than 1/2 the current magnitude of the 10-meter director.

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Current magnitude is not the sole determiner of what occurs with these elements. We must also consider the phase angle of the current. In the monoband versions of these 3-element quads, we find a relative current magnitude on the reflector that varies between 0.81 and 0.86 across 20 meters. The corresponding current phase varies from 126 to 153 degrees. The director current varies from 0.23 to 0.36 in magnitude, with a phase angle range of from -133 to -151 degrees. At the design frequency, the current magnitudes and phase angles are about at the average of these ranges (0.85 at 140 degrees for the reflector and 0.29 at -140 degrees for the director).

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In the tri-band design, at 14.15 MHz, the reflector values are 0.84 at 131 degrees and 0.27 at -149 degrees--well within the range shown for the monoband beam. However, at 21.2 MHz, the tri-band reflector current is down to 0.68 at 133 degrees, while the director current is 0.31 at -150 degrees. The reflector relative current magnitude is low. At the same time, the 20-meter director shows current values of 0.11 at -11.6 degrees. At 28.42 MHz, the 10-meter reflector current is 0.64 at 148 degrees. The 10-meter director current values are 0.36 at -135 degrees. While the combinations are not optimal, the key value is the low reflector relative current magnitude. At this frequency, the 15-meter director shows current values of 0.20 at 20 degrees.

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If the parasitic element current magnitude and phase angle values are not radically out of line (with the possible exception of the 10- and 15-meter reflector magnitudes), then we may still be at a loss to explain why the forward gain drops so much, rather than just a little. The answer lies in understanding how currents and element functions go together. Clearly, reflector currents show a positive phase angle, while director currents show a negative phase angle in 3-element arrays. Although the exact number will change according to the precise design, the monoband ranges of magnitudes and phase angles give us ballpark values for any 3-element parasitic array. We should not neglect the driver current, which in all cases of this modeled sequence is 1.0 at 0 degrees. Essentially, phase angle values near zero yield a driver element, and the two directors with unintended activity are closer to zero degrees than to values appropriate to reflectors or directors. In effect, the parasitically active directors for the next higher band are radiating energy, but without the direct influence of the parasitic elements that have been cut for the band in use.

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The energy must go somewhere. For the subject design, the energy tends to go "up" and "down" relative to the wires in the loop as much as it goes forward and backward. In other words, we end up with wider beamwidth values, not only in the E-plane, but as well in the H-plane. Re-examine the data in Table 3. The tri-band 20-meter beamwidth values are nearly the same as the ones we derived for the monoband beam. In fact, all three monoband 3-element quads have almost identical beamwidth values. However, when we move to 15 meters, the E-plane shows a 4.5-degree wider beamwidth, while the H-plane value increases by about 8 degrees. At 10 meters, relative to the monoband values, the E-plane beamwidth increases by about 13 degrees, while the H-plane beamwidth increases by over 20 degrees. Fig. 9 provides a gallery of H-plane patterns that show clearly the increasing beamwidth as we operate the 3-element tri-band quads on the upper bands.

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The exact degree of pattern deformation, relative to a standard derived from the monoband pattern, will vary with the multi-band quad design. However, every planar and spider 3-element quad design that I have examined has shown the same basic phenomena. At 15 meters, the 20-meter director is active, and at 10 meters, the 15-meter director is active. In both cases, being active means having a current magnitude of at least 10% the value of the driver. The activity is sufficient to prevent the quad from reaching its monoband performance levels on the upper two band. Regardless of the precise design, the upper bands of a 3-element multi-band quad in some cases barely reach 2-element performance levels.

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Planar 3-element, 3-band designs are at a further disadvantage. 2-element designs exhibit only slow changes of performance with variations in reflector-to-driver spacing. However, the driver-to-director spacing (and element circumference) in a 3-element quad reacts to smaller changes in spacing. Hence, a 3-element tri-band quad tends more readily to show that fact that the element spacing is optimal at best on only one of the 3 bands and often not on any of them. As a consequence, tri-band planar designs using 3 elements tend not to achieve a very significant gain over a 2-element quad. Optimized quad designs for the widest bandwidths easily show about 8.5 dBi free-space gain at mid-band. Optimized high-gain monoband quads top 9.0 dBi. A planar quad rarely achieves 7.8 dBi on any band.

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I sampled tri-band 3-element planar quads using 3 different popular spacing values for boom lengths of 18' to 20'. One sample used 10' from reflector to driver and 8' from driver to director, while a second reversed those two numbers. A final sample used 10' for both the reflector-driver and driver-director spacing values. Although it may be possible to refine the performance further, Table 4 shows the range of values at mid-band for the group of designs.

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The element spacing value range favors 15 meters over the other 2 bands. Hence, the overall 180-degree front-to-back ratio level is higher on that band. As well, the lowest gain value is higher than for either of the other bands. The planar design also suffers in beamwidth in both the E- and the H-planes. Optimized monoband designs showed about a 66-degree E-plane beamwidth and a 79-degree H-plane beamwidth. As the table shows, all of the beamwidth values for the tri-band planar design are higher. In addition, the values increase with increasing operating frequency. Finally, the H-plane beamwidth shows considerable growth as the operating frequency increases. Given the associated physical challenges of a 3-element planar multi-band quad construction, most builders have concluded that there is no great sense in deriving 2-element performance from 3 elements.

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Conclusion

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The only definitive point that these notes establish is that multi-band 3-element quads present both physical and electrical challenges that most quad builders find perhaps too daunting. Whether there are any sure-fire ways to overcome both sets of challenges, I frankly do not know. To this point, I have discovered none. Apparently, most quad builders have not found these ways either, since 3-element multi-band quads are far more rare than 4-element multi-band quads.

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With 4 elements, a quad presents no major mounting problems other than the weight of the elements and their support arms. As well, the presence of the second director overcomes to a large measure the pattern distortions that tend to prevent 3-element quads from reaching monoband performance on the upper bands. Nevertheless, 4-element quads present their own challenges--and sometimes the means to overcome them. Virtually all 4-element quads use planar construction. The result will inevitably be that some bands have compromise performance values that emerge from using a boom length that is either too short or too long for optimal wide-band performance. At the same time, the presence of three parasitic elements per band allows the builder to offset some loop dimensions to increase the operating bandwidth with an acceptable SWR value. The challenge lies in finding the correct combination that yields operating bandwidth and reasonable performance that is worth the construction and adjustment effort. Many quad builders have found the benefit-cost ratio favorable in 4-element designs while finding the ratio unacceptable for 3-element multiband quad designs.

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Cubical Quad Notes Vol 1 - 3 available in PDF book format on the Books Page.

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Updated 04-01-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Upper, Quad


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Notes on Full and Shrunken 40-Meter Quads

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L. B. Cebik, W4RNL

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+ Most commercial 40-meter Yagis use half size elements plus a method of loading the elements to achieve some gain and front-to-back ratio on a limited portion of the 40-meter band. Half-size elements, even when spaced optimally at about 20 feet, limit the available gain relative to a full- size 2-element Yagi. However, shortening the elements does increase the available front-to-back ratio relative to a full-size beam. +

The limitations of shortened 40-meter Yagis has raised some interest in the possibilities of a 40-meter quad. The following notes are extrapolations from studies published in Communications Quarterly, Summer, 1997 (pp. 71- 92) (link). The full study focused on 10 meter models and test antennas, with nearly automatic extensions of the ideas to 20 meters. However, a number of variables has required some extensive remodeling for 40-meters.

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40-meters is a wide band. 300 kHz at 40 is electrically the equivalent to 600 kHz at 20 or 1.2 MHz at 10. Hence, it is inherently more difficult sustaining the performance of any type of array across the band, in addition to maintaining an inclusive operating bandwidth. Therefore, for virtually any multi-element antenna design, there will be a region of the band at which performance is peak and other parts of the band where the antenna may be operated with lesser gain and front-to-back ratio.

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This restriction applies equally to quads as to Yagis, either full or half size. Moreover, reduced-size or shrunken quads will be subject to the same types of reduced bandwidth for each of the major antenna performance characteristics of greatest concern to radio amateurs: gain, front-to-back ratio, and SWR bandwidth.

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Let's look at four quad possibilities: a full size model and three versions of shrunken models, and then compare their performance potentials as derived from models. All gain figures are free space gains in dBi.

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In the process of comparing these antenna models, I shall by pass mechanical questions. The quad is requires a significant mechanical support structure. Companies, such as Cubex, to name just one, make support structure hardware available. Whether the resulting assembly is adequate to various climates will have to be a builder decision.

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Full-Size 40-Meter Quad

A full-size 2-element quad for 40 meters has the width of a half-size 40- meter Yagi--about the same width as a full-size 20-meter beam. However, the vertical space requirement and the consequential support structure is very significant. The quad forms a box about 36' top and side, with a front-to-back spacing of about 20 feet. +
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The figure shows the wire dimensions for a full size quad optimized for maximum performance at the lower end of the band. The modeled wire size for this and all models is #14 copper. If you use a fatter wire, do not expect element shortening. As Bob Haviland pointed out, as you increase the wire diameter of the quad or almost any other closed-geometry antenna, element length increases.

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The 20' spacing represents a separation of about 0.14-0.15 wavelength, which is a good compromise among the major performance characteristics of the antenna. Shorter spacings are possible with a consequent narrowing of the operating bandwidth. Larger element spacing tends to increase the ungainliness of the assembly almost exponentially.

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For all quad models, peak gain occurs below 7 MHz. As gain increases, the front-to-back ratio decreases. For all the models shown, a minimum band- edge front-to-back ratio of 9-10 dB was used as a design limit.

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Frequency sweeps of the model show a maximum front-to-back ratio of over 29 dB at 7.1 MHz, where the gain is about 6.9 dBi. Gain is higher at lower frequencies, reaching 7.4 dBi at 7 MHz. Above the design center, both gain and front-to-back ratio show a regular decline down to 5.9 dBi and 10.2 dB at 7.3 MHz.

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Since the feedpoint impedance of the antenna fluctuates around the 100-ohm mark, the antenna was designed for use with a 1/4 wavelength 75-ohm matching section. With the section in place, the antenna has a 50-ohm SWR of less than 2:1 across the band.

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Square Inset-Loaded Shrunken Quad

One method of shrinking a quad is to use voltage-node loading. This method eliminates inductor losses and maintains current levels in the wire elements where they are the highest. However, the design has some limitations. +

First, the current is still high at the corners of a full size quad. Shrinking the loop changes the polarization of the formerly corner current to vertical, where is tends to cancel with fields from the opposite side of the loop. Hence, we can expect lesser gain from every shrunken quad.

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As the figure shows, we can reduce the dimensions of the quad significantly, that is, by 20 to 25%. However, in the square configuration, we are limited by the need for dimensional space for the insets. Further shrinking can be obtained by spreading the inner ends of the insets, thus decreasing their length. However, further shrinkage will be accompanied by further gain reductions.

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With the dimensions shown (retaining the 20' spacing), maximum front-to- back ratio occurs between 7.05 and 7.1 MHz and peaks above 17 dB. Gain in this region is between 6 and 6.4 dBi, climbing to about 6.8 dBi at the lower band edge.

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As with the full-size quad, gain and front-to-back ratio decline from 7.1 to 7.3 MHz, dropping to 4.6 dBi and 6.1 dB, respectively, at the upper band edge. Obviously, peak antenna performance appears over a narrower bandwidth with the smaller antenna.

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The shrunken quad presents a feedpoint impedance apt for a 75-ohm feedline. Therefore, the antenna was designed for this feedline, with expectations of an appropriate transformation either at the antenna feedpoint or at the shack. 2:1 SWR bandwidth just about covers the entire band.

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Diamond Inset-Loaded Shrunken Quad

The builder can obtain further decreases in overall antenna circumference by using a diamond configuration. Unlike the square configurations, where the reflector is purposely made larger than the driven element, the diamond configurations use loops of the same size, varying only the load sizes. A builder can use either scheme with either configuration with very little change in performance characteristics. +
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With an overall reduction of circumference to the 70% of full-size mark, the diamond configuration is at the verge of that point in antenna design where further size reductions are accompanied by much larger decreases in performance, especially with respect to gain and operating band width. Moreover, the maximum cross-arm dimensions and hence both the horizontal and vertical space required by the quad approach the horizontal and vertical dimensions of the square full-size quad. However, the diamond shrunken quad provides more space for the insets, and the configuration will be much lighter and possibly better at shedding ice and snow than wither of the square models.

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The maximum front-to-back ratio of this configuration peaks just above 7.05 MHz at above 17 dB, with a gain of about 6 dBi. Lower band edge gain is close to 6.5 dBi. Gain and front-to-back ratio taper up the band to upper band-edge figures of 3.95 dBi and 4.51 dB, respectively.

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Like the square inset-loaded quad, the antenna is apt for 75-ohm coax feed, and the 2:1 SWR operating band width covers just about the entire band.

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Diamond "Capacity-Hat" Loaded Shrunken Quad

An alternative to inset loading at a voltage node is so-called capacity-hat loading. Instead of an inset, one brings a wire from the left and right corners inward and then branches it in parallel to the main wire to lengths that resonate each loop at the frequencies needed for optimal parasitical performance. +
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As the figure shows, the cap-hat loaded diamond is mechanically equal to the inset-loaded diamond model. The cap-hat wires perform essentially the same function as the insets: to provide the wire length necessary to reach resonance at the desired frequency without adding significantly to the radiation fields. Hence, we would expect performance figures to be equally similar.

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We shall not be disappointed. Maximum front-to-back ratio once more peaks at about 18 dB at 7.05 MHz where the gain is 6.1 dBi. Gain climbs to 6.4 dBi at the band edge. Gain and front-to-back ratio decreases toward 7.3 MHz, where they are 4.1 dBi and 5.4 dB, respectively.

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Insets and cap-hats present the builder with construction challenges of different but comparable sorts. The square and diamond inset models require parallel wires reaching toward (but not reaching and certainly not overlapping) the antenna boom. Lightweight spacers, perhaps 1/2" nominal CPVC, can maintain spacing while UV rated synthetic rope can serve as the insulated link to the hub support. There is no reason why the insets cannot be as much as 15 degrees off-plane without unduly affecting the front-to-side ratio of the antenna pattern. The spread cap-hat wires can be insulated and spaced from the main element wires by similar means: CPVC.

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The dimensions shown are modeled dimensions and will required field alteration to account for the variables of quad construction. Unlike aluminum tubing, which is relatively rigid in length, quads are subject to changes in length depending on the tension applied by the builder during construction. The results may be changes to the insets or the cap-hat spread wires. The amount of metal, if any, in the spreaders may also require small changes in wire length. In short, wire quad dimensions are never as assured as aluminum tubing dimensions.

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Performance Comparisons

To get a better picture of how the antennas modeled above compare with each other, lets look at some graphs of modeled performance across the 40-meter band. +

Gain

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The individual models, when graphed across the band, show that gain is largely a function of percentage of full-size. The full-size quad not only has a higher forward gain than the shrunken models, but the rate of decrease is slower across the band. At the design center--about 7.05-7.1 MHz, the gain approaches that of a short boom or a wide-band 3-element Yagi and exceeds the gain of a full-size 2-element Yagi by over a half dB. (The forward gain of a full-size 2-element quad is still a dB short of the gain of a long-boom optimized 3-element Yagi.)

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The 78% square inset-loaded quad shows good gain across the band relative to the smaller quads and relative to a full size 2-element Yagi. The 2 diamond 70% quads compete well with a full size 2-element Yagi and are superior to half-size Yagis. However, the shrunken quads do show a tendency to more rapidly decrease their gain across the band relative to a full size quad. However, the lowest figures remain about 2 dB better than a dipole.

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Front-to-Back Ratio

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Because the full-size quad has inherently a better front-to-back ratio, it is possible to design its peak further into the 40-meter band and still have about 13 dB at the band edge. This design tactic provide better than a 10 dB front-to-back ratio at the upper end of 40 meters, despite the rapid drop in the ratio above 7.1 MHz.

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All three shrunken models show front-to-back ratio curves that would be indistinguishable in practice. The square 78% model has its peak between 7.05 and 7.1 MHz, which is invisible on this sweep at 0.05 MHz intervals. However, that peak is not significantly above those of the diamonds. with a design limit that set the front-to-back ratio at 9-10 dB at the lower edge of the band, this ratio is sustained only to abut 7.15 MHz for all three models. If a builder desires to center the performance peak within the phone end of the band, he must change element dimensions. However, the antenna may become inoperative at the low end of the band if centered between 7.2 or 7.25 MHz.

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2:1 SWR Operating Bandwidth

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All four antenna models show a wide operating bandwidth, covering all of 40 meters. However, one should understand that the upper half of the band is achieved at significantly lower antenna performance figures.

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The full-size model SWR curve is for a 50-ohm SWR basis. The model was constructed with 1/4 wavelength 75-ohm matching section cut for 7.1 MHz. The 50-ohm SWR never exceeds 1.76 across the band.

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All three shrunken models are inherently 75-ohm antennas, and the SWR curves are based on 75 ohms. The use of 7.05 MHz as a design center is apparent in all of the curves.

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The resonant frequency, at which the antenna shows near-zero reactance, must be set low in the band. To a degree higher than virtually any other antenna design, quads show a very rapid rise in SWR below resonance and a very slow rise in SWR above resonance. The rapid rise in SWR below design frequency is a combination of a rapid drop in the resistive component and a rapid rise in reactance. Above the resonant frequency, both the resistive and reactive components of the feedpoint impedance rise very slowly. This fact can mislead a user into believing that his antenna is performing very well, when, indeed, the low SWR is accompanied by mediocre gain and front- to-back ratio.

+

Consequently, it is never good practice to build a quad without making at least some measurement of the front-to-back ratio across the band in addition to impedance measurements. One can make fairly extensive changes in the driven element without affecting antenna performance. However, changes in the reflector will change the resistive and reactive components of the feedpoint impedance. Hence, for most cases, it is better to begin by establishing the reflector length with respect to front-to-back ratio pattern across the band and then adjust the driven element for the desired SWR characteristics. If the change in the driven element is quite large, it may take one more round of reflector-then-driven-element adjustment to settle on the final dimensions.

+

All of the designs presented can be improved with respect to almost every characteristics. I developed them, not as the last word in 2-element 40- meter quad design, but as typical models on which to base expectations and to make design decisions for one's individual situation.

+

For further information on quads, see at least the following references:

+
    +
  • +

    William I. Orr, W6SAI, All About Cubical Quad Antennas

    +
    • +
  • +

    Bob Haviland, W4MB, The Quad Antenna

    +
    • +
  • +

    John Koszeghy, K2OB, High Performance Cubical Quad Antennas

    +
    • +

+
+
+ +

+
+

Updated 12-30-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Return to Amateur Radio Page
+

Topics: HF Lower, Loading, Quad


+ + diff --git a/content/quad/8040quad.html b/content/quad/8040quad.html new file mode 100644 index 0000000..12a9e40 --- /dev/null +++ b/content/quad/8040quad.html @@ -0,0 +1,17 @@ + + + + + + An 80/40 Quad Design + + + +

An 80/40 Quad Design

+ hr +

An 80/40 Quad Design

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: HF Lower, Quad


+ + \ No newline at end of file diff --git a/content/quad/8040quad.pdf b/content/quad/8040quad.pdf new file mode 100644 index 0000000..804af7b Binary files /dev/null and b/content/quad/8040quad.pdf differ diff --git a/content/quad/bc.html b/content/quad/bc.html new file mode 100644 index 0000000..a9f2247 --- /dev/null +++ b/content/quad/bc.html @@ -0,0 +1,105 @@ + + + + + + The Birdcage Antenna + + + +
+

The Birdcage Antenna

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ The folded X-beam derives its existence from the G4ZU Birdcage antenna. W2EEY viewed the X-beam as half a Birdcage.(1) Although this is historical fact, the logic of antennas goes the other way round: the Birdcage is a double folded X-beam. For reference, Figure 1 provides a free space pattern of an X-beam tuned for maximum front-to-back ratio. +
+ +
+

We may legitimately ask, how much better does the whole Birdcage work compared to an X-beam? When Dick Bird, G4ZU, published his work in 1960, he made some fairly extravagant claims for the antenna, claims that led him to patent it.(2) At this distance and with the calculating power made available by NEC and its offspring, we may decide that the claims for his antenna (and those of many hams who built one) reflect more accurately the low state of home-brew Yagi and quad construction of the time than they do contemporary comparative performance. Models of the Birdcage show little advantage over the X-beam and exaggerate some of its limitations.

+

Bird graphically demonstrated what he took to be the principles of the Birdcage by beginning with the bi-directional pattern of the dipole. Folded into a Vee, the antenna would show, according to his sketches, a strong lobe out the open end and a weak lobe off the apex. Add a Vee reflector (pointed the other way to make an X), double the assembly a quarter wave above or below, bend the X-arms vertically to meet each other as phasing lines, and the Birdcage is born. Figure 2 shows the outline of the Birdcage, with identification of each relevant dimension.

+
+ +
+

Unfortunately, the seeming flaw in the reasoning begins with the Vee itself. Short Vees do not cancel the radiation off the backsides of the elements (the outsides of the V). Thus are born the uneliminable quartering lobes of the X-beam and even larger lobes for the Birdcage.

+

Birdcages come in two forms: with a reflector and with a director. Table 1 shows 10-meter models of each beginning with a self-resonant Birdcage with equal-size elements derived from data given in 1960's literature.(3)

+ 
Table 1.  Modeled Dimensions of the Birdcage Antenna
+
+Dimensions     DE Arm (A)     Parasitic (C)       Vertical (B and D)
+               L (ft)         L (ft)              L (ft)
+Basic
+ Birdcage      5.05           5.05                8.666
+
+DE and Refl
+ Resonated     4.95           5.26                8.666
+
+DE and Dir
+ Resonated     5.16           4.91                8.666
+
+Note:  all models used #14 copper wire in free space at 28.5 MHz on NEC-4.
+
+

Figure 3 shows the performance in free space of the basic Birdcage--a nice 4-leaf clover.

+
+ +
+

G4ZU favored the reflector version, which is perhaps the worse performer of the two possible versions. With a forward gain in free space of under 6 dBi and a front-to-back ratio of about 8 dB, the beam is not the equal of a 2-element Yagi or even of the X-beam. Figure 4 shows its performance in free space.

+
+ +
+

The director version that parallels the development of the X-beam provides more gain and front-to-back ratio: 6.3 dBi and 17 dB, respectively. Figure 5 shows its performance in free space. The direction is reversed, since I simply re-dimensioned the reflector to form a director.

+
+ +
+

As shown in Table 2, the figures for the directed Birdcage surpass both the X-beam and the 2-element Yagi by a small bit, while the reflected Birdcage leaves much to be desired.

+ 
Table 2.  A Comparison of Antenna Performance
+Antenna             TO Angle  Gain      Front-to-      Feedpoint
+ Type               (degrees) (dBi)     Back (dB)      R ñ jX (Ohms)
+A.  Free Space
+Birdcage: DE + Ref  --         5.8       8.0           34 -  0
+Birdcage: DR + Dir  --         6.3      16.9           40 +  4
+Folded X-Beam       --         5.3      39.1           37 -  3
+B.  Height = 5/8 wl
+Birdcage: DE + Ref  22        10.5       8.0           31 -  3
+Birdcage: DR + Dir  22        11.0      17.1           40 +  3
+Folded X-Beam       23        10.5      21.8           35 +  0
+2-El Yagi           23        11.3      10.9           34 -  5
+2-El Quad           22        11.7      18.3           97 -  3
+C.  Height = 1 wl
+Birdcage: DE + Ref  13        11.3       8.6           32 -  2
+Birdcage: DR + Dir  14        11.8      17.0           39 +  2
+Folded X-Beam       14        10.8      31.7           33 -  1
+2-El Yagi           14        11.7      13.5           35 +  0
+2-El Quad           13        12.4      17.9           92 +  8
+Note:  TO angle=the angle of maximum radiation at which azimuth readings of
+calculated gain and front-to-back ratio were obtained.  All calculations
+via NEC-4.
+
+

The pattern of the Birdcage in either version does not meet today's standards of front-to-side ratio or front-to-rear ratio. The quartering rear lobes of the X-beam become virtual side lobes of the Birdcage and are only down from the main lobe by some 4 to 5 dB in the either version. There is little QRM-rejection potential, especially in the reflector version. Over real ground, the pattern devolves into a mound of whip cream. However, over real ground, the director version tends to push its side lobes to the rear, and the pattern begins to resemble that of the folded X-beam.

+

Like the folded X-beam, the Birdcage retains its most optimal pattern only over a small portion of the band of design. The reflector version rapidly grows a tail below design frequency, while the director version grows its tail above design frequency. The SWR bandwidth is also narrow, less than 0.5 MHz at 10 meters for a 2:1 SWR. However, the complex structure of the Birdcage is less amenable to a tunable parasitic element than is the simpler X-beam.

+

All in all, the additional complexities of the Birdcage are not warranted by a significant increase in performance over the X-beam. Gain aside, the side and rear performance of the antenna falls far short of other compact designs. Consequently, while that antenna has a great name and an appealing look, performance models do not recommend the investment of time and resources in this antenna. In some ways, it is a shame to discover this: G4ZU contributed extensively to amateur practice in the field of antennas. Although the Birdcage antenna has had its day, Dick's other work--and his example--will long endure.

+
+

Notes

+
(1) John Schultz, W2EEY, "The G4ZU X Beam for 20," CQ (June, 1965), pp. 26- 28, 102. +

(2) Dick Bird, G4ZU, "The G4ZU 'Bird Cage' Aerial," CQ (April, 1960), pp. 40-42, 117.

+

(3) See George Cousins, VE1TG, "The Tri-Band Birdcage," CQ (July, 1963), pp. 30-33. Another brief reference to the antenna occurs in Orr and Cowan, Cubical Quad Antennas, 3rd Ed. (Lakewood, NJ: Radio Amateur Callbook, 1993), p. 102, where it is shown with a reflector and referred to as a variation of the quad.
+

+
+ +

+
+

Updated 3-18-97 © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Upper, Quad


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+

Sneaking Up on 2-Element Common-Feed Quads
+ Part 1: Monoband Quad Beams as a Starting Point

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Among 2-element quad beam users a question lingers. Which feed system is superior: separate switched drivers or drivers brought to a common feedpoint? The common-feed system is easier for the user, since it eliminates an extra, usually remote, switch box. However, the separate-feed system is usually easier to design and test for proper operation. Many answers to the question abound, ranging from antenna maker claims that users cannot always confirm to simple feelings about the matter.

+

The common-feed 2-element quad is not a simple system, as Fig. 1 tells us. We have the elements for at least 2 bands of operation. The elements interact simply by virtue of proximity. Moreover, we have additional interactions occasioned by the use of a common feedpoint. Finally, we can add to the equation the fact that we usually do not know to what we may be comparing either the common-feed or the separate-feed quad. Little wonder that the question tends to raise more heat than light.

+
+ +
+

Let's revise the basic question so that we can sort out the proper steps on the way to an answer. What happens when we create a multi-band quad and provide it with a common driver feedpoint for all bands?

+

First, we need a set of starting points, namely, monoband quads from which to build the multi-band quad. Every multi-band quad rests on a set of monoband quads which the multi-band design alters to compensate for element interaction. In many cases, the designer may not actually examine the monoband quads that underlie the more complex array, but those quads exist anyway. These notes will designate the monoband quads as the place to start so that we can compare multi-band designs and performance to them.

+

Second, we need to move in logical steps and "sneak up" on the common feed design. After reviewing the performance of the foundational monoband quads, we shall develop from them a series of multi-band designs that use separate feedpoints. These designs will use perfectly square loops for all elements so that the interactions exist at only one level: between reflector wires and driver wires that are equally spaced from each other for the entire perimeter. Only when we know the consequences of this step can we move on to the necessary distortions of the driver wires that occur when we use a common feedpoint.

+

Third, we must set some limits to the study--or we shall never reach a stopping point. One limitation is setting a frequency ratio between adjacent bands in any multi-band design. The closer 2 bands are in frequency, the greater that the element interaction will be. If the operating frequencies are too close, then seemingly inactive elements become very active, sometimes in unwanted ways. When operating on the lower of two frequencies, the seemingly inactive reflector element may form a director in the wrong direction relative to desired beaming. To hold interactions to an accountable level, I shall set a minimum frequency ratio of 1.3:1 between adjacent bands. This ratio allows combinations such as 17 and 12 meters, 20 and 15 meters, and 15 and 10 meters. However, it rules out adjacent bands in the upper HF region of the amateur spectrum. There are successful quad beams using these combinations, but they do not reveal their interactions as readily as more widely space bands. Remember that our goal is to understand what happens as we move toward a multi-band common-feed quad beam. It is not necessarily to design one that we might build.

+

I shall also limit the study (with one exception) to 2-band quad beams, simply to limit the number of different kinds of sample beams. Instead of examining all possible combinations of multi-band quads, we shall look at multiple examples of two-band quads with different frequency combinations in order to find the reliable trends in the physical shape and performance of these beams. These trends will be the keys to understanding what happens along the road to a common feedpoint. As well, the dual-band quads will give us an opportunity to explore an interesting feeding strategy.

+

One situation that I shall avoid is a combination of quads involving a 2:1 frequency ratio, such as a 20-meter and 10-meter dual-band quad. On 10 meters, both of the drivers will be at or near resonance and at or near a low impedance. Hence, we would encounter a greater-than-normal current split between the drivers. However, when used on 10 meters, the 20-meter driver has a circumference of about 2 wavelengths, and radiation is predominantly off the loop edge. The quad works best when radiation is broadside to the loop, a condition that occurs when closed loops are close to 1 wavelength in circumference. By avoiding the 2:1 frequency ratio, we by-pass the need for special compensations to overcome the conflict in pattern formation.

+

The final limitation will involve element spacing. Throughout the multi-banding exercises, I shall maintain the element spacing used in the monoband quads that form our starting points. This specification will result in spider rather than planar quad beams. Planar quad beams have advantages and disadvantages of their own. One primary example is the KC6T quad that I analyzed in volume 1 of Cubical Quad Notes. In terms of wavelengths, the spacing between elements changes as we change bands. Hence, we do not have a ready ability to relate the performance of the multi-band antenna to its root monoband quad components. By preserving element spacing and using what will amount to spider construction with sloping support arms, we can achieve the desired comparisons between original monoband quads and the modifications needed to make them work in various multi-band settings.

+

Getting Started: Monoband 2-Element Quads

+

The multi-element quad beam is essentially a parasitic array with relatively narrow-band performance characteristics. A 2-element driver-reflector design will show a characteristic reduction in forward gain with increasing frequency across the operating passband. This feature the quad shares with the Yagi. (Any well-designed parasitic array with at least one director will show a rising gain with frequency.) However, the key limitations involve the SWR and front-to-back ratio passbands. In Yagi design, 2-element driver-reflector arrays show a low but almost uniform front-to-back ratio across any of the upper HF bands. The SWR passband is often the chief design concern. To widen that passband, we need increased element spacing. The result is a very small reduction in gain at the design frequency, but a wider spread of usable frequencies in which to observe the gain curve.

+

Designing a monoband 2-element quad involves a number of compromises. In volume 2 of Cubical Quad Notes, I described a program and a programmed NEC-Win Plus model that provides optimized 2-element quad beams for any user-selected design frequency and element diameter. The designs rest on extensive hand optimization of models, along with extensive regression analysis to allow use of the designs on wire diameters ranging from 10E-2 through 10E-5 wavelengths and on frequencies from 3 to at least 300 MHz. A number of interested amateurs have added to the array of formats in which one may perform the calculations. For a list of available downloads, see 2-Element Quads as a Function of Wire Diameter Part 2: Automating the Design Process.

+

Fig. 2 shows the general model outline (using an EZNEC graphic), along with a side view of the quad's physical structure. The angle between the support arms is 62 degrees, that is, about 31 degrees each side of a vertical line drawn through the mast and hub. The precise angle will vary a bit from band to band.

+
+ +
+

The angle for the (non-conductive) support arms varies according to the calculated spacing between the elements. The spacing, like all other quad dimensions, is a partial function of the element diameter as measured in wavelengths. In these exercises, I have standardized all quads to the very familiar AWG #14 (0.0641" diameter) copper wire. As measured in wavelengths, the element diameter changes from one band to the next. Since the wire is quite thin, the effects are small. However, the spacing may vary enough to change the overall angle between the reflector and the driver by as much as a full degree or so in the move from 20 down to 10 meters.

+

Based on the equations, I produced a series of models for the upper HF bands. The dimensions appear in Table 1. The spacing entry represents the full dimension. However, for modeling convenience, the loop dimensions appear as 1/2-side lengths. A full side length is twice the value shown, and the loop circumference is 8 times the value in the table. The dimensions are in inches. Multiply these dimensions by 0.0254 to obtain a result in meters.

+
+ +
+

These quad designs model very adequately on either NEC-2 or NEC-4. In fact, I remodeled each quad using EZNEC Pro/4 to check on the results of NEC-Win Plus, which uses NEC-2. The reported performance figures are insignificantly different. Although carrying out measurements in inches to 2 decimal places may seem to be beyond normal construction needs, the original model rests on spreadsheet calculations that carry them out to a dozen decimal places. Rounding to the nearest tenth of an inch is perfectly acceptable. Tenths may be easier to convert to the English system of eighths and sixteenths for use with a tape measure.

+

I selected this particular set of models as the monoband 2-element quads for our study since they provide the widest operating passband of any monoband 2-element quads in my experience. For example, the SWR bandwidth (using the design frequency resonant impedance as a standard) is well below 2:1, even on 10 meters (using the 28-29-MHz span as the antenna passband). However, the 180-degree front-to-back ratio shows a very high peak at the design frequency, but falls off rapidly.

+

On the narrow ham bands (17 and 12 meters), I used the band center as the design frequency. However, on the wider upper HF bands (20, 15, and 10 meters), I selected a frequency below the band center. The design frequency selection criterion was a relatively equal 180-degree front-to-back ratio at both band edges. The 20-meter design frequency is 14.14 MHz. On 15, the frequency is 21.19 MHz. On 10 meters, 28.4 MHz serves as the design frequency.

+

Although we shall look more closely at the performance curves for each monoband quad, Table 2 summarizes the performance characteristics across the band. It lists the band-edge and band-center values. Where the design frequency is not also the center of the band, the table includes those values as well.

+
+ +
+

The design-frequency free-space gain is uniformly 7.04 dBi. The 180-degree front-to-back value at the design frequency tends to climb with frequency, as does the resonant feedpoint impedance. (The reported values result from using calculated figures and do not result from any further modifications to make them "fit" the desired outcome.) The front-to-back ratio at the band edges is about the same for each of the wider bands. (The narrow bands are too narrow and the front-to-back values are too high to be concerned about differences less than 5-6 dB.)

+

Each upper HF amateur band has a different bandwidth when measured as a percentage of the band-center frequency. The table lists those values as well. It is clear from these sample numbers that as the bandwidth increases, the band-edge front-to-back ratio becomes lower. Three-element Yagis on short booms (under 0.25 wavelength) are capable of about 20 dB front-to-back ratios across the wider ham bands. A 2-element quad may match the 3-element Yagi in gain (with a reverse gain curve relative to frequency), but it simply cannot sustain the front-to-back ratio.

+

What the numbers in the table cannot show is how the rearward pattern changes with frequency. (The forward lobe remains well-behaved throughout.) For that purpose, we need a useful gallery of E-plane patterns. Fig. 3 supplies the need. More importantly, it shows the evolution of the rearward lobes as we move away from the design frequency.

+
+ +
+

I selected 10 meters for the gallery since that band gives us the widest operating passband of all the upper HF bands. The patterns show both the frequency and how much that frequency departs from the design frequency. Both 17 and 12 meters are so much smaller than the smallest increment of difference in the figure that we can expect their band-edge patterns to resemble the design frequency pattern with only a small loss on the direct rearward null. 20 meters is only about 70% as wide as 10, and 15 meters is only about 60% as wide as 10 meters. Hence, their band-edge patterns will be intermediate between the pair of patterns marking the farthest extremes on 10 meters.

+

One may debate my use of the 180-degree front-to-back ratio as the desideratum for choosing a design frequency. Admittedly, it is partially a function of modeling convenience, since that figure automatically appears in the basic NEC plot data collection produced by most implementations of the core. However, we should note a significant difference in the overall energy radiated to the rear quadrants both below and above the design frequency. Below the design frequency, we find only a small total area of rearward energy (remembering that we are dealing with only 2 dimensions and ignoring the third). In comparison, above the design frequency, we find a much larger and growing area of total rearward radiation. This condition correlates well with the decreasing forward gain (but continues to ignore the fact that a free-space pattern is actually a 3-dimensional affair). Nevertheless, the band-edge 180-degree front-to-back ratio values--and their equality at the band edges--will serve us well as markers of both similarity and of change when we develop dual-band quad beams.

+

We may collect further detail on the performance changes across each of the upper HF amateur bands by performing frequency sweeps. The graphs to follow emerged from AC6LA's EZPlots Excel function based on EZNEC sweep files. In each case, I subdivided the band into 10 segments to provide the smoothest curves feasible.

+

20 Meters

+
+ +
+

The gain and front-to-back curves in Fig. 4 show the performance on 20 meters. The gain curve is nearly, but not quite, linear in the gain reduction per unit of the passband. The rate of decline is about the same as the rate of climb for a short-boom 3-element Yagi using elements of the same diameter. (Since most Yagis would use fatter elements, practical Yagis of such design will show a somewhat shallower gain-rise curve, ranging from about 6.9 to 7.4 dBi.) The front-to-back ratio peaks at the design frequency and drops to about 16 dB at the band edges.

+
+ +
+

The impedance curves in Fig. 5 have a number of interesting features. The resistance and reactance curves almost parallel each other. Resistance rises about 64 Ohms across the band, while the reactance changes by about 47 Ohms. With AWG #14 wire on 20 meters, the resonant impedance is about 130 Ohms. Using this reference value, we can note that the SWR climbs more rapidly below the design frequency than above it. These features will repeat themselves in subsequent charts, especially for the wider bands.

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17 Meters

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The 17-meter band is only a bit over 1/2% wide. Therefore, we expect flatter gain and front-to-back curves than on the wider 20-meter band. Fig. 6 does not disappoint us. The gain drop is only about 0.2 dB across the band. Because the graph spreads the smaller passband into 10 parts, the front-to-back curve appears flatter. However, it is every bit as steep as the 20-meter curve. However, the front-to-back value remains very high over the whole band, suggesting that the use of a 2-element quad may be well suited to the band.

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Fig. 7 confirms the impression left by Table 2 that the resistance, reactance, and 133-Ohm SWR are for all practical purposes flat across the band. Only automated graphing spreads the SWR values along the Y-axis. The spread is useful in showing that even over a narrow bandwidth, the SWR rises more rapidly below the design frequency than above it. In most cases, construction variables will result in greater SWR deviations than the changes shown in the graph.

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15 Meters

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15 meters returns us to a wider band, but not as wide as 20 meters when measured as a percentage of the band-center frequency. As shown in Fig. 8, the band is wide enough to replicate the 20-meter front-to-back pattern. Both bands show a more rapid decrease in the front-to-back value directly below the design frequency than directly above it. However, by the band edges, the ratio has dropped to about 18 dB on 15 (in contrast to about 16 dB on the slightly wider 20 meters where the wire is also slightly thinner as a fraction of a wavelength).

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As we might anticipate from the fact that 15 meters is slightly narrower than 20 meters, the range of resistance and reactance variation in Fig. 9 is somewhat less than in Fig. 5. The resonant impedance is 134 Ohms. The "spooning" of the SWR curve results from the graph's use of 21.18 MHz as a sampling point, when the actual design frequency is 21.19 MHz.

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12 Meters

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12 meters is the narrowest of the upper-HF amateur bands, when we measure the passband as a percentage of the center frequency (24.94 MHz). Since the band is only 0.4% wide, graphs tend to have a stair-step quality due to the data, which is limited to 2 decimal places. Hence, the gain decrease across the band in Fig. 10 appears somewhat uneven, since the total amount of change is only 0.15 dB. As well, the front-to-back ratio has room only to move slightly off of it peak value. However, if we had used a broader frequency scale, the front-to-back curve would closely resemble the corresponding curves for the wider bands.

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The impedance curves in Fig. 11show barely any change in the resistance and reactance across the band. The resonant design-frequency resistance (135 Ohms) continues to rise as we move upward in frequency and the wire diameter grows when measured as a fraction of a wavelength. The SWR does not reach 1.05:1 within the band. Of course, construction variables suggest that a physical copy of this design might not show the perfection that we can easily obtain in the model.

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10 Meters

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With a bandwidth of about 3.5%, the first MHz of the amateur 10-meter band is the widest within our survey. Therefore, the gain shows the greatest range in Fig. 12. The 180-degree front-to-back ratio drops to a little over 14 dB at the prescribed band edges, even though its peak value is higher than on any other band. One usual marker of a high-performance array in amateur circles is a front-to-back ratio in excess of 20 dB. The 10-meter 2-element quad achieves this value for only about half the band (from 28.2 to 28.7 MHz). However, at the band edges, the front-to-back ratio is higher than we generally achieve with a 2-element driver-reflector Yagi.

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I selected the design frequency to achieve approximately equal 180-degree front-to-back ratios at the band edges. As a consequence of this decision, the 136-Ohm SWR curve--while perfectly acceptable--does not result in equal values at the band edges, as shown in Fig. 13. However, a 2-element quad is a bit less sensitive to driver length changes than a 2-element Yagi. Therefore, we might change the driver length to equalize the band edge SWR value while leaving the reflector length to control the front-to-back peak frequency. However, significant changes in the driver length will require corresponding changes in the reflector.

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The survey has included a collection of equation-designed monoband quad beams for each of the upper HF amateur bands. I have provided extensive information on the modeled performance curves in order to form a detailed baseline against which we can measure multi-band quads to come. However, before we leave the monobanders, we should address at least one or two practicalities. The first matter concerns construction. The models in this sequence presume that all support structures are non-conductive at the operating frequencies. The models also make square corners, although a very small curve at a physical corner to avoid wire crimping would create no operational problems. However, each corner attaches to a support arm. The method of fastening should involve only non-conductive hardware and other components. Metallic clamps, screws, and other fasteners--even if insulated from the element wire--can create 1-turn inductors that may detune the elements, especially since each such conductive fastener is multiplied by 4 for each element. The alternative to a wholly non-conductive fastening system is extensive field adjustment to restore the modeled conditions.

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A second practicality involves feeding quads with feedpoint impedance levels that are considerably higher than standard coax feedline values. The most usual matching system is a simple 1/4 wavelength line using an intermediate characteristic impedance between the feedpoint impedance and the main feedline value. Table 3 provides a sample table of the electrical length of 1/4 wavelength lines at each of the design frequencies. The physical length of the required line requires that we multiply the electrical length by the listed or (better) measured velocity factor of the actual line used. Coaxial cable velocity factors tend to range from about 0.66 to to about 0.80, depending on the dielectric material separating the center conductor from the braid.

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Ideally, the matching section characteristic impedance should be the geometric mean between the two terminal impedance values. We arrive at that value by taking the square root of the product of the terminal impedances. For the range of feedpoint impedances in our models and a presumed 50-Ohm main feedline, the ideal match line would have a characteristic impedance of about 80 to 82 Ohms. 75-Ohm line produces perfectly acceptable 50-Ohm SWR curves. Fig. 14 shows the basic 10-meter SWR curve referenced to a 136-Ohm standard and a 50-Ohm SWR curve that results from using a 1/4 wavelength 75-Ohm match line. The values at any frequency differ, but the overall curve falls well within the range of acceptable SWR values. Remember that the matching system does not alter the antenna performance. Given the linear nature of the 1/4 wavelength match line, it does not add to the total feedline length and hence does not add any significant amount to line losses.

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Conclusion to Part 1

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We have changed the fundamental question that we pose to common-feedpoint multi-band quads. Instead of asking "Which kind of feed system is better?" we asked instead "What happens when we use a common feedpoint for a multi-band quad?" That simple change in question creates a large change in our approach to answers. Instead of directly modeling a common-feedpoint multi-band quad--and drawing all manner of conclusions that might raise more questions than they answer--we have spent the entirety of Part 1 laying a foundation for further steps in the exploration.

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The monoband quads that we have examined--and to which we shall return continually--represent precisely designed 2-element quad beams having the widest operating bandwidth in all operating categories consistent with having a free-space design-frequency gain of at least 7 dBi. Each quad places the peak 180-degree front-to-back value and feedpoint resonance on the design frequency. For ease of future references, the design frequencies result in relatively equal front-to-back values at the upper and lower edges of the wider amateur bands.

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As a practical matter, we may use any of the programs or models that encapsulate the equations derived from hand optimizing an entire system of quads in order to select a different design frequency. One reason for doing so might be to ensure having at least 20 dB of front-to-back ratio across a favored segment of one or another amateur band. The 2-element quad lends itself well to such operational choices. Indeed, if one only wishes to operate on a subsection of a wide amateur band, then one might even prefer other designs that sacrifice operating bandwidth for slightly more gain.

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However, our goal is not to make such selections. Instead, I wish to establish a baseline that we can reliably use in assessing what happens when we attempt to construct multi-band quads. One criticism often leveled against multi-band quads--often based on experience with multi-band Yagis--is that the interaction between elements tends to narrow the operating bandwidth of the antenna on at least one of the bands involved. By starting with a wideband design, we may actually be able to evaluate that claim. As well, we may be able to determine whether the reduction--if actual--results from the basic multi-band process or from trying to use a common feedpoint. We may also note that the criticism that we have recorded is very non-specific in terms of naming which performance parameters might be subject to a narrowing bandwidth in a multi-band quad.

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In one sense, then, we have not yet gotten anywhere in our quest to understand the effects of multi-banding quads and feeding the resulting beam. From a different perspective, we have laid a reasonable foundation for actually going some distance to answer our question. If our extended survey of monoband quad performance is the foundation, then the first floor of the multi-band quad edifice involves creating some quads using separate feedlines for each band. In that way, we may proceed with no shape distortion to any element.

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Cubical Quad Notes Vol 1 - 3 available in PDF book format on the Books Page.

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Updated 12-01-2006. © L. B. Cebik, W4RNL. This item appeared in AntenneX, November, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Return to Amateur Radio Page

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Topics: HF Upper, Quad


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Sneaking Up on 2-Element Common-Feed Quads
+ Part 2: Dual Band Quad Beams With Separate Feedpoints

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L. B. Cebik, W4RNL

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In Part 1 of this series, we defined our basic question about common-feedpoint multi-band quads this way:

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+ What happens when we create a multi-band quad and provide it with a common driver feedpoint for all bands? +
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We also set some limits to the exploration so that we might reduce the task to manageable proportions. We set a 2-band limit for the multi-band quads, although we shall examine one violation of the limit in this part. We also set a minimum frequency ratio of 1.3:1 between the bands included in the dual-band quads. (However, looking at adjacent upper HF ham-band combination might itself make a good study for the future.) We also noted the need to proceed in stages, looking at dual-band quads of 2 elements each using separate feedpoints for each band before we move on to joining the feedpoints. Our goal is to isolate insofar as possible whatever phenomena (physical or electrical) may be functions of using a common feedpoint and which may result simply from placing 2-element quad beams concentrically on a single support system.

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A multi-band quad beam is a combination of monoband quad beams taken through successive modifications until arriving at the final form. To simplify the progression, I adopted spider construction for the beams, as shown in Fig. 1. In this part of our study, we shall use models like the one on the left to determine what modifications result from the proximity of the two antennas. The sketch of a side view of the resulting dual-band beam shows the spider arms and the nearly constant angle created by the driver and reflector elements for each band. Of course, for modeling runs and for operation, only one of the feedpoints would be active at any one time. The use of separate feedpoints and separate driver loops also helps assure that the models will automatically meet Average Gain Test (AGT) standards, so long as we segment each side so that the segment junctions for loops on different bands align reasonably well. A low-band to high-band segment/side ratio of 1.3 to 1.5 to 1 will generally satisfy this requirement by yielding AGT values from 0.998 to 1.002.

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To ease the design process, I selected monoband 2-element quads that have the broadest operating characteristics that I could devise. Table 1 summarizes the dimensions of each beam in the upper HF series at the listed design frequencies. The side dimensions actually list half-sides for modeling convenience. A loop circumference is 8 times the listed length. Keep in mind that any revision to a loop dimension that may appear in subsequent tables will result in a revised circumference that differs by 8 times the listed factor from the monoband loop. The element separation is a full measure.

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Part 1 was devoted to examining these antennas, band by band, in sufficient detail to form a sort of data base that we might use as a reference in tracking the changes that occur (if any) when we form dual-band quads. For ready reference, Table 2 summarizes the performance data for the monoband beams.

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When we combine 2 (or more) quad beams concentrically to form a multi-band array, the elements will interact. Even with a frequency separation of at least 1.3:1 and totally separate loops for each band, we find that the active band elements will induce low-level but significant currents in some of the other loops. Fig. 2 shows the current levels for one of the dual-band beams when operated at each of the 2 design frequencies and after undergoing the required modifications. We should attend mostly to the horizontal wires and their current magnitude curves.

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When operated on the lower band, in the left graphic, the larger loops show high current magnitude at the centers of the horizontal wires. However, note that the smaller loops are not inert. The smaller driver shows a relatively low peak current magnitude, but the peak value on the smaller reflector is appreciable. The element is active enough to become part of the overall radiating structure. The other elements require modification to compensate--if possible--for this activity if we are to restore to the degree possible the performance we obtained from the larger 2-element quad in its monoband form.

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On the right, the smaller loops for the higher band are active, as indicated by the high current magnitude peaks at the centers of the horizontal wires. In this case, the larger driver loop shows a noticeable level of activity, enough to again require modification of the smaller loops to restore so far as possible monoband performance.

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Two consequences follow from the interaction of the elements, even when we use separate feedpoints. One result gives us the design strategy for creating multi-band quads. Each modification to any loop will result in slight changes in the current level on other elements, even for the inert bands. Hence, a small change to a higher-band loop may require a change in previously set lower-band loops--and vice versa. The second result involves intra-band adjustments. Very tiny changes or tweaks to either the driver or the reflector of a monoband quad beam may not require an additional adjustment to the other element. However, larger changes in loop size for either the driver or the reflector will normally require changes in the other element to realign the operating properties across a given band. In most (but not quite all) cases of adjustments that we make in the dual-band quads, we shall have to adjust both the driver and the reflector, since a change in one will itself displace the performance curve.

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The final design strategy usually becomes a random set of moves that we might characterize as "a little of this and a little of that," in each case seeing whether the change moves us in the correct direction. In the present situation, we are using a complex set of operating parameters to define the correct direction. We wish to place the peak 180-degree front-to-back ratio on the design frequency and see roughly equal front-to-back values at the band edges. The monoband quad gain curves give us a good idea of what gain values we should see across the band. As well, we wish to set the design-frequency feedpoint impedance close to resonance.

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A portion of our work will be to see what patterns emerge in the required modifications occasioned by creating a dual-band quad with separate feedpoints. If the patterns are consistent in all of the models, then we might ease the design work of future quad builders. Knowing in what directions to modify the quad loops can save a great deal of time and prevent us from messing up the performance values to a degree that forces us to restart the design from scratch.

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A 17-12-Meter 2-Element Quad Array Using Separate Feedpoints

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Our first example of a dual-band quad beam with separate driver loops is for the narrow 17- and 12-meter band. On this band, we may use the band center frequencies for design (18.118 and 24.94 MHz). The frequency ratio is 1.38:1. Moreover, properties do not shift within the band limits by an amount that will give us any challenges for band-edge performance. If we can peak the performance on each band somewhere within the band, the result will generally be satisfactory across the band.

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Table 3 shows the dimensions of the final version of the 17-12-meter combination. If you compare the numbers with the monoband values in Table 1, the changes seem slight. However, multiply the changes by 8 to see the effects on the circumference of each loop in the beam. In all of our beams, we are holding the spacing constant to reduce the number of variables that we must manipulate.

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The 17-meter driver increases its circumference by nearly 1.5", while the reflector for that band decreases by close to 3-3/8". In contrast, the 12-meter driver requires a circumference reduction of about 1-3/4", but the 12-meter reflector requires no change at all. In the presence of high-band elements, the low-band reflector swells, while the low-band driver shrinks. High-band elements either shrink (driver) or remain unchanged (reflector) in the presence of low-band elements. Let's remember these patterns when we look at other frequency combinations for subsequent dual-band quads.

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Table 4 presents the performance data for our new dual-band 17-12 quad beam. Since both bands are narrow, we may dispense with graphed frequency sweeps, since the curves will be nearly straight lines throughout. Compare the performance values with those for the monoband versions in Table 2.

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Perhaps the first notable performance feature is the seeming rise in the average gain on 12 meters. However, also note the 12-meter front-to-back values. The peak front-to-back value has moved upward in the band and is no longer exactly centered. The shift in the front-to-back curve also indicates a shift in the 12-meter gain curve. Since the gain rises as we decrease frequency, the higher gain levels indicate that the gain and front-to-back curves have moved together in the presence of the 17-meter elements. Comparing the 17-meter gain values in the dual-band quad with those of the monoband version, we find much less slippage. However, the front-to-back back value at the high end of the narrow band is quite a bit lower than in the monoband quad.

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Perhaps the most noticeable difference between the monoband and dual-band versions of the quads involves the feedpoint impedance. The band-center impedance of the 17-meter quad drops about 10 Ohms relative to the monoband value, but the range of resistance across the band remains at 15 Ohms. On 12 meters, we find the greatest impedance decrease: about 30 Ohms resistive or a drop of about 24%. The range of variation in resistance across the band drops by a like amount.

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The chief consequence of the changes in feedpoint impedance lies in the ability of 1/4 wavelength 75-Ohm match-lines to effect a close match to a 50-Ohm main feedline. On 17 and even on 12 meters, the mismatch is not significant. However, if the patterns set by this combination of beams hold for the other combinations that cover wider bands, we may see high 50-Ohm SWR values at the band edges on 20, 15, or 10 meters.

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The 17-12-meter dual-band quad forms a good beginning exercise in combining quads. The narrow bandwidth of the two bands allows us to see patterns of physical and performance alteration without introducing the variables that a wider bandwidth might force upon us. Clearly, we cannot simply slap together monoband beams for 17 and 12 and expect peak performance. However, the physical changes to re-center performance are relatively small. As well, although the performance passband shifts slightly on at least one band, we may easily obtain a full-performance dual-band quad. Matching the lower feedpoint impedances appears to present no significant obstacles.

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A 15-10-Meter 2-Element Quad Array Using Separate Feedpoints

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Our second sample dual-band quads involves wider bands: 15 and 10 meters. As well, the monoband beams for these two bands did not use the band centers as the design frequencies, but slightly lower frequencies: 21.19 and 28.4 MHz. As the dimensions in Table 5 show (when compared to the monoband dimensions in Table 1), we obtain the same patterns of element length adjustment in the 15-10 quad as in the 17-12 quad. The circumference of the 15-meter driver increases by a little over 1", while the 15-meter reflector shrinks by nearly 4 inches. The 10-meter driver decreases its circumference by nearly 2", but the reflector remains unchanged. I shall resist any temptation to create a set of equations for these changes, since we have two moderating changes from the 17-12 quad. First, the wire diameter as a fraction of a wavelength changes from one band to the next, since all models use AWG #14 copper wire. Second, the frequency ratio changes from one dual-band quad to the next. The 15-10-meter combination uses a design-frequency ratio of about 1.34:1.

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Relative to the monoband performance values in Table 2, the dual-band performance numbers in Table 6 reveal some patterns that would only be possible to see with the wider-band quads for bands like 15 and 10 meters. Since 15 and 10 meters have different bandwidths, we must be careful of cross-band transfer of changes. However, relative to the band-edge numbers in the monoband tables, the 15-meter performance in the dual-band design shows a much steeper gain decrease and generally lower band-edge front-to-back values. In contrast, again relative to monoband values, the 10-meter section of the dual-band quad shows a shallower gain curve and higher band-edge front-to-back values. The near-resonant (pre-match) impedance values for the two bands are comparable to those obtained with the 17-12 dual quad.

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As a cross-check on the reality of some of these values, Fig. 3 provides sweep data on the 15-meter gain and 180-degree front-to-back values. Note that the peak front-to-back ratio is close to the band center, higher in frequency than the design frequency. The higher gain value at the low end of 15 meters confirms that the overall performance pattern has slipped upwards in frequency, just as we saw in a much smaller way with the 17-meter quad.

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Fig. 4 graphs the resistance, reactance, and 50-Ohm SWR values for the 15-meter section of the dual-band quad. These values presume a 1/4 wavelength 75-Ohm matchline between the loop feedpoint and the 50-Ohm main feedline. If we examine the pre-match impedance values for 15 meters with the monoband values, we find that the total change in resistance across the band is slightly higher in the dual-band quad, but the total change in dual-band 15-meter reactance is considerably smaller. As a result, the 1/4-wavelenghth matching section has little difficulty in effecting a wholly acceptable impedance situation relative to the 50-Ohm main feedline.

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The 10-meter loops form the inner elements of this dual-band quad, and 10 is the widest of the bands in the upper HF amateur region. The inner position of these loops appears to show some advantage in both gain and front-to-back ratio, as suggested by both the tabular values and the sweep graph in Fig. 5. The performance curves have slipped upward in the band relative to monoband values, similarly to the 12-meter values. However, relative to 10-meter monoband values, the gain curve decreases at a slower rate when the loops are part of the 15-10 quad. As well, the average of the band-edge front-to-back ratios is slightly higher than in the monoband version. (When we turn to a 20-15-meter dual-band quad, we shall be very interested in whether the values for 15 meters show any significant difference from the values that we reviewed earlier, once we give the loops for that band an inner position.)

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The match-line values of resistance and reactance on 10 meters do not show the nearly straight lines that we obtained on 15 meters. One factor in the curves shown in Fig. 6 is the very width of the band--over 1.5 times wider than 15 meters. A second and possibly more significant factor is the fact that the inner position of the 10-meter elements results in a significant departure in pre-matched values relative to the monoband version of the antenna. The total range of pre-match resistance is slightly lower than in the monoband quad, but the dual-band pre-match reactance shows a spread that is more than 1.6 times the range that we found in the monoband 10-meter quad. As a consequence, a simple 1/4 wavelength 75-Ohm line achieves an acceptable 50-Ohm SWR at 28.0 MHz with very little to spare.

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Amateur antenna builders appear to have great difficulty in thinking about match-lines in increments other than 1/4 wavelength. Transmission lines effect a continuous impedance transformation along their length (except when perfectly matched to the antenna feedpoint load). Although the transformation calculations are more complex than for resistive loads, there are numerous aids to permit us to find the impedance transformation for virtually any line length. In many cases, we may obtain a flatter SWR curve across a given bandwidth by selecting a line length other than 1/4 wavelength. As noted in Table 6, a 75-Ohm line with an electrical length of about 100" will achieve a 10-meter SWR curve with more equal band-edge values than a 104" (1/4-wavlength) line. (Remember that all line lengths listed in inches are electrical lengths. Multiply these values by the velocity factor of the line used to obtain the required physical lengths of the match line.)

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A 20-15-Meter 2-Element Quad Array Using Separate Feedpoints

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The 20-15-meter dual quad is similar to the 15-10 quad in that both cover wider amateur bands. However, the frequency ratio is higher (1.5:1), while both bands are narrower that the 10-meter band. Nevertheless, most of the patterns developed as potentials in connection with the first two dual-band quads receive confirmation in the new model. As shown by a comparison of the dimensions in Table 7 with those in Table 1, the outer 20-meter reflector increases its circumference by about 1-1/4", while the outer 20-meter driver circumference shrinks by nearly 3-3/4". The inner 15-meter reflector remains unchanged, but the inner 15-meter driver circumference decreases by about 2-1/8". Although wire size as measured in terms of a wavelength and the frequency ratio may play a role in the precise amount of modification required for any element in the dual quad, the positions of the elements determine the general patterns of increasing and decreasing loop size.

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The performance values in Table 8, when compared to the monoband values in Table 2, again show the same patterns as in the 15-10-meter quad. On 20 meters, the dual-band gain curve shows a steeper decline than does the monoband curve. The 20-meter band-edge 180-degree front-to-back values are lower relative to monoband values. However, the inner 15-meter quad shows the opposite trends. Its gain curve is shallower than is the monoband curve, while the dual-band band-edge front-to-back ratios are equal to or higher than the monoband values. For both bands in the dual-band quad, the pre-match feedpoint impedance values track well with the values for the other dual-band quads in terms of the reductions relative to monoband versions of the antennas.

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Like the 15-meter section of the 15-10-meter quad, the 20-meter section of the new model shows the same drift upward in frequency, as shown in Fig. 7. The steeper gain curve of the 20-meter section relative to the monoband model results in the low end showing higher gain and the high end showing lower gain than in the monoband 20-meter antenna. The 20-meter front-to-back curve now peaks at mid-band rather than at the design frequency, with the low end of the band showing a front-to-back ratio under 13 dB.

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Allowing for a small difference in bandwidth as a percentage of the center frequency, the 20-meter dual-quad matched impedance values are remarkably parallel to those of the 15-meter section of the 15-10-meter quad. The 50-Ohm SWR curve is quite tame, since the outer section elements tend to reduce the reactance excursion across the band, relative to the monoband 20-meter quad. At the same time, the resistance range only moves upward slightly. Hence, SWR curve only peaks at 1.43:1 after a 1/4 wavelength 75-Ohm matching line.

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15-meters becomes the inner loop set on this dual-band quad. Not only is the gain curve somewhat shallower than on the monoband version, but as well, the curve is almost half as steep as the 15-meter gain curve on the 15-10-meter dual-band quad. The inner position of 15 meters also results in differences in the band-edge front-to-back ratio values. They are slightly better than the monoband values, but 4-5-dB better than the values for 15-meters when that band occupies the outer position in a dual-band situation. Compare the curves in Fig. 9 with those of Fig. 5, along with the corresponding values in the relevant tables. Of course, we see the upward overall frequency shift in both performance categories.

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With respect to impedance values, the inner position loses its advantage due to the greater drop in the resonant pre-match feedpoint impedance relative to a monoband quad. However, the fact that 15-meters is only 60% as wide as the first MHz of 10 meters allows the use of a standard 1/4 wavelength 75-Ohm matching line with good results. The matched resistance and reactance curves are relatively flat, despite the 50-Ohm excursion in the pre-matched reactance value. As a result, the 15-meter 50-Ohm SWR curve is almost identical to the SWR curve for 20 meters in this dual-band quad.

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The three dual-band quads that meet the basic requirements for this exploration all show the same patterns in physical and performance modifications relative to their monoband origins. The size of outer reflector increases, while outer drivers diminish. Inner reflectors require no change, whereas inner drivers shrink. The resulting performance patterns tend to shift gain and front-to-back curves slightly upward in the band, while allowing the pre-match feedpoint impedances to be near resonance on the original design frequencies. Both feedpoint impedances decrease, the outer by about 10 Ohms, the inner by about 25 to 30 Ohms. For the antennas derived from the original monoband designs, both bands of the dual-band versions allow use of a standard 1/4 wavelength 75-Ohm line section for matching. However, for some bands, line length adjustment may yield a better match across a given band, especially for the inner quad of the pair.

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The slight upward frequency shift in the gain and front-to-back curves may seem troublesome to someone seeking a perfect reproduction of the monoband curves. Further tweaking might indeed be possible. However, in most cases, I limited loop dimension changes to 0.1" increments, meaning a 0.8" inch change in the overall loop circumference. Anything more finicky would likely be impossible to replicate in most shops, and construction variables will likely override even the level of model precision that I used. Nevertheless, one may be able to move the gain and front-to-back curves downward in frequency slightly by making loop adjustments in 0.01" increments for each half side.

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A 20-15-10-Meter 2-Element Quad Array Using Separate Feedpoints

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The terms of this exercise permit only 1 possible 3-band quad. Although 2-band quads are the main focus of the investigation, all of the basic materials were available to design the 3-band antenna. As well, a 3-band quad would answer--at least provisionally, since we would make only one model--some lingering questions about the 2-band versions. The physical and performance dimensions and values show very distinct patterns depending upon whether the loops for a given band are inner or outer quads. So one might relevantly ask the following questions. 1. Would the outer band loops remain at the same dimensions and with the same performance if we place 2 bands of quad inside? 2. Would the inner band loops retain their dimensions if we add 2 bands of quads outside them? 3. What happens to the dimensions and performance of the middle loops now that they are no longer either inner or outer loops? To obtain a first order set of answers, we must violate one of the guiding restraints. We must use a frequency ratio of 2:1 between the outer quad (20 meters) and the inner quad (10 meters). In advance, we might expect that the 20-meter loop might exert more influence on 10-meter dimensions and performance than the other way around. The 20-meter elements will be close to resonance as 2 wavelength loops when we activate the 10-meter quad.

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The tri-band dimensions appear in Table 9 for comparison with several other dimensional tables in this part of our exploration. The 20-meter dimensions are exactly the same as they were in the dual-band quad using 20 meters as the outer band. The 10-meter reflector is the innermost element of that type and has the same dimensions as both the monoband and the dual-band quads. However, the 10-meter driver undergoes further shrinkage from the monoband 10-meter driver and is now shorter even than the driver for the same band as the inner loop in a dual-band quad. It is quite likely that the further reduction in driver length is a function of two inseparable factors: the presence of the 20-meter driver and the required dimensional change in the 15-meter driver for its middle position in the array.

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On 15 meters, we encounter the most interesting dimensions. The driver is smaller than when it is the outer loop on a dual-band quad but larger than when it is the inner loop. Conversely, the reflector is longer than when it is an outer loop but shorter than when it is an inner loop.

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Table 10 provides a summary view of the performance of the tri-band quad. I shall reserve commentary on the band-by-band performance until we can survey the sweep graphs for each band. However, the pre-match impedances deserve special note. The 20-meter near-resonant impedance is the same as it was when 20-meters served as the outer quad on a 2-band antenna. The 15-meter pre-match impedance at the design frequency is closely comparable with the impedances of all of the inner drivers for the 2-band quads. On 10 meters, the pre-match impedance drops to 92 Ohms, partly due to the further shortening of that element and--most likely--partly due to interactions of the 10-meter elements with the elements of both lower bands.

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The 20-meter performance curves in Fig. 11 are almost indistinguishable from those of the 20 meter elements in the 20-15-meter dual-band quad. The curves show the characteristic slight up-shift in frequency. Even the band-edge front-to-back ratio values are similar to those in the 2-band antenna.

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Equally similar to the curves for 20 meters in the 2-band quad are the tri-band 20 meter matched impedance curves in Fig. 12. The pre-matched resonant impedance on the design frequency is virtually identical to the value for the 2-band model, and the resistance and reactance changes across the band are within a few Ohms of those of the 2-band model. As a consequence, a 1/4 wavelength 75-Ohm matching line provides a very satisfactory SWR curve with a maximum value of 1.42:1.

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Since the 15-meter elements of the tri-band, separate-feed quad differ from both the monoband version and from the 2-band versions using either an inner or an outer position, we expect at least some difference in the performance curves. The rate of change in gain across the 15-meter band is one measure of similarity and difference. In the tri-band quad, the rate is greater than in the monoband 15 meter quad and also greater than when the 15-meter elements form the inner loops of a 2-band quad. However, the rate is lower than when the 15-meter loops form the outer elements of a 2-band antenna. See Fig. 13. Corresponding to these differences--which are small but distinct--are differences in the band-edge values of the 180-degree front-to-back ratio. In the tri-band version, they are lower than in the monoband version and lower than when 15 meters forms the inner elements of a 2-band quad. However, the values are higher than those for 15 meters as the outer quad in a 2-band antenna. Nevertheless, in both categories of performance, the central position of the elements allows us to return the curves to their monoband position, that is, with the front-to-back peak at or very near to the design frequency.

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Despite the normalcy of the gain and front-to-back curves, the pre-matched impedance of the 15-meter band most resembles values that we obtain for the inner quad of a 2-band model, as shown in Fig. 14. As a result, the standard 1/4 wavelength 75-Ohm matchline yields a 50-Ohm SWR curve that is higher a the low end of the band. The curve is similar to the one for the 15-meter section of the 20-15 2-band quad, but with a slightly higher value at the low end of the band and a slightly lower value at the high end of te band. An adjustment to the matchline length would equalize the band edge values and reduce the maximum value below 1.5:1.

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The 10-meter elements form the inner elements of the tri-band quad. The inner elements tend to show the lower rate of gain change in 2-band quads, and this trend continues in the tri-band model. The rate of gain change is lower than in both other models using 10-meter elements. The band-edge front-to-back ratio values match those of the 15-10 meter quad and are higher than the values shown by the monoband model. The overall front-to-back curve has a somewhat shallow appearance, especially when compared to the monoband version. The peak front-to-back ratio occurs on about 28.44 MHz, but it scarcely exceeds 30 dB, compared to a value of nearly 60 dB in the monoband version. (Of course, in a practical quad, the exceptionally sharp and narrow-band peak might not be obtained, even on a monoband quad.)

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The pre-matched impedance of the 10-meter elements starts with a low resonant value (about 92 Ohms) and also shows rather wide excursions of both resistance and reactance across the wide 10-meter band. A 75-Ohm matching line is not ideal for the situation, although using the prescribed length shown in Table 10, the 50-Ohm impedance remains below 1.9:1 at both ends of the passband.

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The most usual strategy employed to improve the 10-meter SWR situation is to revise the 10-meter elements so that they provide a more acceptable--higher--resonant feedpoint impedance. However, the gain or the front-to-back performance may suffer as a result of these changes. Alternatively, one might lower the design frequency and limit the SWR passband to an upper frequency of about 28.8 MHz.

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Despite the strain of obtaining an adequate SWR spread across the 10-meter band, the tri-band quad provides overall performance that is fully adequate to most needs on all 3 bands. Separate drivers and match-lines for each band allow for a remote switching system. As well, one may make fine (in contrast to basic) adjustments to loop lengths without significant change on the other bands. In the end, the performance of the tri-band quad is similar to the performance of the 2-band quads and of the monoband quads.

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Conclusion to Part 2

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In this part of our exploration, we have examined the physical and performance changes occasioned by combining monoband beams into several 2-band beams and one 3-band array, using separate drivers for each included band. Throughout, we remained true to the original monoband designs by retaining the element spacing. Thus, each spider quad shows almost identical angles between the driver and reflector elements for each band. The angles are close enough to each other so that non-conductive spacer rods can easily allow a builder to fix the spacing. However, in a quad (or other parasitic 2-element beam), the spacing tends to be less sensitive to change than the element lengths.

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The exercise has shown us what physical modifications occur as a result of simple element interaction between quads on the same support system when the frequency ratio between quads is between 1.3:1 and 1.5:1. This step has been necessary in order for us to be able to separate alterations of quad dimensions or of performance due to the use of a common feedpoint from alterations that are basic to placing 2 quads on the same arms.

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In the final part of this exploration, we shall deal directly with 2-band quads using a common feedpoint. We shall encounter only 3 new models: 17-12 meters, 15-10 meters, and 20-15 meters. For reasons that will become clear in our examination of these models, we shall set aside the tri-band quad. However, in its place are a series of fundamental modeling questions. Therefore, we shall not begin the last part by looking at 2-band quad performance. Instead, our first question will involve the proper way to model a common-feedpoint quad driver set.

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Updated 01-01-2007. © L. B. Cebik, W4RNL. This item appeared in AntenneX, November, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 3

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Return to Amateur Radio Page

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Topics: HF Upper, Quad


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Sneaking Up on 2-Element Common-Feed Quads
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L. B. Cebik, W4RNL

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Finally. . .we are ready to tackle dual-band quad beams with common feedpoints. Like the dual band beams in Part 2 that used separate feedpoints, our new beams will rest ultimately on the series of monoband beam designs that we examined in Part 1. They will also adhere to the basic limits surrounding the study by using no more than 2 bands per beam where the bands have at least a 1.3:1 frequency ratio. Hence, our new combination beams will include versions for 17 and 12 meters, for 15 and 10 meters, and for 20 and 15 meters.

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Fig. 1 provides a generalized sketch of the physical elements of the new set of beams. Like the versions using separate feedpoints, the new combinations will employ spider construction in order to maintain the spacing on each band used by the monoband beams. The angle between forward and rearward support arms is an average of the angles calculated from the collection of monoband quads. As noted in Part 2, very small variations in spacing make very little difference to performance compared to equally small variations in the element lengths.

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Perhaps the one item in Fig. 1 that requires further comment is the arrangement of the feedpoint. For each combination beam, the inner or higher frequency driver will use a square loop. All loop-shape distortion will involve the driver for the lower frequency of the pair. The design decision rests on a number of factors, not the least of which is relative simplicity compared to finding an intermediate position for the feedpoint that distorts both driver loops equally. In addition, experience suggests (but does not prove) that driver distortion has fewer negative effects on the lower frequency driver than on the inner or higher frequency driver.

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To assess the quads that use a common feedpoint, we shall need some data at hand for reference. Table 1 repeats the dimensions used on the same set of quads when using separate feedpoints. To the information presented in Part 2, I have added the circumference of the driver for each lower frequency quad.

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All common-feed quad combinations sought to achieve the same goal used for the quads with separate feedpoints: restoration to the fullest extent possible of the performance of the monoband quads on which the designs rest. For immediate comparison of the physical results, Table 2 provides the resulting dimensions for the common-feedpoint versions.

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To obtain the circumference of any loop, we normally multiply the listed half-side length by 8. However, the models using a common feedpoint require us to add to the three linear sides the sloping and center sections of wire that creates the feedpoint. Hence, the circumference forms an odd value relative to the half-side lengths.

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Certain general patterns show up in the physical dimensions. For each combination, the inner reflector for the higher-frequency band remains either fully or close to unchanged. However, every inner driver shows increased length relative to the inner drivers for the quads using separate feedpoints. Likewise, the outer reflectors for the lower frequency show virtually no change in length. As well, the circumferences of the outer drivers for the common-feedpoint quads are very close in overall length to the circumferences of the outer drivers for the versions using separate feedpoints. The inner drivers undergo the most extreme change of any element when converting from separate feedpoints to a common feedpoint, and the amount of change is significant. It ranges from a 6" to a 12" overall circumference increase, depending on the models involved. The lower band element exerts much more influence over the higher band driver, despite (or perhaps because of) the distortion in the lower-band driver shape. At the same time, both types of dual band quads use independent loops for reflector elements. In general, the interactions between the reflector elements do not change significantly when moving from separately fed drivers to drivers with a common feedpoint. You may wish to consult Part 1 for the dimensions of the original monoband quads to determine the total amount of variation, although changes in that variation apply mostly to the inner or higher-frequency driver elements.

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We shall also need to compare the performance values for the common-feedpoint quads to corresponding figures for versions with separate feedpoints. Table 3 collects the performance data for all of the 2-band quads into one table for convenient reference. We shall have occasion to refer to this table as we encounter each of the dual-band common-feedpoint quad assemblies.

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The data that we shall develop on the new set of quads comes from NEC models. Although I habitually use NEC-4, all of the quad designs that we have so far explored work well with NEC-2. Nothing in the designs challenges NEC limitations. Hence, each quad so far has shown an Average Gain Test (AGT) score between 0.998 and 1.002, indicating a high reliability. I have also subjected the models to convergence tests. These tests altered the segmentation of each wire uniformly. For dual-band quads, I varied both the inner and the outer wire segmentation so as to maintain the same ratio of segments in corresponding wires relative to inner and outer loops. The goal was always to maintain to the degree possible an alignment between segment junctions. The results showed excellent convergence with relatively modest segmentation. Both the AGT and convergence tests are necessary but not sufficient conditions of model adequacy, but long use of wire quad models has resulted in relatively high reliability. (The reliability of the models presumes that physical implementations do not use construction methods that introduce corner fastening loops and other features that might detune an element relative to its model as a clean square.)

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Given the high reliability of the models that we have used in Parts 1 and 2 of this exploration, we hope to achieve similar reliability for the common-feedpoint quads. However, the modeling itself presents a challenge.

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Modeling Common-Feedpoint Quads

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The only critical region of a dual-band quad model using a common feedpoint is the set of wires coming together at the feedpoint wire. The most common method used for developing the model appears in the upper section of Fig. 2.

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The inner driver "bottom" wire consists of 3 modeled wires. The center wire consists of 3 segments, with the source or excitation placed on the center segment. The adjacent segments are the same lengths as the source segment, providing for equal currents on each side of the source segment. At the ends of this wire, we connect the remaining lengths of the inner driver wire. We segment each of these wires so that the segment lengths are as close as feasible to the segment lengths on the center wire.

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The ends of the center wire also form junctions with the wires for the outer driver. We segment each of these added wires so that the segment lengths are as close as feasible to the lengths of segments in the center wire and in the inner driver wires. For many applications, this technique suffices to produce highly accurate models. The current division between the 2 driver loops does not occur until at least one segment away from the source segment.

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In the case of the quad loops, the inner and outer driver wires form an angle. The angle appears to be fairly wide. In fact, if we were creating a a set of radials symmetrically arranged around a center junction, we might use much smaller angles and achieve high accuracy in the results from either NEC-2 or NEC-4. However, in the present situation, NEC-2 and NEC-4 shows considerable differences in the results that they report from a single quad model. Given a test model for 17 and 12 meters using this modeling scheme, NEC-2 reports a free-space gain at 18.118 MHz of 7.88 dBi and 7.74 dBi at 24.94 MHz. Changing the core to NEC-4 yielded gain reports of 7.19 and 7.06 dBi for the two frequencies. If we check the AGT values, NEC 2 produces values of 1.215 on 17 and 1.212 on 12. These values indicate that NEC-2 gain reports are about 0.85-dB too high. In the same conditions, NEC-4 produces AGT values of 1.037 and 1.038 for the two bands, still overestimating gain by about 0.16 dB. In addition to mis-reporting the gain, the source resistance will also be in error. To correct the source impedance, multiply the reported value by the basic AGT score.

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The initial models of common-feedpoint quads present two challenges. First, we should be able to develop models with a more ideal AGT score, a value much close to 1.0 so that the gain reports require no adjustment. Second, the models should yield the same results under NEC-2 and NEC-4. Some years back, I worked out an alternative scheme for modeling feedpoints that essentially are in parallel with each other. The technique is applicable to common-feedpoint quads, as shown in the lower part of Fig. 2. We begin be retaining the structure of the inner driver wire, but we shall make no wire connections to it from the lower frequency or outer driver. Instead, we shall create parallel 3-segment wires, one for each driver. The sloping wires of the outer driver will connect to their own center wire. We should use enough spacing between the two center wires so that they do not interact significantly. We shall be able to tell the minimum correct spacing from AGT scores for the final model. We can begin with relatively close spacing and increase the spacing until the AGT values approaches 1.0 as closely as we need for a given modeling exercise.

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The next step is to place a source or excitation on the center segment of one and only one of the center wires. Between the source segment and the corresponding center segment on the other center wire, create a transmission line with the NEC TL facility or command. Give the line a characteristic impedance somewhere in the ball park of the anticipated impedance values, although the actual value will not be at all critical. The key to establishing a parallel connection is to assign the transmission line as short a length as a given implementation of NEC will permit. Many programs permit lengths as short as 1e-10 meters if using the TL command directly. You may use the same specification in whatever unit may be in use, if the interface translates those units into meters internally. Some programs have certain minimum values for some or all length specifications. Whatever the lower limit, use it. The goal is to set up a line length that effects virtually no impedance transformation between one end and the other end of the line. Remember that the line length that you specify is independent of the physical distance between the center segments that you set up when establishing the two center wires.

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Using this modeling system, both NEC-2 and NEC-4 return the same gain and impedance reports, with AGT scores very close to 1.0, for the test quad combination for 17 and 12 meters. We shall examine that model's performance in more detail shortly. For the moment, the development of a relatively reliable method of modeling common-feedpoint quads is our concern.

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Despite the nearly ideal AGT score for the revised method of modeling the quads, we cannot claim that the model is as reliable as the monoband models or the dual-band models with separate feedpoints. In this instance, reliability refers to our ability to transfer the results to a physical implementation of the quad designs. The model does not correspond perfectly to the geometry of a typical common-feedpoint as constructed for use. Such common feedpoints normally consist of a center insulator where the wires join. The distance between the junctions of the two drivers is likely to be smaller than the length of the 3 segment center wires unless we use a very high number of segments per wavelength. Therefore, any physical implementation of a common-feedpoint quad should take the modeled data as a starting point for final field measurements and adjustments. However, the revised modeling system should come a good bit closer to field measurements than the initial modeling system.

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A 17-12-Meter 2-Element Quad Array Using A Common Feedpoint

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Because it involves a pair of narrow bands, the common-feedpoint 17-12-meter quad is the natural first experiment. The dimensions appear in Table 2. More pertinent to our interests here is Table 4, which provides the performance data. Compare the figures to those in Table 3 for the 17-12-meter quad using separate feeders.

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Compared to the separate feed model, the common feed 17-12-meter quad front-to-back curves appear to show an additional upward frequency shift. The 17-meter quad appears to reach peak value at the upper end of the band, while the 12-meter peak lies beyond the upper band limit. The gain levels are modest but well within expectations for a 2-element quad. Although the performance does not achieve the full monoband potential, the numbers and the patterns are fully appropriate for these bands. Fig. 3 provides a gallery of free-space E-plane patterns for both bands to confirm this fact.

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The impedance behavior of the common-feed dual band quad holds a surprise: the mid-band feedpoint impedances are very similar for the two bands. The impedances specifically leave remnant reactances due to an interesting potential for the array. A single 75-Ohm match-line can serve both bands in providing a satisfactory match to a 50-Ohm main feedline. The model calls for a 145" (electrical) length, although in practice, a builder may have to experiment with the length that yields the best 50-Ohm SWR curves on both bands. The modeled line is about 0.22 wavelength on 17 meters and about 0.31 wavelength on 12 meters. The matching line is an abbreviated form of series matching, for which Regier's work provides the most general solutions. The worst-case 50-Ohm SWR is 1.32:1, a value that meets the most stringent SWR requirements on the amateur bands.

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The ability to have a common feedpoint and a single match-line--along with the fully adequate performance on both bands--makes the dual-band 17-12-meter quad a prime candidate for actual construction and use. However, remember that the common-feed models require slight distortions of the physical geometry in order to meet modeling constraints. Therefore, one cannot approach such a project is if the model formed a final template.

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A 15-10-Meter 2-Element Quad Array Using A Common Feedpoint

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The proper assessment the band-edge performance of the common-feedpoint quad requires that we examine models designed to cover wider bands. The 15-10-meter common-feedpoint quad provides one of two tests of the performance curves. Table 5 gives us the summary data on the model's performance on both bands for comparison with data for the separate feedpoint models in Table 3.

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On 15 meters, the rate of gain decrease across the band is identical to the rate for the separate feed model. Fig. 4 shows the gain and front-top-back curves for 15 meters. Relative to the separate-feedpoint model, the common-feedpoint version appears to show an added shift of the 180-degree front-to-back curve upward in the band, even though the gain curves for the two types of quads are very similar. The peak front-to-back value occurs just above the mid-band frequency.

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Fig. 5 provides a gallery of free-space E-plane patterns for both the separate- and the common-feedpoint models on 15 meters. The clearest evidence of front-to-back upward frequency shift is the set of rear lobes that occur at 21 MHz. The common-feedpoint lobes are larger in all ways than those for the separate-feedpoint quad.

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In Fig. 6, we see the post-match impedance curves for the 15 meter portion of the quad. The 110" (electrical length) 75-Ohm match-line is about 0.20 wavelength at the 15-meter design frequency. The result is an SWR curve that reaches its minimum value very low in the band. However, the upper band limit shows a maximum value that is under 1.7:1. Although we might change the length for a better match on 15, we have selected the length that yields the best compromise values for both 15 and 10 meters. The technique may not be ideal for the widest amateur upper-HF bands, but it is serviceable.

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As the widest of the bands within our survey, the first MHz of 10 meters presents the greatest challenge to the common-feedpoint dual-band quad. The rate of gain decrease across the 10-meter band is actually lower than it is using separate feedpoints. The curves appear in Fig. 7. Once more, the common-feedpoint quad shows additional upward frequency shifting of the front-to-back curve relative to the separate-feedpoint model. The peak values of the 180-degree front-to-back ratio occurs at about 28.55 MHz.

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The upward frequency drift of the performance curves shows itself most vividly in a comparison of the 28-MHz free-space E-plane patterns for both the separate- and the common-feedpoint models in Fig. 8. The band-edge front-to-back value of the common-feedpoint model is under 13 dB, and the pattern shows significant devolution compared to the 28-MHz pattern for the separate-feedpoint quad. In contrast, at 29 MHz, the separate-feedpoint model shows no signs of a 180-degree null, but the common-feedpoint model has a null that approaches 3 dB.

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Although the pre-match feedpoint impedance values of both 15 and 10 meters are similar in value, the post-match impedances show interesting differences. The post-match impedance performance curves appear in Fig. 9. At 28.4 MHz, the 110" 75-Ohm match-line is about 0.26 wavelength. Once more the minimum 50-Ohm SWR occurs quite low in the band, with 29 MHz showing a value of 1.91:1--just barely within the usual amateur 2:1 standard. The 3.5% bandwidth of 10 meters provides a considerable challenge for a compromise match-line length. However, in principle, the system does work. The quad design is subject to enough variables in the translation into a physical antenna that one could not certify the system with out extensive field adjustment of the element lengths and the line length.

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The 15-10-meter dual-band common-feed quad has its main function as a study model for observing the performance of the antenna under wide-band conditions. 10 meters provides the major challenge for the performance of the inner quad loops. There are potential outer band loops that must cover a wider bandwidth than the 2.1% offered by 15 meters.

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A 20-15-Meter 2-Element Quad Array Using A Common Feedpoint

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To confirm the general tendencies in wide-band performance of dual-band common-feedpoint quads, we may model a version for 20 and 15 meters. This combination places the challenge for coverage on 20 meters, the outer quad in the pair. As well, the frequency ratio is higher for this pair of quads: 1.5:1. Table 6 provides the summary data about the performance of the pair.

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As shown in Fig. 10, the rate of gain decrease across 20 meters is slightly lower for the common-feedpoint quad than for the version using separate feedpoints. However, the front-to-back curve slips further upward in frequency so that the peak value occurs at about 14.25 MHz. This slippage results in a continuing trend toward unequal front-to-back ratios at the band edges relative to the monoband model on which both dual-band quad beams rest.

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The gallery of free-space E-plane patterns in Fig. 11 shows the degradation of the common-feedpoint rear lobe structure at the low end of 20 meters. The 180-degree front-to-back ratio has fallen below 10 dB, a value that is considered low even for a 2-element driver-reflector Yagi. It is not clear whether one may further refine the design to move the front-to-back curve lower in the band and still retain adequate forward gain and a usable feedpoint impedance. Remember that among the 2-element quad performance characteristics, the front-to-back ratio undergoes the greatest change over any bandwidth. Normally, one can more easily obtain a feedpoint impedance curve meeting any of the normal limits than one can obtain a broad front-to-back curve that meets any of the usual standards.

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The pre-match feedpoint impedance values on 20 meters (Table 6) are comparable to those for any of the other bands, with allowances for the bandwidth when comparing values. A 170" 75-Ohm match-line is about 0.20 wavelength at 14.14 MHz. It provides an adequate set of impedances for a 50-Ohm feedline, although the upper band edge shows an SWR of 1.8:1. As in the case of the 15-10-meter combination, the 20-meter minimum SWR value occurs quite low in the band.

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The rate of gain decline on 15 meters in the present combination is lower than when we use separate feedpoints. Although the gain at the low end of 15 meters--as shown in Fig. 13--is lower than for the separate feedpoint version, the gain values at the upper end of the band are nearly the same. The front-to-back ratio curve shows its anticipated upward shift. The separate-feedpoint version of the array showed a peak front-to-back value near mid-band. With a common feedpoint, the peak value occurs at about 21.3 MHz. As well, the peak value does not reach 30 dB. Obtaining very high and narrow bandwidth values of front-to-back ratio is not operationally very significant. However, it is a measure of the degree to which multi-band and common-feedpoint interactions among wires decrease performance peaks.

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The gallery of free-space E-plane patterns in Fig. 14 provides a glimpse at the types of azimuth patterns that one might obtain over ground. Our interest is in comparing the patterns for separate feedpoints with those for a common feedpoint. As in the other wide-band dual-band quads in this part, the pattern at the lower edge of the band (here, 15 meters) shows the greatest change of shape relative to patterns for the monoband and separate-feedpoint 15-meter beams. The front-to-back ratio at 21 MHz is down by about 3 dB relative to the separate feedpoint model. Overall, even though the common-feedpoint quad uses a design frequency of 21.19 MHz, performance appears to be best in the SSB portion of the 15-meter band.

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The pre-match impedance spread resembles the curves for all of the other bands. The total change in resistance is lower than on 20 meters, while the total change in reactance is about the same. However, on 20 meters, we needed a 170" 75-Ohm line to achieve a manageable 50-Ohm SWR curve across that band. This same line length on 15 meters is about 0.31 wavelength, somewhat longer than ideal for use as a single match-line for a common-feedpoint quad. Nevertheless, as shown in Fig. 15, the SWR curve fits, with a maximum value of 1.85:1. The peak value occurs at the low end of the band, and the 50-Ohm SWR never drops below about 1.2:1. Because 20 and 15 meters show peak SWR values at opposite ends of the band, any physical implementation of such a system is likely to require extensive field adjust to work.

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Like the 15-10-meter combination, the 20-15-meter common-feedpoint quad model is most useful in displaying the wide-band behavior of this type of quad. Perhaps the 17-12-meter version is the one most apt for construction, especially since coverage of those bands very often is an afterthought and uses beams of lesser capability than antennas for 20, 15, and 10 meters.

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Conclusion to the Series

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Our efforts to model dual-band common-feedpoint quads have produced a number of results, most of which may be smaller in scope than one might have imagined prior to the step-by-step process that we have gone through to arrive at these models. As we did in Part 2, we retained the spacing of the basic monoband quads and used spider construction so that the angle formed between the reflectors and drivers in a multiband quad remained constant. In all cases, we simply adjusted element lengths to obtain the closest approach possible to monoband performance. Throughout, we used quads with a frequency ratio of at least 1.3:1.

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Part 2 showed that the largest physical adjustments to the dimensions of monoband quads occur by virtue of simple proximity of one quad to the next. Despite the use of separate drivers for each of the 2 bands in each assembly, we had to change some of the element lengths to restore performance. The three dual-band quads that meet the basic requirements for this exploration all show the same patterns in physical and performance modifications relative to their monoband origins. The size of outer reflector increases, while outer drivers diminish. Inner reflectors require no change, whereas inner drivers shrink. The resulting performance patterns tend to shift gain and front-to-back curves slightly upward in the band, while allowing the pre-match feedpoint impedances to be near resonance on the original design frequencies. Both feedpoint impedances decrease, the outer by about 10 Ohms, the inner by about 25 to 30 Ohms.

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The modification of these models for a common feedpoint required only small dimensional changes. For each combination, the inner reflector for the higher-frequency band remains either fully or close to unchanged. However, every inner driver shows increased length relative to the inner drivers for the quads using separate feedpoints. Likewise, the outer reflectors for the lower frequency show virtually no change in length. As well, the circumferences of the outer drivers for the common-feedpoint quads are very close in overall length to the circumferences of the outer drivers for the versions using separate feedpoints. The inner drivers undergo the most extreme change of any element when converting from separate feedpoints to a common feedpoint, and the amount of change is significant. It ranges from a 6" to a 12" overall circumference increase, depending on the models involved. The lower band element exerts much more influence over the higher band driver, despite (or perhaps because of) the distortion in the lower-band driver shape. At the same time, both types of dual band quads use independent loops for reflector elements. In general, the interactions between the reflector elements do not change significantly when moving from separately fed drivers to drivers with a common feedpoint.

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Adding a common feedpoint for a dual-band quad does affect the performance to some degree. The upward shift in the performance curves for gain and the front-to-back ratio continues the progression that we first saw in 2-band quads with separate feedpoints. One result on wider amateur bands, such as 20, 15, and 10 meters, is a degradation of the rear lobe confinement at the low end of each band. In contrast, the near resonant feedpoint impedance at the design frequencies turned out to be very nearly the same for both bands of operation. The value of the resistive component is the value associated with the outer quad of separate-feedpoint dual-band quads. Although interesting, this result has limited utility if the impedance requires transformation in order to match the characteristic impedance of the main feedline. In the course of developing the common-feedpoint models, we saw that a single match-line length might serve 2 bands manageably, if not ideally.

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The single match-line for a 50-Ohm main feedline is not a necessary condition of common-feedpoint quad operation. It is possible to feed the quads with a balanced, shielded parallel line composed of series-connected lengths of 50-Ohm cable. As the SWR curves for the two wide-band models show in Fig. 16, only 10 meters is wide enough to press the limits of the curve, even though the design frequency impedance is close to 120 Ohms. The direct feed system has the advantage of being applicable to common-feed multi-band quads covering 3 or more bands, so long as the impedance curves on each band are similar to those shown for the dual-band models.

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The models that we chose as our baseline are not necessarily the best designs to implement for a multi-band quad using either separate or common feedpoints. I selected them because they presented the widest operating bandwidth of any 2-element quads using common wire elements. They offered us the best chance of seeing the dimension and performance changes that 2-band operation might create, while still maintaining recognizable performance curves. Along the way, the feedpoint impedance was not the limiting factor. The front-to-back ratio remains the quad's most changeable parameter as we scan any of the wider upper-HF amateur bands. If we wish full band coverage of 20, 15, or 10 meters, then we must decide if a relatively low front-to-back ratio at one band edge or the other is a satisfactory condition. If we only wish to cover a portion of these wider bands, then the 2-element quad becomes competitive with a 3-element short boom monoband Yagi and highly competitive with multi-band Yagis using considerably longer booms.

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Updated 02-01-2007. © L. B. Cebik, W4RNL. This item appeared in AntenneX, November, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Upper, Quad


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Notes on the Modified Half-Loop

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Notes on the Modified Half-Loop

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This page exists to include the PDF in the topic index

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Topics: HF Lower, Half Square


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Some Notes on Long-Boom Quads

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L. B. Cebik, W4RNL

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In the course of examining existing designs for long-boom, high-gain monoband quad beams, I have been struck but the "hit or miss" nature of the designs. Although popular since the 1960s, quad design appears to have missed out on anything systematic. The absence of systematic design principles does not apply to the basic nature of loops, which are well covered in books by Haviland and Orr. However, the addition of parasitic elements to achieve gain, front-to-back, and operating bandwidth seems almost devoid of adequate study and full treatment.

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As a step in the direction of such investigations, these notes offer some thoughts on modeling studies into parasitic quad beams. More precisely, they offer three (of many possible) approaches to the design of long boom quad beams. What the designs reveal may be useful to others in further work.

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The baseline for each of the approaches was to produce a quad beam model that yielded 11 dBi free-space gain and about 20 dB or more of 180-degree front-to-back ratio across the operating bandwidth. The operating bandwidth itself would eventually become a consideration, but was not among initial concerns. All antennas were designed and modeled for 20 meters, with a 14.175 MHz design frequency.

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I selected the gain level based on the popular notion that a quad loop can achieve about 1.8 to 1.9 dB more gain than an equivalent dipole. This notion has given rise to the presumption that a quad beam has about the same gain advantage over a Yagi with the same number of elements and a similar boom length. However, the presumption does not work out in reality, largely because quad beams are constructed using thin wire elements in contrast to the fatter tubing used by typical Yagis. Because the thin wire results in lower levels of inter-element coupling, the quad's gain advantage is seriously reduced and is often completely negated in large arrays. Some of the gain advantage can be restored by the use of fatter elements, which in models can be single fat wire elements or multi-wire simulated fat elements. The restoration of gain through the use of dual-wire elements, despite the higher material losses of the dual thin wires, tends to demonstrate the relative dominance of inter-element coupling over wire loss in establishing the gain of a large array. For this reason, the models we shall discuss use a variety of wire sizes, ranging from 1/10 to 1/2 inch.

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The selection of the 20-dB front-to-back criterion rests on the ability of monoband Yagis to achieve this figure routinely across the designed operating passband. Equivalent performance should be possible from a quad if it is to justify itself as a competitor for the Yagi. (This considerations is apart from operational reports that quads have an advantage at band openings and closings. Models cannot simulate the propagation conditions that would either confirm of disconfirm such reports.)

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The approaches taken to designing this collection of long-boom quads are varied. The first design is a direct adaptation of parasitic element placement taken from Yagi design. The second is a wide-band variation of Yagi design sometimes called optimized wide-band arrays (OWA). The third approach uses wide-spaced principles in which elements use approximately the same spacing throughout the design.

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1. The Standard Yagi Approach

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The first approach to quad designs uses standard Yagi spacing as a basis for quad design, with element size and spacing optimized after initial placement. I used the approach to design a 3-element quad with excellent performance over its passband. However, several peculiarities--relative to a comparison Yagi--appeared in the results. First, the element spacing was somewhat larger than for the Yagi, despite elements of the same diameter. Second, the operating bandwidth for both the front-to-back ratio and the SWR were considerably narrower than for the Yagi. Third, instead of the traditional 50 to 100 Ohm quad feedpoint impedance, the 3-element quad showed a feedpoint impedance close to 25 Ohms. All of these conditions and limitations also showed up on a longer version of the antenna.

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For a Yagi model, I took a 3-element 20-meter design developed by K6STI. I enlarged it to 5 elements by adding 2 directors. It is equivalent to a 48' boom length Yagi that would provide about 10.1 dBi free space gain across 20 meters with good front-to-back figures. After optimizing the 0.1" diameter elements and spacing them to achieve 11 dBi free-space gain and the requisite front-to-back ratio, the boom length increased to 50.36'. Fig. 1 presents a side view of the antenna to show the relative element spacing.

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The following table provides dimensions for the antenna (in feet).

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Element           Length/Side       Circumference     Distance from Reflector
+Reflector         18.11             72.45             -----
+Driver            17.77             71.06             11.25
+Director 1        17.38             69.54             22.62
+Director 2        17.38             69.54             34.00
+Director 3        17.38             69.54             50.36
+

Fig. 1A provides a free-space azimuth pattern for the antenna at the design frequency.

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Despite its excellent pattern, the antenna turned out to have a narrow operating bandwidth: a little over 110 kHz on 20 meters. If we accept this restriction, then the antenna has much to recommend it, including the achievement of 11 dBi free-space gain with only 5 elements. (Wider-band designs will require 6 elements for the same achievement.)

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Fig. 2 presents the free-space gain of the 5-element quad over its working bandwidth. The rate of gain change--nearly 0.25 dB over 110 kHz--is quite high, a mark of a narrow-band antenna design. Nonetheless, the gain figures exceed the 11 dBi target everywhere in the passband.

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Fig. 3 shows the front-to-back ratio over the same bandwidth. The peak is over 30 dB, but the rate of decrease from the peak is fairly rapid. With slightly more work, the peak front-to-back ratio might be better centered in the passband. The result would be better than 20 dB across the passband.

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The VSWR curve (Fig. 4) is the 50-Ohm SWR resulting from matching the feedpoint of the model. The resonant 25-Ohm feed impedance was transformed via a 1/4-wl section of 37.5-Ohm coax (presumptively made from parallel sections of 75-Ohm cable). The limits of the graph show values just above 1.9:1 at each end. However, the SWR curve continues to steepen at both ends of the passband so that only about another 10-15 kHz are available before the SWR reaches 2:1.

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The 5-element quad design would be inappropriate for use on 20 meters except for certain operators who use only small portions of the band. However, scaled to 17 or 12 meters, the antenna would provide the same performance and cover the entire 100 kHz band. Indeed, if this design has a home at all, it would be on the WARC bands.

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Of all the quad designs that we shall consider, the 5-element Yagi-based design is the most compact. However, most quad builders shy away from antennas with odd numbers of elements. Performance is not so much the worry as is mounting the antenna. With an odd number of elements, the center-most elements comes quite lose to the tower unless one uses a long mast above the tower-top. One can overcome the problem to some degree by weighting the mast to one side or the other. Still, balancing weight loads and wind loads makes this move uncertain for all but those with considerable mechanical engineering experience.

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The following table is the EZNEC model description for anyone who wishes to experiment further with the design.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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+5 el quad 20 m                             Frequency = 14.175  MHz.
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+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
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+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W4E2  -9.056,  0.000, -9.056  W2E1   9.056,  0.000, -9.056 1.03E-01  21
+2     W1E2   9.056,  0.000, -9.056  W3E1   9.056,  0.000,  9.056 1.03E-01  21
+3     W2E2   9.056,  0.000,  9.056  W4E1  -9.056,  0.000,  9.056 1.03E-01  21
+4     W3E2  -9.056,  0.000,  9.056  W1E1  -9.056,  0.000, -9.056 1.03E-01  21
+5     W8E2  -8.883, 11.248, -8.883  W6E1   8.883, 11.248, -8.883 1.03E-01  21
+6     W5E2   8.883, 11.248, -8.883  W7E1   8.883, 11.248,  8.883 1.03E-01  21
+7     W6E2   8.883, 11.248,  8.883  W8E1  -8.883, 11.248,  8.883 1.03E-01  21
+8     W7E2  -8.883, 11.248,  8.883  W5E1  -8.883, 11.248, -8.883 1.03E-01  21
+9    W12E2  -8.692, 22.623, -8.692 W10E1   8.692, 22.623, -8.692 1.03E-01  21
+10    W9E2   8.692, 22.623, -8.692 W11E1   8.692, 22.623,  8.692 1.03E-01  21
+11   W10E2   8.692, 22.623,  8.692 W12E1  -8.692, 22.623,  8.692 1.03E-01  21
+12   W11E2  -8.692, 22.623,  8.692  W9E1  -8.692, 22.623, -8.692 1.03E-01  21
+13   W16E2  -8.692, 33.999, -8.692 W14E1   8.692, 33.999, -8.692 1.03E-01  21
+14   W13E2   8.692, 33.999, -8.692 W15E1   8.692, 33.999,  8.692 1.03E-01  21
+15   W14E2   8.692, 33.999,  8.692 W16E1  -8.692, 33.999,  8.692 1.03E-01  21
+16   W15E2  -8.692, 33.999,  8.692 W13E1  -8.692, 33.999, -8.692 1.03E-01  21
+17   W20E2  -8.692, 50.360, -8.692 W18E1   8.692, 50.360, -8.692 1.03E-01  21
+18   W17E2   8.692, 50.360, -8.692 W19E1   8.692, 50.360,  8.692 1.03E-01  21
+19   W18E2   8.692, 50.360,  8.692 W20E1  -8.692, 50.360,  8.692 1.03E-01  21
+20   W19E2  -8.692, 50.360,  8.692 W17E1  -8.692, 50.360, -8.692 1.03E-01  21
+21          -0.128, 11.503,  0.000         0.128, 11.503,  0.000 1.03E-01   1
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1    21 / 50.00   ( 21 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+
+1      5/50.0  (  5/50.0)   21/50.0  ( 21/50.0)   11.619 ft    37.5  0.67  N
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

2. The OWA-Yagi Approach

+

The second and third design approaches attempt to see what might be required to achieve a quad beam with full 20-meter coverage. Ideally, this coverage would include the following criteria:

+
    +
  • 1. Less than 2:1 SWR across the band;
    • +
  • 2. Greater than 11 dBi free-space gain across the band;
    • +
  • 3. Greater than 20 dB 180-degree front-to-back ratio across the band.
    • +
+

In the end, I settled for some reasonable compromises. Still, the resulting designs have some aspects that make them less fit for direct construction.

+

The second approach also uses Yagi parasitic element principles, but of a special type. In Yagi design, the originator, NW3Z, refers to them as optimized wide-band arrays. He has developed 20 meter Yagis for 48' booms with about 10.1 dBi average gain and greater than 20 dB front-to-back ratio across 20 meters. These initial specifications sound very much like those of other 5-element Yagis on similar booms. However, the NW3Z design adds one more element, a director. By judicious spacing of the reflector and the added director from the driven element, the Yagi achieves a direct match top to a 50-Ohm feedline with low SWR (under 1.3:1) across the entire band.

+

Adapting the OWA principle to quad design proves to be feasible, although not without certain costs. First, the spacing of the reflector and the first director differ substantially from the Yagi version. As well, the entire array must by longer (61.2') than its Yagi counterpart to achieve the design goal of 11 dBi free-space gain.

+
+ +
+

Fig. 5 shows the side view of the final design to provide a perspective on the required element spacing. Note especially the reflector and first director positions. Fig. 5A is a free-space azimuth pattern for the design at its design frequency, 14.175 MHz.

+
+ +
+

An added cost to achieve the design goals was the use of 0.5" diameter elements in all of the elements. Hence, the design is unlikely to be directly implemented, although alternative element construction is possible. The following table provides the array dimensions for 20 meters. Once more, all dimensions are in feet.

+ 
Element           Length/Side       Circumference     Distance from Reflector
+Reflector         18.54             74.16             -----
+Driver            18.52             74.08              9.06
+Director 1        17.06             68.24             15.32
+Director 2        16.84             67.36             27.39
+Director 3        16.82             67.28             41.38
+Director 4        16.30             65.20             61.20
+

If you compare the element dimensions with those for the 5-element narrow-band quad, you will discover some interesting differences other than spacing. First, the OWA reflector and driver have dimensions that are quite close to each other, with both being somewhat longer than the corresponding elements in the 5-element array. Second, the directors tend to be shorter than those in the smaller beam.

+

For the performance curves, we shall use the entire 20 meter band from 14.0 to 14.35 MHz.

+
+ +
+

The gain of the OWA 6-element quad is quite stable, as shown in Fig. 6. It ranges from 10.99 to 11.11 across the band. This is about 1/3 the variation of the smaller array despite the 3-fold increase in operating bandwidth. The shape of the gain curve, however, suggests that the gain stability limits of the array are not very much wider than the 20 meter band itself. Note the increasing rates of change near the band edges.

+
+ +
+

The front-to-back ratio across 20 meters appears in Fig. 7. Of all the array approaches tested in this exercise, the OWA design is the only one to achieve greater than 20 dB front-to-back ratio for the full passband. Part of the reason for this result stems from the use of very large diameter elements. Single-wire elements of the usual #12/#14 AWG material will not yield the front-to-back operating bandwidth.

+
+ +
+

The OWA 6-element quad provides a direct 50-Ohm match with no matching network components, as shown in Fig. 8. Interestingly, the shape of the pattern resembles that for the corresponding OWA 6-element Yagi, but with higher band-edge values. Despite the ability of the design to cover 20 meters fully, the quad shows itself to be inherently more narrow-banded than counterpart Yagis.

+

The OWA quad is quite possibly a usable design for a high performance, full band coverage array, with one exception. The 0.5" diameter elements are not feasible using standard quad construction techniques that employ relatively lightweight fiberglass or similar element support arms. Significant reductions in the effective element diameter reduce inter-element coupling and result in gain and operating bandwidth reductions. The solution is to redesign the array for dual-wire elements using #14 or #12 wire. However, the substitutions will require extensive re-optimization of element lengths to restore the performance curves. Because the closely-spaced loops would require between 2 and 3 times the number of segments per element, with an increase in the number of modeling wires, the slow process was not endured for this exercise. Nonetheless, more extensive work on 2-element quads, described in past articles, strongly suggests that the substitution is quite achievable.

+

For anyone who wishes to work further with this type of design, the following table is the EZNEC model description.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6 el 20 meter owa quad                         Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W4E2  -9.270,  0.000, -9.270  W2E1   9.270,  0.000, -9.270 5.00E-01  21
+2     W1E2   9.270,  0.000, -9.270  W3E1   9.270,  0.000,  9.270 5.00E-01  21
+3     W2E2   9.270,  0.000,  9.270  W4E1  -9.260,  0.000,  9.270 5.00E-01  21
+4     W3E2  -9.260,  0.000,  9.270  W1E1  -9.270,  0.000, -9.270 5.00E-01  21
+5     W8E2  -8.950,  9.056, -8.950  W6E1   8.950,  9.056, -8.950 5.00E-01  21
+6     W5E2   8.950,  9.056, -8.950  W7E1   8.950,  9.056,  8.950 5.00E-01  21
+7     W6E2   8.950,  9.056,  8.950  W8E1  -8.950,  9.056,  8.950 5.00E-01  21
+8     W7E2  -8.950,  9.056,  8.950  W5E1  -8.950,  9.056, -8.950 5.00E-01  21
+9    W12E2  -8.530, 15.320, -8.530 W10E1   8.530, 15.320, -8.530 5.00E-01  21
+10    W9E2   8.530, 15.320, -8.530 W11E1   8.530, 15.320,  8.530 5.00E-01  21
+11   W10E2   8.530, 15.320,  8.530 W12E1  -8.530, 15.320,  8.530 5.00E-01  21
+12   W11E2  -8.530, 15.320,  8.530  W9E1  -8.530, 15.320, -8.530 5.00E-01  21
+13   W16E2  -8.420, 27.388, -8.420 W14E1   8.420, 27.388, -8.420 5.00E-01  21
+14   W13E2   8.420, 27.388, -8.420 W15E1   8.420, 27.388,  8.420 5.00E-01  21
+15   W14E2   8.420, 27.388,  8.420 W16E1  -8.420, 27.388,  8.420 5.00E-01  21
+16   W15E2  -8.420, 27.388,  8.420 W13E1  -8.420, 27.388, -8.420 5.00E-01  21
+17   W20E2  -8.410, 41.383, -8.410 W18E1   8.410, 41.383, -8.410 5.00E-01  21
+18   W17E2   8.410, 41.383, -8.410 W19E1   8.410, 41.383,  8.410 5.00E-01  21
+19   W18E2   8.410, 41.383,  8.410 W20E1  -8.410, 41.383,  8.410 5.00E-01  21
+20   W19E2  -8.410, 41.383,  8.410 W17E1  -8.410, 41.383, -8.410 5.00E-01  21
+21   W24E2  -8.150, 61.200, -8.150 W22E1   8.150, 61.200, -8.150 5.00E-01  21
+22   W21E2   8.150, 61.200, -8.150 W23E1   8.150, 61.200,  8.150 5.00E-01  21
+23   W22E2   8.150, 61.200,  8.150 W24E1  -8.150, 61.200,  8.150 5.00E-01  21
+24   W23E2  -8.150, 61.200,  8.150 W21E1  -8.150, 61.200, -8.150 5.00E-01  21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

3. The Wide-Spaced Approach

+

A third approach to long-boom quad design employs relatively wide but uniform spacing between elements. Beginning with a driver-reflector spacing that approaches the optimum for a 2-element maximum front-to-back ratio design, the directors are then added at similar spacing from each other. The director element lengths show a consistent decrease in length as one moves forward from the driver. Fig. 9 shows the side view to give some perspective on the overall design of a 6-element array capable of 11 dBi free-space gain.

+
+ +
+

The design-frequency free-space azimuth pattern appears in Fig. 9A. The pattern is as well-behaved at the center of the passband as either of the other designs.

+
+ +
+

As a design exercise, I optimized the 6-element wide-spaced array using #8 AWG wire (0.1285" diameter). In part, I wanted to see what differences might result for the operating bandwidth, especially with respect to the front-to-back ratio. The following table provides the physical dimensions of the model. As usual, all dimensions are in feet.

+ 
Element           Length/Side       Circumference     Distance from Reflector
+Reflector         18.43             73.73             -----
+Driver            17.70             70.80             13.95
+Director 1        17.23             68.92             28.29
+Director 2        16.83             67.32             42.78
+Director 3        16.57             66.27             57.60
+Director 4        16.13             64.51             69.82
+

Immediately apparent is the greater length of the array compared to the OWA version of a wide-band quad: 70' vs. 61'. More subtle are the required variations from uniformity in the element spacing. Although the average spacing is nearly 0.2 wl, the director spacings cannot be set by simple adherence to the average. Performance deteriorates rapidly using mere rules of thumb as guidance.

+
+ +
+

Fig. 10 shows the gain curve across 20 meters for the wide-spaced array. Like the OWA array, the curve shows good stability, with a net variance of only 0.15 dB across the band. Note especially that a wide-spaced design is capable of placing the peak gain of the antenna well within the boundaries of the operating passband.

+
+ +
+

Fig. 11, the front-to-back curve across 20 meters, shows the effect of using small diameter wire for the elements. The band-edge front-to-back ratio is about 17 dB, and the peak value is 21 dB. To the present, I have found no way to increase the front-to-back performance within the constraints of the overall length and the wire size. However, the use of large-diameter elements or dual-wire substitutes shows promise of improving this aspect of performance considerably.

+
+ +
+

The SWR curve for the wide-spaced 6-element array appears in Fig. 12. Unlike the other curves, this one is a 75-Ohm VSWR curve, the inherent feedpoint impedance of the antenna. Matching the antenna to a 50-Ohm feedline requires the use of a simple transmission-line transformer. The band-edge reactance is well under +/-j40 Ohms for mid-band resonance of the driver.

+

The wide-spaced 6-element array has considerable potential for further development through the use of larger diameter elements or substitutes. Nevertheless, the key limiting factor in this direction is the boom length. Comparable Yagi designs with the same boom length would likely use 7 elements and provide equal gain, but superior front-to-back, performance.

+

Those who might wish to further optimize the design can refer to the following EZNEC model description.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6-element wide-spaced 20m quad                      Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+
+1     W4E2  -9.216,  0.000, -9.216  W2E1   9.216,  0.000, -9.216    #  8   21
+2     W1E2   9.216,  0.000, -9.216  W3E1   9.216,  0.000,  9.216    #  8   21
+3     W2E2   9.216,  0.000,  9.216  W4E1  -9.216,  0.000,  9.216    #  8   21
+4     W3E2  -9.216,  0.000,  9.216  W1E1  -9.216,  0.000, -9.216    #  8   21
+5     W8E2  -8.850, 13.945, -8.850  W6E1   8.850, 13.945, -8.850    #  8   21
+6     W5E2   8.850, 13.945, -8.850  W7E1   8.850, 13.945,  8.850    #  8   21
+7     W6E2   8.850, 13.945,  8.850  W8E1  -8.850, 13.945,  8.850    #  8   21
+8     W7E2  -8.850, 13.945,  8.850  W5E1  -8.850, 13.945, -8.850    #  8   21
+9    W12E2  -8.615, 28.289, -8.615 W10E1   8.615, 28.289, -8.615    #  8   21
+10    W9E2   8.615, 28.289, -8.615 W11E1   8.615, 28.289,  8.615    #  8   21
+11   W10E2   8.615, 28.289,  8.615 W12E1  -8.615, 28.289,  8.615    #  8   21
+12   W11E2  -8.615, 28.289,  8.615  W9E1  -8.615, 28.289, -8.615    #  8   21
+13   W16E2  -8.415, 42.775, -8.415 W14E1   8.415, 42.775, -8.415    #  8   21
+14   W13E2   8.415, 42.775, -8.415 W15E1   8.415, 42.775,  8.415    #  8   21
+15   W14E2   8.415, 42.775,  8.415 W16E1  -8.415, 42.775,  8.415    #  8   21
+16   W15E2  -8.415, 42.775,  8.415 W13E1  -8.415, 42.775, -8.415    #  8   21
+17   W20E2  -8.284, 57.600, -8.284 W18E1   8.284, 57.600, -8.284    #  8   21
+18   W17E2   8.284, 57.600, -8.284 W19E1   8.284, 57.600,  8.284    #  8   21
+19   W18E2   8.284, 57.600,  8.284 W20E1  -8.284, 57.600,  8.284    #  8   21
+20   W19E2  -8.284, 57.600,  8.284 W17E1  -8.284, 57.600, -8.284    #  8   21
+21   W24E2  -8.064, 69.822, -8.064 W22E1   8.064, 69.822, -8.064    #  8   21
+22   W21E2   8.064, 69.822, -8.064 W23E1   8.064, 69.822,  8.064    #  8   21
+23   W22E2   8.064, 69.822,  8.064 W24E1  -8.064, 69.822,  8.064    #  8   21
+24   W23E2  -8.064, 69.822,  8.064 W21E1  -8.064, 69.822, -8.064    #  8   21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Conclusion

+

Long-boom, high-performance, wide-bandwidth monoband quad design is not easily obtained. Although only three design approaches have been employed in this exercise, they indicate several trends in large quads:

+
    +
  • 1. A wide operating bandwidth is improbable for quad lengths similar to corresponding Yagi lengths, if superior performance is expected. Wide-band quads with superior performance will likely require greater boom lengths.
    • +
  • 2. A key limiting factor in quad design is the use of small-diameter elements. Large-diameter elements, or suitable substitute dual-wire elements having similar inter-element coupling potential, are necessary for achieving high gain, high front-to-back ratios, and 2:1 SWR curves across the wider amateur bands.
    • +
  • 3. Of the designs so far surveyed, perhaps the OWA version holds the most potential for the wider amateur bands (20, 15, and 10 meters). The 5-element array should be adequate for 30, 17, and 12 meters, assuming that one can compensate for the mechanical difficulty presented by the use of an odd number of elements.
    • +
+

Of course, this exercise is limited by exploring only three design approaches to the development of quads meeting the original design criteria. Hopefully, it will serve as a stepping stone in a more thorough exploration of all relevant design approaches. What seems clear is that the design of high-performance quads can no longer be left to haphazard approaches. Expecting wide operating bandwidths and high performance requires a full appreciation of parasitic element principles. Equally key to the process is an understanding of how quad elements resemble their corresponding Yagi elements and how quad elements differ in the process of inter-element coupling. None of the designs we have investigated can yet be said to have come close to the full potential of long-boom quads. At best, they are merely "pretty good."

+
+ +
+

Updated 06-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Quad List

+

Go to Main Index

+

Topics: HF Upper, Quad


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+

2-Element Quads as a Function of Wire Diameter
+ Part 1: Understanding Some Quad Properties

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

There are some very old formulas for cutting the lengths of 2-element (and larger) quad beam elements, formulas that have persisted since at least the 70s, if not before. The driven element should be 1005/f(MHz) feet long, while the reflector should be 1030/f(MHz) feet long. Spacing should be between 0.14 and 0.2 wavelengths. (ARRL Antenna Book, p. 12-1) Moreover, the quad has been called a very "low-Q" antenna, meaning that it is wide-banded compared to other beam antennas, presumably including Yagis.

+

Unfortunately, using the formulas will result in a relatively poor 2-element quad at any spacing. As well, we should not be too attracted by the so-called low Q of the quad, because that feature has very restricted application.

+

In fact, we should very likely start all over again, beginning with the one piece of information that early quad builders thought was too insignificant to notice: the wire size. In this short series, we shall examine the properties of 2-element quad beams using a driver and reflector based on the wire size we select for the elements. In this part, we shall look at quad properties based on very careful modeling with NEC. In Part 2, we shall provide a way of automating the design process. In the final part, we shall look at a way to improve the operating performance bandwidth of wire quads.

+

There are many operating specifications that we might emphasize for the design frequency we choose. For this exercise, I shall pick two, letting the others become what they will in the designs. First, the driven element will be resonant at the design frequency. Before we are done, we shall show how and why to vary that parameter without significantly affecting the reflector. Second, we shall select a spacing between elements and a reflector length that provides maximum 180-degree front-to-back ratio at the design frequency. These choices are consistent with work done on VHF models by Dan Handelsman and David Jefferies and generally provide the widest operating bandwidth for most of the quad beam's other parameters. Fig. 1 shows the critical 2-element quad dimensions for our work.

+
+ +
+

In order to generalize the results, we shall deal with the wire size, element lengths, and element spacing in terms of fractions of a wavelength. This procedure will allow us later to develop a general set of design equations that will be accurate to within 0.5% for wire sizes greater than 0.0003 wl and within about 1% for wires down to about 0.00003 wl, with resonance and peak front-to-back ratios occurring within about 10 kHz of actual detailed models.

+

To get an idea of how wire diameters when expressed in terms of a wavelength coincide with common physical measures, the following table may be useful. Numbers in () indicate the closest AWG wire gauge, where applicable.

+ 
Dia. in WL               Physical diameter in inches
+               3.5 MHz        14 MHz         30 MHz         144 MHz
+0.00001        0.0337 (20)    0.0084 (32)    0.0039 (38)    0.00082
+0.0000316      0.1066 (10)    0.0267 (24)    0.0124 (29)    0.0026 (40)
+0.0001         0.3372         0.0843 (12)    0.0393 (18)    0.0082 (32)
+0.000316       1.0664         0.2666 (2)     0.1244 (8)     0.0259 (22)
+0.001          3.372          0.841          0.3934         0.0820 (12)
+0.00316        10.664         2.666          1.244          0.2592 (2)
+0.01           33.722         8.431          3.934          0.8964
+

Obviously, few 80 meter quads will be constructed using 0.01 wl wire. However, 2-meter quads using 1" diameter elements are quite feasible. Likewise, a 2-meter quad from 1E-5 (shorthand for 0.00001) wl wire is unlikely, but 3.16E-5 wire is already #10 AWG at 80 meters.

+

The wire diameter steps used in this exercise may seem peculiar. Most antenna characteristics dependent upon wire size tend to vary with the common logarithm of the diameter. The progression of steps in the diameter column translate into a linear progression of logarithms from -5 to -2, with the "316" steps representing -x.5 log values. (A more exact value for the intermediate diameters would be 31622777.)

+

Models for each wire diameter were developed to obtain element lengths and spacing to resonate with driver within +/-j1 Ohm of remnant reactance. As well, the front-to-back peak value had to exceed 50 dB. NEC-2 or -4 are equally adept at this task, since the quad presents no pressure on either core's limitations until the wire size exceeds 0.01 wl. The models used 21 segments per side to ensure good convergence.

+

The models were calibrated for the most common material used in quad beam construction: copper. Test aluminum models showed little change in characteristics relative to the baseline copper models, but the slightly higher wire losses can add roughly an Ohm to the feedpoint impedance--less than 1% of the actual value. The test frequency was 28.5 MHz, about the geometric mean for the combined HF and VHF frequency range.

+

Since copper wire material losses vary with frequency, but at a rate that differs from the changes in wire diameter, there will be slight variations from the results to be shown at the extremes of the frequency range. At very low HF frequencies, the gain will be higher, but only by a maximum of a few tenths of a dB. Since the gain increase results from lower material losses, the source impedance will be lower--perhaps as much a 5 Ohms at 80 meters. Conversely, gain at VHF for a given wire size will be very slightly lower than at 28.5 MHz, while the feedpoint impedance will be correspondingly higher. However, these slight variations occasion no significant changes in the physical dimensions of the quad as a function of a wavelength.

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Before examining the properties of 2-element quad beams in detail, let's take a summary view of the modeling results in the form of a table. All sizes and lengths are in wavelengths. We shall use our shorthand notation for wire sizes. Gain is the free-space value.

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Wire dia.      DE-Ref Space        DE Length      Ref Length     Gain dBi
+1E-5           0.650               0.99920        1.02248        2.95
+3.16E-5        0.142               1.00600        1.05224        6.67
+1E-4           0.156               1.01060        1.06560        6.99
+3.16E-4        0.160               1.01424        1.07976        7.08
+1E-3           0.164               1.01984        1.10000        7.11
+3.16E-3        0.167               1.02744        1.12992        7.16
+1E-2           0.170               1.05016        1.18432        7.21
+

The key element in this table is the value set for the thinnest wire. Notice the gain associated with this wire size. As the wire size increases--given our design criteria of resonance and peak front-to-back value--the frequency at which peak gain occurs decreases. For a wire size of about 3.16E-5, the maximum front-to-back value and the peak gain value occur at about the same frequency. For all wire sizes greater than 3.16E-5, the peak gain frequency is below the design frequency and grows more distant from it with increasing wire size.

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In contrast, for wire sizes below 3.16E-5, the peak gain value occurs at a frequency higher than the design frequency. At the design frequency the gain value may be quite low, since the gain decreases more rapidly at frequency below that at which peak gain occurs. The result is that 2-element quad beams with any performance potential at all and designed to the criteria used in this exercise are not feasible in wire sizes below 3.16E-5. As a result, model results for the thinnest wire in the table have been removed from the graphs to follow.

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The first significant feature appears in Fig. 2, which plots the required element spacing for maximum front-to-back ratio against the wire sizes. The thinner the wire, the closer that spacing must be to achieve maximum front-to-back values at the design frequency. Notice that the curve becomes nearly linear with wire sizes above 1E-4, which is thinner than #14 at 10 meters. The shallowness of the curve above this value indicates that for most practical monoband beam designs, 0.17 wl spacing represents a limit. However, since tuning a 2-element quad for peak front-to-back also tends to result in the widest operating bandwidth for most parameters, it becomes advisable to use the spacing that is correct for the selected wire size.

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Fig. 3 presents the driver and reflector element circumference lengths. Of special note is the fact that the reflector length increases at a faster rate than the driver length. In practical terms, the fatter the wire, the more the length of the reflector must exceed the length of the driver for peak performance.

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Combining the results for spacing and element length yields the conclusion that inter-element coupling increases with wire size. Arriving at the correct value for a given wire size involves both element length and spacing so that the parasitic element currents have the correct magnitude and phase for maximum front-to-back performance. This performance will only be achieved if both the upper and lower wires of the reflector have close to optimal currents at their centers--and thus an optimal current distribution along their length. Part of the reflector sizing curve is a result of this function.

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In Fig. 4 we have the resonant feedpoint impedances of the modeled quads. The general increase in value is apparent. Part of the stair-step nature of the curve results from the fact that close to resonance, the resistive component of the impedance can show significant changes as we change the remnant reactance from close to j-1 Ohm to +j1 Ohm. In the value range of the graph (125-155 Ohms), the stair-step result is visually apparent, but not operationally significant. However, the overall difference between the thinnest and the fattest wire values may be significant for the method chosen to match an optimized quad beam to a given main feed line.

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The change of gain with respect to wire size, shown in Fig. 5, must be read with great care. For wire sizes greater than 1E-4, the gain increase with additional wire thickness would not itself justify using a larger wire size. However, remember that as the wire thickness increases, the frequency of maximum gain becomes increasing lower than the design frequency. One consequence of this fact is that for thicker wires, the amount of gain change across a given amateur band will be less than for thinner wires. For example, consider a 2-element quad at 10 meters with a 28.5 MHz design frequency. Using #14 wire, the gain at 29 MHz will drop to under 6.5 dB, despite the 7+ dB value at the design frequency. With 0.5" elements, the gain at 29 MHz will be above 6.7 dB. In general, fatter elements provide both higher and smoother performance across the ham bands.

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There are other dimensions to operating bandwidth that are worth noticing. Two are included in Fig. 6. The graph shows clearly the VSWR bandwidth as a percentage of the design frequency. Even the thinnest wire on the graph shows a 6.2% operating bandwidth, while the span from 28 to 29 MHz is only about 3.5% of the design frequency. It is the wide SWR range that has given the 2-element quad beam the illusion of being a low-Q antenna.

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However, notice the second curve on the graph, which provides the front-to-back operating bandwidth. Because a 20-dB front-to-back ratio can be commonly achieved with Yagi design across a relatively wide frequency range--that is, a range covering all or almost all of a ham band--the operating bandwidth was defined as the percentage of design frequency over which the model had a front-to-back ratio in excess of 20 dB. These percentages are very low and do not reach the 3.5% level until we have a wire size of about 3.16E-3. This value represents a wire over 1" in diameter at 10 meters. Since quads are rarely made from wires this thick at HF, the quad user will generally have to be content with front-to-back performance at the band edges that is inferior to that which a well-designed Yagi may provide.

+

The narrowness of the operating bandwidth relative to front-to-back performance for the 2-element quad beam demonstrates a number of cautions. First, VSWR operating bandwidth is often a misleading indicator of the operating bandwidth of other antenna properties. The 2-element quad beam is in fact a high-Q (or narrow-band) antenna with respect to its front-to-back performance. Essentially, the loop construction of 2 1/2 wl elements connected at the ends makes the inter-relationship of the driver and the reflector more frequency critical in terms of arriving at the correct current magnitude, phase, and distribution on the reflector for high front-to-back performance--relative to the linear elements of the Yagi.

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(Note: this comparison only suggests that the rate of change of a 2-element driver-reflector Yagi optimally spaced for maximum front-to-back ratio will be less than for a 2-element quad. However, such a Yagi may have a peak front-to-back ratio of only about 12 dB, with lesser values away from the design frequency. As well, the 2-element Yagi will have a lower gain--with a considerable variance across a band as wide as 10 meters. Hence, the 2-element quad will generally outperform a 2-element Yagi when both are designed to the same criteria. The point of these notes about quad performance is not to assess the overall superiority of one antenna type over the other. Instead, these notes call attention to the specific properties of the quad that must be taken into account when designing one or when reaching an overall evaluation of the quad's performance--especially, when considering options within quad design factors.)

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When we initially examined the gain of quads relative to wire size, we noted the frequency position of the gain peak and its influence on the rate of change of gain across an intended band of operation. Fig. 7 formalizes those notes by showing the rate of gain change per 1% of design frequency in terms of dB. Let us use the 1E-4 wire size as a marker, since it is the first data point where peak gain is significantly lower in frequency that the maximum front-to-back frequency. The curve is nearly linear from that point through 1E-2 wire sizes. In fact, for each decrease of wire size by a factor of 10, the rate of gain change across a working passband increases by nearly 1/2 dB. Wherever stable gain is required across a passband, the fattest element diameter feasible is the order of the day.

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Although the graphs based on element wire size have much to teach us about the performance of 2-element quads, they cannot teach everything. For example, once one has designed a 2-element quad for a chosen wire size, it is usually a good procedure to reresonate the driver from the mid-band design frequency to a lower frequency--somewhere between 1/4 and 1/3 the way up from the lower limit of the passband. The obvious questions is this: how do we arrive at such a recommendation?

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The answer can be found by performing a frequency sweep of a given design and looking at selected properties. For an example, let's take one of our 28.5 MHz designs using 3.16E-4 wl wire (about 0.12" in diameter, between #10 and #8 AWG) and sweep it between 27.8 and 30.8 MHz. Then, let's record the results for VSWR and front-to-back ratio on a graph, such as Fig. 8.

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The design frequency values can be easily identified. Let's begin with the VSWR curve. Note that the SWR value increases much more rapidly below the design frequency than above it. If we wish to have roughly equal SWR values at the band edges of a chosen operating passband, then it will be necessary to reduce the resonant frequency of the driver. In fact, the small change in element size needed to effect this change will have negligible effect on the performance of the reflector or the frequency of maximum front-to-back. For example, reducing the resonant driver frequency to about 28.3 MHz will move the front-to-back ratio peak by only a few kHz.

+

Such a move will likely be beneficial (although minimally so) to the overall front-to-back performance within the passband--for example 28 to 29 MHz. Similarly to the SWR performance, but to a lesser degree, the front-to-back value changes more slowly above the design frequency than below it. From the graph, you may determine that 0.3 MHz above design frequency, the front-to-back ratio is above 20 dB, while 0.3 MHz below design frequency, the value is only about 18.5 dB. In fact, using the span from 28 to 29 MHz as a passband definition, there is a 3 dB difference in the front-to-back ratios at the passband edges.

+

It is possible from the graph in Fig. 8 to create an illusion--namely, that there is good performance to be had from the antenna above 29 MHz. However, remember that across the passband, the antenna gain is steadily decreasing, and it continues to decrease as we raise the frequency further. By the frequency at which the SWR approaches 2:1 on the high side of the design frequency, the gain has dropped to about 5.5 dBi, and the front-to- back ratio is only about 7.4 dB. At 29.7 MHz, the gain is down to 6 dB, with a front-to-back ratio of about 10.6 dB. Although usable for some purposes, these figures are down considerably from the design frequency values.

+

The point of the exercise has been to demonstrate the changes in 2-element quad performance as we change wire size. I noted early on that one would have to make some adjustments as we change frequency, since the graphs are calibrated to copper wire. To give you a better sense of the degree of change, let's sample our 3.16E-4 wl diameter wire quad at a number of frequencies. Note that 28.5 MHz is the original design frequency. All of the quads use the same length elements and spacing in terms of fractions of a wavelength.

+ 
Frequency      Gain dBi       Front-to-Back       Feedpoint Z
+  MHz                           Ratio dB          R +/- jX Ohms
+  3.5          7.12           45.37               136.7 + j 0.4
+ 28.5          7.08           51.33               137.4 + j 0.2
+144.0          7.02           47.67               138.6 - j 0.1
+223.0          6.99           43.33               139.2 - j 0.3
+

For thinner wire sizes, the variance will be greater, while fatter wires will show less variance.

+

The small range of the variance should tell us two things. First, the general properties of 2-element quads are indeed largely a function of the diameter of the wire we use for the elements. In general, performance--especially the operating bandwidth of most essential performance specifications--improves with the use of larger diameter elements. Unfortunately, this fact is at odds with the conventional ways in which we construct quads. The supporting structure for quad elements will handle thinner wire but certainly not aluminum tubing. However, there are alternative ways of simulating fat elements that make use of wire. Remember that the inter-element coupling is the key contribution of thicker elements. Material losses are secondary. Hence, if we can increase the coupling through the use of light-weight simulated fat elements, we may generally ignore their slightly higher material losses. We shall defer that task to Part 3 of the series.

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Second, the general reliability of the modeling results as we alter frequency gives rise to the possibility of automating the design process. Suppose that we could simply specify a wire size and a design frequency and have a program that will complete all of the remaining electrical design steps. That will be our project for Part 2 of this short series.

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Updated 11-01-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Lower, HF Upper, Quad, VHF / UHF


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2-Element Quads as a Function of Wire Diameter
+ Part 2: Automating the Design Process

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L. B. Cebik, W4RNL

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In Part 1 of this short series, we examined some of the properties of the 2-element monoband quad beam as they emerged from the wire size. For that exercise, we used a series of graphs based on selected models. The models used wire diameters from 3.16E-5 through 1E-2 wavelengths in diameter so that the X-axis of each graph would follow a linear pattern according to the common logarithm. The Y axes of the graphs explored various properties of the beam. The design specification for each model was that the driver should be resonant within +/-1 Ohm of remnant reactance and that the wire dimensions and element spacing should produce a maximum value of 180-degree front-to-back ratio. Fig. 1 shows the salient quad dimensions.

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The task of finding suitable beam dimensions was considerably eased by the use of "modeling by equation" techniques. The program used was NEC-Win Plus, but any other NEC-2 or NEC-4 program with a similar facility would work as well. All models used copper wire and were in free space.

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Fig. 2 shows the equations page of the model used to explore quad properties. The standard design frequency (variable G) is 28.5 MHz, which is roughly the geometric mean between the lowest HF frequency for which a 2-element quad might be built and the high VHF frequency to be used. By moving the design frequency down from a more perfect 30 MHz, the resulting model beams could be compared more easily to physical beams built for the 10-meter amateur band.

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For each wire size select for variable H (multiplied by the wavelength in cell D3 to provide physical dimensions for the program), it became necessary only to vary three values. A is 1/8 of the driver circumference, while B is 1/8 of the reflector circumference. D is the spacing between elements. As a matter of course, I examined spacing in 0.005 wavelength increments to find highest front-to-back peak and then refined the spacing.

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Fig. 3 shows the equations version of the wires page. The wires corresponding to the variables are clear enough. Each model was swept in 0.01 MHz (10 kHz) increments to track the pattern of both resonance and the maximum front-to-back ratio. The closer to resonance, the smaller the change to the driver length variable A. The closer to maximum front-to-back ratio, the smaller the changes to the reflector length variable B. Then the spacing would be changed, with a further zeroing-in exercise until no further improvements could be made.

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Note the Radiation Pattern entry. The gain and front-to-back ratio were obtained from a tabular readout. Since I needed only the 90-degree mark for gain and the 270-degree mark for rearward gain, I set the parameters for the radiation pattern to produce only 4 values. This set-up will not yield any usable graphical patterns, but it does simplify scanning the tabular readout.

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From this preliminary work, which one might replicate either in greater detail or for other antennas, I obtained the data points for the graphs in Part 1. These graphs are simple "connect-the-dot" constructions that are useful for seeing patterns. However, they do not provide any basis for calculating 2-element quads for other design frequencies.

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I subjected the data obtained from the systematic modeling exercise to regression analysis. At one time, such analysis was painstakingly slow. However, programs like DataFit automate the process, providing both tabular and graphical outputs to test the equations that result. For the 2-element quad, 4th-order equations yielded results that fell within about 0.5% of optimized models throughout the physical wire size limits and the frequency limits of the project, with the exception of very thin wires. Where the common log of the wire diameter in wavelengths was -4 or less, the error rate increase slightly. In all test cases, the resulting model had its resonant frequency and its maximum front-to-back frequency within about 10 kHz of the requested design frequency. These results were judged to be well within the construction variables for most antenna-building situations.

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There is a limit to how well regression analysis can track data points. Higher-order equations tend usually (but not always) to provide a better track than lower-order equations. 4th-order equations were the maximum possible with the limited number of data points used.

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Some data point sequences make easy curve fits for regression analysis. Fig. 4 shows the reflector circumference curve produced by the analysis along with the original data points. A more exacting fit is hard to imagine.

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However, Fig. 5 shows a more difficult fit between the curve and the data points for the rate of gain change. Although the curve comes close to the data points, the reversal of direction for the thinnest wire makes the shape of the curve peak more open to question. Remember that with the thinnest wire used, the 2-element quad reaches a coincidence between the frequency of maximum gain and the frequency of maximum front-to-back ratio. Hence, the rate of change is less than the next thinnest wire sized used. From 0.0001 wavelength wire diameters onward, the frequency of maximum gain is always lower than the frequency of maximum front-to-back ratio. For the purposes of the advisory approximation, the curve and the regression equation is perfectly adequate.

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The equations produced by regression analysis are perfectly adequate for calculating all of the data we examined in Part 1 for all points between the listed data points. However, the equations have no inherent theoretic import for electronics or antennas beyond their ability to calculate.

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The production of a set of calculating equations does have the merit of allowing one to create a small program in any number of media to automate the design process for 2-element quads that meet the basic specifications (resonance and maximum front-to-back ratio on the design frequency). By specifying the wire size and the design frequency, we can let the program generate the remaining data. Therefore, I produced the following little GW Basic program to do just this task.

+ 
10 CLS:PRINT "Program to calculate the dimensions of a resonant square 2-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00336#:BD=.04966518519#:CD=.2731955556#:DD=.6716364021#:ED=1.644147937#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.003173333333#:BR=.0508237037#:CR=.3081977778#:DR=.8663851852#:ER=2.040064444#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AS=-.003#:BS=-.03551851852#:CS=-.1553055556#:DS=-.2902116402#:ES=-.02540079365#
+240 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+250 AZ=1.976333333#:BZ=30.84751852#:CZ=172.4909722#:DZ=419.5162831#:EZ=519.8747579#
+260 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+270 AG=-.06333333333#:BG=-.7203703704#:CG=-3.010277778#:DG=-5.381375661#:EG=3.738769841#
+280 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+290 AW=1.688666667#:BW=23.76837037#:CW=124.9339444#:DW=295.8872328#:EW=281.2755159#
+300 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+310 AF=-.00266666667#:BF=.388#:CF=4.790666667#:DF=19.55485714#:EF=28.76628571#
+320 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+330 AN=-.08333333333#:BN=-.9462962963#:CN=-3.943055556#:DN=-7.582671958#:EN=-5.23234127#
+340 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+350 WL=299.7925/F:PRINT "Wavelength in Meters =";WL
+360 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+370 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+380 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+390 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+400 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+410 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+420 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+430 PRINT "Approximate Resonant Feedpoint Impedance =";ZR;"Ohms"
+440 PRINT "Approximate Free-Space Gain =";GN;"dBi"
+450 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+460 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+470 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+480 INPUT "Another Value = 1, Stop = 2: ";P
+490 IF P=1 THEN 10 ELSE 500
+500 END
+

Line 140 contains something peculiar to GW Basic. "LOG" in GW Basic always mean the natural logarithm. Hence, a conversion factor is necessary to convert the natural log to a common log. If the medium to which this program may be transferred already knows the difference between "LOG" and "LN," the conversion factor can be dropped.

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The program does not contain a module to convert AWG wires gauges into physical diameters, so the following table may be useful.

+ 
AWG Size       Dia. Inches              Dia. mm
+18             .0403                    1.0236
+16             .0508                    1.2903
+14             .0641                    1.6281
+12             .0808                    2.0523
+10             .1019                    2.5883
+ 8             .1285                    3.2640
+
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Fig. 6 provides a truncated view of the screen data produced by the program. The test case is a 28.5 MHz quad using wire just slightly larger than #18 AWG. Conveniently, the selected wire size is 0.0001 wavelength in diameter. The remaining entries show the calculated data. The following table parallels the data from the program and from the test model that served as the 0.0001 data point. ("DF" means "design frequency.")

+ 
Data                                    Calculated          Modeled
+Wire dia. in WL                         .0001 (input)       .0001 (input)
+Driver circumference in WL              1.0103              1.0106
+Refl. circumference in WL               1.0653              1.0656
+DE-Refl. Space in WL                    0.1557              0.156
+Resonant Feedpoint Z in Ohms            133.4               133.9
+Free Space Gain in dBi                  6.99                6.99
+2:1 VSWR Bandwidth in % of DF           7.8                 8.1
+>20 dB F-B Ratio Bandwidth in % of DF   1.71                1.67
+Rate of Gain Change in dB per 1% of DF  1.24                1.25
There are some cautions to be observed in using the program or its equations. At the frequency extremities of the program, that is, at low HF or middle to upper VHF, certain systematic variations will appear between the calculations and actual models of the antenna. They are best illustrated by reference to the following table. The 28.5 MHz reference frequency corresponds to the program design frequency and was used in the table above. + 
Frequency      Wire Size      Dia.      Gain      Feed Z    Efficiency
+  MHz            WL           inches    dBi       Ohms         %
+  3.5          0.0001         3.372"    7.12      131.3     98.82
+ 28.5          0.0001         0.414     6.99      133.4     96.69
+144.0          0.0001         0.0082"   6.79      137.8     92.85
+

The rate of change of material losses in real materials does not occur at the same rate as the change in inter-element coupling. NEC calculates efficiency solely on the basis of material losses, which the table shows to increase with frequency if the wire diameter is held constant as a function of a wavelength. Increased material or resistive losses also appear as increases in the source impedance, not to mention small reductions in the antenna gain. Conversely, well below the design frequency, efficiency increases, gain increases, and the source impedance decreases.

+

Had the program been calibrated for lossless wire, there would have been no difference in the results at any of these frequencies. However, calibrating the program in terms of copper wire provides a more realistic basis for planning. The differences between copper and aluminum will be minimal. It is probably useful to note also that few amateur quads for 80 meters will be constructed from 3.37" diameter wires, and equally few built for 2 meters will use 0.0082" wire (about #32 AWG). Nonetheless, the advice given in Part 1 to use the fattest element diameter possible--or a simulation of a fat wire remains valid.

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For those using a NEC program with a "model by equation" facility, such as NEC-Win Plus, the equations in the GW Basic program can be entered directly into the model itself.

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Fig. 7 shows the equations page for such a model. Columns E, F, and G contain the constants and equations for determining variables A, B, and C. Since each final equation (line 7) produces a value for the driver, reflector, and spacing in wavelengths, line 8 converts these values to physical values using the current dimensional units (inches in the figure). Of course, the values for the driver and reflector are for the total circumference, so the required values for A and B are 1/8 of the line 8 numbers.

+

Although this model has only the dimensional equations entered, there is no reason why one cannot also enter the other equations. The spread sheet is fully functional and has sufficient columns (out of sight to the right) to handle the supplemental calculations. One need only enter the design frequency and the wire size (in current dimensional units) to obtain results for both the model and the supplemental information. (Note that the spreadsheet here does know a LOG from a LN, so the conversion factor has been omitted in column D, line 4.)

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Of course, one also needs to attend to the frequency or frequencies for the model, as noted in the upper left corner of the figure. In this case, a sweep of 0.01 MHz each side of the design frequency provides sufficient data to determine the resonant frequency and the frequency of peak front-to-back ratio. The radiation pattern can be modified for a full azimuth pattern, if one needs it.

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The model itself appears in dimensional form in Fig. 8. The dimensions correspond precisely to the output from the Basic program, once one moves from feet to inches or back the other way.

+

The model in the figure has been set in order to correspond to our initial design case. However, let's survey a few designs using material that may be more likely at the chosen frequency than the constant 0.0001 wavelength wire we have so far used. In the tables below, C means calculated by the program and M means modeled results. In all cases, the reference models on which the program is based show a front-to-back ratio that is greater than 50 dB. Hence, the Front-to-Back column may be used as an indication of program accuracy, understanding the values change very rapidly near the peak. Hence, values of about 40 dB or so indicate a peak within about 10 kHz of the design frequency.

+ 
     Wire Size      Frequency      Gain      Feed Z         F-B Ratio
+     (and log)         MHz         dBi       Ohms            dB
+1.  #12 20-meters
+C    0.0808 (-4.0)  14.175         6.99      133.2          ---
+M    0.0808         14.175         7.05      132.3          41.0
+
+2.  #14 20-meters
+C    0.0641 (-4.1)  14.175         6.95      131.6          ---
+M    0.0641         14.175         7.04      130.3          38.1
+
+3.  #14 40-meters
+C    0.0641 (-4.4)  7.15           6.76      126.2          ---
+M    0.0641         7.15           7.03      121.2          31.1
+
+4.  #14 6-meters
+C    0.0641 (-3.6)  50.5           7.07      138.1          ---
+M    0.0641         50.5           7.04      138.7          47.6
+
+5.  0.5" 2-meters
+C    0.5 (-2.2)     144            7.19      149.3          ---
+M    0.5            144            7.18      150.0          59.6
+

The limitations noted earlier have appeared in full force. Thin wire models tend to show up to 1 to 1.5% errors in some data, while fat wire models come very close to calculated values. The break point falls at about the wire size where the log of the diameter in wavelengths reaches -4. However, the actual frequencies of peak front-to-back ratio are within 10 to 15 kHz of the calculated value. Thin wire models tend to show more rapid decreases in front-to-back ratio relative to the peak value for smaller changes in frequency. Consequently, the calculated values for antenna dimensions would easily fall within construction variables.

+

Because of the number of variables--especially compared to the single dimensional variable needed for a single quad loop--we cannot expect quite the same precision of result for 2-element quad beams. However, the program can go a long way toward easing the guesswork involved in the construction of these antennas. Given the need for field adjustment and in many cases the likely need to change the resonant frequency to place the SWR curve where we want it, the program should provide more adequate guidance to the 2-element quad builder than almost anything else around.

+

Note: A version of the GW Basic program is available in HAMCALC. The following links will take you to a download page where you may download the program as a. a NEC-Win Plus model file, b. a GW Basic program, or c. a VB script generously made available by Randy Frum, AC4FD. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen. An on-line Java script calculator (web.archive.org). is available courtesy of the work of Steven Dick.

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Before we leave our 2-element optimized quads, let's tackle one more question: can we improve the operating bandwidth of 2-element quads (especially the front-to-back ratio bandwidth) and avoid large, heavy, tubular elements? That will be our task in Part 3.

+

Also see the Antenna Modeling Programs page for more information.

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Updated 12-01-2000, 11-14-2002, 03-24-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for November, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to Main Index

+

Topics: HF Lower, HF Upper, Quad, VHF / UHF


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2-Element Quads as a Function of Wire Diameter
+ Part 3: Fatter elements from "Mere Wire"

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L. B. Cebik, W4RNL

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In Part 1 of this series, I suggested that there might be a way to simulate large diameter elements in 2-element quads by using wire. The object was to allow the same performance as a thick tubular element without the very high increase in weight associated with such elements. Quad structures are rarely designed to handle anything but wire.

+

In this part, let's re-examine the reasons for wanting to use fat elements in our quads. Then let's perform a modeling test to see if we can get the simulation to work well.

+

Why a Fat-Element Quad?

+

The simplest way to get a handle on why fatter elements are beneficial to 2-element quads is to examine the performance of a couple of optimized designs. The design frequency will be 28.5 MHz. The design passband will be 28-29 MHz: we shall be interested in performance across that span, and not just at the design frequency.

+

The element diameters chosen are 0.0641" and 0.5". The thinner wire corresponds to #14 AWG copper wire, perhaps the most popular quad element material used in the US. The half-inch size is arbitrary, but sufficiently larger to show major performance differences--differences that can make a difference in operation across the designated passband.

+

Each beam was designed using the automated program presented in Part 2 of this series. The #14 version uses a spacing of 0.158 wl. The driver circumference is 1.012 wl long, while the reflector length is 1.071 wl. The design frequency resonant impedance is 136.1 Ohms. The 0.5" diameter version requires a spacing of 0.164 wl. The driver is 1.020 wl long, while the reflector is 1.103 wl long. The resonant impedance at the design frequency is 141.1 Ohms.

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Fig. 1 shows the gain curves for the two quads. As we have noted, the thinner the wire size for a 2-element quad, the closer in frequency are the maximum front-to-back and the maximum gain points. Hence, the #14 quad starts at a higher gain, being closer to the gain peak. However, the gain of the #14 version decreases more rapidly across the passband of interest in this exercise. In contrast, the 0.5" version has a lower rate of change across the band, which tends to even up gain performance between band edges. If gain were the only parameter in question, then there would likely be no reason to work with fatter elements. However, we should also look carefully at the front-to-back curve, shown in Fig. 2.

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It is tempting to focus on the front-to-back peak, which is the same for both antennas. However, of much greater importance is the front-to-back ratio toward the band edges. The front-to-back ratio of the #14 antenna is barely 12 dB at 28 MHz and 16 dB at 29 MHz. 20 dB front-to-back ratio is a common amateur standard. For the #14 version, we achieve this goal only between 28.26 and 28.78 MHz. In contrast, the 0.5" version of the antenna shows better than 20 dB front-to-back ratio between 28.15 and 28.94 MHz, a 50% improvement in bandwidth between the 20-dB markers. At 28 MHz, the 0.5" antenna improves the front-to-back ratio by 4 dB over the #14 version, while at 29 MHz, the improvement is 5 dB.

+

The operational improvements are sufficiently large to encourage us to try to obtain them. We may not want to go to exceptional lengths mechanically to acquire the improved performance, but if we could modify the standard quad support structure in minor ways, the modifications might be worth the work.

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To complete the record, Fig. 3 shows the comparative SWR curves of the two antennas, each referenced to its own resonant feedpoint impedance. Once more, we see the more rapid increase in SWR below design frequency than above it. Since the SWR never reaches 2:1, we might be satisfied with either curve. However, for very long coax runs, the 0.5" curve is superior in reducing line losses.

+

How Can We Obtain Fat Element Performance from Wire?

+

For any fat element, we may construct an equivalent element from 2 wires spaced by a distance that is not at all arbitrary. When using relatively thin wire to simulate very thick elements, a three wire scheme may be required, but the transition from #14 to 0.5" on 10 meters is far from needing the added wire.

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For linear elements, such as used in Yagis, the technique is simple. We may take each element and find its resonant frequency. Then we construct a wire pair (shorted at the ends and the center) of the same length as the tubular element. We adjust the spacing until we arrive at the same resonant frequency. For most simple arrays of linear elements, the spacing used for one element will generally suffice for all of them.

+

The dual wire element will have a higher material loss than the original tubular element, since its surface area is smaller. However, the performance of a parasitic array depends more upon the inter-element coupling than on material loss (within limits, of course). The dual wire element restores the level of coupling that is reduced in the move from a fat to a thin element. Hence, the modeled performance of Yagis using thick tubular elements and their dual wire equivalents is generally within 0.1 dB gain and indistinguishable with respect to the front-to-back ratio and the impedance curve. These factors apply not only to the design frequency, but as well across the passband.

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For 2-element quads, with their closed element geometry, the construction of a 2-wire equivalent requires a different procedure--more of a trial and error technique. Constructing a 2-wire element for each of the quad's elements requires a trial spacing of the wires and then adjustment of the overall loop sizes to bring the antenna to resonance and to maximum front-to-back ratio at the design frequency. The feedpoint impedance at resonance is a good indicator that the wire spacing is correct: it should be about the same as the fat-element antenna being simulated.

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There are two main ways to construct dual-wire elements, shown in Fig. 4.

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One method, shown on the left, involves placing a cross-piece at the loop support point--a sort of Tee-configuration. Then, for each element, identical loops are built, spaced by the desired amount. At each corner (minimally), bridge wires between loops are required to ensure that each loop in the element has the same current distribution. The mid-point between loops in each element--where the support arm is--represents the point for measuring the spacing between elements.

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The second method is to construct loops in the same plane. This method is illustrated on the right in Fig. 4. The two loops for each element will have different circumferences, one larger and one smaller than the reference length used to calculate them. Once more, bridge wires are necessary at the corners (at least) to ensure equal current distribution along the wires of each loop. In this planar construction method, each element is a constant distance from the other.

+

For our test antenna, I finally settled on a wire spacing of 5" for both the Tee and the planar models. To show what is necessary in quad element adjustment for the simulated fat elements, the following table may be useful.

+ 
Antenna             #14 Single     0.5" Single    #14 Tee        #14 Planar
+Element Spacing     0.158 wl       0.164 wl       0.164 wl       0.164 wl
+Driver Length       1.012 wl       1.020 wl       1.003 wl       1.003 wl
+Refl. Length        1.071 wl       1.103 wl       1.107 wl       1.107 wl
+Resonant Impedance  136.1 Ohms     141.1 Ohms     142.1 Ohms     141.8 Ohms
+

For the Tee configuration, the actual spacing is +/- 2.5" for each of the loops. For the planar configuration, the actual loop lengths are 4 x +/-2.5" for each loop. From the perspective of resonance and maximum front-to-back ratio at the design frequency, it makes no difference whether one uses the Tee or the planar configuration. The results are the same to 4 significant figures, with differences only in the 5th digit for numerical fussiness on my part.

+

More interesting at this point is the fact that each of the dual-wire antennas requires a smaller driver and a larger reflector than the 0.5" antenna which they simulate. In fact, the dual-wire driver is even smaller than that required for the more closely spaced single #14 antenna. Whether these loop size adjustments will affect performance remains to be seen.

+

Modeling dual wire elements involves great care. The 5" spacing at 10 meters presses the limits of NEC-2. To ensure equal current distribution in the driver, one must model a single wire of at least three segments, with the source placed at the center. Then, 1 segment wires move at right angles to the center feed wire to the required spacing limit. For 5" spacing, these wires were each 2.5" long. Since NEC prefers that wires meeting at angles have similar segment lengths, 2.5" became the standard segment length for the entire model. The planar model required different levels of segmentation for the inner and outer loops in order to keep the segment junctions parallel with each other. In the end, the models required between 645 and 670 segments. This level of segmentation still provided a large segment length to wire diameter ratio, also desirable for accuracy.

+

Even with such care, the NEC-2 models pressed the core limits for the close spacing of wires. Initial NEC-2 models showed a systematic 0.3 dB gain deficit relative to the 0.5" model. Applying the average gain test in NEC-Win Plus to all of the models produced values of 1.002 for both of the single wire models. However, the dual-wire models yield values 0.969. Values close to 1.000 indicate a precise model within the limits of the test (which is a necessary, but not a sufficient condition of model adequacy). For many general purposes, values as low as 0.96 and as high as 1.04 are considered very good. However, for correlating models, especially when one design is a proposed substitute for the other, the average gain test values were considered inadequate.

+

The models were reconstructed in NEC-4, which is, while not perfect, considerably better than NEC-2 with respect to close wire situations. Unfortunately, the average gain test was not available in the version of NEC-4 used. However, the gain deficit dropped to 0.1 dB. I suspect, but cannot prove, that the remaining deficit is a function of the core and not a real difference between antennas. (Proof will have to await the next generation of modeling cores.) Part of my suspicion arises from the fact that the dual wire models virtually eliminate material loss as a source of reduced gain. The single #14 wire quad has an efficiency of 97.9% as a function of wire composition, including skin effect. The 0.5" model has an efficiency of 99.7%. Both dial-wire antennas have efficiencies of 99.0%.

+

We shall look separately at the performance of the Tee and the planar versions of the dual-wire 2-element quad. The reason will become apparent before we are done.

+

The Dual-Wire Tee Model

+

Fig. 5 presents a sketch of the elements of the dual-wire quad in the Tee configuration (where "Tee" refers to the unseen supporting structure). The structure, including the feedpoint modeling, are apparent from the sketch.

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+ +
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Since the SWR curve is relatively unimportant to the antenna's performance, we may by-pass that consideration and focus upon gain and front-to-back ratio, compared to the 0.5" antenna which the new version simulates.

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Fig. 6 presents the gain curves across the first MHz of 10 meters for the 0.5" antenna and its counterpart. Of note is the NEC-4 deficit of about 0.1 dB average that we have previously noted. More important however is the shallower curve for the dual wire antenna. The lower rate of change in gain tends to indicate that the 5" spacing between wires is actually simulating a wire somewhat fatter than 0.5".

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The impression given by the gain curve in Fig. 6 is confirmed in the front-to-back curve in Fig. 7. The dual-wire version of the antenna actually increases the passband for better than 20 dB front-to-back ratio from 28.1 to 29.0 MHz. This operating bandwidth is not a function of the very slightly lower peak front-to-back ratio at the design frequency. That difference only indicates that the 0.5" curve is better centered at 28.5 MHz.

+

With respect to gain and front-to-back ratio, then, there is little to choose between the dual thin-wire and the single fat wire models.

+

The Dual-Wire Planar Model

+

The model construction of the planar configuration of the dual-wire quad appears in Fig. 8. The construction of an actual planar antenna using the dual wire technique should parallel the model closely, especially with respect to the use of bridge wires and the feedpoint area of the driver.

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+ +
+

Once more, we shall by-pass the SWR curves and focus our attention on gain and front-to-back performance bandwidths.

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Fig. 9 shows the gain curves of the planar model and the 0.5" standard. The planar model shows the same tendency toward a shallower rate of gain decrease across the band than the single 0.5" element model. Interestingly, the planar model begins 0.03 dB lower than the Tee model at 28 MHz, but ends up at the same gain value at 29 MHz.

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The front-to-back curve in Fig. 10 shows the same performance spread as the equivalent curve for the Tee--a 28.1 to 29 MHz passband for better than 20 dB front-to-back ratio. By now, it should be apparent why I have presented the Tee and planar curves separately: placed on the same graph, we could not see one through the other.

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To illustrate the point, Fig. 11 presents the SWR curves for both dual-wire antennas, along with the curve for the 0.5" model. The Tee and planar curves overlie each other so closely that they are indistinguishable. In fact, for every operating parameter about which we might have concerns, the two versions of the dual-wire antenna are indistinguishable. Moreover, the curves also suggest one more time that the dual-wire antennas are of broader operating bandwidth in every important way than the 0.5" model for which they are a substitute.

+

Finding the exact spacing to be a precise substitute for the 0.5" element model would have been an exercise in unwarranted fussiness. 5" is a nice round number and convenient for modeling. #12 AWG wire (.0808" diameter) would have yielded a different dual-wire spacing for the same equivalence to a 0.5" single element. However, the more likely course of further experimentation should be to find the spacing (in easy-to-handle numbers) that yields a true minimum front-to-back ratio of 20 dB across the entire 1 MHz span of 10 meters.

+

The present exercise has been aimed at establishing the principles of dual-wire simulation of fat-wire elements in the optimized 2-element quad. I suspect that the wider bandwidth of performance with the 5" spacing suggests that a slightly wider element spacing might show further gains. However, that increase would be of the order of 0.001 wl for a total spacing of 0.165 wl at the design frequency. Such differences would likely be lost in the variables of actual antenna construction.

+

More significant to antenna construction are the physical consideration of choosing the planar or Tee models. Initially, the planar version seems more appealing, since it requires fewer parts. There is no need for fixing the Tee support to the main support arm. The absence of any significant difference between the Tee and planar model performance suggests that the planar model would perform equally well on either of the two main types of quad construction: the use of a spider hub and slanting support arms or the use of a boom with flat-plane support arm structures. The only possible deficit for the planar model is the need to have loops for each element that have different circumferences.

+

With proper construction, the dual-wire antennas--especially the planar model--can strengthen the overall assembly for each element by providing dual tensioning of the arms relative to each other. However, by using 2 wires for each element (relative to a narrow banded single #14 wire), we have increased the available wire for ice and snow loading. How the strengthening and the loading potentials balance, one cannot say in the abstract.

+

The dual-wire technique is not restricted to monoband 2-element quads. It is adaptable to 3-band and 5-band quads. I would suspect that single wire elements would satisfy the needs of the narrower bands--17 and 12 meters. However, the use of dual wire techniques might overcome the fall-off of performance on the wider bands--20, 15, and 10 meters. As well, the inherently wider SWR curve for the dual-wire configuration might overcome some of the interaction between bands that makes a shallow SWR curve difficult to obtain on some bands in some multi-band designs.

+

The key to a good multi-band 2-element quad employing dual-wire techniques for the wider bands lies in the balance of the support arm strength and the potential for winter loading. The wire weight would be about 60% greater than for single wire designs, with an equal increase in surface area. Hence, before tackling such a task, one would do well to assess the adequacy of the support structure.

+

In addition, the design of a multi-band 2-element quad using dual wire elements for some bands requires a total redesign of the elements relative to conventional values. Not only must the wire spacing be selected so that the coverage on each band meets design specifications, but as well, the driver and loop sizes must be refigured for the element spacing selected--along with the spacing between elements.

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The design task is far from simple. However, it is feasible and may be one way to bring quad design from the 1960s into the new millennium. There is no good reason why quads should not enjoy the same high front-to-back ratios across the ham bands as the Yagis with which they compete.

+

An Additional Note on Dual-Wire Gain

+

The matter of the gain deficit that appeared in NEC-2 models of the dual-wire wider-band 2-element quads continued to disturb me. Even though the final deficit was small in NEC-4 models, I still wondered if there was a way of rebuilding the dual-wire models to eliminate any question of whether the deficit was real or a product of core limitations.

+

I rebuilt the planar model in the following way: I eliminated the driven element section for the feedpoint and ran both wires continuously from corner to corner. I then placed a source at the center of each lower driver wire to simulate a parallel feed of the two loops. The resulting model could use fewer segments, since the minimum segment size was now about 5" to keep the segment junctions parallel between the inner and outer loops of each element. Slight adjustments of driver and reflector brought the model to the optimal conditions of resonance and maximum front-to-back value. The Average Gain Test in NEC-2 registered 0.9996, a value considered to indicate a highly accurate model.

+

The resulting frequency sweep with the model on both NEC-2 and NEC-4 yielded an average gain differential of 0.025 dB between cores. At 28.5 MHz, the NEC-2 dual wire model gain is now within 0.06 dB of the 0.5" single wire model. There are no significant differences in the front-to-back and the SWR curves.

+

The following table summarizes the differences between the original and the alternative models at the design frequency. NEC-2 performance figures are shown.

+ 
Model                   Original Planar         Alternate Planar        0.5"
+Free-space gain         6.92 dBi                7.07 dBi                7.13 dBi
+Max. front-to-back      51.56 dB                49.44 dB                55.82 dB
+Feedpoint impedance     141.8 + j0.5 Ohms       141.7 - j0.2            141.1 - j0.5 Ohms
+Driver Length           1.003 wl                1.015 wl                1.020 wl
+Reflector Length        1.107 wl                1.108 wl                1.103 wl
+Spacing                 0.164 wl                0.164 wl                0.164 wl
+

The differential in reflector length is under 0.1% and makes no difference in operation. The driver length difference between the original and alternate models is about 1.2%, but falls within the range of field adjustments, since the builder may wish to alter the frequency of resonance within the passband. The feedpoint impedances are identical well-beyond any possibility of measuring a difference.

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The disadvantage of using the alternate model is the requirement to calculate the parallel combination of series R+/-jX impedances for the two loops. However, the simplification of the model, the higher AGT rating, and the far better agreement with NEC-4 models all recommend the alternative. The alternative technique also holds some promise of allowing dual wire versions of long boom quad models, since the segmentation per loop is halved relative to the original planar model.

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Of course, the alternative model tends to confirm my suspicion that there is no significant gain difference--even minusculely--between the dual-wire quads and the 0.5" single element quad.

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Updated 01-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for December, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Topics: HF Lower, HF Upper, Quad, VHF / UHF


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Automating the Design of 3-Element Monoband Quad Beams
+ Part 1: A Wide-Band Model

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+

L. B. Cebik, W4RNL

+

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+

The exercise of automating the design of 2-element quads raised the question of whether a similar technique might be applied to 3-element quads. One answer is in this set of notes.

+

For all quads, from 1 to n elements, performance depends in large measure upon the diameter of the loop wire as measured in terms of wavelength. Indeed, performance varies with the common logarithm of the wire diameter.

+

When we automated the design of 2-element quads, we chose as the primary parameter the spacing between elements such that it yielded the highest front-to-back ratio when the array was resonant. The design equations for 3-element quads retained the same feature, using the same progression of spacings between the reflector and the driven element. This selected spacing not only yields the highest front-to-back ratio, but as well it tends to yield the widest operating bandwidth. As we noted in the discussion of 2-element quads, quad array bandwidth is less a matter of the 2:1 SWR bandwidth and more a matter of the >20 dB front-to-back ratio bandwidth.

+

The director was sized and spaced to yield a good gain with a resonant feedpoint impedance between 70 and 80 Ohms. In general, this procedure does not yield the very highest possible gain or the shortest boom length possible. However, it does produce a very good gain (as judged in quad terms) with the widest possible operating bandwidth. In a general way, the required driver-to-director spacing is nearly double that of the reflector-to-driver spacing. Fig. 1 illustrates the relationship.

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It is certainly possible to emphasize one parameter over another and achieve a different design from the one used in this exercise. In Part 2, we shall examine a higher-gain model. However, the compromise of gain and operating bandwidth in the version under study here yields a very workable 3-element quad design with boom lengths of about 0.4 wavelengths.

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The procedures for developing the design algorithms are the same as for the 2-element quads. I optimized designs in the 10 meter band using wires between 0.0000316 wl and 0.01 wl. I then subjected the resulting curves to regression analysis to produce a series of equations that can be placed into a modeling program with model-by-equation facilities or into a utility program for simple calculation of dimensions and basic operating data. As I have noted in connection with simpler quad designs, regression equations do not have theoretic significance in and of themselves, but they do yield outputs that model as resonant quad arrays for any wire size within the set limits and for any HF or VHF frequency. As with the 2-element equations, the gain figures tend to be higher than the baseline at lower HF frequencies and lower than the baseline at VHF frequencies, since everything has been calibrated at 10 meters for copper wire elements.

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The following GW Basic utility program requires only the entry of the wire size and the design frequency to set the calculations in motion. Since direct entry of AWG wire sizes is not included, the following table makes a good refresher:

+ 
AWG Size          Dia. Inches             Dia. mm
+18                .0403                   1.0236
+16                .0508                   1.2903
+14                .0641                   1.6281
+12                .0808                   2.0523
+10                .1019                   2.5883
+ 8                .1285                   3.2640
+

Besides the usual dimensional outputs, the program will also display the wire diameter as a function of a wavelength. The performance data includes the approximate gain at the design frequency, the feedpoint impedance, the 2:1 SWR bandwidth as a percentage of the design frequency, the >20 dB front-to-back bandwidth as a percentage of the design frequency, and the rate of change of gain over a span of 1% of the design frequency. Remember that the line with the "LOG" entry is, for GW Basic, a natural log and requires a correction factor to create a common log. If you translate the program to another medium, you can drop the conversion factor if the medium recognizes common logs.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 THEN 160 ELSE 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 IF D1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.00064:BD=.01044148148#:CD=.06484444444#:DD=.1886626455#:ED=1.232080635#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0009333333333#:BR=.01915555556#:CR=.13983333333#:DR=.4587492063#:ER=1.64042381#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.0012#:BI=-.0209037037#:CI=-.13021111111#:DI=-.3498137566#:EI=.5941126984#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=-.0033#:BS=-.03927777778#:CS=-.1724583333#:DS=-.3239603175#:ES=-.04951547619#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.004866666667#:BP=-.06262962963#:CP=-.29347222222#:DP=-.6174457672#:EP=-.2289269841#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=-2.227066667#:BZ=-26.75247407#:CZ=-115.9142556#:DZ=-217.8183323#:EZ=-79.59203175#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.07#:BG=-.7877777778#:CG=-3.350833333#:DG=-6.143888889#:EG=5.104166667#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=-.05847333333#:BW=-.5028392593#:CW=-.4586494444#:DW=6.080227037#:EW=17.61091389#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11695666667#:BF=1.717985556#:CF=9.6510925#:DF=25.23848992#:EF=27.78167988#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 AN=-.04666666667#:BN=-.5414814815#:CN=-2.302777778#:DN=-4.364074074#:EN=-3.092777778#
+380 DG=(AN*(D1^4))+(BN*(D1^3))+(CN*(D1^2))+(DN*D1)+EN
+390 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+400 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+410 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+420 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+430 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+440 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+450 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+460 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+470 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+480 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+490 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+500 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+510 PRINT "Free-Space Gain =";GN;"dBi"
+520 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+530 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+540 PRINT "Approximate Rate of Gain Change =";DG;"dB per 1% of Design Frequency"
+550 INPUT "Another Value = 1, Stop = 2: ";P
+560 IF P=1 THEN 10 ELSE 570
+570 END
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Wire size and 3-Element Quad Performance

+

The effects of wire size on gain are as vivid for a 3-element quad as for a 2-element quad, as shown in Fig. 2.

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+

In this figure, wire size is listed in wavelengths, using values that translate into a linear progression of the logarithms of the wire sizes. There is well over a dB difference in the gain of arrays using the thinnest wire size and arrays using the fattest wire size. Moreover, the increase in gain over the corresponding 2-element quad also increases with wire size. The thinnest wire size 3-element quad shows a 1.3 dB improvement in gain over a 2-element quad using the same wire, whereas the fattest wire 3-element quad shows a gain improvement of nearly 2 dB over its corresponding 2-element array.

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Fig. 3 shows the change of maximum front-to-back ratio with increasing wire size. Theoretically, the curve should be smooth and almost linear across the scale. Since the checkpoint models were hand optimized, allowing the maximum front-to-back ratio to occur as little as 10-15 kHz from the design frequency yields the flat portion of the curve. However, in practice, this slightly less than optimal design curve makes no practical difference, since constructing a quad so that its front-to-back ratio maximum is precisely at the design frequency is more hope than reality. Nevertheless, the increase of both gain and front-to-back ratio with wire diameter demonstrates the importance that wire size has in effecting maximum mutual coupling between quad elements. Thin wire quads of the sort we generally construct at HF with #14 or #12 wire simply are not capable of achieving all of the performance that a quad can provide.

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The feedpoint impedances as a function of wire size appear in Fig. 4. Here, the curve is very real and not a function of optimizing variance. With the thinnest wire, the gain peak and the front-to-back ratio peak are very close together, yielding less than a peak feedpoint impedance value. As the wire size increases, the gain peak occurs well below the design frequency so that the front-to-back maximum value dominates the production of the feedpoint impedance.

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Fig. 5 shows the circumference of each of the 3 elements in wavelengths. As with the 2-element quads, the reflector size increases more rapidly than the driver size. However, the required reflector circumference is shorter in the 3-element quad than in the 2-element quad for any given wire size.

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Interestingly, the director circumference does not follow the pattern for the other two elements. As the wire size increases, the required director size decreases. If we were to normalize the driver circumference so that it graphs as a straight line across the page, the director line would move down at almost the same rate as the reflector line moves up.

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The spacing graphic, in Fig. 6, gives some precision to the earlier remark that the driver-to-director spacing is about twice the reflector to driver spacing. In fact, the spacing from the driver to the reflector increases with wire diameter--between about 0.14 and 0.17 wl for the span of wire sizes included in the exercise. In contrast, the required director-to-driver spacing decreases with increases in wire size--from about 0.32 wl for the smallest wire to about 0.25 wl for the fattest wire.

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Sample Frequency Sweeps

+

The full story of what happens as we change wire sizes becomes much more evident if we perform some frequency sweeps. So I designed quads using three wire sizes: 0.0131" (near to #28 AWG), 0.131" (near to #8 AWG), and 1.31". The design frequency was 28.5 MHz, and the wire sizes correspond to 0.0000316, 0.000316, and 0.00316 wl diameters. The frequency sweep used 0.1 MHz intervals from 28 to 29 MHz.

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In Fig. 7, we have the gain curves across the first MHz of 10 meters for the 3 quads. The lowest curve for the thinnest wire shows the gain peak within 0.1 MHz of the design frequency, with a rapid drop in gain at the low end of the band. For the middle-size wire, the gain peak is evident at 28.1 MHz, while for the fattest wire, gain is peak but flat for the first 0.2 MHz of the passband.

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Equally evident to the gain advantage of the fattest wire is the very slow rate of gain decrease compared to the thinner wires. The thinner wires show a full half dB variance in gain across the passband, while the range of gains is only 0.2 dB for the fattest wire.

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The front-to-back curves in Fig. 8 show several things. First, the slight displacement of the curve for the fattest wire downward in frequency by about 15 kHz corresponds to the flattened portion of the front-to-back curve in Fig. 3. Apart from that slight offset, the three curves are remarkable congruent with each other. The rates of decrease from the peak are similar for all three curves and are parallel both above and below the design frequency. Finally, note the steeper rate of decrease below design frequency than above design frequency. These curves are fully consistent with those for 2-element quads.

+

If we select some arbitrary dividing value, such as a 20 dB front-to-back ratio, it is clear that even the fattest wire version of the 3-element quad does not cover all of the 1 MHz passband of the exercise. In this regard, the 3-element quads designed here have slightly narrower front-to-back ratio operating bandwidths than corresponding 2-element models.

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A similar narrowing of the operating bandwidth applies to the 2:1 SWR dividing lined commonly used to denote acceptable performance, as shown in Fig. 9. Only the fattest wire model covers the entire passband. By judiciously lowering the resonant frequency of the middle-size wire model, it can be set to show under 2:1 SWR just about all the way across the passband. This fact results from the more rapid rise in SWR below design frequency than above it. Since the entire set of resonant feedpoint impedance is between 70 and 80 Ohms for all wire sizes at the design frequency, all SWR values in the curves are referenced to 75 Ohms.

+

Some Sample 3-Element Quad Arrays

+

To provide a sample of the program's output, here are some dimensions and performance data for a few 3-element quads.

+ 
1.  20 meters, #14 wire, design frequency: 14.175 MHz
+Wire Diameter:                0.0641" or 7.70E-5 wl
+Reflector Circumference:      73.09'
+Driver Circumference:         70.06'
+Director Circumference:       65.31'
+Refl-Driver Spacing:          10.69'
+Driver-Dir Spacing:           21.58'
+Total Boom Length:            32.27'
+Feedpoint Impedance:          79.5 Ohms
+Free-Space Gain:              8.47 dBi
+SWR Bandwidth:                3.10% or 0.439 MHz
+>20 dB F-B Bandwidth:         1.18% or 0.167 MHz
+Rate of Gain Change:          0.22 dB/1% of design frequency
+

Although the quad array modeled here has an acceptable SWR across all of 20 meters, the front-to-back ratio becomes a limiting factor. On a crowded band such as 20 meters, front-to-back ratio is very often an important antenna design consideration. For most installations, therefore, the antenna would likely be designed for either the CW/digital end of the band or for the phone end of the band.

+ 
2.  10 meters, #12 wire, design frequency: 28.5 MHz
+Wire Diameter:                0.0808" or 1.95E-4 wl
+Reflector Circumference:      36.64'
+Driver Circumference:         34.95'
+Director Circumference:       32.43'
+Refl-Driver Spacing:           5.49'
+Driver-Dir Spacing:           10.30'
+Total Boom Length:            15.79'
+Feedpoint Impedance:          77.2 Ohms
+Free-Space Gain:              8.74 dBi
+SWR Bandwidth:                3.34% or 0.952 MHz
+>20 dB F-B Bandwidth:         1.41% or 0.402 MHz
+Rate of Gain Change:          0.21 dB/1% of design frequency
+

Let's compare this array with another for the same frequency.

+ 
3.  10 meters, 0.5" wire, design frequency: 28.5 MHz
+Wire Diameter:                0.5" or 1.21E-3 wl
+Reflector Circumference:      37.42'
+Driver Circumference:         35.22'
+Director Circumference:       32.39'
+Refl-Driver Spacing:           5.66'
+Driver-Dir Spacing:            9.57'
+Total Boom Length:            15.23'
+Feedpoint Impedance:          72.3 Ohms
+Free-Space Gain:              9.00 dBi
+SWR Bandwidth:                4.42% or 1.20 MHz
+>20 dB F-B Bandwidth:         2.11% or 0.601 MHz
+Rate of Gain Change:          0.10 dB/1% of design frequency
+

The 0.5" wire quad shows all of the dimensional characteristics in comparison to the #12 AWG version that we have seen in the curves. As well, 0.5" performance is slightly up, while the feedpoint impedance is slightly down relative to the #12 wire model. Most significantly, the SWR and front-to-back operating bandwidths for the fat-wire model are 30% or more greater than those of the thin-wire array. Of course, it is impractical to consider construction of a quad array for 10 meters that has half-inch diameter elements. However, we shall return to this problem before we close the book on this exercise.

+ 
4.  6 meters, 0.25" wire, design frequency: 51 MHz
+Wire Diameter:                0.25" or 1.08E-3 wl
+Reflector Circumference:      20.87'
+Driver Circumference:         19.67'
+Director Circumference:       18.10'
+Refl-Driver Spacing:           3.16'
+Driver-Dir Spacing:            5.37'
+Total Boom Length:             8.53'
+Feedpoint Impedance:          72.4 Ohms
+Free-Space Gain:              8.99 dBi
+SWR Bandwidth:                4.14% or 2.11 MHz
+>20 dB F-B Bandwidth:         2.05% or 1.05 MHz
+Rate of Gain Change:          0.11 dB/1% of design frequency
+

The 6-meter version of the 3-element quad is similar in characteristics to the 0.5" 10-meter array, since the wire diameters are similar relative to a wavelength. However, even a wire size of about 0.001 wl is insufficient to provide a full front-to-back operating bandwidth for the wide 6-meter band. Elements closer to 1" in diameter would be necessary for this task.

+ 
5.  2 meters, 0.1" wire, design frequency: 146 MHz
+Wire Diameter:                0.1" or 1.24E-3 wl
+Reflector Circumference:       7.31'
+Driver Circumference:          6.88'
+Director Circumference:        6.32'
+Refl-Driver Spacing:           1.11'
+Driver-Dir Spacing:            1.87'
+Total Boom Length:             2.98'
+Feedpoint Impedance:          72.2 Ohms
+Free-Space Gain:              9.00 dBi
+SWR Bandwidth:                4.24% or 6.19 MHz
+>20 dB F-B Bandwidth:         2.19% or 3.20 MHz
+Rate of Gain Change:          0.10 dB/1% of design frequency
+

The same 4-MHz bandwidth, when moved from 6 to 2 meters, presents less of a problem for a 3-element quad composed of 0.001 wl wire. The >20 dB operating bandwidth now covers about 80% of the band. The use of 0.25" wire would easily permit the achievement of all benchmarks across the entire 2-meter band.

+

Hopefully, these examples will provide some guidance in developing a sense of the requisite wire size to achieve not only a desired gain level, but as well a desired operating bandwidth for 3-element quad arrays of the present design.

+

Simulating Large-Diameter Elements

+

In a past 2-element quad exercise, we looked at the use of spaced #14 AWG wires to simulate fatter single wires. In that effort, we used 2 #14 AWG copper wires spaced 5" apart and joined at the corners. We explored two different configurations and found no significant difference between them. The resulting 2-element quad easily replicated the performance of a 0.5" diameter quad, with a bit to spare. The consequences of substituting 2 thinner wires for one fatter one were a slight enlargement of the reflector and a slight decrease in the driver circumference.

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I repeated the exercise for the 3-element 0.5" wire array noted among the examples. Since the number of variables increases with every new element, I restricted my efforts to planar loops, illustrated in Fig. 10. Note the structure of the planar loops, including the necessary corner wires. Optimizing the model required some further adjustments in director circumference and spacing, since the 2-element array showed the dual-wire version to act like a wire slightly fatter than a half-inch in diameter.

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Here is a comparison of the dimensions (in inches) between the two models. Note that the dimensions for the dual-wire model represent positions halfway between the two wires, so that the actual wire positions are +/- 2.5" relative to the coordinates that would emerge from the listed dimensions.

+ 
Dimension                     0.5" Single Wire              2x#14 AWG Wires
+Reflector Circumference:      449.0"      1.084 wl          449.3"      1.085 wl
+Driver Circumference:         422.7"      1.021 wl          421.4"      1.018 wl
+Director Circumference:       388.6"      0.939 wl          385.3"      0.930 wl
+Refl-Driver Spacing:           67.9"      0.164 wl           67.9"      0.164 wl
+Driver-Dir Spacing:           114.8"      0.277 wl          111.0"      0.268 wl
+Total Boom Length:            182.7"      0.441 wl          178.9"      0.432 wl
+

Although the differences are small, they are significant in arriving at the final operating characteristics of the array. While the dual-wire reflector is slightly larger than the single-wire elements, the dual-wire driver and director are both slightly smaller. As well, the dual-wire director is closer to the driver, resulting in a shorter overall boom length for the array.

+

Performance for the 3-element dual-wire array parallels that of its 2-element cousin. The model shows slightly less gain at the design frequency, but whether this minuscule gain loss is real or an artifact of the closely spaced wires in the model remains uncertain.

+
+ +
+

Fig. 11 shows the gain curves for both versions of the array from 28 to 29 MHz. Immediately apparent is the fact that the dual-wire gain decreases more slowly than the single wire gain. Shallower gain curves are generally characteristic of fatter wires with higher overall gain--a fact which contributes to the uncertainty over the slight gain deficit in the dual wire model at the design frequency. However, the gain differences between versions of the antenna would make no operational difference at all.

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+ +
+

A second piece of evidence that the 5" spacing of the dual wire model acts similarly to a wire somewhat fatter than the 0.5" model appears in Fig. 12. The front-to-back curve of the dual-wire version is slightly wider than that of the 0.5" single-wire model. Again, the differences make no operational difference, but their existence is numerically significant in the process of equating dual-wire arrangements with corresponding diameters of single wires.

+

Comparing the feedpoint impedances between the two version of the array does not permit an easy chart. The dual-wire model uses a dual feed system of driver wires fed essentially in parallel. Hence, the composite feedpoint impedance required hand calculation. However, the following table of values may be useful in exploring the feedpoint situation. Resistances and reactances are in Ohms.

+ 
Frequency               0.5" Single Wire                    2x#14 AWG Wires
+MHz               Resistance  Reactance   75-Ohm SWR        Resistance  Reactance
+28.0              53.10       -43.78      2.13              53.76       -38.55
+28.1              56.78       -34.52      1.80              57.97       -30.44
+28.2              60.57       -25.56      1.54              60.25       -22.55
+28.3              64.44       -16.90      1.33              63.57       -14.86
+28.4              68.33       - 8.51      1.16              66.89       - 7.34
+28.5              72.19       - 0.38      1.04              70.18       - 1.01
+28.6              75.99         7.54      1.11              73.43         7.20
+28.7              79.70        15.28      1.23              76.62        14.32
+28.8              83.31        22.89      1.36              79.73        21.36
+28.9              86.79        30.41      1.49              82.76        28.36
+29.0              90.16        37.88      1.63              85.73        35.37
+

Both antennas would easily cover the first MHz of 10 meters with a VSWR under 2:1, although the 0.5" model might require a slight adjustment of the driver to bring its resonant point lower in the band. (Such adjustments to the driver, if modest, have no significant effects on the other operating characteristics of the array.)

+

Besides looking at raw feedpoint impedance values, it is often useful to examine the swing of both resistance and reactance across the passband in question. The dual-wire array changes resistance nearly 14% less than the single-wire model, while the dual-wire reactance changes nearly 10% less. Both numbers are clear indications that the dual-wire system with its 5" spacing represents a single wire that is larger than the 0.5" diameter used for comparison.

+

The bottom line on the exercise is that a set of dual-wire loops for a quad array can effectively improve 3-element quad performance relative to the customary single #14 AWG quad structure. Even if one discounts the gain advantage of the dual-wire array as operationally marginal, the improvement to both the SWR and front-to-back operating bandwidths is undeniably significant to all except those operators who use only small portions of the wider amateur bands.

+

The following links will take you to a download page where you may download the program as a. a NEC-Win Plus model file, b. a GW Basic program, or c. a VB script generously made available by Randy Frum, AC4FD. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen. An on-line Java script calculator (web.archive.org) is available courtesy of the work of Steven Dick.

+

The process of converting one of the automated designs to a dual-wire version does require hand-optimization at present. However, the automated designs that emerge from the utility program shown in this article provide some useful starting points for developing realistic 3-element monoband quad arrays that live up to their theoretical potential. This wide-band design focuses on one potential; next month's high-gain design focuses on another.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +
+

Updated 02-01-2001, 11-14-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for January, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Quad List

+

Go to Main Index

+

Topics: HF Upper, Quad, VHF / UHF


+ + diff --git a/content/quad/q3le2-1.gif b/content/quad/q3le2-1.gif new file mode 100644 index 0000000..624b4bc Binary files /dev/null and b/content/quad/q3le2-1.gif differ diff --git a/content/quad/q3le2-2.gif b/content/quad/q3le2-2.gif new file mode 100644 index 0000000..924d206 Binary files /dev/null and b/content/quad/q3le2-2.gif differ diff --git a/content/quad/q3le2-3.gif b/content/quad/q3le2-3.gif new file mode 100644 index 0000000..3a68c63 Binary files /dev/null and b/content/quad/q3le2-3.gif differ diff --git a/content/quad/q3le2-4.gif b/content/quad/q3le2-4.gif new file mode 100644 index 0000000..f843985 Binary files /dev/null and b/content/quad/q3le2-4.gif differ diff --git a/content/quad/q3le2-5.gif b/content/quad/q3le2-5.gif new file mode 100644 index 0000000..bf7c6b5 Binary files /dev/null and b/content/quad/q3le2-5.gif differ diff --git a/content/quad/q3le2-6.gif b/content/quad/q3le2-6.gif new file mode 100644 index 0000000..de23525 Binary files /dev/null and b/content/quad/q3le2-6.gif differ diff --git a/content/quad/q3le2-7.gif b/content/quad/q3le2-7.gif new file mode 100644 index 0000000..1debfd4 Binary files /dev/null and b/content/quad/q3le2-7.gif differ diff --git a/content/quad/q3le2-8.gif b/content/quad/q3le2-8.gif new file mode 100644 index 0000000..80609bc Binary files /dev/null and b/content/quad/q3le2-8.gif differ diff --git a/content/quad/q3le2-9.gif b/content/quad/q3le2-9.gif new file mode 100644 index 0000000..10e85c2 Binary files /dev/null and b/content/quad/q3le2-9.gif differ diff --git a/content/quad/q3le2.html b/content/quad/q3le2.html new file mode 100644 index 0000000..03d4f04 --- /dev/null +++ b/content/quad/q3le2.html @@ -0,0 +1,242 @@ + + + + + + Automating the Design of 3-Element Monoband Quad Beams Part 2 + + + +
+

Automating the Design of 3-Element Monoband Quad Beams
+ Part 2: A High-Gain Model

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the first part of this small study on automating the design of 3-element quad beams, we explored a wide-band version of the array--at least, as wide-band a version as we could obtain while still developing reasonably good gain. The results yielded a quite feasible set of potential designs. As with any quad design, the fatter the element used, the better the performance.

+

Dan Handelsman, N2DT, reviewed an early draft of the initial program and design. He pointed out an alternative design that achieved significantly higher gain, had good front-to-back figures, and had a relatively low feedpoint impedance suitable for a direct 50-Ohm match. The sacrifice in operating bandwidth--as defined by the >20 dB front-to-back ratio rather than the 2:1 VSWR ratio--was still far less than with some other high gain designs.

+
+ +
+

The high-gain 3-element quad has a quite different profile than the wide-band model, as revealed in Fig. 1. Although the overall boom-length is similar--about 0.4 wl--the high-gain design spaces the driver considerably farther from the reflector and closer to the director. Ordinarily, in Yagi design, increasing the driver-reflector spacing increases the feedpoint impedance. However, in the case of these quad designs, the feedpoint impedance decreases from the wide-band design values.

+
+ +
+

The high-gain design has a number of other interesting properties. For example, the gain curve is roughly centered in the passband. Fig. 2 shows the gain curves for the design using three wires sizes: 0.0001 wl, 0.001 wl, and 0.01 wl. For the 2 thinner wire sizes, the gain peaks on the design frequency. The fattest wire size shows a peak just above the design frequency (28.5 MHz in this case), as well as a much smaller increase in gain relative to the next smaller wire size. There appears to be a limit in this design to the gain increase with increasing wire size, possibly connected with a maximum degree of inter-element coupling.

+

As well, the front-to-back ratio peaks are not variable from one wire size to the next. Instead, the front-to-back ratio remains constant within +/-0.5 dB of 30 dB throughout the series of optimized models.

+

Automated Design

+

Nonetheless, the high-gain design is amenable to automated design predicated on the entry of the design frequency and the wire size. The performance varies with the common logarithm of the wire size as measured in fractions of a wavelength. By applying regression analysis to optimized models at various wire sizes, it is possible to develop algorithms that produce working designs for any HF or VHF frequency within close tolerances.

+

The following GW Basic utility program encapsulates the design data. As always, LOG in GW Basic means a natural logarithm and requires a correction factor to yield a common log. If the program is entered in another medium that treats LOG as a common logarithm, the conversion factor can be omitted.

+

The program deletes on piece of data useful to the wide-band design: the rate of change of gain per 1% of frequency change. Since the gain peaks at the design frequency rather than outside the passband of the antenna for an amateur band, the rate-of-change figure loses its meaningfulness.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 3-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "Alternate Design",,,"L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 PRINT "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 IF D1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=.000266666667#:BD=.00506666667#:CD=.03633333333#:DD=.1221904762#:ED=1.183285714#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED
+210 AR=.0037333333333#:BR=.05362962963#:CR=.29275555556#:DR=.7424529101#:ER=1.814412698#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER
+230 AI=-.00266666667#:BI=-.033244444444#:CI=-.1550666667#:DI=-.3222793651#:EI=.7283809524#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI
+250 AS=.00033333333#:BS=.004837037037#:CS=.02552777778#:DS=.05643756614#:ES=.2191230159#
+260 SP=(AS*(D1^4))+(BS*(D1^3))+(CS*(D1^2))+(DS*D1)+ES
+270 AP=-.002333333333#:BP=-.03128148148#:CP=-.15586111111#:DP=-.3417669312#:EP=-.05499206349#
+280 IP=(AP*(D1^4))+(BP*(D1^3))+(CP*(D1^2))+(DP*D1)+EP
+290 AZ=4.4029#:BZ=53.43954444#:CZ=239.2408583#:DZ=462.3614437#:EZ=373.3035655#
+300 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+310 AG=-.15#:BG=-1.768518519#:CG=-7.763055556#:DG=-14.78592593#:EG=-.609722222#
+320 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+330 AW=.16666666667#:BW=2.265925926#:CW=11.706111111#:DW=27.93058201#:EW=28.88753968#
+340 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+350 AF=.11933333333#:BF=1.671777778#:CF=8.9885#:DF=22.45931746#:EF=23.68797619#
+360 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+370 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+380 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+390 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+400 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+410 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+420 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+430 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+440 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+450 PRINT "Director Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+460 PRINT "Director Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+470 PRINT "Director-Driver Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+480 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+490 PRINT "Free-Space Gain =";GN;"dBi"
+500 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+510 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+520 INPUT "Another Value = 1, Stop = 2: ";P
+530 IF P=1 THEN 10 ELSE 540
+540 END
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

My preference for setting up utilities in GW Basic rests on the transparency of the programming language. The program structure and the equations used to produce the output values are completely transparent for easy transport to any desired medium. Most spreadsheets use straightforward embellishments of Basic.

+

Some Graphic Results

+

The program outputs can be graphically presented to show the general trends of the high-gain design dimensions. Fig. 3 shows the loop circumference dimensions as a function of a wavelength for wires sizes that are also functions of a wavelength. The reflector and driver curves are familiar to those who have looked at the wide-band design. Although the exact values differ, the growing loop size as wire diameter increases is a familiar feature. The director loop circumference, however, is another matter. It changes very little across the span of wire diameters, with down-turns at both ends of the scale. In fact, as the wire size decreases to the thinnest region, the wide-band and the high-gain design begin to resemble each other, since the gain peak comes closer to the design frequency for each version.

+
+ +
+

The element spacing required for optimized high-gain design follows rules that differ from those applicable to the wide-band design. The reflector-to-driver spacing decreases with increasing wire size--exactly the opposite of the case with the wide-band design. In contrast, the driver-to-director spacing shows a curve similar to the director loop circumference graph, with down-turns at both ends of the wire-size scale. Likewise, the range of variation is very small with the high-gain design. In contrast, the wide-band model showed a significant reduction of required spacing between the driver and director as the wire size increased. The high-gain curves appear in Fig. 4.

+
+ +
+

Some Performance Comparisons

+

Dimensions are not the only parameters that lend themselves to graphical comparisons. As well, we can look at some of the performance predictions for both the wide-band and the high-gain versions of the antenna. Most significant among these parameters are gain, the 2:1 SWR bandwidth, and the >20 dB front-to-back bandwidth.

+
+ +
+

Fig. 5 shows the comparative gains for the two designs. Once we move above the thinnest wires, the high-gain version of the antenna shows an average gain advantage of about 0.5 dB over the wide-band version. In fact, the azimuth patterns of the two designs are quire similar, as shown in Fig. 6.

+
+ +
+

The free space azimuth patterns are predicated on 0.5" diameter copper elements with a design frequency of 28.5 MHz. Because of the rear side lobes are so similar, the differential in front-to-back ratios will not be operationally significant. How significant the gain differential will be must be a user measure based on an assessment of all of the critical parameters.

+
+ +
+

Fig. 7 shows the comparative values of 2:1 SWR bandwidths, as a percentage of the operating frequency. The graph shows an advantage of better than 1.5:1 for the wide-band version of the antenna. However, whether that degree of increase is necessary depends upon the bandwidth required for a given antenna design. For reference, the following table shows the percentage band width of each of the amateur bands from 80 through 2 meters. All frequencies are in MHz.

+ 
Band        Limits                  Center            Bandwidth as a % of
+                                    Frequency         the Center Frequency
+80            3.5   -   4.0           3.75                  13.33%
+40            7.0   -   7.3           7.15                   4.20%
+30           10.1   -  10.15         10.125                  0.49%
+20           14.0   -  14.35         14.175                  2.47%
+17           18.068 -  18.168        18.118                  0.55%
+15           21.0   -  21.45         21.225                  2.12%
+12           24.89  -  24.99         24.94                   0.40%
+10-1 MHz     28.0   -  29.0          28.5                    3.51%
+10-full band 28.0   -  29.7          28.85                   5.89%
+ 6           50.0   -  54.0          52                      7.69%
+ 2          144     - 148           146                      2.74%
+

With respect to the SWR bandwidth, any wire size that is 0.0003 wl will cover any of the wider HF ham bands (excluding 80 meters). For equivalent coverage with the high-gain version, a wire size equal or greater than about 0.004 wl is necessary.

+

For reference in using both Fig. 7 and the tables of ham-band bandwidths, the following wire-size table is repeated from the 2-element quad mini-series. The numbers in () represent the nearest common AWG wire gauge.

+ 
Dia. in WL                          Physical diameter in inches
+                  3.5 MHz           14 MHz            30 MHz            144 MHz
+0.0000316         0.1066 (10)       0.0267 (24)       0.0124 (29)       0.0026 (40)
+0.0001            0.3372            0.0843 (12)       0.0393 (18)       0.0082 (32)
+0.000316          1.0664            0.2666 (2)        0.1244 (8)        0.0259 (22)
+0.001             3.372             0.841             0.3934            0.0820 (12)
+0.00316           10.664            2.666             1.244             0.2592 (2)
+0.01              33.722            8.431             3.934             0.8964
+

Obviously, the thinnest wires are impractical at VHF, and the fattest wires are equally unusable at the lowest HF frequencies. Nonetheless, in the middle region of the table, it may be possible to simulate fatter wires by the use of multiple strands of #14 AWG or similar. The technique would be identical to the exercise noted in Part 1 of this 3- element quad exploration.

+
+ +
+

More critical to many operations than the SWR bandwidth is the >20 dB operating bandwidth. Fig. 8 shows the differences for the two designs. Once one passes the 0.001 wl wire size, the average advantage for the wide-band design is about 20-23%. Full coverage of the first MHz of 10 meters would require a wire size of about 2.5" for the wide-band design, while the high-gain will not quite cover this passband with a diameter (or its equivalent in multiple wires) of over 4". Nonetheless, half-inch wire (or tubing) may suffice for nearly full band coverage of 2-meters using the high-gain design. Moreover, not every 3-element quad application needs to cover the entirety of any of the wider HF ham bands.

+
+ +
+

One significant difference in the designs is related to the feedpoint impedance, as shown in Fig. 9. The wide-band design resonant feedpoint impedance varies by under 10 Ohms across the entire span of wire sizes. However, the high-gain design shows an increasing feedpoint impedance as wire size decreases, from a low of about 48 Ohms with 0.01 wl wire to a high of nearly 73 Ohms for the thinnest wire. As the wire reaches the thinnest values in the progression, the curve is ever more steep. As noted earlier, with the thinnest wire size, the 3-element quad performance values become quite similar for the two designs. The thicker the wire of the high-gain design, the easier it becomes to directly match a 50-Ohm feedline.

+

Some Practical Design Examples

+

To get a better sense of how the two design differ, let's compare some designs between the wide-band and the high-gain designs.

+ 
1.  20 meters, #14 wire, design frequency: 14.175 MHz
+Wire Diameter:                      0.0641" or 7.70E-5 wl
+                              Wide-Band                     High-Gain
+Reflector Circumference:      73.09'                        72.86'
+Driver Circumference:         70.06'                        70.71'
+Director Circumference:       65.31'                        68.04'
+Refl-Driver Spacing:          10.69'                        12.33'
+Driver-Dir Spacing:           21.58'                        15.46'
+Total Boom Length:            32.27'                        27.79'
+Feedpoint Impedance:          79.5 Ohms                     60.6 Ohms
+Free-Space Gain:              8.47 dBi                      9.00 dBi
+SWR Bandwidth:                3.10% or 0.439 MHz            2.07% or 0.293 MHz
+>20 dB F-B Bandwidth:         1.18% or 0.167 MHz            1.12% or 0.159 MHz
+Rate of Gain Change:          0.22 dB/1% of design frequency-------
+
+2.  10 meters, #12 wire, design frequency: 28.5 MHz
+Wire Diameter:                      0.0808" or 1.95E-4 wl
+                              Wide-Band                     High-Gain
+Reflector Circumference:      36.64'                        36.52'
+Driver Circumference:         34.95'                        35.26'
+Director Circumference:       32.43'                        33.89'
+Refl-Driver Spacing:           5.49'                         6.12'
+Driver-Dir Spacing:           10.30'                         7.70'
+Total Boom Length:            15.79'                        13.82'
+Feedpoint Impedance:          77.2 Ohms                     56.1 Ohms
+Free-Space Gain:              8.74 dBi                       9.29 dBi
+SWR Bandwidth:                3.34% or 0.952 MHz            2.26% or 0.644 MHz
+>20 dB F-B Bandwidth:         1.41% or 0.402 MHz            1.32% or 0.376 MHz
+Rate of Gain Change:          0.21 dB/1% of design frequency-------
+
+3.  10 meters, 0.5" wire, design frequency: 28.5 MHz
+Wire Diameter:                      0.5" or 1.21E-3 wl
+                              Wide-Band                     High-Gain
+Reflector Circumference:      37.42'                        37.23'
+Driver Circumference:         35.22'                        35.53'
+Director Circumference:       32.39'                        33.86'
+Refl-Driver Spacing:           5.66'                         6.07'
+Driver-Dir Spacing:            9.57'                         7.70'
+Total Boom Length:            15.23'                        13.77'
+Feedpoint Impedance:          72.3 Ohms                     52.7 Ohms
+Free-Space Gain:              9.00 dBi                      9.50 dBi
+SWR Bandwidth:                4.42% or 1.20 MHz             2.84% or 0.809 MHz
+>20 dB F-B Bandwidth:         2.11% or 0.601 MHz            1.80% or 0.513 MHz
+Rate of Gain Change:          0.10 dB/1% of design frequency-------
+
+4.  6 meters, 0.25" wire, design frequency: 51 MHz
+Wire Diameter:                      0.25" or 1.08E-3 wl
+                              Wide-Band                     High-Gain
+Reflector Circumference:      20.87'                        20.78'
+Driver Circumference:         19.67'                        19.84'
+Director Circumference:       18.10'                        18.92'
+Refl-Driver Spacing:           3.16'                         3.39'
+Driver-Dir Spacing:            5.37'                         4.30'
+Total Boom Length:             8.53'                         7.69'
+Feedpoint Impedance:          72.4 Ohms                     53.0 Ohms
+Free-Space Gain:              8.99 dBi                      9.49 dBi
+SWR Bandwidth:                4.14% or 2.11 MHz             2.80% or 1.43 MHz
+>20 dB F-B Bandwidth:         2.05% or 1.05 MHz             1.76% or 0.90 MHz
+Rate of Gain Change:          0.11 dB/1% of design frequency-------
+
+5.  2 meters, 0.1" wire, design frequency: 146 MHz
+Wire Diameter:                      0.1" or 1.24E-3 wl
+                              Wide-Band                     High-Gain
+Reflector Circumference:       7.31'                         7.27'
+Driver Circumference:          6.88'                         6.94'
+Director Circumference:        6.32'                         6.61'
+Refl-Driver Spacing:           1.11'                         1.18'
+Driver-Dir Spacing:            1.87'                         1.50'
+Total Boom Length:             2.98'                         2.68'
+Feedpoint Impedance:          72.2 Ohms                     52.5 Ohms
+Free-Space Gain:              9.00 dBi                      9.50 dBi
+SWR Bandwidth:                4.24% or 6.19 MHz             2.85% or 4.16 MHz
+>20 dB F-B Bandwidth:         2.19% or 3.20 MHz             1.81% or 2.64 MHz
+Rate of Gain Change:          0.10 dB/1% of design frequency-------
+

Anyone who looked at Part 1 of this exercise will recognize the sample 3-element quads, since I used the same frequencies and wire sizes for the high-gain models in the right-hand column. In each case the dimensional differences are significant. However, for most folks, the gain and the operating bandwidth comparisons will be more interesting. In each case, the high-gain design shows its higher gain. Likewise, the wide-band design shows the wider SWR and front-to-back bandwidths. Selection of a final design requires that the end-user measure all of the operating potentials against a set of operating needs.

+

The following links will take you to a download page where you may download the program as a. a NEC-Win Plus model file, b. a GW Basic program, or c. a VB script generously made available by Randy Frum, AC4FD. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen. An on-line Java script calculator (web.archive.org). is available courtesy of the work of Steven Dick.

+

Conclusion

+

We have surveyed and automated the design of two significantly different 3-element quad beams. Even so, we have not exhausted the possibilities for the antenna type. One may design for even higher gain values, although the operating bandwidth and the feedpoint impedance will continue to decrease. Similarly, one may design for even wider operating bandwidths, but at a cost to array gain. If one pursues this latter course, eventually, the array gain will decrease to the level of a Yagi with a similar bandwidth and element diameter. In that case, the advantages of moving to a quad design would disappear, and the added complexities of quad construction would no longer warrant the effort. Once more, the precise point at which the transition occurs must be determined by the end-user.

+

Nonetheless, these exercises are useful in many ways. Besides the obvious benefit of yielding relatively optimized designs for any HF/VHF frequency and wire size, the programs provide an easy means of designing quads for comparative purposes. The evaluation of antennas at a practical level is very often a matter of comparing available designs. Yagi comparators are easy to find. Up to now, an adequate sampling of comparable quad designs has been hard to find. These utility programs considerably ease the process of uncovering 3-element quad designs and their capabilities.

+

One final caution: the designs are monoband quads throughout. One cannot simply plug them into a multi-band array and expect each quad to perform as specified here. In multi-band quad arrays, virtually all elements are significantly active, adding to or subtracting from the performance of the focal set of elements for any band. Therefore, creating an effective multi-band quad array requires considerably more adjustment than a mere field tweak on the monoband designs.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +
+

Updated 03-01-2001, 11-14-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for January, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Quad List

+

Go to Main Index

+

Topics: HF Lower, HF Upper, Quad, VHF / UHF


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+

40-Meter Wide-Band 3-Element Quad Designs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Let's begin with a pop quiz. Suppose first that you wanted a directional 3-element quad array to cover as much of 40 meters as possible. Suppose further that space for the array is not problem. Finally, suppose that you had a choice among the following three designs: the "Classic #14," "the Single W-B #12," and the "Dual W-B #12." Which would you choose?

+

So far, the question is not fair. So let's provide some grounds for selection with a few performance graphs.

+
+ +
+

Fig. 1 shows the gain curves for the three choices. The classic #14 peaks at about 7.15 MHz, but falls off rapidly on either side of the design frequency, especially the low frequency side. Still, this is a normal curve for a quad beam in almost every performance category. The single W-B #12 has its gain peak at about 7.05 MHz, although the design frequency is higher. It is not clear from the graph whether the dual W-B #12 has a gain peak at 7.0 MHz or somewhat lower in frequency. From the graph, the antenna with the most consistent gain from one end of the band to the other is clear.

+
+ +
+

The front-to-back ratio curves in Fig. 2 are equally clear. The peak front-to-back ratio in all cases occurs between 7.1 and 7.15 MHz. However, the classic #14 does not reach 20 dB (with the possibile exception of a few kHz at its peak). The single W-B #12 does considerably better, but still manages >20 dB front-to-back ratio for only about 85 kHz. The dual W-B #12 has the widest >20 dB front-to-back ratio bandwidth and never drops below 14 dB across the 40-meter band.

+
+ +
+

The classic #14 array is--near the design frequency--a 50-Ohm antenna, and the SWR curve in Fig. 3 is referenced to that value. Unfortunately, the <2:1 SWR region is only about 130 kHz wide. The single W-B #12 version of the antenna covers about 200 kHz with under 2:1 SWR--this time referenced to the array's near-75-Ohm feedpoint impedance. Only the dual W-B #12 model manages under 2:1 SWR (referenced to 75 Ohms) across the entire band.

+

For someone interested in the entire 40-meter band, there is a clear winner in this selection process: the dual W-B #12 model. But, before we look at what this model is, let's review the lesser arrays in the group.

+

The Classic #14 3-Element Quad Design

+

For at least a quarter century, we have been given a set of formulas for constructing 3-element quads:

+ 
Reflector loop circumference in feet = 1030/frequency in MHz
+Driver loop circumference in feet = 1005/frequency in MHz
+Director loop circumference in feet = 975/frequency in MHz
+

Many hams have believed that an independently fed quad loop answers to the driver formula, but it does not--not even close. Likewise, other hams have believed that we can make a 2-element quad using just the driver and reflector formulas. Any such array is less than optimal. Few folks have noticed that the spacing is left vacant, subject to our own construction limitations.

+

In fact, the formulas apply to fairly short 3-element quads using quite thin wire. The formulas are not perfect and require some optimization to bring the gain, front-to-back ratio, and SWR "best" numbers into reasonably close alignment. The following design in #14 AWG copper wire provides good figures at the design frequency (close to 7.15 MHz):

+ 
Reflector loop length:        1719.4"     143.29'
+Driver loop length:           1683.8"     140.31'
+Director loop length:         1634.9"     136.24'
+Reflector-Driver space:        219.5"      18.30'
+Driver-Director space:         284.4"      23.70'
+Total boom length              503.9"      42.00'
+

Although this array is capable of about 8.6 dBi free-space gain at the design frequency, it has a very narrow operating bandwidth in every performance category. The gain drops to about 7.5 dB (1.1 dB off peak) at the low end of the band. The front-to-back ratio is below 10 dB for much of the band. The 2:1 SWR bandwidth covers less than half of the 40- meter band.

+
+ +
+

The selected azimuth patterns that scan 40-meters in 100 kHz intervals tell much of the classic #14's story in graphical detail in Fig. 4. Beyond the center 100 kHz of the band, the pattern of the array is more bi-directional than directional.

+

The use of the classical formulas on 40 meters provides somewhat of an overstatement of the inadequacies of these old numbers. A beam of this design might make a useful array for either the CW or the SSB end of 40 meters, but certainly not both. (This conclusion, of course, references the US 40-meter band. The array might be adequate to European interests in the band.)

+

For those who model and might wish to adjust the design to one or the other end of the 40-meter band, the following model description may be useful:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-element 40-meter classic quad                       Frequency = 7  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1     W4E2 -17.911,  0.000,-17.911  W2E1  17.911,  0.000,-17.911    # 14   11
+2     W1E2  17.911,  0.000,-17.911  W3E1  17.911,  0.000, 17.911    # 14   11
+3     W2E2  17.911,  0.000, 17.911  W4E1 -17.911,  0.000, 17.911    # 14   11
+4     W3E2 -17.911,  0.000, 17.911  W1E1 -17.911,  0.000,-17.911    # 14   11
+5     W8E2 -17.539, 18.296,-17.539  W6E1  17.539, 18.296,-17.539    # 14   11
+6     W5E2  17.539, 18.296,-17.539  W7E1  17.539, 18.296, 17.539    # 14   11
+7     W6E2  17.539, 18.296, 17.539  W8E1 -17.539, 18.296, 17.539    # 14   11
+8     W7E2 -17.539, 18.296, 17.539  W5E1 -17.539, 18.296,-17.539    # 14   11
+9    W12E2 -17.030, 41.998,-17.030 W10E1  17.030, 41.998,-17.030    # 14   11
+10    W9E2  17.030, 41.998,-17.030 W11E1  17.030, 41.998, 17.030    # 14   11
+11   W10E2  17.030, 41.998, 17.030 W12E1 -17.030, 41.998, 17.030    # 14   11
+12   W11E2 -17.030, 41.998, 17.030  W9E1 -17.030, 41.998,-17.030    # 14   11
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           6     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The Single-Wire Wide-Band #12 3-Element Quad Design

+

How might we improve the classic design? First, we should go to a larger diameter wire. However, #12 AWG copper wire is about the largest value that most hams will use. That fact will initially limit the improvements we can make.

+
+ +
+

Fig. 5 illustrates a second design move we can make: enlarge the spacing to something nearer to optimal. The figure shows the profiles of the classic and the improved designs, revealing that it will take another 20+ feet of boom to get significant improvements in operating bandwidth on 40 meters.

+

I used the wide-band version of the automated design program that I presented in an earlier article to obtain the widest-band 40-meter beam I could develop with #12 wire. The dimensions that resulted are these:

+ 
Reflector loop length:        1736.8"     144.73'
+Driver loop length:           1669.2"     139.10'
+Director loop length:         1560.3"     130.02'
+Reflector-Driver space:        246.8"      20.56'
+Driver-Director space:         522.6"      43.55'
+Total boom length              769.4"      64.11'
+

Wide-band design requires a driver-to-director spacing that is greater than the entire boom length of the classic design. Wide-band operation of a 3-element quad beam simply needs considerably greater boom-length than we have thought about using in the past.

+

Even with the longer boom length, the wire diameter we have chosen continues to limit performance. #12 wire is a very thin conductor at 40 meters--about 5E-5 wavelengths. Consequently, optimizing loop dimensions and element spacing will not provide full 40-meter coverage.

+

Gain is not the problem, since it holds to a free-space value of about 8.4 dBi or better across the band. The front-to-back ratio, although significantly improved compared to the classic #14 model, remains less than stellar. It actually falls below 10 dB at the low end of the band and exceeds 20 dB for less than 100 kHz. The 75-Ohm 2:1 SWR passband is only about 180 kHz wide--about 50 kHz wider than for the classic #14 design. Although the single-wire #12 wide-band design provides considerable improvements in gain and front-to-back ratio relative to the classic #14 model, it falls short of covering the band by a wide margin. Just getting full SWR coverage would require a wire about 3-4" in diameter.

+
+ +
+

Fig. 6 shows our situation graphically through spot azimuth patterns across the band. The single-wire array will simply not do the job we specified at the beginning of this exercise.

+

Those who wish to try some adjustments to the array under discussion may benefit from the following model description:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-element 40-meter single-wire wide-band quad               Frequency = 7  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1     W4E2 -18.091,  0.000,-18.091  W2E1  18.091,  0.000,-18.091    # 12   11
+2     W1E2  18.091,  0.000,-18.091  W3E1  18.091,  0.000, 18.091    # 12   11
+3     W2E2  18.091,  0.000, 18.091  W4E1 -18.091,  0.000, 18.091    # 12   11
+4     W3E2 -18.091,  0.000, 18.091  W1E1 -18.091,  0.000,-18.091    # 12   11
+5     W8E2 -17.388, 20.563,-17.388  W6E1  17.388, 20.563,-17.388    # 12   11
+6     W5E2  17.388, 20.563,-17.388  W7E1  17.388, 20.563, 17.388    # 12   11
+7     W6E2  17.388, 20.563, 17.388  W8E1 -17.388, 20.563, 17.388    # 12   11
+8     W7E2 -17.388, 20.563, 17.388  W5E1 -17.388, 20.563,-17.388    # 12   11
+9    W12E2 -16.253, 64.113,-16.253 W10E1  16.253, 64.113,-16.253    # 12   11
+10    W9E2  16.253, 64.113,-16.253 W11E1  16.253, 64.113, 16.253    # 12   11
+11   W10E2  16.253, 64.113, 16.253 W12E1 -16.253, 64.113, 16.253    # 12   11
+12   W11E2 -16.253, 64.113, 16.253  W9E1 -16.253, 64.113,-16.253    # 12   11
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           6     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The Dual-Wire Wide-Band #12 3-Element Quad Design

+

A 40-meter quad beam by any accounting is a sizable structure. The spreaders should easily be able to support 2 #12 AWG wires. Therefore, we may simulate a fat wire by using double-wire elements in a planar arrangement. Fig. 7 shows the general outline for such a beam. Note the connections between each element loop at every corner.

+
+ +
+

It proved possible to cover all of the first MHz of 10 meters with a very good front-to- back ratio using a single 0.5" diameter wire or 2 #14 wires spaced 5" apart. A 40-meter quad with comparable coverage would need wires spaced more than 20 inches apart. As a more modest design project, I aimed simply to achieve an SWR of under 2:1 across the band. This goal required the use of 10" #12 wire spacing.

+

The optimized dimensions for the dual-wire model yields an array that is close to 4' shorter than the single-wire version. The following dimensions list the circumferences of both the inner and outer loops for each element:

+ 
Reflector loop length:  Outer       1823.3"     151.94'
+                        Inner       1743.3"     145.27'
+Driver loop length:     Outer       1725.9"     143.83'
+                        Inner       1645.9"     137.16'
+Director loop length:   Outer       1569.4"     130.79'
+                        Inner       1489.4"     124.12'
+Reflector-Driver space:              287.7"      23.97'
+Driver-Director space:               435.6"      36.30'
+Total boom length                    723.3"      60.27'
+

For our trouble, we obtain a smooth gain curve across the band with under 0.3 dB variation. In addition, the front-to-back ratio is above 14 dB across the band and above 20 dB for over half the band. Finally, the 75-Ohm SWR is less than 2:1 across the entire band. Although still less than perfect, the 10" spacing of the dual-wire elements provides very significant improvements in performance over either of the other models.

+
+ +
+

Fig. 8 provides a graphic sense of the improvements. All of the pattern elements are more tightly grouped than in the comparable azimuth pattern sweeps for the other designs. For those who wish to examine the model structure, the following listing may be useful.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-element 40-meter dual-wire wide-band quad                 Frequency = 7  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+1     W4E2 -17.978,  0.000,-17.978  W2E1  17.978,  0.000,-17.978    # 12   29
+2    W10E1  17.978,  0.000,-17.978  W3E1  17.978,  0.000, 17.978    # 12   29
+3     W9E1  17.978,  0.000, 17.978  W4E1 -17.978,  0.000, 17.978    # 12   29
+4    W12E1 -17.978,  0.000, 17.978 W11E1 -17.978,  0.000,-17.978    # 12   29
+5     W8E2 -17.145,  0.000,-17.145  W6E1  17.145,  0.000,-17.145    # 12   23
+6    W10E2  17.145,  0.000,-17.145  W7E1  17.145,  0.000, 17.145    # 12   23
+7     W9E2  17.145,  0.000, 17.145  W8E1 -17.145,  0.000, 17.145    # 12   23
+8    W12E2 -17.145,  0.000, 17.145 W11E2 -17.145,  0.000,-17.145    # 12   23
+9     W2E2  17.978,  0.000, 17.978  W6E2  17.145,  0.000, 17.145    # 12    1
+10    W1E2  17.978,  0.000,-17.978  W5E2  17.145,  0.000,-17.145    # 12    1
+11    W1E1 -17.978,  0.000,-17.978  W5E1 -17.145,  0.000,-17.145    # 12    1
+12    W3E2 -17.978,  0.000, 17.978  W7E2 -17.145,  0.000, 17.145    # 12    1
+13   W16E2 -18.992,-23.973,-18.992 W14E1  18.992,-23.973,-18.992    # 12   29
+14   W22E1  18.992,-23.973,-18.992 W15E1  18.992,-23.973, 18.992    # 12   29
+15   W21E1  18.992,-23.973, 18.992 W16E1 -18.992,-23.973, 18.992    # 12   29
+16   W24E1 -18.992,-23.973, 18.992 W23E1 -18.992,-23.973,-18.992    # 12   29
+17   W20E2 -18.159,-23.973,-18.159 W18E1  18.159,-23.973,-18.159    # 12   23
+18   W22E2  18.159,-23.973,-18.159 W19E1  18.159,-23.973, 18.159    # 12   23
+19   W21E2  18.159,-23.973, 18.159 W20E1 -18.159,-23.973, 18.159    # 12   23
+20   W24E2 -18.159,-23.973, 18.159 W23E2 -18.159,-23.973,-18.159    # 12   23
+21   W14E2  18.992,-23.973, 18.992 W18E2  18.159,-23.973, 18.159    # 12    1
+22   W13E2  18.992,-23.973,-18.992 W17E2  18.159,-23.973,-18.159    # 12    1
+23   W13E1 -18.992,-23.973,-18.992 W17E1 -18.159,-23.973,-18.159    # 12    1
+24   W15E2 -18.992,-23.973, 18.992 W19E2 -18.159,-23.973, 18.159    # 12    1
+25   W28E2 -16.348, 36.302,-16.348 W26E1  16.348, 36.302,-16.348    # 12   29
+26   W34E1  16.348, 36.302,-16.348 W27E1  16.348, 36.302, 16.348    # 12   29
+27   W33E1  16.348, 36.302, 16.348 W28E1 -16.348, 36.302, 16.348    # 12   29
+28   W36E1 -16.348, 36.302, 16.348 W35E1 -16.348, 36.302,-16.348    # 12   29
+29   W32E2 -15.515, 36.302,-15.515 W30E1  15.515, 36.302,-15.515    # 12   23
+30   W34E2  15.515, 36.302,-15.515 W31E1  15.515, 36.302, 15.515    # 12   23
+31   W33E2  15.515, 36.302, 15.515 W32E1 -15.515, 36.302, 15.515    # 12   23
+32   W36E2 -15.515, 36.302, 15.515 W35E2 -15.515, 36.302,-15.515    # 12   23
+33   W26E2  16.348, 36.302, 16.348 W30E2  15.515, 36.302, 15.515    # 12    1
+34   W25E2  16.348, 36.302,-16.348 W29E2  15.515, 36.302,-15.515    # 12    1
+35   W25E1 -16.348, 36.302,-16.348 W29E1 -15.515, 36.302,-15.515    # 12    1
+36   W27E2 -16.348, 36.302, 16.348 W31E2 -15.515, 36.302, 15.515    # 12    1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          15     1 / 50.00   (  1 / 50.00)      0.707       0.000       V
+2          12     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note in the model the use of two sources which are essentially in parallel. You may use the standard parallel impedance equations to calculate the composite feedpoint impedance. In practice, of course, a builder would bring the two loop wires together at the feedpoint for a single feedline connection.

+

The dual-wire planar loop design is not the answer to all limitations of 3-element quad bandwidth, but it goes a long way toward overcoming them. For such a large initial array, the two-wire loop is fairly straightforward, if not simple, to implement. The cost will be something over 400' in extra wire.

+

A Note on Designing 3-Element Quads

+

I habitually use a mixture of two NEC programs for quad design--NECWin Plus and EZNEC. Although many of the graphics that appear here are from models cross-checked on EZNEC/4, the basic design work was done with NECWin Plus using the model-by-equation facility.

+
+ +
+

Fig. 9 provides a simple illustration--chosen because a quad design with a single-wire structure makes a more compact graphic. (The same illustration using the dual wire model would have required 36 lines in the "wires page" section.) By setting the "half-side" dimensions of the quad in terms of a fraction of a wavelength, the task of hand-optimizing a design is considerably eased. In this case, the director spacing is actually the spacing from the reflector to the director, and finding the distance from the driver to the director is a simple case of subtraction. Alternatively, one might set the driver at zero and use a negative value for the reflector spacing and a positive value for the director. Finding the total boom length then becomes a simple case of addition.

+

The earlier note on the rough equivalency of a 3-4" wire to the 10" double #12 wire arrangement can be verified by using the 3-element wide-band automated design program. A 3" wire is the minimum diameter single copper wire that will yield a 75-Ohm <2:1 SWR curve for a 40-meter array. The model below is one example of such a design. Note that when run on NEC-4, the properties will show a slight displacement (un 50 kHz) in frequency. The curve was developed in NEC-2.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-Element Wide-Band 40-M design:  3" elements         Frequency = 7.15  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1     W4E2 -226.06,  0.000,-226.06  W2E1 226.061,  0.000,-226.06 3.00E+00  11
+2     W1E2 226.061,  0.000,-226.06  W3E1 226.061,  0.000,226.061 3.00E+00  11
+3     W2E2 226.061,  0.000,226.061  W4E1 -226.06,  0.000,226.061 3.00E+00  11
+4     W3E2 -226.06,  0.000,226.061  W1E1 -226.06,  0.000,-226.06 3.00E+00  11
+5     W8E2 -211.88,273.902,-211.88  W6E1 211.876,273.902,-211.88 3.00E+00  11
+6     W5E2 211.876,273.902,-211.88  W7E1 211.876,273.902,211.876 3.00E+00  11
+7     W6E2 211.876,273.902,211.876  W8E1 -211.88,273.902,211.876 3.00E+00  11
+8     W7E2 -211.88,273.902,211.876  W5E1 -211.88,273.902,-211.88 3.00E+00  11
+9    W12E2 -194.11,727.268,-194.11 W10E1 194.109,727.268,-194.11 3.00E+00  11
+10    W9E2 194.109,727.268,-194.11 W11E1 194.109,727.268,194.109 3.00E+00  11
+11   W10E2 194.109,727.268,194.109 W12E1 -194.11,727.268,194.109 3.00E+00  11
+12   W11E2 -194.11,727.268,194.109  W9E1 -194.11,727.268,-194.11 3.00E+00  11
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           6     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

To obtain a >20 dB front-to-back curve for the entirety of the US 40-meter band requires a much greater single-wire diameter: about 20". The following model provides such a curve on NEC-2, with the usual slight frequency displacement in NEC-4.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+3-Element Wide-Band 40-M design:  3" elements         Frequency = 7.15  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1     W4E2 -238.14,  0.000,-238.14  W2E1 238.145,  0.000,-238.14 2.00E+01  11
+2     W1E2 238.145,  0.000,-238.14  W3E1 238.145,  0.000,238.145 2.00E+01  11
+3     W2E2 238.145,  0.000,238.145  W4E1 -238.14,  0.000,238.145 2.00E+01  11
+4     W3E2 -238.14,  0.000,238.145  W1E1 -238.14,  0.000,-238.14 2.00E+01  11
+5     W8E2 -215.68,280.836,-215.68  W6E1 215.680,280.836,-215.68 2.00E+01  11
+6     W5E2 215.680,280.836,-215.68  W7E1 215.680,280.836,215.680 2.00E+01  11
+7     W6E2 215.680,280.836,215.680  W8E1 -215.68,280.836,215.680 2.00E+01  11
+8     W7E2 -215.68,280.836,215.680  W5E1 -215.68,280.836,-215.68 2.00E+01  11
+9    W12E2 -189.54,696.975,-189.54 W10E1 189.536,696.975,-189.54 2.00E+01  11
+10    W9E2 189.536,696.975,-189.54 W11E1 189.536,696.975,189.536 2.00E+01  11
+11   W10E2 189.536,696.975,189.536 W12E1 -189.54,696.975,189.536 2.00E+01  11
+12   W11E2 -189.54,696.975,189.536  W9E1 -189.54,696.975,-189.54 2.00E+01  11
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           6     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Developing a multi-wire equivalent for a 20" diameter wire is likely not feasible with only two wires. Even if the SWR and front-to-back curves can be replicated, the full gain (9.2 dB at design center frequency) will not be available without several wires per loop--perhaps 4 wires on 10" centers (as a speculative guess). The 20" wire in the model presses the limits of wire diameter (0.01 wl) for which the design program has been calibrated.

+

I have been asked why I use an independent value for the wavelength (D3) in most of my equations. When letting software perform a string of calculations, I tend to prefer the most precise value for physical and mathematical constants that I can find. This includes such values as PI, the speed of electromagnetic radiation in free space, and the ratio of natural to common logarithms. I then save rounding for the final step of calculations performed by software programs. Others may wish to use only the least number of significant digits in the weakest input value in all numeric entries.

+

Whatever procedure one finds most comfortable, the process of developing a wide-band 40-meter 3-element quad takes more than a few formulas whose limitations have been lost in the mists of summary, custom, and usage. Even the best of the designs here can be improved by judicious further modeling using either wider spacing of dual wires or larger multi-wire loops. There are many modeling challenges ahead before the quad beam has exhausted its potential.

+
+ +
+

Updated 04-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for March, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Quad List

+

Go to Main Index

+

Topics: HF Lower, Quad


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+

4-Element Monoband Quad Design

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The most common designs of 4-element quads suffer from the urge to retain short booms and thin elements. Consequently, the average 4-element design fails to meet expectations or to match the performance of 4- and 5-element Yagis. A 4-element Yagi is capable of about 9 dBi gain with a good front-to-back ratio, although in practical designs, gain averages of 8.6 dBi (free space) are more typical in the HF bands using elements at 20 meters that average about 1" in diameter.

+
+ +
+

The average monoband 4-element quad has the appearance of Fig. 1. As usual, the discussion limits itself to single feedpoint driver elements with square loops used throughout.

+

A Comparison of 3 Designs for 4-Element Quads

+

Let's begin with a comparison of three designs. The first is a standard design wire quad for 20 meters that has the following dimensions.

+ 
Design Data for a "Standard" 4-Element Quad
+
+Element Diameter:                   #14 AWG
+Reflector Circumference:            72.66'
+Driver Circumference:               70.89'
+Director 1 Circumference:           68.78'
+Director 2 Circumference:           66.72'
+Refl-Driver Spacing:                12.87'
+Driver-Dir 1 Spacing:               10.59'
+Dir 1-Dir 2 Spacing:                10.58'
+Total Boom Length:                  34.04'
+

The free-space gain of this array peaks just above 9.65 dBi at about 14.2 MHz. The front-to-back ratio peaks at about 23 dB at 14.25 MHz, but falls off to about 10 dB at the low end of the band. Indeed, the front-to-back ratio is above 20 dB for only about 150 kHz of the total width of 20 meters. The array has a 50-Ohm 2:1 SWR bandwidth that is just about 300 kHz, not enough to cover the entirety of 20 meters. In short, the array acts in an entirely normal way, with a front-to-back passband (using the 20 dB standard) that is just over half the overall 2:1 SWR passband.

+

If we are willing to use a much longer boom length to account for the higher level of inter-element coupling of loops compared to linear elements, we might arrive at the following design.

+ 
Design Data for an "Optimized" 4-Element Quad
+
+Element Diameter:                   #14 AWG
+Reflector Circumference:            72.91'
+Driver Circumference:               70.50'
+Director 1 Circumference:           67.29'
+Director 2 Circumference:           65.78'
+Refl-Driver Spacing:                11.37'
+Driver-Dir 1 Spacing:               22.07'
+Dir 1-Dir 2 Spacing:                25.27'
+Total Boom Length:                  58.71'
+

Although the "standard" short-boom design resulted from design "formulas," it is clear that no effort was made to make any of the performance peaks coincide in frequency. The present design was placed at 14.15 MHz in order to better equalized band edge performance.

+

This design retains the #14 AWG wire size, but extends the element spacing to the degree feasible before losing the desired antenna properties. Overall, gain is up by about 0.5 dB from the short-boom model, ranging from nearly 9.8 dBi to just under 10 dBi at mid-band. The front-to-back ratio peaks at about 40 dB, but drops to just under 15 dBi at the band edges. The beam is designed for a source impedance between 50 and 75 Ohms, where it misses full band coverage at under 2:1 by about 20 kHz or so. Although no single category of performance is so great as to dictate the longer boom design over the shorter version, the composite of all of the improvements in both gain and operating bandwidth strongly suggest the superiority of the longer-boom model.

+

As we have seen from designing quads with fewer elements, almost every category of performance benefits from enlarging the effective diameter of the elements. Consider the following design using 1" diameter elements. The 1" diameter elements can be synthesized from properly spaced pairs of wires in accord with principles enumerated at length in a past episode of this series.

+ 
Design Data for an "Optimized" 4-Element Quad
+
+Element Diameter:                   1.0"
+Reflector Circumference:            74.84'
+Driver Circumference:               71.04'
+Director 1 Circumference:           67.04'
+Director 2 Circumference:           64.68'
+Refl-Driver Spacing:                11.37'
+Driver-Dir 1 Spacing:               22.07'
+Dir 1-Dir 2 Spacing:                25.13'
+Total Boom Length:                  58.56'
+

For our further efforts, we gain another half dB of gain over the #14 optimized design, with the free-space gain ranging from 10.3 to about 10.45 dBi. The front-to-back ratio peaks at a uselessly high 60 dB, but drops slightly below 20 dB at the band edges. Once more, the optimal feed cable is 75 Ohms, and the array easily holds the SWR below 2:1 across 20 meters.

+
+ +
+

A graphical comparison of the 3 designs can perhaps portray the performance better than words. Fig. 2 shows the free-space gain curves of the 3 arrays. Note that all three arrays place the peak gain within the passband, a mark of having achieved the highest gain feasible from the general design. However, also note that both wire designs show a sharper drop in gain at the low end of the band compared to the gain curve for the 1" model.

+
+ +
+

Often, a series of strategically taken azimuth plots can show the strengths and weakness of designs even better than graphed curves. Fig. 3 shows the azimuth plots for the 20-meter band edges and middle for the short-boom design. Clearly the design has been optimized for the upper end of the 20-meter band, although it is not clear whether this is intentional or accidental. The formulas were applied for a midband frequency of 14.175 MHz. Fatter wire with no change in dimensions would have moved the operating peaks higher in the band, while thinner wire would have narrowed the operating bandwidth of the array.

+
+ +
+

Fig. 4 provides the comparable set of patterns for the #14 optimized long-boom array. In this design exercise, the design frequency of 14.15 MHz provides well-balanced band-edge performance, although the rear lobes become significant at both 14.0 and 14.35 MHz.

+
+ +
+

The rear lobes of Fig. 5 show that the 1" diameter model belongs to the same design sequence as the optimized #14 model. However, the band-edge rearward performance is considerably improved over the thin-wire model. The rear lobe aligned 180 degrees from the forward lobe at 14.175 MHz shows how steep the front-to-back curve is, since the peak occurs at 14.15 MHz. The mid-band front-to-back ratio is about 35 dB compared to the peak 60 dB figure 25 kHz away.

+
+ +
+

In fact. Fig. 6 reveals that same information about front-to-back performance in a different form. The peak front-to-back frequency for the #14 optimized model is just below 14.175 MHz and exceeds 40 dB. Also of note is the fact that the short-boom model achieved such gain as it could at the expense of front-to-back ratio.

+
+ +
+

In Fig. 7, we have the SWR curves, although we must remember which one represents a 50-Ohm value and which ones represent a 75-Ohm value. In large measure, the bandwidth quality of any array--with special attention to quads--is a function as much of the range of feedpoint reactance across a band as it is a matter of the range of the resistive component of the feedpoint impedance. Moreover, the ratio of total change of reactance to the average resistance (or to the desired feed cable) will indicate loosely whether or not a 2:1 ratio can be maintained across the band. The short-boom model has a median resistive component of 48.8 Ohms with a total change of reactance of 85.8 Ohms--a ratio of about 1.76:1. The long- boom wire model has a reactance range that is higher: 96.5 Ohms. However, the median resistance is 66 Ohms, for a 1.46:1 ratio. The 1" model shows a change in reactance of 67 Ohms with median resistance of 59 Ohms, for a 1.13:1 ratio. Although the ratios are not precise indicators of SWR performance, it is clear that a low ratio is a good indicator of better bandwidth. More precise equations can be developed, but the complexity of the SWR formulas make the exercise--already less than precise--somewhat superfluous. A good indicator is sufficient to alert the quad designer to desired directions of improvement.

+

Automating 4-Element Quad Design

+

Both optimized designs emerge from the same sequence of designs that will allow for automated design after regression analysis of the baseline models that spanned wire diameters from 3.16E-5 to 1E-2 wavelengths. As we have added elements to the designs, it has become harder to maintain a wide operating bandwidth with decreasing wire sizes. 4-element design, when applied to HF arrays that typically use wire, significantly benefits from the development of thick-wire substitutes in order to achieve maximum gain, a high front-to-back ratio over the entire chosen band, and an SWR of less than 2:1 across the band. In general, a wire size of 0.005 wavelengths is desirable, which is in the vicinity of 5" at 20 meters. Obviously, a 2-wire--or preferably a 3-wire--substitute is called for. (Narrow-band applications, of course, are immune from this requirement, except for achieving maximum gain and adequate front-to-back ratio.)

+

The selection of a design sequence also calls for some comment. The baseline arrays in the sequence must, of course, be part of a sequence and not merely a set of random spot designs, each of which uses the prescribed wire size. Each array was designed so that, to the degree possible, maximum gain occurred within 1.5% of the design frequency. The maximum front-to-back ratio was set on the design frequency, as was array resonance. Wire size was change in increments that resulted in a sequence of the common logarithms of the wire size in wavelengths of 0.5 increments. This interval ensured a regression analysis that could be carried out to the 4th order.

+
+ +
+

Fig. 8 shows the reflector circumference (more correctly, the value of 1/8 of the reflector circumference) curve developed via regression analysis. Similar curves, not all so precisely fitted as the example, emerged for the other parameters of the 4-element quad design.

+

In practice, the number of true variables in the analysis turned out not to exceed those used for the 3-element quads shown in preceding episodes. The spacing needed between the reflector and driver and between the driver and the first director required very large changes before they resulted in a significant change in array properties. In contrast, each of the other dimensions of the array were quite sensitive to small changes. (These dimensions included all element circumferences and the spacing between director 1 and director 2.) Therefore, the spacing between the driver and its adjacent elements was allowed to stand as a pair of constants (in terms of wavelengths).

+

An additional factor involved in the selection of the model sequence to form the basis for automated design involved the rate of change of the reactance range from the lower to the upper limits of a defined frequency span. Each model in a sequence will show a range of reactance change across an assigned frequency span such that the thinner the wire, the higher the reactance range. The rate of change of this range from one wire size to the next plays a role in the selection of the design sequence: the lowest rate of change with wire size decrease is the most desired sequence. This rate ensures that thinner wire designs--while not matching the performance of thick-element designs in the same sequence--at least provide useful performance.

+

There are, in fact, spot designs that will outperform the models in this sequence, some of which have shorter booms. Dan Handelsman provided me with one such design for 2 meters using a 0.5" diameter element. The design data are as follows:

+ 
Design Data for an N2DT 4-Element Quad
+
+Design Frequency:                   146 MHz
+Element Diameter:                   0.5"
+Reflector Circumference:            92.36"
+Driver Circumference:               84.64"
+Director 1 Circumference:           83.20"
+Director 2 Circumference:           78.80"
+Refl-Driver Spacing:                17.50"
+Driver-Dir 1 Spacing:               17.50'
+Dir 1-Dir 2 Spacing:                18.00'
+Total Boom Length:                  53.00'
+

The dimensions for the corresponding 0.5" diameter model from the selected sequence are these:

+ 
Design Data for a 4-Element Quad from the Sequence
+
+Design Frequency:                   146 MHz
+Element Diameter:                   0.5"
+Reflector Circumference:            89.98"
+Driver Circumference:               83.42"
+Director 1 Circumference:           77.76"
+Director 2 Circumference:           74.35"
+Refl-Driver Spacing:                13.22"
+Driver-Dir 1 Spacing:               25.67'
+Dir 1-Dir 2 Spacing:                28.07'
+Total Boom Length:                  66.96'
+

The N2DT quad actually outperforms the sequenced quad by a small margin, despite the 14" reduction in boom length. The gain is 0.15 dB higher (10.76 vs. 10.61 dBi) at the design frequency. The 20-dB bandwidth is close to 2.8% in contrast to the sequence design's 2.75% value. (The bandwidth of 2 meters is about 2.78%.) Both arrays have a 50-Ohm SWR under 2:1 across the band. (For the VHF range, with large diameter elements whose logs are between -2.5 and -2.0, the feedpoint impedances of the sequenced designs are closer to 50 Ohms than to 75 Ohms.) The natural question is why the N2DT design was not chosen as the basis for the design sequence.

+

The answer lies in the rate of change of the span of reactance with decreasing wire sizes. For the span of wire sizes whose diameters in wavelengths result in common logs of -2.0 to -2.5, the reactance range increased 54% for the N2DT design, but only by 33% for the chosen sequence. Although the rate of change is not a linear curve in all cases, it does provide an indication of the most promising design sequence that is usable over a wide span of wire diameters.

+

Neither the N2DT design nor the sequence design provides the highest possible gain for a 4-element quad. The following dimensions are for a high-gain 4-element quad that also uses 0.5" diameter elements and a design frequency of 146 MHz.

+ 
Design Data for a High-Gain 4-Element Quad
+
+Element Diameter:                   0.5"
+Reflector Circumference:            89.120"
+Driver Circumference:               83.760"
+Director 1 Circumference:           77.760"
+Director 2 Circumference:           74.080"
+Refl-Driver Spacing:                13.200"
+Driver-Dir 1 Spacing:               25.937"
+Dir 1-Dir 2 Spacing:                30.715"
+Total Boom Length:                  69.840"
+

This design will meet the less than 2:1 SWR standard (50 Ohms), but the front-to-back ratio holds above the 20 dB level for only about 3/4 of the 2-meter band. As well, the gain varies about 0.4 dB across the band. The two most prominent factors in the design are its free-space gain, which reaches 11.0 dBi, and its length, which is about 2" short of 6'. It did not exhibit a sufficient bandwidth or a sufficiently low rate of reactance-span change to qualify for the sequence.

+

The Automated Design Program

+

Perhaps the only significant claim that can be made for the sequence of designs that resulted in the automated design program is that they yield close to the widest bandwidth in the listed operating categories, along with the best gain potential as a secondary criterion, of any sequence that I have so far uncovered. Obviously, there may well be other sequences awaiting discovery. Therefore, the program should be used with due appreciation of the tentative nature of its presentation.

+

However, what the program does do is to give due place to element diameter and to quad- loop inter-element coupling in its development. As with the other programs in this sequence, one enters the desired element diameter in a specified unit of measure. The program contains no provision for entering AWG wire sizes. As well, one enters the design frequency. For wide bands, such as the harmonically related HF amateur bands, it may be best to select a design frequency between 0.35 to 0.4 of the way from the lower band edge in order to achieve roughly similar front-to-back and SWR values at both band edges.

+

As with past programs, the listing is for GW Basic, since that format makes all of the mathematics visible to the user.

+ 
       A GW Basic Program to Calculate Dimensions of a Wide-Band 4-Element Quad Beam
+
+10 CLS:PRINT "Program to calculate the dimensions of a resonant square 4-element quad beam."
+20 PRINT "All equations calibrated to NEC antenna modeling software for wire diameters"
+30 PRINT "     from 3.16E-5 to 1E-2 wavelengths within about 0.5% from 3.5 - 250 MHz."
+40 PRINT "L. B. Cebik, W4RNL"
+50 INPUT "Enter Desired Frequency in MHz:";F
+60 PRINT "Select Units for Wire Diameter in 1. Inches, 2. Millimeters, 3. Wavelengths"
+70 INPUT "Choose 1. or 2. or 3.";U
+80 IF U>3 THEN 60
+90 INPUT "Enter Wire Diameter in your Selected Units";WD
+100 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+110 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+120 IF U=3 THEN D=WD
+130 PRINT "Wire Diameter in Wavelengths:";D
+140 L=.4342945*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413:D1=.4342945*LOG(D)
+150 IF D1<-4.5 then 160 else 170
+160 print "Wire diameter less than 3E-5 wavelengths:  results uncertain."
+170 if d1>-2 THEN 180 ELSE 190
+180 PRINT "Wire diameter greater than 1E-2 wavelengths:  results uncertain."
+190 AD=-.00018:BD=-.002359259259#:CD=-.01090277778#:DD=-.01971296296#:ED=.1174938889#
+200 DE=(AD*(D1^4))+(BD*(D1^3))+(CD*(D1^2))+(DD*D1)+ED:DE=DE*8
+210 AR=.0002666666667#:BR=.004237037037#:CR=.02554444444#:DR=.07158756614#:ER=.2119230159#
+220 RE=(AR*(D1^4))+(BR*(D1^3))+(CR*(D1^2))+(DR*D1)+ER:RE=RE*8
+230 AI=-.0002#:BI=-.002525925926#:CI=-.01182777778#:DI=-.02473915344#:EI=.1008246032#
+240 IR=(AI*(D1^4))+(BI*(D1^3))+(CI*(D1^2))+(DI*D1)+EI:IR=IR*8
+250 AT=-.0006#:BT=-.009059259259#:CT=-.04912777778#:DT=-.1152343915#:ET=.01678174603#
+260 TT=(AT*(D1^4))+(BT*(D1^3))+(CT*(D1^2))+(DT*D1)+ET:TT=TT*8
+270 SP=.1635:IP=.481
+280 ATT=.0026666666667#:BTT=.036888888889#:CTT=.177#:DTT=.3386587302#:ETT=1.046738095#
+290 TTP=(ATT*(D1^4))+(BTT*(D1^3))+(CTT*(D1^2))+(DTT*D1)+ETT
+300 AZ=1.2#:BZ=13.92592593#:CZ=60.777777778#:DZ=113.9177249#:EZ=132.618254#
+310 ZR=(AZ*(D1^4))+(BZ*(D1^3))+(CZ*(D1^2))+(DZ*D1)+EZ
+320 AG=-.1#:BG=-1.184444444#:CG=-5.228333333#:DG=-9.831507937#:EG=4.045238095#
+330 GN=(AG*(D1^4))+(BG*(D1^3))+(CG*(D1^2))+(DG*D1)+EG
+340 AW=.07#:BW=1.048518519#:CW=6.173055556#:DW=17.12092593#:EW=21.34722222#
+350 SW=(AW*(D1^4))+(BW*(D1^3))+(CW*(D1^2))+(DW*D1)+EW
+360 AF=-.03#:BF=-.27666667#:CF=-.4475#:DF=2.348809524#:EF=7.853214286#
+370 FB=(AF*(D1^4))+(BF*(D1^3))+(CF*(D1^2))+(DF*D1)+EF
+380 WL=299.7925/F:PRINT "Wavelength in Meters =";WL;"    ";
+390 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+400 PRINT "Quad Dimensions in Wavelengths, Feet, and Meters:"
+410 PRINT "Driver Side =";(DE/4);" WL or";(DE/4)*WF;"Feet or";(DE/4)*WL;"Meters"
+420 PRINT "Driver Circumference =";DE;" WL or";DE*WF;"Feet or";DE*WL;"Meters"
+430 PRINT "Reflector Side =";(RE/4);" WL or";(RE/4)*WF;"Feet or";(RE/4)*WL;"Meters"
+440 PRINT "Reflector Circumference =";RE;" WL or";RE*WF;"Feet or";RE*WL;"Meters"
+450 PRINT "Reflector-Driver Space =";SP;" WL or";SP*WF;"Feet or";SP*WL;"Meters"
+460 PRINT "Director 1 Side =";(IR/4);" WL or";(IR/4)*WF;"Feet or";(IR/4)*WL;"Meters"
+470 PRINT "Director 1 Circumference =";IR;" WL or";IR*WF;"Feet or";IR*WL;"Meters"
+480 PRINT "Director 1-Reflector Space =";IP;" WL or";IP*WF;"Feet or";IP*WL;"Meters"
+490 PRINT "Director 2 Side =";(TT/4);" WL or";(TT/4)*WF;"Feet or";(TT/4)*WL;"Meters"
+500 PRINT "Director 2 Circumference =";TT;" WL or";TT*WF;"Feet or";TT*WL;"Meters"
+510 PRINT "Director 2-Reflector Space =";TTP;" WL or";TTP*WF;"Feet or";TTP*WL;"Meters"
+520 PRINT "Approx. Feedpoint Impedance =";ZR;"Ohms   ";
+530 PRINT "Free-Space Gain =";GN;"dBi"
+540 PRINT "Approximate 2:1 VSWR Bandwidth =";SW;"% of Design Frequency"
+550 PRINT "Approximate >20 dB F-B Ratio Bandwidth =";FB;"% of Design Frequency"
+560 INPUT "Another Value = 1, Stop = 2: ";P
+570 IF P=1 THEN 10 ELSE 580
+580 END
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Note: "LOG" in GW Basic always mean the natural logarithm. Hence, a conversion factor is necessary to convert the natural log to the common log required by the program. If the medium to which this program may be transferred already knows the difference between "LOG" and "LN," the conversion factor can be dropped.

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The program provides supplemental data on the approximate feedpoint impedance at resonance, the free-space gain at the design frequency, the under 2:1 SWR bandwidth as a percentage of the design frequency, and the greater than 20 dB front-to-back ratio bandwidth also as a percentage of the design frequency. Since the latter two curves are not symmetrical on both sides of the design frequency, careful selection of the design frequency is important.

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A version of this program appears in the HAMCALC suite of GW Basic utility programs available from VE3ERP. As well, a version appears at the Nittany Scientific (web.archive.org) web site in the form of a NEC-Win Plus model set up in equations. The supplemental data do not appear in that program, since running a model through a frequency sweep is a superior method of determining passband performance and selecting the optimal design frequency. The following links will take you to a download page where you may download the program as a. a NEC-Win Plus model file, b. a GW Basic program, or c. a VB script generously made available by Randy Frum, AC4FD. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen. Also see the Antenna Modeling Programs page.

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Some Foreshadowings

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The level of inter-element coupling among quad loops requires greater spacing, in general, than comparable linear dipole/Yagi elements in order to optimize array gain. To obtain high gain with a good bandwidth for other operating parameters, the multi-element monoband quad becomes longer faster than potentially competing Yagi-Uda designs. At 4 optimally spaced elements, even with thick element diameters, the quad approaches a possible limit on its ability to provide higher gain with a shorter boom length.

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Yagi designs are only one alternative to the potential 5- and 6-element quad. Dan Handelsman has been working with asymmetrical and symmetrical double rectangles (ADRs and SDRs) as alternatives both to the entire set of simple quad loops and to the reflector and driven elements of such arrays. These designs show promise of adding gain and a very wide operating bandwidth for any given number of elements and boom length. However, the cost appears at present to be greater complexity in the mechanical design of the ADR and SDR elements. The feasibility of such designs may eventually be different for potential HF and VHF applications.

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In short, these design exercises are only a beginning to the process of more fully understanding both the potentials and the limitations of quad designs in all of their forms--some of which we have yet to see.

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Also see the Antenna Modeling Programs page for more information.

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Updated 05-01-2001, 11-14-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for April, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Quad List

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Go to Main Index

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Topics: HF Upper, Quad, VHF / UHF


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Adjacent-Band Quad Behavior

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L. B. Cebik, W4RNL

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In the study of quads that led up to some notes on dual-band antennas using a common feedpoint, I intentionally by-passed an important question. Dual-band quads required a frequency ratio of at least 1.3:1 for inclusion in the earlier notes. As a result, I omitted combinations such as 20 and 17 meters or 12 and 10 meters. That set of notes reached a number of conclusions about quad behavior based on consistent trends shown by the models that I did use. Foremost among the results was the observation that most of the major performance and dimension changes resulted from the simple proximity of the element loops, even when using separate feedpoints. The major dimensional change that occurs when using a common feedpoint instead of separate feedpoints is the lengthening of the inner or higher-frequency driver loop.

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We are now positioned to fill in the gap in our exploration of dual-band quad behavior. The study can restrict itself to quads with separate feedpoints on each band, thus simplifying the required modeling. Most of the dimension and performance behaviors that we shall find interesting occur using separate feedpoints. Fig. 1 shows the general parameters of the models used in this sequence of examinations. Of course, only one of the two feedpoints shown in the sketch will be active at any one time.

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Like the earlier sequence of quad models, the new set will rest on the monoband quad designs derived by equations, as described in Part 1 of that study. Dual band models will presume spider construction, which calls for an angle of about 62 degrees between the driver and the reflector support arms. Indeed, the only restriction that we shall remove is the minimum frequency ratio between bands. Hence, we can now see what trends develop as we change the ratio. By using combinations of 17 and 12 meters, 15 and 10 meters, and 20 and 15 meters, we encountered relatively small interactions that left the performance curves quite similar to those for the monoband beams, with variations only in the limiting values for each band. We also noted small variations that depended upon whether a loop was part of an inner or higher frequency beam or was part of an outer or lower frequency beam.

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To the collection of dual-band quads previously used, we may now add 4 other combinations: 20-17, 17-15, 15-12, and 12-10, where each designation is for an amateur band pair. We shall divide the trends into 2 parts. The first set of trends will involve the physical dimensions. The second (and longer) exploration will deal with performance.

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General Notes on Dual-Band Quad Dimensions

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Table 1 provides a summary of the dimensions, starting with those of the monoband beams. Along side each monoband beam are the dimensions of the loops and the spacing for all of the dual-band quads that we shall examine. As in past notes, all dimensions are in inches. Multiply the values by 0.0254 to obtain dimensions in meters. The loop dimensions appear as circumferences in this table, and a loop side is the value shown divided by 4. Spacing values are the distance between the front and rear loops for each band. As I did for the monoband beams, I used 14.14, 21.19, and 28.4 MHz as offset design frequencies so as to level the band-edge front-to-back ratio values to the degree possible. 17 and 12 meters are narrow enough to allow the band center frequency to serve also as the design frequency. All drivers are resonant at the design frequency within about +/-j1 Ohm of remnant reactance. In anticipation of potential trends, I extended the degree of element size precision to 0.05". All values of element spacing remain constant between the monoband and dual-band quads.

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The dual-band quads are listed according to the bands covered, that is, as 20-17, 20-15, etc. Each combination shows the loop circumferences that result in a peak front-to-back ratio and near resonance at the design frequencies. The entries marked "d-Mono" show the difference between the required circumference of the element in its place within the dual-band quad and the corresponding monoband element. A positive value means that the dual-quad element is larger; a negative value means that it is smaller.

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The dual quads fall into 2 groups. The 20-15, 17-12, and 15-10 models are wide, that is, have a greater spacing between the two element sets due to the larger frequency ratio. The ratios range from 1.34:1 up to 1.5:1. These patterns replicate what we uncovered in the previous study. If a driver is an outer (or lower frequency) elements, then it will increase in length relative to the monoband value. For the upper HF bands used here, the amount and the range is small: 2.2 to 3 inches. If the driver is an inner (or higher frequency) elements, then its length will decrease relative to a monoband quad. Again the amount and range are small: 3.8 to 4.3 inches.

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If a reflector is an outer loop, then it will be shorter than the corresponding monoband reflector. The amount is greater than for the other affected elements: 6.2 to 7.5 inches. In contrast, for the wide dual quads with higher frequency ratios, if a reflector is an inner loop, it requires no change from the monoband length.

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The other group of dual quads includes 20-17, 17-15, 15-12, and 12-10 meters. The frequency ratios for this set run from a low value of 1.14:1 to a high value of 1.28:1. The average ratio is 1.21:1, in contrast to the average ratio for the wide group: 1.42:1. The result, of course, is a 2:1 ratio of ratios.

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For the narrow group, if a driver is an outer loop, then it increases in size relative to the monoband quad element and roughly in proportion to the ratio of ratios. That is, the driver range of increase is 4.0 to 5.3 inches. If the reflector is an outer loop, then it decreases in size, not only with reference to the monoband antenna, but as well by a factor greater than the ratio of ratios. Outer reflectors for the narrow group decrease their circumferences by 12 to 17 inches relative to the monoband models. In general, the closer the spacing between the elements of a dual-band quad, the more rapidly that a reflector becomes shorter to maintain the same performance points.

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If reflector is an inner loop, the wide dual-band quads required no change in circumference. However, with closer spacing, the narrow group of dual-band quads show a small amount and range of increase relative to the monoband quads: 1.3 to 3 inches. Like the wide-group drivers, the narrow group drivers--when forming inside loops--require shortening relative to monoband values. However, the amount is less than proportional to the ratio of ratios. The range of 5.1 to 5.5 inches is only about 30% greater than the amounts required by the wide group.

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Physically, then, the elements of dual-band quads show a varied pattern of changes as we shrink the spacing between loops by creating beams for adjacent bands. Some changes are roughly proportional to the ratio of ratios, while others are not. However, trends that first appeared for the wide group continue in the same direction as we decrease the loop spacing by using adjacent bands. (Of course, the one exception is the inner reflector, which showed no trend for the wide-group dual quads.)

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Within reason, one might use the patterns shown in Table 1 as a design aid if developing a dual-band quad. The exact amounts of change will themselves change if we alter the element diameter, that is, the wire size. A further variable prevents me from trying to codify the patterns into a set of design equations. The performance points listed as criteria for success at the design frequencies--peak front-to-back ratio and driver resonance--are not perfect. The attainment of the peak front-to-back ratio at the design frequency is a judgment call within the limits of the increments of side-length change in the test models. As the frequency goes up, an increment of 0.05" per half-side length may not be sufficient to place the peak with precision. Operationally, such small departures from perfection are superfluous worries. However, they are enough to preclude final codification. Even regression analysis is not feasible, since it would apply to only one fixed wire size. A true set of design equations would require a survey that included a wide range of wire sizes. Such a survey is theoretically possible, and the results would amount to an extension of the existing monoband design equations, showing the modification of a monoband design for a dual-band quad for frequency ratios of perhaps 1.1:1 up to 1.5:1. However, the work involved so far does not seem to to yield a sufficiently useful result.

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Band-by-Band Performance Trends

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The performance side of our adjacent-band behavior question requires a gallery of graphs. For each loop tuned to the design frequency on each of the upper-HF amateur bands, I plotted the following results across the band: gain, 180-degree front-to-back ratio, feedpoint resistance, and feedpoint reactance. Hence, there are 5 graphs for each parameter, one for each band. Each graph also contains the curve for the monoband quad as a reference. In all cases we shall be more interested in the slope or general shape of a curve than in in precise values.

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Each graph covers a different territory because not all wide and narrow group potentials appear in every graph. For example, the 20-meter graphs will show only 3 curves, and the two dual-band curves will apply only to loops that are outer elements, that is lower in frequency than the accompanying band. 10-meter graphs show just the opposite in their 3 lines. Besides the monoband curve, we shall find only instances where the 10-meter elements are inner or higher frequency elements. Only 15 meters shows the full spectrum of potentials, with 2 outer loop and 2 inner loop cases to accompany the monoband curve.

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The dimensional table used a single designation for each combination, for instance, 17-12. The graph legends use a modification of that system. The band of interest to the graph always appears first in the dual-band quad designation. Therefore, in the 17-meter graphs, we shall find the label 17-12, but in the 12-meter graph, we shall designate the same dual-band quad as 12-17.

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Gain

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Both dual-band 20-meter curves in Fig. 2 refer to outer elements in their pairs. The monoband curve shows the lowest rate of gain decrease across the band. Note that as we add a higher band--even widely separated--the rate of gain decrease becomes steeper. In addition, as we reduce the space between the 20-meter elements and the second set in the pair, the rate of gain decrease becomes even greater.

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The 17-meter gain chart (Fig. 3) includes one instance where 17-meters is an inner element. In this case, the rate of gain decrease is slightly less than the rate for the monoband quad. For the two cases in which the 17-meter elements are outer loops, the rate of gain decrease is higher than the monoband rate. Once more, the more closely spaced elements result in a more rapid decline in gain than for the more widely space elements. Indeed, the slope angles for the two outer-loop cases is dramatic. In passing, we may also note that the monoband and the two outer loop curves do not vary in gain by much at the design frequency. However, the inner-loop case shows a numerically noticeable higher gain value (more than 0.1 dB).

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One reason for including graphs of the small 17- and 12-meter bands is that they show some fine detail better than graphs for the wider amateur bands. Fig. 4 covers the gain situation on 15 meters, but some of the detail may be obscured by the wide range of values. When we pair 15 and 12 meters, the outer 15-meter loops show a very steep gain curve with a total gain decrease of nearly 2 dB across the band. When we pair 15 meters with 10 meters, the gain decrease range drops to just over 1 dB. The two cases where 15 meters forms the inner loop set (15-17 and 15-20) show gain decrease curves that are shallower than the monoband curve. With the scales used, it is difficult to see, but the 15-17 curve is slightly shallower than the 15-20 curve. Both inner loop curves show a slightly higher gain at the design frequency than the monoband quad. In short, the 15-meter gain curves reflect all of the trends shown for the other bands surveyed so far.

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The 12-meter gain curves in Fig. 5 provide us with only 1 case where the 12-meter loops serve as outer elements. The narrow spaced 12-10 combination produces a very steep gain decrease curve, even over the 100 kHz of the band. When the 12-meter elements are inner loops, they show slightly higher gain than the monoband quad. However, the curves for the 2 dual-band quads are too close together for any definitive conclusions regarding relative curve flatness.

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Besides the monoband reference gain curve, the 10-meter dual-quad gain curves in Fig. 6 are limited to cases where the 10-meter elements are inner loops. At 28.4 MHz, both dual-quad curves show a higher gain than the monoband quad. As well, the more widely space 10-15 combination shows a steeper curve than the narrow 10-12-meter pair.

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In general, then, the gain of inner loops at the design frequency is higher than the monoband value, but the rate of decrease is greater. Using adjacent amateur bands in a dual-quad results in a high rate of inner-element gain decrease compared to using bands that more widely spaced. The situation for the outer loops in a dual quad is the reverse. Although the gain value at the design frequency does not vary significantly from the monoband value, the outer-loop gain curves are shallower. The closer the element spacing from one band to the other, the shallower the curve. However, outer-loop advantages over the monoband quad are generally too small to be operationally significant.

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180-Degree Front-to-Back Ratio

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Within the limits of modeling described earlier, the 20-meter front-to-back curves are nearly congruent. The monoband curve shows the highest peak value and the highest band-edge values. The dual-band quads show slightly lower peak values (although that appearance may be illusory, given the narrow-bandwidth of the actual peak). They also show very comparable band-edge value. However, as we decrease the frequency ratio of the 2 bands, the band-edge values decrease. Note that these remarks apply to the 20-meter loops as outer elements in the band pairings.

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The front-to-back curves for the very small 17-meter band show the limitations of the data generation technique in Fig. 8. The divisions are 0.01 MHz apart, that is, less than 1/3 the increments used on 20 meters. Hence, peak front-to-back ratio displacements that would be invisible on 20 meters show clearly on the expanded 17-meter scale. The one instance where the 17-meter loops are inner elements (17-20) shows a lower peak value but higher band-edge values than the monoband curve. In both cases where the 17-meter elements are outer loop sets, the band-edge values are lower than the monoband values. As well, as the frequency ratio decreases, the overall front-to-back performance suffers, as shown by the 17-15 curve.

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As we increase the quad frequency, we also encounter limitations in placing front-to-back peaks within the minimum increment of element length change. Hence, not all peaks appear at the 21.19-MHz design frequency, as shown in Fig. 9. Nevertheless, the curves continue to confirm and expand the trends already noted. When 15-meter elements are the inner loops, they show slightly higher band-edge values than the monoband beam--although not by an operationally significant amount. As well, the lower the dual-quad frequency ratio, the higher the band-edge front-to-back ratio. On the other side of the monoband curve, when the 15-meter elements are outer loops, we find significantly lower band-edge front-to-back values. The lower the frequency ratio when 15-meter elements are outer loops, the worse the overall front-to-back curve.

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Unfortunately, the 12-meter band is too small for the graph in Fig. 10 to tell us much in light of the modeling limitations imposed. The monoband curve and the 12-10 curve are well aligned. The 12-10 curve places the 12-meter elements as outer loops and the frequency ratio is small. Hence, we see the typical degradation of the front-to-back curve. Both instances where the 12-meter elements serve as inner loops have displaced peaks, so we can only guess that the band-edge values would be higher than the monoband values if the curves aligned perfectly. However, it is clear that the 12-meter curve for the 12-15 pair is generally higher than the 12-17 curve with which it aligns. Of course, the frequency ratio of the 12-15 pair is lower than the ratio for the 12-17 pair.

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The mis-alignment of the 12-meter monoband curve with the 2 inner-loop cases is not quite accidental. The 10-meter curves appear in Fig. 11. The monoband quad model achieves a very high and steep peak value at the 28.4-MHz design frequency. The 10-12 and 10-15 dual quad pairs have peaks of unknown value near 28.45 MHz. Drawing the peak frnt-to-back ratio downward to the design frequency is a tedious task requiring exceptionally small increments of reflector length change. I have allowed the peak displacement since such tiny changes would be beyond the limits of most home shop facilities. Nevertheless, both inner loop 10-meters element sets show higher band-edge front-to-back values than the monoband quad, if only by a little. As well, the pair with the lower frequency ratio show even more slightly higher band-edge values.

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For all of the operating parameters, we have three interests in the curves that appear in the graphs. First, we are interested in whether or not the curves for one band confirm the trends shown by the curves for another band. Within the limits of the sets, we can generally respond affirmatively, with no exceptions so far.

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Second, we are interested in the differences in the performance levels depending on whether the elements for a given band form the inner or the outer set of quad loops. Throughout the front-to-back sequence, we have seen the outer loop sets generally yield poorer band-edge front-to-back values than the monoband beam. Because a quad front-to-back peak is so high, but only for a very narrow bandwidth, the band-edge values form a better overall marker of performance in this dimension than the peak value. Remember that a typical short-boom 3-element Yagi may be able to provide a 20-dB front-to-back ratio across any of the wider amateur bands. We tend to obtain slightly better band-edge front-to-back performance when the loops for a band are inner elements for a dual-band quad.

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Finally, we are interested in the differences created by the frequency ratio between the loop sets of a dual-band quad. For outer loop sets, decreasing the frequency ratio between bands covered by the beam can result a significant degradation of the front-to-back ratio across the band. Even the wider frequency ratios, such as between 10 and 15 meters, can yield noticeable decreases in the band-edge front-to-back performance. In contrast, when the loop set is an inner element set, the changes are operationally small, with numerically noticeable improvements in the band-edge front-to-back performance as we decrease the frequency ratio.

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Feedpoint Resistance

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The next set of graphs will reveal the trends that we can expect from the feedpoint resistance as we move the position of elements from outer to inner locations in a dual-band quad and as we alter the frequency ratio between the loop sets in a pair. However, a fuller understanding of the overall feedpoint impedance requires attention to this section and to the next section that covers feedpoint reactance.

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Both dual-quad curves for 20 meters in Fig. 12 represent outer locations relative to the other band involved. Both curves show a systematic decrease in the feedpoint resistance relative to the monoband value. The lower the frequency ratio between the bands, the greater the decrease in feedpoint resistance in the outer loop. As well, the lower frequency ratio produces a less linear curve.

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The 17-meter resistance curves in Fig. 13 tend to confirm the patterns that we noted for the 20-meter resistance curves, As well, the new graph introduces the first instance of a curve for the loop set using an inner position. The curve is for a low frequency ratio (17-20), and it shows a progression of resistance values that are also lower than those for the monoband quad. In fact, they are the lowest in the graph.

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Fig. 14 provides the resistance curves for 15 meters. All dual-band quad resistance values are well below the monoband values. When the 15-meter elements form outer loops, they show the same patterns that we saw on 20 and 17 meters. The curves show a growing non-linearity as we decrease the frequency ratio between the bands, and show in addition a greater reduction in value as we decrease the frequency ratio. When the 15-meter elements form inner loops, the curves are more linear, but decreasing the frequency ratio increases the reduction in the resistance values relative to the monoband quad.

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The narrow 12-meter band, shown in Fig. 15, allows us to examine the region of feedpoint resistance near the design frequency. In all cases, the dual-quad resistance is at least 30 Ohms lower than the monoband value. As well, lower frequency ratios produce greater resistance reductions. Near the design frequency, the low-ratio inner loop curve has the lowest resistance. However, the low-ratio outer curves would show (as on 15 meters) a non-linear shape such that wider band edges would show values as low or lower than when the loops form a low-ratio inner element set.

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The 10-meter graph in Fig. 16 allows us only to examine dual-band quad feedpoint resistance when the loops are at inner positions. However, the band is wide enough at 3.5% bandwidth to reveal that even the monoband curve will show some non-linearity. In contrast, the inner-position dual band quads with 10-meter elements are more linear than the monoband curve with respect to feedpoint resistance. Once more, the lower the frequency ratio between the bands in the array, the greater the reduction in feedpoint resistance relative to the monoband values.

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The reductions in feedpoint resistance accompany dual-band quad elements regardless of whether they occupy inner or outer positions. The lower the frequency ratio between loops, the greater the reduction in resistance. This condition leads to attempts to design multi-band quads for direct feeding with 75-Ohm feedline. Whether this tactic is completely feasible depends to a great degree on the reactance excursions across the bands.

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Feedpoint Reactance

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On 20 meters, as shown in Fig. 17, the monoband quad shows the greatest range of reactance. The other curves represent dual-band quads where the 20-meter loops have outer positions. The high-ratio curve for 20-15 has a slightly smaller range of reactance than the monoband curve due to the small non-linear shape. If we decrease the frequency ratio, as in the case of 20-17, the reactance curve flattens, limiting the total range of reactance change across the band. Each of the dual-band reactance curves is accompanied by a reduction in feedpoint resistance. The SWR relative to the resonant source impedance is a complex function of the ratio of reactance to resistance. The reduced range of reactance change offsets the reduction in resistance on 20 meters. Hence, the SWR curves for 20 meters tend to be similar in all 3 cases.

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17 meters is so narrow, as shown in Fig. 18 that we may by-pass curve shape and focus on basic properties. When 17-meter elements are outer loops with a high frequency ratio (17-12), the curve shows the flattening that we saw in the 20-meter loops. Likewise, when the 17-meter elements are inner loops (17-20) we see a higher slope to the reactance curve. However, when the 17-meter elements have an outer position with a low frequency ratio to the other band (17-15), the curve has a reverse slope. This situation provides an expanded view of the reactance behavior in the corresponding 20-meter case in which we saw a major bend in and flattening of the reactance curve as it passed the design frequency.

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The 15-meter reactance curves in Fig. 19 confirm the reactance behavior and allow us to view them over a greater bandwidth. When the 15-meter elements are inner loops, we find a steeper rate of reactance change than we find in the monoband curve. The change in frequency ratio between the 15-17 and the 15-20 cases produces only a small difference, with the lower frequency ratio showing the slightly steeper curve. More interesting are the curves for the 15-meter elements when they take an outer position. The 15-10 curve shows a slightly steeper rate of change below the design frequency. (This region also yields lower values of feedpoint resistance.) For the best SWR curve relative to the resonant impedance, one might wish to purposely detune the 15-meter driver to maximize the flatter portion of the reactance curve across the SWR passband. However, when we reduce the frequency ratio by pairing the 15-meter elements with 12-meters elements, we obtain greater self-limiting of reactance on the low side of the design frequency. Above the design frequency, the reactance shows a fairly steep reverse curve, that is, a curve showing increasing capacitive reactance with increasing frequency.

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On 12 meters, as shown in Fig. 20, we find the expected behavior of the 12-meter loops when they have inner positions. The reactance change across the band is higher than for the monoband quad. However, when the 12-meter loops have an outer position with a low frequency ratio (12-10), they show a dramatic reverse curve across the narrow confines of this band. Indeed, the total change is higher than for any other case, although we should note that the maximum reactance excursion is only about 13 Ohms for the 100 kHz passband.

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The 10-meter curves in Fig. 21 lose all drama because both dual-quads place the 10-meter elements in inner positions. Hence, the curves are nearly linear with a steeper slope than the monoband curve. The lower frequency ratio curve (10-12) shows a slight, nearly negligible, steeper slope than the higher frequency ratio curve (10-15). In both cases, the 1-MHz passband yields a total reactance change close to 100 Ohms.

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The reactance curves for dual-band quads present patterns that are considerably more complex than the patterns for many of the other operating parameters. When we use higher frequency ratios between bands in a multi-band quad, the behaviors are more nearly regular, relative to a monoband quad. Outer-position loops show flatter reactance curves, while inner-position loops show steeper curves. Hence, we may expect to have more difficulty covering all of 10 meters with an acceptable SWR than we encounter on 20 meters. However, the outer position curves are less than linear, and that non-linearity increases as we decrease the frequency ratio between loops. The reverse curves with an increasing capacitive reactance as the frequency climbs offer considerable design challenges to the quad builder.

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Conclusion

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We have taken a long look at dual-band quads using both higher and lower frequency ratios between bands. Our goal has been to detect reliable trends in major performance categories and in loop dimensions. The individual sections provide the best summaries of those patterns. In many categories of performance, the inner and the outer positioning of quad loops tend to produce reverse tendencies. However, the tendencies do not usually fully counter-balance each other for similar frequency ratios. Moreover, as we saw in the case of reactance excursions, the inner and the outer position curves do not always form reverse versions of each other.

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For the novice multi-band quad designer, there is a temptation to loosely believe that if we create a 3-band or a 5-band quad, the loops surrounded by other loops will simply neutralize the influences of the adjacent loops. However, the cautions that I just enumerated suggest that the surrounded loop may require more design effort, not less, in order to balance the unequal effects of the both inner and outer loops. The feedpoint resistance and reactance require special attention if we are to allow full coverage of all bands. The feedpoint resistance declines in the presence of any other loop (within the range of frequency ratios covered in these notes). If we cannot effect a suitable reduction of the total reactance change across the wider bands, the feedpoint SWR referenced to the resonant resistance will show a degraded curve.

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Dual-band quad trends are instructive. However, they are not complete. For example, we have worked exclusively with spider-design quads that maintain a prescribed element spacing based upon calculations performed in wavelengths, not in feet or inches. Hence, these notes may or may not be applicable to planar quads that use a fixed physical distance between all drivers and reflectors. As well, these notes are only suggestive in terms of what actually accurs in 3-band and 5-band quads. As a data compendium, these notes represent only the barest beginning of systematic studies in the behavior of multi-band quad beams.

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Updated 03-01-2007. © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Three Ways to Skin a Quad Loop

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L. B. Cebik, W4RNL

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+ A single quad loop makes a compact and effective bi-directional array for 10 meters. It has somewhat more gain than a dipole, and most users note that it is quiet, that is, not as susceptible to local noise as an open-ended dipole. With some sort of supporting system, the loop is a good choice for many ham back yards. +

A quad loop does its work with the antenna in the vertical plane, like a giant flyswatter. Maximum radiation is off the two broad surfaces and is minimum off the edges.

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Now comes the hard part: deciding what kind of loop to use. There are at least three versions, each with advantages and disadvantages. Let's look at them in order of complexity.

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The Standard Square Loop

The first sketch (Figure 1) shows a standard quad loop made from #12 AWG copper wire. (If you use a different size wire, you may have to change the dimensions just a bit for resonance.) This antenna is a proven performer, with about 3.3 dBi free space gain, which translates into about 8.3 dBi gain at 1 wavelength above ground for the bottom wire (about 35'). The elevation angle of maximum radiation is about 19 degrees, which provides access to low-angle incoming DX signals. +
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The feedpoint impedance is about 125 Ohms at the 28.5 MHz design resonance frequency. A quarter wavelength section of 75-Ohm coax (about 5.7' of standard RG-59 with a velocity factor of 0.66) will provide a very low-loss match for the 50-Ohm coax to the shack and provide less than 2:1 SWR over all of the first MHz of 10 meters, plus a little. With this set-up, the antenna has the broadest operating bandwidth of all of the loops we shall examine.

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The old standard way of making a quad loop is to use criss-cross spreaders of bamboo, fiberglass, or--more recently--PVC. However, there are no rules that forbid you from stretching the quad loop from its corners to trees or other vertical supports. You can also use tubular horizontal members and wires vertical sides, although you may have to adjust the dimensions--most likely to enlarge them a bit.

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The Elongated Loop

In July, 1996, K6STI wrote in QST of an old idea: by elongating the quad loop we can achieve a little more gain and, at the same time, bring the feedpoint impedance close to 50 Ohms for a convenient match with our standard 50-Ohm coaxial cables. +
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Figure 2 shows the dimensions of a #12 AWG copper wire loop meeting these goals. The feedpoint impedance is almost exactly 50 Ohms at 28.5 MHz. However, the 2:1 SWR operating bandwidth is only about 800 kHz, somewhat narrower than the standard loop with a matching section attached.

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The gain of the loop with the bottom wire at about 35' is 8.9 dBi (4.2 dBi in free space), and the taller assembly lowers the take-off angle to 17 degrees. Both the gain and the lower angle of maximum radiation contribute a little extra to our DXing efforts.

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Most likely, you would want to build a fixed version of this kind of loop by supporting the wire from its corners by ropes running to adjacent supports. As an alternative, you can build a rotatable version by using tubular horizontals and wire vertical sides (again, with dimensional adjustments that owe to the fat horizontal elements) attached to (but insulated from) a center mast. With a height about 3' taller than the normal quad loop, support requires a bit more work than the standard loop. Yet, if the top of this loop and the top of the standard loop are level with each other, this elongated loop loses some of its advantages in gain and lowered take-off angle.

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The Hentenna

The Hentenna is an invention of Japanese hams (and "hen" means "what is it?"--or so I am told). It consists of the full wavelength upper loop with a secondary lower loop that allows a close match to 50-Ohm coaxial cable. See figure 3. +
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The gain of this antenna, if the bottom wire is at the same level as the other two loops (1 wavelength or 35'), is about 9.8 dB (5.0 dBi in free space), with a take-off angle of 15 degrees, making it a good DX antenna among loops. However, its performance depends very much on the added height of the upper wire, which is nearly 19' from the bottom. The antenna is 60% as wide but more than twice as tall as the standard square loop. If we lower the top wire to parallel it with the top wires of the other two loop designs, the hentenna turns out to be only a little better than they are.

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The operating 2:1 SWR bandwidth is the narrowest of the three loops, about 600 kHz or a little over half of the first MHz on 10 meters with the design frequency of 28.5 MHz used here. Like the other loops, construction can be all wire, with the corners attached by thin (UV-resistant) rope to supports. Or, you can once more use larger diameter upper and lower horizontal members with wires sides and a wire feedpoint element for a rotatable antenna.

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Pattern Comparison

To give you a better idea of what to expect from each antenna, here are two elevation patterns, each of which contains patterns for all three loops. +
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Figure 4 compares the antennas using a common bottom horizontal wire height of 20'. This arrangement places the elongated loop top wire above that of the square loop, and the hentenna top wire above both the others. The advantage in gain and lowered angle of radiation for the larger loops is clear.

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Figure 5 reverses the procedure and places the top wires of all 3 antennas at 40' up. For many installations, top height is more absolute than bottom height. In this configuration, all three antennas have comparable TO angles, with only small gain advantages as the loops grow larger.

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Whichever loop you choose, assuming that a loop fits your operating needs, give your best ingenuity to construction. If at all possible, figure out how to make the antenna free standing so that you can rotate it by hand (if not by a TV rotator). You will need to turn at most less than a half turn, since the antenna is bi-directional. All of the loops have very deep side nulls on a plane with the wires, and just these nulls along can get rid of more than half the QRM that might get in the way of your QSOs.

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Loops are also handy in contests, where you really do want to hear what is happening in most directions. You never know in advance from where your next contact will come. If you build the loop to be collapsible, you can set it up for Field Day and other hilltopping exercises.

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The basic quad loop is a versatile antenna that lends itself to many construction techniques. If you want a little more performance than a dipole can give and you think it is fun to have a flyswatter waving in the breeze above your QTH, then one of these three designs may be the next antenna to build.
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+ Go to Amateur Radio Page
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Topics: HF Upper, Quad


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+


+ Some Model Quads Index

+

L. B. Cebik, W4RNL

+
+
+ +
+

As a result of a number of requests that I have received for models of quads from my files, I thought that I might make a batch available all at once. Actually, I shall divide the material into 3 sections: full-size 2- element quads, shrunken 2-element quads, and multi-band quads of 2 or more elements. My collection lacks some interesting types, such as a good model of the Swiss quad.

+

I shall not be adding modeling files per se, but I shall add some model descriptions that one can transcribe into any modeling software format. Not many descriptions are necessary, because virtually all models are constructed in the same manner. Initially, all models begin in a free space environment. Each loop is centered on a 0, 0 X (or Y) and Z axis. The loop corners are then defined.

+

For square loops with bottom wires parallel to the ground, a coordinate set consists of two entries, each one-half the side dimension, with + or - signs as dictated by the particular corner of the loop. Hence, the upper left corner of a loop with 9' sides will use -4.5, 0, 4.5 as X, Y, and Z coordinates.

+
+ +
+

Diamond loops require that one multiply one-half the length of a side by 1.414 to arrive at the peak, which will then be at either the X (or Y) or the Z coordinate when the other is zero. The same loop as above, but turn to a diamond configuration, would use for the top coordinates 0, 0, 6.36.

+

The "unused" coordinate, of course, receives the spacing dimension between elements. Simple monoband quads can set any element to zero and count from that point. Multi-band spider-hub quads often use a zero-center point to best advantage. Once one has one element complete and correct, ne may then use an appropriate copy mechanism to replicate the element, changing coordinate numbers (or letters, if symbolic entry is used) to account for dimensional differences.

+

Once the loops have been constructed in a free space environment, adjustment for height above ground is a simple matter of changing all Z-coordinates by the same amount. Of course, the amount will be the height above ground if the height represents the loop center. Other adjustments may be needed if the height represents the bottom of the lowest wire.

+

Despite a few remnant protestations from a few quad designers, antenna modeling programs have proven very effective and accurate for designing and analyzing quads. All programs have some limitations, so let's note the most important ones.

+

MININEC 3.13, the core of such programs as ELNEC, AO, and NEC4WIN, has a problem with corner-clipping as segment centers tend to give the effect of linking and ignoring the small increment to the actual corner junction or pulse. The standard method for reducing this effect to negligible amounts is length tapering. Length tapering can be manually or automatically implemented, and the automatic systems can be visible or invisible to the user who does not look at the post-run wire tables for the antenna. It is a process of reducing the length of segments gradually as corners are approached so that two conditions are met. First, the segments closest to the corner are very short without exceeding the minimum segment length, either absolutely or relative to wire diameter. Second, the changes in length from one segment to the next are within the boundaries set for accurate output from the core.

+

NEC (-2 or -4) (as found in programs like NECWires, EZNEC, and NEC-Win) does not require length-tapering at corners, since the currents are taken from the entire segment. However, NEC has two limitations to note. First, angular junctions of wires having different diameters yield inaccurate results. This is no problem for the standard wire quad loop. However, some quad design use large diameter tubular horizontal members and vertical wires to connect them. NEC has a problem with this configuration. Second, NEC requires that the source be placed on a segment, which presents problems to corner feed points, such as might occur on a diamond shaped quad. We shall look at the alternatives for handling this situation as we proceed through the models.

+

The initial monoband quads will all be for 10 meters. In most instances, I shall not express dimensions in terms of equations of the order "L = 1234/f" since the required length of a quad loop will vary with the wire diameter on any band. The fatter the wire, the larger the quad loop for the same resonant frequency. Therefore, unless one adjust the wire size as well as the length, scaling will be imperfect. Since the models will use #14 AWG copper wire (0.064" diameter"), direct diameter scaling makes for unlikely assemblies (for example, #10 AWG on 20 meters based on the use of #14 AWG on 10 meters).

+

With these reservations in mind, we may look not only at the models, but at their characteristics as well. The exercise will provide some useful expectations of various kinds of quads (but by no means all kinds), including recognition of what may be misleading about showing only peak data without the remainder of the data curves across a band of intended operation. We shall also find some easy ways out of a few seeming blockades to achieving desired performance curves. In the last part, we shall take up the question of remotely switching stubs as a feed system for multi-band quads.

+ +

The following books should be required reading for anyone interested in large or small quads:

+
    +
  • +

    William Orr, W6SAI, and Stuart Cowan, W2LX. Cubical Quad Antennas, 3rd Ed. Lakewood, NJ: Radio Amateur Callbook, 1993

    +
    • +
  • +

    Bob Haviland, W4MB. The Quad Antenna. Hicksville, NY: CQ Communications, 1993

    +
    • +
  • +

    John Koszeghy, K2OB. High Performance Cubical Quad Antennas, 2nd Ed.

    +
    • +
+
+ +
+

Updated 4-2-99, 8-5-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad1.html b/content/quad/quad1.html new file mode 100644 index 0000000..18ffcd8 --- /dev/null +++ b/content/quad/quad1.html @@ -0,0 +1,206 @@ + + + + + + Quad Models Part 1 Full-Size 2-Element Quads + + + +
+

Some Model Quads:
+ 1. Full-Size 2-Element Quads

+

L. B. Cebik, W4RNL

+
+
+ +
+

Models of full size 2-element quad beams are not difficult to make or to optimize for some desired set of maximum performance figures at a design frequency. Almost all 2-element quads use the driver-reflector configuration to maximize the operating bandwidth (relative to driver- director parasitic beams). Since the quad offers a bit of extra gain and a very good front-to-back ratio relative to a 2-element driver-reflector Yagi with the same element spacing, operating bandwidth is the next parameter on the normal list of specifications, and the driver-reflector type of parasitic quad beam offers this feature as well.

+

There are three dimensions to any quad:

+
+ +
+

As Fig. 1 demonstrates, the first dimension is the wire length or loop size of each element. We can specify this in terms of the length of a side, since most quads employ a square configuration for ease of mechanical construction. Hence, the circumference of the loop is simply 4 times the length of a side. As noted in the introduction, the length of half the side can be important in setting up coordinates for a model.

+

As our first exercise below will demonstrate, element spacing will be extremely important to 2-element quad design models. The closer the spacing, the smaller the requisite loops sizes and the lower the source impedance. Since the 2-element quad has a relatively high (compared to 50 Ohms) source impedance, some designers favor close spacing in the attempt to bring the source impedance into a close match with coax. Whether this is wise we shall see.

+

The third dimension of a quad is the wire size or diameter. For a given loop resonant frequency, the fatter the wire, the larger the required loop circumference. This factor is directly opposed to what we encounter with linear elements. It applies not only to completely closed geometries, like the quad loop, but to many other nearly closed geometries, where normally linear free element ends are brought into close proximity to other normally free element ends.

+

Unless otherwise specified, all of the quad models we shall examine will use #14 AWG copper wire. Also, except as noted, the models will be designed for a center frequency of 28.5 MHz. The design center frequency can mean many things, since it does not itself say what parameter or parameters are maximized at this frequency. In general, for 2-element design work, setting the resonant frequency of the driver and the approximate maximum front-to-back ratio for the design frequency is a satisfactory starting point. In any 2-element driver-reflector parasitic array, the gain will describe a descending curve from well below the design center to well above it. Peak gain occurs at a point of virtually useless front-to-back ratio and is attempted only for special purposes. Front-to- back ratio for any design tends to show a peak that is a useful reference mark. Adjustments may be required if the slope of performance away from the peak is not symmetrical.

+

Likewise, it is usually safe to begin with the assumption that the VSWR curve relative to the resonant impedance of the antenna will be roughly symmetrical. Hence, setting the resonant point of the antenna under design to the same frequency as the peak in front-to-back performance is a safe start unless previous analyses indicate otherwise. Adjustments in the driver frequency can usually be made later to compensate for any lack of symmetry in the VSWR curve without unduly upsetting the overall antenna performance. (This is not always true of 2-element Yagis, but is generally true of 2-element quads.)

+

Remember that the basic quad beam is essentially a 4-element array, although we commonly call it a 2-element beam. Each loop is 1 wl long, consisting of two dipoles joined at their ends and spaced relative to their high current regions about 1/4 wl apart. since the spacing is not optimal for achieving maximum gain from two dipoles, we tend to consider the loop a single element with abut 1.9 dB (maximum) gain over the dipole.

+

Remember also that peak performance figures can be misleading. Very often, the only extended frequency information given about an antenna design is the 2:1 VSWR curve. However, every major performance parameter deserves attention.

+
+ +
+

The azimuth patterns in Fig. 2 show significant elements of the performance potential of a monoband quad for 10 meters across the first MHz of the band. If we looked only at the pattern for 28.5 MHz, the design center frequency for this model, we might misunderstand the actual performance. The near-maximum front-to-back pattern might not make clear how that parameter varies across the band. For this model, the low-end front-to- back figure barely exceed 10 dB. Above 28.25 MHz, the front-to-rear performance is at least 15 dB below the maximum forward gain. Only in the vicinity of mid-band is the front-to-rear performance everywhere at least 18 dB below maximum forward gain.

+

The collection patterns also reveals that there is a significant variation in the forward gain across the band--something over 1 dB between 28 and 29 MHz, with the lowest gain at the highest frequency. The decrease in gain with an increase in frequency is a characteristic typical of parasitic 2- element driver-reflector designs, whether Yagi or quad. Parasitic designs having a director typical show an increase in gain as the frequency increases.

+

Quad Performance as a Function of Element Spacing

Let's examine the modeled performance potential of a series of 10-meter 2- element quads that differ chiefly in the spacing between the elements. Each quad was set for near resonance (+/- about 2 Ohms reactance) at 28.5 MHz. In addition, the maximum front-to-back ratio was positioned as near a practicable to this same frequency. Using these two criteria as design specifications, the maximum forward gain of the array was allowed to set itself. In fact, in nearly all cases, the maximum forward gain achievable from the quad falls outside the lower end of the band, that is, below 28 MHz. +

As the spacing increases, placing resonance and the maximum front-to-back ratio at mid-band requires larger loops as the element spacing is increased. The following table shows the essential dimensions for #14 AWG bare copper wire models in this series.

+ 
Spacing   Spacing   L Driver  C Driver  L Reflector    C Reflector
+ WL        feet      feet      feet      feet           feet
+0.125      4.31      8.66     34.64      9.16          36.64
+0.145      5.02      8.70     34.80      9.19          36.77
+0.160      5.50      8.72     34.88      9.23          36.92
+0.174      6.00      8.77     35.06      9.25          37.00
+0.200      6.90      8.82     35.28      9.30          37.20
+

We can get the best idea of performance potential trends by looking at a series of graphs across the first MHz of 10 meters.

+
+ +
+

In Fig. 3, we get a good view of the gain curves associated with each of the spacings used. clearly, the widest spacing yields the lowest gain across the band (although gain is not the only consideration in selecting a design). The gain increases as spacing narrows through to the 5' (0.145 wl) spacing. However, as the spacing narrows to 1/8 wl (4.31'), the overall gain curve shows a slight decrease--beginning on a par with the 0.145 wl curve, but decreasing more rapidly as the frequency increases.

+

Note that the average gain difference between the highest and lowest curves is about 0.4 dB. Operationally, this might be no great loss, but it might be considered to remain above the threshold of significance. In contrast, the differential between any two adjacent curves in the overall plot is truly insignificant. Despite the lack of operational significance, the collection of curves does show the trends in gain--given the design criteria used in constructing the models.

+
+ +
+

In all cases, as shown in Fig. 4, the maximum 180-degree front-to-back value occurs between 28.5 and 28.6 MHz. Interestingly, both the closest element spacing (0.125 wl) and the widest spacing (0.2 wl) show the lowest peak value. In a curve of this sort, where the checked frequencies are 0.1 MHz apart, it is not possible to say with assurance whether there is no sharp peak or whether it is too sharp to appear.

+

Nonetheless, it is not the peak, but the overall performance curve that is most important. All of the antennas show a maximum front-to-back ratio well above 20 dB, but equally, all dip well below the 20 dB mark at the band edges. The widest spacings show the best low end performance, while there is no significant difference in performance at the upper band edge.

+

In general, the quad tends to show a 20 dB 180-degree front-to-back ratio for 500 kHz or less. From the pattern tendencies shown in Fig. 2, the overall front-to-rear performance will be a bit less. Hence, unless one intends to operate over only a very small portion of the band relative to its full span, the deep null that one can obtain at some specific frequency turns out not to accurately indicate the antenna's actual performance potential.

+
+ +
+

Fig. 5 reveals that the closer the element spacing, the steeper the VSWR curve--and vice versa. Also revealed is the fact that, at any spacing in the range of the models, the curve is much steeper below the resonant frequency than above it.

+

What the curves do not reveal is the actual antenna impedance at or near resonance. The following table provides modeled performance figures at 28.5 MHz for the five models as a reference against which to read the graphs.

+ 
Spacing        Free Space     Front-to-Back       Feedpoint Impedance
+ wl/feet       Gain dBi       Ratio dB            R +/- jX Ohms
+0.125/4.31      7.16           23.6                102 - j 1
+0.145/5.02      7.18           28.0                118 - j 0
+0.160/5.50      7.07           40.1                135 - j 2
+0.174/6.00      7.02           30.4                146 _ j 2
+0.200/6.90      6.81           23.8                166 - j 2
+

The three widest spacings show SWR values under 2:1 across the first MHz of 10 meters, relative to their resonant impedances. However, over any of the spacings surveyed in these models, the quad shows a very slow rise in SWR above the resonant frequency. We can use this fact to slightly redesign any of the models for a more even SWR performance. We simply reduce the frequency of resonance by enlarging the driven element.

+ 
Spacing   Spacing   L Driver  C Driver  L Reflector    C Reflector
+ WL        feet      feet      feet      feet           feet
+Original
+0.145      5.02      8.70     34.80      9.19          36.77
+Modified
+0.145      5.02      8.76     35.04      9.19          36.77
+

The change of about 1" per side is sufficient to lower the resonant frequency by about 0.15 MHz. No change is made to the reflector. Let's examine what happens to performance.

+
+ +
+

The change of gain, shown in Fig. 6, is wholly without significance.

+
+ +
+

Likewise, as Fig. 7 reveals, there is no change in the front-to-back ratio performance with the modification of the driven element.

+
+ +
+

Fig. 8 shows the new SWR curve relative to the old one. The SWR across the first MHz of 10 is now well below 2:1. Changing the resonant frequency to about 28.3 MHz has evened out the values to produce a curve more equal at the ends--without otherwise disturbing the antenna's potential performance.

+

The exercise shows more than our ability to adjust the SWR curve. It demonstrates the relative immunity of the reflector to moderate changes in the length of the driven element. Hence, the designer has some freedom to place the front-to-back curve and the SWR curve anywhere along the operating band that yields a set of desired operating characteristics.

+

The models used in this comparative study have used a variable number of segments, range from 7 per side to 21 per side. However, the common 2- element quad converges in NEC with only about 5 segments per side, so differences in gain, front-to-back ratio, and source impedance reports will be minimal.

+

The following EZNEC model description of the modified quad with 0.145 wl element spacing is typical of all of the models whose dimensions have been shown:

+ 
2 el quad 10m 5' sp #14                      Frequency = 28.35  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -4.380,  0.000, -4.380  W2E1   4.380,  0.000, -4.380    # 14   21
+2   W1E2   4.380,  0.000, -4.380  W3E1   4.380,  0.000,  4.380    # 14   21
+3   W2E2   4.380,  0.000,  4.380  W4E1  -4.380,  0.000,  4.380    # 14   21
+4   W3E2  -4.380,  0.000,  4.380  W1E1  -4.380,  0.000, -4.380    # 14   21
+5   W8E2  -4.596, -5.018, -4.596  W6E1   4.596, -5.018, -4.596    # 14   21
+6   W5E2   4.596, -5.018, -4.596  W7E1   4.596, -5.018,  4.596    # 14   21
+7   W6E2   4.596, -5.018,  4.596  W8E1  -4.596, -5.018,  4.596    # 14   21
+8   W7E2  -4.596, -5.018,  4.596  W5E1  -4.596, -5.018, -4.596    # 14   21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+

In programs having provision for symbolic coordinate entry, three variables would suffice for a full free space description of the model: a value for the driver corners, a value for the reflector corners, and a value for the element spacing. An example, using the AO format is shown below. The axes used for the elements are Y and Z, with the driver coordinate designated "de" and the reflector coordinate "ref." The relative positions of the driver and reflector along the X axis are shown as "dep" and "rep." Otherwise, the model is identical to the EZNEC description shown above.

+ 
2-Element Quad
+Free Space Symmetric
+28.3 MHz
+8 copper wires, feet
+ref = 4.596
+de = 4.38
+rp = -5.018
+dep = 0
+1     dep -de -de  dep de -de  #14
+1     dep -de -de  dep -de de  #14
+1     dep -de de   dep de de   #14
+1     dep de de    dep de -de  #14
+1     rp -ref -ref rp ref -ref #14
+1     rp -ref -ref rp -ref ref #14
+1     rp -ref ref  rp ref ref  #14
+1     rp ref ref   rp ref -ref #14
+1 Source
+Wire 1, center
+

A more general format is the .NEC ASCII file used by NEC-Win. The same antenna model (with elements in the X and Z axes) in this format appears in the NEC-Win file:

+ 
CM 2 el quad 5' sp #14 cu
+CE
+GW 1 21 -4.38 0 -4.38 4.38 0 -4.38 2.67060367454068E-03
+GW 2 21 4.38 0 -4.38 4.38 0 4.38 2.67060367454068E-03
+GW 3 21 4.38 0 4.38 -4.38 0 4.38 2.67060367454068E-03
+GW 4 21 -4.38 0 4.38 -4.38 0 -4.38 2.67060367454068E-03
+GW 5 21 -4.596 -5.018 -4.596 4.596 -5.018 -4.596 2.67060367454068E-03
+GW 6 21 4.596 -5.018 -4.596 4.596 -5.018 4.596 2.67060367454068E-03
+GW 7 21 4.596 -5.018 4.596 -4.596 -5.018 4.596 2.67060367454068E-03
+GW 8 21 -4.596 -5.018 4.596 -4.596 -5.018 -4.596 2.67060367454068E-03
+GS 0 0 .3048
+GE 0
+EX 0 1 11 0 1 0
+LD 5 1 1 21 5.8001E7
+LD 5 2 1 21 5.8001E7
+LD 5 3 1 21 5.8001E7
+LD 5 4 1 21 5.8001E7
+LD 5 5 1 21 5.8001E7
+LD 5 6 1 21 5.8001E7
+LD 5 7 1 21 5.8001E7
+LD 5 8 1 21 5.8001E7
+FR 0 11 0 0 28 .1
+RP 0 1 360 1000 90 0 1 1
+EN
+

The wire size (radius) and the material specification (copper) are shown in numerical terms in this file, in the GW and LD lines, respectively. The FR line specified a frequency sweep from 28 to 29 MHz in 0.1 MHz steps.

+

Both the AO and the .NEC file are usable. Simply download this file, extract the model file portion of the text, and save it as an ASCII file. Use the .ANT extension for the AO file and the .NEC extension for the NEC-Win file. These files may then be modified to create other quad configurations.

+

Any modeler should know not to expect precisely the same results from multiple programs. At the outset, input and output rounding conventions will alter numeric values very slightly. The selected values for material resistivity may vary slightly from one program to the next. NEC-2 occurs in 16- and 32-bit versions, with very slightly different outputs. The sum of these variations can yield slight numeric differences while using ostensibly the same core.

+

MININEC differs from NEC in placing pulses at segment junctions. This procedure requires a degree of length tapering in the approach to an angular junction to prevent corner clipping. Depending on the degree of length tapering, MININEC may show a lesser or greater departure from NEC values in the direction of showing result apt to a slightly shorter or higher frequency antenna.

+

To illustrate the difference, the following table lists results from NEC-Win (NEC-2), EZNEC (NEC-2), and AO (MININEC) for a single model-- the 5' spaced antenna modified for resonance near 28.3 MHz. The values for free space forward gain, 180-degree front-to-back ratio, and source impedance are shown for 28, 28.5, and 29 MHz in an X/Y/Z format (except for source impedance).

+ 
Parameter      NEC-Win             EZNEC               AO
+Gain in dBi    7.71/7.18/6.58      7.70/7.18/6.57      7.73/7.29/6.68
+F-B in dB      10.3/28.4/16.3      10.2/28.2/16.4       8.9/23.2/18.0
+Impedance
+  28.0          69.4 - j 35.4       69.2 - j 42.5       62.5 - j 45.1
+  28.5         120.6 + j 19.6      120.2 + j 12.4      111.0 + j 14.0
+  29.0         162.0 + j 45.5      161.5 + j 38.2      154.0 + j 43.0
+

Operationally--which here would include constructing a 2-element quad of the given design--the differences in these programs are insignificant. The two NEC-2 programs are very close, but not exact. Compared to both NEC-2 result sets, the MININEC output is a bit generous with gain and stingy with front-to-back ratio, with a systematically lower source impedance. However, the variables of construction will in virtually all cases exceed any differences among the numbers in the reports.

+

If we hold the wire size constant (#14 AWG copper), then the quad does not directly scale to other frequencies without some adjustment of side lengths for both the driver and the reflector. The following table provides model dimensions for 10 meters through 20 meters for similar performance. The discover the amount of adjustment, you may take the ratio of the new frequency to 28.5 MHz and determine the scaled length of the sides to compare with the dimensions used in the actual model. All models use an element spacing of 0.125 wl.

+ 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Segment
+ MHz       feet      feet      feet      feet      feet      per side
+28.5       4.31      8.66     34.64      9.16     36.64        7
+24.94      4.93      9.91     39.62     10.47     41.86        9
+21.22      5.79     11.64     46.56     12.26     49.04       11
+18.12      6.79     13.62     54.48     14.35     57.40       13
+14.17      8.68     17.42     69.68     18.30     73.20       15
+

The selection of segmentation for each model was determined by my eventual goal of combining them into a single 5-band quad model--a topic which we shall address in a future episode. By taking 1/2 the length of a side, one can get the requisite value of the coordinates for the drivers and the reflectors. The remainder of the model construction is routine.

+

The modeled performance of the resultant monoband quads is tabulated below:

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+28.5            7.16           23.6                102 - j 1
+24.95           7.11           23.9                105 + j 1
+21.22           7.18           23.2                 99 + j 2
+18.12           7.14           23.7                101 - j 1
+14.17           7.15           23.2                 99 + j 0
+

Despite having the narrowest operating bandwidth of the range of element spacings we have surveyed, all of these 1/8 wl spaced models are amenable to the use of a simple 1/4 wl section of 75-Ohm coax as a matching section for a 50-Ohm main transmission line. However, if the characteristics of one of the wider-spaced 10-meter models is desired, proportional enlargement of the spacing and the side lengths will put one very close to the desired model.

+

This collection of models should put one well on to the road of quad modeling throughout the upper HF region. However, it does not exhaust the modeling possibilities for simple, full-size 2-element monoband quads. Next time, let's look at a few variations and some questions of comparison.

+
+ +
+

Updated 2-17-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
Go to Variations and Comparisons +

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad2.html b/content/quad/quad2.html new file mode 100644 index 0000000..8810449 --- /dev/null +++ b/content/quad/quad2.html @@ -0,0 +1,279 @@ + + + + + + Quad Models Part 2 Variations and Comparisons + + + +
+

Some Model Quads:
+ 2. Variations and Comparisons

+

L. B. Cebik, W4RNL

+
+
+ +
+

Rarely is the modeling of a quad beam just an exercise. The modeling activity generally precedes some decision-making about building or purchasing an actual antenna. Hence, we cannot proceed without encountering various kinds of controversies.

+

In this episode, we shall consider two such unsettled matters.

+

Element Spacing and Flexibility

One of them lies wholly within the realm of quads and concerns the best element spacing for quads. Both MININEC and NEC consistently show more closely spaced 2-element quads to exhibit higher gain than more widely spaced models. The contrasting spacings are those close to 0.125 wl on one side and those closer to 0.2 wl on the other. Some have claimed that closely spaced quads do not perform in reality as models predict and that widely spaced quads are superior in gain. +

Unfortunately, this claim is not universally supported. Some builders of closely-spaced quads claim that they obtain the performance predicted by calculations, models, and other quad users. Hence, we have an open question as to the disparity of experiences.

+

One important advantage of more widely spaced quads can be demonstrated by examining the azimuth patterns across a ham band, in this case, the first MHz of 10 meters.

+
+ +
+

In Fig. A, we have patterns every 250 kHz across the lower end of 10 meters for the most widely-spaced quad in our collection, the one with 0.2 wl element spacing. This azimuth pattern exercise can be compared with Fig. 2 in the preceding episode. The rear quadrants of the patterns in Fig. A show far less variation than those of the more closely spaced (0.145 wl) version in Fig. 2. The lesser variation is indicative of the fact that minor variations of structure--whether loop length or spacing--create smaller performance changes when the elements are more widely spaced.

+

Another way to approach the same point is to examine the source impedance of various quad designs across the operating pass band. The following table lists source impedances for three models: the most closely spaced version (0.125 wl), a middling version (0.16 wl) and a widely paced version (0.2 wl). Only three checkpoints are given: 28.0, 28.5, and 29.0 MHz.

+ 
                         Source Impedance:  R +/- j X Ohms
+Frequency              0.125 wl            0.16 wl             0.2 wl
+28.0                 52.6 - j 64.9       86.0 - j 47.3      127.4 - j 29.7
+28.5                101.7 - j  0.9      134.7 - j  2.1      165.7 + j  3.3
+29.0                147.4 + j 30.4      167.5 + j 20.3      184.2 + j 17.5
+     Delta R             94.9 Ohms           81.5 Ohms           56.8 Ohms
+     Delta X             95.3 Ohms           67.6 Ohms           47.2 Ohms
+

Compared to the values for the narrowest spacing, the resistance range for the widest spacing is 40% smaller and the reactance range 50% smaller. Since none of the values obtained for the feedpoint impedance of the 2- element quad is a direct match for the usual 50-Ohm coax feedline, some sort of matching system will be required. Not only will the lesser resistance and reactance excursions make it easier to provide a band-edge- to-band-edge match within a 2:1 SWR range, but as well they will in most system improve efficiency (or, to say the same thing, reduce losses).

+

Replicating the performance of a model with an actual antenna requires more than just obtaining an SWR curve that is similar to that predicted by a model. The parameters of gain and front-to-back ratio must also be replicated by adjustment of the antenna dimensions. Normally, the front- to-back ratio is easier to determine than gain. A helper station or a signal source at least 10 wl distant from the antenna is usually sufficient to find the frequency at which signals from the antenna rear are minimum.

+

Adjustment of a full-size reflector requires alteration of the wire length of a loop that is often already soldered closed. However, two alternative schemes often permit reflector adjustment.

+
+ +
+

As shown in Fig. 9, we may use either inductive or capacitive loading on the reflector. In many past designs, inductive loading has been used because it permits the reflector to be the same size as the driven loop-- about 5% shorter than a full size reflector at the closest spacing. The inductive reactance required to electrically lengthen the reflector to full size can be provided by either an inductor or a length of shorted transmission line. If we choose to use capacitive loading, we must enlarge the reflector and electrically shorten it with capacitive reactance. Ordinarily, a variable capacitor is used to find the correct value and then is replaced by a fixed capacitor.

+

Apart from the matter of loop size, we can wonder if one loading system has an advantage over the other. Here modeling can suggest some answers. I created three alternative models to the 0.125 wl element spacing version of the full size quad. There are two inductively loaded quads with identical loops sizes, one using an inductor with a Q of 300 and the other using a shorted transmission line. Since the inductively loaded models shortened the reflector loop length by 5%, the loop for the capacitively loaded model increase the reflector loop length by a like amount. The table shows the dimensions of the 4 antennas, each of which uses a 4.31' (0.125 wl) spacing between elements.

+ 
Load      L Driver  C Driver  L Refl.   C Refl.   Refl. React.
+Type       feet      feet      feet      feet      Ohms
+None       8.66     34.64      9.16     36.64      ---
+Coil       8.66     34.64      8.66     34.64      140
+TL         8.66     34.64      8.66     34.64      140
+Capac.     8.66     34.64      9.68     38.72      150
+

A coil with a Q of 300 and a reactance of 140 Ohms will have at the design frequency of 28.5 MHz a series resistance of about 0.47 Ohms and an inductance of 0.78 microH. To achieve the same reactance with a 600-Ohm, velocity factor 1.0 transmission line requires a shorted section about 1.26' long. A capacitive reactance of 150 Ohms at 28.5 MHz requires about 37.3 pF.

+

All of these values can be modeled in NEC and all but the transmission line in MININEC using the facilities for mathematical loads. Since the loads are installed at the center point of the reflector lower element, the likelihood of error due to a differential between a mathematical load and a physically modeled load is minimized. Comparing the performance reports across the first MHz of 10 meters for all four models provides some interesting results.

+
+ +
+

Operationally, the gain of the 4 quad models is insignificantly different, as shown in Fig. 10. However, some emergent trends are apparent. Both forms of inductive loading narrow the pass band of the gain curve so that the gain peak is no longer lower in frequency than 28 MHz. There is a noticeably more rapid decrease in gain at the high end of the pass band as well. The gain curve for the capacitively loaded model is insufficiently different from that of the unloaded model to suggest that capacitive loading provides a shallower curve of gain decrease across the band. However, the hint of difference may lead some modelers to experiment with even larger reflectors and heavier capacitive-reactance loading.

+
+ +
+

In contrast to their gain curve, the inductively loaded models provide a higher peak front-to-back ratio than either the unloaded or the capacitively loaded model, as revealed in Fig. 11. The curve for the capacitively loaded model is distinctly shallower than even that of the unloaded model. All of the models show about the same front-to-back ratio at the upper end of the pass band, which makes evident the lower front-to- back ratio at the lower end of the band provided by the two inductively loaded models. As with gain, the inductively loaded models show a narrower pass band for a given performance level, while the larger, capacitively loaded reflector shows a wider pass band for a given level of performance.

+
+ +
+

The SWR (relative to the impedance at resonance) performance of the models appears in Fig. 12. note that the 600-Ohm shorted stub provides an SWR curve that is indistinguishable from that for a coil with a Q of 300. Both curves are significantly sharper than the curves for the unloaded model and the capacitively loaded model. Consistent with the results for gain and for the front-to-back ratio, the capacitively loaded model shows the broadest curve.

+

The SWR curves for all four models can be brought within a 2:1 SWR range by lowering the driver resonant frequency. However, the drivers for the inductively loaded models will have to be resonated at a noticeably lower frequency than those of the unloaded and capacitively loaded models in order to achieve a 2:1 SWR operating bandwidth.

+

For reference, here are the reported performance figures for the design center frequency (28.5 MHz) for the four models.

+ 
Load           Free Space     Front-to-Back       Feedpoint Impedance
+Type           Gain dBi       Ratio dB            R +/- jX Ohms
+None            7.16           23.6                102 - j 1
+Coil            7.13           23.1                 96 + j 0
+Trans. Line     7.15           22.9                 96 + j 1
+Capacitor       7.17           22.7                106 - j 4
+

Both the capacitively loaded and the transmission-line stub loaded models invoke no losses in the modeled load. Hence, their gains are about the same as the unloaded model. The reflector coil has a finite Q (300) and hence shows the effect of the loss. Inductive loading, with its smaller reflector loop size, also lowers the resonant impedance of the model. In contrast, capacitive loading and the larger reflector loop increase the resonant impedance of the array. The variance from the impedance of the unloaded full-size quad is not great, but it indicates another trend to be cataloged for possible later use.

+

Reflector loading provides a convenient method of optimizing the front-to- back performance of the quad beam. Of the two inductive methods, there is little to choose between using a coil and using a shorted transmission line stub. However, capacitive loading provides greater advantages than either form of adding inductive reactance, but at the cost of a physically larger reflector loop. Whether or not the larger loop is mechanically feasible, modeling cannot say.

+

External Comparisons

Besides providing data that is useful in deciding how one might design a 2- element quad beam, modeling can also make a contribution to the decision of whether to construct a quad or some competitive antenna type, such as a 2- element or 3-element Yagi. What modeling can contribute are projections of performance potential. +

However, modeling cannot provide a definitive answer to the typical quad vs. Yagi dispute. Whether there are factors beyond gain, front-to-back ratio, and SWR bandwidth that give one or the other antenna type the edge exceeds the ability of models to determine. Hence, we shall confine modeling analysis to what it can do.

+
+ +
+

Fig. 13 shows the outlines of a short-boom 3-element Yagi, a typical driver-reflector 2-element Yagi, and one of the 2-element quad models--the version using 5' spacing and a driver resonated at about 28.35 MHz to bring the SWR curve within 2:1 limits across the first MHz of 10 meters. The dimensions of the three antennas are as follows:

+ 
Quad
+Spacing   Spacing   L Driver  C Driver  L Reflector    C Reflector
+ WL        feet      feet      feet      feet           feet
+0.145      5.02      8.76     35.04      9.19          36.77
+
+2-Element Yagi
+Spacing   Spacing        L Driver       L Reflector
+ WL        feet           feet           feet
+0.125     4.33           16.06          17.33
+
+3-Element Yagi
+Ref-DE    DE-Dir    Total     L Reflector    L-Driver       L-Director
+Sp-feet   Sp-feet    feet      feet           feet           feet
+ 2.5       5.0       7.5       17.66         16.63          15.44
+

The footprints of these 3 antenna models are clear in Fig. 13. However, the "footprint" figure of speech also reminds us that while the Yagis are flat sandals, the quad is a boot with as much height as width.

+

For reference, here are EZNEC model descriptions of the two Yagis used for this set of comparisons. The models are so simple that translation into any other program format should be easy.

+ 
2-el Yagi 1/8 wl sp 10m                        Frequency = 28.4  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1         -8.667,  0.000,  0.000         8.667,  0.000,  0.000 5.00E-01  31
+2         -8.033,  4.333,  0.000         8.033,  4.333,  0.000 5.00E-01  31
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          16     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+
+3-el Yagi short-boom 10m                        Frequency = 28.5  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1         -8.828,  0.000,  0.000         8.828,  0.000,  0.000 5.00E-01  31
+2         -8.317,  3.000,  0.000         8.317,  3.000,  0.000 5.00E-01  31
+3         -7.721,  7.500,  0.000         7.721,  7.500,  0.000 5.00E-01  31
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          16     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+

Since the Yagis are for study purposes only, their elements are a uniform 0.5" diameter and are aluminum. Slightly different elements lengths would be required for actual Yagis using an element diameter tapering schedule. The quad remains #14 AWG copper wire. The 3-element Yagi is adapted from a K6STI design in the YO collection. I have intentionally used a short boom version that is competitive in gain with the 2-element quad. 3-element Yagis with booms in the vicinity of 11.5 to 12 feet would show about an additional 1 dB forward gain.

+

It is possible to make parallel frequency sweeps with the three designs and compare the performance potential of the three antennas.

+
+ +
+

The free-space forward gain of all three antennas appears in Fig. 14. At the design center frequency (28.5 MHz), the 3-element Yagi and the 2- element quad have almost identical gain figures. However, the gain vs. frequency characteristics of the quad and the larger Yagi are opposing, so that as the gain of one increases, the gain of the other decreases. The 3- element Yagi shows a rather small gain change across the pass band, while the change for the quad is about 0.8 dB.

+

The gain of the 2-element Yagi is significantly lower than that of the 2- element quad--almost a full dB across the band. Because the quad and the 2-element Yagi are both driver-reflector designs, their gain curves parallel. A driver-director 2-element Yagi gain curve would parallel that of the 3-element Yagi, but the operating bandwidth would be much narrower.

+

It may be useful to notice one more property displayed by the gain curves. By judicious selection of data points, one can develop some misleading claims about antennas. for example, if we focus only on the gain at 28 MHz, then the gain differential between the 2-element and 3-element Yagis is only about a third of a dB--hardly a sufficient reason to add the third element. At 29 MHz, the differential is about 1.6 dB, making the 2-element Yagi seem hardly worthwhile in the comparison. As always, the message is the same: do not be satisfied with data points. Instead, demand the curves.

+
+ +
+

If there is one place where the 2-element driver-reflector Yagi suffers, it is in the category of the front-to-back ratio, as Fig. 15 reveals. The flat curve between 10 and 11 dB would be reflected in any defined front-to-rear performance evaluation. This curve does not mean that the 2-element Yagi is not useful. In fact, it can be an advantage to some types of net and contest operations where total rejection of signals from the rear quadrants is not a useful property. Again, a 2-element driver-director design would show a higher front-to-back ratio, but would be usable only over a much narrower bandwidth.

+

However, both the quad and the 3-element Yagi show superior overall performance. The curves are remarkably parallel to each other. At the lower end of the band, the Yagi shows almost 10 dB greater rear rejection, with a lesser advantage in the upper part of the pass band. All-in-all, the quad is clearly intermediate to the Yagis in front-to-back performance.

+
+ +
+

Fig. 16 shows that all three antennas, relative to their resonant impedances, are capable of a 2:1 SWR across the pass band of concern here. Of more interest are contrasting patterns of the SWR curves. The steep quad curve below resonance (28.35 MHz in the example) becomes a very shallow curve above resonance. The 2-element Yagi--resonated at 28.4 MHz to achieve the 2:1 SWR fit--reflects the low-end steep curve of the quad, but is no where near as shallow above resonance. In sharpest contrast stands the 3-element Yagi curve: shallower below resonance and steeper above resonance. Built into these curves are some lessons about the effects of directors on Yagi design.

+

The true business at hand is placing the performance potential of the 2-element full-size quad beam among its normal design competitors. As expected, it comes out somewhere in the middle.

+

However, the competitors on this modeling comparison are full-size monoband Yagis. Monoband quads in amateur use are rarely the norm. Where they are used, the operator often wants minimal size and sometimes resorts to techniques of shrinking the full-size quad. Therefore we shall have to look at shrunken quads and their potential performance. Keeping the Yagi figures and the full-size quad figures in mind will be useful in evaluating the performance potential of scrunched and squashed quads.

+

The other major use of 2-element quads is in multi-band version covering 3 to 5 amateur bands. We shall also have to examine some models of these types of antennas.

+

But first, a small digression.

+

Diamonds, Squares, and Rectangles

Some quad makers prefer the square shape. It occupies the smallest vertical and horizontal dimensions. Other quad builders prefer the diamond shape. They find it more resistant to the rigors of ice and snow than the square shape. Both of these preferences involve factors to which modeling cannot speak. +

With respect to performance, neither shape has an edge. In my collection of quad models, I have found no difference in the performance figures for either shape. To illustrate, let us look at the model description for the diamond equivalent of the 0.125 wl spaced 2-element quad. The model is simple enough not to require replication in other formats.

+ 
2el quad dia. 6.12/6.48/4.31sp               Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2   6.123,  0.000,  0.000  W2E1   0.000,  0.000,  6.123    # 14    7
+2   W1E2   0.000,  0.000,  6.123  W3E1  -6.123,  0.000,  0.000    # 14    7
+3   W2E2  -6.123,  0.000,  0.000  W4E1   0.000,  0.000, -6.123    # 14    7
+4   W3E2   0.000,  0.000, -6.123  W1E1   6.123,  0.000,  0.000    # 14    7
+5   W8E2   6.476, -4.310,  0.000  W6E1   0.000, -4.310,  6.476    # 14    7
+6   W5E2   0.000, -4.310,  6.476  W7E1  -6.476, -4.310,  0.000    # 14    7
+7   W6E2  -6.476, -4.310,  0.000  W8E1   0.000, -4.310, -6.476    # 14    7
+8   W7E2   0.000, -4.310, -6.476  W5E1   6.476, -4.310,  0.000    # 14    7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           7     3 /100.00   (  3 /100.00)      1.000       0.000      SV
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+

The model is fed in one of the two most commonly used ways--with a split feed, one source being placed on each of the segments adjacent to the lowest corner.

+
+ +
+

As shown in Fig. 17, one can also create a special wire of at least 3 segments having equal length with the single source on the center segment. This method tends to shorten the overall loop size by a tiny amount--enough to show up in the performance report decimal columns, but not enough to affect building plans or performance curves.

+
+ +
+

Fig. 18 shows that the gain is systematically within 0.09 dB between the two shapes for the entire first MHz of 10 meters.

+
+ +
+

The front-to-back ratio for the two models is even closer, as most of the reference markers obscure each other in Fig. 19.

+
+ +
+

Although the diamond shaped quad shows a resonant impedance abut 4 Ohms high then the square version, Fig. 20 shows that the two SWR curves overlap each other almost perfectly.

+

One might view the graphing of these overlapping curves as excessive. However, given the degree to which I have argued for showing curves to verify modeling claims about performance, they are simply a matter of practicing what I preach.

+

With the square-diamond comparison complete, we may now turn to another variation: the rectangle. However arranged, the square is not the quad form capable of the highest gain. A vertical rectangle can increase gain significantly.

+

Consider 2-element monoband quads with the following dimensions, where an entry of the order 6.9/11 means 6.9' horizontally and 11' vertically. These models happen to use #12 copper wire, since they occurred as part of a separate modeling experiment.

+ 
Spacing   Spacing   L Driver  C Driver  L Reflector    C Reflector
+ WL        feet      feet      feet      feet           feet
+Rectangular
+0.200      6.91     6.8/11.0  35.60     7.4/11.0       36.80
+0.160      5.50     6.9/11.0  35.80     7.3/11.0       36.60
+Square
+0.200      6.91      8.86     35.44      9.32          37.28
+

For reference, here is an EZNEC model description of the wide-spaced rectangular 2-element quad array.

+ 
2-el. rect. quad                               Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -3.400,  0.000, -5.500  W2E1   3.400,  0.000, -5.500    # 12   11
+2   W1E2   3.400,  0.000, -5.500  W3E1   3.400,  0.000,  5.500    # 12   15
+3   W2E2   3.400,  0.000,  5.500  W4E1  -3.400,  0.000,  5.500    # 12   11
+4   W3E2  -3.400,  0.000,  5.500  W1E1  -3.400,  0.000, -5.500    # 12   15
+5   W8E2  -3.700, -6.900, -5.500  W6E1   3.700, -6.900, -5.500    # 12   11
+6   W5E2   3.700, -6.900, -5.500  W7E1   3.700, -6.900,  5.500    # 12   15
+7   W6E2   3.700, -6.900,  5.500  W8E1  -3.700, -6.900,  5.500    # 12   11
+8   W7E2  -3.700, -6.900,  5.500  W5E1  -3.700, -6.900, -5.500    # 12   15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+
+ +
+

Fig. R1 provides a sketch of the rectangular quad outline. The rectangles in the models shown here have not been shape-optimized for maximum gain, so further improvements might well be made to the mid-band performance shown here for reference.

+ 
Antenna        Free Space     Front-to-Back       Feedpoint Impedance
+               Gain dBi       Ratio dB            R +/- jX Ohms
+Rect: wide sp   7.42           26.7                109 - j 3
+Rect: close sp  7.61           19.8                 94 + j39
+Square          6.85           24.0                167 + j 8
+

Both the close-spaced rectangle and the square were resonated lower in the band (28.3 to 28.35 MHz) to establish an SWR curve with close to equal values at the band edges. (Note: for comparison with the #12 square quad in the table above, the #14 copper version of the square quad, shown in the last episode, had a free space gain of 6.81 dBi, a front-to-back ratio of 23.8 dB, and a source impedance of 166 Ohms.)

+
+ +
+

The gain curves for the three models, shown if Fig. R2, demonstrate the higher gain possible with a 2-element parasitic rectangular beam. At midband, the wide-spaced rectangle shows a 0.5 dB advantage over the square model, and further improvement might be possible by optimizing the rectangle's shape for maximum gain. The ratio of horizontal to vertical dimension will vary with frequency, so optimization would be required for each band on which such a scheme might be used.

+
+ +
+

Although the rectangle provides higher gain, it yields lower front-to-back ratios on average than the square model, as revealed in Fig. R3. Despite the peak in the wide spaced rectangular model, the overall performance is less satisfactory than the square, with the lower end of the band suffering most. some improvement can likely be effected by sliding the front-to-back maximum lower in frequency.

+
+ +
+

Fig. R4 provides some SWR curves. The curve for the square is referenced to the resonant impedance of the antenna (about 152 Ohms) simply to show the flatness of the curve. Without provision for matching, the two rectangular quads both achieve usable 75-Ohm SWR curves, with the wide-spaced model slightly better. As one make a horizontally polarized loop more vertically rectangular, the source impedance decreases. The decrease also shows up in the source impedance for rectangular quad beams.

+
+ +
+

Comparative mid-band (28.5 MHz) free space azimuth patterns appear in Fig. R5. The increased gain and decreased front-to-back ratio are quite clear on the pattern overlays.

+

The point of this particular modeling exercise is to demonstrate that the square quad is simply not the ultimate in quad gain, no matter the spacing or loop size. The rectangular quad is capable of significantly higher gain. Of course, the square has some structural advantages which may override use of a higher-gain configuration. But, then, almost all antennas represent a compromise among all of the factors and specifications that go into their design and construction. The quad is no exception.

+
+ +
+

Updated 2-22-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
Go to Shrunken Quads +

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad3.html b/content/quad/quad3.html new file mode 100644 index 0000000..4add945 --- /dev/null +++ b/content/quad/quad3.html @@ -0,0 +1,385 @@ + + + + + + Quad Models Part 3 Shrunken 2-Element Quads + + + +
+

Some Model Quads:
+ 3. Shrunken 2-Element Quads

+

L. B. Cebik, W4RNL

+
+
+ +
+

The art of creating a miniature quad--that is, any quad significantly smaller than full size--has been around almost as long as the quad itself. There are many techniques for achieving a smaller size quad. Most fundamental--and perhaps the lossiest--is adding either center or corner inductors to each quad loop.

+

My own collection of models has focused on a technique that may owe to Paul Carr, N4PC, and which appears in Lew McCoy's book on antennas from CQ Communications. It consists of insetting the loop wires at the low current, high voltage points at the loop sides. Paul reasoned that this form of "linear loading" would have the least impact on gain and front-to-back ratio. I studied variations of the technique, including building some trial versions, for a piece in Communications Quarterly a few years back (link). The models discussed here will be a selection from the large number accumulated during that study. Like the full-size models we have already examined, all use #14 AWG copper wire. All models will be in free space for consistency with the previous models.

+

Because the techniques for shortening quad loops are many and varied, this collection of model will necessarily be incomplete. However, the progression of models may provide some background for evaluating other types of miniature quads that you decide to model.

+

The 78% Square

At about 78% full size, one reaches a limit for providing single insets on each side of a quad loop. The insets can be made wider or narrower, as well as longer or shorter, in order to fit building techniques. +
+ +
+

Fig. 21 shows the outlines of a single inset square quad beam. The models we shall look at have 6.96' sides on the driven element. Two versions will be compared, one with 4.31' spacing (0.125 wl), the other with 5' spacing (0.145 wl). The reflector sides are 7.24' and 7.40', respectively.

+

For those who wish to replicate the models, the following extracts from EZNEC model description files provide the coordinates.

+ 
2L 3.46/3.62/4.31 lnld                       Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W12E2  -3.460,  0.000, -3.460  W2E1   3.460,  0.000, -3.460    # 14   21
+2   W1E2   3.460,  0.000, -3.460  W3E1   3.460,  0.000, -0.125    # 14   10
+3   W2E2   3.460,  0.000, -0.125  W4E1   0.825,  0.000, -0.125    # 14   21
+4   W3E2   0.825,  0.000, -0.125  W5E1   0.825,  0.000,  0.125    # 14    1
+5   W4E2   0.825,  0.000,  0.125  W6E1   3.460,  0.000,  0.125    # 14   21
+6   W5E2   3.460,  0.000,  0.125  W7E1   3.460,  0.000,  3.460    # 14   10
+7   W6E2   3.460,  0.000,  3.460  W8E1  -3.460,  0.000,  3.460    # 14   21
+8   W7E2  -3.460,  0.000,  3.460  W9E1  -3.460,  0.000,  0.125    # 14   10
+9   W8E2  -3.460,  0.000,  0.125 W10E1  -0.825,  0.000,  0.125    # 14   21
+10  W9E2  -0.825,  0.000,  0.125 W11E1  -0.825,  0.000, -0.125    # 14    1
+11 W10E2  -0.825,  0.000, -0.125 W12E1  -3.460,  0.000, -0.125    # 14   21
+12 W11E2  -3.460,  0.000, -0.125  W1E1  -3.460,  0.000, -3.460    # 14   10
+13 W24E2  -3.620, -4.310, -3.620 W14E1   3.620, -4.310, -3.620    # 14   21
+14 W13E2   3.620, -4.310, -3.620 W15E1   3.620, -4.310, -0.125    # 14   10
+15 W14E2   3.620, -4.310, -0.125 W16E1   0.930, -4.310, -0.125    # 14   21
+16 W15E2   0.930, -4.310, -0.125 W17E1   0.930, -4.310,  0.125    # 14    1
+17 W16E2   0.930, -4.310,  0.125 W18E1   3.620, -4.310,  0.125    # 14   21
+18 W17E2   3.620, -4.310,  0.125 W19E1   3.620, -4.310,  3.620    # 14   10
+19 W18E2   3.620, -4.310,  3.620 W20E1  -3.620, -4.310,  3.620    # 14   21
+20 W19E2  -3.620, -4.310,  3.620 W21E1  -3.620, -4.310,  0.125    # 14   10
+21 W20E2  -3.620, -4.310,  0.125 W22E1  -0.930, -4.310,  0.125    # 14   21
+22 W21E2  -0.930, -4.310,  0.125 W23E1  -0.930, -4.310, -0.125    # 14    1
+23 W22E2  -0.930, -4.310, -0.125 W24E1  -3.620, -4.310, -0.125    # 14   21
+24 W23E2  -3.620, -4.310, -0.125 W13E1  -3.620, -4.310, -3.620    # 14   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+
+2L 3.46/3.7/5 lnld                           Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W12E2  -3.460,  0.000, -3.460  W2E1   3.460,  0.000, -3.460    # 14   21
+2   W1E2   3.460,  0.000, -3.460  W3E1   3.460,  0.000, -0.125    # 14   10
+3   W2E2   3.460,  0.000, -0.125  W4E1   0.740,  0.000, -0.125    # 14   21
+4   W3E2   0.740,  0.000, -0.125  W5E1   0.740,  0.000,  0.125    # 14    1
+5   W4E2   0.740,  0.000,  0.125  W6E1   3.460,  0.000,  0.125    # 14   21
+6   W5E2   3.460,  0.000,  0.125  W7E1   3.460,  0.000,  3.460    # 14   10
+7   W6E2   3.460,  0.000,  3.460  W8E1  -3.460,  0.000,  3.460    # 14   21
+8   W7E2  -3.460,  0.000,  3.460  W9E1  -3.460,  0.000,  0.125    # 14   10
+9   W8E2  -3.460,  0.000,  0.125 W10E1  -0.740,  0.000,  0.125    # 14   21
+10  W9E2  -0.740,  0.000,  0.125 W11E1  -0.740,  0.000, -0.125    # 14    1
+11 W10E2  -0.740,  0.000, -0.125 W12E1  -3.460,  0.000, -0.125    # 14   21
+12 W11E2  -3.460,  0.000, -0.125  W1E1  -3.460,  0.000, -3.460    # 14   10
+13 W24E2  -3.700, -5.000, -3.700 W14E1   3.700, -5.000, -3.700    # 14   21
+14 W13E2   3.700, -5.000, -3.700 W15E1   3.700, -5.000, -0.125    # 14   10
+15 W14E2   3.700, -5.000, -0.125 W16E1   1.140, -5.000, -0.125    # 14   21
+16 W15E2   1.140, -5.000, -0.125 W17E1   1.140, -5.000,  0.125    # 14    1
+17 W16E2   1.140, -5.000,  0.125 W18E1   3.700, -5.000,  0.125    # 14   21
+18 W17E2   3.700, -5.000,  0.125 W19E1   3.700, -5.000,  3.700    # 14   10
+19 W18E2   3.700, -5.000,  3.700 W20E1  -3.700, -5.000,  3.700    # 14   21
+20 W19E2  -3.700, -5.000,  3.700 W21E1  -3.700, -5.000,  0.125    # 14   10
+21 W20E2  -3.700, -5.000,  0.125 W22E1  -1.140, -5.000,  0.125    # 14   21
+22 W21E2  -1.140, -5.000,  0.125 W23E1  -1.140, -5.000, -0.125    # 14    1
+23 W22E2  -1.140, -5.000, -0.125 W24E1  -3.700, -5.000, -0.125    # 14   21
+24 W23E2  -3.700, -5.000, -0.125 W13E1  -3.700, -5.000, -3.700    # 14   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+

The length and width of the inset wires can be derived from simple exercises in subtraction. In making the models, I juggled the inset size and reflector loop length for something approaching best performance, although further tweaking of any of the models is certainly possible.

+

There is a tendency in shrinking quads to shrink the spacing between elements. However, better performance can be obtained with somewhat wider spacing. In these models, 0.125 wl and 0.145 wl spacing are compared. As with past models, 28.5 MHz is the design center frequency for resonance and for maximum 180-degree front-to-back ratio. As we shall see, there are opportunities for sliding either or both of these characteristic to other points within the pass band.

+
+ +
+

Fig. 22 shows a clear gain advantage for the wider-spaced version of the single-inset square, although the actual amount may not be operationally significant. More notable than this gain differential is the fact that with the shrinking of the quad size, the gain curve is steeper, and the gain peak now falls within the pass band (28 to 29 MHz) rather than below it. At the design center frequency, gain is about 0.5 dB below that of comparable full-size 2-element quad beams.

+
+ +
+

Where the added spacing between elements shows up most graphically is in the front-to-back ratio, as Fig. 23 demonstrates. The wider spaced version not only peaks at a higher value (by about 4 dB), but as well is better across the pass band.

+

For reference, here are the modeled performance figures for the two antennas at the design frequency.

+ 
Antenna        Free Space     Front-to-Back       Feedpoint Impedance
+Version        Gain dBi       Ratio dB            R +/- jX Ohms
+0.125 wl        6.42           13.4                 76 - j 1
+0.145 wl        6.56           17.3                 78 - j 0
+
+ +
+

As shown in Fig. 24, wider element spacing also makes the 75-Ohm VSWR curve shallower, especially at the lower end of the band. One aspect of shrinking quads is the fact that it is possible to obtain a low SWR not only at the upper limit of the pass band (29 MHz), but well beyond that point. However, some caution must be used, because the downward curves of both the gain and the front-to-back ratios quickly reduce the antenna performance to just above dipole level.

+

One can judiciously slide the resonant point of the antenna lower in the pass band by lengthening the driver loop or its insets. Equally judicious sliding of the front-to-back peak by similar adjustments to the reflector is also possible. The latter changes can equalize the front-to-back ratio at the pass band limits. Unlike a full size quad, where the adjustments are fairly (although not completely) independent, changes to one element of the shrunken quad tend to affect the properties normally associated with the other element. Hence, even when modeling, care should be used to make adjustments in small amounts.

+

The 72% Diamond

The single inset square is the largest of this collection of shrunken quad models. If we turn the square into a diamond, we obtain additional room for longer insets. This move permits a smaller loop size. +
+ +
+

Fig. 25 shows the general scheme of the diamond version of the shrunken quad. The sides are about 6.36' long. For this antenna, the loop dimensions for both the driver and the reflector were held equal, with all adjustments made to the insets. The following model description files provide the coordinates for both 0.125 wl and 0.145 wl versions of the antenna design.

+ 
2L dia 6.36/side 4.31 sp lnld                Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+             --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W11E2   0.300,  0.000, -4.500  W2E1   4.500,  0.000, -0.125    # 14   21
+2   W1E2   4.500,  0.000, -0.125  W3E1   0.860,  0.000, -0.125    # 14   21
+3   W2E2   0.860,  0.000, -0.125  W4E1   0.860,  0.000,  0.125    # 14    1
+4   W3E2   0.860,  0.000,  0.125  W5E1   4.500,  0.000,  0.125    # 14   21
+5   W4E2   4.500,  0.000,  0.125  W6E1   0.000,  0.000,  4.500    # 14   21
+6   W5E2   0.000,  0.000,  4.500  W7E1  -4.500,  0.000,  0.125    # 14   21
+7   W6E2  -4.500,  0.000,  0.125  W8E1  -0.860,  0.000,  0.125    # 14   21
+8   W7E2  -0.860,  0.000,  0.125  W9E1  -0.860,  0.000, -0.125    # 14    1
+9   W8E2  -0.860,  0.000, -0.125 W10E1  -4.500,  0.000, -0.125    # 14   21
+10  W9E2  -4.500,  0.000, -0.125 W11E1  -0.300,  0.000, -4.500    # 14   21
+11 W10E2  -0.300,  0.000, -4.500  W1E1   0.300,  0.000, -4.500    # 14    3
+12 W21E2   0.000, -4.310, -4.500 W13E1   4.500, -4.310, -0.125    # 14   21
+13 W12E2   4.500, -4.310, -0.125 W14E1   0.430, -4.310, -0.125    # 14   21
+14 W13E2   0.430, -4.310, -0.125 W15E1   0.430, -4.310,  0.125    # 14    1
+15 W14E2   0.430, -4.310,  0.125 W16E1   4.500, -4.310,  0.125    # 14   21
+16 W15E2   4.500, -4.310,  0.125 W17E1   0.000, -4.310,  4.500    # 14   21
+17 W16E2   0.000, -4.310,  4.500 W18E1  -4.500, -4.310,  0.125    # 14   21
+18 W17E2  -4.500, -4.310,  0.125 W19E1  -0.430, -4.310,  0.125    # 14   21
+19 W18E2  -0.430, -4.310,  0.125 W20E1  -0.430, -4.310, -0.125    # 14    1
+20 W19E2  -0.430, -4.310, -0.125 W21E1  -4.500, -4.310, -0.125    # 14   21
+21 W20E2  -4.500, -4.310, -0.125 W12E1   0.000, -4.310, -4.500    # 14   21
+
+             -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           2    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+
+2L dia 6.36/side 5.0 sp lnld                 Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W11E2   0.300,  0.000, -4.500  W2E1   4.500,  0.000, -0.125    # 14   21
+2   W1E2   4.500,  0.000, -0.125  W3E1   0.770,  0.000, -0.125    # 14   21
+3   W2E2   0.770,  0.000, -0.125  W4E1   0.770,  0.000,  0.125    # 14    1
+4   W3E2   0.770,  0.000,  0.125  W5E1   4.500,  0.000,  0.125    # 14   21
+5   W4E2   4.500,  0.000,  0.125  W6E1   0.000,  0.000,  4.500    # 14   21
+6   W5E2   0.000,  0.000,  4.500  W7E1  -4.500,  0.000,  0.125    # 14   21
+7   W6E2  -4.500,  0.000,  0.125  W8E1  -0.770,  0.000,  0.125    # 14   21
+8   W7E2  -0.770,  0.000,  0.125  W9E1  -0.770,  0.000, -0.125    # 14    1
+9   W8E2  -0.770,  0.000, -0.125 W10E1  -4.500,  0.000, -0.125    # 14   21
+10  W9E2  -4.500,  0.000, -0.125 W11E1  -0.300,  0.000, -4.500    # 14   21
+11 W10E2  -0.300,  0.000, -4.500  W1E1   0.300,  0.000, -4.500    # 14    3
+12 W21E2   0.000, -5.000, -4.500 W13E1   4.500, -5.000, -0.125    # 14   21
+13 W12E2   4.500, -5.000, -0.125 W14E1   0.400, -5.000, -0.125    # 14   21
+14 W13E2   0.400, -5.000, -0.125 W15E1   0.400, -5.000,  0.125    # 14    1
+15 W14E2   0.400, -5.000,  0.125 W16E1   4.500, -5.000,  0.125    # 14   21
+16 W15E2   4.500, -5.000,  0.125 W17E1   0.000, -5.000,  4.500    # 14   21
+17 W16E2   0.000, -5.000,  4.500 W18E1  -4.500, -5.000,  0.125    # 14   21
+18 W17E2  -4.500, -5.000,  0.125 W19E1  -0.400, -5.000,  0.125    # 14   21
+19 W18E2  -0.400, -5.000,  0.125 W20E1  -0.400, -5.000, -0.125    # 14    1
+20 W19E2  -0.400, -5.000, -0.125 W21E1  -4.500, -5.000, -0.125    # 14   21
+21 W20E2  -4.500, -5.000, -0.125 W12E1   0.000, -5.000, -4.500    # 14   21
+
+             -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           2    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+

For both models, the source is placed on a special wire on the center of its three segments. for reference, here are the design frequency performance figures for the two models:

+ 
Antenna        Free Space     Front-to-Back       Feedpoint Impedance
+Version        Gain dBi       Ratio dB            R +/- jX Ohms
+0.125 wl        6.14           12.6                 82 + j 0
+0.145 wl        6.24           16.6                 86 - j 3
+
+ +
+

As Fig. 26 shows, the wide spaced version shows a bit more gain than the narrower spaced version. More notable is the fact that the further shrinkage of the design has moved the gain peak farther into the pass band. The lower band edge gain is now significantly lower than the peak gain.

+
+ +
+

The front-to-back curves in Fig. 27 show about the same differential between versions as those for the 78% square. however, the rate of fall- off from the peak value is much faster. As the size of the quad continues to shrink, it become more important to move the peak front-to-back ratio down the band.

+
+ +
+

As one might expect, the SWR curves in Fig. 28 are much steeper below the resonant frequency than for the square. Once more, judicious movement of resonance lower in the band can provide a wider operating bandwidth using the usual 2:1 ratio as a guide. Indeed, by appropriate tweaking, one can so position the resonant point and the front-to-back peak to increase the peak value significantly. However, that move must be balanced against the front-to-back performance across the pass band. A sharper peak may not always result in higher values at the pass band edges.

+

The 68% Double-Inset Square

Paul Carr's original version of the "squad" (squashed quad) employed a double inset for maximum size reduction. A 10-meter double-inset square is shown in Fig. 29. +
+ +
+

The size of this quad is about 68% of full size, with two equal loops that are 6' on a side. Performance was tweaked by adjusting the length of the insets. The model description provides the coordinates for the two loops and their insets.

+ 
2 el square quad, 2 lin load                 Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W20E2  -3.000,  0.000, -3.000  W2E1   3.000,  0.000, -3.000    # 14   21
+2   W1E2   3.000,  0.000, -3.000  W3E1   3.000,  0.000, -0.375    # 14   10
+3   W2E2   3.000,  0.000, -0.375  W4E1   0.580,  0.000, -0.375    # 14   19
+4   W3E2   0.580,  0.000, -0.375  W5E1   0.580,  0.000, -0.125    # 14    1
+5   W4E2   0.580,  0.000, -0.125  W6E1   3.000,  0.000, -0.125    # 14   19
+6   W5E2   3.000,  0.000, -0.125  W7E1   3.000,  0.000,  0.125    # 14    1
+7   W6E2   3.000,  0.000,  0.125  W8E1   0.580,  0.000,  0.125    # 14   19
+8   W7E2   0.580,  0.000,  0.125  W9E1   0.580,  0.000,  0.375    # 14    1
+9   W8E2   0.580,  0.000,  0.375 W10E1   3.000,  0.000,  0.375    # 14   19
+10  W9E2   3.000,  0.000,  0.375 W11E1   3.000,  0.000,  3.000    # 14   10
+11 W10E2   3.000,  0.000,  3.000 W12E1  -3.000,  0.000,  3.000    # 14   21
+12 W11E2  -3.000,  0.000,  3.000 W13E1  -3.000,  0.000,  0.375    # 14   10
+13 W12E2  -3.000,  0.000,  0.375 W14E1  -0.580,  0.000,  0.375    # 14   19
+14 W13E2  -0.580,  0.000,  0.375 W15E1  -0.580,  0.000,  0.125    # 14    1
+15 W14E2  -0.580,  0.000,  0.125 W16E1  -3.000,  0.000,  0.125    # 14   19
+16 W15E2  -3.000,  0.000,  0.125 W17E1  -3.000,  0.000, -0.125    # 14    1
+17 W16E2  -3.000,  0.000, -0.125 W18E1  -0.580,  0.000, -0.125    # 14   19
+18 W17E2  -0.580,  0.000, -0.125 W19E1  -0.580,  0.000, -0.375    # 14    1
+19 W18E2  -0.580,  0.000, -0.375 W20E1  -3.000,  0.000, -0.375    # 14   19
+20 W19E2  -3.000,  0.000, -0.375  W1E1  -3.000,  0.000, -3.000    # 14   10
+21 W40E2  -3.000, -4.310, -3.000 W22E1   3.000, -4.310, -3.000    # 14   21
+22 W21E2   3.000, -4.310, -3.000 W23E1   3.000, -4.310, -0.375    # 14   10
+23 W22E2   3.000, -4.310, -0.375 W24E1   0.425, -4.310, -0.375    # 14   19
+24 W23E2   0.425, -4.310, -0.375 W25E1   0.425, -4.310, -0.125    # 14    1
+25 W24E2   0.425, -4.310, -0.125 W26E1   3.000, -4.310, -0.125    # 14   19
+26 W25E2   3.000, -4.310, -0.125 W27E1   3.000, -4.310,  0.125    # 14    1
+27 W26E2   3.000, -4.310,  0.125 W28E1   0.425, -4.310,  0.125    # 14   19
+28 W27E2   0.425, -4.310,  0.125 W29E1   0.425, -4.310,  0.375    # 14    1
+29 W28E2   0.425, -4.310,  0.375 W30E1   3.000, -4.310,  0.375    # 14   19
+30 W29E2   3.000, -4.310,  0.375 W31E1   3.000, -4.310,  3.000    # 14   10
+31 W30E2   3.000, -4.310,  3.000 W32E1  -3.000, -4.310,  3.000    # 14   21
+32 W31E2  -3.000, -4.310,  3.000 W33E1  -3.000, -4.310,  0.375    # 14   10
+33 W32E2  -3.000, -4.310,  0.375 W34E1  -0.425, -4.310,  0.375    # 14   19
+34 W33E2  -0.425, -4.310,  0.375 W35E1  -0.425, -4.310,  0.125    # 14    1
+35 W34E2  -0.425, -4.310,  0.125 W36E1  -3.000, -4.310,  0.125    # 14   19
+36 W35E2  -3.000, -4.310,  0.125 W37E1  -3.000, -4.310, -0.125    # 14    1
+37 W36E2  -3.000, -4.310, -0.125 W38E1  -0.425, -4.310, -0.125    # 14   19
+38 W37E2  -0.425, -4.310, -0.125 W39E1  -0.425, -4.310, -0.375    # 14    1
+39 W38E2  -0.425, -4.310, -0.375 W40E1  -3.000, -4.310, -0.375    # 14   19
+40 W39E2  -3.000, -4.310, -0.375 W21E1  -3.000, -4.310, -3.000    # 14   10
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+

The more numerous the insets, the higher the number of wires in a model. For those used to modeling antennas with simple geometries, the model size in terms of both wires and segments may seem high. The relatively thin wire (#14 AWG) allows the use of short segment lengths. For NEC models, the segment junctions should align as closely as possible wherever there are closely spaced wires. This is especially important in the insets.

+

The following table provides the performance figures at the design frequency for the 68% double-inset square for an element spacing of 0.125 wl. Also in the table are comparative figures for the single-inset diamond and square, using the same element spacing.

+ 
Antenna        Free Space     Front-to-Back       Feedpoint Impedance
+Version        Gain dBi       Ratio dB            R +/- jX Ohms
+68% square      5.87           10.4                 58 - j 0
+72% diamond     6.14           12.6                 82 + j 0
+78% square      6.42           13.4                 76 - j 1
+

The following graphs will provide similar comparisons across the pass band.

+
+ +
+

The gain curves in Fig. 30 show hoe the gain peak moves more radically toward the design frequency with each reduction in antenna size. Also worth noting is the steeper rate of gain fall-off in the smaller quads in this collection of models.

+
+ +
+

When antenna resonance and peak front-to-back ratio are designed for the same frequency, the curves for all three models are exceptionally congruent, as shown in Fig. 31. Note that the front-to-back ratio is almost non-existent at the lower end of the band for the smallest model.

+
+ +
+

Fig. 32 shows the 75-Ohm SWR curve for the three antennas across the entire first MHz of 10 meters. Besides showing how steep the low end curve is for the 68% square, the graphic actually obscures some interesting properties of the antenna. Therefore, let's eliminate the highest values of SWR.

+
+ +
+

In Fig. 32A, we obtain a clearer picture of the impedance behavior of the smallest quad, relative to its larger single-inset brethren. The lowest SWR occurs close to 28.6 MHz because the resonant impedance of the antenna is below 60 Ohms. However, note the shape of the curve as it moves toward the upper end of the band. The SWR actually decreases by the time we reach 29 MHz. It would be very easy during antenna adjustment to deceive oneself into thinking that all is well by obtaining a relatively flat SWR curve. However, this curve can obscure the fairly narrow pass band for usable gain and front-to-back ratio.

+

The 72% Hat-Loaded Diamond

I first ran into the hat loaded design in HF Antennas for All Locations by Les Moxon, G6XN. My interest was to compare the performance of a hat-loaded antenna to an inset-loaded version. +
+ +
+

Fig. 33 shows the general outline of a diamond version of the hat loaded quad beam. Square versions are also easily possible, although the diamond allows the hat wires to be somewhat longer.

+

A perfect hat would extend outside the loop at the side junction and have two wires exactly end-to-end for relatively perfect radiation cancellation. Placing them inside the loop makes construction easier, since they can be suspended from the normal loop wires. The exact lengths of the wires will vary with their spacing from the loop wires.

+

For the purposes of comparison, the hat model was made from the 72% diamond, using 5' element separation (0.145 wl). At the original insets, the loop was closed and the hat structure added. The following model description will provide guidance for the coordinates used.

+ 
2L dia 6.36/side 5.0 cap load                Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1  W11E2   0.300,  0.000, -4.500  W2E1   4.500,  0.000,  0.000    # 14   21
+2   W3E1   4.500,  0.000,  0.000  W6E1   0.000,  0.000,  4.500    # 14   21
+3   W1E2   4.500,  0.000,  0.000  W4E1   4.000,  0.000,  0.000    # 14    2
+4   W5E1   4.000,  0.000,  0.000         1.589,  0.000,  2.411    # 14   17
+5   W3E2   4.000,  0.000,  0.000         1.589,  0.000, -2.411    # 14   17
+6   W2E2   0.000,  0.000,  4.500  W7E1  -4.500,  0.000,  0.000    # 14   21
+7  W10E1  -4.500,  0.000,  0.000  W8E1  -4.000,  0.000,  0.000    # 14    2
+8   W9E1  -4.000,  0.000,  0.000        -1.589,  0.000,  2.411    # 14   17
+9   W7E2  -4.000,  0.000,  0.000        -1.589,  0.000, -2.411    # 14   17
+10  W6E2  -4.500,  0.000,  0.000 W11E1  -0.300,  0.000, -4.500    # 14   21
+11 W10E2  -0.300,  0.000, -4.500  W1E1   0.300,  0.000, -4.500    # 14    3
+12 W22E2   0.300, -5.000, -4.500 W13E1   4.500, -5.000,  0.000    # 14   21
+13 W14E1   4.500, -5.000,  0.000 W17E1   0.000, -5.000,  4.500    # 14   21
+14 W12E2   4.500, -5.000,  0.000 W15E1   4.000, -5.000,  0.000    # 14    2
+15 W16E1   4.000, -5.000,  0.000         1.324, -5.000,  2.676    # 14   17
+16 W14E2   4.000, -5.000,  0.000         1.324, -5.000, -2.676    # 14   17
+17 W13E2   0.000, -5.000,  4.500 W18E1  -4.500, -5.000,  0.000    # 14   21
+18 W21E1  -4.500, -5.000,  0.000 W19E1  -4.000, -5.000,  0.000    # 14    2
+19 W20E1  -4.000, -5.000,  0.000        -1.324, -5.000,  2.676    # 14   17
+20 W18E2  -4.000, -5.000,  0.000        -1.324, -5.000, -2.676    # 14   17
+21 W17E2  -4.500, -5.000,  0.000 W22E1  -0.300, -5.000, -4.500    # 14   21
+22 W21E2  -0.300, -5.000, -4.500 W12E1   0.300, -5.000, -4.500    # 14    3
+
+             -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           2    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+

The feedpoint is the same as for the single-inset diamond model. For reference, here are the design frequency performance numbers for the two 5'-spaced models.

+ 
Antenna        Free Space     Front-to-Back       Feedpoint Impedance
+Version        Gain dBi       Ratio dB            R +/- jX Ohms
+diamond inset   6.24           16.6                 86 - j 3
+diamond hat     6.23           18.4                 93 + j 0
+
+ +
+

The gain curves in Fig. 34 show a remarkable coincidence, given the physical differences in the load designs. There is nothing to choose in this department.

+
+ +
+

As shown in Fig. 35, the hat model shows about a full dB or slightly greater advantage in front-to-back performance. This amount of added front-to-back ratio would scarcely be noticeable. Moreover, it is not clear that the inset model might not be tweakable to obtain a similar set of values (or the hat model "de-tweaked" by intention or accident to obtain the inset curve).

+
+ +
+

The SWR curves in Fig. 36 show differences partly as a result of the higher resonant impedance of the hat model. (The resistive portion of the source impedance for all of the antennas we have examined drops to 30 Ohms or less at the lower band edge.) Judicious resonance movement would yield an operating bandwidth that covered most of the first MHz of 10 meters.

+

Lest we once more fall into the lethargy that equate performance with the SWR curve, let's close with a gallery of azimuth patterns across the pass band for the hatted model. It is an effective compromise between the large and the small square, as well as being virtually identical to the patterns of the 5' spaced inset diamond. Fig. 37 summarizes the performance characteristics of the category of shrunken quads in the versions we have examined here.

+
+ +
+

Trying to cover all of the varieties of schemes used to miniaturize quad beams would be prohibitive in terms of both time and space. You may add to your collection of shrunken quad models as such models come your way.

+

The models we have looked at have maintained reasonable efficiency and minimized losses in their means of shrinking the quad. The effects of both loop size and of element spacing have been sampled as a guide to further modeling (not to mention building). My own building of some of them suggests that they will perform to modeled specifications, which provides a useful antenna for limited space.

+

The one missing feature of these shrunken quads that is prized by many quad users is the ability to nest antennas of this design to produce a multi-band array. Indeed, the full size 2-element quad remains the chief vehicle for this type of service. For the next episode, I shall try to find some of the multi-band 2-element quads hiding in my files. They shall not be hard to find, I suspect. 5-band quad designs, even with only two elements, require large antenna models.

+
+ +
+

Updated 2-19-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
Go to 2-Element Multi-Band Quads +

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Loading, Quad


+ + diff --git a/content/quad/quad4.html b/content/quad/quad4.html new file mode 100644 index 0000000..c90d6bd --- /dev/null +++ b/content/quad/quad4.html @@ -0,0 +1,409 @@ + + + + + + Quad Models Part 4 Multi-Band 2-Element Quad Beams + + + +
+

Some Model Quads:
+ 4. Multi-Band 2-Element Quad Beams

+

L. B. Cebik, W4RNL

+
+
+ +
+

One of the advantages of the full-size quad is that one can nest the beam within or around others to form a multi-band HF beam of very respectable performance. The total real estate involved is no larger than that required by the largest beam of the group--normally a 20 meter array for upper HF applications.

+

It is possible to model (or design) 5-band quads with about 400 total segments. In past years, the run time for such a model on a PC would have been fairly taxing, especially for frequency sweeps on each of the bands covered by the antenna. Computer speed has sliced the time to the barely noticeable. The major time is now spent on constructing the model.

+

My own collection of 2-element 5-band models is somewhat limited, containing just four different types (and a host of variations on them). However, each may be worth a separate look, since each has some distinctive features.

+

A Spider Quad with 0.125 wl Element Spacing

Although the term "spider" is sometimes used to label any hub device that holds the supports for quad elements, its best use is to label those 8- legged hubs that hold all of the supports for a multi-band 2-element beam. One feature of quads constructed by this method is that the element spacing between the driver and the reflector is constant in terms of wavelengths. Whether this is an advantage, we shall see along the way. +

The first model originated as simply a study item, designed to look at the question of whether multi-band quads should be fed in common or with separate lines for each driver and with the unused driver loops closed. Throughout these notes, I have chosen the latter option for clarity within the models.

+

The study began with separate 2-element quad models for each of the 5 upper HF amateur bands. To refresh our memories, I shall import a small table from the first episode. L means side length, and C means loop circumference.

+ 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Segment
+ MHz       feet      feet      feet      feet      feet      per side
+28.5       4.31      8.66     34.64      9.16     36.64        7
+24.94      4.93      9.91     39.62     10.47     41.86        9
+21.22      5.79     11.64     46.56     12.26     49.04       11
+18.12      6.79     13.62     54.48     14.35     57.40       13
+14.17      8.68     17.42     69.68     18.30     73.20       15
+

When combined, the required dimensional changes to achieve resonance and peak front-to-back performance at the design frequency for each band show up in the following table for the 5-band quad array.

+ 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Segment
+ MHz       feet      feet      feet      feet      feet      per side
+28.5       4.31      8.64     34.56      9.20     36.80        7
+24.94      4.93      9.90     39.60     10.20     40.80        9
+21.22      5.79     11.63     46.52     12.06     48.24       11
+18.12      6.79     13.66     54.64     14.06     56.24       13
+14.17      8.68     17.50     70.00     18.06     72.24       15
+

The reason for using the indicated number of segments per side in the independent quads should be clear. In the combined quad, the segmentation was selected to have--to the degree feasible--identical segment lengths throughout and segment junctions that aligned from one loop to the next.

+
+ +
+

The element spacing of this first model is 0.125 wl, resulting in the proportions shown in Fig. 38. Each loop is full size, with no loading. As with the monoband models, the design called for resonance at each band center and to the degree possible the peak front-to-back ratio at the same frequency.

+

In case anyone would like to replicate the 5-band model, an EZNEC description follows. It is feasible to extract the description as an ASCII document and to modify it to fit the formats required by other programs that use input files in ASCII format. Although many format changes are required, number-entry typing errors are eliminated by this procedure.

+ 
5-band quad:  1/8 wl sp                      Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -4.320,  2.155, -4.320  W2E1   4.320,  2.155, -4.320    # 14    7
+2   W1E2   4.320,  2.155, -4.320  W3E1   4.320,  2.155,  4.320    # 14    7
+3   W2E2   4.320,  2.155,  4.320  W4E1  -4.320,  2.155,  4.320    # 14    7
+4   W3E2  -4.320,  2.155,  4.320  W1E1  -4.320,  2.155, -4.320    # 14    7
+5   W8E2  -4.600, -2.155, -4.600  W6E1   4.600, -2.155, -4.600    # 14    7
+6   W5E2   4.600, -2.155, -4.600  W7E1   4.600, -2.155,  4.600    # 14    7
+7   W6E2   4.600, -2.155,  4.600  W8E1  -4.600, -2.155,  4.600    # 14    7
+8   W7E2  -4.600, -2.155,  4.600  W5E1  -4.600, -2.155, -4.600    # 14    7
+9  W12E2  -5.815,  2.897, -5.815 W10E1   5.815,  2.897, -5.815    # 14   11
+10  W9E2   5.815,  2.897, -5.815 W11E1   5.815,  2.897,  5.815    # 14   11
+11 W10E2   5.815,  2.897,  5.815 W12E1  -5.815,  2.897,  5.815    # 14   11
+12 W11E2  -5.815,  2.897,  5.815  W9E1  -5.815,  2.897, -5.815    # 14   11
+13 W16E2  -6.030, -2.897, -6.030 W14E1   6.030, -2.897, -6.030    # 14   11
+14 W13E2   6.030, -2.897, -6.030 W15E1   6.030, -2.897,  6.030    # 14   11
+15 W14E2   6.030, -2.897,  6.030 W16E1  -6.030, -2.897,  6.030    # 14   11
+16 W15E2  -6.030, -2.897,  6.030 W13E1  -6.030, -2.897, -6.030    # 14   11
+17 W20E2  -8.750,  4.334, -8.750 W18E1   8.750,  4.334, -8.750    # 14   15
+18 W17E2   8.750,  4.334, -8.750 W19E1   8.750,  4.334,  8.750    # 14   15
+19 W18E2   8.750,  4.334,  8.750 W20E1  -8.750,  4.334,  8.750    # 14   15
+20 W19E2  -8.750,  4.334,  8.750 W17E1  -8.750,  4.334, -8.750    # 14   15
+21 W24E2  -9.030, -4.334, -9.030 W22E1   9.030, -4.334, -9.030    # 14   15
+22 W21E2   9.030, -4.334, -9.030 W23E1   9.030, -4.334,  9.030    # 14   15
+23 W22E2   9.030, -4.334,  9.030 W24E1  -9.030, -4.334,  9.030    # 14   15
+24 W23E2  -9.030, -4.334,  9.030 W21E1  -9.030, -4.334, -9.030    # 14   15
+25 W28E2  -4.950,  2.465, -4.950 W26E1   4.950,  2.465, -4.950    # 14    9
+26 W25E2   4.950,  2.465, -4.950 W27E1   4.950,  2.465,  4.950    # 14    9
+27 W26E2   4.950,  2.465,  4.950 W28E1  -4.950,  2.465,  4.950    # 14    9
+28 W27E2  -4.950,  2.465,  4.950 W25E1  -4.950,  2.465, -4.950    # 14    9
+29 W32E2  -5.100, -2.465, -5.100 W30E1   5.100, -2.465, -5.100    # 14    9
+30 W29E2   5.100, -2.465, -5.100 W31E1   5.100, -2.465,  5.100    # 14    9
+31 W30E2   5.100, -2.465,  5.100 W32E1  -5.100, -2.465,  5.100    # 14    9
+32 W31E2  -5.100, -2.465,  5.100 W29E1  -5.100, -2.465, -5.100    # 14    9
+33 W36E2  -6.830,  3.393, -6.830 W34E1   6.830,  3.393, -6.830    # 14   13
+34 W33E2   6.830,  3.393, -6.830 W35E1   6.830,  3.393,  6.830    # 14   13
+35 W34E2   6.830,  3.393,  6.830 W36E1  -6.830,  3.393,  6.830    # 14   13
+36 W35E2  -6.830,  3.393,  6.830 W33E1  -6.830,  3.393, -6.830    # 14   13
+37 W40E2  -7.030, -3.393, -7.030 W38E1   7.030, -3.393, -7.030    # 14   13
+38 W37E2   7.030, -3.393, -7.030 W39E1   7.030, -3.393,  7.030    # 14   13
+39 W38E2   7.030, -3.393,  7.030 W40E1  -7.030, -3.393,  7.030    # 14   13
+40 W39E2  -7.030, -3.393,  7.030 W37E1  -7.030, -3.393, -7.030    # 14   13
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+

All models continue to be in free space. This particular model grew in stages, going from a monoband antenna to a tribander to a full 5-band model. Hence, the wires must be grouped in series of 8 each, with the bands in order being 10, 15, 20, 12, and 17. For each band, change the source to the center of the following wires for each band: 20 = wire 17; 17 = wire 33; 15 = wire 9; 12 = wire 25; and 10 = wire 1.

+

Since 12 and 17 are such narrow bands, graphing performance on them is a fruitless exercise in drawing straight lines across the page. The wider bands (10, 15, and 20) were graphed by running frequency sweeps that divided each band into 10 equal parts (resulting in 11 values). Hence, the graphs record steps from the bottom of the band. Each 20-meter step is 0.035 MHz; each 15-meter step is 0.045 MHz; and each 10-meter step is 0.1 MHz.

+
+ +
+

The gain curves in Fig. 39 show an interesting trend. Although the 10- meter band is wider than the other as a percentage of the center frequency, the gain holds up better on that band than on the lower bands. Indeed, the gain is higher than for the lower bands--higher even than the monoband version of the 10-meter quad.

+

For reference, here is a table of key performance figures for the independent quad beams at the center frequency for each band.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+28.5            7.16           23.6                102 - j 1
+24.95           7.11           23.9                105 + j 1
+21.22           7.18           23.2                 99 + j 2
+18.12           7.14           23.7                101 - j 1
+14.17           7.15           23.2                 99 + j 0
+

For contrast, here is the performance of the combined beam at each band center.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+28.5            7.48           20.3                 40 - j 0
+24.95           7.16           24.7                 42 + j 0
+21.22           7.23           28.9                 53 + j 0
+18.12           7.32           25.8                 61 - j 0
+14.17           7.23           32.4                 84 - j 0
+
+ +
+

As Fig. 40 suggests, the front-to-back ratio is subject to very steep peaks on all but 10 meters. however, the band edge values resemble those of the monoband close-spaced quad beams--fairly low compared to mid-band values.

+

The source impedance values shown in the table are at considerable variance from those of the monoband quad beams, indicating a significant amount of interaction among elements. Those who are interested in the interactions will wish to examine the current tables for the supposedly inactive elements in the quad.

+
+ +
+

Fig. 41 shows the 75-Ohm SWR values for the 3 wide bands. Although this particular 5-band quad might well have been referenced to 50-Ohms, all of the others we shall examine more aptly use a 75-Ohm standard. Hence, the graph was made consistent with the others.

+

In fact, only the 10-meter curve is not movable to fit a 2:1 SWR bandwidth standard. Both the 15-meter and the 20-meter drivers can be adjusted to move their SWR curves. Note the leveling off of the 20-meter SWR above the band center, but also compare that phenomenon with the gain fall-ff at the upper end of the band.

+

Although the constant spacing of the elements in terms of wavelengths seems to be an advantage in the abstract, that appearance fails to reckon with the complex interactions of the elements. The source impedance climbs from the innermost quad to the outermost, which can make matching a complex affair.

+

Moreover, the operating bandwidth of the close-spaced quad is somewhat narrow, suggesting that a wider spacing may be advantageous. So we may turn from this study model to something a little more versatile.

+

A Spider Quad with 0.174 wl Element Spacing and Capacitive Reflector Loading

One direction for overcoming some of the limitation of the close-spaced spider is to increase the spacing. One useful study model in my collection uses an element spacing pf 0.174 wl, which is 6' at 10 meters (28.5 MHz). +
+ +
+

Fig. 42 Shows the general configuration of the model. The inward slope of the elements toward the boom is more extreme than in the close-spaced model. The squares on the reflector elements (all except 10 meters) represent a second attempt to add flexibility: loading capacitors. The reflectors for 20 through 12 meters are made longer than normal and electrically shortened with capacitors. As we noted with monoband beams, this practice permits more precise setting of the front-to-back ratio without altering the reflector loop lengths, and it adds a small degree of widening to the operating bandwidth. Because the 10-meter and 12-meter reflectors are so closely spaced to begin with, enlarging the 10-meter reflector was deemed impractical.

+

The following table lists the dimensions of note to the model, along with the value of the capacitor used. No losses are charged to the capacitor. In the model, it is important to use a Type 0 load that calls for an actual value of capacitance so that frequency sweeps will accurately portray the behavior of the antenna across the pass band. Since the reactance of the capacitor will change as the frequency changes, the use of a type 4 complex impedance (series resistance and reactance) load will not reflect the capacitor's actual effects. In the table, the segments/side column has been omitted, since all the quad models in this collection use the same segmentation scheme as the first one.

+ 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Reflector
+ MHz       feet      feet      feet      feet      feet      cap. pF
+28.5       6.00      8.63     34.54      9.40     37.60        ---
+24.94      6.86      9.88     39.52     10.56     42.23         80
+21.22      8.06     11.72     46.86     12.39     49.56        125
+18.12      9.44     13.77     55.08     14.48     57.92        135
+14.17     12.07     17.67     70.66     18.48     73.90        225
+

In replicating and improving this model, if changes are made to any of the loading capacitors, it is important to check the effects of the change on other bands. The most notable interaction is between 10 and 12 meters, since the loops are so close in length. However, 10 pF change in the 12- meter loading capacitor created operationally insignificant but numerically noticeable changes in the reported values for every other band.

+

For anyone wishing to replicate this particular model, here is the EZNEC model description.

+ 
5-band quad: .174wl sp                       Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1   W4E2 -51.800, 36.000,-51.800  W2E1  51.800, 36.000,-51.800    # 14    7
+2   W1E2  51.800, 36.000,-51.800  W3E1  51.800, 36.000, 51.800    # 14    7
+3   W2E2  51.800, 36.000, 51.800  W4E1 -51.800, 36.000, 51.800    # 14    7
+4   W3E2 -51.800, 36.000, 51.800  W1E1 -51.800, 36.000,-51.800    # 14    7
+5   W8E2 -56.400,-36.000,-56.400  W6E1  56.400,-36.000,-56.400    # 14    7
+6   W5E2  56.400,-36.000,-56.400  W7E1  56.400,-36.000, 56.400    # 14    7
+7   W6E2  56.400,-36.000, 56.400  W8E1 -56.400,-36.000, 56.400    # 14    7
+8   W7E2 -56.400,-36.000, 56.400  W5E1 -56.400,-36.000,-56.400    # 14    7
+9  W12E2 -59.300, 41.138,-59.300 W10E1  59.300, 41.138,-59.300    # 14    9
+10  W9E2  59.300, 41.138,-59.300 W11E1  59.300, 41.138, 59.300    # 14    9
+11 W10E2  59.300, 41.138, 59.300 W12E1 -59.300, 41.138, 59.300    # 14    9
+12 W11E2 -59.300, 41.138, 59.300  W9E1 -59.300, 41.138,-59.300    # 14    9
+13 W16E2 -63.350,-41.138,-63.350 W14E1  63.350,-41.138,-63.350    # 14    9
+14 W13E2  63.350,-41.138,-63.350 W15E1  63.350,-41.138, 63.350    # 14    9
+15 W14E2  63.350,-41.138, 63.350 W16E1 -63.350,-41.138, 63.350    # 14    9
+16 W15E2 -63.350,-41.138, 63.350 W13E1 -63.350,-41.138,-63.350    # 14    9
+17 W20E2 -70.300, 48.350,-70.300 W18E1  70.300, 48.350,-70.300    # 14   11
+18 W17E2  70.300, 48.350,-70.300 W19E1  70.300, 48.350, 70.300    # 14   11
+19 W18E2  70.300, 48.350, 70.300 W20E1 -70.300, 48.350, 70.300    # 14   11
+20 W19E2 -70.300, 48.350, 70.300 W17E1 -70.300, 48.350,-70.300    # 14   11
+21 W24E2 -74.350,-48.350,-74.350 W22E1  74.350,-48.350,-74.350    # 14   11
+22 W21E2  74.350,-48.350,-74.350 W23E1  74.350,-48.350, 74.350    # 14   11
+23 W22E2  74.350,-48.350, 74.350 W24E1 -74.350,-48.350, 74.350    # 14   11
+24 W23E2 -74.350,-48.350, 74.350 W21E1 -74.350,-48.350,-74.350    # 14   11
+25 W28E2 -82.650, 56.623,-82.650 W26E1  82.650, 56.623,-82.650    # 14   13
+26 W25E2  82.650, 56.623,-82.650 W27E1  82.650, 56.623, 82.650    # 14   13
+27 W26E2  82.650, 56.623, 82.650 W28E1 -82.650, 56.623, 82.650    # 14   13
+28 W27E2 -82.650, 56.623, 82.650 W25E1 -82.650, 56.623,-82.650    # 14   13
+29 W32E2 -86.900,-56.623,-86.900 W30E1  86.900,-56.623,-86.900    # 14   13
+30 W29E2  86.900,-56.623,-86.900 W31E1  86.900,-56.623, 86.900    # 14   13
+31 W30E2  86.900,-56.623, 86.900 W32E1 -86.900,-56.623, 86.900    # 14   13
+32 W31E2 -86.900,-56.623, 86.900 W29E1 -86.900,-56.623,-86.900    # 14   13
+33 W36E2 -106.00, 72.408,-106.00 W34E1 106.000, 72.408,-106.00    # 14   15
+34 W33E2 106.000, 72.408,-106.00 W35E1 106.000, 72.408,106.000    # 14   15
+35 W34E2 106.000, 72.408,106.000 W36E1 -106.00, 72.408,106.000    # 14   15
+36 W35E2 -106.00, 72.408,106.000 W33E1 -106.00, 72.408,-106.00    # 14   15
+37 W40E2 -110.85,-72.408,-110.85 W38E1 110.850,-72.408,-110.85    # 14   15
+38 W37E2 110.850,-72.408,-110.85 W39E1 110.850,-72.408,110.850    # 14   15
+39 W38E2 110.850,-72.408,110.850 W40E1 -110.85,-72.408,110.850    # 14   15
+40 W39E2 -110.85,-72.408,110.850 W37E1 -110.85,-72.408,-110.85    # 14   15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1       Laplace Coefficients
+          Seg.     Actual      (Specified)
+
+1           5    13 / 50.00   ( 13 / 50.00)   Coefficients listed below
+2           6    21 / 50.00   ( 21 / 50.00)   Coefficients listed below
+3           7    29 / 50.00   ( 29 / 50.00)   Coefficients listed below
+4           8    37 / 50.00   ( 37 / 50.00)   Coefficients listed below
+
+Load  1  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   8.000E-11   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  2  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   1.250E-10   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  3  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   1.351E-10   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  4  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   2.246E-10   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+

The dimensions of this model are listed in inches. The band-by-band source positions are as follows: 10 = wire 1; 12 = wire 9; 15 = wire 17; 17 = wire 25; and 20 = wire 33. Loads are listed by reference to Laplace transform notation, but the capacitor values can be read directly from the s^1 denominator position.

+

For reference, here are the performance potential reports for the band centers from 10 to 20 meters.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+28.5            7.15           32.4                 58 + j 16
+24.95           7.05           31.0                 70 + j  3
+21.22           7.07           29.1                 80 + j 20
+18.12           7.08           25.8                 94 + j  8
+14.17           7.11           23.8                118 - j  3
+

The resonant points for 10 and 15 meters were intentionally lowered, resulting in the inductively reactive source impedances for those bands at the specified frequencies. More notable is the fact that widening the spider did not overcome the tendency of this design to show an increasing source impedance magnitude as we move from the inner loops to the outer ones. This phenomena alone suggests that matching a spider to a given feedline will present some problems.

+
+ +
+

The gain curves in Fig. 43 show a good correlation to those for the narrow-spaced version of the 5-band quad. The gain curve for 10 meters is overall lower because the design effort aimed to raise the front-to-back ratio. However, gain change across 10 meters is virtually identical to that of the narrower quad. The 20-meter curve is slightly steeper for this model relative to the previous one.

+
+ +
+

Whereas the previous model showed high peak values of front-to-back ratio on 15 and 20, with 10 meters showing a relatively smooth curve, the front- to-back ratio curves in Fig. 45 show just the opposite. 10-meter front-to- back ratios are very good across the band. 15 and 20 show only mild peaks, but with overall performance significantly less than on 10. The performance on 20 at the low end of the band is improved, although the high-end figure is almost identical for the two models. Except on 10 meters (and the narrow WARC bands), attaining a 20 dB front-to-back ratio across the band with the spider design will be difficult.

+
+ +
+

The wider spacing of the present spider design significantly improves the 75-Ohm SWR operating bandwidth, despite the variability of source impedances from band-to-band. As shown in Fig. 45, all bands except 10 meters come in at under 2:1 SWR across the bands, and the 10-meter curve yields about 750 kHz of under 2:1 SWR operation.

+

Wider spacing, then, does provide superior performance over narrow spacing in spider designs. Part of the reason for the improvements involves complex interactions among the elements. The theoretically inactive elements are in practice quite active--at least to the degree necessary to shape the performance curves for the 5-band quad. Removing the loops for 12 and 17 meters would require a complete refiguring of the multi-band quad for effective 3-band operation. Some of loop size changes are small but necessary, suggesting that the multi-band quad is not the broad-banded insensitive beast that its early reputation made it out to be.

+

A "Flat-Loop' Quad with 8' Element Spacing and Capacitive Reflector Loading

In the April, 1992, edition of QST (p. 52), KC6T published a quad design that used flat plane loops spaced 8' apart. The 5-band design employed capacitor loading of the reflector. In addition, the designer used gamma matches on the drivers. +

In my own model of this antenna, some modifications have been made for modeling convenience. The driven elements were resonated at band centers. The reflector loads were optimized for the free space model. The differences between my values and the values used in the two practical versions described in the article reaffirm the importance of determining the actual value of loading required through field adjustment. The 10-meter reflector is not loaded. Fig. 46 shows the general outline of the resultant model.

+
+ +
+

The dimensions for the model follow in tabular form. Note especially the spacing in wavelengths for each band. The 10- and 12-meter loops are farther apart than those in the models explored so far, while 20-meter elements are closer than those in the narrow spider model we first examined.

+ 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Reflector
+ MHz       wl        feet      feet      feet      feet      cap. pF
+28.5      0.232      8.63     34.54      9.40     37.60        ---
+24.94     0.202      9.88     39.52     10.56     42.23         58
+21.22     0.173     11.72     46.86     12.39     49.56         68
+18.12     0.147     13.77     55.08     14.48     57.92         76
+14.17     0.115     17.67     70.66     18.48     73.90         94
+

Here is the corresponding EZNEC model description of the KC6T quad.

+ 
2el quad KC6T QST 4-92, p 52                    Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -4.292,  0.000, -4.292  W2E1   4.292,  0.000, -4.292    # 14    7
+2   W1E2   4.292,  0.000, -4.292  W3E1   4.292,  0.000,  4.292    # 14    7
+3   W2E2   4.292,  0.000,  4.292  W4E1  -4.292,  0.000,  4.292    # 14    7
+4   W3E2  -4.292,  0.000,  4.292  W1E1  -4.292,  0.000, -4.292    # 14    7
+5   W8E2  -4.950,  0.000, -4.950  W6E1   4.950,  0.000, -4.950    # 14    9
+6   W5E2   4.950,  0.000, -4.950  W7E1   4.950,  0.000,  4.950    # 14    9
+7   W6E2   4.950,  0.000,  4.950  W8E1  -4.950,  0.000,  4.950    # 14    9
+8   W7E2  -4.950,  0.000,  4.950  W5E1  -4.950,  0.000, -4.950    # 14    9
+9  W12E2  -5.825,  0.000, -5.825 W10E1   5.825,  0.000, -5.825    # 14   11
+10  W9E2   5.825,  0.000, -5.825 W11E1   5.825,  0.000,  5.825    # 14   11
+11 W10E2   5.825,  0.000,  5.825 W12E1  -5.825,  0.000,  5.825    # 14   11
+12 W11E2  -5.825,  0.000,  5.825  W9E1  -5.825,  0.000, -5.825    # 14   11
+13 W16E2  -6.842,  0.000, -6.842 W14E1   6.842,  0.000, -6.842    # 14   13
+14 W13E2   6.842,  0.000, -6.842 W15E1   6.842,  0.000,  6.842    # 14   13
+15 W14E2   6.842,  0.000,  6.842 W16E1  -6.842,  0.000,  6.842    # 14   13
+16 W15E2  -6.842,  0.000,  6.842 W13E1  -6.842,  0.000, -6.842    # 14   13
+17 W20E2  -8.733,  0.000, -8.733 W18E1   8.733,  0.000, -8.733    # 14   15
+18 W17E2   8.733,  0.000, -8.733 W19E1   8.733,  0.000,  8.733    # 14   15
+19 W18E2   8.733,  0.000,  8.733 W20E1  -8.733,  0.000,  8.733    # 14   15
+20 W19E2  -8.733,  0.000,  8.733 W17E1  -8.733,  0.000, -8.733    # 14   15
+21 W24E2  -4.675, -8.000, -4.675 W22E1   4.675, -8.000, -4.675    # 14    7
+22 W21E2   4.675, -8.000, -4.675 W23E1   4.675, -8.000,  4.675    # 14    7
+23 W22E2   4.675, -8.000,  4.675 W24E1  -4.675, -8.000,  4.675    # 14    7
+24 W23E2  -4.675, -8.000,  4.675 W21E1  -4.675, -8.000, -4.675    # 14    7
+25 W28E2  -5.358, -8.000, -5.358 W26E1   5.358, -8.000, -5.358    # 14    9
+26 W25E2   5.358, -8.000, -5.358 W27E1   5.358, -8.000,  5.358    # 14    9
+27 W26E2   5.358, -8.000,  5.358 W28E1  -5.358, -8.000,  5.358    # 14    9
+28 W27E2  -5.358, -8.000,  5.358 W25E1  -5.358, -8.000, -5.358    # 14    9
+29 W32E2  -6.300, -8.000, -6.300 W30E1   6.300, -8.000, -6.300    # 14   11
+30 W29E2   6.300, -8.000, -6.300 W31E1   6.300, -8.000,  6.300    # 14   11
+31 W30E2   6.300, -8.000,  6.300 W32E1  -6.300, -8.000,  6.300    # 14   11
+32 W31E2  -6.300, -8.000,  6.300 W29E1  -6.300, -8.000, -6.300    # 14   11
+33 W36E2  -7.350, -8.000, -7.350 W34E1   7.350, -8.000, -7.350    # 14   13
+34 W33E2   7.350, -8.000, -7.350 W35E1   7.350, -8.000,  7.350    # 14   13
+35 W34E2   7.350, -8.000,  7.350 W36E1  -7.350, -8.000,  7.350    # 14   13
+36 W35E2  -7.350, -8.000,  7.350 W33E1  -7.350, -8.000, -7.350    # 14   13
+37 W40E2  -9.400, -8.000, -9.400 W38E1   9.400, -8.000, -9.400    # 14   15
+38 W37E2   9.400, -8.000, -9.400 W39E1   9.400, -8.000,  9.400    # 14   15
+39 W38E2   9.400, -8.000,  9.400 W40E1  -9.400, -8.000,  9.400    # 14   15
+40 W39E2  -9.400, -8.000,  9.400 W37E1  -9.400, -8.000, -9.400    # 14   15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1       Laplace Coefficients
+          Seg.     Actual      (Specified)
+
+1           5    25 / 50.00   ( 25 / 50.00)   Coefficients listed below
+2           6    29 / 50.00   ( 29 / 50.00)   Coefficients listed below
+3           7    33 / 50.00   ( 33 / 50.00)   Coefficients listed below
+4           8    37 / 50.00   ( 37 / 50.00)   Coefficients listed below
+
+Load  1  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   5.800E-11   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  2  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   6.810E-11   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  3  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   7.640E-11   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Load  4  s^0         s^1         s^2         s^3         s^4         s^5
+Num   1.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+Den   0.000E+00   9.360E-11   0.000E+00   0.000E+00   0.000E+00   0.000E+00
+

This model gives dimensions in feet, but the order of loops differs. All of the driver loops are listed, followed by all of the reflectors, each in ascending wavelength order from 10 to 20 meters. Hence the source wires are as follows: 10 = wire 1; 12 = wire 5; 15 = wire 9; 17 = wire 13; and 20 = wire 17. Anyone who believes that I should set myself a more consistent set of modeling conventions for 5-band quads would be entirely in the right.

+

The following band-center performance potential reports will serve as a reference for the graphs to follow.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+28.5            7.46           22.8                 75 - j 0
+24.95           7.20           30.6                 77 + j 0
+21.22           7.28           34.4                 70 + j 2
+18.12           7.30           31.7                 70 + j 2
+14.17           7.21           24.0                 77 + j 2
+

The first thing to notice is that this model sustains the higher gain values of the narrow spider with the higher front-to-back ratios (except for 10 meters) of the wide spider. The second and very important thing to notice is the source impedances for all five bands. The band-center 75-Ohm SWR for all bands is insignificant.

+
+ +
+

The gain curves (Fig. 47) for the KC6T design show an overlap at the lower end of the bands. The overlap results from an increase in gain for the lower two bands. The 10-meter gain variance across the band is the lowest of the three designs we have examined. The gain drop-off for any band is equal to or less than the best figures for any of the designs. Nonetheless, the drop-off does run from 1 to 1.2 dB for 15 and 10 meters. I have not yet found a design that does not have this type of curve without setting the gain around 6.5 dBi in the first place.

+

Interestingly, the 10-meter portion of the antenna, when extracted from the overall 5-band environment, is not capable of the gain it shows within the larger set of loops. A free space gain of about 6.5 dBi, with a front-to- back ratio approaching 20 dB is the best I have been able to model from that part of the antenna. Moreover, the independent resonant impedance is over 170 Ohms--a far cry from the 75-Ohm impedance 10 meters shows in the 5-band model. Just how the other loops contribute to the 10-meter gain and source impedance remains to be calculated.

+
+ +
+

As presently structured, the front-to-back performance of the model is somewhat deficient and requires further work. See Fig. 48. It is uncertain whether significant improvements can be made. 10-meter performance begins at about 15 dB and peaks at over 50 dB. 15-meter performance peaks near 35 dB, but decreases to about 15 dB at the band edges in a well balanced curve. 20-meter performance is poorest of all, with the low edge of the band below the 10 dB mark. However, the close spacing of the 20-meter elements at under 1/8 wl may prevent significant improvements. Perhaps only the addition of a 30-meter set of elements to this model will allow some improvement to the 20-meter front-to-back curve.

+
+ +
+

The 75-Ohm SWR curves for the 3 wide bands, shown in Fig. 49, suggest that the antenna has good potential for direct matching to 75-Ohm feedline. The resonant point on 20 meters needs to be moved much lower in the band--with consequent adjustments to every other loop. 10 meters provides nearly 800 kHz of 2:1 SWR bandwidth, even before line losses are used to obscure the remaining mismatch at the antenna terminals.

+

With the increasing use of CATV low-loss hardline for fixed position runs between the antenna location and the shack entry, using a 75-Ohm feed system with an antenna of this design seems quite feasible. Driver switching can be accomplished with either solid or foam core 75-Ohm cable at the antenna end of the line. A single 75:50 Ohm transformer or unun can be used at the operating position to effect a match with equipment inputs and outputs. Alternatively, for use with a low-loss 50-Ohm main feedline, a single wide-band matching device might be located in the remote switch box, with all switching done at 75 Ohms.

+

Although 8-legged spiders and similar designs that keep quad elements spaced the same amount in terms of wavelength have become very popular, modeling exercises may breed a new respect for older fixed spacing designs. The KC6T design forms a very good starting point for improvements--and is a good design to model in its own right.

+

The Square and Its Feedpoint

EI7BA has built a quad somewhat similar to the wide-spaced spider we have examined. However, he has altered the feedpoint for mechanical reasons. +
+ +
+

For a square quad, the normal feedpoint, especially with spider construction, leaves a long run of unsupported feedline from the hub to the center of the element, as suggested in Fig. 50. If we have a multi-band quad, then we might have 5 line lengths, the net weight of which begs for a sky-hook.

+

EI7BA runs his feedlines to the corner(s) of the quad square. One might use the same corner for all or distribute the weight each side of center. The question then arises as to the effect the change of feed position might have upon the antenna pattern.

+
+ +
+

Fig. 51 shows the band-center pattern of the EI7BA quad on 15 meters using the normal centered feedpoint. Performance at this frequency is good with respect both to gain and front-to-back performance. As the figure shows, the vertically polarized component of the total far field is very small--at least 40 dB down from the horizontal and total fields, which are indistinguishable in the pattern graphic.

+
+ +
+

Moving the feedpoint to one corner has some interesting effects, which are displayed infig. 52. First, the vertically and horizontally polarized components of the field have equal forward gain values. Together, they yield a total field that is only down by 0.1 dB relative to the center-feed result. The total field has a wider beam width and extends beyond the 90-degree points we often use to define front-to-side ratio. The normal feed system produces front-to-side values greater than 35 dB down, whereas the front-to-side ratio for the corner feed is about 13 dB.

+

When we set aside simple habits of expectation, it is not at all clear that one can say that one pattern is superior to the other without introducing a good bit of information about the operating goals and style of the individual user. One can develop equal numbers of scenarios favoring each total field pattern. Whether the corner feed offers any advantages or disadvantages relative to propagation, modeling itself cannot say.

+

The repositioning of the feedpoint to the corner does tend to raise the source impedance of the antenna by a small amount. In one example, the change was from 75 Ohms to about 85 Ohms. Such changes will have to be factored into the design itself by anyone using this alternative feed system.

+

When Is Enough Enough?

+

Hopefully, the models made available here will provide a sufficient start to anyone interested in exploring multi-band 2-element quads. However, lest one think of these notes as in any way definitive, here is a list of some questions not tackled.

+
    +
  • 1. Does the diamond shape have any electrical effect (in contrast to obvious mechanical effects) upon a multi-band quad? Models of monoband quads suggest a negative answer, but I have not run any models to verify this suggestion.
    • +
  • 2. What is the optimal spacing for either spider or flat plane quads? The models noted here are only samples, not exhaustive investigations. Hence, there are possibilities yet to be tapped.
    • +
  • 3. What is the effect of using much fatter wire in the multi-band quad? Using #10 aluminum wire or other candidates for the loops has not been explored here. Some loop size changes are inevitable, but the interactions and their consequences for performance and feedpoint impedance figures remains to be figured.
    • +
  • 4. What effect will using metal or partially metal support arms have on quad performance? Metal arms or arm segments were not a part of these models.
    • +
  • 5. What is the effect of using a common feed point for all of the drivers in a 5-band quad? The models used here restricted themselves to feeding one driver at a time, with the unused drivers having closed loops. The common-feed question requires separate exploration.
    • +
  • 6. How will antenna height above ground affect quad performance, especially the source impedance. All of the models we have looked at have been free space versions to make the performance figures comparable. Although quads have a reputation of relative immunity to surrounding objects, every proposed quad should be modeled at its height of intended use.
    • +
  • 7. Can 5-band 3- and 4-element multi-band quads be modeled? In principle, the answer is a deceptively easy "yes." However, each 5-band element adds 20 wires to the model or about 200 segments. Since run times grow exponentially rather than linearly, the resultant models may require modeler patience. (The present generation of PCs has plenty of resources, so that is not a limitation.) Some programs with 500 segment limitations may not be able to handle models of large quads adequately, and reducing the segmentation per loop side in order to fit the model to the program runs the danger of producing inaccurate results.
    • +
+

These are not all of the questions that remain unanswered, but they are enough to remove any sense of definitiveness to these casual notes. My intent has been simply to make available some of the models in my collection to those interested in quad modeling--and to show some of the performance potential and limitations of each of the designs considered.

+

So we have only scratched the surface of the quad question cluster. Nonetheless, I hope my modeling experiences may be useful to those just starting to model their first quad.

+
+ +
+

Updated 2-20-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Monoband Quads of More Than 2 Elements

+

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad4a.html b/content/quad/quad4a.html new file mode 100644 index 0000000..a6357ec --- /dev/null +++ b/content/quad/quad4a.html @@ -0,0 +1,169 @@ + + + + + + Quad Models Part 4a Alternative Common Feeds for Multi-Band 2-Element Quad Beams + + + +
+

Some Model Quads:
+ 4a. Alternative Common Feeds for Multi-Band 2-Element Quad Beams

+

L. B. Cebik, W4RNL

+
+
+ +
+

When we specify an interest in a 2-element 5-band quad beam, we are usually, but not always, saying more than just these facts. Ordinarily, we are also looking for an array that is compatible with a 50-Ohm (or at most a 75-Ohm) coaxial cable system. Under these circumstances, I have on a number of occasions--for reasons we shall presently illustrate--recommended separate feed lines to each driver in the quad array, most often combined at a remote switch near the hub of the antenna. Over the years, a number of individuals have made some discoveries and rediscoveries that are worthy of note as alternatives to the remote switching idea. In the process of looking at these alternatives, we may also understand somewhat better a. what goes on in an array with a common feed system and b. some different ways of overcoming the less-than-optimal parts of what is going on.

+

The Separate-Feed Standard

In order to make some valid comparisons, let's use a single antenna throughout the exercise. Although we shall perform some modifications on the antenna as we proceed, let's begin with these dimensions for the "spider" 2-element, 5-band beams used in Part 4 of this series: + 
Frequency Spacing   L Driver  C Driver  L Refl.   C Refl.   Segment
+ MHz       feet      feet      feet      feet      feet      per side
+28.5       4.31      8.64     34.56      9.20     36.80        7
+24.94      4.93      9.90     39.60     10.20     40.80        9
+21.22      5.79     11.63     46.52     12.06     48.24       11
+18.12      6.79     13.66     54.64     14.06     56.24       13
+14.17      8.68     17.50     70.00     18.06     72.24       15
+

In modeling terms, the following EZNEC description is more complete.

+ 
5-band quad:  1/8 wl sp                      Frequency = 28.5  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -4.320,  2.155, -4.320  W2E1   4.320,  2.155, -4.320    # 14    7
+2   W1E2   4.320,  2.155, -4.320  W3E1   4.320,  2.155,  4.320    # 14    7
+3   W2E2   4.320,  2.155,  4.320  W4E1  -4.320,  2.155,  4.320    # 14    7
+4   W3E2  -4.320,  2.155,  4.320  W1E1  -4.320,  2.155, -4.320    # 14    7
+5   W8E2  -4.600, -2.155, -4.600  W6E1   4.600, -2.155, -4.600    # 14    7
+6   W5E2   4.600, -2.155, -4.600  W7E1   4.600, -2.155,  4.600    # 14    7
+7   W6E2   4.600, -2.155,  4.600  W8E1  -4.600, -2.155,  4.600    # 14    7
+8   W7E2  -4.600, -2.155,  4.600  W5E1  -4.600, -2.155, -4.600    # 14    7
+9  W12E2  -5.815,  2.897, -5.815 W10E1   5.815,  2.897, -5.815    # 14   11
+10  W9E2   5.815,  2.897, -5.815 W11E1   5.815,  2.897,  5.815    # 14   11
+11 W10E2   5.815,  2.897,  5.815 W12E1  -5.815,  2.897,  5.815    # 14   11
+12 W11E2  -5.815,  2.897,  5.815  W9E1  -5.815,  2.897, -5.815    # 14   11
+13 W16E2  -6.030, -2.897, -6.030 W14E1   6.030, -2.897, -6.030    # 14   11
+14 W13E2   6.030, -2.897, -6.030 W15E1   6.030, -2.897,  6.030    # 14   11
+15 W14E2   6.030, -2.897,  6.030 W16E1  -6.030, -2.897,  6.030    # 14   11
+16 W15E2  -6.030, -2.897,  6.030 W13E1  -6.030, -2.897, -6.030    # 14   11
+17 W20E2  -8.750,  4.334, -8.750 W18E1   8.750,  4.334, -8.750    # 14   15
+18 W17E2   8.750,  4.334, -8.750 W19E1   8.750,  4.334,  8.750    # 14   15
+19 W18E2   8.750,  4.334,  8.750 W20E1  -8.750,  4.334,  8.750    # 14   15
+20 W19E2  -8.750,  4.334,  8.750 W17E1  -8.750,  4.334, -8.750    # 14   15
+21 W24E2  -9.030, -4.334, -9.030 W22E1   9.030, -4.334, -9.030    # 14   15
+22 W21E2   9.030, -4.334, -9.030 W23E1   9.030, -4.334,  9.030    # 14   15
+23 W22E2   9.030, -4.334,  9.030 W24E1  -9.030, -4.334,  9.030    # 14   15
+24 W23E2  -9.030, -4.334,  9.030 W21E1  -9.030, -4.334, -9.030    # 14   15
+25 W28E2  -4.950,  2.465, -4.950 W26E1   4.950,  2.465, -4.950    # 14    9
+26 W25E2   4.950,  2.465, -4.950 W27E1   4.950,  2.465,  4.950    # 14    9
+27 W26E2   4.950,  2.465,  4.950 W28E1  -4.950,  2.465,  4.950    # 14    9
+28 W27E2  -4.950,  2.465,  4.950 W25E1  -4.950,  2.465, -4.950    # 14    9
+29 W32E2  -5.100, -2.465, -5.100 W30E1   5.100, -2.465, -5.100    # 14    9
+30 W29E2   5.100, -2.465, -5.100 W31E1   5.100, -2.465,  5.100    # 14    9
+31 W30E2   5.100, -2.465,  5.100 W32E1  -5.100, -2.465,  5.100    # 14    9
+32 W31E2  -5.100, -2.465,  5.100 W29E1  -5.100, -2.465, -5.100    # 14    9
+33 W36E2  -6.830,  3.393, -6.830 W34E1   6.830,  3.393, -6.830    # 14   13
+34 W33E2   6.830,  3.393, -6.830 W35E1   6.830,  3.393,  6.830    # 14   13
+35 W34E2   6.830,  3.393,  6.830 W36E1  -6.830,  3.393,  6.830    # 14   13
+36 W35E2  -6.830,  3.393,  6.830 W33E1  -6.830,  3.393, -6.830    # 14   13
+37 W40E2  -7.030, -3.393, -7.030 W38E1   7.030, -3.393, -7.030    # 14   13
+38 W37E2   7.030, -3.393, -7.030 W39E1   7.030, -3.393,  7.030    # 14   13
+39 W38E2   7.030, -3.393,  7.030 W40E1  -7.030, -3.393,  7.030    # 14   13
+40 W39E2  -7.030, -3.393,  7.030 W37E1  -7.030, -3.393, -7.030    # 14   13
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           4     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+

With separate feedpoints, the array produces the following results at the design frequencies for each of the 5 bands.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+14.17           7.23           32.4                 84 - j 0
+18.12           7.32           25.8                 61 - j 0
+21.22           7.23           28.9                 53 + j 0
+24.95           7.16           24.7                 42 + j 0
+28.5            7.48           20.3                 40 - j 0
+
+ +
+

Fig. 1 shows the 20, 15, and 10 meter free-space azimuth patterns for this array. Note that each is a well-behaved pattern with very distinct side-nulls and a standard rear pattern for antennas of this type. Each is virtually indistinguishable from a monoband quad beam pattern for the same frequency.

+

Common Feed

+
+ +
+

Quad common feed is usually achieved in one of the three ways shown in Fig. 2. At its most simple, the system simply involves connecting the driver wires for each band together at a certain point. Alternatively, we can connect the wires together at the terminals of a balun to adjust the impedance for a match to coaxial cable. A third method is to use a transmission line section to feed the wires in phase with each other. The first two system deform the drivers of some bands by introducing non-horizontal angles to the lower driver wire. The phasing line system does not.

+

At the suggestion of WD8JOL, who has been planning a revision to a GEM quad, I experimented with introducing a 150-Ohm phasing line to the driver of the 0.125 wavelength spaced model above--which is similar in arrangement to the GEM quad. The phase line--as a physical matter--can be constructed from reasonably heavy wire and polycarbonate or similar spacers. For a model, the TL facility does all of the necessary work. Like Parker's model, I obtained best results by connecting the main source or feedline to the 17-meter element. For planar element sets using the same system, connection to the 20-meter element is normally best.

+

The feedpoint impedance for all bands at their design frequencies is close enough to 100 Ohms to presume that the coax line will be fed through a 2:1 balun of some sort. The results obtained from this arrangement are shown in the following table.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+14.17           7.21           23.8                103 - j 20
+18.12           7.21           24.3                 97 - j  2
+21.22           7.15           27.0                100 + j  6
+24.95           7.26           27.1                121 + j 25
+28.5            5.89           21.2                 95 + j 36
+

The results will vary somewhat with the exact element dimensions. For the design used here, the low ends of the bands showed higher than acceptable SWR values. However, the most important thing to notice is the pattern shape, which is shown in free-space azimuth patterns for 20, 15, and 10 in Fig. 3.

+
+ +
+

Typically, with any form of common feed, the first casualty is the front-to-side ratio. Remember that the patterns of Fig. 3 are in free space, and the side nulls are reduced as the antenna is placed closer to the ground. If we begin with reduced front-to-side ratios, matters tend to become progressively worse with lower heights. The reduced front-to-side ratio is evident even at 20 meters and wholly disappears for 10 meters. The particularly poor front-to-side ratio at 10 meters results from the fact that with a single common feed, the 20 meter element uses a significant portion of the fed 10-meter power and radiates at angle wide of the center line. The composite pattern for these two bands (with minor affects from the 12-meter elements) gives us the 10-meter azimuth shape shown in Fig. 3.

+

Many operators may find the pattern and lower 10-meter gain to be complete satisfactory in exchange for the simplicity of a common feed system. Others may wish to discover an alternative which avoids the cost of a remote switch but which also preserves the pattern shape of independently fed drivers.

+

Dual Phase Lines

In the search for a common feed with well-behaved patterns, we often overlook the fact that feeding a quad loop never yields perfect conditions on the top wire, that is an element center with the same current magnitude and phase (adjusted for the reversal of direction) as at the center of the lower element. One way to overcome this imperfection is to feed both the top and bottom element centers. In this case, we shall use phasing lines to both sets of element centers, as shown in Fig. 4. +
+ +
+

If the modeled loop is continuous, and modeled continuously "around the horn," you will discover that the model calls for a half-twist in the feedline junction assembly to achieve in-phase feeding. However, with dual feed, this convention of modeling--which is very useful with single-feed-point-per-loop systems--is not accurate. You must use in reality an untwisted feed. More accurately, you should model dual-feed loops by beginning at the far left center (or far right center) and then model both upper and lower loop halves in the same direction. Then, the model will reflect reality in all details and the in-phase feeding will be straight-forward.

+

With the dual feed system, the result is an almost total absence of current on the 20 meter elements when 10-meter energy is fed to the system. As a result, we obtained the following results from the spider beam rearranged for two 150-Ohm phasing lines.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+14.17           7.27           23.5                 77 + j 38
+18.12           7.19           23.4                 49 - j 14
+21.22           7.20           27.0                 57 + j  5
+24.95           7.49           21.6                 72 + j 35
+28.5            7.77           22.1                104 + j 53
+

The results were obtained using 150-Ohm phase lines, with junction lines of 100 Ohms. At the design frequencies, the junction would be satisfactory for a 75-Ohm main cable for this particular exercise. However, the SWR bandwidth may not be satisfactory at the lower ends of the wider bands.

+
+ +
+

Despite these limitations, great strides have been made in the control of the patterns, as shown by the examples in Fig. 5. For all bands, the front-to-side ratios have been restored. As well, 10-meter performance has improved even beyond the level shown for independently fed drivers. However, I should add a reminder here that in none of the feed systems do we overcome the inherently narrow banded operating characteristics of a 2-element thin-wire quad, whether a monoband version or a multi-band array. The gain changes rapidly across the band, and the front-to-back ratio peaks above 20 dB only for a narrow band segment. These characteristics are inherent in the small diameter elements and the spacing used.

+

Not all versions of the dual-phase-line feed system for 2-element multi-band quad arrays will show impedances that combine for some sort of coaxial cable main feeder. However, in all cases, the system may be used with parallel feedline as the phase-line connectors and as the main feedline. Of course, the user would need a balanced antenna tuner. Moreover, care must be taken in routing the parallel line so that it maintains an adequate distance from the tower or mast and so that it remains distant from the rotator housing as the antenna is turned throughout its cycle. These measures are not difficult, but they may be initially foreign to those most used to handling coaxial feedlines.

+

Single-Loop Feed

If we are going to use a dual-feed system that puts the center of both the upper and the lower horizontal elements in phase--and if we are going to use parallel feedline and a tuner in the process--than we might as well eliminate all but the 20-meter driver. With both horizontal elements fed in phase, the resonance of this element no longer matters. In fact, we may construct a quad array that resembles the simplified sketch in Fig. 6. +
+ +
+

Such a system goes as far back as the 1969 work of DJ4VM and has been recently improved upon by Dr. Hartmut Waldner, DF6PW. Harmut's version of the antenna--in operation--uses a diamond configuration and is likely to be published in the near future. For my modeling investigations, I have applied the principle to the planar array of KC6T and to the 0.125 wavelength spider array. In the latter case, I simply removed all of the driver wires from the model except the ones for 20 meters. I then used 450-Ohm parallel line to feed the top and bottom horizontals of the remaining driver and took impedance reading at their junction. The exercise established that the principle may be applied with equal success to both planar and to spider arrays.

+

The results obtained from the spider array are in line with those from the DF6PW array and are in the following table.

+ 
Frequency      Free Space     Front-to-Back       Feedpoint Impedance
+ MHz           Gain dBi       Ratio dB            R +/- jX Ohms
+14.17           7.21           25.2                 61 + j270
+18.12           7.72           20.1                187 - j544
+21.22           8.02           18.6                 33 - j180
+24.95           8.40           15.0                 14 - j 43
+28.5            8.47           14.7                 11 + j 51
+

Immediately apparent is the higher gain of the system as the frequency is increased. The cost of the higher gain is a loss of some front-to-back ratio from 15 through 10 meters. Only an individual operational goal analysis will tell a prospective builder whether the trade-off is a reasonable one.

+
+ +
+

The patterns are well controlled on all bands, as shown in Fig. 7. Of course, the table makes clear that to obtain these values, the feed system must be based on parallel feedline and a balanced ATU. Indeed, Harmut reports that he has relieved his shack of considerable RF by rebuilding a network tuner into a balanced link-coupled tuner. The lines used in the model tests were 450-Ohm transmission lines. However, any parallel line should work about as well.

+

Overcoming the upper band pattern distortion of a common-feed multi-band quad array, then, has more than one route to solution. For those wedded to coaxial cable feed techniques, the separately fed driver system will continue to be the most attractive. However, dual feed of the driver or drivers holds an equal potential for returning the quad patterns to good behavior on all bands. To sustain the desired peak front-to-back ratios, the dual phase lines to a full array of feeders may be the best route. For added upper band gain at the cost of some of the front-to-back ratio, the single loop driver can be attractive--especially since it does away with 4 ice-gathering wire loops in the array.

+

In none of the exercises did I make any modifications to the dimensions of any of the loops in the 0.125 wavelength spider array. I simply added phase lines and/or removed unneeded elements. Hence, I cannot say that the optimum performance has been achieved. However, it appears from initial modeling tests that closer-spaced arrays attain higher peak gains than more widely spaced arrays. Compared to planar arrays, there might be a slight advantage in single-loop feed systems to the spider version over planar versions.

+

Of course, for many operating purposes, the simpler system of combining feedlines in the most traditional ways may prove satisfactory. In antenna matters, there are always alternatives. Which system is superior requires careful measurement against operating goals and local circumstances by the potential user. These notes are simply a vehicle of making builders aware that there are alternative methods for achieving a combined feed for a multi-band 2-element quad array.

+

My thanks to Dr. Harmut Waldner, DF6PW, for calling my attention to the need to change the way we model quads when going to multiple-feed loops.

+
+ +
+

Updated 7-16-2000, 9-4-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Monoband Quads of More Than 2 Elements

+

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad4b.html b/content/quad/quad4b.html new file mode 100644 index 0000000..d1793b6 --- /dev/null +++ b/content/quad/quad4b.html @@ -0,0 +1,409 @@ + + + + + + Quad Models Part 4b Stacking 2-Element, 5-Band Quads + + + +
+

4b. Stacking 2-Element, 5-Band Quads

+

L. B. Cebik, W4RNL

+
+
+ +
+

Because there appears to be interest in the stacking potential of quads, especially 2-element, 5-band quads, I decided to stack a pair of models and seed what they would do. I used 24' spacing between array centers. I first ran the single array in free space, followed by the pair in free space, for a relative gain and general property check. I then placed the lower quad 50' up and the higher 24' above that to see if ground would create any undesirable effects. Details of the dimensions of the quads used in this preliminary exploration of stacking appear in Part 4 of this series.

+

The KC6T Planar 5-Band Quad

+
+ +
+

The quads used in this initial run are models in NEC-4 of the KC6T quad in April, 1992 QST (p.52), one of the finest planar quad designs I have found with a constant 8' spacing, as shown in Fig. 1. It uses loading capacitance (modeled as a value of C and not as a value of -jX) in the reflector to set the operating frequency and my models are self-resonant without a matching network. The models have been set for the most desirable combination of gain, F-B, and impedance at mid-band to reveal the rate of change of these parameters both above and below the design frequency. Fig. 2 shows an outline of the stacked pair of planar quads.

+
+ +
+

The data consists of gain in dBi, TO angle (where relevant), F-B, beamwidth, feed Z(s) and 75-Ohm SWR (for which the original array had been set).

+ 
KC6T Quad in Free Space
+
+Fq        Gain      F-B       B/W       Feed Z         SWR-75
+14.0      7.6        8.3      69         34.7-45.6     3.10
+14.175    7.2       24.0      73         76.6+ 1.6     1.03
+14.35     6.4       11.6      76        112.2+ 9.4     1.52
+
+18.118    7.3       31.7      74         69.5+ 1.7     1.08
+
+21.0      7.7       12.6      72         47.3-30.0     1.96
+21.225    7.3       34.4      75         69.5+ 1.7     1.08
+21.45     6.7       14.2      77         89.6+19.3     1.34
+
+24.94     7.2       30.6      76         77.0+ 0.3     1.03
+
+28.0      7.7       14.5      75         65.9-54.2     2.15
+28.5      7.5       22.8      77         75.4- 0.3     1.01
+29        7.3       37.1      78         87.1+50.1     1.87
+ 
2 KC6T Quads stacked 24' apart in Free Space:  Z1 (upper entry) = lower
+quad; Z2 (lower entry) = upper quad.  Since both quads are fed on the lower
+element, some differentials in values are normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-75 1/2
+14.0      9.0       11.3      70         64.6-18.9     1.36
+                                         66.7-20.4     1.30
+14.175    8.8       20.4      73        120.8+23.2     1.70
+                                        117.2+13.5     1.60
+14.35     8.3       12.4      75        164.8+14.3     2.22
+                                        154.2+12.3     2.07
+
+18.118    9.5       21.5      73         86.8+ 3.6     1.17
+                                         85.9+ 4.1     1.16
+
+21.0      10.1      12.9      72         56.3-29.9     1.71
+                                         56.1-29.6     1.71
+21.225    9.9       22.3      75         81.3+ 1.3     1.09
+                                         81.1+ 1.8     1.09
+21.45     9.5       13.3      77        104.1+14.6     1.44
+                                        104.2+15.2     1.45
+
+24.94     10.2      23.1      77         84.1- 5.0     1.14
+                                         84.6 -4.9     1.15
+
+28.0      10.8      15.1      75         70.0-57.0     2.16
+                                         70.2-56.7     2.15
+28.5      10.7      23.5      77         79.7- 2.2     1.07
+                                         79.9- 2.0     1.07
+29        10.5      26.8      78         92.5+48.6     1.84
+                                         92.7+48.9     1.85
+ 
Stacking Gain averaged by bands:
+20        17        15        12        10
+1.6       2.2       2.6       3.0       3.2  dB
+ 
2 KC6T Quads stacked 24' apart in 50' and 74' above average ground:  Z1
+(upper entry) = lower quad; Z2 (lower entry) = upper quad.  Since both
+quads are fed on the lower element, some differentials in values are
+normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-75 1/2     TO
+14.0      13.6      11.7      71         64.2-19.1     1.37           15
+                                         66.6-20.0     1.36
+14.175    13.4      20.5      74        117.0+19.6     1.63           14
+                                        120.1+18.5     1.66
+14.35     13.0      12.1      76        156.4+20.5     2.13           14
+                                        162.8+ 8.5     2.18
+
+18.118    14.4      21.6      74         87.7+ 4.5     1.18           11
+                                         85.3+ 3.5     1.15
+
+21.0      15.1      13.1      72         56.7-29.8     1.70           10
+                                         55.8-29.7     1.72
+21.225    15.0      22.0      75         82.3+ 1.1     1.10           10
+                                         80.5+ 2.1     1.08
+21.45     14.6      13.1      78        105.1+13.4     1.45           10
+                                        103.8+16.3     1.45
+
+24.94     15.4      22.1      77         82.7- 5.8     1.13            8
+                                         86.2 -5.5     1.17
+
+28.0      15.9      14.9      75         69.1-56.1     2.15            8
+                                         69.3-57.5     2.18
+28.5      15.8      22.9      77         79.3- 0.9     1.06            7
+                                         78.7- 1.9     1.06
+29        15.7      26.5      79         92.7+50.2     1.87            7
+                                         91.8+49.6     1.86
+

As is clearly evident, the particular quad design explored here does not suffer from being placed over ground at 50' for the center of the bottom array and at 74' for the center of the top array. The front-to-back and impedance values hold closely to their free-space values--sufficiently so that I could not think of recommending a design change. In addition, stacking appears to shift the operating parameters to provide operating bandwidth in the stack that is superior to that of the single array. Assuming that an in-phase feedline harness can be devised, the coax run should bring virtually all SWR values under 2:1 at the shack. For the stacks, they are all well within rig-tuner range without excessive loss.

+
+ +
+

For reference, Fig. 3 shows the azimuth pattern at mid-band in 15 meters for the array over ground.

+

A 0.174 WL Spaced Spider Quad

The following data apply to a stack of 2 spider-construction 2-element, 5-band quads, spaced 24' center-to-center. The element spacing of this model is 0.174 wavelength. The spacing is wider than most commercial spider quads, which range from about 0.11 to 0.13 wavelength. An outline appears in Fig. 4. Clear in the sketch are the reflector loads, similar to those used on the KC6T model. See Part 4 of this series for details. +
+ +
+

As with the KC6T planar model, the series of tables begin with data for a single array in free space, followed by a stack of 2 in free space. The last table places the antennas at 50' and 74', respectively, above good soil. Fig. 5 shows the outline of the pair of spider quads in their stack.

+
+ +
+

The data consists of gain in dBi, TO angle (where relevant), F-B, beamwidth, feed Z(s) and 75-Ohm SWR (for which the original array had been set).

+ 
0.174-WL Spider Quad in Free Space
+
+Fq        Gain      F-B       B/W       Feed Z         SWR-75
+14.0      7.6        9.2      71         76.6-22.8     1.35
+14.175    7.1       23.4      75        117.3- 2.1     1.57
+14.35     6.3       11.8      79        129.7- 1.7     1.73
+
+18.118    7.1       25.3      76         92.8+ 8.7     1.27
+
+21.0      7.6       12.0      73         53.1-13.5     1.50
+21.225    7.1       29.1      77         79.7+20.2     1.31
+21.45     6.5       14.3      80        105.8+36.5     1.70
+
+24.94     7.0       29.8      76         69.3+ 2.2     1.09
+
+28.0      7.4       20.4      77         48.5-39.8     2.17
+28.5      7.2       32.1      79         58.5+16.7     1.42
+29        6.9       18.1      81         70.5+70.1     2.54
+ 
2 0.174-WL Spider Quads stacked 24' apart in Free Space:  Z1 (upper entry) = lower
+quad; Z2 (lower entry) = upper quad.  Since both quads are fed on the lower
+element, some differentials in values are normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-75 1/2
+14.0      8.9       11.4      72        131.1- 1.3     1.83
+                                        136.4-14.9     1.85
+14.175    8.7       26.4      75        196.0- 4.7     2.61
+                                        170.9- 9.5     2.29
+14.35     8.2       16.4      78        196.9-32.2     2.71
+                                        180.6-18.0     2.44
+
+18.118    9.4       26.4      76        119.5+10.0     1.61
+                                        117.9+11.0     1.59
+
+21.0      10.0      12.3      73         62.5-10.7     1.27
+                                         62.2-10.5     1.27
+21.225    9.8       30.3      77         93.6+24.4     1.44
+                                         93.1+24.7     1.44
+21.45     9.3       14.3      80        126.9+35.9     1.89
+                                        126.5+36.6     1.89
+
+24.94     10.1      33.1      78         76.3+ 1.4     1.03
+                                         76.7+ 1.6     1.03
+
+28.0      10.5      20.2      77         49.9-39.5     2.11
+                                         50.1-39.3     2.10
+28.5      10.3      26.4      79         60.1+18.5     1.42
+                                         60.2+18.7     1.42
+29        10.1      17.9      81         73.2+73.7     2.61
+                                         73.3+74.1     2.62
+ 
Stacking Gain averaged by bands:
+20        17        15        12        10
+1.6       2.2       2.7       3.0       3.3  dB
+ 
2 0.174-WL Spider Quads stacked 24' apart in 50' and 74' above average ground:  Z1
+(upper entry) = lower quad; Z2 (lower entry) = upper quad.  Since both
+quads are fed on the lower element, some differentials in values are
+normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-75 1/2     TO
+14.0      13.6      11.8      73        135.1- 3.0     1.80           15
+                                        137.6-11.6     1.85
+14.175    13.4      28.7      76        183.4+ 0.3     2.45           14
+                                        182.1-11.4     2.44
+14.35     12.9      15.8      79        197.1-16.3     2.65           14
+                                        182.9-29.1     2.51
+
+18.118    14.3      28.1      76        121.3+11.0     1.64           12
+                                        116.6+10.3     1.56
+
+21.0      15.0      12.6      74         62.9-10.4     1.26           10
+                                         61.8-10.6     1.28
+21.225    14.9      29.6      77         94.9+24.4     1.45           10
+                                         92.1+25.0     1.44
+21.45     14.4      14.0      80        128.5+34.6     1.89           10
+                                        125.7+38.2     1.90
+
+24.94     15.3      29.8      78         75.5+ 0.2     1.01            9
+                                         78.0+ 1.7     1.05
+
+28.0      15.7      19.9      77         49.1-38.9     2.12            8
+                                         49.4-39.8     2.14
+28.5      15.5      25.5      79         59.6+19.5     1.49            7
+                                         59.3+18.8     1.44
+29        15.4      17.5      81         73.2+75.0     2.65            7
+                                         72.7+74.6     2.64
+

The main line of the numbers for the spider quad are similar to those of the planar quad. However, certain deviations are worth noting. First, the spider quad impedance values for the upper and lower antennas differ somewhat more than comparable figures for the planar model. It would appear that especially the outer bands (17 and most radically 20 meters) are susceptible to changes. Second, the 20-meter--and to a lesser extent, the 10-meter--antennas alter impedance values when placed into the stack-- enough to require retuning of these portions of the arrays. The spider construction leaves the impression that either it leaves the individual band elements more exposed to external influence or that the planar quad is more immune to external influence--perhaps two ways of saying the same thing. The bottom line remains that spider construction quads are likely to need more than a little reformulation when placed in a closely spaced stack.

+
+ +
+

Fig. 6 shows the 15-meter azimuth pattern at mid-band over ground for reference.

+

A 0.125 WL Spaced Spider Quad

The following data apply to a stack of 2 spider-construction 2-element, 5-band quads, spaced 24' center-to-center. The element spacing of this model is 0.125 wavelength, narrower than the preceding spider quad and closer to commercial implementations of the design, which range from about 0.11 to 0.13 wavelength. An outline appearing in Fig. 4 is close enough to the present design not to need a new sketch, although this design uses exactly pruned reflectors with no loading. See Part 4 of this series for details. +

As with the other models, the series of tables begin with data for a single array in free space, followed by a stack of 2 in free space. The last table places the antennas at 50' and 74', respectively, above good soil.

+

The data consists of gain in dBi, TO angle (where relevant), F-B, beamwidth, and feed Z(s). Due to the variability of the feedpoint impedances, an SWR column would be meaningless and has been omitted.

+ 
0.125-WL Spider Quad in Free Space
+
+Fq        Gain      F-B       B/W       Feed Z
+14.0      7.6        7.6      69         40.6-45.1
+14.175    7.2       28.9      73         84.2- 0.1
+14.35     6.4       12.8      76        117.7+ 5.6
+
+18.118    7.2       32.4      73         60.9- 0.5
+
+21.0      7.6       12.0      71         31.5-38.6
+21.225    7.2       24.7      74         52.9+ 0.2
+21.45     6.6       12.3      77         76.4+24.5
+
+24.94     7.3       25.8      74         41.5+ 0.1
+
+28.0      7.8       13.7      72         30.9-61.1
+28.5      7.5       20.3      74         40.0- 0.3
+29        7.2       15.6      76         50.4+54.7
+ 
2 0.125-WL Spider Quads stacked 24' apart in Free Space:  Z1 (upper entry) = lower
+quad; Z2 (lower entry) = upper quad.  Since both quads are fed on the lower
+element, some differentials in values are normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2
+14.0      8.9        9.6      70         72.1-18.4
+                                         73.2-20.7
+14.175    8.8       22.2      73        130.0+24.9
+                                        126.5+13.3
+14.35     8.3       14.8      76        180.0+13.4
+                                        163.1- 9.3
+
+18.118    9.4       21.1      73         74.3+ 5.3
+                                         73.5+ 5.0
+
+21.0      10.0      11.8      71         36.8-37.4
+                                         36.7-37.4
+21.225    9.8       19.3      74         60.3+ 3.0
+                                         60.0+ 3.0
+21.45     9.4       11.7      77         88.7+25.7
+                                         88.2+26.0
+
+24.94     10.3      21.1      74         45.4- 0.8
+                                         45.3- 0.7
+
+28.0      10.8      13.8      72         32.1-62.4
+                                         32.3-62.3
+28.5      10.6      18.1      74         41.5- 0.9
+                                         41.6- 0.7
+29        10.4      14.1      76         52.6+54.5
+                                         52.7+54.7
+ 
Stacking Gain averaged by bands:
+20        17        15        12        10
+1.6       2.2       2.6       3.0       3.1  dB
+ 
2 0.125-WL Spider Quads stacked 24' apart in 50' and 74' above average ground:  Z1
+(upper entry) = lower quad; Z2 (lower entry) = upper quad.  Since both
+quads are fed on the lower element, some differentials in values are
+normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     TO
+14.0      13.6       9.8      70         71.6-18.7     14
+                                         73.1-20.0
+14.175    13.5      23.0      74        125.2+21.4     14
+                                        130.6+18.3
+14.35     13.0      14.3      76        170.4+21.6     14
+                                        172.2+ 4.0
+
+18.118    14.4      21.3      74         74.8+ 6.3     11
+                                         73.2+ 4.2
+
+21.0      15.0      11.9      71         37.0-37.2     10
+                                         36.6-37.4
+21.225    14.9      19.0      75         61.0+ 3.2     10
+                                         59.5+ 3.0
+21.45     14.5      11.5      77         90.0+25.2     10
+                                         87.4+26.7
+
+24.94     15.4      20.9      74         45.1- 1.5      9
+                                         46.0- 0.5
+
+28.0      15.9      13.7      72         31.8-62.0      8
+                                         31.9-62.6
+28.5      15.7      17.8      74         41.3- 0.2      7
+                                         40.9- 0.8
+29        15.6      14.0      76         52.6+55.4      7
+                                         52.1+55.1
+

The narrower spacing of the 0.125-WL spider design results in a narrower operating bandwidth, which shows up most clearly in the front-to-back curves that one can infer from the data. As well, when stacked, the sharp peak of the front-to-back curve does not need to be displaced much to appear as a significantly lower mid-band value, as in the charts for stacked versions of the design.

+

One disaadvantage of the more closely spaced spider design is that equal excursions of reactance across any given band--relative to the wider-spaced spider--will result in steeper SWR curves, due to the lower initial resistive component of the feedpoint impedance. As a result, the problem of obtaining a good match for all portions of all five bands may become a major challenge.

+

Wider Spacing

+

Experimental modeling with larger quad arrays in stacks suggests that wider spacing may effect greater isolation between bays. This intial 24' spacing is between 5/8 and 2/3 wavelength on 20 meters--and proportionally greater on the other bands. Hence, the major effect of modest increases in spacing from one array center to the other would be primarily on 20 and 17 meters.

+

Therefore, I reran the 0.125 wavelength spider array with a spacing of 30' or about 5/6 wavelength on 20 meters. I will provide the entire data set, including the single array free space information, to ease the process of making internal comparisons within the data. However, comparisons with the preceding data set are also very relevant to deciding what spacing may be best for this type of quad array.

+ 
0.125-WL Spider Quad in Free Space
+
+Fq        Gain      F-B       B/W       Feed Z
+14.0      7.6        7.6      69         40.6-45.1
+14.175    7.2       28.9      73         84.2- 0.1
+14.35     6.4       12.8      76        117.7+ 5.6
+
+18.118    7.2       32.4      73         60.9- 0.5
+
+21.0      7.6       12.0      71         31.5-38.6
+21.225    7.2       24.7      74         52.9+ 0.2
+21.45     6.6       12.3      77         76.4+24.5
+
+24.94     7.3       25.8      74         41.5+ 0.1
+
+28.0      7.8       13.7      72         30.9-61.1
+28.5      7.5       20.3      74         40.0- 0.3
+29        7.2       15.6      76         50.4+54.7
+ 
2 0.125-WL Spider Quads stacked 30' apart in Free Space:  Z1 (upper entry) = lower
+quad; Z2 (lower entry) = upper quad.  Since both quads are fed on the lower
+element, some differentials in values are normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2
+14.0      9.3        7.7      69         57.2-39.2
+                                         56.8-39.7
+14.175    9.4       18.5      73        109.5+ 6.9
+                                        106.9+ 6.5
+14.35     8.9       14.5      76        156.0- 0.1
+                                        153.3+ 3.1
+
+18.118    10.1      19.8      74         71.3- 0.7
+                                         71.1- 0.4
+
+21.0      10.6      12.6      71         34.9-39.9
+                                         34.9-40.0
+21.225    10.4      17.8      75         59.6- 1.7
+                                         59.6- 1.6
+21.45     9.9       10.5      77         85.7+17.4
+                                         85.7+17.5
+
+24.94     10.7      23.0      74         43.5- 2.6
+                                         43.5- 2.6
+
+28.0      11.1      15.0      72         31.4-62.3
+                                         31.4-62.4
+28.5      10.9      18.4      75         41.7- 1.8
+                                         41.7- 1.8
+29        10.7      13.3      76         53.2+51.9
+                                         53.3+51.9
+ 
Stacking Gain averaged by bands:
+20        17        15        12        10
+2.1       2.8       3.2       3.3       3.4  dB
+ 
2 0.125-WL Spider Quads stacked 30' apart in 50' and 80' above average ground:  Z1
+(upper entry) = lower quad; Z2 (lower entry) = upper quad.  Since both
+quads are fed on the lower element, some differentials in values are
+normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     TO
+14.0      13.9       8.0      70         56.8-39.4     14
+                                         57.1-39.3
+14.175    14.0      19.2      73        106.7+ 6.5     14
+                                        109.1+ 7.1
+14.35     13.5      14.0      76        153.1+ 3.8     13
+                                        155.6+ 0.0
+
+18.118    14.9      20.0      74         70.9+ 0.3     11
+                                         71.1- 1.2
+
+21.0      15.5      12.6      71         35.2-39.7      9
+                                         34.5-39.9
+21.225    15.3      17.5      76         60.9- 1.2      9
+                                         58.6- 0.9
+21.45     14.8      10.4      78         87.7+16.6      9
+                                         85.5+19.7
+
+24.94     15.7      22.6      75         42.9- 3.4      8
+                                         44.2- 3.4
+
+28.0      16.2      14.7      72         31.1-62.0      7
+                                         31.0-62.1
+28.5      16.0      18.0      75         41.3- 1.0      7
+                                         41.4- 1.3
+29        15.8      13.1      77         52.2+53.1      7
+                                         53.4+52.6
+

The changes created by increasing the spacing are subtle. Increasing the height of the overall array by 6' changes the TO angle by only a fraction of a degree on any one band. If the change shows up in the chart, it is largely a function of rounding to the nearest degree. Gain is up, more on the lower bands than on the upper, but always under an average of a half dB. The front-to-back ratio appears to be down slightly--or the peak may have shifted in frequency so that it no longer coincides with the design frequency.

+

The chief merit of increasing the center-to-center spacing of the arrays to 30' shows up in the impedance column. First, the impedance values are closer to those for the single array in free space. Second, the differentials between upper and lower bay impedances are reduced. The latter effect is greater on the lowest bands but is evident to some degree on all bands. The benefit of this change from the more closely spaced stack is that once you have achieved the best arrangement for matching the main feedline to the drivers for an individual array, you can rely on that arrangement to satisfy the needs of the stack.

+

On paper, the added 6' of stacking space may seem little. However, it can make significant differences in bending forces on the stack mast. Whether it is wiser to shorten the stack and wrestle with the matching or to be assured of matching and increase the strength (and weight) of the mast is a stacker's decision.

+

Conclusion

+

I have been hesitant in the past to recommend stacking multi-band quads, given the fact that a quad is already a stack in itself. However, these figures suggest that--if one can handle the matching, the mechanicals, and the weather--the enterprise may prove worthy, even with relatively close spacing, as used in these models. The results--so far--suggest that planar designs may be the best behaved in a closely spaced stack in the sense of needing the least post-stacking adjustments.

+

There has been a predilection to overestimate the desirability (at least electrically) of the spider design because it provides each band with the same spacing in terms of wavelengths. However, as noted in Part 4, that intuition of benefit encompasses only part of what is going on with a 5-band 2-element quad. Element interaction plays a role in giving the planar design a degree of both stability from band to band and gain that is reduced as we move the elements from a single plane. Indeed, there are limits to this process, and these show up in 3-element designs and in efforts to add VHF frequencies to planar quads using the existing support arms. The mechanical differences in the schemes are, of course, beyond the scope of this modeling study.

+

As always, differences of design may yield different stacking results. As well, different stacking spacings may yield differences. The results also apply only to 5-band quads using separate ot switched feeds. Common feed system stacking results have not yet been explored. Every design should be thoroughly modeled before capital investment.

+
+ +
+

Updated 8-7-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Monoband Quads of More Than 2 Elements

+

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad, Stacking


+ + diff --git a/content/quad/quad5.html b/content/quad/quad5.html new file mode 100644 index 0000000..2102de9 --- /dev/null +++ b/content/quad/quad5.html @@ -0,0 +1,356 @@ + + + + + + Quad Models Part 5 Monoband Quads of More Than 2 Elements + + + +
+

Some Model Quads:
+ 5. Monoband Quads of More Than 2 Elements

+

L. B. Cebik, W4RNL

+
+
+ +
+

My stock of models of quad beams having more than 2 elements is limited to a few published designs, mostly by K2OB and W6SAI. I have played a bit with the 3-element monoband quad design, but I do not claim to have optimized it fully.

+

Nevertheless, some of the modeled properties of published designs may be instructive in terms of setting expectations for what a modeling program is likely to say about a design. As with the remainder of the models in this set, the modeling program is NEC-4, but there are no differences in NEC-2 outputs for the same designs. Except where specifically noted, the designs use #14 AWG copper wire. All are 20-meter models, the band of choice for K2OB, whose designs make up half of those to be examined. As in past episodes, the primary operational properties that we shall graph include free space gain (in dBi), 180-degree front-to-back ratio (in dB), and SWR (referenced as relevant to a fixed value, such as 50 Ohms or 75 Ohms, or to the resonant impedance of the antenna in question).

+

The K2OB designs apparently have been optimized for maximum gain, which does not occur at the same frequency as maximum front-to-back ratio. The W6SAI 3-element design has intentionally reduced gain and striven for broad-band operation. My own 3-element model has striven for a balance among feedpoint impedance, gain, and front-to-back ratio.

+

Since comparisons with Yagi designs are inevitable, I have included a 5- element Yagi design to compare with the 5-element quads. The comparison, of course, is only at the level of modeling and cannot comment upon any perceived operational phenomena that have no correlates in modeling.

+

Throughout, I have discarded any references to wire-cutting formulas. In their place, I have list in tabular form the dimensions of the models themselves. As we shall discover, wire diameter does play a role in the performance curves of a quad beam. Hence, direct scaling must include wire diameter as well as loop length--or else adjustments will be required in the loop length if a certain wire size is retained. Likewise, changing wire size within any given model will require readjustment of loop sizes to return the curves to their original positions on the graphs or performance for gain, front-to-back ratio, and swr.

+

3-Element Monoband Quads

The 3-element monoband quad is simply 3 quad loops so sized and arranged as to maximize gain, front-to-back ratio, or a certain feedpoint impedance--or some combination of 2 or 3 of these parameters. My stock of 3-element monoband quads for 20 meters includes a 24' boom design from K2OB, a 20' design from W6SAI, and a 24' model of my own devising. Interestingly, the loop sizes that I derived from tweaking the model turned out to be within an inch per side of those used by the W6SAI design. (Note: although W6SAI is normally used as a label for the design, the quad book is under dual authorship of W6SAI and W2LX. Hence, dual credit should be given to any design bearing the label "W6SAI" in these notes.) +
+ +
+

Fig. 53 provides an outline sketch of a typical monoband 3-element quad design. Essentially, only loop lengths and element spacing will change from design to design. Here is a table of the dimensions used in the models we shall compare.

+ 
          Reflector           Driver              Director
+Model     Side L    Space     Side L    Space     Side L
+           feet     Re-DE      feet     DE-Di      feet
+K2OB324   18.006    11        17.562    13        17.426
+3LQ2024   18.12     11        17.80     13        17.20
+Orr2012   18.12     10        17.80     10        17.20
+

Note that my own design (3LQ2024) uses the same boom length (24') and element spacing (11' and 13') as the K2OB design, but different loop lengths. The W6SAI design uses the same loop lengths as mine, but on a shorter (20') boom with equal element spacing (10' each). The Orr design specifies #12 wire, while the other models use #14.

+

For reference, here are EZNEC model descriptions for each of the designs.

+ 
K2OB 3el quad 11/13=24                       Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -9.003,  0.000, -9.003  W2E1   9.003,  0.000, -9.003    # 14   21
+2   W1E2   9.003,  0.000, -9.003  W3E1   9.003,  0.000,  9.003    # 14   21
+3   W2E2   9.003,  0.000,  9.003  W4E1  -9.003,  0.000,  9.003    # 14   21
+4   W3E2  -9.003,  0.000,  9.003  W1E1  -9.003,  0.000, -9.003    # 14   21
+5   W8E2  -8.781, 11.000, -8.781  W6E1   8.781, 11.000, -8.781    # 14   21
+6   W5E2   8.781, 11.000, -8.781  W7E1   8.781, 11.000,  8.781    # 14   21
+7   W6E2   8.781, 11.000,  8.781  W8E1  -8.781, 11.000,  8.781    # 14   21
+8   W7E2  -8.781, 11.000,  8.781  W5E1  -8.781, 11.000, -8.781    # 14   21
+9  W12E2  -8.713, 24.000, -8.713 W10E1   8.713, 24.000, -8.713    # 14   21
+10  W9E2   8.713, 24.000, -8.713 W11E1   8.713, 24.000,  8.713    # 14   21
+11 W10E2   8.713, 24.000,  8.713 W12E1  -8.713, 24.000,  8.713    # 14   21
+12 W11E2  -8.713, 24.000,  8.713  W9E1  -8.713, 24.000, -8.713    # 14   21
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+3el quad--Yagi Spacing--20m                  Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -9.060,  0.000, -9.060  W2E1   9.060,  0.000, -9.060    # 14   21
+2   W1E2   9.060,  0.000, -9.060  W3E1   9.060,  0.000,  9.060    # 14   21
+3   W2E2   9.060,  0.000,  9.060  W4E1  -9.060,  0.000,  9.060    # 14   21
+4   W3E2  -9.060,  0.000,  9.060  W1E1  -9.060,  0.000, -9.060    # 14   21
+5   W8E2  -8.900, 11.000, -8.900  W6E1   8.900, 11.000, -8.900    # 14   21
+6   W5E2   8.900, 11.000, -8.900  W7E1   8.900, 11.000,  8.900    # 14   21
+7   W6E2   8.900, 11.000,  8.900  W8E1  -8.900, 11.000,  8.900    # 14   21
+8   W7E2  -8.900, 11.000,  8.900  W5E1  -8.900, 11.000, -8.900    # 14   21
+9  W12E2  -8.600, 24.000, -8.600 W10E1   8.600, 24.000, -8.600    # 14   21
+10  W9E2   8.600, 24.000, -8.600 W11E1   8.600, 24.000,  8.600    # 14   21
+11 W10E2   8.600, 24.000,  8.600 W12E1  -8.600, 24.000,  8.600    # 14   21
+12 W11E2  -8.600, 24.000,  8.600  W9E1  -8.600, 24.000, -8.600    # 14   21
+
+             -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+Orr:  20 m: 3el                              Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -9.060,  0.000, -9.060  W2E1   9.060,  0.000, -9.060    # 12   21
+2   W1E2   9.060,  0.000, -9.060  W3E1   9.060,  0.000,  9.060    # 12   21
+3   W2E2   9.060,  0.000,  9.060  W4E1  -9.060,  0.000,  9.060    # 12   21
+4   W3E2  -9.060,  0.000,  9.060  W1E1  -9.060,  0.000, -9.060    # 12   21
+5   W8E2  -8.900, 10.000, -8.900  W6E1   8.900, 10.000, -8.900    # 12   21
+6   W5E2   8.900, 10.000, -8.900  W7E1   8.900, 10.000,  8.900    # 12   21
+7   W6E2   8.900, 10.000,  8.900  W8E1  -8.900, 10.000,  8.900    # 12   21
+8   W7E2  -8.900, 10.000,  8.900  W5E1  -8.900, 10.000, -8.900    # 12   21
+9  W12E2  -8.600, 20.000, -8.600 W10E1   8.600, 20.000, -8.600    # 12   21
+10  W9E2   8.600, 20.000, -8.600 W11E1   8.600, 20.000,  8.600    # 12   21
+11 W10E2   8.600, 20.000,  8.600 W12E1  -8.600, 20.000,  8.600    # 12   21
+12 W11E2  -8.600, 20.000,  8.600  W9E1  -8.600, 20.000, -8.600    # 12   21
+
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+ +
+

The gain curves across 20 meters for all three models appear in Fig. 54. The Orr and 3LQ designs show very parallel gain curves for their identical loop lengths. Hence, the gain difference is a measure of the shorter Orr boom and the different relative spacing of the elements.

+

The maximum gain for the K2OB model shows a peak at 14.245 MHz. The peak is roughly 0.3 dB higher than the gain of the 3LQ design at the same frequency--for the same boom length. However, the K2OB design shows a low-end fall-off. With judicious adjustment of the loop sizes, the gain curve might well be centered in the band so that it everywhere meets or exceeds the gain value of the 3LQ model on the same length boom.

+
+ +
+

The Orr quad exhibits a very smooth front-to-back ratio curve in Fig. 55. However, values never reach the 20 dB mark. The K2OB design shows a peak above 25 dB, but the band-edge performance is poor, especially at the low end of the band. In conjunction with the gain curve, it appears that the antenna has been designed for the high end of 20 meters and the overall performance can be moved downward in frequency.

+

The 3LQ design on a 24' boom shows a much higher peak front-to-back ratio and a higher average value across the band than the other two designs. Nonetheless, band-edge performance is well below 15 dB, and the range for a front-to-back ratio in excess of 20 dB is only about 150 kHz of this 350 kHz band. It would appear that considerable sacrifice in forward gain performance may be necessary to achieve a relatively smooth front-to-back performance approach 20 dB at the band edges.

+

How much gain can be sacrificed and still have a quad advantage over a Yagi of similar boom length is a difficult question to answer. In my collection of models, I have K6STI 20-meter Yagi designs for 3-element Yagis on 24' booms and 4-element Yagis on 26' booms. The 3-element Yagi shows a mid-band free space gain of about 8.1 dBi, while the 4-element design shows a gain of 8.5 dBi. The peak Orr design gain just exceeds 8.8 dBi, so there is little margin with which to play to increase its front-to-back performance. Despite seeming differences in the gain of the K2OB and the 3LQ designs, when adjusted for a minimal front-to-back performance of 20 dB, the result would be identical designs. With the 3LQ version registering a peak gain just above 9.1 dBi, it shows about a full dB gain over the 3-element Yagi on the same length boom. It might require about half that advantage to yield a significantly better front-to-back performance.

+
+ +
+

The SWR performance of the three designs relative to a 50-Ohm standard appears in Fig. 56. Neither the 3LQ nor the Orr design remains at under 2:1 SWR across 20 meters, although the Orr design comes closer to that goal. The K2OB design--intended for use with a matching circuit--shows the steepest curve of the 3 designs.

+ 
Antenna        Impedance at a Specified Frequency           Delta     Delta
+          14.0           14.175         14.35                 R         X
+K2OB      28.4 - j80.5   25.4 - j29.3   25.4 + j25.1         3.0      105.6
+Orr       34.4 - j37.4   42.4 + j 1.4   40.2 + j39.4         8.0       76.8
+3LQ       36.5 - j34.8   43.2 + j11.5   45.2 + j57.5         8.7       92.3
+

In all three models, the variation in the resistive component of the source impedance is small. We made a similar finding with respect to 2-element quads. Moreover, the pattern is variable, and as the Orr model shows, the peak resistive component may not occur at a band edge. However, the variation of reactance across the band is quite even and, comparatively speaking, very wide. Reducing this range to a more easily accommodated level is no small task indeed. At a basic design level, leaving the reduction to the masking effect of matching circuit losses or to cable losses is no solution at all, even if the process has practical advantages.

+

5-Element Monoband Quads (and a Yagi)

My small collection of 5-element monoband quads consist of K2OB designs for 20 meters. We shall look at two versions, one for 40' boom, the other for an 80' boom. In both cases, the reflector is spaced 10' from the driven element. The shorter boom uses uniform 10' element spacing throughout. The spacing from the driven element to the first director and between the remaining directors in the 80' boom model is 23.3'. Fig. 57 shows the outline of a 5-element monoband quad array. +
+ +
+

Since K2OB specifies the same dimensions for #16 through #12 AWG wire, #14 copper is used in the models. With the spacing already specified, we need tabulate only the loops sizes, expressed in terms of the length of each side, which are used for both versions of the antenna.

+ 
Reflector       Driver        Director 1     Director 2     Director 3
+ 17.786'        17.458'        17.356'        17.332'        17.332'
+

For reference, here is an EZNEC model description of the 80' boom model. To revise it for a 40' boom, make changes only to the Y-axis values for the directors.

+ 
5-el quad: K2OB 80'                            Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -8.938,  0.000, -8.938  W2E1   8.938,  0.000, -8.938    # 14   21
+2   W1E2   8.938,  0.000, -8.938  W3E1   8.938,  0.000,  8.938    # 14   21
+3   W2E2   8.938,  0.000,  8.938  W4E1  -8.938,  0.000,  8.938    # 14   21
+4   W3E2  -8.938,  0.000,  8.938  W1E1  -8.938,  0.000, -8.938    # 14   21
+5   W8E2  -8.729, 10.000, -8.729  W6E1   8.729, 10.000, -8.729    # 14   21
+6   W5E2   8.729, 10.000, -8.729  W7E1   8.729, 10.000,  8.729    # 14   21
+7   W6E2   8.729, 10.000,  8.729  W8E1  -8.729, 10.000,  8.729    # 14   21
+8   W7E2  -8.729, 10.000,  8.729  W5E1  -8.729, 10.000, -8.729    # 14   21
+9  W12E2  -8.678, 33.300, -8.678 W10E1   8.678, 33.300, -8.678    # 14   21
+10  W9E2   8.678, 33.300, -8.678 W11E1   8.678, 33.300,  8.678    # 14   21
+11 W10E2   8.678, 33.300,  8.678 W12E1  -8.678, 33.300,  8.678    # 14   21
+12 W11E2  -8.678, 33.300,  8.678  W9E1  -8.678, 33.300, -8.678    # 14   21
+13 W16E2  -8.666, 56.600, -8.666 W14E1   8.666, 56.600, -8.666    # 14   21
+14 W13E2   8.666, 56.600, -8.666 W15E1   8.666, 56.600,  8.666    # 14   21
+15 W14E2   8.666, 56.600,  8.666 W16E1  -8.666, 56.600,  8.666    # 14   21
+16 W15E2  -8.666, 56.600,  8.666 W13E1  -8.666, 56.600, -8.666    # 14   21
+17 W20E2  -8.666, 79.900, -8.666 W18E1   8.666, 79.900, -8.666    # 14   21
+18 W17E2   8.666, 79.900, -8.666 W19E1   8.666, 79.900,  8.666    # 14   21
+19 W18E2   8.666, 79.900,  8.666 W20E1  -8.666, 79.900,  8.666    # 14   21
+20 W19E2  -8.666, 79.900,  8.666 W17E1  -8.666, 79.900, -8.666    # 14   21
+
+               -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+

The 5-element quad makes a fairly large model if we use plenty of segments per side to ensure convergence. However, it runs rapidly on a current generation computer (300 MHz or higher speed CPU).

+

Because the comparison will be inevitable, we might as well take it on from the beginning. How well does a 5-element quad model do against a 5-element Yagi model? Note that I have expressed the question in terms of modeled performance, not in terms of on-the-air performance. Since we shall restrict our inquiry to what NEC-4 modeling reports, we should not pretend that the answers are perfectly general.

+

The Yagi selected is a 5-element 45' boom model based on a design by W6NGZ. Further modeling studies of this and other long-boom 20-meter Yagis appears in another set of notes in this collection. (See Six Long-Boom Yagis.) The 45' boom length is the shortest of the collection and closest to the 40' K2OB model size. For reference, here is the model description of the W6NGZ Yagi.

+ 
5L45' W6NGZ CQ 10-96 p 22                      Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -215.60,  0.000,  0.000  W2E1 -156.00,  0.000,  0.000 6.25E-01   5
+2   W1E2 -156.00,  0.000,  0.000  W3E1 -120.00,  0.000,  0.000 7.50E-01   3
+3   W2E2 -120.00,  0.000,  0.000  W4E1 -72.000,  0.000,  0.000 8.75E-01   4
+4   W3E2 -72.000,  0.000,  0.000  W5E1  72.000,  0.000,  0.000 1.00E+00  13
+5   W4E2  72.000,  0.000,  0.000  W6E1 120.000,  0.000,  0.000 8.75E-01   4
+6   W5E2 120.000,  0.000,  0.000  W7E1 156.000,  0.000,  0.000 7.50E-01   3
+7   W6E2 156.000,  0.000,  0.000       215.605,  0.000,  0.000 6.25E-01   5
+8        -205.95, 79.800,  0.000  W9E1 -156.00, 79.800,  0.000 6.25E-01   4
+9   W8E2 -156.00, 79.800,  0.000 W10E1 -120.00, 79.800,  0.000 7.50E-01   3
+10  W9E2 -120.00, 79.800,  0.000 W11E1 -72.000, 79.800,  0.000 8.75E-01   4
+11 W10E2 -72.000, 79.800,  0.000 W12E1  72.000, 79.800,  0.000 1.00E+00  13
+12 W11E2  72.000, 79.800,  0.000 W13E1 120.000, 79.800,  0.000 8.75E-01   4
+13 W12E2 120.000, 79.800,  0.000 W14E1 156.000, 79.800,  0.000 7.50E-01   3
+14 W13E2 156.000, 79.800,  0.000       205.950, 79.800,  0.000 6.25E-01   4
+15       -198.21,155.160,  0.000 W16E1 -156.00,155.160,  0.000 6.25E-01   4
+16 W15E2 -156.00,155.160,  0.000 W17E1 -120.00,155.160,  0.000 7.50E-01   3
+17 W16E2 -120.00,155.160,  0.000 W18E1 -72.000,155.160,  0.000 8.75E-01   4
+18 W17E2 -72.000,155.160,  0.000 W19E1  72.000,155.160,  0.000 1.00E+00  13
+19 W18E2  72.000,155.160,  0.000 W20E1 120.000,155.160,  0.000 8.75E-01   4
+20 W19E2 120.000,155.160,  0.000 W21E1 156.000,155.160,  0.000 7.50E-01   3
+21 W20E2 156.000,155.160,  0.000       198.209,155.160,  0.000 6.25E-01   4
+22       -196.55,337.920,  0.000 W23E1 -156.00,337.920,  0.000 6.25E-01   3
+23 W22E2 -156.00,337.920,  0.000 W24E1 -120.00,337.920,  0.000 7.50E-01   3
+24 W23E2 -120.00,337.920,  0.000 W25E1 -72.000,337.920,  0.000 8.75E-01   4
+25 W24E2 -72.000,337.920,  0.000 W26E1  72.000,337.920,  0.000 1.00E+00  13
+26 W25E2  72.000,337.920,  0.000 W27E1 120.000,337.920,  0.000 8.75E-01   4
+27 W26E2 120.000,337.920,  0.000 W28E1 156.000,337.920,  0.000 7.50E-01   3
+28 W27E2 156.000,337.920,  0.000       196.548,337.920,  0.000 6.25E-01   3
+29       -189.90,530.400,  0.000 W30E1 -156.00,530.400,  0.000 6.25E-01   3
+30 W29E2 -156.00,530.400,  0.000 W31E1 -120.00,530.400,  0.000 7.50E-01   3
+31 W30E2 -120.00,530.400,  0.000 W32E1 -72.000,530.400,  0.000 8.75E-01   4
+32 W31E2 -72.000,530.400,  0.000 W33E1  72.000,530.400,  0.000 1.00E+00  13
+33 W32E2  72.000,530.400,  0.000 W34E1 120.000,530.400,  0.000 8.75E-01   3
+34 W33E2 120.000,530.400,  0.000 W35E1 156.000,530.400,  0.000 7.50E-01   3
+35 W34E2 156.000,530.400,  0.000       189.900,530.400,  0.000 6.25E-01   4
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           7    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+

The Yagi model uses an extensive element diameter taper schedule, resulting in many model wires. The segment lengths have been kept as equal as possible throughout the model. The material is aluminum in diameters ranging from 1" down to 0.625". All of the models, both quad and Yagi, are in free space, with gain values in dBi.

+
+ +
+

The gain curves in Fig. 58 show different design goals for the two antenna types. The Yagi has been optimized for roughly the same gain across the 20-meter band, while the quads have been designed to achieve maximum gain. The 80' boom model shows a maximum gain of about 12 dBi peak, but falls below the Yagi level at the low end of the band. The 40' version of the antenna peaks just above the Yagi level, but falls 2 dB below the Yagi at the low end of the band.

+
+ +
+

The modeled front-to-back performance of the quads is significantly below the level achieve by the Yagi anywhere within the 20-meter band, as demonstrated in Fig. 59. Although the 80' boom model peaks at 30 dB, the band-edge performance is below 10 dB. The low-level but rising curve of the 40' boom quad suggests that additional work needs to be done to optimize the model by bringing the front-to-back curve within the band.

+
+ +
+

Only the 50-Ohm SWR curve for the Yagi is shown in Fig. 60. It achieves under 2:1 SWR across the entire 20-meter band. However, some of the other Yagi models in the long-boom collection achieve even better figures.

+

The quad-model source impedances are not amenable to graphing because of their wide variation, especially of the reactive component. The following table demonstrates the difficulty.

+ 
Antenna        Impedance at a Specified Frequency           Delta     Delta
+          14.0           14.175         14.35                 R         X
+80' quad  31.9 - j99.6   25.5 - j47.3   15.6 + j26.6        16.3      126.2
+40' quad  25.6 - j98.0   35.2 - j52.7   26.6 - j20.0         9.6       78.0
+45' Yagi  32.0 - j11.4   33.7 - j 2.3   35.9 - j 7.4         3.9        9.1
+

The ranges of both the resistive and reactive components of the Yagi source impedance are very small indeed, leading to a very stable matching situation. Likewise, the resistive components of the quad source impedances are also quite manageable. However, the quads exhibit (like their 3-element kin) wide swings of reactance across the 20-meter band, leading to very steep SWR curves, whatever the reference impedance value.

+
+ +
+

The relative performance at mid-band for the three antennas can be represented partially by overlaying free-space azimuth patterns, as done in Fig. 61. The superior gain of the 80' boom quad is clearly apparent, as is the relatively insignificant different in gain and horizontal beamwidth of the shorter quad and the Yagi. The Yagi's superior front-to-back performance is also clear.

+

One question bound to arise is why the quads do not exceed the Yagi by much greater margins, since they have been designed for maximum gain. Orr and Cowan, for example, give the quad loop a 1.4 dB advantage over a dipole--an advantage that should be reflected in the models, but is not. The answer to "why" is "wire."

+

Quad Element Diameter

Although quad enthusiasts are fond of providing loop length formulas that disregard wire size, we should not be too hasty in doing so. NEC takes the effects of the wire diameter into account in calculating the operating parameters of an antenna. Let's return to the 3-element K2OB design just because it shows such pronounced peaks in performance. We may run the very same model using #16 AWG wire at one extreme and #12 AWG wire at the other, both copper. #16 AWG wire is 0.0508" in diameter; #12 is 0.0808" in diameter; and the #14 used in most of the models is 0.0641" in diameter. The diameter ratio of #12 to #16 is about 1.6:1 +
+ +
+

Fig. 62 shows the free space gain of the two wire models. Of first note is the movement of the peak gain frequency by about 70 kHz, with the thinner wire showing the lower peak frequency. W4MB makes note in his book of the fact that for closed geometries, increasing the wire diameter also increases the resonant frequency of a loop. It also raises the frequency of peak gain for a multi-element quad. (We shall look into the gain differential in a moment.)

+
+ +
+

As Fig. 63 reveals, increasing the loop wire diameter also increases the frequency of peak front-to-back performance, in this case by about 35 kHz. In short, the operating center design frequency of the entire antenna is increased with each incremental increase in wire diameter.

+

Not only does the antenna operating frequency change with wire diameter, but as well the gain changes. More correctly expressed, the losses increase noticeably with a decrease in wire diameter. Whenever wire diameter makes a significant difference in performance parameters, we must also look at the difference made by the selection of materials for the elements, since the loss differential between, say, copper and aluminum may also make a difference in antenna performance.

+

To get a feel for what is involved, let's make a series of comparisons, first between 10-meter dipoles of radically different diameters. Despite the large difference in diameter, both size materials are used for different antennas. The test frequency is 28.5 MHz.

+ 
Diameter  Length    Material       Free Space     Source Impedance
+ inches    feet                    Gain dBi       R +/- jX Ohms
+ 1        16.32     Zero-loss      2.13           71.7 - j 0.6
+                    Copper         2.13           71.7 - j 0.5
+                    Aluminum       2.13           71.7 - j 0.5
+
+ 0.0641   16.67     Zero-loss      2.14           71.9 - j 1.1
+                    Copper         2.09           72.6 - j 0.4
+                    Aluminum       2.05           73.0 - j 0.1
+

Operationally, the differences are not significant. However, here we want to notice trends. Once the wire diameter reaches a certain region--and 1" is within that region--the difference in efficiency among materials becomes insignificant. However, when the diameter is smaller, differences in material losses can become more readily apparent, as in the case of the #14 10-meter dipole. Not only does the gain vary, but as well the source impedance varies to reflect the added losses in less conductive materials.

+

Typically, HF quads are constructed of wire, which has a small diameter that shows the effects of material losses. Here is the same data for a single 10-meter quad loop for the three materials.

+ 
Diameter  Length    Material       Free Space     Source Impedance
+ inches    feet                    Gain dBi       R +/- jX Ohms
+ 0.0641    9.13     Zero-loss      3.30           125.3 - j 0.7
+           per      Copper         3.24           127.0 + j 0.8
+           side     Aluminum       3.22           127.8 + j 1.5
+

For equal diameters and materials, the gain difference between a square quad loop and a dipole, when both are resonant, is about 1.15 dB in NEC model reckoning. However, the wire loop loses another increment of gain advantage when it competes with a 1" diameter dipole, even if the quad wire is copper and the dipole is aluminum. In multi-element arrays, these small increments add up quickly.

+

Let's do another comparison, this time between models of a 3-element quad beam and a 3-element Yagi. The quad is #14 AWG copper wire, while the Yagi is 1" aluminum. These models happen to be 14.175 MHz versions.

+ 
Antenna        Material       Free Space     F-B       Source Impedance
+                              Gain dBi       dB        R +/- jX Ohms
+3-el. Yagi     Zero-loss      8.14           27.5       25.6 - j 1.1
+               Copper         8.12           27.4       25.7 - j 1.0
+               Aluminum       8.11           27.3       25.7 - j 0.9
+3-el. Quad     Zero-loss      9.49           25.3       40.3 + j 9.3
+               Copper         9.13           28.5       43.2 + j11.5
+               Aluminum       8.95           30.3       44.6 + j12.6
+

The gain change for the wire quad throughout the span of materials from lossless wire to aluminum is 18 times that of the 1" Yagi. Likewise, the other performance parameters in the wire quad change by significantly greater amounts as the materials are changed.

+

The upshot of these modeling comparisons is very basic: as long as quads (or other arrays) use thin wire with real losses, their performance will not achieve the theoretical maximum possible for any given design. In contrast, antennas using elements of appreciable diameter will tend to more closely approach theoretically achievable results, even with materials as lossy as aluminum. The differences between thin and fat wire versions of the same antenna can be significant.

+

Consider the 3-element quad array designated 3LQ2024, a 20-meter 3-element quad using #14 AWG copper wire. Now let us increase only the diameter of the driven element to 0.5" while leaving it copper. This effective diameter might be simulated by using a double wire driver with a spacing between wires of 1" or more. To reresonate the antenna requires an increase in the driver length per side of about 0.1 foot. For reference, here is the model description.

+ 
3el quad--Yagi Spacing--20m                  Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -9.060,  0.000, -9.060  W2E1   9.060,  0.000, -9.060    # 14   21
+2   W1E2   9.060,  0.000, -9.060  W3E1   9.060,  0.000,  9.060    # 14   21
+3   W2E2   9.060,  0.000,  9.060  W4E1  -9.060,  0.000,  9.060    # 14   21
+4   W3E2  -9.060,  0.000,  9.060  W1E1  -9.060,  0.000, -9.060    # 14   21
+5   W8E2  -8.950, 11.000, -8.950  W6E1   8.950, 11.000, -8.950 5.00E-01  21
+6   W5E2   8.950, 11.000, -8.950  W7E1   8.950, 11.000,  8.950 5.00E-01  21
+7   W6E2   8.950, 11.000,  8.950  W8E1  -8.950, 11.000,  8.950 5.00E-01  21
+8   W7E2  -8.950, 11.000,  8.950  W5E1  -8.950, 11.000, -8.950 5.00E-01  21
+9  W12E2  -8.600, 24.000, -8.600 W10E1   8.600, 24.000, -8.600    # 14   21
+10  W9E2   8.600, 24.000, -8.600 W11E1   8.600, 24.000,  8.600    # 14   21
+11 W10E2   8.600, 24.000,  8.600 W12E1  -8.600, 24.000,  8.600    # 14   21
+12 W11E2  -8.600, 24.000,  8.600  W9E1  -8.600, 24.000, -8.600    # 14   21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+

Let's see how the models compare. The #14 wire model is designated 3LQ2024 and the 0.5" model is labeled 3LQ20245.

+
+ +
+

Fig. 64 compares the gain curves for the two models, which are identical except for the driver wire diameter and the small adjustment in length to recenter the curves. The difference is about 0.25 dB. The amount may not be operationally significant, but it is illustrative of the advantage of larger diameter elements.

+
+ +
+

In Fig. 65, we see that the front-to-back performance of the antennas does not change with the change in driver diameter. However, if the reflector and the director on this model were also increased in diameter, then all of the elements would have to be reoptimized to place the performance curves in the same relative positions in the 20-meter band.

+
+ +
+

The 50-Ohm SWR curves in Fig. 66 show a further advantage of the large diameter driven element. The SWR curve for the 0.5" driver model is flatter by far than that of the thin-wire model. Although the curve does not cover all of 20 meters with an SWR below 2:1, the improvement over the thin-wire version of the antenna is apparent, despite the fact that the fat driver shows a lower resonant source impedance (about 41 Ohms).

+

The purpose of these comparisons is not to promote any changes in quad construction. Rather, it is to explain why and to what degree wire diameter and material play a role in quad design and performance potential, as reported by NEC-4 models. Understanding what limits the performance of an antenna type may be as important as understanding what makes it work as well as it does.

+

This foray into larger monoband quad models is necessarily incomplete. We have looked at very few samples, and those samples show only a couple of the many design biases one might use in developing a large quad array. Nevertheless, the exercise may be accounted useful if we have acquired an appreciation for both the potentials and the limitations of this class of large parasitic antenna.

+
+ +
+

Updated 2-26-99, 2-19-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Further Notes on 3-Element Quads

+

Go to Larger Multi-Band Quads

+

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad5a.html b/content/quad/quad5a.html new file mode 100644 index 0000000..bd7415a --- /dev/null +++ b/content/quad/quad5a.html @@ -0,0 +1,98 @@ + + + + + + Quad Models Part 5a Further Notes on 3-Element Quads + + + +
+

Some Model Quads:
+ 5a. Further Notes on 3-Element Quads

+

L. B. Cebik, W4RNL

+
+
+ +
+

In the set of notes on multi-element monoband quads, we examined 3 different models of 3-element quad beams. The basic outlines of such a beam appear in Fig. 1.

+
+ +
+

The main difference among the quads was the boom length and spacing. For a refresher, here are the dimensions of the quads examined.

+ 
Model     Side L    Space     Side L    Space     Side L
+           feet     Re-DE      feet     DE-Di      feet
+K2OB324   18.006    11        17.562    13        17.426
+3LQ2024   18.12     11        17.80     13        17.20
+Orr2012   18.12     10        17.80     10        17.20
+

Note that my own design (3LQ2024) uses the same boom length (24') and element spacing (11' and 13') as the K2OB design, but different loop lengths. The W6SAI design uses the same loop lengths as mine, but on a shorter (20') boom with equal element spacing (10' each). The Orr design specifies #12 wire, while the other models use #14.

+

The Orr design exhibited the lowest gain on its short boom, while the K2OB design showed the highest peak gain--but only over a small operating bandwidth. Only the Orr design showed a feedpoint impedance close to 50 Ohms: the other two designs showed much lower impedances ranging from 25 to 40 Ohms. Interestingly, as the performance extracted from the quad increased at the design frequency, the operating and SWR bandwidths decreased.

+

There are some indicators of quad performance within these models that are worth pursuing a little further. So after we look at a 3-element Yagi as a comparator, we shall examine a 3-element quad that has been optimized beyond the limits set in the initial discussion.

+

A 3-Element Yagi

In the course of discussing the 3 models, I referred to a K6STI-designed Yagi for 20 meters with a free-space gain of just over 8.1 dBi at the design frequency (14.175 MHz). Perhaps we can better grasp a set of reasonable expectations by taking a longer look at a model of this design. The antenna uses 1" uniform-diameter aluminum elements. The description appears in Fig. 2. +
+ +
+

Ignore any dimension numbers past the third decimal place (or second), since everything is in inches. The excess specificity results from deriving the design from a set of simple equations, and eliminating the spurious decimal places from the spreadsheet calculations would be unproductive time.

+

In relationship to our upcoming quad examination, the SWR curve of the beam (relative to its design frequency resonant feedpoint impedance of 26.26 Ohms) is especially interesting.

+
+ +
+

As shown in Fig. 3, the Yagi can be matched so as to operate over the entire 20-meter ham band with less than a 2:1 SWR ratio. How we arrive at this condition is shown partially by Fig. 4.

+
+ +
+

The total difference across the band in the resistive component of the feedpoint impedance is just over 4 Ohms. The reactance passes through a range of 26.3 Ohms. These are fairly small numbers when it comes to a bandwidth of nearly 2.5% of the center frequency.

+

The Yagi free-space gain shows a steady (nearly linear) increase across the band from 7.95 dBi at 14.0 MHz to 8.36 dBi at 14.35 MHz. The design maximizes the front-to-back ratio near the 14.175 MHz design frequency. The actual peak is about 28.2 dB just below the design frequency. At the risk of operating bandwidth, the resonant frequency and the front-to-back peak frequencies can be moved to other points within the passband for the antenna.

+

Although this design should be classified as a high-performance 3-element Yagi for its 22.5' boom and the number of elements, the general properties of the antenna are similar to those of other 3-element designs. They have come to form--rightly or not--the sorts of expectations we have of 3-element parasitic beams of all sorts, including quads.

+

Setting Up a Better 3-Element Quad Design

In trying to optimize a 3-element quad for the same design frequency, several considerations from the main discussion came to mind. Foremost is the relative inefficiency of quad construction methods. The small diameter wire used in most quads (#12-#14 AWG) limits the efficiency of the antenna due to the small surface area available on each element. Therefore, the new design would use larger elements. 1" diameter elements seemed an appropriate size for comparison with the Yagi just described. However, such large elements are not usually realistic for practical quad construction. +

On one level, we might argue that since only a model of a quad is at stake, the element size need not be realistic. We need not resort to such an argument, since this element diameter can be simulated with pairs of wires for each elements spaced a distance that yields for each of the loops the same overall resonant length. Most monoband quad frames can easily support 2 wires per spoke. In test models, there is negligible difference between the 2-wire simulation and the single fat element in terms of performance and efficiency. The numbers will not be absolutely identical, since the surface area of the two wires still does not equal the surface area of the single fat element. However, gain, front-to-back, and impedance numbers generally coincide to the first decimal place, as does the operating bandwidth of the resulting beam. Hence, the use of 1" elements in the design exercise is, in fact, practical--even if rarely used in actual quad building.

+

A second factor in the new design involves element spacing. Quad designs have long languished under two influences which have limited their performance. One is the desire for a near-50-Ohm feedpoint impedance. Effective design dictates that we let go of that goal and see what feedpoint impedance emerges if we optimize the other performance characteristics. Obviously, we can design so as to let the feedpoint impedance get too low. However, if a usable front-to-back ratio of about 20 dB is part of the design parameter set, then early indications are that a value in the mid-20s will emerge. This value, in fact, parallels the feedpoint impedance of good Yagi designs that also include a 20-dB front-to-back ratio requirement.

+

The other limiting factor is the traditional but non-rational urge to use a short boom and equal spacing between all elements. Although these design features have yielded quads with a convenient feedpoint impedance, the designs have not lived up to the so-called theoretical gain advantage of a quad over a similar Yagi of about 1.8 to 1.9 dB.

+

In redesigning the 3-element quad, one might start with new spacings at random and hope that some optimization program might catch a pair of magic distances. However, we need not resort to such measures, since we already have a large collection of parasitic beams with well-established element spacings for good performance. In fact, I took the Yagi we just described as the baseline for a fat-element quad. In the end, I enlarged the reflector-to-driver spacing by an inch and the overall boom length by 30 inches. This occurred in the process of determining the optimum loop circumference for each element in the beam.

+

A Somewhat Better 3-Element Quad

The redesign of the 3-element quad with 1" (or 1"-equivalent) elements resulted in the model description shown in Fig. 5. +
+ +
+

Once more, the design is equation driven, so the numbers in each dimension box are spreadsheet calculations, and not an attempt to be spuriously precise. Round them as you please. The real question is what I got for my pains.

+

At the design frequency of 14.175 MHz, the free-space gain is 9.97 dBi. This represents a gain of 1.84 dB over the Yagi. However, remember that the Yagi is 30" shorter than the 25' long quad. Nevertheless, the Yagi efficiency is about 99.5%, while the use of fat elements has raised to quad efficiency to 98.8%. The remaining difference owes to the fact that the quad elements are twice as long as those of the Yagi, and each increment of that extra length as a certain resistivity.

+

The 180-degree front-to-back ratio of the quad is just over 24 dB at the design frequency, with the quartering rear lobes yielding a worst-case value of 21.5 dB. The feedpoint impedance is just over 26 Ohms.

+

Despite these promising results, there are limitations to the design. Whoever first called a quad beam a wide-band device must have had only low-gain version in mind. As we saw in the K2OB designs, a quad optimized so far as possible to achieve its theoretic advantage over a Yagi has a narrower operating bandwidth, both in terms of SWR and in terms of performance specifications.

+

The present design is no exception. The VSWR curve, centered on the resonant impedance at the design frequency of 14.175 MHz, appears in Fig. 6.

+
+ +
+

Why the curve is so steep becomes evident when we look at the resistance and reactance curves, shown in Fig. 7.

+
+ +
+

Although the resistive component varies by only 3.8 Ohms (similar to the Yagi variation of 4 Ohms), the reactance varies by over 70 Ohms (in contrast to the 26-Ohm variation of the Yagi). The result is a 2:1 VSWR bandwidth of only about 175 kHz within the 20-meter band. There is little that most matching systems can do to widen the operating bandwidth without introducing a set of losses. This design, at least (but in common with the K2OB design), suggests that a high gain quad may indeed be more narrow-banded than a comparable Yagi design of similar proportions.

+

Both the Yagi and the quad have well-behaved azimuth patterns, as shown in the overlay of Fig. 8.

+
+ +
+

By well-behaved, I mean that neither design shows any incipient or real forward lobes other than the main lobe. Many VHF and interlaced HF Yagi designs show secondary forward lobes on each side of the main lobe, but these are absent in these two designs. Moreover the rear quadrants show only the usual set of three lobes.

+

The quad quartering rear lobes are larger than those of the Yagi. This fact suggests that further optimization of the quad design may be possible--perhaps through the use of a generalized optimization routine using both incremental and genetic techniques in combination. As I noted, the present design has been further optimized relative to those in the main discussion, but I did not say that it was finally or ultimately optimized.

+
+ +
+

Fig. 9 compares the gain curves of the Yagi and the quad beams. As we noted earlier, the gain figures for the Yagi continues to increase nearly linearly across the band. However, the quad shows a distinct gain peak between 14.25 and 14.30 MHz. In most 3-element Yagi designs, it is not possible to combine peak front-to-back ratio values and peak gain values within a single HF ham band. However, the quad design (as well as the K2OB design in the main discussion) appears to make the in-band gain peak a more normal feature of a 3-element quad beam.

+
+ +
+

In Fig. 10, we can observe the 180-degree front-to-back curves for the two antenna types. The Yagi front-to-back peak occurs just below the design frequency. However, the quad peak is just above the design frequency. We have some freedom to move the front-to-back peak, but not unlimited freedom. If we move it too close to one or the other of the band edges, the operating bandwidth for either or both the gain and the feedpoint impedance can become very narrow--or we lose a significant part of the gain. (There are other antenna types--for example, the Moxon Rectangle-- where the SWR and the front-to-back curves are quite non-symmetrical, changing more rapidly on one side of the design frequency than the other. In such cases, we may intentionally choose a design frequency that will tend to provide as close as possible to equal values at the band edges instead of optimizing for a band-center frequency.)

+

Although the gain of the 3-element quad design is quite consistent across the band, the front-to-back values do not follow suit. The Yagi hits a low of 17.5 dB, while the quad shows a low of about 13 dB--at opposite ends of the band. In this connection, also note that the Yagi shows a decrease of feedpoint resistance with increasing frequency, but the quad shows an increase of feedpoint resistance as the frequency increases.

+

Conclusions (Tentative)

+

As a narrow-band beam, then, the 3-element quad approaches more closely than other designs I have so far seen the theoretical advantage over a comparable Yagi. (The Yagi still has better wide-band characteristics--and the Yagi design shown here is usually classified as a high-gain, narrow- band design.) The use of fat elements--real or simulated by multiple wires per element--and more typical parasitic element spacing produced a beam with higher efficiency and more gain, while retaining within its limited passband a good front-to-back ratio and a matchable feedpoint impedance.

+

However, the quad beam also revealed some ways in which its behavior is unlike that of a Yagi. The gain and resistance curves show distinctly non-Yagi behaviors. Moreover, designing a quad on the basis of Yagi parasitic element spacing yield an inherently narrow-band design.

+

It remains an open question whether or not it is possible to optimize a 3- element quad so that it exhibits high gain (for an antenna of its type) and broad bandwidth, while retaining the usual standard of a good front-to-back ratio (20 dB) and a usable feedpoint impedance (25 Ohms or more). Unless someone already has such a design in his/her pocket, it is likely that we shall not know until the 3-element quad has been run through optimizing routines as many times as Yagis have.

+

At most this note is a step in that direction. If it has done anything useful, then perhaps it is to have elicited some of the further properties of 3-element quads that may play a role in the "ultimate" design.
+

+
+ +
+

Go to Larger Multi-Band Quads

+

Return to Quad Model Index

+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad6.html b/content/quad/quad6.html new file mode 100644 index 0000000..d46d5fa --- /dev/null +++ b/content/quad/quad6.html @@ -0,0 +1,482 @@ + + + + + + Quad Models Part 6 Larger Multi-Band Quads + + + +
+

Some Model Quads:
+ 6. Larger Multi-Band Quads

+

L. B. Cebik, W4RNL

+
+
+ +
+

My collection of larger (more than 2 elements) multi-band quads is fairly small, consisting of about 3.5 models. However, since one of them is of a 3.5 element 5-band quad, perhaps the score is even. Let's see how this works out.

+

First, I have modeled one of the multi-band quads from recent editions of the ARRL Antenna Book (page 2-12 in the 17th Edition). The antenna is a 4- element 3-band quad on a 40' boom. I count it as 1.5 models, since I have modeled is in both #14 and #12 AWG copper wire. The results, especially in light of my notes on wire size in monoband quads, are interesting.

+

Next, ON7NQ has shared a number of models with me in his efforts to improve the performance of a commercial 3-element 5-band quad on an 18' boom. One model of note simply adjusts the sizes of virtually all of the loops. A second model adds 2 new elements--new drivers for 10 and 12 meters--making approximately a 3.5 element quad--all on the same 18' boom.

+

In looking at these models, we should note a number of things. First and most obvious is the standard set of performance parameters that we have surveyed for all of the quads: free space gain in dBi, 180-degree front- to-back ratio in dB, and VSWR to some specified resistive impedance value. In addition to these matters, we may also wish to note how 3- and 4-element quads are similar to and differ from 2-element multi-band quads in various characteristics. Finally, we may also wish to record some factors related to boom length--at least so far as this small sample of models might suggest about the question.

+

As in all other cases, modeling has been done on NEC-4. The conventions of segmentation used in earlier multi-band quads are repeated here. For each side of a given quad loop, there are 7 segments on 10 meters, 9 segments on 12, 11 segments on 15, 13 segments on 17, and 15 segments on 20. Within practical limits, this scheme approaches the goal of having equal length segments throughout the model. Nonetheless, at least one model will have 724 segment distributed on 68 wires. Although NEC-2 will provide results as accurate as NEC-4 for these models, some implementations are limited to 500 segments and may prove less than fully adequate for the modeling task. MININEC results are also accurate if care is taken to ensure element length segment tapering at each corner of each loop. Without the use of symmetry or core enlargement, however, some of these models may be too large for some available versions of MININEC to handle.

+

As with past multi-band quads, only 20, 15, and 10 meters will undergo frequency sweeps. The 2 WARC bands (17 and 12) are so narrow that antenna performance characteristics do not significantly vary from their mid-band values. Each wide band will be divided into 10 equal segments. On 20, each segment is 0.35 MHz wide, on 15 each is 0.45 MHz wide, and on 10 each is 0.1 MHz wide. Hence, the graphs cover all of 20 and 10 meters and the first MHz of 10 meters.

+

4-Element 3-Band Quads

In recent editions of the ARRL Antenna Book, there is a 3-band, 4-element quad design attributed to W0AIW. It uses a 40' boom, with all elements (20 through 10 meters) equally spaced at 10' intervals. Fig. 67 provides an outline sketch of the antenna. +
+ +
+

The following table lists the element lengths per loop side for each of the three bands.

+ 
Band      Reflector           Driver              Dir. 1             Dir. 2
+          Side L    Space     Side L    Space     Side L    Space    Side L
+           feet     Re-DE      feet     DE-D1      feet     D1-D2     feet
+20        18.104    10        17.604    10        17.271    10       17.271
+15        12.167    10        11.833    10        11.583    10       11.583
+10         8.927    10         8.677    10         8.401    10        8.401
+

These loop lengths are very close to those used in one commercial quad using a shorter boom for a 3-element version. The change from band-to-band appears to be a matter of simple loop length scaling. The elements are shorter than the monoband loop lengths recommended in Orr and Cowan for 3- and 4-element quads. For reference, here is a model description.

+ 
arrl #14                                       Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2  -4.200, 20.000, -4.200  W2E1   4.200, 20.000, -4.200    # 14    7
+2   W1E2   4.200, 20.000, -4.200  W3E1   4.200, 20.000,  4.200    # 14    7
+3   W2E2   4.200, 20.000,  4.200  W4E1  -4.200, 20.000,  4.200    # 14    7
+4   W3E2  -4.200, 20.000,  4.200  W1E1  -4.200, 20.000, -4.200    # 14    7
+5   W8E2  -4.200, 10.000, -4.200  W6E1   4.200, 10.000, -4.200    # 14    7
+6   W5E2   4.200, 10.000, -4.200  W7E1   4.200, 10.000,  4.200    # 14    7
+7   W6E2   4.200, 10.000,  4.200  W8E1  -4.200, 10.000,  4.200    # 14    7
+8   W7E2  -4.200, 10.000,  4.200  W5E1  -4.200, 10.000, -4.200    # 14    7
+9  W12E2  -4.339,  0.000, -4.339 W10E1   4.339,  0.000, -4.339    # 14    7
+10  W9E2   4.339,  0.000, -4.339 W11E1   4.339,  0.000,  4.339    # 14    7
+11 W10E2   4.339,  0.000,  4.339 W12E1  -4.339,  0.000,  4.339    # 14    7
+12 W11E2  -4.339,  0.000,  4.339  W9E1  -4.339,  0.000, -4.339    # 14    7
+13 W16E2  -4.464,-10.000, -4.464 W14E1   4.464,-10.000, -4.464    # 14    7
+14 W13E2   4.464,-10.000, -4.464 W15E1   4.464,-10.000,  4.464    # 14    7
+15 W14E2   4.464,-10.000,  4.464 W16E1  -4.464,-10.000,  4.464    # 14    7
+16 W15E2  -4.464,-10.000,  4.464 W13E1  -4.464,-10.000, -4.464    # 14    7
+17 W20E2  -5.792, 20.000, -5.792 W18E1   5.792, 20.000, -5.792    # 14   11
+18 W17E2   5.792, 20.000, -5.792 W19E1   5.792, 20.000,  5.792    # 14   11
+19 W18E2   5.792, 20.000,  5.792 W20E1  -5.792, 20.000,  5.792    # 14   11
+20 W19E2  -5.792, 20.000,  5.792 W17E1  -5.792, 20.000, -5.792    # 14   11
+21 W24E2  -5.792, 10.000, -5.792 W22E1   5.792, 10.000, -5.792    # 14   11
+22 W21E2   5.792, 10.000, -5.792 W23E1   5.792, 10.000,  5.792    # 14   11
+23 W22E2   5.792, 10.000,  5.792 W24E1  -5.792, 10.000,  5.792    # 14   11
+24 W23E2  -5.792, 10.000,  5.792 W21E1  -5.792, 10.000, -5.792    # 14   11
+25 W28E2  -5.917,  0.000, -5.917 W26E1   5.917,  0.000, -5.917    # 14   11
+26 W25E2   5.917,  0.000, -5.917 W27E1   5.917,  0.000,  5.917    # 14   11
+27 W26E2   5.917,  0.000,  5.917 W28E1  -5.917,  0.000,  5.917    # 14   11
+28 W27E2  -5.917,  0.000,  5.917 W25E1  -5.917,  0.000, -5.917    # 14   11
+29 W32E2  -6.083,-10.000, -6.083 W30E1   6.083,-10.000, -6.083    # 14   11
+30 W29E2   6.083,-10.000, -6.083 W31E1   6.083,-10.000,  6.083    # 14   11
+31 W30E2   6.083,-10.000,  6.083 W32E1  -6.083,-10.000,  6.083    # 14   11
+32 W31E2  -6.083,-10.000,  6.083 W29E1  -6.083,-10.000, -6.083    # 14   11
+33 W36E2  -8.635, 20.000, -8.635 W34E1   8.635, 20.000, -8.635    # 14   15
+34 W33E2   8.635, 20.000, -8.635 W35E1   8.635, 20.000,  8.635    # 14   15
+35 W34E2   8.635, 20.000,  8.635 W36E1  -8.635, 20.000,  8.635    # 14   15
+36 W35E2  -8.635, 20.000,  8.635 W33E1  -8.635, 20.000, -8.635    # 14   15
+37 W40E2  -8.635, 10.000, -8.635 W38E1   8.635, 10.000, -8.635    # 14   15
+38 W37E2   8.635, 10.000, -8.635 W39E1   8.635, 10.000,  8.635    # 14   15
+39 W38E2   8.635, 10.000,  8.635 W40E1  -8.635, 10.000,  8.635    # 14   15
+40 W39E2  -8.635, 10.000,  8.635 W37E1  -8.635, 10.000, -8.635    # 14   15
+41 W44E2  -8.802,  0.000, -8.802 W42E1   8.802,  0.000, -8.802    # 14   15
+42 W41E2   8.802,  0.000, -8.802 W43E1   8.802,  0.000,  8.802    # 14   15
+43 W42E2   8.802,  0.000,  8.802 W44E1  -8.802,  0.000,  8.802    # 14   15
+44 W43E2  -8.802,  0.000,  8.802 W41E1  -8.802,  0.000, -8.802    # 14   15
+45 W48E2  -9.052,-10.000, -9.052 W46E1   9.052,-10.000, -9.052    # 14   15
+46 W45E2   9.052,-10.000, -9.052 W47E1   9.052,-10.000,  9.052    # 14   15
+47 W46E2   9.052,-10.000,  9.052 W48E1  -9.052,-10.000,  9.052    # 14   15
+48 W47E2  -9.052,-10.000,  9.052 W45E1  -9.052,-10.000, -9.052    # 14   15
+
+             -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    41 / 50.00   ( 41 / 50.00)      1.000       0.000       V
+

The model has 48 wires and 528 segments. However, modeling time can be reduced by judicious use of the copy function for identical loops and by symbolic coordinate entries, if available. The source wires for each band are as follows: 20m = wire 41; 15m = wire 25; and 10m = wire 9. Source placement is at the wire center.

+

Because small changes in wire size resulted in noticeable differences in the antenna performance across the bands in question with monoband quads, I modeled this antenna using both #14 and #12 AWG copper wire. Only the #14 model is shown, since wire size is the only difference between the models.

+

As a handy reference, the following table lists the mid-band performance for each band of each version of the antenna.

+ 
Wire-     Freq.     Gain      F-B       Impedance
+ Band      MHz      dBi       dB        R +/- jX Ohms
+#14-20    14.175     9.60     20.8       40.8 + j 3.6
+#12-20               9.74     22.0       38.0 + j 1.7
+#14-15    21.225    10.10     16.8       87.6 + j 4.4
+#12-15              10.16     15.9       85.3 + j 3.9
+#14-10    28.5       8.93      8.3      105.0 - j35.0
+#12-10               8.93      8.0      103.0 - j35.8
+

The differences in performance figures are almost completely insignificant. This fact suggests that element interaction among loops for the various bands may play a stronger role in determining performance characteristics in this 3-band model than modest changes in wire size. The closest loop set to an uninfluenced set is for 20 meters, and the differences in mid-band performance are greatest on that band. The performance curves across the bands bear out this suggestion.

+
+ +
+

The gain curves in Fig. 68 show the virtual identity of the 10-meter gain for the two wire sizes. 15-meter gain does almost as well, and only 20-meter gain shows something interesting. The low-end increase in gain toward the peak value is slightly steeper for the fatter wire.

+

A rising gain curve across the band is natural for virtually any parasitic beam having a director and is the opposite trend from that shown by 2-element reflector-driver designs. However, the 10-meter curve strongly suggests that the performance for this band has not been optimized. The dimensions for 10-meters suggest that the design technique used to arrive at the dimension was simple scaling of the loop length from 20 and 15 meter. The result is, according to the model, relatively mediocre performance at the low end of 10 meters for a long-boom 4-element array.

+
+ +
+

The front-to-back ratio curves in Fig. 69 tend to confirm that--if the model is reasonably accurate--inadequate attention has been paid to 10 meter dimensions. The front-to-back ratio on that band only rises above 10 dB at about 28.6 MHz and continues to climb toward the 29.0 MHz mark, where the scan ceased. In contrast, the front-to-back peaks for both 20 and 15 meters occur within the passband under study. In accord with the suggestion that the 20 meter loops are least affected by the other loops in the array--in other words, act most like a monoband array--the 20-meter front-to-back curves show a frequency displacement that is missing from the 15- and 10-meter curves.

+
+ +
+

The VSWR curves in Fig. 70 are also revelatory. The 20-meter mid-band values suggested that the array might have a low SWR relative to 50 Ohms across that band. However, the curves show that SWR climbs precipitously below mid-band, as the resistive component of the source impedance approaches 20 Ohms. Although the mid-band impedance given for 15 meters suggests a better match to 75-Ohm line, the 50-Ohm SWR remains below 2:1 across that band. On 10 meters, the SWR only approaches 2:1 at 29 MHz. However, if the dimensions of all the 10 meter loops were changed to bring the performance reports within the pass band, it is likely that the 10-meter SWR would also decrease to a more acceptable set of values relative to 50 Ohms.

+

For reference, here is a table of source impedance values for each band, using the #14 model, recorded for the low, middle, and high points of each band.

+ 
Band           Impedance at a Specified Frequency           Delta    Delta
+20 m      14.0           14.175         14.35                 R        X
+          24.2 - j45.8   40.8 + j 3.6   67.7 + j34.5        43.5      80.3
+15 m      21.0           21.225         21.45
+          69.6 - j10.2   87.6 + j 4.4   60.7 + j11.3        26.9      21.5
+10 m      28.0           28.5           29.0
+          92.6 - j94.6   105.0- j35.0   104.9+ j 6.7        12.4     101.3
+

Above 29 MHz, the 10-meter impedance descends once more. It is likely that judicious loop alteration can bring the source impedance within a 2:1 50- Ohm SWR curve that occupies most of the first MHz of 10. Likewise, adjustment to the 20 meter driver length could also move its 2:1 SWR curve lower in the band. There is no reason to touch anything on 15, except perhaps to draw the front-to-back curve more symmetrically within the band.

+

A 3-Element 5-Band 18'-Boom Quad Array

Correspondence with ON7NQ brought to light his efforts to improve the performance of a commercial 3-element 5-band quad he had purchased. The initial dimensions--with allowance for adding 17 and 12 meters and for dropping one element--were similar to those in the 4-element quad just studied. Improvements to 20 meter low-end performance and overall 10-meter performance were the goals of the revisions. Although ON7NQ modeled with a MININEC product, my cross checks with his numbers via NEC-4 showed a very close correlation. The results of one direction of the work yielded the 3- element array sketched in Fig. 71. +
+ +
+

Since the sketch gives no hint of the final dimensions of this model (only one of several we discussed), the following table may help.

+ 
Band      Reflector           Driver              Dir. 1
+          Side L    Space     Side L    Space     Side L
+           feet     Re-DE      feet     DE-D1      feet
+20        18.166    10        17.812     8        17.166
+17        14.134    10        13.874     8        13.458
+15        12.066    10        11.834     8        11.500
+12        10.334    10        10.062     8         9.834
+10         9.100    10         8.800     8         8.684
+

Compared to the dimensions given for the 3-band quad, 15 meters changes scarcely at all. In the case of both 20 and 10 meters, the loops have been enlarged, with the exception of the 20-meter director, which was decreased. The model for this 60-wire, 660 segment model follows.

+ 
ON7NQ 3 el 5 band #14                        Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1   W4E2 -52.100, 96.000,-52.100  W2E1  52.100, 96.000,-52.100    # 14    7
+2   W1E2  52.100, 96.000,-52.100  W3E1  52.100, 96.000, 52.100    # 14    7
+3   W2E2  52.100, 96.000, 52.100  W4E1 -52.100, 96.000, 52.100    # 14    7
+4   W3E2 -52.100, 96.000, 52.100  W1E1 -52.100, 96.000,-52.100    # 14    7
+5   W8E2 -52.800,  0.000,-52.800  W6E1  52.800,  0.000,-52.800    # 14    7
+6   W5E2  52.800,  0.000,-52.800  W7E1  52.800,  0.000, 52.800    # 14    7
+7   W6E2  52.800,  0.000, 52.800  W8E1 -52.800,  0.000, 52.800    # 14    7
+8   W7E2 -52.800,  0.000, 52.800  W5E1 -52.800,  0.000,-52.800    # 14    7
+9  W12E2 -54.600,-120.00,-54.600 W10E1  54.600,-120.00,-54.600    # 14    7
+10  W9E2  54.600,-120.00,-54.600 W11E1  54.600,-120.00, 54.600    # 14    7
+11 W10E2  54.600,-120.00, 54.600 W12E1 -54.600,-120.00, 54.600    # 14    7
+12 W11E2 -54.600,-120.00, 54.600  W9E1 -54.600,-120.00,-54.600    # 14    7
+13 W16E2 -59.000, 96.000,-59.000 W14E1  59.000, 96.000,-59.000    # 14    9
+14 W13E2  59.000, 96.000,-59.000 W15E1  59.000, 96.000, 59.000    # 14    9
+15 W14E2  59.000, 96.000, 59.000 W16E1 -59.000, 96.000, 59.000    # 14    9
+16 W15E2 -59.000, 96.000, 59.000 W13E1 -59.000, 96.000,-59.000    # 14    9
+17 W20E2 -60.375,  0.000,-60.375 W18E1  60.375,  0.000,-60.375    # 14    9
+18 W17E2  60.375,  0.000,-60.375 W19E1  60.375,  0.000, 60.375    # 14    9
+19 W18E2  60.375,  0.000, 60.375 W20E1 -60.375,  0.000, 60.375    # 14    9
+20 W19E2 -60.375,  0.000, 60.375 W17E1 -60.375,  0.000,-60.375    # 14    9
+21 W24E2 -62.000,-120.00,-62.000 W22E1  62.000,-120.00,-62.000    # 14    9
+22 W21E2  62.000,-120.00,-62.000 W23E1  62.000,-120.00, 62.000    # 14    9
+23 W22E2  62.000,-120.00, 62.000 W24E1 -62.000,-120.00, 62.000    # 14    9
+24 W23E2 -62.000,-120.00, 62.000 W21E1 -62.000,-120.00,-62.000    # 14    9
+25 W28E2 -69.000, 96.000,-69.000 W26E1  69.000, 96.000,-69.000    # 14   11
+26 W25E2  69.000, 96.000,-69.000 W27E1  69.000, 96.000, 69.000    # 14   11
+27 W26E2  69.000, 96.000, 69.000 W28E1 -69.000, 96.000, 69.000    # 14   11
+28 W27E2 -69.000, 96.000, 69.000 W25E1 -69.000, 96.000,-69.000    # 14   11
+29 W32E2 -71.000,  0.000,-71.000 W30E1  71.000,  0.000,-71.000    # 14   11
+30 W29E2  71.000,  0.000,-71.000 W31E1  71.000,  0.000, 71.000    # 14   11
+31 W30E2  71.000,  0.000, 71.000 W32E1 -71.000,  0.000, 71.000    # 14   11
+32 W31E2 -71.000,  0.000, 71.000 W29E1 -71.000,  0.000,-71.000    # 14   11
+33 W36E2 -72.400,-120.00,-72.400 W34E1  72.400,-120.00,-72.400    # 14   11
+34 W33E2  72.400,-120.00,-72.400 W35E1  72.400,-120.00, 72.400    # 14   11
+35 W34E2  72.400,-120.00, 72.400 W36E1 -72.400,-120.00, 72.400    # 14   11
+36 W35E2 -72.400,-120.00, 72.400 W33E1 -72.400,-120.00,-72.400    # 14   11
+37 W40E2 -80.750, 96.000,-80.750 W38E1  80.750, 96.000,-80.750    # 14   13
+38 W37E2  80.750, 96.000,-80.750 W39E1  80.750, 96.000, 80.750    # 14   13
+39 W38E2  80.750, 96.000, 80.750 W40E1 -80.750, 96.000, 80.750    # 14   13
+40 W39E2 -80.750, 96.000, 80.750 W37E1 -80.750, 96.000,-80.750    # 14   13
+41 W44E2 -83.250,  0.000,-83.250 W42E1  83.250,  0.000,-83.250    # 14   13
+42 W41E2  83.250,  0.000,-83.250 W43E1  83.250,  0.000, 83.250    # 14   13
+43 W42E2  83.250,  0.000, 83.250 W44E1 -83.250,  0.000, 83.250    # 14   13
+44 W43E2 -83.250,  0.000, 83.250 W41E1 -83.250,  0.000,-83.250    # 14   13
+45 W48E2 -84.805,-120.00,-84.805 W46E1  84.805,-120.00,-84.805    # 14   13
+46 W45E2  84.805,-120.00,-84.805 W47E1  84.805,-120.00, 84.805    # 14   13
+47 W46E2  84.805,-120.00, 84.805 W48E1 -84.805,-120.00, 84.805    # 14   13
+48 W47E2 -84.805,-120.00, 84.805 W45E1 -84.805,-120.00,-84.805    # 14   13
+49 W52E2 -103.00, 96.000,-103.00 W50E1 103.000, 96.000,-103.00    # 14   15
+50 W49E2 103.000, 96.000,-103.00 W51E1 103.000, 96.000,103.000    # 14   15
+51 W50E2 103.000, 96.000,103.000 W52E1 -103.00, 96.000,103.000    # 14   15
+52 W51E2 -103.00, 96.000,103.000 W49E1 -103.00, 96.000,-103.00    # 14   15
+53 W56E2 -106.87,  0.000,-106.87 W54E1 106.870,  0.000,-106.87    # 14   15
+54 W53E2 106.870,  0.000,-106.87 W55E1 106.870,  0.000,106.870    # 14   15
+55 W54E2 106.870,  0.000,106.870 W56E1 -106.87,  0.000,106.870    # 14   15
+56 W55E2 -106.87,  0.000,106.870 W53E1 -106.87,  0.000,-106.87    # 14   15
+57 W60E2 -109.00,-120.00,-109.00 W58E1 109.000,-120.00,-109.00    # 14   15
+58 W57E2 109.000,-120.00,-109.00 W59E1 109.000,-120.00,109.000    # 14   15
+59 W58E2 109.000,-120.00,109.000 W60E1 -109.00,-120.00,109.000    # 14   15
+60 W59E2 -109.00,-120.00,109.000 W57E1 -109.00,-120.00,-109.00    # 14   15
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8    53 / 50.00   ( 53 / 50.00)      1.000       0.000       V
+

This model happens to begin with the 10-meter wires, from director to reflector, and end with the 20-meter wires. The source wires are 20m = wire 53, 12m = wire 41, 15m = wire 29, 17m = wire 17, and 10m = wire 5. Dimensions are in inches in the model description. The wire size is #14 AWG copper.

+

The midband performance values reported by NEC-4 for this model are as follows:

+ 
          Freq.     Gain      F-B       Impedance
+ Band      MHz      dBi       dB        R +/- jX Ohms
+20        14.175     8.08     11.31      43.6 + j 3.2
+17        18.118     8.32     15.2       39.6 + j 3.5
+15        21.225     8.51     21.4       45.5 + j 6.2
+12        24.94      8.52     15.9       47.7 + j 8.9
+10        28.5       9.33     11.3       45.0 + j14.9
+

Relative to the 40' boom 4-element array, gains are down, but each band shows a good match at center to a 50-Ohm feed system. A closer look at each parameter across the wide bands may be useful in understanding the design goals of this model.

+
+ +
+

As shown in Fig. 72, the gain across 15 meters is virtually flat. The gain across 20 meters descends, but only moderately, with design emphasis upon performance at the lower end of the band. Although the 10-meter gain curve still ascends, its peak occurs within the pass band. As we discovered with 2-element multi-band quad arrays, element interaction provides 10-meters with higher gain than might otherwise be obtained in a monoband 18' boom quad, since the elements are very widely spaced for that band. 20 meters seems to "suffer" from its relative independence, with 15 meters showing a "balance" of influence. (How to quantify the terms in "-" remains a task for the future of quad design.)

+
+ +
+

The front-to-back curves (Fig. 73) tell us that the antenna was largely designed for gain, with the source impedance the most important second factor. Front- to-back ratio was largely accepted for what it turned out to be. On 15 meters, where gain performance is exceptionally stable, the front-to-back peak can easily be moved within the passband. 20 and 10 are harder nuts to crack, and their numbers are relatively poor, except for the low end of 20 meters, where they approach being adequate. On 10, the front-to-back performance across the band is similar to a 2-element reflector-driver Yagi.

+
+ +
+

The 50-Ohm SWR performance of the antennas has also been optimized for the low ends of the bands, as is readily apparent in Fig. 74. On 20 and 10, the SWR is below 2:1 for at least 80% of the pass bands, but that figure goes down to 60% on 10 meters. For reference, here are the standard figures across each of the wide bands.

+ 
Band           Impedance at a Specified Frequency           Delta    Delta
+20 m      14.0           14.175         14.35                 R        X
+          45.3 - j19.9   43.3 + j 4.0   32.0 + j43.2        13.3      63.1
+15 m      21.0           21.225         21.45
+          48.1 - j15.6   45.4 + j 6.8   35.4 + j38.3        12.7      53.9
+10 m      28.0           28.5           29.0
+          76.9 - j32.2   45.0 + j14.9   27.0 + j86.7        49.9     118.9
+

Optimizing gain within the pass band for each of the wide bands has resulted in an expansion of the range of reactance across the bands. Like most 3-element parasitical arrays, the lowest impedance is at the upper end of the band.

+

We might accept the 20-15 meter performance as not likely to be improved by more than a small amount due to the limitations of the boom length on those bands. Compared to Yagis, the boom length is short for 20 meters and about right for 15 meters, relative to maximizing gain through the use of three elements. Extending and improving 10 meter performance seems the only further development possible, since the boom is long for 3 elements on that band. The 10' reflector-driver spacing seems especially long.

+

A 3/4-Element 5-Band 18'-Boom Quad Array

ON7NQ added a new spreader midway between the old reflector and driver spreaders. To this, he attached what became driver loops for 10 and 12 meters, with the old drivers becoming first directors. The result is a hybrid 3- and 4-element quad, where the element spacing on the highest two bands more closely resembles that used with comparable Yagis. The overall 18' boom length was retained. The result looks something the sketch in Fig. 75. +
+ +
+

The following table lists the side lengths for the elements in this revised array.

+ 
Band      Reflector           Driver              Dir. 1             Dir.2
+          Side L    Space     Side L    Space     Side L    Space    Side L
+           feet     Re-DE      feet     DE-D1      feet     D1-D2     feet
+20        18.084    10        17.808     8        17.084
+17        14.042    10        13.858     8        13.316
+15        12.066    10        11.834     8        11.500
+12        10.200     5         9.932     5         9.850     8       9.892
+10         9.224     5         8.816     5         8.716     8       8.666
+

Due to the difference in space on 12 and 10 in terms of fractions of a wavelength, the forwardmost director on 12 is actually larger than the first director. Many of the loop size changes are small on the lower bands, and the 15 meter dimensions did not change at all. Here is the model description for this 68-wire, 724-segment model.

+ 
ON7NQ 3/4 el 5 band #12                      Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1   W4E2 -108.50,  0.000,-108.50  W2E1 108.500,  0.000,-108.50    # 12   15
+2   W1E2 108.500,  0.000,-108.50  W3E1 108.500,  0.000,108.500    # 12   15
+3   W2E2 108.500,  0.000,108.500  W4E1 -108.50,  0.000,108.500    # 12   15
+4   W3E2 -108.50,  0.000,108.500  W1E1 -108.50,  0.000,-108.50    # 12   15
+5   W8E2 -106.85,120.000,-106.85  W6E1 106.850,120.000,-106.85    # 12   15
+6   W5E2 106.850,120.000,-106.85  W7E1 106.850,120.000,106.850    # 12   15
+7   W6E2 106.850,120.000,106.850  W8E1 -106.85,120.000,106.850    # 12   15
+8   W7E2 -106.85,120.000,106.850  W5E1 -106.85,120.000,-106.85    # 12   15
+9  W12E2 -102.50,216.000,-102.50 W10E1 102.500,216.000,-102.50    # 12   15
+10  W9E2 102.500,216.000,-102.50 W11E1 102.500,216.000,102.500    # 12   15
+11 W10E2 102.500,216.000,102.500 W12E1 -102.50,216.000,102.500    # 12   15
+12 W11E2 -102.50,216.000,102.500  W9E1 -102.50,216.000,-102.50    # 12   15
+13 W16E2 -84.250,  0.000,-84.250 W14E1  84.250,  0.000,-84.250    # 12   13
+14 W13E2  84.250,  0.000,-84.250 W15E1  84.250,  0.000, 84.250    # 12   13
+15 W14E2  84.250,  0.000, 84.250 W16E1 -84.250,  0.000, 84.250    # 12   13
+16 W15E2 -84.250,  0.000, 84.250 W13E1 -84.250,  0.000,-84.250    # 12   13
+17 W20E2 -83.150,120.000,-83.150 W18E1  83.150,120.000,-83.150    # 12   13
+18 W17E2  83.150,120.000,-83.150 W19E1  83.150,120.000, 83.150    # 12   13
+19 W18E2  83.150,120.000, 83.150 W20E1 -83.150,120.000, 83.150    # 12   13
+20 W19E2 -83.150,120.000, 83.150 W17E1 -83.150,120.000,-83.150    # 12   13
+21 W24E2 -79.900,216.000,-79.900 W22E1  79.900,216.000,-79.900    # 12   13
+22 W21E2  79.900,216.000,-79.900 W23E1  79.900,216.000, 79.900    # 12   13
+23 W22E2  79.900,216.000, 79.900 W24E1 -79.900,216.000, 79.900    # 12   13
+24 W23E2 -79.900,216.000, 79.900 W21E1 -79.900,216.000,-79.900    # 12   13
+25 W28E2 -72.400,  0.000,-72.400 W26E1  72.400,  0.000,-72.400    # 12   11
+26 W25E2  72.400,  0.000,-72.400 W27E1  72.400,  0.000, 72.400    # 12   11
+27 W26E2  72.400,  0.000, 72.400 W28E1 -72.400,  0.000, 72.400    # 12   11
+28 W27E2 -72.400,  0.000, 72.400 W25E1 -72.400,  0.000,-72.400    # 12   11
+29 W32E2 -71.000,120.000,-71.000 W30E1  71.000,120.000,-71.000    # 12   11
+30 W29E2  71.000,120.000,-71.000 W31E1  71.000,120.000, 71.000    # 12   11
+31 W30E2  71.000,120.000, 71.000 W32E1 -71.000,120.000, 71.000    # 12   11
+32 W31E2 -71.000,120.000, 71.000 W29E1 -71.000,120.000,-71.000    # 12   11
+33 W36E2 -69.000,216.000,-69.000 W34E1  69.000,216.000,-69.000    # 12   11
+34 W33E2  69.000,216.000,-69.000 W35E1  69.000,216.000, 69.000    # 12   11
+35 W34E2  69.000,216.000, 69.000 W36E1 -69.000,216.000, 69.000    # 12   11
+36 W35E2 -69.000,216.000, 69.000 W33E1 -69.000,216.000,-69.000    # 12   11
+37 W40E2 -61.200,  0.000,-61.200 W38E1  61.200,  0.000,-61.200    # 12    9
+38 W37E2  61.200,  0.000,-61.200 W39E1  61.200,  0.000, 61.200    # 12    9
+39 W38E2  61.200,  0.000, 61.200 W40E1 -61.200,  0.000, 61.200    # 12    9
+40 W39E2 -61.200,  0.000, 61.200 W37E1 -61.200,  0.000,-61.200    # 12    9
+41 W44E2 -59.950, 60.000,-59.950 W42E1  59.950, 60.000,-59.950    # 12    9
+42 W41E2  59.950, 60.000,-59.950 W43E1  59.950, 60.000, 59.950    # 12    9
+43 W42E2  59.950, 60.000, 59.950 W44E1 -59.950, 60.000, 59.950    # 12    9
+44 W43E2 -59.950, 60.000, 59.950 W41E1 -59.950, 60.000,-59.950    # 12    9
+45 W48E2 -59.100,120.000,-59.100 W46E1  59.100,120.000,-59.100    # 12    9
+46 W45E2  59.100,120.000,-59.100 W47E1  59.100,120.000, 59.100    # 12    9
+47 W46E2  59.100,120.000, 59.100 W48E1 -59.100,120.000, 59.100    # 12    9
+48 W47E2 -59.100,120.000, 59.100 W45E1 -59.100,120.000,-59.100    # 12    9
+49 W52E2 -59.350,216.000,-59.350 W50E1  59.350,216.000,-59.350    # 12    9
+50 W49E2  59.350,216.000,-59.350 W51E1  59.350,216.000, 59.350    # 12    9
+51 W50E2  59.350,216.000, 59.350 W52E1 -59.350,216.000, 59.350    # 12    9
+52 W51E2 -59.350,216.000, 59.350 W49E1 -59.350,216.000,-59.350    # 12    9
+53 W56E2 -55.340,  0.000,-55.340 W54E1  55.340,  0.000,-55.340    # 12    7
+54 W53E2  55.340,  0.000,-55.340 W55E1  55.340,  0.000, 55.340    # 12    7
+55 W54E2  55.340,  0.000, 55.340 W56E1 -55.340,  0.000, 55.340    # 12    7
+56 W55E2 -55.340,  0.000, 55.340 W53E1 -55.340,  0.000,-55.340    # 12    7
+57 W60E2 -52.900, 60.000,-52.900 W58E1  52.900, 60.000,-52.900    # 12    7
+58 W57E2  52.900, 60.000,-52.900 W59E1  52.900, 60.000, 52.900    # 12    7
+59 W58E2  52.900, 60.000, 52.900 W60E1 -52.900, 60.000, 52.900    # 12    7
+60 W59E2 -52.900, 60.000, 52.900 W57E1 -52.900, 60.000,-52.900    # 12    7
+61 W64E2 -52.300,120.000,-52.300 W62E1  52.300,120.000,-52.300    # 12    7
+62 W61E2  52.300,120.000,-52.300 W63E1  52.300,120.000, 52.300    # 12    7
+63 W62E2  52.300,120.000, 52.300 W64E1 -52.300,120.000, 52.300    # 12    7
+64 W63E2 -52.300,120.000, 52.300 W61E1 -52.300,120.000,-52.300    # 12    7
+65 W68E2 -51.995,216.000,-51.995 W66E1  51.995,216.000,-51.995    # 12    7
+66 W65E2  51.995,216.000,-51.995 W67E1  51.995,216.000, 51.995    # 12    7
+67 W66E2  51.995,216.000, 51.995 W68E1 -51.995,216.000, 51.995    # 12    7
+68 W67E2 -51.995,216.000, 51.995 W65E1 -51.995,216.000,-51.995    # 12    7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           8     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+

This model is listed by bands from 20 through 10 meters, with wires within a band given from the reflector forward. Consequently, the source wires are 20m = wire 5, 17m = wire 17, 15m = wire 29, 12m = wire 41, and 10m = wire 57. Dimensions are in inches, and the wire size is #12 AWG copper.

+

To see what basic improvements the addition of the two new drivers has made, let's look at the midband performance reports from the model.

+ 
          Freq.     Gain      F-B       Impedance
+ Band      MHz      dBi       dB        R +/- jX Ohms
+20        14.175     8.30     15.2       44.4 + j 3.6
+17        18.118     8.42     25.5       43.5 - j 0.1
+15        21.225     8.52     21.6       46.6 - j 0.6
+12        24.94      9.22     18.5       42.2 + j 2.9
+10        28.5       9.74     27.9       56.1 + j11.3
+

Overall, gain and front-to-back ratios are up across the board, although only marginally on the lowest bands. Mid-band gain and front-to-back ratio are better on 10 meters especially. 15-meters remains virtually unchanged.

+
+ +
+

In the gain curves in Fig. 76, we may note that 15 remains unchanged in its flat curve, while the decrease in gain at the upper end of 20 meters has decreased. The gain curve for 10 meters remains at about 9 dBi or better for 90% of the pass band, before taking a nose dive.

+
+ +
+

In Fig. 77, we can see the unchanged 15-meter front-to-back curve, which serves as a back drop for the other curves. 20 meters shows a movement of the curve to better center it within the band and give better upper band- edge performance. The biggest improvement occurs on 10 meters, where the front-to-back value is at least 15 dB for more than 3/4 of the pass band. As with the gain, we get a steep slope downward as the frequency approaches 29 MHz.

+
+ +
+

The small adjustments to the lower bands yield 50-Ohm SWR curves (Fig. 78) that are below 2:1 for 90% of 20 and 15 meters. The 10-meter 2:1 curve has been extended to over 80% of the pass band and is consistent with the patterning of the gain and front-to-back figures. 28.8 to 29 MHz has been sacrificed for optimized performance at the low and middle regions of the pass band. You may compare this figure with Fig. 74 to more clearly see the improvement in the 50-Ohm SWR category.

+

It is also noteworthy to compare the performance figures of the 3/4-element 5-band quad with those of the traditional design in Fig. 68 through Fig. 70. Although the 4-element, 40' boom design provides more gain on 15 and 10 meters, the 18' boom 3/4-element design is superior in all other categories, except perhaps 20-meter front-to-back ratio--which was obtained at the cost of a relatively low gain figure over most of the band. The 18' 3/4-element design is also a better match on every band.

+

The results of looking at these models are a few suggestions rather than judgments. First, element interaction in a multi-band quad array remains a strong candidate for being the source of some of its performance. The fact that the current ON7NQ model achieves the performance it does with a boom less than 50% the length of the more traditional models suggests that some of the element interactions can be beneficial.

+

The achievements of the short boom quad also suggest that those interested in quad design may wish to rethink some of presumptions underlying traditional designs. Element spacing taken in terms of fractions of a wavelength plays a role in optimizing performance, although not necessarily in a simple way. Simply adding element collections at somewhat arbitrary points along the boom may be less effective than optimizing the spacing for each major band and then working out whatever compromises may be needed. A 40' boom may be both useful and necessary for higher gain on 20 and 17, but without intermediate elements somewhere along the line, the boom length may be wasted for 10- and 12-meter performance.

+

Even within the realm of these design suggestions, it appears that a quad can be designed for a relatively uniform source impedance for all of the bands covered. Although this feature may not improve absolute performance, it can ease the task of installation, band-switching, and other functions of a more practical nature in constructing and using a large quad array. It also appears possible to better center the SWR curve within both the 20- and 15-meter bands.

+

There may in fact be designs available that achieve all of this. My small sample of models can make no claim to being exhaustive or even representative. However, if those designs are not available at present, then multi-band quad designers have a fertile field of endeavor for some time to come. If someone is going to erect something of the mechanical complexity of a many-element, many-band quad, he deserves to have the optimal performance to be gained from the array--and from the investment he has made in it and in its supporting structure.

+

Stacking the 3/4-Element 5-Band 18'-Boom Quad Array

+

The ON7NQ 3/4 element quad on an 18' boom has attracted a bit of attention, along with questions about stacking a pair of them. Stacking quads is not quite the same as stacking Yagis. For identical monoband Yagis, the best stacking distance tends to increase with individual array gain. Once you find--via models--the best distance apart for maximum gain, then the next hunt is for the distance that gives adequate front-to-back ratio--unless one wishes to redesign the antennas in the array. The higher the gain of the individual Yagis, the more likely it is to be able to find a distance that maximizes front-to-back ratio while only robbing about 0.1 dB from the maximum gain.

+

For quads, we have a different ball game. Although array gain does play a role in the determination of the best stacking distance, this criterion tends to be overridden by considerations of array isolation. By isolation, I mean a stacking distance that allows each array on all bands covered to shows the least changes in feedpoint impedance on each band relative to a single array. Planar arrays tend to show more isolation at close spacings (5/8 to 2/3 wavelength on 20 meters, or about 24') than spider designs. 2-element 5-band spiders tend to achieve satisfactory isolation with a center-to-center spacing of about 30'--at least in the models explored so far. (Remember that all of this work is exploratory.)

+

The ON7NQ array is planar in design, but has more gain than the 2-element planar designs examined so far. Hence, it was likely that the best stacking distance might be more than 24'. In fact, a 30' spacing produced adequate isolation (and convergence of the feedpoint impedances with the single array values). However, 36' proved to be a bit far apart, as the lower-band front-to-back ratio began to decreae--or shift off of the design frequency. Therefore, the following preliminary figures for the single array and the stack in free space use a 30' stack spacing, as measured from the hub of one array to the hub of the other. Fig. 78a shows a profile of the stack.

+
+ +
+

The data consists of gain in dBi, TO angle (where relevant), F-B, beamwidth, feed Z(s) and 50-Ohm SWR (for which the original array had been set). Since the array was designed for 28.0 to 28.8 MHz coverage on 10 meters, The values for that band follow the designer's plan.

+ 
ON7NQ 3/4-Element Quad in Free Space
+
+Fq        Gain      F-B       B/W       Feed Z         SWR-50
+14.0      8.4       11.8      66         37.5-18.4     1.66
+14.175    8.3       15.1      67         44.3+ 4.3     1.16
+14.35     8.1        9.8      67         34.9+36.2     2.48
+
+18.118    8.4       25.5      68         43.5- 0.3     1.15
+
+21.0      8.4       15.2      69         49.6-20.2     1.50
+21.225    8.5       21.0      68         46.4- 0.0     1.08
+21.45     8.5       10.3      65         36.2+30.7     2.17
+
+24.94     9.2       19.0      59         40.9+ 2.2     1.23
+
+28.0      9.0       18.4      65         43.8-31.7     1.97
+28.4      9.6       30.7      59         51.3+ 6.7     1.14
+28.8      9.7       12.4      52         31.2+ 8.0     1.67
+ 
2 ON7NQ Quads stacked 30' apart in Free Space:  Z1 (upper entry) = lower
+quad; Z2 (lower entry) = upper quad.  Since both quads are fed on the lower
+element, some differentials in values are normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-50 1/2
+14.0      10.2      13.5      65         38.7-20.9     1.71
+                                         38.4-20.5     1.70
+14.175    10.2      14.7      65         42.5+ 9.3     1.30
+                                         42.2+ 9.4     1.30
+14.35     9.9        9.4      64         36.9+45.7     2.88
+                                         36.3+45.7     2.92
+
+18.118    10.9      23.3      67         43.9+ 1.5     1.14
+                                         43.9+ 1.5     1.14
+
+21.0      11.2      14.6      68         49.8-19.7     1.48
+                                         49.8-19.7     1.48
+21.225    11.3      21.3      67         49.4+ 2.3     1.05
+                                         49.4+ 2.3     1.05
+21.45     11.1      10.1      64         41.5+32.1     2.04
+                                         41.5+32.2     2.04
+
+24.94     12.0      17.4      59         44.7- 0.9     1.12
+                                         44.8 -0.9     1.12
+
+28.0      12.1      18.9      65         46.0-31.9     1.93
+                                         46.0-31.9     1.93
+28.4      12.6      25.1      59         53.2+ 5.1     1.12
+                                         53.3+ 5.1     1.12
+28.8      12.6      12.2      52         31.9+ 8.4     1.64
+                                         31.9+ 8.4     1.64
+ 
Stacking Gain averaged by bands:
+20        17        15        12        10
+1.8       2.4       2.7       2.9       3.0  dB
+ 
2 ON7NQ Quads stacked 30' apart in 50' and 80' above average ground:  Z1
+(upper entry) = lower quad; Z2 (lower entry) = upper quad.  Since both
+quads are fed on the lower element, some differentials in values are
+normal.
+
+Fq        Gain      F-B       B/W       Feed Z 1/2     SWR-50 1/2     TO
+14.0      14.7      13.5      65         38.7-20.6     1.70           14
+                                         38.4-20.7     1.71
+14.175    14.7      14.5      65         42.5+ 9.5     1.30           13
+                                         42.1+ 9.2     1.30
+14.35     14.4       9.3      65         40.0+45.7     2.88           13
+                                         36.2+45.6     2.92
+
+18.118    15.7      22.7      67         44.1+ 1.4     1.14           11
+                                         43.8+ 1.5     1.15
+
+21.0      16.1      14.7      68         49.8-19.9     1.49            9
+                                         50.0-19.6     1.48
+21.225    16.2      20.9      67         49.3+ 2.2     1.05            9
+                                         49.6+ 2.3     1.05
+21.45     16.0      10.0      64         41.6+32.2     2.04            9
+                                         41.5+32.2     2.04
+
+24.94     17.0      16.5      58         44.8- 1.3     1.12            8
+                                         45.1 -0.9     1.11
+
+28.0      17.1      19.0      65         45.8-32.1     1.94            7
+                                         46.0-32.1     1.94
+28.5      17.6      24.7      59         52.9+ 5.0     1.12            7
+                                         53.2+ 5.1     1.12
+29        17.6      12.2      52         31.6+ 8.8     1.66            7
+                                         31.7+ 8.5     1.65
+

The two quad arrays show good isolation with a 30' spacing in free space, shifting the feedpoint impedance by only a very few Ohms on 20 and much less as the frequency goes up. Front-to-back figures remain roughly centered in the design frequencies. The stacking gain shows a relatively standard progression. Consequently, the stacking process may in some cases--considering mast stresses, mechanical complexity, and weather effects--be a worthwhile project. Greater spacing will show increased array isolation on 20 meters, but greater skewing of the performance curves. Less spacing shows decreased isolation between arrays and higher differentials between feedpoint impedance values for the two feedpoints. For reference, the forward gain of a 5-6 element Yagi on a 0.7 wavelength boom (48' on 20 meters, 24' on 10 meters) is about 10.1 dBi in free space.

+

Above ground, as we might expect, the values of impedance diverge more than in free space (where Z1 is the lower quad and Z2 is the upper and both quads are fed on the bottom wires of their respective drivers). With 30' spacing, the values--even on the lowest bands--do not diverge enough to materially affect a junction. 75-Ohm quarter wavelength sections might be used on each band and join at a Tee prior to connection to a single remote band switch installed on the mast. If connection length is a problem, the lower quad might be fed at its top wire, and 75-Ohm 3/4 wavelength sections are also usable, although with greater losses. Alternatively, but with some complexities of switching, 75-Ohm parallel line can be used to transform the 50-Ohm individual feed impedances to the 100 Ohms needed at each Tee-junction for the stack common feedline.

+

The stacking exercise is shown only as a representative example of possibilities and to illustrate the importance of independence or isolation in quad stacking.

+

Updated 2-26-99, 8-7-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Go to Feeding Multi-Band Quads

+

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+

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+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quad7.html b/content/quad/quad7.html new file mode 100644 index 0000000..6ce8e6d --- /dev/null +++ b/content/quad/quad7.html @@ -0,0 +1,128 @@ + + + + + + Quad Models Part 7 Feeding Multi-Band Quads + + + +
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Some Model Quads:
+ 7. Feeding Multi-Band Quads

+

L. B. Cebik, W4RNL

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A persistent question about multi-band quads, whether 2-element models or larger, is the proper way to feed them. There are several questions associated with this basic inquiry, but only a few have I been able so far to shed any light on through the models in my collection. But perhaps it is worth a note or two on the question to reveal how far I have gotten so far.

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Common Feed

In my collection of models, I have found no way to develop a successful model with a common feedpoint for all bands. I have not found a placement of position that permits all drivers to be brought to this point and still yield a set of patterns and source impedances that are satisfactory. Part of this effort will be described in an upcoming article in Communications Quarterly, so perhaps we can bypass the common-feed question here with only a couple of notes. +

The strongest interactions in 2-element multi-band quads appear to be these: 20 vs. 10 meters when 10-meters is active; 12 vs. 10 meters when 10 meters is active.

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I have modeled 2-band combinations of 12 and 10 meter quads. I am not satisfied with the results, even though the source position distorts the driver shape the least. Finding dimensions that will yield good free space patterns and usable feedpoints on both bands is not easy. The 12-meter driver acts like a 10-meter reflector, but one that either surrounds the 10-meter driver or is ahead of it. The 10-meter reflector acts like a 12- meter director, in conflict with the 12-meter reflector. although I have been able to stabilize 12-meter performance in models, 10-meters still eludes me.

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I have also modeled common-feed 20-10-meter combinations. Here, the problem appears to differ. The 10- and 20-meter drivers interact when 10 is driven, because the 20 meter driver is about 2 wl long and has a low impedance--something like 200 Ohms, when the 20 meter quad is driven away from the presence of the 10-meter elements. The combination on 10 meters not only shows angular side bulges, in line with the pattern of a 2 wl loop, but as well is sensitive to the loop distortions created by the common feed position between the two drivers. In free space, the patterns tilt downward by a considerable degree.

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In a five-band common-feed quad, I have found no satisfactory arrangement that will yield patterns and impedances good on all bands. So far, when the patterns look reasonably clean (meaning that they are similar to the patterns of monoband quads), the impedances become unworkable, and vice versa.

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These notes do not mean that there is no satisfactory arrangement. That is why I have shown no figures here. The net result simply means that I have found no such arrangement, if it exists. However, my criteria are fairly stringent. For an arrangement to be satisfactory, the quad must on all bands have a satisfactory pattern and a satisfactory source impedance. There is some latitude in the impedances that might be acceptable, but the patterns must approach the standards set by quad models using separate feed points for each band. So far, I must admit failure in this quest.

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Remotely Switched Independent Feedpoints

A multi-band quad may be fed through a couple of arrangements using a remote switching system. Perhaps the most common system is to run a section of feedline from each loop to a central remote switch and relay system. Fig. 79 illustrates such a system in simplified (3-band) form. +
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Key to this system is that the unused lines are completely open. Neither their braid nor their center conductors are connected to anything, including the box or each other. Each line, by standard design, is 1/4 wl long at the operating frequency of the unused driver. Depending upon the placement of the remote switch, one may need to use either 0.66 or 0.78 VF feedline to get the closest approximation of the right length (without coming up short).

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The benefit of this system is that all relays are enclosed in a single box that can be effectively weather proofed (while allowing drainage or evaporation of condensation). Whether this system has disadvantages, we shall examine shortly.

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A second system is to short the feedpoint of each driven loop right at the feedpoint itself, as illustrated in Fig. 80.

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In this system, a weatherproofed relay is positioned at the feedpoint. The relays can be "normally closed" types so that the loops are shorted without power to the system. The only energized relay is located at the active driven element. It is opened, thus allowing the feedline to be in series with the element loop.

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This system assures that the unused driver loops are closed--a condition generally considered to be more optimal for achieving good quad patterns and usable source impedances. However, the weight and exposure of the relays when placed at the sources makes this system somewhat more of a mechanical design problem than the single remote box and 1/4 wl stubs. It entails in most designs the use of a separate feedline for each band--or a secondary switching system for the feedline.

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As a consequence of this complexity, the most common design for separately feeding each band of a multi-band quad has been the central switching box and 1/4 wl stubs. However, there are still a few questions which we might pose about this system:

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1. Do we need the stubs to be open-ended to create a short across the loop?

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2. Since the stubs will be 1/4 wl long at the frequency for which the driver is tuned, will they effectively short the loop when the quad is operated at other frequencies?

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To look into these questions together, I remodeled a couple of 2-element multi-band quads that we looked at in Part 4 of this series. One was the study quad that used a constant 0.125 wl spacing between elements. This is a version of the spider-type quad in which elements for lower bands are both ahead and behind elements for higher bands. The second was the KC6T design that uses an 8' boom for all bands, along with capacitive reflector loading. Although 2 models might not be exhaustive as a study, the pair may give us some suggestive results.

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2-Element, 5-Band Quad with 0.125 wl Spacing

The 2-element, 5-band, 0.125 wl spaced quad has the general appearance shown in Fig. 81. Consult Part 4 of this series for the band-by-band dimensions of the model. +
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The data I collected from this model comes in 4 parts, three of which I shall present in tabular form. First is the performance data for the model with the unused driver loops closed. The data includes the Free Space gain in dBi, the 180-degree front-to-back ratio in dB, and the source impedance in Ohms.

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Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           7.48      20.28               40.0 - j 0.3
+24.94          7.32      25.83               41.5 + j 0.1
+21.225         7.16      24.70               52.9 + j 0.2
+18.118         7.23      32.38               60.9 - j 0.5
+14.175         7.23      28.92               84.2 - j 0.1
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We may consider this our base-line data against which we may compare data from modeling variations.

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The first variation was to connect a 1/4 wl line to each driver. The other end of the line of the active driver element was brought to a very short wire used as the remote source point. For this exercise, the TL facility of NEC-4 was used, so the lines are handled as mathematical lines, not as physical lines that may play a desired or undesired role in far field pattern formation. Two subvariations were used. In one, each unused line was set as an open line, which uses a very remote wire and a specified very high impedance (or very low admittance) to create the open circuit. The second subvariation used a remote short, thin wire that serves as the source wire when the element is active. Inactive lines are simply connected to their unique wires without a source. The results between the two systems varied only in the hundredths column of the model output reports, and so only one set of data will be given.

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For reference, the line lengths used are as follows, where the Frequency column indicates the driver element to which a given transmission line stub is connected.

+ 
Frequency      Stub Length    Stub Length
+ Band           in feet        in inches
+10              8.628         103.54
+12              9.859         118.31
+15             11.585         139.02
+17             13.717         164.60
+20             17.347         208.16
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In each case, the source impedance of the element when driven was used as the line characteristic impedance (rather than using some common figure, such as 75 Ohms). The lines use a VF of 1.0, since line loss variations cannot be determined by NEC. Actual lines would be shortened in accord with the actual velocity factor of the line used.

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With the unused lines either brought to their individual short wires or left open, the following performance figures were reported by NEC-4.

+ 
Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           7.43      20.10               39.2 + j 0.0
+24.94          7.33      25.64               41.0 - j 0.0
+21.225         7.17      25.02               51.6 - j 0.1
+18.118         7.23      32.12               60.0 + j 0.7
+14.175         7.23      28.85               85.6 - j 0.1
+

To the degree that NEC can model the situation, the use of 1/4 wl lines-- each set to the operating frequency of the driver--that are open at the remote switch point creates virtually no change in the patterns or the source impedances of the 2-element multi-band quad on any band. for this model, at least, it does not matter that the lines are not 1/4 wl long at the frequency of current operation. They provide sufficient closure to allow standard performance on each band.

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The second variation set each unused driver line (without any other change to the line) at a remote short circuit. In principle, this would open the unused driver loops. The results reported by NEC-4 are the following.

+ 
Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           7.33      19.68               54.9 + j16.9
+24.94          7.17      28.95               71.0 + j 3.7
+21.225         7.07      23.02               79.0 + j 1.1
+18.118         7.20      37.31               78.6 - j 0.7
+14.175         7.23      29.57               88.6 + j 0.7
+

The use of shorted 1/4 wl stubs for this concentric quad model is certainly not catastrophic. There is a slight gain loss with increasing frequency, while the changes in the front-to-back ratio are variable. These mixed results tend to indicate only a small shift in resonant frequency for the driven loops as a result of the inactive loops having shorted stubs.

+

The more noticeable affect is the increase in source impedance for the quad at higher frequencies relative to the impedance with shorted unused loops (or open stubs). Note that this source impedance is the value at the end of the stub for the active band, using a characteristic impedance line equal to the source impedance of the baseline value from the first table. nonetheless, this technique bears watching in other models, since it seems at first appearance a useful result.

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2-Element, 5-Band Quad with 8' Spacing

The KC6T 8'-boom 2-element, 5-band quad model was also given the same treatment. Consult Part 4 of the series for dimensions, load values, and other design considerations for this quad, the outline of which is roughly that shown in Fig. 82. +
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For this quad, the baseline data is as follows.

+ 
Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           7.46      22.81               75.4 - j 0.3
+24.94          7.20      30.63               76.9 + j 0.3
+21.225         7.28      34.40               69.5 + j 1.7
+18.118         7.30      31.71               69.5 + j 1.7
+14.175         7.21      24.01               76.6 + j 1.6
+

As notes in Part 4, one of the interesting aspects of this design is the relatively constant source impedance from band to band. This factor simplifies the stub modeling. The line lengths will be the same as in the first test, but the characteristic impedances will be between 70 and 75 Ohms. For the two subvariations of an open-circuit remote stub end, the results are as follows.

+ 
Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           7.42      22.54               71.7 + j 0.2
+24.94          7.18      31.60               74.0 + j 0.7
+21.225         7.28      35.20               68.2 - j 1.2
+18.118         7.30      31.72               69.0 - j 1.3
+14.175         7.21      23.97               77.0 - j 1.7
+

As with the concentric quad model, the flat-plane model shows no significant difference in any performance parameter between the baseline data set and the open unused stub set.

+

The only test remaining is the one in which the unused driver stubs are short circuited at their remote ends. The data for this test is as follows.

+ 
Frequency      Gain      Front-to-Back       Source Impedance
+ in MHz        in dBi    Ratio in dB         (R +/- jX Ohms)
+28.5           -1.34     14.74                 4.7 + j83.0
+24.94          6.63      28.14                41.7 - j96.5
+21.225         7.13      30.02               183.2 - j23.8
+18.118         7.26      34.61               120.7 - j12.5
+14.175         7.22      24.36                80.8 - j 1.1
+

The flat-plane model obviously suffers far more from the use of shorted stubs for the unused driver than does the concentric model. 12 and 10 meter operation suffers the most and requires considerable redesign before even approaching the performance in the baseline data set.

+

Conclusions

Any conclusions we reach must be very tentative, since only one sample of each quad type (concentric and flat plane) was used. We cannot, for example, assert with any certainty that all spider-type concentric quads would show a similar set of data relative to the model studied. +

What is more assured, although by no means finalized, is the fact that unused driver loop closure is desirable for attaining good performance on all bands of a 2-element, 5-band quad. With relatively equal assurance, we can also suggest that cutting the open-ended stubs to 1/4 wl at the loop's normal operating frequency suffices to allow the array to achieve peak performance on all bands (within, of course, the design limitations inherent in each type of quad). Modeling does not seem to turn up any particular problems with the open-stub system of remote switching.

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This study is very incomplete, being limited to a subset of models in my collection. Nevertheless, the results seemed worth adding to this series, since they do appear to allay any hesitation over using the open-stub remote switching system and to suggest that using shorted stubs may be unwise--or at least not fully predictable for any given situation.

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Updated 4-2-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Return to Quad Model Index

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Return to Amateur Radio Page

+

Topics: HF Upper, Quad


+ + diff --git a/content/quad/quadlist.html b/content/quad/quadlist.html new file mode 100644 index 0000000..93f1b65 --- /dev/null +++ b/content/quad/quadlist.html @@ -0,0 +1,42 @@ + + + + + + New Quad Studies Index + + + +
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+ New Quad Studies

+

L. B. Cebik, W4RNL

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Based on earlier notes at this site, I embarked on a more systematic study of quad beams. The articles below, all but one of which have appeared in AntenneX, represent the core of this approach. Articles containing BASIC file listings now have links to download the monoband quad calculation programs in various formats.

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  1. Calculating the Length of a Resonant Square Quad Loop
    2. +
  2. 2-Element Quads as a Function of Wire Diameter: Part 1: Understanding Some Quad Properties
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  3. 2-Element Quads as a Function of Wire Diameter: Part 2: Automating the Design Process
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  4. 2-Element Quads as a Function of Wire Diameter: Part 3: Fatter Elements from "Mere Wire"
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  5. Automating the Design of 3-Element Monoband Quad Beams: Part 1: A Wide-Band Model
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  6. Automating the Design of 3-Element Monoband Quad Beams: Part 2: A High-Gain Model
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  7. 40-Meter Wide-Band 3-Element Quad Designs
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  8. 4-Element Monoband Quad Design
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  9. Some Notes on Long-Boom Quads
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  10. In Pursuit of Better VHF Quad Beams: A Work in Progress
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Additional articles will be added until the series is complete.

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Updated 11-14-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Quad


+ + diff --git a/content/quad/quadloop.html b/content/quad/quadloop.html new file mode 100644 index 0000000..015904e --- /dev/null +++ b/content/quad/quadloop.html @@ -0,0 +1,177 @@ + + + + + + Calculating the Length of a Resonant Square Quad Loop + + + +
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Calculating the Length of a Resonant Square Quad Loop

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L. B. Cebik, W4RNL

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I have recently received a number of inquiries about calculating the length of wire needed to form the circumference of a single resonant square quad loop at numerous frequencies. Everybody seems to "know" that such a loop in the HF range requires use of the old formula

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They also seem to know that this equation does not work at VHF.

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In fact, this old formula, whose origin I mercifully do not know, does not work at HF either. It has been, is, and always will be wrong for common sizes of bare wire. I have heard by the unreliable grapevine that it is the formula to use at HF for insulated wire, where we have a shortening effect or velocity factor. However, being over 4% short, the formula exceeds the velocity factor effects of most wire insulations with which I am familiar.

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#12 AWG bare copper wire requires a calculation constant of about 1043 at 28.5 MHz and a constant of about 1065 at 146 MHz. However, those numbers individually are good for one wire size at one frequency. There should be a more general solution that will get quad loop builders into the ballpark at any frequency and wire size. Therefore, let's look at the problem of figuring the wire for a single resonant quad loop all over again.

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Fig. 1 shows us the basic ingredients for what we need. A single quad loop in free space has only two directly related dimensions: wire diameter and circumference length. If we express both measures in terms of wavelengths (or fractions of a wavelength), then the required perimeter length of the loop at resonance for lossless wire will be a direct function of the wire diameter. Remember that a fixed wire diameter, like #12 AWG wire (0.0808"), becomes a larger fraction of a wavelength as we increase the frequency. As we increase the wire diameter as a function of a wavelength, the loop circumference will also increase in terms of wavelengths.

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The only reason we also need to know the frequency is so that we can translate the input wire diameter from a common unit of measure, such as inches or millimeters, into a fraction of a wavelength. If we uses feet and/or inches, then a wavelength, L, becomes

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and +
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You can apply the length of a wave at your desired frequency to the wire diameter you select to get its diameter as a fraction of a wavelength.

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For convenience in what follows, the following is a handy little table of the diameters of AWG wire sizes often used for building quad loops.

+ 
AWG Size          Dia. Inches             Dia. mm
+18                .0403                   1.0236
+16                .0508                   1.2903
+14                .0641                   1.6281
+12                .0808                   2.0523
+10                .1019                   2.5883
+

Once we have converted our wire diameter into a fraction of a wavelength, we can determine how long the perimeter of a single resonant quad loop must be in terms of a wavelength.

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To find the relationship between the wire diameter and the perimeter length, I modeled a large number of quad loops and brought them to resonance, where resonance is defined as a feedpoint impedance with less than +/-0.1 Ohm of reactance. The process was considerably eased by using the model-by-equation facilities of NEC-Win Plus. Once I had placed variables for the wire dimensions and the wire diameter, a new model required only that I change two values on the equations page. Using this facility is how I came to realize that no matter what frequency I plugged into the model, the impedance did not change if I defined the variables in terms of a wavelength.

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The restriction on this result is the use of lossless or perfect wire and a free space model. However, changing any model's material into copper or aluminum yields no significant adjustments to the result. The resistive component of the impedance grew to reflect the wire losses (an Ohm or two), and the remnant reactance near resonance remained less than +/-1 Ohm. Of course, ground effects will vary from application to application and must be the responsibility of the builder and user of the antenna. However, quad loops are relatively less sensitive to changes in height above ground than dipoles with free ends.

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Fig. 2 shows the relationship between the wire diameter and the perimeter length, when both are expressed in terms of a wavelength. Note that the wire diameter axis is a log scale, and the "3162" steps are points at which the common log has a value of x.5. The graph is limited to wires sizes from 1.0E-05 to 1.0E-2, which covers the range of #18 on 80 meters to small tubing at VHF. As is evident, the relationship is not at all linear.

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The following equation is a first order approximation of the curve in the graph.

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where QL is the perimeter length of the quad loop and d is the wire diameter, both in wavelengths.

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The approximation is satisfactory for most amateur building projects, since the maximum error is about 2%, relative to the NEC models from which the algorithm was generated. The deviation from precise results can be shown in the following table which lists the reactance of quad loops modeled on the results of the algorithm.

+ 
Wire Size in WL               Reactance of the Calculated Loop
+      .00001                              - 1.1
+      .00003162                           - 7.9
+      .0001                               - 1.3
+      .0003162                            +11.4
+      .001                                +21.0
+      .003162                             - 0.1
+      .01                                 - 1.7
+

The maximum error occurs at a wire size of about 0.001 wl. For larger and smaller wire sizes, the error in the algorithm is far less than 1%. Fig. 3 shows a combination of the modeled curve and the calculated curve as further means of tracing the relative deviations of the algorithm from modeled results.

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Translating the results in wavelengths into normal units of measure is simply a second exercise in applying the relationships in the earlier given equations. The required perimeter length can be transformed into any common unit for the frequency specified at the beginning of the exercise.

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A Utility in GW Basic

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To save you the trouble of doing the transformation and algorithm calculations for each possible quad you may wish to build, I have put the basics of the discussion above into a simple utility program. The listing of the GW Basic program follows.

+ 
10 PRINT "Program to calculate the perimeter length of a resonant quad loop."
+20 PRINT "All equations correlated to NEC antenna modeling software."
+30 PRINT "L. B. Cebik, W4RNL"
+40 INPUT "Enter Desired Frequency in MHz:";F
+50 PRINT "Select Units for Wide Diameter in 1. Inches or 2. Millimeters"
+60 INPUT "Choose 1. or 2.";U
+70 IF U>2 THEN 50
+80 INPUT "Enter Wire Diameter in your Selected Units";WD
+90 IF U=1 THEN WLI=11802.71/F:D=WD/WLI
+100 IF U=2 THEN WLI=299792.5/F:D=WD/WLI
+105 PRINT "Wire Diameter in Wavelengths:";D
+110 L=.4343*LOG(D*10^5):LL=L^2:LM=LL*.0128:LN=LM+1.0413
+120 PRINT "Perimeter Length in Wavelengths =";LN
+130 WL=299.7925/F:PRINT "Wavelength in Meters =";WL
+140 PM=LN*WL:PRINT "Perimeter Length in Meters =";PM
+150 WF=983.5592/F:PRINT "Wavelength in Feet =";WF
+160 PF=LN*WF:PRINT "Perimeter Length in Feet =";PF
+170 END
+

The program let's you enter the wire diameter in either inches or millimeters. Anyone so inclined can add an AWG wire table module for direct entry of wire gauges. However, the table of diameters given earlier should satisfy most needs.

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Line 110 does most of the calculating, with the algorithm broken into steps. You can modify the line to repackage the equation if you prefer that form. The program was written in GW Basic, which only recognizes log-base e (natural logs). But then, GW Basic was a product of the 1980s (my edition is dated 1987). Hence, the log functions contain a conversion factor for log-base 10 (common logs). You can expand the 0.4343 multiplier indefinitely for greater precision of calculation (say, to 0.4342945), but the common conversion factor is precise enough for virtually all applications. If you translate the program into another medium that recognizes both common (LOGx) and natural (LNx) logs, you should remove the conversion factor if you retain the "log" notation. Current spreadsheets--a common substitute for Basic--tend to have both functions.

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Outputs (to screen only) include the input data, the wire size in terms of a wavelength, and the resulting perimeter length, also in terms of a wavelength. In addition, the outputs include the length of a wave in feet and in meters, along with the perimeter lengths in these units. I shall assume that conversion to inches or to mm or cm is a routine hand calculator job. However, you can feel free to doctor the utility program to include these outputs as well.

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I tend to prefer working up utilities in GW Basic, since the listing makes all of the arithmetic transparent, both for error detection and for transferring the information to others. Indeed, if this item is downloaded as an ASCII file and the text trimmed away, most GW Basic programs will run the ASCII program listing.

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Some Examples

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Let's run a few examples through the calculating utility and see how they stack up to NEC models. First, we shall use #12 wire on 20, 10, 6, and 2 meters.

+ 
Frequency   Wire Dia.   Wire Dia    Perimeter   Perimeter
+  MHZ         in.         wl          wl          feet
+ 14.1       0.0808      9.653E-5    1.0537      73.5026
+      Feedpoint Z             Feedpoint Z
+      Perfect Wire            Copper Wire
+      124.6 - j 1.5           126.3 + j 0.0
+
+Frequency   Wire Dia.   Wire Dia    Perimeter   Perimeter
+  MHZ         in.         wl          wl          feet
+ 28.5       0.0808      1.951E-4    1.0626      36.6716
+      Feedpoint Z             Feedpoint Z
+      Perfect Wire            Copper Wire
+      126.3 + j 5.9           127.6 + j 7.1
+
+Frequency   Wire Dia.   Wire Dia    Perimeter   Perimeter
+  MHZ         in.         wl          wl          feet
+ 51.0       0.0808      3.491E-4    1.0718      20.6697
+      Feedpoint Z             Feedpoint Z
+      Perfect Wire            Copper Wire
+      128.2 + j12.6           129.2 + j13.4
+
+Frequency   Wire Dia.   Wire Dia    Perimeter   Perimeter
+  MHZ         in.         wl          wl          feet
+146.0       0.0808      9.995E-4    1.0925       7.3598
+      Feedpoint Z             Feedpoint Z
+      Perfect Wire            Copper Wire
+      132.6 + j21.6           133.2 + j22.1
+

The series of #12 examples shows the "growth" in the wire diameter as a function of a wavelength. As well, the remnant reactance in the models that are based on the calculations reflects the curves shown in Fig. 3. Moreover, we can also see that as the loop circumferences grow, so too does the feedpoint impedance. However, as the wire diameter grows as a function of a wavelength, the losses reduce, as evidenced by the smaller differential between the resistive components of the perfect-wire and the copper wire impedances.

+

Before we leave you on your own, let's make a 146 MHz quad loop from 0.25" diameter copper and see what happens.

+ 
Frequency   Wire Dia.   Wire Dia    Perimeter   Perimeter
+  MHZ         in.         wl          wl          feet
+146.0       0.25        3.093E-3    1.1207       7.5497
+      Feedpoint Z             Feedpoint Z
+      Perfect Wire            Copper Wire
+      138.0 + j20.6           138.2 + j20.8
+

As we pass over the point of maximum error we begin to see a reduction in the remnant reactance. But just how much deviation from true resonance does the 20 Ohms represent? The circumference of the calculated loop is 7' 6.6". A NEC model that brings the antenna to resonance within the specified limits of +/-0.1 Ohm reactance requires a circumference of 7' 5.4". The difference is just over 1% of the overall perimeter length. If we reference the VSWR of the calculated loop to 138 Ohms, the resulting value is 1.16:1.

+

To see the effects of ground on our calculated loop sizes, let's try the #12 28.5 MHz copper wire loop at various heights.

+ 
Height (wl)       Feedpoint Z       VSWR Relative
+                  R +/- jOhms       127.6 Ohms
+Free Space        127.6 + j 7.1     ----
+0.5               125.3 - j 3.9     1.04
+0.75              128.8 + j14.9     1.12
+1.0               126.7 + j 1.2     1.01
+1.25              128.3 + j11.7     1.10
+

The upshot of this table is that calculating the single quad loop via the algorithm will result in usable results for any common antenna height. Since the antenna impedance will slowly stabilize near its free space value as we further increase the height, VHF quad loops especially will show no adverse affects from the divergence between the model and calculation curves in Fig. 3.

+

The result is that the error level in the first order approximation--within the limits of the wire sizes chosen as the extremes--is not operationally significant. In fact, it is likely that construction methods will yield a greater variance from the NEC models than calculations via the algorithm.

+

Better Methods

+

Since developing the initial approximation of the quad loop dimensions, I have redeveloped the algorithm using regression analysis. The revised algoritm appears in Fig. 5 in the form available as a NEC-Win Plus model file for download. A VB script generously made available by Randy Frum, AC4FD, of the regression-based analysis is also available for download. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen.

+
+ +
+

In addition, Herman van Elburg has developed an alternative regression analysis from the NEC data that is also very highly accurate. His equation is somwhat simpler and amenable to both hand calculator and spreadsheet use:

+
+ (loop circumference / L ) = A + B x (wire diameter/L) ^ C +
+

where L is a wavelength in air, and A, B, and C are factors derived from regression analysis. For the quad loop, A = 1.03258; B = 0.6732; and C = 0.37596. The general form of the regression equation appears in Fig. 6.

+
+ +
+

The maximum deviation--which occurs only with the fattest wire diameters--is just over 1/2%.

+

Conclusion

+

It is certainly legitimate to ask why I have gone to such fussy levels of explanation and correlation with NEC models in the presentation of the simple BASIC program to calculate quad loop circumferences. The answer has two parts.

+

1. We began with a traditional wire cutting formula from sources unknown in the dim recesses of amateur radio's history. That formula has always simply been presented as if it were correct, and it has become embedded in the minds of antenna builders. I did not wish this presentation simply to present an alternative in equally simple terms, trusting only to the belief potential of readers.

+

2. The circumference of a single resonant quad loop turns out not to be amenable to a simple cutting formula at all. The required perimeter length is a direct consequence of the wire diameter selected for the loop. Although there are means--as shown in the Basic program--to calculate the required circumference from the wire size, getting used to the idea of how quad loops behave requires some degree of immersion. These notes have been designed to provide a small bath of quad loop calculation.

+

The program, of course, even within the limits of its accuracy, applies only to square and diamond loops that are individually resonant. Dimensions of the loops within a quad beam using 2 or more elements will differ, just as do the linear elements of a Yagi relative to a single resonant dipole.

+
+ +
+

Moreover, the calculations will also require alteration for rectangular loops developed to achieve enhanced gain and a reduction of the feedpoint impedance to something closer to 50 Ohms. In general, the perimeter of such rectangular loops, when fed on the short horizontal elements shown in Fig. 4, will be somewhat longer than the circumference of a resonant square loop. Nevertheless, since squares are the most common form of loops, owing to the greater ease of construction, the little utility program in these notes should be serviceable for many antenna builders.

+

The updated versions of this program, using regression analysis results to derive more exacting dimensions, appears in the HAMCALC collection from VE3ERP. The following links will take you to a download page where you may download the program as a. a NEC-Win Plus model file, b. a GW Basic program, or c. a VB script generously made available by Randy Frum, AC4FD. Randy notes that the script will run natively on Windows ME and Windows 2000 and above and will run on other Windows operating systems (95, 98 and NT) if the Windows Scripting Host is installed (normally installed with IE 5 and above). Simply run the script from the "Run" command on your main screen. An on-line Java script calculator (web.archive.org). is available courtesy of the work of Steven Dick.

+

Also see the Antenna Modeling Programs page for more information.

+
+ +
+

Updated 03-01-2000, 03-23-2000, 11-14-2002, 02-02-2003, 05-02-2005. © L. B. Cebik, W4RNL. This item appeared in AntenneX, February, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Quad List

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Go to Main Index

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Topics: Quad


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+

The "Quad vs. Yagi" Question


+

L. B. Cebik, W4RNL


+
+
+ +
+

The history of beam antennas commonly used by radio amateurs is filled with hyperbole at various stages in the development of each antenna type. The post-war years that saw the rise of the Yagi-Uda parasitic array as the de facto amateur standard in directional beams also witnessed outlandishly hopeful specifications and claims for relatively poor antenna designs. Eventually, ARRL had to ban gain specifications from advertisements for amateur beams. Fortunately, that phase of Yagi development is behind us. The current generation of Yagis--largely designed with the aid of computer software of various types--tends to live up to the stated claims. Computers are not the only source of our improved understanding of parasitic arrays. Books by Lawson and Leeson have contributed some baseline information and ideas that hold in check any tendencies to overstate or imprecisely state what given Yagi designs can and cannot do.

+

The history of the cubical quad antenna is equally fascinating. Bill Orr's 1959 book on the subject devotes a chapter to Clarence Moore's invention to overcome high-altitude problems at HCJB in Quito, Ecuador. After World War II, the quad design gradually spread until it had attracted a diverse group of devoted fans. The 2-element driver-reflector quad beam still rules the quad roost, although much larger arrays have appeared from time to time.

+

One interesting facet of quad lore is the fact that many of the early claims have not gone the way of early Yagi claims. They remain as part of the rationale often given for using quads. In fact, they have become ingrained sound bites, passed along to potential beam users. Among the interesting ones are the following--taken from no particular source, but only from e-mail inquiries to me over the years.

+
+

Any beam's front-to-back ratio tends to vary depending on the installation environment, so the quad's front-to-back ratio is about as good as any beam's ratio.

+

The quad beam shows an absence of high-angle radiation.

+

A 2-element quad has about the same gain as a 3-element Yagi.

+

Quad beams tend to open and close bands, that is, they allow communications both before Yagis can make the same connection and after Yagis can no longer make the connection.

+
+

All of these statements have had proponents and detractors from time to time. I have for many years avoided examining the quad-Yagi dispute in any direct comparison mostly because I had not devised a reasonable test for the last of the claims. To the best of my knowledge, the claim emerged in the early 1970s, while Yagi design still languished in the throes of pure trial and error, with an emphasis upon error. Yet the claim persists to this day, perhaps just because devising a test for it--one that did not rely simply on operator reports--was impractical, if not impossible.

+

The following notes will eventually deal with that claim. However, before we can do so, we must first set up a 2-element quad beam and a 3-element Yagi beam so that we have a fair test. NEC-4 software will be our vehicle so that all tests are replicable by anyone who wishes to perform them.

+

A 2-Element Quad Beam

+

Much of the old design information on 2-element quads, including cutting formulas, still persists in the literature. Most of the design data needs an update. Over time, we have come to appreciate not merely the performance of an antenna on a particular design frequency, but as well, the operating bandwidth of the antenna. Operating bandwidth includes not only the SWR curve, but as well the gain and the front-to-back curves. In some cases, we may even become interested in the operating bandwidth of a directional antenna's vertical and horizontal beamwidth. We shall not need to go quite that far, since both quads and Yagis show relative stability in those parameters within any of the amateur bands. However, a good design for any amateur beam is one that not only performs well on a specified frequency, but as well, performs nearly as well across an amateur band.

+

For our investigation, we shall design beams for the 20-meter band, using 14.175 MHz as the design frequency. However, we shall be keenly interested in how well these beams perform across all of 20 meters. For the 20-meter quad beam design, we shall use a driver-reflector arrangement, with each loop composed of 2-mm diameter copper wire. (2 mm is 0.0787", which falls between the common amateur wires, that is, AWG #14 and AWG #12.) The general outline appears in Fig. 1.

+
+ +
+

The design used here derives directly from the algorithms that I developed some years ago for designing quads for any element diameter within reason and for frequencies between 3 and 300 MHz. The goal of the optimization exercise that results in the algorithms was to develop designs having the widest possible operating bandwidth for both the SWR curve and the front-to-back ratio. In the course of those studies, it quickly became apparent that the SWR bandwidth problem was easier to handle than the front-to-back bandwidth challenge. The results yielded designs that used wider spacing between the driver and the reflector than most of the literature showed. The listed specifications strictly apply only to square loops, although diamond loop dimensions will be almost identical.

+ 
+Physical specifications for the 2-element quad used in these notes
+
+Dimension                   Meters         Feet          Wavelengths
+Reflector side              5.629          18.47         0.266
+Reflector circumference    22.517          73.87         1.065
+Driver side                 5.341          17.52         0.253
+Driver circumference       21.366          70.10         1.010
+Driver-Reflector spacing    3.286          10.78         0.155
+
+

Note that is the wire size changes or the frequency changes, the listed dimensions may not directly scale. For the design frequency, we shall find the following NEC-4 reports of free-space performance. The lower portion of the report includes a matching section that I added to produce an exact 50-Ohm resistive impedance at the design frequency. We shall need this impedance later. The section is a 1/4 wavelength line with an arbitrary impedance necessary to produce the desire source impedance with the listed line length. The resulting source impedance is 50.000 +/- j0.000 Ohms. Any other lossless modeled network would do as well.

+ 
+NEC-4 report of free-space performance for the 2-element quad at 14.175 MHz
+Forward      180-Degree Font-     Beamwidth     Source Impedance
+Gain dBi     to-Back Ratio dB     degrees       R +/- jX Ohms
+7.05         40.59                76            132.1 - j0.01
+
+TL Zo       Line Length
+Ohms        meters
+81.27515    5.28795
+
+

Fig. 2 shows the free-space E-plane pattern for the quad beam. The pattern shows the total field (blue), the horizontal component (red), and the vertical component (green). Although small, the vertical component may have some role to play later in these notes. We may also note in passing that the quartering rear lobes tend to offset the very high 180-degree front-to-back value.

+
+ +
+

To gauge better the merits and limits of the quad beam design, we must perform a frequency sweep of the antenna across 20 meters (14.0 to 14.35 MHz). Fig. 3 graphs the forward gain and the 180 degrees front-to-back ratio of the antenna. Like all driver-reflector parasitic arrays, the quad beam shows a descending gain curve as we increase the operating frequency within the passband. The total change in forward gain across the band is about 0.9 dB, running from a high of 7.5 dBi to a low of 6.6 dBi.

+
+ +
+

Many antenna designers insist upon a minimum 180-degree front-to-back ratio of 20 dB across an operating passband. This goal is almost impossible for any quad design of which I am aware. (I have not been able to trace the 20-dB demand to anyone who happens to dislike quads.) Although the design used here has the widest front-to-back bandwidth of any 2-element that I have encountered, it still falls short of the demand. The low-end ratio is about 15 dB and the high-end ratio is a little under 18 dB. I shall not judge whether these band-edge values are good enough. Rather, I shall just note that most quads designs fall far short of what the present design achieves in front-to-back bandwidth.

+

I noted earlier that the front-to-back bandwidth proved more challenging than the SWR bandwidth. With the matching section in place, the resulting 50-Ohm SWR curve appears in Fig. 4. The SWR is 1.5:1 or less across the entire 20-meter band.

+
+ +
+

I am not recommending this design for replication--although one might build one as easily as any other 2-element design. My purpose has been to set-up a 2-element quad design with very good capabilities within its class. Now we need to turn to the design of a comparable Yagi.

+

A 3-Element Short-Boom Yagi

+

We need not re-invent any wheels when it comes to 3-element Yagi designs. The N6BV collection of Yagis in The ARRL Antenna Book gives us plenty from which to choose. For these notes, I have selected a variation of his short-boom design that in the 20-meter version would fit easily on a 16' boom. For these notes, I eliminated the tapered-diameter schedule and settled on 1" (25.4 mm) diameter aluminum elements. The general outline appears in Fig. 5.

+
+ +
+

I optimized the element length and spacing values for the uniform-diameter material. The results appear in the following physical specifications. Unlike the quad, you may scale the Yagi for different frequencies, so long as you remember to scale the element diameter as well as the element length and spacing values.

+ 
+Physical specifications for the 3-element Yagi used in these notes
+
+Dimension                   Meters         Feet          Wavelengths
+Reflector length            10.82          35.50         0.512
+Reflector-Driver spacing     1.84           6.03         0.087
+Driver length               10.19          33.43         0.482
+Driver-Director spacing      2.81           9.23         0.133
+Reflector-Director spacing   6.45          15.26         0.220
+
+

At the design frequency (14.175 MHz), NEC-4 reports the following performance values. Since the feedpoint impedance is not 50 Ohms, I also added a matching section to the Yagi driver to yield a purely resistive impedance of 50.000 +/- j0.000 Ohms. (The decimal places shown are part of the NEC output report. The version used is the one that accompanies GNEC. In seeking out such precise numerical results, be aware that different compilers and even different computer CPUs may shows very slightly different values. Normally, the differences make no practical difference at all. They only make sense in the context of tests yet to come.)

+ 
+NEC-4 report of free-space performance for the 3-element Yagi at 14.175 MHz
+Forward      180-Degree Font-     Beamwidth     Source Impedance
+Gain dBi     to-Back Ratio dB     degrees       R +/- jX Ohms
+7.18         43.68                68            28.8 + j0.01
+
+TL Zo       Line Length
+Ohms        meters
+37.93215    5.284
+
+

In terms of free-space performance, the only significant difference lies in the E-plane beamwidths of the two antennas. The quad beamwidth is about 8 degrees wider than the Yagi beamwidth. This difference would make a small difference in operation, but only in terms of how often we needed to rotate the beam to place a communications target within the main forward lobe. Fig. 6 provides the free-space E-plane pattern corresponding to the one shown for the quad beam.

+
+ +
+

The most notable difference between Fig. 6 and Fig. 2 lies in the absence of any visible green trace. Unlike the quad pattern, the Yagi pattern shows no evidence of a vertical component that rises to a -40-dB level.

+

We noted this Yagi as a short-boom Yagi, and its gain at the design frequency is less than 0.15-dB higher than the gain of the quad. We may thus comment on one of our original quad claims, namely, that 2-element quad gain is about the same as 3-element Yagi gain. Such a claim applies only to short-boom Yagis, such as the 16' long version that we have examined. The claim would be utterly false is we compared the quad to a longer-boom 3-element Yagi. With a boom closer to 24', a Yagi would have an additional dB of forward gain with an acceptable front-to-back ratio and a workable source impedance. The danger in the original quad claim was its reduction to a sound bite, omitting the context in which it is correct.

+

As we did for the 2-element quad beam, we need to examine the Yagi performance across the entire 20-meter band. Fig. 7 shows the forward gain and the 180-degree front-to-back ratio. Like all parasitic arrays with directors, the Yagi shows a rising gain curve as we increase the operating frequency. Although the gain curve appears to be as steep as the one for the quad--despite the opposing slope--we should carefully note the gain range. The gain varies from about 7.1 dBi to 7.3 dBi, a difference of only 0.2 dB across the band. We may compare this to the 0.9-dB gain range for the quad beam.

+
+ +
+

Unlike the 2-element quad, the 180-degree front-to-back ratio of the Yagi remains well above 20 dB across the entire 20-meter band. Indeed, we may also compare the rearward lobes of the quad and the Yagi. Although the shapes are similar, the Yagi rearward lobes are considerably weaker. These facts lead us back to another of the original claims about quads, namely, that front-to-back ratio is too environmentally dependent for us to make reliable comparisons. Given the data that we have seen so far, this claim has the appearance of being a smoke screen for the quad's somewhat inferior performance with respect to rearward lobes. We shall return to this matter when we eventually place both antennas above ground.

+
+ +
+

Fig. 8 provides the matched 50-Ohm SWR curve for the Yagi across the 20-meter band. The curve is not significantly different from the one for the 2-element quad. In both cases, the antennas used an artificial matching section impedance to achieve the perfect match at the design frequency. Using the nearest real cable in both cases would yield very similar SWR curves between the quad and the Yagi.

+

Quad and Yagi over Ground

+

Our exercise so far has had essentially one purpose: to create comparable 2-element quad and 3-element Yagi designs. Since the models are in free space, we need to bring them down to earth in order to evaluate their relative performance in a more realistic situation. A wavelength at 20 meters is approximately 70', a normal height for beams in amateur service. Therefore, we may create under each beam model an average ground 1 wavelength below. Since the beams are horizontally polarized, the exact ground quality will make only a small difference to the performance numbers. The main requirement is that we assign the same height to both beams.

+

The height of a quad's physical center-point may differ a bit from the electrical height, that is, the height that yields the same elevation angle of maximum field strength (TO angle) as a planar beam, such as a Yagi. In this case, assigning a 1 wavelength height to the quad's center produced the same TO angle as the Yagi.

+ 
+NEC-4 performance report for the 2-element quad and the 3-element Yagi
+at 14.175 MHz at 1 wavelength above average ground
+
+Quad
+Forward     TO Angle    Vertical      180-Degree Font-     Horizontal
+Gain dBi    degrees     Beamwidth     to-Back Ratio dB     Beamwidth
+12.30       14/76       16 deg        30.02                76 deg
+
+TL Zo       Line Length     Source Impedance
+Ohms        meters          R +/- jX Ohms
+82.8        5.32055         50.000 +/- j0.000
+
+Yagi
+Forward     TO Angle    Vertical      180-Degree Font-     Horizontal
+Gain dBi    degrees     Beamwidth     to-Back Ratio dB     Beamwidth
+12.51       14/76       16 deg        28.87                68 deg
+
+TL Zo       Line Length     Source Impedance
+Ohms        meters          R +/- jX Ohms
+37.2155     5.41325         50.000 +/- j0.000
+
+

The data show that the two antennas have gain values that are only about 0.2 dB apart. Both beams show the same TO angle (where the first number is the elevation angle and the second is the theta angle). In fact, both beams show the same vertical beamwidth. The similarity of the elevation or theta patterns is evident in Fig. 9.

+
+ +
+

In both patterns, we find a second elevation lobe at about 45 degrees (theta or elevation). The quad's second lobe appears to be very slightly weaker than the one that appears in the Yagi pattern. In operation, both second lobes would have almost identical affects. The idea in one of the initial claims about quads that they do not produce high-angle radiation appears to be derived from the fact that horizontal antennas vertically spaced by 1/2 wavelength tend to cancel vertical radiation. However, the second elevation lobe is a considerable departure from the vertical. Moreover, the cancellation decreases rapidly as we reduce the spacing between wires. The quad wires are only 1/4 wavelength apart. The combination of these two conditions yields a second elevation lobe that is perfectly normal for any horizontal beam. As we move from the horizon to the zenith, we find that neither beam has significant radiation straight upward.

+

The bottom line with respect to transmitting elevation patterns is that neither antenna shows a significant advantage over the other. Nothing in the relative lobe strength or the vertical beamwidth would account for the supposed ability of the quad to open and close DX bands.

+
+ +
+

Fig. 10 provides us with a comparison of the azimuth patterns for both beams using the TO angle as the pattern reference. As the data attest, the azimuth patterns have the same horizontal beamwidth as they had in free space. 1 wavelength is not a height that maximizes the front-to-back ratio. (3/8, 7/8, and 1-3/8 wavelength are all better heights for that purpose.) Hence, both beams show lesser values of 180-degree front-to-back ratio than they did in free-space. The quad has the higher value by a small margin. However, the quartering rearward lobes are considerably stronger than those of the Yagi. If we were to average the forward gain to rearward gain ratio throughout both rearward quadrants, the Yagi would achieve the better value. Since the antennas occupy the same environment, the smoke-screen claim among our original quad statements reveals itself as a cover-up for the fact that 2-element quads do not control their rearward lobes as well as a 3-element Yagi. A study of parasitic beams will show that the front-to-back ratio of a beam with one or more directors is capable of better rearward lobe reduction than a beam with only a reflector. The quad's complex mutual coupling does a better job at rearward lobe control than a single 2-element driver-reflector Yagi, but we require at least one director to fully tame the rearward lobes to a level at least 20 dB below the forward gain across the entirety of the rear quadrants.

+

A Receiving Test

+

Nothing in the transmitting patterns of the 2-element quad suggests any advantage over the Yagi relative to any of the claims with which we began. Perhaps the only claim not fully tested is the idea of the quad having superiority over a Yagi when the propagation is weak, that is, at the beginning and the ending of a daily cycle. Since the shape of the total field does not indicate any significant difference, we have only one remaining possibility, although it is a weak one. The quad did show a remnant vertical component to its radiation pattern. Years ago, I read a study--long since lost--that suggested that at one or the other end of a daily propagation cycle, the energy might not be as thoroughly skewed with respect to polarization as we take it to be when propagation is strong. Indeed, the study suggested that the dominant polarization might be at a 45-degree angle relative to either the vertical or the horizontal.

+

We can test this hypothesis in NEC-4 by altering the test conditions. Instead of setting up a source on the feedpoint segment, let's instead use a linear plane wave as the excitation. We shall set the source so that the beam's main forward lobe is aligned with it. We may also set the excitation at any vertical angle. We shall try theta angles from 70 degrees to 86 degrees (elevation angles from 20 degrees down to 4 degrees) to be certain that we cover all likely DX skip angles. Fig. 11 shows the general set-up.

+
+ +
+

Instead of placing a source at the former source segment, we shall place a 50-Ohm receiving load at that position. Using the receive pattern (PT) command, we may sample the current at that segment for comparison between the two types of beams. (This set-up is why the two beams used matching sections to produce a source impedance of exactly 50 Ohms resistive.) In all cases, we shall use a plane-wave excitation of 1 V/m for uniformity.

+

We shall go one step further. The linear plane-wave excitation command (EX1) allows us to vary the angle of the plane wave (eta) from 90 degrees (horizontal) to 0 degrees (vertical). Therefore, we may fairly test to see if the quad has sufficient sensitivity at any incoming polarization angle to give it an advantage over the Yagi.

+
+ +
+

Table 1 shows the tabular results of the exercise as applied to the quad beam. To provide a better appreciation of the variation of current magnitude on the antenna feedpoint as we change the polarization, Fig. 12 plots the curves for selected theta/elevation angles.

+
+ +
+

The strongest curve at all plane-wave eta angles (except for 0 degrees) coincides with the TO angle for the antenna. The adjacent curves at 4 degrees above and below the TO angle are nearly equal. As we lower the TO angle to 6 degrees above the horizon, we find a considerable weakening of the current magnitude on the source segment. However, for horizontally polarized signals, the current magnitude is more than half the level we find at the TO angle.

+

We may perform the same exercise for the Yagi. The tabular results appear in Table 2.

+
+ +
+

Once more, we can more clearly see the smooth curves by graphing selected theta/elevation angles--the same ones that we used for the quad. Indeed, Fig. 13 shows the same set of relationships among the curves that we saw in trhe quad graphic. Even at an elevation angle of 6 degrees, horizontally polarized signals have more than half the value of similarly polarized signals at the TO angle.

+
+ +
+

We may go a step further. Let's directly compare the current magnitudes on the source segment for both antennas at the TO angle (76/14 degrees theta/elevation). Fig. 14 shows the resulting dual plot.

+
+ +
+

The plot shows that the curves are congruent throughout the range for eta. (Indeed, we may compare the current values for the TO angle with an eta of 90 degrees. Converting the ratio to dB, we obtain a gain difference of just over 0.2 dB, just the same as we obtained from the transmitting plots.)

+

To ensure that any performance differential is not a function of the signal's incoming angle, let's repeat the plotting process for a 4-degree elevation angle (86 degrees theta). Fig. 15 supplies the outcome.

+
+ +
+

Once again, we have congruent plots with no exceptions at any value of eta. The quad's remnant vertical component proves to be ineffective in improving cross-polarization reception relative to the Yagi with its purely linear elements. Nothing in the receiving test--with plane-wave sources at a variety of elevation angles and a thorough scan of polarization angles--gives us any reason to suppose that one antenna has an advantage over the other.

+

Conclusions and Historical Speculations

+

Both Yagis and quads are highly modelable antennas that do not come close to pressing any limitation of NEC software. If we set up highly comparable beams--a 2-element quad and a 3-element short-boom Yagi--we reach the inevitable conclusions that neither antenna has a decisive advantage over the other, no matter how we test them with the software. Therefore, the remnant claims for quads with which we began our exercise turn out to have little or no foundation. A 2-element quad only matches the gain of a short-boom 3-element Yagi but does not equal the gain of a long-boom 3-element Yagi. The potential for higher-angle radiation is roughly the same with both types of beams. The addition of a director to the Yagi gives it somewhat better control (or attenuation) of the rear lobes than we find in a quad with only a reflector. Finally, nothing in the receiving or transmitting patterns of the two types of antennas lends any support to the idea that one or the other is superior at daily band openings or closings.

+

The quad claims appear to be simple remnants of a bygone era in antenna design. Whereas Yagi proponents have largely grown silent with respect to early exuberant claims, the quad claims have hung around long after they have lost their foundation. There was a day--perhaps a quarter century ago or more (that is, prior to 1985) when such claims might have been true. Yagi home builders often confused front-to-back ratio for forward gain in the absence of adequate range tests. In the preceding decades (the 1960s and 1970s) even ZL-Specials and HB9CVs outperformed many of the existing Yagis. In that case, writers presumed that the Yagis were performing to their theoretical potential and then ascribed to the phased array unreasonably high gain values. (These claims also persisted well past their time.) So it is quite plausible that various quad designs outperformed common 3-element Yagis of earlier days.

+

However, those days are generally over. The present generation of Yagi designs (and not all Yagi makers use present-generation designs) achieve the peak performance of which a Yagi configuration is capable. Indeed, in the world of Yagis, we no longer expect to discover truly new designs with a performance miracle. Perhaps the best progress has appeared in the realm of multi-band Yagis and hybrids that use small or large phased driver arrangements to improve performance bandwidth.

+

A similar situation applies to quad beams. As we learn more about the basic properties of quad beams, we are discovering that they have both advantages and limitations. One of the lessons that we have had to learn is that we cannot simply transfer a Yagi design to quad loops. The mutual coupling between closed loops sets up requirements that may sometimes differ widely from those applicable to the Yagi's linear elements.

+

In the end, there are good reasons to use a quad and good reasons to use a Yagi. However, when it comes to deciding between a 2-element quad and a 3-element short-boom Yagi--when both are monoband beams--the considerations will (or should) not include expectations of great performance differences.

+
+ +
+

Updated 07-23-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Upper, Quad, Yagi


+ + diff --git a/content/quad/trq.html b/content/quad/trq.html new file mode 100644 index 0000000..2193ecd --- /dev/null +++ b/content/quad/trq.html @@ -0,0 +1,65 @@ + + + + + + 12/17-Meter Trap Quad + + + +
+

A Trap Small Quad Beam for 12 and 17 Meters

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In conversations with Paul Carr, N4PC, at the 1997 Huntsville Hamfest, he suggested that--based on some notes in my article on small quads--a duo- band quad ought to be possible using a trap in the wire connecting the hat wires to the diamond quad loop. The loop is resonant on 12, while the loop plus trap plus hat wires are resonant on 17. See Figure 1, Question: can one make a usable 2-element beam on this principle, say for 12 and 17 meters? +
+ +
+

Answer: yes, although it might be a somewhat finicky construction job, especially on 17 meters, where the shortening makes wire lengths somewhat more critical. However, the idea might be worth pursuing, since these are bands where many folks are looking for something better than a dipole, but not as expensive or as large as a full-size commercial beam.

+

Take two of the diamonds of #14 copper wire in Figure 1 and set them 8.15' feet apart. Make the driven element (forward) diamond just about 10' per side (actually, 39' 11 inches in circumference). The rear diamond should be just about 10.4' per side (circumference = 41' 7.5"). The resulting diamond quad is 14' 9" tall and the same size wide, which is fairly compact for a 12 and 17 meter antenna.

+

The capacity hats are the wires starting at the side points of the diamond. They begin with a wire 9" long, from which 2 wires extend parallel to the main loop wires. Each is just about 2' 5" long for each loop.

+

The traps are parallel inductor-capacitor combinations with a target reactance per component of 250 ohms, giving 1.6 microH and 25.5 pF. The design used a target Q of 200. Variations in Q or trap components will affect the required lengths for the hat wires parallel the loop wires for 17-meter resonance.

+

The resulting antenna produces feedpoint impedances in two ranges. For 17 meters, the impedance is just above 100 ohms, while on 12 the impedance is closer to 160 ohms. For a 50-ohm match, one bands wants a 2:1 transformation, while the other band prefers a 3:1 transformation.

+

A series section of 75-ohm coax with a velocity factor of 0.66 can be between 7' and 7.5' long and effect the transformations close enough to provide under 2:1 SWR across both bands. (Note, this is a simple series section chosen for its impedance transforming characteristics. It is not the usual 1/4 wl section.)

+

The predicted performance of the antenna is given in the following table derived from NEC-4 models:

+ 
Freq.    Gain  F-B     Natural     With 7'   SWR     With 7.5'   SWR
+MHz      dBi   dB      Feed Z      RG-59     50      RG-59       50
+
+18.068   5.67  12.71    96 - j11   42 + j 8  1.27    44 + j12    1.34
+18.1     5.62  17.15   114 + j 4   47 - j 1  1.07    47 + j 3    1.08
+18.168   5.35  29.41   149 + j22   44 - j16  1.43    43 - j12    1.34
+
+24.89    6.87  18.37   160 - j 2   34 + j 7  1.54    35 + j14    1.63
+24.95    6.76  20.37   168 + j 3   32 + j 6  1.60    33 + j14    1.69
+24.99    6.68  21.18   172 + j 6   31 + j 6  1.64    32 + j14    1.73
+

The next two figures illustrate the free space azimuth patterns for the mid-12 and mid-17 meter band points. The gain in 12 is quite decent, as is the front-to-back ratio. On 17, gain is down, although the front-to-back ratio holds up--a feature of shrunken 2-element antennas.

+
+ +
+
+ +
+

Both patterns are quite serviceable, although not exceptional. Since the antenna can likely be built on a stressed light PVC frame, in a manner similar to the construction I used for the 10-meter shrunken quad, experimenting with this design should not be a budget buster. If it does not work out to satisfaction, the PVC can be converted into tomato stakes next spring, and the wire used for other antennas.

+

Nothing in these design notes is certified by construction. But the design techniques may have an adaptable idea or two for some other project. Or, with some luck and patience, you might just end up with a usable small quad for 12 and 17 meters.
+

+
+ +

+
+

Updated 9-29-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Upper, Quad, Traps


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+ + + + + +
W4RNL title graphicL. B. Cebik, W4RNL (SK)
+ Knoxville, TN
+
+
+

+

Amateur Radio, Tales and Technicals

+

Amateur Radio is a communications service consisting of operators licensed and regulated in the United States by the Federal Communications Commission. Amateur radio operators, by regulation engage in emergency and other public service communications, maintain technical skills, and foster international good will via communications.

+

My personal interest in amateur radio focuses on research into and education about antennas and antenna modeling. The listings on this page link to some past and present research (and to some past research updated before posting on these pages). Since these are essentially working notebooks and not polished articles (for the most part), they may contain typos, misspellings, and a few grammatical infelicities. Moreover, they are subject to revision and updating whenever I discover something more accurate, more useful, or more interesting.

+


+

+

Tales and Technicals:
+ A Little History and a Lot of Antennas

+

From time-to-time, I shall post some yarns, mostly taken from my collection of old books, manuals, magazines, and handbooks. I shall also occasionally post from the pages of my notebooks some technical information that may be of use to fellow and prospective hams. To keep this index from being too long to use, I have placed many items in collected groups. So be sure to check the listings that appear to collect items together from time to time for additions. Since these are notes and some reprints of casual articles, there will be considerable overlap in places--and many large gaps in other areas. Nevertheless, let's begin with these items:


+

A Little History, a Little Humor, and a Little Seriousness

+
+

Antenna Modeling Software Notes

+ +

See also the Antenna Modeling series


+

Practical Antenna Notes: Lower HF (Mainly) Vertical Antennas

+
+

Practical Antenna Notes: Lower HF (Mainly) Horizontal Antennas

+
+

Practical Antenna Notes: Upper HF (Mainly): Yagis and Relatives

+
+

Practical Antenna Notes: Upper HF (Mainly): Other HF Arrays and Questions

+
+

Practical Antenna Notes: VHF/UHF (Mainly)

+
+

Transmission Lines, Impedance Coupling, and Construction

+
+

Continuing Series

+
    +
  • + Antenna Options: a series of articles appearing on an irregular basis in QEX. The basic theme of the series is that, whatever the interest in antenna design, construction, or use, the amateur always has options. The more we understand our options, the better decisions that we shall make. +
    • +
  • Antenna Modeling: a series of articles on antenna modeling specially prepared for antenneX. The series aim is to help antenna modelers get the most benefit and least anguish from their programs.
    • +
  • + An-Ten-Ten-nas: a series of articles for 10-10 News on antenna basics having special relevance to 10-meter operation. +
    • +
  • + Antennas From the Ground Up: a series of articles on antenna basics originally created for Low Down, the journal of the Colorado QRP Club. The emphasis is largely on lower HF and wire techniques. +
    • +
  • + Amateur Radio Continuing Education: a series of articles prepared over several years for the annual Proceedings of the ARRL National Education Workshop. The pieces range in scope from a full-scale proposal for a technical education series down to using a blackboard more effectively in the classroom. There are also links to some other educational sites. +
    • +
+
+

HAMCALC

+

Numerous articles refer to HAMCALC, a suite of utility calculation programs developed for hams by George Murphy, VE3ERP. The information in the articles gives Murph's address for obtaining the current version on CDROM. Due to a bout of ill-health, HAMCALC is no longer available on CDROM. However, you can obtain HAMCALC from this link to the CQ Magazine site (web.archive.org) and download the current version of the suite in Zipped format. The site provides instructions for installation and use.

+


+ Links to Other Antenna Information +

These links carry a lot of valuable information and ideas, ranging from antenna fundamentals to advanced topics in antenna design, modeling, feeding, and building. In addition, some provide links to other sites.


+
+

Commercial Antenna Manufacturers and Vendors: A collection of known sources, offered because these pages often contain educational as well as commercial information.


+
+
+

Other Amateur Radio Links: A small collection of links to organizations and linkage sites to help you find other good sources of information.


+
+

+

A Final Note

+

You will note an absence of reviews, analyses, and evaluations of commercially made antennas in the notes at this site. It would be inappropriate for me to remark on such antennas without having the antennas at hand and the appropriate range and equipment for testing them. These notes relate to antenna types and designs over which I have design control and are generally aimed to assist you to understand their operation. Even specific designs are not intended for uncritical replication, although a number of them have been successfully built and used. Still, the goal is not to produce a compendium of antennas for you to build. Rather, the object is to assist you to understand the antennas that you do build, use, or simply think about.

+

You may note that I do not attach my name or call to any antenna design. There are 2 main reasons for this action. First, I prefer to call antennas by their technical titles, except where there is already a traditional name that brings ready recognition of the technical features of the antenna. In a few cases, where an antenna's originator deserves recognition and a technical label might be cumbersome, I have given the antenna a name. Hence, I refer to the Moxon rectangle rather than to a 2-element, rectangular, dual-coupled, parasitic array. I claim no originality for any antenna design in these notes and have patented nothing shown in any article. Second, the aim of these notes is to assist you--in small bits--to understand the antennas involved and antennas in general. Hence, most of the designs are derivative from existing designs taken from texts and handbooks. Nothing in the collection deserves re-labeling with my name or call.

+

Please do not attempt to download the entire site using software designed for blind downloading. If you wish a record of the entire site, antenneX periodically produces a CDROM with the entire site on it. However, I have kept most (but, alas, not all) of the items at the site short enough to read at a single sitting. Pick something of interest, read, and digest. Then pick something else. Let your wandering interests be your guide. If you wish to read more on a subject, by all means, select a related item. Or, look in other good sources for information on the subject. This site is collection of items cast at an intermediate level. Hence, it is far from the last word on any subject, whether you think of basic theory underlying a matter or about very practical construction and operation aspects of an antenna or system.

+

When you begin to track the items at this site, you become a companion down the path of antenna explorations that I have followed. Be certain that you are ever alert to pathways that are a function of your own interests. This pathway is not the only one, and it is far from the perfect one. But it has been and continues to be both a good and interesting one.

+

It has been my high pleasure to receive e-mail and regular mail that suggests these materials are of educational and technical service to a broad spectrum of individuals, both in the United States and around the world. Numerous items have appeared in the newsletters and other publications of amateur radio groups. The formal and informal distribution of some of the material, both as written and in translation, in areas where bound publications are unavailable or prohibitively expensive suggests that the energies used to develop and place some of the notes has been productive. So much to learn and so little time to learn it, but always time to share what I have learned along the way--lest it be lost.

+ +

I also receive inquiries into available books. For a list of books that I have put together, see the book page.


+

W4RNL animated graphic


+

-73-

+

LB, W4RNL


+
+
+

Updated 04-04-2008

+
+
+
+
+

Return to Home Page


+

+

Pages by The House of Two Lions

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+

The 40-Meter Bobtail Curtain as An All-Band Wire Antenna

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Sture Lof, SM5DXV, described to me an interesting adaptation of the 40-meter Bobtail Curtain to all-band use. The use was interesting enough to pass along as a possibility for those who use a wire on all bands.

+

Sture did not provide dimensions, so I went back to the SCV series at this site and developed an optimized 40-meter (7.15 MHz) antenna. This frequency is at the high end of the European band, but in the middle of the U.S. Band. Actually, dimensions are not that critical, although the rough proportions will tend to provide the maximum gain on 40. As well, I selected the height for the same goal.

+
+ +
+

Fig. 1 provides the dimensions for the antenna, along with the three feeding options for 40 meters, for bands below 40, and for bands above 40. The technique that Sture passed along was to construct the center wire from parallel transmission line. By judiciously connecting the bottom end of the center vertical line, we can achieve an all-band antenna.

+

The dimensions are quite reasonable and only a little longer than an 80-meter dipole. The total length is 149' (74.5' each side of the center vertical), with vertical legs that are 33.5' long. With the top wire at 44' above average ground, the vertical tips are 10.5' above ground, a safe height to prevent accidental contact with these high voltage points on the antenna. However, for convenient feeding, we bring the center wire close to the ground. Therefore, some form of "fencing" to prevent contact is a wise precaution.

+

The Bobtail on 40 Meters

On 40 meters, the Bobtail curtain operates in its design mode--as three 1/4 wavelength verticals spaced about 1/2 wavelength apart. Instead of using individual feedlines properly phased, we use a top wire that provides the correct phasing. Because the currents on the top horizontal wire are equal and of opposite phase at any distance from the center wire, the horizontal radiation is largely self-canceling. The result is a vertically polarized broadside pattern. +
+ +
+

The current magnitude distribution, shown if Fig. 2, shows that the peak current on the verticals is at the top of the element, a desirable location for a low angle signal. As well, the maximum current on the center wire is twice the value of the maximum value on the end verticals. Of special note is the current distribution on the center wire. With the wire extended down nearly to ground level, where we locate a matching tank circuit, we need have no concern about the center wire's extra length. The current distribution shows the minimum at the same height as the tips of the end verticals.

+

The most common way to feed a Bobtail is still the use of a matching tank circuit that resembles the left option in Fig. 1. The parallel tank circuit would be similar in appearance and component values to an old fashioned plate circuit for a tube amplifier. The coaxial feedline can either tap the low end of the coil, a few turns above ground--and a good RF ground is essential--or one may use a small link coil over the low end of the tank coil. The parallel transmission line forming the center vertical is shorted and connected either to the top of the coil or to a tap near the upper end of the coil--whichever provides the best match. If the system is near resonance, then the reactance will be high. With the extended center vertical, the resistive component is likely to be much lower. Hence, initial set-up will likely involve a good bit of juggling of the two taps and the setting of the variable capacitor. But once set, the match should cover at least half of 40 meters with a 2:1 SWR on the main feeder line. Be certain to weather-proof the assembly when you finalize the settings.

+
+ +
+

The Bobtail should provide about 5.1-5.2 dBi gain at an elevation angle of maximum radiation (Take-Off or TO angle) of 19 degrees. Fig. 3 provides a view of both the elevation and the azimuth patterns of the antenna. In this azimuth pattern, and in all others to follow, the horizontal wires of the antenna stretch from left to right across the graphic. Why many operators prefer a Bobtail to a dipole with the same top height appears in Fig. 4.

+
+ +
+

The elevation patterns are for a 40-meter dipole and the Bobtail, both with a height of 44'. This height is a bit above the average U.S. casual wire height (about 30'-35'), but the dipole pattern is still filled with very high angle radiation. Its maximum gain--6 dBi--occurs at about 44 degrees elevation. The slightly lesser gain of the Bobtail, however, occurs in just those regions favoring DX skip. In addition, the Bobtail has very little high angle sensitivity, and a large amount of QRN and other interfering signals are relatively high-angle incoming energy. For many, the Bobtail is a nearly ideal wire DX antenna, especially considering that it is cheap, low enough for easy maintenance, and durable. Although we need a good RF ground for the base of our matching tank circuit, we do not need a radial system for the antenna on 40 meters. Indeed, you can think of the end verticals as composed of two L-shaped dipoles, while the center vertical is a Tee.

+

If you do not quite have the 150' length needed for the idealized Bobtail, you can make it as short as about 125' by lengthening the verticals to about 38'. The best top height for the shortened Bobtail is about 50' above ground, which places the end vertical tips 12' above the soil. Once again, we can bring the center vertical all the way to the ground without disturbing the pattern. At most, this shortened (lengthwise) version loses only about 0.1 dB of gain or so.

+

However you build your Bobtail for 40, you will discover that setting the matching circuit benefits from a friend with a VHF/UHF transceiver and a field strength meter at least 10 wavelengths distance and broadside to the antenna. Tune for a combination of a good main feedline match and maximum signal strength. It is possible to obtain a good match with most of the energy circulating in the tank and not as much in the antenna.

+

Converting the Bobtail to 80 and 160 Meters

On 80 and 160 meters, we connect the feedline ends together, but set aside the matching tank circuit. We feed the combined lines against a ground radial system to form a shortened top-loaded vertical. We should use very low loss line to the ATU. It may even be possible to use an automatic ATU at the feedpoint. +

The top loading consists of a modified Tee. The horizontal wires and the end verticals form the top hat for the vertical antenna. Radiation tends to be at a fairly high angle, and so the antenna is good mostly for local or regional contacts. Because the end wires interact with the central vertical, the pattern will change as we move across 80 and 75 meters.

+
+ +
+

Fig. 5 shows typical patterns for the ideally shaped Bobtail. As we move upward on the band, the spacing between verticals changes, and so does the overall current distribution. So the pattern can range from a figure 8, with most radiation in line with the antenna, to a clover leaf. The exact dimensions we use for the Bobtail will have a bearing on the exact patterns we achieve. Likewise, the impedance can range from 100 to 1500 Ohms resistively and -1500 to +5000 Ohms reactively. So the matching situation calls for the widest range tuner you can find or make.

+
+ +
+

Fig. 6 shows the general circular pattern that we achieve on 160 meters, where the current on the outer verticals is low and distorts the pattern very little from normal. Of course, the antenna is short, but the Tee hat is just about long enough to bring the antenna close to resonance. Close does not mean a very low reactance, but a manageable one. However, the resistive component will be low--about 10 Ohms before we add in loss factors resulting from the ground quality and the size of our radial system. Hence, a couple of hundred Ohms of reactance yields a very high SWR to match.

+
+ +
+

Fig. 7 shows the current distribution along the wires of our top-loaded short vertical at 1.85 MHz. At a height of less than 0.1 wavelength, the antenna cannot be expected to be a stellar performer. If you need DX performance on 160 meters, you will require a quite different design.

+

While certainly less than optimal for 80 and 160 meters, the adapted Bobtail still permits communications on these bands. Of course, one can build a Bobtail for 80 meters (about 296' long at 3.6 MHz) and shift these patterns downward by one band.

+

The Bobtail Adapted for Use on Bands Above 40 Meters

For all bands above 40 meters, the Bobtail opens up the double center vertical to use the transmission line as what it is: transmission line. so the antenna is no longer a Bobtail curtain. Instead, it becomes a center-fed doublet at 44', with drooping end sections. On some bands, the current in the vertical end sections is insignificant relative to pattern formation. On other bands, it will play a significant role. +

The following table lists the modeled results for the new doublet. The maximum gain is the gain of the strongest lobe in the pattern. All of the patterns (except 30 meters) have multiple lobes, since the doublet is 216' long from tip to tip. The Hor. Angle indicates the angle between the plane of the wire and the strongest first lobe in the horizontal plane. The TO Angle is the elevation angle of maximum radiation. The feedpoint impedance (Feed Z) shows values taken at the junction of the wire and the transmission line that formerly was our center vertical.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Performance of the Modified Bobtail on the Upper HF Bands
+
+Freq.      Max. Gain  Hor. Angle       TO Angle        Feed Z
+MHz        dBi        degrees          degrees         R +/- jX Ohms
+10.125     5.5        90               31               440 - j 1200
+14.1       7.9        57               21              1800 - j 1500
+18.118     8.2        43               17              2500 + j  200
+21.1       8.5        28               15               300 + j  310
+24.94      6.8        21               14               270 - j  125
+28.1       8.5        39               11              1000 - j  800
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Not listed in the table is 80 meters. The user can operate the antenna as a low doublet with drooping ends on 80 meters. 44' is low and yields high angle radiation, but the pattern will be an oval that is nearly circular. So it may complement the use of the antenna in the hatted-vertical mode described above.

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In the chart, bands with the lower gain values tend to have the most activity by the vertical ends sections of the doublet. We can check out 30 meters as an example.

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Fig. 8 shows the azimuth pattern at the TO angle for 10.125 MHz. The total pattern is composed of vertically and horizontally polarized components. If you examine just the horizontal component, you will find a slightly distorted figure 8. However, the vertical end wires are active enough to produce radiation off the ends of the doublet. Hence, the total pattern is bi-directional with significant side lobes less than 10 dB below the strength of the two main lobes.

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Fig. 9 gives us just the total patterns for the remainder of the upper HF bands from 20 through 10 meters. Each pattern uses the TO angle. 20, 17, and 10 meters show the least activity in the vertical end wires. Hence, their patterns have the fewest lobes--commensurate with the length of the antenna in wavelengths--and the deepest nulls in the direction of the plane of the antenna. In all cases, the antenna runs horizontally across the pattern.

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15 and 12 meters show higher levels of activity in the vertical wires. The chief indicator is the ragged pattern outline, indicating many individual lobes, some created by the length of the horizontal wire, others created by the phase relationship between the two active end vertical wires. As well, the null that we would expect off the ends of the doublet is very shallow.

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Let's open up the 12-meter pattern and take another look at how the lobes form. See Fig. 10. The vertically polarized component of the field obviously is at work in making the end null shallow. As we gradually move toward a position broadside to the wire, we can see that some lobes in the total field result from horizontal component lobes, others result from vertical component lobes, and still others are combinations of the two. The complexities of a pattern like this suggest some points to remember.

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First, for wires with even modest geometric complexity, a random guess at the lobe structure based on what a linear doublet might produce is likely not to give too much guidance as to the pattern shape. If you model your antenna, be as precise as possible with every twist and turn to arrive at the most usable result.

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Second, if you ask someone else about your pattern shapes, do not expect precision in the answer that you get. You will receive--in a best-case scenario--only as much precision as you put into the question.

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However, once we reach the bottom line, we get the following result: if we can effect a match with the orders of impedance indicated in the chart, we have a doublet that will be as effective as most other single- wire doublets. For the ham with room for only one wire antenna, then, the Bobtail is not a bad choice.

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However, let's remember that the antenna here emerged from a desire for an effective DX antenna on 40 meters. The other bands were bonuses. Indeed, if one also has a beam for upper HF DX work, then the ability to tune the Bobtail as a doublet on the upper bands gives one a good back-up antenna for when the rotator freezes or when an element breaks, or (more benignly) for a second receiver checking for openings on other bands.

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One caution: only consider the bobtail curtain in any form if you have the room to keep the elements in a straight line and apart from each other as the dimensions suggest. Do not try to bend the bobtail. Even a shallow Vee shape with a 150-degree included angle (where straight is 180 degrees) will reduce gain by a full dB on the primary band. A 120-degree included angle will reduce performance to a nearly circular pattern with a gain level not much different from a single monopole.

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So the all-band Bobtail is not for everyone. But it may serve well for some.

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Updated 05-27-2003, 02-04-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Bobtail Curtain, HF Multi Band, SCV


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Triangulating Bobtail Curtains

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L. B. Cebik, W4RNL

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The bobtail curtain is a vertically polarized array used by many operators on the lowest amateur bands. Essentially a wire antenna, the array requires only 1/4 wavelength for the vertical portion of its elements plus safety clearance from the ground. Hence, it is shorter than most vertical antennas, but provides a very good bi-directional pattern at low elevation angles. This collection of notes has featured the bobtail curtain in several places. In the basic SCV series, see "Part 5: Shorties, Double-Wides, and Twins." As well, see "Voltage Feeding SCV Loop". You may also wish to explore "The 40-Meter Bobtail Curtain as An All-Band Wire Antenna.".

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Recently, Ed Boutwell, W4ZSB, tried a promising arrangement on 20 meters: a triangle of bobtails. I translated the idea to 40 meters, where bobtails are more common and explored its properties in some details. These notes provide the results of that expedition into geometry. However, to provide enough background for those notes in this location, let's begin by reviewing some basic bobtail properties.

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The Single Bobtail Curtain

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The bobtail curtain is actually a set of 3 1/4 wavelength vertical elements that we top-feed in phase. Although developed earlier, the bobtail is an electrical outgrowth of the smaller half-square, a set of 2 vertical 1/4 wavelength elements that we also top-feed and phase-feed. Ideally, a half-square works best when the tops of each element have the same current magnitude and phase angle. A 1/2 wavelength horizontal wire between the two verticals provides the necessary phasing while the radiation from that connecting wire largely cancels itself, leaving only a bi-directional (mostly) vertically polarized radiation pattern broadside to the plane of the wires.

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The bobtail curtain extends the half-square by adding a further half wavelength horizontal wire and a third vertical 1/4 wavelength wire. However, that change produces some interesting changes in the antenna's operation. Fig. 1 shows the outline of a bobtail curtain and indicates one of the major changes.

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The total horizontal length of a bobtail is about 1 wavelength. We can call the antenna an SCV (self-contained vertical array) because its entire structure is above ground and it requires no ground-plane radial system to complete the antenna. As the diagram indicates, we feed the center vertical, and the horizontal phasing wires supply energy to the outer verticals. (The green dots in the diagram simply indicate the segmentation used for this particular model of a bobtail.) As a consequence of the feedpoint, the center vertical requires twice the current of each outer vertical. The relative current magnitude curves show the difference in current between the center and outer vertical in the binomial current distribution.

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The diagram shows the feedpoint at the top of the center vertical. Actually, we may feed the element anywhere along its length. The top-most point may show an impedance that is under 50 Ohms, so we may wish to bring the feedpoint lower to match common coaxial cables. Alternatively, we may feed the vertical at its end using standard voltage-feeding techniques. We may even extend the center element to near ground level (but leave the outer verticals alone) to place the usual high-Z tank tuner more conveniently. In all cases, the current will be highest at the top of the center vertical element.

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The current distribution curves also show the relative phase angle of the currents. The horizontal wires show the reversal of current phase that largely, but not completely, cancels the horizontal radiation component from the antenna. The curves on the end vs. center elements sometimes trouble viewers, who think that the elements may therefore be out of phase. However, the diagram does not show the voltage magnitude and phase along the wires. The simplest way to demonstrate that the bobtail elements are in phase with each other with respect to radiation is to compare what happens when we purposely reverse the phase of the outer verticals with respect to the center vertical.

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The left side of Fig. 2 shows a typical bobtail patterns. It is the same pattern that we get when feeding 3 1/4 wavelength verticals in phase, with the center vertical fed twice the current of each outer vertical. If we phase the outer elements 180 degrees relative to the center vertical, then we obtain the pattern on the right, and the elements become an end-fire array. This is not the pattern that we derive from the bobtail with its single feedpoint.

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I noted that the bobtail curtain horizontal wires largely but incompletely cancel the horizontal radiation component from the array. An array of 3 1/4 wavelength vertical would shows almost no horizontal radiation component--just enough to indicate the effects of the radiation being composed of both direct and ground-reflected components. If the bobtail could cancel all of the horizontal radiation, it would produce a similar set of components to its total field. However, see Fig. 3, which shows the components of the bobtail.

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The brown vertical-component lines show a beamwidth that is somewhat narrower than the total field beamwidth. The difference emerges from the remnant horizontal component, shown in blue. The peak strength of the horizontal component is about 10 dB below the maximum gain level. Because the horizontal lobes are not broadside to the plane of the wires, they do not affect the maximum signal strength--only the beamwidth. In the broadside direction relative to the wire plane, the signal is virtually only vertically polarized.

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One of the reasons why low-band operators favor the bobtail is its radiation pattern. The elevation pattern is the key. Let's place a dipole at 50' above ground for 40 meters. Let's also build a bobtail with the same top height. Fig. 4 overlays the elevation patterns of the two antennas in the specified places.

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Admittedly, the dipole shows the higher maximum gain level. Indeed, a full wavelength wire (the same horizontal length as the bobtail) would show about 1.5-dB higher gain yet. However, note the elevation angle at which the dipole and its longer kin achieve maximum gain: well above 30 degrees. In contrast, the bobtail obtains maximum gain at considerable lower angles, usually below 20 degrees elevation. Since most long-distance ionospherically refracted signals are at angles below 20 degrees, the bobtail has an advantage. In addition, much (but not all) of the atmospheric noise comes from closer sources arriving at higher elevation angles. The dipole is far more sensitive to higher-angle radiation than the bobtail. As a consequence, bobtail users who have properly aimed their antennas to broadside target regions usually report better DX communications, not only with stronger signals, but as well with a better signal-to-noise ratio, especially on the lower HF bands.

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Fig. 1 indicated a set of dimensions applicable to the bobtail. The dimensions include an overall horizontal (h) value, with half of h devoted to each side of the center vertical. The diagram also indicates a vertical dimension (v) for the length of the main radiators. Finally, the dimensions include a base height of the vertical bottoms above the terrain (ht). Let's see how these dimensions play out using the universal AWG #12 copper wire at the center of 40 meters (7.15 MHz).

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In fact, there are two rough forms of the bobtail, one based on conventional general ideas and one based on optimizing the array for maximum gain. Table 1 provides the dimensions and the modeled performance of the bobtails over average ground (conductivity 0.005 S/m, permittivity 13).

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+Table 1. Bobtail array dimensions and modeled performance
+Version        h feet   v feet   ht feet   h wl     v wl     Gain dBi   TO angle    Beamwidth   Impedance
+Conventional   124.8    38.0     12.0      0.907    0.276     4.90      18 deg      54 deg      42.8 + j3.4 Ohms
+Maximum Gain   149.0    33.5     12.5      1.083    0.244     5.05      19 deg      50 deg      29.1 + j0.0 Ohms
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The conventional version rests on using 1 wavelength as the measure of the total length and of each side of the array (center-vertical + horizontal-wire + end-vertical). Of course, the total length of each section rests in part on bringing the verticals to resonance. Hence, the length of each section is 1.006 wavelengths. Since each design has its own optimum height above ground, the conventional design shown has a top height of 50'. Actually, the base height is not too sensitive and +/- a foot or so will not affect performance. However, the feedpoint resistance does go down as the antenna height decreases. For the top-fed version shown, the impedance is adequate for a direct connection to common coaxial cables.

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The maximum-gain versions rests on the empirical work of SM4CAN, which models have confirmed. We can slightly increase the bobtail maximum gain value by extending the value of h and shortening the values of v. The total section length does not significantly increase (1.030 wavelengths). However, for maximum gain, the base height goes down slightly and the shorter vertical sections leave the array top height at 46'. Due to the slight reduction in base height, the improved gain costs us about 1 degree in the elevation angle of maximum radiation. In most circumstances, the ordinary operator might not notice either change.

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The maximum-gain design imposes one noticeable penalty: a significant reduction in the feedpoint resistance when using a top-feed method. In fact, most users of the SM4CAN-type bobtail use a high-voltage feed system, with the tank circuit close to ground. Since differences of impedance become a simple process of selecting the correct tapping points on the parallel tank circuit, the actual impedance at the junction of the center vertical with the horizontal wires becomes a matter of no concern.

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There are slight differences in the patterns produced by the two bobtail versions, although once more, they are not likely to be significant in normal operation. Fig. 5 shows the differences.

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The conventional design elevation pattern shows very slightly less sensitivity to very high-angle signals than does the maximum-gain version. As well, the conventional version shows a very deep null in line with the wires. In contrast, the longer maximum-gain design shows the beginnings of side lobes. These lobes are 25 dB below the level of the main lobes, and they are consistent with what happens when we set up independent in-phase-fed verticals. Perfect 1/2 wavelength spacing produces the cleanest pattern. However, we can squeeze a bit more gain from the set by widening the spacing slightly. The cost is the emergence of those same sidelobes. Eventually, as we further increase the spacing, the sidelobes grow to levels at which they steal significant energy from the main lobes, which become weaker. However, for small increases in length beyond exact 1/2 wavelength spacing, the lobes can emerge only at the expense of the beamwidth of the main lobes. Note that the beamwidth of the conventional design is almost 5 degrees wider than for the maximum-gain design.

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It is now time to look at the idea of triangulating bobtail curtains. I would have had to provide most of the graphics and tabular information to use for comparison with the triangles. So the review of basic bobtail properties has seemed like a productive way to frame the data.

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Bobtail Triangles

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A bobtail feeds the center vertical, allowing the horizontal wire to act as a phase lines relative to the outer verticals. Suppose one wished to work in several directions and not just the pair created by a single bobtail curtain. The most compact installation might be a triangle in which the corner verticals performance multiple duties, depending on which of 3 center verticals would be active at any given moment.

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In principle, by mental visualization only, the verticals at the center of the other two sides and the vertial at the far end across from the actively fed vertical would receive low current levels. As well, they are farther way from the fed vertical and at angles outside the plane formed by the basic bobtail. Would their presence be fatal to the scheme? Or would they somehow enhance the broadside patterns?

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We can easily model the concept of a triangle of bobtails, using the same materials (AWG #12 copper wire) and frequency (7.15 MHz) that we used for the single bobtails. However, we have multiple possibilities that form a small matrix. In one direction, we have two slightly different bobtail designs. We should see if that difference is significant or not when we triangulate the system. In the other direction, we have two ways to handle the unused feedpoints. One way is to leave them open, and the other is to place a short across the unused feedpoint gaps. We obtain a shorted unused feedpoint in a model simply by removing the source from that wire. To create a genuine open circuit at the unused feedpoint, we need to add a very high resistance load. A resistance of 1e10 Ohms is satisfactory to achieve this goal.

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Let's begin with the conventional bobtail design that uses the shorter horizontal lines and longer verticals. Table 2 shows the data for the system with the unused feedpoints both shorted and open. Note that the table gives two gain values, one for the direction toward the triangle apex ("apex") and one toward the flat side ("side") of the triangle. The difference of these values creates a small front-to-back ratio that is also listed in the table. In addition to the two value sets, I have included the data for a single bobtail of the same design dimensions.

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+Table 2. Bobtail triangle modeled performance: convention design
+Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
+Single              4.90 dBi    4.90 dBi    18 deg     0.0 dB              54 deg      42.8 + j3.4 Ohms
+Shorted Feedpoints  5.08        3.81        18         1.27                59          43.1 + j12.6
+Open Feedpoints     5.19        4.52        17         0.67                58          46.5 + j1.0
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The data show only slight variations between the properties of a single bobtail and the triangle. In both cases, the gain of the two lobes of the single bobtail falls about midway between the gain values for the triangles in each direction. The remaining differences show up better in the radiation patterns that appear in Fig. 6.

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Both elevation patterns (representing shorted and open unused feedpoints) show a significant increase of the higher-angle sensitivity in the direction from the feedpoint to the opposite apex of the triangle. Compare these patterns to the elevation pattern in Fig. 5, which shows plots both bobtail designs. For the triangle, the azimuth patterns show greater balance between the two broadside lobes when the unused feedpoints are open relative to when they are closed. Regardless of how we handle the unused feedpoints, the triangular array shows increased radiation off the ends, compared to the deep side nulls of the conventional design azimuth pattern in Fig. 5.

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Before we reach any conclusions about the performance of the bobtail in a triangle, let's perform the same set of modeling tests on the maximum-gain design. Table 3 provides the data.

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+Table 3. Bobtail triangle modeled performance: maximum-gain design
+Version             Apex Gain   Side Gain   TO angle   Front-Back Ratio    Beamwidth   Impedance
+Single              5.05 dBi    5.05 dBi    19 deg     0.0 dB              50 deg      29.2 + j0.0 Ohms
+Shorted Feedpoints  4.41        5.19        20         0.78                49          29.1 - j3.0
+Open Feedpoints     4.59        5.39        19         0.80                48          28.5 - j0.7
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As shown in the patterns in Fig. 7, the higher gain occurs away from the apex and toward the fed side of the triangle. Relative to the conventional design, the maximum-gain version shows less performance difference relative to the handling of the unused feedpoints. However, the azimuth patterns shows some differences that the simple numbers cannot reveal. With the feedpoints shorted, the maximum-gain design shows a much higher level of radiation in the plane of the active bobtail than with open unused feedpoints. In both cases, the small sidelobes that we saw in Fig. 5 for this type of bobtail curtain are clearly evident and not as insigificant.

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The sensitivity to higher angle radiation occurs in the direction of the triangle apex. However, since this direction in the maximum-gain design is slightly weaker, the increase is less pronounced than in the conventional design.

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We may account for many of the differences in performance among the various antennas by looking at the relative current magnitude distribution for each of the triangles. Fig. 8 provides some simple representations.

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Although matters of scale do not permit magnifying the current along the horizontal wires, we can see indications of it on the wires beyond the active bobtail. This current level decreases with distance from the plane of the active bobtail, but is still sufficient to produce higher-angle radiation toward the apex of all of the models.

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For each design type, the two current charts clearly show the difference between shorting and opening the unused feedpoints. With open feedpoints, the side center verticals are relatively inert. Hence, with open unused feedpoints, only the apex vertical contributes to the overall pattern formation. The exact magnitude and phase angle of the current on that vertical element is enough to tilt the pattern in one or the other direction. Remember that the apex vertical is closer to the active bobtail in the conventional design than it is in the maximum gain design. When the mid-side verticals are active, that is, when we short the unused feedpoints, we obtain somewhat different results in the two designs. In the conventional design, the active mid-side verticals contribute to a wide beamwidth in the apex direction, relative to the lobe in the opposite direction. In the maximum-gain design, the active mid-side verticals increase the radiation off the ends of the active bobtail plane.

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Conclusion

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If we wish to operate in many directions with a bobtail curtain, setting up a triangle is one way to proceed. We save the construction of 3 verticals relative to having 3 independent bobtails. As well, the performance differences relative to independent bobtails are functionally rather small and may well be acceptable. In fact, unless we had unlimited space, it is dubious whether we could avoid interaction among the elements of independent bobtails oriented in different directions.

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Perhaps the key limitation of the bobtail curtain triangle is that we cannot cover the entire horizon. The beamwidth is simply too narrow (50-55 degrees) for 3 bi-directional arrays to achieve this goal. However, we may come close enough to satisfy our needs--at least until we need only a few more countries, all of which fall in the crevices between adjacent azimuth patterns.

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My own interest in the array is neither to recommend nor to discommend its use. Rather, the interesting activity for me is to have seen what happens when we triangulate bobtail curtains.

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Updated 03-24-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Bobtail Curtain, HF Lower, SCV


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SCVs Index: A Family Album

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L. B. Cebik, W4RNL

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A class of antennas is noted for its ability to provide low-angle, vertically polarized radiation without need for a ground plane. These antennas, whose basic form requires 1 wavelength of wire, are both common and remarkable--a combination that instantly calls for further study. The following series of notes, based on computer modeling studies, attempts to clarify some of the basic properties, potentials, and limitations of these self-contained, vertically polarized wire antennas--or SCVs for short.

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For a VHF application, see also The Half-Square on 2 Meters: Parts 1-3

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The series is also available as a book in PDF format with accompanying models on the Books Page.


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Updated 05-15-1999, 01-14-2003.

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Go to Main Index Page

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Topics: SCV


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+

SCVs Part 1: The Group Picture

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In ON4UN's remarkable book on Low Band DXing, there are a number of scattered antenna designs worth noting.1 All involve about 1 wavelength of wire, with some 2 wavelength variations on the basic antennas. They share a common feature (besides the relatively low cost of wire) for DXers and world-wide contesters using 160, 80, and 40 meters especially. When properly constructed and fed, they exhibit only low angle, mostly vertically polarized radiation. Figure 1 provides a generalized elevation pattern for a typical SCV. +
+ +
+
+ Figure 1. A typical SCV elevation plot. Gain will vary with the type of SCV used. +
+

Moreover, these antennas do not need ground planes.

+

The Family Portrait

I have elsewhere dubbed these antennas as "self-contained, vertically polarized wire antennas." For short, we can call them all SCVs. Here is a list of some of the things these antennas have in common. +

1. All use about 1 wavelength of wire (except for the doubled versions). As with all 1 wavelength antenna systems, the radiation properties can be altered by changing the feedpoint of the system. A 1 wavelength system is not an SCV unless the feedpoint is selected to maximize vertically polarized radiation.

+

2. SCVs are "closed" systems. A better term might be that they are "complete" systems. They do not require a ground return or ground plane to complete the antenna. Like all vertically polarized antennas near ground relative to the frequency of operation, they do depend to some extent upon the local ground quality for their radiation efficiency. However, they do not depend upon local ground quality for basic operation. Unlike the vertical monopole without its ground plane, the SCVs all model very nicely in free space.

+

3. SCVs come in several varieties, all of which are related. The two most recognizable shapes are the triangle and the rectangle. Triangles (or "deltas") tend to vary from equilateral to right angle. Rectangles can be anything from squares (quad loops) to long flat rectangles, sometimes dubbed "magnetic slot" antennas.2 Quad loops can be either set up as squares or as diamonds.

+
+ +
+
+ Figure 2. Basic types of common 1 wavelength SCVs. For triangles and open- ended antenna types, the horizontal wire may be low or high. The most usual arrangements are shown. +
+

As shown in Figure 2, there is a kissing cousin to these closed loops called the "half square."3 You can in fact trace the evolution from the closed loops to the half square in NEC models. Begin with a triangle fed for maximum vertical radiation. Open the top apex, a voltage maximum, by a very small amount (but not so close at the tips that the program interprets the wires as connected). The properties do not change. The properties evolve as the base wire is extended to a full half wavelength and the open wires are moved to a position at right angles to the base wire.

+

3. For vertically polarized operation, all SCVs need to be fed 1/4 wavelength from a high-voltage maximum, in other words, at a current maximum. For the deltas, this position is 1/4 wavelength from the apex. For rectangles, the proper position is mid-side. This position becomes the side peak for the diamond configuration. In free space models of all these configurations, it makes no difference whether the voltage maximum is up or down, since there is no up or down to free space except in conventionalized graphic plots. However, the apex position may make a considerable difference in performance over real ground, while at the same time creating a challenge for antenna support. The advantage of placing the feedpoint as high as possible may conflict with available physical supports for the wire.

+

4. The horizontal member that each of these antennas share in common functions largely (but not exclusively) as a 1/2 wavelength phasing line. The high voltage maximum in the center of this line effects a phase reversal for currents, so that they are equal in magnitude but opposite in polarity on either side of the maximum. Hence, the resultant radiation cancels to a high but incomplete degree. The feed point and another point opposite it in the structure are current maxima which are approaching 1/2 wavelength separation and which are phased for additive radiation broadside to the wire assembly. Figure 3 illustrates these features with a half square, whose properties are almost ideal.

+
+ +
+
+ Figure 3. Current magnitude and phase on a half square antenna. For each type shown in Figure 2, the 1/2 wavelength phasing line extends from the feedpoint to a similar point on the opposite side of the antenna. +
+

Nonetheless, the resultant radiation pattern is a combination of vertically and horizontally polarized radiation, as illustrated in Figure 4, a typical azimuth pattern for an SCV. This pattern illustrates the degree to which horizontally polarized radiation--either from the "phasing" line or from angled portions of the vertical wires--fails to be cancelled. Although the vertically polarized radiation provides for the antenna's maximum gain, the horizontally polarized radiation increases the beamwidth of this bi-directional array.

+
+ +
+
+ Figure 4. Vertically polarized, horizontally polarized, and total field radiation for a half square. Patterns of the other SCVs are similar. +
+

For those who like terminological mysteries, the rectangles are symmetrical with respect to top and bottom horizontal wires. Which we should call the phase line and which we should call part of the vertical members of the array is a debate best left to medieval scholastics. In effect, both upper and lower horizontal members perform both functions.

+

5. All of the SCVs can be arrayed in pairs (or triplets) aligned broadside for either phased or parasitical operation. Therefore, it is possible to create beam arrays, and with some stubs and relays, make the beams switchable in direction. SCVs follow the common parasitical arrangements that require reflectors to be larger than driven elements, which are in turn larger than directors.

+

For additional bi-directional gain, SCVs can be placed side-by-side with a common feedpoint. The near-1/2 wavelength spacing of vertical members with the requisite phase reversals along the line(s) yields additive radiation broadside to the array. Hence, there have been open double rectangles, open double deltas, and the bobtail curtain.4 Figure 5 illustrates the shapes of these antennas, along with one other: the double magnetic slot--or double side-fed rectangle. This antenna provides feedpoint impedance transformation from a normally very low value to one more favored by hams.

+
+ +
+
+ Figure 5. Several types of 2 wavelength "double" SCVs. +
+

Brief Profiles of the Family Members

To become better acquainted with the basic properties of the different versions of the SVC, let's examine some free space models of some of the family members. Table 1 provides some basic construction data on various SCVs, all cut from #12 wire for 7.15 MHz in our initial comparison. Table 1 also provides the approximate free space maximum gain broadside to the antenna. Also listed is the free-space feedpoint impedance. + 
             Basic Properties and Free-Space Performance of Common SCVs
+
+Antenna Name          Abbreviation 7.15 MHz Dimensions       Free Space      Feedpoint
+                                      (in feet)              Gain (dBi)   Impedance(Ohms)
+
+Equilateral Delta         EQD    48.8'/side, base down, apex up   2.9       120
+
+Right-Angle Delta         RAD    60.8' base, 43' sides, base down 3.3        51
+                                      apex up
+
+Double Right-Angle Delta  DBD    121.6' base, 43' sides (twice),  5.1        35 (note 1)
+                                      base down, apex up
+
+Square Quad Loop          QSQ    36.3'/side                       3.2       130
+
+Diamond Quad Loop         QDI    36.3'/side                       3.1       130
+
+Rectangle (Magnetic Slot) REC    56' horizontal, 12.8' vertical   4.4        15
+
+Double Magnetic Slot      DMS    56' horizontal, 13.0' vertical,  4.7        80 (note 1)
+                                      3' separation
+
+Open Double Magnetic Slot ODS    110.8' horizontal, 11.1' vertical; 5.7    30 (note 1, 2)
+                                    fed on end wire (center-wire
+                                    feed possible)
+
+Half Square               HS     62.4' horizontal, 39' vertical    4.6       65
+
+Bobtail Curtain           BC     125' horizontal, 38' vertical;    6.3     40 (note 1, 3)
+                                    fed on center wire
+
+Note 1:  A 2 wavelength system; unmarked antennas are 1 wavelength arrays.
+
+Note 2:  Impedance value for end-wire feed.  Antenna impedance with center-wire feed
+is about 9 Ohms.
+
+Note 3:  For center-wire feed of the bobtail, impedance is about 40 Ohms at the
+junction with the horizontal wire, about 55 Ohms at 60% up the vertical, and
+about 70 Ohms at the middle of the vertical.
+
+Table 1.  Basic properties and free-space performance of common SCVs.
+

It is clear that the deltas and the squares are very comparable performers, although the right-angle delta (RAD) carries a feedpoint impedance compatible with coaxial cable feedlines. Interestingly, we find also that the rectangle (REC) provides superior gain to the square (QSQ) or diamond (QDI), despite its flattened appearance. However, remember that the sides of the rectangle, where the high current maxima lie, are more nearly 1/2 wavelength apart, providing for better radiation addition. The feedpoint impedance of the single rectangle is, unfortunately, lower than most hams wish to handle. Of the 1 wavelength SCVs, the half square (HS) is the best performer with respect to gain, since its vertical members are a full half wavelength apart, and the feedpoint impedance is coax- compatible.

+

Within Table 1, I have added 2 wavelength wire arrays, namely, the double right-angle delta (DBD), the double magnetic slot (DMS), the open double slot (ODS), and the bobtail curtain (BC). Unlike the side-by-side 2 wavelength models, the DMS winds the loops in parallel, with a mobius crossing at the end away from the feedpoint. Not only does the wire doubling in the double magnetic slot increase the feedpoint impedance, but as well, it adds something to the gain. The spacing between the wires is not critical; the model uses a 3' spacing. The open double slot adds more gain with a moderately usable feedpoint impedance (but only if fed on an end wire, since the impedance of the antenna is about 9 Ohms if fed on the center wire).

+

The final gain winner in the group is the bobtail curtain (BC). Fed about midway up the center vertical toward the horizontal wire, the impedance is about 70 Ohms, while at the junction with the horizontal wire, the impedance is closer to 40 Ohms. With patience, a builder can find an exact 50-ohm point between the two. Of course, the free ends of the half- square and the bobtail curtain lend themselves to voltage feed via a simple tapped high-Q parallel tuned circuit, as shown in Figure 6.

+
+ +
+
+ Figure 6. Typical network for matching low-impedance transmission lines to high impedance feed points on an open-ended SCV (half square or bobtail curtain). +
+

With Feet on the Ground

Although Table 1 suggests the relative differences in performance among the types of SCVs, it does not tell the entire story. To get some sense of real-world performance from these antennas, I set up a little exercise. Since the number of different installations is nearly endless, I established some rules for a hypothetical ham installation. In general, I set 50' as the maximum height of installation for a 40-meter SCV, with a desired minimum height of 20' up. However, this set of restrictions would have eliminated most of the antennas. So for the half square and bobtail. I lowered minimum height to 10' for the free ends. I followed general conventions of placing the horizontal wires of the triangles in the lower position, while the half square and bobtail horizontal wires were high. + 
                Performance of Common 7.15 MHz SCVs Over Average Ground
+
+Antenna    Height Range  Gain in dBi  Front-to-Side  Take-Off Angle  Feedpoint Impedance
+            (in feet)                  Ratio (dB)      (degrees)          (Ohms)
+
+EQD        20 - 62.3      1.5           - 3             18           135 (Note 2)
+
+RAD        19.6 - 50      1.9           - 5             20            60
+
+DBD        19.6 - 50      3.7           -12             20            40
+
+QSQ        20 - 56.3      1.6           - 4             18           145
+
+QDI        20 - 71.4      1.5           - 4             16           135 (Note 2)
+
+REC        37.2 - 50      3.0           -12             17            15
+
+DMS        37.0 - 50      3.3           -12             17            80
+
+ODS        38.9 - 50      4.5           -25             16            30
+
+HS         11.0 - 50      3.4           -15             18            65
+
+BC         12.0 - 50      5.0           -28             18            40 (junction-fed)
+                                                                 56 (60% up center wire)
+                                                                    70 (mid-center wire)
+
+Note 1:  All antenna #12 copper wire over average earth (conductivity
+ = 0.005 S/m; dielectric constant = 13).
+
+Note 2:  This antenna is not physically apt under the terms of the exercise.
+
+
+Table 2.  Performance of common 7.15 MHz SCVs over average ground.
+

Table 2 sets out the results in terms of gain, front-to-side ratio, take-off angle, and feedpoint impedance. Technically, the diamond and square quads must be eliminated for violating the upper height limit, along with the equilateral delta. Their numbers are included for reference. The deltas can be operated with their horizontal wires high, for some improvement in performance. Operating the half-square and the bobtail with their horizontal wires low is possible, but at the cost of performance.

+

The table also provides front-to-side gain ratio numbers that give an indication of the degree of bi-directionalness of the arrays. The higher gain arrays have higher front-to-side ratios and "peanut" patterns, while the lower gain models tend to have more oval patterns.

+

In the immediate family of 1 wavelength SCVs, the rectangle and the half square provide the greatest gain. However, the single rectangle has a very low feedpoint impedance, and the double magnetic slot is recommended in its place. The open double slot almost matches the bobtail, and its smaller vertical-plane footprint allows greater height and a lower take-off angle.

+

However, none of the SCVs permit unlimited heights without losing much if not all of the low angle radiation advantage. As you elevate any of the SCVs, a second lobe appears at a high angle. Eventually, at a height specific to each antenna type, the higher angle secondary lobe becomes the primary lobe.

+
+ +
+
+ Figure 7. Elevation patterns for a right-angle delta antenna at three different heights. +
+

Figure 7 shows the elevation patterns for a 40-meter right angle delta at three heights: with the base at 20, 40, and 60 feet up. Figure 8 shows the same set of elevation patterns for a half square where the lowest heights of the free ends are 11, 31, and 51 feet. The lobe development is virtually indistinguishable between these two antennas (or between any other two of the SCVs).

+
+ +
+
+ Figure 8. Elevation patterns for a half square antenna at three different heights. +
+

The entire purpose in using an SCV is to accept the lower gain of the SCV in exchange for the ability of the antenna's vertically polarized pattern to attenuate signals from high elevation angles. The high angle radiation is generally thought to contain most of the non-DX QRM and also the land-mass QRN that makes hearing low-band DX so difficult. The SCVs form a natural filter. Since modern receivers have gain to spare on the low bands, relative to the basic noise level, the lower gain of the SCV is no disadvantage for reception. The low angle of radiation can also be effective when transmitting.

+
+ +
+
+ Figure 9. Elevation patterns for a dipole and a half square antenna, both with maximum heights of 50 feet. +
+

However, if we elevate an SCV too high, it loses its filtering ability without gaining anything significant in low angle radiation. In fact, for raw gain, a simple dipole at the hypothetical exercise height of 50' would do about. Compare the dipole and half square elevation patterns in Figure 9. Note that the half square very low angle radiation exceeds that of the dipole at the same elevation angles, despite the fact that the dipole has an overall gain advantage. One might almost suggest separate antennas for transmitting (the dipole) and receiving (the SCV)--or at least an A-B switch.

+

What's Left to Tell?

This family portrait has aimed to set up the SCV family tree. However, it leaves many questions unanswered. Here are a few of them. +

1. Although we might simply presume that we can scale the 40-meter results to the other low bands, do the antennas actually perform the same way for each band?

+

2. The rectangle is a crushed square, and the right angle delta is a crushed equilateral triangle. What are the limits of crushing these geometric shapes before performance deteriorates.?

+

3. All of the models in this preliminary family reunion have been over uniform average ground (conductivity = 0.005 S/m; dielectric constant = 13). How do the antennas perform over different types of both local and distant ground for each of the three lowest bands?

+

4. Will any of the changes of soil and shape make any difference in the elevation patterns shapes as they change with antenna height?

+

We shall look at these questions in future episodes. Since I cannot possibly build and test each type of antenna over all the various soils and in all the various shapes possible, we shall do our exploration by modeling in NEC-4, which is reliable for this class of antennas.5 However, we must note at the outset that antenna modeling provides suggestive results relative to the real world. Because modeling programs presume level ground, they cannot provide detailed information about these antennas on the many sorts of terrain where hams live and use them.

+

At the same time, our project is just the sort of thing at which antenna modeling excels: the accumulation of systematic data over a wide range of questions. Antenna building must be very selective due to the cost and effort involved and because of the great care that must be used to obtain repeatable and accurate results. For its results to be definitive, the range test must go beyond the anecdotal: all variables must be accounted for in detail to ensure that the results can be formulated as generalizations applicable to other situations that are relevantly similar.

+

One advantage of modeling in the present case is that each antenna and installation situation can be directly compared with the others, since most of the intervening variables present in real world antennas are equalized in the model set-up. Hence, modeling is a wholly appropriate vehicle for comparing relevantly similar types of antennas--namely, the SCV family.

+

However, the final choice for an antenna at any site is a mixture of performance potential and physical possibility. If you have only one high support point, then a delta may be necessary, since two-point support antennas are automatically ruled out. If available supports are wide- spread but not exceptionally high, then the rectangles and open-ended arrays jump to the forefront.

+

Nonetheless, even if your choice is forced by features of the antenna site, learning more about SCVs in general cannot be a bad thing. You never know when someone may ask you a question.

+

Notes

1 John Devoldere, ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed. (Newington: ARRL, 1994). See especially Chapter 10, "Large Loop Antennas," for information on rectangular and triangular loops. However, half squares and bobtail curtains are relegated to Chapter 12, "Other Arrays." +

2 For the "magnetic slot" and "double magnetic slot," see Russell E. Prack, K5RP, "Magnetic Radiators--Low Profile Paired Verticals for HF," The ARRL Antenna Compendium, Vol. 2 (Newington: ARRL, 1989), pp. 39-41.

+

3 The half square antenna actually appeared after its larger sibling, the bobtail curtain. See Ben Vester, K3BC, "The Half Square Antenna," QST (March, 1974), 11-14. Additional notice appeared in Radio Communications for January, 1977 (p. 36). See also Robert Schiers, N0AN, "The Half-Square Antenna," Ham Radio (December, 1981), 48-50. All three of these early sources show the antenna as voltage-fed from one of the free ends.

+

4 For the bobtail curtain, see Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," CQ (March, 1948), 21-23 and 92-95. See also Smith follow-up articles, "The Bobtail Curtain and Inverted Ground Plane," Parts 1 and 2 in Ham Radio (February, 1983), 82-86, and (March, 1983), 28-30. For the open double magnetic slot, see Lew Gordon, K4VX, "The Double Magnetic Slot Antenna for 80 Meters," The ARRL Antenna Compendium, Vol. 4 (Newington: ARRL, 1995), pp. 18-21.

+

5 NEC-4 is a proprietary code of the Lawrence Livermore National Laboratory, University of California, from whom a user-license must be obtained. Commercial implementations include the following:

+

a. EZNEC Pro: Roy Lewallen, W7EL, P.O. Box 6658, Beaverton, OR 97007; e- mail: w7el@eznec.com.

+

b. GNEC: Nittany Scientific, 1733 West 12600 South, Suite 420, Riverton, UT 84065; sale@nittany-scientific.com.

+

Because the horizontal baseline of many of these antennas is lower than 0.2 wavelengths, MININEC models of them are less likely to be reliable than NEC-2 or NEC-4 models.

+

Also see the Antenna Modeling Programs page.

+
+
+
+ +
+

Updated 4-29-98. © L. B. Cebik, W4RNL. A print version of this note appears in The National Contest Journal September 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

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+ Go to Part 2 +

Return to SCV Index

+

Topics: Bobtail Curtain, Delta Loop, HF Lower, Half Square, Quad Loop, Rectangle, SCV, Voltage Feeding


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+

SCVs Part 2: The Delta Branch

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ In casting about for a reasonable way to organize the material in this series of self-contained vertically polarized wire antennas (SCVs), it finally struck me that the antenna types themselves formed the core of family divisions. Although there are fascinating parallels among the 3 main family branches: the deltas, the rectangles, and the open-ended types, practical considerations often dictate which type of antenna one will install. Deltas go where there is only a single support up high. Rectangles take the least space, considering both height and length, and therefore might be favored most on 160 meters. Half-squares are the tallest and widest and thus favor 40 meters. +

So I decided to treat each branch of the family separately and simply call attention to similarities to their cousins where apt. Today, the deltas get their due. We shall restrict our attention to apex-up configurations, since that is the most common form. Raising the baseline to the top, with the apex down, increases gain a bit over ground. However, with the requirement for a span up high, other members of the SCV family may be better candidates.

+

As a reminder from the first episode, the chief purpose in using an SCV is to acquire a low angle of maximum radiation with little or no response to high-angle radiation from which emerges most of the QRM and QRN that otherwise covers up weak DX signals. Most SCV antennas have significantly less maximum gain than a dipole, but they outdo the dipole at low radiation angles unless the dipole is at least 1/2 wavelength high. For any given path angle, the required height for the dipole to equal the SCV varies with the inherent gain of the SCV in question. Deltas encompass the lower gain members of the SCV family.1

+
+ +
+
+ Figure 1. The two common forms of the delta: the equilateral and the right-angle. +
+

Deltas have two common forms, as sketched in Figure 1: the equilateral and the right-angle versions. It was long ago discovered that the right angle delta has slightly more gain than the equilateral delta (3.3 dBi vs. 2.9 dBi in free space on 40 meters). Moreover, when each is fed 1/4 wavelength down from the apex, the equilateral delta has a feedpoint impedance close to 115 Ohms, while the right-angle delta impedance is close to 50 Ohms, for a direct coax feed system. Note that the equilateral delta requires a feedpoint about 25% up one of the legs to place it 1/4 wavelength down from the apex. For the same 1/4 wavelength spacing from the apex, the right-angle delta feedpoint is about 12% up one of the legs.

+

However, it is not clear that the right-angle delta is the ultimate in gain for the apex-up triangular system. As one drops the height of the triangle and spreads the baseline to compensate in order to maintain resonance, the gain of the triangle increases from the equilateral mode to the right-angle mode. In fact, free space models suggest that a good bit more shortening and spreading is possible before one passes the point of maximum free space gain (which holds up in practice over ground). Figure 2 shows the progression. At a certain dimension, the increase in gain created by bringing the feedpoint and the point opposite to it on the other sloping side closer to 1/2 wavelength apart begins to be off set by reduced vertically polarized radiation do to the radically increasing slope of the upper wires.

+
+ +
+
+ Figure 2. The progression in shape of the delta toward maximum gain and beyond. +
+

Interestingly, the ratio of baseline length to height from the baseline to the apex for maximum gain is frequency dependent. If we let R be the ratio of baseline length to height and F be the frequency in MHz, then

+
+ +
+

This near-equation was derived using #12 AWG copper wire antennas and holds good throughout the HF range. It shows some significant drift as one approaches 2 meters, where the #12 wire diameter becomes a more significant portion of a wavelength.

+

For 40 meters the correct ratio of length to height is about 2.9:1, while at 80 meters the ratio is about 2.6:1. (The right-angle delta, of course, has a ratio of 2:1, while the equilateral triangle has a ratio of about 1.15:1. The loss relative to maximum gain is only a few tenths of a dB.) As the length-height ratio increases, the feedpoint impedance decreases. On 80, resonance yields a resistance of 27 Ohms, while the more radically sloped maximum gain delta for 40 has a feedpoint impedance of about 22 Ohms. In exchange for that decrease in feedpoint impedance, the maximum possible gain for the delta increases, about 3.26 dBi for 80 and 3.43 dBi for 40.

+

The actual shapes of the deltas we build are largely a function of space available. High towers or trees and narrow yards tend to get equilateral (or nearly so) triangles, while lower supports and bigger yards get right-angle (or nearly so) models. But all of these antennas work over ground of varying quality. Because there are some interesting behavioral differences, let's look separately at the two most common types of deltas.

+

The Equilateral Delta

Because equilateral deltas for 80 and for 40 (the bands for which they are most commonly apt) are different percentages off from maximum gain configuration, we should not expect them to behave in an exactly scaled manner. The feedpoint impedances for the two bands are almost identical when scaled for both antenna size and height above ground. However, in some instances, the gain and elevation angle of maximum radiation will shows significant differences. +

I modeled in NEC-4 a series of 80-meter (3.6 MHz) equilateral deltas with the baseline elevated in 10-foot increments from 10 feet through 70 feet.2 Since the model was 96' wide and 83' high, as shown in Figure 3, the maximum height of 153' seemed a reasonable limit for the exercise. Over most soils types, that is already too high for maximum SCV performance.

+
+ +
+
+ Figure 3. Dimensions of the modeled equilateral deltas for 80 and 40 meters. +
+

Table 1 summarizes the results of the exercise for very poor, poor, average, and very good soil as commonly defined in terms of conductivity and dielectric constant:

+ 
Soil Type             Conductivity (S/m)             Dielectric Constant
+Very poor soil           0.001                             5
+Poor soil                0.002                            13
+Average soil             0.005                            13
+Very good soil           0.0303                           20
+

These initial tests presumed a common soil type for many wavelengths in every direction from the antenna, and as always in modeling, level, uncluttered ground.

+ 
  3.6 MHz Equilateral Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor        10             -0.66             25                   186 + j21
+(C=0.001,        20             -0.25             23                   156 - j 7
+  DC=5)          30              0.05             22                   137 - j15
+                 40              0.29             20                   125 - j15
+                 50              0.50             19                   117 - j13
+                 60              0.69             19                   113 - j 9
+                 70              0.86             18                   111 - j 5
+
+Poor             10              0.78             23                   190 + j36
+(C=0.002,        20              1.08             21                   162 - j 0
+  DC=13)         30              1.27             20                   143 - j12
+                 40              1.40             19                   130 - j16
+                 50              1.48             17                   121 - j15
+                 60              1.51*            16                   114 - j11
+                 70              1.49             15                   111 - j 7
+
+Average          10              1.28             22                   196 + j41
+(C=0.005,        20              1.48             20                   167 + j 1
+  DC=13)         30              1.58             18                   147 - j13
+                 40              1.62*            17                   132 - j18
+                 50              1.59             16                   122 - j17
+                 60              1.50             15                   114 - j13
+                 70              1.34             14                   110 - j 8
+
+Very Good        10              3.61             16                   196 + j54
+(C=0.0303,       20              3.85             14                   172 + j 8
+  DC=20)         30              4.04             14                   153 - j10
+                 40              4.20             13                   137 - j17
+                 50              4.29             12                   125 - j18
+                 60              4.32*            12                   116 - j15
+                 70              4.24             11                   111 - j11
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of equilateral delta = 96' baseline length, 83' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 1.  3.6 MHz equilateral delta:  properties over various soils at various heights.
+

For each type of soil, the antenna height that yields maximum gain is flagged--and that height differs for each type of soil. Over very poor soil, maximum gain is not achieved within the table limits, while for poor soil, the maximum gain baseline height is 60 feet. For good soil, that height drops to 40 feet, while over very good soil it increases once more to 60 feet. Hence, if your soil differs from average, then generalizations based on average soil can be misleading.

+

The elevation angle of maximum radiation (or take-off angle) behaves more as one might expect. For any given antenna base height, the take-off angle decrease directly with the improving quality of soil. In contrast, the feedpoint impedances for the antenna show only a trace of change with changes in soil type. Even at the lowest heights, where ground effects are the largest, the spectrum of soil types yields only a 10-Ohm change (about 5%) in the resistive component of the feedpoint impedance.

+

The 40-meter equilateral delta was 48.5' wide by 42' high, as shown in Figure 3. I ran it at 5-foot intervals from a baseline of 5' up to a baseline of 50' at a frequency of 7.15 MHz. Table 2 shows the results. (If you wish to compare the two tables, double the height of the 40-meter entry to find the roughly corresponding 80-meter entry.) Once more, over very poor soil, a maximum gain height is not achieved. However, the maximum gain height is 35-40' for poor soil, 25-30' for average soil, and 25' for very good soil. This continuous downward trend is distinguished from the odder trend in the 80-meter antenna.

+ 
   7.15 MHz Equilateral Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor         5             -0.08             26                   177 + j26
+(C=0.001,        10              0.41             24                   151 + j 1
+  DC=5)          15              0.78             23                   135 - j 7
+                 20              1.09             21                   125 - j 7
+                 25              1.36             20                   118 - j 5
+                 30              1.60             20                   114 - j 2
+                 35              1.80             19                   112 + j 1
+                 40              1.97             18                   112 + j 4
+                 45              2.12             18                   112 + j 7
+                 50              2.26             17                   114 + j 8
+
+Poor              5              1.06             24                   186 + j40
+(C=0.002,        10              1.41             22                   160 + j 6
+  DC=13)         15              1.66             21                   142 - j 6
+                 20              1.85             19                   130 - j 9
+                 25              1.99             18                   121 - j 8
+                 30              2.08             17                   115 - j 5
+                 35              2.13*            16                   112 - j 1
+                 40              2.13*            15                   111 + j 2
+                 45              2.11             15                   111 + j 6
+                 50              2.07             14                   112 + j 8
+
+Average           5              0.96             23                   192 + j42
+(C=0.005,        10              1.24             21                   164 + j 5
+  DC=13)         15              1.41             20                   144 - j 8
+                 20              1.52             18                   131 - j11
+                 25              1.58*            17                   121 - j10
+                 30              1.58*            16                   115 - j 6
+                 35              1.53             15                   111 - j 2
+                 40              1.44             14                   110 + j 2
+                 45              1.33             14                   110 + j 6
+                 50              1.21             14                   112 + j 9
+
+Very Good         5              2.84             18                   198 + j55
+(C=0.0303,       10              3.06             17                   171 + j11
+  DC=20)         15              3.21             16                   152 - j 6
+                 20              3.31             15                   136 - j12
+                 25              3.35*            14                   124 - j12
+                 30              3.31             13                   116 - j 9
+                 35              3.17             12                   111 - j 5
+                 40              2.94             11                   109 + j 0
+                 45              2.63             11                   108 + j15
+                 50              2.27             10                   101 + j 8
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of equilateral delta = 48.5' baseline length, 42' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 2.  7.15 MHz equilateral delta:  properties over various soils at various heights.
+

At most baseline heights, the 40-meter equilateral delta gain over average soil does not come up to its gain over poor soil. However, the TO angles for each soil level show the normal progression lower as the soil quality improves for any given height of the baseline. Moreover, the feedpoint impedances also show their normal progression for any given height from one soil type to the next better. In short, using average soil as a sample of the 40-meter equilateral delta modeled performance sells the antenna somewhat short.

+
+ +
+
+ Figure 4. Typical elevation patterns for the equilateral delta below, at, and above the baseline height for maximum gain. +
+

Although it is not possible to create a single generalization governing elevation pattern shape for every soil type, some general expectations are possible. As illustrated in Figure 4, elevation patterns at baseline heights well below the height of maximum gain tend to be bulbous, with a higher angle of maximum radiation. Elevation patterns at the height of maximum gain tend to show the first signs of a secondary high angle lobe. At heights where the gain declines significantly from its maximum value, the secondary lobe is considerable. At such heights, the advantage of the antenna is lost: rejection of high-angle QRM and QRN diminishes to make the antenna's low gain a distinct disadvantage. In general, for each soil type or its closest approximation, it may be best to hold the baseline height of the antenna at or slightly below the level for maximum gain.

+

The Right-Angle Delta

Because right-angle deltas are closer in shape to the ratio of length to height necessary for maximum gain from the shape, they display higher gain at any given baseline height than the corresponding equilateral delta. The dimensions for the 80-meter right-angle delta are shown in Figure 5. The baseline is 120' long, with a 60' height. +
+ +
+
+ Figure 5. Dimensions of the modeled right-angle deltas for 80 and 40 meters. +
+

Because the right-angle delta is shorter than the equilateral delta, the 80-meter antenna was modeled at baseline heights of 10 through 90 feet without exceeding the maximum apex height of roughly 150 feet. Table 3 shows the results for our four defined soil types. Immediately apparent is the higher gain at lower heights and the higher maximum gain obtainable at each height.

+ 
   3.6 MHz Right-Angle Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor        10             -0.45             28                    94 + j28
+(C=0.001,        20              0.07             26                    76 + j 6
+  DC=5)          30              0.38             24                    66 - j 2
+                 40              0.61             22                    59 - j 4
+                 50              0.81             21                    54 - j 3
+                 60              0.99             20                    51 - j 2
+                 70              1.15             19                    49 - j 0
+                 80              1.29             18                    49 + j 1
+                 90              1.42             18                    49 + j 3
+
+Poor             10              1.05             25                    95 + j38
+(C=0.002,        20              1.46             23                    79 + j10
+  DC=13)         30              1.68             21                    68 + j 1
+                 40              1.83             20                    61 - j 3
+                 50              1.92             19                    56 - j 4
+                 60              1.95             17                    42 - j 3
+                 70              1.97*            16                    50 - j 1
+                 80              1.92             15                    49 + j 0
+                 90              1.85             15                    48 + j 2
+
+Average          10              1.63             24                    97 + j42
+(C=0.005,        20              1.94             22                    81 + j12
+  DC=13)         30              2.08             20                    71 + j 1
+                 40              2.14             18                    63 - j 4
+                 50              2.15*            17                    57 - j 5
+                 60              2.09             16                    53 - j 4
+                 70              1.96             15                    50 - j 2
+                 80              1.77             14                    48 - j 0
+                 90              1.53             13                    47 + j 1
+
+Very Good        10              3.92             18                    94 + j48
+(C=0.0303,       20              4.21             17                    82 + j17
+  DC=20)         30              4.41             15                    73 + j 3
+                 40              4.58             14                    65 - j 3
+                 50              4.72             13                    59 - j 5
+                 60              4.80*            13                    54 - j 5
+                 70              4.80*            12                    50 - j 3
+                 80              4.69             11                    48 - j 1
+                 90              4.48             10                    47 + j 1
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of right-angle delta = 120' baseline length, 60' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 3.  3.6 MHz right-angle delta:  properties over various soils at various heights.
+

Also apparent is the fact that the height of maximum gain parallels roughly the pattern shown for the 80-meter equilateral delta. The height of maximum gain over average soil is less than that for either poor or for very good soil. Nonetheless, the progressions of feedpoint impedances and take-off angles are normal.

+

One of the chief selling points for the right-angle delta is that the feedpoint impedance is generally compatible with coaxial cable feed systems. Because the models used are based on a free space model, the model is not a good approximation of coaxial cable under a baseline height of about 40 feet.

+

The 40-meter right-angle delta charts are based on a free space resonant model with a 60.8' baseline and a 30.4' height. The model was run at 5-foot intervals up to a baseline height of 50 feet, which is well beyond the point at which high angle lobes begin to dominate the elevation pattern. Once more, as shown in Table 4, the gain over average soil is anomalously low relative to the gain over poor and over very good soil. However, take-off angles and impedance progressions are regular as the soil type improves. In addition, elevation patterns follow the same general order as for the equilateral delta. The recommended height to maximize available gain but avoid significant high angle lobes is at or just below the height of maximum gain for the relevant soil type.

+ 
    7.15 MHz Right-Angle Delta:  Properties Over Various Soils at Various Heights
+
+Soil Type       Baseline        Gain            T-O Angle              Feed Impedance
+                Height ft       dBi              degrees               R +/- jX Ohms
+
+Very Poor         5             -0.11             28                    88 + j30
+(C=0.001,        10              0.46             26                    73 + j 9
+  DC=5)          15              0.86             24                    63 + j 2
+                 20              1.19             23                    57 + j 0
+                 25              1.47             22                    53 + j 0
+                 30              1.72             20                    51 + j 2
+                 35              1.94             19                    49 + j 3
+                 40              2.14             19                    48 + j 5
+                 45              2.30             18                    48 + j 6
+                 50              2.45             17                    49 + j 7
+
+Poor              5              1.18             26                    92 + j40
+(C=0.002,        10              1.64             24                    77 + j13
+  DC=13)         15              1.92             22                    67 + j 4
+                 20              2.14             21                    60 + j 0
+                 25              2.29             19                    55 - j 0
+                 30              2.41             18                    52 + j 0
+                 35              2.48             17                    50 + j 2
+                 40              2.51*            16                    48 + j 3
+                 45              2.50             15                    48 + j 5
+                 50              2.46             15                    48 + j 4
+
+Average           5              1.17             25                    95 + j42
+(C=0.005,        10              1.57             23                    79 + j13
+  DC=13)         15              1.77             21                    68 + j 3
+                 20              1.90             20                    61 - j 1
+                 25              1.97             18                    56 - j 1
+                 30              2.00*            17                    52 - j 0
+                 35              1.97             16                    49 + j 1
+                 40              1.90             15                    48 + j 3
+                 45              1.79             14                    47 + j 5
+                 50              1.66             14                    48 + j 7
+
+Very Good         5              3.19             20                    96 + j49
+(C=0.0303,       10              3.49             19                    82 + j17
+  DC=20)         15              3.66             17                    72 + j 5
+                 20              3.79             16                    64 - j 0
+                 25              3.87             15                    58 - j 2
+                 30              3.88*            14                    53 - j 2
+                 35              3.81             13                    50 - j 0
+                 40              3.65             12                    48 + j 2
+                 45              3.39             11                    47 + j 4
+                 50              3.06             11                    47 + j 6
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of right-angle delta = 60.8' baseline length, 30.4' height to apex.
+                Construction:  #12 AWG copper wire.
+
+Table 4.  7.15 MHz right-angle delta:  properties over various soils at various heights.
+

Like the 80-meter right angle delta, the 40-meter right-angle delta approaches coaxial cable compatibility fairly rapidly as the baseline height increases. In fact, a height of about 15' is all that is needed for a direct coax feed system, although a balun choke is likely wise, given the placement of the feedpoint for maximum vertically polarized radiation.

+
+ +
+
+ Figure 6. Feedpoint resistance and reactance of the modeled 80-meter right-angle delta across the band. +
+

Figure 6 shows the free space impedance sweep of the 80-meter right angle delta across the band. Figure 7 shows the equivalent sweep for 40 meters. In both cases, read the value of resistive component from the left Y-axis and the value of the reactance from the right Y-axis.

+
+ +
+
+ Figure 7. Feedpoint resistance and reactance of the modeled 40-meter right-angle delta across the band. +
+

On 80 meters, the resistive component varies a total of about 26 Ohms, well within the range of coax matching. On the narrower 40-meter band, the change is only about 5.6 Ohms. The right-angle delta is indeed a stable antenna relative to its feedpoint resistance.

+

On both bands, the reactance varies much more widely across the band: 126 Ohms on 40 meters and over 475 Ohms on 80 meters. However, in both cases, the reactance changes linearly with frequency. By making the antenna inductively reactive at the lowest frequency of operation, it may be feasible to insert a remotely operated variable capacitor to compensate for the inductive reactance, leaving a net feedpoint impedance that is both resistive and within the range of direct coaxial cable feed.

+

On 80 meters, even a very good capacitor may only permit operation across most, but not all of the band. On 40 meters, most of the band may be covered within a 2:1 SWR limit without any matching components at all. In some cases, built-in antenna tuning units within some transceivers may suffice for any compensation needed, since coax line losses are quite small on the lower bands. However, for equipment sensitive to even fairly low SWR levels, such as numerous linear amplifiers, an external matching system is advisable.

+

Improving the Local Soil

+

A question bound to arise in the minds of some builders whose soil is poor or worse is whether performance improvements can be had by improving soil conditions in the local area of the antenna.3 The answer lies in how much soil the antenna builder controls and how high the antenna is.

+

Soil improvement can consist of a radial system, but it should not be confused with a tuned radial system as might be needed with a monopole connected to it. Soil improvement might also be accomplished by a wire grid or other less exact mesh of wires designed to improve soil quality over a region within which the antenna is generally centered.

+

To see what modeling might suggest about the matter, I took equilateral and right-angle deltas for 80 meters and placed them over very poor soil. Then, I created a radial zone of very good soil centered beneath the antenna. For the first step I used a zone 0.25 wavelength in radius and hence extending just beyond the antenna limits. The second step was a zone with a radius of 0.5 wavelength, followed by succeeding 0.5 wavelength increases in the radius until no further improvement was recorded. Test models were placed with their baselines at 20, 40, and 60 feet.

+

The results of the investigation appear in Table 5 for the equilateral delta and in Table 6 for the right-angle delta. Several interesting features emerge from a comparison of the two tables. First, a short zone of improvement can actually reduce antenna performance from its desired gain vs. take-off angle goals. The effect occurs over a larger improvement zone as the antenna height increases.

+ 
         3.6 MHz Equilateral Delta:  Soil Improvement Performance Changes
+
+In the sample tables below, the antenna is presumed to be over very poor soil (C=0.001;
+DC=5) for an indefinite distance in every direction.  Soil improvement in the
+immediate vicinity of the antenna is achieved at the designated radius to the
+level of very good soil (C=0.0303; DC=20).
+
+Very Good Soil               Gain in dBi             Take-Off Angle
+Radius in feet                                        in degrees
+
+Baseline = 20'
+  0                                -0.25                23
+ 68 (.25 wl)                       -0.06                31
+136 (.50 wl)                        2.32                25
+272 (1.0 wl)                        3.68                19
+408 (1.5 wl)                        3.85*               16
+544 (2.0 wl)                        3.85                16
+680 (2.5 wl)                        3.85                16
+
+Baseline = 40'
+  0                                 0.29                20
+ 68 (.25 wl)                       -0.10                21
+136 (.50 wl)                        0.96                27
+272 (1.0 wl)                        3.31                20
+408 (1.5 wl)                        4.09                16
+544 (2.0 wl)                        4.20*               13
+680 (2.5 wl)                        4.20                13
+
+Baseline = 60'
+  0                                 0.69                19
+ 68 (.25 wl)                        0.55                19
+136 (.50 wl)                        0.55                19
+272 (1.0 wl)                        2.16                20
+408 (1.5 wl)                        3.57                16
+544 (2.0 wl)                        4.14                14
+680 (2.5 wl)                        4.32*               12
+
+Note 1.  *=maximum gain at the baseline height equal that of the antenna over
+continuous very good soil.
+
+
+Table 5.  3.6 MHz equilateral delta:  soil improvement performance changes.
+
+            3.6 MHz Right-Angle Delta:  Soil Improvement Performance Changes
+
+In the sample tables below, the antenna is presumed to be over very poor soil
+(C=0.001; DC=5) for an indefinite distance in every direction.  Soil
+improvement in the immediate vicinity of the antenna is achieved at the
+designated radius to the level of very good soil (C=0.0303; DC=20).
+
+Very Good Soil                   Gain in dBi       Take-Off Angle
+Radius in feet                                      in degrees
+
+Baseline = 20'
+  0                                 0.07                26
+ 68 (.25 wl)                        1.11                38
+136 (.50 wl)                        3.53                25
+272 (1.0 wl)                        4.21*               17
+408 (1.5 wl)                        4.21                17
+544 (2.0 wl)                        4.21                17
+680 (2.5 wl)                        4.21                17
+
+Baseline = 40'
+  0                                 0.61                22
+ 68 (.25 wl)                        0.15                22
+136 (.50 wl)                        2.29                28
+272 (1.0 wl)                        4.30                19
+408 (1.5 wl)                        4.58*               14
+544 (2.0 wl)                        4.58                14
+680 (2.5 wl)                        4.58                14
+
+Baseline = 60'
+  0                                 0.99                20
+ 68 (.25 wl)                        0.74                20
+136 (.50 wl)                        0.74                20
+272 (1.0 wl)                        3.52                20
+408 (1.5 wl)                        4.58                16
+544 (2.0 wl)                        4.80*               13
+680 (2.5 wl)                        4.80                13
+
+Note 1.  *=maximum gain at the baseline height equal that of the antenna
+over continuous very good soil.
+
+
+Table 6.  3.6 MHz right-angle delta:  soil improvement performance changes.
+

Second, the range required for the achievement of maximum gain (equivalent to that of a continuous zone of very good soil) is shorter for the right-angle delta than for the equilateral delta. Since only 0.5 wavelength intervals were checked, the table does not give the precise point where maximum gain over very good soil was attained. However, the half wavelength difference appears consistently at all three antenna baseline heights. At least in part, the differential occurs because of the height of the high current feedpoint of the antennas. The right-angle delta feedpoint is about 7' or so above the baseline, while the equilateral delta feedpoint is about 20' above the antenna baseline. These differences are consistent with the differentials with height changes in the size of the soil improvement zone to achieve maximum gain.

+
+ +
+
+ Figure 8. Elevation patterns of identical equilateral delta over a. continuous very good soil and b. an improved very good soil area with very poor soil beyond. +
+

Third, the maximum achievable gain is that which occurs if the soil were very good continuously from the antenna to the far end of the Fresnel zone. However, this does not mean a full equivalency of performance. Figure 8 shows elevation patterns for two deltas of identical design at identical heights above ground. One is modeled over continuous very good soil, while the other is modeled over an improved (very good) soil zone to 2.5 wavelengths, with very poor soil beyond. Although the upper portion of the two patterns is identical, the area below the angle of maximum radiation is deficient for the soil improvement case. The missing radiation is unfortunately the lowest angle radiation so desired by most SCV users.

+
+ +
+
+ Figure 9. Typical equilateral and right-angle delta azimuth patterns at the elevation angle of maximum radiation. +
+

The SCV Azimuth pattern, as we noted last time, is a broad oval, as representatively shown in Figure 9. The right-angle delta, besides showing a marginal gain benefit, also shows a slight increase over the equilateral model in side rejection. However, both patterns should be interpreted as broad ovals with side performance down only 4 to 5 dB below the main lobes. Beyond the SCV Deltas

+

The are many variations of the delta which we shall not cover. Most variations alter the feedpoint, using either the lower corner or the center of the baseline. These designs gradually lose the dominance of vertically polarized radiation as the feedpoint moves away from 1/4 wavelength down from the apex of the triangle. The resultant total pattern increases in gain, but as well in higher angle radiation. However, the delta in these configurations tends to perform better as an all-band antenna fed by parallel transmission line to an antenna tuner. In addition, the antenna is somewhat simplified mechanically.

+

Since our concern is with SVCs, we shall bypass these variations and turn next time to another family member rightfully called an SCV.

+

Notes

1 These notes should be read as only a slight addition to the excellent material in John Devoldere, ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed. (Newington: ARRL, 1994), especially Chapter 10, "Large Loop Antennas," pp. 10-5 to 10-10. Everyone interested in contesting or DXing on 160-40 meters should have a copy of this remarkable book on the shelf. +

2 All modeling in this particular exercise was done in EZNEC Pro, NEC-4 version, available from W7EL. The ground system used throughout is the Sommerfeld-Norton.

+

3 See also Low-Band DXing, pp. 9-8 to 9-9 and 9-30 to 9-31. Unlike Devoldere, I prefer to call the phenomenon at hand "soil improvement" rather than establishing a radial system. It is not at all clear that lacing the underground area beneath a delta or other SCV with copper wire achieves something close to perfect ground. Hence, I have used more conservative soil improvement figures associated with very good ground (C=0.0303; DC=20).
+

+
+ +

+

Updated 5-19-98. © L. B. Cebik, W4RNL. A print version of this note appears in The National Contest Journal. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 3 +

Return to SCV Index

+

Topics: Delta Loop, HF Lower, SCV


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+

SCVs Part 3: The Rectangular Division

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+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ So far, we have looked at the delta loop SCVs. To review, the SCV antennas are the class of self-contained, vertically polarized, 1 wavelength wire antennas and include deltas, quad loops, and open-ended arrays such as the half-square and bobtail curtain. Basic designs require about 1 wavelength of wire, but doubled versions also work very well. These antennas only become SCVs when their feedpoints are located so as to maximize vertically polarized radiation and minimize horizontally polarized radiation. Under those conditions, they have less raw gain than when fed for horizontally polarized radiation, but they exhibit very low angle bi-directional patterns broadside to the array with very little response to high-angle radiation. Hence, they are favored by many DXers who will trade gain for a better signal-to-noise ratio for distant signals. Moreover, they require no ground plane. +

For 160 meters, where everything is big, the SCV with the smallest vertical and horizontal dimensions is the side-fed rectangle. Squares are much taller with less gain, while half squares are also taller with only a small margin of extra gain over the rectangle. Deltas are also taller, and longer corner-to-corner than the rectangle. Hence, for most installations requiring an SCV, the rectangle should be the antenna of choice.

+
+ +
+
+ Figure 1. The basis of the rectangular SCV in the quad square loop. +
+

The side-fed rectangle was popularized in recent times by K5RP, who called it a magnetic slot in his Antenna Compendium, Vol. 2 article.1 One may get a grip on the side-fed rectangle more easily by deriving it from the side-fed square (or quad) loop. See Figure 1. When used for horizontally polarized radiation, the bottom fed loop has been long known to lower its feedpoint impedance and increase its gain if elongated vertically. K6STI reported some time back in QST on using the loop in this configuration to achieve a 50-Ohm impedance.2 Also, this configuration is the basis for the Hentenna, an elongated loop with good gain and an impedance matching system.

+

In free space, there is no up or down. Therefore, laying the square loop on its "side" gives us the same antenna with the field at 90 degrees to the bottom-fed version. Likewise, tilting the elongated loop over on its side produces the magnetic slot or single rectangle. When placed over the earth rather than in free space, the antenna produces mostly vertically polarized radiation. Like its brother, the square loop, it needs no ground plane.

+

Maximum free space gain from the rectangle occurs when the long unfed sides are about 3 times longer than the short fed side and the loop is brought to resonance. This shows clearly in Figure 2, which tracks free space models (using #12 copper wire). This 3:1 figure is normally not very critical, as the gradual slope of the curve demonstrates. The resonant feedpoint resistance for the 206' long by 68' high version is just above 30 ohms, which is a bit low until we introduce proximity to the earth into the picture.

+
+ +
+
+ Figure 2. Shape vs. gain in the 160-meter rectangular loop. +
+

In fact, the ratio of long side to fed-side of the rectangle for maximum free space gain is frequency dependent. Based on free space models of rectangles resonated at frequencies from 1.8 to 146 MHz, the ratio (R) of the long side to the short side for maximum gain (where F is the frequency in MHz) is as follows:

+
+ +
+

Like the counterpart relationship between the baseline length and the height of deltas, this approximation holds fairly well into the 2-meter region, at which the #12 wire basis for the models becomes an appreciable part of a wavelength.3 However, the curve approaching maximum gain is shallow, and little is lost from being slightly off the ideal mark.

+

Although the ratio of long-to-short side increases for maximum gain in an elongated loop with increases in frequency, the feedpoint impedance follows normal rules: the more extreme the elongation, the lower the feedpoint impedance at resonance for the resulting loop. At 2 meters, where the ratio approaches 6:1, the feedpoint impedance is in the vicinity of 7 Ohms.

+

The Single Rectangle

+
+ +
+
+ Figure 3. Dimensions of the rectangular loops used in this study. +
+

Figure 3 sets the dimensions used in this study for the single rectangle. (We shall look at the K5RP double rectangle a bit farther on.) I shall leave it to builder ingenuity as to how one might hang up this antenna. But before we string a long length of wire, we should ask how high to string it.

+
+ +
+
+ Figure 4. Gain and take-off angle for rectangles at various heights. +
+

Figure 4 provides modeling data on the single rectangle for bottom wire heights ranging from 20' to 140' up. The antenna top wire will be 68' higher. The left axis records gain over average soil for the various heights. Note that as the bottom wire reaches the 90-100' mark, the gain levels off and then decreases with further increases in antenna height. The second curve referenced to the right axis records the continuous decrease in the elevation angle of maximum radiation, which runs from 23 degrees for the lowest height surveyed to 14 degrees for the highest.

+
+ +
+
+ Figure 5. Three elevation patterns of the rectangle at various heights. +
+

On the very dubious assumption that we have some choice in how high to place the rectangle, we can also use elevation patterns of the antenna as a guide. Figure 5 provides three patterns with the bottom wire at 20' up, 100' up, and 140' up. The decrease in gain with the 140' pattern is already evident, along with the reason for that decrease. Above the height for maximum gain, a secondary lobe begins to appear at a very high angle. With sufficient elevation (above 1/2 wavelength or so), the secondary lobe becomes dominant and the overall low angle gain of the antenna begins to decrease dramatically. However, I doubt anyone will ever test this modeling result by placing the bottom wire of the rectangle above 270' up.

+
+ +
+
+ Figure 6. 160-meter rectangle feedpoint resistance and reactance. +
+

We can see the span of expected feedpoint impedances in Figure 6. At 140' up, the feedpoint impedance approaches that of free space models. The resistive component increases in a regular curve as the antenna is lowered to more usable heights, in accord with reductions in gain as the antenna passes the 90' level on its way down. Also notable as an earth-effect is the increase in inductive reactance with lower heights, a fact suggesting that builders of rectangles at low heights might wish to shrink them to bring them to resonance. (However, before adjusting the antenna size, see the notes on matching below.) Notice that the feedpoint resistance of the antenna at its target frequency (here, 1.85 MHz) is well within the range of direct coaxial cable feed.

+
+ +
+
+ Figure 7. Rectangle resistance and reactance across the 160-meter band. +
+

As one might expect, the SWR bandwidth of this antenna, like most 160- meter antennas, is fairly narrow. More important is the information in Figure 7, a track of the resistance and reactance across the band for the antenna when the lower wire is at 20' up. Similar data accrue for higher antenna elevations, but with a shift in the resistance curve according to height.

+

The range of resistance is rather narrow--under 12 ohms across the band, as read from the left axis. Moreover, the reactance (as read from the right axis) changes in a very linear fashion. It would be simple enough to enlarge the antenna until it displays inductive reactance across the band. A remotely tuned series capacitor might then compensate for the reactance, leaving a resistive impedance suitable for coaxial cable.

+ 
160-Meter Single Rectangle Gain and Feedpoint Impedance Over Various Soils
+
+Antenna Height Gain in dBi         Take-Off Angle Feedpoint Impedance
+  (in feet)                           (degrees)          (R +/- jX Ohms)
+
+   20-88'
+Very Poor Soil    0.34             27             65.1 + 30.0
+Poor Soil         1.86             25             62.4 + 34.1
+Average           3.09             22             60.6 + 36.8
+Very Good         5.24             16             55.7 + 37.4
+
+   60-128'
+Very Poor Soil    1.09             23             42.5 -  1.7
+Poor Soil         2.55             21             43.1 +  0.2
+Average           3.63             19             44.0 +  1.3
+Very Good         5.78             14             44.2 +  3.1
+
+  100-168'
+Very Poor Soil    1.24             20             33.3 -  5.1
+Poor Soil         2.67             18             34.3 -  4.8
+Average           3.71             16             35.2 -  4.9
+Very Good         6.16             13             36.1 -  4.4
+
+
+Soil types          Conductivity (S/m)       Dielectric Constant
+
+Very Poor Soil      0.001                     5
+Poor Soil           0.002                    13
+Average             0.005                    13
+Very Good           0.0303                   20
+
+Table 1.  160-meter single rectangle gain, TO angle, and feedpoint
+impedance over various soils, with different antenna heights above ground.
+

The data developed so far has been over average earth, as it is called. Unfortunately, many of use live over earth significantly poorer than average, while a few lucky souls live on very good earth. Table 1 provides some guidance as to expectations for various types of soil ranging from very poor (conductivity (C) = 0.001 S/m; dielectric constant (DC) = 5) to very good earth (C = 0.0303; DC = 20). The figures reflect single side- fed rectangles at base heights of 20, 60 and 100 feet. Similar tables might be drawn up for any vertically polarized antenna and show similar differences from one soil type to the next. However, unlike the delta loops, which showed some aberrant progressions with changes in soil conditions, the course of values shows relative smooth curves from one soil type to the next for rectangles.

+

The tables are based on uniform soil in every direction from the antenna for distance great enough to fully affect the far field. Of great interest is the lack of significant change in the antenna feedpoint impedance with changes in soil type. It is dubious whether one can effect significant performance improvements in this or any other SCV by doctoring the soil in the immediate vicinity of the antenna. On the other hand, the soil at a distance of 2 wavelengths and more form the antenna is usually beyond control.

+
+ +
+
+ Figure 8. Elevation patterns over very poor and very good soil. +
+

The better the distant soil, the better the low angle radiation from the antenna. Figure 8 shows the contrast between very poor and very good soil. Equally important with the gain improvement is the lowered angle of maximum radiation. Were the curves graphically equalized, the higher-angle response would be very little different. However, the low-angle response from the antenna over very good soil is very much enhanced. Intermediate soil types provide intermediate curve shapes.

+

The Double Rectangle

For various reasons, some antenna builders prefer to feed their antennas with parallel transmission line and use an ATU to effect a match. One effective way to do this is to use the antenna as an impedance transformer by doubling it and making a mobius-strip crossing at the end opposite the feedpoint. This is the double rectangle shown in Figure 3, and developed by K5RP. +

The sketch shows two significant features. First, the loop must be slightly fatter vertically for maximum gain relative to the single loop. Second, the spacing between the loops has very little effect on antenna gain. In fact, models of the double loop with a space that ranges from 1' up to 12' showed only a 0.01 dB difference in gain.

+

What did change with changes in spacing was the required total loop size for resonance. The closer the wires, the larger the loop size. Part of this size increase stems from the fact that the crossing wires are longer for wider spacing, thus occasioning smaller outside dimensions. However, the other part is a function of minor interactions between the loops. With a constant length of 206' for the double rectangle array, the loop height was 70' with a 12' spacing and 71' for a 2' spacing.

+

The remainder of the data was generated on the basis of a 2' space between the wires, simply because that is most likely a more convenient construction distance. Spacers can be almost anything that insulates and is light weight. It is essential that the crossing wires at the far end of the array be well insulated from each other, although spacing appears not to be critical.

+
+ +
+
+ Figure 9. Gain and take-off angle of the double rectangle at various heights. +
+

The double rectangle exhibits almost a half dB of additional gain beyond that of the single rectangle. Figure 9 shows the gain and take-off angle for lower-wire heights from 20' to 140' up, which permits direct comparison with the corresponding chart for the single rectangle. The curves are highly congruent, with peak gain at about 100' up (with the top wire at 171' up). Since the resolution of take-off angles is one degree, the "stair-step" form of that curve should be no surprise, and 1-degree differences between the graphs for the single and double rectangles are meaningless.

+
+ +
+
+ Figure 10. Feedpoint resistance and reactance of the double rectangle. +
+

The "transformer" action of the double rectangle configuration appears clearly in Figure 10. The forms of both the resistance and the reactance curves are almost identical to those of the single rectangle, but the double rectangle values are almost exactly 4 times those for the single rectangle. Both resistance and reactance are multiplied.

+

The curve suggests that almost any parallel feedline might be used to feed the double rectangle. A link-coupled tuner should be able to handle the range of resistance and reactance across 160-meters. In fact, the more typical network tuner with its 4:1 output balun should not be heavily challenged by the impedances presented by the double rectangle.

+ 
160-Meter Double Rectangle Gain and Feedpoint Impedance Over Various Soils
+
+Antenna Height Gain in dBi         Take-Off Angle Feedpoint Impedance
+  (in feet)                           (degrees)          (R +/- jX Ohms)
+
+  20-91
+Very Poor Soil    0.54             27             274 + 120
+Poor Soil         2.07             24             264 + 139
+Average           3.30             22             258 + 151
+Very Good         5.46             16             237 + 156
+
+  60-131
+Very Poor Soil    1.38             23             171 -   6
+Poor Soil         2.83             21             174 +   2
+Average           3.90             19             178 +   7
+Very Good         6.06             14             179 +  14
+
+ 100-171'
+Very Poor Soil    1.60             20             131 -  18
+Poor Soil         3.01             18             136 -  17
+Average           4.05             16             139 -  17
+Very Good         6.50             12             143 -  15
+
+
+Soil types          Conductivity (S/m)       Dielectric Constant
+
+Very Poor Soil      0.001                     5
+Poor Soil           0.002                    13
+Average             0.005                    13
+Very Good           0.0303                   20
+
+Table 2.  160-meter double rectangle gain, TO angle, and feedpoint
+impedance over various soils, with different antenna heights above ground.
+

Like the single rectangle, soil quality affects the far field pattern fairly strongly without affecting the feedpoint impedance very much. Table 2 presents data for the double rectangle at the same baseline heights as for the single rectangle in Table 1. The increase in gain for the double rectangle is everywhere apparent in the table. However, the chief effect of the table is likely to be to make many folks wish they lived surrounded by very good earth. I did not have the heart to present the salt-water data.

+

The Result

Unlike the patterns for vertical monopoles and dipoles, the SCV family of antennas display a highly bi-directional pattern. Figure 11 presents the azimuth pattern for a double rectangle over average soil with a baseline height of 100' up and a take-off angle of 16 degrees. The single rectangle presents a similar pattern. Note the cloverleaf in the center of the pattern: it represent remnant horizontally polarized radiation which is not eliminable from any of the SCV configurations. +
+ +
+
+ Figure 11. Azimuth pattern for a double rectangle showing both vertical and horizontal components. +
+

In general, deltas and square loops have more broadly oval patterns with less front-to-side rejection than the rectangle. The half-square pattern is similar to that of the rectangle with a slightly greater front- to-side ratio.

+

To increase gain further--and in the process double the front-to-side ratio--requires no more altitude, but double the linear space for the antenna. K4VX's open double rectangle with a common center wire or the familiar bobtail curtain provide about 1.5 dB added gain and over 20 dB front-to-side ratio, with comparable take-off angles to the single and double rectangles shown here.4 They are certainly antennas worth investigation if one has a linear space well over 400' long.

+

These notes are based on computer models of the rectangle, which itself has already been proven in the field. Where computer modeling is at its best is in developing systematic guidance data, and that has been the aim of these notes. Computer models assume level terrain, but the individual contemplating an antenna such as these might well use terrain analysis software by N6BV or K6STI to adjust expectations for the particular antenna site and its environs. The more data we gather in advance, the more realistic will be our expectations for any antenna we might think about building. The 160-meter rectangle makes a good case-in- point.

+

But What About 80 Meters?

In our haste to review the rectangle at 160 meters, we have bypassed data for 80 meters, where the antenna is certainly a candidate for SCV use. The ideal ratio of length to fed-side for a 3.6 MHz rectangle is about 3.6:1. #12 AWG copper wire models in free space yielded maximum gain with dimensions of about 110' long by 31' high, at a figure about 0.25 dB higher than the 160-meter model. However, the feedpoint impedance was about 8 Ohm lower. These latter two properties result from the narrower shape of the 80-meter rectangle. + 
3.6 MHz Single Rectangle:  Properties Over Average Soil at Various Heights
+
+Soil Type Baseline  Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+
+Average    10        2.21            25            50 + 38
+(C=0.005,  20        2.76            23            40 + 15
+  DC=13)   30        2.98            21            34 +  7
+           40        3.08            20            30 +  3
+           50        3.11*           18            27 +  2
+           60        3.08            17            25 +  2
+           70        3.01            16            23 +  2
+           80        2.88            15            22 +  3
+           90        2.69            14            21 +  4
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of single rectangle = 110' baseline length, 31' height.
+          Construction:  #12 AWG copper wire.
+
+Table 3.  3.6 MHz single rectangle:  properties over average soil at
+various heights.
+

With these variations in mind, you can anticipate the values for the 80-meter rectangle that appear in Table 3. Only the values for average soil are shown, since the values for other soils are proportional, using the 160-meter charts as a guide. The height of maximum gain is just about half that for 160 meters. However, over ground, the gain is not as high as the corresponding 160-meter rectangle at twice the height.

+

Only at low heights is it advisable to feed the 80-meter single rectangle directly with coax. Indeed, the single rectangle above 160 meters is probably a worse choice than its companion double rectangle. Like the 160-meter version of the double rectangle, the 80-meter antenna displays a slight gain over a single rectangle with relative insensitivity to the spacing of the two wires. The sample model placed the wires 1' apart, with the cross-over wires spaced about 0.5' apart. Also like the 160-meter version, the model maintained the same length, but increased the height over the single rectangle by a small amount, ending up with a total height of 32.3' for resonance in free space.

+ 
3.6 MHz Double Rectangle:  Properties Over Average Soil at Various Heights
+
+Soil Type Baseline  Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+
+Average    10        2.40            25           212 + 132
+(C=0.005,  20        2.98            23           164 +  39
+  DC=13)   30        3.23            21           138 +   6
+           40        3.36            19           120 -   8
+           50        3.42            18           107 -  14
+           60        3.43*           17            97 -  15
+           70        3.37            15            90 -  13
+           80        3.26            15            85 -   9
+           90        3.08            14            82 -   5
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of double rectangle = 110' baseline length, 32.3'
+height.
+          Construction:  #12 AWG copper wire.
+
+Table 4.  3.6 MHz double rectangle:  properties over average soil at
+various heights.
+

Table 4 shows the modeled values over average soil at heights ranging from 10 to 90' (with resultant top-wire heights ranging from 42.3' to 122.3'). The added gain over the single rectangle is evident, as is the reduced gain relative to corresponding 160-meter double rectangles. Like the 160-meter models, the height of maximum gain for the double rectangle is slightly and perhaps insignificantly higher than for the single rectangle.

+

The feedpoint impedance at low heights is likely to benefit from the use of parallel feeders and an antenna tuner. At higher levels, a quarter- wavelength matching section of 75-Ohm cable will provide a 50-Ohm coax match over a small portion of the band. However, the large scale changes in reactance suggest that parallel feeders and a tuner may be best for operation over the entire band.

+

This basic data, when combined with sensible adjustments to the 160- meter data, should provide reasonable guidance for our expectations should we decide to build one of these antennas. Before we make such a decision, we shall want to compare these data with those in the last episode on deltas. But let's not be too hasty. Final decisions should await a fuller story on the open-ended cousin to these two loops: the half-square.

+

Notes

1. For the "magnetic slot" and "double magnetic slot," see Russell E. Prack, K5RP, "Magnetic Radiators--Low Profile Paired Verticals for HF," The ARRL Antenna Compendium, Vol. 2 (Newington: ARRL, 1989), pp. 39-41. However, the elongated loop or "oblong" and its relationship to the square quad has been well-known for a long time. See, for example, the reference to this subject in Karl Rothammel, Y21BK, Antennenbuch (Berlin: Militarverlag der DDM, 1984), pp. 230, where a ratio of about 2.4:1 is recommended for the vertically polarized version. Reference is made therein to work by G6LX. +

2. Brian Beezley, K6STI, "A Gain Antenna for 28 MHz," QST (July, 1994), 70.

+

3. In the HF region, we can use a simpler approximation: (2.8 + 1.4 log F), where F = the frequency in MHz for #12 copper wire. When expressed in terms of natural logarithms, R approaches the Fibonacci constant times ln (100 F).

+

4. For the open double magnetic slot, see Lew Gordon, K4VX, "The Double Magnetic Slot Antenna for 80 Meters," The ARRL Antenna Compendium, Vol. 4 (Newington: ARRL, 1995), pp. 18-21.
+

+
+ +

+
+

Updated 5-19-98. © L. B. Cebik, W4RNL. A print version of this note appears in The National Contest Journal. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

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+ +

+
+ Go to Part 4 +

Return to SCV Index

+

Topics: HF Lower, Quad Loop, Rectangle, SCV


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+

SCVs Part 4: The Open-Ended Cousins

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Having examined the low-band properties of the delta and rectangular loop, we next turn to the open-ended cousin of these SCVs: the half square. Although developed after its double-wide brother, the bobtail curtain, the half square is the more fundamental antenna.1 As shown if Figure 1, it consists of two (roughly) 1/4 wavelength vertical legs connected by a (roughly) 1/2 wavelength horizontal wire. The horizontal wire functions as a phasing line between the verticals, although its radiation is imperfectly cancelled. +
+ +
+
+ Figure 1. Basic outline of the half square antenna. +
+

The first question often asked about the half square is whether it really belongs to the SCV family. Like the loops, the half square may operate without a ground plane--in fact, a small ground plane may reduce its gain and other desirable properties. Moreover, one may model the antenna in free space and make versions pointing either up or down for any frequency. For low band use, the down-pointing half square is favored because it places the high-current points at the corners at maximum achievable height.2

+
+ +
+
+ Figure 2. Evolution of the half square from the delta. +
+

One can establish the SCV credentials of the half square by a simple free space modeling project. Begin with a right-angle delta, as shown in Figure 2. Separate the wires at the high-impedance apex point by a little. Then widen the separation, adjusting the model to maintain something close to resonance. Table 1 shows the first steps of this progression. In effect, nothing happens when the wires at the apex do not touch. By gradually, straightening the sloping delta wires toward the vertical and by lengthening the baseline until the feedpoint is in a corner, once evolves the half square. Finally, for low-band use, flip the antenna over so that the open ends point down. Of course, in free space, from which the figures in the table emerge, the flip is gratuitous, since there is no up or down.

+ 
         Partial Evolution of a Right-Angle Delta to a Half Square
+
+Antenna Description           Gain dBi       Feedpoint Impedance
+                                          (R +/- jX Ohms)
+
+Right-angle delta:
+60.8' base; 30.4' height       3.31               51 + j 6
+
+Right-angle delta: apex
+wires separated 0.2'           3.31               51 + j 6
+
+Height increase to 30.41';
+apex spread 0.4'               3.32               51 + j 7
+
+Height increase to 30.7';
+apex spread 2.0'               3.36               51 - j 1
+
+Height increase to 31.1';
+apex spread 4.0'               3.41               53 + j 5
+
+Note:  Frequency:  7.15 MHz; Wire: #12 AWG copper; model in free space.
+
+Table 1.  Partial evolution of a right-angle delta to a half square.
+

The more ideal separation between the vertical elements of the half square produces a sharper bi-directional pattern than the SCV loops develop. The side rejection will vary from 10 to well over 15 dB, for a familiar peanut-shaped pattern. An example appears in Figure 3. Whether the this pattern is an advantage or a disadvantage depends upon the oeprator's needs.

+
+ +
+
+ Figure 3. Basic azimuth pattern of the half square at the elevation angle of maximum radiation when the antenna is at the height of maximum gain. +
+

Like the other SCVs, the half square has a ratio of horizontal to vertical lengths that yields maximum gain in free space (and over ground). However, that ratio appears to be independent of frequency, except for some residual effect of wire size. The ratio of horizontal length to vertical height for maximum gain is about 1.6:1.3

+

For most antennas, there is sufficient band-to-band variation that giving formulas for cutting wires can be more misleading than helpful. However, the relatively invariant relationship between the horizontal and vertical dimensions of the half square for a maximum-gain configuration tends to assure a good utility for such formulas here. Where H is the horizontal length in feet, V is the vertical height in feet, and f is the frequency in MHz,

+
+ +
+

80-Meter and 40-Meter Maximum Gain Half Squares

An 80-meter half square designed for maximum gain at 3.6 MHz requires a horizontal wire about 124.5' long and two vertical end wires, each 77' long, when all wires are #12 AWG copper. The maximum free space gain of this antenna is about 4.6 dBi. When the antenna is placed over ground at some achievable height, the free space gain cannot be realized until the soil is very much better than average. + 
        80-Meter Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        1.74            23            80 + j13
+(C=0.001,  10        1.92            22            74 + j 5
+  DC=5)    15        2.05            22            70 + j 1
+           20        2.14            21            67 - j 3
+           25        2.21            20            65 - j 1
+           30        2.27            20            63 - j 1
+
+Poor        5        3.24            21            80 + j17
+(C=0.002,  10        3.34            20            75 + j 7
+  DC=13)   15        3.40            20            71 + j 2
+           20        3.42*           19            68 - j 0
+           25        3.42*           18            66 - j 1
+           30        3.41            18            64 - j 2
+
+Average     5        3.75            20            81 + j19
+(C=0.005,  10        3.79*           19            75 + j 8
+  DC=13)   15        3.79*           18            71 + j 2
+           20        3.76            18            68 - j 0
+           25        3.71            17            66 - j 1
+           30        3.63            16            64 - j 2
+
+Very Good   5        6.30            15            80 + j20
+(C=0.0303, 10        6.36            15            75 + j 9
+  DC=20)   15        6.40            14            72 + j 3
+           20        6.42*           14            69 - j 0
+           25        6.42*           13            66 - j 2
+           30        6.40            13            64 - j 3
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 124.5' horizontal length,
+77' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 2.  80-meter half square over various soils at various heights.
+

Table 2 shows the results of modeling the 80-meter half square over various soils. The listings can be quite short, since--for all but very poor soil--the half square reaches maximum gain when the vertical ends are quite close to the ground. Indeed, the most desirable height from the point of view of gain is lower for average soil than it is for either poor or very good soil. However, like the other SCVs, the half square shows a consistent pattern of feedpoint impedances for corner-fed models regardless of the soil type immediately beneath the antenna. The antenna is close to resonant in the vicinity of 70 Ohms, although very close proximity to the ground raises that number by as much as 10 Ohms.

+

A corresponding maximum gain half square for 7.15 MHz would be 62.45' horizontally and 39' vertically, using #12 AWG copper wire. Because the #12 wire is a larger fraction of a wavelength in diameter, the antenna's free space maximum gain is nearly 4.7 dBi. However, like the 80-meter model, the 40-meter half square does not achieve this gain over ground unless the soil is far better than average.

+ 
        40-Meter Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        2.41            23            73 + j 4
+(C=0.001,  10        2.72            22            67 - j 1
+  DC=5)    15        2.94            21            64 - j 2
+           20        3.13            20            62 - j 2
+           25        3.29            19            61 - j 1
+
+Poor        5        3.57            21            75 + j 6
+(C=0.002,  10        3.72            20            68 - j 1
+  DC=13)   15        3.78            18            64 - j 3
+           20        3.80*           17            62 - j 2
+           25        3.78            16            61 - j 1
+
+Average     5        3.40            20            76 + j 6
+(C=0.005,  10        3.46*           19            68 - j 1
+  DC=13)   15        3.42            17            64 - j 3
+           20        3.33            16            62 - j 3
+           25        3.20            15            61 - j 1
+
+Very Good   5        5.50            17            76 + j 7
+(C=0.0303, 10        5.51*           15            69 - j 2
+  DC=20)   15        5.44            14            65 - j 4
+           20        5.26            13            62 - j 4
+           25        5.05            12            60 - j 2
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 62.45' horizontal length,
+39' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 3.  40-meter half square over various soils at various heights.
+

Table 3 shows the figures for 40-meter half square performance over various types of soil. Once more, the antenna shows maximum gain when the ends are fairly close to the ground, although that height varies with soil type. Unlike the 80-meter antenna, modeling suggests that the half square for 40 performs slightly better over poor soil than over average soil, although the difference is marginal, since the progression of take-off angles, or elevation angles of maximum radiation, is normal and decreases regularly with improvements in soil type. The progressions of feedpoint impedances is also quite normal to our expectations. Again, because the #12 wire is "fatter" on 40 than on 80, the resonant feedpoint impedance is a few Ohms under that of the corresponding 80-meter half square.

+

Although the tables flag a height (or two) as reflecting maximum gain heights for soils that are poor or better, the entries for very poor soil show no flags. The reason for the absence of a flag is that over very poor soil, half squares for 80 and 40 continue to show increases of gain with increases of height. Table 4 extends the 40-meter "very poor soil" set of values up to a height of 60' for the lowest point of the antenna. The continued increase in gain and lowering of the take-off angle are clearly apparent.

+ 
        40-Meter Half Square Over Very Poor Soil at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        2.41            23            73 + j 4
+(C=0.001,  10        2.72            22            67 - j 1
+  DC=5)    15        2.94            21            64 - j 2
+           20        3.13            20            62 - j 2
+           25        3.29            19            61 - j 1
+           30        3.45            18            61 + j 0
+           35        3.60            18            62 + j 1
+           40        3.76            18            62 + j 1
+           45        3.92            17            63 + j 1
+           50        4.10            16            64 + j 1
+           55        4.29            16            64 + j 1
+           60        4.48            15            64 + j 0
+
+Table 4.  An extension of the 40-meter half square over very
+poor soil at various heights.
+

However, an illusion accompanies this progression, as shown in Figure 4. The elevation patterns in the figure are for antenna base heights of 10, 25, and 40 feet, respectively. As one raises the antenna, gain increases, but so too does a secondary high-angle lobe. In the process of acquiring more gain, the half square users also acquires high-angle radiation in the receive mode, thus decreasing the QRM and QRN filtering benefits of the half square. Whether there is a cut-off point to the height of the antenna over very poor soil--and where that point might be-- is a decision only the antenna builder can decide.

+
+ +
+
+ Figure 4. Elevation patterns of a half square over very poor soil for three heights. Note the increasing gain, but as well, the increasing high-angle secondary lobe. +
+

In general, the half square over almost any soil type provides maximum gain at heights closer to the ground than is true of the other SCVs. Like its relatives, the half square elevation pattern begins to produce secondary high angle lobes as soon as it passes the height of maximum gain. Exceeding that height by very much may yield stronger reception to closer- in, high-angle signals and partially or wholly defeat the basic purpose in using an SCV in the first place.

+

80-Meter and 40-Meter 50-Ohm Resonant Half Squares

From the numbers in Table 3 and Table 4, it is clear that the feedpoint impedance of a maximum gain half square is somewhat distant from 50 Ohms. However, one of the benefits of using a corner feedpoint for the antenna is the ability to feed the antenna with standard 50-Ohm coaxial cable. Therefore, I redesigned the half square models to come somewhat closer to a 50-Ohm feedpoint impedance. +

The 80-meter (3.6 MHz) model required horizontal stretching to 155' with the verticals shortened to only 60' to arrive at a 50-Ohm antenna in free space. This is a horizontal-to-vertical ratio of about 2.58:1, which is a considerable departure from the maximum gain ratio of 1.6:1. When subjected to the same systematic modeling over various soils as the maximum gain models, Table 5 emerged. All of the gain figures are down significantly from the maximum gain model, with the decreases growing worse as the soil type grows worse. Moreover, the heights for maximum gain also decrease, while the take-off angles increase. Whether these reductions in performance warrant the move to a 50-Ohm model is, once more, a user decision.

+ 
80-Meter 50-Ohm Resonant Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5       -0.29            25            66 + j 9
+(C=0.001,  10       -0.12            24            61 - j 1
+  DC=5)    15       -0.02            24            57 - j 7
+           20        0.03            23            54 - j10
+           25        0.06            22            52 - j13
+           30        0.08            21            51 - j15
+
+Poor        5        1.61            23            61 + j16
+(C=0.002,  10        1.66*           22            57 + j 4
+  DC=13)   15        1.66*           22            54 - j 3
+           20        1.61            21            53 - j 7
+           25        1.54            20            51 - j10
+           30        1.46            19            50 - j12
+
+Average     5        2.33*           21            60 + j21
+(C=0.005,  10        2.30            21            56 + j 8
+  DC=13)   15        2.20            20            54 + j 1
+           20        2.08            19            53 - j 4
+           25        1.93            18            52 - j 8
+           30        1.77            18            51 - j11
+
+Very Good   5        5.27*           16            52 + j25
+(C=0.0303, 10        5.17            16            51 + j12
+  DC=20)   15        5.04            16            50 + j 4
+           20        4.89            15            50 - j 1
+           25        4.73            14            50 - j 5
+           30        4.58            14            50 - j 8
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 155' horizontal length,
+60' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 5.  80-meter 50-Ohm resonant half square over various
+soils at various heights.
+

Figure 5 shows the feedpoint resistance and reactance across the 80- meter band for the 3.6 MHz model. Across the band, the change in the resistive component is about 77 Ohms. With some redesign of the antenna, almost all of the band might be fit within a 2:1 SWR curve, assuming that the reactance can be compensated for at the feedpoint. However, the reactance varies by over 500 Ohms, suggesting that additional redesign for a remotely tuned series capacitor might still not yield full band coverage.

+
+ +
+
+ Figure 5. Feedpoint resistance and reactance of a 50-Ohm resonant 80-meter half square across the band. +
+

40-meters presents fewer problems for a half square designed for 50- Ohm feed. The dimensions of the model used for 7.15 MHz, was 70.5' horizontally and 34.5' vertically (with #12 AWG copper wire). The horizontal-to-vertical ratio is about 2:1, which is much closer to the maximum gain ratio than the 80-meter version achieved. As shown in Table 6, the gain reductions for the 40-meter antenna are less severe than for the 80-meter model, and the heights needed for maximum gain are only slightly lower than those for the maximum gain model for each type of soil. Likewise, increases in the take-off angle are less severe. In general, then, a 40-meter half-square designed for 50-Ohm resonance may be more feasible than an 80-meter version.

+ 
40-Meter 50-Ohm Resonant Half Square Over Various Soils at Various Heights
+
+Soil Type Bottom    Gain      T-O Angle      Feed Impedance
+          Height ft dBi        degrees       R +/- jX Ohms
+
+Very Poor   5        1.85            24            58 + j 4
+(C=0.001,  10        2.15            23            53 - j 3
+  DC=5)    15        2.34            21            50 - j 6
+           20        2.51            20            48 - j 6
+           25        2.68            19            47 - j 7
+
+Poor        5        3.19            22            58 + j 8
+(C=0.002,  10        3.30            20            53 - j 1
+  DC=13)   15        3.31*           19            50 - j 5
+           20        3.28            18            48 - j 6
+           25        3.23            17            48 - j 6
+
+Average     5        3.06*           21            59 + j 9
+(C=0.005,  10        3.06*           19            53 - j 0
+  DC=13)   15        2.97            18            50 - j 4
+           20        2.83            17            49 - j 6
+           25        2.68            16            48 - j 6
+
+Very Good   5        5.34*           17            57 + j12
+(C=0.0303, 10        5.24            16            52 + j 1
+  DC=20)   15        5.06            15            50 - j 3
+           20        4.82            14            49 - j 5
+           25        4.54            13            48 - j 6
+
+Note 1.  * = Height of maximum gain
+Note 2.  Dimensions of half square = 70.5' horizontal length,
+34.5' vertical height.  Construction:  #12 AWG copper wire.
+
+Table 6.  40-meter 50-Ohm resonant half square over various
+soils at various heights.
+

The feeding problem is also less severe on 40 meters. The resistive component of the feedpoint impedance, as shown if Figure 6, varies by only 6 Ohms or so, while the reactance varies by a little under 140 Ohms. Therefore, for a corner-fed 40-meter half square, a remotely tuned series variable capacitor becomes a viable option for full band coverage with direct coax feed--assuming the antenna is further optimized to present inductive reactance across the band.

+
+ +
+
+ Figure 6. Feedpoint resistance and reactance of a 50-Ohm resonant 40-meter half square across the band. +
+

End-Feeding the Half Square

+

Corner-feeding the half square eliminates in large measure the need for a more complex matching network when the antenna is used only on the band for which it is designed. Conversely, feeding the antenna in the most traditional manner--at the open end of one of the verticals--requires a parallel tuned circuit resonated on the band of choice. The coil is tapped for coaxial cable feed. An additional tap may be used near the top of the tank circuit to effect the most precise match possible.

+
+ +
+
+ Figure 7. Comparison of azimuth patterns of a corner-fed and an end-fed half square. Except for the feedpoint location, the antennas are identical. +
+

At the fundamental frequency for which the half square is cut, the use of end or corner feeding makes little difference to performance. Figure 7 shows the slight difference in pattern. With corner feed, the bi-directional pattern is closely symmetrical, with gain maxima at 90 and 270 degrees in the pattern shown. When end fed, the antenna shows a slight displacement of about 5 degrees in the maximum gain points, tilted away from the feed point. In practical terms, the user would be hard pressed to tell the difference.

+

End feeding is often recommended by those planning to use the antenna on more than one amateur band.4 If the matching network is remotely tuned, it might be pressed into service as a multi-band tuner. Likewise, there is no rule against feeding the corner with a parallel transmission line and using an antenna tuning unit in the shack for other bands.

+ 
Corner-Fed vs. End-Fed 80-Meter Half Squares at Higher Frequencies
+
+Frequency Max. Gain T-O Angle Az. Angle of   Feedpoint Impedance
+ in MHz    in dBi    degrees   Max. Gain       (R +/- jX Ohms)
+
+3.6
+a. Corner 3.79      18        90               71 + j   3
+b. End    3.93      18        85             4100 - j4000
+
+7.15
+a. Corner 5.35      20        55             1400 - j  30
+b. End    5.17      20        53             1900 - j3000
+
+10.1
+a. Corner 6.59      16        41             1000 - j 600
+b. End    6.46      19        40              350 - j2000
+
+14.1
+a. Corner 6.78      33        31              600 - j 200
+b. End    7.29      34        30              800 - j1000
+
+Note 1.  Dimensions of half square = 124.5' horizontal length,
+77' vertical height. Construction:  #12 AWG copper wire.
+Height 15' minimum.
+
+Table 7.  Corner-fed vs. end-fed 80-meter half squares at
+higher frequencies.
+

Table 7 hints at the anticipated results of using an 80-meter half square on 40, 30, and 20. By comparing corner and end feeding systems for a single model of the half square, we discover that there is no significant difference in the patterns. The slight differences in gain, as well as angles of interest, result from one or the other system yielding larger or smaller "bulges" in the pattern in various directions. The chief differences between the two feed point show up in the anticipated feedpoint impedances.

+
+ +
+
+ Figure 8. End-fed 80-meter half square azimuth pattern on 40 meters. The center-fed pattern is similar. +
+

On 40 meters, the pattern is roughly square for both feed systems, as is evident from Figure 8. Maximum gain is toward the corners most distant from the feedpoint. In contrast, an 80-meter dipole would become something close to a full wavelength on 40, producing a strong bi-directional pattern approaching 9 dBi if the antenna is a half wavelength up on 40 meters. The half square substitutes coverage for gain.

+
+ +
+
+ Figure 9. End-fed 80-meter half square azimuth pattern on 30 meters. The center-fed pattern is similar. +
+

The patterns for the 80-meter half square on 30 and 20 meters are not too different from each other, as Figure 9 and Figure 10 make evident. The square becomes elongated, with further gain in the most favored directions. 20-meter use shows the disadvantage of a high-angle main lobe, although the lobe is very broad vertically. The feedpoint impedances for both bands require the use of a tuner with a considerable range of adjustment.

+
+ +
+
+ Figure 10. End-fed 80-meter half square azimuth pattern on 20 meters. The center-fed pattern is similar. +
+

The patterns are certainly not those favored for DXing. However, they offer the contester and the general operator some advantages in coverage not offered by highly directional (including highly bi-directional) antennas. However, in some applications, the antenna tuner settings will be very sharp and require readjustment with small frequency excursions.

+

Although the half square can be pressed into multiband service, its principle use remains as a vertically polarized low-angle low-gain antenna that offers a fairly high signal-to-noise ratio for DX signals. Of the SCVs surveyed, it shows the strongest preference to be mounted as low as the structure permits for maximum gain over most soil types. However, a maximum gain 80-meter model would top out in the 90 to 100 foot level, while a 40-meter model also designed and installed for maximum gain would need to be 50 to 60 feet high. Except over very poor soil, further increases in height will likely not yield superior performance overall, when we combine considerations of both gain and the elevation angle of maximum radiation.

+

Moreover, unless one needs only a bi-directional pattern, full coverage may require two half squares at right angles to each other. However, with a little remote switching, it is possible to design the right angle array with a common feed vertical and to detune the unused wires. Of course, having the land on which to install such a system is a prior necessity.

+

So far in this series, I have not attempted to compare the various types of SCVs, although I have compared SCVs within each type. Because each type of SCV has its own installation requirements, "better" and "worse" become complex terms that measure not only the performance and feedpoint figures for the antennas, but as well, all of the mechanical properties and their relationship to the prospective user's land. Nevertheless, the prospective SCV user should remember that these antennas as a class are not general purpose antennas. Rather, when installed within the limits suggested for each type within the class, they provide low-gain, low-angle radiation free from higher lobes and thus forming a natural filter against QRM and QRN from closer sources. In some cases, users may want them for receiving purposes only and use a dipole or similar antenna for transmitting (in which application high angle QRM and QRN are not relevant).

+

Installing SCVs too high, especially half squares, can easily defeat the main functional advantage of the antennas. Designing them for 20 meters is a marginal enterprise, and above 20 meters, other antenna types will normally out-perform the SCVs. The SCVs do come into their own again until the VHF region, where they can be mounted many wavelengths above ground and their largely vertical polarization combined with a beamwidth around 60 degrees may be superior in some applications to Yagis turned on their side.

+

Except for these very general comments, I have avoided comparisons with other types of antennas. Although a thorough comparison would be useful, the amount of material there is to present on SCVs and the shortage of space within which to present it suggests that this must be (as they sometimes say in textbooks) "an exercise left to the reader."

+

In fact, there are a number of directly related SCV questions left to look at. Some hams have built shrunken SCVs. Others have built double wides (for example, the double-humped delta, the open double magnetic slot, and the bobtail curtain). Still others have managed some reversible SCV beams. We should take at least a brief look at each of these ideas in one last installment.

+

Notes

1 The half square antenna actually appeared after its larger sibling, the bobtail curtain. See Ben Vester, K3BC, "The Half Square Antenna," QST (March, 1974), 11-14. Additional notice appeared in Radio Communications for January, 1977 (p. 36). See also Robert Schiers, N0AN, "The Half-Square Antenna," Ham Radio (December, 1981), 48-50. All three of these early sources show the antenna as voltage-fed from one of the free ends. For the bobtail curtain, see Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," CQ (March, 1948), 21-23 and 92-95. See also Smith follow-up articles, "The Bobtail Curtain and Inverted Ground Plane," Parts 1 and 2 in Ham Radio (February, 1983), 82-86, and (March, 1983), 28-30. See also John Devoldere, ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed. (Newington: ARRL, 1994), Chapter 12, "Other Arrays." +

2 VHF half-square designs will appear in a forthcoming issue of Communications Quarterly (See The Half-Square on 2 Meters for an earlier version of the article). Unfortunately, some half square users have oversold the antenna, especially for upper HF use. See, for example, Hannes Coetzee, ZS6BZP, "A Visit to the Half Square Antenna," Communications Quarterly (Spring, 1998), 83-90. At normal heights (1/2 wavelength or more), a dipole will usually outperform the half square on the upper HF bands. Its use on the lower bands is, in concert with the other SCVs, to sacrifice gain for a low-angle bi-directional elevation pattern that suppresses high-angle QRM and QRN. Its most apt application is where elevating a horizontal antenna in its entirety above 1/2 wavelength is not feasible.

+

3 If expressed as a ratio of vertical to horizontal dimensions, the ratio is 0.62:1. Allowing for wire thickness effects, this is the Fibonacci constant:

+
+ +
+

(This equation yields a value of about 0.618034, which also yields an inverse ratio of about 1.618034. The numbers are decimally longer for those addicted to transcendental numbers). The reference to Fibonacci is incidental in this context; the basic ratio for the half square holds up at least throughout the HF region.

+

4 See, for instance, Joe Everhart, N2CX, "End-Fed Half-Wave Antennas," QRPp (Spring, 1998), 11-15.
+

+
+ +

+
+

Updated 5-21-98. © L. B. Cebik, W4RNL. A print version of this note appears in The National Contest Journal. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Part 5 +

Return to SCV Index

+

Topics: HF Lower, Half Square, SCV


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+

SCVs Part 5: Shorties, Double-Wides, and Twins

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ We have looked in some detail at deltas, rectangles, and half squares- -the three main types of self-contained vertically polarized wire antennas (SCVs). Unfortunately, space has not permitted a detailed look at all of the antennas and their variations on all of the low bands. But hopefully, the modeling exercises will be suggestive enough for you to carry on independently. +

In our final episode, we shall be even more hurried, and hence must confine ourselves further. We shall look at shortening techniques for some of the SCVs, at open-face double-wide versions of them, and at the basics of parasitical techniques applied to the SCVs. We can only cover the ground by sticking to one band (80), one soil type (Average: C = 0.005 S/m; DC = 13), and limited variations. Again, I hope the data will be enough to let you extrapolate to your specific needs.

+

Shorties

Of all of the SCVs, the delta has proven the most popular antenna to shorten. A full-size equilateral delta for 3.6 MHz is about 96' long at the base, with an 83' height. Add to this the requisite minimum height for adequate to optimal performance, and the antenna becomes a very major enterprise. +

Even some shortening can be beneficial. For reasons that will become apparent, I have limited discussion to 3/4-size deltas, which--at 3.6 MHz-- become 72' wide by 62' high. The 21' height saving alone can make the difference between the antenna being feasible and being impossible.

+
+ +
+
+ Figure 1. Various ways to load a small equilateral delta. +
+

Figure 1 shows perhaps the three most common forms of loading the shortened delta in order to make it resonant once more. In Low Band DXing, ON4UN shows some of these and other loading schemes.1 In some respects, all three techniques are varieties of one technique: adding wire to the highest impedance point possible in order to sustain the high current parts of the antenna for maximum field strength.2 However, the techniques show some interesting differences.

+

One of those differences is the feedpoint, which is distinctly higher up the side for the double-wire top-loaded model than for the other two models. For maximum vertically polarized radiation, the feedpoint was chosen to yield the lowest take-off angle possible (with verifying checks upon the remnant horizontal field to confirm minimal field strength in that polarization). One can fine tuning this point in models by selecting the feedpoint so that the final horizontal field (which is a cloverleaf in azimuth patterns) is as symmetrical as possible.

+

Part of the reason for the higher feedpoint up the side of the double- wire top-loaded model is the current distribution in the loading wire assembly. The current magnitude in each of the two wires at the apex is about 0.8 of the source current. In both the single-wire loaded version of the antenna, the current is about double this value.

+ 
        A Comparison of Shortened Equilateral Delta 80-Meter Loops
+
+Antenna Full Size Delta   Double Wire Top    Single Wire Top    Single Wire Base
+             Loop              Loaded              Loaded             Loaded
+Ht    Gain TO   Feed Z    Gain TO   Feed Z   Gain TO   Feed Z   Gain TO   Feed Z
+feet  dBi  deg. R+/-jX    dBi  deg. R+/-jX   dBi  deg. R+/-jX   dBi  deg. R+/-jX
+
+10    1.28  22  196+j41   0.55  23  87+j39   0.62  23  76+j33   0.33  22  40+j12
+20    1.48  20  167+j 1   0.80  21  72+j12   0.86  21  65+j 7   0.71  21  32+j 0
+30    1.58  18  147-j13   0.92  20  63+j 3   0.96  20  57-j 2   0.81* 19  28-j 4
+40    1.62* 17  132-j18   0.97* 18  56+j 2   0.99* 18  51-j 6   0.80  17  25-j 6
+50    1.59  16  122-j17   0.96  17  51-j 2   0.97  17  47-j 7   0.74  16  23-j 6
+60    1.50  15  114-j13   0.89  16  47-j 2   0.89  16  43-j 7   0.62  15  22-j 6
+70    1.34  14  110-j 8   0.76  15  44-j 1   0.75  15  41-j 5   0.47  14  21-j 5
+
+Note 1:   Full-size delta loop:  96' baseline, 83' height; shortened delta
+          loops (3/4 full size):  72' baseline, 62' height.
+          Double-wire top load is 1' wide by 47.4' long; single wire top
+          load is 54' long; single wire base load is 46.5' long.
+          All antennas: #12 AWG copper wire.  Height entry: baseline height
+          above ground.  Design frequency: 3.6 MHz.
+          All antennas over average soil (C=0.005 S/m; DC=13).
+
+Table 1.  A comparison of shortened equilateral delta 80-meter loops.
+

Table 1 shows the results of modeling each loaded delta, along with a full size equilateral delta for comparison--all over average soil. Immediately apparent is the fact that the top-loaded deltas require the same baseline height as the full size delta for maximum gain. Although the base-loaded delta finds its maximum gain level 10' lower, its overall gain is also lower than either of the top-loaded models. Between the top-loaded models, there is little if anything to choose. Both provide close to a 50- Ohm match (with the base-loaded model having about half the feedpoint impedance of the top-loaded models). The gain of the best loaded delta is down by two-thirds of a dB from the full-size model, an amount which is usually not too significant operationally.

+

Like the full-size right-angle delta, which has a feedpoint impedance and 80-meter height that closely accord with those of the loaded deltas, the feedpoint resistive component does not change radically across the 80- meter band. This makes the loaded delta a candidate for remotely tuned series capacitance compensation for an antenna designed to have inductive reactance at all across the band or across some part of the band of interest. Models also suggest that the antenna gain increases more rapidly as the antenna is "oversized" than is the case with dipoles and similar horizontally polarized antennas.

+

The limitation on the delta used for the modeling sequences is that the single-wire top-loading element had to fit within the delta. In practice, where many delta users install them at angles other than vertical, the wire can be almost any length.3 (However, heed ON4UN's warning about the high voltage on the end of this wire.) Where the wire may seem to require more length than the delta permits, the end can be split, folded back, or coiled, although each of these techniques may increase the need for very careful adjustment.

+
+ +
+
+ Figure 2. Some methods of shortening half squares. +
+

The techniques just listed are more commonly applied to shortened half squares, as illustrated in Figure 2. Half squares tend to lose the least performance when the length of the phasing line is left in tact and only the length of the vertical members is shortened. I ran a series of free space models to check the performance losses with shortening. The full size half squares with 77' verticals showed a gain of 4.6 dBi and a resonant feedpoint impedance of about 63 Ohms. Using the symmetrical hat technique of loading, I shortened the verticals to 60' with horizontal spikes running 10' each way from the element ends. The gain dropped to about 4.45 dBi, with a decrease in the feedpoint impedance to 57 Ohms resistive. Enlarging the hat spikes to 20' each permitted the verticals to be only 46' long: the gain dropped to about 4.1 dBi and the feedpoint impedances decreased to 45 Ohms resistive. Similar decreases could be expected over ground relative to a full-size half square. The design question remaining would center on choosing a compromise between the top height for the lowest take-off angle and the bottom height for maximum gain from the shortened antenna.

+

The key element in successfully obtaining maximum performance from a shrunken SCV is to place the loading at the high voltage, high impedance portion of the antenna, leaving the high current portions as undisturbed as possible. In addition, design work should also include pre-construction modeling exercises to locate the feedpoint at the position which produces maximum vertically polarized radiation and minimum horizontally polarized radiation--assuming that one wishes SCV-type performance.

+

Double-Wides

+

At the other end of the scale from the shorties are the side-by-side double SCV antennas. Versions have been built for each of the major SCV types, so that there are double-humped deltas, open-face double rectangles (also called open double magnetic slot antennas), and double half squares (called bobtail curtains). Each has a tale of its own to tell.

+

The Double Right-Angle Delta. Figure 3 illustrates the design and resonant dimensions of a double right-angle delta cut for 3.6 MHz.4 The single right-angle delta is shown for comparison. Very little difference exists between the dimensions of each of the double's two triangles and the one trinagle of the single delta.

+
+ +
+
+ Figure 3. Single and double 80-meter right-angle deltas. +
+

The key difference lies in the position of the feedpoint. Where the two triangles would meet in the middle, the feedpoint is place between the baseline and the lowest point of the triangles' upper wires. Due to the balance within the overall system, horizontal radiation does not radically increase relative to that within a single delta with optimal feedpoint placement. Moreover, the feedpoint is compatible with a coaxial feed system.

+ 
     A Comparison of Single- and Double-Humped Right-Angle Delta Loops
+
+Antenna:  Single Right-Angle Delta       Double Right-Angle Delta
+
+Height    Gain  TO   Feed Z              Gain  TO   Feed Z
+feet      dBi   deg. R+/-jX              dBi   deg. R+/-jX
+
+10        1.63  24   97+j42              3.97  23   54+j22
+20        1.94  22   81+j12              4.08* 22   47+j 8
+30        2.08  20   71+j 1              4.04  20   43+j 3
+40        2.14  18   63-j 4              3.97  18   40-j 0
+50        2.15* 17   57-j 5              3.89  17   37-j 2
+60        2.09  16   53-j 4              3.79  16   35-j 2
+70        1.96  15   50-j 2              3.66  15   33-j 1
+
+Note 1:   Full-size right-angle loop: 120' baseline, 60' height; double
+          right-angle loop:  242' baseline, 60.5' height.  All antennas:
+          #12 AWG copper wire.  Height entry: baseline height above ground.
+          Design frequency: 3.6 MHz.  All antennas over average soil
+          (C=0.005 S/m; DC=13).
+
+Table 2.  A comparison of single- and double-humped right-angle delta
+loops.
+

Other differences emerge from a comparison of the performance at various heights of the single and double right-angle deltas. Table 2 compares the antennas between 10' and 70' baseline heights over average soil. Two data point stand out. First, a properly constructed double delta is capable of almost 2 dB gain over a single delta. Second, the baseline height for maximum gain is much lower for the double delta than for the single--some 30' lower. However, this extra gain and lower height requirement are purchased at the price of an antenna nearly 240' long that requires at least two high support points. Whether or not this defeats the value of the delta, whose single-hump version requires only one high support point, is a builder judgment.

+

The Double Open Rectangle. K4VX brought the double open magnetic slot--or the double rectangle, for simplicity--to amateur antenna most recently.5 When optimized for gain in free space, the dimensions shown in Figure 4 are best for 3.6 MHz.

+
+ +
+
+ Figure 4. Single and double open rectangles. +
+

The free space gain for the double rectangle was 5.5 dBi, compared to about 5.0 dBi for the double delta. The half dB advantage of the double rectangle also shows up over ground, as the figures in Table 3 demonstrate. However, the double rectangle requires considerably more baseline height to achieve maximum gain than the double delta. At a height of 20' for the baseline of each, performance is quite similar. Compared to the single rectangle, the double rectangle shows a gain advantage of about 1.5 dB, which is also 1 dB higher than the K5RP double-wire rectangle reviewed in an earlier episode.

+ 
            A Comparison of Single and Double Rectangular Loops
+
+Antenna:  Single Rectangle               Double (Open) Rectangle
+
+Height    Gain  TO   Feed Z              Gain  TO   Feed Z
+feet      dBi   deg. R+/-jX              dBi   deg. R+/-jX
+
+10        2.21  25   50+j38              3.72  25   109+j57
+20        2.76  23   40+j15              4.23  23    81+j15
+30        2.98  21   34+j 7              4.44  22    68+j 0
+40        3.08  20   30+j 4              4.53  20    59-j 5
+50        3.11* 18   27+j 2              4.56* 18    53-j 7
+60        3.08  17   25+j 2              4.54  17    48-j 7
+70        3.01  16   23+j 2              4.46  16    45-j 6
+
+Note 1:   Single rectangle: 110' long, 31' high; double rectangle:  208'
+          long, 26.8' high.  All antennas: #12 AWG copper wire.  Height
+          entry: baseline height above ground.  Design frequency: 3.6 MHz.
+          All antennas over average soil (C=0.005 S/m; DC=13).
+
+Table 3.  A comparison of single and double rectangular loops.
+

With dimensions of the rectangle optimized for gain, the preferred feedpoint position is at the center of one end of the assembly. At the height of maximum gain, the feedpoint impedance is about 53 Ohms, whereas the impedance of the antenna if fed on the center wire is only about 17 Ohms.

+

The double open rectangle is about 208' long, some 30' shorter than the corresponding double delta. Moreover, it is over 30' shorter in height. Thus, the high point for maximum gain installations of both antennas is quite similar (about 80'), even though the baseline of the rectangle needs to be higher.

+

The Bobtail Curtain. Of all the double SCVs, the bobtail curtain has the highest gain.6

+
+ +
+
+ Figure 5. The half square and the bobtail curtain. +
+

With the gain-optimized dimensions shown in Figure 5, the antenna has a free space gain of over 6.4 dBi. The gain also appears over ground, as shown in the figures in Table 4. The gain is well over 1.5 dB higher than for the half square and a full dB higher than for the double open rectangle, when each is place at the correct height for maximum gain. In fact, with maximum gain of the bobtail appearing over average soil at a minimum height of 15' or so, the maximum required height is once more about 80' above ground. (In other words, all three double SCVs require about the same upper height to achieve maximum gain.)

+ 
          A Comparison of the Half Square and the Bobtail Curtain
+
+Antenna:  Half Square               Bobtail Curtain
+
+Height    Gain  TO   Feed Z         Gain  TO   Feed Z
+feet      dBi   deg. R+/-jX         dBi   deg. R+/-jX
+
+ 5        3.75  20   81+j19         5.38  21    75+j39
+10        3.79* 19   75+j 8         5.45  20    68+j22
+15        3.79* 18   71+j 2         5.47* 19    64+j12
+20        3.76  18   68-j 0         5.45  18    61+j 7
+25        3.71  17   66-j 1         5.42  18    58+j 3
+30        3.63  16   64-j 3         5.36  17    53-j 2
+
+Note 1:   Half square: 124.5' long, 77' high; bobtail curtain:  296' long,
+          66.45' high.  All antennas: #12 AWG copper wire.  Height entry:
+          baseline height above ground.  Design frequency: 3.6 MHz.  All
+          antennas over average soil (C=0.005 S/m; DC=13).
+
+Table 4.  A comparison of the half square and the bobtail curtain.
+

Unlike the other double SCVs, whose dimensions are close to a simple doubling in length of their single SCV parents, the bobtail requires significant refiguring of the half square dimensions. The dimensions optimized by modeling show a longer and lower antenna: about 296' long and 66.45' high. These figures are close to the proportions recommended by SM4CAN, as cited in ON4UN's book.7 For the added length, one acquires nearly 4 dB gain over a single full size equilateral delta at its optimum height.

+

Feeding the bobtail is best done at the center wire. The high impedance base point of the wire can be fed via a parallel tank circuit. However, the impedance at the center of the wire is close to a coax match. If the height of the antenna yields too high an impedance at this point, one can simple select a higher point on the wire. With the model shown at the height for maximum gain, the top of the center wire shows an impedance of about 33 Ohms. Hence, between the top and the center, there is a good coax matching point for almost any installation.

+
+ +
+
+ Figure 6. Azimuth patterns for double-wides at heights of maximum gain. +
+

A comparison of azimuth patterns--each at the elevation angles of maximum radiation when the antenna is set at the height for maximum gain-- can reveal something further about the differences among the double-wide SVCs. See Figure 6. As the gain of the double-wides increases, the side- rejection also increases. In its maximum gain configuration, the bobtail actually begins to show a side "bulge" in its pattern. For maximum side rejection, the bobtail can be made slightly taller and less lengthy, if a little less gain is acceptable.

+

One caution: only consider the bobtail curtain in any form if you have the room to keep the elements in a straight line and apart from each other as the dimensions suggest. Do not try to bend the bobtail. Even a shallow Vee shape with a 150-degree included angle (where straight is 180 degrees) will reduce gain by a full dB on the primary band. A 120-degree included angle will reduce performance to a nearly circular pattern with a gain level not much different from a single monopole.

+

Twins

The SCV double-wides provide a foundation for higher gain bi- directional arrays on the low HF bands. The cost is longitudinal landscape. The beamwidth between -3dB points grows narrower with increased gain, and side rejection increases. Depending upon operating needs, these features may or may not be advantages. +

Where a higher degree of directionality is needed, one can press the SCVs into parasitical service with fair ease. Deltas will show a directional pattern with some front-to-back ratio and a little gain, and they may be placed at angles sloping from a cross bar placed near the top of a single existing tower. However, the most improvement occurs when one moves up to the half square, and we shall use this SCV as the basis for these notes.

+
+ +
+
+ Figure 7. A 2-element parasitical half square beam. +
+

Figure 7 sketches a feasible 2-element parasitical beam for 3.6 MHz. One useful guideline for half-square beams is to leave the horizontal length of the two elements the same (and to place them at the same height). Adjust the beam properties by altering the lengths of the verticals. In the sketch, the spacing was chosen for convenience: 30' provides a feedpoint impedance that varies between 50 and 55 Ohms as the bottom height of the antenna is raised from 13 to 23 feet (top height range: 87 to 97 feet). A wider spacing would add some gain to the array.

+

The forward gain of the beam over ground is about 6.7 dBi in the favored direction, with about 18 to 23 dBi front-to-back ratio, depending upon height. These figures are for an elevation angle of maximum radiation that runs between 17 and 18 degrees. The beamwidth is about 65 degrees between -3 dB points.

+
+ +
+
+ Figure 8. A 2-element parasitical half square beam with stub reflector loading. +
+

With vertical legs of different lengths, the beam just described is fixed in one direction. The beam becomes reversible if we make both the driven element and the reflector legs the same length. By adding a shorted stub of 50-Ohm coax to the reflector (about 25' for this particular array), as shown in Figure 8, the beam produces the same range of feedpoint impedances, the same range of front-to-back ratios, and the same gain (within 0.1 dB) as the beam in Figure 7. Since the stub may be brought to a center point between the elements, twin stubs may run from each element. With simple switching of both the center conductor and the outer braid, one line becomes a shorted stub and the other becomes just a part of the feed system for the beam. The result is a reversible beam.

+

If the builder prefers, he can use appropriate lengths of open-ended transmission line to place the stub junction point closer to the ground. Even shorted stubs longer than 1/2 wavelength can be used for a ground- mounted junction box. However, the longer the stub, the greater its losses, resulting in a little loss of front-to-back ratio (mostly). Alternatively, the beam can be fed with parallel transmission line, with the stubs cut to suit the higher impedance, higher velocity factor line.

+

Parallel transmission line becomes more attractive as a feed system for those who wish to operate over large regions of the band. The 80-meter model shows a fairly small frequency range for good beam properties. Parallel transmission line to an ATU allows use of the antenna across the entire band, with beam properties set for some "special" segment. Moreover, with only a little more complexity, the reversible beam can be configured for phased feeding to change the properties of the resulting field.

+
+ +
+
+ Figure 9. Azimuth pattern of a 2-element half square beam. +
+

Since the half square is fed at one corner, the azimuth pattern will be slightly tilted, as shown in Figure 9. The two-degree difference in the forward direction is less likely to be noticed than the differential to the rear.

+

With a maximum gain of about 6.6 to 6.7 dBi over average soil, the advantages over a standard wire Yagi may not be immediately apparent. A wire Yagi will have dimension fitting wholly within the width of the horizontal portion of the half square, without the need for vertical legs. When placed at the same height as the half square top wire, the Yagi will show up to 9.4 dBi gain.

+
+ +
+
+ Figure 10. Elevation patterns for a 2-element Yagi and a 2-element half square at 97' high. +
+

Figure 10 shows a comparison between the elevation patterns of the Yagi and the corresponding pattern of the half square beam. The SCV beam shows low angle radiation several dB stronger than the horizontal Yagi. However, perhaps the real advantage of the SCV beam for DX work is most apparent where the Yagi shows high gain and the half square beam shows little or none. The SCV not only rejects signals to the rear by 10 dB more than the Yagi, but as well the forward lobe is relatively unresponsive to high-angle signals above 30 degrees elevation.

+

For those with acres of open land or those who simply like to dream of large wire arrays, the bobtail curtain is also open to treatment as a parasitical beam.8 Using the horizontal dimensions of Figure 5, we can cut driver verticals to 64.4' and reflector verticals to 66' to obtain a 30'- spaced array with some remarkable properties. With a top height of 81.5' (plus or minus a bit), we obtain the azimuth pattern of Figure 11, with a 50-Ohm feedpoint impedance if the center leg is fed at the middle of its vertical length. With a gain of over 8 dBi at a low angle and a worst-case front-to-rear ratio of about 25 dB, the antenna is highly directional. Its narrow 44-degree beamwidth does suggest application in specific directions rather than more general operation. The bobtail beam is susceptible to reversibility in a manner similar to that used with the half square.

+
+ +
+
+ Figure 11. Azimuth pattern of a 2-element parasitical bobtail curtain beam. +
+

Summing Up

In this final installment, we have only been able to illuminate the highlights of supplementary techniques in getting the most out of SCVs, whether within restricted areas or height or with the aim of getting the most performance from the SCV possibilities. If the series has answered some questions about SCVs, it has opened the door a myriad others. +

Remember that in our modeling look at each of the SCV types, we discovered that we cannot automatically scale an antenna from one band to another and expect the same performance or feedpoint impedance. The antennas in this episode have been optimized by modeling for 3.6 MHz and may require considerable adjustment for use on 160 or 40 meters. Anyone considering anything more than casual experimentation with SCVs should invest in one of the NEC programs available to develop some initial guidance for both the feasibility and the construction phases of the enterprise.

+

Moreover, even with the best approximations of local soil type, construction always requires significant field adjustment, both of the antenna and of any special feed system used with the antenna. SCVs require not only a bit of real estate, but as well a good dose of patience. Modeling can provide some detailed preliminary guidance and systematic information about antennas, but it can never install a support tower, hang a wire, or make final adjustments.

+

However, if this series has helped you understand the basic properties of the family of SCVs--with regard both to their similarities and to their unique individual personalities--then it has done what modeling does best.

+

Notes

1 John Devoldere, ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed. (Newington: ARRL, 1994). See Chapter 10, pp. 10-14. +

2 For notes on the functional equivalence of double-wire and single wire end loading, see "Modeling and Understanding Small Beams: Part 7: Shrunken Quads," Communications Quarterly (Summer, 1997), 71-92. See also the work of Frank Witt, W1DTV (now AI1H), "Top-Loaded Delta Loop Antenna," Ham Radio (December, 1978), 57-61.

+

3 See, for example, Walter Schreuer, K1YZW/G3DCU, "The Top-Loaded Delta Revisited," ("Hints and Kinks"), QST (June, 1998), 59-60.

+

4 ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed., p. 12-12. The dimensions shown in Figure 12-15 are for 3.8 MHz.

+

5 Lew Gordon, K4VX, "The Double Magnetic Slot Antenna for 80 Meters," The ARRL Antenna Compendium, Vol. 4 (Newington: ARRL, 1995), pp. 18-21.

+

6 Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," CQ (March, 1948), 21-23 and 92-95. See also Smith's follow-up articles, "The Bobtail Curtain and Inverted Ground Plane," Parts 1 and 2 in Ham Radio (February, 1983), 82-86, and (March, 1983), 28-30.

+

7 ON4UN, Antennas and Techniques for Low-Band DXing, 2nd Ed., p. 12-13.

+

8 A 2-meter bobtail beam design (along with half-square designs using 2 and 3 elements) has appeared in an issue of Communications Quarterly, and the basic designs can be found in the VHF/UHF section of these notes.

+
+ +

+
+

Updated 05-25-1998, 01-14-2003, 02-04-2005. © L. B. Cebik, W4RNL. A print version of this note appears in The National Contest Journal. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 6

+

Return to SCV Index

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Topics: Bobtail Curtain, Delta Loop, HF Lower, Half Square, Quad Loop, Rectangle, SCV


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SCVs Part 6: The Bruce Array: An Update

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L. B. Cebik, W4RNL

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The ARRL Antenna Book has long had some interesting information on the Bruce Array, developed in recent editions (pp. 8-42 to 8-47 in the 19th Edition) by Rudy Severns, N6LF. Nonetheless, I still receive inquiries about the array, most wondering how it stacks up against half-squares and bobtail curtains and whether it is among the class of antennas that I call SCVs (self-contained vertical arrays).

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The short answer to the inquiry is that it does quite nicely. An optimized half-square for 3.6 MHz shows a gain of about 3.8 dBi broadside to the plane of the array at a take-off angle of about 18 degrees when we make it about 0.46 wavelength long and place the base about 15' above ground. A bobtail curtain at the same height above ground requires a length of about 1.08 wavelengths for a gain of about 5.5 dBi at a 19-degree take-off angle, when designed for the same frequency. A 3-element Bruce array, when about 1/2 wavelength long gives the same gain as a half square. When about the same length as a bobtail curtain, it yields nearly 6.3 dBi gain.

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However, for a given length, the Bruce array requires more wire, since the vertical elements are only about 1/4 wavelength apart. As well, since the Bruce array has some of its horizontal wires at the bottom, it tends to show maximum gain--the numbers cited above--when the base is about 0.15 wavelength above ground--about 41' above ground. Hence, the maximum gain placement of the antenna tends to also raise the top level of the antenna to about 0.41 wavelength or 111' at 3.6 MHz. You may wish to compare these numbers with the dimensions of half squares and bobtail curtains in Parts 4 and 5 of the SCV series. You may also wish to compare the dimensions with other forms of the SCV in earlier parts of the series, especially the side-fed rectangle and double-rectangle.

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So simple answers do not tell us the entire story of the Bruce array, since the feasibility of using this array depends very much on local circumstances. However, it may be useful to explore the array to see what some of its potentials and limitations may be.

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What is a Bruce Array and How Does It Work?

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A Bruce array is a continuous length of wire arranged to form 1/4 wavelength vertical wires spaced about 1/4 wavelength apart. To ensure that the array is vertically polarized--at least as a starting principle--we shall feed it at the center of any vertical element. To make a complete vertical dipole, we have to count from the feedpoint 1/4 wavelength, which takes us either to the center of a bottom horizontal wire or to the center of a top horizontal wire. The end vertical require that we add about 1/8 wavelength of wire to the open end to achieve full vertical dipole length. These end wires can be pointed outward, but to save space, most builders fold them back inward. The direction makes only a little difference, since the array shows predominantly (but not exclusively) vertically polarized radiation, with the remnant currents in the horizontal wires canceling to a large degree.

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Fig. 1 shows the most common forms of Bruce arrays used by amateurs, ranging from 2 to 5 vertical elements. In reality, you can build them to virtually any length for which you have the space. The figure also gives us the names of the array parts: horizontal, vertical, and end wire. In each case--at least at the start--we shall feed the antenna on either the center vertical or one of the verticals closest to the center.

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In this exercise, we shall use a design frequency of 3.6 MHz so that the array is more easily comparable to other SCVs. Dimensions will be given in wavelengths or fractions of wavelengths so that you can scale the antenna within the band with no problem. All models will use AWG #12 copper wire, except for one brief set of notes down the line. My initial model of the Bruce used the 4-element version in The ARRL Antenna Book with the recommended dimensions of 1.05 times a standard fraction of a wavelength. Hence, the 1/4 wavelength sections are actually 0.26 wavelength long and the 1/8 wavelength end wires are 0.135 wavelength long. We shall eventually change that a bit.

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The approximate dimensions suffice to show how the Bruce works, and Fig. 2 can help us in this regard. The curved lines show the current magnitude along each element when we feed the antenna at the center of a vertical element. The fields--as indicated by the current magnitudes on the vertical elements--add up to yield a bi-directional pattern broadside to the plane of the array. The horizontal wires show a current minimum at their centers, and of course, the end wires show the current going to zero at their ends--where we find a high voltage, as a safety note.

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What the diagrams to not show is that the current undergoes a 180-degree phase shift from one vertical center-point to the next. We shall use this fact later on in a discussion of alternative feed systems. For now, we may simply note that this continuous shift in current phase from one center to the next sets up a condition in which the radiation from the horizontal wires largely cancels itself, leaving a predominantly vertically polarized array.

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In Fig. 3, we have the elevation pattern overlaid on the outline of the array, when the array is about 0.15 wavelength above ground. The pattern is very well behaved as vertical antennas go and is clearly broadside to the plane of the array.

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However, there is a tendency among hasty builders to reason that the center bottom horizontal wire is much more convenient. Hence, they break the wire at its center and install a parallel feedline. When we make this move, everything changes.

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At first modeling sight, we might not realize that we have change the nature of the array. Fig. 4 shows a pattern of current magnitudes that is very similar to those in Fig. 2. What these current plots do not show here is that the phase along the horizontal wires is not shifting, but is the same at each end of the horizontal wire. The result is a pattern like the one shown in Fig. 5.

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Feeding the Bruce array in series at the center of a horizontal wire changes the pattern from broadside to endfire, and a very considerable decrease in gain--about 3.2 dB for the 4-element array shown. There are ways of feeding the Bruce at the bottom center that will yield the relatively high gain vertical broadside array that we want, but the simple series feed system here will not do the job.

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Fig. 6 shows a more correct way to obtain our vertical array with a center feed. We connect a wire from the center of the bottom wire to ground and feed the wire at its base against ground. We shall look more closely at this feeding system further down the line. Right now, we shall stay with the basic properties of the Bruce and assume that we are feeding it at the center of a vertical wire or in a way that simulates this feed system.

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Fig. 7 presents an SWR sweep for our initial Bruce design for 3.6 MHz. The 250-Ohm SWR curve is interesting, since it shows a usable under-2:1-SWR limit of slightly over 200 kHz. However, the resistance and reactance curves are even more interesting.

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The resistance changes very little with frequency. The reactance changes at a greater rate, but in nearly a linear fashion with rising frequency. Together, these two facts provide the user with a method of expanding the frequency coverage of a Bruce array. First, design the array so that it shows an inductive reactance at the lowest frequency of operation. Second, place remotely tuned variable capacitors in the feedline at the antenna terminals. The capacitors will compensate for the inductive reactance, leaving essentially a resistive impedance close to 250 Ohms (for our test array). Third, add a 4:1 balun and feed the system with 50- or 75-Ohm coaxial cable. Most baluns operate most efficiently when there is little or no reactance at their load terminals, so the balun in this set-up should provide good service. Fig. 8 shows the general scheme for this feed system.

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We shall examine some other feed options before we conclude this exploration of the Bruce array. However, it is now time to refine the Bruce dimensions and mounting situation.

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How Big and How High?

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If we review the common outlines of amateur-size Bruce arrays, something should immediate strike us as odd about the 2-element version. It resembles a side-fed quad loop, but with a gap. We may place the gap at either the top or the bottom. Fig. 9 shows the quad loop and its 2 Bruce cousins.

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Note that the Bruce gap, in either version, is at a high impedance, high voltage, minimal current point. When examining the evolution of the half-square from a closed loop, such as a delta, I discovered that one can open a loop at the high-impedance point with little or no effect upon performance. There is little or no difference between a high-impedance point on the loop circumference and a very-high-impedance gap, if the gap is not too large. In fact, the following table shows the performance figures for a 2-element quad and its Bruce counterparts at a base height of 0.15 wavelength.

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+  Modeled Performance Reports for a side-Fed Quad Loop and Bruce Arrays
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+      Antenna               Gain       TO Angle   Feed Impedance
+                            dBi        degrees    R +/- jX Ohms
+      Quad                  1.87       16         137.0 - j 3.7
+      Bottom-Gap Bruce      1.89       17         134.6 - j25.8
+      Top-Gap Bruce         1.86       17         135.3 - j26.1
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The original 4-element Bruce model using AWG #12 copper wire and the listed dimensions (0.26 wavelength vertical and horizontal wires and 0.135 wavelength end wires) showed an impedance of 248 - j61 Ohms when fed at the center of one of the interior vertical wires. This condition obtained with a base height of 0.15 wavelength or about 41'. The next question was how to go about enlarging the structure to bring the array to resonance.

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The easiest way to accomplish this feat is simply to lengthen the end wires somewhat until the array arrives at something close to resonance on the design frequency. However, this tack drops the gain a bit. The original design showed a gain of 5.20 dBi at a TO angle of 16 degrees, with a feedpoint impedance of 248.6 - j60.6 Ohms. Lengthening the end wires by 0.01 wavelength to 0.145 wavelength brought the array close to resonance with a feedpoint impedance of 259.2 - j 2.5 Ohms. However, the gain dropped to 5.11 dBi.

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A second way is to lengthen the vertical dimension slightly. This tactic seems prima facie more promising, since it promises to add a bit to the overall height of the array. However, this route also decreases gain on the road to resonance. Increasing the vertical lengths by 0.005 wavelength to 0.265 wavelength nearly resonated the array at 261.4 - j3.3 Ohms, but showed a 0.02-dB drop in gain. Although the drop was slight, this was not the desired trend.

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In fact, the best method of sustaining array gain and arriving at resonance is to increase the length of the horizontal wires. Although the increase is only slight, the wider spacing of the elements increases gain. Ideally, verticals achieve their highest gain in a phased array at a spacing of about 1/2 wavelength. We cannot achieve this in the Bruce, because the array consists of dipoles connected end-to-end by bending them around. Still, any reasonable widening that does not decrease the array height shows up as a smidgen of increased gain.

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The following table lists the final values selected for the parts of the Bruce arrays. The slight decrease from the recommended vertical length and the slight increase in the horizontal length optimized gain while bringing the feedpoint impedance close to resonance.

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+                         Bruce Array Dimensions
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+All dimensions in wavelengths
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+No. of     Horizontal       Vertical        End             Total
+Elements   Wire             Wire            Wire        Horiz. Length
+2          0.27             0.255           0.13            0.27
+3          0.27             0.255           0.14            0.54
+4          0.27             0.255           0.145           0.81
+5          0.27             0.255           0.145           1.08
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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With the array at a base height of 0.15 wavelength (and a consequential top height of 0.405 wavelength), the arrays show interesting elevation patterns broadside to the plane of the array. Fig. 10 gives us some modeled snapshots.

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Although the vertical beamwidths of all four versions of the Bruce are similar, the versions with an even number of vertical elements show a deeper null directly above the array. The versions with an odd number of vertical elements have their end wires arranged with one high and one low. Whether this factor is the key to the difference in the depth of the zenith null I have not explored, since the difference is not operationally significant. It is, simply, interesting.

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A relevant question at this point is why I have consistently placed the test models at a base height of 0.15 wavelength. The answer is direct: this height yields the highest gain for the array. I explored the performance of the 4 versions of the Bruce array at base heights ranging from 0.05 wavelength up to 0.25 wavelength in 0.025 wavelength increments. The following tables provide the rationale for my selection of a base height.

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+             Bruce Array Performance at Various Base Heights
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+2-Element (closed loop version)
+Base Ht          Gain       TO Angle        Feedpoint Impedance
+WL               dBi        degrees         R +/- jX Ohms
+0.05             1.60       21              194.3 + j 38.3
+0.75             1.72       19              174.8 + j 15.7
+0.1              1.80       18              159.5 + j  4.0
+0.125            1.85       17              147.1 - j  1.7
+0.15             1.87+      16              137.0 - j  3.7
+0.175            1.87+      16              128.8 - j  3.4
+0.2              1.84       15              122.5 - j  1.5
+0.225            1.77       14              117.8 + j  1.3
+0.25             1.68       14              114.6 + j  4.7
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+3-Element
+Base Ht          Gain       TO Angle        Feedpoint Impedance
+WL               dBi        degrees         R +/- jX Ohms
+0.05             3.52       21              289.7 + j 48.8
+0.75             3.64       20              261.4 + j 22.4
+0.1              3.72       19              239.8 + j 10.1
+0.125            3.77       18              222.5 + j  5.4
+0.15             3.79+      17              208.7 + j  5.2
+0.175            3.77       16              197.8 + j  7.9
+0.2              3.74       16              189.6 + j 12.3
+0.225            3.68       15              183.8 + j 17.9
+0.25             3.58       15              180.2 + j 23.8
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+4-Element
+Base Ht          Gain       TO Angle        Feedpoint Impedance
+WL               dBi        degrees         R +/- jX Ohms
+0.05             4.89       21              356.2 + j 56.8
+0.75             5.03       19              318.9 + j 24.9
+0.1              5.13       18              290.1 + j 10.8
+0.125            5.18       17              267.1 + j  6.1
+0.15             5.21+      16              248.6 + j  7.2
+0.175            5.21+      16              234.2 + j 11.9
+0.2              5.17       15              223.4 + j 18.9
+0.225            5.09       14              216.0 + j 27.2
+0.25             4.98       14              211.7 + j 35.9
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+5-Element
+Base Ht          Gain       TO Angle        Feedpoint Impedance
+WL               dBi        degrees         R +/- jX Ohms
+0.05             5.94       20              425.0 + j 75.8
+0.75             6.10       19              380.4 + j 34.0
+0.1              6.20       18              347.2 + j 14.6
+0.125            6.26       17              321.2 + j  7.0
+0.15             6.29+      17              300.9 + j  7.0
+0.175            6.28       16              285.5 + j 10.2
+0.2              6.23       15              274.2 + j 16.6
+0.225            6.14       15              266.9 + j 24.4
+0.25             6.02       14              262.8 + j 32.6
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The maximum gain heights are marked with a '+' symbol. Note that the versions with an even number of elements are indifferent to heights between 0.15 wavelength and 0.175 wavelength, while the versions with an odd number of elements show one evident--if not operationally significant--maximum gain base height.

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Fig. 11 shows the elevation plots for the 4-element Bruce array at base heights of 0.05, 0.15, and 0.25 wavelength. The plots suggest that selecting the base height for the array may involve more than just the maximum gain values, since the range of gain change is not exceptionally large. Both the lowest and the highest base levels result in patterns with significant high-angle radiation. The more optimal height of 0.15 wavelength results in the least high-angle radiation, which can mean some quieting of shorter-skip QRN during the noisier months of operation.

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In Fig. 12, we can compare the azimuth patterns of the 4 sizes of arrays, with each azimuth pattern taken at the to angle for the antenna with a base height of 0.15 wavelength. As we increase the number of elements, the horizontal beamwidth of the array narrows, which is the main source of the added gain of the larger versions. However, two other factors should call themselves to our attention. First, the 5-element array begins to show side-lobes, which suggests that a truly large Bruce array might require some redesign to keep the growth of these side-lobes in check. Second, none of the patterns are truly symmetrical. The side-lobes of the 5-element version show this fact most vividly, due to their differing sizes. However, if you carefully trace the patterns of the other versions, you will discover that each favors one side over the other. The difference is once more not operationally significant, but interesting as a facet of the basic design of an antenna that is never completely symmetrical.

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Fig. 13 provides us with a composite view of the gain changes with base height for the 4 versions of the array. In each case, the rate of change is not high with changes of base height, although the peak gain points are clear. More significant for this collective gain graph is the fact that we obtain diminishing returns with each added element to the array. At the optimum base height, the 3-element version has a gain advantage of 1.92 dB over the 2-element version. However, adding the 4th element nets us only 1.52 dB of added gain, and adding a 5th element gives us only another 1.08 dB. The progression downward in increased gain continues as we add elements. For any practical installation, of course, there will be a point at which adding elements does not warrant the added wire or other mechanical support requirements for a very large array.

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The changes in take-off angle are consistent for all of the arrays, so we may by-pass a graph of that factor and turn to the feedpoint resistance, shown if Fig. 14. What is most obvious from both the tables and the graph is that the feedpoint resistance increases as the base height decreases. Depending upon the feed system that a designer selects, the change of feedpoint impedance with base height may assume considerable significance.

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However, we should note another interesting aspect of the change, garnered by looking at the 4 lines. The step in resistance for any base height is larger when going from an even number of elements to an odd number than when going from an odd number to an even number. Relative to the total array, the feedpoint of versions with an odd number of elements is horizontally centered. However, when the number of elements is even, the feedpoint is always horizontally off center. Late, we shall show a way to correct for this, but first, we should also examine the reactance curves for the 4 versions of the Bruce array.

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The reactance curves appear in Fig. 15. In each case, the reactance is most capacitive or least inductive at or near the optimal base height. The reactance becomes more inductive as we decrease or increase the height away from the optimum level. In addition, the reactance increases at a higher rate the more elements that we use, especially at lower base heights. However, the amounts of reactance are in step with higher resistive components of the feedpoint impedance that accompany the use of more elements. Hence, we would see very little change in SWR sweeps keyed to the resonant impedance of each version.

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Some Miscellaneous Variables that Affect Performance

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Different builders experience differing circumstances, so we should address at least a few questions relating to differing constructions for the Bruce array. The first question concerns what happens if one chooses a different diameter wire for the array. The answer is simple: not much, although one might be tempted to tweak the design while in the modeling phase of the work. The following table shows the results for using AWG #8 through AWG #14 wire to make the 4-element version of the array.

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+     The Affects of Different Wires sizes on a 4-Element Bruce Array
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+Wire Size             Gain       TO Angle         Feedpoint Impedance
+AWG   Diameter (")    dBi        degrees          R +/- jX Ohms
+ 8    0.1286          5.27       17               243.3 - j 15.4
+10    0.1019          5.24       16               245.8 - j  4.3
+12    0.0808          5.21       16               248.6 + j  7.2
+14    0.0641          5.18       17               251.7 + j 19.0
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The differences in gain are almost wholly a function of the RF losses in the wire, since with lossless wire, there is only a 0.01-dB difference in gain between the thinnest and thickest wires. Likewise, the increases in the feedpoint resistance reflect the same phenomenon. The differences in the TO angle are likely phantoms, occasioned because the actual TO angle is close to 16.5 degrees, resulting in a rounding difference at a 1-degree resolution.

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One should likely avoid the temptation to tweak the model due to a change in wire size within the limits in the table, simply because differences in the ground quality will have a much more profound affect on performance. I ran the 4-element array over the standard set of ground qualities at its 0.15 wavelength optimum base height and obtained the results in the following table.

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+    The Affects of Ground Quality on the Performance of a Bruce Array
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+Ground Quality        Gain       TO Angle         Feedpoint Impedance
+Type  Cond/D.C        dBi        degrees          R +/- jX Ohms
+VP    .001/5          3.96       20               236.7 + j 18.0
+P     .002/13         5.02       18               245.7 + j 12.9
+Ave   .005/13         5.21       16               248.6 + j  7.2
+VG    .0303/20        7.82       13               258.6 + j  2.3
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The changes in the feedpoint impedance with changes in ground quality are far less significant than the changes in the far-field pattern for the array. The chart seems to encourage one to move to a location with better soil for vertical antenna performance. However, the degree of improvement over a standard vertical antenna, such as a ground-mounted monopole with a radial system, will be comparable for each level of soil quality.

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Very often, one receives recommendation for placing extensive radial systems beneath SCV-type vertical arrays. To see what effect such a radial system might have, I placed systems of 32-radials, each 0.25 wavelength long, beneath each of the vertical elements. To keep from having modeled wires intersect at other than wire ends or segment junctions, I placed the radial systems alternately at 0.001 wavelength and 0.0015 wavelength below ground. Fig. 16 shows the resulting model in outline form. For the check, I used the same soil qualities as in the preceding table. The antenna base height remained at 0.15 wavelength above ground.

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The following simple table shows the results. For the sake of easy comparison, I have replicated the results without radials over each ground quality from the preceding table.

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+       Affect of Adding Buried Radials to a  4-Element Bruce Array
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+                 Gain       TO Angle        Feedpoint Impedance
+                 dBi        degrees         R +/- jX Ohms
+Very Poor (conductivity 0.001; dielectric constant 5)
+W/O Radials      3.96       20              236.7 + j 18.0
+With Radials     4.21       20              247.6 + j 25.6
+Poor (conductivity 0.002; dielectric constant 13)
+W/O Radials      5.02       18              245.7 + j 12.9
+With Radials     5.17       18              255.9 + j 16.3
+Average (conductivity 0.005; dielectric constant 13)
+W/O Radials      5.21       16              248.6 + j  7.2
+With Radials     5.33       17              255.0 + j 10.1
+Very Good (conductivity 0.0303; dielectric constant 20)
+W/O Radials      7.82       13              258.6 + j  2.3
+With Radials     7.84       13              260.3 + j  3.1
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The net gain increase for adding the extensive radial field ranges from 0.25 dB over very poor soil to 0.02 dB over very good soil. The chief detectable effect centers on the feedpoint impedance, which becomes less dependent upon soil quality with the addition of the radial system. The far-field effects, however, tend to be minimal. Indeed, the basic soil quality beyond the radials has the greater affect upon far-field strength and take-off angle. The advantages of adding radials come at a cost of 8743' of AWG #12 copper wire for the total of 128 radials. Whether or not to add radials to the Bruce array is, in the end, a builder's decision.

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There is one system of feeding the Bruce array that does demand a radial system, but that will be part of our concluding section on alternative feeding systems for the array.

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Some Alternative Feeding Systems for the Bruce Array

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One alternative feed system that we have already noted is the use of a vertical wire running from the center of a lower horizontal wire to ground, with the feedpoint placed in series with the wire at ground level. Fig. 17 sketches the full required system to feed the Bruce in this way and still obtain a vertically polarized pattern.

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Since the connecting wire is a form of vertical monopole fed against ground, we require a radial system to complete the antenna subassembly. Early versions of this mode of feed used as few as 2 radials, but I have modeled the system (imperfectly) using 32 radials. The imperfections stem from the requirements for a buried radial system combined with the requirements for the segment lengths on either side of the segment on which one places the source or feedpoint. The radials are 0.001 wavelength below ground, and we require a junction at ground level. Ideally, the segment above this junction should also be 0.001 wavelength long, as well as the one above that. Beyond that height, the remaining segment lengths of the vertical wire may taper toward the segment lengths used in the horizontal wire of the Bruce array where the vertical wire joins it. The model that I used is close to meeting these requirements, but may be imperfect at lower heights. The imperfections likely inflate the gain figures by a small amount.

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Over average ground, with a 32-radial system beneath the vertical feed wire, I obtained the results in the following table. The aim of the exercise was to see at what height and length of feed wire the array might approach resonance.

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+          4-element Bruce Array with a Center-Wire Feed System
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+Base Ht          Gain       TO Angle        Feedpoint Impedance
+WL               dBi        degrees         R +/- jX Ohms
+0.15             5.47       16              301.8 - j297.8
+0.20             5.42       15              210.0 - j156.1
+0.25             4.82       13              191.4 + j 12.0
+0.247            4.87       13              190.6 + j  1.5
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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At the optimum height relative to array gain, the center vertical feed wire shows considerable capacitive reactance. One alternative for the builder is to simply run a length of parallel transmission line to an antenna tuner located at the transmitter location. However, a second alternative is to increase the length of the center vertical wire and raise the height of the array until the wire shows a feedpoint impedance near resonance. Hence, I have included those steps in the exercise.

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The results suggest more precision than the model will bear. Nonetheless, a length just under 0.25 wavelength appears to provide the near-resonant feedpoint impedance. However, we should not only note the drop in gain, but as well the increasing rate at which gain drops as we pass through this region. A length change of 0.003 wavelength yields as much gain decrease in this region as the initial change of 0.05 wavelength shown in the table.

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As well, elevating the antenna to a base height in the 0.24 wavelength region creates undesirable pattern effects. Fig. 18 shows the difference in the elevation patterns broadside to the array for 0.15 and 0.24 wavelength base heights. Excepting some possible special operational requirements, I shall assume that the left-hand pattern is the more desirable.

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There will always be array builders who prefer to use coaxial cable from the transmitter location to the antenna. We have already seen that we can accommodate such users with a reactance-compensation and 4:1-balun system. However, we have other choices. Fig. 19 shows one of them that is especially applicable to the 4-element Bruce array.

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The modeled transmission lines from the two center verticals go to a center junction, with one line reversed to achieve a 180-degree out-of-phase current situation between the two elements. With out-of-phase feeding of the two elements, each shows a feedpoint impedance of 125.0 + j 5.4 Ohms. The physical length between elements is 0.27 wavelength, requiring a physical lengths for each feedline of 0.135 wavelength. If we use RG-83 coax (characteristic impedance: 125 Ohms), the electrical length will be about 0.16 wavelength or so. When we reverse one line, the net impedance is close to 65 Ohms with virtually no reactance.

+
+ +
+

Fig. 20 shows the 65-Ohm SWR curve derived from the model of this system. Below it is the SWR curve is we use 50-Ohm coax at the junction. The use of 75-Ohm coax would show an SWR curve canted in the opposite direction from the 50-Ohm curve. Although this system has promise, it depends upon the ability of the builder to place a cable support post for the junction of the RG-83 coax length with the main feed cable. As well, the success of this system also depends upon obtaining close to the ideal feedpoint impedances on the two center vertical wires, and this figure depends upon both array base height and the soil quality below the array.

+

Since most Bruce arrays of modest proportions (up to 5 elements) will likely have only end supports, with non-conductive cables between them to support the array wires, we should also mention the potential for feeding the array at one end. Let's stay with the 4-element Bruce and see what happens when we give this system a try.

+
+ +
+

Fig. 21 shows the general scheme for such an end-vertical feed system. In general, the end support also supports the feedline, which then goes to the center of the vertical. For our 4-element Bruce array using AWG #12 copper wire and placed 0.15 wavelength above ground at its base, we obtain a maximum gain of about 5.3 dBi at a 17-degree TO angle--in other words, essentially the same performance we obtained feeding a center wire. The modeled feedpoint impedance is 254.0 + j22.7 Ohms, very close to what we obtained when feeding a center wire. A 300-Ohm feedline would be a close match for this system and minimize voltage, current, and impedance excursions along the line on its way to the transmitter location.

+
+ +
+

In Fig. 22, we see the modeled azimuth pattern for the array. The only notable feature is the slightly greater pattern tilt toward the fed end, relative to feeding one of the center wires. This tilt results from the slight losses in the wire from one end of the array to the other, but has virtually no operational significance.

+

We can also end-vertical feed the array at the lower corner. The performance does not change, but the impedance rises to 356.7 - 82.8 Ohms, which is natural as we off-center-feed a dipole. The impedance will increase relative to the center-feed impedance, and the length may no longer be resonant. Such a feedpoint is amenable either to standard parallel transmission line feeding techniques or to adjustment of the array dimensions. Once more, the exact value obtained for the corner feedpoint impedance will depend upon array base height and soil quality.

+

Although the length of these notes precludes coverage for other bands, the 80-meter data should provide sufficient guidance for scaling the antenna either to 160 meters or to 40 meters. The Bruce array has good potential among the SCVs in providing higher gain in a shorter overall horizontal length than the bobtail curtain. However, the cost is the need to use a higher base height than required for the open-end array. Ultimately, the choice of vertical array (rectangle, bobtail curtain, or Bruce array) for the low bands may depend upon the layout of user's land both horizontally and vertically.

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+

Updated 01-13-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Return to SCV Index

+

Topics: Bruce Array / Sterba Curtain, HF Lower, SCV


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+

Voltage Feeding SCV Loops

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+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ We have known since the first days of the development of the antenna types that we could feed half squares and bobtail curtains at a high voltage point. The dangling 1/4 wl vertical wires exposed the high-voltage, high-impedance point and placed it within relatively easy reach. +
+ +
+

The circuit for effectively feeding a voltage node of the open-ended SCVs is in Fig. 1. The top--or a tap near the top--goes to one of the half square verticals or to the middle vertical of the bobtail curtain. This remote circuit can be set and weather sealed. If the tips of the vertical are a significant distance above ground, then the center wire of the bobtail may be extended toward the ground. The matching tank circuit is then positioned so that its lower end forms a contact with a good RF ground (which is not the same as a radial system). The current magnitude at the top of the tank circuit will be higher than at the tip of an end vertical, but it will reach close to the zero point in line with those end-vertical tips. Maximum current will still be at the tops of the verticals, where they join the horizontal wire. The maximum center-vertical current magnitude, of course, will be twice the maximum magnitude of the end verticals on a Bobtail current. On a half square, the two top vertical currents will be about equal.

+

Many newcomers to antennas are skeptical about the equality among the feeding systems for the open-ended SCVs, so let's pause to create a small demonstration. Let's feed the center vertical of a bobtail curtain at a series of positions: the top (at the junction with the horizontal phasing lines), at the center of the vertical, at the base of the vertical, and finally at ground level (by extending the center vertical to ground). In terms of some essential data, we obtain Table 1.

+ 
+Table 1. Performance of a bobtail curtain using various feedpoint positions.
+Note:  all dimensions are the same, except for the length of the vertical for ground-level feeding.
+Feed Method          Gain dBi     TO Angle     Feedpoint Impedance
+Vertical top         4.87         18 deg       43 + j5 Ohms
+Vertical center      4.98         18           73 + j8
+Vertical Bottom      4.99         18           4000 - j2400
+Ground level         5.07         18           500 - j5000
+
+

As we lower the feedpoint position, the impedance climbs until we reach the normal tip of the center vertical. Feeding at this point represent the placement of a parallel resonant tank circuit, such as shown in Fig. 1, or its equivalent in the form of a network, at the vertical tip. We may presume that a ground line runs from the tank to a ground rod. However, the tank circuit represents a very high impedance in series with this lead. Therefore, no significant antenna current appears on this line.

+

The table shows only slight variations in gain and none in the TO angle. The current distribution of the relative current magnitude does not change with a change in feedpoint position. Fig. 2 provides a demonstration of this fact.

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+ +
+

The only variation in dimensions for the bobtail occurs with the final case in which we have brought the center vertical to ground level. At this level, we install the parallel resonant tank circuit for matching to a feedline. (I shall assume that anyone using this type of system has taken every useful safety measure to prevent human or animal contact with the high-voltage on the wire.) In the table, the impedance is indicative of the values we might obtain, but it will vary in practice according to the components that for the tank circuit. The model also includes a ground rod for the base of the tank. Note that the matching point is not precisely a true high-voltage point, but occurs below it. Hence, the current rises somewhat at the feedpoint, producing a lower impedance. However, with a tapped tank, we may easily find the correct matching positions for the antenna and for the lower-impedance feedline to the shack. Within the boundaries of the original length of the vertical, we find a completely normal current distribution curve.

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+ +
+

The loop versions of the SCV--the triangles and rectangles--present a different problem, as revealed in Fig. 2. They have no exposed ends. Moreover, the maximum current point of effective SCV operation with a maximum of vertically polarized radiation is way off to the side and elevated.

+

The shame of it all is that the loops can be used as general purpose wire antennas for most of the ham bands above their resonant SCV frequencies. However, they operate better in this role if fed at the center of the bottom. You will need balanced feeders and an ATU, just as you would for a doublet.

+
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+

Just for initial comparative purposes, Table 2 provides some numbers for a right-angle delta, resonant for SCV use at 7.15 MHz, with its base at 35' and its apex at 65' up over average soil, as sketched in Fig. 4. The first numbers list the gain, take-off angle, and source impedance if we attempt to feed the antenna on all bands at the SCV side feedpoint, about 12% up the triangle leg. The second set give the same modeled data if we feed the antenna at the center of its horizontal base leg.

+ 
+Table 2.  Modeled performance of a right-angle delta using side- and bottom-feed
+Right-angle delta:  side fed
+Frequency      Gain dBi       T-O angle      Source Z (R+/-jX)
+ 7.15 MHz      1.97           16 degrees       49 + j   0
+10.1           4.60           57             5700 + j4500
+14.15          6.92           37              115 + j 135
+21.2           6.42           22              270 + j 295
+24.95          7.96           18              790 - j 105
+28.5           8.10           15              435 + j 510
+
+Right-angle delta:  bottom-center fed
+Frequency      Gain dBi       T-O angle      Source Z (R+/-jX)
+ 7.15 MHz      5.83           42 degrees      255 + j  75
+10.1           7.57           29             3510 + j2100
+14.15          7.47           35              175 + j 120
+21.2           7.90           14              235 + j 350
+24.95          8.91           68              665 - j1150
+28.5           8.49           15              615 + j 415
+

Where SCV-type operation is not involved, on every band except 12 meters, the bottom fed loop shows either higher gain or a lower take-off angle than the side fed version. Hence, for general use, the bottom-center position is the better feedpoint. Of course, it is also more convenient than the side position.

+

It would be nice if we could get SCV operation at the same point. We can.

+

For SCV operation, we cannot simply place the feedline in series with the wire, as we would for general operation. Instead, we must separate the wires a bit at the very center of the bottom. This is the equivalent to the first step in converting the antenna into a half square. This position is a high-voltage point where the current reverses polarity. Separating the wires at this point does not materially affect the gain or take-off angle of the antenna. In other words, it does not affect the ratio of vertically polarized to horizontally polarized radiation.

+
+ +
+

However, as shown in Fig. 5, we shall not change the shape into a half square. We shall retain the delta shape. The spacing of the break in the wire is not critical--2" to 6" appears to make no significant difference. For the particular right angle delta model we are using, opening the bottom did not change the gain, take-off, angle, or source impedance. More precisely, the source impedance with side feed changed by only a fraction of an Ohm. Moving the side feedpoint to the bottom changed the impedance, but not the gain or take-off angle.

+

We shall leave one end of the wire at the bottom-center break unattached to anything. The other end, we shall attach to the very same parallel tuned circuit we might used to voltage feed a bobtail curtain. The antenna source impedance will be complex and high, with the resistive component in the 3500 to 4000 Ohm range and the reactance between 8000 and 10000 Ohms. A good high-Q coil with well-spaced turns to prevent arcing and a good variable capacitor, also with wide spacing between plates, will handle the job easily. The only task is patiently finding the right tap points for both the antenna and the feedline so that a coax line sees 50 Ohms.

+

However, since we are making this move to use the antenna with parallel feedline, the situation is not so critical. The use of the parallel tuned circuit is still recommended, since the impedance of the antenna end is still very high even with 600-Ohm parallel line. However, we need only find a tap that approximates the line impedance and let the tuner in the shack do most of the work. In fact, with this system, once we find a good setting, we can replace the variable capacitor with a door knob high-voltage capacitor and protect the expensive variable from the weather. We should also run a wire from the base of the tank to ground--a good RF ground.

+

We shall still need a weather proof case for the capacitor and the coil. So we might as well add either a knife switch for manual operation or a relay for remote operation. The switching job is this: when we wish to use the antenna as an SCV, one side of the base-leg break goes to the tank circuit and the other goes to nothing. The feed line goes across the tap(s) on the coil. When we wish to use the antenna for general operation, the tank is disconnected and each side of the base-leg break goes to each side of the parallel feed line. The switching, suggested in Fig. 6, may require 3 sets of contacts.

+
+ +
+

This system should work equally well on rectangles as well as triangles. If you are inclined to try this system, I recommend that you start with a manually switched system to see if it will suit your needs before you invest in a remote switching system.

+
+ +
+

Updated 08-14-1998, 03-24-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: Delta Loop, HF Lower, HF Upper, SCV, Voltage Feeding


+ + diff --git a/content/scv/vdelt.html b/content/scv/vdelt.html new file mode 100644 index 0000000..6696411 --- /dev/null +++ b/content/scv/vdelt.html @@ -0,0 +1,137 @@ + + + + + + All-Band Use of Vertical-Plane Deltas + + + +
+

Notes on All-Band Use of Vertical-Plane Deltas

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Although the vertical-plane delta loop either pointed up or down and fed virtually anywhere will radiate well enough to provide contacts, it is a relatively poor performer--in any configuration--when stretched to other bands, compared even to the simplest substitute. Modeling of delta loops and similar antennas has proven to be a quite reliable indicator of performance, since nothing in the antenna type even approaches, let alone exceeds, the limits of the software for accurate modeling. So the following notes may be useful. These notes apply to vertical-plane equilateral delta triangles, although with some variation, they apply equally well to vertical-plane right angle deltas. Modeling was done on NEC 4.1. +

First, the antenna. A vertical-plane equilateral delta for 40 meters will be about 48.5' wide and 42' high. This places limits on the height above ground of the lowest point, since with a 35' low-point height, the high point is 77' up. For the examples below, a standardized 15' bottom point is used, with a 57' upper point. See the following sketch for the various configurations of the vertical-plane delta, along with a small, simple antenna with which we might compare it.

+
+ +
+
+

The Vertical-Plane Delta as an SCV

+
a. When fed as a self-contained vertical (SCV), the feedpoint is about 1/4 wl from the delta apex or about 25% away from the horizontal wire along one side. Maximum bottom heights of 20' to 25' yield the highest gain (about 1.45 dBi) with an elevation angle of maximum radiation of between 16 and 17 degrees. The first signs of a secondary higher angle lobe just make an appearance, but do not constitute a problem relative to the antenna's use as a low-gain, low-angle DX antenna with superior signal to noise characteristics due to insensitivity to higher angle radiation. The following elevation patterns are for heights of the bottom wire of 15, 25, and 35 feet. +
+ +
+

b. As the antenna is raised by another 5-10 feet, the secondary lobe increases, so that with a bottom height of 40', the antenna's secondary high angle lobe at 60 degrees is down by only 4 dB or so. As the antenna is lowered, gain decreases very slowly (imperceptibly?), and the elevation angle of maximum radiation increases very slowly (about 1 degree for each 5' of lowering). A 15' lower wire or point height provides good performance within this class of antennas.

+

As the following pattern shows, the azimuth pattern of a vertical plane delta fed as an SCV is a broad oval.

+
+ +
+

c. Moving the feedpoint to a mid-side location increases gain by increasing the amount of horizontally polarized radiation produced by the antenna. This increases the elevation angle of maximum radiation as well as spreading the main lobe vertically to permit considerable amounts of higher angle radiation. In affect, moving too far from the feedpoint prescribed for use of the vertical plane delta as a vertical antenna tends to defeat that purpose. However, the vertical-use feedpoint itself is not critical within say 5% or so of the recommended point.

+

d. Moving the feedpoint to a corner also increases the amount of horizontally polarized radiation. The result is similar to using a midpoint feed. The elevation angle of maximum radiation only increases slightly (approximately 5 degrees), while the gain remains about the same. The elevation pattern becomes a flatted oval showing significant higher angle radiation only a very few dB down from the maximum. The result is the same as for the mid-side feedpoint: a relative defeat of the use of the antenna as a low-angle, low-gain, high signal-to-noise ratio antenna.

+
+ +
+

Every version of the self-contained vertical requires feeding about 1/4 wavelength from a peak position in order to maximize vertically polarized radiation. Selection of some other feedpoint will show an increased proportion of horizontally polarized radiation, with a consequential increase in sensitivity to higher angle radiation and an increase in QRM and QRN levels relative to the strength of low angle DX signals.

+
+

The Vertical-Plane Delta as an All-Band Antenna

+
Let's turn to anticipated performance on other bands, using a standard 15' to 57' height for the delta. For each configuration considered, the tables will list the maximum gain of the antenna model in dBi, the elevation angle of maximum radiation (TO angle), the azimuth angle at which maximum radiation occurs, the approximate feedpoint impedance (subject to variations due to construction), and notes on the pattern shape. +

1. The vertical plane delta fed for maximum vertically polarized radiation 1/4 wl away from the apex on one side.

+ 
Freq      Gain      TO angle    Az Angle       Feed Z     Pattern
+notes
+7.15      1.3       19            90          145-j  20     oval
+10.1      2.0       16            90         2700+j2600     oval
+14.15     5.6       59            90          310+j 100     oval
+18.1      5.2       34            64         1300-j1300     off-center peanut
+21.1      5.1       36            52          480+j 190     off-center peanut
+24.95     5.5       49            99         1200-j1300     boomerang
+28.1      6.3       38            90          360+j 190     bulgy square
+

Although the 30-meter performance is low angle, the gain is low. Otherwise, the elevation angle of maximum radiation is quite high. See the last antenna in this series.

+

2. V-delta, horizontal down, fed at center of the horizontal

+ 
Freq      Gain      TO angle    AZ angle      Feed Z        Pattern
+notes
+7.15      4.7       56            90         115+j  30     oval
+10.1      5.8       33            90        1400+j3900     peanut
+14.15     5.9       60            90         360+j  27     oval
+18.1      8.3       40            90        1300-j1300     long peanut
+21.1      6.4       40            90         185+j 170     oval
+24.95     8.8       47            90        1300-j 750     long, thin oval
+28.1      5.5       40            25         330+j 300     bulgy
+rectangle
+

3. V-delta, horizontal up, fed at bottom apex

+ 
Freq      Gain      TO angle    AZ angle      Feed Z      Pattern notes
+7.15      6.0       37            90         140-j  10     oval
+10.1      7.2       27            90        2700+j1400     oval
+14.15     6.6       71            90         250+j 160     oval
+18.1      6.3       44            90        1000-j1900     oval
+21.1      5.6       69            90         110+j 180     oval
+24.95     7.4       33            90        1500-j1700     bulgy oval
+28.1      8.6       53            90         280+j 230     bulgy oval
+

For these two variations, the radiation angle is quite high. Lower lobes exist, but at lesser strength than the high lobes, except as noted for a few exceptional cases in the tables.

+

Changing the feedpoint from bottom to top does not significantly change the patterns of the center-fed horizontally polarized antennas.

+

4. V-delta, horizontal down, fed at lower corner

+ 
Freq      Gain      TO angle    AZ angle      Feed Z      Pattern notes
+7.15      1.2       27            90         145+j  10     oval
+10.1      1.2       18            90        3500+j1900     oval
+14.15     4.4       43            32         260+j 180     2 lobe, edgewise
+18.1      5.0       39             0         590-j1600     2 lobe, edgewise
+21.1      5.0       36             0         130+j 220     2 lobe, edgewise
+24.95     5.4       25            40        1000-j1400     2 lobe, edgewise
+28.1      6.6       23            36         300+j 280     2 lobe, edgewise
+

Above 30 meters, the pattern of the lower-corner-fed delta becomes two large lobes off the edges of the delta, with nulls off the delta faces that vary with the band. The lobe in the direction away from the feed point tends to be flatter with signs of becoming a double lobe, and on some bands the azimuth angle of maximum radiation is offset from the delta edge. (The elevation patterns for this feed configuration do not appear in the collection of patterns shown below.)

+

5. 48.5' horizontal dipole with 9.1' drooping ends: Let's compare the performance of this simple antenna placed at a height of 57' up. This is the same as the top height of the deltas modeled here. It is center-fed.

+ 
Freq      Gain      TO angle    AZ angle      Feed Z     Pattern notes
+7.15      6.5       33            90          69-j   2     oval
+10.1      8.1       24            90         210+j 800     oval
+14.15     7.8       17            90        5500-j1100     oval
+18.1      9.4       13            90         120-j 900     oval
+21.1      7.7       11            42          55-j 130     4 lobes
+24.95     7.7       10            55         280+j 790     4 lobes
+28.1      7.6        9            65        3050+j1700     4 lobes
+

The 4-lobe patterns have indistinct lobes and hence might have been classified as bulgy rectangles or squares.

+

This simple antenna that takes 1/2 the wire of a delta and spreads no farther than the horizontal wire of the delta has a lower elevation angle of maximum radiation and in all but a couple of cases, higher gain than any of the multiband deltas, when the deltas are set up in the vertical plane. 20 and 10 meters may present matching problems for limited range tuners. To get a sense of the pattern differences involved, the following elevation patterns may be helpful. Each antenna is shown for each band. Elevation patterns are taken at the azimuth angles yielding the highest gain for each model. (The corner-fed models are omitted, since the graphics are already verging on being "cluttered.") The general trend for the simple wire antenna to provide more gain at lower elevation angles is clearly apparent.

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A full-length 40-meter dipole fed with parallel transmission line via and ATU would show slightly better performance. Open wire feeders are recommended for any multi-band wire antenna where the feedpoint impedance varies widely.

+

Again, these numbers apply only to deltas set up in the vertical plane. Deltas and other loops set up in the horizontal plane are another story entirely.

+

The figures and patterns speak for themselves, so no recommendations are needed. However, what was said earlier bears repeating. The delta loop when set up vertically, can be used on all bands, just as can almost any wire antenna that is at least 3/8 wavelength long at the lowest frequency to be used. However, whatever the configuration (apex up or down) and whatever the feedpoint (corner, apex, mid-horizontal, SCV, mid-side), it is unlikely to outperform even a simple center fed wire at the same height as the top of the delta.
+

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Updated 10-13-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +

+
+ Go to Amateur Radio Page
+

Topics: Delta Loop, HF Multi Band


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A Ten-Minute Timer That Just Won't Quit

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L. B. Cebik, W4RNL

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In September, 1980 (pp. 34-38), QST printed a little 10-minute timer circuit that is still (Jan. 2000) in use in my shack. Requests for the circuit diagram led me to reproduce the original diagram--although there are some optional additions noted in other diagrams in the article. (Getting the entire QST CDROM collection from 1915-1995 is a good archive for the shelf.)

+

+

The diagram may be large for the screen, but can be "screen copied" in pieces for downloading. The size is necessary to preserve the legibility of the detail.

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Since the diagram is self-explanatory as to function and descriptions of 555/556 operation abound, I shall add no detail here, but refer you to the original article and various data sheets. Low-current and other updated versions of the 556 chip may be available and should be used. Some of them may require adjustment of components used in linking the sections, etc. However, the basic concept is still sound, despite the age of the circuit.

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Updated 01-29-00. © L. B. Cebik, W4RNL. First published in QST September, 1980. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: Tales


+ + diff --git a/content/tales/amel-1.jpg b/content/tales/amel-1.jpg new file mode 100644 index 0000000..ca030ab Binary files /dev/null and b/content/tales/amel-1.jpg differ diff --git a/content/tales/amel-2.jpg b/content/tales/amel-2.jpg new file mode 100644 index 0000000..2e6e7ea Binary files /dev/null and b/content/tales/amel-2.jpg differ diff --git a/content/tales/amel-3.jpg b/content/tales/amel-3.jpg new file mode 100644 index 0000000..3feb92a Binary files /dev/null and b/content/tales/amel-3.jpg differ diff --git a/content/tales/amelanchier.html b/content/tales/amelanchier.html new file mode 100644 index 0000000..7e7fbc5 --- /dev/null +++ b/content/tales/amelanchier.html @@ -0,0 +1,58 @@ + + + + + + The Serviceberry Tree + + + +
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The Serviceberry Tree

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The serviceberry is a small flowering and berry-producing tree that is prized by wildlife as a source of nourishment and protection. Although once exceptionally widespread in the U.S., we do not hear of it as much as we should. Therefore, I have gathered the following notes as an introduction to this fine addition to any habitat for birds and other wildlife.

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Genus: Amelanchier (meaning blood-red-referring to the bark of new branches that emerge)

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Common names (from the Audobon N.A. Trees book, the Little Golden Guide to Trees, and Trees of the Smokies):

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  • Sarvis-a very old name for the serviceberry
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  • Serviceberry-on the old (colonial) frontier, because it would bloom in early spring, about the time circuit-riding preachers would hold the first religious services of the year or the time the ground thawed to permit burials from winter deaths
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  • Shadblow and Shadbush-in colonial times, the blooms appeared about the time that the shad were running
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  • Juneberry-because in that month, the berries would appear
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There are several major species of the genus amelanchier (in the Rose family):

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  • Alnifolia and Canadensis are mostly (smaller) western types
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  • Arborea or "downy" serviceberry is common in the SE area and throughout the eastern U.S. The leaves are like those of the birch, with a downy underside.
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  • Sanguinea or "roundleaf" serviceberry is common in coastal areas (both northeastern shore areas and Great Lake areas), as well as in the Smokies. The leaves are round but toothed, with a smooth underside.
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  • Laevis or "smooth" serviceberry is listed in Trees of the Smokies, with leaves visually resembling those of the downy, but smooth underneath.
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The flowers bloom as early or earlier than redbuds. The 5-petal white flowers make a great display while the leaves are not fully unfurled.

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The tree has the appearance of a large shrub because it often grows with multiple trunks, each fairly thin, emerging from the same root set. In this property, it resembles a crepe myrtle. However, it can grow to from 20' (roundleaf at some altitude) to 40' (downy).

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The summer leaves are green, but autumn foliage can range from red to golden, depending on the variety. They appear to hold their foliage well.

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The berries are small, but sweet and edible by everyone, ranging from birds to critters to bears and deer (with the latter two also eating some of the foliage in the wild) to humans. Serviceberries were once common enough that folks made serviceberry pies in season.

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The following website have pictures and accounts of the serviceberry in its various forms across the U.S. My Thanks to Tom Shutters, K4FJW, for performing the search that turned them up.

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www.cnr.vt.edu/dendro/dendrology/syllabus/aalnifolia.htm (web.archive.org).

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www.cnr.vt.edu/dendro/dendrology/syllabus/aarborea.htm (web.archive.org).

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ostermiller.org/tree/serviceberry.html

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www.mpelectric.com/treebook/fact15.html (web.archive.org).

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www.dcnr.state.pa.us/forestry/commontr/serviceb.htm

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www.mrgrow.com/plant/plant497.htm (web.archive.org).

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www.yale.edu/fes505b/shadbush.html (web.archive.org).

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www.cmi.k12.il.us/Urbana/projects/apple/service/bpark/serviceberry.html (web.archive.org).

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www.csuchico.edu/~rcooke/serviceberry.html (web.archive.org).

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Topics: Tales


+ + diff --git a/content/tales/bluebird.jpg b/content/tales/bluebird.jpg new file mode 100644 index 0000000..3c80715 Binary files /dev/null and b/content/tales/bluebird.jpg differ diff --git a/content/tales/comsys.html b/content/tales/comsys.html new file mode 100644 index 0000000..2b946e4 --- /dev/null +++ b/content/tales/comsys.html @@ -0,0 +1,226 @@ + + + + + + Socio-Cybernetic Modeling + + + +
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On Socio-Cybernetic Modeling

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L. B. Cebik

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Since the original private publication of this paper in the early 1970s, the work of refining the correlations between the entropic system pair that is the subject of the original work has proceeded to reveal an ever tightening cohesiveness to the fundamental premises of the study. Advances in computer hardware and programming since the 70s have permitted fuller realization of all of the facets and features of a committee system that have been categorized to this date (January, 1999). For example, as computer speed and storage have increased, programming (or procedural counterparts) have enlarged to fill the space and extend the time to its original limits and beyond. Ostensibly designed to speed results, the end result is often slower than with older, slower machines that somehow managed to get their work done. Likewise, the interactions of task-specific programming and the overall operating system reflect virtually all of the interactions of committees in almost any organizational hierarchy. Inter-committee and inter-program relationships--both beneficial and detrimental when viewed from a perspective of the goals of each--reflect more detailed correlations than were ever thought possible in the beginning. The list might go on indefinitely.

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Therefore, it has seemed useful to make the original paper once more available to those interested in modeling entropic system pairs in a rigorous manner. Much research remains to be done, but here is where it began.

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LBC, January, 1999

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This paper presents the fundamental stages of modeling two equivalent entropic frames of reference. As with any paired frames, one may analogize from one to the other and back. This procedure proves especially profitable in developing suitable symbolic and mathematical models of computer systems and committee systems.

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A simple example illustrates the principle. The notorious expression,

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+ +
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which translates for computer programmers as "garbage in, garbage out," may be expressed more rigorously as

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where Go is garbage out, Gi is garbage in, and k is a constant of proportionality (as it will be throughout this exercise). The comparable, but non-equivalent, expression for a committee system is

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where V means "any input." A little thought over the difference yields the realization that equation (2) applies to computer systems without reference to the operator. Since a computer system consists of one or more computers plus one or more operators, equation (2) is a limited subsystem case. A full computer system answers to equation (3).

+

1. Entropic Frames of Reference (COMSYS)

For either system (COMSYS), the equivalency of the output value equations leads to the conclusion that +
+ +
+

where COMSYSo is the assignable system output value and COMSYSi is the assignable system input value. Moreover, equation (4) defines both systems as entropic frames of reference.

+

If the conclusion expressed in equation (4) is to hold, it must have consequences that are valid for either system. Consequences of the precise order required abound. Of most central interest for modeling is the relationship between P and So, where P indicates the length of the procedural or programmatic involvement during system activation and So is the significance of the output of the system activation occurrence.

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Most generally, the relationship between P and So is given by

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For each system type, there are closely related but separable interpretations. For a committee system (COMSYSm), the applicable expression is

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where Pr is the length in time units of the procedural determinations and Sso is the significance of the substantive output. For a computer system (COMSYSp), the applicable expression is

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where Pg is the length of the program and Sdo is the significance of the data output.

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P, whether interpreted as Pr or as Pg, is essentially a time measure. The change of output significance, C, for notable periods of system activation is given by

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where t is an applicable general time measure and Si is a measure of the input significance. The rate of change provides a measure of system effectiveness, E, and is given by

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An accompanying graph (Fig. 1) provides an illustration of the results. Given an arbitrary significance of 1 to the input for any COMSYS activation, C and E will vary as shown. Besides the steep decline of efficiency in a short time, the net result is the leveling off of change and effectiveness at a level which approaches 0. Instantaneous rates of change, Ci, and rates of effectiveness, Ei, are, of course, given by

+
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and

+
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Real effectiveness (the rate of change of significance) and apparent effectiveness mirror each other. Graphically, this is shown in Fig. 2. Apparent effectiveness represents the measure assignable to the system self-appraisals of output significance, which is in no case to be confused with the self- or system appraisal of any individual element in the system. In general terms, apparent effectiveness, Ea, is given by the equation,

+
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Apparent change, Ca, likewise, is given by

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For either system, So, the measure of output significance, is limited to values equal to or less than Si.

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2. Computer Systems Modeling (COMSYSp)

The general equations governing systems are subject to individual refinement. In the process of refinement, variations arise between expression appropriate to each system just to the degree that either a. the two systems are dis-analogous or b. the development of suitable categories is lacking. For computer systems (COMSYSp), equation (5b) holds, namely, +
+ +
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or rewritten

+
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where Pg is the length of the program and Sdo is the significance of the data output. For real systems, this equation is modified by a measure of operator efficiency, epsilon, such that

+
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where n is the number of operators and gamma1, gamma2, . . .gamman are the effectiveness ratings of the individual operators, each of which must be given in within the limits

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for any operator, gammaiota. Together with equation (5b1), the exact expression for So of COMSYSp is

+
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This equation, of course, provides a significance measure of the output of the special case including one and only one computer. Its limiting value is the instance (real or hypothetical) of a single operator with an effectiveness rating of 1, which forces the equation to the form

+
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For rho computers which are interactive, the equation becomes

+
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where all factors are as previously defined and Crho is the total possible combinations of computers.

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Even equation (15) makes certain assumptions. First, it is assumed that operators within any given system are exclusive; that is, no operator forms part of a system with more than one computer. Interactive operators would require a correction factor within equation (15). Second, any necessary interaction programming is absorbed within the Pg measure for each computer. Precision in this regard would also require a correction factor. However, equation (15) will be sufficiently accurate for most purposes, and the derivation of corrective factors is left as an exercise for the reader.

+

The interactive computer super-system presents many difficulties for accurate modeling. For example, under some forms of standard programming, computers will assume data not in evidence. Different CPUs with alternate instruction sets, even operating under the same operating system, may do this without necessarily alerting the operator to the altered data. Variations occur due to differences both at the level of translating program language into machine processes and in the conduct of machine processes.

+

Without suitable correctives, the assumptions and the possible errors stemming from them complicate the evaluation of the output of a super- system. Analogously, members and subcommittees make similar operational variations which complicate the evaluation of a committee's output. Moreover, such members and subcommittees often make assumptions in the absence of data without informing either the chair or the hierarchical "user" (administrator, executive, etc.) of the committee.

+

The resultant errors are closely related to the concept set or language processed by the COMSYS, whether computer or committee. In complex machines with sub-units and multiple computing units (CPUs), the analogy to committees, with subcommittees and individual members--all active language users--is close to exact.

+

3. Committee Systems Modeling (COMSYSm)

For committees, +
+ +
+

or

+
+ +
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where Pr is the length in time units of the procedural determinations and Sso is the significance of the substantive output. More generally and as a limiting case,

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However, committees, as previously noted, have both subcommittees and members. Thus, the limiting case is more precisely specified for real circumstances as

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+ +
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where beta accounts for subsystem activation.

+
+ +
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where mu is the number of members, nu is the number of subcommittees, and the expression Cnu+1 represents the total combinations of subcommittees plus the committee as a whole. The final equation is thus

+
+ +
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As with computer systems, equation (19) is limited by assumptions. If, for example, subcommittees have unique procedures of their own, a correction factor will be needed within equation (19). This derivation is left to the reader as an exercise.

+

The nature of the correction factor will depend in part upon the nature of the subcommittee procedural activities. Robert's Rules of Order (RROO) is the most common committee program. If used uniformly throughout proceedings of all subcommittees and of the committee itself, then a generalized accounting correction factor is possible for equation (19). If, on the other hand, special procedural rules are introduced into one or more of the subcommittees, two analyses become required. first, the effects of the deviant procedure on the subcommittee output must be evaluated. Second, the compatibility of the sub-outputs with each other--when produced under differing procedures--must be evaluated. Just as some deviants of the same program may turn out to be incompatible, so too may be outputs resulting from the use of variant procedures. The analogy of FORTRAN and RROO is more than accidental.

+

An interesting historical phenomenon is that although there exist no operational rules for human relationships to computer systems (HrCOMSYSp), ancient operational rules exist for human relationships to committees (HrCOMSYSm). This fact owes probably to the antiquity of committees and the recentness of computers. The more recent the development of a system, the more complex the rules, which is evident from a comparison of the operating instructions for a computer with its mix of procedural and relational matters and operational rules for committees.

+

Operational rules, of course, are imperatives often representing the accumulated experiential wisdom of a group and may be passed from one generation to the next in aural or written form. When distorted due to accident in the transmission or by virtue of motivated obscurity, such operational rules may comprise one core of magic and witchcraft. In more pure form, they undergird what has become modern science. To this day, we persist in calling them "laws."

+

Perhaps the most ancient extant operational rules come from a collection of sayings originating--or at least aggregating--along the Danube River. The following list is freely translated and updated in light of RROO.

+

Laws (Operational Rules) Governing Human Relationships to Committees

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1. If asked to serve on a committee, refuse.

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2. If forced to serve on a committee, be absent.

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3. If forced to attend committee meetings, be silent.

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4. If forced to speak, move for a termination of discussion.

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5. If the motion to terminate is defeated, move to remand the issue to its source for action.

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6. If the motion to remand is defeated, move for adjournment and/or disbandment.

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7. If all else fails, leave the meeting on the grounds of having another committee meeting to attend.

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The historical list of operational rules contains numerous additional rules,, laws, and advice, much of it ad hoc at first sight. for example, there is a cryptic note:

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8. What you chair, you must sit in.

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More problematical is the rule,

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9. To be absent is to be elected,

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which seems initially to contradict rule 2., unless interpreted as an implicit power which may force attendance. A recent (1970s) New Yorker cartoon has perhaps made the only significant summary contribution to this ancient list with its caption:

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10. There are no great individuals, only great committees.

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For socio-cybernetic modeling, perhaps the most mathematically interesting rule is 7. Whatever the case among those who created this aggregate of rules, in modern institutions, following this rule will never create ethical guilt for lying. It follows from adherence to this rule that the existence of some certain number of committees will have identical consequences of there being no committees, since the number will effectively preclude the conduct of business, indeed, preclude even strictly procedural activation. In the abstract, the equation for this situation is

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For the real world, some finite time, t, is required even to record presence, convene, and adjourn. Therefore, there is an empirical equivalent of the abstract equation which takes the form

+
+ +
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where COMtheta is a quantity of committees so large that the effective t allowable to each is less then the t required to convene, record, and adjourn, or

+
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which thus defines the threshold for the maximum possible number of real committees.

+

The threshold condition leads to some interesting consequences, namely,

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and

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etc., or more generally,

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This result may be of only historical interest for inter-cultural studies, since for any given time and place, there is one and only one number x such that x is theta.

+

4. The Future of Socio-Cybernetic Modeling

Every set of models must have empirical application if it is to have more than idle interest. The present case is no exception. The application of these models rests on certain fundamental principles. +

1. There is an analogy between COMSYSp and COMSYSm (and any other COMSYS member). In other words, all members of COMSYS are equivalent entropic frames of reference.

+

Several points follow from this principle alone. First, every equation for COMSYSp may have an analogue in COMSYSm, and vice versa. In exact form, such equations will be equivalent. Thus, every extant relationship within one member set provides a potential insight into another member set. Likewise, every inexactitude in one member set may find a means of correction in another member set. Second, the analogy may be systemic rather than particularistic, thereby permitting individuality to the equations describing elements of the system.

+

2. Equivalent frames of reference are convertible.

+

Since what is herein modeled is an empiric reality, convertibility extends beyond the generation of conversion equations. There is, in effect, a potential for converted reality. Since both COMSYSp and COMSYSm are social realities with the same conceptual foundations, the possibility of merging adds itself to mere conversion. This fact makes possible the creation od scenarios of futuristic import.

+

For example, we earlier noted the limit theta to the possible number of committees. By principle 1, above, we should also seek an equivalent limit phi to the number of interacting computers. This limit may be a function of time tIA such that the addition of further computers does not permit passing beyond the ENTER-EXIT procedure into data processing. Future generations of computers may suppress the effect by increasing computer speed and by bypassing ENTER-EXIT procedures through common machine and program languages.

+

Such speed elevating procedures hold promise for committees in accord with principle 2. tCRA can be shortened in a number of ways. The most likely is through a merger of COMSYSm with COMSYSp. Thus, rather than requiring the physical co-presence of members, committees may convene via CRT terminals. Conference telephone calls already accomplish such ends. Computer terminals provide enhanced speed by automatically recording proceedings. Thus, the limit theta for committees can be increased by several orders of magnitude.

+

3. Every problem contains the seeds of its own solution.

+

The enhancement of the limit "theta" is close to reality. The next step, however, requires a review of the model equations set out herein. First, since So = k (Si/P), and since no COMSYS exists without a significant P factor, the entropic limit, So = Si, can never in practice be reached. In fact, the opposite limit, So = 0, is the more likely prospect. Moreover, not only does P affect So adversely, so too does beta, as noted in equations (17) through (19). likewise, COM0, or its equivalent, COMtheta, is unlikely to be permanently achieved for two reasons. First, no COMSYS, once in existence, ever goes out of existence. Hence, COM0 is unobtainable directly. Second, tactical gains in pressing the limit "theta" have appeared whenever needed throughout history. Hence, exhausting the mechanical gains of computer terminal meetings is not likely to exhaust theta.

+

The solution lies in a systems merger of a more complete sort. Systems merger would include the following steps.

+

1. For every COMSYSm, let there be a COMSYSp assigned each member such that

+

a. each COMSYSp is equipped with identical machines and languages;

+

b. RROO is made part of the COMSYSm and the COMSYSp;

+

c. every computer of COMSYSm/p (merged COMSYSm and COMSYSp) is interactive.

+

2. Let operational rules 3 through 7 be programmed into every computer of COMSYSm/p.

+

3. Let each computer memory of COMSYSm/p contain a large quantity of random discussion statements, key word selected by rapid scan of the preceding discussion statement in the meeting record such that

+

a. for any point of discussion, every system scans;

+

b. scanning proceeds from end to beginning, with the first to hit a key word being the next to discuss; and

+

c. in the event of identical timing, discussion goes to the memory with the longest elapsed time since its last recorded discussion.

+

4. Let all meetings occur via preset timing and system keying.

+

5. Let adjournment be a function of completion of business or of falling below a quorum due to other meetings.

+

6. Let the program and the procedure be as long as human intervention can make them, with all terminals dedicated in non-meeting hours to extending both and to automatically introducing extensions as meeting topics.

+

7. Let the "off" switch be removed from each terminal.

+

The immediate consequences of these procedures will be to place all matters of substance and action into the hands of individual humans. However, since COMSYSm/p would no longer require human relationship in order to function, there ought to be plenty of time to perform these simple tasks of substance.

+
+ +
+

Updated 1-20-99. © L. B. Cebik. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index Page

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Topics: Tales


+ + diff --git a/content/tales/comsys1.gif b/content/tales/comsys1.gif new file mode 100644 index 0000000..b6cd10d Binary files /dev/null and b/content/tales/comsys1.gif differ diff --git a/content/tales/comsys2.gif b/content/tales/comsys2.gif new file mode 100644 index 0000000..1e08537 Binary files /dev/null and b/content/tales/comsys2.gif differ diff --git a/content/tales/cq.html b/content/tales/cq.html new file mode 100644 index 0000000..315289e --- /dev/null +++ b/content/tales/cq.html @@ -0,0 +1,54 @@ + + + + + + Why Call "CQ"? + + + +
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Why Call "CQ"?

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+
+

L. B. Cebik, W4RNL

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+ +

+
+ This morning (June 19, 1998), a thoughtful and oddly interesting question arrived via e-mail: what is the deepest reason for someone to call "CQ" when that person has no idea of who may answer or whether anyone will answer at all? The following notes were my reply.
+
+
+ +

+
+ Peter, +

I do not know if there is any single deepest reason for calling "CQ." I can only guess at such deep motivations, but here are a few thoughts.

+

For the brand new ham, there is a sense of wonder at the possibility of having a radio signal actually being heard and responded to. That alone is enough motivation to try, just to see what happens. In a way, it parallels the SETI project efforts to listen to outer space, just in case there is something to be heard and the efforts to place special identifying materials on some deep probe space craft, just in case someone out there may someday find the probe.

+

I also suspect that as the new ham becomes experienced, two things happen. First, wonder turns into curiosity, especially as replies become routine, but from where they come and from whom they come remain unknowns until the reply actually happens. Second, the first response has an excitement that can become addictive in the sense of one wanting to repeat the first experience over and over again.

+

Although subsequent experiences are never quite like the first, since they do not have that initial anxiety of the totally unknown attached, new adventures into calling "CQ" have new dimensions, especially the human dimension. Every reply creates a new strand in a web of links among widely separated but still kindred spirits. Amateur radio, despite its internal disputes and diversity of activities, is still a community of human beings that cuts across all divisions of race, nationality, religion, and other things that divide us around the world. A "CQ" knows no such boundaries: our mutual interest in radio communications does not even break barriers: the barriers are simply not there. (I am sure this is truer in your region of the world, where boundaries are close in, than in the US, where a ham might spend his entire career talking only to folks within his own country.)

+

Interest in radio communications may offer a further contributing factor to the motivation for calling "CQ." Such interest tends to mark a person out as an individual, someone a little different from most of his or her friends, neighbors, and co-workers. Hence, there is a natural desire for camaraderie, a sense that one is not alone, but linked to a community. That is why hams tend to form clubs and anticipate "eye-ball QSOs." That same urge for linkage results in calling "CQ' as an invitation to and a hope for a new strand in the linkage that tells us we are not alone and that hence gives meaningfulness to all our efforts to master the art, science, and craft of radio communications.

+

Linkage to a community brings out in us at least two different and opposing urges, and they occur in different proportions in different individuals. One urge is to compete with others in our broad community. so we compete in contests for points or for countries worked, or for anything else. The other urge is to help, aid, assist any other member of the community who needs what we may have to offer: advice, knowledge, materials, other links we may have to services not available--the list is endless. The only condition I have ever known a true ham to place on rendering assistance was this: NOT that the recipient repay, but rather that the recipient be prepared to assist some other who may someday need what can be rendered.

+

Both of these twin urges make calling "CQ" more meaningful, for we may never know in advance whether we might receive a reply that either helps our score or gives us an opportunity to help someone else.

+

I personally believe that the most mature reason for calling "CQ" is the chance to be of assistance, even if that is only to give another the pleasure of a QSO, but more if the one who replies needs more. That is why I maintain my web site--it is one way in which I can help those in our community of hams who may need what is there.

+

There are, I am sure, those who would like to invert my remarks by leaning too heavily on the idea of being alone and seeing the "CQ" as a way to merely relieve loneliness. But I think one can only make this move at the expense of ignoring the initial sense of wonder and the more mature and thoughtful dimensions of being a ham and calling "CQ." It is at root not a demand for an answer, but an invitation to communicate, and that communication is a sharing. Sometimes we share only perfunctory data; sometimes we share news, information and ideas; sometimes we share joys and successes; and sometimes we share needs and solutions. In short, we share all that makes us a community, although not too much at any one time. Granted, some few may make "CQ" into a demand for reply, or even into a desperate plea for a reply, but for most, it is an invitation and a question: How can I assist?

+

I do not know if this is responsive to your question, but it is how I think about "CQ." In fact, over my 45 years as a ham, I have not too often called "CQ" myself (except to see of a quiet band had any listeners). Instead, I have tended to listen for "CQs" and replied to them. Listening is also a way of being ready to serve.

+

-73-

+

LB, W4RNL
+

+
+ +

+
+

Updated 6-20-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

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+ +

+
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Topics: Tales


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PVC Gurneys for All Occasions

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L. B. Cebik, W4RNL

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Roll-around carts or gurneys tend to come in two varieties: a. cheap, short-lived, and wobbly, or b. strong, durable, and expensive. Commercial grade good units run well over $100 and often over $200. The $20 to $50 units rarely last more than a year or so before the wheels go, the metal rusts, or something breaks under the loads we put on them.

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The following notes describe some gurneys we designed and built for a special purpose: to hold Jean's wild bird rehabilitation cages. However, the general principles of the two major designs are applicable and adaptable to a wide variety of uses. So I am summarizing the thinking that went into them. Since they are not precisely an "antenna item," I am placing these notes in the first catch-all category of the index.

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The drawings bear the initials "J. R." for Jean, since we designed the gurneys to hold a number of her cages. Our object, in part, was to elevate the cages so that there would be no stooping over to feed and care for orphaned and injured birds. However, we also wanted to be able to roll the cages into the sunlight on warm, good weather days and then to roll them back into the shop where the birds spent their time protected from bad weather and chill.

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Because showers and other water are a way of life in bird rehabilitation, we also wanted the gurneys to be weather proof. Hence, except for the casters, there is almost no hardware in the gurneys--only Schedule 40 PVC (1.25" nominal diameter). As well, there are no openings into the PVC pipes, so the interior of the structure remains as dry as the day of assembly.

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The key to making a PVC gurney is to collect many fixtures to go with the pipe itself. Ls handle the outside corners. Ts handle 3-way junctions for surfaces. Where you must go in a pair of directions, then one direction must be higher than the other. In a special gurney, we used Xs or cross junctions, along with a pair of 45-degree couplers. Of course, end caps are necessary for the leg bottoms. Before we finish, I shall show how we solved the challenge of applying caster to the end caps.

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The "Care Cage Gurneys 1-3" figure shows the piping and coupling layout for the most basic gurney. I have built several of these units in various sizes to handle different cage needs. As we look at the layout, we shall also discover why these units are adaptable to other uses.

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The first thing to note is that many coupling, especially on the legs, abut each other. We handle this with a short length of PVC cemented into both couplings, using a length that the couplings totally hide. Incidentally, the double thickness of the coupling and the linking pipe piece makes an exceptionally strong joint. Of course, joint quality depends partly on our use of the right cleaner and cement.

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Note also that a number of the adjacent Ts are at right angles to each other. My technique for making such joints is simple. Around the shop, I have pre-located a number of good right angles, for example, the floor and workbench legs. I insert dry a length of pipe in each direction. When I cement the joint, I quickly press the extensions against the right angle structure. It only takes a few seconds for PVC cement to weld the junction into a whole, so pre-planning where to go and what to do to establish a good right angle is essential. When cutting pipe lengths, remember to measure the amount of insertion length for each coupling so that you end up with the correct final dimensions.

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Since the cages did not require a top surface (we used cable ties to secure the wire cages to the perimeter PVC), the structure is open with only a single cross member to keep the lengths of pipe at about 2' or under. This length is very sturdy. The bottom shelf is another matter, so you might give some preliminary thought on how you wish to use the area. We have used a variety of techniques to make the bottom area into storage space for rehabbing supplies, unused transportation cages, and various kinds of seeds for the large variety of birds that Jean took in. In one case, I took a scrap sheet of plywood--it happened to be 1/2" thick, but 3/8" thick stock would be very adequate--and by cutting notches in the corners for the legs, fit it into the lower space as a shelf. This option did not require any hardware, since the legs locked it into place.

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On another version, I used some scrap 3/8" plywood that did not cover the entire space. However, a pair of small sheets, side by side, filled the area. These sheets required stainless steel (non-rusting) sheet metal screw to hold the shelf in place. You may as easily use coated steel or aluminum mesh or other shelving materials. However, be sure that all metal and hardware is non-rusting. As well, you may apply any of these ideas to the top level. In fact, you may wish to look at the stock of plastic bins available at Walmart, K-mart, etc. There are a number of very large units intended for under-bed storage. Hence, they have walls only about 6" high--a combination that makes a good unit for either the upper or lower level. Use a minimum number of sheet metal screws into the PVC rails to fix them in place.

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The photograph to the left shows a 2-cage unit. (Yes, although almost invisible, there are birds in the cages. Those unfamiliar with wild bird rehabilitation should know that it requires a federal license to hold migratory songbirds in a cage, and then only for a limited period of rehabilitation. Many states--such as Tennessee--also require state licensure of facilities. However, state laws tend to be quite variable from state to state, with differing assigned jurisdictions, as well. In general, capturing native species of migratory song birds without such a license and purpose happens to be against the law. So if you are thinking of making your favorite songbird into a pet, please don't.) The objects in the cages are materials that Jean added as enrichments for the birds, each designed from her extensive observations of birds in the wild to be something that would get orphaned nestlings used to the typical habitat they would one day find when they were released.

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Note that the top level of the gurney extends a few inches beyond the end legs. These extensions make convenient handles for rolling the gurney around. The amount of extension is a function of what makes a comfortable grip in your own application.

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The next photo to the right shows the double-length cage that Jean designed and had built for her work. The cage is long enough so that very small song birds--such as chickadees, titmice, wrens, and sparrows-- can get some end-to-end flight exercise as a preliminary to being moved into flight cages or an aviary. During the peak of orphan nestling season (about April through August in Tennessee), the numbers of birds might increase to a load of 50. In these times, the long cage's center divider would roll into place, making 2 cages out of one (for species who by virtue of age difference or natural feistiness did not get along together).

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The photo also shows the use of the lower shelf as a supply storage area. The bottom lining in the cage(s) above provides a natural umbrella over the shelf, so a plywood shelf is sufficient. However, if you use plastic or other materials for a bottom shelf, consider the following idea. Find containers with low walls but the largest areas that will fit in the space. Fasten these down to the rails. Then, for parts, provisions, or other items stored, let each item have its own plastic container that fits into the big container. These sub-containers should mesh together to make maximum use of the space and may have higher walls (that is, be deeper) than the low-walled retaining containers. There are a myriad of plastic containers available at very low prices, and the present-day quality of the plastic materials has reached the stage of being as durable as the basic frame.

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The next basic design for a gurney emerged from the need to hold and move a 4' by 4' by 4' small flight cage. Actually, the cage served as a basic (but not final) flight cage for very small species and as a rehabilitation cage for large species, such as quail, doves, and killdeer. Such a cage is ungainly to handle, so we designed a special gurney not only to reorient it indoors, but as well to wheel it outdoors.

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The key features of this gurney are the use of cross couplings or Xs, the use of short legs, the use of capped uprights to prevent the cage from sliding, and the provision for a handle for rolling the cage about. The crosses provide a rigid basic structure. The short legs provide a home for the casters, about which we shall say more soon. The capped uprights are sized to the cage, and the caps make the entire structure water- tight.

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The handle section consists of upright PVC lengths, with two cross bars, one about half way up and the other forming the handle. The handle is offset from the cage wall by the use of a pair of 45-degree couplings. In this application, the handle assembly will show some flex, but not enough to harm anything unless you load the gurney with a refrigerator.

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The photograph shows the gurney in use with its cage, filled with perching limbs and other enrichments to prepare the recovering or growing bird(s) for eventual freedom. (With a rehabber in the household, pruning limbs was less a matter of cleaning up trees than it was a gathering of perches for bird who ranged in size from 4" to 15" long.)

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Although this style of gurney may seem less apt to other uses, consider it as a potential base for a complete station on wheels. You may design the framework for holding the equipment and then redesign the gurney to hold the framework. Now you have a completely mobile station--or test lab, or whatever. (No, these gurneys are not designed for installing a small engine to make them self-propelled.)

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I have mentioned casters for the gurneys in several places. There are two things to note about them: quality and mounting.

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First, use only high quality casters. I learned from experience that the cheapest caster wheels will last only a very short time on concrete and asphalt. They may seem strong and economical in the hardware store, but they will amount to money lost when placed in use. Obtain high quality casters with wheels designed to stand the stresses, grinding, and wear of rough surfaces. You will discover that these units also have better bearings and hence roll more smoothly from day 1.

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The sketch introduces the subject of mounting casters. The end caps for PVC are too small for using the type of caster that mounts on a plate with small bolts. Since you may not be able to obtain flat-top caps, but have to settle for rounded types, you likely cannot even mount a plate onto the cap at all.

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My solution was to use insertion casters that come with a housing that press fits into a hole. However, the hole must be in solid material for the length of the caster housing and the caster shaft.

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My procedure was to cement together the end cap and the length of pipe necessary to join the cap to the leg assembly--ordinarily a T that abutted the end cap. I used auto-repair epoxy (Bondo) to fill the cap and linking pipe. I discovered through experience that the hole that I eventually drilled would hold the caster housing or shell better if I placed fiberglass repair cloth or simple wood chunks into the hole as I filled it with epoxy. Be certain to use the correct proportions of the two parts of the epoxy and to mix them thoroughly to ensure that the filling cures. Give the filled assembly a couple of days to cure before drilling, since the epoxy is in a confined space.

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When fully cured, drill the leg end from the cap side to fit the caster shell tightly--but not so tightly as to prevent the caster from snapping in place. Do not drill all of the way through the epoxy fill. Tap home the shell and then insert the caster. If a caster housing later wants to begin to come loose, you can dribble some epoxy into the hole, let it cure, and then re-drill the shell hole.

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If something breaks--and it never did for us--you can always effect a repair with some PVC couplings and short pipe lengths.

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The cost of these gurneys was about $40-$50 each, with nearly half that cost going to casters and perhaps a fourth to left-over couplings and pipe. That is why I have some yard benches made from PVC frames and treated lumber, not to mention a 10-meter beam boom. Yes, you can find small gurneys and roll-around carts for a bit less, but not ones of the size and durability of these units.

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Besides, the challenge of making something that custom fit the need was worth the investment. I have elsewhere stated that PVC is tinker-toys for adults, and so it is. A pipe structure from PVC, along with all of the fittings, is adaptable to many needs. Perhaps these gurneys will inspire you to even better structures for your own home, garden, shop, radio, antenna, and other needs. You can, for example, take the upright retainers from the second style of gurney and apply them to the upper and lower levels of the first gurney type. In that way, you might do away with fasteners altogether for holding in place the basic shelving trays. Hmmm. . . Now that is an interesting idea. I wonder how many couplings and how much pipe I have around the shop to try that.

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Updated 12-09-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: PVC, Tales


+ + diff --git a/content/tales/howto.html b/content/tales/howto.html new file mode 100644 index 0000000..2f74eea --- /dev/null +++ b/content/tales/howto.html @@ -0,0 +1,70 @@ + + + + + + A Guide to Assisting Songbird Babies + + + +
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A Guide to Assisting Songbird Babies

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Jean R. Cebik

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Is the baby really an orphan?

Each spring many people call wildlife rehabilitators because they have found a baby bird alone on the ground. People usually think that the animal needs their help, and they want to bring it in. Most babies are still under the watchful eye of their parents and do not need help from well-meaning humans. +

Fledgling Baby Birds

People often see baby birds that are partially or fully feathered sitting on the ground below a tree or shrub and automatically assume that the baby fell out of the nest and needs to be helped. At this stage in a bird's development, they are considered fledglings. Fledglings NORMALLY jump or fall out of the nest and spend several days on the ground or on tree limbs waiting for their parents to bring them food. This is their "flight training" stage. The parent birds will continue to feed their babies until the babies build their flight skills. This stage usually takes only a few days. Unless injured, these birds should be left where they are. Humans can help by keeping cats, dogs, and curious children away from the bird so that the mother can continue to feed it and teach it the necessary survival skills. +

If a dog or cat is threatening the baby bird, do not instantly bring the baby bird in. Rather, keep the pet restrained for the short time the baby is there. However, if a cat or dog has already attacked the bird (either a juvenile or an adult bird), please take the bird immediately to a wildlife rehabilitation intake center. They will accept injured wildlife, evaluate its condition, treat it, and then turn it over to a wildlife rehabber for the nursing care the animal needs until it is ready to be released back into the wild.

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Nestling Baby Birds

Baby birds that are mostly featherless are considered to be nestlings. These birds stay in the nest and the parents come to feed them there. These babies, when found, are usually on the ground directly below the nest. This often occurs when a wind storm blows the baby out of the nest, a sibling pushed the nestling out, or the baby simply falls from the nest. Occasionally, a crow, blue jay, or grackle will take a nestling from the nest and, for whatever reason, drop it on the ground. If you find a nestling on the ground, the absolute best thing to do is to place the bird back in its nest. If the nest cannot be reached or if you find an entire nest with nestlings in it on the ground, the following procedure often works well: Create a "makeshift" nest out of a clean berry basket or margarine tub with holes punched in the bottom for drainage. Line the berry basket or bowl with pine needles or paper towels. Then tack the makeshift nest back up in the tree as close to the original nest as possible. Finally, place the nestlings into the nest and leave. The parents will usually come back in a short time and will feed the babies just as if they were in their original nest. If a bird has built a nest in an awkward location (for example, on the grill of your car), carefully remove the nest with the babies in it and place it as close to its original location as possible. For example, place it on a carport shelf, hidden from open view, or place it in a nearby tree or shrub. The mother bird will likely hear her babies chirping for food and will find the nest quickly and continue feeding them. +

It is a myth that birds will abandon their nests if a human has touched the nest or babies. Birds in general (with the exception of vultures) have a very poor sense of smell and will not be aware that you have touched their nest or babies. However, they will be bothered by the sight of humans near their nest. If you have had to move a nest or replace nestlings, watch from a distance to ensure that the parents find it and continue feeding their nestlings.

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The only time we recommend bringing the baby birds to a wildlife rehabilitator is if you KNOW that the parents are dead or if the babies are injured in any way. The natural parents do a much better job of raising their young than any human could ever do. The natural parents can also teach their youngsters how to find food and avoid predators. A featherless baby bird that is brought to a wildlife rehabilitator must be fed every 15-20 minutes from dawn to dusk. This obviously requires a tremendous commitment of time and energy, and there is a severe shortage of songbird rehabilitators in our area. So please make every effort to keep baby birds with their parents and protect them from family pets.

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If you do find a REAL orphan or an injured bird, please do the following:

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1. Get it to a licensed wildlife rehabilitator (orphan) or to a wildlife rehabilitation intake center (if injured) AS SOON AS POSSIBLE. The longer the delay, the less chance it has of surviving.

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2. Keep the baby bird WARM and in a quiet, dark place until you can bring it in (a small cardboard box lined with paper towels or toilet tissue works well).

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3. DO NOT give the baby bird any liquids (they get all they need from their food and very often will inhale any liquid and aspirate). If you cannot get the baby bird to a qualified caretaker for several hours, moisten some dry cat or dog food in warm water. Let it soak for about 15 minutes until the food is soft, and then feed the baby bird just one nugget of food at a time. If it is featherless, it needs to be fed every 15 minutes. If it is fully feathered, it should be fed once per hour. Handle the bird as little as possible, and remember that birds are very fragile. Although not a complete diet, the moistened cat or dog food will keep the bird alive until it can get to a qualified caretaker.

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The designated wildlife intake center for injured birds and other wildlife is currently the University of Tennessee Vet School on Neyland Drive. Ijams Nature Center maintains a hotline to provide information on how to contact rehabilitators.

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How does one become a wildlife rehabilitator?

If you are interested in becoming a wildlife rehabilitator, you need to contact a licensed rehabber. You must train with a licensed rehabber for one year and then set up your facility. Tennessee Wildlife Resources Agency must come and inspect your facility after you apply for your license. If they approve your license, you must then apply to the U.S. Fish and Wildlife Service in Atlanta for a permit to rehabilitate migratory birds (if you are interested in rehabbing mammals only, you do not need a federal permit). The Migratory Bird Treaty Act protects our native birds, and only licensed wildlife rehabilitators are permitted to hold a bird captive even for the purpose of nursing it back to health. +

Locally, the East Tennessee Council of Wildlife Rehabilitators meets once a month from September through April to further our education and training. They sponsor many programs and courses to keep us up-to-date in our knowledge of how to care for injured or orphaned wild animals. Two organizations, the International Wildlife Rehabilitation Council (IWRC) and the National Wildlife Rehabilitators Association (NWRA), publish journals that contribute to our continuing education in this fascinating field. IWRC also offers courses of study and examinations in basic and advanced wildlife care. Becoming a licensed wildlife rehabilitator requires a large commitment of time, energy, and resources. No funding is provided by the state or federal government for this activity, and rehabbers are volunteers committed to helping our wild neighbors since human activity often causes harm to animals. This is one way of helping the wild creatures who share our planet. There are many other ways to help.

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What Can I Do To Help?

As concerned human beings, there are some things that we can do to help the songbirds that add so much beauty and such sweet music to our lives. A few helpful actions are listed below. +

1. Plant trees, shrubs, and vines known to attract birds because they provide food sources or cover for nesting. Some of the plants native to the Southeast region of the U.S. that birds find most attractive are these:

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      A.  Trees             B.  Shrubs             C.  Vines and Flowers
+          Dogwood               Pyracantha             Trumpet Vine
+          Maple                 Barberry               Morning Glory
+          Holly                 Holly                  Honeysuckle
+          Mulberry              Ligustrum (Privet)     Coneflower
+          Magnolia              Viburnum               Zinnia
+          Oak                   Nandina                Sunflower
+          Cedar                 Serviceberry*          Virginia creeper
+          Hemlock               Rose                   Black-eyed Susan
+          Pine                  Cotoneaster            Coreopsis
+          Sassafras             Photinia
+          Crabapple             Euonymus
+          Hackberry             Flowering quince
+          Cherry
+          Plum
+          Mountain Ash
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*The serviceberry is considered a tree in the Southeast, but a shrub in other parts of the U.S. In Tennessee, it reaches the size of a mature dogwood or redbud tree.

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These are just a few of the plants that birds use. As you can see, many of these plants add beauty to our yards while providing food and cover for the birds. If you are interested in learning more about plants that attract birds, consult any of the many books available at gardening centers or home centers (such as Lowe's, Mayo's, Home Depot).

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2. Avoid the use of chemicals on your lawns. Pesticides and herbicides are poisonous to birds and other wildlife (and not very good for humans, either).

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3. Easiest of all, leave a place for wildlife in your yard. Choose a corner of your property and let it revert to nature. Some of the plants that humans dislike provide important sources of food for wildlife. For example, wild blackberry plants, sumac, black cherry, pokeweed, hay grasses, and honeysuckle may be weeds to homeowners, but they are food for birds and small mammals such as chipmunks and squirrels.

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4. Watch carefully the things that you throw away to ensure that they do not pose a danger to birds or other wildlife. Do not discard fishing line where birds or turtles can get entangled in it; many animals lose limbs when they become entangled in fishing line and their circulation is impeded. Do not discard plastic rings from soft drink cans without cutting them apart so that animals cannot get entangled in them. Do not pour out oil or other petroleum distillates; take them to a service station for proper disposal. Do not throw away out-of-date computers; they contain many toxic substances such as lead and mercury. Instead, find someone in need of a computer, even if it isn't the latest model, and donate it to a worthy cause or individual.

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5. Provide a source of water in your yard. It can be as simple as a birdbath or as elaborate as a fountain. Keep your source of water filled with clean water.

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6. Provide bird feeders. A wide variety of attractive and useful bird feeders are available at low cost. Remember to keep your feeders filled and clean them frequently.

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7. Do not cut down a tree or shrub during spring or summer months without first checking thoroughly to be sure there are no birds nesting in it.

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Jean R. Cebik
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Formerly Federal and State Licensed and IWRC-Certified Songbird Rehabilitator

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Topics: Tales


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10-10 and Lindbergh

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L. B. Cebik, W4RNL

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Imagine yourself on the 22nd of May, 1927, about 0200 Paris time. What would you be thinking? Much of the North American and European world was wondering whether Charles Augustus Lindbergh had successfully crossed the Atlantic solo in his Spirit of St. Louis. Somebody knew, and he was later to become a 10-10er.

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That night, my father, Jim Cebik, KA1TXF, #53363, was operating under the call 1ATG from Fairfield CT (he now lives a few miles away in Stratford). For international contacts, he added the informally agreed upon prefix NU. He was in contact with 8AKL, that is, F8AKL (the "F" was also informal then) in the Paris area. The wavelength was 42 meters with minimum QRM and no QRN. The French operator sends QRX, please wait. He steps outside his shack to investigate a noise overhead. He returns to the air with the report that Lindbergh has passed overhead on his way to Le Bourget airport. Jim is quite possibly the first American on this side of the Atlantic to know that Lindbergh has made it.

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F8AKL's name is illegible on the QSL card he sent. Detailed name and mailing address (not to mention county, 10-10 number, grid square, etc.) had not yet become standard parts of the card's format. Nevertheless, he confirmed passing on the information with this comment at the bottom of his card: "TNX for QSO OM--gld to kan give u news fm Lindbergh just wen is coming to Paris--PSE QSL." For both operators, the QSO was as exciting as the news of Lindbergh.

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For those curious about the date and time, Lindbergh took off from the US (Roosevelt Field) at 7:52 AM EST, May 20, 1927. He flew for 33 hours and 32 minutes. In terms of Eastern time in the US, it was May 21, about half-past 5 in the early evening. In Paris, it was nearly 2 AM, the next day, give or take some looseness in log keeping in those days. (Another 1927 QSL card just lists the time as "night.")

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Jim is 90 this year, still licensed, but not as active as he once was on the air. Off the air, his schedule makes me look feeble by comparison. And, yes, he clearly remembers this 1927 QSO--and many others, such as working Admiral Byrd's supply ship in the Arctic, a ship he finally set eyes on at Old Mystic Seaport in the 1950s during a family outing there.

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I wonder what other historically interesting facts lie buried in the QSL cards of our members.

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This item first appeared in 10-10 News, July, 1996.

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Return to Amateur Radio Page

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Topics: Tales


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In Memory of Jean

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L. B. Cebik, W4RNL

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Jean Robeson Cebik was my wife and so much more. A life-long resident of the Knox County, Tennessee, she passed away Monday, November 4, 2002, at the age of 59 after a 13-month struggle with cancer. Jean worked for many years at the University of Tennessee in office administration and at Technology for Energy as a technical editor before returning to UT and earning a master's degree in French literature. Afterwards, she taught a number of years at Pellissippi State College and then retired to become a licensed wild songbird rehabilitator. In addition, Jean was an accomplished craftsperson whose creations grace our home, with Christmas a special occasion for the display of her wreaths, flower arrangements, and ornaments.

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Jean held an amateur radio license (N4TZP), and we often operated as an OM-YL team on 10 meters. She was my constant companion at every hamfest to which we traveled. The dedication that appears in each of my books available from antenneX--volumes of antenna studies--bears witness to Jean's importance in my life and to my work:

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+ "All of the volumes of my antenna studies are dedicated to my wife, my friend, my supporter, and my colleague, all of whom are Jean. Her patience, understanding, and assistance gave me the confidence to retire early from academic life to undertake full-time the continued development of my web site. The site is devoted to providing, as best I can, information of use to radio amateurs and others--both beginning and experienced--on various antenna and related topics. Each volume grew out of that work--and hence, shows Jean's help at every step." +
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Jean was a state and federally licensed and IWRC certified wildlife rehabilitator specializing in songbirds. Songbird rehabilitation came Jean's way after her varied career during which was an avid bird watcher who did not so much wish to create a long life list as she wished keenly and sensitively to observe songbird behavior. She became a rehabilitator in the mid-1990s after retiring from her career path, and she carried her observations and sensitivity to the work. Specializing in smaller songbirds, she used her observations to create cage and aviary enrichments for both orphan and injured birds, in some years single-handedly caring for over 300 birds. Jean achieved a 70% success rate for release, and nothing satisfied her more than to discover nests of a few of her former charges in the 1-acre home that she developed into a habitat for songbirds and other small wildlife. She favored smaller songbirds, with eastern bluebirds, barn swallows, gold finches, chickadees, house wrens, and Carolina wrens among her special favorites. However, she also nurtured killdeer, quail, robins, doves, and blue jays with equal success. Each species of bird had special properties to be honored in their care and to inspire us as they flew to their renewed lives. Still, Jean cried for each of her charges who did not survive. (See "A Guide to Assisting Songbird Babies," her notes distributed in the Knoxville, TN, area.)

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Jean was selflessly devotion to songbird and wildlife rehabilitation. She so loved songbirds that she devoted her life to nourishing, protecting, and rehabilitating them. They thanked her well by singing and flying to freedom. Jean used her background in research to ferret out information for fellow rehabilitators, including internet searches for the latest data and for sources of materials and supplies. To the Eilertsen-MacLeod manual, A Flying Chance, Jean contributed extensive observations and numerous photographs. She was also a member of the East Tennessee Wildlife Rehabilitation Council, which--in conjunction with Knoxville's Ijams Nature Center--planted on December 7 a serviceberry tree as an enduring, useful, and living memorial to Jean.

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Perhaps no other tree or shrub could honor Jean more than the serviceberry. A native North American genus (amelanchier), the serviceberry appears in almost as many species as it has common names: serviceberry, shad bush, shadblow, juneberry, sarvis. Most of the names come to us from colonial and early pioneer times, when the tree bloomed in early Spring, about the time circuit-riding preachers could once more hold services, and when the shad began their runs and incidentally provided food for colonials. In June, its berries emerged to fill the crops of birds and the pies of pioneers. Its foliage sheltered and nourished wildlife ranging from birds to bears.

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The ETWRC-Ijams planting grew out of Jean's final wish, which I had added to notes on her passing to both amateur radio and wildlife rehabilitation organizations. Jean's last wish was simple: that everyone she knew should plant a tree or shrub in his or her yard to nourish, nurture, and protect the songbirds that she so much loved and so ably rehabilitated. Upon hearing of Jean's final wish, one individual pensively noted: "How thoughtful! How sensitive! How selfless! How typical!"

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Jean's wish reached both wildlife rehabilitators and amateur radio operators throughout the U.S. and beyond. Response has been overwhelming, with Autumn plantings or promises of Spring plantings amounting to a large grove, if not a small forest. The East Tennesse DX Association has fulfilled a promised second planting at Ijams for early 2003, and the Oak ridge Amateur Radio Club has contributed a third tree. There are plantings as far way from Jean's Knoxville, TN, home as Australia, where the planter of a Golden Wattle noted that the sun should never set upon Jean's memory or her work. Although Jean's innate modesty might not have let her say so, nothing would have pleased her more than the response to her final wish, except perhaps that the plantings might become a precedent to similar gestures to honor each future fallen rehabilitator.

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Together we lived and learned, each from and with the other. I am much less than I was, now that I am without her, but much more than I could have been had I not met her. Jean was my wife, my friend, my life, and my love. She is not here. I shall miss her.

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December 8, 2002

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Topics: Tales


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What's in a Name?

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L. B. Cebik, W4RNL

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The antenna owes its name to a certain visual similarity that some kinds bear to the "movable, segmented organ of sensation on the head of insects, myriapods, and crustaceans." We rarely confuse the two generic types of the antenna for plural reasons. An insect has two antennae, but an amateur radio operator often has two (or more) antennas. (Many British experts preserve the alternative name, aerial, perhaps because the term is less arcane and captures something of the antenna's lofty position in the air and something of its ethereal role in radio communications.) "What's in a name?" wrote Shakespeare. An antenna by any other name would radiate as well--and confuse the heck out of amateur radio operators.

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Confusion reigns within the field of antenna names largely due to history--more specifically, the history attached to how each antenna type received its name. Some antennas have received the names of their creators or developers, such as the (W)8JK. Others have received names because of what they look like, such as the J-pole. Still others received names from their original uses, such as the Zepp(elin). Some few antennas hide technical information behind their names, such as the dipole. Since the history of antennas includes strong elements of mixing, matching, and adaptation, the result has become almost a free-for-all of naming that can leave us breathless, wondering what a name really means.

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We can obtain some useful information--or at least a bit of entertainment--by looking at the names of antennas apart from most of our normal concerns for their performance under the circumstances of their installation. Ultimately, the option that we shall face is whether to call an antenna by its common name--often a misnomer--or by a technical description that best places the antenna within the total body of antenna types. Shall we refer to a certain antenna as an endfire bi-directional array of a pair of horizontal center-fed collinear 2-half wavelength wires 180° out of phase or simply as a W8JK flattop? The answer seems obvious until we explore some of the ways in which common names can get us into trouble.

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So let's explore some of the types of names that we give antennas. This space is too small for detailed histories of names, but along the way, we can suggest avenues of further exploration for those interested. As a convention, I shall italicize each antenna name that we consider. Mercifully, I shall omit from consideration most merely cute names, such as the myriad of antennas that have borne the name "signal squirter." ("Squirt," however, once had a common use in amateur radio to designate newcomers who usually used lower power than more experienced hams.)

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Antennas Named for People

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In earlier radio days--say the late 1920s through about 1940--antenna designs emerged largely from two sources: Bell Labs and RCA. Engineers would publish their developments--after their companies obtained patents--in the Proceedings of the IRE (later supplanted by the array of IEEE publications) or in a house organ, such as the RCA Review. Both are excellent sources of information on antenna developments, and most college libraries have collections. If you wish to look at the original papers, you may obtain specific references by looking at the footnotes or references in any of the standard college texts, such as Kraus' Antennas.

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If an antenna design took hold, users would tag the antenna with the developer's name. Such was the case for Bruce and Sterba, whose antennas appear in outline form in Fig. 1. Both antennas are bi-directional arrays in which the beamwidth and gain emerged from the number of bays in the system. The feedpoints shown varied, with a more central feedpoint removing a slight azimuth tilt produced by end wire or corner feeding.

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Both antennas have interesting histories. Although both have passed from commercial use, the Bruce array has found renewed interest among amateurs, especially in the Northwest corner of the U.S, with its tall supportive Douglas firs. However, Kraus is reputed to have reported that Edmond Bruce himself confessed that he would have preferred his name be attached to another of the many types of antennas that he developed in his distinguished career.

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Sterba's work has also passed from use, but not from legend. It also illustrates how easy it is to confuse categories of antenna names. We shall soon look at the naming of antennas in terms of what they resemble. The Sterba curtain is not one of those antennas--although it sort of looks like a curtain. Nonetheless, as the diagram shows, the antenna has some specific requirements, such as the 1/2 wavelength dimensions and the vertical parallel sections that form phasing (transmission) lines. However, I have seen on the web an "all-band Sterba curtain." Yes, the antenna will load up on all HF bands, even when cut for 10 meters. However, the phase relationships that make the antenna a Sterba curtain hold only for the narrow band of frequencies for which the basic properties hold. Just because an antenna looks like a Sterba curtain does not mean that it is a Sterba curtain. Off the design frequency, it may become simply a random tangle of wires with dubious radiation properties.

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Perhaps the most famous and still widely used antenna-naming event has been the Yagi, one version of which appears in Fig. 2. The original work on parasitic element relationships appeared in the late 1920s as a joint publication of Yagi and Uda. Hence, one historically correct name for the antenna is the Yagi-Uda parasitic array. It is unclear just why the name was shortened to simply the Yagi. A number of engineers are bothered by references to the antenna by its shortened name, since Uda may have been more central to the development of ideas that are still in use today. They appear to fear that the shortened name reflects our bad habit of the giving of credit to or the taking of credit by an academic or staff senior member, when the work is actually the product of a younger creative mind. However, the more probable reason for the truncation is that it is simply easier to say the first of the two names--and what is easiest to say often sticks as a label.

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I must confess to a small contribution to the name-by-development enterprise. In the 1990s, I began examining Les Moxon's development of the VK2ABQ square into a rectangle with more reliable performance characteristics. (The antenna has precedents in the 1930s, but it appears that both VK2ABQ and G6XN were unaware of them.) As I developed the outlines of the rectangular antenna that used both parallel-element and element-tip coupling to yield some useful properties, I called the antenna the Moxon rectangle. Les' contributions to understanding antennas among radio amateurs seemed to warrant the label for the antenna. See his HF Antennas for All Locations. The name for the rectangular antenna appears to have gained some currency.

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Some antenna names appear to have been either self-generated or self-promoted by individual developers. Perhaps the classic case appears in Fig. 4. John Kraus, W8JK (or simply 8JK in some older circles), has never avoided any opportunity to promote his own work, which was highly creative over his long career. In his works, you will find innumerable self-references, even in texts that we might expect to take a more objective or remote perspective on matters.

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The (W)8JK array is a bi-directional horizontal endfire array consisting of 2 elements, each of which is anywhere from 1/2 wavelength to 1.25 wavelengths long. The elements are 180 degrees out of phase with each other, as suggested by the center main feed line and the fact that one of two connecting lines to the elements has a half twist. The antenna appears in many variations of element spacing and length, and some versions have used multiple-wire elements. The antenna still has numerous applications.

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At the opposite end of the scale are antennas with only partial names, so that the name of the developer has been lost, except among those with enough interest to dig out the information. The ZL Special, shown in 3 variations from the 1950s in Fig. 5, is a case in point. Many folks view this antenna simply as a development from down under rather than as the work of an individual. The antenna emerged in 1949 from the work of George Prichard, who was ZL3MH at the time and later became ZL2QQ. F. C. Judd, G2BCX dubbed the antenna the ZL Special in 1950 in his article describing his initial experimental results. Specific identifying marks to indicate Pritchard as the originator simply disappeared after that. (There are some similar developments during World War II, but they were not accessible to--or usable by--radio amateurs at the time.)

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The ZL Special is a basic version of a 2-element horizontal phased array with principles of operation similar to those used by its Swiss counterpart, the HB9CV. Unfortunately, the sad state of affairs in the development of amateur Yagi beams of the period gave the simpler 2-element antenna an unwarranted reputation for very high gain (over 9 dBi in modern terms) to go with an excellent front-to-back ratio. (It deserved the latter judgment.) Variations on the design still appear today.

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Naming antennas for their developers is a long, honored, and honorable tradition in radio communications work. However, we should remember that such names tell us virtually nothing about the antenna itself--unless we happen to be familiar with the antenna by having studied it--however briefly. Hence, as we saw with the Sterba curtain, the combination of a named antenna and too little information about what the antenna really is (and how it does its work) carries the danger of perpetuating either wrong labels or--worse yet--faulty impressions and information.

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Still, we find a persistent ego-borne effort by some writers to name antennas after themselves. In amateur circles, the naming usually involves a call sign. There are occasions on which the practice is appropriate. For example, if one is comparing an already named antenna design to some variation or refinement of one's own devising, then distinguishing the comparators may require something like a pair of calls, one of which will be the author's. Apart from such circumstances, I prefer to let history take its toll. Understanding what an antenna is and how it works is more significant than giving the antenna a catchy name.

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Antennas Named for What they Look Like

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Antennas often received names based on their appearance. What they look like determines the label, which comes in one of two general forms: alphabetic and geometric. Fig. 5 shows typical examples of each kind of name. The J-pole not only resembles the letter J, but originally made use of pipe sections to result in a self-supporting VHF vertical antenna.

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Clarence Moore, W9LZX, holds the patent for the cubical quad antenna. The closed loop structure originally overcame coronal discharge problems at HCJB in Quito, Ecuador in 1942. The name obviously derives from the appearance--virtually a cube using 4-sided elements. An X-brace supports the 4 corners and allows the loops to have a square (shown) appearance or to take on a diamond shape. Because the basic name applies to a 2-element version of the antenna, individual elements often bear the name quad loop, while arrays with 2 or more elements become quad beams.

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Alphabetic names are perhaps the most numerous, since many basic antennas resemble common letters. To the alphabet, we may add another piece of U.S. history that plays a role in antenna naming: cattle branding. Brands had to be simple to meet the capabilities of frontier blacksmith shops, but maintain a unique identity for each rancher. From those origins have emerged a few antenna names, such as the pair in Fig. 7.

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The lazy-H is a relatively old bi-directional beam consisting of 2 collinear elements spaced originally 1/2 wavelength in a vertical arrangement. The cross bar of the H is the phase line, which feeds the two elements in phase. Other feeding schemes are possible for monoband versions of the antenna using 1 wavelength element lengths and an electrical half wavelength phase line (taking the velocity factor into account). However, the 1960s brought the realization that if the elements are 1.25 wavelengths long and spaced 5/8 wavelength apart, the beamwidth will be narrower and the gain higher. As well, the antenna will operate reasonably down to the point where the elements are only 1/2 wavelength long, with a spacing of 1/4 wavelength. With a wide-range antenna tuner, the lazy-H became a multi-band bi-directional broadside array.

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Much younger than the lazy-H is the lazy-N. The tilted N structure is all part of the radiating element (unlike the lazy-H that combines elements and phase lines to make its letter shape). The antenna zigzags the element with angular fold-backs to reduce the total height of the vertical. To overcome the lowered feedpoint impedance of this arrangements, the antenna uses an offset feedpoint experimentally determined to be close to 50 Ohms.

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Both the lazy-H and the lazy-N tell a sad tale from the historical perspective. With such easy names, few--if any--people remember who the developers may have been or where to find the original articles describing the first incarnations.

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Alphabetic antenna names very quickly become alphabet soup. Fig. 8 shows us why. Consider a resonant half wavelength antenna fed at the center. Rather than creating a linear element, we shall bend the antenna at the center to form a 90-degree angle. What do we get? Fig. 9 shows us some of the territory.

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At the bottom left are 4 views of antenna with our eyes parallel to the ground plane. Hence, the antenna extends vertically. We may make an L or an inverted-L. (We often bring the latter antenna to the ground and feed it at that point, sometimes using a radial system.) The next two views shows us a V (rarely used except for TV rabbit ears) and the very common HF inverted-V. The last entry allows us to suspend an HF wire with only one high support. Although the Ls require a 90-degree angle, Vs and inverted-Vs often use wider angles. If we change our viewing point to a position above the antenna and arrange it parallel to the ground, we obtain a horizontal V, also called a quadrant antenna. The last name seems to apply only to single element horizontal wires.

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The upper part of the sketch shows a bit of the terminological morass created by the letter V (a part of the letter's story intentionally omitted by Sesame Street). On the upper left is a long-wire V-beam. The end wires return to ground or to just above ground with a terminating resistor to create a directional traveling wave antenna. Each leg may be from 2 to n wavelengths long, depending upon the available wire and terrain. At the center is a second V beam, this time composed of elements that are swept forward to form the V shapes. V-ing elements tends to degrade rather than enhance the performance of 1/2 wavelength elements, but may provide some pattern control of 1.25 wavelength elements. (In some designs, the 1.25 wavelength dimension is between the element end points and results in a need for physical elements totaling close to 1.5 wavelength.) Just to add to the potential confusion in the V name, the right-hand V-beam consists of inverted-V elements. In most cases, the seeming simplicity of a letter name leads to its use for antennas that may have very distinct arrangements and properties.

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Geometric shapes are not without their own oddities of use or of history. Fig. 9 shows 3 vertically polarized self-contained verticals. On the left in each case is the electrically simpler version. The delta is any triangle, although equilateral and right triangles are the most common shapes. The side feed point is 1/4 wavelength from the apex to provide a vertically polarized pattern. Below it is the side-fed rectangle, again vertically polarized given the feedpoint.

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To the right of each single antenna is a doubled version. Since each of the left-side shapes forms a pair of vertical monopoles fed in phase (roughly), the doubled versions act like a bank of 3 vertical monopoles fed (roughly) in phase. The bi-directional pattern is broadside to the plane of the wires.

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At the top of the figure we find the half square, so named because it seems to lack the bottom half that would make a full square. To the right is the doubled version, called in a mixed metaphor the bobtail curtain by its developer. Each antenna uses true vertical elements properly spaced for maximum gain. However, to achieve this goal, the half-square is somewhat out of square, with a 5:8 ratio between vertical and horizontal sections. The bobtail curtain requires significant elongation of the horizontal sections and shortening of the legs for maximum broadside gain. Whereas the simple delta and rectangular shapes predate their doubled versions, the bobtail curtain historically precedes the half square. See Woodrow Smith, W6BCX, "Bet My Money on the Bobtail Beam," CQ (March, 1948), 21-23 and 92-95, and Ben Vester, K3BC, "The Half Square Antenna," QST (March, 1974), 11-14, for the seminal articles on each antenna. In place of the upper high-current, low voltage feedpoints shown, one may bring the tip of one vertical to ground and use standard voltage-feeding methods.

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The odd name of the doubled half-square results from combining two different look-alike ideas. The idea of a curtain goes back to the 1920s and rests on the resemblance of the array of elements (and support lines) to a curtain. The verticals do not reach the ground, giving rise to the idea of bobbing the tail of a horse. The composite picture of a horse's tail covering a living room window, however, is not a pretty sight. When we stray from using strictly alphabetic or geometric names, we often open the door to confusion. Fig. 10 shows a different kind of example.

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The sketches show 3 different kinds of bow-ties. In the left, feeding across the center points of the top and bottom wires yields a vertically polarized signal. We find such bow-ties ahead of many planar reflectors in UHF FM repeater service. If we feed across the center horizontally, the wings of the bow-tie act like very fat horizontal element halves. This configuration also bears that name fan, but it should not be confused with fans of dipoles for two or more frequencies, fed at a common point. On the right is an alternative shape for the horizontal bow-tie. Both the center and the right versions may have a straight horizontal section running across the overall shape and supporting lighter spread wires in the HF region. UHF bow-ties sometimes consist of solid surfaces.

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The bow-tie at the right is a bow-tie only if we feed it horizontally, as shown. If we separate the upper and lower wire structures and feed across the two at the center--following the system used at the far left, then the bow-tie becomes a vertically polarized double diamond. However, diamonds have their own foundations for confusion.

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Fig. 11 shows the outline of a terminated long wire array. In 1931, Bruce called this a diamond. However, others preferred a more purely geometric name and called it the rhombic. Bruce adopted this label in his 1935 article, co-authored by Beck and Lowry. The dimensions of the antenna combined the leg length and the angle called alpha in various equations to result in a highly directional array with a very narrow beamwidth. Matching the terminating resistor of this traveling wave antenna to the feedpoint impedance yields a wide-band array with consider performance--but also with very strong sidelobes. Although few remain in use, the antenna served point-to-point communications across the oceans for several decades. Incidentally, this is the array that Bruce apparently would have liked his name attached to instead of the array shown in Fig. 1.

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Although many other geometric labels exist, these suffice to show the simplicity--and therefore the danger--of using names that rest simply on what an antenna may resemble. Merely calling out the alphabetic or geometric name of an antenna does not yet tell us anything significant about the antenna itself in most cases.

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I have vowed to omit from these notes labels that are merely cute. However, there is a trend in antenna labels that has an alphabetical flair. It occurs when we mix antenna types and try to come up with a unique name for the hybrid result. Perhaps no basic antenna has seen more variations than the Yagi (or Yagi-Uda, if you prefer). Fig. 12 shows some of the labeled hybrids.

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The quagi combines some quad loop elements--usually the driver and the reflector--in an effort to improve performance by at least the level of a quad loop over a dipole. Results have been mixed, although the idea continues to attract experimenters in VHF and UHF antenna work. The zagi is a yagi with zigzag elements that use linear compression to shorten the width of at least small beams. The zigzagging may use triangular or square sections. Since a Yagi does not care much about its driver, we may use a J-pole to drive a vertical beam. The result is the jagi. Finally (at least for the moment), we may drive a Yagi with two drivers, phase-fed, in order either to increase gain over a narrow bandwidth or to increase the natural bandwidth of a driver-director array. The result becomes the phagi (also called the log-cell Yagi). The quest for short memorable names is almost as unstoppable as the effort to name an antenna after oneself.

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Antennas Named for Their Initial Use

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Of all the antennas named for their original applications, we need only one example to show what can happen to a name, once we give it some currency. Consider the Zeppelin, a hard-frame lighter-then-air ship of the 1920s and 30s. For radio communications, the simplest HF antenna that we might use would be a long wire trailing from the ship. Of course, we would have to feed it at one end of the wire. We might use an antenna tuner today to match the high-impedance of the wire's end, but in earlier days of high-impedance vacuum-tube amplifiers, we might also find a way to connect the antenna directly to the transmitter. The top sketch in Fig. 13 shows the antenna itself.

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The feasibility of this antenna gave rise to ground-based applications. Two modifications emerged. First, to keep the antenna as high as possible, we employed a high impedance transmission line between the equipment and the antenna end. Second, we shortened the antenna name to the Zepp. With a wide-range antenna tuner, we found that we could operate the antenna over a considerable span of frequencies if the wire was at least 1/2 wavelength long at the lowest frequency. At high frequencies, the antenna wire became longer as measured in wavelengths.

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Eventually, the center sketch in Fig. 13 acquired a longer name: the end-fed Zepp. Given its origins, we should not have needed the label expansion. What occasioned the enlargement was a curious turn of linguistic events. If we take the same length of wire, we can also feed it in the center. This arrangement is convenient for many home installations where the house and the operating room may be centered on the available property. Unfortunately, many folks began calling the mid-point feeding arrangement the center-fed Zepp. The original use that gave rise to the name for the antenna had disappeared, lost in the human penchant for short snappy names. However, if you are prone to mental pictures, consider a Zeppelin trying to use a center-fed arrangement with very long wires on either side of the feedpoint. Pictures aside, one center-fed antenna has permanently acquired a Zepp association. If the element is about 1.25 wavelengths, then we have an extended double Zepp (or EDZ--in some literature, a DEZ), even though the vertical monopole version (at 0.625 wavelength) is not called an extended Zepp or any kind of Zepp at all.

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Like all of the antenna names or labels that we have so far considered, a name based upon an initial application tells us almost nothing about what the antenna is technically. Such names obscure rather than reveal where an antenna fits within the overall set of structures that we use to radiate and receive signals. Indeed, it sometimes amazes me how few antenna names actually do reveal what the antennas do and how they do it. Even those antennas that do bear technical names are subject to dangers of label misuse.

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Antennas Whose Names Carry Technical Information

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If we look closely at a few of the basic antenna names, we can find some technical information. To find the information, we must treat the label as a noun with a meaning and not just as a convenient name. Radio amateurs tend to have difficulty in this regard because they enter antenna studies in the middle. Basic licensing requirements tend to insist that the individual undergoing a test recognize some antenna shapes, not that they understand basic antenna principles.

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Consider the dipole. At the most rudimentary level, this antenna serves both theoretical and practical purposes. The most rudimentary dipole is very short and has the general properties shown in Fig. 14. The level of charge increases constantly from the centered feedpoint outward, reaching a peak value at the element ends. In contrast, the current distribution is maximum at the feedpoint and decreases toward zero at the wire ends.

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If a dipole is to be a dipole, then it must preserve its basic properties as we lengthen it to a value that is practical. Current must be highest at the center and decrease once along the wire length toward the wire ends. Essentially, the maximum length of a true dipole is an electrical half wavelength. This antenna is perhaps the most common and fundamental antenna used by radio amateurs if we combine a number of properties to form a label for the antenna that is truly accurate. What we normally call a dipole is actually a center-fed resonant (or nearly resonant) 1/2 wavelength dipole. The term "dipole" indicates the current (and the charge) distribution. The term "center-fed" indicates where along the wire that we place the energy source, that is, the feedpoint. (Other feedpoints for the length of wire involved will produce the same current distribution as the center feedpoint.) The reference to being "resonant" indicates that at the feedpoint, the measured impedance shows no reactance, but is instead purely resistive. (The note on being nearly resonant recognizes that a small amount of reactance at the feedpoint is acceptable under normal conditions of use.) The wire length (1/2 wavelength) may seem redundant, but it does give us information needed to replicate the conditions on other frequencies. The combination of ingredients that make up the commonly used dipole are very convenient. It allows us to use a coaxial cable as a feedline for monoband operation, and the impedance of a well-matched system coincides closely with the output or input impedance of standard transmitting and receiving equipment used for many decades.

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What happens if we make the center-fed wire longer? We do not need to do any physical work, but only to increase the operating frequency. Then the wire can be several wavelength long, even though it is 1/2 wavelength at the initial or lowest frequency. Typical of the results is the current distribution curve shown in the lower part of Fig. 15.

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With many transitions of current from maximum to minimum and back again, we no longer have a dipole. Instead, we have a 4 wavelength center-fed antenna whose feedpoint may or may not be nearly resonant. Indeed, the only trait that the antenna has at the listed frequency with the original dipole is the fact that both antennas have a centered feedpoint. For a half century, we have called such antennas doublets. The name only tells us where to find the feedpoint. The rest we shall have to add to arrive at a reasonable technical description of the antenna.

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There is an unfortunate tendency among radio amateurs especially to label an antenna by what it looks like and not by what the antenna is doing. Even seasoned antenna veterans persist in calling any center-fed wire a dipole, except for some few who call it a center-fed Zepp. However, the antenna shown in the lower part of Fig. 15 is a doublet and requires further specification to capture its functioning. Now let's make the story just a bit more complex. In the 1930s, we likely could not have used the term "doublet" as a label for the antenna. In that decade, some handbooks used the term for a very specific antenna. If we use parallel feedline as the line to a 1/2 wavelength center-fed wire, we do not obtain a close impedance match between the antenna and the feedline. To effect a match, builders would spread the feeder ends and connect them to the wire at a distance from the wire center and eliminate the gap that we might ordinarily find at the center point. Within a decade or so, handbooks gave this arrangement a more specific name: the delta match, because the spread of the feedline formed an inverted Greek letter in shape. The term "doublet" had been freed to indicate a center-fed wire of indeterminate length, but certainly one that is longer than a strict dipole.

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The 4 wavelength center-fed wire at 28.4 MHz that we viewed in Fig. 15 is not only longer than a strict dipole, it qualifies as a long-wire antenna. You may ask fairly the following question: How long must a wire antenna be to qualify as a long-wire antenna? The answer is not illuminating: we are not sure. Most antennas that we classify as long-wire antennas do not begin to show desirable properties until they are at least 2 wavelengths long--sometimes 3 or more. Practical long-wire antennas used in the 1930s through today tend to be at least 5 wavelengths long. However, I know of no text that sets a dividing point between the long-wire antenna and the antenna that is not a long-wire. (However, note that we do not divide the world of antennas into 2 classes: the dipole and the long-wire. The two terms do not form a true contrasting pair.)

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Most long-wire antennas also use end feedpoints. With the feedpoint at one end, we can add a terminating resistor at the other end of the wire array to convert a standing-wave antenna with bi-directional properties into a traveling-wave antenna that is highly directional. Fig. 16 shows three commonly used long-wire arrays: the simple 1-wire long-wire, the V beam, and the rhombic. All three use terminating impedances to arrive at the sample azimuth patterns that I have overlaid on the antenna sketches. Both the V beam and the rhombic make use of the angles of the single wire's main lobes to arrive at the correct wire angle to achieve the high gain and narrow beamwidth of their main lobes.

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"Long-wire" then is both a generic label for any antenna that is numerous wavelengths long and a more specific label for one kind--the simplest kind--of generic long-wire antenna. So the 4 wavelength center-fed unterminated doublet of Fig. 15 is a generic long-wire antenna, but not specifically a long-wire antenna of the end-fed sort.

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Some technically informative labels become so long that we create abbreviations. Then we proceed to use the abbreviations in antenna writings, often assuming that the reader can translate the label. Hence, we find articles and specification sheets on LPDAs, sometimes further abbreviated to LPDs. LPDA stands for log periodic dipole array, and some writers believe that the word "array" (and its abbreviating letter) are superfluous. (We also have LPMAs or LPMs, meaning log periodic monopole arrays.) The LPDA label indicates not just a set of antenna properties, but as well an entire design procedures for creating antenna of the required type. Fig. 17 shows some of the basic design elements as well as the general outline of an LPDA.

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The elements of the LPDA are substitutes for short sections of arc in a circle. By using initial values that define the angle formed by the element outlines, the relative length of any two adjacent elements and the spacing between adjacent elements, and the initial spacing of the rearmost two elements, we can design a complete LPDA. The design will include a transmission line between elements that undergoes a single half-twist at each new element working from the forward feedpoint to the rear. The line partly determines the antenna's properties and also the feedpoint impedance, which will be close to resonant in adequate designs. In fact, the antenna falls into a class of antenna called frequency-independent antennas. However, practical LPDAs set upper and lower frequency limits in normal applications. Entire books exist on the design and properties of LPDAs--and their cousins, the LPMAs. However, this brief overview may suffice to indicate just how much technical detail a very specific antenna label may indicate.

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Now let's become complex again. Many practical designs for LPDAs may add a parasitic director at the forward of the array to raise the gain at the high end of the operating passband without the need for numerous short elements. Sometimes, practical designs will also use a parasitic reflector to aid low-end performance. Now we have a quandary. Is the resulting antenna a supplemented LPDA or something else.

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The "something else" might be a log-cell Yagi, as illustrated in Fig. 18. In this antenna, we find a driver section that answers to LPDA rules, plus a pair of parasitic elements. The driver section usually does not enhance gain, but it can yield an improved front-to-back ratio over a Yagi with a single driver element. Most significantly, the log-cell can broaden the operating bandwidth of the antenna allowing relatively even performance over all of the widest amateur bands, such as 10, 6, and 0.7 meters.

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In fact, we often distinguish between a supplemented LPDA and a log-cell Yagi by reference to the frequency coverage. If the parasitic elements aid performance at very disparate frequencies but are inert for other parts of a wide operating spectrum, then we generally have a supplemented LPDA. If the parasitic elements are effective across the entire passband (usually restricted to a single band, such as 10 or 20 meters), then we have a log-cell Yagi. However, like all separations between labels, the distinction is not absolute. For example, there are pure LPDAs designed for single bands, such as 10 or 6 meters.

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Let's add one final complexity. Fig. 12 showed one sample of a phagi, a Yagi using a pair of phased driver elements. Now we can pose a further fair question: When do we have a phagi and when do we have a log-cell Yagi? The most general answer will die a death of a thousand qualifications. Usually, a true log-cell Yagi will design the driver section using LPDA design procedures. In contrast, most simple phased driver sections tend to find their dimensions experimentally, that is, by trial and error. As well, the phagi driver section might use a common feedpoint with transmission line section going both forward and rearward (with the half-twist only on the rearward section). A true log-cell always places the feedpoint at the forward element in the cell.

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So much for generalities. In practice, the phased driver section of a phagi may result in values that would meet LPDA rules. The log-cell that originates using LPDA design procedures may require modification to meet the needs of the overall log-cell Yagi. In the end, we do not find a sharp dividing line between the two antennas and their labels. Instead, we find only a fuzzy gray area of indeterminacy. Such is the life of labels and names.

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Conclusion--of Sorts

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We certainly might extended our list indefinitely. Among abbreviated antenna names is the DDRR. Antennas named for developers include the Windom, the Beverage, and the Adcock. Geometrically based names include the bi-square and the four square. Common antennas taking their names from various everyday shapes encompass the fishbone and the bazooka, not to mention whips, folded elements in various forms and antenna elements with hats. As the list of labels grows longer, the more we realize just how uninformative most of them are.

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If these notes have a conclusion, it might be in the form of a rule. Antenna labels, when properly used, mask a wealth of information about what the antenna does and how it does it. Labels are not for simple visual recognition, since visual appearance can deceive as often as it enlightens. When you encounter a new (or old) antenna label or name, take time and devote energy to learning everything that you can about the antenna. Only then will the antenna's name become truly meaningful.

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What's in a name? Everything--or nothing at all, depending upon the effort you put into learning about the thing named.

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Updated 12-26-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Tales


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Antenna Newcomers and the Language of Antennas

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L. B. Cebik, W4RNL

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The antenna forums and discussion lists often have occasion to answer inquiries from individuals who are relative newcomers to the study of antennas. As well, many other newcomers "lurk" in the background, reading the stream of questions, notes, and replies, but rarely sending a message.

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Antenna newcomers deserve a hearty welcome, but also some understanding. Most are not EE students using the various information sources as an adjunct to "Antennas 101." Rather, they are individuals who already have embarked on life's journey through work in other areas. They may have become interested in RF communications and now find that antennas are interesting if only because they seem the most mysterious part of the path between the key, computer, or mike on one side and the speaker, headphones, or computer on the other side. The curbs at the edge of the road that signals must cross are the antennas. Still others may already be involved in electronics, but have now been re-assigned to work with antennas--and they cannot remember a word of what happened in "Antennas 101." I have had the good fortune to meet these and many other types of individuals who are relatively new to antennas.

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One of the oldest and worst postures that experienced antenna workers (teachers, engineers, 50-year hams, etc.) can take is the attitude of superiority that says, "I have made it this far. It is up to you to catch up." Rather, we should all be amazed at what the newcomer has to learn just to get started. Let's make a short list of what it takes just to get going in this fascinating arena. We can divide the areas of "getting-started information" into 3 general categories. Our list is strictly practical.

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  • 1. Basic conventions and concepts related to antenna representation;
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  • 2. Some basic concepts applicable to antenna operation; and
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  • 3. Some basic concepts of antenna performance in numerical and graphical form.
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Basic conventions and concepts related to antenna representation

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More experienced antenna workers typically sketch antennas incompletely and casually. For example, the 3 forms of dipole sketching on the left in Fig. 1 have all appeared in these pages. The straight lines are obviously the antenna wire or tubing parts. But what about the center section--the so-called feedpoint?

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Somehow, because no one ever comes right out and says so, the newcomer must realize that the 3 sketches of the same antenna are highly presumptive about the feedpoint. First, we have the transmitting convention: most antenna parts go by names based on the antenna's use as a transmitting transducer, one that transforms RF (AC) energy into ever-expanding electromagnetic fields. Hence, we call the terminals the feedpoint to indicate that we are supplied with energy from a source (which always has a series resistance or impedance). We forget to footnote the name with the fact that the antenna works the other way around as well, intercepting electromagnetic fields and converting that energy into RF electrical energy. The device using that energy forms a load resistance or impedance for the antenna as a source.

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We also generally fail to mention to newcomers that we have at least 2 ways to handle the antenna's source and its load. We can place the transmitter and/or the receiver directly at the antenna terminals, or we can remotely site the source and/or the load and use a transmission line to connect the two. Of course, the moment we mention a transmission line, we are into one of the mysteries of antennas that takes a longer time to bring into the light. Since we are just getting started in the area of antennas, we can simply think about the sloping antenna that we throw up during amateur field operations, or the collapsible whip on the FM receiver (or 2-m transceiver), to imagine how we may connect the source or the load directly to the antenna.

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We also presume that newcomers can automatically and correctly read our conventional representation of the antenna's terminal impedance, whether resonant, inductively reactive, or capacitively reactive. The left part of Fig. 2 shows how we conventionally draw the situation for an antenna with an inductively reactive terminal impedance.

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The right side of the figure redraws the terminal situation for a balanced dipole antenna and for a single-ended monopole termination. Many newcomers only much later realize that the dipole drawing is as legitimate a representation as the monopole sketch. For the dipole, we can show half the resistance and half the reactance on each of the two balanced terminals, since the antenna terminals are in series with the source or the load. If one of the two terminals connects to ground, then we may use the single-ended form. The sketches also show the way we handle reactance at the antenna terminals in the most usual cases. We compensate with an equal reactance of the opposite type. However, if we must also transform the resistive component to effect a match, then we enter another set of mysteries called networks (or more casually, antenna tuners). This arena is also one that takes time to master.

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A perennial question that arises from antenna newcomers--especially those trying to build an antenna based upon an article they have read--is the gap between the terminals. How big or small should the gap be? Do we add the gap size to the antenna element length or is it included in the length? Fig. 3 illustrates the problem and part of the solution.

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Except under direct interrogation, no one tells the newcomer that the smallest gap should be just wide enough to keep the half-elements from shorting together. But wider gaps will do, with due attention to frequency. On 80 meters, a foot-wide gap is fine, but at VHF, we want the smallest practical gap--perhaps as wide as the spacing of the conductors of the transmission line connected to the terminals. At lower frequencies, where the gap is wider than the transmission-line conductor spacing, the leads from the line to the terminals of the element become part of the element. There are limits to gap size at any frequency, but generally, the size of the gap has no effect on the element length from tip-to-tip.

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These sample quandaries reflect the types of questions that newcomers often have (and are almost as often afraid to ask) about the casual and conventional ways in which we sketch antennas. There are others, but we should look at a few ideas involving basic antenna operation.

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Some basic concepts applicable to antenna operation

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If a newcomer asks how a dipole really operates, some respondents will send the individual to a basic college text for a "review" of Maxwell's Laws, Poynting Vectors, and the entire theoretical foundations of antenna theory. (At least an equal number of others will either admit that they do not know or provide a smoke screen of odds and ends to cover up that fact.) What we often forget is that the newcomer--if not in an EE class--may simply be looking for a reasonably accurate way to visualize the operation in order to develop some rational expectations of antennas and some foundation for understanding what appears in mid-level articles and handbooks. Something as simple as the sketch in Fig. 4, adapted from many texts, may do the basic job. It may also leave room for the individual to move at personal speed both back to the fundamentals and forward to the construction project.

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When the question-and-answer session is informal, we can stress only a few points and still get across the basic ideas. First, the concentration of charges is an instantaneous phenomenon, with polarity shifts in tune with the operating frequency. However, the concentration tells us why the ends of a wire antenna can be dangerous to anyone touching them during a transmission. Second, the current curve is a standing wave. If the antenna is a dipole, then the peak current occurs at the center of the element, right at the terminals. Third, the sketch omits the source's series resistance, which we assume is matched to the impedance of the dipole at its terminals, however long the dipole might be. Fourth, a true dipole can never be longer than 1/2 wavelength electrically, since if it grows longer, then current peaks occur on either side of the center point and not at the center. (This is a good time to remind the newcomer about how antenna terminology is often thrown about casually, so that we often name as a "dipole" almost any center-fed antenna.) Finally, we can enter into a discussion of the relationship between the center-fed wire's length and the terminal impedance conditions.

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There is much more that we can reasonably say without ever introducing an equation, and it may all be helpful in developing reasonable expectations about antennas. Equations are also good, but only if the student is ready for them. However, we can also illustrate what we say. A well-wrought experiment is ideal, but usually the questions arise when we are not close to our materials and test equipment. However, if we have some modeling software, we can show the student what he or she needs to see. The materials in Fig. 5 show especially the current magnitude and phase of the current standing wave on a resonant half wavelength dipole when it is transmitting or radiating.

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The particular set of diagrams happens to come from EZNEC. Other software may represent current in a similar way or the software may use a color coding to represent the maximum and minimum levels. Either technique can be equally effective in answering basic question, so long as the individual understands the conventions of the representation.

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The transmitting situation of the current on a dipole is fairly easy to represent, since the model is simple. This one happens to be in free space, so everything is very nicely symmetrical about the antenna terminals. Actually, we can also represent the current situation on a receiving antenna with fair ease. Simply start with the transmitting antenna. Then create an identical dipole about a mile away. Do not forget to provide the receiving antenna with a load that is equal to its resonant impedance. After you run the model, examine the currents on the receiving antenna. You likely will see a current magnitude and phase angle curve like the one in Fig. 6.

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You can actually go into a good bit of detail here based on the modeling data. For example, if you look at the current calculation tables, you will find that the ratio of current magnitude between the tips and the center of both antennas is the same. This may also be a good time to open the question of aligned and cross polarization between linear antennas. All you have to do is change the axis along which you create either the transmitting or the receiving antenna. (Actually, the demonstration is most effective when you conduct it both ways.)

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From this point, you can go in many directions. Usually, you will have to lead the newcomer to the right questions to ask. For example, what happens to the current along the wire if we make the wire longer, longer yet, and exceptionally long? Is there any regularity not only to the current curves but also to the development of lobes? (Here you may be in for a long session on the operation of a multi-band center-fed antenna, perhaps an 80-meter dipole operated on 10 meters, for example.) Are there ways to control the current phase along a center-fed wire that is very long? Suddenly you are working with collinear arrays. Why must the antenna be center-fed? How do lobes develop if we feed the wire at its end when it is multiple wavelengths long. Finally (for the moment), here is the best question: how is a vertical monopole like a dipole and how is it different?

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One well-placed question leads to others. Education of newcomers lies in the questions, not just the answers. To further the process, every answer should lead to the next question(s).

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Some basic concepts of antenna performance in numerical and graphical form

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Although we might have continued the questions that arose from the simple dipole demonstration, we cannot forget that our goal is to orient the newcomer to read with understanding. The dipole discussion has already led us to look at antenna patterns and use terms like "polarization." These terms are part of a third cluster of ideas that a newcomer must naturalize: the conventions and concepts used to represent antenna performance.

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Today, we tend to use graphical representations of antenna performance as much or more than numerical reports. Nevertheless, both rest upon measuring or calculating the far-field radiation pattern produced by the antenna (among other things). In turn, these patterns rest on some fundamental ideas that relate the antenna to its environment.

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The most fundamental environment for an antenna is free-space, a limitless region in all possible directions with no up or down, since it lacks any references to make sense of these notions. Hence, we must use the antenna itself as a reference. Antennas with linear elements are handy in this regard, because we can distinguish an E-plane and an H-plane, as shown at the top left in Fig. 7.

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The E-plane is the plane of the antenna's electric field--the one of greatest importance to the far field--which occurs in a plane parallel to the axis of the element. As shown at the top right, a simple dipole has an indefinitely large number of possible E-planes. However, we tend to use the one that parallels the E-plane of flat multi-element arrays. The antenna's H-plane occurs at right angles to the element in alignment with the magnetic field. At the lower left in Fig. 7 is the E-plane and the H-plane far-field radiation pattern for a typical 3-element Yagi. We may note that the two fields touch at the forward-most point of the pattern and again at the rear-most point. We should also note that the E-plane and the H-plane patterns have different shapes.

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When we place the antenna over ground, say 1 wavelength above ground, our orientation changes. Now the ground and the pattern behavior together determine how we handle the performance representation. Instead of an H-plane pattern, we have an elevation pattern. Note the formation of elevation lobes and nulls that derive from the combining of the direct or incident waves from the antenna and from the ground reflections that may add or subtract from the incident waves. We call the elevation angle above the horizon where the radiation is strongest or the gain is the highest the take-off (TO) angle. In this case, the angle is 14 degrees.

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The pattern that circles the antenna is the azimuth pattern. The pattern corresponds in this case to the E-plane pattern of the free-space situation. Since the plane of the elements is horizontal relative to ground, and since all of the elements are linear, we can also say that the antenna is horizontally polarized. However, if we had set up the antenna with the elements vertical with respect to ground, we would take the azimuth pattern that corresponds to the H-plane pattern of the free-space situation. As well, the antenna is now vertically polarized.

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We do not take the azimuth pattern at the level of the horizon. Instead, we normally take the pattern at a higher angle, most usually the TO elevation angle, although we may use other elevation angles as the need arises. The azimuth pattern actually forms a conical section from the origin of the system with a 14-degree angle. With such low angles, transferring that conical section to a flat graph causes negligible distortion, but at very high angles, the distortion may be considerable.

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The more complex the patterns, the more parts we have to consider, and every part has two aspects: a name and some associated numbers. The top section of Fig. 8 shows some of the parts of the typical azimuth pattern. This pattern is laid out on a circular grid. The angular notations are clear. The pattern strength numbers of the various rings may be less clear initially. This pattern uses a logarithmic ring scale. Other patterns may use a linear scale. Proponents of linear scales believe that they show pattern detail more realistically, but they do require that the user determine a minimum gain value for the innermost ring. In contrast, the log scale is uniform from one application to another.

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The pattern is also normalized. To normalize a pattern, we set the gain of the outer ring to the maximum gain of the antenna. All other parts of the pattern show how much weaker the gain is relative to maximum gain. To find out the maximum gain, we must consult the numerical data. For our pattern, the maximum gain is about 12 dBi. A dB is 10 times the common log of the ratio of any two powers in the same units. We generally record gain vales in dB relative to some standard antenna, either real or theoretical. The most common standard today is the gain in decibels above an isotropic source, that is, one that radiates equally well in free space in every possible direction. A few decades ago, most amateur antenna articles showed the gain in dBd, the gain over a free-space dipole. By definition, a free-space ideal dipole has a gain of 2.15 dBi. So the two measures are supposedly interchangeable. The use of dBi prevents confusion over whether a gain recorded in dBd is the gain of a free-space dipole or the gain of a real test dipole in the same position as the antenna being considered. When we encounter a gain in dB with no reference, we know that some comparison is being made, perhaps between two antennas. (If the gain value in "bare" dB appears in an advertisement, then we know to be suspicious.)

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Every lobe of interest in a radiation pattern has a beamwidth. We are generally interested in the main forward lobe of directional antennas, although other lobes may interest us for special reasons. We conventionally define the beamwidth in degrees between points on the pattern that show half the power of the point of maximum gain. Half the power means -3 dB. For a maximum gain of 12 dBi, the beamwidth is the angle between points on the lobe where the gain is 9 dBi. Note that I have been referring to the main forward lobe and not simply to the forward lobe. Although this pattern has only one forward lobe, many antennas have secondary lobes in the generally forward direction.

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The rear quadrants are especially interesting. The present antenna shows 3 rearward lobes; other antennas may shows from 1 to very many lobes. We call the ratio of power gains in the forward direction and the rear direction the front-to-back ratio. However, there are numerous ways to obtain the ratio and multiple names for some ways. If we take a bearing 180 degrees opposite the bearing of the strongest forward gain, then we have the 180-degree front-to-back ratio. In some cases, the 180-degree direction does not show the strongest rearward lobe. We can also compare the gain of the forward lobe with the strongest rearward lobe and arrive at a worst-case front-to-back ratio (which some call the front-to-rear ratio). More commonly, the front-to-rear ratio averages all of the gain values in the rearward quadrants and compares that value with the forward gain. (But some call this value an average front-to-back value.) The lesson is to obtain not only the numbers, but also the foundation for those numbers before reaching any conclusions about antenna performance.

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The elevation pattern, shown at the bottom of Fig. 8, also uses a log ring scale and it also has parts. Here, I have changed the antenna to a vertical dipole with its center point (or terminals) 1/4 wavelength above ground. The elevation patterns shows a stronger lower lobe with a TO angle. This lobe has a vertical beamwidth that rests on the same half-power points that we used to obtain the azimuth pattern beamwidth. The vertical beamwidth gives us an idea of over what range of propagation angles the antenna may be effective.

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Compare the elevation pattern in this figure for a vertical dipole with the outline of the elevation pattern for the horizontal Yagi in Fig. 7. Although horizontal antennas produce distinct lobes and nulls based mostly on the height of the antenna above ground, vertical antenna below a few wavelengths above ground are less orderly in the development of secondary elevation lobes. The higher-angle lobe of the vertical dipole has only a shallow null between it and the lower main lobe. In some cases, the two lobes may merge and obscure just where the null should be.

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Although I shall not add them here, we may graph almost any data about antenna performance on rectangular graphs. Even the pattern data is apt for such treatment. More usually, we find rectangular graphs that show important performance information over a spread of frequencies or a "sweep." We might graph over the selected frequencies such data as the maximum forward gain, the TO angle, the front-to-back ratio, the strength of any forward sidelobes, the feedpoint impedance, or the SWR relative to a standard, such as 50 Ohms.

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Conclusion

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These brief notes only scratch the surface of the basic concepts and conventions that the newcomer to antennas must eventually master to appreciate fully the great mass of literature that is available. Nothing here is at all complete or adequate. I have only said enough to indicate the importance of some of the ideas, terms, conventions, and representations. I have not presented any kind of cohesive treatise. Still, we can note that nomenclature and conventions interweave with substantive antenna operation basics, so that to learn one is to learn the other. Learning to talk rightly is one step toward learning to talk sensibly.

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Indeed, when I look even at this truncated list of terms and conventions applicable to antennas, I am somewhat surprised that any newcomer does master them. But they do! The learning curve is longer or shorter, depending upon the help available and the impediments to learning that abound in some quarters. Readers of amateur journals and participants in the discussions have access to expert assistance, even for basic matters. Remember that all of the expert assistance available from the experienced antenna workers comes from folks who once upon a time were also newcomers. At one time or another, we have all had the same basic questions to ask--and have hesitated to ask them, lest we look ignorant. However, there is only one bad question, and that is the one that goes unasked.

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Antennas are less a problem than they are a challenge. For many the challenge is fascinating, an endless field of things to be learned. In a sense, we are all newcomers to what has yet to be discovered.

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Updated 06-15-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Everything Old Is New Again

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L. B. Cebik, W4RNL

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Sometimes an old article in a ham magazine shows you that some of your finest achievements are only extensions of much older work. That lesson came home to me in an article (actually, 2 articles in one) in QST for October, 1937. Peter Dodd, G3LPO called my attention to the piece, because it had a forerunner of the VK2ABQ square. Actually, the articles had a lot more.

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The composite article, called "Concentrated Directional Antennas for Transmission and Reception," (pp. 27-30), was put together because "Rhombics and multiple arrays of conventional form give high gains--but even for the 14-Mc band, they take considerably more yardage than most of us have available. Therefore, concentrated directional systems which are more readily fitted into the usual back yard have a distinct appeal. . .." It is interesting that the editor chose to call these small and possibly directional antennas "concentrated." The term conjures many images, although nothing clearly electronic. Such imagery--sometimes useful, sometimes misleading--was more common in the 1930s than it is today.

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The second thread that connects the two articles is that the first is by John L. Reinartz, W1QP. The second is by Dr. Burton T. Simpson, W8CPC, based on some suggestions made to him by Reinartz.

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The Half-Wavelength Loop

Reinartz writes on "Half-Wavelength Loop Antennas." One of his basic designs is a square, 1/8 wl on a side. The square is open for the feedline in the middle of one edge, and in the middle of the opposite edge is a gap. Reinartz analyzes the antenna to have a low feedpoint impedance, and uses 72-Ohm line to feed it. The basic design appears in Figure 1. +
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Interestingly enough, in another notebook item in this collection, The IL-ZX Antenna for 40 Meters, I presented a compact loop of intermediate size. The major difference between the Reinartz design and the one in my notes is the use of a double winding. The double IL-ZX winding acts as an impedance transformer to raise the very low loop impedance to coax levels. The double loop, if brought to something of a point on each side of the gap, permits easier antenna adjustment for resonance.

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Nonetheless, it is good to know where (or perhaps only approximately where) the design had its start. The field strength noted by W1QP is recorded as "about 28%, as compared to a straight half-wave dipole." The double loop shows a better performance level, being down from a modeled free space dipole by only about 1.1 dB and just a little more than that when set up near ground as a vertically polarized antenna. Since it is not possible to devise a perfectly comparable placement vertically over ground for both the loop and a linear dipole, gain comparisons are elusive. The antenna shows about a 4 dB front-to-side ratio, but not more than about 0.1 dB front-to-back. Reinartz believed he got a significantly higher front-to-back ratio, which I have not been able to replicate in models.

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In 1937, the typical amateur station tuned both the antenna and the rig together, adjusting the antenna and the coupling to the final tank (parallel tuned) circuit simultaneously. The era of fixed or even narrow range of output impedances for transmitters had yet to emerge. Further adjustment of the impedance match involved simply widening the feedpoint gap, which provided spread the feedline and increased its impedance at the antenna terminals. Hence, determining the actual operating conditions of the W1QP 1/2 wl loop is nearly impossible without further precision in the account. However, such precision, even if available, would have been spurious to the ordinary ham of the era, since the means of achieving maximum power output without exceeding (catastrophically) the plate current ratings of the final amplifier tubes varied considerably among stations.

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Finding the origins of one antenna design is a nice day's work. Finding two is serendipity.

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The 1-Wavelength Square

Between the work of Fred Caton, VK2ABQ, and recent developments employing its offspring, the (Les) Moxon (G6XN) rectangle, there is a continuity. (Some minor improvements appear in other notes of this collection, for example, Moxon Rectangles for 40-10 Meters and An Aluminum Moxon Rectangle for 10-Meters. However, as Peter Dodd has pointed out in the 2nd edition of his Antenna Experimenter's Guide (pp. 99-100), there is a more distant predecessor, "A Square 'Signal Squirter' for 14 Mc." W8CPC credits W1QP for the suggestions that led to his proto-VK2ABQ square. The basic suggestion was that most of the radiation from a standard 1/2 wl dipole emerges from the center half of the antenna wire. The lower current end portions might be bent back with little loss. +

The expression "signal squirter" seems today to be almost baby talk. However, in the 1930s. new operators were often called "young squirts," not just because many were very young (which is incidentally true), but because they were new to the game of "squirting" RF around the world. Imagistically, the rig and antenna formed the world's most perfect atomizer, with a mist finer than any perfumer ever dared dream. Note how easy it is to get carried away by the everyday metaphors of 1930s amateur radio.

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The Simpson electrical design is shown in Figure 2. We can bypass the extensive reinforced and rotatable wooden square on which the antenna turned.

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Simpson specifies a spacing of 16' 6" from front to back, and the wood frame he used, bristling with ceramic insulators to support the 1/4" diameter copper tubing suggest a similar dimension side-to-side. What affect the many metal reinforcement plates had on antenna performance is impossible to tell at this distance.

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Like the VK2ABQ square, the W8CPC antenna separates two folded-back dipoles with a small end gap. The tubing ends were 18" apart, but each end had a brass rod insert to adjust the gap. Tuning up the antenna involved simultaneous adjustments to both the transmitter and antenna, using an RF ammeter across a temporary gap in the reflector. Again, the feedpoint gap was fairly large by current standards, allowing a variable length spread in the feeders as an aid to matching--where matching means maximum power transfer to the antenna. In this case, the transfer was measured in terms of reflector element current levels. When tune-up was complete, another brass rod closed the gap left by removing the RF meter.

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Having modeled a number of VK2ABQ designs, I am aware of the critical nature of the gap in the end of the two elements. There are actually two gap settings that provide forward gain and a front-to-back ratio. The narrower gap provides more gain but what we would today consider mediocre front-to-back ratio, while a much wider gap provides a current on the reflector that is nearly perfect in magnitude and phase to yield a maximum rear null (>30 dB), but at the cost of over a dB of gain. (Similar results accrue to the Moxon rectangle, but with considerably greater ease of finding the right dimensions to use with no post-assembly adjustment required.)

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The gap required for a maximum front-to-back ratio exceeds by a wide margin the range of adjustment available in the W8CPC design. Hence, I have to conclude that he adjusted his antenna for a quite narrow gap, something close to 1". The trick is the position of the gap. Using a 16' 6" square, one can terminate the driver 4" forward of the side-to-side center line. If the reflector is then brought within an inch of the driver, the loop can yield about 5.1 dB forward gain and about 5.0 dB front-to-back ratio. If the same gap size is transferred to the 8.5 and 7.5 inch positions, the gain drops to about 4.7 dB, but the front-to-back ratio exceeds 8.0 dB. This is about the maximum movement forward of the center-line within the +/-9" range of adjustability in the antenna. For both cases, the source impedance is less than 150 Ohms, considered low in those days, and both settings are within 18 Ohms reactance of resonance at the target frequency.

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I cannot be certain that my models have captured the Simpson design exactly, especially in view of his claim of about a 7 S-unit difference in a DX report of his signal forward and reverse. However, they are indicative of the kind of performance that might be typically achieved by the antenna type. The numbers from these models are consistent with models of the 1" coat-button spaced wire antennas in the VK2ABQ collection. Clearly, the Simpson square is a close match to the VK2ABQ squares, apparently without direct lineal connection. And it follows that all contemporary variations on the square and the folded-back rectangle share a common root going back at least to 1937.

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Appreciation of the Past

Am I finished with these antenna designs from the past? Not completely. If nothing else, there is that elusive front-to-back ratio claimed by both authors. So far I have not been able to reproduce it an models. Rather than conclude hastily that it is not there, I prefer to think that perhaps there are more models to try. If I find anything, I shall certainly add the results to this note. +

Some antenna designers and analysts might be disturbed--even discouraged--by the discovery that their seemingly new offspring are intimately related to designs of the more distant past. I do not share that view. Instead, I am happy to pay homage to past work and to grow in my appreciation of how well basic design principles were known 6 decades ago. The 1930s comprise a fertile decade for design thinking in antennas, and vast strides were made in pressing wire antennas to their limits.

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It would take the 1980s and 1990s to yield new techniques of software to allow some of the older design principles to be implemented with assured performance. Moreover, new ground is being broken daily in antenna design. However, we should not let contemporary development rates lead to the impression that "they knew hardly anything back then." They knew a very great deal--and developed ingenious ways of making it work in the absence of the complex antenna analyzers and other test equipment we have at our disposal today.

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It is no slur against current design and analysis efforts to suggest that they mostly carry out the details of principles long known. Those details are crucial to making antennas perform to the peaks that the principles promised but that older measurement and calculation limitations could not assure. (One might get a sense of the importance of recent developments by asking when the 1920s work of Yagi and Uda started yielding really good antenna designs instead of really good antenna claims.) Perfecting the implementation of basic principles is a worthy enterprise in any era.

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At the same time, new principles and techniques are also emerging today. Someday, they will be the more distant past to which we look with admiration. But at just this moment, October, 1937, will do as a past worth at least my own appreciation.

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I want to thank W6TOY, W6ZH, W3/V31FA, and KE6RIE, all of whom came to my rescue in locating a copy of these studies. Several of these gentlemen expressed the hope that I could do something good with the articles. However, it is truer to say that the articles did something good for me.

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Updated 10-28-1998, 10-28-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Historical Q Signals

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L. B. Cebik, W4RNL

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For those who have an interest in history or who are building a time machine, here are the international communications Q-signals from the 1930 American Radio Relay League Handbook.

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1930 ARRL Handbook Q-Signal List (pp. 198-200)

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+ Meanings abbreviated. With ?, = question; without = statement +
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Q-SignalExplanation
QRAName of station
QRBApproximate distance from your station to mine
QRCAccounts for charges to station liquidated by xxx private company
QRDWhere are you going; I am going to xxx
QRENationality of station
QRFWhere do you come from; I come from xxx
QRGYour exact wavelength in meters or frequency in kilocycles
QRHMy exact wavelength of frequency
QRIIs my tone bad; my tone is bad
QRJCannot receive you, signals too weak
QRKReceive you well, signals good
QRLAre you busy; I am busy
QRMBeing interfered with
QRNTroubled by atmospherics
QROIncrease power
QRPDecrease power
QRQSend faster
QRSSend more slowly
QRTStop sending
QRUHave you anything for me; I have nothing for you
QRVSend series of Vs
QRWAdvise xxx that I am calling him
QRXMust I wait; wait!
QRYWhich is my turn; your turn is xxx
QRZWho is calling me; you a being called by xxx
QSAStrength of signal (1-5)
QSBStrength of signal varies
QSCSignal disappears entirely at intervals
QSDIs my keying bad; keying is bad
QSESignals distinct? Signals run together
QSFAutomatic transmission good? Automatic transmission fades out
QSGTransmit telegrams by series of 5, 10, or xx
QSHSend telegram one at a time
QSISend telegrams in alternate order without repetitions
QSJCharge to be collected per word
QSKSuspend traffic and call again at (time)
QSLAcknowledgement of receipt
QSMReceived acknowledgement of receipt
QSNCan you receive me now; cannot receive you now
QSOCan you/I can communicate with xxx
QSPRelay free of charge
QSQSend each word or group once
QSRDistress call from xxx has been attended to by yyy
QSUSend on xxx meters (kilocycles) waves of Type A1, A2, A3, or B
QSVShift to wave of xxx meters (kilocycles) for rest of communications
QSWI will send on xxx meters (kilocycles) waves of Type A1, A2, A3, or B
QSXWavelength (frequency) varies
QSYSend on xxx meters (kilocycles) without changing type of wave
QSZSend each word or group twice
QTACancel telegram # xxx if not yet sent
QTBAgree with word count? I do not agree with word count
QTCNumber of telegrams sent
QTDWord count that you are confirming is accepted
QTETrue bearing is xxx degrees
QTFPosition of your station based on bearings is xxx
QTG1 minute call signal for radio compass bearings
QTHPosition in latitude/longitude (or any other indication)
QTITrue course
QTJSpeed in knots
QTKTrue bearing relative to me is xxx degrees
QTLSending signals to permit bearing with respect to the radio beacon
QTMSending radio and submarine sound signals to permit bearing and distance
QTNCannot take bearing of your station
QTPGoing to enter dock or port
QTRExact time
QTSTrue bearing of my station relative to you
QTUStation open from xxx to yyy (times)
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The 1930's list from the American Radio Relay League Handbook is only a partial listing of Q-signals, even at that early date. Like lists in more current ARRL handbooks and operating manuals, the 1930 list contains only those signals thought to be of most use to radio amateurs.

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A later (world War II) listing is fairly common among CW fans. My copy of the Combined Operating Signals, a joint U.S.-British production, dates from 1944 and contains only Q-signals, omitting the Z- series and, of course, ARRL's later N- series. My thanks to VE3DNY for sending me a photocopy. Virtually the entire set of combinations appears, with only a few left blank for future use. Each signal is listed twice: once on a left-hand alphabetical listing page and again on a right-hand topical page. The system begins to fold back upon itself. For example, QQP means "Check correctness of last QDR given." This is opaque unless one knows that QDR means "Your magnetic bearing in relation to me is xxx." However opaque the system may seem, the document contains the following warning: "These operating signals possess no security and must be regarded as equivalent to plain language. This must be borne in mind by all users and great care must be taken to avoid giving away information of value to the enemy." The enemy that the authors of the manual had in mind was NOT users of telephony in any of its forms or even non-hams.

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Updated 02-10-1998, 01-08-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ + diff --git a/content/tales/rem.html b/content/tales/rem.html new file mode 100644 index 0000000..5cfd99d --- /dev/null +++ b/content/tales/rem.html @@ -0,0 +1,39 @@ + + + + + + A Time to Reminisce + + + +
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A Time to Reminisce
+ (Christmas, 1997)

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L. B. Cebik, W4RNL

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+ When I was very young and could tell a flea from a gnat with my bare eyes, they gave me radio components that I could hold in my hands and from which I could build a super-regenerative 10-meter receiver and squeeze out a little 10-meter power by adding another multiplier after the crystal oscillator. +

The next time I looked, I could barely distinguish without glasses a mole from a vole from a mouse, and they gave me transistors to hold with my needle-nose pliers when soldering and reminded me that I still needed to neutralize my 10-meter finals.

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Now that I can just barely tell a horse from a camel even wearing my glasses, they give me parts to hold with tweezers while plugging them into circuit board holes smaller than human hairs and offer me complete 10-meter rigs that fit in my hand.

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I do not know which I miss more: those big warm parts or those good eyes. Thank goodness 10-meter operators have not changed much over the years-- still the best part and heart of hamming. And if they happen to be running CW QRP from a hilltop, then my heart runs warm, even if the parts run cool.
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Updated 2-21-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. This item first appeared on TENTEN-L and in The County Line RoadRunner Feb, 1998.
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The RST Standard of Reporting

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L. B. Cebik, W4RNL

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Part 1: The RST System Itself

The RST (Readability-Strength-Tone) system of reporting with which we are all familiar (or are we?) goes back to 1934. The S-meter name was derived from the S in RST. Before (and for some time after) that, receiver meters were sometimes called R-meters (and sometimes just "signal" meters) after an earlier system proposed for amateur use and terminated at either 5 or 9. The difference in the 2 scales results directly from the change brought about in the standard RST report system between 1925 and 1936. These vacuum-tube voltmeters inside the receiver were used as much to align the receiver as to determine the strength of incoming signals. +

Most S-meters were and are still a derivative function of AGC (called AVC by many in those days) and thus cannot exactly parallel the RST system. Few S-meter circuits are able to meet the proposed standard of S9=50 microvolts, with each S-unit equaling a 6 dB reduction from that level. The more signal processing we insert before the detection of a voltage roughly corresponding to signal strength, the more troubles we encounter with the accuracy of the system. Moreover, receiver gain distribution tends to vary from band to band (which is why QST product reviews rate sensitivity on various bands). Hence, the standard proposed in the early 1940s was never adopted by manufacturer's, even though S-meters are given printed scales as if the system were universal.

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Between S1 and S9, a well-calibrated meter can provide a reasonable indication of signal strength that parallels the original RST system. In contrast, S9+40 is a sort of meaningless extra in conversation relative to the system. It is extraneous precision for the term "extremely strong signals" on an electronic system (the receiver) that has been shown time and time again to be quite imprecise. Hence, S9+40 is almost the SSB equivalent of Dave's World talk--and of a world where the thing rules the operator rather than the operator ruling the thing (the meter).

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Unfortunately, few if any transceivers have well-calibrated S-meters. For a review of the performance of some recent transceivers, see the website of Greg Ordy, W8WWV www.seed-solutions.com/gregordy/ (web.archive.org) and look at two special items: "S Meter Blues" and "S Meter Lite." The latter is an attempt to overcome transceiver S-meter limitations with better-calibrated software.

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The only way for the meter to be precisely in tune with the RST reporting system at the low end is to have S1 as the left needle rest marking. Then, you give S1 if you can hear the non-needle mover and give nothing if you cannot hear him. If S1=a certain number of microvolts of signal strength, the needle does not move until there is that number +1 (or +.001, etc.). Everything else that is lower is still S1. Or it is silence, since a person cannot give a report to a station he does not hear (nets and contests not included). This means of meter calibration would make the meter again partially track the RST standard.

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If we turn the question around and require that the reporting system parallel the action of meters, then we need a new standard by which to report. The RST system of reporting is a standard and was developed to be a standard. It is not and was never intended to be a large collection of individual interpretations and inventions. Rather, it is a standard agreed upon and promulgated to everyone for standard use, in essence, an ITU standard paralleling all those used in physics and electronics that have been agreed upon by recognized bodies representative of all users.

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Until a new standard exists, the current standard places the RST system ahead of meter readings and "S" runs from 1 to 9. Those who insist upon putting their own revisions into practice--however widespread--only create confusion--like inventing a new set of meanings for voltage, current, and resistance such that E=2IR: quite possible, but confusing to casual readers.

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A following notes may form some historical background to my comments concerning RST as a standard.

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The earliest system of signal reporting emerged from the Q-signal system and included QSA (signal strength). In the May, 1925, issue of QSI, we find in the back pages (specifically, page 63, following correspondence) the following note.

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+ It has been suggested that the R system of indicating audibility be used instead of the ineffective QSA-QRZ-QRK arrangement in practice now. This has been suggested by a number of correspondents and isundoubtedly an improvement so the list is given below. Hang it by your set and make use of it.
+ R1--Faint signals, just audible.
+ R2--Weak signals, barely readable.
+ R3--Weak signals, but readable.
+ R4--Fair signals, easily readable.
+ R5--Moderately strong signals.
+ R6--Strong signals.
+ R7--Good strong signals. Would be readable through heavy QRN and QRM.
+ R8--Very strong signals. Several feel-from-phones stuff.
+ R9--Extremely strong signals. +
+

From the QST text, it is clear that the R-system existed informally and for some time before this mention by ARRL. From this system emetged the ealiest reference to signal strengh meters as R-meters. The system is not the full RST system that was soon to emerge.

+

In the 1930 ARRL Handbook, there is no mention of RST. Rather, the standard log page shows reference to QSA (Strength of signals on a scale of 1 to 5) and tone, given as a set of remarks (pp. 195-96). An alternative to the word "tone" was QRI? ("Is my tone bad?" as if the expected reply would be "yes.") Q-signals were the universal means of conveying complex questions and information quickly in early radio, augmented by the Phillips code, Navy signals, and a few other sources.

+

The 1936 ARRL Handbook (the next in my collection) reports (p. 323) that the basic version of the modern (?) RST system was proposed in 1934 by W2BSR. (See Arthur M. Braaten, W2BSR, "A New Standard System of Reporting signals," QST, (October, 1934), pages 18, 19, 106, 108.) Braaten's article followed a piece in August, 1934, by D. C. Redgrave, KA1NA, that emphasized the need for a change in the reporting of signals due to inconsistencies of usage. His proposal ("FRAME") was far more complicated than the W2BSR proposal. The original RST system used a 559 scale to preserve the QSA range. "T" was very detailed, since the achievement of a "Purest d.c. note" was a function of many factors, including poor or nonexistent power supply filtration and what was then known as musical modulation and whistle. A recent article in Funkamateur shows a pair of QSL cards from W2BSR, a 1934 version using QSA and a 1935 update using RST. See Wolf Harrath, OE1WHC, "Wie gut, wie stark, wie rein? 72 Jahre RST-System," Funkamateur, (November, 2006), pages 1260-1262. Braaten's original set of signal strength categories were as follows (from page 19 of the QST article). Compare the categories to those appearing in the tables later in these note.

+
+ Signal Strength
+ 1. Faint--signals barely perceptible
+ 2. Weak signals
+ 3. Fairly good signals
+ 4. Good signals
+ 5. Very strong signals +
+

ARRL enthusiatically adopted the RST system of signal reporting as "logical and brief," not to mention "increasingly satisfying as you keep using it" (from the prologue to the Braaten article by ARRL's Communication Manager).

+

"Some time later," W2BSR made a second proposal to expand the strength scale to 1 to 9 to accommodate finer gradations of perceived signal strength. (This step must have occurred either late in 1934 or early in 1935, since the copyright date of the '36 Handbook is October, 1935.) In 1936, an RST followed by "X" for the appearance of crystal control (for frequency stability) already existed, but there is no mention of "K" for key clicks is given. The 1947 Handbook adds "C" for chirp (p. 466), while retaining the 1936 meaning for the T-numbers. By 1952 the "K" appears, but the RST system had become such a standard part of amateur operations, that the editors moved the chart to the "Miscellaneous Data" chapter without any accompanying textual comment (p. 547).

+

To receive a report in 1936, one sent "RST?" or "QRK?" ("Are you receiving me well?") RST was an evolving standard, and reports were not yet sent by everyone as part of the first exchange. The '36 Handbook refers to the RST system as "the present standard recommended for your use" (p. 323).

+

Between 1936 and 1995, the meanings of the 5 R-numbers and the 9 S-numbers did not change. Sometime between 1970 and 1978 (the space between Handbooks in my collection), the T-numbers took on their current meanings. The T-scale was altered in wording to reflect changing problems in achieving pure CW. In the 30s, T represented what the ham constructor had achieved. In modern times, it largely indicates a malfunction of some stage in a transmitter. T-6 now means "Filtered tone, definite trace of ripple modulation." Between 1934 and the early 70s, it was interpreted as "Modulated note, slight trace of whistle." See the accompanying table for further details on "T" and a reminder of the meanings of the rest of the numbers.
+

+
+

Table. 1. The RST system in 1936 and in 1995.

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ R: Same in '36 and '95 +
+ 		+
+ S: Same in '36 and '95 +
+
1 Unreadable1 Faint signals, barely perceptible
2 Barely readable, occasional words distinguishable2 Very weak signals
3 Readable with considerably difficulty3 Weak signals
4 Readable with practically no difficulty4 Fair signals
5 Perfectly readable5 Fairly good signals
6 Good signals
7 Moderately strong signals
8 Strong signals
9 Extremely strong signals
+
+ T: 1936 +
+ 		+
+ T: 1995 +
+
1 Extremely rough hissing note1 Sixty-cycle ac or less, very rough and broad
2 Very rough a.c. note, no trace of musicality; broad2 Very rough ac, very harsh
3 Rough, low-pitched a.c. note, slightly musical3 Rough ac tone, rectified but not filtered
4 Rather rough a.c. note; moderately musical4 Rough note, some trace of filtering
5 Musically modulated note5 Filtered rectified ac, but strongly ripple-modulated
6 Modulated note, slight trace of whistle6 Filtered tone, definite trace of ripple modulation
7 Near d.c. note, smooth ripple7 Near pure tone, trace of ripple modulation
8 Good d.c. note, just a trace of ripple8 Near perfect tone, slight trace of modulation
9 Purest d.c. note9 Perfect tone, no trace of ripple or modulation of any kind

+
+
+
+

Does the RST standard system of reporting need change? Perhaps "R" is not to be changed, since it represents a measure of readability to the receiving operator. Is "S" a strict measure (a standardized meter reading), a relative measure (based on how signals sound compared to each other on a given occasion with given band conditions), or a subjective measure (of how the receiving operator feels about the incoming signal)? What can "S" be as a standard for the next century? Does "T" need revision, omission, or mention only when the note is other than purest d.c.? Perhaps QRP operators are in the best position to contribute to a revised standard applicable to them or to everyone since they work at power levels where the report is most meaningful.

+

If good QRP practice does require a new standard for RST, then let there be a deliberative body representative of all the QRP organizations, and let this body study the problem, receive input from all interested operators, consider all the aspects of the problem, and develop a new standard. Further, let all QRP organizations making studies, issuing awards, and publishing operating accomplishments formally adopt the new standard and insist that all data input to them be in accord with the new standard. At that time, deviant input must be rejected or revised to meet the new standard.

+

Until then, the de facto standard is that which appears in handbooks and which takes precedence over meters. Until we go through the process of creating a better standard, we can either report in accord with the standard to the best of our operating skill or we can be deviant (or "cool"). If the latter, we owe it to other QRP operators to let them know which we are doing so that operator may discount our report. If the former, then we are committed to applying our best efforts and skills to master the art of reporting uniformly with others who are also committed to the standard. The uniformity cannot be perfect, but it can be reliable.

+

"R" reports may improve as we better master the art of copying CW (or SSB). Recognizing CW signal faults may require much practice in this day and age when almost all rigs produce clean CW. Strength reporting may be the most controversial part of the process. If the RST system is the standard, then the use of meters is an aid to reporting signal strength, but it is not as the standard itself. Should anyone report my signal as S0, I shall stop transmitting, since that is--by the standard--evidence of non-contact, and except for CQ and QST (no, not the magazines), non-contact transmissions except for brief tests and known beacons are not regulatorily approved. If someone gives me an S9+anything, then that is only a cue to reduce power. Only the S9 goes in the logbook/disk.

+

Of course, virtually all BIG contest reports and dx pile-up reports are meaningless. But that fact does not say that QRP operators must adopt the meaningless. They can still adhere to the operative standard for maximum information transferral until such time as a better standard is adopted--if there is one.

+

Anyone care to lead the effort to form an international body to study the question and develop a new standard for the 21st century?

+

Whatever may transpire, I recommend that we always keep the other operator in mind as we use the present RST system for the transferal of the most precise information permitted by the standard. We can always add notes in our own logs for impressions of the band conditions, etc. But as the 1936 Handbook notes, the RST system is a complete and efficient report in its own right to the other operator.

+

The S-Meter System

Although derived from the "S" in "RST" and its preceding Q-signals, the S-meter system of reporting signal strength has taken on a life of its own. Because the system is mathematically derived from a base signal level of S9 that corresponds to a received signal strength that can be measured in micro-volts or in dBm, the S-meter system can give meaning to a report that S is zero--or even below zero. +

When originally proposed, the S-meter system would use 6-dB increments below the base level for each S-level lower than 9. As noted earlier, difficulties in setting band-to-band receiver response led to the proposal falling into a limbo in which receiver manufacturers adhered to a general sense of the system, but S-units varied considerably (by up to a full dB) in increments between S-levels as we move from one receiver maker to another (using the same frequency for testing).

+

More recent events have renewed interest in standardizing the S-meter system. Reports of interfering signals and noise from amateurs to regulatory agencies have become common and provide a source of data for at least some of these agencies. However, most such agencies are more familiar with signal levels registered in micro-volts or in dB(uV)/dBm than in amateur S-levels. Hence, a reliable conversion scheme is once more in order. What the future of DSP and similar receiver developments may hold in store for overcoming the once insurmountable problem of variable receiver response (especially as related to the AGC system from which S-meter readings were derived), I cannot say.

+

A precise system of conversion requires--if it is to handle both signal and noise sources--a bandwidth for measurement as well as a signal strength reading. I am indebted to Hans-Joachim Brandt, DJ1ZB, leader of the study group of DARC (Deutscher Amateur Radio Club) for providing the table that they are submitting to the German national standards organization. Once fully accepted in Germany, the table may well be distributed widely among national government agencies and (hopefully) among receiver makers.

+

The following graphic presents the table exactly as I received it, including the European convention of using a "," instead of the U.S. "." to represent a decimal. I have not wished to change anything in the table. However, I shall update the table should I receive a revision from DARC or any U.S. regulatory source accepting a similar standard. An alternative version (from IARU Region 1 Recommendation R1, 1990) appears in Tabelle 4 and Tabelle 5 of the 2006 Funkamateur article referenced earlier in these notes. The differences are small, mostly representing a rounding of values. However, Tabelle 5 is interesting since it presents an alternative set of values for frequencies above 30 MHz. Values for the upper range are 0.1 times the received voltages for HF, a change of 20 dB. A second difference is that the magazine tables omit S0.

+
+ +
+
+ +
+

For careful reporting involving the strength of signals in a variety of circumstances, the proposed S-meter system--or a reasonable variant of it--makes eminent sense. The relevant activities include not only reporting to interfering signals and noise to regulatory agencies, but also matters such as equipment and antenna system tuning, antenna comparisons, etc. Nevertheless, one should not confuse the S-meter system and its functions from the use of the RST system in report exchanges between amateurs communicating with each other. Where the other operator's signal is in question, the RST system--rightly used--provides a very compact way of reporting a wealth of information. However, it has relied and always will rely on the training and experience of the receiving operator to set the information into the proper alpha-numeric characters to provide maximum useful information to the sender.

+
+ +

+
+

This item first appeared in QRP Quarterly, October, 1995. Updated 12-10-2001. Part 2 was added April 19, 2004, with further additions on September, 24, 2006 and November 29, 2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Tales


+ + diff --git a/content/tales/scilit.html b/content/tales/scilit.html new file mode 100644 index 0000000..c756385 --- /dev/null +++ b/content/tales/scilit.html @@ -0,0 +1,170 @@ + + + + + + Understanding and Producing Scientific and Technical Articles + + + +
+

Understanding and Producing
+ Scientific and Technical
+ Articles, Proposals, and Reports

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

As I retired and cleaned out an office of some 26 years' use, I uncovered a number of antique nuggets. I wished they had been gold and convertible into cash, but alas, they were only wisdom encapsulated. Some are more than 25 years in my possession--and may have been old when I received them. Their ultimate origins are wholly unknown, since my sources are burred photocopies of nearly as blurry photocopies. While my sight remains good enough to decipher them, I shall place them here. Read at your own peril.

+
+ +
+

Understanding Scientific and Technical Discussion and Literature

The following list speaks for itself--and, unfortunately, for all too many of us upon occasion. Let he or she who has never used any of these expressions (or their first cousins) cast the first aspersion. +
+ A Key to Understanding Scientific Literature +
+ 
     What he/she said                        What he/she meant
+
+1.  It has long been known that. . .    I haven't bothered to look up the
+                                        original reference but. . .
+
+2.  Of great theoretical and            Interesting to me
+     practical importance. . .
+
+3.  While it has not been possible      The experiment did not work out,
+     to provide definite answers to     but I figure I could at least get
+     these questions. . .               a publication out of it. . .
+
+4.  The W-PO system was chosen as       The fellow in the next lab had some
+     especially suitable to show        already made up. . .
+     the predicted behavior. . .
+
+5.  Three of the samples were chosen    The results on the others didn't
+     for detailed study. . .            make sense. . .
+
+6.  Accidentally strained during        Dropped on the floor. . .
+     mounting. . .
+
+7.  Handled with extreme care           Not dropped on the floor. . .
+     throughout the experiment. . .
+
+8.  Typical results are shown. . .      The best results are shown. . .
+
+9.  Agreement with the predicted
+     curve is. . .
+          excellent                          fair
+          good                               poor
+          satisfactory                       doubtful
+          fair                               imaginary
+
+10.  It is suggested that. . .
+     It is believed that. . .
+     It may be that. . .                I think. . .
+
+11.  It is generally believed           A couple of other guys think so
+      that. . .                         too. . .
+
+12.  It is clear that much additional   a.  I don't understand it. . .
+     work will be required before a     b.  My grant is up for renewal. . .
+     complete understanding. . .
+
+13.  Unfortunately, a quantitative      a.  Nobody else understands it either.
+     theory to account for these        b.  Guess the subject of my grant
+     results has not been formulated.       proposal.
+
+14.  Correct within an order of         Wrong. . .
+     magnitude. . .
+
+15.  Thanks are due to Joe Glotz for    Glotz did the work, and Doe
+     assistance with the experiments    explained what it meant.
+     and to John Doe for valuable
+     discussion.
+
+16.  It is intuitively obvious to       Well I saw the derivation for this once,
+     the most casual of observers.      but I can't find it now, and it is
+                                        way too complicated to add in the book,
+                                        and anyway, I'm not very casual today.
+
+17.  The derivation is left to the      I couldn't find the derivation in any of my
+     reader.                            reference books, and I couldn't figure it
+                                        out, so you go figure it out! (And when you
+                                        do, please send it to me).
+
+
+ +
+

Buzz-Wordsmanship

After recently distributing the "Keys to Understanding Scientific Discussion and Literature," I received a wonderful array of appreciative notes, equally divided between those who vaguely remembered the list and welcomed an old friend and those who had never before seen it and felt guilty for having used a column-1 expression on at least one occasion. Two separate sources sent me copies of another item originating at the same time (about a quarter century ago, I think, and likely even older--I cannot be sure because I wore out my copy using it). While equally fascinating, it had more to do with administration and management than it did with electronics of the sort that interests us. +

However, if necessity is the mother of invention, then play is surely the father. So let's review the original item and then see what electronic damage we may do to it.

+
+
+
+ How To Win At Wordsmanship +
+

After years of hacking through etymological thickets at the U.S. Public Health Service, a 63-year-old official named Philip Broughton hit upon a sure-fire method for converting frustration into fulfillment (jargonwise). Euphemistically called the Systematic Buzz Phrase Projector, Broughton's system employs a lexicon of 30 carefully chosen "buzzwords":

+ 
Column 1                 Column 2                 Column 3
+
+0.  integrated           0.  management           0.  options
+1.  total                1.  organizational       1.  flexibility
+2.  systematized         2.  monitored            2.  capability
+3.  parallel             3.  reciprocal           3.  mobility
+4.  functional           4.  digital              4.  programming
+5.  responsive           5.  logistical           5.  concept
+6.  optional             6.  transitional         6.  time-phase
+7.  synchronized         7.  incremental          7.  projection
+8.  compatible           8.  third-generation     8.  hardware
+9.  balanced             9.  policy               9.  contingency
+

The procedure is simple. Think of any three digit number, then select the corresponding buzzword from each column. For instance, number 257 produces "systematized logistical projection," a phrase that can be dropped into virtually any report with that ring of decisive, knowledgeable authority. "No one will have the remotest idea of what you are talking about," says Broughton, "but the important thing is that they're not about to admit it."

+
+
+

Two facts struck me. First, every ham wishes he or she could come up with the key electronic invention that would solve the world's problems, make one rich beyond belief, and write one's name large in all future history books. Second, all that is needed is inspiration.

+

Since the first premise is set, all we need is a source of inspiration. That's where Broughton's word-play device comes into play. By judiciously selecting words for 3 columns, we can inspire ourselves to create the electronics of tomorrow. So I made up my list of inspirational concepts.

+ 
Column 1                 Column 2                 Column 3
+
+0.  integrated           0.  encoded              0.  optimizer
+1.  asynchonous          1.  programmable         1.  converter
+2.  analog               2.  monitored            2.  reactor
+3.  parallel             3.  reciprocal           3.  transducer
+4.  functional           4.  demodulated          4.  interface
+5.  transferable         5.  logic-based          5.  buffer
+6.  digital              6.  transformational     6.  filter
+7.  synchronized         7.  incremental          7.  instrument
+8.  compatible           8.  fifth-generation     8.  regenerator
+9.  balanced             9.  time-phase           9.  generator
+

Be careful: some 3-digit inventions may already exist, such as 654. However, I have never seen a 770 or a 334. You may revise the list to suit your special interests. But there is fertile inventive ground, even in this preliminary cut. So while you rewrite the list, I am off to the shop. I do not know today if I shall try to make an 898 or a 542.

+
+ +
+

Mastering the Grammar of Technical and Scientific Literature

+

The third (and final?) entry is a set of general guidelines sufficient to lead anyone through the grammatical morass of technical writing. Specialists try to make the task seem more difficult than it is, but the following rules cover almost all of the cases you will encounter in a lifetime of writing and editing. Again, the exact origin is unknown, although the list has been plaguarized many times. One more time will likely not hurt.

+
+ Rules of English for Technical Article, Proposal, and Report Writers +
+
    +
  • 1. Don't use no double negatives.
    • +
  • 2. Make each pronoun agree with their antecedent.
    • +
  • 3. Join clauses good, like a conjunction should.
    • +
  • 4. About them sentence fragments.
    • +
  • 5. When dangling, watch them participles.
    • +
  • 6. Verbs has to agree with their subject.
    • +
  • 7 Just between you and I, case is important, too.
    • +
  • 8. Don't write run-on sentences they are hard to read.
    • +
  • 9. Don't use commas, which are not necessary.
    • +
  • 10. Try to not ever split infinitives.
    • +
  • 11. Its important to use your apostrophe's correctly.
    • +
  • 12. Proofread your writing to see if you any words out.
    • +
+

Enough is enough. Or is it. . .?

+
+ +
+

Updated 7-28-1999, 10-21-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Tales


+ + diff --git a/content/tales/sea.html b/content/tales/sea.html new file mode 100644 index 0000000..6ff085b --- /dev/null +++ b/content/tales/sea.html @@ -0,0 +1,49 @@ + + + + + + To the Sea Again + + + +
+

To the Sea Again

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+
+

I must go down to the sea again
+ Where the conductivity is high.
+ All I need is a tall array
+ And a rotor to steer her by.

+

I must go down to a south sea isle
+ Where the population is low,
+ And work DX without a rest. . .
+ --Pardon my QRO.

+

I must go down to the seaside dunes
+ And operate in the sand.
+ When I return, my log is full
+ Of QSOs from every land.

+

I must go down to the sea again
+ To watch the waves and swells,
+ And leave to someone else the task
+ Of answering QSLs.

+

(with apologies to John Masefield)

+
+
+ +
+

Updated 08-21-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Tales


+ + diff --git a/content/tales/sell-1.gif b/content/tales/sell-1.gif new file mode 100644 index 0000000..b327905 Binary files /dev/null and b/content/tales/sell-1.gif differ diff --git a/content/tales/sell-10.gif b/content/tales/sell-10.gif new file mode 100644 index 0000000..cf37996 Binary files /dev/null and b/content/tales/sell-10.gif differ diff --git a/content/tales/sell-11.gif b/content/tales/sell-11.gif new file mode 100644 index 0000000..08ab776 Binary files /dev/null and b/content/tales/sell-11.gif differ diff --git a/content/tales/sell-12.gif b/content/tales/sell-12.gif new file mode 100644 index 0000000..43e4a3d Binary files /dev/null and b/content/tales/sell-12.gif differ diff --git a/content/tales/sell-13.gif b/content/tales/sell-13.gif new file mode 100644 index 0000000..11cc285 Binary files /dev/null and b/content/tales/sell-13.gif differ diff --git a/content/tales/sell-14.gif b/content/tales/sell-14.gif new file mode 100644 index 0000000..ef6cf34 Binary files /dev/null and b/content/tales/sell-14.gif differ diff --git a/content/tales/sell-15.gif b/content/tales/sell-15.gif new file mode 100644 index 0000000..47a5db2 Binary files /dev/null and b/content/tales/sell-15.gif differ diff --git a/content/tales/sell-16.gif b/content/tales/sell-16.gif new file mode 100644 index 0000000..34aecfc Binary files /dev/null and b/content/tales/sell-16.gif differ diff --git a/content/tales/sell-2.gif b/content/tales/sell-2.gif new file mode 100644 index 0000000..e405329 Binary files /dev/null and b/content/tales/sell-2.gif differ diff --git a/content/tales/sell-3.gif b/content/tales/sell-3.gif new file mode 100644 index 0000000..e28c6f8 Binary files /dev/null and b/content/tales/sell-3.gif differ diff --git a/content/tales/sell-4.gif b/content/tales/sell-4.gif new file mode 100644 index 0000000..9cfd9c8 Binary files /dev/null and b/content/tales/sell-4.gif differ diff --git a/content/tales/sell-5.gif b/content/tales/sell-5.gif new file mode 100644 index 0000000..e372b33 Binary files /dev/null and b/content/tales/sell-5.gif differ diff --git a/content/tales/sell-6.gif b/content/tales/sell-6.gif new file mode 100644 index 0000000..db45753 Binary files /dev/null and b/content/tales/sell-6.gif differ diff --git a/content/tales/sell-7.gif b/content/tales/sell-7.gif new file mode 100644 index 0000000..acb6a0d Binary files /dev/null and b/content/tales/sell-7.gif differ diff --git a/content/tales/sell-8.gif b/content/tales/sell-8.gif new file mode 100644 index 0000000..4d4a89b Binary files /dev/null and b/content/tales/sell-8.gif differ diff --git a/content/tales/sell-9.gif b/content/tales/sell-9.gif new file mode 100644 index 0000000..e0d857f Binary files /dev/null and b/content/tales/sell-9.gif differ diff --git a/content/tales/sell.html b/content/tales/sell.html new file mode 100644 index 0000000..3255354 --- /dev/null +++ b/content/tales/sell.html @@ -0,0 +1,176 @@ + + + + + + Sell an Antenna + + + +
+

So You Want to Sell an Antenna. . .

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The following notes are not what they seem. My tongue was firmly in my cheek as I wrote these notes. In fact, I bit it several times just to bring me back to reality.

+
+ +
+

You have been working in your garage/basement/barn shop for days/weeks/months. The antenna design on which you have been working is finished. When you install it in the field, it actually works.

+

At this stage, most hams would simply operate and enjoy the contacts they make, whatever the context: contests/QRP/rag-chewing/etc. A subset of these operators would begin to catalog the things that the antenna will not do and begin research on the next antenna to replace this one. However, a few antenna builders will reach the conclusion that they can make up kits or packages and sell the antenna to other hams. But there are many antennas already on the market.

+

How do you make your antenna stand out so that people will buy it?

+

America is not only the the land of the free, it is also the land of marginal advertising. We began the tradition of claiming that toothpaste, deodorant, shaving cream, and cars will attract women to men and that hair dye, perfume, and mascara would attract men to women. Biology, health, intelligence, and personality had nothing to do with the matter. An interesting facet of the history of advertising is that we began to believe such things. Once belief set in, the facts no longer mattered.

+

So it is with antennas, although I am not aware that any amateur radio device has formed the attractive function between the genders. Still, effective advertising emphasizes the positive. Indeed, it puts the positive in bold-face, surrounds it with a frame, and then lights the frame so that it outshines all other considerations. The merely neutral and certainly the negative lurk silently in the shadows, unexpressed, unmentioned, unacknowledged.

+

A good engineer will want to tell a complete unvarnished story to anyone who may wish to use a given antenna. The story will be filled with facts and figures, and told without similes or metaphors. That is simply good engineering ethics. It is also why large corporations carefully separate their engineering and their marketing departments. Nothing kills a quick and irreversible sale like the whole plain story.

+

So the first step in learning how to sell your antenna--your magic antenna--is to come in from the shop, take a shower, put on clean clothes, and become your own marketing department. The second step is learning how to selectively express truths about your antenna to make it appeal to a collection of consumers who are waiting to hand someone their money. The decisive element in whether that money goes to you is not the intrinsic quality of your product. Instead, it is the show that you give them to acquire a belief in your product. Once you have that, even mediocre performance will not convince them that they did not buy the best that there is.

+

The following notes are designed to show you ways in which you can present some kinds of antenna products so that they engender belief in the product. In no case will any of the techniques falsify a fact. Indeed, for each case that we present, we shall see both the whole unvarnished story and the fact to present. After all, there are laws against false advertising--not to mention a plethora of ethical and religious traditions.

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A Wire Antenna Example

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Let's start out simply. In our shop, we have developed an off-center-fed 137.5' AWG #14 copper wire antenna. The feedpoint is 42.88' from one end and 94.62' from the other. At the feedpoint, we install a 4:1 balun and use coaxial cable as the main feedline. What can we possibly say about such an antenna that will distinguish the product from all of the other wire antennas on the market? Of course, we can use plastic insulators having exotic names, such as polycarbonate (and the many various trade names for the material). Or we can emphasize the fixture used for connecting the feedline to the wire and extol its virtues for durability. But most antenna buyers want to hear something about performance. They do not want an antenna that merely radiates. They want a "gusher," a "signal pusher," a veritable "RF volcano." How can we give them what they want?

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First, we can emphasize the gain on 10 meters--without necessarily saying that we are talking only about 10 meters. Remember that silence is golden in selling. We can say that the gain potential is higher for our OCF than it is for a mere or plain center-fed doublet. We shall not be falsifying in the least. Fig. 1 compares the free-space E-plane (azimuth) patterns of a 135' doublet and our OCF at 28.5 MHz. The maximum gain of the OCF's strongest lobes is indeed numerically greater than the maximum gain of the strongest lobes of the center-fed doublet.

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Of course, we shall also be silent about the fact that the OCF has a non-symmetrical pattern, compared to the doublet's symmetrical pattern. We shall also simply fail to mention that the OCF has more lobes and consequently more nulls than the doublet. And we shall certainly not mention that the OCF has many weaker lobes than the doublet on 10 meters, especially broadside to the wire itself (which runs across the page in the pattern).

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If we are up on some antenna theory, we can make a stronger claim, again simply being silent about the fact that we are talking only about 10 meters. We may claim with numerical justification that the maximum gain is greater than we can obtain from a 2-element Yagi. Once more, we are falsifying nothing, as shown in the comparative free-space E-plane (azimuth) patterns that appear in Fig. 2. The black line indicates the pattern for a relatively standard 10-meter 2-element Yagi.

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We shall not mention that the maximum gain differential is only 0.4 dB. Nor shall we mention that the maximum-gain lobes of the OCF are very narrow compared to the broad main lobe of the Yagi. We shall also be silent concerning the fact that the Yagi has a significant front-to-back ratio (10-11 dB across 10 meters) and is designed to be turned directly toward the desired station. (Pushing a 137.5' length of wire around in a circle for aiming is a daunting task, to be sure.) And we shall also not compare the element lengths (17.5' maximum for the 10-meter Yagi vs. 137.5' for the OCF).

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Very likely, we shall also fail to mention that the gain of the OCF decreases as we reduce frequency. At 80 meters, the bi-directional pattern is virtually indistinguishable from a center-fed doublet pattern, although the doublet shows about 1.5-dB more gain. We shall also not mention that with the OCF configuration chosen, the lobes develop twice as fast as in the doublet. So the doublet, when 1 wavelength long, still has only 2 main lobes broadside to the wire, but the OCF shows a non-symmetrical cloverleaf. A symmetrical 4-leaf clover appears for the doublet at 20 meters, but the OCF has 8 lobes on this band. All of this information is likely only to confuse the potential buyer, so we shall refrain from mentioning such unimportant details.

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More important to selling our OCF is the fact that we intend to feed it with a length of coax. If we model the antenna for 200 Ohms impedance, we shall obtain a fair picture of the SWR curves at 50 Ohms once we install the balun. Fig. 3 shows these curves.

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The initial curves are not promising, although we can cover parts of the harmonically related ham bands with under 2:1 50-Ohm SWR with the balun. In fact, we are likely to measure better performance once we install the balun. First, if we measure the SWR at the far end of RG-58 coax (nearly the lossiest coax that will handle amateur transceiver power levels), we shall obtain better SWR figures. Second, the balun itself may introduce losses that reduce the SWR values. The actual losses will depend upon balun design and its ability to handle higher levels of reactance. As a sample, I inserted an arbitrary 50-Ohm load in series with the feedpoint to simulate possible balun losses. The result is a revised set of SWR curves, shown in Fig. 4.

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Note that all levels are considerably lower. The antenna covers the CW portion of 80 meters and just about all of 40 and 20 meters with 2:1 SWR or less. As well, the antenna covers the main activity regions of 10 meters. These are all facts we might wish to stress, and a lossy test coaxial cable, such as RG-58, might even improve the coverage. Of course, we shall not show the actual curves, although we might show a sample if it is below 2:1 across an entire band.

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At the same time, we shall not mention that balun and cable losses take their toll on the energy available at the antenna itself. The arbitrary loss insert into the system reduces 10-meter gain on the OCF by well over 1 dB. We might well just omit any reference to losses in the feedline and impedance transformation system and extol the virtues of the coverage we obtain using a coaxial cable. Besides, the tuners we find inside rigs can extend the coverage to all of the listed bands.

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Many hams mis-label the type of antenna used here as a Windom. However, that 1929 invention used only a single wire as the feeder, and--of course--it radiated. The antenna that we are manipulating is an off-center-fed doublet, or OCF. Radiation from the feedline is minimal, although there are at least small imbalances in current on the two lines (whether we use parallel line or coax). The main radiation is from the horizontal wire, so we can safely say that the OCF is better than a Windom. If folks wish to believe that it is better than other marketplace OCFs that call themselves Windoms, that is their responsibility.

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Every product needs a name. To sound truly professional, the name needs to leave the impression that it is descriptive. Since the antenna covers the HF bands, the letters "HF" are ready to use. Numbers--up to but not over 3--leave a good impression. So we can use 137, which is the rough length of the wire. So we have The All-Band OCF HF-137 as a perfectly plausible name. Note that we have avoided non-professional terms like "gusher" and "volcano." Those names belong to unlicensed users of the RF spectrum, not to relatively newly licensed radio amateurs with FCC-assigned call letters. The upward move in status calls for an antenna that has been engineered.

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Our small ad in a magazine might look like Fig. 5. You can always enlarge it with testimonials, once they begin to roll in. Note that the ad seems to appeal not only to the beginning antenna user, but also to the experienced advanced user of complex expensive antennas. That gives the antenna's high quality and performance claims verisimilitude, even if no advanced antenna user ever buys one or even seriously considers using one. The claim is not false, since an all-band wire is in fact a good back-up and emergency antenna for complex stations.

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I have not suggested a price for the antenna (actually, the antenna kit with wire, insulators, and balun). Do not make the price too low. First, you will find that the income does not cover the parts you buy plus the time it takes to make up kits and mail them out. Second, too low a price smacks of not being a professional-grade antenna. On the other hand, do not price the antenna too high and put it out of reach of your target market.

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Remember that it makes very little difference that the highly positive impression that we leave with our emphases and our silences might just be a misimpression. Wire antenna buyers tend to be newer hams (in contrast to many experienced hams who build wire antennas from scratch) who normally do not have a comparable second antenna for making A-B tests. Hence, they will not be able to determine that the OCF is overall no better than or worse than a center-fed doublet, and they will thank us for not needing a separate antenna tuner. Nor do wire antenna buyers have test equipment capable of measuring system losses either directly or indirectly. They are only interested in what the SWR meter says and what they hear. Going from no antenna to our magical OCF design will let them hear a lot. We can even anticipate receiving testimonials praising the antenna, and we can always add excerpts to our advertising. User judgment counts, especially when highly favorable, regardless of the user's technical qualifications for making such judgments.

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A Wire Bi-Directional Array Example

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Our second example of selling an antenna involves a very old bi-directional beam called the Sterba curtain. The outline of this venerable array appears in Fig. 6. The core consists of one or more half wavelength long sections, where each section requires 2 horizontal wires vertical spaced by 1/2 wavelength, with the whole array at least 1/2 wavelength above ground. To complete the array, we have on each end a pair of vertically stacked 1/4 wavelength wires.

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At each end of the array, we connect the top and bottom ends of the horizontal runs with a single wire to close the array. However, the sections between the ends are connected with parallel transmission lines that are 1/2 wavelength long with a half-twist to ensure that the top and bottom wires in any section are in phase with each other. The sections should be open-wire (ladder) line for a velocity factor as close to 1 as possible. The actual impedance of these lines is not critical: any high value will do, and the array works fine with lines that are spaced from 3" to a foot. There are 2 possible feedpoints. We can place the feedpoint at a lower extreme corner for convenience. However, the natural losses even of copper wire will bend the bi-directional beams by about a degree or two. The version shown in Fig. 6 uses an odd number of interior sections and places the feedpoint at the exact center of the lower wire. The antenna ideally requires a 600-Ohm feedline to an antenna tuner for effective use with modern amateur equipment. However, since we shall specify the use of a tuner, virtually any high-impedance parallel transmission line will work well.

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Fig. 7 shows the free-space E-plane or azimuth pattern for the array at its design frequency. For a 5-section Sterba, 2 wavelengths long at the design frequency, we obtain two main lobes, each with a free-space gain of about 10.4 dBi. The Sterba curtain has more gain than a 5-element Yagi. Of course, a 5-element Yagi has a beamwidth that is twice as wide as the Sterba, and the Yagi is designed to be rotated. However, we shall not let these facts deter us.

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Commercial services stopped using Sterbas long ago. They found better large wire arrays, such as the rhombic, for point-to-point and SW broadcast services. Only hams still build occasional Sterbas. As well, virtually all Sterbas in commercial and government service were large and used in the lower HF region. However, you may note from Fig. 7 that our design sample is in the middle of 10 meters.

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The Sterba for 10 meters is 69' long and 17.25' high. The minimum height above ground for effective service on 10 meters is 17.25', a half wavelength. That places the top wire at 34.5' above ground. The interior wires in this model are 1' apart. In the end, the Sterba curtain requires about 1/2 the field space required by a 135' center-fed doublet. The fact that it requires almost 3 times as much wire as the 135' doublet (310' vs. 135') will not slow us down in the least.

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The comparison of overall length between the 10-meter Sterba and the 135' doublet is critical to the discovery that will make the antenna a hot seller among wire users. That discovery is a simple one: we can use the feedline and tuner system to load up the antenna on all bands from 80 to 10 meters. We have invented The All-Band Sterba Curtain.

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Fig. 8 shows the patterns of the 10-meter Sterba on the remaining HF bands. None of these bands yields a pattern with the high-gain bi-directional beams that we obtain on 10-meters. The Sterba curtain is a high-gain bi-directional beam only on its design frequency, where the half-twist interior connecting lines ensure that the current magnitude and phase are the same for each pair of top and bottom wires. On all other bands, the lines are no longer 1/2 wavelength, and so each pair of top and bottom wires will have different current conditions. As well, adjacent sections of the array have different current conditions. The result is that even the currents in the lines are no longer equal in magnitude and opposite in phase. Hence, the interior vertical wires may radiate to one or another degree of efficiency.

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In the end, for all bands from 80 through 10 meters, we obtain the free-space performance levels shown on the left in the following table. The total pattern is composed of vertical and horizontal components, and the second data column list the dominant component.

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+A Comparison of Free-Space Gain and Feedpoint Impedance Values:  A 10-Meter Sterba Curtain and a 135' Center-Fed Doublet
+                          10-Meter Sterba Curtain                               135' Center-Fed Doublet
+Frequency        Maximum Gain  Dominant    Feedpoint Impedance           Maximum Gain     Feedpoint Impedance
+   MHz              dBi       Polarization   R +/- jX Ohms                      dBi         R +/- jX Ohms
+28.5              10.41        horizontal    570 + j 20                        5.27         2600 - j 850
+24.94              5.43        vertical      930 + j 170                       4.70         130 - j 1000
+21.225             4.29        vertical      2300 - J 1700                     4.58         2900 + j 980
+18.118             2.17        mixed         20 + j 80                         4.66         130 + j 15
+14.175             2.32        vertical      3700 + j 1800                     3.83         4100 + j 130
+10.125            -1.20        mixed         110 - j 470                       3.49         90 - j 320
+7.15               2.30        horizontal    250 + j 1800                      3.73         5000 - j 2400
+5.358              0.52        horizontal    30 - j 360                        2.67         430 + j 120
+3.75               1.78        horizontal    95 - j 180                        2.08         90 + j 100
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Of course, if we place the antenna in the vertical position prescribed for lower-HF versions of the array--that is, 1/2 wavelength above ground at the design frequency--the antenna will be much too low for more than NVIS operations below 20 meters. But let's not dwell on that difficulty. The chart tells us that we can load the antenna on all HF bands with not too much strain on the tuner limits with any common parallel transmission line.

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The table's right-most columns provides us with the free-space performance of the usual 135' center-fed doublet. The impedance listings show us why some doublet users prefer somewhat shorter or longer lengths for the antenna wire. At 135', the antenna is nearly resonant at the center of 80 meters. Hence, on 40, 20, 15, and 10 meters, it is very close to a perfect even number of wavelengths long, resulting in extremely high values of impedance. If we shorten the antenna to about 125', the antenna is closer to resonance at 4 MHz, with even harmonics that fall outside the ham bands. Hence, the impedances within the ham bands give the tuner a little less pressure on its matching limits. We may also note in passing that the Sterba curtain feedpoint impedances are in almost all cases more amenable to common parallel transmission lines.

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Fig. 9 presents the free-space E-plane patterns for the 135' center-fed doublet for comparison with those of the all-band Sterba curtain. Although we cannot prevent the emergence of multiple lobes, note that the lobes evolve in an orderly and predictable progression as we move from 80 to 10 meters. The table tells us that the doublet actually has a higher maximum gain on all but 2 bands. However, newer wire users are more interested in an easy match than they are in the gain numbers (except for 10 meters), so we may simply pass over the gain columns in silence.

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We are now ready to advertise our all-band Sterba curtain. In accord with good wire antenna marketing principles, we shall stress the positive aspects of the array and hold our tongues with respect to anything that someone might cite as a negative. The result might be a small ad like the one in Fig. 10.

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You will recognize most of the claims from the discussion, including the potential misimpression left by the gain claim. We shall not worry about of oxymoron of calling a Sterba curtain (essentially, a monoband array with a fairly narrow frequency range for maximum performance) an all-band antenna solely on the basis of the ability to effect a match. The ad also stresses the all-copper construction of the antenna, since copper has a good reputation as a conductor. Of course, aluminum would do as well, except for the difficulty of creating junctions. However, we shall package the kit as a single length of wire to start and stop at the feedpoint. We shall throw in a handful of 1' plastic rods to create the vertical phase lines. You can reserve the directions for staking out the lawn to construct the antenna for a paper instruction sheet: words and paper are cheap.

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A Yagi Example

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In our wire-antenna examples, we have moved from marginal and dubious claims to blatant misimpression. However, when we turn to beam antennas, we change directions and slide into the realm of the downright subtle. In the marketing arena of beam antennas, the name of the game is gain--with a little bit of front-to-back ratio thrown in to cloud issues that might otherwise be clear. The heyday of gain claims for Yagis and other beams occurred in the 1980s, before the emergence of antenna modeling software. Indeed, for decades, some Yagi marketers tried to deny the validity of antenna modeling software in order to sustain overzealous gain claims. Such marketers would argue that models did not reflect adequate range tests, and if their antennas failed to show well in actual range tests, they claimed that the tests were flawed from an engineering perspective. Those were halcyon marketing days, indeed. One common habit was to make a simple sum of each gain advantage. For example, adding a reflector to a dipole added about 4 dB of gain. Adding a director to a dipole added about 4 dB of gain. Therefore, adding both a director and a reflector to a dipole driver must add about 8 dB to the dipole's inherent gain. Note that in the 1980s (and later) many marketers (whether of antenna products or ideas) refused to reference the decibel to any particular comparison or to a standard. Instead, they would claim a gain of XX dB and let the reader try to figure out what that meant. Of course, they hoped that most readers would be so impressed by the number XX that they would forget to ask about the standard of measurement.

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In Europe, it is still popular--if not standard--to express the gain of a beam in terms of dBd, that is, gain in decibels over a dipole. However, even dBd contains an ambiguity that we shall explore. One rendering--the most usual--of the term is the dB gain over a theoretically perfect dipole in free space. The perfect dipole has an infinitesimal wire diameter with no wire losses, and hence its value is always 2.15 dBi, where dBi is the gain in dB over an isotropic source. So a gain claim for a 3-element beam over ground might by given as 11 dBd, instead of the US custom of reading the value as 13.15 dBi. Of course, the dBd gain is not the gain over a real dipole at the same height as the tested Yagi. It would show a gain of about 7.65 dBi or 5.5 dBd. Hence, the performance improvement of the Yagi over a real dipole at the same test height would be the same in both dBd and dBi terms: 5.5 dB. However, a claim of 5.5 dB improvement over a dipole does not sell as many beams as a claim of 11 dBd. The dBd purveyors, of course, defend themselves by claiming that a gain of 13.15 dBi is too high and too theoretical a number, conveniently forgetting that the basis of dBd is equally theoretical and equally misleading unless we also cite the gain of a dipole at the same height above ground in the same terms of measurement.

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In this part of the exercise, we shall not try to sell a re-named dipole with a gain of 7.65 dBi or 5.5 dBd. Instead, we shall embark upon a more difficult task. First, we shall develop a fairly standard 3-element Yagi for 10 meters. In fact, it will be no better or worse than most of the 10-meter Yagis on the market. However, our task will be to make our Yagi stand out above the crowd.

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Fig. 11 shows the general outline of our Yagi. The 3 elements fit on an 11.2' boom (12' with the necessary allowance for boom-to-element hardware). The sample uses 1/2" aluminum elements, which is impractical in actual construction. But the performance of a version with stepped element diameters will not vary significantly from the baseline model. The design frequency gain is about 8.11 dBi in free-space. The gain is about a full dB greater than the standard Yagi in the ARRL Antenna Book. Of course, that Yagi fits on an 8' boom, but we need not emphasize the smaller size of the comparator.

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Yagis in this class have resonant feedpoint impedances in the mid-20-Ohm range. Therefore, this design shortens the driver to provide some capacitive reactance in series with the feedpoint resistance. By connecting an inductive reactance of the correct value across the feedpoint, we obtain an L-network matching section that raises the impedance at the terminals to 50 Ohms resistive. The inductive reactance has the form of a shorted transmission line stub, which we also call the hairpin or beta match. There are 3 general ways to elevate an impedance in the 25-Ohm range to 50 Ohms. With a resonant driver, we might use a 1/4 wavelength section of 37-Ohm coax (parallel sections of RG-59). We may use the capacitively reactive driver with a gamma match, with its rod and series capacitor. By comparison with the beta match, the gamma is mechanically more complex with more junctions to weather over time. The beta match introduces the fewest mechanical junctions to suffer from the long-term effects of weather. There is no evidence that any one of the 3 matching systems has any more or less loss when new and solidly constructed than any other system.

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The 3-element high-gain Yagi performs in a normal fashion. A completely fair description of the Yagi would show the performance curves of the antenna across the intended operating range, 28.0 to perhaps 29.0 MHz. Fig. 12 shows the gain pattern and the front-to-back pattern. The curve marked "front/back ratio" shows the 180-degree value, while the curve marked "front/side ratio" provides the worst-case values for the front-to-back value.

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The curves not only give us the operating characteristics of the antenna on 10 meters, but as well, they provide us with the information we need for the first set of marketing claims about the antenna. For example, the gain climbs in nearly linear fashion as we raise frequency from 7.87 dBi in free space to 8.44 dBi. The average gain is 8.13 dBi. However, in the passband, the Yagi has a gain potential of 8.44 dBi maximum. The curves show an average front-to-back value of nearly 22 dB (180-degree or worst-case) across the band. We may remain silent about the fact that front-to-back ratio drops below 20 dB at both ends of the band, and certainly we shall not talk about the under-15-dB value at 29 MHz. Instead, we shall note that the maximum front-to-back value is over 29 dB at 28.4 MHz. We may also forget to note that the values for maximum gain and for maximum front-to-back ratio do not occur at the same frequency. We shall be in good company with some Yagi makers on the commercial market if we simply cite the maximum values for these parameters.

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Fig. 13 shows the free-space E-plane (azimuth) patterns for the Yagi at the design frequency and at the band edges. If we wish to display a pattern, we shall certainly use the mid-band pattern, leaving the band-edge patterns to the users imagination. However, as we continue our marketing research, we may find an even more attractive pattern.

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To complete the picture, Fig. 14 graphs the feedpoint resistance and reactance of the Yagi, along with the 50-Ohm SWR curve. The graphs include the beta match. Due to the transformation of complex impedances, fixed-component matching networks tend to reverse the direction of curves that we might obtain of the feedpoint impedance components without a matching section. The resistance would rise with frequency, and the reactance would form a curve with more capacitive reactance at the low end of the band and more inductive reactance at the high end. These details are significant for understanding more fully how the Yagi operates in this configuration. However, they are much too detailed for advertising the beam.

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The SWR curve does not cover the entire band at the antenna terminals with a value that is below 2:1. However, the 50-Ohm SWR is below 2:1 across the most active region of 10 meters, which many operators terminate just above 28.8 MHz.

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Besides stressing the positive attributes of our beam, we may also wish to compare its performance with a dipole as a more graphic demonstration of its stellar quality. The best way to do this is by testing or modeling the Yagi over ground and comparing it with a dipole at the same height above ground. The best test heights to use for this simple ploy are about 7/8 wavelength or 1.375 wavelengths. Otherwise, we may fail to arrive at the best marketing numbers in the comparison.

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The following table shows the basic performance figures for the compared antennas over average ground. On the left are the numbers for the dipole. On the right are the numbers for the Yagi. The Yagi data includes a front-to-back ratio, which is not relevant to the dipole. Like the Yagi, the dipole is made from 1/2"-diameter aluminum. The + and - signs record the maximum and minimum values of selected parameter values within the limits of the height increment used.

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+A Comparison of Dipole and 3-Element Yagi Performance at Various Heights Aboce Average Ground at 28.5 MHz
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+                   Dipole                                             3-Element Yagi                   Yagi - Dipole
+Height   Gain    TO Angle   Feed Impedance         Gain     TO Angle   Front-Back     Feed Impedance    Delta Gain
+WL       dBi     degrees    R +/- jX Ohms          dBi      degrees    Ratio dB       R +/- jX Ohms        dB
+0.3      5.73     48        85.59 + j5.95          10.47     35        29.17          52.44 + j0.83       4.74
+0.4      6.27     35        80.53 - j8.28          11.45     29        30.69 +        50.32 - j1.84       5.18  +
+0.5      7.23     28        68.14 - j9.14          12.19     25        25.63          48.21 - j1.98       4.96
+0.6      7.76 +   23        63.47 + j0.35          12.69     22        24.74 -        46.78 - j0.59       4.93  -
+0.7      7.51     20        69.82 + j7.09          12.95     19        30.72          47.63 + j1.33       5.44
+0.8      7.14 -   17        77.27 + j3.78          13.09     17        38.70 +        49.40 + j1.02       5.95
+0.9      7.20     15        76.67 - j3.40          13.21     15        28.13          49.65 - j0.38       6.01  +
+1.0      7.63     14        70.44 - j5.04          13.34     14        24.77 -        48.54 - j1.25       5.71
+1.1      7.91 +   13        67.09 - j0.22          13.41     12        25.17          47.63 - j0.58       5.50  -
+1.2      7.77     12        70.37 + j4.17          13.48     11        29.62          47.86 + j0.61       5.71
+1.3      7.52 -   11        75.15 + j2.57          13.54     11        32.71 +        48.93 + j0.70       6.02
+1.4      7.52     10        75.15 - j2.08          13.60     10        27.75          49.30 - l0.15       6.08  +
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A dipole's gain undulates as we raise the dipole height, with peaks at about 5/8 wavelength and every half wavelength above that level (1.125, 1.625, etc.). The peaks become less pronounced with increasing height, and above 2 wavelengths are not especially discernable. Likewise, the dipole shows minimum gain values at about 3/8 wavelength and every half wavelength above that level (0.875, 1.375, etc.). With its inter-element coupling and the projection of the reflected wave forward of the structure, a beam shows less sensitivity to the height above ground, although we can detect differences in the rate of gain change between increments as we elevate the antenna. More sensitive to changes in height is the front-to-back ratio, with peak values (meaning least rearward radiation) corresponding roughly to the dipole heights of minimum gain.

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When comparing a Yagi to a dipole, pick a test height that will provide the best marketing numbers while falling within the range that users might place their antennas. At a test height of about 7/8 wavelength, our 3-element Yagi shows over 6-dB gain beyond that of a dipole. Being able to honestly claim more than 6-dB gain advantage will attract buyers more surely than a claim of 5 dB or even of 5.5 dB, both of which are equally honest numbers, but relevant to different test heights. Note that between heights of 0.5 wavelength and 1.0 wavelength, the gain differential varies by more than a full dB. (If we were interested in selling a dipole, we might pick a test height of 0.5 wavelength and then claim that our dipole's gain is less than 5 dB lower than a 3-element Yagi. Or, preferably, we would select a short boom Yagi and claim the gain was less than 4 dB lower. Even better still, we might claim the dipole to by down by only about a half S-unit relative to a 3-element Yagi.)

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We may also use a selected test height to obtain a radiation pattern to use in some of our advertising. The selected pattern must use a test height that yields the highest front-to-back ratio. Fig. 15 shows the azimuth pattern at the TO angle listed in the table for a height of 0.8 wavelength. We shall not be concerned that the height is not the same level from which we derived our gain differential number. The azimuth pattern is normalized to the maximum gain within it. Hence, it does not show the gain value associated with it. Some programs print that value to the side, but we can always graphically delete the number. An azimuth patterns with a very high front-to-back ratio almost always leaves the impression of superior performance, even in the gain category.

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We now have accumulated enough positive facts to warrant calling our beam "The Superior 3-Element Yagi." So our ad might take the form of Fig. 16. I have omitted the pattern shown in Fig. 15, but you may wish to fit it into the space.

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Of course, we shall not in the ad tell anyone that the use of a beta match requires elements that are well insulated and isolated from the boom. Hence, the construction uses one or another means of achieving this goal. We shall also not mention that some methods are better than others, since our ad does not discuss this facet of the beam at all. Performance and tough durability are the hallmarks by which we want to attract customers to this antenna. Even though all antennas deserve preventive maintenance at least once a year--if not more often--most antenna buyers want to believe (without having to say so out loud) that they can install the antenna and have it work to specification indefinitely.

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Conclusion

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The principles folded into the three examples in this exercise should guide you, whatever the type of antenna that you wish to market from your garage or workshop. They are not fantastical products of a fertile or even a cynical imagination. Every one of these principles has appeared in printed advertisements for antennas sold somewhere in the last 2 decades. The exercise antennas differ from the sources, and I have applied the principles in a concentrated fashion to the samples. Therefore, anyone who has used any of the principles can always say "That is not me."

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Nevertheless, the principles sell antennas and yield what marketing and advertising count as being factual and evidentially based claims. Remember that selling an antenna depends as much on what we do not say as it does on the claims we put into print.

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Note also that we have not appealed to any untested, unproven, or even controversial theories of operation for our antenna. While such theories appeal to a small market segment, they limit sales among the largest part of the antenna-buying public--our target consumer group. Most folks want to relate to the antenna by using terms that they have heard and that they think they understand. The more positive links between buyer and product, the stronger is the buyer's belief in the product.

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Some skeptics--usually found among buyers rather than sellers and engineers rather than marketing experts--might ask whether these principles are fair. A discussion of that question would need another exercise entirely.

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Updated 08-02-2002. © L. B. Cebik, W4RNL. This item appeared in AntenneX, July, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Tales


+ + diff --git a/content/tales/shack.gif b/content/tales/shack.gif new file mode 100644 index 0000000..980bd02 Binary files /dev/null and b/content/tales/shack.gif differ diff --git a/content/tales/shack.html b/content/tales/shack.html new file mode 100644 index 0000000..461da99 --- /dev/null +++ b/content/tales/shack.html @@ -0,0 +1,28 @@ + + + + + + When Shacks Were Shacks + + + +
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When Shacks Were Shacks

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L. B. Cebik, W4RNL

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Go to Main Index

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Topics: Tales


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Thoughts on Caring for a Terminally Ill Loved One

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By one who has been there and learned the hard way

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  • There is nothing harder than caring for a terminally ill loved one--except not having the loved one to care for.
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  • If you choose to become the care giver--even with the assistance of a hospice program--know that this will be not merely an important job, not merely the most important job, but instead, the one and only job that you have for so long as you have it.
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  • If you cannot accept the job on these terms, then do not accept it at all.
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  • All else is secondary to the tasks of caring. Learn to treat everything else you must or should do as a respite, as recreation, as rest.
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  • By all means, enroll in a hospice program. Then you may call for help and be assured of regular visitation, advice, encouragement, and understanding.
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  • Learn from the hospice nurses about current conditions, but do not expect a detailed or guaranteed prognosis.
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  • Learn from the hospice aids how to do things, but do not expect them to do everything needed.
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  • Adapt techniques of care that you learn to the one for which you care--for you know that person and love that person more than even dedicated hospice helpers, aids, volunteers, and nurses possibly can.
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  • So long as the one you care for can express his or her desires, use them as a guide to what you do and how you do it.
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  • Do not let a question linger: ask for an answer from hospice personnel or medical personnel. There is no such thing as a dumb, foolish, or stupid question, except for the question that goes unasked.
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  • Learn to sleep in short sessions. It is not easy and it is not too good for you. But long sleep periods may be worse for the loved one in your care. When your term of service is over, be prepared to spend a considerable time trying to re-establish your normal sleep cycle.
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  • Prepare yourself to do jobs that you cannot now imagine doing. Changing diapers and cleaning up messes that you are accustomed to thinking of as private and often foul will become routine. Washing private areas of your loved one is both necessary and routine. In all such matters, re-assure the loved one, for his or her privacy, dignity, and self-respect are at stake.
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  • Learn to accept the sight of unbearable things, such as blood, stool, urine, stomach bile, un-healing sores, and vomit. Learn not to react negatively to them. Learn to take them in stride.
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  • Do not chastise the loved one for what he or she cannot control. Likewise, do not present the loved one with a falsely cheerful face. Take the serious seriously. Take the unpleasant in stride (and curse the walls of another room, if necessary). Make the situation pleasant and even tell a funny story whenever the loved one is prepared to hear such things.
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  • Keep the loved one informed about his or her situation and about the wider world around him or her. Find the loved one's interests--which may now not be identical to the interests shown when the loved one was able to be active--and feed those interests with information, anecdotes, and conversation.
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  • Make special occasions, like an early "mini-Christmas," for the loved one. But, make sure that it is an exchange, not a one-way street. Let the loved one give as well as receive.
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  • Let visitors be alone with the loved one, especially if the visitor is a special friend. Instruct the visitor to call you at the earliest sign of a need. Do not overly restrict the duration of the visit. Your loved one may be tired out from the visit, but you will discover that the loved one is also strengthened after a little rest. And the loved one will be cheered if the visitor is sensitive enough to focus on their mutual interests and not on your loved one's condition.
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  • Inform key family members of any change of condition. Indeed, find a family member who will act as the relay to the rest of the family. Recommend visits from family members at each change of condition. Do not withhold family visits, even when you think that the end is near. It is better to be wrong and allow family to visit your loved one an extra time than to be right and not let the family visit if they wish.
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  • A cordless telephone is a wonderful instrument for letting the loved one stay in touch with family and friends as long as possible.
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  • A hospital bed and the loved-one's own bed will become a serious matter for decision. If the loved one can move or roll, then a full size or larger bed may be preferable. A hospital bed is narrow but has head and leg adjustments for when the loved one can no longer effectively roll from side-to-side.
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  • Learn with the loved one to handle many care chores cooperatively. Changing bed linens and protective pads may require special "roll-over" techniques. The best way to do them is the way you learn together.
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  • Learn to wash the loved one gently and in ways acceptable to the loved one. Learn to wash legs, feet, and private areas effectively but sensitively. Learn to apply the loved one's favorite lotions and creams, as well as any others deemed necessary by hospice or medical personnel.
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  • Learn to administer medications accurately, effectively, and on time.
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  • Learn to assist with feeding, but do not force food--not even water. Your loved one may stop eating altogether--or go on a liquid diet. If you fear dehydration, ask for advice and assistance.
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  • Monitor breathing and, if you are worried, ask for assistance.
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  • Insist on effective and prompt pain management. Accept no avoidable delays.
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  • Do not try to reform the loved one. If he or she smokes, this is no time to change that, unless smoking hinders necessary medications. Instead, think about safety. If the patient can no longer sit up to smoke, then be present at every smoking episode--even to holding the cigarette.
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  • Do not sit and stare at the loved one. Instead, engage in conversation with the loved one, even if the conversation is somewhat one-way.
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  • Hold hands--a lot!
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  • Be prepared for the nearing of the end. Expect delirium, short attention spans that grow increasingly shorter, non-responsiveness, non-eating, refusal of water despite a growing amount of dried bile in the mouth, labored breathing that you wish you could ease.
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  • The nearing of the end is a time of growing care-giver fatigue and aversion. You will experience heart-break every time that you look in on your loved one--almost to the point of not being able to bear to see him or her in that condition. This is the time to find the extra strength to look in more often, even if it means feeling helpless at not being able to do anything just then. This is the time to talk with trusted friends or family members to share those feelings so that you can muster the strength to carry on until the end has arrived.
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  • Do not expect to be present, or feel guilty if you are not present, in the room at the exact moment of passing. That moment is beyond your control. But call for help if you sense that moment is near.
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  • You will have questions for a considerable time after the end. Did I do all that could and should have been done? Did I do things right? Did I do something wrong that made things worse? Do not dwell on these questions, because there are no answers except this one: If you did all that you could in the best way that you knew how, then you did very well indeed.
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  • Let the professionals care for your loved one after he or she has passed away.
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  • You will feel empty once the end has come. Tears are natural to men and to women at this time. Find time among the necessary chores and phone calls to simply sit and grieve--although, for many, a family member or friend near by is an aid to grieving.
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  • Every sense of loss has two sides. You may be much less than you were, now that you are without your loved one, but you are much more than you could have been had you not loved him or her.
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L. B. Cebik

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In memory of my courageous Jean

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November 4, 2002

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Go to Main Index

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Topics: Tales


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The Wouff-Hong, the Rettysnitch, and the What?
+ The Uggerumph

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L. B. Cebik, W4RNL

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"There were three gadgets that were devised by the amateurs of those early days to keep Young Squirts constantly reminded of these three important don'ts of amateur radio.. A Squirt who used too much of what we used to call "Lake Erie Swing," or sent with a slobbery fist, or cluttered up the air with too many CQ's, or garbled his call letters so that they had to be guessed at, was called upon by a committee, the chairman of which was a big brute with a positive manner and who exhibited and explained the workings of an instrument known as an Uggerumph.

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"A Squirt who was a band-jumper, or who failed to maintain an intimate acquaintance with a reliable wavemeter, was politely knocked on the head with a base-ball bat, dragged out into the nearest sand lot, and subjected to a surgical operation with a thing called a Rettysnitch. . . .

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"Last but by no means least, a Squirt who even thought of using a false call, let alone actually using one, or used profane language on the air or who willfully broke up other legitimate amateur traffic, was taken for a certain kind of ride during which an instrument of torture known as a Wouff-Hong figured very prominently. No Young Squirt ever returned from one of those rides."

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+ from "Rotten Young Squirts" by The Old Man, QST, February, 1932, p. 27 +
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+ We have seen the Wouff-Hong. +
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+ Those who have seen it, dread it. +
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+ Most of us have seen the Rettysnitch. +
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+ Those who have seen it, fear it. +
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+ But, can anyone tell us what the Uggerumph looks like? +
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+ Is it real--or just a mythical something that goes "bump" in the night? +
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The Revelation

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I quickly learned from a number of victims of the Uggerumph that, unlike the Wouff-Hong and the Rettysnitch, this third instrument of torture for rotten operating may not be an inanimate object. It can chase you around and leaves scars on both body and psyche. It has a mean disposition, so mean that appropriately descriptive terms cannot be repeated in polite company (although I am assured that it loves its mother). Apparently, more modern accounts viewed of the Uggerumph as a creature, while T.O.M. himeself called it an "instrument." Hence, cyborgs, robots, and androids are not out of the question as proper categories for the Uggerumph. It has been referenced, but not pictured, in QST, CQ, and 73, but always by cartoonists and humorists who seem immune to its bite, claw, sting, scratch, gouge, rip, or whatever (or all of the above) (and possibly more).

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From ARRL HQ, I received the following note: "Although the Uggerumph was not initially a "thing", in T.O.M.'s writings, he later turned it into one. Although we don't have a photo on the web page, we do have it on display here at HQ in the same case as the Wouff-Hong and Rettysnitch. It looks like a cross between a bear trap and a straight key, with a bone mounted on it (a vertebrae segment)." My thanks go to Dan Miller, K3UFG, Michael Tracy, KC1SX, and Joe Bottiglieri, AA1GW, for a chain of events that quickly brought to me several photographs of the Uggerumph. It is customary at this point to note that the photos are explicit and may be unsuitable for viewing by children.

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The First Mystery

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How the Uggerumph originated was answered in a note accompanying the photographs.

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"This mysterious object was made shortly after Hiram Percy Maxim wrote his story "Rotten QRM" in 1917. Whether the device was symbolic of QRM in those days or was supposed to cure its evils is left to the imagination, although strong hints were given by The Old Man."

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The "editorial" was reprinted in the December 1940 issue of QST. The word "ugerumf"--while mentioned in this writing, was actually part of poorly sent exchange by a "poor gink."

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A portion of the text reads:

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"BIRRGRMP BRU ROTARY GE GE UGERUMF OM WITH MY SET RETTYSNITCH SPITTY TONE HIT IN POTIMUS? Now what do you suppose the poor gink was trying to say when he unreeled that? You have to guess a lot in wireless, and how would you guess this?" (TOM)

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Yes UGERUMF--not the more popular spelling--UGERUMPH--was used (at least in the 1940 reprint) Perhaps the "ph" modifies this to a noun?

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Why Uggerumph (or ugerumf)? From Jim Wade, WB8SIW, I received the following account:

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Perhaps some additional information on early spark technology would be helpful. Early Spark Transmitters produced a "damped oscillation." The electrical discharge of a high voltage transformer across a gap in an LC circuit excited the LC circuit, which then oscillated at it's resonant frequency. The process is not unlike ringing a bell. Tapping the bell starts it ringing at it's resonant frequency, and the amplitude decreases over a period. The more often the "clapper" rings the bell, the greater the average amplitude.

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Early spark transmitters utilized a "straight" spark gap. The audio frequency one would hear in a receiver was typically a result of the the adjustment of an interruptor or other device at the primary of the transformer. Typically a low, rough, note.

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Eventually, radio engineers figured out that one could increase the efficiency of the spark transmitter by placing a rotary gap in the LC circuit. This device was essentially a "spoked" wheel that rotated on a motor shaft (insulated from the motor, of course), that interrupted the spark at a much higher rate (e.g. ringing the bell faster). This improved efficiency and provided a somewhat more pleasing high frequency tone in the receiving operators phones; it also cut through interference easier.

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The "zenith" (no reference to "9ZN" intended) of spark technology was the "synchronous" rotary spark gap. This was typically a spark-wheel on the shaft of a motor that rotated at a multiple of the AC frequency at the input of the spark transformer primary (e.g. a multiple of 50 or 60 hz). This device improved efficiency above the non-synchronous rotary spark gap for two reasons:

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1) The spark gaps were aligned at the peak of the AC wave form, therefore delivering more power to the LC circuit.

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2) The tone was more pleasing to the ear and cut through interference better, since the discharges were evenly synchronized.

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All of this having been said, a common "trick" utilized by radio amateurs when sending "30" (di-di-di-dah-di-dahhhhhh) at the close of a QSO was to open the "transmit/receive" switch (usually a big knife witch), allowing the spark to die during this last prosign. The result was an unusual "growl." Likewise, an improperly adjusted rotary gap or an inexpensive "straight" gap typically had a rough, unpleasant note in the receiving operators headphones. Therefore, I suspect, the term "Uggerumph."

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By the way, the reason we refer to radiotelegraphy as "CW" is related to spark technology. Unlike early spark transmitters, which produced a "damped oscillation", vacuum tube transmitters produced an "undamped" oscillation or "continuous wave." Therefore, when vacuum tube transmitter technology came into favour in the early '20s, the term "CW" became synonymous with radiotelegraphy. In reality, all modern modes utilize a continuous wave, but we continue to associate "CW" with radiotelegraphy.

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Anyway, I hope that explanation of early spark transmitter technology helps.

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The Second Mystery

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The remaining mystery is why so many hams believe that the Uggerumph is animated, self-propelled, and no longer needs the oversight of the "big brute" with the "positive manner." After all, TOM clearly refers to the device as an instrument. However, in many stories, the animate take on the role of instruments of fate, of justice, of revenge, of . . .. Likewise, the Uggerumph is secretive and stealthy, attacking without being seen in advance and knowing precisely its target.

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So let's do a little history. In 1932, the year of TOM's reference in this note, most equipment still used highly functional but aesthetically crude structures. Amateur radio equipment was no exception. However, by the end of the decade, culminating in the 1939 New York World's Fair, the geometries of art deco styling had given way to the sleek lines of a moving futurism. In automobiles, the Cord opened new vistas in disguising the chaos of the engine compartment under a smooth metallic veneer. Belching steam locomotives with their exposed boilers and steam lines suddenly looked like Buck Rogers space ships that simply preferred to hug a pair of tracks. After WWII, the futurism took on a note of power. For example, the styling that in the 1980s we called "the hatchback" was--for the 1948 Oldsmobile--a "torpedo back." Imagine the possibility of applying a skin of smooth metal over the Uggerumph. Perhaps by the late 1960s, it even has fender fins adapted from the Desoto. By 1990, I can imagine an Uggerumph with perfected stealth technology that evades even our visual senses.

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I should not ignore the genius of TOM or his cohorts. The original Uggerumph bears the imprint of "J. H. Bunnell & Co., New York, U.S.A." J.H.'s role in the development is not clear, but his contribution appears to be the "key" to the Uggerumph. Remember that TOM's initial acquaintance with and development of the Uggerumph stems from the era of spark, and sparks have yet to tell their full story. Indeed, they are lightning quick and do not sit still to tell tales. Could spark have infused something animate into the device? Or could TOM have been so far ahead of his time as to develop the same technology that was to make the Mars' Sojourner a self-guiding rover? The technology in the photo of the Uggerumph appears to be solid state.

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But is the Uggerumph more than manufactured, more than programmed? Is it self-evolving? The eminent science publisher, Hugo Gernsbach issued many reports of self-replicating and evolving "things" that appeared to be objects--but that were more. If the Uggerumph could self-replicate or even breed, then it might also self-evolve. I have heard rumors of devices called electromagnetic hunters, "E. H." for short. One breed of them becomes riled whenever it encounters especially bad and illegal operations. There must be more than one of them, because the breed has been spotted (but not identified for what they are) all across the country. They present themselves as mild-mannered makers of speeches at ham conventions. Generically, we call the breed the "Rile-E-H." If I interpret their behavior correctly, they have elevated torture for rotten operating to a new level. The original Uggerumph would send its victim to a doctor for repairs. The new generation of the Uggerumph, the Rile-E-H, now requires that victims go to someplace worse--the office of a lawyer.

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This line of history and speculation, of course, cannot be proven. It can, however, serve as a warning to the same group of rotten operators against whom TOM railed. In the night, in the dark, in the mist may lurk an Uggerumph to wreak havoc upon those who infect the amateur bands with foul operating practices and plain stupid activities.

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How Do They Do Their Work?

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I have been asked how the Uggerumph, Rettysnitch, and Wouff-Hong do their work of exacting fair and just punishments upon those who foul the airwaves with stupid, unethical, and/or illegal operations. My answer must be speculative, since no one upon whom these instruments/creatures of justice have performed their surgery will confess to exactly what happened. Perhaps they remember only the pain, but not the details. If so, that may be for the best, since amateur radio justice is firm and effective, but not vengeful. Speculatively then, we might let the shape of the instrument be the guide to its use.

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Remember that the Uggerumph essentially is a treatment for uncaring ignorance--whose proper name is "stupidity." The Uggerumph is obviously a shocking hole-cutter, the depth being determined by the severity of the offense. Some hams describe the Uggerumph as a "bear trap," something capable of taking a bite out the victim. Although I do not see hinges in the photographs, neither do I see the hinges in the jaws of folks who speak to me. So a biting device or creature is certainly an allowable view of the Uggerumph. The size of the bite of which the Uggerumph is capable indicates use on the main torso, with the exact position being optional. However, since young squirts were on the mind of TOM, I suspect that the most common placement is one that would prohibit sitting for a while. For all its ferocity, the Uggerumph is the gentlest of the torturing trio.

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"The Rettysnitch. . .is used to enforce the principles of decency in operating work," according to the 1930 ARRL Handbook. The Rettysnitch is a much more specific instrument, also able to make holes, but smaller and deeper ones. It is capable of trepanning and even brain scrambling--or perhaps descrambling those whose operating habits begin scrambled. However, it can also be used on the key (or mike) arm to inflict a tatoo of scar tissue. Since it is the instrument of ethical conduct, it might also be used for heart reversal, and the Rettysnitch's missing teeth suggest that it might have encountered some very hard hearts in its past.

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According to the same 1930 ARRL Handbook, "The Wouff-Hong is amateur radio's most sacred symbol and stands for the enforcement of law and order in amateur operation." The Wouff-Hong's nearest analog is the old-fashion but still effective can opener. Now every can opener requires an initial insertion point, and (if you picture the human anatomical form) you can choose between upper and lower points. The object is to open up the miscreant and expose his evil to himself. This requires the subject to be supine and all opening to be done on the front side, where the victim can indeed see the results: the exposure of his own evil. The beauty of the wood Wouff-Hong lies in the fact that it leaves splinters in places from which they cannot be removed. Thus is the scoundrel reminded for life of his misdeeds and what lies ahead if any one of them should ever be repeated.

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History has it that the applications of the three instruments are unimaginable. However, I have spent my life imagining the unimaginable. Should protocol dictate or should you be too overcome with dread, you may destroy this note. However, you may also keep it in secret so that, if someone really needs to know, you can tell him what is in store if he does not change his operations for the better.

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Updated 04-15-2000, 04-18-2000, 04-27-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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The Wouff-Hong and the Rettysnitch: Lost Traditions?

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L. B. Cebik, W4RNL

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  • "The Wouff-Hong is amateur radio's most sacred symbol and stands for the enforcement of law and order in amateur operation."
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  • "The Rettysnitch. . .is used to enforce the principles of decency in operating work."
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+ The Radio Amateur's Handbook, 1930, p. 11 +
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In 1930, the Handbook had pictures of both instruments of enforcement. By 1936, only the Wouff-Hong appeared, and by 1947, the Handbook had deleted both photos. Just when we needed traditions of law and order and of decency in amateur operations to guide its growth in the post World-War-II explosion of technology and easier licensing, the symbols had disappeared from view.

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Many of today's hams have no idea what a Wouff-Hong and a Rettysnitch look like. To rectify that gap in hamdom's essential history, I have used my very limited CAD abilities to make sketches of the two instruments. Figure 1 is the Wouff-Hong. The two main pieces appear to be wood banded by metal strapping and by heavy wire. What the sketch cannot convey is the darkness at the upper end of the longer wood piece, as if stained by blood or purified for its grave duties in the fires of purgatory--or both.

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Figure 2 is a sketch of the Rettysnitch, an all-metal tool. Of the 5 teeth around the disk near the pointed end, only three remain. According to tradition, the other two have done their work and perished in the effort. Again, my limited skills in rendering the Rettysnitch rob the device of its terrible demeanor, and therefore of its force to ensure operating decency among amateurs.

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Perhaps the last time the story of the Wouff-Hong and the Rettysnitch was told was in 1934. Thanks to Ed Guilford, AA7HQ, in Bothell, Washington, I have the May, '34, QST in which Rufus P. Turner--famous in the annals of electronics writings--recounted "Hamdom's Traditions: A Bedtime Story for Young Squirts." But even by Turner's time, the Rettysnitch was relegated to a paragraph on the story's continuation page in the back of the magazine, with no picture. Somehow, even then, folks had forgotten that you can never have law and order without first having decency. Some pessimists think that we now have neither.

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I do not subscribe to the pessimist's view. Sure, the number of rotten operators has skyrocketed, but not their proportion to the main corps of good, legal, and decent operators, capable and courteous to a fault. We should not be troubled by the size of the job of curing amateur radio of its illegalities and indecencies, for we have more folks to help use the Wouff-Hong and the Rettysnitch just where and how they ought to be used. No, not on others, but on ourselves--to make sure that we set a model for how amateur operations ought to be conducted.

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Turner offers no prescription for using either device, but thought the Wouff-Hong able to beat out King Kong's brains or easily plow up acres of Manhattan bedrock. That will tell you something of the power of these machines. But it won't tell you how they came to be.

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Remember T.O.M.--The Old Man--who wrote in earliest days of "Rotten QRM." His very first article in 1917 blasted concocted abbreviations just coming into use. Among the almost unintelligible gibberish in his headphones were words like "wouff hong" and "rettysnitch," surely instruments of terrifying punishment. By mid-1917, ARRL was besieged by orders for these contraptions, orders that could not be filled because the League staff had never seen either device.

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In 1919, after World War I (then called simply the Great War since no one could imagine doing all that destruction and killing all over again), the League once more took up its work in earnest. At just this critical time, the Directors received from The Old Man a package containing an authoritative and well-preserved specimen of Wouff-Hong. Turner described the contents of the package as "the gruesome instrument of torture." By order of the Directors, it was hung in the office of the Secretary-Editor, within easy reach. Its first portrait appeared in QST for July that year. At each Board meeting, the Wouff-Hong stood on display, to the blanched looks of the humbled Directors.

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The Old Man also presented the world with its first glimpse of the Rettysnitch. In 1921, the monstrous machine was presented to the League traffic manager by the Washington, D.C., Radio Club, ostensibly after receiving it from T.O.M. Even at its first public appearance, two of its teeth were missing, suggesting a long history of necessary and effective use. However, to this day, the Rettysnitch has lost no other teeth. It was ordered to hang by its mate.

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In the 20s and 30s, many a reproduction of both instruments, but especially the Wouff-Hong, materialized across the country. (The photograph of one such replica of a Wouff-Hong is courtesy of Joe Holstein, N8EA.) A group of hams in Flint, Michigan, created the mystic society called the Royal Order of the Wouff-Hong. The society endures to this day, according to legends to which I have so far not been privy. And The Old Man has been given a name: Hiram Percy Maxim, W1AW. At least, legend tells the story that way, perhaps based on the fact that T.O.M. glared at "Kitty" while reflecting on the "rottenness" of everything. Maxim did have a cat. However, true to feline nature, Maxim's cat never spilled the beans.

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But what has become of the Wouff-Hong and the Rettysnitch? More important, what has become of their power to enforce both decency and law and order on the ham bands? Hams used to cringe at the thought, let alone the sight, of these dreadful tools of enforcement. But, we do not hear of them much anymore. Oh, a tremor of curiosity every now and again brings out a ripple of questions and speculation. But not much more than a ripple.

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You see, today, we have much more terrifying weapons, things like Oozies and H-booms and the like. They scare us in ways that seem to make the Wouff- Hong and the Rettysnitch tame and toothless. However, even in Maxim's day, objectively more powerful weapons were used in France, like tanques and gas more poisonous than that made by Texas chili. Why were the Wouff-Hong and the Rettysnitch so powerful to those early hams?

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Because those hams cared about amateur radio in their hearts. They wanted what they knew they could never have: a perfectly law-abiding and decent radio service that would inspire young and old alike to become hams or, lacking the inclination to electronics, to become admirers of hams. Every minute of on-the-air time was a chance to show how noble a pursuit amateur radio was and should always be. They feared the Wouff-Hong and the Rettysnitch as instruments of their own consciences, as they strove to meet the standards they set for themselves.

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And that is where today you will find both the Wouff-Hong and the Rettysnitch--deep in your own conscience. If they seem to hold no power, then you know it is time once more to elevate your standards a notch higher, and then to strive to achieve them perfectly. Each of us has a secret and private office where no one else may go. Above the door, facing our individual operating tables, hang two instruments, one of law and order, the other of decency. However much the outside world may neglect the tradition of these terrible reminders of responsibility, each of us posses our own Wouff-Hong and Rettysnitch. May you never deserve their sting.

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Like all legends, this one, too, must end with special words: pass it on.

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Updated 2-16-99. Versions of this item have appeared in 72, the newsletter of the New England QRP Club and in QST, the journal of the American Radio Relay League. Photographs of both the Wouff-Hong and the Rettysnitch may be seen at the Sparks Telegraph Key Review pages, along with a vast array of telegraphy keys.

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Return to Amateur Radio Page

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Topics: Tales


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Topic Index

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Balun

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Batwing

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Beamwidth

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Big Wheel

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Bobtail Curtain

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Books

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Boom Effects

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Bowtie / Fan

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Broadcast

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Bruce Array / Sterba Curtain

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Closed and Interrupted Loop

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Collinear

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Corner Reflector

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Delta Loop

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Design

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Dipole

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Dipole Curtain Array

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Discone

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Doublet

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EDZ / Zepp

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Education

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G5RV / ZS6BKW

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HB9CV / ZL Special

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HF Lower

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HF Multi Band

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HF Upper

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Half Square

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Hardware

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Helix

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Hex Beam

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Horizontal Loop

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Inverted L

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Inverted U

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Inverted V

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J-Pole

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LPDA

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Lazy H

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Lindenblad

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Links

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Loading

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Longwire

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MF

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Magazine Columns

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Matching

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Modeling

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Moxon

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NVIS

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Noise / Receive

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Off Center Fed Dipole

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PVC

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Phased Array

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Planar Reflector

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Portable

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Prismatic Polyhedron

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Quad

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Quad Loop

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Rectangle

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Reversible

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Rhombic

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SCV

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Satellite

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Small Beams

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Stacking

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Stepped Diameter

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Tales

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Transmission Line

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Traps

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Turnstile

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VHF / UHF

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VOACAP

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Vertical

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Voltage Feeding

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W8JK

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X Beam

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Yagi

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The Impedance-Transformation Properties
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L. B. Cebik, W4RNL

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Baluns, as we commonly construe them in amateur radio, have three main functions. First, they convert an antenna feedpoint or a parallel transmission line from a balanced circuit to a single-ended (sometimes called an unbalanced) configuration, where the single-ended configuration is necessary for cables and equipment using coaxial connectors in which the outer conductor is connected to ground somewhere in the system. Second, we often employ baluns to attenuate common-mode currents to keep them out of equipment and off the surface of coaxial cable braids or sheaths.

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Third, we employ some baluns to transform load impedance values to an alternative value. Although there are designs for baluns capable of many impedance ratios (from 1:1 upward), the most usual balun impedance ratio is 4:1. Indeed, the amateur radio marketplace offers dozens of 4:1 units from different makers, with many different styles of construction for many different applications.

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Although many measurements exist for the power handling capabilities of existing 4:1 balun, with additional measurements for their ability to attenuate common-mode currents, I have seen no measurements of the impedance transformation properties of baluns across the full HF spectrum from 3 to 30 MHz. The AIM 4170 antenna analyzer unit and associated software provides a convenient method of filling this vacuum, at least partially. The notes in the following series of preliminary measurement reports make a start toward characterizing different types of balun designs with respect to impedance transformation.

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Part 1: Essential Background

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Part 2: The Dual-Ferrite-Bead HF Balun: Some Preliminary Measurements

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Part 3: Voltage Baluns: Some Preliminary Measurements

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Part 4: Toroidal Current Baluns: Some Preliminary Measurements

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Since each item in the sequence is in PDF format, you will have to use the "Back" button to return to this page to access the following item.

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Updated 04-01-2008.© L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Balun


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Antenna Design

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L. B. Cebik, W4RNL

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Over the years, I have developed a number of highly accurate design aids for some very basic antennas, such as the Moxon rectangle, quads from 1 to 4 elements, 3-element Yagis, and a dual-element wideband dipole. Although the aids are available in a variety of forms, I have decided to combine all 11 calculation programs into a single spreadsheet. You may download the spreadsheet using the following links:

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Antenna-Design in .XLS format (Excel)

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Antenna-Design in .QPW format (Quattro Pro)

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Almost all of the calculating programs are also available as NEC-2 antenna models in NEC-Win Plus (.nwp) format. This format is perhaps the most preferred because it allows you to see antenna patterns and the calculated feedpoint impedance as you enter the design frequency and the element or wire diameter. Some are available as programs (AC6LA's Moxgen), scripts (Moxon), and may appear elsewhere on-line. However, the Quattro-Pro and Excel spreadsheets may make them available as a group to some antenna builders who lack modeling software.

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All of the programs have some of the same limitations. They all presume that the antenna uses a uniform diameter element material throughout. This provision is normally not a problem for quad antennas, but many HF and lower VHF Moxons and Yagis will use stepped diameter elements. The programs have no provisions for stepped-diameter elements and so will be useful only as a starting point for significant additional design work. As well, all of the programs presume that the wire is bare; insulated wire will required significant adjustments. Finally, all of the programs presume that all elements are insulated and electrically isolated from any conductive support structure. The calculations do not consider boom effects for elements directly connected to a conductive support structure.

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The spreadsheet pages also have limitations, the foremost of which is that nothing has been protected from accidental or intentional change. You may wish to store an archival copy of the spreadsheet you download and use only a work copy.

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All of the programs rest on a common set of procedures for each type of antenna. For each basic design, I developed a large number of optimized NEC models translating each design for measurements in wavelengths. I then subjected each dimension collection to regression analysis to obtain working equations that allowed me to "connect the dots." The equations have no electrical significance in themselves, but provide continuity between the steps in the optimized models. In virtually all cases, the difference between a calculated model and an independently optimized model at the same intermediate place resulted in less than 1% variation. The calculations have been calibrated for use between 3 and 300 MHz. However, I have successfully designed antenna from these equations for frequencies as low as 1 MHz and as high as 900 MHz.

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Unlike a large number of oversimplified antenna design aids (including those notoriously inaccurate "cutting formulas"), the programs take seriously the fact that the dimensions of an antenna design of any complexity will change as we change the element or wire diameter. In fact, the user must enter only two pieces of numerical data. One is the design frequency in MHz. The other is the diameter of the wire or element. The programs have been calibrated for wire diameters as small as 1E-5 wavelength up to about 1E-2 wavelength. However, you will enter the wire diameter in a selected unit of measure. Each program provides options for AWG wires sizes as well as diameters given in inches or in millimeters. The program calculates the wire diameter as a fraction of a wavelength. With 3 entries (frequency, unit of wire size, and the wire size itself), each program produces a set of dimensions given in wavelengths, meters, feet, and inches. You may not be able to take them to the bank, but you will be able to take them to any NEC modeling software and confirm the performance. Then, you may build the antenna.

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Every program page contains a reference diagram to identify each dimension against the sketch. However, since these floating diagrams may not translate to all versions of either Quattro Pro or Excel, we shall run down the programs briefly in these notes. Page A of the spreadsheet contains two programs for Moxon rectangles, the antenna that started me down the path of using regression analysis on optimized models. Page B has programs for 1 and 2 element quads. Page C provides calculations for 3-element quad beams, with a wide-bandwidth and a high-gain version. Page C supplies calculations for a high-performance 4-element quad. Page (E) provides calculations for three different 3-element Yagi designs: one for maximum practical gain, one for maximum front-to-back ratio, and one for very-wide-band operation. The final page (F) contains the equatrions for the dual-element wideband dipole. It is unlikely that I shall be able to add further programs to this set of 11, because every additional increase in design complexity multiplies the number of variables to be tracked when optimizing designs for various increments of wire diameter.

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The Moxon Rectangles

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The Moxon rectangle is a compact two-element driver-reflector parasitic array that delivers almost the gain of a 2-element Yagi with significant improvement of the front-to-back performance. Because the element ends fold toward each other, we must create some calculation dimensions in addition to the usual element-length and element-spacing pair. Fig. 1 diagrams the dimensions.

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The tails are dimensions B and D, and the fairly critical gap is dimension C. E is simply the sum of B through D as an arithmetic check. A, of course, is the maximum side-to-side dimension of the antenna. In its normal form, it is about 70% as wide as a comparable 2-element Yagi.

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By normal form, I mean simply a version that has a resonant feedpoint of about 50 Ohms. This form appears in the first of the two programs. A 50-Ohm feedpoint impedance allows direct connection to a 50-Ohm main feedline, although the use of a common-mode current suppressor is advisable.

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An alternative form uses a somewhat squarer structure to yield a feedpoint impedance between 90 and 100 Ohms. This form is useful when creating circularly polarized turnstile pairs of Moxons for fixed satellite antenna use. RG-62 makes a good phase line, and the net impedance allows use with a 50-Ohm main feedline. The gain is somewhat lower than for the 50-Ohm version, but when placed over ground and pointed straight up, ground reflections wash out the differences. The second program on Page A calculates the required dimension. Note that each program is separate and requires new user inputs.

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For further information on Moxon rectangles, see the index of articles on Moxon Rectangles and Online Calculator. Alternatively, see my volume on Moxon Rectangle Notes on the Books Page.

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The Quads

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Volume 2 of Quad Notes or the index of "New Quad Studies" provides references to the articles relating to the calculation aids for the entries in this category. The process began with single-element quad loops and progressed into beams. Fig. 2 shows the critical dimensions of the smallest quad components. One- and two-element calculations appear on Page B of the spreadsheet.

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With a square quad loop, we are usually concerned with the length of each side to see how much room the antenna will occupy and with the loop circumference to see how much wire we need to make the antenna. I included the single loop since cutting formulas for single quad loops are so very far off the mark. If you make a diamond loop, you may use the same side and circumference calculations and simply rotate the array 45 degrees. The 125-Ohm feedpoint impedance is ripe for a quarter wavelength section of 70-75-Ohm cable as a matching section for our normal 50-Ohm main cable.

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When we turn to 2-element quad beams, we encounter a major quad limitation, the relatively narrow operating bandwidth for its feedpoint impedance and front-to-back ratio. Therefore, I optimized the 2-element quad for maximum front-to-back ratio and for maximum operating bandwidth. As a result, the calculated spacing between the elements will be somewhat wider than we find in most articles and handbooks. Narrower spacing may raise the gain at the design frequency by a very small amount, but the SWR and front-to-back bandwidth will drop very noticeably. The wide-band 2-element quad does have a fairly high feedpoint impedance--about 135 Ohms. A quarter wavelength section of 93-Ohm RG-62 will usually provide a good match to the main feedline.

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Fig. 3 shows the outline of critical dimensions for a 3-element quad beam. When we add a third element (a director), we are faced with options. We may design for maximum operating bandwidth or we may design for maximum gain--but we can not do both within the same design. Page C of the spreadsheet, however, does give you a chance to design quads of each type and to compare their dimensions.

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The wide-bandwidth version at the top of the page shows reduced gain (by about 0.7 dB) relative to the high-gain version at the bottom of the page. However, for any operating parameter, such as the SWR curve or the front-to-back ratio, the bandwidth of the high-gain version is only 60-70% of the value for the wide-band version. The wide-band version of the beam has a 75-80-Ohm feedpoint impedance, while the high-gain version is closer to 50-Ohms.

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On page D of the spreadsheet, we find calculations for a high-performance 4-element quad. Obtaining over 10-dBi free-space gain with the widest possible operating bandwidth requires fairly wide spacing among the elements. There have been spot-frequency designs of equal performance using shorter booms, but they do not lend themselves to smooth curves that allow a very wide range of wire diameters and frequencies. The feedpoint impedance values of the 4-element quad design hover in the 60-Ohm region. Fig. 4 shows the outline of the beam for parts identification.

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Like the Moxon rectangle, the quad and its calculations presume a monoband beam. Since the dimensions all rest on fractions of wavelengths, combining them into a concentric multi-band quad is no easy task. Elements interact so that the monoband dimensions may not be right as a foundation for the more complex array.

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3-Element Yagis

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All 3-element Yagi designs share some common features, most notably, the ones shown in Fig. 5. We have 3 elements, with 2 spacing values to consider. However, spreadsheet page E has three separate calculation programs, indicating that there is more to 3-element Yagi design than having 3 elements.

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Over the years, I have identified 3 fairly distinct species within the genus of 3-element Yagi: a high-gain type, a maximum front-to-back ratio type, and a very-wide-band type. The top of the spreadsheet calculates the dimensions of the high-gain Yagi. With a free-space gain of about 8.1 dBi, it still has a design-frequency front-to-back ratio of about 25 dB. However, it is somewhat narrow-banded, straining to cover the first MHz of 10 meters. The resonant feedpoint impedance is 25 Ohms, a convenient value for use with a quarter wavelength matching section, a beta match, or a gamma match.

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Immediately below the graphic on the spreadsheet are the calculations for the maximum front-to-back version of the antenna. Although the gain drops to about 7.8 dBi, the rear lobe has a deep null on the design frequency. The null may approach 60 dB below the forward lobe. Hence, the antenna is useful for single-frequency direction finding. The typical resonant feedpoint impedance is close to 30 Ohms.

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At the bottom of the page is the wide-bandwidth version of the antenna. The gain is about 7 dBi on the design frequency, although the front-to-back ratio remains above 20 dB. The antenna's key advantage is its ability to maintain most of its design-frequency performance across a wide bandwidth, such as all of 10 meters or all of 2 meters. A second advantage is the 50-Ohm resonant feedpoint impedance, a direct match for the typical 50-Ohm main feedline.

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Each of these 3-element Yagi designs has applications for which it is most suited. The key limitation lies in the programs. They calculate for uniform-diameter elements, restricting their use to VHF and UHF beams, and possibly some low-HF wire Yagi installations. To create a stepped-diameter version of any of the Yagis requires the use of NEC-type software. Ordinarily, stepped-diameter elements do not require any changes of element spacing. However, having the Leeson corrections available can ease the problem of arriving at equivalent-length stepped-diameter elements relative to the uniform versions used in the calculations.

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For additional information on these antenna designs, see "Modeling Yagis by Equation"

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The Dual-Element Wideband Dipole (DEWD)

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UR0GT developed an interesting wide-band dipole antenna that employs 2 elements in an interesting close-spaced relationship. See Fig. 6. The center cross-wire, marked "spacing," contains the feedpoint, normally a 50-Ohm coaxial cable. Each end of the antenna consists of 2 wires, one longer and one shorter. By judicious selection of the 3 wire lengths, one can cover all of the 80-75-meter band using common wire sizes. Fatter wire sizes (or tubing) yield even broader bandwidth values. For example, one might make a single vertical antenna to cover both the 10- and 11-meter bands. Likewise, one can easily broaden the bandwidth of a UHF planar reflector array with a DEWD driver.

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The design program is based on using the center resonant frequency (with other resonant points at the low and high ends of the passband) set to about 70 Ohms for a 50-Ohm SWR at that point of less than 1.5:1. By entering the element diameter and the center or design frequency, the spreadsheet calculates the length of the spacing wire and the two pairs of end wires to produce a wideband dipole with under 1.5:1 50-Ohm SWR for the calculated bandwidth shown as the last entry. The bandwidth is simply the upper frequency of a 1.5:1 SWR minus the lower frequency with the same SWR divided by the center frequency and multiplied by 100 to arrive at a percentage.

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The calculation program is not a final design product unless you want it to be that. It will also provide starter values for modeling wider-band DEWDs that use a higher center SWR (perhaps 2:1) or special purpose very low SWR DEWDs, such as an element designed just to cover the entire 10-meter band with less than 1.1:1 50-Ohm SWR.

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Conclusion

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The 11 calculation programs included in these spreadsheet pages represent an advance beyond the over-simplified formulas all too often used to design antennas with marginal performance. Each system rests on careful optimized modeling and regression analysis and has been spot checked with physical prototypes. When used within their limitations, they can speed the design of utility antennas of the types included in the collection. However, like any system of calculation, they do not account for the set of construction variables that accompany the building of any antenna. Those variables are the user's responsibility.

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For an additional set of spreadsheets that may be useful when matching antenna feedpoints to main feedlines, see "Antenna Matching"

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Updated 06-26-2006, 04-04-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Design, Dipole, Matching, Moxon, Quad, Yagi


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Antenna Matching

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L. B. Cebik, W4RNL

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The following notes have a very limited purpose: to orient you to the calculation aids available in spreadsheet form for determining the dimensions of a few common ways of matching an antenna--especially a beam--to your feedline. You may download the spreadsheet using the following links:

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Antenna-Match in .XLS format (Excel)

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Antenna-Match in .QPW format (Quattro Pro)

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The spreadsheet pages include series matches (including the 1/4 wavelength transformer, the Bramham system, and the Regier system), the beta or hairpin match, the gamma match (using separate sheets for the Healey-Wheeler system and the Tolles-Nelson-Leeson system), and finally the match-line and stub method. The pages themselves are simple and direct, with only numerical content, plus a few notes here and there. There are no hidden entries, so you may alter them as you wish--although accidental ruination is also possible. Be sure to have entries for each input data slot, or the results will not be usable. The sheets have very few protections against non-calculable situations, such as division by zero. All pages have undergone reasonably extensive testing via antenna models.

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The following notes orient you to the pages, but do not provide extensive explanations of how each matching system work.

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Series Matching

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Series matching includes 3 system, ranging from the most specific to the most general.

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1. The 1/4 Wavelength Transmission-Line Transformer

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The 1/4 wavelength transmission-line transformer is perhaps the best known of the series matching systems. Fig. 1 outlines the basic application of the system.

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We may insert a 1/4 wavelength section of transmission line between a resonant antenna impedance and a feedline if the transformer section Zo is the geometric mean between the antenna and the feedline impedance. For example, if a beam has an impedance of 25 Ohms and we have a 50-Ohm feedline, then a transformer section of 35-37 Ohms will effect the required impedance transformation. We may use RG-83 or parallel sections of RG-59 to create the transformer. We may also step up or step down: the only requirement is that the transformer Zo be roughly the geometric mean of the two end values.

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For further information on the 1/4 wavelength transmission-line transformer, as well as ways to use variations of it, see "When is a Quarter Wave Not a Quarter Wave?".

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2. The Bramham System

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The Bramham system of series matching tackles a special problem: matching a resonant antenna impedance to a different feedline Zo. The basic problem and solution appear in outline form in Fig. 2.

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By using two inserted line sections (that never total more than 1/4 wavelength), we can arrive at a perfect match. However, we require that the initial antenna impedance be resonant. For further information on the Bramham system, see "Series Matching: A Review".

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3. The Regier General Series-Matching Solution

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3 decades ago, Regier developed a general solution to series matching any antenna impedance to a given line with a single line insertion. The general outline appears in Fig. 3.

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There are limits to what combinations of Zo and Z1 we may use and still obtain a desired match. In general, the closer the values of Zo and Z1, the smaller the range of antena impedance values that we can match. Note that we can combine parallel and coaxial lines in creating the match. For further information on the Regier system, see "Series Matching: A Review"."

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The spreadsheet page for series matching has undergone many modeling tests using the NEC TL facility. The results are exact. All series matching systems presume a driven element that is insulated and isolated from any conductive support boom.

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The Beta or Hairpin Match

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On a separate spreadsheet page, you will find calculations for the beta or hairpin match. Essentially, the beta match is a form of L-network specifically arranged to transform a higher line Zo to a lower antenna impedance. In the process, the network uses a shortened element that has capacitively reactance in the feedpoint impedance as one of the reactive components in the L-network. Fig. 4 shows the general evolution of the beta or hairpin match.

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For the highest level of effectiveness for a given resistive component of feedpoint impedance, the beta match requires a certain capacitive reactance. We obtain this value by adjusting the element length. The only component that we need to add to the system is the parallel or shunt element. If the element has a capacitive reactance, the shunt element must be inductive (and vice versa).

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Some folks distrust the beta match because one form of shunt inductance seems to be a short circuit across the feedpoint. Fig. 5 shows 3 typical forms of adding inductive reactance across the feedpoint terminals, which are insulated and isolated from any conductive support boom.

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A solenoid inductor is feasible and generally has little loss, since its reactance will normally be quite low. However, shorted transmission-line stubs may generally provide the same inductive reactance with even lower loss. The hairpin or shorted parallel transmission line section is the version that most worries new users. However, the beta match in any form is as effective as virtually any other system in effecting a low-loss match between the element and the feedline--when the element resistive component is less than the feedline Zo. In addition, one may also lengthen an element to make it inductively reactive. Then the shunt component becomes a capacitance. Both versions of the beta match have undergone extensive modeling confirmation.

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For further information on the beta or hairpin match, see "The Beta Match: 2 Views"."

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The Gamma Match

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Two pages devote themselves to gamma match calculations. The gamma match differs from the previous matching systems in that the calculations are not precise. Rather, they produce starter values that will require careful field adjustment (the gentler sounding term for trial and error). Fig. 6 shows some of the reasons why the calculations are less than fully precise.

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The gamma system begins with a larger number of variables, some of which are the physical dimensions of the assembly components. We need to know or decide upon the main element diameter, the gamma rod diameter, and the center-to-center spacing between these two parts. Calculations usually proceed (although there have been variations) by treating the gamma assembly as a section of parallel transmission line, shorted at the far end. The end result is a change in the position of the antenna feedpoint relative to the element without the gamma assembly. Most calculation systems do not take into account the far-end shorting bar structure or the structure that supports the feedline connector.

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Practical gamma matches also include a number of variations on the ideal situation used in calculations. The rod may extend beyond the shorting bar. The required series capacitor may not be at the feedpoint, but be somewhere along the gamma rod. The gamma system is the only matching system in this group that permits a direct connection of the main element center to the boom. However, we cannot easily obtain the initial feedpoint impedance when we connect the element to the boom, and the boom will have an affect upon the feedpoint impedance.

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The two calculation systems have different sources but similar starting points. The Healey-Wheeler system derives from some of the earliest work on the gamma and requires the user to insert trial values of the gamma rod length until the resulting resistive component at the new feedpoint matches the target line Zo. The Tolles-Nelson-Leeson system (distributed in Basic format by ARRL with The ARRL Antenna Book) calculates the gamma rod length.

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The two systems do not produce identical results. As well, the results differ from the results of antenna modeling. Because NEC cannot effectively handle the gamma match, only a highly corrected version of MININEC (such as Antenna Model) is adequate to the modeling taks. However, even MININEC cannot show the required variations that emerge from connecting the element to a central boom. Since gamma matches receive only spot checks rather than systematic comparison of calculations and/or models with physical antennas, all three methods are tentative guides, useful for beginning the process of designing a gamma match, but always needing extensive field adjustment.

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For further information on the beta or hairpin match, see "Some Preliminary Notes on the Gamma Match"." Despite the lesser precision of the calculations relative to building a gamma matching assembly, the gamma match itself is capable of matching a wide range of antenna impedance vales--both resonant and non-resonant--to standard feedlines.

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The Match-Line and Stub Matching System

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Of all of the matching systems included in the spreadsheet pages, the match-line and stub system may be the oldest. We use it to match odd antenna impedance values--such as values we might obtain from an extended double zepp antenna--to a standard feedline. Fig. 7 outlines what we require.

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If we select a match-line Zo that is high enough relative to the antenna resistive component, at some line length, the resistive component will be the Zo of the feedline. In almost all cases, there will be a remnant reactance for which we may compensate with a shorted or open stub of the same type of line that we use for the match-line section. In most cases, there will be a solution in which the combined length of the match-line and the stub is less than 1/4 wavelength. In fact, the match-line and stub system is a variation of the Regier series matching system, but it is sufficiently special to deserve separate treatment.

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There are values of match-line impedance that will not effect the desired match. The spreadsheet shows how to detect them. Wherever we may create the desired match, we shall find two match-line lengths that will do the job. Each line length will have both open and shorted stub reactance compensation values. Of the four options, we normally select the one that yields the shortest combined match-line and stub length. (In fact, it is possible by adding 1/2 wavelength match-line sections to bring the main feedline connection point close to ground level--so long as we do not let the stub drag on the ground.)

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For further information on the match-line and stub method, see "Stub Matching: A Review"."

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Conclusion

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I am making these spreadsheet pages available solely as an aid to amateurs and others who may have occasion to calculate one or more common matching systems. Despite subjecting them to numerous tests, I cannot certify that they will always produce precise results, since I have not tested all possible cases. (Gamma match results, of course, will not be precise, although the two versions shown yield results that coincide with their sources.) Even where the results are good, every antenna builder must remember that construction variables may call for field adjustments in even the most precise systems.

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There are many more ways to match antennas than I have included in these few sheets. General L-, T-, and PI-network solutions appear in many programs, and so I have omitted them. Instead, I have chosen methods that, despite their wide use, have not usually been included in matching programs. Applying them to situations more significant than satisfying curiosity about the calculations is a user responsibility.

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For an additional set of spreadsheets that may be usful when designing some kinds of antennas, see "Antenna Design"

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Updated 06-26-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching


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The Beta Match: 2 Views

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L. B. Cebik, W4RNL

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The beta or hairpin match is so deceptively simple in appearance that many radio amateurs distrust it immediately. Surely adding a coil across the feedpoint terminals--and nothing else except the coax--must foul up the performance and produce dreadful results. The coil or the hairpin is so small that it must act like a short circuit.

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Unlike a gamma match, which permits the builder to make a direct connection between the driver and the boom, the beta-matched driver requires insulation and isolation from a conductive boom. But, beyond that, the driver connections are simpler. In fact, we can use the same terminals to connect both the beta match and the coax. Every reduction in something that can degrade with time and weather is a blessing in home-built antennas.

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The two common forms of the beta match appear in Fig. 1. The antenna terminals connect to a coaxial cable, usually 50 Ohms. The beta component is anything that produces a required inductive reactance. How much inductive reactance we need will appear shortly. The two most common ways to produce an inductive reactance are with a solenoid inductor or coil and with a shorted transmission-line stub. The stub form is responsible for the name "hairpin" match. Apparently, the term "beta match" was originally copyrighted by Hy-Gain, a company that has used the system extensively over the years. Sensitivity to that situation has led some folks to avoid the simple term "beta match" and to use only the expression "hairpin match." The result has been some odd locutions. For example, the solenoid or coil method of producing the required inductive reactance has been called a "hairpin inductor." Since I have acknowledged the potential copyright holder and have no commercial interests, I shall call the system by its simplest name.

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The ARRL Antenna Book has long had a correct explanation of how a beta match works, along with the conditions for setting up the system. Part of what we shall see here parallels that account. However, there is also a second way to look at the beta match, one that takes us back to even more basic terms. By looking at the beta match in two ways, perhaps we can give you a way to avoid confusion about the system.

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First things first: we call the system a matching system. This label implies that we have an antenna whose feedpoint impedance is not a good match for the ubiquitous 50-Ohm coaxial cable that we so often use as our feedline. We only use the beta match when the antenna feedpoint impedance is less than the cable impedance. For this case, we are talking of impedances well under 50 Ohms. Although we can use a beta match with impedances as high as 35 Ohms, we normally reserve the system for impedances of 25 Ohms or less.

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If our driver is resonant at about 25 Ohms, then we do not need a beta, gamma, or Tee match. Instead, we can use a 1/4 wavelength section of 37-Ohm cable to effect an impedance match. Although there is a 35-Ohm coaxial cable available, it is not easy to find and runs about $3.00/foot. A simpler scheme is to connect 2 lengths of 70-Ohm cable in parallel, with the center conductors connected and the braids connected at both ends. A pair of RG-59 cables in parallel will just fit inside of the common male UHF connector shell without significant deformation. Hence, we can create and waterproof the required cable with fair ease. Remember to account for the velocity factor of the line that you actually use when constructing such a cable.

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Of course, the line length will vary not only according to the line's velocity factor, but also as a function of the frequency that you use as your design frequency. The design frequency is normally the center frequency of the span of frequencies for the antenna (assuming a monoband antenna). If the passband (another name for the spread of frequencies used) is wide and the antenna has any odd properties, you may adjust the design frequency so that you achieve satisfactory performance at the edges of the span. For wider amateur bands, I often recommend that an antenna like the Moxon rectangle be designed for a point about 1/3 the way up from the low end of the passband. Other antennas may require different treatment.

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I used to calculate the length of a wave at the design frequency from scratch. 299.7925/F in MHz gives a wavelength in meters. Divide that by 0.3048 for the length in feet. Multiply by 12 for the length in inches. Of course, if you need the length in cm or mm, then simply make an adjustment by 100 or 1000 to the length in meters. Nowadays, I simply keep my antenna modeling program running and let it do the calculating for me.

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If we opt for a 1/4 wavelength matching section, then we have no need to use a beta match. That situation would mean that this little article would end right here. So let's assume that we do not have any 70-Ohm cable or do not want to cut a section out of our cable TV system. What we do have is some leftover house wiring material, specifically, some AWG #12 copper wire with a 0.0808" diameter. Ultimately, we shall apply it to a 3-element 10-meter Yagi. However, we first need a general procedure for calculating everything that we need for the beta match.

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A Beta Match: the Network Way

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One of the conventional representations of a beta matched antenna element appears on the left in Fig. 2. Let's examine it more closely, because it tells us part of what we have to do to set up the antenna's driven element to receive a beta match.

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Although the figure shows stubs to indicate that we are dealing with an antenna element, the load for the energy arriving via the coaxial cable is essentially between the terminals. Note that we must have a complex load. First, there is a series resistance (Rs). Next, there is a series capacitive reactance (XCs). That much alone tells us that the antenna element itself must not be resonant. If we lengthen the element beyond resonance, it will present a complex impedance composed of a series resistance and an inductive reactance. That condition is a possible one for a beta match, but by habit, amateurs want lighter elements, not heavier ones. So they traditionally use an element that is shorter than resonant. That physical situation results in a complex impedance consisting of a series resistance and a series capacitive reactance, as shown in the sketch. If we had started with a 1/2-inch resonant 10-meter element about 196.97" long, then we must reduce its length to about 192.2" to obtain a usable combination of resistance and capacitive reactance.

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Before we look at why my measurements are so fussy, let's clear up another misconception, this one bred by the appearance of the left-hand sketch in Fig. 2. Because we have only 1 capacitor symbol, numerous newcomers tend to think of the beta match as an unbalanced system. Now the gamma match is inherently an unbalanced system, but the beta match is a balanced system. The center part of Fig. 2 shows a way of drawing the situation that gives us a balance of capacitor symbols. We have 1/2 of the capacitive reactance on each side of the resistor. (If we were using real capacitors as lumped components, we would make each one be twice the value of the virtual capacitor in the left-hand sketch, so that each one has 1/2 the total series reactance. But remember that we are not using a lumped component. Instead, we are using the reactance of an element that is shorter than its resonant length.)

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Now we can return to the fussy element length measurements. How long or short we make the element is a function of the series resistance that it presents. If we know that value, then we can calculate everything else using some very simple equations that apply to an L-network when the energy source has a higher resistive impedance than the load (antenna element). To see how this works, look at the right-hand part of Fig. 2. There, I have redrawn the center sketch in the form of a balanced L-network. You calculate a balanced network the same way as an unbalanced one, except that you later divide the series capacitive reactance into 2 equal parts, one part for each side of the line.

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The L-network consists of a series capacitive reactance (XCs) and a parallel inductive reactance (XLp) across the line on the source or cable side of the network. XLp is the beta-match component, either a solenoid inductor or a shorted transmission-line stub. (Note: XLp is also called a shunt component, but I shall stick to the term parallel. I do not want to confuse matters by using too many terms beginning with "s.")

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There are several ways of calculating the required values of XCs and XLp, but at root, they depend on knowing the value of Rs, the resistive part of the antenna or load impedance. Let's create and define a term having the name "delta." Nowadays, we call this term the loaded Q, the working Q, or the network Q, but its original name was delta. In equations, we represent the name with the lower case Greek letter. We can show the definition of the delta of a down-converting L-network by a simple equation (and down-converting simply means that the source-end impedance is higher than the load-end impedance).

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How do we find out the antenna feedpoint resistance. If we have our antenna set up for a field test, we can always measure the impedance with one of the several antenna analyzers on the market. Or we can go to an antenna modeling program and let it calculate the impedance. Let's suppose that we come up with 25 Ohms. The ratio of the 50-Ohm source end impedance to 25 Ohms is 2:1. Subtract 1 from that and you get the square root of 1, which is 1. That is the value of delta.

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Next, let's figure out how much capacitive reactance we need in series with the 25-Ohm resistive value to satify the network requirements. This step is also an easy calculation.

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We simply multiply the value of delta by the value of the series resistance that is the load, and the answer appears. 1 times 25 gives us 25 Ohm reactance. Notice that in this network calculation, we do not obtain a + or - sign. The absence of a sign simply means that the reactance can be either inductive or capacitive under a special condition. The condition is that the parallel reactance that we will next calculate must be (for ordinary cases) the opposite type from the series reactance. Since we want a shorter element with capacitive reactances as the series reactance, we must use an inductive reactance for the parallel reactance.

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The source-side or parallel reactance is simply the value of the source resistance (50 Ohms) divided by the value of delta. Since delta = 1, then the parallel reactance must be 50 Ohms. Remember that these steps apply to the situation in which we are matching a higher impedance (the 50-Ohm cable that is the source of emergy) to a lower value of resistive impedance (the value of Rs that is the resistive component of the antenna element impedance). When receiving, the situation is reversed. the antenna element is the source of energy at a lower resistive impedance that we up-convert to the 50-Ohm cable impedance. The same component values apply. However, to help keep things straight, we usually only think in terms of transmitting. So the cable end becomes our energy source and the antenna becomes the load.

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That is all there is to doing the basic calculations for the beta-match as a down-converting L-network. We have not yet translated these reactance values into physical components. Of course, we have only one component needing the translation: the parallel inductive reactance across the terminals. The capacitive reactance is contained in the antenna feedpoint impedance. However, before we effect the translation, let's step back and take another look at what we just did.

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A Beta Match: the Parallel-Circuit Way

One of the shortcomings of most handbooks designed for radio amateurs is that they do not give enough space to a fundamental fact about impedances. We receive the information about the antenna feedpoint impedance and do not stop to think about the orientation of the information. In our ideal case, the shorter antenna elements has an impedance of 25 - j25 Ohms. We normally forget that the values for each component of the impedance are series values. +

Why is the qualification necessary? The answer lies in the fact that for every series impedance, there is an equivalent parallel combination of impedance values. Although the handbooks give the conversion equations in each direction, they do not give enough practical examples of using them. Our beta match presents us with a very significant use, since it may teach us something about impedances at the same time that it allows us to flex those long-dormant equations. What we shall do is convert the left side of Fig. 3 into a form that reflects the right side.

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Note that the L-network consists of source and load resistances, with a combination of series and parallel reactances. Suppose that we converted the series antenna impedance components into their parallel equivalent values. For reference, here are the series-to-parallel equations. Note the similarities that let you simplify the actual key presses needed on a hand calculator.

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Since both the series resistance and series reactance values had numerical values of 25, we can quickly arrive at the parallel equivalent resistance (50 Ohms) and the parallel equivalent reactance (-j50 Ohms). Now note that something amazing has occurred. The parallel resistive component of the load--with its associated capacitive reactance at work--yields a 50-Ohm resistance.

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Now be amazed by a fact that is well known to people to match things up for a living: The series and parallel values of the resistive component of an impedance are the same when the is no series reactance or there is an indefinitely high parallel reactance. We cannot simply re-resonate the antenna element, because that would yield a 25-Ohm resistive impedance. We need a way to keep the capacitive reactance working while getting rid of the series reactance net value-- or driving the parallel reactance upward and off scale for all practical purposes.

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One very practical way to accomplish this is to place a parallel reactance of the opposite type scross the initial parallel reactance value. Parallel reactances that are equal make up a resonant circuit. Parallel reactances operate in the same manner as parallel resistances with respect to arriving at a net value for 2 values.

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Since the reactances are equal within this idealized case, the denominators add up to zero, because the two reactance values have opposite signs. Division by zero is not possible, of course. But we know that the value of the result becomes higher without limit as the denominator approaches zero. One common computer program technique of handling division by zero, when zero is within a range of possible values, is to set the result at an arbitrary but very high number. Typically, programs use 1E10. We may use that number here in order to see what has happened to the series values for R and X that we might encounter as the impedance at the coax terminals.

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The equations tell us how to back calculate into the more familiar series forms of resistance and reactance at the coaxial cable terminals. Remember that Rp is still 50 Ohms. Adding the square of 50 to the square of 1E10 has no effect. Any hand calculator will return 1E20 as the result because the square of 50 (2500) only appears at the far end of the result, outside the range of what the readout will show. The resistance numerator is 50 times 1E20. When we divide this by 1E20, we end up with 50 Ohms as the series resistance. The reactance conversion back into a series value has a quite different result. We end up with 2500 times 1E10 divided by 1E20. The result is 2.5E-7 or about 250 nano-Ohms. Effectively, the reactance is zero, just as we predicted.

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The calculations that we have just performed are commonplace in matching situations. In another item at the site are ways to calculate the match-line-and-stub system of matching. We find the place along a transmission line at which the parallel resistive impedance is 50 Ohms. Then we add a parallel transmission-line stub to match the parallel reactance value at that point, but use a stub that produces a reactance of the opposite type. The result is a parallel resistive impedance in paralel with a very high value of parallel reactance. When we reconvert to series values, the series resistance equals its parallel counterpart, and the reactance goes to zero or very close to it. Then we can run coax from that point back to the transmitter. Of course, there is no magic in using 50 Ohms as the desired impedance. It just happens to be the most common line impedance to which we normal gear our matching efforts.

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Although the series-parallel-series conversion equations seem more complex than the simplified L-network equations, they are in fact more fundamental. Indeed, you now have a more complete idea of what those network equations are actually calculating.

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One of the main questions facing the would-be beta matcher is knowing what length to make the antenna element. One of the advantages of the L-network equations is that they provide guidance here, where the series-parallel conversions require that we almost hunt out the correct series reactance value by trial and error. Since we most often calculate for a 50-Ohm source resistance, let's make a small chart of beta-match reactance values using small increments of change in the series load resistance.

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+     Some Beta-Match Resistance and Reactance Values
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+Rso = 50 Ohms for all cases
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+Rs (Ohms)        35     25     17     12.5    10     8.3
+Delta            0.65   1.0    1.4    1.7     2.0    2.2
+Xs (Ohms)        22.9   25.0   23.6   21.7    20.0   18.6
+Xp (Ohms)        76.4   50.0   35.4   28.9    25.0   22.4
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One way to use this chart is as a guide to setting the length of the driven element in an array that might use a beta match. If you have antenna modeling software, you can try shorter elements relative to resonance to arrive at vaue very close to the optimum for the match. It is also likely that you might be able to interpolate between listings for the entire set of reactance values for your own installation.

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Finishing the Job

Let's set up a worked problem so that we can track the techniques and finish the job of creating all of the beta-match components. We may use the 3-element Yagi shown in Fig. 4 as an example that is not far from the idealized numbers that we have used. The antenna uses 1/2" aluminum elements. +
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+3-Element 10-Meter Yagi Dimensions in Inches
+Design Frequency:  28.5 MHz     Elements: 0.5" aluminum
+Element              Length        Spacing from Reflector
+Reflector            206.28        ----
+[Driver (resonant)   196.97        62.40]
+Driver (shortened)   192.20        62.40
+Director             185.33        134.54
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The dimension table shows the original resonant driver. With this element, the feedpoint impedance was 25.7 Ohms. In the process of shortening the element for the beta match, the resistive component dropped a bit to 23.76 Ohms, with a capacitive reactance of -j24.27 Ohms. The numbers that I am citing are too precise for practical purposes, but they certainly cannot hurt our progression of calculations. Both the resistive and reactive components of the modeled feedpoint impedance fit the table nicely, being slightly below those in the column for a 25-Ohm resistive component.

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To calculate delta, we would take the ratio of 50 Ohms, the cable or source resistive impedance, to the value of Rs at the antenna, 23.76 Ohms. The value for delta is (again, in overly precise terms) 1.051. Delta times Rs gives us the series reactance: -j24.97 Ohms or very close to the modeled value, and certainly too close to require any more trial changes of the antenna length. The source resistance divided by delta gives us the reactance of the parallel inductive component or j47.58 Ohms.

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To check out work, lets convert the series impedance terms at the antenna terminals to their parallel equivalents. With the series-to-parallel value equations, we can use the modeled feedpoint series values to obtain equivalents. Rp = 48.55 Ohms. Xp = -j47.53 Ohms. To compensate for the capacitive reactance, we need an inductive reactance of j47.53 Ohms in parallel with the equivalent parallel capacitive reactance. This value is only 0.05 Ohm different from the value we calculated with the network equations. Quite frankly, I know of no one who could build the difference. However, let's use that very slight difference to calculate the net parallel reactance. We end up with a net reactance of j45,229.55 Ohms

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We can now apply the parallel-to-series conversion equations to the new values: Rp = 48.55 Ohms and Xp = j45229.55 Ohms. The value for the new Rs is 48.549, that is, 48.55 Ohms. The final value for Xs is j0.052 Ohms, that is, so close to zero that it does not matter.

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Our work can now go in two directions. We may construct a solenoid inductor or a shorted transmission-line stub to give us the required parallel inductive reactance. Let's begin with a coil. The relationship between a value of inductive reactance and the inductance that produces it at a given frequency is given in common equations.

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Since we know the frequency (f = 28.5 MHz) and the inductive reactance (XL = j47.58 Ohms), we can use the right-side version to obtain an inductance: L = 0.2657 uH. I have purposely used too many decimal places for practical purposes, but they never hurt an example on paper.

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The next step is to calculate a coil that has this inductance. Remember at the beginning of these notes, I specified that we had some AWG #12 copper house wire. We can build a coil from this material. However, when installing it, we must be certain that the copper does not touch the aluminum elements. Otherwise, we shall see corrsion from electrolysis. However, we can use stainless steel hardware (including washers) both to make a secure connection and to separate the two reactive materials.

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There is an age-old equation for calculating the inductance of a coil from its construction, so long as the coil is a single-layer solenoid. Of course, we already know the inductance, and so we can turn the equation around to obtain the number of turns. We shall assume a coil diameter of 1" and a total length of 1". These number assure us of a reasonable Q for the coil. As well, the 1" coil length will coincide with the spacing between the connecting bolts and still leave room for a small gap between the element halves.

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In the equations, L is the inductance in uH and n is the number of turns. The length of the coil is l, and the diameter is d, both in the same unit of measure. We are using inches. Since the values of l and d are both 1, the value of n is the square root of the inductance times 58 or the square root of 15.41. So n = 3.93 turns. Of course, wwe shall raise that to 4 turns so that the leads both head for the element terminals.

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Note that the coil-winding equation does not take the wire size into consideration and does not account for the inductance in the coil leads. We shall, of course, keep the leads as short as feasible. Then we may fine tune the coil inductance by spreading or squeezing the turns as needed.

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Next, let's replace the coil with a shorted transmission-line stub or hairpin. We shall use our AWG #12 wire for the hairpin, using the same precautions at the element connections that we applied to the coil. First, we need to determine the characteristic impedance (Zo) of the parallel line that we shall create. Let's suppose that we retain the 1" center-to-center spacing. The diameter of AWG #12 wire is 0.0808". We can calculate the Zo from another standard equation, where S is the center-to-center spacing and d is the diameter when both are in the same unit of measure.

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The equation gives us 276 times the log of 2/.0808 or 384.64 Ohms. Again, the sense of precision in the 2 decimal places is spurious and only reminds us that we are working a paper example. We shall assume a velocity factor of 1.0 for our short line that will be self-supporting. However, we need to know how short--or long--the line must be. Since we want an inductive reactance, we shall use a shorted transmission line. Again, we have some standard equations that relate the inductive reactance (XL) to the line length (l).

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Note that the equation requires that we use a trig function on our hand calculator. "Arctan" is simply the inverse of the "tan" function. So we divide 47.58 (XL) by 384.64 (Zo) to get 0.1237 and then take the inverse of the tangent of that number. The result is a line that is 7.052 degrees long. We are now only 2 short steps from the final length.

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The first step is to divide the electrical length in degrees by 360 to find the fraction of wavelength that the line happens to be: 0.0196 wavelength. That is the equation on the left.

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The length in inches will be this fractional length times the length of a wave in inches. At 28.5 MHz, a wavelength is 414.135". So our AWG #12 1"-wide stub will be 8.112" long. One reason that the excessive number of decimal places is spurious lies in the various ways in which we construct beta stubs. Fig. 1 showed a rounded end, which is commercially common, since it is easy to create a smooth curve by bending the wire around a cylinder. However, the equation for the electrical length assumes that the shorting wire has effectively zero length and plays no role in the functioning of the stub. Even a flat end to the stub will have a small effect on the inductive reactance, and so too will the connection eyes at the element end. Like the coil, we can also spread or squeeze the stub line into submission.

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Nevertheless, we may test our calculation of the hairpin by adding a shorted transmission line across the terminals of the Yagi with the shortened driver. We shall specify in NEC's transmission line facility a Zo of 384.64 Ohms and a length of 8.112". (The actual TL command requires the measurement in meters. Many commercial implementations of NEC allow user entry in the same dimensions as the wire entries for the elements. The program then converts this value to 0.2060 meters before turning the core loose to perform its calculations.)

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Remember that when we performed our series-to-parallel-to series calculations, we ended up with an impedance of 48.55 + j0.05 Ohms. With the hairpin in place within the model, we obtain a NEC-calculated impedance of 48.55 - j0.05 Ohms. Those values are too close (j0.1 Ohm apart) to be coincidental. Indeed, you may wish to run this exercise through a number of trial value combinations just to become familiar with the process and to get a firm grasp on the relationship of the network calculations to those we performed to convert the feedpoint situation into an equivalent pure parallel circuit.

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Does a beta matched Yagi have an advantages or disadvantages relative to one with a resonant driver? Fig. 5 overlays the 27.5-Ohm SWR curve of the version with a resonant driver on the 50-Ohm SWR curve of the final beta-match version using a shorted transmission-line stub. As you can see, the SWR curves are almost indistinguishable. The Yagi will cover between 28.0 and almost 28.9 MHz with under 2:1 SWR at the feedpoint. The curve will be slightly broader at the transmitter end of the coax line.

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Both versions of the antenna show a free-space gain of 8.11 dBi. There is a divergence in the 180-degree front-to-back ratio: 27.12 dB vs. 27.13 dB. The pattern in Fig. 4 applies equally to both versions of the antenna.

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This small exercise has tried to accomplish 2 things at the same time. First, it has tried to outline the procedure for creating a beta match, including the initial determination of whether or not such a matching system is in order. We calculated the required element capacitive reactance and the required parallel inductive reactance. Then we converted the inductive reactance into a practical beta inductor and also into a beta shorted transmission-line stub.

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Our second goal was to understand better how a beta match does its work. We began with the standard L-network treatment, which is very handy for calculating the required reactances once we know the resistive component of the driver feedpoint. However, we supplemented that perspective by converting the circuit into an equivalent purely parallel circuit so that we could see some basic facts about matching situations of all sorts. We seek a series combination of resistance and reactance that--when converted to their parallel equivalents--yields a parallel resistive component of 50 Ohms. Then we parallel the reactance with the opposite type having the same absolute value. When reconverted back into series values, the reactance goes to zero or very close to zero. Under those conditions, the series and parallel resistive components are, for all practical purposes, the same. In the case of the beta match, we obtained a resistive impedance too close to 50 Ohms to notice any fussy numerical difference.

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One final caution: the Yagi that we used for our example is a very good design. However, the uniform 0.5" diameter elements are impractical In effect, we would need a combination of 5/8 and 1/2 inch elements or, for lighter duty, a combination of 1/2 and 3/8 inch elements. However, even those values, which seem so close to 1/2", will require a complete refiguring the the element lengths. As well, since the beta match results in a balanced set of terminals, use a common-mode supressor at the feedpoint. Something like a W2DU-type bead choke will work fine in the transition from the balanced terminals to the single-ended coaxial line.

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Updated 02-02-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching


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How Accurately Must We Aim a Beam?

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L. B. Cebik, W4RNL

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We may divide the question of beam aiming accuracy into two parts: how accurate we can be and how accurate we must be.

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How Accurate Can We Be?

The accuracy with which we can aim a directional beam array depends largely on two factors. +

1. The accuracy of the beam assemblies initial alignment: A beam's initial direction depends upon the heading on which we lock down the boom and mast within the rotator and upon the accuracy of the rotator's registry of that direction. Consequently, some installers go to great pains to establish the direction of true North and the departure of the beam from that bearing at the point of installation. Once these values are known, the rotator indicator is also set to this heading. Presumably, when everything is set, we lock down the system. The heading will at least be accurate when the beam is pointed in this initial direction.

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2. The accuracy of the beam heading indicator, normally as registered on the rotator control box meter or translated into a computer numerical value. Regardless of the readout system, the accuracy of the heading indication depends upon the accuracy with which the indications system follows the changes of heading relative to the initial alignment.

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Many rotator systems use a potentiometer in the rotator motor assembly housing, along with a control voltage from the control box. A perfectly linear potentiometer with no dead region at either end of the turning circumference would provide a very accurate indication of the departure of the beam heading from the setting at initial alignment. However accurate the circuitry for translating the voltage returned by the potentiometer to the control box, the potentiometer itself has an accuracy limit, normally expressed as a potential range of error. A +/-1% error range would translate into a +/-3.6-degree range of heading error. Given the environmental stress under which such potentiometers operate--in terms both of temperature and humidity extremes and of the motor and gear operation--it is dubious that even a 1% potentiometer would long uphold that level of accuracy.

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We have presumed that the circuitry that translates the incoming voltage from the potentiometer has no error, an unsafe assumption to be sure. Taking all possible sources together, it is unlikely that a rotating system using a potentiometer in the rotator motor housing and standard sorts of indicator circuitry will be better than +/-3% accurate (and possibly less accurate). This accuracy percentage translates into a possible error of up to +/-10.8 degrees. The error is likely to be variable across the horizon in several ways. First, the error level may shift with the bearing. Second, the error level may shift with the direction of rotation, as the wiper contact changes direction. Third, the error level may shift with changes in temperature and humidity. Fourth, the error level may shift with time and the changing conditions of operation of the potentiometer--not to mention the rotator control box indicator circuitry.

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It is not difficult to resolve the voltage returned by the indicator potentiometer down to several decimal places. Translating this voltage into beam headings in tenths of a degree--as read out on a numeric display--is also routine. However, since the basic accuracy of the return voltage is subject to so many potential error-inducing factors, such a display would be more a satisfying illusion than a true registry of the beam's actual heading.

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Obtaining a more accurate readout of the beam heading would require an independent measurement system. One such system would include a self-correcting sensing and indicator system of true North or some other preset bearing. It would then measure the difference between the known or reference bearing and the beam heading, possibly taken by real or virtual measurements of the boom vs. the preset heading. Laser interception of the boom and a fixed reference bar could easily achieve 1-degree accuracy for the beam system. However, for almost all installations, the cost would be prohibitive. Likely, it would also require alignment before each use.

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In the end, the bulk of amateur operations will have to be satisfied with an accuracy of beam heading read-out somewhere in the +/-1 to +/-5 percent region.

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How Accurate Must We Be?

The answer to our second question depends upon several factors regarding the beamwidth of directional antennas. Most amateurs are familiar with the registration of antenna beamwidth in terms of half-power or -3 dB power points. Relative to the bearing of maximum forward gain, we may obtain a beamwidth in degrees by determining the bearings on either side of the maximum gain heading at which the gain decreases by 3 dB. +

However, the -3dB beamwidth is too broad for those types of operation most concerned with maximum precision of beam heading readouts. No standard beamwidth currently exists to evaluate the question at hand. Therefore, solely for the sake of discussion and with absolutely no pretense of adoption, I shall create a standard. For standard voice and CW operation, a drop in gain of 0.5 dB is too small to detect. However, for some of the newer modes of operation, such a drop may mean the difference between a signal being received and not being received. A 0.5-dB change of gain represents a change of less than 0.1 S-unit as currently set into meters at 5 to 6 dB per S-unit. Although not detectable in many types of communications, let's take this unit as the hypothetical least detectable change of gain for at least some types of operation.

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Using such a standard will allow us to re-evaluate antenna beamwidths by yielding new values. If someone wishes to adopt a more liberal standard, the resulting beamwidths will always be greater than the +/-0.5 dB beamwidth. Hence, any conclusions reached in the following notes can be readily adjusted to the revised standard.

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With a standard at hand, we have only to apply it to typical antennas used by the amateur community. As a sampling, I scanned several dozen beam antennas from my collection of models to determine both the standard -3 dB and the suggested -0.5 dB beamwidths. The standard figure was produced by the modeling software--NEC-4 as commercially implemented. However, the -0.5 dB beamwidth was determined by exploring the azimuth pattern until the gain decreased by half a dB. Since pattern exploration occurs in increments, I chose as the demarcating value the heading on which the gain was at or just above -0.5 dB relative to the maximum forward gain so as not to be too liberal with the recorded beamwidth value.

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Using NEC models of beam antennas is convenient, since measurement of the -0.5 dB heading would be difficult, at best. Models presume certain conditions that may or may not be true of real antennas. For instance, the models of standard beam designs all produce symmetrical patterns. The symmetry of the pattern of a real antenna, especially as it increases in frequency and within the tight limits of -0.5 dB points, would be open to question. The models all use free- space gain as the reference in order to fairly compare antennas having vastly different gain values. Over real ground, the take-off angle--or elevation angle of maximum radiation--will vary slightly as we increase the gain of a directional beam, which would make comparisons a bit more difficult.

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The table below provides model figures for antennas of 2 types: monoband Yagis and monoband quads. Yagis are far more numerous in the listing--numerous enough not only to show progressions, but as well to show occasional slight departures from progression main lines. The collection of quads is barely large enough to form a progression, but it is sufficiently extensive to allow some comparisons with the group of Yagis.

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+                   Representative Beams and Their Beamwidths
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+Free-Space Gain         +/-3 dB B/W       +/-0.5 dB B/W     No. Elements
+    dBi                   degrees            degrees
+Yagis
+ 6.13                   70.0              28                 2
+ 6.27                   68.8              20                 2
+ 6.48                   68.8              28                 2
+ 7.12                   66.6              26                 3
+ 7.80                   63.6              26                 3
+ 8.11                   62.8              24                 3
+ 8.48                   61.2              24                 4
+ 8.90                   59.8              24                 4
+ 9.25                   58.8              24                 4
+ 9.71                   55.6              22                 4
+10.05                   54.6              22                 5
+10.21                   52.6              22                 5
+10.22                   53.6              22                 5
+10.23                   53.6              22                 6
+10.23                   52.6              20                 6
+10.28                   52.4              20                 5
+10.53                   51.8              20                 5
+11.07                   49.2              20                 7
+11.33                   49.8              20                 6
+11.89                   44.6              18                 8
+12.25                   46.2              18                 6
+12.54                   42.5              18                 8
+13.27                   36.7              16                 9
+13.33                   40.2              16                 8
+13.89                   37.4              16                10
+14.21                   35.8              14                11
+15.22                   32.6              14                13
+15.68                   32.0              14                14
+15.68                   31.2              12                14
+16.27                   29.0              12                16
+17.62                   25.0              10                21
+18.59                   22.6              10                26
+18.66                   22.4               8                25
+19.64                   20.4               8                31
+Quads
+ 7.06                   75.0              30                 2
+ 7.49                   74.0              30                 2
+ 8.88                   65.4              26                 3
+ 9.56                   61.6              24                 4
+ 9.74                   60.2              24                 3
+ 9.96                   57.8              24                 4
+10.00                   57.0              24                 6
+11.16                   49.6              20                 5
+11.34                   49.2              20                 5
+11.89                   45.2              18                 6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The table reveals several notable items about gain vs. beamwidth.

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1. The general trend: As shown in Fig. 1, the general trend in each group of directional beams is a narrower beamwidth for a higher gain. This fact has been known since beam antennas first appeared in the dim recesses of radio history. However, few amateurs have a due appreciation of the quantification of this phenomenon. Therefore, the table is worth reviewing. Note also that, within limits, the gain-beamwidth relationship is independent of the number of elements within an array. Rather, the gain derived from the beam is the chief determinant of both -3 dB and -0.5 dB beamwidth--or anything in between. Indeed, the exact boom length is also secondary to the beamwidth, since some nearly equal-gain arrays have differences in operating bandwidth: narrower bandwidth arrays can often achieve a peak gain on a shorter boom. Of course, excessively widening the beamwidth standard can easily let the check points encounter secondary lobes-- although not for the reasonably well-behaved patterns in Fig. 1--and thus empty the figure of meaning.

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For the most part, HF operators work with antennas with less than 12 dBi free- space gain, in other words, less than 8-9 elements on a long boom. The majority work with antennas yielding between 7 and 9 dBi free-space gain. Consequently, the available -0.5 dB beamwidth will be at least 20 degrees (+/- 10 degrees of the desired heading for most operators. Even those working with beams capable of 12+ dBi free-space gain will have a -0.5 dB beamwidth of 18 degrees.

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The situation differs as we increase gain, as is common in VHF and UHF operation. Beamwidths at the -0.5 dB level shrink to single digit levels, increasing the difficulty of accurately aiming an array. Indeed, independent references are often needed to precisely position a very high gain array on its target.

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2. Quad vs. Yagi beamwidth: At every level sampled where the gain of a quad array could be roughly equated with the gain of a Yagi array, the quad exhibited wider -3 dB and -0.5 dB beamwidths. As shown in Fig. 2, the difference is most dramatic at lower gain levels: the plots show antennas with 7+ dBi free-space gain levels. The linear plot is necessary to display the two patterns clearly.

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As the gain of the array increases, the differential in beamwidth between Yagis and quads decreases. However, it never disappears entirely within the range of arrays sampled here for the quads. However, since no quad with a free-space gain above 12 dBi was used in the listing (since I do not have any in my collection of models), there may well be a point at which the differential disappears from view.

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What applies to the differential between Yagis and quads also applies to other types of arrays. It is always unwise to assume from a glance at an azimuth pattern that a directional beam has a certain order of beamwidth at any level used as the standard. Careful checking of each design is necessary to know for certain.

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3. Exceptions to the trend: Within the list of directional arrays, there are a few exceptions to the general progression of gain vs. beamwidth correlations. Moreover, the progression would not graph out as a smooth curve for either the - 3dB or -0.5 dB levels. Fig. 3 demonstrates why the curve would be irregular. Not all patterns are the smooth ovals that we associate with "perfectly designed" parasitic arrays. Although the curve on the left resembles in its main forward lobe outline the middle pattern of Fig. 1, the forward secondary lobes make it difficult to know for sure whether the main lobe has been distorted from the most "well-behaved" condition. Hence, ripples in the general progression are bound to occur wherever secondary forward lobes are present.

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As the right side of Fig. 3 demonstrates, even when the secondary lobe structure seems invisible, it may exert an effect on the beamwidth. For equal-gain antennas, the "bullet" pattern to the right has a narrower beamwidth by noticeable amounts at both levels of interest in these notes. The widening of the pattern as the bearings approach the side nulls is an indication of secondary lobe formation.

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In fact, changes in the azimuth pattern that can affect the beamwidth may occur across the operating bandwidth of an antenna, even though gain changes are small to negligible. For well-designed arrays with limited operating bandwidths, such differences are likely to be only of academic interest. However, they do exist and may play a role in performance wherever designs are pressed beyond their limits.

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Some Tentative Conclusions

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The second portion of these notes was designed to graphically and tabularly demonstrate the relationship between gain and beamwidth for a span of array gains that cover most amateur operations. However, the basic question for the second part of these notes was how accurate our beam aiming must be to achieve the strongest signals between locations. If we combine the notes for the two portions of this preliminary investigation, some tentative answers emerge.

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1. For lower gain, wide beamwidth arrays--typical of most (but not all) HF operations--excessive concern with the precise heading of a beam seems to be beyond the level of necessity. The potential errors of heading indicators are offset by the very wide -0.5 dB beamwidth--in most cases, better than 20 degrees. Unless on the cusp of detectability, most changes of 5 degrees in beam heading will not yield any change in signal strength that will show up on a meter. For this class of arrays, simply point at "Europe" or "Southeast Asia" (for the U.S. operator) will be accurate enough, although a final tweaking to compensate for unquantified indicator system errors may be useful. For voice and CW operations, where the -0.5 dB standard for detectable signal strength change is too stringent, the available beamwidth before a change of beam direction would make a difference can be considerably wider.

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2. For very high gain system with inherently narrow beamwidths, such as those above 12 dBi free-space gain, the indicator system error and the -0.5 dB beamwidth begin to merge. For such systems, adjunct aiming accessories are certainly warranted as a matter of course for each change of beam direction. Such auxiliary systems may involve manual or automated fine aiming relative to signal strength, or they may make use of adjunct directional aids derived from precise navigation work.

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3. For the intermediate level system with free-space gain levels between 8 and 13 dBi, we have a situation that is difficult to define in terms of operational actions. When used for casual or slow-rate operations, manual system tweaking based on signal strength of the target station (and possibly QRM from other competing stations) often suffices. However, for high-speed and competitive operations with definite target stations, even an operating assistant may not be able to keep pace with the need for adjusting headings to be as precise as necessary for the highest efficiency. It is in these kinds of cases that we find appropriate concern with precision installation settings, indicator system error levels, and (automated) adjunct heading adjustments.

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However, system error potential and antenna beamwidth alone--even when all normal variables are taken into account--do not tell the full story. To these factors we must add the propagation conditions and paths that exist at any given moment of operation. This final collection of variables can sometimes (but certainly not always or even most of the time) void the best results of the most precise system that does not rely on careful listening and re-aiming for the strongest signal.

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In the end, each operator must make his or her own decisions on how much effort to place into each phase of the problem of aiming a directional array. These notes--especially the beam data--are designed to help with, but not substitute for, the process through which each station operator must go in directing his or her array.

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Updated 01-22-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Beamwidth, Quad, Yagi


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A Common-Mode Current Picture Show

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L. B. Cebik, W4RNL

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Common-mode currents on transmission lines come in two varieties: good ones and bad ones. Of course, if we do not know what a common mode current is, then we would have a difficult time telling the two apart.

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On a normal transmission-line, free of anything other than the energy that we wish to transfer from one end to the other, we find on the 2 conductors (of a 2-conductor transmission line) currents of equal magnitude and opposite phase angle. The field between the conductors ideally prevents the line from radiating any energy. However, if we introduce energy onto the lines that has a common magnitude and phase angle on both lines, then the transmission lines becomes a simple antenna wire that happens to be composed of two wires. Many amateurs have pressed old lengths of 300-Ohm TV ribbon cable into antenna use by joining the wires at each end and using the cables as a single wire. Under these conditions, the wires have only antenna currents. We might also call them radiation currents. Finally, we can call them common-mode currents, since the two wires have a common current magnitude and phase angle.

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Now suppose that we could combine transmission-line currents and antenna/radiation/common-mode currents on the same pair of wires. We do so every time we construct or use a folded dipole or a folded unipole (monopole). In "Unfolding the Story of the Folded Dipole", I noted that a folded dipole is also a transmission line, and I showed a method for sorting the radiation from the transmission-line currents. The transmission-line currents turned out to have a phase angle of just about 90 degrees, indicating a non-power-consuming current. Hence, the energy that we supply to the folded dipole becomes radiation just as efficiently as similar energy supplied to a standard dipole. (An identical relationship exists between the two types of current in a folded monopole and a standard or 1-wire monopole.)

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Note that we want to call the non-transmission-line currents radiation currents when we have a devise like a folded dipole, where our main interest is in the radiation. We tend to call those very same currents common-mode currents when we have a transmission line that we do not wish to radiate. There is another reason for the name change. Common-mode currents exist all along the transmission line (until we attenuate them sufficiently). The end of the line that enters the house and the operating room radiates these currents into other nearby wires and devices, including the transmitting equipment. These currents can cause some metering circuits, such as the one measuring SWR, to produce erroneous readings. It does not take much current to create problems in solid-state circuitry. We may experience the RF energy on sharp corners of equipment cabinets in the form of small surprising shocks. This "bite" is only a small version of what we might experience if we were to touch the antenna wire itself while transmitting. For all of these reasons, common-mode currents tend to represent the bad side of radiation currents. Nevertheless, the two are in principle the very same when contrasted to transmission-line currents.

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Every transmission line has the potential for carrying common mode currents. Common-mode currents occur whenever we have an imbalance between either the magnitude or the phase of the currents along a transmission lines, where we measure such an imbalance at any facing points along the line. The two most common sources of common-mode currents in lines on which we do not want them are an imbalance at the antenna feedpoint and induced currents from the antenna field. Parallel transmission lines show imbalances whenever we feed a wire antenna away from a point of maximum current. This point is normally the center point on a half wavelength antenna. If we move the feedpoint on this wire off-center or to the end, we shall find a current imbalance and resulting common-mode currents (and what we sometimes call feedline radiation). On a parallel transmission line, we can induce common-mode currents by improper routing (that is, routing the line at other than a 90-degree angle to the antenna element). We can sometimes create them by running the line too close to a metallic object, like a down spout. If we have different coupling levels between each wire and the metallic object, an imbalance may result, and so too may common-mode currents.

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In a parallel transmission line, we rarely can easily sort the transmission-line from the common-mode currents. (In fact, few amateurs are equipped to even measure the currents on a parallel transmission line.) Even when we use NEC or MININEC to model a transmission line as a set of wires, the program reports a single set of currents, one for each wire at any facing segment or pulse pair. However, in a future episode of my continuing series on antenna modeling (#123), I shall describe the necessary steps to set up a simple spreadsheet or similar calculating aid to do the sorting.

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Coaxial cables are another matter when it comes to sorting transmission-line from common mode currents. Since introduced by Walt Maxwell, W2DU, in the early 1980s, we have seen pictures like Fig. 1 in various handbooks. The sketch portrays the junction of a common dipole or other center-fed wire antenna with a coaxial cable feedline.

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The sketch shows a cutaway view of the coax so that we have a braid line on each side of the center conductor. Between facing surfaces of the coaxial cable, we have transmission-line currents, as suggested by the arrows that have opposite directions. Since the currents are RF (a form of AC), they change direction periodically, so any arrows indicate the directions at one instant of time. At that instant, the currents in the antenna wire have a direction in common with the conductors of the cable, since the cable and its source are in series with the antenna feedpoint.

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The sketch shows, on the right side for convenience (but actually extending all around the braid) an extra arrow having the same direction as the arrow in the antenna wire connected to the braid. The idea that the sketch portrays is that the coax braid forms a second path for antenna currents, otherwise called common-mode currents. Those new to antennas and feedlines may ask how this can be so. Others may ask whether such currents are always a problem.

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Fig. 2 may help us answer the first of the two questions. Within the coaxial cable, we have two surfaces of concern: the outer surface of the center conductor and the inner surface of the braid or outer conductor. We are concerned about surfaces due to skin effect, which holds the current activity very close to the conductor surface. The indicated field allows the cable to act as a transmission line, since the current magnitudes are the same on any facing points along the way, but the phase angles are 180 degrees apart.

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Any common-mode or radiation currents have the same phase angle, regardless of how they originate. The same phenomenon--skin effect--holds common-mode current activity on the outermost surface of the conductor, in this case, the outer surface of the braid. (The intervening dielectric or insulation in the cable does not disrupt this process. In fact, the fields that force RF to the near-surface area make any interior region a poor conductor for the RF of the common-mode current. Hence, we use tubes for beam elements rather than solid rods. The same effect also allows stranded wire to serve with equal effectiveness as solid wire in antennas.) Essentially, the near-surface RF currents on the coax braid are separated from the transmission-line currents on the inner braid surface (and the center conductor) by the material between those surfaces. In effect, when we use a coaxial cable feedline, common-mode and transmission-line currents are self-separating.

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Getting Ready for a Picture Show

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The second question wondered whether common-mode currents are always a problem. Some amateurs have never used an attenuator for them and still not experienced any problems. Others have had major problems. We need to see if we can find some of the probable causes, at least in principle. To provide some preliminary glimpses into the world of common-mode currents, we can either measure the currents on many dozens of antennas or we might try to construct a model of the common-mode situation.

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In episode 100 of the antenna modeling series ("The Dipole and the Coax"), I pointed out some of the difficulties in constructing a completely adequate model of a simple center-fed dipole antenna connected to a coaxial cable. The problems are especially acute using NEC, since we must construct the coaxial cable wire a a single wire having the properties of the coaxial cable's outer-surface. Even then we shall not have captured the coax completely, since coax normally has an insulating outer jacket. In addition, the coaxial-cable diameter is normally different from the diameter of the regular antenna element wire, and NEC (both -2 and -4) has accuracy difficulties when we have angular junctions of wires having dissimilar diameters. Finally, the source will not be at the exact point where the antenna wire and the simulated coax wire form a junction. The source is on the source segment, but the junction must occur at the end of the source segment. Moreover, NEC is most accurate when the length and diameter of the source segment is the same as the length and diameter of the segments adjacent to the source segment. If we connect the coax wire to the end of the source segment, we violate this condition, but if we add a segment on each side of the source segment before creating the junction of antenna wire and coax wire, we increase the problem of displacement between the source and the junction of interest.

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By comparing models from both NEC and MININEC systems, I reached the conclusion that models may be good enough to show the common-mode phenomenon, but we cannot fully trust their detailed data reports in the absence of a large (and largely unconducted) set of laboratory and/or field measurements. Since our goal is not to evaluate a specific situation involving an antenna element with a certain diameter and a coaxial cable with a certain diameter, we can minimize most of the problems to an acceptable level.

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Fig. 3 outlines the conditions of the models that we shall use in our picture show. We shall create a resonant dipole (within +/- j1 Ohm) at 29.97925 MHz, that is, exactly at 10 meters. The wire will be lossless (or perfect) and will have a 5-mm (0.1968") diameter. To avoid angular junctions of wires with dissimilar diameters, the simulated coax wire will also be 5-mm in diameter. (The selected diameter falls between the outer-braid diameter of RG-174 and RG-58. Hence, the set-up may not be normal in the everyday sense of amateur installations, but it falls within the range of possible installations.)

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Constructing the antenna will require 3 wires. The first wire has 51 segments and extends beyond the exact center point by half the length of a single segment. (A segment turns out to be 0.047624 m long, about 10 times longer than the wire diameter to ensure good calculating accuracy in NEC.) The source goes on Segment 51 of Wire 1. Hence, it is at the exact element center. Wire 2 extends from the end of wire 1 to the outer end of the element and uses 50 segments. Hence, all segments in the antenna wire have the same length. The coax wire (wire 3) extends downward from the junction of wires 1 and 2. It length will be variable, depending on our demonstration needs, but it will be segmented so that the length of a segment is as close as possible to the length of a segment in the element proper.

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One possible way to model a dipole and its coaxial cable is to also model a transmission line using the TL facility within NEC. We then place the source on the wire that terminates the feedline. However, we do not know in advance what characteristic impedance to use for the line. Moreover, we have a choice of velocity factor values. We shall return to the affects of a transmission line on the situation before we close. For now, we may simply place the source at the position indicated in Fig. 3.

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Unlike our normal concerns for feedlines, which ordinarily require us to pay close attention to the velocity factor, we need only concern ourselves with the physical length of the simulated coax wire in the model. With respect to common-mode or radiation currents, the electrical length of the coax wire is a function of 3 factors: the physical length, the diameter, and the small adjustment for the outer insulating weather jacket. The antenna velocity factor of insulated wire tends to run between 0.95 and 0.98. Since we need not be ultra-precise in selecting coax wire lengths for these demonstrations, we can ignore both the antenna velocity factor and the effects of diameter without losing track of the major shifts in performance.

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In fact, using EZNEC software and NEC-4, we can directly vary the lengths of the coax simulation wire in 1/8 wavelength increments. At the test frequency, exactly 10 m per wavelength, we can always determine the length of any line in meters by multiplying the length in wavelengths by 10. As well, EZNEC's graphic facilities allow us to produce some simply-to-read illustrations suited to these exercises.

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The exercises will consists of paired tables and graphics. Hence, it will amount to a picture show of sorts. Indeed, the pictures may be more significant than some of the precise data, although we shall pause now and again to comment on where the data is adequate and where it may be more questionable.

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Exercise 1: Free Space

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Let's begin our examination of potential common-mode currents by placing the dipole in free space. Although this environment is not realistic for the average amateur installation, it will provide us with one advantage. We may record an average gain test (AGT) score for each model in the series. We shall begin with a zero-length coax wire, that is, a simple dipole with no appendage. Then we may add the coax wire dangling "below" the dipole to approximate an ideal right-angle position. (The term "below" is relative only to the Z-axis of the coordinate system. Free-space, of course, has no inherent above or below.)

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For each length of coax wire, we shall record several items of data. The feedpoint impedance will be useful to know, as well the maximum gain and the AGT score. In addition, we shall record the relative current magnitude and phase angle on selected segments. The source segment will always have a value of 1.0 at 0 degrees. Our interest will lie in the adjacent segments. On one side, we have a single segment (wire 1). On the other side, we have two segments that join (wires 2 and 3). (The pure dipole, of course, lacks a wire 3.) These current values may seem tedious to gather, but they will turn out to be informative.

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The results of our expedition appear in Table 1.

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Although the text omits quotation marks, all tables use them around the expression "coax wire" to ensure that we do not forget that the wire is a stand-in for a length of coax that serves as both the feedline and the source of added radiation currents. Within the free-space set-up, the lengths of coax used are convenient measures, even if they do not represent lengths we might encounter in an amateur installation. In fact, the free end of the coax wire might be an actual wire end or it might be the point at which a longer coaxial cable is subjected to one or another type of attenuator so that the remaining coaxial cable length is effectively isolated from the length under test.

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Within the data, two coax-wire lengths should attract our attention: 1/4 wavelength and 3/4 wavelength. Of the sampled lengths, only these two show oddly aberrant feedpoint impedance values, lower current magnitude on wire 2, elevated current magnitude on wire 3, less than ideal AGT values, and lower maximum gain levels. The AGT scores are of special note, since they represent a modeling limitation. When wire 3 shows relatively insignificant current levels (less than 0.1 of the maximum value), the AGT score indicates a reliable model requiring no corrective for either the gain value or the reported feedpoint impedance. However, when wire-3 current is significant, the AGT value departs from the ideal by a significant amount, suggesting that the model's numerical data are not reliable. Even if we use the AGT value to correct the gain figure, we find lower than normal maximum gain. Under the prescribed conditions, common-mode currents are sufficient to significantly alter the dipole radiation pattern relative to our expectations.

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One area in which the AGT does not disturb the results is in the calculation of the net current magnitude and phase angle on the right side (wires 2 and 3) of the dipole. The vector sum of the currents on that side should equal the reported current on the left side of the source. We may expect a small and systematic difference, since the sum of the surface areas of wires 2 and 3 is double that of wire 1. However, we anticipate a general coincidence between the net current values. Table 2 will inform us of whether or not the models achieve this end.

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The columns marked "wE" provide the required calculated net current values, while those marked "w1" record the current for the single-wire side of the dipole. The pure dipole, of course, shows no difference between the two. For every entry in which we have a coax wire, we find a consistent 0.07 to 0.08 degree difference in the phase angle for all entries. For all entries with an AGT value of 1.000, the wire-1 value for the phase angle is slightly higher than for the simple dipole. I have bold-faced the values for coax wire lengths of 1/4 and 3/4 wavelength, because the phase angle values are out of line with the other values in the list.

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Despite the questions of data reliability, the general phenomenon of common-mode currents shows well in the table. We may also represent the data in more graphical form. For each tabular entry, we may generate E-plane and H-plane patterns for the free-space model. In addition, we may also represent the pattern of current magnitude along the antenna elements and the coax wire. Fig. 4, Fig. 5, and Fig. 6 provide a catalog of the current and radiation patterns applicable to the entries in Table 1.

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Let's first look at the current magnitude portions of each figure. For all coax-wire lengths except 1/4 and 3/4 wavelength, the current all along the coax wire is small. I have magnified the levels so that a definitive curve shows for each coax wire length. However, the peak current is never above about 0.2 of the maximum value. Therefore, the current distribution on the antenna element wire remains virtually undisturbed by the presence of the coax wire. In contrast, with 1/4 and 3/4 wavelength coax wires, the current peak for the coax wire occurs at the junction with the antenna element. Hence, we find a significant current division between wire 2 and wire 3. The current in wire 2 (to the left in the graphical representations) is low enough that we might expect to find considerable alteration of the normal dipole free-space pattern.

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The E-plane and H-plane patterns (azimuth and elevation in conventionalized modeling terms) provide us with two types of data. First, the patterns show both the vertical and the horizontal components of the total field patterns. In virtually all cases, most of the horizontal component disappears beneath the line that records the total field. However, the vertical component is instructive. For example, the pure dipole with no coax wire shows no vertical component in free space. When we add the coax wire, we obtain a distinct vertical component to both patterns. For all but two of the pattern sets, the vertical component is about 20 dB or more down from the maximum gain. In addition, the indicated patterns show side nulls that are at least 20 dB or more lower in gain than the main lobes. The two aberrations are the patterns for 1/4 wavelength and 3/4 wavelength coax wires. The peak vertical components in these cases may be less than 10-dB down from maximum gain values, with strong consequences for the total field dipole radiation pattern. The patterns for lengths of 1/4 and 3/4 wavelength differ, but both equally distort what we think of as the normal dipole pattern.

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Exercise 2: 1 Wavelength above Average Ground

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Before we draw any conclusions about common-mode currents, let's repeat the exercise with a small difference. For the second run, we shall set the dipole exactly 1.01 wavelength above average ground. (The use of 1.01 wavelength as the antenna height ensures that the 1 wavelength coax wire does not touch the ground. We shall look at that option in a separate exercise.) Since we are now dealing with a lossy ground, we cannot make use of AGT score values, since those values require the removal of all resistive losses, using either a free-space or perfect-ground environment. However, we may record the reported gain value and the TO angle (take-off or elevation angle of maximum field strength). In all other ways the models remain intact. Table 3 records the results of this exercise. Remember that the "zero-length" model is a simple dipole with no wire 3.

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In this exercise, coax-wire lengths of 1/4 and 3/4 wavelength again show anomalous results compared to the results for other lengths. At all other coax-wire lengths, we obtain about the same maximum gain and very similar feedpoint impedance values. Note that the impedance for the simple dipole entry shows a small reactive component because I did not change the dipole length when moving it from free space to a position above real ground. The impedances for the two sensitive coax-wire lengths are between 20 and 30 Ohms lower than for the other lengths. As well, the maximum gain is more than a dB lower. In the current-value columns, we find the same general pattern of current values on the first segments of wires 2 and 3 that we found in the free-space exercise

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We may translate the tabular results into the same sorts of patterns that we developed for the first exercise. We omit the current portions of the graphics, since they are virtually identical whether in free space or over real ground. However, Fig. 7, Fig. 8, and Fig. 9 provide the elevation and azimuth patterns for each of the entries in Table 3.

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The first difference to note in the patterns relative to free-space models is that even the simple dipole shows a small vertical component over real ground. When we compare this component with the corresponding components for most of the models with coax wires, we find that the strength of the component does not change. It remains about 20 dB below the maximum gain, although the exact shape of the component changes somewhat with the length of the coax wire. In contrast, the maximum gain for the vertical components for 1/4 and 3/4 wavelength coax wires is only about 10 dB down from the maximum gain value. The consequences for the total field elevation patterns are not dramatic. However, we find distinct distortions in the azimuth patterns for coax wire lengths of 1/4 and 3/4 wavelength. These distortions do not make the antenna unusable, but when combined with the gain reduction, they do make a difference. Note that even with the pattern distortions, the TO angle for all of the patterns remains at 14 degrees elevation.

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At this point, we might be tempted to draw some hasty conclusions. One such conclusion is that we can avoid coaxial cable common mode currents by avoiding line lengths that are odd multiples of 1/4 wavelength. However, this conclusion would be warranted only for cases in which the coax end was either free or was isolated by some attenuation device to the degree that it acted like a free end. In most amateur installations, we do not find these conditions at work. We need to set up a model that might more adequately represent installation conditions.

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Exercise 3: Coax Wire to Ground, with and without a Ground Rod

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In most cases, the coax wire will come to the level of the ground. The route may be direct or indirect. One such indirect route is through the equipment cases to a station grounding system. I cannot represent each possible case. However we might explore some stand-in cases. For example, we might set the dipole at various heights from 3/4 wavelength up to 1-1/4 wavelength, with coax wires that just reach the ground. For this set of cases, we shall expect elevation patterns that show different TO angles, since each entry places the dipole at a different height.

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We also have two ways to handle the fact that the coax wire just reaches the ground. One way is to simply let the wire end at Z=0. This type of model may not be wholly reliable, since NEC typically shows an inaccurate source impedance under these conditions. So we might (in NEC-4) create a 1/4 wavelength ground rod, using the same 5-mm diameter wire that we have used in the remainder of the model.

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Table 4 records the NEC reports for both type of models. In addition, it also records reference values of simple dipoles (with no coax wire) at each of the heights for the other cases in this exercise.

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The table immediately shows some very interesting results. When the coax wire touches the ground, with or without a good ground rod, the sensitive lengths are no longer odd multiples of 1/4 wavelength. Instead, the sensitive lengths become multiples of 1/2 wavelength--in this case, a length of 1 wavelength. Our previous hasty conclusion turns out to have been far from universal.

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The second notable feature is the difference in the dipole performance with a 1 wavelength coax wire between having a ground rod and only touching the ground. The no-rod situation shows the greater reduction in the feedpoint impedance and the maximum gain. In comparison, the other coax-wire lengths show only modest differences between a rod and a no-rod condition. Additionally, the gain with a ground rod and a 1 wavelength wire shows the greatest reduction in maximum gain of all the cases when we compare the values with the gain values for a modeled dipole with no coax wire. If we were to carry out the exercise in even smaller increments, we might expect to see the gain differential curve show a non-linear curve to a peak difference at 1 wavelength and then a non-linear downward trend, with repetitions every half wavelength.

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We may sample the current magnitude and distribution curves, as in Fig. 10. The curves for coax-wire lengths of 0.75 and 1.25 wavelengths begin at the feedpoint junction with very low current values, and those values remain very low all along the coax wire. The samples use ground rods, which are a constant 0.25 wavelength for each case. The curves for the 1 wavelength coax wire begin at the feedpoint with high current on the coax wire. Indeed, the current magnitude is high enough so that we find unequal current curves on the two halves of the antenna element itself. The current pattern presents two significant peaks at heights of 1 wavelength and 1/2 wavelength: these maximums are strong enough to affect the overall radiation pattern.

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Before we turn to the patterns, let's take note of the current distribution on the ground rod. Although the ground rod is physically 1/4 wavelength, its electrical length within the selected ground medium (conductivity 0.005 S/m, permittivity 13) is longer. Hence, the current undergoes 2 peak values. (An underground dipole would not have to be very long physically to be a resonant half wavelength electrically, although the precise physical length will vary with the ground medium.)

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Fig. 11 translates the tabular data for the models with ground rods into elevation and azimuth patterns. Despite the half-dB gain loss in the model with a 1 wavelength coax wire, we find nothing unusual in either the elevation or the azimuth pattern. The vertical component of the patterns is only slightly greater than for the other patterns. Indeed, with the well-grounded termination of the coax wire, we find that the feedpoint impedance is not very far off the mark for a dipole at a 1 wavelength height with no coax wire at all.

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We may fairly ask at this point what all of the pictures might be telling us with respect to common-mode currents on the outer side of a coaxial cable' braid. We have examined two sorts of cases, one in which the coax wire had a free end and another in which the coax wire terminated at ground. Both cases have used straight coax wires projecting at a 90-degree angle from the junction with one side of the feedpoint of the dipole antenna element. Within these conditions, we discovered two different situations in which common-mode currents appeared to be significant. With a free end to the coax wire, sensitive coax lengths appeared to be odd multiples of 1/4 wavelength. With the coax terminated at ground, sensitive lengths appeared to be multiples of 1/2 wavelength.

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One initial impression might be that under one or the other condition, we have a good chance of not incurring common-mode currents to any significant degree. However, as we noted near the beginning of our picture show, we do not require common-mode current levels that distort the radiation pattern to experience unwanted coupling into equipment or household devices making use of solid-state circuitry. Since we do find some common-mode currents on coax braids in nearly all circumstances, the potential for problems exists under nearly all coax-wire conditions.

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The picture show also suffers severe restrictions. It does not cover a myriad of cable routings that are typical of almost any antenna installation. Cables may travel horizontally for considerable distances at a variety of heights ranging from underground to a considerable distance above ground. Cable routing and switching may make the calculation of the total cable length to a ground connection nearly impossible. As well, we may not be certain of the quality of the cable ground, since a good ground for lightning protection may or may not also be a good ground for RF at the operating frequency.

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On top of all this, we have not investigated whether non-ideal cable routing may have an affect on a cable's susceptibility to common-mode currents.

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Exercise 4: Coax Wire to Ground with a Ground Rod But Sloping Under the Antenna Element

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We have long believed that improper or non-ideal routing of a coaxial cable may increasing the potential for incurring common-mode currents due to coupling between the antenna element fields and the outer surface of the cable. (A similar situation would also induce common-mode or radiating currents on a parallel transmission line.) We can gather some idea of the level of interaction by a simple demonstration. We must note from the start, however, that the variations on the situation that we shall set up are nearly endless. So the exercise will show only that some influence does exist, but it will not go any further.

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Let's use a model in which the coax wire reaches the ground and terminates in a 1/4 wavelength 5-mm diameter ground rod with average ground. The coax wire will slope at a 30-degree angle directly under one of the dipole legs. When the angled portion of the coax is at the end of the antenna element, the coax will drop straight down to the ground. The total length of the coax wire is 1 wavelength. Since the sloping leg is 1/4 wavelength, the sloping end is 1/8 wavelength below the end of the dipole. With the remaining 3/4 wavelength of coax wire, the antenna height will have to be about 0.875 wavelength to satisfy the overall geometry.

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The top portion of Fig. 2 shows the antenna model geometry and also shows the current magnitude and distribution. The lower portion of the figure shows a straight coax run with an equivalent total length of coax-wire, that is, 1 wavelength. Since the antenna heights differ, the total field elevation pattern differences do not reflect any effects of the different coax-wire routings. Any dipole at a height of 7/8 wavelength will show the large upward lobe structure.

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More significant is the vertical component within the pattern. The peak value for that component appears to be somewhat higher with the sloping coax wire than with the straight one. A similar condition appears on the current distribution section of the graphic. Indeed, the two current portraits seem somehow anomalous. Both raise the peak current value to as close to the same level as feasible. The sloping coax wire appears to show higher current peaks than the straight 1 wavelength coax wire, although as we discovered in the preceding exercise, a coax-wire length of 1 wavelength showed the highest coax-wire current peaks of any of the sampled lengths. In contrast to this appearance, the straight-wire model shows a reduced current magnitude on the dipole leg sharing a connection with the coax braid. However, the sloping-coax model shows a seemingly smooth curve of current magnitude across the feedpoint junction.

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To resolve the visual situation, we may turn to the data in Table 5. The table lists the modeled data for the sloping case and for two straight-coax cases, the 0.875 and the 1 wavelength coax runs. All three cases use a ground rod.

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The table entries for the sloping-coax model indeed show that the current magnitude of wire 2 is very close to the magnitude on the single-wire side. What the graphic did not show was the very significant difference in phase angles between the two current magnitudes. As a consequence, the current magnitude on wire 3 is about 30% higher than we find on the same segment in the case of a 1 wavelength straight coax wire. Because the graphic omitted the phase-angle data (a necessity for me to provide 2-D representations), it only appears anomalous. With the phase-angle data added, we can see that the sloping-coax situation increases the common-mode current magnitude on the coax braid. In addition, the situation in the model reduces the maximum gain of the dipole at a 7/8 wavelength height by about 0.6 dB relative to the straight coax dipole at the same height.

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The single demonstration does not provide a comprehensive picture of how non-ideal cable routing may affect both antenna performance and the level of common-mode currents. However, it does tell us that non-ideal routing can alter antenna performance and provide increased common-mode current levels. We have already seen that we may have difficulty in determining whether we have a sensitive coax length due to problems in measuring the length of the coax between the antenna and ground and uncertainties about the quality of the ground. The safest procedure is to install some form of attenuation for common-mode currents as a standard operating procedure with all coax-fed antennas.

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Exercise 5: Coax Wires with Attenuation

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Common-mode current attenuation generally comes in two forms: the 1:1 balun or transmission-line transformer and the ferrite-bead choke. Simulating a 1:1 balun is beyond the capabilities of the EZNEC implementation of NEC-4. However, the W2DU-type ferrite bead choke is quite simple. It provides an inductive reactance on the outside of the coax braid without disturbing what occurs inside the coaxial cable. Hence, it does not affect transmission-line currents, but it attenuates common-mode currents.

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With a properly constructed bead balun for the frequency used, it is possible to obtain at least j750 Ohms of inductive reactance. (See the current ARRL Antenna Book, p. 26-25. As well, see Bill Sabin, W0IYH, "Exploring the 1:1 Current (Choke) Balun," QEX, July, 1997, as well as Chapter 21 of Walt Maxwell, W2DU, Reflections II, for background on the ferrite bead choke.) Therefore, we shall use a simple load on the coax wire consisting of j750 Ohms.

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In the first part of our new exercise, we shall use the model of a coax wire with a free end. We found that when the coax wire was 3/4 wavelength long, it showed a high sensitivity to common mode currents. We may install the load (that is, the bead choke simulation) anywhere along the wire. Let's place it at the feedpoint and then at 0.25 wavelength intervals, including the far or open end of the coax wire. Table 6 shows the numerical results of the exercise.

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The table includes values for the case without the bead choke for comparison. When we place the choke 0.25 and 0.75 wavelengths away from the feedpoint, it has virtually no effect on the common mode current values. However, when we place it either at the feedpoint or at a point 1/2 wavelength distant from the feedpoint, it reduces the current on the coax wire to nearly equally low levels. To see this situation graphically, we may examine Fig. 13.

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The current distribution graphics for no-load and for loads at 1/4 and 3/4 wavelength positions are virtually indistinguishable from each other, except for the square marking the load location. When we place the load at the feedpoint, common mode current drops to near-zero. When the load is 1/2 wavelength from the feedpoint, the current level between the feedpoint and the load is not quite zero. But, it is very much attenuated compared to the no-load or the misplaced load conditions.

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We may repeat the experiment using the model with a ground rod and a straight 1 wavelength coax wire. This model showed the greatest sensitivity to common mode currents in its series of samples. Once more, we shall use a j750-Ohm load and move it from a position at the feedpoint along the line in 0.25 wavelength increments. Hence, the last position will be just about at ground level. Table 7 gives us the outcome of the modeling exercise.

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With the load positioned at the 0.25 and 0.75 wavelength points along the coax wire, we obtain little or no benefit. The impedance reflects the value for a no-load (that is, a no-attenuator) condition. However, when we place the load at the feedpoint or at multiples of 1/2 wavelength from the feedpoint, the antenna impedance and gain values return to the levels that we expect of a dipole at 1 wavelength above average ground with no coax wire in the model. Fig. 14 provides a set of current distribution portraits that reflect these conditions.

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The portraits reveal the same general patterns as the portraits in Fig. 13. When the choke is at the feedpoint or at a distance that is a multiple of 1/2 wavelength from the feedpoint, we obtain maximum attenuation of common-mode currents. When the choke is at a distance, the common-mode currents do not go to zero between the feedpoint and the load, but they are very much attenuated relative to their value with a no-load or a misplaced-load condition.

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The feedpoint is the most common location for the installation of a common-mode current attenuator. In fact, commercially made devices often combine the attenuator and a dipole center insulator assembly in one. In terms of reducing common-mode currents on coax braids to a minimum, the feedpoint position is universally the best. However, the demonstration has only covered cases of straight-line coax runs. It has not covered the case of a sloping or otherwise erratic coax run. For this reason, it is not unwise to install a second bead choke at the point where the coax enters the house or equipment room. A good earth ground running from the braid on the equipment side of the attenuator is an additional method to maximize the supplemental attenuation.

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Exercise 6: Coax Wires and Transmission Lines

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One of the markers that we have used to initially spot a coax-wire length that was sensitive to common-mode currents is the feedpoint impedance. In virtually all cases where common-mode currents have been high, the feedpoint impedance has dropped significantly from a more normal dipole value. We have been using the feedpoint impedance as modeled at the center segment of the dipole element. The potentially misleading idea that this situation may suggest is that a normal dipole impedance at the equipment end of the coaxial cable indicates relative freedom from common mode currents, while a lower-than-normal impedance may indicate their presence.

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Unfortunately, this idea does not necessarily play out in real situations. The electrical length of the coax outer braid is a function of its physical length and its diameter. The outer jacket may contribute an antenna-level velocity factor that might range from 0.95-0.98, depending on the jacket material and its thickness.

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In contrast, the transmission line currents and the impedance transformation that may occur between the center conductor and the inside of the coax braid have very different velocity factors. For 50- and 70-Ohm cables, we find two common velocity factor values: about 0.66 for solid dielectrics and about 0.78 for foam dielectrics. As a result, a given physical length of a coaxial conductor will have an electrical length in practice that is considerable loger than the electrical length of the outer braid for common-mode currents.

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Table 8 provides a simple example using the dipole and a 3/4 wavelength coax wire with a free end. To the model we can add a 3/4 wavelength 70-Ohm transmission line, with a short terminating wire on which we place the source. The table shows a reference line with the values for the same model but with the source located on the center of the dipole. If we arbitrarily assign the transmission line a velocity factor of 1.0, we discover that the line transforms the 52-Ohm impedance up to about 94 Ohms.

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With realistic values for the velocity factor, we obtain different values for the source impedance, values that are not likely in isolation to give us clues to the common-mode current situation. In an actual situation, we are faced with perhaps two alternatives. One direction in which we can go is to devise means by which to measure the level of common-mode currents. If we lack proper measuring equipment, we might rely upon other signs, such as the presence of interference with communications equipment functions of other household devices.

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The other alternative is to install common-mode current attenuation devices, such as bead chokes, during the installation of the antenna system. The antenna system includes both the antenna and the transmission line. As we noted earlier, the most use position for a common-mode attenuator is the junction of the coaxial cable and the antenna element. However, a secondary attenuator at the house or equipment-room entry point can provide additional protection against potentially harmful effects from even low levels of common-mode currents.

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Conclusion

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Our common-mode-current picture show has reached its end, even though it has surveyed only a few of the possible combinations of antennas and feedlines that might make up an amateur installation. Along the way, we discovered that the level of common-mode currents depends upon several factors, including the length of the coaxial cable and the nature of its termination. Cables with free ends have sensitive lengths that differ from cables that terminate at the ground. Cables that do not leave the antenna feedpoint at right angles tend to be more susceptible to common-mode currents.

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Although the tabular data is indicative of actual conditions, we should remember that the models used are subject to some restrictions. We had to use a single wire diameter for both the antenna element and the coax wire to minimize model inadequacies. Even with this departure from the reality of most antenna installations, we still encountered non-ideal AGT values when common-mode currents were relatively high. The chief cause for the deviation from an ideal AGT value is the position of the junction between the coax wire and the element wire immediately adjacent to the source segment. Such models fail to implement the conditions under which NEC calculates most accurately the current on the source segment. The problem does not show up when common-mode currents are very low and most of the source current appears on the antenna element with almost none on the coax wire.

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Notwithstanding the limitations that the situation imposes on the numerical data, the general portrait of common-mode currents shows generally accurate patterns of currents and the conditions that tend to either promote or suppress their development. However, in most amateur installations, we have no accurate method for determining the exact electrical length of our coaxial cable as it proceeds from the antenna to the equipment and then via an earth ground line to the actual ground. For the average amateur antenna installation, the safest strategy relative to common-mode currents is prevention. Adding a common-mode current attenuator to the system should be a standard part of any installation involving a coax-fed antenna.

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Updated 08-21-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Balun


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ATUs, Delta, and Losses

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L. B. Cebik, W4RNL

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+ Losses from the insertion of antenna tuning units or transmatches between transmitters and transmission lines have bothered numerous folks for some time. There are two questions: how much loss can I expect? and how do I minimize the loss? Both are good questions with good answers. Unfortunately, they are not super simple answers. But some old material combined with some new material can make the answers easier to come by. Those who like the math involved can focus on the equations, while those interested in operational matters can concentrate on the tables and the resulting rules of thumb to minimize losses. +

Most ATUs used today are L-C networks. The most common configuration is the C-L-C Tee network. However, L-C-L Tees and C- L-C PIs are in use, as are SPC and Ultimate Transmatch designs. Loss figures can be calculated for all such networks.

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Delta: The old material that contributes to determining ATU losses appears in Terman's Radio Engineers' Handbook (McGraw-Hill, 1943), pages 210-215. Based predominantly on work done in the 1930s by W.I. Everitt, Terman's analysis of classic impedance-matching networks is still referenced by current handbooks. The relevant part for considering ATU losses is the term, delta, which is a justifiably simplified measure of power dissipation in networks. For any impedance matching network, the primary power dissipation culprit is the inductance, and inductor losses can be calculated.

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The efficiency of L-C networks is dependent upon the impedance transformation ratio and the phase shift. PI networks and L-C-L Tees generally exhibit a large angle of phase retardation, while the C-L-C Tee circuit shows a large angle of phase advance. In contrast, simple L-networks show small angles of phase advance or retardation. Losses increase with increasing transformation ratios and tend to be larger when the phase shift is either very large or vary small. The delta-figure takes both into account. (Note, in some explanations of networks, but not in all, Terman's delta goes under the name of "working Q," "circuit Q," or "network Q.")

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The concept of delta has certain limitations. First, it ignores capacitor losses. This is justified for well-designed capacitors at HF and below, but capacitor losses may become significant at the boundary between HF and VHF (about 30 MHz). Second, the loss figure ignores the effects of strays, both capacitive and inductive, within a real ATU, especially one cramped inside a metal case. At 10 meters, the principal L and C in a matching circuit may be composed more of strays than of component values. Third, the technique will assume we know the coil Q in figuring ultimate efficiency and losses. On this score, we mostly guess, but a figure of 100 for good air wound coils is a conservative guess. Good powdered iron core toroids may yield more. Of course, the "suck out" effect of shorted coil turns is also ignored. Moreover, only networks, and not inductively coupled ATUs, are covered.

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Within these limits, the Terman-Everitt delta yields a fair estimate of loss and efficiency. As Terman notes,

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In other, equally approximate terms, network efficiency = 1 - delta/Q. (Multiply this figure times 100 for a percentage value of efficiency).

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Now if we only knew how to calculate delta, the rest would be simple. Terman provides graphs for estimating delta. Each type of network requires its own calculation, and it can be a bit tedious to calculate delta for several combinations of component settings. However, Brian Egan, ZL1LE, has derived equations for delta- calculations and added them to his program TUNER.BAS. This versatile program is now included in the collection of programs called HAMCALC.

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Among the networks for which ZL1LE includes calculations are PIs, C-L-C Tees, SPCs, Ultimates, and L-C-L Tees. By running the program through a selection of values, one can learn the trends of tuning that will minimize losses. Operationally, that is the best we can hope for with a fixed set of impedance conditions presented by the transmission line from the antenna and with ATU components that we cannot modify, that is, with a coil whose Q we cannot improve. From the general relationship of power lost to power delivered, it is clear that we always want to tune for minimum delta.

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For CLC T networks, a more complete analysis of losses (or efficiency) appeared in July, 1997, QEX, by Kevin Schmidt, W9CF. In fact, ZL1LE has included Schmidt calculations for this network in his suite of programs, so that you can not only calculate network values for a given match, but also calculate the efficiency of the coupling. Delta turns out to be a good approximation of Schmidt losses for networks with coil Qs above 50.

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As a preliminary sample, consider a CLC T network of the kind so common in commercial tuners. With an input impedance of 50 ohms resistive and a sample load impedance of 400 + j100 ohms (SWR=8.53:1) at 3.5 MHz, calculations give a maximum transmitter end C1 of 343.7 pF. Using various values of C1 (depending on the components in the tuner we have), we can find the following table of values. Efficiencies are calculated by Schmidt means and delta values by Terman means. A more detailed analysis of CLC networks appears below, along with Figure 2 to make clearer the components C1, C2, and L.

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C1             343 pF              250            150
+L (Q=250)      6.58 microH         7.16           10.77
+C2             305pF               99             51
+Efficiency     98.8%               98.1           96.8
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+C1             343                 250            150
+L (Q=100)      6.46                7.15           10.82
+C2             263                 96             50
+Efficiency     97.1                95.4           92.0
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+Delta          2.7                 4.5            8.0
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Note that efficiency is always higher for the coil with the higher Q and also for the lowest value of delta for any given coil Q. Using delta alone to calculate the efficiencies would have given us 98.9 for the Q = 250 case and 97.3 for the Q = 100 case in the first column.

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If we work the same problem for 1.8 MHz, we find that the maximum capacitance for C1 is 668 pF. Let's arbitrarily choose 645 pF for this capacitor, but also work the cases where C1 = 250 pf and 150 pF.

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C1             645 pF              250            150
+L (Q=250)      12.48 microH        24.11          39.35
+C2             418 pF              84             50
+Efficiency     98.7%               96.2           93.7
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+C1             645                 250            150
+L (Q=100)      12.36               24.26          39.83
+C2             393                 82             47
+Efficiency     96.9                90.6           84.4
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+Delta          3.0                 9.4            15.9
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Both of the earlier trends are repeated: efficiency is highest with the highest coil Q and the lowest value of delta. Delta remains a very close approximation of losses (or, in Schmidt terms, efficiency). Note, however, the range of values needed to achieve the highest levels of efficiency.

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I ran TUNER.BAS through a number of exercises using different types of networks, and here are some results for some configurations. I chose 10.1 MHz, because I was working on a network problem for that band. To standardize the tests, I chose the following load conditions for each network: 150 ± j0 ohms, 150 + 100 ohms, and 150 - j100 ohms. Looking at a straight 3:1 SWR purely resistive load is a good beginning point, while exploring the network with both capacitive and inductive reactances indicates limitations of the network with certain types of loads. This test is limited, since a higher delta at a 3:1 impedance transformation ratio is not indicative of the network's overall capability. Some networks are more efficient with lower transformation ratios, while others grow more efficient as the transformation ratio increases.

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PIs: This familiar low-pass network configuration appears in Figure 1.

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For those interested, the Egan equation for delta for a PI network (where omega = 2piF wherever it occurs) is the following:

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Here is a small table of results for 10.1 MHz:

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Input = 50 ohms  Output = 150 ± j0 ohms  Maximum permitted L = 1.365 µH
+       L  1.364     C1  172      C2  179      delta  2.2
+or        1.364         192          185             2.5
+       L  1.2       C1   36      C2  150      delta  1.5
+       L  1.15      C1   15      C2  149      delta  1.5
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+Input = 50 ohms  Output = 150 + j100 ohms  Maximum permitted L = 1.640 µH
+       L  1.639     C1  140      C2  197      delta  2.5
+       L  1.6       C1   84      C2  187      delta  2.2
+       L  1.5       C1   26      C2  182      delta  1.9
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+Input = 50 ohms  Output = 150 - j100 ohms  Maximum permitted L = 1.640 µH
+       L  1.639     C1  140      C2  100      delta  2.5
+       L  1.6       C1   84      C2   90      delta  2.2
+       L  1.5       C1   26      C2   85      delta  1.9
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In all three cases, the lists stop where one of the values approaches the minimum usually obtainable with ordinary components. In this case, a value for C1 lower than about 20 pF is not normal for most ATUs. In many instances, as illustrated by the very first entry, two solutions to the matching problem are possible. After the first entry, only the more promising set of values is shown. PI networks are, within limits, equally capable of handling capacitive and inductive reactances in the load, with the limits of both being related to the range of C2. Notice that efficiencies of 98% are possible within the limits of the method. As Terman notes, increasing the ratio of the impedances to be matched increases the value of delta and decreases efficiency. For example, when the resistive component of the output impedance is 300 ohms, with or without a reactive load, the lowest value of delta is about 2.3. To achieve the highest efficiency possible for any given matching situation, we must use the following rule of thumb:

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+ PI networks: Use the lowest value of L that still permits C1 to be effective. +
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C-L-C Tees: This most common ATU network configuration appears in Figure 2.

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To determine delta, use the Egan equation

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Input = 50 ohms   Output = 150 ± j0 ohms     Maximum permitted C1 = 222.9 pF
+       C1  222.8    C2  6027     L  1.65      delta  1.4
+       C1  222      C2  1468     L  1.59      delta  1.5
+       C1  220      C2   992     L  1.56      delta  1.5
+       C1  210      C2   362     L  1.43      delta  1.8
+       C1  200      C2   262     L  1.39      delta  2.0
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Note that although a very low value of delta is theoretically possible, a realistic value of 2.0 or higher is to be expected with common components used in ATUs. As in the case of the PI network, the C-L-C Tee yields higher values of delta as the output impedance is increased. At 6:1 ratio of output-to-input impedance, delta does not go below 2.1 with normal ATU components.

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Input = 50 ohms  Output = 150 + j100 ohms  Maximum permitted C1 = 222.9 pF
+       C1  222.8    C2  154      L  1.65      delta  1.4
+       C1  220      C2  132      L  1.54      delta  1.6
+or         220          196         1.85             1.3
+       C1  210      C2  110      L  1.43      delta  1.8
+or         210          279         2.12             1.2
+       C1  200      C2   98      L  1.39      delta  2.0
+or         200          396         2.34             1.2
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Note in this table that two sets of matching values are possible, even within the range of normal ATU components. One set drives toward maximal efficiency as C1 is decreased, while the other set moves away from the highest efficiency under the same condition. The primary setting to watch, therefore, is that of C2.

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Input = 50 ohms  Output = 150 - j100 ohms  Maximum permitted C1 = 172.6 pF
+       C1  172.5    C2 91080     L  1.37      delta  2.5
+       C1  150      C2   456     L  1.42      delta  3.0
+       C1  130      C2   223     L  1.52      delta  3.6
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With respect to efficiency, the C-L-C Tee is less effective with capacitively reactive loads than with inductively reactive loads. With some load conditions, here a capacitive reactance of 100 ohms combined with our standard 150-ohms resistive component, a very low delta will not be possible with normal components. The best we can do is to keep delta as low as possible by following the common advice for C-L-C Tee tuners:

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+ C-L-C Tees: Use the maximum capacitance possible, especially for C2, for a given matching situation. +
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However, even with a delta of 3.6 to 4, efficiency with a coil Q of 100 will be in the neighborhood of 96%.

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SPC: The SPC (series-parallel capacitance) network is the more general case of which the C-L-C Tee is a specific instance. Note that the C-L-C results from the SPC if we lower the value of the capacitor in parallel with L to zero. Ordinarily, the parallel capacitor is ganged as a dual unit with either C1 or C2. The requirement for a high-voltage dual-section capacitor has limited commercial production of SPC tuners. Figure 3 shows the more common configuration, with Cp and C2 ganged as equal-value units.

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The SPC departs from the C-L-C Tee in two significant operational characteristics. First, the actual values required for a given impedance transformation will differ. Second, the SPC tends to tune much more sharply. I recommend the use of verniers on the capacitors for ease of tuning. However, the equation for determining delta for the SPC is the same as that given for the C- L-C Tee.

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Input = 50 ohms  Output = 150 ± j0 ohms    Maximum permitted C1 = 222.9 pF
+       C1  222.8    C2  6027     L  0.04      delta 58.8
+       C1  210      C2   362     L  0.64      delta  4.7
+       C1  180      C2   176     L  0.69      delta  4.6
+       C1  170      C2   152     L  0.75      delta  4.7
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+Input = 50 ohms  Output = 150 + j100 ohms  Maximum permitted C1 = 222.9 pF
+       C1  222.8    C2  154      L  0.82      delta  2.9
+       C1  220      C2  137      L  0.85      delta  2.8
+       C1  215      C2  118      L  0.87      delta  2.9
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+Input = 5 0ohms  Output = 150 - j100 ohms  Maximum permitted C1 = 172.6 pF
+       C1  172.5    C2 91080     L  0.01      delta 1256
+       C1  140      C2  305      L  0.52      delta  9.1
+       C1  120      C2  172      L  0.76      delta  8.2
+       C1  110      C2  136      L  0.88      delta  8.3
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The SPC tuner improves the harmonic rejection characteristics of the C-L-C Tee (which is inherently a high-pass filter), but apparently at the cost of lower efficiency. All three tables show the values surrounding the lowest value for delta obtainable under the given load conditions. The SPC appears to do better with inductive loads than with purely resistive transformations or capacitive loads. The value of delta increases for resistive and inductive loads as the ratio of output-to-input impedance increases, but shows a slight decrease for capacitive loads at higher ratios. Because tuning points are quite specific, no general rule of thumb is possible for the SPC.

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L-C-L Tees: The L-C-L Tee, shown in Figure 4, has suffered from neglect until recent years. It is a natural low-pass filter, like the C-L-C PI shown earlier. However, whereas the intermediate impedance of the PI is lower than either the input or output impedances, the intermediate impedance of the L-C-L Tee is higher than either the input or output impedances. This results in higher voltages and lower currents at the junction of the three components.

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Determining delta for the L-C-L Tee requires attention to both inductors, which for simplicity are assumed to have the same Q in the following Egan equation:

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Input = 50 ohms  Output = 150 ± j0 ohms    Minimum permitted L1 = 1.114 µH
+       L1  1.115    L2  0.07     C  152       delta  1.4
+       L1  1.12     L2  0.20     C  157       delta  1.5
+       L1  1.20     L2  0.77     C  176       delta  1.8
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+Input = 50 ohms  Output = 150 + j100 ohms  Minimum permitted L1 = 1.438 µH
+       L1  1.439    L2  0.01     C  181       delta  1.8
+       L1  1.50     L2  0.16     C  180       delta  2.0
+       L1  2.00     L2  1.30     C  159       delta  3.1
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+Input = 50 ohms  Output = 150 - j100 ohms  Minimum permitted L1 = 1.114 µH
+       L1  1.115    L2  1.51     C  145       delta  2.1
+       L1  1.12     L2  1.38     C  140       delta  2.0
+       L1  1.14     L2  1.16     C  129       delta  1.9
+       L1  1.43     L2  0.02     C   85       delta  1.8
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Despite the use of two theoretically lossy inductances in the L-C-L Tee, it maintains low values of delta over a wide range of load conditions and transformation settings. Delta climbs more rapidly with inductive loads than with capacitive loads away from optimal settings. The operative rule of thumb for maximum efficiency is this:

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+ L-C-L Tees: Choose the lowest value of L2 that permits a match. +
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This operative rule holds true at higher ratios of output-to-input impedance, even though values of delta increase at those ratios. L-C-L Tees are subject to losses from circulating currents in the shorted turns of either switched or rotary solenoid or toroidal coils, losses that the value of delta cannot take into account. Therefore, construction of this network requires special care.

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Ultimate Transmatch: Lew McCoy's Ultimate Transmatch (UT) is an interesting variation on the C-L-C Tee. It places a dual capacitor at the input of the network, one section in series with the signal path, the other section to ground. Figure 4 shows the general outline of the network.

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Calculating delta for the UT design requires the following Egan equation:

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Input = 50 ohms Output = 150 ± j0 ohms  Maximum permitted C1 = 750 pF per section
+       C1  749      C2   168     L  0.57      delta  5.8
+       C1  600      C2   161     L  0.68      delta  5.0
+       C1  400      C2   143     L  0.90      delta  4.1
+       C1  250      C2   113     L  1.17      delta  3.8
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+Input = 50 ohms Output = 150 + j100 ohms Maximum permitted C1 = 750 pF per section
+       C1  749      C2   81      L  0.57      delta  5.8
+       C1  400      C2   75      L  0.90      delta  4.1
+       C1  250      C2   66      L  1.17      delta  3.8
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+Input = 50 ohms Output = 150 - j100 ohms Maximum permitted C1 = 546 pF per section
+       C1  545      C2 >350K     L  0.73      delta  4.7
+       C1  300      C2  615      L  1.06      delta  3.8
+       C1  250      C2  400      L  1.17      delta  3.8
+       C1  200      C2  256      L  1.30      delta  3.9
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Like other series-capacitance designs, the UT appears most effective with purely resistive and inductive loads: Required values for a match fall easily within the ranges of normal components just as the network approaches maximum efficiency. (If C1 is lowered further in these cases, delta increases.) However, with capacitively reactive loads, maximum efficiency has passed by the time C2 enters the range most normal for ATUs.

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Although the values for delta are higher than with some other designs, efficiency remains in the 96% ballpark. In fact, the efficiency of the Ultimate Transmatch appears to increase (at least to some limit) with increases in the ratio of output-to-input impedance. Using a 300-ohms output resistance with either no reactance or 100 ohms of inductive reactance, the UT achieved values of delta in the neighborhood of 2.8, while with 100 ohms of capacitive reactance, delta was about 3.5. The rule of thumb for the UT design is not as simple as with some other designs:

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+ UT: With normal ATU components (Cmax less than 400 pF), choose the highest value of C2 that permits a match within the range of C1. +
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Remember that, for any of the network designs, as the frequency decreases, some of the efficiencies achieved in these 10.1 MHz tables may not be reached, since proportionately greater values of C and L may be needed for the same load conditions. Moreover, switched inductors may not provide the values necessary for highest efficiencies. This limitation is rarely a problem, since the value of delta in most cases "bottoms out" over a fairly wide range. Nonetheless, the rules of thumb continue to apply.

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Moreover, remember that these figures are based solely on losses in the inductor, one assumed to have a Q in the range of 100 or more. Additional losses due to poor components, bad wiring and switching, stray inductances and capacitances, and coil "suck-out" are not accounted for by the calculations. If components get warm or arc under matched conditions at 100 watts, even though the calculations indicate less than 5% losses, believe your senses. Then analyze the components and construction of your ATU. Something other than network choice is very wrong.
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First printed in QRP Quarterly, January, 1996. Updated 3-25-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Return to Amateur Radio Page

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Topics: Matching


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Some Preliminary Notes on the Gamma Match

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L. B. Cebik, W4RNL

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My e-mail regularly contains a question that appears in various forms, but has one theme: Why have I not written anything about the gamma match? There are notes at my personal website on various forms of series matching systems and notes on the beta match. These two types of matching systems represent alternatives to the gamma match, especially when the task is to transform the generally low impedance of a Yagi array up to the value of 50 Ohms, as required by the most common feedlines used in amateur and other services.

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Compared to a gamma match, series and beta matching systems are both simple and precise. Both systems make no alteration to the driven element, but add networks composed of transmission lines (usually) to the element feedpoint. The beta match does require that we initially set the driven element length to arrive at an optimal value of reactance relative to the feedpoint resistance, but the beta component is or is equivalent to adding a simple reactance across the feedpoint. The matching systems do not affect the radiation properties of the element.

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As a consequence of these conditions, we may calculate the required values for series-matching or beta-matching components very precisely. In practice, the key factor affecting field adjustment of the systems is the accuracy of the velocity factor that we use in the calculations relative to the value that actually applies to the line used. If we know the velocity factor with measured accuracy (in contrast to the values we find in lists and specification sheets), we can often obtain the desired result with no need for further adjustment.

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These fundamental matching systems are therefore amenable to automated formulation, that is, a utility program or a spreadsheet page that will tell us the required values if we input the feedpoint conditions and other values related to the components. In fact, I keep a spreadsheet on hand in my computer for just such calculations. It contains calculations for 1/4 wavelength matching sections, Bramham transformations, and Regier series matching calculations. In addition, it allows beta-match calculations and returns results for using either a shorted transmission-line stub or a solenoid inductor as the most common beta components. However, it also yields open lines and capacitance values should one choose to lengthen the driven element rather than shortening it. I have also added a page for the match-line and stub system of matching, used with higher-impedance antenna elements. I wrote the pages in Quattro Pro (.qpw), but have also saved them in Excel (.xls). You may download the sheet of your choice from the following addresses.

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Antenna-Match in .XLS format (Excel)

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Antenna-Match in .QPW format (Quattro Pro)

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The Gamma Difference

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The gamma match differs fundamentally from the other matching systems because it alters the physical properties of the driven element in ways indicated by Fig. 1. First, it adds new wires to the element, giving the element a more complex shape. Second, it changes the element feedpoint relative to the original element. The simple element uses a feedpoint position that normally is at the center of the element. The gamma-matched element places the feedpoint on a wire that joins the gamma rod to the main element.

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One gamma-match advantage to many builders is the fact that the element may now connect directly to the boom. Both series and beta matching systems require driven elements that are insulated and isolated from any conductive support boom. In the era in which so-called "plumber's delight" construction methods ruled amateur Yagi construction, the gamma match equally ruled impedance transformation for coaxial feedlines. However, connecting the element to the boom changes its electrical length and therefore the feedpoint impedance prior to creating a gamma match. Therefore, most gamma match users began their calculations or experiments with only an estimated feedpoint impedance for the pre-matched element. NEC and MININEC antenna-modeling software offer no assistance here, since these programs only model axial currents (that is, along the element) and thus could not account directly for boom effects. Some builders have come to believe that a gamma match requires a direct connection between the boom and the element center. However, the connection is only an option, not a mandatory condition for the matching system.

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One criticism of the gamma match accuses it of displacing the pattern in the direction of the match due to the size of the assembly. Effectively, as some believe, the assembly increases the diameter of the gamma side of the element, and this asymmetry of the driven element results in the main lobe's re-aiming. To test this notion, I constructed models of 28-MHz beams with identical reflectors and element spacing. One beam uses a simple driven element. The other uses a driver with the same overall length, but with a gamma match assembly (of course, with no boom). The gamma assembly is in the plane of the two elements and projects forward of the driver. The results of the test appear in Fig. 2.

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The slightly lower forward gain of the gamma-matched version of the beam is an artifact of certain limitations of NEC (which we shall review shortly). The key factor in the overlaid patterns is the degree of lobe displacement, indicated by the lines that I added to the sides of the lobe. Displacement does indeed occur, but at a level too small for any user ever to notice in operation. The two patterns to the right show that the gamma match also has an affect on the free-space side nulls for the array. The simple beam has side nulls that show no limit. However, the gamma-matched beam has limited side nulls that are a mere 40-dB down from the level of maximum gain. I am unaware of any operational use of a beam in which one might be able to detect the difference.

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The modeled test case assumes by its mathematical basis relatively perfect construction of the gamma-match driven element. I have in past years seen range-generated patterns for gamma-matched beams with a significant displacement of the main forward lobe. It would not be possible to perform a full analysis of such patterns without being able to model currents within the driven element and along the boom--if the elements makes a direct connection to the boom. However, in principle and assuming careful construction, pattern displacement is not a hindrance to the use of a gamma match.

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Calculating the Gamma Match

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H. H. Washburn, W3MTE, introduced the amateur community to the gamma match in his September, 1949, QST article, "The Gamma Match" (pp. 20-21, 102). D. J. Healey, W3PG, provided the first mathematical analysis of the match in "An Examination of the Gamma Match," QST, April, 1969 (pp.11-15, 57). Healy's treatment, however, required the use of nomographs and a Smith chart.

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Since these seminal articles, several alternative analyses have appeared in amateur journals. H. F. Tolles, W7ITB, presented a purely mathematical analysis in "How to Design Gamma Matching Networks" in Ham Radio for May, 1973 (pp. 46-55). Because the Tolles equations proved tedious to many gamma designers, R. A. Nelson, WB0IKN, set them into a Basic program in "Basic Gamma Matching," Ham Radio, January, 1985 (pp. 29-33). ARRL converted Nelson's Apple-Basic program into a version suitable for IBM computers, and a listing appears in The ARRL Antenna Book, 16th Ed. (p. 26-20). In 2000, Dave Leeson, W6NL, corrected portions of the program so that it more accurately serves as a design vehicle to calculate gamma matches. This program is also available within the HamCalc collection of Basic utilities edited by George Murphy, VE3ERP. Fig. 3 shows the GW Basic listing for the version of the program distributed by ARRL.

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Since the work of Tolles and Nelson, two alternative mathematical analyses have appeared. Ron Barker, G4JNH, presented "A New Look at the Gamma Match" in QEX, May/June, 1999 (pp. 23-31). Barker changes some of the fundamental assumptions about the key factors in a gamma match to arrive at his results. Unfortunately, his work is less amenable to easy placement in a Basic utility or a spreadsheet, since the calculations require the solution to simultaneous equations. In contrast, Roger Wheeler, G3MGW, returned to the Healey analysis and converted the graphical techniques back into mathematical methods that allow a straightforward spreadsheet set of calculations. Both of these later analyses rely on something that was unavailable to earlier gamma calculations. In most cases, the determination of the initial or pre-match driver feedpoint impedance rested on assumption, guesswork, or rudimentary measurement. Measurement became difficult if the builder connected the driver to the boom and did not allow for a feedpoint gap, even if it would later be closed. Both Barker and Wheeler require the use of antenna modeling software to determine the pre-match driver impedance. Other methods exist, for example, the Brian Beezley, K6STI, module in the overall program YO. However, Beazley has never published his procedures.

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The downloadable spreadsheet contains pages for the Healey-Wheeler (HW) and the Tolles-Nelson-Leeson (TNL) methods of calculating gamma match rods and series capacitors. Every gamma-match calculating system tries to yield a physical value for the length of the gamma rod and a series capacitance value at the feedpoint to leave a pure resistive impedance. The required inputs appear in Fig. 4. We need to know the diameters of the main element in the region of the gamma assembly and of the proposed gamma rod, tube, or wire. As well, we must input the center-to-center spacing between the main element and the gamma rod. Ordinarily, the physical dimensions for the inputs and the outputs are in the same units of measure. The spreadsheets use inches.

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In addition, we require two impedance values. One value is for the simple driven element, designated Ra and jXa in Fig. 4. We also need to specify a desired feedpoint impedance, Rf, which is the target resistive impedance that matches the main feedline. For our samples, we shall use 50 Ohms, since it is the most common value that we encounter in amateur radio applications. However, we may apply the gamma match for virtually any reasonable line impedance.

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Fig. 4 also shows some of the points in the gamma assembly that exhibit derived impedances calculated somewhere within the system. Z1 is the transformed impedance based on the fact that the gamma assembly forms a shorted transmission line stub. (One misguided criticism of the Healey system was that it treats the gamma assembly as a folded dipole. Every folded dipole exhibits both radiation and transmission-line currents. In the calculation of the gamma line, we are concerned with the transmission-line performance of the assembly.) We can derive the characteristic impedance (Zo) of the stub using conventional equations that involve only the physical dimensions of the line. S is the center-to-center line spacing, and d1 and d2 are the diameters of the gamma rod and the main element, respectively.

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The TNL system uses more fundamental equations involving havercosines. However, in the typical range of Zo (perhaps 200 to 600 Ohms), the differential in results between equations is less than 1% and normally only about 0.1%.

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While we are using only the physical dimensions that we input to the calculation system, we can also calculate a step-up ratio between the original simple-driver impedance and the value shown as Z1 in Fig. 4. The most usually form of the equation again employs the three input physical values, S, d1, and d2.

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Once more, the TNL system uses more fundamental equations, but the differential in result, compared to the more usual engineering formulation is well under 1%. Both the HW and TNL systems use this equation to calculate the value of Z1 (R1 +/- jX1) simply by multiplying Ra and jXa by the value of r. If the diameters of the main element and the gamma rod are the same, then r = 4. If the gamma rod is thinner than the main element, then r > 4. If the gamma rod is thicker than the main element (an unusual but possible situation), then r < 4 but r > 1.

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We may add two side notes here. First, the Barker calculation system does not use the step-up ratio derived from the usual equation. Barker uses the impedance ratio between a simple driver element in isolation (essentially a dipole) to the impedance of the simple driver in service within the beam antenna. Second, at least the HW system does not account for the fact that the impedance undergoes not only a step-up in value, but also a shift in phase angle when we move from the driver without the gamma assembly to the driver with the assembly. If we model a gamma system and place the feedpoint at the position it would occupy on the pre-gamma driver element, we can observe the phase-angle shift in the impedance.

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The HW system calculates the value of Z2, the impedance presumed to exist at the far end of the gamma assembly. If we assume that the current distribution is sinusoidal--which is close to correct but not precise--then we may use a standard equation to determine the values of R2 and X2.

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Theta is the electrical length of a gamma assembly either in degrees or in radians at the design frequency. Since we cannot determine the value of theta without a physical gamma rod, the HW system calls for a trial length. In concert with the remaining calculations, we simply adjust the trial length until the value of Rf becomes 50 Ohms, if that is the target feedpoint impedance.

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The TNL system operates differently. By addressing the required impedance and phase angle at the feedpoint, it calculates the required rod length using the factors already derived plus some ratios that appear in the listing in Fig. 3. The original Tolles article in Ham Radio provides the source of these ratios as they are applicable to the calculations. The Barker system uses neither of these methods, but creates an assumption of what must be the relative impedance at the gamma junction with the main element. He then calculates actual values from the initial driver impedance in a set of simultaneous equations.

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The HW system derives the feedpoint impedance from two values in parallel. One value is the impedance of the gamma assembly as a shorted transmission-line stub having the length, theta, and the characteristic impedance Zo.

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The other values are the values of Z2 as transformed by the same length of transmission line back to the new feedpoint. Wheeler follows Healey in using the following equation for this part of the impedance combination.

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To resolve the equation, of course, one must break it into real and imaginary parts and then recombine them to arrive at the final value of Z3. (The TNL system essentially reverses the procedures and calculates the rod length from the required transformation.) We combine the parallel combination to arrive at an impedance that is the desired Rf in series with a value of Xf that is inductive. From this inductive reactance and the design frequency, we may determine the required series capacitance to leave us with a purely resistive feedpoint impedance.

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I have tracked some of the rudimentary elements of gamma calculating systems to show what sort of thinking goes into them. However, the treatment is in no way complete, nor does it touch a number of the dimensions of the TNL and Barker systems. Instead, it is simply complete enough to allow one to track through the attached spreadsheet formulations of the HW and the TNL systems, in case one wishes to calculate a few typical gamma assemblies.

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Testing the Gamma-Calculating Systems

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Virtually all published gamma-calculating systems use one or two examples of the system's application and then declare the system adequate. Wheeler applied his formulation to gamma assemblies on quad loops. Tolles preferred VHF Yagis using gamma rods considerably thinner than the main element. Barker uses a single 20-meter beam as his test case. Of course, trying to develop a systematic set of test cases would be nearly impossible if we were restricted to constructing physical antennas having an interesting range of feedpoint impedance values for transformation.

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It is possible to construct a series of antenna models to serve as a surrogate for the physical antennas. However, we cannot do the job in NEC-2 or even NEC-4. As suggested in Fig. 5, the gamma assembly presents NEC with two problems. First, unless the gamma and main elements are the same diameter, we encounter angular junctions of wires with dissimilar diameters. Although NEC-4 improves on the performance of NEC-2 under these circumstances, the results are insufficiently accurate for use as a comparator to the calculated values. In addition, gamma spacing is rather narrow for most beams that use relatively fat element diameters. Under these conditions, NEC tends to yield less than precise results. The relative unreliability appears in the average gain test (AGT) scores, which generally are no better than 0.92 when a perfect score would be 1.00. Since arriving at a feedpoint impedance of 50 Ohms is critical to the comparisons, AGT values in the range of 0.92 are too far from ideal to be useful. Values of 0.98 to about 1.02 are more valuable to the task of comparison.

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Fortunately, MININEC is not sensitive to angular junctions of wires with differing diameters. However, in its raw form, it is subject to limitations related to close wire spacing and to angular junctions in general. One version of MININEC, Antenna Model, has introduced correctives that make it suitable for some first-order comparisons with the calculation systems. Note that I do not call the models "standards" against which we test the calculation systems. At best, the models are comparators so that we may observe some general trends as well as similarities and differences in outcomes.

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Fig. 6 shows the general set-up for the modeling process. Although unnecessary for the pre-match model, I have assigned to each element the same number of segments used in the gamma model. The number of segments for each element derives from the test values of gamma spacing. All test models will use 28 MHz as the design frequency. The gamma spacing will use 4" as a center value and require 2 segments in the feedpoint wire to place the feedpoint at that wire's center. Hence, a 2" segment length becomes the standard. For some tests, we shall use gamma spacing values of 2" and 6", but the segment length differential will not prove too detrimental to the AGT scores. In fact, in the accumulated data, I shall show not only the modeled gamma rod length and the indicated series capacitor, but as well the AGT score to permit you to reach your own conclusion about the model's reliability.

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From the very start, we recognize some important differences between the models and the calculation systems. Foremost among the differences is the fact that the models contain actual physical structures for the gamma far end shorting bar and for the feedpoint connecting assembly. In all models, I shall use end wires that have the same diameter as the main element, since in gamma assemblies applied to Yagis, the shorting bar and the coax connector plate tend to be substantial. Neither the HW not the TNL calculation system includes any allowance for such structures. Barker does add some fudge factors to his system, and the HW spreadsheet page includes an optional fudge-factor section at the end. The reason for the fudge factors is that calculations tend to call for capacitance values that are too high, and the models will reflect this fact by requiring lower capacitance values than the calculations indicate.

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Test 1: A Simple Scaling Project

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As an initial test, let's compare 3 perfectly scaled antennas with gamma matches. The test frequencies are 7, 14, and 28 MHz. For each frequency, I created a basic 2-element driver-reflector Yagi with a feedpoint impedance of 29.84 - j25.73 Ohms (typical of 0.12 wavelength element spacing). To ensure perfect scaling, the elements are lossless. (The calculation systems do not take material losses into account, and given the small size and generally large element surface areas used in beams, the losses would indeed be small.) The 10-meter antenna uses a 0.5" main element diameter, with a 0.375" gamma rod. The element-to-rod spacing is 4". All of these dimensions also scale upward as we lower the test frequency. Therefore, the 7-MHz version of the antenna uses a 2" main element, a 1.5" gamma rod, and 16" spacing. Even though the 40-meter dimensions may be somewhat larger than realistic, they will serve well in this test. The top section of Table 1 provides a more detailed run-down of the beam dimensions.

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The lower portion of the table shows the calculated length of the gamma rod and the calculated series capacitance using the Healey-Wheeler and the Tolles-Nelson-Leeson system. It also shows the modeled values in the AM MININEC program. Because all dimensions are perfectly proportional, the calculated values of the gamma-line characteristic impedance, Zo, and the step-up-ratio, r, are the same for all three antennas. A review of the basic equations shown earlier will confirm this result.

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As a consequence, we find that the two calculation systems also produce scaled values for both the gamma rod length and the required series capacitance. Likewise, the modeled gamma rod and series capacitance also internally scale within the limits that I set for modeling precision. I adjusted the rod length and the series capacitance until the feedpoint impedance reached 50 Ohms resistive, +/-0.1-Ohm, and j0 Ohms reactive, +/-j0.1 Ohm.

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For this test case, the two calculating systems yield quite similar values for the gamma rod length. However, both values are 16-17% shy of the modeled value. One reason that I selected this initial test case was the fact that the calculation systems yield values smaller than the model. Theoretically, if we simply assume that the calculation system does not take the shorting bar into account, we would expect the calculated lengths to be slightly long. Hence, the systems and the model must have other differences.

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As we expected from general gamma-match experience, both calculation systems over-estimate the required amount of series capacitance needed to bring the feedpoint impedance to a resistive 50-Ohm value. In this early test, we may also note that the two systems yield very different series capacitance values. Therefore, a single method of adding fudge factors into the determination of the final series capacitance value will not work for both systems.

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However, I have to insert a reminder here. The modeled gamma match is only a comparator in this test (and in those yet to appear). It is not a standard against which to measure the adequacy of the two calculating systems. With the exception of the gamma-rod length, the 3 systems of determining the required gamma-rod length and the series capacitance merely yield different results.

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Test 2: Changing the Ratios among Element Diameter, Rod Diameter, and Spacing

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For a second test, let's modify the initial beam so that it is very close to resonant, with a feedpoint impedance of 32.07 - j0.05 Ohms. For this test, we may use a 28-MHz beam. Like the beam in the first test, the element spacing is 0.12 wavelength, so the only change is to the driver length. The main element diameters are 0.5". Once more, we shall explore the HW and TNL calculating system results and compare them with AM MININEC modeling results.

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This test will be somewhat more complex. We shall explore 3 element-to-rod spacing values: 2", 4", and 6". As well, we shall look at gamma-rod diameters from 0.125" to 0.625" in 1/8" increments. A gamma rod that is fatter than the main element is unusual in reality, but certainly possible. Because we are changing both the diameter ratio between linear parts of the gamma assembly and the spacing between those parts, the values of both Zo and r will change with each sample case. The value of Zo will range from about 233 Ohms (for the 0.625" rod at a 2" spacing) to nearly 465 Ohms (for the 0.125" rod with a 6" spacing). The versions using 2" spacing will show the widest range of step-up ratio (r) values, running from about 3.6 for the fattest rod to 7.1 for the thinnest.

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Table 2 catalogs the data for the series of tests. The top part of the table provides the initial antenna dimensions, along with the near-resonant pre-match feedpoint impedance. The next part of the table provides results for the three methods of determining the required gamma parameters. The AM section provides an additional column that lists the AGT score for each model in the set. The models using a 2" spacing are the farthest from ideal. It is not wholly clear that MININEC follows the same general AGT rules as does NEC. Hence, we cannot claim with assurance that the 50-Ohm impedance derived from the models (within the limits used in the first test) is off by no more than about 1.25 Ohms. However, the parallels among values for all three spacing values suggest that the models are generally reliable within the limits of the average gain test.

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The three methods of finding gamma parameters differ in almost every category. The HW and TNL systems show various degrees of gamma-rod length increase as we increase the rod diameter, regardless of the spacing. The models show virtually no change in length within each of the spacing groups. The HW system shows a considerable increase in length as the rod diameter increases, while the increase is fairly modest for the TNL system. In all cases, the calculating methods show longer rods than the models. However, we cannot draw conclusions until we review the second part of this test series, using a different initial or pre-match feedpoint impedance.

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The series capacitance values produced by each method present an equally befuddling array of differences within each method and between any two methods. The HW system produces only small changes in value across the span of rod diameters for wide-spacing values, but larger changes for narrow spacing values. The HW changes within spacing groups are in all cases smaller than for the TNL intra-group changes. The modeled values partially parallel the HW values in terms of the amount of change within each spacing group. However, the trends are not consistent between the calculating systems and the modeling system.

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Before we rush to conclusions, we should repeat the very same tests using a different pre-match impedance. We shall retain every other beam detail, except that we shall use the version of the beam that shows a pre-match impedance of 29.84 - j25.73 Ohms. The results of this second survey appear in Table 3.

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With respect to gamma rod length, within each group, the HW system shows an increasing length as we increase the rod diameter. Both the TNL system and the AM models show a decreasing rod length as we increase its diameter. Despite the different trends for the initial impedance of the antenna, the HW and TNL lengths are not very different from each other for any given element-to-rod spacing. However, the rod lengths required by the models are systematically longer. (This fact is exactly the reverse of what we saw when the beam's pre-match impedance was nearly resonant.)

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With the high capacitive reactance of the pre-match impedance, the gamma-rod lengths remain relatively stable for all 3 methods within each increment of element-to-rod spacing. However, the series capacitance is another matter. The HW system shows the greatest rate of increase with increasing rod diameter, while the AM models show the smallest rate of increase. Both calculating systems produce much higher series capacitance values than the models, with the HW system showing values that are 100-150% too high. The TNL and AM series capacitance values are more closely--but not too closely--aligned.

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The trends shown within each of the two test situations generally failed to parallel each other, despite the fact that the only difference between system inputs is the initial or pre-match impedance values. It would appear that we need a further type of test situation.

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Test 3: Varying the Input Impedance

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The goal of this test sequence is to determine--at least in a preliminary way--the effects of varying the pre-match feedpoint impedance, with special reference to the reactance. We already have sample of resonant and highly capacitively reactive impedances. We may use the same basic model of a 28-MHz 2-element Yagi and vary the driver length to create a reasonably fair sequence of reactance values. We need a positive limiting reactance value that is close to the negative limiting value. As well we need reactance values close to +/-13 Ohms as intermediate values between resonance and the limits. We can arrive at these values just by varying the length of the initial beam driver, as shown in the top section of Table 4. The resistive component of the pre-match feedpoint impedance will increase as the driver grows longer. However, the amount of increase should not be enough to invalidate this highly preliminary test sequence. We shall survey two gamma-rod diameters in order to assure ourselves that any trends are not mere quirks.

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The lower portion of Table 4 shows the results of calculating the gamma parameters and of modeling them. Let's examine the results, separating the gamma length from the series capacitance, and also separating the two different gamma-rod diameters. Fig. 7 graphs the gamma-rod lengths for the 0.125" diameter gamma rod.

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Both the HW and the TNL calculating systems show roughly equal rod lengths at the extremes of the test series, with the inductively reactive initial driver requiring a considerably longer length than the capacitively reactive driver by a factor of about 2:1. However, between these extremes, the two systems show curves with almost exactly opposite tendencies. Moreover, when we examine the modeled gamma-rod lengths, we find a quite different curve. The rod is shortest when the pre-match impedance is closest to resonance, with increases in length as the impedance becomes more reactive, regardless of the type of reactance.

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When we increase rod diameter to 0.375", as shown in Fig. 8, the same tendencies repeat themselves, although the calculated lengths increase the ratio between the most inductive and the most capacitive reactance values. However, the modeled gamma-rod lengths show virtually the same values as shown in the curve for the 0.125" rod.

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If we graph the series capacitance values for the 0.125" rod across the spread of pre-match impedances, the curves become quite interesting, as suggested by Fig. 9. Each method of reaching a capacitance value shows a peak, and the peak occurs at a different impedance for each method. The HW system arrives at a peak capacitance value at the intermediate capacitive reactance value, while the TNL system peaks at (or close to) resonance. The modeling method shows its peak near the intermediate inductive reactance value. We should remember that the model contains gamma end wires that are not a part of the calculating systems.

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The capacitance curves for the 0.375" rod diameter show similar traits to those for the 0.125" rod. See Fig. 10. The calculating systems appear to show peaks with higher levels of reactance than we found to be the case for the thinner gamma rod. Once more, the TNL gamma matches show peak series capacitance values close to an initial resonant impedance, with the HW peak in the capacitive reactance region and the modeled match's peak in the inductively reactive region, relative to the initial or pre-match driver impedance.

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Perhaps more vividly than any other test, the final series of tests shows one of the chief sources of differences among the three systems. The two calculating systems respond to differences in the feedpoint reactance in similar ways, although the length curves show opposite tendencies as the pre-match impedance approaches and passes resonance. If the test is representative, then we have established that the two systems are the same in principle, although they differ in detail. However, for changes in the gamma-rod length, neither system correlates well with the modeling method of designing a gamma assembly. Otherwise expressed, the modeling system of design fails to correlate well with the methods of calculation.

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Note that I have emphasized the conditional nature of the test series. We have examined only the impedances that tend to apply to Yagi beams, that is, impedances below the feedpoint impedance. Establishing that the results are in fact representative would require a very large series of test sequences involving many possible impedance combinations relative to the feedpoint target and the pre-match values. At most, this test has established the importance of the pre-match impedance as a factor governing the results from each method.

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Some Tentative Conclusions

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I approached the gamma match out of curiosity. My inquisitiveness arose from the difference between series matching and beta matching calculation systems and the calculation of gamma matching systems. The first two methods produce precise results so that the most significant limitation when implementing one of them surrounds the physical properties of the components involved. For transmission line lengths, the accuracy of the velocity factor (or our ability to make linear measurements of the line) becomes the chief source of error.

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The gamma matching system calculation methods show far less precise results. Some writers have ascribed most of the error to the lack of end wires in the calculated values. For many implementations, this convenient explanation seemed too weak to account for the differences. Therefore, I took two of the systems that are amenable to straightforward calculation progressions and compared their results to MININEC models using the most reliable version available of that software. The results of our preliminary series of tests--restricted to a 50-Ohm target feedpoint and to pre-match impedance values typical of Yagi arrays--show something else entirely.

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The two calculation systems--HW and TNL--produce seemingly divergent results, especially with respect to variations among the main element diameter, the gamma rod diameter, and the spacing. However, if we employ a range of pre-match impedance values that vary mostly with respect to reactance, we begin to see an emerging pattern in which the calculated gamma lengths converge at high pre-match reactance values and diverge when the pre-match impedance approaches resonance. (We may bypass capacitance calculations, since they depend on the calculated gamma rod length.)

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Perhaps the most disturbing aspect of the test series is the fact that neither calculation method approaches--either in values or in trends--what we find when we model a gamma match using MININEC models with nearly ideal AGT scores. However, we cannot in this case give automatic priority to the modeled results because they have not undergone confirming field tests. They simply serve here as a third method that differs in principle from the basic presumptions underlying the two calculation systems that we examined. Nevertheless, the differences in results among the methods strongly suggests that the present methods of calculating gamma match components fall seriously short of being precise.

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We have had occasion to note that one point at which both the HW and TNL systems make a questionable assumption lies in the use of standard equations for calculating the transformed pre-match impedance to arrive at a value that we have called Z1. Remodeling the gamma to move the feedpoint to the main element at the junction of the gamma-half-element with the non-gamma-half-element suggests at least a phase shift and also significant variation from the calculated value of r that depends only on the physical properties of the assembly. The transformation also appears to relate to the pre-match impedance--especially the reactive component--although our test series is too small to reach two important conclusions. One conclusion would be the derivation of a revised step-up function, either as a correction factor on the usual calculation or as a substitute formulation. The other conclusion that we cannot draw is the adequacy of the modeled gammas to serve as source for such correctives.

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Even if we could revise the available calculation systems, they would still fall short of the precision that we obtain from the calculations associated with series and beta matching systems. The methods by which we implement a gamma match include significant variables relative to even a precise calculation system. Fig. 11 shows some of the factors involved.

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The upper portion of the sketch shows the general situation presumed by all of the methods that we have examined. The elements have a uniform diameter and thus most closely approximate sinusoidal current distribution. The end wires at the gamma far end and at the feedpoint have no weight in the calculation--except as post-facto fudge factors. Third, the series capacitance is precisely at the feedpoint of the gamma system.

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The lower portion of the sketch shows some typical variations in the theoretical arrangement used in calculations. The elements in the HF range may use stepped-diameter structures that may vary the usual expectations for current distribution. The gamma rod normally extends beyond the shorting bar, leaving a small but definite radiating structure. The shorting bar at the gamma far end and the plate holding the coaxial cable connector have significant proportions that will vary from one installation to another. The sketch also shows the use of a tubular capacitor, a common HF technique to provide the series capacitance without concern for the voltage and current levels on the component and without concern for the effects of weathering. Once set, we may effectively seal the capacitor so that it requires only long-term maintenance. However, equally important to the type of capacitor used is its position. Typically, without regard to the type of capacitor used, gamma-match builders install the component on the gamma rod rather than at the actual feedpoint. Fig. 12 illustrates a sample of commercial gamma-match construction. By virtue of its position along the gamma line, the capacitor modifies both its influence on the feedpoint impedance and on the structure of the gamma line. As well, the physical implementation of the gamma must take into account any affects of the boom, if one chooses to connect the driven main element to the boom.

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Therefore, even if we were to perfect gamma-matching system calculations, they would not yield the precision that we associate with other matching system calculations. Rather, they would serve only as a general guide to begin a process that only field adjustment can perfect. Indeed, for any selection of main element diameter, gamma rod diameter, and spacing between the two, there is a gamma length and a series capacitance that will effect a usable match to a desired main feedline over a wide range of pre-match impedance values--although not a completely unlimited range. As well, the gamma match will work either with or without a direct connection of the driven element to the boom.

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Whatever the complexity of the calculation system, its output is simply a starting point to the process. We might as easily replace it with a table encompassing all of the successful implementations of gamma-match systems arranged by frequency, main element diameter, gamma rod diameter, and element-to-rod spacing (with annotations on the method of implementing the series capacitance). Such an archive--if it existed--would likely provide as much guidance to gamma-match dimensions as the current methods of designing them.

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Updated 10-01-2006. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Sep., 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching


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Some Further Notes on the Gamma Match
+ What MININEC Models Report

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L. B. Cebik, W4RNL

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In "Some Preliminary Notes on the Gamma Match," I began (but certainly did not conclude) a comparison between two methods of calculating gamma-match dimensions (specifically, the length of the gamma rod and the required series capacitance) with additional comparisons to a set of MININEC models. Once I translated the two calculation methods (the Healey-Wheeler and the Tolles-Nelson-Leeson systems) into handy spreadsheet formats, they stood ready to deliver any amount of required data on a moment's notice. However, modeling is far less handy in this regard, since each new case requires a new model.

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The original investigation revealed some anomalies between the modeling and the calculation methods of finding gamma-match dimensions. For example, both calculation systems show a significant variability in gamma-rod length as we change the ratio of the main element diameter to the gamma-rod diameter. However, the models showed virtually no change for gamma rods ranging from 0.25 up to 1.25 of the main element diameter. Even more interesting was a very preliminary check of gamma rod lengths relative to the initial feedpoint reactance. Calculation methods showed a virtual continuous increase in gamma rod length as the reactance went from a significant capacitive value up to an equally significant inductive value. Models showed a minimum gamma rod length at or near a resonant initial element impedance with increases that vary with reactance, whether capacitive or inductive.

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The original survey--driven by a comparison among gamma design methods--had many limitations. Perhaps the primary restriction concerned the very small region of initial antenna impedances used in the examples. The resistive component of the initial antenna element impedance was about 30 Ohms. Gamma matches are capable of matching a wide range of impedances to a given feedline impedance. Hence, further systematic modeling seemed in order. Since even a small survey will involve many models, these notes will focus entirely upon what models have to tell us.

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Modeling Issues

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One reason for focusing solely upon models in these notes has to do with the basic structure of a gamma match and its representation within an antenna modeling system. Fig. 1 provides the outline of the gamma match structure in contrast to the element structure without the match in place.

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We normally obtain a value for the impedance of a driven element at the element's center, as shown in the upper portion of the sketch. A gamma match adds further wires to the structure and moves the feedpoint, as indicated in the lower half of the sketch. Calculation systems of determining gamma dimensions treat the wire that is parallel to the main element as a transmission line and use equations appropriate to that conception. As a consequence, they do not directly account for the connecting wires at the feedpoint and at the far end of the gamma system. To model a gamma match as a physical structure requires that we include these connecting wires, or else the model will not work. For all models in this study, the end wires will use the same diameter material as the main element.

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The input data for a gamma match forms a relatively complex set.

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    1. The main element diameter

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    2. The gamma rod diameter

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    3. The center-to-center spacing of the main element to the gamma rod

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    4. The initial feedpoint impedance of the driven element, usually given in series format: R +/- jX Ohms

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    5. The target matched impedance, given solely in resistive terms and usually the characteristic impedance of the main feedline

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To simplify our initial work, we shall use a single spacing throughout the exercise. As well, the main element diameter and the gamma rod diameter will be the same. As we review some old data, we shall see some justification in these simplifying maneuvers. Again, to simplify matters, we shall use 50 Ohms as the standard target impedance for the match. This is perhaps the most common value for which we find gamma-match designs.

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Where the new work will depart significantly from previous work is by beginning with a larger range of initial antenna impedance values. Since we cannot survey everything in one exercise, we shall explore resistive impedance between 15 and 60 Ohms in 15-Ohm increments. We shall also explore reactance values between -j24 and +j24 Ohms in j8-Ohm increments to subdivide the curves more finely.

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As in the earlier exercise, we shall use MININEC models. NEC models are simply not up to the task of modeling a gamma match. Fig. 2 suggests why.

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If we were using models with gamma rods that varied in diameter from the main element diameter, NEC would reveal its well known weakness at angular junctions of wires having different diameters. However, the models in this study will use equal diameters for all wires. Nevertheless, with relatively close spacing of wires, NEC also begins to yield errant results, as indicated by average gain test (AGT) scores that depart widely from the ideal value of 1.0000.

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Raw MININEC 3.13 (the version available in the public domain) would be equally incapable of accurately modeling gamma matches due to some inherent weaknesses. Unmodified MININEC has difficulties with corner junction, close-spaced wires, and some other aspects of many model geometries. However, Antenna Model has introduced correctives for these problems. In addition, it produces a readily accessible AGT score so that the modeler can evaluate the model undergoing work. Therefore, all models used in this study employ Antenna Model as the operative software.

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All models in these notes begin with a "gamma-less" 2-element Yagi having a desired (or usable) driver-element feedpoint impedance, as shown in the upper half of Fig. 3. The models will be in the vicinity of 30 MHz. In this frequency region, using 100 segments per element yields segment lengths in the vicinity of 2". This segment length easily accommodates the range of main element and gamma rod diameters that we would normally use in samples--and in regular construction. The gamma-match version of the model makes no change in the reflector element. The driver element retains its initial length, but become 3 model wires. The sketch shows that the number of segments in the gamma-match region is N, so that the total number of segments in this half of the element is 50. However, the value of N will vary according to the required gamma length so that the segments in all 3 parts of the driver have as close to equal lengths as may be feasible. The gamma rod will also have N segments.

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The result of these measures produces an internally consistent set of models. However, the data set has not been validated against a set of physical antennas with the modeled properties. Hence, we cannot and do not claim that the exercise reflects the reality of gamma match implementation. That portion of the work is available to anyone with sufficient patience and aluminum stock to build and measure the requisite range of antennas.

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Nevertheless, the modeling data provide a mass of information that is ripe for physical testing. As well, they provide a collection of cases against which anyone may compare the results of calculating gamma systems via any of the extant methods.

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A Review of Some Previous Results

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The original foray into modeling gamma matches used a test frequency of 28 MHz. As well, dimensions appeared in inches. The fundamental model of a 2-element Yagi used 0.12 wavelength spacing between two 0.5" elements. The feedpoint impedance prior to adding a gamma match was 29.84 - j25.73 Ohms for the non-resonant version and 32.07 - j0.05 Ohms for the resonant model. The only difference between the models was the length of the driver element.

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The initial test models examined two variables: the spacing between the gamma rod and the main element as well as the size of the gamma rod relative to the main element. I varied the gamma rod diameter between 0.125" and 0.625" in 0.125" increments. I also varied the gamma spacing, using 2", 4", and 6" center-to-center. For each model in the series, I varied the gamma-rod length until I reached a new feedpoint impedance of 50 +/-j0 Ohms, +/-0.1 Ohm in both the resistive and reactive components.

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Fig. 4 graphs the outcome of the test for the resonant model with respect to the length of the gamma rod. (The tabular data appear in the original article.) The graph uncovers two interesting results. First, the modeled gamma rod undergoes almost no change in length, regardless of the ratio between the element and rod diameters. This outcome runs contrary to the trends shown by calculation systems. More important for our work here, it suggests that further modeling need not be concerned with the element-to-rod diameter ratio during first-order investigations into modeled gamma trends.

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The second result is the regularity of the change in gamma-rod length with increasing spacing. The gamma rod length is inversely proportional to the spacing, but not in a simple arithmetic fashion. The open question is whether the proportions will hold for other initial impedance values, including those containing a significant reactive component.

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Virtually every gamma match requires a series reactance to compensate for the remnant feedpoint inductive reactance. All models placed the series capacitance at the feedpoint, although physical construction practices may vary from this position. Fig. 5 shows the progression of series capacitance values for the three spacing values, with the variations in the element-to-rod diameter ratio. Here, the curves are not linear. It is possible that the curves might meet for any reasonable spacing value with a gamma rod that is very thin. However, as the rod becomes thicker, the required series capacitance varies inversely according to spacing and directly with an increasing rod diameter.

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I repeated the same sequence of models using the beam design that had a non-resonant feedpoint impedance. The feedpoint impedance phase angle approaches 41 degrees, which we may record as a very significant departure from resonance. However, the modeling procedures followed the same steps as used for the resonant model. The graph of the modeled gamma lengths appears in Fig. 6. (Once again, the full tabular data appear in the original article.)

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The curves for each spacing increment show a definite "tilt" and become shorter as the gamma rod becomes thicker. However, the amount of length change for the change in the element-to-rod ratio is quite small: a 2% length change for a ratio change of 5:1. This result suggests that one might explore other directions in gamma-match variables by using a single element-to-rod ratio with confidence that the results for other ratios would not jeopardize the validity of the trends uncovered.

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In addition, the change in gamma length for the changes in spacing follows very closely the relationships applicable to the resonant model. This result is also useful for further work, since it implies that one might use a single spacing value for further work and later derive conversion equations for transferring the results to other spacing values. The numerical values might change, but the trends would be reliable.

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The shapes of the curves for the required series capacitance in Fig. 7 are virtually identical to those for the resonant model in Fig. 5. For all three spacing values, the resonant model required series capacitance values about 1.6 times higher than the ones for the non-resonant model using the thinnest gamma rod. The ratios only grow to between 1.7 and 1.8 using the fattest gamma rod. Within broad but usable limits, then, we may rely upon the trends of other modeling directions to be indicative of all spacing values and all element-to-rod ratios, even if we restrict ourselves to a single element-to-rod ratio and a single spacing value.

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One of the most interesting results to emerge from the initial models of gamma matches at 28 MHz involved a rudimentary exploration of what happens if we systematically vary the initial feedpoint impedance between a fairly large capacitive reactance and a fairly large inductive reactance. To sample that situation, I varied the driver lengths of the pre-match models to arrive at impedances values that have nearly 26-Ohm reactances and nearly 13-Ohm reactances--of both types--with the resonant model at the center. To create these models, I varied the driver length until I reached acceptable feedpoint values and froze the dimensions at each step. This procedure is slightly inexact, since the resistive component will vary a small amount as the driver length changes without varying the other beam dimensions. However, for the purpose of looking at some basic trends, the variations in resistance are relatively harmless. To reduce the work involved, I checked the results using a constant 4" spacing between the element and the rod and looked at 0.125" and 0.375" gamma rod diameters. (The tabulated data appear in the original article.)

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With respect to gamma-rod length, as shown in Fig. 8, the size of the gamma rod makes virtually no difference. More significant is the shape of the curve itself. First, the shortest gamma-rod length occurs at or close to an initial resonant feedpoint. As we add either capacitive or inductive reactance to the initial feedpoint impedance, we require a longer gamma rod. This trend runs counter to results that we might obtain from calculation systems. Extant systems tend to show a continuous increase in gamma-rod length for the entire sequence of initial impedance values.

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Also interesting is the tilt of the curve. The tilt might be a function of at least two phenomena. First, it might be a result (wholly or partially) of the rising resistive component of the initial impedance. Second, it might be a function of that fact that the shortest gamma-rod length does not occur at resonance, but perhaps on the capacitive side of resonance. Hence, we have an open question that deserves further investigation.

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As we would expect from the previous trends in modeled gamma match assemblies, the required series capacitance increases as we increase the gamma-rod diameter. Fig. 9 shows the degree of increase as it varies according to the initial feedpoint reactance. Of equal interest is the fact that the required series capacitance reaches a peak value at the intermediate inductive reactance, and then begins to decline. The decline is greater for the thinner gamma rod than for the thicker one. Hence, we are once more left with a question of whether the peak occurs at the same initial feedpoint reactance in both cases.

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We may add to these questions a further one: do the trends that we found in the gamma models apply equally to a wide range of potential initial feedpoint impedance values? The initial results suggest that we need a broader study of modeled gamma dimensions. We may set aside questions of gamma rod diameters and spacing and perhaps usefully focus on gamma assembly dimensions as we systematically vary the feedpoint impedance.

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Basic Parameters of a Second Gamma Modeling Study

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The added investigations into gamma-match behavior as modeled in Antenna Model's version of MININEC began with a different premise than the one used for the initial studies. The fundamental model properties should be transferable to any frequency with ease. Indeed, it might be possible to codify the results via regression analysis into design equations. Although this potential did not materialize, it did establish the parameters of the models.

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The design frequency selected was at the middle of the span of frequencies in which we typically find gamma matches. For precision, I selected 29.97925 MHz, which we may round to 30 MHz. At the design frequency, every meter is 0.1 wavelength. Hence, all dimensions are metric. For the initial models in this group, we shall use a constant spacing: 0.1 m (3.937"), again, close to the 4" spacing used as a base line in the first series. The gamma rod will have the same diameter as the main element.

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One important reason for freezing some of the model dimensions is to permit a survey of others. The initial models in this new study used a range of element and gamma-rod diameters ranging from 1 mm to 31.623 mm. Although the range may seem strange at first sight, the steps (1, 3.1623, 10, and 31.623) are equivalent to base-10 logarithms of -4 through -2.5 as a function of wavelength. The range of the coverage is from close to 0.04" (AWG #18 wire) up to nearly 1.25". Hence, the range of element diameters does not extend on either end very far beyond the range of materials from which we find gamma-match applications in the test frequency region (10 meters). The second axis of the survey involved a span of initial resonant element impedances. Although gamma matches may cover a wider range, 15 through 60 Ohms seemed to be a good range for conversion to a target feedline impedance of 50 Ohms. Indeed, it was possible to create initial 2-element Yagis with the desired feedpoint impedances, as shown in Table 1. As in previous models, the initial beams, when gamma-matched, produced a 50-Ohm driver impedance +/- 0.1 Ohms for both resistance and reactance.

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In all cases, I held the reflector at a length of exactly 0.5 wavelength. The spacing varied as needed to yield a resonant driver. Fig. 10 shows the driver half-lengths required for each impedance level as the element diameter increased. Note that there is virtually no difference between the 45-Ohm and the 60-Ohm driver lengths for any given element diameter; the spacing alone is sufficient to create the impedance difference. In the development of these models, the actual performance of the resulting beam is not in question and was not recorded. For gamma-match considerations, only the feedpoint impedance is significant.

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Fig. 11 examines the required gamma rod lengths for each impedance level as we increase the element diameter. The curves show two results. First, the use of logarithmic increments results in relatively tame curves without requiring an unnecessarily large number of steps (and models). Second, the curves, while appearing to be congruent, do not achieve sufficient coincidence to allow effective regression analysis into a single set of design equations.

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Table 2 shows the data set behind the curves in Fig. 11 and following graphs. The table includes a column listing the AGT score of each model. The AGT score improves toward an ideal value of 1.0000 as the number of segments is set to yield equal segment lengths along the driver. However, unlike the similar test in NEC, we cannot use the AGT value to correct the impedance value. Changing the proportions of segments in the gamma section and the remainder of that element half might not change the AGT at all or only by 0.0001. However, the gamma feedpoint impedance might change by as much as 2 Ohms. AGT values of 1.0000 are rare, since the gamma segment count can only increase by an integer. In many cases, the truly ideal number of segment would be a decimal value, resulting in a small but definite departure from equal-length segments along the driver as I put in place the closest integer value. In all cases, the gamma side of the driver used 50 segments.

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As the table shows, each gamma length and accompanying series capacitor produced a feedpoint impedance of 50-Ohms resistive +/-0.1 Ohm of resistance or reactance. It is useful to examine the data by re-grouping it according to element diameters so that each curve represents the progression of resonant initial driver impedance values. Fig. 12 provides a graphic perspective of the gamma length when viewed from the altered perspective.

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As we increase the element diameter, the curve of gamma lengths becomes steeper, increasing with the initial feedpoint impedance. For each curve, the slope decreases as the initial feedpoint impedance comes closer to the target impedance, although the required length continues to increase. Table 3 provides a reference table of the data in the graph, re-grouped for easy correlation.

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Fig. 13 graphs the series capacitance data with separate curves for each initial impedance level. All curves show a rising series capacitance as we increase the element diameter. The lowest initial feedpoint impedance requires the highest series capacitance values. Once more, the curves are nearly but not quite congruent.

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If we re-group the data by element diameters, we can see the degree of required capacitance decrease as we increase the initial feedpoint impedance for all wire diameters. The graph in Fig. 14 has a quite different appearance than the one in Fig. 13, although both graphs cover the same overall data set. Looking at only one of the two graphs might well leave a misimpression of the changes that occur from one step to the next.

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The data that we have surveyed expands previous examinations of gamma assembly models by expanding the range of resonant initial feedpoint impedance values. The cost of expanding the impedance range was a restriction to a single gamma-rod spacing: 0.1 m. As well, the entire survey uses a uniform target impedance of 50 Ohms resistive. Nonetheless, the tabulated and graphed data provide insights into what MININEC models report about the required gamma rod length and the required series capacitance value across the range of resonant initial feedpoint resistance level that one is most likely to encounter in beam construction. By using graphs with alternating orientations, one might easily infer values for other initial resonant feedpoint impedance between 15 and 60 Ohms. As well, one might then scale the models to other frequencies, although the gamma spacing might become too large or too small at very wide excursions from the test frequency.

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Varying the Initial Feedpoint Reactance

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One important reason for expanding the range of initial feedpoint impedance values was to gain a better understanding of the consequences of varying the initial feedpoint reactance. To perform this further study, it was necessary to restrict at least one of the variables in the examination of basic parameters. I chose to freeze the element and gamma rod diameter at 0.01 m (0.3937"). In addition, the models in this collection use the 0.1-m spacing of the previous set at the same test frequency.

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For each impedance level, I reset only the driver length to achieve the desired reactance values. In order to include more increments within the set, I used an increment of j8 Ohms of reactance for the models. The resulting set of models for each target impedance level includes 7 models with limiting reactance values of -j24 and +j24 Ohms. Because the driver length changes, the resistance value of the initial feedpoint impedance will change slightly from one end of the model span to the other for each target value. However, for simplicity, we may still find the tilted graphs both usable and perhaps instructive. Table 4 tabulates the models in this set prior to the addition of gamma assemblies.

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As the table shows, I used the same +/-j0.1-Ohm limit in setting the driver length (the table shows half-lengths) for each model in each target impedance group. Interestingly, the span of resistance values from -j24 Ohms to +j24 Ohms does not increase in proportion to the target impedance. The maximum target impedance is 4 times the minimum value. However, the 15-Ohm span is 1.26 Ohms, while the 60-Ohm span is 8.73 Ohms, a ratio of nearly 7:1. For reference, Fig. 15 shows the driver lengths that accompany the changes in reactance for each target impedance group.

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As we saw for the case of resonant initial impedances, there is virtually no difference between the driver lengths for 45 and for 60 Ohms, regardless of the reactance. Indeed, were it not for the slight changes in the resistive component of the initial impedance, the graphed lines might be arithmetically linear.

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For each of the 28 initial models, there is an accompanying gamma-match model. Each of these models uses a gamma rod length and series capacitance that brings the gamma feedpoint impedance to 50 Ohms resistive within the usual limits imposed on the exercise. Table 5 provides a record of the data in progressive form. The gamma rod length was varied until the resistive component was 50 Ohms and the reactance was recorded. Although one might simply use this information to calculate the required series capacitance, I modeled it in place and recorded both the capacitance value and the remnant reactance. The AGT scores are also part of the tabular record.

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Graphs for the required gamma lengths are perhaps more vivid in showing the changes as we move from one initial impedance level to the next. Fig. 16 provides the required information.

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The graph uses enough increments and enough initial impedance levels to be instructive, at least so far as we may interpret the MININEC models. First, the higher the initial impedance level, the shallower will be the curve of required gamma-rod lengths from -j24 to +j24 Ohms reactance. The ratio of maximum gamma length to minimum gamma length is about 4 times greater for the 15-Ohm curve than for the 60-Ohm curve. It is likely no accident that the ratio of initial impedance levels is also 4:1. It is probable that the curves would better approach congruence had we set up the exercise by reference to the impedance phase angle rather than using definite values of reactance.

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Second, the curves strongly indicate that the shortest gamma rod length does not occur precisely at a resonant initial feedpoint impedance. As we increase the initial target impedance toward 60 Ohms, we find that the lowest recorded gamma lengths occur with an initial feedpoint reactance of -j8 Ohms. It is very likely that the lower two impedance levels would show the shortest gamma-rod lengths with reactances somewhere between j0 and -j4 Ohms.

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Fig. 17 shows what happens to the required series capacitance values as we move from one target impedance group to the next and as we change the initial feedpoint reactance in j8-Ohm increments. In all cases, we find a rising curve. However, by including the curve for the 15-Ohm target impedance level, we clearly see the S-shape of the curve, a detail that might elude us had we used only values closer to the feedline impedance. The curves meet and cross in the region of reasonably high capacitive reactance.

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In general, the models suggest that the closer the initial impedance is to the feedline impedance, the less critical will be the dimensions of the gamma assembly. Small changes in gamma length and small changes in the series capacitance will alter the gamma feedpoint performance less and less as the initial impedance is at or above about 30 Ohms. As well, the initial feedpoint reactance will have a smaller impact upon the required rod and capacitor values if the initial resistive component is greater. In this region of initial feedpoint impedance values, construction variables will very quickly outweigh differences among modeled variations. However, as we encounter initial impedances below 30 Ohms, small variations in reactance, gamma length, and series capacitance can very significantly affect the gamma feedpoint impedance and its match to the feedline.

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Tentative Conclusions

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These notes only tell us what carefully constructed MININEC models report. In each case, I have had to restrict the number of operative variables in order to arrive at doable modeling tasks. Even so, the model collection passed 150 files long ago.

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The data does reveal useful trends within the modeled assemblies. Nevertheless, the models have two shortcomings of which we must be constantly aware. First, the models presume an idealized gamma structure that may differ from actual gamma assemblies. Fig. 18 indicates some of the points of difference.

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It is possible to model some of the physical variations between the ideal configurations that we have used for systematic data and actual gamma assemblies. Preliminary models suggest that the rod extension is not a major difficulty if the models are reasonable approximations of the actual gamma assembly. I added rod extensions beyond the far end of the gamma assembly in 50-mm increments. At an extension length of 150 mm (about 6"), selected models showed only about 1.5 Ohms difference between the feedpoint impedances of the ideal assembly and of the extended assembly. The series capacitance required no change.

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We may also change the modeled diameter of the near- and far-end connector wires or bars with fair ease. Using models with a 0.01-m element and gamma-rod diameter, I varied the end wire diameters between about 3 mm (about 1/8") and 50 mm (about 1"). The required change in the gamma-rod length was only about 1%. The required capacitance change also fell into the 1% range.

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Much more striking is the amount of change in both gamma-rod length and in the series capacitance value as we change the series capacitor position from its ideal location at the feedpoint. Antenna Model allows only limited locations for load positions, so I checked the ideal position, a capacitor location at the beginning of the gamma rod, and a position at the center of the rod. The last position coincides approximately with capacitors made from concentric tubes and hence distributed along the gamma-rod length. I used both a resonant and a non-resonant initial impedance for the sample checks. The models involve beams using 0.01-m diameter elements with a spacing of 0.12 wavelength. Table 6 shows the results of these first samplings.

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The samples suggest that the degree to which a non-ideal capacitor position changes the gamma dimensions may vary with the amount of reactance in the initial beam impedance. However, in both sets, the trend is the same: the farther away from the feedpoint that we place the gamma capacitor, the greater will be the variation from the ideal configuration values for both the gamma rod length and the series capacitor. Most series capacitor designs can handle the variation within standard field adjustments. However, if we do not account for the capacitor position, we might discover that we need to re-construct the gamma rod to arrive at the desired target feedpoint impedance.

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The second shortcoming of the ideal models continues the theme of construction discoveries. The models have not been subjected to careful comparisons with physical models that replicate the gamma features. Indeed, this difficulty is endemic to all gamma-match design systems. At best, they have been subjected only to spot checks. Hence, we cannot tell the difference between systematic and accidental coincidence of results.

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Nevertheless, patient modeling has strongly suggested the presence of some trends in gamma behavior that we might easily have overlooked had we only used one of the calculation methods of obtaining gamma design values. As well, the modeling data is now available for comparison with the results of those methods. Hence, the modeling task has made at least a small contribution to the study of gamma matches.

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Nevertheless, there remain many questions, even within the realm of gamma-match models. Does the model's insensitivity to changes in the ratio of the gamma rod diameter to the main element diameter hold up across the same span of target initial driver impedance values--and across the same span of reactance values? Does the seeming regularity of gamma rod changes also hold up across the range of target impedances and reactance variations?

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What modeling may have to say to these questions--and others left in silence--will have to await one of two events. One possibility is the absorption of the task by another modeler. The other possibility is my own recovery from the fatigue that accompanies all extended adventures into systematic modeling.

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Updated 11-01-2006. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Oct., 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching


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A GAP in Our Understanding of Feedpoints

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L. B. Cebik, W4RNL

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One enduring cluster of questions often raised by newer antenna builders involves the gap at the center of an element at the feedpoint connection. Apparently a number of misconceptions have arisen to create concerns, especially if a person who writes an article about an antenna does not specify how wide the gap should be for that antenna. These notes hope to at least partially dispel some of the misconceptions.

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You may note that I am placing this set of notes in the section of the index concerned with transmission lines. There are 2 reasons for this placement, one a matter of convenience, the other a matter of fundamentals. Because the subject does not strictly belong in any of the other sections--which I have divided according to antenna types and frequency ranges, it is convenient to place it here. The general principles apply to any antenna for any frequency whatsoever. More important, newer antenna builders tend to think of the feedpoint gap as a function of the antenna element. As we shall see, the feedpoint gap is a function of the transmission line. More specifically, it is a function of the feedpoint-antenna connection point as a remote source for the antenna.

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Let's begin by clearing the air in terms of the two most common questions that newer antenna builders pose about the feedpoint gap.

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Considering the Gap, How Long Is an Antenna Element?

Let's consider 2 antenna elements, each one composed of wires, rods, or tubes on each side of the feedpoint gap. Lengths L1 and L2, as shown in Fig. 1 can be equal, but need not be. The considerations that apply to center-fed elements also apply to off-center-fed elements. +
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The only difference between the 2 elements in the figure is the size of the feedpoint gap. So the question transforms it self into this one: Is the element length L1 + L2 or is it L1 + L2 + Gap?

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The general answer that applies in almost all cases appears in Fig. 2. The element length is the total tip-to-tip length of the element, regardless of the size of the gap. There are some practical building constraints that we should observe, but for almost all cases where the gap represents an opening for connecting the feedline, the answer in Fig. 2 applies.

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What Really is the Feedpoint Gap?

Since feedpoint gaps may vary in size, even for antennas of similar design for the same frequency, the general answer we have just given sometimes causes confusion. Individuals sometimes have a difficult time trying to formulate what the confusion is, but it usually boils into this question: what precisely is a feedpoint gap. The answer to this question involves an understanding of what goes into building an antenna element with a feedpoint. +

Ordinarily, we have 2 element halves or sections plus a center insulator or cable connector. This description omits one set of critical elements--the wires that connect the element sections to the feedline or connector. In many amplifier and similar circuits, we tend to think of connecting wires as conveniences to ensure that all of the components meet all other relevant components. Most of our concerns are focused on eliminating stray effects by keeping the leads or connecting wires as short as possible or routed where they can neither emit nor receive anything harmful to the circuit's operation.

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Antenna-to-feedline connecting wires, however, have a very different place in life. Most often, they are part of the antenna. Sometimes--by accident or by intention--they may be part of the feedline as well. But let's start by looking at them as part of the antenna element. Fig. 3 illustrates the basic case.

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The "real" or "actual" gap is simply the distance between the wires of the feedline. (Now we know why I have placed this note among the transmission line notes.) The connecting wires are parts of the antenna elements. For a parallel transmission line, the gap is simple to see and appreciate. When using coaxial cables, the use of a connector at the feedpoint can obscure the fact that the real gap is the distance between the center conductor and the braid that make up the feedline. Note that in both cases, I have created an ideal situation in which the connecting wires are in the same plane as the antenna element. I even created a small gap in the braid oval so that you can see that the center conductor connecting wire does not touch the braid.

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Ideally, then, the connecting wires are a part of the antenna element. So we may think of those wires as an extension inward of the antenna element section until it reaches the proper side of the feedline. Since the feedline transfers energy from the source or transmitter to the antenna (and conversely from the antenna to a receiver), we may think of the gap as the energy source. Fig. 4 provides this picture for the transmitting situation. We may replace the source symbol with a load symbol to capture the receiving condition.

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Let's look at Fig. 4 from 2 perspectives. First, from the point of view of the antenna builder, the gap disappears electrically, even if it is required physically for the feedline connection. The source is in series with the element regardless of whether we make a direct connection to the antenna or use a transmission line. Since a source has no dimension of its own, outside of the physical requirements for connection, the antenna element is continuous from tip-to-tip.

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Second, let's take another look at the source point of the antenna element. Making connections of any sort requires that we interrupt the continuity of the element to insert the source. Hence, we necessarily have a gap. There will be element material ends that face each other across the gap, and these ends will exhibit a capacitance relative to each other. For HF antennas using normal materials, we tend--as practical builders--to ignore the very small gap effects. However, those who design antennas for UHF frequencies and those who experiment withh very fat elements become very much aware of the capacitance. In fact, antenna modeling software calculates gap properties using the source segment as the gap. The software then factors these calculations into the overall model of the antenna, just as it does the special calculations for effects that occur at the outer ends of the element.

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Does the Second Look at the Gap Have Any Effect on How We Treat the Feedpoint Connection?

If you are copying a design from an article in a journal or a handbook, then following the construction instructions ensures that you will take any gap effects into account, since the prototype antenna did so. However, let's look at construction practices a little more closely to see what these notes imply for a practical antenna. We may begin with a coaxial cable as our feedpoint connector. Fig. 5 shows the outlines of a UHF connector, but the same general rules of thumb apply to BNCs, SMAs, Ns, and any other coaxial-cable connector. +
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We can divide the connecting wires into 2 segments for each one. Segments A and A' are the ones that are inward extensions of the antenna element. Ideally, they should be the same length. This requirement is not critical if both sections are very short and we are using an HF frequency. In addition, the current of a half wavelength element does not change rapidly at the element center. Hence, a very small amount of off-center placement makes no difference to antenna performance. However, ideally, we should keep the amount as low as permitted by the connector type that we are using.

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Practical building constraints often dicate that we must use the connecting-wire sections labeled B and B'. Keeping these segments as short as possible is the ideal. Also ideal is making them the same length. However, connectors tend not to cooperate fully, since most coax connectors have a projecting center pin and a shell below it. As well, the only convenient place to make a connection between the shell and the element section is at a point lower than the upper lip of the shell. Once more, at HF, these slight differences between B and B' make little difference.

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In fact, we often have occasion to stretch the ideal situation. We can do so with no harm at HF, since a wavelength is so long and the actual leads are only a tiny fraction of a wavelength. Fig. 6 illustrates a few variations on the ideal theme.

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On the left is a simplified representation of a feedpoint with a beta match hairpin at the feedpoint. The hairpin or shorted transmission-line stub has a width and length calculated to provide a certain inductive reactance across the feedpoint. For very practical reasons we may wish to use a common connection point on each element half for both the hairpin and the feedline connector. The fewer connections we create, the fewer connections we have to worry about in terms of degradation by weathering.

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Some builders use a plastic housing to provide some weatherproofing for the pin-side of the connector. This treatment lets us avoid slathering waterproofing goop over this vulnerable side of the connector. (The cable side also needs waterproofing, but allows us to install it in a more orderly fashion with an eye toward periodic removal and renewing.) Adding a waterproof housing to the connection may require us to use longer than normal leads for our connections, even if they are inside a plastic or RF-transparent box.

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From an idealistic perspective, the relatively thin leads do not distribute current in the same pattern as the fatter main element halves. However, at HF, these leads are only a very tiny fraction of a wavelength. Hence, they do not disturb the current distribution on the element in any measurable way.

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At UHF, we may become concerned with the cumulative effects of the leads. In such cases, we have an alternative shown on the right in Fig. 6. We may directly connect the coax to the element using as close to zero-length leads as feasible. As well, we may take great care in dressing and soldering the connections so that we do not have solder lumps and other construction anomalies.

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Let's pause here to reconsider the effects of the connecting wires labeled B and B' in Fig. 5. We have noted that the length of B and B' were not critical in the HF range, but might be so in the UHF range. Consider the fact the B and B' form a parallel transmission line section that runs from the coax connector to the antenna element. Now let's specify that we have so arranged the antenna element that it has a feedpoint impedance of 50 +/- j0 Ohms at the gap point where the horizontal wires (A and A') turn downward into the parallel transmission line formed by B and B'. We may ask what the impedance is at the other end of the line B-B' where the actual 50-Ohm coax line begins.

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The answer to that question depends on 4 factors: 1) the diameter of the connecting wires; 2) the spacing between the wires; 3) the length of the wires B and B'; and 4) the frequency of operation. The characteristic impedance of the transmission line B-B' is a function of the first 2 factors. Let's use #12 wire (0.0808" diameter) and set the wires 0.111" apart center-to-center. These specifications set the characteristic impedance at 100 Ohms. The actual spacing is likely to be wider, with a resulting higher characteristic impedance, but these values will do for a simple example.

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Next, let's choose 14 MHz as a mid-range HF frequency and 432 MHz as a UHF frequency. Finally, we shall evaluate the transformation of our 50-Ohm antenna feedpoint impedance with the length of B-B' set at 1", 2", and 3". The following small table gives us the results.

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+Sample Impedance Transformation for Parallel Leads at 2 Frequencies
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+     Lead Length       14 MHz                 432 MHz
+     (Inches)          (R +/- jX Ohms)        (R +/- jX Ohms)
+       0               50.0 +/- j0            50.0 +/- j0
+       1               50.0 + j0.6            52.0 + j17.3
+       2               50.0 + j1.1            58.7 + j35.0
+       3               50.0 + j1.7            71.8 + j52.9
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Clearly, lead length in the form taken by B-B' as a short section of parallel transmission line makes virtually no difference in the HF region. However, even 1" leads at the improbably close spacing of the leads in the example produces a significant impedance transformation, especially in terms of the inductive reactance, at the beginning of the true coaxial cable run. As a result, the higher the operating frequency, the more important it becomes the keep the leads designated as B and B' as short as possible. The scheme on the right in Fig. 6 represents one way to approach the desired UHF goal of zero-length leads.

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What About Wire Element Connections?

Fig. 7 shows a typical wire-antenna center set-up. The sketch omits refinements that will add mechanical strength to the feed-line-antenna junction. The actual connection fixture can be as simple as an insulator with end loops for connecting the wires. Alternatively, it may be a fancy fixture with the feedline compressed inside to relieve the wire connections of bending stresses that eventually result in a broken connection. For open construction, we often solder the wrap region to preserve and protect the electrical continuity between the 3 pieces of wire that we have wrapped into a single line. +
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Essentially, we have a nearly ideal situation where there are no leads to be labeled B-B'. The only discontinuities along the antenna element are the slight changes in diameters at the soldered section, the loop through the insulator, and the short wire lengths from the end of the transmission line to the insulator loop openings. At HF, these small variations make no practical differences in the operation of the antenna element.

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There is a variation of the system that deserves a quick look. It is possible to have an antenna element at some higher impedance (let's say 800 Ohms) and to effect a match to a lower-impedance transmission line (perhaps 600 Ohms) by a simple technique. We simply spread the 600-Ohm line gradually as we approach the antenna feedpoint. The left side of Fig. 8 shows the general scheme.

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The system works best under 2 conditions. First, the impedance change is not too great. Second, the length B is considerably longer than the ultimate gap length A. The right side of Fig. 8 gives us an equivalent circuit in arbitrary step sizes. The actual analysis would use step sizes that are each infinitesimal. However, a useful sketch would not then be possible. Along the spreading line length designated as B, each change of spacing between the line introduces a new line segment with a slightly higher characteristic impedance. Hence, the spreading line has the form of a large cluster of transmission line segments, each with a slightly different characteristic impedance.

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However, each step introduces a small but definite length of wire that is parallel to the antenna wire itself. Therefore, each step yields some radiation. I have not given any particular dimensions for the lines, and certainly not the dimensions that we might physically calculate as yielding an 800-Ohm parallel transmission line. The mixed function of the spreading line will change the required dimensions with respect to the overall A length necessary for an 800-Ohm impedance at that end of the line. Experiment and experience are generally the best guides to setting the dimensions for a spreading line.

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We should not confuse the type of impedance conversion in Fig. 8 with some others. In the case that we have been examining, the antenna impedance is higher than the characteristic impedance of the line before spreading, and the element has the normal source gap at its center. There are some other related schemes that work in the other direction, matching a lower antenna impedance to a higher feedline impedance. Fig. 9 provides some samples that rarely appear in the same drawing. However, the Delta, Tee, and Gamma match systems are members of the same family.

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The oldest of the sibling matching systems is the Delta, although we do not find many practical uses for it today. In earlier radio days, home-made parallel transmission lines ruled most amateur antenna installations. Suppose that we have a 70-Ohm resonant 1/2 wavelength dipole, but a 600-Ohm transmission line. How do we effect a match?

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Let's start by not opening the antenna element center. Instead, let's attach a spreading transmission line to points on the antenna so that we achieve a matched condition. The length of the spreading line (that forms an inverted Greek Delta) and the spread interact so that experimentation becomes the most reliable guide to finding the right attachment points. As well, just like the earlier case, the angled wires have vectors that are parallel to and at right angles to the transmission line. The right-angle vector, of course, is parallel to the antenna wire and represents a source of radiation in addition to the antenna wire. Since we use coaxial cable for virtually all monoband resonant dipoles these days, the Delta match has mostly historical interest.

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However, if we bring the transmission line close to the antenna wire and run a wire on each side and parallel to the antenna, we transform the Delta match into a Tee match. The wires or tubes of the Tee section are parallel to and radiate just like the main radiating element. Note that just like the Delta match situation, the main element has no gap because we are not inserting the source (transmission line) at that point.

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The Tee match system has many practical complexities outside the scope of this particular set of notes. The parallel Tee rods or tubes are normally thinner than the antenna element itself. In fact, the Tee match finds its most general use with Yagi antennas where the feedpoint impedance (if we opened the element at the center) would be considerably lower than 50 Ohms, the standard value for the most used coaxial cables. We find a number of commercially made UHF Yagis still using the Tee-match system. In the HF range, some builders use a Tee match to elevate low element impedances up to 200 Ohms. At that point, they insert a 4:1 balun at the element, thus bringing the impedance down to 50 Ohms and effecting a change from a balanced feed system to a single-ended coaxial cable feed system.

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For many choices of length and diameter for the Tee-bars/tubes, the impedance at the feedline terminals will show some inductive reactance. So a number of installations will use series capacitors so that the terminals shows a purely resistive impedance. However, with judicious calculation, planning, and experimentation, we can usually find Tee-bar length and spacing values that will allow capacitor-less connections.

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An added advantage of the Tee match system is that it allows the Yagi element to be continuous. In that condition, we may pass it through the boom in the same way that we pass the parasitic elements. In most cases today, only HF antennas make direct connections between the boom and the element. VHF and UHF Yagis tend to use insulated bushings at the boom pass-through points. Direct element connections with the boom have ways of weathering and aging, with a resultant increase in self-generated noise. However, even with an insulating plate to separate the element from the boom, a Tee-match system is still serviceable.

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A variant of the Tee is the Gamma match, shown on the right in Fig. 9. It also functions to match a low element impedance to a higher feedline impedance, and the most common use is with low-impedance Yagi drivers and coaxial cable feedlines. The Gamma match is designed for driven elements that directly connect to the boom. However, the Gamma match is inherently single-ended, with the coax braid connected directly to the element center, which is also the boom. For the range of materials used to make a Gamma match, a series capacitor is a normal part of the system at the junction of the feedline center conductor and the Gamma rod.

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In the present context, the only reason for looking briefly at the Tee and Gamma matches is to note their kinship to the older Delta match. All three use a continuous, that is, no-gap element and find connections that will raise a lower impedance antenna center to a higher value at the feedline junction.

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When we began these few notes on the gap at the center of driven antenna elements, we thought of the gap as simply a break of the antenna element. In the end, the gap is a function of the feedline, which supplies energy to the antenna. Any gap in the element itself has some effect on the feedpoint impedance, but with normal materials at HF, these effect is negligible for practical installations. Gap effects become noticeable with outsized materials or very high frequencies. The actual gap is the distance between the conductors of a feedline, viewed as the energy source for the antenna element. We examined a few of the complexities that typical installations encounter, some of which are unintentional and others of which are intentional.

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For most cases, changing the way we look at the feedpoint gap in an antenna element removes most of the questions about standard installations. As well, understanding the role of the connecting wires may allow us to construct antennas that present fewer problems during the field tune-up phase. We can then place our questions and concerns at the point where they will do the most good for the final product.

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Updated 01-16-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Modeling


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Notes on Home-Built Antenna Hardware

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L. B. Cebik, W4RNL

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In the course of writing the many items at this site, I have scattered a number of notes on antenna materials or hardware. As the site has grown, the odds of a reader encountering a relevant note have decreased accordingly. Therefore, this note attempts to coalesce a number of thoughts on antenna hardware in one place.

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The notes represent a set of practices that I prefer. The collection is not the only way to do things, but it is one fairly good way among the many acceptable practices. Nevertheless, I recommend that you examine various antenna handbooks for alternatives. We all have different skills and our access to materials may vary. The more techniques that you have at your disposal, the easier it will become to find the ones that fit your circumstances.

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I have divided the material into two major divisions that cover hardware and techniques: beam antennas and wire antennas. The notes focus on HF antennas in the main.

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Beam Antenna Hardware

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My preferences for beam construction all focus upon one word: quality. Quality construction is a synonym for durability, that is, the ability of the beam antenna to perform for a long period with all of the capabilities it had when you first put it in place. Quality beam construction breaks down into three main materials: stainless steel, aluminum, and polycarbonate.

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Stainless Steel

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I prefer to use only one material for all antenna hardware: stainless steel. Not many years ago, we had to use mail order or on-line sources for stainless steel nuts, bolts, and washers. However, these items are now regular stock in many home centers. The reason why I prefer stainless steel is simple. Virtually all beam antennas bring together at least two materials: aluminum and copper. Dissimilar materials are subject to electrolysis, the corrosion of materials due to a difference in the atomic electrical potential of each material. Copper and aluminum are both conductors, but we cannot durably join the two at a connection point. When some home builders resorted to cheaper aluminum AC wire, they had to find connectors that would prevent electrolysis between the aluminum wire and the brass (mostly copper) screws at the terminals. Only power companies use aluminum wire these days and homes have returned to an all-copper status.

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The rate of corrosive effects between dissimilar metals depends on their "nobility." The more distant the metals on the chart (see Table 1), the greater the potential between them, even in the most weather-protected conditions. As the table notes, a difference of only +/-0.3 volts between the atomic potential of two metals at a junction indicates the strong possibility of significant corrosion at the junction. Note how far apart that aluminum and copper fall on the table.

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Stainless steel is generally inert to electrolysis. Hence, it makes the best simple buffer between different metals that might show significant corrosive effects. Fig. 1 shows a sample connection at possibly the feedpoint of a beam's driven element. Note that the system uses not only a stainless nut and bolt, but also stainless washers. Hence, the copper wire is isolated physically but not electrically from the aluminum tube.

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Two washers deserve special mention. I place a washer under the bolt head to spread the force that the head exerts on the softer aluminum tube. Excess tightening will not result in the bolt head widening the hole in the tubing. In most cases, I add a fiberglass rod within the rube to strengthen the assembly. If I butt-join tubes, I add an inner tube for the same reason. The other notable washer occurs next to the nut. I use a stainless lock washer to ensure that the assembly does not come apart after a season of flexing in the weather.

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Aluminum

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The subject of aluminum bothers many a newer antenna builder because of its cost if we buy it new from reputable sources. Due to cost, many builders resort to wire beams, while others build only antennas for which they can find used TV antenna elements. At one time, home centers carried a large and varied stock of aluminum tubing, but in recent years, the centers have shifted their stocking philosophies from "do-it-yourself-in-your-own way" to "do-it-as-pre-packaged." Some antenna builders have shifted to the use of L-stock and square stock.

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First, round tubing is the best material available for HF antenna elements, since it tends to slip the wind best. Flat surfaces tend to increase wind resistance. Second, I do not recommend even home-center tubing for antennas designed to withstand many seasons of rough weather. The tubing available in home centers is of dubious lineage, and its strength data is often wholly unavailable. Most of all, I do NOT recommend the use of aluminum conduit for antenna elements. Conduit is a form of softer pipe. It not only weighs more than tubing, it also bends permanently under loads.

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The best material for U.S. antenna builders is 6063-T832 aluminum tubing, available from various outlets. The tubing is strong, and the most common wall thickness for the home antenna builder is 0.058". It is also available in outer diameter increments of 1/8" (0.125"). If we used a wall thickness of 0.0625"--that is, 1/2 the increment between tubing sizes--we would ideally have a perfect fit from one size to the next. However, this approach fails to recognize that even computer-controlled industrial processes have allowances. Hence, the 0.058" wall thickness allows the closest practical size for nesting one tube inside the next larger size, as suggested in Fig. 2.

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The lower portion of the figure suggests the use of home-center tubing, which usually has a wall thickness of 0.050" or less. Note the larger spacing between the nested segments. The larger spacing yields more wiggle room, which calls for special measures to ensure a tight mechanical bond between element sections. The upper portion of the sketch with the standard 6063-T832 tubing would allow the use of a simple pair of sheet metal screws to bond the sections--stainless steel sheet metal screws, of course.

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The sketch also specifies an overlap of 2" to 3" at the junction. There are special cases in which it is wise to double tubing. For example, the centermost part of a 20-meter beam element might use about 3' of 1.25" stock. The next exposed length might be only 24" or so, but the 1.125" tubing would go all the way to the element center, giving the middle of the element extra strength to bear higher wind loads. Where we do not need doubling strength, 2" to 3" of overlap is sufficient to provide a strong connection without adding unnecessary weight to the element.

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Some antenna makers prefer to use thinner-wall tubing to create equally strong but lighter and more flexible element assemblies. Other makers use swaging techniques to decrease the element diameter by either 1.5 or 2 steps, relative to our standard 1/8" increments. In most cases, the home builder does not have access to the necessary equipment to handle such techniques, and the lighter tubing in the requisite aluminum type may not be readily accessible. Hence, the use of the tubing that we have noted is almost the de facto American standard. In contrast, European antenna makers tend to prefer heavier tubing (in metric increments, of course). Their antennas tend to bear larger ice and snow loads, but may require a larger rotator to turn effectively.

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Polycarbonate

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Since I use antenna modeling software to design antennas that I build, I always plan on insulating and isolating the elements from the supporting boom. NEC and MININEC calculate only axial currents along an element and hence cannot show the effects of the boom, were we to make a direct connection. All beam designs that appear at this site either use non-conductive booms or use plates to insulate and isolate the elements from the boom.

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At HF, the best plate material in my experience is polycarbonate. Lexan is a GE trademark and trade name for the material. Do not confuse the material with acrylic materials that ball up under a saw blade. As well, polycarbonate differs from Plexiglas, another trademarked material. All of these materials are related chemically, but we can obtain "true" polycarbonate from on-line sources in convenient size sheets that we can then saw and drill with woodworking tools. Simply be certain that the polycarbonate is UV protected. The plate size will vary with the amateur band, which generally determines element size and weight. ¼" thick material generally satisfies most upper HF requirements. Although polycarbonate is satisfactory well into the lower UHF range, many VHF and UHF beam builders prefer Delrin and other later materials for insulating plates and shapes.

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To use polycarbonate plates effectively requires that we design an assembly that makes best use of their strengths. The assembly requires a variety of parts. Table 2 provides a key to the parts that appear in the sketches in Fig. 3 and Fig. 4.

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The plate itself is oblong, extending 6 to 12 inches along the element axis and perhaps 4 to 6 inches along the boom axis. The larger numbers, of course, apply to bands like 20 and 17, while the smaller dimensions are for 12 and 10 meters. As suggested by Fig. 3, the use of a longer dimension along the element axis places the element U-bolts at a larger distance to allow for assembly work at the element center.

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Stainless steel U-bolts attach the element to one side of the plate, while similar U-bolts clamp the plate to the boom on the other side. I prefer the type of U-bolt that comes with a cast saddle over other types. The absence of any saddle tends to allow element slippage over time. Muffler-clamp type saddles contact the element in two lines, which can more easily deform the element tube than the solid cast saddle. In most cases, the boom U-bolts will be larger than the element U-bolts, since booms may range from about 1.25" for lighter beams to perhaps 2" for longer ones. Boom materials can be either 6063-T832 or 6061-T6. For anything heavier than a 2-element beam, it is useful to use thicker tube walls, perhaps 0.125". For smaller beams, you can nest 1.125" tubing with 0.058" walls inside 1.25" tubing with the same wall thickness. If you need a longer boom than the stock available, you may stagger the junctions of the inner and outer tubes to achieve a stronger boom with a uniform diameter.

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For parasitic elements, you may use a single center element section or you may link two sections with an inner strengthening tube. Even where you do not need doubling, the inner tube should extend at least to the edges of the polycarbonate plate so that the U-bolts go around a double thickness of tubing to help avoid crushing. The driver element replaces the linking tube with a non-conductive rod or tube, such as fiberglass. The rod helps align the element and provides for the required driven element gap. Note that the gap in any antenna is a part of the total element length. It is NOT an an addition to the length. The gap size is not critical, since the leads from either side of the gap to the feedline connector make up any missing length. Essentially, the final gap size is the spacing between the conductors in the feedline.

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All hardware (except for U-bolt cast saddles) is stainless steel. Fig. 4 shows an exception to this rule. The support for the coax connector consists of a short length of 1" by 1" by 1/16" thick L-stock. The length is just enough to serve as a U-bolt keeper bar. At the center, a 5/8" hole allows you to mount a through-chassis coax UHF connector. Leads to the element are short and direct. Use a "liquid" (plastic) electrical tape product to seal the coax connector rear end--and the coax junction once you install the feedline.

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The general ideas in these sketches permit any number of variations. Besides studying alternative techniques that appear in articles and handbooks, you may also examine various commercially made beams that you encounter. Very often, manufacturers place their assembly manuals on line for the benefit of prospective buyers and those who obtain beams second hand. These manuals are excellent sources of ideas ready for your local adaptation.

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Whichever system of mounting that you use, be certain that the assembly has the quality necessary for durable service. Most beams operate at the tops of expensive towers with equally expensive rotators to direct them. The antenna itself should not be a weak link in this otherwise sturdy system.

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Wire Antenna Hardware

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Wire antennas deserve as much attention as beams, although the hardware may differ. Hard-drawn copper wire is generally satisfactory for most wire antennas, although copper-clad steel is perhaps the most durable material. However, it is harder to use, since it does not want to straighten out from its packaged coil shape. Beware of soft-drawn copper wire, since it will stretch and eventually break from its own weight. Although the merits of solid vs. stranded wire have sometimes led to abstract debates, I have never encountered any difference between the two for equivalent sizes. Most wire antennas may use insulated wire, although you will have to adjust the element length. Insulation adds an antenna (not a feedline) velocity factor that ranges from about 0.93 to about 0.98, depending on the insulation type and thickness. Hence, insulated elements will be physically shorter than equivalent bare wire elements. The concern for the length adjustment needed for wire insulation applies only to antennas that use precisely designed element lengths, such as wire Yagis. If you are setting up a multi-band center-fed doublet, the precise length is not critical, since you will be using parallel feedline and an antenna tuner.

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Center or Feedpoint Connections

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For simple dipoles or other antennas with low feedpoint impedances that require coax connectors. there are numerous inexpensive commercially made feedpoint connectors constructed from various plastic materials. Some units include a 1:1 balun to attenuate common-mode currents--a wise precaution for any antenna directly fed by coaxial cable. However, our selections are fewer when we use a parallel feedline. Very often, wire antenna builders use a simple insulator and just solder the feedline to the antenna wires. Unfortunately, this common practice results in feedline flexing at the junction, with a line break in almost no time. A better system is to devise a center insulator that also provides strain relief for the parallel feedline.

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The polycarbonate UV-protected plate in Fig. 5 has some critical holes that we can easily fashion at the workbench. All of the holes and slots through which we pass wires should be filed to produce smooth rounded edges. The antenna wire holes will benefit from short lengths of plastic tubing through which the antenna wire passes. The effect is similar to the use of a thimble used with rope and wire cable ends. The stress on the wire is distributed over a small length rather than being concentrated at a single point.

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The slots allow you to weave the feedline and thereby virtually eliminate the stress at the line ends. Hence, we may use simple wraps or solder lugs to terminate the line and to provide a separate lead to solder to the antenna wire. Note that the feedline connection to the antenna wire occurs at the place where we normally wrap and solder the antenna wire. This system prevents antenna wire movement from stressing the feedline. Use stainless steel nuts and bolts, of course. You may cover the junctions with products designed as "liquid" electrical tape.

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The simple plate achieves the same goal as the few commercially made assemblies for joining antenna wire to parallel transmission line. Fig. 5 shows the general principles used by such devices. Because the units can consist of two molded pieces clamped together by assembly screws, they tend to replace the slots in the homemade version with alternating bars molded into the casing. Once we close the case, the parallel feedline cannot move. The other difference from the homemade assembly is the use of eye-bolts for the antenna wire.

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The Other End(s) of the Wire

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Whether home-made or commercially made, these connectors are applicable to any wire antenna feedpoint using parallel feedline, whether we locate the feedpoint at the center, off center, or at the end of the wire antenna. However, wire antennas have either 1 or 2 loose ends that we need to join to a support rope. Fig. 7 shows one of my favorite types of insulators and strain-relief devices for wire antenna ends. The sketch portrays a cutaway view of an "egg" insulator. The antenna wire and the support rope at right angles to each other. Hence, by showing the wire, the rope disappears from view.

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We might use a common bar insulator in this application. When we used guy wire as the chief antenna end support material, we often needed bar insulators to prevent the high voltage at the antenna ends from arcing to the guy wire as the assembly gathered grunge from the atmosphere. However, since rope supports are now nearly universal, the egg insulator is both usable and beneficial. The egg insulator creates its own thimble for stress relief by the molded slots in its ceramic structure. Additionally, if the egg should crumble, the wire and rope are linked until we can replace the insulator. (However, I have never broken an egg insulator, even by dropping one in the shop.)

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I have noted the universal use of rope as a support material for wire antennas. Not all ropes are created equal. For antenna support, use one of the multi-layered UV-protected ropes designed expressly for this job. Almost anything else (except perhaps for Phillystran) will eventually break either from sun exposure or from the effects of precipitation.

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Supporting the Wire

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When we think of supporting the ends of a wire antenna, we often let haste make great waste. Never tie off the end of a wire antenna to a tree limb. The same applies to wire loop antenna for which we may use various trees and similar structures as intermediate supports. Under the continuous force of variable winds, the wire can act like a saw blade. Under certain conditions, high voltage can actually ignite wood. We think of wood as an insulator. Properly treated, it can be an effective insulator in the lower HF region. However, live trees and raw wood are more like a semiconductor, where the resistance varies with the wetness of the material, both inside and outside.

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In addition to durability and safety, we should also think of convenience when we install a wire antenna. Every antenna deserves a close inspection every 6 months. If we can easily lower the antenna, we can reduce maintenance time to under an hour, including cleaning the insulators and wire and applying a thin coat of non-conductive liquid polish to the antenna wire. Fig. 8 shows some (but not all) ways of adding convenience to our list of antenna assembly properties.

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At the upper end of the system, we have the wire termination (using a bar insulator in this case), with the support rope passing over a limb or through an eye-ring attached to a post or trunk. If you use a screw-type fixture with a tree, expect the tree to over-grow it within a few years. The rope then proceeds nearly to ground level. The sketch shows 3 different ways of handling the loose end. For short-term use, we can wrap the excess rope around the trunk or post. However, if the tree is living, then we must re-wrap the rope once a year to prevent girdling the tree. We can also install a weight that will let the rope slide as the tree sways. However, this technique requires us to create a safe system that will not let the weight harm people or pets. The third system uses a stainless steel cleat with the rope forming an effective nautical wrap. We do not have to keep all of the rope needed to lower the antenna at the termination point of the system. Rather, we keep only enough excess to create a good lock. When we need to lower the antenna for maintenance, we can add rope to the end before we lower the antenna.

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A popular and effective wire antenna is the inverted-L. The antenna structure includes both a vertical and a horizontal portion. One mistake often made by first users is to run the vertical section next to a tree trunk. The result is usually very poor antenna performance and a tree that is overstuffed with RF.

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As shown in Fig. 9, we need to devise an installation that places the vertical section of wire as far from the tree trunk as may be feasible. We can use the same general support system, but notice that the wire does not run over the tree limb. Rather, it runs through a ring supported by the rope that we attach to the tree and pass over a handy limb. If you have two trees, then suspending a rope between them and running the inverted-L wire up to a center point would further reduce losses from RF-eating trees. These same principles would apply to suspending a wire vertical monopole from a high point in the tree canopy.

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Near-Ground Concerns

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Vertical monopoles and inverted-Ls ordinarily place their feedpoints at near-ground level. Our thoughts at this junction should include mechanical and electrical soundness, as well as safety. The termination on the left in Fig. 10 shows a good use for the modern generation of waterproof remote antenna tuners. Placing the tuner at the feedpoint of the multi-band antenna allows a buried coax run to the shack. However, I very often see antenna builders connect the antenna wire directly to the tuner terminal. If certain things go wrong, the tuner might be mechanically damaged from excess strain exerted by the antenna wire. Hence, the sketch also shows a rod and non-conductive plate that serves as an intermediary. A short line goes from the tuner to the plate, which bears the stress of the antenna wire.

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In addition, the rod also serves as a focal point for grounding at the tuner-antenna junction. The tuner's ground terminal connects to the rod via the plate, while a set of radials extends from the rod outward. The radials may serve only the needs of the antenna. However, a smarter procedure would be to set up the radials in accord with standards for dissipating lightning energy as well. The terminals on the plate should have a means of shorting the antenna to ground and disconnecting the tuner when an electrical storm is in the area (or, better, whenever the antenna is not in use).

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The right side of the sketch shows the far end of an wire antenna, which might be any wire antenna that needs to bring that end toward the ground. For safety, the end is at least 8' to 10' above ground, that is, above the highest point that a person or pet might jump. A rope keeps the wire end taut by virtue of being anchored to the ground.

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The picture is not yet complete. The anchor has a portion above ground that might prove physically hazardous. The antenna tuner terminals and the plate terminals are both exposed to touching, either intentionally or accidentally. Fig. 11 shows one type of remedy for these conditions. The tall non-conductive conduit protects an individual from making physical contact with the antenna. At the other end of the wire, it would prevent an individual from tripping over the anchor. As a second line of defense, one might also plant a small circular flowerbed around the conduit, complete with a small (6"-8") picket fence or other border.

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At the feedpoint end of the system, the tuner has an additional protective housing connected to the conduit. The housing serves several purposes. First, it prevents contact with the antenna terminals. Second, it allows us to elevate the tuner above ground to prevent the unit from lying in water. Third, it keeps rain and snow from falling directly on the unit, reducing the test load that we place on its waterproof claims.

+

Implementing all of these wire-antenna techniques--or any reasonable variations upon them--is not very expensive. However, they can together keep our antennas working longer with less potential for harm to people, pets, or property.

+

Conclusion

+

This collection of notes represents some of the HF practices that seem to have serve me well over a large number of years. They do not show the only way to achieve our goals when building beams and wire antennas. Instead, they show only one set of ways. However, with the explanations of why I do what I do in the way that I do it, you should be able to develop methods for arriving at the same goals with different and even better methods.

+
+ +
+

Updated 06-14-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Hardware


+ + diff --git a/content/trans/lclatu.html b/content/trans/lclatu.html new file mode 100644 index 0000000..9e921d1 --- /dev/null +++ b/content/trans/lclatu.html @@ -0,0 +1,77 @@ + + + + + + A Junkbox L-C-L/L-C ATU + + + +
+

A Junkbox L-C-L/L-C ATU for $3.00

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Having built C-L-C Tees, inductively coupled balanced ATUs, SPCs, and a couple of 10-meter L-C-L Tees, I have intended to build an all-band version of the L-C-L network for quite a while. The addition of a QRP+ to the station gave me the incentive to go ahead. Learning of the potential front-end problems that might result from integrating the rig into the switching system that lets me select among my other rigs, the QRP+ would have to be a separate station on the side, with its own WM-1 wattmeter and its own ATU. +

I needed a station unit, not a super compact field unit. It had to have enough heft to support the RG-213 I use to feed the antennas (a GAP-VI and a Butterfly beam). And it had to be soon. That meant finding what I needed in the junk box, rather than making up a design and exploring hamfests for several years to find the parts.

+

Here is what I found: 2 10 µH LaPointe rotary inductors from a remotely tuned EDZ beam project, a few HF-100 variable capacitors, a 550- 550 pF 2 section capacitor from my father's junk box (probably from a military rig), a ceramic multi-wafer 7-position rotary switch about 7" long, knobs galore, some 3/4" aluminum L-stock from a portable antenna no longer in use, and about 2.5 square feet of Plexiglas the previous owner of my house left behind. I also found a bicentennial quarter and two long- lost screwdrivers among the junk. That was almost everything I needed for an L-C-L Tee tuner.

+

The Plexiglas would make the panels and chassis, supported and bound by the L-stock. That decision alone would save almost $160 (the cost of 2 new turns-counters). Since Plexiglas is transparent, I could count the turns myself. Well-wired ATUs do not radiate, consisting of passive components only, so a metal case is not required. All I needed were 4 insulated shaft couplings, which I obtained from Buckeye Electronics for $3.00.

+
+

The Circuit

+
Figure 1 shows the schematic for my L-C-L Tee tuner. It is straightforward in almost every respect. The 100 pF variable capacitor is always in the circuit, while the 550 pF sections switch in, one at a time, as needed. When using the larger capacitor values, the 100 pF unit becomes a fine-tuning vernier. Hence, I had no need for an expensive reduction drive. +
+ +
+

The inductors have spread turns at one end to maintain Q at low inductance values. Therefore, the short from the rotary contact goes to the close-spaced end of the coil.

+

10 µH coils are sufficient for most situations, down to 80 meters. However, I can imagine some load types for which they might not provide an efficient match on the lower bands. If you short out all of the output coil, you have an L-circuit, suitable for end-fed random wires. Alternatively, to get more inductance into the circuit, I added S2 to move the capacitor set to the output terminal and use both coils. On low bands, one coil might be at full inductance and the other varied for the match.

+

Although the schematic shows 3 switches, all switching can be combined in a single multi-section rotary switch. Ceramic wafers are best.

+
+

Construction

+
Plexiglas offers several advantages as a case material for an ATU: it reduces stray couplings to metal; it allows see-through tuning; and it cost me nothing. The "chassis," top, and front and rear panels are all 5.75 x 11 inch 0.125" thick Plexiglas, with "cut-to-fit" end pieces. A sabre saw and a sander shape the Plexiglas well. It handles like wood for cutting and drilling. I use masking tape at cutting and drilling points to minimize scratching. +

Front Open View

+
+ +
+

A front view of the ATU without the top, end-plates, and case rim, showing the parts placement. All parts except the rotary switch are mounted to the plexiglass base plate. The switch is mounted between the front and rear panels.

+

Rear Closed view

+
+ +
+

A rear view of the ATU with the case fully assembled, showing final assembly materials, the rear mount of the rotary switch, and the cut-out and plate for the input and output connectors.
+

+

Two strips of L-stock hold the chassis plate off the table. The coils and capacitors mount on this plate. A set of "ground" connections run under the plate and link all parts, as well as the rails and a small aluminum plate at the rear on which the input and output coax connectors are mounted. Exact techniques depend on the components one finds in a junk box. A handful of 6-32 machine screws, nuts, and lock-washers (with a few 8-32 pieces to mount the coils) is all the hardware the project requires.

+

The ceramic wafer switch had enough positions and sections to handle the switching jobs shown in the schematic. I shortened the rods (and re-threaded them) so that with the shaft mounted to the front panel, the rods just projected through the rear panel. This technique keeps the switch from sagging, reduces strain at the front mounting, and holds the front and rear panels apart at the correct distance. I read switch position by a pointer knob that aligns with the visible detents in the switch support plate behind the front panel.

+

I wired the chassis components first, the switch second, and made interconnections when I mounted the switch. Quarter-inch wooden dowel provides the coil and capacitor shaft extensions through the front panel to hold the tuning knobs.

+

Aluminum L-stock pieces around the case perimeter link the sides and bottom of the case, with an independent top piece of plexiglass and a rim of L-stock to hold it in place. Vertical L-stock at the corners is electrically connected to the grounded chassis rails. Only the top perimeter pieces float, but have shown no detectable RF, either to my finger tips or by detuning the circuit from semi-assembled settings. There are no panel markings because none are needed.

+
+

Operation

+
An L-C-L Tee is an inherent low pass filter capable of a wide range of matching. Some writers have feared coil "suck-out" in the shorted turns of the coils and both inter-turn and stray capacitance. This effect has not been experienced in comparisons of received signal strength on all HF bands between the QRP+-L-C-L combination and the main station rigs and their tuners (and SPC and a C-L-C). Switching over to the L-C L-network has enabled me to load random wires, aluminum gutters, and aluminum sliding door frames. +

Despite the use of two inductors, L-C-L tuners are capable of high efficiencies. W. I Everitt, in the 1930s, provided the basic analysis of fundamental networks, including their losses. His work is summarized in Terman's Radio Engineers' Handbook (McGraw-Hill, 1943, pp. 210-215). The key term for determining losses is delta, based on inductor losses in each type of network. Although Terman provides graphs of delta, popular in the days before computers and pocket calculators, Brian Egan, ZL1LE, has derived the delta equations and added them to his very useful program, TUNER.BAS. This versatile program is now included in the collection of programs called HAMCALC, made available by George Murphy.

+

In general,

+
+ Power lost in network/Power delivered to network = delta/Q +

+ In other, equally approximate terms, network efficiency = 1 - delta/Q. (Multiply this figure times 100 for a percentage value of efficiency). Figures for the delta of an L-C-L network range from 1.5 to 2 for loads of 150 ohms, with or without reactances up to ±100 ohms. These figures are similar to those of the more common C-L-C tuner. Both networks will show an increasing delta with increases in the ratio of impedances to be matched. A delta of 2 yields about 98% efficiency, ignoring bad wiring, power switch contacts, lossy connectors, poor capacitor construction, and strays. In short, efficiency is not an issue in deciding whether an L-C-L network should be used as an ATU. +

Using an L-C-L (or any other ATU) circuit effectively requires some forethought. Multiple matching settings are possible, and we always want to tune for minimum delta and maximum efficiency at the best match (lowest SWR to the transmitter). The operative rule of thumb is this: Choose the lowest value of L2 (the antenna-side inductor) that permits a match. This setting will ensure the lowest obtainable value for delta, whatever its actual value.

+

The L-C-L ATU has met all my design specifications and is doing its work well with the QRP+. The fact that the transparent case reveals the components and connections and, therefore, mystifies shack visitors is simply an unintended but welcome bonus.
+

+
+ +

+
+

First printed in 72: The New England QRP Newsletter, April, 1996. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Return to Amateur Radio Page

+

Topics: Matching


+ + diff --git a/content/trans/lclatu1.gif b/content/trans/lclatu1.gif new file mode 100644 index 0000000..c0f8b6c Binary files /dev/null and b/content/trans/lclatu1.gif differ diff --git a/content/trans/lineimp.html b/content/trans/lineimp.html new file mode 100644 index 0000000..560c61b --- /dev/null +++ b/content/trans/lineimp.html @@ -0,0 +1,223 @@ + + + + + + Voltage, Current, and Impedance Along a Transmission Line + + + + +
+

Voltage, Current, and Impedance

+
+

Along a Transmission Line

+
+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ A few years ago, I made up a little utility program in GW BASIC to satisfy my curiosity about--and later my need to know--what happens to voltage, current, and impedance along a transmission line. The program used lossless lines, since I was interested in identifying the recurring and nonrecurring values along the line. If someone needs to know the values with line losses factored in, N6BV has an excellent program on the ARRL bulletin board. +

What I wanted was less a specific value for a predetermined cut of line (although the program figures that, too), but a table of values about every 5 degrees to show me how and at what rates the voltage, current, and impedance were changing under various matches and mismatches between the antenna and transmission line.

+

I wanted not only to examine the impedance--our obsession with which has fouled up many an antenna analysis--but as well to observe the changes in voltage and current, along with their phase angles. These latter figures are essential to understanding phase lines and other matters of matching. For example, in a ZL Special, it is crucial to set up the elements and the phasing line so that the rear element sees a current magnitude and phase that is correct relative to the values on the forward element, which also yields a certain value of voltage at the feedpoint common to both element feed systems. Although the characteristic impedance of the line plays a critical role in the transformation, the actual element impedances are secondary.

+

Because someone else may get interested in charting such data for lossless lines, the utility program is listed below. It is messy programming, because different parts of the data stream were added at different times. Impedance and phase are derived from values for R and +/-jX, which are separately calculated. Voltage and current, along with their phase angles, are redundantly calculated independently of each other and of impedance (just to see if I could get all the angle correction factors to work).

+

The program produces on screen 90 degrees of values. Hard copy produces 180 degrees--not much more will fit on a single piece of paper. To examine the other 180 degrees of a full cycle, simple make another run, plugging in the values for the 180-degree mark as the initial values.

+

Some of the values will surprise you. You may not realize how high voltages and currents can rise under seriously mismatched antenna-to-line conditions. You might not have known that, when the antenna exhibits a very high resistance and reactance, the line spends most of its length at very low values, with only brief rises to the heights. There is much to be learned from these tables.

+

A version of this program, smoothed in appearance by George Murphy, VE3ERP, is contained in HAMCALC, now in its 25th version. If you do not want to deal with this program directly in your own copy of BASIC, you can obtain a copy of the latest version of HAMCALC.

+

The other alternative is simply to clip off everything but the program from a downloaded ASCII version of this page. BASIC will read a program in ASCII, and you can then save it as a regular BASIC program. Replace the last line (1140) with your own favorite ending: I keep all my BASIC utility programs in a master menu for ease of finding and using them. In any event, have fun with the following morass of lines.
+

+
+ +

+
+ 
10 'FILE: "LINEIMP.BAS"
+20 CLS:COLOR 11,1,3:CLS
+30
+IL=0:EL=0:THI=0:THE=0:THIR=0:THER=0:IIM=0:IRL=0:IPOL=0:IPHS=0:IPHSD=0:EIM=0
+:ERM=0:EPOL=0:EPHS=0:EPHSD=0:RL=0:XL=0:ZO=0:VF=0:F=0:LD=0:LM=0:LF=0:LR=0:T=
+0:TS=0:DA=0:DB=0:DN=0:RS=0:XS=0:XL=0:XM=0:XN=0:RZ=0:XZ=0:RI=0:XI=0:LN=0:LG=
+0:RA=0:XA=0:LL=0
+31 XXX$=STRING$(79,32)
+40 PRINT"      Ein, Iin, Rin, and Xin for Line Lengths, given Antenna E, I,
+R,and X"
+50 PRINT "                              L. B. Cebik, W4RNL"
+60 PRINT:PRINT "Calculates Input E, I, R, and X for specified transmission
+lines, given the     'terminal' E, I, R, and X of the antenna.
+Calculations can be for a specific   length of line (in degrees, feet, or
+meters) or, more generally, for every five
+70 PRINT "degrees of an unspecified line length (up to 90 degrees on screen
+or 180 degreeson a print out).  Data can be from MININEC, NEC or
+measurements.":PRINT
+71 INPUT "Enter Antenna R in Ohms  ", RL
+72 INPUT "Enter Antenna X in Ohms  ", XL
+73 PRINT"Do you wish to enter (v)oltage and current or (p)ower?"
+74 AA$=INKEY$:IF AA$="v" OR AA$="V" THEN 100 ELSE IF AA$="P" OR AA$="p"
+THEN 75 ELSE 74
+75 LOCATE 12,1:PRINT XXX$:LOCATE 12,1:INPUT "Enter Load Power in Watts
+",PWR
+76
+IL=SQR(PWR/RL):THI=0:EL=IL*SQR((RL^2)+(XL^2)):THER=ATN(XL/RL):PI=3.141593:T
+HE=(THER*180)/PI
+77 LOCATE 12,1:PRINT XXX$:LOCATE 12,1:PRINT "Antenna Load Current in Amps
+",IL
+78 PRINT "Load Current Phase Angle in Degrees  ",THI
+79 PRINT "Antenna Load Voltage in Volts  ",EL
+80 PRINT "Load Voltage Phase Angle in Degrees  ",THE
+81 GOTO 140
+100 LOCATE 12,1:PRINT XXX$:LOCATE 12,1:INPUT "Enter Antenna Load Current in
+Amps (usually 1)  ",IL
+110 INPUT "Enter Load Current Phase Angle in Degrees  ",THI
+111 INPUT "Enter Antenna Load Voltage in Volts  ",EL
+112 INPUT "Enter Load Voltage Phase Angle in Degrees  ",THE
+113 PWR=IL*RL
+140 INPUT "Enter Line Characteristic Impedance in Ohms  ", ZO
+150 INPUT "Enter Line Velocity Factor as a decimal  ", VF
+160 INPUT "Enter Frequency in MHz  ", F
+170 INPUT "Do you wish to use a specific line length?  (Y)es or (N)o?  ",A$
+180 IF A$="Y" OR A$="y" THEN 200
+190 IF A$="N" OR A$="n" THEN 500 ELSE 170
+200 INPUT "Specify units for line length: (D)egrees, (F)eet, (M)eters  ",U$
+210 INPUT "Line Length  ",LL
+220 IF U$="D" OR U$="d" THEN LD=LL
+230 IF U$="F" OR U$="f" THEN LD=((.3660131*F)*LL)/VF
+240 IF U$="M" OR U$="m" THEN LD=((1.200831*F)*LL)/VF
+250 GOTO 750
+260 INPUT "Do you wish a hard copy? (Y)es or (N)o? ",PR$
+270 IF PR$="Y" OR PR$="y" THEN PR=1 ELSE PR=0
+280 CLS:PRINT "               Line Input R and X for Frequency ";F;"MHz"
+290 IF PR=1 THEN LPRINT "               Line Input R and X for Frequency
+";F;"MHz"
+300 PRINT:PRINT "Ant I=";IL;"Amps at ";THI;"degrees;  Ant E=";EL;"Volts at
+";THE;"degrees"
+310 IF PR=1 THEN LPRINT:LPRINT "Ant I=";IL;"Amps at ";THI;"degrees;  Ant
+E=";EL;"Volts at ";THE;"degrees"
+320 PRINT "Ant R=";RL;"Ohms","   Ant X=";XL;"Ohms","  Power=";PWR;"Watts"
+330 IF PR=1 THEN LPRINT "Ant R=";RL;"Ohms","   Ant X=";XL;"Ohms","
+Power=";PWR;"Watts"
+340 PRINT "Line Zo=";ZO;"Ohms","   Vel Fctr=";VF
+350 IF PR=1 THEN LPRINT "Line Zo=";ZO;"Ohms","   Vel Fctr=";VF
+360 PRINT:PRINT "    Line E      Phase     Line I    Phase    Line Z
+Phase"
+370 IF PR=1 THEN LPRINT:LPRINT "    Line E     Phase     Line I    Phase
+Line Z     Phase"
+380 PRINT USING "#######.##";EPOL,EPHSD,IPOL,IPHSD,Z,THZD
+390 IF PR=1 THEN LPRINT USING "#######.##";EPOL,EPHSD,IPOL,IPHSD,Z,THZD
+400 PRINT:PRINT "Degree","Feet","Meters","Rin","Xin"
+410 IF PR=1 THEN LPRINT:LPRINT "Degree","Feet","Meters","Rin","Xin"
+420 PRINT LD,LG,LN,:PRINT USING "#####.##";RI;:PRINT "     ";:PRINT USING
+"#####.##";XI
+430 IF PR=1 THEN LPRINT LD,LG,LN,:LPRINT USING "#####.##";RI;:LPRINT "
+";:LPRINT USING "#####.##";XI:LPRINT:LPRINT
+440 PRINT:PRINT:PR=0
+450 INPUT "Would you like another run? (Y)es or (N)o?  ",R$
+460 IF R$="Y" OR R$="y" THEN GOTO 480
+470 IF R$="N" OR R$="n" THEN 1140 ELSE 450
+480 PRINT:PRINT "Press (n) to create a whole new entry; press (z) to begin
+with a new line       characteristic impedance; press (l) to begin with a
+new line length.":PRINT
+490 I$=INKEY$:IF I$="N" OR I$="n" THEN GOTO 20 ELSE IF I$="Z" OR I$="z"
+THEN GOTO 140 ELSE IF I$="L" OR I$="l" THEN GOTO 200 ELSE 490
+500 INPUT "Do you wish a hard copy? (Y)es or (N)o? ",PR$
+510 IF PR$="Y" OR PR$="y" THEN PR=1 ELSE PR=0
+520 CLS
+530 PRINT "Values of I, E, Phase Angles, R, and X for Frequency ";F;"MHz"
+540 IF PR=1 THEN LPRINT "Values of I, E, Phase Angles, R, and X for
+Frequency ";F;"MHz"
+550 PRINT:PRINT "Ant I=";IL;"Amps at ";THI;"degrees;  Ant E=";EL;"Volts at
+";THE;"degrees"
+560 IF PR=1 THEN LPRINT:LPRINT "Ant I=";IL;"Amps at ";THI;"degrees;  Ant
+E=";EL;"Volts at ";THE;"degrees"
+570 PRINT "Ant R=";RL;"Ohms","   Ant X=";XL;"Ohms";"  Power=";PWR;"Watts"
+580 IF PR=1 THEN LPRINT "Ant R=";RL;"Ohms","   Ant X=";XL;"Ohms";"
+Power=";PWR;"Watts"
+590 PRINT "Line Zo=";ZO;"Ohms","   Vel Fctr=";VF,"Freq=";F;"MHz
+600 IF PR=1 THEN LPRINT "Line Zo=";ZO;"Ohms","   Vel Fctr=";VF:LPRINT
+610 PRINT "Degree   Feet     Ein      Phase   Iin     Phase    Rin      Xin
+ Z Phase   Z"
+620 IF PR=1 THEN LPRINT "Degree   Feet     Ein      Phase   Iin     Phase
+Rin      Xin   Z Phase   Z"
+630 IF PR=1 THEN DE=180 ELSE DE=90
+640 FOR LD=0 TO DE STEP 5
+650 GOTO 750
+660 PRINT USING "#####.##";LD,LG,EPOL,EPHSD,IPOL,IPHSD,RI,XI,THZD,Z
+670 IF PR=1 THEN LPRINT USING
+"#####.##";LD,LG,EPOL,EPHSD,IPOL,IPHSD,RI,XI,THZD,Z
+680 NEXT
+690 IF PR=1 THEN
+LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT:LPRIN
+T:LPRINT:LPRINT:LPRINT:LPRINT:LPRINT
+700 INPUT "Do you wish another run? (Y)es or (N)o?  ",B$
+710 IF B$="Y" OR B$="y" THEN 730
+720 IF B$="N" OR B$="n" THEN 1140 ELSE 700
+730 PRINT:PRINT "Press (n) to create a whole new entry; or press (z) to
+begin with a new line    characteristic impedance.  "
+740 I$=INKEY$:IF I$="N" OR I$="n" THEN GOTO 20 ELSE IF I$="Z" OR I$="z"
+THEN GOTO 140 ELSE 740
+750 PI=3.141593:LR=(PI*LD)/180:THIR=(PI*THI)/180:THER=(PI*THE)/180:IF
+THER=0 THEN THER=.0000001
+760 IIM=(IL*(SIN(THIR)*COS(LR)))+((EL/ZO)*(COS(THER)*SIN(LR))):IF IIM>-.001
+AND IIM<(.001 then iim=0
+770 irl=(il*(cos(thir)*cos(lr)))-((el/zo)*(sin(ther)*sin(lr))):if irl=0
+then irl=.0000001
+780 ipol=sqr((irl*irl)+(iim*iim)):iphs=atn(iim/irl)
+790 iphsd=(iphs*180)/pi
+800 if iim=>0 AND IRL=>0 THEN IPHSD=ABS(IPHSD)
+810 IF IIM=>0 AND IRL<0 then iphsd=180-abs(iphsd)
+820 if iim<0 and irl<0 then iphsd=180+abs(iphsd)
+830 if iim<0 and irl=>0 THEN IPHSD=360-ABS(IPHSD)
+840 EIM=(EL*(SIN(THER)*COS(LR)))+((IL*ZO)*(COS(THIR)*SIN(LR))):IF EIM>-.001
+AND EIM<.001 then eim=0
+850 erm=(el*(cos(ther)*cos(lr)))-((il*zo)*(sin(thir)*sin(lr))):if erm=0
+then erm=.0000001
+860 epol=sqr((erm*erm)+(eim*eim)):ephs=atn(eim/erm)
+870 ephsd=(ephs*180)/pi
+880 if eim=>0 AND ERM=>0 THEN EPHSD=ABS(EPHSD)
+890 IF EIM=>0 AND ERM<0 then ephsd=180-abs(ephsd)
+900 if eim<0 and erm<0 then ephsd=180+abs(ephsd)
+910 if eim<0 and erm=>0 THEN EPHSD=360-ABS(EPHSD)
+915 IF RL=0 THEN RL=1E-08
+920 RA=RL/ZO
+930 XA=XL/ZO
+940 T=TAN(LR)
+950 TS=T*T
+960 DA=(1-(XA*T))*(1-(XA*T))
+970 DB=(RA*T)*(RA*T)
+980 DN=DA+DB
+990 RS=RA*RA
+1000 XS=XA*XA
+1010 RN=RA*(1+TS)
+1020 XK=XA*(1-TS)
+1030 XM=((1-RS)-XS)*T
+1040 XN=XK+XM
+1050 RZ=RN/DN
+1060 XZ=XN/DN
+1070 RI=ZO*RZ
+1080 XI=ZO*XZ
+1085 Z=SQR((RI*RI)+(XI*XI))
+1090 THZD=(ATN(XI/RI)*180)/PI
+1100 LN=(LD*VF)/(1.200831*F)
+1110 LG=(LD*VF)/(.3660131*F)
+1120 IF A$="N" OR A$="n" THEN 660
+1130 IF A$="Y" OR A$="y" THEN 260
+1140 RUN "C:\basic\menu.bas"
+

+
+
+ +

+
+

Updated 4-1-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Return to Amateur Radio Page

+

Topics: Transmission Line


+ + diff --git a/content/trans/match0.gif b/content/trans/match0.gif new file mode 100644 index 0000000..bc22b77 Binary files /dev/null and b/content/trans/match0.gif differ diff --git a/content/trans/match1a.gif b/content/trans/match1a.gif new file mode 100644 index 0000000..dda10ff Binary files /dev/null and b/content/trans/match1a.gif differ diff --git a/content/trans/match2a.gif b/content/trans/match2a.gif new file mode 100644 index 0000000..896841a Binary files /dev/null and b/content/trans/match2a.gif differ diff --git a/content/trans/match3a.gif b/content/trans/match3a.gif new file mode 100644 index 0000000..3b6baf0 Binary files /dev/null and b/content/trans/match3a.gif differ diff --git a/content/trans/matcha.html b/content/trans/matcha.html new file mode 100644 index 0000000..0953669 --- /dev/null +++ b/content/trans/matcha.html @@ -0,0 +1,146 @@ + + + + + + A Little Matching + + + +
+

Who's Afraid of a Little Matching?

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Several times in the last few months I have seen articles and notes on Yagis and quads with a similar theme: I'd prefer to take a little less gain to have a direct 50-ohm feed point impedance and avoid those lossy matching systems. I began wondering: how much gain is an acceptable reduction to equal the loss removed by omitting a matching system? +

This is not a simple question. First, we need to set some frequency limits to the considerations. Upper HF (10 meters) appears to be a good stopping point for a first cut at the question. Above 10 meters in the ham bands, coaxial cable losses begin to become quite significant, even when perfectly matched. Additionally, capacitors begin to show losses that are negligible at HF. These and other factors strongly suggest that a separate set of design thoughts might be apt for VHF. So I shall confine my thinking to HF for the moment.

+

Second, the original question appears to pertain to gain antennas of parasitical design, such as Yagis and quad beams. These are the main types of antennas that are commonly used and which tend to have feedpoint impedances other than 50 Ohms. Hence, these are the types of antennas for which a designer might genuinely have a choice between a 50-Ohm lower gain design and a non-50-Ohm higher gain design.

+

Third, the antenna mechanicals are not in question here. Yagis and quads are assumed to be well designed mechanically so that their initial properties endure. If this is the case, then we shall in all fairness make the same assumption about the construction design of any matching system: it is mechanically designed to have and hold the properties its initial electrical design gives it. Bad practices are not what the question is about. If the question were about bad construction practices, then the answer is simple: construct better antennas and networks or find a better constructor. But the question seems instead to be about a principle, namely, the losses inherent in matching system designs, losses that cannot be designed out of the matching system.

+

Fourth, we are talking of contemporary, late 1990s, antenna designs. At one time, it was common to find Yagis with feedpoint impedances in the teens. The best optimized commercial and personal designs now typically run above 20 to 25 Ohm feedpoint impedances. Therefore, basic antenna efficiency is not significantly lowered by the materials resistance. However, I think it may be wise to hold this consideration in abeyance until the remainder of the thinking is done.

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If we use models of parasitical beam designs and specify the material (normally copper or aluminum), we may by-pass the question of antenna efficiency. NEC-based modeling systems take materials losses into account in the calculation of antenna gain. for a given design, the materials losses are given in the difference between the antenna gain using lossless wire and the antenna gain using a specified wire material. Moreover, the question of network losses presumes that the antennas compared are made of comparable materials.

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There are many matching schemes used with Yagis and quads. Many of them are not subject to easy calculation of losses. However, three typical schemes are easily calculated. Since all are widely (but not universally) used, they will make interesting test cases. I shall assume that if anyone has evidence that some fourth or fifth scheme is even more efficient than any of the ones discussed, he or she will certainly use the new system in place of the three I shall examine.

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One common system is the Tee-match, which consists of a bar in parallel with the driven element. We feed the center point of the bar and attach its ends outward along the driven element so that we obtain a desired feedpoint impedance.

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Another is the common beta match, also called the hairpin match, which is nothing but an L-circuit network where the series reactive component is constituted by a series reactance at the antenna feedpoint.

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The final system for which we can easily calculate losses is a quarter- wavelength and related lengths of coax that may be used to transform impedances.

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As an aid to gauging the significance of losses, the following graph compares power losses expressed as percentages of the original power and as dB.

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The Tee-Match:

The basic structural elements of the Tee-match are shown in Figure 1. +
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We can investigate losses when using the Tee match, because the structure can be effectively modeled in MININEC. In fact, just such a preliminary study was conducted and posted in this collection (The Tee-Match). When modeled directly, the losses of the Tee-match are included in the antenna gain and front-to-back figures. Therefore, significant losses will show up as decreases in antenna forward gain, whether in free space or over ground.

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The conclusions of that study are revealing. Assume a 5-element Yagi with 1" diameter aluminum elements in free space. Then develop Tee-matches to raise the impedance from the antenna reference source impedance (with no matching element wires) to the vicinity of 200 Ohms. The purpose of the high impedance at the source is to enable the use of a 4:1 toroidal balun of Sevick design for a resultant match with 50-Ohm coax. In the following table, the "Reference" line refers to the antenna without a matching section. The remaining lines refer to Tee-match bars of the indicated diameter in inches.

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Model                Gain in dBi                 F-B in dB            Source Z (R +/- jX)
+Reference            9.827                       22.15                 25.5 - 0.96
+T: 0.50"             9.855                       21.71                209.7 + j0.85
+T: 0.75"             9.789                       21.81                210.7 + j1.36
+T: 1.00"             9.817                       21.86                209.7 + j2.49
+T: 1.25"             9.832                       21.86                198.6 - j1.27
+T: 1.50"             9.853                       21.92                205.2 + j1.41
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The maximum variation in gain is 0.066 dB, and the maximum variation in front-to-back ratio is 0.44 dB. Given the wandering nature of the figures from one model to the next, there is no compelling reason to believe that the differences are anything more than artifacts of the modeling process, since for each Tee match used, a slightly different Tee bar length and main driven element length were required.

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In addition, Sevick reports that when properly constructed with due attention to the impedance of the winding, the transmission-line transformers he has designed are better than 99% efficient. At 99% efficiency, the loss would be about 0.04 dB.

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4:1 coax baluns of the 1/2 wavelength design may run slightly higher losses, depending upon the type of coax used. Low loss coax in the 1/2 wavelength fold-back portion of the balun may have a loss of about 0.08 dB (under 2% of power).

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Therefore, the use of a well designed and constructed Tee-match incurs only a very minor loss. If we assume that the network consists of both the Tee- system and the transmission line transformer, then losses resulting from the electronic aspects of the composite network amount to about 1-2% of power or about 0.04-0.08 dB.

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The Beta Match:

The beta match is outlined in Figure 2. +
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The Beta match has been extensively described and explained. The current basic reference is The ARRL Antenna Book, pp. 26-9 to 26-11. Also insightful is "The Hairpin Match: A Review," by Thomas Cefalo, Jr., WA1SPI, Communications Quarterly, Summer, 1994, pp. 49-54, to which I wrote a follow-up (Communications Quarterly, Winter, 1995, pp. 51-54). Despite these efforts, a reputation for lossiness persists with the beta match.

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Part of the problem lies in the fact that is the parallel or shunt inductor is a coil, the operating bandwidth of the match is wider than with the use of a hairpin or shorted transmission line. since a wider operating bandwidth indicates greater resistive losses, many folks have assumed without calculation that the requirement for an inductance of any sort makes the beta match inherently lossy. Actually, no assumptions are needed, since all the critical aspects of the beta match can be fully calculated.

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Let's look at a few antennas and determine the losses incurred by this matching system.

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a. A Two-Element Yagi

Actually, the number of elements and basic gain of an antenna are largely Irrelevant--except as base-line numbers--to the question of losses from a beta match. What is of critical importance is the feedpoint impedance. For the beta match, using 28.5 MHz as the design center frequency, I have chosen upper and lower frequency limits of 1.25% away from center. This figure fully covers all the HF ham bands except 80/75 and 10 meters. The resulting upper and lower frequencies for our explorations will be 28.144 and 28.856 MHz. +

The following table summarizes the calculations performed for a beta match, where the driven element was first sized to provide close the an ideal series capacitive reactance for the system. Then, the required shunt coil was created and becomes a constant for all frequencies within the limits. The reactance at each limit was converted into an equivalent capacitance and, with the beta inductor, used to calculate the resulting SWR relative to 50-Ohms. Also given for each frequency is "delta," the loss or working Q figure for the frequency and impedance transformation desired.

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Network delta is predicated on losses associated with the inductive reactance, based on the premise that, for HF at least, capacitors have comparatively negligible losses. The capacitive reactance of the antenna is not directly comparable to a lumped-constant capacitor. However, losses associated with the capacitive reactance at the antenna feedpoint are already accounted in the antenna materials losses and the final gain figure for the antenna.

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All figures are derived from a combination of NEC-2 for the antenna performance figures and ZL1LE's ladder (L-network) module of his ATU network program suite included in HAMCALC, supplemented and cross checked with a hand calculator.

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Frequency (MHz)                           28.144               28.500               28.856
+Gain (Free Space, dBi)                    6.66                 6.38                 6.13
+F-B (dB)                                  10.10                11.06                11.14
+Feed Z (R Ohms)                           27.56                33.14                38.57
+Antenna reactance CX (Ohms)               -36.77               -24.31               -12.72
+Equivalent capacitor Ca (pF)              153.8                229.7                433.6
+Inductor used La (micro-H)                0.391                0.391                0.391
+SWR relative to 50 Ohms                   1.57                 1.02                 1.40
+Delta                                     0.90                 0.71                 0.54
+

Remember that the driven element was set to a length at 28.5 MHz to provide the reactance just about on the nose for a beta match and a coil calculated from the required inductive reactance in shunt to provide a close match to 50-Ohm coax. The SWR of 1.02 shows a close match. The inductor becomes a constant across the band, with the series capacitive reactance changing with frequency. At the edges of our limits, the resistive component also changes, calling for a different component set to effect a 1:1 match. However, the available components are the coil just put in place and the series reactance of the antenna at the new frequency. Since these values are not ideal, the beta match presents the coax feedline with an impedance resulting in the SWR figures shown. For this particular antenna design, the beta match provides a very decent SWR operating band width.

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Now let us look at losses. We need go no further than the worst case losses, which result when the delta is highest--in this case 0.90. Actual power losses are a function of the ratio of delta to Q, the figure of merit of the inductor. Loss as a percentage of power is 100 x (delta/Q).

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The question then is one of the Q of the inductive reactance. Coils with a minimum Q of 100 are easily hand-wound, and Qs exceeding 200 are certainly possible. Hairpins--shorted transmission lines--have far lower losses, although not zero losses. Let us arbitrarily take a Q of 500 as representing the worst hairpin we might construct; carefully crafted hairpins may have Qs exceeding 800. With these numbers, we can perform a few simple calculations.

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Delta         Inductance Q         Loss (% power)       Loss in dB
+0.90          100                  0.90                 0.039
+0.90          200                  0.45                 0.020
+0.90          500                  0.18                 0.0078
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Clearly the (worst-case) hairpin has far lower losses than any inductor. However, the inductor-based beta match cannot be classified as extremely lossy.

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Let us look at two more examples with lower impedances to be matched, and therefore higher values of delta.

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b. A Three-Element Yagi

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Frequency (MHz)                           28.144               28.500               28.856
+Gain (Free Space, dBi)                    7.15                 7.21                 7.38
+F-B (dB)                                  22.12                35.45                23.54
+Feed Z (R Ohms)                           29.43                27.95                23.80
+Antenna reactance CX (Ohms)               -32.63               -24.85               -15.05
+Equivalent capacitor Ca (pF)              173.1                224.7                366.5
+Inductor used La (micro-H)                0.314                0.314                0.314
+SWR relative to 50 Ohms                   1.32                 1.00                 1.51
+Delta                                     0.84                 0.89                 1.05
+

Worst-Case losses:

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Delta         Inductance Q         Loss (% power)       Loss in dB
+1.05          100                  1.05                 0.046
+1.05          200                  0.53                 0.023
+1.05          500                  0.21                 0.0091
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c. A Five-Element Yagi

+ 
Frequency (MHz)                           28.144               28.500               28.856
+Gain (Free Space, dBi)                    9.11                 9.26                 9.40
+F-B (dB)                                  21.67                26.67                28.54
+Feed Z (R Ohms)                           19.71                17.54                13.58
+Antenna reactance CX (Ohms)               -35.55               -25.89               -13.32
+Equivalent capacitor Ca (pF)              159.1                215.7                414.1
+Inductor used La (micro-H)                0.205                0.205                0.205
+SWR relative to 50 Ohms                   1.90                 1.12                 2.05
+Delta                                     1.24                 1.36                 1.64
+

Worst-Case losses:

+ 
Delta         Inductance Q         Loss (% power)       Loss in dB
+1.64          100                  1.64                 0.072
+1.64          200                  0.82                 0.036
+1.64          500                  0.33                 0.014
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The highest loss encountered in this sequence of Yagis is 0.072 dB as a result of the electronic aspects of the beta matching system, and this only occurs when the antenna has a very low impedance and the beta inductor is in the low-Q region of 100. Higher-Q coils and hairpins reduce these losses considerably.

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The Quarter-Wavelength Matching Section:

The quarter wavelength matching section is illustrated in Figure 3. +
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For antennas with a feedpoint impedance of about 100 Ohms resistive or of about 25 Ohms resistive--and close to resonance, the quarter wavelength matching section can be an effective matching system. For higher impedances, 70-Ohm and 75-Ohm cables are commonly used for matching sections. For impedances close to 25 Ohms, 35-Ohm line can be used. RG83A/U is available, but at $3.00 a foot, it is not as commonly used as it might well be in this application. Fortunately, its 0.66 velocity factor cuts necessary costs somewhat.

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Consider the following 3-element Yagi with the driven element close to resonance, with a 1/4 wavelength section of 35-Ohm line used for a match and cut for 28.5 MHz. The actual section used was cut to 93 electrical degrees length to ensure an SWR under 2:1 at the upper end of the test frequency spread. Losses in the matching section were calculated with N6BV's TLA; they include only the additional losses arising from the use of the line as an impedance transformer, since the line itself constitutes part of the overall length of feedline from the transmitter to the antenna.

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Frequency (MHz)                           28.144               28.500               28.856
+Gain (Free Space, dBi)                    7.93                 8.10                 8.34
+F-B (dB)                                  20.76                25.74                17.56
+Feed R (Ohms)                             27.09                25.74                22.89
+Feed X (Ohms)                             -13.3                - 0.85               +13.24
+Matching Z (R +/- jX Ohms)                37.67 + j18.04       47.65 - j0.03        36.43 - j22.62
+SWR relative to 50 Ohms                   1.65                 1.05                 1.84
+Loss (dB)                                 0.030                0.004                0.037
+

Losses, of course, increase as the frequency moves away from the the design center for which the matching line is cut. Nonetheless, losses for this particular application do not exceed 1% of power or 0.04 dB.

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SWR Bandwidth:

In selecting a matching scheme, losses in the network are not the only consideration. The SWR operating bandwidth that results from the matching section is also of some electrical importance. Those matching schemes that show higher SWR at the edges of the frequency spread of interest may in some cases be worse choices than other systems with higher initial losses but a lower average SWR relative to the main coax feedline. Losses in the main line increase with SWR. The precise losses will vary with frequency, line type, and line length. Hence, no generalizations are possible. However, in performing calculations of the order just presented, one should also account for main line losses as well before selecting a matching system. +

Conclusions:

There is little to choose among the matching schemes explored here, which only sample a few of the schemes--the ones most easily calculated for electrical design losses. The maximum loss encountered was about 0.08 dB, or about 2% of the total radiated power. (Lesser materials or poor physical design, of course, might result in greater losses.) We may therefore use the 0.08 dB figure as the amount of reduction that one might be willing to accept in an antenna design to achieve a 50-Ohm direct match. +

Unfortunately, I know of no antenna designs with a 50-Ohm direct feed system that are only 0.08 dB less than their higher-gain counterparts. Normally, the gain differential tends to approach 1.0 dB. There are no electrical reasons for suffering such a loss, if the sole aim is to avoid network losses associated with matching networks.

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There remain, however, some good reasons for settling on a lower gain design in the interests of a direct 50-Ohm feed:

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1. Operating bandwidth: Some designs--such as the 6-meter design in another note in this collection--show a very wide 2:1 SWR operating bandwidth. For some operating needs, operating bandwidth is much more important than gain, and these designs may certainly become the design of choice.

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2. A ham's first home-brew Yagi: For the beginning constructor, a design that represents a sure thing is often important. A 50-Ohm design without the mechanical and electrical details of a matching network can approach the ideal of a "sure thing."

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For the experienced antenna builder without need for more than a moderate operating bandwidth, however, there should be no need to shy away from matching networks. They cannot be classified as electrically lossy, if one designs them properly--and many good design aids are available. If good design is accompanied by good construction practice (at least as good as that put into the antenna proper), then the matching network should approach in operation its electrical potential for efficiency.

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The first step in this process is to set aside any reputations matching networks may have and actually to perform the calculations that provide an accurate picture of losses and of efficiency. Matching networks at the antenna terminals have gotten a poor reputation that has largely emerged from bad physical design, bad construction, and bad maintenance, all of which are highly curable antenna diseases. Electrically, the matching systems explored here have so little inherent electrical design loss that it may safely be ignored--with one exception. Do not take my word for any of this, but perform the calculations yourself. You may be amazed at how many interesting and useful things we can learn from such exercises.

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For further comparisons among matching systems, see "The Matching Question Redux".

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Updated 04-04-1998. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching, Quad, Yagi


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The Matching Question Redux

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L. B. Cebik, W4RNL

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Back in 1998, I took a look at the matching question, especially as applied to the driver element of typical amateur beam antennas, such as the Yagi-Uda array of various sizes. See "Whose Afraid of a Little Matching?". In those notes, I used a set of external utility programs to calculation the components and the losses of some common types of matching systems applied normally to the feedpoint of antennas to change the natural impedance of the driver to the standard 50-Ohm coaxial cable. In virtually all cases, the losses turned out to be negligible.

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The appearance of the latest version of EZNEC Pro/4 (version 5) has provided an interesting opportunity to revisit the question and to make reasonably fair comparisons among most of the matching system candidates. Author Roy Lewallen has included in the user interface of the program a special set of facilities. In addition to the standard transmission line facility, upgraded to include line losses, Roy has added new facilities to create ideal transformers and L-networks. In fact, we can place back-to-back L-networks together to obtain 3-component networks such as PIs and Ts. Roy's system allows the user to specify resistance, inductance, and capacitance to the legs of the networks, so we can explore the effects of the components with any level of component loss (or low-Q) that we wish. Those who know how to handle the NT command can already do this, but on a single-frequency basis. In Roy's interface, for each change of frequency in a sweep, the interface calculates the correct NT commands for the specified component values before executing the core run for each frequency step. The result is a unique ability for the user to evaluate a total antenna system within any model, including matching networks and coaxial cables.

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The new version of EZNEC gives a chance to look at most (but not all) of the common matching systems that we apply to beams using a common set of antenna elements and changing only the matching system and its components. For example, let's begin with a common 3-element Yagi that uses 0.5"-diameter aluminum elements for 28.5 MHz. Initially, we shall set the driver to resonance at the design frequency, even though the impedance will be about 25 Ohms. Fig. 1 shows the Yagi dimensions, along with its outline and its free-space E-plane pattern.

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In our exercises, we may use the free-space environment, since we are only examining the effects of matching systems applied at the feedpoint. In actual installations above a real and lossy ground, there will be other losses. However, these will vary with the antenna height and the quality of ground. Moreover, they will be constant for a given installation. Therefore, the differences that we are seeking will not change and show up most vividly by comparing them in free space.

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Table 1 provides the basic performance information that we shall glean from each model. In this case, with no matching system, we obtain a certain forward gain and a 180-degree front-to-back value. As well, we obtain the feedpoint impedance. The next two figures show the SWR at 28 MHz and at 29 MHz. For the basic antenna, we used a reference impedance that equaled the resonant impedance of the driver at the design frequency. When we add matching systems to the antenna, we shall use 50 Ohms as the reference value. The two SWR values give us a rough estimate of the operating bandwidth of the antenna. Significant increases in the SWR values at either end of the 1-MHz span indicate a shrinking 2:1 SWR bandwidth. The final value is the radiation efficiency as calculated by NEC based on the sum of all losses, whether from the material losses (aluminum) of the elements or any losses in the components that we shall eventually add to the antenna system. Since our basic antenna has only material losses, the 99.2% efficiency is the highest value that we may obtain in this exercise. We shall encounter the value many times, since for each matching system, we shall begin with an idealized matching system with lossless components.

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We may note in passing that this antenna design is a very good monoband performer for the number of elements and the length of the boom. In addition to this basic antenna, we shall eventually introduce a variant to test beta-match systems. However, our initial matching efforts will use a resonant driver.

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Impedance Transformers

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Our first methods of transforming the natural driver impedance to 50 Ohms will involve two types of transformers, as suggested in Fig. 2. The first is a 1/4 wavelength section of transmission line whose characteristic impedance (Zo) is the geometric mean between the antenna terminal load impedance (at Ld and Ld') to the cable or source impedance (at So and So'). Since the ratio of the load and the source impedance values is 1:2, we may also employ a low-loss or nearly ideal transformer of any desired construction.

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The 1/4 wavelength matching section requires a 37-Ohm Zo, which we may obtain by parallel to pieces of 70-75-Ohm cable. The cables that we choose for the job are generally either RG-59 or RG-11, which have different loss values. The new version of EZNEC let's us introduce losses from any cable chart by entering the loss per 100' (or meters, if we choose that unit of measure for the model) at the nearest listed frequency. For 10 meters, the 10 MHz value is the useful one. The program then scales the losses to the selected model frequency. This technique is very effective except at very low frequencies and ultra high frequencies, and our sample cases will not press either limit. Table 2 provides the results of our modeling.

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As we progress from the zero-loss case to RG-59, we discover a descending gain curve. The lossiest of the cables yields a forward gain that is down by 0.14 dB, an amount that we would have a very difficult time measuring in a range test, let alone detecting on normal operation. The front-to-back ratio is (and will be for all our models) virtually unchanged. The design frequency impedance values are well within acceptable limits relative to the ideal 50-Ohm value. As we add cable losses to the matching system, we note that the SWR at 28 MHz decreases very slightly, indicating that the cable losses broaden the SWR bandwidth--although we likely would not be able to measure the difference using the equipment generally available to radio amateurs. We also discover that the total antenna system efficiency has dropped from a maximum of 99.2% down to 96.1% for the RG-59 implementation. The 3% drop (or about 3-watts added loss for a supplied power of 100 watts) shows up in the gain and the bandwidth numbers, which made no detectable dent in anticipated performance.

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Table 3 shows the result of employing a 1:2 impedance transformer in place of the 1/4 wavelength matching section. The transformer implementation in EZNEC is an idealization with a fixed very small loss. It might represent a very high-efficiency 2:1 balun and likely has less loss than a wide-band conventional transformer using a powdered iron toroidal form. Well-constructed conventional transformers may show a 2-3% loss, placing them in the general range of results obtained from the two types of real ("lossy") cables used in the 1/4 wavelength transformer exercise.

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L-Networks

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An alternative to using either transformer method to raise the natural 25-Ohm driver impedance to a 50-Ohm cable value is to place an L-network at the feedpoint of the antenna. Normally, we would use fixed components and calculate their values from an external utility program. When looking from the source to the load, we are down converting, which mean placing the shunt or parallel component of the L-network on the source side of the arrangement. As shown in Fig. 3, we have two main options for the required L-network.

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The sketch shows the approximate component values required by each version of the L-network. For each case, we may begin by using lossless components. Although we might assign Qs to the capacitors, the value would by over 1000 and more typically 5000. Such values will show no changes in the output. For practical cases, we can limit losses to the inductor. As a sample, I selected a Q of 200. This value is somewhat low for very carefully constructed coils, but may be typical of coils as we normally construct them and then house them for weather protection. Table 4 provides the results of our models using both lossless and lossy inductors.

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The use of either type of L-network yields the same result. With a coil Q of 200, the efficiency drops to 98.7%, for a net gain decrease of 0.02-dB. The SWR bandwidth is numerically slightly below the limits we found for the pre-matched antenna, but the difference would be very difficult to measure under the best range conditions. L-networks, then, can be a highly effective method of achieving a match between a resonant driver and a 50-Ohm cable when the transformation ratio is about 2:1.

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3-Component Networks

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In practice, we would likely not go beyond the 2-component L-network in effecting a match between the 25-Ohm driver and a 50-Ohm cable. Every extra component is one more source of system failure due to any number of conditions. However, because we encounter many claims that suggest significant inefficiencies for 3-component networks, relative to the simple 2-component L-network, we should at least see what the models might suggest.

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Fig. 4 outlines the main candidates for matching service. We have low-pass PI and T configurations and a high-pass T arrangement. (A low-pass T is also possible but hardly ever appears in practical systems.) The outlines show the components used in the model. I have not tried to optimize the components for the lowest value of delta or loaded network Q, but selected components that might be close to those employed by radio amateur implementations of these networks.

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The version of EZNEC used in this exercise creates 3-component networks by placing two L-networks back-to-back. The center component is split between the two Ls. In some cases, this creates a parallel set of components in each L, and in other cases, it splits the center component into series elements. For practical cases, you may divide the center component of the 3-element network into two equal values whose combination results in the calculated component value.

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Table 5 presents the results of modeling each 3-component network as a lossless network and then as a network where the inductors have a Q of 200. The lowest efficiency obtained (from the low-pass PI network) is 96.9%, which decreases the gain to 8.01 dBi. Even though the gain decrease is only 0.1-dB relative to a lossless system, we might be able to improve the value by selecting components for the PI that result in a lower value of delta. The practical question becomes the feasibility of the component values under network re-calculation vs. the small improvement we might see in the model numbers, given that the lossy and lossless versions would show no detectable operational differences. Perhaps the greatest improvement might be in the SWR bandwidth values.

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The T networks have lower values of delta and thus show slightly higher gain values, along with slight improvements in the 28-MHz and 29-MHz 50-Ohm SWR values. The bottom line is that a three-component network need not show operationally detectable reductions in performance over the simpler 2-component networks, although the numerical results may show some differences. Nonetheless, for practical reasons, such as reducing the number of items that might fail under operational duress, the simplest possible networks are preferable.

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The Beta Match

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What we now generically call the beta match originated from work at HyGain. The "beta" moniker has stuck, although a number of writers avoid the term to skirt any copyright or patent issues. However, it is convenient to use the term and then to break down methods of implementation according to the type of so-called beta component. All forms of the match rest on the same basic principle.

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We begin with a slight revision to the basic antenna we set up at the start of these exercises. As shown in Fig. 5, we simply shorten the driver element until it exhibits approximately the "right" impedance as a value of R - jX Ohms. The performance of the pre-matched antenna does not differ from the performance of the same antenna with a resonant driver.

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The "right" driver impedance is a composite of source resistance and a series capacitive reactance. The required capacitive reactance is a function of two factors. One the the resistance that we want to convert to 50 Ohms. The other is the calculated value of a series capacitor in an L-network that would effect the impedance transformation. Since the antenna feedpoint impedance contains both the load value of R and the L-network C-equivalent value of the series XC, we only need to add a single shunt or parallel component across the feedpoint terminals to complete the L-network. (By lengthening the element, we might work in the other direction, obtaining a value of R and an inductive reactance. Then the shunt component would be a value of C. This system has application, but the series XC version is the more common.) Fig. 6 shows some common variations in typical beta matching schemes.

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The feedpoint portion of the sketch shows the source impedance that we shall use for our exercises. It is close to but not precisely optimal, a fact that will give use a view of the beta-match flexibility. The lower left sketch replicates one of the most common forms of beta components, the so-called hairpin. The hairpin is simple a parallel transmission line length, shorted at the far end, and designed to show the required inductive reactance across the terminals of the driver. (Some versions of the hairpin ground the center of the short to bring the driver to a DC and static discharge ground. Theoretically, the ground should make no difference in the length of the line, but some sources show different calculation sets for ungrounded and grounded hairpins. In all cases, the length of the hairpin requires adjustment for resonance of the antenna system at the design frequency, so the difference may be academic.) For the hairpin versions of the system (ungrounded), a chose 600-Ohm line, with a resulting very short required length. Presuming that the line is uninsulated, I used 600-Ohm ladder line loss factors in checking the seemingly lossy version of the hairpin.

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An alternative version of the hairpin of transmission-line inductive reactance uses simple coaxial cable for the beta component. A 50-Ohm line requires almost 10 times the length of the high-impedance hairpin. Like the parallel line, the far end is shorted to create a transmission-line inductively reactive stub. The effectiveness of this system depends on the line we choose and its losses.

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The final version of the beta match replaces the transmission-line inductively reactive shorted stub with a simple solenoid inductor having an inductance at the design frequency that yields the required reactance across the driver terminals. Some writers have criticized the use of a beta inductor as too lossy compared to a hairpin. We may test this claim by using another new EZNEC feature, the ability to place a load in a shunt or parallel connection across the source and still maintain R-L-C load components and frequency nimbleness. The interface recalculates the NT equivalent of the shunt-connected load for each frequency step in a sweep.

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Table 6 shows the results of testing the three types of beta components across the driver terminals. Even with its typical loss factor entered in, the 600-Ohm open line shows no loss in gain. The beta inductor with a Q of 200 also shows almost no gain loss and only a 1.5% decrease in efficiency. The most questionable beta component of the lot is the 50-Ohm RG-58 shorted line. With a loss of 1.3 dB/100' at 10 MHz, the line drops the array gain to 7.96 dBi, 0.15-dB lower than the pre-match antenna. The efficiency is 95.7%.

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Conclusion

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Although we might suggest that, if a builder prefers to use 50-Ohm cable for the beta shunt inductive reactance, a lower-loss cable might be superior, the actual perceptible performance loss would be virtually non-existent. Other factors, such as the loss in the cable between the antenna system, including its beta match (or any of the other matching systems modeled), and the transceiver would be higher than the losses in the matching system. Indeed, the lesson of these models is that a requirement for impedance matching at a beam's feedpoint is not necessarily a count against the beam design.

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Other performance factors for the beam, such as its performance bandwidth (including gain and front-to-back ratio as well as SWR), the evenness of gain across a band, etc., may count for more than the need for a matching system. In fact, the physical construction of the beam and its ability to survive adverse weather may be more significant to a choice of beam designs than the feedpoint impedance. Of course, these priorities assume that the matching system, whatever the specific type, uses high quality components and houses them (where necessary) in ways that do not shorten their life or yield increasingly poor performance with time.

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These notes have not included the gamma match among the matching systems considered because gammas require additional lengths of tubing or rod, and NEC does not handle well junctions of wires having different diameters. However, for modeling information of gamma matches, see the pair of gamma studies in this section of the index.

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To repeat the question I posed nearly a decade ago: "Who's Afraid of a Little Matching?" When carefully done for lower-impedance Yagi beams, no one should be.

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Updated 05-25-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching


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Some (Old) Notes on Home-Brew Parallel Transmission Lines

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L. B. Cebik, W4RNL

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Many hams have the urge to home-brew parallel transmission lines. The process seems simple enough, since all we need is a. some wire and b. some spacers to place periodically along the wire, positioned to maintain a relatively constant spacing. However, there is often a gap between the easy physical process and a knowledge of what it is that we have made. So the following notes are devoted to 2-wire parallel transmission lines with the hopes of clarifying a few ideas and bringing the product and its understanding a bit closer together. In the process, I have included some interesting material (at least interesting to me) drawn from handbooks that are between 60 and 70 years old.

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Parallel feeders go back to the beginnings of radio. By 1930, the "two-wire untuned feeder system" was a standard ARRL Handbook feature. The Jones Radio Handbook of 1937 provides a table of line losses showing the advantages of open-wire feeders (a 440-Ohm line in the table) over lower impedance twisted-pair feeders (p. 70). The use of 600-Ohm lines was fairly standard, using a spacing of about 6". "To reduce radiation from the feeders to a minimum, the two wires should not be more than 10 to 12 inches apart." (The Radio Amateur's Handbook, 7th Ed., ARRL, 1930, p. 162.) Rarely did hams exceed the 6" spacing.

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A number of rules of thumb emerged to remind hams of the 6" standard, and some of them evolved into rather vague "justifications." Rather than rehearse these old saws, let's simply look at the relationship between transmission line wires and the characteristic impedance of the resulting line.

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A Review of Some Basics

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Every transmission line has a characteristic impedance, and parallel transmission lines are no exception. The characteristic impedance (Zo) of a line depends on the physical properties of the line. For a 2-wire set, we have only two properties of note (assuming the use of a very conductive material, such as copper): the diameter of the wire and the spacing between the wires, as shown in Fig. 1.

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There are a number of equations you may encounter for determining the characteristic impedance of a parallel transmission line, using the physical characteristics of the line as a basis. As we have noted, the key physical characteristics are the center-to-center spacing of the wires and the wire diameter. All basic equations involve the use of logarithms, either natural logs or common logs.

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The most precise expression for the characteristic impedance (Zo) of a parallel transmission line, based on the physical spacing and diameter of the wires, is usually given in terms of an inverse hyperbolic cosine and the fundamental numerical constant e, which has a value of 2.718281828459 (as far as it is carried out here: the decimal string is endless).

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where S is the center-to-center spacing between wires and d is the wire diameter, both in the same units. As well, S is considered to be very much larger than d.

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The right side of equation 1 is the conventional algorithm for solving the equation to the left. It involves the use of natural logarithms (to base e) and can be initially simplified to the following expressions if A is equal to or greater than 1:

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where +
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and +
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A more common equation that is useful in determining the characteristic impedance of parallel transmission lines involves common logarithms (to base 10):

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where S and d have the same meaning as in the first equation. This equation provides adequately accurate results for most home constructed transmission lines, where the wire spacing is relatively wide compared to the wire diameter. For closely spaced wires or surfaces, the first equation is generally considered the more precise.

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The equations apply to round wires only. When using square conductors or flat surfaces facing each others, the equations must be corrected.

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where d is the effective diameter of the material and w is the width of the facing surface. Since square or flat-face conductors are used almost exclusively for low-impedance lines that cannot be obtained with round conductors, we shall note them here and pass on to more ordinary lines.

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None of these equations account for the very small wire losses involved in using real materials, such as copper. There is some evidence that the greatest concentrations of electrons are on the facing surfaces of the parallel wires, with the consequence that losses may be larger for a given wire size in a transmission line than in other uses of similar wire. The result may be a need to de-rate the current carrying capacity of a wire by an AWG step or two. Nor do the equations account for the very small inductive reactance component of the characteristic impedance.

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The equations for determining the characteristic impedance of a transmission line from the spacing and wire diameter can be tedious work. Much of this has been automated in a module of the HAMCALC suite of GW Basic electronics utility programs, available from George Murphy, VE3ERP. It is also useful simply to get a feel for the range of impedances values as they relate to common (round) wire sizes and common spacings. To that end, the following table may be useful to some folks.

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                             Parallel Wire Transmission Lines
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+Wire Size (AWG)         #8          #10         #12         #14         #16
+Wire diameter (inches)  0.128       0.102       0.081       0.064       0.051
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+Spacing (inches)              Characteristic Impedance (Zo) in Ohms
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+0.5                     246.0       273.7       301.5       329.3       357.1
+1.0                     329.0       356.8       384.6       412.4       440.2
+1.5                     377.6       405.4       433.2       461.0       488.8
+2.0                     412.1       439.9       467.7       495.5       523.3
+2.5                     438.9       466.7       494.5       522.3       550.0
+3.0                     460.9       488.5       516.3       544.1       571.9
+3.5                     479.2       507.0       534.8       562.6       590.4
+4.0                     495.2       523.0       550.8       578.6       606.4
+4.5                     509.3       537.1       564.9       592.7       620.5
+5.0                     522.0       549.7       577.5       605.3       633.1
+5.5                     533.4       561.2       589.0       616.8       644.6
+6.0                     543.8       571.6       599.4       627.2       655.0
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The calculated values in the table are far more precise than we shall encounter in reality. However, within a percent or two, they accurately portray what we can expect from carefully constructed open-wire lines--that is lines using occasional spacers rather than a solid or perforated dielectric (insulation) that surrounds the wires and fills the space between them.

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While some of us are drawn to tables, others prefer and benefit from more graphical presentations of the same information. The graph in Fig. 2 presents the same data as in the table.

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Two facts are initially most notable about the graph. First, the progression of even wire sizes in the AWG scale yields linear increments of impedance for any given spacing. Second, as the spacing increases, the upward change in impedance grows smaller. The difference between impedances for 0.5 and 1.5 inch spacings is over 130 Ohms, but between 5 and 6 inch spacings, the difference is down to about 22 Ohms. Wide-spaced lines are therefore less critical relative to minor imperfections of construction.

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Some Magical Numbers: 300, 450, and 600

We are used to encountering parallel transmission line with these values of characteristic impedance: 300, 450, and 600 Ohms. From the table of values, it is clear that constructing a 300-Ohm line in open-wire fashion would be difficult. First, the spacing is narrow and may require more spacers to keep the wires aligned. Second, small changes of spacing will create larger changes of impedance than with wider-spaced lines. +

Commercial 300-Ohm cable usually overcomes these difficulty by encasing the wires and the space between with a vinyl material having good RF characteristics--that is, introducing minimal losses at all frequencies of use. Fig. 3 shows the cross section of two commercial options for 300-Ohm line, along with the cross section of what might be our home-brew open wire line.

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The use of a solid dielectric around and between the wires creates two phenomena of note. The first is a slightly higher loss than with open-wire lines. For most general purposes, the loss is small enough to neglect. However, under wet weather conditions, moisture on the line can change the characteristic impedance and introduce further losses. As well, the line can gather foreign materials that may also change the line's characteristics.

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Second, the use of a dielectric around and between the wires lowers the velocity factor of the line. Typical 300-Ohm TV cable has a velocity factor of about 0.8, meaning that a wavelength of line is about 0.8 times the free-space wavelength for the frequency of use. In contrast, open wire line tends to have a velocity factor close to 1.0, depending on the number and type of spacers used. Rarely does well-constructed open-wire parallel transmission line have a velocity factor lower than about 0.98.

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Although it is possible to construct 450-Ohm open wire transmission line, the most common commercial form also uses a vinyl dielectric. To reduce the losses and to increase the velocity factor, the line usually has windows, that is, openings in the material between the coated wires. The windows are structured to preserve the wire spacing while allowing the maximum air dielectric between wires. For these lines, velocity factors tend to range between 0.9 and 0.95. These commercial lines are inexpensive and convenient to use. In fact, the convenience may outweigh the cost differential relative to home brew lines, given the time required to construct lines.

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Open wire lines of home-brew construction are generally called for under the following conditions:

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  • 1. When the power level to be used may exceed the current carrying capacity of available commercial lines.
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  • 2. When the antenna to be used may be better matched to an impedance value that is not commercially available.
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  • 3. When the amateur has more material and time than money.
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Also on the commercial market are pre-prepared 600-Ohm open-wire lines, usually with plastic spacers. The bottom sketch of Fig. 3 is a cross-section of common commercial 600-Ohm line. Like 450-Ohm line, commercial open-wire line tends to use small diameter conductors and narrower spacers. While suitable for moderate amateur power levels, the line can introduce resistive losses at higher power levels. This product was formerly more plentiful than today.

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Which Impedance and Why

Constructing an open wire transmission line is a balance of two factors: the optimal impedance for the line and the ease of construction. Let's spend a moment on the first of these factors. +

Besides being cheaper to manufacture, TV-type transmission line uses a 300-Ohm impedance for convenience. Remember that the 300-Ohm figure is "nominal," meaning it is an approximation and may vary by 10% to 20%, depending upon the quality control of the manufacturing process. Its convenience stems from the emerging television industry in the post-WWII era. Folded dipole elements provided a rough match for the line, and TV sets were engineered to have 300-Ohm inputs. Outside of this industry, the line was used for its price and handiness, with little regard to matching. Amateurs used an antenna tuner (ATU) to compensate for reactance at the shack end of the line and to change the impedance to the emerging 50-Ohm coaxial cable standard. However, except for some briefly available transmitting versions of the line, the typical 300-Ohm line available today is composed of thin wires closely space (under 3/8").

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Also available at one time was 75-Ohm transmitting line. With two round conductors capable of carrying significant power, an open wire 75-Ohm line is not possible, since the calculations would show the wires overlapping. The use of a dielectric material between and around the wires permitted the construction of the low impedance wire. In the U.S., only remnants of this cable remain.

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Since we can more easily build 450-Ohm and 600-Ohm open-wire line, let's look at some reasons for choosing one value over the other.

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  • 1. Wider spacing of the 600-Ohm line tends to make construction less critical than for 450-Ohm line.
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  • 2. Some antenna types for which we might use a given line tend to be better matched to one value than the other. Here are some examples. +
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    • a. A doublet used for all bands may encounter very high and very low impedances. A 600-Ohm line is often a good intermediate value to limit the voltage and current peaks on the line under the conditions of a mismatch on every band. However, if the highest impedance is about 1200-Ohms and the lowest is about 70 Ohms, then a 300-Ohm line is closest to the geometric mean between the extremes. If 300 Ohm line is impractical (for any of the reasons noted along the way), then 450-Ohm line may be the next best option.
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    • b. Some antennas exhibit feedpoint impedances close to the characteristic impedance of one or the other line. Remember that a fairly wide range of resistance and reactance values can be presented to these high-value lines with a VSWR of under 2:1 (here used as a measure of voltage and current peaks). Although we tend to think in terms of 50-Ohm antenna feedpoint impedances, many good arrays have impedances ranging from 100 to 800 Ohms.
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    • c. In some applications where the VSWR is low along the parallel line, a 450-Ohm line permits the use of transmission line transformers at the shack end rather than an ATU. A 9:1 transformer will yield a 50-Ohm match to a 450-Ohm impedance. (In fact, there are installations that use such transformers at both the shack and tower ends of long runs of 450-Ohm transmission line to reduce losses that would be incurred with an all-coax system.) In contrast, a 600-Ohm line matched to the antenna presents a 12:1 impedance ratio to the common 50-Ohm system, and matching may be restricted to the use of an ATU.
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These examples only illustrate the need for analyzing all the factors at both ends of the transmission line to determine what line is best for the job at hand. The line is part of a system, and every system is only as good as its weakest part. Careless adoption of a transmission line impedance value may rob a given system of some measure of efficiency.

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Building Open-Wire Lines

If this were 1931, we would receive the following advice on building parallel transmission line: +
+ "An impedance of 600 ohms is both convenient and standard, however, and is entirely satisfactory for amateur systems. The proper spacing for a 600-ohm transmission line is computed to a sufficient approximation by the following formula: +
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where D is the distance between the centers of the feeder wires and d is the diameter of the wire." (The Radio Amateur's Handbook, 7th Ed., ARRL, 1930, p. 166)

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Unfortunately, the simple formula results in a spacing that is too wide for common wire sizes, such as AWG 12 or 14. The old equation gives us spacings of 7.9" and 6.3" for a 600-Ohm line, whereas the more exacting equations (which were in all of the Handbooks by 1936) show spacings of 6" and 5", respectively. (The Jones Radio Handbook of 1937 uses a figure of 150 X r, where r is the radius. For #12 and #14 wires, this simplified formula is more accurate. Pacific Radio Publishing, 1936, p. 54.) However, notice that erring on the high side for spacing introduces a smaller deviation from the desired impedance than using too narrow a spacing.

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We may refer to either our table or graph to determine the approximate spacing for either 450-Ohm or 600-Ohm transmission lines. #14 wire requires about 1.5" for 450 Ohms and about 5" for 600 Ohms. #12 wire needs about 1.75" for 450 Ohms and about 6" for 600 Ohms. We may always resort to the equations for more exacting figures, but greater accuracy is rarely required at these impedance levels.

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When we translate our computations into construction, we find the following 1930 recommendations:

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+ "In building a two-wire feeder the wires should be separated by wooden dowels which have been boiled in paraffine. In this way, the feeder is given a tendency to swing in windy weather as a unit. When heavy glass or porcelain spacers are used the tendency is for each wire to vibrate with respect to the other, so causing changes in capacity between the wires and consequent changes in the emitted frequency. The wooden dowels can be attached to the feeder wires by drilling a small hole in the dowels, then binding them to the feeders with wire." (The Radio Amateur's Handbook, 7th Ed., ARRL, 1930, p. 169) +
In the 1936 ARRL Handbook (13th Edition), we find the same information (p. 281), but the "e" has been dropped from "paraffin." We also find a recommendation for unbroken lengths of either #12 or #14 hard drawn copper wire for the feeders. +

In 1930, antenna feeders were coupled directly or inductively to the final tank circuit. Hence, changes in the feeder conditions affected the frequency of the keyed oscillator of which the tank was a part. Although we do not design our stations in this manner any more, the principle of using light dowels remains valid in terms of maintaining a constant characteristic impedance for the line. However, our choices in dowel material have vastly increased due to the introduction of a plethora of plastic materials that we can press into service.

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Among the spacer materials in use today for home-brew open-wire feeders are the following:

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  • 1. Wooden dowels, more usually marine varnished than boiled in paraffin.
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  • 2. Plastic rods of sundry sources, including Walmart coat-hangers and similar non-radio devices. However, polycarbonate rods with assured RF characteristics are inexpensive enough to replace materials of more questionable origins.
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  • 3. PVC and CPVC thin-wall tubing.
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  • 4. Strips of vinyl siding.
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We can extend the list, but the principle is clear. The spacer can be any light-weight material with reasonable good RF resistance in the HF region. Additionally, the material should be impervious to water. The material should also be durable under direct sun (high ultra-violet) conditions. Since the spacers of most open-wire transmission lines are under far less stress than such devices as insulated antenna supports, some materials (such as PVC) may prove more durable in transmission line uses than in other antenna applications.

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The construction of lines has also not changed much over the years. Fig. 4 shows two methods of using rod, dowel, and tubular spacers. At the top is the standard hole, used with a bridge-wire, as shown at the bottom. In the middle is a convenient variant, using a narrow slot plus a hole and bridge wire. This second technique permits the builder to "snap" the wires into place, rather than threading them down the entire length of the feeders. The third technique, useful when using plastic plates as spacers, has insets at each end for a tight wire fit. The wires is then pinned in places with a thin wire through the hole and is wrapped around the wire, with a solder fix. This method of construction also eliminates the task of threading each plate down the whole length of the feeder, but allows for pinning the wires in place permanently.

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In Fig. 5, we see how we might effectively use flexible strip materials. Drill a pair of holes at each end of each strip. Then, flex the strip and thread the wire through the holes. Releasing the strip should provide sufficient friction to hold the strip in place indefinitely.

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Upon these basic methods there are innumerable further variations, as hams adapt almost anything to the task of setting feedline spacing. Whatever the spacer material and technique of construction, the distance between spacers should be as great as possible while still being close enough together to keep the distance between wires constant.

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Although adapting non-radio materials to use in constructing parallel feeders is an old ham tradition, it may be better to invest in materials with known RF properties. To preserve light weight and good weather and sun resistance--without boiling dowels in paraffin--perhaps polycarbonate or equivalent rods may be the best feeder spacers available today. Nevertheless, this advance in materials technology is still very small compared to venerableness of open-wire transmission lines as a whole.

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A Final Note

These notes have been devoted to considerations that go into the construction of a parallel transmission line. Installing them is another equally important matter. Current handbooks have excellent accounts of good engineering practice to use for installations, and I shall not review them here. +

However, I often hear of hams who violate these good engineering practices. They believe--sometimes rightly, sometimes erroneously--that a. they have gotten away with something and b. they are justified in recommending such practices to others. Whether or not a. is true, it is always bad electronics and bad amateur practice to recommend other than good engineering practice to other hams. These other folks may not be so lucky as the person who makes the recommendation thinks he or she has been, and they may not yet have the background to know why.

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Nothing ruins the performance of beautifully made parallel transmission line like careless installation.

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Updated 1-6-2000, 12-28-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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When is a Quarter Wave Not a Quarter Wave?

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L. B. Cebik, W4RNL

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The quarter wavelength coax matching section is a common technique for matching two impedances for which an available coax type represents an intermediate value. Figure 1 shows the technique, matching in both cases to a 50-ohm coax line. The 100-ohm load uses 75-ohm coax to effect its match, while the 25-ohm load uses 35-ohm coax for the matching sections.

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The quarter-wave matching sections are a fourth of a wavelength long at the operating frequency. To calculate the length in feet, we can use the following simple equation:

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where L is the length in feet, F is the frequency in MHz, and VF is the velocity factor of the transmission line used for the quarter- wavelength section.

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Likewise, figuring the impedance relationships is a matter of knowing two out of the three following items: Zload, the load impedance; Zsource, the source or line impedance; and Zo, the characteristic impedance of the matching section. Then we can use the following equations:

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Unfortunately, most folks memorize this formula as an isolated fact, also knowing it applies only where the load and source impedances are purely resistive, with no reactance. They forget two important facts.

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1. The quarter wavelength matching section is a special case and condition of coax line. Actually, the impedance--in terms of both resistance and reactance--is constantly changing down the line. At the 1/4 and 1/2 wavelength points, a resistive load will show up as a resistive impedance. At the 1/4 wavelength point, it will be a transformed value, while at the 1/2 wavelength point, it will be the original load value.

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2. The quarter wavelength section is also a special case of the series matching system pioneered by Frank Regier, OD5CG, a system which has appeared in ARRL antenna publications since the 1970s. A complex system would require a length of the main feedline between the load and the matching section. However, when the load is resistive and the transformation matches the coax rules above, the length of the "in- between" section goes to zero.

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If the load has some reactance, you can always perform the Regier calculations to make up a matching section. However, there is--for mild cases where the line SWR is not beyond about 3:1 and the load reactance is only up to 50% of the load resistance--a simpler way to design a quarter wave matching section with no "in-between" section. The technique is simpler if you have the right tools, in this case, some common software. A version of NEC-2, such as NECWin, EZNEC, or NECWires, will be needed for running some frequency sweeps later. A copy of HAMCALC from VE3ERP will provide you with the impedance transformation values along transmission lines. The specific program title is "Transmission Line Performance." Or, Alternatively, you can down load and isolate the GW Basic utility program from the "Voltage, Current, and Impedance Along a Transmission Line" see Index.

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Transforming Upward

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The final tool that you need is a slight change of approach: free yourself from the idea that the matching section will be always be 1/4 wavelength long. Figure 2 shows why. It graphs the resistive part of the impedance along a 35-ohm transmission line for a half wavelength (180 electrical degrees). The three loads are as follows: exactly 25- ohms resistive, a complex load of 28 + j15 ohms (inductively reactive), and a complex load of 28 - j15 ohms (capacitively reactive).

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The purely resistive load of 25 ohms become a resistive load of 49 ohms at the 1/4 wavelength point along the 35-ohm line. This matches the short formula exactly, even though the program that calculated this value used the complete complex equation for impedance transformation. (You can find versions of the transformation equations in almost any antenna handbook. The ones used here are for lossless lines, which have more than enough accuracy in view of the short lengths of line used.)

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Notice that the inductive load reaches a peak resistive value closer to the load. Although we are not yet positioned to freeze a precise length of 35-ohm cable for the matching section, we know that it will be in the 50-degree length vicinity. Likewise, the capacitive reactance load requires a matching section longer than 90 degrees, more like 130 degrees. Although the precise lengths needed will differ as the load values change, it will be generally true that when transforming load impedances with reactance upward, inductive reactance will call for shorter matching sections and capacitive reactances will call for longer sections.

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Notice also that the peak resistance values for the inductive loads are higher than 50 ohms. This is a function of the fact that the reflection coefficient and SWR are higher with these loads than with the 25-ohm load. From this graph, however, we cannot determine either what the SWR is or precisely what the best line length will be. These decisions require that we know what happens to the reactance along the line.

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Figure 3 shows both the resistance and reactance (using separate Y-axis scales) for the 28 + j15 ohm (inductively reactive) load. The reactance curve is interesting since it clearly shows that the reactance does not vary in a nice sinusoidal curve. Rather, it ramps, meaning that it changes value slowly for one direction in the curve and more rapidly in the other direction. This fact means that if you must choose a line length where the curve is changing more rapidly, the working bandwidth may shrink for your matching section. Likewise, the higher the reactance--and hence, the higher the SWR--the more rapid the change and the narrower the operating bandwidth for the matching section.

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Nevertheless, for modest values of reactance, we can find a satisfactory length of line at which the reactance is close to zero and the resistance is close enough to 50 ohms to give us a perfectly usable match. The length here is 50 degrees.

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Figure 4 shows the resistance and reactance curves for the 28 - j15 ohm (capacitively reactive) load. Since we are interested in a resistive value close to 50 ohms and a reactance close to zero, we will select a length of about 130 degrees.

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Incidentally, we can from these graphs estimate closely the SWR on the line. Select the point where the reactance is zero. Now determine the resistance as closely as the graph will permit. The SWR is simply the resistance divided by the 35-ohm line impedance--or that line impedance divided by the resistance: whichever way yields a number greater than 1. The SWR on the matching section used for both examples so far is under 1.7:1, which ensures a low loss matching system, considering the overall short line lengths.

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From Degrees to Feet or Meters

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The graphs are good for illustrating the background of our matching sections. However, the tables produced by the BASIC programs are better for determining the actual line length needed for the match. They let you plug in the load values and the matching line characteristic impedance (Zo) and velocity factor (VF), and frequency. Even though the principles apply at any frequency, all of the examples in this note use a design frequency of 28.5 MHz.

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In addition, the graphs are plotted every ten degrees, while the tables provide values every five degrees along the line. Hence, with calculations, you can decide on a line length that will be so close that any difference from calculational precision will make no operational difference at all.

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As a sample, here are a few lines from the chart produced for the 28 + j15 ohm load and a phase line having a characteristic impedance (Zo) of 35 ohms and a VF of 0.66 (with voltage and current magnitude and phase data omitted for clarity):

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Degrees   Feet      Meters    R(in)     X(in)     Z mag     Z phase
+ 40       2.53      0.77      55.44     11.17     56.55     11.40
+ 45       2.85      0.87      57.94      6.39     58.29      6.29
+ 50       3.16      0.96      59.01      0.91     59.02      0.89
+ 55       3.48      1.06      58.46     -4.66     58.65     -4.55
+ 60       3.80      1.16      56.38     -9.72     57.22     -9.78
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From the chart, using the lowest reactance values shown (less than 1 ohm), the matching section for the inductive load should be 3.16' (0.96 m) long. A similar table shows that the matching section for the capacitive load should be 8.23' (2.51 m) long (again, for a 28.5 MHz design situation).

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The examples used here are adaptations from a real antenna situation--a phased Yagi I was designing. The 35-ohm cable is RG-82A with a VF of 0.66. However, RG-82A sells for about $3.00 per foot, since it is not a widely used cable in quantity. An alternative cable would be common 75-ohm RG-59 or RG-11, with two lengths in parallel to make up a 37.5- ohm cable.

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Figure 5 shows the curves for the 28 + j15 ohm load, while Figure 6 shows the curves for the 28 - j15 ohm load, both using the 37.5-ohm matching line. In both cases, we can find satisfactory matching sections (about 55 degrees or 3.5' [1.05 m] and about 125 degrees or 7.9' [2.4 m], respectively), assuming we are not so hyper as to demand a perfect 50-ohm match. In fact, it will not be the lowest SWR that is of greatest concern, but the overall SWR curve that will interest us most.

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Transforming Downward

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Before we turn to the SWR curve, let's look at the use of 70 or 75 ohm cable as a match between 50-ohm line and resistive loads of about 100 ohms. (We shall remain at 28.5 MHz throughout this section.) The 70- ohm line will match a 100-ohm resistive load to 50-ohm line almost perfectly, while--as shown in Figure 7--the 75-ohm matching section is not sufficiently far off the mark to make us worry for a second.

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But what about reactive loads? Let's set up an inductive load of 85 + j25 ohms. In the downward transformation shown in Figure 8, we see the opposite effect of transforming upward: now the inductive load calls for a matching section longer than 90 degrees. For this example, the length is 120 degrees. From the tables, we can read 7.59' or 2.31 meters.

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As we might expect, and as Figure 9 shows, a capacitive load of 28 - j25 ohms calls for a line length that is shorter than 90 degrees to effect the match, in this case, about 60 degrees, or 3.80', which is 1.16 meters. As with the earlier up-transformation cases, we can use the point where the reactance is zero to calculate the approximate SWR on the matching section line (about 1.4:1).

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To demonstrate what happens at slightly higher SWR levels, let's take a quick look at loads of 100 + j50 ohms and 100 - j50 ohms in Figures 10 and 11. Notice the steeper reactance curves with higher peak values, both of which facts promise a narrower operating bandwidth. Notice also that even though the load resistance is 100 ohms, the transformation does not hit 50 ohms where the reactance crosses the zero line. Rather, the transformed value is close to 40 ohms (a 1.25:1 SWR for the 50-ohm main feedline to which we are matching).

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For the comparison, Figure 12 shows just the resistance curves for the 85 + j25 ohm and the 100 + j50 ohm loads. Notice that even the resistive part of the impedance does not form a sine wave curve for either case. Rather, peaks occur over a smaller portion of the total line length, while nulls are spread out over a longer portion of the total line length. The higher the reactance, the higher the peak and the smaller portion of the line to which it is confined.

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SWR Curves

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So far, we have restricted ourselves to a specific design frequency, 28.5 MHz. However, in the examples, I was interested not in one frequency, but in the entire first MHz of the 10-meter band. Hence, a 1:1 SWR at 28.5 MHz was less interesting than getting a satisfactory SWR curve from 28 to 29 MHz.

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The rates of resistance and reactance change of the cable away from the design center frequency will affect the operating bandwidth of the match. Likewise, the characteristics of the antenna that create feedpoint impedance changes over that same frequency range will also play a role in the effective operating band width of the matching section. Let's look at two examples and see what happens.

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The phased Yagi used in the upward transformation through a 35-ohm matching section presented a load of 28 + j15 ohms. Using NEC-2, I added the matching section to the model. The technique, for those who have not used it, is simple. I created a one-segment thin (#14) wire a large distance from the antenna proper. Since NEC transmission lines need a terminating point, I had to have the wire, which became the new antenna feed point. However, the actual transmission line is only mathematical and not physical in the model. Hence, in specifying the line properties, I also specified its length. This is the length used in NEC calculations, and the actual location of the terminating wire is irrelevant, except that it pays to keep it well clear of the antenna fields.

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Figure 13 shows a pair of SWR curves. One is the curve for the line length chosen on the basis of initial considerations from the tables (3.16' or 0.96 m). It is quite non-symmetrical, rising much more rapidly above the design frequency than below it. So I adjusted the matching section length, shortening it so that it provided the minimum SWR at about 28.6 MHz. Now the curve provides roughly equal SWR values at both ends of the band of interest. The actual length of line is 2.85 feet (0.87 meters), selected by trying several lengths of line until I was satisfied with the SWR curve. Your satisfaction may come with a different curve.

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Notice that the SWR never goes to 1:1, but that is unimportant. It is far more important to my design goals that the matching section provides a 1:7 or less SWR over the entire first MHz of 10 meters. Although the effect is not dramatic and no harm would have resulted from leaving the line as first calculated, I let my sense of perfectionism take hold. And, by performing the modeling exercise, I was able to establish well before building that either length would do the job needed.

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With feedpoint values of 20 to 30 ohms and either inductive or capacitive reactance, our choices for matching have been few. Gamma matches thrive on inductive reactance, while beta matches prefer capacitive reactance (unless we wish to use a shunt capacitor for the match). Balun-transformer users prefer, for good reasons, to adjust the driven element length to resonance. Whatever the reactance type, we may now add a coax matching section to our list of techniques for feeding low-impedance parasitical arrays. They provide a very low-loss option.

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A similar situation exists for quad beams, which typically have feedpoint impedances in the 80 to 120 ohm range, with or without reactance. Figure 14 shows the results of running SWR curves for the 100 + j50 ohm load I encountered with a model quad beam. The longer-than-90-degree matching length of 75-ohm line was just about right to reach the center hub of the antenna assembly.

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As the graph lines show, once more, I adjusted the matching line length to provide a reasonable symmetrical SWR curve to give me comfortable matching as close to both 28 and 29 MHz as possible. The original design length of 7.28' (2.22 m) became 6.01' (1.83 m) after only a couple of adjustments in the NEC model.

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Notice that in this design exercise, I sacrificed the lowest obtainable SWR on the 50-ohm line (about 1.16:1 at 28.4 MHz) in order to spread the 2:1 SWR limits just as wide as they would go with this situation. The 2:1 SWR operating bandwidth almost, but not quite, covers all of the first MHz of 10 meters. (With any significant length of 50-ohm coax from the matching section to the station equipment, the station SWR meter would read less than 2:1 from 28-29 MHz.) The minimum SWR rises to about 1.5:1. In terms of line losses from the coax run to the shack, these values are quite satisfactory in the HF range. However, there are pieces of equipment that begin to cut power in the presence of SWR values well below 2:1: in such cases, my design would not be satisfactory.

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All of these calculations can be worked out on Smith Charts, when supplemented by a pocket calculator. The advantages of the techniques shown here are several. First, the transmission line tables show the full range of resistance and reactance values for a 180-degree length of line. Hence, they actually suggest from the numbers whether or not a single series matching section is a good way to go in matching the load to the line. Second, the technique is quick, since tables based on a modeled or measure feedpoint impedance take only a moment to generate from the BASIC program, and the frequency sweeps to obtain the desired SWR curve take only moments longer. In the latter case, one can run through some intuitive moves with respect to matching section length without further calculations and see the results almost instantly on most programs.

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Whichever technique you use to develop the numbers for a single series matching section, do not forget that such a section may be a good route to a simple, low-loss match, even when the load has some reactance and the required match-line length is not a pure quarter wavelength.

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Updated 2-20-98, 7-15-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. A version of this item has appeared in AntenneX.

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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Rotator Direction Controllers

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L. B. Cebik, W4RNL

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About 20 years ago, I built a rotator control for a CD-44 rotator. The circuit was roughly based on some basic ideas of K9AZG's prior work, but it included some significant improvements. It appeared in 73 ("Elegant Rotating," 73 Magazine, 285 (June, 1984), 60-64). A few years later, when I acquired an HD-73 rotator, I redesigned the controller for that system. It appeared in CQ ("An Automatic Beam-Aimer for the HD-73 Antenna Rotator," CQ, 47 (January, 1991), 11-16).

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Many, but not all, basic rotator control boxes are still somewhat primitive. At the other extreme, I have seen some very sophisticated circuits, a few of which are computer controlled and require only that one type in the DX prefix to re-aim the beam. Somewhere between is a happy medium: the operator simply twists a dial to a desired heading and the rotator completes the job. For rotators that still use a "hold-it-down-until-it-arrives" system, extra circuitry is required.

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In the belief that the original simple circuits that I developed for my stations might still be serviceable, I am placing the original pencil schematics here for reference. They are not the clearest in the world. That is the price of scanning pencil lines that are 15-20 years old. However, I think they can be read well enough to get the ideas across. Printing them may require that the page be set "landscape" rather than "portrait" orientation.

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Both units use voltage comparators--LM311s in the original. Everything is supplied with +/-12 volts, since power is simple enough to obtain and at least one of the versions needs the dual supply. The comparators drive switching transistors that drive relays. 5-amp contacts are the safest, but 2-amp contacts will do and allow smaller relays. Besides some cross wiring of the output terminals to the original controller, defective driver transistors have been the chief troubleshooting problem. We buy them in cheap batches and solder them in without testing. Hence, some turn up bad, often with very odd symptoms.

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In the "CD" version of the rotator control, the third LM311 is needed only if the rotator has a separate braking line. Omit that portion of the circuit for versions without such a line. The circuit shown can be adjust from a fraction of a second to several seconds delay.

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The basic principle is simple: we sample the "heading" voltage from the pot in the rotator head. We connect a much higher value pot across this voltage source to create a reference voltage. These two voltages go to the voltage comparators. When the reference is more positive than the heading value, one comparator activates and sends (via the relay) voltage to the rotator motor to rotate the beam until the values match and the comparator shuts down. If the reference is more negative than the heading value, the other comparator activates. When the two voltages are the same--within a user-set adjustment range--nothing happens.

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The two systems differ in this way. The CD-type rotator uses a 26-volt indicator spread. Hence, reference and control voltage can go directly to the comparator input pins. The HD-type uses a very low positive voltage for the heading meter value. Hence, we add a combination DC amplifier and difference circuit between the two source values and the comparator pins. These two variations on a theme should suffice to allow redesign for whatever kind of system might be encountered. For example, you might wish to use solid state devices rather than relays, although you would have to ensure that they do not create stressful voltage drops in the motor operating voltage.

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There are in both circuits all kinds of trimmer pots for initial set-up to permit smooth operation. The HD unit contains a power interlock system that I would now incorporate into the CD unit. The key to satisfying operation, however, is the quality of the reference pot, which will have panel marks to indicate the desired beam direction. It must be linear, and the smaller the amount of dead (no change in value) space at the ends of rotation, the wider the spacing between heading marks in the center region. I have heard of continuous rotation pots that eliminate the dead-region problem, but my own unit uses a standard high quality pot of normal design.

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My own HD unit has never required maintenance in 15 years of service, and I have heard of CD units giving equally durable service. Construction layout is not critical. Connections to the rotator box used by the builder are a builder responsibility, since terminal strips and rotator models have undergone changes over the years.

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Refer to the original articles for further details of the designs and adjustments. These schematics are provided simply to demonstrate the level of simplicity that can still provide effective control of a rotator for one-twist beam heading settings. However, you still have to know what direction J3 is from your QTH.

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The "CD" Controller

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The "HD" Controller

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Updated 01-21-01. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Beamwidth


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Series Matching: A Review

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L. B. Cebik, W4RNL

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When the load impedance of an antenna does not match the characteristic impedance of the transmission line feeding the antenna, we often wish to effect a match. Similarly, where we wish to shift from one kind of transmission line to another having a different characteristic impedance, we must also effect a match. The are numerous means of obtaining matching conditions including (with deference to the limitations of each) an L-C network, a standard transformer, and a transmission-line transformer (balun). Often overlooked in the search for a matching system is the "series-section" transformer or series matching system.

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A series matching system consists of several elements: a load impedance (Zl), a characteristic impedance of a line to be match to the load (Zo), and up to two lengths of transmission line constituting the impedance transformer to effect a match between the load impedance and the line impedance. The transmission line(s) used to effect the match can be specified in terms of their characteristic impedances, which we may call Z1 and Z2, where Z1 is always the section closest to the load. Figure 1 sketches the typical series matching situation.

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The advantages of using a series matching system are many. First, for almost any set of conditions, one can find commercially made transmission lines to serve as the elements of the system. Second, losses are generally low because the required lengths for Z1 and Z2 are short. Third, connections between the line lengths can be made with standard commercial connectors. We can weatherproof these connectors by standard means. The result is that we can avoid using fixed and variable lumped components (coils and capacitors) to create the impedance transformation, components which are often more difficult to weatherproof.

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The key limitation to all series section matching systems is that they are frequency specific. Since all are composed of lengths of transmission line that will be specified in electrical degrees, the physical length of the lines will vary with frequency. In most cases, the effective operating bandwidth of these systems will be quite sufficient to cover any of the ham bands (at least above 80 meters). However, they are not broad-banded systems in the sense that a well-designed impedance-transforming balun or unun is broad-banded.

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One way to get a handle on series matching systems and their utility is to do a little history, but only as far back as 1961. Depending on the age of the reader, those 37 years may seem like a very long time or only yesterday.

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Bramham's Coaxial Line Matching System

In Electronic Engineering for January, 1961 (pp. 42-44), B. Bramham published a paper on "A Convenient Transformer for Matching Coaxial Lines," based on work he had done for a CERN report in 1959. His problem and his solution are sketched in Figure 2. Essentially, he wanted to match two coaxial transmission lines having different characteristic impedances, and he wanted to use only the materials at hand, namely, the two types of line to be joined. +
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He recognized that other matching systems, some of them falling into the series category, were available, such as impedance tapering line sections, single and multiple quarter wavelength transformer sections, and slug and stub matching techniques. (Balun and unun techniques were not well-developed in 1961, although--as Sevick has shown in his several books and many articles--the principles were available.) However, all of these methods required special materials besides the two line types to be joined.

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Note the special conditions that apply to Bramham's problem. The connection is between two types of transmission line. The initial line is presumed to be matched to the load so that the VSWR is 1:1. Hence, the impedances in question are resistive, with no significant reactive component.

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Bramham's solution was to develop a means for calculating equal lengths of the two lines, Z1 and Z2, that would effect the impedance transformation for a given frequency. The solution is elegantly simple. First, let's define a special term, M

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where Z1 and Z2 are the values of the two lines to be joined in the scheme shown in Figure 2.

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The only question is how long to make the two equal section of line inserted between the line to the load and the line to the source. The answer is available on a calculator:

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where L1 is the length if the matching line Z1 and L2 is the length of the matching line Z2. I have transposed Bramham's equation to the "tan" form useful with calculators, although his original was expressed as a "cot" equation.

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The answers will be given in either degrees or radians, depending on how you set your calculator. If you wish the answer as a fraction of a wavelength, divide the answer in degrees by 360 and the answer in radians by 2pi. Multiply that figure by a wavelength at the frequency of interest, and you have the required line lengths with a velocity factor of 1.0. You can then multiply each line length by the relevant velocity factor for that line to reach the final line lengths to be used.

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The line lengths will never exceed 30 degrees (1/12 of a wavelength) each, which represents the limiting case of the two lines approaching the same impedance. The operating bandwidth of the system is almost equal to that of a single quarter wavelength matching system and is widest where the two lines are closest in characteristic impedance. However, unlike the quarter wavelength system, which often cannot be implemented because a suitable intermediate impedance line does not exist, the Bramham system can always be implemented where the load matches the initial line. Moreover, it can be implemented at any convenient point down the initial line and need not be placed at the terminals of the load.

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The applications are obvious. For example, one might run surplus 75-Ohm hard line from the shack to a tower. At an convenient point at either end, one may use a Bramham series section transformer to effect a match to 50-Ohm cable to be run at one end into the shack and at the other up the tower or around the rotator to the antenna. However, this technique would apply only to a monoband installation. VHF adaptations of the same technique are obvious.

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As is often the case, someone can come along and show a given matching technique to be a special case of a more general solution. Such was the fate of the Bramham series transformer section.

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Regier's Series-Section Transformer

Between 1971 and 1978, Frank A. Regier, OD5CG, presented at least three papers on a general solution to the series matching question. Figure 3 sketches the general conditions of the overall problem. +
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Taking any load that is not matched to a desired feed line, we may attach a specific length of the desired feedline. That specific length will transform the impedance to another value. That value will, in turn, be transformed by the second line of a certain characteristic impedance to a value that is a match with the desired system feedline. The two lengths of line for the series matching sections depend on frequency, and the solution is frequency specific with a certain operating band width. The lengths are also dependent on the characteristic impedance selected for the special section of line.

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The details of Regier's solution can be found in the following references:

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  • "Impedance Matching with a Series Transmission Line Section," Proceedings of the IEEE (July, 1971), 1133-1134.
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  • "The Series-Section Transformer," Electronic Engineering (August, 1973), 33-34.
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  • "Series-Section Transmission-Line Impedance Matching," QST (July, 1978), 14-16.
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I list these important references in the text rather than in a footnote because experience has taught me that most folks simply pass over footnotes. These items are too important to the subject to ignore. A summary of Regier's work is available in almost any edition of The ARRL Antenna Book. In the 18th Edition, the basic information appears on pages 26-4 ff. Those interested in design series section transformers with the aid of Smith Charts should see pages 28-12 ff or the QST article.

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Regier's solution is best used in "normalized" form, where the ratios of one impedance to another are first reduced to single values. Otherwise, the calculation equations tend to look terribly opaque. So let's define a few quantities.

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where the load impedance is specified as RL +/- jXL and Z1 is the selected impedance of the special matching section. Note that we shall let L1 be the electrical length in degrees of the line Zo between the load and the special matching section, while L2 is the electrical length in degrees of the special matching section.

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Now we can calculate the two lengths, starting with L2, since it plays a role in calculating L1.

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Although this equation looks a bit forbidding, it can be handled on a calculator. The equation produces two good results, plus and minus. The positive result gives a shorter length for L1 and hence is preferred. If the result is an imaginary number, then the value of n must be changed. You can do this by increasing the value of Z1, the characteristic impedance of the special matching section. Remember that the series matching technique can use parallel transmission line sections as well as coaxial cables, so using a length of 300-Ohm or 450-Ohm line as the special matching section is perfectly appropriate.

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Now let's turn to L1.

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In some cases, a calculator will return a negative value for the electrical length of L1. To arrive at the correct positive value, simply add 180 degrees to the calculated result. For example, should L2 return a value of -62 degrees, the correct result will be 118 degrees.

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Since the lengths L1 and L2 are in electrical degrees, divide them by 360 to arrive at a fraction of a wavelength. Then, for the frequency of interest, multiply the fraction times a wavelength for a set of physical lengths with a velocity factor of 1.0. Finally, for the lines actually to be used, multiply each physical length by the velocity factor of actual line, and arrive at the actual line lengths.

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For those who shy away from math, Regier's equations appear to be too complex for the average ham to use. Taking this viewpoint leads the builder often to miss a simple and useful load-to-line matching procedure for monoband antennas. To make the Regier series-section equations more accessible to every ham, they are available as one of the utility programs available in the HAMCALC collection.

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Notes and Applications

The common quarter wavelength matching section is actually a special case of Regier's general solution. For the required intermediate value of characteristic impedance of the special matching section, Z1, the length goes to 90 degrees, while the require length of system feedline between the load and the special section (L1) goes to zero. +

Likewise, the Bramham alternating section system is also a special case of the Regier solution. If you examine the equations, first let x go to zero, since the Bramham system presumes a matched load with no reactance. Then n and r become equal, since the load or the line to the load has the same impedance value as the characteristic impedance of the special matching section.

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Unlike the Bramham system, the Regier series matching system permits matching to many type of loads, with or without a reactive component. Let's take a look at a few sample cases, as sketched in Figure 4.

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Our first antenna is a ground plane antenna cut for 28 MHz and fed with 50- Ohm RG-213 coaxial cable. The antenna presents a source impedance of 35 - j10 Ohms. Although we might live with the natural VSWR of the antenna, we are artificially reducing the 2:1 VSWR bandwidth, because the lowest value is nearly 1.5:1. To achieve a lower minimum SWR value, we can introduce a series matching system consisting of a 141.8-degree length of our main cable (9.09') connected to the antenna. Follow this with a 28.6-degree length of RG-11 (1.84'). Finally, return to the main RG-213 cable to the shack. The main cable sees, at the design frequency, a 50-Ohm resistive impedance.

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Case 2 consists of a wire dipole cut for 7.1 MHz and presenting a feedpoint impedance of 75 + j100 Ohms. The 300-Ohm feedline presents a very high value of VSWR. We can overcome this high SWR, if we use a 1.48-degree length of the 300-Ohm line (0.55' at a velocity factor of 0.97) from the antenna, followed by a 25.1-degree length of 75-Ohm RG-11 (6.35'), and return to our 300-Ohm line, the line to the shack sees a 1:1 SWR at the design frequency.

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All of these Regier calculations can not only be verified by measurements of actual antenna-cable systems, they can also be modeled on NEC using the TL facility as a pre-construction cross-check on the initial calculations.

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Our final example is a 14,175 MHz Yagi that presents a source impedance of 25 - j25 Ohms. Such antennas often use beta-match systems to arrive at a match with a 50-Ohm feedline. As an alternative, we can also use a Regier series matching system consisting of a 153.3-degree length (19.4') of RG- 213 from the antenna, followed by a 6.4-degree length of 450-Ohm parallel line (1.2' at if VF = 0.97), before returning to the RG-213 that goes to the shack. The line to the shack sees a 50-Ohm load at the junction with the parallel section. This case uses the high-impedance line for the special section because the minimum characteristic impedance that would satisfy the calculations is 80 Ohms for higher Zo matching sections. Although there are 92-Ohm coaxial cables, the 450-Ohm line is easily made from shop scrap and works just as well with a shorter length. (If a choke balun to block common mode currents from the main feedline is to be used, it should be installed on the shack side of the special section. The higher SWR and mismatch along the first two sections of cable may not be suitable for some types of choke balun designs.)

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Alternatively, as pointed out to me by Roger Johnson, N1RJ, one might use a parallel run of RG-213 for the matching section, giving 25 Ohms for a lower Zo matching section. In this solution, the initial single RG-213 would be 6.5' long (51.3 degrees), followed by a 4.3' 25-Ohm section (33.7 degrees) and finally the main RG-213 line to the shack. For almost all cases, there are multiple solutions, which fact allows you to select from a reasonable range of lines to achieve the electrical and mechanical goals of your matching challenge.

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Additional monoband applications for Regier series-section matches abound, especially at VHF, where antennas are normally monoband affairs. For example, in stacked arrays of odd numbers of antennas, it is often not possible to arrive at reasonably low-loss values of impedance through 1/4 wavelength matching sections that then combine in parallel to yield a central 50-Ohm feed system. Using series matching-sections may well permit arriving at a junction of three 150-Ohm impedances, which then combine to yield the desired 50-Ohm feed. Equally, it is possible to arrive at a value for each line of 210 Ohms so that they then combine to match a 70-Ohm surplus low-loss hard line directly, without need for further matching.

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A utility program, such as the one included in the HAMCALC collection, makes it easy to run through innumerable combinations in quick order and then to devote most of your time selecting the one offering the best performance. Performance might in some cases be a measure of VSWR operating band width. In other cases, it might be a matter of total system cable losses (which can be checked on a program such as TLA or TLW by N6BV, available without cost via ARRL.

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The series-section matching system deserves addition to any antenna builders repertoire of methods for matching loads to feedlines.

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Updated 2-5-99, 4-4-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Jan., 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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Some Aspects of Series and Parallel Coaxial Cable Assemblies

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L. B. Cebik, W4RNL

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In the course of developing this collection of notes, I have had occasion to use and to refer to both series and parallel coaxial cable assemblies. Perhaps a few notes specifically devoted to this subject might be useful to those who have never used coaxial cables in this way.

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Basic Transmission Line Properties

Among these notes is a discussion of the basic properties of transmission lines: 12 Ways to See and Love Your Feeders. That discussion is the background for these notes. However, let's review the salient properties of transmission lines as they are important to us in this context. +

First, all transmission lines consist of two or more conductors so arranged that they do not radiate RF energy. Whatever the exact arrangement of conductors, 2-wire lines have equal current magnitude and opposite current phase at every point along the line, thus resulting in the confinement of RF fields to the region of the line. Since the lines do not radiate (when installed correctly), the energy applied at one end of the line is available for controlled use at the other end of the line.

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All transmission lines exhibit a characteristic impedance that is a function of the capacitance between the wires and the inductance along the wires for any unit of length. Since this ratio is the same, no matter how many units of length we put together, the impedance is the same for any line length. Since the impedance is a function of reactance rather than resistance, the characteristic impedance does not represent a loss or a using-up of the energy. There are small elements of resistance and conductance that also play a role in forming the characteristic impedance of transmission lines, but line makers strive to keep these as low as feasible. These latter factors determine the basic loss per unit measure of a transmission line.

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Second, we have two generally used types of transmission lines. (There are far more than two types, but most common applications in amateur radio and related areas of antenna work use only these two types.)

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a. The parallel transmission line: the parallel line consists of two wires of constant and equal diameter with a constant spacing. To maintain constant spacing, line makers use various techniques, ranging from periodic non-conductive cross bars (ladder line) to molded coatings of special RF-rated vinyl (TV ribbon cable or "windowed" parallel line).

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The insulating material between the wires, where the RF fields are most intense, creates a velocity factor (VF) for the line, so that the physical length of a wavelength of line is shorter than the electrical length of that line. Ladder line--using mostly air as the medium between wires--has a VF close to 1.0. Windowed lined, with a mixture of air and vinyl between the wires, may have a VF of 0.9 to 0.95. Ribbon cable, once widely used for TV antenna lead-in, has a VF of about 0.8.

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Parallel line has the lowest inherent loss of the common transmission lines. Ladder line has the lowest loss of all. Therefore, as we use these lines in highly mismatched situations--with high SWR values on the line--the loss multiplier created by the SWR does not create significant total energy losses in the HF region.

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However, we must install parallel transmission line free and clear of anything that might disturb the balance between the lines or penetrate the fields around the wires to couple energy to unwanted objects. This requirement is often the limiting factor in the use of parallel transmission line.

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b. Coaxial cables: a coaxial cable consists of a center conductor and a surrounding conductive cylinder. Since the fields are wholly confined to the space between the inner wall of the cylinder and the outer surface of the center wire, the line is more immune to what occurs beyond the outer wall of the cylinder.

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We often use braided wire for the outer cylinder of coaxial cables to obtain a flexible cable. However, the use of solid outer cylinder material has become common in VHF and UHF applications, with some HF uses.

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Like any transmission line, we must maintain a constant spacing between the center conductor and the outer cylinder. The most common RF-rated plastics resulted in cables with a VF of about 0.66. Later foam insulating spacers raised the VF to about 0.8. The lowest-loss UHF solid-shell lines use spacers and an inert gas as the dielectric, with a VF between 0.8 and 0.9.

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The losses of the best hard-shell coax lines rival those of ladder line. However, common coax lines have an inherent loss level much higher than that of parallel lines. In the HF region, the losses are largely a function of the limited current-carrying ability of the center conductor. As a result, the loss multiplier created by operating the lines at high values of SWR can result in significant loss of energy along the coaxial cable. The losses vary with frequency, increasing as we raise the frequency. And, of course, they increase with the length of the line.

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Coaxial cables find their best uses in situations where the antenna feedpoint impedance--either naturally or as adjusted by a network at the antenna terminals--is a close match for the characteristic impedance of the transmission line. Where the impedance is highly variable, such as with a multi-band doublet or loop antenna, parallel transmission line is the generally recommended method of transferring power from the transmitter to the antenna. Parallel line, of course, usually requires an impedance transformation system, such as an ATU, at the transmitter end of the line, since transmitters tend to have output impedances that allow for only limited variation.

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Varieties of Coaxial Cable

Most of us are familiar with only two varieties of coaxial cable: 50-Ohm cable and 70-Ohm Cable. However, coaxial cable comes in a variety of characteristic impedances (Zo). The following incomplete list samples the available possibilities. + 
Zo (Ohms)        Cable Types (in ascending order of power capacity)
+35               RG-83
+50               RG-174, RG-58, RG-213 (RG-8)
+70-75            RG-59, RG-11
+93               RG-62
+125              RG-63
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Many of these cable types are available in different versions, using solid or foam insulation and having different velocity factors. There are also additional cables, especially in the 70-75-Ohm region, that have only manufacturer numbers. The list shows no 70-Ohm cable as thin as RG- 174, but there are video cables in the 0.15" total diameter region that we can easily use for low power amateur applications in the VHF and UHF region.

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There are also special versions of the common 50-Ohm and 70-Ohm cables with certain characteristics of interest to users. Maritime-rated outer jackets are available on some cables. As well, we can find outer jackets designed especially for burial. A number of new low-loss flexible cables have appeared on the market.

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Some of the cables with special construction features require that we turn to a dealer who specializes in cables. As well, 35-Ohm, 93-Ohm, and 125-Ohm cables are sufficiently uncommon to require us to inquire with a dealer. The WireMan, Inc (of South Carolina) has proven highly reliable in my experience and carries in stock many of the uncommon cable that I have noted.

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Series-Connected Coaxial Cables

There are applications in which we need a parallel transmission line that is shielded, that is, that is relatively immune to the unbalancing influences of very nearby conductive materials. For such applications, we can create a series-connected coaxial cable. +
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Fig. 1 shows the basic elements of a series-connected coaxial cable. In this application, we use the center conductors of two coaxial cables that run side-by side--to ensure that they are of the same length. We can separate the lines, since the currents and voltages on each leg of the line are functions of the center conductor and the outer cylinder. By connecting the outer cylinders (or braids) together at the top and bottom, each line will have comparable current magnitudes in opposite phases at each measurement point along the cable length. Many applications permit only a ground connection for the braid at the lower end of the cable. However, if a grounding point is available at the upper end of the line, it is useful for sustaining the balance between the currents on the two center conductors.

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The characteristic impedance of a series connected coaxial cable is twice the impedance of a single cable of the same type. However, the power rating will be about the same as for a single cable, since the current- carrying ability of the center conductors has not changed. However, in higher impedance situations--for which series cables are often used--the current level may be naturally lower than when the same cable is used in a well matched situation. On the other hand, the series cable may be used in highly mismatched situations, resulting in high peak currents resulting from the high SWR level.

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Fig. 2 illustrates two common applications for series-connected coaxial cables. The top portion of the sketch shows a multi-band antenna calling for parallel transmission line. However, the metallic structure and the variable spacing created by the rotator require some insurance that the line's balance will not be disturbed. The sketch shows the use of series- connected coax used for the critical region, with standard parallel line used thereafter.

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Since the series-connected coax section has a much high loss level than standard parallel line, we wish to use it only where necessary, with standard parallel line used wherever we can maintain it in a fixed and proper position relative to the tower or other objects. One European maker of a 2-element quad using a single driver for all bands uses the series-connected cable for the rotating driven element.

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Perhaps the best cable for such applications is series-connected RG-63. The single-line Zo of 125 Ohms results in a 250-Ohm series-connected cable. The relatively high impedance makes the transition to and from 450-Ohm windowed or ladder line a small matter. Indeed, new users of transmission lines should be aware that there are no special losses created by linking two transmission lines of different Zo values. The new line simply encounters an impedance value at its terminals and proceeds in perfectly normal fashion to transform that impedance according to its own characteristic impedance.

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The Wireman at last report had stocks of RG-63 that we can use for series-connected applications--and he was contemplating carrying a dual version with the outer jackets molded together for use as a shielded parallel line.

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A second use for the same type of series connected cable occurs at the shack end of the line. Very often, there are innumerable metallic wires, conduits, and masses within our homes that make it nearly impossible for use to eliminate unwanted coupling from standard parallel transmission lines, even in the short distance between the wall and the ATU. We can turn to a section of series-connected RG-63 for the indoor run. Here, we should be sure to ground both ends of the shield to the master station ground system that goes to a deep ground rod in the shortest feasible distance.

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Although "twin-RG-63" is perhaps the most versatile series-connected coax cable (or shielded parallel line, as it is sometimes called), some applications may call for a custom impedance value, such as 100 Ohms or 140 Ohms. Fig. 3 illustrates one such application.

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The antenna represents a specifically designed 2-element horizontal phased array. The boom is metallic, so we might well encounter difficulties using an open-wire phasing line between the two elements. Since the array was designed to use a 100-Ohm phase line, series connected 50-Ohm coax cable neatly fulfills the requirement. In fact, the phaseline is run within the boom for weather protection, and the braids may be grounded to the boom at both ends. The system is currently being used on commercial phased arrays for 30 and 40 meters.

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In all of these applications, designers are fully aware of two factors that may play a role in their use of series connected coaxial cables. First, is the velocity factor of the cable. It is not especially important in the applications in Fig. 2, but it is critical to the use of such lines in a phased array such as outlined in Fig. 3.

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The second factor is the higher losses per unit of length of series- connected coaxial cable than of standard open-wire parallel transmission line. These losses are not significant in the short line length used in Fig. 3, but they do have a bearing on the applications shown in Fig. 2. In general, where series connected parallel line is used solely to avoid unwanted coupling to a parallel transmission line, we should use it only for those distances where the coupling may occur. Wherever we can control such coupling by proper installation of standard parallel transmission line, we should use that low-loss line.

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Parallel-Connected Coaxial Cables

The use of parallel-connected coax cables of the same length normally involves cases where we need a cable of 1/2 the Zo of a single line of the same cable. Obviously, this opens up the door to having cables of some odd but useful characteristic impedances. Two 50s in parallel give us a 25-Ohm cable--a value not commercially available. Two 70s give us 35 Ohms, a value very useful in 1/4 wavelength matching sections. Two 93s give us 46.5 Ohms, again useful in matching sections. Two 125s give us 62.5 Ohms, once more useful in matching sections or as a main line. +
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Fig. 4 provides data on how to hook up cables to achieve a parallel connection. The two center wires are soldered together at both ends. As well, the two braids are soldered together at both ends. If you are using RG-58 (50-Ohms) or RG-59 (70 Ohms), the two cables will--with proper preparation of the ends--fit inside the barrel of a standard coax male connector. You can seal the spaces with a non-reactive, non- conductive sealant--after everything is properly soldered.

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However, consider using direct splices between the parallel coax section and any main cable to which you connect it. If you work in the VHF/UHF region, especially with small cables, you may be able to avoid the introduction of small reactances by using a carefully constructed direct cable splice. You can always strengthen the junction by adding some surface stiffening between the linked sections. Heat shrink tubing with a little epoxy inside (but not on the junctions of wires) can add strength to spliced thin lines.

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Paralleled cables will provide roughly twice the power handling capacity of a single cable in the HF region. The surface area of the center wires is doubled. However, be sure to calculate your power limit for the new impedance and the current peaks that will be present at this impedance.

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One of the main uses of parallel-connected coax cables is to form a 1/4- wavelength matching section with an impedance that is correct for the desired match. The ideal matching section impedance is the square root of the product of the input and output impedances. Here are a few examples of common matching section applications.

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Antenna               Impedance        Line Zo    Match Section Zo
+2-element Quad        115              50         76 (use 70 Ohm cable)
+3-element Yagi         25              50         35 (use RG-83 or
+                                                  paralleled
+                                                  70-Ohm cables)
+2-element Yagi         40              50         45 (use paralleled
+                                                  RG-62 sections)
+Dipole                 72              50         60 (use paralleled
+                                                  RG-63 sections)
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Fig. 5 illustrates the general matching section situation. The matching section--whether composed of 1 line or paralleled lines--is simply inserted between the odd antenna impedance and the main feedline, with center conductors connected and with braids or outer cylinders connected.

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Let's take an example that may be finicky. Suppose I had a 2-element Yagi with a feedpoint impedance of about 41 Ohms at mid-band. Such an array would give me under 2:1 SWR across the band. However, we can do a bit better. Let's make up a parallel section of RG-62 and make it 1/4 wavelength. The net impedance of the paralleled lines is 46.5 Ohms. At the design frequency, I obtain an impedance of about 52 Ohms. Moreover, the section helps my make the SWR curve more symmetrical across the operating passband. See Fig. 6 for the relative SWR curves as they apply to a specific Yagi design.

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Even though common practice tries to get away with minimal work, nothing in good engineering practice--except possibly excessive cost--says that I may not be as finicky as I desire. The symmetrical curve for the array with the section added will likely prevent an SWR sensitive rig or amplifier from reducing power at the low end of the band--if one needs a reason other than personal satisfaction for adding the section.

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As noted in another item ("When is a Quarter Wavelength Not a Quarter Wavelength?), the sections that we add can be length-adjusted to provide the most desirable SWR curve for a given situation. Hence, we are not limited to using matching sections only when we have ideal input and output impedances to go with ideal paralleled coax matching sections. Antenna modeling software is perhaps the fastest way to adjust the length of "slightly off" sections so that we can effect the best possible match.

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We can, of course, use paralleled coax as the main feedline for special situations. In some cases, we may wish to use the odd impedance values that happen to match an antenna to create feedlines that run all the way into the shack, where we might apply the final impedance transformation. The decision to use this option will depend on numerous factors, such as the losses in the lines that form our options, the weight of the paralleled lines relative to a single line, and the cost of the line.

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In the End. . .

. . .both series-connected and parallel connected coaxial cables have a place in the array of transmission line techniques at our disposal. Careful measurement and fabrication go a long way toward making our use of them successful. +

In the process of thinking about feedline needs, do not overlook some of the available lines other than the 50-Ohm and 70-Ohm lines we most often think about. The odd-values--either alone or in series or parallel combination--may provide just the characteristic impedance for a given job.

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Updated 12-26-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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Some Notes on Modeling Hybrid Transmission Line Stubs

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L. B. Cebik, W4RNL

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What is a Hybrid Transmission Line Stub?

The hybrid transmission line stub is composed of a length of transmission line with (usually) a capacitor connected across the "far" or terminating end of the stub. The capacitor serves as either a modification of the basic stub or as a means of tuning the stub. In either case, the reactance that we normally find at the circuit or antenna end of the stub acquires a new values as a result of the insertion of a reactance at the terminating end. Fig. 1 shows the general layout. +
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There are many uses for hybrid transmission line stubs, but they tend to fall into two categories. First, the use of a hybrid stub allows the designer to place the terminating end of the stub at a desired distance from the circuit or antenna end of the line. Second, the hybrid stub allows the user to modify the stub reactance with fixed reactances so as to achieve a wide range of desired values of either inductive or capacitive reactance.

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How Shall We Treat Hybrid Stubs?

The general layout in Fig. 1 has opened the hybrid stub to alternative interpretations. Fig. 2 shows one of them. +
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The general treatment of the hybrid stub underlying Fig. 2 is as an open stub with a capacitive reactance across the far terminals. This reactance is viewed as equivalent to a parallel capacitor placed across the antenna (or circuit) terminals of the stub. Unfortunately, this treatment appears to misconstrue the hybrid stub.

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Fig. 3 shows a more useful interpretation of the hybrid stub. The capacitive reactance across the terminating end of the stub is in series with the reactance of a shorted stub. Although the insertion of a capacitor creates an open DC circuit, the RF path remains complete. Hence, the net reactance of the hybrid stub is simply the sum of the stub reactance and the capacitive reactance.

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If the (shorted) stub is less than 1/4 wavelength long, then its reactance is inductive. Between 1/4 and 1/2 wavelength, the stub is capacitively reactive, returning to an inductive reactance for length between 1/2 and 3/4 wavelength.

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The fixed reactance at the far end of the stub can be, in principle, either inductive or capacitive. Inductive reactances are rarely used, since the Q of inductors tends to be low enough to introduce unwanted losses in the hybrid stub. The higher Q of capacitors tends to offer much lower loss and greater ease of varying the net reactance of the hybrid stub. (Remember that the stub itself is not without some loss.)

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The hybrid stub, according to this construal, is always shorted, with a series reactance at the far terminals. Perhaps a test NEC-4 model can both test and illustrate the hybrid stub principle.

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What Are the Requirements for a Satisfactory Model of a Hybrid Stub?

The surest way to model a hybrid stub is to use a stub transmission line constructed of wires continuous with the antenna element itself. For the test situation, I used AWG #14 copper wire (0.0641" diameter) as both the antenna element and the transmission line stub material. The element is set for 3.6 MHz in the test case, although the actual length of the element will vary according to the nature of each test case. To avoid any tuning ambiguities occasioned by placing the stub on the same segment as the antenna source, I created a set of 2-element wire Yagis, using the stub to tune or detune the parasitic element. +
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Fig. 4 shows the general layout of the hybrid stub. At a frequency of 3.6 MHz, a wavelength is about 273.2' long. The recommended minimum segment length is about 0.001 wavelength, calling for a separation of the transmission line wires of minimally 0.273'. For the tests, I used a spacing of 0.33' or 3.96". To ensure that I introduced no inaccuracies be virtue of having adjacent segments of significantly different lengths, I used 3 segments per foot for both the transmission lines wires and the antenna element wires. The result was a series of Yagi test models having between 800 and 850 total segments.

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One caution is useful at this point. Because the transmission line wires have equal and opposite currents, their net radiation is virtually nil. Under these conditions, a poor model of a transmission line stub will not show itself in the average gain test (AGT). Poor to precise models all showed an AGT of 1.0 on NEC-4, indicating that the value is almost solely a product of the wire antenna elements themselves. Remember that the AGT is a necessary and not a sufficient condition of model adequacy. Therefore, I can only recommend that the test cases used here not be replicated in software having an insufficient total segment count.

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The reason for using AWG #14 wire for both the element and the transmission line is to ensure that NEC yields accurate results. NEC has a known potential error weakness wherever there are angular junctions of wires with different diameters.

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We can calculate with very good precision the characteristic impedance (Zo) of the #14 wires spaced 3.96" apart.

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The most accurate equation (1) for the calculation defines S as the center-to-center spacing of the round conductors and d as the conductor diameter, assuming conductors of the same diameter. Although we may invoke this equation for any parallel transmission line, it is only necessary where wires are very closely spaced. Most often--for more widely spaced wires, we use a more familiar equation (2) to calculate the Zo of the line:

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There are many operating aids to perform the calculation for us, and the Zo of the stub line used in these exercises is about 577.6 Ohms.

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From the Zo, along with the line velocity factor (VF)--which is 1.0 in this case--we can calculate both open and closed (shorted) stub lengths to arrive at any desired reactance. As well, we can calculate the required stub length for a desired reactance. However, the calculations will require that we register the line length in electrical degrees.

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Equation (3) is handy for determining the electrical length in degrees from the line length in either meters or feet. To go the other way, we use equation (4):

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where K is 1.20 for lengths in meters and 0.366 for lengths in feet,

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Once we can work with electrical lengths in degrees, we can handle the correlation of stub length and reactance. For a closed or shorted stub, we use the equations in (5):

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where Xc is the reactance of the closed or shorted stub. Note that the equation applies to any line length, as the tangent of the ratio will change signs as we pass the 90-degree point. However, when calculating lengths, we shall have to adjust the lengths by adding 180 degrees when the length values are negative.

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Likewise, we can move from line length to reactance and back again by using the equations in (6):

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where Xo is the reactance of the open stub. Again, we shall have to add 180 degrees to line lengths when the results are negative.

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There are two phenomena not accounted for in the calculation of the lines by means of the classical equations. First, the calculations do not account for the small line losses that result from the less-than-perfect conductivity of copper wire. These losses are quite small, but will show themselves as slight modifications of the feedpoint impedance, whether the stub attaches to the driven element or to a parasitic element. Second, the equations do not account for stub-end phenomena, such as the characteristics of the wire that shorts a closed stub. These effects are small and show themselves most vividly when the stub is very short. In such cases, the shorting wire becomes a more significant percentage of the total length of wire in the stub.

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Test 1: A 2-Element Wire Yagi with a Hybrid Stub in the Reflector

My first test case used a 2-element wire Yagi of the driver-reflector type. Fig. 5 shows the outline of the model and its variants using hybrid stubs. +
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I first modeled the antenna to a set of free-space operating characteristics at 3.6 MHz. The driver used 393 segments and reflector used 411. The NEC-4 results are as follows.

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Gain (dBi)            Front-to-Back         Feedpoint Impedance
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+5.94                  10.55                 37.18 - j 1.709
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Because this is an exercise involving numerical progressions rather than an operating design, reported values use the full set of decimal places.

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I then added to the reflector a shorted stub as described earlier. I calculated the stub in increments of 10 Ohms inductive reactance. On the shorting wire, I introduced a capacitive reactance of the same absolute value as that calculated for the stub. (The reactance can be replaced by its corresponding capacitance with no change of results for this single-frequency test.) The following table provides the results.

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Stub Xl    Stub L     Gain       F-B Ratio        Feedpoint Impedance
+(Ohms)     (feet)     (dBi)      (db)             (R +/- jX Ohms)
+ 10        0.753      5.98       10.48            36.45 - j 1.988
+ 20        1.505      5.98       10.47            36.47 - j 2.001
+ 30        2.257      5.97       10.47            36.57 - j 1.980
+ 40        3.007      5.96       10.47            36.71 - j 1.947
+ 50        3.755      5.95       10.48            36.88 - j 1.901
+ 60        4.501      5.93       10.49            37.17 - j 1.817
+ 70        5.244      5.92       10.49            37.28 - j 1.797
+ 80        5.985      5.90       10.49            37.53 - j 1.729
+ 90        6.722      5.89       10.49            37.70 - j 1.691
+100        7.455      5.88       10.49            37.88 - j 1.650
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Overall, the introduction of a capacitive reactance at the far-end terminals of the shorted stub results in a confirmation of the construal of the hybrid stub, since the antenna returns in each case to its original operating characteristics when the introduced capacitive reactance compensates for the calculated value of the inductive reactance of the stub. Fig. 6 overlays the free-space E-plane patterns of the original array and of the version using a 100-Ohm stub and a corresponding capacitive reactance in the shorting wire.

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The progression of feedpoint impedance values shows in part the effect of the increasing (although operationally insignificant) losses as the stub wires grow longer. However, there is an ambiguity in the results if we read them from the gain and front-to-back columns. The gain of the version with the shortest stub is actually higher than that of the original beam without any reflector stubbing. However, if I add a reflector load to the original beam consisting of -1.5 Ohms (capacitive reactance), then the gain becomes 5.98 dBi with a front-to-back ratio of 10.49 dB and a feedpoint impedance of 36.48 - j 1.961 Ohms.

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The source of the slight offset might arise from several sources. 1. The characteristic impedance calculation might be slightly off relative to NEC-4's calculation of the effects of paralleling the wires. 2. The shorting wire may contribute to the offset in part or in whole. 3. The length calculations may not correspond with absolute precision between the calculations and the NEC-4 calculations.

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The practical output from the existence of the offset is simple: always use a variable capacitor when initially setting a system following these general parameters. This practice can also compensate for minor differences between the actual line velocity factor and the value assumed for calculations.

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However, in principle, the system used to construct a model of the hybrid transmission line stub shows excellent results both as a confirmation of the operation of the stub and as an illustration of what is possible.

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Test 2: Controlling a Wire Yagi Reflector

Very often, we do not simply wish to cancel out two forms of reactance. Instead, we wish to leave a remnant reactance. The net reactance may be either inductive or capacitive, but in either case, we may use a hybrid stub, that is, a shorted stub with a capacitor at the short. +
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As a test case, let's consider the driver-reflector Yagi shown in Fig. 7. The basic Yagi consists of a driver and a parasitic reflector that is the same length as the driver. The basic configuration requires a reflector load of 65 Ohms for the array to yield the following free-space operating properties.

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Gain (dBi)            Front-to-Back         Feedpoint Impedance
+                      Ratio (dB)            (R +/- jX Ohms)
+6.09                  10.30                 34.75 - j 0.603
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The load for this Yagi consists of a shorted stub having the same characteristics as the one used in the preceding example. Everything is AWG #14 wire, with the stub using a spacing of 0.33' (3.96").

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Now let's lengthen the stub to a calculated length for a 100-Ohm inductive reactance. The theoretically required capacitive reactance for returning the stub to a net of 65 Ohms inductive reactance is -35 Ohms. The following table shows the reported operating properties with a small range of capacitive reactance values.

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Cap. Xc          Gain       F-B Ratio       Feedpoint Impedance
+(Ohms)           (dBi)      (db)            (R +/- jX Ohms)
+-35              6.07       10.04           34.32 - j 1.090
+-34              6.05       10.15           34.81 - j 0.849
+-33              6.03       10.25           35.31 - j 0.614
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Although the differences are well below the level of practical concern, they are interesting. The simply calculated value of inductive reactance restores the array gain, but shows a lower front-to-back ratio and lower resistive component to the impedance. Subtracting 1 Ohm of capacitive reactance restores the feedpoint impedance, but lowers gain and does not bring the front-to-back ratio back near its original value. Subtracting a second Ohm of capacitive reactance restores most of the front-to-back ratio and sets the feedpoint reactance very close to its original value, but at a cost of slightly lower gain and a slightly high feedpoint resistance. The question (of academic interest, mostly) is which of the 3 options best reflects array performance.

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Essentially, the last option of using -33 Ohms of capacitive reactance seems most accurate to reality. Lengthening the stub slightly increases wire losses in the array. These losses will slightly reduce gain and--even though the loss is in the reflector--slightly elevate the feedpoint resistance. However, the front-to-back ratio will be sustained. Hence, moving toward an equality of feedpoint reactances appears to best equate the altered array with the original.

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As we noted in the first test, there is a slight offset between the calculated value of capacitive reactance and the value required for the best level of equality, even with an appreciable stub length. The 2 Ohm differential is well within the range of practicality, but once more suggests that when implementing any hybrid stub, a variable capacitor best serves the needs of initial testing.

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Despite the use of a hybrid stub, the resulting pattern shows no aberrations. Fig. 8 overlays the free-space E-plane patterns for the original and the modified arrays using the -35 Ohm option.

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Test 2: Controlling a Wire Yagi Director

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Let's turn the tables and create a driver-director Yagi using a near-resonant driver and a director of the same length, as shown in Fig. 9. To function as an effective director, we shall have to add capacitive reactance as a director load. For the free-space operating values in the following table, I added a load of -60 Ohms to the director.

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Gain (dBi)            Front-to-Back         Feedpoint Impedance
+                      Ratio (dB)            (R +/- jX Ohms)
+5.85                  22.28                 22.16 + j 1.188
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Now let's add to the director a shorted stub with an inductive reactance of 60 Ohms. Using our #14 wire and 3.96" spacing, our line has a Zo of 577.6 Ohms, calling for a stub length of 4.50'. Theoretically, we must now increase the loading capacitor (at the stub short) to -120 Ohm capacitive reactance. The following values emerged from the exercise.

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Cap. Xc          Gain       F-B Ratio       Feedpoint Impedance
+(Ohms)           (dBi)      (db)            (R +/- jX Ohms)
+-120             5.87       18.58           20.12 + j 3.626
+-124             5.80       21.85           22.37 + j 1.392
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Although the use of the theoretically correct value best preserves array gain, it results in off-target values for the front-to-back ratio and the feedpoint impedance. One of the benefits of using a driver-director array as a test vehicle is that the closely spaced elements exhibit a narrower passband than a driver-reflector array. Hence, smaller changes in component values yield larger changes in performance.

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Increasing the capacitive reactance by 3% restores virtually all of the array performance except for that small amount lost in the resistivity of the stub wire. Once more, the implementation of a hybrid stub would require a variable capacitor for initial testing before replacing the unit with a fixed value. (Of course, one might retain the variable capacitor and remotely tune it to maximize array performance over a wider frequency range than would be possible with a fixed capacitor.)

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The version of the array using the stub and -124 Ohms of capacitive reactance performs in practical terms as well as the original array. Fig. 10 overlays the free-space E-plane patterns for this version and the original array as a demonstration of the operational equivalence of the two designs.

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A Special Note on Modeling Hybrid Stub Systems

Throughout these exercise, I have used a stub composed of wires. This practice placed some restrictions on the ultimate precision of the results relative to standard calculating means for determining stub lengths. Although the wire stubs correlate very closely the calculated lengths and the NEC-4 analysis, there may be slight alterations in the results of the model due to small differences in the calculation means and the presence of the shorting wire in the model. Hence, there remains a small (operationally insignificant) ambiguity as to the source of the difference between values calculated using classical equations and those introduced by trial and error into the model. +

However, using wire stubs is necessary. The NEC TL facility for creating non-radiating transmission lines cannot be directly employed for the exercise. Ideally, the TL facility would permit the use of any diameter element and would remove the wire losses of the stub from consideration when evaluating the results. (However, those losses are real and a designer must account for them when constructing an actual array using stubs.)

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Fig. 11 shows why the TL facility is not apt to the present task. The models require that we place a load on the stub terminating wire. With wire stubs, the load is centered within the wire space with the parallel lines terminated at the wire ends. However, loads are always in series with transmission lines created by the TL facility of NEC. As a result, a load added to the wire used to terminate a stub would actually fall outside the lines making up the stub itself.

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There are means of placing a load on the terminating wire in series with the terminals. However, not all implementations of NEC permit its use. We may specify admittance values (called real and imaginary for the more common terms of conductivity and susceptance) at the TL termination. Susceptance is simply the inverse of reactance. Hence, it is possible to load a transmission line in some implementations of NEC.

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The use of such terminating loads is always in terms of admittance and never in terms of capacitance or inductance. Consequently, the values are applicable to one select frequency and do not vary with changes in frequency, as do LD-type loads specified in terms of capacitance and reactance. Since admittance loads at the terminations of TL transmission lines are not commonly used by beginning modelers, I have not used them in this exercise, but have let the ambiguities stand.

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Applications

There are numerous applications for hybrid transmission line stubs. The following sample only begins the creative search for uses where the hybrid stub may prove more useful than some alternative means of implementing reactances in antenna arrays. +

1. Reversible wire arrays: Consider a 3-element parasitic array with identical lengths for the elements. In most cases, the reflector will require a shorted stub to optimize its electrical length. The director will require an open stub to optimize its length. Assuming, of course, that we choose to use stubs for this work.

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However, we have an alternative. Let's use hybrid stub systems throughout. We may lengthen the reflector stub by an amount od reactance equal to the minimum reactance available from a capacitor (or system of paralleled capacitors), plus a bit more. Then we may use the capacitor to reduce the net inductive reactance and possible to tune the reflector.

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We may also treat the director similarly, by using a shorted stub equal to the capacitors minimum reactance and then adding capacitive reactance in the amount necessary to tune the director for optimal array performance.

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If we choose to do so, we may lengthen each stub by 1/2 wavelength with no change in the tuning range of each variable, thus placing the variable components near to ground level for easier weather protection. However, we must take into account the added losses of the longer stub lines when evaluating the aptness of these design moves. Line losses from the system may be acceptable at 160 or 80 meters, but they may become excessive in the upper HF range.

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Reversing the array is a simple matter if the lines extend to a central location. We may simply switch the director and reflector capacitors, including in the reflector side that added line length for that operation. At 160 meters, such a tunable/switchable system may permit a doubling of the normal operating passband with wire beams--and permit the user to achieve a higher front-to-back ratio away from the initial design frequency.

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2. Positioning a loading component: A length of shorted transmission line stub in conjunction with a capacitive loading element can be used to electrically lengthen an antenna element. As well, proper selection of the line length and the capacitor reactance hold two advantages. For a fixed capacitor termination, we may change the electrical length of the element simply by changing the capacitor. As well, we may run both the capacitor and stub within the physical element, thus using the ready weather protection offered by the element. My old GAP VI appears to use just this sort of system to achieve a narrow-band 80- or 75-meter resonance.

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3. Tuning a short monopole: Most vertical monopoles for 80 and especially 160 meters are shorter than 1/4 wavelength. Hence, tuning them for optimal operation involves one or more of a number of techniques to overcome the low feedpoint resistance and rapidly changing feedpoint reactance. The complexity of some tuning systems is a wonder to behold.

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Fig. 12 shows an alternative system that applies to monopoles longer than 1/8 wavelength and shorter than 1/4 wavelength. We shall explore that restriction in a moment. Let us use a system by which we can establish resonance across one of the lower ham bands.

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Over the range of 160 meters, a 1/8 wavelength monopole changes its resistance by only abut 2 Ohms or so. Hence, if we could control the reactance, we might use a fixed network to match the low feedpoint impedance to a standard 50-Ohm coaxial cable. Such fixed networks are normally more weather durable than networks requiring the remote tuning of variable components--assuming that both are assembled within equally weather-resistant packages.

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Instead of using a loading coil or other means of electrically lengthening the radiator, let's use a hybrid stub system. With the correct combination of line length and capacitors, we can alter the inductive reactance at the monopole by wide amounts--and take into account the potential shifts in frequency. The line length--alone or plus multiples of 1/2 wavelength--might even permit the capacitor system to be indoors with the operator.

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There are some restrictions in the use of this type of system. For shorter monopoles, we require stub lengths providing higher values of inductive reactance. Stub lengths close to 1/4 wavelength show rapid changes of reactance with small changes of length. (Remember that stub length is a tan function, which goes to an indefinitely high value at exactly 1/4 wavelength.) Indeed, working with lengths close to 1/4 wavelength at the lowest frequency of use may result in a line already longer than 1/4 wavelength at the highest used frequency. Hence, keeping the required inductive reactance as low as may be practically possible gives the system more flexibility. One way to do this is to increase the monopole height well above the 1/8 wavelength point.

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As well, the capacitor tuning system requires calculation of its reactance span for both the lowest and highest frequencies of use, and these values must be correlated with the basic stub length to ensure that the capacitors will have sufficient range to tune the antenna across the entire span of frequencies to be used.

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If one can live within these restrictions, then there is an added advantage to the system. Tuning need only locate the lowest SWR point, given the fixed network at the antenna base. The fixed network may use the lowest working Q obtainable for maximum efficiency. Despite the losses in the stub line, the hybrid system is likely to have lower losses than most (but certainly not all) other means of electrically lengthening the antenna.

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These sample applications only scratch the surface of the potential for hybrid transmission line stub systems. You may already know of others.

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At root, however, this exercise has aimed at better understanding and properly modeling the hybrid transmission line stub system.

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Updated 05-01-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Matching, Reversible, Transmission Line


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Transmission-Line and Tuner Calculation Aids

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L. B. Cebik, W4RNL

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There are numerous aids for the antenna builder to help him or her calculate what will happen along the transmission line from the antenna to the shack and within the antenna tuner inside the shack (or, remotely speaking, at the base of the antenna or its support). Since most of the utility programs are free for the download, they are readily accessible. Still, many antenna system builders do not make use of the resources available. Perhaps a review of some of the most common programs might be useful as an introduction that will encourage their use.

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We shall proceed in two steps. First, the most common transmission-line programs are TLW from the ARRL's Dean Straw, N6BV, and TLD from Dan Maguire, AC6LA. They form a nice pair to compare and contrast. Then there are network matching programs. We shall sample 3 programs that differ in how they proceed.

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Transmission-Line Programs: TLW and TLD

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If we have a transmission line between an antenna and the shack (which we shall sometimes call the "measuring point") there is only one condition under which we know with reasonable precision the impedance at the shack end of the line. That condition is where the antenna feedpoint is perfectly matched to the line that we are using. Even then, unless we have hand-calculated the figure, we do not know the line loss at the frequency we are using. Most often, we do not have a perfect match between antenna and feedline, and every bit of difference between the line and the antenna increases our uncertainty about the impedance at the measuring point.

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However, every condition that we can throw at the antenna-end of the transmission line can be calculated all along the line. This includes not only the impedance changes along the line, but the losses as well--and the effect those losses have on the impedance that appears at the shack end. The equations have been around for a long time, and Terman's Radio Engineers' Handbook (McGraw-Hill, 1943) has versions of the equations for both lossy (normal) and lossless lines. The latter equations are simpler to implement and use, but the former represent reality much more closely. So the programs that we need to use calculate for lossy lines.

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One of the more common programs is TLD (Transmissioon Line Details) by AC6LA. You can obtain a copy at no cost by visiting Dan's web site (www.ac6la.com/tldetails1.html). Fig. 1 shows the main screen of TLD.

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What you input is only a part of what the screen shows, with the rest calculated by the program. You may select one of the common lines available commercially from a long list of options. The list of lines includes the characteristic impedance (Zo), the line velocity factor (VF) and the loss figures, given in TLD as K1 and K2 values. You will enter the length of the line in either a common unit of measure (for example, feet or meters) or in wavelengths. Of course, you will also enter the frequency of concern, since transmission line losses and transformations vary with frequency. If you need to make some conversions either before or after the program does its work, you may go to the conversion screen, shown in Fig. 2. You will also enter the load impedance in series resistance and reactance values. You may set the power input (at the shack end of the line). The program does the rest.

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The upper part of the screen toward the right shows the matched loss of the line shown--for RG-8X and 30 MHz, 5.398 dB/100 m. The losses of the 5-m line we are using are 1/20 of that value.

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Perhaps the greatest amount of information appears in the lower part of the main screen. The program attempts to place as much information on a single screen as possible. At the lower left, we have tables of values for both the source and load ends of the line. Both columns appear, not only to give us SWR values, but as well because we had a choice when setting in the impedance values earlier: they can be the antenna feedpoint values or the set of values measured at the shack-end of the line.

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Note the 2 SWR entries. The upper entry is relative to the Zo of the line, listed at the bottom of the table. The second SWR value is relative to a resistive impedance that we set into the box below the Smith Chart graph in the lower center region of the screen. To the right of the Smith chart, we find a pair of loss columns, one calculated in terms of dB and the other based on the power that we set into the box in the upper screen half. TLD calculates separate values for the losses due to the finite conductivity (mostly of the center conductor of a coax cable but of both conductors of a parallel line) and due to the finite resistivity of the cable dielectric that separates the conductors. In addition, if the line has more than zero-length and we do not have an exact match between the load and the line, there will be added losses due to the effects of SWR, that is, due to the peak voltage and current values that appear along the line. To save you from calculating the percentage of loss due to each factor, the lower right corner of the TLD screen contains a bar graph calibrated to yield the percentage of loss due to each factor.

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We can change any of the input values according to the needs of our investigation. For example, we can compare the losses for a specific length of line using RG-8, RG-58, RG-8X, RG-213, and some of the commercial low-loss lines, all by a simple change in the line selection. Even though these are all nominally 50-Ohm lines, we can track the differences in actual characteristic impedance values as we change lines. Many other exercises are equally easy to implement. In addition to coaxial cables, the list of options includes some typical parallel lines.

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If we wish to survey the conditions along a length of line, we might wish to try TLW (Transmission Line Program for Windows). The program comes with the current edition (20th as I write) of the ARRL Antenna Book on the enclosed CDROM. Fig. 3 shows the main screen for TLW.

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The data that we need to supply is essentially the same as for TLD: line selection; length in meters, feet, or wavelengths; frequency; and impedance as series resistance and reactance values. Note that we can specify the impedance for calculation as either the impedance at the load end of the line or at a given measuring point. Since this screen calculates only in dB, we do not need to specify a power level, although we shall later do so when we explore the "tuner" calculations available to us.

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The program revises the line characteristics and the other calculations as we revise any of the input entries. And now we may compare the results between TLD and TLW. For the screen grabs, I supplied both programs with load values of 300 + j100 Ohms and selected RG-8X, using the Belden version of the line. Both line lengths are 5 meters at 30 MHz. However, TLD gives us a shack-end impedance of 23.28 - j61.63 Ohms, while TLW shows 19.36 - j51.65 Ohms. As well, TLD shows a total line loss of 0.742 dB, while the corresponding figure in TLW is 0.854 dB.

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Where do the differences come from? What do they mean?

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There are differences in the way each program arrives at its final values. However, those difference, whan applied to half wavelength perfect lines, result in differences that are under 0.2%. The major differences occur with respect to the input data cataloged by the program. Note first the difference in velocity factor between the two programs. That small 0.02 difference results in TLW showing a much closer coincidence to TLD values (or vice versa) when the TLW line length increases to 5.1 m. There are also differences in the calculation of matched line losses between the two programs: 5.398 dB/100m vs. 6.320 dB/100 m. There is even a small difference in the listed Zo of the Belden RG-8X: 50.0 - j 0.405 Ohms vs. 50.1 - j 0.47 Ohms. Hence, even using identical calculation procedures, the results would differ.

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The important question for the user is whether these difference make a difference? The answer in most cases is "No." Cable specifications represent optimal values given by the manufacturer, and may differ from one batch of cable to the next over a small range. If we change the maker, then the range of difference may be considerably larger. I have measured the VF a non-Belden RG-8X cable as 0.72, which is far from the value used in either program. Perhaps the most divergent figure for the RG-8X cable used in the example is the matched-line loss value.

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The upshot of these considerations is that the seeming exact values calculated by the programs are subject to real-world variables, mostly of cable manufacture. (Further deviation between calculations and measurements may also occur due to cable age and conditions of storage, which are user responsibilities.) Calculations within either TLD or TLW are highly useful for study, planning, and designing, but in the end must give way to measurements and adjustments based on those measurements.

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For study and planning, TLW has two graphing features that are highly useful. Fig. 4 shows the voltage and current graph that allows you to determine where along the line the peak values occur. Note that I set the power at 1000 watts for both programs for the exercise. The peak voltage with the given load is about 527 Vrms, while the peak current is 10.5 Arms. The peak current on the RG-8X relatively thin center conductor is, of course, a matter of concern, and a more robust cable would normally be used at the frequency and power level of the exercise.

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Fig. 5 shows the alternative graph that plots the resistance and reactance along the 5-meter length of transmission line. As in the voltage/current graph, the load end of the cable is at the right, with the transmitter (or tuner) on the left. The line is about 5/8 wavelength. For each half wavelength of the line, notice the length of line over which the resistive component takes on a very low value. As well, notice the reduction in the peak values of both resistance and inductive reactance closer to the source end of the line compared to the comparable values at the load end of the line.

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TLW also permits the user to specify a line, such as the one shown in Fig. 6. The screen calls for a relatively complete set of specifications, even for the perfect 450-Ohm line shown here. Proper specification of a line requires not just a resistive impedance, but as well, a reactive component, if there is one. It also calls for a frequency of operation and the attenuation per unit of line, here 100 m. Of course, a velocity factor is mandatory, since even ladder line with only periodic spacers shows a value less than 1.0. As well, every line has a maximum voltage rating that depends on many factors.

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The line shown on the sample screen is a perfect 450-Ohm line, that is, a line with no reactance in its Zo, no losses, and a velocity factor of 1.0. Interestingly, when such a line is plugged into TLD at 30 MHz, a load of 2000 - j 2000 Ohms returns the same values at a distance of 1/2 wavelength. In TLW, the calculation process returns 1994.87 - j 1999.86 Ohms for the same initial conditions. The difference is too small to make a difference and is noted simply to show the difference in the calculation procedures for the two programs.

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These notes have not covered all of the program features. For example, both programs either show or give an option to show the reflection coefficient as an alternative to the SWR value that amateurs so commonly use. TLD has loss values applicable to the Sonata suite of engineering modeling programs, and it provides a graph of matched line losses for a wide range of frequencies. TLW has calibrated results based on noise-bridge or Autek antenna analyzer measurements. The unique features of each program justify having both available for ready use, especially since they come at essentially no cost (or, in the case of TLW, at no extra cost).

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Clemens Paul, DL4RAJ, has reminded me that there is a free on-line program (Transcalc) by Kevin Schmidt, W9CF, at his website: w9cf.github.io . Although the program notes that it uses a number of features from TLW, the calculation procedure appears to resemble more the one used by TLD in terms of results from specifying lossless or perfect lines. TLD does not calculate SWR's above 999, but Transcalc does. Additionally Transcalc shows graphically what is happening along the line like TLW, and also has a zooming feature. The W9CF applet contains instructions for downloading two files that together allow storage of the program locally for use with your browser in the off-line mode. For offline use of Transcalc with newer Windows versions (such as XP), you have to download the (free) MS virtual machine or the java plug-in from Sun. For basic transmission-line calculations and a graph of voltage, current, and power along a long length of line, the W9CF program can be very useful as an alternative to the ones reviewed in these notes.

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Tuner Analysis

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The analysis of antenna tuners is at root the analysis of networks effecting an impedance match between a user-specified load impedance and either a given or user-specified source impedance. Most usually, the source impedance (Rin) is 50-Ohm resistive. However, the load impedance may be complex.

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Programs vary in how many networks they include. For example, TLW includes the most common networks used in tuners used by radio amateurs: the low- and high-pass L, the low-pass (CLC) PI, and the high-pass (CLC) T. A suite of utility programs by Brian Eagn, ZL1LE, adds the low-pass (LCL) T as well as a collection of 2-element networks. A more general program called the "Impedance Matcher" includes a total of 16 networks, including a number of "double Ls" (which may go under different names in other contexts, such as the PI-L sometimes used in power amplifier design).

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We shall examine briefly the 3 programs noted, but not because they vary in the number of networks offered. Rather, each program begins its calculations at a different point, and these differences are notable in terms of the responsibility they place on the user.

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Network analysis begins with two sets of numbers besides the impedances to be matched. For convenience, the sample load (Zout) will always be 300 + j 100 Ohms, and the input impedance (Rin) will be 50 Ohms. One additional set of figures is the unloaded or component Q (or Qu) of the capacitor(s) and inductor(s) in the network. For the purposes of this survey, inductor Qu will be 250, and capacitor Qu will be 5000. Each of those values will vary according to the component quality and to the circumstances of use. With a roller inductor or a tapped coil, the Q may vary widely over the frequency range as the ratio of coil length to coil diameter changes, and the contribution to inductance of the leads rises with frequency. The component Q-values that I have chosen are generous.

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The other figure of importance is delta (as defined in Terman). Where available, the Greek letter uses the lower case. To avoid finding a lower case delta on a keyboard, the term now has a variety of names, all using the letter Q: effective Q, loaded Q, network Q, and operating Q, to name a few. Vacuum-tube amplifier output PI networks tend to use delta values around 10-12, while solid-state amplifiers aim for values closer to 1. The value of delta makes a difference to tuner losses. In general, power lost/power delivered to the load is equal to delta/Qu (where for first order approximations, one might use the Qu of the inductor). Therefore, network efficiency as a percentage equals 100 * (1 - delta/Qu). Therefore, the higher the component Q and the lower the delta, the more efficiently the tuner will transfer power from the source to the load. (The load, of course, is usually a system that includes an antenna plus a transmission line, and the line--as we have seen--may have losses of its own.)

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One factor not included in network calculations is the fact that for very low values of delta, the settings of components for a perfect match to a 50-Ohm source and the settings for maximum power transfer may differ slightly. When delta is greater than about 10, the differential is virtually undetectable. However, when delta drops down to the 1-3 range, those settings may differ by amounts detectable from variable component settings. (See Chapter 6 of recent editions of The ARRL Handbook for more on this phenomenon in parallel tuned circuits.) Because most tuners do not include relative output indicators, most users settle for a perfect impedance match rather than for maximum power transfer. Nevertheless, the most ideal tuner component values are those that yield the lowest value of delta.

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TLW includes--besides the transmission-line analysis--a supplementary module for tuner analysis. The module is based on the older DOS program, AAT. In the TLW context, it uses for its impedance input the values calculated for the source end of the transmission line. However, if you wish to directly input a value, just specify any transmission line with a length of zero. Then the load impedance from the main screen will also appear at the load terminals of the network.

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Fig. 7 shows the tuner selection screen, with its options. The power setting also applies to the main page. The component Q values are the default values, although for this exercise, we have altered them. As well, the selections provide a value for stray capacitance at the network output, using a default value of 10 pF. In the following exercises, I have reduced this value to zero so that calculations among programs will correlate to the degree possible. However, for practical tuner analysis, the stray capacitance value can be very useful, especially when looking at the performance of a given tuner on the 12- and 10-meter bands, where 10 pF is a large percentage of a network's output capacitance.

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The calculations for high-pass (Cs-Lp, where Cs is a series capacitor followed by Lp, a parallel or shunt inductor) and low-pass (Ls-Cp) L networks are quite standard. Fig. 8 shows both screens for a tuner load impedance of 300 + j100 Ohms. If we first calculate the delta (or effective Q, in this program), then there is only one set of component values that will meet that delta calculation and still yield a match to the 50-Ohm input.

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TLW, as shown in Fig. 7, allows matching calculations for only 2 other tuner networks in common use: the low-pass (Cp-Ls-Cp) PI and the high-pass (Cs-Lp-Cs) T. Fig. 9 shows the calculations for both of these networks for the specified conditions. It also shows the approach taken to solving the requisite equations for these networks.

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Note that each network has an output-side capacitor whose value is an integer. For each network, the user must select the value of that component, and the program completes the calculations, including deriving the delta or effective Q of the network. If the goal is the most efficient transfer of power, then the user must try different values for the output-side component until the effective Q value reaches its lowest value. The required value may not be the highest or lowest value for which there is a solution to the network equations. For example, output capacitance values between 35 and 45 pF all calculated a delta of 1.6 for the high-pass T network. However, there may be values for which there are no solutions, and the program prompts you for a different value.

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A program that takes quite a different approach to the calculations is known as Impedance Matcher (or more correctly, as Impedance Matching Network Designer). This program is a scripted on-line calculator, but you may download the entire file, with its subdirectory of graphics, and run the program locally on your browser. The URL is bwrc.eecs.berkeley.edu/Research/RF/projects/60GHz/matching/ImpMatch.html (web.archive.org). The script covers 16 networks, of which Fig. 10 shows the most common ones used in amateur antenna tuners.

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The page shows only solutions for the low-pass and high-pass L networks. The reason for this condition is the required input data. Besides the input and output impedances and the frequency (in basic units), the user must supply a target value for delta called the Desired Q in this treatment. The value prescribed is 2.0. The L network calculations provide the values for the closest value of desired Q, but the other networks make use of the specified Q. Hence, they have no solutions. There are solutions for a delta of 2.4, and we shall shortly look at them in comparison with the values produced by the other programs.

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Fig. 11 shows the remainder of the single long page of possible networks in the program. For a desired Q of 2.0, there are some solutions among the "LL" circuits, although we normally do not find these in antenna tuners. However, all of the more complex matching networks have places in solid-state amplifier designs and in numerous other applications.

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So far, we have looked at two approaches to network calculations. For networks having 3 components, TLW has the user specify the output-side component value and search for the lowest delta. Impedance Matcher has the user select a desired Q and then adjust that value until the program provides a solution in terms of component values. There is a third route to network solutions, the one used in one of the GW Basic HamCalc suite of utilities. You can find the latest version of Hamcalc at www.cq-amateur-radio.com/HamCalcem.html (web.archive.org). In the index, find the program called Transmatch Design by Brian Egan, ZL1LE. Because Basic screens do not register as graphics on my operating system, we shall have to content ourselves with text-grabs from those screens.

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The calculations for L networks (called Ladder networks in the program) generally do not stray far from the techniques used in the other programs. The following example of a low-pass L (Cs-Lp) makes that clear. We begin by entering the required input data, and the program specifies which type of network will provide a solution. Note that the components are specified simply as reactance positions. The program will not only provide solutions involving the usual cases in which we have a series reactance of one type and a shunt reactance of the other type. There are conditions of load impedance that may require series and parallel reactances of the same type. However, we shall not encounter them with our simple 300 + j100 Ohm load transformed to 50 Ohms resistive. The text-grabs will not reproduce the special characters used to show some of the network diagrams (created by HamCalc's master, George Murphy, VE3ERP). Still, you likely can infer what goes where. R1 always refers to the input impedance and R2 and X2 refer to the output or antenna-side impedance.

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+                   2-ELEMENT LADDER MATCHING NETWORK PROGRAM
+---------------------------- by Brian Egan, ZL1LE ------------------------------
+    TYPE 'A' LADDER NETWORK               TYPE 'B' LADDER NETWORK
+
+      o--- Xa ---------o                    o--------- Xa ---o
+                 |                                |
+      ---»       Xb   ---»                  ---»  Xb       ---»
+      R1         |   Load                   R1    |        Load
+       ----------------                      ----------------
+-------------------------------------------------------------------------------
+                   +------------------------------+
+                   |  NETWORK DESIGN PARAMETERS:  |
+                   +------------------------------+
+
+1.   ENTER frequency of operation in MHz:   30
+2.   ENTER value of input resistance, R1, in ohms:  50
+3.   ENTER value of load resistance, R2, in ohms:   300
+4.   ENTER value of load reactance, X2, in ohms:    100
+
+-------------------------------------------------------------------------------
+a TYPE A network is required to match prescribed source and load.
+-------------------------------------------------------------------------------
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The network requires a Type A network, but it has two forms, as shown by the following grabs of the solutions.

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+                   2-ELEMENT LADDER MATCHING NETWORK SOLUTIONS
+-------------------------------------------------------------------------------
++------------------------------------------------------------------------+
+| DESIGN PARAMETERS:                           LOAD SWR  =   6.68        |
++------------------------------------------------------------------------|
+| Frequency (MHz)    =    30           Load Resistance  =  300.0 _       |
+| Source Resistance  =    50.0 _       Load Reactance   =  100.0 _       |
++------------------------------------------------------------------------+
+-------------------------------------------------------------------------------
+    SOLUTION 1.              o--- Ca ---------o
+    ----------                          |
+Ca (pF) =   44.6             ---»       Lb   ---»
+Lb (uH) =  0.864             R1         |   Load
+delta   =  2.05               ----------------
+-------------------------------------------------------------------------------
+    SOLUTION 2.              o--- La ---------o
+    ----------                          |
+La (uH) =  0.631             ---»       Cb   ---»
+Cb (pF) =   43.2             R1         |   Load
+delta   =  2.38               ----------------
+-------------------------------------------------------------------------------
+
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The differences between the ZL1LE approach and the others that we have encountered show up once we work with 3-component networks. Let's begin with the low-pass PI (Cp-Ls-Cp). In the text-grab below, the component graphics do not show correctly. As well underlines appear instead of the omega for Ohms and the delta for the effective or network Q.

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+                         PI-COUPLER TRANSMATCH DESIGN
+--------------------------------------------------------------------------------
+                                       L
+                          R1 »-------_____-------» RL
+                          input  |           |   load
+                                -+- C1      -+- C2
+                                 |           |
+                           grnd ///         ///
+--------------------------------------------------------------------------------
+        Transmatch Input Impedance R1................   50.00 _
+        Load Resistance RL...........................  300.00 _
+        Load Reactance...............................  100.00 _
+        Frequency....................................   30.000 MHz
+        Inductor L...................................    0.684 uH
+        SWR..........................................    1:1
+ SOLUTION 1:  ( _[delta] = 2.9 )
+        Capacitor C1.................................   35.72 pF
+        Capacitor C2.................................   45.64 pF
+ SOLUTION 2:  ( _[delta] = 3.1 )
+        Capacitor C1.................................   46.57 pF
+        Capacitor C2.................................   47.27 pF
+--------------------------------------------------------------------------------
+
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Note that the inductor value appears above the section of the screen devoted to solutions. The reason for the placement is that the program first calculates the maximum value of inductor, in this case 0.685 uH. Due to rounding, the program may not always accept this value as the user input, and so, as shown above, you must select a notch lower than maximum. The procedure has two goals. First, it allows direct calculation to the lowest feasible value of delta--2.9 in this case. However, that goal must also coincide with the derivation of multiple solutions, if they exist. Hence, in some case, you may be able to adjust the value of the networks required component input value and arrive at one of the two solutions with a marginally lower value for delta.

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Transmatch Design also provides calculations for the low-pass T (Ls-Cp-Ls), an underused but effective tuner network. In this case, the program pre-calculates the minimum value for the input-side inductor. In the following text-grab, you will find that I had to replace the minimum 0.631 uH value with 0.632 uH.

+ 
+                         LOWPASS TEE TRANSMATCH DESIGN
+--------------------------------------------------------------------------------
+                                  L1       L2
+                          R1 »---____-----____---» RL
+                          input        |         load
+                                      -+- C
+                                       |
+                                      /// grnd
+--------------------------------------------------------------------------------
+        Transmatch Input Impedance R1................   50.00 _
+        Load Resistance RL...........................  300.00 _
+        Load Reactance...............................  100.00 _
+        Frequency....................................   30.000 MHz
+        Inductor L1..................................    0.632 uH
+        SWR..........................................    1:1
+ SOLUTION 1:  _[delta]=  2.4
+        Capacitor C..................................   43.20 pF
+        Inductor L2..................................    0.00 uH
+ SOLUTION 2:
+        No second solution
+--------------------------------------------------------------------------------
+
+

For this network, there is only one solution, and the value of delta is quite in line with values that we have seen for other networks. Hence, despite the erroneous impression that "too many" inductors will ruin tuner efficiency, the value of delta tells a different story. However, note that for the matching condition specified, the output inductor goes to zero. The result is an L-C-L T that is effectively a low-pass L network.

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In his original formulation of the high-pass T (Cs-Lp-Cs) network calculations, ZL1LE used equations comparable to those used for the other 2-component networks. However, he revised his calculations following the QEX article "Estimating T-Network Losses at 80 and 160 Meters" by Kevin Schmidt, W9CF (July, 1996). [This article is often mis-referenced as appearing in July, 1997.] For further notes on this network, see "Understanding the T-tuner (C-L-C) Transmatch" by William E. Sabin, W0IYH, QEX (December, 1997).

+

ZL1LE's re-formulation of the high-pass T calculations now yield a table of values based on the inductor Q values.

+ 
+ HIGH-PASS TEE TRANSMATCH (with finite Q inductor)
+--------------------------------------------------------------------------------
+
+                        Input >---|+---------|+---> Load
+                                  C1    |    C2
+                                  +_____+
+                                  |  L
+                                \\-\\
+
+--------------------------------------------------------------------------------
+ ENTER: Input impedance in ohms......? 50
+ ENTER: Load resistance in ohms......? 300
+ ENTER: Load reactance in ohms.......? 100
+ ENTER: Frequency in MHz.............? 30
+--------------------------------------------------------------------------------
+
+ HIGH-PASS TEE TRANSMATCH (with finite Q inductor)
+--------------------------------------------------------------------------------
+ DESIGN PARAMETERS:| R1=  50.0 _| RL= 300.0 _| XL= 100.0 _| Freq.=  30.000 MHz
+--------------------------------------------------------------------------------
+                      TABULATION OF TRANSMATCH PARAMETERS
+         +-----------------------------------------------------------+
+         |    Q    |  L(uH)  |  C1(pF) |  C2(pF) |Loss (dB)| Eff.(%) |
+         +---------+---------+---------+---------+---------+---------|
+         |Infinite |  0.699  |   47.4  |   47.1  |  0.00   |  100.0  |
+         |   250   |  0.680  |   47.4  |   40.2  |  0.04   |   99.0  |
+         |   200   |  0.677  |   47.4  |   39.2  |  0.05   |   98.8  |
+         |   150   |  0.673  |   47.4  |   37.8  |  0.07   |   98.4  |
+         |   100   |  0.665  |   47.4  |   35.6  |  0.11   |   97.6  |
+         |   50    |  0.649  |   47.4  |   31.3  |  0.22   |   95.0  |
+         +-----------------------------------------------------------+
+--------------------------------------------------------------------------------
+
+

Using the values for an inductor Q of 250, we can back calculate the value of delta at 2.4. The ZL1LE calculation procedure aims directly at the lowest feasible value of delta to produce component values capable of maximum power transfer. In tuners--but not in all applications of networks--this is the user's goal in setting variable components.

+

We should pause to examine a significant question apart from the procedures necessary within each program to yield component values for the lowest feasible value of delta. The question is simply a matter of whose calculation to believe. To point toward an answer--without necessarily arriving at a final decision--let's catalog the values for networks where at least 2 of the programs produce solutions. We can work through the networks in order, remembering that in each case, the design frequency is 30 MHz, the source impedance is 50 Ohms resistive, and the load impedance is 300 + j100 Ohms. The inductor Qu is 250 and the capacitor Qu is 5000, wherever those figure may play a role in the calculations. You may calculate the efficiency and the loss from the equations with which we began these tuner network notes.

+ 
+1.  High-Pass (Cs-Lp) L Network
+Parameter         TLW             Imp. Matcher        Trans. Design
+Cs (pF)           44.8            44.6                44.6
+Lp (uH)           0.86            0.863               0.864
+delta             2.4             2.38                2.05
+
+

The only difference among the 3 is the Transmatch Design calculation of the delta value. However, the difference results only in a 0.2% change in efficiency, an amount that would not be detectable by ordinary means of measurement.

+ 
+2.  Low-Pass (Ls-Cp) L Network
+Parameter         TLW             Imp. Matcher        Trans. Design
+Ls (uH)           0.63            0.631               0.631
+Cp (pF)           43.4            43.2                43.2
+delta             2.4             2.38                2.38
+
+

So far, we have nothing to choose relative to the 3 programs. Perhaps there will be some significant differences among the 3-component networks.

+ 
+3.  Low-Pass (Cp-Ls-Cp) PI Network
+Parameter         TLW             Imp. Matcher        Trans. Design
+Cp (pF)           17.2            37.8                35.7     46.6
+Ls (uH)           0.66            0.684               0.684    0.684
+Cp (pF)           44.0            45.9                45.64    47.27
+delta             2.7             2.40                2.90     3.10
+
+

The Transmatch Design double solution values bracket those produced by Impedance matcher. Although the TLW values appear on the surface to be more distant, note the 11 pF spread between the two Transmatch Design solutions. The TLW input capacitor value is not so far out of range as it may seem, when we consider that for low values of delta, tuning is often very broad. Had I chosen a different output capacitor value, the input capacitor value would have come into closer alignment without unnecessarily disturbing the value of delta. Again, a few tenths difference in delta will make no significant difference to the tuner's efficiency.

+ 
+4.  Low-Pass (Ls-Cp-Ls) T Network
+Parameter         TLW             Imp. Matcher        Trans. Design
+Ls (Ls)           ----            0.636               0.632
+Cp (pF)           ----            43.3                43.2
+Ls (uH)           ----            0.036               0.0
+delta             ----            2.40                2.40
+
+

Once more, there is no significant difference between the two programs that provide results for the low-pass T network.

+ 
+5.  High-Pass (Cs-Lp-Cs) T Network
+Parameter         TLW             Imp. Matcher        Trans. Design
+Cs (pF)           47.6            44.2                47.4
+Lp (uH)           0.69            0.651               0.680
+Cs (pF)           45.0            ----                40.2
+delta             1.6             2.40                2.40
+
+

The anomalous solution to the C-L-C T appears in the Impedance Matcher program. In the output capacitor value box, it lists "NaN," indicating that there is no calculable value. Varying the desired Q over a wide range makes no difference to that solution box. In contrast, the values produced by TLW and Transmatch Design are closely coincident, despite the difference in the calculated value of delta. (After I wrote this item, TLW incorporated revisions that should eliminate differences in the calculation of delta.)

+

In the end, there is little to differentiate the final calculations among the 3 styles of network calculation programs. The main differences lie in the approach to the calculations. For network calculations that aim directly at the lowest feasible value of delta, perhaps Transmatch Design is the most straightforward. However, its GW Basic format is far less convenient than the Windows format used by TLW.

+

In addition, TLW provides extensive information about probable component losses as well as the total tuner loss. It also supplies the peak voltages across capacitors and the RMS current through inductors--for the power setting chosen--as a guide for safe design or use of the tuner. Consequently, as a package, TLW may be the most complete tuner analysis program around, even if the user must fish a bit to arrive at the lowest effective Q or delta.

+

Since the three programs are no cost items (or for TLW, a no-cost extra), you can afford to have all of them available in order to use each where it may be strongest. As well, both TLD and TLW provide complementary coverages of transmission-line analyses at no cost to the user. In essence, then, we have a suite of calculation programs that can go a long way toward giving us a complete picture of what is occurring electrically between the antenna feedpoint and the transceiver input/output. What the birds and weather may be doing to the system is another matter entirely.

+
+ +
+

Updated 01-01-2005. © L. B. Cebik, W4RNL. This item first appear in antenneX for December, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Matching, Transmission Line


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+

Notes on a Wide-Band 50/75-Ohm Coax Feed System for Low HF Band Dipoles and Vees

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Back in 1997, Dave Leeson, W6NL, brought to my attention an interesting technique for achieving wide-band operation on the lower HF bands, especially the 80/75-meter band. The technique derived from mentions in texts and from references in ARRL publications by Frank Witt, AI1H, a noted experimenter and evaluator of low-HF broad-banding methods. Suppose that we have two desired operating frequencies, one in the 80-meter CW portion of the band and the other near the upper end of the 75-meter SSB portion of the band. A normal dipole would provide a single SWR minimum and would reach high values of SWR at the band edges. Alternatively, we might select one or the other end of the band and possibly use an antenna tuner to work the other band edge.

+
+ +
+

The broadbanding method begins by selecting the geometric mean between the two desired frequencies (that is, the square root of the product of the two frequencies). Suppose that we cut a dipole to be resonant at this frequency. Next, for the dipoles design frequency, we should cut a length of 50-Ohm coax that is a multiple of a half wavelength so that its length is perhaps from 0.5 wavelength to 2.0 wavelengths. Of course, the physical length will be the line's velocity factor times the electrical wavelength at the design frequency. To the shack or source end of this line, we connect a 1/4 wavelength 75-Ohm transformer line section, again multiplying the electrical length by the line's velocity factor to arrive at a physical length. Fig. 1 shows the general scheme.

+

The result is a well-establish broadening of the operating SWR-bandwidth. These notes are a bit of follow-up that seemed interesting as the numbers emerged from some modeling exercises. I used a dipole resonant at 3.75 MHz, ignoring the geometric mean part of the scheme, since I had no two special frequencies in mind. Actually, the scheme provides a certain wide-banding effect about whatever center frequency is chosen, and the available bandwidth is independent of any desired pair frequencies. My initial dipole was AWG #12 copper wires 128.8' long and fed at the exact center. My intention in 1997 was to provide a modeling demonstration that the technique was indeed feasible.

+

A decade ago, NEC software was limited to the calculation of transmission lines on a lossless basis. The most recent version of EZNEC has corrected this limitation and now allows the modeler to make use of lossy transmission lines by entering from convenient tables the loss per 100' (or meters) at the nearest frequency to the model's design frequency. I have interpreted the notion of "nearest frequency" to use a center line between tabular entries based on the geometric mean between entry frequencies. Therefore, in the following notes, we shall use the following cables and loss factors:

+
+

50 Ohms: RG-213, VF 0.66, Loss 0.6 dB/100' @ 10 MHz

+

75 Ohms: RG-216, VF 0.66, Loss 0.7 dB/100' @ 10 MHz

+
+

We shall proceed in 2 steps. First, we shall examine the general principles of the matching system using lossless cables, as I did in the last century. Second, we shall repeat the exercises using cables with real loss figures attached in order to see in what ways we may have to modify the conclusions drawn using only lossless lines. As a final step, we shall compare the results to Frank Witt's very interesting "Transmission Line Resonator" or TLR that he explained in detail in "Broadband Matching with the Transmission Line Resonator," The ARRL Antenna Compendium, Vol. 4 (1995), pp. 30-37. Since its initial publication, the TLR matching system has been a regular part of The ARRL Antenna Book, Chapter 9, where you will find an explanation and evaluation of a large collection of broadbanding systems. System evaluation includes not only how much of a band like 80/75 meters that we can cover with less than 2:1 SWR, but as well what losses we might incur due to our efforts.

+

1. Broadbanding a 3.75-MHz Dipole with Lossless Transmission Lines

+

Let's begin our journey by reviewing the properties of a 3.75-MHz AWG #12 resonant dipole at various heights above ground. We shall avoid the usual backyard 35' height, since that level is even below the height for maximum NVIS gain. Instead, we shall look at heights between 90' and 120' in 10' increments. One of the often-ignored features of horizontal antennas is that they change their feedpoint impedance as we change antenna heights, especially in the range from 1/4 wavelength to 1 wavelength. Table 1 provides some modeled data using average ground.

+ 
+Table 1.  Modeled performance of a 3.75-MHz 128.8' AWG #12 dipole over average ground
+
+Height   Height   Feed Impedance   Max. Gain   TO Angle
+feet     wl       R+/-jX Ohms      dBi         degrees
+120      0.458    74.8 + j 0.0     7.30        31
+110      0.419    82.5 + j 0.6     6.88        34
+100      0.381    88.7 + j 4.2     6.51        37
+ 90      0.343    93.1 + j10.6     6.24        41
+
+

The feedpoint impedance values are the modeled values taken at the antenna terminals and only at 3.75 MHz. In general, the resistance goes lower with a rising capacitive reactance below the design frequency. Above the design frequency, the antenna terminal impedance shows a higher resistance with a gradually rising inductive reactance. As the performance numbers show, the design-frequency impedance changes relatively rapidly even though the height range amounts to just over 0.1 wavelength. As well, in this height range, the gain and take-off angle (the elevation angle of maximum gain) also vary considerably.

+

The first order of business in broadbanding the antenna is to add 50-Ohm coax to the feedpoint in lengths from 0 to 2 wavelengths, using 1/2 wavelength increments. We shall initially omit the 1/4 wavelength 75-Ohm transformer, since the 50-Ohm lines have much to tell us on their own. We shall also keep the antenna at 120' above ground. With 5 different line lengths, let's take 50-Ohm SWR sweeps from 3.5 to 4.0 MHz in 0.05-MHz increments. The results will be the chart in Fig. 2 Only the last of the set of 5 lines shows clearly, since they overlay each other with perfection.

+
+ +
+

At first sight, it appears from the SWR that it does not matter how many half wavelength sections of 50-Ohm cable that we add. The results seem to be the same. However, that is the first illusion that we must overcome in understanding how the matching system works. When the line is lossless and used only at the frequency for which it is exactly 1/2 wavelength, then the source-end impedance (both the resistance and the reactance) are the same as at the antenna end of the line. However, when we move the operating frequency below 3.75 MHz, the operating wavelength is longer. Therefore the line becomes shorter relative to its length at 3.75 MHz. In this case, the different lengths of line will return different values of resistance and reactance, since the line is a different fraction of a wavelength in each case. Likewise, when we increase the operating frequency, the operating wavelength becomes shorter. The fixed line length then becomes longer than prescribed for the design frequency. Again, the different line lengths return different values of resistance and reactance.

+

The most general equation for calculating the impedance at the source end of a line for lossless lines is this one:

+
+ +
ZL is the load or antenna terminal impedance in this case. ZS is the source end impedance. Z0 is the characteristic impedance of the transmission line. The script "l" is the length of the line at the calculating frequency in degrees or radians. From similar equations, we can also derive the resistance and reactance components of the impedance. As an exercise, let's plot the resistance at the source end of the line for half wavelength sections from 0 to 4, as shown in Fig. 3. Note that within about 100 kHz of the center frequency, the values do not vary much as we add sections of line. However, as we approach the band edges, the resistance values show more radical changes. +
+ +
+

We may perform a similar exercise with respect to the reactive component of the source-end impedance. Fig. 4 shows the results. The curve for a single half wavelength section almost overlays the feedpoint curve. However, as we add more sections, the departure from that curve becomes far more extreme.

+
+ +
+

The resistance and reactance at each potential frequency and for each length of 50-Ohm line determine the load-end values for the 75-Ohm 1/4 wavelength impedance transformer. Ideally, for the transformer to function simply, the load-end impedance should be resistive and about 112.5 Ohms. Under these conditions, the transformer will show its source end value as 50 Ohms according to the standard simplified equation,

+
+ +
However, if the impedance values at the load end are complex or if the length of the transformer is more or less than exactly 1/4 wavelength, then the precise calculation reverts to the complex form shown earlier. Of course, the source end of the 50-Ohm section--whatever its length--becomes the load end of the transformer. The impedances at this junction are complex, and the transformer is only 1/4 wavelength at 3.75 MHz. Therefore, the transformer only approximates the ideal condition where the simplified equation is accurate. +

The matching system that we are exploring does not die from these conditions. In fact, these conditions are essential to making it work as a broadbanding system. When we combine the impedance range of 1/2 wavelength sections with the transformer, we obtain some possibly useful results. Fig. 5 presents the SWR curves for the complete system using lossless lines and 50-Ohm sections from 1/2 wavelength to 2.0 wavelengths.

+
+ +
+

With lossless lines, each curve has a potential use. For example, if we wish to have minimum SWR values at 3.65 and 3.85 MHz, a 2 wavelength section of 50-Ohm cable might be in order. However, the SWR values rise more rapidly beyond those frequencies than with a 1.5 wavelength 50-Ohm section. The line for a single 1/2 wavelength 50-Ohm section shows a single dip. Of the group, a 1 wavelength section of 50-Ohm cable provides the widest operating bandwidth: from below 3.55 MHz to above 3.95 MHz.

+

My dipole at 120' over level average ground had an independent feedpoint impedance of about of 75 Ohms. If we lower the antenna in 10' increments, we obtain the following data on approximate bandwidths between 2:1 50-Ohm SWR points. Despite the changes in the antenna terminal impedance values from one height to the next, Table 2 shows the matching system to be stable. At every height, curves for the various lengths of 50-Ohm cable remain congruent with the set shown for 120'.

+ 
+Table 2.  50-Ohm 2:1 SWR bandwidth of a 3.75-MHz dipole at various heights
+with various lengths of 50-Ohm cable in the broadband matching system
+
+50-Ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
+     0.5wl          3.57           3.96        0.39              1.45
+     1.0            3.55           3.96        0.41              1.30
+     1.5            3.57           3.93        0.36              1.10
+     2.0            3.58           3.91        0.33              1.07
+110' up"  Z=82 Ohms
+50-Ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
+     0.5wl          3.55           3.97        0.42              1.35
+     1.0            3.54           3.96        0.42              1.25
+     1.5            3.56           3.93        0.37              1.10
+     2.0            3.58           3.91        0.33              1.05
+100' up"  Z=89 Ohms
+50-Ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
+     0.5wl          3.53           3.97        0.44              1.26
+     1.0            3.54           3.97        0.43              1.15
+     1.5            3.56           3.93        0.37              1.04
+     2.0            3.58           3.90        0.32              1.09
+90' up"  Z=93 Ohms
+50-Ohm Length  Lower limit    Upper limit    Bandwidth      Lowest SWR
+     0.5wl          3.53           3.99        0.46              1.25
+     1.0            3.54           3.96        0.42              1.10
+     1.5            3.56           3.93        0.37              1.01
+     2.0            3.58           3.90        0.32              1.05
+
+

The graphs and tables so far go only as far as did the entire modeling analysis of 1997. The question remains open as to what sort of SWR curves we might obtain when using real coaxial cables, such as RG-213 and RG-216.

+

1. Broadbanding a 3.75-MHz Dipole with Lossy Transmission Lines

+

"Lossy" is a term that we apply to all real transmission lines. As such, it does not specify how much loss is involved, but only that more complex equations are necessary to calculate the source-end impedance for a given load impedance and factor in the real losses of the lines. The values for RG-213 and RG-216 come from the table on page 24-19 of the 20th Edition of The ARRL Antenna Book. There are lines with higher and lower losses than these relatively standard lines.

+

Let's replace the lossless lines in our initial models with these real lines and let NEC calculate the results. In both cases, the listed velocity factor of the lines is 0.66. Since a wavelength at 3.75 MHz is 262.286', the 1/4 wavelength section will be 65.572' * 0.66 or 43.277'. Each half wavelength of the 50-Ohm line will be 86.554' long.

+

We may now repeat the exercise by inserting into the model the physical length of the line, the velocity factor, and the 10-MHz loss factor for each of the two cables in the system. If we do this and run the model for each step shown in Fig. 5, we wind up with the set of 50-Ohm SWR curves shown in Fig. 6.

+
+ +
+

The cable losses do not significantly alter the curves for 50-Ohm sections that are 0.5 wavelength and 1.0 wavelength long. Both curves now provide complete coverage of the 80/75-meter band with SWR values of 2:1 or less. The more interesting results involve the use of 1.5 wavelength and 2.0 wavelength sections of 50-Ohm cable ahead of the 75-Ohm 1/4 wavelength transformer. The SWR minimums using the longest 50-Ohm section no longer reach the low values that we obtained for lossless cable. In addition, the minimum SWR values for a 1.5 wavelength 50-Ohm section move away from the center frequency on both sides of the center frequency.

+

One of the major reasons for the shift in the curves is the altered transformation of the feedpoint impedance along the now-lossy 50-Ohm cable sections. We may compare the results obtained with lossless cable in Fig. 2 with the results for lossy cables in Fig. 7. The top line shows the SWR curve for the antenna terminals themselves. Each lower line represents a 1/2 wavelength increase in the length of the 50-Ohm cable. With lossless lines, we could not separate the curves. With lossy lines, we can easily identify each curve, with the implication that at every point along each curve, the resistance and reactance values have also changed. When we combine the new impedance component values with the lossy transformer, the resulting SWR curves across the band also change their shape.

+
+ +
+

As we lower the height of the antenna and raise the pre-match feedpoint resistance, then lossy cables in the matching system show further variations from the lossless cable situation. Fig. 8 shows the curves for a height of 90' above average ground. The half wavelength and 1 wavelength 50-Ohm sections still provide the best band coverage. However, the double SWR minimum values are lowest with the 1 wavelength line. Both longer lines show a continued reduction in SWR bandwidth.

+
+ +
+

No broadband matching system is immune to losses. When we model lossy lines as a part of the model, the system losses show up as reduced maximum gain for the antenna. Most of the losses are a direct function of the matched cable losses plus a small multiplier due to the SWR value on each cable at each operating frequency. We may summarize the losses by checking the maximum antenna gain at the design frequency (3.75 MHz) and at the band edges. Table 3 presents the data, using the antenna itself with no matching system as a base line. The table is instructive, although it has limitations that we shall later note. The total line length value is the sum of the 50-Ohm and 75-Ohm cables used for each matching system variation. The loss value is relative to the antenna gain prior to adding the matching system.

+ 
+Table 3.  Maximum gain and TO angle of a 3.75-MHz dipole at 120' above average ground with variations of the 50-75-Ohm matching system
+
+Total Line      3.5-MHz   TO angle  Loss     3.75-MHz   TO angle  Loss     4.0-MHz   TO angle  Loss
+Length feet     Gain dBi  degrees   dB       Gain dBi   degrees   dB       Gain dBi  degrees   dB
+0               6.91      33        ----     7.30       31        ----     7.68          29    ----
+129.83          5.67      33        -1.24    6.77       31        -0.56    6.61          29    -1.07
+216.39          5.05      33        -1.86    6.43       31        -0.87    5.87          28    -1.81
+302.94          4.46      33        -2.45    6.09       31        -1.21    5.21          28    -2.47
+389.49          3.89      33        -3.02    5.76       31        -1.54    4.61          28    -3.01
+(values for 220' of RG-213 50-Ohm cable)
+                4.92      35        -1.99    6.42       30        -0.88    5.77          30    -1.91
+
+

Since the cable has at the design frequency about a 0.45-dB loss per 100' when matched, the losses at 3.75-MHz show the approximate minimum loss obtainable from the cable under nearly matched conditions. However, at the band edges, we have seen sizable excursions in the feedpoint resistance and reactance, some above the 2:1 SWR values that we associate (rightly or wrongly) with good amateur equipment practice. The SWR value forms a (complex) multiplier on the basic cable loss, increasing the losses at the band edges.

+

We may repeat the exercise using a height of 90' above average ground to see whether the losses for each length of 50-Ohm cable remain consistent. Table 4 provides the results of this survey.

+ 
+Table 4.  Maximum gain and TO angle of a 3.75-MHz dipole at 90' above average ground with variations of the 50-75-Ohm matching system
+
+Total Line      3.5-MHz   TO angle  Loss     3.75-MHz   TO angle  Loss     4.0-MHz   TO angle  Loss
+Length feet     Gain dBi  degrees   dB       Gain dBi   degrees   dB       Gain dBi  degrees   dB
+0               6.10      44        ----     6.24       41        ----     6.44          39    ----
+129.83          5.07      45        -1.03    5.68       41        -0.56    5.36          39    -1.08
+216.39          4.52      44        -1.58    5.31       41        -0.93    4.63          38    -1.81
+302.94          4.00      45        -2.10    4.95       41        -1.29    3.98          39    -2.46
+389.49          3.48      44        -2.62    4.59       41        -1.65    3.39          39    -3.05
+
+

Lowering the antenna height reduces losses at the lower end of the band, but the losses at mid-band and at the upper band edge remain relatively constant. The explanation is straightforward once we review Table 1. Without changing the length of the dipole element, the antenna is slightly long at 90', long enough to show up as a slight imbalance in band-edge losses.

+

The tables have one misleading aspect. They do not account for the actual cable length between the antenna and the actual transceiving equipment. Rather, they treat the antenna and any matching system as a unit. In practice, the serially linked cables would count as part of the cable run to the equipment. Only if the required cable run from the antenna to the equipment is shorter than the prescribed matching system will the matching system create additional losses. For example, if the required cable run is about 220', then the 1.5 wavelength and the 2.0 wavelength matching systems will create losses necessarily in excess of the losses in a simple cable run. The 0.5 wavelength and the 1.0 wavelength systems will create losses associated with the matching system plus the additional length needed to reach the equipment. Since these systems result in low SWR values across the band for a remaining 50-Ohm cable, these added losses will be limited to about the matched-loss value for the cable used. In this sense, the baseline gain values for the antenna are equally unrealistic, since they presume a perfect match at each frequency with a lossless cable. If we use our sample 220' length of RG-213, then the losses at the band edges will be higher if we employ no matching network at all. Table 3 has a special line of values for the antenna at 120' using 220' of RG-213 50-Ohm cable. Note that the loss values are not very different from those for the 1 wavelength matching system with a total cable length of 216'.

+

Lossy transmission lines used in the matching system may well alter our initial perceptions of the wide-band 50-75-Ohm matching system. Although lossless cables seemed to favor the longer system for some applications, the best lengths turn out to be either 0.5 wavelength or 1.0 wavelength of 50-Ohm cable prior to the 75-Ohm 1/4 wavelength transformer. Fig. 9 provides the outline of the system most favored by the use of cables with real losses. The system provides the widest coverage and the lowest losses possible.

+
+ +
+

The 50-75-Ohm matching system is simple and convenient. In most cases, we can tailor the version to match reasonably closely with the required cable run from the antenna to the shack. All connections are serial, with no hanging stubs or other appendages to add weight to the feedline. One remaining question is whether the system provides the greatest efficiency feasible.

+

The AI1H TLR Broadband Matching System

+

In 1995, Frank Witt, AI1H, presented an alternative to the 50-75-Ohm transmission-line broadband matching system. He called the system the Transmission-Line Resonator (TLR). It consisted of three lengths of 50-Ohm cable. We shall continue to use RG-213 with a velocity factor of 0.66 and a loss factor of 0.6 dB/100' as our implementation, which coincides with Witt's own version. A length of cable connects the antenna terminals to the source, which can be the station equipment or a further length of 50-Ohm cable that reaches the equipment. At the antenna terminals, he connects an open stub across the terminals, effectively adding a shunt capacitance (more correctly, a capacitive reactance) to the antenna terminal impedance. At the source end of what Witt calls the "link" line, he adds a shorted stub across the line, effectively adding a shunt inductance (or inductive reactance). With the proper proportions, shown for the 80/75-meter band in Fig. 10, the combination yields a broadband 50-Ohm match for the dipole.

+
+ +
+

The calculation details appear both in Witt's original article and in The ARRL Antenna Book. Our goal here is simply to model the Witt broadband TLR match and then to compare the results we obtain with the results we obtained from the 50/75-Ohm system that we have been examining. Witt requires a somewhat different length for his self-resonant dipole. He based his initial calculations on a frequency that was the geometric center of the band. However, as he refined the dimensions, he lowered the resonant dipole frequency from 3.742 MHz to 3.710 MHz. The model is based on a resonant dipole at Witt's frequency composed of AWG #12 copper wire at both 120' and 90' above average ground.

+
+ +
+

Fig. 11 shows the 50-Ohm SWR curves applicable to the model of the TLR system. The top line is the pre-match SWR curve, which reveals the minimum value that is below the center of the band. The next line down is the 50-Ohm SWR with Witt's dimensions for an antenna height of 120' above average ground. The lowest line is for the antenna at 90'. To optimize this curve, I reduce the source-end shorted-stub length from 20.1' down to 19'. Indeed, it appears that one can make fine adjustments to the TLR system simply by changing the length of the most convenient appendage to the link line, which for the modeled situation would be at or close to ground level.

+

The shape of the curve and its maximum and minimum values are very similar to those for the 50/75-Ohm series system when we use either a 0.5 wavelength or a 1.0 wavelength section of 50-Ohm cable. With respect to the SWR curves, the curves may show no advantage or disadvantage for each system. Structurally, the 50/75-Ohm system requires only serial connections of cables. The TLR system requires two appended stubs. The TLR physical length total 101' (ignoring the parallel-connected stubs), while the 50/75-Ohm system requires 130' of cabling for the 0.5 wavelength 50-Ohm section and 216' for the 1.0 wavelength section. Making a decision based on mechanical considerations would likely require consideration of the specific installation layout.

+

We may also compare losses in each system by using the data that the model provides for the two most eligible versions of the 50/75-Ohm system and the specified TLR systems. Table 5 shows the values at the band center and edges at both antenna heights. The lengths listed in the TLR entry include the stub lengths, which contribute to the overall loss picture.

+ 
+Table 3.  Maximum gain and TO angle of a 3.75-MHz dipole above average ground with variations of the 50-75-Ohm matching system and the TLR system
+
+Total Line      3.5-MHz   TO angle  Loss     3.75-MHz   TO angle  Loss     4.0-MHz   TO angle  Loss
+Length feet     Gain dBi  degrees   dB       Gain dBi   degrees   dB       Gain dBi  degrees   dB
+Height = 120'
+0               6.91      33        ----     7.30       31        ----     7.68          29    ----
+129.83          5.67      33        -1.24    6.77       31        -0.56    6.61          29    -1.07
+216.39          5.05      33        -1.86    6.43       31        -0.87    5.87          28    -1.81
+TLR (134.2)     5.51      33        -1.40    6.72       30        -0.58    6.41          29    -1.27
+Height = 90'
+0               6.10      44        ----     6.24       41        ----     6.44          39    ----
+129.83          5.07      45        -1.03    5.68       41        -0.56    5.36          39    -1.08
+216.39          4.52      44        -1.58    5.31       41        -0.93    4.63          38    -1.81
+TLR (133.1)     4.91      45        -1.19    5.58       41        -0.66    5.16          39    -1.28
+
+

At both heights, the losses are almost wholly dependent upon the line length and the degree of mismatch between the antenna terminals and the characteristic impedance of the line. With an intermediate length of transmission line between the two versions of the 50/75-Ohm system, the TLR shows intermediate loss levels. Indeed, one might suggest that for a broad but highly usable SWR characteristic, the 0.5 wavelength version of the 50/75-Ohm system is superior. However, certain types of equipment demand tighter SWR limits, for example, amplifiers with a 1.5:1 fold-back limitation. For such equipment, the TLR system offer the lowest losses possible.

+

Both the 50/75-Ohm and the TLR systems are adaptable to any frequency range in which a 13% operating bandwidth is required and the initial impedance is in the dipole range. As well both systems can be applicable to other antenna terminal impedance values by the proper selection of cables in the system. Our goal has only been to expand the initial modeling feasibility study to include loss factors, not to provide a generalized theory of cable matching. The range of available transmission-line characteristic impedances, of course, will always limit the 50/75-Ohm system.

+

Of course, if we are not confined to the use of coaxial cables, we may always attach a 450-Ohm parallel transmission line to the antenna and employ a well-balanced ATU in the shack. 220' of such line will have a loss of about 0.05-dB/100' (or about 0.11 dB for the total line length) in a matched condition on the band. The SWR values are not likely to incur great losses. Indeed, for the line itself, the losses will amount to between 0.3 and 0.4 dB across the band. However, the total system losses will depend upon the efficiency obtainable within the antenna tuner, and that value will change with the tuner design.

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+ +
+

Updated 11-29-1997, 06-27-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Lower, Matching, Transmission Line


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+

An SWR-Feedline-Reactance Primer
+ Part 1. Dipole Samples

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Introduction: The Dipole, SWR, and Reactance

Let's take a look at a very common antenna: a 67' AWG #12 copper wire dipole for 7.15 MHz, that is, the center of the 40-meter band. We shall place the antenna at a height of 50' above average ground, which is ground with a conductivity of 0.005 S/m and a dielectric constant of 13. Fig. 1 shows the general outline of the small antenna system. +
+ +
+

If I model this antenna, I obtain a feedpoint impedance of 87.12 - j2.98 Ohms. There is nothing wrong with either the model or the antenna. The near-resonant impedance is not very close to 70 Ohms because it is not supposed to be. The resonant impedance (and the resonant length) of a dipole varies with the height of the antenna above ground. At some heights, the impedance will be greater than 70 Ohms, while at other heights, the impedance will be under 70 Ohms. The value undulates up and down between a height of 1/4 wavelength and 1.25 wavelengths, but gradually smooths out as the antenna height increases above 1.25 wavelengths.

+

Normally we would expect the antenna to perform over the entire 40-meter band from 7.0 to 7.3 MHz. So let's perform a frequency scan and graph the results. Fig. 2 shows what we get for our effort.

+
+ +
+

Examine the blue lines first. The antenna provides us with a better SWR curve using a 75-Ohm reference than with a 50-Ohm reference. Given the near-resonant impedance of about 87 Ohms, the curves are exactly what we should expect.

+

The red lines show us why the SWR curves increase their value away from the near-resonant frequency of 7.15 MHz. The resistive component (upper red line) does not change much across the 40-meter band. However, the reactance describes a nearly linear curve between 7.0 and 7.3 MHz. At the low end of the band, the reactance is mostly capacitive, indicating that the antenna is short for resonance at 7.0 MHz. At 7.3 MHz, we find the highest value of inductive reactance, indicating that the antenna is too long to be resonant at that frequency.

+

Everything that we have examined is such commonplace knowledge that some instructions sets that accompany SWR meters and antenna analyzers cite some rules of thumb.

+

1. If you lower the frequency and the SWR goes down, then the antenna is long and the reactance at the feedpoint is inductive. If you raise the frequency and the SWR goes down, then the antenna is short and the reactance at the feedpoint is capacitive.

+

2. If your meter gives you a value for reactance but does not tell you whether the value is inductive (+) or capacitive (-), you can use Rule 1 to tell the difference. If a lower frequency yields a lower value of reactance, then the reactance is inductive. If a higher frequency gives a lower reactance value, then the reactance is capacitive.

+

Unfortunately, such rules of thumb usually fail to mention two important facts that give the rules some validity. First, the rules apply to near-resonant antennas based on a half wavelength center-fed element. Second, the rules apply to the antenna feedpoint and to certain other situations, but not to all measurement situations. Like most rules of thumb, these ignore the fact that we also have fingers.

+

In this case, the "fingers" represent that fact that we ordinarily make our SWR and resistance/reactance measurements some distance from the actual antenna feedpoint. Between the feedpoint and the measuring instrument, we normally have a length of feedline. In my experience, a large number of newer antenna builders have no idea what happens to the impedance value between the antenna feedpoint terminals and the other end of the feedline connected to the measuring instrument.

+

Most builders know that if there is a good match between the antenna feedpoint and the feedline, the impedance will be almost the same everywhere along the line. From Fig. 2, we can see that we almost have a perfect match at 7.15 MHz between the antenna and the 75-Ohm cable. However, that match becomes worse each side of the near-resonant mid-band frequency. If we try to use a 50-Ohm cable, then we do not have even a 2:1 SWR at the band edges. The increasing reactance, inductive or capacitive, increases the SWR value and presents the line with a complex impedance at the antenna terminals.

+

At this point, most texts would introduce a set of equations to use for calculating what happens along the feedline. Of course, few readers actually perform the calculations. So we shall try a different tack. The following notes will present a series of graphs--all resembling in format Fig. 2. However, each one will use a different feed line characteristic impedance and a different line length. We shall look at 50-Ohm cable, the most commonly used feedline for dipoles, and then at 75-Ohm coax, the better match for the 40-meter dipole at a 50' height. Finally, we shall examine a special hybrid case.

+

For all of our exercises, we shall presume that the cable has a velocity factor of 1, which we can easily do in modeling. In real situations, the electrical lengths of the cables would be multiplied by the velocity factor of the cable we actually use. However, should you replicate these exercises using actual coaxial cables, be certain to measure the velocity factor rather than relying upon published figures. I have found reputable cables as much as 5% off the published figures.

+

We shall look at cables from 1/4 wavelength to 3/4 wavelength long. The electrical lengths of these cables are as follows, assuming that they are calculated based on a wavelength at 7.15 MHz (137.562').

+ 
Length in                 Length in
+Wavelengths               Feet
+1/4                        34.39
+3/8                        51.59
+1/2                        68.78
+5/8                        85.98
+3/4                       103.17
+

The values that we shall derive will be for lossless cable. As the cable becomes longer, losses will reduce the SWR value at the source end, with commensurate changes in the resistance and reactance values that result in the reduced SWR value. The losses will vary with the cable ratings. At one end of the scale, there are very lossy cables, although not especially at 7 MHz. At the opposite extreme are hardlines with losses that rival the best open-wire parallel feedlines. For our purposes, which focus around understanding the feedpoint reactance at the source end of the lines, the losses in real lines will not be significant.

+

The 40-Meter Dipole with a 50-Ohm Cable

+

Our first two major sample situations involve the use of the dipole with a single feedline, as shown in outline form in Fig. 3.

+
+ +
+

The first of the two situations described by the sketch makes use of 50-Ohm feedline. We shall examine the resistance, reactance, and the 50-Ohm and 75-Ohm SWR values for each of the sampled feedline lengths in the table.

+
+ +
+

The 1/4 wavelength feedline shows an impedance at 7.15 MHz of 28.66 + j0.98 Ohms. We know that a 1/4 wavelength transmission line forms a transformer so that the source impedance is the square of the line impedance divided by the load or antenna impedance, assuming we have nothing except resistive impedance. The presence of reactance complicates the calculation considerably, but at the near-resonant frequency of 7.15 MHz, the reactance is too low to make a difference in the outcome. 2500 divided by 87.12 equals 28.69.

+

However, off the resonant frequency, we have a rapidly rising reactive component to the antenna terminal impedance. Therefore, even though the antenna terminal impedance shows a slowly rising curve in Fig. 2, the impedance curve for the resistive component describes an arc, with band edge values both lower than the band-center value.

+

With a 1/4 wavelength feedline, we can also notice a radical change in the reactance curve. Instead of showing a "rising" curve from capacitive to inductive reactance, the 1/4 wavelength line curve descends from an inductive value at the low end of the band to a capacitive value at the high end. The rules of thumb that apply to the antenna terminals reverse themselves with the line in place.

+

Because the 50-Ohm coax performs a downward transformation on impedance across the band, neither the 50-Ohm nor the 75-Ohm SWR curves are very heartening for operating the antenna.

+
+ +
+

The values for the 3/8 wavelength 50-Ohm feedline in Fig. 5 are no better when it comes to the SWR cures. The impedance at the source end at 7.15 MHz is 44.46 + j26.01 Ohms. (Incidentally, I am giving the impedance values to two decimal places, as reported by the modeling software, so that anyone who wished to replicate the modeling exercise can compare results without ambiguity. The values are about 2 decimal places too precise for measuring instruments generally available to amateurs.) Although the resistive component of the impedance seems to favor 50-Ohm cable, the reactive component sets the impedance at a value quite distant from 50 Ohms.

+

Interestingly, the reactive component of the impedance remains entirely inductive across the band. The curve generally descends except for the last graphed increment, where it shows a very slight rise. Given the very slight change in reactance across the band, not to mention the reverse direction of the curve relative to the curve for the antenna terminals, the rules of thumb become entirely useless in determining the type of reactance in a real measurement situation.

+
+ +
+

The curves for the 1/2 wavelength 50-Ohm line in Fig. 6 should seem familiar. With a 1/2 wavelength line, the impedance at the design frequency should reproduce the impedance at the antenna terminals. The reported value of 87.12 - j3.04 comes within 0.05 Ohm of reactance of being perfect. As well, the reactance and resistance curves show the same general tendencies as those for the antenna feedpoint.

+

However, as we move away from the design frequency toward the band edges, the line length will no longer be 1/2 wavelength. At 7 MHz, the line will be short and at 7.3 MHz, the line will be long. If you closely compare the resistance and reactance curves in Fig. 2 with those in Fig. 6, you discover an interesting phenomenon. The resistance curve for the 1/2 wavelength line case shows a wider span than the spread at the antenna terminals--about a 6.5 Ohm differential. In contrast, at the end of the 1/2 wavelength line, the reactance shows a narrower span than at the antenna terminals, nearly 21 Ohms (or about 32%) narrower. As a result, the SWR curves are somewhat flatter with the 1/2-wavleength line, although perhaps not enough to make an operational difference.

+
+ +
+

As we increase the line length to 5/8 wavelength, as shown in Fig. 7, we lose the reactance curve that tracks the one for the antenna terminals. In fact, the new reactance curve is almost a mirror image of the curve for 3/8 wavelength. As well, the reactance values are all capacitive, in contrast to the all-inductive values for the 3/8 wavelength line. The 7.15-MHz impedance of 41.89 - j24.53 Ohms reflects the mirror imaging. And once more, the curve descends in value with rising frequency, although the very small change in reactance itself would suffice to make the rules of thumb quite useless.

+

Once more, neither the 50-Ohm nor the 75-Ohm SWR curves are very promising for full-band operation of the antenna. In contrast to their 3/8 wavelength line mirror images, the 5/8 wavelength lines yield peak 75-Ohm SWR values at the high end of the band, rather than at the low end.

+
+ +
+

Fig. 8 shows the curves for a 3/4 wavelength 50-Ohm transmission line. We are taught quite correctly that at the design frequency for which the line is exactly 3/4 wavelength, the impedance will be the same as for a 1/4 wavelength line. The reported value is 28.66 + j0.97, only j0.01 Ohm reactance different from the report for the 1/4 wavelength line.

+

However, away from the design frequency in either direction, the line is no longer 3/4 wavelength. Still, the amount (as a percentage) by which it departs from 3/4 wavelength is less than the same frequency departure for the 1/4 wavelength line. Therefore, the reactance spreads for the two lines differ, with the longer line showing a little over 30% less of a reactance spread across the band. Nonetheless, the SWR curves for the 3/4 wavelength line are no more promising for full-band operation than the ones for the 1/4 wavelength line.

+

We have seen two cases in which we have separate graphs for line lengths that are separated by 1/2 wavelength: the case of no transmission line and a 1/2 wavelength line, and the case for 1/4 wavelength and 3/4 wavelength lines. In both instances, we noted identical trends in the curves. The major difference between the curves within each case is that the longer line produced a narrower spread of the reactance over the full width of the 40-meter band.

+

As a result, we would expect the the curves for a 7/8 wavelength line would show the same trends as those for a 3/8 wavelength line and the curves for a 1-1/8 wavelength line would show the same trends as for the 5/8 wavelength line. The reactance spreads would simply be somewhat narrower in each case. Of course, the longer we make the line physically, the more that actual line losses will modify these values, with the actual amount of modification depending on the loss per unit length of the chosen line. Nonetheless, the span of values that we have examined should be sufficient to provide a fairly clear picture of the impedance transformations that occur along a 50-Ohm transmission line with the starting terminal impedance values for the 40-meter dipole at a 50' height. As well, they show fairly clearly the limitations of the rules of thumb that gave rise to the exercise.

+

The 40-Meter Dipole with a 75-Ohm Cable

We should never accept a set of data without having a means to confirm its general validity. So far, you have only my word that transmission lines perform in the manner described. In order to provide some confirmation that the general ideas are correct, let's re-run the same set of exercises. Instead of a 50-Ohm cable, this time we shall use a 75-Ohm transmission line. As in the first case, we shall use a velocity factor of 1, since the velocity factors of existing 75-Ohm cables vary as much as do those for 50-Ohm cables. Conveniently, the same table of fractional wavelengths at 7.15 MHz will serve us well for the re-run. +
+ +
+

If we replace the 50-Ohm cable with a 1/4 wavelength section of 75-Ohm feedline, as shown in Fig. 9, we obtain a mid-band impedance of 64.49 + j2.19 Ohms. This value is a product of the same simplified calculation that we used with the 50-Ohm line. However, this time, we divide the square of 75 (5625) by the antenna terminal resistance (87.12) to arrive at a calculated impedance of 64.6, just a little off from the value we get when we factor in the very small reactive component at the antenna terminals.

+

The band-edge resistance values are in the 50s while the reactance varies from j23 to -j12 Ohms. The result is a set of SWR curves that are usable across the 40-meter band. We shall have occasion just a bit further down the road to use this system within a larger antenna-feedline system.

+

For the moment, we may note that the direction of the reactance curve is the same as with the 1/4 wavelength 50-Ohm line. This provides part of the confirmation that we needed, namely, that the 50-Ohm results were--with respect to trends--perfectly general.

+
+ +
+

The 3/8 wavelength 75-Ohm transmission line also reflects the trends shown by its 50-Ohm counterpart. Compare Fig. 10 with Fig. 5 for the 50-Ohm cable of the same length. The reactance is wholly inductive. As well, reactance curve shows a slight downward trend, except for the highest end of the operating passband. The 7.15-MHz impedance is 76.72 + j11.56 Ohms. Hence, the 75-Ohm SWR curve remains exceptionally good, but the 50-Ohm curve has taken a tilt for the worse.

+
+ +
The 1/2 wavelength 75-Ohm line yields curves in Fig. 11 that closely resemble those in Fig. 2 and in Fig. 6, the graphs of the antenna with no transmission line and the graph for a 1/2 wavelength 50-Ohm line. The 7.15-MHz impedance is 87.12 - j3.08 Ohms--within an eyelash of the impedance reported for the antenna with no transmission line at all. However, let's look at the band-edge impedances for the 3 cases: + 
TL Situation               7.0 MHz                7.3 MHz
+No Line                   82.48 - j35.20         91.86 + j29.15
+1/2-WL 75-Ohm Line        87.71 - j34.89         96.54 + j26.96
+1/2-WL 50-Ohm Line        89.92 - j30.12         98.24 + j21.34
+

Although the differences are small, the trends are clear. As we reduce the characteristic impedance of the 1/2 wavelength line, the band-edge resistance increases, but the band-edge reactance decreases. Does this trend hold for transmission lines with impedances above 87 Ohms? There are 93-Ohm and 125-Ohm coaxial cables, so let's replicate the chart using those lines.

+ 
TL Situation               7.0 MHz                7.3 MHz
+No Line                   82.48 - j35.20         91.86 + j29.15
+1/2-WL 93-Ohm Line        86.80 - j37.21         95.80 + j29.62
+1/2-WL 125-Ohm Line       85.81 - j40.50         94.96 + j33.27
+1/2-WL 87.12-Ohm Line     87.06 - j36.51         96.01 + j28.82
+

As we increase the transmission line characteristic impedance, using a 1/2 wavelength line, the resistance decreases and the reactance increases. However, the resistive portion of the band-edge impedance does not decrease relative to the antenna terminal impedance, but rather to the band-edge values of a hypothetical 87.12-Ohm line, shown in the last line of the new table. The reason for this reference line is that even the perfectly matched line loses its perfection of match as we move away from the frequency at which it is exactly 1/2 wavelength. The lesson here is that we must--when setting trends with any precision--compare truly comparable items. The no-line case is satisfactory for some comparisons, but for seeing the resistance-reactance trend in 1/2 wavelength lines, we need to make our reference also a 1/2 wavelength line, in this case perfectly matched at the design frequency.

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The 5/8 wavelength 75-Ohm line in Fig. 12 reflects the trends shown for the 50-Ohm line in Fig. 7 and is the virtual mirror image of the graph for the 3/8 wavelength line in Fig. 10. The mid-band impedance is 71.69 - j10.85 Ohms. The reactance is wholly capacitive and has such a shallow curve as to negate any possible application of the rules of thumb that gave rise to this exercise. The 75-Ohm SWR curve remains very good, but the 50-Ohm SWR curves reaches excessive values at the high end of the 40-meter band. Once more, our 75-Ohm work confirms the general trends, but not the specific values, revealed by the earlier 50-Ohm work.

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The 3/4 wavelength line, graphed in Fig. 13, shows once more that the values and trends tend within limits to replicate themselves every 1/2 wavelength down a lengthening transmission line. The 7.15-MHz impedance is 64.49 + j2.19 Ohms, the same value that we obtained for a 1/4 wavelength line. However, as we noted for the 50-Ohm line case, the band edge values will vary somewhat between 1/4 wavelength and 3/4 wavelength lines, due to differences in how much each line differs from its length at band center.

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Although the data for resistance and SWR in our sequence of graphs is interesting, our main goal has been to explore what happens to reactance as we increase the length of a transmission line away from the antenna feedpoint. Sometimes graphing phenomena can give us a better set of long-term intuitively correct expectations than a series of simple calculations in numerical form. If we remember the general trends shown by the graphs, then we shall be in a better position to apply or to withhold application of the rules of thumb with which we started.

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The 40-Meter Dipole with a 75-Ohm Matching Section and a 50-Ohm Cable

The case in which we placed a 1/4 wavelength 75-Ohm transmission line from the antenna terminals to the source presented us with the best overall 50-Ohm SWR curve. Before we leave our dipole altogether, let's explore a possibility: let's use the 75-Ohm line as a matching section and then let the remainder of the line be 50 Ohms. Fig. 14 outlines the system. +
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As our work so far has shown us, we might as easily have used a 3/4 wavelength section of 75-Ohm cable as the matching section. In either case, we would expect that 50-Ohm SWR curves would be superior to any that we experienced when we connected the 50-Ohm cable directly to the antenna terminals. Let's do a complete survey, so that we can detect oddities, if they should occur.

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Remember that the 7.15-MHz impedance at the end of the 75-Ohm matching section is 64.49 + j2.19 Ohms. Hence, with a 1/4 wavelength length of 50-Ohm cable added to the system, we shall obtain an impedance that is roughly 2500 divided by 64.5, or about 38.8 Ohms. As shown in the graph in Fig. 15, the impedance at 7.15 MHz is 38.72 - j1.32 Ohms.

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Despite the impedance conversion, the 50-Ohm SWR never rises to 1.6:1. As well, we find a rising reactance curve, the same trend--with different values--that we found at the antenna terminals. The reason is straightforward: the first 1/4 wavelength section reversed the direction of the curve, and the second 1/4 wavelength section reversed it once more.

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The 3/8 wavelength 50-Ohm cable addition, graphed in Fig. 16, shows what should be by now very familiar characteristics. The 50-Ohm SWR curve once more does not rise to 1.6:1. The reactance curve is wholly inductive, but is so flat as to make the rules of thumb irrelevant to any practical application to this situation. The 7.15-MHz impedance is 46.86 + j12.08 Ohms. The resistive component is closer to 50 Ohms than was the 1/4 wavelength line value, but the reactance is higher. The result is the same--a mid-band SWR of 1.29:1.

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Fig. 17 shows the curves when we add a 1/2 wavelength 50-Ohm line to our matching section of 75-Ohm cable. The 75-Ohm SWR curve shows a very low mid-band value, but rises rapidly toward the band edges, although the peak values is well under 2:1. However, the 50-Ohm SWR curve has not changed, with a 1.29:1 mid-band value and a peak value of 1.57:1.

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The reactance curve has its typical downward slope, replicating the curve that we would obtain at the end of the 75-Ohm matching section. Also as expected, the mid-band impedance is 64.49 + j2.23 Ohms, the value that we found at the end of the matching section.

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At the end of a 5/8 wavelength 50-Ohm line added to the matching section, we obtain the values shown in Fig. 17. The resistance and reactance graph lines are virtual mirror images of those we saw in Fig. 16 for the 3/8 wavelength line. The mid-band impedance is 50.03 - j12.92 Ohms, which yields a 50-Ohm SWR value of 1.29:1. The peak band-edge value at 7 MHz is 1.57:1.

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The graph for a 3/4 wavelength 50-Ohm addition to the matching section in Fig. 19 replicates--within limits that we have previously noted--the results for the 1/4 wavelength line in Fig. 15. The reactance shows a rising line, while the mid-band impedance is 38.72 - j1.32 Ohms. The 50-Ohm SWR at 7.15 MHz is 1.29:1, while the peak value (at 7 MHz) is 1.57:1.

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Perhaps the most notable feature in this sequence of graphs is the fact that the 50-Ohm SWR curve did not change at all as we increased the length of 50-Ohm cable that followed the 1/4 wavelength 75-Ohm matching section. Our previous comparison of 1/4 wavelength and 3/4 wavelength line sections showed a smaller spread for the reactance across the band. Perhaps we can lower the band-edge peak 50-Ohm SWR values if we replace the shorter matching section with a longer one.

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Fig. 20 shows the results of the replacement. The minimum 50-Ohm SWR value does not change; it is still 1.29:1. However, the maximum value is now 1.49:1, perhaps a small decrease, but one that may bring the maximum value under the amplifier power reduction or shut-down value.

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Remember that the matching technique that we used in this example applies to a specific "situated-antenna." That is, the feedpoint impedance at the antenna terminals had to be close to the 87-Ohm mid-band value. This condition exists for a 40-meter dipole at 50' or about 0.36 wavelength up. Since the impedance of a resonant dipole will vary with its height above ground at least to about 1.25 wavelengths, changing the antenna height will require a different matching technique.

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Nevertheless, the example does illustrate at least two different properties of focal interest in this introduction to transmission line transformations. First, it illustrates a simple application of series matching using only transmission lines. For a more detailed account of series matching techniques, see "Series Matching: A Review".

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Second, the sample matching situation further illustrates what happens to the SWR curves, the resistance curve, and especially the reactance curve at the source point when we place various types and combinations of feedlines between the antenna terminals and the measuring point, that is, the source. The matching-section example shows that having a good working familiarity with these transformations has multiple benefits. Familiarity with the curves tells us when to apply the overworked rules of thumb and when to ignore them because they are irrelevant to a situation. The same familiarity also tends to give us intuitively correct expectations and understandings of the measured results we obtain. Final, the familiarity also opens avenues of opportunity for effecting the level of matching required by a given antenna situation.

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For these reasons, we should let familiarity grow into downright intimacy with the phenomena that we are exploring. Therefore, we need a second part to this primer to explore other situations than that of a simple dipole. Even then, we shall not be complete in our knowledge, but, then, intimacy never is.

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Updated 12-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for November, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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An SWR-Feedline-Reactance Primer
+ Part 2. Some Interesting Antennas and Matching Systems

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L. B. Cebik, W4RNL

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Where We Have Been and Where We Are Going

In Part 1 of this primer, we examined 40-meter dipoles with several types and lengths of feedline in order to look intensively at what happens under various conditions to the resistance, reactance, and SWR values. Our starting point was a pair of rules of thumb about relating the type of reactance, capacitive or inductive, to the changes in either the reactance absolute value or the SWR as we shift frequency from our initial reading. We discovered right away that these rules of thumb have very limited application. Once we add feedline that is not a perfect match with the antenna impedance, the reactance curve may change direction, depending on the length of the line. +

However, we also began to develop a more visual and hopefully a more intuitively correct understanding of the behavior of resistance and reactance along a transmission line. As well, we saw from the models that we used to explore this territory the ways in which the line length, even apart from line losses, can affect resistance and reactance as we move away from the design frequency toward band edges. Along the way, we encountered some interesting uses of feedline transformers that are an odd multiple of a quarter wavelength.

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In this episode, we shall do more of the same, but with a difference. Part of our survey will involve looking at different antennas, including a 1 wavelength doublet, a single quad loop, a three-element Yagi, and an extended double Zepp (EDZ). The first 3 of these antennas are resonant at the design frequency, but the EDZ is inherently non-resonant. As well, we shall examine further the quarter wavelength of feedline as an impedance transformer used to effect a match between an antenna and a main feedline that do not initially match. This exploration will lead us to look at at least two other matching systems: the beta or hairpin match and the match line-and-stub system. In each case, we shall be interested in the behavior of resistance and reactance as we place these systems between the antenna terminals and the main feedline.

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Our main goal is to refine our working understanding of resistance, reactance, and SWR behavior on a feedline relative to the same parameters when measured at the antenna terminals. Granted that all of these items can be calculated by the use of handbook equations: in fact, we shall be using NEC-4 to perform our calculations (on lossless lines). Nevertheless, graphical analysis can potentially add some clarity and vividness to the numbers so that we may gradually develop more correct expectations of the situations that present themselves to us.

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The 1-Wavelength Doublet

Let's begin our series of antennas with a 1 wavelength doublet. We may have many reasons for using such an antenna. It provides somewhat more gain and a narrower beamwidth than a 1/2 wavelength dipole. Occasionally, we simply press into service an 80-meter dipole on 40 meters, where the wire is close to 1 wavelength. +

However, for our work, we shall use a more precisely cut 1 wavelength doublet: it will be 133.4' long and use AWG #12 copper wire. We shall place this 7.15-MHz (40-meter) antenna at 50' above average ground. Fig. 1 shows the outlines of our simple antenna system.

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The top portion of the sketch shows our baseline antenna with no feedline. We shall throughout these notes always begin at a comparable situation. Fig. 2 outlines the resistance and reactance behavior across 40-meters. (Since the resistance and reactance are both so high, SWR curves would be useless, at least at this stage in our exploration.)

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The feedpoint impedance at the design frequency is 4784 + j0.42 Ohms. The increments along the left Y-axis of the graph cover a sizable range of values, so the shallow curves actually are sharper than any of those that we encountered in Part 1. Especially notable is the fact that the reactance goes from being considerably inductive to being considerably capacitive across the 40-meter band. This curve is precisely the opposite of the reactance behavior of a 1/2 wavelength dipole. However, in the vicinity of an integral multiple of a wavelength, the reactance must reverse its curve and be inductive when the antenna is short (under 1 wavelength) and be capacitive when the antenna is long (more than 1 wavelength). This phenomenon occurs only for a small range either side of the 1 wavelength (or any integral wavelength) mark. Indeed, the toughest job in creating a 1 wavelength antenna will be finding the exact length--for the materials, height, and environment--at which the transition occurs.

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A common question regarding 1 wavelength doublets is how to feed them. Why not use common 50-Ohm coaxial cable? Of course, we shall need a means of transforming 4784 Ohms to 50 Ohms (both resistive), but that is a task for the quarter wavelength matching section of feedline. Since the antenna is resonant (by modeling design), we can use the simple equation to find the required matching section impedance. Multiply the two impedances (input and output) together to get 239,200 and take the square root: 489.1 Ohms. Essentially, this is the geometric mean between the two impedance values.

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A 489-Ohm impedance transmission line is fairly easy to build. Two lengths of AWG #16 spaced 1.5" apart or two lengths of AWG #10 spaced 3" apart will do the job just about perfectly. There are, of course, equations and utility programs to perform the calculations, or you can arrive at a very workable approximation from some graphs in "Some (Old) Notes on Home-Brew Parallel Transmission Lines". Let's build such a line and use a perfect 1/4-wavlenegth section between the antenna terminals and the measuring point or source. (As we did in Part 1, we shall assume that the velocity factor is 1.0, since we can always trim our open-wire home-made line if the value is slightly lower.) Fig. 3 shows the outcome for the resistance, reactance, and the 50-Ohm SWR.

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As the 1/4 wavelength lines did in Part 1, this new line reverses the direction of the reactance curve. Notice that the total spread of reactance across the band is just under 60 Ohms. Combined with the almost changeless resistance line, the reactance allows a 50-Ohm SWR curve that remains well under 2:1 from one band edge to the other. The 1 wavelength doublet is often discounted as a monoband antenna on the grounds that it is too hard to match to standard cables and too sharply tuned to use without an antenna tuner. Neither of these grounds is true, and the 1 wavelength doublet is an extremely cheap and relatively broadband 40-meter antenna--with a couple of dB of extra gain. Of course, add a 1:1 choke or balun at the junction of the match line and the feedline to suppress common-mode currents.

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A 1-Wavelength Single Quad Loop

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Let's change gears and move to a 1 wavelength single quad loop. For most wire sizes in common use, an HF self-resonant loop will require a cutting formula like this one: L(ft) = 1041/Fr(MHz). Of course, the exact length will vary with the wire size or element diameter and with the frequency, since the wire size as a fraction of a wavelength varies with frequency. However, accurate algorithms for designing a self-resonant square (or diamond) loop are available. See "Calculating the Length of a Resonant Square Quad Loop", for background: the utility program is available in various formats from various sources.

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We shall look at a self-resonant quad loop for 10 meters, with a 28.5-MHz design frequency. The loop uses AWG #14 copper wire, and the model places it in free space for this exercise. The circumference of the loop is 36.52' Fig. 4 outlines the two ways in which we shall examine the loop: as a "bare" antenna and with a matching line.

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The basic antenna provides resistance and reactance curves as they appear in Fig. 5. The 50-Ohm SWR curve is somewhat gratuitous, but does show that we do not have a close match between the antenna feedpoint impedance and our 50-Ohm feedline.

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The impedance of the bare quad loop is 127.0 + j0.76 Ohms at 28.5 MHz. Unlike the 1 wavelength doublet, the reactance curve has a normal direction, since a quad loop is essentially two 1/2 wavelength dipoles with their ends bent toward each other until they touch. They form two 1/2 wavelength antennas in phase (except for wire losses) and spaced 1/4 wavelength apart.

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If we wish to match the loop to a 50-Ohm coax main feedline, we shall need a 1/4 wavelength section of 79.7-Ohm line (SQRT (50 * 127)). 75-Ohm line is about the closest value that we might readily find. (Building a 75-Ohm line with air insulation would require square conductors spaced very close to each other. The lowest obtainable value using round wires and air insulation is about 80 Ohms, and it is impractical in terms of maintaining the spacing.) If we use this line in a 1/4 wavelength matching section--the right side of Fig. 4--we would obtain the impedance behaviors shown in Fig. 6.

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The resistance and reactance curves are perfectly normal for the situation. Because the line is only 1/4 wavelength at 28.5 MHz, the resistance shows a peak value there with declining values at the band edges. The reactance curve is the reverse of the one for the bare antenna. Since the matching section is not a perfect geometric mean between the input and output impedances (as it was in the 1 wavelength doublet case), the SWR does not reach 1.0:1 at the center of the operating passband. However, even with the less than perfect value, it only rises to about 1.5:1 at the band edges.

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2-element monoband quad beams very often have impedances in the same range as the single quad loop. Hence, the 1/4 wavelength 75-Ohm matching section has seen wide use with these arrays. The graphed results of the model suggest that we can handle a considerable range of impedances with 75-Ohm cable, which ideally would match 112.5 Ohms to a 50-Ohm coax main feeder. Antenna feedpoints from 100 to 130 Ohms have used them. However, two cautions are in order. First, it may pay to model the actual situation before cutting any 75-Ohm cable to 1/4 wavelength to confirm that acceptable results will emerge. Second, one may use lengths that are not 1/4 wavelength at the antenna design frequency, but somewhat longer or shorter. Very often, modeling will allow one to find the best length to effect a match with equal 50-Ohm SWR values at both band edges. For further details on this idea, see "When is a Quarter Wavelength Not a Quarter Wavelength?".

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A 3-Element 20-Meter Yagi

So far, we have looked at antennas that exhibit self-resonant impedances above the impedance of our 50-Ohm main feedline. Let's turn to an antenna with a lower self-resonant impedance: a 3-element Yagi. The antenna consists of a reflector, a driver, and a director for 14.175 MHz, the center of the 20-meter band. The elements use 1" diameter aluminum on a 22.5' boom. Fig. 7 outlines the antenna, along with three ways in which we shall handle the driver. Throughout the examination, we shall not touch the length of either the director or the reflector, nor shall we alter the element spacing. +
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The "bare" element treatment uses a 198" driver. With that length, the array has a feedpoint impedance of 25.71 - j0.93 Ohms at 14.175 MHz. The resistance, reactance, and 25.71-Ohm SWR appear in Fig. 8.

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The SWR curve appears to tilt more toward the high end of the band because the impedance is essentially flat between 14.175 and 14.20 MHz. However, the SWR rises more slowly below the design frequency than above it. Hence, the band-edge SWR at 14 MHz is lower than at 14.35 MHz. Nonetheless, a good 25.71-Ohm SWR curve is not a good match for a 50-Ohm feedline.

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Otherwise, the behavior of the resistance and reactance are normal--for a parasitic array with a director. The reactance shows a rising characteristic with frequency. The resistance, however, decreases with increasing frequency: that is the mark of a director-controlled parasitic array. Single wire antennas and even Yagis having a driver and reflector show the reverse resistance curve: rising resistance with increasing frequency. See, for example, the bare 40-meter dipole in Part 1 or the bare quad loop in Fig. 5 of this part.

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We shall need to add a matching network of some kind to effect an impedance transformation to match our 50-Ohm main feedline. We have three main choices--although a few others are possible. First is the gamma match, often used when we want to directly connect all elements to a conductive boom. Due to modeling limitations, we shall pass over this matching system in this exercise. Although we can model a gamma in principle, using the same diameter for all wires in the system, normal gamma construction uses several different wire diameters. NEC-2 and NEC-4 tend to yield inaccurate results when we insist on using angular junctions of wires having different diameters.

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A second option is to use a 1/4 wavelength matching section. The ideal characteristic impedance for this section would be the square root of 25.71 * 50, or 35.85 Ohms. We can approximate a 36-Ohm transmission line by paralleling two 1/4 wavelength sections of 72-Ohm cable, connecting together the two center conductors at both ends and the two braids at both ends. In fact, a pair of RG-59 cables will just fit inside a normal UHF coax connector without deformation, making such a matching section both easy to construct and easy to use.

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The impedance behavior, graphed in Fig. 9, is strictly normal for a 1/4 wavelength matching section. Because the line is short at 14 MHz and long at 14.35 MHz, the resistance curve peaks at mid-band. The reactance curve has the opposite slope of its counterpart for the bare driver. The 50-Ohm SWR curve replicates the general appearance of the 25.71-Ohm curve for the bare element. Note that the SWR at 14 MHz is 1.66:1, while at 14.35 MHz, it is 1.75:1, a reasonably well-balanced curve for full 20-meter coverage.

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An alternative matching scheme is the beta or hairpin match. For more detailed information on beta matches in general, see "Beta Coils and Hairpins". Essentially, a beta match is an L-network consisting of a series capacitive reactance on the antenna side and a shunt inductive reactance on the feedline side. To simplify construction, we provide the series capacitive reactance at the antenna terminals by shortening the driver element enough to provide the right reactance value. Instead of using the self-resonant length of 198", we can use a 193" driver to provide about 25 Ohms capacitive reactance.

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To match a 50-Ohm line to a 25-Ohm load, we need, in addition to the 25-Ohm series capacitive reactance, a shunt inductive reactance of about 50 Ohms. We can provide the reactance using any means that shows inductive reactance. For example, we might place a coil across the antenna terminals, so long as the coil's inductive reactance at 14.175 MHz was 50 Ohms. Alternatively, we can use a shorted transmission line stub. Since we can derive more inductive reactance from a shorter stub using a higher characteristic impedance for the transmission line, most builders use parallel open-wire transmission line sections, with the end result resembling a large hairpin.

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To produce 50 Ohms inductive reactance from a 600-Ohm transmission line, we must make it a little over 11" long at 14.175 MHz. So our first attempt at a beta match will use the 193" driver with an 11" 600-Ohm hairpin across the feedpoint terminals. The results appear in Fig. 10.

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In contrast to the 1/4 wavelength matching section system of effecting the match, the beta match or L-network shows a large change in resistance across the 20-meter band. Conversely, the reactance shows very little change. The previous system showed just the opposite characteristics--a large change in reactance but only a small change in resistance. Nevertheless, the resulting 50-Ohm SWR curve has almost the same shape for both systems. With the beta match, the 50-Ohm SWR at 14 MHz is 1.65:1, and at 14.35 MHz, it is 1.79:1.

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The use of a 600-Ohm hairpin inductively reactive stub raises a natural question: will any of the operating parameters change is we use a different characteristic impedance for the stub. For example, we might want to use a 50-Ohm stub, although it will have to be 104.1" long. The line is physically impractical and is likely to be lossy compared to the short 600-Ohm stub. However, for this small side-exercise, we can ignore losses and impracticality.

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The graph for the impedance behavior of our replace stub appears in Fig. 11. The graph is virtually indistinguishable in every respect from Fig. 10, the behavior of the 600-Ohm stub. Indeed, even the bend-edge values of 50-Ohm SWR are the same in both cases.

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Throughout this exercise, we have ignored actual gain and front-to-back values, since they are not germane to our interests. The 3-element Yagi used for the models appears in several guises (element diameter taper schedules) at my web site, for anyone interested. It is a very good monoband 3-element Yagi with its design origins in the work of Brian Beezley, K6STI. In fact, a version of the beam appears in his classic MININEC program, AO.

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A 10-Meter Extended Double Zepp

The extended double Zepp (EDZ) holds interest for us in this context, because it is an inherently non-resonant antenna. At about 1.25 wavelengths, the antenna provides about the highest gain that we can achieve from a single wire before the lobes split into multiple lobes, none of which are broadside to the wire. It has been a popular antenna for use with parallel feedline that terminates at an antenna tuner. +

Let's examine a 10-meter version of the EDZ, 44' of AWG #14 copper wire, about the right length for 28.5 MHz as a somewhat arbitrary design frequency. The design frequency is arbitrary in the sense that we have no special marker to indicate an appropriate goal for that frequency. In all of our other antennas, we used resonance, the condition where reactance goes to zero, as our marker. With the EDZ, we shall always have reactance. At best, we can roughly optimize the wire length for maximum gain at the design frequency, but so long as we are close to maximum gain, we can use a convenient wire length. Hence, we shall use 44'. Our models will all be in free space.

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After we examine the characteristics of a bare EDZ (with no feedline as part of our model), we shall explore a type of matching system sometimes called the match-line and stub system. Fig. 12 shows the two possible versions, one using a shorted stub, the other using an open stub. Both require a transmission line length between the antenna and the stub. The combination yields an impedance at the junction of 50 Ohms, so the portion labeled main feedline can be 50-Ohm coax. However, before we can build a mathing system, we must find the impedance that requires matching.

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The bare EDZ shows an impedance of 142.90 - j690.50 at 28.5 MHz, as shown in Fig. 13. The resistance changes hardly at all across the 28-29-MHz span. The reactance shows a rising characteristic, being more capacitively reactive at the low end of the band and less so at the upper end of the operating passband. Of course, a 50-Ohm SWR curve would be useless at this stage of antenna system development.

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For any impedance to be matched, whether simple or complex, there will be a length of transmission line for a pre-selected characteristic impedance such that the addition of a compensating stub will yield a desired impedance. For the 142.9 - j690.5 Ohm antenna terminal impedance, we must find the combination that will give us 50 Ohms to match out coaxial cable. (Not all transmission line characteristic impedances will provide a solution to this requirement, although most higher values will do the job. Hence, most match-line and stub systems use parallel transmission line for the task.)

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In fact, there are at least 8 solutions to our problem. There will be two match-line lengths. Each of these line lengths will have two parallel stub solutions, one for an open stub and one for a shorted stub. As well, there will also be for each line length a pair of series stub solutions, although they are less commonly used. Parallel transmission line lends itself to the use of parallel stubs.

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For detailed information on the calculation of match lines and stubs, see the special appendix to "The EDZ Family of Antennas". The account provides a detailed analysis of the math behind the system. Previously, the system had in virtually all antenna handbooks been left to cut-and-try techniques or to visual means, such as a Smith chart. My motivation for looking more intensively at the match of the method arose from the fact that if the solution could appear on a Smith chart, then it also had to have a calculable foundation. However, should the system have any interest to future antenna projects, you need not replicate the calculations with pencil. The HAMCALC collection contains a version of the utility program that I wrote to simplify the work and to show at least all of the parallel stub solutions.

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For a shorted-stub solution, we shall use 450-Ohm transmission line. The matchline length will be 5.302' long, while the shorted stub will be 1.348' long. The alternative matchline length is not much longer, but the shorted stub is considerably longer. In most cases of match-line and stub matching, we select the solution that results in the shortest combination of lines.

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Fig. 14 provides a view of the resulting impedance behavior. The new feedpoint impedance at the junction of the lines and stub is 49.99 - j0.02 Ohms, a result that is not likely to be achieved in a real application of the system. The reactance shows a rising curve (like the bare-wire curve), while the resistance curve has the opposite slope. Both exhibit considerable variation. The result is a 50-Ohm SWR curve that is below 2:1 only from 28.1 MHz through 28.9 MHz. We might ask whether we would get better results from an open-stub combination. Let's continue to use 450-Ohm line for both the match line and the stub.

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The match line for the open stub system is 5.758' long, while the stub length is 7.220'. I selected the second match-line length because its open stub is about 2.5' shorter than the one for the first match-line length. The combination results in a 28.5-MHz feedpoint impedance of 50.02 - 0.01 Ohms, once more, a pleasant mathematical outcome, but not one to expect of real wires and lines.

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As shown in Fig. 15, the reactance curve has a rising characteristic, similar to the curve for the shorted stub. But, the range of reactance across the first MHz of 10 meters is about 30% less than for the shorted stub. The resistance curve for the open stub has the opposite slope from the one for the shorted stub. However, the total range of source resistance is about 20% greater than the range for the shorted stub version of the system.

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The consequence of these contrary curve spans is a 50-Ohm SWR curve that is virtually identical in both cases. Once more, the passband with less than a 2:1 50-Ohm SWR extends from about 28.1 to 28.9 MHz. In most cases, the precise values of resistance and reactance will not make an operational difference to the use of the system. Hence, in principle, the two versions of the match-line and stub system are equivalent. However, the shorted stub version has a slight physical advantage in requiring a slightly shorter match line and a considerably shorter stub.

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Conclusion

Of course, our interest has not aimed directly at building a physical antenna. Instead, we have focused on watching the behavior of resistance, reactance, and SWR curves as we connect various transmission lines and different lengths of each type to the antenna feedpoint. The rules of thumb that motivated our initial investigation are long gone. They apply over a too limited range of cases to be very useful. +

Connecting a single transmission line to a mismatched antenna terminal set--even with only a small mismatch--resulted in very regular behavior for the resistance and reactance curves. Indeed, it is possible to mentally catalog the general characteristics of the curve and to use the catalog to assist our expectations in real antenna work.

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When we began the process of adding matching networks that used transmission lines, but not in simple ways, the curves became less regular and hence less predictable without using some form of calculating system. Our primary system has been antenna modeling software using NEC-2 or NEC-4 within the limits of that software. (Adhering to those limits means that there are some cases that we cannot effectively model in detail, as well as factors that will not appear in the results, such as transmission line losses.) The advantage of antenna modeling software (and adjunct graphing software) is that it provides both graphical and numerical outputs together. In this exercise, we have used EZNEC in combination with EZPlots to calculate and present the frequency sweeps. Other software will do an equal job.

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With such software or its equivalent, we can inspect the behavior of the impedance components and derivatives as we add transmission lines to the antenna feedpoint. The need for rules of thumb disappears whenever we can actually calculate the result. The more we actually calculate, the more nearly correct will be our intuitions about a situation. When we see clearly the sort of result that we should obtain--even if we cannot mentally calculate the numbers involved--the mystery that surrounds transmission lines gradually disappears, replaced by understanding. The goal of these exercises has been a set of small steps toward understanding the impedance behavior of transmission lines when connected to antennas.

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Updated 12-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for December, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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Notes on Calculating Input Values from Load Values
+ Along a Transmission Line

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L. B. Cebik, W4RNL

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+ Note: This is a version of a presentation to college student-hams in 1994. Due to limitations in both the drawing system and the HTML system, substitute characters have been used in places. Greek letters are usually spelled out in the text (but not in equations). "L-script" is simply "l" in the text. In places, the standard footed slash that introduces a phase angle has been replaced by "@". Meanings should generally be clear for all other symbols and abbreviations used in the text.
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The input values of voltage, voltage phase angle, current, current phase angle, resistance, and reactance (along with impedance and impedance phase angle, if desired) depend upon two properties: the load value of these parameters and the length and characteristics of the transmission line. The load may be an antenna, a junction with one or more other transmission lines, a dummy load, or anything similar. Those with little experience in dealing with these concepts and quantities may be interested in reading the following review of the relationships among the various transmission line properties.

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Everything begins by speaking the same language. Figure 1 schematically represents most of the elements of transmission lines, while Table 1 (at the end of the text) defines many of the abbreviations to be used in the text and the equations to follow. Since all calculations will be done in terms of degrees (or radians) along a wavelength of RF, let us note in passing the standard conversion equations:

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and

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where Lm is the initial length in meters and Lf is the initial length in feet. The constants can be rounded to 1.2 and 0.366 respectively, but I usually prefer to save rounding for the last step in a series of calculations, despite the predilection of many to initially round everything to the smallest number of significant figures to be found in the data group.

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Should you wish to write a basic program incorporating any of the material to follow, you will have to convert degrees into and out of radians. For quick reference, the conversion equations are these:

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and

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where thetad is any angle (or l) in degrees, and thetar is any angle (or l) in radians.

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Impedance Transformation

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Let's begin with the transformation of impedance along the transmission line, beginning at the load. For every degree of travel, the impedance takes on a new value, with one exception. If the load is purely resistive and exactly matches the characteristic impedance of the line, then the impedance along the line is constant. However, if the load has any reactance or if the load does not match the characteristic impedance of the line, then resistance and reactance go through a cycle of changing values that repeat themselves every 180°. All of what follows, of course, applies to lossless lines, which provides accurate enough results for the short lengths involved in most amateur applications.

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Terman (Radio Engineer's Handbook, p. 186) provides the most general impedance equation:

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where l is the length of the line and lambda is the length of a wavelength, both in the same units, that is, both in feet, meters, or degrees. The terms of the equation are therefore in radians automatically.

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As a matter of completeness, we should note that Keucken (Exploring Antennas and Transmission Lines by Personal Computer, p. 181) provides the appropriate expansion of this equation for use in a computer:

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Keucken's procedure is to calculate the numerator and denominator independently, converting each into polar notation. Zin then equals ZO times the ratio of the polar amplitudes, while the phase angle is simply the numerator angle minus the denominator angle. Rectangular coordinates emerge from standard sine and cosine calculations.

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However, it is very often more useful to begin with and end with the resistive and reactive components of an impedance separately given (that is, given in rectangular rather than polar form). The ARRL Handbook for the early 1990s (p. 16-3) provides separate resistance and reactance equations:

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and +
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Equation 8 will return values with the correct signs, + for inductive reactance and - for capacitive reactance.

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To obtain the impedance, simply take the square root of the sum of the squares:

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and obtain the phase angle from

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From the values of Rin and Xin, we can easily calculate the VSWR using the most general equation:

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Since equations (7) and (8) are for lossless lines, the same VSWR value will result from Rin and Xin values taken at any length, from the antenna terminals on down the line. A few sample calculations should convince skeptics who have experienced changes in SWR readings in the shack with changes in line length that those changes arose from factors external to the basic antenna-feedline configuration. Adding loss factors to the Rin and Xin calculations will result in progressively lower VSWR values as the line length increases. Loss amendments or supplements to the basic equations are important at VHF or with very long line lengths at HF, but short HF lines used in many simple matching or phasing solutions rarely need the added complexities for results that are within measurement or construction accuracy limits. To explore the losses along a line and their effect upon VSWR readings, obtain a copy of the program TLA/TLW by N6BV, available from the ARRL.

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Solving equation (11) for Rin and Xin, of course, will not return unique values. Instead, the equation will return families of values. The families of values--or curves--form the basis for the well-known Smith charts and its more recent computerized extensions, for example, the W7ZOI/ARRL program, MicroSmith.

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Although SWR is the most familiar term used to describe the imedance matching situation in much literature, it is not the only term or even the most fundamental. More basic is the ratio of the reflected voltage to the incident voltage at any given position along a transmission line. An identical ratio applies to the reflected current and the incident current. Thus we may derive from the load resistance (Rin), the load reactance (Xin), and the line characyeristic impedance impedance (R0) a complex term called the reflection coefficient. (Note that because most transmission lines have negligible reactance, that we may reduce the line impedance to its resistive component.) Under these condition, we may calculate the reflection coefficient magnitude (|rho|) .

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However, rho is a complex term with real and imaginary components. In other words, rho has a phase angle, that we may also calculate. For most basic work, we tend to overlook the phase angle of the reflection coefficient and make use only of its magnitude.

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In many tests and handbooks, we find that authors then derive VSWR from the value of rho:

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You may recongnize equation 11 as an expansion of equations 11a and 11c. Essentially, SWR and the magnitude of the reflection coefficient measure the same thing, but use different scales. The list of ways in which we may handle ratio of reflected to incident voltage or current has a third entry called the return loss (RL), which we measure in dB:

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Some texts handle the return loss as a negative quantity, but most instruments that measure return loss treat the quantity as positive, resulting in the leading negative sign in equation 11d.

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Stubs

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If the load end of the line is short circuited so that RL = 0, and XL = 0, then

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and the reactance is inductive. If XL = (an open circuit), then

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and the reactance is capacitive. Equations 12 and 13, of course, are the standard equations for calculating the reactance of a length (less than 90°) of transmission line. The results may be obtained directly from equation (8), assuming that it has been plugged into a BASIC program or something similar, by letting RL = 0.00000001 (as a place holder for 0.0, which may yield "Division by Zero" messages) and XL = 0 for inductive, shorted stubs. For capacitive, open stubs, plug 999,999,999 into both RL and XL.

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Often, we know the reactance to be cancelled by a stub and desire the corresponding line length. If we let lL = the length of an inductive stub (in degrees) and likewise let lC = the length of a capacitive stub (in degrees), then the equations become

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and

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The terms of equation (15), of course, can be inverted and the arctan taken of the result, a procedure common to calculator operations. To determine the physical length of the transmission line, apply equations (1) or (2), solving for Lf or Lm, as appropriate.

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Although we may apply stubs wherever compensatory reactance is required in an antenna-feedline system, the more general stub matching situation is presented in Figure 2. Here, we introduce a transmission Line between the antenna and the junction of the Feed line to the shack or rig. (Capitalized words here refer to elements in Figure 2.) The length of Line is chosen so that at the junction, the resistive component will be the same as the characteristic impedance of the Feed line. However, in most instances, there will be also be a reactive component which the addition of a parallel stub cancels. Note that under the condition of no series reactance, the series and parallel values of feedpoint impedance are identical and purely resistive. In the most general situation, there is no requirement that the Line, Stub, and Feed sections have the same characteristic impedance.

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Although calculation of line length for the Line and the Stub have been largely left to graphical solutions, there is no reason why we should not directly calculate them, especially via a short computer program. The Line length calculation simply requires us to solve equation (7) for l and to convert that length in radians into degrees and feet via equations (1) through (4) as appropriate. The rewrite of (7) yields a quadratic:

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Solving for lr, we obtain

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Note that there are two solutions, since for every 180° of line length (under mismatch conditions), there will be two points at which the resistive component has the same value. Applying equation (8) to the two lengths will yield opposing values of reactance. The limiting case is where the value under the radical goes to less than zero: this condition indicates that with the combination of line values chosen for the antenna values measured or derived from a modeling program, the resistive component never reaches the chosen Feed line characteristic impedance.

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Converting the remnant series reactance into a parallel value provides the magnitude, with a sign change, that the stub reactance must equal to leave the junction with a purely resistive impedance that matches the Feed line ZO.

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This excursion into stub-matching calculations simply illustrates the utility of equations (7) and (8). Knowing the impedance at the end of a length of a feedline terminated in a load, a short, or an open-circuit has too many uses to catalog here.

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Current and Voltage Transformation

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A knowledge of resistance and reactance along a transmission line will not answer every important question about a feed system. Often neglected are the classic and very useful equations for calculating the voltage and current, along with their respective phase angles, along a transmission line. Terman (p. 185) gives the basic current equation as

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where l and lambda have the same meaning as with equation (5).

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Note that the calculation of current at any point along a transmission line requires knowledge not only of the current and its phase angle, but as well of the voltage and its phase angle. Such information, if not measured, best comes from information provided by antenna modeling programs, which generally collect together EL, thetaE, IL, thetaI, RL, and XL in one listing or report. Although such data comes from a model and is often limited by being calculated over perfect, rather than real, ground, it may turn out to be more accurate than the output of the measuring instruments found in most ham shacks.

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Expanding the Terman equation for load currents and voltages that are at other than a 0° phase angle, we can first let ratio EL/ZO = IZ. Then,

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and

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Substituting into equation (18), we arrive at the most general equation,

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Let IH be the "real" component solution and IJ be the "j" component solution. Then

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and

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Unlike reactance that varies ±90°, the phase angle of the current along a transmission line varies through a 360° cycle. Since tangents are ambiguous, a corrective is in order, especially if these equations are loaded into BASIC or some similarly restricted language. Table 2 provides a set of general correctives applicable to either voltage or current calculations.

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The Terman (p. 185) equation for finding the voltage anywhere along a lossless transmission line is

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Letting ILZO = EZ, expanding, and then gathering terms, we arrive at an equation exactly comparable to (21), and we proceed as in (22) and (23) to arrive at Ein and thetaEin. Likewise, the correctives in Table 2 are required to follow the voltage phase angle through its 360° swing.

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Equations (7), (8), and (19) through (24) can put into a single program for simultaneous calculation for any specified collection of voltage, current, and impedance conditions at the load of a transmission line. To prevent division by zero, do not let IH or EH go to 0, but make it read some tiny fraction, such as 0.00000001. Likewise, force IJ and EJ to zero if either is between 0.001 and -0.001.

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Given an operating frequency and the characteristic impedance and velocity factor of a transmission line, you can calculate the voltage, current, and impedance conditions for any length of line. Likewise, with a simple "FOR-NEXT" loop, you can produce a screen or a page of values to explore rates of change for any of the values. A very few such sheets will convince the hardiest skeptic that with complex loads, neither voltage nor current nor their phase angles change in symmetrical sine curves associated with basic AC theory. In general, values from 0° to 90° in 5 increments just about fill a monitor screen, while 0° to 180° in 5 increments will almost fill a sheet of paper. For paper printing, you can simply plug in the values on the 180° line for a new run to complete an entire cycle. One of the easiest ways to check the accuracy of the equation transcriptions into the programming language is to add phase angles thetaZ and thetaI; they should equal thetaE, although you may on occasion have to subtract 360° from a sum to arrive at values of thetaE that have started a new cycle. You can also spot check amplitude values with Ohm's law, although it may require calculation of Zin from Rin and Xin, if Zin is not part of the charted values.

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Feedpoint Conditions

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(Note: equations 25 through 27 have been omitted from this version of the presentation, since they deal with a specialized application and are less generally useful.)

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2-element arrays, where the forward element is directly driven, require a phasing line that has a half-twist between two driven elements. In the case of the ZL Special, the line is approximately 45° long with respect to transformation of the current, where the half-twist in effect places the rear element current 180° minus the line length (45°) out of phase with respect to the forward element current. The net effect is a reversed rear element current 315° (or -45°) out of phase with the forward element current. The general ZL Special configuration appears in Figure 3. We shall limit our interest in the antenna to the feedpoint conditions.

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The input end of the phasing line for the 2-element horizontal array is in parallel with the forward element source. At this point, the voltage is the same for each branch of the current division, although the currents themselves may be quite different. If we calculate or derive from antenna modeling software the phase line input impedance and the forward element impedance, they will be given in series form. To obtain a single source impedance for this antenna, we shall require 1. a transformation to parallel values, 2. a parallel combining of the two, and 3. a return to series form for obtaining the feedpoint impedance of the combination relative to any feedline connection.

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Converting the pair of series impedances into parallel form requires the standard conversion equations:

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and

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It is usually arithmetically easier to invert these values into conductance and susceptance values, each parallel component of which may be added for a combined value and then to invert each result to obtain the parallel values for the resultant resistive and reactive components of the feedpoint impedance. Finally, use these standard equations to reconvert the combination to series form:

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The calculations associated with feedpoint impedances of a horizontal 2-element array are amenable to BASIC and other utility program languages.

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This exercise has aimed to demonstrate the mathematics of calculating feedline input values from load values for any transmission line and of calculating the length of matching stubs, along with the feedpoint impedance of rudimentary arrays. None of the equations are in any sense new, although only a few of the crucial ones--for example, those involving values of current and voltage, along with their phase angles--appear in any of the current handbooks readily available to radio amateurs. Once there was a point to these omissions, since Smith charts obviated some (but by no means all) of the tedious hand calculations. Without diminishing the utility of Smith charts, even the most rudimentary form of programming--that is, BASIC--can reduce the work of making direct calculations down to a matter of inputting data. Moreover, familiarity with the equations provides insight into what the Smith Chart is doing and how. Thus, it is perhaps time once more to place these very useful equations before the amateur community in readily available form for use by the ham interested in antennas and feedlines.

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Most of the equations cited in this set of notes have been placed into utility programs among the HAMCALC collection, developed and regularly updated by George Murphy, VE3ERP. Since the collection of programs uses GWBasic, the equations (or their break down for implementation) is readily accessible to interested users. For an intersting and insightful way of looking at the elements of a Smith Chart, beginning with the reflection coefficient, see "Speedometers, Thermometers, SWR Meters, and Smith Charts" by Dan Maguire, AC6LA.
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Updated 11-25-1998, 10-16-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Return to Amateur Radio Page

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Topics: Matching, Transmission Line


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A 2-Meter/70-Centimeter Dual-Band Yagi for the Home Builder

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L. B. Cebik, W4RNL

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The popularity of dual-band 2-meter/70-centimeter transceivers is high and still growing. VHF and UHF activity of all sorts on both bands is also growing. Indeed, both bands are fully populated with repeaters, and hilltop operations are becoming regular weekend events for all modes. Over the last year or so, I have received numerous inquiries into antennas that cover all of both bands. Two-band and three-band Yagis are readily available for the HF bands, so why not for the 2-m and the 70-cm bands.

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When most amateurs think of a dual-band Yagi, they envision something like the version shown on the left in Fig. 1. The elements are interlaced, and the beam uses either a single driver element or two elements closely coupled. Interlacing the elements seems to promise a short boom, not much longer than required by the lower band of the pair. In the HF region, such designs are both common and highly successful.

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One of the reasons that interlaced multi-band beams work so well in the HF region is that the maximum frequency ratio between the highest and the lowest band covered is about 2:1. The 2-m/70-cm combination presents a different challenge because the frequency ratio is about 3:1. Consider two dipoles, cut for 20 and 10 meters. We can easily use both dipoles with a common feedpoint. The reason is fairly simple: when one dipole shows a low impedance, the other shows a high impedance. The two dipoles do interact, but normally, we can prune each pair to show a satisfactory low impedance on each band. When rightly done, each dipole is active on its own band and relatively inert on the other band. However, if the frequency ratio is 3:1, we have a different situation. At resonance on the higher band, both dipoles show a low impedance. The activity of the longer element has many possible effects, ranging from detuning the upper-band element to dominating the far-field pattern of the combined antenna. Even where we can obtain some satisfactory performance on both bands, the operating bandwidth on the higher band tends to be very narrow.

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When we try to interlace 2-meter and 70-cm elements in a Yagi design, the results are usually disastrous. As well, the high level of interaction between elements for the two bands requires that all dimensions--and everything else that has an effect on the electrical length of the elements--become so sensitive that even the smallest variation can ruin the performance relative to the desired level. One solution is to create isolation by setting the elements for each band at right angles to each other. Arrow Antennas has a hand-held satellite antenna that uses this principle. The right-angle orientation of the elements minimizes interactions. However, the antenna is not useful for using common modes on both bands. Digital and SSB operation on both bands requires horizontal polarization, while FM activity uses vertical polarization. The need expressed by my e-mail is for a beam that uses the same polarization on both bands.

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The solution to the conundrum is to give up the idea of a vest-pocket beam for both bands and return to the fundamentals portrayed by the sketch on the right side of Fig. 1. In this design scheme, the lower band elements all appear at the rear. The shorter higher-band elements are either inert or nearly so when the lower band elements are active. The forward higher-band elements essentially interact only with the nearby lower-band director, which functions as a nearly inert added reflector. Note that each section of the beam has its own driver and therefore its own feedline.

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The Basic Design and Its Performance

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For a variety of reasons, my own design predilections run toward wide-band designs capable of covering all of a desired band. This tendency carries a limitation. First, for a given boom length and number of elements, the gain will not be as high as we can obtain from the same boom length over a narrower bandwidth. However, the seeming penalty also has an advantage. Once designed, broadband beams are more forgiving of the slight variations that occur in every replication due to small differences in the materials used or the shop skills available.

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The design that we shall examine uses 3 elements on 2 meters and 4 elements on 70 centimeters. Each section of the beam covers the full band with acceptably small changes in performance level across each band. The sections each show an very good 50-Ohm SWR curve over the full band (144-148 MHz and 420-450 MHz) with less than 1.5:1 SWR. Because we are separating the two sections, the dimensions are almost (but not quite) identical to those we might employ for independent beams on each band. The final design requires a boom that is less than 50" long.

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Fig. 2 shows the complete dimensions of the dual-band Yagi design. It includes element lengths and element spacing values, as well as spacing values for the combined array. Note that these dimensions apply only to the specified 1/8"-diameter elements in the sketch. Changing the element diameter will require considerable redesign of both element lengths and spacing values within each section of the beam. In a multi-band arrangement, there is no single reliable adjustment factor for changes in element diameter vs. element length and spacing. Re-design for different element diameters is best done with antenna modeling software in small and patient steps to obtain performance curves that are satisfactorily like those we shall show for this design.

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With the dimensions shown, we may sample the performance on each band. Table 1 shows the free-space data and also the data for performance when the antenna is 20' above average ground with a vertical orientation.

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+2-Meter Performance of the Dual-Band Yagi
+Free Space
+Frequency     Gain     F-B Ratio     Feedpoint Z     50-Ohm
+MHz           dBi      dB            R +/- jX Ohms   SWR
+144           7.05     18.35         48.7 - j 9.6    1.22
+146           7.08     18.38         49.4 + j 0.7    1.02
+148           7.18     17.62         48.7 + j11.7    1.27
+20' above Average Ground
+Frequency     Gain     TO Angle     F-B Ratio     Feedpoint Z     50-Ohm
+MHz           dBi      degrees      dB            R +/- jX Ohms   SWR
+144           10.71    4.3          18.34         48.7 - j 9.7    1.22
+146           10.77    4.2          18.35         49.4 + j 0.7    1.02
+148           10.89    4.2          17.60         48.7 + j11.3    1.27
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To correlate these numbers to anticipated antenna patterns, Fig. 3 provides both free-space patterns and patterns over ground. If we assume that the primary use of the antenna will be with a vertical orientation, the free-space H-plane pattern becomes the azimuth pattern for the antenna when used over ground. However, if we rotate the antenna 90 degrees to a horizontal orientation, then the free-space E-plane pattern becomes the azimuth pattern for the beam. The figure does not show the elevation patterns for the beam in horizontal use above ground.

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The fact that the patterns for three sampled frequencies do not change much is promising for consistent performance across the band. We can perform a similar evaluation by sampling the data and patterns across the much wider 70-cm band. Table 2 provides the numerical data (with the beam vertical above ground), while Fig. 4 supplies the patterns.

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+70-cm Performance of the Dual-Band Yagi
+Free Space
+Frequency     Gain     F-B Ratio     Feedpoint Z     50-Ohm
+MHz           dBi      dB            R +/- jX Ohms   SWR
+420           7.36     19.38         51.7 - j19.2    1.46
+435           7.48     20.99         54.2 - j 2.3    1.10
+450           7.87     22.28         49.5 + j17.1    1.41
+20' above Average Ground
+Frequency     Gain     TO Angle     F-B Ratio     Feedpoint Z     50-Ohm
+MHz           dBi      degrees      dB            R +/- jX Ohms   SWR
+420           12.49    1.6          19.36         51.7 - j19.2    1.46
+435           12.63    1.5          20.99         54.2 - j 2.3    1.10
+450           13.05    1.5          22.55         49.5 + j17.1    1.41
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The 4-element design used for the 70-cm section of the beam has slightly more gain than the 3-elements used on 2 meters. That slightly higher gain translates into a numerically more noticeable gain improvement at 20' above ground because on 70 cm, the beam is higher above ground than on 2 meters when we measure the height as a function of a wavelength. In these terms, the forward section (at about 9 wavelengths) is 3 times higher than the rear section (at only 3 wavelengths).

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Special Note: When horizontally oriented, antennas show an initially rapid increase in forward gain as we elevated the antenna to and above 1 wavelength. The rate of gain increase slows down with further increases in the antenna height. When vertically oriented, the same antenna shows much more modest gain (largely due to the wider beamwidth), but as we raise the antenna above ground, the gain of the vertically oriented antenna increases more rapidly. By a height of about 20 wavelengths, the two gain values are nearly identical.

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The patterns also return some interesting information. Although the sample patterns from across the 70-cm band are well controlled and similar, the rear lobes show more complexity than the rear lobes of the 2-meter section, especially in the E-plane free-space patterns. We can see the effects of the more complex rear-lobe structure in the H-plane patterns as well. Some of the complexity is a function of interaction with the 2-meter director, which is nearly three times longer than the 70-cm reflector. How much complexity is acceptable from a design standpoint is a compromise between lengthening the boom further, on the one hand, and developing significant impacts upon the overall pattern shape and the feedpoint impedance, on the other hand. The specified distance allows full band coverage with wholly acceptable values and lobe formation.

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Since spot-sample data can sometimes be misleading, we should also perform some frequency sweeps with the dual-band array model to determine whether the performance is as smooth across both bands as the data seems to promise. Fig. 5 provides 2-meter curves for the free-space forward gain and the 180-degree front-to back ratio. Be sure to read the curves with reference to the appropriate Y-axis scale. For example, the gain curve looks like it takes a major turn upward. However, the total gain variation across the band is only 0.13 dB. Likewise, the front-to-back curve appears to be severely peaked. The actual range of front-to-back ratio is less than 1 dB. Both variations would be unnoticeable in operation.

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The smoothness of performance over a given passband is a function (for Yagi arrays) of the gain, the pattern shape, the front-to-back ratio, and finally the feedpoint impedance. Fig. 6 shows the sweep curves for the feedpoint resistance, reactance, and 50-Ohm SWR across the entire 2-meter band. The resistance varies by about 1 Ohms, while the reactance shows a normal curve with a 21-Ohm range. As a consequence, the 50-Ohm SWR never exceeds 1.3:1.

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Obtaining smooth performance on the 4-MHz 2-meter band is one thing, but attaining a similar goal on the wider 70-cm band is another. Allowing for the frequency differential, the 70-cm band is over 4 times wider than 2 meters. Two factors that assist in obtaining wide-band performance on 70 cm are the addition of the fourth element and the use of an element diameter that is physically equal to the 2-meter element diameter. At 70 cm, the 1/8" elements are equivalent to 3/8" elements at 2 meters. In addition, we do not always add elements to a Yagi beam to obtain gain. By careful design, an added element can improve our control of the Yagi's properties across a given passband.

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As shown in the 70-cm sweep graph for free-space gain and the front-to-back ratio in Fig. 7, the Yagi exhibits a normal set of curves. The total gain range is 0.51 dB, a very small variation for a 7% bandwidth. As well, the front-to-back ratio varies by 2.9 dB, also a relatively small change over a 30-MHz spread. Operationally, we could not detect the performance difference by switching from one end of the band to the other.

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The feedpoint impedance values are equally smooth across the band. As shown in Fig. 8, the source resistance varies by only 5 Ohms, while the change in reactance across 30 MHz is about 36 Ohms. As a consequence, the 50-Ohm SWR remains below 1.5:1 throughout the band.

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Remember that a broadband beam is not just for individuals who wish to use it everywhere within a given band. For the relatively new antenna builder, broadband beams have another advantage. Small variations (I shall not call them errors) from the design very often allow virtually full performance with a broadband design, but the same variations are often enough to detune a narrow-band design to the point of ruining the anticipated performance.

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Some Notes on Building a Beam Like This One

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These design notes are not a construction article. You should use the materials and techniques that you have mastered. However, a few notes drawn from the design of many dozens of Yagis and the construction of many operating and prototype antennas may be useful to newer builders.

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The design shown and analyzed in these notes emerged from NEC-4 models that fall well within the software guidelines for accurate models, that is, models that perform to expectations when constructed so as to coincide with the parameters of the model. All NEC models presume that all elements are insulated and isolated from any conductive boom material or use a non-conductive boom, such as a PVC or a fiberglass tube. (If you use PVC, then be sure that the type you use is well protected from UV. The UV protection of white PVC tends to vary by region of the country.) In fact, NEC has no way to model directly the effects of a boom on elements that contact it or that pass through it via insulating sleeves.

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The design specifies the use of 0.125" (1/8") diameter elements throughout. Even changing the diameter to a 3/16" diameter rod amounts to a 50% change in the diameter, enough to require considerable redesign to restore the performance curves in all categories. Larger diameter changes will require patient redesign of the element lengths and spacing values to re-center all of the performance curves. I occasionally receive e-mail asking if I can redesign an array for someone's local material. Unfortunately, my time does not permit custom design work. At a certain point, a prospective builder has to master the skills needed to redesign a beam or simply pass up a design as interesting but not feasible. About the only elements susceptible to diameter changes are the drivers. Fatter drivers normally only require a change in length to restore their SWR curves and do not usually affect performance in other categories.

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The construction of this beam likely should avoid virtually all nut-bolt combinations. In the HF region, even #10 hardware (stainless steel, of course) creates no measurable detuning effects. However, at frequencies 10 or more times the upper end of the HF region, the lumps created by #6 hardware may make a noticeable difference in performance. The closer the hardware lump is to the center of the element, the more it will likely detune the element relative to its modeled performance.

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Similar cautions apply to cutting and spacing elements. The builder of UHF antennas needs to master the art of measuring to 32nds of an inch, and preferable to 64ths of an inch. (Better yet is the use of a rule that calibrates the space between inch marks in tenths and hundredths.) A 64th of an inch is about 0.4 mm. Such precision, especially from 70 cm upward, requires that we set aside our woodworking concepts of cutting elements in favor of a "sneakier" process. If we measure our element material, then we should cut it with the entire mark showing. Then we can trim the ends down while smoothing them. For aluminum elements, use a bench sander. For harder metals, you may use a grinding wheel (which will gall up if used on aluminum).

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For the present beam--as much as I like aluminum rod--I would likely recommend brass rod. The reason for this choice is the fact that we shall add very small solder "blobs" to the parasitic elements (reflectors and directors). Fig. 9 shows the general idea. In a non-conductive boom tube (round or square), drill a 1/8" hole to pass the element. More precisely, drill a hole just large enough to pass the element with difficulty until it is centered with the centerline of the boom tube. On each side of the tube, add a very small amount of solder to the element to prevent the element from moving in the hole, but not enough solder to make a significant "lump." As an alternative that will work equally well with either brass or aluminum, you may obtain from a local home center one of the epoxies rated for adhesion to metal. Most of these epoxies will be non-conductive, but use only enough to prevent the element from moving under the most severe stresses that nature might eventually throw at the beam.

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The driver elements require somewhat different treatment. We must split these elements to allow direct connection of a 50-Ohm coaxial cable (with a few ferrite beads near the feedpoint to attenuate common-mode currents). Fig. 10 shows one system that has proven effective. Construct a small plate to support the element. Plate size will vary with the size of the element, but it should be long enough (from side to side) to keep the driver in line and parallel to the other elements. At the same time, it should not be so large (especially on 70 cm) that it forms a significant substrate for the element. A substrate with a dielectric constant that differs from the value of air will detune the driver element. A pair of sheet metal screws through the plate and boom should hold it in place.

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Very close to the center, drill two small (1/8") holes through the plate. Each driver half will make a very small bend at the hole and penetrate into but not through the plate. The function of the bends is only to lock the driver element position at the boom. The spacing between the holes should be the same as the spacing between the center conductor and the braid of the coaxial cable used. (Remember that the driver lengths are from tip-to-tip and include the gap created for feedline connection.) Solder the cable center conductor and braid to the element halves using zero-length leads. Coating the cable end and connections with a plastic dip-type coating (such as Plasti-Dip) will weather proof the cable end and solder joints. The length of the cable will depend on a subsequent step. However, clamp the coax to the plate or the boom to remove all stress from the connections.

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Without further pinioning, the driver elements will swing. One step in preventing the swing is to cut a shallow groove in the plate from one end to the other so that the element can rest in the groove. At the ends of the plate, you can cut small block with an inset just large enough to pass the element. With the correct epoxy or plastic cement, weld the plate and the end blocks together.

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Making all of the mechanical connections and drilling holes in the boom requires careful alignment. I recommend that you make up from scrap wood a jig to firmly hold and align the boom while adding the elements. For holes, a drill press--even the rudimentary type that clamps a hand drill--is almost a necessity. However, it will prove invaluable for many future antenna and household projects.

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Any other system that achieves the same goals with minimum metal connected to or in very close proximity to the driver elements will do as well.

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The beam needs support. If you use the beam horizontally oriented, you can place a standard fitting at the center of the boom to mate it with the mast or the stub that attaches to the mast. The center point of the boom lies between the 2-meter driver and director. The two coax leads from the drivers can lie along the boom or within the boom to emerge at the hub.

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The greater challenge lies in using the beam vertically oriented. In most cases, the safest routing for the coaxial cables is to the rear of the 2-meter reflector so that the lines do not detune the elements of the beam. Fig. 11 shows one scheme for accomplishing this goal. Since the boom will be about 50" long on one side of the mast, it will require some form of brace (or counterweight) on the other side of the mast for balance. This configuration also places a limitation on the choice of boom material. It must be rigid enough not to sag significantly with the added weight of the elements. The elements will usually be an insignificant addition to the weight of such boom materials as PVC, so a length of boom that remains straight when supported at one end will likely be sufficient.

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The sketch shows the brace installed on the side of the mast away from the antenna. This system is more apt to PVC and similar materials in which the cements virtually weld the junctions of pipes and fittings together to form a continuous length. However, a triangular support that meets the boom on the antenna side of the mast will also work if it does not interfere with the beam elements.

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The sketch in Fig. 11 also shows a device called a duplexer. If you use the antenna with separate 2-m and 70-cm rigs or if the transceiver has separate 2-m and 70-cm input/output connectors, you may run the individual cables all the way to the rig. However, if the transceiver covers both bands with a single input-output connector, you will need a duplexer to combine the single paths on the transceiver side but to isolate the two antennas from each other on their side of the device. Feeding a 70-cm signal to both antennas at once will divide power between the two sections of the beam with very serious degradations to performance on that band.

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A cross-band duplexer essentially consists of a pair of filters: a low pass filter for 2 meters and a high-pass filter for 70 cm, as shown in general form in Fig. 12. The cut-off frequency for each filter is a frequency that can be almost anywhere between the two bands. The key is that the cut-off frequency must allow the filter to exhibit virtually maximum attenuation at one frequency while showing virtually no attenuation at the other. The number of filter sections and their exact design will vary from one unit to the next. However, for dual-band rigs with a single input/output connector, the device is essential.

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You may place the duplexer anywhere behind the 2-meter reflector. The most convenient mounting position will vary with the construction of the support system. You now also know the lengths of the feedline cables to the individual antennas: just long enough to reach from the driver element to the duplexer. Most commercial units will use cable connectors on both the antenna and rig sides of the unit. However, if you build your own duplexer, you may solder the antenna-side cables directly to the board holding the filters and simply seal the protective box openings--being careful to clamp the cables to remove stress from these connections.

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Conclusion

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We have examined a design for a dual-band directional antenna for 2 meters and 70 cm. The antenna falls into the category of utility beams, since it has modest forward gain, good front-to-back ratio, and a very wide operating bandwidth in all performance categories. Using separate 2-meter and 70-cm section arranged for minimal interaction results in a beam that one might reproduce with relatively good reliability and assurance of performance to specifications.

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Just as important to the success of the beam as the electrical specifications is the care that we put into the construction of such a beam. Attention to all of the construction and support suggestions--or to variations that yield the same results--will allow the beam to achieve the performance of which it is capable.

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Updated 08-08-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: VHF / UHF, Yagi


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A Collection of 220-MHz Yagi Designs:
+ Part 1: Utility Beams: Boom Lengths under 100"
+ and from 3 to 8 Elements

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L. B. Cebik, W4RNL

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The first collection of Yagi designs for 222-225 MHz might be called utility beams, since they are all of relatively small size. The boom lengths range from 21" to just over 80", which translates into boom material lengths between 2' and 7'. Element lengths run from 22" to 27". This range will not change, since it is a function of the frequency of operation.

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In the following notes, we shall introduce each design with a very short commentary and an outline sketch captured from EZNEC. Then, we shall present a table of dimensions, a table of performance data, and free-space azimuth patterns taken at 222, 223.5, and 225 MHz. Some patterns will be pointed right, others will point straight up. Since these models originate over a long period of time, the conventions of arranging elements on the X and Y axes have varied. However, the pattern shapes are unaffected by their modeled orientation.

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Please note the element diameter for each design. It will change from one design to another. Do not use an alternative element diameter without first optimizing the design for the new size. Performance will suffer--often dramatically. As well, note that elements are presumed to be well isolated from the boom. If you wish to use through-mounting for the elements with a metallic boom, consult other sources for applicable correction factors. However, for these shorter arrays, you may well wish to consider alternative boom materials, such as polycarbonate rods or tubes.

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220-3: A 3-Element Yagi

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+ +
+

The smallest Yagi in the group, but not the shortest, is a 3-element array that follows the general parameters of a Bill Orr HF design from the 1980s. A 50-Ohm wide-band match is obtained almost solely by the spacing between the reflector and the driver, as well as the element lengths themselves. At HF, this array is capable of just over 7-dBi gain in free space using standard element sizes. However, the 3/8" diameter elements used her place the free-space gain closer to 8 dBi. However, the Yagi design achieves a 180-degree front-to-back ratio of between 19 and 20 dB. The 50-Ohm SWR is very low across the band.

+ 
Model 220-3 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        25.92                 ----
+Driver           24.40                 12.06
+Director         21.68                 21.45
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              7.80             7.88            7.96
+180-deg F-B           19.40            19.93           19.69
+-3dB Beamwidth        65.0             64.7            64.4
+Impedance (R+/-jX)    41.9 - j 1.1     41.5 + j 3.4    40.8 + j 8.2
+50-Ohm SWR            1.19             1.22            1.31
+
+ +
+

220-4: A 4-Element "OWA" Yagi

+
+ +
+

Model 220-4 is a 4-element "optimized wide-band antenna" (OWA) Yagi, the smallest number of elements to which OWA design can be applied. Note the position of the first director in the outline sketch. The reflector and first director are sized and spaced relative to the driver to provide a very wide-band SWR curve at the desired feedpoint impedance--in this case 50 Ohms. The 1/8" element design shown here is scaled from a 2-meter design. It yields a shorter boom than the 3-element design with an even flatter SWR curve across 220. Despite the short boom, it achieves a bit higher gain than the 3-element model. Consequently, using a 4th element may be worth the investment in aluminum and mounting hardware. However, note the rate of change in gain across the band, which is higher than with the 3-element model due to the use of a thinner element. At just over 20" long, this array promises excellent performance.

+ 
Model 220-4 Dimensions (in inches):  Element Diameter 0.125"
+
+Element          Length          Space from Reflector
+Reflector        26.51                 ----
+Driver           25.78                  8.14
+Director 1       24.16                 10.82
+Director 2       22.70                 20.19
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              8.16             8.22            8.29
+180-deg F-B           23.91            22.07           20.19
+-3dB Beamwidth        62.8             62.5            62.2
+Impedance (R+/-jX)    47.2 - j 2.0     47.6 - j 0.2    47.4 + j 1.0
+50-Ohm SWR            1.07             1.05            1.06
+
+ +
+

220-6: A 6-Element "OWA" Yagi

+
+ +
+

Application of the OWA design is more easily implemented as the number of elements increase. The 6-element design shows the same general arrangement of reflector-driver-first director, although the precise dimensions will be a function of the overall design. The increase in boom length to just under 3' yields an additional 2 dB of gain using 1/8" elements. Note directors 2 and 3: a common phenomenon in OWA design is that these directors will have the same length or director 3 may be slightly longer than director 2. Note the evenness of gain across the band. This design was scaled from a 2-meter design.

+ 
Model 220-6 Dimensions (in inches):  Element Diameter 0.125"
+
+Element          Length          Space from Reflector
+Reflector        26.47                 ----
+Driver           26.10                  6.62
+Director 1       24.42                  9.36
+Director 2       23.72                 16.94
+Director 3       23.72                 24.35
+Director 4       22.84                 35.42
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              10.19            10.22           10.21
+180-deg F-B           28.77            34.98           26.47
+-3dB Beamwidth        53.2             52.6            52.0
+Impedance (R+/-jX)    47.3 + j 9.7     50.1 + j 9.4    50.9 + j 4.0
+50-Ohm SWR            1.23             1.21            1.10
+
+ +
+

220-7: A 7-Element "OWA" Yagi

+
+ +
+

Also scaled from a 2-meter design is a 7-element OWA Yagi on a 4.5' boom. The extra boom length adds about 1.3 dB of gain, with other parameters sustained. The original design used quarter-inch elements, so for 220, 3/16" elements worked best in the adaptation. As in the 6-element design, directors 2 and 3 have the same length, with the forward 2 directors returning to a normal set of tapered lengths. As a personal aside, note the incipient secondary forward lobes in the azimuth patterns. Although almost all designers would considered them insignificant, I continue to believe that a "perfect" Yagi design would eliminate them.

+ 
Model 220-7 Dimensions (in inches):  Element Diameter 0.125"
+
+Element          Length          Space from Reflector
+Reflector        26.79                 ----
+Driver           25.62                  5.82
+Director 1       23.93                  8.84
+Director 2       23.48                 16.67
+Director 3       23.48                 26.59
+Director 4       23.35                 39.94
+Director 5       22.24                 54.30
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              11.52            11.55           11.51
+180-deg F-B           25.34            30.28           27.04
+-3dB Beamwidth        47.2             46.2            45.2
+Impedance (R+/-jX)    41.6 + j 2.9     44.3 + j 5.2    48.5 + j 3.7
+50-Ohm SWR            1.22             1.18            1.09
+
+ +
+

220-8: An 8-Element Yagi

+
+ +
+

The first of 2 8-element designs uses a relatively short boom, only 7" longer than the 7-element OWA design. As well, it does not use OWA design practices, but derives the source impedance largely by virtue of the spacing between the reflector and the driver. Hence, the SWR curve is steeper than for the OWA design, and the gain is only about 0.4 dB higher. Part of the gain originates in the large (3/8") elements. This design is a scaling of a relatively standard handbook design for 432 MHz. It achieves its pattern largely by the taper of the directors. Note the continuing decrease in the -3 dB horizontal beamwidth as we increase the gain.

+ 
Model 220-8 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        25.60                 ----
+Driver           25.50                  8.62
+Director 1       23.97                 11.41
+Director 2       23.29                 17.35
+Director 3       22.76                 25.57
+Director 4       22.45                 35.77
+Director 5       22.15                 47.64
+Director 6       21.90                 61.04
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              11.87            11.90           11.88
+180-deg F-B           27.21            21.76           18.41
+-3dB Beamwidth        45.8             45.2            44.6
+Impedance (R+/-jX)    34.9 + j 8.7     42.6 + j 7.4    44.4 - j 2.7
+50-Ohm SWR            1.51             1.25            1.14
+
+ +
+

220-8A: A Second 8-Element Yagi

+
+ +
+

The final Yagi in our utility collection is a scaled derivative from the classic DL6WU designs for 432 MHz. Bringing the frequency downward required the use of 3/8" elements (as the closest correspondent to the 4 mm elements in the higher-frequency original), plus other adjustments. One mark of this design is the 81" boom length and the consequential increase in gain over the shorter 8-element design just reviewed. Guenter Hoch designs are noted for long boom lengths and a sequence of directors such that the full-size original (26 elements in my files) can be broken almost anywhere to yield a fairly well optimized Yagi of the new shorter length. For the best SWR curve, the reflector spacing often needs tweaking. However, DL6WU designs are very broad-banded and can be made to work acceptably over the entire 420-450 MHz band. So the challenge of scaling the design to 222-225 MHz is to align the best front-to-back ratio region of the curve with the flattest SWR for the desired feedpoint impedance. Needless to say, we shall encounter other DL6WU derivatives as we explore arrays for longer booms in succeeding episodes.

+ 
Model 220-8A Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        26.20                 ----
+Driver           25.20                 11.36
+Director 1       23.50                 14.99
+Director 2       23.19                 24.68
+Director 3       22.91                 36.24
+Director 4       22.65                 49.68
+Director 5       22.42                 64.75
+Director 6       22.00                 80.88
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              12.75            12.75           12.60
+180-deg F-B           20.03            23.58           22.01
+-3dB Beamwidth        40.4             39.6            38.8
+Impedance (R+/-jX)    35.0 - j 5.7     39.9 + j 5.0    56.4 + j 9.9
+50-Ohm SWR            1.46             1.29            1.25
+
+ +
+

This completes the set of utility 220 Yagis from my files. If I had to select favorites from the list, it would be the OWA designs adapted from various 144 and 432 MHz designs. Despite the seeming sensitivity of the position and length of the first director in obtaining the desired feedpoint impedance, the broad-banded nature of these arrays tends to make them reasonably straightforward to replicate with success. As well, each provides even performance across the band in most categories.

+

Nevertheless, many applications on 220 require considerably more gain than provided by any of the antennas shown in this utility collection. Therefore, in the next collection, we shall look at beams using boom lengths from about 12' to about 18'. We shall not greatly increase the element count: in fact, we shall stay in the 12-14 element range throughout the exercise. However, a few of the designs will have "something different."

+
+ +
+

Go to Part 2: Boom Lengths from 140" to 220" and from 12 to 14 Elements

+

Return to Index

+

Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


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+

A Collection of 220-MHz Yagi Designs:
+ Part 2: Medium-Length Boom Beams: Boom Lengths from
+ 140" to 220" and from 12 to 14 Elements

+

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The second collection of 222-225 MHz Yagis consists of arrays with 12 to 14 elements. The boom lengths vary from 12' to about 18' overall, which is beginning to get into the territory of serious operation on the band. We call them "medium length" booms, because we shall look at a few serious booms in the next section. But for the moment, the medium-size Yagi will be interesting to explore.

+

As we did in the first collection of utility beams, we shall introduce each design with a very short commentary and an outline sketch captured from EZNEC. Then, we shall present a table of dimensions, a table of performance data, and free-space azimuth patterns taken at 222, 223.5, and 225 MHz. Some patterns will point to the right, others will point straight up. Since these models originate over a long period of time, the conventions of arranging elements on the X and Y axes have varied. However, the pattern shapes are unaffected by their modeled orientation.

+

Please note the element diameter for each design. It will change from one design to another. Do not use an alternative element diameter without first optimizing the design for the new size. Performance will suffer--often dramatically. As well, note that elements are presumed to be well isolated from the boom. If you wish to use through-mounting for the elements with a metallic boom, consult other sources for applicable correction factors.

+

220-12: A 12-Element Yagi

+
+ +
+

The first Yagi in the new group is the shortest, a 12-element array that fits on a 147.5" boom--just over 12'. It is another derivative from a DL6WU 432-MHz design and uses 1/4" elements. Like all the beams in the Guenter Hoch series, it is broad-banded, which gives the scaler a choice of where in the operating range to place the 223-225 MHz range. Hence, the dimensions are not as constant in the series of beams derived from the 432-MHz design as they would be in the original. Because the beams are broad-band arrays, they do not squeeze out of a given boom length and number of elements all of the gain that is possible. However, they tend to be reliably replicated.

+ 
Model 220-12 Dimensions (in inches):  Element Diameter 0.25"
+
+Element          Length          Space from Reflector
+Reflector        25.40                 ----
+Driver           24.61                  10.35
+Director 1       22.49                  14.23
+Director 2       22.31                  23.55
+Director 3       22.04                  34.67
+Director 4       21.79                  47.60
+Director 5       21.56                  62.10
+Director 6       21.36                  77.62
+Director 7       21.19                  93.92
+Director 8       21.04                 111.00
+Director 9       20.91                 128.85
+Director 10      20.79                 147.48
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              13.87            14.11           14.32
+180-deg F-B           24.05            22.96           20.08
+-3dB Beamwidth        38.2             37.2            36.4
+Impedance (R+/-jX)    47.4 - j 5.0     51.9 - j 0.7    57.7 + j 1.8
+50-Ohm SWR            1.12             1.04            1.16
+
+ +
+

220-13B: A 13-Element Yagi

+
+ +
+

Model 220-13B is also a DL6WU derivative using 1/4" diameter elements. Theoretically, it ought to have the same dimensions except for the additional director. However, as noted, adjustments have been made to the dimensions to align the performance figures. Hence, the dimension chart below will vary a bit from the one for the 12-element version of the array. Of added interest is the fact that as we add more elements, the number of secondary forward and rearward side lobes increases. Although still over 15 dB down from the main forward lobe, they are a noticeable features of almost all long-boom Yagis. The 13th element extends the boom length to nearly 170" but yield about 0.8 dB more gain than the 12-element Yagi.

+ 
Model 220-13B Dimensions (in inches):  Element Diameter 0.25"
+
+Element          Length          Space from Reflector
+Reflector        25.80                 ----
+Driver           25.00                  10.52
+Director 1       22.85                  14.46
+Director 2       22.67                  23.92
+Director 3       22.39                  35.23
+Director 4       22.14                  48.36
+Director 5       21.91                  63.09
+Director 6       21.70                  78.86
+Director 7       21.53                  95.42
+Director 8       21.38                 112.77
+Director 9       21.24                 130.91
+Director 10      21.12                 149.83
+Director 11      21.02                 169.55
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              14.72            14.95           15.13
+180-deg F-B           39.67            27.18           20.59
+-3dB Beamwidth        34.8             34.0            33.2
+Impedance (R+/-jX)    50.4 + j 1.4     55.7 + j 6.6    63.9 + j 7.8
+50-Ohm SWR            1.03             1.18            1.32
+
+ +
+

220-14A: A 14-Element Yagi

+
+ +
+

Let's complete this sequence of DL6WU design with a 14-element version of the Yagi on a 191" (nearly 16') boom. The set of patterns will show the beam's lineage, since the side lobes are nearly identically placed for all three of these medium boom-length Yagis. Again, we shall use quarter-inch elements. However, we shall not this time gather an extra 0.8 dB gain. The gain boost is closer to about 0.4 dB over the 13- element array. As well, the dimensions will not coincide with either of the preceding designs due to the need for adjustments in the move from 432 to 223.5 MHz as the design frequency and in the imperfect scaling of 4 mm elements to 1/4" elements.

+ 
Model 220-14A Dimensions (in inches):  Element Diameter 0.25"
+
+Element          Length          Space from Reflector
+Reflector        25.92                 ----
+Driver           25.11                  10.56
+Director 1       22.95                  14.52
+Director 2       22.77                  24.03
+Director 3       22.49                  35.39
+Director 4       22.24                  48.58
+Director 5       22.01                  63.37
+Director 6       21.79                  79.21
+Director 7       21.63                  95.85
+Director 8       21.47                 113.28
+Director 9       21.34                 131.50
+Director 10      21.22                 150.51
+Director 11      21.11                 170.31
+Director 12      21.00                 190.91
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.16            15.41           15.63
+180-deg F-B           22.61            29.71           25.64
+-3dB Beamwidth        33.0             32.4            31.4
+Impedance (R+/-jX)    48.7 - j 1.6     50.8 + j 6.0    58.1 + j 12.5
+50-Ohm SWR            1.04             1.13            1.32
+
+ +
+

220-14: A 14-Element Yagi

+
+ +
+

The last of our broad-band scaled Yagis is an interesting, but largely impractical design from some 432-MHz studies. The key question that I was looking at concerned the effects of element diameter on both bandwidth and gain. In scaling the study array for 220, the element diameter increased to a full inch. Increasing the element diameter has-- to a certain point--a positive effect on array gain, but it is easy to reach a point where elements are over-coupled unless we increase their spacing. Therefore, this array uses a 18' boom--and extra 2' of boom to achieve about a half dB gain over the DL6WU-derived 14-element array. A 15-element Dl6WU array using thinner elements would end up with close to the same boom length. Hence, we must consider this design as simply an object of study rather than as a candidate for construction.

+ 
Model 220-14 Dimensions (in inches):  Element Diameter 1.0"
+
+Element          Length          Space from Reflector
+Reflector        26.00                 ----
+Driver           23.00                  12.18
+Director 1       22.12                  19.90
+Director 2       21.23                  31.63
+Director 3       21.23                  48.86
+Director 4       20.34                  66.53
+Director 5       19.75                  85.39
+Director 6       19.50                 104.25
+Director 7       19.26                 123.10
+Director 8       19.07                 141.96
+Director 9       18.95                 160.82
+Director 10      18.77                 179.69
+Director 11      18.53                 198.54
+Director 12      18.38                 217.39
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.80            15.92           15.97
+180-deg F-B           24.28            23.31           19.86
+-3dB Beamwidth        31.6             30.8            30.2
+Impedance (R+/-jX)    44.4 - j 3.7     37.1 + j 2.0    43.6 + j 7.0
+50-Ohm SWR            1.47             1.35            1.23
+
+ +
+

220-13A: A 13-Element Yagi

+
+ +
+

Very often, when designing for a narrower operating bandwidth, one can arrive at a gain value with either a shorter boom or with fewer elements than when designing for broad-band operation. SM5BSZ developed an interesting array that I have scaled to 220 in two stages. This first stage uses 1/8" elements on a 212" boom. The boom length is close to that of the 14-element array we just visited, but there is one fewer element. Yet performance is about the same for the two arrays. Note the last 3 forward directors: they actually increase in length rather than adhering to the constant taper of the array we have looked at so far. Check the element length list for other unexpected changes in the directors. That the array is designed for narrower-band use than some of the other arrays that we have examined is shown in the rate of change of gain, front-to-back, and feedpoint impedance in the chart below. If all we wish to do is save weight relative to the 14-element array above, then this design will do the job. However, as a preview of things to come, we shall take a second look at the design.

+ 
Model 220-13A Dimensions (in inches):  Element Diameter 0.125"
+
+Element          Length          Space from Reflector
+Reflector        25.60                 ----
+Driver           25.40                   7.29
+Director 1       24.00                   9.82
+Director 2       23.63                  20.41
+Director 3       22.91                  38.18
+Director 4       22.46                  58.28
+Director 5       22.71                  79.45
+Director 6       22.50                 101.40
+Director 7       22.23                 124.01
+Director 8       22.10                 147.92
+Director 9       22.21                 171.06
+Director 10      22.46                 192.22
+Director 11      22.50                 212.01
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.44            15.92           16.27
+180-deg F-B           20.79            30.26           18.69
+-3dB Beamwidth        30.2             28.8            27.4
+Impedance (R+/-jX)    39.7 + j 3.9     49.0 + j 9.6    63.8 + j 0.1
+50-Ohm SWR            1.28             1.22            1.28
+
+ +
+

220-13: A 13-Element Yagi

+
+ +
+

The Yagi with which we shall finish this medium-boom-length collection may seem to be identical to the one that we just finished. However, there is a significant set of changes. The driver and the first 4 directors have been increased in diameter--in this scaling, to 0.25". Only one element length has been changed--the driver--in order to bring the impedance curve back into good order. However, the overall performance of the array has improved by about 0.4 dB--a good increase in gain for the small change made in the design. In effect, the wholesale increase of element diameter may not be completely necessary to improve array performance. With the right element lengths, increasing the diameter of only certain key elements can achieve the same goal without requiring that we increase the boom length by the amount we saw required in the Yagi with 1" elements. Moreover, the side lobes in the version using only 0.125" elements are considerably stronger than those in the design version that employs 0.25" elements in key places. Thus, the SM5BSZ design--as scaled and adjusted for 220--holds more than construction interest in the evolution of Yagi design work. (Indeed, SM5BSZ has developed a challenging set of papers on the foundations of Yagi calculations.)

+ 
Model 220-13 Dimensions (in inches):  Element Diameter 0.125"  (* = 0.25")
+
+Element          Length          Space from Reflector
+Reflector        25.60                 ----
+Driver           24.79                   7.29 *
+Director 1       24.00                   9.82 *
+Director 2       23.63                  20.41 *
+Director 3       22.91                  38.18 *
+Director 4       22.46                  58.28 *
+Director 5       22.71                  79.45
+Director 6       22.50                 101.40
+Director 7       22.23                 124.01
+Director 8       22.10                 147.92
+Director 9       22.21                 171.06
+Director 10      22.46                 192.22
+Director 11      22.50                 212.01
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.96            16.36           16.55
+180-deg F-B           25.98            28.62           18.38
+-3dB Beamwidth        30.0             28.8            27.6
+Impedance (R+/-jX)    31.6 - j 2.4     46.9 + j 5.7    69.4 - j 0.7
+50-Ohm SWR            1.59             1.14            1.39
+
+ +
+

The SM5BSZ-derived 13-element Yagi completes my collection of medium-boom arrays between 12 and 14 elements on booms from 12' to 18' long. Other designs certainly exist, although they do not happen to be at hand. However, the ones we have examined give a reasonably fair picture of what is possible within the range of boom lengths and element numbers that define the collection. Remember that you can, by judicious optimizing, move the point of maximum gain or any other operating parameter to any point within the 223-225 MHz band to meet special operating needs.

+

In addition, we have seen a few of the limitations and a few added possibilities beyond those we ordinarily think about when designing Yagis. There are a few more radical possibilities for this range of arrays, but we shall defer them until Part 4 of the collection. In between here and there, namely, in Part 3, we shall take an abbreviated look at some truly long-boom Yagis--up to 60' in boom length. However impractical they may seem, they are worth a look.

+
+ +
+

Go to Part 3: Boom Lengths from 235" to 596" and from 16 to 33 Elements

+

Return to Index

+

Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/220-21o.gif b/content/vhf/220-21o.gif new file mode 100644 index 0000000..9d587f1 Binary files /dev/null and b/content/vhf/220-21o.gif differ diff --git a/content/vhf/220-21p.gif b/content/vhf/220-21p.gif new file mode 100644 index 0000000..d848c57 Binary files /dev/null and b/content/vhf/220-21p.gif differ diff --git a/content/vhf/220-26ao.gif b/content/vhf/220-26ao.gif new file mode 100644 index 0000000..99117e8 Binary files /dev/null and b/content/vhf/220-26ao.gif differ diff --git a/content/vhf/220-26ap.gif b/content/vhf/220-26ap.gif new file mode 100644 index 0000000..5e25f80 Binary files /dev/null and b/content/vhf/220-26ap.gif differ diff --git a/content/vhf/220-26o.gif b/content/vhf/220-26o.gif new file mode 100644 index 0000000..d4672e1 Binary files /dev/null and b/content/vhf/220-26o.gif differ diff --git a/content/vhf/220-26p.gif b/content/vhf/220-26p.gif new file mode 100644 index 0000000..e6da5b9 Binary files /dev/null and b/content/vhf/220-26p.gif differ diff --git a/content/vhf/220-27o.gif b/content/vhf/220-27o.gif new file mode 100644 index 0000000..10e0bcd Binary files /dev/null and b/content/vhf/220-27o.gif differ diff --git a/content/vhf/220-27p.gif b/content/vhf/220-27p.gif new file mode 100644 index 0000000..6e86093 Binary files /dev/null and b/content/vhf/220-27p.gif differ diff --git a/content/vhf/220-3.html b/content/vhf/220-3.html new file mode 100644 index 0000000..50e4f8e --- /dev/null +++ b/content/vhf/220-3.html @@ -0,0 +1,258 @@ + + + + + + 220-MHz Yagis Part 3: Very Long Yagis + + + +
+

A Collection of 220-MHz Yagi Designs:
+ Part 3: Very Long Yagis: Boom Lengths from 235" to 596"
+ and from 16 to 33 Elements

+

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The third collection of 222-225 MHz Yagis consists of arrays with 16 to 33 elements. The boom lengths vary from 20' to about 50' overall, which is at the high end of the territory of serious operation on the band. These are truly "long-boom" Yagis. Virtually all of them are outside the realm of practical building projects, although there are some HF Yagis with booms of this length. Whatever their practicality, these big Yagis are interesting as designs to study.

+

As we did in the first and second collections of beams, we shall introduce each design with a very short commentary and an outline sketch captured from EZNEC. Then, we shall present a table of dimensions, a table of performance data, and free-space azimuth patterns taken at 222, 223.5, and 225 MHz. Some patterns will be pointed right, others will point straight up. Since these models originate over a long period of time, the conventions of arranging elements on the X and Y axes have varied. However, the pattern shapes are unaffected by their modeled orientation.

+

Please note the element diameter for each design. It will change from one design to another. Do not use an alternative element diameter without first optimizing the design for the new size. Performance will suffer--often dramatically. As well, note that elements are presumed to be well isolated from the boom. If you wish to use through-mounting for the elements with a metallic boom, consult other sources for applicable correction factors.

+

220-16: A 16-Element Yagi

+
+ +
+

The first 3 Yagis in out long collection are all DL6WU derivatives. Each one uses 3/8" diameter elements. However, the first one is a variant in its element lengths and spacings. As we have noted, the DL6WU beams are truest in their scaling when the element diameter can be to exact scale with the original. When we change the element diameter to accommodate available materials, the designs are thrown slightly off their ability to be pruned and used without readjustment. The more elements to the array, the truer the design plays despite slight changes in element diameter. However, the shorter versions--like the 20' 16-element design at hand--require the most adjustment. Nevertheless, the array described here shows some very good performance figures--as the chart below the dimensions will attest.

+ 
Model 220-16 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        26.18                 ----
+Driver           24.97                  10.83
+Director 1       23.11                  14.82
+Director 2       22.92                  24.39
+Director 3       22.65                  35.82
+Director 4       22.39                  49.11
+Director 5       22.16                  64.00
+Director 6       21.94                  79.94
+Director 7       21.77                  96.69
+Director 8       21.62                 114.24
+Director 9       21.48                 132.58
+Director 10      21.36                 151.72
+Director 11      21.25                 171.65
+Director 12      21.14                 192.39
+Director 13      21.05                 213.66
+Director 14      20.91                 234.92
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              16.52            16.60           16.46
+180-deg F-B           20.13            23.70           20.74
+-3dB Beamwidth        27.8             27.2            26.6
+Impedance (R+/-jX)    41.8 - j 3.0     51.2 + j 8.2    72.6 - j 1.5
+50-Ohm SWR            1.21             1.18            1.45
+
+ +
+

220-21: A 21-Element Yagi

+
+ +
+

If we add 5 elements to the preceding Yagi design--with a few minor alterations here and there--we can gain nearly 1.5 dB more gain from the resulting array. However, those 5 new elements will occupy about 8 more feet of boom length. A practical 220 EME antenna may require at least 30' of boom. While reviewing this design, it may be worth while to also examine some other progressions--most notably the decrease in beamwidth that accompanies the increases in gain. Consequently, aiming the array moves progressively from the realm of the casual through the area of carefulness and finally into the region of the finicky. A second trend to notice is the strength of the secondary forward lobes. Those lobes, which we called brief attention to in the second section of this collection, continue to increase in strength faster than the main lobe itself. By the time we reach 21 elements, the secondary lobes are down from the main lobe by less than 17 dB.

+ 
Model 220-21 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        26.03                 ----
+Driver           25.22                  10.61
+Director 1       23.05                  14.58
+Director 2       22.87                  24.14
+Director 3       22.59                  35.54
+Director 4       22.33                  48.80
+Director 5       22.11                  63.66
+Director 6       21.89                  79.56
+Director 7       21.72                  96.27
+Director 8       21.57                 113.78
+Director 9       21.43                 132.08
+Director 10      21.31                 151.18
+Director 11      21.20                 171.06
+Director 12      21.10                 191.76
+Director 13      21.00                 212.97
+Director 14      20.93                 234.19
+Director 15      20.85                 255.40
+Director 16      20.78                 276.62
+Director 17      20.70                 297.84
+Director 18      20.64                 319.06
+Director 19      20.58                 340.28
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              17.87            17.99           17.90
+180-deg F-B           21.17            26.38           22.91
+-3dB Beamwidth        24.2             23.6            23.0
+Impedance (R+/-jX)    46.5 + j 2.5     56.0 + j 11.7   70.6 - j 1.0
+50-Ohm SWR            1.09             1.28            1.41
+
+ +
+

220-26: A 26-Element Yagi

+
+ +
+

The next longer array uses a boom length of just over 37' and 26 elements. The design is the last in our sequence of those derived from the work of DL6WU. Like the 21-element Yagi, this design uses 3/8" diameter elements. In fact, the number of elements is now sufficiently large that no adjustments are required between the two arrays to arrive at satisfactory performance across the 223-225 MHz spread. (In fact, the 26-element 432 array was the original DL6WU design and smaller versions were pruned from it.) The extra 9' of boom nets us about 1 dB of further gain, with front-to-back ratio and feedpoint impedance remaining stable.

+ 
Model 220-26 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        26.03                 ----
+Driver           25.22                  10.61
+Director 1       23.05                  14.58
+Director 2       22.87                  24.14
+Director 3       22.59                  35.54
+Director 4       22.33                  48.80
+Director 5       22.11                  63.66
+Director 6       21.89                  79.56
+Director 7       21.72                  96.27
+Director 8       21.57                 113.78
+Director 9       21.43                 132.08
+Director 10      21.31                 151.18
+Director 11      21.20                 171.06
+Director 12      21.10                 191.76
+Director 13      21.00                 212.97
+Director 14      20.93                 234.19
+Director 15      20.85                 255.40
+Director 16      20.78                 276.62
+Director 17      20.70                 297.84
+Director 18      20.64                 319.06
+Director 19      20.58                 340.28
+Director 20      20.52                 361.50
+Director 21      20.45                 382.72
+Director 22      20.41                 403.93
+Director 23      20.35                 425.15
+Director 24      20.30                 446.36
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              18.88            19.01           18.93
+180-deg F-B           23.01            29.84           22.98
+-3dB Beamwidth        21.8             21.2            20.6
+Impedance (R+/-jX)    48.5 + j 3.0     59.3 + j 8.5    63.7 - j 6.5
+50-Ohm SWR            1.07             1.26            1.31
+
+ +
+

220-26A: A Longer 26-Element Yagi

+
+ +
+

In the medium-length-boom collection, we looked at a "study design" using 1" elements. The use of such large elements at VHF and UHF frequencies seems odd to many. However, some very effective designs are possible. SM5BSZ developed a fairly narrow-band design for 432 MHz using 10-mm (0.394") elements. The design scales to 220 with 0.75" elements, about 0.004" below optimal, with a loss of only a little of the gain. The design shows a very sharp peak gain value, but that evaluation is somewhat relative to the 20 dBi free-space gain of the array: the peak is about 0.5 dB above the band-edge values. In the 220 version, the peak gain is about 20.33 dBi and occurs just below the upper end of the band. With judicious adjustment, a designer can move it to any place in the band. For this extra dB above the preceding 26-element design, we need another 10' of boom length--about 47.5' total. SM5BSZ designs do not rely on a constant element-length taper. Therefore, in the dimension chart below, you will note some forward directors that are longer than the ones immediately to their rear.

+ 
Model 220-26A Dimensions (in inches):  Element Diameter 0.75"
+
+Element          Length          Space from Reflector
+Reflector        24.44                 ----
+Driver           24.80                  21.79
+Director 1       23.18                  27.31
+Director 2       22.02                  41.22
+Director 3       21.48                  59.34
+Director 4       20.95                  79.38
+Director 5       20.51                 102.17
+Director 6       20.25                 125.78
+Director 7       20.06                 149.33
+Director 8       19.89                 173.44
+Director 9       19.75                 197.56
+Director 10      19.59                 221.89
+Director 11      19.44                 246.62
+Director 12      19.32                 271.44
+Director 13      19.23                 296.28
+Director 14      19.14                 321.14
+Director 15      19.03                 346.04
+Director 16      18.88                 371.21
+Director 17      18.74                 396.56
+Director 18      18.67                 421.84
+Director 19      18.66                 447.24
+Director 20      18.78                 471.91
+Director 21      19.06                 495.67
+Director 22      18.78                 521.11
+Director 23      18.65                 545.90
+Director 24      19.84                 568.25
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              19.55            20.01           20.32
+180-deg F-B           26.12            20.04           22.82
+-3dB Beamwidth        20.4             19.2            18.0
+Impedance (R+/-jX)    33.3 - j 4.7     31.9 - j 2.9    48.7 + j 12.2
+50-Ohm SWR            1.53             1.58            1.28
+
+ +
+

220-33: A 33-Element Yagi

+
+ +
+

The final array in our collection of super-boom Yagis derives from a HyGain design, the original for which came from Joe Reisert, W1JR. It is an older design relative to some of the others and shares some properties in common with both the DL6WU and the SM5BSZ designs. Like the Guenter Hoch designs, it can be pruned to almost any desired length and yield a quite usable and competent Yagi of the new shorter length. However, in common with the designs of Leif Asbrink, it does not rely upon a constant taper to the director lengths. In the dimension chart, you will find many succeeding directors using the same length as the preceding one. Using 3/8" diameter elements, the array achieves about the same gain as the 26-element SM5BSZ design, but has much more broad-band characteristics. In the performance table, note the smaller range of gain change and beamwidth change across the band. The cost of broad-banding the performance is 7 elements and 2.3' of extra boom length. We have now hit the 50' mark in booms. As with all these derivative designs, additional tweaking is certainly possible. For example, the low SWR value can be spread across the 220 band without material harm to the other performance figures.

+ 
Model 220-33 Dimensions (in inches):  Element Diameter 0.375"
+
+Element          Length          Space from Reflector
+Reflector        26.34                 ----
+Driver           26.00                   9.66
+Director 1       23.93                  13.54
+Director 2       23.44                  23.21
+Director 3       22.95                  34.55
+Director 4       22.71                  47.87
+Director 5       22.48                  62.55
+Director 6       22.11                  78.53
+Director 7       21.81                  95.20
+Director 8       21.81                 112.63
+Director 9       21.57                 130.96
+Director 10      21.32                 150.07
+Director 11      21.20                 169.85
+Director 12      21.14                 189.94
+Director 13      21.02                 210.49
+Director 14      20.90                 231.49
+Director 15      20.90                 252.72
+Director 16      20.77                 273.95
+Director 17      20.77                 295.26
+Director 18      20.65                 316.49
+Director 19      20.65                 337.80
+Director 20      20.24                 359.03
+Director 21      20.12                 380.26
+Director 22      20.12                 401.57
+Director 23      20.12                 422.80
+Director 24      19.88                 444.11
+Director 25      19.94                 465.34
+Director 26      19.94                 486.57
+Director 27      19.82                 507.88
+Director 28      19.82                 529.11
+Director 29      19.82                 550.42
+Director 30      19.82                 572.50
+Director 31      19.82                 595.52
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              19.92            29.99           19.91
+180-deg F-B           23.27            25.63           27.69
+-3dB Beamwidth        20.2             19.8            19.5
+Impedance (R+/-jX)    41.2 + j 4.4     47.7 + j 4.2    32.2 - j 6.1
+50-Ohm SWR            1.24             1.10            1.59
+
+ +
+

In terms of boom length, we have reached the end of the collection. In general, we achieve higher gain with longer boom arrays. As we strive for more gain, the higher that we go, the more added boom length is needed for each extra dB of gain. However, we must make allowances for variations in that general rule of thumb. First, the selection of element diameter will have a bearing on just how long a boom needs to be in order to achieve a given gain level, with the possibility that we may reach a point where the element diameter increases the boom length faster than it increases gain. Second, there will be variations in boom length for a given gain that relate to the performance bandwidth characteristics of the array, with broader bandwidth Yagis generally needing more boom length for a given gain level than narrow-band models.

+

Despite these general trends, we have not yet reached the limits of our overall collection of designs. There are some design and construction facets of 220 Yagi design that we have not encountered. We may try some construction variations because they offer performance improvements. Or, to reverse the coin, we may sacrifice performance in order to simplify construction and adjustment. Finally, we might take an interest in some performance factors other than gain and front-to-back ratio. We shall sample these variations on the Yagi theme in our final episode.

+
+ +
+

Go to Part 4: Special Designs: Equal-Length Directors, Quagis, and Multiple Reflectors

+

Return to Index

+

Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/220-33o.gif b/content/vhf/220-33o.gif new file mode 100644 index 0000000..2572941 Binary files /dev/null and b/content/vhf/220-33o.gif differ diff --git a/content/vhf/220-33p.gif b/content/vhf/220-33p.gif new file mode 100644 index 0000000..b990b2c Binary files /dev/null and b/content/vhf/220-33p.gif differ diff --git a/content/vhf/220-3o.gif b/content/vhf/220-3o.gif new file mode 100644 index 0000000..9c3a206 Binary files /dev/null and b/content/vhf/220-3o.gif differ diff --git a/content/vhf/220-3p.gif b/content/vhf/220-3p.gif new file mode 100644 index 0000000..38befee Binary files /dev/null and b/content/vhf/220-3p.gif differ diff --git a/content/vhf/220-4.html b/content/vhf/220-4.html new file mode 100644 index 0000000..df4313a --- /dev/null +++ b/content/vhf/220-4.html @@ -0,0 +1,228 @@ + + + + + + 220-MHz Yagis Part 4: Special Designs + + + +
+

A Collection of 220-MHz Yagi Designs:
+ Part 4: Special Designs: Equal-Length Directors, Quagis,
+ and Multiple Reflectors

+

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Our final collection of Yagi designs for 222-225 MHz contains some special-interest designs. Since there are almost innumerable aspects of Yagi design and performance in which we might take interest, we can only sample a few possibilities. In fact, the number of possibilities equals the number of remaining designs in my collection of models. Nevertheless, we can look at some special construction methods designed either to improve antenna performance or to make construction and adjustment easier for the newer builder. We can also briefly explore at least one way to improve some performance figures other than gain and front-to-back ratio. From that point forward, you will be on your own.

+

As we have done throughout this exploration of 220 Yagis, we shall introduce each design with a very short commentary and an outline sketch captured from EZNEC. Then, we shall present a table of dimensions, a table of performance data, and free-space azimuth patterns taken at 222, 223.5, and 225 MHz. Some patterns will be pointed right, others will point straight up. Since these models originate over a long period of time, the conventions of arranging elements on the X and Y axes have varied. However, the pattern shapes are unaffected by their modeled orientation.

+

Please note the element diameter for each design. It will change from one design to another. Do not use an alternative element diameter without first optimizing the design for the new size. Performance will suffer--often dramatically. As well, note that elements are presumed to be well isolated from the boom. If you wish to use through-mounting for the elements with a metallic boom, consult other sources for applicable correction factors.

+

220-27: A 27-Element Yagi (22 Directors and 4 Reflectors)

+
+ +
+

DJ9BV developed a 27-element Yagi design for 432 MHz, from which the design below is adapted. It consisted--as shown in the outline sketch--of 4 reflectors in a plane at right angles to the plane of the driver and 22 directors. Overall, the array is nearly 33.75' long, which places it about in the range of a 24-element DJ6WU design. With 22 directors, that length is for a 24-element Yagi if it had only a single reflector. The elements are 0.25" in diameter in this adaptation. The aim of the array was to improve performance over standard Yagis. In the gain department, the array models at values one might expect from a DJ6WU 24-element Yagi. However, the DJ9BV excels in two other categories. First, the front-to-back ratio is superior to that of the standard Yagi of the same length and number of elements. Second, the feedpoint impedance is more stable across the entire band than even the DL6WU arrays. Whether these two improvements justify the added mechanical work of installing a 4-reflector system depends largely on the potential user's operating needs.

+ 
Model 220-27 Dimensions (in inches):  Element Diameter 0.25"
+
+Element          Length/Height   Space from Reflector
+Reflector 1      25.99/17.20           ----
+Reflector 2      25.99/ 5.73           ----
+Reflector 3      25.99/-5.73           ----
+Reflector 4      25.99/-17.20          ----
+Driver           25.00                  10.61
+Director 1       23.47                  14.58
+Director 2       23.01                  24.14
+Director 3       22.63                  35.54
+Director 4       22.47                  48.80
+Director 5       22.32                  63.66
+Director 6       22.09                  79.56
+Director 7       21.86                  96.27
+Director 8       21.55                 113.78
+Director 9       21.55                 132.08
+Director 10      21.55                 151.18
+Director 11      21.25                 171.06
+Director 12      21.25                 191.76
+Director 13      21.25                 212.97
+Director 14      21.02                 234.19
+Director 15      21.02                 255.40
+Director 16      21.02                 276.62
+Director 17      20.79                 297.84
+Director 18      20.79                 319.06
+Director 19      20.79                 340.28
+Director 20      20.64                 361.50
+Director 21      20.64                 382.72
+Director 22      20.64                 403.93
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              18.12            18.39           18.62
+180-deg F-B           29.28            34.05           23.78
+-3dB Beamwidth        24.2             23.6            23.0
+Impedance (R+/-jX)    47.4 - j 2.6     51.0 - j 4.6    45.8 - j 7.8
+50-Ohm SWR            1.08             1.10            1.20
+
+ +
+

220-15: A 15-Element Yagi

+
+ +
+

The following 15-element Yagi design is only for comparative purposes with the array to follow. It places 15 3/16" elements on a boom nearly 18' long. The key design property being tested is the use of directors of equal lengths from the second director forward to the last. The reflector, driver, and first director have been set for a 50-Ohm match at the feedpoint across the band. The result of this experiment is a beam with gain slightly below that of the DL6WU 14-element Yagi explored in Part 2, even though the boom is 20" longer for the present design. The purpose in using uniform-length directors for almost all of them is to simplify construction for the newer builder. If that goal is worthy in any given situation, then the 1/4 dB loss in gain may be acceptable.

+ 
Model 220-15 Dimensions (in inches):  Element Diameter 0.1875"
+
+Element          Length          Space from Reflector
+Reflector        26.00                 ----
+Driver           24.44                  19.33
+Director 1       22.80                  30.74
+Director 2       22.11                  50.75
+Director 3       22.11                  61.32
+Director 4       22.11                  77.07
+Director 5       22.11                  92.87
+Director 6       22.11                 108.87
+Director 7       22.11                 124.73
+Director 8       22.11                 140.38
+Director 9       22.11                 156.17
+Director 10      22.11                 171.97
+Director 11      22.11                 187.77
+Director 12      22.11                 203.62
+Director 13      22.11                 219.36
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              14.47            14.76           14.90
+180-deg F-B           20.17            30.76           20.37
+-3dB Beamwidth        28.6             27.4            26.2
+Impedance (R+/-jX)    45.7 - j 13.2    41.2 - j 5.8    37.2 + j 5.9
+50-Ohm SWR            1.34             1.26            1.39
+
+ +
+

220-15Q: A 15-Element Quagi

+
+ +
+

Bill Buchanan, WB4WEN, sent me the design of the array from which the above Yagi was derived. It is a design expressly for 220: a 15 element quagi, as shown in the outline sketch. It has all of the features of the Yagi that I generated for purposes of comparison, except that the driver and the reflector are quad elements. In many cases, quagis show no better performance than comparable Yagis, but in this special case, it does. Remember that directors 2 through 13 are all the same length for construction simplicity. The design shows better than 1 dB gain over the Yagi of the same design, with a few inches saved on the boom, since the quagi reflector and driver can be closer spaced for the 50-Ohm feedpoint match. The gain of the array falls directly between the values for the 14-element and the 16-element DL6WU designs, and the boom length is also between the two. What the uniform elements may give up in maximum gain is restored by the use of quad elements for the driver and reflector.

+ 
Model 220-15Q Dimensions (in inches):  Element Diameter 0.1875"
+
+Note:  Reflector and Driver dual numbers represent the length of a quad
+element side and the circumference of the element.
+
+Element          Length          Space from Reflector
+Reflector        14.53/58.14           ----
+Driver           14.00/55.99            13.63
+Director 1       22.79                  23.60
+Director 2       22.11                  43.60
+Director 3       22.11                  54.18
+Director 4       22.11                  69.93
+Director 5       22.11                  85.72
+Director 6       22.11                 101.58
+Director 7       22.11                 117.37
+Director 8       22.11                 133.28
+Director 9       22.11                 149.02
+Director 10      22.11                 164.82
+Director 11      22.11                 180.61
+Director 12      22.11                 196.46
+Director 13      22.11                 212.20
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.82            15.99           16.05
+180-deg F-B           20.01            23.63           24.93
+-3dB Beamwidth        28.2             27.2            26.2
+Impedance (R+/-jX)    61.7 - j 20.1    53.9 - j 9.0    43.6 + j 9.8
+50-Ohm SWR            1.51             1.21            1.28
+
+ +
+

220-18: 18-Element Yagis With 0.1875" and 0.25" Diameter Elements

+
+ +
+

If you examine the arrays in Parts 2 and 3 (and in this part so far), you will discover that there are secondary forward lobes of considerable proportions. They range in strength from 11 to 17 dB below the level of the main lobe, depending upon Yagi design. In general, the higher the overall gain, the larger the secondary lobes relative to the main lobe. As well, various design variants may suffer higher strength secondary forward lobes as the cost of working toward other goals. The 15-element quagi (and the comparative Yagi) are cases in point. In addition, in many designs, the feedpoint impedance drifts from optimal for a 50-Ohm feed cable as the challenge of gain yields beams with narrow operating bandwidths. The design that we shall present here is the result of a study in striving toward two goals at the expense of gain. One technique of obtaining a wide operating bandwidth is to employ OWA principles around the driver end of the array. A technique of reducing the strength of the secondary lobes is to use enough elements for a given boom length.

+

The following 2 Yagis differ only in their element size (3/16" and 1/4"), but that occasions small changes in element length and spacing. Nonetheless, they both use 18 elements on a 19' boom. Their performance is comparable, with the larger-diameter elements producing a modicum more gain. However, in both cases, the 50-Ohm SWR is less than 1.2:1 across the band. As well, the secondary forward lobes are always more than 21 dB below the main forward lobe. The suppression of secondary lobes also shows up in the beamwidth of the main lobe. Note that the main lobe is wider than the main lobe of the 15-element quagi and Yagi, despite their comparable gains and boom lengths. The two 18-element designs achieve in gain almost what one might expect from the a 15-element DL6WU Yagi on a boom of similar length to these arrays. Thus, the cost of better control is not so much gain as it is the need for 3 extra elements. The performance charts and the pattern displays--when compared to those for other arrays in this collection--are sufficient demonstration of the control obtained by the 18-element OWA Yagis.

+ 
Model 220-18 Dimensions (in inches):  Element Diameter 0.1875"
+
+Element          Length          Space from Reflector
+Reflector        26.67                 ----
+Driver           25.30                   6.58
+Director 1       23.79                   9.19
+Director 2       23.34                  16.70
+Director 3       23.34                  26.83
+Director 4       23.21                  40.11
+Director 5       22.82                  53.61
+Director 6       22.64                  63.06
+Director 7       22.36                  74.35
+Director 8       22.11                  87.47
+Director 9       21.88                 102.18
+Director 10      21.67                 117.92
+Director 11      21.50                 134.46
+Director 12      21.35                 151.79
+Director 13      21.21                 169.90
+Director 14      21.09                 188.80
+Director 15      20.99                 208.48
+Director 16      20.89                 228.96
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              15.98            16.04           16.00
+180-deg F-B           23.47            26.94           39.63
+-3dB Beamwidth        30.4             29.8            29.4
+Impedance (R+/-jX)    42.7 - j 4.2     45.9 + j 1.9    58.6 + j 4.7
+50-Ohm SWR            1.20             1.10            1.20
+
+ +
+ 
Model 220-18 Dimensions (in inches):  Element Diameter 0.25"
+
+Element          Length          Space from Reflector
+Reflector        26.40                 ----
+Driver           25.23                   6.52
+Director 1       23.56                   9.10
+Director 2       23.11                  16.80
+Director 3       23.11                  26.57
+Director 4       22.98                  39.72
+Director 5       22.59                  53.08
+Director 6       22.41                  62.45
+Director 7       22.14                  73.62
+Director 8       21.89                  86.61
+Director 9       21.66                 101.18
+Director 10      21.46                 116.77
+Director 11      21.29                 133.14
+Director 12      21.14                 150.31
+Director 13      21.01                 168.24
+Director 14      20.89                 186.95
+Director 15      20.78                 206.45
+Director 16      20.69                 226.72
+
+Modeled Performance
+
+Parameter             222 MHz          223.5 MHz       225 MHz
+Gain dBi              16.04            16.08           16.03
+180-deg F-B           22.47            23.87           29.85
+-3dB Beamwidth        30.0             29.6            29.2
+Impedance (R+/-jX)    42.1 - j 2.6     43.6 + j 2.8    53.5 + j 8.6
+50-Ohm SWR            1.20             1.16            1.20
+
+ +
+

These two versions of the 18-element Yagi give you a chance to choose your favored element material: 3/16" rod or perhaps lighter 1/4" tubing. However, they should not be considered to be the most fully optimized designs possible either in their boom length category or in the degree of pattern and impedance control. Improvements are always possible.

+

Similar comments apply to all of the Yagis in this collection. The survey of designs is mostly an idea base. More design possibilities exist in various publications and books devoted to VHF and UHF operation. Indeed, ARRL's brand new publication, Yagi Antenna Classics, has a beam for 220 that I will someday check out.

+

In the meantime, I hope that this collection of designs for the 223-225 MHz region provides enough data to satisfy one's curiosity about the sorts of things that are possible. Then you can invent some new possibilities.

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+

Return to Index

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Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


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+

A Collection of 220-MHz Yagi Designs

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+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

I have received numerous requests over the years for VHF Yagi designs, with the 220-MHz band (222-225 MHz) receiving the most requests. The reason for the emphasis upon 220 MHz owes perhaps to the fact that fewer designs are published for this band than for the more popular 144-MHz and 432-MHz bands.

+

I do not have many designs of my own for 220. However, I have collected a good number of Yagi designs for 144 MHz and for 432 MHz. Since scaling a design is routine work for most modeling programs, I freely adapted the designs in my collection for the new frequency. In the collection that follows, we shall see adaptations of designs by DL6WU, SM5BSZ, DJ9BV, and WB4WEN. In addition, we shall see some adaptations of the OWA principle, most noted in the NW3Z designs for HF. Most of the OWAs are from my own work, as are a few others.

+

In the collection, there will be 20 sample designs, ranging from 3 elements to 33 elements and in boom lengths from 20" to 596". All but the last few designs are standard Yagis. But we shall look at a quagi design, a Yagi with uniform-length directors, and a Yagi with multiple reflectors. These are certainly not all of the design possibilities, but they may be enough to provide a foundation for many a construction project.

+

Throughout, every design will presume that elements are well insulated and isolated from the supporting boom. There are too many options in boom diameters to try to provide correction factors for each design. As well, each design is composed of aluminum elements of the assigned diameter. Do not try to build a design using elements with a different diameter without first redesigning the element lengths and spacing to optimize performance.

+

Every design has been set up for a direct 50-Ohm feed. With insulated elements, a direct coaxial feed (with a means of suppressing common mode currents before they travel down the coax) seems most natural--not to mention simple. As well, all designs aimed for a minimum worst-case front-to-back ratio of 20 dB everywhere in the band. This goal was met in all but 4 designs, which dropped no lower than 18 dB at one or the other end the band.

+

A special note on materials: it has become customary for many Yagi builders to use only 0.1875" or 0.25" diameter rods for elements on 220. The usual excuse is that larger tubing weighs too much. Unfortunately, the justification is simply false. 0.1875" 6061 rod weights 0.032 pounds per foot, while 0.25" 6061 rod weighs 0.058 pounds per foot. However, 0.375" 6063 tubing weights 0.044 pounds per foot--less than quarter-inch rod. So we shall throw out the custom and use for each design the diameter tubing that best seems to optimize scaled performance.

+

Narrative will be minimal, except to provide a general characterization of a design and to acknowledge the design's origin. Emphasis will be placed on a. the beam dimensions, b. a chart of key performance characteristics, and c. free-space azimuth plots across the band. Here is the way in which I shall subdivide the beam collection.

+ +

For each sample design, there may well be better choices of element diameters and boom lengths. This collection is simply a starter for design efforts, not a finished product. Run them through your modeling and optimizing programs to change element diameter, element spacing, and overall boom length. Combine ideas to see whether you can squeeze more out of a given boom length and set of elements.

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+ +
+

Updated 03-29-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


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+

The OWA Family Moves to 220

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+
+

L. B. Cebik, W4RNL

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+
+ +

+
+

In the June and July (2002) issues of AntenneX, I presented a family of wide-band 2-meter Yagis ranging from 6 to 12 elements. (See "An OWA Family of 2-Meter Yagis From 6 to 12 Elements," Parts 1 and 2.) The arrays had the following basic characteristics:

+
    +
  • Gain commensurate with the boom length and--at the longest length--within 0.3 dB of the best performing arrays on file.
    • +
  • Direct 50-Ohm feed
    • +
  • 50-Ohm SWR under 1.25:1 across the 144-148-MHz range
    • +
  • Significantly reduced forward side lobes--worst case more than 20 dB down, typically more than 25 dB down
    • +
  • 180-degree and worst-case front-to-back ratio more than 20 dB
    • +
+

The arrays employed 3/16" (0.1875") diameter aluminum elements and were developed via NEC-4 modeling software. All elements are presumed to be insulated and isolated from any conductive boom.

+

The 220-MHz amateur band has in recent times awakened from previous slumber. The activity results in part from the shrinkage of the band to 222-225 MHz, a blow to amateur pride in the U.S. As well, a number of simple transverters have emerged to permit operation on the band. Finally, a cadre of dedicated operators has gone public, developing interest via local club and hamfest activities.

+

Therefore, to serve this growing collection of operators, I have adapted the designs of the 2-meter OWA family to the 222-225-MHz range. The process was not as arduous as it might appear at first site. I scaled all dimensions of the arrays from 146 MHz to 222 MHz, the new design frequency. I then adjusted the element diameter to 1/8" (0.125") and made any final necessary adjustments. (The scaled diameter was not too far off the mark, since the frequency ratio is close to 1.5:1 or its inverse for dimensions, 0.6667:1.)

+

The 220 versions of the OWA family preserve all of the characteristics of their 2-meter cousins. Because the 220-MHz band is smaller as a percentage of the design frequency, the arrays actually cover well over the old 220-225 MHz band limits. The chief advantage is that the greater precision required in building arrays for frequencies approaching UHF is offset somewhat by the slightly wider latitude of acceptable tune-up.

+
+ +
+

Fig. 1 presents in graphical form the forward gain of the 7 members of the family. Perhaps the foremost feature to note is the relatively small change of gain across the band. I designed the arrays to place the highest gain at or just above 222 MHz. Since the principal use of these arrays would be for point-to-point communications, which occurs at the low end of the available band, highest performance belongs in this region.

+

As the number of elements increases, the increment of gain advantage decreases. Therefore, the user may enter construction criteria as well as gain into the formula for determining which version to construct. The smallest--6-element--Yagi is under 3' long in this incarnation. The 9-, 10-, and 11-element versions are under 8', 10', and 12' long. These lengths lend themselves to the use of a variety of boom materials and boom-construction techniques.

+

The widest gain increment occurs between the 6- and 7-element versions of the array. In fact, as later element dimension tables will reveal, the versions from 7 to 12 elements are very closely related so that as we add an element, we change only the length and spacing of the former forward-most director and then optimize the length and spacing of the new forward-most director. This technique simplified the preservation of the 50-Ohm SWR curve and the front-to-back ratio.

+

However, the 6-element array is a cousin, designed on the same basic principles, but using an independent set of dimensions to achieve its performance within a certain boom length--under 5' on 2 meters and under 3' at 220. The gain graph shows that the design is slightly better at preserving gain across the entire band, although the front-to-back ratio will show more variation--ranging from a low of 21 dB to a high of 35 dB. In contrast, the other members of the family aimed for slightly higher gain for the boom length, so long as the front-to-back ratio remained above 20 dB. The result is a set of front-to-back figures ranging from 21 to 25 dB and a noticeable but not very significant peak in gain.

+

Since the SWR curves of the arrays would form a morass of tightly packed lines on a graph, I shall present instead two contrasting cases. See Fig. 2.

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+ +
+

The OWA SWR curve, when extended to its limits, shows 2 low points. The first is a shallow dip near the lower frequency limit of designed operation. The second is a deep dip near the upper operating limit. Below the lower dip, the SWR increases relatively slowing, while above the upper dip, SWR increases rather sharply as the feedpoint impedance drops precipitously. The 220-MHz versions of the OWA family are designed for operation closer to the upper frequency dip to ensure a worst-case SWR of 1.25:1 for the most carefully constructed array. (Construction variables are likely to raise the entire set of SWR values as leads between the feedline and the element introduce some reactance into the impedance seen by the feedline proper.)

+

We may approach the upper frequency dip in two ways, illustrated most vividly by the 7- and 10-element arrays. The 7-element version of the antenna shows the lowest ultimate SWR, but the cost of achieving it is a higher SWR at the band edges: about 1.22:1. The 10-element array has a much shallower dip, but the SWR (without consideration of construction-induced additions) never exceeds 1.15:1.

+

In thinking about the differences between the two curves and the low overall design SWR, line loss is not the principle consideration. The differences in line loss between a 1.1:1 and a 1.25:1 are insignificant. However, the lower the design SWR, the less critical the final construction, since there is greater room for the introduction of otherwise unwanted reactances.

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+ +
+

Fig. 3 samples the patterns of the 6-, 9-, and 12-elements versions of the array. The shortest beam shows the cleanest pattern. The forward lobe is smooth, with no visible secondary forward lobes. The beamwidth of the pattern is wide enough that any tendencies toward the development of secondary forward lobes are encompassed by the overall forward pattern.

+

As we increase gain, we decrease the beamwidth, permitting secondary forward lobes to reveal themselves. The 9-element array shows them as slight bulges. The 12-element array not only shows identifiable secondary lobes, but tertiary bulges as well. One aim in the design of these arrays was to minimize these secondary lobes, and the patterns show the degree of success.

+

The rear lobes are equally susceptible to multiple lobes. Indeed, the 6-element beam shows a clear triple-lobe structure. The more closely knit family from 7 to 12 elements all show the type of structure of the overlapping 9- and 12-element versions in Fig. 3. A central rear lobe has two small side lobes. Although these arrays have more energy to the rear than the 6-element version, they should prove entirely serviceable in terms of operation or even a G/T (gain vs. thermal temperature) analysis.

+

The simplest way to present the individual family members is in a systematic presentation of dimensions and performance. Therefore, most of what follows will be tabular in format, with some free-space azimuth patterns to illustrate the performance expectations from the arrays.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+6 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.45       -----
+Driver            26.28        6.66
+Director 1        24.58        9.42
+Director 2        23.88       17.05
+Director 3        23.88       24.52
+Director 4        22.99       35.66  ( 2.97'--0.67 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See Fig. 4.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               10.22             35.09             50.0 + j 9.4      1.21
+223               10.22             28.86             51.1 + j 7.0      1.15
+224               10.19             24.70             49.5 + j 2.5      1.05
+225               10.14             22.10             43.4 - j 1.9      1.16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+7 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        22.72       55.02  ( 4.59'--1.03 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See fig. 5.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               11.55             29.59             46.4 + j 8.5      1.21
+223               11.51             26.76             49.7 + j 6.9      1.15
+224               11.43             23.18             50.6 + j 1.0      1.02
+225               11.26             20.60             43.6 - j 6.4      1.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+8 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        23.15       56.88
+Director 6        21.83       74.32  ( 6.19'--1.40 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See Fig. 6.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               12.34             23.52             46.6 + j 8.0      1.20
+223               12.32             23.98             49.5 + j 7.4      1.16
+224               12.22             23.04             51.7 + j 2.5      1.06
+225               12.04             21.15             46.7 - j 6.6      1.17
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+9 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        23.15       56.88
+Director 6        22.56       76.29
+Director 7        21.18       94.70  ( 7.89'--1.78 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See Fig. 7.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               13.00             21.92             45.2 + j 5.5      1.17
+223               12.99             22.56             46.0 + j 6.1      1.16
+224               12.92             23.00             47.5 + j 4.7      1.02
+225               12.76             22.60             46.4 - j 1.2      1.08
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+10 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        23.15       56.88
+Director 6        22.56       76.29
+Director 7        22.10       96.41
+Director 8        20.26       114.43  ( 9.54'--2.15 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See Fig. 8.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               13.48             22.40             46.4 + j 4.6      1.13
+223               13.48             22.37             46.3 + j 4.2      1.12
+224               13.43             22.32             46.0 + j 2.8      1.10
+225               13.29             21.98             43.7 - j 1.0      1.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+11 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        23.15       56.88
+Director 6        22.56       76.29
+Director 7        22.10       96.41
+Director 8        21.64       117.33
+Director 9        21.05       134.82  (11.24'--2.54)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See fig. 9.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               14.01             25.70             47.2 + j 6.3      1.15
+223               14.03             25.23             48.6 + j 5.1      1.11
+224               13.99             23.91             48.5 + j 1.5      1.04
+225               13.86             22.25             43.8 - j 4.0      1.17
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12 Elements:  1/8"  (0.125") diameter aluminum
+
+Element           Length      Distance from
+                    (")       Reflector (")
+Reflector         26.90       -----
+Driver            25.98        5.78
+Director 1        24.33        8.86
+Director 2        23.89       16.69
+Director 3        23.94       26.78
+Director 4        23.81       40.37
+Director 5        23.15       56.88
+Director 6        22.56       76.29
+Director 7        22.10       96.41
+Director 8        21.64       117.33
+Director 9        21.18       138.11
+Director 10       20.52       156.52  (12.79'--2.94 wl)
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Performance Expectations:  See Fig. 10.
+
+Frequency         Free-Space        Front-Back        Feedpoint Z       50-Ohm
+ MHz              Gain dBi          Ratio dB          R +/- jX Ohms     SWR
+222               14.34             24.65             47.5 + j 6.1      1.14
+223               14.37             24.77             48.7 + j 4.8      1.11
+224               14.34             24.23             48.4 + j 1.1      1.04
+225               14.24             23.08             43.6 - j 4.2      1.18
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Construction of Yagi arrays requires increased attention to detail as we increase frequency. HF is very forgiving of relatively sloppy construction methods. However, even by 6 meters, the effects of loose leads, casual measurement, and unwise choices of materials become all too apparent.

+

The arrays presented here call for great care in three areas of effort, all of which together re-affirm the construction principle of going slowly and getting it right. First, obtain the right materials. Do not alter the element diameters without redesigning the entire array. A change in diameter of the elements will throw off the inter-element coupling and thus the entire operation of the array. Beware of boom materials susceptible to UV degradation or other adverse weathering affects. The longer the model you may choose to build, the more critical material selection becomes.

+

Second, measure element lengths and spacing very carefully, and cut precisely. Cutting a 16th long and sanding the element ends to precision is wise if you lack a precision shop. If you use any through mounting of elements, use a drill press--even a small fixture that accepts a hand drill will do. The object is precise alignment of all of the elements. Keeping everything on a single plane is likely more of an aesthetic ideal than an electrical necessity. However, keeping the elements as exactly parallel to each other as possible is a necessity.

+

Third, plan carefully the mounting of the driven element and the attachment of the feedline or a connector to this element. If at all possible, keep the driver in line with the other elements, since even a 1" displacement will slightly change the H-plane pattern of the array. Over ground, this slight change may wash out as ground reflections add and subtract from direct radiation, but the gain may suffer slightly. Equally or perhaps more important, use extreme care with driver leads to the feed cable stub or connector.

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The only element in the array which may be altered without significant changes in the performance of the array is the driver. Use of a fatter driver will call for element shortening, but will otherwise not adversely affect performance--or improve it. However, this available latitude does give the builder options for construction that may be useful in view of available materials.

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1/8" aluminum rod is often obtainable from local home centers, but may be purchased from outlets like Texas Towers at very reasonable prices. I shall leave boom construction and element mounting systems to the many handbooks on the market. The most promising methods will vary from one size array to the next.

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None of these array approach the size needed for moon-bounce work, although a quad array of the longest ones might approach the threshold for such operations. Nevertheless, the arrays do promise more effective point-to-point communications in the 222-225-MHz region. That is enough of a service to keep any family busy.

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Updated 09-02-2002. © L. B. Cebik, W4RNL. This item appeared in AntenneX, August, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: VHF / UHF, Yagi


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Multiple Reflectors for Long-Boom Yagis

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L. B. Cebik, W4RNL

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+
+ +

+
+

On occasion, I have received inquiries of the following type: How much will the gain of my Yagi for [VHF/UHF] improve if I just add some additional reflectors?

+

From the start, such inquiries have usually struck me as strange, since I do not generally think of a reflector as a key element in the improvement of an array's gain. The reflector, in concert with the driver--and in OWA designs, all in concert with the first director--tends to function so as to set the Yagi feedpoint impedance. In designs within which the first director is primarily a gain and directivity element, the length and spacing of the reflector, relative to the driven element, tends to set the impedance such that a wider spacing increases the impedance and vice versa.

+

As well, the reflector may play a variable role in setting the front-to-back ratio of a Yagi. In some designs, the reflector plays only a small role: in concert with the forward-most director, change the lengths of the two elements can smooth out (or peak) the font-to-back ratio across a given design passband. However, the directors themselves tend to control the level of the front-to-back ratio. In one design exercise for 12 meters, a set of phased drivers with an inherent front-to-back ratio barely above 7 dB returned a front-to-back ratio of well over 20 dB when a director was added to the array. In other cases, the reflector specifications may be crucial in obtaining a desired front-to-back level.

+

Adding reflectors, then, seems most apt to obtaining a desired driver impedance or to obtaining a desired front-to-back performance. Gain improvements would seem secondary from the perspective that I normally take. However, we might reformulate the question to see if some design work might give us something useful by way of answer.

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Defining the Supplemental Reflector Question

+

Suppose that we start with a very reasonable Yagi design. Since the question of multiple reflectors arises most normally in the VHF and UHF region, let's use a 12-element Yagi with a boom length of about 2.94 wl. The design employs an OWA driver/reflector/first-director combination to provide a 50-Ohm impedance with an SWR under 1.2:1 across the 222-225-MHz spread. Hence, in the arena of setting the feedpoint impedance, there is little that additional reflectors could do to improve the situation.

+

As well, the array--ignoring any construction variables that might alter modeled specifications--shows better than 23 dB front-to-back ratio across the band--whether we take a 180-degree or worst-case slant on the front-to-back ratio. Although 20 dB is a typical radio amateur boundary between good performance and otherwise in this department, it is possible that further improvement might tweak a G/T (gain vs. thermal loss) calculation.

+

The array gain in free-space models runs between 14.24 dBi at the upper end of the band and 14.34 dBi at the lower end, with a peak of 14.36 dBi at band center. These figures have more precision than operationally useful, but do indicate the slope of the gain curve. Hence, we may retain them for this study.

+

Equally of note in the initial Yagi design is the secondary forward lobe performance. Many high gain designs have secondary forward lobes that are down by only 12-18 dB from the main forward lobe. The OWA-based design provides additional attenuation of these lobes to the -25 dB or better level.

+

To the existing array, we shall make no changes. Instead, we shall simply add a pair of reflector elements above and below the existing reflector. We shall seek out the length and position that optimizes performance best. Position here shall mean two things: the alignment of the reflectors with the original reflector and the vertical distance between the original and new reflectors. The general outline of the two arrays appears in Fig. 1.

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Due to the graphing limitations in the software from which the outlines are taken, the "std" or original array does not line up exactly with the corresponding elements on the "ref" or supplemented array. However, the dimensions and positions of the original 12 elements have not changed.

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Fig. 2 provides an EZNEC Pro wire table for the original array, with all dimensions in inches. This wire structure, using 1/8" aluminum elements, is the basis for what follows.

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Fig. 3 shows the corresponding wire table for the 14-element array, with the 2 new reflectors listed as wires 1 and 2. Notice that they are slightly behind the original reflector and considerably separated from it vertically. The 13' long Yagi now becomes nearly 2' high as a result of adding the reflectors.

+

Besides their positions, also note the length of the added reflectors, which are significantly longer than the original reflector. I adjusted the position and length of the reflectors to obtain the best combination of gain, front-to-back ratio, and feedpoint impedance possible. In their present positions, changes of new reflector length shows a slight drop in gain. However, it might also be possible to continue working with the reflector specifications to obtain further increases in performance. These notes are a preliminary investigation and the results are suggestive, but in no way final. However, see the added notes near the end.

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Potential Performance Comparisons

+

One critical factor remained a constant: the added reflectors should result in a feedpoint impedance range that resulted in a 50-Ohm SWR curve no worse than that of the original array. Fig. 4 shows the remarkably coincident curves that resulted.

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+ +
+

The following table compares the impedance and SWR values at the band edges and center.

+ 
Antenna                 STD                           REF
+  Frequency       R+/-jX Ohms       SWR         R+/-jX Ohms       SWR
+  222             47.5 + j 6.1      1.14        49.5 + j 6.8      1.15
+  223.5           48.9 + j 3.3      1.07        51.2 + j 3.4      1.07
+  225             43.6 - j 4.2      1.18        45.5 - j 5.3      1.16
+

Then what, if anything, did we obtain for our trouble? To answer this question, let's look at the relevant data in both tabular and graphical formats.

+

In the following table, the following column headings will apply: GN = free-space forward gain in dBi; B/W = -3 dB horizontal beamwidth in degrees; FB 180 = 180-degree front-to-back ratio in dB; FB W-C = worst case front-to-back ratio in dB; S/L = front-to-(forward)-side-lobe ratio in dB.

+ 
Parameter         GN          B/W         F-B 180     F-B W-C     S/L
+STD
+  222             14.34       36.8        24.65       24.53       27.85
+  223.5           14.36       36.2        24.59       24.12       26.57
+  225             14.24       35.4        23.08       23.08       24.97
+REF
+  222             14.44       36.8        31.25       31.25       28.09
+  223.5           14.46       36.2        34.73       34.16       26.64
+  225             14.34       35.6        34.21       31.41       24.88
+

The constant gain increase resulting from placing and optimizing the 2 new reflectors is 0.10 dB. As expected, the gain increase is itself not significant enough to call for the additional two elements. Likewise, the beamwidth does not change at all (0.2 degrees at 225 MHz). Moreover, the forward side lobe performance also fails to change significantly.

+

However, the front-to-back ratio shows a more dramatic increase with the addition of the new elements. The average increase in the 180-degree ratio is 9.3 dB, while the average improvement of the worst-case value is nearly 8.4 dB. (It may be useful to note that in optimizing the front-to-back ratio, the worst-case value was equalized to the degree possible at the band edges.)

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Before commenting further on these results, let's examine them as annotated free-space azimuth (E-plane) patterns. Comparing the std and ref patterns may provide additional insight into what has happened as a result of adding the new reflectors.

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Fig. 5 shows the corresponding patterns at 222 MHz. Most notable is the shrinkage of the main rear lobe, but without significant effect on the rear side lobes. The strongest rear side lobes remain virtually as strong in both patterns, although the main lobe shrinkage makes those lobes more vivid for the ref model. In fact, a new set of rear side lobes, swallowed by the main lobe in std, becomes evident in ref.

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Fig. 6 reveals something about the main rear lobe of both models. The seemingly insignificant spread of the main rear lobe for std turns out to have some importance, as revealed by the "fan" shape of the main rear lobe in ref. At 223.5 MHz, the ref array reaches peak performance in both forward and rearward directions. Hence, the secondary rearward lobes also show some noticeable improvement--however marginal the exact numbers--relative to those same lobes in std. However, there is virtually no change on the forward lobe structure of the array.

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Fig. 7, the comparison at 225 MHz, shows a continuation of the features so far noted. The rear quadrants show considerably less energy in ref than in std, despite an absence of change to the forward lobe structure. One reason--subject to full analysis of a 3-dimensional pattern set--that so little gain is added to the forward lobe is that the original rear lobes initially had so little energy. At well over 20 dB down from the main lobe, a further increase in front-to-back ratio of 10 dB leaves little energy to add to the array's forward gain.

+

Indeed, even had the new reflectors reduced all side lobes to near-zero values, the array would still have shown little further forward gain. The key to adding such gain would be a further reduction in the -3 dB beamwidth, which seems beyond the powers of new reflector elements to influence. Essentially, only the director structure of the array might accomplish that feat.

+

However, for some possible applications, the absence of a significant increase in forward gain may not be sufficient reason to ignore the addition (and further perfection) of the new reflector elements. To the degree that the best weak signal reception performance requires us to minimize all pattern lobes except the main forward lobe, the improvements in front-to-back ratio may be operationally significant. Indeed, the rear lobe structure of ref suggests that some further reductions may be possible without jeopardizing other performance factors.

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Exploring Supplemental Reflector Performance With Model Variables

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Perhaps the simplest way to accomplish this task as an initial modeling design effort is to transfer the model to a program accepting variables and equations. Despite the graphical representation of results in EZNEC Pro, I actually did the design revisions using NEC-Win Plus, using the model-by-equation facility.

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Fig. 8 shows the very simply equations page, with 3 variables, A, B, and C. A is the element half length in meters (the default unit of .NEC-format conversion from EZNEC to NEC-Win). B is the distance along the Y-axis, where a value of zero would align the new reflectors with the old. C is the vertical separation of each reflector above and below the plane of the other elements.

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The wires page, Fig. 9, shows the variable placement for the two new elements. The element length coordinates appears as A and -A. Likewise, the upper and lower new reflectors are at C and -C. Note that in this initial exercise, I did not alter the placement of length of the original reflector. In a full scale study, one might wish to convert this element to a set of variables and adjust its specifications. (Since the original reflector was crucial to obtaining the impedance curves across the passband, I left it unchanged as the simplest means of sustaining those curves.)

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Since NEC-Win Plus uses NEC-2, I transferred the final optimized dimensions back to EZNEC Pro, using NEC-4, so that all numbers would emerge from the same calculating engine.

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The Performance of a Single Added Reflector

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Although the improvements to the front-to-back ratio are directly attributable to the added reflectors forming a roughly vertical plane with the original reflector, the question arose as to whether we might obtain similar results with a single new in-plane reflector. I therefore simplified the model in NEC-Win and tried to optimize a single reflector placed immediately behind the original. Fig. 10 shows the resulting wire table.

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Wire 1 is the new reflector. Note that it is shorter than the original. As well, it is at a considerable distance from the original reflector, lengthening the boom by over 9". The position and length of the new reflector were the best obtainable without modifying the original reflector. The following table summarizes the data from the model (omitting the impedance and SWR data, which did not change).

+ 
Parameter         GN          B/W         F-B 180     F-B W-C     S/L
+1-REF
+  222             14.39       36.8        25.81       25.81       27.61
+  223.5           14.43       36.2        26.23       26.00       26.28
+  225             14.29       35.4        25.01       25.01       24.61
+

Once more, gain does not change by much--0.05 dB above std. As well, the beamwidth and side-lobe performance remain constant with std. The average 180-degree front-to-back ratio improves by only 1.6 dB, while the average worst-case front-to-back ratio improves by 1.7 dB. In short, the addition of an in-plane reflector provides little improvement in overall performance while lengthening the array weight and length. Fig. 11 provides E-plane patterns for comparison with the one marked std and ref.

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No fixed and final conclusions emerge from this preliminary study of adding reflectors to long VHF and UHF Yagis. The work does suggest that relative to reasonably well-designed single-reflector in-plane Yagis, added vertical plane reflectors offer little to improve gain, beamwidth, side-lobes, or impedance concerns. Some of the illusion that they might create notable improvements in any of these areas certainly stems from lack of complete information on the part of inquirers. However, some of the impression may also result from comparing lesser in-plane designs with perfected designs using added reflectors.

+

At this juncture, subject to change with time and further investigation, the real contribution of added reflectors appears in the reduction of rear lobe radiation. In many single-reflector designs, the interests of maximizing gain has resulted in relatively poor rearward performance. Even the design called std in these notes can use improvement if employed in the most demanding weak signal applications. to this end, the addition of vertical-plane reflectors can improve the antenna performance without detracting from other performance goals of the design. And it is here that added vertical-plane reflectors may have their best use.

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Supplemental Notes on "Ultimate Front-to-Back" Performance

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It struck me that the data presented in the above notes is incomplete. We have not explored the H-plane (or free-space elevation) pattern results of adding the supplemental reflectors. At the same time, the failure to reach something close to ultimate front-to-back performance also bothered me (or my sense of orderliness in bringing the small and provisional test to completion).

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Therefore, I returned to the NEC-Win model and its variables, seeking the maximum front-to-back performance that I could generate with 2 supplemental reflectors--without jeopardizing the improvements, such as they are, in forward performance. Fig. 12 provides a wire table (in EZNEC format) for the results of these attempts to "perfect" the model.

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If you compare this model with the earlier provisional supplemental reflector model, you will discover that only one parameter has changed: the vertical distance between each new reflector and the plane of the standard Yagi. The increase is nearly 25%. The reflector lengths remain within 1% of their previous values. Also constant is the distance from the original reflector in the array plane, although this distance is less sensitive to change than the element length.

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The resulting SWR curve is well within the project specifications, as revealed by the following table (where STD represents the original Yagi and ULT refers to the freshly modified version).

+ 
Antenna                 STD                           ULT
+  Frequency       R+/-jX Ohms       SWR         R+/-jX Ohms       SWR
+  222             47.5 + j 6.1      1.14        49.4 + j 5.9      1.12
+  223.5           48.9 + j 3.3      1.07        50.8 + j 2.5      1.05
+  225             43.6 - j 4.2      1.18        44.8 - j 5.8      1.18
+

The following table compares the performance values of all 3 arrays, with STD giving us a reference baseline, while REF and ULT let us see what further improvements we may make and where the limits may lie.

+ 
Parameter         GN          B/W         F-B 180     F-B W-C     S/L
+STD
+  222             14.34       36.8        24.65       24.53       27.85
+  223.5           14.36       36.2        24.59       24.12       26.57
+  225             14.24       35.4        23.08       23.08       24.97
+REF
+  222             14.44       36.8        31.25       31.25       28.09
+  223.5           14.46       36.2        34.73       34.16       26.64
+  225             14.34       35.6        34.21       31.41       24.88
+ULT
+  222             14.44       36.6        38.28       32.96       27.49
+  223.5           14.45       36.0        47.19       30.31       26.07
+  225             14.32       35.6        38.31       28.50       24.36
+
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Fig. 13 provides sample free-space azimuth (E-plane) patterns for the array at each frequency. Of special note with respect to our project of increasing the front-to-back ratio is the fact that, although we indeed significantly increased the 180-degree front-to-back ratio, we did not improve the worst-case value. In fact, above 222 MHz, the worst-case value actually goes down. However, the total energy to the real remains lower, as may be evident from comparing the rearward quadrants of ULT and REF in their respective azimuth patterns.

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Whatever the improvement, it comes at a cost. First, the forward gain shows signs of a decrease--as yet imperceptible in operation, but numerically significant in terms of optimizing an array. Second, the sidelobe performance is beginning to deteriorate slightly, as revealed by a comparison of the side-lobe values in REF and ULT. In the ULT model, neither of these decreases has yet reached a level that would count against carrying the supplemental reflector design process to the ULT values.

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The supplemental reflectors also have a benefit for the free-space elevation (or H-plane) pattern of the array. Fig. 14 shows that benefit.

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The figure compares the 223.5-MHz elevation patterns for STD and ULT. The improvement in the rear-most portion of the pattern is clear, as the large main rear lobe of STD devolves into a collection of smaller lobes. However, we should also attend to the secondary forward lobes in the H plane--a pair above and below the plane of the array. Each member of the set shows at least 2-dB improvement due to the presence of the added reflectors. At the same time, the main forward lobe shows a slight increase in beamwidth. Yagi design has, to a very large measure, tended to ignore H-plane performance, since it has been viewed as somewhat beyond effective control. The element ends in the E-plane constitute the chief controls in forming the azimuth pattern. To the degree that the azimuth pattern shows a stronger forward lobe, the beamwidth and the side lobes in the H plane follow suit, although imperfectly, if the evidence of the STD pattern is any indicator. The supplemental reflectors outside the main array plane provide some added control of the H-plane side lobes. However, it remains to the future to see what other steps might be taken to reduce the vertical side-lobes even further. The Yagi has been traditionally viewed as a 2-dimensional array, and modern long-boom Yagi design is approaching the limits of what can be obtained by varying only element lengths and spaces. The addition of supplemental reflectors has shown some promise of improved front-to-back performance, but only up to a limit. Perhaps the key break in past Yagi thinking lies in the potential of supplemental elements above and below the plane of the directors to improve both vertical side-lobe performance. What form Yagi-Uda arrays may someday take lies in future design efforts as we begin to think of the parasitic array as a 3-dimensional antenna.

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Updated 10-09-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: VHF / UHF, Yagi


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Expanded Coverage for the 6-Element 2-Meter OWA Yagi
+ 142-150 MHz

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+
+

L. B. Cebik, W4RNL

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In December, 2004, QST published my adaptation of OWA to VHF Yagis ("Building a Medium-Gain, Wide-Band 2 Meter Yagi," pp. 33-37). I had designed the antenna to cover the entire 2-meter band (144-148 MHz) with relatively even gain and at least 20 dB 180-degree front-to-back ratio all across the span. Those design features allowed the beam to be used either horizontally or vertically without having to build specialized antennas for different services. The free-space gain ranged from 10.1 to 10.3 dBi, a variation of only 0.2 dB. The 50-Ohm SWR curve was extremely flat and never exceeded 1.25:1 across the band. I used 3/16" aluminum rods for elements, except for the driver. To allow for through-boom construction (using a PVC boom), I used 1/2" aluminum tubing for the driver, with a 3/8" section of fiberglass rod aligning the two halves of the directly fed driver. The design required no matching network or assembly, because the inherent feedpoint impedance of the antenna is close to 50 Ohms.

+

Since the appearance of the article, I have received two kinds of questions. The first group wonders if the beam is adaptable to operation outside the 2-meter band, where we find special services, such as MARS. The other group has wondered about adapting the design to 3/8" tubing, which may be easier to obtain than the aluminum rod material. I have combined both inquiries into a re-design of the array so that it covers 142 to 150 MHz. The SWR above 149.5 MHz climbs steeply, and the front-to-back ratio below 142.5 MHz begins to fall somewhat. However, the resulting design with 3/8" diameter aluminum elements (except for the driver) retains the relatively smooth gain performance and usable front-to-back and SWR values across the specified passband.

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Table 1 shows the original dimensions of the array along with the dimensions of the version using 3/8" elements. Although the element lengths have changed, I have retained the element spacing. Fig. 1 shows the general outline of the beam to give a sense of its proportions. As with all OWA designs, the first director actually serves as a secondary driver and tends to control the upper half of the passband. As well, OWA designs use the second and third directors (with equal or close to equal lengths) to control the shape of the forward lobe. For longer OWA Yagis, the control directors tend to suppress and not merely attenuate emerging forward sidelobes. Since this design uses a boom that is less than 1 wavelength, there are no sidelobes to control. However, many similar size designs tend to show a small emerging forward sidelobe at the upper end of the passband.

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As we move to Fig. 2, we find my preferred construction method for VHF: passing elements through the boom and securing them on either side with hitchpin clips (also called hairpin cotter pins). You may select your own favorite assembly method or refer to the original article for construction details. You may even wish to increase the diameter of the PVC tube used in the original by one tubing size to accommodate the increased diameter of all parasitic elements in the array. My goal in these notes is to review the performance potentials of the re-design.

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One detail that bears repeating is the arrangement of the 1/2" fed driver element. As shown in Fig. 3, I used a BNC connector with a small bent plate crafted from some 1" by 1" by 1/6" L-stock that I had on hand. The BNC center pin uses a standard soldered jumper to one side of the driver. The shell and the mounting plate form a curve to fit the PVC boom and make a direct connection to the other side of the element. Since the mounting hardware for the element has a minimum size (perhaps #6), the fiberglass rod that separates and aligns the driver halves has to be about 3/8" in diameter so as to maintain its strength once drilled for the hardware. That makes the 1/2" driver element tube very sensible.

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+

How well does the array actually perform? I have promised expanded coverage, but does the beam deliver adequate performance outside the amateur 2-meter allotment? To answer these questions, we may look at some sample data and frequency sweep curves. The first graph (Fig. 4) shows the free-space gain and the 180-degree front-to-back ratio across the widened passband.

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The gain varies from a low value of 10.0 dBi to a maximum value of 10.27 dBi, or about a quarter-dB variation across the entire operating spectrum. The OWA design allows one to place the peak gain inside the passband, which tends to reduce the level of variation within the band. Standard designs tend to show a rising gain curves across the band. Hence, while such designs may show a peak gain the exceeds to OWA gain (but not by much), the gain at the low end of the spectrum may be much lower.

+

One limitation of a very wide-band Yagi design is that it is not usually possible with shorter booms (compared to very large boom Yagis used for serious point-to-point DXing) to sustain a front-to-back ratio at the 20-dB level everywhere in the band. Hence, the front-to-back performance falls off at the lower end of the new wider band, but is still in excess of 15.5 dB. For most general purposes, this value provides satisfactory performance.

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To give us a different view of the graphed data, we can examine the selected free-space E-plane (azimuth) patterns in Fig. 5. The patterns reveal that the array is very well behaved across the entire passband with no unexpected lumps or aberrations. The free-space E-plane patterns generally reflect very precisely the sorts of patterns we will obtain with the antenna horizontally oriented above ground. Of course, if we set the antenna to a vertical orientation, the beamwidth will be significantly wider, since a Yagi always exhibits a narrower beamwidth in the plane of the elements.

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Table 2 provides the modeled data reports to go along with the graphs and the E-plane patterns. You can correlate the tabular entries with both the individual plots and the proper positions on the graph in Fig. 4. The data table holds no surprises, except perhaps for the impedance and SWR values at 150 MHz. They seem high and represent the other limitation of wide-band design. The OWA impedance curve shows a rather rapid decline in resistance above the final SWR minimum. The passband then is a joint function of limiting values of SWR at the high end of the band and limiting values of the front-to-back ratio at the low end of the band. Fig. 6 shows how the resistance and the SWR change across the operating passband.

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Across the entire 8 MHz spread for the expanded beam, the feedpoint reactance varies by no more than about 16 Ohms. For almost all of the passband, the resistance hovers within a 12-Ohm range. However, as we pass 148 MHz, the resistance begins a rapid decline, with a commensurate rise in the 50-Ohm SWR. However, at 149.5 MHz, the SWR is only about 1.5:1. If the primary operation is the 2-meter amateur band and above, then one might reduce the lengths of both the fed driver and the first director/secondary driver to raise the resistance and lower the SWR at the upper end of the band, while sacrificing some performance below the amateur band.

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My goal, however, was to see if I could redesign the 2-meter 6-element OWA to use 3/8" tubing and--at the same time--expand coverage on both sides of the amateur band. The design shown here achieves both goals in an acceptable manner. If you need the coverage and wish to use only one beam for all purposes in the 2-meter range, then this design just might work for you.

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+

Updated 01-04-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/2mowa1.html b/content/vhf/2mowa1.html new file mode 100644 index 0000000..c31420e --- /dev/null +++ b/content/vhf/2mowa1.html @@ -0,0 +1,206 @@ + + + + + + OWA Family of 2-Meter Yagis Part 1: A Comparison of 12-Element Yagi Designs + + + +
+

An OWA Family of 2-Meter Yagis From 6 to 12 Elements:
+ Part 1: A Comparison of 12-Element Yagi Designs

+

+
+
+

L. B. Cebik, W4RNL

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+ +

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+

These notes present a family of Optimized Wide-band Antenna (OWA) Yagis developed as a simple design exercise and not necessarily intended to be implemented. The boom lengths range from 4.5 to 20 feet, with 6 to 12 elements. What differentiates these Yagis from a large collection of other excellent designs is not only the design principles (OWA) invoked, but as well the design specifications. Rather than aim solely for gain, front-to-back ratio, and feedpoint impedance, the designs also set specifications for control of secondary forward lobes. In this first part, we shall compare a 12-element 2-meter Yagi derived from DL6WU design to its corresponding OWA design to gather a perspective on what the use of OWA principles may gain and lose. In Part 2, we shall examine the entire set of OWA designs individually.

+

Background

+

In the quest for better long-boom Yagis for VHF, gain has been the leading criterion. Obtaining the most gain from the least number of elements on the shortest possible boom has been a hallmark of design efforts. Some writers, such as Zack Lau, W1VT, have set aside front-to-back ratio (unimportant to most operations) and feedpoint impedance (obtainable by a suitable match) in order to achieve maximum gain from minimum aluminum.

+

Other designers have taken a more balanced approach, combining calculated element lengths and placement with an easily matched feedpoint impedance (normally 50 Ohms). The work of pioneer Guenter Hoch, DL6WU, and Leif Asbrink, SM5BSZ, have contributed much to this effort. If the boom length is long enough, the front-to-back ratio tends to follow the gain, and the usual standard of a 20 dB front-to-back ratio has been part of the design.

+

We can illustrate the design conceptions involved with a 12-element Yagi based on work by DL6WU, whose designs are still the standard by which other efforts are measured. In principle, one may take a DL6WU design and cut it off anywhere among the set of directors and wind up with a usable Yagi with a gain that is close to the maximum for the resultant boom length. This principle is only partly correct by virtue of the broad operating bandwidth designed into the DL6WU array. If one removes one or more directors from a given design, the forward-most remaining director must be adjusted to reset the operating parameters. Since these parameters may individually peak anywhere within the broad limits of the design, further work is usually required to bring the peak gain, peak front-to-back ratio, and an acceptable feedpoint impedance range within the desired operating range. There are two easily used strategies in addition to modifying the forward-most director. One is to locate the desired set of parameters within the overall range of the array and then frequency scale them into the desired operating range. The second move is to adjust the driver length to set the balance of reactance around the center frequency of the desired operating range so as to yield the best 50-Ohm SWR curve for that range.

+

All of these maneuvers were applied to a shortened 12-element design from DL6WU's original work. My desire to use a 12-element array as the model is that the longest array in the set to be presented uses 12 elements. Hence, the potential for comparison is obvious. Moreover, 12 elements will easily fit on a 20' boom, a convenience for US builders. Whether the resulting revised DL6WU design is fair to the originator is a judgment for others to make. The outline of the array appears in below, followed by 2 charts: one provides the dimensions in inches of the array, while the other summaries the NEC-4 modeled performance properties. The charts are followed by the 50-Ohm SWR curve across 2 meters and free-space azimuth patterns for the design. All of the values for this design and for all succeeding designs presume elements that are well insulated and isolated from the boom.

+
+ +
+ 
DL6WU-Derived Design
+
+No. of elements:  12
+Element diameter:  0.157"  (4mm), except the driver: 0.197" (5mm)
+Boom length:  232.17"  (19.35')
+Maximum 50-Ohm SWR:  1.28:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.34                 ----
+Driver           38.74                  15.24
+Director 1       36.55                  21.69
+Director 2       36.35                  36.35
+Director 3       36.15                  53.94
+Director 4       35.96                  74.46
+Director 5       35.57                  97.32
+Director 6       35.18                 121.95
+Director 7       34.79                 147.74
+Director 8       34.59                 174.71
+Director 9       34.40                 202.85
+Director 10      32.38                 232.17
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.46            14.67           14.54
+Max. 2ndary Lobe      -18.60           -17.76          (-24.03)*
+180-deg F-B           18.21            20.22           46.63
+-3dB Beamwidth        35.6             33.8            32.4
+Impedance (R+/-jX)    55.5 - j 11.3    47.1 - j 7.0    53.4 + j 10.5
+50-Ohm SWR            1.27             1.17            1.24
+*Value is for the 2nd secondary lobe.
+
+ +
+
+ +
+

The design revision strove to place both the maximum gain peak and the maximum front-to-back ratio within the operating passband (144-148 MHz) with only partial success, since the front-to-back ratio peaks at the upper band edge. The front-to-back ratio exceeds 20 dB over at least half of the band, with the 144-MHz value being the worst case.

+

The SWR curve would be deemed acceptable for almost all applications. In fact, many of the broadband VHF and UHF Yagi designs from the 1970s forward have employed an intuitive OWA arrangement of the reflector, driver, and first director. As the SWR curve shows, the SWR value meanders at a low level, with a dip in the upper portion of the band. There is a peak inside the lower band edge, indicating a second dip just below the usable band.

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The final graphic shows the modeled free-space azimuth patterns for the array. The progression of patterns is typical for a Yagi with its gain peak within the operating passband. The normal "oval" forward lobe gradually becomes a more "bullet-shaped" lobe. The transition brings with it a narrowing of the -3 dB beamwidth.

+

The change of shape of the forward lobe is due to the devolution of the first secondary forward lobe. Although this lobe is clearly evident in the patterns for 144 and 146 MHz, it is only a "swelling" of the main lobe at 148 MHz. For this reason, the modeling software did not detect it as a lobe and identified the second secondary lobe as the main one. The DL6WU design used in this illustration has a fairly good set of figures for secondary forward lobes. Many other designs that I have explored have had much worse--from -17 dB to -11 dB.

+

All-in-all, the DL6WU design represents a very fine array of its type relative to a comparison of the boom length and number of elements with the modeled performance figures. For US builders, the array presents some practical problems, since 4 mm rod is not only not available, but as well is almost the arithmetic mean between available sizes (0.125" and 0.1875"). Therefore, some redesign would be necessary to obtain the performance promised by the array. Nevertheless, the result would have the same number of elements and still fit a 20' boom.

+

An Expanded Set of Specifications

+

The DL6WU-derived design presents a sufficient number of theoretical problems to occasion a new set of specifications for 2-meter Yagi design. Rather than leading with gain, we shall lead with pattern control in an effort to eliminate to the degree possible secondary lobes. As it turns out, the same technique that gives us an increased measure of pattern control also provides a means for obtaining the lowest possible 50-Ohm SWR across the band. OWA techniques provide the basis for both achievements. A high front-to-back ratio will also be a part of the specifications, while gain will be simply peaked within the band. This specification set requires more detailed discussion.

+

1. Pattern control: Secondary forward lobes generally obtain their power by a reduction in the -3 dB beamwidth of the main forward lobe. For example, a roughly comparable array with secondary lobes reduced to the -24 dB level will have a nearly 3 degrees wider beamwidth than the example just shown. The beamwidth advantage is even greater compared to Yagis of the same size and gain with even stronger secondary forward lobes. Note that this increase in beamwidth does not come at the expense of main lobe forward gain--although designs that use pattern control as a primary specification may for other reasons end up with slightly less gain--perhaps 1/3 dB less than an array designed expressly for gain within the wide-band category of designs.

+

Therefore, a specification for the present design exercise is a series of arrays with all secondary forward lobes at -22 dB or more relative to the main forward lobe. There may be other Yagi design techniques available to permit further reduction of the secondary lobes without appreciable detriment to other operating parameters. However, as a start, the application of an OWA drive set for the array has permitted a considerable improvement over common designs.

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2. Feedpoint Impedance: The OWA techniques refined by NW3Z and WA3FET for HF use are equally applicable to VHF and UHF arrays. As noted, they are almost implicit in a number of the classic 50-Ohm long-boom designs. In fact, the DL6WU design uses a wider than optimal spacing of the reflector from the driver for OWA purposes. The result is that the reflector tends to control the impedance level more than the combination of the reflector and first director, resulting in a larger than desired swing in reactance. The 2-meter band is an excellent place to use them, since the bandwidth as a percentage of the center frequency (2.74%) is almost the same as the bandwidth of 20 meters (2.47%) for which the initial OWA designs were developed.

+

Obtaining a very low 50-Ohm SWR across a considerable bandwidth requires careful sizing and placement of the reflector, driver, and first director elements. The exact element lengths and the spacing between them are a function of the element diameters. However, in long boom arrays, once these elements have been set, only the forward-most elements need juggling to obtain virtually the same SWR profile across the band. The SWR curve of the OWA 12-element design to be discussed further on is an example of the desired curve.

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+ +
+

Note the general similarity of the curve to that of the DL6WU design. Although not apparent in this curve, many OWA SWR curves show a second dip just at the lower edge of the band (or just below that). However, the SWR curve itself does not tell the entire story. Part of the OWA benefit lies in the reduced reactance excursion across the band. For the 12-element design, the reactance changes by a total of less than 10 Ohms, compared to the DL6WU net change of nearly 22 Ohms. (Other 50-Ohm Yagi designs do considerably worse than the DL6WU design used as an illustration here.)

+

The relative size and space among the reflector, driver, and first director do not complete the OWA picture. Wide band Yagi designs can be obtained with 3, 4, and 5 elements, but the OWA design becomes most stable with 6 or 7 elements. Director 3 is often the same length as or slightly longer than director 2--as a matter of course. This feature is not possible to implement on a true DL6WU design in which the directors are all tapered according to a formula.

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As a sample--but not the only possible one, the following dimensional chart shows the first 5 elements of the longer-boom models to come. There may be slight changes made in some array designs to polish the curves, but the set illustrates both the reflector-driver-first-director arrangement, as well as the amount by which the 3rd director may exceed the 2nd in length.

+ 
Element Diameter:  0.1875"
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+

For this particular situation, where the element diameter is 3/16" (0.0023 wavelength) and the design frequency is 146 MHz, the reflector is 0.109 wavelengths behind the driver, while the first director is 0.058 wavelengths in front. The element lengths from reflector to first director are 0.506, 0.489, and 0.458 wavelengths. To date, I have arrived at no single equation set that will settle all cases where OWA drive sets are desired.

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As we add elements to the array, returning to the basic SWR curve and the reducting the reactance excursion to a minimum requires an added design step beyond those required by DL6WU and similar designs. Terminating a DL6WU design required only that we adjust the forward-most director--normally shorter than its length as part of a longer array. For an OWA design, the 2 forward-most directors require adjustment of both length and spacing to refine performance and re-establish the SWR curve.

+

3. Front-to-back ratio: For this set of Yagis, a 20-dB worst-case front-to-back ratio was set as a requirement for all versions at all frequencies within the operating passband. In fact, it is possible to achieve higher overall values of front-to-back ratio (whether taken as the 180-degree, worst-case, or averaged value) than those within the designs to be examined. However, this move comes at the expense of either the forward gain, the desired SWR curve, or both.

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4. Gain: Within the boundaries of this exercise, the gain value was not a primary objective. In many instances, the gain value was balanced against the front-to-back performance of the array. However, the resulting difference from the maximum obtainable gain was not great--perhaps 0.1 to 0.2 dB at most.

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More significance was placed on centering the gain peak within the operating passband. This placement is normal for OWA designs and has the benefit of reducing the variation of gain from one end of the band to the other. Maximum gain excursions of under 0.3 dB are normal for the beams within this collection.

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Applying the specification set roughly in the order given in the list yielded a range of 7 Yagis from 6 to 12 elements, all with similar characteristics. The dimensions cannot be simply summarized because of the need to adjust multiple elements as one moves from one size to the next. However, we can provide a view of the peak performance obtained by looking at the final Yagi in the sequence, the 12-element OWA design.

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The 12-Element OWA 2-Meter Yagi As with the DL6WU design, we begin with the array outline, followed by the dimensions and modeled performance of the array. We have already examined the SWR curve, so the final graphic will complete the picture with free-space azimuth patterns for the design.

+
+ +
+ 
No. of elements:  12
+Element diameter:  0.1875" (3/16")
+Boom length:  238.00"  (19.67')
+Maximum 50-Ohm SWR:  1.20:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       33.60                 146.60
+Director 8       32.90                 178.40
+Director 9       32.20                 210.00
+Director 10      31.20                 238.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.07            14.35           14.27
+Max. 2ndary Lobe      -25.15           -28.04          -25.04
+180-deg F-B           23.22            24.66           23.17
+-3dB Beamwidth        38.4             36.8            35.6
+Impedance (R+/-jX)    43.1 + j 4.8     47.4 + j 6.1    43.9 - j 3.9
+50-Ohm SWR            1.20             1.15            1.17
+
+ +
+

The gain deficit of this array relative to the DL6WU ranges from 0.27 to 0.32 dB. In exchange for this small deficit, we obtain a 20-dB front-to-back ratio or better as the worst-case value across the band. The feedpoint impedance undergoes less change of reactance for a lower overall shift in the 50-Ohm SWR value. However, the improvement in this category relative to the DL6WU is, at best, marginal.

+

The free-space azimuth pattern graphic shows perhaps the greatest advantage of the present design: a better than 7 dB improvement in the suppression of forward side lobes to a worst-case value of -25.04 dB. All three patterns show a "normal" shape, with little or no tendency toward a bullet shape. The beamwidth is an average of 3 degrees wider than the standard long-boom Yagi design.

+

It perhaps would be foolhardy to make any claims to the effect that the increased beamwidth offered by better pattern control would yield significant operational benefits. It is the goal of a design exercise to explore what is possible, not to try to convert the possible into the operationally necessary.

+

An ideal Yagi would show no secondary lobes at all, either forward or rearward. In a survey of some 40 designs in my collection, I found the following pattern of lobe formation on each side of the main forward lobe to be generally, but not exclusively, true.

+ 
No. of Elements       No. of Secondary
+                      Forward Lobes
+3-6                   0
+7-10                  1
+11-12                 2
+13-16                 3
+17-19                 4
+20-21                 5
+22-25                 6
+26-28                 7
+>28                   9 or more
+

The table does not tell the entire story, since some designs showed as many as 4 additional side lobes relative to the numbers in the chart. As well, some designs displayed many small lobes, while others showed fewer wider lobes. In some cases, the lobes flowed into each other rather than being separately identifiable by intervening nulls. Nevertheless, of all of the original and modified designs in my collection of models, the best values of secondary lobe suppression ran 18.5 dB and lower--usually considerably lower.

+

The "Extra Element" OWA Question

+

The fact that the 12-element OWA Yagi comes as close as it does to the gain of a standard wide-band Yagi raises one question about the foundations of OWA design as practiced in the HF region. The NW3Z/WA3FET designs for 20 meters use a 48' boom with 6 elements to achieve the gain and front-to-back values inherent in better 5-element designs of the same boom length. The OWA advantage lies in its control of the feedpoint impedance across the entirety of the 20-meter band, along with some smoothing of the gain and front-to-back values. In fact, the basic 6-element design can be scaled to 2 meters and then adjusted for the use of the (relatively) fatter 3/16" elements used throughout this series of Yagis. The results of this work appear in the graphics and tables that follow. We may note in passing that this 4.5' long Yagi is ripe for construction using a non-metallic boom.

+
+ +
+ 
No. of elements:  6
+Element diameter:  0.1875" (3/16")
+Boom length:  54.22 (4.52')
+Maximum 50-Ohm SWR:  1.23:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.52                  ----
+Driver           39.96                  10.13
+Director 1       37.38                  14.32
+Director 2       36.31                  25.93
+Director 3       36.31                  37.28
+Director 4       34.96                  54.22
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              10.13            10.23           10.16
+180-deg F-B           22.01            35.36           22.19
+-3dB Beamwidth        54.0             52.6            51.4
+Impedance (R+/-jX)    44.8 + j 7.6     50.0 + j 9.6    43.8 - j 1.6
+50-Ohm SWR            1.22             1.21            1.15
+

If we compare the dimensions of the 6-element OWA Yagi with those of the "core" of the present series, we shall see differences that go beyond detail. The reflector is further back--0.125 wavelength behind the driver, while the first director is closer--0.052 wavelength in front. The element lengths also differ. The reflector is shorter (0.501 wavelength); the driver and first director are longer (0.494 and 0.467 wavelength, respectively). As well, the second and third directors are of equal length, in contrast to the longer second director of the long-Yagi core.

+

The difference in design lowers the overall gain of the array to what one might achieve in standard designs with 5 elements. However, the 6-element array decreases the gain change across the band to about 0.1 dB. The remaining values are comparable to those yielded by the selected core, as illustrated by the SWR curve.

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+ +
+

The free-space azimuth patterns for the 6-element array do not directly reveal anything about the suppression of secondary lobes, since a 6-element Yagi does not ordinarily show any development in this direction. However, it may be well to keep these patterns at hand as we examine in Part 2 the full family of Yagis in the sequence headed by the 12-element version. Note that the 6-element patterns show no tendency toward a "bullet-shaped" pattern at the high end of the band. As a result, the -3 dB beamwidth changes by only 2.6 degrees across the 2-meter band.

+
+ +
+

We shall see in the next section of these notes that the 7-element Yagi that forms the foundation of the sequence has an inordinate gain improvement over the 6-element OWA Yagi we have just examined. We shall also see that achieving this extra gain--which obviates the need for an extra element--also pushes the pattern shape across the band toward a "bullet" pattern at the high end. As we add more elements, the bullet gradually diminishes so that by the time we reach the 12-element array at the head of the line, the pattern has returned to a well-behaved shape resembling that of the pattern at the low end of the band.

+

The question that remains--but which will not be addressed in these notes--is whether we might have obtained even better pattern control by using the 6-element Yagi as the foundation and holding the resulting arrays to normal or non-bullet patterns altogether. The decision to use the core that we examined earlier was based on the very significant improvement it offered. Further improvements using OWA techniques can be developed by other designers.

+

Thus, we have the rationale for the present exercise: to discover to what degree at least one OWA technique enables us to further suppress secondary lobes and "clean up" the typical long-boom Yagi pattern. In Part 2, we shall survey the entire set of Yagis for two purposes. First, we shall see to what degree the technique works at each Yagi size. Second, we shall look at some designs that may be suited to those who cannot go the entire route toward a 20' boom.

+
+ +
+

Updated 08-02-2002. © L. B. Cebik, W4RNL. This item appeared in AntenneX, July, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: The Entire Family

+

Return to Index

+

Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/2mowa10o.gif b/content/vhf/2mowa10o.gif new file mode 100644 index 0000000..86d6947 Binary files /dev/null and b/content/vhf/2mowa10o.gif differ diff --git a/content/vhf/2mowa10p.gif b/content/vhf/2mowa10p.gif new file mode 100644 index 0000000..00801d6 Binary files /dev/null and b/content/vhf/2mowa10p.gif differ diff --git a/content/vhf/2mowa10s.gif b/content/vhf/2mowa10s.gif new file mode 100644 index 0000000..c7388f6 Binary files /dev/null and b/content/vhf/2mowa10s.gif differ diff --git a/content/vhf/2mowa11o.gif b/content/vhf/2mowa11o.gif new file mode 100644 index 0000000..0f41214 Binary files /dev/null and b/content/vhf/2mowa11o.gif differ diff --git a/content/vhf/2mowa11p.gif b/content/vhf/2mowa11p.gif new file mode 100644 index 0000000..5886815 Binary files /dev/null and b/content/vhf/2mowa11p.gif differ diff --git a/content/vhf/2mowa11s.gif b/content/vhf/2mowa11s.gif new file mode 100644 index 0000000..bc3fd70 Binary files /dev/null and b/content/vhf/2mowa11s.gif differ diff --git a/content/vhf/2mowa12o.gif b/content/vhf/2mowa12o.gif new file mode 100644 index 0000000..015246b Binary files /dev/null and b/content/vhf/2mowa12o.gif differ diff --git a/content/vhf/2mowa12p.gif b/content/vhf/2mowa12p.gif new file mode 100644 index 0000000..953e50b Binary files /dev/null and b/content/vhf/2mowa12p.gif differ diff --git a/content/vhf/2mowa12s.gif b/content/vhf/2mowa12s.gif new file mode 100644 index 0000000..ad68633 Binary files /dev/null and b/content/vhf/2mowa12s.gif differ diff --git a/content/vhf/2mowa2.html b/content/vhf/2mowa2.html new file mode 100644 index 0000000..b8f9eb2 --- /dev/null +++ b/content/vhf/2mowa2.html @@ -0,0 +1,281 @@ + + + + + + OWA Family of 2-Meter Yagis Part 2: The Entire Family + + + +
+

An OWA Family of 2-Meter Yagis From 6 to 12 Elements:
+ Part 2: The Entire Family

+

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The family of Yagis that are directly linked by the use of the OWA core described in Part 1 of these notes begins with a 7-element design. The remaining members of the family were developed by the addition of a new director. The addition required readjustment of both the length and the spacing for the two forward-most directors. The general trend required that the former lead director be lengthened and spaced further forward in order to retain the desired SWR curve that is indicative of reducing the reactance excursions to a minimum across the 2-meter band. The interactive process required that one adjust the length and the spacing of new forward-most director to center the gain curve within the passband and to achieve the 20-dB front-to-back ratio across the band. One of the interesting features of the family members is that each succeeding array is just about 30" longer than its shorter kin.

+

All of the following designs presume that the elements are well insulation and isolated from a metallic boom, although some of the shorter ones might be placed on non-metallic booms. There is a further issue: the designs were considered complete when they met all of the specifications outlined in detail in Part 1. Virtually every individual design can be further perfected within that specification set by running them through an optimizing program of one or another sort. In addition, one can achieve better gain or better front-to-back ratios by additional optimizing, although the cost may be slight degradations of the SWR curves or pattern control. The levels of control on these two factors allow considerable room for some performance improvements by simply reducing these requirements. All of the designs show less than a 1.25:1 SWR across the band and better than -22 dB secondary lobe strength (with some exceptions noted in the text). Where these values are not required by a set of operational specifications, the other performance parameters may be improved.

+

For each design step, we shall present an outline sketch of the Yagi and a brief narrative, followed by both dimensional and performance tables. An SWR curve and a set of free-space azimuth patterns will complete the description. As a point of reference early in the progression, you may wish to have at hand the information on the separately designed 6-element OWA Yagi described at the end of Part 1.

+
+

A 7-Element OWA 2-Meter Yagi

+
+ +
+

The 7-element version of the OWA provides the core of the family, as described in Part 1. The first 5 elements are common to all of the family members. These particular elements, along with their spacing, creates an independent array that is just under 7' long. Especially noticeable is the gain increase over the 6-element Yagi in Part 1--better than 1.25 dB on average. This increase is considerably more than one might expect from the addition of a single element if we also sustain all of the specifications in the set we examined. For example, the SWR curve is fundamentally a well-behaved OWA curve.

+

The reason for the increase in gain is a shift in the operating curve with respect to forward pattern shape. The 146 and 148 MHz patterns show a tendency toward the bullet shape. As a result, the -3 dB beamwidth changes across the band by 4 degrees, a 50% increase over the change in beamwidth that accompanies the wholly "normal" patterns of the 6-element array. As a consequence of moving toward bullet patterns, the emerging secondary lobe devolves from a definitive lobe into a bulge. As with the succeeding versions of this Yagi family, the "-s" in the secondary lobe column of the performance data indicates that the lobe is a "swelling" of the main forward lobe; therefore, a value for the lobe is a rough estimate. When the final column gives a dash rather than a value, the bulge is too small for quantification. Although that bulge-shaped lobe may seem an advantage in terms of its integration into the main forward lobe, it reduces the beamwidth of the main lobe. As well, the gain change across the band increases to about 0.26 dB (compared to 0.1 dB for the 6-element Yagi). Whether these levels of reduction in pattern control are acceptable for any particular application is a user judgment based on operational specifications. For the present design exercise, these limitations were considered acceptable.

+ 
No. of elements:  7
+Element diameter:  0.1875" (3/16")
+Boom length:  83.67 (6.97')
+Maximum 50-Ohm SWR:  1.24:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       34.54                  83.67
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              11.46            11.56           11.30
+Max. 2ndary Lobe      -26.16           -22.98-s        (See text)
+180-deg F-B           21.26            29.62           20.70
+-3dB Beamwidth        48.0             46.2            44.0
+Impedance (R+/-jX)    40.7 + j 2.8     46.2 + j 8.5    44.0 - j 6.2
+50-Ohm SWR            1.24             1.21            1.20
+
+ +
+
+ +
+
+

An 8-Element OWA 2-Meter Yagi

+
+ +
+

The 8-element Yagi required readjustment of the 5th director, moving it about 3" forward and lengthening it by over an inch. The new director is shorter than the previous forward-most director. The final length is a bit over 29" longer than the 7-element version and will fit nicely on a 10' boom. Nevertheless, the SWR curve has remained virtually unchanged. There are inevitable slight movements in the exact frequency at which the lowest SWR occurs, but the dip is within the last half MHz at the upper end of the band. The forward portions of the azimuth patterns for the 8-element Yagi are similar to those for the 7-element array, but the rearward patterns show the more definite emergence of the secondary lobes. To some degree, the shift toward a bullet forward pattern disguises the secondary lobe emergence in that direction, and the 3.8-degree change in beamwidth tends to confirm the disguise. However, the array shows a nearly 0.8 dB increase in average gain across the band, although the change in gain across the band remains above 0.2 dB.

+ 
No. of elements:  8
+Element diameter:  0.1875" (3/16")
+Boom length:  113.00 (9.42')
+Maximum 50-Ohm SWR:  1.20:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       33.20                 113.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              12.24            12.36           12.07
+Max. 2ndary Lobe      -24.45           -21.64-s        (See text)
+180-deg F-B           20.54            23.51           41.40
+-3dB Beamwidth        45.2             43.2            41.4
+Impedance (R+/-jX)    42.5 + j 3.9     46.4 + j 7.9    47.1 - j 6.2
+50-Ohm SWR            1.20             1.20            1.15
+
+ +
+
+ +
+
+

A 9-Element OWA 2-Meter Yagi

+
+ +
+

The 9-element member of the family shows the same growth symptoms as the preceding Yagi. The 6th director is moved forward by about 3" and increased in length. The most forward director winds up at the 12' mark, a relatively convenient building size. The SWR curve shows the small dip near the lower end of the band, since the deeper minimum has been shifted upward in frequency be about 0.25 MHz. This move gives some idea of the room the individual designer has for "tweaking" any design to achieve more favorable numbers, in this case, an SWR value that does not exceed 1.17:1 across the band. Design flexibility does not mean that a builder will achieve the precise modeled figures in the constructed version. However, it does indicate that a builder has room for maneuver in obtaining acceptable measured performance from an array. The gain increment of the 9-element Yagi over its 8-element brother averages 0.65 dB. We should expect lesser gain increases with each added director. An additional feature to notice from the azimuth patterns is the first hint at the emergence of a second secondary lobe at the upper end of the band. As well, the patterns show a trend toward "normalization" at all frequencies tested.

+ 
No. of elements:  9
+Element diameter:  0.1875" (3/16")
+Boom length:  144.00 (12.00')
+Maximum 50-Ohm SWR:  1.17:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       32.20                 144.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              12.85            13.01           12.80
+Max. 2ndary Lobe      -24.46           -22.21-s        (See text)
+180-deg F-B           21.32            21.91           22.73
+-3dB Beamwidth        43.0             41.2            39.5
+Impedance (R+/-jX)    43.8 + j 3.8     45.2 + j 5.4    46.6 - j 0.8
+50-Ohm SWR            1.17             1.17            1.08
+
+ +
+
+ +
+
+

A 10-Element OWA 2-Meter Yagi

+
+ +
+

The 10-element Yagi adds about 0.5 dB gain over the 9-element version for an increase in length to a 14.5' boom. The pattern shapes continue the trend toward normalization. In this particular case, note the very shallow SWR curve. Achieving such constancy has a cost, in this instance, a very slight reduction in the total gain that one might be able to glean from the array. Additional markers of this fact at the mere 2.6" movement of the 7th director and the very short length of the 8th (forward-most) director. I have left this condition as another indicator of the flexibility available to the builder who may revise the design by additional adjustments to the two most forward directors.

+ 
No. of elements:  10
+Element diameter:  0.1875" (3/16")
+Boom length:  174.00 (14.50')
+Maximum 50-Ohm SWR:  1.18:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       33.60                 146.00
+Director 8       30.80                 174.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              13.29            13.49           13.33
+Max. 2ndary Lobe      -24.91           -23.58          (See text)
+180-deg F-B           22.91            22.41           22.07
+-3dB Beamwidth        41.4             39.6            38.2
+Impedance (R+/-jX)    43.8 + j 4.5     46.4 + j 4.6    43.8 - j 0.7
+50-Ohm SWR            1.18             1.13            1.14
+
+ +
+
+ +
+
+

An 11-Element OWA 2-Meter Yagi

+
+ +
+

With the addition of the 9th director, we return to the typical OWA SWR curve, and we add another 0.5 dB gain to the array. Note, however, that from the 9-element version to this one, we have been moving the lowest gain from the high end of the band to the low end of the band--although the net difference remains 0.25 dB or lower. The shift sets the best front-to-back ratio at mid-band, aligned roughly with the highest gain figure. As well, the shift tends to shrink the first secondary lobe as we increase frequency on the band, yielding suppression of all secondary lobes to the -25 dB or better level. This 14-dBi Yagi is 17.1' long, with changes in the directors as well. The former forward-most director is 4.4" farther forward, and the new director is proportionally longer than the one on the 10-element array. Although maneuvers as precise as the ones made in these models are unlikely to be replicated with equal precision in the workshop, they do suggest that the performance of the model can be brought to the desired level with the manipulation of a very limited number of variables.

+ 
No. of elements:  11
+Element diameter:  0.1875" (3/16")
+Boom length:  205.00 (17.08')
+Maximum 50-Ohm SWR:  1.20:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       33.60                 146.00
+Director 8       32.90                 178.40
+Director 9       32.00                 205.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              13.77            14.02           13.90
+Max. 2ndary Lobe      -25.17           -26.36          -25.76
+180-deg F-B           23.27            25.72           22.35
+-3dB Beamwidth        39.4             37.8            36.4
+Impedance (R+/-jX)    42.8 + j 4.4     47.1 + j 6.4    44.1 - j 3.7
+50-Ohm SWR            1.20             1.16            1.16
+
+ +
+
+ +
+
+

A 12-Element OWA 2-Meter Yagi

+
+ +
+

For family unity, the 12-element Yagi graphics and tables are repeated from Part 1. With a length just under 20', the 12-element array provides only about 0.35 dB additional gain, although pattern control continues to improve. The strongest secondary lobe is -25 dB compared to the main lobe. Fuller discussion of the features of this member of the family appears in Part 1.

+ 
No. of elements:  12
+Element diameter:  0.1875" (3/16")
+Boom length:  238.00 (19.67')
+Maximum 50-Ohm SWR:  1.20:1
+
+Dimensions (in inches):
+
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       33.60                 146.00
+Director 8       32.90                 178.40
+Director 9       32.20                 210.00
+Director 10      31.20                 238.00
+
+Modeled Performance
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.07            14.35           14.27
+Max. 2ndary Lobe      -25.15           -28.04          -25.04
+180-deg F-B           23.22            24.66           23.17
+-3dB Beamwidth        38.4             36.8            35.6
+Impedance (R+/-jX)    43.1 + j 4.8     47.4 + j 6.1    43.9 - j 3.9
+50-Ohm SWR            1.20             1.15            1.17
+
+ +
+
+ +
+
+

The family of Yagis in these notes represent a design exercise that has been based on using a set of specifications somewhat unlike those common to amateur designs. Pattern control was given top priority, even if the end result was not the ideal goal of the elimination of all secondary lobes. However, the following set of free-space azimuth patterns may give some indication of the degree to which pattern control has been improved. Each pattern represents a different VHF Yagi having either 12 or 13 elements. Each pattern also represents a different design and designer, and all show good gain performance with adequate front-to-back ratios throughout. Nevertheless, the -3 dB beamwidths are significantly narrower than the values shown for the 12-element array in our new family. Comparing this collection of azimuth patterns with those for the 12-element OWA Yagi will give some idea of the improvements that are possible for Yagis from 19 to 22 feet in boom length.

+
+ +
+

As almost an incidental specification, the use of OWA techniques also permits a very tight control on the feedpoint impedance of the arrays. All of the Yagis in the collection were designed for 50-Ohm direct matching to coaxial cable (with the usual common-mode suppression techniques applied).

+

The achievement of front-to-back ratios that exceeded 20 dB as a worst-case value and the gain levels attained by the arrays at any boom length are an indication that the designer can apply to long-boom Yagi design a more complex set of specifications than most designers have applied in the past.

+

In the end, however, this has only been a design exercise, not a prelude to construction. Still, it may be serve as a springboard toward even better designs, and so the family portrait may have some utility down the road. We are a long way yet from the development of the ideal Yagi-Uda array for 2 meters.

+
+ +
+

Updated 08-02-2002. © L. B. Cebik, W4RNL. This item appeared in AntenneX, August, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Topics: VHF / UHF, Yagi


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+

Extending the 2-Meter OWA Family
+ Part 1: 13 to 20 Elements and a Self-Limiting Design

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In a past 2-part series devoted to developing the optimized wide-band antenna (OWA) concept to full-band Yagi antennas for 2 meters, we examined a connected series of antennas ranging from 7 to 12 elements. See "An OWA Family of 2-Meter Yagis from 6 to 12 Elements," (Part 1 and Part 2).

+

That series elicited a number of requests for longer versions of the antenna, given its adequate but stable gain, very good front-to-back ratio, exceptional SWR curve across the band, and general attenuation of sidelobes to more than 20 dB down from the main forward lobe. The development of the next set of beams had to await available time, since the optimizing process is unlike a number of Yagi designs that use a single algorithm to calculate each added element. The OWA series requires resetting the former forward-most element and then placing a new (added) element at the correct position. However, the work of extending the sequence from 13 through 20 elements is now complete.

+

The results, using a design frequency of 146 MHz, have yielded some surprises. First, as the boom gets longer, the addition of new elements is almost stable in its requirements, with each new addition requiring a 5" spacing jump for the former forward-most elements, along with the 1" lengthening. The new element would be about 28" ahead of the previous director for a total boom length increase of about 33". The forward-most element would be about 1.5" shorter than the preceding director.

+
+ +
+

Fig. 1 shows the general outline of the shortest and longest Yagis in the new series. Below is a table of boom lengths for the series of antennas, including the 12-element version as a reference. Although the dimensions of the boom length are given in several units of measure, future tables of element lengths and spacing will all be in inches, since the conversions should be second nature to any antenna enthusiast.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            OWA Yagi Series Boom Lengths:  12 to 20 Elements
+
+Note:  Wavelength measurement is for a frequency of 146 MHz.
+
+No. of                      Boom Length
+Elements         Inches     Feet       Meters     Wavelengths
+12               238        19.83       6.05      2.94
+13               271        22.58       6.88      3.35
+14               304        25.33       7.72      3.76
+15               337        28.48       8.56      4.17
+16               370        30.83       9.40      4.58
+17               403        33.58      10.24      4.99
+18               436        36.33      11.07      5.39
+19               469        39.08      11.91      5.80
+20               502        41.83      12.75      6.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

OWA Basics and The Criteria of Design

+

The key elements in a true OWA design are the reflector through director 3, that is, the rear-most 5 elements of the array. There are numerous wide-band Yagi arrangements that essentially involve only the rear-most three elements, for example the well-known DL6WU design. For a 50-Ohm wide-band match with a single linear driver elements, Guenter Hoch used a reflector-to-driver spacing of 0.200 wavelength and a driver-to-director-1 spacing of 0.075 wavelength. The element lengths depend upon the diameter of the individual elements. In any wide-band design (including the OWA design), the first director acts as a secondary driver, and its current magnitude exceeds that of the driver over the upper (approximate) half of the operating passband.

+

The OWA system begins with a different combination of element spacing. The reflector-to-driver spacing may range from 0.10 to 0.13, while the driver-to-director-1 spacing might range from 0.05 to 0.06 wavelength, depending upon both the element diameter and the disposition of directors 2 and 3. These controlling directors are either the same length or the forward of the two is slightly longer than the rearward. The benefits of having the controlling directors is to permit the gain peak and the front-to-back peak to occur at roughly the center of the operating passband without significant disturbance to the SWR curve for the passband. As one increases the number of elements of an OWA Yagi, it becomes more difficult to achieve true centering so that designers are generally required to settle for a slightly lesser standard: that the peaks both occur within the passband, even if they lean toward the upper passband edge.

+

In designing the family of 2-meter OWA Yagis, I have used several criteria to mark success--even if a relative rather than an absolute success. These criteria include the following items.

+

1. The 50-Ohm SWR curves for the antennas in the family should not exceed 1.2:1 anywhere within the pass band. Fig. 2 shows the curves for the 13-element and the 20-element members of the family. The two curves are so coincident that their difference is scarcely visible. (Telling which curve is which is an exercise left to the reader. However, the later modeled performance data at 146 MHz will provide a small clue as to which line belongs to which antenna.)

+
+ +
+

2. The front-to-back ratio, whether taken as the 180-degree value or the worst-case value, should exceed 20 dB throughout the operating passband. Fig. 3 compares the 50-Ohm front-to-back curves for the 13-element and the 20-element members of the family. As is readily apparent, both curves--and by extension, the curves of intermediate family members--easily meet the criterion. However, as we increase the number of elements, the slope of the curve diminishes.

+
+ +
+

3. The front-to-sidelobe ratio should exceed 20 dB by the highest possible margin. The front-to-sidelobe ratio is the ratio, in dB, between the maximum forward gain and the gain of the strongest forward sidelobe. In most cases where a longer-boom Yagi is involved, there are forward sidelobes as well as the main lobe. In most conventional Yagi designs, the strongest sidelobe--usually the first, but occasionally the second--will be down by only 15 to 18 dB relative to the maximum forward gain. The OWA design permits an additional 5- to 10-dB improvement, reducing sensitivity of the antenna to off-axis signals.

+

The worst-case value of the front-to-sidelobe ratio occurs in the shorter members of the family, hovering between 23.5 and 24 dB at 144 MHz, when a new sidelobe emerges. (The number of forward sidelobes--and rear sidelobes as well--tends to be a function of the boom length. The number of sidelobes is roughly equal to the boom length in wavelengths, reduced to an integer.) The most general worst-case value occurs at 148 MHz. It ranges from about 24.3 dB for the shortest Yagi in the group to close to 27 dB for the longest Yagi in the family.

+

4. The gain of the array should peak as close to the passband center as is feasible and will be whatever the other design considerations permit it to be. As is evident in Fig. 4, the longer we make the boom and the more elements that we add in the prescribed design sequence, the more the gain peak shifts upward within the passband.

+
+ +
+

One result of the shifting gain peak is an increasing gain differential across the band as we increase the number of elements. The shortest Yagi has a differential of just over 0.35 dB across the passband, while the longest OWA has a differential of about 0.55 dB. However, these values tend to be considerably smaller than the differentials obtained from many other types of designs over a similar passband. A typical 20-element DL6WU Yagi might show as much as a full dB differential in gain across 2 meters, although the design has sufficient operating bandwidth to allow one to select an operating point with less gain differential. However, obtaining this result with a well-centered front-to-back maximum may be difficult.

+

Because the OWA series is designed for other than maximum gain as the primary criterion of success, we shall discover that the series is self-limiting in effective boom length or the number of elements. Indeed, 20 elements may exceed the maximum practical length for the design--when compared to others--by 4 or 5 elements for all but a special purpose antenna in which sidelobe attenuation is a paramount concern.

+

The Family Dimensions

+

The design of the added members of the OWA 2-meter family proved to be a more stable operation than the design of the members with 7 through 12 elements. Indeed, the 12-to-13-element range seems to be a turning point in the design work. The addition of each new element requires that the previous forward-most element be moved further forward by about 5". The length required an average 1" addition. The new forward director required an average 28" space from the repositioned director, so that the total boom growth for the 146-MHz designs was 33" on average. This value is close to 0.4 wavelength at the design frequency, a value similar to the spacing used in DL6WU arrays. The length of the new forward-most director is about 1.5" (average) shorter than the re-adjusted preceding director.

+

The deciding factors in settling upon a set of dimensions for each member of the series included the coincidence of the SWR curves, the maintenance of front-to-back ratios across the passband, and the achievement of a worst-case front-to-sidelobe value equal to or better than the next shorter member of the overall family. All of the antennas in the new series--like their shorter brethren--use 0.1875" (3/16") aluminum elements. For elements up to about 1.5 times fatter or .67 times thinner, the standard element adjustment factors in manual may be applied. However, if the new elements are twice as fat or half as thin, then the array may require re-design of the element spacing throughout.

+

The following table presents all of the dimensions together. For each added element, the table shows only those elements requiring changes from the original and subsequent entries preceding the entry in focus.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+         OWA 2-Meter Yagi Dimension Table From 12 to 20 Elements
+
+Note:  after the initial listing, only the last two elements in each
+design change--hence, the abbreviated listings.
+
+Element diameter:  0.1875" (3/16")          Maximum 50-Ohm SWR:  1.20:1
+
+Dimensions (in inches):
+
+12-Elements
+Element          Length          Space from Reflector
+Reflector        40.90                 ----
+Driver           39.50                   8.79
+Director 1       37.00                  13.47
+Director 2       36.33                  25.38
+Director 3       36.40                  40.72
+Director 4       36.21                  61.38
+Director 5       35.20                  86.49
+Director 6       34.30                 116.00
+Director 7       33.60                 146.00
+Director 8       32.90                 178.40
+Director 9       32.20                 210.00
+Director 10      31.20                 238.00
+
+13 Elements
+Director 10      32.20                 243.00
+Director 11      30.00                 271.00
+
+14 Elements
+Director 11      30.80                 276.00
+Director 12      29.00                 304.00
+
+15 Elements
+Director 12      30.40                 309.00
+Director 13      29.20                 337.00
+
+16 Elements
+Director 13      30.00                 342.00
+Director 14      28.40                 370.00
+
+17 Elements
+Director 14      29.20                 375.00
+Director 15      28.00                 403.00
+
+18 Elements
+Director 15      28.80                 408.00
+Director 16      27.60                 436.00
+
+19 Elements
+Director 16      28.40                 441.00
+Director 17      27.40                 469.00
+
+20 Elements
+Director 17      28.40                 475.00
+Director 18      27.40                 502.00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For example, if we want to build a 20-element version, we would use the first 11 elements from the initial table, followed by the last value shown for each added element. This procedure boils down to using the upper director length and spacing for each entry except the last, in which case, we use the values of both the 17th and 18th directors. The spacing, of course, is the cumulative spacing from the reflector, which is set to zero for counting purposes. The lengths are full element lengths and should be halved if one wishes to reconstruct the NEC-4 models that formed the basis of these designs.

+

As was true of the initial family members in this OWA Yagi group, the dimensions presume that the elements are well-insulated and isolated from any conductive boom material (by at least 1 boom diameter distance). There are algorithms for calculating the element length adjustments necessary when using insulated through-boom construction. Direct element-to-boom construction requires further element-length adjustments, but is not recommended unless one has access to industrial-grade welding equipment that can assure a very durable bond with high and constant conductivity.

+

Individual Performance and Pattern Portraits

+

Perhaps the most direct way to show the potential performance of the extended OWA series of Yagis is simply to show selected tabular performance reports from the NEC-4 models, along with free-space E-plane (azimuth) patterns. For each design, the data will cover 144, 146, and 148 MHz.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  13 Elements (See Fig. 5)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.32            14.64           14.59
+180-deg F-B           23.13            25.57           24.54
+Impedance (R+/-jX)    42.8 + j 4.4     46.8 + j 6.9    45.4 - j 4.5
+50-Ohm SWR            1.20             1.17            1.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  14 Elements (See Fig. 6)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.50            14.84           14.82
+180-deg F-B           23.22            25.65           25.15
+Impedance (R+/-jX)    42.9 + j 4.2     46.4 + j 6.9    45.8 - j 4.2
+50-Ohm SWR            1.20             1.18            1.13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  15 Elements (See Fig. 7)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.68            15.04           15.05
+180-deg F-B           23.97            25.96           24.27
+Impedance (R+/-jX)    42.8 + j 4.4     46.8 + j 6.7    45.2 - j 3.9
+50-Ohm SWR            1.20             1.17            1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  16 Elements (See Fig. 8)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.82            15.19           15.21
+180-deg F-B           24.08            26.34           24.18
+Impedance (R+/-jX)    42.8 + j 4.5     47.0 + j 6.7    44.9 - j 4.0
+50-Ohm SWR            1.20             1.16            1.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  17 Elements (See Fig. 9)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              14.93            15.32           15.35
+180-deg F-B           24.00            26.55           24.45
+Impedance (R+/-jX)    42.8 + j 4.4     46.9 + j 6.7    44.9 - j 4.2
+50-Ohm SWR            1.20             1.17            1.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  18 Elements (See Fig. 10)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              15.03            15.42           15.47
+180-deg F-B           24.12            26.37           24.94
+Impedance (R+/-jX)    42.8 + j 4.4     46.8 + j 6.7    45.1 - j 4.2
+50-Ohm SWR            1.20             1.17            1.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  19 Elements (See Fig. 11)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              15.11            15.52           15.58
+180-deg F-B           24.44            26.20           25.07
+Impedance (R+/-jX)    42.9 + j 4.5     46.8 + j 6.7    45.1 - j 4.1
+50-Ohm SWR            1.20             1.16            1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Modeled Performance:  20 Elements (See Fig. 12)
+
+Parameter             144 MHz          146 MHz         148 MHz
+Gain dBi              15.19            15.61           15.68
+180-deg F-B           24.50            26.18           25.11
+Impedance (R+/-jX)    42.9 + j 4.5     46.8 + j 6.6    45.1 - j 3.9
+50-Ohm SWR            1.20             1.16            1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Some Curiosities of the Family

+

The OWA family becomes downright sedate as we increase the number of elements and the boom length. For example, for the 20-element version, we can extend the forward-most director an additional 5" without noticeable change in any of the performance figures. Moreover, the gain increase does not match the boom-length increase when we compare it to other design series. As a quick example, the following table compares the gain increase with each new element in the OWA series with the corresponding gain increase in a typical DL6WU series. The example is suggestive because the boom lengths for the two series, while not identical, are close enough to be comparable. In addition, each column uses simply the modeled gain value at mid-band, not the peak achievable gain.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    Change of Gain per Added Element
+
+Note:  Free-space gain values taken at 146 MHz, which is not the peak
+gain for either antenna series, but a representative mid-band value.
+Boom lengths for each value are comparable, but not exactly the same.
+20-element boom length for the OWA series is 41.83' and for the DL6WU
+series is 40.52'.  Hence, the comparison is suggestive, but not
+definitive.
+
+Antenna          OWA Series                       DL6WU Series
+Elements   Gain (dBi)       Delta Gain      Gain (dBi)      Delta Gain
+12         14.35            -----           14.70           -----
+13         14.64            0.29            15.22           0.52
+14         14.84            0.20            15.62           0.40
+15         15.04            0.20            15.91           0.29
+16         15.19            0.15            16.20           0.29
+17         15.32            0.13            16.52           0.32
+18         15.42            0.10            16.85           0.33
+19         15.52            0.10            17.13           0.28
+20         15.61            0.09            17.34           0.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The OWA series at the 12-element baseline already has a gain about 1/3 dB less than a comparable DL6WU design. At 16 elements, the differential is a whole dB. At 20 elements, the differential is 1-3/4 dB. Clearly, we have embarked upon a trail of diminishing returns with respect to array gain.

+

Part of the reason behind the smaller increment of gain increase for each added OWA director is the lesser activity on the directors in the OWA design. Activity refers to the relative current magnitude on the sequence of forward directors, especially those from 11 or 12 up to 18. Fig. 13 shows in roughly equal scale the current magnitude on the elements of three 6 wavelength boom Yagis. On both of the non-OWA designs, we can immediately see the higher current magnitude on each of the forward directors, relative to the lower values for the OWA model.

+
+ +
+

A second curiosity concerns the side and rear lobe development as we increase the boom length and the number of elements. Ordinarily, we expect to see a number of forward side lobes that is roughly equal to the number of wavelengths of boom length, rounded to an integer. However, examine Fig. 14. The 13-element design is about 3.35 wavelengths long and shows 3 forward sidelobes (and three rearward sidelobes, if we count bumps carefully). The 6.21 wavelength 20-element version should show us 6 sidelobes. However, we can count only 4, including the extremely minute first sidelobe closest to the main lobe itself. The rearward sidelobes are equally deficient relative to expectations. Relating the number of forward sidelobes to gain instead of boom length should still net us at least 5. Moreover, the figures do give us a better impression of just how well the OWA design attenuates or suppresses sidelobe development compared to more traditional designs in the field.

+
+ +
+

These questions bear further investigation, and hence a Part 2 (and Part 3) to this continuing saga of the OWA 2-meter family of Yagis. We need to make more detailed comparisons, looking at not only boom length, but the element population as well as we seek means of suppressing forward sidelobes and achieving more adequate gain values.

+
+ +
+

Updated 08-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for July, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: Gain, Element Population, and Hybrid Designs

+

Go to Main Index

+

Topics: VHF / UHF, Yagi


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+

Extending the 2-Meter OWA Family
+ Part 2: Gain, Element Population, and Hybrid Designs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

We concluded the first section of this report on the extended (13-20 elements) OWA family with a list of curiosities. The curiosities related to limitations of gain performance of the extended series relative to other wide-band long-boom Yagis, where "long-boom" represents an approximate 6 wavelength boom. They are also related to the formation of sidelobes on various design types.

+

It is worth repeating the table that compares the gain growth of the OWA series with the gain growth of a DL6WU-type array, since the boom lengths for each new element--while not exactly the same--are quite comparable.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    Change of Gain per Added Element
+
+Note:  Free-space gain values taken at 146 MHz, which is not the peak
+gain for either antenna series, but a representative mid-band value.
+Boom lengths for each value are comparable, but not exactly the same.
+20-element boom length for the OWA series is 41.83' and for the DL6WU
+series is 40.52'.  Hence, the comparison is suggestive, but not
+definitive.
+
+Antenna          OWA Series                       DL6WU Series
+Elements   Gain (dBi)       Delta Gain      Gain (dBi)      Delta Gain
+12         14.35            -----           14.70           -----
+13         14.64            0.29            15.22           0.52
+14         14.84            0.20            15.62           0.40
+15         15.04            0.20            15.91           0.29
+16         15.19            0.15            16.20           0.29
+17         15.32            0.13            16.52           0.32
+18         15.42            0.10            16.85           0.33
+19         15.52            0.10            17.13           0.28
+20         15.61            0.09            17.34           0.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As is evident, the rate of gain increase generally decreases for both beam types as the total number of elements increases. This follows from the fact, first made clear by Lawson, that the overall gain is a function of boom length more than the number of elements, so long as we have a minimum element population needed to provide performance over a desired operating bandwidth. Each new element, with roughly equal spacing between the forward-most 6 elements or so, adds a smaller percentage increment of boom length. Hence, the rate of increase per element is less as we increase the total number of elements.

+

More notably for our present situation is the fact that the rate of increase of gain per element in the OWA series is only about half (or less) that of the DL6WU-type series. Hence, by the 20th element or a boom length just in excess of 6 wavelengths, the OWA series shows a 1.73 dB deficit in gain relative to the DL6WU-type series. (The number is overly precise, given the conditions of comparison listed at the top of the table. However, it is certainly indicative of the deficit level.)

+

We initially traced the gain deficit to the lower level of relative current magnitude on the forward directors of the array--at least as that level compares to the relative current magnitude on the directors of other Yagi series in the same boom-length ballpark. As we can see in Fig. 1, where the maximum array current magnitudes are roughly equal in strength, the DL6WU-type and the VK3AUU-type arrays show considerably higher forward director maximum current levels.

+
+ +
+

Related to the gain deficit for a given boom-length is the development of sidelobes. As a general rule of thumb, the number of sidelobes on each side of the forward main lobe--and the number of rear sidelobes on each side of the main rear lobe--will be roughly equal to the boom length in wavelengths when we reduce that length to an integer value. Hence, we expect to see 6 forward and 6 rearward sidelobes on each side of the main array axis.

+
+ +
+

Fig. 2 shows the sidelobe development of 6 wavelength boom DL6WU-type and VK3AUU-type arrays. Although the newest sidelobe close to 90 degrees off the main forward bearing is very small, even in the expanded patterns in the figure, we can count 6 clear lobes for both antennas. The rear sidelobes also add up to 6, although the main rear lobe of the DL6WU pattern is obscured by the fact that the first sidelobe on each side is so much stronger than the main or 180-degree lobe that we have the impression of a mere depression. However, if that main rear lobe were truly minuscule or missing, the rear gain 180 degrees opposite the main forward lobe would show a deep depression.

+

The OWA series sample, also with a 6 wavelength boom, is an exception to this general rule of thumb. At most, we might count 4 forward sidelobes and perhaps 3 rear sidelobes on each side of the pattern. As well, we may note that the first forward sidelobe is very much weaker than the second and third sidelobes. Indeed, for all three arrays, the sidelobe strengths are directly comparable. The VK3AUU-type array uses 25 elements on its 6 wavelength boom to significantly reduce sidelobe strength relative to the DL6WU-type array, even though both have roughly the same forward gain. However, the OWA series at the same boom length effects not only a suppression of sidelobe formation, but as well reduces the sidelobe strength even further. Also, it does so with 20 elements--that same number as in the DL6WU-type array.

+

At the simplest level, we might leave matters as they stand. The OWA series of Yagis sacrifices gain for the sake of a cleaner pattern with fewer sidelobes and weaker ones as well. We might even attribute that condition to the combined effects of the OWA core--with its critical first 5 elements (Reflector through Director 3)--and to the method of adding new elements to restore both the 50-Ohm SWR curve and the low level of sidelobe development. However, even these propositions leave us with a number of questions.

+
    +
  • 1. Which of the two OWA design concepts--the core or the method of adding new elements--has the dominant effect on side-lobe development?
    • +
  • 2. Is there a method of obtaining more gain from the OWA series without sacrificing sidelobe suppression and attenuation?
    • +
  • 3. What role does element population play in sidelobe attenuation?
    • +
+

None of these questions is simple, especially in light of the fact that the method of investigation will involve comparisons among available Yagi designs. We have used the DL6WU-type design as one kind of standard because it has a long and respected history. W1JR and K1FO designs have similar performance levels, especially with respect to gain and sidelobe development, although they use different algorithms for generating new elements along the boom. Hence, for 20 elements on a 6 wavelength boom, the DL6WU-type antenna will form one axis of comparison. By way of contrast, the newer VK3AUU-type design--less familiar to Yagi builders--achieves considerable sidelobe attenuation, apparently from the higher element density for a given boom length. It packs 25 elements on a 6 wavelength boom and reduces forward sidelobe to more than 20 dB down from the main forward lobe. Hence, it raises the third question in our list and requires comparison to both the OWA series and the DL6WU series.

+

Add to the relativity and complexity of comparisons another factor--the variety of methods by which we might achieve higher OWA series (and other series) gain levels. We may use fatter elements to increase the level of coupling between elements, but even this technique is subject to certain requirements to have any positive effect. We may also use different algorithms for new-director placement. The simplest way of approaching this technique is to create some hybrid designs. We may graft the forward directors onto the OWA core. Here, we may use the first seven OWA elements, since at the transition between elements 7 and 8 (director 5 and 6), we find the closest correlation of element lengths for both the DL6WU and the VK3AUU arrays. The hybrid may go some distance in letting us know whether the array gain is limited by the core or by the method of adding OWA directors. In addition, it may give us some insight into whether the core or the new directors are chiefly responsible for the suppression of new sidelobes and the attenuation of existing sidelobes.

+

The exploration will not be at all a neat progression. We shall have to backtrack and cross our own trail numerous times along the way. We shall also be dealing with numerous standard and non-standard variations on the original designs from our comparators. In a modeling jungle, we can only go where the undergrowth permits.

+

As a marker, the DL6WU designs are the work--before any of my modifications--of Guenter Hoch, the renown developer of long-boom Yagis for VHF and UHF work. His efforts are too well-known to require a full record. VK3AUU is David Tanner, whose work is more recent and involves different techniques of achieving wide-band performance and sidelobe attenuation than the ones used by earlier designers. I have adapted David's designs directly from models that he has personally shared with me. My DL6WU designs come from 3 sources. One is the basic program DL6WU-G, which has been the developed over the years by the efforts of KY4Z, W6NBI, G3SEK, and DL6WU himself. There is another DL6WU GW Basic program called antdl6wu.bas, developed by WA2TIF on the heels of previous developments by a large number of contributors. More recent is an EXCEL spreadsheet initially developed by VK3AUU. I have used all of these programs in generating models of DL6WU-type arrays for this study. Since many of the designs involve adaptations to the needs of this study, tracing one or another to a specific program may be difficult. But all of this is part of the undergrowth.

+

Let's begin by examining the antennas used for comparisons a bit more closely.

+

The Comparators

+

The DL6WU long-boom Yagi series has gone through several stages of evolution. The examples used here derive from an initially scaled 432-MHz model that resulted in 11.8-mm or 0.466" diameter elements. When I ran the 20-element model through the dl6wu-g.bas program, the returns were insignificantly different from the scaling. I then ran a 4-mm or 0.1575" diameter version of the antenna through the program to arrive at new dimensions. In all cases, the DL6WU design uses the same element spacing. Differences in element diameter answer to a set of equations for deriving the element reactance and from that figure and the new diameter, deriving new element lengths. The equations appear in the RSGB publication The VHF/UHF DX Book, edited by Ian White, G3SEK, and are replicated in an article at my web site on scaling VHF and UHF arrays (../vhf/scales.html). As well, George Murphy has encapsulated them in a convenient utility among his HAMCALC GW Basic suite, now available for download from the CQ Magazine web site.

+

The following table provides the dimensions of the two models whose element diameters show an almost 3:1 ratio.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+         20-Element DL6WU Yagis:  Element Lengths Only Re-scaled
+
+Note:  Element spacing is the same for both versions, resulting in a
+6.02 wavelength boom. Both versions are derived with only minor
+adjustments from the program dl6wu-g.bas.  All dimensions in inches.
+
+                      Cumulative            Element Diameter
+Element               Spacing    0.1575" (4 mm)        0.466" (11.8 mm)
+Reflector               ----           39.78                39.68
+Driver                 16.17           39.16                38.44
+Director 1             22.23           36.39                35.13
+Director 2             36.78           36.09                34.85
+Director 3             54.17           35.75                34.44
+Director 4             74.37           35.41                34.04
+Director 5             97.01           35.11                33.69
+Director 6            121.26           34.85                33.36
+Director 7            146.73           34.62                33.11
+Director 8            173.41           34.42                32.87
+Director 9            201.30           34.24                32.66
+Director 10           230.43           34.07                32.48
+Director 11           260.71           33.93                32.32
+Director 12           292.24           33.80                32.15
+Director 13           324.58           33.67                32.01
+Director 14           356.92           33.56                31.90
+Director 15           389.27           33.46                31.78
+Director 16           421.58           33.35                31.66
+Director 17           453.92           33.26                31.55
+Director 18           486.26           33.18                31.45
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Immediately apparent is the fact that the 18th director shows a much larger differential in length relative to the two element diameters than the reflector. Since the element reactance increases as it shortens, the length adjustment becomes larger. Had the reflector been longer than about a resonant half wavelength, then the fatter version would have actually been longer than the thinner one.

+

By keeping a constant relative reactance in each element, the mutual coupling between elements remains close to the same as we move from one element diameter to another. We can observe this from the similarity of modeled performance reports for the two antennas.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  20-Element DL6WU Yagis
+
+4-mm Diameter Elements
+Parameter                   144 MHz         146 MHz         148 MHz
+Gain dBi                    16.70           17.34           17.62
+180-deg F-B                 17.53           23.74           17.23
+Front-Sidelobe              16.11           17.03           17.23
+Impedance (R+/-jX)          55.4 - j 6.1    50.9 + j 6.9    68.1 + j 4.1
+50-Ohm SWR                  1.17            1.15            1.37
+
+11.8-mm Diameter Elements
+Parameter                   144 MHz         146 MHz         148 MHz
+Gain dBi                    16.90           17.45           17.68
+180-deg F-B                 18.44           25.56           20.80
+Front-Sidelobe              16.46           17.19           17.23
+Impedance (R+/-jX)          52.2 - j 8.4    50.4 + j 5.0    68.0 + j 0.5
+50-Ohm SWR                  1.19            1.10            1.36
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The fatter element version shows an average gain advantage of only about 0.12 dB, which is quite insignificant. Because we have used such a large change of diameter (3:1) between versions, the equations begin to lose their precision. They are best applied to element diameter ratios of about 1.5:1, especially for narrow-band designs. They are successful in wide-band designs for diameter ratios up to about 2:1. A sign that we have in the DL6WU design an operating bandwidth that is larger than normal, even for standard wide-band designs--and yet have reached or surpassed the limits of adequacy for length adjustment--appears in the 180-degree front-to-back figures. Here, the fat-element version shows a clear advantage that borders on being operationally detectable.

+

More recently, VK3AUU has proposed a different algorithm for calculating the required element lengths and spacing for long-boom Yagis. His arrangement uses a considerably different reflector-driver-director-1 arrangement to achieve wide-band operation in terms of the 50-Ohm SWR. As well, he employs a higher element population per unit of boom-length in order to attenuate sidelobe development. His original array that he shared with me used 41 10-mm diameter elements on a 24-meter boom. I have cut off the design at 20 elements and changed the element diameter to 3/16" (0.1875"). The resulting array underwent further adjustments to yield the model used here for comparisons. The following table shows the modeled dimensions. Of course, anything of merit in the design belongs to VK3AUU, and any deficiencies belong to my adjustments.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                         25-Element VK3AUU Yagi
+
+Note:  Model derived from a 41-element original with 10-mm diameter
+elements.  All dimensions in inches.  Boom length is 6.11 wavelengths.
+
+                      Cumulative       Element Diameter
+Element               Spacing          0.1875"
+Reflector               ----           40.41
+Driver                 16.10           40.60
+Director 1             18.88           37.15
+Director 2             28.63           36.66
+Director 3             41.29           36.23
+Director 4             56.01           35.81
+Director 5             72.34           35.38
+Director 6             89.95           35.03
+Director 7            108.69           34.68
+Director 8            128.38           34.39
+Director 9            148.93           34.04
+Director 10           170.21           33.83
+Director 11           192.16           33.54
+Director 12           214.77           33.33
+Director 13           237.94           33.12
+Director 14           261.63           32.91
+Director 15           285.84           32.70
+Director 16           310.49           32.55
+Director 17           335.58           32.34
+Director 18           361.07           32.20
+Director 19           386.96           32.06
+Director 20           413.21           31.99
+Director 21           439.83           31.85
+Director 22           466.76           31.71
+Director 23           494.03           31.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Because the driver and first director make up a closely coupled element pair that constitutes the actual array driver, the driver is actually longer than the reflector. Nonetheless, the remaining elements show a regular, although not simple, increment of length decrease. The array packs 25% more elements on about the same boom length as used in the DL6WU 20-element arrays. The resulting modeled performance appears in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  25-Element VK3AUU Yagi
+
+0.1875" Diameter Elements
+Parameter                   144 MHz         146 MHz         148 MHz
+Gain dBi                    16.91           17.22           17.27
+180-deg F-B                 25.00           35.65           23.61
+Front-Sidelobe              20.10           22.28           24.17
+Impedance (R+/-jX)          56.4 + j 2.7    59.6 + j 3.9    49.6 + j 6.6
+50-Ohm SWR                  1.14            1.21            1.14
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Perhaps the most significant feature of the performance figures are the higher front-to-sidelobe ratios all across the band, relative to the figures for the DL6WU array. The difference becomes visually apparent by a review of Fig. 2.

+

We may appreciate the design goal differences between the DL6WU arrays and the VK3AUU Yagi by looking at a few overlaid curves. Fig. 3 shows the anticipated free-space gain values derived from frequency sweeps of all three models. Although the DL6WU antennas show a higher peak value, note the rather narrow range of the Y-axis. In practical terms, both antennas fit the same operational ballpark.

+
+ +
+

As wide-band designs, the DL6WU values do not necessarily fall as we move beyond the high band edge, although we seem to see a peak just below that frequency. The DL6WU designs have multiple gain, front-to-back, and SWR peaks and valleys, and their relative positions on a frequency sweep vary with the number of elements in the design. The VK3AUU design shows a much narrower range of gain variation over the 2-meter band, with a peak that also is close to the upper passband limit.

+
+ +
+

Fig. 4 shows that the VK3AUU 180-degree front-to-back peak values occur close to the design center for the array--146 MHz. The DL6WU peak values are but one of several peaks within the overall operating passband for the array, and the frequency position and peak values vary with the number of elements. 20 elements is not one of the recommended array sizes for peak front-to-back performance, although it is the size required for comparison with the largest of the OWA series developed so far.

+
+ +
+

Fig. 5 overlays the 50-Ohm SWR curves for the three modeled comparators. Like the gain and front-to-back curves for the DL6WU Yagis, the SWR curves show a relatively close coincidence, with just enough departure to indicate the limits of the length adjustment equations. The VK3AUU curve shows that it is possible to obtain less than 1.25:1 SWR at 50 Ohms across the entire 2-meter band with proper spacing of the reflector, driver, and first director, without need for special treatment of the subsequent 2 directors, as is done in the OWA array.

+

The VK3AUU array achieves about the same gain as the DL6WU, but with better than 20 dB values for both the 180-degree front-to-back ratio and the front-to-sidelobe ratio. However, the VK3AUU array design shows all of the sidelobes typical for a 6 wavelength boom, but attenuated relative to the DL6WU (and similar designs). It does not show any sidelobe suppression, that is, a failure for the sidelobes to emerge.

+

This feature of the VK3AUU array permits us to answer at least one of our questions: whether the OWA core or the method of adding new elements is responsible in the main for the sidelobe suppression that we find in the 20-element, 6 wavelength boom version. To answer the question, we shall need to create some hybrids.

+

A Tale of Two Hybrids

+

The most direct--but far from the simplest--way to sort out the effects of the OWA core from the effects of the method of adding elements to the OWA series 6 wavelength boom Yagi is to create one or more hybrid designs. By judicious manipulation, it is possible to append the forward director structure of either the VK3AUU design or the DL6WU design onto the core of the OWA.

+

Circumstances dictated that I use the first 7 elements of the OWA design as the core. First, it was on this original design that I had begun the process of adding new directors by modifying the length and spacing of the former forward-most director and then adding the new one. Second, the length of the 8th element (Director 6) in the OWA corresponded most closely to an element in the grafted director structure. In all cases, the process required considerable juggling of the overall structure in two ways. One way led to slight frequency scaling to bring the overall hybrid antenna into a near replica of the OWA SWR curve and to center--as best possible--the operating characteristics. Further refinements required changes to the reflector, driver and first director, along with the forward-most director to complete the process well enough to achieve a usable array.

+

The VK3AUU director structure from about 100" of cumulative spacing forward presented the simpler of the two graftings. However, the move required some overall adjustment by frequency scaling and some touch-up of the reflector-driver portion. The following table presents the final dimensions--which might well undergo further optimizing.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    24-Element OWA-VK3AUU Hybrid Yagi
+
+                      Cumulative            Element Diameter
+Element               Spacing          0.1875"
+Reflector               ----           41.04
+Driver                  8.91           39.61
+Director 1             13.65           37.08
+Director 2             25.46           36.45
+Director 3             40.86           36.52
+Director 4             61.59           36.30
+Director 5             86.49           35.04
+Director 6            108.69           34.68
+Director 7            123.37           34.39
+Director 8            143.91           34.04
+Director 9            165.19           33.83
+Director 10           187.15           33.54
+Director 11           209.75           33.33
+Director 12           232.93           33.12
+Director 13           256.61           32.91
+Director 14           280.83           32.70
+Director 15           305.47           32.55
+Director 16           330.56           32.34
+Director 17           356.05           32.20
+Director 18           381.94           32.06
+Director 19           408.19           31.99
+Director 20           434.81           31.85
+Director 21           464.56           31.71
+Director 22           487.64           31.41
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The final boom length at the 23-element mark was 6.03 wavelengths, about 0.08 wavelength shorter than the VK3AUU original and 0.19 wavelength shorter than the original 20-element OWA design. The reason for the element decrease is the smaller spacing between the early elements of the original VK3AUU design.

+

The performance is a fair--but not perfect--match for the performance of the original VK3AUU-derived design, as shown by the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  24-Element Hybrid OWA-VK3AUU Yagi
+
+0.1875" Diameter Elements
+Parameter                   144 MHz         146 MHz         148 MHz
+Gain dBi                    16.92           17.18           16.95
+180-deg F-B                 23.43           29.06           25.99
+Front-Sidelobe              20.02           22.57           24.00
+Impedance (R+/-jX)          45.0 + j 4.5    48.8 + j 6.0    34.8 - j 6.7
+50-Ohm SWR                  1.15            1.13            1.49
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The peak gain is better centered than in the original design. Hence, we have reduced the upper passband-edge gain below the value for the original design. The SWR curve reflects OWA characteristics, with a relative fast rise in value at the upper passband limit.

+

The use of a single hybrid would only hint at an answer to the question that gave us a reason to create a hybrid--namely, to what extend either the OWA core or the method of adding new directors is responsible for the OWA Yagi's tendency to suppress sidelobe formation. A second hybrid, using a different forward structure predicated on a different algorithm for adding new directors might turn the hint into a strongly suggestive answer. So I tried the same technique of starting with 7 OWA elements and adding a DL6WU-type director structure.

+

The ensuing design challenge required the use of 0.375" diameter elements, twice as fat as the 0.1875" OWA and VK3AUU originals. This move further entailed some frequency scaling and element scaling so that the final result may not closely resemble at first site the DL6WU design from which I took the initial grafts. The array turned out to be shorter at the 20-element mark than originally planned and required the addition of 3 elements to bring the boom length above 6 wavelengths. The final 23-element length is 6.07 wavelengths.

+

The final dimensions for this exercise--but not necessarily for a fully adequate practical array--appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    23-Element OWA-DL6WU Hybrid Yagi
+
+                      Cumulative            Element Diameter
+Element               Spacing          0.375"
+Reflector               ----           40.60
+Driver                  9.95           38.60
+Director 1             13.91           35.80
+Director 2             25.67           35.31
+Director 3             40.59           35.31
+Director 4             60.68           35.11
+Director 5             81.09           34.52
+Director 6             95.40           34.24
+Director 7            112.48           33.83
+Director 8            132.32           33.44
+Director 9            154.57           33.10
+Director 10           178.39           32.78
+Director 11           203.40           32.53
+Director 12           229.62           32.30
+Director 13           257.02           32.09
+Director 14           285.61           31.91
+Director 15           315.39           31.75
+Director 16           346.37           31.60
+Director 17           380.98           31.47
+Director 18           412.85           31.27
+Director 19           438.99           31.07
+Director 20           465.13           30.88
+Director 21           491.00           29.80
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Despite the modifications, the array performs in a manner reasonably close to that of a DL6WU Yagi designed in perfect accord with the original algorithms. The modeled free-space performance appears in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  23-Element Hybrid OWA-DL6WU Yagi
+
+0.375" Diameter Elements
+Parameter                   144 MHz         146 MHz         148 MHz
+Gain dBi                    16.94           17.18           17.13
+180-deg F-B                 36.86           22.30           20.39
+Front-Sidelobe              22.51           21.92           20.12
+Impedance (R+/-jX)          38.9 + j 2.2    52.4 + j 4.5    58.3 + j 4.1
+50-Ohm SWR                  1.29            1.10            1.19
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Like many lengths of DL6WU designs, the peak gain appears near one end of the passband while the peak front-to-back ratio appears near the other.

+
+ +
+

We can contrast the gain curves for the two hybrid arrays by examining Fig. 6. The DL6WU-hybrid places its peak--at least for this portion of its total operating passband--near the passband upper limit. The VK3AUU-hybrid centers its gain curve very close to the design frequency. Given the narrow range of values on the Y-axis of the graph, the overall gain performance is comparable.

+
+ +
+

Like the VK3AUU-hybrid gain curve, the array's front-to-back curve, shown in Fig. 7, is also quite well centered in the passband. In contrast, the DL6WU-hybrid's front-to-back curve dwindles considerably above the lower end of the passband. However, both array designs maintain a front-to-back ratio of better than 20 dB across the 2-meter band.

+
+ +
+

Fig. 8 compares the 50-Ohm SWR curves for the two hybrids. The VK3AUU- hybrid curve has distinct OWA features. However, the DL6WU-hybrid curve is relatively featureless in terms of identifying marks. Nevertheless, without further modification of the hybrid arrays, it is slightly superior. If neither the gain nor the front-to-back ratio could be well-centered in the passband, the DL6WU-hybrid SWR curve is well-centered.

+

In many ways, the initial listings and comparisons are preliminary to our central question. They establish several facts to give us confidence in our answer to the question. First, hybrid designs are certainly possible and promise performance close to that of the original designs. Second, the two arrays are quite comparable in both size and performance. Hence, at a point short of being definitive but close to one of confidence, we can look at the sidelobe development of the two hybrid arrays.

+
+ +
+

Fig. 9 provides expanded views of the sidelobes of the free-space patterns for both hybrid arrays. In each of them, we can count 6 forward and 6 rearward sidelobes, although a couple of them are very diminutive. In no way is the OWA core itself able to suppress the formation of the sidelobes. The forward director structure is at least the dominant influence on their formation.

+

The VK3AUU-hybrid and the original derived VK3AUU 25-element array show very similar front-to-sidelobe values. However, the DL6WU-hybrid further attenuates its sidelobes by 3-5 dB relative to the original 20-element DL6WU presented at the beginning of this exploration. The most likely source of that further attenuation is the increased element (or more properly, director) population on the 6 wavelength boom for the hybrid. Although designed to different algorithms, the two director structures end up with close to the same number of directors in the same boom space. And the result appears to be an increase in the attenuation of sidelobe strength.

+

Conclusions

+

The conclusions that we may draw with reasonable confidence place responsibility for side-lobe attenuation on the density of directors. As well, sidelobe suppression appears also to be a function of the director structure, since neither the DL6WU nor the VK3AUU structures achieved any sidelobe suppression. Without claiming that these answers are more than strongly suggestive, we have cleared two of the three questions from our initial list.

+

However, we have one remaining question: is there a way to improve the gain performance of the original 20-element OWA Yagi? As a clue to where we might turn for an answer, I might note the unexplained increase in the diameter of the DL6WU-hybrid elements to 0.375" (3/8"). Because the route to the answer contains some necessary by-ways, I suspect that we had best devote a full third part in this series to the question.

+
+ +
+

Updated 09-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for August, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: Increasing OWA Gain vs. Preserving Sidelobe Suppression

+

Go to Main Index

+

Topics: VHF / UHF, Yagi


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+

Extending the 2-Meter OWA Family
+ Part 3: Increasing OWA Gain vs. Preserving Sidelobe Suppression

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In our preceding discussion, we developed tentative answers to two out of our three inquires that emerged from the extension of the OWA 2-meter family to 20 elements. By way of quick review, the low gain but high sidelobe suppression of the 20-element version of the array left us with these questions.

+
    +
  • 1. Which of the two OWA design concepts--the core or the method of adding new elements--has the dominant effect on side-lobe development?
    • +
  • 2. Is there a method of obtaining more gain from the OWA series without sacrificing sidelobe suppression and attenuation?
    • +
  • 3. What role does element population play in sidelobe attenuation?
    • +
+

The development of some hybrid models, combining the core of the OWA Yagi with the forward director structures of DL6WU and VK3AUU designs, suggested strongly that the forward director structure more than the core is responsible for the strong sidelobe attenuation. As well a key to sidelobe attenuation appears to be a higher density of well-regulated directors than has typically been used on past (pre-VK3AUU) long-boom Yagi designs.

+

Although incidental to the exercise, I would not especially recommend the use of the hybrid designs in practice. The DL6WU design and some of its peer designs provided the most wide-band gain for the fewest elements. For sidelobe attenuation, the VK3AUU array--even severely modified to fit this exercise--is a good standard for future designs.

+

We are thus left with only one question: whether it is possible to obtain more gain from the OWA 20-element Yagi without significant damage to its sidelobe suppression abilities. As a guide to the level of sidelobe development in the various arrays, the sample DL6WU design in its 4-mm element diameter version averaged a front-to-sidelobe ratio of 16.8 dB, while the version with 11.8-mm elements averaged 17.0 dB. The 0.1875" element diameter version of the VK3AUU array achieved an average front-to-sidelobe ratio of about 22.2 dB, or 5 dB better than the DL6WU. The OWA 20-element Yagi, despite a gain deficit of about 1-3/4 dB relative to the other arrays managed an average front-to-sidelobe ratio of 28.7 dB, about 6.5 dB better than the VK3AUU array and 11.5 dB better than the DL6WU.

+

If sidelobe suppression is important to any application of a long boom Yagi, then we would accrue an advantage if we could squeeze further gain from the OWA array without losing a significant amount of the sidelobe attenuation. As well, we should recall that the OWA Yagi not only attenuates sidelobes, but also tends to suppress them, since we could observe fewer sidelobes--either forward or rearward--on the OWA pattern than on the patterns for the other arrays.

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Sidelobe suppression may not be so straightforward as we might initially think from pattern observation. All of the anticipated 6 sidelobes for a 6 wavelength boom may be present. However, if the array's structure directs one or more of them so that two or more coincide, then the seemingly suppressed sidelobes will be present, but weak and invisible. This possibility, however, has little practical difference from true suppression, since it is the shape of the resulting pattern and the strength of the visible sidelobes that will determine an array's sensitivity to signals that are off axis.

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How OWA Gain and Sidelobe Attenuation May Be Related

+

A Yagi array consists, normally, of a driven element and one or more parasitic elements, that is, elements which derive the energy directly or indirectly from the driven element. Since the intent of a Yagi is to provide a directional beam of energy, those elements on the side of the array away from the main forward beam are called reflectors. In the most common designs, there will be a single reflector, since its task is less to reflect and more to set--by virtue of its spacing and length--the feedpoint impedance of the driver. In large arrays, the reflector is normally more influential on the performance at the low end of the desired passband than the upper. We can also add other reflector elements, ordinarily in a plane at right angles to the orientation of the remaining elements. By creating a planar reflector, we can improve the front-to-back ratio of the array. This improvement often shows up in the attenuation of vertical sidelobes--a subject for a wholly different treatise.

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Elements forward of the driver in the direction of the main beam are called directors. We may add a virtually endless number of directors ahead of the driver. Before we turn to these forward directors, let's pause to note some special relationships. The first director in a narrow band Yagi tends to function solely as a director. The driver maintains the highest current magnitude throughout the passband of the array. In wide-band designs, however, the first director normally has a position closer to the driver. In the upper portion of the passband, the first director will show a higher relative current magnitude than the driver itself and thus tends to control the performance of the array in that region of the passband. With certain spaces between the driver proper and the first director as a secondary driver--due to the close element coupling--we may even see a reversal of normal expectations for driver feedpoint reactance. That is, as we shorten the first director, we may find the reactance at the driver feedpoint becoming less capacitive and more inductive. In the OWA design, the 2nd and 3rd directors perform controlling functions and may be the same length--or the 3rd director may be slightly longer than the 2nd director. The controlling function receives its name from the ability of the OWA design to center the peak gain and the peak front-to-back ratio close to the design frequency and within the operating passband.

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Beyond the 3rd director, the remaining forward directors generally show a regular--although not necessarily simple--progression of reduced lengths until we reach the end of the array. Some director pairs may be the same length, but the general tendency is reduced length as we move away from the driver. The result is an overall taper of the Yagi shape for a given boom length.

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As Lawson showed, the basic forward gain of a Yagi is determined less by the absolute number of elements and more by the boom length. For a given boom length, of course, we require a certain minimum number of elements to achieve the mutual or inter-element coupling necessary to establish current levels on the entire set of directors that allow us to obtain the gain that is theoretically possible. One of the prices that we pay for using a minimalist configuration is a narrow operating passband, not only in terms of the feedpoint impedance excursions, but as well in terms of the available gain and front-to-back ratio.

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Wide-band designs, such as the DL6WU and VK3AUU Yagi series, free the home Yagi builder from many of the ultra-precise construction tasks that face someone building a narrow-band design with a minimalist configuration. The cost is twofold: the use of more elements and the use of a relatively mild taper to the element lengths. The 6 wavelength boom of a DL6WU array uses a taper in the range of 0.79 to 0.83 as we take the ratio of the most forward director to the reflector. The 25-element VK3AUU array on the same length boom uses a taper on the vicinity of 0.78.

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As we discovered in the last episode, even within the realm of wide-band designs, we can distinguish minimal from "fully-packed" Yagi designs. The DL6WU design--and a number of kindred Yagis--achieve maximum wide-band gain from the fewest practical number of elements, but suffer fairly large fully developed sets of forward and rearward sidelobes. On the same boom length, the addition of 5 directors, using the VK3AUU algorithm, attenuates sidelobes by an average across the 2-meter band of 5 dB relative to the DL6WU design. In fact, compressing the DL6WU director structure to allow the addition of 3 more directors shows a sidelobe attenuation level close to that of the VK3AUU design.

+

For a given gentle taper in the range of the DL6WU and VK3AUU Yagi designs, gain is largely a function of boom length, since both element populations achieve similar gain levels. Both arrays achieve within their design algorithms comparable levels of mutual coupling from one element to the next. However, the 20-element OWA Yagi achieved considerable less gain, but accompanied by not only further attenuation of sidelobe energy, but as well by an apparent suppression of sidelobes. Moreover, most of the forward director structure uses element spacing that is quite similar to that in the DL6WU design. The next step is to search for a critical difference.

+

The most evident difference lies in the overall element taper of the two arrays. Instead of a 0.79-0.83 taper, typical of DL6WU 6 wavelength arrays, the OWA series array shows a taper close to 0.67--a much more radical level of element shortening as we move forward along the beam. One obvious effect of the more radical tapering of element lengths is to reduce the mutual coupling among adjacent elements, which plays a key role in the reduced additional gain that we achieve with each added director. Fig. 1 shows the OWA outline with the relative current magnitude levels indicated for each element.

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+ +
+

The first line of correction might seem to be to simply increase the mutual coupling between elements. However, as we shall see in our efforts to restore some of the lost gain to the OWA 20-element, the element taper will play a considerable role in sidelobe formation. Although we shall not go all the way in restoring gain, we shall go far enough to illustrate some of the limitations that we encounter along the way. Understanding limitations of Yagi design is significant to the design of series that attempt to combine across a given operating passband maximum forward gain, maximum front-to-back ratio, minimum feedpoint SWR, and minimum sidelobe development.

+

Standard Element Scaling The first inclination might be to use fatter elements in an effort to achieve a higher level of mutual element coupling. Of course, a change in element diameter requires that we re-calculate the element lengths. The standard equations involve a 2-step process. The first step is to calculate the reactance of each element from this following equation.

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+ +
+

L is the original element length, D is the original element diameter, lambda is a wavelength at the design frequency, and X is the resulting reactance. Then we plug the calculated reactance along with lambda and a new element diameter, D, into the second equation.

+
+ +
+

The result is a new length, L, applicable to the new element diameter.

+

These handy equations are part of the HAMCALC suite of GW Basic utilities--now available for download from the CQ Magazine web site. Let's use them to design revised versions of the 20-element OWA Yagi using 0.375" and 0.75" diameter elements. The following table shows the results of the re-design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           20-Element OWA Yagis:  Scaled Element Lengths and Spacing
+
+Note:  All dimensions derived from standard element scaling equations while
+maintaining the same element spacing.  All dimensions in inches.
+
+                  Cumulative                    Element Diameter
+Element           Spacing           0.1875"           0.375"            0.75"
+Refl.               ----            40.90             40.98             41.08
+Driver              8.79            39.50             39.35             39.15
+Dir. 1             13.47            37.00             36.46             35.71
+Dir. 2             25.38            36.33             35.68             34.78
+Dir. 3             40.72            36.40             35.76             34.88
+Dir. 4             61.38            36.21             35.54             34.62
+Dir. 5             86.49            35.20             34.37             33.22
+Dir. 6            116.00            34.30             33.33             31.98
+Dir. 7            146.60            33.60             32.51             31.02
+Dir. 8            178.40            32.90             31.70             30.05
+Dir. 9            210.00            32.20             30.89             29.09
+Dir. 10           243.00            32.20             30.89             29.09
+Dir. 11           276.00            30.80             29.27             27.16
+Dir. 12           309.00            30.40             28.82             26.61
+Dir. 13           342.00            30.00             28.34             26.05
+Dir. 14           375.00            29.20             27.41             24.95
+Dir. 15           408.00            28.80             26.95             24.40
+Dir. 16           441.00            28.40             26.49             23.85
+Dir. 17           475.00            28.40             26.49             23.85
+Dir. 18           502.00            27.40             25.33             22.47
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The results of this exercise should theoretically net us the same performance from each version of the array, since the equations will yield the same inter-element coupling, using shorter lengths for fatter elements and the original element spacing throughout the array. The following table indicates a somewhat different story.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  20-Element OWA Yagi:  Standard Element Scaling
+
+0.1875" Diameter Elements
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.19             15.61             15.68
+180-deg F-B             24.50             26.18             26.74
+Front-Sidelobe          28.26             31.07             26.74
+Impedance (R+/-jX)      42.9 + j 4.5      46.8 + j 6.9      45.1 - j 3.9
+50-Ohm SWR              1.20              1.16              1.14
+
+0.375" Diameter Elements
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.18             15.51             15.52
+180-deg F-B             24.81             25.86             24.37
+Front-Sidelobe          32.15             30.44             26.11
+Impedance (R+/-jX)      43.7 + j 5.0      47.2 + j 4.8      40.0 - j 7.9
+50-Ohm SWR              1.19              1.12              1.32
+
+0.75" Diameter Elements
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.07             15.30             15.24
+180-deg F-B             24.74             25.06             23.43
+Front-Sidelobe          31.86             29.48             25.39
+Impedance (R+/-jX)      44.4 + j 4.3      46.6 + j 0.4      33.2 - j 9.1
+50-Ohm SWR              1.16              1.07              1.59
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although we see a decreasing gain as we increase the element diameter, Fig. 2 makes the decrease more readily apparent. With each doubling of element diameter, we end up with increasingly less gain.

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+ +
+

However, the front-to-back ratios do not significantly differ among the variations of the 20-element OWA Yagi. As Fig. 3 shows, the decline from one diameter to the next larger is much less noticeable than the change in gain.

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+ +
+

Part of the problem stems from the limitations of the equations themselves. They work best--achieving very close to perfectly equivalent arrays--when the ratio of the two elements is 1.5:1 or less. We have pushed the equations to 2:1 and 4:1 ratios. As well, the OWA core requires somewhat careful optimizing of the driver and first director (especially) to hold the passband within the same limits. Without this adjustment, the SWR passband slides downward in frequency with increasing element diameter. Fig. 4 makes this slide readily apparent.

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+ +
In the process of using standard conventions for adjusting the element lengths for the new diameters, we did alter another--often overlooked--feature of the array. We increased the rate of taper of the array, as indicated by the ratio of the most forward director length to the reflector length. The 0.375" version shows a taper ratio of 0.62, while the 0.75" version has a ratio of 0.55. The significance of these further reductions appears in Fig. 5, which shows the 146-MHz sidelobe structure for free-space models of the three array versions. +
+ +
+

Although the 0.1875" version clearly shows a 4th forward sidelobe, despite its minuscule size, the fatter versions of the array with their increased taper obscure any definite identification of a 4th forward lobe. Since the overall sidelobe attenuation is not better than with the thinnest of our Yagis, the apparent disappearance of the 4th sidelobe has little practical consequence. However, the progression does suggest that element length taper does play a role in sidelobe formation and suppression.

+

An Alternative Technique of Increasing Mutual Coupling

+

There is a second strategy available for scaling the element lengths for fatter elements. We can initially substitute the new element diameter for the old. The resulting array will no longer show its performance peak or its passband limits at the same frequency as the original array. However, we can locate those limits and then re-scale the entire array so that the design frequency is once again 146 MHz.

+

The 20-element OWA Yagi underwent this treatment, with 4 versions as the result: the original 0.1875" diameter array plus three others using 0.375", 0.5" and 0.75" diameter elements. The following table shows the dimensions that resulted from the exercise.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+         20-Element OWA Yagis:  Compressed Element Length Adjustments
+
+Note:  Element lengths and spacing derived from scaling and compression
+techniques described in the text.  All dimensions in inches.
+
+                  Cumulative        El. Dia.          Cumulative        El. Dia.
+Element           Spacing           0.1875"           Spacing           0.375"
+Reflector           ----            40.90               ----            40.19
+Driver              8.79            39.50               8.64            38.81
+Director 1         13.47            37.00              13.24            36.36
+Director 2         25.38            36.33              24.94            35.69
+Director 3         40.72            36.40              40.01            35.76
+Director 4         61.38            36.21              60.31            35.58
+Director 5         86.49            35.20              84.98            34.59
+Director 6        116.00            34.30             113.98            33.70
+Director 7        146.00            33.60             144.04            33.01
+Director 8        178.40            32.90             175.29            32.33
+Director 9        210.00            32.20             206.34            31.64
+Director 10       243.00            32.20             238.76            31.64
+Director 11       276.00            30.80             271.19            30.26
+Director 12       309.00            30.40             303.61            29.87
+Director 13       342.00            30.00             336.04            29.48
+Director 14       375.00            29.20             368.46            28.69
+Director 15       408.00            28.80             400.88            28.30
+Director 16       441.00            28.40             433.31            27.90
+Director 17       475.00            28.40             466.72            27.90
+Director 18       502.00            27.40             493.25            26.92
+
+                  Cumulative        El. Dia.          Cumulative        El. Dia.
+Element           Spacing           0.5"              Spacing           0.75"
+Reflector           ----            39.85               ----            39.31
+Driver              8.57            38.48               8.45            37.96
+Director 1         13.12            36.05              12.95            35.56
+Director 2         24.73            35.39              24.39            34.91
+Director 3         39.67            35.46              39.14            34.98
+Director 4         59.80            35.28              58.99            34.80
+Director 5         84.26            34.29              83.12            33.83
+Director 6        113.01            33.42             111.49            32.97
+Director 7        142.82            32.73             140.89            32.29
+Director 8        173.81            32.05             171.46            31.62
+Director 9        204.59            31.37             201.83            30.95
+Director 10       236.74            31.37             233.54            30.95
+Director 11       268.89            30.01             265.26            29.60
+Director 12       301.04            29.62             296.97            29.22
+Director 13       333.19            29.23             328.69            28.83
+Director 14       365.34            28.45             360.41            28.06
+Director 15       397.49            28.06             392.12            27.68
+Director 16       429.64            27.67             423.84            27.29
+Director 17       462.77            27.67             456.51            27.29
+Director 18       489.07            26.69             482.46            26.33
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Since each new array involved total frequency scaling, including element spacing, each version requires a cumulative spacing column as well as an element length column. The compression scaling name results from the fact that the scaling results in slightly shorter boom lengths for each fatter version. Hence, besides the effects of increasing the element diameters, we also have very slightly closer element spacing at work in increasing the mutual coupling among elements. The following table summarizes the modeled free-space performance data for the 4 versions of the array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  20-Element OWA Yagi:  Compressed Element Scaling
+
+0.1875" Diameter Elements:  Boom length 6.21 wavelengths
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.19             15.61             15.68
+180-deg F-B             24.50             26.18             26.74
+Front-Sidelobe          28.26             31.07             26.74
+Impedance (R+/-jX)      42.9 + j 4.5      46.8 + j 6.9      45.1 - j 3.9
+50-Ohm SWR              1.20              1.16              1.14
+
+0.375" Diameter Elements:  Boom length 6.18 wavelengths
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.72             16.07             16.07
+180-deg F-B             23.31             26.29             26.35
+Front-Sidelobe          31.35             30.76             26.85
+Impedance (R+/-jX)      36.5 - j 0.5      41.0 + j 2.6      46.3 - j 7.2
+50-Ohm SWR              1.37              1.29              1.18
+
+0.5" Diameter Elements:  Boom length 6.05 wavelengths
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                15.95             16.25             16.20
+180-deg F-B             22.59             25.88             26.70
+Front-Sidelobe          32.91             30.54             24.17
+Impedance (R+/-jX)      33.7 - j 1.8      38.3 + j 1.3      45.7 - j 9.2
+50-Ohm SWR              1.49              1.31              1.24
+
+0.75" Diameter Elements:  Boom length 5.97 wavelengths
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                16.25             16.48             16.34
+180-deg F-B             21.54             24.70             27.07
+Front-Sidelobe          24.16*            28.78*            23.82
+Impedance (R+/-jX)      29.6 - j 4.3      34.1 - j 0.5      44.5 - j12.8
+50-Ohm SWR              1.71              1.47              1.33
+Note:  * means the appearance of a new sidelobe.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Fig. 6 shows us the gain curves for all 4 versions of the compression-scaled array. Since the exact passband limits used in the scaling is a judgement call and not a simple calculation, we should not expect a perfectly congruent set of curves. However, all of them place the gain peak well within the operating passband. It is clear that increasing the element diameter increases the gain. In just the range of the trial diameters, we have restored the peak gain to within about 1 dB of the gain achieved by DL6WU and VK3AUU arrays. We have not made our array very much heavier in the process, since 3/8" 6061-T832 tubing is actually lighter per unit length than 3/16" rod.

+
+ +
+

The front-to-back ratio data, shown in Fig. 7, suggests that we have made no operationally significant changes in this performance category. The exact peak position is a function of the scaling choices made, and one might easily align all of the peaks by slightly different selections. In general, I chose to scale the array versions so that the SWR curves would align their minimum values with fair coincidence. In addition, I also selected the scaling factors to achieve the same taper factor for each version.

+
+ +
+

As Fig. 8 shows, all of the arrays have minimum 50-Ohm SWR values at about 147.5 MHz. Although all versions of the array have passband end-to-end SWR values well below 2:1, the overall SWR curves degrade as we increase the element diameter without further adjustment to the core of the array.

+

If we take sidelobe suppression as well as attenuation as one of our design criteria--as we have in this exercise--we encounter a limit as to how much we may increase the mutual coupling among elements. All of the arrays have the same taper ratio of forward director to reflector: 0.67. (In fact, the values range only from 0.6698 to 0.6699.) However, the sidelobe structures are not identical.

+
+ +
+

As we increase the mutual coupling among adjacent elements by virtue of the element diameter and the element spacing, we can notice the incipient development of a new lobe. See Fig. 9. It shows itself as a shifting "bulge" in the forward patterns of the arrays using larger than 3/16" elements. In the rearward patterns, the main rear lobe corners are actually sidelobes for the purposes of counting. In the 0.75" version of the array, we can clearly count 5 sidelobes. Although this number remains 1 less than we find in our comparators, the DL6WU and the VK3AUU, the emergence of a new lobe also signals a reduction in the average sidelobe attenuation across the entire band.

+

Hence, our increase in gain via increased mutual coupling comes at a price, despite the maintenance of the element taper value. At a certain point in the process of increasing the coupling, we begin to lose the advantages of the element taper.

+

Perhaps the version of the array with the best all-round performance (including sidelobe suppression and attenuation with the more standard performance categories) is the one using 0.5" elements. Fig. 10 shows the free-space E-plane (azimuth) patterns for this array across the 2-meter band at frequencies corresponding to those in the table of performance values.

+
+ +
+

As a rough measure of the increase in mutual coupling, you may compare Fig. 1 for our original array with 3/16" elements to Fig. 11 for the version with 0.5" diameter elements. The increased relative current magnitude on the forward directors should be relatively clear.

+
+ +
+

However, we are still a dB below the gain of the DL6WU and VK3AUU arrays. Certainly, we can go through further iterations to further increase the array's gain while preserving the sidelobe suppression. However, it is unlikely that we shall attain full gain with full sidelobe suppression without significant elements of re-design. For example, it is not immediately clear how to increase the element population in balance with an element taper that will both attenuate existing sidelobes and suppress further sidelobe development while improving gain and sustaining front-to-back performance.

+

One Last Experiment in the Series

+

If we can scale element diameters upward, perhaps we may return to our initial 3/16" diameter elements by scaling downward from the 0.5" version of the array. Actually, the optimizing process required 3 steps and remains imperfect. First, I applied the standard element diameter-to-length equations for a new set of values. Next, I did some compression scaling--in this case, expansion scaling--to re-center the performance values. Finally, I re-adjusted the core elements to obtain a 50-Ohm SWR curve with values no higher than 1.2:1. The following table compares the dimensions of the original and the final versions of 3/16" 20-element OWA Yagis.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+     20-Element 0.1875" Diameter Element OWA Yagis:  Original and Revised
+
+Note:  All dimensions in inches.
+
+                        Original                            Revised
+                  Cumulative        El. Dia.          Cumulative        El. Dia.
+Element           Spacing           0.1875"           Spacing           0.1875"
+Reflector           ----            40.90               ----            40.90
+Driver              8.79            39.50               8.79            39.50
+Director 1         13.47            37.00              13.47            37.06
+Director 2         25.38            36.33              25.37            36.48
+Director 3         40.72            36.40              40.35            36.54
+Director 4         61.38            36.21              60.56            36.41
+Director 5         86.49            35.20              85.10            35.61
+Director 6        116.00            34.30             113.96            34.90
+Director 7        146.00            33.60             143.87            34.34
+Director 8        178.40            32.90             174.96            33.79
+Director 9        210.00            32.20             205.85            33.25
+Director 10       243.00            32.20             238.11            33.25
+Director 11       276.00            30.80             270.38            32.15
+Director 12       309.00            30.40             302.64            31.83
+Director 13       342.00            30.00             334.90            31.52
+Director 14       375.00            29.20             367.16            30.88
+Director 15       408.00            28.80             399.42            30.57
+Director 16       441.00            28.40             431.68            30.25
+Director 17       475.00            28.40             464.92            30.25
+Director 18       502.00            27.40             491.32            29.49
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Since the initial mode of re-scaling was application of standard scaling equations, the final revised beam is imperfect. It has an element taper of 0.72, which is below the values for the DL6WU and VK3AUU arrays, but well above the taper in the compression-scaled models. As we shall see, this difference makes a difference in the modeled performance data.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Modeled Performance:  Revised 20-Element OWA Yagi
+
+0.1875" Diameter Elements:  Boom length 6.08 wavelengths
+Parameter               144 MHz           146 MHz           148 MHz
+Gain dBi                16.03             16.39             16.20
+180-deg F-B             24.53             27.92             24.86
+Front-Sidelobe          29.26             26.20*            23.80*
+Impedance (R+/-jX)      42.7 + j 3.7      45.6 + j 7.5      47.3 - j 7.7
+50-Ohm SWR              1.19              1.20              1.18
+Note:  * means the mergence of a new lobe.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Fig. 12 shows the free-space gain and 180-degree front-to-back ratio across the band. The peaks are just above the design frequency. The front-to-back ratio shows roughly equal values at the band edges. The gain values show another small increment of increase beyond those of the 0.5" array version on which this design is based.

+
+ +
+

The 50-Ohm SWR curve is pure OWA in its shape and low values across the band, as Fig. 13 clearly illustrates. The deepest dip at 147.5 MHz is correctly placed.

+

However, the new taper value of 0.72 has taken its toll. See Fig. 14.

+
+ +
+

The increased taper value allows us to count 5 sidelobe peaks or bulges in both the forward and rearward directions for each of the 3 sampled patterns. Although at 144 MHz, we have a front-to-sidelobe ratio that reflects the best OWA values, the sidelobe attenuation at 146 MHz is 4 dB lower than the value for the 0.5" compressed-scaling array. For maximum sidelobe suppression and attenuation, the 0.5" diameter element version of the largest of our OWA series Yagis remains unsurpassed. . .for the moment.

+

Conclusion

+

Our initial task was simply to extend the OWA series of Yagis to 20 elements. However, the curiosities left by the results of that project have led us a considerable distance away from Yagis to build into the basic properties of Yagis. Some of these properties--for example, sidelobe suppression in contrast to simple attenuation--may have no immediate implications for practical antenna construction and use. However, these notes do indicate some directions for further investigation into the inter-relationship of the entire set of Yagi properties, if for no other reason than to understand them better.

+

Some of the properties are physical. This list includes the director structure algorithm, the element length taper, and the overall element population for a given boom length. Some of the properties are electrical, including forward gain, sidelobe attenuation, sidelobe suppression (or development), and mutual coupling. We may add to this list the various ways in which we construct the core to achieve a given feedpoint impedance over a considerable passband and the role of the core in establishing the positions of gain and front-to-back peaks. With this number of variables--plus others not listed or not yet appreciated--it is unlikely that Yagi development has reached its final stage. We have much more to learn before we can justify a claim that an ultimate Yagi is in hand. However, we are closer to being able to tailor a Yagi design for a more complex set of operational specifications.

+
+ +
+

Updated 10-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for September, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: VHF / UHF, Yagi


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+

2-Meter Yagi Stacks
+ Part 1: 6- to 18-Element OWA Examples

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+
+

Note: This series of notes prepresents a preliminary study of stacking questions. Much fuller data and analysis appears in my book, Long-Boom Yagi Notes. These preliminary notes may be useful to those who do not have access to that volume.

+
+

Stacking VHF Yagi antennas increases gain by a hypothetical 3 dB over the gain of a single Yagi unit. Of course, the stacker must subtract any losses that accrue to the power splitting system for in-phase feeding of the two units. The key question for the would-be stacker has always been a simple one: how far apart should I stack two (or more) Yagis to optimize the gain of the system.

+

Some Background

+

HF modeling generally uses shorter Yagis, when measured in terms of either the number of elements or the boom-length. Most data involves 3- to 8-element Yagis. I have looked at the HF question in the past, and the results are at my site: Stacking Yagis. Two conclusions emerged. First, the required stacking space between two Yagis depends on the gain of the individual units. The higher the gain, the wider the spacing that we need to obtain maximum gain from the stack of 2. Second, the spacing that yields maximum gain is not necessarily the spacing that yields maximum front-to-back ratio. Maximum front-to-back ratio for a stack of 2 is usually close to the value of maximum front-to-back ratio for a single unit. Hence, failure to preserve the maximum front-to-back ratio results normally in a degradation of that value.

+

Similar conclusions are shown in the discussion of stacking in The ARRL Antenna Book, 20th ed., in the VHF discussion on pages 18-10 through 18-12. There are graphs of both the gain and the front-to-back ratio (called the front-to-rear ratio and meaning the worst-case front-to-back ratio rather than an averaged front-to-rear ratio). However, the samples do not show a regular progression from which one might draw more detailed conclusions other than the seemingly random variations in the front-to-back lines.

+

RSGB's The VHF/UHF DX Book contains an interesting discussion of the same topic. On page 7-8, the author presents a way of calculating the required spacing for maximum gain:

+
+

Dopt = lambda / (2 sin (phi / 2))

+
+

where lambda is a wavelength in any desired unit of measure, and phi is the relevant half-power beamwidth of a single antenna unit in degrees or radians, as preferred. Dopt is the optimal distance or spacing between Yagis in the same unit of measure as specified for lambda. The equation produces very plausible numbers that require increased spacing with a narrowing beamwidth. Of course, the half-power beamwidth is related to forward gain such that the higher the forward gain, the narrower that the beamwidth tends to be. Before we close this discussion, we shall return the the equation in the RSGB source.

+

Unfortunately, vertical stacks of horizontally oriented Yagis tend not to be quite so neat an affair as the equation suggests, but may be more orderly than the Antenna Book discussion might lead us to believe. So a systematic modeling exercise appears to be in order if we are to find the middle ground.

+

Setting Up the Models

+

The first step in the process of developing a useful modeling exefcise involves setting its limits. For this exercise, we shall limit ourselves to stacks of 2 identical Yagis. The antennas will be horizontally oriented and stacked vertically. Very often, such exercises are conducted in a free-space environment, where Yagis are hardly ever used. For this collection of models, we shall use a base height of 5 wavelengths or about 33.68' or 10.27 m above average ground. The second beam in the stack will be spaced above the first by a distance that we shall specify in 10ths of a wavelength as the increment of change. Limiting the base height to 5 wavelengths allows accurate elevation plots when the pattern uses a 0.1-degree increment. As we increase the height further, we reach a level for which the 0.1-degree increment of elevation is insufficiently accurate to capture the maximum gain and its take-off (TO) angle. The height is also sufficient to ensure that the feedpoint impedances of the upper and lower Yagis do not differ from each other in any degree likely to occasion problems with standard in-phase feeding systems.

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As a measure of the front-to-back ratio, we shall use the 180-degree ratio value. For this exercise, the 180-degree value is the most sensitive to change and hence will yield a clear indication of maximum and minimum values as we check different spacing values between the upper and the lower Yagi. Because the front-to-back ratio is taken at the same elevation angle as the record of maximum gain, there is a minor and generally insignificant vaguery to the value at certain points in tables of results. As we raise the height of the upper Yagi--or, in other words, increase the spacing--the TO angle will slowly decrease. Between two entries with angles that differ, the change in front-to-back value may be off the mark by up to 0.1 dB. However, the trends remain accurate reflections of beam performance.

+

The second major step in the set-up process is to select a coherent set of Yagis to test. The ones that I chose come from the 2-meter OWA series. You may obtain the physical specifications for each beam from other articles that presented the series. See An OWA Family of 2-Meter Yagis from 6 to 12 Elements and Extending the 2-Meter OWA Family. The family consists of a unified collection of Yagis using OWA design techniques. As a result, all of the family members have very similar patterns of gain, front-to-back ratio, and SWR values across the band, with gain adjustments varying with the boom length and the resulting number of elements. Fig. 1 shows 2 sample SWR curves across 2-meters for represetatives of the family.

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From the total family, I selected Yagis having 6, 9, 12, 15, and 18 elements. Table 1 shows the modeled performance of single units both in free space and at a height of 5 wavelengths above average ground at the design frequency of 146 MHz. The individual Yagis cover the entire 2-meter band with only small changes in values between maximum and minimum values. The boomlengths vary from 0.67 wavelength for the smallest Yagi in the set up to 5.39 wavelengths for the 18-element version. Gain is largely a function of boomlength rather than the number of elements. Hence the rate of gain increase dwindles rapidly for the longest members of the family. However, the selection will prove useful in eliciting some significant factors in the separation of Yagis in a stack of 2.

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+ +
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Since height above ground is the leading determinant for the TO angle, and since all of the single-unit Yagis are at the same height, they all show the same TO angle. However, we we look at stacks of 2 Yagis, the situation changes. The effective height relative to the TO angle for a stack of 2 antennas is about 2/3 of the upward distance between the antenna units. Hence, as we increase separation, the TO angle will slowly decrease. The information in Table 1 is also sufficient to verify that the antenna height is enough to avoid any changes in feedpoint impedance relative to free-space design values. Finally, the data shows that ground reflections increase the gain--relative to the free-space value--by between 5.8 and 5.9 dB. We shall return later to the gain over ground values vs. free-space gain after we have had a chance to look at 2-stacks of each Yagi in the group.

+

The modeling test procedure is straightforward. For each Yagi stack, I shall increase spacing in 0.1 wavelength increments. Each set of tests will extend beyond peak gain and peak front-to-back ratio values by at least one step to verify that a peak has occurred. I shall record the results using the spacing between Yagis as a reference. In all cases, the lower Yagi remains at 5 wavelengths above ground. Hence, the height of the upper Yagi is simply 5 plus the tabulated spacing.

+

Modeling Exercise Results For each Yagi, I shall present both a table and a graph of the key stacking data. Tabular information is more precise to the eye, but trends are clearer in graphical form.

+

Model owa2m616x2: Although all of the longer Yagis in this group of OWA designs use the same first five elements, the 6-element Yagi uses a somewhat different set of dimensions. Hence, its 180-degree front-to-back ratio shows a higher maximum value than the other designs. When stacked, the maximum-gain spacing is between 1.0 and 1.1 wavelength. However, the maximum front-to-back separation is 1.3 wavelength, as shown in Table 2 and in Fig. 2.

+
+ +
+
+ +
+

As we shall see in subsequent Yagi stacks, the maximum front-to-back spacing is a constant. All designs will show a front-to-back maximum at a spacing of 1.3 wavelengths. We shall also note some other key spacing values related to the front-to-back ratio. The maximum gain spacing, however, is a variable. For the short Yagi (0.67 wavelength boom), the maximum gain occurs with a smaller spacing than the first front-to-back maximum, so--from a practical perspective--we have no reason to carry the curves further.

+

Model owa2m916x2: The 9-element Yagi uses a 1.78 wavelength boom, and we naturally expect that we need a wider spacing for maximum gain. The modeling evidence does not disappoint us. The boom is nearly 3 times the length of the first Yagi in the set, and the required spacing becomes about 1.5 wavelength. See Table 3 and Fig. 3.

+
+ +
+
+ +
+

Since the gain changes slowly as we move the spacing on either side of the maximum gain value, we do not lose much if we select a compromise spacing between the maximum gain and the maximum front-to-back values. In this case, a spacing of about 1.4 wavelengths would be a very practical value.

+
+ +
+

The differences in the designs of the 6-element and 9-element Yagis yield different patterns for the rear quadrants. As a result, the difference between a maximum gain and a maximum front-to-back spacing have diffeent effects on the rearward pattern. Fig. 4 shows something of the difference. The 9-element design (along with all of the larger Yagis in the set) has a single major rearward lobe with only small sidelobes. Hence, the 180-degree front-to-back ratio and the worst-case front-to-back ratio are the same. The range of variation from minimum to maximum front-to-back ratio is only about 3.5 db at worst.

+

In contrast, the design-frequency front-to-back ratio of the 6-element design shows a deep null directly opposite the forward lobe. As we move away from the design frequency, the pattern becomes more rounded into a single lobe at lower frequencies and becomes multi-lobe at high frequencies. Nevertheless, at stacking spaces widely divergent from the maximum front-to-back value, the entire rear-lobe structure grows larger, as shown in the figure that shows the pattern for maximum gain. Hence, by any interpretation of the concept of front-to-back ratio, a lower front-to-back value in dB indicates a considerable increase in the gain of the rearward lobes.

+

Model owa2m126x2: The boomlength of the 12-element design is 2.94 wavelengths, about 65% longer than the boomlength of the 9 element design. However, the gain increase of the longer over the shorter Yagi is only about 1.3 dB. As a result we would expect that the required increase in spacing for maximum gain would be somewhat smaller than the increase between 6- and 9-element designs. However, the maximum-gain separation is not a smooth function. The required separation for maximum gain is only 1.6 wavelength, just 0.1 wavelength wider than for the smaller beam. Table 4 and Fig. 5 provide the details.

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+ +
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I have carried out the spacing values further in this instance for 2 reasons. First, the curve above the maximum gain value shows a flattening. It seemed wise to determine whether there might be a secondary peak in the gain-vs.-spacing curve. Despite the flat region of the curve between 1.8 and 2.1 wavelengths, no secondary peak appeared. Nevertheless, this region of the curve will become important as we look at still longer Yagis.

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The second reason for extending the range of trial spacing values is to locate the minimum and next maximum front-to-back spacing values. The minimum occurs at a spacing of 1.7 wavelength, very close to the spacing for maximum gain. The second maximum front-to-back value occurs at a spacing of 2.4 wavelength. Like the front-to-back maximum value at 1.3 wavelengths, these new values are also constant for any Yagi in the set under test.

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Model owa2m156x2: Even though the boomlength of the 15-element Yagi is 40% longer than the length of the 12-element design, the gain increase for a single unit is only about 0.7 dB. Theoretically, we should see an even smaller increment in spacing increase to achieve maximum gain. However, the actual required spacing--as shown in Table 5 and in Fig. 6--is considerably larger: between 2.1 and 2.3 wavelengths.

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The gain-vs.-spacing curves for the 12-element and the 15-element Yagis deserve closer inspection. Both curves have similar properties, but nearly in mirror image. There is in both Fig. 5 and in Fig. 6 a rise near the 1.6 wavelength mark, followed by a relatively flat region. For the shorter beam, the flatter region leads to a more rapidly decreasing gain value at a spacing of about 2.1 wavelengths, although some leveling is apparent until we reach 2.3 wavelengths. For the 15-element Yagi. the gain-value flattening after a space of about 1.6 wavelength is actually a very slowly rising curve that peaks in a very broad way between 2.1 and 2.3 wavelength.

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The net effect for the set of Yagis is a stacking-space region of some interest. If the single unit gain is only a bit lower, the required stacking space for maximum gain is smaller than previous spacing increments would suggest. However, with only a small increase of gain, the required spacing "jumps" to a larger-than-expected values. Once over the "forbidden" zone between 1.8 and 2.0 wavelength spacing, we might anticipate a smaller increment for the next Yagi in the set.

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Model owa2m186x2: The 18-element Yagi has a boomlength of 5.39 wavelengths and a gain improvement of about 0.35 dB over the 15-element design. As noted in earlier articles on this family of Yagis, the gain increments are somewhat smaller than for other design series, such as the DL6WU Yagis. The smaller growth in gain is the price paid for maintaining very small sidelobes across the entire 2-meter band.

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As shown in Table 6 and in Fig. 7, the required spacing for maximum and minimum values of front-to-back ratio have not changed from those associated with any of the smaller Yagis. However, the spacing required for maximum gain continues to grow, reaching a peak-gain value at 2.4 wavelengths. Interestingly, this spacing coincides with the spacing required for a front-to-back ratio peak.

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Although the gain-vs.spacing curve is shallow, its peak is distinct at a single spacing value. The relevant portion of the curve in the maximum gain region shows a behavior similar to the curves for the smallest Yagis in the tested set. However, the "double-hump" (or flat region or forbidden zone) continues to appear between 1.6 and 2.0 wavelengths in the form of a decreased rate of gain increase, followed by a faster rise in gain as we approach the spacing that yields maximum gain.

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Some General Trends

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As we increase the length and gain of the individual Yagis, we see that the amount of gain from the stack of 2 decreases steadily. Table 7 tracks the steady decrease in stack-gain. The decrease is not serious enough to suggest not using a stack, although split feed losses must be added to the decrease to arrive at a final value for what a stack of 2 can do for us. At the limits of practical boom lengths, stacking offers an increase of gain that would require highly impractical boomlengths to achieve.

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Many stack users are unfamiliar with the elevation patterns that emerge from stacks. An individual Yagi beam tends to produce a series of lobes at regular angular intervals. A stack, however, produces an irregular elevation pattern, as shown in the patterns for the test beams in Fig. 8. The interactions between vertically spaced elements both locally and at the points where the individual patterns merge (including both incident and reflected components) result in deep nulls that tend to vary with the individual beam gain values and with the spacing between them. As we increase the spacing between the beams, the number of lobes lower than the first major stack-null tends to decrease.

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Azimuth patterns for 2-stacks, on the other hand, tend to retain almost all of the characteristics of the individual beams when used alone. Fig. 9 provides a comparative view of the 15-element Yagi when used alone and in a 2-stack spaced for maximum gain. In addition, the figure provides band-edge paterns as well as design-frequency patterns. In all cases, the modifications to the sidelobe structure are minor.

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Finally, we should return to the equation for calculating the optimal beam separation for a stack of 2 Yagis. Table 8 shows the calculated and the modeled spacing required for each beam in the test series. The calculated optimal spacing is based on a regular sin function of the free-space H-plane (vertical) beamwidth. For the calculations, the vertical beamwidth is derived from a free-space model of the array.

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The calculated values fall short of the modeled space over ground in every case. Of greater importance may be the fact that the calculated spacing cannot show the irregularity in the development of the maximum-gain spacing curve and the seeming "forbidden zone" effect. Indeed, in the final analysis, anyone contemplating creating a 2-stack for beams of significant length owes it to himself to obtain modeling software and to re-create to the degree possible the stacking conditions.

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Perhaps the most important trends that we have seen in this set of beams deserve further attention. Especially notable are the differences between calculated and modeled optimal spacing distances and the double-humped curve associated with longer booms and their wider-than-expected spacing. One possible explanation for both phenomena is ground effects, that is, unexpected irregularities in the optimal spacing that result from the ground reflections. Therefore, I modeled the entire set of OWA Yagis in free space to see if there might be some significant differences.

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The shorter (6- and 9-element) Yagis showed no differences in either the required spacing for maximum gain or in the spacing for maximum front-to-back ratio. At the other end of the scale, the 18-element Yagi also showed no differences in maximum gain and front-to-back spacings. Table 9 shows the tabulated values for both the free-space version and the model with a base height of 5 wavelengths.

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Maximum 180-degree front-to-back ratio occurs at a spacing of 1.3 wavelengths and again at 2.4 wavelengths. The minimum front-to-back ratio occurs in the 1.7-1.8 wavelength region. Gain peaks in the 2.4-2.5 wavelength region, with the free-space model show a slightly more distinct peak relative to adjacent values.

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As we move downward to the 15-element OWA Yagi, we encounter a more significant difference in the required spacing for maximum gain. Contrary to possible expectations, the free-space model does not show a smaller required spacing for maximum gain. Instead, the free-space model requires a wider spacing, as shown in Table 10 and in Fig. 10.

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The model whose base height is 5 wavelengths above ground shows a broad peak gain between 2.1 and 2.3 wavelengths spacing. However, the free-space version places the optimal separation for maximum gain between 2.4 and 2.5 wavelengths. In both cases, the adjacent values are sufficiently close to optimal so the the difference has no great significance in practice. However, the fact that it is counter-intuitive does have some significance. Rather than expanding the stack spacing, ground effects appear to narrow it slightly for some longer-boom Yagis.

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The most dramatic effects appear in connection with the 12-element Yagi. The original graph of gain vs. separation for the 12-element antenna 5 wavelengths above ground (Fig. 5) showed a peak gain with 1.6 wavelength spacing. Beyond that point, the gain remained level or descended very slowly until we reached a spacing of about 2.3 wavelengths. The level area for this model combined with the nearly level curve as the 15-element Yagi approached optimal spacing to produce the rough notion of a "forbidden zone." The notion does not indicate that a practical pair of Yagis might not use the spacings in the zone. Rather, it only indicated that we could expect no gain peak in the zone.

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Table 11 and Fig. 11 provide comparisons of the free-space and above-ground models of the 12-element OWA Yagi.

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The free-space model not only preserves the forbidden zone, but places maximum gain at a spacing of 2.3 to 2.4 wavelengths, far above the 1.6 wavelength spacing indicated by the model with a 5 wavelength base height. Again, the gain differentials are small enough across the spacing region from 1.6 to 2.4 wavelengths to permit a set-up at any height in the region. Indeed, the best height--apart from physical constraints--might be a spacing that yields the best combination of gain and front-to-back ratio. In practical terms, the forbidden zone might also be called the ideal zone. However, from the perspective of understanding stacking phenomena, the zone appears to forbid maximum gain values from appearing in models. Calculated spacing values, of course, do not acknowledge such a zone, but then, calculations tend to err on the low side compared to models for all of the Yagis in the set.

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Throughout both the free-space and above-ground modeling of OWA Yagi 2-stacks, the front-to-back maximums and minimums occur at the same separations, with an occasional deviation of 0.1 wavelength. There are two possible explanations for this phenomena. First, it might simply be a relatively universal condition for all stacks of 2 Yagis. Second, it might be a function of the particular desgn considerations that guided the development of the OWA series. In Fig. 1 we saw the coincidence of the SWR tracks across 2 meters, as exemplified by the curves for the 9- and 15-element versions. Further design guidelines--possible with few other types of Yagi designs--included centering to the degree possible both the gain and front-to-back curves within the 144-148-MHz passband. Fig. 12 provides gain and 180-degree frnt-to-back ratio curves for the 12- and 18-element versions of the OWA Yagi.

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The 12-element OWA Yagi show both peak gain and peak front-to-back ratio at 146.5 MHz. For the 18-element version of the antenna, peak gain occurs at 147.25 MHz, while peak front-to-back ratio appears at 146.75 MHz. As Yagi designs go, both sets of figures represent well-centered curves that minimize differences at the band edges. The centering of the front-to-back curves (especially) may be resonsible for the constant value of separation for stacked-Yagi maximum and minimum front-to-back ratios. The free-space tables show that ground effects are not responsible for those values or their relative constancy across the range of Yagi boom lengths.

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With respect to gain, I have referred to the erstwhile forbidden zone as a double-humped curve. For arrays with a base height 5 wavelengths above ground, the actual double hump occurs somewhere between 12 and 15 elements. In fact, as shown in the gain plots in Fig. 13, the 13-element Yagi in the OWA series provides a true double peak, with maximum gain occuring at spacing values of 1.6 to 1.7 wavelengths and again at 2.0 to 2.1 wavelengths. The continuum of 12 through 15 elements provides added evidence that a peak gain value does not occur in the 1.8- to 1.9 wavelength region, although for the 13-element version of the OWA Yagi, the gain values in the region are highly usable, except for the lower front-to-back ratio in this region.

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Although the relative constancy of the spacing values for both maximum and minimum front-to-back ratios hardly needs further evidence, it was convenient to gather this data for the sequence with smaller boomlength steps. Fig. 14 shows the 4 relevant curves of front-to-back vs. spacing between the two beams in each stack. The deviation from the statistical norm is no more than 0.1 wavelength for either minimum or maximum values.

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Modeling one coherent set of beams is neither a necessary nor a sufficient condition for establishing the trends that we have seen as relatively universal. To obtain a sense of their universality, we need to sample other coherent lines of Yagi designs. If the trends are replicated in a second line of Yagis, we do not have yet a sufficient condition of universality. However, we may at least have a stronger suggestion in that direction. And even if the trends do not hold up, we may reach a better understanding of what may be responsibile for the stacking phenomena that we uncover.

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Hence, this study has a second part--and as many parts as a reader might like to add until he or she runs out of coherent lines of Yagi designs.

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Updated 09-01-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: 9- to 18-Element DL6WU Examples

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Go to Main Index

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Topics: Stacking, VHF / UHF, Yagi


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2-Meter Yagi Stacks
+ Part 2: 9- to 18-Element DL6WU Examples

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L. B. Cebik, W4RNL

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In the first part of this exercise, we examined a set of OWA Yagis for 2 meters with 6 through 18 elements. Along the way, we discovered that some of the relatively accepted optimal spacings for stacks of 2 vertically spaced Yagis did not correspond to modeled results, either in free-space or when the antennas had a base height of 5 wavelengths, that is, the height of the lower of the 2 Yagis in the stack. The initial investigation showed some general trends that deserve further exploration.

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First, the optimal spacing for maximum gain shows a region in which a gain maximum does not occur: between about 1.8 and 2.2 wavelengths spacing between Yagis. We called this region the "forbidden zone," but only because the absolute gain maximum value does not occur in this region. From a practical perspective, the curve is relatively flat for 12- to 15-element Yagis with corresponding boomlengths (2.9 to 4.2 wavelengths). Hence, one may select almost any spacing within this fregion for the subject Yagis and--commensutrate with selecting a good spacing for the front-to-back ratio--the results may be indistinguishable from selecting the maximum gain spacing. However, from the investigation of one coherent set of Yagi designs, it is not clear to what degree the forbidden zone is inherent to Yagis of the requisite boomlength or to what degree it is Yagi-design dependent.

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Second, the OWA series of Yagis showed beam separations for maximum and minimum front-to-back ratio that are constants for all of the designs in the set. These spacing values applied whether the model was in free space or over ground. Hence, ground reflections are not the source for the uniform front-to-back spacing values. However, investigating only one type of Yagi designs leaves open the question of whether the 180-degree front-to-back rasults are endemic to Yagis or specific to the OWA design sequence. As noted in Part 1, all of the OWA designs yield similar SWR curves as well as similar curves for both gain and front-to-back ratios. In both of the latter cases, the peak values are designed as close as possible to the center of the design bandwidth to minimize the total range of gain and front-to-back values across the operating passband. Not all Yagi designs use such a tight set of design specifications.

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Therefore, as a first-order test of the general trends that we have so far noted, it is necessary to sample a set of Yagis with a similar number of elements and similar boomlengths in order to see what emerges for vertically stacking 2 of them. For this exercise, we shall retrace our steps using samples from the venerable DL6WU Yagi design sequence. As we shall see, almost no set of Yagi designs could be more distant from the OWA series.

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Some Basic Properties of DL6WU Yagis

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The DL6WU Yagi designs evolved over a 2-decade period. The modern builder can obtain a design program called dl6wu-gg.exe in order to design Yagis of almost any long length. The only restriction is that the shortest coutenanced length is about 2.15 wavelength, that is, 10 elements. We shall press this limit just a bit.

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The DL6WU Yagis are designed to have very good forward gain combined with a resonable front-to-back ratio. The impedance-setting cell--composed of the reflector, driver, and first director--is designed to provide a very wide bandwidth. Using 3/16" (0.1875" or 4.76 mm) elements on 2 meters, the operating bandwidth is at least 14-15 MHz, well beyond the limits of the 2-meter band. Hence, obtaining a reasonably successful operating version of a DL6WU Yagi is almost assured, even if a particular incarnation is off the design frequency by some measure that depends on the level of shop skill.

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Table 1 shows the dimensions of the 18-element version of the DL6WU Yagi used in this exercise, with all dimension values derived from dl6wu-gg.exe. One of the seeming beauties of the DL6WU Yagi is that to make a shorter-length version, we need only remove directors. Hence, the 9-, 12-, and 15-element versions of the array use the same dimensions as shown in the table, minus the excess directors. Table 2 shows the boomlengths of the set of Yagis used in this exercise, along with the modeled single-unit performance in both free space and 5 wavelengths above average ground.

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The 9-element version of the array is, of course, past the authorized smaller limit of these Yagis, but the operating data is entirely reasonable and acceptable for our purposes. The 4 Yagis in the set have boomlengths of 1.81, 2.85, 4.01, and 5.22 wavelengths. The corresponmding OWA Yagis had boomlengths of 1.78. 2.94, 4.17, and 5.39 wavelengths for 9 through 18 elements. Hence, the 2 sets of Yagis fall within a range of ready comparisons for vertical stacking.

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At this stage, the gain advantage of the DL6WU sequence over the corresponding memebers of the OWA sequence is relatively unimportant. The DL6WU sequence also has a much higher level of forward sidelobe strength compared to the OWA models. OWA sidelobes are down by about 25 dB from the main forward lobe. DL6WU sidelobes are down only by about 16 dB. These facts are for the most part also unimportant to our work. However, toward the end of these notes, we shall mention one consequence of the differential in forward sidelobe strength. But for the moment, we may let these differnces merely exist.

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More significant are the different performance curves produced by the DL6WU Yagis across the 2-meter band as we increase the number of elements and the boomlength. Fig. 1 shows the gain and front-to-back curves for each of the Yagis in the test sequence, with modeled data taken 5 wavelengths above average ground.

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Unlike the similarity of curves for the OWA sequence of Yagis, every one of the DL6WU curve pairs differs from every other one in the total set. Likewise, we find a comparable difference in the 50-Ohm SWR curves for the DL6WU Yagis, in contrast to the nearly perfectly overlaid SWR curves for the set of OWA Yagis. Fig. 2 shows the SWR values across 2 meters for each of the 4 DL6WU Yagis.

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The variability of the performance curves for various lengths of DL6WU Yagis is almost impossible to grasp without looking at the performance of the Yagis across the entire operating bandwidth. For the element diameter used in these models, that bandwidth extends nearly down to 138 MHz and nearly up to 153 MHz. Therefore, we may look at wider-band properties of selected versions of the antenna.

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Fig. 3 shows frequency seeep data for the 12- and 18-element versions of the DL6WU Yagis across the entire operating passband. Note that for both versions, maximum gain occurs at about 148 MHz, at the top of the 2-meter band but well above the 146-MHz design frequency. The front-to-back ratio data is much more fascinating, since the two curves are quite different. The 12-element Yagi has two peak value frequencies, 142 and 149.7 MHz, about 7.5 MHz apart. (For reference, the 9-element version of the Yagis also has 2 front-to-back peaks that are 8 MHz apart.) The 18-element version has 3 peaks, with 2 notable apsects. The first peak occurs further up the band from the lower operating limit: 144.5 MHz. The second peak at 149.5 MHz is only 5 MHz distant from the first peak. The third peak--a small one--occurs 3 MHz higher at 152.5 MHz.

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In terms of general properties of the DL6WU Yagi series, the more elements that we add, the closer to each other grow the front-to-back peaks. The first peak moves further up the band with each additional director. Because the lower end of the operatian passband shows slower development of these curves than the upper end of the passband, it is not possible to note that at a certain boom length, a new front-to-back peak will appear at the lower frequency limit. As well, as we add more elements, the upper end of the passband is subject to more closely spaced peaks and nulls. Since we may make DL6WU Yagis up to 30 and perhaps even 40 elements, our sample cannot show the full complexity of the front-to-back curves that may emerge. For additional information on the broadband properties of the DL6WU designs, see "Appreciating DL6WU Wide-Band, Long-Boom Yagis for 420-450 MHz".

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The 50-Ohm SWR curves for the 12- and 18-element DL6WU Yagis show a similar pattern to the front-to-back curves. Fig. 4 shows the cruves. The 12-element curve shows 3 dips toward minimum value, while the 18-element curve shows 4 distinct dips. As well, the first dip for the 18-element version occurs at a higher frequency than does the first dip of the 12-element Yagi. This pattern coincides with the basic properties of the front-to-back curves. The article mentioned above provides (for the 70-cm band) information relating the resistance and reactance curves to the front-to-back curves.

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The key point to note is that, although the curves for any length DL6WU Yagi are similar, as we add more elements, the curves become more compressed within the total operating passband. As a result, the operating performance curves for any limited section of the total passband--for example, 144 through 148 MHz--will not correspond from one boom length to the next. However, if you carefully examine the front-to-back curves in Fig. 1 and the SWR curves in Fig. 2, you can generally see where along the total span of the curves that these segments fit. The DL6WU series of Yagis forms a coherent set so long as we understand both the design criteria and the general trends of the operating curves as we add more elements.

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The variability of front-to-back and SWR performance from one Yagi to the next in the DL6WU series is very much what we need to test the outstanding questions left over from the first installment. Because within the 2-meter band, there are significant performance differences from the values obtained for the OWA series, we can put both the forbidden zone phenomena and the seeming universality of front-to-back maximums and minimums to a fair test for 2-stacks.

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The DL6WU Yagis in Stacks of 2

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To determine the optimal spacing for maximum 2-stack gain and to find the maximum and minimum front-to-back spacing values, I ran each of the 4 DL6WU Yagis through the same range of separation. In all cases, coincident with the OWA tests, the lower Yagi is 5 wavelengths above average ground. The upper Yagi uses spacings of 1.2 wavelengths through 3.0 wavelengths. If our goal were only to find the spacing for maximum gain, we might easily have skipped many spacing values for each Yagi in the set. However, the values obtained may tell us something about our unanswered questions.

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Table 3 presents the data from the 9-element version of the DL6WU Yagi. Remember that this beam is 1 element and about 0.3 wavelength shy of the minimum recommended length for the design sequence. However, the gain is good, and the front-to-back ratio is equal in general to the value produced by the 12-element version. Remember that the Yagi series was not designed for front-to-back ratio, and a high value in this category is a function of how close the peak occurs relative to the test frequency. In this instance, the peak values of front-to-back are well above and well below the test frequency.

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The gain peaks at a spacing of 1.6 wavelengths. The front-to-back ratio shows peaks at spacing values of 1.4 and 2.5 wavelengths, with a null at 2.0 wavelength. Interestingly, and as shown in Table 4, the gain peak for the 12-element version of the beam also occurs with a spacing of 1.6 wavelengths. However, the front-to-back peak values occur with slightly more separation than required by the 9-element version: at 1.5 and 2.6 wavelengths. The front-to-back minimum value occurs with a spacing of 2.0 wavelengths. The average front-to-back ratio for the 12-element version is slightly lower than for the 9-element model.

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The gain data for the 15-element DL6WU array, shown in Table 5, gives evidence of the forbidden zone at work. Maximum gain occurs with a spacing between 2.4 and 2.5 wavelengths, but with an almost level set of values down to a spacing of 1.9 wavelengths. The data for the front-to-back maximum and minimum values shows perhaps the most variability in the set of tested designs. There are front-to-back peaks with spacings of 1.3, 1.6, and 2.7 wavelengths, although the 1.6 wavelength peak is a one-shot peak. Minimum values occur with spacing values of 1.5 and 2.2 wavelengths.

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The data for the 18-element DL6WU Yagi appears in Table 6. Maximum gain occurs with a spacing of 2.5 wavelengths. Spacing values of 1.5 wavelength and 2.3 wavelengths produce maximum front-to-back values. Minimum values occur with spacing values of 1.8 and 2.9 wavelengths.

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The best way to summarize these results is in separate graphs of the gain and of the front-to-back curves across the range of separation values. Fig. 5 shows the gain curves for the 4 test models.

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The so-called forbidden zone appears in the DL6WU gain graphs as vividly as it does in the corresponding graphs for the OWA series of Yagis. Spacing values between about 1.9 and 2.2 wavelengths produce a relatively flat line and show no peak values for any of the test models. Indeed, the DL6WU test series is interstring because the two shorter versions show the same spacing for maximum gain, while the two longer versions show almost identical spacing values for maximum gain. There is a gap between 1.7 and 2.3 wavelengths, and standard means of estimating optimal spacing suggest that the 12- and 15-element versions of the beam should have shown gain maximum values within this range.

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Fig. 6 provides a composite graph of the front-to-back behavior of the DL6WU 2-stacks across the range of spacing values. The shorter pair of models have overlapping curves that look similar to those for the OWA series. However, although the maximum points correspond fairly cosely to those of the OWA Yagi series, the minimum at a spacing of 2.0 wavelengths does not. The OWA Yagis showed a consistent minimum front-to-back value with a spacing of 1.7 wavelengths.

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The curves for front-to-back maximums and minimums for the longer two versions of the DL6WU Yagi differ frm the shorter Yagi curves and from each other as well. At most, we can detect in both of the long-boom front-to-back curves a maximum associated with closer spacing and a maximum associated with wider spacing of the Yagis in the stack. However, anything resembling the neatness that we found in the OWA curves seems remote, at best.

+

The DL6WU tests put to rest the idea that the front-to-back curves for a 2 stack form a set of relatively constant spacing values for maximum and minimum values. The net result is that there are no reliable guides for Yagis of certain numbers of elements or certain boomlengths for the spacing values needed to maximize the front-to-back ratio. Indeed, this note also applies to the required spacing for maximum gain. Whatever the Yagi design, to find the optimal spacing for any desired condition--or for the best compromise between gain and front-to-back ratio--we must model the specific Yagi designs in the proposed stack at the proposed height above the type of ground at the installation.

+

The OWA and DL6WU Yagis do share something in common: the amount of gain yielded by a 2-stack for Yagis of similar boomlength and numbers of elements. Table 7 summarizes the results for the DL6WU series. Within about 0.01 dB, the results are identical to those for the OWA series.

+
+ +
+

There is a second shared property in the modeled OWA and DL6WU Yagi 2-stacks: the inadequacy of standard calculations to predict what modeling suggests as the optimal spacing for maximum gain. Table 8 summarizes the results. In both cases, the vertical beamwidth applied to the standard equation comes from a free-space model of the beam. The standard equation comes up shy of the modeled mark in virtually every case. The DL6WU estimates of optimal spacing include an extra set of figures drawn from the dl6wu-gg.exe program. The beamwidth values tend to coincide closely with those modeled (with the 9-element value being merely an estimate, since the program does not countenance so short a boom). Hence, the algorithm used in the program differs from the standard equation from the RSGB book and yields even narrower spacing values that are thus further from the modeled values.

+
+ +
+

The standard equation comes closest to the modeled value for the 12-element DL6WU design, even though the modeled 1.6 wavelength spacing appears to be narrower than if there were no forbidden zone. In general, the standard equation yields greater separation values for the DL6WU antennas than for the OWA beams due to the narrower main-lobe beamwidth of the DL6WU Yagis. The narrower main-lobe beamwidth is in turn a function of the strong sidelobes associated with the design. These sidelobes are down only 16 to 17 dB from the main forward lobe, in contrast to the OWA series, in which the sidelobes are down by about 25 dB. The absence of strong sidelobes results in wider main lobe beamwidths. The OWA series shows H-plane beamwidths that run from 12% to 25% wider than beamwidths for corresponding DL6WU models. Interestingly, the disparity in modeled optimal spacing values for maximum gain does not match the difference in beamwidths.

+

From a practical standpoint of planning a 2-stack of 2-meter Yagis, the differentials noted in this study may seem far too finicky. Still, the object of the exercise is not to set standards for the construction of effective Yagi stacks. Rather, the goal is a better understanding of Yagi operation in 2-stacks when we move from the relatively short HF beams to the longer booms that are both possible and common on 2 meters. To achieve that aim, we should be as precise as possible within the limits of the method of investigation.

+

Some Supplementary Notes on DL6WU Front-to-Back Spacing Values

+

The general conclusion to be reached from the study is that every Yagi design deserves 2-stack modeling prior to making final decisions about the spacing to be used between the beams. While general equations and esitmates may work, they also may leave some disappointments relative to optimal stack performance expectations. The differences in modeled spacing values for the best compromise between gain and front-to-back ratio that emerge from looking at the OWA and the DL6WU Yagi series make a strong recommendation for some pre-construction modeling work.

+

Having reached that conclusion still leaves a few remnant questions concerning the diversity of front-to-back results for the DL6WU series of Yagis. There are a number of possibilities that might form the strongest reason for the diversity. Although we may not be able to reduce the list to a single item, we might with a little extra work reduce the list and understand in a slghtly more firm way what the main influence is (or influences are).

+

We might begin by listing some possibilities, along with the conclusions provided by our work so far.

+

1. One possible source of the front-to-back curve variability in the DL6WU Yagi set is the placement of the stack above real ground. However, as we saw in the OWA series tests, the use of free space makes virtually no difference to the spacing required for maximum and minimum front-to-back ratios. Hence, if there is any effect at all, it is likely to be very small.

+

2. A second possible cause of the variability is where in the wide-band front-to-back curve we place the test situation. The 146-MHz test frequency is in the downslope of the front-to-back curves for the 9-, 12-, and 18-element Yagis, but in the upslope for the 15-element model. If we allow for differences of absolute values and for some variations at the limits of the graphs in Fig. 6, the upslope graphs following generally similar tracks. The 15-element upslope model shows the greatest difference from its downslope cousins.

+

3. The position of the test frequency in the wide-band front-to-back curve alone would not likely create the differences in the required spacing values for front-to-back maximum and minimum values without some other effect, such as a frequency shift in the curves. Fig. 7 shows the wide-band front-to-back curves for the 12-element DL6WU Yagi using a selected minimum and maximum spacing. Note that the maximum spacing curve shows its peaks at a slightly lower frequency (perhaps about 0.3 MHz or so) than the peaks in the minimum spacing curve.

+
+ +
+

For comparison, Fig. 8 shows a corresponding set of wide-band front-to-back curves for the 15-element DL6WU Yagi. In this case the exact spacing values for maximum and minimum values of front-to-back at 146 MHz differ from those used in the 12-element graph. However, we find the same result: the maximum spacing curve places its peak values at a lower frequency the the peaks of the minimum spacing curve.

+
+ +
+

In order to correlate these curves with the reported values, we cannot perform a simple uniform frequency shift. Rather, the upslope models, such as 15-element Yagi, find their corresponding front-to-back values at a frequency higher than the test frequency. In contrast, the downslope models, such as the 12-element DL6WU array, find their corresponding values at a frequency lower than the test frequency.

+

This first-order account of the variability in the required spacing for maximum and minimum frnt-to-back values is far from complete. At best, it describes the penomena. Ultimately, the reasons for the phenomena will involve a detailed analysis of the interactions between the two beams in each stack. Such an account might permit the redesign of the stacked beams to maximize front-to-back at the same spacing as required for maximum gain. However, that task does not reduce to a simple adjustment of the reflector. In fact, as other studies have shown, the front-to-back ratio and pattern is as much or more a function of the directors as it is of the reflector. The reflector's chief tasks are setting the lower limit to the passband and setting (in conjunction with the driver and first director) the feedpoint impedance across the passband.

+

From a practical perspective, making such adjustments to the DL6WU Yagis would be futile, since the range of front-to-back values between minimums and maximums is so small. For all but the 15-element version, the front-to-back range is 1.5 dB or less. Hence, from a practical standpoint, the difference hardly makes a difference to operation. For the 15-element DL6WU Yagi, only the high value of front-to-back ratio at the closest spacing tested yields a significant difference in front-to-back ratio between maximum and minimum values--about 3.7 dB. Above smaller spacing, the differential shrinks to the levels noted for the other members of the group.

+

In contrast, the OWA series of beams, when stacked, show variations ranging from 3.4 to 3.8 dB from maximum to minimum. In many practical cases, this range is entirely acceptable. However, from a perspective of theoretical interest, the differentials keep the question alive.

+

Conclusion

+

Perhaps this study may arrive at two tentative cnclusions based on the divergent sets of Yagi designs modeled in stacks of 2 at 2 meters. Since the study has not surveyed all Yagi series and desgns, the conclusions are more suggestive than firm.

+

1. As we increase the boomlength and the number of elements in a Yagi design, the required spacing for maximum gain increases in a somewhat surprising way. At shoter boomlengths (perhaps 3 wavelengths or less), the required spacings are fairly close, but still greater than those predicted by standard equations. As the boomlength reaches about 4 wavelengths, the required spacing for maximum gain increases both suddenly and considerably.

+

Between the shorter and longer boom values for maximum gain, the gain values are fairly constant with only slow increases or decreases, according to the boomlength. Although no peak gain values show up in the spacing region from about 1.8 to 2.2 wavelengths, this region represents a set of useful separations that is not subject to more than tiny changes in gain with significant changes in spacing. It may be especially useful for stacks of Yagis having boomlengths between 2.5 and 4.5 wavelengths.

+

2. The required spacing for maximum front-to-back ratios is only rarely the same as the spacing required for maximum gain. The spacings may be relatively uniform with changing boom lengths--as in the case of the OWA series of Yagis--or vary considerably from one boomlength to the next--as in the case of the DL6WU series. Whether the spacing for maximum front-to-back is a constant or a variable depends on fundamental Yagi design considerations, as shown by the contrasting criteria used for the two tested Yagi series. However, the maximum spread of front-to-back values for the worst case in the 2 series was under 4 dB. Hence, from a practical perspective, the front-to-back ratio may be a very secondary consideration, especially for design that yield ratios in the 20-dB or greater range.

+

In all cases, the variability of the required spacing for both maximum gain and an acceptable front-to-back ratio requires the stack-builder to look beyond simple standard equations if he or she is to obtain peak array performance. Hence, my earlier suggestion applies as perhaps the most general conclusion of these notes: in all cases, the builder should invest some time in detailed and correct modeling to determine the best spacing for a stack relative to a. the exact Yagi design, b. the boomlengths and number of elements, c. the height above ground, and d. the type of ground and terrain in the antenna region. The builder must then weigh the modeling data against a. any physical constraints of the antenna installation and b. the operating goals and specifications for the stack.

+
+ +
+

Updated 09-01-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: 70-CM Yagi Stacks, Part 1: 10- to 40-Element DL6WU Examples

+

Go to Main Index

+

Topics: Stacking, VHF / UHF, Yagi


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+

Notes on 6-Element Wide-Band 2-Meter Yagis

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

I have in several past notes discussed a VHF antenna to which I must confess some partiality. The antenna is a 6-element Yagi that covers all of 2-meters with at least 10 dBi free-space gain, at least 20 dB 180- degree front-to-back ratio, and better than 1.2:1 50-Ohm SWR from 144 to 148 MHz. The antenna boom length is less than 56" (1.4 m), which lends itself to the use of a non-conductive boom, for which the element lengths and spacings are designed. The use of a direct 50-Ohm feed reduces the number of mechanical connections in the path between cable and element, thus reducing the number of potential loss sources. (However, a common-mode current suppression "choke" is advisable.) Fig. 1 shows the general outline of the array.

+
+ +
+

The design is an adaptation of Optimized Wide-band Antenna (OWA) principles used at HF by a series of HF antennas designed by NW3Z and WA3FET. For a given boom length and gain level, the design requires one extra director that has the main function of controlling--in concert with the reflector--the impedance of the array over a wide frequency span. One may design OWA arrays for almost any reasonable feedpoint impedance. The main difference among such designs is that the space required by the reflector, driver, and first director tends to increase with increases in the design feedpoint impedance.

+

OWA designs also tend to have second and third directors that are the same length. However, in some designs, the third director may be slightly longer than the second. The fourth or final director is the shortest. Changing its length will alter performance at one or the other end of the design passband, with some alteration of the SWR curve as well.

+

In other places, I have published notes on the design of a family of OWA-type Yagis for 2 meters. The sizes ranged from 6 to 12 elements, with boom lengths running from 4.5' to 20'. Among the advantages that accrue to the family is the excellent control of secondary forward lobes, which remain generally better than 20 dB below the level of the main lobe. The result is a naturally wider horizontal beamwidth without gain loss, relative to designs in which the secondary forward lobes are down from the main lobe by only 12 to 18 dB.

+

My return to the 6-element version of the OWA Yagi results from inquiries that I have received on this useful utility design. Similar questions have arisen concerning other antenna designs that I have published. The question runs something like the following: I cannot obtain the specified diameter material at the local hardware store. Can I use the alternative size material that they carry?

+

The answer to this question carries us in two directions. The first kind of answer involves learning what sources there are for various materials used in constructing good antennas. For example, there are several outlets, such as Texas Towers (http://www.texastowers.com) from which we can order many basic antenna element materials. One advantage of using these sources is that they carry 6061 and 6063 rods and tubes, generally the best aluminum types to use for antenna elements. The material obtainable from hardware outlets rarely has the aluminum type specified on the label. The other advantage is the availability of a wide range of rod and tubing diameters.

+

The second kind of answer involves adapting a given antenna design to a new diameter material. Suppose that a designers specifies 0.1875" (3/16" or 4.76 mm) elements. The builder has a stock of either 0.125" (1/8" or 3.18 mm) rods or 0.25" (1/4" or 6.35 mm) rods. Will he or she need to adjust the element lengths of spacings?

+

The answer is "yes." In fact, without making such adjustments, the antenna will not perform as originally designed. There are two major reasons for this result. In general and first, both driver and parasitic elements lengths require adjustment with every change of diameter. The general goal is to arrive at elements whose self-resonant frequencies are the same as in the original array. Second, the inter-element coupling changes for a given spacing of two elements if we change the element diameter. Element spacing does not change as rapidly as the element length for a given level of coupling when we change element diameter. However, it changes enough so that we cannot ignore the effects.

+

One of the simplest ways to accommodate a revised element diameter is to resort to a Yagi optimizing program. We simply plug into the program the existing design and specify the new element diameter. The program then churns out the revised design.

+

More antenna builders have general antenna modeling programs than have optimizing programs. There is a procedure that we can use to re-optimize a design for a new element diameter, although it has a pitfall from which we must guard ourselves. Here is how the procedure works.

+

1. Create a model of the original design and establish its operational characteristics.

+

2. Revise the model to use the new element diameter.

+

3. Find the frequency at which the new model shows the same operating characteristics as the original model did at its initial design frequency. If we are moving to a larger-diameter element, the new frequency will be lower than the old one. If we are moving to a smaller-diameter element, the new frequency will be higher than the old one.

+

4. Frequency scale the revised antenna model from the new design center to the original design center. Retain the new element diameter: the amount of performance change occasioned by the small frequency movement will usually not require a reiteration of this step. However, when enlarging or shrinking elements by more than a factor of 2, it may pay to make the change in two steps of scaling and checking.

+

At this stage, check the performance of the antenna across the passband used by the original design. In many instances, the model will suggest that we need not make any further changes. However, in some cases, we may need to adjust some element lengths to center the gain, front-to-back, and SWR curves as closely as possible to their original form (assuming that the original curves are the most desirable ones for our application). The driver length will have the greatest effect upon the SWR curve. Juggling the reflector length and the most forward director lengths can smooth out the performance across the passband, although rechecking the SWR curve may be necessary. For a given band-edge adjustment, alter the element that moves gain and/or front-to-back performance values in the desired direction with least adverse affect on the SWR curve. Finally, when reducing element diameters, you may need to increase the reflector spacing from the driver to raise the general impedance level back to that of the larger elements with which you began.

+

The pitfall in this procedure involves stopping at this point. Although the initial detection of the revised design center frequency and scaling that back to the original center produced element lengths that are very close to optimum, the element spacing moved in the wrong direction. The thin-element model increased element spacing, while the fat element model decreased the spacing. However, as element diameter increases, element spacing must increase to maintain the same level of coupling. Because we have adjusted element lengths, the spacing adjustments may not be dramatic, but they will be noticeable. Therefore, we need one more step.

+

5. If increasing element diameter, increase the spacing among elements by about twice the amount that the initial scaling decreased them. If decreasing the element diameter, do the opposite. Do not use a simple additive method, but instead find a multiplier based on the scaling ratio used in step 4. Take into account any revised positioning of the reflector in step 4. As well, check the driver, reflector, and most forward director lengths to re-establish the performance curves for the array.

+

To illustrate these steps, I took my original 6-element OWA Yagi, designed for 3/16" elements, and revised it for more commonly available 1/8" and 1/4" element materials. First, however, I tweaked the design for slightly better optimized performance.

+

I next used the steps above to obtain the best possible performance in NEC-4 models for the thinner and thicker elements. The design criteria remained constant throughout the exercise:

+

Gain: greater than 10 dBi free-space gain from 144-148 MHz with a maximum range of about 0.1 dB between maximum and minimum gain;

+

Front-to-back ratio: greater than 20 dB 180-degree front-to-back ratio with worst-case front-to-back ratios also greater than 20 dB;

+

50-Ohm VSWR: less than 1.2:1 50-Ohm VSWR from 144 to 148 MHz.

+

The design work--being hand-done--does not necessarily represent the absolute best that one might obtain from the design. Still, the designs meet all of the performance criteria with ease. The following table presents the resulting design dimension, first in inches.

+ 
              Dimensions of 3 6-element Wide-Band Yagis (Inches)
+
+Note:  All elements aluminum and are presumed well insulated and isolated
+from a conductive boom or mounted on a non-conductive boom.  The driver
+will be split for a direct feed with 50-Ohm coaxial cable.  The
+separation of the feedpoint ends is included in the overall element
+length shown, and the split is non-critical between 1/8" and 3/4".
+
+Dimension               1/8" el.          3/16" el.         1/4" el.
+Element Length in Inches
+Refl.                   40.80             40.67             40.38
+Driver                  40.10             39.92             39.47
+Dir. 1                  37.63             37.38             36.99
+Dir. 2                  36.56             36.31             36.10
+Dir. 3                  36.56             36.31             36.10
+Dir. 4                  35.20             34.96             34.50
+Spacing from Reflector in Inches
+Driver                  10.20             10.18             10.25
+Dir. 1                  14.27             14.39             14.48
+Dir. 2                  25.95             26.06             26.22
+Dir. 3                  37.39             37.47             37.70
+Dir. 4                  54.44             54.49             54.82
+

Because the design has drawn interest from a few individuals who work in the metric system, the following table repeats the dimensions in millimeters. The most common European 2-meter element diameter appears to be 4 mm (0.1575"). Although I did not optimize a 4-mm version of the antenna, the differences between the 1/8" and 3/16" versions should provide reasonably close guidance.

+ 
            Dimensions of 3 6-element Wide-Band Yagis (Millimeters)
+
+Dimension               3.175 mm el.      4.763 mm el.      6.35 mm el.
+Element Length in Millimeters
+Refl.                   1036              1033              1026
+Driver                  1019              1014              1003
+Dir. 1                   956               949               940
+Dir. 2                   929               922               917
+Dir. 3                   929               922               917
+Dir. 4                   894               888               876
+Spacing from Reflector in Inches
+Driver                   259               259               260
+Dir. 1                   362               366               368
+Dir. 2                   659               662               666
+Dir. 3                   950               952               958
+Dir. 4                  1383              1384              1392
+

Note that all element lengths shrink as the element diameter increases. The total element length difference between 1/8" and 1/4" elements approaches 0.5" (12 mm). Between steps, the 0.25" (6 mm) difference will make a difference in performance, displacing the performance curve significantly. As well, all but 1 of the element spacings increase as diameter increases. The exception is the 1/8" reflector, which I moved back to raise overall impedance of the array closer to 50 Ohms. Increasing the element spacing to a near optimal level allows the array to yield its maximum gain while providing the least difference in gain within the operating passband.

+

The 1/8" Model

+
+ +
+

Fig. 2 provides spot checks on the free-space azimuth patterns of the array with 1/8" elements--with the antenna horizontally positioned. The following table presents performance values across the band, as reported by NEC-4.

+ 
                0.125"-Diameter 6-Element OWA Yagi Performance
+
+Frequency   Gain        Front-to-Back     Feedpoint Impedance     50-Ohm
+  MHz       dBi         Ratio dB          R +/- j X Ohms          VSWR
+144         10.06       22.62             47.9 + j 6.3            1.14
+145         10.12       28.35             49.4 + j 7.9            1.17
+146         10.17       32.85             50.7 + j 7.9            1.17
+147         10.17       26.48             49.8 + j 4.8            1.10
+148         10.12       22.44             42.0 + j 0.2            1.19
+

Although the 1/8" model proved easy to tame with respect to roughly equal front-to-back performance at both edges of the passband, gain equalization proved more difficult. For those unfamiliar with a typical OWA SWR curve, Fig. 3 shows the anticipated performance of the 1/8" model. Note that there is a peak value near 145.5 MHz, with lower values above and below that frequency. The typical OWA SWR curve tends to show two minima, with the rise in SWR becoming steep above the null at the higher frequency.

+
+ +
+

The 3/16" Model

+
+ +
+

Fig. 4 shows sample free-space azimuth patterns for the mid-size model. As element diameter increases, the deep front-to-back rear null may vary above or below the design center frequency, although the gain increases smoothly. The following table shows the anticipated performance of this version of the array.

+ 
                0.1875"-Diameter 6-Element OWA Yagi Performance
+
+Frequency   Gain        Front-to-Back     Feedpoint Impedance     50-Ohm
+  MHz       dBi         Ratio dB          R +/- j X Ohms          VSWR
+144         10.15       23.77             45.3 + j 6.5            1.18
+145         10.20       31.03             47.6 + j 8.4            1.19
+146         10.24       32.41             50.3 + j 8.0            1.17
+147         10.23       25.04             50.7 + j 3.4            1.07
+148         10.17       21.30             42.7 - j 3.2            1.19
+

Although the performance advantages would not be detectable in operation, we would not have obtained performance even equal to that of the 1/8" model had we not at least adjusted the element lengths. For most utility purposes, adjustments to the element spacing might be superfluous effort. However, unless we in fact perform the necessary modeling, we could not make such a judgment. Although the judgment holds in this case, it might not hold in others. Fig. 5 shows the VSWR curve across 2 meters.

+
+ +
+

The 1/4" Model

+
+ +
+

Fig. 6 shows the free-space azimuth patterns for the 1/4" version of the array. The differences of these patterns from the preceding sets are subtle and not of great operational performance. However, as the following table of anticipated performance figures shows, the largest diameter model in this sequence also shows the least relative gain change across the passband.

+ 
                 0.25"-Diameter 6-Element OWA Yagi Performance
+
+Frequency   Gain        Front-to-Back     Feedpoint Impedance     50-Ohm
+  MHz       dBi         Ratio dB          R +/- j X Ohms          VSWR
+144         10.19       21.85             44.2 + j 3.4            1.16
+145         10.24       26.59             47.6 + j 5.4            1.13
+146         10.27       29.63             51.2 + j 4.6            1.10
+147         10.25       25.64             52.8 - j 0.4            1.06
+148         10.18       22.05             47.0 - j 8.0            1.19
+

Fig. 7 shows the SWR curve for this version of the array, perhaps the shallowest of the entire lot. Indeed, the numerical progressions displayed by this design exercise illustrate the principles of array redesign, although for the limited set of element diameters, they do not produce operationally detectable differences in results. However, I cannot stress enough that the element length adjustments are absolutely necessary to obtain the basic performance level of the 1/8" model, with adjustments to other elements to center the performance curves and assure satisfactory SWR performance.

+
+ +
+

Optimizing vs. Changing Designs

+

Let's begin with an observation about OWA SWR curves. For a given passband, the higher frequency minimum is normally a prelude to a steep rise in SWR. The designer normally positions the minimum close to the upper edge of the design passband. For the two thinner models, the minimum occurs at about 147.5 MHz. For the 1/4" version, the minimum is set at 147 MHz. That difference is a larger difference than we might think at first sight.

+
+ +
+

Fig. 8 presents the SWR curves for all three versions of the array from 140 to 150 MHz. Although the gain and front-to-back performance fall off below the design limits of this exercise, the antenna is still usable 4 MHz below the design limit. One use we might make of this information is the following: should we wish to cover the 2 MHz region above the 148-MHz design limit, we might scale the antenna or readjust the elements most affecting the impedance performance of the OWA Yagi.

+

The relative similarity of the 1/8" and 3/16" curves--when added to the performance tables for these arrays--generally establishes that each is an optimized version relative to its element diameter. However, note the slight difference in the shape of the SWR curve for the 1/4" version. Its upper-end rate of increase is shallower than we might expect based on the other two curves. As well, the lower minimum is not so much a null as it is simply a decrease in the rate of SWR increase as the frequency goes below the 2-meter band edge.

+

To achieve an SWR curve that is truly congruent with the 1/8" and 3/16" curves, we would need to do some further design work. As it stands, one might well consider the 1/4" version of the antenna a slightly revised design rather than simply an optimization of the other designs for the new diameter of material.

+

Perhaps the most evident consequence of the differences in the curves is that fact that the exercise cannot provide any convenient formulas for adjusting element lengths and spacings. The element diameter ratios were 3/2 (3/16:1/8) and 4/3 (1/4:3/16). The element length decreases with increasing diameter were about 1% per step, with special attention given to advisable further adjustments to the reflector, driver, and most forward director. The spacing adjustments amount to about 0.5% per step, again with special attention to the reflector-drive space and the position of the most forward director.

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At best, then, this design exercise has yielded only a small catalog of matters on which to use care when changing the diameter of an element while retaining the performance of the original design. However, a catalog is usually better than a mere guess.

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Updated 12-26-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for December, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: VHF / UHF, Yagi


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The 3-D Corner Reflector

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L. B. Cebik, W4RNL

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Back in 1999 (seems like a century ago), I examined some properties of the corner reflector (See "Corner Reflectors Revisited".) Since that time, a number of scattered ideas for improved performance have come my way. Among them was a 3-dimensional corner array that first appeared in the IEEE Transactions on Antennas and Propagation, July, 1974. The article was "Three-Dimensional Corner Reflector Array" by Naoki Inagaki (pp. 580-582). I am indebted to Gene Wood, WA4PGI, for supplying me with both the article and his experiences in building a version of the antenna for the mid-UHF region.

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The 3-D corner is calculated by the authors to have considerably more gain than a conventional corner array. I wondered how the claim might appear in NEC-4 models, so I built up a couple to see the results. Let's review the state of the corner array and then explore further the 3-D corner.

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The Conventional Corner Array

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The conventional corner array consists of two flat planes forming a triangle. The most commonly used angle is 45 degrees, although others are usable. The apex of the angle may be sharp or somewhat rounded. As well, the forward edges of the plane may continue linearly or be slightly folded toward the line formed by the apex of the triangle through the dipole that usually serves as the fed element.

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Modeling the conventional corner array generally follows construction practices, as shown in Fig. 1.

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For consistency, let's call the length of the wire at the apex in either version of the model the width. The distance between the forward edges of the two planes is the aperture. The distance from the apex through the driving element to the forward edge of the reflector planes will be the depth.

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Many corner reflectors use bars or rods to form the plane of the reflector. The rods are parallel to the fed dipole element. Models following this technique tend to be smaller in terms of the total number of wires and segments than models simulating solid or screen wire reflector planes. The required wire-grid structure is a highly effective simulation of solid planes, but requires far more wires and segments.

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The need for many more segments arises from the recommended maximum spacing between wires in a grid: 0.1 wavelength. Using a maximum wire diameter that is the segment length divided by PI results in wires thick enough to simulate a solid surface without violating NEC recommendations for segment length to radius ratios. However, the spacing between wires results in segment lengths that are in excess of conservative recommendations. However, tests using shorter segment lengths in corner reflector planes (0.05 wavelength) yield no significant differences in performance data, despite the 4-fold increase in the total number of segments in the model.

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The use of corner reflectors in amateur radio service has tended to produce skimpy reflector planes, well under 1.5 wavelength per side. However, corner reflectors perform partially as a function of the size of the reflector planes. Let's consider a reflector with a width of about 1.5 wavelengths, an aperture of 3 wavelengths and a depth of about 1.5 wavelengths.

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Fig. 2 shows the H-plane polar plot of a good design using these proportions. The 13.75 dBi gain figure is for free space. Note that this pattern would be equivalent to setting up the reflector in the form of a Vee with the aperture toward the right. As we shall see from the E-plane pattern in Fig. 3, the planes of the reflector are less able to suppress side lobes than the edges of the rods in the reflector of this model and the tips of the dipole. However, the general level of H-plane sidelobes is less than from most conventional large Yagi designs with equivalent gain.

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The E-plane pattern is a paragon of good pattern behavior. The beamwidth to the half-power points is just over 40 degrees. The oval pattern is the dream of Yagi designers. The array shows consistent characteristics over a very wide bandwidth, as illustrated by the SWR curves shown in Fig. 4. Unlike long-boom Yagis of conventional design, corner reflector arrays lack strong forward sidelobes. Hence, they exhibit less off-axis sensitivity. I have used the 420-450 MHz amateur band as a modeling convenience. For many purposes, the physical structures required by the corner reflector might be too large to permit home workshop construction. However, the results are easily transportable to higher frequency ranges by simple scaling.

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The natural impedance of the dipole in the array is about 70 Ohms. We may control this value to some extent by the position of the dipole relative to the apex of the triangle. Still, there will be some change in performance with a repositioning of the dipole, and the design goal is always the best compromise between performance and feedline matching. Nonetheless, for this design example, a feedline composed of low loss 75-Ohm TV hard-line would be close to ideal.

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To some extent, the operating bandwidth of the array is a function of the diameter of the dipole. Some designers have used solid-surface fan dipoles to achieve very wide bandwidths. Others have used phase-fed dipoles and similar structures to achieve more gain from the array.

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Perhaps the most interesting direction of corner reflector studies has been taken by John Regnault (G4SWX) and John Sager, who have constructed some interesting models based on the fact that a corner reflector--especially of bar construction--acts somewhat like an optical reflector and somewhat like a parasitic reflector array. Using a reflector about 1.44 wavelengths wide with a 2 wavelength depth and an aperture of about 2.6 wavelengths, they obtain nearly 15.8 dBi free-space gain. The most fascinating aspect of their design work is the variable lengths used for reflector rods, with some being in the vicinity of 1/2 wavelength.

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These notes provide some background into what we can expect of and achieve with corner reflectors designed in the conventional manner, along with variations on that theme. However, their function in the context of this small study is to provide a setting for considering the potentials of the 3-dimensional corner array.

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The 3-D Corner Reflector Array

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The 3-dimensional corner reflector array makes two key changes in the conventional corner array. First, it uses 3 planes as reflector surfaces, as shown in Fig. 5. Second, it places a monopole on one of the surfaces. The length of the monopole is variable, but something close to 3/4 wavelength yields a good match for common feedlines.

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Fig. 5 shows the plane of the array used as the ground plane for the monopole in a horizontal position. The other two planes are vertical. I should note in advance that this arrangement will not be the operating position of the array. However, the arrangement did simplify the construction of wire grids for the reflector surfaces.

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Modeling the 3-D corner reflector requires wire grid techniques. There is simply no effective way to use rods and still make all of the required wire junctions along the joined edges of the 3 planes. Hence, the models for this array tend to be fairly large: 1403 segments for the smaller of the two models that we shall study and 2468 segments for the larger.

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The model sizes result from using 0.1 wavelength spacing between wire centers-lines. Although this spacing is satisfactory for simulating solid or screen structures for the reflector planes, it limits the placement of the monopole to X and Y values in steps of 0.1 wavelength per step. As measured from the deep corner of the reflector planes, these steps increase to 0.1414 wavelength each. Fortunately, the step-size permits a close approximation of the monopole position to what is required for both maximum performance and for a good match to common feedlines. The result is that positioning the monopole becomes a matter of care, but not one of critical finickiness.

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The patterns yielded by the 3-D corner reflector array are themselves worthy of study. The simpler of the two patterns is the H-plane pattern, a sample of which appears in Fig. 6.

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All free-space H-plane patterns tend to have the same general features as the sample. The area immediate to the rear will tend to be depressed or show a bulge, depending upon the 180-degree front-to-back ratio of a given design. However, the broad shoulders and general "bullet" shape are common to most design variations. Despite this feature, we should not assume that the array will shows the same H-plane pattern shape when used over real ground. Note the very small horizontal component in the "butterfly" at the center of the polar plot. The line for the vertical component is hidden beneath the heavier line used to track the total pattern of the antenna.

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Of special note is the fact that the 3-D corner reflector array--as modeled--is a vertically polarized antenna relative to the bottom plane of the reflector assembly. The conventional corner array is usable to good effect when either vertically or horizontally polarized--a matter of tilting the reflector. The 3-D corner reflector may also be tilted for horizontal polarization, so long as the monopole is parallel to the ground surface.

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The reference sketch in the lower left corner of Fig. 6 shows the orientation of the antenna and reflector relative to the pattern produced. As expected from right-angle vertical planes, the pattern center-line points to a bearing of 45 degrees. However, the elevation angle for the plot does not appear. If you initially think that it is the standard zero degrees of free-space azimuth patterns, you would have failed to account for the effect of the third plane upon the antenna pattern.

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If we take E-plane patterns along the center-line of the radiation field, we end up with what modeling conventionally refers to as elevation patterns--even if that term seems usually to be out of place in free space. Fig. 7 shows three design variations and their resulting H-plane patterns. Although the H-plane pattern at the elevation angle of maximum radiation is consistent, the structure of the E-plane patterns is subject to considerable variation, both in the shape of the main lobe and in the size and shape of the side lobes. Hence, for minimal problems from potential side lobes structures, the design should be set for minimal strength in all but the main forward lobe. Not all combinations of monopole length and placement favor a clean E-plane pattern.

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We shall address later the question of orienting the antenna in practice. For the moment, the key matter for design concerns the placement of the monopole on the bottom plane and the length of the monopole. In all cases, the monopole is fed on the lowest segment, the one that joins the junction of wires in the wire-grid plane.

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As a test of potential performance, I tracked these variables using two different reflector plane dimension sets. The smaller set used planes that are 1.5 wavelength on each edge. The larger set uses 2.0 wavelength plane edges. The difference is sufficient to see if the plane size makes a significant performance difference.

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The data for these modeling tests appears in the table below. The coordinates for the monopole position are given as X and Y values in wavelengths from the axis. However, these coordinates result in distances from the deep corner that are 1.414 times either of the coordinates. The test frequency is 432 MHz (the same as used with the corner reflector models).

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Model 3c1r5:  1.5 wavelength per reflector-plane edge
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+Monopole length:  0.7 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      12.36      46         25.47            55        85 - j 27
+.6x.6      14.06      49         23.83            53        56 - j 38
+.7x.7      12.40      53         18.64            55        47 - j 26
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+Monopole length:  0.75 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      14.15      40         31.47            45        99 + j 13
+.6x.6      14.39      47         25.76            50        73 + j  5
+.7x.7      13.03      53         19.49            55        59 + j 21
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+Monopole length:  0.8 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      14.70      37         34.81            42        125 + j 32
+.6x.6      14.44      46         27.15            48         93 + j 40
+.7x.7      13.20      54         20.03            57         79 + j 67
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+Model 3c2r0:  2.0 wavelength per reflector-plane edge
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+Monopole length:  0.7 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      14.55      46         40.26            43        83 - j 26
+.6x.6      15.89      48         33.64            41        54 - j 36
+.7x.7      14.91      55         27.46            48        44 - j 23
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+Monopole length:  0.75 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      15.70      40         46.02            37        98 + j 12
+.6x.6      16.19      46         35.67            39        71 + j  7
+.7x.7      15.59      53         27.72            45        57 + j 27
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+Monopole length:  0.8 wavelength
+Position   Gain       TO angle   Front-Back       Beamwidth Feedpoint Z
+(wl)       (dbi)      (deg)      Ratio (dB)       (deg)     (R+/-jX Ohms)
+.5x.5      16.14      37         43.78            34        123 + j 32
+.6x.6      16.37      45         37.48            38         91 + j 42
+.7x.7      15.77      52         27.90            43         78 + j 77
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These sample modeling figures reveal some interesting trends in the performance of the 3-D corner reflector array.

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1. As we increase the size of the reflector--at least in the 2 steps shown here--gain and front-to-back improve, but the source impedance of the monopole does not significantly change for any given position or length.

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2. As we increase the length of the monopole for a given position and reflector size, the gain increases and the signal elevation angle relative to the bottom plane increases.

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3. As we move the monopole outward from the reflector deep corner, the gain peaks in all but one case at a coordinate set of 0.6x0.6, a distance from the deep corner of about 0.85 wavelength.

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4. The lowest reactance for either size reflector set occurs with a monopole about 0.75 wavelength long and placed at coordinates 0.6x0.6 or 0.85 wavelength from the deep reflector corner. The impedance is close to 70 Ohms for use with either 50 or 70 Ohm cables.

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5. The monopole position and length most apt to yield an elevation angle at or very close to 45 degrees is the 0.75 wavelength version spaced 0.85 wavelength from the reflector deep corner. As shown in Fig. 7, this combination also offers the cleanest E-plane pattern structure at close to maximum obtainable gain.

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6. As we move the monopole further from the deep reflector corner, the front-to-back ratio decreases. As we increase the reflector size, the front-to-back ratio increases.

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With either size reflector planes, the 3-D corner array is a wide-band antenna. The following tables shows performance values at 420, 435, and 450 MHz to sample the rates of change across this amateur band. All monopoles use coordinates 0.6x0.6 (wavelength) and are 0.75 wavelength tall at 432 MHz.

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+Model 3c1r5:  1.5 wavelength per reflector-plane edge at 432 MHz
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+Frequency  Gain       TO angle   Front-Back       Feed Z
+ MHz       (dBi)      (deg)      Ratio (dB)       (R+/-jX Ohms)
+420        14.17      48         23.72            69 - j 11
+435        14.44      47         26.17            73 + j  9
+450        14.66      47         27.49            76 + j 30
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The performance values increase (along with the feedpoint impedance) because the reflector and monopole have a constant set of physical dimensions, enlarging them slightly with increasing frequency. Fig. 8 shows both the 75-Ohm and the 50-Ohm SWR curves for the smaller reflector array across the entire band at 5 MHz intervals.

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+Model 3c2r0:  2.0 wavelength per reflector-plane edge at 432 MHz
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+Frequency  Gain       TO angle   Front-Back       Feed Z
+ MHz       (dBi)      (deg)      Ratio (dB)       (R+/-jX Ohms)
+420        15.93      46         34.73            66 - j 10
+435        16.26      46         35.82            72 + j 11
+450        16.61      47         36.52            76 + j 33
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Fig. 9 shows the 75-Ohm and 50-Ohm SWR curves from 420 to 450 MHz in 5 MHz intervals. In general, the performance values for the array change by well under 5% while the impedance remains well within appropriate ranges for matching to standard coaxial cables.

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The performance values and operating bandwidth of the array are to some extent a function of the monopole diameter. In this design exercise, I used a 0.03 wavelength diameter, which translates into 20.8 mm or 0.82". A standard piece of copper tubing in the vicinity of these values would easily replicate the performance.

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With respect to raw performance, the 2 wavelength reflector assembly yields the best values. A 0.75 wavelength monopole spaced about 0.85 wavelength from the deep reflector corner or at coordinates 0.6 x 0.6 wavelength from the bottom reflector edges offers the best compromise between gain and feedpoint impedance. The monopole length at 432 MHz will be about 20.5" or 520.5 mm.

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At 432 MHz, the 2 wavelength reflector will have edge lengths of 51.9" or 1318.5 mm. These lengths may be ungainly for practical installations. The 1.5 wavelength reflector assembly has edge lengths of 38.25" or 971.5 mm, which may be more feasible. Since the source impedance does not change significantly with increases in the size of the reflector, the best reflector is the largest one that will endure local weather conditions. This suggestion applies up to the 2 wavelength version, since I have not modeled larger reflector assemblies.

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With a 2 wavelength reflector assembly, the 3-D corner reflector array offers superior performance to the standard corner reflector occupying a similar volume. How much superior depends to some degree on the techniques applied to the conventional corner reflector. Nonetheless, for vertically polarized signals, the 3-D corner array offers a degree of simplicity along with its performance that may appeal to many backyard antenna builders.

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Some Practical Considerations

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There are two major categories of practical concerns that any potential 3-D corner array builder must address: construction and orientation.

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Construction can employ any set of proven UHF techniques. For frequencies above 900 MHz, it is feasible to form the reflector from a single sheet of copper flashing. Two edges can be simple bends, with the final joint formed from an overlap that one solders securely. Raw edges can use fold-over lips with solder to stiffen and secure the junction of the lip with the flashing surface.

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One advantage of a solid reflector surface is that anything done to the "backside" usually has no effect upon performance. Hence, the bottom plane can be stiffened to the degree necessary for the installation of both the monopole (with its cable connector) and a mounting system.

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An alternative construction method to the use of solid reflectors surfaces appears in Fig. 10. The antenna belongs to WA4PGI and is designed for 1296 MHz. It employs 1/4" aluminum hardware cloth supported at the edge-junctions by L-stock. Each diagonal along the reflector planes receives further support from a length of U-channel. The pieces are riveted together. Hardware cloth has the advantage of slipping the wind more effectively than a solid plane.

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Fig. 11 provides a closer view of the monopole and its mounting. Essentially, a plate backs up the hardware cloth and permits the mounting of a coax connector to which one might solder or braze the monopole. The plate system does not disturb the overall reflector operation since it lies behind the plane. However, it also serves as a mount for attachment of the array to a mast with U-bolts. In these photographs, the array is horizontally polarized and has been used to good effect by WA4PGI for weak signal work.

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Because the main beam takes off at an angle of about 45 degrees to the bottom plate, the bore sight bisects the angle formed by each of the pairs of planes in the reflector assembly. Hence, the entire array must be tipped downward about 45 degrees in vertically polarized service along a line formed from the deep corner of the reflector through the monopole to the front far corner of the bottom plane. For horizontally polarized service, rotate the tilted assembly 90 degrees around the apex of the corner (the deep reflector corner) until the monopole is parallel to the ground surface.

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In Fig. 12, we can get a sense of the performance potential of the WA4PGI array, even though the patterns are for 432 MHz with the antenna only 5 wavelengths (about 3.5 m or 11.5') above ground. Both the model and the 1296-MHz array use 2 wavelength reflector planes. The sidelobe imbalance that we saw in the E-plane patterns in Fig. 7 reappears, although the strongest sidelobe is nearly 22 dB below the main forward lobe. The gain at 2.8 degrees elevation is 21.95 dBi, with a 180-degree front-to-back ratio of nearly 39 dB.

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Fig. 13 is a representation of the array in vertically polarized service. The line of red dots mark the position of the monopole within the reflector planes. (The technique I used to obtain the tilted arrays was to save the EZNEC/4 file in .NEC format and then to import it into NEC-Win Plus. There, I blocked all of the wires and performed successive rotation steps. I rotated around the Z-axis by 45 degrees to place the bore sight along the Y-axis. I then rotated the array around the X-axis to obtain the tilt required for the vertically polarized model. Rotating the result by 90 degrees around the Y-axis yielded the horizontally polarized version. I saved the results as .NEC files and opened them from within EZNEC for the pattern runs (for consistency with earlier patterns).

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In Fig. 14, we see the patterns of the array in vertically polarized service. The gain at an elevation angle of 2.6 degrees is 20.64 dBi. The differential between the horizontal and vertical orientation gains is a function of the relatively low height above ground. As the height increases, the two gain values gradually merge. As the free-space patterns suggested, the array has slightly better side lobe performance when vertical, with the strongest sidelobe down about 25.5 dB relative to the main forward lobe. Note that the free-space bullet-shaped pattern has given way to a more conventional pattern shape. It is not always safe to assume that free-space patterns will replicate themselves in azimuth patterns over ground. The sidelobe "ears" are a function of using a 3/4 wavelength monopole. (Similar ears show up on extended double Zepp arrays, although the ears for the corner reflector array are exceptionally modest.) The current along the monopole shows two peaks, rather than the single peak to which we are accustomed when using 1/4 wavelength monopoles.

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From the patterns above ground, it is clear that the 3-D corner reflector array is capable of very high performance, whichever way we orient the array. It features a very narrow beamwidth, relatively low side-lobe levels, and high gain to go along with the relatively simple construction, wide operating bandwidth, and easily-matched feedpoint impedance.

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I would recommend a gimbal or other adjustable mounting system that permits final adjustment of the angle to occur at the installation height. Select several distant targets at various headings and align the array with each. Then adjust the tilt and rotation angles for maximum signal strength. Tighten the assembly at either the average of the angles required or by reference to the most important of the sources/targets. Since the exact angle may depend upon the antenna height, the local terrain features, and the specific operating needs of the station, no single recommendation would cover all possible cases. However, an error of 1 or 2 degrees will reduce gain at the target only in the hundredths column of the gain figures.

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For upper UHF service, the 3-D corner reflector offers the possibility of arranging several arrays, each pointed toward a specific target. Nothing in the performance figures suggests that one cannot arrange several reflectors in close rearward proximity to each other. Indeed, the use of this antenna design in commercial service might find them surrounded by RF-transparent housings. A cubical housing would encase the antenna well and place a point into potential winds, allowing the wind to by-pass the reflector and monopole. Other aerodynamic shapes are also possible. The small size of the array at frequencies over 900 MHz gives the 3-D corner array excellent potential for high gain, point-to-point, wide-bandwidth communications, as might be required in spread spectrum wireless applications.

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As an emergency reflector system, the 3-D corner reflector also has possibilities. you may line 3 sides of a cardboard box with aluminum foil and poke the antenna of a hand-held unit through one plane. Although this procedure ignores all of the conditions for optimal service, you may still experience an increase in signal strength to your target. At a more formal level, you can preplan the reflector for your intended frequency range and then construct 3 panels that will assemble and interlock at the field site. You may even design the individual panels so that they fold up into a compact mass for transport.

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My thanks once more go to Gene Wood for bringing the 3-D corner reflector antenna design to my attention. I recommend that anyone who holds an interest in the 3-D corner reflector system consult the original IEEE article by Naoki Inagaki for reference to the design equations and general theory underlying a most promising array.

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Updated 07-01-2003, 02-05-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Corner Reflector, VHF / UHF


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+

LPDAs for the 400-800-MHz Television Range
+ Part 1: An Ideal But Impractical Antenna

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

The advent of High-Definition television has brought about some anticipation of the need for wide-band high-gain UHF antennas for areas of the country where the population density--and the station density--is high. Each television channel will in fact occupy two channels to carry all of the necessary data to make current and projected systems work well. With a two-channel signal, reception will require an antenna of considerably higher reliability (gain) than we presently use. The search for both ideal and practical antennas is underway.

+

In this first part of the 2-part series, we shall examine the properties of the log periodic dipole array (LPDA) to serve the need. Next time, we shall examine a much more practical antenna that meets existing requirements with room to spare while leaving a good bit of physical room to spare as well.

+

An "Ideal" LPDA for 400-800 MHz

+

The 400-800-MHz range has a 2:1 frequency ratio. An LPDA is fully capable of superior performance in this range. However, the LPDA often receives poor marks for performance owing to deficient design. The chief problems in most extant designs are the following:

+

1. The urge to use as few elements as possible from the beginning of design. This urge results in the selection of a low value of Tau--often in the 0.80-0.89--range, with a correspondingly low Sigma value (less than 0.05) to keep the boom as short as possible.

+

2. The tendency to design an LPDA by the traditional book, using only a 2% margin below the lowest operating frequency and a 30% margin above the highest operating frequency.

+

Both of these design trends result in low-gain LPDAs with highly uneven performance across the intended operating passband. Gain fall-off at the lower and upper ends of the operating spectrum results from uncritical adherence to standard design criteria. In addition, low values of Tau and Sigma result in wide variations in gain across the operating passband, as well as wide excursions in the feedpoint impedance. A highly variable gain defeats the goal of dual channel reliability in having gain to spare at both frequency channels to ensure adequate reception of all required data.

+

In the present design exercise, let's reverse the usual procedure. Instead of beginning with the smallest possible LPDA and then wrestling with the design to make it work, let's begin with an ideal design that will easily do the job. Later, we can think about the practical limits of size reduction to make a more practical antenna.

+

For the "ideal" design, I used the following criteria:

+

1. I selected values for Tau and Sigma that are nearly the maximum permitted by design equations. Tau was set at 0.97. For this value of Tau, the ideal value of Sigma is near 0.18, so I also used this value.

+

2. The higher the value of Tau, the less need there is to set a lower limit to the design that is several percent below the actual lowest operating frequency. Therefore, the lowest design frequency was set at 400 MHz, using the standard 2% allowance that determines the length of the longest element.

+

3. Because of high-frequency truncation, setting the design limit for the array at 1.3 times the top operating frequency is usually inadequate. Since all elements forward of the one nearest resonance are active, as we change operating frequency upward, fewer elements are active. At the top of the operating range, as few as 2-3 elements will be active if we use the standard design specifications. The result is a decrease in gain of severe proportions in many LPDA designs. A more adequate figure for a pure LPDA is 1.6 times the upper operating frequency. If one uses standard design software for initial calculations, the 1.3 factor may be built into the system. Using an upper design frequency of 1.25 times the upper operating frequency usually results in a shortest element cut for 1.6 times the upper operating frequency. Therefore, the upper design frequency was set for 1000 MHz.

+

4. Although practical LPDAs might used several element diameter steps, the basic design work used a 0.125" element throughout for simplicity.

+

The resulting design uses 40 elements on a boom that is about 10.6' long. Since we are not here interested in commercial practicality in this initial effort, we can work with a design proportioned like the outline in Fig. 1.

+
+ +
+

Physically, the antenna can be described using the EZNEC antenna model descriptions, if we remember that element length values in the Y-columns are for element half lengths:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+400-800 MHz T=.97 S=.18 40 el      Frequency = 400  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1            0.000, -7.528,  0.000         0.000,  7.528,  0.000 1.25E-01  29
+2            5.420, -7.302,  0.000         5.420,  7.302,  0.000 1.25E-01  29
+3           10.677, -7.083,  0.000        10.677,  7.083,  0.000 1.25E-01  27
+4           15.777, -6.870,  0.000        15.777,  6.870,  0.000 1.25E-01  27
+5           20.723, -6.664,  0.000        20.723,  6.664,  0.000 1.25E-01  27
+6           25.521, -6.464,  0.000        25.521,  6.464,  0.000 1.25E-01  25
+7           30.176, -6.270,  0.000        30.176,  6.270,  0.000 1.25E-01  25
+8           34.690, -6.082,  0.000        34.690,  6.082,  0.000 1.25E-01  23
+9           39.069, -5.900,  0.000        39.069,  5.900,  0.000 1.25E-01  23
+10          43.317, -5.723,  0.000        43.317,  5.723,  0.000 1.25E-01  23
+11          47.438, -5.551,  0.000        47.438,  5.551,  0.000 1.25E-01  21
+12          51.434, -5.385,  0.000        51.434,  5.385,  0.000 1.25E-01  21
+13          55.311, -5.223,  0.000        55.311,  5.223,  0.000 1.25E-01  21
+14          59.072, -5.066,  0.000        59.072,  5.066,  0.000 1.25E-01  19
+15          62.719, -4.914,  0.000        62.719,  4.914,  0.000 1.25E-01  19
+16          66.258, -4.767,  0.000        66.258,  4.767,  0.000 1.25E-01  19
+17          69.690, -4.624,  0.000        69.690,  4.624,  0.000 1.25E-01  19
+18          73.019, -4.485,  0.000        73.019,  4.485,  0.000 1.25E-01  17
+19          76.248, -4.351,  0.000        76.248,  4.351,  0.000 1.25E-01  17
+20          79.381, -4.220,  0.000        79.381,  4.220,  0.000 1.25E-01  17
+21          82.419, -4.093,  0.000        82.419,  4.093,  0.000 1.25E-01  17
+22          85.367, -3.971,  0.000        85.367,  3.971,  0.000 1.25E-01  15
+23          88.225, -3.852,  0.000        88.225,  3.852,  0.000 1.25E-01  15
+24          90.999, -3.736,  0.000        90.999,  3.736,  0.000 1.25E-01  15
+25          93.688, -3.624,  0.000        93.688,  3.624,  0.000 1.25E-01  15
+26          96.298, -3.515,  0.000        96.298,  3.515,  0.000 1.25E-01  13
+27          98.829, -3.410,  0.000        98.829,  3.410,  0.000 1.25E-01  13
+28         101.284, -3.307,  0.000       101.284,  3.307,  0.000 1.25E-01  13
+29         103.665, -3.208,  0.000       103.665,  3.208,  0.000 1.25E-01  13
+30         105.975, -3.112,  0.000       105.975,  3.112,  0.000 1.25E-01  13
+31         108.216, -3.019,  0.000       108.216,  3.019,  0.000 1.25E-01  11
+32         110.389, -2.928,  0.000       110.389,  2.928,  0.000 1.25E-01  11
+33         112.497, -2.840,  0.000       112.497,  2.840,  0.000 1.25E-01  11
+34         114.542, -2.755,  0.000       114.542,  2.755,  0.000 1.25E-01  11
+35         116.526, -2.672,  0.000       116.526,  2.672,  0.000 1.25E-01  11
+36         118.450, -2.592,  0.000       118.450,  2.592,  0.000 1.25E-01  11
+37         120.316, -2.514,  0.000       120.316,  2.514,  0.000 1.25E-01   9
+38         122.127, -2.439,  0.000       122.127,  2.439,  0.000 1.25E-01   9
+39         123.883, -2.366,  0.000       123.883,  2.366,  0.000 1.25E-01   9
+40         125.586, -2.295,  0.000       125.586,  2.295,  0.000 1.25E-01   9
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1            0.000,-191.20,  0.000         0.000,191.201,  0.000 3.18E+00  29
+2          137.665,-185.47,  0.000       137.665,185.465,  0.000 3.18E+00  29
+3          271.200,-179.90,  0.000       271.200,179.901,  0.000 3.18E+00  27
+4          400.728,-174.50,  0.000       400.728,174.504,  0.000 3.18E+00  27
+5          526.371,-169.27,  0.000       526.371,169.269,  0.000 3.18E+00  27
+6          648.245,-164.19,  0.000       648.245,164.191,  0.000 3.18E+00  25
+7          766.462,-159.27,  0.000       766.462,159.265,  0.000 3.18E+00  25
+8          881.133,-154.49,  0.000       881.133,154.487,  0.000 3.18E+00  23
+9          992.364,-149.85,  0.000       992.364,149.853,  0.000 3.18E+00  23
+10         1100.26,-145.36,  0.000       1100.26,145.357,  0.000 3.18E+00  23
+11         1204.92,-141.00,  0.000       1204.92,140.996,  0.000 3.18E+00  21
+12         1306.43,-136.77,  0.000       1306.43,136.766,  0.000 3.18E+00  21
+13         1404.90,-132.66,  0.000       1404.90,132.663,  0.000 3.18E+00  21
+14         1500.42,-128.68,  0.000       1500.42,128.684,  0.000 3.18E+00  19
+15         1593.07,-124.82,  0.000       1593.07,124.823,  0.000 3.18E+00  19
+16         1682.95,-121.08,  0.000       1682.95,121.078,  0.000 3.18E+00  19
+17         1770.12,-117.45,  0.000       1770.12,117.446,  0.000 3.18E+00  19
+18         1854.68,-113.92,  0.000       1854.68,113.923,  0.000 3.18E+00  17
+19         1936.71,-110.50,  0.000       1936.71,110.505,  0.000 3.18E+00  17
+20         2016.27,-107.19,  0.000       2016.27,107.190,  0.000 3.18E+00  17
+21         2093.45,-103.97,  0.000       2093.45,103.974,  0.000 3.18E+00  17
+22         2168.31,-100.85,  0.000       2168.31,100.855,  0.000 3.18E+00  15
+23         2240.93,-97.829,  0.000       2240.93, 97.829,  0.000 3.18E+00  15
+24         2311.36,-94.894,  0.000       2311.36, 94.894,  0.000 3.18E+00  15
+25         2379.69,-92.048,  0.000       2379.69, 92.048,  0.000 3.18E+00  15
+26         2445.96,-89.286,  0.000       2445.96, 89.286,  0.000 3.18E+00  13
+27         2510.25,-86.608,  0.000       2510.25, 86.608,  0.000 3.18E+00  13
+28         2572.60,-84.009,  0.000       2572.60, 84.009,  0.000 3.18E+00  13
+29         2633.09,-81.489,  0.000       2633.09, 81.489,  0.000 3.18E+00  13
+30         2691.76,-79.044,  0.000       2691.76, 79.044,  0.000 3.18E+00  13
+31         2748.68,-76.673,  0.000       2748.68, 76.673,  0.000 3.18E+00  11
+32         2803.88,-74.373,  0.000       2803.88, 74.373,  0.000 3.18E+00  11
+33         2857.43,-72.142,  0.000       2857.43, 72.142,  0.000 3.18E+00  11
+34         2909.37,-69.977,  0.000       2909.37, 69.977,  0.000 3.18E+00  11
+35         2959.75,-67.878,  0.000       2959.75, 67.878,  0.000 3.18E+00  11
+36         3008.63,-65.842,  0.000       3008.63, 65.842,  0.000 3.18E+00  11
+37         3056.03,-63.867,  0.000       3056.03, 63.867,  0.000 3.18E+00   9
+38         3102.02,-61.951,  0.000       3102.02, 61.951,  0.000 3.18E+00   9
+39         3146.62,-60.092,  0.000       3146.62, 60.092,  0.000 3.18E+00   9
+40         3189.89,-58.289,  0.000       3189.89, 58.289,  0.000 3.18E+00   9
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           5    40 / 50.00   ( 40 / 50.00)      0.707       0.000       V
+
+                -------- TRANSMISSION LINES ---------
+
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  100.0  1.00  R
+22    22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist  100.0  1.00  R
+23    23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist  100.0  1.00  R
+24    24/50.0  ( 24/50.0)   25/50.0  ( 25/50.0)  Actual dist  100.0  1.00  R
+25    25/50.0  ( 25/50.0)   26/50.0  ( 26/50.0)  Actual dist  100.0  1.00  R
+26    26/50.0  ( 26/50.0)   27/50.0  ( 27/50.0)  Actual dist  100.0  1.00  R
+27    27/50.0  ( 27/50.0)   28/50.0  ( 28/50.0)  Actual dist  100.0  1.00  R
+28    28/50.0  ( 28/50.0)   29/50.0  ( 29/50.0)  Actual dist  100.0  1.00  R
+29    29/50.0  ( 29/50.0)   30/50.0  ( 30/50.0)  Actual dist  100.0  1.00  R
+30    30/50.0  ( 30/50.0)   31/50.0  ( 31/50.0)  Actual dist  100.0  1.00  R
+31    31/50.0  ( 31/50.0)   32/50.0  ( 32/50.0)  Actual dist  100.0  1.00  R
+32    32/50.0  ( 32/50.0)   33/50.0  ( 33/50.0)  Actual dist  100.0  1.00  R
+33    33/50.0  ( 33/50.0)   34/50.0  ( 34/50.0)  Actual dist  100.0  1.00  R
+34    34/50.0  ( 34/50.0)   35/50.0  ( 35/50.0)  Actual dist  100.0  1.00  R
+35    35/50.0  ( 35/50.0)   36/50.0  ( 36/50.0)  Actual dist  100.0  1.00  R
+36    36/50.0  ( 36/50.0)   37/50.0  ( 37/50.0)  Actual dist  100.0  1.00  R
+37    37/50.0  ( 37/50.0)   38/50.0  ( 38/50.0)  Actual dist  100.0  1.00  R
+38    38/50.0  ( 38/50.0)   39/50.0  ( 39/50.0)  Actual dist  100.0  1.00  R
+39    39/50.0  ( 39/50.0)   40/50.0  ( 40/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The wire table appears in both English (inches) and metric (millimeters) forms for ease of translation. The phase line is 100-Ohms throughout, since a low-impedance line yields a completely stable LPDA, given the high values of both Tau and Sigma.

+

We shall examine the operating characteristics of the 40-element LPDA more closely as we proceed. However, at this stage, let's quickly examine the free-space azimuth patterns in Fig. 2, since they give us a fair sampling of the antenna's performance.

+
+ +
+

The total gain variation across the passband of use is under 1 dB. As well, the front-to-back ratio is 30 dB or better. The -3 dB beamwidth is relatively even, running between 42 and 44 degrees through the operating range. Needless to say, these are all positive attributes of the antenna design. However, no LPDA should be accepted on too scanty a set of performance samplings. Therefore, let's look more closely at how the antenna sweeps the entire operating range.

+

Fig. 3 presents data for the design with several goals. First, with a 50 MHz interval between sweep steps, the graphs will show with fair--but not final--reasonableness the antennas capabilities. Should anyone have a more serious intent for the design, then samplings at much smaller intervals are necessary.

+

Second, the graphs sweep beyond the edges of the operating passband to show the trends in performance at the extremes. Normally, LPDAs show a rapid decline in performance below the lower edge of the design frequency (with very low-Tau, high-Sigma design being somewhat of an exception). Beyond the upper operating frequency, the performance decline is slower, although impedance excursions may be greater proportionally than gain and front-to-back excursions.

+
+ +
+

Fig. 3 gives us the gain and front-to-back values across the swept frequencies. Within the 400-800-MHz range of operation, the gain is remarkably stable, with a gradual decrease immediately outside the operating passband. However, above 900 MHz, the gain decreases very rapidly. Had we not specified a very high upper design frequency, the radical slope of the gain decrease would have occurred within the operating passband.

+

Below the operating passband, the front-to-back ratio dwindles quickly, with a slower decrease above the upper end of the operating range. The peaks (450 and 700 MHz) of front-to-back ratio within the operating range are natural to virtually all LPDA designs.

+
+ +
+

Typical of LPDA performance--unless masked by matching devices such as baluns and the like--the resistance and reactance of the array show increasingly large excursions as we approach and pass the upper design frequency. The general trend in these parameters is opposite below and above the design range. Below 400 MHz, both resistance and inductive reactance increase. Above the design range, resistance decreases and capacitive reactance increases.

+

Within the design range--when the upper limit is extended to overcome truncation effects--changes in the source resistance are modest. Reactance remains predominantly capacitive, although quite low. The graph does not show this completely due to the wide intervals between readings. However, if we sweep more tightly, the inductive reactance reports will be fewer in number than the capacitive reactance reports. As well, if we had tapered the element diameters to smaller values with shorter elements, the overall capacitive reactance dominance would also have shown itself.

+
+ +
+

The overall consequences of the resistance reactance excursions appear more dramatically in the 50-Ohm and 75-Ohm curves of Fig. 5. Within the operating range of the antenna, we may operate with cables of either characteristic impedance. However, the median feedpoint impedance of the array is closer to 75 Ohms than to 50. In fact, the higher that we set the combined values of Tau and Sigma, the closer the feedpoint impedance will approach the characteristic impedance of the phasing line (100 Ohms in this design example).

+

In passing, we may note that the antenna will show a reasonable line match down to 350 MHz and up to 900 MHz. However, the degradation of the other performance figures suggest that this SWR margin will net little by way of good antenna operation.

+

The "Ideal" LPDA in Operation

+

Since the antenna--should someone ever build one of them--will operate many wavelengths above ground, the resistance, reactance, and SWR figures will remain applicable in virtually can circumstance. However, there are limitations to the gain and front-to-back reports. The use of free-space is quite useful for establishing performance characteristics. However, all of the work was done in the antenna E-plane, which corresponds to a horizontal orientation above a real ground. Perhaps it may be useful to briefly examine the antenna design above real ground in both horizontal and vertical orientations.

+

Initially, the LPDA model was set horizontally above real ground at a height of 20' (240" or 6.1 m). I chose the height as representing an installation above a 1-story average American home.

+
+ +
+

Fig. 6 present representative azimuth patterns for the array at 400, 600, and 800 MHz. These far field patterns are representative of point-to-point communications, with the lowest lobe angle descending with rising frequency from 1.8 degrees to 0.9 degrees.

+

The patterns themselves closely approximate the free-space patterns, with the added gain of ground reflections. since a desired minimal level of gain for the requirements of urban and suburban television is about 7-8 dB, these antennas have excess gain--a result that we expected. The beamwidth requires careful aiming of these antennas for maximum response. However, the narrow beamwidth has the bonus of reducing ghosting that results from signals reflected from or refracted by buildings and other objects.

+

If we flip the array 90 degrees into a vertical orientation while leaving the boom at the 20' mark, we obtain the patterns shown in Fig. 7.

+
+ +
+

The first thing to note about the patterns in Fig. 7, relative to those in Fig. 6, is that they have lower gain and wider beamwidths. The gain deficit is half to 3/4 of a dB, while the average increase in -3 dB beamwidth is 3-4 degrees.

+

Although the 180-degree front-to-back ratio remains the same for both orientations, the rear lobe structure changes considerable as we change orientations. Rejection at 90 degrees to the main forward lobe decreases although it remains well above 25 dB. In addition, as the 600-MHz pattern shows, when vertically oriented, LPDAs may show a tendency to display very minor secondary forward lobes at some frequencies.

+

Conclusions

+

Our small design exercise into a nearly ideal LPDA for the 400-800 MHz range suggests that the LPDA principle is entirely serviceable for the express needs of high-definition television. The design has only 2 drawbacks. First, it is 10.6' long, much longer than anyone wishes to use in a residential situation. (The length may not be detrimental to many research situations.) As well, the 40-element design does not lend itself to economical construction.

+

One might well use a pair of U-channels as combination booms and phase lines for the array, following a common practice in LPDA design. However, with 80 half elements to install--mostly likely by pressure fitting--assuring long-term reliability commensurate with the initial cost of such an antenna would be difficult. Mounting the array would present similar challenges, since rear-end mounting is likely unfeasible and the close spacing of the elements would call for a complex mid-boom mounting scheme.

+

Such problems--at first sight daunting--are surmountable by careful engineering. However, except for specialized uses, such an antenna would lie beyond commercial feasibility for the general television consumer market. (However, if we were to gold-anodize the structure and claim special properties for the array equal to those claimed for the battery cables with gold contacts used by some audiophiles for speakers, we might capture a fetish market among the growing numbers of aficionados of "home theaters" and designated "media rooms." I shall leave such speculations to those who develop midnight-to-dawn infomercials.)

+

What we need at the practical level is an antenna no more than about 2' square--or, more accurately for LPDAs, 2' on a side of a triangle. We should also reduce the number of elements. Still, we need to have something of a margin relative to the gain needs of high-definition television.

+

In short, we need Part 2, "A Practical Antenna."

+
+ +
+

Updated 03-01-03. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Feb., 2003). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Go to Main Index

+

Topics: Broadcast, LPDA, VHF / UHF


+ + diff --git a/content/vhf/48lppr-1.gif b/content/vhf/48lppr-1.gif new file mode 100644 index 0000000..c832012 Binary files /dev/null and b/content/vhf/48lppr-1.gif differ diff --git a/content/vhf/48lppr-2.gif b/content/vhf/48lppr-2.gif new file mode 100644 index 0000000..1bbec5f Binary files /dev/null and b/content/vhf/48lppr-2.gif differ diff --git a/content/vhf/48lppr-3.gif b/content/vhf/48lppr-3.gif new file mode 100644 index 0000000..685ab9d Binary files /dev/null and b/content/vhf/48lppr-3.gif differ diff --git a/content/vhf/48lppr-4.gif b/content/vhf/48lppr-4.gif new file mode 100644 index 0000000..9d68142 Binary files /dev/null and b/content/vhf/48lppr-4.gif differ diff --git a/content/vhf/48lppr-5.gif b/content/vhf/48lppr-5.gif new file mode 100644 index 0000000..6fa78e6 Binary files /dev/null and b/content/vhf/48lppr-5.gif differ diff --git a/content/vhf/48lppr-6.gif b/content/vhf/48lppr-6.gif new file mode 100644 index 0000000..26ccc98 Binary files /dev/null and b/content/vhf/48lppr-6.gif differ diff --git a/content/vhf/48lppr-7.gif b/content/vhf/48lppr-7.gif new file mode 100644 index 0000000..5cca01c Binary files /dev/null and b/content/vhf/48lppr-7.gif differ diff --git a/content/vhf/48lppr-8.gif b/content/vhf/48lppr-8.gif new file mode 100644 index 0000000..0bf9ce0 Binary files /dev/null and b/content/vhf/48lppr-8.gif differ diff --git a/content/vhf/48lppr.html b/content/vhf/48lppr.html new file mode 100644 index 0000000..58fb994 --- /dev/null +++ b/content/vhf/48lppr.html @@ -0,0 +1,190 @@ + + + + + + LPDAs for the 400-800-MHz Television Range Part 2: A Practical Antenna + + + +
+

LPDAs for the 400-800-MHz Television Range
+ Part 2: A Practical Antenna

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In Part 1, we examined a nearly ideal log periodic dipole array (LPDA) for the 400-800-MHz range, which is anticipated by some to be the main home of high definition television in densely populated areas of the US. The antenna showed over 18 dBi of gain with better than 30 dB front-to-back ratio and a beamwidth under 45 degrees throughout its frequency range in either vertical or horizontal orientation, when modeled 20' over real ground. With a Tau of 0.97 and a Sigma of 0.18, the antenna approaches the theoretical limit of the performance of which an LPDA is capable with 0.125" diameter aluminum elements.

+

Unfortunately, the antenna has a set of significant disadvantages for residential use, even though it is likely a good research antenna. The 40 elements and the 10.6' boom place the antenna beyond the feasibility limit in terms of being a consumer product.

+

The question is whether we can design an antenna capable of 7-8 dBi free-space gain that is small enough to constitute a candidate for commercial use--or home fabrication. Small LPDAs abound, but most suffer from too small an element population and either have consequential wide variations in performance within the operating passband or suffer performance degradation at the edges of the passband. One requirement for our antenna that differs from spot use--that is, use on a single frequency at any given moment--is the need to have roughly equal performance on two separated channels of operation at any given time.

+

An antenna meeting these--and other--needs for the 400-800-MHz frequency range is indeed possible. If it were not, this series would have ended with Part 1.

+

A Practical LPDA for 400-400 MHz

+

In designing a smaller LPDA, we shall use some of the same design criteria that we employed on the ideal version.

+

1. We shall choose a relatively high value for Tau: 0.95. By doing so, we obtain good performance at the low end of the operating spectrum and therefore do not have to make allowances for performance tail-off. The standard 2% extra for the longest element will suffice with a low-frequency design specification of 400 MHz.

+

2. We shall set the upper frequency limit at 1000 or 1.25 times the highest operating frequency. This assignment will guarantee that the inherent design calculation allowance of 1.3 times the upper operating frequency will result in a 1.6 upper limit multiplier. This maneuver will result in sustained performance near the 800-MHz end of the operating passband without significant truncation effects.

+

3. We shall choose an intermediate value for Sigma, one which constrains the overall length of the array while permitting high performance. Since the specifications of a relatively confined boom length and maximum performance are at odds, a compromise value for Sigma is required. 0.056 results in acceptable performance and size.

+

The sum of these design parameters results in an LPDA with the general outline shown in Fig. 1.

+
+ +
+

Although there are 24 elements in the array--a number that many designers would shy away from--we shall accept the number and comment on construction challenges and opportunities at the end of these notes. For modeling purposes, the elements are all 0.125" in diameter and assigned the conductivity of aluminum.

+

The resulting model appears below in EZNEC format. Remember that the element lengths listed in the Y-column are in fact half-lengths.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+400-800 MHz T95 S056                    Frequency = 400  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1            0.000, -7.528,  0.000         0.000,  7.528,  0.000 1.25E-01  29
+2            1.686, -7.151,  0.000         1.686,  7.151,  0.000 1.25E-01  27
+3            3.288, -6.794,  0.000         3.288,  6.794,  0.000 1.25E-01  27
+4            4.810, -6.454,  0.000         4.810,  6.454,  0.000 1.25E-01  25
+5            6.256, -6.131,  0.000         6.256,  6.131,  0.000 1.25E-01  23
+6            7.629, -5.825,  0.000         7.629,  5.825,  0.000 1.25E-01  23
+7            8.934, -5.533,  0.000         8.934,  5.533,  0.000 1.25E-01  21
+8           10.173, -5.257,  0.000        10.173,  5.257,  0.000 1.25E-01  21
+9           11.351, -4.994,  0.000        11.351,  4.994,  0.000 1.25E-01  19
+10          12.469, -4.744,  0.000        12.469,  4.744,  0.000 1.25E-01  19
+11          13.532, -4.507,  0.000        13.532,  4.507,  0.000 1.25E-01  17
+12          14.542, -4.282,  0.000        14.542,  4.282,  0.000 1.25E-01  17
+13          15.501, -4.068,  0.000        15.501,  4.068,  0.000 1.25E-01  15
+14          16.412, -3.864,  0.000        16.412,  3.864,  0.000 1.25E-01  15
+15          17.277, -3.671,  0.000        17.277,  3.671,  0.000 1.25E-01  15
+16          18.100, -3.487,  0.000        18.100,  3.487,  0.000 1.25E-01  13
+17          18.881, -3.313,  0.000        18.881,  3.313,  0.000 1.25E-01  13
+18          19.623, -3.147,  0.000        19.623,  3.147,  0.000 1.25E-01  13
+19          20.328, -2.990,  0.000        20.328,  2.990,  0.000 1.25E-01  11
+20          20.998, -2.841,  0.000        20.998,  2.841,  0.000 1.25E-01  11
+21          21.634, -2.699,  0.000        21.634,  2.699,  0.000 1.25E-01  11
+22          22.239, -2.564,  0.000        22.239,  2.564,  0.000 1.25E-01   9
+23          22.813, -2.435,  0.000        22.813,  2.435,  0.000 1.25E-01   9
+24          23.358, -2.314,  0.000        23.358,  2.314,  0.000 1.25E-01   9
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1            0.000,-191.20,  0.000         0.000,191.201,  0.000 3.18E+00  29
+2           42.829,-181.64,  0.000        42.829,181.641,  0.000 3.18E+00  27
+3           83.517,-172.56,  0.000        83.517,172.559,  0.000 3.18E+00  27
+4          122.170,-163.93,  0.000       122.170,163.931,  0.000 3.18E+00  25
+5          158.890,-155.73,  0.000       158.890,155.734,  0.000 3.18E+00  23
+6          193.775,-147.95,  0.000       193.775,147.948,  0.000 3.18E+00  23
+7          226.915,-140.55,  0.000       226.915,140.550,  0.000 3.18E+00  21
+8          258.398,-133.52,  0.000       258.398,133.523,  0.000 3.18E+00  21
+9          288.308,-126.85,  0.000       288.308,126.847,  0.000 3.18E+00  19
+10         316.721,-120.50,  0.000       316.721,120.504,  0.000 3.18E+00  19
+11         343.714,-114.48,  0.000       343.714,114.479,  0.000 3.18E+00  17
+12         369.357,-108.76,  0.000       369.357,108.755,  0.000 3.18E+00  17
+13         393.719,-103.32,  0.000       393.719,103.317,  0.000 3.18E+00  15
+14         416.862,-98.152,  0.000       416.862, 98.152,  0.000 3.18E+00  15
+15         438.848,-93.244,  0.000       438.848, 93.244,  0.000 3.18E+00  15
+16         459.734,-88.582,  0.000       459.734, 88.582,  0.000 3.18E+00  13
+17         479.577,-84.153,  0.000       479.577, 84.153,  0.000 3.18E+00  13
+18         498.427,-79.945,  0.000       498.427, 79.945,  0.000 3.18E+00  13
+19         516.334,-75.948,  0.000       516.334, 75.948,  0.000 3.18E+00  11
+20         533.347,-72.150,  0.000       533.347, 72.150,  0.000 3.18E+00  11
+21         549.508,-68.543,  0.000       549.508, 68.543,  0.000 3.18E+00  11
+22         564.862,-65.116,  0.000       564.862, 65.116,  0.000 3.18E+00   9
+23         579.448,-61.860,  0.000       579.448, 61.860,  0.000 3.18E+00   9
+24         593.305,-58.767,  0.000       593.305, 58.767,  0.000 3.18E+00   9
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           5    24 / 50.00   ( 24 / 50.00)      0.707       0.000       V
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  100.0  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  100.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  100.0  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  100.0  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  100.0  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  100.0  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  100.0  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  100.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  100.0  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  100.0  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  100.0  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  100.0  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  100.0  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  100.0  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.0  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist  100.0  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist  100.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist  100.0  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist  100.0  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist  100.0  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist  100.0  1.00  R
+22    22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist  100.0  1.00  R
+23    23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist  100.0  1.00  R
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The wire table appears twice, the first time in English units (inches), the second time in metric units (millimeters). The source, transmission line (phase line), and ground data are identical for both versions. Our initial look at the model's potential performance will be via the free-space E-plane, which is a horizontal orientation within modeling software.

+

The array forms a triangle that is a little over 15" at the base (along the longest element) with a boom just under 24" long. The array size is certainly more manageable that the 10.6' long boom of the ideal array.

+

As we did for the ideal LPDA, let's begin with a simple survey of representative free-space azimuth pattern for the smaller LPDA. See Fig. 2.

+
+ +
+

The free-space gain of the array varies by under 0.7 dB across the passband, with a front-to-back ratio that is consistently better than 25 dB. The average gain is above 8.5 dBi, sufficient for the application for which the antenna is designed. Although the rear lobes do expand as the frequency increases, the worst-case front-to-back ratio remains at 25 dB or more. Because the array has lower gain than the ideal array (about 4.5 dB less), the resulting -3 dB beamwidth is greater by about 15 degrees at an average value of 60 degrees. The sum of the potential performance characteristics suggests that we might well take a closer look at the antenna by sweeping its operating range.

+

As we did for the ideal range, we shall sweep in 50 MHz intervals from 350 through 1000 MHz. By exceeding the edges of the operating range, we get some insight into the sensitivity of the design to tiny variations that always occur when translating a modeled design into a physical antenna. The region below the lowest operating frequency shows large changes; hence, we may use a smaller region to sample. In contrast, in the frequency range above the highest used frequency, changes occur more slowly. Thus, we shall look at a full 200 MHz beyond the 800-MHz upper operating limit.

+
+ +
+

Fig. 3 provides gain and front-to-back data for the array. Within the operating region, the gain exceeds 8.4 dBi at every frequency checked. Had we not specified a higher-than-standard upper frequency limit, the portions of the gain curve that are under 8 dBi would have appeared within the operating range of the antenna. Although not so radical, the front-to-back ratio curve would have equally suffered without the high frequency design limit.

+

At the low end of the scale, we find that both gain and front-to-back ratio tail off rapidly below 400 MHz. Since the descent in values is nearly linear, the design has a 25 MHz "buffer" of usable performance below 400 MHz.

+
+ +
+

In Fig. 4, we find the excursions of the feedpoint resistance and reactance across sweep range from 350 to 1000 MHz. The resistance shows a very small range of variation centered around 50 Ohms within the 400-800-MHz operating range. However, for this design, the feedpoint resistance drops to a low value both above and below the main operating passband. Note that it returns to a more desirable value at 1000 MHz: such phenomena reinforce the need to take readings at rather small frequency intervals to determine the potential for undesired values.

+

The reactance curve within the operating passband shows only one excursion into the inductive region, with all other readings being capacitive. However, with values so close to zero, some inductively reactive readings may occur between the sweep points. Outside the working passband, the reactance follows the typical pattern of becoming very inductive below the lower limit and very capacitive above the upper limit.

+
+ +
+

Fig. 5 presents both 50-Ohm and 75-Ohm SWR curves. From 400 to 900 MHz, the curve is essentially flat. With a lower Tau and Sigma than used in the ideal array, the feedpoint impedance is not as close to the value of the phase line characteristic impedance. In the ideal array, a 100-Ohm phase line yielded a curve whose median impedance value was close to 75 Ohms. In this smaller LPDA, the median value is close to 50 Ohms for the same 100-Ohm phase line.

+

The excursions in resistance and reactance in Fig. 4 easily prepare us for the very high SWR values at 350 MHz. At the upper end, the low SWR at 1000 MHz is still another reminder to use a small enough sweep interval to detect undesired values, in this case at 950 MHz. Otherwise, we might harbor an illusion of using the region above 800 MHz as added operating territory.

+

As with the ideal array, some of the peaks and valleys in the operating performance curves will change frequency somewhat if we taper the effective diameter of the elements, reducing their diameter in the most forward area of the LPDA. This region also has the shortest and most tightly packed set of elements. The most forward element is a scant half inch forward of the next element.

+

The Practical LPDA over Real Ground

+

As we did with the 40-element LPDA, we set the smaller array at a height of 20' (240" or 6.1 m) above real ground to sample the performance under more realistic conditions. Of course, modeling software presumes level ground with no buildings, trees, towers, or other structures unless we create wire-grid models of them.

+
+ +
+

Fig. 6 shows the azimuth patterns of the array oriented horizontally. The azimuth pattern shapes are almost identical to the free-space E-plane patterns used in the basic description of the antenna. The far-field elevation angle ranges from 1.7 degrees at 400 MHz to 0.9 degrees at 800 MHz. At the given height, the gain varies by only about 0.6 dB across the operating spectrum, with a consistent front-to-back ratio of well over 25 dB. The average gain is about 15.8 dBi, or a little more than 4 dB less than the gain of the 10'-long array. However the gain should easily meet--with surplus--the requirements that we set forth for the project.

+

The average 60-degree -3 dB beamwidth is about 15 degrees wider than the corresponding beamwidth for the ideal array. The wider beamwidth of the smaller array eases the task of aiming the antenna, but may show a slight increase in ghosting potential.

+
+ +
+

Fig. 7 presents the same data collection with the array set to a vertical orientation. The average gain is about 0.5 dB less than when the beam is set horizontally, but with a very small gain change across the operating passband. The gain deficit relative to the ideal array is the same as for the comparison of the two arrays when horizontal: a little over 4 dB.

+

The array beamwidth when vertically oriented averages about 87 degrees. This value is almost double the beamwidth of the ideal array when set vertically. As well it is more than 15 degrees wider than the small array in the horizontal position. It is a fact of life with arrays composed of parallel linear elements that the increase in beamwidth as we reduce the overall gain of the system will have different rates for horizontal and vertical orientations. The vertical position will show a higher rate of beamwidth increase for an given reduction in system gain than will the horizontal orientation.

+

Construction Challenges

+

If we accept that the LPDA design, as modeled here, is adequate to the performance needs of urban and suburban high definition television (and similar working situations), then the remaining questions are practical. Is it feasible to build such an array for potential residential use?

+

The most common LPDA construction in the UHF region tends to use a pair of U-channels as the booms. The facing solid surfaces form the phasing line. Half-elements press fit into alternating upper and lower channel holes. An example of this construction style appeared in "An LPDA for 2 Meters Plus," QST (Oct., 2001), pp. 42-46. The arrangement was beefed up for mid-VHF use.

+

Even with a total boom length of about 24", the construction style would be expensive in a 24-element array. However, with sufficient materials engineering at the front end, simpler alternatives are possible. Fig. 8 shows the general features of one possibility.

+
+ +
+

The first step is to find the etched-copper strip equivalent for the elements in the modeled design. NEC and MININEC models, of course, are restricted to round-wire elements. In the process of conversion to the flat strips of copper on a suitable substrate, one might well undertake the task of finding the optimal diameter for each element in the array.

+

The array lends itself to construction by joining two identical half arrays, thus reducing fabrication complexities at one point in the production process. Each half LPDA consists of alternating upper-side and lower-side half elements, with one of the etched strips used as the phase line. If we flip one section, it would join with the other to form a complete array. Of course, the fabrication effort that we saved earlier, we now expend in joining the two sections and soldering the loose element ends to the phase line strips.

+

The phase line calls for some comment. If we simply etch a line on a solid substrate, we must be careful to determine if the consequent velocity factor of the resulting phase line will disturb the performance curves significantly. It will certainly affect the characteristic impedance of a line of a set width when compared to the same line with only air between the strips. (Most handbooks for radio amateurs, for example, omit the dielectric constant from equations for calculating the impedance of transmission lines from the physical element diameters and spacing, since air is presumed to be the dielectric for home-built lines.) Fig. 8 shows one possible solution. Most of the region below the line is cut away, allowing a higher velocity factor and a dielectric constant closer to air for the phase line. Periodic projections in between elements provide some mechanical linkage between the two halves of the array.

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The substrate itself requires investigation prior to commitment to manufacture. G-10 glass board material is one of the standard substrates for etched circuit production. However, such boards may prove too heavy for the application if the array requires significant spacing between the phase line strips. Light-weight substrates, including some with ribbed hollow cores may be possible.

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Of course, we use modern glues or epoxies to join the substrate halves permanently. As well, we weather-protect the entire assembly. In addition, we add a cable connector at the front point and devise a suitable support system.

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Creating a simple and relatively inexpensive array of adequate performance thus involves a few R&D challenges. It is likely that much of this work already exists in scattered form. Nevertheless, once the design translation into an etched-board form is complete, then the 24-element array becomes no more complex than an array with half the number of elements and one-fourth the performance potential. The result is a durable, light-weight antenna with a very broad operating passband and considerable performance.

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Updated 03-10-03. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Mar., 2003). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: Broadcast, LPDA, VHF / UHF


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A 100-1000 MHz "Utility" LPDA

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L. B. Cebik, W4RNL

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In a pair of articles in QEX ("Notes on Standard Design HF LPDAs," May-August, 2000), I explored some of the problems and pitfalls of designing LPDAs with a wide passband--something of the order of a 10:1 frequency range. The notes focused on antennas for the 3-30 MHz range and ran from 60 to 164 feet long with 20 to 43 elements. Essentially, the bottom line was that if the boom length is too short and if Tau or Sigma--the design constants for an LPDA--are too low, the resulting LPDA will exhibit one or more of the following flaws:

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  • 1. The overall gain will be too low to be significantly useful.
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  • 2. The gain will be uneven across the passband, with serious drops in gain at either the low or high end of the passband.
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  • 3. With increasing frequency, the azimuth patterns will become misshapen relative to the normal or "well-behaved" pattern due to harmonic activity on elements behind the most active element.
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  • 4. The chance of weakness--frequency regions in which the forward gain deteriorates and even reverses direction due to excessive harmonic activity of elements behind the most active element--increases, if the phase line impedance becomes too low in an effort to increase overall gain.
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  • 5. The feedpoint impedance will become erratic, with wide excursions of both the resistive and reactive components, so that it may not be possible to yield an SWR under 2:1 for any center impedance value.
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Although impractical for amateur installations, the 164' 26-element model of a standard design LPDA--with slight modifications to even out performance--proved to be among the most promising designs that used the minimum number of elements necessary to suppress nearly all of the difficulties and still yield an average gain of about 7 dBi--about that of a 2-element quad, but spread over a 3+ octave span. Although not perfectly tamed in all respects, the design was deemed at least acceptable.

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Interestingly, utility LPDAs are routinely designed for a 10:1 frequency span at VHF-UHF frequencies. Among the common designs are those for 100-1000 MHz. However, in most cases they are short (30-60 inches boom length) and have a low element population (10-14). Such antennas are about half the minimum acceptable size--when rightly scaled--of the HF arrays examined. I have modeled a number of possibilities in the VHF/UHF frequency region, varying the number of elements and the overall boom length in the most common region. All are equally poor performers. 12-element 30" boom-length LPDAs for the frequency span rarely achieved more than 5 dBi free-space gain--a full dB less than a 2-element Yagi--with ragged and irregularly shaped patterns that emerged at less than half way up the passband. Even longer boom models fail to pass muster with low element densities.

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For example, the LPDA whose 75-Ohm SWR curve appears in Fig. 1 is designed with a Tau of 0.77 and a Sigma of 0.11 to place 12 elements within a 60" boom. Once more, irregular pattern shapes emerge very quickly with increasing frequency. Note the spike in the SWR curve. It indicates a potential weakness, that is, a pattern that may even reverse direction.

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Fig 2 shows the pattern at 140 MHz. Indeed, it is pointing in the wrong direction due to harmonic activity on elements well to the rear of those which are normally active at the working frequency. The antenna required redesign in an effort to remove the offending anomaly in performance.

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In Fig. 3, we have the 75-Ohm SWR curve for one variation on the 60" 12-element LPDA for 100-1000 MHz. The SWR spike appears to be reduced relative to the one in Fig. 1.

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However, the spike is just as great. It has only moved away from the marker frequencies used by the SWR curve (every 20 MHz). The peak anomaly occurs at about 135 MHz, as shown in the free-space azimuth pattern in Fig. 4. Once more, the effective beam direction has reversed and the source impedance has reached unusable values.

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Satisfactory--if not completely perfect--performance across the 100- 1000 MHz region is more easily achieved if we use more elements, a better choice of Tau and Sigma values, and a sufficiently high phase line impedance. The 164' 26-element 3-30 MHz HF array used a Tau of 0.9024 and a Sigma of 0.0519. Certain element lengths and spacings--especially at the low end of the spectrum--had been modified for improved low-end performance while retaining good gain at the upper end of the passband.

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Fig. 5 shows the outline of the resulting array. It also shows the outline of the array scaled for use in the 100-1000 MHz range. The most significant changes required in the scaling process were a stepping of the element diameters, with 0.25" elements used at the low end of the spectrum. The diameter stepped downward in 0.0625" increments until the most forward and shortest elements used 0.0626" (about #14 AWG) diameter elements. The overall scaled length is just about 60". The following table shows the wire set-up for the model.

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+60", 26-el 100-1000 MHz LPDA              Frequency = 1000  MHz.
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+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
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+              --------------- WIRES ---------------
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+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)  Dia(in) Segs
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+1          -29.400,  0.000,  0.000        29.400,  0.000,  0.000 2.50E-01 107
+2          -27.210,  6.969,  0.000        27.210,  6.969,  0.000 2.50E-01  97
+3          -24.525, 12.610,  0.000        24.525, 12.610,  0.000 2.50E-01  87
+4          -22.133, 17.700,  0.000        22.133, 17.700,  0.000 2.50E-01  79
+5          -19.675, 22.293,  0.000        19.675, 22.293,  0.000 2.50E-01  71
+6          -18.027, 26.439,  0.000        18.027, 26.439,  0.000 2.50E-01  65
+7          -16.269, 30.181,  0.000        16.269, 30.181,  0.000 2.50E-01  57
+8          -14.683, 33.557,  0.000        14.683, 33.557,  0.000 2.50E-01  53
+9          -13.251, 36.605,  0.000        13.251, 36.605,  0.000 1.88E-01  47
+10         -11.959, 39.355,  0.000        11.959, 39.355,  0.000 1.88E-01  43
+11         -10.793, 41.837,  0.000        10.793, 41.837,  0.000 1.88E-01  39
+12          -9.740, 44.077,  0.000         9.740, 44.077,  0.000 1.88E-01  35
+13          -8.791, 46.099,  0.000         8.791, 46.099,  0.000 1.88E-01  31
+14          -7.933, 47.924,  0.000         7.933, 47.924,  0.000 1.88E-01  29
+15          -7.160, 49.570,  0.000         7.160, 49.570,  0.000 1.88E-01  25
+16          -6.462, 51.056,  0.000         6.462, 51.056,  0.000 1.25E-01  23
+17          -5.832, 52.397,  0.000         5.832, 52.397,  0.000 1.25E-01  21
+18          -5.263, 53.608,  0.000         5.263, 53.608,  0.000 1.25E-01  19
+19          -4.750, 54.700,  0.000         4.750, 54.700,  0.000 1.25E-01  17
+20          -4.287, 55.686,  0.000         4.287, 55.686,  0.000 1.25E-01  15
+21          -3.869, 56.576,  0.000         3.869, 56.576,  0.000 6.25E-02  15
+22          -3.491, 57.379,  0.000         3.491, 57.379,  0.000 6.25E-02  13
+23          -3.151, 58.103,  0.000         3.151, 58.103,  0.000 6.25E-02  11
+24          -2.844, 58.757,  0.000         2.844, 58.757,  0.000 6.25E-02  11
+25          -2.566, 59.347,  0.000         2.566, 59.347,  0.000 6.25E-02   9
+26          -2.316, 59.880,  0.000         2.316, 59.880,  0.000 6.25E-02   9
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+              -------------- SOURCES --------------
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+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
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+1           5    26 / 50.00   ( 26 / 50.00)      1.000       0.000       V
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The actual element lengths are double those shown in the X-column. The element size steps are shown in the second column from the right side of the table. The initial model used a 150-Ohm phase line characteristic impedance throughout. Therefore, that portion of the model table can be omitted in the interests of space.

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As shown in Fig. 6, the resulting array yields a quite acceptable 75-Ohm SWR curve for the entire passband. The 20-MHz check points on which the curve is based may hide weaknesses. Therefore, suspect regions were checked at closer intervals. For example, the flat peak in the 600 MHz region might hide a high peak between check points. However, it turned out to yield a smooth line when checked at intervals less than 1 MHz apart.

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The average free-space gain for the array is just over 7 dBi, with values lower than that at the low end of the pass band and also in the 700 MHz region. The range of gain variation for the array is just over 1 dB. The overlaid free-space azimuth patterns at 100-MHz intervals in Fig. 7 demonstrate how consistent the performance is.

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Slight pattern irregularities begin to emerge at about 900 MHz, with a slight "spade" shape to the forward lobe and ripples in the rear lobes. However, by maintaining a 150-Ohm phase line, these affects are minimized while sustaining the highest gain obtainable from the given design.

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For some applications, the builder may desire to effect a direct 50-Ohm match for the array. The standard procedure for achieving this goal is to reduce the phase line impedance to 100 Ohms or less. Unfortunately, if the impedance is lowered consistently to this value, weaknesses appear and some patterns display considerable irregularities.

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A more modest approach is to use a tapered characteristic impedance for the phase line. If the array were to be constructed using 3/4" U-channel (2 pieces) for the element supports and phase line, forward channel separation can be closer than the rear separation. Separations of the 3/4" channel phase lines ranging from about 0.3" (8 mm) to 0.9" (23 mm) along the 60" line length will provide an impedance range of about 75 to 150 Ohms.

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The following table shows the simulation of the continuously changing phase line impedance within the model.

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+                -------- TRANSMISSION LINES ---------
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+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
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+1      1/50.0  (  1/50.0)    2/50.0  (  2/50.0)  Actual dist  152.5  1.00  R
+2      2/50.0  (  2/50.0)    3/50.0  (  3/50.0)  Actual dist  148.0  1.00  R
+3      3/50.0  (  3/50.0)    4/50.0  (  4/50.0)  Actual dist  143.7  1.00  R
+4      4/50.0  (  4/50.0)    5/50.0  (  5/50.0)  Actual dist  139.5  1.00  R
+5      5/50.0  (  5/50.0)    6/50.0  (  6/50.0)  Actual dist  135.5  1.00  R
+6      6/50.0  (  6/50.0)    7/50.0  (  7/50.0)  Actual dist  131.5  1.00  R
+7      7/50.0  (  7/50.0)    8/50.0  (  8/50.0)  Actual dist  127.7  1.00  R
+8      8/50.0  (  8/50.0)    9/50.0  (  9/50.0)  Actual dist  124.0  1.00  R
+9      9/50.0  (  9/50.0)   10/50.0  ( 10/50.0)  Actual dist  120.4  1.00  R
+10    10/50.0  ( 10/50.0)   11/50.0  ( 11/50.0)  Actual dist  116.8  1.00  R
+11    11/50.0  ( 11/50.0)   12/50.0  ( 12/50.0)  Actual dist  113.4  1.00  R
+12    12/50.0  ( 12/50.0)   13/50.0  ( 13/50.0)  Actual dist  110.1  1.00  R
+13    13/50.0  ( 13/50.0)   14/50.0  ( 14/50.0)  Actual dist  106.9  1.00  R
+14    14/50.0  ( 14/50.0)   15/50.0  ( 15/50.0)  Actual dist  103.8  1.00  R
+15    15/50.0  ( 15/50.0)   16/50.0  ( 16/50.0)  Actual dist  100.8  1.00  R
+16    16/50.0  ( 16/50.0)   17/50.0  ( 17/50.0)  Actual dist   97.9  1.00  R
+17    17/50.0  ( 17/50.0)   18/50.0  ( 18/50.0)  Actual dist   95.0  1.00  R
+18    18/50.0  ( 18/50.0)   19/50.0  ( 19/50.0)  Actual dist   92.2  1.00  R
+19    19/50.0  ( 19/50.0)   20/50.0  ( 20/50.0)  Actual dist   89.6  1.00  R
+20    20/50.0  ( 20/50.0)   21/50.0  ( 21/50.0)  Actual dist   86.9  1.00  R
+21    21/50.0  ( 21/50.0)   22/50.0  ( 22/50.0)  Actual dist   84.4  1.00  R
+22    22/50.0  ( 22/50.0)   23/50.0  ( 23/50.0)  Actual dist   82.0  1.00  R
+23    23/50.0  ( 23/50.0)   24/50.0  ( 24/50.0)  Actual dist   79.6  1.00  R
+24    24/50.0  ( 24/50.0)   25/50.0  ( 25/50.0)  Actual dist   77.3  1.00  R
+25    25/50.0  ( 25/50.0)   26/50.0  ( 26/50.0)  Actual dist   75.0  1.00  R
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Fig. 8 shows the resulting 50-Ohm SWR curve for the modified array. So far, no peaks in SWR above 2:1 have been found in searches between the 20-MHz check points used to form the graph. However, the development of a 50-Ohm match is not without some cost.

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Fig. 9 shows the overlaid patterns for the 100-MHz check points in the frequency sweep of the array. Note that a greater number of the patterns show the development of minor side lobes. As well, more of the rear patterns show a widening that reduces the worst-case front-to-back ratio for the upper frequencies to below 20 dB, despite a consistent 23-28 dB 180-degree front-to-back ratio.

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Tapering the phase-line characteristic impedance has one beneficial effect. It raises the array gain above 200 MHz by an average of 0.5 dB. The curves in Fig. 10 compare the gain of the array designs. The general shape of the curve is preserved by the tapered phase line version, including the drop in the 700 MHz region. However, the overall level is higher except for the lowest frequencies in the span.

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As seen in Fig. 11, the front-to-back ratio is not harmed or enhanced by the phase line impedance tapering technique. The gain and front-to-back ratios, when examined in greater detail than used in the graphic shown here, exhibit periodic peaks and valleys. However, the gain and front-to-back for any given design do not show coincident peaks and valleys, and the exact frequencies of maximums and minimums will shift with minor design changes. Hence, the exact values in Fig. 11 should not be interpreted as giving one version of the array a significant advantage over the other.

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The higher gain of the tapered phase line impedance version of the array and its cost in terms of pattern behavior deserve a further note. A well-behaved azimuth pattern for an LPDA design has the appearance of a standard directional array pattern, for example, as might be produced by a Yagi. Fig. 12 shows the free-space azimuth pattern at 200 MHz for the untapered version of the array as a simple demonstration of a well-behaved pattern.

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Observe the element with the highest relative current magnitude. Forward of that element, virtually all the elements are active. Behind the most active element, only two are very active (or have a significant current magnitude), and behind them, activity virtually disappears. This is the conditions for a very well-behaved pattern, such as the one in Fig. 12.

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Fig. 13 shows the free-space azimuth pattern at 1000 MHz of the tapered phase line version of the model in order to demonstrate how far from well-behaved the patterns might go. To a lesser degree, the patterns at 900 and 1000 MHz of the constant impedance phase line model show some elements of the pattern distortion. However, in the tapered phase line model, the distortions appear at much lower frequencies. The degree of distortion is proportional in the main to the rising frequency.

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The forward lobe shows the development of small side lobes. As well, the main portion of the forward lobe has lost its smooth oval and has taken on the appearance of a common garden trowel. The rear lobes have spread so that they are down from the main lobe by only about 17.5 dB at their peaks. Additionally, they show considerable ripple in their outline.

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The graph of the relative current magnitude on the elements provides the reason why the pattern has grown distorted. Behind the most active element, there is considerable activity on a number of elements, although the current level decreases smoothly. However, there is also a region of increased current magnitude, indicating harmonic activity of the affected elements. In the main, it is this activity that yields the pattern distortion.

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Fig. 14 compares the free-space azimuth patterns of the two versions of the LPDA at 600 MHz. In this mid-passband region, the fixed impedance model shows greater pattern control, even though there are hints of potential irregularities compared to the well-behaved pattern of Fig. 12. The tapered impedance model shows incipient secondary forward lobes and a greater ripple to the rear lobes than the fixed impedance version.

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Carried to high levels of current, relative to the most active element, active elements behind the most active element would yield a potential weakness that might go so far as to produce a pattern reversal and an unusable feedpoint impedance. However, in the present designs, these consequences have been avoided. Still, an important user question remains.

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Just how much pattern distortion is acceptable for an LPDA design? There is no simple answer to this question, since it necessarily involves goals and specifications brought to the antenna design be the user. For general utility purposes, the pattern distortion shown in Fig. 13 might well be considered to be well within needs. For other purposes, the most well-behaved pattern achievable might be required. For utility purposes, either version of the 26-element LPDA shown here would be serviceable, with the final selection perhaps dictated by the desired feedpoint impedance.

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There is a considerable difference between the 12-element sample models that were rejected and the 26-element models that proved to be reasonably successful. How many fewer elements than 26 might one use and obtain the necessary performance in terms of gain, an absence of weaknesses, and an acceptable SWR curve across the passband? There is, once more, no simple answer to the question. Each trial design may alter the value of Tau and Sigma, the total boom length, and the low and high frequencies used in the design exercise. For lower values of Tau, a lower minimum frequency should be used to ensure adequate gain near 100 MHz. As well, altering the length and spacing of the longest elements in accord with circularizing techniques may be useful in increasing low-end gain. If high end gain tapers off too badly, the design may use a higher maximum frequency or also employ circularizing techniques to adjust the most forward elements with respect to length and spacing.

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When we combine the variables of both basic design and useful modifications, a general answer to the question of how few elements we may use and still achieve a desired level of performance becomes impossible. The examples of LPDA design given here represent but two of many possibilities. However, they do illustrate well the general guidance of using a long enough boom and using enough elements to ensure that we get the job done.

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Updated 12-1-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for November, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: LPDA, VHF / UHF


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The 64-(Euro-)Dollar Question

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L. B. Cebik, W4RNL

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U.S. amateur operators have access to the 6-meter (50-54-MHz) band. However, they do not have access to a small band open to UK hams: the 4-meter (70-70.5-MHz) band. Only some Region 1 countries share that middle ground between 6 and 2 meters. UK amateur also generally have smaller plots on which to erect antenna farms. Very often, a chimney-supported mast is the only available antenna support. Hence, multi-band antennas for small spaces are always popular reading (and building) projects.

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A reasonable combination of bands for the chimney top is 6 and 4 meters. The relationship between bands is roughly equivalent to the relationship between 20 and 15 meters: about a 0.75:1 frequency ratio. Hence, there are numerous options open to UK ham in need of a combined 6/4-meter antenna. As a bonus, I shall throw a single feedline into the mix.

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Most roof-top antenna mounters also add a special caveat into the mix: keep the boom length to about 6'. This desire opens a different door on the problem of multi-band antennas: the antenna mythology arising out of the 1960s through the 1980s. If my reading has been representative, it is fraught with misdirection. So, although we shall try to stick to the 6' boom limit, we shall not always succeed.

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In fact, we shall look at two directions of design for 6/4-meter antennas. One path will lead us into LPDA and related designs. The other road will have a "Yagi" label. Neither direction will give us a perfect antenna--where perfect also means easy to build--but both will lead to usable solutions for the careful antenna builder.

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The Path to LPDAs

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Much of the foundation for LPDAs, log-cell-Yagis (also called LPYs or log-Yagis), and similar structures comes from the era just before the advent of very good antenna modeling software. As a result, the material found in many amateur journals and books is filled with misconceptions arising from one-of-a-kind successes generalized well beyond the limits of what analysis will bear.

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For example, in LPDA design (whether for an entire array or for the driven cell in an array with reflectors and/or directors), we encounter the idea that if we make an element resonant for each desired band within the array, we shall improve performance in some way. Unfortunately, that idea stems from the old and erroneous assumption that an LPDA operates like a selective 3-element Yagi. The element just longer than the resonant one is a reflector and the element just shorter than the resonant one is a director. This idea is faulty on at least two counts, as illustrated in Fig. 1.

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1. Although an individual element may be somewhat more active--as determined by the peak current magnitude on it--multiple elements show high current levels in a well populated LPDA. The 70-MHz portion of Fig. 1 is especially graphic on this point, where 3 elements have very nearly equal current magnitudes.

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2. Virtually all of the elements forward of the most active element on any frequency are significantly active in terms of showing high current magnitudes (in contrast to the relatively inert elements well behind the most active one). The 3-element Yagi analogy simply does not apply to an LPDA.

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Another misconception follows on this first one. Most calculating programs for LPDA designs set the resonant frequency of the shortest element about 1.3 times the highest frequency in the operating pass band. Although this formula might work with LPDAs using very long booms, very many elements, a very high value of Tau, and an ideal value of Sigma, the multiplier is too small for the smaller, less populated LPDAs designed by amateurs. As a result, the smaller LPDAs experience considerable high-end performance degradation relative to performance in the middle of the passband. A value closer to 1.6 times the highest frequency used is closer to reality for a design with comparable performance throughout the passband.

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As a result of these and other misconceptions about LPDAs, most LPDAs and log cells designed by amateurs tend to have too few elements and unsatisfactory performance at the high end of the scale. But before we enter the actual task of redesigning the LPDA for 6 and 4 meters, lets examine another problem: misguided expectations. Many amateurs expect LPDAs to provide smooth performance across their entire passbands. Hence, if a performance number is out of line with the expected single value set, something must be wrong.

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What is wrong is the idea of expecting smooth LPDA performance with the types of values of Tau, Sigma, and element count typical of amateur LPDAs. LPDAs show cyclical performance, with peaks and valleys of gain and front-to-back ratio, as illustrated in Fig. 2.

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The particular LPDA only has a 1.5:1 frequency range and therefore shows only two gain cycle. Do not make too much of the depth of the visual curve, since it only represents a change of 0.24 dB. The 180-degree front-to-back line shows more numerous peaks and valleys--and they do not necessarily coincide with the peaks and valleys in the gain curve. (The front-to-side line in the graph actually represents the worst-case front-to-back ratio and is much more constant than the 180-degree curve.) The exact performance of an LPDA depends on both the directly fed power to the elements and the mutual coupling among the elements. Hence, it is natural that, in this environment where the ratio of the two changes with every small change in operating frequency, the gain and front-to-back curves do not coincide.

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The resistance, reactance, and SWR curves also reflect these conditions, as shown in Fig. 3. Resistance and reactance do not show resistive peaks and inductively reactive peaks at the same frequencies. A well design LPDA tends to show its highest values of reactance (either inductive or capacitive) when the resistance is closest to the median value for the array. Equally, the lowest reactance values tend to occur when the resistance is furthest from its median value. Hence, although subject to ups and downs of its own, the LPDA's SWR value--in a well-designed array--tends to be acceptable (relative to some design standard) across a very wide passband.

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So what can we do for the 50-70 MHz span? The answer is that we can design a fair number of different LPDAs to cover this spread. Each version uses a design frequency range of 50 to 87 MHz. The calculations give us a lower frequency longest element and a higher frequency shortest element.

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The end result is a series of LPDAs each of which has the following physical properties:

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1. A longest element that is 120.4" from tip to tip.

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2. A shortest element that is 53.25" from tip to tip.

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3. A total element length of 70", which allows a bit of space on a 72" boom for mounting hardware.

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4. A variable number of elements, from 8 through 12, with consequential variations in overall performance, performance curve shapes, and values of Tau and Sigma.

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In all cases, the performance at 6 meters is very comparable to the performance at 4 meters. The frequencies in between are largely allocated to television, so the antenna will handle to channels below about 75 MHz.

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Full dimensions--as presented in model description format--appear at the end of the article. However, Fig. 4 provides the outlines for the 4 sample LPDAs.

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As the outline sketch makes apparent, the only difference in appearance among the 4 LPDA designs is the element population. The following table provides of the basic design and performance information about the arrays.

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+              Design and Performance Data for the 6/4-Meter LPDAs
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+      No. El.     Tau   Sigma       51-MHz            70-MHz
+                                    Gain  180-F-B     Gain  180-F-B
+       8          0.89  0.06        6.58  20.25       6.69  18.41
+      10          0.91  0.05        6.85  35.42       6.94  22.06
+      12          0.93  0.04        7.01  31.64       6.80  18.68
+      14          0.94  0.03        7.13  27.02       6.94  21.04
+All gain values are for free-space.  All data from NEC-4 models.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Do not cheer too loudly at some of the very high 180-degree front-to-back ratios, since they are subject to spikes. Indeed, construction variations can easily move the high peak away from the listed frequency and present only a more modest value. However, in general, the arrays show--across their entire passbands--an increasing level of performance as we increase the element count. However, we cannot proceed indefinitely, because the value of Sigma is decreasing. With that decrease comes a need for employing other optimizing techniques to sustain performance at 70 MHz.

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Fig. 5 shows azimuth patterns at 50.5 and 70 MHz for the 10-element array. The patterns are typical and completely well behaved, since the small operating frequency span does not stress the design in any way. Note in the lower-frequency pattern that the 180-degree front-to-back value does not show the true rearward performance as well as would a worst-case value using the strongest rearward lobe gain. With that figure, there is little difference between the 50- and the 70-MHz patterns.

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All of the arrays use a 150-Ohm phase line so that the target feedpoint impedance is 50 Ohms without need for any conversion. A few ferrite beads on the coax at the feedpoint will suppress any tendencies toward common-mode currents on the feedline to the array. However, using the same characteristic impedance for the phase line between elements does not guarantee that all of the versions of the LPDA will yield the same SWR curves. See Fig. 6.

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If you carefully track the lines for each array, you will discover that the 14-element array has the smoothest performance and the lowest average value of 50-Ohm SWR. The 8-element version shows one peak (outside any ham band) above 2:1 and also reveals the most erratic progression. The conclusion that higher values of Tau tend to smooth the impedance curves is a correct one on which to generalize--within overall design limits.

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The following table provides modeled performance for the 10-element version at heights of 20' and 35' above average ground. you can extrapolate both for the other models and for other heights.

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+                          10-Element LPDA Performance
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+                        50.5 MHz                            70 MHz
+Height      Gain dBi    F-B dB      Feed Z      Gain dBi    F-B db      Feed Z
+F.S.         6.8        28.2        88 - j 4     6.9        22.1        60 - j17
+20'         12.1        22.1        84 - j 2    12.5        23.8        58 - j15
+35'         12.4        33.2        89 - j 6    12.7        23.9        59 - j16
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The values are better directional performance figures than they are raw gain figures. Since they are far field figures at the elevation angle of maximum radiation (TO angle), the performance in point-to-point use may differ somewhat.

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A final misconception attaching to many types of arrays is the gain potential. Gain potential is largely a matter of boom length and not the number of elements. As the range of LPDA populations shows, adding elements may show a slight increase in forward gain, but the true merit of using more elements within a given boom-length lies elsewhere. Whether an LPDA or a Yagi, further elements on the same boom gives the designer more flexibility in setting the feedpoint impedance level at maximum gain and also permits a wider operating bandwidth within the pre-set SWR limits. If you want more gain, you will have to use a longer boom. For Yagis, one can extend the boom length almost without limit. However, an LPDA will peak out at a gain of about 12 dBi (free space).

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Can I build any of the LPDAs? There are at least two ways to build an LPDA for the VHF range and upward: using 1 boom and a separate phase line assembly and using 2 booms and letting them double as the phase line. In both cases, we must ensure that we have a phase reversal of the phase line with each element. That means give the line a half-twist between each pair of elements. Actually, there are better ways to perform the reversal technique while sustaining the line's integrity and characteristic impedance.

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However, it is very important to use a phase line impedance of 150 Ohms or slightly less. A higher impedance will raise the average impedance at the feedpoint and may not yield a direct 50-Ohm feed for the array. In addition, increasing the phase-line characteristic impedance will also lower the array performance, with low figures for both gain and front-to- back ratio.

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+                Phase Line Structures and Dimensions:  150 Ohms
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+      Conductors        Center-to-Center Distance     Gap Distance
+      #12 copper              0.153"                    0.072"
+      #14 copper              0.121"                    0.057"
+      1" square tubes         2.222"                    1.222"
+      3/4" square tubes       1.667"                    0.917"
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The first two line types are for the 1-boom version of the array. The final two are for the twin-boom version.

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The 1-boom LPDA: A 6' length of aluminum tubing or PVC forms a good boom for the 1-boom LPDA. The dimensions at the end of this article are for elements that are well insulated and isolated from any conductor, including a boom. Therefore, the use of non-conductive plates to support the elements is essential. Fig. 7 shows the general layout.

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The sketch omits the usual U-bolts that connect the plate to the boom and the nuts and bolts that connect the elements to the plates. Please use stainless steel hardware throughout the assembly to avoid bimetallic electrolysis and hardware rusting.

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Every element in an LPDA is split, with a small gap at the center. As the sketch indicates, we can support the phase line on small pillars or blocks. At each element junction, we add very short jumpers to the element halves. On odd numbered elements, we use direct jumpers, while on even numbered elements, we use crossing jumpers. (Or vice versa.) This technique ensures that we reverse the phase line with each element while keeping the actual phase line straight and true. Since I am presuming the use of copper wire phase line materials, soldering the jumpers to the lines is wise, while screws or nut-and-bolt combinations attach the jumpers to the elements. Use stainless steel washers or a similar technique to prevent a copper-to-aluminum contact.

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At the forward end of the array, where the element density is high, the mounting blocks may suffice to maintain the spacing between phase line wires. However, at the rear end of the array, you may need to use thin spacers and perhaps glass tape to keep the line exactly spaced and parallel. In all cases, you may wish to seal the spaces and the jumper junctions with Plasti-DipTM or a similar product. Plasti-Dip is also handy for sealing the end of a length of coax soldered to the froward-most terminals or to seal the rear side of a coax connector that you attach to the front end of the boom.

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The original designs of the LPDA family used no rear shorting stub. However, you may attach one to the center of the longest element by extending the line and soldering its free ends together. The length of the line will vary from 1 to 6 inches in most cases. Construction variables will determine how long a stub to use. The stub will affect performance, including impedance, at the lowest frequencies of use, so select a line length that gives you the best operating and SWR performance. The stub is not necessary for operation of the array. However. it does place both sets of half-elements at the same potential, thereby reduce noise from static charge build-up on the elements.

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The 2-boom array: A twin-boom version of the LPDA family is certainly possible using techniques that I used on a 2-meter LPDA that appeared in QST a couple of years ago. There, I used U-channel for 3/16" rod elements. In these arrays, all elements are 1/2" aluminum tubes, so we need a variation on that technique. Incidentally, for the longest elements, using inner sections of 5/8" aluminum tubing, with outer sections of 1/2" diameter material will not affect overall performance, but may move the peaks and valleys in the performance curves to slightly different frequencies.

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Fig. 8 shows the basic ingredients of twin-boom construction using 1" square tubes. For each element, we drill through both sides of each tube with 1/2" holes. We mount each half element in a hole, alternating which half goes on top and which on the bottom. This mounting method ensures a phase reversal with each new element in the set. We can secure each tube in place with a sheet metal screw that penetrates the element. The screw heads go on the outside of the tubes, not on the sides facing each other. The heads would disturb the impedance of the phase line formed by the precisely spaced tubes.

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To space the tubes, we place periodic non-conductive plates along the twin-tube assembly, using either sheet metal screws or through hardware at each point. Use a plate on each side of the tubes to reduce stress on the plates. As well, use a stiff non-conductive plate to connect the booms to the mast. My personal preferences for all such plates is polycarbonate (also called LexanTM). However, other materials will also do the job if they are UV protected.

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At the front end of the array, at the forward-most elements, you will need to attach a length of coax (with common-mode current attenuating beads) or a coax connector for the main feedline. As with the 1-boom mode, Plasti-Dip or similar materials seal the connections.

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The 2-boom version eases the problem of making a reliable phase line, but involves more metal work and results in a heavier antenna. Which method you choose depends on available materials and your own skills. However, let's not make a choice until we see what a Yagi may have to offer to dual-band operation.

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The Road to a Yagi

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Because the Yagi array is by nature narrow band, with rarely more than about a 10% operating bandwidth, it tends to yield more gain per unit of boom length. However, we shall not quite make our 6' limit with the design that will follow. Essentially, the 6-meter portion of the array requires about 73.5" between the rear and forward elements for its performance. The upper-band forward-most director is at 79" from the 6-meter reflector. If we add a bit more for the boom-to-element assemblies, the length may end up about 82-84 inches long.

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The real challenge in creating a 2-band array is placing the elements so that the array performs well on both bands. As well, we need a technique to allow us to use a single feedline. The feed technique is some-times called direct feed, but I prefer the term "closed-sleeve coupling." Like open-sleeve coupling, used on many Force 12 HF beams, the two drivers are close enough together so the mutual coupling determines a good part of the effectiveness and impedance at the feedpoint on the upper band. However, rather than just using mutual coupling, we also use a short length of transmission line between the actual feedpoint on the longer driver and the shorter driver. Hence, we have a dual driver system, similar to that used on current production models of the Bencher Skyhawk and the HF series of arrays by Optibeam.

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The line that I specify in the model is 100-Ohms at a velocity factor of 1.0. To form this line, you can use short, thin, square bars of brass or copper. However, you can also press into service RG-62 coax at 93 Ohms. The line is so short that the performance of the array will not change significantly. Even 75-Ohm twin lead will work.

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In Fig. 9, we can see the general layout of the array. It uses 3 elements on 6 meters. The elements are set for very wide-band operation that covers all of the 6-meter band with about 7 dBi of free-space gain and an average front-to-back ratio of nearly 20 dB. We can get more gain from three elements on the boom size we are using, but I opted for a bit less gain and more operating bandwidth. The full beam dimensions--in model format--appear at the end of these notes. Once more, all elements are specified as 1/2" diameter. However, on the 6-meter elements, you can use inner sections of 5/8" diameter tubes. Likely the only needed change will be a slight readjustment of the 6-meter driver to obtain under 2:1 50-Ohm SWR at both ends of 6 meters.

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On 4 meters, we need more elements to make the beam work. I chose 4, although one might even make a case for 5. Fig. 10 shows why.

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If we examine the current magnitudes on the left portion of the figure, we can see a very large differential between current peaks on the longer 6-meter elements and the shorter 4-meter elements. However, the right side of the figure, for 4-meter operation, tells a different story. We see the peak currents on the short elements, but it is the longer ones that tell us about the design challenges. We might expect to see significant current on the 6-meter driver due to its direct connection to the feedline. However, notice that its curve has an odd shape compared to the curve we get when we use it on 6 meters, as the current tries to go to zero before it reaches the element end.

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The directors are our primary focus. The first 70-MHz director shows a very high current level and in fact operates somewhat as a slaved 2nd driver for the array. Even more interesting is the 6-meter director, which has very significant current on it, even though dominated by the 4-meter director immediately ahead of it. One could make a case for adding a director behind the 6-meter director to "capture" the mutual coupling from the preceding director. However, since the array provided adequate performance without the missing director, I omitted it. (The added director will broaden the bandwidth and slightly increase the front-to-back ratio. Since 4 meters is such a narrow band, I let construction simplicity outweigh these small improvements. However, if you decide to experiment by modeling the array with an added 70-MHz director just short of the 6-meter director, you should be aware that the new director will requires adjustments to the length and spacing of nearly every element in the array.)

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The following table provides the performance figures of the free-space model on both bands. I extended the limits of 4 meters to provide a sense of the operating passband on the higher frequency range.

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+                  Performance of the 7-Element 6/4-Meter Yagi
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+Freq.       Gain dBi          F-B dB            Feedpoint X       50-Ohm
+MHz                                             R +/- jX Ohms     SWR
+6 Meters
+50          7.14              16.3              41 - j 23         1.71
+51          7.06              20.1              46 - j 15         1.38
+52          7.09              21.4              50 - j  4         1.09
+53          7.24              19.9              54 + j 11         1.26
+54          7.49              16.6              59 + j 34         1.90
+4 Meters
+69.5        7.72              14.3              48 - j  9         1.19
+70          8.04              17.0              43 - j  4         1.18
+70.5        8.40              17.9              41 - j  0         1.23
+71          8.77              16.4              36 + j  1         1.40
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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For use only on the lower part of 6 meters, one may simply lengthen the 6 meter driver slightly to reduce the SWR in that region (and lose the upper end of the band). By changing only the driver length, we do not significantly change the gain and front-to-back along the band.

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Note that, on 70-MHz, the gain and front-to-back ratio together oppose the progression of impedance rather than paralleling the impedance. This fact--natural to a slaved-driver system--makes adjustment of the upper band a good bit more finicky than the lower band. Any wholesale change in element diameter on 4 meters will require complete re-design of the array. Nevertheless, once set up, the operating bandwidth on both bands is very good, as evidenced by the 50-Ohm SWR curves shown in Fig. 11.

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As well, the azimuth patterns for the array are quite well behaved, with patterns typical of a dual-band Yagi. See Fig. 12 for some representative examples.

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There are no special notes for construction of the Yagi, since it follows standard handbook practices. The modeled dimensions presume that the elements are well insulated and isolated from a conductive boom. Hence, the plate technique shown for the 1-boom LPDA is completely adaptable to the Yagi.

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However, mounting the array to a mast will present a challenge. The 6-meter driver and the surrounding 4-meter elements are at the center of the array. Rather than risk detuning the array--since the 4-meter elements are fairly sensitive--it may be better to place the boom-to-mast plate behind the driver assembly and to counter-weight the boom at the rear for balance.

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So, which way should I go?

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There are some who are drawn to LPDAs and some who are loyal to Yagis. Overall, on the two amateur bands, the Yagi is a slightly better performer, especially on 4 meters. However, it is also more sensitive on the 4-meter band and requires careful construction and field adjustment. The LPDAs should perform with no significant field adjustment except for finding the most desirable length of stub, so long as you use care in building the independent phase line for the 1-boom version. As well, the LPDAs provide good performance between the bands for receiving purposes.

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In either case, if you develop a flipping mechanism to orient either array vertically for use with the FM protion of 6 meters, be sure to use a non-conductive mast. When the elements are close to and parallel with a conductive mast, you likely will expience severe detuning effects.

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In the end, I shall leave the choice to your preferences. As well, there are undoubtedly many other antenna possibilities, including dual-band quads. Sometimes having too many choices can be worse than having none at all. . .

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Model Descriptions of Antennas Cited in These Notes

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1.  LPDAs:  Note:  Element half-lengths appear in the Y column, with element spacing
+(from the longest element) recorded in the X column.  All element lengths are tip-to-tip, and
+the center gaps are a part of the overall length.
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+50-70 8el t89 s06                            11/3/03     8:45:45 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 51 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,-60.221,      0                  0,60.2208,      0       0.5   25
+2                13.8096,-53.593,      0            13.8096,53.5926,      0       0.5   23
+3                26.0992,-47.694,      0            26.0992,47.6939,      0       0.5   19
+4                37.0362,-42.444,      0            37.0362,42.4445,      0       0.5   17
+5                46.7694,-37.773,      0            46.7694,37.7728,      0       0.5   15
+6                55.4313,-33.615,      0            55.4313,33.6154,      0       0.5   13
+7                63.1399,-29.915,      0            63.1399,29.9155,      0       0.5   13
+8                     70,-26.623,      0                 70,26.6228,      0       0.5   11
+
+Total Segments: 136
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       8        50.00      50.00    6        .70711      0         V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF  Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      1           50.00     50.00    2           50.00     50.00    Actual dist  150     1      R
+2      2           50.00     50.00    3           50.00     50.00    Actual dist  150     1      R
+3      3           50.00     50.00    4           50.00     50.00    Actual dist  150     1      R
+4      4           50.00     50.00    5           50.00     50.00    Actual dist  150     1      R
+5      5           50.00     50.00    6           50.00     50.00    Actual dist  150     1      R
+6      6           50.00     50.00    7           50.00     50.00    Actual dist  150     1      R
+7      7           50.00     50.00    8           50.00     50.00    Actual dist  150     1      R
+
+Ground type is Free Space
+===============
+50-70 10el t91 s05                           11/4/03     4:38:47 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 70 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,-60.221,      0                  0,60.2208,      0       0.5   25
+2                10.8784,-54.999,      0            10.8784,54.9995,      0       0.5   23
+3                20.8137,-50.231,      0            20.8137,50.2308,      0       0.5   21
+4                29.8875,-45.876,      0            29.8875,45.8757,      0       0.5   19
+5                38.1746,-41.898,      0            38.1746,41.8981,      0       0.5   17
+6                45.7431,-38.265,      0            45.7431,38.2654,      0       0.5   17
+7                52.6555,-34.948,      0            52.6555,34.9477,      0       0.5   15
+8                58.9685,-31.918,      0            58.9685,31.9176,      0       0.5   13
+9                64.7342, -29.15,      0            64.7342,29.1502,      0       0.5   13
+10                    70,-26.623,      0                 70,26.6228,      0       0.5   11
+
+Total Segments: 174
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       10       50.00      50.00    6        .70711      0         V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF  Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      1           50.00     50.00    2           50.00     50.00    Actual dist  150     1      R
+2      2           50.00     50.00    3           50.00     50.00    Actual dist  150     1      R
+3      3           50.00     50.00    4           50.00     50.00    Actual dist  150     1      R
+4      4           50.00     50.00    5           50.00     50.00    Actual dist  150     1      R
+5      5           50.00     50.00    6           50.00     50.00    Actual dist  150     1      R
+6      6           50.00     50.00    7           50.00     50.00    Actual dist  150     1      R
+7      7           50.00     50.00    8           50.00     50.00    Actual dist  150     1      R
+8      8           50.00     50.00    9           50.00     50.00    Actual dist  150     1      R
+9      9           50.00     50.00    10          50.00     50.00    Actual dist  150     1      R
+
+Ground type is Free Space
+
+===============
+50-70 12el t93 s04                           11/3/03     8:46:48 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 51 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,-60.221,      0                  0,60.2208,      0       0.5   25
+2                8.97321,-55.914,      0            8.97321,55.9139,      0       0.5   23
+3                17.3047,-51.915,      0            17.3047,51.9151,      0       0.5   21
+4                25.0403,-48.202,      0            25.0403,48.2022,      0       0.5   19
+5                32.2226,-44.755,      0            32.2226,44.7549,      0       0.5   19
+6                38.8913,-41.554,      0            38.8913,41.5541,      0       0.5   17
+7                45.0831,-38.582,      0            45.0831,38.5822,      0       0.5   15
+8                50.8321,-35.823,      0            50.8321,35.8229,      0       0.5   15
+9                56.1699,-33.261,      0            56.1699,33.2609,      0       0.5   13
+10               61.1259,-30.882,      0            61.1259,30.8821,      0       0.5   13
+11               65.7275,-28.674,      0            65.7275,28.6735,      0       0.5   11
+12                    70,-26.623,      0                 70,26.6228,      0       0.5   11
+
+Total Segments: 202
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       12       50.00      50.00    6        .70711      0         V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      1           50.00     50.00    2           50.00     50.00    Actual dist  150     1      R
+2      2           50.00     50.00    3           50.00     50.00    Actual dist  150     1      R
+3      3           50.00     50.00    4           50.00     50.00    Actual dist  150     1      R
+4      4           50.00     50.00    5           50.00     50.00    Actual dist  150     1      R
+5      5           50.00     50.00    6           50.00     50.00    Actual dist  150     1      R
+6      6           50.00     50.00    7           50.00     50.00    Actual dist  150     1      R
+7      7           50.00     50.00    8           50.00     50.00    Actual dist  150     1      R
+8      8           50.00     50.00    9           50.00     50.00    Actual dist  150     1      R
+9      9           50.00     50.00    10          50.00     50.00    Actual dist  150     1      R
+10     10          50.00     50.00    11          50.00     50.00    Actual dist  150     1      R
+11     11          50.00     50.00    12          50.00     50.00    Actual dist  150     1      R
+
+Ground type is Free Space
+=============
+50-70 14el t94 s03                           11/3/03     8:47:26 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 51 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                      0,-60.221,      0                  0,60.2208,      0       0.5   25
+2                7.63568,-56.556,      0            7.63568,56.5559,      0       0.5   23
+3                14.8067,-53.114,      0            14.8067, 53.114,      0       0.5   21
+4                21.5412,-49.882,      0            21.5412,49.8816,      0       0.5   21
+5                 27.866,-46.846,      0             27.866,46.8459,      0       0.5   19
+6                33.8058,-43.995,      0            33.8058, 43.995,      0       0.5   19
+7                39.3841,-41.318,      0            39.3841,41.3176,      0       0.5   17
+8                 44.623,-38.803,      0             44.623,38.8031,      0       0.5   15
+9                 49.543,-36.442,      0             49.543,36.4416,      0       0.5   15
+10               54.1636,-34.224,      0            54.1636,34.2239,      0       0.5   15
+11                58.503,-32.141,      0             58.503,32.1411,      0       0.5   13
+12               62.5783,-30.185,      0            62.5783, 30.185,      0       0.5   13
+13               66.4056,-28.348,      0            66.4056, 28.348,      0       0.5   11
+14                    70,-26.623,      0                 70,26.6228,      0       0.5   11
+
+Total Segments: 238
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       14       50.00      50.00    6        .70711      0         V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF  Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      1           50.00     50.00    2           50.00     50.00    Actual dist  150     1      R
+2      2           50.00     50.00    3           50.00     50.00    Actual dist  150     1      R
+3      3           50.00     50.00    4           50.00     50.00    Actual dist  150     1      R
+4      4           50.00     50.00    5           50.00     50.00    Actual dist  150     1      R
+5      5           50.00     50.00    6           50.00     50.00    Actual dist  150     1      R
+6      6           50.00     50.00    7           50.00     50.00    Actual dist  150     1      R
+7      7           50.00     50.00    8           50.00     50.00    Actual dist  150     1      R
+8      8           50.00     50.00    9           50.00     50.00    Actual dist  150     1      R
+9      9           50.00     50.00    10          50.00     50.00    Actual dist  150     1      R
+10     10          50.00     50.00    11          50.00     50.00    Actual dist  150     1      R
+11     11          50.00     50.00    12          50.00     50.00    Actual dist  150     1      R
+12     12          50.00     50.00    13          50.00     50.00    Actual dist  150     1      R
+13     13          50.00     50.00    14          50.00     50.00    Actual dist  150     1      R
+
+Ground type is Free Space
+===============
+2.  Yagi:  Note that the elements are grouped by band, with the 70-MHz elements shown first.
+Half-element lengths appear in the X column, with the spacing from the 6-meter reflector
+shown in the Y column.  All element lengths are tip-to-tip, and the driver gaps are a part of the
+overall length.
+
+6m/4m Yagi                                   11/3/03     8:49:13 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 70.25 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+(4-meter elements)
+1                  -41.5,   10.5,      0               41.5,   10.5,      0       0.5   21
+2                  -40.5,     34,      0               40.5,     34,      0       0.5   21
+3                  -38.7,   48.5,      0               38.7,   48.5,      0       0.5   21
+4                  -38.5,     79,      0               38.5,     79,      0       0.5   21
+(6-meter elements)
+5                  -58.4,      0,      0               58.4,      0,      0       0.5   31
+6                  -54.6,   40.7,      0               54.6,   40.7,      0       0.5   31
+7                  -47.9,  73.45,      0               47.9,  73.45,      0       0.5   31
+
+Total Segments: 177
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       6        50.00      50.00    16       1           0         V
+
+No loads specified
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF
+Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (in)        (ohms)
+1      2           50.00     50.00    6           50.00     50.00    Actual dist  100     1      N
+
+Ground type is Free Space
+
+ +
+

Updated 01-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Dec., 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index +

Topics: LPDA, VHF / UHF


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+

Route 66
+ 6-Meter 6-Element OWA Yagis in 9 Versions

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The low end of 6 meters has an appeal to many newcomers to the band and to amateur radio. In this region, communications is usually by way of CW or SSB with horizontally polarized beams operating point-to-point for everyday purposes and via skip during one of the band's many propagation phenomena. Unlike HF beams, Yagis for 6 meters have a reasonable size. One person can usually assembly, test, and install a 6-m beam with fewer worries about accidents or weather wreckage. As well, the smaller beam size reduces the cost of initial construction or repair. Although smaller than HF beams, 6-m Yagis are still large enough that the adjustments are less finicky than on 2-m or 70-cm versions. Hence, they make good projects for the less experienced builder.

+

Perhaps the one factor that inhibits home construction of 6-m beams is the builder's inability to obtain precisely the materials used in available designs in books and magazines. Although I would always recommend the use of 6063-T832 aluminum tubing (available from mail order sources such as Texas Towers and others), many first-time beam builders wish to obtain aluminum tubing from local hardware outlets. This tubing tends to have a slightly thinner wall thickness than 6063-T832. Hence, the fit from one size to the next is slightly looser than for the standard antenna material. However, it is otherwise serviceable and is durable for the light weight of 6-m beams. Given the ready availability of hardware outlet tubing, would-be builders want to translate published designs into their favorite local tubing size.

+

Of course, the process is fraught with dangers. Changes in element diameter create changes in the performance of any Yagi. With every change in the diameter of the elements, a Yagi requires redesign to re-optimize the performance. This requirement applies not only to the feedpoint impedance, but as well to the curves for gain and front-to-back ratio across a desired passband. There are some element-length adjustment programs available, but new builders usually are unaware of them.

+

So we have a quandary: how can we adjust the dimensions of a 6-m Yagi to suit local materials? The process is straightforward but daunting for the backyard builder. With a suitable antenna modeling program, we can adjust the element lengths and spacing to obtain the performance of an original design to match the proposed tubing size for the project. Since lack of building experience usually is matched by an equal lack of antenna modeling experience, we are no better off than when we started thinking about building a 6-m beam.

+

One Solution (of Many)

To ease the design process, I have taken a good design and performed the necessary redesign for a wide variety of tubing sizes. The basic design is a 6-element OWA Yagi, outlined in Fig. 1. The OWA design has some special features and limitations. The limitations apply to ideas one might have about modifying it. +
+ +
+

The 6-element OWA has a little over 10 dBi forward gain in free space. (Add 5-6 dB further gain depending on the height over ground.) At the center of the passband the front-to-back ratio is well over 20 dB, regardless of whether we use the 180-degree front-to-back or the worst-case front-to-back figure. To avoid complex matching structures with many metallic junctions that increase their losses due to weathering, the feedpoint impedance is 50 Ohms. Finally, the design is broadband, that is, has a wide operating passband. This last quality is very useful to the new builder who likely lacks equipment to finely tune a narrowband beam. Hence, the design tends to assure successful replication, even allowing for all of the construction variables that arise as we move from one builder to the next.

+

The design depends on the use of the first director as a secondary (non-fed) driver to broaden the operating passband. The system also allows the designer to center the peak gain and the maximum front-to-back ratio close to the center of the operating passband. The simultaneous centering of these properties also depends upon the 2nd and 3rd directors. As a result, you cannot shorten the beam simply by removing a forward director. All 6 elements operate in concert to produce the performance curves. So these notes are relevant only if you need a 6-m beam with a boom length from about 12.5 to 13.5 feet.

+

All of the design specifications in the following tables apply to elements that are well insulated and well isolated from a conductive boom. At the beam size we are considering, an aluminum boom seems most appropriate. Non-conductive materials are either too heavy or sag too much for effective use. Therefore, you will have to consider obtaining suitable tubing for the boom and plate material on which to mount the elements. We shall look at element mounting in more detail toward the end of these notes. However, the aluminum boom should have a diameter of 1.25" to 1.5" with a wall thickness of about 1/8" You can create such a boom from normal (0.58" wall) stock by placing the next smaller size tubing inside the size you decide to use. Since tubing normally comes in sizes that are less than the required total boom length (adding a few inches to each end to hold the element mounting plates), you can use a staggered construction method. Suppose that you want a 14' boom. Cut outer 1/16" wall tubing lengths of 4', 6', and 4'. Cut inner sections of 6', 6', and 2'. After thorough cleaning to allow easy nesting of the two tubing sizes, mate them and secure with a few stainless steel sheet metal screws in places where the elements themselves will not go. (We do not want the sheet metal screws to interfere later with the element mounting plates or their hardware.)

+

6063-T832 aluminum tubing has a standard wall thickness of 0.058" or slightly under 1/16" (0.0625"). Hence, it nests well when clean, with a good tight fit. 6061-T6 tubing tends to use tolerances that are not quite a rigorous as the other material. If you have trouble nesting two tubes in the boom, warm one and cool the other. The hot summer sun and an air conditioning vent are usually sufficient to remove binding. In winter, place the inner tube in the outdoor chill and the outer tube over a heating vent to achieve the same effect.

+

While we are considering boom-tube nesting, let's note that most hardware store tubing has a wall thickness of 0.050". Hence, the nesting of successive sizes will be looser. Although that may ease the nesting process, it will also reduce the boom's strength.

+

You can use a single tube with a 1/8" wall thickness. However, there are some materials to avoid for both the elements and the boom. Do NOT use electrical conduit. The material has 2 drawbacks. First, it is soft and will bend easily. That property is desirable for its primary application in protecting electrical house wiring. However, for a Yagi boom, the softness can be a disaster. Second, the material is unnecessarily heavy for antenna applications. There is no need to stress a rotator assembly more than the amount needed to achieve a certain antenna strength.

+

As well, avoid 6061-T6 pipe. The same material used to make some tubes is more readily available as fence or railing material. However, in this application, the material meets piping standards of measurement. A specified diameter is the nominal (or minimum) inside diameter, with the wall thickness added to arrive at an outside diameter. In most cases, the wall thickness is greater than 1/8", adding unnecessary weight to the beam.

+

Uniform-Diameter Element Designs

One typical request that I receive contains the builder's intention to use a single tubing diameter for all of the elements. The longest element in a 6-meter OWA Yagi is under 10' total. We can link 2 5' tubing sections at the center by adding a short section of the next smaller size tubing inside the junction. Thus we preserve continuity and maintain a uniform element diameter. We shall tackle the feedpoint questions later on. +

We shall look at tables of element lengths and spacings for uniform-diameter elements ranging from 3/8" to 1" in diameter. The tables will list the spacing values from the center of the rear element forward to the current element in the list. In fact, all spacing values are element-center to element-center. However, between element length and element spacing, spacing is the less critical. A spacing change of 1/4" will make no detectable difference to performance, but element lengths should end up as close as feasible to the listed value.

+

Element lengths appear in 2 forms for convenience. The half-length listing counts from the boom centerline outward to the element tip. The full-length listing goes from one element tip to the other. This method of measurement includes the driver. Since you will need to create a small gap in the driver for connecting the coax center conductor and braid, remove the material from the center without changing the tip-to-tip measurement. In effect, the true gap of an antenna is the spacing between the 2 conductors of the feedline. If you make a wider gap, then the leads from the coax or the coax fitting become part of the element. You will noeed only a quarter to a half inch gap in the tubing at the center.

+

Each table is actually 2 tables, one for dimensions and one for modeled performance. The design frequency for each beam is 51 MHz. Most horizontal Yagi activity on 6 meters occurs at the low end of the band. Many hams center the activity at about 50.1 MHz, while other cover the entire first MHz by centering the passband at 50.5 MHz. The beams in this collection will perform very well at 50 MHz. That is one reason for using a broadband design. However, you can scale the designs to a lower frequency by multiply the dimensions in the table by a proper amount. To center the passband at 50.5 MHz, multiple all element lengths and element-spacing values by 1.01. If you wish the performance peak to occur at about 50.1 MHz, multiply all length and spacing values by 1.018. In all scaling activities, we normally also use the multiplier on the element diameter. However, the 1% to 1.8% deficit in ideal tubing diameter will not affect performance in any way that you will be able to detect. As well, they fall within the range of normal construction variables, so you would not be able to tell the difference between a scaling error and some other kind of small variation during construction.

+

In fact, the designs are not optimized to the absolute limit. Rather, they are optimized to achieve the same performance curves and patterns, regardless of the element diameter--within the range shown in the tables. Fig. 2 shows the free-space azimuth patterns for 50, 51, and 52 MHz. Note the transition of the rear lobes across the operating passband. Although the patterns are for the 5/8" diameter element version of the beam, all of the versions show the same evolution of the rear lobes and the same clean forward lobe with no sidelobes. Sidelobes begin to emerge as an antenna grows to a boomlength of 1 wavelength or more. They also appear at the highest operating frequency of some shorter boomlengths if we press a narrow-band design into wider operation.

+
+ +
+

Fig. 3 gives us a broader picture of the forward gain and front-to-back ratio behavior of the antenna, again using the 5/8" element version as a sample of what is true for all of the versions. The forward gain curve looks steep, but notice the very small increment in the left-hand Y-axis scale. In fact, the maximum difference in gain across the 2-MHz passband is only 0.17 dB, an amount you could not detect in any kind of operation. Notice also that the peak value is within 0.25-MHz of the design center. That position is part of the reason for the very small change in gain across the passband. Other types of Yagi designs tend to show a rising gain curve across the entire passband, resulting in a much large total gain change from maximum to minimum.

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There are two blue curves, one labeled front-to-back ratio and one labeled front-to-side ratio. The front-to-back ratio curve is for the 180-degree front-to-back ratio. Since the forward lobe has no side lobes, the front-to-sidelobe ratio in EZNEC actually records the worst-case front-to-back ratio. In Fig. 2, notice the angled line in the rear lobe for 51 MHz. That is the program's way of recording the strongest lobe other than the main forward lobe--which for our beams is the worst-case front-to-back ratio. As you might expect, the ratio is lower than the 180-degree value. At the passband center, the value is still well above 20 dB. At the band edges, the two ratios are virtually the same, given the shape of the rear lobe(s). Note that there is a 0.25-MHz offset between peak gain performance and peak front-to-back performance. Both curves are well centered, but do not expect absolute perfection from a mere mortal designer.

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Fig. 4 provides a view across the entire passband of the feedpoint resistance and reactance, as well as the 50-Ohm SWR. These curves are typical for any OWA design. Because we are pressing the limits of the design, the SWR at the high end of the passband reflects the rapid decrease in feedpoint resistance. Below about 51.5 MHz, SWR values range from 1.1:1 to 1.3:1. Because the resistance drops rapidly above the final crossing of the 50-Ohm mark, we tend to design OWA Yagis for peak gain and front-to-back performance at a lower frequency, as shown in Fig. 3. Although the curves shown apply to the 5/8" diameter version of the beam, the curves for every size element are remarkably similar.

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The dimension table (Table 1) below provides the dimensions, with the guidelines for understanding them in accord with the notes near the beginning of the article. One facet of the dimensions not given earlier applies only to a few readers who may not be used to working with dimensions given as decimal inches. In the U.S., we typically work with rulers providing inch subdivisions in 16ths. Therefore, the following brief table provides a convenient conversion for moving the dimensions from the tables to your rulers. The differences will not make a difference to antenna performance.

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+Conversion of Decimal Inch Subdivisions to the Nearest 16th Inch
+   10th   0.1   0.2   0.3   0.4   0.5   0.6   0.7   0.8   0.9
+   16th   2     3     5     7     8     9     11    13    14
+         (1/8)                   (1/2)                   (7/8)
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The dimension table provides 6 different 6-element OWA Yagi designs centered on 51 MHz. Table 2 provides spot modeled performance values for each design. Note that in each case, the increasing element diameter results in a numerically noticeable but operationally insignificant improvement of gain at the design center. As well, each design centers the peak gain and peak 180-degree front-to-back ratio close to the design center. With increasing element diameter we also find that the total gain change across the band goes down. However, the band-edge front-to-back ratio tends to remain constant or dwindle just slightly. This phenomenon occurs because the element spacing remains fairly constant from the driver forward. As I noted earlier, the optimizing process ceased when each version of the Yagi with uniform-diameter elements achieved the desired set of curves.

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The SWR curves change shape slightly as the element diameter increases. The key factor in this process was keeping a relatively constant 50-Ohm SWR value at the upper edge of the passband. Since the beams become slightly more broadbanded with increasing element diameter, this factor brought the 51-MHz impedance values slightly closer to the last crossing of the resistance curve with 50 Ohms. As well, the driver and director 1 (the secondary unfed driver) do not change their relative lengths. Hence, the increasing spacing of the reflector can only go so far in yielding an ideal OWA SWR curve over the 4% passband. Nevertheless, for a large region on either side of the design frequency (51 MHz), the curves and numbers indicate excellent 50-Ohm performance.

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Stepped Diameter Element Versions of the 6-Element OWA Yagi

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For a variety of reasons--ranging from available materials to increased wind ratings--some builders prefer to use stepped diameter elements. Therefore, I created 3 variations on this theme. For each element, there is a 24" inner half element (full inner length = 48"). The remainder of the element, often called the "tip section," uses the remaining length of the half-lengths listed in Table 5 plus 2" for overlap (insertion into the inner section). Fig. 5 shows the general scheme for each element.

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The right side of the sketch shows 3 methods of pinning the element sections together. For most purposes, a pair of stainless steel sheet metal screws about 1/2" inward from the end of the inner tube and 1/2" from the limit of the inserted tip tube will provide a satisfactory junction with durable continuity. When constructing elements in this fashion, clean the mating surfaces well, but without materials that might inhibit electrical continuity. If you uses a scrubbing pad, you will have less chance of bi-metallic corrosion that might result from doing the same job with steel wool. Parasitic elements will use a continuous 48" section of inner tubing. We shall address the split driver and its gap in more detail in the final notes on construction.

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The tables will consider beams using the following combinations of tubing diameters: 1/2" inner with 3/8" tips, 5/8" inner with 1/2" tips, and 3/4" inner with 5/8" tips. Even minor cases of diameter stepping result in physically longer elements for the same performance as uniform-diameter elements. Therefore, using the reflector as an example, the fattest stepped diameter element requires a longer physical length than the thinnest uniform-diameter reflector. Diameter stepping also results in slight changes in the element interactions. Hence, the curves for the stepped-diameter versions of the 6-element OWA Yagis will show some subtle differences relative to those for the uniform-diameter versions.

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To sample the performance of the stepped-diameter Yagis, I used the mid-sized model with 5/8" inner sections and half-inch outer or tip sections. Fig. 6 provides 3 free-space azimuth patterns. In general, the 50- and 52-MHz patterns are virtually identical to those for the uniform-diameter models, but the 51-MHz design shows slightly less 180-degree front-to-back ratio. Because the front-to-back ratio at 52 MHz holds up better in this wide passband, I was able to slide the gain and front-to-back curves downward to achieve a 20-dB front-to-back ratio at 50 MHz. This move lowered the frequencies of both the peak gain and the peak front-to-back performance levels slightly. Hence, the deep (>30 dB) front-to-back ratio occurs slightly below the design frequency.

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Fig. 7 shows the gain and front-to-back curves for the same sample beam. You may compare the curves to those in Fig. 3 to see the slight differences from the uniform-diameter models. Despite the slight movement in the curves downward in frequency, the total gain change across the band is comparable to the change for the uniform-diameter versions of the Yagi. The overall 180-degree front-to-back curve is slightly flatter than the corresponding uniform-diameter element curves, but the band edges show slightly superior performance (although nothing that you could measure from on-the-air performance).

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To obtain the very good OWA-type performance curves for gain and front-to-back ratio, the SWR curves suffer slightly. The values for 50 and 51 MHz shows a decrease in 50-Ohm SWR as we increase the element diameters. However, the value for 52 MHz show increases with larger elements. However, the highest value modeled is comparable to the highest value modeled for the uniform-diameter elements. See Fig. 8.

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To scale the designs down to 50.5 or to 50.1 MHz, use the same factors applied to the uniform-diameter elements (1.01 and 1.018, respectively). Apply these only to the tip sections, leaving the inner sections at 24" for a half length (or 48" for a full length). In fact, a 1%-2% change in the length of the inner sections will make no noticeable difference to beam performance. Remember to scale the element spacing as well as the element lengths.

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Table 3 and Table 4 present the data on dimensions and on spot performance for the 3 stepped-diameter versions of the 6-element OWA Yagi. The dimensions confirm the relationship of stepped diameter element lengths to uniform-diameter versions. As well, the element spacing differs slightly, but grows at the same rate as for the uniform-diameter Yagis in this collection. The performance tables show the same general characteristics as their uniform-diameter counterparts.

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Along the way, we have covered aspects of beam construction, including the best materials, boom construction, and stepped-diameter element construction. We should add one more element to the notes, even though there may be almost as many construction methods as there are builders. I have strongly recommended that you insulate and isolate the elements from the boom. Direct connection has 2 major problems, even for parasitic elements. First, the boom represents a major swelling in the element diameter at that point, one that modeling cannot show. Therefore, directly connected elements must be refigured--as best possible--relative to the insulated/isolated elements shown in the designs. Second, directly connected elements tend to weather at the junction of boom and elements, ultimately resulting in increased noise on reception. Since most of the elements and element combinations in this exercise are too large for insulated through-boom construction, the use of a mounting plate for each elements is perhaps the best method for construction. Fig. 9 shows one good way to implement the scheme.

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The heart of the mounting system is a polycarbonate plate at least 1/4" thick. I have omitted exact length and width dimensions, since they will vary with the element size. To save a bit of weight, you may trim the plate corners. Each plate requires U-bolt holes for the boom fasteners. Although the sketch shows 4 U-bolts holding the element in place, 2 will normally do the job toward the long ends of the plate. The stainless steel U-bolts should all have saddles to reduce the chances of boom or element crushing and to increase the surface area in contact with the boom or the element.

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The version of the mounting system shown in the sketch applies to the split driver. Leave (trim) a gap (without changing the required tip-to-tip length) and insert a section of non-conducting material. The material may be a polycarbonate, Fiberglas, or PVC rod or tube. The insert does several jobs. It keeps the gap in place, especially when we add stainless steel through-bolts for connections from the coax cable or the connector. The insert also aligns the element so that a single pair of stainless steel element-fixing U-bolts will provide the required mounting. Finally, if we make the insert as long as the plate, it aids us in preventing element crushing.

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For uniform-diameter parasitic elements, simply bring the tubing ends together with a short section of the next smaller tubing diameter to form the insert and electrical link. Fasten the exposed tubing to the link insert with stainless steel sheet metal screws. If you use a continuous section of tubing--as you well might for the inner sections of stepped diameter elements--simply use great care not to crush the element under the stainless steel U-bolts.

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Did I mention that all metal hardware should be nothing less than stainless steel? Not only does it prevent corrosion, it also is largely immune to bi-metallic contact electrolysis.

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Well, there you have it: 9 versions of a 6-element OWA Yagi for 6 meters. Among the collection may be a design that you can build. However, if you want more or fewer elements, you are on your own. If you want a significantly different stepping schedule for the eleet diameters, you are also on your own. Even in these cases, the kinds of changes that occur from one element size to another might serve as resonable starting guides to your own efforts to use modeling software to create a custom design for your needs and your materials. Besides getting you on the air with a usable 6-meter beam of fairly considerable size, these notes have also tried to show by example some of what you can accomplish by designing antennas with a suitable modeling package.

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Addendum

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Since writing these notes, I have had several reports of successful construction, each one a bit different from all the others, embodying the special skills and preferences of the builder. Lenny Wintfeld, W2BVH, sent me some photos of his version. Fig. 10 shows the element-to-boom plate used while in the construction process.

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Fig. 11 gives you a good idea of the antenna size during the mounting process. The installers and the long boom 2-meter antenna provide a good perspective on the antenna.

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Your own 66 beam may differ in detail, but since this is not a commercial beam that you just assemble from supplied parts, you should be suitably proud of your own craftsmanship.

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Updated 05-01-2005, 10-20-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: VHF / UHF, Yagi


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Special Needs Call for Special Antennas: The X-Array

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L. B. Cebik, W4RNL

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Consider the following scenarios and Fig. 1.

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1. A repeater station is located on the coastline of a given area. The desired coverage area is inland, with no maritime activity.

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2. Another repeater station is located near or at the base of a hill or mountain. It suffers from reflected signals returning from the hill surface. The desired coverage area lies in front of the hill and to the sides of the repeater antenna site.

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3. A proposed repeater antenna site (and frequency allocation) lies close enough to another repeater's coverage area on the same or a nearby frequency to promise overlapping coverage and mutual interference. The new station desires an area of coverage that lies in the region not covered by the existing repeater.

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These samples of special needs have in common a very similar desired region of coverage, but very different reasons for wanting that coverage. We might nearly endlessly create other plausible scenarios to provide other avenues to the same need. In each case, we need at least a semi-circle of coverage, with extensions to the rear. However, we need to diminish the signal to the rear for at least 60 degrees either side of a hypothetical center line.

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We can, of course, design a complex array of multiple antennas to create the semi-circle-plus. However, if we can develop a single antenna to do the job, we obtain a maintenance advantage in terms of the mechanical and electrical simplicity of the installation.

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Notice that forward gain is not one of the criteria for the antenna installation. Anything close to the gain of a vertical dipole at an equivalent height would suffice. The major specification for this antenna installation--whatever the reasons behind it--is the pattern shape.

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The X-Array

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Steve Giess, a UK radio astronomer and experimenter in long-range TV reception, introduced me to an interesting commercial antenna from days past. The Antiference "Antex" antenna provided service for British 405-line television, channel 2, with the audio at 48.25 MHz and the video at 51.75 MHz. The antenna is vertically polarized. It is an X-array.

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I call it an array to distinguish it from various forms of X-beam that have been used in horizontal service in the amateur bands. Among the many forms are the full X, the Roman X, and the folded X-beam. (See "Modeling and Understanding Small Beams: Part 1. The Folded X-Beam," Communications Quarterly (Winter, 1995), pp. 33-50.) All of these design had relatively narrow operating bandwidths and only marginal performance levels to recommend them.

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The Antiference X-array stands vertically, with two shorter arms to one side and two longer arms to the other. See Fig. 2.

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As shown in the figure, we initially leave the center area of the array open, with no connection among the arms. Of course, in this pre-use condition, we also have no drive, so the antenna simply forms a big mechanical X.

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The initial British TV frequencies are close enough to the U.S. 6-meter band to allow for simple scaling. As well, the array may have application on 2 meters, so I adjusted the dimensions for that band as well. In the following table of dimensions--keyed to the designations in Fig. 2, the element lengths (LS for the shorter elements and LL for the longer elements) are calculated from the hypothetical crossing point of the elements. For the actual physical element, subtract .70" (18 mm) from each 6-meter element and 0.35" (9 mm) from each 2-meter element.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Scaled antiference X-array dimensions for 6 and 2 meters
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+6 Meters:  element diameter: 0.5" or 12.7 mm
+Dimension    HS          LS           HL           LL          W            SP
+Inches       74.8        52.9         81.9         57.9        78.4         1.0
+Millimeters  1900        1343.5       2080         1470.8      1990         25
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+2 Meters:  element diameter: 0.25" or 25.4 mm
+Dimension    HS          LS           HL           LL          W            SP
+Inches       27.6        19.5         29.9         21.2        28.7         0.5
+Millimeters  700         495          760          537.5       730          13
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Each beam is shorter than a vertical dipole for the frequency, but much wider, of course.

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The azimuth pattern for the array is oriented with the main axis in line with the X frame, with the weakest signal--the rear--on the long element side. Fig. 3 shows the general orientation of the pattern. Note that the pattern is very wide. In some options for interconnecting elements and feeding the array, the maximum gain is not in perfect alignment with the frame axis, but off set symmetrically to each side. However, the broad forward lobe is generally equal to or within 0.5 dB of maximum strength along the main aiming axis.

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What we derive from the X-array depends upon how we feed the antenna and how we interconnect the element centers. Fig. 4 shows us several options of interest, although the maker countenanced only the first two.

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In option A, the array forms a relatively standard driver-director array. The other two versions are free-space mirror images of each other. Whatever the selected option, the antennas cover the two amateur bands with under 1.5:1 50-Ohm SWR. To achieve the best patterns across the FM portions of the 6- and 2-meter bands, I used design frequencies of 52.5 and 146.5 MHz.

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In options B and C, shorting bars link three out of the 4 elements. A feedpoint link or wire connects the free element and the junction of the other two links. This ingenious scheme has some interesting consequences, as we shall see.

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The most ordinary configuration--the parasitic driver-director array--produces easily anticipated free-space patterns. The plots appear in Fig. 5.

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One of the disadvantages of the X-beam in horizontal service is the fact that the rear lobes are very large. This feature shows clearly in the "elevation" plot--actually the E-plane pattern for the array. However, this feature is no particular impediment to vertical service for the array over ground. Fig. 6 shows the azimuth and elevation patterns of the option-A version of the antenna at a center height of 2 wavelengths above average ground (37.5' or 11.42 m). The following table provides both the free-space and the over-ground performance of the array at the design frequency.

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+                   6-Meter Performance of the X-Array:  52.5 MHz
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+Option A Feed
+Parameter                Gain   TO Angle    Horiz BW     F-B Ratio    Feedpoint Z
+                         dBi    degrees     degrees      dB           R+/-jX Ohms
+Free Space               4.5    ---         204          8.4          65 + j 6
+2-WL Above Ground        7.3    6           204          8.2          65 + j 6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Options B and C, when modeled in free space, provide a lesson in modeling: do not always judge the performance of an antenna by its free space model unless you plan to use it in free space. Instead, verify its performance at the proposed height above real ground. Fig. 7 provides the free-space elevation or E-plane patterns for the X-array when connected as shown in options B and C in Fig. 4.

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We shall initially promise better performance over real ground than appears to be the case from the free-space patterns. However, the two patterns, although mirror images in free space, do not produce identical patterns over ground. Option B connects the lower long leg to the forward elements and yields a rearward free-space lobe that is--by graphical convention downward. Option C does the opposite, connecting the upper long leg to the forward elements and yielding a rear upward lobe. Over real ground, the rear lobes interact with the ground differently, producing differing amounts of rearward energy. As shown in Fig. 8, option C wastes considerable energy in high-angle rearward lobes, while the rearward portions of the option-B pattern are much better behaved. There is little wonder why the antenna makers countenanced option B but not option C.

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With respect to the forward lobes, there is little on the surface to choose between the azimuth patterns of either option. Fig. 9 provides the two patterns for comparison.

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However, there are--besides the matter of upward rear-lobe energy--some significant differences in the performance of the two arrays. The following table present both free-space and 2 wavelength height performance numbers for both options B and C.

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+                   6-Meter Performance of the X-Array:  52.5 MHz
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+Option B Feed
+Parameter                Gain   TO Angle    Horiz BW     F-B Ratio    Feedpoint Z
+                         dBi    degrees     degrees      dB           R+/-jX Ohms
+Free Space               2.7    ---         236          9.3          55 + j 9
+2-WL Above Ground        5.7    6           246          10.2         53 + j 8
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+Option C Feed
+Parameter                Gain   TO Angle    Horiz BW     F-B Ratio    Feedpoint Z
+                         dBi    degrees     degrees      dB           R+/-jX Ohms
+Free Space               2.7    ---         236          9.3          55 + j 9
+2-WL Above Ground        5.2    6           253          8.2          55 + j 8
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The free-space reports are the same in both cases. However, option B provides about a half-dB more gain along the axis of the array than option C. In both cases--as indicated by the blue and green line in the patterns of Fig. 9--maximum gain does not occur along the axis. In option C, there is a 0.8 dB difference between gain along the axis and maximum gain. That differential is under 0.5 dB for option B.

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In both cases, the forward gain over ground is less than for the option-A simple parasitic array. However, the horizontal beamwidth of both B and C is significantly wider, providing much smoother signal strength or reception sensitivity for a greater arc.

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Nevertheless, either option A or option B will provide quite good service is meeting the needs specified at the beginning of these notes. The rearward signal is down about 10 dB relative to a very broad forward signal area. As well, both will provide very good 50-Ohm SWR curves across the band, as shown in Fig. 10.

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Equally good are curves for the 2-meter version of the array. The 50-Ohm SWR curves appear in Fig. 11.

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However, in the process of optimizing the 2-meter design, I encountered a temptation that the designer should overcome. The change in relative element diameter to something fatter as a fraction of a wavelength required some adjustment of element lengths from their originally scaled values. The aim was to replicate as closely as possible the design frequency feedpoint impedances for both feedpoint options A and B. In the process, I obtained the following free-space performance values.

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+                  2-Meter Performance of the X-Array:  146.5 MHz
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+Free-space
+Parameter                Gain   TO Angle    Horiz BW     F-B Ratio    Feedpoint Z
+                         dBi    degrees     degrees      dB           R+/-jX Ohms
+Option A Feed            4.7    ---         160          20.1         61 + j 2
+Option B Feed            3.8    ---         186          19.5         50 + j 8
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The front-to-back ratios in both cases are superior to those of the 6-meter model. However, the horizontal beamwidth values are well down from the 6-meter values. In short, there is a price to pay for the added peak front-to-back values.

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From Single Frequency Design to Frequency Sweeps

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Since the ratio of gain and front-to-back ratio to the horizontal beamwidth of the array can make a difference to our design decision--given the initial premises for these notes--let's examine what happens to these parameters somewhat more systematically. We might begin by adjusting the dimensions of the 52.5-MHz array in its option-A, free-space version. The following table provides some steps in the evolution of the design working toward maximum front-to-back ratio at the design frequency.

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+                   6-Meter Performance of the X-Array:  52.5 MHz
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+Free-space
+Element Lengths          Gain         Horiz BW     F-B Ratio          Feedpoint Z
+LL / LS                  dBi          degrees      dB                 R+/-jX Ohms
+1471 / 1344 mm
+57.9 / 52.9 in           4.5          204          8.4                65 + j 6
+1471 / 1358 mm
+57.9 / 53.5 in           4.8          189          10.5               62 - j 1
+1478 / 1372 mm
+58.2 / 54.0 in           5.2          173          14.0               56 - j 4
+1492 / 1379 mm
+58.7 / 54.3 in           5.4          165          17.1               54 + j 1
+1499 / 1386 mm
+59.0 / 54.6 in           5.6          157          21.8               49 + j 2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Certain trends become obvious in the design process. Lengthening the director increases the gain and front-to-back ratio. In the process, the feedpoint resistance decreases, and so does the reactance. It is necessary to lengthen the driver to restore the near-resonant condition of the array. Small driver adjustments do not affect gain, but do slightly increase the front-to-back ratio.

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If we focus on the gain and front-to-back ratio alone, then the last set of dimensions in the sequence appears to be the best. However, that judgment is premature, given that one crucial parameter in the exercise is the -3-dB horizontal beamwidth of the array. As we raise the gain and the front-to-back ratio, the beamwidth diminishes--by 50 degrees over the span of the adjustments in the chart.

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For a given spot frequency (or repeater frequency pair, since the performance of the array does not vary significantly over a relatively small frequency span), we must reach a decision regarding the optimal combination of gain, front-to-back ratio, and horizontal beamwidth. That decision, of course, will rest upon factors outside the exercise itself.

+

We may explore the array properties in another manner: by taking selected performance readings at frequencies within the overall amateur band to which we might apply the array. Let's look at the first and the last steps in the design evolution and take modeled performance readings at each MHz marker in the 6-meter band.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            Free-Space 6-Meter Performance of 2 Versions of the X-Array
+
+Original Version:  LL = 1471 mm/57.9"; LS = 1344 mm/52.9"; Option A
+Parameter                50           51           52          53           54
+Gain (dBi)               3.5          3.8          4.2         4.8          5.5
+Hor. B/W degrees         280          247          218         189          161
+Front-Back dB            3.9          5.1          7.0         10.4         19.7
+Feed R+/-jX Ohms         54-j10       60-j1        65+j4       64+j6        53+j9
+
+Optimized Version:  LL = 1499 mm/59.0"; LS = 1386 mm/54.6"; Option A
+Parameter                50           51           52          53           54
+Gain (dBi)               4.0          4.5          5.2         6.0          6.2
+Hor. B/W degrees         231          202          172         143          118
+Front-Back dB            5.9          8.6          14.4        21.3         7.6
+Feed R+/-jX Ohms         61-j6        63-j2        57-j1       40+j9        26+j33
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

In the process of optimizing the gain and front-to-back performance of the 6-meter X-array, we managed to radically alter the SWR curve for the array across the band. Fig. 12 gives us a dramatic comparison of the 50-Ohm SWR curves for both the original and optimized versions of the array. Apart from any other parameter that we might question, the optimized version of the array is clearly usable only at spot frequencies, since the bandwidth for matching a 50-Ohm cable and obtaining the higher performance is considerably narrowed. Above the design frequency, the 50-Ohm SWR rises steeply. Below the design frequency, performance falls off rapidly.

+
+ +
+

Apart from the question of 50-Ohm SWR, the chart re-confirms that as we increase the gain and front-to-back ratio of the array, the optimized version loses 40-50 degrees of beamwidth. For a spot frequency, we may press optimization to the limit of whatever balance we have struck in terms of our need for both gain and beamwidth. However, if we need an array for full band coverage, we must accept a more modest set of performance figures with fewer radical changes across the operating passband.

+

In our initial evaluation of the design, we noticed that option B regularly produced a wider beamwidth than option A, despite option-A's ability to provide higher gain. It is worthwhile to see how those design frequency values work out in a full sweep of the 6-meter band. This time we shall use values taken at 2 wavelengths above average ground at a TO angle of 6 degrees.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 6-Meter Performance of 2 Versions of the X-Array
+
+Option A; Original Version
+Parameter                50           51           52          53           54
+Gain (dBi)               6.1          6.5          7.0         7.6          8.3
+Hor. B/W degrees         281          248          218         190          161
+Front-Back dB            3.8          5.0          6.8         10.2         19.1
+Feed R+/-jX Ohms         54-j10       60-j1        64+j5       64+j7        53+j10
+
+Option B; Original Version
+Parameter                50           51           52          53           54
+Gain (dBi)               5.7          5.9          6.1         6.4          7.3
+Hor. B/W degrees         270          262          252         236          199
+Front-Back dB            5.1          6.5          8.6         12.3         19.6
+Feed R+/-jX Ohms         44-j8        49+j0        52+j6       53+j10       48+j12
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Only at the lowest frequency of the band--below the region where vertical antennas are the norm--does the beamwidth of option A exceed that of option B. As well, the option-B rate of decline in beamwidth across the band is less than that of option A. The differential in gain favoring option A increases with frequency, a fact that tells us that the option-B gain is more stable across the band.

+

The consequences of the comparison are suggestive. For spot frequency use, a partially or fully optimized version A of the X-array may be most apt. However, for general coverage that includes a desire to sustain the pattern shape as well as possible, option B feeding offers the best choice.

+

These recommendations might hold for any band to which we might scale the X-array if the practicalities of antenna construction and durability allowed us also to scale the element diameter in a true fashion. However, for durability, 2-meter elements must generally be fatter than the true scale diameter. Therefore, for the 2-meter version of the X-array, we chose 0.25" (6.35 mm) diameter elements. Let's performance a sweep of the 2-meter amateur band to see what results we obtain for option A and option B with the array in free space.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 2-Meter Performance of 2 Versions of the X-Array
+
+Option A; Original Version
+Parameter                144          145          146         147          148
+Gain (dBi)               4.1          4.3          4.6         4.9          5.1
+Hor. B/W degrees         186          176          166         155          146
+Front-Back dB            11.0         13.4         17.1        24.8         26.3
+Feed R+/-jX Ohms         72-j3        69-j2        64+j0       57+j3        51+j8
+
+Option B; Original Version
+Parameter                144          145          146         147          148
+Gain (dBi)               2.8          3.1          3.5         4.0          4.4
+Hor. B/W degrees         224          210          194         178          162
+Front-Back dB            11.5         13.8         17.1        22.3         22.7
+Feed R+/-jX Ohms         55-j7        55+j7        52+j8       48+j9        44+j12
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 2-meter design, as presented, shows little difference between the two methods of feeding the array. The standard parasitic feed system in option A yields a little more gain, and the price of gain is a reduction in the beamwidth. For a spot frequency design, the selection between the two designs is a matter of the need for gain vs. the need for horizontal beamwidth.

+

More generally, the conclusion that emerges is that if beamwidth needs in excess of 200 degrees form a major criterion for the array, then the designer will have to reset the element lengths to decrease the array gain and store the wider beamwidth. The fastest route to this result is a reduction in the length of the shorter elements, with adjustments as needed to the driver to set the 50-Ohm SWR curve at an acceptable level across the operating passband.

+

Conclusion

+

The vertically oriented X-array, although not widely used in any service in the US, should not be forgotten. It offers a simple solution to special needs that may arise in repeater operations in the VHF range where beamwidth may sometimes be a major consideration. Perfecting the design to provide an acceptable level of gain, front-to-back ratio, and beamwidth is straightforward. The ingenuity of the Antiference designers in developing the alternative feed system that we have labeled option B provides further flexibility to the array and to the potential user. Etched into a substrate in miniature form, the array may even have applications above 500 MHz for a variety of situations calling for control of the beamwidth and smooth gain values across that beamwidth. The X-array is not for everyday use, but should not be forgotten when the special needs arise for which the antenna is well suited.

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+ +
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Updated 11-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for October, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: VHF / UHF, X Beam


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+

70-CM Yagi Stacks
+ Part 1: 10- to 40-Element DL6WU Examples

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+
+

L. B. Cebik, W4RNL

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+

The 2-part series on 2-meter Yagi stacks showed an interesting anomaly with respect to the optimal vertical spacing for stacked beams. The required spacing for maximum gain did not form a smooth curve. Instead, it displayed a region between about 1.8 and 2.2 wavelengths spacing, a zone I called the "forbidden zone." Regardless of the Yagi design and boom length, no gain peaks occurred with spacing in this region. The curve of gain vs. stacking space is generally flat in the region, with a small peak below the region for a shorter boom Yagi and a small peak above the region for longer Yagi. So there is a theoretical possibility that a hypothetical beam of just the right boomlength and number of elements might have two peaks of equal strength: one at the lower edge of the zone and one at the upper edge. However, most real Yagi designs do not happen to come in just the right combination of ingredients to display that possibility.

+

The so-called forbidden zone is actually a boon to Yagi stack designers. The level and near-peak gain that exists in this region makes physical stack design less critical. Indeed, for arrays like the DL6WU design--where the front-to-back ratio varies considerably with the addition of each new director--the builder can choose the spacing within the zone that yields the highest front-to-back ratio and still be very close to peak gain for the stack.

+

The 2 series of Yagis tested in the stacking exercises--the OWA and DL6WU designs--limited the maximum boomlength to between 5.2 and 5.4 wavelengths, a little under 11 meters and a little over 35'. This length region exceeds the practical limit of 2-meter Yagis for almost all stack builders. Nevertheless, some questions remain about the forbidden zone, questions that we can only answer by trying longer boomlengths. Perhaps the most outstanding question is whether there are additional forbidden zones as we increase the size of the Yagi as a function of both the boomlength and the number of elements. To remain within the realm of the nearly practical, I shifted the frequency range to the 70-cm band. The 420-450-MHz band allows beams with up to 40 elements and 14 wavelength booms in the same space that our 18-element 2-meter Yagis occupied.

+

The change in band also requires a few changes in the procedure for the NEC-4 modeling exercise. 4 mm is a popular element size in Europe, and the DL6WU 70-cm Yagis initially used this element. At about 0.1575", it falls between the common US rod diameters of 1/8" and 3/16". However, relative to a wavelength, 4 mm represent an element that is nearly 3 times larger than the 3/16" elements used in the 2-meter beams.

+

For DL6WU designs, as calculated via the program dl6wu-gg.exe, element spacing remains unchanged, regardless of the element diameter. The arrays are sufficiently broadbanded that optimizing spacing for changes in the element diameter is unnecessary to produce a successful beam. Still, the change in element diameter does alter the inter-element coupling to a degree for which simply adjusting all element lengths cannot compensate. The most evident results will be changes in the pattern of front-to-back peaks and 50-Ohm SWR dips across the band as we change element diameter and recalculate the elements for the same boomlength.

+

Changing the modeling frequency also necessitates another change of procedure. It was possible at 2 meters to set the beams at a base height of 5 wavelengths above average ground. By setting the elevation plot increment to 0.1 degree, we obtained quite accurate forward gain reports for the main lobe of the radiation pattern. As well, the height of about 35' or 10.5 meters was realistic for numerous installations.

+

As we increase the height of an array, we increase the number of elevation lobes, and each lobe is correspondingly narrower. If we place the antenna too high above ground, as measured in wavelengths, the lobes can grow so vertically thin that even 0.1 wavelength increments of elevation can miss the peak gain of the lowest lobe. We encounter precisely this situation in raising the design frequency to 432 MHz. 35' represents about 15 wavelengths above ground in the 70-cm band. To obtain the same resolution as we obtained on 2 meters, we would need an elevation increment no greater than 1/3 the value used on 2-meters, with consequential increases in the run time for each model at each trial stack spacing.

+

Any Yagi design that we use at 432 MHz will employ 11 models ranging from 10 to 40 elements for each of the 2 Yagis in the stack. (The sequence of models--for convenience--will use the number of elements as markers, resulting in models having 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, and 40 elements.) To conserve overall run-time, I shall place all models in free space. The gain adjustment for placement over ground is just under 6 dB. With all models in free space, we can obtain all of the necessary information from a single azimuth pattern using pattern increments of 1 degree.

+

The procedure carries with it one limitation. In the 2-meter sequence, we saw that the difference between a free-space environment and placement over ground resulted in a shift in peak-gain spacing for one model on the fringe of the forbidden zone. The 12-element OWA model showed optimal stack separation at about 1.65 wavelengths 5 wavelengths above ground but at about 2.35 wavelengths when in free space. The actual difference in gain between the two separation values is small in both cases. Nevertheless, this phenomenon should be kept in mind when evaluating the results of this study.

+

Selecting a Yagi series for this 70-cm study initially presents no problems. Although there are no OWA designs beyond 20 elements, the DL6WU series of Yagis has no practical limit other than a physical limit specified by the builder. Hence, the extended study of 2-stack separation reasonably begins with this classic set of Yagi designs.

+

Notes on Long-Boom DL6WU Yagis for 432 MHz

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All DL6WU designs used in this study emerge from the program dl6wu-gg.exe. As noted in the 2-meter study, we only need a single set of dimensions, the ones for the longest version of the beam series. In this case, the limit is 40 elements. Table 1 presents those dimensions for an element diameter of 4 mm. The dimensions appear in millimeters, inches, and wavelengths.

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The longest boom in the set is just over 14 wavelengths (about 31.9' or 9.73 meters). The shortest version of the Yagi set, at 10 elements, falls within the boomlength range countenanced by the program. Each trial version of the antenna adds 3 elements, so there are 11 total Yagis in the set. The study uses the number of elements as its baseline in order to yield a linear X-axis scale for all graphs. However, the boomlength does not increase linearly because the impedance-setting core and early directors of the design do not increase the length in a linear manner. Since the gain is a function of boomlength rather than the number of elements, gain does not increase in a linear manner with the number of elements. Fig. 1 shows the 432-MHz free-space gain range for the test series of Yagis in terms of their single-unit performance.

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The DL6WU series of Yagis becomes ever more stable in performance as we increase the boomlength and the number of elements. Table 2 supplies the free-space performance values for the set of trial designs, and includes values for both the vertical and horizontal beamwidths and sidelobe ratios. The beamwidth values will become significant later when we compare the calculated stacking spacing values to the modeled values. The front-to-sidelobe ratio is the differential between the main forward pattern lobe and the strongest forward sidelobe.

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In conventional Yagi designs, sidelobes form at a rate of about 1 forward and 1 rearward--each side of the beam's centerline--for every wavelength of boom. Fig. 2 shows representative patterns for the 10-, 25-, and 40-element versions of the DL6WU Yagi. The corresponding boomlengths are 2, 8, and 14 wavelengths. As an idle-time activity, you may wish to count both the forward and rearward sidelobes and obtain the rerquisite number for each category. However, the actual count may require an enlargement of the pattern and a finer pattern increment, since the lobes very close to 90 degrees off axis are very small and narrow, especially in the E-plane.

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Because the front-to-sidelobe values do not form a consistent curve, we may for reference take their average values. The average horizontal sidelobe ratio is 17.7 dB, while the average vertical sidelobe ratio is 14.7 dB. Of course, in free-space, the notion of horizontal applies to the antenna's E-plane, while the idea of vertical applies to the H-plane, as if the antenna were horizontally polarized over ground. Fig. 3 provides a more detailed graphical look at the front-to-sidelobe ratio values. From 10 to 19 elements (2.1 to 5.6 wavelength booms), the horizontal and vertical sidelobe ratios almost form inverse curves. However, above 19 elements, both curves show a decreasing front-to-sidelobe ratio.

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The DL6WU Yagi series uses an impedance-setting cell with relatively wide spacing to establish a native 50-Ohm feedpoint impedance for direct feed. The reflector-driver spacing is 0.20 wavelength, and the driver-director-1 spacing is 0.075 wavelength for all versions in the trial series. The result is a very wide operating passband, relative to the usual 2:1 50-Ohm SWR standard. Although the impedance column of Table 2 shows some variability of the 432-MHz impedance, especially with shorter boomlengths, the SWR curves for the entire set of designs shows a lower limit just above 405 MHz and and upper limit just under 460 MHz.

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Fig. 4 displays SWR curves for the first 4 Yagis in the series. Note that within the extended passband of the design, the number of dips in SWR value increases from 3 to 6 between 405 and 460 MHz. These dips are a function of the undulations in both resistance and reactance at the feedpoint. As we increase the number of elements, the frequency increment between dips decreases. At the lower end of the specturm, adding elements tends to force the first dip higher in frequency, while the higher-end dips compress in frequency spacing before disappearing. At the low end of the spectrum, when the former first dip is too far from the passband edge, a new dip forms. Since the frequency span between SWR dips is larger at the lower end of the operating passband, the "new dip" formation is easier to see.

+
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Fig. 5 shows the SWR curvers for Yagis with 22 through 40 elements. The ratio of the longest boom to the shortest in this set is similar to the boomlength ratio for the first 4 Yagis in the set. However, the entire set shows only 6 or 7 dips, depending upon boom length. Still, the set of curves does show clearly the gradual compression of passband space between dips and the development of a new lower-end dip.

+

To graphically illustrate the wide-band performance, we may examine for reference graphs of free-space gain and 180-degree front-to-back performance for each of the Yagis in the trial series. Fig. 6, Fig. 7, and Fig. 8 present the relevant graphs in clusters to permit easier reproduction.

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Perhaps the only non-undulating set of wide-band values occurs in the category of forward gain. Table 3 presents the gain behavior data for the set of trial designs. It lists the peak gain and its frequency, along with the differential between the peak gain and the design frequency (432 MHz) gain.

+
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Note that there is a changing value for the frequency of peak gain for each size beam. That value drifts upward, although not in a fully consistent manner. Fig. 9 translates the tabulated data into graphical form, showing the curves for peak and design-frequency gain. The right-hand Y-axis provides the values for the third curve--the differential between peak and design-frequency free-space gain.

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Much more undulating are the data sets for 180-degree front-to-back behavior. These data are more intrinsically connected to the changes in feedpoint resistance and reactance. Hence, as the data in Table 4 show, they are subject to the same compression phenomena as the SWR curves. The pattern is a bit different from the pattern shown by the SWR curves. If we increase the number of elements and boomlength, the lowest peak varies in frequency, with the other peaks growing closer to the first peak. New peaks appear at the upper end of the passband. The tabulated pattern shows remarkable consistency.

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The general trends among the test versions of the DL6WU Yagi apply to designs of similar boomlengths. However, there will be variations in details as we change the element diameter. Those changes are evidence of the remnant differentials in inter-element coupling that are not removed by changes in the element spacing.

+

2-Stack Data

+

We have lingered over the properties of the extended family of DL6WU Yagis for 2 major reasons. First, the 2-meter study displayed only a limited subset of the total family. The 70-cm models provide a wider view of the family's fundamental characteristics. Second, the main focus of this study--the 2-stack behavior of the Yagis--rests upon an understanding of the single-unit performance for each change in the number of elements and the boomlength.

+

The 2-meter study examined at some length the patterns of front-to-back undulations that occur with changing values of stack spacing. The present study cannot add significantly to that account, however incomplete it might be from an explanatory perspective. What the 70-cm exercise can do is to explore in some detail the question of whether there may be additional forbidden zones as we expand the range of Yagi sizes and the consequential stacking space values.

+

With the exception of restricting data to free-space values, the procedure for determining the optimal spacing for maximum gain of a 2-stack at 432-MHz was the same as used in the 2-meter study. The increment for each trial was 0.1 wavelength. Table 5 lists the output of those trials. In some cases, the spacing is listed as n.n5 wavelengths. This notation indicates that two adjacent spacing values yielded the same maximum gain value. Hence, the average is listed. However, the associated front-to-back value is for the lower of the two heights.

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The notations "flat up" and "flat down" indicate that, above (up) and below (down) the optimal maximum gain spacing, the gain remained almost constant for a considerable range of spacing values. The "flat" gain value was rarely more than about 0.05 dB lower than the peak value. The existence of these flat regions strongly suggests that there are multiple forbidden zones. Fig. 10 shows the maximum stack gain and compares it with the gain for a single unit at the design frequency. The increase, as shown in the tabular data, is remarkably consistent across the range of boomlengths, running between 3.12 and 3.16 dB.

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A more vivid portrait of the modeled optimal (maximum-gain) stacking space values appears in Fig. 11. The 3 separate forbidden zones or spacing-value jumps appear between 10 and 13 elements, between 19 and 22 elements, and between 34 and 37 elements. As a function of the number of elements, the large steps make little intuitive sense. As well, if we examine the associate values of free-space gain values, the steps lack a sense of intuitive order. However, if we look at the median boomlength values, we find values approximating 3, 6, and 12 wavelengths for the three steps. Then, if we look at the median spacing value in the forbidden zones, we obtain the (approximate) sequence of 2, 3, and 4 wavelengths. Although one can create a progression from these pairs of values, the basic values are too crude to permit anything but speculation. Hence, we shall have to content ourselves with only the pattern at present.

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Also evident from Fig. 11 is the fact that the modeled values of optimal stack spacing for maximum gain far exceed the standard calculations of those values. Table 6 provides the data behind the graphed lines.

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The RSGB equation comes from The VHF/UHF DX Book, page 7-8.

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Dopt = lambda / (2 sin (phi / 2))

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Lambda is a wavelength in any desired unit of measure, and phi is the relevant half-power beamwidth of a single antenna unit in degrees or radians, as preferred. Dopt is the optimal distance or spacing between Yagis in the same unit of measure as specified for lambda. The dl6wu-gg.exe calculations are based on lines 2630 to 2710 of the original program (in pre-compiled Basic):

+ 
+2630 BH = 30 - 3.14 * (G1 - 14)  'Correlation from published patterns of DL6WU yagis
+2640 PRINT #1, USING "        Horizontal beamwidth = ##.# deg"; BH
+2650 BV = BH / COS(BH / (2 * 57))  'Over-estimates BV for shorter yagis
+2660 PRINT #1, USING "          Vertical beamwidth = ##.# deg"; BV
+2670 SH = 51 / BH
+2680 PRINT #1, "      Suggested stacking distances for 2 yagis:"
+2690 PRINT #1, USING "                  Horizontal = #### mm = ###.# inches = #.## wavelengths"; SH * MM; SH * INCH; SH
+2700 SV = 51 / BV
+2710 PRINT #1, USING "                    Vertical = #### mm = ###.# inches = #.## wavelengths"; SV * MM; SV * INCH; SV
+
+

BH and BV are the horizontal and vertical beamwidths for the calculated Yagi design. The horizontal beamwidth derives from published DL6WU design patterns, and the vertical beamwidth is calculated as a simple function of the horizontal beamwidth. The calculated estimates of spacing are them simply 51 / beamwidth for the horizontal and the vertical cases. Both the vertical beamwidth and the stacking distance formulas used in dl6wu-gg.exe are ad hoc developments from small bits of apparent emprical experience.

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The simplified calculation of stack spacing within dl6wu-gg.exe produces the smallest values. The RSGB equation produces larger values. However, neither set of computations comes appreciably close to the modeled values. This condition applies whether we examine 2-stacks over ground--as in the 2-meter study--or stacks in free-space--as in the present exercise. Moreover, neither system of calculation predicts the forbidden or "no-peak-gain" zones or describes their location in terms of boomlength or spacing values. Nonetheless, the repetition of the zones through 2 series of 2-meter beams and this extended 70-cm study produces a consistent body of modeling results that appear both in free-space and over-ground environments.

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A Special Note on DL6WU Yagi Element Calculations

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The program dl6wu-gg.exe is readily available from the website maintained by Ian White, G3SEK. See "Technical Notebooks". The information focuses on VHF/UHF and contains important antenna, filter, moonbounce, and circuitry data. Ian writes the highly respected monthly RadCom "In Practice" column. The program for calculating DL6WU elements is in a ZIP file that includes the compiled program that runs under DOS and a text (.txt) file containing the original Basic code for the program. The latest revisions appear to have been made in 2003. Lines 1369 through 1547 contain the element calculations in conjunction with data from lines 2100 to 2220.

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The element spacing in the program is a frozen set of data values. Hence, only the element lengths are adjusted for differences in diameter. There are also adjustments for direct contact with metallic booms and for insulated through-boom construction. For these note, the dimension presume a non-conductive boom or elements that are well insulated and isolated from the boom. When you add the log functions that determine element length taper along the boom to the adjustment factors, the resulting equations are beyond the discussion scope of these notes, but readily accessible in the program.

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The standard DL6WU Yagi uses a reflector-to-driver spacing of 0.20 wavelength, with a driver-to-director-1 spacing of 0.075 wavelength. These values are not the only ones possible. David Tanner, VK3AUU, has developed an alternative design program for DL6WU beams using a different set of element spacings in the impedance-setting cell. His reflector-to-driver spacing is 0.183 wavelength, with a driver-to-director-1 spacing of 0.081 wavelengths. As a consequence, his element spacing and element length algorithms differ somewhat from those in dl6wu-gg.exe. Fig. 12 provides a comparison between his values and those of dl6wu-gg.exe for Yagis up to 40 elements for our exercise design frequency of 432 MHz, where a wavelength is about 694 mm. The tables in the graphic are aligned so that the differing element designations create minimal confusion. As well, VK3AUU's dimensions are in centimeters, while the dl6wu-gg.exe-derivatives are in millimeters.

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The differences in overall boom and element lengths are small, but not wholly insignificant, especially for elements closer to the impedance-setting cell. The calculations are available in an Excel spreadsheet. For further information, contact David Tanner, Korumburro Road, Drouin South 3818, Australia, or (via e-mail) at vk3auu@vic.australis.com.au.

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Conclusions

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Extending the study of long-boom Yagi 2-stacks to 40 elements and 14 wavelengths of boom, while using a wholly different element diameter, has achieved several suggestive modeling results.

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1. The new set of DL6WU Yagis confirms the modeled 2-meter forbidden zone found in the vicinity of a 3 wavelength boom and a stack space of 2 wavelengths.

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2. The extension of the Yagi series to boomlengths of 14 wavelengths uncovered 2 more forbidden zones, one with a 6 wavelength boom and a spacing of 3 wavelengths, the other with a 12 wavelength boom and a spacing of 4 wavelengths (approximately).

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3. The modeled optimal stacking distances for maximum gain considerably exceed values produced from earlier techniques for estimating the value of Dopt.

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The extensive examination of the properties and characteristics of the DL6WU series of Yagis represented a necessary pre-condition of ascertaining that the series form a sufficiently reliable sequence to validate the results, at least in terms of NEC-4 modeling output. Indeed, the DL6WU series of Yagis is worth investigation as not only a classic design scheme, but also as an opening into understanding Yagi properties in general. Especially significant are the design criteria in terms of what parameters are held to close tolerances (for example, feedpoint impedance, operating bandwidth, and maximum gain). Equally important are parameters allowed to seek their own values or to undulate, such as the feedpoint resistance and reactance and the 180-degree front-to-back ratio. Since the question most asked about 2-stack spacing concerns maximum gain, the reliability of the maximum gain point relative to the design frequency and the repeatability of that relationship from one boomlength to the next qualified the DL6WU series as a reasonably reliable indicator of 2-stack spacing behaviors.

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For the more limited 2-meter study, we examined at least 2 Yagi design series--each having different design criteria--in order convert an initial finding into something suggestive of general stack behavior. We owe it to the study of longer Yagis to do the same. The generalized question is whether or not--for some other sequence of Yagi designs--the forbidden zones will appear with the same boomlengths and the same stack spacing. Since finding a suitable Yagi design sequence is half the battle, we shall have to await part 2 to see what emerges.

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Updated 09-01-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: 10- to 40-Element VK3AUU Examples

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Go to Main Index

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Topics: Stacking, VHF / UHF, Yagi


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70-CM Yagi Stacks
+ Part 2: 10- to 40-Element VK3AUU Examples

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L. B. Cebik, W4RNL

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Part 1 of this study of stacked 70-cm Yagis explored the properties of DL6WU beams ranging from 10 to 40 elements or 2.15 to 14.0 wavelengths of boom. After looking extensively--but incompletely--at the properties of single units, we found that 2-stacks exhibited an interesting characteristic hinted at by the earlier 2-meter study of shorter-boom Yagi stacks. The so-called forbidden zone of spacing distances between Yagis in the stack proved to be periodic. It occurred with boomlengths of approximately 3, 6, and 12 wavelengths and stacking space values of about 2, 3, and 4 wavelengths, respectively.

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Redoing the work with a different Yagi series is a necessary condition of transforming a characteristic of a particular Yagi series into a more general characteristic of long-boom Yagis. If the same characteristic appears with a second Yagi series--especially if the design principals differ from those applied to the first series--then the characteristic is most likely more general. However, re-appearance of the characteristic is not a sufficient condition of total generality. Rather, the results are suggestive and perhaps even usable in the form of expectations of Yagis in general.

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At the same time, study of a second Yagi series opens the way to seeing in what ways the characteristic may change form as the beam design principals vary. Lack of change is not a certification that the characteristic does not change for any Yagi design series. However, the presence of change might offer suggestive insights into the characteristic pattern of the so-called forbidden zone phenomenon.

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Critical to the extended study is the selection of a suitable second Yagi design series. The OWA series of Yagis used in the 2-meter study has not been extended beyond 20 elements. Hence, that series is out, despite the intersting design facet of very low forward side-lobe strength and even the disappearance of some sidelobes. I also have on file an old long-boom Hy-Gain model for 432 MHz, reportedly based on a Joe Reisart, W1JR design. Unfortunately, the maximum length available to me is 32 elements. Although I can shorten the design, I do not have the algorithms for lengthening it to 40 elements.

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Another possible series is the product of Steve Powlishen, K1FO. This series has appeared for many editions of The ARRL Antenna Book, and appears on pages 18-28 through 18-40 of the 20th edition. The original design algorithms appear in QST for December, 1987, and January, 1988. Hence, the work is nearly 20 years old. One drawback to the use of this series is that the element lengths require adjustment as one uses the beam in specified lengths. Moreover, boom lengths are almost the same as those used in the DL6WU series. A 40-element 432-MHz K1FO design has a boomlength of 9360 mm, compared to a boomlength of 9726 mm for the same number of elements in a DL6WU design. The K1FO impedance-setting cell is designed for an inherently lower feedpoint impedance--perhaps close to 30 Ohms--with the intention of using a Tee match and balun.

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Perhaps a better choice for extending the study of 2-stack behavior in long-boom Yagis is a design that, for for any given number of elements, ends up with a boomlength that differs from the corresponding DL6WU design. David Tanner, VK3AUU, was noted in the previous episode of this study for his variant design algorithms for DL6WU-type Yagis. Why we might call these Yagis DL6WU variants rather than a distinct Yagi series involves a number of Yagi features. First, the elements form a continuous length taper defined by the design algorithms. Second, for any set number of elements, the boomlength will be very close to the length of a standard DL6WU Yagi. Distinct long-boom Yagi designs tend to vary one or the other of these properties. The overall length may differ for a given number of elements. Alternatively, the element taper may differ from the steady rate of shortening of new directors. Some designs show pairs of equal-length elements periodically in the director series. Other designs have shown up to 4 equal-length directors occurring periodically in the sequence. A third reason for treating the VK3AUU series as a DL6WU variant is that this is the way in which VK3AUU has labeled this part of his work.

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However, VK3AUU also shared a different Yagi design that deserves more attention from US builders than it appears to have received to this date. The design effort arose out of a desire to exert more control over the Yagi properties, while simultaneously limiting the boom length to about 8 meters. The original design used 42 elements in the 8-meter space with 1/8" (0.125" or 3.175 mm) diameter elements. This beam seemed appropriate as the foundation for the present study, but with a few modifications for more direct comparison with the DL6WU series presented in Part 1.

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VK3AUU 432-MHz Beam Characteristics

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In order to make sense out of the results of stack modeling in NEC-4, it is first necessary to understand the properties of the VK3AUU 432-MHz design. In fact, what we shall examine is an unauthorized variation of the initial design that first enlarges the element diameter to 4 mm, to coincide with the element diameter used by the DL6WU series of Yagis. The process of re-sizing the beam also involved returning the feedpoint impedance to very close to 50 Ohms. The result tends to displace the gain peak slightly, since in the original version, the gain peak occurred at the design frequency.

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Table 1 shows the dimensons of the altered design up through 40 elements. Although not expressly countenanced by the designer, the beam is amenable to trimming by the removal of directors and no other changes. Hence, from the chart, we may also derive and create models of beams with 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, and 40 elements for use in our stacking survey.

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As with the DL6WU Yagi series, this exploration will confine itself to free-space models. Regardless of Yagi design differences, the new Yagi series suffers the same modeling limitations as the earlier series. A 70-cm wavelength is short enough that placing the antenna at a reasonable height above ground--say 30' to 50'--requires a very small increment of elevation angle change in the pattern readout in order to accurately capture the maximum gain of the lowest lobe. The use of free-space patterns allows data extraction with 1-degree intervals in the pattern, reducing the time required for each trial stacking separation value. For gain over ground, add nearly 6 dB to the free-space values to obtain the corrected figure.

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Table 2 lists the free-space performance of single VK3AUU nits for each boom length and number of elements. The table contains the same information that we gathered for the DL6WU series, so you may directly compare the entries for each increment of element numbers.

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As we raise the number of elements, the gain rises smoothly, but, of course, not linearly, and for the same reasons that apply to any Yagi series. See Fig. 1. Gain is largely a function of boomlength and not the number of elements. The DL6WU series used a constant space between directors from the 10th onward. However, the VK3AUU series alters the director spacing as well as the director length for each new forward element. The corresponding DL6WU gain values appear on the graph for reference.

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The gain values achieved by the VK3AUU Yagis for any given number of elements are lower than for the corresponding number of elements in a DL6WU array. That fact results from the shorter boomlength used by the VK3AUU series. Fig. 2 compares boomlengths for each increment of element numbers in both series. The VK3AUU boomlength averages about 0.75 of the DL6WU boomlength, but varies from about 71% at 13 elements to about 77% at 40 elements.

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The boom lengths for the 2 series of Yagis do not coincide for the samples except occasionally. However, the few cases in which boomlengths roughly correspond do confirm the dependence of gain on the boomlength rather than on the number of elements. Here are 3 widely separated cases.

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+VK3AUU                                       DL6WU
+Boomlength     Number of      Free-Space     Boomlength     Number of      Free-Space
+wavelengths    Elements       Gain dBi       wavelengths    Elements       Gain dBi
+3.117          16             15.17          3.225          13             15.28
+6.882          28             17.91          6.815          22             17.82
+10.792         40             19.46          10.415         31             19.35
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In Table 2, the horizontal and vertical (E-plane and H-plane) front-to-sidelobe values are especially interesting. In the VK3AUU series, the horizontal ratio averages 19.56 dB, while the vertical ratio averages 16.94 dB. We may contrast these values to those for the DL6WU series: 16.73 dB horizontally and 14.68 dB vertically. The improvement not only includes a significant reduction in sidelobe strength, but as well the beginning of some suppression. Fig. 3 shows representative E-plane (azimuth) and H-plane (elevation) patterns for the 10-, 25-, and 40-element versions of the array. Due to the differences of boom length for any number of elements, do not expect the same number of lobes as in the corresponding patterns for DL6WU arrays. See Fig. 2 in the last episode. Instead, attend to the shape of the lobes. In the free-space patterns for the DL6WU series, each lobe has a corresponding very deep null. In contrast, the nulls between lobes in the VK3AUU series are shallower, indicating an incipient merging of lobes and the possible disappearance of some lobes in very long-boom versions.

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Sidelobe control is one aspect of the VK3AUU overall specifications for long-boom Yagi design. The design also provides tighter control over the feedpoint impedance than exercised by the DL6WU series. In that series, the impedance-setting cell used a reflector-to-driver spacing of 0.20 wavelength and a driver-to-director-1 spacing of 0.075 wavelength. The VK3AUU series uses a reflector-to-driver spacing of about 0.192 wavelength, with a driver-to-director-1 spacing of about 0.033 wavelength. These changes result in differences in the spacing of the early directors. More significantly, they also result in a stronger control over the variations in feedpoint resistance and reactance, with a consequential widening of the total bandwidth over which one may operate the beam. The total bandwidth increase to a range from just over 400 MHz to just under 460 MHz. Because variations in the SWR curves are small from one size beam to the next, we may represent the curves by selected samples at element numbers of 10, 25, and 40. See Fig. 4.

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As we increase the number of elements, we also gradually increase the number of SWR dips toward a 1:1 value. However, the minimum-to-maximum value ranges, especially within the 420-450-MHz amateur band, tend to be smaller than for the DL6WU series. The revision to the impedance-setting cell thus creates a greater degree of control over the feedpoint performance of the array.

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Wide-band gain and front-to-back performance are also more completely controlled in the VK3AUU series. To illustrate this fact, we may again use only a few samples, this time for 16, 28, and 40 elements. Fig. 5 shows the wide-band gain and front-to-back curves for these representative members of the series. In general, the range of gain across the wide passband is only marginally smaller than for the corresponding DL6WU designs. As well, the range does not change very much for eather series as we change the number of elements and the resulting boomlength. The variation runs from nearly 4 dB up to about 5.5 dB across the span of all beam sizes.

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To the degree possible, the VK3AUU design attempts to place maximum gain at the design frequency. In frequency sweeps of all of the trial models over the full SWR passband of the beam, the peak gain fregency varies by a much smaller amount than in DL6WU designs, relative to the design frequency. Some of the departure is a function of the modifications made in order to use elements with the same diameter in both series. Some of the departure is simply a function of the fact that the initial design was for 42 elements, with resultant variations in performance that emerge from uncorrected director removal. Table 3 shows the gain performance of the VK4AUU series.

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Fig. 6 shows the small variation between design frequency gain and peak gain in these modified models. Note especially the curve for the differential, the value of which appears on the right-hand Y-axis. Compared to the corresponding curve for the DL6WU series of Yagis, the rate of change is much more regular, as well as having a much smaller range of values.

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Because the range of boomlengths for the VK3AUU Yagis is smaller than for the DL6WU set, the front-to-back ratio tends to show fewer peaks for any given number of elements. Table 4 provides data on the front-to-back performance. Despite differences in the number of front-to-back peak values (for the 180-degree front-to-back ratio), the behavior is similar to that of the DL6WU series. It shows the same compression, movement of peak frequencies, and emergence of new peaks as we increase the number of elements in the array. However, within the 70-cm amateur band, the VK3AUU Yagis tend to show a minimum front-to-back ratio in excess of 20 dB for all except the two shortest versions. The DL6WU series showed a higher variability in the front-to-back values, even when werestrict the data to the amateur band limits.

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The VK3AUU Yagi series has some features in common with the DL6WU series. The front-to-back behavior and the variation of gain across the widest usable passband (as defined by a 2:1 50-Ohm SWR ratio) are cases in point. However, the VK3AUU series exerts greater control in many areas of beam performance, especially in the smoothness of the in-band SWR curve (and the resistance and reactance curves from which the SWR curves result), in the achievement of good working values of front-to-back ratio for virtually all boom lengths, and in the coincidence of the maximum gain frequency and the design frequency. Using more elements for a given boomlength provides for the greater control, at the expense of gain, of course.

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2-Stack Characteristics

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As with all of the trials designs to obtain the 2-stack optimal spacing for maximum gain, each free-space stack of VK3AUU Yagis went through numerous models. Each new trial increased the stacking distance by 0.1 wavelength. The data presented is only a small part of the data gathered. Table 5 shows the stacking performance in a form that allows direct comparison with the tabulated data for the DL6WU Yagi series in the preceding phase of the study. Some of the DL6WU data appears at the right to facilitate comparisons. Spacing entries of the for n.n5 wavelengths indicate that the 0.1 wavelength increments on either side of that value showed the same peak gain. In some cases, the curves for the VK3AUU series are shallow enough to have 3 spacing increments with the same peak gain. The associated front-to-back ratio is for the smallest separation in those cases.

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The gain of the 2-stack over the gain of a single unit in free-space varies over a small range: from 3.08 to 3.16 dBi. Fig. 7 shows the progression of gain values for both single units and for 2 stacks.

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Because the boomlengths of VK3AUU arrays do not reach the 12 wavelength mark, we find only 2 forbidden zones. They appear at approximate boomlengths of 3 and 6 wavelengths, with corresponding separations of about 2 and 3 wavelengths, respectively. These forbidden zones coincide--at least roughly--with those for DL6WU Yagis having similar boomlengths. The key to finding those zones in the tabulatred data is to find the entries that list "flat up" and "flat down" notations. As with all other cases of forbidden zones, there is a region of level gain just above or just below the peak value. The level gain value is usually within about 0.1 dB of the peak value and the flat curves represent a highly usable and non-critical region of stack spacing.

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The VK3AUU Yagis tend to show much smaller variations in the 180-degree front-to-back value across the region. For example, the 25-element Yagi 2-stack shows a peak gain of 20.46 dBi at 2.6 wavelengths of separation. For spacing above that level up to a separation of 3.6 wavelengths, the gain drops only to 20.42 dBi. From separations of 2.6 through 3.6 wavelengths, the front-to-back ratio varies from a minimum of 21.22 dB to a maximum of 21.98 dB. The next Yagi in the series uses 28 elements. Peak gain appears over a broad region from 3.2 to 3.5 wavelengths of separation. The flat region below those values down to about 2.6 wavelengths of spacing has a gain of no less than 20.96 dBi. Over the same region, the front-to-back ratio varies from 21.83 dB to 22.76 dB. In both cases, the total front-to-back variation is under 1 dB. The 28-element VK3AUU Yagi 2-stack is very close to being a true double-hump case, having two peaks with a slightly lower gain in the region between the separations yielding peak values. As noted in earlier episodes, however, the exact peak behavior of free-space models and of models taken at some operating height above ground may vary. Hence, the boomlength that shows the double-hump phenomenon in free space may be slightly longer than the boomlength for the same phemoenon over ground.

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The differences in design between the VK3AUU and DL6WU series of beams do not affect the relative inadequacy of standard methods of estimating the stacking spacing. Table 6 shows both the calculated and modeled optimal spacing values for maximum gain. The calculated value uses modeled beamwidths and the same RSGB equation used in preceding episodes, where lambda is a wavelength and phi-h is the vertical or H-plane beamwidth.

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Fig. 8 provides a more dramatic presentation of the same data. The smooth curve represents the calculated values of optimal separation for the beams. The stepped curve shows the modeled values. In all cases, NEC-4 models indicate a wider spacing than the standard calculations. For the longest boomlength, the difference amounts to a full wavelength.

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As a handy reference, Fig. 9 shows the spacing graphs for both the VK3AUU and the DL6WU series of 2-stacked Yagis. Once more, the X-axis uses the number of elements. However, the true coincidence between the separation curves appears when we translate those registrations into the boomlengths that apply to the individual beams in each series. One fact that the graph makes evident is that the rate of required increase in spacing for an increasing boomlength that does not reach the next jump or forbidden zone is lower than the calculations suggest.

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A 2-stack of Yagis calls for in-phase feeding of the Yagis. To see what the effects of such a system might be, I created a model using one of the numerous systems available to effect a single feedpoint. The test case was the 25-element VK3AUU design that calls for a spacing of 2.6 wavelengths. The in-phase feeding system consisted of two equal lengths of 70-Ohm transmission line. Since each line must transform the 50-Ohm Yagi feedpoint impedance to 100 Ohms for parallel connection at the junction, the required electrical length for each line is 1.75 wavelengths. This specification allows for cables with velocity factors as low as 0.743 if the lines run vertically between driven elements.

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The net effect of the use of in-phase feeding--apart from losses--is to reduce the operating passband of the array somewhat. The exact reduction for any Yagi 2-stack will depend upon the level of resistance and reactance excursions at the individual feedpoints. For the 25-element array, the passband was 410 to 455 MHz, a reduction of 10 MHz at the lower end of the spectrum and 5 MHz at the upper end.

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Fig. 10 shows the frequency sweep of the array with respect to free-space gain and front-to-back ratio. For all frequencies, the stack gain curve shows between 3.0 and 3.1 dB additional gain over a single unit. Stacking does not significantly effect the gain improvement across the usable passband. The front-to-back ratio curves do not change from those associated with a single unit. Peak values occur in the vicinity of 423, 439, and 454 MHz points on the graph. See Table 4 for the single-unit front-to-back frequencies.

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With in-phase feeding systems that effect an impedance transformation, the operating passband width depends on the stability of the feedpoint resistance and reactance at each Yagi driver. The VK3AUU impedance performance is very stable and results in a wide stacked passband. Fig. 11 presents the resistance, reactance, and SWR excursions at the junction of the two phaselines that yield close to a 50-Ohm impedance for use with a standard coaxial cable or hardline.

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Like all impedance transformation systems based on odd-multiples of a quarter wavelength, the reactance curve changes its orientation, showing increased inductive reactance below the design frequency and increased capacitive reactance above the design frequency. Note that both the resistance and reactance curves undulate. The range between minimum and maximum values should be as low as possible in a well-controlled system. The VK3AUU impedance setting cell described earlier achieves a high degree of control so that SWR values are very low throughout the 70-cm amateur band (420-450 MHz). The single-unit SWR curve showed dips (minimum values) at 420, 432, 449, and 457 MHz. The corresponding dips in the stacked array appear at 432, 444, and 450 MHz. These dips correspond to the last 3 dips in the single-unit sequence. The lowest single-unit dip at 420 MHz is missing from the stack performance curve.

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The stacking gain must in all cases be decreased by the losses in the in-phase-feed lines. The total physical line length that would not be present for a single unit is 3.5 wavelengths. Apart from small losses attaching to connectors and connections, hardline calculations suggest a loss of about 0.1 dB. High quality 70-75-Ohm coaxial cables may present losses approaching 0.2 dB. Lower grade coaxial cables increase the loss to between 0.4 and 0.5 dB. You may estimate the phase-line losses (and any cable losses) with programs like TLD (AC6LA) and TLW (N6BV/ARRL). However, be certain to add a small increment for connection imperfections and for weathering. For the system at hand, line losses in the in-phase feeding system do not present a serous challenge to the use of a 2-stack. In any event, the challenge is not nearly so great as the mechanical chellenge of building and support a long-boom 2-stack.

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A Special Note on the Original VK3AUU 42-Element Yagi

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Since these notes on stacking VK3AUU-type arrays used a modified version, it seems only fair to the beam's originator to present a bit of data on the basic design. It used 0.125" diameter elements in a design for 432.1 MHz, with maximum gain at the design frequency. For reference, Table 7 presents the original dimensions in millimeters, inches, and wavelengths.

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The design-frequency performance--using lossless elements as originally supplied in the model--is a free-space gain of 19.87 dBi, a front-to-back ratio of 36.91 dB, and a feedpoint impedance of 52.2 - j0.5 Ohms. The horizontal front-to-sidelobe ratio is 19.74 dB. Fig. 12 provides a set of free-space patterns for the array at its design frequency.

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The original array has thinner elements than the modifications used in this study. As well, the SWR curve is not centered around the design frequency. Hence, the passband shows a relatively sharp cut-off just above the upper end of the 70-cm amateur band. The source resistance drops to about 25 Ohms, although the reactance shows a remarkably small range (just over 10 Ohms) across the band. The gain remains within 0.5 dB of the peak value throughout the band, and the minimum front-to-back ratio is about 28 dB.

+

The concept of using more elements on a shorter boom has a long history in Yagi design. The VK3AUU array uses them to exert control over more operating characteristics than most other Yagi designs. When boomlengths reach the 8- to 10-meter mark, 1 to 2 extra elements per wavelength represent an almost insignificant weight and windload addition to an already unwieldy boom. Consequently, the VK3AUU Yagi design techniques deserve considerable study by all early 21st-century Yagi designers.

+

Conclusions

+

Exploration of the VK3AUU Yagi series provided us with beam samples that use a different boomlength for the same number of elements as a DL6WU design. As a result, they serve as a means of confirming--in at least a strongly suggestive way--the generality of some of the stacking behaviors that we have observed. The forbidden zones reappear at the same boomlengths and associated spacing distances in both series of Yagis. For the Yagi stacker, the fruits of the forbidden are 1. a relatively broad range of spacing in which gain is at or near peak value and 2. a set of non-finicky adjustments.

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The higher control over antenna operating characteristics exhibited by the VK3AUU Yagi series does reduce the front-to-back value excursions and thus contributes to the generally broad range of options for the stacker. As well, the VK3AUU series shows as broad or slightly broader SWR operating passband than the DL6WU series, helping to ensure that the beams can be replicated in a home workshop and stacked with relative confidence in the operating results.

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In the end, the 2-meter and 70-cm explorations of 2-stacks also suggest strongly that the various means of estimating the proper stacking distance that are in popular use today require considerable revision. If the modeling in this study bears out in carefully designed and executed range tests, then the optimal spacing separation in a 2-stack will be considerably wider than present equations tend to predict. An adequate equation will have to take into account the forbidden zone and the consequential jump in spacing value. As well, such an equation would need to account for the relatively slow rise in separation that occurs between jump points.

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One limitation of this study of both the DL6WU and VK3AUU Yagi series is that they both use samples at every 3-element increment of boomlength increase. As a result, these preliminary notes miss considerable fine detail in the development of both single-unit and stack properties from the shortest to the longest Yagis in each series. A fuller modeling study would have to investigate the Yagis for each new element added. That body of data would exceed by a wide margin the available space for these notes. However, I have undertaken such a study for the DL6WU and other series of large Yagis. The results appear in Long-Boom Yagi Studies, which is available from antenneX on CDROM.

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Although this episode marks the completion of the study--so far as it has gone--much territory remains for fertile exploration. 3-stacks and 4-stacks of long-boom Yagis are not unknown. As well, many long-boom Yagi users create horizontal pairs, squares, and diamonds of Yagis to maximize gain. Hence, much more investigation remains for the explorer with the patience to probe the various combinations of Yagis that make up present and future stacks. The 2-stack is only a fascinating beginning.

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Updated 09-01-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Stacking, VHF / UHF, Yagi


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6-Meter B-Antennas
+ A Dipole and a 2-Element Beam

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+
+

L. B. Cebik, W4RNL

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Some years ago (1998, to be precise), I described a 10-meter B-antenna. The exercise began as a dare, following some articles on the L-antenna. (Yes, there is also a C-antenna that has been used for many decades in special circumstances.) After the "initial" exercise, I did not expect to find any actual users, although the design work is itself informative. However, some weeks ago, Allison Parent, KB1GMX, reported on her success in building at least two of the antennas for 6 meters, using the rounded configuration shown in the photo. The antennas fit her special need--to have an antenna for portable work on SSB with a size that would fit the bed of her pick-up truck when she went into the field. Her tests showed that other stations could not tell the difference between her B and a normal dipole in horizontally oriented service. 6-meter hilltopping--often tied to other VHF and UHF efforts--has become very popular in the present mid-decade slump in sunspots. Antennas for 2 meters and up generally fit into pick-up beds or the rear of vans. A good performer for 6-meter work is often the limiting factor.

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Therefore, I decided to explore the B-antenna once more, this time for low-end 6-meter work. In the process, I worked up both a dipole and a 2-element driver-reflector Yagi. Both give very respectable performance and lend themselves to various forms of space-saving transport. Reviewing the B-dipole version will instruct us in why the B-configuration is superior to some other forms of element shortening. The B-beam will open up some further applications.

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The B-Dipole

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The basic B-dipole is a form of shortened 1/2 wavelength element that uses a fold back portion to reduce the required length. Generally, fold-back portions of an element that are in close proximity to the central portion of the element incur considerable loss in performance. Therefore, the B-dipole bends the central portion away from the centerline. The fold back occurs along the centerline, keeping it well spaced from the central portion of the element. The result is an improvement in performance and a more usable feedpoint impedance.

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On 6-meters, a dipole is about 10' long. As shown in Fig. 1, the B-dipole reduces that length to just under 6'. The cost is a width of 17" in either the angular or the round versions of the antenna. The angular version requires a fold back of 17", exactly the distance from the feedpoint to the peak of the angle. (The rounded version requires a smaller fold back length because the circumference of the semi-circle is greater than the combined length of the two straight sides of the angular version.)

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Of course, the rounded version of the antenna looks most like the letter B if we set the antenna vertically. As well, the angular version turned around vertically looks like a sigma. But these a small points are applicable only to someone who wishes to use the idea but change its name to sound more original. Actually, the angular version may be easier to build from the 0.125" rod used in all models shown here. Before we are finished, we shall consider a few construction ideas.

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The dimensions shown provide a design frequency of 50.3 MHz, which is adequate to provide full coverage of the entire first MHz of 6 meters. Dipole performance does not change rapidly as we use the antenna off its self-resonant frequency. Therefore, the pattern in Fig. 2 and the accompanying SWR curves give a good picture of what we can expect from 50 to 51 MHz. The free-space E-plane pattern is broadside to the element plane as defined by the triangular structure. The broadside gain is about 1.7 dBi in free space, down by only about 0.4 dB from a full-length dipole.

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The self-resonance feedpoint resistance is just about 32.5 Ohms, although the diameter of the element material will have a small effect on that value. The 50-Ohm SWR curve shows that we may use the element with a direct feed, especially in portable operation, where coaxial cable lengths are generally fairly short. The 32.5-Ohm SWR line would be similar to a 50-Ohm SWR curve if we introduce one of the feedpoint matching systems, such as a Regier series-matching scheme.

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It is possible to re-design the B-dipole for vertical service in the FM region of 6 meters. However, element shortening does take its toll on the operating bandwidth available. It is likely that, even with a matching system, the B-dipole would cover only about 1.5 MHz of the band.

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The B-Beam

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The B-antenna is susceptible to use in a 2-element driver-reflector Yagi-Uda beam with only slight modifications to the two required B-dipoles. Because the dipole impedance is already only about half the value of a full size dipole, I selected a boom length of 36", close to 0.15 wavelength at the design frequency. This spacing provides a feedpoint impedance of about 25 Ohms with the 1/8" diameter element material. Fatter materials may require additional spacing to achieve the same impedance, since the greater mutual coupling between elements will not only change the lengths of the individual elements, but also reduce the feedpoint impedance without modification to the spacing.

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Fig. 3 provides the outline of the B-beam and the changes required relative to a self-resonant B-dipole. The main element dimensions do not change--only the fold back portions. Some newer amateurs tend to believe that they can make a 2-element beam simply by adding a longer reflector to an existing dipole. Unfortunately, such a procedure tends to yield very poor performance. To optimize the array for the maximum obtainable front-to-back ratio as well as forward gain, the driver element requires shortening to go with the longer reflector element.

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The dimensions shown apply specifically to 1/8"-diameter element material. As guidance for versions of the beam that may use other materials, the driver--when not in the presence of the reflector--is self-resonant at about 51.3 MHz. The reflector, if fed independently of the driver, is self-resonant at about 49.45 MHz. The goal, whatever the element material, is beam resonance at just about 50.3 MHz. The lower portion of the figure shows the 25-Ohm SWR curve, as well as a 50-Ohm curve when we add some necessary matching.

+

The geometric mean between the natural 25-Ohm resonant feedpoint impedance and the 50-Ohm characteristic impedance of our standard coaxial feedline is about 36 Ohms. If we parallel-connect two lengths of 70- to 75-Ohm feedline, such as RG-59, we can obtain an effective impedance of 35-37 Ohms. We can create such a parallel cable by taping together two length of cable. At each end, we connect the two center conductors together and also the two braids together. The electrical length that we need is 58". However, this value assumes a velocity factor of 1.0. All coaxial cables have velocity factors of less than 1.0. To find the required physical length of paralleled cable, we multiply the line's velocity factor times the required electrical length. If we use cables with a solid dielectric, the velocity factor will be close to 0.67. Hence, this type of cable needs to be about 38.9" long. Foam cables have a velocity factor close to 0.8, resulting in a required physical length of about 46.4". In all cases, if you have a more precise value for the cable that you plan to use, substitute its velocity factor for the two samples here and multiply times the 58" electrical length. The result should be an SWR curve very similar to the 50-Ohm curve shown in the figure.

+

Impedance matching has no effect on the radiation pattern developed by the 2-element beam. Unlike the broadband performance characteristics of a simple dipole, the characteristics of a Yagi (of any type whatsoever) will change more rapidly as we move away from the design frequency. Fig. 4 provides free-space E-plane patterns for the B-beam at 50, 50.3, 50.6, and 51 MHz. Since most SSB and similar activities that call for a horizontally oriented beam occur very low in the band, performance peaks in that range.

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The free-space gain and 180-degree front-to-back ratio values below each polar plot provide a gauge of the performance change across the operating passband. They also show that on average, we increase the forward gain by about 3 dB relative to the B-dipole. The front-to-back values are modest by quite adequate to most hilltop operations.

+

In fact, the forward gain of the B-beam comes within about 0.2-0.3-dB of the gain of a similar Yagi with full size elements. (Such a Yagi might not need a matching system for a 50-Ohm feedline.) The full-size Yagi would only have a front-to-back ratio of about 10-11 dB. An interesting fact about 2-element Yagis of this general design is that shortening the elements by almost any means generally increases the front-to-back ratio, despite the falling gain. The front-to-back advantage of the B-beam is modest, since the elements are designed to sustain as much as possible of the performance of full size elements.

+

The performance values shown occur with each element face-to-face. Performance may differ if the elements are edgewise to each other, since that orientation will change the mutual coupling between them.

+

Building B-dipoles and B-Beams

+

The construction of a B-antenna is subject to the available materials and the ingenuity of the individual builder. This section provides some ideas, but they are by no means the only ones that will work--or even the best of what will work. For simple antennas, my favorite support material is PVC, which should be RF transparent well into the VHF range, if not higher. We can obtain the material cheaply from home centers, along with 1/8" rod of any conductive material from copper to aluminum to brass.

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Fig. 5 outlines the general properties of one possible portable set-up for a B-element. Let's take two 3' sections of PVC tubing and a T connector. The neck of the T is for either the beam-boom or for a dipole-mast. The top or T portion holds the PVC that supports the element halves. In most cases, a pressure fit will hold the PVC tubing in place for the duration of most hilltop operations. Therefore, we can disassemble the elements and end up with a 3' long transport package (except for whatever mast we use). Remember that the beam boom is also 3' long.

+

Some materials are springy enough to form rounded B half-elements without collapsing. Angular elements can be pre-bent to half-element shape. I recommend that the bend angle be about 100 degrees so that the element will be under tension when fitted to the support. However, the fold-back section should be fixed at its 45-degree angle relative to its adjacent side.

+

Near the T fitting, you can drill a hole at a 45-degree angle through the PVC to accept the feedpoint end of the half element. At the far end, sawing a 45-degree slot in the PVC is best for angular elements. If the slot angles into the PVC, then the tension of the installed element will hold it in place. (For rounded element halves, a pair of holes would suffice, since you can pass the element through them. However, for rounded elements, the holes should pass straight through the PVC.)

+

At the feedpoint center, the element should extend beyond the support tube far enough for connections. In most cases, you can use short pigtail leads from a coax connector and fasten them to the element center ends with pressure clips or a screw-down clamp of any small and convenient sort. On a parasitic element, a single clip or clamp will complete the element.

+

Variations on this central construction theme are as endless as the variety of available materials and your own ingenuity. The goal of the ideas used here has been to describe a method of assembly that requires perhaps 5 assembly minutes to go from the pick-up truck bed to an operating antenna, even allowing for the time it takes to screw on the coax cable connectors. As well, the parts for the antenna--dipole or beam--would fit inside of a transport case made from two (worn?) bath towels sewed together at three of the 4 edges. (Clips or clamps, of course, go inside an additional small bag, along with extras, since Murphy will dictate that at least one gets lost in the grass or gravel on every outing.)

+

The tale of the B-antenna for 6 meters is not a long one. But then, neither is the antenna.

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+ +
+

Updated 04-04-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, VHF / UHF, Yagi


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Modeling Biconical Antennas

+ hr +

Modeling Biconical Antennas

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This page exists to include the PDF in the topic index

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+

Topics: Dipole, VHF / UHF


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Notes on the Batwing
+ Part 1: Basic Batwing Properties

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L. B. Cebik, W4RNL

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Ever on the lookout for wide-band antennas, I was pleased when John Magliacane, KD2BD, called my attention to the "batwing." Long used in a turnstile and phased-vertical-array configuration, the basic batwing is little understood among amateurs and hence, little used. Perhaps it deserves a better fate.

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This series will consist of 3 sessions. The first will examine the basic properties of the batwing as a very broadband dipole antenna. The second will examine two major applications of the batwing. The final section of these notes will deal with a few modeling issues.

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The Basic Batwing

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Fig. 1 shows the general layout of the batwing dipole. It consists of dipole elements, each of which is fed from a common feed/phase line. This arrangement has been used at HF, most notably by OptiBeam, as a way of feeding drivers for 3-band Yagis arrays. However, the gain-array lays the elements out on the horizontal plane. The batwing itself places each element on the vertical plane--and has a symmetrical mate for each one. I have seen log-periodic arrays tipped toward ground and used as a wide-band array of dipoles, and the principles are similar--up to a point.

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The point of departure is the fact that the batwing doubles the LPDA structure--and connects the element ends. As well, the dipoles appear to be equally spaced, meaning that they do not describe the LPDA taper of both element length and spacing. Instead, the feed system is a combination of mutual element coupling and feedpoint drive, with the termination of the most active elements at any frequency being somewhere between elements.

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Fig. 2 shows the distribution of current--in magnitude terms only--along the elements of a batwing at widely diverse frequencies: 375 and 475 MHz. The batwing is a very broadband antenna. There are slight differences in the current magnitude curves at these extremes, especially along the longest horizontal elements. As well, the current magnitude shift at each connection point on the feed/phase line is also apparent.

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Fig. 1 has 3 pairs of dots indicating connection points. The most common implementations of the batwing, which we can also build from solid plates rather than from rods, use a central conductive mast. The top and bottom elements and the ends of the feed/phase line connect to the mast--mostly as a form of lightning protection. Antenna current on the mast is negligible. The center pair of dots form the feedpoint connection. Connecting the two terminals of the feeder to these two points connects the two feed/phase lines and the elements in series with the source energy.

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KD2BD developed a set of dimensions for a batwing from the two sources noted in Fig. 1: Johnson, Antenna Engineering Handbook, 3rd Ed., and Kraus, Antennas, 2nd Ed. These references provide some background reading sources on the batwing:

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    +
  • G. H. Brown in Electronics, March and April, 1936
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  • R. W. Masters in Broadcast News, January, 1946
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  • H. E. Gihrig in RCA Review, June 1951
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  • Sato, Kawakami, & Masters, Trans. IECE (Japan), May, 1982
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  • H. Kawakami in IEEE Trans. Antennas Propagat., Dec., 1984
    • +
+

For about 435 MHz, the individual batwing would be 6.25" from feed/phase-line to end, with the shortest dipole 2.31" from its feed/phase-line to its end. The total vertical length is 17.66". KD2BD did not specify the size of the mast or the distance either from its center or its edge to the feed/phase-line.

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I used the KD2BD dimensions to construction a model of the batwing for the 70-cm band. For the exercise, I omitted the mast, since one may build a batwing using a non-conductive mast. I separated the feed/phase lines by 0.5", which adds 0.25" to each outer dimension for the longest and shortest dipoles. I segmented the array so that each segment is as close to 0.5" as possible, allowing the use of a 1-segment wire for the connected long dipoles and across the feedpoint so addition of a source. The wire in the model is 0.125" in diameter. My initial models used aluminum, but there is little difference in performance ranging from perfect or lossless wire through copper to aluminum. Fig. 3 is an outline sketch of the test model, with the dimensions shown as sample sets of coordinates (in inches).

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The segments are all about the same length and each is 4 times the wire diameter. I placed the dipoles equi-spaced from each other, with lengths derived from the need for a straight line from the shortest to the longest. Most photos of the batwing show rounded corners, but the pointed ones do no harm in this proof-of-principle model. As a standard of comparison, I made from 0.125" aluminum a dipole 12.7" long for 435 MHz.

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The following table summarizes the results of a free-space comparison between the two antennas.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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+               Comparison Between 70-cm Dipole and Batwing
+
+Dipole
+Freq. MHz                   420             435             450
+Gain dBi                    2.09            2.12            2.15
+-3-dB Beamwidth degrees     79.2            78.5            77.6
+Feed Z: R+/-jX Ohms         64.5 - j25.0    72.1 + j 0.3    80.7 + j25.5
+75-Ohm SWR                  1.47            1.04            1.40
+
+Batwing
+Freq. MHz                   420             435             450
+Gain dBi                    5.09            5.22            5.36
+-3-dB Beamwidth degrees     80.0            79.2            78.4
+Feed Z: R+/-jX Ohms         76.9 - j15.6    80.2 - j 8.8    83.9 - j 4.3
+75-Ohm SWR                  1.23            1.14            1.13
+
+Note:  Antennas as described in text using 0.125"-diameter elements.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The batwing manages about 3-dB greater gain than the simple dipole at all frequencies, but maintains a very similar -3-dB bandwidth across the 70-cm band. How the batwing accomplishes this feat becomes evident from Fig. 4, a set of comparative E-plane and H-plane patterns for the antennas in free space.

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The vertical arrangement of matching dipoles in the batwing places the most active elements in the vicinity of 1/2 wavelength from each other. A wavelength at 435 MHz is 27.133", and the overall height of the array is 17.66" or somewhat over 1/2 wavelength. The effective distance between in-phase-fed dipoles is somewhat under 1/2 wavelength, as evidenced by the fact that there are not deep nulls in the H-plane pattern along the Z-axis. However, the spacing is close enough to 1/2 wavelength to significantly compress the radiation along the Z-axis, and this energy shows up as higher gain in the E-plane pattern.

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Although the model used a phase-line separation that prevents a true batwing resonance within the 70-cm band, the 75-Ohm SWR curve is much flatter than that of a comparable dipole. Fig. 5 shows the 75-Ohm SWR curves for both antennas from 400 to 470 MHz.

+

It is important to remember that the model under test here has no center conductive mast. With the same dimensions, a center mast to which the inner ends of the longest elements connect might change the equivalent uniform-diameter elements lengths by a small degree. As well, the essentially ground potential center mast might also alter the inherent characteristic impedance of the feed/phase line and would require considerable remodeling to effect the impedance shown in the modeled results. We shall do a preliminary exploration of issues surrounding a conductive mast in Part 3 of these notes. However, the model that we are using here should play true to a physical batwing using a non-conductive mast.

+

Changing Element Diameter

+

For many would-be batwing builders, the 1/8" diameter elements used in the test model would not be satisfactory. Since the array requires soldering or brazing elements together, some with end to mid-wire junctions, one might prefer to use larger-diameter elements. So I ran a free-space comparison of the batwing--without any dimensional changes--using 1/8", 3/16", and 1/4" elements. Of course, all connected wires in a NEC model should be the same diameter to prevent errors emerging from angular junctions of wires having dissimilar diameters. Hence, the diameter of the wires forming the feed/phase line also increased in diameter. The consequence of this move was to alter the resistive component of the feedpoint impedance, as the fatter wire increased the capacitive reactance of the array. As well, the fatter wire in the feed/phase lines with no change in the center-to-center spacing of those lines decreased the characteristic impedance of the line. (We shall explore some issues related to feed/phase line characteristic impedance in Part 3.)

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+       Comparison Among 70-cm Batwing Using Various Wire Diameters
+
+0.125" diameter elements
+Freq. MHz                   420             435             450
+Gain dBi                    5.09            5.22            5.36
+-3-dB Beamwidth degrees     80.0            79.2            78.4
+Feed Z: R+/-jX Ohms         76.9 - j15.6    80.2 - j 8.8    83.9 - j 4.3
+75-Ohm SWR                  1.23            1.14            1.13
+
+0.1875" diameter elements
+Freq. MHz                   420             435             450
+Gain dBi                    5.13            5.26            5.39
+-3-dB Beamwidth degrees     80.2            79.4            78.5
+Feed Z: R+/-jX Ohms         70.5 - j28.6    71.9 - j22.5    73.4 - j18.4
+75-Ohm SWR                  1.49            1.36            1.28
+
+0.25" diameter elements
+Freq. MHz                   420             435             450
+Gain dBi                    5.15            5.28            5.41
+-3-dB Beamwidth degrees     80.4            79.6            78.6
+Feed Z: R+/-jX Ohms         66.2 - j37.1    66.3 - j31.3    66.6 - j27.3
+75-Ohm SWR                  1.49            1.36            1.28
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The lower resistive components of the feedpoint impedances suggest that the increased diameter of the feed/phase line with no change of spacing is resulting in a lower characteristic impedance for the line. Hence, before scaling the antenna dimensions, it would be wise to alter the spacing of the feed/phase line to bring the resistance back up and to determine the consequences on the reactance. The reactance seems to show a regular shift of about 30 MHz for each 0.0625" increase in element diameter, but some of that effect is a consequence of the altered characteristic line impedance. Revised spacing between the lines to adjust the feedpoint resistance may well change the accompanying reactance.

+

The 70-cm band has a 6.9% bandwidth relative to the center frequency of 435 MHz. The batwing's gain across the band varies by just over 0.25 dB, with less than a 2-degree change in beamwidth.

+

The Batwing Above Ground

+

For a horizontal antenna high above ground, the gain increases be close to 6 dB relative to the free-space gain as a result of ground reflections. Although this fact is seemingly very well known, it may be useful to take the trouble to run both our reference dipole and the batwing an exercise of placing each--at its center--10 wavelengths above average ground. The results appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+     Comparison Between 70-cm Dipole and Batwing 10 WL Above Ground
+
+Dipole
+Freq. MHz                   420             435             450
+Gain dBi                    8.08            8.08            8.08
+Take-Off Angle degrees      1.5             1.4             1.4
+-3-dB Beamwidth degrees     79.2            78.4            77.6
+Feed Z: R+/-jX Ohms         64.0 - j24.7    72.0 - j 0.2    81.2 + j25.6
+75-Ohm SWR                  1.47            1.04            1.40
+
+Batwing
+Freq. MHz                   420             435             450
+Gain dBi                    11.04           11.17           11.32
+Take-Off Angle degrees      1.5             1.4             1.4
+-3-dB Beamwidth degrees     80.0            79.2            78.2
+Feed Z: R+/-jX Ohms         76.8 - j15.5    80.2 - j 8.8    83.9 - j 4.3
+75-Ohm SWR                  1.23            1.14            1.13
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The exercise has changed the numbers virtually not at all, except for the gain and for adding the elevation angle of the lowest and strongest lobe of the pattern over ground. A 10 wavelength height is 271.33" (22.61') at 435 MHz.

+
+ +
+

There are significant differences between the elevation patterns of the dipole and the batwing that do not show up in the tabulated numbers. Fig. 6 shows the elevation patterns of the dipole. For each of the 3 test frequencies, the total lobe pattern would fit inside (with allowance for a difference in strength) of the upper half of the free-space circular H-plane pattern. Essentially, the dipole provides not only a low-angle signal, but very high angle signals of nearly equivalent strength.

+
+ +
+

The free-space pattern of the batwing showed considerably less energy at high angles relative to the zero-degree angles at which we took the E-plane pattern. That same phenomenon appear over ground in the form of the pattern shown in Fig. 7. The high-angle lobes are very much weaker than the low-angle lobes, contributing to the gain advantage of the batwing over the dipole. Like the dipole, the lobe structure of the elevation pattern over ground would fit inside the upper portion of the H-plane pattern in free space, with allowance for the gain differential.

+

Although incidental to the situation, we may note that the lobe structure in detail is a function of frequency and height above ground. For a fixed height (22.61'), the lobe structure changes as we move across the band. This fact is most evident in the changing structure to the very highest-angle lobes. Note that while the strength of these lobes differs for the two antennas, the lobe structure itself is the same for both antennas in terms of the position of maximums and minimums.

+

Stacking a Pair of Batwings

+

A popular use of batwings--especially when turnstiled--is to create vertical stacks of them to increase gain. We may look at some of the basic properties of the batwing stack simply by stacking 2 of them in free space.

+
+ +
+

Fig. 8 shows the outline of such a stack, along with two of the key parameters. The spacing between the centers of each array is limited by the vertical dimension of each antenna. It makes no sense to have them overlap. So we shall be as concerned with the end-spacing as with the center-to-center spacing of the arrays.

+

The most popular spacing used by most batwing-makers is 1 wavelength center-to-center. At 435 MHz, this amounts to 27.133". The resulting end-to-end spacing is 9.473" or 0.35 wavelength. Under these conditions, we obtain the following free-space performance from a stack of 2 batwings. The feedpoint impedance reports are for each of the two in-phase-fed sources.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+          Free-Space Performance of a Stack of 2 70-cm Batwings
+
+Batwing
+Freq. MHz                   420             435             450
+Gain dBi                    8.43            8.62            8.80
+-3-dB Beamwidth degrees     80.2            79.4            78.4
+Feed Z: R+/-jX Ohms         71.4 - j12.6    75.2 - j 3.7    80.5 + j 2.7
+75-Ohm SWR                  1.20            1.05            1.08
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

At a center-to-center separation of 1 wavelength, the outer edges of the batwing are vertically about 1.6 wavelengths apart. The net effect is to produce "ear-lobes" on the H-plane pattern. Fig. 9 shows the H-plane ear lobes clearly.

+
+ +
+

The side lobes give the pattern a similarity to the normal E-plane pattern of an extended double Zepp (a 1.25 wavelength center-fed wire). With the Zepp, we know that shortening the wire to 1 wavelength or less will yield a pattern free of these lobes. Therefore, it may be useful to examine trends in lobe development as we select a closer and a more distance spacing for the two batwings in the stack. Throughout, we shall assume in-phase feeding of the arrays. As well, for this test, we may use 435 MHz as the test frequency.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                 Batwing Stack of 2:  Varying Separation
+
+                            Closer          Standard        Farther
+Center-to-Center (WL)       0.816           1.0             1.184
+End-Separation (WL)         0.165           0.349           0.533
+Gain dBi                    8.20            8.62            8.41
+Front-to-Sidelobe (dB)      -13.83          -12.65          -7.65
+-3-dB Beamwidth degrees     79.5            79.4            79.0
+Feed Z: R+/-jX Ohms         72.9 - j 9.7    75.2 - j 3.7    84.1 - j 4.9
+75-Ohm SWR                  1.14            1.05            1.14
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

With respect to array gain, the 1 wavelength center-to-center spacing appears close to optimum. As we decrease spacing, we find an increase in the front-to-sidelobe ratio, but by only a small amount. As we increase spacing, the ear lobes increase, as indicated by the decrease in the front-to-sidelobe ratio. For this particular model, with all of the physical features described at the beginning of these notes, the 1 wavelength center-to-center spacing also yields the most convenient feedpoint impedance.

+

Over ground, the stack shows a very usable gain increase over a single batwing. The following performance table tells the entire story. The lower batwing has its center 10 wavelengths above average ground. The feedpoint impedance reports are for each of the 2 arrays, fed in phase.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+         Performance over Ground of a Stack of 2 70-cm Batwings
+
+Batwing
+Freq. MHz                   420             435             450
+Gain dBi                    14.36           14.50           14.73
+Take-Off Angle degrees      1.4             1.4             1.3
+-3-dB Beamwidth degrees     80.2            79.2            78.4
+Feed Z: R+/-jX Ohms         71.4 - j12.6    75.2 - j 3.8    80.6 + j 2.7
+75-Ohm SWR                  1.20            1.05            1.08
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The stack over ground shows the anticipated 6 dB gain over its free-space counterpart. The gain over a single batwing at 10 wavelength center height is slightly more than 3 dB, due partly to the second antenna being 11 wavelengths above ground. Otherwise, there are no significant changes in the remaining reported values.

+
+ +
+

Fig. 10 shows the elevation pattern of the batwing 2-stack at 435 MHz. The key element in this pattern is the high-angle radiation that is not present with a single batwing. However, the strongest of this high-angle radiation is 15 dB below the strength of the main lobe. For many applications, this level of high-angle radiation presents no problems to successful use of the batwing stack.

+

Stacking 4 Batwings

+

To gain an additional 3 dB of gain, it is necessary to double the 2-stack. A stack of 4 batwing antennas spaced 1 wavelength center-to-center would have the general appearance of the outline sketch in Fig. 11.

+
+ +
+

When building vertical stacks of arrays, there is a common misconception that there is an equality of performance in all categories for each of the arrays. However, that is not quite the case. The inner arrays couple to at least 2 other arrays, while the outer arrays couple only to arrays toward the center of the stack. This yields some slight differences of performance, as indicated in the table below by the feedpoint impedances. The stack has its lowest antenna centered at 10 wavelengths (22.61') above average ground, with the remaining arrays centered at 11, 12, and 13 wavelengths (24,87', 27.13', and 29.39'). Each array is fed in phase with the others.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+         Performance over Ground of a Stack of 4 70-cm Batwings
+
+Batwing
+Freq. MHz                   420             435             450
+Gain dBi                    17.59           17.75           17.89
+Take-Off Angle degrees      1.3             1.2             1.2
+-3-dB Beamwidth degrees     80.2            79.4            78.4
+Outer 2 Antennas
+Feed Z: R+/-jX Ohms         71.9 - j10.6    76.5 - j 2.7    82.0 + j 2.9
+75-Ohm SWR                  1.16            1.04            1.10
+Inner 2 Antennas
+Feed Z: R+/-jX Ohms         65.3 - j 8.5    70.5 + j 2.2    77.7 + j 9.9
+75-Ohm SWR                  1.20            1.07            1.14
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The resistive component of the impedance across the 70-cm band differs by about 6 Ohms between an outer (top or bottom) or an inner position, a difference of about 8.5%. The modeled performance presumes that each array is fed in phase. A standard phasing harness for a stack of 4 arrays would not provide such perfection of energy distribution, and the results would show up as slightly altered gain figures.

+
+ +
+

The differences between a 2-stack and a 4 stack are not confined to gain and power distribution. Fig. 12 shows the elevation pattern of the 4-stack at the base-antenna center-height of 10 wavelengths above average ground. Although the secondary high-angle lobes remain 15-20 dB below the lowest main lobe far-field strength, they do show a change of distribution, relative to the pattern of high-angle lobes in Fig. 10 for the 2-stack.

+

From Basics to Applications

+

In this portion of my notes on the batwing antenna, we have examined some of its basic properties as a very wide-band dipole antenna. It holds promise of being useful for applications in the UHF range, where we can make good use of constant performance characteristics across a wide area of the spectrum. The models used a 435-MHz design frequency and cover all of the 70-cm band with less than a 1.2:1 75-Ohm SWR in most cases and cover 400-470 MHz (a 16% bandwidth relative to 435 MHz) with about 1.5:1 or less 75-Ohm SWR. Because most batwing applications use horizontal polarization, we have confined ourselves to that orientation.

+

In the second part of this series we shall examine two principal applications of the batwing. The first is with a planar reflector to obtain uni-directional performance. The second is as a turnstile array to obtain omni-directional performance. In the UHF range, hardly anyone is satisfied with bi-directional performance, the basic property of a single batwing and its stacks.

+
+ +
+

Updated 02-01-2004. © L. B. Cebik, W4RNL. This item originally appeared in antenneX Jan., 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Go to Main Index

+

Topics: Batwing, Stacking, VHF / UHF


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+

Notes on the Batwing
+ Part 2: Uni-Directional and Omni-Directional Batwings

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In Part 1 of this short series of notes on the batwing antenna, we examined the basic dipole-like properties of the antenna. We found it to have about 3 dB gain over a conventional dipole, along with a very wide bandwidth. The gain is a function of the compression of higher angle radiation due to the antenna's vertically symmetrical structure. The wide bandwidth results essentially from having very closely coupled dipoles of different lengths.

+

The model that we used--and shall continue using--differs from most commercial implementations of the batwing. It uses no conductive center mast to which the uppermost and lowermost dipoles connect. Hence, the feed/phase lines are closer together than in common versions, but do not have a ground-potential center bus--the mast. The 435-MHz design is 17.66" high by 13.0" wide at the top and bottom and 5.12" wide at the center.

+

In this part of my notes, we shall explore two typical directions in which one might wish to take the batwing. One direction is the beam antenna. Using a planar reflector, we can obtain a uni-directional horizontally polarized antenna of some promise. The other direction is the application for which the batwing is most famous: as a "super-turnstile" antenna, often stacked for greater gain. The nearly circular omni-directional pattern has proven useful for commercial television transmitting and may prove useful for ATV applications.

+

The Batwing Beam

+

Virtually any dipole-like antenna is suitable for use with a planar reflector, that is a solid sheet, screen, or set of closely spaced rods forming a rectangle at a useful distance behind the antenna proper. Almost any size planar reflector that extends at least a bit beyond the boundaries of the driven antenna will provide some gain and front-to-back ratio. However, for many antennas, there is an optimum reflector size in terms of both width and height.

+

The Double-Diamond

+

As a sample that we may use for comparative purposes, we may review the double-diamond and its reflector that appear in another item at this site: "Modeling the Double-Diamond for UHF." The double-diamond is actually a pair of side-fed quad loops fed at a common point--the inner corner of the diamonds. As a side-fed quad in duplicate, the antenna is vertically polarized. Fig. 1 shows the outlines of the double-diamond and its reflector.

+
+ +
+

The reflector is 42" wide by 32" high, the version providing maximum gain with a double-diamond 4" in front of the plane at 435 MHz. The diamond has been shape-adjusted for a combination of maximum gain and a near-resonant feedpoint impedance of 50 Ohms at the design frequency. The reflector model uses 0.1 wavelength spacing between wires whose diameter is sized relative to the spacing. A larger model using 0.05 wavelength spacing was tested and yielded results that are numerically so close to those of the smaller model that it made no sense to wait out the runs of a model 4 times the size.

+

The results of the runs produced the following free-space performance table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+     Performance of a Double-Diamond and Optimized Planar Reflector
+
+Freq. MHz                   420             435             450
+Gain dBi                    11.15           11.25           11.32
+Front-to-Back Ratio dB      20.96           21.28           21.64
+-3-dB Beamwidth degrees     51.2            50.6            50.2
+Feed Z: R+/-jX Ohms         38.3 - j30.0    45.1 - j 6.4    55.6 + j17.0
+50-Ohm SWR                  2.06            1.19            1.40
+
+Note:  The antenna is vertically polarized.
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Antennas that are capable of covering all of the 70-cm band are not so common that the one may casually bypass the double-diamond with a planar reflector. Fig. 2 shows the H-plane and E-plane patterns in free-space for the array. When placed well above ground, these patterns translate into well-behaved azimuth and/or elevation patterns, depending on the orientation of the antenna.

+
+ +
+

The SWR curve for the antenna is easily adjusted to better center the 50-Ohm minimum. As Fig. 3 shows, it is a bit off center in the proof-of-principle design used for the antenna. Obtaining a desired impedance and resonance at the design frequency is a matter of adjusting both the driver size and the distance from the reflector. At 5 inches, there is a shape to the double diamond that yields a 50-Ohm impedance.

+
+ +
+

The Batwing Array

+

The batwing is a more complex structure. Therefore, for the exercise at hand, I decided not to attempt to re-size the antenna. Instead, I sought a distance from the reflector that yielded resonance at whatever impedance emerged. At 5" from the planar reflector, the 435-MHz batwing is resonant at 170 Ohms. A 4:1 impedance transformation yields 42.5 Ohms, which might be satisfactory for 50-Ohm cable.

+

Finding the optimum size reflector is often a matter of trial and error. In this exercise, some of the sizes tried include those in Fig. 4. In each case, the first size figure is the width and the second is the height.

+
+ +
+

The results on which I based a final selection for a reflector plane appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+         Performance of a Batwing and Various Planar Reflectors
+
+R1:  30" wide by 30" high
+Freq. MHz                   420             435             450
+Gain dBi                    10.27           10.44           10.62
+Front-to-Back Ratio dB      19.11           19.30           19.46
+-3-dB Beamwidth degrees     56.2            55.0            54.0
+Feed Z: R+/-jX Ohms         157.4 + j24.2   170.2 + j 1.9   169.3 - j25.6
+170-Ohm SWR                 1.18            1.01            1.16
+
+R2:  40" wide by 40" high
+Freq. MHz                   420             435             450
+Gain dBi                    10.51           10.49           10.49
+Front-to-Back Ratio dB      23.60           24.64           25.64
+-3-dB Beamwidth degrees     56.2            57.8            59.2
+Feed Z: R+/-jX Ohms         155.9 + j25.7   170.1 + j 3.7   170.4 - j24.5
+170-Ohm SWR                 1.20            1.02            1.16
+
+R3:  50" wide by 50" high
+Freq. MHz                   420             435             450
+Gain dBi                    10.00           10.00           10.02
+Front-to-Back Ratio dB      28.38           28.81           29.24
+-3-dB Beamwidth degrees     65.5            66.6            67.6
+Feed Z: R+/-jX Ohms         156.9 + j25.9   170.9 + j 3.4   170.8 - j25.1
+170-Ohm SWR                 1.20            1.02            1.16
+
+R4:  60" wide by 40" high
+Freq. MHz                   420             435             450
+Gain dBi                     9.73            9.76            9.83
+Front-to-Back Ratio dB      32.93           34.21           30.15
+-3-dB Beamwidth degrees     70.0            70.6            70.6
+Feed Z: R+/-jX Ohms         156.5 + j24.9   170.0 + j 2.8   169.9 - j25.0
+170-Ohm SWR                 1.19            1.02            1.16
+
+R5:  40" wide by 60" high
+Freq. MHz                   420             435             450
+Gain dBi                    10.39           10.38           10.39
+Front-to-Back Ratio dB      25.09           25.89           26.57
+-3-dB Beamwidth degrees     56.7            57.9            58.9
+Feed Z: R+/-jX Ohms         155.2 + j26.1   169.8 + j 4.6   170.8 - j23.9
+170-Ohm SWR                 1.20            1.03            1.15
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

There are trends evident in this series of trial reflector sizes. Below a certain size (and the 30" by 30" reflector is below that size), neither the gain nor the front-to-back ratio reach maximum obtainable values. Above a certain size (which the 40" by 40" sample may mark provisionally), an increase in the width of the reflector results in an increase in both the front-to-back ratio and the -3-dB beamwidth. However, gain tends to decrease, as shown in reflectors R3 and R4. Below a certain height (which the 40" by 40" sample may mark provisionally), the beamwidth and the front-to-back ratio decrease, but if too high, the gain goes down.

+

Although the final size is provisional, it likely falls into the range around 40" by 40" unless a particular application requires that we place more emphasis upon the front-to-back ratio than upon the forward gain. With a larger reflector, we may sacrifice half to three quarters of a dB for the sake of an added 4 to 10 dB front-to-back ratio.

+
+ +
+

Fig. 5 shows the E-plane and H-plane patterns for the free-space model using the 40" by 40" reflector. With slightly less gain but higher front-to-back ratios, these patterns are quite similar to those of the double diamond, our standard of comparison. Indeed, in terms of these performance figures, there is little to choose between the two designs. Both not only show balanced performance, but as well sustain that performance across the 70-cm band.

+

However, in a wide-band antenna, the SWR curve may be for some applications as important as the general level of performance. Fig. 6 shows the 170-Ohm SWR plot for the batwing planar array from 400-470 MHz.

+
+ +
+

Over this extended range, the 170-Ohm SWR never reaches 1.5:1. It is likely that ice, snow, and whatever chemicals the atmosphere may deposit upon the antenna surface will not be noticed in operation as detuning source with the batwing planar array.

+

A 2-Stack Batwing Array

+

The batwing array is a natural for a vertical stack of at least two arrays. A 1 wavelength center-to-center spacing yielded the best results for a batwing stack without the reflector, so I modeled the new array using this separation. One structural simplification that this arrangement produces is an overlapping reflector, using the 40" by 40" version as our starting point. The final vertical dimension was 67", which yields an extension of the reflector above the top array and below the bottom array that is equal to the extension in a single-bay array. Fig. 7 shows front and side outline views of the model.

+
+ +
+

The individual batwings in the 2-stack are identical to those used throughout this exercise. As well, the 2-stack array maintains the same distance from the reflector as in the single-bay model: 5". One consequence of these moves is a centering of the feedpoint impedance in the vicinity of 160 Ohms, which becomes the new standard for SWR reports. The following table summarizes the performance data.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+          Performance of a Batwing and Planar Reflector 2-Stack
+
+40" wide by 67" high
+Freq. MHz                   420             435             450
+Gain dBi                    13.46           13.48           13.50
+Front-to-Back Ratio dB      23.73           24.66           25.59
+-3-dB Beamwidth degrees     56.0            57.6            59.1
+Feed Z: R+/-jX Ohms         146.9 + j23.8   160.6 + j 6.9   163.8 - j17.0
+160-Ohm SWR                 1.19            1.04            1.11
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The stack adds about 3 dB to the array gain, but preserves the front-to-back ratio and beamwidth of the single-bat R2 reflector version. Although 160 Ohms may not be convenience as a feedpoint impedance, judicious re-design of the feed/phase line might easily establish a better impedance for transformation to a convenient coaxial cable value. However, using 125-Ohm coax for a phasing line will yield about 100 Ohms for the individual impedances at their parallel junction with a 50-Ohm main feedline. (For the performance over ground at a 10 wavelength height, add about 6 dB to the free-space gain used in this exercise.)

+
+ +
+

Fig. 8 shows the E-plane and H-plane patterns for this free-space model of the directional 2-stack. The E-plane pattern is almost a replica of the single-bay pattern. However, the H-plane pattern shows side lobes at approximately 30 degrees off the main lobe and down by only about 17 dB. These side lobes are the result of the stacking "ears" that we encountered in H-plane patterns derived from batwing stacks without reflectors. With the reflector, the bi-directional ears on each side of the main lobes become single side lobes. These patterns are similar to those that emerge from parasitic extended double Zepp arrays and result from the overall vertical distance between the topmost antenna dipole and the bottommost antenna dipole element. Commensurate with some experimental long-element parasitic beams, it may be possible to tilt each batwing so that the top and bottom project forward of the remainder of the active antennas. There are experimental possibilities for the batwing array that only the future will determine as worthy or not.

+
+ +
+

The final figure (Fig. 9) in this portion of the notes is a 160-Ohm SWR plot for the 2-stack from 400 through 470 MHz. The curve shows that for each of the two sources, the feedpoint impedance is as stable as that of the single-bay version of the directional batwing. (However, in terms of a flat SWR curve, the flattest remains to be seen.)

+

The batwing array with a planar reflector offers a horizontally polarized beam antenna of good performance in a package that is relatively compact in its horizontal dimensions. It is 40" wide by 5" front-to-back. If constructed, the support mast should lie behind the reflector. Indeed, the mast may form a backbone for the reflector. The 67" height of the 2-stack reflector or the 40" height of the single bay may seem large for an essentially utility array. However, lying close to the mast, the reflector and the overall array offer some reduction of snow and ice loading effects that tend to snap many 70-cm Yagis. As well, few Yagis can boast the evenness of the batwing array's performance from one end of the band to the other.

+

The Batwing Turnstile

+

The other application for the batwing that appeals to potential users is as an omni-directional horizontally polarized array, possibly suited to ATV and other wide-band uses. Almost any horizontally polarized antenna can be turnstiled, and the batwing is no exception. Of course, the most basic turnstile antenna consists of two simple dipoles at right angles and fed so that the current magnitudes are equal but 90 degrees out of phase. A similar treatment applies to folded dipoles, to quad loops, and to the batwing. Since the turnstiled dipole array is the most basic, let's begin with a comparison between it and what we get when we turnstile a batwing of the 435-MHz dimensions that we have used throughout this exercise.

+

Dipole vs. Batwing

+

As shown in Fig. 10, the turnstiled dipole pair is deceptively simple. We take two dipoles, each of which is resonant at the design frequency. We cross them at their centers, displacing them so that they do not touch each other. We (current) feed one dipole. From that dipole to the other, we run a 90-degree current phase-shift network. The network can be a simple or complex as desired. For our model--since it takes no physical space--we may run a 1/4 wavelength transmission line having an impedance equal to that of a single dipole at resonance. The net impedance of the dipole pair is 1/2 the impedance of a single dipole.

+
+ +
+

The batwing appears more complex, but most of that impression comes from the basic structure of the antenna. The model outline shows (although hardly visible) that we have displaced one structure vertically from the other by enough for the center wires to clear each other. We feed each batwing in the 90-degree pair at its normal feedpoint. Our feedline goes to one feedpoint. From there to the other, we run our 1/4 wavelength phase line. However, the native impedance of a batwing of the modeled design is about 80 Ohms. We used 70-Ohm transmission line, the same characteristic impedance used with the dipole turnstile. The mismatch yields pattern distortions. The simplest way around this problem is to use a length of line that minimizes the pattern distortions. In this case, with a design frequency of 435 MHz, instead of using 6.78" of line (with a velocity factor of 1.0), we used 6.4".

+

For our free-space models, we obtained the follow results, tabulated in terms of the maximum and minimum gain and the differential. The last figure--in addition to the squaring of dipole turnstile patterns--is a measure of the non-circularity of the pattern--designed to be omni-directional.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                   70-cm Dipole and Batwing Turnstiles
+
+Dipole Turnstile
+Freq. MHz                   420             435             450
+Max. Gain dBi               -0.53           -0.76           -0.04
+Min. Gain dBi               -3.45           -1.85           -3.36
+Gain Difference dB          2.92            1.09            3.40
+
+Batwing Turnstile
+Freq. MHz                   420             435             450
+Max. Gain dBi                2.41            2.57            2.83
+Min. Gain dBi                1.01            1.24            1.28
+Gain Difference dB          1.40            1.33            1.55
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the dipole turnstile shows a more circular pattern at 435 MHz, it degrades toward the band edges to produce about 3 dB differential in the maximum and minimum gain levels. The batwing turnstile has much smoother performance across the band, as we might expect from an antenna design that is inherently broad band. As well, the batwing turnstile averages about 3 dB higher gain across the band than its dipole counterpart, a figure which is consistent with our comparisons in Part 1 between a single dipole and a single batwing.

+
+ +
+

Fig. 11 shows comparative E-plane and H-plane patterns at 435 MHz for the two types of turnstile antennas. We can easily see the reason for the higher gain of the batwing version, given the H-plane compression of the high-angle radiation that is typical of the dipole turnstile. However, for a more comprehensive view of pattern distortions, we need to compare E-plane patterns across the band.

+
+ +
+

Before examining those patterns, let's take a glance at the comparative SWR patterns in Fig. 12. A turnstile antenna exhibits a very wide SWR bandwidth. The dipole turnstile shows less than 1.4:1 35-Ohm SWR from 400 to 470 MHz, well beyond the band limits. The turnstiled batwings show a 37-Ohm SWR of under 1.11:1 across the same span, despite the 10-Ohm mismatch between the phase line and the batwing feedpoint impedance.

+

As I had occasion to note in my QEX article, "Some Notes on Turnstile-Antenna Properties" (Mar/Apr, 2002, pp. 35-46), it is never safe to use the SWR curve of a turnstile antenna for any purpose. A turnstile antenna reaches the limits of an acceptable pattern long before it reaches unusable SWR values. Fig. 13 tells us something of that story.

+
+ +
+

Fig. 13 provides the necessary free-space patterns to make a proper evaluation of the adequacy of the two types of turnstiles as omni- directional antennas for all of the 70-cm band. The combined patterns in Fig. 11 appear as separate patterns in the center column of Fig. 13. The effects of the closer line match are evident in the peaks of the dipole pattern. Equally apparent are the pattern degradations at 420 and 450 MHz. No longer are these patterns close to a flatted circle. Instead, they form distorted ovals with high front-to-side differentials. On the other hand, the batwing turnstile maintains its overall pattern shape across the entire band.

+

How well the batwing turnstile performs over ground appears in the following table. As we have done throughout these notes, we placed the center of the batwing 10 wavelengths (271.33" or 22.61') above average ground.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+          Performance of a Batwing Turnstile 10 WL Above Ground
+
+Freq. MHz                   420             435             450
+Gain dBi                    8.33            8.51            8.78
+TO Angle degrees            1.5             1.4             1.4
+Feed Z: R+/-jX Ohms         37.1 + j 0.1    37.2 + j 0.0    37.2 + j 0.0
+37-Ohm SWR                  1.004           1.006           1.006
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The gain differential across the band is only 0.45 dB, and, of course, the 37-Ohm SWR is negligible. Variables of weather that may affect the antenna tuning have no significant effects on the performance of the antenna.

+
+ +
+

Fig. 14 shows the elevation patterns of the antenna. In shape, these patterns are virtually identical to those shown for a single batwing along its line of maximum bi-directional gain. The slight changes in the radiation lobes near the zenith angle are evident as we move across the band.

+

A common practice is to stack turnstiles in an effort to achieve more omni-directional gain. Stacking batwing arrays is also common. Therefore, I modeled two vertically stack turnstiled batwings with 1 wavelength center-to-center spacing. One caution derived from the study of single batwings is the fact that the impedance changes slightly for each batwing in a stack relative to the impedance of an isolated batwing. To see if the changes made any difference, I left the 6.4" phase line used with the single batwing turnstile antenna. The free-space pattern results appear in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+              70-cm Batwing Turnstiles: Free-Space 2-Stack
+
+Freq. MHz                   420             435             450
+Max. Gain dBi                5.45            5.65            6.08
+Min. Gain dBi                4.42            4.53            4.40
+Gain Difference dB          1.03            1.12            1.68
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The seemingly improve performance derives in part from the direction in which the impedance changes when two batwings are in a 1 wavelength stack. It decreases. Hence, the 70-Ohm phase line is a better match for the array than when used with a single turnstiled batwing. As a result, the pattern distortion is lower for two-thirds of the band. Changing the phase line length would have permitted me to optimize the pattern, or at least center the distortion level.

+

The desirability of optimizing the phase line appears in the following table of values taken with the stacked batwing turnstiles 10 and 11 wavelengths above average ground.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+      Performance of a Batwing Turnstile 2-Stack 10 WL Above Ground
+
+Freq. MHz                   420             435             450
+Gain dBi                    11.31           11.57           12.02
+TO Angle degrees            1.4             1.3             1.3
+Feed Z: R+/-jX Ohms         37.2 + j 0.0    37.4 + j 0.0    37.5 + j 0.2
+37-Ohm SWR                  1.004           1.010           1.014
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The trend that we saw in the free-space E-plane gain readings re-appears in the performance table for the batwing turnstile stack above ground. Although slight, the degradation of the nearly ideal readings appears in the upper portion of the band. Between 420 and 435 MHz, we see only a 0.26 dB change of gain, but between 435 and 450 MHz, the gain rises 0.45 dB. The 37-Ohm SWR curve shows a comparable set of changes. Even a turnstile design as promising as the batwing array can use careful optimizing.

+
+ +
+

Fig. 15 shows the elevation patterns across the 70-cm band for the stack of turnstiled batwings. Once more, the shape of these patterns is almost identical to the shape of the elevation patterns for single batwings stacked above ground, when we take those patterns along the axis of maximum gain. Nonetheless, the overall omni-directional gain of the turnstiled batwings is well under that of the bi-directional single array, as is true whenever we turnstile a horizontal antenna to achieve omni-directional performance.

+

Given the fact that the single and turnstiled batwing results are comparable at every point, we can repeat a caution mentioned when we stacked 4 single batwings. The impact of mutual coupling will be greater on the inner antennas of the stack than on the outer antennas. Hence, preservation of an omni-directional pattern may require careful attention to the phase line or whatever other means are used to effect phasing in order to avoid pattern distortions. The SWR curve of the composite phased array may not itself give much clue. Hence, careful design analysis, normally via good modeling practices, may be the best pre-construction and pre-measurement procedure to achieve as pure an omni-directional pattern as possible.

+

Conclusion: Not Quite Yet

+

Although we have examined the basic properties and the two main applications of the batwing, we are not quite done with the antenna. Our model uses no common mast, a feature of many batwing antennas. That fact leaves a number of unanswered questions. As well, the changes in performance that we observed in Part 1 when we arbitrarily changed the wire diameter raises further questions. It may well be that the batwing is susceptible to some modeling alternatives that may give us a few added insights into the antenna. So, let's spend one more session on our batwing notes.

+
+ +
+

Updated 03-01-2004. © L. B. Cebik, W4RNL. This item originally appeared in antenneX Feb., 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

Go to Main Index

+

Topics: Batwing, VHF / UHF


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+

Notes on the Batwing
+ Part 3: Modeling Issues with the Batwings

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In most antenna articles, we usually encounter models used for design or analysis. In most cases, we receive the models as if they were perfect, with the possible exception of a few minor variables related to the construction side of the ledger.

+

However, few models are perfect, not only relative to the physical implementation of the antenna, but as models themselves. Antennas with linear and uniform-diameter elements come closest to perfection, but when we complicate the geometry, model adequacy--as a model--becomes a question that we cannot--or at least, should not--ignore. The batwing antenna is a case in point. Its complexity--both physically and electrically--demands that we examine how good the models are on which we have based our discussion.

+

Some Basic Modeling Issues

+

Throughout this series, we have presented the models of the batwing as "proof-of-principle" models. That is, we developed a model adequate for certain analytical purposes, but without some of the details of the usual physical batwing antennas. A minor variant is the pointed corners on the model, when most implementations use rounded corners. A far more major item is the omission of the central mounting mast common to most implementations. As a result of these changes and omissions, the models can show us the potentials of the antenna, but they are not adequate design vehicles, except for sharp-cornered batwings that use a non-conductive support mast.

+

The basic model that we used throughout Parts 1 and 2 of this series used a 435-MHz design frequency and had the following physical specifications, with all dimensions on this EZNEC model description in inches.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+batwing 435                                     Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1    W15E1  -6.500,  0.000,  8.830 W21E1  -0.250,  0.000,  8.830 1.25E-01  12
+2    W15E2  -5.180,  0.000,  5.880 W21E2  -0.250,  0.000,  5.880 1.25E-01  10
+3    W16E2  -3.880,  0.000,  2.940 W22E2  -0.250,  0.000,  2.940 1.25E-01   7
+4    W17E2  -2.560,  0.000,  0.000 W23E2  -0.250,  0.000,  0.000 1.25E-01   4
+5    W18E2  -3.880,  0.000, -2.940 W24E2  -0.250,  0.000, -2.940 1.25E-01   7
+6    W19E2  -5.180,  0.000, -5.880 W25E2  -0.250,  0.000, -5.880 1.25E-01  10
+7    W20E2  -6.500,  0.000, -8.830 W26E2  -0.250,  0.000, -8.830 1.25E-01  12
+8    W27E1   0.250,  0.000,  8.830 W33E1   6.500,  0.000,  8.830 1.25E-01  12
+9    W27E2   0.250,  0.000,  5.880 W33E2   5.180,  0.000,  5.880 1.25E-01  10
+10   W28E2   0.250,  0.000,  2.940 W34E2   3.880,  0.000,  2.940 1.25E-01   7
+11   W29E2   0.250,  0.000,  0.000 W35E2   2.560,  0.000,  0.000 1.25E-01   4
+12   W30E2   0.250,  0.000, -2.940 W36E2   3.880,  0.000, -2.940 1.25E-01   7
+13   W31E2   0.250,  0.000, -5.880 W37E2   5.180,  0.000, -5.880 1.25E-01  10
+14   W32E2   0.250,  0.000, -8.830 W38E2   6.500,  0.000, -8.830 1.25E-01  12
+15    W1E1  -6.500,  0.000,  8.830 W16E1  -5.180,  0.000,  5.880 1.25E-01   6
+16    W2E1  -5.180,  0.000,  5.880 W17E1  -3.880,  0.000,  2.940 1.25E-01   6
+17    W3E1  -3.880,  0.000,  2.940 W18E1  -2.560,  0.000,  0.000 1.25E-01   6
+18    W4E1  -2.560,  0.000,  0.000 W19E1  -3.880,  0.000, -2.940 1.25E-01   6
+19    W5E1  -3.880,  0.000, -2.940 W20E1  -5.180,  0.000, -5.880 1.25E-01   6
+20    W6E1  -5.180,  0.000, -5.880  W7E1  -6.500,  0.000, -8.830 1.25E-01   6
+21   W39E1  -0.250,  0.000,  8.830 W22E1  -0.250,  0.000,  5.880 1.25E-01   6
+22    W2E2  -0.250,  0.000,  5.880 W23E1  -0.250,  0.000,  2.940 1.25E-01   6
+23    W3E2  -0.250,  0.000,  2.940 W24E1  -0.250,  0.000,  0.000 1.25E-01   6
+24   W41E1  -0.250,  0.000,  0.000 W25E1  -0.250,  0.000, -2.940 1.25E-01   6
+25    W5E2  -0.250,  0.000, -2.940 W26E1  -0.250,  0.000, -5.880 1.25E-01   6
+26    W6E2  -0.250,  0.000, -5.880 W40E1  -0.250,  0.000, -8.830 1.25E-01   6
+27   W39E2   0.250,  0.000,  8.830 W28E1   0.250,  0.000,  5.880 1.25E-01   6
+28    W9E1   0.250,  0.000,  5.880 W29E1   0.250,  0.000,  2.940 1.25E-01   6
+29   W10E1   0.250,  0.000,  2.940 W30E1   0.250,  0.000,  0.000 1.25E-01   6
+30   W41E2   0.250,  0.000,  0.000 W31E1   0.250,  0.000, -2.940 1.25E-01   6
+31   W12E1   0.250,  0.000, -2.940 W32E1   0.250,  0.000, -5.880 1.25E-01   6
+32   W13E1   0.250,  0.000, -5.880 W40E2   0.250,  0.000, -8.830 1.25E-01   6
+33    W8E2   6.500,  0.000,  8.830 W34E1   5.180,  0.000,  5.880 1.25E-01   6
+34    W9E2   5.180,  0.000,  5.880 W35E1   3.880,  0.000,  2.940 1.25E-01   6
+35   W10E2   3.880,  0.000,  2.940 W36E1   2.560,  0.000,  0.000 1.25E-01   6
+36   W11E2   2.560,  0.000,  0.000 W37E1   3.880,  0.000, -2.940 1.25E-01   6
+37   W12E2   3.880,  0.000, -2.940 W38E1   5.180,  0.000, -5.880 1.25E-01   6
+38   W13E2   5.180,  0.000, -5.880 W14E2   6.500,  0.000, -8.830 1.25E-01   6
+39    W1E2  -0.250,  0.000,  8.830  W8E1   0.250,  0.000,  8.830 1.25E-01   1
+40    W7E2  -0.250,  0.000, -8.830 W14E1   0.250,  0.000, -8.830 1.25E-01   1
+41    W4E2  -0.250,  0.000,  0.000 W11E1   0.250,  0.000,  0.000 1.25E-01   1
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1    41 / 50.00   ( 41 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The model is a NEC model, with all modeling done on NEC-4 (both EZNEC and GNEC). It has 41 wires and 271 segments. Of course, when we stacked and turnstiled batwings, we multiplied the number of segments and wires. Adding wire-grid reflectors produced some models with well over 1,000 segments. Hence, adequate study of a batwing antenna system requires a modeling program with a considerable segment limit.

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Fig. 1 shows the outline of the model that corresponds to the description above. From the beginning, we have a number of modeling decision that we must make. First, we must choose a segment length. The smallest gap between the two halves of the antenna sets the segment length at about 0.5". Since it is advisable to have all segments within an inter-connected model the same length, we used 0.5" as the standard segment length. It is especially important to keep the segment number and length the same on the wires that parallel each other at the array center, since they are closely spaced. However, the dipoles within the array are not so far apart that we can completely ignore alignment.

+

Because we wished to center the source on the most central wire in the antenna, we used a single segment for it. It would have been better to have 3 segments on this wire in order to separate the 4-way junctions from the source segment by at least one segment. But here, we encounter another limitation. It is desirable to keep segment length at least the same, and preferably longer, than the maximum wire diameter used in the model. Some models used up to 0.25" diameter wire (and some trial models used even fatter wire). 3 segments on a 0.5" wire reduces the segment length to 0.167", too short for the larger wire sizes--indeed too short for wires above about 1/8" in diameter. As well, the more complex the geometry, the more important it usually is to keep the segment length considerably longer than the wire diameter. So the decision to use a single segment for the 3 connecting wires between the wings is a compromise, and we shall examine the consequences of that compromise as we proceed.

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We not only modeled the batwing in NEC, but also in MININEC, using Antenna Model. Fig. 2 shows the MININEC version of the model. Since MININEC requires that we place a source at a segment junction or pulse, the connecting wires use 2 segments. As the diagram shows, we restricted the MININEC models to versions of the array in which the spacing between the central wires is wider, thus achieving close to a 1:1 length ratio for the segments in those wires and the segments in adjacent wires. However, in some models, we were forced to press the desired limit of having segments at least 1.25 times the wire diameter. Otherwise, the models are the same in terms of the dimensions, coordinates, and segmentation of the other 38 wires.

+

In both models, straight wires terminate at junctions to simplify the process of modifying a model. It is permissible to terminate one wire at the segment junction within another. However, any slight change to the wire whose segment junctions form termination points results in a requirement to change many wires. Using wire junctions exclusively tends to simplify the modification procedure.

+

UHF models present a limitation we normally do not encounter with HF antennas. Small diameter elements are quite large when viewed in terms of a fraction of a wavelength. The use of short segments (here, about 0.5") can result in surpassing NEC limitations at corners. See Fig. 3 for samples of acceptable and unacceptable corner treatments.

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If the outer surface of one wire penetrates to the inner third or thereabouts of another wire, the results will either be inaccurate for that junction or the program will flag an error and refuse to run (depending upon the implementation). As we increase the diameter of a wire beyond about 5/16" (0.3125"), we incur this problem. The net result is to limit the range of wire diameters that we can use effectively with the 435-MHz batwing.

+

A similar problem occurs in NEC and MININEC if we try to increase just the diameter of the vertical central feed/phase line wires. In NEC, we must be cautious of angular junctions between wires having dissimilar diameters, and so all of the NEC models changed wire diameter uniformly throughout the model. However, MININEC is less sensitive to this situation, allowing us to increase the diameter of just those wires making up the central feed/phase lines (wires 21-32 in the model description). For a given spacing (always center-to-center in a model), there is a limit to the size we may use. Fig. 4 shows why.

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Modeling programs based on round wires do not permit one wire to penetrate to the centerline of the other and, indeed, do not permit even shallow penetration of one wire surface into the surface of the other. Even very close wire proximity tends to yield errors. Some MININEC programs, such as Antenna Model, have correctives for very closely spaced wires, but NEC will yield systematic errors under these conditions. The result is that an adequate model should maintain a good space (several radii) between the surfaces of two parallel wires in addition to keeping the segment junctions as well aligned as feasible.

+

The batwing antenna is an electrically complex affair, consisting of several dipoles that are closely coupled and connected at their outer ends, along with a feed/phase line that has a characteristic impedance based upon the wire diameter and the spacing between wires. It is not just a mass of wires soldered together to make an odd-shaped antenna.

+

Since the antenna is a broad-band array, it is natural for us to perform frequency sweeps of its characteristics across a band of interest. In this case, we are interested in the 70-cm band from 420-450 MHz (and possibly beyond). By using program supplements, such as EZPlots by Dan Maguire, AC6LA, we can obtain impressive graphs.

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Fig. 5 shows the gain and front-to-side ratio--as relevant data for a dipole--across the band for the 0.125" version of the array. In Fig. 6, we find the feedpoint resistance and reactance data, along with the 75-Ohm SWR curve for the antenna model.

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What I neglected to add to the preceding paragraph was that the graphs are of data directly reported by the program. However, we may well ask how reliable the data may be relative to the model used to generate it. (This is not the same question as asking how accurate a model is to physical reality. At this stage, we are asking for an adequacy of model evaluation--as a model.) One of the tools that we have at our disposal for making an evaluation is the Average Gain Test (AGT).

+

Some AGT Test and Design Strategy Exercises

+

The AGT tests a lossless model either in free space (used here) or over perfect ground (useful with monopoles and arrays of them) to record from a fair number of equally spaced samples the ratio of the average of the power reported as radiated to the power supplied to the model. We can receive this value as a simple number--the ratio. We can also convert it into dB by taking the log of the AGT number and multiplying by 10.

+

If and only if the AGT value is 1.0 will the numbers that we derive from the graphs be reliable modeling reports. However, we may use the AGT values to correct some of those figures. In general, if the AGT in dB is greater than 0, then the reported gain of the antenna is too high and we must subtract the AGT in dB from the reported value to arrive at a more nearly correct value. Likewise, if the AGT value in dB is less than 0, we must add its absolute value to the reported gain to have our more nearly correct figure.

+

The AGT score given as a unit-less ratio is also useful. When the reactance at the feedpoint is not too high, we may use the AGT score to correct the resistive portion of the impedance. Simply multiply the AGT value times the resistive component of the impedance to arrive at a more nearly correct value. If we perform this calculation on the impedance values with the AGT score for the 0.125" batwing, we shall discover that the SWR curve must also change. As well, the AGT impedance corrective does not tell us by how much the reactance may be off the mark.

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I should note that none of the models used in the first two parts of this series scored a perfect 1.0 on the AGT test. However, as we shall see, the scores were sufficiently close that the trends shown in those parts are quite reliable. Difficulties only emerge when we require fine shading of results to determine whether a particular design maneuver will yield an improvement or when we compare models made on two different systems of modeling.

+

Let's go through a small exercise, one relevant to the batwing. I increased the wire size successively on the batwing from 0.125" through 0.1875" to 0.25" (1/8" to 3/16" to 1/4"). In the process, I widened the spacing between the feed/phase lines in an attempt to see if that process would equalize the feedpoint impedances among models. Here is the raw data for this exploration.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                Batwing Performance with Various Wire Diameters
+
+0.125" Wire with 0.5" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.09              5.22              5.36
+Feed Z R+/-jX Ohms            76.9 - j15.6      80.2 - j 8.8      83.9 - j 4.3
+75-Ohm SWR                    1.23              1.14              1.13
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.29              5.43              5.56
+Feed Z R+/-jX Ohms            75.6 - j14.1      77.9 - j 7.6      80.6 - j 3.0
+75-Ohm SWR                    1.21              1.11              1.09
+
+0.25" Wire with 0.9" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.46              5.59              5.72
+Feed Z R+/-jX Ohms            75.4 - j11.3      77.2 - j 4.9      79.5 - j 0.3
+75-Ohm SWR                    1.21              1.11              1.09
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

At first sight, it appears that the experiment was a grand success, since the impedances do achieve a fair degree of equalization. However, note the great gain increases with wire size--over a third of a dB just from increasing the wire size by a factor of 2.

+

When we go back and perform an AGT test on the three models, we obtain--from thinnest to thickest wire--the following values: 0.964 (-0.16 dB), 1.005 (0.02 dB), and 1.043 (0.18 dB). Now, let's go back and correct the gain and resistance values in a new table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+       Batwing Performance with Various Wire Diameters:  AGT Corrections
+
+0.125" Wire with 0.5" Feed/Phase Line Spacing            AGT: 0.964 (-0.16 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.25              5.38              5.52
+Feed R Ohms                   74.1              77.3              80.9
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing            AGT: 1.005 (0.02 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.27              5.41              5.54
+Feed R Ohms                   76.0              78.7              81.0
+
+0.25" Wire with 0.9" Feed/Phase Line Spacing              AGT: 1.043 (0.18 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.28              5.41              5.54
+Feed R Ohms                   78.8              80.5              82.9
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

First, we may notice that the gain advantage of the 0.25" diameter wire batwing has shrunk to a couple of hundredths of a dB at most. Gain would not be a reason for moving from one wire diameter to another with the batwing--although there might be others reasons for doing so.

+

Second, the resistive components of the impedances are not quite so close together as we had at first suspected from the raw data. The disparity may lead us in another direction of investigation.

+

Using standard parallel transmission line calculations, we can find the characteristic impedance (Zo) of the feed/phase line for each model. The basic 0.125" wire model with a 0.5" line spacing shows a Zo of 247 Ohms. The 0.1875" wire model with a wire spacing of 0.7" gives a Zo of 239 Ohms. The fattest (0.25") model with a spacing of 0.9" yields 234 Ohms. What would happen if we equalized the impedances, using the 0.125" model as a baseline with a Zo of 247 Ohms. If we retain the same line spacing for the larger models (0.7" and 0.9"), we obtain two new wire diameters: 0.175" (instead of 0.1875") and 0.225" (instead of 0.25"). The following table provides the corrected results for the new feed/phase lines, remembering that in these NEC models, all of the wires change diameter as the feed/phase lines change diameter.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+       Batwing Performance with Various Wire Diameters:  AGT Corrections
+
+0.125" Wire with 0.5" Feed/Phase Line Spacing            AGT: 0.964 (-0.16 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.25              5.38              5.52
+Feed R Ohms                   74.1              77.3              80.9
+
+0.175" Wire with 0.7" Feed/Phase Line Spacing             AGT: 1.003 (0.01 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.26              5.40              5.54
+Feed R Ohms                   76.9              79.6              82.7
+
+0.225" Wire with 0.9" Feed/Phase Line Spacing             AGT: 1.037 (0.16 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.27              5.40              5.53
+Feed R Ohms                   79.8              82.2              85.0
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The exercise initially tells us that increasing the Zo of the larger model feed/phase lines actually sends the feedpoint impedances farther apart than the initial descending values for these numbers. However, the initial readout is not the whole story. For we now know that we have two design strategies for bringing those values closer together--and closer to a 75-Ohm design-frequency value. As we increase the wire diameter in the model, we may decrease the feed/phase line Zo and/or we may adjust the outer dimension of the batwing. There is no such thing as a failed test, but only test from which we fail to learn.

+

We may also ask what might happen if we increased the diameter of the feed/phase line without increasing the diameter of the dipole and outer perimeter wires. For this task, we must use MININEC (Antenna Model, in this case), since NEC become erroneous when faced with junctions of wires with dissimilar diameters.

+

For the test, I used the 0.25" wire diameter model as a baseline, since it used a feed/phase line separation of 0.9", adequate for having 2 segments at the crossing wires. The combination of 0.25" wire and 0.9" separation yields a Zo of 234 Ohms. Keeping the spacing but increasing the wire diameter to 0.35" for just the feed/phase line gives a Zo of 192 Ohms. With 0.45" diameter wire, the Zo is 158 Ohms. For these three cases, MININEC returned the following uncorrected data.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+          Batwing Performance with Various Feed/Phase Line Diameters
+
+0.25" Wire with 0.9" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.11              5.23              5.35
+Feed Z R+/-jX Ohms            84.1 - j18.8      85.6 - j13.7      87.3 - j 9.4
+75-Ohm SWR                    1.30              1.23              1.21
+
+0.35" Wire with 0.9" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.06              5.19              5.32
+Feed Z R+/-jX Ohms            78.9 - j22.1      79.7 - j16.7      80.6 - j13.3
+75-Ohm SWR                    1.34              1.26              1.21
+
+0.45" Wire with 0.9" Feed/Phase Line Spacing
+Freq MHz                      420               435               450
+Gain dBi                      5.05              5.16              5.27
+Feed Z R+/-jX Ohms            73.6 - j23.8      73.8 - j18.6      74.2 - j15.2
+75-Ohm SWR                    1.38              1.28              1.23
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The decreasing gain values with no changes in the dipole diameters should make us suspicious that something is amiss with the modeling. If the actual gain values were relatively constant, then the reported values would indicate a decreasing AGT value. In fact, this is the case, as the following table of corrected gain and resistance values shows.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ Batwing Performance with Various Feed/Phase Line Diameters:  AGT Corrections
+
+0.25" Wire with 0.9" Feed/Phase Line Spacing            AGT: 0.9524 (-0.21 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.32              5.44              5.56
+Feed R Ohms                   80.1              81.5              83.1
+
+0.35" Wire with 0.9" Feed/Phase Line Spacing            AGT: 0.9437 (-0.25 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.31              5.44              5.57
+Feed R Ohms                   74.5              75.2              76.1
+
+0.45" Wire with 0.9" Feed/Phase Line Spacing            AGT: 0.9348 (-0.29 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.34              5.45              5.56
+Feed R Ohms                   68.8              69.0              69.4
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We should never expect perfect agreement, even when employing correction factors, between NEC and MININEC results. However, within a very small ballpark, the MININEC exercise permits us to extend our design strategies. The reduction in feed/phase line Zo results in a consequential reduction in the feedpoint impedance. In fact, the feedpoint resistance reduction is about 1/6 the reduction in Zo for a constant set of dipole diameters. We now have another means of controlling the feedpoint impedance of the batwing.

+

The Conductive Mast Question

+

All of our models have omitted the central conductive mast that is part of most commercial implementations of the batwing antenna, especially in dipole or turnstile applications. Modeling such a mast presents both NEC and MININEC with difficulties. The mast ordinarily has a diameter that is several times the diameter of the wire diameter used in the antenna proper. With the short segment lengths required for the antenna, the mast diameter is usually larger than the antenna segment length. Even smaller masts are limited by virtue of the corner junction penetration into the center portion of NEC segments.

+

At most, then, NEC models might give us an indication of the effect of a central mast simply by modeling a center wire between the two sets of wires used as the feed/phase lines of the antenna. However, even this model requires some special treatment, since the central mast wire joins only the top and bottom of the batwing horizontal wires. The source wire must be allowed to cross between the feed/phase lines without interruption or junction with the mast wire.

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+ +
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Since the aim of the model is to get an indication of the likely effect of the central mast, precision is not the goal. Fig. 7 indicates in an edge and a face view how I built the model for this goal. The mast wires are vertical as they extend above the top horizontal and below the bottom horizontal wires in the array. Between those points, the mast consists of two wires that join in the vicinity of the source wire, but displaced 0.5" to avoid contact with the source wire. Despite the distortions from a physical implementation that would use a straight mast and wrap the feedpoint contacts around the mast, we ought to be able to see some effect. Indeed, by varying the diameter of the mast wire, we might even observe some trends.

+

For the test, I used the 3/16" (0.1875") diameter wire model of the batwing antenna. The reasoning behind this choice is that this version has the best AGT rating, 1.005. I first used a 3/16" mast wire so that there would be no wire junctions between dissimilar diameter wires. However, I then increased the mast wire diameter to 0.25" and then to 0.3125" (5/16"). Beyond this diameter, I encountered warnings concerning the angular penetration of one wire into the central region of another.

+

The following table summarizes the outcome of these models.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                 Batwing Performance with a Central Mast Wire
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing and No Mast Wire
+AGT:  1.005 (0.02 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.29              5.43              5.56
+Feed Z R+/-jX Ohms            75.6 - j14.1      77.9 - j 7.6      80.6 - j 3.0
+75-Ohm SWR                    1.21              1.11              1.09
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing and a 0.1875" Mast Wire
+AGT:  1.007 (0.03 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.31              5.44              5.58
+Feed Z R+/-jX Ohms            75.7 - j15.6      77.9 - j 9.0      80.5 - j 4.3
+75-Ohm SWR                    1.23              1.13              1.09
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing and a 0.25" Mast Wire
+AGT:  1.007 (0.03 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.31              5.44              5.58
+Feed Z R+/-jX Ohms            75.7 - j15.6      77.9 - j 9.0      80.5 - j 4.3
+75-Ohm SWR                    1.23              1.13              1.09
+
+0.1875" Wire with 0.7" Feed/Phase Line Spacing and a 0.3125" Mast Wire
+AGT:  1.007 (0.03 dB)
+Freq MHz                      420               435               450
+Gain dBi                      5.31              5.44              5.58
+Feed Z R+/-jX Ohms            75.7 - j15.6      77.9 - j 9.0      80.5 - j 4.3
+75-Ohm SWR                    1.23              1.13              1.09
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The data shown is uncorrected for the AGT. However, the difference between the AGT with and without the mast wire is too small to make a difference in the results.

+

The first comparison should be between the top two entries, with and without a central mast wire. The differential between the two data sets is too slight to see that a thin wire makes a difference to the performance of the batwing model.

+

The second comparison should be between the second and third data sets. Because the wire junctions between the 0.1875" antenna wires and the 0.25" mast occur at points that make no difference in the currents within the mast or the antenna wires, the junction of wires having different diameters creates no problems. The constant AGT between these two data sets provides the evidence of this, as does the identity of the gain and impedance values. (A similar effect is noticeable with symmetrical sets of radials forming ground planes or element end hats for monopoles or dipoles.)

+

The final comparison should be among all three sets of data for the changing diameter of the central mast wire. If a central mast is to have some effect on the overall performance of the array, it should show in some variations in the performance data. However, there is no change of performance at all across the 70-cm band.

+

There are, of course, limitations to the model. The mast extends only 10" above and below the antenna proper. Nevertheless, there is negligible mast current (less than 5E-6 relative to a source current of 1.0). Although there may be a "magic" mast length (or diameter) that shows significant increases in antenna currents, that length (or diameter) is likely avoidable.

+

The key limiting factor in the use of a central conductive mast will be physical. Such a mast will force the two lines making up the feed/phase system farther part, calling for a recalculation of the line Zo to achieve, with a given set of batwing dimensions, a desired feedpoint impedance. Hence, the strategies developed earlier in this modeling exercise would prove useful in the ultimate design of a practical batwing array.

+

Of course, one may use a non-conductive mast that is slightly offset from the arrays to permit more freedom in the design of the feed/phase line system. Conductive mounting brackets connecting the support mast to the central tower mast may have connections to the center of the batwing top and bottom horizontal elements for lightning protection.

+

Conclusion--or a Beginning

+

We have focused in this episode on the modeling issues. The limitations of the modeling software may preclude an absolutely precise model of an ultimate batwing design for a particular application. However, they can offer design strategies so that the field adjustments that we make have some initial sense of direction and potential result.

+

Translating the potentials of the batwing antenna into physical implementations offers too many turns for inclusion in this series of short notes on the antenna. If the modeling exercises have given some indication of the potential for this antenna, then perhaps they have done its work. The batwing has a large variety of possible wide-band applications beyond the television transmitting industry that it has long served. For amateur and commercial directional point-to-point communications or omni-directional horizontally polarized service, the batwing antenna may be among the best very wide-band antennas available. Especially at UHF, where we tend to lose more power in cable runs than anywhere else, the ability to achieve very low SWR values across a wide frequency range, when combined with the wide-band gain performance of the batwing, may give this antenna renewed life in many incarnations.

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+ +
+

Updated 04-01-2004. © L. B. Cebik, W4RNL. This item originally appeared in antenneX Mar., 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Batwing, VHF / UHF


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+

A 70-CM Wide-Band, Long-Boom Yagi with High Sidelobe Suppression

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L. B. Cebik, W4RNL

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The following small table shows the free-space forward gain and the front-to-sidelobes for both the E-plane and the H-plane for 3 long-boom Yagis. The boomlength is about 13.2 wavelengths in each case, although it will vary slightly, since we can only add elements in whole units. Each design is standard for its type. The DL6WU entry emerges from the program DL6WU-GG.EXE. The entry labeled "LB" (for "long-boom") comes from a modified and extended version of a VK3AUU array. The N6BV entry is an optimized Yagi for the 420-440-MHz range. The first two Yagis, although centered on 432 MHz, cover the entire 70-cm band. The N6BV Yagi used 3/16" (0.1875") diameter elements, while the other two arrays use 4-mm (0.1575") diameter elements. These are, of course, NEC-4 values for 432 MHz and would require adjustment for comparison with any test-range figures.

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+Series   Elements   Boomlength    Gain    E-plane Front-to-    H-plane Front-to-
+                    Wavelengths   dBi     sidelobe Ratio dB    sidelobe Ratio dB
+DL6WU      38       13.215        20.18       15.91                14.84
+LB         47       13.327        20.78       14.53                13.71
+N6BV       38       13.104        20.69       14.81                14.00
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The front-to-sidelobe ratio values shown for the 3 Yagis are typical for beams having this boomlength, although there are not too many designs that reach this length. The numbers are based on NEC-4 models of each array. They come from an archive of data that I developed for a large number of basic designs. I modeled the design for every length of boom within each design series from 2 wavelengths to either as far as the series goes or 14 wavelengths, whichever came first. The data appear in Long-Boom Yagi Studies, available from antenneX.

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The DL6WU Yagi is perhaps the standard against which we measure all other long-boom arrays. The top portion of Fig. 1 shows the E-plane (horizontal) and H-plane (vertical) patterns of the 38-element version of the array in free space.

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What would you pay for a long-boom Yagi of about the same boomlength that yielded the patterns in the lower portion of Fig. 1? In this context, I am not speaking of money. Rather, I am talking in Yagi terms. One way of paying is in dB of reduced gain. The other means of payment is in terms of element weight and wind load. The lower portion of the figure shows sidelobes in both planes that are suppressed by 10 dB or more from the corresponding sidelobes of the upper pattern. For any application in which reduced off-axis sensitivity to noise or signals is important, the sidelobe reductions may be important. As well, Guenter Hoch, DL6WU, reports that at higher UHF frequencies, atmospheric particulates may create enough diffraction to reduce overall gain if sidelobes are not more than 17 dB down relative to the main lobe. So the question remains: what would you pay for front-to-sidelobe ratios that are more than 20 dB over almost the entire 70-cm band?

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The Background and Dimensions of the C50 Yagi

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The C50 array uses 50 elements in the space that held only 38 elements in older Yagi designs. Fig. 2 shows the outline of the C50. You may note--despite the difficulty of picking out fine detail--that the element spacing and length values do not adhere to a fixed rate of increase or decrease. There are some cyclical elements built into the design.

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The history of the C50 begins with a 41-element 2-meter design by David Tanner, VK3AUU. His design used a higher element density per boomlength unit than more tradition designs, such as the DL6WU or the W1JR/HyGain beam. The original version of his beam, when transported by scaling to 70 cm, showed promise of raising the front-to-sidelobe ratio in both planes, but especially in the E-plane. Initial variations of his design showed promise of exceeding 19 dB at 432 MHz, but with a decrease in performance away from that design frequency.

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However, two principle components of his design remain in the C50. One is the interesting wide-band impedance-setting cell composed of the reflector, driver, and first director (mainly). Note that the reflector in Fig. 2 is shorter than the driver, and the first director is spaced close to the driver in a primary-secondary driver arrangement. His array covered all of the 70-cm band with an exceptionally low 50-Ohm SWR with a direct feed.

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The second feature of the VK3AUU array retained in the C50 is the compressed element spacing. However, the element spacing is even more compressed in the C50. (The C in C50 stands for Compressed spacing.) Compressed spacing is anther way of referring to high element density for a given boomlength. Whereas the DL6WU and N6BV Yagis used 38 elements in 13 wavelengths, the LB entry uses 47 and follows the VK3AUU spacing schedule--almost. The C50, of course, packs 50 elements on the same boom. So the weight penalty paid for the C50 is almost a half-pound of aluminum rod, relative to the oldest designs with proven wide-band properties, like the DL6WU. Although the DL6WU design uses a different impedance-setting cell design, it, too, is capable of full 70-cm band coverage with a direct feed and low 50-Ohm SWR values.

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However, not every design is susceptible to spacing compression with a good outcome in terms of gain and sidelobe performance. My experiments on the DL6WU series came to naught. Rather, the array must use a certain variability of both spacing and element length to eventually yield high sidelobe performance combined with adequate performance in all other categories that apply to wide-band Yagis. I would love to be able to present a series of calculation equations that perfectly describe the structure of the C50. However, the design emerged from what engineering calls manual iterative experimentation. We know it as trial and error.

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The dimensions of the C50 appear in Table 1. Both the element spacing and the element length values appear in millimeters, inches, and wavelengths. The last of the 3 forms may be useful for scaling the beam to other bands. However, remember to scale the element diameter as well as the cumulative boomlength and element length values. The model presumes a non-conductive boom or elements that are well insulated and isolated from a conductive boom. For through-boom construction, adjust the element lengths according to principles shown in "Scales". The element lengths appear as whole lengths for guidance to any construction and as half-lengths as guidance to modeling the antenna.

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How does the C50 stack up against the 3 representative designs using essentially the same boomlength? The patterns in Fig. 1 give some idea, and we may supplement those patterns with a performance report from the NEC-4 model. The data apply to the design frequency of 432 MHz. E BW and H BW refer to the E-plane and H-plane beamwidths, while E F/SL and H F/SL refer to the E-plane and H-plane front-to-sidelobe ratios. The other columns should be self-explanatory.

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+Elements  Boomlength   Gain   180-Deg Front-to-  E BW   E F/SL    E BW   H F/SL     Feedpoint Z     50-Ohm
+          wavelengths  dBi    Back Ratio dB      deg.   Ratio dB  deg.   Ratio dB   R +/- jX Ohms   SWR
+50        13.242       20.26    27.89            19.2   25.91     19.8   24.35      52.96 + j1.49   1.066
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The C50 forward gain in free-space is between the values for the DL6WU and the remaining 2 entries among the standard designs. Among all of the designs, the C50 shows a gain deficit of not more than 0.5 dB relative to the best designs in the group. (Of course, we can obtain more gain at the listed boomlength by using a narrower bandwidth, but that is not one of the goals for this design.) The possible gain deficit is the other cost for the 10-dB improvement in front-to-sidelobe performance.

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But are the costs worthwhile? I can give no fixed answer to this question. However, we can perhaps sort out some of the considerations. Consider first installing the beam parallel to the earth, horizontally polarized. Let's compare the DL6WU beam from Fig. 1 to the C50 at the same height. For modeling purposes, I selected a height of 10 wavelengths above average ground. The height is low--between 22' and 23' at 432 MHz. However, the height is also about as high as we can go and still obtain accurate indications of lobe maximums using an elevation plot with an increment of 0.1-degree. If we compare the elevation plots for both beams we obtain the patterns shown in Fig. 3.

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I have enclosed the multi-lobe elevation pattern structure inside the free-space envelope for several reasons. First, too few folks realize that the fit is perfect, once we adjust for the greater maximum gain of the antenna over ground. However, the peak values of the lobes result from reinforcing combinations of incident and reflected energy. Each one is offset by a null created by cancellation between incident and reflected energy. The result for the antenna over ground is an outline to the multiple lobes that exactly matches the free-space pattern.

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Second, there is no significant difference between the cluster of elevation lobes the fit inside the main free-space forward lobe for each Yagi. The significant differences appear in the first 2 sidelobes at higher elevation angles for the DL6WU array. The first sidelobe is less than 15 dB down, while the second is less than 20 dB down. For the C50, both lobes are nearly 25 dB lower than the strength of the main lobe.

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Over ground, the main lobe has a gain of over 25 dBi. We may determine the gain of the sidelobes by subtracting the front-to-sidelobe ratio from the forward gain. For a sidelobe that is down by 15 dB, the sidelobe gain is 10 dBi. For a sidelobe ratio of 20 dB, the sidelobe gain is 5 dBi. When the sidelobe ratio reaches 25 dB, the sidelobe gain is about 0 dBi. In terms of basic transmitting and receiving, none of these values is insignificant. However, gains of 5 and 10 dBi are certainly less desirable in sidelobes than a gain of 0 dBi.

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How important these sidelobe gains are to a particular operation depends on the operational specifications and needs. For point-to-point terrestrial communications, the high-angle lobes might not be very significant, especially if the beam has excess gain relative to the needs of a given communications path. However, if we angle the antenna upward, we might reach a different conclusion. With the antenna pointed straight up, all sidelobes are in play and the beam gain is essentially the same as the free-space gain. Even at a 45-degree angle, we find the free-space gain (without the benefit of ground reflections) and all sidelobes. Since we have both E-plane and H-plane sidelobes of similar strength, we can picture them as a kind of halo around the main beam. The stronger the sidelobe, the more the antenna is susceptible to off-axis noise and signals. Hence, for operations with non-terrestrial targets--such as EME work--the sidelobe structure may acquire a different level of importance.

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The C50 as a Broad-Band Yagi

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We have so far concerned ourselves with the performance of the C50 at the design frequency, 432 MHz. However, the C50 design covers of the entire 70-cm band. It is certainly possible to wring more gain out of fewer elements if we are willing to settle for a narrow bandwidth. For expert builders with high precision shops and high precision tune-up equipment, a narrow bandwidth antenna may be suitable to operations that never exceed some small subsection of the band. Most builders do not have access to this level of precision. If nothing else, a wide-band Yagi design tends to assure the careful home builder that the design will likely work at midband and with performance close to the specifications.

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When working toward the C50, I used the following design specifications.

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  • 1. Forward gain: >19.6 dBi free space
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  • 2. 180-degree front-to-back ratio: >20 dB and desirably >25 dB
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  • 3. Front-to-sidelobe ratio: >20 dB in both E-plane and H-plane
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  • 4. Feedpoint impedance: 50 Ohms with <1.25:1 SWR
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  • 5. Bandwidth: all specifications met from 420 to 450 MHz.
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Although I would like to report that the C50 passes all tests, it actually misses a couple of them by a smidgen or 2. Still, it comes closer to meeting all of these specifications than any other long-boom Yagi with which I have any acquaintance. For that reason and despite its imperfections, the design is still worth passing along.

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When examining broadband characteristics for any beam, many modelers are content to set the frequency sweep increments wide and to cut off the sweep at the exact band edges. However, I prefer to use a wider sweep passband in order to watch the trends in performance degradation outside the operating portion of the sweep range. Because Yagis tend to show a slower rate of degradation below the lower band limit, I tend to extend that range further than I do the upper end of the sweep, where performance decays more rapidly. The wide-band plots come from AC6LA's EZ-Plots program.

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Fig. 4 shows the wide-band gain and front-to-back performance of the array from 400 to 460 MHz in 1-MHz increments. The gain peaks in the 431-433-MHz span, exactly around the design frequency. The peak value of 20.26 dBi compares to 19.76 dBi at 420 MHz and 19.69 dBi at 450 MHz. The maximum change of gain across the 70-cm band is 0.57 dB. Gain falls off very slowly beyond the operating limits and still exceeds 17 dBi at 400 MHz.

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The 180-degree front-to-back ratio is the easiest parameter to determine automatically in a frequency sweep. Since the lobe structure to the rear changes with frequency, determining a worst-case front-to-back ratio requires a manual investigation at each frequency. Yet, we can obtain a good picture of the worst-case front-to-back ratio simply by connecting dots, specifically the dots at the lowest level of each dip in the 180-degree front-to-back value. Within the operating passband, the lowest front-to-back value exceeds 25 dB. Even at 400 MHz, we still have a front-to-back ratio that exceeds 13 dB.

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The wide-band feedpoint data appear in Fig. 5. As with all long-boom Yagis that I have examined in detail, there are as many peaks in the resistance and reactance curves, and as many (largely invisible) dips in the SWR curve, as there are peaks in the 180-degree front-to-back curve across equal sweep ranges. In all wide-band impedance-setting cell designs, the resistance peaks and the inductive reactance peaks are offset, which tends to level the SWR. (The capacitive reactance peaks, of course, show up as visual dips, but they are equally offset.)

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The resistive component of the feedpoint impedance begins to drop significantly above 450 MHz. Hence, the SWR curve is only usable to about 455 MHz. At the low end of the sweep range, the SWR is usable all the way down to the lowest swept frequency. Between 420 and 450 MHz, the 50-Ohm SWR value only climbs above the specification limit of 1.25:1 at 2 frequencies: 446 and 447 MHz, but it remains below 1.3:1.

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In the present context, Fig. 6 may be the critical sweep. It shows the front-to-sidelobe ratio for the array in both the E-plane and the H-plane. The E-plane ratio remains above 20 dB all the way down to 420 MHz. The H-plane value drops slightly below 20 dB between 422 and 423 MHz, and at the band edge is 19.15 dB. The sidelobe ratios maintain a high ratio above the upper end of the 70-cm band.

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The jagged nature of the curves calls for some explanation. If we examine the region from 430 to 432 MHz as an example, we shall encounter what amounts to a limitation in the way a modeling program identifies lobes in a pattern. Fig. 7 presents E-plane patterns for 3 frequencies to show the situation. The graph curves for each plane are nicely parallel so that the explanation also applies to H-plane sidelobe curves.

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In the pattern for 431 MHz, the sidelobe line identifies the strongest sidelobe. Modeling programs identify a lobe by detecting the fact that the gain value for a given direction in the pattern is higher than the gain values for both adjacent headings in the pattern. As earlier noted, the front-to-sidelobe ratio is the difference between the maximum forward and the gain at the identified sidelobe.

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The most critical part of the exercise lies in the transition to 432 MHz. Sidelobes do not pop in and out of existence. Rather, they evolve. The first forward sidelobe both diminishes and folds into the main lobe as we increase the operating frequency. At a certain point in its life, it no longer presents a lower gain value on both sides of a peak value for some given increment of pattern survey. The patterns shown used an angular increment of 1 degree. At 432 MHz, the sidelobe does not show a lower gain value at this increment as we move toward the main-lobe bearing. (It might show such a lower gain value if we use a finer survey increment, such as 0.1 degree.) As a result, we may only view the remnant of the sidelobe as a "bulge" in the main lobe. In general, virtually all long-boom Yagis have "impure" main lobes, especially away from their design frequencies. Rather, the main lobe is the sum of numerous bulges. For shorter boomlengths, Yagi patterns at the upper ends of their operating ranges often show a "bullet" shaped pattern rather than the "tear-drop" pattern that appears at the design frequency.

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The evolution of sidelobes affects not only the first forward sidelobe, but all sidelobes. Since the array shows its highest forward gain at a certain frequency (here, 432 MHz), the gain deficit at the band edges represents energy going elsewhere. Below the design frequency, part of this energy appears as a wider beamwidth. At 420 MHz, the beamwidth is over 1 degree wider than at 432 or 450 MHz. As well, some of the energy appears in the collection of sidelobes, both fore and aft of the headings at right angles to the main lobe heading. The result is often a more complex arrangement of lower order sidelobes. Fig. 8 shows the E-plane and H-plane patterns of the C50 for both the E-plane and the H-plane. Compare the patterns to the lower part of Fig. 1, especially for the H-plane in which the geometry of the element tips along the total boomlength exerts less control over the sidelobe direction.

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Although the patterns shown have too small a scale to give more than a general impression, sidelobe analysis is significant to the overall evaluation of a Yagi design. For every wavelength of boom, there will be 4 sidelobes, 2 forward and 2 aft. Hence, the longer the boomlength, the more difficult it becomes to evaluate all sidelobes, especially if we examine patterns at low angular resolutions. (There are exceptions to the 4-lobe-per-boom wavelength rule. Some Yagi design techniques may result in overlapping lobes so that the total number is fewer than the norm. However, techniques of true sidelobe suppression, rather than the attenuation shown by the C50, are still in their infancy and of uncertain utility.)

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The extended sweep of the C50 shows that it almost meets every design specification. Where it falls short, it does so only in a minor way. Hence, as a long-boom Yagi for 432 MHz and surrounding frequencies, it appears to have adequate gain and other basic properties combined with high sidelobe attenuation. As I reported at the beginning of these notes, the sidelobes are down about 10 dB relative to more standard Yagi designs. The cost is small: a maximum forward gain level that is very slightly less than the maximum I have been able to squeeze from standard designs and the added weight of several more elements.

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The C50 as a "Trimming" Yagi

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The classic DL6WU Yagi design has some interesting properties. Foremost among them is the fact that it forms a "trimming" Yagi series. That is, to form a perfectly usable Yagi with a sorter boomlength than may be at hand, simply remove the forward-most directors down to the desired boomlength. The resulting Yagi will perform at the gain appropriate to the new boomlength and will have an adequate front-to-back ratio and a wide-band feedpoint impedance curve. In the history of long-boom Yagi design, there have been numerous other trimming Yagi series. They tend to result from the fact that a well-designed impedance-setting cell and the immediate directors ahead of it remain relatively stable, regardless of the number of added directors. For example, the DL6WU series is rated for booms from about 2 wavelengths up to about 39 wavelengths.

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We may treat the C50 in the same manner, trimming directors one at a time down to a boomlength of about 2 wavelengths (12 elements). I do not recommend the trimming unless the operating properties are adequate to a particular application. Indeed, for the shortest lengths in the series, you may wish to optimize a particular design within whatever operating specifications you set. In the present context, the trimming exercise has a different function. It may tell use something about the design itself.

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The exercise is simple enough at the design frequency. I simply removed the forward-most director and recorded data on the slightly shorter model at 432 MHz. The results of that exercise appear in tabular form in Table 2.

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Because the data may form a confusing mass, I have also constructed a few graphs to chart the progressions with increasing numbers of elements. (Graphing by pure boomlength would have added a complication to the graphs, and we can effectively only add a whole element at a time.) Fig. 9 shows the free-space forward gain and the 180-degree front-to-back ratio.

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The gain curve is entirely normal, with gain levels comparable to standard Yagi designs for each boomlength represented by the element count. The front-to-back ratio curve (or picket fence?) perhaps calls for a note. The 180-degree front-to-back peak value shifts in frequency for each added element. Sometimes, the peak is at or very close to the design frequency, and sometimes it is more distant, resulting in a lower value at 432 MHz. For any range of boomlengths (represented by the element count in the graph), the number of peaks that occur from the shortest to the longest boom is a function of the element density or average number of elements per unit of boomlength. Equally dense Yagi designs, even if different in in element placement and length, tend to show the same number of peaks for the same range of boomlengths. Both the DL6WU and the N6BV series of Yagis would show about 5 peaks for the range in which the C-series shows 16. Both of those other series use 38 elements total, whereas the C-series uses 50 total. The rise in the number of peaks is hence exponential with increases in element density.

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Fig. 10 provides use with the feedpoint data across the range of possible C-series Yagis from 12 to 50 elements. Although the values are useable for the entire set, the fluctuations tend to flatten out noticeably somewhere close to the 28-element mark. The leveling out is not solely a function of the 50-Ohm SWR, but also appears in the resistance and reactance curves. Perhaps the most significant reason for showing this graph is to note that the number of peaks in either the resistance or the reactance (taking either the inductive or capacitive peak values) curve is close to the number of peaks in the front-to-back curve, usually the same or only 1 more or less. In our frequency sweep of the C50, we noted a similar relationship between the feedpoint conditions and the 180-degree front-to-back ratio value.

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In Fig. 11, we find something very normal: a smooth curve of both the E-plane and the H-plane beamwidth values. The longer the boom, the narrower the beamwidth, with the E-plane value always slightly narrower than the H-plane value. The longer the boom, the closer the two values grow toward each other. At the longest booms, we find a limitation within the modeling environment. The technical definition of a half-power point is that point in the pattern where the gain is 3-dB below the highest gain. With a limited sample of directions, the reported -3-dB points will rarely appear with precision. Therefore, any program must do one of two things. First, it can simply use the closest value to -3 dB or perhaps even the value that first exceeds -3 dB. Or, more complexly, it can interpolate the -3 dB point from the values at sampled headings just above and below that value, with a resulting interpolation of the heading at which the calculated values would occur. For such cases, it does not make much sense to carry the heading values (and the angular distance between them) to many decimal places. Whatever the system actually used, EZNEC gives the beamwidth heading values to 1 decimal place, with a resulting step of 0.2 degrees per total beamwidth change (a 0.1-degree change in heading on each side of the main lobe).

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Most standard design Yagis would end the sequence of graphs at this point. Traditionally, Yagi designers have let the front-to-sidelobe ratio be what emerged from the design. However, we have treated the C-series as a design for applications where higher sidelobe attenuation is needed. Hence, Fig. 12 is a necessary addition to the record of data trends.

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First, let's tackle the sudden drop in the H-plane front-to-sidelobe ratio between 20 and 19 elements. The drop is not nearly so sudden as the graph makes it appear. At 20 elements, the main sidelobe is actually a bulge of the order that we examined earlier. However, it is the main bulge, with other sidelobes very much weaker. At 19 elements, the modeling program can detect with a 1-degree pattern increment a lower gain on either side of the bulge. Hence, the bulge takes its place among the identified sidelobes. However, the bulge is large enough to make the use of the C-series questionable with respect to sidelobe reduction for many elements longer than the 20-element transition point.

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In fact, the imperfection of the C-series as a trimming-Yagi series shows itself at the opposite end of the scale. The sidelobe ratio in both planes is on a rising curve relative to increasing boomlength at the 50-element mark. Every unit shorter reduces the sidelobe performance by a small amount. At the design frequency, the sidelobe properties level off in the 20-dB region, with usable lengths down to perhaps 31 elements (a little under 7.4 wavelengths of boom). However, expect sidelobe performance that is poorer as we move away from the design frequency, especially downward. Hence, the shorter the C-series Yagi, the more it becomes a spot-frequency Yagi in terms of its sidelobe performance, even though it retains quite usable performance in all other categories for even shorter versions. As well, in general, the sidelobe performance will exceed that of most other designs from the 25-element range upward. For truly wide-band use with very high sidelobe performance, perhaps the minimum recommended element count is 43 (or 11 wavelengths of boom).

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A more perfect Yagi with sidelobe performance as one of the design specifications would show more level properties of front-to-sidelobe ratio throughout more of its range. Whether achieving this goal is possible in a trimming series is not known at this time. Detailed revisions to both element spacing and element length are the routes to discovering if the C-series is amenable to being a truly adequate trimming Yagi in all respects. However, it may also be the case that for each length of boom, individual optimization may be required to achieve the added 10 dB of sidelobe attenuation attained by the C50 itself. Of course, anyone is free to develop a C60.

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The design exercise that we have examined in these notes has aimed to show that it is possible to design a long-boom Yagi with high sidelobe performance while retaining both wide-band operation and reasonably good gain and front-to-back performance. The compression of element spacing combined with a usable element-length schedule has produced such a design, whatever the practicality of its use. But the study also shows that we still have a considerable ways to go before we can master the art of long-boom Yagis. Along that route, the techniques used to develop the C50 are but clues to a complex set of design parameters.

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Updated 07-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX June, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: VHF / UHF, Yagi


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CAP Emergency-Beacon Direction-Finding Antennas

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L. B. Cebik, W4RNL

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The Civil Air Patrol has acquired a new urgency to monitor the emergency radio beacons of downed aircraft. These beacons operate at 121.5 MHz, with a strong third harmonic at 364.5 MHz.

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I have long held CAP in high regard, since in the 1950s, my father and mother were CO and Exec for the Bridgeport, CT, squadron. Indeed, among my parents and two brothers, I was the only family member not to obtain a pilot's license, although I did serve the USAF in the late 1950s and early 1960s as an air traffic controller. I guess I always wanted to be able to tell my brothers where to go.

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When asked if I had any designs adaptable to the new requirement, not only to monitor the emergency beacons, but to perform direction finding (DF) work in the field to locate downed aircraft, I came up with a pair of serviceable designs. Each design has versions for 121.5 and 364.5 MHz, exact 3:1 scalings. In addition to being good DF antennas, an added requirement was that the antennas may be assembled and disassembled, the latter need a function of having to carry them in aircraft to a search site.

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A good DF antenna--short of a Doppler multi-antenna DF array--needs to have an adequate forward gain lobe and a deep rear null. The forward gain acquires the signal. However, the deep rear null allows a more accurate determination of the direction to the signal, since the null is much sharper, that is, narrower in terms of the headings at which the signal disappears or is weakest. Like all CAP skills, it takes practice to use a DF antenna effectively.

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We shall divide our work into 3 parts. First, we shall look at a simple design--a Moxon rectangle--that is smaller: only 35" by 13". Then, we shall examine a 3-element Yagi. It is larger: 49" by 30". These numbers apply to the 121.5-MHz version. The 364.5-MHz antennas are exactly 1/3 size. Whichever frequency we choose, each design has advantages and disadvantages. Finally, we shall examine some construction suggestions, many of which apply to either design.

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DF Moxon Rectangles for 121.5 MHz and for 364.5 MHz

The Moxon rectangle is a simple 2-element array composed of a driver and a reflector. Because it folds its element ends toward each other, it obtains a smaller footprint than a comparable 2-element Yagi. As well, the combined coupling of the parallel elements and the tail tips provides a deep front-to-back ratio that provides a good DF rearward null. +
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Fig. 1 provides the outline of the Moxon rectangle. The proportions apply to the versions for both frequencies. The following table provides the dimensions in inches for each frequency. A is the total side-to-side length. B is the length of the forward or driver tail. C is the gap between tails. D is the reflector tail. E is the sum of B, C, and D, giving the total front-to-back dimension.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      DF Moxon Rectangle Dimensions
+           Dimension        121.5 MHz             364.5 MHz
+           Diameter         0.375                 0.125
+           A                34.77                 11.59
+           B                 4.36                  1.45
+           C                 1.87                  0.62
+           D                 6.74                  2.25
+           E                12.97                  4.32
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The Moxon dimensions are dependent upon the element diameter, so they will be somewhat off if you choose a different material. We shall discuss my recommendation for 3/8" diameter 121.5 MHz elements in the construction section. The most critical dimension is the gap between tail tips. They need to be well aligned and maintain their spacing during antenna use.

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The Moxon rectangle has modest gain with a broad forward lobe. The following performance table applies equally to the 121.5-MHz and 364.5-MHz versions. The gain is for free-space and is provided as a comparison with the Yagi design to come later.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              Modeled Performance Data:  DF Moxon Rectangle
+
+Category                                    Performance
+Free-Space Gain in dBi                        5.9
+180-Degree Front-to-Back Ratio               34
+Horizontal Beamwidth, Degrees                79
+Vertical Beamwidth, Degrees                 144
+Feedpoint Impedance, R+/-jX Ohms            54 - j0
+50-Ohm SWR                                  1.08
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The Moxon rectangle supplies moderate gain in a very broad forward lobe, whether held vertically or horizontally. (With a downed aircraft, one may have to hold the antenna in either manner--or at an intermediate angle--for the strongest forward signal.) The direct front-to-back ratio provides a deep rear null. Fig. 2 shows the patterns for both horizontal and vertical orientations of the antenna.

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The Moxon has less gain than a 3-element Yagi, but it is smaller and lighter to wield. As well, its design allows direct connection of a 50-Ohm coaxial cable with no matching considerations. Since we use the antenna only in receiving applications, we do not need to consider a balun device. Fig. 3 shows the SWR curve from 120-MHz to 123 MHz. A similar curve, centered on 364.5 MHz would apply to the smaller antenna.

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The Moxon is one route to effective DF work, if the gain is adequate to the field situation. However, if we need more forward gain to acquire the emergency beacon signal, we should turn to a larger array.

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3-Element DF Yagis for 121.5 MHz and for 364.5 MHz

Standard Yagi designs strive for maximum forward gain from a given number of elements and boom length. However, we may also design a Yagi for maximum front-to-back ratio, sacrificing some gain for the good DF null to the rear. That is the operative design specification that produces the 3-element Yagi outlined in Fig. 4. +
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Note that the driven element is fairly well centered between the reflector and the director. The following table provides the dimensions for both frequencies, again using 3/8" elements for 121.5 MHz and 1/8" Elements for 364.5 MHz. Because we need two spacing columns, one for inter-element spacing and the other for cumulative spacing, we divide the dimensions into separate tables for the two frequencies. All dimensions are in inches.

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+                      3-element DF Yagi Dimensions
+
+Element          Length          Spacing          Cumulative Spacing
+
+121.5 MHz (0.375" diameter elements)
+Reflector        48.66           -----            -----
+Driver A         44.29           15.31            15.31
+(Driver B)       46.00           15.31            15.31
+Director         42.11           13.92            29.23
+
+364.5 MHz (0.125" diameter elements)
+Reflector        16.22           -----            -----
+Driver A         14.76            5.10             5.10
+(Driver B)       15.36            5.10             5.10
+Director         14.04            4.64             9.74
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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With the dimensions shown, the Yagi--whichever the frequency--has the performance characteristics shown in the table that follows.

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+              Modeled Performance Data:  3-Element DF Yagi
+
+Category                                    Performance
+Free-Space Gain in dBi                        7.7
+180-Degree Front-to-Back Ratio               45
+Horizontal Beamwidth, Degrees                65
+Vertical Beamwidth, Degrees                 108
+Feedpoint Impedance, R+/-jX Ohms:
+  Driver A with matching stub               51 + j2
+  Driver A 50-Ohm SWR                       1.05
+  Driver B without matching stub            32 + j2
+  50-Ohm SWR                                1.55
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The gain of the Yagi is nearly 2 dB greater than for the Moxon rectangle. The rear nulls of both are so deep that there is no practical difference in the two numbers for this category. The Yagi forward beamwidth in either a horizontal or a vertical position is considerably narrower than the Moxon. Hence, for the added antenna area and weight, we obtain more gain and a somewhat better ability to stay on course when pointing the antenna at the target. Fig. 5 clearly shows the narrower beam angle of the Yagi, relative to the Moxon.

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You have a choice between two drivers. They differ in length but use the same spacing from the reflector and director. Driver A is designed for use with a shorted stub placed across the feedpoint terminals. It is a 37.5-Ohm transmission line stub constructed from parallel section of RG-59 or other 75-Ohm coaxial cable (or even some old 75-Ohm parallel transmission line). Driver B is the length if you choose not to use a matching section.

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The matching section allows a near-perfect match between the feedpoint and a 50-Ohm main feedline, using the Driver A length. With the alternate length, B, the SWR is about 1.55:1, which is adequate for almost all purposes and simplifies construction. Fig. 6 shows the comparative SWR curves for the two versions of the antenna.

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The following table lists the physical lengths of shorted stubs using two different velocity factors. The 0.8 value applies to most foam insulation versions of RG-59 or similar 75-Ohm cables. 0.67 applies to standard solid dielectric cables. Note that when paralleling cables for a lower impedance, we cut each to the specified length and tie the braid to the braid and the center-conductor to the center-conductor. Of course, at the shorted end, we tie everything together. To tie lines together means to establish a good physical junction that we then solder and seal. Dimensions are in inches.

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+                 Driver A Matching Shorted-Stub Lengths
+
+Length                           121.5 MHz             364.5 MHz
+Electrical: VF = 1.0             14.90                 4.97
+Foam:  VF = 0.8                  11.92                 3.97
+Solid:  VF = 0.67                 9.98                 3.33
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Because constructing an accurate short stub of paralleled transmission line at 364.5 MHz is quite tricky and more than a little bit finicky, I recommend that you use Driver B for the upper frequency antenna. For the 121.5-MHz version, you have your choice.

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The Yagi is bigger, heavier, but performs somewhat better than the Moxon. However, either is capable of giving good performance within the gain needs of the situation.

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Building a DF Antenna

A DF antenna for the field must be as light as feasible, durable in use, but able to be disassembled for transport in a small package. Although these requirements are not easy to implement, we have a major advantage. Since the antenna will remain disassembled except during use, we need not concern ourselves too much with eliminating contact between dissimilar metals. That fact opens up some potentials of the local home center hardware sections. +

Let's begin with the 3-element Yagi for 121.5 MHz. I recommend the use of 3/8" elements because we can obtain good 6063-T832 aluminum tubing from standard mail order sources, such as Texas Towers. It comes in 6' lengths for UPS shipping, so 3 lengths will meet our needs.

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Note that the boom is shorter than the elements. Therefore, if we can have a boom with the element centers permanently attached, we can take off the outer ends of the elements and pack them in line with the boom for a transport package about 30" long. See Fig. 7 for the general idea of how this might work for the director and the reflector (as well as for the Moxon reflector).

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The boom should be 1/2" nominal PVC, which has an outer diameter close to 1". We shall treat the driver element separately, so let's begin with the reflector and the director. Obtain some threaded brass rod, 5/15" in diameter. (Steel is fine, but harder to cut, while aluminum is hard to find.) Cut two 3" or so lengths. Drill the boom just under 5/16" and either tap the hole for threads that match the rod or use the rod itself to cut threads. Install the reflector and director threaded rods in the PVC.

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Now cut two pieces of 3/8" aluminum tubing in half. Tap the ends to create 5/16" threads to match the rod. Do not tap much beyond the end of the threaded rod projections from the PVC (about 1") or you will create a weak point in the element. Now thread the elements on the rod projections. Measure the total length of the reflector and the director so that the tip-to-tip length equals the dimension chart. Trim the ends.

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Of course, I am omitting from each step the need to have clean smooth ends. The threads need to be especially clean, since we do not wish to destroy the interior threading of the tubes with metal burrs. The outer ends need to be smooth for operator and bystander safety.

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We can use the same system on the smaller 364.5-MHz Yagi. However, lets use threaded 1/8" brass rod for both elements. After tapping the boom at the correct positions, we can simply thread the element into place. Since this antenna is only 16" by 10", once assembled, it can stay assembled for transport. So a drop of epoxy at the boom-element junctions should hold things in place permanently.

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The driven elements require different treatment. See Fig. 8 for some ideas.

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For the driven element of the 121.5-MHz antenna, we shall need a non- conductive plate, perhaps a 2" by 4" piece of 1/4" Lexan, plexiglas, or similar. The 4" dimension projects to the sides of the boom. Fasten the plate to the boom with sheet metal screws into the boom--or use nuts and bolts. Lock the nuts with sealer, since they will stay in place.

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From the 5/16" brass rod, cut two 3" pieces. With a drill press, drill a pair of holes to pass through the rod and into each side of the plate. We now have two rod sections with a small gap between them and extending over the plate ends. Tap two more sections of aluminum tubing, place them over the rod ends, and trim to length--either A or B, depending on your choice.

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The brass rod will accept solder. Therefore, you may solder the main feedline directly to the rod at the gap--the braid to one side and the center conductor to the other. For this operation, it pays to remove the rod from the plate and use a temporary wood plate instead. The heat of soldering may deform the plastic material. Alternatively, you can install solder lugs under the bolts closest to the gap and use these for attaching the feedline. When you re-assemble the driver plate, if you use a matching stub, you can tape it to the boom. There is no need in this antenna to waste coax connectors.

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The 364.5-MHz antenna requires somewhat different treatment. A 1/2" thick plate of plastic will serve as the feedpoint and driver mount. We only need a piece about 1.5" wide by about 2" side-to-side. Use screws through holes in the block to attach it to the boom.

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The trickier part is the element mount. Drill a hole (it can be threaded to match the brass rod) from one side of the block to the other. Or drill separate holes from each side limit inward. Now drill a larger hole on each side of the center line to give you access to the half element that you will insert or thread into the long holes. Use these holes to solder the transmission line to the two halves of the driver. Solder quickly and carefully with a well-heated iron to prevent damage to the plastic block. I am assuming you are using Driver B and only need to trim the length so that the driver matches the dimension sheet from tip-to-tip.

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You may coat soldered connections with Plasti-Dip or similar material for weather protection. The only step left is to add a handle. For the small Yagi, you can use a PVC coupling--either cemented or threaded--and add PVC sections of your choice to make a convenient handle. Remember that you may have to use the antenna at any angle from vertical to horizontal.

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The large Yagi can also use an end handle, although the weight may be more tiring. An end handle lets you stand behind the antenna which creates less pattern distortion. However, for taking null readings, you may have to hold it overhead.

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Alternatively, you can break the PVC boom and add a Tee fitting (making sure that the reassembled boom maintains the correct element spacing). From the Tee, you can add PVC fittings of your choice to create the most comfortable grip to keep the antenna overhead. Height does make a difference in both forward signal acquisition and in null determination.

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The Moxon rectangle can use many of the same techniques as the Yagi. For 121.5 MHz, the threaded brass rod at the reflector allows you to attach the reflector halves without going around corners through the element hole. At the forward or driver end, the brass rod permits soldering directly to the coax able pig-tails. PVC makes a good boom, with the same handle-fitting considerations as on the larger Yagi.

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The key is bending corners. However, most plumbers tubing benders will handle up to 3/8" material. Go slowly to prevent crimping. If necessary, fill the tube with fine sand before bending. Use slow and steady pressure.

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Allow excess tubing at both ends of each half element. Then fit the pieces together to align the tail tips and assure measurements. From the boom center line, each driver should measure a total of 1/2 A plus B, and each reflector should measure 1/2 A plus D. Use a small piece of nylon tubing or similar to keep the tips aligned and properly gapped.

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The 364.5-MHz Moxon can use the same driver assembly method as the Yagi for that frequency, except that the ends will bend pack. You can use a single piece of brass rod for the reflector if you use a rear handle. Simply cut a slot into the boom rear and align all of the pieces, including the tips with the positioning nylon tubing. Since the smaller Moxon will be a unit, you can then use epoxy at the slot-to-reflector junction to fix the position. Then add couplings for a rear handle.

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For the larger Moxon at 121.5 MHz, consider a Tee fitting at the boom center for a centered vertical handle. See Fig. 9. Cement only one side of the Tee onto the boom. Since the nylon tip tubes can slide off and since one side of the boom can slide off, you can break the Moxon into 2 pieces for bagging and transport.

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I have debated whether to add more than the three sketches of these construction ideas. I decided not to do so. The sketches are only suggestions of some, but certainly not all, ideas. You will have to adapt them to local circumstances in any event. Therefore, anything that is not perfectly clear in words, you will have to think through, and that may open to you many new ideas to use materials to which you have access and with which you have some facility.

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So these notes present at least two types of antennas, with complete dimensional data, that will serve the beacon monitoring and direction finding needs for most CAP filed operations. There are other antenna systems that you might use, but these are inexpensive and amenable to basement or garage shop construction at a small cost using easily obtained materials. Nevertheless, cheap does not mean careless. The utility of the antenna in the field, both in terms of performance and durability, will depend on the care that you use in construction. Pooling talent is a good way to obtain the best construction.

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Eventually, commercial antenna makers will discover that there is a market for antennas of these types or similar ones, given the intensification of the requirements on CAP and possibly other agencies for monitoring and field antennas for the beacon frequencies. Until then, these designs provide a nice challenge for the home workshop--not to mention a very important public service from CAP and other volunteers.

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A Note on 2-Observer DF-Fixing

Radio direction finding (DF) remains an art filled with maps and grease pencils in many circles. The standard technique, illustrated in Fig. 10, shows a target--with a radiating emergency beacon or other radio signal--at the center of an array of observers. +
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Each observer takes a reading and conveys it to a central location. There, a map reader who knows the location of each observer draws a heading line from that observer across the map. Where the lines intersect must be the target.

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Initial observations are often limited to single approach area, so the differences between heading readings may be small. Under these conditions, the single-dot target becomes a target area.

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Since the initial approach area may often be restricted, let's see if we cannot develop a different approach to the problem of locating the target. The approach will be based on taking reading on the fly with the use of highly directional antennas and accurate compass work. This phase of the work is always a limiting factor in any target location operation. We require the most accurate heading--usually taken by reference to a deep null in the antenna pattern--accompanied by the most accurate possible compass reading.

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In the late 1950s, USAF control towers were fitted with a UHF DF device to give the bearing of any radio transmission used by USAF pilots on any of the UHF channels. If the pilots navigation receivers were out, we could steer him toward the base. About 1960, two interesting things occurred. First, Sgt. Achee (my memory does not have his first name on file) and I developed a 1-station DF-fix calculator and submitted it through channels. Second, the idea, while praised, was not acted upon, because the DF gear was systematically removed from control towers. However, our tests with aircraft stationed at the base (Webb AFB in Big Spring, TX, now closed) proved the technique to be sound.

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The technique we used was to create an initial bearing. Then we had the plane fly for 1 minute at right angles to the heading. The airspeed and time gave us the distance flown. We took a second bearing. Finally, we calculated the distance of the aircraft from the base. Back then (1959-60), we modified a circular slide rule with the necessary scales to make the calculation a 30-second affair.

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Now suppose that we have two ground observers fitted with highly directional antennas and compasses. Further, let them be have two other small pieces of gear: a GPS receiver to determine highly accurate positions and a pocket-size programmable calculator. If our target is a downed aircraft with a radiating beacon, we can achieve the same DF fix on the fly.

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Since I do not have access to CAP or USAF training materials dealing with locating downed aircraft, the following notes may be replicating an existing wheel. However, on the chance that the notes might be useful, I'll go through the procedure anyway. Who knows where the ideas may not yet be known and hence prove useful.

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Fig. 2 sets forth an idealized situation of 2 observers, each roughly equidistant from the target. Each observer takes a heading to the target. If the two headings are close to identical, then the first step is to send one of the observers at a roughly right angle to the heading for a specified distance, perhaps 1/10 the initial estimate of the possible distance from the target. When the second observer takes a new reading, the triangle will be a closer approximation to the ideal.

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At this point, we know several things of very great interest.

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  • 1. From either (or both) GPS readings or known positions, we know how far apart the two observers are. That is, in terms of our triangle in Fig. 2, we know side c.
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  • 2. From the difference between the two readings of the target heading, we know the angle C.
    • +
  • 3. From our right angle maneuver, we know that the distances between observers to the target are about the same. In other words, side a = side b.
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That is all of the information that we need to do a rough calculation of the position of the target in terms of its distance from the observers--remembering that we already have the headings.

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The key is a much overlooked simple trig relationship called the law of sines:

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The letter designations correspond to those in Fig. 2.

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Under the assumption that the two sides, a and b, are about the same length, we can calculate angle A (or angle B), since it is one half the difference between 180 degrees and angle C. Hence, we can calculate the approximate length of side a from the following equation.

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We can plug this equation into a programmable calculator. We only need to enter the difference between the readings of the two observers and the distance apart of the two observers, and a distance to the target will emerge. Together with the headings, we can place the target--at least well enough for the observers to leap forward toward it.

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The benefit of the technique is that it does not require transferring data to a map--not always an easy task in the field. As well, even if initial readings are not precise, the observers can move at least 50% of the way toward the target at the highest feasible field speed before taking the next set of readings.

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An Example

Suppose that we let the distance between observers by 5 (in whatever units you choose). Also suppose that the difference between headings taken by the observers is 20 degrees. The sine of 20 degrees is 0.3420, as any pocket calculator will tell. +

Assuming that both observers are about the same distance from the target, then angle A (or angle B) will be (180-20)/2 or 80 degrees. The sine of 80 degrees is 0.9848.

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If we plug this information into equation (2), the calculator gives us a result of 14.398 in the same units as we used for the side c value.

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As a check, the ratio of side c to sin(C) is 14.6199. The ratio of our calculated side a to sin(A) is 14.6202.

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The smaller the value of angle C, the higher the potential error. As we initially noted, the readings of the observers with respect to the heading to the target also affect the reliability of the results.

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Nevertheless, the technique does allow two observer teams to proceed at a fairly rapid pace toward a target with almost instantaneous checks on their positions with respect to the target. The technique cannot overcome canyons, cliffs, and other impossible terrain, but it might help speed the process of locating a target without having to transfer data to a map while on the move.

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Updated 05-05-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Moxon, VHF / UHF, Yagi


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The Case of the Curly Collinear

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L. B. Cebik, W4RNL

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Sometimes only a couple of back-to-back questions about the same antenna will spark my interest in it. The curly collinear is just such an antenna. Everyone has seen them mounted on cars, trucks, and SUVs. But apparently, not everyone is familiar with how they work.

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Fig. 1 shows a sketch of a typical curly collinear. The upper section is about 5/8 wavelength. The lower section can be a 1/4 wavelength or 5/8 wavelength monopole--with and without radials in commercial implementations--or even a 1/2 wavelength dipole. Some folks have believed--without looking--that the coil creates a 2-band antenna. However, the coil is actually a method of getting the upper and lower sections in phase, in part, by compensating for the heavy capacitive reactance of the upper 5/8 wavelength section, and in part by separating the two sections to increase the gain.

+

The beauty of commercial versions of the antenna is that we can fabricate the two vertical sections and the "phasing" coil from a single piece of stainless steel or other suitable antenna material. By removing mechanical connectors along the antenna length, we increase the durability of the antenna. It will survive almost anything except closing the garage door on it.

+

Having said what the antenna is and having given the core of how it works, I suppose that I could stop here. Had I received only one question about the antenna, I might have quit at this point. But multiple questions got me to wondering. 1. Why do we use these antennas when we can make compact monopoles? 2. What principles of collinear arrays are involved in these antennas? 3. Can I model them adequately--at least adequately enough to show reliably the general trends of performance? Those are enough questions to fill an article.

+

The Standard Vertical Antennas

+

The standard antennas used by amateurs for mobile work are the 1/4 wavelength monopole and the 5/8 wavelength monopole, both with radials, along with variations on the 1/2 wavelength dipole. Fig. 2 shows their relative sizes.

+
+ +
+

Some of the monopoles are mag-mount versions that use the vehicle surface in lieu of a radial system. Nonetheless, antennas of each type--whatever the advertising hype--tend to perform similarly, with allowances for the quality of construction and, hence, the losses in the assembly.

+

To answer our first question of why we might use a vertical collinear array, let's explore the operating characteristics of the standard antennas. We shall use some common characteristics for all of the antennas to be explored. The material will be 1/8" (0.125") diameter aluminum. The operating frequency will be 435 MHz, the center of the 70-cm band. The operating frequency shows why the use of aluminum is harmless; that is, it covers virtually all materials we might use. The diameter is fat enough to reduce differences among materials from silver to stainless steel to a negligible level. As well, the 70-cm band is wide enough so that SWR curves covering the entire band from 420 to 450 MHz give us a useful benchmark.

+

For each antenna, I shall present a table of dimensions, including the length of any vertical sections and the length of the radials, if used. The table will also include performance data, including a take-off angle. The base height of each antenna will be 60" (2.21 wavelengths) above ground to simulate a small truck or SUV mount. I shall explain any special table entries as they appear. Since the figures are predicated on NEC-4 models of the antennas, I also provide the Average Gain Test (AGT) score for the model in order to establish its reliability. Interestingly, every one of our models will have a score just under 1.0, so the absolute value of the gain correction factor--given as a gain deficit--can be added to the reported gain. The amount is in all cases too small to be range-measured, let alone detected in operation.

+

Following the tables will be some graphics. One set will include elevation and azimuth plots for the antennas as situated above average ground. Most, but not all, of the azimuth patterns will be boring circles. At least initially, we shall be mostly interested in the elevation patterns, especially as they bear on our first question. We shall also record the 70-cm band SWR curve for each antenna, since most of these antennas find use in the widest portion of the band devoted to FM service.

+

The 1/4-Wavelength Monopole: Our 1/4 wavelength monopole model is the baseline due to its familiar nature and almost universal use. We have all learned how to make such an antenna with nothing more than a coax connector and a few scraps of house wiring.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+1/4-Wavelength Monopole
+
+Vertical length       6.75"                       AGT: 0.959 = -0.18 dB
+Radial length         6.35"
+
+Gain:  4.63 dBi  TO angle:  5.2 deg.   Feed Z:    24.6 - j 0.5 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+
+ +
+

The quarter wavelength monopole has a low main lobe, but it places most of its energy in much higher and relatively useless lobes. The elevation pattern in Fig. 3 displays this property clearly. The 25-Ohm SWR curve in Fig. 4 tells us that with a simple matching section or system, we can cover virtually the entire 70-cm band with under 2:1 SWR. We may droop the radials to raise the impedance closer to 50 Ohms to directly match our coax feedline.

+

The 5/8-Wavelength Monopole: The popularity of the 5/8 wavelength monopole arose initially from advertising hype of a 3 dB improvement based on the theoretical capabilities of the antenna. Unfortunately, over real ground of any sort, the antenna does not achieve its theoretical potential. This becomes clear in both the tabular and graphic data. In urban mobile use, the 5/8 wavelength monopole sometimes shows superiority over its short cousin because the maximum current region is higher and may be above the level of surrounding vehicles.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+5/8-Wavelength Monopole
+
+Vertical length       17.00                       AGT: 0.951 = -0.22 dB
+Radial length         6.35"
+
+Gain:  4.76 dBi  TO angle:  4.8 deg.   Feed Z:    77.8 - j 215 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+
+ +
+

As shown in Fig. 5, the lobe structure of the 5/8 wavelength monopole is only slightly different than the corresponding lobe structure of the 1/4 wavelength monopole. Considerable energy heads upward at angles beyond usefulness for most VHF and UHF mobile purposes. The SWR curve in Fig. 6 used a simple inductive load to compensate for the high capacitive reactance. The resulting matched 75-Ohm SWR curve then turns out to be as broad as the corresponding 25-Ohm curve for the short monopole.

+

The 1/2-Wavelength Dipole: Despite complexities of feeding a vertical dipole for mobile or portable use, it remains a standard antenna type and requires coverage with our monopoles. So we shall include it for reference. Of course, it uses no radial system.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+1/2-Wavelength Dipole
+
+Vertical length       12.70                       AGT: 0.999 = -0.00 dB
+Radial length         -----
+
+Gain:  5.43 dBi  TO angle:  5.0 deg.   Feed Z:    72.1 + j 0.4 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+
+ +
+

The dipole shows a small improvement over the monopoles, but likely insufficient to warrant any special efforts required for the feedpoint and the cable to prevent the occurrence of common mode currents. As the elevation pattern in Fig. 7 shows, the upper lobes are a bit weaker than those of the monopoles, but still filled with largely wasted energy. One clear advantage of the dipole appears in Fig. 8. The 75-Ohm SWR curve shows a maximum SWR at the band edges of about 1.5:1.

+

The sum of our brief review of standard antenna types amounts to this: they all exhibit wasted energy at high elevation angles. If we could recover some of that energy and re-direct it at a low elevation angle, we might improve the performance of our vertical antennas, whether or not in mobile service. And that is where the collinear array enters the picture.

+

The Traditional Collinear Array

+

Essential background on the collinear array appears in Chapter 8 of the current (19th) edition of The ARRL Antenna Book (pages 8-35 to 8-39), written by Rudy Severns, N6LF. The original home for the collinear array was the HF region, where one might piece together a number of horizontal 1/2 wavelength wires, end-to-end. The key to obtaining gain is to operate them in phase, and the natural link between sections was the 1/4 wavelength shorted stub or phasing section.

+

Adaptation to VHF vertical applications in the 1960s was initially simplistic. The horizontal wires were center-fed. If we cut the array in half and stood it vertically (with help to prevent the wire array from sagging), we might obtain gain. Unfortunately, as I learned from copying a magazine design in the 1970s, the so-called phasing section was not a simple matter at all, as most of my radiation went skyward and my trusty house-wire monopole regularly outperformed the rudimentary collinear array.

+
+ +
+

Fig. 9 shows two different kinds of designs that we might terms fundamental. The standard design uses a ¼ wavelength monopole topped by a 1/2 wavelength section. The monopole requires standard length radials. However, the phasing section is perhaps the most surprising feature. It is too wide from the top wire to the bottom wire to view as a transmission line stub, even though the horizontal dimension is about ¼ wavelength. Its vertical width contributes to the radiation, and the horizontal sections of the flag-like section also influence the pattern. The spacing between the lower and upper sections is necessary to obtain maximum gain in the lowest elevation lobe of the pattern.

+

The alternative design is based on the fact that we can feed a dipole--of which the monopole with a set of radials is a variation--anywhere along the dipole length as an off-center-fed antenna. Hence, we may reduce the radial lengths to the point where just the mounting base will suffice for that service. The remaining dimensions will change to yield both the desired pattern and the feedpoint impedance.

+

In vertical use, then, the collinear array has additional properties besides contributing to broadside gain. Elevation angle and feedpoint impedance are also matters of concern, since we normally operate these antennas with coaxial cable and no antenna tuner. The combination of functions, focused in the phasing section of the array, yield a pattern of current distribution quite unlike the idealized patterns we sometimes see in texts.

+
+ +
+

Fig. 9A shows the current magnitude distribution on the two variant designs that we shall individually examine. Ideally, we might expect the current magnitude curve in the vertical portion of the phasing section to be symmetrical, with descending currents along the horizontal wires. Quite another pattern appears in reality such that the entire system lacks balance. Even the upper half wavelength does not have its peak at the center, but somewhere above that point. Such patterns are typical of phasing sections in vertical arrays, and we saw similar patterns in various J-pole designs. (See "Some J-Poles That I Have Known", Parts 1-4.)

+

The two designs sketched in the graphics are only two of many possible designs for a fundamental 1/2-over-1/4 wavelength collinear vertical array. My interest in these stems from my desire to know if one can adequately model a collinear array. In flag-phase-section form, they are perhaps the simplest to model and among the most tedious to tweak on the way to optimizing the pattern. Both designs are geared toward a 100-Ohm feedpoint impedance, with the idea of using a quarter wavelength 70-75-Ohm matching section on the way to a 50-Ohm main feedline. In each dimension table, we shall encounter 3 vertical lengths, as designated in Fig. 9. As well, we shall note the horizontal length of the phasing flag.

+

The Standard "Flag" 1/2-Over-1/4 Collinear Array: We might easily build the standard design from a 35.4" length of 1/8" rod, assuming that we can make good, sharp bends and that our modeled design translates into a physical antenna having the same dimensions. One advantage held by commercial makers is that they can run through many prototypes on the way to final factory fabrication. The average backyard builder must find alternative uses for failed 1-wire versions if he is to not feel guilty for wasting the aluminum rod.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Standard 1/2-Over-1/4 Collinear Array
+
+V3 length             13.0"                       AGT: 0.951 = -0.22 dB
+V2 length              4.0"
+V1 length              6.0"
+Horizontal length      6.2"
+Radial length          6.35"
+
+Max. Gain:  7.33 dBi  Gain Differential:  2.17 dB      Mean Gain: 6.25 dBi
+TO angle:  4.8 deg.   Feed Z:    96.8 + j 0.4 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The pattern for the standard flag collinear array is a broad oval with over 2-dB difference between maximum and minimum gain levels. The tabulated data provides one measure of the imbalance. The current distribution in Fig. 9A goes a long way toward showing the source of the non-circular pattern, with unbalanced current levels everywhere on the structure, especially in the radials and the phasing wires.

+
+ +
+

Both the elevation and the azimuth patterns in Fig. 10 are interesting as they reveal the results of the current imbalance. The azimuth pattern is not only non-circular, but as well shows a slight egg-shaping to the oval. The elevation pattern, taken along the axis of maximum gain, shows considerable dissimilarity in the lobe structures on each side of the vertical assembly.

+

The Alternative "Flag" 1/2-Over-1/4 Collinear Array: The alternative structure provides a partial correction to the misshapen azimuth pattern provided by the standard model. Although the phasing wires appear to have a greater imbalance than on the standard design, the very short radials have a much more equal set of currents. However, the short radials require that the upper section of the antenna use about 38.3" of rod, an inconvenient length for the home builder who tries to get something useful from every 6' length of rod purchased from mail order houses or home centers.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Alternative 1/2-Over-1/4 Collinear Array
+
+V3 length             13.7"                       AGT: 0.958 = -0.19 dB
+V2 length              6.0"
+V1 length              6.0"
+Horizontal length      6.3"
+Radial length          2.0"
+
+Max. Gain:  7.48 dBi  Gain Differential:  1.36 dB      Mean Gain: 6.80 dBi
+TO angle:  4.7 deg.   Feed Z:    116.4 - j 3.2 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The ovalization of the azimuth pattern, shown in Fig. 11, is only a little more than half that of the standard design. However, the elevation pattern shows as much imbalance left and right of the vertical center line as did the corresponding pattern for the standard design.

+
+ +
+

In practice, there is not much to choose between the two designs. The SWR curves in Fig. 12--based on a reference impedance of 112 Ohms, an idealized value for a 75-Ohm quarter-wave matching section--show that either design will cover the entire 70-cm band, if only barely within the 2:1 standard so often used for SWR values.

+
+ +
+

The question with which we are faced is how to make a collinear array with a truly circular pattern.

+

Folding the Phasing Section of a Traditional 1/2-Over-1/4 Collinear Array

+

One early measure taken to prevent harm to the flag-like phasing section of a traditional 1/2-over-1/4 wavelength collinear array was to fold the section around the central vertical elements. To see what this measure might do to and for the collinear arrays that we have just examined, I revised the models in the general shape shown in Fig. 13.

+
+ +
+

The key difference in the new models is the squared fold-around phasing section. The section is 2" on a side, with a spacing of 1" from the central vertical sections. Due to the diameter of the wires (0.125"), I terminated the section 0.15" short of closing the gap. Hence, the total horizontal length of the phasing section is 8.85", and with one model, further revisions of dimensions proved necessary to bring it into line with respect to pattern shape, gain, and feedpoint impedance.

+

The Standard 1/2-Over-1/4 Collinear Array with a Fold-Around Phasing Section: The standard collinear array required only a slight lengthening of the top vertical section to bring it into usable shape, as shown by the tabulated information.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Standard 1/2-Over-1/4 Collinear Array
+
+V3 length             14.2"                       AGT: 0.953 = -0.21 dB
+V2 length              4.0"
+V1 length              6.0"
+Horizontal length      8.85"
+Radial length          6.35"
+
+Max. Gain:  7.08 dBi  Gain Differential:  0.33 dB      Mean Gain: 6.75 dBi
+TO angle:  4.7 deg.   Feed Z:    97.7 + j 5.0 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The top vertical section grew by 1.2", and the mean gain of the array also grew a bit. The non-circularity of the pattern is down to only 0.33 dB, a value with which virtually any user can live. Equally apparent in the patterns in Fig. 14 is the much better balance in the elevation lobes left and right of the vertical center line. As well, there appears to be an overall decrease in the high angle radiation levels.

+
+ +
+

The Alternative 1/2-Over-1/4 Collinear Array with a Fold-Around Phasing Section: The alternative basic collinear array also benefits from the fold-around phasing section. However, as the following tabulated data shows, its dimensions show a much larger departure from the initial dimensions. It is likely that some of these variations might have been avoided by using a slightly larger set of outer dimensions for the phasing section. As previously noted, there is no single design maneuver one must use in arriving at a useful--or at least plausible--array design.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Alternative 1/2-Over-1/4 Collinear Array
+
+V3 length             14.4"                       AGT: 0.968 = -0.14 dB
+V2 length              6.0"
+V1 length              7.6"
+Horizontal length      8.85"
+Radial length          2.0"
+
+Max. Gain:  7.75 dBi  Gain Differential:  0.20 dB      Mean Gain: 7.65 dBi
+TO angle:  4.5 deg.   Feed Z:    111.7 - j 5.8 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Lengthening both vertical sections yields a small increment of overall gain improvement, with a reduction in gain differential to only 0.2 dB. The patterns in Fig. 15 show the results. Indeed, the alternative 1/2-over-1/4 wavelength array shows the best performance achieved so far in this modeling exercise.

+
+ +
+

The SWR curves in Fig. 16 uses a 100-Ohm reference impedance to more closely correspond to the results we might obtain using a 70-Ohm quarter wavelength matching section for our main 50-Ohm feedline. A 112-Ohm reference would have reversed the positions of the lines on the graph. With either standard, we can observe one significant effect of using a fold-around phasing section for the array: the 2:1 SWR bandwidth has undergone significant narrowing in the process.

+
+ +
+

Throughout this section, I have called the middle part of the array simply a "phasing section." Perhaps it is not excessive repetition to note once more that the section does more than establish correct phasing between the two main vertical portions of the antenna. It also separates the sections to increase overall low-angle gain and works with the lengths of the two central sections to establish a usable feedpoint impedance.

+

The traditional collinear array is a fairly complex structure to construct. Field adjustment suggests separate pieces for the sections, but durability for mobile or heavy-weather uses suggest one-piece construction. The search for a workable solution to this conundrum--at least as we approach the GHz range of frequencies--resulted in the ubiquitous curly collinear.

+

Finally, the Curly 5/8-Over-1/4 Wavelength Collinear Array

+

The curly collinear, sketched in Fig. 1, takes a different approach to placing a 1/2 wavelength element above the base element. By extending the element to about 5/8 wavelength, it yields an impedance at the lower end that has a resistive component below 100 Ohms and a capacitive reactance that can run from -200 to -300 Ohms, depending upon the precise length selected.

+

If we add an inductor to the lower end of the upper linear section, we can do several things. First, we can compensate for the capacitive reactance of the 5/8 wavelength section. Second, we can use the length of the inductor to effect a physical separation of an eighth wavelength or more between the upper and lower sections to enhance the array gain. Third, we can match the entire array to a desired impedance, depending upon the design of the lower section.

+

The lower section in the trial models is about 1/4 wavelength. Using slightly short radials (relative to 1/4 wavelength), we can extend the lower section, and then add a bit more so that the reactance at the top end of the section is also capacitive. The inductor then provides compensation for that reactance as well. The net required inductance is sufficient to require a coil long enough to provide something close to optimal spacing without lowering the inductor Q too much.

+

The Initial Model of the 5/8-Over-1/4 Collinear Array: Fig. 17 shows the outline of my initial model of the curly collinear. It shows the current magnitude distribution along the antenna, as well as marking the sections of the antenna. The current minimums noted on the sketch show the results of selecting section lengths that create the conditions suited to the use of an inductor as a separator, as a matching coil, and as a means of keeping the two sections in phase.

+
+ +
+

My initial phasing section consisted of NEC loads, both R-X and later R-L-C types. I loaded each segment of the 3-segment wire in the section with 1/3 of the total load to reflect the fact that a coil filling the total space of the wire would act similarly. The following tabulated data shows the total reactance and inductance at 435 MHz. I arbitrarily chose a Q of 300 for the inductor.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Initial Model of 5/8-Over-1/4 Collinear Array
+
+V3 length             14.7"                       AGT: 0.972 = -0.12 dB
+V2 length              3.15"
+V1 length              8.25"
+Radial length          5.0"
+V2 Total Load:        R = 1 Ohms       Xl = 300 Ohms   L = 0.33 uH
+
+Max. Gain:  7.26 dBi  TO angle:  4.6 deg.   Feed Z:    50.4 - j 1.9 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The performance of the initial model of the curly collinear--with non-radiating loads rather than a physically modeled coil--shows that the design is practical. As revealed in Fig. 18, the azimuth pattern is circular, since there are no bent wires in the array except for the symmetrical radials. The elevation pattern shows a considerable reduction in high-angle radiation compared to the monopoles and the dipole which we originally set up as standards of comparison. The gain falls well within the range of values that we obtained for traditional collinear designs.

+
+ +
+

The 50-Ohm SWR curve for the array shows--in Fig. 19--that the antenna should cover just about all of the 70-cm band.

+
+ +
+

Two questions regarding antenna performance remained after tweaking the initial model to the shape shown in the tables and graphics. First, with a physical radiating coil, will the high-angle radiation remain at the low level shown in Fig. 18? Second, would the operating passband remain as wide as shown in Fig. 19 with a physical coil? Finally, of course, a modeling question remained: could I model a physical coil and still have a model that would have an AGT close to 1.0?

+

The Model of the 5/8-Over-1/4 Collinear Array Using a Physical Coil: To ensure that I kept the turns of the physically modeled coil sufficiently separated, I increased the spacing between the upper and lower section to about 4". I then modeled a physical coil with a pitch of 0.8" per turn or 1.25 turns per inch. The coil used an octagonal shape so that each wire in each turn would not be excessively different in length than the segment lengths used in the vertical wires above and below the coil.

+

Including the leads from the vertical wires to the coil ends, the resulting 5-turn coil has a calculated inductance of about 0.29 uH. The deficiency, relative to the 0.33-uH NEC coil simulation, required that I lengthen the upper section somewhat to reduce the capacitive reactance for which the coil provides compensation. To achieve close to a 50-Ohm feedpoint impedance, I also had to lengthen each radial by an inch. Fig. 20 shows an outline of the final model, along with an expanded view of the coil section.

+
+ +
+

The resulting model shows the same type of current distribution as the initial model. The current minimums occur within the straight sections of the array. However, the coil--both as a radiating element and as a longer physical separator between the two vertical sections--does alter performance somewhat.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Model of 5/8-Over-1/4 Collinear Array with a Physical Inductor
+
+V3 length             15.4"                       AGT: 0.964 = -0.16 dB
+V2 length              4.05"
+V1 length              8.25"
+Radial length          6.0"
+Inductor:        5 turns, 1" diameter, 4.05" total length, 1/2" leads
+
+Max. Gain:  7.55 dBi  TO angle:  4.5 deg.   Feed Z:    47.8 + j 0.8 Ohms
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Despite concerns over the effects of the coil upon the adequacy rating of the model, the 0.964 AGT value falls very much within the range of values obtained by the entire set of models used in this exercise. The added separation between the vertical array sections is the most likely source of the half-dB increase in gain at the lowest angle. However, it is likely that the coil structure contributes to both the gain and to higher angle radiation, as shown in the elevation plot in Fig. 21. (Compare elevation plots in Fig. 21 with those in Fig. 18.)

+
+ +
+

It would also appear that the coil, when physically modeled, shows a higher effective Q than the assumed value of 300 used in the initial model. The 2:1 50-Ohm SWR bandwidth of the model shrinks to about 20 MHz, as shown in Fig. 22.

+
+ +
+

Establishing an actual coil Q would be a daunting task, since the conditions under which the coil operates do not fit classical inductor theory, which presumes a constant current throughout the coil turns. In fact, the current distribution changes from one modeled coil wire section to the next. Hence, the effective Q is best estimated from the coil's effect on operating bandwidth. Rather than quantifying on the basis of the SWR curves, we may simply note that the bandwidth narrows considerably with a physically modeled coil in place of the idealized NEC load simulations.

+

The end result, nonetheless, is a highly effective collinear array. As we noted at the start, for frequencies at least twice our 70-cm test frequency, the design of curly collinears shows many variations, including no-radial versions. Most have an integrated total structure so that the only weak point is at the junction of the collinear and its base.

+

Conclusion

+

We have largely answered the questions with which we started this exploration. The collinear array provides a significant gain increase over the normal standard antennas used for omni-directional vertically polarized service in the UHF region of the spectrum. It does so by reducing high-angle radiation and increasing the gain in the lowest elevation lobe. Hence, the collinear array fulfills the promise originally made but ineffectively kept by the simple 5/8 wavelength monopole.

+

We have also seen that developing a collinear array is not a simple matter, especially when we vertically orient the antenna and play it against a presumed ground plane. What some view simplistically as a quarter wavelength matching "stub" turns out to be a somewhat complex section of the antenna, even if the wire structure seems simple. The current distribution within the section--especially as it effects a physical separation between the main radiating portions of the array--has both phasing and matching functions, with the latter one important when we wish to arrive at a working feedpoint impedance.

+

The 5/8-over-1/4 wavelength collinear design actually simplifies both the electrical and physical design requirements by providing capacitive reactance at the coil ends for compensation by the inductive reactance in the coil. For a coil of "ball-park" inductance (and inductive reactance at the design frequency), we may adjust the lengths of the vertical sections (and the radials, if used) to obtain a relatively high performance collinear array with a desired feedpoint impedance.

+

Moreover, NEC-4 appears well suited to modeling the entire structure so long as we use the same diameter wire throughout. Indeed, modeling the coil section rather than using NEC non-radiating loads appears to present a more realistic view of the antenna's potential performance. However, careful modeling of the coil is essential to sustaining close to an ideal AGT rating for the model.

+

For the 70-cm band, it is likely that backyard builders would employ separate upper and lower sections, with a stiff insulating section between to support an inductor. Such an array would permit considerable experimentation on the road to perfecting a design. However, the 3-part curly collinear has 2 main areas of caution. One of them is electrical: sustaining as close as possible to lossless junctions between adjacent sections. The second concern is mechanical: creating a structure that will stand up to the rigors of its working environment. These two concerns are likely the reasons that we do not see many amateur band versions of the curly collinear--at least, not at 70 cm and lower.

+

Whether or not we actually build a curly collinear, understanding its operation and its place within the general spectrum of collinear designs is a worthy enterprise. These notes have only scratched the surface of what we may learn about collinears, and the ideas involved in their workings may prove useful in other antenna design work.

+
+ +
+

Updated 06-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Collinear, VHF / UHF, Vertical


+ + diff --git a/content/vhf/coco.html b/content/vhf/coco.html new file mode 100644 index 0000000..a0f0191 --- /dev/null +++ b/content/vhf/coco.html @@ -0,0 +1,17 @@ + + + + + + Is COCO (Coaxial-Collinear) Your Cup of Tea? + + + +

Is COCO (Coaxial-Collinear) Your Cup of Tea?

+ hr +

Is COCO (Coaxial-Collinear) Your Cup of Tea?

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: Collinear, VHF / UHF, Vertical


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+

Corner Reflectors Revisited
+
+ Part 1: A Comparison With a Good Yagi

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

In the museum of overlooked antennas lies the corner reflector. Once a bastion of TV reception and occasional ham use, this antenna has given way to TV cable and ham Yagis. In the 70 cm band (420-450 MHz), where TV and amateur radio almost meet, the corner reflector had its heyday and has passed largely into history.

+
+ +
+

The most common etching of the corner reflector is shown in Fig. 1. When not adapting a TV antenna, most hams used screen wire and frames for the reflector planes.

+

I recently had occasion to revisit the corner reflector and to model it. One version showed very nice gain from 400-500 MHz, along with a feedpoint impedance that was convertible across the operating range to something close enough to either 50 or 70 Ohms within less than a 2:1 SWR. I began to wonder why the antenna had been discarded.

+
+ +
+

Part of the answer shows up in Fig. 2. A 10-element DL6WU log-calculated Yagi for 432 MHz appears roughly in scale with an optimized corner reflector of similar performance. The footprints are indeed different. Still we have the nagging question of whether the corner reflector might have something to offer that the Yagi does not. To develop some sort of answer, let's look at each antenna briefly.

+

The antenna description file for the DL6WU Yagi appears at the end of this part of the story , in case someone wishes to replicate the antenna. The originator is most noted for the logarithmic technique for calculating element lengths and spacings. Modeling can tweak his results, but not by much--and not without ruining some other features of his designs. First, the designs were all geared to a 50-Ohm feedpoint impedance, even if we are shifting to 70-Ohm hard-line scrounged from the cable industry. Second, the designs were broadbanded both in source impedance and in overall antenna characteristics. Third, the designs were generated in large models--the original for this 10-element version had 26 elements. At most points down the boom, the home builder could snip off the directors he did not want to build and still have a good Yagi with a 50-Ohm feedpoint impedance.

+

The antenna description will list the dimensions in inches for direct comparison with the corner reflector. However, the originals are given in millimeters, with 4 mm as the element diameter. The entire array comes in at under 5' long and a maximum width of just over 13" at the reflector.

+

The corner array we shall look at in some detail is bigger than most amateur source recommend. The dotted lines of Fig. 2 indicate the rough reflector size one commonly sees, but that set of dimensions yields fairly mediocre performance. The larger reflector allows optimizing the array for 432 MHz as a design frequency for maximum gain and very adequate front-to- back ratio.

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+ +
+

In Fig. 3, we can find dimensions enough to start a building project, although it is wise to supplement this figure with data from the model description file at the end of Part 2 of these notes. Note that the 2 reflector planes are each virtually square. Their dimensions are between 1.4 and 1.45 wl. The design is a standard 90-degree reflector and uses 3/8" (about 8 mm) aluminum tubing. For simplicity, a 3/8" diameter dipole is the driver, although the widest-band corner reflectors use(d) bent Brown-Woodward bow-tie drivers. We shall discuss the driver placement further down this note pad.

+

Two sets of numbers have emerged regarding corner reflectors: minimums and optimums. Unfortunately, the minimum numbers have received wider distribution among hams, while the more optimal numbers lie buried in Kraus, Antennas, 2nd Ed. (Section 12-3) and his sources. W8JK hold the patent for the corner reflector. Kraus specifies numbers as high as 1.62 wl for rod lengths and 1.5 wl for the length of each reflector plane--not far off the numbers used to develop the model used here. The rod diameters and spacing used here are also well within his limits. We should remember that most of the information on corner reflectors was developed long before modeling software was developed.

+

The numbers in Fig. 3 reflect the results of modeling with the rod construction. A different type of reflector plane may require adjustment. Preliminary models using wire grid techniques to fill the plane more fully suggest that these planes might need to be slightly larger than the dimensions shown for the rods. It appears that adequate modeling of corner reflectors has just begun.

+

Some Patterns

If the corner reflector, with all its size, will only just match the more compact Yagi, why bother with it? To get some idea of why we might consider the corner reflector design, let's do some comparisons between the excellent DL6WU Yagi and the corner challenger. +
+ +
+

Fig. 4 combines 420-450 MHz (5 MHz increments) azimuth patterns for the Yagi, oriented horizontally, with the antenna 30' (over 13 wl) above average earth, using an elevation angle of 1.1 degrees. Three features of the pattern overlays should call themselves to our attention. First, the front-to-back ratio is highly variable across the band. Second, the gain shows significant variation across the band. Third, the side lobe structure varies considerably as we move from one frequency to the next.

+
+ +
+

In Fig. 5 we have the same situation, but with the antenna oriented vertically. The side lobes are very much stronger in this configuration, with some less than 15 dB below the forward lobe. As expected, both gain and front-to-back ratio show patterns similar to those for the horizontal orientation.

+
+ +
+

We turn to the horizontally oriented corner reflector in Fig. 6 with a similar set of patterns. However, the lack of significant variation in any of the noted parameters (gain, front-to-back ratio, and side lobe structure) makes it hard to believe that there are seven azimuth patterns overlaid in the graphic. Especially evident is the act that the front-to- back ratio never reaches a worst-case value as bad as 25 dB.

+
+ +
+

When vertically oriented, the corner reflector cannot quite match the rearward performance of the horizontally oriented version. As shown in Fig. 7, however, the side lobes exceed -20 dB at only one test frequency. moreover, the overall beamwidth is remarkably constant for a vertically oriented array. Compare this figure to Fig. 5, the corresponding pattern for the 10-element Yagi.

+
+ +
+

Fig. 8 makes the Yagi-corner comparison in the horizontal mode from a slightly different angle. Here we have elevation patterns for the Yagi and corner reflector overlaid, with color as our only hope of sorting out the lobe structure. In general, the Yagi wastes more energy at higher elevation angles than the corner reflector (at the 432 MHz design frequency). While the differences may not be yet decisive for any particular application, one begins to view the corner reflector as a well- behaved antenna.

+

Some Graphs

Although patterns can indicate some overall properties of the antennas, they do not permit sorting out the patterns as well as might some graphing. so let's investigate some of the features we have noted through the magic of spreadsheet graphing. +
+ +
+

The gain chart in Fig. 9 illustrates a number of things. First, even at a height above 13 wl, antennas designed for horizontal polarization show less gain when oriented vertically--over 0.5 dB. Otherwise, the gain curves are congruent for each type of antenna.

+

Second, the Yagi shows a rather distinct peak in gain, with significantly lower values (about 0.9 dB) toward the band edges. In contrast, the gain figures for the corner reflector vary by less than 0.4 dB across the band. We should also point out that systematic frequency sweeps earn their tedium time when they turn up unsuspected turns in the curves, for example, the corner reflector gain dip above 435 MHz. I have not investigated this dip to see if it is general for any type of reflector plane or whether it is unique to the choice of lengths and diameters used in this model.

+
+ +
+

The 180-degree front-to-back curves in Fig. 10 reveal a common Yagi trait: the peaking of the front-to-back value at a single frequency, with lower values elsewhere in the band. Although the DL6WU design has excellent gain across the band, the front-to-back ratio exceeds 20 dB for only a small portion of the spectrum.

+

In contrast, the corner reflector design varies by only 3 dB in front-to- back ratio across the entire 70 cm band. Unlike the Yagi curves for vertical and horizontal orientation, where the curves exactly overlay each other, the corner reflector shows some slight variations between orientations--but never enough to be noticed in operation.

+
+ +
+

In Fig. 11, we look at a property seldom mentioned in amateur antenna circles: -3 dB beam width. Here, we notice that the Yagi beamwidth decreases regularly across the band. In contrast, the curves for the corner reflector are much flatter, with slight peaks at those frequencies where we found the gain to fall off slightly. In general, we can add the beamwidth regularity to the evidence for the claim that corner reflectors are very well-behaved across a wide operating band width.

+
+ +
+

Accessing the operating advantages of each antenna type across a wide band, like the 420-450 MHz spread, necessarily involves taking the 2:1 VSWR curves of each antenna into account. Since the curves for each orientation within each antenna type are identical, only a single curve for each antenna type appears in Fig. 12.

+

If we think solely in HF terms, then the Yagi curve appears acceptable. For a field operation with short cable runs, the Yagi may be usable. However, for lowest losses in a fixed station environment with longer cable runs--even with high quality hard-line--the SWR values over 1.5:1 (for a 50- Ohm standard, the design impedance of the antenna) can give one pause. In contrast, the corner reflector never exceeds 1.4:1 relative to the 70-Ohm driver design and placement for this particular model.

+

Some Initial Conclusions

I purposely chose what I consider a good Yagi design with which to compare an equally competent corner reflector design. The DL6WU design combines a workable feedpoint impedance with characteristics that are as broad-band as any I have seen for Yagis at UHF. I also picked the design to have a comparable gain to the corner reflector. By lengthening the boom and adding directors, one can increase the Yagi's gain, but mostly at the expense of some operating bandwidth. +

In contrast, there is little one can effectively do to increase the gain of a corner reflector. Different angles from the 90-degree reflector used here promise spot gain increase, but not very much and usually with a degradation of one or more other parameters. Placing parasitic arrays in the driver position is also of limited benefit, since the corner array is a "4-plane" design. Radiation rearward, upward, and downward all reflect forward, and predicting portions of the radiation pattern normal to a dipole does not yield enough gain to justify the reduction on operating bandwidth. In short, the corner reflector (within the limits of easily replicated designs) is yielding almost all that it can.

+

However, the corner reflector yields the same performance across the entire band. The 70-cm band is actually no challenge for a corner reflector, which has seen effective service over 2:1 frequency ranges. Let us make one last note of the categories in which we have seen consistent performance:

+
    +
  • 1. Forward gain;
    • +
  • 2. Front-to-back ratio;
    • +
  • 3. -3 dB beamwidth;
    • +
  • 4. SWR; and
    • +
  • 5. All of the above in both horizontal and vertical orientations.
    • +
+

Within its gain limits, the corner reflector is a paradigm of a well- behaved antenna with consistent performance across an entire amateur band. For that reason alone, it is worth exploring a little further into the design featured in this part of these notes. Whether or not one wishes to built such a large antenna relative to its gain, what goes into the design should be intrinsically interesting.

+

However, one forewarning before we move onward. This part of the notes contains every last one of the pictures and graphics. Part 2 will feature tables instead. They are not as attractive, but they may be even more informative. Abandon aesthetics, all ye who enter Part 2.

+
+ +
+ 
DL6WU Original, 10 el 432 MHz           Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1            0.000,  6.705,  0.000         0.000, -6.705,  0.000 1.57E-01  19
+2            5.465,  6.496,  0.000         5.465, -6.496,  0.000 1.57E-01  19
+3            7.512,  5.937,  0.000         7.512, -5.937,  0.000 1.57E-01  19
+4           12.433,  5.890,  0.000        12.433, -5.890,  0.000 1.57E-01  19
+5           18.307,  5.819,  0.000        18.307, -5.819,  0.000 1.57E-01  19
+6           25.134,  5.752,  0.000        25.134, -5.752,  0.000 1.57E-01  19
+7           32.787,  5.693,  0.000        32.787, -5.693,  0.000 1.57E-01  19
+8           40.980,  5.638,  0.000        40.980, -5.638,  0.000 1.57E-01  19
+9           49.587,  5.594,  0.000        49.587, -5.594,  0.000 1.57E-01  19
+10          58.606,  5.555,  0.000        58.606, -5.555,  0.000 1.57E-01  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+ +
+

Updated 4-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Part 2 +

Return to Main Index

+

Topics: Corner Reflector, VHF / UHF


+ + diff --git a/content/vhf/corn2.html b/content/vhf/corn2.html new file mode 100644 index 0000000..e0eec88 --- /dev/null +++ b/content/vhf/corn2.html @@ -0,0 +1,155 @@ + + + + + + Corner Reflectors Revisited Part 2: The Evolution of a Model + + + +
+

Corner Reflectors Revisited
+
+ Part 2: The Evolution of a Model

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The model of a corner reflector used to make the comparison with the DL6WU Yagi in Part 1 emerged from a process of manual optimizing. For this exercise, I chose to stay with the 90-degree reflector corner, although other angle are possible--some with reportedly a bit more gain. I also chose to stay with the rod-style reflector construction. I have experimented with wire grid structures to better simulate a screen or solid reflector plane, but I am not yet happy with those models. (There is always further modeling one can do, which means that someday this sequence might have more parts.)

+

The evolutionary portion of the work concerns two elements of the antenna (which actually does not many more elements than two). First is the size and shape of each reflector plane. Second is the choice and position of the driver dipole. We should look at these elements in order.

+

The Reflector Planes

For reference, let's repeat Fig. 3 from the first part: +
+ +
+

The initial dimensions for the reflector were 18" across and 31" along the edge. To achieve these dimensions, I simply stair-stepped 3/8" aluminum tubes at 2" increments in the X and the Z axis. Hence, rods occur at 2.8" intervals as measured along the edge of the plane. Each plane has 11 rods, plus a center one directly behind the driver.

+

These dimensions were already larger than the planes used with the rod corner reflector list in the ARRL Antenna Book, which calls for rod lengths of 16.25" and a plane side length of 27" (compared to my initial 18" and 31"). The performance of the initial model was disappointing. The only route to improving performance was to enlarge the reflector plane. The first step was to increase the rod lengths, which I did in 4" or 6" increments. The plane kept the same side length throughout this phase. The following table shows what happened.

+ 
Rod Length     Gain      F-B Ratio      Feed Impedance
+  inches       dBi         dB           R +/- jX Ohms
+  18           10.05     25.08          87.0 + j 7.7
+  22           10.30     31.99          91.4 + j 1.9
+  28           10.78     35.08          92.6 - j 2.4
+  32           11.25     29.86          92.6 - j 4.0
+  38           13.03     27.62          90.1 - j 5.3
+

With rods longer than about 38 inches, the gain began to fall off, and so the 38" rod dimension was frozen. note that I could have narrowed the peak gain rod length even further, but for the purpose of this study, that step would have been superfluous, since these models are not for a production run of corner reflectors.

+

The progression of gain figures is not wholly revealed by the table, since the increments are variable. However, the progression is fairly linear until peak gain is achieved and then begins to fall off slowly.

+

The next step was to optimize the side dimension of each plane by increasing the number of rods in single 2" stair steps (length increase = 2.8") until gain began to fall off. The following table shows what happened--all with the new 38" rod length.

+ 
Number of      Side Length    Gain      F-B Ratio      Feed Impedance
+  Rods           inches       dBi         dB           R +/- jX Ohms
+  11           31.2           13.03     27.62          90.1 - j 5.3
+  12           34.0           13.22     26.23          91.1 - j 5.4
+  13           36.8           13.42     27.23          91.3 - j 6.2
+  14           39.6           13.55     28.21          90.7 - j 6.6
+  15           42.4           13.53     26.84          90.4 - j 6.0
+

At 14 rods (ignoring the common center rod in the reflector), gain peaks and then slowly falls off. The rate of increase to the peak is slower, because one dimension has already been optimized. The 14-rod plane was checked at 42" wide, in case changing the side length altered the peak rod length dimension. However, 42" rods produced lower gains, giving me confidence that the resulting plane was reasonably close to optimal for a 432 MHz corner reflector.

+

In passing, it is interesting to note that the apparent maximum gain occurred when each plane was approximately square. Of course, one example--namely the present model--does not make a general case for anything. Hence, it is not clear what, if any, significance this fact may have.

+

The following number are often encountered for designing corner reflectors.

+ 
Designator     Dimension           Recommended              Used Here
+Lmin           Minimum rod length       0.6 wl              1.40 wl
+S              Side length              2* driver spacing   1.45 wl
+                                        or > 2 wl
+D              Distance from apex       0.25 - 0.7 wl       see below
+               of corner to driver
+G              Spacing between rods     < 0.06 wl           0.1 wl
+r              rod diameter             0.02 wl             0.014
+

The distance of the driver from the apex to achieve feedpoint impedance ranging from 50 to 100 Ohms was about 8.3" to 11.76" with no influence upon gain or other operating parameters. These distance correspond to 0.3 to 0.4 wl, a small range indeed.

+

In Kraus, we can find some design factors for a 2:1 frequency range corner reflector using a Brown-Woodward bent bow-tie driver. For the low and high frequencies of the range, we find these dimensional recommendations:

+ 
Designator     Dimension                Low Freq.           High freq.
+Lmin           Rod length               0.81 wl             1.62 wl
+S              Side length              0.75 wl             1.50 wl
+D              Distance from apex       0.27 wl             0.54 wl
+               of corner to driver
+G              Spacing between rods     0.061 wl            0.122 wl
+R              Rod diameter             0.01 wl             0.02
+

The dimension used in this 432 MHz model are actually in the middle to slightly into the high region of the overall dimensions. The free space gain listed for the low frequency end of the spectrum was 11.0 dBi, while the high frequency end yielded about 14.0 dBi. The 13.55 dBi figure of the optimized model corresponds to the general placement of the dimensions.

+

The frequency range required by the 432 MHz model is far less than the 2:1 ratio of the model described by Kraus (only about 7%). Within that narrower span, we have already seen that the performance characteristics ar remarkably stable.

+

However, some design factors are not fully clear from the limited modeling done so far. First, wire grid screen reflector planes appear to need to be larger than the rod model developed here. An initial model had reduced gain until reaching about 440 MHz, at which point the gain equal that of the rod model, with improvement to the front-to-back ratio (worst case front-to-back ratio > 30 dB). However, it is not yet clear whether the initial wire grid screen models are adequate to capture a screen reflector plane.

+

What is clear is that the fuller the reflector plane coverage, the higher the gain. Reducing the rods to #12 wires reduced gain by nearly a full dB in one test run. The real modeling test is to be able to develop a range of models, each of which captures closely the performance of real antennas built to the same geometry specifications. In this department, there remains much work to do.

+

Finally, the gain maximum yielded by the nearly square reflector planes does not achieve the theoretic 14 dB gain suggested by the figures in Kraus. We shall look at this question in further detail in Part 3.

+

Feeding the Corner Reflector

Given the fairly narrow frequency coverage required of this corner reflector, a fat dipole, 3/8" in diameter seemed adequate to the task. The stability of the operating parameters seems to confirm this reasoning. +

Although many corner reflectors are operated at a feedpoint impedance of 300 Ohms or more, this test model was restricted to the range of 50 to 100 Ohms. The selection followed these guidelines:

+
    +
  • 1. 50-Ohms is the most common characteristic impedance for coaxial cables used by amateur operators, even though losses are considerable at 432 MHz for all except very expensive 50-Ohm hard-line.
    • +
  • 2. 70-Ohm hard-line, obtained from the cable television industry, has become the coaxial line of choice wherever it can be obtained.
    • +
  • 3. 100 Ohms as a feedpoint impedance is convenient for use with a 1/4 wl 70-Ohm impedance transformer section for use ultimately with 50-Ohm coaxial cable.
    • +
+

First, let's look at the physical placement and length of driver need to achieve each of these impedance within the optimized reflector. We can also see whether the driver variations had an significant affect upon the performance parameters of the antenna at the 432 MHz design frequency.

+ 
Driver length  Dist from Apex Gain      Front-to-Back       Feed Impedance
+  inches         inches       dBi         dB                R +/- jX Ohms
+  11.28          8.3          13.63     25.85                49.8 + j 0.9
+  11.32          9.6          13.60     27.27                69.7 - j 1.4
+  11.76         11.3          13.54     28.28               100.4 + j 1.1
+

The driver placement has little affect on the antenna performance, at least within the small range of movement occasioned by the impedance choices we made. However, every movement of the driver requires that one readjust its length for resonance.

+

Of equal importance to obtaining a desired feedpoint impedance at the design frequency is the stability of that impedance across the band, here from 420 to 450 MHz. For this exercise, the 50-Ohm and 70-Ohm SWR curves were directly plotted. However, the 100-Ohm model was fitted with a 1/4 wl 70-Ohm line (6.83" at 432 MHz with a velocity factor of 1.0) to yield essentially a 50-Ohm SWR curve.

+
+ +
+

The graph in Fig. 13 tells an interesting story. At the band extremes, the 50-Ohm impedance driver yields SWR figures sufficient to make one worry about added line losses. This curve results from a large swing in the reactance at the lower impedance--approximately 43 Ohms across the band for a resistance change of only 22 Ohms.

+

In contrast, the reactance swing of the 70-Ohm driver position is a little over 38 Ohms with a resistance swing of less than 17 Ohms. At the higher impedance, these swings alter the SWR value by a far lower amount than at the 50-Ohm level.

+

However, for a 50-Ohm main line, I would recommend the 100-Ohm driver position in concert with a 70-Ohm transformation line. The 50-Ohm SWR curve for this arrangement is very flat, with only a 14 Ohm change of resistance and a 6.5 Ohm change of reactance across the band. In general, the higher the feedpoint impedance, the more stable it is across the desired bandwidth. Certainly 300-Ohm feedpoint impedance can be achieved within this general configuration and may be advantageous to some operations.

+

Remaining Work

These notes are about a work in progress. Much remains to be done, but I have included my progress to this point in hopes that there may be some suggestive ideas among progression of modeling that led to the results in Part 1. +

I have already mentioned the need to complete the development of a satisfactory wire grid arrangement to simulate wire screens in the reflector. Already, someone as asked what the optimal spacing might be for a phased array of corner reflectors, possible for EME work. I shall tackle this problem as soon as 1 GHz CPU computers are available in my price range.

+

However, there are some interesting lesser phenomena worth investigating as well. The pattern of current peaks along the rods forms a fascinating topography worth some more detailed looks. It will also be interesting to compare this topography to that upon a screen of crossing wires. But all of these questions will have to wait for some available time. In the interim, I hope this much is useful in getting a better grip on the corner reflector.

+

In the interim, we can at least look at the question of maximum gain that we might obtain by further attempts to optimize this model. In fact, the optimizing efforts expended on this present model were casual, and a more rigorous exploration of dimensions might yield something useful--even if nothing more than a couple of guidelines for manually optimizing models. To that task we turn in Part 3.

+
+ +
+ 
Corner refl + dipole: 432 MHz             Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1         -5.660,  9.600,  0.000         5.660,  9.600,  0.000 3.75E-01  11
+2        -19.000,  0.000,  0.000        19.000,  0.000,  0.000 3.75E-01  31
+3        -19.000,  2.000,  2.000        19.000,  2.000,  2.000 3.75E-01  31
+4        -19.000,  4.000,  4.000        19.000,  4.000,  4.000 3.75E-01  31
+5        -19.000,  6.000,  6.000        19.000,  6.000,  6.000 3.75E-01  31
+6        -19.000,  8.000,  8.000        19.000,  8.000,  8.000 3.75E-01  31
+7        -19.000, 10.000, 10.000        19.000, 10.000, 10.000 3.75E-01  31
+8        -19.000, 12.000, 12.000        19.000, 12.000, 12.000 3.75E-01  31
+9        -19.000, 14.000, 14.000        19.000, 14.000, 14.000 3.75E-01  31
+10       -19.000, 16.000, 16.000        19.000, 16.000, 16.000 3.75E-01  31
+11       -19.000, 18.000, 18.000        19.000, 18.000, 18.000 3.75E-01  31
+12       -19.000, 20.000, 20.000        19.000, 20.000, 20.000 3.75E-01  31
+13       -19.000, 22.000, 22.000        19.000, 22.000, 22.000 3.75E-01  31
+14       -19.000, 24.000, 24.000        19.000, 24.000, 24.000 3.75E-01  31
+15       -19.000, 26.000, 26.000        19.000, 26.000, 26.000 3.75E-01  31
+16       -19.000, 28.000, 28.000        19.000, 28.000, 28.000 3.75E-01  31
+17       -19.000,  2.000, -2.000        19.000,  2.000, -2.000 3.75E-01  31
+18       -19.000,  4.000, -4.000        19.000,  4.000, -4.000 3.75E-01  31
+19       -19.000,  6.000, -6.000        19.000,  6.000, -6.000 3.75E-01  31
+20       -19.000,  8.000, -8.000        19.000,  8.000, -8.000 3.75E-01  31
+21       -19.000, 10.000,-10.000        19.000, 10.000,-10.000 3.75E-01  31
+22       -19.000, 12.000,-12.000        19.000, 12.000,-12.000 3.75E-01  31
+23       -19.000, 14.000,-14.000        19.000, 14.000,-14.000 3.75E-01  31
+24       -19.000, 16.000,-16.000        19.000, 16.000,-16.000 3.75E-01  31
+25       -19.000, 18.000,-18.000        19.000, 18.000,-18.000 3.75E-01  31
+26       -19.000, 20.000,-20.000        19.000, 20.000,-20.000 3.75E-01  31
+27       -19.000, 22.000,-22.000        19.000, 22.000,-22.000 3.75E-01  31
+28       -19.000, 24.000,-24.000        19.000, 24.000,-24.000 3.75E-01  31
+29       -19.000, 26.000,-26.000        19.000, 26.000,-26.000 3.75E-01  31
+30       -19.000, 28.000,-28.000        19.000, 28.000,-28.000 3.75E-01  31
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+
+ +
+

Updated 4-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Part 3 +

Return to Main Index

+

Topics: Corner Reflector, VHF / UHF


+ + diff --git a/content/vhf/corn3.html b/content/vhf/corn3.html new file mode 100644 index 0000000..6583fa7 --- /dev/null +++ b/content/vhf/corn3.html @@ -0,0 +1,146 @@ + + + + + + Corner Reflectors Revisited Part 3: Optimizing the Model + + + +
+

Corner Reflectors Revisited
+
+ Part 3: Optimizing the Model

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Let's begin our look at optimizing the model corner reflector further by looking at its construction, as sketched in Fig. 2 from Part 1.

+
+ +
+

The enlargement of the reflector consists in making at least one of two moves. First, one may uniformly change the length of each rod in the reflector. Second, one may add rods at 2" horizontal and vertical increments (2.8" along the 45-degree side-line).

+

The development of the model used in Parts 1 and 2 of this study employed only the most casual means of optimization. Changes in rod length encompassed several inches at a time until an approximate "best" length was achieved. Even though rods were added at the minimum possible rate of one per plane, the optimizing task was ended as soon as a single downturn in gain was noted. The resulting dimensions and performance were as follows (with allowance for very small numerical differences occasioned by moving the driver to a position that provides the desired feedpoint impedance.

+ 
Freq      Rod L     No. of    Side L    FS Gain   F-B Ratio Feed Impedance
+MHz       inches    Rods      inches    dBi       dB        R +/- jX Ohms
+432       38        14        39.6      13.60     27.27     69.7 - j 1.4
+

The use of this model for the comparative study rested upon several considerations. First, the modeled reflector was considerably larger than many published dimensions. Second, the model exhibited very good gain and other performance characteristics, not the least of which was the relative stability of the properties across the 420-450 MHz frequency range.

+

However, a number of concerns remained after working with the model. It did not achieve the maximum free space gain of 14 dBi listed in some sources. Second, the optimizing technique was sufficiently casual as to permit confusion between a gain plateau and a gain maximum. This possibility is hinted at in the gain curves in Fig. 9 by the upturn in gain at the high end of the frequency range covered by the plot.

+

Careful optimizing--whether manual or automated--must include sufficient tests to ensure that a gain plateau followed by a gain drop is not interpreted automatically as having passed the point of maximum gain for an array. Several systematic increments of dimensional change must follow the detection of maximum gain to give confidence in the peak figure. Alternatively--as found in some genetic optimizing routines--one can use a method of "jumping" over regions of decreased gain to see if there is a different geometry that produces an even higher gain.

+

Therefore, let's return to the model and see if further optimizing is possible. After an initial "jump" in dimensions, we shall look very closely at small changes in gain. Optimizing is one of those modeling enterprises in which it makes sense to carry out reported values to whatever number of decimal places it takes to see a difference, even if operationally, a particular change may seem to make no difference.

+

(Those who insist upon reducing all gain and other NEC output figure uniformly to integers or other units that make operational differences may in fact be missing an entire dimension of what NEC makes available when used analytically. The level of precision that may be spurious to operational considerations can be vital wherever numerical trends make a difference to a design or analysis project. On the other hand, suggesting that the antenna which I built in my garage has a gain of 13.783 dBi would only make sense as an exercise in humorous hyperbole.)

+

Optimizing the Corner Reflector

+

The present task is to see if the gain of a corner reflector can be raised to about 14 dBi free space at 432 MHz, the design frequency. An added constraint is that the gain must be reasonably stable between 420 and 450 MHz.

+

We may set aside several potentially complicating factors with the following notes. First, the changes to be made to the reflector planes in terms of the number of rods and their length have no significant effect upon the feedpoint impedance when the driver is left in the positions noted in Part 2 for 50, 70, and 100 Ohms feedpoint impedance. Even when surveyed across the band, the SWR limits remained very tightly matched to the figures given in Part 2, with changes only in the hundredth's column. Once the horizontal dimension of the corner array is considerably more than double the distance from the driver to the reflector apex, source impedance appears to remain very stable.

+

Second, the front-to-back figures for all models showed a minimum 180- degree ratio of 25 dB. Therefore, variations in these figures were considered insignificant for the present enterprise. Related to this feature is the fact that the pattern shape also remained stable, with -3 dB beamwidths in the 36-40 degree range throughout. Hence, the shapes shown in Part 1 of this exercise remain good indicators of the patterns derived from further optimizing efforts.

+

Throughout, the basic model structure has been retained, including the use of 3/8" diameter aluminum tubing for all elements of the corner reflector, including the driver. Hence, the optimizing efforts are valid only for this structure. The use of smaller or larger diameters of reflector rods may require re-optimizing the model. Nonetheless, within this limits, we may focus our attention to the gain patterns yielded by the model with different rod lengths and different numbers of rods.

+

A gain peak emerges as the side length of the reflector planes approaches 2 wl. Therefore, optimizing efforts were concentrated in this region, using (without counting the apex rod) 19, 20, and 21 rods for side lengths of 53.7" (1.97 wl), 56.6" (2.07 wl), and 59.4" (2.17 wl at 432 MHz). This spread represents about a 10% overall change of side length for the reflector planes. For each of the side length options, I looked at rod lengths of 36, 37, and 38 inches.

+
+ +
+

The first gain curve (Fig. 14) is for 19 rods. Immediately apparent is that the curve for the 37" rod length yields a curve whose shape is similar to the one shown in Part 2, with a peak near the design frequency, a gain decrease above that frequency, and a final upturn at the highest frequency tested. Use care in interpreting steep curves, since the range of gain for the entire graph is 1 dB.

+

Of equal importance are the other two curves. In fact, they show a frequency displacement of relatively similar curves. The curve for the 36" rods shows its peak higher in the passband. The curve for the 38" rods moves the gain decrease region lower in the passband to encompass the design frequency.

+
+ +
+

When each reflector plane is lengthened by one rod (2.8"), we obtain the curves in Fig 15. They are quite similar to those in the preceding graphic, but with slightly higher gain peaks for all three curves. The fact that the curves are being displaced slightly lower in frequency (relative to the preceding graph) is almost invisible.

+
+ +
+

Increasing the reflector plane to 21 rods and 59.4" yields Fig. 16. By this time, the lowering of the curves in frequency with increases in reflector length is more readily apparent. Also apparent is the fact that the 37" rod length--for the overall structure under study--is closest to optimal for achieving the maximum gain at the design frequency and the most even gain across the frequency span covered.

+
+ +
+

Fig. 17 combines the gain curves for the 37" rod lengths for a comparison of the three side lengths. The peak free space gain of the longest reflector exceeds 14.25 dBi. However, the true peak is below 430 MHz, and the curve is on a downward trend, so that the 432 MHz gain of the intermediate reflector actually numerically exceeds it.

+

However, a new trend is also appearing. In the models in Part 2, the maximum differential between a gain peak and null was under 0.4 dB. The differential at the new longer reflector side length begins to exceed 0.5 dB. Even if more gain is obtainable with further increases in the side length of the reflectors, it may be purchased at the cost of smooth gain response across the frequency spread of interest.

+

One might continue the progression of optimizing studies further, especially if one is interested in a particular frequency of operation. further adjustment of reflector rod length and reflector side length may yield perhaps another 0.2 dB of gain increase. However, due to the increasing size of the models involved, I decided to stop at this point.

+

Let's compare the result of this exercise with the model with which we began.

+ 
Freq      Rod L     No. of    Side L    FS Gain   F-B Ratio Feed Impedance
+MHz       inches    Rods      inches    dBi       dB        R +/- jX Ohms
+432       38        14        39.6      13.60     27.27     69.7 - j 1.4
+432       37        20        56.6      14.21     29.23     70.2 - j 1.4
+

We have gained 0.6 dB gain. Before we end the optimization exercise, we should ask, "At what cost?"

+

Physically Implementing the Corner Reflector

+

Finding the maximum gain peak and then setting it right on 432 MHz might require a very precise rod length. For those so inclined, a length just below 37" will move the curves upward in frequency. Each side length will require a unique rod length. This fact has implications for physically implementing the design using real materials. When modeled dimensions become too finicky, it does not bode well for constructing an antenna that matches the model in performance, since numerous construction variables may intervene.

+

Apart from this question, the general size of the corner reflector has significantly increased with the addition of 5 to 7 new reflector rods. Fig. 18 indicates the approximate growth, using the intermediate optimized model in comparison with the model used in Parts 1 and 2.

+
+ +
+

Interestingly, the side length has increased by a factor of about 1.4, which results in an aperture increase of the same amount. There is a weight increase of about 40%. More importantly, the area encompassed by the side dimensions has doubled. The implications for balance, weight, wind loading, and other factors affected by the larger structure should be immediately apparent. Moreover, maintaining precision construction over the larger structure--and over the lifetime of the structure in service-- also become a factor in deciding whether or not to go for maximum possible gain.

+

Moreover, the 0.6 dB gain does not accumulate in stacks of corner reflectors. It is rather a one-time gain that may in fact increase the overall physical difficulty of implementing the entire stack.

+

Nonetheless, the exercise has been far from idle. When combined with the models used in Parts 1 and 2, the new work suggests that there is a degree of periodicalness in gain vs. reflector structure. Hence, reflector plane size is not a matter of arbitrary selection once certain limits have been observed. Instead, the development of corner reflector designs deserves all of the detailed attention we give to other antenna types. Modeling, while limited in some respects, can be useful with this class of antennas. However, there are material selections that may require careful field testing to obtain precisely the right dimensions for the reflector planes so that the antenna provides--at any size--all of the performance of which it is capable.

+
+ +
+ 
Corner refl + dipole: 432 MHz           Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1           -5.660,  9.600,  0.000         5.660,  9.600,  0.000 3.75E-01  11
+2          -18.500,  0.000,  0.000        18.500,  0.000,  0.000 3.75E-01  31
+3          -18.500,  2.000,  2.000        18.500,  2.000,  2.000 3.75E-01  31
+4          -18.500,  4.000,  4.000        18.500,  4.000,  4.000 3.75E-01  31
+5          -18.500,  6.000,  6.000        18.500,  6.000,  6.000 3.75E-01  31
+6          -18.500,  8.000,  8.000        18.500,  8.000,  8.000 3.75E-01  31
+7          -18.500, 10.000, 10.000        18.500, 10.000, 10.000 3.75E-01  31
+8          -18.500, 12.000, 12.000        18.500, 12.000, 12.000 3.75E-01  31
+9          -18.500, 14.000, 14.000        18.500, 14.000, 14.000 3.75E-01  31
+10         -18.500, 16.000, 16.000        18.500, 16.000, 16.000 3.75E-01  31
+11         -18.500, 18.000, 18.000        18.500, 18.000, 18.000 3.75E-01  31
+12         -18.500, 20.000, 20.000        18.500, 20.000, 20.000 3.75E-01  31
+13         -18.500, 22.000, 22.000        18.500, 22.000, 22.000 3.75E-01  31
+14         -18.500, 24.000, 24.000        18.500, 24.000, 24.000 3.75E-01  31
+15         -18.500, 26.000, 26.000        18.500, 26.000, 26.000 3.75E-01  31
+16         -18.500, 28.000, 28.000        18.500, 28.000, 28.000 3.75E-01  31
+17         -18.500, 30.000, 30.000        18.500, 30.000, 30.000 3.75E-01  31
+18         -18.500, 32.000, 32.000        18.500, 32.000, 32.000 3.75E-01  31
+19         -18.500, 34.000, 34.000        18.500, 34.000, 34.000 3.75E-01  31
+20         -18.500, 36.000, 36.000        18.500, 36.000, 36.000 3.75E-01  31
+21         -18.500, 38.000, 38.000        18.500, 38.000, 38.000 3.75E-01  31
+22         -18.500, 40.000, 40.000        18.500, 40.000, 40.000 3.75E-01  31
+23         -18.500,  2.000, -2.000        18.500,  2.000, -2.000 3.75E-01  31
+24         -18.500,  4.000, -4.000        18.500,  4.000, -4.000 3.75E-01  31
+25         -18.500,  6.000, -6.000        18.500,  6.000, -6.000 3.75E-01  31
+26         -18.500,  8.000, -8.000        18.500,  8.000, -8.000 3.75E-01  31
+27         -18.500, 10.000,-10.000        18.500, 10.000,-10.000 3.75E-01  31
+28         -18.500, 12.000,-12.000        18.500, 12.000,-12.000 3.75E-01  31
+29         -18.500, 14.000,-14.000        18.500, 14.000,-14.000 3.75E-01  31
+30         -18.500, 16.000,-16.000        18.500, 16.000,-16.000 3.75E-01  31
+31         -18.500, 18.000,-18.000        18.500, 18.000,-18.000 3.75E-01  31
+32         -18.500, 20.000,-20.000        18.500, 20.000,-20.000 3.75E-01  31
+33         -18.500, 22.000,-22.000        18.500, 22.000,-22.000 3.75E-01  31
+34         -18.500, 24.000,-24.000        18.500, 24.000,-24.000 3.75E-01  31
+35         -18.500, 26.000,-26.000        18.500, 26.000,-26.000 3.75E-01  31
+36         -18.500, 28.000,-28.000        18.500, 28.000,-28.000 3.75E-01  31
+37         -18.500, 30.000,-30.000        18.500, 30.000,-30.000 3.75E-01  31
+38         -18.500, 32.000,-32.000        18.500, 32.000,-32.000 3.75E-01  31
+39         -18.500, 34.000,-34.000        18.500, 34.000,-34.000 3.75E-01  31
+40         -18.500, 36.000,-36.000        18.500, 36.000,-36.000 3.75E-01  31
+41         -18.500, 38.000,-38.000        18.500, 38.000,-38.000 3.75E-01  31
+42         -18.500, 40.000,-40.000        18.500, 40.000,-40.000 3.75E-01  31
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           6     1 / 50.00   (  1 / 50.00)      1.000       0.000       V
+
+ +
+

Updated 4-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Main Index

+

Topics: Corner Reflector, VHF / UHF


+ + diff --git a/content/vhf/corner-1.gif b/content/vhf/corner-1.gif new file mode 100644 index 0000000..cf3b5e7 Binary files /dev/null and b/content/vhf/corner-1.gif differ diff --git a/content/vhf/corner-10.gif b/content/vhf/corner-10.gif new file mode 100644 index 0000000..074448c Binary files /dev/null and b/content/vhf/corner-10.gif differ diff --git a/content/vhf/corner-11.gif b/content/vhf/corner-11.gif new file mode 100644 index 0000000..0d53688 Binary files /dev/null and b/content/vhf/corner-11.gif differ diff --git a/content/vhf/corner-2.gif b/content/vhf/corner-2.gif new file mode 100644 index 0000000..496bef9 Binary files /dev/null and b/content/vhf/corner-2.gif differ diff --git a/content/vhf/corner-3.gif b/content/vhf/corner-3.gif new file mode 100644 index 0000000..90322a5 Binary files /dev/null and b/content/vhf/corner-3.gif differ diff --git a/content/vhf/corner-4.gif b/content/vhf/corner-4.gif new file mode 100644 index 0000000..88db61d Binary files /dev/null and b/content/vhf/corner-4.gif differ diff --git a/content/vhf/corner-5.gif b/content/vhf/corner-5.gif new file mode 100644 index 0000000..9d10762 Binary files /dev/null and b/content/vhf/corner-5.gif differ diff --git a/content/vhf/corner-6.gif b/content/vhf/corner-6.gif new file mode 100644 index 0000000..57b98a6 Binary files /dev/null and b/content/vhf/corner-6.gif differ diff --git a/content/vhf/corner-7.gif b/content/vhf/corner-7.gif new file mode 100644 index 0000000..ffa78b3 Binary files /dev/null and b/content/vhf/corner-7.gif differ diff --git a/content/vhf/corner-8.gif b/content/vhf/corner-8.gif new file mode 100644 index 0000000..f8daa87 Binary files /dev/null and b/content/vhf/corner-8.gif differ diff --git a/content/vhf/corner-9.gif b/content/vhf/corner-9.gif new file mode 100644 index 0000000..a8b83db Binary files /dev/null and b/content/vhf/corner-9.gif differ diff --git a/content/vhf/corner.html b/content/vhf/corner.html new file mode 100644 index 0000000..fc25fe0 --- /dev/null +++ b/content/vhf/corner.html @@ -0,0 +1,210 @@ + + + + + + Corner Reflectors Revisited Again Part 1: A Systematic Look at Planar Reflector Sides + + + +
+

Corner Reflectors Revisited Again
+
+ Part 1: A Systematic Look at Planar Reflector Sides

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The corner reflector array has been around since 1938, and Kraus described his initial experiments and analyses in paper published in 1939 and 1940. Indeed, he applied for a patent on the corner reflector antenna in 1942. Since then, the antenna has had an on-and-off career among radio amateurs, television broadcasters, and other VHF and UHF users.

+

In the preceding century (1999), I developed some preliminary modeling studies of corner reflectors for the 70-cm band. See "Corner Reflectors Revisited". In that 3-part exercise, I examined primarily reflectors composed of 0.375" diameter rods spaced 2" center-to-center. The reflectors suggested--over the limited number of sizes explored--that with rod construction, reflector arrays exhibited minor periodic variations in gain as the reflector dimensions varied. Between 2 peak gain levels, the horizontal side length of a reflector might grow considerably, with a minor gain minimum between the peaks.

+

Although rod-based reflectors served well over a good period of time, they have passed out of favor to other antenna types. However, for upper VHF regions, they are still quite serviceable. UHF reflectors would more likely use closely spaced screens or solid surfaces. Naturally, the idea arose for an exploration of these reflectors using wire-grid models similar to the ones used to study planar reflectors. The modeling techniques exist to simplify systematic studies of such arrays. As well, I wondered if the periodic behavior of the rod reflector would also show up in wire-grid reflectors.

+

The Basic Study Set-Up

+

As in the study of planar reflectors, I used 299.7925 MHz as the test frequency so that 1 meter = 1 wavelength. The wire-grids consist of 0.1-m (wavelength) segments using a diameter of 0.0159 m (segment length / PI). As demonstrated in the course of studying planar reflectors, there is no need to use closer spacing of the wires in the grid, since tightening the grid by even a factor of 4 did not alter the results significantly.

+

The 90-degree corner reflector is a somewhat different beast than a simple rectangular planar reflector. It consists of two planes, normally at right angles to each other. Centered in the array is a driver, normally a simple dipole, because one can derive all of the performance desired from the array by adjusting the reflector dimensions. Fig. 1 shows the general layout of a small reflector and its driver, along with an identification of some of the key terms applied to the reflector.

+
+ +
+

In modeling terms, I shall lay out each reflector so that its apex--the wire formed at the reflector center--lies on the +/-Z axis, or in conventional terms, vertically. Hence, the dipole will also be vertical. The apex wire will have X- and Y-axis coordinates of 0, 0. Hence, the dipole will be spaced from the apex by a distance registered along the X-axis, and the reflector will spread open left and right in the +/-Y dimension.

+

The vertical dimension will thus provide the array height or the length of the apex wire. The horizontal dimension will usually refer to the length of each side from the apex of the reflector to the open end. Since each side makes a 45-degree angle to the coordinate axes, the actual forward dimension (in the X direction) will be 0.707 times the side length. The total distance between wires at the open ends of the sides is the aperture and is 1.414 times the length of a side.

+

As I did in the study of planar reflectors, I shall assume a priority for a 50-Ohm feedpoint system. You may set the dipole feedpoint impedance at almost any reasonable impedance (say, between 50 and 100 Ohms) simply by changing the space between the dipole and the apex, with some small adjustments of the dipole length to restore resonance. As shown in the earlier study, higher impedance drivers tend to produce wider 2:1 SWR bandwidths. For the present survey, I shall use the same 0.008 m (8 mm) dipole diameter used in the study of planar reflectors. Fatter dipoles will likely yield wider SWR bandwidths, although we shall not have space to examine that potential in this initial exploration.

+

As I did for the planar reflector study, I shall use a set of Green's files to separately model the reflectors. The benefit is that the Green's file produced by the reflector models can be used in a variety of models using other than the standard dipole driver--all without having to re-run the largest part of the model, that is, the reflector itself.

+

Although more complex than the basic rectangles of the planar reflectors, the corner reflector models are still quite simple. The following lines show the NEC file for the smallest of the reflectors used. It has a vertical height of 1.0 m (wavelength) and horizontal dimensions of 0.5 m (wavelength) on each side of the reflector apex.

+ 
CM Basic Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM T1 = center line, T2, T3 = verticals + GM
+CM T4, T5 = horizontal centers + GM
+CM Density = 0.1 m x 0.1 m
+CM Size = 1.0 m x 1.0 m, File = C-Vn-Hn.WGF
+CE
+GW 1 10 0 0 -.5 0 0 .5 .0159
+GW 2 10 0 -.1 -.5 0 -.1 .5 .0159
+GM 0 4 0 0 0 0 -.1 0 2 1 2 10
+GW 3 5 0 0 0 0 -.5 0 .0159
+GM 0 5 0 0 0 0 0 -.1 3 1 3 5
+GM 0 5 0 0 0 0 0 .1 3 1 3 5
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 4 10 0 .1 -.5 0 .1 .5 .0159
+GM 0 4 0 0 0 0 .1 0 4 1 4 10
+GW 5 5 0 0 0 0 .5 0 .0159
+GM 0 5 0 0 0 0 0 -.1 5 1 5 5
+GM 0 5 0 0 0 0 0 .1 5 1 5 5
+GM 0 0 0 0 -45 0 0 0 4 1 0 0
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG c-v10-h05.WGF
+EN
+

GW 1 sets up the apex wire. GW 2 and the following GM line establish the vertical wires on one side of the reflector. GW 3 and the following 2 GM lines set up the wires in the horizontal direction. Finally, the last GM line bends the array from GW 2 onward the requisite 45 degrees. GW 4, GW 5, and their associated GM lines do the same thing on the other side of the apex wire. After specifying the free-space medium and the test frequency, the partial results are saved into a designated WGF file for use with various drivers.

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The basic model sets up 10 vertical grid squares and a total of 10 horizontal grid squares (5 on each side of the apex. The largest reflector in the set uses a vertical dimension of 2.0 m (wavelengths), with side lengths of 1.6 m (wavelengths). The result is a set of squares that runs 20 vertically by 32 horizontally. As the following lines show, the reflector model is no larger as a file, although the number of segments and the resulting .WGF file are both many times larger than for the small reflector.

+ 
CM Basic Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM T1 = center line, T2, T3 = verticals + GM
+CM T4, T5 = horizontal centers + GM
+CM Density = 0.1 m x 0.1 m
+CM Size = 2.0 m x 3.2 m, File = C-Vn-Hn.WGF
+CE
+GW 1 20 0 0 -1 0 0 1 .0159
+GW 2 20 0 -.1 -1 0 -.1 1 .0159
+GM 0 15 0 0 0 0 -.1 0 2 1 2 20
+GW 3 16 0 0 0 0 -1.6 0 .0159
+GM 0 10 0 0 0 0 0 -.1 3 1 3 16
+GM 0 10 0 0 0 0 0 .1 3 1 3 16
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 4 20 0 .1 -1 0 .1 1 .0159
+GM 0 15 0 0 0 0 .1 0 4 1 4 20
+GW 5 16 0 0 0 0 1.6 0 .0159
+GM 0 10 0 0 0 0 0 -.1 5 1 5 16
+GM 0 10 0 0 0 0 0 .1 5 1 5 16
+GM 0 0 0 0 -45 0 0 0 4 1 0 0
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG c-v20-h16.WGF
+EN
+

All models use NEC-4 (GNEC). NEC-2 models may require slight revisions of the GM lines and should invoke the EK command.

+

The model that adds the dipole is a paragon of simplicity:

+ 
CM Dipole .331 m from planar reflector
+CE
+GF 0 c-v10-h05.WGF
+GW 101 11 .331 0 -.2116 .331 0 .2116 .004
+GE 0 -1 0
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The sample version calls up the Green's file for the smallest reflector. To call up any other reflector in the set, you only need to change the GF line to specify the file name of that reflector. Hence, you may have--if you wish--a single model, or as many models as there are reflectors in the survey set. If you counted up the models required to handle the horizontal dimension changes (12) and the number needed to handle the 0.2-m (wavelength) increments of the vertical dimension (6), the total set of reflectors numbers 72. This set is twice the number used in the planar reflector study.

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The corner-reflector study also makes a few other adjustments. First, because we have so many horizontal increments, the main graphs of performance will reverse the conventions used in the planar study. Each vertical dimension will have its own line, and the X axis will record the steps in the horizontal dimension. Second, I "reset" each new collection of models, where a new set uses a new horizontal increment and covers vertical dimensions from 1.0 to 2.0 m (wavelengths). The resetting process consisted of adjusting the spacing of the dipole from the apex and the dipole's length to arrive at a 50-Ohm SWR value of 1.00:1. This procedure allowed somewhat more sensitive (but not perfectly sensitive) readouts of variations in the feedpoint resistance and reactance with changes in the vertical dimension of the reflector.

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Some Basic Performance Parameters of Standard Corner Reflector Arrays

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By a standard corner reflector, I mean only one that has a 90-degree angle. The dipole itself varies in its closest approach to the reflector from 0.228 m to 0.234 m, a distance just slightly longer than each half of the dipole itself. The following table lists the reflector horizontal dimensions, the distances from the apex to the dipole, and the dipole length to achieve the noted 50-Ohm SWR value with the shortest vertical dimension in each group. Every dipole has a 0.008-m diameter. The distance of closest approach to the reflector is 0.707 times the spacing from the apex.

+ 
+Horizontal Side          Spacing from        Dipole Length
+Length (m/wl)            Apex (m/wl)         (m/wl)
+0.5                      0.331               0.4232
+0.6                      0.325               0.4232
+0.7                      0.323               0.4238
+0.8                      0.324               0.4240
+0.9                      0.325               0.4238
+1.0                      0.324               0.4238
+1.1                      0.323               0.4239
+1.2                      0.324               0.4242
+1.3                      0.325               0.4242
+1.4                      0.326               0.4238
+1.5                      0.325               0.4234
+1.6                      0.323               0.4236
+

As the table makes clear, the required spacing of the dipole from the reflector apex fluctuates in a very small but regular way. The dipole lengths are simply those needed to zero out the reactance to the degree possible until the 50-Ohm SWR reads 1:1. Although none of the fluctuations makes a significant operational difference, the numerical progressions are interesting in their own right.

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We may characterize the performance of a corner reflector--at least over the range of reflector sizes sampled--as very well-behaved. We shall encounter a vertical dimension of maximum gain potential, although the exact vertical dimension will vary a small amount with the horizontal dimension. For any group of vertical dimensions, the average gain increases as we increase the reflector horizontal dimension. The only place where the array may find energy for increased gain is in the beamwidth. The H-plane beamwidth shows the greatest decrease as we enlarge the horizontal dimension of the reflector. This makes sense, since this beamwidth is at right angles to the dipole and extends on either side of the maximum gain heading in the direction of the reflector sides. The E-plane patterns show lesser influences of changes in horizontal reflector size, and this pattern emerges "out the open ends" of the reflector structure. Fig. 2 samples the E-plane and H-plane patterns of the smallest and the largest reflectors horizontally. Both pattern sets use the reflector vertical dimension producing maximum gain.

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Immediately noticeable in the figure is the fact that the vertical dimensions producing maximum gain differ for the two sizes of horizontal reflector sides. Equally noticeable is the fact that as we move from small to large reflectors, the H-plane beamwidth--as indicated by the red lines--changes much more than the E-plane beamwidth. We may pass over the changes in shape of the forward lobe, since the transition from an essentially round forward lobe to a bell-shaped lobe is common to most planar reflector situations. More significant is the rear lobe structure, as viewed with an eye toward the worst-case front-to-back ratio. With the small reflector, the worst-case front-to-back ratio is just over 20 dB. The larger reflector yields a worst-case front-to-back ratio that is over 30 dB. Although (as we shall see) the 180-degree ratio fluctuates considerably, the worst-case values tend to progress steadily as we lengthen the sides of the reflector.

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The corner reflector shares an important feature with its planar cousin. Once we establish a spacing of the dipole from the reflector apex, the SWR curve does not vary significantly as we change the size of the reflector. Fig. 3 overlays two curves from very different size reflectors to demonstrate the similarity of the curves.

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The curve passes through the 2:1 SWR level at about 288 MHz and again at 315 MHz, for a total span of 27 MHz. This value represents a 9.0% SWR passband for a driver with a 0.008-m diameter. We shall not be able to examine what may happen with other element diameters within this initial study. Instead, we need to examine more closely some of the detailed data from the survey of reflector array performance. Since free-space forward gain is always of interest, we may begin with Fig. 4.

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The gain chart X-axis records the length of individual reflector horizontal sides, so the overall physical length that one would use for planning materials is twice the value shown. Each line represents a different vertical reflector height. The meaning of each line is self-explanatory. If you wish to scan what happens for any given horizontal dimensions with a changing vertical height, simply scan the values vertically on the chart.

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If we do some vertical scanning, we shall notice that the changes of reflector height produce similar ranges of gain numbers for every increment of horizontal side length. Actually, there is an interesting and somewhat subtle curve, which we can show in the following table. The two lines indicate, first, the horizontal dimension increment (Horizontal Length) and, second, the range of gain from 1.0 to 2.0 m (wavelength) of height (Delta Gain).

+ 
+Horizontal Length in m/wl   0.5    0.6    0.7    0.8    0.9    1.0    1.1    1.2    1.3    1.4    1.5    1.6
+Delta Gain in dB            0.80   0.96   1.05   1.06   1.07   1.16   1.28   1.38   1.38   1.30   1.22   1.19
+
+

The curve indicates in a suggestive, if not a definitive, way the overall effect of increasing the vertical dimension of a reflector for any given horizontal dimension. The lowest gain always corresponds to a vertical height of 1.0 m. Maximum gain occurs with a vertical height of either 1.4 m (for the smaller reflectors) or 1.6 m (for reflectors with sides at least 0.9 m). The maximum gain differential occurs with horizontal dimensions of 1.1 and 1.2 m.

+

Throughout the range of horizontal lengths surveyed, the longer the sides, the higher the peak gain and the higher the average gain, taking into account all of the values for vertical dimensions. The only cross-over occurs between the vertical lines for 1.4 and 1.6 m, between horizontal increments of 0.8 and 0.9 m. If the curves were steeper, we would see that the vertical height required for maximum gain actually undergoes a continuous increase across the span of horizontal dimensions. The amount by which the preceding and succeeding vertical heights show a decrease from the peak value varies gives an indication of the likely height of the peak value between the surveyed vertical heights. Using simple proportional parts, we obtain a continuous increase in vertical height throughout the gain chart as we increase the horizontal dimension. When the side length reaches about 1.7 or 1.8 m, the required vertical height for maximum gain will increase to 1.8 m, assuming that the trends hold beyond the chart limits.

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Another way to look at the gain curves with respect to maximum gain is to examine the rate of gain increase from one peak to the next. The following 2-line table provides the data, with the proviso that we have already established that the graphs and survey do not in all cases reveal the actual peak gain. Where the gain is almost the same at two successive surveyed points, the actual peak is likely somewhere between the two points and has a value higher than either of the two listed values.

+ 
+Horizontal Length in m/wl         0.5    0.6    0.7    0.8    0.9    1.0    1.1    1.2    1.3    1.4    1.5    1.6
+Successive Gain Increase in dB    ----   0.63   0.47   0.34   0.33   0.39   0.39   0.32   0.18   0.09   0.11   0.15
+
+

We find the expected general decrease in the rate of change between steps as we move away from the smallest reflectors, where each step is a significant increase in the horizontal dimension. However, after the changeover in the vertical height required for maximum gain, we find an increase in the successive gain rise, followed by a rapid decline. However, the decline returns to an increase at the upper end of the chart. Part of the periodic behavior can be accounted for in the fact that we have surveyed distinct points along the continuum of possible vertical and horizontal dimensions. However, part may also be due to the dimensions themselves.

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In the earlier study of rod-based reflectors, we found elements of periodic behavior in the dimensions of those arrays, even to seeing gain reductions. With continuous surface reflectors, simulated here by wire-grid constructs, we do not encounter gain reductions. However, we do find changes in the rate of gain increase that suggest at least some residual periodic behavior.

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At first sight, the curves for the 180-degree front-to-back ratios in Fig. 5 may appear to be a senseless morass. However, we can make some good sense out of the curves by some judicious vertical and horizontal scanning. Of course, horizontally, the shortest vertical heights and the shortest horizontal sides yield the lowest front-to-back values. However, above a horizontal side length of about 0.7 m, the valleys of the curves give a good approximation of the worst-case front-to-back ratio, regardless of how high a peak value may rise. In general, larger the reflector in terms of both vertical and horizontal dimensions, the better the overall front-to-back performance.

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For any size parasitic reflector, such as those on a wide-band Yagi (the DL6WU designs, for example), a fixed reflector length over a wide frequency range will show multiple peaks in the 180-degree front-to-back ratio. The reflector size changes shown in Fig. 5 represent an obverse manner of showing similar information, this time by keeping the frequency constant and varying the reflector size. All of the reflector sizes--using the vertical increments to distinguish them--show at least two peaks. The shortest reflector peaks at a side length of 0.7 m. The next 3 vertical sizes (1.2 through 1.6 m) peak with a side length of 0.8 m. The 1.8-m reflector peaks at 0.9-m side length. Interestingly, when the vertical height reaches 2.0 m, the side length must reach 1.2 m for a peak 180-degree front-to-back ratio.

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Second peaks show a somewhat different pattern. The shortest (1.0-m) reflector shows its peak with a 1.2-m side length. The 1.2-m vertical reflector has its peak at the same side length, although the peak is almost indistinct. The reflectors with vertical dimensions of 1.4, 1.6, and 2.0 m show a second peak at a side length between 1.4 and 1.5 m. However, the vertical 1.8-m reflector has a very distinct peak at 1.4 m side length.

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From the perspective of an optical analogy to the corner reflector, the seeming irregularities of the changes in gain rates and the front-to-back peaks would be anomalies. However, the corner (and the planar) reflectors are somewhat hybrid beasts, exhibiting partial optical properties and partial parasitic element properties. If we change the position of the dipole with respect to the reflector apex, we change the front-to-back ratio behavior. However, changing the reflector dimensions also changes that behavior, but in ways that suggest parasitic element behavior. The rod-based reflector structures appear to show a higher proportion of parasitic behavior, since they are capable of periodic gain reductions as we increase reflector size. In the more solid wire-grid reflector models, those changes are reduced to changes in the rate of gain increase. However, the front-to-back behavior of the planar facets of the corner reflector suggest that parasitic element behavior remains the dominant mode of reflector operation.

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Beyond Just the Gain Behavior

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So far, we have surveyed the most common aspects of array behavior to which many antenna evaluators attend: the forward gain (in free-space terms), the front-to-back ratio, and the SWR curves. However, there are other facets of the ways in which corner reflectors perform that give us some interesting insights into their operation. We shall pay close attention to two such facets: the -3 dB (half-power) beamwidth in both the E- and H-planes, and the small but interesting changes in the feedpoint impedance as we change the reflector's vertical dimension.

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Fig. 6 orients us to the difference between the E-plane and the H-plane patterns with a corner reflector. The dipole driver is parallel to the apex wire of the reflector. The E-plane pattern is one that is in the planes formed by these two wires. It is not confined by the reflector sides directly. Rather, it is confined mostly by the forward directivity of the array. A dipole in free space has an E-plane beamwidth of about 75-80 degrees. We may use this figure as a reference point when examining E-plane patterns for the corner reflector.

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The H-plane pattern is at right angles to the dipole. In free space, the dipole's H-plane pattern is a circle. When we place the dipole within the confines of the corner reflector, the dipole fields and the reflector sides strongly interact to confine the resulting pattern.

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Fig. 7 presents the E-plane beamwidth data using the convention set up for the gain and front-to-back information. The beamwidth data has an additional limitation. It emerges as a post-core-run calculation and is normally presented to the nearest integer in degrees. Therefore, we find the graph has the appearance of a multiple set of stairways. Nonetheless, we can glean some valuable information from the graph.

+

If we scan the graph vertically as a start, we discover that the range of values for the span of vertical reflector heights is limited. The smallest reflector horizontally shows a spread of 8 degrees decrease as we increase the vertical height. With a side length of 1.6 m, we increase the change of beamwidth to only 14 degrees.

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Looking at the chart horizontally, we find that the 1.0-m high reflector changes its E-plane beamwidth by only 4 degrees as we extend the sides from 0.5 m to 1.6 m. With a vertical height of 2.0 m, the difference in beamwidth between the shortest and the longest reflector side length is 10 degrees.

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From a composite perspective, the shortest and smallest reflector yields the widest E-plane beamwidth, about 58 degrees. The minimum E-plane beamwidth is 40 degrees, a value that occurs at the maximum gain vertical and horizontal dimensions: 1.6-m vertically and 1.5 and 1.6 m horizontally. Above the maximum gain point, the beamwidth tends to increase by about 2 degrees. The total beamwidth span of 18 degrees reflects the somewhat narrow gain span of the array: 4.2 dB from minimum to maximum.

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The H-plane beamwidth changes by a much greater amount overall, as shown in Fig. 8. The total range runs from 74 down to 34 degrees, or about 40 degrees. Some curves show a very slight dip (never more than 2 degrees) at the reflector size yielding maximum gain for any curve. However, it is clear that the H-plane beamwidth is almost wholly a function of the reflector side length. As we would expect, the rate of decrease slows down with increasing side lengths, since each new increment of side length becomes progressively a smaller fraction of the overall reflector size increase.

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A well-controlled 10-element Yagi has about the same gain as the largest corner reflector in our survey. Such an array has a boomlength in the 2.15-wavleength range. By way of comparison, the highest gain corner reflector of our series has sides that are 1.6 wavelength long for a 1.13 wavelength front-to-back dimension. The aperture is about 2.26 wavelengths, with a vertical height of 1.6 wavelengths. The gain levels are very comparable. So, too, are the E-plane beamwidths--about 40 degrees. However, the Yagi has an H-plane beamwidth that is over 44 degrees, compared to the 34-degree beamwidth of the corner reflector. In addition, the Yagi displays forward sidelobes in the H-plane, while the corner reflector exhibits a single forward lobe, as shown in Fig. 2. This comparison does not recommend one antenna over another. Instead, it brings to the fore characteristics that may prove significant to one or another set of design specifications.

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The final data set at which we should take a look concerns the feedpoint behavior of corner reflectors. For the survey, the dipole length and its spacing from the reflector apex was set to provide a 50-Ohm SWR of 1.00:1 using a vertical dimension of 1.0 m. I reset the dipole length and spacing for each new increment of the horizontal or side length. However, I maintained the dipole length and position as the vertical dimension grew through its six increments.

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The resulting data showed an interesting variability in terms of stability. In no case did the values change radically with changes in vertical height. However, there are cases that we might consider more stable and others that we might consider less stable. In terms of the SWR range, the most stable case (horizontal side length = 1.3 m) showed a range that never exceeded 1.02:1. The least stable case showed a peak value of 1.05:1. Fig. 9 shows the patterns with changes in the vertical reflector dimension. Although the overall range is small, the differences in the peak values for the two cases show a 2.5:1 difference.

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Interestingly, the difference is, for the most part, not a matter of changes in the resistive component of the impedance. As shown in Fig. 10, the most stable case has a maximum resistance range of 0.86 Ohm, while the least stable case has a range of 0.92 Ohm. Moreover, the two curves--within the limitations of the modeling techniques used to establish them--show good congruence.

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The culprit, that is, the source of the SWR divergence between the two cases is the range of reactance at the feedpoint of the two dipoles driving the different size reflectors. As Fig. 11 shows, there is a considerable differential between the maximum ranges of reactance for the two cases. The 1.3-m reflector displays a reactance variation of 1.15 Ohms. However, the range for the 1.5-m reflector is nearly double, at 2.22 Ohms,

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Although the most stable and least stable cases occur with reflector sizes that are close to each other, no two successive increments of horizontal side length show the same pattern. Nor is there a clearly identifiable repetition of patterns. In short, the feedpoint behavior of the corner reflector is not a simple matter of reflector dimensions. (However, the patterns, if any, might be a complex matter of reflector dimensions, involving the area of the two planes and the regions of illumination or maximum reflector currents within them.)

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The interest in the feedpoint behavior of the corner reflector, even though it is below the level of operational significance, arises out of the fact that we have been accumulating a collection of variable behaviors. The two most evident ones involved the range of gain across each set of vertical dimensions as we increased the horizontal side dimension and the amount of gain increase at maximum gain for each successive increment of side-length increase. Unfortunately, the available beamwidth data was not sufficiently sensitive to show similar undulations, if any exist.

+

Bar-based reflector structures displayed a wider range of behaviors, especially with respect to gain. With wire-grid planes, the variations reduce to small undulations that this survey has only imprecisely identified.

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Unfinished Business

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In the course of our survey of corner reflector sizes, we have by-passed a number of interesting questions in order to remain focused on the continuum of reflector size increases with a simple dipole driver. Within the focus of our efforts using wire-grid reflector planes to simulate closely spaced screens or solid surfaces, we may fairly reach the following conclusions.

+
+ 1. For the range of horizontal side lengths studied, a dipole-driven corner reflector reaches maximum gain with a vertical dimension between 1.4 wavelengths and 1.6 wavelengths, with the likely precise vertical size growing as the horizontal side length grows. +

2. The maximum gain obtainable from a corner reflector shows continuous growth from horizontal side lengths of 0.5 wavelength through 1.6 wavelengths. However, there appear to be variations or undulations in the rate of growth with linear increases in the side length.

+

3. The worst case front-to-back ratio shows generally increasing values with the overall size of the reflector surfaces. The maximum value of 180-degree front-to-back ratio shows at least two distinct peaks across the span of side lengths used in the survey, although those peaks show differences in the peak value and in the side length of occurrence relative to the vertical dimension.

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4. E-plane beamwidth shows only small and steady decreases with increases side length, with minimum values occurring at of near reflector size yielding maximum gain for a given side length. H-plane beamwidth is almost completely a function of the horizontal side length and shows a steady decrease with increasing side-length increases.

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5. Operationally, a 50-Ohm 8-mm diameter dipole driver shows a 9.0% 2:1 SWR bandwidth. Reflector size makes virtually no difference to the SWR curve. Feedpoint behavior is operationally stable, but shows some interesting minor undulations.

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Despite the long list of conclusions that we may draw from the survey, others remain for further study. For example, one might wonder if there is a reflector size that would show an actual decrease in gain with a further increase in reflector side length. As well, from time to time, investigators have suggested some slight revisions to the general corner reflector shape in order to improve array performance.

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The driver has also occasioned some suggested revisions, such as the use of a bi-conical or a fan driver element. As well, one might try to press into service driver systems that display some bi-directional gain in the H-plane and see if they are suitable for service with a corner reflector.

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Sampling these questions deserves more than one additional foray into the angular world of corner reflectors.

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Updated 06-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX May, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: Corner Reflector, VHF / UHF


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Corner Reflectors Revisited Again
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+ Part 2: A Non-Systematic Look at Some Corner Variations

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L. B. Cebik, W4RNL

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In Part 1 of this return visit to the corner reflector, we examined a series of 72 reflectors, all modeled as wire grids using 0.1-m (wavelength) segments of 0.0159-m (wavelength) radius wire. In the discussion of planar reflectors, we had established that this method of forming a model of a closely spaced screen or a solid surface is quite accurate, at least, relative to assemblies using wires on a grid that is up to 4 times more dense.

+

The series of reflectors used vertical dimensions along the apex and the sides forming the aperture from 1.0 to 2.0 m (wavelengths). 1 m = 1 wavelength, because the test frequency is 299.7925 MHz. Each side length ranged from 0.5 m to 1.6 m long. Each successive model varied either the vertical dimension by 0.2 m or the horizontal side length by 0.1 m (for a total increase of 0.2 m in the overall sum of the two sides). For each of the 72 reflectors forming the matrix of sizes, the driver was a simple dipole using a 0.008-m diameter. Its length and position provides a very close 50-Ohm resonant match at the feedpoint.

+

On the basis of the detailed survey, we reached the following conclusions.

+
+ 1. For the range of horizontal side lengths studied, a dipole-driven corner reflector reaches maximum gain with a vertical dimension between 1.4 wavelengths and 1.6 wavelengths, with the likely precise vertical size growing as the horizontal side length grows. +

2. The maximum gain obtainable from a corner reflector shows continuous growth from horizontal side lengths of 0.5 wavelength through 1.6 wavelengths. However, there appear to be variations or undulations in the rate of growth with linear increases in the side length.

+

3. The worst case front-to-back ratio shows generally increasing values with the overall size of the reflector surfaces. The maximum value of 180-degree front-to-back ratio shows at least two distinct peaks across the span of side lengths used in the survey, although those peaks show differences in the peak value and in the side length of occurrence relative to the vertical dimension.

+

4. E-plane beamwidth shows only small and steady decreases with increases side length, with minimum values occurring at of near reflector size yielding maximum gain for a given side length. H-plane beamwidth is almost completely a function of the horizontal side length and shows a steady decrease with increasing side-length increases.

+

5. Operationally, a 50-Ohm 8-mm diameter dipole driver shows a 9.0% 2:1 SWR bandwidth. Reflector size makes virtually no difference to the SWR curve. Feedpoint behavior is operationally stable, but shows some interesting minor undulations.

+
+

There remain a number of outstanding questions, which we may divide into two groups. First are questions concerning performance using a dipole driver. Because the spacing of the driver from the sides of the reflector plays a role in the array performance, we are limited with the corner reflector in selecting drivers. We do not have the freedom that was possible with the simple flat planar reflector to choose any driver that might fit forward of the reflector surface. Nevertheless, we have a number of options, including fatter dipoles, folded dipoles, and fan dipoles that might either improve the forward gain or increase the SWR bandwidth of the array from its 9% value using the 8-mm dipole.

+

A second set of questions surround the reflector itself and rest on the fact that in our survey, even 1.6-m sides did not register the highest gain feasible from the corner reflector composed of tight screens or solid surfaces. So we are left with the question of whether there is in fact a corner reflector size beyond which the gain decreases.

+

It is not possible to perform a complete survey of all of the objects of study before us. Therefore, we shall be somewhat selective on the premise that, just as the driver showed regular progressions of values as we changed reflector sizes, any replacement drivers will show similar progressions. We shall shortly show the reason why we have adopted the premise. A reflector size that is 1.4-m vertical with 0.8-m side lengths will form our main test vehicle, although we shall employ other sizes from time to time. Using the same reflector will permit judicious comparisons among a number of the driver candidates without bogging us down in an excess of data that does not directly contribute to the comparison.

+

The following lines form the Green's file model for the main reflector in this part of the study.

+ 
CM Basic Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM T1 = center line, T2, T3 = verticals + GM
+CM T4, T5 = horizontal centers + GM
+CM Density = 0.1 m x 0.1 m
+CM Size = 1.4 m x 1.6 m, File = C-Vn-Hn.WGF
+CE
+GW 1 14 0 0 -.7 0 0 .7 .0159
+GW 2 14 0 -.1 -.7 0 -.1 .7 .0159
+GM 0 7 0 0 0 0 -.1 0 2 1 2 14
+GW 3 8 0 0 0 0 -.8 0 .0159
+GM 0 7 0 0 0 0 0 -.1 3 1 3 8
+GM 0 7 0 0 0 0 0 .1 3 1 3 8
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 4 14 0 .1 -.7 0 .1 .7 .0159
+GM 0 7 0 0 0 0 .1 0 4 1 4 14
+GW 5 8 0 0 0 0 .8 0 .0159
+GM 0 7 0 0 0 0 0 -.1 5 1 5 8
+GM 0 7 0 0 0 0 0 .1 5 1 5 8
+GM 0 0 0 0 -45 0 0 0 4 1 0 0
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG c-v14-h08.WGF
+EN
+

By appropriate number replacements, you may create any size reflector without lengthening the file itself. However, the stored WGF file will vary in size according to the total number of segments in the reflector wire grid.

+

Increasing the Bandwidth

+

A corner reflector does not change its gain and front-to-back characteristics very rapidly as one moves away from the design frequency. For a simple dipole driver, such as the 8-mm diameter dipole used in Part 1 of our work, the performance passband outstrips the SWR bandwidth by a wide margin. Therefore, we shall initially look at some suggested ways of expanding the SWR passband, keeping an eye out for performance changes along the way. I shall resonate each candidate driver at either 50 Ohms or at an impedance suited to the use of that driver. (There will be an exception to this rule along the way.)

+

1. Fatter Dipoles

+

The most immediate apparent solution to increasing the SWR bandwidth of a corner reflector is to employ fatter dipoles. To investigate this option, I selected our initial 8-mm dipole plus 12-mm and 16-mm dipoles as comparators. The 2:1 diameter ratio between the smallest and the largest in the group should provide an indication of using this route as a means to expanding the operating bandwidth while remaining well within the limitations of NEC-4 regarding the segment length vs. the wire radius.

+

The basic model for any dipole-driven corner reflector--using the Green's files generated by reflector models--has the following form.

+ 
CM Dipole 50-Ohm
+CE
+GF 0 c-v14-h08.WGF
+GW 101 11 .324 0 -.212 .324 0 .212 .004
+GE 0 -1 0
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The GW line will be the only difference among the dipoles. In fact, we may isolate the GW lines for the three drivers under comparison.

+ 
+GW 101 11 .324 0 -.212  .324 0 .212  .004     8-mm driver
+GW 101 11 .326 0 -.2075 .326 0 .2075 .006    12-mm driver
+GW 101 11 .328 0 -.2035 .328 0 .2035 .008    16-mm driver
+
+

To obtain a resonant 50-Ohm feedpoint required a slightly different spacing from the reflector apex and a slightly different dipole length. The length, which shrinks from 0.424 m down to 0.407 m, is a function mostly of the increasing element diameter. However, since the element surface comes closer to the reflector surface as we increase the diameter, we have also to compensate for the change in mutual coupling. Increasing the spacing allows us to restore the 50-Ohm impedance, but that spacing change also affects the dipole length. In the end, a resonant driver requires a balance between the effects of coupling and of element length. The total spacing change was 4 mm for a radius change of 4 mm. The closest approach of the dipole surface to the reflector plane remains virtually unchanged.

+

To determine whether I needed to survey the alternative drivers over the entire set of reflectors, I initially chose two reflectors of very different sizes as test cases. One reflector is the version already noted, with a 1.4-m vertical dimension and 0.8-m side lengths. The second test reflector used a 1.6-m vertical dimension with 1.6-m side lengths--twice as long. The similarity in the vertical dimension stems from the fact that both reflector sizes represent the peak gain performance for the selected side lengths, as derived from the survey in Part 1. For the three drivers, the two reflectors yielded the following performance figures. In the table, E-BW is the E-plane -3 dB beamwidth, and H-BW is the corresponding value for the H-plane. Gain values are for free space, and the front-to-back value is for 180 degrees.

+ 
+Reflector     Dipole       Gain     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Size          Dia. mm      dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V14-H08       8-mm         11.42    38.27             46         54         49.63 - j1.56   1.03
+              12-mm        11.42    38.24             46         54         49.90 - j0.20   1.00
+              16-mm        11.41    38.19             46         54         49.96 - j0.47   1.01
+V16-H16       8-mm         13.38    37.35             40         34         48.82 - j1.69   1.04
+              12-mm        13.37    37.51             40         34         50.08 + j0.37   1.01
+              16-mm        13.37    37.47             40         34         50.14 + j0.09   1.00
+
+

Since there is no change in performance at the extremes of reflector sizes, we may let a single reflector size stand in for all sizes with respect to the SWR bandwidth. As shown in Part 1, reflector size makes virtually no difference to the SWR performance of the corner reflector design.

+
+ +
+

As Fig. 1 shows, we obtain the expected increase in SWR bandwidth as we increase the dipole diameter. However, the rate of increase is not very great. Whereas the 8-mm dipole has a 9.0% bandwidth between 2:1 SWR points, the 12-mm dipole shows an increase of only 1% and the 16-mm dipole has an increase of 1.7% over the initial size. Between the thinnest and fattest dipoles, we obtain only a 5-MHz increase in the passband.

+

The end result of the modeling experiment is simple: a fat dipole is beneficial, but does not achieve the desired goal of a significant widening of the SWR bandwidth.

+

2. The Bi-Conic Dipole

+

An alternative to the fat dipole is the bi-conic dipole. Fig. 2 suggests its shape and relationship to our primary reflector.

+
+ +
+

The bi-conic (or biconical) dipole is one that tapers from a thin center to a thicker pair of outer ends. For our test, segment-length vs. wire-radius limitations allowed only a relatively simple sample of this dipole type, with the center section at 8-mm diameter and the outer ends at 16-mm diameter. The following lines show the model used, along with the GC entries used to effect the taper.

+ 
CM bi-conic dipole
+CE
+GF 0 c-v14-h08.WGF
+GW 101 5 .335 0 -.1753 .335 0 -.02 0
+GC 0 0 1 .016 .004
+GW 102 1 .335 0 -.02 .335 0 .02 .004
+GW 103 5 .335 0 .02 .335 0 .1753 0
+GC 0 0 1 .004 .016
+GE 0 -1 0
+EX 0 102 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The geometry continuation entries allow for a uniform increase in diameter as we move from one segment to the next working from the center outward. The result is a dipole that is 0.3056-m long, about 25% shorter than the uniform-diameter dipoles. A bi-conic dipole has a significantly lower feedpoint impedance than a uniform-diameter dipole and hence requires more spacing from the reflector apex to achieve a 50-Ohm feedpoint impedance. The following simple table compares the performance of our original model and the new driver.

+ 
+Reflector     Dipole               Gain     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Size          Dia.                 dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V14-H08       8-mm uniform         11.42    38.27             46         54         49.63 - j1.56   1.03
+              8-16-mm bi-conic     11.04    38.00             46         54         50.07 - j0.13   1.00
+
+

The very slightly reduced gain performance is a mutual function of the shorter overall length of the dipole and the increased spacing from the reflector apex. Otherwise, there is nothing to distinguish the two drivers.

+
+ +
+

Unfortunately, neither is there any significant difference between the SWR performances of the original dipole and the new bi-conic driver, as illustrated by the SWR curve in Fig. 3. The bi-conic driver has an SWR passband of 10.0%, about the same as for the 12-mm uniform-diameter driver. We must look elsewhere for a means to increase the corner reflector SWR bandwidth.

+

3. The Folded Dipole

+

A third candidate for increasing the SWR bandwidth is the folded dipole. Essentially, a folded dipole--in addition to its impedance transformation function--also acts like a piece of fat wire. Fig. 4 shows our test set-up.

+
+ +
+

The dimensions of the folded dipole in the test are themselves interesting. The spacing between the two wires--each reduced to a 4-mm diameter--is 0.01 m, close to the value of the 12-mm uniform-diameter dipole. The spacing from the reflector apex--0.326 m--is the same value used with the 12-mm dipole. However, since the folded dipole effects a 4:1 impedance transformation, the reference standard will be 200 Ohms instead of 50 Ohms. The folded dipole length is 0.4158 m, only about 0.4 mm longer than the 12-mm dipole. The following lines show the model of the driver, ready for use with the standard reflector file.

+ 
CM Folded Dipole
+CE
+GF 0 c-v14-h08.WGF
+GW 101 11 .326 0 -.2079 .326 0 .2079 .002
+GW 101 1 .326 0 .2079 .326 .01 .2079 .002
+GW 101 11 .326 .01 .2079 .326 .01 -.2079 .002
+GW 101 1 .326 .01 -.2079 .326 0 -.2079 .002
+GE 0 -1 0
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The performance of the folded dipole does not vary the uniform-diameter dipole, as evidenced by the following simple table.

+ 
+Reflector     Dipole               Gain     Front-to-Back     E-BW       H-BW       Impedance
+Size          Dia.                 dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V14-H08       8-mm uniform         11.42    38.27             46         54         49.63 - j1.56   1.03 (50 Ohms)
+              folded dipole        11.41    38.27             46         54        199.79 - j0.21   1.00 (200 Ohms)
+
+

As a result of these comparisons, we should already suspect that the folded dipole will yield an SWR passband no smaller than for the 8-mm dipole and no larger than for the 12-mm dipole. In fact, as shown in Fig. 5, the SWR passband (at 200 Ohms) is exactly between the values for the two normal dipoles: 9.5%.

+
+ +
+

I chose the 200-Ohm impedance for its compatibility with the 50-Ohm drivers that we have so far surveyed, and because a simple 4:1 transformer would permit a match to standard coaxial cable. By increasing the spacing from the reflector apex and with minor adjustments to the overall folded-dipole length, one may adjust the impedance to 300 Ohms with little fall-off in performance. Since the increased impedance will be only about 1.5 times the impedance used for our test, the increase in the passband will be small. Nevertheless, the possibility does put us in touch with another strategy sometimes used to increase the SWR passband.

+

4. Changing the Dipole Feedpoint Impedance

+

Although we have been focusing on 50-Ohm drivers for our corner reflectors, we should not forget that we have considerable control over the feedpoint impedance of a corner reflector driver simply by changing its distance from the reflector apex and then adjusting the dipole length to resonance. As an experiment, I took our original 8-mm dipole and moved it to positions that yielded 70 Ohms and then 100 Ohms as the resonant feedpoint positions. Fig. 6 sketches the relative positions of the dipole for the 3 cases, along with the values for spacing and length.

+
+ +
+

As we increase the distance from the reflector apex, we must lengthen the dipole to compensate for the reduced mutual coupling between the dipole and the reflector. The total increase in spacing for a 2:1 change in impedance is over 10 cm, which is informative in another direction. At the 300-MHz test frequency, the amount of movement of the dipole to arrive at the desired feedpoint impedance is well within the range of careful manual adjustment. In short, the corner reflector--while requiring careful handling--is not so finicky as to defy effective field adjustment.

+

The following lines simply present the individual GW lines of the models used for each test and replicate the data in Fig. 6 within modeling form.

+ 
+50-Ohm Dipole
+GW 101 11 .324 0 -.212  .324 0 .212  .004
+70-Ohm Dipole
+GW 101 11 .37  0 -.2134 .37  0 .2134 .004
+100-Ohm Dipole
+GW 101 11 .436 0 -.2194 .436 0 .2194 .004
+
+

The following table provides a performance comparison among the three drivers at the test frequency.

+ 
+Reflector     Dipole               Gain     Front-to-Back     E-BW       H-BW       Impedance
+Size          Dia.                 dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V14-H08       8-mm--50-Ohm         11.42    38.27             46         54         49.63 - j1.56   1.03 (50 Ohms)
+              8-mm--70 Ohm         11.37    37.86             46         54         70.04 - j0.19   1.00 (70 Ohms)
+              8-mm--100 Ohm        11.28    36.08             46         54        100.15 - j0.17   1.00 (100 Ohms)
+
+

As we move the driver away from the reflector apex, we see both a rise in the feedpoint impedance and a small drop in performance. However, within the boundaries of this test, the performance decrease would not be within the range of operational detection. Nonetheless, the decline does suggest that there is a limit to the progression before performance reaches the point of being unacceptable (as defined by design goals and alternative designs).

+

If we are willing to accept the small decrease in performance and the "trouble" of working with a 100-Ohm feedpoint impedance, we may be in for a pleasant surprise when it comes to the array's SWR passband. See Fig. 7.

+
+ +
+

As we have noted in several places, the 8-mm dipole yields a 9% SWR passband when set for a 50-Ohm feedpoint impedance. If we are willing to work with 70-Ohm cables--such as surplus television cables and hardlines--we can increase the SWR passband by 40% to a total value of 12.7%. If a 100-Ohm impedance is not troublesome, the passband expands to 25%, that is, a 2:1 100-Ohm SWR that extends from about 275 to 350 MHz. Such a passband is sufficient to cover the entire FM broadcast band (about 20%, using the usual 88-108-MHz markers).

+

For many designers, 100 Ohms presents problems of losses within matching networks. Hence, there remains a quandary: can we obtain a similar SWR bandwidth and still have a 50-Ohm feedpoint impedance?

+

5. The Fan Dipole

+

In fact, there is a technique for obtaining both a 50-Ohm feedpoint impedance and a wide SWR bandwidth, and it has been around for perhaps a half-century. One may use a "bow-tie" or fan dipole in place of the dipoles that we have been exploring. A fan dipole can consist of a solid surface or a simple outline. In past commercial practice, planar fan dipoles have been widely used, some with part folded forward. For the purposes of modeling, a simple outline fan is the one to use, since we may construct it from 8-mm wire. The fat wire provides the closest approach to a solid surface, but does not completely simulate it. Fig. 8 shows the general outlines and the dimensions.

+
+ +
+

The Fan is 0.24 m wide overall, with a maximum width of 0.22 m. Independent fan dipoles have their widest bandwidth when the main frame sections are at or near a 45-degree angle, and this fan approaches that goal. However, such a fan dipole has a low impedance (in the 20-25-Ohm range). As a consequence, it is necessary to space the fan considerably father from the reflector apex than the uniform-diameter dipoles. A spacing of 0.5 m proved necessary to achieve a 50-Ohm impedance at the test frequency. The following lines show the model for this driver system. The center section (GW 102) is 0.03 m long so that its wire length is approximately equal to the length of the segments in the sloping wires.

+ 
CM Fan dipole
+CE
+GF 0 c-v14-h08.WGF
+GW 101 5 .5 .11 -.12 .5 0 -.015 .004
+GW 101 5 .5 -.11 -.12 .5 0 -.015 .004
+GW 101 7 .5 .11 -.12 .5 -.11 -.12 .004
+GW 102 1 .5 0 -.015 .5 0 .015 .004
+GW 103 5 .5 0 .015 .5 .11 .12 .004
+GW 103 5 .5 0 .015 .5 -.11 .12 .004
+GW 103 7 .5 .11 .12 .5 -.11 .12 .004
+GE 0 -1 0
+EX 0 102 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The following table compares the performance of the fan dipole driver with the initial 8-mm driver at the test frequency.

+ 
+Reflector     Dipole               Gain     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Size          Dia.                 dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V14-H08       8-mm uniform         11.42    38.27             46         54         49.63 - j1.56   1.03
+              fan dipole           11.16    32.32             48         52         51.47 - j0.78   1.03
+
+

Performance is down a bit for two reasons. First, the dipole is only a little over half as long as the 8-mm dipole (0.24 m vs. 0.424 m). As well, the element actually terminates at the center of the horizontal end pieces. Hence, part of the current--although only a small part--is at 90 degrees to the general E-plane of the antenna. The second reason for a small decline in performance is the increased distance between the driver and the reflector apex. The fan dipole is even further from the reflector apex than the 100-Ohm dipole that we just surveyed. Although the decline is not especially significant from an operational perspective, it is great enough to show up in the beamwidth columns.

+
+ +
+

The reason for using a fan dipole becomes immediately clear from the 50-Ohm SWR curve in Fig. 9. The 2:1 or less SWR span goes from about 271 to 362 MHz, for a 30.3% passband. Solid fan dipoles may be able to cover even more territory, but the 91 MHz of coverage by the outline fan is a sufficient increase over all of the other driver systems. As is true for virtually any array based on a half wavelength driver, the SWR climbs more slowly above the design frequency than below it. The fact that it occurs with a direct 50-Ohm feedpoint impedance is an added bonus. The question now is just the opposite from the one raised about uniform-diameter drivers: will the performance match the SWR passband. The following table of values for the standardized reflector used in all of these modeling tests gives us the data to evaluate. As in all tables in these notes, the gain is for free space, and the table uses the 180-degree front-to-back ratio. E-BW and H-BW are the E-plane and H-plane -3 dB beamwidths, respectively. Although the passband is between 271 and 363 MHz, the table counts in 10s starting at 270 MHz.

+ 
+Frequency     Gain     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+MHz           dBi      Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+270           10.72    27.02             50         58         36.96 - j28.33  2.04
+280           10.93    28.20             48         56         41.80 - j18.34  1.55
+290           11.08    29.90             48         54         46.65 - j 9.10  1.22
+300           11.16    32.39             48         52         51.57 - j 0.61  1.03
+310           11.18    36.22             48         52         56.51 + j 7.04  1.20
+320           11.16    43.28             50         50         61.26 + j13.77  1.38
+330           11.13    57.08             50         48         65.57 + j19.66  1.54
+340           11.09    41.04             52         48         69.21 + j24.92  1.70
+350           11.06    36.07             54         46         72.05 + j29.81  1.84
+360           11.01    33.16             58         44         74.07 + j34.64  1.97
+
+
+ +
+

Fig. 10 summarizes the gain and front-to-back data in graphical form. Although the gain curve looks steep, the maximum gain variation across the passband is 0.46 dB, a very acceptable figure for many applications. Note that maximum gain occurs slightly above the design frequency. The 180-degree front-to-back figure shows an expected peak at a frequency still higher in the overall passband. The front-to-back values at the passband edges are more representative of the worst-case front-to-back values across the operating range.

+

The combination of front-to-back data and beamwidth data suggest that the E-plane and H-plane patterns show some variation as we change frequency. For example, the E-plane beamwidth varies by a total of 10 degrees across the band. To sample whether the E-plane patterns are uniformly acceptable, Fig. 11 presents 4 sample patterns at 30-MHz intervals.

+
+ +
+

The greatest rate of pattern shape change occurs in the upper 30 MHz of the passband. The E-plane beamwidth changes by 8 degrees in that span, and by the top end of the operating spectrum, the pattern has taken on a bit of a spade shape. In contrast, the H-plane beamwidth shows a steady decline from the lowest to the highest frequency. In large measure, this narrowing of the H-plane beamwidth--the side-to-side beamwidth if we use the array in a vertical orientation--results from the fact that the reflector side increases in length as a function of a wavelength as we increase the frequency. Fig. 12 shows the resulting patterns at the same 30-MHz intervals.

+
+ +
+

The pattern evolution is in every way well-behaved. Indeed, the wide-band reflector array exhibits in these patterns one of its hallmarks: a clean forward lobe in both planes with no secondary forward lobes. In addition, the front-to-back ratio and the front-to-rear ratio are high enough to satisfy almost any application specification.

+

The fan dipole satisfies the need for a reflector array driver that provides an SWR passband that closely matches the performance passband of the antenna. The spacing of the driver and its short overall length do reduce maximum performance by about a quarter dB relative to the maximum gain provided by the best of the uniform diameter dipole drivers. As well, had we used a larger reflector, we would have obtained nearly 2 dB higher gain from any of our test cases. However, that fact only reminds us that we have some unfinished business with the reflector itself.

+

Is There a Maximum Reflector Size?

+

First, let's take stock of where we stand. We are exploring 90-degree corner reflectors composed of planar surfaces simulated in models by a wire-grid structure. The structure uses 0.1 wavelength cells, with a wire radius that is the cell length divided by 2 times PI or 0.0159 m. The basic driver for the array is a simple dipole, although we have seen that there are many ways to make a simple dipole into something more complex and still have a dipole. Driver structures other than dipoles, such as some of the phased dipole and monopole arrays used aptly with a flat or planar reflector, are not applicable to the corner reflector, because of their breadth. Maintaining a usable minimum spacing of closest approach by the outer elements to the reflector calls for a spacing from the reflector apex that severely reduces performance. In the end, some form of single dipole works best with the 90-degree reflector. For the following work, we shall return to our initial 8-mm dipole.

+

In the initial survey of reflectors, we used sizes that appeared to fall within the range that one might well build. The vertical dimension ranged from 1.0 to 2.0 m (wavelengths), and the maximum gain for the survey fell within this range. It occurred for smaller side lengths at a vertical dimension of 1.4 m (wavelength) and for larger side lengths at 1.6 m (wavelength). At the longest side length within the survey, we noted two interesting features. First, the maximum gain from the array had not achieved a detectable maximum. Second, the vertical dimension for maximum gain was on the verge of appearing at the 1.8-m (wavelength) mark.

+

Therefore, it seemed appropriate to continue the survey for side lengths beyond 1.6 m. Since every increase in a reflector dimension increases the size of the Green's file, and Green's files are very large, computer time and storage space become active considerations. However, there is another issue to which the curves for vertical dimensions of 1.2 m and 1.4 m will become relevant. Therefore, I took the following tack. I created new reflectors for vertical heights of 1.2 through 2.0 m (wavelengths). As well, I increased the increment between side lengths to 0.4 m (wavelength). Combining the new results with older results gives us a portrayal of array performance from a side length of 1.2 m to 3.2 m, with vertical heights of 1.2 through 2.0 m.

+
+ +
+

As the curves show, the vertical height for maximum gain passes from the 1.6-m mark to 1.8 m somewhere between side lengths of 2.0 and 2.4 m. A vertical height of 2.0 m never shows the maximum gain derivable from a side length within the survey range. In fact, the curve for 2.0 m is almost coincident with the curve for a vertical dimension of 1.4 m. More significantly for our quest, maximum gain occurs with a side length of about 2.4 m (wavelengths). The fact that the values for side lengths of 2.0 m and 2.8 m are nearly equal suggests that a side length of 2.4 m is nearly optimal for maximum array gain. The highest gain value in the data set is 13.77 dBi.

+

The issue that makes the curves for 1.2-m and 1.4-m vertical dimensions especially interesting is the very smoothness of those two curves as they reach their respective peak gain levels and then decrease in gain with further increases in the vertical dimension. I checked some intermediate horizontal dimensions to ensure that I missed no aberrations. For example, with a horizontal dimension of 3.0 m, the 1.2-m vertical curve passes through 13.04 dBi, the free-space gain between the values for 2.8 m and 3.2 m. Likewise, the 1.4-m vertical curve registers 13.26 dBi, a figure intermediate between the 13.40 dBi at 2.8 m and 13.19 dBi at 3.2 m. When we examine rod-based corner reflectors in Part 3 of this series, we shall not find such smooth curves at the extremes of reflector side length.

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The front-to-back curves in Fig. 14 also tell an interesting tale, although the jagged lines may obscure it. If we trace the lowest values and ignore the high peaks, then we can see that the overall value--taken as the worst-case front-to-back ratio or the averaged front-to-rear ratio--continues to climb as we enlarge the reflector. Very interestingly, with a horizontal side length of 2.4 m, the 180-degree front-to-back ratios tend to come together into a tight cluster of values between 37 and 40 dB. What gives the cluster interest is the fact that all of the corresponding gain figures are at or very close to their peak values with a side length of 2.4 m.

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Since the power is not increasing the forward gain above a side length of 2.4 m, but the rearward power continues to decrease, there are few other places for the power to go than in terms of increasing values of E-plane and H-plane beamwidth. Although the graph beyond the side length of maximum possible gain is too short to make this fact evident in patterns, the numbers tell the story. If we average the 3 E-plane beamwidth values for the surveyed vertical dimensions at each side length, a side length of 2.4 m shows the lowest average (39.3 degrees). By the time we reach the maximum side length of 3.2 m, the average has grown (to 40.0 degrees). The H-plane figures are more dramatic. At a side length of 2.4 m, the average H-plane beamwidth for the 3 vertical dimensions is 32.0 degrees. At a side length of 3.2 m, the value becomes 36.7 degrees.

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The H-plane beamwidth values are indicators of performance to the sides of the reflector aperture. Up to the point of maximum gain, these values had steadily descended, inviting the idea that the extending sides of the reflector had a confining effect on the "side-to-side" radiation relative to the aperture. However, beyond a certain side length, the seeming confinement begins to weaken.

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The corner array turns out to be perhaps more complex than its appearance may indicate. The reflector is--within the limitations of this study and the physical implementations anyone is ever likely to build--perhaps not simply a pair of plane surfaces. For example, we might wonder if the corner reflector, when composed of rods or bars instead of closely spaced screens or solid surface, has both the same performance and the same limitations as the wire-grid models suggest for solid surfaces. As well Kraus' early work suggested alternative reflector angles, and some antenna builders have suggested some alternative shapes. Perhaps, before we close the book on corner reflectors, we had better spend a little more time on the reflector and its corner.

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Updated 07-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX June, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 3

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Go to Main Index

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Topics: Corner Reflector, VHF / UHF


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Corner Reflectors Revisited Again
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+ Part 3: Rod-Based Corner Reflectors

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+

L. B. Cebik, W4RNL

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In the first two parts of our exploration of corner reflectors, we examined 90-degree reflectors composed of modeled wire-grid structures to simulate closely spaced screens or solid surfaces. Of course, the preceding studies of planar reflectors are technically also a study of corner reflectors having an angle of 180 degrees. Both sets of studies are relevant to the next move in our progression.

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In this part, we shall examine rod-based corner reflectors. From the study of rod-based planar reflectors, we may extract the parameters of the reflector model. It will use 0.015-m radius rods spaced 0.1-m apart, where a meter is also a wavelength at our 299.7925-MHz test frequency. In planar reflectors, these dimensions--although using fatter rods than past recommendations--provide the closest coincidence between wire-grid and rod reflectors with respect to the spacing of the driver from the apex and general array performance in test models.

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The key assumption of past recommendations that we want to test is whether the rod-based reflector replicates the performance of the wire-grid models. In other words, does the rod-based reflector simulate accurately the solid surfaces upon which the foundations of corner reflector theory rest? As we discovered in the case of planar reflectors, there is reasonably close coincidence, with only a small performance reduction for rod-based reflectors. However, we also discovered that when a planar reflector uses rods about 1.4 m (wavelengths) long, certain driver types that require close spacing to the reflector result in aberrant current distributions on the reflector rods and consequential variations from expected performance. Reflector illumination appears to be normal with longer and shorter rods. So we have one "alert" before us: does anything comparable occur with the 90-degree rod-based corner reflector.

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There are some significant differences in the operation of planar and corner reflectors. With every driver assembly tested, the planar reflector showed maximum gain for any given horizontal length with a vertical dimension of 1.2 m (wavelength). This figure held good for both wire-grid and rod reflectors. Since the vertical dimension of maximum gain is less than the vertical dimension that created anomalies for some planar drivers, the gain curves for planar reflectors at maximum gain are very well behaved. In general, the horizontal length of maximum gain was one in which the reflector extended electrically beyond the driver by about 0.5-0.6 m (wavelength).

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In contrast, the wire-grid models for the corner reflector required side lengths in the vicinity of 2.4 m (wavelengths) for maximum gain with any selected vertical dimension. A vertical dimension in the region of 1.6 to 1.8 m (wavelengths) showed the maximum gain with wire-grid reflectors when using the 2.4-m side length. So, we have a second significant question: will a rod-based corner reflector show maximum gain in the same way as the wire-grid models? Or, will the differences in the maximum gain performance between the planar reflector and the corner reflector result in differences between the wire-grid and rod-based corner reflector performances?

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The Basic Rod Reflector Corner Reflector

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The rod-based reflector is considerably easier to model than the corresponding wire-grid model. The following lines show the Green's file model for one of the reflectors.

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CM Rod Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM Size = v1.0 m x h1.0 m
+CE
+GW 1 10 0 0 -.5 0 0 .5 .015
+GW 2 10 0 -.1 -.5 0 -.1 .5 .015
+GM 0 4 0 0 0 0 -.1 0 2 1 2 10
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 3 10 0 .1 -.5 0 .1 .5 .015
+GM 0 4 0 0 0 0 .1 0 3 1 3 10
+GM 0 0 0 0 -45 0 0 0 3 1 0 0
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG cr-v10-h10.WGF
+EN
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GW 1 sets up the apex rod. GW 2 and GW 3 set up the first rods on each side of the apex. Each of these wires has a following GM entry to copy the wire the desired number of times at the specified 0.1-m distance. In this example, we copy each side wire 4 time to give us an overall horizontal length of 1.0 m. The file name coding follows this total length prior to bending. For each of the side wires, there is also a second GM entry. This entry tilts the entire set of rods on each side by the required 45 degrees. (In a future episode, we shall explore some other angles simply by altering the tilt angles in these two lines.) The result is a 90-degree rod-based corner reflector, with side lengths that are half the total initial horizontal length in the file-name code. Fig. 1 shows the difference between this simpler model and what a wire-grid model requires for the same corner structure. The vertical and horizontal dimensions for the samples in the figure are arbitrary.

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We may alter the vertical dimension by making a few easy changes in GW 1 through GW 3. Since the reflector is vertically oriented relative to the modeling coordinate system, the dimensions of each rod show up as +/-Z coordinates, -0.5 and 0.5 in the example. Raising these values to +/-0.6 yields a reflector with 1.2-m rods, and we would change the number of segments from 10 to 12 for a constant 0.1-m segment length. For each side wire (GW 2 and GW 3), we would also change the last entry in the following GM entries to 12 so that every rod in the reflector has the same new length.

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Changing the horizontal size of the reflector is even easier. We simply increase the number of replicated wires by one for each 0.1-m increase in side length. To go from a side length of 0.5 m in the example to 0.6 m, each initial GM entry would start GM 0 5 instead of the value in the example (GM 0 4). Of course, we would change both the CM reference information and the file name in the WG line to correspond to the new dimensions.

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The file that we need in order to make use of the collection of reflectors created by the technique just outlined is also very simple. With corner reflectors, the diversity of driver assemblies used with planar reflectors is not feasible. So we only need to create a file for a dipole, such as the one we used with the wire-grid reflectors. A sample, set up for the rod-based reflectors, appears in the following lines.

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CM Dipole
+CE
+GF 0 cr-v10-h60.WGF
+GW 101 11 .324 0 -.2119 .324 0 .2119 .004
+GE 0 -1 0
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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All dipoles use an 8-mm diameter. As noted early on in the study of planar reflectors, the wire conductivity is perfect or lossless, since adding material losses makes no significant difference in the performance figures, given the large surface area of all conductors in the model. With the wire-grid reflectors, I varied the dipole length and spacing from the corner reflector apex. The range of required spacing rang from 0.323-m to 0.326-m for a 50-Ohm impedance using the smallest reflector in the sequence. Only the smallest reflector with a vertical height of 1.0 m and side lengths of 0.5 m required more spacing, 0.331 m. The required dipole length varies from 0.4232 m up to 0.4242 m.

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The present exercise varied the technique used to set the dipole length and spacing. For each vertical dimension covered from 1.0 m to 2.0 m, I set the dipole length and spacing using a large reflector side length, a region in which the impedance is very stable from one increment to the next of side length. I wanted to see what the impedance curve would be as we shorten the side length down to its minimum 0.5-m size. In fact, regardless of the vertical dimension, the 50-Ohm SWR turned out to be 1.00:1 for all side lengths greater than about 1.0 m. Below that value, the SWR increased very slowly, reaching 1.05:1 with a side length of 0.5 m. The following tables shows the spacing and dipole length dimensions for each of the vertical rod lengths explored in this study.

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+Reflector Vertical         Spacing from          Dipole Length
+Length m/wl                Apex m/wl             m/wl
+1.0                        0.324                 0.4238
+1.2                        0.322                 0.4244
+1.4                        0.323                 0.4248
+1.6                        0.324                 0.4247
+1.8                        0.324                 0.4246
+2.0                        0.3235                0.4246
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The required values, allowing for the different premise set between the wire-grid and rod reflector models, are nevertheless tightly clustered and very comparable to each other. The comparability between the wire-grid and rod reflector driver dimensions tends to confirm the selection of 0.015-m rods on 0.1-m centers for the new reflector structure.

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In each exercise, I have spent considerable initial time showing all of the facets of the modeling involved. This procedure, while delaying the results, serves two important purposes. First, it allows anyone who wishes to do so to replicate the models, not only within NEC, but as well within any other modeling program, including some of the proprietary hybrid programs. As always, I shall note that the runs here use NEC-4 (GNEC). If translated into NEC-2 models, one should invoke the EK command, given the marginal segment-length to radius ratio in the driver. Of course, the second purpose in exposing the modeling that underlies the study is to permit critique and model improvement.

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The Rod Reflector with a Linear Dipole Driver

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Let's begin our look at the performance of a rod reflector with a linear dipole driver at the end, that is, with a summary of the gain peaks using the new reflector and the wire-grid models.

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+                             Wire-Grid Model                         Rod Reflector               Difference
+Reflector Vertical    Peak Free-Space    Side Length         Peak Free-Space    Side Length      Relative to
+Length m/wl           Gain dBi           m/wl                Gain dBi           m/wl             Wire-Grid
+1.0                   12.78              2.8                 11.59              2.0              -1.19
+1.2                   13.16              2.4-2.8             12.94              2.5              -0.22
+1.4                   13.48              2.4                 13.73              2.6              +0.25
+1.6                   13.73              2.4                 13.41              2.0-2.3          -0.32
+1.8                   13.77              2.4                 13.33              2.1-2.3          -0.44
+2.0                   13.57              2.4                 13.39              2.3-2.4          -0.18
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Overall, the small drop in performance--hardly noticeable operationally--is comparable to the differences in performance recorded for wire-grid and rod-based planar reflectors. However, the table reveals two significant oddities. First, the side lengths are generally comparable between the reflector types, especially given the increment of side-length change (0.4 m) used in the wire-grid study with its large and slow-running models. However, the 1.0-m tall reflector is an interesting exception. To reach maximum gain with a wire-grid reflector required a side length larger than average, but with the rod reflector, the side length was well-below average for the other cases.

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The second--and perhaps more significant--anomaly is the 1.4-m tall reflector. Here, the rod reflector shows a gain actually higher than the maximum value reached with the wire-grid counterpart. In fact, we shall discover some other oddities to the behavior of both the 1.2-m and 1.4-m tall reflectors. Indeed, the 1.0-m tall reflector and the larger versions between 1.6-m and 2.0-m tall form a group of well-behaved arrays, that is, comparable to each other except for the precise gain and front-to-back values. However, we shall keep our eyes open when examining the 1.2-m and 1.4-m tall reflectors.

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Because the models were smaller and required less storage for the Green's files, I created rod reflectors for each vertical dimension using side lengths from 0.5 m up to 3.0 m in 0.1-m increments. This procedure permitted me to keep a close watch for possible small variations in performance, since experiences with planar reflectors--along with the table just presented--have suggested that we might encounter some.

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The gain performance is a good case in point. See Fig. 2 for the gain curves.

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The curves for reflectors that are 1.0-m tall or 1.6-m to 2.0-m tall are very smooth. The overall gain deficiencies with the shortest reflector suggest that one should not use this size in rod form. However, other than this obvious recommendation, exceeding 1.6-m as the rod-reflector vertical dimension does not seem warranted, given the tightness of the curves for the 3 largest sizes of reflector. In addition, note the changing rate of gain differential between increments of side length. The region for side lengths less than about 1.4 m--a somewhat arbitrary cut-off point--are perhaps too small to obtain anything close to the performance of which the corner reflector is capable. Older recommendations tended to call for side lengths about twice the distance between the dipole driver and the reflector apex. That distance would perhaps apply to a very high impedance version of the corner reflector, since--as shown with the wire-grid reflectors--the impedance increases with the distance of the dipole from the apex. However, for the low-impedance (50-Ohm) arrays to which I have confined myself, the old recommendation is inapplicable. The arbitrary cut-off side length that I suggested is 4-5 times the spacing of the driver from the apex.

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In an earlier and highly preliminary study of rod reflectors, I suggested that there might be some periodic effects in terms of gain changes vs. reflector size. The present, more systematic modeling study begins to reveal where those effects occur. With a vertical height of 1.2 m, we find the gain peak at a side length of 2.5 m. However, we can see that as we pass the limit of the study at a side length of 3.0 m, the gain is again on the rise. In the region of side lengths from 1.3 m to 2.5 m, we can also see changes in the rate of gain increase with each added increment of side length. The curve stands in sharp contrast to the smooth curves for the other vertical dimensions that we have classified as well-behaved.

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The curve for a vertical dimension of 1.4 m is even more varied. It shows variations in the rate of change per increment of side length throughout the span. In the side-length region from 1.7 m to 2.6 m, we find at least 4 gain peaks, with the highest value actually exceeding the value obtain from a wire-grid reflector. (Note: it might be easy to think that we could capitalize on this behavior by simple selection of the right height and side length. However, construction variables such as rod radius and reflector connections are likely to introduce further variables into the performance curve of a physical reflector.)

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The earliest gain peak with a side length of 1.7 m is accompanied by a one-time reduction in both the E-plane and the H-plane beamwidth. Although the steps are small, these are the only anomalous results that occur in this category of performance. In general, H-plane beamwidth shows a continuous shrinkage as we lengthen the reflector sides until we reach the side length of maximum gain. Then it increases by 2 degrees for the remaining increases in side length. The E-plane beamwidth shows a continuous decrease, with only a few cases of a 2-degree increase just at the 3.0-m side length that ends the progression.

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The gain curve for the 1.4-m tall reflector actually shows a smooth curve downward with side lengths longer than 2.6 m. In contrast, the shorter 1.2-m reflector was just beginning to show its peak gain variations as we passed a side length of 2.5 m. Therefore, it is likely--but untested--that there is a relationship between the vertical dimension and the side length in this region of fluctuation.

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Because the 180-degree front-to-back curves tend to have so many peak and valleys, I have presented only 3 of the 6 in Fig. 3. However, they suffice to show the general trends in the rearward direction. If one were to draw a line connecting the lowest values in each cycle, the resulting curve would well represent the worst-case front-to-back values for the individual curves.

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The relationship between the curve for the 1.0-m tall reflector and for the 1.8-meter tall reflector is interesting. As noted for the gain curves, the shortest reflector and the three tallest belong in a single group. The taller the reflector, the longer the side length for each front-to-back peak. Between the two sizes shown, there is an approximate 0.3-m lengthening of the sides for each peak shown by the taller reflector. In addition, both reflectors show a decreasing differential between adjacent peaks and valleys as the sides grow longer. Although there is a slight increase in the average of the 180-degree front-to-back values among the reflectors from 1.6-m through 2.0-m tall, the increase per increment of vertical dimension is too small to make a significant difference.

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The odd curve is the one for the 1.4-m tall reflector. It undergoes many more peaks and valleys over the span of side lengths than either of the other curves. However, the additional peaks do not form a 2:1 ratio with the peaks and valleys for the other two curves over any extended portion of the graphed curves. Unlike the gain curve for the 1.4-m tall reflector, the front-to-back peaks do not show their fluctuations in a limited portion of the curve's span (1.7 m through 2.6 m of side length for the gain curve). Instead, the fluctuations begin with a side length of about 1.0 m and are continuously in fluctuation for every side length longer than that. The curve for the 1.2-m tall reflector is more like the one for its smaller counterpart; however, the gain fluctuations for the 1.2-m reflector only began with the longest side lengths.

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The curves that we have shown are reflected in the patterns for the various reflector sizes. As interesting as are the pattern shape changes in both the E-plane and the H-plane for each increment of size change, whether vertical or horizontal, we can only sample the field.

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Selected patterns appear in Fig. 4 for the 1.0-m vertical reflector for side lengths of 1.4 m, 2.2 m, and 3.0 m. Below a side length of 1.4 m, all of the gain curves decline too steeply to form recommended reflector sizes. The E-plane patterns, which are parallel to the dipole and to the rods in the reflector, form a closely overlapping set. The H-plane patterns, at right angles to the dipole and across the reflector aperture, show somewhat greater variation, but mostly in the region near 90 degrees to the main forward heading. In both cases, the rate of change of the beamwidth is very slows, despite the 2:1 ratio of side lengths between the shortest and the longest reflectors in the series used to generate the patterns, about 4 degrees for both the planes.

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The patterns for the 1.0-m tall reflector are also stand-ins for the patterns produced by the tallest reflectors from 1.6 through 2.0 m. There are differences, of course. For example, the taller reflectors have such a high front-to-back ratio that only a few peaks appear past the -40-dB cut-off of the GNEC pattern plots. As well, the E-plane patterns for the taller reflectors tend to develop 5 rearward lobes, rather than just 3 for the 1.0-m tall reflector. The beamwidths for both the E- and H-plane patterns are proportionately narrower. The E-plane beamwidth for the 1.0-m reflector is about 60 degrees, but is only 44 degrees for all three of the tall reflectors. Similarly, the H-plane pattern has a beamwidth of about 42 degrees when the reflector is 1.0-m tall, but about 38 degrees for the 1.6-m through 2.0-m reflectors. Still, the rate of change of beamwidth for each size reflector with increasing side lengths is relatively constant at both ends of the size spectrum.

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The patterns for the 1.2-m tall reflector, shown in Fig. 5, depart from the norms set up by the patterns for the 1.0-m tall reflector. Although the E-plane patterns overlap well, note the gain deficiency for the shortest side length. Then compare that pattern with the gain curve in Fig. 2. The gain curve for the 1.2-m tall reflector has a slower than normal rate of rise with increasing side length for nearly 2/3 of the total span of side lengths surveyed.

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In the H-plane, the pattern becomes almost pear-shaped. Although the -3 dB response forms a narrower beamwidth than for the smaller reflector, the side-lobe bulges are noticeably larger by about 2 dB. As well, as the side length increases, the peaks in the side-lobe bulges tends to move forward. Between the smallest and the largest side lengths for which patterns appear in the figure, the change is between 15 and 20 degrees.

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The patterns for the 1.4-m tall reflector form an especially interesting group. See Fig. 6. The oddities that we saw in the gain and front-to-back curves do not result in unusable patterns in any sense of that term. Rather, we find a more usable set of patterns than for the 1.2-m tall reflector. The E-plane patterns overlap well. However, if you examine the rear lobes carefully, you will see in the red curve for 2.2-m side length the emergence of the 4th and 5th rearward lobes. The same lobes appear in the green curve for the 3.0-m side length, but are the same strength as those for, and hence hidden by, the red curve.

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The H-plane patterns make the side-lobe bulges more apparent, but only because the main forward lobe has returned to the straight sides that we saw in the patterns for the smallest reflector. The actual strength of these side-lobe bulges is less than for either of the smaller reflector heights. In fact, tiny remnants of the side-lobe bulges remain in the narrow beamwidth patterns for the larger reflectors, but become small enough to be simple ripples in the shape of the forward lobe. Nevertheless, the more distinct side-lobe bulges in the 1.4-m tall H-plane patterns do show a forward migration as we increase the side length.

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The survey of the performance of rod-based corner reflectors with dipole drivers has turned up some anomalous behavior at just the reflector height where we might expect it--1.4-m (wavelength). The deviant behavior relative to the smallest reflector and to the largest set of 3 is certainly noticeable, especially in the gain behavior, where the near-resonant parasitic effects of the reflector bars create a gain potential that might exceed that of a close-space screen or solid-surface reflector simulated by the ire-grid models. Nevertheless, the abnormalities in the performance progressions in no way make the 1.4-m tall rod reflector unusable. Indeed, it is likely for most applications to be close to the rod length of choice--at least with a suitably long side length.

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In the case of the planar reflector, where the optimal length of the rods is between 1.2 and 1.3 m, some driver assemblies produced perhaps unacceptable results with a 1.4-m set of reflector rods because the driver was too closely spaced to the reflector, creating an over-coupling condition. However, the corner reflector can use only a simple dipole, and it is quite reasonably spaced from the reflector. Hence, any performance deviations show up as mere ripples in the curves compared to the curves that set the norms. Indeed, as shown in Fig. 7, the rods give every indication of normal illumination, as indicated by the uniform color except in the region closest to the driver element (the red dipole at the center). There are variations in current on the rods, but they are too small to show up in a 256-color range that spans 2 orders of magnitude.

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+ +
+

Basic plane-reflector theory would suggest a continuum between planar and corner reflectors, as well as no significant difference between solid and rod-based reflectors. However, we have seen the smooth curves associated with wire-grid models give way to some mildly aberrant behavior in at least two sizes of rod-base reflectors. However, unlike the planar reflectors, where we would normally avoid the problematical size reflector, with a corner reflector, the same size becomes the size of choice to enhance performance. The difference, of course, stems from a more basic aspect of reflector array performance. For planar arrays, peak performance for any horizontal dimension occurred with a vertical dimension less than the vertical dimension at which oddities crept into the picture. For wire-grid corner reflectors, the vertical dimension at which peak performance occurred is larger than 1.4 m (wavelength). Hence, the oddities associated with 1.4-m (wavelength) rods represent an opportunity rather than a deficit.

+

The Rod Reflector with a Fan Dipole Driver

+

One performance figure that does not change in the shift from wire-grid to rod reflector models is the 2:1 SWR bandwidth of the array when driven with an 8-mm diameter linear dipole. For both sets of reflectors, regardless of size, the SWR bandwidth is about 9%. For optimized designs at the test frequency, about 300 MHz, the passband extends from approximately 288 MHz to about 315 MHz, or about 27 MHz total. This value is sufficient to cover regions like the 70-cm amateur band (when we scale the array dimensions) with enough extra to allow for significant construction variability. However, when we studied wire-grid reflectors and replaced the linear dipole with a fan dipole, we tripled the operating passband. We should explore whether we may obtain similar results with a rod-based reflector. Fig. 8 shows similar rod-based reflectors with the placement of the linear and the fan dipoles.

+
+ +
+

Since out primary interest is in bandwidth characteristics, I simplified the exercise in several respects. First, the fan dipole has a uniform size and spacing from the reflector throughout. The following lines serve two purposes: to show the model used for the replacement driver and to provide a record of its relevant dimensions.

+ 
CM Fan dipole
+CE
+GF 0 cr-v20-h60.WGF
+GW 101 5 .49 .11 -.12 .49 0 -.015 .004
+GW 101 5 .49 -.11 -.12 .49 0 -.015 .004
+GW 101 7 .49 .11 -.12 .49 -.11 -.12 .004
+GW 102 1 .49 0 -.015 .49 0 .015 .004
+GW 103 5 .49 0 .015 .49 .11 .12 .004
+GW 103 5 .49 0 .015 .49 -.11 .12 .004
+GW 103 7 .49 .11 .12 .49 -.11 .12 .004
+GE 0 -1 0
+EX 0 102 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The vertical and horizontal dimensions of the fan dipole are the same ones used with the wire-grid reflector: 0.24-m tall by 0.22-m wide (at the widest spread), using 8-mm diameter wire. The spacing of the dipole from the reflector apex is 0.49 m, 0.01-m less than for the wire-grid reflector. The increased spacing relative to the linear dipole derives from the lower independent impedance of the fan dipole relative to the independent impedance of a linear dipole.

+

Because the systematic survey of the rod reflector with a linear dipole showed the smallest side lengths to be well outside the region for acceptable performance--when measured against the peak performance one might obtain--I shrunk the range of side lengths covered for each vertical dimension in the current survey. The side length for the fan dipole driver will vary from 1.0 m to 3.0 m. As well, I used side length increments of 0.2 m. However, I performed spot checks using 0.1-m increments in regions where performance fluctuations might occur. The sample model is set up to cover the largest array checked, as indicated by the GF entry and the Green's file name: 2.0 m (wavelengths) vertically, with an overall horizontal dimension of 6.0 m (wavelengths, indicating 3.0-m (wavelength) side lengths.

+

As a start in our new survey, we may compare in a brief table the performance of the fan and the linear dipoles with identical rod reflectors.

+ 
+                           Fan Dipole Model                      Linear Dipole Model             Difference
+Reflector Vertical    Peak Free-Space    Side Length         Peak Free-Space    Side Length      Relative to
+Length m/wl           Gain dBi           m/wl                Gain dBi           m/wl             Linear Dipole
+1.0                   11.53              2.8                 11.59              2.0              -0.06
+1.2                   13.04              2.6 and 3.0         12.94              2.5              +0.10
+1.4                   13.68              2.3                 13.73              2.6              -0.07
+1.6                   13.11              2.3                 13.41              2.0-2.3          -0.30
+1.8                   12.94              2.4                 13.33              2.1-2.3          -0.39
+2.0                   12.96              2.4                 13.39              2.3-2.4          -0.43
+
+

Because the fan dipole array performance falls off, relative to the linear dipole and especially for the vertically tallest reflectors, it likely makes little sense to use a fan dipole with a rod reflector that is taller than about 1.4 m (wavelength). The gain of the 1.4-m reflector is a full half-dB stronger than for adjacent vertical reflector sizes, with an optimum side length near 2.3 m (wavelengths). However, we shall eventually qualify this general statement.

+
+ +
+

Fig. 9 confirms the general free-space gain performance reported as peak values in the table. The curve for the 1.4-m tall reflector is significantly higher than for any of the other reflector sizes. What appear as nearly a linear progression of gain values is an illusion based on the increase in the side-length increment used. Had we used a 0.1-m increment, we would have found a set of three gain value peaks between side lengths of 1.7 m and 2.6 m. The gain curve for the 1.2-m tall reflector shows its double peak in the region of the longest side values used in the survey.

+
+ +
+

We may remove the fluctuations in the curves in a different manner. Let's use the side length range of 1.0 m to 3.0 m as a test bed. Then, let's take the average gain across that span for each vertical size of reflector. If we perform the simple math, we obtain the curves shown in Fig. 10. At the test frequency, the average gain for the 1.4-m reflector becomes visually apparent. However, for that size and for larger vertical reflector dimensions, the linear dipole advantage also becomes apparent, if the SWR bandwidth is not a concern.

+
+ +
+

When we turn to the 180-degree front-to-back figures for the fan dipole, Fig. 11 reveals that they fall into two rather distinct groups. The three shorter reflectors have similar performance levels, as do the three taller reflectors. However, both groups show smaller peaks and valleys than we encountered with the linear dipole, but that is partly due to the fact that we have eliminated the shortest set of side lengths from the graph.

+
+ +
+

If we use the average 180-degree front-to-back values for the span of side lengths in the present survey and compare the linear and fan dipole arrays, we obtain some interesting results. See Fig. 12. The linear dipole is superior for every vertical reflector dimension except 1.6 m. Here, the fan dipole matches the linear dipole. The steep rise in the front-to-back ratio for the 1.6-m reflector with a fan dipole driver accounts for the separation of the two groups of ratios shown in Fig. 11.

+

At the level of general performance at the test frequency, the fan dipole patterns exhibit completely normal characteristics compared to the patterns for the linear dipole. All patterns are "bullets" except for the ones for the 1.2-m and 1.4-m tall reflectors. The 1.2-m vertical reflector shows its pear-shape, and the 1.4-m vertical reflector has its side-lobe bulges. In both cases, as we increase the side length, the bulges progress to a more forward angle. Hence, the patterns in Fig. 4 through Fig. 6 accurately represent the patterns for the fan dipole with equal size reflectors.

+

The conclusions that we can draw from the comparison of linear and fan dipoles with rod reflectors are essentially that same ones that we drew for wire-grid reflectors. The fan dipole does show a small performance decline in general, relative to the linear dipole. However, the decline is in most cases too small to be operationally detected. Hence, it forms a very reasonable exchange for the anticipated increase in operating bandwidth, both at the SWR and performance level.

+
+ +
+

For all of the fan dipole arrays tested, I obtained the same 50-Ohm SWR bandwidth using rod reflectors. The passband extended from about 271 MHz to 355 MHz, or about 84 MHz. See Fig. 13 for a sample 50-Ohm SWR sweep. This sweep results in an SWR bandwidth of 28%. Across the span of sampled reflector sizes, the band edges may shift either upward or down ward by perhaps 1 MHz without adjusting the size or the position of the fan dipole. However, the total bandwidth remains unchanged. By way of contrast, the 50-Ohm SWR passband for the wire grid reflectors extended from 271 MHz to about 362 MHz, a 91-MHz total, or about 30.3%. Both bandwidth percentages are calculated using the design frequency of about 300 MHz, not the passband center frequency, which would be slightly higher than 300 MHz in both instances.

+

However, the SWR passband does not tell the entire story in the design of a wide operating passband array. Besides the SWR limits, we must also consider the characteristics of the gain and the front-to-back ratio across that passband. A well-designed array will be one that combines a number of factors in the best possible compromise.

+
+ 1. The total gain differential across the passband. +

2. The total front-to-back differential across the passband.

+

3. The evenness of gain and front-to-back performance at the passband limits.

+
+

Of course, special requirements may alter this list of factors. For example, if the anticipated signals at the highest frequency used are weaker than those at the lowest frequency, we may wish to design an array with a rising gain figure.

+

The performance of a rod-reflector fan-dipole array tends to vary with both the vertical and the side-length dimensions of the array. To sample the variation, I created 5 different arrays, all of which have the same SWR passband. Fig. 14 shows the modeled free-space gain performance for the arrays. The legend codes the reflector sizes by indicating the vertical dimension (V12 = vertical 1.2 m) followed by the side length (H12 = side length 1.2 m).

+
+ +
+

All five arrays use the very same fan dipole at the same spacing from the reflector apex. Only the reflector dimensions differ. Hence, the performance curves are a function of the differences in those dimensions. The smallest reflector (V12-H12) shows the greatest differential in gain across the passband (2.25 dB) with a rising curve that shows a double peak at the high end of the passband. The largest reflector (V16-H19) shows a contrasting descending gain curve, although the differential across the band is only 0.8 dB.

+

Other reflector sizes yield other characteristics that may be useful in some situations. For example, the curve labeled V14-H12 has band-edge gain values that are most closely matched (0.12 dB differential). Almost as well matched (0.17 dB differential) is V14-H15, but the average gain is about 1.2-dB higher than V14-H12. However, of the samples provided, V14-H19 shows the highest average gain.

+
+ +
+

The front-to-back characteristics may also be of interest to a designer of wide-band corner arrays. The values for the 5 samples in Fig. 15 show a considerable spread of characteristics. V16-H19 has the least change in ratio across the passband, about 3 dB. The other reflectors show various trends favoring one or the other end of the band. However, even the smallest reflector, V12-H12, has a front-to-back ratio of over 24 dB, more than adequate for most communications functions, even if 10 dB less than the lowest value for V16-H19.

+

Therefore, the tentative conclusion drawn on the basis of data from the test frequency alone requires modification for a wide-band array. Although optimal for the design frequency, a reflector with a vertical dimension of 1.4 m (wavelength and a side length of 2.3 m (wavelengths), the proper reflector size for a given wide-band array may vary considerably from those figures. The samples--designed solely to show differences among the performance of different size reflectors and not intended to show the best performance--are only a beginning for the designer. The end result will be a melding of design specifications with what various corner reflector sizes will produce.

+

Is There More?

+

So far we have examined only 90-degree corner reflectors using both wire-grid and rod-based models. All of the reflector designs have used uniform reflector planes, that is, planes forming smooth rectangles. Other possibilities do exist, including reflectors with variable-length rods to enhance the parasitic performance of the reflector elements.

+

As well, we have examined reflectors with a 90-degree angle. (The study of planar reflectors handles the case of the 180-degree "corner" reflector.) Basic corner reflector theory allows for potentially higher gain levels if we reduce the angle further, perhaps down to 60 degrees.

+

Experimenters have also claimed two advantages to cutting off the apex to form a trough. One advantage is a smaller reflector structure. The other is the possibility of more gain for the same vertical size and the same virtual side length, that is, the side length if extended back to the apex.

+

Although we cannot give the same detailed systematic treatment to each of these variations on the corner reflector, we certainly can do enough sampling to test the hypotheses and proposals involved. So we shall add one more part to this series to examine these possibilities.

+
+ +
+

Updated 08-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX July, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 4

+

Go to Main Index

+

Topics: Corner Reflector, VHF / UHF


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+

Corner Reflectors Revisited Again
+
+ Part 4: Variations on Standard Corner Reflectors

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Our next foray into corner reflectors will actually be a sampler of sorts. As we move away from the standard 90-degree reflector with plane sides, whether modeled as wire grids or as a set of rods, the individual topics become more specific, each with a smaller set of design interests. On the other hand each topic might well expand into the semi-complete coverage that I have extended to the standard corner. Remember, though, that the coverage of even the standard corner has restricted itself to 50-Ohm drivers in order to be able to track various performance variations over a large range of reflector sizes. The bottom line is that, no matter how extensive I might make a modeling compendium for corner reflectors, the coverage would still be incomplete. There is always a variant that deserves coverage but remains uncovered.

+

Nevertheless, the coverage may be sufficient to provide a useful level of general guidance. Based on that guidance, perhaps the samples that we shall explore in this session will be enough to allow you to expand any topic of interest by specific modeling or field experiments of your own.

+

In this exercise, we shall take brief looks at the following topics.

+
+ 1. Narrowing the corner reflector angle. +

2. Enhancing parasitic effects of reflector bars.

+

3. Aperture fold-in.

+

4. Trough reflectors

+

5. Collinear dipole drivers

+
+

The rationale for the selection and order of the topics will become apparent as we scurry through them. To level the sampling field, I shall continue to use 50-Ohm drivers throughout. As well, I shall largely restrict the reflector size used in the sampling to a vertical dimension of 1.4 m (wavelengths) and a side length of 2.4 m (wavelengths), at our test frequency of 299.7925 MHz, where 1 m = 1 wavelength. My selection of the reflector size is not arbitrary. For 90-degree rod reflectors, this reflector size yields the peak performance, and the wire-grid reflectors peak about 0.2 m taller. As a result, improvements and degradations of performance should show up with minimal ambiguity. In some cases, however, we shall be left with unanswered questions concerning whether a longer side length might have yielded better performance. This question is but one part of the unfinished business that I must leave to your own modeling.

+

Narrowing the Corner Reflector Angle

+

Classic corner reflector literature tends to focus upon the standard or 90-degree reflector, but also notes that this angle may be too large to produce the maximum gain that we might achieve from the angled array. Therefore, the first sampling calls for a brief survey of some possibilities, as sketched in Fig. 1. I actually carried the survey down to 50 degrees, starting from 90 degrees and working in 10-degree increments.

+
+ +
+

The survey involved, for this case only among our present topics, using both wire-grid and rod-based reflectors in order to determine if there might be any significant variations. The modeling used the reflectors saved from earlier investigations simply by modifying two lines in the Green's file model. The following sample will show the ease of setting up new corner angles.

+ 
CM Rod Corner Reflector: 299.7925 MHz; 1 m = 1 wl
+CM Size = v1.4 m x h4.8 m (2.4-m side)
+CM 70-degree apex angle
+CE
+GW 1 14 0 0 -.7 0 0 .7 .015
+GW 2 14 0 -.1 -.7 0 -.1 .7 .015
+GM 0 23 0 0 0 0 -.1 0 2 1 2 14
+GM 0 0 0 0 55 0 0 0 2 1 0 0
+GW 3 14 0 .1 -.7 0 .1 .7 .015
+GM 0 23 0 0 0 0 .1 0 3 1 3 14
+GM 0 0 0 0 -55 0 0 0 3 1 0 0
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG cr70-v14-h48.WGF
+EN
+

The final GM entries for each side of the rod reflector simply change the angle of tilt from a true planar reflector to enclose an angle of 70 degrees. The treatment of the wire-grid reflector is identical. The dipole model making use of this partial result simply changes the GF entry to record the proper Green's file that it will access.

+

Let's begin by summarizing the survey results in a table. For each new angle, I adjusted the apex-to-dipole spacing (listed as "Space") and the dipole length (listed as "Length") for 50-Ohm resonance, as registered by an SWR report of 1.00:1. The performance figures are the same as presented in all other tables in this series, where the free-space gain is in dBi, the 180-degree front-to-back ratio is in dB, and the beamwidths (E-BW and H-BW) are for the dipole/array E- and H-planes.

+ 
+Wire-Grid Reflectors
+Space     Length     Angle      Gain     Front-Back     E-BW       H-BW        Impedance        50-Ohm
+m/wl      m/wl       degrees    dBi      Ratio dB       degrees    degrees     R +/- jX Ohms    SWR
+0.325     0.4248     90         13.49    38.00          40         34          50.10 + j0.20    1.00
+0.364     0.4226     80         14.19    46.29          38         30          50.11 + j0.20    1.00
+0.4135    0.4202     70         14.27    45.35          38         28          50.10 + j0.03    1.00
+0.480     0.4174     60         14.15    43.40          38         32          50.20 + j0.03    1.00
+0.573     0.4140     50         13.66    32.86          40         36          50.03 + j0.03    1.00
+
+Rod Reflectors
+Space     Length     Angle      Gain     Front-Back     E-BW       H-BW        Impedance        50-Ohm
+m/wl      m/wl       degrees    dBi      Ratio dB       degrees    degrees     R +/- jX Ohms    SWR
+0.323     0.4248     90         13.70    34.05          42         36          50.22 - j0.03    1.00
+0.361     0.4226     80         14.25    36.69          40         32          50.18 - j0.11    1.00
+0.410     0.4202     70         14.63    40.55          38         30          50.08 + j0.02    1.00
+0.4765    0.4172     60         14.70    43.41          38         30          50.09 - j0.21    1.00
+0.569     0.4140     50         14.46    38.77          38         34          49.88 + j0.03    1.00
+
+

The first noticeable trends involve the dipole length and spacing from the apex. As we shrink the angle of the reflector, the dipole requires more spacing from the apex and decreases its length. Both phenomena are natural, since the dipole will have a closer approach to and increased mutual coupling with the reflector planes. In this region of reflector size, the dimensions make virtually no distinction between the wire grid or the rod reflectors, as indicated by the trend graphs in Fig. 2. The tightness of the dimensional fit for both space and length is clearly evident.

+
+ +
+

Because the reflector size used in the survey is more optimal for rod reflectors than for wire-grid reflectors, as recorded in the surveys in preceding sections of this study, we should expect some difference in the gain curves for the two types as we shrink the angle. The table and the gain graph in Fig. 3 show the differences.

+
+ +
+

The wire-grid version peaks with an angle of 70 degrees, while the rod reflector peaks at 60 degrees. The table data on the front-to-back ratio also shows a wire-grid reflector peak at a wider angle than for the rod reflector. In addition, we also find that the minimum beamwidth values tend to correspond with the maximum gain values. Whether the wire-grid would also show a peak in gain at 60 degrees with its more optimal reflector vertical dimension (1.8 m) is one of those remnant unanswered question.

+

Changing the corner reflector angle apparently has a limit in its ability to increase gain for a given set of reflector dimensions. Both types of reflector show significant gain reductions as we decrease the reflector angle below 60 degrees. Whether there is a more optimal reflector size for narrower angle is also a question left to specific design interests.

+

The corner reflector angle also has a bearing on the exact pattern shapes that we obtain from the array. Fig. 4 provides wire-grid samples for 90, 70, and 50 degrees in both the E-plane and the H-plane.

+
+ +
+

In the E-plane, we do not see the beginnings of side "bulges" (incipient secondary forward lobes) until we pass the reflector angle for maximum gain. However, comparable bulges are an inherent part of the H-plane pattern. As we decrease the reflector angle, these side lobes increase in strength and move forward. The 50-degree pattern comes close to being pear-shape.

+
+ +
+

Fig. 5 provides the comparable patterns for the rod reflector series of models. In both the E-plane and the H-plane, the patterns show similar but less-developed side lobe bulges. In part, the slow development is the result of the fact that the size of the reflector (especially the vertical dimension) coincides more closely with the optimal size for this type of reflector.

+

One facet of performance does not change with the type of reflector: the SWR bandwidth. SWR bandwidth is largely a function of the dipole spacing and length, although these parameters are influenced by the reflector angle. However, just as the graph of dimensions showed a very close overlap of values, so too do the 50-Ohm SWR curves for the two types of reflectors. Therefore, Fig. 6 shows the curves only for the rod reflector.

+
+ +
+

For both reflector types, the 2:1 SWR bandwidth shrinks from 9.0% with a 90-degree reflector angle down to 8.3% with a 50-degree angle. The shrinkage, although small, runs contrary to our experience with the 90-degree reflector when we moved the dipole further from the reflector apex. However, in that case, increasing the spacing decreased the dipole's coupling to the reflector surfaces. In the present survey of shrinking angles, the increased spacing still results in increased coupling and a narrowing of the SWR bandwidth.

+

Enhancing Parasitic Effects of Reflector Bars

+

Although the survey of shrinking angles for 50-Ohm corner reflectors leaves numerous unanswered questions, let's turn to a different technique of changing corner reflector performance. Here, I shall report on the work (with permission) of John Regnault (G3SWX) and John Sager (G0ONH), as conveyed in private correspondence. Beginning with a rod reflector that uses a 75-degree angle, they systematically altered the length of the reflector rods for a reflector that is close to the general size that we are using as are sample: 1.4-m vertically by 2.4 m for each side. The end result was a reflector that used different lengths for virtually every reflector rod.

+

In a preceding part of this series, I showed a typical rod reflector in terms of its current distribution. Except for the region immediately behind the dipole driver, the remaining portions of the reflector show so little current variation that it does not register on the color scale used for the relative current magnitude display: 5e-003 down to 1e-005. Compare that illustration with Fig. 7, which uses the very same scale of relative current magnitudes and the same level of excitation.

+
+ +
+

The location of the all-red driver dipole differs slightly in each case, since I tilted the original graphics to slightly different angle in order to reveal the state of relative current distribution on the apex rod. However, more striking is the fact that in both cases, the reflector rods show a range of current distribution that is a product of the careful selection of reflector rod lengths.

+ 
CM corn6a.nec
+CM G4SWX 2001 design
+CM Corner reflector center freq 299.8MHz
+CM 75 degree apex corner 2.4WL panels 1.4WL wide
+CM corn6a.nec: 0.3WL rod spacing design
+CM Rods spaced .2 .1 .1 .2 .3 .3 .3 .3 .3 .3
+CM single dipole drive 50 ohm optimized
+CE
+GW 0 40 0.0793 -.690 0.0609 0.0793 0.690 0.0609 0.0108
+GW 0 40 0.2380 -.695 0.1826 0.2380 0.695 0.1826 0.0108
+GW 0 40 0.3173 -.689 0.2435 0.3173 0.689 0.2435 0.0108
+GW 0 40 0.4760 -.676 0.3653 0.4760 0.676 0.3653 0.0108
+GW 0 40 0.7140 -.682 0.5479 0.7140 0.682 0.5479 0.0108
+GW 0 40 0.9520 -.702 0.7306 0.9520 0.702 0.7306 0.0108
+GW 0 40 1.1900 -.697 0.9132 1.1900 0.697 0.9132 0.0108
+GW 0 40 1.4280 -.700 1.0958 1.4280 0.700 1.0958 0.0108
+GW 0 40 1.6660 -.689 1.2784 1.6660 0.689 1.2784 0.0108
+GW 0 40 1.9040 -.692 1.3200 1.9040 0.692 1.3200 0.0108
+GW 0 40 0.0793 -.690 -0.0609 0.0793 0.690 -0.0609 0.0108
+GW 0 40 0.2380 -.695 -0.1826 0.2380 0.695 -0.1826 0.0108
+GW 0 40 0.3173 -.689 -0.2435 0.3173 0.689 -0.2435 0.0108
+GW 0 40 0.4760 -.676 -0.3653 0.4760 0.676 -0.3653 0.0108
+GW 0 40 0.7140 -.682 -0.5479 0.7140 0.682 -0.5479 0.0108
+GW 0 40 0.9520 -.702 -0.7306 0.9520 0.702 -0.7306 0.0108
+GW 0 40 1.1900 -.697 -0.9132 1.1900 0.697 -0.9132 0.0108
+GW 0 40 1.4280 -.700 -1.0958 1.4280 0.700 -1.0958 0.0108
+GW 0 40 1.6660 -.689 -1.2784 1.6660 0.689 -1.2784 0.0108
+GW 0 40 1.9040 -.692 -1.3200 1.9040 0.692 -1.3200 0.0108
+GW 0 40 0.0 -.710 0.0 0.0 0.710 0.0 0.0108
+GW 1 15 0.363 -.199 0.0 0.363 0.199 0.0 0.0108
+GE
+GN-1
+FR 0,1,0,0,299.8,0.
+EX 0 1 8 1 1.00000 0.00000
+RP  0, 1, 361, 1001, 90., 0., 1., 1.,10000.
+RP  0, 361, 1, 1001, 0., 0., 1., 1.,10000.
+EN
+

The model shown above is for the reflector on the left in Fig. 7. It uses what I tend to call a mild or modest set of variations in the reflector rod length. However, notice also that the rod spacing also changes to enhance the parasitic effects. The dipole used in these models is fatter than the ones on our survey (0.0216 m vs. 0.008 m), but the rod diameters are a bit smaller (0.0216 m vs. 0.03 m). The only adjustments that I made to the model are 2. First, I strung out the reflector wires as individual units rather than using the symmetry entries in the original. Second, I adjusted the dipole spacing and length for a 50-Ohm SWR of 1.00:1 on NEC-4.

+

The second model uses a much more radical set of reflector rod adjustments in an attempt to squeeze a bit more gain from the system. Fig. 7 on the right shows not only the relative current magnitude distribution, but also the fact that certain rods have been reduced in length to approximate parasitic reflectors. The following lines provide the model (with similar adjustments to the first one) and its relevant dimensions. You may identify the short reflector rods as the ones with only 15 segments, the same number as used in the driving dipole.

+ 
CM corn6b.nec
+CM G4SWX 2001 design
+CM Corner reflector center freq 299.8MHz
+CM 75 degree apex corner 2.4WL panels 1.4WL wide
+CM corn6b.nec: 0.3WL rod spacing design
+CM Rods spaced .2 .1 .1 .2 .3 .3 .3 .3 .3 .3
+CM Rods 1 and 4 0.5WL others 1.5WL
+CM single dipole drive 50 ohm optimized
+CE
+GW 0 15 0.0793 -.260 0.0609 0.0793 0.260 0.0609 0.0108
+GW 0 45 0.2380 -.702 0.1826 0.2380 0.702 0.1826 0.0108
+GW 0 45 0.3173 -.717 0.2435 0.3173 0.718 0.2435 0.0108
+GW 0 15 0.4760 -.252 0.3653 0.4760 0.252 0.3653 0.0108
+GW 0 45 0.7140 -.691 0.5479 0.7140 0.691 0.5479 0.0108
+GW 0 45 0.9520 -.702 0.7306 0.9520 0.702 0.7306 0.0108
+GW 0 45 1.1900 -.697 0.9132 1.1900 0.697 0.9132 0.0108
+GW 0 45 1.4280 -.700 1.0958 1.4280 0.700 1.0958 0.0108
+GW 0 45 1.6660 -.689 1.2784 1.6660 0.689 1.2784 0.0108
+GW 0 45 1.9040 -.692 1.3200 1.9040 0.692 1.3200 0.0108
+GW 0 15 0.0793 -.260 -0.0609 0.0793 0.260 -0.0609 0.0108
+GW 0 45 0.2380 -.702 -0.1826 0.2380 0.702 -0.1826 0.0108
+GW 0 45 0.3173 -.717 -0.2435 0.3173 0.718 -0.2435 0.0108
+GW 0 15 0.4760 -.252 -0.3653 0.4760 0.252 -0.3653 0.0108
+GW 0 45 0.7140 -.691 -0.5479 0.7140 0.691 -0.5479 0.0108
+GW 0 45 0.9520 -.702 -0.7306 0.9520 0.702 -0.7306 0.0108
+GW 0 45 1.1900 -.697 -0.9132 1.1900 0.697 -0.9132 0.0108
+GW 0 45 1.4280 -.700 -1.0958 1.4280 0.700 -1.0958 0.0108
+GW 0 45 1.6660 -.689 -1.2784 1.6660 0.689 -1.2784 0.0108
+GW 0 45 1.9040 -.692 -1.3200 1.9040 0.692 -1.3200 0.0108
+GW 0 45 0.0 -.720 0.0 0.0 0.720 0.0 0.0108
+GW 1 15 0.378 -.1955 0.0 0.378 0.1955 0.0 0.0108
+GE
+GN-1
+FR 0,1,0,0,299.8,0.
+EX 0 1 8 1  1.00000  0.00000
+RP 0 1 361 1001 90. 0. 1.00000 1.00000
+RP 0 361 1 1001 0. 0. 1.00000 1.00000
+EN
+

The following brief table will show some of what we derive from the difficult and likely tedious task of optimizing the length of each reflector rod. The 70-degree standard rod reflector appears as a point of reference.

+ 
+Array       Angle     Gain     Front-Back     E-BW        H-BW        Impedance        50-Ohm
+            degrees   dBi      Ratio dB       degrees     degrees     R +/- jX Ohms    SWR
+Standard    70        14.63    40.55          38          30          50.08 + j0.02    1.00
+Corn6A      75        15.66    32.13          34          22          49.91 - j0.04    1.00
+Corn6B      75        15.78    26.26          34          22          49.99 - j0.08    1.00
+
+

Both reflectors with optimized rods provide better than a dB of additional gain over the standard reflector with a nearly optimum angle. In the process, they lose a bit of front-to-back ratio, although virtually any communications service would be satisfied with the levels achieved. In addition, both arrays effect additional and quite noticeable reductions in the E-plane and the H-plane beamwidths. In fact, the beamwidth reductions are so sizable that we need to examine the patterns of the arrays to see how they emerge. Since the original models use a horizontal orientation relative to the modeling coordinate system (in contrast to our standardized vertical orientation), the individual patterns will point in different directions from the remainder in this part of the series.

+
+ +
+

The cost associated with adjusting individual reflector rods for better parasitic performance is the emergence of sidelobes, both fore and aft. The E-plane pattern in Fig. 8 for Corn6A, the mild adjustment, shows that the worst-case front-to-back ratio is closer to about 25 dB due to rearward sidelobes. E-plane bulges that appear only when standard reflectors pass the angle of optimal gain are plainly appearing in this optimized model. The H-plane shows the most significant departure from the well-behaved patterns associated with standard reflectors. Once more, the sidelobes that appear in strength only when a standard reflector has passed the angle of optimal performance are a standard part of the optimized model. In addition, the pattern shows ripples indicating a whole cluster of incipient sidelobes, undoubtedly the result of the variable length of the reflector rods. Having noted the variations from the norm for standard reflectors, I should add that these phenomena are not inherent drawbacks to the design. That judgment rests on comparing standard and optimized patterns against a set of design criteria for a particular communications task.

+
+ +
+

Fig. 9 shows the patterns for the more radically altered version of the reflector with optimized rod lengths. The use of some reflector rods that function more distinctly as parasitic reflector elements creates some significant changes in the patterns. Both the 180-degree and the worst-case front-to-back ratios show further reductions, as illustrated both by the performance table and by the H-plane pattern. The H-plane pattern also shows that the rippled side bulges of Corn6A are now a pair of distinct forward sidelobes on each side of the main forward lobe of Corn6B. In the E-plane pattern as well, the incipient sidelobes of Corn6A are now fully fledged secondary forward side lobes in Corn6B.

+

Whatever the fine points of the performance figures and patterns, the fact remains that Regnault and Sager have demonstrated that by optimizing the length and spacing of the reflector rods in a corner reflector that is 1.4 m (wavelengths) vertically with 2.4-m (wavelength) sides, we can gain at least a full dB of further gain from the structure. It remains somewhat a moot point whether we call the reflector a modified corner or a hybrid parasitic-corner reflector.

+

Perhaps more significant is another seemingly minor detail in the two corner reflectors that we have just noted. The most forward rod in each reflector does not continue the straight line formed by the preceding rods back to the apex rod. Instead, the rod forms a "fold-in," a shift in position that effects a slight reduction in the expected aperture. Since this represents a third way in which we may modify a standard reflector, we should add it to our survey.

+

Aperture Fold-In

+

Fig. 10 shows the general concept of side-length fold-in. Essentially, the fold-in portion of the reflector adds a reflector plane that is parallel with the line formed by the dipole driver and the apex. Although we can implement a fold-in with either wire-grid or rod reflectors, our survey will limit itself to a sampling of rod reflector steps.

+
+ +
+

Each new rod in the reflector maintains the same inter-rod spacing: 0.1 m. Hence, for a given starting side length, each rod increases the side length without changing the aperture. In order for us to have a relevant stand of comparison to see what happens as we add rods to a fold-in, let's re-examine some older data for standard 90-degree corner reflectors that are 1.4 m vertically with several side lengths.

+ 
+Reference Values for 90-Degree Corner Reflectors 1.4-M Vertically
+Side-Length     Free-Space    Front-to-Back     E-BW        H-BW       Impedance       50-Ohm
+m/wl            Gain dBi      Ratio dB          degrees     degrees    R +/- jX Ohms   SWR
+2.3             13.66         35.78             42          36         50.22 - j0.02   1.00
+2.4             13.70         34.05             42          36         50.20 - j0.03   1.00
+2.5             13.70         34.84             42          36         50.20 - j0.03   1.00
+2.6             13.73         34.71             40          36         50.20 - j0.01   1.00
+2.7             13.68         35.59             42          36         50.22 - j0.02   1.00
+
+

When adjusted to have a 50-Ohm SWR of 1.00:1, the performance shows a mild peak with a side length of 2.6 m, although the entire region from 2.4 m to 2.6 m might be considered as virtually identical in performance. Note that the free-space gain peaks at about 13.7 dBi. The beamwidths are comparable throughout the entire range of side lengths in the small table.

+

Next, let's take a reflector with a 2.4-m side length and begin to add fold-in rods, one at a time to each side of the reflector. The reflector aperture remains 3.39 m, but the distance from the apex to the aperture line grows from 1.70 m up to 2.10 m as we add up to 4 fold-in rods. The following table shows the modeling results for each additional fold-in rod.

+ 
+Adding a fold-in to a 90-Degree Corner Reflector 1.4-M Vertically With a Basic
+Side Length of 2.4 M:  Each fold-in step is 0.1-m forward, but no wider than the initial
+aperture (3.39 m).
+
+No. of Fold-    Free-Space    Front-to-Back     E-BW        H-BW       Impedance       50-Ohm
+In rods         Gain dBi      Ratio dB          degrees     degrees    R +/- jX Ohms   SWR
+No added rods   13.70         34.05             42          36         50.20 - j0.03   1.00
+1 fold-in rod   13.76         35.31             42          34         50.21 - j0.07   1.00
+2 fold-in rods  13.98         43.45             40          32         50.08 - j0.14   1.00
+3 fold-in rods  14.00         44.27             40          30         50.10 - j0.15   1.00
+4 fold-in rods  14.23         33.60             40          28         50.03 - j0.03   1.00
+
+

Most notable is the fact that gain continues to increase even through the 4th added fold-in rod, with no signs of decrease. The front-to-back ratio remains strong. Although the E-plane beamwidth shows a marginal decrease, the H-plane beamwidth shows a much sharper curve downward.

+

Let's take one more step and begin with a reflector that is 2.3 m per side. Then we may add fold-in reflector rods up to a total of 4. The aperture for the slightly smaller initial reflector is 3.25 m. The distance from the apex to the aperture line will grow from 1.63 m to 2.03 m.

+ 
+Adding a fold-in to a 90-Degree Corner Reflector 1.4-M Vertically With a Basic
+Side Length of 2.3 M:  Each fold-in step is 0.1-m forward, but no wider than the initial
+aperture (3.25 m).
+
+No. of Fold-    Free-Space    Front-to-Back     E-BW        H-BW       Impedance       50-Ohm
+In rods         Gain dBi      Ratio dB          degrees     degrees    R +/- jX Ohms   SWR
+No added rods   13.66         35.78             42          36         50.22 - j0.02   1.00
+1 fold-in rod   13.79         32.97             42          34         50.26 - j0.03   1.01
+2 fold-in rods  13.88         35.43             42          32         50.30 - j0.13   1.01
+3 fold-in rods  14.13         38.59             40          30         50.12 - j0.29   1.01
+4 fold-in rods  14.47         31.40             38          26         50.01 - j0.07   1.00
+
+

The second case is interesting because it begins with a lower gain value than the first. However, by the time we add a single rod, the array has a higher gain then the first case, and with 4 fold-in rods, the difference has grown to about a quarter dB, with no signs of impending decrease. As well, the final case in the list, even though technically smaller than the final case in the first list, has narrower beamwidth values.

+

If we draw lines from the aperture limits back to the apex, the largest array on the first list forms an effective angle of just about 80 degrees. For the second and smaller array, the angle becomes a little over 77 degrees. Now let's go all the way back in this exercise to the beginning. The gain of an 80-degree corner array with 2.4-m sides was about 14.25 dBi, virtually the same value as the largest fold-in model using 1.4-m initial sides. The gain value for a 70-degree array was 14.63 dBi, somewhat higher than for our 77-degree (effective) fold-in model that began with 2.3-m sides. In effect, the fold-in technique does more than just hold the aperture at some fixed final value. It also narrows the effective angle of an array, whatever its starting angle.

+

To test this way of looking at the fold-in structure on corner arrays, let's perform one more test. The 60-degree corner using 2.4-m sides yielded the highest gain of the set of shrinking corners tested. Let's use the 60-degree angle and go in two directions. First, we shall extend the sides by one increment to 2.5 m. Second, we shall move the new rods inboard instead to create a 2.5-m side length, but retain the aperture of the original model with 2.4-m sides. The following table shows what we get.

+ 
+Options for a 60-Degree Corner Reflector 1.4-M Vertically With a Basic
+Side Length of 2.4 M:  A. Extending the side length to 2.5 M, or B. Adding a fold-in rod.
+Each fold-in step is 0.1-m forward, but no wider than the initial aperture (3.0 m).
+
+No. of Fold-           Free-Space    Front-to-Back     E-BW        H-BW       Impedance       50-Ohm
+In rods                Gain dBi      Ratio dB          degrees     degrees    R +/- jX Ohms   SWR
+60 deg, 2.4-m side     14.70         43.40             38          30         50.37 + j0.15   1.01
+60-deg, 2.5-m side     14.80         42.65             38          30         50.43 + j0.17   1.01
+60-deg, 2.4 + fold-in  14.80         39.41             38          30         50.47 + j0.17   1.01
+
+

I chose the case specifically to be at the edge of performance increase with changes of the corner angle. Adding 0.1-m to each side increased the gain by about 0.1 dB. Note that the fold-in did no better, but actually shows a slight reduction in the front-to-back ratio. The beamwidths do not change for either modification relative to their initial values.

+

The data suggest strongly that there is a limit to the amount by which fold-in structures can improve the performance of a corner array. When the effective angle produced by the fold in approaches or reaches the corner angle of optimal performance for a plane-sided corner array, improvements will disappear. Since a 90-degree corner is distant from the smaller angle that marks the maximum gain that might be achieved for a given side-length, fold-ins show excellent potential for improved performance. However, if we begin with the optimal angle, there will be little difference between a fold-in and a simple side extension.

+

One might question the wisdom of using a fold-in, since it complicates reflector construction. However, a wide corner, such as the 90-degree reflector, does allow for easy implementation of a wide-band driver, such as a fan dipole. In such cases, preserving the wide-band characteristic while obtaining additional gain may call for the use of a fold-in. Its complications may be less than trying to implement a fan with a narrow corner angle.

+

Trough Reflectors

+

As the side length needed for best corner reflector performance increases, the array grows more ungainly, especially in view of its 3-dimensional nature. One solution offered to counteract this effect is the trough reflector. The basic principle appears in Fig. 11. We replace the pointed apex end of the reflector with a flat region that simply cuts off the apex. The result is supposed to preserve, if not enhance gain, while sustaining the other major characteristics of the corner reflector.

+
+ +
+

Guidance on the creation of trough reflectors seems somewhat vague, general, and perhaps even misguided. At the very least, it seems directed toward corner designs other than the 50-Ohm driver that is and has been our standard system throughout this study. To test the merits of trough reflectors, I modified the 90-degree 1.4-m high rod reflector in the following ways. I replaced the apex and sidebars in steps of 2 rods on each side of the apex bar for a series of test models. Keeping the spacing between bars in the flat part of the trough at 0.1 m actually widens the overall size, although not enough to jeopardize the results. The following sample model, labeled T4, provides an example of the process.

+ 
CM Trough Reflector and Dipole
+CM Version T4
+CE
+GW 1 14 .4 0 -.7 .4 0 .7 .015
+GW 2 14 .4 -.1 -.7 .4 -.1 .7 .015
+GW 3 14 .4 -.2 -.7 .4 -.2 .7 .015
+GW 4 14 .4 -.3 -.7 .4 -.3 .7 .015
+GW 5 14 .4 -.4 -.7 .4 -.4 .7 .015
+GM 0 19 0 0 0 .07071 -.07071 0 5 1 5 14
+GW 12 14 .4 .1 -.7 .4 .1 .7 .015
+GW 13 14 .4 .2 -.7 .4 .2 .7 .015
+GW 14 14 .4 .3 -.7 .4 .3 .7 .015
+GW 15 14 .4 .4 -.7 .4 .4 .7 .015
+GM 0 19 0 0 0 .07071 .07071 0 15 1 15 14
+GW 101 11 .572 0 -.2188 .572 0 .2188 .004
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The 14-segment reflector rods confirm that the vertical dimension is 1.4 m. The flatted part of the trough has been moved 0.4 m from the former apex. Hence, it must extend 0.4 m each side of the apex rod (GW 1) to preserve the 90-degree angle toward the virtual apex point at X=0. The 19 rods in each GM entry complete the structure that is very close to 2.4 m on each total side (angled portion plus 1/2 of the trough). Obviously, T2 would move the trough only 0.2 m from the former apex, while T10 would move the trough "bottom" 1.0 m from the apex. Twice the displacement measures the width of the flat part of the trough reflector. For each case, I adjusted the spacing of the dipole from the trough centerline to yield a 50-Ohm impedance.

+

The models of trough reflectors provided the following performance reports--in the format with which we have grown familiar. T0 is a standard 90-degree rod reflector and forms a reference point for comparing the various trough models.

+ 
+Trough       Free-Space    Front-to-Back     E-BW        H-BW       Impedance       50-Ohm
+Model        Gain dBi      Ratio dB          degrees     degrees    R +/- jX Ohms   SWR
+T0           13.70         34.05             42          36         50.22 - j0.03   1.00
+T2           13.56         30.45             42          34         49.97 - j0.10   1.00
+T4           13.74         27.75             44          30         49.88 - j0.16   1.00
+T6           12.80         27.84             42          36         50.01 - j0.22   1.00
+T8           11.12 split   23.89             56          68         49.97 + j0.04   1.00
+T10          11.51 split   18.00 (approx)    88          68         49.95 - j0.23   1.00
+
+

The trough reflector obviously has very limited applications for a 50-Ohm driver. Above the T4 level, the gain decreases severely, and by the T8 level, the H-plane pattern has split into two lobes, each displaced from the centerline with a large null between them. The high H-plane beamwidths represent the sum of the two lobes, although each is about 20 to 25 degrees wide and significantly more than 3 dB down at the H-plane forward heading.

+
+ +
+

Fig. 12 shows that even the T4 version of the trough offers no improvement in the 50-Ohm 2:1 SWR passband. The reason is fundamental to the trough design and its relationship to the dipole driver. Note the dimensions in the following table for the test models. All dimensions are in meters.

+ 
+Trough       X-axis        Space between     Net space       Dipole
+Model        Displacement  dipole & apex     dipole to ref.  length
+T0           0             0.323             0.323           0.4248
+T2           0.2           0.378             0.178           0.4310
+T4           0.4           0.572             0.172           0.4376
+T6           0.6           0.778             0.178           0.4367
+T8           0.8           0.975             0.175           0.4367
+T10          1.0           1.176             0.176           0.4367
+
+

Once we create even a small fatted portion of a trough, the required spacing of the driver from the reflector no longer corresponds in any way to the results that we obtain from either a wire-grid or a rod corner reflector. Instead, the spacing is almost exactly the spacing required from a dipole to a planar reflector. The dipole no longer has its closest approach to the plane surface of the angled reflector.

+

However, up to the T4 level, a trough reflector makes a viable alternative to a standard corner reflector. To check on the stability of performance, I swept both the standard corner and the T4 trough--both represented in Fig. 12--through their passband and a little beyond to end up with 5-MHz increments. Fig. 13 shows the results of a gain comparison of the two arrays from 285 through 320 MHz.

+
+ +
+

The gain changes so little across the passband in either case (about 0.5 dB), that we have very little to choose between the two models. However, the front-to-back curve in Fig. 14 suggests that the true corner reflector is consistently 3 dB or more superior to the trough reflector. The beamwidths for the T4 and the true corner show virtually no difference at any frequency.

+
+ +
+

For 50-Ohm driver systems, the trough design has very limited application. A T4 trough reflector is viable and may provide one kind of mechanical advantage over the true corner. You may attach a mounting mast directly to the rear side of the flat area and achieve a more secure installation than with a true corner. However, do not expect improvements in performance. If you use a basic reflector size that significantly differs from the size used in our sample survey, you will need to subject the array to considerable modeling and field testing before pronouncing it optimal in any sense of the term.

+

Collinear Dipole Drivers

+

To this point, we have focused on modifications that we may perform on the reflector structure, focusing on a standardized rod-reflector that is 1.4 m vertically and that has a side length of 2.4 m. Before we close the book on 50-Ohm corner reflector arrays, we should note one driver modification that we can perform. We have noted throughout that alternative drivers having a significant H-plane dimensions (across the aperture) tend to perform erratically or poorly compared to their performance with planar reflectors. When we examined planar arrays, we discovered that phased dipoles side-by-side and 1/2 wavelength apart provided good broadside gain. When fed in phase, they also provided a considerable bandwidth compared to a single dipole driver.

+

Although we cannot place a similar driver across the H-plane of a corner reflector, we can devise a collinear form of dipole driver where we feed the dipoles in phase. Fig. 15 shows the general outline of the system.

+
+ +
+

In the test models, the inner dipole ends are 1/4 wavelength apart. The spacing from the apex is 0.393 m to give each dipole a resonant 100-Ohm impedance. In concert with the broadside planar array, the individual feedpoints connect to a central feedpoint via 100-Ohm transmission lines. The parallel combination at the junction provides a good match for 50-Ohm cable. Each dipole is 0.433-m long, and so the overall length of the driver assembly is 1.116 m. The dipoles use the 8-mm diameter also used for single dipole drivers.

+

The separation of the dipoles is not designed to provide the maximum gain possible. Instead, my focus is upon other properties of the overall array. For example, with a single dipole driver, the 1.4-m vertical reflector extended nearly 0.49 m beyond the end of the driver. Will we need a similar extension to derive maximum gain from the collinear pair of dipoles? To find an answer, I tested reflectors with vertical dimensions ranging from 1.4 m to 2.4 m. Each rod reflector used a side length of 2.4 m.

+
+ +
+

Fig. 16 provides a graph of the results in terms of both gain and front-to-back ratio. Note that the X-axis of the graph records the vertical dimension of the reflector. The free-space gain increases until it reaches 14.95 dBi with a 2.2-m high reflector. The extension of the reflector beyond the collinear dipole limit is about 0.54 m, close to the extension value required for a single dipole. Additional extension space for the 2.4-m rod reflector shows a small decrease in gain. Interestingly, the 180-degree front-to-back ratio shows a small dip at the maximum gain point with respect to array vertical size. However, the values (36-42 dB) are already so high that differences no longer make much of a difference.

+
+ +
+

Fig. 17 illustrates the degree to which the rearward radiation of the collinear dipole array is approaching total insignificance in both planes. As well, the patterns are extremely well behaved, with no detectable forward sidelobes or bulges. The quality of the patterns holds up very well across the 2:1 50-Ohm SWR passband, shown in Fig. 18. The acceptable SWR level exists from 275 to 350 MHz, a 75-MHz passband. Expressed in other terms, we have a 25% passband with respect to the 2:1 50-Ohm SWR standard.

+
+ +
+

The collinear array maintains its performance across the SWR passband. The free-space gain peaks at about 15.2 dBi at 310 MHz, just above the design frequency, with a very slow roll-off above that frequency. On the low-frequency side, we have a steeper curve, but the total gain variation is about 0.7 dB. As shown in Fig. 19 the 180-degree front-to-back ratio displays its usual variations, but no value goes below about 37 dB.

+
+ +
+

Although the sample array makes no pretense of achieving the maximum performance from a collinear dipole driver system, it does establish a few important characteristics. First, the collinear systems requires--like a single dipole--about 0.5 m of reflector beyond the dipole ends to achieve maximum gain. As a result, the system shown here requires a 2.2-m tall reflector. At some size, and especially if one enlarges the spacing between dipoles, the system might better be served by two independent corner reflectors.

+

Second, the passband of the phase-fed collinear dipoles is similar to that of the broadside driver used in the study of planar reflectors. Combined with other techniques, such as the use of fan dipoles, one might increase the passband even further. However, in all cases, the designer will have to balance the operating passband against any rates of decrease in gain, front-to-back ratio, or desired pattern shape.

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However, we are not done with the quest for increased operating bandwidth using corner reflectors.

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Almost Done, But Not Complete

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The survey of modification techniques to corner reflectors and their drivers provides a number of techniques by which a designer might reliably squeeze the last modicum of performance from a corner array. Some techniques, such as the collinear driver scheme, seem broadly based. Others, such as the use of a trough reflector, appear to have limited utility. Still others, such as modifying reflector rod length and spacing for maximum gain, require painstaking care, not to mention trial and error. Combining techniques, such as adding fold-ins to the collinear driver array, may well break new ground in corner reflector design. Still others, such as developing a collinear array with a narrower angle, may require special attention to the mechanical aspects of the resulting antenna.

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This episode of my exploration of corner arrays has a slightly different purpose than the other parts of the series. They were designed to provide general guidance of what is likely to work and what is likely not to work within the realm of standard corner reflector designs. This session has been devoted to some very general guidance of where one might next go in corner reflector design. There is no telling how much we have yet to learn about this fascinating hybrid of optical and parasitic properties.

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One continuing challenge is the quest to expand the operating passband of a corner array beyond the 25% value achieved by both the collinear driver and by the fan dipole driver from past episodes. So we might well spend one more episode seeing just how far we can stretch a 50-Ohm feedpoint in a corner array and still have both an SWR under 2:1 and some usable performance.

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Updated 09-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX August, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 5

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Go to Main Index

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Topics: Corner Reflector, VHF / UHF


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Corner Reflectors Revisited Again
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+ Part 5: The Very-Wide-Band Corner Reflector

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L. B. Cebik, W4RNL

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In the course of our meanderings through the properties of corner reflectors, we have found only two driver assemblies that would expand the 2:1 SWR bandwidth to slightly over 25%: the fan dipole and a pair of in-phase-fed collinear dipoles. The latter driving option required a considerable expansion of the vertical dimension--or the rod length for rod-based reflectors--to achieve its peak performance.

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A standard feature of some texts that deal with corner reflectors is a UHF television receiving array with a claimed 2:1 frequency range. Developed about a half century ago, the array now receives truncated descriptions in such volumes as Kraus, Antennas, 2nd Ed., pp. 557-559, and Johnson (ed.) Antenna Engineering Handbook, 3rd Ed., pp. 29-21 to 29-24. The Johnson volume provides some of the measured data for the array, while the Kraus text supplies some interesting dimensional detail. However, the principles behind the array appear not yet to have been modeled as a means of comparing the antenna to other reflector arrays.

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Obviously, the array holds considerable interest, if for no other reason than the challenge of modeling its key features. That task will be the chief effort of this fifth episode on corner reflectors. The job is subject to a number of qualifications. First, this entire series is based upon a feedpoint of 50 Ohms for builder convenience and to confine the scope of our work into a series of projects that we can compare, one with another. However, Kraus reports that the design was intended for use with a "300 or 400 Ohm twin line." We shall model the driver assembly as a 50-Ohm system when placed within the confines of a 90-degree corner reflector.

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Second, we have throughout used a 2:1 SWR standard as marking the edges of the operating passband when examining the band width of the arrays under scrutiny. Since the wide-band corner array of yore was designed for television reception nearly a half century ago, it is likely that a 2:1 standard was not applicable. It is more likely that some form of measure of signal strength at the television terminals, measured or calculated, provided the terms of bandwidth specification. However, in our work, we shall continue to use the 2:1 50-Ohm SWR value as marking passband limits. However, we shall also discover that even with those limits, the gain and front-to-back performance of a reflector array may extend considerably beyond the widest limits that we shall use.

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Third, for practical reasons, I shall call any guidance provided by the modeling in this episode less general and more "proof-of-principle" in nature. As we shall see, my model for the driver of the array will only capture some of the essential features, enough to isolate what makes it the key element in expanding the flat-fan dipole driver passband from something over 25% to about 40%. As well, my rod reflector will also differ from the published versions, although it is close enough to replicate the essential ingredients of the original's performance. Finally, I shall by-pass the commercially appropriate procedure of designing to an upper and lower frequency limit, with a resultant mid-frequency. Instead, as with all of the other arrays in this series, I shall design the model for near resonance at 299.7925 MHz, so that 1 wavelength at the design frequency will equal 1 meter. Then, we shall discover where the passband will end in each direction and what the performance will be across the range of frequencies between those limits.

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Let's begin by seeing what the consequence of those changes might be. The passband that we shall encounter will be shaped just like the ones that we have so far reviewed, with a steeper curve below the design frequency than above it. Hence, a true design mid-frequency will be significantly above our design frequency, about 8.3% to be more precise (325 MHz). Let's survey the dimensional results of these numbers. The "Kraus" column uses mid-frequency values derived from Kraus' description. The "Design" column gives the values as a function of our 299.7925-MHz design frequency. The final "Mid-Frequency" column adjusts those values to the passband mid-frequency. All dimensions are in wavelengths,

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+Dimension                  Kraus            Design            Mid-Frequency
+Dipole-to-apex spacing     0.40             0.50              0.54
+Reflector rod length       1.20             1.20              1.30
+Reflector rod diameter     0.015            0.030             0.0325
+Reflector rod spacing      0.092            0.10              0.108
+Reflector side length      0.113            1.20              1.30
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The individual reflector measurements do not create any significant problems. The slightly wider reflector rod spacing is compensated for by the much larger diameter of the modeled rods. Otherwise, the dimensions of the listed model reflector and the design reflector are quite close. However, the mid-frequency adjustment to those values suggests that we are beginning with a reflector that is overall a bit larger than the original.

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The one figure that does not jive well with the listed dimensions is the spacing from the driver to the reflector apex, with a 20% to 30% difference, depending on how one counts. Reconciling that much difference requires that we take a closer look at both the original and the modeled driver. However, since the driver design is the key to the array's wide-band performance, that is just where we ought to begin anyway.

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The Forward-Bent Fan Dipole

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We are familiar by now with a fan dipole. We have used one with both wire-grid and rod reflectors in past episodes. What converts the standard flat fan dipole into a Brown-Woodward "bow-tie" dipole is bending the dipole down its axis so that, relative to a corner reflector, it bends forward at a 90-degree angle. Fig. 1 shows the difference.

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Contrary to existing literature, that describes a horizontal version of the subject array for television reception, I shall continue our convention of using a vertical orientation, in light of anticipated 21st century best uses for a corner reflector. The change of orientation is the least of the list of matters with which we need to be concerned with respect to the model. First, note the addition of an "axis" wire running from end to end. This wire alters the performance of the bent model relative to the flat design. In the flat model, the terminating point is always at the exact center of each wire end between the tips of the triangle. With a center wire added, the end point may shift somewhat.

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The bent fan dipole requires some dimensional adjustment to align it with the flat fan. The side-to-side dimension, as measured from the centerline to a tip, shrinks from 0.11 wavelength to 0.108 wavelength. However, the overall length of the dipole increases from 0.24 wavelength for the flat version to 0.262 wavelength for the bent version. The bends in the fan are designed so that they will be parallel to the plane of the reflector itself when finally situated.

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Sketches of the Brown-Woodward (B-W) dipole show 3 differences from the modeled version. First, the angle taken by the perimeter edge is shallower in the sketches than in the model. The model approaches a 45-degree angle relative to the centerline, while sketches give no clear indication of the B-W angle. The smaller angle of the sketched design may account for the fact that its listed mid-frequency length is 0.8 wavelength, rather than the 0.242- wavelength value of the model at the design frequency. Second, sketches seem to indicate that instead of a sharp bend, such as used in the sketch, there may be a flat area along the center line, with bends beginning at some point away from the centerline. Third, the B-W bow tie is a solid sheet. The model is a set of perimeter wires. However, the wire is the same 8-mm diameter wire used for the flat fan. Hence, some of the effect of the actual flat area may be captured by the wire diameter along the centerline of the antenna, while the wire thickness may capture something of the solid surface.

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Nevertheless, the differences are enough to make the notes on the very-wide-band corner array less than useful for general design guidance. At most, they may serve to prove the principle of using a forward-bent dipole as a driver for the corner reflector. As well, the bends in the dipole create a rise in the average gain test value for the new driver. Because we shall work within a 2:1 SWR range, we may apply a corrective to all gain values that we derive from the models (about -0.67 dB) to arrive at more accurate values. Even with all of these cautions and precautions, we shall not be able to see what gives the forward-bent fan dipole its advantage in the corner reflector by examining the driver alone.

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As the comparative SWR graph shows, the forward-bent dipole shows only a small advantage over the flat fan dipole. Both have a resonant impedance between 28 and 30 Ohms. The comparative 50-Ohm passband are 13.3% for the flat version and 14.7% for the bent version.

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Fig. 3 gives us the E-plane patterns of a flat fan and a bent fan. (The H-plane patterns of these dipoles in isolation are circles in both cases.) First, ignore the relative strengths of the patterns. It is the shape that interests us here. The flat fan shows the deep side nulls that we expect of a dipole. However, the bent dipole side-nulls do not reach 20 dB. This feature will reappear in a modified way when we finally reach the forward-bent fan dipole driven corner array.

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The shallow depth of the bent fan side nulls is a clue to the error in the pattern graph, since both dipoles have identical drive levels. The flat fan should show a peak gain slightly greater than the peak gain for the bent version. The reason that these values are reversed is that the polar plot uses uncorrected gain values. The flat fan free-space gain varies from 2.04 to 2.16 dBi from 290 to 335 MHz. The bent fan gain varies (when corrected) from 1.84 to 1.93 dBi, an accurate reflection of the increased power off the ends of the antenna.

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Perhaps the most notable fact that we have gleaned from our preliminary look at the flat and bent fans in isolation is the difference in the pattern shape in the E-plane (parallel to the axis of the antenna). For any further insights into why one might want to use a B-W dipole in a corner array, we shall have to model the driver in its working position.

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The Very-Wide-Band Corner Reflector Array

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When we place the drivers into their places within a corner array, the result resembles the pair of sketches shown in Fig. 4.

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In both cases, the reflector is 1.2-m (wavelengths) vertically, and the side length is also 1.2 m (wavelengths). The flat fan is 0.49 m (wavelength) away from the reflector apex, while the centerline of the bent fan is 0.5 m (wavelength) distant from the same point. The following lines present a complete model of the bent fan driver and its rod reflector. If you wish to replicate the flat fan model, simply extract the driver geometry lines from a past episode's model and replace the bent fan rod geometry with them. The model that follows is set up for a complete frequency sweep.

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CM Bent fan dipole-12-12-rods
+CE
+GW 1 12 0 0 -.6 0 0 .6 .015
+GW 2 12 0 -.1 -.6 0 -.1 .6 .015
+GM 0 11 0 0 0 0 -.1 0 2 1 2 12
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 3 12 0 .1 -.6 0 .1 .6 .015
+GM 0 11 0 0 0 0 .1 0 3 1 3 12
+GM 0 0 0 0 -45 0 0 0 3 1 0 0
+GW 101 5 .57778 .075 -.131 .5 0 -.015 .004
+GW 101 5 .57778 -.075 -.131 .5 0 -.015 .004
+GW 101 3 .57778 .075 -.131 .5 0 -.131 .004
+GW 101 3 .5 0 -.131 .57778 -.075 -.131 .004
+GW 101 4 .5 0 -.131 .5 0 -.015 .004
+GW 102 1 .5 0 -.015 .5 0 .015 .004
+GW 103 5 .5 0 .015 .57778 .075 .131 .004
+GW 103 5 .5 0 .015 .57778 -.075 .131 .004
+GW 103 3 .57778 .075 .131 .5 0 .131 .004
+GW 103 3 .5 0 .131 .57778 -.075 .131 .004
+GW 103 4 .5 0 .015 .5 0 .131 .004
+GE 0 -1 0
+FR 0 14 0 0 265 10
+GN -1
+EX 0 102 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+FR 0 14 0 0 265 10
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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GW entries 101 through 103 give the driver details, while the preceding lines set the reflector geometry. The FR entries that supply frequency details give away the results to come. They specify a frequency sweep from 265 to 395 MHz for the array. Fig. 5 gives the results of that sweep for both the flat and the bent dipole drivers.

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For the bent dipole driver, the 2:1 SWR passband edges are 265 MHz at one end of the range and 385 MHz at the other end. This 120-MHz range is a 40% bandwidth relative to the design frequency or about 37% relative to the center-frequency of the defined passband. The bent dipole clearly provides a very significant increase in the passband relative to what a flat fan dipole can provide. According to the literature, the difference is a function of the fact that the planes of the bent fan parallel the planes of the reflector. However, that fact alone does not tell us what changes with respect to array performance. Hence, we should begin an exploration of the performance reports for the two types of drivers.

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Fig. 6 gives us a comparative view of the forward gain values that we can derive from the array, using corrected values for the free-space gain. In effect, the graph tells us that there is no difference whatsoever in gain performance. Indeed, if the graph reveals anything, it is the fact that with the flat fan driver, the array performance passband extends well beyond the SWR limits set by the driver. If a 2.41-dB difference between the lowest and the highest values of gain is satisfactory for an application and if SWR is not a matter of concern, then either driver would provide the same gain service.

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The situation is less simple when it comes to the 180-degree front-to-back ratio (Fig. 7). The 180-degree values, taken as a composite across the band, do reflect the overall increased rearward radiation of the bent-fan driver system. The difference ranges from 3 to over 5 dB across the passband, and the lines are almost perfectly congruent. If we wish to probe these numbers in greater details, we must examine some patterns for the array. In the following samples, we shall find patterns in both the E-plane and the H-plane taken at the sweep extremes and at 335 MHz, the frequency of highest gain. Since the sweep extremes fall outside the SWR passband, we expect slightly weaker forward gain peaks than for the peak gain frequency.

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For an array with such a wide operating passband, the fat-fan patterns are quite well-behaved, as shown in Fig. 8. The E-plane patterns show equal half-power beamwidths at the sweep extremes--58 degrees--although the high frequency pattern has an overall broader appearance. The beamwidth shrinks to 42 degrees at the peak power frequency. Throughout the span, the rear lobes are both modest and normal, that is, well within our expectations for a high-gain array.

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The H-plane patterns show more visual variation across the frequency span. The "bullet" pattern at 265 MHz evolves into a narrower forward lobe with distinct sidelobes as we move higher in frequency. By the time that we reach 300 MHz, the pattern has developed deep nulls to separate the forward lobe from two major sidelobes. These sidelobes do not change their maximum strength by much as we continue to increase frequency, even though the H-plane beamwidth shows a gradual reduction from 48 degrees at the lower end of the passband to 32 degrees at the upper end. In fact, note that the side-to-side extent of even the low-end "bullet" pattern has roughly the same strength as the sidelobes.

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The E-plane patterns for the forward-bent fan dipole driver, shown in Fig. 9, are somewhat less tidy than those for the flat fan. Immediately apparent are the larger rear lobes at every sampled frequency, a fact that showed up in the front-to-back graph in Fig. 7. Also apparent is the wider pattern at 395 MHz with a beamwidth of 66 degrees in contrast to 58 degrees for the flat fan. However, perhaps the most notable feature is the one most easily missed. Compare the two sets of E-plane patterns for the depth of the side nulls. The shallower side nulls for the bent fan that we first saw when looking at the antenna in isolation (Fig. 3) remain a part of the E-plane patterns when we use the bent fan to drive a corner reflector.

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In contrast, the H-plane patterns for the bent fan are almost the same as for the flat fan. The only difference of significance is the slightly larger size of the rearward lobes or structures.

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Nothing in the graphs or patterns has helped us to understand why the SWR curves for the flat and the bent fan driver systems have such different 2:1 bandwidths. The differing shapes of the drivers, including the fact that the planes of the bent fan parallel the reflector surfaces, do not create changes in the patterns that we may directly tie to the SWR level. Only one set of parameters remains to explore: the source or feedpoint impedance.

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With respect to the feedpoint reactance, the very sizable difference in SWR goes unexplained. Both drivers show very normal reactance curves, beginning with a considerable capacitive reactance and ending with an equally considerable inductive reactance. There is a difference in the total reactance range: 87.02 Ohms for the flat fan and 67.28 Ohms for the bent fan. However, this difference alone does not suffice to widen the SWR bandwidth by the amount that we saw in the SWR curve in Fig. 5. Let's graph the respective feedpoint resistance curves and see if an answer lies there. See Fig. 10.

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The curve for the flat fan shows a very normal curve that climbs steadily upward, although it slows the rate of climb as the frequency approaches the upper limit. The bent-fan curve tells a much different tale, as it reaches a maximum value at about the same frequency as the point of highest gain. Then, as we further increase the frequency, the curve levels off and actually declines. If we re-examine Fig. 5, we can see that had we specified higher SWR limits of 2.5:1 or 3:1, we would have garnered considerably more territory at the high end of the band with only small increased at the low frequency end. However, note the slightly upsweep at the high end of the passband for the bent fan curve. The reactance near the upper end of the passband is increasing faster than for the flat fan system.

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The mystery of the bent-fan benefit becomes somewhat clearer as we digest the resistance data. The parallel planes of the driver and the reflector likely increase coupling between the two surfaces as we increase frequency, with the normal result of a lower overall impedance in the driven element. The effect is sufficient to partially counteract the tendency toward higher impedance values with increasing frequency, at least enough to broaden the SWR bandwidth. Our little experiment--even with all of its differences from the original antenna--suffices to uncover the principle of the B-W bow-tie's prowess in serving as the focal point for a very-wide-band corner reflector. Indeed, controlling the width of the fan's projections, with consequential adjustments to its overall length, would give the designer a degree of further control over the bandwidth. In addition, one might also experiment with the angle of bend or, in other words, the level of parallelism between the driver and reflector planes as another means of controlling bandwidth.

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A Brief Note on Higher Impedance B-W Bent-Fan Dipole Drivers

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I have noted that the original B-W bent-fan dipole driver required 300- to 400-Ohm feedline. Physically, it is longer, end-to-end, than the 50-Ohm driver that we have used, and its spacing also differs from the value required in our modeled bent fan. Of course, the original driver used a relatively thin solid sheet, while our model used a perimeter substitute with 8-mm diameter wire. However, something more than these differences is at work to explain the major differences in shape and length.

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As an experiment, I used a 1.2-m vertical wire-grid reflector with a side length of 2.4 m, where these dimensions are also in wavelengths at the design frequency. As we shall see further on, the 50-Ohm bent fan model driver works well with such a reflector. However, my goal differed. I wanted to find out what sort of changes I would have to make to arrive at a 300-Ohm driver within the reflector.

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Essentially, I had to increase the length of the driver to 0.6 m overall, more than twice the length of the 50-Ohm driver. The other driver dimensions remained unchanged. The resulting driver has a much shallower angle between the center and the ends. Using the same 8-mm wire, the shallower angles formed by the 3 joining wires on each side of the center segment reduce the adequacy of the model. As a result, the following notes are only suggestive and fall short of being a proof-of-principle model.

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With a 300-Ohm design frequency impedance and very little reactance, the 2:1 SWR passband of the modified array increases from 120 MHz up to 212 MHz (with a range from about 248 MHz up to 460 MHz). In other words, the passband increases from 40% to slightly over 70%. The peak gain appears at about 440 MHz, with a corrected value of about 14.2 dBi. The position of the peak gain value tends to coincide extremely well with field measurement results reported in the Johnson volume. The gain differential across the band is about 1.9 dB.

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Front-to-back values range from 23 to 32 dB. The E-plane beamwidth shows a very regular progression from 50 degrees at the low end of the scanned spectrum to 38 degrees at the upper end. By 420 MHz, the E-plane pattern shows a distinct spade shape, and at the uppermost frequency sampled, it takes on distinct side bulges, suggesting incipient secondary forward lobes.

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These results strongly suggest that a B-W bent-fan dipole designed for about a 300-Ohm feedpoint impedance will further increase the operating passband of a corner array without serious performance or pattern degradation. The modeled driver shows trends in its length and shape that lean toward the sketches of the B-W driver. Nevertheless, the results are extraordinarily tentative and insufficiently reliable to be more than suggestive. The high average gain test values place the impedance values at the passband edges into some doubt, especially as the reactance levels rise to prevent corrections. As well, even the corrected gain and other performance values are subject to adjustment. Even with all of these serious qualifications and modeling limitations, the exercise gives the very-wide-band television reflector array at least a partial confirmation.

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Understanding what role the B-W bent-fan dipole plays in achieving the SWR bandwidth and also discovering that it plays little role in determining the gain and front-to-back performance figures, is not only useful, but as well opens the door to further experimental work, whether conducted through modeling or field experiments--or both. The potential for an antenna using a single driver that covers a 2:1 frequency range (even at the cost of expanding SWR limits above the 2:1 value used here) has potential for a number of applications, especially above the GHz level. At those frequencies, however, one might be inclined to use solid surfaces or closely spaced screens for the reflectors. In addition, most descriptions of the very-wide-band corner reflector array note an economic and performance compromise in the setting of the reflector size. So we have at least two questions that we might pose before leaving this version of the corner reflector. 1. What do we obtain if we use large reflectors? 2. What can we expect from a reflector using a wire-grid as the modeled simulation of a solid or screened set of planes?

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Bigger and Tighter Reflectors

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The 1.2-m vertical by 1.2-m side-length rod reflector used to approximate the listed very-wide-band array produces good gain, but not the maximum gain of which the forward-bent fan dipole is capable. As we saw in previous episodes, there is a practical limit to the vertical dimension. Ideally, a vertical dimension (rod length) of 1.4 wavelengths yields maximum gain, but in a very-wide-band design, that dimension must occur well above the design frequency and close to the middle of the frequency range actually covered by the array. Therefore, the vertical dimension of 1.2 wavelengths appears to work best by placing the peak array gain in the middle of the passband.

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Of course, the steps used for the vertical dimension are at 0.2 wavelength intervals. In the course of tests with reflectors using different vertical dimensions, the 1.4-wavlength size consistently yielded free-space gain values that peaked below the design frequency. The longer the side lengths of the reflectors, the lower the frequency of peak gain. In contrast, maintaining a vertical dimension or rod length of 1.2 wavelengths kept the peak gain value in the vicinity of 325 or 335 MHz. The resulting gain curve tends to place the lowest gain value at the low end of the passband, but sustains an appreciable gain all the way to the top of the passband.

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Fig. 11 compares the gain levels of our initial model using a side length of 1.2 wavelengths and a second model having the same vertical dimension, but sides that are twice as long: 2.4 wavelength (as measured at the design frequency, where 1 wavelength = 1 meter). The coding on the legend indicates the vertical dimension and the side length in meters, where those values are also wavelengths at the design frequency. The peak corrected free-space gain of the expanded array is 13.99 dBi. The average gain increase across the passband--which is identical for both arrays--is about 0.67 dB. However, the larger array better centers the peak gain so that the differential from lowest to highest gain value is 2.12 dB, in contrast to the 2.41-dB differential for the smaller version of the array.

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Increasing the vertical dimension to 1.4 wavelengths and retaining the new 2.4 wavelength side length produced a peak gain value of 14.08 dBi at 275 MHz. Above that frequency, the gain gradually falls off so that the top-end gain value is down to 12.15 dBi. The average gain is higher, and the differential between highest and lowest value is less: 1.93 dB. However, the lowest value for the array occurs at the highest frequency, where the E-plane beamwidth also expands to 76 degrees. For some applications, the more even forward gain value may be useful, but in most UHF applications, a rising or level gain curve is desirable.

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Even at the 1.2 wavelength vertical dimension, the added gain comes at a fabrication cost that is considerable. The reflector would require a much more robust construction, whether supported behind the reflector apex or at the center of mass. In the field of UHF television reception for which the original array was designed, the lesser gain of the smaller reflector effected very good performance between 450 and 900 MHz with a practical size. Indeed, memories of UHF antenna installations suggest that the array had surplus gain, since a more common sight were planar reflectors with narrower-band drivers, one pointed at each UHF station in the region. These arrays general showed less gain by 2 to 3 dB, but provided fixed and less expensive installations. The corner array seems to have been reserved for the viewer with more funds to expend on a rotatable system.

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Of course, in terms of television, all of these last notes are historical, as cable and satellite television now supply the needs of television viewers. However, the television experiences of the 1950s through the 1980s may be useful to track for anyone who may contemplate applications in the upper UHF range.

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The advantage of the corner reflector with longer sides in the front-to-back department is apparent from Fig. 12. In the lower half of the SWR passband, the longer sides provide a considerable increase in the front-to-back ratio. However, as we increase frequency and the sides grow longer as a function of a wavelength, we arrive at a limit, beyond which the front-to-back value increases no further. Using the 180-degree figure makes the task of identifying a specific frequency or even a small frequency span almost impossible. However, the graph makes it clear that for the upper half of the passband, the longer side length yields no advantage.

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As we have seen in past episodes, the rod reflector has a peculiar characteristic. The gain peaks in a noticeable manner as the vertical dimension of the array reaches the vicinity of 1.4 wavelengths. If we extrapolate from the curves for the very-wide-band array curves for all of the rod reflectors using that value, it is likely that a vertical dimension of 1.30 to 1.35 wavelength may come closer to the peak gain vertical dimension. However, the exact value will vary with the rod diameter, which determines to a major degree the electrical length of the reflector rods. The physical length of our 1.4 wavelength rods would yield a significantly higher electrical length, given the 0.03 wavelength diameter. To some degree, the rod spacing will also play a role, since the spacing determines the mutual coupling between the individual rods. Although the initial theory of corner reflectors is based upon image theory, when we construct corner reflectors using rods, we cannot ignore parasitic effects that modify the results of the basic formulations.

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Solid surface and closely spaced screens used as reflector surfaces showed a different set of curves as we increased both the vertical dimension and the side length of the reflector. Our model for these reflectors uses wire-grid techniques that we carefully checked in the study of planar reflectors. In general, as we increased the vertical dimension and/or the side length, we obtained smooth curves, with shallow peaks in the vicinity of a vertical dimension of 1.6-1.8 wavelength and a side length in the 2.4-2.8 wavelength region. Based on that modeling experience, I constructed a model using our forward-bent fan dipole with a 1.4-wavlength vertical dimension and a 2.4 wavelength side length at the design frequency, where these values become meters. The array size grows with increasing frequency and shrinks with decreasing frequency. The following lines provide the model used to sweep the array across the anticipated passband. As always, you may extract the model from the text, strip aways the opening and closing HTML codes, and use it directly in any version of NEC accepting .NEC-format files. You may modify the reflector size using the guidance of past episodes of this series.

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CM Bent fan dipole-14-24-wiregrid
+CE
+GW 1 14 0 0 -.7 0 0 .7 .0159
+GW 2 14 0 -.1 -.7 0 -.1 .7 .0159
+GM 0 23 0 0 0 0 -.1 0 2 1 2 14
+GW 3 24 0 0 0 0 -2.4 0 .0159
+GM 0 7 0 0 0 0 0 -.1 3 1 3 24
+GM 0 7 0 0 0 0 0 .1 3 1 3 24
+GM 0 0 0 0 45 0 0 0 2 1 0 0
+GW 4 14 0 .1 -.7 0 .1 .7 .0159
+GM 0 23 0 0 0 0 .1 0 4 1 4 14
+GW 5 24 0 0 0 0 2.4 0 .0159
+GM 0 7 0 0 0 0 0 -.1 5 1 5 24
+GM 0 7 0 0 0 0 0 .1 5 1 5 24
+GM 0 0 0 0 -45 0 0 0 4 1 0 0
+GW 101 5 .57778 .075 -.131 .5 0 -.015 .004
+GW 101 5 .57778 -.075 -.131 .5 0 -.015 .004
+GW 101 3 .57778 .075 -.131 .5 0 -.131 .004
+GW 101 3 .5 0 -.131 .57778 -.075 -.131 .004
+GW 101 4 .5 0 -.131 .5 0 -.015 .004
+GW 102 1 .5 0 -.015 .5 0 .015 .004
+GW 103 5 .5 0 .015 .57778 .075 .131 .004
+GW 103 5 .5 0 .015 .57778 -.075 .131 .004
+GW 103 3 .57778 .075 .131 .5 0 .131 .004
+GW 103 3 .5 0 .131 .57778 -.075 .131 .004
+GW 103 4 .5 0 .015 .5 0 .131 .004
+GE 0 -1 0
+FR 0 14 0 0 265 10
+GN -1
+EX 0 102 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+FR 0 14 0 0 265 10
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
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Fig. 13 compares the 50-Ohm SWR curves for the new wire-grid model and for the large rod reflector that we have just reviewed. Any differences fall in the region of the subtle. At most, the wire-grid curve is displaced upward in frequency by under 1 MHz. There is a slight difference in curve shape in the area where the rod reflector rod lengths are near 1.4 wavelengths. In that area, the rod reflector shows a lower SWR value. However, at the upper end of the passband, the rod-reflector curve becomes steeper than the curve for the wire grid model, suggesting that the wire-grid version would sustain an SWR value below 3:1 for a greater frequency span than the rod version of the array.

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With narrow-band corner arrays, we noted that wire-grid models showed a peak gain that is slightly less than the peak gain available from a rod reflector with a 1.4 wavelength vertical dimension, due to the absence of a parasitic effect. We shall encounter the same phenomenon when examining the gain curves for the two arrays in Fig. 14.

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Peak free-space gain for the wire-grid model is about 13.48 dBi and occurs between 335 and 345 MHz, where the vertical dimension of the reflector is close to 1.6 wavelengths. These values are consistent with earlier results for narrower-band arrays using simply dipole drivers. At these frequencies, the side length is about 2.7 wavelengths. Quite clearly the peak gain of the rod reflector is noticeably higher. However, the rod reflector gain differential across the scanned passband is over 2 dB. The wire-grid model shows a gain differential of only 0.52 dB, and this differential includes the band-edge values that fall slightly outside the 2:1 SWR passband.

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The E-plane -3-dB beamwidth of the wire-grid version has a much narrower range of values than for the rod reflector. The beamwidth falls between 46 degrees at 265 MHz and 40 degrees in the 350-MHz region, followed by a gradual increase back to 46 degrees at the top of the SWR passband. However, by the time we reach the end of the scanned range, about 8 MHz higher than the end of the SWR range, the beamwidth increases to 54 degrees. The rod reflector starts with a wider beamwidth at the low end of the passband--54 degrees--and ends at 58 degrees at 395 MHz. The minimum value is 40 degrees at 315 MHz. The changes in beamwidth create an inverse curve relative to the gain values, with a sharp peak near the high-gain frequency. In contrast, the wire-grid model produces a shallow inverse of the equally shallow wire-grid gain curve.

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In contrast, H-plane curves coincide more closely with the front-to-back curves, when we smooth the latter to remove the peaks and valleys that appear when using 180-degree values. Both the rod and the wire-grid reflectors show a gradual shrinkage of the beamwidth by 8 degrees across the scanned frequency range. However, the rod reflector range goes from 36 down to 28 degrees, with a small dip in the vicinity of the frequency of highest gain. The wire-grid version ranges from 32 degrees down to 24 degrees, with no discernable dip.

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The advantage in front-to-back ratio of the wire-grid reflector over the rod reflector shows itself very clearly in Fig. 15. The wire-grid values show an ascending curve well into the upper third of the passband. However, in the area of 385 MHz, the vertical dimension is about 1.8 wavelengths and the side length has grown to more than 3 wavelengths. As we saw when scanning the large collection of narrow-band arrays, these are values marking the point where continued reflector growth becomes self-defeating.

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The sample overlaid patterns in Fig. 16 provide a glimpse at potential performance of the wire-grid version of the enlarged forward-bent fan dipole driver array. The tighter limits of gain variation show up in both the E-plane and the H-plane patterns. The E-plane patterns show a worst-case front-to-back ratio that is consistently in the 24-26 dB range, despite the use of the bent fan driver. The green line marking the pattern for the array at 8 MHz above the 2:1 SWR passband limit shows clear signs of degradation from the perspective of a clean single-lobe pattern. The increase in beamwidth that we have seen with previous wide-band patterns at the upper end of the range begins to bulge in development of what will become distinct forward side lobes, similar to those one derives from arrays using extended double Zepp (1.25 wavelength) elements. At 395 MHz, we are still a considerable ways from the appearance of such distinct side lobes, but they show as incipient (or, dare I say it, pregnant) bulges. In contrast, the H-plane patterns are completely normal relative to those we have viewed for the rod reflectors in this series.

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To avoid the upper-frequency E-plane pattern distortion, you may select a slightly smaller vertical dimension for the wire-grid reflector. A similar reflector using a 1.2 wavelength vertical dimension and 2.4 wavelength side lengths produces a cleaner--less bulgy--E-plane pattern at the upper end of the scanned range with no change in the SWR curve. The cost is slightly less gain across the passband--about 0.25 to 0.5 dB, depending on the frequency. As well, the front-to-back ratio is also slightly lower. However, the E-plane beamwidth changes by only 4 degrees across the entire frequency range scanned. Wherever pattern shape carries a high weight in the specifications for a wide-band antenna, the 1.2 wavelength vertical solid or screened reflector may be a good choice.

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The wire-grid reflector model is more likely to fit applications of very-wire-band applications of the corner array above 1 GHz. Hence, it has been useful to see in what ways solid surface or closely spaced screens will show differing performance curves from rod reflectors. One of the emergent sub-themes of these studies has been the differing behaviors of the two types of corner reflectors. Applying a very-wide-band driver to the corner reflector has both extended our understanding and confirmed earlier conclusions regarding these differences.

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One Has to End Somewhere

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The study of corner reflectors--even a modeling study using the techniques of this series or improved techniques--does not end here. However, for the level of general guidance and proof of principle, we should end at this point. Further work would not so much uncover added design principles as it would refine them. For many, the further work would be simply more of the same, while for a few, with task-driven design interests, the work would become too specific for general guidance.

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However, I hope that these studies do contribute in a small way to the understanding of corner reflectors, including the 180-degree version that I have dubbed the planar reflector. The design has untapped potential in 21st century applications. It is relatively simple to build and adjust, compared to other designs requiring finicky pruning of every element. In the UHF range, especially above 1 GHz, one can build arrays that are both sturdy and adjustable using essentially hardware store components. Moreover, for a very small investment in materials, we acquire a field ripe for endless experimentation.

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Whether oriented vertically for FM and similar services or aimed horizontally for point-to-point communications, the corner array likely deserves more than the archival treatment that it has received in the last two decades. Hopefully, these notes make a contribution to its revival.

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Updated 10-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX September, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Corner Reflector, VHF / UHF


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Corner Arrays for Personal Communications

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L. B. Cebik, W4RNL

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Corner arrays are much neglected antennas with wide-spread applications. They are inherently broad-banded: a simple dipole driver with a properly sized reflector is capable of about 100 MHz of consistent pattern properties and under 2:1 SWR in the 500 MHz region. As well, gain can be excellent for the antenna simplicity, ranging from over 10 dBi to about 14 dBi free space gain, depending upon the reflector size.

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An added advantage of the corner reflector is that it lends itself to somewhat casual building practices in the home shop--as long as one seeks only good or adequate performance rather than absolute peak performance. With the casual building and adjusting technique that we shall suggest, look for 10-11 dBi gain rather than the 14 dBi figure. In addition, many hardware, craft, and kitchen supply store materials can be pressed into service.

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In this design exercise, we shall explore corner reflectors for two frequency ranges: 800-900 MHz and 1800-2000 MHz. Both bands are used for personal communications. A common problem is home use of low power transmitting and receiving devices: from many suburban or country locations, they do not quite provide reliable communications with the nearest local relay tower. A few dB of gain over the built-in stub antenna can make a big difference in reliability. Of course, there will be a cable between the indoor antenna and the transceiver, so a few more dB are useful to overcome line losses.

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The corner reflector can be set for either horizontal or vertical polarization simply by turning the assembly 90 degrees. We can then use a 2-step procedure that I call "aim and adjust" to set up a corner reflector. Of course, having commercial test and measurement equipment on hand can peak the system, but the simple procedure often suffices for reliable communication.

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Corner Reflector Basic Ingredients

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Fig. 1 shows the basic ingredients of a monoband corner reflector. It consists of the pair of panels that form a 90-degree angle behind a simple dipole driver. The reflector can be sets of rods that parallel the driver, a screen, or a solid panel. For outdoor use, rods and screens that pass the wind are favored. However, for indoor use, solid panels will do well and are easier to obtain. Raiding the kitchen supply counter for cookie sheets is one easy route to reflector material.

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The size of the panels for this design exercise is about 8.3" across with an individual length of about 16.1". Such panels will yield a reflector that is 22.8" top-to-bottom and 11.4" front-to-back. We shall later discuss some home construction methods, but feel free to innovate. All dimensions will be given in inches. However, you can translate these into millimeters by multiplying all of them by 25.4.

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The exact size of the reflector is not critical, although the given dimensions are about the smallest that I would recommend. Rounding the dimension upward will do no harm. In fact, 9" by 12" sheets for the upper and lower sections would be very good indeed. We shall use the present reflector for both bands of interest--and one might use it for any band in between them.

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The dipole is cut for resonance near the middle of desired passband. My practice is to choose a frequency between 1/3 and 1/2 the way up the passband, since the SWR curve may not be completely symmetrical, rising slightly faster below the design frequency than above it. Of course, one needs a way to support the dipole. For the frequencies in question, a polycarbonate tube is likely best, but simple wood will work. There is no rule that the tube must be round: square and rectangular cross sections will work as well. For reasons that we shall spell out near the end, you might consider using brass or copper tubing for the driver element.

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Pass the tube and the feedline through the rear of the reflector. Add some mounting brackets. Then aim and adjust.

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A 800-900 MHz Version

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Modeling corner reflectors can typically use two techniques that reflect construction practices. One is to create a reflector from individual rods. A second is to create wire-grid assemblies for the two plates. I have modeled the present antennas on NEC-4 using both methods, along with wire grids with various size grid squares and grid-wire diameters. In general, the results coincide quite closely--closely enough to require no adjustments to the dimensions to achieve acceptable results. The calculated result presented here to illustrate corner reflector properties for the bands in question emerge from wire-grid models of the reflector.

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The only semi-critical element is the driver. For broadest bandwidth, fatter is better. The design frequency impedance will be in large measure a function of the distance of the driver from the reflector apex. I have somewhat arbitrarily set the mid-band SWR standard (resonant impedance) at 88 Ohms. Lower impedances result from moving the driver closer to the reflector apex; higher impedances require a larger spacing.

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For the 800-900 MHz range at the 88-Ohm impedance level, the distance of about 5.7" is fine. For most purposes, a 0.5" diameter dipole will require a 5.7" length. Reducing the dipole to 0.25" requires a length of 5.85". The broad-banded nature of the antenna allows rough interpolation and extrapolation for other driver diameters.

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Fig. 2 provides a mid-band azimuth pattern for the corner reflector. For the intended application, the pattern, gain, and beamwidth are quite good, allowing for precision aiming using signal strength alone as a guide. Showing further patterns would be an exercise in sameness, so the following table lists the performance reports of the model from 800-900 MHz. The driver is 0.25" in diameter.

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Frequency        Gain       F-B Ratio       Feed Impedance        88-Ohm
+  MHz            dBi          dB            (R +/- jX Ohms)       VSWR
+800              11.53      30.39           67.3 - j 18.7         1.434
+810              11.61      30.51           71.9 - j 13.2         1.299
+820              11.68      30.52           76.7 - j  8.0         1.184
+830              11.76      30.42           81.6 - j  2.9         1.086
+840              11.83      30.28           86.8 + j  1.9         1.026
+850              11.91      30.08           92.1 + j  6.4         1.088
+860              11.98      29.89           97.6 + j 10.7         1.167
+870              12.06      29.68           103.2 + j 14.6        1.247
+880              12.13      29.52           109.0 + j 18.2        1.327
+890              12.21      29.37           114.9 + j 21.5        1.406
+900              12.28      29.27           120.8 + j 24.4        1.483
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The total change of gain across the passband is about 0.75 dB, with a change of front-to-back ratio of 1.25 dB. The SWR curve appears in Fig. 3. Its smoothness results from the fact that the feedpoint resistance shows a total change of only about 53 Ohms, while the reactance range is about 43 Ohms.

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It is possible to design Yagis with similar gain values for the same range, but their front-to-back ratio values will generally be inferior by considerable amounts. Although such Yagis (generally about 12 elements) will show a flatter vertical dimension, they will be considerably longer: close to 48" long compared to the 1' front-to-back dimension of the corner reflector. Moreover, a Yagi requires careful replication of the design length and spacing of each element down to about a millimeter, which is often beyond casual home workshop capabilities.

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A 1800-2000 MHz Version

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The most standard practice to follow in designing a high-band version of the corner reflector would be to scale every dimension and obtain similar performance to the 800-900 MHz model just examined. However, to make the 1800-2000 MHz design worth noting, let's follow a different procedure. We shall retain the same corner reflector assembly and simply position a different driver to see what we get.

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Since the reflector is nearly twice as large as it needs to be as a recommended minimum, we should expect some changes in the upper-band pattern relative to what we saw for the lower band. Fig. 4 shows the mid-band pattern, which is typical of the patterns for all frequencies in the passband.

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Note that the pattern is not only a bit stronger, it also maintains that strength across a wider beamwidth--thus easing the aiming problem somewhat. The front to back ratio is above 40 dB across the passband, which makes differences from one frequency to another largely irrelevant.

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The driver for the assembly is spaced 2.5" from the reflector apex. A 0.25" diameter driver requires a 2.5" length, while a 0.125" driver needs to be about 2.55" long. Again, the arbitrary SWR standard will be 88 Ohms, although changing the driver spacing from the reflector apex can raise or lower this value to suit user needs.

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The following table provides passband data from the NEC-4 model to give some idea of the performance stability across the 200 MHz passband, using a 0.25" diameter driver.

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Frequency        Gain       F-B Ratio       Feed Impedance        88-Ohm
+  MHz            dBi          dB            (R +/- jX Ohms)       VSWR
+1800             12.58      42.35           65.5 - j 10.2         1.382
+1820             12.52      43.02           70.0 - j  7.7         1.282
+1840             12.46      44.22           74.7 - j  5.4         1.193
+1860             12.40      45.34           79.6 - j  3.4         1.115
+1880             12.33      46.53           84.6 - j  1.7         1.045
+1900             12.26      46.52           89.7 - j  0.3         1.020
+1920             12.22      49.20           95.0 + j  0.6         1.080
+1940             12.22      48.53           100.3 + j  1.2        1.140
+1960             12.22      48.64           105.6 + j  1.4        1.201
+1980             12.23      48.44           111.0 + j  1.1        1.261
+2000             12.24      49.28           116.3 + j  0.4        1.321
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The total gain change is only 0.36 dB, with a front-to-back range of 7.2 dB. The resistance range is 51 Ohms, while the reactance range is only 12 Ohms. The small reactance range results from using the out-sized reflector. The progression shows a reversal in the expected direction of reactance change at the high end of the band. The resulting SWR curve appears in Fig. 5.

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Had we reduced the diameter of the driver to 0.125", we would have seen a more normal reactance curve with a net change of 39 Ohms. Reducing the diameter of the driver, with adjunct changes in its length, increases the band-edge SWR value. Halving the diameter value given would increase the band-edge value by about 0.1 to 0.2. The corner reflector thus shows its stability with varying materials across a wide frequency range.

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Vertical Polarization

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The azimuth patterns that we have so far viewed are free space patterns. Reduce their values by about 2.1 dB to obtain the antenna's gain over a dipole. The resulting numbers will apply for any given height over any given terrain.

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For most Yagi designs below lengths that can be considered very long, positioning the antenna to obtain vertical polarization tends to yield a significantly wider beam width than when placed for horizontal polarization. In addition, side-lobe development--both forward and rearward--becomes quite pronounced, although hardly ever reaching the point of making the antenna unusable. Without element ends to confined side-lobe development, the vertically polarized Yagi places significant energy into them.

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Corner reflector are not immune to these effects, although in some cases, the effects are smaller than with Yagis of corresponding gain. See Fig. 6.

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The 850 MHz pattern of the vertically positioned corner reflector shows a considerable amount of energy to the sides. However, the -3 dB beamwidth is actually narrower than when the antenna is horizontally positioned (see Fig. 2). The high-band model also shows a similar phenomenon, although less pronounced due to the very high front-to-back ratio of the design used here. Compare the pattern in Fig. 6 with the one in Fig. 4. The narrowed beamwidth is especially notable, but not as much as the ovalization of the forward lobe.

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Nevertheless, both corner reflectors make excellent arrays to use with either horizontal or vertical polarization for the bands in question.

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A 2-Band Version

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A question that arose in course of these design studies was whether it is possible to develop a 2-band version of the array in order to be able to cover both bands with a single reflector. In general, the project seemed initially doomed because the high-band driver appeared to require a position closer to the reflector apex than the low-band driver. The result is excessive "illumination" of the low-band driver, which placed a small null in the center of the high-band pattern.

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However, if we are willing to accept some pattern changes on the high band, we can design a 2-band version of the corner reflector. The pattern changes appear in Fig. 7.

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The low band pattern changes are too slight to mention. The high-band changes show the results of the low-band driver playing a role in the formation of the pattern. The forward side lobes result from the fact that the low-band driver approaches the length of an extended double Zepp relative to the high-band frequencies.

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Fig. 8 shows the relative current magnitudes on the dual driver elements for the middle of the low band and the middle of the high band. On the low band, the current (about 40% of that on the low-band driver) on the forward short driver has little effect, since it functions at best as a low-efficiency director. On the high band, however, the rearward low-band driver with about 40% of the main driver current exerts a more significant effect on the pattern, largely because the peak current positions lie beyond the edges of the shorter driver.

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The actual driver system is a pair of phase fed dipole elements. Both are 0.25" in diameter, with the low-band driver spaced 5.7" from the reflector apex. The shorter high-band driver is 9.0" from the apex. The low-band driver is 5.7" long, while the high-band driver is 3.3" long. Note that the low-band driver is positioned normally relative to the independently driven array we have already examined. The high-band driver is longer than it would be for independent use in an array.

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The two drivers are connected by an 80-Ohm phase line, with a reversal of connections. Such a line can be constructed of aluminum or other metal straps or bars. For 0.5" wide straps, the required spacing is about 0.23". For 0.375" straps, the spacing is 0.17", while 0.625" straps need 0.28" of spacing. One set of elements requires holes in the facing strap to effect the reverse connection, and the dipole ends will be slightly out of alignment vertically so that the elements can pass each other. Because any given deviation from "perfect" construction tends to have larger effects with increasing frequency, I would recommend that the offset construction be applied to the low-band driver.

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The assembly is design for a 75-Ohm feed system, with the feeder connected to the front or high-band driver. Fig. 9 shows the 75-Ohm SWR curves for the two bands. Although not truly outstanding, these curves should be quite serviceable for the array.

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The following table provides band-edge and mid-band performance figures for the 2-band corner reflector array.

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Frequency        Gain       F-B Ratio       Feed Impedance        75-Ohm
+  MHz            dBi          dB            (R +/- jX Ohms)       VSWR
+Low-Band
+800              11.51      31.34           64.2 + j 17.8         1.349
+850              11.88      30.99           61.2 + j  0.2         1.225
+900              12.26      29.74           51.4 - j  4.7         1.469
+High-Band
+1800             13.34      29.27           75.6 - j 21.7         1.333
+1880             14.90      30.92           69.0 - j 23.6         1.401
+1900             15.15      30.83           67.7 - j 29.0         1.517
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The low-band performance almost exactly tracks the performance of the monoband version we studied. Of course, there are variations in the feedpoint impedance values relative to the monoband version. However, for the high band, note the increasing gain and the fairly wide range (1.8 dB) of variation across the band. Since all gain values exceed those of the monoband high-band model, the variation is likely to be acceptable.

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In general, I would not recommend attempting construction of the 2-band corner reflection in anything less than a very well-equipped shop that permits both precision construction and accurate measurement for adjustment. The number of variables involved in the driver assembly call for more than casual assembly of approximate component pieces.

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A Few Construction Suggestions

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Casual construction of either monoband version of the corner reflector array is another matter--one well within shop capabilities. Fig. 10 sums up a few initial suggestions.

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The reflector plates can be formed from flat plate by using a metal brake or even a bench vise with metal or wooden extensions to create the angular edges. A 0.5" to 1.0" edge lip on each plate, bent to 45 degrees, will allow mating of the two plates to create the correct assembly. A series of nuts and bolts along the joined edges will secure the reflector well-enough for indoor use.

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Before assembly--indeed, before bending--it is wise to plan for the feeder tube. The right portion of the sketch shows a hole in the center of the reflector apex. Although a round tube is shown, a square or rectangular polycarbonate or substitute version can be used. Each plate from the bend forward needs to be opened for half the tube. In general, extend the opening about 1.414 times the radius of the tube (or half the vertical face of a rectangular tube). Also remove metal from the edges so that the tube can pass all the way through the reflector apex.

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You can secure the tube to the edge flange with metal strips that form clamps. For indoor use, such clamps will be more than secure enough if they are simply very tight across the tube. Being able to loosen the clamps to permit driver positioning is wise. Added metal straps can be placed at the outer corners of the reflector apex flange to hold u-bolts or other mounting hardware.

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The dipole might well be made from copper tubing (or craft-store brass) so that you can solder the feedline leads directly to each half of the dipole. Avoid adding excessive lumps to the dipole. As well, a toothpick or other short piece of wood dowel (fiberglass would be best if available in this thin diameter) can run across the gap in the dipole inside the tubing to ensure alignment of the two sides. How the dipole is affixed to the tube depends on the material at hand, but a very slightly undersized slot at the front of the tube might allow a useable pressure fit.

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Setting up the corner reflector involves aiming and adjusting. First, set the reflector for the correct polarization. Next, aim the reflector array at the target relay antenna, using signal strength as a guide. Then, slide the dipole forward and backward from its initial position until both the transmitted and received signal are maximum. Finally, clamp the dipole tube in place. Although this procedure does not qualify as precision adjustment, it may well suffice to bring signals in both directions well above the threshold of reliability.

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If a 9 by 12 by 22 inch assembly can fit available space and if greater signal reliability is needed on either of the two bands we have considered (or anywhere in between as well), then a corner reflector array from the pantry and plumbing shop might be the easiest (and cheapest) route to success.

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Updated 10-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for September, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Corner Reflector, VHF / UHF


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Circling the Square Quad

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L. B. Cebik, W4RNL

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A question posed to me every now and then is whether the circumference of a circular quad loop and the circumference of a square quad loop--both with the same diameter wire and the same resonant frequency--are the same. It is an interesting question, since without any analysis, it seems to have a simple answer. However, like most questions of its type, it hides numerous complexities, some related to the motivation for the question, others related to the variables involved in developing some kind of reliable answer.

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Setting the Circular Loop in Its Context

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Since the most common form of quad loop used by VHF operators is square, one must wonder why the urgency to turn to a circular loop. The square loop normally uses 4 non-conductive spokes to support the corners of a wire square, where the wire may run from AWG #14 copper to about 0.25" thin-wall tubing. At 2-meters (146 MHz, as a target frequency), this diameter range runs from 0.0031 wavelength to 0.00079 wavelength, a 4:1 ratio between the largest and smallest diameters in the set. Smaller wires present the fewest construction complications, although they show the smallest operating bandwidth for a given quad design.

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Circular loops, on the other hand, challenge the builder. There are some commercial 2-meter quads using flat strap loops in order to obtain a round shape with only 1 mounting point to a boom. However, we shall have to confine ourselves in these notes to round wires, which do not enter a perfectly round shape--or sustain it--with great ease. Hence, we once more must inquire into the motivation for building a quad array with circular loops.

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Among novice antenna builders, there lurks a danger: learning something as a one-line generalization. The applicable general statement most often quoted to me is that a circular loop has the highest gain possible, higher than a square loop. Hence, it makes sense to strive for a circular-loop quad rather than settling for a square-loop quad. There are only 2 difficulties opened by this generalization.

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First, as portrayed in Fig. 1, the generalization is incomplete in its context. As shown in the top portion of the figure, it is more proper to say that among symmetrical loops, the circular shape has the highest gain of all of the possible polygon substitutes. The greater the departure from circularity, the lower the gain, if we maintain a regular polygon shape.

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The lower half of the figure expands the context. It shows the symmetrical or regular polygon in the center--with a feedpoint shown--between two alternative configurations, one with higher gain and one with lower gain. As shown in numerous sources, as we stretch the axis between the feedpoint and its opposite side--maintaining resonance throughout--the rectangle increases in gain as those sides approach a separation of 1/2 wavelength. There are limits to this process. One is physical: we cannot make a rectangle that is 1/2 wavelength long and still have a resonant rectangle. A second reason emerges from the properties of the necessary wire implementation of the rectangle. Wire losses will set a point, one that varies with wire diameter and composition to the shape of the rectangle, that yields the highest gain. A final consideration is the feedpoint impedance that decreases as we stretch the rectangle to increase gain. At some point, the resonant impedance becomes too low for effective use.

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At the other end of the figure are rectangles fed along their longer sides. These rectangles show lower gain and higher feedpoint impedances than symmetrical polygons. The stretched rectangles with feedpoints on the short side, especially vertically polarized versions, are widely used in the lower HF region, to obtain gain over simple vertical antennas in a bi-directional pattern. They require construction techniques that fall within the abilities of many amateur antenna builders and so have developed a niche for themselves.

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The stretched rectangle offers a considerable gain advantage over a square loop, about 1 dB for versions presenting a feedpoint impedance close to 50 Ohms. (A resonant square loop has a feedpoint impedance in the 120-130-Ohm range, depending upon wire size.) What we are missing in the case of comparing a circular loop to a square loop is a quantification of the amount of gain advantage that it has over a square. As well, we have no translation of the gain of a single circular loop over a square relative to the gain advantage of a circular-loop quad beam over its counterpart square-loop version.

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As well, we have no easy answer to the question of whether a circular loop having the same circumference as a counterpart square loop will also have the same resonant frequency. If not, we shall need an adjustment factor. This factor will normally be relative to the loop circumference of a square, since most available quad designs in the literature use square loops.

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I have in the past suggested an empirical method of determining the adjustment factor. At 2-meters (146 MHz will be our design frequency throughout this exercise), build a single resonant square quad loop. Then, using the same wire, build a circular loop, adjusting its circumference for resonance at the same frequency as the square. The ratio of the two circumferences will be the adjustment factor for all of the elements in the array being rounded--if there are no other design variables to consider.

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A modeling approach to the question is necessarily limited, since NEC and MININEC models must use straight-wires to form a polygon that approaches circularity. However, even within this limitation, modeling offers some advantages over the empirical approach, since we may use as our subject antennas arrays of some complexity. Remember that part of our question involves--beyond a simple adjustment factor for loop circumference--an inquiry into whether there may be additional design considerations in the conversion. In other words, will a circular-loop beam have the same operating characteristics as its square counterpart across a given operating passband?

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Arbitrarily--although based on some experience in designing quad beams--I selected a 3-element quad beam optimized for maximum gain at the center of the 2-meter band as a worthy test case. The use of a high gain design means that the gain, front-to-back, and impedance curves will be sharp enough to observe any shifts between square and near-circular versions. As well, a 3-element beam would provide an indication of the gain advantage of going circular, relative to the square, and do so in a context that would preclude a common error. If we developed a gain advantage for a single loop over a square, then some novice antenna buffs would simply add that gain for each new loop appended to the array. Unfortunately, antennas tend not to work that way. A geometry-based gain increase occurs once, and that advantage tends to be the total that we may gain for a parasitic array of any complexity.

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Now for a limitation: we shall not be able to model a circle. However, we may model both a hexagon and an octagon. In this way, we may approach the situation with a circle, and the trends developed by modeling both a hexagon and an octagon as the loops for a 3-element quad beam may be of some assistance in extrapolating values for a circle.

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Some Basic Geometry of Loops

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On the road from a square to a circle, we shall initially wish to develop quad beams having the same loop circumferences for all versions. Then, by adjusting the loop sizes, we may determine the required hexagon and octagon loop circumferences needed. We may next calculate an adjustment factor, and possibly even extrapolate to a reasonably reliable adjustment factor for circular loops.

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The first step in the process is to understand something about the geometries of our subject loop shapes. Fig. 2 summarizes the results of a little exercise in trigonometry.

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We know that the circumference of a circle is 2 times PI times the radius of the circle, and that the inverse lets us compute the radius from the circumference. The figure gives us the final numbers to 4 decimal places.

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We may use simple trig relationships to find the relationship between the circumference of almost any polygon and a focal line, if we first determine what we shall call the focal line. The simplest line runs from the polygon center to a corner--the fx lines for the 3 shapes shown. We shall use the same type of focal line in each case for consistency.

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For the case of the square, the line designated fs is 1/2 the square root of 2 (that is, 0.5 SQR(2)) times the length of a side, which is 1/4 of the total circumference. That means the circumference is the given value in the sketch relative to a focal line, fs, of any length.

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The hexagon is the easy case, since we can build one by using a collection of equilateral triangles. Hence, the focal line, fh, is the same length as any one side. The circumference is 6 times the length of fh.

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The octagon seems more complex simply because we are not used to working with 22.5-degree angles. However, 1/2 the length of any side is the sine of 22.5 degrees times the length of the focal line, fo. Once we have the length of a half-side, we multiply by 16 to obtain the circumference.

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Notice that the relationship between the circumference and focal line of the octagon is rapidly approaching the relationship between the circumference and radius of a circle. For many purposes, modelers often use octagons as adequate approximations of a circle. However, we shall not stop with the octagon. We shall use the trends developed by going through the hexagon to see if we cannot approximate what a circular loop should use as its circumference. The result will not be precise, because our steps from the square to the circle--in terms of the ratio of C to fx--are not regular. As well, our modeling will itself be subject to some limitations of precision. Nevertheless, we may be able to produce a reasonable value for the backyard builder, along with some other considerations for him to evaluate.

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A Matter of Process

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To start on our process, we need a source of square quad designs. I used the NEC-Win Plus equation-based model for a 3-element "high gain" quad (in contrast with a "wide-band" design using the same number of elements). The model is available from the Nittany Scientific (web.archive.org) web site, and a simple calculating program in Windows form can be downloaded from the web site under "New Quad Studies".

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Also see the Antenna Modeling Programs page.

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Fig. 3 shows the equations screen for the model for a square 146-MHz quad using 0.125" diameter elements. This model requires only the revision of the variables for the wire diameter in the units of measure selected for the model and the design frequency (variables G and H). The remaining variables are calculated to yield half-side lengths and reflector to driver or director spacing for use in the model itself.

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By multiplying the side half-lengths times 8, we obtain the circumference of each element. We may then use the relationships in Fig. 2 to obtain the focal line values for either hexagon or octagon versions of the model having loops with the same initial circumference. However, each type of model requires its own set-up.

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Fig. 4 shows the basic set-up for a hexagon model. Each loop has two end point at Z=0 and X = fh. The upper and lower points on the perimeter of the hexagon require an X-value that is the sine of 30 degrees and a Z-value that is the cosine of 30 degrees, with +/- signs as appropriate to the position of a point relative to the central or boom line (Y-axis). Fig. 5 shows the variables on the equations page. One might more fully automate the process, but this method was simple enough for our test cases.

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The hexagon array requires 18 wires for a 3-element quad, compared to only 12 for the square-loop version. Each side of the square quad used 11 segments, and each loop has 44 segments. A comparable number of segments per side for the hex is 7, resulting in 42 segments per loop. The use of an odd number of segments on each side ensures that the feedpoint segment is exactly centered on one side wire of the driver loop. The octagon loops use 5 segments per wire, for a total of 40 per loop. The total number of wires in the octagon model grows to 24.

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However, before moving to the octagon model, let's note in advance that the converted models do not resonate at 146 MHz, despite using loops with the same wire diameter, circumference length, and element spacing as the square models. To facilitate global re-scaling and then return the wire size and element spacing to their original values, I transferred the initial hex model to EZNEC. This program is also compatible with EZPlots, by AC6LA, from which I could make rapid graphs of gain, front-to-back ratio, feedpoint resistance and reactance, and SWR after making a frequency sweep across 2 meters at 0.25-MHz intervals. Fig. 6 shows the final wire table, after all adjustments, for one of the test cases.

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Note the X-coordinate in line 2. From zero to this point is the half-length of one side of the hexagon. Hence, 12 times the absolute value of the coordinate yields the circumference of the loop. It was thus possible to adjust the model for near resonance at 146 MHz and later return to find the resulting loop circumferences and what degree of adjustment was necessary relative to the square model. In all cases, element spacing and wire diameter are the same between models in a test sequence.

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When we move to the octagon version of the 3-element quad, we need a different set-up for the 8 wires in each loop. Fig. 7 shows the general set-up. You can correlate the variables A, B, and C to the focal line lengths calculated for the octagon to the values for the initially used loops with the same circumference in the square quad base-line model. Variables D and E designate the element spacing, counting from the reflector forward. Variables G and H simply list the sine and cosine of the relevant angles involved in calculating the corner coordinates. That angle was 30 degrees for the hexagon and is 22.5 degrees for the octagon. All octagon coordinates are functions of either the sine or the cosine of 22.5 degrees applied to the focal line length for each of the three loops. All of these variables for the octagon appear in a sample equations page in Fig. 8.

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For ease of multiple-wire adjustments and some graphing via EZPlots, I once more transferred the model to EZNEC. The final values for one of the test models appear in Fig. 9. Note once more the X-coordinate in line 2 of the wire table. The absolute value of this coordinate is 1/2 the length of one side of the octagon. Hence, 16 times that value yields the circumference of the loop. As with the hexagon arrays, I brought each octagon array to the same near resonant condition as in the square array original, using the same element spacing and the same wire diameter. (Note that the screens used to illustrate the process do not necessarily represent the same test model.)

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A Sample Test Run

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The 3-types of loops yield quads that look both similar and oddly different. Fig. 10 provides to-scale outlines of each type of 3-element quad.

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Although the main elements of comparison among the square, hexagon, and octagon arrays are easily observable from data tables, it may be useful to do a bit of graphic analysis on at least one array as a guide to interpreting the tables. For this sample run, I shall use 0.125" diameter wire and look at the square and the octagon versions of the quad after optimizing the octagon version for resonance at 146 MHz.

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Beginning with the square quad properties over the 2-meter band, we may look at the gain and front-to-back curves in Fig. 11. Note that the gain and front-to-back peaks are well centered in the passband. The front-to-sidelobe ratio is a measure of the worst-case front-to-back ratio for the array. It will always be a curve that either overlays the 180-degree front-to-back curve or departs from it in a shallower curve at somewhat lower values.

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Fig. 12 shows the comparable curve for the adjusted octagon array using the same wire size and element spacing. For the same resonant frequency, the octagon version shows a 180-degree front-to-back peak slightly above mid-band and a gain peak very much above mid-band. This pattern appears in all of the quasi-rounded versions of the arrays and indicates that changing shape has consequences for the performance curves.

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Fig. 13 shows the original square quad with its near resonance at 146 MHz. Although we may trace with care the feedpoint resistance and reactance curves, we may use the band-edge 50-Ohm SWR as check points referenced to the right Y-axis scale. Now examine Fig. 14 for the same points. This graph of feedpoint values is for the octagon version of the array. We note that the band-edge SWR values are higher than for the square quad, indicating that the quasi-rounded quads have slightly narrower passbands than the initial square version. As we examine the tabular results, we shall note that the narrowing passband applies to more categories of performance than just the 50-Ohm SWR.

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The Tabulated Results

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I created 2-meter 3-element quads with wire diameters of 0.25", 0.125" and 0.0625". The 2:1 wire size differentials provided a large wire-size range with a small number of samples. Each quad initially used a square version developed from the automated model program, with derived and adjusted hexagon and octagon versions. The models used perfect/lossless wire, although the differences between this selection and either copper or aluminum are not significant. Each derived model was adjusted until nearly resonant at 146 MHz, the near-resonant frequency of the original square model.

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The following tables provide modeled free-space data at 144, 146, and 148 MHz for each of the models. Each model was subject to the Average Gain Test (AGT) to verify its adequacy. The worst value was 1.005, representing a maximum gain report error of 0.02 dB.

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+                  0.25" Diameter Wire:  3-Element Quads
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+Square:  AGT: 1.005 = 0.02 dB
+Frequency                   144             146             148
+Gain dBi                    9.53            9.62            9.61
+180-deg F-B dB              18.27           30.10           18.68
+Feed Z (R+/-jX Ohms)        44.5 - j29.0    49.7 - j 0.7    54.1 + j28.6
+50-Ohm SWR                  1.851           1.015           1.732
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+Hexagon:  AGT:  1.005 = 0.02 dB
+Gain dBi                    9.66            9.78            9.79
+180-deg F-B dB              17.14           26.50           19.57
+Feed Z (R+/-jX Ohms)        44.2 - j29.7    49.2 - j 0.3    53.7 + j30.5
+50-Ohm SWR                  1.884           1.017           1.794
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+Octagon:  AGT:  1.004 = 0.02 dB
+Gain dBi                    9.69            9.82            9.85
+180-deg F-B dB              16.64           25.13           19.88
+Feed Z (R+/-jX Ohms)        44.0 - j30.6    48.9 - j 0.7    53.3 + j30.5
+50-Ohm SWR                  1.919           1.027           1.796
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+                 0.125" Diameter Wire:  3-Element Quads
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+Square:  AGT: 1.004 = 0.02 dB
+Frequency                   144             146             148
+Gain dBi                    9.48            9.56            9.52
+180-deg F-B dB              17.26           30.91           17.24
+Feed Z (R+/-jX Ohms)        45.2 - j32.8    51.4 - j 0.2    56.2 + j33.1
+50-Ohm SWR                  1.980           1.028           1.868
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+Hexagon:  AGT:  1.003 = 0.01 dB
+Gain dBi                    9.61            9.73            9.72
+180-deg F-B dB              15.95           27.10           18.52
+Feed Z (R+/-jX Ohms)        44.7 - j34.9    50.6 - j 0.9    55.5 + j34.0
+50-Ohm SWR                  2.074           1.022           1.901
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+Octagon:  AGT:  1.002 = 0.01 dB
+Gain dBi                    9.65            9.78            9.78
+180-deg F-B dB              15.70           25.79           18.70
+Feed Z (R+/-jX Ohms)        44.7 - j34.9    50.4 - j 0.6    55.3 + j35.0
+50-Ohm SWR                  2.078           1.013           1.935
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+                 0.0625" Diameter Wire:  3-Element Quads
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+Square:  AGT: 1.003 = 0.01 dB
+Frequency                   144             146             148
+Gain dBi                    9.42            9.50            9.43
+180-deg F-B dB              16.31           31.58           16.07
+Feed Z (R+/-jX Ohms)        45.8 - j37.0    53.1 - j 0.4    58.3 + j36.7
+50-Ohm SWR                  2.138           1.062           1.981
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+Hexagon:  AGT:  1.002 = 0.01 dB
+Gain dBi                    9.56            9.69            9.65
+180-deg F-B dB              15.36           28.49           17.14
+Feed Z (R+/-jX Ohms)        45.5 - j38.3    52.3 - j 0.1    57.8 + j38.9
+50-Ohm SWR                  2.199           1.046           2.060
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+Octagon:  AGT:  1.002 = 0.01 dB
+Gain dBi                    9.60            9.74            9.71
+180-deg F-B dB              14.85           26.70           17.63
+Feed Z (R+/-jX Ohms)        45.3 - j39.7    51.9 - j 0.9    57.3 + j38.7
+50-Ohm SWR                  2.264           1.043           2.053
+
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+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1. Changes in Performance: For each wire size, we can observe 2 phenomena. First, the operating passband in each category of performance narrows a small amount as we move from the square to the hexagon to the octagon. Second, the peak performance shifts upward in frequency relative to the resonant frequency of the array.

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The most likely reason for these changes in performance as we gradually round the shape of the quad loops is that the mutual coupling between elements also changes. Remember that we scaled the loops but retained the spacing of the initial square-quad version.

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Therefore, although a quad adapted from a square to an octagon (and, by extension, a circle) may provide satisfactory performance for a given design passband, further optimizing to center the performance peaks at the design frequency is both possible and recommended.

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2. Changes in Peak Gain: As we gradually round the corners of a quad, we see an increase in peak gain. From a square to an octagon, the rise is about 0.24 dB for each of the wire sizes. about two-thirds of the rise occurs in the shift from a square to a hexagon. Hence, the further rise from an octagon to a circle is only likely to create a total gain increase of 0.3 dB over a square quad.

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Whether the gain increase--assuming that one also re-optimizes the array to place performance peaks at the design frequency--is justified is a builder/user decision, most likely based upon the degree of difficulty in the re-design and the construction of the circular elements. A 0.3-dB change of forward gain would not normally be detectable in array operation, since it is just about 5% of 1 S-unit.

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The following table provides element circumferences and element spacing for the arrays whose performance data we have just observed. All dimensions are in inches. Element spacing is listed only once for the square loop, since it is the same for all 3 arrays in each set.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+                  0.25" Diameter Wire:  3-Element Quads
+
+Element or Spacing               Square           Hexagon         Octagon
+Reflector                        88.552           86.793          86.070
+Driver                           83.749           82.085          81.401
+Director                         79.243           77.669          77.022
+Reflector-Driver Spacing         14.150
+Reflector-Director Spacing       32.174
+Circumference Ratio Relative to Square Loops      0.9801          0.9720
+
+                 0.125" Diameter Wire:  3-Element Quads
+
+Element or Spacing               Square           Hexagon         Octagon
+Reflector                        87.515           85.957          85.359
+Driver                           83.349           81.865          81.296
+Director                         79.300           77.888          77.347
+Reflector-Driver Spacing         14.193
+Reflector-Director Spacing       32.243
+Circumference Ratio Relative to Square Loops      0.9822          0.9754
+
+                 0.0625" Diameter Wire:  3-Element Quads
+
+Element or Spacing               Square           Hexagon         Octagon
+Reflector                        86.739           85.402          84.840
+Driver                           83.042           81.761          81.222
+Director                         79.337           78.114          77.599
+Reflector-Driver Spacing         14.244
+Reflector-Director Spacing       32.277
+Circumference Ratio Relative to Square Loops      0.9846          0.9781
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As we increase the wire diameter, the required amount of circumference shortening increases. To determine if the increase was predominantly a function of wire size or whether array design played a significant role on the adjustment factor, I turned to a second 3-element array for which there is an automated design model and program. The wide-band design calls for dimensions significantly different from those of the high gain design so that a variation ought to appear in the correction factor, at least for the octagon version. Therefore, I created a wide-band model using 0.0625" diameter lossless wire for a square-loop array centered at 146 MHz. I then re-calculated the array for octagon loops and adjusted it for near-resonance at 146 MHz, using the same procedure as on the previous arrays.

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The following tables summarize the performance data and the dimensions of square and octagon versions of the wide-band quad beam. Since the feedpoint impedance is close to 70 Ohms, both 50-Ohm and 75-Ohm SWR values are listed.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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+            0.0625" Diameter Wire:  3-Element Wide-Band Quads
+
+Square:  AGT: 1.003 = 0.01 dB
+Frequency                   144             146             148
+Gain dBi                    9.11            8.99            8.78
+180-deg F-B dB              15.78           34.02           17.76
+Feed Z (R+/-jX Ohms)        55.7 - j37.2    72.6 - j 0.6    88.6 + j31.6
+50-Ohm SWR                  2.012           1.452           2.081
+75-Ohm SWR                  1.891           1.034           1.520
+
+Octagon:  AGT:  1.002 = 0.01 dB
+Gain dBi                    9.33            9.29            9.12
+180-deg F-B dB              14.07           26.01           20.06
+Feed Z (R+/-jX Ohms)        54.8 - j40.3    70.8 - j 1.0    87.3 + j34.6
+50-Ohm SWR                  2.132           1.416           2.121
+75-Ohm SWR                  1.992           1.061           1.568
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+            0.0625" Diameter Wire:  3-Element Wide-Band Quads
+
+Element or Spacing               Square                Octagon
+Reflector                        87.086                85.179
+Driver                           82.320                80.517
+Director                         75.922                74.260
+Reflector-Driver Spacing         13.155
+Reflector-Director Spacing       35.914
+Circumference Ratio Relative to Square Loops           0.9781
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The octagon version of the wide-band array shows a variable increase of gain over the square version, because the true gain peak of the square version lies just below the lower limit of the operating passband. However, a peak increase of about 0.3 dB appears possible. As with the high gain design, we note a slight narrowing of the operating passband as we round the square into an octagon.

+

Since the octagon circumference ratio relative to the square version is identical for both the high gain and the wide-band designs to 4 decimal places, it is likely that we may ascribe the changes in the ratio values to the wire size changes alone.

+

From Octagon to Circle

+

The circumference ratios derived from the exercise are listed to 4 decimal places as a simple function of the calculations involved. It is unlikely that any backyard builder would be able to use values of more than 2 significant figures. In general, then, if the wire size is greater than about 0.1", a correction factor of 0.97 is adequate and for wires 0.1`" and less, 0.98 is adequate.

+

However, these values apply only so far as we round a square to an octagon. If we return to Fig. 2, we shall find that an octagon has a ratio of focal line to circumference that is only about 3/4 of the way from the corresponding ratios for a square and for a circle. Further extrapolation may be necessary to arrive at factors applicable to a circle, if we use the square loop as a starting point.

+

It is therefore likely that for wire sizes greater than about 0.1" diameter, a final correction factor of 0.96 would apply, and for wires sizes less than 0.1" diameter, a correction factor of 0.97 would be closer to the mark--when moving all the way from a square quad to its circular counterpart. (See the Appendix for a further refinement of these numbers based upon a 16-sided loop model.)

+

The design considerations that we have observed from the compilation of performance data place a further caution on the application of any such correction factors. The movement of the peaks in the performance curves as we made the transition from a square through a hexagon to an octagon strongly suggest that a circular design requires careful optimization to return those peaks to the vicinity of the design frequency. This process may result in changes to the element spacing and the loop circumferences. Hence, the correction factor may turn into different numbers for each of the loops in the array, plus a pair for the element spacing.

+

As a simple example of further optimization, we can restore the position of the front-to-back ratio peak by scaling the element spacing as well as the loop sizes once we discover where the initial octagon's resonant frequency is. However, as shown in Fig. 15, the gain peak remains high in the passband (even though the total gain change across the band is only 0.13 dB). This model is a further modification of the high gain quad with 0.25" diameter elements. On balance, relative to our earlier octagon model, we give up a tiny bit of gain but acquire a better bandwidth for higher front-to-back ratios.

+
+ +
+

As well, the resistance, shown in the feedpoint graph in Fig. 16, reaches 50 Ohms well above the mid-band point, suggesting slight changes in the size or spacing of the reflector. However, these changes will create changes in the other curves that we are trying to balance in a perfectly optimized quad array.

+
+ +
+

For reference, the following tables present a comparison of the performance and the dimensions of the 0.25" element octagons under our initial assumptions and with the further refinements of element spacing.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+      3-Element High Gain Octagon Quad Performance: 0.25" Diameter
+
+With Square Version Element Spacing
+Frequency MHz               144             146             148
+Gain dBi                    9.69            9.82            9.85
+180-deg F-B dB              16.64           25.13           19.88
+Feed Z (R+/-jX Ohms)        44.0 - j30.6    48.9 - j 0.7    53.3 + j30.5
+50-Ohm SWR                  1.919           1.027           1.796
+
+With Scaled Element Spacing
+Frequency MHz               144             146             148
+Gain dBi                    9.67            9.78            9.79
+180-deg F-B dB              18.39           30.67           19.08
+Feed Z (R+/-jX Ohms)        43.6 - j29.2    48.2 - j 0.0    52.0 + j30.5
+50-Ohm SWR                  1.876           1.038           1.805
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+         3-Element High Gain Octagon Dimensions: 0.25" Diameter
+
+Element or Spacing               Square Spacing        Scaled Spacing
+Reflector                        86.070                86.185
+Driver                           81.401                81.510
+Director                         77.022                77.125
+Reflector-Driver Spacing         14.150                13.772
+Reflector-Director Spacing       32.174                31.314
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

These maneuvers, of course, apply to the octagon. Given the changes in the curves as we moved from the square to the octagon, we can expect further movement in the same directions as we approach a true circle for the quad loops. Hence, optimization of the octagon is an indicator of, but not a guarantee of, the performance of a quad with perfectly circular loops.

+

Anyone who wishes to design a true circular element quad with NEC or MININEC software should therefore begin with a polygon of at least 12 to 16 sides. Although the dimension shown in this exercise form a starting point for the design, they will require careful re-sizing to arrive at a truly satisfactory design that assures that we obtain the full 0.3 dB gain over a square that circular loops offer at the frequency on which we wish to have that gain.

+

Appendix: Going to 16-Sided Loops

+

After adjusting the element spacing for the 8-sided loop to restore some of the performance curves as we round the square loop quad beam, I decided to create a 16-sided loop version of the array. The techniques for generating a 16-sided loop are an extension of those used to create the octagon, so we may by-pass them and go straight to the results. These results will be based on adjusting or re-scaling the element spacing along with the loop circumference as we bring the array to near resonance at 146 MHz.

+

As suspected, the 16-sided version of the array required further adjustment beyond the 8-sided loop version. The following table provides the dimensions in parallel columns for the initial square version, the octagon, and the added 16-sided version, all using lossless 0.25"-diameter wire.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+         3-Element High Gain Octagon Dimensions: 0.25" Diameter
+
+Element or Spacing               4 sides        8 sides      16 sides
+Reflector                        88.552         86.185       85.418
+Driver                           83.749         81.510       80.784
+Director                         79.243         77.125       76.438
+Reflector-Driver Spacing         14.150         13.772       13.649
+Reflector-Director Spacing       32.174         31.314       31.035
+Adjustment Factor Relative to Square Loops      0.9733       0.9646
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

A 16-sided loop has a focal-line-to-circumference ratio of 0.1602 compared to a circle's 0.1592. The inverse values are 6.2832 for the circle and 6.2429 for the 16-sided loop. The 16-sided loop is close enough to a circle that we may reaffirm the recommended correction factors developed only by going to an 8-sided loop model. When moving from a square to a circle, for wires fatter than about 0.1" diameter, multiply all dimensions (that is, circumferences and element spacing) by about 0.96. For wires less than about 0.1", use a multiplier of 0.97. These values tend to confirm the extrapolation performed on the basis of the octagon version of the quad. However, we now strongly suggest that the builder apply the adjustments to the element spacing as well as the element circumference.

+

The modeled free-space performance of the 16-sided model appears in the following table.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+      3-Element High Gain 16-Sided Quad Performance: 0.25" Diameter
+
+Frequency MHz               144             146             148
+Gain dBi                    9.67            9.78            9.80
+180-deg F-B dB              18.39           31.26           19.19
+Feed Z (R+/-jX Ohms)        44.0 - j30.1    48.1 - j 0.4    51.4 + j30.5
+50-Ohm SWR                  1.901           1.040           1.809
+
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As the table suggests, the gain curve continues to move higher in the passband as we further round the corners of the loops. However, it is possible to use the adjustment factor to center the front-to-back curves, as shown in Fig. 17.

+
+ +
+

The form of adjustment developed here also allows the SWR curve to remain well centered in the passband, as revealed in Fig. 18. However, as we saw in the move through the hexagon and the octagon, the operating passband continues to narrow. As well, the resistive component of the feedpoint impedance continues to slowly decrease. However, nothing in the progression of charts suggests that a true circular loop version of the array would not--using 0.25" diameter elements--meet a 2:1 50-Ohm SWR limit at the band edges.

+
+ +
+

The bottom line, then, is that we may adjust a square quad to a circular loop quad by adjusting both the loop circumferences and element spacing. However, we should expect a slight reduction in the operating bandwidth. As well, the design might well use further optimizing to return the gain peak to the design frequency.

+
+ +
+

Updated 05-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for April, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Quad, VHF / UHF


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Modeling the Double-Diamond for UHF

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+

L. B. Cebik, W4RNL

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+
+

The double-diamond quad has become a "hot" antenna in Europe. Introduced in Germany some years ago, the antenna has "taken off" and become somewhat a darling among home-brew antenna fans, especially on 432 MHz, where the usual double-diamond array can cover all of the band.

+

Two recent articles in antenneX have featured the double twin quad in various arrays, along with certain circumspectly veiled claims for its gain. As well one of the articles noted that I would try to model the antenna, so I guess I had better do some work. But first, we need to straighten out a few misimpressions.

+

1. According to one article, by using phasing, one seemingly gets a directional 9-dbi gain. Adding a reflector nets you another 4 dB. The problem in this line of thinking is the belief--common even in commercially made quads--that if you have a collection of techniques at hand to improve antenna performance, what you get is the sum of all of the theoretically possible improvements. Unfortunately, this simply does not happen. If a technique provides gain by suppressing rear quadrant radiation, then another technique that also suppresses rear quadrant radiation will have little or no work to do. Indeed, the combination of techniques may in fact spoil things. The only way to proceed is the following: remain silent about the theoretic gains, model the antenna as a design aid, build a prototype, and then range test it. Then you will know what the sum of the techniques yields. In most antennas, the total performance will normally be less than the sum of techniques used to produce it.

+

2. The double-diamond quad is not at all new in the world of antennas. Perhaps its application to UHF is relatively recent, but not the double quad. In fact, the double quad, fed across the junction of side points, is simply a variant on the double-loop SCVs used in the MF and lower HF range to obtain gain over single loop versions of the same antennas. Hence, we have the double-delta--a lower gain, but much more practical version of the double-diamond where wire height is a major challenge to 80 and 160 meter operators. Likewise, we have the rectangle and its double, sometimes (mis-)called the "double magnetic slot" and heavily studied by David Jefferies and Dan Handelsman. The open loop versions of the SCVs originated in reverse order: the bobtail curtain preceded the half square. But both belong to the 1 wavelength club. See Fig. 1 for some old and common SCV "doubles."

+
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+

Here is why double-diamonds belong to the SCV family: all of the SCVs, when fed for dominantly vertically polarized radiation, consist--in single loop form--of two 1/4 wavelength verticals connected by horizontal phasing lines that are roughly 1/2 wavelength long. A closed loop suffers a small gain deficit resulting from the necessity of placing the vertical wires closer together than 1/2 wavelength. As Dan Handelsman has shown, we can endure a great deal of vertical shortening in the interests of wider spacing before the vertical elements become too short to radiate well. In fact, Kent Svensson, SM4CAN, in his 1988 booklet on Bobtails, empirically derived the need to shorten the verticals and extend the spacing even beyond a pure half wavelength between elements to achieve maximum gain from the array.

+

3. The double-quad is not the first use of SCV techniques on the VHF and UHF bands. Quads have been common. A few years ago, I had occasion to design and build some half-square and bobtail curtain parasitic arrays for 2-meters. What is original about the double-quad is just that--the use of the double quad in diamond form as a bi-directional broadside array at UHF. We should not diminish the achievement or insight involved, but we should also expect the antenna to behave like it should, given its SCV electrical heritage.

+

Work on VHF applications of the double-quad goes back at least to 1983 with the publication in the SAIEE journal of "A Broadband High-Gain Antenna for VHF-UHF," by Michael Stringfellow, then ZS6BUF, now AA7CT.

+

In fact, we shall look at the double-diamond quad in a few different configurations, and then re-introduce a long lost technique that offers even more potential with a bit less critical construction.

+

Evolving the Double Diamond Quad on 432 MHz

+

For some of the notes that follow, I shall use metric notations, and for some I shall use English units. I should apologize--or at least convert everything to one system. However, the exercise in units conversion will likely do everyone some good in refreshing those conversion constants that keep slipping from memory.

+

At the outset, let's note that this is a modeling exercise designed to establish some basic operating principles for the antennas. Since all of the models will be perfect, with no lumps, leads, or other disturbances, they are limited in their guidance for construction or prototypes. However, the trends will play true, and in those trends lies our keenest interest. Nevertheless, we shall keep our eyes open for limitations of the modeling systems used.

+

The evolution that we shall track goes from the simple vertical dipole to the single side-fed diamond loop, to the full double-diamond quad, as shown in Fig. 2.

+
+ +
+

The beginning of the double-diamond quad loop abides in the simple vertical dipole. A 4-mm diameter aluminum vertical dipole for 432 MHz in free space will show a gain of about 2.1 dBi and a resonant feedpoint impedance of about 72.5 Ohms. These values are the touchstone for all further work, and the circular H-plane pattern of Fig. 3 serves only as a reminder.

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+ +
+

Now let's build in modeling form a single diamond loop and feed it on the side to obtain dominantly vertically polarized radiation. The model has the following form:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                        A Side-Fed Single Diamond Loop
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1     W3E1   0.000,-318.07,  0.000  W2E1   0.000,-159.03,111.478 4.00E+00  15
+2     W1E2   0.000,-159.03,111.478  W5E2   0.000,  0.000,  4.000 4.00E+00  15
+3     W1E1   0.000,-318.07,  0.000  W4E1   0.000,-159.03,-111.48 4.00E+00  15
+4     W3E2   0.000,-159.03,-111.48  W5E1   0.000,  0.000, -4.000 4.00E+00  15
+5     W4E2   0.000,  0.000, -4.000  W2E2   0.000,  0.000,  4.000 4.00E+00   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     5 / 50.00   (  5 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Many antenna workers are familiar with the E-plane pattern of the single loop, which resembles the E-plane pattern of a dipole, but without the ultimate front-to-side ratio of a dipole in free space. However, the H-plane pattern of the side-fed 1 wavelength loop is less familiar. As Fig. 4 shows, it is an oval.

+
+ +
+

Once we look back to the dipole's H-plane pattern, the oval becomes quite logical. The free-space gain of the single resonant side-fed diamond loop, again using 4-mm diameter material at 432 MHz, is about 4.1 dBi according to NEC-2 and about 3.7 dBi according to NEC-4, with a half-power beamwidth of about 105 degrees. The feedpoint impedance is 80-85 Ohms. Using the more conservative and more accurate NEC-4 value, a (vertically polarized) quad loop has only about 1.6 dB more gain than the vertical dipole.

+

We must note that as one reaches the UHF range, NEC-2 and NEC-4 begin to diverge in their results. For antennas with only linear elements, the divergence is often minuscule, especially for simple antennas, such as a 3- to 4-element Yagi. However, as the antenna geometry grows more complex, the divergence becomes significant, as in the case of a quad loop, with its enclosed form and 4 90-degree corners. The greater the number of elements and the more complex the geometry, the greater the divergence between the older core and NEC-4.1.

+

The models in this sequence were developed to a great extent using the variables-and-equations features of NEC-Win Plus. However, all have been cross checked on GNEC and EZNEC-4. The improved algorithms of the NEC-4.1 core have in all tests performed by the software developers proven more accurate than then those of NEC-2. However, I make no presumption that they are perfect. That is why we are looking at trends rather than placing our bets solely on individual performance numbers.

+
+ +
+

Fig. 5 shows that the single diamond loop is--using a 4-mm diameter--a potentially wide-band antenna. The SWR curve is partly a function of the large element diameter when measured as a fraction of a wavelength.

+

Now we are ready to grow into the double-diamond quad array. However, before we jump into making two diamonds with identical vertical and horizontal corner-to-corner measurements per loop, let's pause for a practicality. We want a 50-Ohm feedpoint, if for no other reason than tradition. (Of course, cable makers will happily have you pay full price for 50-Ohm hardline rather than have you scrounge up usable sections of 75-Ohm hardline from the cable-TV company left-overs.)

+

A square-loop version of the double-diamond will have an impedance in the 80-Ohm range when resonant. To lower that impedance to 50 Ohms requires that we squish the squares so that the horizontal dimension of each loop is longer than the vertical dimension by roughly a 1.43:1 ratio. However, this should be no problem, because as N2DT has shown for the rectangle and SM4CAN has shown for the bobtail, squishing in this direction yields a bit of extra gain in addition to setting the resonant feedpoint impedance at a lower value.

+

As the following table of model dimensions shows, we feed the diamond pair with a short wire across the gap that we purposely make for just that function.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+            A Double-Diamond (Twin-Quad) Antenna with 4-mm Elements
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1     W5E1   0.000,-318.07,  0.000  W2E1   0.000,-159.03,111.478 4.00E+00  15
+2     W1E2   0.000,-159.03,111.478  W3E1   0.000,  0.000,  4.000 4.00E+00  15
+3     W9E2   0.000,  0.000,  4.000  W4E1   0.000,159.033,111.478 4.00E+00  15
+4     W3E2   0.000,159.033,111.478  W8E2   0.000,318.066,  0.000 4.00E+00  15
+5     W1E1   0.000,-318.07,  0.000  W6E1   0.000,-159.03,-111.48 4.00E+00  15
+6     W5E2   0.000,-159.03,-111.48  W7E1   0.000,  0.000, -4.000 4.00E+00  15
+7     W9E1   0.000,  0.000, -4.000  W8E1   0.000,159.033,-111.48 4.00E+00  15
+8     W7E2   0.000,159.033,-111.48  W4E2   0.000,318.066,  0.000 4.00E+00  15
+9     W6E2   0.000,  0.000, -4.000  W2E2   0.000,  0.000,  4.000 4.00E+00   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     9 / 50.00   (  9 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The H-plane pattern of the double-diamond is an extension of the single-loop pattern, as shown in Fig. 6. The front-to-side ratio increases, the beamwidth decreases, and the maximum gain increases.

+
+ +
+

The impedance of the double-diamond is a function of the length-to-height ratio of each loop. As noted, a ratio of about 1.43:1 is close to optimal for 4-mm elements. At 432 MHz, the impedance of the basic model is just over 50 Ohm resistive with negligible reactance. However, if we increase the diameter of the element material, the ratio changes. Because a closed loop increases in circumference with increases in element diameter, the dimensions will both increase, as shown by the following dimensional table for 6.35-mm (1/4") diameter elements.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           A Double-Diamond (Twin-Quad) Antenna with 0.25" Elements
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1     W5E1   0.000,-322.89,  0.000  W2E1   0.000,-161.45,114.924 6.35E+00  15
+2     W1E2   0.000,-161.45,114.924  W3E1   0.000,  0.000,  4.000 6.35E+00  15
+3     W9E2   0.000,  0.000,  4.000  W4E1   0.000,161.445,114.924 6.35E+00  15
+4     W3E2   0.000,161.445,114.924  W8E2   0.000,322.890,  0.000 6.35E+00  15
+5     W1E1   0.000,-322.89,  0.000  W6E1   0.000,-161.45,-114.92 6.35E+00  15
+6     W5E2   0.000,-161.45,-114.92  W7E1   0.000,  0.000, -4.000 6.35E+00  15
+7     W9E1   0.000,  0.000, -4.000  W8E1   0.000,161.445,-114.92 6.35E+00  15
+8     W7E2   0.000,161.445,-114.92  W4E2   0.000,322.890,  0.000 6.35E+00  15
+9     W6E2   0.000,  0.000, -4.000  W2E2   0.000,  0.000,  4.000 6.35E+00   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     9 / 50.00   (  9 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

However, the ratio of length to height of each loop has decreased to about 1.40:1 to achieve a 50-Ohm resistive resonant impedance. From this point forward, we shall use our 1/4" (6.35-mm) elements for further models. The 420-450-MHz 50-Ohm SWR plot in Fig. 7 shows that the double-diamond is--like the single side-fed loop--a wide-band antenna.

+
+ +
+

Over the entire 420-450-MHz band, the performance of the double-diamond remains quite stable, with only about a 0.2 dB change in maximum free-space gain from one end of the band to the other. The following table also shows that the half-power beamwidth is also quite stable, varying only about 2-3 degrees across the band.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Double-Diamond (0.25" Elements) Performance
+NEC-2
+Freq.       Gain        Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         degrees     R+/-jX Ohms       SWR
+420         6.22        56.0        44.1-j19.0        1.52
+430         6.29        56.0        48.3-j 6.6        1.15
+440         6.36        54.0        53.1+j 1.1        1.14
+450         6.44        54.0        58.7+j18.9        1.47
+NEC-4
+Freq.       Gain        Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         degrees     R+/-jX Ohms       SWR
+420         5.41        55.0        52.7-j25.9        1.65
+430         5.48        54.0        57.5-j10.9        1.28
+440         5.55        53.0        63.1+j 4.3        1.28
+450         5.63        52.0        69.7+j19.9        1.60
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Even though the specific values between the NEC-2 and NEC-4 models are not coincident, the trends displayed by the figures do coincide. The free-space gain of the double-diamond is about 5.5 dBi. This is a net gain of 1.8 dBi for the doubling of the loops. Note that when we went from a dipole to a single loop, we acquire 1.5 dB of added gain, short of the 2.1 dB theoretically possible. Likewise, when we doubled the loops, we fell considerable short of the 3-dB advantage that theory might tell us is possible. When using real materials, such as aluminum, and shapes that are optimized for some parameter other than gain (in this case, feedpoint impedance), we rarely come close to theoretical maximums.

+

Nonetheless, the potential performance of the double-diamond is similar to that of a bobtail curtain or a double rectangle. As such, especially for a vertically polarized antenna from which we desire something narrower than the beamwidth provided by the Yagi laid on edge, the SCV class of double loops offers significant performance. 5.5 dBi free-space gain with a 54-degree beamwidth provides not only a directional pattern, but as well freedom from some ghosting effects that infect vertically oriented small Yagis with beamwidths in excess of 80 or 90 degrees.

+

Double-Diamond Quad Arrays

+

The potential use of the double diamond quad in arrays is as unlimited as the use of linear elements. Therefore, we shall look at only a couple of variations: the 2-element parasitic double-diamond quad beam and the use of a double-diamond with a flat reflector.

+
+ +
+

From the 1/4" material, I modeled a 2-element parasitic array consisting of a driver and a reflector, as outlined in Fig. 8. Like standard quads, the reflector of a double-diamond quad must be further to the rear of a driven element than for a Yagi with linear elements. The final spacing was about 0.22 wavelength.

+

There was also a limiting factor with respect to the elements. Using the Belgian array as a guide, I placed imaginary supports between the two elements at the horizontal limits of the antenna elements. This decision dictated that the two elements have the same horizontal dimension and differ only in the maximum height of the two loops. As well, the array is designed for a direct 50-Ohm feed, which further restricts the range of heights and the ratios of length-to-height. The maximum element lengths horizontally are 0.51 wavelength. The driver height is about 0.228 wavelength, while the maximum reflector height is 0.27 wavelength. These dimensions presume a 5/8" (about 8 mm) gap between the joined loops for the coax feedpoint. The following dimensional model table shows the final model developed for this exercise.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  A 2-Element Parasitic Double-Diamond Array
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+1     W5E1 351.492,153.347,  0.000  W2E1 175.746,153.347, 78.397 6.35E+00  15
+2     W1E2 175.746,153.347, 78.397  W3E1   0.000,153.347,  4.000 6.35E+00  15
+3     W9E2   0.000,153.347,  4.000  W4E1 -175.75,153.347, 78.397 6.35E+00  15
+4     W3E2 -175.75,153.347, 78.397  W8E2 -351.49,153.347,  0.000 6.35E+00  15
+5     W1E1 351.492,153.347,  0.000  W6E1 175.746,153.347,-78.397 6.35E+00  15
+6     W5E2 175.746,153.347,-78.397  W7E1   0.000,153.347, -4.000 6.35E+00  15
+7     W9E1   0.000,153.347, -4.000  W8E1 -175.75,153.347,-78.397 6.35E+00  15
+8     W7E2 -175.75,153.347,-78.397  W4E2 -351.49,153.347,  0.000 6.35E+00  15
+9     W6E2   0.000,153.347, -4.000  W2E2   0.000,153.347,  4.000 6.35E+00   1
+10   W14E1 351.492,  0.000,  0.000 W11E1 175.746,  0.000, 93.042 6.35E+00  15
+11   W10E2 175.746,  0.000, 93.042 W12E1   0.000,  0.000,  4.000 6.35E+00  15
+12   W18E2   0.000,  0.000,  4.000 W13E1 -175.75,  0.000, 93.042 6.35E+00  15
+13   W12E2 -175.75,  0.000, 93.042 W17E2 -351.49,  0.000,  0.000 6.35E+00  15
+14   W10E1 351.492,  0.000,  0.000 W15E1 175.746,  0.000,-93.042 6.35E+00  15
+15   W14E2 175.746,  0.000,-93.042 W16E1   0.000,  0.000, -4.000 6.35E+00  15
+16   W18E1   0.000,  0.000, -4.000 W17E1 -175.75,  0.000,-93.042 6.35E+00  15
+17   W16E2 -175.75,  0.000,-93.042 W13E2 -351.49,  0.000,  0.000 6.35E+00  15
+18   W15E2   0.000,  0.000, -4.000 W11E2   0.000,  0.000,  4.000 6.35E+00   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     9 / 50.00   (  9 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

At 432 MHz, the array shows a free-space gain of 8.7 dBi, a gain of 3.2 dB over the bi-directional double-diamond alone (NEC-4 results). The front-to-back ratio is below 20 dB at mid-band but approaches 20 dB at 440 MHz. Fig. 9 shows the mid-band H-plane pattern (the modeling azimuth pattern) for the array.

+
+ +
+

The following table of values taken across the full 420-450 MHz band shows that the performance peaks at mid-band and falls off toward the band edges. Maximum gain occurs about 5 MHz below the maximum front-to-back frequency, a common phenomenon with any 2-element quad array. The performance curve is not unlike that of a 4-element Yagi designed to cover the entire 420-450 MHz band.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  Double-Diamond Parasitic Array Performance
+NEC-2
+Freq.       Gain        Front-Back  Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          degrees     R+/-jX Ohms       SWR
+420         9.70         9.33       48.0        33.8-j11.4        1.61
+430         9.61        16.91       50.0        49.7-j 8.0        1.17
+440         9.24        18.08       50.0        53.8-j10.8        1.25
+450         8.81        11.99       48.0        50.7-j 7.0        1.15
+NEC-4
+Freq.       Gain        Front-Back  Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          degrees     R+/-jX Ohms       SWR
+420         8.75         8.05       47.5        37.4-j19.0        1.68
+430         8.77        14.70       47.2        58.2-j10.6        1.28
+440         8.44        19.88       47.8        67.0-j14.3        1.47
+450         8.01        13.17       47.7        64.0-j11.8        1.38
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

Fig. 10 provides the 50-Ohm SWR curve for the array. SWR reaches about 1.7:1 at the low end of the band, but from 425 MHz upward, it levels off in the 1.28:1 to 1.50:1 range. Like most quad beams, the SWR operating curve is much flatter than the performance (gain and front-to-back ratio) curves.

+

For a wider and more stable set of performance curves, the double diamond benefits from the use of a simple flat reflector. Fig. 11 shows the general scheme, using a modeled wire grid screen behind a single double-diamond array.

+
+ +
+

The double diamond does not benefit from a corner array, because each virtual vertical element is a different distance from the reflector. However, we shall return the corner reflectors before we complete these preliminary notes. With simple dipole feed systems, flat and corner arrays can use a system of bars for simplified modeling. Extensive modeling tests have shown that an adequate system of bars and a wire-grid screen yield results too close to each other to make a difference. However, with a double-diamond, one MUST use a screen for adequate results, even if the result for a modest wire grid is over 1100 segments. The reason that we require a wire-grid screen relates to the shape of the double- diamond elements. Whether square or diamond, a side-fed quad element has small but significant radiation in the E-plane. With only vertical bars as the elements of a flat or corner reflector, the gain and impedance do not change relative to a full screen of the same outer dimensions. However, the front-to-back ratio will report as much as 8 dB lower than with a full screen.

+

Switching to inches as our unit of measure, the optimum distance between the double diamond and a flat screen reflector proved to be about 4 inches. This distance permitted revision of the double-diamond dimensions to achieve a 50-Ohm impedance.

+

The gain performance of a double-diamond with a flat reflector is dependent upon the overall dimensions of the reflector screen. The following table provides an indication of the degree to which gain will vary with screen size.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+      432-MHz Performance of a Double-Diamond Quad with a Flat Reflector
+
+Screen width      Free-Space  Front-Back  Beamwidth   Feed Impedance    SWR
+vs. height (")    Gain dBi    Ratio dB    degrees     R +/- jX Ohms
+
+44 by 32          10.70       28.0        50.1        55.9 + j 2.0      1.13
+32 by 24          10.10       29.5        52.8        55.8 + j 2.1      1.13
+24 by 20           9.65       29.5        54.0        56.6 - j 5.3      1.17
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The front-to-back ratio and the impedance undergo only small changes relative to the high correlation between gain and screen area.

+

The following table of dimensions includes a small adjustment to the double-diamond horizontal and vertical dimensions to make the SWR curve favor the upper end of the band, where a vertically polarized antenna is most likely to be used. This particular model used the 4-mm (0.1575") double-diamond. The screen wires are omitted after the first few, since no one (except the modeler) needs to read another thousand lines of antenna model wires. The screen is composed of wires spaced 1" apart using 0.1" diameter wire.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             A Double-Diamond Driver With a Flat-Screen Reflector
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1     W5E1 -11.000,  4.000,  0.000  W2E1  -5.500,  4.000,  4.300 1.57E-01  15
+2     W1E2  -5.500,  4.000,  4.300  W3E1   0.000,  4.000,  0.157 1.57E-01  15
+3     W9E2   0.000,  4.000,  0.157  W4E1   5.500,  4.000,  4.300 1.57E-01  15
+4     W3E2   5.500,  4.000,  4.300  W8E2  11.000,  4.000,  0.000 1.57E-01  15
+5     W1E1 -11.000,  4.000,  0.000  W6E1  -5.500,  4.000, -4.300 1.57E-01  15
+6     W5E2  -5.500,  4.000, -4.300  W7E1   0.000,  4.000, -0.157 1.57E-01  15
+7     W9E1   0.000,  4.000, -0.157  W8E1   5.500,  4.000, -4.300 1.57E-01  15
+8     W7E2   5.500,  4.000, -4.300  W4E2  11.000,  4.000,  0.000 1.57E-01  15
+9     W6E2   0.000,  4.000, -0.157  W2E2   0.000,  4.000,  0.157 1.57E-01   1
+10   514E1 -12.000,  0.000,-10.000 W11E1 -11.000,  0.000,-10.000 1.00E-01   1
+11   534E1 -11.000,  0.000,-10.000 W12E1 -10.000,  0.000,-10.000 1.00E-01   1
+12   554E1 -10.000,  0.000,-10.000 W13E1  -9.000,  0.000,-10.000 1.00E-01   1
+13   574E1  -9.000,  0.000,-10.000 W14E1  -8.000,  0.000,-10.000 1.00E-01   1
+14   594E1  -8.000,  0.000,-10.000 W15E1  -7.000,  0.000,-10.000 1.00E-01   1
+. . .
+1011 441E2  12.000,  0.000,  7.000 W1012  12.000,  0.000,  8.000 1.00E-01   1
+1012 465E2  12.000,  0.000,  8.000 W1013  12.000,  0.000,  9.000 1.00E-01   1
+1013 489E2  12.000,  0.000,  9.000 513E2  12.000,  0.000, 10.000 1.00E-01   1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     9 / 50.00   (  9 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The pattern for the antenna does not change significantly from one end of the band to the other. The H-plane pattern in Fig. 12 is typical for every frequency across the band. In fact, there is under a 0.2 dB change in gain across the band.

+
+ +
+

The following table of modeled values shows the flatness of performance of the array when used with the smallest of the screen sizes.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Double-Diamond With Small Flat Reflector Performance
+
+Freq.       Gain        Front-Back  Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          degrees     R+/-jX Ohms       SWR
+420         9.58        28.90       54.8        47.0-j33.2        1.96
+430         9.64        29.38       54.2        52.3-j16.1        1.37
+440         9.70        29.66       53.6        58.4+j 0.9        1.17
+450         9.72        29.72       53.2        65.4+j17.7        1.50
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+ +
+

The resulting SWR curve in Fig. 13 shows excellent coverage of the band, especially the upper end. By judiciously altering the dimensions of the single double-diamond, one can adjust the resonant position and hence the shape of the SWR curve to favor any part of the band.

+

To test the note at the beginning of this collection to the effect that techniques do not necessarily add up when chasing gain with an array, I modeled the parasitic double-diamond array in front of the same small (24" by 20") flat reflector. The array yielded 8.9-dBi gain with a 16.9 dB front-to-back ratio with the double-diamond reflector 4" ahead of the flat reflector, no better than the performance of the parasitic array without the screen reflector. Decreasing the distance from the flat reflector slowly increased gain, but at the cost of the front-to-back ratio. Increasing the spacing of the two reflectors raised the front-to-back ratio to over 24 dB at a distance of 12". However, the gain fell to below 8.6 dB. The doubling of reflectors does not necessarily improve performance. The fact that the feedpoint impedance did not significantly change during this exercise suggests that the closely coupled parasitic double-diamond reflector remained the dominant influence on the pattern shape of the array.

+

Equally, a phased array will also fail to benefit from the flat reflector if it already has significant gain and front-to-back ratio. Indeed, direct phasing and parasitic phasing are simply electrical and geometric means to the same end: the establishment of the proper relative current magnitude and phase on the two elements to increase forward gain and to decrease rearward gain.

+

A Neglected Alternative

+

The outcome of the modeling exercise with respect to the double-diamond quad loop is twofold. First, in carefully constructed models, the antenna behaves just as one might expect a double loop element to behave. Second, among directional array possibilities, the use of a single double diamond loop ahead of a flat reflector of significant size is perhaps the most efficient route to a broadband array with good gain, excellent front-to-back ratio, narrow beamwidth, and a very wide SWR curve. Indeed, a flat reflector provides (among alternatives checked) the widest and most stable set of performance characteristics.

+

Nonetheless, there is no magic in the double-diamond loop array. It does not provide the most gain that we may obtain from an array of its size (assuming a flat reflector). Nor is it the simplest to construct, given the many bending angles required to fabricate the double-diamond shape with the proper length to height ratio. By comparison, trimming a fat dipole (say, about 0.5" in diameter) is far simpler.

+

Enter the corner array, outlined with a bar reflector in Fig. 14.

+
+ +
+

Like the double diamond arrays, the corner array shows a gain that is (almost) directly proportional to the size of the reflector. (The performance shows periodic variations as one systematically increases the reflector size.) A reflector with an aperture width of 44" and a height of 32" (the same as the largest flat reflector) has the potential for a free-space gain of about 11.25 dBi, with a 26.9 dB front-to-back ratio and a 51.5-Ohm feedpoint impedance. If we reduce the aperture to 32" with a 24" height and a 16" depth, we obtain performance very similar to that of the smallest flat-screen reflector with the double diamond: 9.74 dBi gain, 36.9 dB front-to-back ratio, and a 50.3-Ohm impedance at 432-MHz. The table below gives the various dimensions for the single dipole and the bar reflectors in this smaller array.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  A Small Corner Reflector and Dipole Driver
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1            0.000,  8.500, -5.500         0.000,  8.500,  5.500 5.00E-01  11
+2            0.000,  0.000,-12.000         0.000,  0.000, 12.000 3.75E-01  25
+3            2.000,  2.000,-12.000         2.000,  2.000, 12.000 3.75E-01  25
+4            4.000,  4.000,-12.000         4.000,  4.000, 12.000 3.75E-01  25
+5            6.000,  6.000,-12.000         6.000,  6.000, 12.000 3.75E-01  25
+6            8.000,  8.000,-12.000         8.000,  8.000, 12.000 3.75E-01  25
+7           10.000, 10.000,-12.000        10.000, 10.000, 12.000 3.75E-01  25
+8           12.000, 12.000,-12.000        12.000, 12.000, 12.000 3.75E-01  25
+9           14.000, 14.000,-12.000        14.000, 14.000, 12.000 3.75E-01  25
+10          16.000, 16.000,-12.000        16.000, 16.000, 12.000 3.75E-01  25
+11          -2.000,  2.000,-12.000        -2.000,  2.000, 12.000 3.75E-01  25
+12          -4.000,  4.000,-12.000        -4.000,  4.000, 12.000 3.75E-01  25
+13          -6.000,  6.000,-12.000        -6.000,  6.000, 12.000 3.75E-01  25
+14          -8.000,  8.000,-12.000        -8.000,  8.000, 12.000 3.75E-01  25
+15         -10.000, 10.000,-12.000       -10.000, 10.000, 12.000 3.75E-01  25
+16         -12.000, 12.000,-12.000       -12.000, 12.000, 12.000 3.75E-01  25
+17         -14.000, 14.000,-12.000       -14.000, 14.000, 12.000 3.75E-01  25
+18         -16.000, 16.000,-12.000       -16.000, 16.000, 12.000 3.75E-01  25
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           6     1 / 50.00   (  1 / 50.00)      0.707       0.000       V
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The high front-to-back ratio promises interesting H-plane patterns, and Fig. 15 confirms the promise.

+
+ +
+

Like the double-diamond, the corner reflector array offers full coverage of the band, as evidenced by the curve in Fig. 16.

+
+ +
+

Equally, like the double-diamond array, the performance characteristics promise to be very consistent across the entire 420-450-MHz spectrum. The follow tables provides samples.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      Small Corner Reflector Performance
+
+Freq.       Gain        Front-Back  Beamwidth   Feed Impedance    50-Ohm
+MHz         dBi         dB          degrees     R+/-jX Ohms       SWR
+420         9.63        35.61       60.0        41.8-j14.9        1.45
+430         9.72        35.90       59.0        48.8-j 1.8        1.05
+440         9.81        36.38       58.0        56.6+j11.1        1.27
+450         9.90        37.05       57.1        65.4+j23.7        1.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Essentially, then, the corner reflector offers similar performance with slightly more screening material and much less complexity in the driven element. By using a considerably larger corner screen, we can obtain a lot more gain and even greater bandwidth. With the dipole moved to a position yielding about a 100-Ohm impedance, and using the largest of the screen noted, we can obtain usable performance with a 2:1 100-Ohm SWR for almost the entire range from 400 to 500 MHz. With a bow-tie-shaped driver, we can spread the usable bandwidth still wider, all with excellent gain and superlative front-to-back characteristics.

+

Conclusion

+

Even though this preliminary investigation is only a modeling study, it may have yielded some useful results. Some of those results had to do with the cautions necessary when modeling and the limitations of the available modeling programs. However, in the main, the trends do indicate something useful about the double-diamond or twin-quad loop antenna in the UHF region.

+

The double-diamond twin-quad array has excellent potential as a UHF wide-band array with reasonably good characteristics when used with a flat screen reflector. However, it is far from the ultimate in gain, in front-to-back, in SWR bandwidth, or performance bandwidth. The venerable corner reflector provides strong competition with a much simpler driver assembly, although a bit larger reflector assembly.

+

We must always make sure that we do not over-estimate a "hot" antenna design, merely because it is in fashion. The double-diamond does well enough without exaggeration of its properties. We may be able to squeeze a bit more out of the double-diamond in some array configuration or another, but I doubt that it will be much more.

+
+ +
+

Updated 12-1-2001, 11-12-2002. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for December, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: Quad, VHF / UHF


+ + diff --git a/content/vhf/diamond.html b/content/vhf/diamond.html new file mode 100644 index 0000000..1d2c858 --- /dev/null +++ b/content/vhf/diamond.html @@ -0,0 +1,17 @@ + + + + + + A Diamond Jubilee + + + +

A Diamond Jubilee

+ hr +

A Diamond Jubilee

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: Quad Loop, VHF / UHF


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+

Phased Yagis, EDZ Beams, and Landstorfer Yagis
+ 2-Meter Birds of a Feather

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Although there are some hints on the subject in other notes, it seemed useful to me to review for my own edification the relationship between Phased Yagis and Extended Double-Zepp (EDZ) beams. That review might position us to understand another type of antenna, the Landstorfer-Sacher Yagi.

+

Ever since the amateur community was introduced to EDZ beams in a QST article by Hugo Romander, W2NB, in June, 1938 ("The Extended Double Zepp Antenna"), perhaps too many hams have thought of the EDZ as a special type of 1.25 wl antenna. In fact, it is simply a way of doing some things that we can do with ordinary half wavelength antenna elements. So let's begin with antennas using half wavelength elements. A 2-meter 3-element Yagi seems straight-forward enough for our purposes. We shall set 145 MHz as our design frequency, hoping for at least 2 MHz of coverage on the band.

+

Side-by-Side Phased Yagis

Let's set up 2 3-element Yagis side-by-side with about 1/4 wl of spacing between them. We shall feed them in phase by the basic method of running equal length feedlines to a central point. The general outline appears in Fig. 1. +
+ +
+

As a reference, here is the EZNEC model description of the antenna pair:

+ 
2 Yagis, 3-el, 3/16" el                      Frequency = 145  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -52.092,  0.000,  0.000       -11.868,  0.000,  0.000 1.88E-01  31
+2        -51.142, 13.295,  0.000       -12.818, 13.295,  0.000 1.88E-01  31
+3        -49.995, 27.413,  0.000       -13.965, 27.413,  0.000 1.88E-01  31
+4         11.868,  0.000,  0.000        52.092,  0.000,  0.000 1.88E-01  31
+5         12.818, 13.295,  0.000        51.142, 13.295,  0.000 1.88E-01  31
+6         13.965, 27.413,  0.000        49.995, 27.413,  0.000 1.88E-01  31
+7         -0.100,  0.000,-20.000         0.100,  0.000,-20.000    # 14    1
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     7 / 50.00   (  7 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1   Length     Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)              Ohms Fact Norm
+1     2/50.0  (  2/50.0)    7/50.0  (  7/50.0)   61.050 in    50.0  1.00  N
+2     5/50.0  (  5/50.0)    7/50.0  (  7/50.0)   61.050 in    50.0  1.00  N
+
+Ground type is Free Space
+

Note that the array of Yagis at its widest point is about 104.2" wide or a little over 1.25 wl at the design frequency (where a wl is about 81.4"). Wire 7 in the model is the junction wire for the two transmission lines. Since the two feedpoints are more than 1/2 wl apart, the feedlines are each 3/4 wl long. Phasing line losses and velocity factor are not accounted for in the model. Each Yagi has a natural feedpoint impedance of about 25 Ohms at resonance, so the 50-Ohm lines transform the impedance to 100 Ohms, for a parallel combination that matches a main 50-Ohm feedline.

+

The antenna material is aluminum and the element diameter is 3/16", and both figures will remain constant in this exercise. Likewise, all modeling will be done in free space.

+

The modeled performance of the antenna pair is recorded in the following table:

+ 
Freq.     Gain dBi       F-B dB         R +/- jX       50-Ohm
+MHz                                       Ohms          VSWR
+144       10.9           24.3           45 + j14       1.35
+145       11.0           23.9           51 - j 1       1.04
+146       11.1           20.0           46 - j18       1.47
+

The SWR curve indicates that we might have moved the design frequency up by a half MHz and had a 2:1 SWR from 144 to 147 MHz. However, for our purposes, it is not the precise numbers that matter so much as the relative currents on the antenna elements. Fig. 2 shows the relative values of current for the reflector, director and driver for each antenna. Not surprisingly, the two antennas show the same values.

+
+ +
+

The free space azimuth pattern for the array appears in Fig. 3. Note the "ears" or "wings" in both the forward and rear quadrants. These minor lobes are typical of side-by-side arrays of this type. The wider the spacing between elements (to a point), the higher the overall gain, but as well, the stronger the side lobes.

+
+ +
+

Achieving the full gain of the antenna relative to a remote power source depends on the losses accrued in the phasing lines (as well as the main feedline). Standard coax cables become noticeably lossy at 2 meters, and low-loss types or even hardlines are recommended for this application. The phased pair of Yagis is our baseline against which we shall compare the other antennas in this exercise.

+

2 Yagis with a Common EDZ Driven Element

Our second antenna can be viewed in two ways, depending on how we look at Fig. 4. +
+ +
+

We can focus on the parasitic elements and see the antenna as two Yagis with a common EDZ driven element. Or, we can focus on the driver and see the antenna as an EDZ beam with separate sets of parasitic elements. The particular model we shall examine is described in the following table:

+ 
2 Yagis w/ EDZ driver                         Frequency = 145  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1        -49.200,  0.000,  0.000        49.200,  0.000,  0.000 1.88E-01  31
+2        -49.200,-12.000,  0.000        -9.700,-12.000,  0.000 1.88E-01  13
+3          9.700,-12.000,  0.000        49.200,-12.000,  0.000 1.88E-01  13
+4        -49.200, 12.000,  0.000       -12.500, 12.000,  0.000 1.88E-01  13
+5         12.500, 12.000,  0.000        49.200, 12.000,  0.000 1.88E-01  13
+
+             -------------- SOURCES --------------
+Source    Wire     Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          16     1 / 50.00   (  1 / 50.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1          16     1 / 50.00   (  1 / 50.00)       2.000       608.000
+
+Ground type is Free Space
+

The overall width of the antenna is about 98.4" wide, with all the elements meeting this boundary. The constant outside dimension means that the reflector inside ends are closer together than the director inside ends. (Note also that for modeling convenience, the driver is listed as wire 1.) Since the EDZ driver is very capacitively reactive, an inductive load of 608 Ohms is required at the feedpoint to produce resonance. However, this resonant value is very close to 50 Ohms. The 2-Ohm resistive component of the load is to set the Q at about 300.

+

The following table of values is not strictly correct, since an impedance load was used. For precision, a series R-L load should have been put in place. However, the following values are indicative (with a very slight optimism at the band edges) of performance:

+ 
Freq.     Gain dBi       F-B dB         R +/- jX       50-Ohm
+MHz                                       Ohms          VSWR
+144       10.6           22.6           63 - j32       1.85
+145       10.7           27.5           52 + j 0       1.05
+146       10.8           19.9           43 + j33       2.04
+

This configuration produces a narrower operating bandwidth than the phase-fed independent Yagis. The gain figures of the two models should be considered as very comparable, since this model includes the load inductor losses, while the independent Yagis omit the phase line losses.

+
+ +
+

Fig. 5 shows perhaps the most significant difference between the arrays. The driven element has an additional smaller current peak at the wire center, but this peak contributes little or nothing to the overall gain of the system. The current patterns in the lines formed via bisecting each Yagi in the pair are virtually identical to those of the independent phase- fed Yagis.

+
+ +
+

The azimuth pattern for this model, while differing a bit in rear detail, has all the same features as the pattern for the independent Yagis. The main forward and rearward lobes are accompanied by side lobes. In this case, the size of the rear side lobes is a function of setting the element dimensions to achieve a 50-Ohm feedpoint impedance. Smaller rear side-lobes are possible, but at a different feedpoint impedance.

+

In the end, this model with an EDZ driver is simply an extension of the initial model. The EDZ driver functions as 2 end-fed half wavelength wires with a (roughly) 1/4 wl phasing section between them.

+

There is a second version of this same antenna that is worth noting in passing. It is possible to design the EDZ driver to be self-matching to a 50-Ohm feedline. The method involves adding to the inner ends of the Yagi drivers matching sections of some transmission line or other. The sections can be either coaxial lines or parallel lines. In the model in Fig. 19, the matching section uses parallel line with 1" spacing of the same 3/16" material used for the elements. This particular antenna model is for the 220 MHz band. Note the gap in the unfed side of the matching section.

+
+ +
The model follows: + 
Dual Yagis with EDZ Driver                   Frequency = 223.5  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -30.313,  0.000,  0.000  W2E1 -10.034,  0.000,  0.000 1.88E-01  21
+2     W3E1 -10.034,  0.000,  0.000        -0.500,  0.000,  0.000 1.88E-01   9
+3     W1E2 -10.034,  0.000,  0.000  W4E1 -10.034,  1.000,  0.000 1.88E-01   1
+4     W3E2 -10.034,  1.000,  0.000  W5E1  10.034,  1.000,  0.000 1.88E-01  19
+5     W4E2  10.034,  1.000,  0.000  W6E2  10.034,  0.000,  0.000 1.88E-01   1
+6            0.500,  0.000,  0.000  W7E1  10.034,  0.000,  0.000 1.88E-01   9
+7     W5E2  10.034,  0.000,  0.000        30.313,  0.000,  0.000 1.88E-01  21
+8          -35.113,  8.450,  0.000        -9.295,  8.450,  0.000 1.88E-01  23
+9            9.295,  8.450,  0.000        35.113,  8.450,  0.000 1.88E-01  23
+10         -29.513,-13.203,  0.000        -8.978,-13.203,  0.000 1.88E-01  20
+11           8.978,-13.203,  0.000        29.513,-13.203,  0.000 1.88E-01  20
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          10     4 / 50.00   (  4 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

As shown in Fig. 20, the element currents are essentially the same as those for the loaded EDZ driver version of the antenna. Only the currents in the matching section show a variation.

+
+ +
Performance of this version of the antenna does not reach the levels of the basic model. However, it is not certain to what degree the close spaced wires (a possible NEC limitation) are depressing the gain figure and to what degree the antenna requires further optimization. That is a future project. + 
Freq.     Gain dBi       F-B dB         R +/- jX       50-Ohm
+MHz                                       Ohms          VSWR
+222       10.1           14.2           45 - j16       1.42
+223.5     10.1           15.1           44 + j 6       1.20
+225       10.1           15.6           43 + j27       1.81
+

The mid-band free-space azimuth pattern appears in Fig. 21 for reference.

+
+ +
+

Although the technique of using a self-matching section in the driver provides for a mechanically simpler antenna than one employing loading inductors, the design is not without its own limitations. The parallel line spacing and the gap in the driver interact. So too do the overall driver length amd the required length of the matching line. As well, and unlike the loaded driver version of the antenna, careful left-right alignment of the parasitic elements is necessary to achieve maximum performance. Within these limitations, as an all-mechanical alternative to other all-mechanical designs below, the self-matching array has possibilities.

+

A "True" or Full EDZ Beam

It is not necessary to use separate wires for the parasitic elements each side of center in the array. Instead, we may use full-length wires, as in Fig. 7. +
+ +
+

The result is a beam composed of 3 equal length EDZ wires. Of course, each wire will have to be loaded in accord with its function. The loading and the antenna dimensions appear in the table below:

+ 
3 el edz loaded 3/16" dia                   Frequency = 145  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+1        -49.200,-12.000,  0.000        49.200,-12.000,  0.000 1.88E-01  31
+2        -49.200,  0.000,  0.000        49.200,  0.000,  0.000 1.88E-01  31
+3        -49.200, 12.000,  0.000        49.200, 12.000,  0.000 1.88E-01  31
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          16     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1          16     1 / 50.00   (  1 / 50.00)       2.200       665.000
+2          16     2 / 50.00   (  2 / 50.00)       1.900       565.000
+3          16     3 / 50.00   (  3 / 50.00)       1.600       465.000
+
+Ground type is Free Space
+

Like the preceding model, the overall antenna width is about 98.4" with 3/16" diameter aluminum elements. It is simply coincidental that the loading of each element works out to be about 100 Ohms different than the adjacent element--a function of balancing the antenna for peak performance at a near-50-Ohm feedpoint impedance. The modeled performance is captured in the following table:

+ 
Freq.     Gain dBi       F-B dB         R +/- jX       50-Ohm
+MHz                                       Ohms          VSWR
+144       10.5           17.5           56 - j26       1.65
+145       10.6           39.5           51 + j 0       1.01
+146       10.7           18.2           42 + j27       1.84
+

Relative to our initial pair of Yagis, the performance of this EDZ beam suffers about 0.25 dB as a result of element loading at a Q of 300 (compared to the previous model's loss of a little under 0.2 dB as a result of loading only the driver). Once more, an inexact loading system was used, but it does indicate a slightly wider operating bandwidth than the EDZ-driver-only model.

+
+ +
+

As we might expect, all three elements (in Fig. 8) show the center current peak inherent to an EDZ element. These peaks are not correctly phased to contribute to the overall array gain. The main work occurs in the 1/2 wl segments on either side of the feed and phasing area, and these curves show about the same relative strengths as in the corresponding earlier graphs.

+

The upshot is that an EDZ beam is actually two Yagis fed in-phase side-by- side with about 1/4 wl of spacing between them. The connecting wires are essentially phasing wires for the end feed of each element-end section.

+
+ +
+

The free-space azimuth pattern (Fig. 9) of the antenna model in question bears out this situation by showing all of the features of the other patterns. (The azimuth pattern reflects the potential of the antenna with zero-resistance loads.) What might otherwise be called the main rear lobe is, of course, almost non-existent, and only the rear side lobes show with prominence. It would not be stretching the point to note that all three of the beams we have examined so far are electrically of the same type, with only a few differences of implementation.

+

The Landstorfer-Sacher Yagi

An antenna that deserves more attention is the Landstorfer-Sacher Yagi (the most commonly-used name), shown in outline form in Fig. 10. +
+ +
Steve Stearns, K6OIK, reports the following relative to the origin and correct label for the antenna: "Landstorfer published the antenna in 1976. Years later he published a book with R. R. Sacher that included the antenna. Sacher was a coauthor on the 1985 book, not an inventor of the antenna. For this reason, I think the term "Landstorfer-Sacher" mis-credits the antenna. It is properly called a "Landstorfer array." +

This 3-element array appears initially unusual because of its curved geometry--almost a line of pelicans fishing off the southern U.S. coastline. However, upon closer examination, we can fairly easily figure the function of various parts of the antenna. The model appears in the following table:

+ 
Landstorfer-Sacher 2M Yagi                  Frequency = 145  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1         16.417,-50.197,  0.000  W2E1  15.157,-39.252,  0.000 1.88E-01   5
+2   W1E2  15.157,-39.252,  0.000  W3E1  12.323,-29.331,  0.000 1.88E-01   5
+3   W2E2  12.323,-29.331,  0.000  W4E1   6.339,-20.906,  0.000 1.88E-01   5
+4   W3E2   6.339,-20.906,  0.000  W5E1  -2.008,-14.843,  0.000 1.88E-01   5
+5   W4E2  -2.008,-14.843,  0.000  W6E1 -10.354, -8.780,  0.000 1.88E-01   5
+6   W5E2 -10.354, -8.780,  0.000  W7E1 -15.748, -0.984,  0.000 1.88E-01   5
+7   W6E2 -15.748, -0.984,  0.000  W8E1 -15.748,  0.984,  0.000 1.88E-01   1
+8   W7E2 -15.748,  0.984,  0.000  W9E1 -10.354,  8.780,  0.000 1.88E-01   5
+9   W8E2 -10.354,  8.780,  0.000 W10E1  -2.008, 14.843,  0.000 1.88E-01   5
+10  W9E2  -2.008, 14.843,  0.000 W11E1   6.339, 20.906,  0.000 1.88E-01   5
+11 W10E2   6.339, 20.906,  0.000 W12E1  12.323, 29.331,  0.000 1.88E-01   5
+12 W11E2  12.323, 29.331,  0.000 W13E1  15.157, 39.252,  0.000 1.88E-01   5
+13 W12E2  15.157, 39.252,  0.000        16.417, 49.488,  0.000 1.88E-01   5
+14        23.622,-45.079,  0.000 W15E1  22.362,-33.780,  0.000 1.88E-01   5
+15 W14E2  22.362,-33.780,  0.000 W16E1  20.315,-24.173,  0.000 1.88E-01   5
+16 W15E2  20.315,-24.173,  0.000 W17E1  15.709,-15.472,  0.000 1.88E-01   5
+17 W16E2  15.709,-15.472,  0.000 W18E1   7.953, -9.409,  0.000 1.88E-01   5
+18 W17E2   7.953, -9.409,  0.000 W19E1  -1.417, -6.457,  0.000 1.88E-01   5
+19 W18E2  -1.417, -6.457,  0.000 W20E1  -8.858, -0.984,  0.000 1.88E-01   5
+20 W19E2  -8.858, -0.984,  0.000 W21E1  -8.858,  0.984,  0.000 1.88E-01   1
+21 W20E2  -8.858,  0.984,  0.000 W22E1  -1.417,  6.457,  0.000 1.88E-01   5
+22 W21E2  -1.417,  6.457,  0.000 W23E1   7.953,  9.409,  0.000 1.88E-01   5
+23 W22E2   7.953,  9.409,  0.000 W24E1  15.709, 15.472,  0.000 1.88E-01   5
+24 W23E2  15.709, 15.472,  0.000 W25E1  20.315, 24.173,  0.000 1.88E-01   5
+25 W24E2  20.315, 24.173,  0.000 W26E1  22.362, 33.780,  0.000 1.88E-01   5
+26 W25E2  22.362, 33.780,  0.000        23.622, 45.079,  0.000 1.88E-01   5
+27        31.575,-39.094,  0.000 W28E1  30.394,-29.567,  0.000 1.88E-01   5
+28 W27E2  30.394,-29.567,  0.000 W29E1  28.898,-20.079,  0.000 1.88E-01   5
+29 W28E2  28.898,-20.079,  0.000 W30E1  25.276,-11.181,  0.000 1.88E-01   5
+30 W29E2  25.276,-11.181,  0.000 W31E1  18.740, -4.173,  0.000 1.88E-01   5
+31 W30E2  18.740, -4.173,  0.000 W32E1   9.449, -1.654,  0.000 1.88E-01   5
+32 W31E2   9.449, -1.654,  0.000 W33E1   0.000, -0.984,  0.000 1.88E-01   5
+33 W32E2   0.000, -0.984,  0.000 W34E1   0.000,  0.984,  0.000 1.88E-01   1
+34 W33E2   0.000,  0.984,  0.000 W35E1   9.449,  1.654,  0.000 1.88E-01   5
+35 W34E2   9.449,  1.654,  0.000 W36E1  18.740,  4.173,  0.000 1.88E-01   5
+36 W35E2  18.740,  4.173,  0.000 W37E1  25.276, 11.181,  0.000 1.88E-01   5
+37 W36E2  25.276, 11.181,  0.000 W38E1  28.898, 20.079,  0.000 1.88E-01   5
+38 W37E2  28.898, 20.079,  0.000 W39E1  30.394, 29.567,  0.000 1.88E-01   5
+39 W38E2  30.394, 29.567,  0.000        31.575, 39.094,  0.000 1.88E-01   5
+
+             -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1    20 / 50.00   ( 20 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

I owe the initial version of the model to another ham who took the trouble to measure out the dimensions and to translate them into a usable first model. (The e-mail exchange became lost in my system, so I hoped he would contact me so that I could credit the source of the tough part of the work of generating a model of the antenna. After many moons, Dr. Duncan Cadd, G0UTY, finally emerged to let me know that he was the one who had done all of that careful work to create a usable model of the Landstorfer) My work has been confined to optimizing the model for a 50-Ohm resonant feedpoint impedance, with some adjustments to increase gain a bit. However, I will not claim that this is a fully adequate model of the antenna. Further improvements in converting an essentially curved set of wires into straight wire segments may well be possible.

+

Note that I have not transposed the model to be consistent with the others. I have left the side-to-side dimensions in the Y column (in contrast to their position in the X column for the other models). The overall width of about 100.2" is consistent with the other models, although the antenna has a much more sizeable front-to-back dimension.

+

The performance figures for the antenna model at its present state of development are these:

+ 
Freq.     Gain dBi       F-B dB         R +/- jX       50-Ohm
+MHz                                       Ohms          VSWR
+144        9.7           23.8           50 - j11       1.25
+145        9.7           20.3           55 - j 2       1.10
+146        9.7           18.2           56 + j 7       1.18
+147        9.8           17.1           53 + j16       1.38
+148        9.8           16.5           46 + j28       1.80
+

The first attribute of the L-S Yagi is its broad bandwidth, despite its high gain. Full coverage of 2-meters is easily achieved.

+

The antenna width and coverage together gives us clues to the functions of various parts of the antenna. The outer portions of each elements are the main radiating portions, providing both gain and front-to-back ratio with an overall side-to-side width consistent with EDZ elements. The middle portions function both as phasing and matching sections so that without any spot loading, the antenna provides a feedpoint impedance close to 50 Ohms for direct connection to coaxial cable. Each element ends up using in the neighborhood of 1.5 wl of wire, although the actual situation is a bit more complex than the simple assumption that the wires have a natural low impedance resonant point at center. The wires form a complex variation on the delta feed system. However, each function also transitions seamlessly into the next due to the curved arrangement of the elements.

+
+ +
+

The current curves, shown in Fig. 11, bear out the EDZ-nature of the overall antenna. The magnitude and phasing of the currents in the outer 1/2 wl portions of each element provide the main source of the antenna's pattern.

+
+ +
+

Fig. 12 shows the free space azimuth pattern for the antenna--at least as modeled here. Since side-to-side dimensions are along the Y-axis, the main lobe points to the right side of the graphic. The figure also shows an interesting consequence of the curved structure, which is the reduction of the side lobes to very small proportions, almost as small as those of the N6LF capacitively adjusted EDZ (Antenna Compendium, Vol. 4, pp. 78-80). The rear lobes fold into a single curve, which can only be resolved into 3 lobes by examining the rate of change of gain (rather than the gain itself) in the rear quadrants.

+

As a wide-band variation on the EDZ beam with a natural 50-Ohm feedpoint impedance, the L-S Yagi has much to recommend it. However, fabricating its complex curves and supporting its more extensive front-to-back dimensions may give some home constructors reason to pause.

+

A Late Addition: The G0GSF Vee-ed L-S Yagi

In April, 1999, Brian Austin (G0GSF) and Wen-Chung Liu reported on an interesting variant of the Landstorfer-Sacher Yagi. Their work is interesting in two respects. First, they simplified the complex L-S Yagi curves to a simple Vee structure for each element. Second, they use a genetic algorithm optimizer to produce the design. The outline of their design appears in Fig. 13. +
+ +
+

Since their specifications were in terms of wavelengths, the following model description follows suit.

+ 
g0gsf modified L-S Yagi                      Frequency = 146  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : wl)  Conn.--- End 2 (x,y,z : wl)  Dia(wl) Segs
+
+1         -0.579,  0.321,  0.000  W2E1   0.000, -0.165,  0.000 5.00E-03  31
+2   W1E2   0.000, -0.165,  0.000         0.579,  0.321,  0.000 5.00E-03  31
+3         -0.571,  0.479,  0.000  W4E1   0.000,  0.000,  0.000 5.00E-03  31
+4   W3E2   0.000,  0.000,  0.000         0.571,  0.479,  0.000 5.00E-03  31
+5         -0.584,  0.679,  0.000  W6E1   0.000,  0.255,  0.000 5.00E-03  31
+6   W5E2   0.000,  0.255,  0.000         0.584,  0.679,  0.000 5.00E-03  31
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          31     3 /100.00   (  3 /100.00)      1.000       0.000      SI
+
+Ground type is Free Space
+

The specifications gave no element diameters in the 2nd-hand source available to me, so I used a diameter (0.005 wl) that gave something close to the source impedance listed. However, genetic algorithms are fond of producing designs in which each element has a different diameter. So my approximation is simply that.

+

The length of each element measured from the centerline, from the reflector forward are 0.756 wl, 0.745 wl, and 0.722 wl. The reflector is 0.165 wl behind the driver, while the director is 0.255 wl ahead. The reflector and driver are bent forward of linear by 40 degrees on each side (50 degrees from the boom line), while the reflector is bent forward only 36 degrees (54 degrees from the boom line), according to a report in RADCOM for September, 1999 (p. 56-57). The side-to-side dimension of the array is a bit under 1.2 wl, but still within the EDZ aperture range.

+

In Fig. 14, we see the relative current levels on each element. It is interesting to note that the current level on the central portion of each element are higher than on any of the other models run. EDZ designs, such as the G0GSF modified L-S Yagi, are about the shortest-element arrays which--to my experience--show benefits of either impedance or gain from Vee-ing elements.

+
+ +
+

Fig. 15 shows a pattern that corresponds fairly closely to the G0GSF plot, even though its gain is about 0.3 dB higher than my model. Even the lower gain of my model is superior to that of all of the preceding models, although the front-to-back ratio is somewhat lower. The front-to-back ratio is about 17 dB, and the source impedance about 20 + j 20 Ohms, ripe for a Tee or gamma match.

+
+ +
+

Once full details of the antenna are available to the amateur community, it is likely that we shall see a number of replicas for 6 meters and up. Despite the fact that it does not achieve the pleasant 50-Ohm feedpoint impedance of the Lansdorfer-Sacher Yagi, the simplicity of construction and the freedom from dependence on loading components is likely to make the design attractive.

+

Family Resemblances: Back to In-Phase Yagis

One of the features of the G0GSF Vee-ed EDZ parasitic beam is the wider element spacing relative to other models in this series. I wondered what performance might be obtained from a pair of in-phase-fed Yagis using a spacing of 0.165 wl from the reflector to the driver and 0.255 wl from the driver to the director. Fig. 16 shows the arrangement. +
+ +
+

The result was an array having the description shown below, with all dimensions in fractions of a wavelength rather than in inches, in order to correspond with the description of the G0GSF antenna. Note that the element diameter is smaller, corresponding to about 3/16".

+ 
3 el Yagis, fed in phase                     Frequency = 145  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : wl)  Conn.--- End 2 (x,y,z : wl)  Dia(wl) Segs
+
+1         -0.796,  0.000,  0.000        -0.310,  0.000,  0.000 2.30E-03  21
+2         -0.788,  0.165,  0.000        -0.317,  0.165,  0.000 2.30E-03  21
+3         -0.770,  0.420,  0.000        -0.336,  0.420,  0.000 2.30E-03  21
+4          0.310,  0.000,  0.000         0.796,  0.000,  0.000 2.30E-03  21
+5          0.317,  0.165,  0.000         0.788,  0.165,  0.000 2.30E-03  21
+6          0.336,  0.420,  0.000         0.770,  0.420,  0.000 2.30E-03  21
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+2          11     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

The spacing between Yagi center lines is about 90" and the total overall width is just under 130". This width is similar to width that the G0GSF antenna would have if its elements had been linear.

+

The current distribution on the Yagi elements is very similar to that on the outer portions of the G0GSF antenna, as shown in Fig. 17.

+
+ +
+

The family resemblance goes further than current distribution. The in- phase-fed Yagis show a free-space gain of nearly 12 dBi (using aluminum elements), with a front-to-back ratio of over 12.7 dB. Each Yagi has a feedpoint impedance of 21.9 + j16.2 Ohms, values similar to the source impedance of the G0GSF antenna. The azimuth pattern appears in Fig. 18.

+
+ +
fig. 18 +

Several consequences follow from this exercise. First, folks often forget that genetic optimizing algorithms can identify hitherto unused configurations, but so far they have not produced new antenna types. The G0GSF antenna belongs to the general class of EDZ arrays, which are forms of phased Yagi arrays. Second, the Vee-ed elements, while initially appearing to yield significant gains in performance, turn out to be marginal adjuncts compared to comparable arrays with linear elements. At best, Vee-ing the elements permits a slightly improved front-to-back ratio for the array, but the phased Yagi pair has not been fully optimized.

+

Of course, the use of genetic algorithms is still quite new, and the production of viable designs is a significant achievement for a technique so new. Nonetheless, neither the optimizing technique nor advanced forms of phased arrays--under whatever name they go--should obscure the interrelationship of antenna types.

+

And So. . .

I undertook this little exercise to try to understand better the relationships of some interesting antennas and arrays that were about 1.25 wl wide. They turn out to be intimately related, having differences of implementation more than differences of basic electrical properties. +

At the same time, and without fanfare, I modeled these antennas on 2 meters to check out their feasibility at VHF. EDZ-based antennas are often thought of as principally HF antennas of thin wire construction. 3/16" rod construction at 2 meters and above is certainly practical. They are only 6-meter size in side-to-side dimension, and much less in front-to-back size. All of the long elements are easily adjusted for the use of larger diameter tubing. These antenna types may have their niches in the array of available VHF radiators.

+
+ +
+

Updated 7-28-99, 9-16-99, 4-10-2000, 2-14-2004, 3-14-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: EDZ / Zepp, Phased Array, VHF / UHF, Yagi


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+

Experimental Omni-Directional Antennas for 6-Meters

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +
+

Although our subject matter refers to the 6-meter band--more specifically, 50.5 MHz as a design frequency--the ideas in the following notes are applicable to any other band on which we wish to use any of the antenna designs to obtain a horizontally polarized omni-directional pattern.

+

We shall do a brief review of turnstiles and their limitations, followed by the introduction of some different types of omni-directional antennas.

+

Turnstiles

The basic idea of a turnstile is not dependent upon any one type of antenna. Any horizontally polarized antenna is a fit subject for turnstiling. The most common type of turnstile employs two dipoles, as sketched in Fig. 1. +
+ +
+

The dipoles are set at right angles to each other. We then run a 90-degree long phasing line between the two to obtain quadrature, that is 90-degree phasing. There are more complex systems of achieving the required phasing, but each is subject to the same limitations. The key requirement for the simple phasing system is that the characteristic impedance (Zo) of the phasing line must be very close to the natural resonant impedance of the individual dipoles. A 70-Ohm line is a good match for the dipole turnstile. The net feedpoint impedance will be 1/2 of the impedance of the individual dipoles, or about 35 Ohms for the antenna sketched in Fig. 1.

+

A dipole has a limited -3 dB beamwidth. Therefore, the pattern that is produces in a turnstile antenna will be less than perfectly circular. The gain variation around the rim of the pattern is a little over 1 dB for an ideally constructed turnstile. Fig. 2--on the left--shows the squared but usable dipole turnstile azimuth pattern.

+
+ +
+

The azimuth pattern--whether a free-space E-plane pattern or an azimuth pattern over real ground--does not change except for the increase in signal strength created by ground reflects and the elevation angle of maximum radiation over ground. All of the antennas that we shall discuss have take-off angles of 13 degrees when mounted 1 wavelength above ground.

+

The H-plane pattern in free space becomes the elevation pattern over ground. Fig. 2--to the right--shows the free space H-plane pattern for the dipole turnstile. From it, we should draw a clue as to one major limitation of the dipole turnstile: it radiates better broadside to the plane of the wires than off the edges--and it is the edge radiation which makes horizontally polarized communications possible from point-to-point.

+
+ +
+

Fig. 3 shows the resulting elevation pattern when we place the dipole turnstile 1 wavelength above ground. At 50.5 MHz, this is a height of about 20'. The strongest lobe is not the lowest lobe, but the second lobe. The lowest lobe of the dipole turnstile has a gain of only about 4.8 dBi. While adequate for many purposes, designers have felt that we can do somewhat better. However, we must always remember that when we create a nearly or perfectly omni-directional pattern, we should always expect lower gain than from a dipole. The dipole achieve between 7.5 and 8.0 dBi gain at the same height because it has only two lobes, with deep nulls off the ends. The dipole turnstile uses that same power evenly in all directions, so there will be lower power in each direction than in the bi-directional main lobes of the solitary dipole.

+

Low gain is not the sole limitation of the dipole turnstile. As we vary the frequency, the turnstile gives us the illusion of being a simple antenna, because the SWR remains almost constant for a very wide frequency span. However, the pattern does not stand still. As we vary the frequency off the design frequency, the pattern grows increasingly less circular. Fig. 4 shows the dipole turnstile patterns 1 MHz off the design frequency.

+
+ +
+

The patterns in Fig. 4 would also be good illustrations of other deviations from perfect construction. For example, if the phase line is too long or too short, we shall obtain non-circular patterns. If the line has a higher or lower Zo than the individual antennas, we shall obtain non-circular patterns. There are a number of schemes for obtaining a 50-Ohm feedpoint impedance by using differential lengths of line to each dipole. However, it is not impedance that sets the pattern. Instead, it is the current at each dipole being equal in magnitude and different in phase angle by 90 degrees that yields a circular pattern. Virtually all of the matching schemes result in distorted patterns.

+

The dipole turnstile, then, is a somewhat precision instrument that is not amenable to casual construction unless we can live with a non-circular azimuth pattern. If we can achieve good precision in our element measurements and in the construction of the phase line, we can make some improvements over the dipole elevation pattern and achieve a bit more gain.

+
+ +
+

Fig. 5 shows one direction that we might go: the quad turnstile. Essentially, the quad turnstile is two quad loops--shown in diamond configuration--fed at the base just as we would feed two dipoles. However, the impedance of the resonant quad loop at 6 meters composed of #14 copper wire is about 125 Ohms. Hence, we must make our phasing line out of RG-63, about the only available 125-Ohm coax. The net impedance will be about 62 Ohms, which yields an adequate coax match, especially since the quad SWR curve will be as flat as the dipole curve. Indeed, SWR tells us almost nothing about the performance of a turnstile, with two exceptions. It may tell us that we have an open circuit or a short circuit somewhere along the line. As well, it may reveal the need for some means of suppressing common mode currents.

+

Because the lobes of an individual quad loop are somewhat wider than those of a dipole, the E-plane or azimuth pattern will be somewhat more rounded. Fig. 6 shows the free space azimuth pattern (on the left) for the quad turnstile. The maximum-to-minimum gain variation is somewhat under 1 dB for the quad turnstile.

+
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The H-plane pattern on the right reveals the advantage of the quad over the dipole as an antenna to put into turnstile operation. The gain in the vertical direction does not exceed the gain in the horizontal direction. As a result, the elevation pattern of a quad turnstile with the center hub 1 wavelength above ground will exhibit a main lobe that is significantly stronger than the second lobe upward. As well, the radiation directly upward drops by about 5 dB. Fig. 7 provides a sample elevation pattern.

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The quad turnstile shows a gain (over ground at 13 degrees elevation) of about 5.7 dB, almost a full dB stronger than the dipole turnstile. However, the quad turnstile is subject to all of the same sensitivities to imprecise construction and design as the dipole turnstile. QEX ran an article in Mar/Apr, 2002, covering those sensitivities in detail.

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Updating a Practical 6-Meter Turnstile Quad

In May, 2002, I published in QST some notes on a practical 6-meter turnstiled quad for omni-directional horizontally polarized communications ("A 6-Meter Quad Turnstile," pp. 42-46). The general outline and dimensions of the antenna appear in Fig. QT-1. You will find details and background in the article. +
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+

The key elements for these update notes are the particular construction methods that I used, with crossed CPVC arms to spread the wires. Fig. QT-2 shows some of the details. Note especially the use of holes in the main mast and bolts to secure the cross arms.

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Fig. QT-3 shows the method that I used to join the phase-line and main feedline, with a plate that surrounds the mast at the bottom of the loops. The orioginal article provides explanations for all of the abbreviations in the sketch.

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Ivan Cook, K4SRB, has built an interesting variation on the turnstile quad for 6. His version uses some ingenious twists on PVC--literally. Fig. QT-4 shows Ivan explaining his antenna to a local club. In terms of construction, perhaps the most notable feature is the absence of nuts and bolts at the center junction of the support arms with the mast. Instead, Ivan uses a set of elbows and short PVC links to put the arms at the same level. He cements most joints, but leaves a few using only a friction fit.

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The reason for the friction fit is that Ivan uses his turnstile quad in the field. To transport it, he can twist the elements into a flat plane. In addition, he has used soldered connections--covered by the PVC--for the phase-line and the main feedline connections. These moves effectively eliminate the need for a mast extending from the ground to the base of the antenna. In lieu of a mast, Ivan has put a hook at the top of the central arm and hangs the antenna from a tree limb. Fig. qt-5 provides a general idea of the antenna in use.

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Ivan's variations show two things of importance to antenna experimenters. The first item is the versatility of PVC as a general support structure that is RF invisible at least through 2 meters and for many purposes through 70 cm. The second item is the ingenuity of the individual experimenter in adapting an antenna design to a specific set of needs and goals. Ivan has converted a somewhat ungainly structure into one that is field-friendly both in use and in transport.

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The quad turnstile is not necessarily an ideal antenna. It does have a disadvantage. Its loop construction essentially places two dipoles an average distance apart of 1/4 wavelength. It is the double or phased dipoles that account for the stronger lower elevation lobe of the antenna, relative to the dipole turnstile. However, it is not usually practical to place two quad turnstiles in a vertical stack. The practice is common with dipole turnstiles, but with a degree of usual carelessness that results in relatively poor performance. The pair of dipole turnstiles will interact with each other. If the stack is to have a nearly ideal circular pattern, the individual dipoles must be re-resonated in the stack. Only under this condition will they provide a circular pattern.

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For better control of the feedpoint impedance, some quad-turnstile builders have turned to the vertical rectangle as the base antenna. If we increase the verical dimension of a square and decrease the horizontal dimension, we can change the feedpoint impedance from the square's 125-Ohm value to something closer to what we need. In fact, we can arrive at 50 Ohms, but that is not our goal here. Instead, we want an impedance of between 95 and 100 Ohms so that the turnstile phaseline will give us a direct 50-Ohm feedpoint impedance. Fig. R1 provides an outline of such a turnstile using AWG #14 copper wire and set for 50.5 MHz.

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The vertical sides are about 1.3 times the length of the horizontal wires. The phaseline is 49" of RG-62, which has a velocity factor of 0.84 (for a 58.33" electrical length). The feedpoiont impedance is so close to 50 Ohms that the SWR does not rise above 1.1:1 across the first MHz of 6 meters. However, SWR is never a problem with turnstiled elements. The SWR remain nearly constant over a bandwidth that is much wider than the bandwidth over which the pattern holds its omni-directional shape.

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Fig. R2 shows the elevation and azimuth patterns of the rectangular quad turnstile. The pattern is virtually identical to the pattern for the diamond quad-turnstile version. Because the rectangles are so little out of square to arrive at individual loop impedances near 100 Ohms, the gain does not increase sgnificantly. In this case, the average gain is about 5.5 dBi with a 1-dB variation between maximum and minimum points.

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The finickiness of turnstile antennas--as well as their relatively large size at 6 meters and below--has led designers to look for other options in producing a horizontally polarized omni-directional antenna.

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Unclosed Loops

It is possible to create an omni-directional horizontally polarized antenna by employing a interrupted loop less than 1 wavelength in total wire length. There are two sorts of these loops--which resemble triangles or rectangles: larger loops with a total wire length that is about 3/4 wavelength and smaller loops with a wire length in the vicinity of 1/2 wavelength. There are interesting differences between the larger and smaller loops, so we shall look at them separately. +

Larger Loops

In any of the open-loop designs, one key to success is to find the right shape so that the radiation from the center-portion and the radiation from the legs balances into a circular pattern overall. For this reason, only certain relationships between the center portion and the end pieces will work. The current on the center and end portions is not equal. Therefore, in general, the shaping of the larger loops will be triangular. Bending the end portions towards each other is one way to fine tune the balance of currents and the resulting pattern. +
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Fig. 8 shows two examples of larger loops: the wide-gap and the narrow gap versions. The versions result from giving precedence to one of the other goals of the exercise in addition to pattern shape. The other two goals are the feedpoint impedance and the distance between the tips of the loop ends. In general, with larger loops, the two goals are not compatible.

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The top wide-gap triangle in Fig. 8 sacrifices the convenience of closely spaced tips for a 50-Ohm feedpoint impedance. In fact, like all of the loops that we shall examine, there is a high inductive reactance at the feedpoint. However, we may compensate for this with series capacitance at the feedpoint, using methods that we shall describe further on. The wide-gap model shows a 50-Ohm impedance after compensation, with a 1 MHz 2:1 SWR bandwidth.

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The antenna material for the initial design is 1/4" aluminum. Dimensions will vary with the diameter of the element. The center portion is 68" long, with 53.7" ends. The bending of the ends to make a near triangle results in a 47" dimension from the center section to the element tips. The tips are 16" apart. The pattern shows a maximum azimuth pattern gain variation of well under 0.1 dB. With the antenna 1 wavelength up, the gain over average ground at a 13-degree take-off angle is 6.0 dBi, about 0.3 dB higher than the quad turnstile.

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The top of Fig. 9 shows the elevation pattern of the antenna at the 1 wavelength height. The vertical radiation (straight up) is several dB lower than for the quad loop.

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Let's return to Fig. 8 an examine the lower loop. Here the gap is narrowed to 0.5" so that aligning the ends becomes a much simpler mechanical process. To sustain a circular pattern, the 1/4" diameter element is 62" long in the center portion. The ends are 52.9" long, resulting in a 43" distance between the center element section and the tips.

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The azimuth pattern for this version of the interrupted loop is circular within 0.6 dB around the horizon. As the lower half of Fig. 9 shows, the secondary lobes are further reduced, with vertical radiation running nearly 18 dB below the strength of the main lobes. The gain--again at a 13-degree take-off angle with the antenna 1 wavelength up--averages about 6.3 dBi, a further increase over the wide-space loop.

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Like the wide-spaced loop, the feedpoint of the narrow-gap version of the antenna has a high inductive reactance, calling for compensation. The resistive component of the impedance is about 23.3 Ohms. Therefore, we require a further method of matching this antenna--even with the reactance compensated--to a 50-Ohm coaxial cable. The simplest method is to use a 35-Ohm 1/4 wavelength section of cable. We can construct the section from 38.5" of RG-83 (with a velocity factor of 0.66, for an electrical length of 58.4") or from parallel sections of 70-Ohm cables (which come in various velocity factors, depending upon the use of solid or foam dielectrics).

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The result at the design frequency is a very close match to 50-Ohm coax. However, the 2:1 SWR bandwidth is only about 540 kHz at the antenna terminals. Due to cable losses, SWR measured at the transmitter end of the line would likely show a wider bandwidth.

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Both loops require that we place series capacitors in the line at the feedpoint terminals. The total capacitance for the wide-gap version is 4.98 pF, while the total for the narrow-gap version is 5.48 pF. These numbers are unduly precise, because construction variables will create considerable differences in the feedpoint inductive reactance.

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Perhaps the best way to arrive at the required capacitance with maximum trimming control is to install capacitors in each side of the line, using double the required total capacitance for this series set-up. We can experiment with small fixed capacitors or trim the antenna with variables and replace them with fixed values when tune-up is complete. However, for maximum control, we might consider running insulated wire or thin tubing snugly against the split fed element on each side of the line. The capacitance of the wire and the element depend upon several variables: the facing areas of conductor, the distance between conductors, and the dielectric constant of the insulation on the wire or thin tube. Since a builder will likely use materials on hand, it is impossible to provide detailed guidance. It likely pays to start with wire lengths that are too long and to prune them--evenly on each side--until the reactance disappears at the design frequency.

+

Smaller Loops

The larger loops just described will have a center-section length between 5 and 6 feet. This size is a considerable saving over a dipole or quad turnstile antenna. However, it is still considerable for many installations. Therefore, one may wish to explore interrupted loops in the 1/2 wavelength total wire region. +

There are on the commercial market single element broken loops of the smaller sort. They measure about 41" at the center, with 49" legs--approximately and use a narrow gap between ends. I do not have all of the physical specifications of these antennas--made by Par Electronics in North Carolina. Therefore, the following notes do not necessarily apply to these antennas.

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Most intermediate-size interrupted loops using single elements tend to have very low resistive components to the feedpoint impedance, while sustaining considerable inductive reactance. By compensating for the reactance first, one can use a balun or a broad-band toroidal transformer to raise the impedance to coaxial cable levels. However, at the feedpoint itself, the low impedance raises the potential of resistive losses for the home builder without a well equipped shop. Every fraction of an Ohm in a connection converts a higher percentage of supplied power into heat than with a higher impedance at the feedpoint. Therefore, one might leave such assemblies to the pros and for home construction take a cheaper and easier-to-build approach.

+

In 1997, I introduced as a limited-space 40-meter antenna the IL-ZX, the intermediate or interrupted loop impedance transforming antenna. This link will lead you to that item for background. We can apply the same approach to a 6-meter version of the IL-ZX.

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Fig. 10 shows the general outline of the rectangle forming the IL-ZX. The short portions are 25" long per side, while the longer sections are 41". There is a gap, which is set at 1". Note that the loop resembles a mutilated folded dipole. Only one wire of the over-under pair is fed. The gap consists of parallel wires, each 4" long, the spacing between the upper and lower wires.

+

In several design models, the spacing between wires was varied from 1" to 4" with only minor changes in the remnant inductive reactance at the feedpoint. As well, changing the wire from AWG #14 to AWG #12 resulted in similar minor variations in feedpoint reactance. In fact, one might well control the reactance by making the wires at the gap into arrow points, thus reducing the rate of change of capacitance between ends as the gap spacing is changed. However, changing the gap spacing with the present arrangement also creates only slow changes in feedpoint reactance.

+

The key to the design--and the reason why it is a rectangle rather than a square--lies in the need to have a circular azimuth pattern and a feedpoint impedance with a resistive component near 50 Ohms. The dimensions noted above result in a pattern with about 0.1 dB variation. The top portion of Fig. 11 shows how nearly circular the pattern is with the antenna 1 wavelength over average ground. The elevation pattern is equally well-controlled.

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Since the antenna is smaller than the larger loops that we discussed, the average gain of 5.8 dBi may seem surprising. The resistive portion of the feedpoint impedance is about 58 Ohms, and the 2:1 SWR bandwidth is about 500 kHz. Thus, the operating bandwidth matches the narrow-gap large loop, but not the wide-gap larger loop. The gain levels of all three are comparable.

+

The IL-ZX loop has a considerable inductive reactance, and required about 4.32 pF of total capacitance--or 8.64 pF per feedpoint terminal. The notes given earlier on methods of providing the required series capacitance for the larger loops are equally applicable for the IL-ZX.

+

One of the advantages of the loops that we have been discussing is the ease with which we may stack them. Unfortunately, many folks still labor under the mistaken rule of thumb that a stack nets the user 3 dB of gain. In fact, the gain advantage that we get from a stack depends on the spacing between antennas. For dipoles, 5/8 wavelength yields about the highest gain advantage over a single antenna, and with practical materials, this amounts to a little over 2.5 dB.

+

The goal in stacking a pair of IL-ZX antennas might initially be to further suppress vertical radiation, since that is the most useless part of the elevation radiation pattern. A spacing of 1/2 wavelength yields maximum vertical radiation suppression, but the gain advantage over a single array drops to under 2.4 dB. Although this is highly usable gain, it is simply not the theoretical 3.0 dB bandied about by so many.

+

Equally important is the fact that a stack will lower the overall take-off angle of the array. If the lower antenna is at 1 wavelength height and the upper is at 1.5 wavelengths, then the take off angle will drop from 13 degrees to 10 degrees. For a stack of 2 IL-ZXs, the gain will be about 8.2 dBi.

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Fig. 12 shows the azimuth and elevation patterns for a stack of two IL-ZX antennas. The circular azimuth pattern appears solely to confirm that we may stack these types of loops without redesign, as is required by stacked dipole turnstiles.

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The elevation pattern shows the results of using the 1/2 wavelength spacing between antennas. All lobes except the lowest have reduced strength, a desirable effect for omni-directional horizontally polarized local and regional communications.

+

The stacking harness requires careful construction. Two lengths of 70-75-Ohm coax, each electrically 3/4 wavelength long (because 1/4 wavelength sections would not meet) will transform each pre-compensated 50-Ohm impedance to 100 Ohms. A Tee fitting parallels the two impedances to result in a 50-Ohm match to the main feedline.

+

Uniform-Current Loops

+

An overlooked design emerged in 1944 (Donald Foster, "Loop Antennas with Uniform Current, IRE, Oct, 1944). Recently, Robert Zimmerman resurrected the idea in "Uniform Current Dipoles and Loops," in antenneX for April, 2006. The principle is to divide the circumference of a loop into sections such that the inductance of each wire length is offset by a periodic capacitor and so that the loop exhibits a 50-Ohm impedance--without need for any form of matching. Let's divide a square of wire into 7 sections. Each section wil be 0.12 wavelength long, for a total circumference of 0.84 wavelength. At each wire junction, we shall insert a capacitor. The capacitor size will vary with the wire diameter. AWG #14 calls for 9.63-pF units, whereas AWG #10 needs 10.31 pF capacitors. The design comes closest to an even 10 pF with AWG #12 wire.

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In real terms for 50.4 MHz, each AWG #12 wire section is 28.1" long. The square is 49.2" on a side for a circumference of 196.7". Note that the sections (7) do not correspond to the sides (4), which is no hindrance to effective antenna operation. One model of the antenna looks like the outline in Fig. 13.

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Note that it does not matter if the feedpoint is placed mid-side or offset, so long as the feedpoint is in the middle of a wire section. The figure also shows the relative current magnitude along the circumference of the loop. The level changes by under 4% all along the perimiter. (Initially, this phenomenon appears to have been the goal of the open-ended CCD long doublet, but the open ends preclude obtaining that result.).

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The uniform current square loop provides horizontally polarized radiation. Although only a little larger than the triangles, the results are equal in omni-dfirectionality and superior in gain. At 1 wavelength above average ground, the antenna gain averages about 6.8 dBi, with a total variation in gain of about 0.6 dB. The gain is almost a dB better than the best triangle. Fig. 14 shows the elevation and azimuth patterns and also reveals one significant reason for the improved gain from the loop.

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If you compare the elevation patterns with the one shown for the triangle, you will see that the loop produces virtually no radiation straight upward, leaving more energy for the lower lobes. Since the antenna does not need to compensate for rapidly changing reactance values, it shows a reasonable SWR bandwidth. As shown in Fig. 15, the 2:1 50-Ohm SWR range is 50 to 50.85 MHz. Once you arrive at a usable wire section length and employ the most precise and well-matched set of capacitors that will handle the anticipated power level, you can change the exact center frequency by altering the wire length, since the same capacitance within about 0.1 pF will hold good for nearly a 400-kHz change in center frequency.

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Among the experimental designs shown, the uniform-current square loop is perhaps the "best in show."

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Conclusion

The interrupted-loop and the uniform-current square-loop designs shown here are experimental. Any builder should expect to spend considerable time adapting local materials to the needs of the design of choice. As well, field adjustment will also require considerable care and effort. In the end, the goal is to produce a truly circular horizontally polarized pattern with a feedpoint impedance compatible with the main feedline. Hence, much work will be devoted to proportioning the antenna for pattern shape, and an equal amount of work will go into compensating for the reactance and arriving at a usable resistive impedance. +

In the end, it is doubtful whether the loop designs are any less finicky than the turnstiles. Instead, they simply change the places in construction and design that require close attention to detail. Producing a circular pattern that is horizontally polarized is no mean feat, whatever the design direction we take.

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For frequencies above 400 MHz, the design concepts can be applied to circuit-board construction techniques, since the elements and capacitors are easily fabricated with these methods. The antenna would be only a few inches per side. However, detailed design would require FDTD or comparable techniques that are not at my disposal.

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Updated 12-28-2001, 01-20-2006, 03-31-2006, 04-03-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Turnstile, VHF / UHF


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The Flat-Plane Reflector for 432 MHz
+ Alternatives to Vertically-Oriented Yagis for Broad-Band Use

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L. B. Cebik, W4RNL

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The search for a good wide-band vertically polarized antenna with utility-level performance goes on and on, with various candidates being offered as the current champion. Perhaps a review of some alternatives might be useful, starting with a Yagi as a usable standard, and then looking at some flat-reflector alternatives, and closing with a modest corner reflector.

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A 6-Element Wide-Band Yagi

In the summer of 2001, I published a set of designs for wide-band Yagis for 420-450 MHz using from 4 to 8 elements, each 0.5" in diameter. See Wide-Band Utility Yagis for 420-450 MHz: 1. 4- and 6-Element Models. From the set, I shall take the 6-element version because it present a good set of utility figures and is comparable in length to at least one dimension of some of the antennas to follow. Fig. 1 presents the Yagi outline. +
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The following table gives the dimensions in inches:

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       6-Element Wide-Band 435-MHz Yagi
+Element                 Length            Space from
+                        Inches            Reflector (Inches)
+Reflector               13.46             -----
+Driver                  12.32              5.94
+Director 1              11.10              9.72
+Director 2              10.79             16.18
+Director 3              10.20             24.94
+Director 4               9.80             33.94
+Elements are 0.5" diameter aluminum and should be considered well insulated and
+isolated from any conductive boom material.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The Yagi provides a very low SWR across the entire band, as evidenced by the 50-Ohm SWR plot in Fig. 2. For this antenna and those to follow, all data is from NEC-4 models of the antenna 20' above average ground.

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The following table gives a spot check of performance across the band when used as a vertically polarized antenna. At 20' up, all of the antennas have TO angles (elevation angles of maximum radiation) between 1.5 and 1.6 degrees, assuming a clear path and flat, uncluttered ground.

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+                 6-Element Wide-Band 435-MHz Yagi Performance
+Freq.       Gain        Front-Back  Beamwidth   Feedpoint Z       50-Ohm
+MHz         dBi         dBi         degrees     R+/-jX Ohms       SWR
+420         15.86       18.26       65.2        44.5-j 9.6        1.27
+435         16.62       25.79       59.6        45.1+j 4.3        1.15
+450         17.25       17.32       53.4        50.7+j 9.7        1.21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the Yagi exhibits a very flat SWR, some other figures show considerable variation, even within the relaxed standards one might associate with a utility antenna. For example, the gain varies by almost 1.4 dB, while the front-to-back ratio varies by almost 8.5 dB. Even the half-power beamwidth varies by almost 12 degrees from one end of the band to the other.

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As well, Fig. 3 exhibits a considerable variation in the azimuth pattern, especially among lobes other than the main forward lobe. As we raise the frequency, the single rear lobe at 420 MHz splits into two lobes that gradually work forward until at 450 MHz we have a new single rear lobe with two prominent rearward sidelobes. The forward sidelobes are down from the main forward lobe by only 14 to 15 dB across the band.

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The Yagi's strong suit is gain, which averages about 16.5 dBi. However, some wide-band vertical antenna users may wish to achieve better patterns with less variation in operating properties as we change frequencies. If we take the 3' by 1' dimensions of the utility Yagi as a general building limit guide, then we must begin to think of other antenna arrangements.

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The Flat-Panel Reflector and 3 Driver Systems

Until recently, the flat-panel reflector has been largely ignored in the amateur community. However, it offers the potential for providing a basis for some antennas with good performance, accompanied by minimal changes in operating characteristics across the entire 420-450-MHz band. In addition, the actual performance level can be improved simply by increasing the size of the reflector without change to the lengths of driver elements or their spacing from the reflector. Of course, this latter phenomenon occurs with certain limits of reflector size, although I do not know exactly what the limits might be. In each specific antenna case, we shall examine a small reflector (24" wide by 20" high) in some detail, but also sample a larger reflector (44" wide by 32" high) with about twice the surface area. +

For all but one of the antennas that we shall examine, it makes no difference whether we construct the reflector from a series of vertical bars about 2" apart, from a screen mesh, or from a solid panel. (The double-quad version will require either a screen or a solid panel.) Construction considerations, along with the ease of obtaining materials, will largely determine the selection of the flat-reflector type.

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A flat reflector has a special advantage: we may mount it close to the supporting mast, thus easing certain (but not all) challenges of structural durability.

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A Single-Dipole Driver

Let's consider the flat-panel reflector and single dipole in Fig. 4. +
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The driver dipole is 0.5" in diameters and spaced 4.7" from the reflector. One of the flexibilities offered by the flat-reflector + driver system is that you can adjust the feedpoint impedance of the array by juggling the reflector-driver spacing and driver length for any vale between 50 and 100 Ohms without serious harm to the overall performance figures.

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Fig. 5 shows that we can obtain a 1.5:1 SWR maximum across the entire band. Should you wish to emphasize only part of the band, you may adjust the driver spacing and length to move the SWR curve in either direction.

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The following table provides modeled performance figures for the single-driver array.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Flat Reflector with Single Dipole Driver Performance
+Freq.       Gain        Front-Back  Beamwidth   Feedpoint Z       50-Ohm
+MHz         dBi         dBi         degrees     R+/-jX Ohms       SWR
+420         13.36       15.66       84.4        40.4-j15.5        1.50
+435         13.42       16.24       84.0        48.7+j 3.1        1.07
+450         13.44       16.79       83.8        58.5+j21.5        1.53
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Across the entire band, the gain varies by less than 0.1 dB, although the average value is 2 dB below that of the Yagi. The front-to-back ratio varies by just over 1 dB, while the beamwidth varies by just over a half degree. Hence, the user can expect virtually identical performance from the antenna anywhere in the band. For that reason, a single sample azimuth pattern suffices to illustrate the well-controlled pattern created by the antenna. See Fig. 6.

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+ +
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The reflector dimensions for the antenna just shown are 24" by 20". If we enlarge the reflector to 44" by 32", creating just over double the surface area, we increase the gain at 435 MHz to 14.22 dBi and the front-to-back ratio climbs to 19.18 dB, with a beamwidth of 82.8 degrees. These are gains over the smaller model of about 0.8 dB for gain and 3 dB for the front-to-back ratio, with a beamwidth loss of just over 1 degree. Fig. 7 shows that the rear portion of the pattern draws inward without creating problems for the forward part of the pattern.

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As Fig. 8 shows, the SWR curve does not significantly change despite the increase in reflector area.

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The single-dipole-driver version of the flat-plane reflector array provides smooth performance, but remains noticeably lower in gain than the Yagi. However, the flat-plane reflector lends itself to a number of interesting driver variations.

+

A Dual-Dipole Driver with In-Phase Feeding

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A pair of dipoles at least 1/2 wavelength apart and fed in phase will provide considerable bi-directional gain over a single dipole. If we place these 2 dipoles in front of a flat reflector, we may accrue most of this gain in the form of a stronger main forward lobe for a flat-plane reflector array.

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For our design experiment, let's use the same small 24" by 20" reflector. Then the final array will have the appearance of the sketch in Fig. 9.

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The dipoles are longer and spaced further away from the reflector than the single dipole in our first attempt at a flat-plane reflector array. These dimension arise from the requirement for in-phase feeding of the dipole pair. The dipole length and spacing emerge from design goal of achieving a 100-Ohm resonant impedance for each dipole. One of the flexibilities of the array (which also applies to the corner reflector) is the ability to adjust the driver element(s) spacing for virtually any desired impedance in the 50 to 100 Ohms range, with suitable changes in length to eliminate reactance at the design frequency.

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The 100-Ohm dipoles are nearly an exact match for a 100-Ohm transmission line running from each dipole to a center point, where they join in parallel. The result is a 50-Ohm impedance for the main feedline. We achieve a very broadband array in terms of SWR by matching the "phasing" line to the dipole. Had we used 50-Ohm dipoles with a 75-Ohm line to transform the impedances to 100 Ohms, we would shrink the bandwidth somewhat, since the required 1/4 wavelength lines would be the required length for only a small part of the 30-MHz bandwidth.

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Constructing the required dipoles and their phase lines is likely best done with a version of a glass board. Given the match of dipole impedance to line impedance, the 100-Ohm lines can be any length, so long as the lines to each dipole ar identical. Strips on each side of the board would allow straight-line phase line design. The dipoles might also be composed of strips on the board. However, translating the 0.5" diameter round conductors of the NEC-4 model into flat strips and finding the exact line width for a 100-Ohm impedance with whatever might be the exact thickness and composition of the glass board very likely would call for use of an FDTD program--well beyond my current economic means, since virtually all FDTD programs are proprietary and expensive.

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Should you be able to meet the physical challenges of construction for the dual-dipole flat-reflector array, you will achieve an SWR plot for the 420-450-MHz range like the one in Fig. 10. The parallel reactances of the dipoles as you move away from the design frequency grow at a slower rate than would be the case for a single driver. Consequently, band-edge SWR values well below 1.25:1 are certainly possible. The following table provides the performance samples that we have gathered so far for each antenna.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+             Flat Reflector with a Dual-Dipole Driver Performance
+Freq.       Gain        Front-Back  Beamwidth   Feedpoint Z       50-Ohm
+MHz         dBi         dBi         degrees     R+/-jX Ohms       SWR
+420         14.93       16.52       53.4        56.4-j 7.6        1.21
+435         15.11       16.81       52.0        47.5-j 4.0        1.10
+450         15.25       17.06       50.6        41.8+j 1.0        1.20
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Across the band, the gain varies by about 0.3 dB, with a 0.5 dB front-to-back ratio variation. The beamwidth changes by less than 3 degrees, and is the only variation significantly higher than for a single dipole.

+
+ +
+

If we use the small reflector for the array, we pay a cost for the added gain over a single dipole (about 1.7 dB). As Fig. 11 shows, we acquire two rearward quartering sidelobes similar in strength to the main rear lobe. The rearward lobes derive in part from the dipole spacing: greater than 1/2 wavelength in order to achieve maximum gain. With such wide spacing, the individual dipoles move quite close to the edge of the reflector plane, reducing its benefits.

+
+ +
+

We may better control the rearward lobes and obtain further forward gain by using a larger reflector. If we place the array--with no changes in dipole length of spacing--ahead of the 44" by 32" reflector, we obtain the much better controlled pattern of Fig. 12. all rearward lobes are down by 20 dB. In addition we add another 1.35 dB to the gain for a total of 16.45 dBi at a half-power beamwidth of about 46 degrees. At this size reflector, the array become very competitive with the 6-element Yagi that we employed as a standard against which to measure performance. Although the flat-plane reflector dimensions are greater than those of the Yagi, the array requires no special consideration of its distance from a supporting mast. In addition, the greatest support occurs in the region of greatest mass for the array, a feature that offers lower bending moments in the wind.

+

A Dual-Quad Driver

Those uncomfortable with phase-feeding at UHF may wish to consider using a more complex driver with a single feed. In recent years, the dual-quad arrays has achieved some popularity. It is simple two diamond-shaped quads brought together and fed across the junction at the center. Fig. 13 shows the dimensions of a suitable dual-quad with our small reflector. +
+ +
+

The dual-quad is a UHF adaptation of dual loops that have been common for many years in the lower HF region. Dual deltas, dual rectangles, and dual half-squares (called bobtail curtains) have a long history of providing considerable bi-directional gain over their single-section counterparts. Like the antennas used at lower frequencies, a UHF dual quad is subject to the same rules of composition.

+

A dual quad loop, when composed of two squares, has a feedpoint impedance of about 80 Ohms. To lower this impedance to the design figure of 50 Ohms, we must change the length (side-to-side) to height (bottom to top) ratio of each loop from a square 1:1 ratio to a value of about 1.4:1. As shown in the antenna sketch, the loops in the final design are 11" by 8.6", about 1.28:1. The alteration from the free-standing ratio arises from the presence of the reflector. The reflector-to-driver spacing of 4" dictates loop alteration to maintain the 50-Ohm feedpoint impedance. The design shown in the sketch is subject to alterations in spacing, if you also change the loop dimensions to sustain the desired feedpoint impedance.

+
+ +
+

As a single-driver system, the dual-quad array cannot produce the exceptionally flat SWR curve of the dual-dipole array. As the curve in Fig. 14 reveals, the array is capable of holding a 50-Ohm SWR well under 2:1 across the band. This curve applies to the 4-mm (0.1575") diameter loop element used in the design example. Increasing the loop element diameter will yield a flatter SWR curve, but at a cost of increased loop circumference and a change in the length-to-height ratio. Practical considerations, such as the feasibility of bending the loop element material into the desired shape, may well limit the diameter of the element. In contrast, there is no practical limit to the diameter of the dipoles used in the preceding array designs.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              Flat Reflector with a Dual-Quad Driver Performance
+Freq.       Gain        Front-Back  Beamwidth   Feedpoint Z       50-Ohm
+MHz         dBi         dBi         degrees     R+/-jX Ohms       SWR
+420         14.71       28.99       54.8        47.0-j33.2        1.96
+435         14.81       29.61       54.0        55.2-j 7.6        1.19
+450         14.89       29.78       53.2        65.4+j17.8        1.50
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The table of sampled values reveals why the SWR curve for the dual-quad driver is steeper than for the other arrays: the reactance at the feedpoint changes more rapidly as we change frequency within the operating passband. However, the gain and front-to-back ratios are very stable, changing by under 0.2 dB and under 1 dB, respectively. The beamwidth variation over the entire band is only about 1.5 degrees.

+
+ +
+

Fig. 15 shows the azimuth pattern of the array at mid-band 20' above average ground at an elevation angle of 1.6 degrees. The very well-behaved side and rear lobes deserve special attention. We may obtain a high front-to-back ratio only by use of a screen or solid reflector. If we use a reflector composed of vertical bars, the front-to-back ratio will decrease by as much as 8 dB. The quad loop driver is only dominantly vertically polarized. Some horizontally polarized radiation remains owing to the driver shape. A reflector composed only of vertical bars is relatively ineffective on such radiation.

+

As well, the use of a larger reflector--the 44" by 32" sample--does not yield the dramatic improvement that it did for the dual-dipole array. The small-reflector gain values are similar for the two arrays. However, the larger reflector yields only about a 0.5 dB gain addition for the dual-quad driver (compared to the 1.35 dB addition for the dual-dipole array). Hence, even with a large reflector, the dual-quad array shows a full dB gain deficit relative to the 6-element Yagi uses as a standard.

+

A Corner Array

An alternative to the flat-plane reflector is the corner reflector. Composed of two planes at a 90-degree angle (in its most common incarnation), a corner reflector array requires only a single dipole driver. Fig. 16 shows perhaps the minimum size reflector needed for adequate basic performance as a wide-band vertically polarized array. +
+ +
+

The individual planes--whether composed of vertical bars, a screen, or a solid surface--is about 16" high and 22.6" long. The resulting aperture or distance from one extreme edge to the other is 32". The driver is a 0.5" diameter element that is 11" long and spaced 8.5" from the reflector apex.

+
+ +
+

As shown in Fig. 17, the corner reflector is capable of good SWR bandwidth. The use of a "bow-tie" or bi-conical driver elements can increase the operating bandwidth of the array. As well, increased spacing and the consequential increase on the feedpoint impedance to the 100-Ohm range can also increase the SWR bandwidth.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+               Corner Reflector with a Dipole Driver Performance
+Freq.       Gain        Front-Back  Beamwidth   Feedpoint Z       50-Ohm
+MHz         dBi         dBi         degrees     R+/-jX Ohms       SWR
+420         14.75       35.54       60.0        41.8-j14.9        1.45
+435         14.91       36.05       58.4        52.6+j 4.7        1.11
+450         15.04       36.99       57.0        65.4+j23.7        1.63
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Part of the reason why the corner reflector SWR curve is flatter than that of the dual-quad flat-reflector array owes to the smaller excursion of reactance across the band. The gain figures for the corner array are comparable to those of the dual-quad array, but the front-to-back ratio continues to improve. The variation in gain is only about 0.3 dB, with a 3-degree change in beamwidth.

+
+ +
+

Fig. 18 shows the mid-band azimuth pattern for the corner array, a version of a high-gain cardioid pattern. Increasing the reflector size can increase gain quite dramatically. If we increase the reflector size to achieve a 44" aperture with a 32" height, we achieve a mid-band gain of 16.45 dBi, once more highly competitive with the Yagi. Fig. 19 shows the resulting higher-gain azimuth pattern,

+
+ +
+

One of the interesting facts about the corner reflector is that it shows parasitically tuned behaviors. Consequently not all performance parameters increase uniformly or remain constant. The front-to-back ratio of the larger reflector model is lower (26.49 dB) than for the smaller reflector, despite the rise in gain. Moreover, the performance changes show some periodicalness: they either rise and fall or change the rate of rise as we increase the reflector dimensions either in height or in aperture. See the notes on corner reflectors for further modeling experiments (Corner Reflectors Revisited: Parts 1-3).

+

Despite the variations in the rate of gain change and the rise and fall of front-to-back values, increasing the reflector size generally increases gain. The best gain value that I have modeled would translate into a 20-dBi gain over ground, although the reflector may reach prohibitive size for the 420-450-MHz band. Nevertheless, the construction difficulties are likely no greater--even if quite different qualitatively--than those associated with long-boom Yagis of the same performance potential.

+

Conclusion

This brief survey has sought to place various forms of flat-plane reflector arrays within the context of other array forms of known characteristics. I have surrounded the flat-plane reflector antennas with a Yagi on one side and a corner reflector on the other in order to provide a reasonable assessment of performance potential, at least as best this potential can be derived from preliminary NEC-4 modeling studies. +

The notes have omitted many details that would be a normal part of any antenna design project prior to actually constructing an array. Many facets of design work for the future have received warnings or hints, but much more remains to be done before we can draw any definitive conclusions about any of the arrays discussed. Nevertheless, the flat-plane-reflector array can be a useful alternative to corner-reflector arrays and Yagis as a utility antenna for the 420-450-MHz band. The dual-dipole version of the array is especially interesting, since it can--with a larger or perfected reflector--compete easily with the best of wide-band Yagi designs and with corner reflectors with comparable reflector areas.

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Updated 11-08-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Corner Reflector, Quad, VHF / UHF, Yagi


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Some Notes on FM BC Antennas
+ Part 1: A Few Basics

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+
+

L. B. Cebik, W4RNL

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The past 4 decades since I was a DJ for a small west Texas AM radio station have seen a continuous process of trivialization of broadcast radio. The trend conquered AM first, but has since overrun FM as well. Listeners have decreased just in proportion to the rise in hype for stations--once known proudly by FCC-issued call signs, but now going under aliases such as "poop 102" or "pasture apple 88."

+

As local FM stations sound increasingly alike, one has to search far and wide for a station to suit one's listening desires. Hence, searchers have acquired an interest in antennas to increase the range of their searches. Questions about FM antennas show up in my e-mail at a rate of a couple a month. This past month, I received 4 messages, which suggested that some notes may be in order.

+

In this small set of notes, I shall cover some basics about FM antennas and antenna systems. Then we shall turn to some strategies for covering the 88-108-MHz band with high-gain, directional antennas that one can build at home. Among the antenna types that we shall examine are Yagi directional beams and log periodic arrays. Both of these antenna types a horizontally planar, that is, they are wide and long, but not vertically thick. We shall also examine an antenna that is wide and high, but does not share the long boom length of the other arrays.

+

Antenna and Antenna Systems

Fig. 1 shows the distinction between an antenna and an antenna system. The antenna device itself is only one part of the system. The system includes the antenna, the feedline (properly, the transmission line), and the FM receiver, plus some auxiliary devices. +
+ +
+

Let's start at the FM receiver. Most AM receivers come with a built-in antenna, usually a ferrite bar wound with a long stretch of thin wire. The antenna is adequate for local reception and occasionally for some catch-as-catch-can nighttime DX.

+

FM receivers normally lack antennas. Some may use a short lead to a piece of thin metal folded over the line cord (for AC-powered receivers). Some may have rabbit ears. And some may include that ubiquitous folded dipole that hangs limply because no one keeps the instructions on how to hang it and use it.

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If you feel the need for an external antenna, either in the attic or above the roof, it pays to begin with a simple antenna and work upward to something fancier. One reason (but not the only one) for this strategy is that some FM receivers are subject to overload from strong signals. If you add an external antenna for improving the reception of weak signals, you will discover that local signals may be proportionately stronger. How well your receiver handles very strong signals varies from one model to another, with low-end receivers being most susceptible to various forms of distortion and false signals. So proceed slowly as you progress toward antennas with higher gain.

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It may be the case that simply having a simple antenna in a higher location may provide all of the sensitivity increase that you need. FM reception is largely line-of-sight, and increasing the antenna height increases its "seeing" distance to the horizon. In addition, the main floors of most houses are filled with metallic objects that can shield the antenna from its desired signals. By raising the antenna to an area that is mostly free and clear of metallic clutter, we can often obtain the performance we want. (Of course, once we get used to this performance level, we may yearn for even higher levels.)

+

Between the receiver and the antenna is the transmission (or feed) line. Fig. 2 shows the two most common types: parallel line, sometimes called TV twinlead, and coaxial cable. TV twinlead is inexpensive and--when properly installed--low loss. Coaxial cable tends to have higher losses, although the loss levels vary considerably from one type to the next. However, if you experience unwanted interference pick-up on twinlead, you may need coaxial cable. Again, it may pay to begin simply and inexpensively and then proceed to higher-cost materials as needed.

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TV twinlead has a characteristic impedance around 300 Ohms (although I have seen some very cheap stuff with an impedance closer to 200 Ohms). If your run has any section exposed to weather, use a high quality line. Your receiver may have one or both of two types of antenna connectors. One type is a set of screw terminals: these are designed for TV twinlead connection. The other type is a connector, normally type F, for a coaxial cable. F-connectors are standard in the cable industry and cheap, although quite effective when installed correctly. Their size is suited to 75-Ohm cables: I recommend that you use the cable type rated for cable TV service rather than RG-59 for lower losses. The longer a coaxial cable run, the more important it becomes to use a low-loss cable type.

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Suppose that you wish to use coax, but have only screw leads. Or vice versa. There are inexpensive feedline transformers available from Radio Shack and other outlets to transform 300 Ohms to 75 Ohms or 75-Ohms to 300 Ohms. These are actually 4:1 ratio transformers, and so they will also do a decent job transforming between 50 and 200 Ohms. However, they are power rated only for receiving applications.

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So now we have progressed from the receiver through the transmission line and any required transformers to the antenna proper.

+

Some Antenna Basics

FM broadcast signals--like television signals--are normally horizontally polarized. Therefore, a vertical antenna is unlikely to do much good in the quest for better reception. Instead, the most likely antenna that you might use will be a dipole or an antenna based on a dipole. +
+ +
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Fig. 3 shows a dipole and a directional beam in outline form, along with the general shape of the patterns of reception for each. On the pattern graph, the line shows an equal level of receiving sensitivity all the way around the antenna. It is called an azimuth pattern. Since virtually (but not quite) all reception is line-of-sight, this pattern is a fairly good guide to what you can expect from a given antenna type. Of course, each antenna model will have its own unique pattern, although the two shapes shown are typical.

+

The dipole has a bi-directional pattern roughly shaped like a figure 8. The directional pattern from the beam is stronger in one general direction than the dipole, but considerably weaker in most other directions. Both types of antenna exhibit very weak sensitivity directly off the ends of the element (or elements, for the beam).

+

Comparing antenna performance is a matter of comparing the maximum power gain of one antenna to another. For reception, we measure the maximum sensitivity in the most favored direction against a standard. For most purposes, the standard is an isotropic radiator that radiates equally well in all possible directions. So we set down the maximum gain in decibels relative to an isotropic radiator or dBi. The dipole might have a gain of 7 dBi while the beam might have a gain of 12 dBi. In the favored beam direction, a received signal will be 5 dB stronger than a signal from a dipole.

+

Decibels are a logarithmic function. Hence, 3 dB comparative gain advantage means a signal that is twice as strong. A 6-dB advantage is a power gain of 4. A 10 dB gain advantage is a power gain of 10. From these handy checkpoints, you can interpolate other values without calculating the a power gain in dB equals 10 times the log of the power ratio. In the other direction, to be 3 dB weaker is to be half as strong, etc.

+

I have specified dBi as the standard that I shall use in these notes. There are older standards, like dBd, or decibels gain over a dipole. However, that figure is a conventionalized gain for a dipole in free-space. Hence, the gain in dBd is always simply 2.15 dB less than the gain in dBi. One reason for using dBi is that dBd can be confusing. For example, our sample dipole, when placed high over real ground, has a gain of about 5 dBd or dB over a dipole. That is to say, the gain of our dipole over ground is about 5 dB better than the gain of a perfect dipole in free space (away from any reflective ground surfaces).

+

Both of the antennas in Fig. 3 are directional. That is, each is more sensitive in some directions and less sensitive in others. We simply call "uni-directional" antennas directional. The dipole is an example of a bi-directional antenna, that is, one equally sensitive to two directions. Note that the directions of sensitivity are broadside to the dipole, with a total lack of sensitivity off the element ends. In contrast, the beam favors a single direction. However, it has a less sensitive rearward structure to its pattern. For directional beams, we can specify a second performance characteristic besides maximum forward gain. The new parameter is front-to-back ratio, usually specified as the ratio of sensitivity in the forward direction to the sensitivity rearward. Hence, we specify it in dB. The higher the ratio, the better the rejection of unwanted signals to the rear of the antenna. Of course, the dipole has a ratio of 1:1 or zero dB. Hence, we never mention front-to-back ratio when thinking of dipoles.

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Directional and bi-directional antennas require a method of pointing our antenna at a desired station. If we have only one station for which we need more sensitivity. then we can mount our antenna so that it points toward that station. However, if we want to scan the horizon, then we shall need to add to our antenna system a method for turning the antenna. TV rotators are available for this purpose. So we have another auxiliary piece for our antenna system. The rotator will not only require the motorized turning unit, but as well a multi-wire cable connecting the motor unit to the control unit, which is usually installed near the receiver. Fig. 4 shows a typical system in outline form. The more demands that we put on our antenna system, the more complex and expensive it becomes.

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The Dipole

Let's begin our investigation of antennas with the most rudimentary: the dipole. A dipole is a center-fed, resonant (or near-resonant), half- wavelength antenna. However, the moment that we turn from abstract definitions to actual antenna practice, we meet with two types of dipoles: the straight and the folded. See Fig. 5. +
+ +
+

There is no basic difference in the performance potential for the two types of dipoles. Indeed, most of the advantages assigned to one or the other disappear into a fog on the frontiers of antenna performance. Perhaps the folded dipole has one advantage: since it forms a complete loop, the element does not build up a static charge between element tips. However, the azimuth patterns for each are the same.

+

The chief advantage of one over the other is the feedpoint impedance. The straight dipole has an impedance at resonance of about 70-72 Ohms, a good match for 70-75-Ohm coaxial cable. A folded dipole of standard design has a resonant impedance of about 280-288 Ohms (4 times that of a straight dipole), and the impedance is a good match for 300-Ohm twinlead. However, if we wish to mix and match our dipoles and transmission lines, we can always insert one of those 4:1 transformers so that we obtain a good match.

+

The FM broadcast band is very wide, since it extends from 88 to 108 MHz. The band has about a 20% bandwidth (the difference between the upper and lower end frequencies, divided by the center frequency, times 100 to get a percentage). Over that range, the sensitivity of a dipole--straight or folded--will not significantly change. However, the feedpoint impedance will change. That fact leads us to the subject of Standing Wave Ratio or SWR.

+
+ +
+

The SWR is a measure of the closeness of the match between the antenna feedpoint impedance and the characteristic impedance of the transmission line. The lower the SWR value, the closer the match. As Fig. 6 shows, there is no difference between the curves of a straight dipole connected to a 75-Ohm coaxial cable and a folded dipole connected to 300-Ohm twinlead. (If we mix and match, a high-quality transformer will add nothing to the SWR.)

+

We cut our dipoles for 98 MHz, the center of the band. Incidentally, a 98-MHz straight dipole made from 0.25" diameter rod will be about 57.2" long end-to-end. The same dipole made from thinner wire, say AWG #14 house wire, will require 58.0" A typical twinlead dipole will be about 57" end-to-end. A common question I receive is whether the gap at the center where we connect our transmission line in series with the wire is part of the overall length or adds to the overall length. It is part of the overall length and is not very critical. Gaps from a quarter inch to nearly 1 inch do not affect the end-to-end length. If you wish to move the SWR minimum lower in the FM band, then add about 4 inches to the lengths suggested. If you prefer the upper end of the band, subtract about 4 inches. If you wish to be more precise about the length to which you cut your dipole or folded dipole, then the following table will serve as a guide. The 91-MHz version will cover the low end of the band with a good match to 70-75-Ohm coaxial cable, while the 105-MHz version will do the same for the upper end of the band.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                             FM Band Dipoles
+
+                                       Length in inches
+Straight Dipoles            91 MHz          98 MHz          105 MHz
+Diameter
+0.25"                       61.6            57.2            53.4
+AWG #14 Wire                62.5            58.0            54.1
+
+Folded Dipole
+Twinlead                    61.4            57.0            53.2
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

I may seem to be a bit cavalier in my treatment of lengths in the face of the fact that the curves show end SWR values around 4:1. In fact, these SWR values are not of great concern for receiving purposes--although they might be for transmitting. SWR is an indicator of, but not a measure of, losses in the antenna system from the antenna to the receiver. If you use good quality transmission line and the lead is well-installed and not too long, then you will not likely detect any difference of performance between the band edges and the band center.

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Note that this generalization applies to dipoles, but it may not apply to other antenna types. Some directional antennas have inherently narrow operating ranges, that is, the range through which the pattern characteristics of the antenna are approximately the same. So some beam antennas will show significant differences in performance as we move from one end of the band to the other. We shall examine both narrow- and broad-band beams in the course of our little safari through the antenna jungle.

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If bi-directional reception is suitable for your needs and if you only need more sensitivity, then a dipole in the attic or on top of the roof may be all the antenna that you need. You can make an assembly from PVC and use wire or rod inside of it for weather protection. With a Tee fitting at the center, you can drop your cable down the center and use the vertical PVC section as the mast. Compared to hanging a dipole in the basement or living room, the added height it takes to reach the attic or roof can add considerably to received signal strength.

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You can make folded dipoles from TV twinlead or from bent rod, wire, or tubing. If you plan to mount the antenna out of doors, I do not recommend use of the folded dipoles often packed inside the FM receiver box. Their durability in weather is always suspect. However, you can hang a wire folded dipole in the attic by tying cord to the two ends and nailing the cord to roof beams. However, in any attic installation, be sure that the roof is not lined with foil-faced insulation above the antenna. Such insulation can be like throwing the antenna inside an old coffee can in terms of shielding it from its real work.

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An Omni-Directional Antenna

Suppose that you wish to have an attic or rooftop antenna for increased sensitivity, but do not want to add a rotator to a directional beam. Then you may need an omni-directional antenna. However, as we noted in the beginning, we shall need a horizontally polarized antenna, and verticals do not meet this need. So our antenna becomes somewhat more complex. +

The most common type of antenna used for omni-directional antenna is the dipole turnstile. The antenna derives its name because the elements resemble an old-fashioned turnstile used in stadiums and subways. Fig. 7 shows the general outline of a dipole turnstile using straight elements.

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The figure also shows the pattern of the turnstile along with a dipole pattern for comparison. An antenna has a fixed overall sensitivity. The dipole shows that sensitivity in two lobes, one on each side of the wire. However, if we take that same sensitivity and spread it around in a nearly perfect circle, then the sensitivity level at an given point is less than maximum gain of a dipole (but stronger than the minimum gain of that dipole).

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The turnstile consists of two dipoles that do not touch each other. We send our main feedline to the feedpoint of one dipole. From those terminals to the feedpoint of the other, we run a 70-75-Ohm transmission line that is 1/4 wavelength long and called a phase line. At 98 MHz, the center of the FM band, 1/4 wavelength is 30.11". However, every transmission line has a velocity factor that makes it electrical length longer than its physical length. If we use foam-type coax for our phaseline, then the velocity factor will be about 0.78. So we multiply our true 1/4 wavelength by the velocity factor to come up with 23.5", the physical length for our phase line.

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The main feedpoint impedance will be 1/2 the value for a single dipole. That value will be about 36 Ohms for our straight dipole turnstile. A 50-Ohm coax lead would provide an adequate match for the system at both ends of the line.

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We can also substitute folded dipoles for our straight dipoles. In this case, we would make our phase line from 300-Ohm twinlead. Many types of twinlead have a velocity factor of 0.8, which would make our 1/4 wavelength line 24.1" long. The main feedpoint impedance will now be about 140 Ohms. If we install a 4:1 transformer, we end up with a 35-Ohm impedance for the same 50-Ohm coaxial cable transmission line to the receiver.

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Before you run out and build or buy a straight or folded dipole turnstile, lets examine one more property of the antenna. The SWR curve for a turnstile is very shallow, so in terms of its ability to match a feedline, it is a very broadband antenna. However, its pattern is actually very narrow-banded. To see what I mean, examine Fig. 8.

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The graphic shows the nearly circular pattern at 98 MHz, the frequency for which I designed the array. However, as we move away from that frequency, the pattern becomes less and less circular. By the time we reach the band edges, the pattern has evolved into deformed peanuts, indicating a bi-directional sensitivity in differing directions at the two band edges. The pattern distortion results from the fact that the phase line is no longer exactly 1/4 wavelength at the lower and the higher frequencies, and so the phasing is imperfect.

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This property is not necessarily fatal to the antenna. However, the pattern shifts may mean that you will do a lot of fine antenna turning before locking it in place. The turning is to locate your most favored stations at each end of the FM band. If you are lucky, you may hit them all in the most sensitive areas of the antenna pattern.

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An alternative is to create a dipole turnstile for the portion of the FM band that you most prefer. Use the dipole lengths from the earlier cutting table for the bottom, middle, or top of the band. The 91-MHz straight dipole turnstile would need a 25.3" length of 0.78 VF coax for its phase line, while the 105-MHz version would need a length of 21.9". The folded dipole turnstile using TV twinlead uses a 25.9" phase line for 91 MHz and a 22.5" length for 105 MHz.

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Bigger Antennas

If you cannot fit your listening desires into what the turnstile or the dipole have to offer--or if you desire even greater sensitivity--then you may need to think in terms of a directional antenna along with its rotator. In the next episode, we shall look at some strategies for using directional antennas to improve FM weak signal reception. However, be forewarned that beam antennas are not a simple cure-all for every situation. They have limitations, complexities, and expenses. +

Directional beams are for the very serious FM DXer who needs or deeply wishes to capture weak signals. For those who simply need a boost to their reception capabilities, an attic or roof-top version of one of the simple antennas that we have so far covered will likely do the job. Even if you think that you may wish to go to a bigger antenna, one of these antennas is a good intermediate step so that you can evaluate your situation. You can set up a dipole on a temporary mast that extends just over your roof-top. Mount the mast securely, but not so tight that you cannot turn it.

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Now listen to the quality of reception to you get. Check for strong local station overload of your receiver. Check weaker stations and see if you can null out stronger ones that are near in frequency and that seem to want to capture the frequency of the weak one. Turn the dipole slowly to see if the strong station weakens significantly when the dipole end points toward it. If you have a distant station that you wish to hear, check its performance with the dipole and see if you need further improvement to arrive at comfortable and quality FM reception.

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Once you have performed a thorough evaluation of you listening needs (if any) above and beyond a simple elevated dipole, you can decide if you need to explore the realm of directional beams--and the following episodes of this series. Even if you decide not to go further, you will have learned some important things about the performance of antennas. The first lesson is that bigger is only better if you really need it and have the wherewithal to go after it.

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Special Note: Brian Beezley, K6STI, has done some extensive design and modeling of both simple and complex FM antennas, with a special emphasis on circular polarization. All of the articles are inter-linked. so you may begin with any one of them. For example, he designed a simple circularly polarized attic antenna (web.archive.org). that makes a good starting point.

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Updated 04-09-2003, 01-12-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: Broadcast, Dipole, Turnstile, VHF / UHF, Yagi


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Some Notes on FM BC Antennas
+ Part 2: A Few Possible Yagi Beam Designs

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L. B. Cebik, W4RNL

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Suppose we decide that we need--whatever the reason--a directional beam in order to search for and enhance the reception of distant FM broadcast band stations. What are our choices? In the realm of antennas that we might build for ourselves, there is the Yagi-Uda beam and the log periodic dipole array (LPDA). As well, there are esoteric antennas normally outside the scope of home construction, as well as some over-hyped commercial offerings.

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Before looking at some other options, let's first examine the most popular antenna choice, especially for the listener who may wish to build his or her own antenna: the Yagi. We shall first orient ourselves toward this interesting and useful antenna type. Then, we shall look at a number of different designs. This episode will be filled with many tables, hopefully informative ones, but we shall stop short of actually trying to build a Yagi antenna. That subject will be worth an entire episode in itself.

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Some Yagi Basics

The Yagi-Uda array--or simply the Yagi--appeared in the late 1920s. However, it did not become popular for many communications uses until after World War II with the advent of television. As we entered the 1990s, computer antenna modeling software appeared in civilian circles, and the design of Yagi antennas reached new heights of performance and advertising honesty. Most Yagis available to communications services today begin life as a computer model. +
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Fig. 1 will give us an orientation to some of the key dimensions and operative terminology associated with the Yagi. Note that there is only one feedpoint for the antenna, on the driver or driven element. All of the other elements are parasitic. They derive their function to form the Yagi's directional characteristics from the coupling of energy to and from adjacent elements.

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Relative to the main forward lobe of the antenna, elements to the rear of the driver are called reflectors. Elements forward of the driver are called directors. As we have come to better understand the function of the elements, these names have become simply conventional designators and the label does not necessarily indicate the exact function. It is unwise to try to apply anything like a flashlight and lens analogy to the Yagi. Nonetheless, reflector elements are normally longer than the driver and directors are shorter. However, it is not necessary for the directors to be progressively shorter in any simplistic way. A Yagi designer will place an element and set its length to maximize performance without regard to its length relative to surrounding elements.

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There are three sets of critical dimensions with respect to Yagi design. One of them is the diameter of the elements. Every element that changes its diameter also affects its position in the array and its length. Hence, for the designs that we shall examine in detail, changing the element diameter to some more convenient material may well destroy the performance of the antenna.

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The second set of dimensions of critical importance is the element length. As we have seen, length will depend on element diameter--and also upon its position in the array. The third group is element position. There are several conventions for listing element position. In this episode, we shall designate position by the distance forward of the reflector.

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The distance of the most forward director from the reflector is the element boom length. When building a Yagi, select a boom a little bit longer than this measurement in order to have room to hold any mounting hardware and perhaps to cap the boom ends.

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Why element diameter, length, and position are so interactive is an interesting question that could take us a book to answer. In the context of our entry into Yagi-land, let's just note that changes in any of the dimensions will change the level and distribution of energy coupled into and out of any given element. Any change in one element ripples throughout the array and ends up changing the performance of the array as a whole.

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There are a number of performance specifications that are of considerable interest in Yagi design. Fig. 2 illustrates some new and old ones.

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The maximum forward gain of a Yagi is largely a matter of its boom length--up to a limit. Of course, for a given boom length, we need to have some sort of minimum element population. Once we meet those criteria, the longer the boom, the higher the maximum forward gain. Fig. 2 shows the azimuth patterns of a shorter-boom and a longer-boom Yagi, and the gain differential is readily apparent.

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A second basic property of Yagis is the beamwidth. We normally measure beamwidth between points on each side of the direction of maximum strength or sensitivity (or power gain in transmitting terms). We extend our measurement on either side of that heading until the radiated power is 1/2 the level in the maximum power direction. For receiving, the signal is at half strength. The angle between those two points is the beamwidth of the antenna. In general, the higher the maximum forward power or receiving sensitivity of a beam antenna, the narrower the beamwidth. High gain, narrow beam antennas are better at rejecting stations near to the heading of the desired station. However, the narrow beamwidth makes them more finicky to aim.

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We may often use more than the minimum number of elements on a given boom length to achieve a desired gain. That decision results from wanting to tailor other characteristics. For a given boom length and gain level, the fewer the elements, the narrower the operating bandwidth of the antenna. Operating bandwidth often refers to the frequency coverage over which the antenna maintains its gain, front-to-back ratio, and matched feedpoint impedance, since these are either reasons for using the antenna or conditions necessary to its effective use.

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The Yagi is inherently a narrow-bandwidth antenna. In most Yagi designs, the gain tends to change continuously. If we have 1 or more directors, the gain goes up with frequency until it reaches a peak. Then it rapidly descends and, at a certain frequency, the pattern actually reverses so that the antenna is most sensitive to the rear. In most designs, by the time we reach that pattern-reversal frequency, the feedpoint impedance has changed radically enough to make the antenna unmatchable to the remainder of the overall antenna system.

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The front-to-back ratio is a measure of how well signals are rejected when their direction is in the rear quadrants of the antenna. The most conventional measure simply compares the maximum forward gain to the gain in exactly the opposite direction. We can record the difference in dB as the front-to-back ratio. Some designers take note of the fact that the rear pattern often has lobes, some of which are stronger that the sensitivity to the exact rear of the main lobe. So they use a worst-case value for the entire rear quadrants in making the comparison. Still others average the strength of all of the rearward radiation or sensitivity and make the comparison with that figure. In this episode, as a matter of convenience, we shall use the most conventional figure, the 180-degree front-to-back ratio.

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What Shall We Look For in a Yagi?

The needs of FM listeners who also may wish to build their own antennas are as varied as the types of antennas themselves. Some want something simple that will still give a boost to the desired signal and some rejection of unwanted signals. At the opposite end of the spectrum are listeners who wish maximum gain and maximum unwanted signal rejection regardless of the challenge level in constructing the desired antenna. We shall sample both types of antennas. +

What everyone wants is a single antenna that covers the entire FM band with smooth, even performance across the entire band. If we stick to Yagis, you may not be able to realize that desire in a conventional design. However, we shall show you how close we might come to that goal.

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One requisite for a good receiving antenna is a reasonably good match between the antenna feedpoint and the feedline. All of the antennas that we shall explore will--within their operating passbands--provide a good match to 50-Ohm coaxial cable. This means a 50-Ohm SWR value of 2:1 or less across the passband. In one case, we shall reduce the peak SWR value to under 1.3:1. The results for the antenna builder and installer are the following ones. If you have 50-Ohm coaxial cable, use it and connect it directly (with the correct connector) to the input of the receiver. It will not matter even a little that the receiver has a 75-Ohm input impedance: the difference is too small to make a difference in overall antenna system performance. If you have "cable company" coax (75-Ohm material with good weathering characteristics), feel free to use it. Again, the SWR on the line will be too small to create any losses that could be noticed by the listener. If you want to use TV twinlead of very good quality and know how to install it correctly, then you may use a 4:1 transformer at both ends of the line and still have a successful system.

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A word about the gain values we shall use to characterize Yagi performance. We shall report the gain in free-space terms using the dBi standard. A free-space dipole has a gain of 2.15 dBi. For any two horizontal antennas placed over real ground, the reflections from the ground will add about 5.5 dB to the free-space figure. Hence, a dipole will have about 7.6 dBi gain at reasonable heights. A Yagi with a free space gain of 6 dBi will have a gain of about 11.5 dBi over ground. Although the numbers have changed, the advantage over the dipole (nearly 4 dB) does not change. Hence, the use of free-space figures allows us to compare one antenna with another with confidence.

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Now we are ready to explore a few Yagi designs, beginning with some very simple ones.

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3-Element Yagis

A typical Yagi of conventional design has a bandwidth of about 3% or so, where we define the bandwidth as the difference between the upper and lower limits of operating frequency divided by the median frequency between the two, times 100, of course, to arrive at a percentage. Since the middle of the FM broadcast band is nearly 100 MHz, such designs would give us only about 3 MHz of bandwidth. Unless we had a very confined interest in the FM band, it would take nearly 7 antennas to cover the band. +

By careful design--and the sacrifice of some forward gain--it is possible to more than double the operating bandwidth of even so simple an antenna as a 3-element Yagi. In the process, we may still use conventional element materials, such a 0.25" diameter aluminum. In fact, except for the last of our Yagi designs, all of the antennas in this episode will use quarter-inch aluminum.

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A 3-element Yagi, as outlined in Fig. 3, can cover about 1/3 of the FM band. Hence, if one is only interested in the lowest part of the band, where many (but not all) public radio stations broadcast, and if only modest gain is required, then a single 3-element Yagi may be perfectly satisfactory--and quite easy to build out of home center materials. Should we wish to cover the entire FM band, we might stack three of these light-weight antennas at about 5' intervals on a single mast. Separate feedlines are required for each antenna. However, one might install a switch near the receiver to select the antenna suited to the part of the band under search.

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The designs are not suitable for interlacing on one boom. Indeed, the design of interlaced Yagis is a complicated affair due to the complex interactions of the elements with each other.

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The following table presents the dimensions for 3 3-element Yagis that together cover the entire FM band.

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+                      3-Element Yagis:  Dimensions
+
+All Elements 0.25" diameter aluminum.  Element Length in inches.  Element
+Spacing from Reflector in inches.  Spacing to D1 = Boom Length
+
+           Low:  88-95 MHz       Mid:  95-102 MHz      High:  102-108 MHz
+           Space      Length     Space      Length     Space      Length
+Ref        ----       66.39      ----       61.67      ----       57.85
+Dr         23.12      61.44      21.48      57.07      20.15      53.54
+D1         41.74      54.62      38.78      50.74      36.38      47.60
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that the longest boom length--for the lowest portion of the band--is just over 41" or well under 4'. As we shall see in the next episode--devoted to home construction techniques--the antenna is well within basement and garage shop capabilities. Since the longest element is under 6', common materials are suitable for the task. The driver is forward of the center of the overall boom length, so mounting will not be a significant problem.

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For a Yagi with about a 7% bandwidth, the little 3-element Yagi design provides fairly even performance across its passband. The following table lists typical performance values for the passband (not the overall FM band) for the lowest and highest frequencies covered, as well as the center frequency of the passband. There will be slight variations from one version to the next, so these values are typical rather than absolute.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       3-Element Yagi Performance
+
+Lo = Low end of passband (88 or 95 or 102 MHz)
+Mid = Middle of passband (91.5 or 98.5 or 105 MHz)
+Hi = High end of passband (95 or 102 or 108 MHz)
+Gain = Free-space gain in dBi
+Front-Back = 180-degree front-to-back ratio in dB
+
+                 Lo              Mid              Hi
+Gain             6.9             6.9              7.3
+Front-Back       15              20               19
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The antenna provides almost 5 dB more gain than a dipole at the same height, along with excellent reduction of signal sensitivity to the rear of the antenna. Another way to view the performance is to examine azimuth patterns for the antenna. Fig. 4 provides us with typical patterns at the same passband intervals as those in the table.

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For those who need only modest gain, the simplicity of the 3-element Yagi is difficult to beat.

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4-Element Yagis

For just a few more inches of boom length, we may increase the gain of our Yagi by over a dB. The gain improvement will cost us one more element, as shown in Fig. 5. +
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The element placement of the 4-element Yagi is quite different than that for the smaller 3-element array. The driven element is closer to the reflector, and the first director is very close to the driver. In fact, it is so close, that for the upper part of the passband, it tends to carry more current and to dominate performance. You may also note that designing a Yagi is not simply a matter of tacking on another element. Not only does the spacing of elements differ from the smaller array, but as well the element lengths are also different, even though we are using the same diameter material (0.25" diameter aluminum rods or tubes).

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Perhaps the one drawback to the 4-element design is the fact that the first director is virtually on the center point of the boom. However, the antenna is so light, when properly made, that setting the mounting point a few inches ahead of the first director should create no major mechanical problems in the wind and weather.

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The following table lists the dimensions for this type of Yagi, again using 3 antennas to cover the entire FM band.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      4-Element Yagis:  Dimensions
+
+All Elements 0.25" diameter aluminum.  Element Length in inches.  Element
+Spacing from Reflector in inches.  Spacing to D2 = Boom Length
+
+           Low:  88-95 MHz       Mid:  95-102 MHz      High:  102-108 MHz
+           Space      Length     Space      Length     Space      Length
+Ref        ----       64.36      ----       60.39      ----       55.79
+Dr         17.93      63.29      16.82      59.38      15.54      54.86
+D1         21.45      59.15      20.13      55.51      18.60      51.28
+D2         43.21      56.70      40.55      53.21      37.46      49.15
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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For each version of the antenna, the boom length is only about 2" longer than required for the 3-element Yagi--and still well under 4'. The version for the high end of the FM band is just over 3' long.

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As the following table of typical performance values shows, for each part of the passband of each antenna, we increase the forward gain over the 3-element beam, with an average advantage of 6 dB over a dipole at the same height.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                       4-Element Yagi Performance
+
+Lo = Low end of passband (88 or 95 or 102 MHz)
+Mid = Middle of passband (91.5 or 98.5 or 105 MHz)
+Hi = High end of passband (95 or 102 or 108 MHz)
+Gain = Free-space gain in dBi
+Front-Back = 180-degree front-to-back ratio in dB
+
+                 Lo              Mid              Hi
+Gain             7.8             8.1              8.4
+Front-Back       14              20               11
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The 4-element Yagi does not have the nearly equal front-to-back ratio across the band that we obtained for the smaller beam. Perhaps the decision as to which of the two designs may be more suitable may, in the end, depend on the need for gain vs the need for reducing the strength of signals from the rear of the antenna. Fig. 6, which shows the azimuth patterns for each antenna at low, middle, and high frequencies within its passband, may be useful in visualizing performance and thus making the decision easier.

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Both the 3- and the 4-element Yagis are simple antennas with good performance for their physical size. Both provide a good match (SWR less than 2:1) across their passbands for a 50-Ohm coaxial cable transmission line. However, some listeners may require both higher gain and a narrower beam angle to satisfy their needs.

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6-Element Yagis

In a longer Yagi, we generally cannot cover the entire FM band in 3 steps. We shall require 4 steps and hence, 4 Yagis to do the job. For our pains in this category, we shall obtain beams with about 10 dBi gain (about 8 dB better than a dipole) and an excellent match to common 50-Ohm coaxial cable--with an SWR of better than 1.3:1. Fig. 7 shows the outline of our 6-element Yagis. +
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The designs are optimized wide-band antenna (OWA) Yagis, which have found use on both the HF and VHF amateur bands. The longest version uses a boom that is a little over 7' long, still within manageable size for a fairly light-weight installation. The following table provides the dimensions for each of the four versions needed to cover all of the FM band.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      6-Element Yagis:  Dimensions
+
+All Elements 0.25" diameter aluminum.  Element Length in inches.  Element
+Spacing from Reflector in inches.  Spacing to D4 = Boom Length
+
+                 Low:  88-93 MHz            Mid-1:  93-98 MHz
+                 Space      Length          Space      Length
+Ref              ----       65.36           ----       62.03
+Dr               16.53      64.37           15.68      61.08
+D1               23.37      59.71           22.17      56.66
+D2               42.30      58.13           40.14      55.16
+D3               60.83      58.13           57.73      55.16
+D4               88.41      55.61           83.90      52.77
+
+                 Mid-2:  98-103 MHz         High:  103-108 MHz
+                 Space      Length          Space      Length
+Ref              ----       59.02           ----       56.29
+Dr               14.92      58.12           14.23      55.43
+D1               21.10      53.91           20.12      51.41
+D2               38.19      52.48           36.42      50.05
+D3               54.92      52.48           52.38      50.05
+D4               79.83      50.23           76.13      47.89
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Like the 3- and 4-element beams, the OWA Yagi designs shown here have a 50-Ohm feedpoint impedance. Actually, the feedpoint resistance and reactance wander a bit, or the SWR would be a perfect 1:1 across the passband. However, no other Yagi design comes closer to the ideal than the OWA Yagi within its 5% operating passband.

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The following table provides typical performance figures for each of the 4 antenna designs in the dimensions table.

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+                       6-Element Yagi Performance
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+Lo = Low end of passband (88 or 93 or 98 or 103 MHz)
+Mid = Middle of passband (90.5 or 95.5 or 100.5 or 105.5 MHz)
+Hi = High end of passband (93 or 98 or 103 or 108 MHz)
+Gain = Free-space gain in dBi
+Front-Back = 180-degree front-to-back ratio in dB
+
+                 Lo              Mid              Hi
+Gain             9.9             10.2             10.1
+Front-Back       15              27               21
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The forward gain varies by only 0.3 dB across the operating passband. The front-to-back ratio shows a minimum of 15 dB, with higher values across most of the passband. As the azimuth patterns in Fig. 8 demonstrate, the pattern is clean and well behaved everywhere in the passband.

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As we try to increase antenna gain, the boom length tends to increase faster than the gain. We virtually doubled the boom length to add 2 dB of gain relative to the 4 element Yagi. It is possible to design Yagis with higher gain and still have about the same operating passband. However, their length may quickly outstrip our ability to support the antenna. The 6-element OWA Yagi will likely have a self-supporting boom. That is to say, we shall not need additional trussing to keep the boom from sagging and from snapping with the first high wind or ice of the season. However, by the time we reach about 10' of boom length, added truss-work will likely be advisable, unless we are prepared to use weightier boom tubes with thicker walls. Then, we acquire a new problem of supporting a much greater mass. If we wish to go to the trouble of using a truss with a lighter boom or using a heavier boom, then perhaps we should obtain something more than simply another dB of gain.

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An 8-Element, Long-Boom, Wide-Band Yagi

For the adventurous antenna builder, I shall add one more Yagi design to this collection. It has 8 elements on a 14' boom. Instead of 0.25" diameter rods, the elements are 0.75" tubing--which seems fitting to the larger boom material required. Regardless of the boom, the element diameter is necessary if we are to obtain the chief benefit of the design: the ability to cover the entire FM band with one Yagi. Fig. 9 shows the antenna outline. +
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The center of weight of the array is forward of director 5. The exact position will depend on the ratio of boom weight to element weight. The principle of operation is a modification of the OWA principle in which the first director is very close to the driven element. Indeed, for the upper half of the FM band, the first director controls performance more than the driver. The following table shows the dimensions.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  8-Element Wide-Band Yagi:  Dimensions
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+All Elements 0.75" diameter aluminum.  Element Length in inches.  Element
+Spacing from Reflector in inches.  Spacing to D6 = Boom Length
+
+                 Space           Length
+Ref               ----           65.37
+Dr                26.76          60.14
+D1                30.86          50.11
+D2                51.82          49.20
+D3                75.17          48.52
+D4               102.50          47.61
+D5               136.67          46.70
+D6               167.42          40.55
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

As notable as the close spacing between the driver and the first director is the fact that the forward directors become very short. Director 6 is only about 3/8 of a wavelength long at the mid-band frequency (98 MHz). The combination of the feed system, the element lengths, and the long boom length does net us a Yagi with an operating passband of more than 20% and less than 2:1 50-Ohm SWR across the band.

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We cannot expect a Yagi with such a wide operating passband to have as even a set of performance values as its narrow-band cousins. The following table samples performance at the bottom, middle, and top of the entire FM band.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                  8-Element Wide-Band Yagi Performance
+
+Gain = Free-space gain in dBi                          Frequency in MHz
+Front-Back = 180-degree front-to-back ratio in dB
+
+Frequency        88              98               108
+Gain             9.2             10.3             11.2
+Front-Back       14              17               12
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The gain shows a rising value across the band, with the peak value in the 103-105-MHz range. Front-to-back performance is modest compared to some of the narrow-band designs, but still adequate in all but severe cases of strong rearward signals.

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As shown in Fig. 10, the wide-band design does not have the well-behaved or smooth patterns that we typically associate with narrow-band designs. Nevertheless, the overall design does what it claims: it covers the entire FM band with good gain and adequate front-to-back values, along with a satisfactory match to 50-Ohm coaxial cable. The cost is a long boom and fat elements.

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We have at our disposal an array of FM band Yagis. All are technically wide-band designs, but only one is wide enough to cover the entire band. We have not covered all of the possible antennas that we might use on the FM band, but first we must pause for an important question.

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How would we go about building one or more of these Yagi designs? That is our next episode in the FM saga.

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Updated 04-09-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 3

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Go to Main Index

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Topics: Broadcast, VHF / UHF, Yagi


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Some Notes on FM BC Antennas
+ Part 3: Some Ideas for Home-Built Beam Antennas

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L. B. Cebik, W4RNL

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In the previous episode, we examined a number of practical designs for FM band Yagi antennas. Most of the designs lend themselves to home construction using basic shop tools. In this episode, we shall examine a variety of techniques that you might apply to that construction.

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We shall not provide detailed construction notes for each beam, since that would lead to an excessive amount of repetition. Instead, we shall look at general construction techniques that apply to some or all of the antennas. Indeed, for every technique, there are alternatives, and we shall look at a few options that you may have for any given stage in the building process. You may know a number of techniques that I do not.

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The process of building your own antenna involves the creative application of your own special skills, new skills that you may wish to acquire, and the adaptation of materials that are available to you. One key to the process is understanding the electrical requirements of the antenna under construction and making sure that you honor those. A second key--especially as you build for the VHF region of the spectrum--is being as careful and precise as you can. The last key is making up your mind to give the task a go and then following up with patient, careful work.

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With these preliminaries under our belts, let's begin the process.

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Elements and Booms

All but one of the Yagi designs calls for the use of 0.25" aluminum rod as the element material. Along the way, we noted that the performance of a Yagi depends upon three interlocking factors: the element length, the element placement, and the element diameter. Changing any one of these factors will alter the performance of the antenna design--or call for a redesign to account for the change. Since it is not possible for me to redesign the Yagis to suit every possible combination of materials that a builder may have, the safest path for both you and me is for me to recommend that you not change the element diameter recommended for any of the designs. +

Likewise, do not arbitrarily change the length or placement of any of the elements. (Later in these notes, we shall discuss one change that you can make.) When you cut the elements, try to be precise to 1/16" or better. The most common tool used to cut aluminum rod is the hack saw. Cut the element about 1/16" long and sand the ends down. You will both clean up any cutting burrs and refine the length in the process. Although you can use a file for the task, I prefer sandpaper. A small bench-top disk sander with medium aluminum oxide grit (100 to 150) is ideal. You can safely round the cut edge a bit for ease of handling without altering the dimension.

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If you opt to try the wide-band design that uses 3/4" diameter tubing, you may wish to use a pipe cutter to establish the element length. The pipe cutter makes a clean line and does not tend to cut at an angle, as is often the case with my hack-saw cuts. You can even up the ends with the disk sander after doing an initial deburring of both the inside and the outside of the cut end with a sharp knife.

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Aluminum rod and tubing in the sizes that these designs use may be available at home centers. However, I prefer to use antenna-grade aluminum that I purchase from mail order houses, such as Texas Towers. They sell 6063-T832 tubing in 6' lengths (for UPS shipping), which is deal for FM band projects. Their rod material is 6061-T6. The elements in our Yagis ranges from just about 4' to just under 6'. The advantage of using rods and tubes from such sources s that the electrical and mechanical properties are well known. For example, in a project that requires slipping one size tube inside another larger size, the 0.55" wall thickness allows clearance but also a close fit. Home center tubing tends to have thinner walls, making a close fit harder to achieve. As well, these materials have known strengths, and so you can estimate how well your antenna will stand up to your weather.

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Next comes the boom that supports the elements. Essentially, within the limits of these projects, you have two choices, illustrated in Fig. 1.

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If you use a non-conductive boom, you may drill it so that the elements pass through its center line. If you plan to use a conductive boom, such as aluminum tubing, then you should plan on adding insulating plates with the boom on one side and the elements on the other.

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It is possible to use through-boom element mounting with a metallic boom and still effect insulation of the elements with non-conductive bushings. However, the close proximity of the element to the metallic boom will require adjustment to the element lengths. The calculation for adjusting the element lengths is contained in an article at this site (../scales.html). However, we shall not cover those adjustments in these notes. Instead, let's focus on your two main options.

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For booms up to about 8' in length, Schedule 40 PVC is a good material to use for a boom. Since the boom will live in the weather and sunshine, be alert to an interesting fact about the standard white PVC. In some parts of the country, such as the southeastern U.S., the white plumbing PVC is quite well UV protected. I have some ten-year-old pieces in daily sunshine that are just now becoming brittle enough that I would not try to cut them with a chop saw. However, in other parts of the country, white PVC appears to have less UV protection and may last only a year or two in the sun. If your local white PVC is not UV protected, consider using the gray material in the electrical conduit section of the home center.

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PVC has an entire family of junctions, couplings, and adapters. The greatest number of these are available in plumbing white. Even where there are similar white and gray couplings, they may not be identical in both inner and outer dimensions. It pays to wander the aisles of a home center getting a good feel for what is available and adaptable to service.

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Remember that Schedule 40 PVC is sized to piping standards, not tubing standards. If you order 0.75" aluminum tubing, that is the outer diameter. If you pick up a piece of similarly sized PVC tubing, you will find that it is listed as 3/4" nominal, meaning that the inner diameter is at least 3/4". The outer diameter will be just over 1". Likewise, 1" nominal PVC has an outer diameter closer to (but certainly not exactly) 1-1/4". For the FM band antennas, I recommend either 3/4" or 1" nominal PVC for the boom.

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The reason that I do not recommend PVC for the 14' wide-band Yagi is that PVC is heavy and tends to sag in long unsupported lengths. For long-boom Yagis, aluminum tubing is standard. To make a long boom, you can use 6' lengths by combining two sizes of 0.55" wall thickness tubing. Use either a combination of 1.25" and 1.125" tubes or a combination of 1.125" and 1" tubes. For a 14' boom, we shall need 2 6' lengths of each, plus 2' or so more. (Remember my recommendation that you make the support boom a bit longer--say 6"--than the element boom length listed in the dimension charts.) Simply stagger the junctions of the two tubing sizes. You can lock the tubes together with stainless steel sheet metal screws (stainless steel, of course). However, be sure to pre-plan the screw placement so that these fasteners do not interfere with any of the element assemblies.

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The conductive boom system requires one more basic material: the plate. I tend to prefer polycarbonate (trade name Lexan), which is available from numerous mail sources, such as McMasters-Carr. It is available in 1' x 2' sheets in various thicknesses. 1/4" thick material is more than adequate for element-to-boom plates, but you may want a sheet of 3/8" thick material if you wish to make an insulated boom-to-mast mounting plate.

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Element Mounting

Let's return to our PVC boom and prepare to mount elements through it. First, we have to drill holes in the boom for the elements. Let's initially drill for only the parasitic elements, that is, every element except the driver. +

It is imperative that we keep the elements well aligned. Hence, it pays to do two things before drilling. One step is to obtain some kind of drill press. If you do not otherwise need a floor or bench mounted drill press, purchase one of the fixtures that allows you to mount your electrical drill in it. It will work well for this purpose if you also take the second step. Create from scraps of lumber a jig to hold the boom. You need to be able to lock it in two dimensions. The tubing should not be able to rotate between drillings, and the drill bit should come down for each hole at the exact center line of the tube.

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Although we shall not perform this next action until we finish all of the work on the boom, let's deal with the challenge of holding the element in place once we push it through the boom hole.

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Fig. 2 shows one way to lock the parasitic elements in place. Obtain small hitch-pin clips from your home center, hardware outlet, or mail-order source. Be sure that the 1/4" rod size is within the clip range. Pre-fit the rod to the boom and mark point on the rod where the rod meets the PVC wall. Allow about 1/32" on each side for the thickness of the pin. With a jeweler's file, create a small flat spot at this point so that your drill bit will not slip. Drill a hole that just passes the hitch-pin clip. When you are ready to assemble the beam, you can slip in the tube and add the clips. Their tiny metal mass will not affect the element's performance. However, use stainless steel clips, not the plated ones that will eventually rust when subjected to continuous weathering.

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The driver element requires special treatment, since we need to split it into two halves and make a gap between the halves for electrical connections. Let's consider two systems.

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Fig. 3 shows one system. It consists of an insulating polycarbonate plate with the two element halves mounted with brackets. Because tiny u-bolts may not be easy to obtain for the 1/4" diameter elements, you may have to make up your own brackets out of strips of aluminum. Examine the brackets used to fasten electrical conduit to walls, and copy the construction in miniature. For fasteners, use 6-32 stainless steel nuts, bolts, and lock-washers.

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Alignment will be important so that the element is parallel with the others. (The half-inch or so distance out of plane with the other elements will make no difference at all.) One technique that I have used is to rout a shallow groove in the plate so that the element is self-aligning. Do not rout the line so deeply that it weakens the plate.

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To make connections, simplicity is usually best. One simple system is to drill a hole in the gap end of each half elements--about 1/2" deep. Tap this hole for 6-32 hardware. Add a solder lug (and lock-washer, if not part of the solder lug) for making connections between the half element and the coaxial cable connector. As in every construction step, use stainless steel hardware (except for solder lugs).

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You can mount the cable connector to the boom by using 1" aluminum L-stock to make a bracket. 1/16" thick material works well. I tend to do my drilling with a piece of stock larger than I need. Then I cut it to size and finally shape the edges to suit the job.

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Fig. 4 shows an alternative driven element mounting system that does away with the need for a plate. However, it requires that we make the driver from 0.5" diameter aluminum tubing. At the driver position on the boom, we drill a 3/8" hole and insert a 5" to 6" length of 3/8" diameter fiberglass or similar rod. We can glue the rod in place. Then we slip the element halves over the rod. When we make connections to the tube halves, we lock them into position over the rod.

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We have selected these rod and tube sizes because they are large enough to accept 6-32 stainless steel bolts without weakening them. Smaller diameter materials will not leave enough rod material after drilling for the hardware. Smaller hardware is available, although 2-56 hardware may not be readily available in stainless steel, and 2-56 solder lugs tend to be quite tiny.

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The driver element has become thicker, so its tip-to-tip dimension must be shorter. If you opt for this system, then for each of the narrow-band Yagis, shorten the driver's overall length by 1%. (The actual figure is closer to 0.8%, but that difference will make no operational difference in antenna performance. Note that this adjustment applies only to the driver and not to the parasitic elements. If you wish to use fatter elements, then each element will have its own unique length, as calculated by a means described in the earlier noted article on adjusting VHF beam dimensions and through-boom mounting of elements.)

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The sketch also shows a connector mounting bracket that I shaped to the boom. It connects to the shell of the connector and to the element without needing any additional solder connection. Only the center pin needs to use a soldered wire that runs from the connector to the element half.

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You are now ready to assemble the beam. Simply put all of the pieces together as indicated and you are almost ready for mast mounting. However, our first mounting will be to test the antenna. Once we are satisfied that all is well for the long term, coat the driven element connections with Plasti-Dip or Brushable Electrical Tape (trade names for insulating protective coatings). Use 2 or 3 thin coatings to be sure that weather cannot penetrate to the connections, but avoid excessive amounts that will detract from the appearance of the finished product.

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To mount the beam to a mast, you may use a standard mounting plate or you may take advantage of the collection of PVC junctions. See Fig. 5 for the basic idea.

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You can estimate the center of weight for the 6-element Yagi. For the 3- and 4-element models, the weight is not critical, so you can place the center Tee fitting anywhere close to the center point. If you use this system, install the Tee fitting prior to drilling the element holes.

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From the Tee, you can use a series of threaded adapters to change the size of the mast stub. PVC has a complete array of adapters, some that are combinations of male and female threaded fitting for changing size, and some that have a threaded end and a cemented end (for the final pipe size). You may. for example, increase the pipe size to 1-14" nominal, which fits loosely over standard TV mast. A bolt through both the pipe and mast locks the two together.

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There are also cross fittings, some of which have one size pipe in one direction and a different size pipe in the other. You can likely find one that will fit the boom horizontally while sliding over the vertical mast.

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The Wide-Band Yagi

In the process of exploring construction options for the smaller Yagis, we have encountered virtually every idea that we need in order to make the wide-band Yagi, with its 0.75" diameter tubing elements. +
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Fig. 6 reveals that the task is largely a matter of finding enough polycarbonate plate and u-bolts for the job. The element, boom, and mast sizes are generally amenable to the use of marine (stainless steel) u-bolts. However, for extra security, companies like DX Engineering make such U-bolts with saddles to support the tubes and prevent crushing.

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Since the wide-band Yagi's boom will be conductive, you may use an aluminum plate for the boom-to-mast fixture. 1/4" thick aluminum stock is available, but may be more difficult to cut than polycarbonate.

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The driver element will use a mixture of techniques. It will mount on a plate. If you insert a short length of fiberglass rod (0.625" diameter) or a length of CPVC (1/2" nominal will just fit inside 3/4" tubing), you need only have the outer u-bolts, and the element will stay aligned. Make connections to the connector on its bracket with 6-32 stainless steel hardware and soldering lugs. As always, keep any wire leads as short as feasible. Coat the final connections after testing.

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The figure also gives you 2 options for element placement: above or below the boom. Letting the elements hang below the boom tends to make element alignment more durable when using u-bolts. Gravity tends to aid the maintenance of correct element positioning.

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A Sample PVC Yagi

Let's examine briefly a test Yagi using a PVC boom. The photo in Fig. 7 shows the overall structure of the 6-element antenna that is a scaled version of the design in Part 2. +
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Besides counting elements, there are two features worth noting in this photo. First, I have capped the boom ends to keep insects and dirt from finding a home inside the boom. Second, note the collection of adapters running from the mast stub on the boom and the larger PVC used as a test mast.

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Fig. 8 gives us a closer view of the unique double-boom section that I designed into the assembly--and a clue to why it is there. If you make a mental line from the element on the main boom, it runs through the Tee connector on the lower boom section. To avoid having to run the element through a Tee fitting, I preplanned the assembly to add the lower secondary boom section. In fact, I constructed the entire boom before drilling any holes in order to be certain that everything was straight and true. A side benefit of the secondary boom section is that it shortens the lengths of PVC boom extending to the end caps. The shorter the PVC run, the less the sag.

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A close-up of one boom end appears in Fig. 9. It shows the boom cap and the hitch-pin clips securing the element in place. Some builders have used compression C or E clips, but I have found the hitch-pin clip to be more secure in the long haul.

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The final photo--Fig. 10--is a close-up of the fat-driver and connector assembly. The connector in the photo is a BNC to suit the cables to my test equipment. However, similar brackets would suit F connectors, which tend to be standard in TV applications since the advent of cable. Incidentally, do not use slip-on F connectors. Instead, use screw-on versions to ensure a long-term connection. After all testing, coat the junction for weather protection--or use one of the newer connectors that are weather secure. However, for the chassis-mounted connector on the bracket, coat the exposed connections.

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Part of my object in developing the antenna in the photos was to minimize the number of nuts and bolts required by the antenna. Besides non- critical hitch-pin clips, the antenna needs only two sets of 6-32 hardware for the driver junctions at the gap and two #8 sheet metal screws to fasten the connector bracket to the boom. Whenever you use a sheet metal screw in PVC, make the pilot hole a drill-bit size smaller than you would for metal. This practice allows the sheet metal screw to get a good secure bite into the plastic material. Of course, even the sheet metal screws are stainless steel.

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Stainless steel hardware serves two purposes. It does not rust. In addition, it avoids reactive bi-metallic contact between two metals. Bi-metallic contact that permits electrolysis eventually weakens the connection mechanically and tends to add electrical resistance to the contact.

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There are enough construction ideas and principles in these notes to get you started on your own antenna building project. However, do not think that these notes are the final word on home antenna building. Use and adapt your own shop equipment and skills to the task. You are likely to come up with even better, more secure, and simpler techniques. However, always keep in mind the electrical requirements of the antenna itself.

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With these notes as complete as I can make them, we can turn to our first alternative to the Yagi: the log periodic dipole array (LPDA). However, when we cover the construction aspects of this antenna, many of these notes will be very relevant to that antenna as well.

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Updated 04-09-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 4

+

Go to Main Index

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Topics: Broadcast, PVC, VHF / UHF, Yagi


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Some Notes on FM BC Antennas
+ Part 4: Some LPDA Options

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+

L. B. Cebik, W4RNL

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We have examined both the potentials and the limitations of Yagi antennas for enhancing reception on the 20-MHz-wide FM band. Most Yagi designs of reasonable size and common construction have the ability to cover no more than about 1/4 to 1/3 of the band. The one Yagi that was capable of covering the entire band used very fat elements and a very long boom.

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For full band coverage with a single antenna, one popular option is the log periodic dipole array (LPDA). The LPDA is inherently a wide-band antenna and falls in a class sometimes called frequency-independent antennas. We shall examine this option by looking at two different designs: a modest length (7.3') version with good performance and a long-boom version (14') for excellent performance. In both cases, we shall instantly notice from azimuth patterns that the LPDA at any good gain level has a smooth and regular forward lobe with no lumps or side lobes. As well, compared to the wide-band Yagi we explored, the rear lobes of an LPDA are much smaller. In other words, the LPDA exhibits a much better front-to-back ratio for the suppression of signals from the rear.

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For a given boom length, a well-designed LPDA will require more elements than a comparable Yagi. Our 7' LPDA will have 8 elements, although the narrow-band OWA (actually considered a broadband antenna among Yagis) used only 6 for the same length boom. The wide-band Yagi used 8 elements in 14' of boom, but our LPDA of the same length will use 16.

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Commercial LPDAs for FM reception come in many sizes and shapes. Some use a structure that forms a vertical V, although no particular advantage accrues to that shape. Others get by with short booms and/or fewer elements. Some sweep their elements forward, a practice that actually reduces their potential performance level. Unfortunately, marginal design is a hallmark of consumer-grade LPDAs. The two designs that we shall examine might be considered to be over-designed, but they exhibit smooth performance across the entire band, each at its own level.

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Before we jump into actual designs, let's pause for a moment to understand somewhat the basic principles and parts of an LPDA.

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A Few LPDA Basics

The log periodic dipole array differs from a Yagi in that we feed direct signal to each element. Hence, compared to a Yagi, the antenna has extra parts. See Fig. 1. +
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An LPDA has numerous elements, all of which grow longer in a very regular fashion as we move from front to back. The feedpoint is at the front end of the array. The LPDA uses a transmission line to directly feed power to each elements in the array. The current distribution on any element is thus a combination of the supplied power and the coupled power from adjacent elements. Note in the figure that as we move from one element to the next, we reverse the feedline. There are different ways of achieving the phase reversal, so some designs might not seem to twist a line. Some designs may require the use of a stub at the rear element gap, and others may not.

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The foundations of the LPDA go back to the late 1960s, with the identification of 3 critical and interlocking design factors given the names alpha, tau, and sigma. How these factor inter-relate appears in Fig. 2.

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The LPDA starts with a section of a circle. Since we will use straight elements, we can think of the LPDA as a triangle. If we draw a line down the center of the array, we shall create an angle with a line drawn along the outside tips of the array. We call the angle alpha and measure it in degrees.

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Any two adjacent elements in the array will form a ratio between the length of the shorter and the length of the longer. That ratio also describes the spacing between any two elements and the next two elements rearward. We call that ratio tau.

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The relationship of the spacing between any two elements and the length of the rearward one is called sigma. As the figure suggests, knowing any two of the three design figures let's us algebraically derive the third one. In fact, most LPDA designs begin with the designer selecting values for tau and sigma and therefore letting alpha become whatever the mathematics dictate.

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Most cursory glances at LPDAs tend to stop once we have these numbers. However, LPDA design depends on much more than these factors alone. In any LPDA, at any operating frequency within its range, there will be a most active element, that is, one showing the highest level of current magnitude. Contrary to what designers once thought, all of the elements forward of the most active element will also be active. We knew from the beginning that we needed a rearmost element that was longer than 1/2 wavelength at the lowest operating frequency so that it could be moderately active in order for the LPDA to give full performance at that lowest operating frequency. However, assumptions about how long to make the shortest element were considerably off the mark until recent times. We used to make it resonant at a frequency about 1.3 times the highest operating frequency, but that practice proved to provide too few active elements ahead of the most active one at the upper operating limit. Increasing the resonant frequency of the shortest element to about 1.6 times the upper operating frequency drastically improves high-end performance--but it also adds to the number of necessary elements in an array for a given set of tau and sigma values.

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In addition, we have learned that we may modify the lengths and spacings of the elements at the rear and the front of an array to better tailor the set of operating characteristics. We may also vary the characteristic impedance of the phase line feeding the elements to change the performance level. Indeed, as we lower the characteristic impedance, we improve gain, but at a certain point for any design, we destabilize performance. Destabilization occurs when the array--at some frequency within its operating range--shows a reduction in gain and front-to-back ratio, and sometimes shows an actual reversal of pattern. This problem also occurs if we try to cover too wide a frequency range with too few elements.

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The most complete up-to-date coverage of LPDA design appears in the 2-volume set of books, LPDA Notes on the Books Page. For a succinct technical coverage of LPDA basics, see Chapter 10 of the ARRL Antenna Book, 19th or later edition.

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These brief notes on LPDA basics tell us that a designer must not only select values of tau and sigma in order to create an LPDA. He must also consider the element population, the phase line characteristic impedance (which will have a strong influence on the impedance at the feedpoint), the employment of modifications, and a possible stub in order to come up with a complete working design. A good design should provide the following performance characteristics:

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    1. A smooth gain curve: in the FM band, perhaps no more than 1 dB variation across the entire band;

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    2. A certain minimum front-to-back ratio: that ratio tends to increase as the forward gain increases; and

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    3. A good match to a given feedline selection: under 2:1 SWR within the FM band is normal.

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Since every small change in frequency alters the current phasing difference between two adjacent elements, we do not expect a perfect flat curve. In addition, we do not expect that the gain, front-to-back, and SWR curves will coincide in terms of their peaks and valleys. Instead, we speak in terms of falling within good operating limits.

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Although these notes are not adequate to let you design your own LPDA from scratch, they may be enough to let you understand each of the two designs that we shall examine in detail.

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An 8-Element 7.3'-Long LPDA for Good Performance

Our first example of an LPDA for the FM broadcast band is modest in LPDA circles. It uses 8 elements distributed along a 7.3' boom and has the general proportions outlined in Fig. 3. +
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The following table lists the dimensions of the LPDA, element-by-element. Each element will require a center gap, and the length dimension gives the tip-to-tip length including the gap. The overall length is the element boom length. As always, you will need a support boom slightly longer to allow for element mounting hardware.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                 An 8-Element FM Band LPDA:  Dimensions
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+All dimensions in inches.  Element spacing is listed as the cumulative
+distance from the rearmost element.  All elements 0.25" diameter.
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+El. #            Length          Space from Rear
+1                68.43                 ----
+2                63.06                 15.85
+3                58.11                 30.46
+4                53.54                 43.93
+5                49.34                 56.33
+6                45.46                 67.76
+7                41.89                 78.29
+8                38.00                 88.00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The array uses an initial tau of about 0.92 and a sigma of about 0.12. The antenna is designed for a phase line using standard 300-Ohm good-quality TV twinlead with a velocity factor of 0.8. The feedpoint impedance will be close enough to 200 Ohms to permit the use of a 4:1 transformer at the feedpoint and preferably a 50-Ohm coaxial cable from that point to the receiver. The array also employs a 3" shorted stub of 300-Ohm twinlead across the rear element gap. A builder can leave the stub unsupported so long as it does not touch the support boom. As we shall see in a bit, the array is designed for a support boom and an independent phase line.

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We can sample the performance of the array across the FM band from the following table of values.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                   8-Element FM Band LPDA Performance
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+Gain = Free-space gain in dBi                          Frequency in MHz
+Front-Back = 180-degree front-to-back ratio in dB
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+Frequency        88              98               108
+Gain             8.1             8.4              7.9
+Front-Back       24              48               25
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Compared to the wide-band Yagi, explored in part 2, the LPDA has a little over 2 dB less gain. However, the front-to-back performance is much superior throughout the band. We can gain a better appreciation of these sample numbers be looking at some graphs of both the gain and front-to-back performance.

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From Fig. 4, we seem to see a gain level (red line) that has a major fluctuation. However, examine the left axis values and you will discover that the gain changes by only 0.5 dB across the entire band. In terms of equal sensitivity to signals across the entire FM band, this performance is far superior to what we could obtain from the wide-band Yagi. As well, the front-to-back performance of the LPDA is also superior to that of the wide-band Yagi at any frequency of operation. The minimum value is about 24 dB. An interesting side note is a comparison of the 180-degree ratio with the worst-case ratio, indicated by the line labeled front-to-sidelobe ratio. Although the exact rearward gain shows a deep dimple, the overall front-to-back ratio in worst case terms tends to remain stable across the entire band.

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We can get a better view of the difference between the two ways of listing front-to-back performance by examining the azimuth patterns in Fig. 5. The 98-MHz pattern has the deep dimple directly to the rear, but rearward angling lobes that are a bit stronger. However, even the minimum value of 24 dB assures very high rejection of signals from the rear quadrants of the antenna.

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Equally apparent in the azimuth patterns of Fig. 5 is the clean shape at all frequencies of the forward lobe. There is virtually no change in the shape of this forward lobe at any frequency across the FM band.

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Fig. 6 shows us the changes in feedpoint resistance, reactance, and 200-Ohm SWR as we move along the FM band. By choosing the reference value of 200 Ohms for the SWR curve, we obtain the anticipated SWR values relative to 50 Ohms after we insert a 4:1 transformer at the feedpoint. The highest SWR is about 1.9:1 at the upper end of the band, a product of the design procedure that reduced the top frequency of design from the ideal 1.6 times 108 MHz in order to obtain more gain within the band from the 8 elements on the 88" boom.

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The design promises very good performance across the entire band with 1 antenna, if we can only build it. Although I shall not provide complete construction details, here are some ideas.

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First, you will need a boom. 1" to 1.25" diameter aluminum tubing is ideal, although obtaining an 8' length from which to cut the boom down to size may be difficult if you use mail order sources. You can use 6' lengths in the following way. Whatever the outer diameter you choose, cut a 6' and a 3' section. Then obtain the next size smaller that just fits inside the outer tube. Cut a 6' and a 3' section. However, when joining the tubes, let the outer 3' length and half the outer 6' length slip over a 6' length of the inner tube. Then slide the inner 3' length inside the remaining part of the 6' outer tube. Secure the tube sections with sheet metal screws. Before you nest the tubes, you will have some cleaning work to ensure that there are no burrs or other impediments that will leave you with two partially nested tubes that will not either nest in their final position or unnest for further preparation.

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Once you have a boom, prepare a set of element mounting plates. I prefer UV-protected polycarbonate (trade name Lexan), but other materials will also work. The plate dimensions are not critical. Make each one wide enough to support each half element with two mounting brackets or very small u-bolts. Some folks like to scribe a groove into the plate just deep enough so that the element rides in it, but no so deep as to weaken the plate. The plate dimension along the boom should be large enough so that the u-bolts that go around the boom are at least an inch or so from the element going the other direction on the plate.

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Once we have cut, mounted and positioned each element, it is time to consider the phase line. The gap at the center of each element can be narrow, since the space between the wires of good-quality TV twinlead is only about 3/8". Find or create solderable lugs at least an inch or so long--to separate the phase line from the boom. You can mount the lugs to the element by drilling and tapping a #6 or #8 threaded hole in the inner end of each half elements. Use a stainless steel bolt and lock-washer to fix the lug in place. Then open the vinyl insulation on the line just enough top permit soldering to the lug.

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Fig. 7 is provided mostly as a reminder for these notes, but not as a detailed drawing of all of the details.

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Note: be certain to give the line a half twist and only a half twist between each element.

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Note: Be sure to stretch the line firmly enough so that it does no sag downward to touch the boom. If necessary, add an insulator at the midpoint between elements to support the line. A piece of plastic rod drilled at each end to accept cable ties will allow fastening to both the boom and the line.

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At the rearmost element, let the line extend 3" (not very critical) beyond the last element. Solder the two line wires together to short the stub. At the front end (just in front of the shortest element), add a small plate and the kind of connector that will mate with your 4:1 transformer. If the transformer has leads instead of a connector on the high-impedance side, shorten the leads until you have just enough lead length to solder them to the short-element lugs.

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Of course, add whatever further support is needed for the transformer and the coaxial cable. Be certain--after testing--to coat all of the connections with something like Plasti-Dip or Brushable Electrical Tape to seal these connections from the weather.

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When mounting the antenna, you will use some sort of plate or other fixture to attach the rough center of the boom (away from elements) to the mast. You may have to tip a phase-line support between elements away from the mast to assure good spacing that does not disrupt the balance of the line along its length.

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Vary the construction as fits your own special skills and available suitable materials, but only after you think through what combined electrical and mechanical functions each recommended construction detail fulfills.

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A 16-Element, 14'-Long FM Band LPDA for Excellent Performance

Not only did the wide-band Yagi use a 14' boom, but as well, I have seen more than one FM narrow-band Yagi use a boom approaching this length. So I wondered what we might achieve with an LPDA designed for a 14' boom. The design required 16 elements, but like the short LPDA, performance promises to be outstanding. Fig. 8 shows the general outline. +
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The outline reveals that we will not need a stub with this design, although, as in every LPDA, we need a feedpoint. The array is designed to a tau of about 0.96 and a sigma of 0.11. The following table lists the dimensions using the same conventions that we applied to the short LPDA.

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+                 A 16-Element FM Band LPDA:  Dimensions
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+All dimensions in inches.  Element spacing is listed as the cumulative
+distance from the rearmost element.  All elements 0.25" diameter.
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+El. #            Length          Space from Rear
+1                68.43                  ----
+2                65.87                  14.43
+3                63.40                  28.33
+4                61.03                  41.70
+5                58.74                  54.57
+6                56.54                  66.96
+7                54.43                  78.89
+8                52.39                  90.36
+9                50.43                 101.41
+10               48.54                 112.05
+11               46.72                 122.29
+12               44.97                 132.14
+13               43.29                 141.62
+14               41.67                 150.75
+15               40.10                 159.54
+16               38.60                 168.00
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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What we gain for our effort reveals itself in the following table of sampled performance results anticipated from the design.

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+                   16-Element FM Band LPDA Performance
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+Gain = Free-space gain in dBi                          Frequency in MHz
+Front-Back = 180-degree front-to-back ratio in dB
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+Frequency        88              98               108
+Gain             11.0            10.7             10.3
+Front-Back       32              29               30
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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The overall gain performance is better than that of the wide-band Yagi (but at a cost of more but thinner elements). Moreover, we also obtain further improvement in the front-to-back ratio, with an average value of 29 dB. As with the shorter LPDA, we can better appreciate the performance by examining graphs of these performance values.

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Because we are working with more elements, we see that the gain and the front-to-back curves have two peaks apiece in Fig. 9. The 180-degree and worst-case front-to-back curves overlie each other, with a minimum value of about 25 dB. The gain curve looks more extreme, but once more the range is narrow--from 10.1 to 11.0 dB. These gain values approximate the best values obtained from the wide-band Yagi.

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Unlike the wide-band Yagi, we obtain the gain values with azimuth patterns that are well shaped at all frequencies, as sampled by the patterns on Fig. 10. The very diminutive rear lobes promise excellent attenuation of strong rearward signals.

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The 16-element LPDA design uses a 125-Ohm phase line so that it will yield a feedpoint impedance close to 75-Ohms for use with standard cable TV coaxial cable. See Fig. 11 for some details of the results.

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Although the resistance and reactance curves appear to be simply wiggly lines, the importance of these red curves is to reveal variations that occur within quite narrow limits. Hence, the SWR never reaches 1.5:1 for a 75-Ohm reference.

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One reason for developing the design along the indicated lines is to illustrate a different method of LPDA construction. Instead of using a support boom and an independent phase line, we shall let the boom do double duty, serving as the element support and the phase line. Fig. 12 illustrates the general principles of this method of construction.

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First, we need two 14' lengths of boom, here presuming 1" diameter round tubing or 1" face square tubing. We shall have to join shorter lengths of tubing with the next smaller size as inserts. In general, it is best if the junctions do not occur at exactly the same place long the total boom length. Binding the two tubes together into a single assembly requires that we add some plates periodically along the boom. 1/4" polycarbonate will generally do the job, with bolts through the plate and the tubes. Do not use bolts in the vertical direction, since they would short out the phase line.

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The spacing between the tubes needed for a 125-Ohm assembly differs according to the geometry of the tube. For the 1" round tubes, a center-to-center spacing of 1.59" or a gap of 0.59" gives us a fat transmission line with a characteristic impedance of 125 Ohms. Because square tubes present more surface area to each other, they require a center-to-center space of 1.86" or a gap of 0.86" for the same characteristic impedance.

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You will mount a half-element to each of the two tubes. To do this, use a die to thread the 0.25" rods to accept standard stainless steel nuts (and lock-washers). You will have to add a little over 1/2" to each half element to allow for the part that goes through the second half of the tube and outward to receive the nut. Tighten each element securely, but do not deform the phase line/boom tubes or strip the aluminum threads. (I always start at the rear with the longest element so that if I do strip some threads, I can use the rod for a shorter element.)

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Be certain to alternate the element halves as you move along the array. Designate one side as left. If you start with the left half element on the top boom, then the second left element goes on the bottom, the third on top, etc.

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You can mount a plate on either of the booms at the front and mount on it your coaxial cable connector. Run a lead from the connector center pin to the other boom tube.

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Mounting the array to a mast requires care, since the mast needs to be insulated from and separated from a metal mast. You can top a metal mast with a short section of non-conductive mast--such as PVC--and use a standard polycarbonate mounting plate. Alternatively, you can use thicker (3/8") polycarbonate with a longer vertical dimension so that the metal mast mounts well below the booms of the antenna. Whatever mounting system that you use, do not short out the two boom tubes.

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Test the antenna at ground level, not only for electrical performance, but also to see if you will need any truss work to keep the vertical stresses on the twin boom to a safe minimum.

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Within the gain classes of their respective designs, each of these LPDAs should provide excellent full-band coverage for the FM listener seeking distant stations. With respect to the 14' LPDA, some prospective builders may be hesitant to place so much mass so far from the supporting mast. So in our final installment of these notes, we shall examine an alternative antenna design, one that places most of the mass up and down on the mast. We call the antenna the batwing.

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Updated 04-09-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 5

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Go to Main Index

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Topics: Broadcast, LPDA, VHF / UHF


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+

Some Notes on FM BC Antennas
+ Part 5: The Batwing Antenna and Array

+
+
+

L. B. Cebik, W4RNL

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In all of the preceding episodes of this series, we have looked at conventional antennas whose elements were all in the same horizontal plane. As we move toward higher and higher gains in these antennas, the boom lengths grow ungainly and more difficult to support, especially if one is using a light mast system. In a neighborhood of non-hams, even 7' of boom extending from each side of a most can look dangerous and threatening.

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There are ways to shorten the boom. The chief means is to begin with an antenna that has width and height instead of length and width. Enter the batwing, one of the broadest band dipole-type antennas available. With suitable construction, the batwing can cover the FM band either as a dipole or as a directional beam.

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As we shall see from the dimensions, it may not be easy to build a batwing. However, for some, it may offer a construction challenge and fool the neighbors into thinking that your home is a cell tower.

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Let's take matters a step at a time, and begin with the simple batwing.

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The Batwing Dipole

To understand why the antenna bears the name "batwing," we only need to look at Fig. 1. +
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The outline sketch shows the general shape of the antenna. It consists of dipoles of different lengths, with all of them connected at the outer edge, left and right. Although fed at the very center, the inner vertical lines form a transmission line to distribute energy. As we change frequency, the most active elements above and below the vertical midpoint also change, with longer elements being more active at lower frequencies. However, to some degree, every element is active on every frequency within the design range.

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The sketch shows that the transmission line is shorted at its upper and lower ends. Performance is not affected by this short. However, the top and bottom shorts do make handy points for attaching the batwing dipole to a non-conductive mast.

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The letter designations mark out the most important dimensions. A is the broadest width, and b the shortest at the center. C marks the total height. The two intermediate horizontal elements above and below the center element are equally spaced. Hence, one may deduce their exact lengths by taking a line between the outer end of A and B and using either 1/6 or 1/3 of C (upward or downward) as their vertical positions.

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D is the center-to-center spacing between the phase lines. The distance between these lines is designed for 0.5" diameter material. The remaining structure can use materials from 0.1 to 0.5 inches in diameter. However, it is wise to make the top and bottom shorting "bars" of the larger material to form solid support points for the entire antenna. Below is a table of dimensions for a batwing dipole suitable for 88-108 MHz.

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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                        Batwing Dipole Dimensions
+
+   Dimension                Length in Inches
+      A                          57.70
+      B                          22.73
+      C                          78.39
+      D                           2.22
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The batwing dipole is nearly 5' wide and over 6.5' high. However, if you have a non-conductive mast section, you may mount the antenna directly to it without disturbing the performance. Hence, the mass of the antenna is well centered directly down the mast. Whether the connected elements hold up in the weather will depend upon the quality of construction.

+
+ +
+

Fig. 2 overlays the azimuth patterns of the batwing at 88, 98, and 108 MHz. Although the 3 patterns are within about 0.8 dB of each other, the 108-MHz pattern is the strongest. In fact, Fig. 3 provides the free-space gain curve for the batwing within the FM band.

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+ +
+

Now let's solve a bit of an initial mystery. The patterns in Fig. 3 are virtually identical in shape to those of a simple dipole. In effect, the batwing has about the same beamwidth as a dipole, as indicated by the figure-8 pattern. However, a dipole in free space, when made from real materials, has a gain of about 2.1 dBi. The graph in Fig. 3 shows a mean gain of about 5.2 dBi, about 3 dB higher. Whence cometh the gain?

+

Had we shown a free-space H-plane of elevation pattern for a dipole, it would be perfectly circular. In contrast, the H-plane patterns for the batwing resembles a peanut, with depressed gain at high angles above and below the antenna. The energy is not lost, but simply redirected broadside to the batwing plane.

+

As a consequence, the batwing antenna, besides being inherently broad- banded, has quite significant gain over a simple dipole. In some applications where rotation is not required and where there is no appreciable interference from the rear, relative to the direction of the desired station or stations, a batwing dipole may be quite sufficient as a receiving antenna. One may also rotate the mast, if the mast is sturdy. Rotation of 180 degrees is enough to cover the entire horizon. As noted earlier, however, we require a non-conductive mast in the region of the antenna itself. Alternatively, we may mount the antenna to a conductive mast by using non-conductive stand-off insulated braces connected to the top and bottom phase line shorting bars of the phase line portion of the antenna. We need to place the antenna a few inches away from the conductive mast so that it will not disrupt the characteristic impedance of the phase line.

+

With the suggested phase line, the antenna shows an inherent feedpoint impedance of about 75 Ohms. Hence, we may use standard cable industry coaxial cable as a feedline across the phase line position marked by the B dimension in Fig. 1. Fig. 4 shows the benign 75-Ohm SWR curve for the basic batwing dipole.

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+ +
+

The curve is based on the use of 0.5" diameter material throughout the batwing structure. Such a structure would likely be too weighty for practical use, especially if soldered together with copper. Going to 0.1" diameter material for all but the phase line portions of the dipole array does not hamper the gain; nor does it do more than slightly lower the frequency of the lowest SWR for the antenna.

+

The phase line has a particular characteristic impedance using materials of the specified diameter and spacing. If we change the diameter of the phase line material, we would need to redesign the dimension for the entire array, especially the spacing between the wires. With round wires, about the lowest characteristic impedance that we can obtain is about 80 Ohms. A closer spacing would lower the impedance, but unfortunately let the two phase line wires inter-penetrate each other. The surfaces of the listed phase line wires are about 1.72" apart (2.22" center-to-center), for a characteristic impedance of about 260 Ohms. The feedpoint impedance for this antenna is nominally about 1/4 the characteristic impedance of the phase line.

+

If you construct the phase line from copper tubing, be sure that the outside diameter is 0.5", not the inside diameter. L-couplings allow soldering a complete and quite strong center for the array. If you use 0.1" diameter (about AWG #10) copper wire for the remainder of the structure, then the construction of junctions becomes the main issue. Wire bends upward or downward for soldering to the phase line tubes on the portions away from the parts facing each other will have virtually no effect on the phase line impedance. In fact, the soldered portions might easily be strengthened with fasteners to the phase line tubes.

+

The goal is a strong final structure able to withstand the effects of weather. I have not tested the effects of adding a thin (for example, sprayed on) protective coating. However, bare copper will degrade under the influence of the chemical soup of the modern atmosphere, despite the pleasing green patina that might give the antenna an antique appearance.

+

Commercial manufacture of a batwing can use modern welding techniques to produce a very strong assembly with materials more impervious to atmospheric variables. However, the home craftsman is more limited in the available materials and techniques for assembly. Hence, the batwing dipole array is a distinct challenge.

+

Adding a Reflector

We may increase the forward gain of almost any single dipole or planar array of dipoles by the simple expedient of adding a sheet reflector behind the active antenna. The batwing is no exception. Adding a planar reflector at a given distance will convert the bi-directional batwing into a directional beam of considerable performance. Fig. 5 shows the outlines of such a system. +
+ +
+

The sketch is tilted to make as clear as possible the different parts of the array, namely the batwing dipole and the reflector. The batwing portion has exactly the same dimensions as the independent dipole array that we have been exploring. Immediately apparent in the figure is the fact that the reflector outside dimensions are considerably greater than the 57" by 78" outline of the dipole array itself.

+

In fact, the gain of the system is dependent to a large degree on the size of the reflector behind it. Our test case uses a reflector that is about 133" on a side--or about 11', that is, about 5.5' each side of the mast. For improved performance over the figures that we shall encounter with this model, extending the reflector screen horizontally will do more good that extending it vertically.

+

However, with the planar reflector shown, the batwing beam provides very good performance. Fig. 6 shows the anticipated gain and front-to-back data with the dipole array about 22.2" in front of the reflector.

+
+ +
+

Except for a few frequencies at which there is a very slight difference between the 180-degree and worst-case front-to-back ratios, the two curves are one. The front-to-back curve parallels the gain curve, as the array copies the basic batwing characteristic of showing increasing gain with frequency. In fact, the gain increases by about 0.9 dB across the FM broadcast band, ranging from 10.0 dBi at 88 MHz to 10.9 dBi at 108 MHz. Over the same range, the front-to-back ratio increases from 19 to 20 dB. These changes are not likely to be detectable in terms of reception of distant FM stations.

+
+ +
+

In Fig. 7, we find a very desirable trait in antennas. Over the operating range of the array, the shape of the azimuth pattern, both fore and aft of the array, does not change at all. The forward lobe is a single oval that has a somewhat narrower beamwidth than an LPDA of comparable gain. The rear triple lobes are of modest strength. (Indeed, for comparative purposes, we might note that the narrower beamwidth of the batwing beam might be useful if interfering stations are forward but off to the side of the desired station. In contrast, the very high front-to-back ratio of the LPDA would be more desirable if interfering signals are to the rear of the array.)

+

The limiting factor for the batwing beam is the match to a common feedline value. The mid-band resistive component of the feedpoint impedance is about 170 Ohms. A 4:1 transformer would lower this value to about 42 Ohms, a reasonable match for 50-Ohm coaxial cable. However, the resistance value tends to decrease both above and below the design frequency, and there is also some reactance. The result is a 200-Ohm SWR curve that is quite steep (where the 200-Ohm reference value is a stand-in for the 50-Ohm reference after we add the 4:1 transformer).

+
+ +
+

As shown in Fig. 8, the SWR never reaches a 1.9:1 value, although it rises higher than the values we might associate with a large LPDA. Nevertheless, the indications are that the batwing array would serve very well as a receiving antenna for the entire FM broadcast band.

+

The fact that we are accustomed to antennas that extend mostly in the horizontal plane may give the batwing directional beam an imposing, if not daunting, appearance from the perspective of the home builder. We can alleviate some of the dread in a couple of ways.

+

First, the reflector need not be a solid surface. In fact, a solid surface would not only be too heavy for most home installations, but as well give enough wind resistance to destroy the array in one or two major storms. Fairly wide aluminum mesh, commonly called chicken wire, should be sufficient to form a fully reflective surface. As long as the openings in a mesh are less than about 0.1 wavelength across any dimension, the screen will likely serve as an electrical solid. 12" openings represent to upper limits, although something of the order of 1-3 inches is more desirable from a structural standpoint. As well, the wire need not be very thick, just thick enough so that it does not deform readily within the frame. The object is to slip as much of the wind as possible while maintaining electrical and structural integrity.

+

Essentially, construction of the reflector will consist of an aluminum frame within which we attach the screen wire. The design of the frame will vary with the screening selected or available. A central vertical rib of some sort is necessary for two reasons. We may attached the rib directly to the mast, since the reflector can be at ground potential. As well, from this central rib, we need to provide supports for the batwing dipole portion of the beam.

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+ +
+

Fig. 9 shows in barest outline form the critical support points for the array. Although the sketch shows the reflector separated from the mast in order to designate connection points, the reflector may attach directly to the mast. The more critical connections are the required non-conductive supports that attach to the top and bottom of the batwing dipole and hold it 22.2" ahead of the reflector. If we run the transmission line through a non-conductive tube at the center, we acquire a third mechanical support.

+

Conclusion

We have not come near to covering all of the antenna designs that we may apply to the FM broadcast band to improve reception sensitivity. Our goal has been to move toward a better understanding of the problems involved. +

First, there is the question of what sort of reception improvement we need. A simple improvement in general sensitivity allows us to place a basic simple antenna in the attic or on the roof. However, if we need to separate stations at a considerable distance from potentially interfering local stations, we may need a directional beam placed as high as we can effectively support and maintain, with the additional potential need to rotate the antenna.

+

In the arena of directional beams, we need to decide what frequency coverage we must have and how best to obtain it. Standard Yagi designs--narrow-band in FM terms but relative broadband in Yagi design terms--will let us select the level of gain and the portion of the FM band we need.

+

For full band coverage, we turn to more complex antenna designs. We can choose a Yagi if we are willing to have a considerable gain change across the band, accompanied by only moderate front-to-back performance and rather fat elements. If we wish to achieve maximum front-to-back performance to reject stations to the rear, then a long LPDA may be in order, although its construction is more complex than building a Yagi. If we prefer to have the gain with a level of front-to-back performance between the Yagi and the LPDA, but without the long boom needed for either one, we may opt to try a batwing directional beam.

+

For full band coverage, moderate gain, very good front-to-back performance, good matching, and only reasonable levels of complexity in construction, the 8 element 88" long LPDA may prove to be the best all-round antenna. However, be aware that FM DXing can become addictive. Once we can comfortably listen to all of the first order targets we had in mind before we built the antenna, we shall then discover other stations at a greater distance that we cannot quite bring to full quieting. The discussion that follows is never of the order of whether or not to bother with those stations. Instead, we present ourselves with the following alternatives: to construction a taller and more complex support system to extend the current antenna's horizon or to build a larger antenna with high gain. Eventually, the addicted FM DXer does both.

+

As well, there are other antenna designs to explore, each with its own potential and with its own challenges. FM DXing takes on a life of its own. These notes are only a start in that direction.

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+ +
+

Updated 04-09-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Batwing, Broadcast, VHF / UHF


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Improved Antenna Performance for VHF FM
+ Some Basics, Some Options, Some Hurdles

+
+
+

L. B. Cebik, W4RNL

+

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+

FM operations in the amateur VHF region principally use vertical polarization. The ever-enlarging FM repeater and related simplex operation in the upper 3 MHz of 6 meters and 2 meters has expanded operator goals. Once, amateurs were content to work only local stations and repeaters. However, time has increased the desired repeater range, but with due regard to not causing interference to repeaters operating on the same frequency pair or an adjacent pair. The solution has been less a matter of increased power--since that one factor does not help reception. Instead, the solution has been the use of better antennas. Rubber duckies and other simple antennas will always have a place on handheld units, but home stations require something better.

+

Let's look at a few options for better antenna systems for FM operations, beginning with some basic antennas and their limitations. Next, let's turn to ways in which we can increase gain and directivity to obtain full coverage of the horizon. Along the way, we shall examine some of the practical hurdles that we must overcome to achieve the goal.

+

Since we shall examine several different antenna options, let's place everything on a relatively level playing field. We shall use 6 meters--specifically, 51 to 54 MHz--for a band on which to do our sampling. Although we might place an antenna at virtually any height--the higher the better--let's limit ourselves to 1 wavelength. At 52 MHz, a wavelength is about 225" above ground. When we deal with a vertical antenna, its base, feedpoint, and ground plane radials will be at the 225" level. When we deal with vertically polarized directional antennas, the boom will be at that height.

+

Some Basics

+

FM and repeater operations normally begin with a vertical antenna of some sort. In most cases, operators replace the rubber ducky with a vertical monopole (and sometimes a vertical dipole). Fig. 1 shows the outlines of three such antennas, ranging from the ubiquitous quarter wavelength monopole and proceeding to more complex antennas. The 5/8 wavelength monopole is about 2.5 times longer than the quarter wavelength version. The collinear on the right is only one of many similar phased vertical arrays that use a vertical element structure that does not spread in the X-Y plane.

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At 52 MHz, a quarter wavelength monopole is about 57" long--nearly 5'. The longer 5/8 wavelength counterpart is about 142" long or nearly 12'. The collinear array in the illustration uses a 5/8 wavelength section over a 1/4 wavelength section, with an intervening phasing/matching inductor (or transmission line section). The total height is over 230" or about 19' tall. All of these heights are in addition to the 225" (18.75') base height that we stipulated at the beginning. At that height, the 3 antennas provide the performance shown in Table 1. Each antenna uses a 4-radial ground plane, and each radial is about 1/4 wavelength long.

+ 
+Table 1. Relative performance of 3 vertical antennas on 6 meters with a 1 wavelength base height
+Antenna                   Max. Gain dBi      TO Angle degrees
+1/4 wavelength monopole      2.58              9.3
+5/8 wavelength monopole      3.44              8.2
+5/8-over-1/4 collinear       5.83              7.0
+
+

The gain of the antennas increases in small increments as we lengthen the array. The rising height of the maximum current portion of the antenna results in a gradual decrease in the take-off (TO) angle. Fig. 2 shows the patterns for these three sample vertical antennas.

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At 1 wavelength above ground, we do not obtain the best elevation patterns possible for the two single-element monopoles. There is a higher-angle second lobe with considerable strength but limited utility. The collinear array overcomes this limitation to a considerable degree. However, its length is greater than the supporting mast that we have stipulated for our exercise.

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On the far right of Fig. 2, we see the azimuth pattern that all of these vertical antennas share: an omni-direction pattern. The advantage of this pattern is that it simplifies the antenna structure. None of the antennas requires a rotator to point the antenna in a desired direction. That very property can be--under some circumstances--a disadvantage. Another repeater or station using the same or a nearby frequency (or frequency pair) may interfere with communications to a desired distant repeater or station, or you may interfere with the operation of that station or repeater. In such cases, a directional antenna is desirable or even necessary.

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The moment we think of directional antennas, the Yagi comes to mind. However, a persistent misconception often accompanies the Yagi. Most of the patterns that we see for Yagi antennas are azimuth patterns of the Yagi when it is horizontally oriented. However, FM and repeater services call for vertically oriented antennas. Physically, the change is simple: we simply rotate the antenna 90 degrees around the axis formed by its boom. Unfortunately, many newer amateurs fail also to rotate the pattern.

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Fig. 3 shows the azimuth patterns of a simple 2-element reflector-driver Yagi for 6 meters. In both cases, the boom is 225" above ground. Table 2 shows the data that goes with each of the patterns.

+ 
+Table 2. Performance of a wide-band 2-element reflector-driver Yagi when oriented horizontally and vertically
+Orientation       Max. Gain dBi    TO Angle degrees     Front-to-Back Ratio dB     Beamwidth degrees
+Horizontal           11.11           14                    11.58                      72
+Vertical              6.41           10                    10.28                     153
+
+

When horizontal, the Yagi shows about 4.5-dB higher gain than when oriented vertically. The difference lies to a considerable degree on the manner in which the ground-reflected radiation adds and subtracts from the direct radiation. Note that the maximum gain of the horizontal version is at 14 degrees elevation, but the vertical version has its maximum gain at only 10 degrees. A second important factor in determining the gain is the beamwidth. The vertical version has more than twice the half-power beamwidth of the horizontal version.

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For those unfamiliar with reading radiation patterns, the similarity of the front-to-back ratio numbers may seem initially confusing. The pattern shows a considerable difference in the rearward gain lines. The front-to-back ratio is the difference between the maximum forward gain and the gain 180 degrees opposite. For a difference of 10 to 11 dB, the horizontal forward gain is higher than the vertical forward gain and so the rearward gain of the horizontal version must be similarly higher. Otherwise, the front-to-back ratios would be significantly different from each other.

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If we carry in our heads only the pattern of the horizontally oriented Yagi, then the use of a Yagi immediately brings to mind a collection of associated machinery to direct the antenna. Among that gear is a rotator, a control cable, a control box, and some way to mount the rotator to the support mast (or tower). This equipment may cost many times more than the antenna that it turns, especially if we use relatively simple directional antennas. The rotator motor assembly may weigh many times as much as the antenna, sometimes forcing us to use a sturdier central support--for example, a tower instead of a mast. The motor also has moving parts that require periodic preventive maintenance as they undergo alternative periods of baking and freezing.

+

On the other hand, if we stare intently at the radiation pattern for the same antenna when vertically oriented, other options may come to mind. The beamwidth is especially attractive. As we increase the overall boomlength and gain of a Yagi, both the beamwidth values shown for the 2-element antenna will shrink, and as the boom gets very long and the number of elements grows to a high order, the two values will almost (but never quite) come together. The element tips will confine the E-plane beamwidth of the antenna to a slightly tighter value than the flat surfaces that we see when the beam is vertically oriented. Nevertheless, for small, low-gain Yagis and similar arrays, the beamwidth of the vertical version will be much greater than the beamwidth of a corresponding horizontal version. This is a useful property for many installations.

+

Covering the Horizon with Multiple Vertically Oriented Directional Antennas

+

One way to cover the horizon with directional antennas without using a rotator is to mount multiple antennas at a given height and to switch from one to the next. This technique is most apt to VHF FM service where we meet several conditions.

+
    +
  • 1. The individual antennas are fairly small and light and therefore do not load the support arms.
    • +
  • 2. The size of the antennas lets us mount each one a distance away from the central support mast.
    • +
  • 3. The beamwidth of each antenna is large to reduce the number necessary for full horizon coverage.
    • +
+

One reason for choosing 6 meters as our sampling band is that it falls near the limit of practical construction for such a system. In fact, it will show us some of the limitations and hurdles that we must overcome to put such a system in place. To illustrate the technique, I have selected two small directional beams that might be serviceable on this band. Fig. 4 shows their outlines and relative sizes.

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+ +
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The antenna on the left is a Moxon rectangle, a parasitic 2-element array with a driver and a reflector. The beam to the right is a 3-element Yagi that uses a pair of phased drivers and a director. The driver pair uses a 250-Ohm phase line with a single half twist. Since the elements of the 3-element Yagi do not fold back, the antenna is slightly larger than the Moxon and has slightly more gain. Table 3 provides some data for 52 MHz for versions of both beams when using 0.5"-diameter elements.

+ 
+Table 3.  Performance of a Moxon rectangle and a wide-band 3-element phased-driver Yagi at 52 MHz at 225" above ground
+Antenna          Length inches  Width inches  Max. Gain dBi  TO Angle degrees   Front-to-Back Ratio dB   Beamwidth degrees
+Moxon Rectangle    82.3           30.6          6.46           9.8                20.92                    151
+3-Element Yagi    108.9           34.8          7.65           9.5                20.03                    123
+
+

Both antennas will provide a 50-Ohm SWR below 2:1 across the 51-54-MHz span for FM operation. However, the two SWR curves, shown in Fig. 5 have quite different curves. Phased drivers tend to have a more equal growth of SWR above and below the design frequency (or lowest SWR frequency). In contrast, a single driver tends to show more rapid changes in SWR on one or the other side of the design frequency. Hence, the Yagi places its design frequency a little above the band center. In contrast, the Moxon design frequency is below mid-band so that the SWR is acceptable across the desired spectrum, even though it rises rapidly toward 50.0 MHz.

+
+ +
+

Each antenna uses a single parasitic element. The Moxon uses a reflector. Therefore, its gain decreases as the operating frequency increases. The 3-element Yagi uses a director, so its gain increases as the operating frequency increases. (Standard design Yagis using both a reflector and one or more directors show the rising gain feature, indicating that the directors tend to control the array gain more than the reflector.) Fig. 6 provides graphical verification of the gain situation for both antennas.

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+ +
+

Before we become too enamored with the rising gain characteristic of the 3-element Yagi, we need to evaluate the antennas in the type of service that we intend. We shall create a symmetrical arrangement of the antennas around and away from a central support mast. The beamwidth of the individual antennas suggests that we only need 3 arrays, equally spaced at 120-degree intervals to cover the horizon. (Of course, we shall switch from one antenna to the next, since operating them all together would give us a single lumpy pattern with no gain advantage over a vertical monopole or dipole. Remember that the goal is to obtain some gain and some directivity, and operating the 3 antennas at the same time would defeat both goals.)

+

One key question is how far out on a support boom or arm each antenna must be for effective operation. The answer partly depends on the antenna design. However, 1/4 wavelength appears to be an approximate minimum distance. As we shall see, this minimum will not work for every design, but it does give us a starting point. If the antennas are any closer together on shorter arms, the interactions between them can ruin their performance, since they are all the same in any given installation. Hence, they are more susceptible to interaction than antenna designs for different frequency ranges.

+

1/4 wavelength is nearly 60" (5') on 6 meters. Hence, the support booms must be a total of over 90" for the Moxon and over 95" for the Yagi. 8' booms are equivalent to each half-element of a 10-meter beam, so the project is not implausible by any means. Before we close, we shall look at some construction cautions to observe. If we move the operating frequency to 2 meters or higher, then we can use a separation from the mast that is greater than 1/4 wavelength with virtually no stress on the support arms. The individual antennas are smaller and lighter. We shall also see that some designs require greater spacing from the mast.

+

The Moxon Rectangle Triangle

+

Let's create a set of 3 Moxon rectangles at 120-degree intervals, with each Moxon reflector 60" (5') from a central support mast. The top of the mast in the design models is at the boom level (225"). The left side of Fig. 7 shows the layout of the array.

+
+ +
+

The right side of Fig. 7 shows the patterns that result from each antenna in this configuration. The maximum gain of each antenna is about 6.6 dBi. At the points where we switch from one antenna to the next, the drop in gain is under 2 dB. Two data points relative to the system show us that we are using the bare minimum of separation of the antenna from the center point. One feature is the front-to-back ratio. It has dropped from nearly 21 dB down to between 16 and 17 dB. For this type of service, the drop is not serious, but it does indicate that there is still some interaction between the antennas, even when two of the three are unfed. There is a second indicator of interaction among the antennas. The beamwidth has dropped from over 150 degrees down to about 143 degrees. Again, the decrease in beamwidth is not serious enough to defeat the goal of full horizon coverage with acceptable directivity. However, it strongly suggests that where feasible, the individual antennas should be more than 1/4 wavelength away from the centerpoint.

+

In general, even at 6 meters, a triangle of Moxon rectangles can provide directional coverage of the horizon with a good front-to-back ratio as a safeguard against interference.

+

The Triangle of 3-Element Phased-Driver Yagis

+

The Yagi that we have selected for our design test has a beamwidth of 123 degrees when used in isolation, but at the same height as a triangle of beams. We may set up a symmetrical arrangement of 3 such antennas using the same scheme that we used with the Moxon rectangles. The booms are at 225" above ground, and the rear elements are 60" from the center point or support mast. Fig. 8 shows the general layout in the left portion of the graphic.

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+ +
+

If we successively feed one Yagi at a time, we obtain the coverage shown by the patterns at the right. The forward gain of each antenna has risen by a small amount to just about 8 dBi. The front-to-back ratio holds at about 20 dB. Hence, we must ask where the extra gain comes from. Part of the answer is a reduction in the beamwidth for each antenna in the array. The beamwidth has decreased from 123 degrees to about 109 degrees. That decrease is sufficient to affect the gain where the patterns overlap. Relative to each antenna's maximum gain, the crossover points show nearly 5 dB lower gain. For some installations, the crossover points may not be significant, especially if they are not directed toward desired communications targets. However, relative to full horizon coverage, the drop is significant.

+

The Square of 3-Element Phased-Driver Yagis

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When the beamwidth is not sufficient to cover an area, we have two choices. One is to extend the antenna support booms and move each antenna further out from the feedpoint. That action is certainly feasible at 2 meters and above. However, let's assume that we have reached our physical limit (60") on 6 meters. The second course of action is to add additional antennas. Some cellular and wireless services use this technique with many high-gain Yagis in the UHF range. We shall be modest and add a single antenna to create a square of 4 Yagis, each 60" from the center point and support mast. The left side of Fig. 9 shows the revised arrangement.

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The front-to-back ratio of the square array holds at just above 20 dB. However, the gain of each antenna has increased by another half-dB. The primary source of the added gain is a further reduction in the beamwidth of each pattern. The beamwidth has dropped to about 95 degrees (down from 109 degrees in the triangle and from 123 degrees for an isolated Yagi of this design). As a result, we do not obtain the seamless coverage of the horizon that we might have expected. Rather, as shown on the right in Fig. 9, the cross-over points for the patterns are between 3.5 and 4 dB lower in gain than the maximum forward gain values.

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In setting up this exercise, we did not create a limit on the decrease in gain that we would accept for any switched arrangement of vertically oriented antennas. Therefore, we can only note that the crossover gain-decrease for the Yagi square is between the values obtained for the Yagi triangle and for the Moxon rectangles. From the gain increases shown by the Yagis, it is clear that these antennas interact to a greater degree than we found in the Moxon rectangles. One notable feature of the Moxon rectangle is its highly effective reflector. That element limits interaction between a given rectangle and others facing in different directions. In contrast, the rearmost element of the Yagi is one of the drivers. Hence, structures similar to one of the antennas and beside or behind it are likely to serve as distant reflectors and couple with the active antenna. The result is a slight increase in gain and an attendant reduction in beamwidth.

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The solution to the problem is to increase the separation of the antennas from each other by increasing the distance from the centerpoint. At higher frequencies, this solution is relatively easy to implement. However, we set that solution aside at 6 meters for an important reason: we needed to see that some antenna designs are inherently more interactive in this type of service than other designs. As a result, the simple "trick" of creating a triangle of antennas to cover the FM and repeater horizon turns out to be somewhat less than an automatic or easy design exercise.

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The Question of the Mast

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If some antenna designs are more sensitive than others with respect to interactions, we may also be able to detect that sensitivity in terms of the influence of the support mast on the performance of our arrays. Therefore, I simulated three mast conditions. One case uses no mast in the models, which simulates a non-conductive mast. The actual mast need not be totally non-conductive, but might use PVC or similar materials in the top section from the lower tips of the antenna elements upward.

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The second and third cases use 1.25"-doameter masts with only one difference between them. In one case, the mast goes all the way to ground. In the other case, the mast terminates 1" above ground to simulate either an insulated base or one that is highly resistive. The important difference between these two cases shows up in Fig. 10.

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On the two masts, the peak relative current magnitude is less important than the pattern of current distribution. With the mast isolated from ground, and nearly 1 wavelength long, the current shows 2 distinct peaks and three nulls. However, if we ground the mast, one current peak occurs at ground level, reducing the current magnitude at the top of the mast in the vicinity of the antenna elements. The lower current level should show up as a difference in the modification of antenna performance relative to an isolated antenna. In all of the cases that we shall examine, the top of the mast is at boom height, that is, 225" above ground.

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The Moxon Rectangle Triangle

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We can summarize the relevant information concerning the triangle of Moxon rectangles in tabular form. See Table 4.

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+Table 4.  Performance of a Moxon rectangle triangle with and without a center mast.
+Antenna/Mast                Max. Gain dBi  TO Angle degrees   Front-to-Back Ratio dB   Beamwidth degrees
+Isolated Moxon                6.46            9.8               20.92                    151
+No or non-conductive mast     6.56           10.3               16.91                    143
+Grounded mast                 6.58           10.1               16.38                    143
+Ungrounded mast               6.38           10.1               16.84                    146
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The differences in performance are very small among the options. The similarity in performance of the 3 triangles suggests that the key factor in Moxon triangular performance is the presence of the insert antennas and not the mast. However, the ungrounded mast with a current peak higher up on the mast does appear to be the source of the slightly lower gain and the accompanying increase in beamwidth.

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The Triangle of 3-Element Phased-Driver Yagis

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The absence of a reflector element in the 3-element phase-fed Yagi might lead us to suspect that we would find greater differentials among the three trial models of a triangle of Yagis. To see if reality matches our suspicions, we may examine the data in Table 5.

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+Table 5.  Performance of a triangle of 3-element phase-fed Yagis with and without a center mast.
+Antenna/Mast                Max. Gain dBi  TO Angle degrees   Front-to-Back Ratio dB   Beamwidth degrees
+Isolated Yagi                 7.65            9.5               20.03                    123
+No or non-conductive mast     8.00            9.8               19.44                    105
+Grounded mast                 7.97            9.8               20.60                    109
+Ungrounded mast               7.49            9.8               21.63                    119
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The gain range among the 3 mast scenarios is over 0.5 dB (compared to the 0.2-dB range for the Moxon rectangles). The similarity between the values for a non-conductive mast and for a ground mast is suggestive that the upper grounded-mast current levels are not high enough to seriously change antenna behavior within the triangle of Yagis. However, the ungrounded mast yields a lower gain and a wider beamwidth in noticeable amounts.

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The Square of 3-Element Phased-Driver Yagis

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Whether the behavior of the Yagi square is similar to the Yagi triangle requires another data table, namely, Table 6.

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+Table 6.  Performance of a square of 3-element phase-fed Yagis with and without a center mast.
+Antenna/Mast                Max. Gain dBi  TO Angle degrees   Front-to-Back Ratio dB   Beamwidth degrees
+Isolated Yagi                 7.65            9.5               20.03                    123
+No or non-conductive mast     8.48            9.6               21.73                     95
+Grounded mast                 8.52            9.6               20.91                     95
+Ungrounded mast               8.43            9.7               21.45                     96
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Once more, the values for the non-conductive mast and the grounded mast are very similar. However, when we leave the mast ungrounded, the values for the square of Yagis change much less than they did in the triangle. In fact, the gain changes by less than 0.1 dB, and the beamwidth changes by only 1 degree across the three tested cases. The most likely source of the difference between the triangle and the square is the closer proximity of the Yagis within a square of 4 antennas. As a result, the interaction between antenna structures tends to override any effects of even an ungrounded mast.

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Since we did find some significant differences of mast-to-antenna interactions between the Moxon rectangles and the Yagis, the lesson is simple. These notes are not usable as a design document. Rather, they establish the need to carefully model the actual antennas and mast to be used in a horizon-covering switched array at the height to be used and at the distance from the support mast to be used.

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A Few Construction Hurdles

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The basic idea of an array of directional vertical antennas symmetrically placed around a central mast is not new by any means. The number of antennas required for full horizon coverage depends on the antenna design, the spacing of the antenna from the centerpoint, and the degree of reduced gain that is acceptable at the pattern cross-over points. For most amateur applications, an array of three--perhaps four--antennas is about the maximum array size before a rotator becomes the more attractive option. Part of the reason lies in the cost of numerous antennas, and part of the reason lies in the growing complexity of construction as the number of antennas increases.

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Fig. 11 summarizes a few of the most rudimentary construction considerations. The support mast should be well grounded, if for no other reason than lightning safety. However, if antennas use the minimal 1/4 wavelength spacing between the rearmost element and the array centerpoint, a grounded or a non-conductive upper mast may have significant influence upon the performance of the individual antennas in the collection.

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For the lower VHF region, especially 6 meters, the booms may require a triangular brace to reduce the stress moment along the horizontal support. For all-metal construction, the braces may be straps or L-stock, depending on the actual antenna weight and its distance from the mast. Upper VHF assemblies may be able to omit the bracing. Indeed, as the frequency increases, the use of UV-protected PVC (or similar) boom materials becomes attractive.

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These notes are not so much a guide to construction as they are a reminder that the physical assembly requires as much planning as the electrical performance of the antennas in the array. Equally important is the switching method. Here we have at least three alternatives.

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  • 1. We may run separate feedlines from each antenna into the shack for convenient switching. This option is perhaps most attractive for its simplicity and is most applicable where the coax runs are fairly short. A basic coaxial-cable switch near the equipment position allows the operator to select the favored direction with the fewest mechanical complexities.
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  • 2. We may run short feedlines to a single position at the centerpoint of the array. At that position, we may install a remote coaxial-cable switch. This system requires only one long cable run from the antennas to the shack. The savings in cable may also allow us to purchase the lowest-loss coax that we can find. The system is likely most applicable where the distance between the operating position and the antennas is fairly long. The system has two disadvantages to weigh in the balance. One is the placement of a remote electro-mechanical device at the antenna site, where it will require suitable weather protection. The second disadvantage is the need to run a power line to the remote switching unit.
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  • 3. Those who are very adept in electrical circuitry may create a polling system out of the array. Essentially, in the receiving mode, the system continuously scans at a given frequency until its receives the strongest signal. It locks upon this signal with the antenna that yields the highest signal strength. Such systems are most applicable at repeater installations. Normally, they are used only for receiving, with the transmitted signal on its own channel going to an omni-directional antenna (since the receiving station for the repeated signal may be in any direction and may involve multiple directions for a round-table discussion). With suitable time constants, the system may capture signals with no interruption, even from a mobile station that passes from the field of one antenna to the next.
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Essentially, a switched FM-repeater service antenna system can be as simple or complex as our skills, ingenuity, and inclinations dictate. With the correct antennas properly spaced from the centerpoint of the array, it provides an alternative to the rotator. In some circumstances, it may prove to be superior, since we do not need to wait on the slow-moving rotator in order to communicate. Although we have explored 6 meters as a kind of worst-case scenario in terms of the support vs. antenna interaction equation, the use of a triangle of vertically polarized directional antennas may be easier to implement at higher VHF and UHF ranges for full horizon coverage.

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Updated 04-01-2007. © L. B. Cebik, W4RNL. This item appeared in AntenneX, March, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Moxon, VHF / UHF, Vertical, Yagi


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Notes on Fixed Satellite Antennas

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L. B. Cebik, W4RNL

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Fig. 1 illustrates some of the complexities facing the VHF and UHF operator who wishes to do everything (except use local repeaters, a topic for another day). Initially, the operator imagines a simple fixed omni-directional antenna. But capturing the distant point-to-point station and the rapidly moving satellite in the presence of ground clutter raises questions. It seems that even to receive weather maps around 137 MHz requires an antenna that is high enough to see over the trees and buildings to catch the satellite while it is at a low elevation angle. Similar considerations apply to the distant station, within the gain limits of an omni-directional antenna. I would not disturb this blissful formula for success if it always worked. As we shall see, it does not always work, and for reasons related to basic antenna performance in the presence of the very thing that supports all of that clutter--the ground.

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Fixed Omni-Directional Antennas

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When amateurs first start to dream of satellite communications or of receiving weather information from satellites, they tend to think simple and inexpensive thoughts. They want to install a basic omni-directional antenna with enough gain to allow error-free reception from and a solid connection to a communications satellite. Since satellites may appear almost anywhere in the hemisphere surrounding a given location, an ideal pattern emerges, as portrayed in Fig. 2. The small square on the Z-axis is an arbitrary antenna, since the pattern is not achievable.

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There are two problems that prevent us from obtaining the ideal omni-directional pattern. One difficulty is ground clutter (see Fig. 1). It absorbs, reflects, or refracts very low angle signals. That fact prompts us to raise the antenna to "see over" the clutter in order to reach the horizon. Height improvement works to some extent for point-to-point communications, although intervening clutter may still provide interfering reflections unless we place the antenna very high indeed. However, for satellite work, the technique is not only relatively futile, it can be self-defeating. Satellites are in the extreme far field of any antenna, and the very existence of the ground at any distance will prevent us from creating an ideal omni-directional pattern.

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We might here go back to the textbooks and supply an array of equations by which to prove our point. However, it may be more instructive simply to model some of the most widely used omni-directional antennas and sample their patterns at various heights above ground. Each sample will use 1.5-mm diameter aluminum elements at 300 MHz (more precisely, 299.7925 MHz, where 1 meter = 1 wavelength). Each 2-element antenna will use a 90° phase-difference between elements to achieve the omni-directional pattern. There are numerous techniques to achieve turnstiling--or what engineers prefer to call quadrature feed--but most amateurs will likely use a ¼ wavelength electrical section of transmission line with the same impedance as the individual elements in the antenna. The net feedpoint impedance will be ½ the impedance of the individual element. When we place the antenna above ground, we shall use average soil (conductivity 0.005 S/m, relative permittivity 13). In this initial part of our work, we shall only be interested in the total far field of the antenna. We shall save the vertical, horizontal, and circular components for the last part of our work.

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1. Turnstiled Dipoles: Perhaps the oldest quadrature-fed antenna is a pair of turnstiled dipoles. A version of this antenna has appeared in every ARRL Antenna Book since satellites first appeared, and the antenna predates that event by decades as an upper HF and lower VHF omni-directional antenna. The antenna found wide use in the days before repeaters, when virtually all VHF communications in the amateur bands used horizontally polarized antennas.

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The upper portion of Fig. 3 shows the outline of the dipole turnstile. The appearance gave us the antenna name and that name eventually transferred to the simple feed method. Be certain that the feed system is properly matched at every step, because the SWR curve will remain impressively low long after the free-space patterns to the upper right have gone to pot. The beamwidth of a dipole prevents a perfect E-plane circle, but the squared circle varies only by about 1 dB from maximum to minimum. The H-plane pattern shows that the simple turnstile radiates more strongly broadside to the antenna than off the edges, an important reason why folks tried other designs.

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The lower part of Fig. 3 contains the critical information about the elevation patterns of a simple dipole turnstile as we gradually raise the height of the wires above average ground. Table 1 summarizes the data.

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The elevation pattern of the dipole turnstile has deep nulls between elevation lobes at any height above ground. Even at a height of 10 wavelengths, the null regions where a signal may drop more than 3-dB relative to the lobe value is larger than the region where the signal is less than 3-dB below peak lobe value. Note also that the zenith region (directly overhead) changes as a function of the antenna height, with a deep null at integral height multiples of ½ wavelength and a lobe at odd multiples of ¼ wavelength. In general, the basic dipole turnstile is quite unsatisfactory for general satellite communications and for weather satellite reception, even though it might be useful for local horizontal point-to-point communications.

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2. Turnstiled Dipoles with a Planar Reflector Screen: The immediate amateur development to improve the dipole turnstile was to add a screen below the antenna. The impression that this maneuver leaves is that obtaining more gain cures everything. A proper planar reflector extends at least 0.5-? beyond the limits of the driven antenna elements in every direction. In this case, we may arrange the element to point toward the corners of a square screen in order to minimize excess screen size. Nevertheless, an adequate planar reflector will be about 1.4 wavelength per side, as shown at the top left of Fig. 4. The free-space patterns should suffice to forewarn us that this antenna system will have very limited utility. The antenna shows good gain and an excellent free-space front-to-back ratio. But as the data in Table 2 reveal, along with the patterns in the lower half of Fig. 4, the antenna is good only for satellites directly above us and is worse than the simple turnstile dipole system near the horizon.

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The table lists the half-power beamwidth of the antenna patterns at each height, as a measure of how much of the 180° hemisphere might be missing from coverage. The patterns in Fig. 4 also show several other interesting facets of pattern development with increasing height. For example, note the pattern for a height of 10 wavelengths above ground. It shows 2 peaks that represent what amounts to a circle of maximum gain with a null at the exact zenith angle. As well, the low angle lobes and nulls, although smaller than those for the simple dipole turnstile, remain in place, since they are a result of the antenna's height and not of its specific design.

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The third aspect of pattern development with increasing height for antennas that point generally upward is the development of high-angle ripples in the main forward lobe. These ripples tend to be most prominent in antennas that use crossed elements to achieve circular polarization. However, we shall encounter them to one degree or another in the patterns of all antennas raised to the vertical.

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In the end, the dipole turnstile with an adequate planar reflector does not serve well as a fixed position omni-directional antenna for any service. However, in the upper UHF region (70 cm and upward), it may serve as a simple and effective aimable antenna, if 8 to 8.5 dBi is adequate gain for the operation. Do not skimp on the screen size, because gain will drop quite rapidly as we downsize the reflector dimensions.

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3. Turnstiled Quad Loops: We can generally create a turnstile pair out of any element that has a linear dimension and makes no more than a flat plane. The quad loop is a variation on the dipole. In fact, it is roughly 2 dipoles spaced ¼ wavelength vertically, each bent so that the ends just touch. If we set two quad loops at right angles so that the feedpoints are close but do not touch, we can add a ¼ wavelength phasing line between them, but we must adjust the characteristic impedance of the line to match the individual self-resonant impedance of the loop--about 125-130 Ohms. The feedpoint impedance of the turnstiled quad will be half that value. It appears not to matter if the top crossing points do or do not touch.

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Turnstiled quads came into play as omni-directional antennas with slightly more gain than the dipole turnstile. They come in two varieties, depending on whether we start with square quad loops or with diamond quad loops. Fig. 5 shows the general outline of both versions, along with free-space patterns. Notice that in each case, the patterns form a nearly perfect sphere, rather than showing the egg-shape of the dipole turnstile. Hence, we expect a small increase of gain in the E-plane. The square loop version unfortunately arose in a decade in which cute names were more important to antennas than performance. Hence, someone dubbed the antenna the "eggbeater," a name best forgotten, lest someone rename the turnstiled diamond loops the "whisk."

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As Table 3 shows, there is very little performance difference between the two versions of the same antenna. Since the heights of the antennas depend on the bottom-most point or the feedpoint, the slightly taller diamond loop antenna shows values that reflect the small increase in average height. See Fig. 6 for the patterns of the square quad loops over ground and Fig. 7 for the corresponding diamond loop quad patterns. Note that in both cases, the maximum gain applies to the lowest elevation lobe in the pattern. The maximum gain in this lobe is about 1 dB greater than for a dipole turnstile at the same feedpoint height. As the catalog of patterns shows, the gain improvement is not as significant as it might initially seem. In general, we choose between the 2 versions of the turnstiled quads most often due to a preference for certain construction methods. The models used here at 300 MHz use 1.5-mm diameter elements, but common wire sizes will do as well.

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Unlike the dipole turnstile, the zenith-angle domes occur at integral multiples of a half wavelength, with upward nulls occurring at odd multiples of ¼ wavelength. Otherwise, we have no reason to consider the turnstiled quad loops further as candidates for fixed satellite communications service. They display all of the nulls shown by the dipole turnstile for all practical heights. Therefore, they suffer from the same variability of signal strength as a satellite moves across the sky.

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4. Turnstiled Moxon Rectangles: The number of lobes and nulls in any turnstile horizontal antenna is a function of the height of the antenna above ground. Hence, we cannot eliminate them. However, we can go some distance in reducing the null depth by selecting the right kind of antenna to fit into the turnstile. One key factor is the inherent H-plane beamwidth of the antenna element in isolation. The Moxon rectangle is a 2-element parasitic beam with the element ends folded back toward each other. It has a very broad beamwidth in the H-plane, and has enough side radiation off the element tails to partially fill the nulls at low angles. The resulting pattern is far from perfect, but it goes a considerable distance in the right direction.

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Fig. 8 shows the outline of a turnstiled pair of Moxon rectangles at the upper left. Although the driver centers require enough separation for the phase line, the reflector elements may touch at their centers. We can design the rectangle for a 50-Ohm feedpoint. The phase line will require a 50-Ohm section of coax, but the 25-Ohm net feedpoint impedance will require transformation back to 50 Ohm. Alternatively, we may design the rectangle for a 95-Ohm feedpoint and use coax of that value for the phase line. The resulting net feedpoint impedance is close enough to 50 Ohms not to require any special matching.

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The free-space patterns show the wide beamwidth that results in the more modest nulls in the patterns taken above ground. As revealed in Table 4, the beamwidth of the upper dome is always at least 90°.

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The turnstiled Moxon rectangles achieve much superior evenness of performance at higher elevation angles than any of the fixed antenna candidates that we have so far surveyed. The maximum gain is remarkably consistent regardless of the height of the antenna above ground, largely due to the fact that the antenna has its own highly effective reflector. Direct downward radiation is almost non-existent.

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However, as shown by the elevation plots in Fig. 8, the antenna only goes part way toward smooth performance at lower elevation angles. The antenna configuration limits, but does not eliminate the nulls between elevation lobes. As we increase the height of the antenna above ground, we encounter the same growth in the numbers of lobes and nulls that we have seen in all of the fixed satellite antenna candidates. If we cannot satisfy our operating needs at angles higher then about 30° above the horizon, then we must continue the search for a better fixed-position antenna.

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5. The Modified Lindenblad: In 1941, N. E. Lindenblad developed and patented a design for a circularly polarized antenna to use at the television station atop the Empire State Building. The necessities of World War II delayed the actual construction of a Lindenblad antenna until after the war, and then, the builders intended it for possible aviation use. The Lindenblad has undergone re-invention and modification in recent times without due credit to the original developers. The references should rectify this situation. See Appendix 1 for a comparison of the original Lindenblad with the modified version shown here.

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Fig. 9 shows the outline of the modified Lindenblad on the left, along with instructions on how to model it. It consists of 4 dipoles forming a square. However, each dipole is slanted 45°. Since one may easily mess up the model, the orientations of the elements and the sequence of current source phasing appear in the diagram. Note that we select one element as the prime element and progressively increase the phase angle of each succeeding source by 90° in a clockwise direction to obtain the desired "up" series. (The original Lindenblad fed each dipole in phase to achieve low-angle circular polarization. However, as the Appendix will show, the resulting antenna has severe limitations for satellite use. Hence, the use of progressive quadrature feed has advantages in satellite service.) If we leave the elements oriented as before but use a counterclockwise progression of phase angle increases, we obtain the less-desired "down" series. (Reversing both the element orientations and the progression of phase angles will result in an "up" series.)

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The right side of Fig. 9 shows the differences between the up and down series. (The original Lindenblad has a free-space pattern that is symmetrical with respect to the array centerline.) The differences are vivid in the free-space pattern, but less so in the patterns above ground by 1 wavelength. However, the gain is smoother as we increase the elevation angle in the up series, and the differences between maximum and minimum gain in the azimuth pattern are smaller. The modified Lindenblad was not designed to create a high angle dome, but to provide omni-directional television transmission suitable for reception by both horizontal and vertical antennas in the early days of urban TV. Hence, the upward null was not considered a hindrance to good performance.

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The optimal spacing for the dipoles in a modified Lindenblad array has come in for some discussion. The upper portion of Fig. 10 provides some guidance. The spacing values reflect a center point, so the actual spacing between facing dipoles is twice the listed value. A spacing of 0.5 wavelength provides perhaps the best obtainable pattern over average soil for elevation angles up to about 50°. 0.6 wavelength? spacing might extend the elevation angles 10° further upward, but with somewhat higher ripple in the signal strength.

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The lower part of Fig. 10 provides data for the effects of soil quality on the pattern shape, using a spacing of 0.5 wavelength between facing dipoles with the feedpoints 1 wavelength above ground. Very poor soil shows some pattern degradation, but the patterns for average and better soil are remarkably consistent.

+

Table 5 provides data on the modified Lindenblad array set at various heights above average ground. See Fig. 11 to correlate the data with elevation patterns. In general, the Lindenblad is subject to the same variations in zenith-region radiation as the single turnstile dipole. However, the antenna excels in evenness of performance at lower elevation angles.

+
+ +
+

Even though the modified Lindenblad provides superior low elevation angle performance, the array has limits in terms of the height at which we should position it. Note that the lowest elevation lobe begins to dominate by a height of 2 wavelengths above ground. At heights of 5 wavelengths and upward, the lobes and nulls at very low angles become serious phenomena. Although 3-5 wavelengths is an appreciable height for a 2-meter antenna, the same height in wavelengths may not be sufficient at 70 cm to clear ground clutter. Hence, for all of its other virtues, the modified Lindenblad remains subject to the same pattern formation influences that informed the patterns of the other candidate antennas. (However, the lobe development is severely retarded relative to the original design.)

+

Of all the candidates for a fixed-position satellite antenna in our survey, the modified Lindenblad achieves the best low angle performance, where we understand "low angle" to mean a range of angles in the sky that a satellite is likely to traverse. (We must set aside some of our HF antenna ideas to grasp the needs of satellite communications.) Between 10° and about 50° elevation, no other candidate achieves an equivalent evenness of gain. For angles from about 30° up and higher across the sky, the turnstiled Moxon rectangles take honors among the candidates in the survey. Still, no single antenna type achieves the ideal of a dome across the sky with equal gain in every possible direction and at every possible height.

+

The survey has not been all-inclusive. It has featured some historically important first attempts at usable satellite antennas adapted from omni-directional terrestrial antennas. It finished with two more recent entries, one geared toward smooth higher-angle gain, the other designed 60 years ago for lower elevation angles. In all of the exercises, we have seen that height above ground presents the fixed-antenna user with a conundrum. Greater antenna heights clear the ground clutter, but produce considerable numbers of lobes and nulls. Lower heights tend to clean up the pattern, but may block lower elevation angles due to intervening structures, both man-made and natural. Unless we have specific interests that allow a simple fixed antenna to serve us well, eventually, we shall begin to look at antennas that we can aim and that are worth aiming. We may begin with simple hand-held antennas that we point from our patios. Even while claiming total satisfaction with simplicity, we keep on checking the prices of Az-El rotator systems and dreaming of long-boom antennas with high gain and narrow beamwidths.

+

Appendix 1: The Original Lindenblad Circularly Polarized Dipole Array

+

The modified Lindenblad dipole array is one possibility for a fixed-position satellite antenna especially suited to capturing satellites at lower elevation angles relative to the horizon. Its origins lie in the pioneering work of N. E. Lindenblad, who first proposed the antenna design almost off-hand in a broad article on television transmitting antennas. (See N. E. Lindenblad, " Antennas and Transmission Lines at the Empire State Television Station," Communications, vol. 21, April, 1941, pp. 10-14 and 24-26.) After World War II, Brown and Woodward (who made numerous contributions to VHF and UHF antenna design) developed the idea in detail from Lindenblad's patent papers. (See G. H. Brown and O. M. Woodward, "Circularly Polarized Omnidirectional Antenna," RCA Review, vol. 8, June, 1947, pp. 259-269.) They envisioned possible aviation uses for the antenna. The overall goal for the antenna was omni-directional coverage in the X-Y plane (parallel to ground) with circular polarization. They did not design the antenna for overhead coverage.

+
+ +
+

Fig. A1-1 shows on the left the fundamental principle behind the Lindenblad dipole array. To achieve circular polarization, we need vertically and horizontally polarized components--shown as currents in the wires--such that they result in exactly equal fields at any distance from the antenna in any direction. The sketch shows right-hand circular polarization. The conceptual diagram is almost impossible to realize as a physical antenna. Lindenblad reasoned that an array of tilted dipole, fed in phase, would approximate the ideal situation. The right side of Fig. A1-1 shows the solution, highlighting 1 of the 4 dipoles. If we select the proper angle for the dipole relative to the horizontal (a), then the vertical and horizontal components will be equal. The design is subject to limitations, since we have facing dipoles. The tilt angle, a, depends in part on the distance between facing dipoles. In terms better suited to calculation, the required tilt angle depends upon the radius of the circle connecting the feedpoint positions of the dipoles. Since the fields between adjacent dipoles overlap, the required tilt angle for the dipole also depends on whether we measure fields tangential to the dipole faces or at angles that bisect two dipoles. The following table shows a few of the Brown-Woodward tilt-angle calculations.

+
+ +
+

The modified Lindenblad array using progressive quadrature feed uses a radius of 0.25 wavelength. Therefore, we may simply change the phase angles of the individual feedpoints to put them all at the same phase angle. However, this seemingly simple change results in a need to change the length of the dipoles to restore resonance to each dipole. As well, we need to re-angle the dipoles in the opposite direction from those in the modified version to achieve right-hand circular polarization. Fig. A1-2 shows what we get.

+
+ +
+

In its original configuration, the free-space elevation or theta patterns for the Lindenblad array are quite symmetrical. The slight variation in the patterns facing a dipole and the patterns at 45° to any dipole reflects the requirement for optimizing the tilt angle. In these patterns, the tilt angle is constant at 45°. The phi or azimuth pattern shows a slight squaring, comparable to the pattern of an ordinary turnstile pair of dipoles.

+

Over ground, we obtain elevation patterns that reflect the original uses planned for the antenna. As shown in Fig. A1-2 and in Table A1-2, the strongest lobe is always the lowest lobe. As well, beamwidth of the strongest lobe is always quite narrow. The array produces a very deep null directly overhead.

+
+ +
+

As a consequence of these pattern features, the original Lindenblad array is not especially suitable for satellite work, although it may serve as an omni-directional antenna for point-to-point communications. Unless the target stations are using the same polarization, results are likely to be little better than with a simple dipole turnstile. If the target station is using a comparable antenna, but with left-hand circular polarization, then the two antennas may be blind to each other.

+

Nevertheless, the Lindenblad array achieves a close approximation to circular polarization relative to point-to-point targets in the X-Y plane, that is, parallel to the earth's surface. At angle facing the dipoles (0°, 90°, and 180°), the axial ratio is close to 0.9. Between dipoles (at 45° and 135°) the ratio drops below 0.7, again suggesting the need to change the tilt angle for more nearly circular polarization. In all cases, the sense of polarization is right-handed.

+ 
+Lindenblad Radiation Pattern Reports in Free-Space for Phi Angles 0 to 180°
+- - - RADIATION PATTERNS - - -
+
+  - - ANGLES - -          - POWER GAINS -        - - - POLARIZATION - - -    - - - E(THETA) - - -    - - - E(PHI) - - -
+  THETA     PHI        VERT.   HOR.    TOTAL      AXIAL     TILT   SENSE     MAGNITUDE    PHASE      MAGNITUDE    PHASE
+ DEGREES  DEGREES       DB      DB      DB        RATIO     DEG.               VOLTS     DEGREES       VOLTS     DEGREES
+   90.00     0.00      -3.37   -2.33    0.19    0.88674   -88.70  RIGHT     1.07851E+02    85.59    1.21611E+02    -4.72
+   90.00    10.00      -3.43   -2.13    0.28    0.86140   -89.08  RIGHT     1.07138E+02    85.57    1.24368E+02    -4.70
+   90.00    20.00      -3.58   -1.66    0.50    0.80191   -89.60  RIGHT     1.05333E+02    85.53    1.31350E+02    -4.65
+   90.00    30.00      -3.75   -1.15    0.75    0.74144   -89.88  RIGHT     1.03279E+02    85.47    1.39295E+02    -4.60
+   90.00    40.00      -3.86   -0.83    0.92    0.70553   -89.99  RIGHT     1.01937E+02    85.44    1.44483E+02    -4.57
+   90.00    50.00      -3.86   -0.83    0.92    0.70553   -89.99  RIGHT     1.01937E+02    85.44    1.44483E+02    -4.57
+   90.00    60.00      -3.75   -1.15    0.75    0.74144   -89.88  RIGHT     1.03279E+02    85.47    1.39295E+02    -4.60
+   90.00    70.00      -3.58   -1.66    0.50    0.80191   -89.60  RIGHT     1.05333E+02    85.53    1.31350E+02    -4.65
+   90.00    80.00      -3.43   -2.13    0.28    0.86140   -89.08  RIGHT     1.07138E+02    85.57    1.24368E+02    -4.70
+   90.00    90.00      -3.37   -2.33    0.19    0.88674   -88.70  RIGHT     1.07851E+02    85.59    1.21611E+02    -4.72
+   90.00   100.00      -3.43   -2.13    0.28    0.86140   -89.08  RIGHT     1.07138E+02    85.57    1.24368E+02    -4.70
+   90.00   110.00      -3.58   -1.66    0.50    0.80191   -89.60  RIGHT     1.05333E+02    85.53    1.31350E+02    -4.65
+   90.00   120.00      -3.75   -1.15    0.75    0.74144   -89.88  RIGHT     1.03279E+02    85.47    1.39295E+02    -4.60
+   90.00   130.00      -3.86   -0.83    0.92    0.70553   -89.99  RIGHT     1.01937E+02    85.44    1.44483E+02    -4.57
+   90.00   140.00      -3.86   -0.83    0.92    0.70553   -89.99  RIGHT     1.01937E+02    85.44    1.44483E+02    -4.57
+   90.00   150.00      -3.75   -1.15    0.75    0.74144   -89.88  RIGHT     1.03279E+02    85.47    1.39295E+02    -4.60
+   90.00   160.00      -3.58   -1.66    0.50    0.80191   -89.60  RIGHT     1.05333E+02    85.53    1.31350E+02    -4.65
+   90.00   170.00      -3.43   -2.13    0.28    0.86140   -89.08  RIGHT     1.07138E+02    85.57    1.24368E+02    -4.70
+   90.00   180.00      -3.37   -2.33    0.19    0.88674   -88.70  RIGHT     1.07851E+02    85.59    1.21611E+02    -4.72
+   90.00   190.00      -3.43   -2.13    0.28    0.86140   -89.08  RIGHT     1.07138E+02    85.57    1.24368E+02    -4.70
+
+
+ +
+

Fig. A1-3 shows the elevation patterns for the original Lindenblad at a height of 7.5 wavelengths above average ground. Although the right-hand circular polarization component dominates the pattern at the right, the multiplicity of lobes and nulls tends to disqualify the original array from satellite service. Compare these patterns to corresponding patterns for the modified Lindenblad with progressive quadrature feed. Although the modified version of the antenna has slightly less gain, the evenness of its pattern suggests more satisfactory satellite service at lower elevation angles.

+

The exploration of original Lindenblad literature is not either idle or merely historical. Some antenna builders have tried closer dipole spacing than the value recommended in the main text. To obtain satisfactory patterns, they may wish to attend to the calculations of the more nearly correct tilt angle for these closer spacings. We may yet learn much more about the modified Lindenblad array.

+
+ +

+
+

Updated 05-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

+

Topics: Lindenblad, Moxon, Quad, Satellite, Turnstile, VHF / UHF


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+

Notes on Axial-Mode Helical Antennas in Amateur Service
+ Part 1: Helix Basics, Modeling Issues, and Short Helical Antennas Over Perfect Ground

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The axial-mode helical antenna has become a popular choice for radio amateurs engaging in satellite communications. We may construct helical antennas using straightforward methods with easily available materials. However, the individual builder faces a number of questions about helix size for a given frequency. Past literature has focused mainly on the gain that the axial-mode helix can attain for a given size. We should also examine other facets of the helix, such as the sensitivity to feedpoint impedance change with very small variations in size and the development of sidelobes with changing helix size.

+

In addition, the axial-mode helix generally receives attention in the context of very broadband antennas. In contrast, the amateur seeking circular polarization for satellite communications normally uses a very small bandwidth on any one of several bands, each band requiring a separate antenna. To answer the questions that face the potential amateur helix builder, we must we change our orientation to the antenna. Then we may be able to answer not only the question of how large to build the antenna, but as well whether the axial-mode helix is the right choice for a circularly polarized antenna for some specific use.

+

There are a number of background sources for information on axial-mode helices. The following list is a start, with most of the items having extensive bibliographies.

+
+ John D. Kraus, Antennas, 2nd Ed. (1988), pp. 300-310. +

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd Ed. (1998), pp. 231-239.

+

C. A. Balanis, Antenna Theory, 2nd Ed. (1997), pp. 505-512.

+

H. E. King and J. L. Wong, "Helical Antennas," Chapter 13 of Antenna Engineering Handbook, 3rd Ed., R. L. Johnson, Ed. (1993), pp. 13-1 ff.

+

Darrel Emerson, AA4FV, "The Gain of an Axial-Mode Helix Antenna," The ARRL Antenna Compendium, Vol. 4 (1995), pp. 64-68.

+
+

The fundamental question posed by virtually all of these sources is the gain of the helix relative to its proportions over a significant bandwidth. In the notes to follow, I shall purposely restrict the number of size considerations and also reduce the bandwidth to a single frequency: 299.7925 MHz. At this frequency, 1m = 1WL. Therefore, all measurements will be in meters. The properties of any sample helix will scale to any desired frequency so long as you also scale the wire diameter.

+

My investigation will use NEC-4D as the chief modeling tool. For most purposes, NEC-2 will also work, although the helix formation command has a different entry system for the critical dimensions. NEC results in the past have appeared to yield lower gain reports than some indirect gain calculations based on empirical results. However, there are both modeling and theoretical calculation issues related to the interpretation of the modeling reports, and we shall examine both before we are done.

+

Some Helical Antenna Basics

+

A typical axial-mode helical antenna has the form shown in Fig. 1. It consists of a number of turns, usually rising from a ground plane. The graphical representation of the helix shows the modeling form that I used to generate the basic sections of these notes. The bottom end of the helix connects directly to a perfect indefinitely large ground plane. Peak forward gain occurs close to or at the vertical axis of the helix. However, as we shall see, the pattern of a helix is not always perfectly symmetrical. There are numerous construction variations. Some builders bring the bottom turn of the helix back to the center of the helix circle. Others surround the base with a cup connected to the ground plane. Of course, an actual ground plane will have a finite dimension, usually a full wavelength in diameter or along the sides of a square.

+
+ +
+

The helices with which we shall work are straight sided. King and Wong have worked with both stepped and uniformly tapering helix diameters, but most amateur builders will choose the simpler uniform structure shown in Fig. 1.

+
+ +
+

Fig. 2 shows the basic dimensions of a helix. S is the turn spacing or the linear length of 1 turn of the helix. R is the radius, and 2R the diameter. If we stretch a single turn flat, we obtain the right triangle shown on the right side of the figure. C indicates the circumference of the turn, while L' indicates the length of wire required to obtain a full turn. Angle alpha is the pitch of the helix. For helices having multiple turns, we shall also be interested in the total helix length.

+

The dimensions are all interrelated by a few trig equations. All dimensions refer to center-to-center distances relative to the wires.

+
+ 
+R = radius of the helix, center to wire-center
+C = circumference of the helix                   C = 2 p R
+S = spacing between turns                        S = C tana
+alpha = pitch angle                              alpha = tan-1 (S/C)
+N (or n) = number of turns
+L = axial length of helix                        L = n S
+D = conductor diameter
+L' = Conductor length for a single turn          L' = SQRT(C2 + S2) = C/cos alpha = S/sin alpha
+
+
+

To design of an axial-mode helix, we need select only a few of these dimensions and the rest will following automatically. Perhaps the two most critical dimensions are the pitch angle and the circumference. In fact, basic helix theory tends to restrict axial-mode operation of the helix to pitch angles between 12° and 14°. As well, various texts restrict the circumference to ranges from either 0.8WL to 1.2WL (Kraus) or from 3/4WL to 4/3WL (Balanis). The number of turns in a helix is a builder selection, with gain (for any given pitch and circumference) rising with the number of turns. As well, selection of a wire diameter is also a builder choice. Although not mentioned in any serious way in most literature, we shall discover that the conductor size does make a difference to helix performance.

+
+ +
+

Modeling a helix in either NEC-2 or NEC-4 involves approximating a circular form with a series of straight wires. Fig. 3 shows one limitation of this process. The straight-wire segments are inscribed within the circle defined by the specification of a radius for the helix. Hence, the sum of the wire segments will always be less than the length of the wire in an actual single turn. If we raise the number of segments sufficiently high, the error diminishes to insignificance. A level of about 20 wires per turn is large enough for virtually all applications.

+

The following two lines compare otherwise identical 5-turn helices with a circumference of 1.0WL and a 12° pitch at the test frequency.

+ 
+Segmentation    Reported Gain   Impedance               Average Gain Test               Corrected Gain
+Segments/turn   dBi             R +/- jX Ohms           Value           dB              dBi
+20              8.39            225.5 - j 39.8          1.815           -0.42           8.81
+40              8.30            213.2 - j 71.2          1.762           -0.55           8.85
+
+

Ultimately, the corrected gain values (reported gain - AGT in dB) coincide very well. However, given the model set-up, the impedance values (even if corrected by multiplying half the AGT value times the resistive component) will not coincide. To gather trends, but not actual values, of the terminal impedance of the helix, I placed the source on the very first segment. However, NEC places a source on the entire segment. Changing the number of segments per turn places the actual position of the source either closer to or further from the ground plane. Hence, the more segments per turn, the lower the resistive component of the source impedance.

+

The use of the first segment as a source position has a second effect on the model. A NEC model is most adequate when the segments on either side of the source are equal in length or when the source segment is vertically oriented to a perfect ground plane. The helix meets neither of these conditions. Hence, the average gain test (AGT) value for a helix over perfect ground is not 2.0. However, we may correct the reported gain value (in dBi) by subtracting the AGT value in dB from the reported value. The following lines compare the 5-turn 12° 1.0WL helix with the source placed on segments 1, 2, and 3.

+ 
+Source          Reported Gain   Impedance               Average Gain Test               Corrected Gain
+Placement       dBi             R +/- jX Ohms           Value           dB              dBi
+Seg. 1          8.39            225.5 - j 39.8          1.815           -0.42           8.81
+Seg. 2          8.79            238.2 + j 44.2          1.995           -0.01           8.80
+Seg. 3          8.79            263.1 + j147.3          2.000            0.00           8.79
+
+

Using the AGT value to correct the gain figure is thus a completely effective means of arriving at the modeled helix gain. However, had we used the impedances at segments 2 or 3 instead of going through the process of correcting the model for its AGT value, we would not see the impedance trends as well at the terminal end of the structure. Although the reported values will still be off the mark by a distance roughly equal to half the length of a segment, they will still be adequate to let us examine trends. Because we only need to see trends, we do not need to correct the resistive component of these values, especially since this corrective becomes less secure with high values of reactance.

+

NEC-4 models of helices are deceptively simple, as the following sample reveals.

+ 
+CM General Helix over Perfect Ground
+CE
+GH 1 100 5 1.24664 .159155 .159155 .001 .001 0
+GE 1 -1 0
+GN 1
+EX 0 1 1 0 1 0
+FR 0 1 0 0 299.7925 1
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
+
+

The entire 100-segment model of the 5-turn helix is contained in the single GH entry. It specifies 100 segments in 5 turns with an overall length of 1.24664 m (WL) using a starting and ending radius of 0.159155 m (WL) with starting and ending wire radii of 0.001 m (or 1 mm). The remainder of the model specifies the test frequency (FR), the source position (EX), the perfect ground (GN), and the requests for 2 theta (elevation) patterns at 90° phi (azimuth) angles from each other. The 2 patterns allow us to see the slight non-symmetry of the helix pattern over a perfect ground. (We shall examine the usual NEC-2 version of the GH command before we conclude these notes.) It is possible to create a helix using individual wires, and some programs include, either as part of the program or as an adjunct program, methods of creating helices. However, these systems will produce individual wires for each segment of the helix. Using the GH command, the NEC core calculates and produces the required segments internally. The ability to change the size of a helix with only a few keystrokes allows a larger database in a shorter time. However, before we conclude these notes, we shall change techniques, since rapid methods of helix formation also have their limitations.

+

There is such a thing as presenting too much data in compressed form for effective absorption. Many of the engineering charts developed for axial-mode helices suffer from this syndrome. Therefore, I shall restrict my investigation in several ways. First, I shall use (except for a single demonstration) a constant wire diameter of 2 mm (0.002WL or about 0.07874"). Second, I shall restrict the pitch angles to 14° and 12° (again, except for a single demonstration). These pitches represent the limits recommended for axial-mode helix operation and suffice to show trends based upon changing the pitch. Third, I shall look at helixes using 5, 10, and 15 turns only, since these represent short, medium, and long antennas. Most reference books place a lower limit of about 4 turns for axial-mode operation, so the shortest helix in our batch is close to the limit. 15 turns can result in helices up to 5WL long. Finally, we shall examine changes in performance of the prescribed helices using circumferences from 0.75WL up to 1.35WL. Extending the circumference to the Balanis 3/4WL-4/3WL limits lets us view some properties of these antennas that we might otherwise overlook. Because wire losses are so small in a helix, we shall use perfect (lossless) wire throughout. Let's begin with the smallest of our samples.

+

A 5-Turn Helix Using 2-mm Diameter Wire

+

The first test model is a 5-turn helix that uses 2-mm diameter lossless wire. The initial test used 4 separate pitches: 14°, 12°, 10° and 8°. For any small circumference, the gain increases as the pitch diminishes (and with it, the turn spacing and the total length). I wanted to uncover what the consequences might be of extending each pitch through larger circumferences. 14° is the recommended maximum pitch angle. The minimum circumference in the survey is 0.75WL. The maximum circumference is generally 1.35WL, although one data table uses 1.4WL as the maximum to confirm that the gain begins to drop beyond 1.35WL.

+

Table 1 shows the numerical data for the 4 series of modeling runs. The table derives from a simple spreadsheet used to calculate the required dimensions for the models. "Circum" means the helix circumference, while "Radius" is self-explanatory and is calculated by the spreadsheet. My spreadsheet actually uses 16 numeric positions per calculated number, although the table shows only 8. The extra positions are more of an inconvenience to data copying than they are an aid to precision. "T-space" means the turn spacing, again, as calculated from the pitch angle and the circumference. "Length" is the total length of the antenna, in this case 5 turns times the turn spacing.

+

Recorded data begins with "Gain Rp," the reported gain from the initial modeling. "BW-90" is the beamwidth as viewed down the Y-axis, while "BW-0" is the beamwidth down the X-axis, where beamwidth for both is the -3dB value. "R" and "X" are the components of the source impedance in Ohms. "AGT #" is the calculated average gain test value over perfect ground, where a value of 2.0 represents a fully adequate model as measured by this test. (Note that AGT is a necessary but not a sufficient condition of model adequacy.) "AGT-dB" is the same value converted to dB to serve as a correction factor for the reported gain. When calculated over perfect ground, use half the value of the report AGT, take the log10 of that number, and multiply by 10 to arrive at the AGT-dB value. Since both values are rounded, a digit of deviance is possible. The final or "Gain-Cor" column gives the adjusted forward gain value by subtracting the AGT-dB value from the reported gain value. Since all AGT-dB values in these notes are negative, all corrected gain values will be higher than the reported values.

+

AGT values will vary slightly from one model in a series to the next and, as a block, from one set of runs to the next. The chief source of the low AGT value is the relationship of the source segment to the ground plane. This relationship changes slightly with every increase in circumference, since the source segment becomes slightly longer. As we change pitch to a smaller angle, the source segments again change their relationship to the ground plane. Hence, the AGT # and AGT-dB values both tend to decrease as the pitch becomes smaller.

+
+ +
+

Scanning the tables for patterns can be somewhat daunting, so I have graphed some of the key values, beginning with the maximum forward gain--using corrected gain values. The trends would not have changed had I used the initially reported values.

+
+ +
+

Fig. 4 shows the maximum forward (upward) gains for the 4 pitch angles as we increase the circumference from 0.75 to 1.35WL. (The table shows the 14° 1.4WL circumference value to verify that the 1.35WL circumference value on the graph is a maximum that falls off with a larger circumference.) The trend in the gain graph suggests that we would do well with any of the 4 pitches up through a circumference of about 1.2WL. The lower the pitch, the higher the gain we obtain for any circumference below 1.2WL. It is most interesting that the gain is lowest (for the 12° and 14° pitch angles) where the circumference is close to 1.0WL. Note, however, that as we reduce the pitch angle, minimum gain tends to become associated with smaller circumferences. If we were to move either upward or downward from the design frequency, any circumference (and radius) of choice would change with the new frequency. Therefore, the curves represent a tracking of the gain at frequencies some distance from the design frequency. The 0.75WL and 1.35WL cut-off circumferences limit the tracking to a corresponding frequency range relative to the test frequency.

+

The gain curves do not tell the entire story concerning helical antennas operated in the axial mode. For example, one desirable feature of an antenna that we might wish to build is that all of the key properties should remain stable and predictable over a generous frequency span. We do not need them to be unchanging so long as we can easily predict the direction and amount of change. Small physical changes that yield large changes in a performance property tend to result in an antenna that is difficult to replicate within the tolerances of the usual home shop.

+
+ +
+

For this reason, graphs of the resistive and reactive components of the source impedance become important. Fig. 5 and Fig. 6 present the data for the 4 pitches relative to the 5-turn helix. Although the precise values are subject to adjustment as terminal impedance values, the trends may show us something of the helical antenna's stability.

+
+ +
+

Both the resistance and the reactance curves for the 10° and the 8° curves show significant fluctuations at virtually any circumference of helix, especially as compared to the 14° and the 12° curves. Even these curves have their limits. Above about a 1.2WL circumference, the high-pitch curves show very significant fluctuations. Reactance swings of 70 Ohms are common with a circumference change of as little as 0.05WL. For the 5-turn helix, 14° and 12° pitch helices less than 1.2WL long appear to present the most stable designs with respect to source impedance. Circumferences below about 0.8WL for 12° and 14° pitches also begin to show the instabilities of very large circumferences, but to a lesser degree.

+
+ +
+

A second factor often overlooked in helix performance is the development of sidelobes. Fig. 7 shows the Y-axis elevation patterns of the 5-turn helix with a 12° pitch over stepped circumferences. Although the sidelobes at circumferences of 1.05WL and 1.15WL appear small, note that they are less than 10 dB below the level of the maximum forward gain. As we increase the circumference, the sidelobes become stronger, and by a circumference of 1.35WL, we have a double set, with the forward-most sidelobe only about 6 dB below the main lobe. At the low end of the circumference scale, patterns for sizes below 0.95WL tend to remain as well behaved as the first pattern in Fig. 7.

+

Another feature of the helix's sidelobe development is the fact that neither the main lobe nor the sidelobes are symmetrical with respect to the centerline. Even the 1.05WL circumference pattern shows the asymmetry. In fact, the patterns are more symmetrical as viewed along the Y-axis than along the X-axis. If you return to Fig. 1, you can see that the terminal end of the model is off center when viewed along the Y-axis. The result is larger secondary lobes on one side than the other side of the helix.

+

The sidelobe development, when added to the source impedance data, suggests that in many ways, we would derive better performance overall from a 5-turn helix with a circumference above 0.8WL and under 1.2WL. This practical restriction lowers the maximum gain that we may obtain from the antenna to under 10 dBi with a beamwidth of about 50 degrees or so.

+

At this point, we must wonder if the same trends hold up for 10-turn and 15-turn helices. However, before examining that data, let's examine another overlooked aspect of helix design.

+

A 5-Turn Helix Using 5-mm Diameter Wire

+

Let's increase the wire diameter from 2 mm to 5 mm. 2-mm wire is between AWG #12 and AWG #14 in diameter. 5-mm wire is about 0.1969" in diameter, a little larger than 3/16" rod. At 2.5 times the diameter of our first models, it represents a way to discover whether element diameter makes a difference to helix performance.

+

One limitation of the investigation is the fact that the AGT values continue to drop further below the ideal 2.0 value. Nevertheless, the data are sufficiently accurate to reveal trends as we run through 14° and 12° pitch 5-turn helices. Table 2 has the complete data, but a few graphs can focus our attention on a number of key factors.

+
+ +
+

Fig. 8 presents the gain data for the two subject models for the standard range of circumferences. Both curves closely parallel their counterpart curves for 2-mm wire. The tabular data for 1.4WL will confirm that the 1.35WL gain for the 14° curve is a peak value.

+
+ +
+

In Fig. 9 and Fig. 10 we can see the instabilities of the resistance and reactance performance for circumferences below about 0.85WL and above 1.2WL. However, should we wish to compare the curves for smaller circumferences with the corresponding 2-mm curves, we shall see similar variations (and similar stability) for the two wire sizes. (Note: differences in the Y-axis range on the graphs may leave a misimpression of the actual amount of change.) In general, then, wire size does not make a great deal of difference to the selection of a helix circumference. Indeed, the patterns for the 5-mm helices are too close to those for the 2-mm versions to need repetition.

+
+ +
+
+ +
Wire diameter does make a difference in the forward gain of a 5-turn helix, especially over the range of circumferences that we have so far listed as stable with respect to source impedance and relatively free of sidelobe development, that is, 0.85WL up to about 1.2WL. Fig. 11 shows gain curves for the two wire sizes using a 12° pitch. Note that, besides gain, the only notable feature is the circumference associated with the minimum gain value. The movement of that gain "null" is similar to the effect of reducing the pitch angle with a constant wire size. (See Fig. 4.) Inter-turn coupling thus becomes a possibility for explaining the movement of the gain-null circumference size. +
+ +
+

Within the "stable" range, the average gain advantage for 5-mm wire is about 0.5 dB. The largest differences occur with circumference sizes between about 0.95WL and 1.15WL. Although one may dispute just how much advantage a half dB makes operationally, the result does have a bearing on most of the methods for estimating axial-mode helical antenna gain. None of those techniques takes wire diameter into account. In applying this data to scaled versions of the helices under study, we should remember that 2 mm and 5 mm represent 0.002WL and 0.005WL wire diameters, respectively.

+

Next Time. . .

+

In this initial foray into axial-mode helical antennas for radio amateurs, we have examined helix basics, setting up NEC-4 models over a perfect ground, and the main characteristics of 5-turn helix performance. However, as we move up the amateur bands, we find longer helical antennas. Therefore, we need to look at 10-turn and 15-turn helices in the same environment. We shall see if there are any significant differences in performance beyond the anticipated gain increase and beamwidth decrease. Since a significant part of our investigation involves how to model these antennas, we shall also explore what we need to do if we only have NEC-2 with which to work.

+
+ +
+

Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: 10- and 15-Turn Helical Antennas Over Perfect Ground and Modeling Helices in NEC-2

+

Return to Index

+

Topics: Helix, Satellite, VHF / UHF


+ + diff --git a/content/vhf/gh2.html b/content/vhf/gh2.html new file mode 100644 index 0000000..370a3d8 --- /dev/null +++ b/content/vhf/gh2.html @@ -0,0 +1,141 @@ + + + + + + Axial-Mode Helical Antennas Part 2: 10- and 15-Turn Helical + + + +
+

Notes on Axial-Mode Helical Antennas in Amateur Service
+ Part 2: 10- and 15-Turn Helical Antennas Over Perfect Ground and Modeling Helices in NEC-2

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

In our introduction to axial-mode helical antennas for radio amateurs, we examined helix basics, setting up NEC-4 models over a perfect ground, and the main characteristics of 5-turn helix performance. However, as we move up the amateur bands, we find longer helical antennas. Therefore, we need to look at 10-turn and 15-turn helices in the same environment. We shall see if there are any significant differences in performance beyond the anticipated gain increase and beamwidth decrease. Since a significant part of our investigation involves how to model these antennas, we shall also explore what we need to do if we only have NEC-2 with which to work.

+

A 10-Turn Helix Using 2-mm Diameter Wire

+

A 5-turn helix is just barely larger than the 4-turn limit for the application of axial-mode theory to antenna performance. Doubling that length to 10 turns yields a middle-size antenna, perhaps long for the amateur 2-meter band, but still shorter than those in use at 1296 MHz. Using 2-mm diameter wire and restricting ourselves to pitches of 14° and 12°, we obtain helical antennas that vary from 1.6WL to almost 3.4WL in total length. Our primary question will be whether there are any changes in the characteristics of these antennas other than the anticipated increase in maximum gain.

+
+ +
+

Table 3 provides the modeling data for the series of 10-turn helices. The overall increase in gain is accompanied by an equally expected reduction in beamwidth as we compare data for each level of circumference. However, for the smaller circumferences, the source impedance does not change by any very significant amount, a fact that is consistent with established helix theory and measurement. As well, for this modeling investigation, the AGT values for both helix lengths are consistent with each other.

+
+ +
+

Fig. 12 presents the gain data for the range of circumference covered by this study. Note that, compared with the 5-turn helices, both pitch versions reach their peak gain values at circumferences about 0.1WL smaller. The 12°-pitch version reaches peak gain at a circumference of about 1.2WL. Small-circumference gain values approach the peak gains of large-circumference versions. However, we suspect in advance that the usable region of the curves is smaller than the total span. As well, the minimum gain values occur at about 0.95WL circumference levels. The tilt of the curves in this area suggests that the actual minimum value for the 12° curve occurs with a slightly smaller circumference than for the 14° model.

+
+ +
+

The source resistance and reactance data also show some degree of stability shift toward the smaller circumference values. The 12°-pitch version of the helix begins to show wider variations of both resistance and reactance at a circumference of about 1.15WL. The lower gain 14°-pitch model appears stable with respect to reactance to about 1.2WL, but the resistance begins to show instabilities just shy of that circumference. These trends appear in Fig. 13 and Fig. 14. At the low end of the scale, instabilities begin to appear only for the smallest circumference within the survey.

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+

The end result is that the 10-turn helix appears to be stable to almost the same circumference as the 5-turn helix when we restrict ourselves to 14° and 12° pitch levels. At most, we shrink the stability limit by one step, down to a circumference of 1.15WL.

+

We are as interested in pattern shapes as we are in other performance factors. Here, Fig. 15 can be useful, as it presents the Y-axis elevation patterns for the 12° pitch 10-turn helix at the same circumferences used in Fig. 7. The patterns make several things clear. First, past the gain peak, a 10-turn helix is quite unsatisfactory as an axial mode antenna. In fact, the single dome pattern reappears at various larger circumferences, but it has lost the consistency that marks axial mode operation.

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+ +
+

Second, just as the gain peaked at a smaller circumference than for the 5-turn antenna, the sidelobes begin their appearance at a smaller circumference in 10-turn antennas. The sidelobes of the 10-turn helix with a 0.95WL circumference are nearly as distinct as the ones that we encounter in the 5-turn helix only at a circumference of about 1.15WL.

+

Third, the sidelobe structure becomes more complex, even if we restrict our attention to patterns for circumferences up to 1.15WL. Rather than having single or double side lobes, we have a wider sidelobe that suggests the inclusion of several overlapping sidelobes. Although the peak values are not as high as in the case of some 5-turn patterns, the total energy within the sidelobes may be equal to single stronger lobes. In terms of the pick-up of unwanted noise and signals in directions other than the focus of the main lobe, the effects may be similar.

+

Whether the trends continue or whether the helices have stabilized requires one more set or models.

+

A 15-Turn Helix Using 2-mm Diameter Wire

+

At the design frequency, 15-turn axial-mode helices with circumferences between 0.75WL and 1.35WL yield antennas between 2.4WL and 5.0WL long. We may generally classify these antennas as long helices. Longer helical antennas are possible, but these would be quite rare in amateur service. The long antennas yield their anticipated further increase in gain along with the accompanying decrease in beamwidth. Despite the increased length, the long helices do not yield perfectly aligned patterns, as evidenced by the continuing divergence between X-axis and Y-axis beamwidth data in Table 4.

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+

The gain data captured in Fig. 16 shows a further compression of the gain curve toward the smaller circumferences. The gain peaks are at least one step smaller in circumference, with more precipitous declines in gain above the circumference of peak gain. Even if we press the circumference for maximum gain, the limit of utility is well below the maximum circumference (about 1.3WL) for which axial-mode helical antenna theory is most often rated.

+
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+

The 15-turn source impedance data also suggest that circumferences below 1.15WL are best suited for stable operation, as shown in Fig. 17 and Fig. 18. With respect to source resistance, the 14° version is more stable. The variations in the 12°-pitch version are not an artifact of modeling, since the AGT values of the 15-turn helices are comparable to those of the 5-turn and 10-turn antennas for each pitch shown. However, it is notable that the region of relatively stable resistance values continues to move toward small circumferences.

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+
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Although the resistance of the 14° model shows the greater stability, reactance is the opposite. With respect to reactance, the 12° version shows greater stability, but not by much. At the upper end of the circumference scale, both pitches show radically divergent values with respect to the stable region, suggesting that the longer the axial-mode helix, the more that circumference limits represent a sudden threshold rather than a gradual transition into unreliable operation.

+

The net result of the data is the suggestion that the home builder of a long helix should use great care if he wishes to press the limits of gain and source impedance at the 15-turn level. Construction variables may easily push the antenna over the limits of stable performance. Conservative design using smaller circumference values may make the resulting antenna easier to tame than versions using large values for the circumference.

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+

The trends in pattern formation that we have observed through the 5-turn and 10-turn helices continue in the longer version. Sidelobes development occurs at smaller circumferences, with a definitive and an incipient sidelobe already apparent in the pattern in Fig. 19 for a circumference of 0.95WL. The pattern is relatively free of side lobes only at the smallest circumferences surveyed in these notes. Only the patterns through a circumference of 1.15WL are suitable for axial-mode operation. (Note from the pattern for a circumference of 1.25WL that a narrow half-power beamwidth does not clearly indicate a desirable axial-mode pattern.) Even with single central forward lobes, the sidelobes of the long helices should be a matter of concern, since they are down from the main lobe by less than 10 dB in these models using a perfect ground as the modeling ground plane.

+

Some Comparisons

+

To summarize part of what the data show, we may compare the gain curves for both the 14° and the 12° versions of the three levels of helices studied here. Fig. 20 compares the gain curves for the 14° antennas, while Fig. 21 does the same for the 12° models. For both pitches, note that there is strong parallel among the three curves. However, the longer the helix, the greater is the displacement of the curve toward the smaller values of circumference.

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Equally apparent is the parallelism among curves with respect to the gain decrease above the peak gain point. As the pattern graphics have shown, operation above the peak gain level yields generally unsatisfactory axial-mode radiation patterns, not to mention operation in regions of unstable source resistance and reactance values. How far one may push the circumference smaller than the limit shown on the graph to capitalize on a clean pattern and higher gain on this side of the main minimum would require further study. However, in terms of real helices using a self-contained ground plane and positioned some distance above the actual ground, there will be limitations that the perfect-ground models do not show.

+

We may also compare the gain values derived from this exploration with at least a couple of the shirt-pocket estimation schemes proposed in basic literature about axial-mode helical antennas. Similar calculation systems for gain and the half-power beamwidth appear in Kraus (p. 310) and in Stutzman and Thiele (p. 237). The terms for these calculations have the following meanings. CWL = Circumference of helix in WL. SWL = Turn spacing of helix in WL. n = number of turns in helix. WL = wavelength(s)

+ 
+1. Gain (Directivity):             Kraus                        Stutzman & Thiele
+                                   D = 12 CWL^2 n SWL           D = 6.2 CWL^2 n SWL
+Note:  Gain (dBi) = 10 log10(D)
+
+2. -3dB (half-power) Beamwidth:    Kraus                        Stutzman & Thiele
+                                   HPBW = 52°/(CWL SQRT(n SWL)  HPBW = 65°/(CWL SQRT(n SWL)
+
+3. Terminal Resistance:            R = 140 CWL                  R = 140 CWL
+
+

The original coefficient for directivity in Kraus was 15, but he had reduced this number to 12 by the release of the 2nd edition of Antennas. Although the equation for terminal resistance equation is common to virtually all systems, we shall not try to evaluate it, since the source values for a NEC model do not occur at the true terminal point of a helix.

+

As a test case, let's examine the data for helices with a 1.15WL circumference (using 2-mm wire) and compare the modeled values for 5-, 10-, and 15-turn versions. Gain is in dBi and BW (half-power beamwidth) is in degrees. Modeled data also appear for the 5-turn, 5-mm wire helix.

+ 
+Turns           LWL = n SWL             Modeled                 Kraus                           Stutzman & Thiele
+                                        Gain    BW              D       Gain    BW              D       Gain    BW
+5               1.222WL                 9.93    53              16.9    12.3    41              8.7     9.4     51
+5 (5-mm)        1.222WL                 10.62   53
+10              2.444WL                 12.23   39              33.7    15.3    29              17.4    12.4    36
+15              3.666WL                 13.76   28              50.6    17.0    24              26.1    14.2    26
+
+

As a second test case, let's evaluate helices with 0.85WL circumferences in the same manner.

+ 
+Turns           LWL = n SWL             Modeled                 Kraus                           Stutzman & Thiele
+                                        Gain    BW              D       Gain    BW              D       Gain    BW
+5               0.903WL                 9.49    71              9.2     9.6     58              4.8     6.8     76
+5 (5-mm)        0.903WL                 9.75    69
+10              1.807WL                 10.69   58              18.4    12.7    46              9.1     9.8     57
+15              2.710WL                 11.42   50              37.2    14.4    27              14.2    11.6    47
+
+

The calculating schemes can grow to into fairly complex affairs, as is evident in the more elaborate equations found in the Emerson and the King and Wong references. However, none take the wire radius (or diameter) into account. Hence, all remain shirt-pocket estimators and not precise calculators of the properties of axial-mode helical antennas, at least as modeled in this study. For practical purposes, that is, initial planning and the like, the Stutzman and Thiele simple formulas are as good as any. However, they remain seriously off the mark for shorter helices with smaller circumferences that fall on the curve below the gain minimum. The two simpler schemes presume a steadily rising gain across the span of allowed axial-mode circumferences, and that presumption is not correct with respect to the models surveyed here..

+

This exercise has used NEC-4 to produce the modeled results. NEC-2 also has a helix command, although its structure is quite different from the one used in NEC-4. The GH command does not appear in the original NEC-2 manual (NOSC TD 116, Vol. 2), but does appear in numerous implementations of NEC-2. The only significant difference between the model that we showed for NEC-4 and the NEC-2 counterpart appears in the GH entry in the following sample. (The GE entry also has a slight difference between the NEC-2 and NEC-4 versions.)

+ 
+CM  NEC-2 GH helical antenna over perfect ground
+CE
+GH 1 100 .249328 1.24664 .159155 .159155 .159155 .159155 .001
+GE 1
+GN 1
+EX 0 1 1 00 1 0
+FR 0 1 0 0 299.7925 1
+RP 0 181 1 1000 -90 90 1.00000 1.00000
+RP 0 181 1 1000 -90 0 1.00000 1.00000
+EN
+
+

Fig. 22 shows GNEC and NEC-Win Pro help screens for the GH entry to aid in explaining the differences. Whereas the NEC-4 entry uses the number of turns and the total helix length to internally calculate the turn spacing, the NEC-2 version uses the turn spacing and total length to calculate the number of turns. NEC-4 uses a single helix radius (at both top and bottom), but NEC-2 requires entries of radius for both X- and Y-axes to allow for oval spirals. Restricting the helix to a circular form in NEC-4 opens a floating decimal position that permits one to choose between log spirals and Archimedes spirals, which yield a difference in the turn positions only if the radii differ at the top and bottom of the spiral.

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The GH command in both systems yields a wire segment structure that runs from Z=0 to a Z-value that equals the total length of the helix. The circumference of the helix is centered at X=0 and Y=0. In both systems, the modeler must use the GM command to change the position or orientation of the helix, a maneuver that we have not yet needed for this exercise.

+

The key question is whether we can expect any significant differences in the reported output between NEC-2 and NEC-4. Table 5 provides a negative answer with respect to 5-turn helices using 2-mm diameter wire for pitches of 14° and 12°. (The table repeats the data from Table 1 to facilitate the comparison.) I ran the series using the sample model shown and with the additional EK (extended thin-wire kernel) command that is useful in NEC-2 when the segment length begins to approach the wire diameter. The EK command made no difference to the data output. This test also confirms that the chief source of low AGT values is the position of the source and the orientation of the wire segment on which it is placed. The bottom line is simply that NEC-2 is fully adequate for modeling axial-mode helices so long as the modeler uses the AGT value to correct the gain reports and recognizes the limitation inherent in the source impedance report.

+
+ +
+

Next Time. . .

+

In this episode, we explored longer helixes to identify how their characteristics vary from those of the initial set of 5-turn helices. Besides seeing the gain curves rise in peak value and generally slide to smaller circumferences, we also saw the increase in sidelobe development at smaller circumference levels. Finally, we made some comparisons, including a brief primer on how the NEC-2 and NEC-4 GH (helix) commands differ.

+

However, the entire study has a major limitation. Few amateur antennas have the opportunity to operate over indefinitely extended perfect grounds. Therefore, we need to explore, if only partially, how axial-mode helical antennas perform over self-contained ground planes that are elevated from the actual ground. That exercise will put us a position to do a rudimentary comparison between helices and other antennas amateurs might use the obtain high-gain circular polarization.

+
+ +
+

Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: Axial-Mode Helices above Real Ground and Alternatives to the Helix for Circular Polarization

+

Return to Index

+

Topics: Helix, Satellite, VHF / UHF


+ + diff --git a/content/vhf/gh3.html b/content/vhf/gh3.html new file mode 100644 index 0000000..6d253df --- /dev/null +++ b/content/vhf/gh3.html @@ -0,0 +1,104 @@ + + + + + + Axial-Mode Helical Antennas Part 3: Axial-Mode Helices + + + +
+

Notes on Axial-Mode Helical Antennas in Amateur Service
+ Part 3: Axial-Mode Helices above Real Ground and Alternatives to the Helix for Circular Polarization

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L. B. Cebik, W4RNL

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In past episodes of this series, we examined the basic dimensions of axial-mode helical antennas and initially cataloged the properties of 5-turn helices with different wire diameters over perfect ground. We went on to explore longer helixes to identify how their characteristics vary from those of the initial set of 5-turn helices. Besides seeing the gain curves rise in peak value and generally slide to smaller circumferences, we also saw the increase in sidelobe development at smaller circumference levels. Finally, we made some comparisons, including a brief primer on how the NEC-2 and NEC-4 GH (helix) commands differ.

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However, the entire study had a major limitation. Few amateur antennas have the opportunity to operate over indefinitely extended perfect grounds. Therefore, we need to explore, if only partially, how axial-mode helical antennas perform over self-contained ground planes that are elevated from the actual ground. That exercise will put us a position to do a rudimentary comparison between helices and other antennas amateurs might use the obtain high-gain circular polarization.

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Elevated Self-Contained Ground Planes

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The notes that we have examined so far present an idealized portrait of the axial-mode helix. Gain curves are smooth over the region that we have termed "stable." Within that region, the modeled values of source impedance have also varied within quite small limits. With the stepped increases in helix length, the patterns have shown a progressive development, especially with respect to sidelobe production.

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However, the helical antennas that amateurs and others build do not have the benefit of a perfectly reflecting ground plane that is indefinitely large. Instead, in accord with the general outlines of Fig. 23, they appear on self-contained ground planes of finite size with the entire array placed above ground by an amount determined by operational needs and practical feasibility.

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As noted near the beginning of these notes, a square ground plane is not the only possible helical antenna configuration. However, from the perspective of practical modeling, it is perhaps the most appropriate for initial modeling efforts. As shown in the graphic, we may terminate the helical portion of the model at the nearest intersection of wires making up the wire-grid ground plane. Hence, the source may remain on the very first segment of the helix itself. The technique holds the promise of allowing some comparisons between the models constructed over perfect ground and the new series of models.

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The new models do not come without an associated cost. The models over perfect ground made use of the GH command that permitted very simple model structures. However, if we use the same circumference steps with the new series of models, we need to move the terminal point of the first helix segment from its natural location to the nearest junction of ground-plane wires. We cannot do that and still keep the models simple and uniform from one step to the next.

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The workaround for this problem is to construct individual models for each helix-wire-grid combination. As note at the beginning of these notes, several programs are available to allow the construction of both parts of the antenna on a 1-wire-per-segment basis. For example, EZNEC Pro/4's current version has both facilities. The resulting models are not any more segment intensive than using the GH and GM commands to create and replicate wires under a single tag number. However, they do result in one-model-per-situation. Hence, instead of using 1 model for all 12° antennas, we have one model for each combination of helix pitch, circumference, and length, plus the selected size of wire-grid ground plane.

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Fig. 24 shows the EZNEC helix-creation sub-screen. Essentially, it allows entering the same set of variables as the GH command in either NEC-2 or NEC-4. However, the output is a set of 200 wires, each a GW entry. The wire-grid structure for this exercise is 1.2WL by 1.2WL on a side, with the wires spaced at 0.1WL intervals. Wire 1 of the helix shifts from its position on the X-axis as created to the nearest intersection of wires, normally either X=0.1 or X=0.2.

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The models are limited by the factors that go into their creation. For example, the misalignment of the first helix wire creates a very small error component. More serious is the fact that the helix wire approaches the wire-grid wires at a severe angle: 12°. The normal wire diameter for a wire-grid that simulates a solid surface is the segment length divided by pi. However, this fat a wire results in some larger-circumference models having a first wire that penetrates into the center section of the wire-grid wire that it meets at a junction. To overcome this problem, I reduced the wire-grid diameters to 0.015WL. Although not a perfect simulation of a solid plane, the resulting data was--for models that could handle both thin and thick wires--only a slight change in performance.

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Due to these constraints, I created models only for the 12° versions of the helical antennas, using 5, 10, and 15 turns, with radii ranging from 0.75WL to 1.35WL. Each helix connects to a wire-grid that is 1WL above average ground (conductivity 0.005 S/m, permittivity 13). The goal is to determine to what degree these models may differ from the models created over a perfect ground. Table 6 provides the complete data on the modeling results. The AGT values tends to vary much more widely in these elevated ground-plane models than in the earlier set, but the values remain well within the range of what is usable to obtain suggestive (rather than definitive) trends.

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The general utility of the models shows up in Fig. 25, which tracks of gain levels for both types of models. Over the region that we termed "stable" with the initial set of models, the new models show identical characteristics, with a gain minimum occurring very close to where it occurred over perfect ground. As well, once the models use circumferences that place them outside of effective axial-mode use, the curves overlap fairly precisely. At the small-circumference end of the scale, the new models show lower gain than their perfect-ground counterparts as the circumference reaches a value to Ohms small for axial-mode duty. Within the more central portions of the circumference rage, the two curves for each length of helix parallel each other. The two differences are 1. the elevated models have a higher average gain than the perfect-ground models, and 2. the elevated models show a less severe dip in gain at the minimum point.

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Fig. 26 and Fig. 27 provide data for the elevated ground-plane models on the source resistance and reactance, respectively. The overlap in the curves for a good portion of their length suggests that--with one exception--they portray the source impedance trends quite well. The curves for circumferences above 0.90WL and those for 0.90WL and lower have slightly different slopes. 0.90WL is the last circumference using a 0.1WL grid-wire connection; from 0.95WL upward, the connection is to the 0.2WL grid wire junction.

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The upper limit of source impedance stability is a circumference of about 1.15WL. At the lower end of the scale, the short (5-turn) helix deviates significantly below 0.8WL circumference. However, the other two sizes of helix appear to be stable to the limit of the survey. These results are consistent with the gain behaviors of the three sizes of helix.

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The use of smaller circumferences for 12° helical antennas receives support from the evolution of patterns. Fig. 28 presents a set of three patterns for the 10-turn model at 0.85WL, 1.0WL, and 1.15WL circumferences. EZNEC provides circularly polarized patterns, although the present set has maximum values that do not differ materially from a total-field pattern. All antennas in the series use right-hand circular polarization. Because reverse orientation pattern lobes occur in null areas of the dominant orientation, the total field patterns would show more complex structures in the region of the secondary lobes.

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For most cases, the elevated ground-plane models show slightly less severe sidelobe strength, down from 1 to 1.5 dB relative to patterns for models over a perfect ground. Nevertheless, the sidelobe structure of the 1.15WL circumference model is sizable and peaks only about 10 dB below the main lobe of the pattern. In contrast, the 0.85WL circumference model has scarcely any sidelobe structure at all. However, pattern cleanliness will cost about 1 dB in maximum gain.

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The end result of our survey of 12° helices over elevated ground planes is a set of data that differs in detail but not in main lines from the data for helices over perfect ground. Pressing for maximum gain by using a larger circumference results in a pattern with a much higher sidelobe content. As well, the helix may approach a region of unstable operation where small physical changes may yield large and unexpected changes in the source impedance. Leaning toward smaller circumferences sacrifices some gain for the sake of cleaner patterns and more predictable source impedance behavior.

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Is There a "Best" Ground Plane Size?

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Within the context of square ground planes, the 1.2WL by 1.2WL wire grid used in the survey of 12° helices was both arbitrary and reasonable. I selected a size that I presumed was large enough to perform well in its function. However, without comparators, the ground plane that I used is not certifiably the best. To see if there might be a better size, I performed a final survey using 4 different square ground planes, with sides that are 0.8WL, 1.0WL, a.2WL, and 1.4WL long. Fig 29 shows their relative sizes with respect to a standard helix.

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The ground planes all use 0.1WL wire spacing and 0.015WL wire diameters. This arrangement allows a standard relocation of the first wire in the helix. All first wires for 0.85WL circumference helices go to the 0.1WL position, while each of the two larger sizes (1.0WL and 1.15WL) move to the 0.2WL junction. A finer gradation of wire-grid sizes is desirable. However, such grids would create one or two problems. The use of standard 0.1WL wire spacing moves the first helix wire termination to a different position, creating deviations in the data and the AGT values. Creating a grid that places a wire at both the 0.1WL and 0.2WL position changes the performance of the grid for intermediate outside dimensions. Nevertheless, the 4 samples are enough to establish a basic trend.

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Fig. 30 provides a view of the results of the sampling, while Table 7 gives the complete tabular results. Although nothing significant happens in the realm of source impedance, the 10-turn helices used in the survey show small but definite differences in gain as we change the size of the ground plane. The larger the circumference of the helix, the smaller is the ground-plane size that yields maximum gain. Each of the three sizes of helix--as measured by circumference--has its peak gain with a different size ground plane. What the survey cannot show is whether the overall length of the helix plays a role in the ground-plane size for peak gain, since the smaller circumference models also have a shorter total length.

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The gain difference for the widest helix is not great across the span of ground-plane sizes. However, as we reduce the circumference of the helix, the curves grow steeper. Since the survey stops at a 1.4WL side length for the ground plane, it is not clear whether or not the 0.85WL circumference helix has reached its peak value. Still, ground-plane size is another of those factors that basic helix literature tends to overlook. The amateur who intends to build his own axial-mode helix should not ignore this factor. For the 0.85WL circumference helix, the gain difference between the smallest and largest ground planes in the series is over 1 dB.

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Is the Helical Antenna the Best Choice for Amateur Radio Circularly Polarized Communications?

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These notes have recorded some interesting limitations in the stability and the patterns of axial-mode helical antennas. Calculating the required helix dimensions turns out to be the simplest part of the planning process. Much more hangs upon the decisions we make with respect to selecting the circumference and ground plane sizes, as we weigh the contributing factors in a compromise between having the cleanest pattern, the most stable source impedance, and the maximum gain. A single set of dimensions may not satisfy all possible operating conditions.

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Most engineering sources classify the axial-mode helical antenna as a broadband array. Within this classification, we expect limitations of the sort that we encountered. However, amateur communications calling for circular polarization generally require only narrow-band antennas. Before we close the notes, we should at least do a preliminary comparison of alternative antennas that an amateur might use in satellite communications.

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Fig. 31 presents the outlines of three antennas. All are designed for the test frequency of 299.7925 MHz. The helix, selected from the cluster that we have studied, uses 10 turns, 2-mm wire, and a 12° pitch. The 1.15WL circumference results in a total length of 2.44WL. to make the model coincide with the other antennas, I elevated the terminal end of the helix and created a 1.2WL by 1.2WL wire grid as an elevated ground plane. Other ground plane structures are possible. I experimented with 32- and 64-radial ground planes. However, the need to terminate the first segment of the helix at the center of the radial system established quickly that the helix must be almost perfectly centered over its ground plane structure. Off-setting the radial planes by less than 0.2WL reduced main lobe gain by 3 dB and produced a major secondary lobe only 4-5 dB weaker than the main lobe.

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The helix over the square wire grid was centered, with only the first segment moved slightly (about 0.017WL) to intersect a grid-wire end. The gain (corrected for an AGT-dB value of -0.66 dB) was 12.71 dBi with a beamwidth of 37°. The impedance (corrected for an AGT of 0.859) was about 245 Ohms, although the impedance at the actual junction will be somewhat lower still.

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The other two antennas in the set are a 4-element quad with a turnstiled driver and an 8-element crossed Yagi with turnstiled drivers. The quad is only 1.87WL long from reflector to the forward-most director. Using 1-mm diameter wire for the elements, it has a gain of 10.35 dBi when placed 1WL above average ground. The beamwidth is 58°. Because a quad allows some flexibility in the placement of the driver without undue adverse effects on the array gain, we may arrive at a single-source impedance of about 95 Ohms resistive. Hence, a 1/4WL section of 93-Ohm cable forms a proper phase line run between successive corners of the driver. The result is a circularly polarized antenna. We may reverse the polarization simply by connecting the main feedline at one or the other end of the phase line. The result is a 50-Ohm impedance for the main feedline. The 4-element quad in the outline sketch has a 2:1 50-Ohm SWR bandwidth of more than 25 MHz, which eases the problems associated with construction variables. (Redesigning the antenna for fatter elements would yield a larger bandwidth.) Obviously, longer versions are possible for the quad if one desires more gain.

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The 8-crossed-element Yagi is 2.42WL long, very close to the length of the sample helix. It uses half-inch (12.7-mm) elements. As the sketch shows, the parasitic elements meet at the center, although the drivers require a small separation to effect the turnstile feed. In this particular design, the single driver source impedance is 50 Ohms. Hence, the turnstile phase-line is also 50 Ohms. The resulting impedance presented to the main feedline is close to 25 Ohms. A length of 35-Ohm line (or a pair of 70-Ohm lines in parallel) provides the required match for a 50-Ohm main feedline. As with the quad, one may change polarization simply by swapping phase-line ends for the junction with the matching section and main feedline. To center the design frequency within the overall 2:1 50-Ohm SWR passband, the line lengths for both the phase line and the matching line are not true quarter wavelengths electrically. The electrical length of the phase-line is a bit over 0.22WL, while the matching line is close to 0.215WL. The 2:1 SWR passband runs between 270 and 330 MHz, a 60-MHz spread that should make home construction less critical.

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The Yagi produces a modeled 12.58 dBi gain when the antenna reflectors are 1WL above average ground. The modeled beamwidth is 44°. Compare these values to the shorter quad values of 10.35 dBi and 58°. Anyone interested in either type of antenna can make the appropriate comparisons that weigh performance differences against construction complexity.

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The Yagi and the helix are equivalent performers in terms of gain, while the shorter quad lags in performance while leading in simplicity. Regardless of the actual gain of each antenna in the field, we have another interest in the three antennas: the pattern shape and the sidelobe production.

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The Yagi has a front-to-sidelobe ratio of about 16.6 dB. The corresponding ratio for the quad is about 14 dB. In contrast, the axial-mode helix has a front-to-sidelobe ratio of only 11.1 dB. Note the improvement of the sidelobe performance relative to the models over perfect ground. The elevated 10-turn helix shows a front-to-sidelobe ratio improvement of about 1.6 dB. Nevertheless, the helical antenna sidelobe structure bears watching. Equally important is the distribution of energy to the sides. For this purpose, I remodeled the helix (along with the quad and Yagi) in EZNEC Pro/4, since it provides pattern plots that distinguish the left-hand and right-hand circular polarization of any test antenna. Fig. 32 shows the plots for the three sample antennas.

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Both the Yagi and quad show diminutive side lobes at low angles. The total energy in these sidelobes, as measured by the area they occupy, is quite small. In contrast, the higher-angle lobes of the helix occupy a broad front on each side of the main lobe. Hence, their sensitivity to signals and noise not associated with the communications target is considerably higher than the comparable sensitivity of the parasitic arrays.

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In addition to having smaller sidelobes, both the quad and the Yagi show less reverse polarization energy as well. (Reciprocally, transmitted energy becomes receiving sensitivity.) Once past the 4-element stage, quads tend to require more boom length for a given gain, due to the increased coupling at the corners. Hence, the proper "rival" for the helix is the crossed-element Yagi, and its gain-to-boom-length ratio is virtually identical to that of the helix. If the Yagi's smaller sidelobes make a difference to communications quality, then it might make a better choice than the helix. If switching polarization is necessary, then the Yagi and the quad have an advantage over the helix, with its permanent spiral. With respect to gain, none of the models in this sample comparison squeeze the last fraction of a dB from the designs. Because the aim of this final section is only to show alternatives to the helix and their potential relative performance, I have omitted quad and Yagi dimensions.

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Conclusion

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I began this study because the available literature on axial-mode helical antennas seemed somewhat oblivious to matters other than the maximum potential gain. Pattern shape went largely ignored except in the context of a broadband antenna in the King and Wong treatment. Performance stability for the spot frequency applications that mark amateur use of these antennas also passed in relative silence. These notes have tried to focus on these aspects of helix performance by using a limited number of cases to establish some definite trends that apply to the home construction of axial-mode helices.

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The net result has been to see that for most cases, it is unwise to try to derive the maximum gain of which a helix is capable by widening its base. Unstable source-impedance conditions and serious sidelobes develop before the antenna reaches the maximum gain size. In the end, a practical axial-mode helix has only the gain of a well-designed crossed-element Yagi of a similar boom length, and the Yagi tends to have smaller sidelobes and switchable polarization.

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These results, of course, cannot contend with raw curiosity, which alone will lead many amateur antenna builders to construct helices. At most, these notes can temper enthusiasm with an appreciation of the limitations of the helix. It remains about the best high-gain broadband circularly polarized design available. However, to obtain the best from the design, one must attend to the costs and limits of the design as well as to its potentials.

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Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Helix, Satellite, VHF / UHF


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Horizontal Polling Arrays

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L. B. Cebik, W4RNL

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Rotators are slow-moving devices--advisedly so, because spinning an antenna at high speed can induce large stresses, even at VHF and UHF frequencies. The chief stresses will be due to acceleration and deceleration whenever we start or stop the system. Moreover, rotators are generally not built for continuous operation. Rather, they prove to be most durable when used sporadically to move a directional antenna toward a desired communications target.

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The rotator problem presents a challenge to the growth of PSK and related digital operations in the VHF region. Activity on the low end of 2-meters has increased, and ranges that are impossible for voice and improbable for standard CW are proving to be routine for PSK. Skip Teller, KH6TY, reports regular contacts in the 300-mile range on this mode using moderate power and relatively standard modest beam antennas. The difficulty is that the digital transmission may come and go faster than the operator can move a beam to detect, let alone decode, the signal.

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The solution may lie in using a polling array. A polling array is simply a collection of antennas angularly spaced to cover the horizon within the beamwidth of each antenna. Each antenna's feedline terminates at a central controlling position. By digital control of various sorts, the system activates one antenna at a time in a prescribed order and at a rate much faster than a rotator can move. When the system detects a signal (either of any sort or of a prescribed sort), the system locks onto it with the antenna providing the best signal strength. From this point, the user has many design options. He can leave the lock in place and release it manually after communication. Or the system may return to scanning all antennas after a time delay. The latter system works best with reception-only systems, such as on a repeater. The former system is better for 2-way communication over a single path and on the same or closely related frequencies.

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Polling arrays are in regular use in cell and similar services, where the user has two advantages. First, the antennas are small, and spacing them from a central mast by a wavelength is only a matter of inches. Second, the antennas generally use vertical polarization, and we have no element tips to interfere with each other. However, the needs at the low end of 2 meters tend to be for horizontally oriented antennas.

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Because there may be a tendency to simply transfer vertical polling-array wisdom to the use of horizontal antennas, it may be useful to examine the behavior of horizontal antennas in this kind of service. I shall leave it to others to develop the control devices for scanning a polling array. We shall have quite enough work to do seeing how horizontal antennas respond to polling activities.

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Basic Antennas and Considerations

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Every antenna design has its own properties. The key ones for VHF PSK are gain, front-to-back ratio, and beamwidth in the horizontal plane. Since we cannot possibly cover every antenna that one might use, let's consider two divergent designs. One antenna will be a Moxon rectangle, which has modest gain, an excellent front-to-back ratio, and a fairly large beamwidth. The other antenna will be a 6-element Yagi with higher gain, a very good front-to-back ratio, and a narrower beamwidth. Fig. 1 shows the outlines of the two antennas. Both antennas are designed for direct 50-Ohm feedpoint connections, and so we may set aside that operating parameter as a concern.

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For uniformity, let's place each antenna--and every following polling array that we construct with them--1 wavelength above average ground. Although this height is low for the 2-meter band--our test range--performance at the antenna will not change much if we change heights upward. We may gain a clear path between line-of-sight targets with a higher antenna position, but we would not significantly change the gain or beamwidth. At the selected 1 wavelength height, the two antennas show the following performance potentials in isolation.

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+Individual Modeled Performance Values for 2 Diverse Antenna Types in Horizontal Service
+Antenna Type        Gain dBi    Front-to-Back Ratio dB     Beamwidth degrees
+Moxon rectangle     11.32       28.16                      79.2
+6-Element Yagi      15.20       37.23                      53.0
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To scan the horizon, we would require fewer Moxons than we would 6-element Yagis. However, the Moxons offer about 4-dB less gain than the Yagis. Which parameter--the number of required antennas or the gain--takes precedence is among the earliest user decisions to make. In both cases, a 20-dB minimum front-to-back ratio ensures that few, if any, signals could create a false system lock at reduced strength

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Ideally, we may cover the horizon with 5 Moxon rectangles. We may examine an ideal situation simply by turning the Moxon in 72-degree increments and taking a new pattern along the way. Fig. 2 shows this idealized situation for the 2-element antenna.

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By using the antenna's beamwidth as a measure of angular separation, we may ideally enjoy full horizon coverage with a maximum of 3-dB fluctuation in signal strength (all other things being equal) with only 5 antennas. To achieve a similar result with the 6-element Yagi, we must use 7 antennas, as shown in Fig. 3.

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However, this initial modeling exercise has a significant limitation. It makes use in each case of a single antenna that we rotate around a common center. Hence, each pattern is identical to the adjacent pattern. Missing from the model are some crucial parts of a real polling array. A polling array will consist of several antennas arrayed round a common central support or mast. We cannot simply create a vertical stack of virtually identical antennas. Even with 1/2 wavelength spacing, the antenna will interact sharply. The centermost antennas will show feedpoint impedances seriously off the value for an isolated single antenna. To minimize interactions among antennas--or to bring them down to an acceptable level--the antenna in polling arrays normally have a certain spacing from the central mast. Hence, as shown in Fig. 4, we have at least two critical dimensions to consider when planning a polling array.

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How these two dimensions interact will become a major point of study. However, the very fact that the antennas must be spaced from the mast by a certain distance should remind the planner that a polling array has physical as well as electrical characteristics. Whatever the required distance from the mast to the array rear element, the Moxon rectangle only requires about 14-15 inches more of boom for support. In contrast, the 6-element Yagi requires about 5' of additional boom for support. The higher the gain of the antenna, the narrower the beamwidth, which means more antennas. As well, it means ever-longer booms to support each antenna.

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One reason for specifying the distance dimension as the space from the mast to the rear element is the fact that a reflector tends to act as a screen between the antenna and the mast or other antennas to the rear. However, what the reflector cannot prevent is interaction between the tips of elements in adjacent antennas in the collection. (A vertically oriented polling array is not faced with tip-to-tip coupling, but it does encounter coupling by the parallel orientation of elements in adjacent antennas within the collection.) Since our subject antennas have quite different geometries, let's see what we may learn about them one at a time.

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Some Basic Moxon Rectangle Properties in Polling Arrays

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Since our main concern involves an active antenna and the inactive antennas adjacent to it, we may simplify our initial study by creating only 3 Moxon rectangles. We shall use 72 degrees as the angular separation of the antennas, and the active antenna will be the middle of the 3. We shall proceed by stepping the distance between the mast and the rear element in 1/8 wavelength increments, since an eighth wavelength is just about 10" at 2 meters.

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If we begin with 1/4 wavelength between the mast and the rear element, we end up with the outline shown in Fig. 5. The rear corners of the arrays nearly touch. The coupling is so great that we arrive at a 3-lobe pattern rather than with a single Moxon main lobe. The gain of the main lobe is about 2-dB lower than for an isolated Moxon, and the front-to-back ratio is negligible. The beamwidth has also shrunk to an unusable level.

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If we increase the mast-to-rear-element space by 1/8 wavelength (another 10"), we obtain the pattern shown in Fig. 6.

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The increased spacing places the rear elements at a respectable distance from each other. As well, we see a return to the single-lobe forward pattern. In fact, the gain is a small amount higher than for the antenna in isolation. The front-to-back ratio, while still below the value for an isolated Moxon, is above 20 dB. The added gain comes largely as a result of the narrowing of the beamwidth for a Moxon with adjacent antennas. The beamwidth has shrunk from over 79 degrees to just over 70 degrees. The new beamwidth is below the angular separation between antennas in the system. As a consequence, the lowest gain value where patterns overlap will be an additional dB lower than for the ideal patterns shown in Fig. 2.

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The Moxon with 3/8 wavelength spacing between the mast and the rear element is usable. However, let's see if we garner any significant improvements by increasing the spacing by another eighth wavelength to 1/2 wavelength.

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As shown in Fig. 7, the additional spacing does not change the gain by much. The front-to-back ratio increases by about 3 dB. The beamwidth shows a small growth to just over 72 degrees, just above the level necessary to achieve a maximum pattern gain variation of 3 dB. Whether the increased beamwidth justifies the added 10" of required boom length is a user decision.

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These models go some distance in showing that the proximity of inactive adjacent antennas of the same design can reduce the beamwidth of the active antenna unless we use a sufficient distance between the mast and the rear element. Of course, for a fixed angular separation, every increase in mast-to-antenna spacing sets the individual antennas in the array farther apart, with a consequent reduction in coupling. In the UHF region, we can easily use much greater mast-to-antenna spacing values without incurring much mechanical stress. However, at 2 meters, we are pressing the limits of what we might achieve with common materials. Hence, looking for the minimal values that also promise to be practical values is a sensible exercise.

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Some Basic 6-Element Yagi Properties in Polling Arrays

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Before we increase the Moxon array to full size, let's explore the comparable properties that might accompany a set of 3 6-element Yagis in a polling array. Due to the narrower beamwidth, the required angular separation is 51.43 degrees. As a consequence, we obtain element overlap for considerably larger spacing values from the mast to the rear element. In addition, the Moxon elements side-to-side are only about 70% of the length of the fully extended (unbent) elements of the subject Yagi. As one consequence, we must use a bit of vertical separation between adjacent Yagis if we are to explore potential interactions with fairly short mast-to-antenna distances. Therefore, wherever necessary in this 3-antenna exercise, I have increased the height of the inactive antennas by 6" to prevent element inter-penetration within the models.

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Our first model uses 1/4 wavelength spacing between the mast and the rear element. Our experience with the Moxon at this distance suggests that we may end up with an unusable situation. Fig. 8 confirms our expectations.

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As we found in the case of the Moxon, the Yagi array yields a pattern with 3 forward lobes due to coupling between elements, even with the 6" vertical spacing. The front-to-back ratio is quite usable, but the forward gain is 3 dB below the value for the Yagi in isolation. In addition, the beamwidth is down to 32 degrees, an unacceptable value for the intended service.

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Moving the mast-to-antenna spacing up to 3/8 wavelength does not remove element overlap, as it did for the Moxon. Hence, this model also uses a 6" vertical separation. Fig. 9 shows the results of this modeling experiment.

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The main lobe has re-appeared, but the gain is still about 1 dB shy of the value in isolation. The 180-degree front-to-back ratio is a respectable 26.5 dB, but the rearward sidelobes are strong enough to fall below the desired 20-dB limit. In addition, the forward lobe is not well-shaped and shows only a 44-degree beamwidth, well under the desired 51.4-degree value. As a result of this exercise, we may view the 3/8 wavelength spacing value as still short of being acceptable.

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When we increase the spacing to 1/2 wavelength, we still encounter some element overlap. Therefore, the model shown in Fig. 10 still requires the 6" vertical spacing between adjacent Yagis.

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Under the specified conditions, the forward gain has returned to a nearly normal level. Reduced rearward side lobes accompany the outstanding 180-degree front-to-back ratio so that we obtain the desired 20-dB minimum to the rear. The small forward sidelobes are of no great import to polling performance. However, the beamwidth is still under 50 degrees. At best, this step in the progression of increasing mast-to-antenna distances is marginal.

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By taking the next step, we will increase the mast-to-antenna space beyond the amount required by the Moxon rectangle. Fig. 11 shows what happens when we use 5/8 wavelength (50") as the spacing value.

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The elements now are clear of each other and do not require vertical separation. The pattern has a more normal look, with good gain and only some insignificant side lobes to distort the overall appearance. The front-to-back value has returned to nearly the value for the isolated Yagi with rearward sidelobes well below 20-dB down from the main forward lobe. The beamwidth has increased to 50.8 degrees, a growth of 1 degree. Since we are close to the desired mark (51.43 degrees), perhaps we should take another step in increasing the mast-to-antenna spacing.

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The next step places the rear element of the antenna 3/4 wavelength from the mast (60"). Hence, the total boom length is about 120" (10') to include both the antenna and the spacing. Fig. 12 shows what emerges.

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In fact, we gain almost nothing for our efforts. The gain and front-to-back ratio have leveled off. The side lobes have shrunk a bit, but in this service, they are not a concern. Perhaps the most disappointing fact is that the beamwidth has grown only 0.2 degrees, still shy of the desired value.

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Let's make one more step and see if the beamwidth comes up to expected values. By increasing the mast-to-rear-element spacing to 7/8 wavelength (70"), we obtain the results shown in Fig. 13.

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Once more, hope gives way to disappointment. The patterns grow a bit cleaner, but the beamwidth remain at 51 degrees. For polling service, the 3-antenna exercise suggests that distances between the mast and the antenna of 5/8 wavelength to 7/8 wavelength are just about equivalent. When we consider that every increase in spacing increase the stress on the boom with the antenna on its outer half, a tradeoff may be acceptable. We would find an increased variation in signal strength created by the failure to achieve the full desired beamwidth.

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This part of the exercise has demonstrated that adjacent antennas in a polling array narrow the beamwidth of the active antenna relative to its value in isolation. That fact is important to consider when designing an array for this service. Even with a considerable separation between the central mast and the rear of each antenna, the beamwidth values do not reach their isolated values.

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However, we have two deficiencies to overcome in this exploration. First, we have not examined what happens when we provide a full set of antennas in the array. Second, we have not yet determined the actual number of antennas that we need for either the Moxon or the Yagi array. These two tasks will become the final steps in our journey through horizontally oriented polling arrays.

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The Full Circle

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The 3-antenna models acquaint us with some basic properties of antennas used in polling arrays, but they do not establish what happens when we have a complete circle of antennas. Rather than try to replicate every variation in the progression that we have just examined, I shall select one variation from each of the two antenna types and work through the complete array models. Since the antenna designs are only examples and unlikely to be the actual antennas that someone uses, the principles of the task outweigh a voluminous data collection.

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Perhaps the first matter to strike us from a practical or building perspective is the fact that both idealized arrays called for odd numbers of antennas in the array. For most builders, an even number of antennas simplifies construction, since each boom may extend in opposite directions through (or past) the boom and carry two antennas. For example, compare the 5- and 6-antenna arrays shown for Moxon rectangles in Fig. 14. The array uses 1/2 wavelength spacing between the mast and the rear element of each antenna.

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The angular separation differs between the two array, of course. From 72 degrees, the 6-antenna version drops to 60 degrees. Although we find a slight drop in forward gain--too small by be significant--we also find that the beamwidth has increased marginally by nearly 1 degree. Rather than falling under the desired value, in the 6-antenna array, the beamwidth is actually nearly 12 degrees wider than the minimum required value.

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The increase in beamwidth combined with the higher number of antennas in the array does reduce gain variation between maximum and minimum values. However, the improvement may not be as great as one might expect. Fig. 15 shows the overlapping patterns of the circle of antennas, not as an idealized rendering of the type in Fig. 2, but as a model of the full set of antennas activated sequentially.

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Because the forward lobes are nearly circular, the gain must decrease toward the positions where patterns overlap. The decrease is only 2 dB. If we combine the decrease in gain variation with the probable improvement in construction ease for the assembly, then the enhancements very likely justify building the 6th rectangle for the collection.

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The 6-element Yagi presents us with a different sort of situation. 7 antennas may be more difficult to mechanically stabilize than an array of 8. The angular separation would drop from 51.43 degrees to 45 degrees, allowing the use of 4 booms for the entire set. Since each Yagi is nearly 5' long, I selected the minimally adequate distance from the mast for the model: 5/8 wavelength. With the 3-antenna models we found very little difference in performance as we moved from a 5/8 wavelength distance to a 7/8 wavelength distance. Hence, 5/8 wavelength seems natural at first sight. The outline and pattern on the left in Fig. 16 for the 7-antenna array shows very little practical performance difference relative to the 3-antenna model.

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However, if we reduce the angular separation to 45 degrees and still retain the 5/8 wavelength (50") spacing between the mast and the rear element, then we obtain the outline and pattern on the right in Fig. 16. Note that shrinking the angular separation pulls the elements tips closer together. As a consequence, the interactions increase. The performance figures for each antenna in the 8-antenna array--on the far right--show decreases in gain and front-to-back ratio relative to the individual antennas in the 7-antenna array. As well, we see an increase in the side-lobe structure, although the side lobes are not strong enough to be troublesome in this type of service. Equally, we see a bit of squaring in the forward lobe pattern, despite an increase in the beamwidth.

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As a consequence of the pattern squaring, we find only a half-dB reduction in gain variation between maximum and minimum gain values, despite the fact that we have decreased the angular separation to 45 degrees. Fig. 17 shows the differences in the full-circle 7-antenna and 8-antenna patterns for the 6-element Yagi. In order to smooth the forward pattern and to reduce the gain variation further, we would require additional distance between the mast and the rear elements in the 8-antenna array. It is likely that a distance between 7/8 wavelength and 1 wavelength would be necessary. Again, since the actual antennas planned for such an array should be the subjects of analytical modeling exercises, I have brought the present set of models to a close. These notes have not tried to present a pair of arrays calling for replication. Rather, they have striven to show the principles involved and some antenna behaviors for which the modeler should be alert.

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Conclusion

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These notes have shown how antenna behavior may change between a single antenna in isolation and that same antenna as part of a polling array designed to cover the entire horizon. They have focused on horizontally oriented antennas, specifically, 2-meter beams design for such applications as PSK and other digital modes. The two beams chosen for the study offer contrasts in gain and beamwidth--not to mention antenna size. The Moxon rectangle is an example of a compact 2-element antenna with a small front-to-rear dimension as well as a side-to-side dimension that is only about 70% of the length of a linear 2-meter element. The 6-element Yagi offers significantly more gain, but with a wider side-to-side dimension and a much longer boom requirement.

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Planning for a polling array of horizontal antennas requires an initial decision of the gain required by the anticipated communication paths. Higher gain automatically increases boomlength and equally automatically decreases beamwidth. Hence, the higher the gain that we select, the more antennas that our array must have for full horizon coverage with a user-selected limit to the gain variation around the horizon.

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We have also seen that placing the antenna in an outward-pointing circle tends to reduce the beamwidth relative to the value shown by the same antenna in isolated use. Moreover, arrays calling for odd number of antennas to cover the horizon may prove more difficulty to construct (for stability and durability) than arrays with an even number of antennas. Increasing the number of antennas to an even number decreases the angular separation between antennas.

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For some antennas--including virtually all Yagis with linear elements--increasing the number of antennas within the total array may require an increase in the distance between the mast and the rear element in order to avoid excessive interaction between the active unit and the adjacent inert units. The Moxon array of 6 antennas proved satisfactory within its gain class with a distance of 1/2 wavelength. In contrast, the longer-boom, longer-element Yagis required perhaps 3/4 wavelength as the spacing that might yield well-behaved patterns in an array of 8.

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Each builder will have a set of physical limits to the structure that he or she constructs with confidence. The structure must also match up with the desired gain level, as well as the allowable amount of gain variation. These notes cannot make such decisions for the builder, but only show how to gather some of the data necessary to make them.

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In addition, each polling-array builder must have access to the appropriate sequencing, controlling, and locking circutry necessary to make the system effective. As in almost all of the history of radio communications, it is likely that the control circuitry will become commonplace long before most folks who desire a polling array become familiar with the antenna constraints involved. These notes are an effort to fill--if only partially--a few of the gaps on the antenna side of the issues involved.

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Updated 07-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Jun, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Moxon, VHF / UHF, Yagi


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The Half-Square on 2 Meters

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Part 1: A Bi-Directional Vertical Antenna

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L. B. Cebik, W4RNL

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If you need a vertically polarized bi-directional 2-meter antenna with deep side nulls for direction finding or nulling out adjacent channel interference, try the half-square.

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The half-square (see Figure 1) offers a vertically polarized pattern with the figure-8 pattern usually found only with horizontally polarized antennas. Although the gain of a half-square in the desired direction (broadside to the array) over a vertical dipole is about 2.5 dB, the gain is less important than the front-to-side ratio (edgewise to the array), which offers a minimum of three S-units of rejection even for sloppy construction. The half-square also offers a direct match for 50-ohm coax. This property simplifies construction and minimizes the number of connections to gradually go bad in the weather.

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The horizontal wire of the half-square is a phase line in which two things occur. First, the current and its phase at the far end of the line allow the fields from the two vertical elements to produce a strong signal broadside to the assembly, with deep nulls in the plane of the array. Second, the fields from the horizontal wire largely cancel themselves, leaving the antenna strongly vertically polarized.

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Positioning the horizontal wire above or below the half-square vertical wires makes no difference to antenna operation either in free space or several wavelengths above ground. At HF, builders usually find it more convenient to suspend the vertical wires below the horizontal wire. A VHF, self-supporting vertical elements suggest placing the horizontal wire on the bottom so that the feedline is removed as far as possible from the antenna fields.

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In general, the most critical dimension is the length of the horizontal wire. For most construction methods, it is best to set this length and then trim the verticals for resonance. The result will be an antenna with close to a 50-ohm feedpoint impedance.

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My test antenna used a highly flexible construction method: supporting #12 copper wire (stripped house wiring) with a light, adaptable PVC frame. Figure 1 shows the main features of the structure. The antenna proper consists of two pieces of wire: a 61.5" piece for the horizontal leg and the far vertical leg and a 21.5" piece for the directly fed vertical leg. (For actual construction, it is best to begin with slightly long wires.) There are only two connections, one to each side of the coax feedline.

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The basic PVC structure uses lengths of 1/2" nominal SDR-13.5 light duty PVC for most parts. This lighter PVC uses the same Tee connectors and glue as the sturdier Schedule 40 material, which is used wherever strength is needed. Each short leg of PVC from the Tees has a 1/8" hole to pass the #12 wire. The holes pass the wire freely, since the function of the legs is only to position the wire and resist wind-bending. The main vertical support on the right uses Schedule 40 that transitions with couplers up to 1 1/4" nominal schedule 40 PVC, which slips over a standard 1-1/4" diameter steel mast.

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The test antenna is a top-mount assembly. The offset mount allows the coax weight to counter-balance the longer run to the other vertical side of the antenna. The feedpoint connection is simple, consisting of a 1" by 2" scrap of 1/8" Plexiglas with two holes to pass short bends at the ends of the antenna wires. The coax center conductor and braid are soldered to these wire ends. A half grommet is placed over the coax and the grommet-coax combination clamped in place with a cable tie. The connections are well coated with coax sealant.

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Before soldering the connections, I passed the coax through a 1/4" hole drilled in the short section of PVC extending to the right of the main PVC mast. I cut open a 1/4" inside diameter grommet and used contact cement to lock it to the coax above the hole. The fixed grommet protects the antenna connections from downward forces.

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Two points on the diagram are marked as Mod. A and Mod. B. Modification point A is for side mounting the antenna to a tower. A builder could replace the short right thin-walled PVC with a longer length of Schedule 40 material. Modification point B is for mounting the antenna broadside to a tower. A builder may choose to cut the horizontal PVC at the center and insert a Tee with the opening facing the tower. A length of Schedule 40 PVC would again provide the strength for supporting the antenna from the tower legs.

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The test antenna performs as modeled. Tuning consisted trimming the two vertical elements for minimum SWR on 146 MHz. Excursions across 2-meters show well below a 2:1 SWR at heights from 5' upward. The side nulls are sharp enough to make the antenna useful for direction-finding exercises. Adjacent channel repeater interference from the antenna sides is easily eliminated by careful antenna aiming. See Figure 2

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Models suggest that the antenna is relatively unaffected if side mounted to a tower, that is, with the tower in a plane with the elements. Hence, for a true bi-directional pattern, the edge-wise mounting scheme of Mod. A is recommended. Models also suggest that a non-resonant mast or tower can distort the pattern of the antenna if mounted broadside, as suggested in Mod. B. A distance of 16-18" from the mast raises the gain away from the mast by about 1 dB and yields a front-to-back ratio of about 6 dB.

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The half-square is simple, effective, easy, and cheap, a pretty good ham combination.

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However, we have not exhausted the possibilities with the half square: we can make from it 2 and 2 element parasitic beams, also predominantly vertically polarized, but without the very wide beam width of a Yagi turned vertical.

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Updated 12-12-96, 5-15-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. This item first appeared in Rack Panels, December, 1996. A more extended technical discussion of the antenna appears in Communications Quarterly (Spring, 1999) 65-70.

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Go to Part 2: Half Square Beams

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Return to Main Index

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Topics: Half Square, VHF / UHF


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The Half-Square on 2 Meters

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Part 2: Half Square Parasitic Beams

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L. B. Cebik, W4RNL

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The half square, like any other linear-element antenna, can be set up in a parasitic arrangement to create a uni-directional array with gain and significant front-to-back ratio. In short, we have a 2-meter half square beam.

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Between the time I made my original test 2-meter half square and the time I tried out the beams, I change construction to something more permanent. The horizontal member increased to 3/4" diameter. I have used both aluminum U-channel and tubing, and tubing has less tendency to twist. The vertical elements are 1/8" diameter rod. I have used both brass and aluminum, and recommend aluminum for long-term installations.

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Figure 1 shows the dimensions of the tube-and-rod half square. Construction details will appear in the Communications Quarterly article.

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Figure 2 is an azimuth pattern of the antenna at 30' above ground at an elevation angle of 3 degrees. The vertical and horizontal components of the total pattern are clearly visible, and the revised half square performs as well as its predecessor--but handles wind with less tendency to reshape itself.

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I have noted in the past that parasitic versions of the half square are possible. The number of requests for at least a few details is large enough that I am adding this note to the collection.

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A 2-element half square appears in Figure 3. The arrangement is a typical driver-reflector array, with the spacing chosen to achieve a 50-Ohm feedpoint impedance. Note that the horizontal elements are identical in length, with only the vertical elements adjusted to achieve the pattern and feedpoint impedance. Actually, the spacing is not too critical: 12-13 inches shows no change in the SWR curve.

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Figure 4 shows what we get for our efforts in adding a second element. The forward gain for this plot (taken under the same conditions as the plot for the basic half square) is about 13 dBi, 3.6 dB better than the single half square. The 180-degree front-to-back ratio is over 18 dB. The slight offsets in the pattern result from feeding one corner. The feedpoint impedance report from NEC-4 is 49.4 - 1.4 Ohms, which the limits of my measuring equipment confirms. The beam covers virtually all of 2-meters.

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If we can have 2 elements, why not 3?

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Figure 5 shows a 3-element version of the antenna, along with dimensions. Once more, the horizontals remain at 40" while the verticals change length according to their function. The element spacing also grows larger in the search for a balance between performance and feedpoint impedance.

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The azimuth pattern in Figure 6 (same modeling conditions) shows the added gain (1.4 dB) and the improved front-to-back ratio (22.6 dB). The feedpoint impedance is about 43 Ohms at resonance, and the operating bandwidth is a bit narrower than the 2-element antenna.

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Also notable is the gradual narrowing of the beamwidth of the antenna. A Yagi set vertically will have a very wide beamwidth, defeating some of the directionality we desire from a beam. The half square beams have beamwidths comparable to a Yagi set horizontally, but the half-squares are mostly vertically polarized. This is the chief reason for building a parasitic half square: to achieve relatively high directionalness while being vertically polarized.

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Whether the 3-element version is a justified endeavor depends upon a judgment that balances the added gain and front-to-back ratio against the added mechanical complexity. Six vertical rods makes a bristly array. I use lots of 1/2" Schedule 40 PVC, with the horizontals passing through Tee joints and pinned in place. Again, details will appear in Communications Quarterly. This note is only to whet your creative whistle and not to provide detail construction details.

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Stacking the 2-element Half-Square Array

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A second way to add gain to the system is to stack arrays. Our original 2-element half square array provided about 13 dBi gain when at a height of 360" (30') What happens when we stack a pair in the manner shown in Fig. 7.

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The sketch shows a recommended separation of 90", that is with the second array placed at a height of 450" (using the horizontal part of the array as a reference). Actually, this separation distance does not yield the highest gain. That comes with a separation of about 70" and reaches 16.4 dBi. However, the front-to-back ratio is only 14.0 dB. If we increase the separation to 90", we drop to about 16.2 dBi gain, but improve the front-to-back ratio to 19.6 dB. As well, the feedpoint impedance for each array shows a value closer to the impedance of an independent array: about 56 -j3 Ohms. These values should permit stacking with standard coax-cable methods.

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Fig. 8 shows the azimuth and elevation patterns for the stack. Other separations are possible, but the recommended 90" separation (about 1.1 wl) yields a good pattern with the shape of the original pattern for one array and 3 dB of added gain. We can apply the same technique to similar arrays, such as the one in the next episode.

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If you are feeling really creative, consider this fact: a half square can be doubled to make a bobtail curtain with added gain. Will it also work at VHF?

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Updated 4-12-99, 7-18-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. A more extended technical discussion of the antenna has appeared in Communications Quarterly.

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Go to Part 3: Bobtail Curtain Beams

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Return to Part 1: The Basic Half Square

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Return to Main Index

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Topics: Half Square, VHF / UHF


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The Half-Square on 2 Meters

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Part 3: Bobtail Curtain Parasitic Beams

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L. B. Cebik, W4RNL

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A bobtail curtain is two half squares with a common element. The common element is the center element of the array, and a convenient feedpoint is its junction with the long horizontal member. Essentially, the bobtail curtain is 3 phased vertical 1/2 wl apart, where the horizontal line forms the phasing line. As with the VHF half square, this is an antenna to consider if the need is for directional performance with vertically polarized signals.

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Figure 1 shows a 2-meter bobtail curtain composed of 3/4" horizontal aluminum stick and 1/8" diameter vertical rods. I thread the rods and add nuts above and below the horizontal tube. I support the tube with a PVC assembly, but the only contact is with two Tee joints that pass over the horizontal tubing. This allows a center break, bridged by 1" L stock that holds the coax connector and supports the center rod.

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For a very narrow beamwidth (Figure 2) in a bi-directional vertically polarized array, the bobtail curtain is hard to beat. compare it pattern to that of the half square in the preceding section of these notes. The narrowing of the beamwidth yields added gain, about 0.75 dB more than the single half square. although the side insets are not quite so deep as those of the half square, the narrow beam width compensates. This antenna is quite good as a fixed vertical for repeater reception in areas that are troubled by interfering repeaters from the side. The gain is about 3 dB greater than a vertical dipole at the same height, and offending repeaters to the side can be as much as 25 dB below those toward which the antenna is aimed. The basic single bobtail has a feedpoint impedance of about 39 Ohms, and more exact matching to a 50-Ohm cable will be largely optional.

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If one bobtail is good, will 2 be better?

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Figure 3 sketches the main elements of a 2 element bobtail curtain in a driver-reflector array. This parasitic extension of the half square beams requires only a foot of spacing, making the task of bracing the two horizontals fairly simple. The horizontals have the same length, while the verticals have different heights according to function. All 3 driver verticals are the same lengths as are all 3 reflector verticals. Feed arrangements for the driver are identical to those for the single bobtail.

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As shown in Figure 4, the bobtail beam provides a very interesting azimuth pattern (and all such patterns use the same 30 height, 3-degree elevation angle). The gain is about a half way between the gains of the 2- and 3- element half squares, and the front-to-back ratio exceeds 18 dB in a clean pattern. Feeding the center element gives the bobtail beam a symmetrical pattern. The feedpoint impedance is 51 Ohms according to both the model and prototype tests.

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If one has a need for narrower beamwidth and the half square beams provide, then the bobtail beam may be a reasonable candidate among vertically polarized directional antennas. Like the 3-element half square, the antenna has 6 bristles to its hairdo, and this has led me to stop developments at this level. Actually, models of 3-element bobtails have not yielded good working feedpoint impedances to this date. However, some added gain and front-to-back ratio is feasible.

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Whether the half square or bobtail beam are the right antennas to build depends on many variables of operating mode and conditions. They do present some overlooked possibilities--and even some further possibilities beyond these notes. In a year or two, it may be interesting to compare notes on the innovative methods of construction that might be used in building these parasitic vertical arrays.

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Updated 4-12-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author. A more extended technical discussion of the antenna has appeared in Communications Quarterly.

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Return to Part 2: Half Square Parasitic Beams

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Return to Main Index

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Topics: Bobtail Curtain, Half Square, VHF / UHF


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Some J-Poles That I Have Known

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Part 1: Why I Finally Got Interested in J-Poles and Some Cautions in Modeling Them

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L. B. Cebik, W4RNL

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Although used on many bands from 20 meters on up, the most wide-spread use of the J-pole antenna is on 2 meters. It covers the entire band with under 2:1 SWR, provides a nearly circular azimuth pattern, requires no radials, and matches a 50-Ohm feedline with fair ease. The nearly 3/4 wavelength height of the antenna is not a significant problem for most installations. Versions of the antenna have used everything from TV twinlead to copper water pipe a materials, all with roughly equal success.

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Despite the success of the antenna, disputation about the antenna persists. This disputation has largely put me off the J-pole as an object of study, since much--but certainly not all--of it has lent more smoke than fire to the understanding of J-poles. As well, almost everyone has his or her own favorite version of the J-pole. There are as many versions of the J-pole antenna as there are versions of the letter J in the collection of type fonts supplied with modern computers. Some variations are subtle, others are bold. How much differences each variation makes in actual performance seems to depend upon who has built the antenna.

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Some J-Pole Background

By tradition, we tend to picture the J-pole in the manner of Fig. 1. +
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The classic J-pole has three parts of note: the radiator, the matching section, and the feedpoint.

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1. The radiator is a simple vertical 1/2 wavelength element, with the physical length adjusted for the diameter of the material used. The fatter the material, the shorter the physical length of an electrical half wavelength. As well, insulation will also create a velocity factor that shortens the physical length of an electrical half wavelength.

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Ideally--with a lossless infinitesimally thin wire half wavelength radiator, the impedance at the ends will go to a theoretically indefinitely high value. In practice, with wires of significant diameter, the impedance will be high, but not indefinitely high. The actual impedance will vary with the wire thickness. If the wire end joins another wire end, then the impedance is likely to be still lower, while remaining in the high category.

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2. The matching section of a J-pole consists of a parallel transmission line section about 1/4 wavelength long. A quarter wavelength section has the property of transforming an impedance presented at one end to another impedance at the other end in accord with the simple equation

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such that the characteristic impedance of the line forms the geometric mean between the high and low impedance values. The characteristic impedance, Zo, of the line depends on an equally familiar textbook equation:

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where S is the center-to-center spacing of the parallel conductors and d is the diameter of the conductors--assuming that both conductors have the same diameter. Missing from the equation is the dielectric constant of the material surrounding and between the conductors, since the value is 1.0 for a vacuum or dry air. Hence, vinyl-covered lines such as TV twinlead may have a different Zo than an air-spaced line using the same wire size and spacing.

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We tend to modify this relationship among impedances at the ends of the matching section for practical antenna reasons. By shorting out the bottom of the matching section, we send the impedance at the center of the short to zero--in theory. We also obtain an antenna that is physically connected at all points relative to discharging any static charge build-up. Finally, for J-poles constructed from tubing, we may add an extension below the J-pole proper that forms a handy mounting post.

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The matching section has certain limitations as a true transmission line. The upper ends of the section see quite different impedances, one merely high, the other exceptionally high, although not indefinitely high due to the thickness of the wire used in the open-end leg. Therefore, while it is possible to obtain a generally good transmission line--one in which the currents magnitudes at any point are close to equal and the current phases are close to 180 degrees apart--a perfect balance is not feasible for standard J-pole design.

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3. Since the impedance at the low end of the matching section is very low, matching a 50-Ohm line requires that we place taps across the matching section at some small distance up the line. Because currents are not perfectly equal in magnitude and perfectly out-of-phase, a theoretical J-pole may not show a 50 Ohm impedance that is perfectly resistive. However, by tap adjustment, we can arrive at an acceptable impedance, as determined by the ubiquitous SWR meter. For a more perfect match, we may alternately adjust the total radiator length and the matching section length until the impedance is virtually a purely resistive 50 Ohms at the design frequency. Normally, this procedure is easier to perform with wire versions of the J-pole than with version made from 3/4" hard copper pipe.

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Because the current at the feedpoint is not perfectly balanced, builders run the danger of encountering significant common-mode currents on the transmission line. Therefore, for any version of a J-pole, a 1:1 choke balun of any acceptable design is a necessary precaution. Placed at the feedpoint, such devices tend to do a very good job of suppressing common-mode currents and preventing the feedline from playing a significant role in the radiation pattern of the antenna or in transferring disruptive RF currents to the transmitting equipment.

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Theoretically, it should make no difference to which side of the matching section legs one connects the coaxial cable center conductor. However, because currents are not balanced perfectly, it may in some cases make a difference. Most builders of J-poles tend to try the connection both ways, opting for whichever they discover or believe to provide superior performance.

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As we move from theory to practice, then, the J-pole is an imperfect antenna that happens to do a very good job as a practical antenna. It has served well for many decades as an omni-directional vertical antenna that most users can build from materials available in the home shop or garage--or from materials available at the local hardware depot. Because the antenna has been so successful, a myriad of builders have developed their own magic formulas for calculating the parts of the J-pole. Some of these systems work very reliably, especially if we restrict ourselves to material sizes and leg spacings from which the formulas derive.

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Why I Became Interested in J-Poles

With respect to building J-poles, I had nothing to add to the many schemes by which builders might successfully construct a J-pole. Hence, I took little interest in the antenna. However, when I was asked to design a J-pole for 10 meters by a ham with very limited yard space, my interest began to increase. The design that emerged was shorter overall than the standard J-pole. As well, the matching section was longer than standard. Finally, the feedpoint was not a small distance above the bottom, but instead was directly at the bottom of the J-pole. +

Since 2-meters is the most natural home of the J-pole, it would be unfair to throw in 10-meter dimensions and expect one to understand how standard and non-standard J-poles differ. So I have rescaled the 10-meter design to 2 meters--146 MHz to be exact--in order to make some preliminary comparisons with a standard design J-pole.

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Consider the standard design first. The material is 3/8" aluminum, although at material diameters above about 1/8", the performance differences of aluminum and copper at 2 meters are truly insignificant. The overall length of the antenna is 57.87" or .72 wavelength. The free radiator section is 38.37" long, about .475 wavelength. This length is about normal for a dipole of this diameter. The matching section is 19.5" long, about .24 wavelength. This gives us a velocity factor of about 0.96, which again seems quite normal for air lines with a small loss factor. The center-to-center spacing is 1.2", which yields a Zo between 220 and 225 Ohms. The matching section is shorted at the bottom, with the feedpoint tapped 1.4" above the bottom.

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The scaled 146-MHz non-standard J-pole has a total length of 46.46" or .58 wavelength. The material is 0.195" diameter aluminum. The free-radiator (above the matching section) is 23.82" or .29 wavelength. The matching section itself is 22.64" or .28 wavelength. The matching-section legs are 0.976" center-to-center, for a calculated Zo of about 275 Ohms. The feedpoint is centered in the bottom wire connecting the two matching-section legs.

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Fig. 2 shows perhaps the most striking difference between the two antennas. The standard J-pole on the left shows its current minimum in close proximity to the top of the matching section. Here we can clearly see that while the current at the open end of the matching section goes to zero--or thereabouts--the current on the radiator end connected to the matching section remains well above zero. Hence, there is a small but determinate difference in the current magnitudes and phase angles, relative to a perfect transmission line. The circle near the antenna bottom represents the feedpoint, and the two lines above that circle are the current magnitudes at the bottom short and at the feedpoint line. All-in-all, the standard J-pole reflects our understanding of J-pole performance as outlined above.

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On the right, we have the current distribution of the non-standard J-pole. The lower current minimum for the radiator occurs well below the top of the matching section. The current at the feedpoint, as shown by the line above the feedpoint circle, is rising in magnitude and peaks partway up the open-end matching-section leg. The length of the open-end leg of the matching line from the current peak to the upper end is almost a perfect .25 wavelength. However, the length of the radiator, counting from the upper end current minimum to the lower current minimum, is about .39 wavelength. Counting from the current minimum on the radiator side, the total length of the matching section wires is about .47 wavelength.

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Adjusting the feedpoint impedance of the design involves a juggling of the matching-section and the radiator lengths. If we hold the matching-section open end length constant and change only the length of the radiator upward, then the feedpoint resistance decreases while the feedpoint reactance increases. If we hold the total antenna length constant and increase only the length of the matching-section open-end leg, then both resistance and reactance increase at the feedpoint. The common reactance response to length increases together with the opposing resistance response to length increases permits one to find a purely resistive 50 Ohms for the feedpoint. However, since the currents on either side of the feedpoint are not balanced, a choke balun is mandatory to suppress unwanted currents on the feedline.

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In short, the non-standard design has intercepted the 50-Ohm feedpoint along a complex combination of radiator and matching line. The overlap of the open-end leg of the matching line with the radiator does not adversely affect performance, because the overlap occurs within the low-current region of the radiator. Fig. 3 shows the azimuth patterns for the two antennas. They both show almost identical amounts of pattern displacement toward the open-end leg of the matching section, although the overall pattern distortion from a perfect circle is far too small ever to be noticed operationally. I point out the difference because the standard J-pole design uses a slight wider spacing between the matching-section legs. It appears to be a general property of J-poles that the greater the spacing between matching-section legs, the greater the pattern distortion--or the greater the "front-to-back" ratio.

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Both the standard and non-standard J-pole designs are capable of providing perfectly acceptable 50-Ohm SWR curves. Fig. 4 overlays the curves for both designs. Had I juggled the standard design just a bit more, its curve would have been virtually indistinguishable from the curve for the non-standard design. Both antennas will easily cover 2 meters with very acceptable performance relative to antenna in the J-pole and vertical dipole class.

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The free-space gain of both these antenna is in the vicinity of 2.5 dBi, just above the vertical dipole level. 2.5 dBi represents the maximum gain, and the gain on the opposite side of the pattern is .5 dB lower. At right angles to this axis, the gain is closer to the overall average: about 2.3 dBi. The slight increase over a dipole's gain (about 2.15 dBi) represents the small contribution to the pattern made by the current imbalance on the matching section. Indeed, the current imbalance tends to add more to pattern distortion than to overall antenna gain.

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I have lumped together the gain values of the two J-pole designs for 146 MHz. However, if you model them, even in NEC-4, you might find a seeming difference as much as a half dB. That leads us to some notes on modeling J-poles.

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Cautions in Modeling J-Poles

Modeling a J-pole antenna seems on the surface to be a straightforward task. However, casual modeling can lead to inaccurate models. So a few notes for modelers may be in order before proceeding any further in this small project. +
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Fig. 5 shows some of the areas where we need to think through our modeling efforts. Let's go through them, one at a time.

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1. The source wire: the source wire connects the two legs and should run from a wire junction to a wire junction. This forces each leg of the matching section to be split into at least 2 wires, one above and one below the source wire. The source wire itself should have at least 3 segments initially. (After checking all parts of the model, you might reduce it to a single segment for closely spaced legs, but confirm that this modeling move makes no significant change in the source impedance relative to a more heavily segmented source wire.

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For closely-spaced matching-section legs, the length of the source wire segments may set the standard segment length used throughout the model.

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2. The distance between the source wire and the bottom shorting wire along the matching-section legs: depending on the antenna design, this distance may be either shorter or longer than the space between the legs. 1-segment wires are usable, but in coordination with the length of the segments in the source wire. Since these wires form right angles, it is good practice to have segments in these wires be as equal in length as circumstance permits.

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3. The wire radius/diameter: the ratio of the length of the segments to the diameter of the wire in all wires should be at least 2:1. In some fat-wire/close-spaced J-pole designs, it may be difficult to achieve this ratio. If the design permits, then the ratio should be higher than 2:1. 4:1 is not too high for the angularity of parts of the J-pole structure.

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4. Feed and shorting portions of the model: the wires forming the matching-section legs and the shorting and source wires for the design should be of the same diameter. NEC (-2 or -4) has difficulties with angular junctions of dissimilar diameter wires. Moreover, the segment lengths should be long enough so that the angularly intersecting wire does not penetrate more than about 25-30% into the end of the wire to which it connects.

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5. Tapered-diameter radiators: although tapered diameter elements are common in practical dipoles, they will yield inaccurate models on NEC-2. Because the J-pole structure falls outside the limitations imposed on the Leeson correction facility of programs like EZNEC and NEC-Win Plus, that maneuver is blocked from the modeler. For most purposes, using the diameter of the matching-section legs for the entire structure is the best course to follow, with the knowledge that the radiator section length will require field adjustment if it uses an element diameter tapering schedule.

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NEC-4 can model stepped-diameter elements with quite good accuracy, so long as the steps are relatively small.

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6. The Average Gain Test: subject all models to the average gain test--a facility available on both EZNEC 3.0 and NEC-Win Plus. The average gain test (AGT) provides a figure of merit for the model as well as a gain adjustment for the reported output value. A basic AGT result might be .995 or 1.012. you can translate those numbers into dB by taking 10 times the log of the AGT value. This would give values of -.02 dB and +.05 dB for the two same AGT values. These new values tell you by how much to increase or decrease the reported gain of the model to arrive at a reasonably accurate figure. AGT values greater than 1 indicate that the reported gain is too high and must be decreased by the AGT adjustment. AGT values less than one indicate that the reported gain is too and must be adjusted upward by the amount of the AGT in dB.

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If the AGT value is less than about .85 or more than 1.15, then even the adjusted values may be suspect. The situation may call for refinements of the model before proceeding further.

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Consider the standard and non-standard designs that we compared earlier. NEC-4 reported the maximum gain of the standard model as 2.99 dBi in free space. However, the model showed and AGT value of 1.131 or 0.53 dB. If we reduce the gain as indicated by the test, the truer maximum gain of the standard model is about 2.46 dBi. In contrast, the non-standard model reported a maximum gain of 2.56 dBi in free space. The AGT value was 0.999, for a 0-dB adjustment. Hence, despite initial appearances of a half-dB advantage for the standard version, the adjusted values show the two design to promise virtually identical performance.

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7. Reading J-pole gain from models: because we expect a J-pole to behave like a vertical dipole with a circular pattern, do not mistake the maximum gain for the gain in every direction. You can estimate the average gain around the near circle in two ways. First, you can check the gain in the opposite direction from the bearing of maximum gain and average the two. Second, you can check the gain at headings 90 degrees off the maximum gain heading. The two values should be very close. If you prefer to be even fussier, you can take the average of all four gain readings. Rarely will a J-pole that does not involve collinear radiator sections show more than about 2.3-2.4 dBi average gain. These values, of course, are derived from the adjusted values emerging from the AGT test.

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With these cautions, you can construct very usable models of J-poles. In fact, in my next effort, I shall be working with some close-spaced, thin wire models, looking for any distinguishing features among the many varieties of twinlead J-poles. Initially, I shall be using bare wire, and the models will not correspond closely to the real ones with their vinyl insulation. That will give us a chance to try out the insulated wire facility of NEC-4 and see what difference insulation can make on J-pole performance and design.

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That is ultimately the trouble with J-poles. Once you start working with the design, it adheres to you and will not let go.

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Updated 1-1-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: J-Pole, VHF / UHF, Vertical


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Some J-Poles That I Have Known

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Part 2: The Varieties of Twinlead J-Poles and Some Performance Standards

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L. B. Cebik, W4RNL

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One of the fascinating aspects of J-pole design is the number of slightly different designs that builders have constructed from common 300-Ohm parallel feedline, the most common form of which is TV twinlead. The question that occurred to me is whether there are any significant or at least detectable differences among these design variants. Modeling might shed some light on the question.

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However, modeling is restricted to "proof-of-principle" models. Parallel feedline comes in a variety of physical forms, as illustrated incompletely in Fig. 1.

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The open wire feedline with periodic spacers generally presents no problems for antenna modeling. The wire is bare, and the spacers are usually widely enough spaced that a simple bare-wire model comes very close to a precise model of the physical antenna.

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The vinyl-covers twinleads are another matter. NEC-4 has the ability to handle insulated wires, each wire having a larger radius than the conductor within. We may assign reasonable values to the permittivity and conductivity of the insulating sheath.

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However, these insulations do not account for either of the two varieties of twinlead shown in the figure. Flat 300-Ohm TV twinlead has a continuous vinyl strip between insulated wires. The location is within the most intense portion of the field between wires when used as a transmission line. At present, there are no clear guidelines on how to estimate the thickness of the circular cross-section sheath in the model to approximate the effects of the strip. In contrast, the tubular twinlead version has an air pocket between wires to raise the velocity factor of the line. Nonetheless, the connecting vinyl still occurs where the field between wires is strong.

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Therefore, models of twinlead must begin with bare-wire versions, with the caution that the dimensions that emerge may not be close to the dimensions demanded by vinyl-covered twinlead.

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A second modeling caution involves the very close spacing of twinlead wires--usually AWG #20 wire (0.032" diameter) at a cent-to-center spacing of about 3/8". Then we add to the problem the fact that, for standard J-pole designs, the feed wire will be within 1.5" to 2.5" of bottom of the antenna. Obtaining in NEC-4 a model with a reasonable average gain test (AGT) value occupies as much of the design time as finding dimensions that yield a near-resonant 50-Ohm antenna.

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One of the known work-arounds for excessively tight angles and close- spaced wires tends to fly against normal modeling procedures. Convergence tests tend to add segments until the antenna's gain and source impedance no longer change values between steps in the process. However, to arrive at an acceptable AGT value for models of twinlead J-poles often requires a reduction in segmentation density. Hence, the emergent dimensions become further suspect, since convergence testing and average gain testing are at odds. Nevertheless, we may derive some significant information from the exercise.

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The Single-Wire Radiator Version of the J-Pole

The most straightforward way to obtain a J-pole from a length of TV twinlead is to retain the double line to serve as the matching section. Then, we strip away one wire from the upper portion, leaving a single radiator wire. The outline of a bare-wire version of this type of J-pole appears in Fig. 2. +
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As the dimensions on the sketch indicate, the radiator is 33" long and combines with a 22.5" matching section. The required distance above the bottom short in the section is 1.85". The right side of Fig. 2 shows the current distribution along the antenna. Unlike the standard model of Part 1, the current minimum for the radiator does not align well with the top of the matching section. Instead, it occurs somewhat below the top of the open-end of the matching section.

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The free-space model for this antenna yielded an AGT value of 1.008, indicating that gain reports would be about 0.04 dB too high. The maximum free-space gain of the antenna is about 2.45 dBi, when adjusted, with an average gain of about 2.38 dBi. The total pattern distortion created by the presence of the matching section is about 0.1 dB, as revealed by the top portion of Fig. 3. The narrow-spaced twinlead J-pole yields a very circular pattern.

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The patterns in Fig. 3 emerge from a model whose bottom-most portion is at 10' or 120" above ground. Most commonly, we use 2-meter J-poles at heights ranging from 5' to 20 above ground, so the 10' position seems a fair sample. Remember that the high current portion of the radiator is another 40" above that base level.

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The elevation pattern has a main lobe that is 6 degrees above the horizon. The maximum gain is about 5.1 dBi, subject to terrain features that clutter reality for most operations. While we examine the elevation plot, note the secondary or higher-angle lobes for comparison with other models that will appear in this part of our investigation.

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The test model showed a source impedance at 146 MHz of 53.4 - j3.0 Ohms.

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The Loose-Wire Radiator Version of the J-Pole

One natural variation on the single-wire radiator J-pole is the loose-wire radiator version. The sketch at the left of Fig. 4 shows the general construction and the modeled dimensions. +
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The loose-wire J-pole emerges from the desire to use the twinlead intact for added strength. Therefore, instead of removing the wire that is parallel to the normal radiator, we leave it in place, cutting out only a small portion to allow one side of the matching section to be open. Interestingly, the total length of the matching section does not change. Instead, the tapping point for the source wire moves up a very small amount to arrive ar a near 50-Ohm feedpoint impedance. The test model showed a source impedance at 146 MHz of 47.4 + j2.9 Ohms.

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The change of source wire position results from the slight lengthening required for the radiator--about 1" in the bare-wire proof-of-principle model. As the right side of Fig. 4 shows, the connected-radiator current minimum still occurs below the open end of the matching section. As we might expect, the closely-coupled loose wire show considerable current so that we should think of the two upper wires together as the radiating portion of the antenna. (We should, of course, never forget that the imbalance of current on the matching section wires results in some radiation from this portion of the antenna.)

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The model yielded an AGT value of 1.002, indicating only a 0.01 excess in the gain reports. The adjusted maximum free-space gain was 2.45 dBi, with an average gain of 2.40 dBi. Once more, the distortion of circularity of the pattern amounted only to about 0.1 dB.

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Fig. 5 shows azimuth and elevation patterns of the loose-wire twinlead J-pole with the base 10' above average ground. The upper pattern confirms the essential circularity of the pattern, while the lower elevation pattern seems initially indistinguishable from that of the single-wire twinlead J-pole. Indeed, the gain at a 6-degree elevation angle is about 5.1 dBi. The only difference between patterns that overlaying them can reveal is insignificant: the loose-wire version shows slightly larger lobes at the near-vertical angle just before the zenith null than the single-wire version. The difference of about 2 dB in lobes that are down in the -20 dB range could not be measured in any real situation.

+

The Top-Wire Radiator Version of the J-Pole

Twin-lead J-pole come in many physical varieties. Some builders design them to hang from the top, while other affix them to non-conductive supporting poles. One version has even been packed inside a length of Schedule 40 PVC. All seem to work quite acceptably so that the only choices facing the new builder is the preferred physical arrangement to suit operating needs. +

From this array of variations has emerged one more variant of the twinlead J-pole. It creates a gap and retains the second wire in the radiator section. However, it folds over the two radiator wires at the top and joins them. Since the current goes to zero--in theory--at the top of the radiator, this arrangement should not disturb the current distribution on the radiator wires.

+
+ +
+

Fig. 6 shows the dimension of the proof-of-principle model needed to obtain a resonant feed point. The modeled impedance was 51.7 - j8.2 Ohms. Note that the overall height relative to the loose-wire version has grown only 0.1". However, the matching section is now 22.9" long, with the gap extending another 0.8". The feedpoint tap wire moved upward to 2.4" above the antenna bottom. Clearly, the top wire added some complexity to the operation of the J-pole without necessarily creating any significant construction problems.

+

The current distribution graphic on the right of Fig. 6 shows what has happened. The gap that defined the end of the second radiator wire occurs above the current minimum for the connected wire. Therefore, two current excursions along the connected radiator wires must move the middle current minimum downward from the tip on the connected radiator wire. The tip region of the antenna shows a rising current magnitude.

+

The chief result of the current distribution is the alter the required dimensions of the J-pole relative to the other two versions. The difference does not show up in operation. The model showed an AGT value of 0.965, indicating that gain reports would be about 0.16 dB low. The adjusted maximum gain report is about 2.51 dBi, with an adjusted average gain report of 2.45 dBi. The minuscule difference between these values and those reported for the other two models results mostly from the fact that the AGT value is further from a perfect 1.0 value. The correction factor becomes less accurate as the AGT departs further from the ideal value.

+
+ +
+

Fig. 7 shows the azimuth and elevation patterns for the top-wire twinlead J-pole with a base height of 10'. The gain at an elevation angle of 6 degrees is once more about 5.1 dBi. The pattern is once more circular within about 0.1 dB. The elevation pattern is truly indistinguishable from that of the loose-wire version of the antenna.

+

Insulating the Wires

Nothing in the variant construction methods for the twinlead J-poles shows any sign of changing performance by even the most sensitive antenna range measurement, assuming that each antenna receives due care in the building and adjustment process. However, all of the models used to establish this fact used bare wire. The question remains as to the effects of insulation on the wires. +

Some advanced NEC-4 programs provide an program control input labeled IS, for insulated sheath. The modeler can specify a second radius for each wire, one that is larger than the conductor radius itself. In addition, the modeler can specify values of conductivity and permittivity (relative dielectric constant) for the additional radius.

+

As a test, I began with the single-wire version of the twinlead J-pole. I added to every wire in the model an insulated sheath with a diameter of 0.047", about 1.5 times the diameter of the wire itself (0.032"). I assigned a conductivity of 1E-10 s/m to the sheath, on the assumption that the sheath is an excellent insulator. In fact, in other tests of the IS input, dipole performance did not show any noticeable change until the conductivity reach the 1E-6 s/m level. Hence, for most exploratory purposes, assigning a very low conductivity level will not affect the results. The selected permittivity value was 2.5, about in the middle of the range of most plastic materials used to insulate wires.

+

This model is only a first-order exploration into the performance of twinlead J-poles with insulated wires. The insulating sheaths do not touch--in fact, they leave a considerable air space between wires in the matching section. However, the model is sufficient to "see what happens" with insulated wires.

+
+ +
+

Fig. 8 shows the dimensional differences between the bare and insulated single-wire radiator J-poles. The source impedance of the revised model was 50.6 + j9.7 Ohms with the feedpoint tap wire at just about the same height above the antenna base as for the bare-wire version. In fact, the only required change for this performance was to shorten the height by just over 3.5". The matching section legs remain the same in both models.

+

Although a fully developed model of the matching section might show some required changes in dimensions to account for the velocity factor of actual twinlead, the key result of using insulated wire on the assembly lies in the necessary shortening of the radiator section. To some degree, the matching section is self-compensating, since the current minimum of the radiator now occurs further down the connected leg of the matching section. Unfortunately, the software on which the insulated-sheath model was run does not permit a current distribution graph of the types shown for the other models.

+

Free-space performance of the antenna changes hardly at all. The pattern remains circular within the 0.1 dB level, and the average gain is about 2.4 dBi. In short, insulated-wire twinlead J-poles are every bit as good as bare wire versions and only require attention to the dimensions that result from the wire insulation.

+

Some Standards of Comparison

Throughout this exploration of twinlead J-poles, we have placed the base of the antenna at 10' above average ground to find a sample of its performance potential. In all cases, a gain of 5.1 dBi at a 6-degree elevation angle emerged to make each version the equal of the others. +

The question we might raise, since we have these figures at hand, is how the J-pole stacks up against other common antennas used in the same service. To answer this question, I looked at file models of both 1/4 wavelength monopoles with radials and 1/2 wavelength vertical dipoles. We use the former most commonly when we wish to place the feedline beneath the model. The latter serves well when side-mounting is required.

+

However, we have to examine a matter of test fairness. The J-pole is longer than either of the two comparison antennas, and its region of highest current is well above the antenna base. Simply placing the comparison antennas at a base height of 10' might not result in a fair comparison.

+

Therefore, I performed 2 tests. The first placed the comparison antenna base at 10' above ground. The second raised the antenna until it showed a take-off angle (or elevation angle of maximum radiation) of 6 degrees.

+
+ +
+

The 1/4 wavelength monopole with 4 radials yielded the elevation patterns shown in Fig. 9. (I have omitted azimuth patterns, since the comparison antennas have perfectly circular patterns in the absence of nearby objects.) The upper pattern--with a 10' base for the antenna--has a gain of about 3.4 dBi at 7.1 degrees above the horizon. We can obtain a 6-degree take-off angle by raising the antenna to a base level of 12.9'. The gain rises to just above 4.0 dBi. Clearly, the J-pole is superior by at least a full dB. Moreover, the near-3' increase in monopole height to achieve the 6-degree take-off angle places the monopole and J-pole high current regions at just about the same distance above ground.

+
+ +
+

Fig. 10 shows the comparable results for a vertical dipole. With the vertical base at the 10' level, the gain is just above 4.5 dBi with a 6.7-degree take-off angle. To achieve a 6-degree take-off angle, we must raise the antenna by about 1.7' or 20". It is not accident that this increase elevation corresponds roughly to the length of the matching section of our twinlead J-poles. The resulting gain is about 4.9 dBi, only about 0.2 dB lower than gain of the J-poles. Indeed, to ascribe the added J-pole gain to radiation from the matching section would likely not be wrong. However, to think that one could detect the 0.2 dB gain difference in operation would likely be very wrong indeed.

+

The J-pole, then, performs very much like a vertical dipole, with departures from its electrical mate's pattern that result from the presence of the matching section and its slight imbalance of currents. The departures are slight for very closely spaced thin wires, such as we find in a twinlead version of the antenna. However, the thin wires do not detract from the operating bandwidth of the antenna--one of its chief merits.

+
+ +
+

Fig. 11 shows the SWR curves for the 3 bare-wire models of J-poles that we explored. Conveniently, the curves are displaced sufficiently for ready examination. Clearly, the single-wire and loose-wire curves would overlap almost perfectly had we fussed the 146-MHz impedance to a perfect 50 Ohms. Both curves would show a 50-Ohm SWR of about 1.6:1 at the band edges had we done the additional work.

+

The top-wire curve is interesting, because its low point has a higher SWR value due to the high impedance of the antenna at 146 MHz and because its band-edge values are only about 1.5:1. The curve is shallower. At this point, it is unclear whether the top wire plays a significant role in this minor effect. Obviously, any significant length of 50-Ohm coaxial cable will wash out any differences among the curves.

+

The broadness of the SWR curves, despite the thinness of the radiator wire and despite construction changes that add virtual thickness to the wire for some of the models, raises some questions. The classic dipole model shows a rapid change of current and voltage at the ends as we change frequency. However, those changes do not show up at the feedpoint end of the matching section. We have noted the fact that for all of our models, the radiator current minimum occurs below the top of the matching section.

+
+ +
+

Fig. 12 shows the current distribution for the single-wire J-pole at 2-MHz intervals from 142-150 MHz. If you examine the curves carefully, you will see that the radiator current minimum point slowly climbs upward with frequency increases. The net effect is to change the combined lengths of the matching section legs, as well as the current magnitude in the small portion of the matching section below the feedpoint tap wire. Moreover, there is a changing current magnitude differential from one end of the feedpoint tap wire to the other as we increase frequency.

+

In effect, there is a degree of self-adjustment between the radiator and the matching section that increases the operating bandwidth beyond what we might expect from the wire size alone. The amount of self-adjustment is limited, as the 50-Ohm SWR is just above 2.5:1 at 142 and 150 MHz. Nonetheless, the degree to which the combined radiator and matching section exhibit a broad operating bandwidth in the J-pole adds one more dimension to our appreciation of this seemingly simple antenna.

+

More?

The SWR curve question that we have just begun to explore leaves us with another: what is the effect of element thickness (for both the radiator and the matching section) on the operation of a J-pole? Does the operating bandwidth change? Does the antenna gain change? +

We have also alluded to another interesting aspect of J-poles. The narrow-space versions show a nearly perfectly circular pattern, which the wider-spaced version in Part 1 shows noticeable (but not harmful) distortions from circularity. We are left with the question of whether the degree of non-circularity of the pattern is directly related to the spacing of the legs in the matching section.

+

Each of these 2 questions calls for a bit of detailed modeling to see if the beginnings of a set of answers emerges. As I noted, once one gets hold of a J-pole, it does not let go. So a Part 3 seems inevitable.

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+ +
+

Updated 1-3-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 3

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Go to Main Index

+

Topics: J-Pole, VHF / UHF, Vertical


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+

Some J-Poles That I Have Known

+
+
+

Part 3: The Effects of Element Diameter and Match-Section Leg Spacing
+ on Standard and Non-Standard J-Poles

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Our examination of twinlead J-pole design variations restricted us to thin-wire, close-spaced J-poles. However, an alternative design direction makes use of tubular elements--sometimes copper water pipe. The larger diameter of the elements naturally leads to wider spacing between the legs of the matching section. The general question we might want to ask is whether there are any significant performance differences that result from either enlarging the element diameter or widening the spacing. Even f we do not find operationally significant differences, the trends that we might find in systematically looking at these two variables can give us some proper expectations when building and adjusting a J-pole.

+

To sample the arena--still using 146 MHz as a design frequency--I looked at the performance of both standard and non-standard J-poles--as specified in Part 1 of this exploration. I modeled a number of J-poles using a standard spacing of 1" between match-section legs in diameters from 0.125" to 0.5" in 1/8" increments. Then I did the same for a J-pole using 0.375" diameter elements, increasing the spacing from 1" to 4" in 1" increments. The material throughout was aluminum, although the results would have been virtually identical for copper.

+

Changing any of the design variables results in an overall change in J-pole dimensions. Therefore, the sketches in Fig. 1 can be a guide to dimensional references from this point forward.

+
+ +
+

A applies only to standard dipoles and is the distance from the base of the antenna to the feed-wire. B is the distance from the antenna base to the open end of the short match leg, while C is the distance from the antenna base to the top of the radiator. All dimensions will be in inches. As we saw in Part 2, the difference between C and B does not necessarily define a full half wavelength, even for a standard J-pole, since the current minimum marking the bottom of the radiator may occur below the top of the shorter match section leg of the antenna.

+

As the figure indicates, non-standard designs will always be shorter than standard designs. One consequence of this fact is that with a constant base height for the antenna over ground--say, 10' (120")--the take-off angle or elevation angle of maximum radiation will be slightly higher for the non-standard design than for a standard J-pole. The higher angle results from a slightly lower height for the region of maximum current on the radiator.

+

Non-standard designs have another requirement that does not apply to standard J-poles: the mount should be insulated. Most builders presume that in a standard J-pole, the lower cross piece is at zero impedance. Technically, this is true of only a point along the cross wire. However, the differences in impedance--and hence current--on the wire will be small and likely only to require a very small adjustment of the source wire to re-establish a 50-Ohm resonant feedpoint impedance. Therefore, extending the long leg of the standard J-pole downward to form a mounting extension for a metal mast generally creates no operational problems.

+

With a non-standard J-pole design, the connection of the base of either leg of the matching section to a mounting extension of mast would most likely upset the current distribution along the matching section, resulting in unpredictable results--with the exception of the prediction that the antenna mostly likely would no longer operate in accord with models. constructing a mounting from PVC or similar non-conductive materials is quite simple and expedient for most J-pole element diameters and spacings. If one wishes to make a connection to discharge static build-up on the antenna, then one should apply standard static discharge methods to the design.

+

In the notes that follow, all performance figures will employ models with the antenna base placed 10' above average ground. Although free space is a very usual environment for comparing design variations in antenna work, it will not be useful for J-poles with matching legs separated by an inch or more. Fig. 2 shows us why.

+
+ +
+

The presence of inevitably unbalanced currents on the legs of the matching section does more than create some radiation from the lowest portion of the antenna. The current imbalance also changes the free-space angles of maximum radiation, as exemplified by the free-space elevation (E-plane) pattern in the figure. In the direction of the short leg, the pattern angle is above the hypothetical horizon, while in the direction of the longer element, the pattern angle is below that same horizon. The difficulty arises from the fact that the maximum strength bearings for the two lobes are not 180 degrees apart. The greater the spacing between the legs, the more divergent the angles. Hence, for antennas fatter than or more widely spaced than the twinlead designs we examined in Part 2, the free-space patterns do not give results that we can compare from one design variation to the next.

+

Providing a ground and a constant antenna-base height resolves the problem, especially since virtually all J-poles are used over real ground (although a few aeronautical and aerospace versions might exist). We have already alerted you to the differential that will exist between standard and non-standard designs due to differences in the effective height of the radiator section. However, we can still examine general performance trends that emerge by varying either the element diameter or the matching-leg spacing.

+

These trends are subject to limitations in modeling J-poles. Although the trends that we shall see in the dimensions will be correct, the exact dimensions will not be directly transferable without further adjustment to a physical antenna. Close spacing of wires having different length tends to provide offset results in NEC. As well, the feedpoint regions of both types of J-poles sets certain limits to segmentation. The result will be a requirement that all reported gain figures be adjusted by reference to the average gain test (AGT) value as recorded in dB. The tables that supply the data for each systematic run of models also include the AGT value. A positive value indicates that the NEC reported gain is too high by about the AGT figure. Hence, a truer gain value results from adjusting the reported gain by subtracting the AGT value from the report. The reverse applies to AGT values less than 0.0 dB. The tables provide adjusted rather than raw gain reports.

+

Theoretically, the AGT value expressed as a simple average gain value--with values either higher or lower than the ideal of 1.0--may also be used to correct source impedance reports. We simply multiply the resistive portion of the source impedance by the AGT value to obtain a truer impedance. This technique applies to resistive impedances rather than to complex impedances. For simplicity in determining operating bandwidth for the antennas, the NEC reported impedance figures have been used. Hence, the impedance of a physical antenna answering to the modeled dimensions may by somewhat off for a true 50-Ohm impedance. Adjustments may be small in most cases, but they will be necessary. However, the use of NEC-reported impedances is sufficient to show with good accuracy the most important trends.

+

And trends are the key to this exploration. Our goal is to understand better J-pole behavior, not to provide blueprints for building one. The literature and the web are full of J-pole plans, most of which have stood the test of repeated replication. These notes have a different goal altogether.

+

Varying the Element Diameter of J-Poles

To see what trends might accompany variations in the diameter of the material from which we construct J-poles, I set up basic designs of both standard and non-standard J-poles using a fixed center-to-center spacing of 1" between the matching section legs. Then I varied the diameter of the aluminum elements from 1/8" to 1/2" in 1/8" increments. +

The results appear in both tabular and graphical form in the following notes. The following table provides a reference to the lines labels for the tables in this section and the next. The table also indicates the performance areas in which I took the keenest interest.

+ 
                          Label Reference Table
+A          Dimension A: bottom to feedpoint in inches (standard J-pole)
+B          Dimension B: bottom to open end of match section in inches
+C          Dimension C: bottom to open end of radiator
+Zo         Calculated matching section characteristic impedance in Ohms
+AGT        Average Gain Test value in dB
+M-Gain     Maximum adjusted gain in dBi at take-off angle
+A-Gain     Average adjusted gain in dBi at take-off angle
+TO /_      Take-off or elevation angle of maximum gain in degrees
+F-B        Front-to-back ratio in dB in plane of J-Pole
+Dia.       Element diameter in inches
+Space      Element spacing in inches
+

The dimensions are of great interest, since they indicate trends in relative lengths as we change element diameter (or, later, spacing). The calculated characteristic impedance (Zo) of the matching section may be mostly of archival interest. The maximum gain value, as adjusted by the AGT, is always in the direction of the short leg of the antenna. The average gain values are simply the gain of the antenna at 90 degrees to the bearing for the maximum gain. Further averaging might be applied, but was unnecessary in this first order exploration. The TO angle applies to the antenna when its base is 10' above average ground. finally, the front-to-back ratio indicates the degree of distortion of the azimuth pattern from a perfect circle--as one might obtain from a ground-plane monopole or a vertical dipole.

+

The following tables provides the results for both standard and non-standard J-poles in the diameter-variation test.

+ 
        Constant 1" Element Spacing, Increasing Element Diameter
+
+Standard J-Pole
+Dia.       0.125"           0.25"           0.375"          0.5"
+A           1.25             1.20            1.20           1.30
+B          19.75            19.75           19.60           19.65
+C          59.50            57.90           57.60           57.50
+Zo         332              249             200             166
+AGT        -0.28            -0.53           -0.89           -1.52
+M-Gain     5.12             5.28            5.35            5.41
+A-Gain     4.95             5.07            5.08            5.08
+TO /_      6.1              6.1             6.1             6.1
+F-B        0.43             0.55            0.68            0.81
+
+Non-Standard J-Pole
+Dia.       0.125"           0.25"           0.375"          0.5"
+B          22.50            22.50           22.50           21.60
+C          48.30            45.50           42.50           39.40
+Zo         332              249             200             166
+AGT        -0.05            +0.04           +0.89           +1.66
+M-Gain     5.07             5.04            4.97            4.92
+A-Gain     4.86             4.77            4.64            4.57
+TO /_      6.6              6.6             6.6             6.6
+F-B        0.46             0.60            0.70            0.76
+

The standard J-pole shows very little variation in the required height of dimension B, the length of the short matching leg. As well, there are only small variations in the distance from the antenna base to the source wire, dimension A. The major changes relate to the overall length of the radiator section, which shows modest decreases with each increase in element diameter. For the entire 4:1 increase in element diameter, the overall antenna height decrease is only 2".

+

In contrast, for the same change in element diameter, the non-standard J-pole requires a height reduction of nearly 9". Interestingly, the short leg requires no change until we reach the 0.5" diameter material. However, in physical antennas, we should expect some changes to sustain a 50-Ohm feedpoint impedance, since the AGT value differs for each model.

+

Throughout, each model was set for a feedpoint impedance of 50 Ohms as determined by an SWR of less than 1.01:1 at 146 MHz. We shall examine SWR curves for both types of J-poles near the end of this section of the notes.

+
+ +
+

Fig. 3 plots the maximum and average gain values for both antenna types throughout the range of element diameters. In general, the corresponding values for the standard J-pole are slightly higher than those of the non-standard model due to the differences in the height of the maximum radiation region of the antennas. The differences would make no operating difference at all, although the trends are interesting in and of themselves.

+

The standard design tends to show a rising gain curve with increases in element diameter--although the rise is too modest to alone be a reason for changing a planned material. The increase in diameter raises the region of maximum radiator current faster than the height reduction lowers it. The opposite is true for the non-standard J-pole: the reduction in overall height is more extreme with each increment of increase in element diameter, resulting in a marginally lower overall gain for the same 10' base height of the antenna. In short, the differences in the gain values are almost completely the result of changes (or lack of changes) in the height of the maximum current region of the radiator.

+
+ +
+

More interesting is Fig. 4, which plots the front-to-back ratio for the antenna types through the increases in element diameter. Both types of J-pole show an increasing difference between the gain in the direction of the open matching leg and the direction of the long radiator. Although the amount of differential is not very significant, the curve shapes are. The standard J-pole shows a virtually linear track of the increase in front-to-back ratio, while the curve for the non-standard design tapers the rate of increase with each increase in element diameter. By a diameter of 1", the non-standard design would almost cease to show further increases in the front-to-back ratio.

+

Examining elevation patterns for the antenna types along the axis in plane with the two elements provides some further insights into differences in the behavior of the two types of J-poles. Fig. 5 tells the story.

+
+ +
+

At the top is the elevation pattern for the single-wire twinlead J-pole from the preceding episode. There is for the thin-wire, closely-spaced design only a hint of a difference between the forward lobe structure and the rearward lobe structure. As well, the front-to-back ratio measure a minuscule 0.1 dB. The standard J-pole shows a much more radical difference between forward and rearward lobes structure--much larger a difference than we find for the non-standard design despite the similarity in the front-to-back ratios for the two antennas. At the take-off angles recorded in the table, the azimuth pattern does not suffer as a result of these variations, and the azimuth pattern shown in Fig. 6 suffices as a representation for all of the antenna models in the tables.

+
+ +
+

The feedpoint impedance behavior of the different types of J-poles does show some semi-significant variations and interesting trends. In Fig. 7, we find at the top the 50-Ohm SWR curve for the standard J-poles having the largest and smallest diameter elements. There is virtually no difference in these curves despite the 4:1 difference in element diameter.

+
+ +
+

In contrast, the lower section of Fig. 7 shows the 50-Ohm SWR curves for the largest and smallest diameter elements as used in the non-standard J-pole. Overall, we can see that the smallest diameter element has a wider operating bandwidth than the largest diameter element version of a standard J-pole. At the same time, increasing the diameter of the non-standard design results in further widening of the operating bandwidth.

+

The operating bandwidth, as registered in 50-Ohm SWR curves, is not an isolated fact, but relates closely to the dimensional changes we examined as the first item of interest. The standard J-pole dimensions changed very little over the range of element diameter increases, and the similarity of SWR curves reflects that fact. In contrast, the overall height of the non-standard design changed by a much greater amount, indicating that element diameter would have a much more marked effect on other operating characteristics. Of all the performance parameters checked, operating bandwidth was the one most closely related to the dimensional changes in the designs.

+

Varying the Element Spacing of J-Poles

It is likely somewhat inaccurate to refer to the two legs of a J-pole as elements, since the short leg is part of a matching section and not intended as a radiator. However, the short leg does radiate--as evidence by the free-space elevation pattern in Fig. 3--and it is usually more compact to refer to the two legs of the J-pole as elements. +

The systematic examination of the spacing between J-pole legs or elements used constant diameter 0.375" aluminum elements throughout and varied the spacing in 1" increments from 1" to 4". Using the same labels as in the preceding section, the following table presents the recorded data.

+ 
      Constant 0.375" Element Diameter, Increasing Element Spacing
+
+Standard J-Pole
+Space      1.0"             2.0"            3.0"            4.0"
+A           1.20             1.50            1.95           2.80
+B          19.60            19.60           19.60           19.60
+C          57.60            57.60           58.60           60.30
+Zo         200              284             332             367
+AGT        -0.89            -0.06           +0.26           +0.47
+M-Gain     5.35             5.45            5.43            5.25
+A-Gain     5.08             5.14            5.14            5.05
+TO /_      6.1              6.3             6.3             6.3
+F-B        0.68             0.94            1.17            1.35
+
+Non-Standard J-Pole
+Space      1.0"             2.0"            3.0"            4.0"
+B          22.50            21.80           20.70           19.80
+C          42.50            47.50           50.60           52.10
+Zo         200              284             332             367
+AGT        +0.89            +0.29           +0.06           +0.13
+M-Gain     4.97             5.32            5.52            5.61
+A-Gain     4.64             4.88            5.06            5.17
+TO /_      6.6              6.6             6.5             6.4
+F-B        0.70             1.07            1.35            1.60
+

Regardless of the J-pole type, the overall length of the radiator side increases with increases in spacing between the match-section legs. The standard design increase is modest: under 3" for a 3" increase is spacing. The non-standard design radiator side length increases nearly 10" for the same increase in leg spacing. The large increase is matched by a gradual shortening of the short-leg side--a little over 2.5" for the spans tested. The short leg on the standard design remains constant. However, the distance between the antenna base and the feed-wire increases from 1.2" to 2.8" as the space between legs goes from 1" to 4".

+

Note that the overall radiator-side length follows an opposing curves with respect to increasing element diameter and increasing the spacing between elements.

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The maximum gain and average gain curves follow the changes in the overall length of the radiator-side in both designs, as shown in Fig. 8. The standard design shows a decrease in gain at the upper end of the spacing range, although operationally insignificant. The gain does increases very slightly as we move from a 1" spacing to a 2" spacing, although the overall length does not change in that span. However, to suggest that a 2" spacing might be optimal would be to ignore the many construction variables that would modify the nearly flat curve.

+

The non-standard design shows a rising gain curve, but one that is consistent with the increase in length of the radiator with increasing distance between match-section legs. More significant is the fact that the non-standard J-pole shows a faster rise in the front-to-back ratio than does the standard design, for the same range of match-leg spacings. See Fig. 9.

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The patterns for the J-poles become increasingly interesting as we increase the spacing between the match-section legs. Fig. 10 compares the elevation patterns with the antenna at a 10' height, using the standard J-pole with a 4" spacing--the most dramatic example. In the plane of the 2 elements, with the short leg being the forward direction, the elevation pattern shows marked differences between the forward and rearward set of lobes. When we take an elevation pattern at 90 degrees to the front-back line, we obtain the symmetrical pattern in the lower half of the figure.

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As we increase the spacing between match-section legs, we find a growth in the disparity between the forward and rearward lobe sets. Fig. 11 compares the elevation patterns of the standard J-pole with element spacings of 1" and 4".

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The non-standard design shows a comparable but less radical growth in elevation lobes sets with increases in element spacing. Fig. 12 compares the patterns for 1" and 4" match-leg spacing.

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If we remember the free-space elevation pattern in Fig. 2, we can understand the lobe-set disparity. The forward lobe of the free-space pattern for the standard J-pole showed a distinct upward tilt. Consequently, over ground, the standard J-pole tends to show relatively high energy at higher elevation angles. In contrast, the non-standard free-space pattern shows less tilt and the elevation patterns over ground show somewhat less total high-angle energy.

+

However, there may be a limit as to the maximum advisable spacing between the legs of a J-pole. Almost all of the azimuth patterns for the J-poles in the spacing series shows the same characteristics as the one in Fig. 6. The maximum gain lies on a heading that exactly follows the plane of the elements, with minimum gain in the reverse direction.

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+ +
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However, as we set the spacing of the standard J-pole at 4", the pattern begins to change, as shown in Fig. 13. Maximum gain appears at two points in the relative forward direction, each separated from the in-plane direction. It is likely that as we would further increase element spacing, the points of maximum gain would more widely diverge from the presumed forward direction, eventually resulting in an oval pattern with the strongest points almost broadside to the plane of the J-pole. Just how much pattern distortion one can tolerate is a user judgment based upon the operational goals for the antenna.

+

With the standard J-pole, the operating bandwidth, as reflected in 50-Ohm SWR curves, did not change as we increased the diameter of the element material. However, as we increase the spacing between the legs of the J-pole, the operating bandwidth does increase, as shown in the top half of Fig. 14. With a leg spacing of 4", the 50-Ohm SWR remains below 1/5:1 across the entire 2-meter band. At the 1" minimum spacing used in the survey, the maximum SWR is just above 1.7:1 at the band edges.

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+ +
+

The non-standard J-pole design once more shows an inherently wider operating bandwidth than the standard design. The worst-case SWR shown in Fig. 14 for the non-standard design is under 1.3:1. However, the bandwidth actually decreases as we increase the spacing between the match-section legs. This result seems contrary to the result for increasing the element diameter. However, the bandwidth does correlate quite well with the changes in the overall length of the radiator. The bandwidth increases with decreases in radiator-leg length and decreases with increases in the radiator-leg length.

+

Conclusions, But Not THE Conclusion

The trends that this small survey has uncovered may be useful to the J-pole designer, but they do not approach the level of making a significant difference in the operational use of a J-pole. Over the range of element diameters and match-section leg spacings modeled, a user would be very hard pressed to detect any difference in performance between J-pole types or between designs taken from the most extreme cases. +

Perhaps the most significant conclusion to reach from the data is the need to have some degree of adjustability built into a J-pole that departs from one of the cookie-cutter sets of plans for them. If you change the material diameter or the leg spacing from one of those plans, you likely will have to adjust at least the length of the radiator side. In addition, for standard designs, placing the taps for the feedpoint remains a field exercise--meaning that the taps should be adjustable and tried until one obtains a satisfactory result. For the non-standard design on its insulated base, being able to adjust the length of both sides of the assembly will facilitate the discovery of dimensions that yield a 50-Ohm resistive feedpoint impedance.

+

We have examined standard and non-standard J-pole designs with respect to element diameter and leg spacing. Only one other dimension remains to be explored: the overall length of the radiator. Indeed, since the lower portion of a J-pole is mainly a means of providing power to the radiator section, the J-pole is as much a candidate for lengthening into various collinear vertical arrays. As well, it may be useful as the driven element for modest--or even immodest--Yagis. Therefore, one more episode seems in order to explore these potentials--and possibly compare the results to more standard designs for collinear and parasitic arrays.

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+ +
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Updated 1-6-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 4

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Go to Main Index

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Topics: J-Pole, VHF / UHF, Vertical


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+

Some J-Poles That I Have Known

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Part 4: Some Things We Can and Cannot Do With a J-Pole

+
+
+

L. B. Cebik, W4RNL

+

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+ +

+
+ In this final episode of the saga of the J-pole, we shall examine some interesting variations on the basic J-pole. These ideas will complete my personal investigations into this intriguing antenna--at least for the moment. However, there are many other sources of information on practical J-poles and techniques for improving them--both in terms of performance and in terms of matching them easily to 50-Ohm feedlines. +

First, we shall look into some suggestions for improving standard J-pole performance by increasing the length of the radiator. Our goal will be to understand why most of them do not hold promise of success.

+

Second, we shall look at a longer version of the J-pole that does work: the collinear J-pole. Along the way we shall look at the question of how well it works.

+

Finally, we shall examine a model of the Jagi, the J-pole-driven Yagi. Why it does work will become the final exam to see if we really do understand the J-pole.

+

Longer is Not Necessarily Better

Over the years, I have heard many suggestions for improving the standard J-pole's performance by simply making the radiator section longer. Since the basic J-pole radiator is a 1/2 wavelength wire--end fed, perhaps some of the longer wires with better performance in other contexts will help the J-pole to do better than it does--which is pretty good to begin with. +
+ +
+

Fig. 1 illustrates the most common suggestions for increased length that I have heard. The 5/8 wavelength radiator idea emerges from ground-plane antenna ideas. A 5/8 wavelength vertical has theoretically the highest gain of any ground-plane monopole. The 1 wavelength suggestion emerges from the idea that if 1 half wavelength radiator is good, then 2 must be better. As well, each half wavelength section ends in a high impedance, which is what the matching section needs to see. The 1.25 wavelength notion stems from the extended double Zepp (EDZ), which is essentially 2 half wavelength sections at the outer ends with a phasing section in the middle.

+

Unfortunately, none of these ideas promises much when modeled either in free-space or over ground. As I have throughout these notes, I shall place each antenna in this final section 10' or 120" above average ground. (Whenever we compare an antenna to a J-pole, the comparator will be elevated to a height that places its region of highest current at about the same height as the equivalent region of the J-pole. For a standard J-pole at 146 MHz, that region is about 30"-40" above the antenna base.) As well, unless otherwise specified, all J-pole variants in this final set of notes will use 0.375" diameter aluminum elements, and the matching section will use a 2" spacing. This construction is both feasible and allows models in NEC-4 that result in average gain test (AGT) values close to ideal (1.00 or 0.0 dB).

+

To see what happens if we simply extend the length of the J-pole radiator, let's model the suggested new versions in free space. We shall be especially interested in the elevation patterns, which correspond to the E-plane patterns of vertically polarized antennas like the J-pole.

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+

Fig. 2 contains a wealth of data, since it contains both the free-space E-plane patterns and the current distribution representations for all three antennas. However, by combining the data, we can begin to see the way in which end-fed linear elements differ from center-fed elements of the same length.

+

The 5/8 wavelength pattern gives us our first warning. We begin to see the emergence of multiple lobes at roughly 45-degree angles to the horizontal and vertical axes of the pattern plot. As we increase the length of the radiator to a full wavelength, the emergent lobes become fully formed. We are used to seeing such lobe formation in wires without the matching section only when the wire length was about 2 wavelengths.

+

The corresponding current distribution graphics to the right of Fig. 2 verify the wire length--that is, that I am not presenting models that falsify performance. The 5/8 wavelength graphic shows a single full half wavelength rise and fall of current magnitude above the minimum close to the matching section. Of course, the matching section does not start at a current minimum. Therefore, the currents in that section show very significant imbalance--to the point that the section almost functions as a simple antenna fold-back rather than as a transmission line.

+

The full wavelength current graphic shows 2 full excursions of current above the matching section, with a current null about in line with the top of the matching line pair. Since the currents are better balanced, the radiator itself largely controls the lobe formation. Nevertheless, with end feed, the pattern shows 4 distinct lobes.

+

The pattern for the 1.25 wavelength radiator version of the J-pole resembles the pattern we might expect from a center-fed 1.5 wavelength wire. The 6 lobes represent in a 1.5 wavelength wire the emergence of the 4 corner lobes of a 2 wavelength wire and the decrease of the horizontal axis lobes typical of a wire 1 wavelength or less. The corresponding current distribution graphic seems to confirm this analysis if we take the lowest current excursion as being completed by the unbalanced match line section.

+

Those interested in lobe formation for end-fed wires may wish to read the short Appendix to this episode to develop the full portrait of current magnitude and phase along a wire longer than 1/2 wavelength in order to fully appreciate the lobes in the E-plane patterns for the suggested J-pole improvements. What the models tell us is that the longer radiators are likely to produce more high-angle radiation than low-angle radiation when we place them over a ground.

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Fig. 3 confirms our suspicions. Each J-pole model has its antenna base at 120" above average ground. Each elevation plot lies along the plane of the antenna legs so that a small front-to-back ratio is detectable. In each case, the strongest lobes are at much higher angles above the horizon than we would desire for point-to-point communications on 2 meters. The 5/8 wavelength pattern is usable, but at a lower level than a standard J-pole. The gain at a 6-degree elevation angle is about 2.5 dB lower than for a standard J-pole (2.6 dBi vs. 5.1 dBi). The 1.25 wavelength version does show a low angle lobe--corresponding to the free-space lobe along the horizontal plot axis. However, this lobe is about 1.5 dB weaker than the main lobe of the standard 1/2 wavelength J-pole (3.5 vs. 5.1 dB). The main lobe of the 1.25 wavelength J-pole is indeed quite strong at about 6.4 dBi, but the 42-degree elevation angle is hardly ever useful for point-to-point communications.

+

The lesson that we might take from these models is that the standard-type J-pole's best radiator length is in the vicinity of 1/2 wavelength--as adjusted for the match section requirements and the element diameter. Hence, for a 146-MHz design frequency, the radiator will be somewhat shorter than the 40.2" true half wavelength. Still, this lesson does not mean that we cannot make longer improved-performance J-poles. It simply means that we must make them in a more nearly correct manner.

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The Collinear J-Pole

To prevent the formation of lobes the yield high-angle radiation over ground, we must establish the correct current phase relationships between radiator sections of long J-poles. One age-old technique is to insert a shorted transmission-line stub between the 1/2 wavelength radiator sections that will effect a 90-degree phase shift between the top end of the lower radiator and the bottom end of the upper radiator. The result is a J-pole version of a rather standard collinear vertical array. +
+ +
+

Fig. 4 shows the modeled version of the collinear array. As with many of the models in this series, it is a proof-of-principle model, not a construction blue-print. All the wire sections composing the model are 0.375" diameter, even though one might ordinarily build the 18.5"-long 2"-wide phasing section of thinner material, such as 0.1" diameter wire. Indeed, the selection of the 2" width resulted from modeling needs to keep the wires sufficiently far apart so as not to result in modeling errors.

+

All dimensions are in inches in the figure. If you compare the model with the corresponding 2"-wide 3/8" diameter J-pole in the preceding segment of these notes, you will discover that the short leg has grown from 19.6" to 23.6", with the feed tap moved upward by 4". The half wavelength radiator sections are not of equal length: 41" for the upper and 35.4" for the lower. In part, the differential results from adjusting the upper section to achieve the desired 50-Ohm feedpoint impedance (in addition to the matching section adjustments) without harming the overall gain of the system.

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Fig. 5 shows the current distribution along the antenna, at least in terms of magnitude. The phase-line section changes the current phase by 90.5 degrees, and its placement and length are critical to obtaining full performance from the antenna. Ideally, the current magnitudes at the two junctions of the phase-line should be equal. However, lengthening the upper radiator results in a detectable variance. The 90-degree phase shift is more significant in this application than equalization of current magnitudes.

+

The lower radiator current minimum coincides nicely with the top open end of the matching section. However, since the current magnitudes are not equal between the lines at the top end, considerable imbalance exists along the matching section. The result is a spurious lobe that will become evident in elevation patterns for the antenna.

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In Fig. 6, we find the elevation patterns for the 102" long collinear J-pole with the base 10' above average ground. In the plane of the elements, the antenna shows a maximum gain of about 7.7 dBi, with a small (0.4 dB) front-to-back ratio. The average gain of the antenna shows up by looking at the pattern at 90 degrees to the plane of the elements, as shown in the lower half of the figure. The gain is about 7.4 dBi. This value is about 2.3-2.4 dB higher than the average gain of a single-radiator J-pole. Indeed, although many folks like to bandy the gain advantage of a collinear arrangement as 3 dB greater than a single section, we rarely obtain in real antennas more than about a 2.0-2.5 dB increase in gain.

+

Compared to many vertical antennas, the collinear J-pole shows a remarkable reduction in high-angle radiation. For any vertical collinear array, the only place from which to obtain energy for increased gain at lower elevation angles is from the high-angle energy of a single section. If the single section lacks high angle radiation, creating a collinear version of the antenna will rarely yield improvements in performance that justify the added structure.

+

The upper portion of Fig. 6 shows the spurious lobe that results from both the imbalance in currents in the matching section and from the imbalance of currents in the phasing line. For the model, the phasing section protrudes in a straight line in the direction of the open end of the matching section. In a physical implementation of the design, the phasing section would likely wrap around the main element axis in a circle.

+

To evaluate the collinear J-pole--especially in terms of whether the increased height and complexity of construction is warranted--we should compare its performance with some antenna or other. since the J-pole is 102" long, the vertical extended double Zepp, which is about 100" at 146 MHz, is a good comparator.

+

The EDZ used in this test is 0.375"-diameter aluminum and 100" long. The length allows the model to set the base at 120" above ground, since an exact correlation to the collinear J-pole regions of maximum radiation is not feasible. In the J-pole, those regions are roughly centered in each of the two radiator segments. In the EDZ, the regions of maximum current are located about 1/4 wavelength inward from each end--when we feed the antenna at the center. (End-feeding the EDZ results in a somewhat different distribution of current--enough to disrupt the anticipated lobe formation.)

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Fig. 7 shows the elevation pattern for the EDZ. Since nothing in the structure disrupts the circularity of the pattern, this single plot suffices for all possible axes along which we might take elevation patterns. The gain at 5.5 degrees (about the same elevation angle as for the collinear J-pole) is just under 7.6 dBi, that is, only about 0.2 dB higher than the average gain of the collinear J-pole. The high-angle lobes are reflections of the typical ears that accompany any EDZ pattern. They shrink as we reduce the length of the antenna--but so to does the overall antenna gain. If we extend the length much beyond 1.25 wavelength, the ear-lobes will grow to dominate the pattern, resulting in a pattern with predominantly high-angle radiation.

+

For the version shown, the feedpoint impedance is about 120 - j380 Ohms. There are many schemes for matching an EDZ to a 50-Ohm feedline. One way to do it with lowest loss is to use a section of parallel transmission line and a shorted stub. One might also place a network of fixed or variable components at the feedpoint. Finally, one can employ transmission line sections for the inner portion of the antenna to effect an impedance transformation within the antenna itself. The latter two matching methods tend to reduce overall system gain--that is, to create some loss of radiated energy--more than the match-line-and-stub system. However, the match-line-and-stub system tends to narrow the operating bandwidth of the antenna. (There are notes on feeding EDZs among the collection at this site.)

+

I note the matching requirements for the EDZ so that one might make a fair comparison between the EDZ and the collinear J-pole. For roughly equivalent performance, we have roughly equivalent size and construction complexity--a not too unusual situation for antennas. In which direction one goes may ultimately rest upon which antenna most closely coincides with one's favorite shop techniques.

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The collinear J-pole does offer one advantage over many other types with which it might compete: a wide operating bandwidth. Fig. 8 shows the 50-Ohm SWR curve for the modeled collinear array. The band-edge SWR values are 1.41:1 at 144 MHz and 1.35:1 at 148 MHz. I suspect most users would find these values tolerable.

+

The Directional J-Pole

The current distribution along the radiator section of a J-pole is perfectly normal, with a maximum level at the center and diminishing levels toward the ends. The only variation from what we might expect of a center-fed 1/2 wavelength wire is that at the lower end of the radiator, the current does not go to zero. In fact, the current may be as high as 20% of maximum value at the radiator center. +

Since the current distribution is normal, we might wish to use the J-pole as the driven element in a vertically polarized parasitic array. In The ARRL Antenna Compendium, Vol. 5, Michael Hood, KD8JB, presented a 3 element Jagi (J-pole driven Yagi) (pp. 62-65), using his plumbing-pipe J-pole (from Vol. 4 of the Antenna Compendium) as the driven element. Rather than try to model the complex arrangement of various pipe sizes that he used, I took a standard J-pole model that used 0.375" diameter aluminum with a 2" match-leg spacing as the driven element for a model of a 3-element Jagi.

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Fig. 9 shows the dimensions of the final model. I aligned the elements of the driven element, since the degree of misalignment of element centers was not severe. Each parasitic element also uses 0.375" diameter aluminum. The final dimensions resulted from juggling element spacing and lengths along with the J-pole feed to obtain the best performance and a 50-Ohm feedpoint impedance.

+

The dimensions for the elements emerged initially from a 3-elements Yagi of standard design, but using 0.5" diameter elements. Therefore, in checking the performance of the Jagi, I used this standard Yagi for comparison, placing the center line at about 140" above ground. The Jagi base is 120" above ground, so the center lines are in crude alignment.

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Fig. 10 shows the comparative elevation patterns of the two antennas. Over ground, they both exhibit a maximum forward gain of about 10.3 dBi. As the traces show, the standard Yagi has a slightly smaller set of rearward lobes.

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As shown in Fig. 11, at an elevation angle of 6.2 degrees, both antennas share the same forward gain and beamwidth (about 110 degrees), typical of Yagis turned for vertically polarized use. The front-to-back ratios of the two antennas differ by only about 3 dB (17.4 vs. 20.3 dB), with the standard Yagi having the advantage. Considering the liberties I took in modeling the Jagi, the difference is neither unexpected nor operationally significant.

+

The standard Yagi had a feedpoint impedance in the neighborhood of 40 Ohms at 146 MHz, suitable for direct feed, but likely not for maximum bandwidth without some form of matching. In contrast, the Jagi had a design frequency impedance of almost exactly 50 Ohms. The band-edge 50-Ohm SWR values were 1.74:1 at 144 MHz and 1.83:1 at 148 MHz. The addition of the parasitic elements does affect the operating bandwidth of a J-pole used as its driver, but not sufficiently to prevent full band coverage on 2 meters. Fig. 12 shows the full 50-Ohm SWR curve.

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Yes, the Jagi is not only feasible, but is--as well--an interesting variation on the Yagi that solves the feedline dress question for many vertically polarized applications.

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Conclusion--Yes, THE Conclusion

One could go on almost indefinitely evaluating and analyzing J-pole designs and variations. The number of ways in which individuals have successfully constructed J-poles over the years probably exceeds the number of variations in almost any other antenna type. As well, numerous folks have developed variations on the feeding scheme for either standard or non-standard J-pole types to eliminate the need for pruning or adjusting the long and short legs and moving the standard J-pole feedpoint tap. +

As well, the collinear and parasitic J-pole applications that we examined only scratch the surface of what has been done and what might be done with the J-pole as the starting point. However, my interest in the J-pole was not to form a catalog of antennas to build. Instead, the goal has been to understand a bit better than I did before what is going on in the operation of a J-pole. These notes simply formalize a bit what I learned along the way.

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This conclusion does not mean that I shall never add to this series of notes. It simply means that for the moment, other antennas are exerting a stronger call.

+

However, I know of no other antenna that has its own limerick:

+ 
      I know a wonderful aerial:  the J-pole.
+      You can build one without stealing a payroll.
+        When you tune it to peak,
+        You'll hear signals so weak,
+      That from work you'll likely go AWOL.
+

Appendix 1: Linear-Element Equivalents to Long-Radiator Standard J-Poles

To verify the effects of elongating the standard J-pole radiator in terms of the modeled patterns, I examined a series of linear vertical elements. The closest equivalent linear element to a given J-pole antenna design would yield a free-space pattern very similar to the ones shown in Fig. 2, allowing for the non-symmetry of the J-pole patterns. I fed each linear equivalent element near the bottom, creating an off-center feed system as close to equaling the J-pole feed as possible. The exact position does not correspond to the length of the open-end match-section leg. Instead, it roughly equates with the effective length of the matching section legs as radiators, given the imbalance of current (considering both magnitude and phase angles) on those legs. Fig. 13 shows the general scheme of the equivalency test. +
+ +
+

The results of the test were interesting. The J-pole with a 5/8 wavelength radiator has a free space elevation (E-plane) pattern very similar to a linear element 3/4 wavelength long and fed about 5-10% up from the bottom, as shown in the top pattern of Fig. 14. The J-Pole with a 1 wavelength radiator shows a free-space elevation pattern very similar to that of a 1.25 wavelength linear element fed about 15-20% upward from the bottom. The middle pattern of Fig. 14 shows the result. Finally, the J-pole with a 1.25 wavelength radiator has a free-space elevation pattern very close to that of a 1.75 wavelength linear element fed 10-15% up from the bottom, as shown in the bottom plot.

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Compare the plots in Fig. 14 to those in Fig. 2. As well, compare the current distribution graphics in both figures. In all cases, the elements show zero current at the top end, with typical 1/2 wavelength current curves proceeding downward from the top. The variation in the normal curve occurs at or near the bottom end. In the linear elements, the current below the feedpoint describes a sharply tapering curve toward zero. The curves in this region and just above the feedpoint represent the equivalent linear element behavior of the corresponding J-pole within the matching-section region, given the specific current imbalance for each of the elongated models.

+

The lessons from this exercise are two. First, the imbalance of currents in the J-pole matching section make this section part of the total radiating system. Only in the case of the 1/2 wavelength radiator are the currents within the matching section sufficiently balanced to yield elevation patterns that are close enough to those of a center-fed linear element the same length as the radiator to allow us to generally ignore the matching section. As we saw in Fig. 2 of Part 3, if the wires are not very closely spaced--as with a twinlead J-pole--the resulting free-space pattern is offset from the horizontal plotting axis to be useless in determining antenna behavior. Elements as close together as 1" at 146 MHz are far enough apart to require that we perform all analyses above a ground. Hence, in the end, we cannot ignore the radiation from the matching section even for the classic J-pole with a 1/2 wavelength radiator.

+

Second, we cannot expect J-poles to perform like rough analogs of their radiator sections alone. The version with a 5/8 wavelength radiator does not perform like a 5/8 wavelength monopole with a ground plane system. The 1 wavelength and 1.25 wavelength radiator versions of the J-pole do not perform like elements of similar length in free-space when fed at their centers. The only correct equivalents of J-poles are ones that take into account the radiation from the matching section of the antenna.

+

Appendix 2: Non-Standard Long-Radiator J-Poles

+

All of the test models of long-radiator J-poles used standard J-pole configurations in the notes thus far. It is possible to develop a non-standard J-pole--that is, a J-pole with no shorting strap for the feed point, but instead a single feed point at the base strap--using longer than a 1/2 wavelength radiator. Consider the following published design for a 5/8 wavelength J-pole: The elements are 3/8" tube or rod, with the long radiator about 59.5" long and the short rod about 14.25" long. The rod spacing is about 6.375". As with all of our J-pole models, we shall place them about a wavelength above real ground for deriving patterns.

+

The resulting antenna will show a 50-Ohm SWR well under 2:1 across all of 2 meters and the adjacent CAP frequencies as well. However, as we saw in the last episode, very wide spacing tends to yield significant pattern distortion relative to the ideal of a circular azimuth pattern. See Fig. 15.

+
+ +
+

The pattern distortion ends up producing a pattern with a significant departure from an azimuth circle, and the higher angle of much of the radiation gives no more gain at the lowest lobe than we might obtain from a shorter non-standard J-pole. The gain at a 3.1-degree angle averages about 5.1 dBi, with peaks that are 70 degrees off a line made by the long and short radiator rods. The peak gain is 5.8 dBi. The gain in the direction of the short rod is 5.4 dBi, with a gain of only 3.7 dBi in the opposite direction.

+

The upshot is that the possibility of making a longer J-pole in non-standard form does not yield the benefits of lengthening a vertical monopole over a buried ground plane. The J-pole configuration tends to increase high angle radiation so as to negate the value of the added radiator length. The very wide spacing may give us some ease of construction, but it contributes as well to pattern distortion. A closer spaced standard or non-standard J-pole with a 1/2 wavelength radiator will perform as well with respect to low-angle gain and better with respect to pattern circularity.

+
+ +
+

Updated 1-8-2002; 2-4-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Go to Main Index

+

Topics: J-Pole, VHF / UHF, Vertical


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+

Preliminary Studies of Long-Boom Yagis for 420-450 MHz--Or
+ Fly Me to the Moon. . .

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

There are numerous long-boom Yagi designs, but little study of them using the latest antenna modeling software (NEC-4). This study is a small beginning of the process of analyzing the salient performance features of the various designs using models from my small collection. The effort arose from my own interest in determining if one might develop a "perfect" Yagi, and for this reason, it is strictly preliminary. The perfect Yagi does not yet exist.

+

Long-boom Yagis have an equally long history, but the late 1980s and the early 1990s are the period of the most rapid advances in their design. DL6WU, K1FO, DJ9BV, W1JR, and SM5BSZ are only some of the most noted calls associated with individual or families of Yagis susceptible to mathematical design algorithms. We shall sample efforts from each of these groundbreaking designers. Indeed, we shall sample 10 Yagis, 9 of which are long boom efforts, and one is an explanation of why these notes are only preliminary.

+

My procedures will be straightforward. I modeled each Yagi design using NEC-4. Some wide-band designs covering all or most of the 70-cm band required slight re-scaling to center the passband. In some instances, the designs had been optimized for one or the other end of the band. In a few cases, the initial model had used NEC-2. By the time we increase frequency to the 70-cm band, there is an offset between NEC-2 and NEC-4 amounting to 5-10 MHz. NEC-4 has revised algorithms for element ends and for the feedpoint split, and is considered more accurate in critical cases. To be fair to the potential of a given design, it was necessary--wherever possible--to so center a design within the band that the operating or 2:1 SWR bandwidth either is in the band or covers all of it and that the peak performance characteristics lie within the band. This latter factor allows anyone to re-scale an array's peak performance region to any desired portion of the band.

+

Since the models do not include conductive booms, the model descriptions appended to this study represent arrays whose elements are well insulated and isolated from any conductive boom. One can construct an array directly from the model adhering to those conditions. However, if alternative element diameters or alternative boom-mounting methods are required, the builder must apply appropriate compensation techniques. A summary of those techniques and some of the algorithms required for the work appear in "Scaling and Adjusting VHF/UHF Yagis" at my web site (..), with some of the techniques appearing in Chapter 7 of the RSGB volume The VHF/UHF DX Book, edited by Ian White, G3SEK.

+

For each array, I shall provide similar data. First comes a set of vital statistics giving both the physical size of the array and any special modeling notes, followed by an outline sketch of the antenna. Except for a couple of narrow-band designs, each antenna will have a table of modeled performance figures for 420, 435, and 450 MHz. The data will include both horizontal and vertical beamwidths and forward-to-sidelobe ratios in addition to the more expected gain and front-to-back ratios. Following each table will be sample E-plane and H-plane (free-space) patterns for the arrays. I shall add a frequency sweep of the gain and the 180-degree front-to-back ratio and another sweep of the resistance, reactance, and SWR curves. Finally, I shall add some commentary on the array, although the data itself should make most of the commentary obvious.

+

Because the long-boom Yagis come in various sizes with respect to both the number of elements and the overall boomlength, direct comparison from one design to the next is at best an uncertain enterprise. However, the aggregate results will permit us to draw a number of interesting conclusions about the present state of design and the future of long-boom Yagi design.

+

Evaluating Long-Boom Yagi Designs

Although somewhat tedious, the process of developing both physical and performance data on long-boom Yagis is very straightforward. Evaluatively interpreting that data is another matter. Evaluation often rests upon the intended communications task for which one creates a beam. Even within the confines of a given task, there is no fixed agreement on the order in which to place the various facets of Yagi performance. +

Forward gain and the front-to-back ratio (taken either as the 180-degree ratio or the worst-case front-to-back ratio) are the most common prime performance figures. Very often, beamwidth--both horizontal and vertical--are simply presumed and go unexamined. Until recently, the forward front-to-sidelobe ratio has been ignored. (See "Long-Boom Yagi Sidelobe Suppression" in the Proceedings of the 2002 Southeastern VHF Society, pp. 67-124, for a discussion of this topic.) Nonetheless, some aspects of overall pattern shape as it shifts from one end of the operating passband to the other require non-quantitative commentary at the present stage in the development of studies of long-boom Yagi performance.

+

It is possible to develop some ad hoc measures of Yagi size that permit a few comparisons and detection of some general trends. Therefore, we shall look at the element density of the designs, using the first 21 directors as a guide--since 21 directors comprise the shortest of the designs that we shall examine. We shall also take a measure of the gain-to-element ratio and the gain-to-boom-length ratio. We shall develop these numbers for either 432 MHz (for the narrow-band designs) or 435 MHz (for the wide-band designs). None of these figures has any long-term merit, but they do permit us to reach a few interesting conclusions about the designs at hand. We shall also look at the range of gain and the range of front-to-back ratios across the operating passband wherever these numbers are notable for the builder.

+

In the end, comparison and evaluation can only be suggestive and not authoritative, especially for the radio amateur. Every long-boom Yagi goes through two phases in amateur hands. First is the feeling that there is nothing superior to "this" beam as it passes its final tests and adjustments and is declared operational. After some use, the inveterate beam builder acquires the equally strong feeling that there must be a superior design that just has to be built. I shall reserve further general comments for the concluding section.

+

The tabular data on the performance for each array will include the following categories.

+
    +
  • Forward Gain (dBi): The free-space gain of the forward lobe.
    • +
  • 180-Deg F-B (dB): The 180-degree front-to-back ratio.
    • +
  • Worst-Case F-B (dB): The worst case front-to-back ratio relative to the entire rear
    • +
  • horizontal semi-circle.
    • +
  • Horiz. B-W (deg): The E-plane -3-dB beamwidth of the forward lobe.
    • +
  • Vert. B-W (deg): The H-plane -3-dB beamwidth of the forward lobe.
    • +
  • Horiz. F-SL (dB): The E-plane forward main-lobe-to-strongest-secondary-lobe ratio.
    • +
  • Vert. F-SL (dB): The H-plane forward main-lobe-to-strongest-secondary-lobe ratio.
    • +
  • Note: The notation (+B) indicates forward pattern bulges or merged lobes.
    • +
  • Feed Z (R+/-jX Ohms): The driven element feedpoint impedance.
    • +
  • SWR (n Ohms): The SWR relative to a given reference impedance.
    • +
+

1. A 32-Element DL6WU Yagi

Guenter Hoch, DL6WU, is perhaps the most noted designer of long-boom VHF and UHF Yagis. His work appears in its most developed form in Chapters 7 and 10 of The VHF/UHF DX Book. In addition, there are numerous programs for designing his beams, the most recent of which is an interesting EXCEL spreadsheet available from David Tanner, VK3AUU, whose own designs will appear later in this study. Since the algorithms describing the DL6WU beams are so well known, we may focus on the data instead of the theory. As with all succeeding data, any references to dimensions in wavelengths are for 432 MHz. + 
Basic Data:
+No. of Elements: 32                     Boom Length: 7505.2 mm or 10.81 WL
+Element Diameter: 4 mm                  Model Segmentation: 19 segments/element
+Element Density: .00454 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              18.07                   19.75                   19.21
+180-Deg F-B (dB)                20.61                   25.28                   29.35
+Worst-Case F-B (dB)     20.61                   25.28                   23.44
+Horiz. B-W (deg)                23.0                    19.8                    18.6
+Vert. B-W (deg)         23.6                    20.2                    19.0
+Horiz. F-SL (dB)                13.52                   16.46                   21.76 (+B)
+Vert. F-SL (dB)         12.31                   15.44                   19.20 (+B)
+Feed Z (R+/-jX Ohms)    49.96 - j 9.24          52.24 + j 4.98          39.83 + j 9.64
+SWR (50 Ohms)           1.203                   1.113                   1.367
+
+435-MHz Gain/Element:                   0.617
+435-MHz Gain/Boom Length (WL):          1.827
+
+ +
+
+ +
+
+ +
+

The gain of the wide-band DL6WU array varies by over 1.8 dB across the band, with the peak gain at 440 MHz. Near-peak gain and maximum front-to-back ratio coincide at 438 MHz. For narrow-band use, one may re-scale the array from about 438 MHz to the desired operating frequency within the 70-cm band. Since the frequency sweeps are at 2-MHz intervals, some peaks do not appear. Flattened curves normally mean that a peak value occurs between the point of the flattened line.

+

The change in the pattern shape--especially evident in the H-plane patterns--as we move across the band reflects the changing roles of the driver and the first director. As we increase frequency, the myriad of secondary lobes shifts rearward as the current magnitude on the first director exceeds that on the driver itself, making the first director a slaved driver for the array. This phenomenon is a common feature of almost all wide-band Yagi arrays.

+

The front-to-sidelobe ratio of the DL6WU array is fairly low--well under 20 dB--for all but the last 5 MHz of the band. Again, in common with many wide-band arrays, the first forward sidelobes become bulges on the main lobe, changing its shape from a "tear drop" into a "bullet." Hence, at 450 MHz, the first distinct forward sidelobe is actually the second forward sidelobe in both the E-plane and the H-plane.

+

The DL6WU array, at whatever length the builder chooses, has become a sort of touchstone against which to measure virtually all long-boom Yagis. Its wide bandwidth, easy scaling, and generally good performance for any number of elements from about 10 upward have made this array popular. Perhaps the strongest reservation concerns the relatively low front-to-sidelobe performance, but the DL6WU array is not alone in this difficulty.

+

2. A 31-Element HyGain/W1JR Yagi

When I picked up the following HyGain Yagi design from their former web site, Joe Reisert, W1JR, wrote me to note that he had done the original design for the company. I have adapted the model to 4-mm elements from the original HyGain model that used 3/16" elements (0.1575" vs. 0.1875"). The SWR curve proved smoother using the 4-mm elements. W1JR has published other long-boom Yagi designs in various journals, so this sample is but one expression of his work over the years. The element density is roughly similar to that of the DL6WU design, although the arrangement of elements differs. See the appended model descriptions for details of the director placement. With respect to the reflector, driver, and first director arrangement, DL6WU wide-band designs use element spacings of 0.20 wavelength and 0.075 wavelength for these rearmost elements. The W1JR design uses spacings of 0.178 wavelength and 0.0715 wavelength to achieve its feedpoint impedance control. The long-boom Yagi designer has a wide variety of reflector/driver/first-director arrangements from which to choose, even within the category of 50-Ohm driven elements. + 
Basic Data:
+No. of Elements: 31                     Boom Length: 6990.0 mm or 10.07 WL
+Element Diameter: 4 mm                  Model Segmentation: 19 segments/element
+Element Density: .00471 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              17.23                   18.97                   19.60
+180-Deg F-B (dB)                20.64                   32.41                   23.77
+Worst-Case F-B (dB)     20.51                   26.40                   23.77
+Horiz. B-W (deg)                25.2                    22.4                    20.2
+Vert. B-W (deg)         26.2                    23.0                    20.8
+Horiz. F-SL (dB)                13.31                   16.95                   19.45
+Vert. F-SL (dB)         11.99                   15.72                   18.40
+Feed Z (R+/-jX Ohms)    40.81 - j14.01          46.99 - j 8.68          29.65 - j 7.17
+SWR (50 Ohms)           1.446                   1.208                   1.739
+
+435-MHz Gain/Element:                   0.612
+435-MHz Gain/Boom Length (WL):          1.883
+
+ +
+
+ +
+
+ +
+

The HyGain/W1JR array has characteristics quite similar to those of the DL6WU version. The gain peaks high in the overall passband at 19.64 dBi, although the shorter boom and 1-smaller element count results in a 2.4-dB range of gain across the band. The 180-degree front-to-back ratio shows peaks, although the worst-case value remains fairly constant above the low end of the band. The 50-Ohm SWR is not as uniformly low as in the DL6WU wide-band array, but the values are generally acceptable. However, the SWR begins to climb in the region of highest gain.

+

As one might expect, the gain per boom length unit is higher, but the gain per element is lower. Overall, the element density is similar to that of the DL6WU design, even though the element placement differs between the two designs. As we shall gradually discover, element density has a role to play in the more general pattern shape. The present sample has front-to-sidelobe ratios very comparable to those of the DL6WU Yagi. Finally, the beamwidth across the band is slightly wider than one might generally expect from a reduction in element count of only 1 and a boom reduction of only 7% relative to our first sample Yagi.

+

Nevertheless, one can re-scale the array for any desired frequency within the passband in order to maximize performance in that region. If operation above that frequency is necessary, the next step would be to adjust the reflector, driver, and first director lengths and spacing to achieve an acceptable feedpoint impedance.

+

3. A 27-Element DJ9BV Yagi

Rainer Bertelsmeier, DJ9BV, championed the use of a multiple-reflector Yagi, claiming better performance. The sample that I have uses 27 elements, but 4 of them are reflector elements set out in a flat plane perpendicular to the remaining elements. Hence, the array has only 22 directors. The natural presumption is that the added reflectors will enhance the front-to-back ratio. However, if the flat-plane reflectors assist the array, it is more likely in the gain category. Both operating bandwidth and the front-to-back ratio tend to degrade relative to our first two sample arrays. + 
Basic Data:
+No. of Elements: 27                     Boom Length: 5295.0 mm or 7.63 WL
+Element Diameter: 4.6 mm                        Model Segmentation: 19 segments/element
+Element Density: .00434 elements/mm of boomlength
+
+
+
+ +
+ 
+
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              17.52                   18.74                   17.43
+180-Deg F-B (dB)                19.00                   22.59                   16.94
+Worst-Case F-B (dB)     19.00                   22.59                   16.94
+Horiz. B-W (deg)                25.6                    22.2                    21.6
+Vert. B-W (deg)         26.6                    23.0                    22.4
+Horiz. F-SL (dB)                15.49                   17.25                   20.77 (+B)
+Vert. F-SL (dB)         13.76                   15.45                   18.25 (+B)
+Feed Z (R+/-jX Ohms)    37.66 - j26.66          36.30 - j19.92          25.18 - j22.46
+SWR (50 Ohms)           1.994                   1.751                   2.488
+
+435-MHz Gain/Element:                   0.694
+435-MHz Gain/Boom Length (WL):          2.546
+
+ +
+
+ +
+
+ +
+

I set the dimensions of the DJ9BV array for mid-band to test the overall operating bandwidth. The design falls somewhere between a narrow-band and a wide-band design, covering about 2/3 of the 70-cm band with acceptable front-to-back ratio and 50-Ohm SWR values. However, with judicious revision of the reflector/driver/first-director region, one might improve the SWR curve considerably. The array arose in an era still wedded to the folded dipole driven element as a means of maximizing gain while establishing a 50-Ohm SWR curve.

+

Relative to our first two samples, the overall pattern shape shows improvements to the front-to-sidelobe ratio. However, the 450-MHz pattern has bulges that one likely should not ignore and which show a melding of the main lobe and the first forward sidelobes. Hence, the high front-to-sidelobe ratio at that frequency has dubious value.

+

The gain peaks between 435 and 440 MHz, although the front-to-back ratio peaks at a lower frequency. The high levels of gain per unit of boom length and per element have two facets. First, they are naturally higher than the longer arrays with more directors. However, they are especially high, given that the director count is so low relative to the overall design. The design ultimately shows that by narrowing the operating passband, one can achieve a higher gain figure with fewer elements.

+

Nonetheless, as we shall see in a later sample, there may be better configurations for multiple reflectors in order to suppress forward sidelobes more effectively, especially in the H-plane.

+

4. A 40-Element K1FO Yagi

Steve Powlishen, K1FO, has developed a series of VHF and UHF Yagis that ARRL has featured in the Antenna Book for several editions. (See pp. 18-21 through 18-32 in the 19th edition.) One of the strong merits of his work is that he provides both basic information and detailed adjustments for constructed versions, thus guiding the builder in great detail. The sample that we shall explore here is a 40-element free-space version, that is, a modeled version with no correctives for a system of element-to-boom mounting. + 
Basic Data:
+No. of Elements: 40                     Boom Length: 9251.9 mm or 13.33 WL
+Element Diameter: 4.7 mm                        Model Segmentation: 19 segments/element
+Element Density: .00506 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              19.06                   20.80                   20.48
+180-Deg F-B (dB)                21.89                   32.81                   23.55
+Worst-Case F-B (dB)     21.86                   29.93                   23.55
+Horiz. B-W (deg)                20.8                    18.2                    16.4
+Vert. B-W (deg)         21.4                    18.4                    16.6
+Horiz. F-SL (dB)                13.52                   15.97                   24.77 (+B)
+Vert. F-SL (dB)         12.58                   15.16                   22.79 (+B)
+Feed Z (R+/-jX Ohms)    27.43 - j12.56          31.05 - j 0.89          20.73 + j11.47
+SWR (28 Ohms)           1.568                   1.114                   1.744
+
+435-MHz Gain/Element:                   0.520
+435-MHz Gain/Boom Length (WL):          1.560
+
+ +
+
+ +
+
+ +
+

The gain factors of the K1FO design naturally decrease relative to earlier sample designs, since the addition of each new director shows a decreasing increment of gain advance. However, the array shows better than 20-dBi free-space gain over more than half the 70-cm band, with peak gain appearing in the 440-442-MHz region. By now, it should be apparent that standard wide-band long-boom Yagi design has this characteristic. Both the 180-degree and the worst-case front-to-back ratios are better than 21 dB across the band.

+

The gain advance in the long K1FO design is offset partially by generally poorer suppression of the forward side lobes. Indeed, relative to forward sidelobe suppression, the best region of operation appears to be at the upper end of the band, where the pattern takes on the bullet shape, but the narrow beamwidth tends to ameliorate the effect of the bulges created by merged forward lobes. In this case, there may be two sets of forward lobes merged with the main lobe. In concert with the earliest of our samples, as we increase the operating frequency within the design passband, the front-to-side ratio at about 90 degrees to the main lobe decreases, as the first director takes greater control of the current distribution in the directors.

+

Although the K1FO design has relatively wide operating characteristics, with less than 2-dB change in gain across the band, there is one troublesome aspect to the design. The low design feedpoint impedance--between 25 and 30 Ohms--doubles the losses incurred by any less-than-perfect mechanical junctions at the feedpoint. Models do not analyze the reduction in gain occasioned by such losses. Hence, it becomes important for the user to perform tests and analyses that will determine the total power loss of these factors. The division of power between the radiation antenna and the losses always degrades as we lower the feedpoint impedance. Folded dipoles do not cure the problem, since the impedance transformation includes loss as well as radiation resistance. The ultimate cure, beyond perfecting every mechanical connection in the system, lies in minimizing the number of such connections.

+

5. A 26-Element SM5BSZ Yagi

Although wide-band Yagis offer advantages in terms of replication ease and the ability to move a selected operating point to a desired frequency, they do not obtain the maximum gain from a given number of elements. Lief Asbrink, SM5BSZ, has developed (among his many contributions to VHF and UHF work) a narrow-band long-boom Yagi. He uses 26 elements on a 7429-mm boom, that is, 6 fewer elements on the same boom length used in the DL6WU array that we explored at the beginning. The cost of the exercise is a beam with a very narrow operating bandwidth. In fact, the design is not much good only a couple of MHz away from the 432-MHz design frequency. But at that frequency, it shines. +

In part, the effectiveness of the design stems from the use of fatter than usual elements: 10 mm. As well, note the lower density level of the elements in the following table of basic data. Within the performance data--given only for 432 MHz--note the relatively high values of the gain per element figure and the gain per wavelength of boom figure. Because the array is for narrow-band use, the pattern data will only be for 432 MHz, and the performance graphs will cover only 430-434 MHz.

+ 
Basic Data:
+No. of Elements: 26                     Boom Length: 7429.4 mm or 10.70 WL
+Element Diameter: 10 mm                 Model Segmentation: 19 segments/element
+Element Density: .00353 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        432
+Forward Gain (dBi)              20.52
+180-Deg F-B (dB)                21.29
+Worst-Case F-B (dB)     21.26
+Horiz. B-W (deg)                18.0
+Vert. B-W (deg)         18.4
+Horiz. F-SL (dB)                17.14
+Vert. F-SL (dB)         16.21
+Feed Z (R+/-jX Ohms)    36.69 - j 1.36
+SWR (37 Ohms)           1.038
+
+435-MHz Gain/Element:                   0.789
+435-MHz Gain/Boom Length (WL):          1.916
+
+ +
+
+ +
+
+ +
+

It is likely that only a master antenna builder may replicate this antenna adequately, especially if one must make adjustments for the method of element-to-boom mounting. However, the array does illustrate how much gain one may squeeze out of the least number of elements on a given boom length. As well, comparing this array's peak performance to the wide-band arrays of relevantly similar lengths, we can obtain some idea of how much performance at a given frequency that we sacrifice to obtain the wide-band characteristics designed into those arrays. These are aspects of array performance too little appreciated by many operators trying to decide upon an array for a given task. In the end, if one builds the antenna oneself, the final decision must be a considered balance of the desired performance level vs. the degree of difficulty in replicating a design, with an honest consideration of one's shop skills and tools. Since SM5BSZ is "in the industry," he undoubtedly has access to the finest fabrication tools and has a track record that suggests his skills are unsurpassed.

+

6. A 43-Element VE7BQH Yagi

VE7BQH, Lionel Edwards, developed a "ladder" array that Bill Buchanan, WB4WEN, brought to my attention. To provide some basis for comparison, I adapted the design to the 70-cm band, although that was not its original band. As a result, the model that we shall explore uses a wire diameter close to that of AWG #18 wire. (Re-scaled for the 220-MHz band, the wire size would approximate #12.) One must picture the structure of the antenna as two ropes with wire elements between them. This array is the longest in the collection we are examining, both in terms of the number of elements and in terms of boom length. However, its element density is similar to the values obtained from the DL6WU and W1JR arrays. Unlike all of the other Yagis in this collection, it does not use aluminum tubing, but instead employs copper wire. Like the SM5BSZ entry, we shall restrict our glimpse to its design frequency, 432 MHz, although we shall extend the performance sweeps to include 428 to 441 MHz. The reference impedance for the SWR curve is 28 Ohms. + 
Basic Data:
+No. of Elements: 43                     Boom Length: 10042.1 mm or 14.47 WL
+Element Diameter: 1.1 mm                Model Segmentation: 19 segments/element
+Element Density: .00499 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        432
+Forward Gain (dBi)              20.95
+180-Deg F-B (dB)                30.26
+Worst-Case F-B (dB)             29.93
+Horiz. B-W (deg)                15.2
+Vert. B-W (deg)         15.4
+Horiz. F-SL (dB)                13.55
+Vert. F-SL (dB)         12.87
+Feed Z (R+/-jX Ohms)    31.66 - j13.84
+SWR (28 Ohms)           1.610
+
+435-MHz Gain/Element:                   0.487
+435-MHz Gain/Boom Length (WL):          1.448
+
+ +
+
+ +
+
+ +
+

Although the original 2-meter version of this array was designed to solve the boom-length problem at that lower frequency region, the 70-cm version that I have modeled gives us an example of what we can do with wire. Although it is much longer than the SM5BSZ narrow-band array, the VE7BQH Yagi uses very thin elements. Element diameter and the level of mutual coupling between elements play important roles in developing gain from a given arrangement of elements. I am often surprised by the number of arrays that I encounter where one or more directors are almost inactive. If you wish to hand optimize a Yagi design, pay close attention to the current levels on each element and watch for pattern changes as the levels vary during your adjustments. Of course, we can monitor current on all elements of a Yagi more easily in models than we can with physical elements.

+

The SM5BSZ and the VE7BQH Yagis are two radically different approaches to narrow-band Yagi design. Both produce high gain, but both are deficient in terms of overall pattern shape, especially with respect to the suppression of side lobes. Perhaps other design approaches can yield somewhat better results.

+

7. A 41-Element VK3AUU Yagi

David Tanner, VK3AUU has done some extensive design work in a somewhat different direction from the one taken by other designers of wide-band Yagis. First, he has striven to improve--at least for part of the operating passband--the overall pattern shape, including the suppression of forward sidelobes. Second, he has attempted to optimize the spacing of the reflector, driver, and first director in an interesting manner to achieve a very low 50-Ohm SWR across the passband--that is, all of the 70-cm band. Although the effort is related to the WA3FET/NW3Z techniques for the optimized wideband antenna set-up (OWA), there are certain distinct features to the VK3AUU design. +

DL6WU used spacings of 0.200 and 0.075 wavelength, respectively, for the reflector/driver and driver/first-director. Most other designers have followed suit, with minor variations in the reflector/driver spacing, but with a driver/first-director spacing above 0.075. The typical OWA array will use a reflector/driver spacing of just over 0.1 wavelength, with a driver/first-director spacing in the vicinity of about 0.055 wavelength. Of course, the exact spacings depend to some extent upon the length-to-diameter ratio of the elements in order to achieve a smooth 50-Ohm SWR curve with maximum values under about 1.3:1 across a passband. On a band as wide as 70 cm, obtaining the desired curve with normal element diameters (1/8" to 1/4") is not easy. As well, the second and third directors of a standard OWA configuration have roughly equal lengths.

+

VK3AUU employs a wider reflector/driver spacing (0.19-0.20 wavelength) together with a very narrow driver/first-director spacing (0.033 to 0.038 wavelength) to obtain very broad SWR curves. The models that we shall examine are adapted from 2-meter versions, and the elements have been standardized at a 4-mm diameter. We shall start with a planar Yagi having 41 elements.

+ 
Basic Data:
+No. of Elements: 41                     Boom Length: 7723.3 mm or 11.13 WL
+Element Diameter: 4 mm                  Model Segmentation: 19 segments/element
+Element Density: .00622 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              18.56                   19.73                   19.67
+180-Deg F-B (dB)                22.30                   26.35                   25.17
+Worst-Case F-B (dB)     22.30                   26.35                   25.17
+Horiz. B-W (deg)                22.8                    20.6                    19.8
+Vert. B-W (deg)         23.6                    21.2                    20.2
+Horiz. F-SL (dB)                15.74                   19.52                   17.51
+Vert. F-SL (dB)         14.57                   18.51                   16.26
+Feed Z (R+/-jX Ohms)    49.14 - j 4.41          50.56 - j 1.41          44.39 - j 3.53
+SWR (28 Ohms)           1.095                   1.031                   1.150
+
+435-MHz Gain/Element:                   0.481
+435-MHz Gain/Boom Length (WL):          1.773
+
+ +
+
+ +
+
+ +
+

One feature that the VK3AUU design shares in common with standard OWA techniques is the ability to center the performance characteristics of an array within an operating passband. Although not completely centered, the gain curve peaks at about 440 MHz, lower than most other wide-band designs.

+

The forward sidelobe suppression is not yet a full-band phenomenon. Rather, it peaks in the center third of the band and tapers off on either side of that region. Suppression is nearly 20 dB in the E-plane and slightly less in the H-plane. The suppression is superior to other wide-band designs in this study at 420 MHz. Unfortunately, the change of pattern in those designs from a teardrop to a bullet defeats an effective comparison at 450 MHz. However, it is notable that the VK3AUU design retains its tear drop pattern throughout the 70-cm band.

+

One key to the improvement of pattern shape is the higher element density used by VK3AUU. The element density of 0.00622 elements per mm is about 23% higher than the next most dense array (0.00506) in the collection of Yagis that we have so far studied. The boom length is barely longer than the DL6WU design, but VK3AUU includes 9 more elements, resulting in closer element spacing and consequential increases in element-to-element coupling. Since the weight of the elements is not a major factor in UHF arrays, adding more elements for a given boom length in order to improve pattern shape shows up mostly in fabrication time. The gain levels are equal or superior to those of the DL6WU array, with only a 1.3-dB variation across the 70-cm band.

+

8. A 32-Element VK3AUU Yagi With Added Reflectors

VK3AUU adapted the reflector scheme that I described in the sidelobe suppression study to his basic element scheme in an effort to further reduce forward sidelobes, especially in the H-plane. The result is a 32-element array with 3 reflectors and 28 directors on a 5500-mm boom. (Once more, my model is a 70-cm re-scaling of the designer's 2-meter array.) The 2 added directors are angled slightly to the rear of the normal reflector and produce significant results. In the original design using OWA techniques, I set the reflectors to have minimal effects on the feedpoint impedance relative to a basic array that used only 1 reflector. VK3AUU has chosen to slightly modify the rearmost elements to achieve the same results. The dimensions appear in the model descriptions appended to this study. + 
Basic Data:
+No. of Elements: 32                     Boom Length: 5464.5 mm or 7.87 WL
+Element Diameter: 4 mm                  Model Segmentation: 19 segments/element
+Element Density: .00595 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              17.98                   18.45                   18.08
+180-Deg F-B (dB)                27.98                   35.41                   31.97
+Worst-Case F-B (dB)     25.33                   32.65                   31.97
+Horiz. B-W (deg)                25.4                    23.6                    23.0
+Vert. B-W (deg)         26.4                    24.4                    23.8
+Horiz. F-SL (dB)                19.59                   23.02                   22.26
+Vert. F-SL (dB)         17.87                   21.18                   20.04
+Feed Z (R+/-jX Ohms)    44.81 - j11.26          46.02 - j 5.89          39.94 + j 2.43
+SWR (28 Ohms)           1.299                   1.160                   1.438
+
+435-MHz Gain/Element:                   0.577
+435-MHz Gain/Boom Length (WL):          2.343
+
+ +
+
+ +
+
+ +
+

In this array, the gain curve is almost perfectly centered in the overall passband. However, the patterns at 450 MHz have degraded slightly so that they are approaching the bullet shape that merges forward sidelobes into the main pattern. In some sense, then, the development of this offshoot array is not fully complete.

+

Nevertheless, the array improves both horizontal and vertical front-to-sidelobe ratios by over 4 dB relative to the 41-element planar array that we just examined. Except for the lowest portion of the band, the front-to-sidelobe ratio is better than 20 dB. The only other array with a similar boom length is the DJ9BV Yagi with its plane of 4 reflectors. The VK3AUU array with its "tilt-back" reflector system achieves nearly 6 dB better front-to-sidelobe ratios with only about 0.5 dB gain variation across the passband and comparable gain levels to the DJ9BV Yagi. The improvements accrue not only to the redesign of the added reflectors in accord with principles I laid out in the sidelobe suppression study, but as well to the increased element density. For similar boom lengths, the VK3AUU Yagi employs 6 additional directors.

+

9. A 12-Element OWA Yagi

We now come to the point of showing why the present study is preliminary. The search for a "perfect" Yagi includes not only the standard operating parameters of gain, front-to-back ratio, and SWR bandwidth. As well, it encompasses pattern shape. Pattern shape refers partly to the visual shape, that is, the ideal tear drop pattern. It also refers partly to the suppression of all sidelobes to the degree feasible. +

To set a reference point for such a shape, I am adding to this study a Yagi design that is not a long-boom array as defined by the preceding examples. Indeed, the boom is under 3 wavelengths. The design is an OWA array scaled and adjusted from past 2-meter examples, but with 4-mm diameter elements. Stretching the 2-meter passband to cover the 70-cm band requires considerable adjustment, since the 4 MHz of 2 meters is only 12 of the 30 MHz of 70 cm. Still, it is a possible task.

+ 
Basic Data:
+No. of Elements: 12                     Boom Length: 1997.7 mm or 2.88 WL
+Element Diameter: 4 mm          Model Segmentation: 19 segments/element
+Element Density: .00601 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              13.16                   14.08                   13.95
+180-Deg F-B (dB)                20.51                   23.59                   20.06
+Worst-Case F-B (dB)             20.51                   23.59                   20.06
+Horiz. B-W (deg)                41.8                    38.4                    35.6
+Vert. B-W (deg)         47.2                    42.5                    39.2
+Horiz. F-SL (dB)                20.81                   27.70                   23.63
+Vert. F-SL (dB)         15.96                   18.60                   15.31
+Feed Z (R+/-jX Ohms)    31.32 + j 5.34          48.76 + j14.78          30.05 - j 1.62
+SWR (28 Ohms)           1.626                   1.349                   1.666
+
+435-MHz Gain/Element:                   1.173
+435-MHz Gain/Boom Length (WL):          4.890
+
+ +
+
+ +
+
+ +
+

Translating the 2-meter 12-element OWA Yagi to 70 cm has left some work yet to be done. The gain curve is not fully centered in the passband. As well, although the SWR curve has the characteristic OWA shape, the band-edge values are higher than desired. Moreover, the average value of the resistive component of the impedance might be increased slightly.

+

Nevertheless, the horizontal front-to-sidelobe ratio is greater than 20 dB across the band. As with the 2-meter version of this Yagi, the vertical front-to-sidelobe values lag seriously behind, although adding tilt-back reflectors would effect considerable improvement. The pattern shapes are consistently tear-drop across the band, although there is a bit of evidence at 420 MHz of main and sidelobe merging.

+

The use of this short-boom array (as measured on the 70-cm band) is to set a quasi-standard. The array shows what can be done across the band, especially with respect to pattern shape and horizontal sidelobe suppression. Although the VK3AUU 41-element array achieves equivalent horizontal sidelobe suppression for part of the band, it does not sustain that level of suppression across the entire band. Hence, there is further work to be done.

+

10. A 41-Element Hybrid OWA/VK3AUU Yagi

One key element in the OWA Yagi's ability to suppress horizontal sidelobes is the construction of the entire 5-element main cell of the array. The rearmost 3 elements largely set the feedpoint impedance and bandwidth. However, the 2nd and 3rd directors--sometimes called stabilizing directors--are of equal or near equal length. Together with the elements to the rear, they provide a pattern-shaping effect that contributes to the sidelobe suppression. The VK3AUU 41-element Yagi achieves its results in part due to the element density. Perhaps it might be possible to create a hybrid using the first 5 elements from the OWA array and elements 6-41 of the VK3AUU array. With some adjustments, the result is our final design of the study. The question is whether we can use this technique to create a design with all of the desired properties of a nearly perfect Yagi. + 
Basic Data:
+No. of Elements: 41                     Boom Length: 7727.3 mm or 11.14 WL
+Element Diameter: 4 mm                  Model Segmentation: 19 segments/element
+Element Density: .00621 elements/mm of boomlength
+
+
+
+ +
+ 
+
+Basic Performance Data: Frequency
+Category                        420                     435                     450
+Forward Gain (dBi)              18.31                   19.36                   19.24
+180-Deg F-B (dB)                27.18                   28.78                   30.36
+Worst-Case F-B (dB)     27.18                   28.78                   25.35
+Horiz. B-W (deg)                22.6                    20.4                    20.0
+Vert. B-W (deg)         23.4                    21.0                    20.4
+Horiz. F-SL (dB)                16.01                   20.57                   16.67
+Vert. F-SL (dB)         14.87                   19.59                   15.37
+Feed Z (R+/-jX Ohms)    46.14 - j 5.15          45.42 + j 2.34          45.64 + j 5.38
+SWR (28 Ohms)           1.143                   1.114                   1.156
+
+435-MHz Gain/Element:                   0.472
+435-MHz Gain/Boom Length (WL):          1.738
+
+ +
+
+ +
+
+ +
+

The hybrid array achieves about 1 dB of further sidelobe suppression over the original VK3AUU 41-element Yagi, but the suppression is not close to uniform across the entire band. As well, the gain has suffered a small decrease, although this is both marginal and expected relative to the OWA core of elements. As well, the gain curve is not well centered, but parallels the curve for the original VK3AUU beam design. The front-to-back ratio--taken as either the 180-degree or the worst-case value--is smoother across the band. Hence, the results of the experiment are mixed, with some improvements and some deficiencies, but all at the margins of the performance of the 41-element VK3AUU Yagi.

+

In a more important sense, the experiment is a major failure. The creation of a hybrid array did not provide smooth sidelobe suppression all across the 70-cm band, as in the case of the small 12-element Yagi. However, this result was not wholly unexpected. The family of OWA Yagis for 2-meters grew in length by a complex procedure of adding one element at a time and adjusting it and the preceding director to achieve the desired combination of pattern shape, gain curve, and SWR curve. So far, I have uncovered no algorithm to automate this process. The spacing for each additional element is variable, and it may even be the case that the usual rule, by which we place a new director at an equal or greater space than the preceding one, might require discarding.

+

The entire study, then is preliminary, because much more work remains ahead in the search for the nearly perfect Yagi.

+

Conclusions (So Far)

We may summarize the results of this preliminary study in the following set of entries in our notebooks. +

Gain: We may obtain forward gain with an adequate front-to-back ratio in a variety of ways, depending on the operating bandwidth that we desire. The SM5BSZ array shows how to do this with a minimum number of fat elements for a given boom length, while the long VE7BQH ladder Yagi shows how to replicate the gain using thin wire. For wide bandwidths, there is little to choose among the DL6WU, W1JR, or K1FO arrays--adjusted for similar boom lengths and number of elements--except for certain preferences of feedpoint impedance or other minor factors.

+

Operating Bandwidth: For most long-boom UHF Yagi operations, bandwidth is not a major concern, since operations tend to cluster near certain specific frequencies. However, for the home beam builder, a wide bandwidth offers greater assurance of successful replication of a given design, as well as ease of scaling the array from an initial design frequency to the one specifically desired. As well, it is more likely that the recalculation of elements for new element diameters or for insulated through-boom mounting will result in a working array whose performance is close to the values reported by the initial model.

+

Modeling: Almost all of the models in this study require more than 500 total segments to achieve adequate convergence of results. As well, for serious design work at UHF frequencies, NEC-4 is the modeling core of choice to avoid the frequency offset of NEC-2. (Even the best version of MININEC tend to calibrate the necessary frequency corrections to NEC-2. Hence, before using any MININEC program for serious UHF array design, be sure to calibrate it to NEC-4.) The upshot is that serious design efforts require a serious investment in software and the licenses that may go with a package.

+

Pattern Shape: The most interesting challenge yet to be faced in the improvement of long-boom Yagis lies in the area of achieving a consistent tear-drop pattern across the 70-cm band with improved forward sidelobe suppression. Initial experiments suggest that increased element density can go some distance toward this goal, but that element density alone may not achieve results that cover the entire band. Hence, there are an unlimited number of experiments that await us in the arena of using variable element spacing to see if we can extend the consistent E-plane patterns of shorter Yagis to long-boom arrays. Once we have reached the goal for E-plane patterns, improving the H-plane patterns should be straightforward through the use of added tilt-back reflectors.

+

In the end, I can do little better than to repeat myself: much more work remains ahead in the search for the nearly perfect long-boom Yagi.

+
+

Appendix: EZNEC Model Descriptions of Yagis Used in This Study

+
+ 
+=============================================================================
+
+1.  DL6WU 32 el 435 MHz                Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,170.300,  0.000         0.000,-170.30,  0.000 4.00E+00  19
+2          138.800,165.000,  0.000       138.800,-165.00,  0.000 4.00E+00  19
+3          190.800,150.800,  0.000       190.800,-150.80,  0.000 4.00E+00  19
+4          315.800,149.600,  0.000       315.800,-149.60,  0.000 4.00E+00  19
+5          465.000,147.800,  0.000       465.000,-147.80,  0.000 4.00E+00  19
+6          638.400,146.100,  0.000       638.400,-146.10,  0.000 4.00E+00  19
+7          832.800,144.600,  0.000       832.800,-144.60,  0.000 4.00E+00  19
+8          1040.90,143.200,  0.000       1040.90,-143.20,  0.000 4.00E+00  19
+9          1259.50,142.100,  0.000       1259.50,-142.10,  0.000 4.00E+00  19
+10         1488.60,141.100,  0.000       1488.60,-141.10,  0.000 4.00E+00  19
+11         1728.00,140.200,  0.000       1728.00,-140.20,  0.000 4.00E+00  19
+12         1977.80,139.400,  0.000       1977.80,-139.40,  0.000 4.00E+00  19
+13         2238.00,138.700,  0.000       2238.00,-138.70,  0.000 4.00E+00  19
+14         2508.70,138.000,  0.000       2508.70,-138.00,  0.000 4.00E+00  19
+15         2786.30,137.400,  0.000       2786.30,-137.40,  0.000 4.00E+00  19
+16         3063.90,136.900,  0.000       3063.90,-136.90,  0.000 4.00E+00  19
+17         3341.40,136.400,  0.000       3341.40,-136.40,  0.000 4.00E+00  19
+18         3619.00,135.900,  0.000       3619.00,-135.90,  0.000 4.00E+00  19
+19         3896.60,135.400,  0.000       3896.60,-135.40,  0.000 4.00E+00  19
+20         4174.20,135.000,  0.000       4174.20,-135.00,  0.000 4.00E+00  19
+21         4451.80,134.600,  0.000       4451.80,-134.60,  0.000 4.00E+00  19
+22         4729.40,134.200,  0.000       4729.40,-134.20,  0.000 4.00E+00  19
+23         5007.00,133.800,  0.000       5007.00,-133.80,  0.000 4.00E+00  19
+24         5284.50,133.500,  0.000       5284.50,-133.50,  0.000 4.00E+00  19
+25         5562.10,133.100,  0.000       5562.10,-133.10,  0.000 4.00E+00  19
+26         5839.70,132.800,  0.000       5839.70,-132.80,  0.000 4.00E+00  19
+27         6117.30,132.500,  0.000       6117.30,-132.50,  0.000 4.00E+00  19
+28         6394.90,132.250,  0.000       6394.90,-132.25,  0.000 4.00E+00  19
+29         6672.50,131.950,  0.000       6672.50,-131.95,  0.000 4.00E+00  19
+30         6950.10,131.650,  0.000       6950.10,-131.65,  0.000 4.00E+00  19
+31         7227.60,131.400,  0.000       7227.60,-131.40,  0.000 4.00E+00  19
+32         7505.20,131.150,  0.000       7505.20,-131.15,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+2. HyGain/W1JR 432 31 el                      Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,167.290,  0.000         0.000,-167.29,  0.000 4.60E+00  19
+2          122.738,162.653,  0.000       122.738,-162.65,  0.000 4.60E+00  19
+3          172.028,151.925,  0.000       171.905,-151.93,  0.000 4.60E+00  19
+4          294.763,148.832,  0.000       294.763,-148.83,  0.000 4.60E+00  19
+5          438.765,145.739,  0.000       438.765,-145.74,  0.000 4.60E+00  19
+6          607.891,144.193,  0.000       607.898,-144.19,  0.000 4.60E+00  19
+7          794.413,142.742,  0.000       794.413,-142.74,  0.000 4.60E+00  19
+8          997.366,140.425,  0.000       997.366,-140.43,  0.000 4.60E+00  19
+9          1209.02,138.491,  0.000       1209.02,-138.49,  0.000 4.60E+00  19
+10         1430.33,138.491,  0.000       1430.33,-138.49,  0.000 4.60E+00  19
+11         1663.25,136.944,  0.000       1663.25,-136.94,  0.000 4.60E+00  19
+12         1905.82,135.398,  0.000       1905.82,-135.40,  0.000 4.60E+00  19
+13         2157.09,134.624,  0.000       2157.09,-134.62,  0.000 4.60E+00  19
+14         2412.24,134.239,  0.000       2412.24,-134.24,  0.000 4.60E+00  19
+15         2673.18,133.466,  0.000       2673.18,-133.47,  0.000 4.60E+00  19
+16         2939.91,132.692,  0.000       2939.91,-132.69,  0.000 4.60E+00  19
+17         3209.55,132.692,  0.000       3209.55,-132.69,  0.000 4.60E+00  19
+18         3479.19,131.919,  0.000       3479.19,-131.92,  0.000 4.60E+00  19
+19         3749.79,131.919,  0.000       3749.79,-131.92,  0.000 4.60E+00  19
+20         4019.43,131.146,  0.000       4019.43,-131.15,  0.000 4.60E+00  19
+21         4290.03,131.146,  0.000       4290.03,-131.15,  0.000 4.60E+00  19
+22         4559.67,128.536,  0.000       4559.67,-128.54,  0.000 4.60E+00  19
+23         4829.31,127.763,  0.000       4829.31,-127.76,  0.000 4.60E+00  19
+24         5099.91,127.763,  0.000       5099.91,-127.76,  0.000 4.60E+00  19
+25         5369.54,127.763,  0.000       5369.54,-127.76,  0.000 4.60E+00  19
+26         5640.15,126.217,  0.000       5640.15,-126.22,  0.000 4.60E+00  19
+27         5909.78,126.605,  0.000       5909.78,-126.61,  0.000 4.60E+00  19
+28         6179.42,126.605,  0.000       6179.42,-126.61,  0.000 4.60E+00  19
+29         6450.03,125.831,  0.000       6450.03,-125.83,  0.000 4.60E+00  19
+30         6719.66,125.831,  0.000       6719.66,-125.83,  0.000 4.60E+00  19
+31         6990.27,125.831,  0.000       6990.27,-125.83,  0.000 4.60E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+3. DJ9BV BV70-7L 432 MHz                        Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,-170.00,225.000         0.000,170.000,225.000 4.00E+00  19
+2            0.000,-170.00, 75.000         0.000,170.000, 75.000 4.00E+00  19
+3            0.000,-170.00,-75.000         0.000,170.000,-75.000 4.00E+00  19
+4            0.000,-170.00,-225.00         0.000,170.000,-225.00 4.00E+00  19
+5          115.000,-160.00,  0.000       115.000,160.000,  0.000 4.00E+00  19
+6          170.000,-153.50,  0.000       170.000,153.500,  0.000 4.00E+00  19
+7          295.000,-150.50,  0.000       295.000,150.500,  0.000 4.00E+00  19
+8          445.000,-148.50,  0.000       445.000,148.000,  0.000 4.00E+00  19
+9          620.000,-147.00,  0.000       620.000,147.000,  0.000 4.00E+00  19
+10         815.000,-146.00,  0.000       815.000,146.000,  0.000 4.00E+00  19
+11         1025.00,-144.50,  0.000       1025.00,144.500,  0.000 4.00E+00  19
+12         1245.00,-143.00,  0.000       1245.00,143.000,  0.000 4.00E+00  19
+13         1475.00,-141.00,  0.000       1475.00,141.000,  0.000 4.00E+00  19
+14         1715.00,-141.00,  0.000       1715.00,141.000,  0.000 4.00E+00  19
+15         1965.00,-141.00,  0.000       1965.00,141.000,  0.000 4.00E+00  19
+16         2225.00,-139.00,  0.000       2225.00,139.000,  0.000 4.00E+00  19
+17         2495.00,-139.00,  0.000       2495.00,139.000,  0.000 4.00E+00  19
+18         2775.00,-139.00,  0.000       2775.00,139.000,  0.000 4.00E+00  19
+19         3055.00,-137.50,  0.000       3055.00,137.500,  0.000 4.00E+00  19
+20         3335.00,-137.50,  0.000       3335.00,137.500,  0.000 4.00E+00  19
+21         3615.00,-137.50,  0.000       3615.00,137.500,  0.000 4.00E+00  19
+22         3895.00,-136.00,  0.000       3895.00,136.000,  0.000 4.00E+00  19
+23         4175.00,-136.00,  0.000       4175.00,136.000,  0.000 4.00E+00  19
+24         4455.00,-136.00,  0.000       4455.00,136.000,  0.000 4.00E+00  19
+25         4735.00,-135.00,  0.000       4735.00,135.000,  0.000 4.00E+00  19
+26         5015.00,-135.00,  0.000       5015.00,135.000,  0.000 4.00E+00  19
+27         5295.00,-135.00,  0.000       5295.00,135.000,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     5 / 50.00   (  5 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+4. K1FO Free-Space 432 design                   Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,168.055,  0.000         0.000,-168.05,  0.000 4.71E+00  19
+2          102.810,165.089,  0.000       102.810,-165.09,  0.000 4.71E+00  19
+3          144.330,155.698,  0.000       144.330,-155.70,  0.000 4.71E+00  19
+4          221.437,151.249,  0.000       221.437,-151.25,  0.000 4.71E+00  19
+5          328.201,147.789,  0.000       328.201,-147.79,  0.000 4.71E+00  19
+6          460.668,145.812,  0.000       460.668,-145.81,  0.000 4.71E+00  19
+7          614.883,143.835,  0.000       614.883,-143.84,  0.000 4.71E+00  19
+8          788.870,142.847,  0.000       788.870,-142.85,  0.000 4.71E+00  19
+9          978.673,141.858,  0.000       978.673,-141.86,  0.000 4.71E+00  19
+10         1182.32,140.870,  0.000       1182.32,-140.87,  0.000 4.71E+00  19
+11         1397.82,139.881,  0.000       1397.82,-139.88,  0.000 4.71E+00  19
+12         1623.21,138.892,  0.000       1623.21,-138.89,  0.000 4.71E+00  19
+13         1857.50,137.904,  0.000       1857.50,-137.90,  0.000 4.71E+00  19
+14         2097.72,137.410,  0.000       2097.72,-137.41,  0.000 4.71E+00  19
+15         2345.85,136.915,  0.000       2345.85,-136.92,  0.000 4.71E+00  19
+16         2598.92,136.421,  0.000       2598.92,-136.42,  0.000 4.71E+00  19
+17         2856.93,135.927,  0.000       2856.93,-135.93,  0.000 4.71E+00  19
+18         3117.91,135.432,  0.000       3117.91,-135.43,  0.000 4.71E+00  19
+19         3382.85,134.938,  0.000       3382.85,-134.94,  0.000 4.71E+00  19
+20         3650.75,134.444,  0.000       3650.75,-134.44,  0.000 4.71E+00  19
+21         3921.61,133.950,  0.000       3921.61,-133.95,  0.000 4.71E+00  19
+22         4193.46,133.455,  0.000       4193.46,-133.46,  0.000 4.71E+00  19
+23         4468.28,132.961,  0.000       4468.28,-132.96,  0.000 4.71E+00  19
+24         4743.10,132.961,  0.000       4743.10,-132.96,  0.000 4.71E+00  19
+25         5020.89,132.467,  0.000       5020.89,-132.47,  0.000 4.71E+00  19
+26         5298.67,132.467,  0.000       5298.67,-132.47,  0.000 4.71E+00  19
+27         5577.45,131.973,  0.000       5577.45,-131.97,  0.000 4.71E+00  19
+28         5857.21,131.973,  0.000       5857.21,-131.97,  0.000 4.71E+00  19
+29         6137.96,131.478,  0.000       6137.96,-131.48,  0.000 4.71E+00  19
+30         6419.70,131.478,  0.000       6419.70,-131.48,  0.000 4.71E+00  19
+31         6701.44,130.984,  0.000       6701.44,-130.98,  0.000 4.71E+00  19
+32         6983.18,130.984,  0.000       6983.18,-130.98,  0.000 4.71E+00  19
+33         7265.90,130.490,  0.000       7265.90,-130.49,  0.000 4.71E+00  19
+34         7548.63,130.490,  0.000       7548.63,-130.49,  0.000 4.71E+00  19
+35         7831.36,129.995,  0.000       7831.36,-130.00,  0.000 4.71E+00  19
+36         8115.08,129.995,  0.000       8115.08,-130.00,  0.000 4.71E+00  19
+37         8398.79,129.501,  0.000       8398.79,-129.50,  0.000 4.71E+00  19
+38         8682.51,129.501,  0.000       8682.51,-129.50,  0.000 4.71E+00  19
+39         8966.22,129.007,  0.000       8966.22,-129.01,  0.000 4.71E+00  19
+40         9251.92,129.007,  0.000       9251.92,-129.01,  0.000 4.71E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+5. SM5BSZ 26-el 432 MHz                         Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,161.689,  0.000         0.000,-161.69,  0.000 1.00E+01  19
+2          199.598,156.474,  0.000       199.598,-156.47,  0.000 1.00E+01  19
+3          272.708,153.315,  0.000       272.708,-153.32,  0.000 1.00E+01  19
+4          456.677,145.693,  0.000       456.677,-145.69,  0.000 1.00E+01  19
+5          696.427,142.075,  0.000       696.427,-142.07,  0.000 1.00E+01  19
+6          961.601,138.577,  0.000       961.601,-138.58,  0.000 1.00E+01  19
+7          1263.05,135.693,  0.000       1263.05,-135.69,  0.000 1.00E+01  19
+8          1575.39,133.940,  0.000       1575.39,-133.94,  0.000 1.00E+01  19
+9          1887.06,132.676,  0.000       1887.06,-132.68,  0.000 1.00E+01  19
+10         2206.07,131.604,  0.000       2206.07,-131.60,  0.000 1.00E+01  19
+11         2525.12,130.660,  0.000       2525.12,-130.66,  0.000 1.00E+01  19
+12         2847.01,129.601,  0.000       2847.01,-129.60,  0.000 1.00E+01  19
+13         3174.21,128.579,  0.000       3174.21,-128.58,  0.000 1.00E+01  19
+14         3502.56,127.808,  0.000       3502.56,-127.81,  0.000 1.00E+01  19
+15         3831.20,127.191,  0.000       3831.20,-127.19,  0.000 1.00E+01  19
+16         4160.04,126.592,  0.000       4160.04,-126.59,  0.000 1.00E+01  19
+17         4489.54,125.870,  0.000       4489.54,-125.87,  0.000 1.00E+01  19
+18         4822.54,124.914,  0.000       4822.54,-124.91,  0.000 1.00E+01  19
+19         5157.94,123.992,  0.000       5157.94,-123.99,  0.000 1.00E+01  19
+20         5492.39,123.535,  0.000       5492.39,-123.54,  0.000 1.00E+01  19
+21         5828.46,123.460,  0.000       5828.46,-123.46,  0.000 1.00E+01  19
+22         6154.77,124.262,  0.000       6154.77,-124.26,  0.000 1.00E+01  19
+23         6469.18,126.082,  0.000       6469.18,-126.08,  0.000 1.00E+01  19
+24         6805.75,124.226,  0.000       6805.75,-124.23,  0.000 1.00E+01  19
+25         7133.67,123.389,  0.000       7133.67,-123.39,  0.000 1.00E+01  19
+26         7429.41,131.275,  0.000       7429.41,-131.27,  0.000 1.00E+01  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+6. VE7BQH 43-el "ladder" Yagi                        Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,170.873,  0.000         0.000,-170.87,  0.000 1.06E+00  19
+2          104.400,165.673,  0.000       104.400,-165.67,  0.000 1.06E+00  19
+3          145.546,162.555,  0.000       145.546,-162.55,  0.000 1.06E+00  19
+4          224.865,159.242,  0.000       224.865,-159.24,  0.000 1.06E+00  19
+5          333.284,155.954,  0.000       333.284,-155.95,  0.000 1.06E+00  19
+6          470.410,155.767,  0.000       470.410,-155.77,  0.000 1.06E+00  19
+7          624.401,153.524,  0.000       624.401,-153.52,  0.000 1.06E+00  19
+8          803.685,153.354,  0.000       803.685,-153.35,  0.000 1.06E+00  19
+9          993.819,153.932,  0.000       993.819,-153.93,  0.000 1.06E+00  19
+10         1200.61,151.128,  0.000       1200.61,-151.13,  0.000 1.06E+00  19
+11         1422.07,151.171,  0.000       1422.07,-151.17,  0.000 1.06E+00  19
+12         1645.73,150.329,  0.000       1645.73,-150.33,  0.000 1.06E+00  19
+13         1886.25,149.556,  0.000       1886.25,-149.56,  0.000 1.06E+00  19
+14         2132.79,149.182,  0.000       2132.79,-149.18,  0.000 1.06E+00  19
+15         2382.16,148.885,  0.000       2382.16,-148.88,  0.000 1.06E+00  19
+16         2623.40,148.528,  0.000       2623.40,-148.53,  0.000 1.06E+00  19
+17         2901.15,147.908,  0.000       2901.15,-147.91,  0.000 1.06E+00  19
+18         3167.57,147.526,  0.000       3167.57,-147.53,  0.000 1.06E+00  19
+19         3433.98,148.885,  0.000       3433.98,-148.88,  0.000 1.06E+00  19
+20         3705.32,148.443,  0.000       3705.32,-148.44,  0.000 1.06E+00  19
+21         3974.44,146.583,  0.000       3974.44,-146.58,  0.000 1.06E+00  19
+22         4249.19,146.404,  0.000       4249.19,-146.40,  0.000 1.06E+00  19
+23         4524.94,147.747,  0.000       4524.94,-147.75,  0.000 1.06E+00  19
+24         4806.30,145.640,  0.000       4806.30,-145.64,  0.000 1.06E+00  19
+25         5080.16,147.135,  0.000       5080.16,-147.14,  0.000 1.06E+00  19
+26         5355.87,145.325,  0.000       5355.87,-145.33,  0.000 1.06E+00  19
+27         5631.46,145.410,  0.000       5631.46,-145.41,  0.000 1.06E+00  19
+28         5905.37,146.787,  0.000       5905.37,-146.79,  0.000 1.06E+00  19
+29         6189.16,144.832,  0.000       6189.16,-144.83,  0.000 1.06E+00  19
+30         6471.13,144.459,  0.000       6471.13,-144.46,  0.000 1.06E+00  19
+31         6738.14,144.323,  0.000       6738.14,-144.32,  0.000 1.06E+00  19
+32         7011.75,146.234,  0.000       7011.75,-146.23,  0.000 1.06E+00  19
+33         7287.17,144.680,  0.000       7287.17,-144.68,  0.000 1.06E+00  19
+34         7565.60,144.764,  0.000       7565.60,-144.76,  0.000 1.06E+00  19
+35         7855.32,146.149,  0.000       7855.32,-146.15,  0.000 1.06E+00  19
+36         8126.24,144.008,  0.000       8126.24,-144.01,  0.000 1.06E+00  19
+37         8397.17,144.153,  0.000       8397.17,-144.15,  0.000 1.06E+00  19
+38         8656.70,146.209,  0.000       8656.70,-146.21,  0.000 1.06E+00  19
+39         8939.55,147.160,  0.000       8939.55,-147.16,  0.000 1.06E+00  19
+40         9226.88,145.801,  0.000       9226.88,-145.80,  0.000 1.06E+00  19
+41         9515.61,147.976,  0.000       9515.61,-147.98,  0.000 1.06E+00  19
+42         9808.55,144.960,  0.000       9808.55,-144.96,  0.000 1.06E+00  19
+43         10042.1,150.015,  0.000       10042.1,-150.01,  0.000 1.06E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+7. VK3AUU 41 el                        Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,-167.05,  0.000         0.000,167.054,  0.000 4.00E+00  19
+2          133.100,-169.89,  0.000       133.100,169.890,  0.000 4.00E+00  19
+3          156.082,-153.60,  0.000       156.082,153.597,  0.000 4.00E+00  19
+4          236.694,-151.55,  0.000       236.694,151.550,  0.000 4.00E+00  19
+5          341.372,-149.79,  0.000       341.372,149.795,  0.000 4.00E+00  19
+6          463.106,-148.04,  0.000       463.106,148.039,  0.000 4.00E+00  19
+7          598.160,-146.28,  0.000       598.160,146.284,  0.000 4.00E+00  19
+8          743.727,-144.82,  0.000       743.727,144.822,  0.000 4.00E+00  19
+9          898.641,-143.36,  0.000       898.641,143.359,  0.000 4.00E+00  19
+10         1061.50,-142.19,  0.000       1061.50,142.189,  0.000 4.00E+00  19
+11         1231.37,-140.73,  0.000       1231.37,140.726,  0.000 4.00E+00  19
+12         1407.31,-139.85,  0.000       1407.31,139.849,  0.000 4.00E+00  19
+13         1588.86,-138.68,  0.000       1588.86,138.678,  0.000 4.00E+00  19
+14         1775.79,-137.80,  0.000       1775.79,137.801,  0.000 4.00E+00  19
+15         1967.38,-136.92,  0.000       1967.38,136.923,  0.000 4.00E+00  19
+16         2163.19,-136.05,  0.000       2163.19,136.046,  0.000 4.00E+00  19
+17         2363.43,-135.17,  0.000       2363.43,135.168,  0.000 4.00E+00  19
+18         2567.18,-134.58,  0.000       2567.18,134.583,  0.000 4.00E+00  19
+19         2774.67,-133.71,  0.000       2774.67,133.706,  0.000 4.00E+00  19
+20         2985.42,-133.12,  0.000       2985.42,133.120,  0.000 4.00E+00  19
+21         3199.45,-132.54,  0.000       3199.45,132.535,  0.000 4.00E+00  19
+22         3416.52,-132.24,  0.000       3416.52,132.243,  0.000 4.00E+00  19
+23         3636.62,-131.66,  0.000       3636.62,131.658,  0.000 4.00E+00  19
+24         3859.30,-131.07,  0.000       3859.30,131.073,  0.000 4.00E+00  19
+25         4084.78,-130.78,  0.000       4084.78,130.780,  0.000 4.00E+00  19
+26         4312.59,-130.49,  0.000       4312.59,130.488,  0.000 4.00E+00  19
+27         4542.98,-129.90,  0.000       4542.98,129.903,  0.000 4.00E+00  19
+28         4775.93,-129.61,  0.000       4775.93,129.610,  0.000 4.00E+00  19
+29         5011.69,-129.32,  0.000       5011.69,129.318,  0.000 4.00E+00  19
+30         5221.61,-129.03,  0.000       5221.61,129.025,  0.000 4.00E+00  19
+31         5435.15,-128.73,  0.000       5435.15,128.733,  0.000 4.00E+00  19
+32         5652.20,-128.73,  0.000       5652.20,128.733,  0.000 4.00E+00  19
+33         5872.77,-128.44,  0.000       5872.77,128.440,  0.000 4.00E+00  19
+34         6096.85,-128.15,  0.000       6096.85,128.148,  0.000 4.00E+00  19
+35         6321.51,-127.86,  0.000       6321.51,127.855,  0.000 4.00E+00  19
+36         6552.60,-127.56,  0.000       6552.60,127.562,  0.000 4.00E+00  19
+37         6787.21,-127.27,  0.000       6787.21,127.270,  0.000 4.00E+00  19
+38         7020.65,-126.98,  0.000       7020.65,126.977,  0.000 4.00E+00  19
+39         7257.59,-126.98,  0.000       7257.59,126.977,  0.000 4.00E+00  19
+40         7488.69,-126.68,  0.000       7488.69,126.685,  0.000 4.00E+00  19
+41         7723.30,-126.39,  0.000       7723.30,126.392,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+8. VK3AUU 32 el, triple reflector               Frequency = 432  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1          -16.312,-195.75,203.576       -16.312,195.747,203.576 4.00E+00  19
+2          -16.312,-195.75,-203.58       -16.312,195.747,-203.58 4.00E+00  19
+3            0.000,-169.97,  0.000         0.000,169.973,  0.000 4.00E+00  19
+4          138.980,-169.16,  0.000       138.980,169.158,  0.000 4.00E+00  19
+5          165.406,-155.94,  0.000       165.406,155.945,  0.000 4.00E+00  19
+6          247.293,-153.82,  0.000       247.293,153.824,  0.000 4.00E+00  19
+7          356.585,-151.87,  0.000       356.585,151.867,  0.000 4.00E+00  19
+8          483.820,-150.07,  0.000       483.820,150.072,  0.000 4.00E+00  19
+9          625.084,148.278,  0.000       625.084,-148.28,  0.000 4.00E+00  19
+10         777.114,-146.81,  0.000       777.114,146.810,  0.000 4.00E+00  19
+11         938.931,-145.18,  0.000       938.931,145.179,  0.000 4.00E+00  19
+12         1109.23,-144.04,  0.000       1109.23,144.037,  0.000 4.00E+00  19
+13         1286.71,-142.41,  0.000       1286.71,142.406,  0.000 4.00E+00  19
+14         1470.38,-141.59,  0.000       1470.38,141.590,  0.000 4.00E+00  19
+15         1660.26,-140.29,  0.000       1660.26,140.285,  0.000 4.00E+00  19
+16         1855.68,-139.47,  0.000       1855.68,139.469,  0.000 4.00E+00  19
+17         2055.67,-138.49,  0.000       2055.67,138.491,  0.000 4.00E+00  19
+18         2260.22,-137.51,  0.000       2260.22,137.512,  0.000 4.00E+00  19
+19         2469.67,-136.70,  0.000       2469.67,136.696,  0.000 4.00E+00  19
+20         2682.38,-136.04,  0.000       2682.38,136.044,  0.000 4.00E+00  19
+21         2899.33,-135.07,  0.000       2899.33,135.065,  0.000 4.00E+00  19
+22         3119.55,-134.58,  0.000       3119.55,134.576,  0.000 4.00E+00  19
+23         3343.03,-133.92,  0.000       3343.03,133.923,  0.000 4.00E+00  19
+24         3570.09,-133.60,  0.000       3570.09,133.597,  0.000 4.00E+00  19
+25         3800.09,-132.94,  0.000       3800.09,132.945,  0.000 4.00E+00  19
+26         4032.71,-132.46,  0.000       4032.71,132.455,  0.000 4.00E+00  19
+27         4268.25,-132.13,  0.000       4268.25,132.129,  0.000 4.00E+00  19
+28         4506.41,-131.80,  0.000       4506.41,131.803,  0.000 4.00E+00  19
+29         4746.86,131.150,  0.000       4746.86,-131.15,  0.000 4.00E+00  19
+30         4990.56,-130.82,  0.000       4990.56,130.824,  0.000 4.00E+00  19
+31         5242.09,-130.50,  0.000       5242.09,130.498,  0.000 4.00E+00  19
+32         5464.59,-130.33,  0.000       5464.59,130.335,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     4 / 50.00   (  4 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+9. 12-el OWA Yagi 432 MHz                       Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,173.000,  0.000         0.000,-173.00,  0.000 4.00E+00  19
+2           74.760,167.500,  0.000        74.760,-167.50,  0.000 4.00E+00  19
+3          114.010,152.013,  0.000       114.010,-152.01,  0.000 4.00E+00  19
+4          213.913,148.577,  0.000       213.913,-148.58,  0.000 4.00E+00  19
+5          342.638,148.577,  0.000       342.638,-148.58,  0.000 4.00E+00  19
+6          515.959,147.985,  0.000       515.959,-147.99,  0.000 4.00E+00  19
+7          726.597,142.822,  0.000       726.597,-142.82,  0.000 4.00E+00  19
+8          974.179,138.231,  0.000       974.179,-138.23,  0.000 4.00E+00  19
+9          1230.90,134.650,  0.000       1230.90,-134.65,  0.000 4.00E+00  19
+10         1497.68,131.088,  0.000       1497.68,-131.09,  0.000 4.00E+00  19
+11         1762.79,127.507,  0.000       1762.79,-127.51,  0.000 4.00E+00  19
+12         1997.69,122.402,  0.000       1997.69,-122.40,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+10. OWA-VK3AUU Hybrid Yagi                       Frequency = 435  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            0.000,180.000,  0.000         0.000,-180.00,  0.000 4.00E+00  19
+2           78.760,167.500,  0.000        78.760,-167.50,  0.000 4.00E+00  19
+3          112.000,152.000,  0.000       112.000,-152.00,  0.000 4.00E+00  19
+4          217.913,147.000,  0.000       217.913,-147.00,  0.000 4.00E+00  19
+5          346.638,147.000,  0.000       346.638,-147.00,  0.000 4.00E+00  19
+6          467.107,-148.04,  0.000       467.107,148.039,  0.000 4.00E+00  19
+7          602.160,-146.28,  0.000       602.160,146.284,  0.000 4.00E+00  19
+8          747.727,-144.82,  0.000       747.727,144.822,  0.000 4.00E+00  19
+9          902.641,-143.36,  0.000       902.641,143.359,  0.000 4.00E+00  19
+10         1065.50,-142.19,  0.000       1065.50,142.189,  0.000 4.00E+00  19
+11         1235.37,-140.73,  0.000       1235.37,140.726,  0.000 4.00E+00  19
+12         1411.31,-139.85,  0.000       1411.31,139.849,  0.000 4.00E+00  19
+13         1592.86,-138.68,  0.000       1592.86,138.678,  0.000 4.00E+00  19
+14         1779.79,-137.80,  0.000       1779.79,137.801,  0.000 4.00E+00  19
+15         1971.38,-136.92,  0.000       1971.38,136.923,  0.000 4.00E+00  19
+16         2167.19,-136.05,  0.000       2167.19,136.046,  0.000 4.00E+00  19
+17         2367.43,-135.17,  0.000       2367.43,135.168,  0.000 4.00E+00  19
+18         2571.18,-134.58,  0.000       2571.18,134.583,  0.000 4.00E+00  19
+19         2778.67,-133.71,  0.000       2778.67,133.706,  0.000 4.00E+00  19
+20         2989.42,-133.12,  0.000       2989.42,133.120,  0.000 4.00E+00  19
+21         3203.45,-132.54,  0.000       3203.45,132.535,  0.000 4.00E+00  19
+22         3420.52,-132.24,  0.000       3420.52,132.243,  0.000 4.00E+00  19
+23         3640.62,-131.66,  0.000       3640.62,131.658,  0.000 4.00E+00  19
+24         3863.30,-131.07,  0.000       3863.30,131.073,  0.000 4.00E+00  19
+25         4088.78,-130.78,  0.000       4088.78,130.780,  0.000 4.00E+00  19
+26         4316.59,-130.49,  0.000       4316.59,130.488,  0.000 4.00E+00  19
+27         4546.98,-129.90,  0.000       4546.98,129.903,  0.000 4.00E+00  19
+28         4779.93,-129.61,  0.000       4779.93,129.610,  0.000 4.00E+00  19
+29         5015.69,-129.32,  0.000       5015.69,129.318,  0.000 4.00E+00  19
+30         5225.61,-129.03,  0.000       5225.61,129.025,  0.000 4.00E+00  19
+31         5439.15,-128.73,  0.000       5439.15,128.733,  0.000 4.00E+00  19
+32         5656.20,-128.73,  0.000       5656.20,128.733,  0.000 4.00E+00  19
+33         5876.77,-128.44,  0.000       5876.77,128.440,  0.000 4.00E+00  19
+34         6100.85,-128.15,  0.000       6100.85,128.148,  0.000 4.00E+00  19
+35         6325.51,-127.86,  0.000       6325.51,127.855,  0.000 4.00E+00  19
+36         6556.60,-127.56,  0.000       6556.60,127.562,  0.000 4.00E+00  19
+37         6791.21,-127.27,  0.000       6791.21,127.270,  0.000 4.00E+00  19
+38         7024.65,-126.98,  0.000       7024.65,126.977,  0.000 4.00E+00  19
+39         7261.59,-126.98,  0.000       7261.59,126.977,  0.000 4.00E+00  19
+40         7492.69,-126.68,  0.000       7492.69,126.685,  0.000 4.00E+00  19
+41         7727.30,-126.39,  0.000       7727.30,126.392,  0.000 4.00E+00  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+
+=============================================================================
+
+
+ +
+

Updated 04-28-2003. © L. B. Cebik, W4RNL. First prepared for the South-East VHF Society, April 26, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: VHF / UHF, Yagi


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+

Some Basics of Very-Wide-Band Yagi Design
+ Part 1: A Study of Very-Wide-Band Crossed-Element Yagi Performance

+

+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Purpose: The goal of this series is to explore just how far we may extend the operating bandwidth of the Yagi-Uda antenna. Historically, Yagis were initially designed for maximum gain, a phenomenon that seemed to be limited to a narrow bandwidth. Wide-band Yagis--nost notably of the DL6WU VHF/UHF type--appeared in the 80s and 90s, with variations appearing in the HF region. A special variation, called the OWA or optimized wide-band antenna, appeared in the 1990s. Its special features included a tight control of peformance as well as feedpoint impedance across a moderately wide frequency spectrum--as much as 4-5% of the center or design frequency. The DL6WU Yagis, however, are capable of at least 7% bandwidths and possibly up to 10%, depending on design.

+

Wide-band design does not have a definite border that separates it from very wide band design (VWB). However, we shall use any operating bandwidth over 20% of the design center frequency as falling distinctly within the very wide band region. The question then is simply this one: is it possible to design a Yagi array that provides usable performance over a bandwidth greater than 20% of the design center frequency with a feedpoint impedance that varies within 2:1 SWR limits? The idea of "usable performance" depends, of course, on the particular application for the antenna. Therefore, our initial foray into VWB design will be application-specific.

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The initial study examines the fundamental operation of very-wide-band crossed element Yagis antennas, ordinarily designed for satellite communications. I shall use a self-designed 8-element Yagi for 250-317 MHz as a vehicle for exploring both basic operation of the antenna and its performance potential. Included will be a discussion of very-wide-band Yagi design principles. The second part of the micro-series will examine the design of standard planar Yagis in the very wide band mode.

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The Test Antenna: Design and Operation: The test antenna is a crossed-element Yagi employing 8 element sets: 1 reflector set, 1 driver set, and 6 director sets. Fig. 1 shows the outline of the final array.

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The parasitic elements all meet that their center points, which would normally occur at a boom--whether or not conductive. No performance figure is altered by either joining or isolating the linear parasitic elements at their centers.

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The drivers are quadrature fed, that is, fed with roughly equal currents at a 90-degree phase angle by the use of a simple phasing line approximately but not exactly 1/4 wavelength long at the center frequency on the band. The actual length of line specified was adjusted for the smoothest impedance curve.

+

The individual antennas in the crossed set each have source impedances of about 50 Ohms. Therefore, a 50-Ohm phase line is specified. The net impedance of the driver set is about 25 Ohms. Therefore, a 35-Ohm matching line was added to the feedpoint to raise the impedance to 50 Ohms. Like the phase line, this match line is approximately but not exactly 1/4 wavelength at the center of the operating band, due to adjustment for the smoothest impedance curve across the band.

+

The operating band for this design is 250-317 MHz, with a center frequency of 283.5 MHz. The operating 67 MHz bandwidth is about 23.63% of the center frequency.

+

The design of the individual Yagis was derived from highly modified DL6WU wide-band Yagi design criteria. Elements were recalculated for a diameter of 0.5" to achieve the widest natural bandwidth within the range of potentially usable materials. However, the bandwidth might be achieved with elements only half the diameter used, since the principles of true wide-band design apply to the antenna.

+

Quadrature feed provides one method of increasing the SWR bandwidth, but does not itself improve the bandwidth of such parameters as gain, front-to-back ratio, and pattern shape. Those parameters require careful design of the element sequence in the Yagi.

+

Crucial to an understanding of very-wide-band design is a survey of the current on the driven element and the first director of each Yagi in the set. In VWB design, the first director is set about 0.075 wavelength ahead of the driver. The actual spacing--as is true for all other element spacing in the design--is a function of the element diameter and the variations in mutual element coupling that occur as a result of varying that diameter. The combination of driver-to-director-1 spacing and driver-to-reflector spacing together set the general operating source impedance for the array. The spacing used is roughly optimal for an individual Yagi source impedance of approximately 50 Ohms.

+

When designing the antenna for VWB service, the drive system makes use of a phenomenon that inter-relates the spacing and relative lengths of the driver and the first director. At the low end of the defined operating band, the driver exhibits a current magnitude that is considerably higher than that of the first director. However, at the upper end of the defined operating band, the first director current magnitude exceeds that of the driver. In effect, the first director becomes the effective driver at the upper end of the operating band. So long as the fed driver can couple energy to the first director, the upper end of the spectrum will operate with usable amounts of gain and front-to-back ratio and with a satisfactory pattern shape. Ordinarily, there is a fairly sharp high-end cut-off point at which the first director is too long to sustain its driver function, and the overall performance of the antenna degrades rapidly. The escalating SWR is often accompanied by a pattern distortion that yields multiple peaks in the forward lobe.

+

At the upper end of the operating spectrum, the driver and reflector show reduced influence on the Yagi performance figures and pattern shape. So long as the driver is not too long to couple energy efficiently to the first driver, its length becomes optional with respect to upper-end performance. The main element on which to make fine adjustments in upper-end performance becomes the forward-most director: director 6 in the case of the subject antenna. Changes in the length of the reflector have almost no effect on upper-end performance.

+

At the low end of the operating spectrum, where the driver shows a significantly higher current magnitude than the first director, the driver and reflector tend to control lower-end performance parameters. The driver may be lengthened to extend the lower-end limit to a satisfactory source impedance. Lengthening the reflector in tune to the driver extends the range of acceptable gain and front-to-back performance. Changes in these elements--up to a limit--result in negligible changes in the upper-end performance of the antenna.

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By combining the elements of VWB Yagi design (in concert with quadrature feed), it is possible to obtain a crossed-Yagi design that covers the entire subject band of 250-317 MHz. Fig. 2 shows the NEC-4-modeled SWR curve for the test antenna.

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The upper portion of the curve shows the 50-Ohm SWR values at 2-MHz intervals between 250 and 318 MHz. The upper-end curve rises very rapidly above 318 MHz. The curve rises somewhat less rapidly below the set lower limit of the operating band.

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Notable in the curve are the 5 minimums at 250, 278, 298, 310, and 318 MHz. The broader the operating bandwidth and the greater the element coupling, the higher the number of minimums in the curve, with 5 being the maximum that I have so far been able to obtain. The upper end of the band shows a greater level of fluctuation than the lower end. The lower portion of the figure shows an expansion of the graph between 314 and 316 MHz to confirm that the SWR does not rise above 2.0:1 in this region. The position and level of this curve can be partially controlled by the spacing and length of the forward-most driver.

+

The objective in any design is to assure as best possible a coincidence between the SWR and impedance curves and the other operating parameters. Initially, these factors include the source resistance and reactance.

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Fig. 3 shows the source resistance across the band with the antenna model in 3 different environments used to test the design. One curve presents the modeled free-space source resistance. Another models the resistance with the antenna pointed vertically upward with its reflector about 1 wavelength above the ground at mid-band. The height of about 41.5" is roughly coincident with what might be a standard desk-top operating height. The final curve shows the source resistance with the antenna angled upward 45 degrees, with the center of the reflector at the 41.5" level. This corresponds to desk-top operation for a satellite well below zenith. As with the SWR curve, the source resistance shows increasing fluctuation toward the upper end of the operating spectrum.

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Reactance across the entire operating spectrum varies by less than 15 Ohms, as shown in Fig. 4. Above 317 MHz, the reactance rises sharply, effectively cutting off use of the antenna within the 2:1 SWR limits most often used as a standard. The reactance changes more slowly below the lower end of the operating spectrum. Once more, the curves are virtually identical for all three environments. Together with the overlapping resistance curves, these two graphs show why a single SWR curve (actually modeled with the antenna in the vertical condition over real ground) suffices to demonstrate that parameter. The impedance and SWR figures represent the net values presented to the main feedline after all phasing and matching have been implemented at the antenna feedpoint.

+

These results were obtained with the dimensions shown in the following table.

+ 
               Dimensions of the 8-Crossed-Element Yagi for 250-317 MHz
+
+All elements:  0.5" diameter 6063-T832 aluminum.  Dimensions apply to each linear element in each set
+of two "wires" making up the crossed element.
+
+Element                             Tip-to-Tip              Distance from                       Distance from
+                                    Length (")              Reflector (")                       Preceding Element (")
+ Reflector                           21.80                   ------                              ------
+ Driver                              19.50                    8.27                                8.27
+ Director 1                          16.82                   11.10                                2.83
+ Director 2                          16.56                   18.19                                7.09
+ Director 3                          16.32                   26.65                                8.46
+ Director 4                          16.09                   36.48                                9.83
+ Director 5                          15.88                   47.50                               11.02
+ Director 6                          15.29                   59.30                               11.80
+Phase line length:  9.344", 50-Ohm cable, VF=1.0.  Match line length:  8.948", 35-Ohm cable, VF=1.0.
+
+Table 1.  Dimensions of the 8-crossed-element satellite Yagi for 250-317 MHz.
+

The phase line provides quadrature feed, which in turn provides the antenna with roughly circular polarization. With a fixed phaseline and a potential feed connector at each end, the direction of circularization reverses simply by connecting the match line and main feedline to one or the other connector. Because the phase line is perfect for only one frequency, the strength of the fields will vary slightly as one moves away from the design frequency of the phase line. However, for satellite work, the degree of departure from perfection is below the significance level.

+

Performance: The standard tests for modeled antennas usually include free-space performance and performance over ground in some single configuration. However, satellite antennas may be used at any angle with respect to ground from nearly parallel with the earth's surface to pointed straight upward. To sample the performance of the antenna over real ground, with the lowest end of the boom about 1 wavelength above ground, I set the antenna in two positions: straight up and angled at 45 degrees. These two orientations yield very interesting differences in performance, especially when contrasted with the free-space performance. When antennas are placed parallel to the earth's surface, whether horizontally or vertically polarized, the patterns obtained--with gain adjustments--tend to match the corresponding free-space E-plane and H-plane patterns. This expectation does not apply to antenna placed in a vertical or angled orientation.

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1. Gain: The free-space gain varies from about 9.75 dBi to 12.6 dBi, with the band edges reasonably well matched. Fig. 5 shows the free space gain curve, as well as curves for a vertical and an angled environment above ground. The 45-degree curve closely parallels the free-space curve, but at a strength level well below what we normally expect from ground reflections. The average difference in gain between the angled antenna and the free-space model is about 0.75 dB.

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The curve for the vertical antenna has two interesting features. At the low end of the spectrum, the curve flattens. The larger rear lobes at the lower gain levels become part of the forward radiation when reflected off the ground, thus limiting the gain reduction. Higher in the band, the peak gain does not coincide with the peak for the other curves. This, too, is a function of rearward radiation: the peak gain coincides roughly with the peak front-to-back ratio. When vertical, the antenna has less total radiation upward when the forward and reflected radiation are summed.

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2. Front-to-Back Ratio: The specification of a front-to-back ratio (in dB) applies only to the antenna when in free space or angled over ground. Because the antenna, when angled, does not operated exactly like the same antenna parallel to the earth's surface, the peak front-to-back level shows a frequency shift owing to the differences in the interception of reflected waves with incident waves. The actual peak is at a frequency somewhat above 269.9 MHz, but well below 303.6 MHz. As well, the effects of ground and the angle of the antenna alter fluctuations that we find in the free-space front-to-back ratio from the lower end of the spectrum to the mid-band frequency. See Fig. 6.

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+

Taking the gain and front-to-back values together, we find an emergent design specification for the antenna over the entire spectrum: a gain for all uses in excess of 10 dBi and a front-to-back ratio of greater than 12 dB. For the application, a high front-to-back ratio is not necessary, and its presentation here is mainly to explain various phenomena associated with vertically oriented and angled antennas. With only 2 band-edge exceptions, the design meets or exceeds these specifications.

+

3. Take-Off Angle: With the Yagi angled along its boom at 45 degrees with respect to the earth's surface, the elevation pattern of the antenna shows an angle of maximum radiation that fluctuates only in minor ways from the angle of the antenna itself. Except for the highest frequency sampled, the total fluctuation is only 6 degrees. Even at 317 MHz, the 33-degree take-off angle presents no problems of alignment, since the vertical beamwidth--as measured at -3 dB points away from the bearing of maximum strength--is sufficiently wide so as to require no readjustment. See Fig. 7.

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+

4. Beamwidths: In free-space and pointed straight upward, the differences between the beamwidths of the patterns as measured parallel to each type of element set are too small to require individual treatment. Hence, Fig. 8 graphs only a single beamwidth value for each of these two conditions.

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The free-space beamwidth values are almost solely a function of the forward gain of the array. Hence, the beamwidth curve is almost the inverse figure of the gain curve. When the antenna is pointed straight up, there is a variable amount of power devoted to moderate to incipient side lobes. The stronger the side lobe, the narrower the beamwidth for any given gain level. Hence, at the lower end of the operating band, where side lobe formation is generally highest, the beamwidth narrows more rapidly than in free space.

+

When the antenna is at a 45-degree angle with respect to earth's surface, we must consider both the vertical and the horizontal beamwidth of the pattern. In a general way, both curves follow the free-space curve, with slight adjustments for the effect of the varying front-to-back ratio above the mid-point of the operating band. The presence of the earth's surface restricts the vertical beamwidth to levels roughly comparable to those of the antenna pointed straight up. The 49-degree vertical beamwidth between -3 dB points at 317 MHz points to the reason why the seemingly low 33-degree take-off angle presents no aiming problems for the array. The horizontal beamwidth tends to be higher than we would expect from a horizontally polarized Yagi of the same boom length, but less than that we would expect of a vertically polarized Yagi, if both were parallel to the ground surface. However, the crossed-element beam tends to take on a value intermediate between these two cases.

+

Patterns: It may be useful in understanding the behavior of the crossed-8-element Yagi to examine selected patterns.

+

1. 250 MHz: The patterns for 250 MHz include the free-space pattern, the elevation pattern for the antenna when vertically oriented 1 wavelength above ground, and azimuth and elevation patterns for the antenna when the reflector center is 1 wavelength above ground. See Fig. 9. These patterns give us a portrait of antenna behavior at the low end of the operating band.

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+

Although the antenna exhibits only 10 dB of front-to-back ratio in free space, the rearward lobe contributes to good forward gain performance when the antenna is set vertically above ground. The vertical pattern also shows the incipient side lobes that narrow the beamwidth in this mode. When we angle the antenna 45 degrees, the pattern shows a very broad wave front in both the horizontal and vertical dimensions, as well as improved front-to-back performance relative to free space. Because phasing at this frequency is not quite ideal, the azimuth pattern shows elements of non-symmetry.

+

2. 283.5 MHz: At mid-band, the array shows a well-controlled pattern with forward side lobes about 16 dB below the level of the main forward lobe. When we place the antenna vertically over the ground, the side lobes appear as near-ground-angle lobes. However, the main forward (upward) lobe is very well shaped for its intended application.

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When we tilt the antenna 45 degrees relative to the ground, we obtain the patterns at the right of Fig. 10. It is no accident that the azimuth pattern shows good (although less than absolutely perfect) symmetry, since the phasing line is close to its optimal length. As well, the azimuth pattern resembles that of a 2-element horizontally polarized single Yagi with 2 elements. The resemblance goes beyond appearances, since the forward gain of the array is also quite similar to the gain of a 2-element Yagi.

+

The greatest departure from the 2-element horizontal Yagi pattern occurs with the elevation pattern. The crossed-element Yagi has a strong vertical component and, at about 1 wavelength above ground, it shows the double-lobe structure of a vertically polarized Yagi. The rearward lobes of the array remain quite well-controlled relative to the application of satellite communications.

+

3. 303.6 MHz: In free space, the 303.6 MHz pattern shows the highest front-to-back ratio--about 34 dB, as is evident in Fig. 11. This particular condition results in an actual reduction of gain (relative to the peak gain that we may obtain from the array) when we place the antenna in the vertical position. There is very little energy for the rear lobes to contribute to the upward forward lobe. The vertically positioned antenna shows a higher gain at a slightly lower frequency (see Fig. 5). The side-lobes, both forward and rearward, in the free space pattern contribute to small sidelobes in the vertical pattern, although these remain both narrow and of low amplitude.

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+

When we place the antenna at a 45-degree angle, ground reflection effects result in a front-to-back ratio that is less than the peak value. The azimuth pattern shows a small rearward lobe. As well, the azimuth pattern is again nearly symmetrical, since the frequency is also close to optimal for the phase line. Because the antenna is now higher than 1 wavelength above ground, the vertical pattern shows a decrease in the strength of the lower of the two main forward vertical lobes. The pattern actually shows an incipient third forward lobe developing. Hence, the take-off angle is about 5 degrees above the aiming angle. However, the signal strength at the 45-degree angle is down by well under 0.3 dB compared to the maximum possible strength.

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4. 317 MHz: The patterns for 317 MHz appear in Fig. 12. The free-space pattern remains well-behaved, with the main rearward lobe at least 17 dB lower than the main forward lobe. For this reason, when we set the antenna vertically above ground, the pattern is quite satisfactory for the application. The incipient side lobes have risen in elevation on the forward lobe, but create no unacceptable pattern distortions.

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The azimuth and elevation patterns for the antenna, when tipped 45 degrees, are especially interesting. First, the azimuth pattern shows some degree of non-symmetry in the side lobes, since the phase line is long for this frequency. However, the forward lobe remains aligned within 1 degree of the desired bearing and hence presents no operational problems whatsoever.

+

The elevation pattern requires some special comment. The angle of maximum radiation is 33 degrees above the horizon, although the antenna is pointed 45 degrees above the horizon. A secondary lobe occurs at 49 degrees, with a strength of 10.26 dBi, compared to the main lobe value of 11.01 dBi. At a 45-degree angle, the gain still exceeds 10.0 dBi, thus exceeding the minimum standard set for the antenna design.

+

The elevation pattern also shows considerable low-angle lobing. This phenomenon indicates a growing imbalance of horizontally polarized radiation over vertically polarized radiation. Although not yet harmful to the intended use of the array, the ripples are a clear indicator that the antenna is approaching the upper frequency limit of being serviceable in the intended application.

+

Indeed, the fall-off of gain and front-to-back ratio at the lower end of the operating spectrum and the pattern decay at the upward end of the spectrum suggest that the present design is stretch close to the limits for the overall bandwidth covered. Subjecting the design to further optimization--whether manual or automatic--might increase the usable bandwidth a bit further and indeed might improve one or more of the operating parameters across the band spread. However, it is not anticipated that such improvements would yield operationally significant improvements over the present design.

+

Conclusion: The 8-crossed-element Yagi design with quadrature feed provides about 10 dBi or more gain from 250-317 MHz, with adequate beamwidth for easy satellite aiming and with an acceptable 50-Ohm SWR across the entire spectrum. However, its chief merit as a design lies in its ability to help us understand the design and operation of VWB Yagis. The fundamental mechanism of VWB Yagi design lies in the relative independence of adjustments for upper and lower end performance enhancement due to the function of the first director as a secondary driver. The independence of the adjustments allows the designer to arrive at a closer coincidence in band-edge performance. Even with quadrature feed, arriving at a 23.6% operating bandwidth with acceptable performance--taking into account the need for aiming the antenna at different angles relative to the ground--is an interesting and potentially useful result.

+

The crossed-element Yagi design achieves part of its operating bandwidth from the use of quadrature feed. If we extract from the array a planar Yagi using the same element lengths and spacing, the net bandwidth between 2:1 SWER points shrinks from greater than 67 MHz down to 55 MHz. Although this bandwidth is on the cusp of truly VWB design (19.4%), we may inquire into whether the planar Yagi array is capable of covering the same 250-317 MHz spread that we demanded for our satellite communications design. The inquiry may also reveal some additional principles of VWB Yagi design. Hence, we have reason enough to create Part 2 of this investigation.

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Updated 11-01-2002. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Sep., 2001). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: VHF / UHF, Yagi


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+

+ Simplifying the Turnstile Moxon Rectangle Fixed-Position Satellite Antennas

+

L. B. Cebik, W4RNL

+

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+

Recently, I presented some information on building turnstiled Moxon rectangle antennas for use as fixed-position amateur satellite antennas. The basic article appeared in QST, (Aug. 2001), pp. 38-41 (Find it on the Magazines Page), with some supplemental information in the Technical Correspondence column of QST, Oct, 2001, pp. 78-79. In reading the following notes, I recommend these articles as background.

+

The basic principle of the turnstiled Moxon rectangles appears in Fig. 1. The two antennas are placed at right angles to each other, with the feedpoint separated. (The centers of the reflectors may be touching or separated. No change of performance is detectable between the two options.)

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+

A main feedline connects to one rectangle driver. From that elements a 1/4-wl phase-line composed of a transmission line runs from the fed driver to the second driver. The phase-line should have a characteristic impedance (Zo) that is the same as the natural resonant feedpoint impedance of a single rectangle when used independently. The rectangles used in the initial designs were 50-Ohm versions, calling for a 50-Ohm phase-line between drivers.

+

The condition that we obtain is called quadrature. That is, each rectangle receives the same power level or current magnitude. However, the two feedpoints show a current phase angle of 90 degrees under ideal conditions. Because the Moxon rectangles have such a wide -3 dB beamwidth, when we point the turnstiled array straight up, we obtain an almost perfect circle if we take an azimuth pattern. As well, the elevation pattern shows a very wide and smooth dome of radiation with a beamwidth in excess of 100 degrees. The exact -3 dB beamwidth depends in part on the height of the antenna above the ground surface. Heights up to 2 wl provide smooth coverage of the sky from about 30 degrees above the horizon in any direction. The horizontal and vertical components of the pattern are very nearly equal, suggesting good performance as a satellite changes polarization relative to the ground station as it traverses the sky.

+

One limitation of the satellite Moxons is the need for a matching section between the main feedline and the element terminals. The feedpoint impedance of a perfectly phased turnstile antenna of any type is one-half the impedance of the individual resonant antennas when set up independently. The 50-Ohm Moxons result in a feedpoint impedance of 25 Ohms.

+

The solution used in the original articles was to employ a 35-37-Ohm 1/4-wl matching section to raise the impedance from 25 to 50 Ohms. This system works well if carefully constructed. I originally used 75-Ohm video cable that was about 0.15" in diameter (along with even thinner RG-174 50-Ohm cable for the phase-line). The thin 75-Ohm cable is not usually available in amateur outlets, although the Wireman (in South Carolina) has a stock. The thin cables simplified the physical arrangement of the cables around the feedpoint, since they permit short connecting leads and easy manipulation to keep them separate. A number of difficulties have arisen wherever individuals have tried using fatter RG-58 and RG-59 cables, especially for the 435.6-MHz antenna. Indeed, where thin cables are not obtainable, I have suggested using a single Moxon rectangle directly fed with a 50-Ohm cable. The beamwidth off the edges of the antenna is not as wide, but overall performance may be better than that of a UHF version of the antenna that has wads of cable attached.

+

The matching section consists of two 1/4-wl sections of cable connected in parallel, that is, with their braids connected together and their center conductors connected together at each end of the line. I have recommended that these sections be spliced to a length of main feedline to avoid errors introduced by the use of cable connectors. BNC connectors would be satisfactory, but UHF connectors in this application would be metallic overkill.

+

An alternative method of returning the Moxon feedpoint impedance would be to employ a hybrid coupler-power splitter of the basic design shown in Fig. 2.

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+

For the present application, Zb in the sketch would be a 50-Ohm line and Za in the sketch would be 35-Ohm line. At the design frequency, the hybrid coupler achieves the desired equality of impedances at the 4 corners--one of which is unused. The hybrid coupler achieves the desired 50-Ohm main feedpoint impedance at terminal 1. The current at terminal 2, the unused input port, is negligible, that is more than an order of magnitude less than the current at the main feedpoint. The model of this arrangement uses lossless lines, although the line lengths suggest that losses would not distort matters more than the slight vertical separation of the Moxon rectangles forming the turnstile array.

+

The hybrid coupling system offers no advantage over the simpler system used in the original models, but it does introduce two more line lengths. See Fig. 3.

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When we operate the turnstile off its design frequency, the nearly circular patterns begin to pick up severe azimuth distortion. Fig. 3 shows the basic and hybrid coupling systems at 144 MHz. There is no significant difference in the degree of distortion, although the direction of the main lobes reverses between the two schemes. Consequently, the hybrid couple scheme offers nothing but additional complexity for the satellite arrays.

+

However, the exercise is a reminder that turnstile arrays require careful construction so that we end up with two virtually identical antennas, both of which are resonant at the design frequency. Achieving quadrature requires equal current magnitudes on the two elements with as precise a 90-degree phase shift as we can obtain. Significant distortion, as shown in Fig. 3, begins to appear at under a 1.5% frequency shift from the design frequency, and the condition worsens with added shifts of frequency, whether created by operating the array off frequency or by failure to use sufficient care to ensure that all components of the array are well within 1% of their ideal sizes. Consequently, it is unwise to change materials without careful redesign to account for the altered electrical properties.

+

In the original article, I suggested the use of 3/16" (0.1875") diameter elements for the 145.9-MHz array and AWG #12 (0.0808" diameter) copper wire for the 435.6-MHz array. Those recommendations resulted in the following table of dimensions, keyed to Fig. 4, the general outline of a Moxon rectangle used in most of notes on the antenna.

+
+ +
+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+               Dimensions for Moxon Rectangles for Satellite Use
+
+See Fig. 4 for letter references.  All dimensions in inches.
+Dimension               145.9 MHz: 3/16"        435.6 MHz: AWG #12
+  A                     29.05                   9.72
+  B                      3.81                   1.25
+  C                      1.40                   0.49
+  D                      5.59                   1.88
+  E (B + C + D)         10.80                   3.62
+1/4 Wavelength          20.22                   6.77
+0.66 VF phase and
+      match lines       13.35                   4.47
+Dimensions for 145.9 and 435.6 MHz Moxon Rectangles.  Two are required for each
+antenna.  The phase-line is 50-Ohm coaxial cable and the matching line is parallel
+sections of 75-Ohm coaxial cable.  Low power cables less than 0.15" in outer
+diameter were used in the prototypes.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Due to many requests for dimensions suited to the use of other materials for the 2-meter version of the antenna, I placed the following table in the supplemental information on the arrays.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Dimension                     Stock Diameter for the 145.9-MHz Antenna
+      1/8 (0.125)"      3/16 (0.1875)"    1/4 (0.25)"       0.1575" ( 4 mm)
+ A    29.122            29.052            29.000            29.082 (739 mm)
+ B     3.930             3.806             3.712             3.861 ( 98 mm)
+ C     1.285             1.398             1.484             1.348 ( 34 mm)
+ D     5.580             5.594             5.604             5.588 (142 mm)
+ E    10.794            10.798            10.800            10.796 (274 mm)
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Because there was considerable interest in adapting the array for use on 137 MHz, I also provided dimensions for that frequency.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Dimension                     Stock Diameter for the 137-MHz Antenna
+      1/8 (0.125)"      3/16 (0.1875)"    1/4 (0.25)"       0.1575" ( 4 mm)
+A     31.025            30.951            30.896            30.983 (787 mm)
+B      4.204             4.074             3.975             4.137 (105 mm)
+C      1.350             1.469             1.560             1.417 ( 36 mm)
+D      5.940             5.955             5.966             5.949 (151 mm)
+E     11.494            11.499            11.501            11.497 (292 mm)
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

No added dimensions have been provided for the 435.6-MHz version, since AWG #12 wire is so prevalent in the U.S. We shall look at further UHF construction methods before closing this note.

+

The notes so far summarize the state of Moxon rectangle turnstiles for satellite use to this point. However, the title of these notes implies a simplified assembly, and to that we next turn.

+

Simplifying the Arrays--Slightly

The Moxon rectangle designs used in the initial arrays derived from now standard designs originally developed for HF and VHF use. The designs achieved a direct 50-Ohm feed. However, it is possible to design a Moxon rectangle for virtually any feedpoint impedance well above 100 Ohms, at which point the array becomes more square, resembling the VK2ABQ square array from which G6XN originally developed his rectangular version. +

Moreover, it is also possible to optimize a series of models using stepped wire diameters and from those models and some regression analysis to develop a model- by-equation master model that requires only the element diameter and the design frequency in order to create output models that are accurate from 3 to 500 MHz. Fig. 5 shows the NEC-Win Plus equation page for the 50-Ohm version of the master model. The equations can also be applied independently to a spreadsheet, although placing them in a model-by-equation spreadsheet permits instant NEC-2 analysis of the resulting dimensions.

+
+ +
+

Now the simplification. Although the phase-line must be present in the turnstiles antenna (of whatever type), we may eliminate the matching section if we design Moxon rectangles with an inherent resonant feedpoint impedance of about 93 Ohms. Under these conditions, we may employ RG-62 (Zo: 93 Ohms; velocity factor: 0.84) as the phase-line. The resulting system feedpoint impedance will be close to 50 Ohms (46.5 Ohms), and we may omit the matching section.

+

To permit such design work, I created a series of optimized models having feedpoint impedance between 90 and 95 Ohms and performed standard regression analysis upon them. All optimized models maximized the 180-degree front-to-back ratio at resonance as defined by less than 1 Ohm reactance. As with the 50-Ohm master model, third-order equations proved sufficient for dimensions a through C, while a second-order equation sufficed for D, which changes slowly. The result was the master model, whose equation page appears in Fig. 6.

+
+ +
+

The range of wire diameters allowed by both master models is 1E-5 wl through 1E-2 wl. A diameter of 1E-5 is smaller than anyone will ever use, while 1E-2 is fatter than one will use, even at UHF. Therefore, the fact that the impedance of the perfect wire model drops to 89.8 Ohms for the thinnest wire at 30 MHz and rises to 100.2 Ohms for the very fattest perfect wire poses no design problem.

+

The following tables replicate those for the lower impedance Moxons presented earlier, but with the design set for a 90-95-Ohm feedpoint impedance.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+           Dimensions for 93-Ohm Moxon Rectangles for Satellite Use
+
+See Fig. 4 for letter references.  All dimensions in inches.
+Dimension               145.9 MHz: 3/16"        435.6 MHz: AWG #12
+  A                     24.77                   8.28
+  B                      6.74                   2.24
+  C                      3.00                   1.04
+  D                      7.97                   2.67
+  E (B + C + D)         17.71                   5.95
+1/4 Wavelength          20.22                   6.77
+0.84 VF phase-line       16.99                   5.69
+Dimensions for 145.9 and 435.6 MHz Moxon Rectangles.  Two are required for each
+antenna.  The phase-line is 93-Ohm coaxial cable
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+
+Dimension                     Stock Diameter for the 145.9-MHz Antenna
+      1/8 (0.125)"      3/16 (0.1875)"    1/4 (0.25)"       0.1575" ( 4 mm)
+ A    24.84             24.77             24.72             24.80  (630 mm)
+ B     6.80              6.74              6.69              6.77  (172 mm)
+ C     2.84              3.00              3.12              2.93  ( 74 mm)
+ D     7.96              7.97              7.98              7.96  (202 mm)
+ E    17.60             10.71             17.79             17.66  (448 mm)
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Dimension                     Stock Diameter for the 137-MHz Antenna
+      1/8 (0.125)"      3/16 (0.1875)"    1/4 (0.25)"       0.1575" ( 4 mm)
+A     26.46             26.39             26.34             26.42  (671 mm)
+B      7.26              7.19              7.14              7.22  (183 mm)
+C      2.99              3.16              3.30              3.09  ( 78 mm)
+D      8.47              8.48              8.49              8.48  (215 mm)
+E     18.72             18.83             18.93             18.79  (476 mm)
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Although the differences in dimensions from one material to the next may seem small, 1% precision in construction remains an important goal, if we are to obtain the correct performance from the array.

+

Several things should be clear from a comparison of the 50-Ohm and the 93-Ohm tables. First, the new arrays are squarer or less elongated than the 50-Ohm versions. Second, the gap sizes are larger. These two factors correlate in the design of a Moxon rectangle for any desired feedpoint impedance. Hence, it is in principle possible to design an even longer, narrower Moxon rectangle for a 35-Ohm feedpoint impedance or a squarer model for a 125-Ohm impedance.

+

Changing the shape of the Moxon rectangle to achieve a desired feedpoint impedance also changes the gain and the -3 dB beamwidth of the array. The maximum achievable front-to-back ratio does not change significantly throughout a reasonable set of shapes. The square the array, the longer the element tails that face each other and the shorter the parallel portions of the elements. Hence, as we make the array more square, gain drops and beamwidth increases.

+
+ +
+

Fig. 7 compares the elevation pattern of the 50-Ohm Moxon 2-meter array with a 93-Ohm array, both 1 wl above ground at 145.9 MHz. The new array shows about 0.5 dB less gain, but increases the beamwidth by about 5 degrees. Neither change should alter practical operation significantly, since there are more intervening variables in the average back yard than between versions of the array.

+

However, the higher impedance Moxon rectangles to permit us to simplify construction by using only the 93-Ohm phase-line and a master 50-Ohm feedline, with no required matching section.

+

Why Simplify?

The simplification of the arrays by elimination of the matching section is likely to occasion few benefits at 137 MHz and 145.9 MHz. However, the somewhat cramped quarters of a wire-based 435.6-MHz array may yield easier overall construction and more reliable replication of the prototypes. Eliminating the parallel line section and the splices removes more than one point of potential construction error from the process. +

The simplification also should ease the task of creating arrays for UHF an up, especially if such arrays follow the recommendation of being constructed of foil strips on a fiberglass or other suitable substrate. As I have noted in the past, development of such antennas requires considerable materials investigation and experimental work. Correlating the strip elements to modeled round-wire dimensions is the first step. It is likely that the required gap distances will take on a new correlation to the element length dimensions, since the end capacitance of a strip varies significantly from that of a round wire.

+

However, the use of strip construction on a substrate also permits one to etch the phase-line on one of the two interlocking board forming the turnstile array. The key element here is likely to be finding the velocity factor created by the substrate separating the phase-line strips in a two-sided etching process.

+

Solid boards, of course, create a wind-block situation. Hence, the very small UHF and up versions of the array might well have unused sections of board cut away to slip the wind. Alternatively, we might cover the antenna with an RF transparent dome. Polycarbonate should be serviceable up to several hundred MHz.

+

The turnstile Moxon rectangle array offers some interesting further applications, especially for aeronautical signal transmission, reception, or both. As we move some services formerly in the VHF range upward toward the GHz region, etched- board arrays may become very practical. The system is applicable wherever we need a dome of radiation or reception without nulls. The following possibilities seem especially apt:

+
    +
  • Airport and airways communications
    • +
  • Data and other identification or positioning signaling, wherever a vertical null is not desired.
    • +
  • Communications from aircraft.
    • +
+

The last application is especially interesting, since the satellite array need be only turned upside down and mounted beneath an aircraft to provide the dome of coverage relative to ground communications and other signal points. The array eliminates any "over-station" nulling of signals--assuming that the station antenna does not itself have a vertical null. The high front-to-back ratio of the antenna should make the aircraft itself relatively invisible to the antenna, and even a large wing structure should offer minimal change in the pattern shape or omni-directionality. for some modern aircraft with non-conductive surface "skins," the antenna may be mounted wholly within the aircraft surface boundaries. For slower aircraft, a small dome on the underside of the fuselage should provide good service.

+

The simplified 93-Ohm Moxon rectangle as the basis for turnstiled arrays should ease the development of such systems. Indeed, one might even etch on the interlocking antenna boards both the phase-line and the main feedline, using only a single coax line board-mounted connector just ahead of the reflector. Indeed, it is likely that the reflectors can be connected together at the center and connected to the aircraft system master ground bus, thus providing good immunity from lightning and other discharge damage.

+

The end result is that the turnstiled Moxon rectangles have a good bit of untapped potential. Indeed, every time I think that the array has run the gamut of possibilities and needs a design rest, I encounter a new potential that sets me to work again. I once described the Moxon rectangle as a "niche" antenna. However, it now appears that the array may profitably occupy quite a few niches, if not an entire shelf in the antenna store.

+

An On-Line Calculator for the 93-Ohm Moxon Rectangle Dimensions

+

The Moxon Rectangles and Online Calculator page includes an online calculator with a 93 ohm option.


+
+ +
+

Updated 10-01-2001; 06-01-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: Moxon, Satellite, Turnstile, VHF / UHF


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+

Some Basics of Very-Wide-Band Yagi Design
+ Part 2: Very-Wide-Band Planar Yagi Performance

+

+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Purpose: In Part 1 of this small study of very-wide-band (VWB) Yagis, we examined an 8-element parasitic array using crossed elements and quadrature feed with potential application to satellite communications in the 250-317-MHz region. In the course of our examination, we encountered some of the principles underlying VWB yagi design. However, those principles in part were compromised by the bandwidth-broadening effect of the quadrature feed system. The Yagi described there, if set out as a planar structure without the crossing elements shows a significant reduction in operating bandwidth.

+

In this part of our investigation, we shall pose a simple question: can the bandwidth of a planar Yagi be extended to cover the same 67-MHz bandwidth with usable performance? Unlike the crossed-element Yagi, with its implicit satellite communications application, the planar Yagi has no defined application other than those in which we generally use parasitic arrays. Hence, whether a given level of performance attained is indeed usable will remain a user judgment.

+

In addition to our first question, we shall pose a second question predicated on the very large element diameter (1/2") used in the crossed-element array: can we achieve the desired operating bandwidth with thinner elements, perhaps half the diameter of those in the initial design? We shall be interested not only in the attainment of the desired operating bandwidth in terms of an SWR value, but as well in the consequences for the usual performance criteria of gain and front-to-back ratio.

+

Background and Principles of VWB Design: The earliest Yagis strove for maximum gain, sacrificing bandwidth to obtain it. The emergence of the DL6WU design principles for VHF and UHF Yagi-Uda arrays ushered in (unnoticed by many) the era of wide-band Yagi performance. DL6WU designs were capable often of covering the entirety of the amateur 420-450-MHz band with under 2:1 SWR (relative to a reference impedance of 50 Ohms). The gain generally peaked high in the operating bandwidth, and the front-to-back ratio described a two-peak curve, with one peak low in the band and another just a bit higher than the gain peak. For a review and appreciation of the DL6WU designs, see "Appreciating DL6WU Wide-Band Long-Boom Yagi Design."

+

In the 1990s, there emerged from the work of NW3Z and WA4FET a set of HF Yagis using principles that the authors labeled as OWA or optimized wide-band antennas. The OWA Yagi differs in some important respects from the ordinary or DL6WU wide-band Yagi. Both use the reflector-driver-director-1 portion of the array to set the feedpoint impedance. Standard wide-band Yagis tend toward an element spacing in the vicinity of 0.2 wavelength and 0.075 wavelength for the reflector-driver and the driver-director-1 arrangement. The OWA Yagi uses much closer spacing among these elements, so that the first director becomes almost an extra element in some designs. That is to say, the OWA often uses 6 elements on the length of boom where standard design may use 5. In part, the close spacing of the rearmost elements results from the attention paid to the placement of the second and third directors, which often have the same length. The result is a 5-7% operating bandwidth--sufficient for most amateur bands--but far short of the 10% bandwidths attained by DL6WU designs. In return for the more modest bandwidth, the OWA designs are capable of rather tight control of operating parameters, showing only small changes of gain and front-to-back ratio across the passband. As well, one can design OWA Yagis with improved sidelobe suppression and with 50-Ohm SWR values that never rise above 1.25:1. For further information on OWA Yagi design, see "Notes on the OWA Yagi."

+

Very-wide-band (VWB) design is in effect an extension of DL6WU design, with attention to some special requirements of the VWB situation. The best way to illustrate the principles involved is to try to design VWB Yagis for the same 250-317-MHz band used for the crossed-element Yagi. Initially, we shall use the 1/2" diameter elements of the satellite Yagi in our planar version. However, we shall also explore what happens if we reduce the element diameter to 1/4", or half the initial size.

+

The Yagis will be designed to obtain a 50-Ohm SWR of under 2:1 across the 23.63% operating bandwidth. As well, the Yagis have as a general goal obtaining as smooth as possible a gain and front-to-back curve set for the band. Fig. 1 shows the general outlines--to scale--of the arrays that emerged from the initial exercise. Since there is no single final Yagi design when it comes to meeting a set of specifications, these arrays should be considered as typical, but potentially capable of further optimizing.

+
+ +
+

The Effects of Element Diameter, Length, and Spacing: The following table lists the dimensions for Yagis using both 1/2" and 1/4" diameter elements, with the dimensions of the crossed-element Yagi added for comparison.

+ 
      1.  Dimensions of the 8-Crossed-Element Yagi for 250-317 MHz
+
+All elements:  0.5" diameter 6063-T832 aluminum.  Dimensions apply to
+each linear element in each set of two "wires" making up the crossed
+element.
+
+Element          Tip-to-Tip      Distance from    Distance from
+                 Length (")      Reflector (")    Preceding Element (")
+Reflector        21.80           ------                ------
+Driver           19.50            8.27                  8.27
+Director 1       16.82           11.10                  2.83
+Director 2       16.56           18.19                  7.09
+Director 3       16.32           26.65                  8.46
+Director 4       16.09           36.48                  9.83
+Director 5       15.88           47.50                 11.02
+Director 6       15.29           59.30                 11.80
+Phase line length:  9.344", 50-Ohm cable, VF=1.0.  Match line length:
+8.948", 35-Ohm cable, VF=1.0.
+
+    2.  Dimensions of the 1/2" 8-Element Planar Yagi for 250-317 MHz
+
+All elements:  0.5" diameter 6063-T832 aluminum.
+
+Element          Tip-to-Tip      Distance from    Distance from
+                 Length (")      Reflector (")    Preceding Element (")
+Reflector        22.90           ------                ------
+Driver           20.10            7.99                  7.99
+Director 1       16.72           11.10                  3.11
+Director 2       16.58           18.19                  7.09
+Director 3       16.32           26.65                  8.46
+Director 4       16.08           36.48                  9.83
+Director 5       15.70           47.50                 11.02
+Director 6       14.58           59.30                 11.80
+
+    3.  Dimensions of the 1/4" 8-Element Planar Yagi for 250-317 MHz
+
+All elements:  0.25" diameter 6063-T832 aluminum.
+
+Version A
+Element          Tip-to-Tip      Distance from    Distance from
+                 Length (")      Reflector (")    Preceding Element (")
+Reflector        22.60           ------                ------
+Driver           20.79            9.25                  9.25
+Director 1       17.32           10.67                  1.42
+Director 2       16.85           17.72                  7.05
+Director 3       16.69           26.14                  8.42
+Director 4       16.22           35.94                  9.80
+Director 5       15.98           47.05                 11.11
+Director 6       14.65           57.87                 10.82
+
+Version B
+Element          Tip-to-Tip      Distance from    Distance from
+                 Length (")      Reflector (")    Preceding Element (")
+Reflector        22.60           ------                ------
+Driver           20.79            9.25                  9.25
+Director 1       17.32           10.67                  1.42
+Director 2       17.01           17.91                  7.24
+Director 3       16.77           25.98                  8.07
+Director 4       16.46           35.43                  9.45
+Director 5       16.16           47.24                 11.81
+Director 6       14.02           57.87                 10.63
+
+Version C
+Element          Tip-to-Tip      Distance from    Distance from
+                 Length (")      Reflector (")    Preceding Element (")
+Reflector        22.20           ------                ------
+Driver           20.70           10.60                 10.60
+Director 1       17.05           12.10                  1.50
+Director 2       16.93           18.10                  6.00
+Director 3       16.72           26.80                  8.70
+Director 4       16.52           36.20                  9.40
+Director 5       16.20           46.80                 10.60
+Director 6       15.30           57.40                 10.60
+
+Table 1.  Dimensions of the 8-element Yagis for 250-317 MHz.
+

The adjustments made in moving from the crossed Yagi to the planar version--both using 1/2" elements--fall into two groups. First, the first director and the forward 3 directors are shorter in the planar version. These adjustments extend the upper-frequency bandwidth without materially affecting the lower-frequency performance. There is some effect, but it is taken care of when adjusting the reflector and driver, the second group of modifications. The reflector in the planar Yagi is closer to the driver, and both elements are longer than in the crossed-element design. The two sets of adjustments, while not wholly independent of each other, do have minimal impact on each other.

+

The greatest amount of change occurs when downsizing the elements from 1/2" to 1/4" diameter. Since there is no single set of dimensions that will yield a Yagi with the operating bandwidth specified as the goal, I have developed 3 related designs. Version A had the goal of yielding the smoothest resistance and reactance curves across the 250-317-MHz span. Bunching of the gain peak at the high end of the band led to version B, which attempts to move the gain peak lower in frequency and to increase performance in the lower half of the passband. Version C attempts to compress more systematically the spacing between elements than either of the other versions.

+
+ +
+

Fig. 2 provides a graphical representation of the element lengths used in the 4 planar designs. As one might expect, the 1/4" elements are all longer than the corresponding 1/2" element, except for the reflector, which is longer than 1/2 wavelength and thus requires greater length in the fatter version.

+

Among the 1/4" element designs, Version C--with its systematic element spacing--yields the smoothest perimeter curve of element length. Its forward-most director is actually longer than not only the other 1/4" directors, but as well the corresponding 1/2" forward director. In contrast, Versions A and B show considerable variability of element length from one element to the next, with the forward-most director of version B being significantly shorter than any other element in the entire series.

+
+ +
+

Fig. 3 provides a similar graph of the spacing between adjacent elements for the designs. Most readily apparent are the changes in the reflector- driver-director-1 spacing. The 1/2" element design employs relatively close spacing of the reflector with wider spacing of the first director, relative to the driver. The 1/4" diameter designs require very close spacing of the driver and first director, with Version C using slightly wider spacing than the other two versions. However, version C also requires the widest spacing to the reflector.

+

There appears to be a minimum element diameter that will yield a VWB Yagi with up to 25% bandwidth. 1/4" appears to be very close to the limit in the frequency range tested. 1/4" is about 6E-3 wavelength relative to the band-center, 5.3E-3 wavelength at 250 MHz, and 6.7E-3 wavelength at 317 MHz. This diameter is insufficient in any of the three versions tested to yield the level of independence of adjustment at the upper and lower band edges compared to the larger 1/2" element. The 1/2" reflector and driver can be adjusted without significant effect on upper-end performance, and likewise the 1/2" forward-most two directors can be altered to change performance at the upper end of the spectrum with little significant effect on the low end of the band. However, in the 1/4" versions of the array, all adjustments aimed at one end of the band have smaller but significant effects on performance at the other end of the band.

+

Driver and First Director Current Magnitude: In common with all Yagi wide-band design techniques, the first director becomes the major source of energy for the forward elements at a certain point along the operating passband. In effect, it changes its role from that of the standard parasitic director to that of a secondary or slaved driver. In VWB design, the transition point at which the first director shows a current magnitude that is greater than the current magnitude on the driver occurs about 60% of the way from the lower to the upper end of the passband, with some variability depending upon other elements in the overall design. The curves of first-director current magnitude relative to a standard driver magnitude of 1.0 appear in Fig. 4.

+
+ +
+

Below the change-over point, the curves for all four of the planar designs are very similar. However, above the change-over point, the curves show interesting differences. The relative current magnitude for the 1/2" element design shows a steep climb, giving the first director a dominance over high frequency performance that is not shared fully by any of the 1/4" element designs. Version A of the thinner element designs shows the smoothest curve, without any vestige of the sudden rise that marks the fat element curve. The element length and spacing adjustments made to bring the gain peak lower in frequency for version B result in a sudden rise in first-director current magnitude, followed by a leveling off of the value. Version C of the 1/4"-element designs shows the beginnings of steep current magnitude climb only in the upper 10% of the passband.

+
+ +
+

Fig. 5 shows the 50-Ohm SWR curves that result from the various design manipulations. The curve for the 1/2" element design presents 3 SWR minimums across the passband, with the frequency steps between minimums shrinking with increasing frequency. In common with all VWB designs, the SWR minimum off the edge of the graph is followed by a rapid rise in SWR, yielding a sharp upper-end cut-off for the design. The rate of rise at the low end of the passband is always more shallow. Hence, when translating a design from one frequency range to another--especially if relative element diameter changes are involved--the most prudent design procedure is to scale the frequency at or near the upper end of the operating passband and then to make such other adjustments as may be needed to complete the design work for the new passband.

+

In the lower portion of Fig. 5, none of the 1/4" element designs can achieve the low value of SWR attained by the 1/2" design and still arrive at under 2:1 SWR across the entire band. Once more, inter-element coupling forms the basis for this phenomenon. The wide-spacing required by the reflector with thinner elements does not permit the low value of both resistive and reactive components of the feedpoint impedance 25% above the lower end of the band. Indeed, the minimum SWR value for the thinner element designs occurs within 10% to 15% of the low end of the passband.

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The smooth impedance curve of version A of the 1/4" element designs results in a swamping of all but one SWR minimum. This minimum corresponds to the unseen minimum for versions B and C that occurs just above the upper chart limit, although the rate of rise in SWR for Version A above 314 MHz is slower than the rise in the other curves in the region of 319-320 MHz. The adjustments made to version B to lower the gain peak frequency result in a curve that is nearly congruent with the curve of the 1/2" element design. The price for congruence, however, is that the SWR values never go as low as those at the upper end of the version A curve. The redesign of the 1/4" element Yagi for version C results in a mixed curve relative to the preceding versions. The multiple dips at the upper end of the spectrum result in a descending SWR value that reaches a minimum near 320 MHz before a very rapid rise out of the range that makes the array usable. However, the minimum SWR in the lower half of the pass band never reaches down to 1.45:1.

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Because the inter-element or mutual coupling situation is so different between the 1/2" and 1/4" element versions of the array, the adjustments to the Yagi with thinner elements is much more sensitive to minor variations in element length and spacing. With greater inter-element coupling, the 1/2" element array is far less finicky in the adjustment process.

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Fig. 6 tracks the feedpoint resistance for all 4 designs. As expected, the resistive component of the feedpoint impedance for the 1/2" element design traces a tame range of 40 to 77 Ohms across the passband, with a ripple in the curve around the frequency at which the first director becomes the more dominant driving element. Among the 1/4" element designs, version A shows the smoothest resistance curve, with a resistance range of 35 to 88 Ohms. Both of the re-designed 1/4" arrays show much high peaks in resistance--95-98 Ohms--with much greater variability in the progression of values.

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Corresponding feedpoint reactance curves appear in Fig. 7. The 1/2" curve is generally smooth, with a peak in the region of 303 MHz. By way of contrast and by design, the curve for version A of the 1/4" designs shows the least variability of any curve, with the reactance fluctuating between -j5 and +j5 Ohms for the entire upper half of the spectrum. In the same region, the reactance values for version B and C of the 1/4" arrays show considerably greater ranges of variation and more rapid changes in reactance for a given frequency step.

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The variations in reactance serve as signals to the designer that one or another limitation on operating bandwidth is approaching. Nevertheless, all three thin-element designs achieve the required operating bandwidth of under 2:1 50-Ohm SWR across the entire region from 250-317 MHz. As previously noted, the reduced mutual coupling among elements for the thinner elements results in a more difficult task of realizing the design physically, relative to the 1/2" design.

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Performance: The key performance parameter over and above SWR bandwidth is the level of usable gain for the array across the passband. For the following section, free-space gain will serve as the performance marker. In general and as one might expect, the 1/2" element design is capable of a higher low-end gain and a higher peak gain than any of the thin-element designs. At 250 MHz, the fat-element design achieves about 9.5 dBi gain, with a peak gain approaching 12.3 dBi at 303 MHz. In contrast, the best low-end gain for the 1/4" element designs is 9.0 to 9.1 dBi, with a peak value that ranges from 11.75 to 12.05 dBi. Fig. 8 shows the gain curves for all 4 designs.

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Among the 1/4" designs, version A best tracks the 1/2" design, with the highest peak gain. However, that peak occurs 10% higher in the band than for the other arrays, the price for the design concentration on smooth resistance and reactance curves. The corrective element length and spacing adjustments made to version B lower the frequency of peak gain to correspond more closely with the 1/2" design. The result is slightly better performance by up to 0.25 dB over the entire lower half of the operating spectrum. The redesign of version C places the peak gain frequency between those of version A and B, with intermediate improvements in gain at the low end of the passband.

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Although the curves for all three 1/4" designs show some variability, their inability to achieve the overall gain values of the 1/2" design across the entire spectrum of operation suggests once more a relative deficiency of adequate mutual coupling among elements. Whether that deficiency is sufficient to set the designs below the level of usability depends, of course, on the application specifications brought to the design process.

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Fig. 9 provides a glimpse into the more highly variable situation with respect to the array 180-degree front-to-back ratios. All of the curves show at least two front-to-back maximums, although the double dip in the curve for version A of the thin-element designs is not apparent in the 10% frequency steps used in the graph. The 1/2" design attains a minimum front-to-back ratio of better than 15 dB. The peak value is for the 180-degree ratio, and the worst-case front-to-back ratio at 303 MHz is closer to 20-21 dB.

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All of the 1/4" designs shows a weaker front-to-back ratio at the low end of the band, with version C barely achieving 10 dB at 250 MHz. Version A best tracks the 1/2" design, with its peak occurring 10% higher in frequency, in concert with its peak gain. The readjustments used to lower the frequency of peak gain in version B result in a dip in front-to-back ratio in the upper 20% of the operating spectrum. How significant the front-to-back ratio is, of course, will vary with the particular application.

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As a secondary gauge on the potential performance of these arrays, we may examine selected free-space E-plane patterns. We shall look at the low end of the band, the mid-point, the frequency of highest gain, and the upper band edge.

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Fig. 10 provides patterns for the 1/2" element design. Operationally, all of the patterns are well-behaved. The forward side lobes of the mid-band pattern grow from -24 dB top -18 dB at the peak-gain frequency. However, they again diminish as the first director dominates array energy supply at the upper end of the band. In contrast, the rearward side lobes enlarge at the upper band limit.

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Because all of the patterns for the 1/4" designs are so similar, the ones presented in Fig. 11 will suffice as a suitable sample for the thin-element arrays. Most interesting is the fact that they are in every way normal, despite the stretch of the operating bandwidth relative to the element diameter. The side lobes--both forward and rear--do not reach the level of development of those for the 1/2" design. Indeed, side lobe development is in part a function of the degree of excess mutual coupling among elements in an array. At its peak gain frequency, version C shows forward side lobes approaching the -20 dB level, a partial function of the closer spacing between forward parasitic elements.

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Conclusion: The design exercise has demonstrated that it is indeed possible to create Yagi arrays with an operating bandwidth of 23.6% or greater, even using elements as thin as 1/4". However, elements as thin as 0.006 wavelength at the design center frequency may approach the limit for such operating bandwidths due to the reduction in sufficient inter- element coupling to sustain operation and due to the reduction in low-end performance that attends reduced element diameters. The 1/2" element design, with an element diameter of about 0.003 wavelength, provides a tamer SWR curve and superior performance curves across the entire span.

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The principle design feature of the VWB design is the shift in dominance of the driver and the first director relative to control of the performance characteristics as one moves from the low to the high end of the operating spectrum. The critical spacing and length setting of the reflector, driver, and first director are considerably eased with fatter elements. Indeed, it may be possible to design an array using 1/2" elements for these functions, with thinner elements comprising the remaining directors. However, that task remains to be tested.

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Within the limits of the test arrays used for this study, the fatter the elements, the greater the independence between upper and lower frequency adjustments to the array. Thinner elements in the reflector-driver-director-1 section of the array require closer spacing of the driver and first director to achieve sufficient coupling for the desired spectrum coverage, with a consequential need to increase the reflector spacing. Hence, adjustments become more critical, with consequences for the physical implementation of such arrays.

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There is no single value of spacing between the driver and first director that will achieve VWB performance. Rather, the spacing is critically dependent upon two interactive variables: the element diameter for a given operating band width and the desired operating bandwidth for a given element diameter. The length and spacing of the remaining directors will then show interactive variables of their own as the designer seeks to achieve a set of particular performance goals within the operating passband.

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This study is by no means a final word on VWB design. Instead, it is only an initial exploration into an intriguing venture: to achieve from a parasitic array the widest possible operating bandwidth with usable performance from one end to the other. Much remains to be investigated.

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Updated 11-01-2002. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Oct., 2001). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: VHF / UHF, Yagi


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High-Gain, Wide-Band Yagis for 10, 6, and 2 Meters

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L. B. Cebik, W4RNL

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There is a very interesting 20-meter Yagi design called the Optimized Wideband Antenna, or OWA. Although only one of several designs within this genre, developed by Nathan Miller, NW3Z and Jim Breakall, WA3FET, using an optimizer program no longer available, the 20-meter version is one of the most adaptable. It employs 6-elements in the space that many other designs use 5. Fig. 1 shows the general proportions of the antenna.

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The 20-meter antenna has several features that deserve special note. Director 1 is perhaps the most significant, since it represents the added element to previously standard 5-element designs. By the use of this parasitic element, the driver can be more closely spaced to the reflector and still show a feedpoint impedance very close to 50 Ohms resistive. Moreover, the antenna shows wideband VSWR characteristics, with values less than a 1.3:1 from 14.0 through 14.35 MHz.

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Not only is the feedpoint impedance quite stable, so too are the other main operating characteristics, including both gain and the front-to-back ratio. The antenna shows better than 10 dBi forward gain in free space models across the entire 20 meter band, with more than a 20 dB front-to-back ratio across the same span. Many 5-element designs show much larger variations in all three of the main Yagi parameters: gain, front-to-back ratio, and feedpoint impedance.

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The remaining elements of the OWA are also interesting. Directors 2 and 3 are either the same length or the forward director is slightly longer than the rearward member of the pair. Director 4 and the reflector are available for making small changes in the upper and lower frequency limits of the design to spread the operating characteristics across the desired bandwidth. The 20-meter band is about 2.5% of its center frequency. The OWA is capable if significantly greater operating bandwidths with little loss in any of its main characteristics.

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The reason for making extensive note of the OWA design is that it scales quite easily (but not without some readjustment) to create very usable Yagis for 10, 6 and 2 meters. Although only a few hams have the wherewithal to construct a 48' boom Yagi for 20 meters, 24'-boom Yagis for 10 are more common--and more manageable. The same antenna, scaled and adjusted for 6 meters sits on a boom just over 13' long. On 2 meters, the boom is only a small bit longer than 4.5'. In all cases, the resultant beams show free space gains above 10 dBi across the bands, front-to-back ratios always in excess of 20 dB, and very low 50-Ohm VSWR ratios for direct coax feed systems.

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Let's look at the designs for each band, one at a time.

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A 10-Meter, 6-Element OWA Yagi

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Scaling the initial OWA to 10 meters involved two approaches. One was the direct approach of frequency scaling each element of the original, along with the element spacing and the element diameters. The elements of the 20 meter version used a complex array of tubing sizes from 0.5" to 1.0" in 1/8" increments. For 10-meters, the roughly half size tubing required by direct scaling is not either usual or recommended for most Yagi designs.

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The second approach was to convert the 20-meter design into its equivalent uniform diameter element equivalent, scale this antenna, and then create a set of tapered diameter elements suitable for 10 meters, adjusting their lengths to be equivalent to the substitute model. The following table lists, in order, the overall element length, the spacing from the reflector, and the exposed tubing lengths of each size tubing used on one side of the element. (Be sure to double the length of the largest size tubing and to have extra inches on the remaining sections for the tubes to nest.) All dimensions are in inches.

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Element   Overall        Spacing        0.5"           0.375"         0.25"
+          Length         from Refl.     Inner          Middle         Outer
+Reflector 216.8          ------         35.75          35.75          36.9
+Driver    209.2           44.68         35.75          35.75          33.1
+Dir 1     199.36          69.26         35.75          35.75          28.18
+Dir 2     193.23         132.40         35.75          35.75          25.12
+Dir 3     193.24         192.83         35.75          35.75          25.12
+Dir 4     186.05         282.96         35.75          35.75          21.53
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The antenna was scaled and reset to cover the span from 28 to 29 MHz. Some adjustment of the reflector and 4th director was required to achieve the added bandwidth. The first MHz of 10 meters represents a 3.5% operating bandwidth, about 40% greater than demanded of the 20-meter version of the antenna. The following table shows representative modeled figures for 5 points across the band. All figures are based on free space models using NEC-4.1 with Leeson corrections invoked for greatest accuracy.

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Parameter      28.0      28.25     28.5      28.75     29.0
+Gain dBi       10.00     10.10     10.19     10.26     10.27
+F-B dB         20.29     26.57     30.22     24.47     21.34
+Feed Z:
+   R           38.4      41.9      44.4      44.6      36.5
+   jX          +5.0      -1.1      +1.3      +0.5      -2.6
+50-Ohm SWR     1.33      1.20      1.13      1.12      1.38
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The greater bandwidth demanded of the 10-meter design shows most clearly in the rise in SWR and decrease in feedpoint impedance at the low and high ends of the passband. Nonetheless, the design meets all of the objectives. The gain changes only by about a quarter dB across the band. With further tweaking, the feedpoint impedance might be brought upward toward 50 Ohms a bit, but the reactance figures are extremely low for an antenna covering a full MHz of 10 meters. All of this suggests that the OWA design concept is capable of significant expansion beyond its original implementation.

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The antenna pattern itself is a model of good behavior, with no undesirable side or rear lobes. Note in Fig. 2 the change in the shape of the rearward lobe across the band, which is a normal progression for well-behaved antennas of this type.

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Just for the drama, Fig. 3 shows the 50-Ohm SWR sweep, taken at 0.1 MHz intervals across the band. There are no impedance spikes anywhere in the passband of the antenna.

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As a high-performance 10-meter antenna covering all of the first MHz of the band, the 24' 6-element OWA is a worthy monoband competitor with other designs for the band.

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A 6-Meter, 6-Element OWA Yagi

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The (re-)design goal that I set for myself on 6 meters was to see if the antenna could be reset to hold its characteristics across the first 2 MHz of the band. Centered on 51 MHz, the design sought to have a free space gain of at least 10 dBi, a front-to-back ratio of more than 20 dB, and a low 50-Ohm VSWR from 50 to 52 MHz. The operating bandwidth is 3.9% of the center frequency, or 62% wider than the original 20-meter version.

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At 6 meters, the element taper can be simplified to two steps: 0.5" for the center section and 0.375" for the outer sections. Here is a table of the final dimensions used in the design exercise. As always, physical dimensions are in inches.

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Element   Overall        Spacing        0.5"         0.375"
+          Length         from Refl.     Inner          Outer
+Reflector 119.00         ------         24.50          35.00
+Driver    116.61          29.56         24.50          33.80
+Dir 1     109.07          41.79         24.50          30.03
+Dir 2     105.95          75.65         24.50          28.48
+Dir 3     105.96         108.79         24.50          28.48
+Dir 4     101.80         158.21         24.50          26.40
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The overall antenna length is just about 13.2' which permits construction of the antenna on a 14' boom. The operating characteristics of the model are summarized in the following table.

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Parameter      50.0      50.5      51.0      51.5      52.0
+Gain dBi       10.06     10.16     10.24     10.26     10.17
+F-B dB         20.25     26.51     30.45     23.71     20.34
+Feed Z:
+   R           46.6      49.2      51.8      50.3      34.2
+   jX          +5.2      +8.2      +8.9      +3.7      -0.0
+50-Ohm SWR     1.14      1.18      1.20      1.08      1.46
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The source impedance is closer to 50 Ohms than was true of the 10-meter version of the antenna, but the reactance values are also higher than on 10 meters. Instead of a continuous rise in gain across the band, the 6-meter version of the design shows a distinct gain peak between 51.0 and 51.5 MHz. The front-to-back curve parallels that of the 10-meter version. I note these similarities and differences should someone be of a mind to further optimize these adapted designs from the original OWA.

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The azimuth patterns for the antenna are virtually identical to those for the 10-meter version, as shown in Fig. 4. This includes the slight bulge in the forward pattern near the 90-degree mark (relative to the forward gain bearing) at the high end of the band.

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The SWR sweep in Fig. 5 shows a different pattern than the corresponding 10-meter sweep. The SWR figure, always low, tends to meander across the band, hitting a low point before ascending to 1.46 at the high end of the band. Although the figures are all quite acceptable, further optimizing might bring down the figure at the high end of the band by raising the resistive component of the impedance.

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Most high gain work on 6 meters occurs at the lowest end of the band. This fact may limit the utility of the OWA design. However, the 2 MHz operating bandwidth of the design does demonstrate the reasonably high and well-behaved gain can be attained across a considerable portion of 6 meters.

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A 2-Meter, 6-Element OWA Yagi

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2-meters is filled with Yagis and variants that provide mediocre gain and operating bandwidth on longer than necessary booms. An adaptation of the OWA for 2 meters can provide 10 dBi free space gain on a 4.5' boom, which is under two-thirds of a wavelength. At 2-meters, we can use uniform element diameters for ease of construction.

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The adaptation of the OWA to 2 meters employs 3/16" diameter elements (presumably aluminum rods). The following table summarizes the dimensions, again in inches.

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Element   Overall        Spacing        0.1875"
+          Length         from Refl.
+Reflector  40.52         ------         20.26
+Driver     39.96          10.13         19.98
+Dir 1      37.38          14.32         18.69
+Dir 2      36.31          25.93         18.16
+Dir 3      36.31          37.28         18.16
+Dir 4      34.96          54.22         17.48
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As in all of the tables of physical dimensions, the numbers are fussier than reality. However, the extra decimal place may be useful in letting the builder round off in the direction he or she deems most fitting to the particular construction method being used.

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The design goal of this exercise was to attain an operating bandwidth covering all of the 2-meter band. Although 4 MHz sounds impressive, it is only 2.7% of the center frequency (146 MHz), so the exercise proved fairly easy. The following table lists the modeled operating characteristics across the band.

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Parameter      144       145       146       147       148
+Gain dBi       10.13     10.19     10.23     10.22     10.16
+F-B dB         22.01     28.12     35.36     26.77     22.21
+Feed Z:
+   R           44.8      47.2      50.0      50.9      43.7
+   jX          +7.6      +9.6      +9.5      +5.2      -1.7
+50-Ohm SWR     1.21      1.23      1.21      1.11      1.15
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The narrower passband requirements of this version of the OWA yielded a peak gain and front-to-back ratio very close to the design center frequency. The figures, in fact, are very similar to those for the original 20-meter version which is the basis for all of these scalings.

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The free space azimuth patterns in Fig. 6 for the band edges and center are virtually indistinguishable from those of the other two designs. Only the slightly improved front-to-back levels at the band edges show up as something noticeable on the plots.

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The SWR sweep across 2 meters in Fig. 7 is similar to that of the 6-meter beam, although the smaller passband does not require us to use the steeper portion of the curve above 148 MHz.

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For a high-performance, compact (4.5' boom), and inexpensive 2-meter beam, one could do far worse than the adapted OWA design shown here. With some further optimizing, one might even do a wee bit better.

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Conclusion

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All credit for the OWA design belongs to its originators. This exercise has only shown that one of the implementations of the basic design can be advantageously adapted to other bands. None of the models presses any limit of the NEC and, therefore, they are quite reliable, both as analyses of the antennas and as guides to construction. Of course, using other element diameter taper schedules than the ones shown will require resetting the element lengths to accommodate the materials used.

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The OWA has the following positive characteristics:

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  • Smooth gain across each band, with a value of at least 10 dBi free space
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  • At least 20 dB front-to-back ratio across each band
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  • Direct 50-Ohm feed with less than 1.5:1 SWR across each band
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  • Straightforward construction with readily available materials
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  • Above 20 meters, a manageable (and even modest) size
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In addition to being rather good Yagis of their size, the OWA designs may also serve as a standard against which to measure other designs that present themselves. Even if you never build one of these designs, the data provided here may be useful for comparative purposes.

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Updated 9-1-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Aug., 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: HF Upper, VHF / UHF, Yagi


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The Prismatic Polyhedron and the Planar Reflector

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L. B. Cebik, W4RNL

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Let's begin with notes on two antenna concepts that meet in these notes.

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1. From about June, 2001 through November, 2002, Dan Handelsman and David Jefferies presented a series of articles in antenneX on an interesting concept in broadband antennas: the prismatic polyhedron. Dan eventually patented the idea. Some of the versions were capable of 3:1 frequency ranges with a 2:1 SWR or under at the listed antenna impedance. (In bandwidth percentage terms, a 3:1 frequency range translates into a 100% bandwidth.) Some of the relevant articles and their links are the following:

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"Plate Dipoles and Prismatics," by Dan Handelsman and David Jefferies
(http://www.antennex.com/archive5/Apr02/Apr402/pdp.html : No copy on web.archive.org - page required login)

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"Plate Dipoles and Prismatics Revisited," by David J. Jefferies and Dan Handelsman
(http://www.antennex.com/archive5/May02/May402/pdp2.html : No copy on web.archive.org - page required login)

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"Prismatic Polyhedron Antenna Measurements at Low GHz Frequencies," by David J. Jefferies
(http://www.antennex.com/archive5/Nov02/Nov502/pms.html : No copy on web.archive.org - page required login)

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"Cage Dipoles and the Prismatics," by Dan Handelsman and David Jefferies
(http://www.antennex.com/archive5/Dec02/Dec402/cage.html : No copy on web.archive.org - page required login)

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The third item contain links to further articles on the broadband antenna.

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2. Some time back I published a series of articles on planar and corner reflector arrays that resulted in a book of the same title (Planar and Corner Reflector Arrays, available from antenneX). A planar reflector is a solid sheet, screen, or curtain of wires or rods, optimally sized for the driver and spaced to achieve the best compromise between gain and the feedpoint impedance. Almost all of the modeled drivers increased their SWR and operating bandwidths when used with a planar reflector. In each case, the bandwidth increase occurred mostly on the high side of the design frequency. However, the SWR bandwidths were generally less than about 10% relative to the center or design frequency.

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However, a pair of dipoles spaced 1/2 wavelength and fed in phase achieved an SWR bandwidth of about 26% (about 75 MHz at a center frequency of 300 MHz) while retaining its pattern shape and other operating characteristics. A batwing dipole formed a contrast to the phased dipole pair. An independent batwing shows an SWR bandwidth of over 50% (about 150 MHz at a center frequency of 300 MHz). When provided with a planar reflector, the bandwidth dropped to about 33%, that is, it showed a loss of about 50 MHz. The two wide-band designs left open a number of questions, some specific to the driver types and some generic to the use of planar reflectors.

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The most fundamental question in the present context concerns the useful frequency range for a given planar reflector. Planar reflectors with ordinary drivers having modest bandwidths showed remarkably stable operating characteristics across the SWR bandwidths. However, none of the drivers stressed either the spacing between the driver and the reflector or the reflector size within the limits of operation. Hence, none of the drivers provided data on the potential limits of a planar reflector.

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David Jefferies recently called my attention to the prismatic polyhedrons, and so I decided to explore at least some of these very wide-band antennas in the context of creating a directional array using a planar reflector. The results so far have proven to be interesting and possibly general.

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The P3 Antenna

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Most of these notes employ one of Dan Handelsman's designs, the P3 cut for a lower limit of about 300 MHz. Fig. 1 shows the outline of the antenna and includes dots to indicate segmentation of the wires. The P3 consists of 3 dipoles, each center fed, with triangular junctions at the outer ends. Unlike a cage dipole, where we draw the cage to a center feedpoint, the P3 uses continuous elements. From the center of each element to a central feedpoint, we employ short transmission lines, all the same length and impedance. Thus, we end up with three dipoles fed in phase with relatively close spacing and connected outer ends.

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The test antenna replicated one of the existing designs. The wires are all 0.015 m (1.5 cm) in diameter. Fatter wires increase the operating bandwidth, but the requirements of modeling limit the usable wire diameter. Since the antenna has corners, some as narrow as 60 degrees, using too fat a wire places the surface of one wire within the center region of an adjacent wire segment, a situation that results in NEC warning or error messages. The modeled antenna height (or the length of each long wire) is 0.32 m. Each face (or top/bottom wire) is 0.083 m. The transmission lines from the dipole centers to the common feedpoint are each 300 Ohms, and with a velocity factor of 1.0, the length is 0.05 m. All modeling for the P3 and subsequent arrays used free-space as the environment.

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The modeled P3 showed a 50-Ohm SWR curve with approximate limits of 300 and 760 MHz, for better than a 2.5:1 frequency ratio or about an 87% bandwidth. Dan achieved slightly better results by judicious model tweaking, while some lab versions of the antenna tested by David showed a measured frequency range of more than 3:1. However, for our inquiry, the 2.5:1 range is more than satisfactory. Fig. 2 graphs the progression of feedpoint resistance and reactance, as well as the 50-Ohm SWR across the swept passband. The resistance and reactance values vary over small ranges and undulate, resulting in a wide SWR curve with two low points (similar to the SWR curves of paired driver-first-director elements in an OWA Yagi).

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The wide SWR bandwidth of the P3 does not result solely from the antenna geometry. The selection of the phase-line Zo and length also help to shape the SWR curve and the impedance to which we reference the SWR.

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Table 1 lists the reported data for the P3 as an independent antenna. The table uses 100-MHz increments from 300 through 800 MHz as sampling points. The left-most columns show the growth of the antenna across the sampling range when we measure the elements in terms of wavelengths.

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You may correlate the impedance data in the table to the information in Fig. 2. However, the table includes other significant information for those wishing to model the P3 and similar antenna. The column labeled AGT provides the NEC-4 AGT score for the antenna at each sampled frequency. The adjacent column lists the amount by which to decrease the reported gain to arrive at a more accurate figure. Since we are looking for relatively gross trends, corrections less than 0.1 dB in the gain and 2% or less in the feed resistance column are not significant. (In other modeling exercises, they might become important.)

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As we increase the frequency of operation without altering the physical structure of the P3, we note an increase in the free-space gain. By 800 MHz, the gain has risen almost 1.3 dB. Fig. 3 provides an indications of why this occurs. As the frequency increases, the E-plane (or elevation, given that the model stretched along the Z-axis) patterns show a decreasing beamwidth. (The H-plane or azimuth patterns would show simple circles, so I omitted them.) Between any two adjacent patterns, the change is hardly noticeable, but if we compare the 300-MHz and the 800-MHz patterns, the elevation "squeeze" in the pattern is readily evident.

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The triangular P3 would serve well as either a horizontal or a vertical dipole, especially in UHF applications. Since the SWR bandwidth does vary with the diameter of the wires composing the structure, its use in HF applications, where wires are very thin (relatively speaking), is uncertain, although Dan has addressed such uses in some of his articles. At 30 MHz, the triangle face would be 0.83 m, and at 3 MHz, it would be 8.3 m. These values, of course, rest on also scaling the wire diameter to .15 m at 30 MHz and to 1.5 m at 3 MHz. Fortunately for our goals in these notes, we may simply use the model that we have described.

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The P3 with a Planar Reflector

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Providing the P3 with a planar reflector is, in principle, a relatively straightforward project. Extensive modeling with many types of antennas--ranging from lower HF NVIS aerials to UHF arrays--has yielded a rough rule of thumb. For maximum gain and a good front-to-back ratio, the reflector should extend beyond the limits of the antenna by between 0.45 and 0.55 wavelength in both planes. Therefore, the initial reflector had a size of 1.0 m side-to-side across the face of the P3. The reflector height used was 1.2 m.

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A wire-grid rectangle will generally simulate a solid surface if its wires are no longer than 0.1 wavelength between junctions. To achieve the solid-surface simulation, each wire must have a diameter determined by dividing the wire length between junctions by PI. However, we must introduce a caution here. Make the calculations at the highest frequency to be used. Using a lower frequency may result in a leaky grid or one in which the wires approach resonance. For our very wide-band project, the caution is very significant. Using 800 MHz as the wire-grid construction frequency results in models with many more segments, in some cases approaching 2000. Serious modelers should consider investing in advanced software if their entry-level packages have lower segment limits.

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Fig. 4 shows the outline of the P3 and reflector as modeled. Note that two long legs of the P3 are equidistant from the reflector, while the third leg is about 0.07 m farther forward. I selected a spacing between the driver and the reflector that results in the best compromise between the impedance and the pattern performance. The final value was 0.2 m. Table 2 shows the distance in wavelengths for each of our sampling frequencies. Note that at 800 MHz, the spacing has grown to over 1/2 wavelength. Most designers of wide-band HF dipole curtain arrays use a design-frequency spacing of about 0.3 wavelength. The test array reaches this level before the frequency increases to 500 MHz.

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The selected spacing does not yield the best possible impedance curve. A spacing of 0.22-m is slightly better, but at a cost in other performance categories. Fig. 5 shows the resistance, reactance, and 50-Ohm SWR using the selected spacing between the driver and the reflector. The 2:1 SWR bandwidth has increased its range to 285-820 MHz. The increase is about 15 MHz on the low end, but 60 MHz at the upper end of the range--compared to the independent P3. A single graph of impedance performance is sufficient for all of the models that we shall use. Although we shall vary some of the reflector dimensions, the spacing between the driver and the reflector will not change. As a result, the feedpoint impedance values do not change by more than very small amounts that we may track in the data tables. For any given planar reflector array, the driver feedpoint impedance is relatively insensitive to changes in the size of the reflector.

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Adding the large planar reflector has increased the SWR bandwidth of the P3. However, we do not yet know if the increase is worthwhile in terms of the radiation patterns produced by the antenna. One way to present such data might be to use a frequency sweep curve. Unfortunately, such curves become very misleading if the maximum gain happens to occur at an angle other than the bore sight of the antenna. In such cases, recorded 180-degree front-to-back ratio values will reference the maximum gain heading. Hence, they will not give a true indication of the direct rearward performance of the array. For this reason, we shall explore the performance of the P3+reflector by using both tables and galleries of patterns, each at successive 100-MHz sampling steps. The front-to-back value shown in the table will be the ratio of maximum gain to a direction tangent to the rear of the planar reflector. Table 3 provides our first overdose of data.

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The table has 4 types of entries. Regular type indicates that a pattern is normal, with a forward lobe and only smaller rearward radiation pattern structures. Italic type points to patterns with a single large forward lobe, but with two main headings, each equally off the axis of the array. Boldface entries indicate that the main lobe has split into two lobes, each off axis by the same amount but on opposite sides of the bore sight line. What distinguishes a two-lobe pattern from one with two main headings is the fact that each main lobe has its own beamwidth. In other words, the null between lobes is greater than 3 dB. Finally, entries that are both bold and italic indicate the presence of three distinct lobes, each of which is very significant.

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You may best examine the tabular data in conjunction with an associated gallery of H-plane (azimuth) patterns. For our initial, seemingly optimal reflector size, the patterns appear in Fig. 6. Note that for large reflector, only the pattern for 300 MHz is perfectly well behaved, that is, having a single forward and a single rearward lobe. At 400 MHz, the main lobe already shows two main bearings, with a slight decrease in gain along the main axis of the array.

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The remaining patterns in Fig. 6 provide a fairly good commentary on lobe splitting and widening and on the development of increasing numbers of forward lobes. Interestingly, the rearward lobe remains singular and quite weak. The general conclusion that one might reach is that for the P3, a large or full-size reflector limits the effective operation of the P3 to somewhere between 400 and 500 MHz, despite the fact that the SWR bandwidth is much wider.

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At this stage, the potential for improvement is limited. We cannot change the spacing from the reflector to better optimize that spacing at higher frequencies without radically altering the SWR curve. To restore the SWR curve--assuming that it is amenable to restoration--would require considerable redesign of the P3 itself. Numerous flatter drivers have quite different dimensions when optimized for planar reflector use than we find when we use the driver as an independent antenna.

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If we retain the given dimensions of the P3--which we shall do--then we have only one significant option: to change the size of the reflector. Spot checks of the model suggested that below the design limit (about 300 MHz at the low end of the passband), the patterns remain well behaved, even though the feedpoint impedances are not usable. The suggestive consequence of these checks is that we might widen the operating passband with improved pattern shapes if we reduce the size of the reflector. Rather than using a series of slow steps, I simply halved the reflector size to 0.5 m in the H-plane (horizontally) and 0.6 m in the E-plane (vertically). Again, I set the wire-grid dimensions at 800 MHz to ensure a structure that would not resonate at some intermediate frequency. Table 4 and the gallery of H-plane patterns in Fig. 7 provide the results of this modeling experiment.

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In one sense, the experiment is a success, since patterns are quite normal through 600 MHz. Even though the 500-MHz pattern is technically a dual-heading plot, the decrease in gain along the array main axis is insufficient to make the antenna less than fully functional. However, the patterns show a considerable reduction of gain. At 300 MHz, the gain is down by 1.5 dB compared to the value with the large reflector.

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In addition, the rearward radiation structure shows considerably greater development with the smaller reflector, resulting in somewhat mediocre front-to-back values. The beamwidth of the rearward lobe is much greater than for the rearward lobe with the full-size reflector. Perhaps the single relatively stable dimension of performance lies in the feedpoint impedance. If you compare the Feed R and Feed X values in Table 3 and in Table 4, you will find only relatively insignificant differences. The 2:1 50-Ohm SWR bandwidth still extends from 285 to 820 MHz.

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The data make clear that finding a compromise reflector size is one key to extending the performance of the P3 driver. However, the required reduction in reflector size results in degraded performance relative to both forward and rearward radiation. The limit of what we might call (without criteria to impose a definition) "adequate" performance is perhaps 550 MHz at most. This somewhat arbitrary limit frequency value results in a frequency range that is less than 2:1 (although it is wider than the best obtained for the batwing antenna as a driver). The bandwidth in percentage terms is under 60%.

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Past studies of planar reflectors indicate that for the normal range of driver assemblies (all 2-dimensional), variations of reflector dimensions did not equally affect both the forward gain and the front-to-back ratio. Peak gain occurs at a reflector size that is below the optimal E-plane (vertical) dimension that yields the best front-to-back ratio. Both dimensions contribute to the front-to-back ratio, but the vertical dimensions seemed more pronounced in its effect. Whether we can make a similar differentiation with the P3 is an interesting question. Therefore, let's begin again with the large reflector (Table 3) and see what results from changing only one of the dimensions at a time.

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Table 5 and the gallery of patterns in Fig. 8 supply the results of shrinking only the H-plane or horizontal dimension to 0.8-m. The vertical dimension remains at 1.2-m.

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Except for the gain at 300 MHz, the reduction in reflector width appears to have yielded an improvement. The first appearance of dual headings is at 500 MHz (instead of 400 MHz, as in the original reflector exercise). In addition, the front-to-back ratio remains universally good, and the rearward patterns remain small and distinct. However, from somewhere just below 500 MHz upward in frequency, the patterns become unusable, if the goal is maximum gain on a forward direction.

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We may repeat the experiment, this time reducing the vertical dimension to 0.9-m. The horizontal dimensions returns to its original 1.0-m value. The results of this experiment appear in Table 6 and in Fig. 9.. One conclusion that we can draw from both new experiments is that the impedance values are well within the range of those resulting from the use of the full-size large reflector and from the small reflector. Since we did not change the spacing between the P3 and the reflector surface, the 2:1 50-Ohm SWR range is still 285 to 820 MHz.

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The results of the experiment are complex when we make multiple comparisons. The gain values at the lower end of the spectrum are lower than for either of the two comparators just discussed. However, the pattern at 400 MHz has more gain than the pattern with a shrunken horizontal dimension. Despite this apparent improvement, the table shows that the 500 MHz pattern introduces a double forward heading just as did the pattern with a reduced horizontal dimension. As well, the forward lobes above 500 MHz are split to roughly the same degree.

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The effect of the vertical dimension reduction in the reflector on the rearward pattern is less a matter of numbers than of structure. The shape of the rearward pattern at 300 and 400 MHz is somewhat of a teardrop, rather than the distinct rearward lobe that we obtained from reducing the horizontal dimension of the reflector. Although the 180-degree values remain reasonably good for a planar reflector array, the rearward lobes have taken on a more complex form at higher frequencies. In general, the rearward patterns show a greater beamwidth than did the rearward patterns created by shrinking only the horizontal dimension.

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Both experimental intermediate reductions in reflector dimensions fall short of extending the operating range of the array to the extent of the half-size reflector. However, they do indicate directions for experimentation, depending upon the limits of gain reduction and the limits of rearward performance reduction that we bring to the experiment. Each intermediate dimension reduction extended the operating range by at least 100 MHz over the full-size reflector. However, the small reflector extended the range well past 500 MHz--but with further performance reductions. What compromise is best for a potential application depends upon the project requirement we bring to any further modeling.

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In addition, these notes have restricted themselves to strict planar reflectors. Hence, they provide no clue to what might occur with the use of a corner reflector or a parabolic reflector.

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The P2 without and with a Planar Reflector

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I purposely began with the 3-dimensional driver in order to evaluate its potential for use in a planar reflector array. The P3 has only 2 elements that are 0.2 m from the reflector. The third element is another 0.07 m farther away. Given the fact that a change of as little as 0.002 m could change the array's SWR curve, we likely should not underestimate the consequences of placing a 3-dimensional driver array in front of a planar reflector.

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One way to perform a quick check on the difference between a 2-D and a 3-D driver is to perform at least a perfunctory evaluation of the P2 antenna. The P2 forms a rectangle. In our application, the long legs are 0.356 m, while the short sides are 0.075 m. The wire diameter is 0.015 m (1.5 cm). Using Dan's formulations as a guide, I aimed for a feedpoint impedance centered on 75 Ohms. As shown in Fig. 10, the central feedpoint required two transmission lines, each with a characteristic impedance of 280 Ohms. Each line, with a velocity factor of 1.0, is 0.06 m long.

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As Fig. 11 reveals, the SWR behavior referenced to 75 Ohms is not quite as neat as for the P3. Nor is the 2:1 SWR bandwidth as great. The range for the P2 is 305 to 760 Ohms, very slightly less than for the P3. Nevertheless, the shapes of the resistance and the reactance curves are very close to those that we saw with the independent P3; only the values differ.

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Table 7 summarizes the data for the P2, beginning with the dimensions given in wavelengths at each sampled frequency. To the right are the AGT scores and the required correction of the raw gain reports. Due to the relative simplicity of the P2 structure, these values are superior to the values we obtained for the P3.

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The P2 gain values require some explanation. At first sight, they appear to be universally higher than the gain values obtained for the P2. However, the P3 develops an essentially circular H-plane (azimuth) pattern. The P2 does not. Since P2 consists of two dipoles fed in phase with a small space between, the broadside gain is higher than the edgewise gain. The amount of broadside-to-edgewise difference increases with frequency, since the face distance also increases with frequency. The gallery of free-space H-plane patterns appears in Fig. 12. The gallery omits the elevation or E-plane patterns since these are so similar to the ones we saw in connection with P3 in Fig. 3. In general, averaging the maximum and the minimum gain for each patterns yields a value similar to the corresponding P3 gain value at each sampled frequency.

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For the purposes of comparison, I created only a single planar reflector using the small dimensions that produced the most extended operation of the P3 driver. The reflector is 0.5 m horizontally by 0.6 m vertically. The P2 is 0.2 m ahead of the reflector, the same spacing used for the P3. However, the P2 driver proved to be not as well behaved as the P3. It required a change in both the Zo and the length of the phase lines: 250 Ohms and 0.07 m. Fig. 13 outlines the full array model.

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The array SWR bandwidth relative to 75 Ohms shows both an increase and a shift relative to the curve for the independent P2. The 75-Ohm SWR is 2:1 or less from about 315 to 800 MHz. The frequency ratio is a little over 2.5:1, while the bandwidth is close to 87%. Fig. 14 graphs the feedpoint resistance and reactance, as well as the 75-Ohm SWR, across the potential operating passband. Although detailed values differ from those of the independent P2, the array curves show essentially the same shape.

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The core question is whether the P2 performs as well as the P3 using the same small reflector. See Table 4 and Fig. 7 for the relevant P3 array values. The P2 array performance reports are in Table 8, with a gallery of H-plane patterns in Fig. 15.

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The gain values for the P2 array are superior to those for the P3 array for the 300- to 500-MHz range, before the appearance of a double heading. However, the gain change between the two main bearings at 600 MHz is so slight that the array is fully usable at this frequency. (The P3 array had shown a more severe gain reduction along the array axis at 600 MHz.) The rear lobe structure at all frequencies from 300 through 800 MHz is consistent, simple, and quite similar to the rear lobes for the P3 with the small reflector. Hence, we might conclude that the P2 array is useful over at least a 2:1 frequency range.

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It is likely, although models cannot show it, that the planar structure of the P2 driver contributes to the pattern cleanliness. However, since the broadside gain of the P2 is higher than the edgewise gain, it is equally likely that this aspect of the driver behavior also contributes to the potential extension of the P2 array's operating bandwidth.

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Special Note: the patterns shown for all planar reflector arrays in these notes are H-plane or azimuth patterns with the driver element vertical. E-plane patterns would count as elevation patterns with the element vertical, but would be azimuth patterns if we set the element horizontally. These latter patterns have complexities in addition to those shown here. Since most of the complexities occur at or above frequencies at which we encounter dual headings or split lobes, that is, beyond the range of operational utility, I have not introduced the E-plane patterns to these notes. However, for modelers, the patterns make an interesting study on their own ground.

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Conclusion

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Although we may conclude the article, I am not as certain that we may conclude the investigation. The P2 and P3 antennas are indeed very broadband aerials, especially when we use fat enough conductors. Their inherent bandwidth has provided us with an instrument to test the bandwidth that we may expect from a planar reflector. Here we ran into a conflict between the impedance and the performance requirements. To preserve the impedance curves, we had to set a fixed physical distance between the driver and the reflector. However, because this distance changes in terms of wavelengths as we increase the operating frequency, the frequency range of acceptable radiation patterns was limited. The best operating spread that we were able to obtain was a 2:1 frequency range--using the P2 driver and the small reflector.

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To obtain even this range required compromises, especially with respect to the reflector size. Extending the operating range required the use of a smaller-than-normal reflector, which results in poorer gain and front-to-back performance at the lowest frequency. However, it did enable us to obtain more usable performance at higher frequencies than we could derive from a seemingly more optimal reflector size.

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Given something like a 2:1 frequency range, one might well try to optimize further the elements of the array to provide added gain, increased front-to-back ratio, or smoother impedance curves. Such work might result in changes to the driver dimensions and/or phase-line structure. Of course, besides experimenting with various sizes of reflectors, one might also try other reflector shapes, especially a P3 with a corner reflector. These notes have only scratched the surface of what one might do to refine our understanding of converting a prismatic polyhedron into a directional array.

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Attached to this item is an entry with supplemental data relating to the P3 and planar reflectors. As well, Part 2 covers the P3 used with corner reflectors.

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Updated 06-16-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: Supplementary Data

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Go to Part 3

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Return to Main Index

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Topics: Planar Reflector, Prismatic Polyhedron, VHF / UHF


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The Prismatic Polyhedron and the Planar Reflector
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L. B. Cebik, W4RNL

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The main article on prismatic polyhedrons and planar reflectors bypassed at least two interesting P3 driver possibilities in the interests of conserving space. These supplementary notes will fill in the gap for the P3 triangular driver, at least partially. Throughout these added notes, we shall employ the small planar reflector that is 0.5 m wide (across the face of the triangular P3 structure) and 0.6 m high (along the length of the P3 driver). In all cases, the reflector will set its wire-grid lengths by reference to the highest frequency in the sampling sequence, 800 MHz.

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In addition, we shall not alter the dimensions of the P3 wire structure. In a few cases, we may change the characteristic impedance or the length of the phase lines that lead to a central feedpoint, but these changes will not affect the radiation patterns produced by the P3 driver itself.

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Fig. 1 shows one of the variables that we may introduce to the P3 driver in conjunction with a planar reflector. The original article set the driver as shown on the left. Version 1 places two legs of the triangle equidistant from the reflector surface at the closest approach. Version 2, on the right, shows the alternative orientation that places a single leg at the point of closest approach to the reflector, with the remaining legs more distant but still equally spaced from the reflector. From the triangle apex to the center of the opposite side, we have a distance of about 0.072 m (given the face dimension of 0.083 m). Variations in spacing for version 1 as small as 0.02 m produced noticeable changes in performance. Therefore, we might see performance variations just by changing how many legs are at a prescribed distance from the reflector.

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In the main article, we also fixed the spacing between the reflector and the driver's closest approach to 0.2 m, using only version 1 of the set-up. This restriction yielded consistent SWR curves for all modeling tests that changed the size of the reflector. However, we may equally fix the size of the reflector, as noted in our opening lines, and vary the spacing between the reflector and the driver. For these supplemental notes, we shall examine spacing values of 0.15 m and 0.12 m. Table 1 translates these physical distances into distances in wavelengths for each of the sampled frequencies. As we did in the main article, we shall use 100-MHz increments and sample performance from 300 to 800 MHz.

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If we combine the two sets of variations, we arrive at a matrix with 6 elements for our survey. The galleries of patterns shown in the main article provide us with a good familiarity with the patterns that we might obtain. Therefore, we may use Fig. 2 as a reference or guide and show pattern variations as a set of notes attached to each sample. We shall continue to use azimuth or free-space H-plane patterns for a consistent set of references to the radiation characteristics for the modeled antennas.

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The "normal" pattern consists of one forward lobes and one rearward lobe, as shown at the upper left. The beamwidth may vary, but the general outline does not change. At some higher frequency, the beamwidth grows to a point where the maximum gain does not appear along the main axis or bore sight of the antenna. Instead, we obtain two main headings, each angularly equidistant from the main axis. However, the forward lobe remains singular with a depression in gain along the bore sight that does not exceed 3 dB. A depression of 3 dB or more results in the pattern at the lower left. Since 3 dB marks the half-power point, each main heading now has its own calculated beamwidth. The depth of the null along the main array axis depends on two factors: the beamwidth of the individual lobes and the angular separation from the main axis. Of course, the dividing line between a 2-heading and a 2-lobe pattern is arbitrary, since it uses the half-power beamwidth convention as the dividing line. In reality, if we use small enough frequency increments, we may show patterns that approach a main-axis null of 3 dB and then pass it, and the progression will be smooth, with only lines on the plot to register the passage. A main-axis null of 2.9 dB and one of 3.1 dB will show not detectable differences in operational performance. Nevertheless, the distinction is useful. In the tabular data for 2-heading patterns, I shall indicate the depth of the main-axis null to provide an indication of how closely the pattern approaches the 3-dB limit.

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As the main lobes of a 2-lobe pattern diverge from the array axis, we find the development of a third forward lobe along the bore sight. When very small in strength compared to the 2 main lobes, we may ignore it. However, when the lobe approaches a strength that is only about 6 dB down from the maximum gain of the array, it is strong enough to affect operational performance. At roughly that point, we may call the radiation plot a 3-lobe pattern. The center lobe will increase in relative strength with further increases in frequency until the central lobe equals or exceeds the strength of the angular lobes. As long as the angular lobes have a strength that is within about 6 dB of the central lobes, we still have a 3-lobe pattern. Once the angular lobes fall below the arbitrary 6-dB limit, we may simply call them forward sidelobes. None of the patterns that we shall survey will even reach lobe-strength parity, so we shall not need to invoke the language of forward sidelobes. We should also note that a 3-lobe pattern may also show the beginnings of a 3-lobe rearward pattern, as illustrated by the lower right plot in Fig. 3.

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The significance of these differences shows up in trying to set the frequency limits of a given array configuration. In general, 2-lobe and 3-lobe patterns are unusable for applications that call for maximum forward gain along the main array axis. Normal patterns, of course, are the most desirable. The 2-heading pattern represents a frontier between the usable and the unusable. Since the main-axis gain may range from 0.01 dB up to 3 dB lower than the peak gain value, the utility of the array for a given application depends upon the acceptable gain depression and the beamwidth that we can also accept. That decision rests upon project specification brought to the design process. Hence, we can make no judgment in the abstract. By noticing the frequency at which the 2-heading patterns emerge, we can mark the frontier region between the useful and the useless, leaving finer gradation for project-directed exercises.

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Version 1 Data

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Table 2 through Table 4 present the free-space modeling data for the version-1 P3 configuration with 2 legs toward the reflector. The tables progress from a driver-reflector spacing of 0.2 m to 0.12 m. We used the 0.2-m spacing in the main article to illustrate the effects of using the small reflector. Each table lists the sampled frequency, the maximum forward gain, and a front-to-back ratio. In all cases, the front-to-back ratio is the ratio in dB of the direct rearward gain at a tangent to the rear of the reflector to the maximum gain, at whatever angle that gain occurs. Each table also records the feedpoint resistance and reactance in Ohms. Only one of the tables (Table 2) records a 50-Ohm SWR value. The other tables record NA for "not applicable." As the spacing between the driver and the reflector decreases, no phase-line Zo and length combination yields an SWR bandwidth at any reference value that covers a significantly wide portion of the total passband in the survey. It might be possible to reset the physical dimensions of the P3 driver to yield a wide SWR bandwidth at some reference impedance, but this exercise does not explore that aspect of redesign. The redesign might also achieve its goal by using fatter element wires than the 0.015-m value used in these models. That option, however, falls outside what acceptable models can show.

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The final column of each table notes the type of H-plane pattern that appears on each of the sampled frequencies. Refer to Fig. 2 for an orientation to the appearance of the patterns.

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For version-1 arrays, several trends emerge from the tables. First, the maximum gain increases at virtually all frequencies with a closer spacing to the reflector. Second, the average front-to-back ratio also increases with a closer spacing between the driver and the reflector. Perhaps most notable among the consequences of closer spacing is the increasing frequency at which we obtain normal patterns. With a spacing of 0.12 m, we find normal patterns through 700 MHz, and even the 2-heading pattern may--under some circumstances--be declared usable.

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Offsetting the performance improvements that we obtain from bringing the driver and reflector closer together is the fact that the feedpoint impedance increases its range of values, a fact that precludes obtaining a standard and acceptable 2:1 SWR curve. For resistance values, the 0.2-m spacing yields resistances between 32 and 80 Ohms. At a 0.15-m spacing, the range increase to values of 26 and 117 Ohms. Further compressing the spacing gives us 18 to 132 Ohms. To obtain the performance benefits of the closest spacing, we would need to solve a rather complex matching challenge.

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Version 2 Data

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Table 5 through Table 7 present the free-space modeling data for the version-2 configuration, with only one leg of the P3 driver closest to the reflector. Except for the specific data, the tables are identical in structure to the tables for the version-1 arrangement.

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Internally, the version-2 tables show the same progressions that we found in the version-1 tables. Maximum forward gain levels increase with smaller spacing values, as do front-to-back values. These improvements are especially notable for normal patterns, which increase in number as we close the driver-reflector spacing.

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In addition to these gains, we discover that with a spacing of 0.15 m between the driver and the reflector, we may obtain a broadband 50-Ohm SWR curve, something that we could not achieve with the version-1 counterpart. This result is important, since it indicates that the effective spacing between the driver and the reflector is not a function of the closest leg alone. Rather, it is a function of (roughly) the average distance of all 3 legs to the reflector. We may further appreciate this fact by examining several other columns in the tables for both version 1 and version 2. First, the version-2 patterns show a smaller benefit in lobe structure than the version-1 patterns for the same physical spacing. The version-1 models show a 100-MHz improvement in acceptable patterns relative to the version-2 models at the same distance. (The improvement is only approximate due to the use of such widely spaced frequency increments.) Second, the version-2 gain values for a given spacing correspond most closely to the versions-1 gain values for the next wider spacing. Indeed, the impedance values for the version-2 array with a spacing 0.12 m (Table 7) closely coincide with the impedance values for the version-1 array with a spacing of 0.15 m (Table 3).

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The P2 Driver and Variations in Spacing

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In general, based upon our work in the main article, we should expect the P2 driver to act more like version 1 of the P3 than like version 2. The P2 driver is a rectangle, with phase-lines emerging from the center of each long wire to a central feedpoint. Fig. 3 provides the outline of the P2 with a wire-grid planar reflector, which uses the 0.5-m by 0.6-m dimensions. As we did for the P3, we shall begin with a review of the performance with a driver-reflector spacing of 0.2 m, followed by surveys using 0.15 m and 0.12 m as the closer spacing values.

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In some ways, we might expect the P3 driver to act as if it is closer to the reflector than the version-1 P3 driver, since the average distance to the driver is strictly 0.2 m. In contrast, even the version-1 P3 array underwent some effect from the single leg that was farther forward. Table 8 through Table 10 provide the data for the P2 array using the designated spacing values.

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If we compare the gain values in these tables with the gain values in Table 2 through Table 4, we can confirm our expectation. The best way to make the comparison is to select a frequency at which we obtain a normal pattern for all options, perhaps 400 MHz. For each spacing value, the P2 array shows a higher gain and a higher front-to-back ratio. Of course, we cannot clearly sort the gain advantage that arises from the broadside pattern of the P2, but at 400 MHz, that effect is close to minimal. Hence, the P2 driver gives every appearance of acting like a driver that is closer to the reflector than either version of the P3.

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The broadside gain effect of the P2 driver shows up more significantly as we increase the operating frequency and therefore obtain a greater differential between broadside and edgewise gain. At 500 MHz, the version-1 P3 driver with a spacing of 0.2 m is just entering the 2-heading phase of pattern evolution. However, the corresponding P2 array provides us with a normal pattern. In fact, regardless of spacing, the P2 array shows a slower development of multiple lobes than the version-1 P3. At the closest spacing, the P2 array provides normal patterns from 300 to 800 MHz.

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The improved pattern development comes at a cost in terms of the feedpoint impedance. To obtain the improved pattern formation over a wider passband, we must accept (without altering the P2 shape) an ever-widening range of feedpoint impedance values within the passband. Whereas the version-1 P3 at 0.12 m showed feedpoint resistance values between 18 and 132 Ohms, the P2 array at the same spacing shows a range between 17 and 250 Ohms, with the extreme values occurring at adjacent frequencies in the survey (300 and 400 MHz). As a consequence, the SWR bandwidth no longer matches the pattern behavior bandwidth, even with the intermediate 0.15-m spacing value.

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There is a general trend in gain values that also deserves note, since it occurs for all three arrays. The highest gain values occur at frequencies well above the 300-MHz starting point. The closer the spacing, the higher the frequency becomes for the highest gain that still yields a normal pattern. This phenomenon results from our use of the small reflector size, which is more apt to about 600 MHz than to 300 MHz. It also leaves considerable territory for future exploration, that is, finding the optimum size reflector for the portion of the overall spectrum on which we might wish to operate a P2 or P3 array.

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Conclusion

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Experimenting with various configurations of the P3 array and examining alternative driver-reflector spacing values for both P2 and P3 arrays has turned up a number of further general conclusions. First, as we reduce the distance between the driver and the reflector, we increase the forward gain and the front-to-back ratio. As well, we increase the frequency span over with any configuration yields normal patterns. Comparing the two versions of the P3 and adding in the P2 driver showed that the effective distance from the reflector to the driver is roughly the average distance, accounting for all driver long legs.

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Nevertheless, once we try to access the improved pattern behavior by shrinking the distance between the driver and the reflector, we almost immediately encounter significant variations in the SWR bandwidth curve. Adjusting the Zo and the length of the phase lines does not provide a means of compensating for this variation. Unless one could find an alternative set of driver dimensions that would restore the impedance values with a closer spacing between the driver and the reflector, the prismatic polyhedron will not achieve both good pattern behavior and a wide and usable SWR bandwidth simultaneously. The absence of coincidence between pattern behavior and SWR is the chief limitation in exploiting the prismatic polyhedron as a driver for an exceptionally wideband planar array.

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From here, you may return to Part 1 to review the main text on planar reflectors and the P3. Or, you may proceed to Part 2, which covers the P3 used with corner reflectors.

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Updated 06-16-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Part 1

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Go to Part 3

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Return to Main Index

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Topics: Planar Reflector, Prismatic Polyhedron, VHF / UHF


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The Prismatic Polyhedron and the Corner Reflector

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L. B. Cebik, W4RNL

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In "The Prismatic Polyhedron and the Planar Reflector," and with some supplementary data later added to the version at my web site, I explored the potential of converting the prismatic polyhedron very wide-band dipole into a directional array using a planar or flat reflector. In the course of those explorations, I discovered that the array offered us a choice: either we could retain the very broad 50-Ohm SWR curve (300 to 800 MHz) but with adequate patterns over only a limited part of the range or we could obtain a range of adequate patterns over a 2:1 frequency range, but with far less control of the feedpoint SWR. These results applied equally to the rectangular P2 element and to the triangular P3 element.

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More specifically, with a fixed spacing between a P3 driver and the planar reflector (0.2 m), we preserved the SWR curve from 300 through 800 MHz at values close to those of the P3 used as an independent element. However, depending upon the reflector size, the usable pattern shapes extended only from 300 to about 400-500 MHz. By closing the spacing between the driver and the reflector, the usable pattern range extended to 600 MHz (and in one case all the way to 800 MHz). However, closing the spacing produced highly erratic 50-Ohm SWR curves, even with adjustments to the P3 phase lines. In all cases, the driver elements used only one set of dimensions, leaving one set of variables for future exploration.

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In that safari through the many variables in creating the array, I left open the possibility that we might also wish to examine the prismatic polyhedron, especially the P3, in the context of a corner reflector. The option seemed on the surface to apply especially to the P3 triangular elements, with a single leg toward the apex of the corner reflector and the remaining two legs farther forward. In these notes, I shall trace some preliminary modeling experiments to see if we obtain any useful results from mating the P3 with a 90-degree corner reflector.

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The P3 Driver

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The P3 driver element emerged from the work of Dan Handelsman and David Jefferies. See the original article for a bibliography of articles on the prismatic polyhedrons. The P3 consists of 3 dipoles, each center fed, with triangular junctions at the outer ends. Unlike a cage dipole, where we draw the cage to a center feedpoint, the P3 uses continuous elements. From the center of each element to a central feedpoint, we employ short transmission lines, all the same length and impedance. Thus, we end up with three dipoles fed in phase with relatively close spacing and connected outer ends. Fig. 1 shows the general outline, plus a free-space 50-Ohm SWR curve.

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The copper wires are all 0.015 m (1.5 cm) in diameter. Fatter wires increase the operating bandwidth, but the requirements of modeling limit the usable wire diameter. Since the antenna has corners, some as narrow as 60 degrees, using too fat a wire places the surface of one wire within the center region of an adjacent wire segment, a situation that results in NEC warning or error messages. The modeled antenna height (or the length of each long wire) is 0.32 m. Each face (or top/bottom wire) is 0.083 m. The initial transmission lines from the dipole centers to the common feedpoint are each 300 Ohms, and with a velocity factor of 1.0, the length is 0.05 m. Mating the P3 to corner reflectors required some alterations in both the phase-line characteristic impedance (Zo) and the line length. All modeling for the P3 and subsequent arrays used free-space as the environment.

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Modeled as an independent dipole, the P3 showed a 50-Ohm SWR curve with approximate limits of 300 and 760 MHz, for better than a 2.5:1 frequency ratio or about an 87% bandwidth. Dan achieved slightly better results by judicious model tweaking, while some lab versions of the antenna tested by David showed a measured frequency range of more than 3:1. The resistance and reactance values vary over small ranges and undulate, resulting in a wide SWR curve with two low points. The wide SWR bandwidth of the P3 does not result solely from the antenna geometry. The selection of the phase-line Zo and length also help to shape the SWR curve and the impedance to which we reference the SWR.

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The Corner Reflectors

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The corner reflectors for the P3 driver consist of two plane surfaces forming a 90-degree angle behind the driver. The apex of the angle forms a line that is parallel to the longer legs of the driver. In general, the distance from the apex of the reflector to the driver modifies three properties of the total array. 1. The spacing between the driver and the apex of a normal corner reflector sets the driver impedance in conjunction with the dimensions of the driver. In a narrow-band (less than 15% bandwidth) array, reducing the spacing also reduces the resistive component of the driver feedpoint. Since we shall retain a fixed driver dimension set--for reasons that will soon be very apparent--obtaining a satisfactory 50-Ohm SWR curve requires careful attention to the spacing. Small variations in the curve are possible by altering the phase-line length and Zo.

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2. Changes in the driver-to-apex distance also create changes in the maximum forward gain of an array, given a specific frequency of operation. Resetting the spacing to a larger value tends to reduce array gain, while closer spacing (up to a certain point) yields higher array gain. 3. Larger driver-to-apex spacing values tend to yield broader operating bandwidths. For relatively narrow operating ranges, the operational bandwidth for gain and front-to-back ratio will normally exceed the 2:1 SWR bandwidth. In conventional corner reflector designs (covered extensively in Planar and Corner Reflector Arrays, available from antenneX), the designer must balance the three trends to yield a satisfactory performance level for a given application.

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Conventional (that is, solid or screen) corner reflectors also tend to have ideal sizes relative to a design frequency. An E-plane dimension (that is, one in line with the driving element) should be about 1.4 wavelengths for maximum gain and very good front-to-back ratio values. Gain tends to increase for reflector side lengths (H-plane dimensions) up to about 2.4 wavelengths, although the rate of increase levels off above about 1.8 wavelengths. The H-plane dimensions is the length of each corner reflector plane. The distance across the reflector opening will be about 1.4 times the H-plane length of the reflector surfaces. The distance from the apex to the opening will be about 0.7 times for H-plane dimension for 90-degree reflectors.

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The P3 driver seemed to be a fit candidate for a broadband corner reflector in part because of its triangular shape. With one leg forming the spacing between the reflector apex and the driver, the other legs form an angle, although not perfectly aligned with the angle of the reflector surfaces. The Brown-Woodward bent fan dipole achieved considerable operating bandwidth with a conventional corner reflector, and the P3 in part replicates the same driver shaping. However, before we see if it achieves its apparent promise, we have several reflector modeling issues to consider.

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Like the planar reflectors shown in the earlier article, it is necessary to create wire-grid corner reflectors at 800 MHz so that the structure will not be self-resonant at any frequency within the sampling range (300 to 800 MHz). Because each grid segment will be shorter than had we set the wire-grid design frequency at 300 MHz, the models acquire considerable size very rapidly. Therefore, I settled on two reflector sizes to use in these initial notes, which form at most an initial feasibility study. Fig. 2 outlines the two reflectors.

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The larger of the two reflectors still falls far short of optimal dimensions as defined by narrow-band models of such arrays. The individual sides are 1 m long (although doubling the length would have brought the model closer to ideal at 300 MHz). The height is 1.2 m, a bit short of the 1.4-m ideal for 300 MHz. Nevertheless, with a P3 driver, the model contains 3715 segments, resulting in relatively long NEC run times, especially when performing a frequency sweep. Therefore, I reserved this model structure for special checks after initial modeling with a smaller reflector.

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The smaller reflector is half size. That is, it uses a height of 0.6 m and side lengths of 0.5 m. The resulting model still requires 1411 segments. Like planar reflectors, corner reflector sizes do not radically affect the driver feedpoint impedance. However, the half-size reflector is actually small enough to allow some variation in that antenna property. Nevertheless, the model proved sufficient for the initial feasibility study and also saved considerable time in making adjustments to easily varied dimensions, such as the apex-to-driver spacing and the phase-line dimensions. However, varying the physical dimensions of the P3 to obtain (if possible) superior SWR curves fell outside the range of variables tackled in this study. Indeed, that project is best accomplished within the context of a set of application specifications and goals rather than in a more abstract feasibility exploration.

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Small-Reflector Results

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Because the patterns at some frequencies will show multiple lobes, the best procedure for studying the modeling results is to use a series of tables and galleries of H-plane patterns at selected frequencies. In this way, I can provide true 180-degree front-to-back ratio values relative to the bore sight of the array, rather than opposite an off-axis main lobe. The exception to this non-graphing procedure will be the 50-Ohm SWR curves for the arrays.

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Using the small reflector, I selected two of the apex-to-driver spacing values for comparison: 0.30 m and 0.32 m. The 8" difference in spacing makes a considerable difference both to radiation performance and to the 50-Ohm SWR. The latter property appears in Fig. 3. In both cases, the driver uses 340-Ohm phase lines, each with a 0.06-m length. (The shortest physical length between a P3 leg and the central junction of phase lines is about 0.048 m.) The closer spacing value seems to offer the wider bandwidth before rising steeply. However, the wider spacing value yields lower 50-Ohm SWR values in the lower half of the spectrum, which will prove to be the vital end for acceptable radiation patterns.

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For the version of the array with a spacing of 0.30 m between the driver and the reflector apex, Table 1 and Fig. 4 supply the relevant data and H-plane patterns.

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Interpreting the data requires an orientation and initial comparison with the data for corresponding planar reflectors. The small planar reflector used in the initial article was 0.5-m horizontal by 0.6-m vertical. This screen yields forward gain values between 6 and 8 dBi, with front-to-back ratios between 9 and 12 dB. The small corner reflector has the same height as the small planar reflector. However, each of the two angled sides of the corner reflector is as large as the complete planar reflector. In addition, the angled structure of the corner increases the shadow area behind the array and better focuses the rays in the forward direction. Hence, the forward gain ranges from a little under 9 dBi up to over 11 dBi for patterns with single forward lobes. The major advantage of the corner reflector occurs in the front-to-back category. Its values now range from 15 to 24 dB.

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Table 1 does show evidence that the corner reflector falls short of optimal size at the lower end of the operating spectrum. Maximum gain for patterns with a single forward lobe occurs at 600 MHz. For reference, the corner size is about 1 wavelength per side horizontally and about 1.2 wavelengths in height at that frequency. Nevertheless, the relatively strong rear sidelobes in the patterns at the middle frequencies indicate two problems. First, the reflector remains somewhat undersized when compared to ideal dimensions. Second, at 600 MHz, the driver is about 0.6 wavelength forward of the corner apex, a considerable distance if a tight pattern is desired.

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The operational limits of the small-corner array with the smaller of the 2 sampled spacing values (0.30 m) is perhaps 600 MHz or so. Above 600 MHz, the patterns show more complex lobe structures. In addition, the SWR values relative to a 50-Ohm reference exceed 2:1 by noticeable amounts. Even though some receiving applications accept SWR values up to 3:1, the combination of pattern complexity and SWR combine to suggest that we might do further work on the model. The goal should be to retain the 2:1 operating range for the corner array, but to obtain as well an SWR curve with values less than 2:1 at least through 600 MHz.

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Fig. 3 revealed that if we increase the spacing between the driver and the corner apex by 0.02 m (to 0.32 m), we need make no other changes to the array to produce a satisfactory SWR pattern through 600 MHz. In fact, the 50-Ohm SWR remains below 2:1 through 700 MHz, although the pattern at that frequency is not especially desirable. See Table 2 and Fig. 5 for the relevant data and gallery of H-plane patterns.

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The data and patterns show only small changes in the operating values and pattern shapes over the 2:1 frequency range that we obtained with slightly smaller spacing. On average, but not for every sampled frequency, the gain and front-to-back ratio are down numerically, but the amount is not operationally significant. However, as we closely examine the patterns from 600 MHz upward, we find interesting trends. The tiny emergent forward sidelobes at 600 MHz have become more noticeable, and their growth at 700 MHz is very evident for a mere 8" change in the driver position. In fact, as the 700-MHz sidelobes have grown, the strength of the center lobe has decreased by 2 dB.

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Nevertheless, with the small corner reflector, it has been possible to obtain over a 2:1 frequency range (a 67% bandwidth) relatively acceptable corner array performance in terms of both radiation performance and SWR. We had been unable to achieve both goals together using a planar reflector. The results of these initial models with an inadequately sized reflector provided incentive to construct large models with a more adequate reflector structure.

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Large-Reflector Results

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The large corner reflector uses sides that are 1.0 m long, with a height of 1.2 m. Each corner-reflector size is equal to the large planar reflector described in the original article. The planar reflector produced gain values that ranged from 7 to 9 dBi, with front-to-back ratios running from 17 to 20 dB. These values are consistent with the values produced with a dipole driver optimally spaced ahead of an optimally sized reflector. We should expect improvements using the large corner reflector in place of the flat screen. However, the large corner reflector produces challenges relative to the 50-Ohm SWR curve.

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Fig. 6 shows the SWR curves for two spacing values of the driver from the corner apex: 0.28 m and 0.30 m. With the larger reflector, the phase lines return to a Zo of 300 Ohms, but use a 0.55-m length. Without altering the driver structure, these curves are about the best obtainable from the array, although one might continue systematically searching for other combination of Zo and length that might do slightly better.

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The curve for the closer spacing value shows a low SWR value at 800 MHz. However, the values over the primary region of concern from 300 to 600 MHz are uniformly higher than the SWR values for the wider spacing. Even the wider spacing was unable to produce a curve with all values less than 2:1, although the maximum SWR in the 400-MHz region is about 2.06:1. Although the result is less than perfect, it is adequate enough to let us examine the remaining data for the two large-reflector models.

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The information for the model with closer spacing (0.28 m) appears in Table 3, with an associated gallery of H-plane patterns in Fig. 7.

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As we expected, the increased corner reflector size provides three advantages over the smaller version. First, the gain values increase by an average of almost 2 dB, with the most significant increases occurring at the lowest frequencies. At 300 and 400 MHz, the smaller reflector was seriously undersized, but is now closer to a more optimal size. The fact that the highest gain does not occur at 300 MHz indicates that further reflector size increases might be useful, since the frequencies at which maximum gain does occur have higher than optimal apex-to-driver spacing values.

+

Second, the front-to-back ratios increase by an average of about 15 dB. The smaller reflector produced values that ran from 15 to 24 dB; the larger array range runs from 31 to 42 dB. Related to the improvement in rearward performance is the size of rearward sidelobes: they have decreased by 8 to 10 dB relative to levels using the smaller reflector.

+

If the SWR curve had cooperated, the patterns with the 0.28-m spacing of the driver to the reflector apex would have allowed us to use this version of the P3+corner through 700 MHz. The 600-MHz pattern shows no emergent sidelobes, and the forward sidelobes at 700 MHz are small enough to be tolerated in many applications. Only at 800 MHz does the pattern break into multiple forward lobes and thereby lose its utility.

+

To improve the SWR curve to the degree possible, we increased the apex-to-driver spacing to 0.30 m. Note that this spacing value is the smaller of the two values used with the diminutive reflector. We expect that the increased spacing will change the performance values in areas other than SWR alone. Table 4 and Fig. 8 provide the information on how much change occurs.

+
+ +
+
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The 8" change in spacing does not seriously affect the performance values from 300 through 500 MHz. From 600 through 800 MHz, we do find quite significant changes, especially in the categories of forward gain and pattern structure. The gain at 600 MHz drops by a full dB relative to the closer driver spacing, even though the pattern does not identify any significant forward sidelobes. However, note in the pattern gallery the severe bulges in the sides of the forward lobe, bulges that become very significant sidelobes at 700 MHz. With closer spacing, the 700-MHz forward sidelobes had shown very small development. With the increased driver spacing, the sidelobes are less than 5 dB weaker than the main forward lobe. As a comparison of the gain columns in Table 3 and Table 4 will show, they obtain their energy at the expense of the central forward lobe.

+

The exercises using the larger corner reflector suggest that we may have lost more in the pursuit of a more perfect SWR curve than we actually gained in overall performance, especially since the curve is still not below 2:1 from about 350 to 450 MHz. We lost significant gain at 600 MHz and we also lost the possible use of the 700 MHz pattern. (Adding 700 MHz to the range of usable patterns would have increased the frequency range to 2.3:1, for a 13% bandwidth increase to 80%.) The peak SWR values were 2.06:1 for lesser 600-MHz performance and 2.20:1 for performance through 700 MHz.

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Modifying the P3 Driver

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Using the larger corner reflector, we might set as an interim goal trying to improve the 50-Ohm SWR curve to match at least the level achieved with the 0.30-m driver-to-apex spacing, while preserving the patterns obtained for the closer 0.28-m spacing. We would want to obtain the improved SWR curve for at least the 300-600-MHz range to allow a 2:1 frequency range. Two strategies remain untried. One, as noted, lies outside the range of these notes, since it involves modifying the P3 driver wire structure in small increments until this avenue of effort is exhausted in terms of improved performance curves. The size of the reflector model makes this a somewhat daunting endeavor. For each new set of dimensions, we shall also have to check various phase line impedance values and lengths for the best results.

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Some preliminary modeling using the smaller reflector is suggestive. Without altering the length of the P3 (in the model's Z-axis, that is, 0.32 m), we may obtain some improvement by enlarging the face dimension. The present face dimension is 0.083 m. Enlargements up to about 1.10 m appear to flatten the SWR curves within the lower 300 MHz of the total passband, but each dimension change requires finding the correct phase-line Zo and length. Since there are differences in the P3's behavior depending upon which of our two reflectors we use. We may leave this option at this suggestive stage.

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However, there is a second alternative that might initially escape attention. As shown on the left in Fig. 9, we have imported the P3 driver just as it was when used as an independent dipole. Each phase line (A, B1, and B2) is identical in length and Zo, as is appropriate to independent use as a complete antenna in itself. However, within the context of the corner reflector, the mutual coupling between the individual legs of the P3 and the reflector differs relative to leg A on the one hand and to legs B1 and B2 on the other. (B1 and B2, of course, undergo equivalent mutual coupling.) Therefore, one may wish to experiment with adjusting the lengths of the phase lines by reference to each specific leg. The sketch on the right in Fig. 9 suggests that making line A longer than lines B1 and B2 may provide improved results.

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In a trial model, I retained the P3 dimensions with respect to the wire structure. I also used the large reflector and a driver-to-apex spacing of 0.28 m. The line Zo remained 300 Ohms. However, lines B1 and B2 increased their length to 0.06 m, while line A became 0.08 m. The physical routing of these lines may present some challenges, since the distance between the legs and the physical center point within the legs is about 0.048 m. However, for the present feasibility test, we may bypass this challenge.

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Fig. 10 presents the 50-Ohm SWR curve for the array using the modified unequal phase lines. Compare these curves to the ones appearing in Fig. 6. Over the range from 300 to 600 MHz, the new curve is superior in general to either of the previous curves, with a maximum SWR values of 2.03:1 at 380 MHz, but at the narrower driver-to-apex spacing.

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+

The smaller spacing between the driver and the apex promises better pattern behavior. In fact, the patterns for the modified P3 are so close to those in Fig. 7 that we do not need an additional gallery. Any pattern shape differences would be virtually invisible at the scale of the plots used in the galleries. We may detect the small differences by examining the data in Table 5. Except for the impedance columns, there are no significant differences between the reported performance potentials in the present table and in Table 3, which reported on the model prior to modification.

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+

The development of a smooth SWR curve for the P3+corner reflector array is not--unfortunately--a matter of selecting a different reference impedance. In all of the tables, we find a series of resistive values less than 50 Ohms, but with a set of resistance values higher than 50 Ohms in the 350-450-MHz region. The goal is to minimize the range of variation as much as may be possible. Compare the values in Table 3 with those in Table5 to see the degree of improvement and potential directions for additional improvement.

+

The modified P3 phase lines do not necessarily provide us with the last word in performance improvement. Rather, the use of unequal phase lines in conjunction with optimized dimensions may allow additional improvements in the overall performance curves for the cornered P3.

+

Conclusion

+

These initial modeling studies suggest that the P3 driver may in fact provide wider-band directional performance with a corner reflector than with a planar reflector. With a planar reflector, the effects of changing the spacing between the driver and the reflector yielded opposing tendencies with respect to SWR on the one hand and to radiation patterns on the other. In contrast, a 90-degree corner reflector appears to yield usable SWR curves and a set of radiation patterns that are acceptable at least through 600 MHz, that is, through a 2:1 frequency range. These results use fairly tight criteria of acceptance. Although some past corner-reflector arrays have claimed a 2:1 frequency range, the results appear to rest on relaxed SWR requirements associated with television reception (in ancient times that required outdoor antennas). The results shown in these preliminary notes use a 2:1 SWR limit with a 50-Ohm reference. As well, the gain values--with an adequately sized reflector--are close to normal for comparable narrow-band reflector arrays.

+

Slightly larger reflector sizes would likely yield better gain at the 300-MHz end of the passband. In addition, taller (E-plane) dimensions might improve rearward performance--mostly in terms of further reductions in rearward sidelobes. Such investigations remain for more dedicated application-specific modeling, since the model size grows exponentially with each increase in any reflector dimension. In addition, once the designer selects a satisfactory reflector model, the driver dimensions require experimental modification to arrive at the best performance, both in terms of radiation patterns and in terms of the flattest SWR curves for a selected reference impedance. In addition, one may also wish to explore narrower corner-reflector angles so that the reflector planes better parallel the sides of the driver structure.

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Like all initial feasibility studies, this one ends with notes on possible further work. However, we have gone some distance in establishing that using a P3 prismatic polyhedron driver with a 90-degree corner reflector can achieve a true 2:1 operating frequency range with good performance in the key operating parameters.

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+

Updated 06-16-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Part 1

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Return to Main Index

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Topics: Corner Reflector, Prismatic Polyhedron, VHF / UHF


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+

A 3-Moxon Polling Array for 914 MHz

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+
+

L. B. Cebik, W4RNL

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+
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+

The use of multiple antennas in a polling system--especially for repeaters--is common practice. Independent receiving antennas can be placed at specially selected sites to overcome terrain and other problems that reduce received signal strength and prevent effective use of the repeater. Fig. 1A shows the basic outline of such a system.

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The actual polling in a system of this order occurs at a central receiving site, which is ordinarily the transmitting site as well. Signal strength, easily measured in terms of audio fed to the central station via phone or other hard-wire lines (or even via RF links), determines which antenna-receiver is allowed to send its signal to the repeater transmitter.

+

A one-tower alternative, used in public service communications, appears in Fig. 1B.

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The principle of this system is to use a collection of relatively high gain antennas--such as multi-element Yagis--in a polling system located at atop a single tower. The number of antennas required is a direct function of the gain of the individual antennas. More accurately, the number is determined by the horizontal beamwidth so that coverage is overlapping with no excluded sectors. Since gain tends to be roughly proportional to boom length and element numbers in well-designed arrays and since beamwidth tends to be inversely proportional to these numbers, the higher the gain of individual antennas, the more we require to provide the desired coverage.

+

In most systems, the user antenna will be vertically polarized, so the Yagis in the polling system will also be vertically polarized. The beamwidth in this mode tends to be greater than the beamwidth of the same antenna when horizontal, so fewer antennas can do the job.

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However, arrays of long-boom Yagis tend to show rear lobes that interact with other antennas in the array of Yagis. This phenomenon tends to force a large physical separation of the antennas so that an effective array can have a considerable radius, even at frequencies nearing 1 GHz. In many cases, the gain of long-boom Yagis is unnecessarily high for a desired level of coverage. However, short boom (2-element) Yagis tend to have poor front-to-back ratios (10-12 dB maximum), enforcing the same wide separation of antennas.

+

For lower gain (6 dBi or about 4 dBd) systems, the polling array can be simplified and physically compressed through the use of vertically oriented Moxon rectangles. To test what is possible, I took a long modeling look at the Moxon rectangle scaled and adjusted for maximum performance at 914 MHz (in the amateur 33 cm band). A single rectangle for this band is a very small affair. Fig. 2 outlines the basic Moxon rectangle, with dimensions in millimeters and element diameters standardized at 4 mm.

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+ +
+

The model description for this antenna provides more detail on the element dimensions and coordinates.

+ 
914 MHz Moxon Rectangle                     Frequency = 914  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : mm)  Conn. --- End 2 (x,y,z : mm)   Dia(mm) Segs
+
+1            4.300,  0.000,-57.200  W2E1  17.200,  0.000,-57.200 4.00E+00   3
+2     W1E2  17.200,  0.000,-57.200  W3E1  17.200,  0.000, 57.200 4.00E+00  19
+3     W2E2  17.200,  0.000, 57.200         4.300,  0.000, 57.200 4.00E+00   3
+4           -4.300,  0.000,-57.200  W5E1 -27.300,  0.000,-57.200 4.00E+00   5
+5     W4E2 -27.300,  0.000,-57.200  W6E1 -27.300,  0.000, 57.200 4.00E+00  19
+6     W5E2 -27.300,  0.000, 57.200        -4.300,  0.000, 57.200 4.00E+00   5
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

The Moxon rectangle measures under 2" wide and under 5" side-to-side at 914 MHz. It shows a free-space gain of about 6.0 dBi. with a front-to-back ratio of over 29 dB, as shown in the azimuth pattern in Fig. 3. This particular version of the rectangle was optimized for a 50-Ohm feedline and shows a feedpoint impedance of 50.8 - j0.6 Ohms on the target frequency. Of special note is the -3 dB horizontal beamwidth of nearly 141 degrees. The antenna becomes a serious candidate for a simple one-tower polling array.

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The antenna can be scaled to any of the amateur or other service bands by the usual means of multiplying the element dimensions by the ratio of the baseline frequency to the new frequency. A 2-meter version of the antenna will be about 6 time larger than the 914 MHz models, with the element diameter scaled to about 1". If other element diameters are used, dimensional adjustments will be required along the lines of charts of values presented in past articles on this antenna.

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A Minimum-Spacing 3-Moxon Polling Array

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Because the Moxon rectangle is relatively insensitive to influences to its rear, it is a candidate for a very small radius array. The wide beamwidth of the antenna suggests that an effective array can be constructed using only three of the antennas. A typical experimental array for 914 MHz appears in Fig. 4.

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The model for these tests is described in the following lines.

+ 
914 MHz 3-Moxon Polling Array                     Frequency = 914  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1            0.082,  0.000, -0.057  W2E1   0.094,  0.000, -0.057 4.00E+00   3
+2     W1E2   0.094,  0.000, -0.057  W3E1   0.094,  0.000,  0.057 4.00E+00  19
+3     W2E2   0.094,  0.000,  0.057         0.082,  0.000,  0.057 4.00E+00   3
+4            0.073,  0.000, -0.057  W5E1   0.050,  0.000, -0.057 4.00E+00   5
+5     W4E2   0.050,  0.000, -0.057  W6E1   0.050,  0.000,  0.057 4.00E+00  19
+6     W5E2   0.050,  0.000,  0.057         0.073,  0.000,  0.057 4.00E+00   5
+7           -0.041,  0.071, -0.057  W8E1  -0.047,  0.082, -0.057 4.00E+00   3
+8     W7E2  -0.047,  0.082, -0.057  W9E1  -0.047,  0.082,  0.057 4.00E+00  19
+9     W8E2  -0.047,  0.082,  0.057        -0.041,  0.071,  0.057 4.00E+00   3
+10          -0.036,  0.063, -0.057 W11E1  -0.025,  0.043, -0.057 4.00E+00   5
+11   W10E2  -0.025,  0.043, -0.057 W12E1  -0.025,  0.043,  0.057 4.00E+00  19
+12   W11E2  -0.025,  0.043,  0.057        -0.036,  0.063,  0.057 4.00E+00   5
+13          -0.041, -0.071, -0.057 W14E1  -0.047, -0.082, -0.057 4.00E+00   3
+14   W13E2  -0.047, -0.082, -0.057 W15E1  -0.047, -0.082,  0.057 4.00E+00  19
+15   W14E2  -0.047, -0.082,  0.057        -0.041, -0.071,  0.057 4.00E+00   3
+16          -0.036, -0.063, -0.057 W17E1  -0.025, -0.043, -0.057 4.00E+00   5
+17   W16E2  -0.025, -0.043, -0.057 W18E1  -0.025, -0.043,  0.057 4.00E+00  19
+18   W17E2  -0.025, -0.043,  0.057        -0.036, -0.063,  0.057 4.00E+00   5
+19           0.000,  0.000, -0.100         0.000,  0.000,  0.100 2.54E+01  37
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1          10    14 / 50.00   ( 14 / 50.00)       0.000         0.000
+2          10     8 / 50.00   (  8 / 50.00)       0.000         0.000
+
+Ground type is Free Space
+

I modeled the array for a 50 mm separation of each antenna from a central axis. The radius of the result is under 100 mm (4"). The sketch shows a central mounting pole, and loads (squares) at the feedpoints of the unused (or inactive) antennas. In fact, I modeled the system in 4 separate ways: with and without a metal central mounting pole (25 mm), and with the feedpoints of the unused antenna both closed and open. To open the unused feedpoints, I simply inserted a resistive load of 10E10 Ohms. In tabular form, the results of the variations are as follows.

+ 
        Table 1:  Array Performance with Antennas 50 mm from Center
+Arrangement    F-S Gain       Front-to-Back       B/W       Feedpoint Z
+                 dBi           Ratio dB           deg.      R +/- j X Ohms
+1. No pole,
+ closed f-p    6.69           15.95               120       52.3 - j 1.6
+2. No pole,
+ open f-p      6.56           16.58               123       52.0 - j 1.6
+3. Pole,
+ closed f-p    6.70           14.39               114       53.4 + j 0.6
+4. Pole,
+ open f-p      6.60           15.96               119       53.4 + j 0.5
+

Overall, the close proximity of the individual antennas in the array is reaching a limit. The effects of the unused antennas show up as increased gain in the active antenna, accompanied by a decrease in the front-to back ratio. Fig. 5 shows the overlapping azimuth patterns of the three antennas in the array for case 2, which presumes a form of RF-transparent mounting. The pattern cross-over points are almost precisely at -3 dB points on the individual patterns. The front-to-back ratio should be sufficient to prevent any "falsing" of the system.

+
+ +
+

Despite the small differences in whether the unused antennas have open or closed feedpoints and whether or not a metal mounting pole is used, option 2 remains the method of choice for any implementation of this system. The addition of a metallic mounting pole decreases the front-to-back ratio significantly and, as well, reduces the -3 dB beamwidth below the desired 120-degree value. The modeled mounting pole does show a small but more than insignificant current magnitude.

+

Using open feedpoints for the unused antennas provides the highest front-to-back ratio and the widest beamwidth for the array (123 degrees). Given the usual disruptive influences in normal antenna mounting situations, beginning with the best configuration reduces the effect of unpredictable factors that may degrade system performance.

+

This smallest feasible system offers some physical advantages to installations. At the test frequency, the entire set of 3 antennas, plus a small electronic changeover unit or central cable terminal block, can be installed under an RF-transparent dome for complete weather protection. The diameter of the dome could be as small as 200 mm (about 8"), and the height would be determined more by the electronics and connectors than by the 120 mm (5") need to clear the antennas. Indeed, it would be feasible to use more than one Moxon spaced up to 1 wl center-to-center to increase the gain in each direction without creating a structural problem in the dome.

+

Widening the System

+

The degree of isolation among the antennas increases rapidly as one widens the spacing of each antenna from the center point. If we double the distance from 50 mm to 100 mm, the array radius grows to about 150 mm (about 6"). At the same time, the individual patterns come closer to their form when tested as isolated single antennas. See Fig. 6.

+
+ +
+

The patterns shown are for the use of a non-metallic mounting pole and for open unused feedpoints. The following table compares the array values at the wider spacing with both open and closed unused feeders.

+ 
       Table 2:  Array Performance with Antennas 100 mm from Center
+Arrangement    F-S Gain       Front-to-Back       B/W       Feedpoint Z
+                 dBi           Ratio dB           deg.      R +/- j X Ohms
+1. No pole,
+ closed f-p    6.14           23.94               135       50.3 - j 0.6
+2. No pole,
+ open f-p      6.23           26.60               130       50.3 - j 0.6
+

Either open or closed feeders would be equally useful, and the wider beamwidths in both cases ensure pattern cross-over points at about -2.5 dB signal levels. Front-to-back ratios are close to the value for an independent rectangle, and gain reductions simply reflect the lesser interactions among the three antennas. If a radius as large as 6" is acceptable, the wider-spaced version of the array is to be recommended.

+

In either form, the 3-Moxon polling array shows a fairly broad operating bandwidth. In terms of operating parameters, here are the numbers for the edges and center of a 50 MHz range from 890 to 940 MHz

+ 
   Table 3:  Array Performance with 3 Antennas from 890 to 940 MHz
+Frequency      F-S Gain       Front-to-Back       B/W       Feedpoint Z
+                 dBi           Ratio dB           deg.      R +/- j X Ohms
+890            7.08           21.63               109       34.8 - j14.8
+915            6.19           25.85               131       50.9 - j 0.1
+940            5.14           19.41               158       66.8 + j 9.7
+

For this table, I used the no-pole, open-unused-feedpoint option. As the frequency increases, the beamwidth also increases, while the gain decreases--both fairly linearly. The front-to-back ratio is near maximum at the center of this operating range. Although it would be desirable to optimize the antennas in the array for a target operating frequency, small discrepancies will not adversely affect the array's performance to a noticeable degree.

+
+ +
+

The VSWR bandwidth of the array is not severely tested by the 50 MHz bandwidth of the modeling test, as shown in Fig. 7. It peaks at about 1.6:1 at the low end of the range and does not reach 1.4:1 at the high end. In setting up an array such as this one, operating characteristics other than SWR will be the dominant concerns.

+

Conclusion

+

The 3-Moxon polling array shows considerable promise as a simple polling array for one tower with full horizon coverage in only three steps. The gain of 4 dB over a vertical dipole or equivalent antenna offers a level of reception in specific areas that might otherwise require a separate remote antenna installation. The front-to-back ratio of each antenna permits close spacing of the individual antennas in the array, as well as freedom from false signal control of the polling electronics.

+

In the 900 MHz region, the array can be placed under a protective dome of no more than 12" diameter. Of course, the array can be scaled for the amateur 432, 223, or 146 MHz bands, becoming no larger than 6 times the size of the 914 MHz test antenna system. At the larger sizes and lower frequencies, the individual antennas can be mounted with even greater separation on each leg of a support tower in a unified structure with balanced stresses upon the tower. This type of system would make a polling repeater on the receive side very practical for almost any installation.

+

The individual antennas lend themselves to many forms of construction, with increasing versatility as the frequency increases. At lower VHF frequencies, tubing or rod elements are practical, and an RF-transparent mounting system is quite practical for the antenna boom. As we move above 500 MHz, circuit board traces become feasible antenna elements and feedlines to a center "plug-in" terminal. Of course, the antenna dimensions would require re-optimization for circuit board trace implementation.

+

One factor might be overlooked in this discussion. The individual antennas of each array were unchanged for all dimensions relative to the original isolated Moxon rectangle. This fact makes the fabrication and testing of individual antennas in the array a very simple matter. If the antenna works properly in isolation, it will work within the array.

+

The 3-Moxon polling array may have other applications than repeater use. But that use alone makes the array well worth some further experimentation.

+
+ +
+

Updated 8-1-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for July, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Moxon, VHF / UHF


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Planar and Corner Reflectors Revisited

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Planar and Corner Reflectors Revisited

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This page exists to include the PDF in the topic index

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Topics: Corner Reflector, Planar Reflector, VHF / UHF


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Planar Reflectors
+ Part 1: The Planar Reflector and the Dipole

+
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+

L. B. Cebik, W4RNL

+
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+ +

+
+

2 years ago or so, I did some preliminary investigations into the use of flat-plane or planar reflectors for a few simple 432-MHz band antennas. ("The Flat-Plane Reflector for 432 MHz: Alternatives to Vertically-Oriented Yagis for Broad-Band Use") The designs, although perfectly functional, used somewhat arbitrary reflector sizes. I have been intending to return to the planar reflector, and now is as good a time as any.

+

The planar reflector may seem bulky, and the resulting array--whatever the driver--is a 3-dimensional affair, compared to the essentially 2-dimensional nature of a Yagi. However, the planar reflector array has some advantages for the home builder. First, the reflector construction is simple: a sheet or screen of any good conductor (copper or aluminum) works well. Second, the mast can attach directly to the rear side of the reflector and does not significantly interact with a vertical driver. Third, the only adjustments required are to the length of the driver and to its spacing from the reflector. By judicious pruning, we can obtain a 50-Ohm impedance with little affect on the overall array performance. Even for a simple dipole driver, the result will be an array with the performance of a 3-4-element Yagi without the need to carefully adjust each element. So for upper VHF and lower UHF use, the planar reflector and a suitable driver have much to recommend them.

+

However, in the earlier preliminary look at the planar reflector, I left many questions unanswered. Perhaps the most prominent question is whether there is an ideal size for the reflector to provide maximum performance. It turns out that there is an ideal reflector size, but that the size depends on what parameter you wish to feature--and that question depends on the design specifications and goals. The two most obvious goals that we can choose are the forward gain and the front-to-back ratio. Even for a simple dipole driver, the required reflector sizes are not the same. The impedance of the driver, however, does not vary significantly with changes in the reflector size, so there will be at least one "set-and-forget" adjustment for the array.

+

In this first part of the study, we shall look closely at the simple dipole driver with various size planar reflectors. Our goal is to get a good feel for planar reflector array properties and modeling techniques that can adequately capture them. In future parts, we shall explore what we might gain by using other drivers and what sizes of reflectors yield maximum performance from them. But for utility work, the simple dipole driver is a good starting point.

+

All of the work that follows is set for 300 MHz. Actually, the frequency is 299.7925 MHz, so that 1 wavelength is 1 meter. As a result, the dimensions will easily scale to any frequency that you want. I shall note other special properties of the designs and their models as we move along.

+

The Basic Outlines of a Planar Reflector Array and Its Models

+

The most basic planar reflector array uses a simple dipole as its driver. For all of the models that we shall explore, the dipole will be vertical, and the entire array will be in free space. Fig. 1 shows the basic outline, tilted in the sketch to show the dipole amid with modeled wires that make up the reflector. The dipole is actually centered both vertically and horizontally relative to the reflector.

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+ +
+

For this exercise at 300 MHz, the driver has an 8-mm (0.31") diameter and is 0.436-m long (or 0.436 wavelength). (We shall later see that this diameter is about 1/3rd the effective diameter of the 435-MHz dipole in the earlier article, and this fact will have an effect on the operating bandwidth of the resulting antenna).

+

The reflector model consists of a standard wire-grid structure using 0.1 wavelength segments with a diameter that is the segment length divided by PI, or about 0.0318 m. Such a structure simulates a tight screen or a solid surface quite well. Since the grid is a parasitic structure, it functions most accurately of all the possible ways in which to use a wire grid. The AGT scores of the models were between 0.997 and 0.998, for only about a 0.01-dB deficit in gain. (Wire-grids function with less adequacy but still well within the usable range when they function as a ground plane to which an antenna is attached, and with least adequacy when the wire grid is part of the antenna itself. The modeling results may still be quite usable, but the modeler needs to pay close attention to adequacy tests the more directly the wire grid is connected to the source.)

+

Because the reflectors will be used in numerous models of planar arrays, I used the numerical Green's file (NGF) system of incorporating them into models. There are 36 reflectors used in this exercise, each one having a different vertical and horizontal size. The dimensions vary by 0.2 m (0.2 wavelength) in either the vertical or the horizontal dimension from one reflector to the next. The set used here ranges from 1.0 to 2.0 m (1.0 to 2.0 wavelengths) in each dimension. I have coded the models, for example, D-H12-V14 to indicate a dipole driver with a reflector that is 1.2 m horizontally and 1.4 m vertically.

+

The use of the GM command simplifies reflector construction. I used a central wire, segmented to match the length in 0.1-m increments. Then, 2 GM commands complete the wire collection by replicating the wire enough times to match the opposing dimension. A sample for the H1.2 by V1.4 reflector results in the following NGF file.

+ 
CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.2 m;  Z = 1.4 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H12-V14
+CE
+GW 1 12 0 -.6 0 0 .6 0 .0159
+GM 1 7 0 0 0 0 0 -.1 1 1 1 12
+GM 1 7 0 0 0 0 0 .1 1 1 1 12
+GW 12 14 0 0 -.7 0 0 .7 .0159
+GM 1 6 0 0 0 0 -.1 0 12 1 12 14
+GM 1 6 0 0 0 0 .1 0 12 1 12 14
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG R-H12-V14.WGF
+EN
+

See the series on Antenna Modeling for an episode on the rudiments of creating and using numerical Green's files. Since the results of running the model above is only a file of data, we need a second file with the driver, excitation, and output requests. The model corresponding to the reflector just shown and set up for the dipole driver has the following entries.

+ 
CM Dipole .175 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.2 m;  Z = 1.4 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H12-V14
+CE
+GF 0 R-H12-V14.WGF
+GW 24 11 .175 0 -.218 .175 0 .218 .004
+GE 0 -1 0
+EX 0 24 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The file starts by calling up the data in the stored output of the Green's file. In fact, the reflector portions of all planar arrays will never need to be re-run, since other array models using the reflector need only access the reflector information in storage. Although for small reflectors, we do not save any significant time, for large reflectors, we may save considerable run time.

+

The dipole (GW 24) is 0.436 m (or wavelength) long with an 8 mm diameter. I have spaced it 0.175 m (or wavelength) in front of the reflector and adjusted its length to provide a feedpoint impedance of 50 Ohms resistive. The currents that it induces in the reflector wire grid appear in Fig. 2.

+
+ +
+

I have rotated the sketch just slightly to visually offset the dipole so as not to obscure the currents on the wires that it would otherwise hide. I also set the current span from 1E-003 maximum to 1E-017 minimum in order to show relative variations in current levels on the wire grid. Hence, the dipole is uniformly red (the highest current level) since its current exceeds the maximum in the selected range. Blue indicates the lowest current levels.

+

Because the dipole is vertical, most of the horizontal wire segments in the grid show the lowest current levels. The vertical wire segments show a central region of higher current levels that tapers off as we move away from the positions closest to the dipole. However, there are some values at the reflector edges where we show a slight rise in current relative to what one might think of as an expected progression. The sample shows the smallest reflector used in the exercise, and the patterns are not precisely the same for all reflector sizes. That variation is part of the reason why array performance changes from one reflector size to the next, whether we make the change horizontally or vertically.

+

E-Plane and H-Plane Performance Variations

+

One way to sample the performance variations is to examine the free-space patterns of the dipole/planar-reflector array. There are two polar plots of special interest. The E-plane patterns are those taken in a plane parallel to the dipole itself. If the array were over ground, then these patterns would be very close to those azimuth patterns taken with the dipole set horizontally or parallel to the ground surface. The H-plane patterns are taken in a plane at right angles to the dipole. If the array were over ground, then these patterns would be very close to those azimuth patterns taken with the dipole set vertically or at right angles to the ground surface.

+
+ +
+

Fig. 3 shows some selected E-plane patterns illustrating the evolution of the pattern across the span of sampled reflectors. The upper left pattern with 3 large rear lobes is typical of reflector sizes that are smaller than or equal to, in any progression, the size needed for maximum gain. As the reflector size increases past the size needed for maximum gain, the rear lobes shrink to the ones shown in the upper right pattern. Note the emergence of two added lobes. If we continue the progression to larger reflector sizes, the 180-degree rearward lobe disappears, as shown in the lower left pattern. In the lower right pattern, we see the highest 180-degree front-to-back ratio, created by a deep null to the rear of the heading for maximum gain. However, note that once we pass the reflector size needed for maximum gain, the worst-case front-to-back ratio remains relatively constant in the 22-24-dB range.

+
+ +
+

In Fig. 4, we have a progression of H-plane patterns. The wider beamwidth results from the fact that these patterns are at right angles to the dipole. Not every progression shows all of the shapes indicated in the drawing, but once more, they show a sort of averaged evolution. The smallest reflectors vertically tend to begin with an inverted pear shape pattern, as shown in the upper left. The pattern tends to evolve with increases in the vertical dimension to a more squared rear lobe structure, as illustrated at the upper right. Maximum front-to-back ratio for any progression of the vertical dimension tends to end with the nearly cardioidal pattern at the lower left, with only a rain drop for a rearward lobe. However, as we increase the horizontal dimension, we encounter a widening of the H-plane beamwidth. At the widest and tallest reflector sizes, the forward lobe begins to split. The forward-line null created by the split is never great (about 0.3 dB maximum), but is apparent in the lower right pattern.

+

We can follow the pattern data by also viewing the E-plane and the H-plane -3 dB (half-power point) beamwidths. Fig. 5 shows the progression of beamwidths for the E-plane patterns. In this and subsequent data graphs, I have somewhat arbitrarily placed the horizontal reflector dimension increments into separate lines, while using the X-axis for the increments of the vertical dimension. One could reverse the convention, but the data would not change.

+
+ +
+

The range of variation among all of the data for all reflectors is small for the E-plane beamwidth. There are two main clusters of lines because the data appears as integers with 1 degree each side of the centerline being the minimum. Hence, the beamwidth changes in steps of 2 degrees. Only as we increase the vertical dimension of the reflector to and beyond 1.8 m (or wavelength) do we obtain distinct values for most of the horizontal sizes.

+

However, note that as we increase the reflector size vertically, we obtain a minimum beamwidth value at a reflector height of 1.2 m (or wavelength). Minimum E-plane beamwidth tends to coincide with maximum gain and increases regularly beyond that point.

+
+ +
+

H-plane beamwidth, graphed in Fig. 6, shows a similar correspondence between maximum gain and minimum beamwidth, at least until we reach to two widest horizontal dimensions. The horizontally smaller reflectors also show another interesting feature: beyond a certain vertical height, the H-plane beamwidth remains constant. The two horizontally largest reflector change the progression by showing a continued increase in beamwidth as we increase the vertical dimension of the reflector. These are precisely the reflector dimensions that also show the beginnings of a split in the forward lobe.

+

Resistance, Reactance, Gain, and Front-to-Back Ratio

+

The reflector size may undergo a 4:1 variation in area (from 1.0 m by 1.0 m to 2.0 m by 2.0 m) without requiring any change either in the length of the driver or its spacing from the reflector. As the sample model showed, the driver remains at a spacing of 0.175 m from the reflector throughout the exercise. The highest SWR encountered at the design frequency was 1.03:1.

+
+ +
+

Fig. 7 shows a composite of the SWR curves for the smallest and the largest reflectors, along with the curve for the situation yielding the highest gain. The three curves are so coincident that the individual lines are indistinguishable. The 2:1 SWR passband is about 29-30 MHz or about 10% of the design frequency. The limited SWR passband results in part from the 8 mm (0.31") diameter dipole. One can easily expand the SWR passband by increasing the element diameter. In the earlier article, I used a 0.5" element at 435 MHz, which is electrically about 2.3 times fatter than the one used in this exercise. The result was an SWR curve under 1.5:1 across all of the 70-cm amateur band. The length of that fatter element was 0.416 wavelength, compared to 0.436 wavelength for the dipole used in this exercise. The thickness of the dipole driver--once brought to a 50-Ohm resonance--has virtually no affect upon array performance.

+
+ +
+

Although Fig. 8 may seem to present a jumble of lines, it actually shows some interesting facets of the behavior of the feedpoint resistance as we change the reflector size. The narrowest reflectors horizontally tend to have marginally higher feedpoint resistance values than the widest reflectors. Feedpoint resistance is not a strict function of gain, as was the E-plane and H-plane beamwidths. The minimum feedpoint resistance values occur one to two increments of vertical reflector height beyond the maximum gain dimension.

+
+ +
+

Reactance values more closely parallel gain performance, with all horizontal widths showing the maximum capacitive reactance at the vertical dimension that corresponds to maximum gain. Only the widest reflector (2.0 m horizontally) shows a small variation from this pattern. As well, the reduction in the capacitive reactance is not a constant curve as we increase the vertical dimension of the reflector. Note that all of the reactance values show a slight increase in capacitive reactance as the reflector reaches its maximum vertical length (20 m for this exercise). However, the variations in both the feedpoint resistance and the feedpoint reactance would be difficult to measure under the best circumstances. In both cases, the maximum variation is only a bit over 1 Ohm.

+

I have reserved the gain and front-to-back data for last. My goal has not been to create suspense, but rather to enforce attention to facets of array behavior that we often overlook in our haste to encapusulate array performance in one or two figures. However, the time has come to examine the array gain using a dipole with varying sizes of reflectors.

+
+ +
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The curves in Fig. 10 parallel each other, except for the minor deviations of the curve for the smallest reflector. For maximum gain, there is a numerically clear winner: the reflector having a vertical dimension of 1.2 m and a horizontal dimension of 1.2 m. With this reflector, the modeled free-space gain is 9.31 dBi, about the same value as a long-boom 4-element Yagi. However, note that the reflectors one step smaller and one step larger approach this value so that there would not be an operationally detectable difference. Hence, we might wish to withhold our declaration of the "winner" for a moment.

+

Note that as we increase the horizontal dimension beyond about 1.4 m (or wavelength), gain decreases with any size reflector vertically. As well, as we increase the vertical dimension beyond 1.2 m (or wavelength) the gain also decreases. The gain never decreases to below the level of a long-boom 3-element Yagi, but the decrease from peak value is clearly evident.

+
+ +
+

The 180-degree front-to-back ratio curves in Fig. 11 demonstrate why I suggested withholding a declaration of a winning reflector size. Most evident is the fact that the narrower reflectors show the highest 180-degree front-to-back ratios when combined with the tallest vertical dimension. However, review the E-plane patterns in Fig. 3, with special attention to lower right pattern. Although the 180-degree front-to-back ratio is very high (nearly 31 dB), the worst case front-to-back value is no different from the other patterns (about 22-24 dB).

+

Except for the widest reflectors, there is a general trend toward higher front-to-back ratios with increasing reflector height. The values at the height of maximum gain (1.2 m vertically) tend to be lower due to the prominent 3-lobe rear structure of the pattern, also shown in Fig. 3. However, as we increase the horizontal dimension at the maximum gain vertical dimension, the front-to-back ratio tends to increase. With a horizontal dimension of 1.6 m and a vertical dimension of 1.2 m, we lose only 0.17 dB of forward gain, but arrive at a front-to-back ratio over 20 dB.

+

Changing the Dipole Diameter and Spacing

+

I have noted in passing that changing the diameter of the dipole in front of the planar reflector will have little effect on array properties other than to change the 50-Ohm 2:1 SWR passband. Although this assertion may seem intuitively obvious, we should check it. The process only requires that we alter the dipole in selected models in order to bring it to resonance at the test frequency (299.7925 MHz).

+

Since there is a reflector that yields a distinct gain peak (H = 1.2 m, V = 1.2 m), we may use this model as a first-order check to see if the claim is confirmed or refuted. I simply took the model for this reflector and applied it to both the original dipole and two replacements. Of course, changing the dipole diameter required changing its length. As well, the process required very small changes in the spacing between the reflector and the dipole.

+

The following table shows the resulting dimensions and performance reports from the exercise.

+ 
Dipole          Dipole      Space from      Free-Space     Front-to-Back     Impedance        50-Ohm
+Diameter        Length      Reflector       Gain dBi       Ratio dB          R +/- jX Ohms    SWR
+ 8 mm (0.31")   0.436 m     0.175 m         9.31           18.33             49.44 - j1.25    1.03
+16 mm (0.63")   0.422 m     0.176 m         9.30           18.29             49.45 + j1.09    1.02
+24 mm (0.94")   0.412 m     0.177 m         9.31           18.24             49.32 - j0.91    1.02
+

As with all dimensions in meters in this exercise, a length in meters is also a length in terms of a wavelength. Hence, scaling to a desired frequency is simplified. As predicted, the change in diameter over a 3:1 diameter ratio yields no significant change in performance. The 50-Ohm SWR curves in Fig. 12 are equally revealing.

+
+ +
+

Obviously, the fatter the dipole, the broader the SWR curve. The 8-mm diameter dipole shows a 2:1 SWR between about 287 and 316 MHz, or a 9.7% passband. Doubling the diameter to 16 mm increases the lower and upper limits to about 284 and 319 MHz, respectively, for an 11.7% passband. A further increase to 24 mm sets the limits at 282 and 232 MHz, for a 13.7% passband. In critical applications, a fatter dipole may indeed be advantageous.

+

If we scale the dipoles for the 70-cm band, the smallest diameter dipole would be between 3/16" and 1/4". The mid-sized dipole would be equivalent to about 7/16", and the fattest dipole modeled would be just over 5/8". You may divide these values by 2 and by 3 for rough diameters serving 903 and 1296 MHz.

+

A second premise of this study has been that the designer will normally select the element spacing from the reflector to arrive at a convenient or target feedpoint impedance. Given that amateur practice tends to focus upon 50-Ohm coaxial cables, I used 50-Ohms as the study target.

+

The spacing of the driver from the reflector does tend to control two factors: the gain for a given reflector size and the feedpoint impedance. To bring the driver to resonance for any given spacing will be a necessary step in redesigning for an alternative feedpoint impedance. The following table provides data on three sample reflector-to-driver spacings for our simple dipole array. The reflector used for the samples was the smallest of the lot (1.0 m by 1.0 m). The driver is 8-mm in diameter throughout.

+ 
Reflector-to-      Element     Free-Space     Front-to-Back     Impedance
+Driver Space       Length      Gain dBi       Ratio dB          R +/- jX Ohms
+0.135 m (wl)       0.438 m     9.05           17.78             33.02 - j0.99
+0.175 m (wl)       0.436 m     8.86           17.31             49.85 - j0.24
+0.25 m (wl)        0.444 m     8.31           15.94             80.44 + j0.89
+

The gain and the 180-degree front-to-back ratio tend to increase with closer spacing between the reflector and the driver. Conversely, both values tend to decrease with wider spacing. When starting this study, I decided that the gain increase with closer spacing was not sufficient to warrant a requirement for a complex matching system. However, some of the more complex driver systems yet to be explored may require a wider spacing to obtain a desired feedpoint impedance, suggesting that we may not derive all of the possible gain from them. With the home antenna builder in mind, I have accepted this imperfection to focus on designs that one might produce as physical antennas with some ease.

+

Conclusions So Far

+

Our exploration of a simple dipole placed in front of a planar reflector has produced a number of interesting results.

+

1. Although the feedpoint resistance and reactance show some interesting data curves, the range of variation is so small as to allow the conclusion that the feedpoint impedance does not change materially with changes in reflector size.

+

2. The SWR passband is a function of the driver diameter and not a function of the reflector size.

+

3. For maximum gain, there is an ideal reflector size, namely 1.2-m (wavelength) by 1.2 m (wavelength). Horizontal variations from 1.0 m to 1.6 m show only a small reduction in gain, although variations in the vertical dimension show more evident gain reductions.

+

4. The larger the horizontal dimension, the higher the initial front-to-back ratio with the smaller vertical dimensions. However, a 20-dB front-to-back ratio is easily achieved at the ideal vertical dimension of 1.2 m (wavelength), with a horizontal dimension of 1.6 m (wavelength). Still, with the ideal horizontal dimension for maximum gain (1.2 m or wavelength), the front-to-back ratio is well above 18 dB.

+

This summary does not tell the complete story in the data, but it hits the most essential points. A simple dipole in front of a planar reflector--whether solid or a screen to slip the wind--constitutes a very useful and buildable utility antenna for the UHF range, especially. But the exercise does leave us in a quandary.

+

If we change the type of driver that we use for the array, will the ideal reflector size also change? Some drivers, such as a pair of dipoles in phase or a rectangle, have multiple vertical elements that are not centered. Will they need a full 0.6 m (wavelength) spacing of reflector beyond the outer driver edge to achieve maximum gain? Will such drivers show greater or lesser coincidence between the ideal reflector size for gain and front-to-back ratio? Will these drivers be equally insensitive to reflector size with respect to the feedpoint impedance?

+

It looks like I'll have further use for those reflectors whose data is stored in Green's files.

+

How Reliable Are These Models Relative to Their Purpose?

+

The models used in this exercise are designed to provide general guidance relative to the performance trends of planar reflector arrays. They are not designed to provide specific design parameters for a physical antenna. Design-specific models would require prototypes using the intended construction methods to confirm or modify the generalized features of the models.

+

However, even in the realm of providing general guidance, we may distinguish between two types of conclusions drawn from the data collected from the models. The first type of conclusion focuses upon the general trends in performance as we change the size of the reflector. These conclusions are likely to be quite accurate. The second type of conclusion identifies specific reflector sizes for peak (or null) performance in some category or another. These conclusions are subject to variation within some yet to be specified range.

+

There are tests that are relevant to the type of project being conducted, tests that we can perform within the context of modeling. In the present case, we may construct a series of reflectors using a much closer spacing of the wire-grid elements. The changes of performance reports or the changes that we may need to make in the model to achieve a given target performance can provide an indication of how much a physical antenna may vary from the models. The normal procedure would be to use a much more dense wire-grid, perhaps twice as dense as the standard wire-grid structure. Since the original models used wire-grid segment 0.1 m long, with a radius of 0.0159 m, we can rebuild the reflectors using segment lengths that are 0.05 m long with a radius of 0.008 m. The process also facilitates reflector growth in 0.1-m steps, allowing the modeler to refine certain judgments concerning what size reflector yields a certain peak performance value.

+

To test the present models, I constructed denser reflector wire-grids for the region surrounding the peak forward gain report. That report identified a 1.2-m vertical dimension and a 1.2-m horizontal dimension as the peak free-space forward gain size, using 0.2-m increments between steps. Therefore, I constructed denser reflectors with vertical dimensions that ran from 1.1 m to 1.3 m, with horizontal dimensions between 1.1 m and 1.5 m. Although the reflectors vary from the originals, the driver (dipole) itself remains unchanged: 0.436 m long with an 8-mm diameter and spaced 0.175-m from the reflector.

+

Since the data covers only a limited span of the total covered in the initial model sweeps, we may survey it in tabular form. In this instance, the table has 3 sections, separated by the levels of the reflector's vertical length. Each data grouping within a section proceeds according to increases in the horizontal length of the reflector.

+ 
Vertical = 1.1 m
+Horizontal    Free-Space    Front-to-Back    E-BW       H-BW       Impedance        50-Ohm
+Length        Gain dBi      Ratio dB         degrees    degrees    R +/- jX Ohms    SWR
+1.1 m         9.05          17.96            56         82         49.77 - j0,92    1.02
+1.2 m         9.09          18.39            56         82         49.70 - j1.01    1.02
+1.3 m         9.11          18.90            56         82         49.62 - j1.04    1.02
+1.4 m         9.09          19.49            56         82         49.56 - j1.09    1.02
+1.5 m         9.06          20.16            56         84         49.53 - j1.01    1.02
+Vertical = 1.2 m
+Horizontal    Free-Space    Front-to-Back    E-BW       H-BW       Impedance        50-Ohm
+Length        Gain dBi      Ratio dB         degrees    degrees    R +/- jX Ohms    SWR
+1.1 m         9.22          18.17            54         82         49.53 - j1.29    1.03
+1.2 m         9.26          18.45            54         80         49.44 - j1.36    1.03
+1.3 m         9.27          18.82            54         82         49.35 - j1.36    1.03
+1.4 m         9.25          19.28            54         82         49.28 - j1.33    1.03
+1.5 m         9.20          19.85            54         84         49.25 - j1.27    1.03
+Vertical = 1.3 m
+Horizontal    Free-Space    Front-to-Back    E-BW       H-BW       Impedance        50-Ohm
+Length        Gain dBi      Ratio dB         degrees    degrees    R +/- jX Ohms    SWR
+1.1 m         9.30          18.85            54         82         49.17 - j1.38    1.03
+1.2 m         9.32          18.93            54         82         49.09 - j1.42    1.03
+1.3 m         9.32          19.11            54         82         49.01 - j1.40    1.04
+1.4 m         9.29          19.41            54         84         48.97 - j1.35    1.03
+1.5 m         9.23          19.84            54         84         48.96 - j1.30    1.03
+

The data cover in more detail a much smaller span of reflector variations, so the small variations from step to step are natural. For example, the E-plane and H-plane beamwidths vary by only 2 degrees in either plane across the entire set of models.

+

The denser grid structure suggests that both vertical and horizontal reflector dimensions of 1.3 m (wavelength) are closer to the precise dimensions for maximum overall gain from the planar reflector array using a single dipole driver. The 0.2-m increment used in the initial modeling could not have revealed such a result. We may also note that a horizontal dimension of 1.2-m (wavelength) also yields the reported 9.32-dBi maximum gain value.

+

The two points within the table that correlate to points of our original grid dimensions use horizontal dimensions of 1.2 m and 1.4 m with a vertical height of 1.2 m. In both cases, the denser grid yields gain values that are lower than the original, but only by 0.02 to 0.05 dB. The 180-degree front-to-back ratios also differ for the two points, both being up by about 0.1 dB. The resistance values are the same, with a reactance variation of only about 0.1 Ohm. Both E-plane and H-plane patterns would overlay each other to hide one beneath the other.

+

The results of this test--although limited to a small span of array sizes--suggest that the 0.1 wavelength per segment wire grid is quite reliable as a simulation of either a tightly-spaced screen or of a continuous surface. Indeed, one of the reasons for using fairly large diameter wire in the grid is to achieve the effect of a solid surface. The internally available tests of the initial models suggest that the numerical results with respect to gain and front-to-back are good to the first decimal place. As well, one may have good confidence in the features of the E-plane and H-plane patterns.

+

Our future episodes in this saga will use the wider spacing of grid wires throughout for consistency and ease of data gathering. As we halve the length of each segment within a grid of constant perimeter dimensions, the number of segments expands by a factor of nearly 4. Hence, it is possible to exceed the capabilities either of the core or of one's patience. Nevertheless, before we have reached the end of the final episode in this series, we shall again return to the question of model reliability. As well, nothing in the confidence that the test yields for the models is a substitute for careful prototype construction and measurement.

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+ +
+

Updated 02-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX January, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: Planar Reflector, VHF / UHF


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Planar Reflectors
+ Part 2: Phased Dipoles and Rectangles

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+
+

L. B. Cebik, W4RNL

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+
+ +

+
+

In part 1 of this exercise, we explored models of a planar reflector using vertical and horizontal dimensions that varied from 1.0 to 2.0 wavelengths per side. The test frequency was 299.7925 MHz so that a wavelength equaled 1 meter. The overall goal of the set of tests was to determine if there is an "ideal" size of planar reflector relative to the particular driver used to complete the simple array.

+

In the initial test set, we used a single dipole as the driver. We set its length and spacing from the reflector to achieve a 50-Ohm feedpoint impedance. (The dipole diameter was 8 mm, which has a major effect on the length and a minor effect on the required spacing from the reflector.) We set the dipole vertically relative to the reflector dimensions so that the free-space E-plane corresponds to the vertical reflector length and the H-plane corresponds to the horizontal reflector length. By surveying reflector sizes in a matrix of dimensional variations, we reached the following tentative conclusions.

+

1. Although the feedpoint resistance and reactance show some interesting data curves, the range of variation is so small as to allow the conclusion that the feedpoint impedance does not change materially with changes in reflector size.

+

2. The SWR passband is a function of the driver diameter and not a function of the reflector size.

+

3. For maximum gain, there is an ideal reflector size, namely 1.2 m (wavelength) by 1.2 m (wavelength). Horizontal variations from 1.0 m to 1.6 m show only a small reduction in gain, although variations in the vertical dimension show more evident gain reductions.

+

4. The larger the horizontal dimension, the higher the initial front-to-back ratio with the smaller vertical dimensions. However, a 20-dB front-to-back ratio is easily achieved at the ideal vertical dimension of 1.2 m (wavelength), with a horizontal dimension of 1.6 m (wavelength). Still, with the ideal horizontal dimension for maximum gain (1.2 m or wavelength), the front-to-back ratio is well above 18 dB.

+

The data accumulated for the dipole driver left us with a number of questions for which we require further investigation.

+

1. The ideal reflector horizontal dimension is 1.2 m (wavelength) in the initial test. This dimension extends the reflector 0.6 m (wavelength) each side of the dipole. If we replace the dipole with a more complex driver, will the extension remain constant or will the overall horizontal reflector length remain constant-- or neither?

+

2. The dipole that we used had a diameter of 8 mm and a length of 0.436-m (wavelength). The ideal reflector vertical dimension--in line with the dipole--was 1.2 m (wavelength). The extension of the reflector beyond the dipole at each end was 0.382 m. The remaining question is whether the vertical dimension of the ideal reflector is a function of the dipole length or a function of the frequency of operation. If the vertical dimension is a function of frequency, then the dimension should remain relatively unchanged if we use drivers with different vertical dimensions. If the reflector vertical length is a function of the driver length, then it would likely vary if we use drivers with, for example, significantly shorter vertical dimensions.

+

3. The resistance and reactance--along with the SWR passband--proved to be functions of the driver's physical and electrical properties and did not vary significantly as we changed the dimensions of the reflector. Will these feedpoint properties prove to be generic to the reflector-driver array or will they change if we use a more complex driver?

+

The interest in using a more complex driver owes in part to the structure of a planar reflector array. With a simple dipole driver, we obtained a maximum free-space gain of 9.31 dBi, about the level of a 4-element Yagi of good design. However, the planar reflector and its driver form a 3-dimensional structure, in contrast to the essentially 2-dimensional Yagi structure. If we can replace the driver with one that yields more gain, we might increase the justification for using a 3-D structure, especially in light of the fact that we can produce a relatively strong antenna by mounting the reflector directly to the support mast.

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The Next Step

+

In this episode, we shall begin some explorations of more complex drivers that yield more gain than a simple dipole. The drivers included in this part of the study will include the following ones.

+
+ 1. A pair of in-phase-fed dipoles. +

2. A single side-fed rectangle.

+

3. A double rectangle.

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+

Phased dipoles will provide a bi-directional pattern and hence higher maximum gain than a single dipole. A side-fed rectangle uses a wire loop about 1 wavelength total to effectively provide two shortened dipoles for which the horizontal wires then provide the requisite phasing. If we place two rectangles end to end and use a common side, then we effectively have three dipoles in phase. The rectangles provide the shorter vertical dimension by which we can approach an answer to our question on the ideal vertical dimension for the reflector. Each of the arrays has a different horizontal dimension, and that fact will give us a start toward answering the question of the reflector's horizontal dimension. The variations among the driving requirements for the 3 new study drivers will provide a test of whether the resistance, reactance, and beamwidth functions remain as constant as for the simple dipole driver. Finally, we shall be able to see if we acquire sufficient gain increase to warrant the extra construction effort.

+

Our modeling procedure, described more fully in Part 1, simplifies the data collection. We have already established that the AGT scores for the driver plus wire-grid reflector fall in the high-confidence range, since the reflector is not connected directly to the fed element. Hence, the modeling results should provide good general guidance relative to the questions that we have posed.

+

Data gathering for a matrix of 36 models is simplified by the modeling strategy used in Part 1. The 36 reflectors are already modeled as numerical Green's files. A sample for the H1.2 by V1.4 reflector results in the following NGF file.

+ 
CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.2 m;  Z = 1.4 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H12-V14
+CE
+GW 1 12 0 -.6 0 0 .6 0 .0159
+GM 1 7 0 0 0 0 0 -.1 1 1 1 12
+GM 1 7 0 0 0 0 0 .1 1 1 1 12
+GW 12 14 0 0 -.7 0 0 .7 .0159
+GM 1 6 0 0 0 0 -.1 0 12 1 12 14
+GM 1 6 0 0 0 0 .1 0 12 1 12 14
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG R-H12-V14.WGF
+EN
+

The reflector files are identical except for the dimensions and segmentation of the center wires for each reflector size and for the number of replications in the corresponding GM commands. Although I was prepared to create further reflector models using larger dimensions, this set of tests did not require them.

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Each new driver requires a master model for its elements, as well as excitation specification and output requests. The only variation among the models is the GF line that calls up the pertinent reflector. Hence, the modeler may use 36 models or a single modeled varied 36 times. The choice rests upon whether one needs to go back and review the data in the NEC output file after recording the initial outcome. All modeling for this study used GNEC with its NEC-4D core. However, NEC-2 should provide comparable results, although one may wish to invoke the EK command for situations where the segment length to wire radius ratio is less than about 8:1.

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2 In-Phase-Fed Dipoles Plus a Planar Reflector

+

If we place 2 dipoles 1/2 wavelength apart and feed them in phase, we obtain a bi-directional H-plane pattern with a maximum gain that is considerably higher than we can achieve with a single dipole. The maximum gain occurs at right angles to the plane formed by the 2 dipoles, that is, broadside to the pair. The directions that are in line with the dipoles show deep far-field pattern nulls. If we place the dipoles forward of a planar reflector, we should be able to capitalize on a good portion of that gain improvement. Fig. 1 shows the general outline of the scheme.

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+ +
+

The separation of the dipoles is 0.5 m (wavelength). The dipole lengths are 0.466 m (wavelength) each, using the same 8 mm element diameter that we applied to the single dipole. However, the separation of the dipoles from the reflector by 0.25 m (wavelength) requires some explanation, since we used a separation of 0.175 m for the single dipole.

+

Feeding two dipoles in phase in most installations will require equal lengths of a feedline from the individual dipoles to a center point between them. I shall continue to assume a 50-Ohm main feedline impedance. Hence, when we join the feedpoints in parallel at the center point, each should show 100 Ohms. In general, we can obtain this impedance value in two ways. First, we can place the individual dipoles away from the reflector at a position that yields a 50-Ohm impedance. Then we can run 70.71-Ohm 1/4 wavelength matching sections from each feedpoint to the center junction. This strategy will yield the required 100-Ohm impedance for the parallel junction, but has a number of practical problems. First, constructing a 70-Ohm feedline as a parallel line is not practical with round wires. Flat surfaces can achieve this characteristic impedance with very close spacing. To maintain the spacing, we generally need to use a supporting surface or substrate which will reduce the velocity factor to less than 1.0. However, the distance from each dipole to the centerline is a physical 1/4 wavelength. Hence, for lines with a velocity factor of less than 1.0, the line will not reach. Using 3/4 wavelength lines may be impractical if we wish to avoid unwanted interactions with the lines.

+

For this exercise, I chose an alternative procedure. By setting the dipoles farther away from the reflector, we can obtain a 100-Ohm feedpoint impedance at resonance. Then we can run 100-Ohm lines to the center junction. The velocity factor no longer makes a significant difference to array operation, since the lines are not effecting an impedance transformation. We lose a small increment of gain in the greater spacing between the reflector and the driver assembly, but we gain a considerable amount of construction simplification.

+ 
CM In-Phase Dipoles .25 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.0 m;  Z = 1.0 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H10-V10
+CE
+GF 0 R-H10-V10.WGF
+GW 24 11 .25 -.25 -.233 .25 -.25 .233 .004
+GW 25 11 .25 .25 -.233 .25 .25 .233 .004
+GE 0 -1 0
+EX 0 24 6 0 1 0
+EX 0 25 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The sample model file--which calls up the smallest reflector--illustrates the ease of data gathering with the techniques used and confirms the dimensions used for the study of in-phase-fed dipole drivers. Note that data gathering allowed each driver to be independent to confirm the 100-Ohm individual feedpoint impedance.

+

I shall not present resistance, reactance, and beamwidth graphs, since those in Part 1 accurately reflect the behavior of the in-phase-fed dipoles. At the design frequency, the feedpoint resistance varies by only about 2 Ohms maximum, with a similar 2 Ohm variation in reactance across all 36 reflector models. The feedpoint reactance is minimum at the reflector vertical height that yields maximum gain. The feedpoint resistance is minimum with a vertical reflector height 1 increment larger. The E-plane beamwidth varies between 56 degrees and 78 degrees across the span of reflectors, with the tallest reflectors showing the widest beamwidth values. The E-plane beamwidth narrows at the reflector height for maximum gain by 4 degrees relative to the values for adjacent reflector vertical sizes. The major difference in the E-plane beamwidth behavior, relative to the single dipole driver, is that we find a larger increase in beamwidth as we move from a vertical height of 1.4 m (wavelength) to 1.6 m (wavelength). For the single dipole driver, the increase between these reflector sizes was not distinguishable from a smooth curve. However, for the dual driver, the increase is 6 to 8 degrees, which amounts to a noticeable jump.

+

Of course, the H-plane beamwidth values differ from those associated with the single dipole driver. The dipole driver showed values between 82 and 104 degrees, with signs of forward lobe splitting at the widest beamwidths. The pattern focus associated with the in-phase-fed dipole pair yields nearly constant beamwidth values that vary only between 54 and 60 degrees. For any reflector horizontal dimension, the variation over the span of vertical dimensions is only 4 degrees.

+
+ +
+

Fig. 2 shows the data for the free-space gain of the dual-dipole array for the entire data set. As I did in Part 1, I have assigned different horizontal reflector dimensions to different graph lines and assigned the changes in reflector height to the X-axis. Perhaps the most striking fact is that the maximum gain occurs with a vertical reflector dimension of 1.2 m (wavelength). The highest gain occurs with a horizontal dimension of 1.6 m (wavelength). Maximum gain is 10.85 dBi, about 1.54 dB higher than we obtained with the single dipole driver. However, horizontal reflector sizes from 1.4 m to 1.8 m are too closely nested with the maximum value to represent detectable differences. As we increase the horizontal dimension of the reflector, the gain decreases more rapidly once we pass the vertical reflector height of maximum gain. The increasing rate of decrease is evident from the slope of the lines for the horizontally largest reflectors.

+

If we use the horizontal dimension of 1.6 m as the peak gain size, then the extension of the reflector on either side of the dipole pair is about 0.55 m. Within the limits of the increments of reflector size change that we are using (0.2 m), the extension is comparable to the extension each side of the single dipole (0.6 m) for maximum gain. The vertical dimension of maximum gain (1.2 m) remains unchanged from the single-dipole value.

+
+ +
+

The twin-dipole driver array shows peak values of front-to-back ratio--in Fig. 3--within the range of vertical dimensions for the reflector, at least for the two smallest reflectors horizontally. These peaks differ from the single dipole curves in Part 1, where for all reflector sizes horizontally, the front-to-back curves remained on an up-swing through the vertical limit of the exercise. As well, with only a single dipole driver, the widest reflectors actually showed a leveling or downward trend in the front-to-back ratio for the two widest reflectors. However for the dual-dipole driver, the front-to-back ratio continues its upward swing through all of the widths of reflector.

+

The key to the difference lies in the narrower H-plane beamwidth of the dual-dipole driver itself. In essence, the rearward energy is more focused toward the reflector, resulting in a faster rise in the front-to-back ratio. With a single driver element that has an omni-directional pattern without the reflector, the array requires more horizontal area, relative to any vertical size, to reflect the energy forward and therefore to effect a high front-to-back ratio. However, this account is at best partial, since the rise in the front-to-back ratio is actually slower for each increment of vertical increase as we make the reflector wider (horizontally longer). This latter phenomenon holds true of both drivers, at least within the exercise limits for reflector size.

+

One advantage of in-phase-feeding the dual dipoles is extended operating bandwidth. With a single dipole driver, the array showed a 9.7% operating passband between 2:1 50-Ohm SWR points using the 8-mm diameter element. With 2 dipoles of the same diameter, the array shows a 26% operating passband between 50-Ohm 2:1 SWR points, as shown in Fig. 4. As with the single driver system, the SWR curves coincide within very tiny limits for all reflector sizes. As virtually always, the SWR increases more rapidly below the design frequency than above it.

+
+ +
+

The broader SWR bandwidth for the array allows the user to take advantage of the fact that other performance figures also change slowly across the passband. The following table shows the modeled performance of the array at the limits of its SWR coverage. For this exercise, I remodeled the highest gain version of the array using the TL facility to create two 100-Ohm lines to a central junction. The junction wire is the model feedpoint.

+ 
Frequency         Free-Space        Front-to-Back         Impedance
+MHz               Gain dBi          Ratio dB              R +/- jX Ohms
+270               10.45             18.94                 36.4 + j26.6
+300               10.85             19.15                 51.1 + j 0.9
+349               11.00             19.97                 25.1 - j 5.4
+

Because the beamwidths for the dual-dipole driver differ from those for the single-dipole driver, we may usefully examine a set of free-space patterns for the array. Fig. 5 shows a set of roughly evolutionary E-plane patterns, that is, patterns that are aligned with the plane of the individual dipoles.

+
+ +
+

The top two patterns, plus the one on the lower left, show the progression of pattern development from below, through, and above the maximum gain point until we achieve a maximum front-to-back ratio. These patterns come from a smaller reflector horizontally in order to be able to show the maximum front-to-back ratio. Note the emergence and development of a new set of rearward lobes during the progression. As we increase the horizontal dimension of the reflector, we do not reach the point of maximum front-to-back ratio, but we do increase the beamwidth slightly. The lower right pattern shows that condition, with its array of 5 roughly equal-strength rearward lobes. Note that under these conditions, the gain is down by about a dB from its maximum possible value, but the worst-case front-to-back ratio value improves.

+
+ +
+

In the H-plane, the same first 3 patterns show a different sort of development, with only 1 significant rearward lobe. As we pass through and beyond the maximum gain point for the array, the lobe diminishes until it disappears in the maximum front-to-back plot. As we increase the horizontal dimension of the reflector, the rearward deep null cannot appear within the exercise limits. However, with the widest and tallest reflector used, the rearward quadrants take on a rounded appearance in the 30-dB front-to-back ratio category, which exceeds the worst-case values for the other patterns.

+

The end result is that selecting the reflector size for maximum gain may not achieve the maximum front-to-back values possible when we measure the entire rear area. Hence, the designation of the 1.6-m (horizontal) by 1.2-m (vertical) reflector as optimal applies only to forward gain. An array designer may give to the rearward lobes whatever weight the design specifications may demand. What the current test array has in common with the original simple model is this: maximum gain does not occur at the same reflector size as maximum front-to-back ratio.

+

A Side-Fed Rectangle Plus the Planar Reflector

+

Builders who do not wish to contend with the complexities (both electrical and physical) of a phasing system for dual dipoles have a number of potential substitutes. Among the simplest is a single 1 wavelength resonant rectangle, with shorter vertical sides and a longer horizontal dimension. When fed at the center of one of the vertical sections, the array simulates a pair of phased vertical dipoles. The end vertical sections are less than 1/2 wavelength apart, and so the rectangle does not achieve the full gain of the dipole pair. Nevertheless, the rectangle requires only a single feedpoint and thus simplifies the feed system.

+

The question is how much gain we may retain and still have an array that balances spacing from the reflector with the rectangle shape for a 50-Ohm feedpoint. Rectangles tend to show increased gain with shorter vertical sections and longer horizontal sections that better approximate the optimal half wavelength spacing. However, as we shorten the vertical dimensions, the resonant impedance tends to decrease. In principle, one might select almost any rectangle proportions and achieve a 50-Ohm impedance by judicious selection of the driver-to-reflector spacing. However, as we increase the spacing, we reduce array gain. Hence, any set of dimensions will be a compromise.

+

For this exercise, I chose a set of rectangle dimensions that permitted closer spacing to the reflector (0.186 m) and a rectangle that is 2.1 times horizontally wider than it is vertically high. The vertical sections are 0.172 m and the horizontal dimension is 0.362 m for 50-Ohm resonance at the test frequency. Fig. 7 shows the general outlines of the antenna in front of its reflector. For the rectangle, the wire diameter was reduced to 4 mm to reflect what are likely to be actual construction practices.

+
+ +
+

The following lines show a sample master model for the rectangle.

+ 
CM Rectangle 0.186 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.0 m;  Z = 1.0 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H10-V10
+CE
+GF 0 R-H10-V10.WGF
+GW 24 5 .186 -.181 -.086 .186 -.181 .086 .002
+GW 25 9 .186 -.181 .086 .186 .181 .086 .002
+GW 26 5 .186 .181 .086 .186 .181 -.086 .002
+GW 27 9 .186 .181 -.086 .186 -.181 -.086 .002
+GE 0 -1 0
+EX 0 24 3 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The behavior of the rectangle with respect to the source impedance at the test frequency does not vary enough to call for comment, except in one category. With the single and dual dipole drivers, we were able to correlate the most capacitively reactive value to the maximum gain point along any of the reflector size variations. However, the minimum resistance value at the feedpoint did not correlate to anything specific. With the rectangle, one can detect a partial correlation with a slight increase in the H-plane beamwidth. The correlation is tentative for two reasons. First, the increase is small and does not show for every level of horizontal dimension as we pass one or two steps of vertical increase beyond the maximum gain reflector size. Second, the beamwidth is recorded in integers and hence only shows itself if the beamwidth increase is sufficiently great. As noted, the H-plane beamwidth is very stable over the range of reflector sizes. Hence, confirmation of the correlation would require further refinements in the data gathered.

+

However, for the rectangle, we shall not achieve quite the gain level of the dual-dipole driver. Therefore, the H-plane (but not the E-plane) beamwidth is somewhat wider over the entire range of reflector sizes. The average increase is about 10 degrees (from an average in the upper 50s to an average in the upper 60s). Hence, the peak value has a better chance to show itself--and does in most of the data gathered from the models.

+
+ +
+

Despite the fact that the vertical dimension of the rectangle is less than half that of either type of dipole driver, the peak gain occurs with a reflector vertical dimension of 1.2 m (wavelength), as shown in Fig. 8. The ideal reflector size (for maximum gain) is 1.4 m (wavelength). Since the rectangle is 0.362-m wide, we have about 0.52-m overhang of reflector beyond the rectangle at maximum gain. This figure correlates well with the 0.6-m value for the single dipole and the 0.55-m value for the dual-dipole driver, when each is set against the reflector size that shows maximum gain.

+

In all other respects, the gain curves replicate the appearance of those for the other driver systems. The maximum free-space gain for the rectangle is 10.37 dBi, about a half-dB less than for the dual-dipole driver. We expected this result from the increased H-plane beamwidth figures.

+
+ +
+

The front-to-back curves in Fig. 9 also add pieces to the puzzle of planar reflector array performance. The peak front-to-back value for the horizontally smallest reflector occurs between the recorded point--about a vertical height of 1.7 m. The next size larger horizontally does not reach a peak front-to-back value within the exercise limits. In contrast, the dual-dipoles reach a peak front-to-back value at a vertical height of 1.6 m with the 1.0-m horizontal reflector size and also reached a peak value within the scope of the reflector sizes for the next larger horizontal dimension.

+

The lower gain of the rectangle coincides naturally with the wider H-plane beamwidth. As we saw when comparing the single and dual dipole drivers, narrower beamwidths tend to show greater energy focus to the rear toward the reflector and hence a higher front-to-back ratio at its peak. As we gradually reduce the focus, that is, widen the beamwidth, we require a larger reflector vertically to reach the peak 180-degree front-to-back ratio within a given horizontal dimension.

+

The rectangle, besides showing slightly reduced gain relative to the dual-dipole driver, has a second disadvantage: a much narrower 50-Ohm SWR operating pass band. Fig. 10 shows the data.

+
+ +
+

The 2:1 passband extends from about 293 to 307 MHz, for a 4.7% operating bandwidth. Performance checks beyond the SWR passband suggest that the gain and front-to-back ratio hold up equally to the dual-dipole array. For many applications a 4.7% passband may be more than sufficient. However, the amateur 70-cm band is about 6.8% wide. Hence, one might well have to increase the wire diameter of the rectangle in order to provide full-band coverage. The comparison in Part 1 among wire sizes will be a general guide to expected levels of SWR passband improvement with fatter rectangle construction.

+

Throughout this exercise, I have been using lossless (perfect) wire for all of the models. One may question the practice, since real wire will have losses. Therefore, I rewrote the maximum gain model for the rectangle to apply copper wire losses to both the rectangle and to the reflector. The following 2-line table provides the results.

+ 
Material      Free-Space      Front-to-Back      Impedance          E-BW         H-BW
+              Gain dBi        Ratio dB           R +/- jX Ohms      degrees      degrees
+Perfect       10.37           19.43              49.76 + j 0.39     56           63
+Copper        10.36           19.43              49.96 + j 0.57     56           63
+

At the test frequency (about 300 MHz), the smallest wire diameter is still large as a function of a wavelength. Hence, skin effect, while mathematically noticeable, is not significant relative to array performance.

+

A Double-Rectangle Plus a Planar Reflector

+

An alternative to the single rectangle as a driver that does not require the fabrication of transmission lines is the double rectangle. Fig. 11 shows the general outline of the new driver with its planar reflector.

+
+ +
+

The double rectangle consists of two rectangles with one common vertical side shared by both. The feedpoint is the center of the middle vertical section of the driver. Like the single rectangle, the vertical sections form phased dipoles, with the horizontal wires acting as phase lines. Radiation from the horizontal sections is nearly (but not quite completely) self-canceling. Since the dipoles are short and the spacing less than 1/2 wavelength between pairs of verticals, we cannot realize all of the gain that we might get from properly phased full-size dipoles. However, we might obtain enough to equal at least a pair of phased full size dipoles.

+

An added difficulty to overcome in the basic design is the fact that the feedpoint impedance of an optimized double rectangle (without a reflector) is around 16 Ohms, using 4-mm wire for the elements at our test frequency. As a result, the driver must be further from the reflector than in any other array so far: 0.235 m (wavelength). In addition, just as an optimized Bobtail curtain is vertically shorter than its optimized little brother, the half-square, so too the double rectangle will be shorter than the single rectangle. In this case, the height is 0.1492 m (wavelength), about 13% shorter than the driver we just examined. The overall length (horizontal dimension) is 0.7 m (wavelength). The following lines show a sample model of the double-rectangle driver.

+ 
CM Double rectangle 0.235 m from planar reflector
+CM Planar Reflector 299.7925 MHz (WL=1 m)
+CM Y = 1.0 m;  Z = 1.0 m
+CM standard wire-grid:  Seg L = 0.1 m; radius = L/PI = 0.0159 m
+CM NGF file:  R-H10-V10
+CE
+GF 0 R-H10-V10.WGF
+GW 24 5 .235 0 -.0746 .235 0 .0746 .002
+GW 25 12 .235 0 .0746 .235 .35 .0746 .002
+GW 26 12 .235 0 -.0746 .235 .35 -.0746 .002
+GW 27 5 .235 .35 -.0746 .235 .35 .0746 .002
+GW 28 12 .235 0 .0746 .235 -.35 .0746 .002
+GW 29 12 .235 0 -.0746 .235 -.35 -.0746 .002
+GW 30 5 .235 -.35 -.0746 .235 -.35 .0746 .002
+GE 0 -1 0
+EX 0 24 3 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

Once established, the dimensions yield a 50-Ohm impedance that remains constant within 1.5 Ohm resistance and 1 Ohm reactance across the span of reflector sizes at the test frequency. Otherwise put, the 50-Ohm SWR never exceeds 1.03:1 in the models used in the exercise. The beamwidth values are virtually identical to those for the dual-dipole driver, with one small exception: the H-plane beam width tends to show a small (2 degree) peak when the vertical dimension is about 1.6 m, consistently one increment of vertical height larger than the reflector size that shows the minimum feedpoint resistance. The E-plane beamwidth minimum value continues to coincide with the vertical height needed for maximum gain.

+
+ +
+

The peak gain occurs, as shown in Fig. 12, with a reflector that is 1.6 m horizontally and 1.2 m vertically. However, the peak gain values for horizontal dimensions between 1.4 m and 2.0 m are so tightly grouped, that the difference in gain among them is not distinguishable. Equally difficult to distinguish is the rate of decrease as we increase the vertical dimension of the reflector. Only the two narrowest reflectors show distinct lines in the graph. The gain values generally coincide with those for the in-phase-fed dual dipole driver, although the rate of decrease after the peak value is a bit more rapid for the double rectangle. The horizontal extension of the reflector when using the peak gain size is 0.45 m past each outer vertical wire, a slightly smaller amount than for the other arrays. However, the convergence of the peak gain values for the 1.6-m and 1.8-m wide reflectors suggests that a true peak gain occurs in the vicinity of about 1.7 m for the reflector horizontal dimension. If that holds true, then the required extension would be closer to 0.5 m, or about the same as for the single rectangle and well within the cluster of extensions required by any of the arrays that we have so far surveyed.

+
+ +
+

The 180-degree front-to-back ratio of the double rectangle shows peaks for the two narrowest reflectors within the range of the reflector sizes tested. With a horizontal dimension of 1.0 m, the front-to-back peaks with a vertical dimension of 1.6 m, and with a horizontal of 1.2 m, the peak occurs with a vertical that is 1.8 m. In all of the wider reflectors, the peak front-to-back ratio occurs at or above a vertical dimension of 2.0 m. Note that, just as the gain peak values converge tightly at a single reflector vertical dimension, the front-to-back peak values also converge into a tight group at or slightly above a vertical dimension of 2.0 m.

+
+ +
+

The 50-Ohm SWR operating passband extends from about 290 to 311 MHz, a 7% passband, using the 4-mm double rectangle. The passband is wider than the one for the single rectangle, but still considerably smaller than the passband for the phase-fed vertical dipoles. Increasing the wire size to 8 mm (and adjusting the rectangle dimensions and spacing accordingly) would extend the passband, but it would not approach the wide-band capabilities of the phase-fed dipole driver.

+

Using the center vertical section of the double rectangle as the driving point is not only a convenience, but it also ensures a symmetrical H-plane pattern. A typical pattern appears in the left portion of Fig. 15. Theoretically, we can also feed the array on one end. The end-fed version would have the advantage of presenting a higher resonant impedance for similarly sized driver assemblies. The result would be a closer spacing of the driver from the reflector and a resulting increase in gain. However, see the right portion of Fig. 15.

+
+ +
+

Even using perfect or lossless wire, side-fed double rectangles that are optimized for maximum gain are not correctly sized to yield ideal currents among the vertical elements. Ideally, a double rectangle coincides with basic phased dipole theory when the center vertical has twice the current magnitude of the outer verticals. When we use the center element as the feedpoint, the error introduced by the slightly short spacing of the verticals is equal on both end verticals. Hence, the pattern is symmetrical. However, when we use the end wire as the feedpoint, the error accumulates down the line, and the pattern shows an asymmetrical form.

+

Tentative Conclusions

+

Our further exploration of planar reflector arrays yields a number of tentative conclusions, although some of them appear to be sufficiently justified to be used as generalizations.

+
+ 1. The feedpoint properties of any driver so far, once established, remain the same regardless of the reflector size. +

2. The ideal maximum gain height of the reflector is about 1.2 m (wavelength), regardless of the driver vertical or horizontal dimension.

+

3. The ideal maximum gain reflector is one that extends horizontally beyond the driver system by about 0.5 m to 0.6 m (or wavelength).

+

4. The rectangular drivers provide simpler array construction, but much narrower 50-Ohm SWR operating passbands than the phase-fed dual dipole driver.

+

5. So far, the phase-fed dual dipole driver and the double rectangle provide the maximum gain from the array.

+

6. In none of the arrays does the maximum front-to-back ratio coincide with the maximum gain in terms of reflector size. If we use a front-to-rear ratio, averaging the rearward gain across the 180 degrees of rearward directions, it appears that the larger the reflector, the lower the average rearward gain and the higher the front-to-rear ratio.

+
+

Planar reflector arrays have used a wide variety of driver assemblies. Some of them are based upon the quad loop as a driver, in both single and multiple versions. Therefore, before we freeze these conclusions, we should undertake at least one more round of modeling and data gathering.

+
+ +
+

Updated 03-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX February, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

Go to Main Index

+

Topics: Planar Reflector, VHF / UHF


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+

Planar Reflectors
+ Part 3: Bobtails and Diamonds

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In this series so far, we have examined several types of planar arrays, including a simple dipole driver, a phase-fed dual-dipole driver, and both single and double rectangle drivers. Our goals has been to see how the properties of these driver assemblies vary across a wide range of reflector sizes ranging from 1 to 2 wavelengths per vertical and per horizontal side. All of the NEC-4 models employ a standard wire-grid reflector using 0.1 wavelength segments. As well, all models are designed for a 50-Ohm feedpoint impedance. The test frequency is 299.7925 MHz so that 1 m = 1 wavelength throughout the exercise.

+

Within the limitations of the modeling techniques involved, we have arrived at a number of tentative conclusions.

+
+ 1. The feedpoint properties of any driver so far, once established, remain the same regardless of the reflector size. +

2. The ideal maximum gain height of the reflector is about 1.2 m (wavelength), regardless of the driver vertical or horizontal dimension.

+

3. The ideal maximum gain reflector is one that extends horizontally beyond the driver system by about 0.5 m to 0.6 m (or wavelength).

+

4. The rectangular drivers provide simpler array construction, but much narrower 50-Ohm SWR operating passbands than the phase-fed dual dipole driver.

+

5. So far, the phase-fed dual dipole driver and the double rectangle provide the maximum gain from the array.

+

6. In none of the arrays does the maximum front-to-back ratio coincide with maximum gain in terms of reflector size. If we use a front-to-rear ratio, averaging the rearward gain across the 180 degrees of rearward directions, it appears that the larger the reflector, the lower the average rearward gain and the higher the front-to-rear ratio.

+
+

To the collection of driver assemblies, we should add at least two more entries: the bobtail curtain and the double diamond. Both are adaptations of antennas used in the lower HF range and belong to the general class of SCVs or self-contained vertical antennas. Although the double diamond driver has appeared in at least some articles on UHF utility antennas, the bobtail has--to my knowledge--not seen wide use above the lower HF region.

+

The Bobtail Curtain and a Planar Reflector

+

A bobtail curtain consists of three 1/4 wavelength vertical antennas fed in phase. To effect phasing and to complete the 1/4 wavelength sections, horizontal lines about 1/2-wavlength long connect one vertical element to the next. Each half wavelength line acts as a pair of 1/4 wavelength completions for its vertical section and as a phase reversal section (reversing both voltage and current so that the verticals remain in phase with each other). In the lower HF region, where wire versions of the antenna are common, the horizontal lines are elevated, with the verticals hanging downward. This system places the high current region of the vertical sections as high as feasible. When used at VHF and UHF frequencies, the entire antenna is normally many wavelengths above ground. Hence, the placement of the horizontal wires becomes a matter of building choice. For an article in Communications Quarterly some years ago (See The Half-Square on 2 Meters for an earlier version of the article) I constructed parasitic beams using both half-squares and bobtail curtains with the horizontal wires downward.

+

Although horizontally polarized radiation from the phase-wires is not completely canceled, it is very weak compared to the vertically polarized component. Hence, we may think of both the 2-legged half-square and the 3-legged bobtail curtain as essentially vertical antennas. As a result, they are apt candidates as drivers for a planar reflector. By feeding the junction of the bobtail's center vertical and the phase-wires extending on each side toward the end verticals, we obtain a symmetrical or balanced feed for the end verticals. The required corner feedpoint for a half square does not permit such balance, and therefore, I have by-passed it in favor of the bobtail curtain. When we examined the single and double rectangles, we noted that for optimal performance, a double rectangle would be (for each section) horizontally longer and vertically narrower than the counterpart single rectangle. We find that a similar situation applies to the bobtail curtain relative to the half-square. For the driver assembly used in our model, the vertical legs will be 0.271 m (wavelength) long, while the individual horizontal wires will be 0.45 m (wavelength) long--for a total horizontal length of 0.90 m (wavelength). As shown in Fig. 1, the required spacing from the reflector is 0.185 m (wavelength). As with the rectangles, the wire diameter is 4 mm.

+
+ +
+

As the sketch shows, I have placed the horizontal lines at the model top. However, in these free-space models, the placement is arbitrary and has no direct bearing on array gain. However, it does have a bearing on certain pattern properties that we shall note before leaving this driver. The following lines show the master model for the bobtail curtain driver, calling up one of the Green's files for a reflector.

+ 
CM Bobtail curtain 0.185 m from planar reflector
+CE
+GF 0 R-H16-V12.WGF
+GW 24 5 .185 0 -.136 .185 0 .136 .002
+GW 25 8 .185 0 .136 .185 .45 .136 .002
+GW 27 5 .185 .45 -.136 .185 .45 .136 .002
+GW 28 8 .185 0 .136 .185 -.45 .136 .002
+GW 30 5 .185 -.45 -.136 .185 -.45 .136 .002
+GE 0 -1 0
+EX 0 24 5 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The 0.185-m spacing of the driver assembly from the reflector stems in part from the fact that by itself, the array shows a feedpoint impedance of about 40 Ohms when fed at the junction of the center vertical with the phasing lines. The resistance and reactance behavior of the array tends to be independent of the reflector size, with the exception--noted for all planar reflector arrays so far--that we find a small drop in resistance and a tilt of the reactance toward the inductive side as we pass through the vertical dimension of the reflector that yields maximum gain for any given horizontal dimension. Likely as a result of the "loose ends" of the bobtail, which are non-symmetrical vertically, we find a slightly larger than normal swing of the 50-Ohm SWR as we pass through all of the 36 reflector sizes used in the survey. SWR values range from 1.01:1 up to 1.09:1 as we change reflector sizes at the test frequency. For most of the driver assemblies that we have explored, a range of 1.01:1 to 1.04:1 is more the norm.

+

Likewise, beamwidth behavior closely resembles that of the double rectangle in terms of both actual values and changes as we alter the reflector size. The H-plane beamwidth varies between 48 and 52 degrees for the entire set of sample reflector sizes and changes by no more than 2 degrees for any single increment of either the horizontal or the vertical dimension. However, as with the other drivers, the E-plane beamwidth shows a 4-degree decrease as the vertical dimension passes through the length that yield maximum gain. As well, when the reflector vertical dimension passes from 1.4 m (wavelength) to 1.6 m (wavelength), we see a 6-7-degree jump in the E-plane beamwidth, with a more orderly and slower progression of increases for larger vertical dimensions. The total span of E-plane beamwidths runs from about 57 degrees (at maximum gain) to 73 degrees, with the largest figure occurring with the largest vertical dimension, regardless of the horizontal dimension of the reflector.

+
+ +
+

As shown in Fig. 2, the bobtail curtain driver shows a very orderly set of curves for gain across the set of reflector sizes. As in all of these exercises, the individual graph lines represent increments of the horizontal dimension, while the X-axis shows the increments along the vertical dimension. Maximum gain occurs--consistent with every other driver sampled--with a vertical dimension of 1.2 m (wavelength), regardless of the horizontal dimension. However, overall, the highest free-space forward gain achieved (11.31 dBi) occurs with the largest reflector size sampled. Because the value for the 1.8-m horizontal dimension is so close (11.30 dBi), it is unlikely that the gain rises any higher with reflectors that are longer horizontally. The 0.55-m extension of the reflector beyond the limits of the outer vertical radiators at maximum overall gain is consistent with values obtained for other drivers that we have explored.

+
+ +
+

Unique among the drivers that we have examined, the bobtail curtain shows 180-degree front-to-back peaks within the limits of vertical dimensions for almost all of the range of horizontal dimensions. Only a horizontal length of 2.0 m places the front-to-back peak definitively outside the range of reflector sizes used. When interpreting the curves, if two adjacent peak values are very nearly the same, you may assume that the actual peak value occurs between them at a higher value than for either value shown. This is true for the horizontal dimensions of 1.2 m and 1.4 m especially.

+

The gain and the front-to-back curves give the bobtail curtain driver a sense of orderliness that belies an anomaly occasioned by its vertically asymmetrical structure. In fact, the E-plane patterns for the array shows a distinct tilt that ranges from a maximum downward tilt of 7 degrees to a maximum upward tilt of 5 degrees. Maximum downward tilt occurs with the smallest horizontal dimensions. In the mid-range of horizontal dimensions, the tilt swing is between -2 and +4 degrees. As the horizontal dimension reaches its 2.0-m limit, the tilt is most positive as the vertical dimension also reaches its 2.0-m limit.

+
+ +
+

Fig. 4 illustrates--on the left--the degree of E-plane pattern distortion created by the tilt with a smaller reflector. However, the distortion is minimal in the pattern on the right, which uses the same vertical height, but is nearly twice as wide horizontally. The H-plane patterns for these two cases, shown in Fig. 5, display none of the asymmetry, since the array driver is perfectly symmetrical from one outer vertical to the other one.

+
+ +
+

To reverse the tilt, one need only move the horizontal phase lines from the model driver top to its bottom. It is unlikely that the tilt would be great enough to allow pattern direction for a particular application. However, for the bobtail driver, one cannot assume a perfectly normal set of elevation patterns over ground. Rather one must accurately model or measure the elevation lobe structure before freezing a design.

+
+ +
+

The 50-Ohm SWR curve for the bobtail curtain driver with its planar reflector follows the pattern of all of the other drivers in this exercise. One curve stands in for all, since the feedpoint resistance and reactance behaviors change so little as we vary the reflector sizes. The 50-Ohm 2:1 SWR passband extends from about 288 to about 310 MHz, for a 7.3% bandwidth. This value marginally exceeds the values obtained by the rectangles, but is less than 1/3rd the passband values achieved by the dual-dipole driver system.

+

The unique features of the bobtail curtain driver are three. a. It achieves the highest modeled gain of any of the driver systems. b. It places most of the maximum front-to-back peaks within the range of reflectors sizes used in the exercise. c. It tilts the E-plane patterns slightly, although not enough to detract from its use. Like the other driver systems, it achieves maximum gain with a vertical reflector height of about 1.2 wavelength and with a horizontal reflector width that represents between a 0.5- and 0.6 wavelength extension of the reflector beyond the limit of the driver. As well, the feedpoint impedance behavior is in line with the other drivers.

+

The Double Diamond Plus a Planar Reflector

+

Our final driver system is not the last possible candidate for the task. Instead, it is simply the last one that we shall survey. The double diamond is also an SCV, but at lower HF, we usually see it in the form of a double delta. It consists of two diamond-shaped quad loops joined at the hip, that is, joined at a side peak dimension. Fig. 7 shows the outline of the double diamond applied to our planar reflector study.

+
+ +
+

The model for the double diamond follows construction practice for the antenna. A short vertical wire forms the junction of the individual diamond quads, and we place the feedpoint on that short wire. Essentially, we are feeding two quad loops in phase with each other. We obtain maximum gain from the double diamond when we squash it slightly, as we did for both the bobtail curtain and the rectangles. Hence, the vertical dimension is 0.323 m (wavelength) from peak to peak. However, each diamond is 0.4024 m (wavelength) from peak to center wire, horizontally. Hence, the total horizontal dimension is 0.8046 m (wavelength) from outer peak to outer peak. The following lines show a sample model for the double diamond.

+ 
CM Double diamond 0.148 m from planar reflector
+CE
+GF 0 R-H16-V12.WGF
+GW 24 1 .148 0 -.005 .148 0 .005 .002
+GW 25 30 .148 -.4024 0 .148 -.2012 .1615 .002
+GW 26 30 .148 -.2012 .1615 .148 0 .005 .002
+GW 27 30 .148 -.4024 0 .148 -.2012 -.1615 .002
+GW 28 30 .148 -.2012 -.1615 .148 0 -.005 .002
+GW 29 30 .148 .4024 0 .148 .2012 .1615 .002
+GW 30 30 .148 .2012 .1615 .148 0 .005 .002
+GW 31 30 .148 .4024 0 .148 .2012 -.1615 .002
+GW 32 30 .148 .2012 -.1615 .148 0 -.005 .002
+GE 0 -1 0
+EX 0 24 1 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The model uses a spacing of 0.148 m (wavelength) from the driver to the reflector. With the dimensions shown, the test frequency 50-Ohm SWR varies only from 1.00:1 to 1.03:1 across the entire range of reflector sizes used in the study. Resistance behavior is very uniform, with a slight (1 Ohm) dip in value one vertical reflector increment beyond the vertical size yielding maximum gain. The reactance reaches its most capacitive value at the vertical reflector height that corresponds to the maximum gain for any given horizontal dimension. It reaches its most inductive value at a vertical height of 1.8 m. However, the total modeled reactance range is only about 0.8 Ohm.

+

The beamwidth is equally well-behaved. The E-plane beamwidth range runs from 56 degrees to a maximum of 72 degrees. The lowest value, of course, occurs when the vertical reflector dimension is right for maximum array gain. We find the jump in beamwidth (6 to 8 degrees) in the shift of the vertical reflector dimension from 1.4 m to 1.6 m. The H-plane beamwidth varies over a smaller range--from 52 to 58 degrees across the span of sampled reflector sizes. There is no definitively identifiable peak value, although there is a growth in beamwidth as the vertical reflector dimension increases.

+
+ +
+

The gain curves for the double diamond form a coherent set, as shown in Fig. 8. The line for the largest horizontal dimension (2.0 m) shows that it is beyond the size to yield maximum overall free-space gain by that fact that it descends more rapidly than the other curves after passing the vertical dimension that yields maximum gain. As we may have grown to expect, the double diamond achieves maximum gain with a vertical reflector dimension of 1.2 m.

+

The maximum gain achieved by the double diamond (11.13 dBi) is second only to the bobtail curtain. In fact, as a way of reviewing the driver assemblies that we have looked at, we can create a table of maximum free-space gain performance.

+ 
Driver Type              Maximum Gain       Vertical Reflector       Horizontal Reflector
+                         dBi                Dimension (m and wl)     Dimension (m and wl)
+Single Dipole             9.31              1.2                      1.2
+Phase-Fed Dual Dipoles   10.85              1.2                      1.8
+Single Rectangle         10.37              1.2                      1.4
+Double Rectangle         10.89              1.2                      1.8
+Bobtail Curtain          11.31              1.2                      2.0
+Double Diamond           11.13              1.2                      1.6
+

The horizontal extension of the reflector beyond the limits of the double diamond does not match the 0.5- to 0.6-meter value that we have associated with the other drivers. Because the maximum gain value for a horizontal reflector dimension of 1.8 m is so close to that of the recorded peak dimension of 1.6 m, we might even assume that the actual peak gain occurs at 1.7 m. However, that inferred value leaves only a 0.45-m extension. The shortness of the extension is just what we should expect of a vertical element that extends in a V inward from its peak limit. Although maximum current magnitude occurs at the outer side peak, the values just short of maximum occur further inward from the reflector edge. The functional average current, reflecting what a single vertical dipole might produce, occurs about 2/3 of the way between the diamond vertical peaks and the outer horizontal peak. By this general reckoning, the effective extension is between 0.5 and 0.52 meters--roughly. The rough estimate is very much in line with the horizontal extensions we found for the other driver assemblies.

+
+ +
+

The double diamond's front-to-back behavior in Fig. 9 shows at least the horizontally smallest reflectors--if not the third also--with peak 180-degree values within the range of reflectors used in this exercise. The shape of the curves for the various horizontal dimension lines suggest that there is a "favored" width, namely, 1.2 m. However, this conclusion would required a considerable number of additional reflectors to confirm it. Peak values are not the sole interest that we might have in the graph. If we compare the curves for both the bobtail curtain and double diamond in this episode with the front-to-back curves for the other drivers covered in Part 1 and Part 2, we shall discover that the latest driver assemblies are the only ones with minimum values above 20 dB. Nevertheless, we should hold this note in abeyance until we reach the final part of this portion of the study, where we shall examine some alternative reflector wire grids.

+
+ +
+

The double diamond is no exception to the emerging rule that the 50-Ohm SWR curve is independent of the reflector size. The version shown in Fig. 10 for the maximum gain reflector would not vary in any detectable way had we used any other reflector size. The 2:1 passband extends from about 288 to 314 MHz, an 8.7% passband. Although this value is larger than most, it still is only about 1/3 the passband available to the phase-fed dual-dipole driver.

+
+ +
+

The E-plane patterns in Fig. 11 illustrate vividly a general property of planar reflectors, at least with respect to the wire-grid models that we have been using. The two patterns employ the smallest and the largest reflectors of the series. The excellent behavior of the double diamond allows us to see more clearly than with almost any other array what happens as we enlarge a reflector. The total energy in the rearward direction tends to decrease. The peak rearward lobes are down only about 20 dB with respect to the forward gain when using the smallest reflector. For the largest reflector, the peaks (noting that there are now 5 rather than 3) are down about 28 dB. In exchange--since the energy must go somewhere--the forward lobe develops a wider beamwidth as the reflector grows. The growth is modest--from 60 to 72 degrees--but is still noticeable.

+
+ +
+

The most interesting changing property of H-plane patterns requires that we use a constant vertical size with a varying horizontal dimension, as shown in Fig. 12. As we increase the horizontal dimension of the reflector, the pattern changes in the regions that are about 90 degrees off the heading for maximum gain. With a narrow reflector (H = 1.0 m), there are no 90-degree nulls, but only a tapering off of gain as we move through the region toward the rearward area. However, by the time we reach the widest reflector, the front-to-side ratio has reached a very high value, as the pattern insets clearly show.

+

With respect to the models used in this exercise, the double diamond driver array counts as a high-performance star within the group. It almost matches the bobtail curtain in maximum possible gain, but has none of the bobtail's pattern aberrations. At a reflector size yielding maximum gain, it exceeds most of the other drivers in front-to-back ratio. Of the higher-gain drivers, it has the widest SWR bandwidth with the exception of the phase-fed dual dipoles. Indeed, if the need is operating bandwidth, the dual-dipole driver with its 100-Ohm phase lines would be the top selection. For spot frequency use, the double rectangle, the bobtail curtain, and the double diamond might be the best choices. However, for construction simplicity, the single rectangle and the single dipole offer good performance. For H-plane beamwidth, the single dipole has a 20-30-degree advantage over the higher-gain arrays within the group. Remember that there is only a 2 dB forward gain difference between the worst and the best performers in the entire collection of planar reflector arrays.

+

From Tentative to Fairly Definite: Some Conclusions

+

At the beginning of this episode, we repeated some tentative conclusions reached on the basis of the first two parts of this study. Given our excursions through two more candidates as drivers with no significant changes of behavior trends, we may now convert those conclusions into something definite.

+
+ 1. The feedpoint properties of any driver so far, once established, remain the same regardless of the reflector size. Across the span of 36 reflectors used in the exercise, the maximum change in 50-Ohm SWR was from 1.01:1 to 1.09:1, although a range of 1.01:1 to 1.04:1 is more typical. +

2. The ideal maximum gain height of the reflector is about 1.2 m (wavelength), regardless of the driver vertical or horizontal dimension. The dense wire-grid exercise in Part 1 of the study suggests that the actual "ideal" vertical dimension may be closer to 1.3 wavelength.

+

3. The ideal maximum gain reflector is one that extends horizontally beyond the driver system by about 0.5 m to 0.6 m (or wavelength).

+

4. The phase-fed dual-dipole driver provides the widest SWR passband of any driver assembly, and at a good gain level. However, the other driver systems all offer somewhat simpler construction and fewer field adjustment challenges.

+

5. The bobtail curtain and the double diamond driver systems provide the maximum gain from a planar reflector array. However, almost all of the driver systems provide gain equal to what we might derive from various long-boom 5-6 element Yagis.

+

6. In none of the arrays does the maximum front-to-back ratio coincide with the maximum gain in terms of reflector size. If we use a front-to-rear ratio, averaging the rearward gain across the 180 degrees of rearward directions, it appears that the larger the reflector, the lower the average rearward gain and the higher the front-to-rear ratio.

+

7. E-plane beamwidth is generally controllable by the selection of the horizontal reflector dimension. H-plane beamwidth, once beyond the single dipole driver, is relatively constant and lacks the secondary forward sidelobes that are typical of Yagis in the same gain category.

+
+

These conclusions appear to be reasonably reliable for planar reflectors. Of course, we have not surveyed all of the possible driver systems. For example, with more complex phasing arrangements, we might use 3, 4, or more phase-fed dipoles, along with a reflector that extends horizontally about 0.5 wavelength beyond the limits of the dipole array. Despite the incompleteness of the survey, we appear to have covered most of the array types likely to be useful to the home antenna builder.

+

Back to Model Reliability

+

In Part 1, I performed an initial test on the reliability of the models used in this survey by constructing alternative reflector wire-grid structures. A fairly standard wire grid consists of wire segments that are each 0.1 wavelength long and have a diameter that is the wire segment length divided by PI. In part 1, for a limited set of denser wire grids, I used a segment length of 0.05 wavelength, with the diameter of the wires also halved. The test showed--over the span of reflectors modeled--that the gain and front-to-back values for the new reflectors do not vary from the ones for the standard reflector up to the first decimal place in the reports. As well, resistance and reactance reports varied at most by a few hundredths of an Ohm.

+

Before we leave the study of planar reflectors, we might carry that investigation further to cover--at least in sample form--all of the drivers that we have examined. As well, we might--by judicious selection of a reflector size--look at not only the standard and the first increase in wire-grid density, but as well at a second density increase.

+

Every doubling of wire-grid density increases the number of segments in the reflector by a factor of about 3.9. I began with a reflector that is 1.4 m (wavelength) horizontally and 1.2 m (wavelength) vertically. The standard wire-grid with 0.1 wavelength segments produces a reflector with a modest 362 segments. Doubling the density by using 0.05 wavelength segments increases the number of reflector segments to 1396. The final step to a 0.025 wavelength segment requires 5480 total reflector segments. Modeling run time increases exponentially with the number of segments. Hence, I chose a single sample reflector size to use on all of the drivers. As well, a 2.0 by 2.0 wavelength reflector would have required 12,960 segments, which exceeds the limits of the NEC-4 core (unless one uses GX or symmetry techniques). Fig. 13 shows a comparison of a sample wire-grid and its double-density counterpart to illustrate the rate of segment growth.

+
+ +
+

In spite of the limitations of the test, the results are worth scanning in tabular form. Each driver apears in the order presented, with data for the sample reflector using the 3 degrees of density.

+ 
Single Dipole
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        50-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  9.27           19.19             54         82         49.29 - j1.18    1.03
+X2                  9.25           19.28             54         82         49.28 - j1.33    1.03
+X4                  9.24           19.25             54         82         49.36 - j1.34    1.03
+Max. Difference     0.03            0.09             --         --          0.08    0.16    ---
+Phase-Fed Dual Dipoles
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        100-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  10.82          19.03             56         54         97.91 - j2.29    1.01
+X2                  10.77          19.18             58         54         97.96 - j2.32    1.01
+X4                  10.75          19.22             58         54         98.05 - j2.39    1.01
+Max. Difference      0.07           0.19              2         --          0.14    0.10    ---
+Single Rectangle
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        50-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  10.37          19.43             56         63         49.76 - j0.39    1.01
+X2                  10.34          19.59             56         63         49.79 - j0.32    1.01
+X4                  10.32          19.60             58         63         49.87 - j0.31    1.01
+Max. Difference      0.05           0.17              2         --          0.11    0.08    ---
+Double Rectangle
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        50-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  10.86          19.48             58         54         49.59 - j0.30    1.01
+X2                  10.82          19.69             60         54         49.62 - j0.33    1.01
+X4                  10.80          19.75             60         54         49.69 - j0.36    1.01
+Max. Difference      0.06           0.27              2         --          0.10    0.06    ---
+Bobtail Curtain
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        50-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  11.20          22.83             57         48         49.70 + j3.41    1.07
+X2                  11.16          23.25             57         48         49.68 + j3.31    1.07
+X4                  11.14          23.40             57         48         49.74 + j3.27    1.07
+Max. Difference      0.06           0.57             --         --          0.06    0.14    ---
+Double Diamond
+Density             Free-Space     Front-to-Back     E-BW       H-BW       Impedance        50-Ohm
+Level               Gain dBi       Ratio dB          degrees    degrees    R+/-jX Ohms      SWR
+X1                  11.10          21.24             56         52         49.63 - j0.61    1.01
+X2                  11.06          21.50             56         52         49.61 - j0.72    1.02
+X4                  11.04          21.54             56         52         49.71 - j0.74    1.02
+Max. Difference      0.06           0.30             --         --          0.10    0.13    0.01
+

Besides giving us a comparison among reflector wire-grid densities as one (but not the only) test of model reliability, the table provides a snapshot of some of the differences among the arrays in terms of typical beamwidths, gain levels, and front-to-back values. It is clear, for example, that the single dipole provides the greatest H-plane beamwidth, while the bobtail curtain provides the narrowest. The E-plane beamwidth varies with reflector size, but does not vary significantly among the types of drivers. Although only one of the drivers shows its maximum possible gain with the reflector size used in the test, the gain levels accurately show what each driver can achieve in relative terms.

+

The internal differences for each driver are minuscule as a function of the density of the wire-grid used in the modeled reflector. Only the bobtail curtain shows a noticeable range of front-to-back ratios, and that result stems from the pattern tilt. In practical terms, the re-modeling of the reflector tends to validate the values yielded by the standard (X1) grid, and certainly the trends hold good whatever the numbers in the final decimal places of the modeling reports. How close the values are to each other shows up clearly in Fig. 14, which overlays the E-plane and H-plane patterns for the single rectangle driver. Beneath the red line is a blue-line pattern having the identical shape throughout for both orientations.

+
+ +
+

Remember that this test only shows that the results of using the standard wire-grid with 0.1 wavelength segments are valid witin the context of what NEC-4 can calculate as the performance of the arrays. The average gain test values (all above 0.99, where 1.00 is perfect) provide additional evidence of model adequacy. However, the tests do not provide an external confirmation of the models by comparison with carefully constructed and measured lab or range antennas. That added confirmation lies beyond the scope of this study, but would be a necessary step, should one wish to develop operational planar reflector arrays.

+

Nevertheless, the models used in this study can provide guidance to anyone wishing to build a one-of-kind planar reflector array for some specific use. It is likely that, at UHF especially, the lumps and bumps called construction variables will occasion more field adjustment than any lack within the models.

+
+ +
+

Updated 04-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX March, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 4

+

Go to Main Index

+

Topics: Planar Reflector, VHF / UHF


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+

Planar Reflectors
+ Part 4: Rod or Bar Reflectors

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In the first 3 parts of this study of planar reflectors, we employed wire-grid simulations of closely spaced screens or solid surfaces. Over the life span of planar reflector use, bars or rods have substituted for solid or screen surface. Bars pass the wind easily while having a somewhat better durability than screens, at least in the realm of commercial manufacture. The bars are normally aligned with the dominant polarization of the driving element. For many applications, we would find the bars set horizontally, relative to the earth's surface. However, because anticipated applications of planar reflectors in the 21st century will largely involve services such as the amateur FM repeater system, I have set all drivers vertically. Hence, the bars of a reflector will follow suit.

+

In the literature on reflectors using planar surfaces, beginning with Kraus, we find an assumption that a set of bars will simulate a solid surface or a closely spaces screen if we use bars that are large enough in diameter and spaced closely enough. Fig. 1 shows the key elements in effecting an equivalence between our wire-grid reflectors and a reflector based on bars or rods.

+
+ +
+

The reflector outer dimensions will be the same for both versions. We can also find some recommendations for the rod diameter and spacing, although they are derived from corner-reflector applications. In general, the rod diameter should be at least 0.02 wavelength at the highest frequency used. As well, the spacing between rods should be no greater than 0.125 wavelength at the highest frequency used. Since these recommendations appear in rather vague format, we can assume that the spacing is center-to-center of the rods. As in past episodes, we shall use 299.9725 MHz as the test frequency so that 1 m = 1 wavelength. All conductors will be without loss.

+

Using these or similar bar dimensions, we can create models of rod-based reflectors that hold none of the misgivings that we spent a good bit of time overcoming in the preceding 3 planar episodes. The modeled rods will have the same dimensions as actual rods. Their spacing is great enough to meet any NEC requirements for highly accurate results. Moreover, the reflector models will be relatively small in terms of the number of segments required.

+

Therefore, we are positioned to test our set of planar reflector drivers with the alternative style of reflector. We shall examine the following drivers:

+
+ 1. A single dipole, +

2. 2 dipoles fed in phase,

+

3. A single side-fed rectangle,

+

4. A double rectangle fed on the center vertical element,

+

5. A bobtail curtain, and

+

6. A double diamond driver.

+
+

Because we have extensive data already at hand, we shall be able to take some short-cuts in the investigation in terms of locating the reflector sizes for maximum array gain. Hence, we may by-pass some extensive graphing in favor of a number of short tables that we can easily scan. Nevertheless, we shall want to make the new survey sufficiently complete so that if aberrant behavior does appear, we shall be certain to catch it. (In fiction and theater, a sentence like the preceding one is called "foreshadowing," setting the stage for the discovery of some aberrant behavior.)

+

Before we actually conduct our survey, we have a preliminary task. I noted that the recommendations for the diameter and spacing of the rods in the reflector carried with them a bit of vagueness, since they apparently have emerged from antenna practice at least a half century ago and have little justification other than what might then have passed for successful designs. We are positioned to do a bit of verification to determine if the recommendations result in the best possible reflector designs. We may also discover that there are factors in addition to just rod diameter and spacing that enter into the considerations of designing a rod-based reflector that is equivalent to the wire-grid structures.

+

Establishing Rod-Based Reflector Design

+

Modeling a planar reflector composed of bars is not difficult. The following lines establish a Green's file for the set of bars composing the reflector. The reflector consists of a center bar plus equal numbers of bars on each side of center.

+ 
CM Rod Planar Reflector: 299.7925 MHz; 1 m = 1 wl
+CM Size = 1.0 m x 1.0 m
+CE
+GW 1 10 0 0 -.5 0 0 .5 .015
+GM 0 5 0 0 0 0 -.1 0 1 1 1 10
+GM 0 5 0 0 0 0 .1 0 1 1 1 10
+GE 0 -1 0
+FR 0 1 0 0 299.7925 1
+GN -1
+WG pr-v10-h10.WGF
+EN
+

The GW line allows any level of segmentation needed for the rod length and centers the initial wire at Z=0 for free-space models. The last entry in the line indicates the wire radius, in this case, 0.015 m (wavelength). The following GM lines replicate the wire as many times as needed (here 5 on each side) at the selected interval, center-to-center (here 0.1 m). The GW line in this model uses 10 0.1-m segments so that the segment length equals the center-to-center spacing. The reflector is not connected to the driver, so replicating the segmentation used on a driver assembly is not necessary. Tests using up to three times the segment density per rod yield results that are insignificantly different from the test level of segmentation on the reflector wires.

+

The simple model shown allows for any vertical dimension desired, as well as for any number of rods, normally expanded by one on each end with each incremental change to the reflector. As in earlier test models, the need for a finite number of tests suggests that increments of 0.2 m (wavelength) in each dimension provide enough test points for general guidance.

+

The next step in the process of is to find a vehicle for determining the optimal wire radius (diameter) for the rods and their optimal spacing. Previous work with a simple dipole and the wire-grid reflector indicated that a reflector that is 1.2 m by 1.2 m yields approximately the maximum gain achievable from the dipole when it is spaced 0.175 m from the reflector. A rod-based reflector should yield closely similar results. Therefore, I set up three reflectors as an initial test. Each used a height of 1.2 m. The horizontal dimension--produced by the GM lines in terms of the number of wires and the increment between them--was based on the use of a total of 11, 13, and 15 wires, with a spacing of 0.12 m, 0.1m, and 0.857 m, respectively. Each reflector surveyed reflector wire radii from 0.005 m through 0.025 m in 0.005-m increments.

+ 
CM Dipole
+CE
+GF 0 pr5-v12-h12-r005.WGF
+GW 101 11 .1495 0 -.2188 .1495 0 .2188 .004
+GE 0 -1 0
+EX 0 101 6 0 1 0
+RP 0 361 1 1000 -90 0 1.00000 1.00000
+RP 0 1 361 1000 90 0 1.00000 1.00000
+EN
+

The GF line calls up the relevant reflector file. The file name indicates the structure of the relevant reflector. the initial "pr5" designation indicates 5 reflector wires each side of the center wire, for a total of 11 wires and a spacing of 0.12 m between them. The "v12-h12" portion indicates of vertical and horizontal outer dimensions. The final entry, "r005" represents a wire radius of 0.005 m.

+

The GW line specifies the dipole for that reflector. As in the wire-grid reflector tests, the dipole has a diameter of 8 mm. For each case, the dipole length and spacing from its reflector was adjusted to a 50-Ohm impedance, as registered by a 50-Ohm SWR no greater than 1.01:1. The following table provides the dimensions of the dipole and its spacing from the reflector for each of the test cases. The dipole is always centered both horizontally and vertically with respect to the reflector, where "vertical" represents the +/- Z axis, and "horizontal" represents the Y-axis. Reflector-dipole spacing is on the X-axis.

+ 
11-Wire Reflector:  0.12-m center-to-center reflector rod spacing
+Reflector Wire     Dipole Spacing from     Dipole Length
+Radius m/wl        Reflector m/wl          m/wl
+0.005              0.1495                  0.4376
+0.01               0.1625                  0.437
+0.015              0.1745                  0.4368 *
+0.02               0.177                   0.4366
+0.025              0.181                   0.4366
+13-Wire Reflector:  0.1-m center-to-center reflector rod spacing
+Reflector Wire     Dipole Spacing from     Dipole Length
+Radius m/wl        Reflector m/wl          m/wl
+0.005              0.1564                  0.4372
+0.01               0.168                   0.4368
+0.015              0.1745                  0.4368 *
+0.02               0.1795                  0.4368
+0.025              0.1835                  0.4368
+15-Wire Reflector:  0.0857-m center-to-center reflector rod spacing
+Reflector Wire     Dipole Spacing from     Dipole Length
+Radius m/wl        Reflector m/wl          m/wl
+0.005              0.1615                  0.4370
+0.01               0.171                   0.4368 *
+0.015              0.177                   0.4368 *
+0.02               0.1815                  0.4368
+0.025              0.185                   0.4368
+

Several features of this limited table are noteworthy. First, as we increase the number of wires and decrease the spacing between them, the dipole length stabilizes at 0.4368 m more quickly, that is, at a smaller reflector-wire radius. Second, as we increase the number of reflector wires and decrease their spacing, the required distance between the reflector and the dipole increases for any given reflector-wire radius. Thus, the number of wires in the reflector--or their spacing--has a bearing on the required distance from the reflector to the dipole to achieve a 50-Ohm impedance. Third, note the starred entries. For each of these entries, the distance between the reflector and the dipole most closely approximates the required spacing using the wire-grid model: 0.175 m. All of these entries call for a dipole that is 0.4368 m long. The corresponding dipole with a wire grid reflector is also 0.4368 m when the dipole is corrected to lower its SWR from the values in the tables in earlier episodes.

+

The following table provides the performance data that accompanies the dimension listed above. (Space prevents me from using a single table to place all of the dimensional and performance data values on single lines.) The tables (throughout this exercise) use the 180-degree front-to-back ratio. E-BW and H-BW are the E-plane and H-plane half-power beamwidths, respectively.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   9.31           18.33             54         80         49.72 - j0.15   1.01
+
+11-Wire Reflector:  0.12-m center-to-center reflector rod spacing
+Reflector Wire     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Radius m/wl        Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+0.005              9.13           14.16             54         76         50.16 - j0.02   1.00
+0.01               9.26           16.57             54         76         50.04 + j0.03   1.00
+0.015              9.28 *         17.79             54         78         50.21 + j0.05   1.00
+0.02               9.26           18.31             54         80         50.21 - j0.12   1.00
+0.025              9.24           18.40             54         80         49.95 - j0.06   1.00
+13-Wire Reflector:  0.1-m center-to-center reflector rod spacing
+Reflector Wire     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Radius m/wl        Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+0.005              9.19           15.59             54         76         50.05 - j0.05   1.00
+0.01               9.26           17.47             54         78         50.13 - j0.09   1.00
+0.015              9.27 *         18.24             54         80         50.01 + j0.09   1.00
+0.02               9.24           18.47             54         80         50.01 + j0.14   1.00
+0.025              9.21           18.36             54         80         49.01 + j0.16   1.00
+15-Wire Reflector:  0.0857-m center-to-center reflector rod spacing
+Reflector Wire     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+Radius m/wl        Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+0.005              9.22           16.52             54         76         50.15 - j0.07   1.00
+0.01               9.26 *         17.93             54         78         50.00 - j0.02   1.00
+0.015              9.25 *         18.42             54         80         50.02 + j0.07   1.00
+0.02               9.23           18.49             54         80         50.06 + j0.10   1.00
+0.025              9.19           18.31             54         82         50.03 + j0.10   1.00
+

The starred entries represent more than just the fact that the spacing between reflector and the dipole is close to the same as for the wire-grid version of the planar array. As well, these entries also indicate a performance level that is closest to the performance reported for the wire-grid model. The tiny gain differential (0.04 dB at its minimum for the 13-wire reflector) is not a function of differences in average gain test scores. All of the rod-based reflectors using a 0.015-m radius rod wire have an Average Gain Test value that shows a 0.015 dB gain deficit in the reported value. The wire-grid Average Gain Test value shows a 0.013 dB gain deficit, eliminating any differential in the reported and adjusted values for the two model types. Operationally, all of this fine tuning would make no sense at all. However, in this exercise, we are striving to correlate model data reports, and using the full extent of the raw and adjusted data--even to 4 significant figures--makes eminent sense.

+

The reflector model using reflector-wires with a 0.015-m radius and also using a 0.1-m spacing turns out to most closely approach the wire-grid version of the array, including gain, front-to-back ratio, and both E-plane and H-plane beamwidths. As well, the required dipole dimensions are the same as in the wire-grid model. Note that in the past 3 episodes, we took considerable pains to establish the internal validity of that model. Hence, using its closest rod-based analog to the wire-grid makes good sense--and also provides an easy way to obtain the same increments between horizontal dimensions as we used when testing wire-grid reflectors.

+

The data suggest that--at least with respect to NEC-models of planar arrays--reflector rod spacing should be only slightly less than the 0.125 wavelength value found in recommendations. However, the rod diameter--0.03 wavelength in the data just shown--is about 50% greater than the value used in older recommendations. However, the values that we shall use in this set of tests are derived for a specific feedpoint impedance: 50 Ohms. The tests used here do not establish that the same rod-based reflector specifications apply equally to all feedpoint impedances. Also clear is that within the scope of this test, the distance from the reflector to the dipole also plays a role in the reflector performance in the balance between the feedpoint impedance and the performance reports. This factor finds no mention in any literature that has crossed my path.

+

Testing the Drivers

+

The reflectors that we shall use in testing each of the drivers will use 0.1-m spacing between 0.015-m radius rods. Hence, the horizontal dimension of the reflector will use the same steps as the wire-grid models used--0.2 m per step. The vertical dimension will use the same steps, even though we have the freedom to use any step whatsoever.

+

Our survey can be significantly simplified relative to the hunting expedition that formed the work we did with wire-grid models. Establishing the proper size for the reflector rod assembly also established the fact that the peak gain performance of wire-grid reflector models and bar reflector models shows a close coincidence. Therefore, we need not replicate the entire data series between 1.0 and 2.0 m (wavelengths) for each dimension. Instead, we may simply surround the most likely reflector dimensions with enough possibilities to establish the gain peak dimensions for the bar reflectors. Each reflector will go though vertical dimensions of 1.0, 1.2, and 1.4 m, with horizontal dimensions including one increment above and one increment below the size that yielded maximum gain. As we proceed, we shall keep an eye open for anomalous results. In practical terms, the reduced data gathering will allow us to use some simple tables rather than extensive graphs.

+

1. A Single Dipole Driver

+

Although we have already established some aspects of peak performance using a simple dipole driver, we have not run it through the series of alternative reflector sizes. The key dimensions for the array used in these bar-reflector tests appear in Fig. 2. The corresponding wire-grid dipole used a 0.175-m spacing as the only difference in array dimensions.

+
+ +
+

In the data to follow, the "Reflector Size" column uses a truncated system to record the size. For example, V10-H12 indicates a vertical dimension of 1.0 m and a horizontal dimension of 1.2 m. These values translate to a 13-rod reflector where each vertical rod is 1.2-m long. An H-value of 14 would have 15 rods, and an H-value of 20 would have 21 rods.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   9.31           18.33             54         80         49.72 - j0.15   1.01
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V10-H10            8.78           17.64             60         82         50.33 + j0.90   1.02
+V10-H12            8.89           18.67             60         80         50.17 + j0.76   1.02
+V10-H14            8.89           19.94             60         80         50.04 + j0.81   1.02
+
+V12-H10            9.16           17.75             54         80         50.18 + j0.18   1.01
+V12-H12            9.27 *         18.24             54         80         50.01 + j0.09   1.00
+V12-H14            9.23           19.12             54         82         49.92 + j0.18   1.00
+
+V14-H10            9.18           19.83             54         86         49.68 + j0.11   1.01
+V14-H12            9.16           20.19             56         90         49.55 - j0.11   1.01
+V14-H14            9.14           19.98             56         90         49.37 - j0.05   1.01
+
+

The starred entry indicates the highest gain achievable from the single-dipole driver version of the planar reflector, with the very same dimensions as we encountered with the wire-grid version. In fact, the 2:1 50-Ohm SWR bandwidth is also identical for this size reflector: about 9.7%. Indeed, the rod-based reflector is so well-behaved, the one can scarcely distinguish the patterns between it and the wire-grid reflector, as shown in Fig. 3. If there are any differences, they lie in the rearward quadrants, showing especially as a pair of slight "bulges" in the pattern for the bar reflector. However, note the complete absence of such bulges in the wire-grid H-plane pattern.

+
+ +
+

There can be little doubt that for the single-dipole driver, the use of a rod-based reflector is completely acceptable for virtually any application in which we might use the wire-grid reflector or its closely spaced screen or solid surface physical implementations. Of course, we have used a carefully selected set of bars with respect to their diameter and spacing.

+

2. 2 Dipoles Fed in Phase

+

The dual-dipole driver that we fed in phase in Part 2 of this series is also adjustable to the use of a rod-based reflector. Fig. 3 provides the essential dimensions. The only change that we needed to make was to lengthen the dipoles from 0.466 m to 0.4682 m. As with the single dipole, the driver diameter remains 8 mm.

+
+ +
+

The wire-grid version of this modeled planar array required a reflector that was vertically 1.2 m by horizontally 1.8 m to achieve maximum gain. Once more, we may simplify the data gathering by surrounding this reflector size in the rod-based version with adjacent sizes. The following table provides the results.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       100-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   10.82          19.56             58         54         97.77 - j2.25   1.03
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V10-H14            10.44          18.33             62         54         101.9 + j1.51   1.02
+V10-H16            10.49          18.78             62         54         101.8 + j1.42   1.02
+V10-H18            10.49          19.35             62         54         101.7 + j1.45   1.02
+
+V12-H14            10.76          19.06             58         54         100.1 - j0.06   1.00
+V12-H16            10.79 *        19.23             58         54         99.99 - j0.17   1.00
+V12-H18            10.76          19.68             58         56         99.92 - j0.16   1.00
+
+V14-H14            10.69          21.21             60         56         98.13 + j0.87   1.02
+V14-H16            10.74          20.44             60         56         98.00 + j0.81   1.02
+V14-H18            10.69          20.66             60         58         97.92 + j0.84   1.02
+
+

The dual-dipole driver array with a rod reflector tracks the wire-grid version extremely well, with one exception. Maximum gain in the rod-reflector version occurs with a horizontal dimension of 1.6 m, one increment smaller than with the wire-grid reflector. However, the change in gain for either version of the array is very small (about 0.03 dB) as we move either way horizontally from the maximum gain dimension. Hence, small variables, such as the alignment of the dipoles with the rods of the reflector may alter the peak reflector dimension slightly.

+
+ +
+

As revealed in Fig. 5, the patterns of the wire-grid and rod reflector versions of the dual-dipole driver array are even more tightly matched than those for the single dipole array. As well, both types of reflectors yield the same SWR bandwidth: 26%. For the VHF and lower UHF region, where barred reflectors may prove more practical in some applications than screens or solid surfaces, the dual-dipole driver array, phased as describe in Part 2, provides both performance and bandwidth that matches what we might obtain from a solid or screen reflector.

+

3. A Single Side-Fed Rectangle

+

With the single side-fed rectangle driver, we change the element diameter from 8 mm to 4 mm (that is, from more than 1/4" down to between 1/8" and 3/16"). This move would reflect building tendencies at the 300-MHz test frequency. In the conversion of the rectangle from a wire-grid reflector to a set of rods, only the spacing of the driver from the reflector changed--by 3 mm. Fig. 6 shows the essential dimensions for the rectangle with its new reflector.

+
+ +
+

The wire-grid version achieved maximum gain with a reflector that was 1.2-m high by 1.4-m long. As the following table shows, the same size rod-based reflector also produces maximum gain for the single-rectangle driver. The two maximum-gain versions of the array also have the very same 50-Ohm SWR bandwidth: a somewhat narrow 4.7%. However, it also shows something else that will prove more interesting.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       100-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   10.37          19.43             56         63         49.76 + j0.39   1.01
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V10-H12            9.87           18.99             62         62         49.96 - j1.06   1.02
+V10-H14            9.93           19.44             62         62         49.90 - j1.13   1.02
+V10-H16            9.92           20.09             62         62         49.85 - j1.11   1.02
+V10-H18            9.88           20.71             62         63         49.84 - j1.08   1.02
+
+V12-H12            10.12          19.14             56         59         50.23 + j0.20   1.01
+V12-H14            10.23 *        19.11             56         59         49.98 + j0.15   1.00
+V12-H16            10.23 *        19.53             56         59         49.87 + j0.32   1.01
+V12-H18            10.15          20.27             56         61         49.95 + j0.45   1.01
+
+V14-H12            7.93           26.46             96         99         57.41 - j20.3   1.49
+V14-H14            9.12           30.87             78         80         52.02 - j4.07   1.09
+V14-H16            8.20           16.96             82         85         66.82 + j12.7   1.44
+V14-H18            10.46          14.06             44         37         57.27 - j19.8   1.48
+
+

The table has 4 lines per vertical reflector size because the peak gain of the array occurs at two adjacent sizes: 1.4 m and 1.6 m horizontally. With vertical sizes of either 1.0 m or 1.2 m, the array shows performance virtually identical to the wire-grid version. However, if we increase the vertical dimension of the rods to 1.4 m, the array's behavior changes radically. Every increment of horizontal size shows a major shift in performance, rather than the more evolutionary changes that we encounter with the vertically smaller reflectors and with every array surveyed so far. At a vertical height of 1.4 m, the wire-grid array is well-behaved. Fig. 7 contrasts wire-grid and rod reflector performance for a size of 1.4 m vertically and 1.2 m horizontally.

+
+ +
+

Maximum gain in either plane does not occur in a direct forward direction with the rod-reflector. E-plane peak gain is 7 degrees off axis, while H-plane maximum gain is 20 degrees off axis. As the beamwidth numbers will suggest, the pattern shape will change with each increment of horizontal dimension increase. Also notable in the H-plane (side-to-side, if the array is used with a vertical orientation) pattern is the absence of nulls at 90 degrees to the forward bearing. Instead, we find large side lobes the maximum headings for which are slightly behind the 90-degree points. (You may remember that I pointed out tiny bulges in the E-plane pattern for the single dipole driver.)

+

Rather than speculate on the source of the odd behavior, it may be best to temporarily withhold judgment and gather more data. We still have 3 more drivers to canvass.

+

4. A Double Rectangle Fed on the Center Vertical Element

+

The double rectangle, fed at the center of the middle vertical element, required no change of any dimension when transferred from the wire-grid to the bar-based reflector. Fig. 8 provides the dimensions used for this array.

+
+ +
+

Except for the factor of balance, the double rectangle shares many properties in common with the single rectangle. However, as the following table demonstrates, it falls in the category of very well-behaved arrays when used with a rod reflector.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       100-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   10.90          19.31             58         54         49.58 - j0.37   1.01
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+
+V10-H14            10.49          18.85             64         54         51.26 - j0.10   1.03
+V10-H16            10.53          18.99             64         52         51.25 - j0.13   1.03
+V10-H18            10.54          19.29             64         52         51.23 - j0.13   1.02
+
+V12-H14            10.77          19.36             58         52         50.32 - j0.29   1.01
+V12-H16            10.83 *        19.18             58         52         50.25 - j0.29   1.01
+V12-H18            10.82          20.36             58         52         50.24 - j0.23   1.01
+
+V14-H14            10.68          21.07             62         52         49.83 + j0.11   1.00
+V14-H16            10.69          20.17             62         52         49.96 + j0.05   1.00
+V14-H18            10.63          21.32             64         54         49.70 - j0.02   1.01
+
+

The data curves are smooth, even for the same span of 1.4-m vertical reflectors across which the single rectangle showed erratic behavior. Indeed, the double rectangle varies in no significant way, whichever type of reflector accompanies it. Fig. 9 demonstrates how closely the two reflector types are in terms of the resulting E-plane and H-plane patterns for the highest-gain reflector sizes.

+
+ +
+

At worst, the rod-reflector produces the same sort of bulges just past the side bearings as the single dipole, although they have now grown into "jowls." The 7% SWR bandwidth is also identical to the SWR curve for the wire-grid version.

+

5. A Bobtail Curtain

+

The bobtail curtain holds the distinction of being the only driver in our collection that is horizontally symmetrical, but vertically asymmetrical. Consisting of three phased vertical monopoles with a single horizontal phasing wire between each pair, it will be open-ended in either the up or down direction. For our exercise, we have closed the top (+Z) portion of our models. Fig. 10 shows the relevant dimensions of the array, including the one change needed to set the impedance at 50 Ohms as we changed reflectors: the spacing between the reflector and the driver decreased from 0.185 m to 0.180 m.

+
+ +
+

The bobtail curtain, over the relevant subset of reflector sizes, shows many of the same characteristics with a rod reflector as it showed with a wire-grid reflector, including a 7% 50-Ohm SWR bandwidth. The list of similarities also includes the range of angular tilt to the E-plane patterns. However, as the following table shows, we once more encounter difficulties when we change the reflector height to 1.4 m.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       100-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   11.31          21.45             58         48         49.95 + j3.23   1.07
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+
+V10-H18            10.93          21.00             62         46         51.02 - j1.62   1.04
+V10-H20            10.94          21.11             62         44         51.02 - j1.62   1.04
+V10-H22            10.94          21.24             62         44         51.02 - j1.62   1.04
+
+V12-H18            11.19          21.25             57         44         50.13 + j0.08   1.00
+V12-H20            11.21 *        21.23             57         44         50.11 + j0.11   1.00
+V12-H22            11.20          21.40             57         44         50.13 + j0.14   1.00
+
+V14-H18            9.74           31.26             79         60         53.54 - j4.51   1.12
+V14-H20            10.44          33.70             70         52         51.76 + j5.68   1.12
+V14-H22            9.78           19.25             69         52         64.52 + j15.6   1.45
+
+

Although the data for a 1.4-m high rod-reflector appears simply to trade a bit of gain for a vastly improved 180-degree front-to-back ratio, the situation is not nearly so simple. As Fig. 11 shows, the rearward quadrants again show the considerable development of side-to-rear lobes that do not show up in 180-degree front-to-back numbers. In the case shown, for a 2.0-m reflector horizontally, the 33-dB 180-degree value gives way to worst-case values that are far less than 20 dB. As well, the rearward lobe development has a strong front-to-side component in common with the single rectangle.

+
+ +
+

The data suggest that we now have two aberrant cases among our driver assemblies, at least with respect to rod reflectors with a 1.4-m (wavelength) vertical dimension.

+

6. A Double Diamond Driver The final candidate on our list of drivers to go with a planar reflector is the double diamond. To effect the transition to a rod reflector, we need only reduce the spacing from the reflector from 0.148 m to 0.146 m, a 2-mm difference that allows the feedpoint impedance to be very close to 50 Ohms resistive. Fig. 12 shows all of the essential dimensions.

+
+ +
+

The wire-grid version of this array reached maximum gain with a vertical dimension of 1.2 m and a horizontal dimension of 1.6 m. Since the rod-reflector version shows equal peak values at two successive horizontal increments, I have add a fourth line to each of the table categories.

+ 
+Reference Wire-Grid Reflector
+                   Free-Space     Front-to-Back     E-BW       H-BW       Impedance       100-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+                   11.13          21.22             56         52         49.63 - j0.65   1.02
+
+Reflector Size     Free-Space     Front-to-Back     E-BW       H-BW       Impedance       50-Ohm
+                   Gain dBi       Ratio dB          degrees    degrees    R +/- jX Ohms   SWR
+V10-H14            10.69          20.49             60         52         50.44 + j1.02   1.02
+V10-H16            10.73          20.75             60         52         50.42 + j1.00   1.02
+V10-H18            10.73          21.14             60         52         50.41 + j1.00   1.02
+V10-H20            10.70          22.47             60         52         50.41 + j1.01   1.02
+
+V12-H14            10.97          20.96             56         52         50.00 + j1.42   1.03
+V12-H16            11.02 *        20.88             56         50         49.93 + j1.41   1.03
+V12-H18            11.02 *        21.19             56         52         49.91 + j1.46   1.03
+V12-H20            10.98          21.67             56         52         49.94 + j1.50   1.03
+
+V14-H14            11.13          18.96             52         48         54.83 + j11.3   1.26
+V14-H16            10.66          16.42             52         50         65.57 + j13.1   1.42
+V14-H18            9.84           40.62             74         68         52.02 + j3.90   1.09
+V14-H20            10.48          29.52             64         60         54.65 + j11.51  1.27
+
+

The double diamond driver is both horizontally and vertically balanced. Nevertheless, it shows problems when the reflector grows to 1.4 m vertically. The table shows the numerical deviations from the kinds of values we would expect from a wire-grid reflector. Fig. 13 shows a comparison of both E-plane and H-plane patterns for a vertical reflector height of 1.4 m and a horizontal dimension of 1.6 m. The E-plane pattern shows considerably more rearward radiation for the rod reflector than for the wire-grid version. The H-plane pattern shows the rear quadrant lobe development, a pattern that is roughly common to all three of the arrays that produce problems when the rod reflector is 1.4-m high.

+
+ +
+

In common also with the other problem drivers, the double diamond shows the same erratic progression of values, unlike the smooth progressions with shorter reflectors. Fig. 14 translates the set of numerical values into patterns that show the same erratic development as we change the horizontal dimension of the rod reflector. On the left is a wire-grid version of the model, and it shows an orderly and tight progression from one reflector increment to the next. However, the rod-reflector version on the right displays the erratic growth and shrinkage of the H-plane pattern.

+
+ +
+

Conclusions and Recommendations

+

We may reach some tentative conclusions regarding the use of bar reflectors as substitutes for solid-surface or closely spaced screen reflectors in planar arrays.

+
+ 1. The bar diameter should be about 0.03 wavelength, with an inter-rod spacing of about 0.1 wavelength for best results. However, variations on these dimensions are permissible to the extent that they allow the driver to reach its proper impedance (using the 50-Ohm level that is common to the entire exercise) with the same approximate spacing as it would have with a wire-grid reflector. +

2. The single dipole, the phase-fed pair of dipoles, and the double rectangle drivers are stable for all tested vertical reflector dimensions and perform very much like their wire-grid counterparts. However, the single rectangle, the bobtail curtain, and the double diamond should be used with great caution for vertical reflector dimensions greater than 1.2 m (wavelength).

+
+

These conclusions handle the obvious outcomes of the data gathering, but they do not touch our remaining question of why the vertical dimension of 1.4 wavelength yields aberrant array behavior. Let's begin by examining the current distribution on wire grid and rod reflectors.

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Fig. 15 provides a glimpse into the current distribution over the reflector, using 1.4 wavelengths as the vertical height and 1.6 wavelengths as the horizontal dimension. To set the current distribution in bolder relief, I set the maximum value at 7.5E-2 for the brightest red. The value is less than the peak current at the feedpoint of the drivers involved. Hence, the dipoles at the far right will show no color change until well along their length, since the feedpoint region has a higher current level than the level set for bright red. In the double diamonds, only the short common feedpoint segment shows an equivalently high current magnitude, while the multiple paths of the upper and lower legs show more modest currents. However, note that both double diamonds share the same color distribution--and hence, the same current magnitude distribution--across their structures.

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More significant for our work is the current distribution on the reflector segments of the models. The wire-grid model on the far left shows an almost uniformly low current level throughout, with only a slight rise in current magnitude immediately behind the double diamond--as indicated by a slightly lighter shade of blue. The well-behaved phase-fed dipoles at the right show a similar pattern, even though the reflector elements are now rods. The model segments closest to the dipole centers are technically 1 shade of blue lighter than the remaining segments, but that difference is too little to show on the small graphics. The conclusion that we can draw from the left and right current distribution graphics is that for most stable operation, the driver must illuminate the reflector in a relatively uniform manner.

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The center model's morass of color illustrates what happens when we do not achieve relatively uniform illumination. The individual rods act like individual parasitic elements coupled to the driver. Hence, we find current peaks that exceed the levels at most places on the double diamond structure itself. The current in each region of each rod will be a function not only of the direct coupling from the driver, but also of inter-element coupling among the rods.

+

Why the vertical dimension of 1.4 wavelengths marks a point of sensitivity also relates to the length of the rods: given the element diameters, they are approaching 3/2 wavelengths. The shorter vertical dimensions show less tendency to this effect. The aberrant behavior also disappears when we use a vertical dimension of 1.6 m (wavelengths), although this value carries the array further away from its optimal gain size. Rod length, however, is at most a necessary but not a sufficient condition to the aberrant behavior of the reflector. For only some of the driver assemblies is it a problem.

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The remaining factor necessary to trigger the unwanted effect is what we might call "over-coupling" between the driver and the reflector rods, where over-coupling is a mutual function of two factors. One of them is rod length. The other one is the spacing of the driver to the reflector, relative to the independent gain of the driver apart from the reflector effects. Let's review some of the data that we have encountered. All of the data will be for reflectors that are associated with the highest gain obtainable for each driver and hence will vary in size from line to line in the following table.

+ 
+Driver Type                Maximum Free-        Driver Spacing from
+                           Space Gain dBi       Reflector m/wl
+Single Dipole               9.27                0.1745
+Phase-Fed Dipole Pair      10.79                0.25
+Single Rectangle           10.23                0.183
+Double Rectangle           10.83                0.235
+Bobtail Curtain            11.21                0.185
+Double Diamond             11.02                0.148
+
+

Of the complex drivers having the equivalent of two or more elements, the well-behaved types have reflector-to-driver spaces well over 0.23 wavelength. Complex drivers showing aberrant behavior use distances well below 0.19 wavelength. The one exception to this general progression is the simple single-dipole driver, with its lesser gain--at least 1 dB below the next lowest level. The reflector-to-driver spacing, early on noted as significant in the selection of proper rod diameter and inter-rod spacing, is the most common factor among the arrays susceptible to a 1.4-m rod length sensitivity and those immune to the effect.

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Undoubtedly, other factors may play a role in the problematical situation. For example, the independent beamwidth of the driver may yield greater or lesser coupling to a region of a rod, and it may be in some measure apart from the maximum gain of the driver when away from the reflector. There is, of course, a limit to the independence of beamwidth and maximum gain in driver assemblies, since two are normally intimately linked.

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The goal here is not to provide a final answer to the limitations of rod-based reflectors. Rather, these notes are simply designed to set the limitations into a perspective on driver assemblies that we may wish to use with reflectors of various sizes. Rod behavior is not identical to wire-grid or solid surface behavior, which shows good immunity from parasitic coupling or over-coupling effects. Regardless of the limitations, we can derive the maximum achievable gain from any of the drivers by holding the rod length to optimal levels.

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Or, we may simply use a solid surface or closely spaced screen in lieu of the rods that have occupied our efforts in this episode.

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Updated 05-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX April, 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: Planar Reflector, VHF / UHF


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Notes on Medium-Length 2-Meter Quads and Yagis

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L. B. Cebik, W4RNL

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Choosing a medium-length (7 to 10 foot boom) 2-meter antenna to build involves a number of choices: gain, front-to-back ratio, band coverage, smoothness of performance across the band, feedpoint impedance, and ease of building, to name a few of the factors. The choices typical fall into the quad vs. Yagi category, since planar and corner reflector arrays tend to require excessive volume at 2 meters. These notes are designed to provide a set of preliminary comparisons of what is possible for a medium-length array, but they do not cover every aspect of the decision-making process.

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We shall look at three antennas: a 7-element OWA Yagi, an 8-element OWA Yagi, and a 7-element quad. My rationale is simple: the required boom length of the 7-element quad falls between the boom lengths of the 2 Yagis--and so does the peak gain. With boom lengths from 7.14' to 9.58', perfect for our pre-set definition of a medium-length antenna for 2 meters.

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Virtually all (but not absolutely all) 2-meter communications is point-to-point or line-if-sight. Because skip communications is such a small part of 2-meter work, one of the vaunted advantages of the quad disappears--the ability to open and close a band (on HF) due to the combination of horizontally and vertically polarized radiation. In general, then, the quad competes at VHF based upon its basic properties and not by virtue of interaction with the ionosphere.

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Let's begin with the quad

+

A 7-Element Quad

Designing a quad from ordinary materials, like AWG #12 (0.0808" diameter) copper wire is not a trivial exercise. To save weight, most quads use wire elements. Because a quad uses closed loops and requires bends, aluminum and copper tubing tend not to be used. Aluminum tubing is difficult to close durably into a loop, while copper is very heavy, relative to aluminum. Hence, both materials tend to give way to thinner wire. However, a wire quad has a narrow operating bandwidth relative to one with fatter elements. In the end, a many-element quad is a series of compromises. +

Perhaps the primary compromise involves the front-to-back ratio. For virtually all quad beam designs, the bandwidth of the front-to-back ratio--as measured against traditional amateur standards--is narrower than the SWR bandwidth--again, as measured against usual amateur standards. The SWR standard is normally a 2:1 ratio relative to the resonant SWR impedance. We can develop a medium boom-length quad with a 50-Ohm resonant impedance--or close enough to achieve an SWR under 2:1 at the edges of the 2-meter band.

+

However, we shall not be so fortunate with the front-to-back ratio, where a 20-dB ratio registers the most commonly used standard. At the band edges of 2-meters, we shall have to settle for a front-to-back ratio closer to 15 dB if we design carefully. (We should keep in mind that the designs shown here are intended to cover the entire 2-meter band.

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The following tables list the dimensions of the 7-element quad, all in inches. The element length is the circumference. Each side of the square design is 1/4 the length listed in the table. The second table samples the free-space performance of the antenna. If used horizontally and several wavelengths above ground, the usable gain will be about 6 dB higher than the listed value (in dBi). If used vertically, the gain will be less but the beamwidth will be wider.

+ 
1. 7-Element Quad Dimensions in Inches (AWG #12 Copper Wire)
+
+Element                 Circumference           Distance from Reflector
+Reflector                       86.80                   ----
+Driver                  83.20                   12.36
+Director 1              80.80                   29.19
+Director 2              78.96                   46.18
+Director 3              77.76                   63.57
+Director 4              76.80                   77.50
+Director 5              76.00                   95.99
+
+2. Performance Characteristics
+
+Parameter                       144 MHz                 146 MHz                 148 MHz
+Gain dBi                        11.85                   12.10                   12.13
+180-degree F-B dB               15.30                   22.10                   16.24
+Hor. B/W degrees                48.4                    47.0                    45.2
+Vert. B/W degrees               52.4                    50.5                    48.2
+Feed Z R+/-jX Ohms              44.8 - j30.4            50.7 - j 0.7            49.4 + j32.3
+50-Ohm SWR              1.899                   1.020                   1.896
+
+ +
+

Fig. 1 shows the curves for gain and front-to-back ratio across the band. The front-to-sidelobe ratio provides a measure of the worst-case front-to-back ratio wherever the forward sidelobes are weaker than the rearward radiation, as they are with the quad design. Note that the gain peaks at about 147.25 MHz, although the front-to-back ratio peaks about mid-band.

+

The gain differential across the band is only 0.30 dB, while the front-to-back differential is only 6.8 dB. However, the average front-to-back ratio is only 19.2 dB, with serious decreases at the band edges.

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Fig. 2 shows the feedpoint resistance and reactance, along with the 50-Ohm SWR curve across the 2-meter band. The design achieves full band SWR coverage, but just barely. The feedpoint resistance does not change much, but the feedpoint reactance undergoes a 60-Ohm swing from one end of the band to the other.

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Fig. 3 shows the E-plane (azimuth) patterns of the array across the band. Two features are notable. First, the forward sidelobes are better than 20-dB down all across the band. Second, at the band edges, the rearward radiation is considerable across a significant beamwidth.

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A 7-Element OWA Yagi for 144-148 MHz

The smaller of the two Yagis uses a variation of the optimized wideband antenna (OWA) arrangement pioneered at HF by WA3FET and NW3A. It consists of a reflector about 0.13 wavelength behind the driver and a fairly closely spaced 1st director 0.06 wavelength or less ahead of the driver. (The exact spacing depends upon the desired operating bandwidth and the diameters of the elements.) These elements essentially control the feedpoint impedance. The 2nd and 3rd directors are of equal length and stabilize the array's performance across a design passband (in this case, 144-148 MHz), and have a role to play in suppressing forward sidelobes. The remaining directors control the array gain and front-to-back ratio. +

The following tables list the dimensions of the 7-element OWA Yagi, all in inches. The element length is the overall linear length of each 3/16" diameter aluminum rod. The second table samples the free-space performance of the antenna.

+ 
1. 7-Element OWA Yagi Dimensions in Inches (3/16" [0.1875"] diameter aluminum)
+
+Element                 Length                  Distance from Reflector
+Reflector                       40.70                   ----
+Driver                  39.66                   10.81
+Director 1              37.00                   15.47
+Director 2              36.32                   27.38
+Director 3              36.32                   42.72
+Director 4              36.20                   63.38
+Director 5              34.50                   85.67
+
+2. Performance Characteristics
+
+Parameter                       144 MHz                 146 MHz                 148 MHz
+Gain dBi                        11.50                   11.61                   11.37
+180-degree F-B dB               21.06                   28.73                   20.35
+Hor. B/W degrees                47.8                    46.0                    44.0
+Vert. B/W degrees               57.8                    54.8                    51.6
+Feed Z R+/-jX Ohms              45.7 + j 3.4            51.1 + j 9.0            47.0 - j 6.9
+50-Ohm SWR              1.122                   1.195                   1.168
+

From the tables, we can glean some interesting information. For example, the 7-element Yagi has a horizontal beamwidth that is less than that of the quad. However, the vertical beamwidth is wider than that of the quad.

+

The remaining data is suggestive of what will emerge in the frequency-sweep graphs to come.

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Fig. 4 shows the gain and the 180-degree front-to-back ratio. The worst-case front-to-back does not appear because the higher general levels of front-to-back performance of the 7-element Yagi leave some forward lobes that are stronger than any rearward lobe. Hence, the front-to-sidelobe ratio would alternate between a forward and a rearward lobe.

+

The array gain varies by only 0.24 dB across the band. Its average gain level is almost exactly 0.5 dB less than the longer 7-element quad. On the other hand, the Yagi's front-to-back ratio is everywhere above 20 dB, with an average value of 24.7 dB, about 5 dB better than the quad. Unlike the quad, the OWA Yagi's gain and front-to-back peaks both occur about in the center of the band.

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Fig. 5 shows the resistance, reactance, and 50-Ohm SWR associate with the 7-element Yagi feedpoint. The OWA feedpoint system of elements provides a very wide operating bandwidth with less than a 1.25:1 50-Ohm SWR all across the band. Note that the typical OWA SWR curve shows more than one minimum: a broad one at the low end of the band and a sharper one at the high end. Above 148 MHz, the 2:1 SWR limit appears quickly, but below the lower end of the band, the SWR remains low for several MHz. However, gain and front-to-back ratio are both reduced below 144 MHz.

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+ +
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Fig. 6 shows the E-plane (azimuth) patterns of the 7-element Yagi. Especially interesting are the much diminished rearward radiation lobes, compared to those of the 7-element quad.

+

An 8-Element OWA Yagi for 144-148 MHz

The 8-element OWA Yagi is an extension of the 7-element design and uses essentially the same first 6 elements. Only slight changes have been made to perfect the operating passband. However, unlike some Yagi families, adding an element requires a very significant adjustment to the previously forward-most element. Compare element 7 in the dimension tables for the two designs. +

The following tables list the dimensions of the 8element OWA Yagi, all in inches. The element length is the overall linear length of each 3/16" diameter aluminum rod. The second table samples the free-space performance of the antenna

+ 
8-Element OWA Yagi Dimensions in Inches (3/16" [0.1875"] diameter aluminum)
+
+Element                 Length                  Distance from Reflector
+Reflector                       40.70                   ----
+Driver                  39.50                   10.81
+Director 1              37.00                   15.47
+Director 2              36.32                   27.38
+Director 3              36.32                   42.72
+Director 4              36.20                   63.38
+Director 5              35.20                   88.50
+Director 65             33.30                   115.0
+
+4. Performance Characteristics
+
+Parameter                       144 MHz                 146 MHz                 148 MHz
+Gain dBi                        12.28                   12.42                   12.15
+180-degree F-B dB               20.26                   23.41                   21.42
+Hor. B/W degrees                45.0                    43.0                    41.2
+Vert. B/W degrees               52.6                    49.8                    47.2
+Feed Z R+/-jX Ohms              47.2 + j 0.4            49.6 + j 4.9            49.6 - j 9.0
+50-Ohm SWR              1.106                   1.104                   1.197
+
+ +
+

As shown in Fig. 7, the gain varies by only 0.27 dB across the band, with its peak at mid-band. The front-to-back ratio peaks slightly above the mid-band point but is everywhere greater than 20 dB. As with the 7-element OWA, the front-to-sidelobe ratio does not reliably shows the worst-case front-to-back ratio and is therefore omitted.

+

The average forward free-space gain of the 8-element Yagi is 12.42 dBi, about 1/3 dB higher than the 7-element quad. The front-to-back ratio averages about 4 dB greater than the values for the quad.

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+ +
+

The resistance, reactance, and 50-Ohm SWR curves for the 8-element Yagi, shown in Fig. 8, are very similar to those for the 7-element Yagi. The minimum SWR values occur at 144.25 and 147.25 MHz. For both the Yagi designs, both the resistance and the reactance undergo very small excursions within the 2-meter band.

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+ +
+

Fig. 9 shows the E-plane (azimuth) patterns of the 8-element Yagi, once more revealing well controlled rearward radiation lobes and forward sidelobes.

+

Horizontal or Vertical?

It is well known that when a horizontally oriented beam is placed above ground, its azimuth pattern is almost identical to the free-space (E-plane) counterpart, including the beamwidth. Less well known is the fact that when we vertically orient an array well above ground, its pattern will also closely resemble its free-space counterpart, the H-plane pattern. As well, the more elements or the longer the boomlength of an array, the closer together grow the horizontal and vertical beamwidth values. +
+ +
+

Fig. 10 provides 146-MHz azimuth patterns of the 3 antennas. Each is 5 wavelengths above average ground--somewhere between 33 and 34 feet. In each case, the height is the height of the boom. Each antenna is vertically oriented. Each has a beamwidth that is the same as the vertical beamwidth listed in the free-space performance charts.

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The quad begins to show an improved pattern relative to the Yagis in this orientation, especially with respect to sidelobes--about a 3 dB improvement on maximum strength. As well, one may more easily experiment with circular polarization with a quad than with a Yagi. For circular polarization of a Yagi, we need essentially two Yagis at right angles to each other with some form of quadrature feed. We also need quadrature feed with the quad, but we may run the line or network from one standard feedpoint to another 90 degrees away. This system is often inconvenient with a square quad, but if we use a diamond-shaped quad, we may place the two feedpoints at the corners and use the element support as additional bracing. We can change the direction of circular polarization simply by placing the main feedline at one or the other junctions of the quadrature network or line.

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The Bottom Line

There is no effective bottom line to this analysis. There are many variables in the building situation for each beam-maker that may make one design easier to execute than the other. As well, special needs or operating foci may give one design an advantage over the other. Hence, the data must speak for themselves to the situation of the builder. +

Interpreting the data requires a few cautions. First, as modeled arrays, the elements presume insulation and isolation from conductive booms--although for the Yagis, a non-conductive boom is not out of the building picture. The quads may use a central metal boom with non-conductive element supports. If one wishes to build one of the Yagis using insulated through-boom techniques, then element length adjustments will be needed. Information on that topic appears elsewhere in the VHF/UHF notes at my web site. See Scaling and Adjusting VHF/UHF Yagis .

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Second, the designs each use a specific size material for the elements. Changes in the element lengths are required for changes in the element diameters. Yagi adjustments that are good for at least a 1.5:1 increase or decrease in diameter also appear elsewhere at my website (see Scaling and Adjusting VHF/UHF Yagis ), as well as in VHF/UHF antenna literature. Quad adjustments are less well formulated for changes in diameter. However, for fatter elements, expect each element to be somewhat shorter in circumference.

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When a proposed diameter change exceeds about 2:1 relative to the original, it is time to re-design both the element lengths and their spacing. The mutual coupling between elements changes to the point where it is no longer optimum to preserve and enhance performance. For example, two 6-element OWA Yagi designs, one by me and one by Dean Straw, N6BV, are nearly 6" different in length, with the longer version having elements about twice as fat as the shorter Yagi design. Likewise, a fat-element quad will likely require a significantly longer boom that the AWG #12 model shown here.

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Automated programs for calculating the dimensions of quads exist for 1 to 4 elements. See New Quad Studies. However, the number of variables involved in longer-boom quads--such as the 7-element antenna shown here--have so far precluded automation of the design process. A new generation of optimizing software is beginning to appear for general antenna design, so the future may ease the design process considerably.

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In the interim, I hope these notes are useful in the process of selecting a 2-meter beam to build.

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+

Updated 01-24-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: Quad, VHF / UHF, Yagi


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+

Quagi and Yagi on 2 Meters
+ Some Preliminary Notes

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+

L. B. Cebik, W4RNL

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As soon as one begins to analyze or design Yagis for VHF, someone (or many ones) will inevitably ask about the quagi, the hybrid parasitic array that usually consists of a quad loop driver and reflector with linear directors. In the past numerous claims have been made about the quagi, most based on operational success stories but without suitable comparisons.

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Therefore, I took a step or two into the investigation, and the results appear in these preliminary notes. work is far from done, since I have looked at only some fairly short quagis--in the 11 to 13 foot boom-length range with 7 and 8 elements. I compared them with some Yagis that bracketed the quagi lengths, using models ranging from 9 to 14.5 feet in length and using 8 to 10 elements. The differential in element count for roughly corresponding boom lengths is one of those topics that will bear further study later on.

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It is clear that I plan to compare the two antenna types over comparable boom lengths. However, every comparison proceeds on the basis of a method and a set of specifications by which to make the comparison. My vehicle of comparison will be NEC-4, which is perfectly adequate to the task, since nothing in either basic quagi or basic Yagi design presses it limitations.

+

More important perhaps are the categories and criteria of comparison. Many antenna builders of high gain antennas for VHF design for the highest gain over a very narrow bandwidth. This practice meets certain operational needs for point-to-point work. However, my own categories of comparison range over a broader set of categories:

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+

1. Operating bandwidth: I shall be interested in the SWR bandwidth over the entire 2-meter band (144-148 MHz). At VHF, the 2:1 HF standard is often still used, but I shall be interested in how much better than that we can achieve with an array. All arrays in these notes are designed for a direct 50-Ohm feedline connection, which simplifies comparisons.

+

2. Pattern control: The absence of forward side lobes generally yields the widest -3 dB beamwidth possible for a given gain level. The presence of significant forward side-lobes tends to decrease horizontal beamwidth, a factor not generally taken into account in some of the traditional simplistic means of calculating beamwidth from gain. I shall be interested in the level of side-lobe suppression--how far down in dB from the main lobe the strongest forward side-lobes are. As well, I shall be looking at the -3 dB beamwidth.

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3. Front-to-back ratio: Although many VHF operators ignore the front-to-back ratio due to the relative absence of rearward QRM in many point-to-point operations, a more general set of criteria must attend to this figure. We shall use the 20 dB standard as a marker, giving figures in terms of the 180-degree front-to-back ratio, with special notes on the worst-case value or the averaged rearward value if required.

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4. Gain: Forward gain will be whatever the array yields, as measured across the passband of 2 meters. We shall be interested not only in the maximum gain to be achieved from an array, but as well in the variation of gain across the test passband. Hence, many of our illustrations will be in the form of performance graphs.

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Certainly, anyone who wish to redo the comparisons using other categories or a restricted set of the ones enumerated is free to do so, and the results might look somewhat different from the ones to appear. However, in every such comparison, there should be an initial explanation--like the one above--of the basis for the comparison. Unfortunately, such explanations of the criteria of comparison are still all too often lacking from discussions of large arrays in every frequency range.

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Quagis:

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Fig. A is the outline of a 7-element quagi and shows the quad loop driver and reflector, along with the linear directors. Such antennas have been built with wire or thin (up to 3/16" rod or tubing). The use of quad loops for the reflector and driver arise from several considerations:

+

1. The reflector loop derives from some evidence that even standard Yagis can benefit from multiple reflectors. In effect, multiple reflectors are approximated by the quad loop that provides two reflectors spaced 1/4 wl apart. Although many claims have been made for the multiple reflector arrangement, the chief advantage appears to be in the category of front-to-back ratio.

+

2. Many older designs of Yagis wound up with very low feedpoint impedances, necessitating the use of matching sections: Tees, gammas, and the like. with a quad loop driver, one can achieve a 50-Ohm feedpoint impedance without the use of additional matching schemes.

+

3. The combination of driver and reflector loops eases the problem of arriving at a reasonably broad operating bandwidth--at least in terms of SWR. The reflector-driver spacing (as well as the loop circumferences) can be used to set the operating source impedance of the array.

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In looking for a suitable quagi to use as a basis for these notes, I turned to the ARRL Antenna Book, 18th Edition, page 18-33. There, I found quagi designs that go back to the 1970s. (The same material is on a different page in the 19th Edition.) My modeling efforts required that I reduce the wire size to #14 from the originally specified #12 AWG in order to bring the array to some semblance of performance across the 2-meter band. The following extract from the EZNEC model will provide dimensions:

+ 
Handbook Quagi                                       Frequency = 144-148  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1     W4E2   0.000,-10.770,-10.770  W2E1   0.000,-10.770, 10.770 6.41E-02   7
+2     W1E2   0.000,-10.770, 10.770  W3E1   0.000, 10.770, 10.770 6.41E-02   7
+3     W2E2   0.000, 10.770, 10.770  W4E1   0.000, 10.770,-10.770 6.41E-02   7
+4     W3E2   0.000, 10.770,-10.770  W1E1   0.000,-10.770,-10.770 6.41E-02   7
+5     W8E2  20.900,-10.600,-10.600  W6E1  20.900,-10.600, 10.600 6.41E-02   7
+6     W5E2  20.900,-10.600, 10.600  W7E1  20.900, 10.600, 10.600 6.41E-02   7
+7     W6E2  20.900, 10.600, 10.600  W8E1  20.900, 10.600,-10.600 6.41E-02   7
+8     W7E2  20.900, 10.600,-10.600  W5E1  20.900,-10.600,-10.600 6.41E-02   7
+9           36.570,-17.930,  0.000        36.570, 17.930,  0.000 6.41E-02  15
+10          69.550,-17.750,  0.000        69.550, 17.750,  0.000 6.41E-02  15
+11          86.980,-17.560,  0.000        86.980, 17.560,  0.000 6.41E-02  15
+12         112.980,-17.370,  0.000       112.980, 17.370,  0.000 6.41E-02  15
+13         138.980,-17.180,  0.000       138.980, 17.180,  0.000 6.41E-02  15
+

The boom length is 11.58' for a relatively low element count of 7.

+

The thin elements result in deficiencies in performance when measured over the 2-meter passband. (See my "New Quad Notes, especially the item on VHF quads, for fuller notes on the effects of element diameter on quad performance.) Therefore, I also adapted a WB4WEN design for 220 MHz to 2 meters, shortening it to 7 elements and using 1/4" diameter elements. One might build such an antenna out of copper tubing or aluminum rod (or aluminum tubing, if the small diameter material is available). The following partial model description shows the salient features of this array.

+ 
Modified WB4WEN Quagi                                    Frequency = 146  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1     W4E2   0.000,-11.199,-11.197  W2E1   0.000, 11.199,-11.197 2.50E-01   7
+2     W1E2   0.000, 11.199,-11.197  W3E1   0.000, 11.199, 11.199 2.50E-01   7
+3     W2E2   0.000, 11.199, 11.199  W4E1   0.000,-11.199, 11.199 2.50E-01   7
+4     W3E2   0.000,-11.199, 11.199  W1E1   0.000,-11.199,-11.197 2.50E-01   7
+5     W8E2  21.000,-10.700,-10.700  W6E1  21.000, 10.700,-10.700 2.50E-01   7
+6     W5E2  21.000, 10.700,-10.700  W7E1  21.000, 10.700, 10.700 2.50E-01   7
+7     W6E2  21.000, 10.700, 10.700  W8E1  21.000,-10.700, 10.700 2.50E-01   7
+8     W7E2  21.000,-10.700, 10.700  W5E1  21.000,-10.700,-10.700 2.50E-01   7
+9           36.369, 17.563,  0.000        36.369,-17.563,  0.000 2.50E-01  11
+10          67.200, 17.038,  0.000        67.200,-17.038,  0.000 2.50E-01  11
+11          83.492, 17.038,  0.000        83.492,-17.038,  0.000 2.50E-01  11
+12         107.769, 17.038,  0.000       107.769,-17.038,  0.000 2.50E-01  11
+13         132.109, 17.038,  0.000       132.109,-17.036,  0.000 2.50E-01  11
+

The Buchanan array has several features of note. First, boom length is just over 11', a half foot shorter than the Handbook array, although its performance will be superior in every category. Second, for ease of new-builder success, Bill Buchanan designed all but the first director to be of the same length.

+

To see what a quagi that is just longer than the Handbook array might do, I added a further director to the 7-element model. This move required a director that is quite a bit shorter than the preceding ones, with adjustments also required to the driver loop circumference. The result is a 13.6' boom length, with the other details shown in the partial model description that follows:

+ 
8-element Quagi                                          Frequency = 146  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1     W4E2   0.000,-11.199,-11.197  W2E1   0.000, 11.199,-11.197 2.50E-01   7
+2     W1E2   0.000, 11.199,-11.197  W3E1   0.000, 11.199, 11.199 2.50E-01   7
+3     W2E2   0.000, 11.199, 11.199  W4E1   0.000,-11.199, 11.199 2.50E-01   7
+4     W3E2   0.000,-11.199, 11.199  W1E1   0.000,-11.199,-11.197 2.50E-01   7
+5     W8E2  21.000,-10.650,-10.650  W6E1  21.000, 10.650,-10.650 2.50E-01   7
+6     W5E2  21.000, 10.650,-10.650  W7E1  21.000, 10.650, 10.650 2.50E-01   7
+7     W6E2  21.000, 10.650, 10.650  W8E1  21.000,-10.650, 10.650 2.50E-01   7
+8     W7E2  21.000,-10.650, 10.650  W5E1  21.000,-10.650,-10.650 2.50E-01   7
+9           36.369, 17.563,  0.000        36.369,-17.563,  0.000 2.50E-01  11
+10          67.200, 17.038,  0.000        67.200,-17.038,  0.000 2.50E-01  11
+11          83.492, 17.038,  0.000        83.492,-17.038,  0.000 2.50E-01  11
+12         107.769, 17.038,  0.000       107.769,-17.038,  0.000 2.50E-01  11
+13         132.109, 17.038,  0.000       132.109,-17.036,  0.000 2.50E-01  11
+14         163.000, 15.500,  0.000       163.000,-15.500,  0.000 2.50E-01  11
+

How these physically comparable quagis stack up against each other will be apparent from the follow performance graphs.

+

Gain

+
+ +
+

Fig. 1 shows the gain curves of the three arrays across 2 meters. The two quagis using 1/4" elements have curves that are almost congruent, with a 0.3 to 0.4 dB differential--the improvement we derive from the added director. The gain differential from on end of the band to the other is under 0.6 dB. However, the Handbook version, with its thinner elements, not only shows a much lower gain level by 0.4 to 0.5 dB, but as well shows a full 1 dB variation in gain across the band.

+

Front-to-Back Ratio

+
+ +
+

The Handbook array and the 7-element WB4WEN-derived quagi show similar front-to-back curves, as displayed in Fig. 2. The 180-degree figures are generally representative of front-to-rear performance, since the deep null just above the center of the band is accompanied by a reduction in rear side lobes. However, the Handbook quagi drops below 20 dB at the lower end of the band. Of course, in parasitic design, it is fairly straight forward to move the peak front-to-back ratio to a favored portion of a given band. However, note that above the peak value frequency, the value drops more rapidly than below the peak value frequency.

+

The 8-element quagi was designs for a relatively constant front-to-back ratio across the band with all values above 20 dB, whether we are speaking of the 180- degree front-to-back ratio or an average or worst case value. Should a builder wish to bring the higher gain at the upper end of the band down to the low-end point-to-point operating region of 2 meters, the array can be scaled slightly larger to preserve all of the other operating characteristics.

+

Pattern Control

+
+ +
+

The -3 dB beamwidth, shown in Fig. 3, is a partial measure of pattern control. The decrease in beamwidth across the band is partially a function of the increasing gain across the band, although the drop in beamwidth is somewhat greater than the increase in gain. In this regard, the arrays are comparable, although the Handbook array has the widest beamwidth.

+
+ +
+

Not all of the beamwidth differential among the arrays is solely a function of gain. Fig. 4 shows the Forward-to-Side-Lobe ratio in dB. The Handbook array shows considerably higher side-lobe reduction than the two WB4WEN designs (partly a function of using equal-length directors). Suppression of side lobes tends to increase the beamwidth.

+

To this point in my look at quagis, I tend to find that most designs (which are more numerous than the ones examined here) show stronger forward side lobes than the best Yagi designs. In a broad and incomplete summary, quagis have values range from 11 to 17 dB, while most Yagis run from 16 to nearly 20 dB.

+
+ +
+

Fig. 5 shows overlaid patterns for the 7-element WB4WEN-derived quagi. The patterns illustrate the forward side-lobe development of the array--and the other quagis as well--as gain increases across the band. Note also the confirmation of the reduction in overall rear gain near the peak 180-degree front-to-back ratio frequency.

+

SWR Bandwidth

+
+ +
+

Unfortunately, the thin-wire Handbook array does not provide under 2:1 50-Ohm SWR across the entire 2-meter band, as shown in Fig. 6. However, this achievement was likely not among the design goals for the array. Both of the other quagis provide under 1.9:1 50-Ohm SWR values across the band, partly as a result of the use of larger-diameter elements.

+

The quagis, especially the 2 updated designs, represent perfectly usable arrays for either spot or general 2-meter use. They are capable of good gain and generally acceptable performance figures in most categories of comparison. However, part of our initial exploration is to see how they might stack up against pure Yagis.

+

Yagis

There are many types of long-boom Yagis, ranging from the classic DL6WU designs to more recent efforts to improve upon that standard. For the comparison here, I have used three members of a family of OWA Yagis that I designed in an effort to achieve reasonable levels of pattern control. Their gain levels for a given boom length may be up to 0.3 dB below those of classic DL6WU designs, but they are broad-band antennas in every sense of the term. Fig. B shows the general outline of one of the series. + 
8-el OWA Yagi 146 MHz                                    Frequency = 148  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -20.450,  0.000,  0.000        20.450,  0.000,  0.000 1.88E-01  21
+2          -19.750,  8.792,  0.000        19.750,  8.792,  0.000 1.88E-01  21
+3          -18.501, 13.471,  0.000        18.501, 13.471,  0.000 1.88E-01  21
+4          -18.164, 25.379,  0.000        18.164, 25.379,  0.000 1.88E-01  21
+5          -18.199, 40.722,  0.000        18.199, 40.722,  0.000 1.88E-01  21
+6          -18.106, 61.382,  0.000        18.106, 61.382,  0.000 1.88E-01  21
+7          -17.600, 86.489,  0.000        17.600, 86.489,  0.000 1.88E-01  21
+8          -16.600,113.000,  0.000        16.600,113.000,  0.000 1.88E-01  21
+

The 8-element array is about 9.4' long. The use of 8 elements in this space derives in part from the OWA driver section and in part from the need for enough directors to effect pattern control.

+ 
9-el OWA Yagi 146 MHz                                    Frequency = 146  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -20.450,  0.000,  0.000        20.450,  0.000,  0.000 1.88E-01  21
+2          -19.750,  8.792,  0.000        19.750,  8.792,  0.000 1.88E-01  21
+3          -18.501, 13.471,  0.000        18.501, 13.471,  0.000 1.88E-01  21
+4          -18.164, 25.379,  0.000        18.164, 25.379,  0.000 1.88E-01  21
+5          -18.199, 40.722,  0.000        18.199, 40.722,  0.000 1.88E-01  21
+6          -18.106, 61.382,  0.000        18.106, 61.382,  0.000 1.88E-01  21
+7          -17.600, 86.489,  0.000        17.600, 86.489,  0.000 1.88E-01  21
+8          -17.150,116.000,  0.000        17.150,116.000,  0.000 1.88E-01  21
+9          -16.100,144.000,  0.000        16.100,144.000,  0.000 1.88E-01  21
+

The 9 element array is 12' long. Hence, the 8- and 9-element arrays bracket the 7-element quagis in boom length. Since Yagi gain tends to be a function of boom length, we would expect the Yagis to have gain levels just below and just above the quagis of intermediate length. However, as we shall see, raw gain value is not everything to the design of a parasitic array.

+ 
10-el OWA Yagi 146 MHz                                   Frequency = 148  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -20.450,  0.000,  0.000        20.450,  0.000,  0.000 1.88E-01  21
+2          -19.750,  8.792,  0.000        19.750,  8.792,  0.000 1.88E-01  21
+3          -18.501, 13.471,  0.000        18.501, 13.471,  0.000 1.88E-01  21
+4          -18.164, 25.379,  0.000        18.164, 25.379,  0.000 1.88E-01  21
+5          -18.199, 40.722,  0.000        18.199, 40.722,  0.000 1.88E-01  21
+6          -18.106, 61.382,  0.000        18.106, 61.382,  0.000 1.88E-01  21
+7          -17.600, 86.489,  0.000        17.600, 86.489,  0.000 1.88E-01  21
+8          -17.150,116.000,  0.000        17.150,116.000,  0.000 1.88E-01  21
+9          -16.800,146.600,  0.000        16.800,146.600,  0.000 1.88E-01  21
+10         -15.400,174.000,  0.000        15.400,174.000,  0.000 1.88E-01  21
+

The 10-element Yagi is 14.5' long. Its gain value should be just above that of the 8-element quagi, at least in theory. All of the Yagis use 3/16" diameter elements. As well, elements 1-7 are identical. Indeed, the entire family--from 7 to 12 elements--was developed using that same core elements with each added director requiring adjustment of only the two forward-most directors to stabilize performance. Details of the entire collection and its theory of design will appear sometime in 2002 in antenneX. For now, our first step is to make a few comparisons among the Yagis set forth here.

+

Gain

+
+ +
+

Yagi design can be set to place the maximum gain of the array within the operating passband, as shown in Fig. 7. This practice results in the least variation in gain across the band. As we increase the number of elements, the variation in gain decreases. The range is about 0.25 dB in the 8-element design and only 0.2 dB in the 10-element version.

+

Front-to-Back Ratio

+
+ +
+

The graph of front-to-back curves in Fig. 8 appears to be a maze of lines. However, note the very small range of values on the Y-axis--only 4 dB total. Had I graphed the curves on a larger scale, say 20 dB total, the lines would be difficult to distinguish from each other. In general, the graph simply demonstrates that all 3 of the Yagis achieve a 20 dB front-to-back ratio across the entire band. Nor part of the rearward pattern exceeds the -20 dB mark relative to the gain of the forward lobe.

+

Pattern Control

+
+ +
+

The first step in looking at pattern control is to examine the -3 dB values for beamwidth in Fig. 9. Like the values for the quagis (in Fig. 3), the curves all show a relative constant rate of decrease across the operating passband. However, if we refer to Fig. 7, we see that at the upper end of the band for all three antennas, the gain is decreasing slightly. Thus, beamwidth is not solely a function of gain.

+
+ +
+

The graph of relative side-lobe strength in Fig. 10 shows in part why the beamwidth continues to decrease even though gain no longer increases. For all three designs, maximum forward side-lobe suppression is greatest at the low end of the band. It decreases across the band. The stronger forward side lobes tend to narrow the beamwidth of the array, regardless of gain. Hence, parasitic array beamwidth is a function of at least two (if not more) factors: gain and forward side-lobe strength.

+
+ +
+

Fig. 11 shows the overlaid free-space azimuth patterns of the 9-element version of the Yagis used here for comparative purposes. The patterns are typical of those for all three Yagis. Of especial note is the fact that forward side lobes can be disguised and hence not recognized in casual observation. The overlaid patterns show how a definite forward side lobe at 144 MHz becomes a seemingly simply bump in the pattern at 148 MHz. However, that side-lobe has effects that are just as definite as the clearly evident strong side lobes of the quagis. Note the main forward lobe at 148 MHz: it is clearly narrower from the -10 dB point onward than the other main forward lobes.

+

SWR Bandwidth

+
+ +
+

The family of OWA Yagis was designed for relatively constant performance characteristics across the 2-meter band, including gain, front-to-back ratio, side-lobe suppression, and SWR. The highest value of 50-Ohm SWR shown in the graph in Fig. 12 is about 1.20 to 1. A mark of OWA performance is a double dip in the SWR curve--a weak dip low in the band and a deep dip near the upper end of the band. Either dip can be disguised, as is the large dip in the 9-element Yagi, which actually occurs between 147.5 and 148 MHz.

+

In general, the Yagis shown here represent a quite usable family sub-group that meets all of the design goals set for them

+

Some Relevant Comparisons and Some Remaining Questions

+

In comparing the quagis to this family of Yagis, it is unnecessary to overlay SWR patterns. The fundamental design principles used in the Yagi designs ensured a flatter set of SWR curves and any of the quagis. Indeed, it is unclear at this point in the investigation whether one can design a quagi for equivalent SWR performance, although it is likely that improvements in the current quagi SWR curves are possible with redesign. However, that work is for the future.

+

Likewise, the front-to-back curves also need no overlaying, since all but the Handbook array meet the 20 dB standard.

+

For the remaining comparisons, we shall use the 2 updated quagis (11' and 13.6') and the 9- and 10-element Yagis (12' and 14.5'). Adding in all of the antennas would make the graphs confusing.

+
+ +
+

In Fig. 13, we can see the different gain curves for the two types of antennas. The Yagis, with their longer booms, have higher average gains, although the quagi gain values rise to meet the Yagis at the upper end of the band. That rise--in contrast to the relatively even gain of the Yagis across the band--suggests that further design work may be possible to better center the quagi gain peak within the band. However, centering the gain within the operating passband often has the effect of reducing maximum gain by 0.1 to 0.2 dB from its out-of-band peak. Only further design work will tell of one can equalize quagi gain in the way in which Yagi gain can be equalized.

+

Despite the differences in the curves, it is clear that for a given boom length, the quagi has no especially advantage over a Yagi. At least, this holds true for the quagi versions so far analyzed. Whether a real gain improvement over a comparable Yagi is possible with a quagi design remains to be seen.

+
+ +
+

The comparative -3 dB beamwidth curves in Fig. 14 are especially interesting from the perspective of pattern control. The 8-element Quagi and the 9-element Yagi have closely matched curves. The quagi gain surpasses that of the 9-element Yagi for most of the band, suggesting that it should have a narrower beamwidth. However, a glance at Fig. 15 shows that the Yagis decrease their forward side-lobe suppression more rapidly than the quagis, which tend to have uniformly strong forward side lobes. Hence, where gain would increase the beamwidth of the Yagi, the development of side lobes of significance reduces it.

+
+ +
+

However, neither gain nor side lobes fully account for the close tracks of the 8-element quagi and the 9-element Yagi. It presently appears--subject to further exploration of quagi designs--that the quagi design itself yields for a given boom length a "naturally" wider beamwidth than a comparable Yagi. It is not clear at this stage of investigation what factors are at work--the loops, the special director set, etc.--or to what degree.

+

This initial investigation, thus, has ended by raising more questions than it has answered. Perhaps the only fairly definite conclusion we can reach is that, all other things being equal, quagis and Yagis have similar gain potential for given boom lengths. With proper design, either antenna can be designed for a front-to-back in excess of the standard (20 dB). Likewise, both can be designed for under 2:1 50-Ohm SWR throughout the operating passband. Whether the quagi can rival the OWA SWR figures remains to be discovered.

+

In the realm of pattern control, beamwidth and side-lobe suppression remain open questions for further design or design analysis--depending on what designs come my way and what I may be able to concoct. Whether adding further elements will allow better gain centering and pattern control is, again, a matter for further investigation.

+

Moreover, I have stayed with rather modest boom lengths so far. It is not clear what the development of very long-boom quagis may hold by way of performance characteristics.

+

Finally, remember that these notes are based on a set of analysis categories and criteria that may or may not be applicable to a given operating circumstance. I tend to think in fairly broadband terms. If you think in other terms, feel free to develop a comparable analysis from your own perspective. Nothing has been claimed as an absolute, and alternative perspectives are not only fair, but also welcome.

+
+ +
+

Updated 04-16-2001. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: Quad, VHF / UHF, Yagi


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+

Modeling the Dual Rhomboid
+
+ Part 1: The 1296 MHz Version from QST

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Some Background on the Dual Rhomboid

In the late 1950s, Edmund Laport of RCA hand calculated a number of improved rhombic-type antennas. The improvements for a dual rhomboid consisted in the main of higher gain (with claims of 27 dB over a dipole) and lower side lobe values. The horizontal beamwidth was calculated at about 11 degrees to -3 dB points. Thus the antennas represent appropriate choices for fixed point-to-point communications or reception. +

Interest in the design has periodically peaked in various parts of the overall communications field, including amateur VHF and UHF efforts and the TV reception (cable and individual) industry. For either application arena, improved rhombics offer the potential for an inexpensive antenna (some wire and wood) with high gain and relatively easy construction.

+

Cliff Buttschardt, K7RR, graciously provided me with some background material appearing in the October, 1976 CATJ, and other information has appeared in 73 and QST. The article's references include several Radio-Electronics articles between 1953 and 1960, mostly referenced to TV uses of the rhombic. As well, there are references to Laport's original papers in the RCA Review (March, 1952, and March, 1960). Bill Parker, W8DMR, wrote on the "Dual Rhombic for VHF-UHF" in 73 for August, 1977, and the information there was edited and relayed by Emil Pocock, W3EP, in his VHF column (p. 89) in QST for March, 1997. The reason for the resurgence of interest in 1997 stems from the 1296 MHz version of the dual rhomboid built by Dayton Johnson, W0OZI, which won the 1996 Central State VHF Conference antenna gain test with a measure 17.3 dBi gain value. (See QST for December, 1996, p. 90.)

+

Although Laport developed several advanced multi-element rhomboid antenna designs (hand-calculated), the most favored for its ease of implementation is the dual rhomboid. (The elements are rhomboids, but not true rhombi, since the sides are not necessarily perfectly parallel.) It is on the dual rhomboid that I shall concentrate, since it presents a number of challenges to the antenna modeler.

+

In this note, I shall focus on the 1296 MHz version of the antenna derived from the work of W8DMR as revised by W3EP, since that is likely the antenna design most accessible to most hams. Apparently, W3EP scaled the antenna design from a 1255 MHz ATV version in Parker's article. Among the claims made for the antenna are the following of interest to an inveterate modeler. 1. The gain may be 20 dB better than a dipole. 2. The antenna allows for "sloppy" construction without jeopardy to success.

+

In all of this background material, no mention is made of the antenna's front-to-back ratio. Moreover, Laport's theoretical calculations and HF applications of the antenna suggested that terminating resistors for each section of this traveling wave design should be about 660 Ohms and yield a net feedpoint impedance of about 330 Ohms. In ham writings, this has been uncritically translated into 600 Ohm resistors and a 300-Ohm feedpoint impedance.

+
+ +
+

To see how this works, see Fig. 1, a general outline--with dimensions--of the 1296 MHz version appearing in QST. The two rhomboids are offset from each other--left and right--by a small distance at their terminating points so that the separate patterns maximize the main forward lobe and minimize troubling side lobes that are characteristic of single rhombic designs. Both rhomboids are fed in parallel. Laport's original designs called for no separation between the "upper" and the "lower" wires, but only insulation at the crossing points. Typical ham practice has mounted the two rhomboids on opposite sides of a frame, usually about 3/4" to 1" thick (at UHF, a minimum size for sturdiness).

+

At 1296 MHz, a wavelength is about 9.11" long, so the length of the antenna from feedpoint to terminating resistors is about 8.4 wl and the maximum width is about 4.7 wl. (This may account for the fact that no ham has yet constructed a rotating HF version of the antenna.) At 1296 MHz, the antenna is about 77" long and 42.5" wide--quite manageable dimensions.

+

There are two sets of antennas to be explored: the QST model and the CATJ versions derived directly from Laport's analysis. In this part, I shall look only at the QST model. One important reason for this is that modeling the antenna is tempting for anyone with a basic modeling program using NEC-2. However, creating a useful (I shall not use the term "precise") model of the Laport dual rhomboid is not so easy a task as it may seem, and I shall point to some dangers in the enterprise before seeing what the QST model yields.

+

Modeling a Dual Rhomboid

A single rhombic antenna that is 8 wl long will tax many basic NEC-2 modeling programs. The core will handle the geometry easily, but the number of segments required to achieve a relevant degree of convergence (as a test of model adequacy) may quickly approach the standard 500-segment limit attached to basic programs. If we create a dual rhomboid antenna with closely spaced wires crossing each other and sharp angles, the number of segments required for convergence to even a reasonable degree quickly passes the 1000 mark, and some of my models approached 1600 segments before achieving an acceptable level of convergence. +

Modeling a rhomboid shape with a feedpoint and two terminating resistors also requires small distortions of the ideal acutely angled points to the geometry. For the 1296 MHz model, I used 1" multi-segment wires at the points in which to place the resistors and the source. Although an inch seems small compared to a total length of 77", it is 11% of a wavelength and thus cannot be neglected as a potential error source. These wires used at least 3 segments (and some as high as 7) to ensure centering of the source and resistors and to ensure that segments adjacent to the source and load were the same length of the source and load segments.

+

The wires for the longer and shorter sides are equally highly segmented. I developed two models, the chief difference between them appearing in Fig. 1A.

+
+ +
+

Model A brings the two wires on each side of the feedpoint to a common junction. This is a somewhat dangerous modeling practice, since the wire segments closest to the junction intersect--even for small diameter wire--along an appreciable portion of the segment. This can create modeling errors. Convergence to a reasonable, but not perfect, degree required models using nearly 1600 segments.

+

Model B changes all of the angles to right angles, minimizing the mutual wire penetration effect. It may also reflect ham construction using a wood frame. These models converged reasonable with about 800 segments.

+

However, the results obtained from just the change in feedpoint area treatment differ by enough to warrant presentation of both sets of figures. For many purposes, the differences may not make a difference, but that is not something that a modeling exercise can establish from the outset. For example, the feedpoint impedance of Model A is higher than the theoretical 300 Ohms by about as much as the feedpoint impedance of model B is below that value.

+

In all azimuth patterns, to add to the slowness of model runs, I used a 0.1 degree resolution. The patterns of rhombics of any form are too complex for the 1-degree resolution we habitually use with Yagis.

+

Interestingly, in no case did I obtain anything close to the 20 to 27 dB gain over a dipole. All modeling was done in free space using copper wire losses, so a comparison with a free space dipole should reduce the reported figures by about 2.1 dB. This does not make the dual rhomboid a poor antenna, since 16 dBi free space gain from a hank of wire and a few slats of wood is still excellent performance potential.

+

For reference, here is the description of Model B as used below.

+ 
Dual Rhombic-QST 3-97, p89                Frequency = 1296  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in)  Dia(in) Segs
+
+1   W8E2  -0.500,  0.000,  0.000  W2E1  -0.500,  0.000,  0.500    # 12    2
+2   W1E2  -0.500,  0.000,  0.500  W3E1 -15.250, 27.500,  0.500    # 12   75
+3   W2E2 -15.250, 27.500,  0.500  W4E1   5.500, 77.000,  0.500    # 12  120
+4   W3E2   5.500, 77.000,  0.500  W5E1   6.500, 77.000,  0.500    # 12    3
+5   W4E2   6.500, 77.000,  0.500  W6E1  21.250, 50.000,  0.500    # 12   75
+6   W5E2  21.250, 50.000,  0.500  W7E1   0.500,  0.000,  0.500    # 12  120
+7   W6E2   0.500,  0.000,  0.500  W8E1   0.500,  0.000,  0.000    # 12    2
+8  W15E2   0.500,  0.000,  0.000  W9E1  -0.500,  0.000,  0.000    # 12    3
+9   W1E1  -0.500,  0.000,  0.000 W10E1  -0.500,  0.000, -0.500    # 12    2
+10  W9E2  -0.500,  0.000, -0.500 W11E1 -21.250, 50.000, -0.500    # 12  120
+11 W10E2 -21.250, 50.000, -0.500 W12E1  -6.500, 77.000, -0.500    # 12   75
+12 W11E2  -6.500, 77.000, -0.500 W13E1  -5.500, 77.000, -0.500    # 12    3
+13 W12E2  -5.500, 77.000, -0.500 W14E1  15.250, 27.500, -0.500    # 12  120
+14 W13E2  15.250, 27.500, -0.500 W15E1   0.500,  0.000, -0.500    # 12   75
+15 W14E2   0.500,  0.000, -0.500  W7E2   0.500,  0.000,  0.000    # 12    2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           2     8 / 50.00   (  8 / 50.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           2     4 / 50.00   (  4 / 50.00)     600.000         0.000
+2           2    12 / 50.00   ( 12 / 50.00)     600.000         0.000
+
+Ground type is Free Space
+

Modeling Results

The data derived from the models will appear mostly in tabular form, with a few patterns interspersed. This is a consequence of my usual procedures of systematically exploring certain variables in the antenna design. +

One question of interest is whether wire size plays any significant role in antenna performance. The easiest way to find out is to run identical antenna dimensions with various wire sizes. Here are the results for 1296 MHz, using the prescribed 600-Ohm terminating resistors. In the tables that follow, gain is the free space value in dBi, F-B is the 180-degree front-to-back ratio in dB, B/W is the -3 dB beamwidth in degrees, F/S is the ratio of the forward lobe to the most major side lobe in dB, and the Feed Z is the source impedance.

+ 
Model A  (1581 segments)
+
+AWG       Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+12        16.23     15.99     10.0      10.24     347 - 81
+14        16.25     16.55     10.0      10.23     372 - 58
+16        16.29     16.90     10.2      10.26     391 - 46
+18        16.22     17.49     10.2      10.23     411 - 33
+20        16.17     18.18     10.2      10.21     429 - 23
+

Although the gain does not change in practical terms, it does show a peak with #16 copper wire. Interestingly, the QST article suggested that #12 would be the smallest wire likely to be used. I am not certain that is a sound statement, since the #16 version of the model also showed the highest front-to-side lobe ratio. Note also the increasing front-to-back ratio and feedpoint impedance as the wire size decreases. These phenomena are likely effects of increasing wire losses, which do not affect gain significantly.

+ 
Model B  (797 segments)
+
+AWG       Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+10        15.71     14.98     10.3      10.74     186 - 17
+12        15.76     15.54     10.4      10.66     200 -  8
+14        15.80     16.20     10.4      10.57     213 -  1
+16        15.81     16.92     10.4      10.48     226 + 10
+18        15.81     17.71     10.4      10.40     239 + 18
+20        15.80     18.59     10.4      10.33     251 + 26
+

The antenna gain for this model is systematically about a half dB lower than for Model A, and the reported source impedance is below 300 Ohms. Interestingly, the front-to-back ratio is almost identical for each wire size between the two models. One of the reasons that I tend to trust Model B more than Model A is the smaller excursion of reactance with the changes in wire size (noting that I added #10 wire to Model B just to see what would occur). Moreover, the gain peak is less pronounced and the front-to-side ratio makes a steady progression downward as the front-to-back ratio climbs.

+
+ +
+

Fig. 2 provides a free space azimuth pattern for Model A, which is virtually identical to the pattern for Model B with a slight adjustment of gain. Despite the careful calculations made by Laport, this version of his work cannot suppress the main side lobe by more than 10 dB relative to the main lobe.

+
+ +
+

It is interesting to compare the azimuth plot to a free space vertical (or elevation) plot for the antenna (Fig. 3). In this plane, we see a broadening of the main forward and rear lobes (to about 30 degrees between -3 dB points). We may also note that the largest side lobe also appears in this pattern, giving the impression that it may form a cone around the main lobe.

+
+ +
+

A 3-D view of the pattern, shown in Fig. 4, can give us a better view of what is happening with the main side lobe--or side lobes. First, we must allow for the fact that the reduced resolution of the 3-D pattern converts smooth petals into crystalline points. Nonetheless, we can see that the main side lobe is actually a series of undulating lobes and nulls around the main lobe. (Those given to such things can make any sort of desired Rorschach test out of the 3-D pattern.)

+

To some degree, then, the dual rhomboid is sensitive to wire size in the 1296 MHz model we are examining. We may increase the front-to-back ratio by decreasing the wire size. We should also wonder what effect we might achieve by changing the values of the terminating resistors. The next data set for both models explores two versions of each model: #12 wire and #16 wire--that latter because it coincides with the gain peaks shown by the preceding data. One of the basic questions to pose is whether there is a value of terminating resistor that will maximize the front-to-back ratio. The following data set systematically reduces the terminating resistor values in 100-Ohm increments from 600 to 200 Ohms.

+ 
Model A  (#12 wire; 1581 segments)
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       16.23     15.99     10.0      10.24     347 - 81
+500       16.21     17.77     10.0      10.17     338 - 81
+400       16.17     20.23     10.0      10.07     327 - 83
+300       16.14     21.97     10.0       9.95     313 - 85
+200       16.09     18.31     10.0       9.77     295 - 89
+
+Model A  (#16 wire; 1581 segments)
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       16.29     16.90     10.2      10.26     391 - 42
+500       16.26     19.15     10.2      10.17     379 - 46
+400       16.23     21.91     10.2      10.06     364 - 51
+300       16.20     21.50     10.2       9.92     346 - 58
+200       16.17     16.37     10.2       9.74     323 - 68
+

Despite differences occasioned by the smaller wire size occasioning more rapid property changes than the larger wire size, the two tables show an interesting coincidence. The maximum front-to-back ratio occurs with a load between 300 and 400 Ohms--closer to 300 Ohms for the #12 wire and closer to 400 Ohms for the #16 version. Fig. 5 shows the resultant azimuth pattern for the #12 version with terminating resistors of 300 Ohms.

+
+ +
+ 
Model B  (#12 wire; 797 segments)
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       15.76     15.54     10.4      10.66     200 -  8
+500       15.74     17.64     10.4      10.55     194 -  8
+400       15.72     20.92     10.4      10.42     186 -  8
+300       15.69     24.15     10.4      10.23     177 -  9
+200       15.67     18.91     10.4      10.00     165 - 10
+
+Model B  (#16 wire; 797 segments)
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       15.81     16.92     10.4      10.48     226 + 10
+500       15.79     19.64     10.4      10.37     218 +  9
+400       15.77     23.64     10.4      10.23     209 +  8
+300       15.75     23.11     10.4      10.06     197 +  7
+200       15.74     16.59     10.4       9.83     182 +  5
+

As with Model A, Model B shows its maximum front-to-back ratio with terminating resistors between 300 and 400 Ohms. The consistency between the source impedance values for the two wire sizes gives me additional reason to trust Model B more than Model A, even though the primary trends coincide.

+

Whether the source impedances reported by Model B are accurate to a real antenna involves a number of variables. Some of those variables include limitations of the model itself, as described earlier. Other variable emerge from the construction process itself. Ideally, the support structure for the antenna should be RF-transparent at 1296 MHz. Likewise, construction practices should involve no metal supports--not even nails--close to the wire. Even a few 1-inch brads can add up to a wavelength of nails very quickly. As a consequence, any real version of the dual rhomboid is likely to show a source impedance somewhat at variance of even the most precise model.

+

One final question that occurred to me resulted from the claims that the dual rhomboid forgives sloppy construction. In more precise form, one may ask to what degree the antenna may be frequency sensitive. As a partial answer to this question, I ran Model A through a few wire sizes but on the ATV frequency of 1255 MHz, about 3% lower. (Some claims for the broad-banded nature of the antenna suggested that +/- 40% of the design frequency would be usable.) The following table compares the results for Model A at 1296 and 1255 MHz for 3 wire sizes, using the standard 600-Ohm terminating resistors.

+ 
Model A  (1581 segments)
+
+Freq.     AWG       Gain      F-B       B/W       F/S       Feed Z
+MHz       Size      dBi       dB        deg       dB        R+/-jX
+1296      12        16.23     15.99     10.0      10.24     347 - 81
+1255      12        16.20     19.37     10.6      10.30     313 -108
+
+1296      16        16.29     16.90     10.2      10.26     391 - 46
+1255      16        16.26     21.48     10.8      10.20     362 - 80
+
+1296      20        16.17     18.18     10.2      10.21     429 - 23
+1255      20        16.14     23.96     10.8      10.12     409 - 61
+

With respect to gain, no especially frequency sensitivity can be found. However, the front-to-back ratio with a given value of terminating resistor is quite frequency sensitive. At the lower frequency, the 600-Ohm terminating resistors are close to optimal for maximizing the front-to-back ratio. Moreover, the added capacitive reactance at the source is quite evident for all of the wire sizes.

+

Whatever the final evaluation of the adequacy of these models, it is clear that the Laport dual rhomboid antenna is not quite the "set-and-forget" item that some sources portray it to be. Its properties vary with wire size, terminating resistor value, and frequency. Whether any of those variations are significant to a given operation can only be judged by reference to the operating specifications.

+

Moreover, the realizable gain from at least the QST version of the antenna is considerably less than claims derived from theory (which rarely takes into account wire losses). What I hope to squeeze time for is a look at the dimensions derived more directly from Laport's work--perhaps something in the 100 MHz range (about 8 times longer than the 1296 MHz model). When I am semi-satisfied with models of that antenna, I shall add Part 2 to this report on modeling the dual rhomboid.

+
+ +
+

Updated 8-14-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: Will the Real Laport Please Stand Up

+

Return to Main Index

+

Topics: Rhombic, VHF / UHF


+ + diff --git a/content/vhf/rhh.html b/content/vhf/rhh.html new file mode 100644 index 0000000..7cd764e --- /dev/null +++ b/content/vhf/rhh.html @@ -0,0 +1,213 @@ + + + + + + Modeling the Dual Rhomboid Part 2: Will the Real Laport Please Stand Up + + + +
+

Modeling the Dual Rhomboid
+
+ Part 2: Will the Real Laport Please Stand Up

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The CATJ Models

In looking at the CATJ article referenced in Part 1 of these notes, I was initially struck by the fact that the author tried to show as exactly as possible the dimensions of a true Laport dual rhomboid. Modeling this antenna might provide a comparison with the 1296 MHz QST model examined in Part 1. +

Of course, some scaling would be necessary. The CATJ versions were cut for the television channels, with a 100 MHz model for reference (or for FM reception use). So we can expect in this part to find antennas over 12 times larger than the 1296 MHz model. Replacing inches with feet for the Part-1 model will give an idea of the size difference.

+
+ +
+

Fig. 6 repeats the sketch in Part 1, but without dimensions. Just why will become immediately apparent.

+

Sometimes a casual reading must give way to a close reading, and in the process, what seemed clear becomes a bit muddy. The CATJ article provides dimensions in two ways: approximations of the distances from the feedpoint to the supporting cross members and angles between the two short legs and between the two long legs. (There is a further ambiguity because the picture of the angles refers to angles A and B but references a table where the only angles given are called X and Y.) The result was two sets of dimensions. One was based on using the prescribed leg lengths plus sines and cosines of the angles given, which resulted in what I call the narrow model. The second version was based on the approximated cross member dimensions, which yielded what I call the wide model. We shall look at a third model before we are done.

+

The dimensions for the narrow and wide models are as follows, using #12 AWG copper wire and the prescribed 600-Ohm loads. Refer to Fig. 6 to place each dimension.

+ 
Narrow Model
+0-A  31'            A-A'   30.30'
+0-B  56'            B-B'   38.12'
+0-C  88.5'          C-C'   7.8'
+
+Wide Model
+0-A  31'            A-A'   31.50'
+0-B  56'            B-B'   39.35'
+0-C  88.5'          C-C'   7.8'
+

For model construction in each case, I used the method of creating right angles among wires at the feedpoint area as perhaps yielding a more trustworthy model than bringing the wires together at a very shallow angle. The following model description table illustrates the modeling technique.

+ 
Dual Rhomboid:  Laport-CATJ                  Frequency = 100  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W8E2  -0.100,  0.000,  0.000  W2E1  -0.100,  0.000,  0.100    # 12    1
+2   W1E2  -0.100,  0.000,  0.100  W3E1 -15.750, 31.000,  0.100    # 12   75
+3   W2E2 -15.750, 31.000,  0.100  W4E1   3.800, 88.500,  0.100    # 12  125
+4   W3E2   3.800, 88.500,  0.100  W5E1   4.000, 88.500,  0.100    # 12    3
+5   W4E2   4.000, 88.500,  0.100  W6E1  19.670, 56.000,  0.100    # 12   75
+6   W5E2  19.670, 56.000,  0.100  W7E1   0.100,  0.000,  0.100    # 12  125
+7   W6E2   0.100,  0.000,  0.100  W8E1   0.100,  0.000,  0.000    # 12    1
+8  W15E2   0.100,  0.000,  0.000  W9E1  -0.100,  0.000,  0.000    # 12    3
+9   W1E1  -0.100,  0.000,  0.000 W10E1  -0.100,  0.000, -0.100    # 12    1
+10  W9E2  -0.100,  0.000, -0.100 W11E1 -19.670, 56.000, -0.100    # 12  125
+11 W10E2 -19.670, 56.000, -0.100 W12E1  -4.000, 88.500, -0.100    # 12   75
+12 W11E2  -4.000, 88.500, -0.100 W13E1  -3.800, 88.500, -0.100    # 12    3
+13 W12E2  -3.800, 88.500, -0.100 W14E1  15.750, 31.000, -0.100    # 12  125
+14 W13E2  15.750, 31.000, -0.100 W15E1   0.100,  0.000, -0.100    # 12   75
+15 W14E2   0.100,  0.000, -0.100  W7E2   0.100,  0.000,  0.000    # 12    1
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           2     8 / 50.00   (  8 / 50.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           2     4 / 50.00   (  4 / 50.00)     600.000         0.000
+2           2    12 / 50.00   ( 12 / 50.00)     600.000         0.000
+
+Ground type is Free Space
+

Before looking at the results of modeling these 100 MHz models, let's review Fig. 7. This is a free space azimuth pattern for one of the best 1296 MHz models, using #12 wire and 300-Ohm terminating resistors to achieve maximum front-to-back ratio. Remember that #12 wire is about 12 times fatter at 1296 MHz relative to a wavelength than it will be at our new test frequency of 100 MHz.

+
+ +
+

At 100 MHz, with 600-Ohm terminating resistors, the basic numbers given by NEC-4 for the performance of the narrow and wide models are as follows:

+ 
Model     Gain      F-B       B/W       F/S       Feed Z
+          dBi       dB        deg       dB        R+/-jX
+Narrow    14.96     21.94     12.2      11.56     388 - 144
+Wide      15.26     24.11     11.8      11.36     364 - 148
+

The respective free-space azimuth patterns are shown in Fig. 8 and Fig. 9.

+
+ +
+
+ +
+

Both models show less gain than the 1296 MHz model, but considerably better front-to-back ratio with the prescribed 600-Ohm terminating resistors. The beamwidth at 100 MHz is wider by a small amount, and the front-to-side lobe ratio is better, also by a small amount. Perhaps the major fact that becomes evident, especially in the narrow model, is the reduction in the amount of power overall in the rearward lobes. Every lobe past 60 degrees from the main lobe is down by at least 20 dB and mostly more. One goal of the Laport dual rhomboid design is at least partially met in these models.

+

To see what effect wire size might have on performance, I ran the wide model using wire sizes from #12 through 0.5" in diameter. Throughout the exercise, the dimensions remained constant and the terminating resistors were a constant 600 Ohms.

+ 
Wire      Dia.      Gain      F-B       B/W       F/S       Feed Z
+Size      In.       dBi       dB        deg       dB        R+/-jX
+12        0.0808    15.26     24.11     11.8      11.36     364 - 148
+10        0.1019    15.29     25.39     11.8      11.29     345 - 147
+ 8        0.1285    15.31     26.81     11.8      11.21     327 - 145
+ 6        0.1620    15.33     28.27     11.8      11.13     309 - 144
+ 4        0.2043    15.34     29.69     11.6      11.04     292 - 143
+ 2        0.2576    15.35     31.07     11.6      10.95     275 - 141
+--        0.3       15.36     31.94     11.6      10.89     264 - 140
+--        0.4       15.40     33.49     11.6      10.76     242 - 136
+--        0.5       15.49     33.62     11.6      10.66     222 - 131
+

Obviously, the performance of the dual rhomboid benefits from the use of fatter wire, whether used as a single wire or as a simulated fat wire composed of separated parallel wires. The chart does not peak within the range of values checked (nor does a similar chart for the narrow model). As we saw with the 1296 MHz model, the front-to-side lobe ratio and the feedpoint impedance both decrease with increases in the front-to-back ratio and gain.

+

It may be the case that using a single wire size of #6 AWG may be the most practical compromise for a 100 MHz dual rhomboid. Wire of this size or larger might best be aluminum for weight saving. Therefore, I compared the performance figures for both #12 and 0.5" wire in copper and aluminum.

+ 
Wire      Wire      Gain      F-B       B/W       F/S       Feed Z
+Size      Type      dBi       dB        deg       dB        R+/-jX
+12        copper    15.26     24.11     11.8      11.36     364 - 148
+12        alum.     15.24     24.10     11.8      11.39     364 - 148
+
+0.5"      copper    15.49     33.62     11.6      10.66     222 - 131
+0.5"      alum.     15.49     33.59     11.6      10.68     222 - 131
+

Since the performance differences between copper and aluminum wire are non-existent at the limits of the chart, any wire size within the chart will give equivalent performance, whether copper or aluminum.

+

As I did with the 1296 MHz model, I checked the new models to determine whether different values of terminating resistors would yield better performance than the standard 600-Ohm values. As a quick reference, here are numbers for the wide models using #12 wire and using #6 wire (copper).

+ 
#12 Copper Wire
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       15.26     24.11     11.8      11.36     364 - 148
+650       15.26     27.13     11.8      11.34     356 - 146
+700       15.27     30.13     11.8      11.33     350 - 145
+750       15.27     31.06     11.8      11.30     344 - 143
+800       15.27     29.15     11.8      11.28     338 - 142
+
+#6 Copper Wire
+
+Res.      Gain      F-B       B/W       F/S       Feed Z
+Size      dBi       dB        deg       dB        R+/-jX
+600       15.33     28.27     11.8      11.13     309 - 144
+650       15.33     31.22     11.8      11.10     304 - 142
+700       15.34     31.05     11.8      11.09     299 - 141
+

The gain of this model (and likewise, the narrow model) rises very slowly (insignificantly so) as the value of the terminating resistors increases. However, the front-to-back ratio shows a peak that results from the interrelationship of the wire size and the terminating resistor values. The 650-Ohm value for #6 wire is close to the value recommended by Laport's original design. For reference, Fig. 10 shows the azimuth pattern for the #6 wire wide model with the optimal terminating resistor values.

+
+ +
+

The Scaled QST Model

There remains the question of what happens if one simply scales the 1296 MHz model to 100 MHz, while retaining the #12 wire. The dimensions will be somewhat different from those of either the narrow or wide models, with a shorter overall length and somewhat wider cross supports at all positions. The scaled dimensions are these: + 
Scaled QST Model
+0-A  29.7'          A-A'   32.94'
+0-B  54.0'          B-B'   45.90'
+0-C  83.16'         C-C'   11.0'
+

To translate the model to 100 MHz, certain modifications were necessary. Relative to pure scaling, the spacing between rhomboids had to be reduced (to 0.2') and the spacing between feedpoint area leg junctions also had to be reduced to manageable values (0.2'). For reference, here is the model description.

+ 
Dual Rhombic-QST 3-97, p89                 Frequency = 100  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W8E2  -0.100,  0.000,  0.000  W2E1  -0.100,  0.000,  0.100    # 12    2
+2   W1E2  -0.100,  0.000,  0.100  W3E1 -16.470, 29.700,  0.100    # 12   75
+3   W2E2 -16.470, 29.700,  0.100  W4E1   5.940, 83.160,  0.100    # 12  120
+4   W3E2   5.940, 83.160,  0.100  W5E1   7.020, 83.160,  0.100    # 12    3
+5   W4E2   7.020, 83.160,  0.100  W6E1  22.950, 54.000,  0.100    # 12   75
+6   W5E2  22.950, 54.000,  0.100  W7E1   0.100,  0.000,  0.100    # 12  120
+7   W6E2   0.100,  0.000,  0.100  W8E1   0.100,  0.000,  0.000    # 12    2
+8  W15E2   0.100,  0.000,  0.000  W9E1  -0.100,  0.000,  0.000    # 12    1
+9   W1E1  -0.100,  0.000,  0.000 W10E1  -0.100,  0.000, -0.100    # 12    2
+10  W9E2  -0.100,  0.000, -0.100 W11E1 -22.950, 54.000, -0.100    # 12  120
+11 W10E2 -22.950, 54.000, -0.100 W12E1  -7.020, 83.160, -0.100    # 12   75
+12 W11E2  -7.020, 83.160, -0.100 W13E1  -5.940, 83.160, -0.100    # 12    3
+13 W12E2  -5.940, 83.160, -0.100 W14E1  16.470, 29.700, -0.100    # 12  120
+14 W13E2  16.470, 29.700, -0.100 W15E1   0.100,  0.000, -0.100    # 12   75
+15 W14E2   0.100,  0.000, -0.100  W7E2   0.100,  0.000,  0.000    # 12    2
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     8 / 50.00   (  8 / 50.00)      1.000       0.000       I
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           2     4 / 50.00   (  4 / 50.00)     600.000         0.000
+2           2    12 / 50.00   ( 12 / 50.00)     600.000         0.000
+
+Ground type is Free Space
+

Here is a small chart comparing #12 models with 600-Ohm terminating resistors for all three models:

+ 
Model     Gain      F-B       B/W       F/S       Feed Z
+          dBi       dB        deg       dB        R+/-jX
+Narrow    14.96     21.94     12.2      11.56     388 - 144
+Wide      15.26     24.11     11.8      11.36     364 - 148
+Scaled    15.52     32.65     10.4      10.12     293 -  96
+
+ +
+

Fig. 11 presents the free-space azimuth pattern for the scaled QST model as adjusted. Note the slightly higher gain and front-to-back ratio, but the narrower beamwidth and lower front-to-side lobe ratio. Among the more subtle features to notice when comparing patterns is the first lobe off the main lobe. In the narrow and wide CATJ models, it is a low-level distinct lobe. In the scaled QST model, the first lobe is stronger and melds with the main lobe. Whether features like these make an operational difference in most ham circumstances is dubious. However, they are interesting theoretically when considering what Laport was trying to accomplish with his design.

+

If the side lobes are not especially troublesome, the scaled QST 1296 MHz model may be the more advantageous design, considering the gain, front-to-back ratio, and feedpoint impedance. However, if the power to the rearward lobes is of concern for a particular operation, the CATJ version may end up as more suitable.

+

A Note on Feedpoint Reactance

Virtually all of the models have shown a remnant capacitive reactance of proportions to disturb a match with 300-Ohm or similar line. Because of limitation in the models, it is not certain to what degree this reactance will appear in a real antenna. However, modeling uncovers a simple technique for changing the reactance. See Fig. 12. +
+ +
+

Where the wires of the legs join, the spacing between leg pairs can be widened or narrowed. Narrowing the spacing tends to push reactance further into the capacitive region. Widening the spacing pushed the reactance less capacitive and more toward inductive. Although the models may not predict the exact reactance value to be encountered with a dual rhomboid, the trends should be quite reliable in field adjusting the feedpoint reactance.

+

Conclusion

By judiciously using the figure that emerged from the 1296 MHz model and those that emerged with these 100-MHz models, it is possible to estimate the properties of scaled versions of the dual rhomboid for 144-, 225-, and 440-MHz versions of the antenna. The key item to remember is that the "standard" #12 wire becomes effectively fatter relative to a wavelength as the frequency increases. +

The dual rhomboid models produce consistent narrow beamwidth gains between 15 and 16 dBi in free space. At 100 MHz, the require length is 83-89 feet, with a 38 to 45 foot maximum width. What these numbers do not tell us is whether the antenna is worth building. So far we have produced no standards of comparison. For example, what would be the performance of a simpler single wire rhombic at 100 MHz? Does the dual rhombic have enough of a gain advantage to warrant the added construction difficulties? How large would a Yagi or equivalent gain be?

+

It may be useful to add one more part to this series to provide some basis for the individual to decide if the dual rhomboid is indeed the way to go.

+
+ +
+

Updated 8-16-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: Some Standards of Comparison

+

Return to Main Index

+

Topics: Rhombic, VHF / UHF


+ + diff --git a/content/vhf/rhhh.html b/content/vhf/rhhh.html new file mode 100644 index 0000000..1611ebb --- /dev/null +++ b/content/vhf/rhhh.html @@ -0,0 +1,215 @@ + + + + + + Modeling the Dual Rhomboid Part 3: Some Standards of Comparison + + + +
+

Modeling the Dual Rhomboid
+
+ Part 3: Some Standards of Comparison

+
+


+
+

L. B. Cebik, W4RNL

+
+
+ +
+

In thinking about building a dual rhomboid, we should carefully evaluate whether the results will be worth the effort involved. Despite its inexpensiveness at UHF, the dual rhomboid is not the simplest antenna to build.

+

Moreover, the dual rhomboid does not offer in modeled performance the gain theoretically claimed for it. Consistent gain figures between 15 and 16 dBi free space have emerged from the models. Even if we allow that the models have not caught the precise dimensions by which the side lobes come in for complete control, it is dubious that any constructed version of the antenna will achieve much more than 16 dBi free-space gain.

+

Therefore, it is reasonable to look at some other antennas in order to make some evaluative comparisons. In this note, I shall explore only two: the single-wire rhombic and a standard Yagi.

+

The Single-Wire Rhombic

The ARRL Antenna Book has carried an HF rhombic since time immemorial. It is possible to scale this antenna to 100 MHz and to use #12 wire in order to see by how much the dual rhomboid outperforms it. +
+ +
+

Fig. 13 provides the essential dimensions for the 100 MHz single-wire rhombic. At 79.3' long by 38.6' wide, the antenna occupies a footprint just a tad smaller than the dual rhomboids. The model description follows.

+ 
ARRL rhombic scaled to 100 MHz                  Frequency = 100  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W6E2  -1.200,  0.000, 14.469  W2E1   1.200,  0.000, 14.469    # 12    7
+2   W1E2   1.200,  0.000, 14.469  W3E1  19.291, 39.638, 14.469    # 12  100
+3   W2E2  19.291, 39.638, 14.469  W4E1   0.344, 79.275, 14.469    # 12  100
+4   W3E2   0.344, 79.275, 14.469  W5E1  -0.344, 79.275, 14.469    # 12    3
+5   W4E2  -0.344, 79.275, 14.469  W6E1 -19.291, 39.638, 14.469    # 12  100
+6   W5E2 -19.291, 39.638, 14.469  W1E1  -1.200,  0.000, 14.469    # 12  100
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           4     1 / 50.00   (  1 / 50.00)      0.707       0.000       V
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+1           2     4 / 50.00   (  4 / 50.00)     600.000         0.000
+
+Ground type is Free Space
+

The values in the Z columns are remnants of the source of this scaled model and can be replaced by zeroes for free space analysis. The wide spacing of the wires near the feedpoint represent an attempt to control some of the capacitive reactance at the feedpoint.

+

As I did for the CATJ dual rhomboid models, I ran the scaled single-wire rhombic through various wire sizes to develop a sense of the trends in performance. Note the reduction of the terminating resistor to 600 Ohms from the HF value of 800 Ohms. Here are the results.

+ 
Wire      Dia.      Gain      F-B       B/W       F/S       Feed Z
+Size      In.       dBi       dB        deg       dB        R+/-jX
+12        0.0808    13.85     45.30     11.4       8.50     625 -  96
+10        0.1019    13.93     34.76     11.4       8.53     606 - 105
+ 8        0.1285    14.01     29.84     11.4       8.56     585 - 114
+ 6        0.1620    14.09     26.68     11.4       8.59     563 - 122
+ 4        0.2043    14.16     24.40     11.4       8.61     540 - 130
+ 2        0.2576    14.24     22.57     11.4       8.65     516 - 137
+

Fig. 14 presents the free space azimuth pattern for the single-wire rhombic using #12 wire, where the terminating resistor has been optimized for maximum 180-degree front-to-back ratio. Obvious from the figure is the fact that a 180-degree front-to-back ratio reveals the rearward lobe behavior over only a very small portion of the rear quadrants. The number is impressive on paper only.

+
+ +
+

Optimizing the front-to-back ratio for wire sizes other that #12 AWG will require adjustment of the terminating resistor. Larger wire versions may be preferable to the #12 model in order to increase both the antenna gain and the front-to-side lobe ratio.

+

The front-to-side lobe ratio numbers can be misleading if one does not also account for the strength of the main lobe. In fact, the lower front-to-side lobe numbers for the single-wire rhombic--relative to the dual rhomboid models--only indicate lobes that have about the same intrinsic strength as those of the dual rhomboids. We can see this by overlaying patterns, as in Fig. 15.

+
+ +
+

The red and blue patterns in Fig. 15 clearly show the higher gain of the dual rhomboid. However, with respect to the other lobes in the pattern, only the positions and not the strengths change from one pattern to the next. With respect to the secondary lobes, there is not much to choose between a single-wire rhombic and a dual rhomboid. Of course, this must be qualified with the recognition that the models in this collection may not have caught the precise dimensions that yield maximum lobe control. However, we have looked at enough models to suggest that if there is such a "perfect" dimension set, it is unlikely to be replicated in the home workshop.

+

In terms of forward gain, the difference between the best 100 MHz #12 wire dual rhomboid and the #12 wire single rhombic is less than 1.7 dB.

+

A 16-Element Yagi

A second standard of comparison one might use in evaluating the dual rhomboid is a standard design Yagi of comparable gain. DL6WU designs have been around for a long time. They feature 50-Ohm feedpoint impedances and fairly broad-banded characteristics. One interesting facet of the DL6WU design is that one can cut off a longer design and still end up with good characteristics and a 50-Ohm feedpoint impedance. +

For this exercise, I cut off a 26 element DL6WU design at 16 elements and then scaled the result to 100 MHz to provide a comparator for the dual rhomboid. The antenna has the appearance of Fig. 16.

+
+ +
+

For reference, here is the model description.

+ 
DL6WU Original, 26 el 432 MHz             Frequency = 100  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1          0.000,  2.414,  0.000         0.000, -2.414,  0.000 6.80E-01  19
+2          1.967,  2.339,  0.000         1.967, -2.339,  0.000 6.80E-01  19
+3          2.704,  2.137,  0.000         2.704, -2.137,  0.000 6.80E-01  19
+4          4.476,  2.120,  0.000         4.476, -2.120,  0.000 6.80E-01  19
+5          6.591,  2.095,  0.000         6.591, -2.095,  0.000 6.80E-01  19
+6          9.048,  2.071,  0.000         9.048, -2.071,  0.000 6.80E-01  19
+7         11.803,  2.049,  0.000        11.803, -2.049,  0.000 6.80E-01  19
+8         14.753,  2.030,  0.000        14.753, -2.030,  0.000 6.80E-01  19
+9         17.851,  2.014,  0.000        17.851, -2.014,  0.000 6.80E-01  19
+10        21.098,  2.000,  0.000        21.098, -2.000,  0.000 6.80E-01  19
+11        24.491,  1.987,  0.000        24.491, -1.987,  0.000 6.80E-01  19
+12        28.032,  1.976,  0.000        28.032, -1.976,  0.000 6.80E-01  19
+13        31.720,  1.966,  0.000        31.720, -1.966,  0.000 6.80E-01  19
+14        35.556,  1.956,  0.000        35.556, -1.956,  0.000 6.80E-01  19
+15        39.491,  1.947,  0.000        39.491, -1.947,  0.000 6.80E-01  19
+16        43.425,  1.940,  0.000        43.425, -1.940,  0.000 6.80E-01  19
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          10     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+Ground type is Free Space
+

This model happens to be symmetrical in the X axis. The longest element is under 5' and the element diameter for the model is a little larger than 5/8". Note that the boom length is only about 43.5' long or about half the length of a dual rhomboid.

+
+ +
+

Fig. 17 presents the free space azimuth pattern for the 16-element Yagi. For comparative purposes, the modeled performance figures at 100 MHz are these.

+ 
Gain      F-B       B/W       F/S       Feed Z
+dBi       dB        deg.      dB        R+/-jX
+16.30     17.98     29        17.41     48 - j4
+

Although the front-to-back ratio of this particular model is under 20 dB, the overall power found in side lobes is much smaller than that in any of the rhomboid models. The front-to-side ratio is very good for rejection of QRM from those regions.

+

The beamwidth (29 degrees between -3 dB points) makes the antenna considerably easier to aim than any of the rhomboid models, whose beamwidths are only a third as wide. The Yagi's wider beamwidth can be either an advantage or a disadvantage, depending upon the operating requirements for the antenna.

+

The DL6WU antennas scale easily, so long as one remembers to scale the element diameter as well as the lengths and spacings. At 432 MHz, the element diameter for optimal performance is 4 mm.

+

Conclusion

I have not presented the single-wire rhombic or the DL6WU Yagi either to encourage or discourage construction of a dual rhomboid. That decision belongs to the individual user. However, making that decision requires reference to relevant comparators, and the ones we have examined here seem like good choices with which to start. +

A More Precise Laport Dual Rhombic

Although the models examined in these notes will likely provide highly satisfactory dual rhomboid antennas, I have remained unsatisfied with the presentation of numbers for the builder to use. The "narrow" version of the Laport in Part 2 used a combination of lengths calculated from angles and some of the "approximations." So I decided to see what we might obtain by calculating from ground zero. +

The basic information is this:

+ 
L1 = 3.5 wl = 34.425' at 100 MHz
+L2 = 6.0 wl = 59.014' at 100 MHz
+Angle A (for L1) = 26.1 degrees
+Angle B (for L2) = 18.85 degrees
+

Let us assume that Laport used true rhombi, with parallel sides. The result is a set of calculations, sketched in Fig. 18.

+
+ +
+

The figure shows only one of the two rhombi. The horizontal line will have coordinates 0,0 at the left.

+

Side a, from the through horizontal line upward to the end of L1 will equal sin A * L1 = 15.144'. Side b, from the through horizontal line downward to the end of L2 will equal sin B * L2 = 19.067'. If the sides are parallel, the distance c will equal side b - side a = 3.923'. Distance d from the origin to the end of L1 will equal cos A * L1 = 30.915'. Distance e from the origin to the end of L2 will equal cos B * L2 = 57.031'. Distance f from the origin to the far peak of the rhombus will equal d + e = 87.946'.

+

These numbers provide us with coordinates for both rhombi of the Laport antenna. They appear in the model description below.

+ 
Dual Rhomboid:  Laport-CATJ                 Frequency = 100  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn.--- End 2 (x,y,z : ft)  Dia(in) Segs
+
+1   W4E2   0.000,  0.000,  0.100  W2E1 -15.144, 30.915,  0.100    # 12  150
+2   W1E2 -15.144, 30.915,  0.100  W3E1   3.923, 87.946,  0.100    # 12  257
+3   W2E2   3.923, 87.946,  0.100  W4E1  19.067, 57.031,  0.100    # 12  150
+4   W3E2  19.067, 57.031,  0.100  W1E1   0.000,  0.000,  0.100    # 12  257
+5   W8E2   0.000,  0.000, -0.100  W6E1 -19.067, 57.031, -0.100    # 12  257
+6   W5E2 -19.067, 57.031, -0.100  W7E1  -3.923, 87.946, -0.100    # 12  150
+7   W6E2  -3.923, 87.946, -0.100  W8E1  15.144, 30.915, -0.100    # 12  257
+8   W7E2  15.144, 30.915, -0.100  W5E1   0.000,  0.000, -0.100    # 12  150
+
+            -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1     1 /  0.00   (  1 /  0.00)      1.000       0.000      SV
+2           1     5 /  0.00   (  5 /  0.00)      1.000       0.000      SV
+
+              --------------- LOADS ---------------
+
+Load      Wire      Wire #/Pct From End 1      R (Ohms)       X(Ohms)
+          Seg.     Actual      (Specified)
+
+1         257     2 / 99.81   (  2 /100.00)     300.000         0.000
+2           1     3 /  0.33   (  3 /  0.00)     300.000         0.000
+3         150     6 / 99.67   (  6 /100.00)     300.000         0.000
+4           1     7 /  0.19   (  7 /  0.00)     300.000         0.000
+
+Ground type is Free Space
+

You may notice several alterations in this model relative to those used in preceding parts of these notes. First, two independent rhombi are used, each with its own feed and load. This move preserves the geometry of the rhombi. Second, to avoid flat wires at either end of the rhombi, split loads are used for the terminating resistors and split feed is used for each rhombus. This technique involves a compromise and a modeler's judgment of priorities. In this case, preservation of wire geometry was given priority over exact equalization of segment lengths for each fed and load segment. The model employs a high number of segments (1648), but may still not be perfectly converged. The segment lengths are equal to two decimal places, but very slight differences in segment length for split loads and feeds can prevent convergence until a very high number of segments is used in a model.

+

Despite these potential shortfalls of perfection, certain trends make the results close to precise. First, for all stages of convergence testing from about 800 segments upward, the same terminating resistor values produced maximum front-to-back ratio in each model tested with different wire sizes. Gain, beamwidth, and front-to-side lobe ratio remained very close during the tests, although the higher the number of segments, the better the reported front-to-back ratio. Only the feedpoint impedance remained somewhat variable.

+

The following results were obtained for #12 and #6 copper wire. In the table, the given value of terminating resistor--chosen for the best front- to-back ratio--represents a series combination of two load resistors in the model description. The feedpoint impedance given is the composite parallel impedance for the two sources connected in parallel. The rhombi are vertically separated 0.2' (2.4").

+ 
Wire  Dia.     Res.      Gain      F-B       B/W       F/S       Feed Z
+Size  In.      Ohms      dBi       dB        deg       dB        R+/-jX
+12   .0808     600       15.01     23.38     12.4      12.10     398 - 122
+ 6   .1620     550       15.08     23.48     12.4      11.94     348 - 130
+

The most interesting facet of the exercise in trying to make the Laport antenna model more precise does not appear in the tabulated numbers. Rather, it appears in the azimuth pattern of Fig. 19.

+
+ +
+

The Laport antenna does indeed have potential for controlling the side lobes of the rhombic configuration. Only 3 forward side lobes rise much above -20 dB relative to the main lobe, and they are down by more than 12 dB. The reduction in rearward lobes is significantly improved relative to any of the preceding models used in these notes. Whether or not this model has succeeded in capturing the Laport dual rhombic in exact precision, it is clear that Laport was on the right track in his efforts to reduce side lobes from rhombic antennas. Perhaps the only thing not yielded by the design is the absolute maximum in gain.

+

Spacing between the two rhombi does make a difference in performance characteristics, including the feedpoint impedance, which rises as the wires are brought closer together. If the spacing is increased, we obtain a lower source impedance, higher gain, high front-to-side lobe ratio, and--up to a peak value--higher front-to-back ratio. I ran a small table of ever-increasing spacing using the #12 wire, 600-Ohgm terminating resistor model, and I obtained the following results.

+ 
Space  Space     Gain      F-B       B/W       F/S       Feed Z
+Feet   WL        dBi       dB        deg       dB        R+/-jX
+0.2    0.020     15.01     23.38     12.4      12.10     398 - 122
+0.4    0.041     15.05     29.04     12.4      12.18     342 - 105
+0.6    0.061     15.07     34.27     12.4      12.23     316 -  88
+0.8    0.081     15.08     35.21     12.4      12.26     303 -  77
+1.0    0.102     15.10     33.13     12.4      12.30     295 -  68
+1.2    0.122     15.11     31.45     12.4      12.32     290 -  62
+

The gain rises continuously with increasing space, although the peak cannot be far off the chart. The front-to-back ratio increases until the spacing reaches 0.8' (0.081 wl). There is no sign where the increase in front-to-side lobe ratio may peak. Given the reported impedance figures, a spacing in the region of 0.081 wl may be most optimal for a balance of operating characteristics. Why increased spacing tends to improve performance appears to be a function of the fact that the wires of the two rhombi cross at less than right angles. THus, there is significant coupling between them. For any given geometry for the individual rhombi, there is likely a spacing that optimizes the operating characteristics. Fig 20 provides an azimuth pattern of one of the most fully optimized Laport dual rhombic antennas obtained in this series of experiments. Even so, note the fact that, relative to the rear lobes in Fig. 19, some of the rear lobes in this pattern are beginning once more to grow.

+
+ +
+

The Laport design deserves further study, with special reference to the designer's original papers. These notes have gone only so far as the available information will permit. Hopefully, they have indicated some useful directions for additional effort.

+
+ +
+

Updated 8-17-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Main Index

+

Topics: Rhombic, VHF / UHF


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Some Overlooked Antenna Basics for DX and Off-World Communications

+ hr +

Some Overlooked Antenna Basics for DX and Off-World Communications

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: Satellite, VHF / UHF


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+

The Quad Beam as an Amateur Satellite Antenna

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

US amateur satellite operators use a variety of antennas for frequencies just below 146 MHz and in the 435.6-MHz area. Most often, if the operator desires a circularly polarized signal, he uses crossed quadrature-fed Yagis. The 3:1 frequency ratio of the two satellite sub-bands tends to create difficulties in constructing interlaced crossed Yagis. Therefore, most serious satellite operators use widely separated antenna booms. The mechanical issues associated with such a structure, especially when controlled by an elaborate AZ-EL rotator control system, are well known.

+

An alternative to the crossed Yagi is the quadrature-fed quad beam. The technique of feeding a quad loop to obtain circular polarization is quite simple and long known. A version of a quadrature-fed quad loop appears in the sample models in the MININEC program AO by K6STI. One simply feeds signals 90 degrees out of phase but of equal current magnitude to points on the quad loop that are also 90 degrees apart. These can be adjacent corners or adjacent side-centers.

+

In the following design notes, we shall look at some of the issues involved in both the electrical design and the physical implementation of concentric quads for 146 MHz and for 435.6 MHz. If we can arrange the quads concentrically, we may mount both on a single boom and relieve the greater part of the mechanical issues associated with the use of crossed Yagis.

+

A Dual-Band Quadrature-Fed Satellite Quad Beam

+

The design goals of the effort are the following.

+
    +
  • 1. A minimum of 10 dBi forward gain on each band with a reasonably well-shaped pattern.
    • +
  • 2. Reversible circular polarization.
    • +
  • 3. 50-60° -3-dB beamwidth with under 1° variation for ease and reliability of aiming.
    • +
  • 4. Minimal structure using a single boom and common materials, commensurate with performance goals.
    • +
  • 5. Simple quadrature feed for each quad, with a 50-Ohm main feedline impedance.
    • +
+

A square quad loop drivers may be fed at the center of adjacent sides or at proximate corners with a 90° current phase shift to achieve circular polarization. Parasitic elements do not require separate treatment for each component of the polarization. The result is remarkably even current magnitudes along the quad loops, with considerable latitude for physical or frequency inexactness before the resulting pattern takes on enough distortion to be unusable. The limiting factor in combining satellite arrays for 146 and 435.6 MHz is the almost precise 3:1 frequency ratio between the two satellite allocations. A wavelength at 146 MHz is about 80.84", while a wavelength at 435.6 MHz is 27.10". Combined Yagis often interact in uncontrollable ways. However, it is possible to control the interactions between concentric quads to minimize unwanted interactions. The keys to successful 435.6-MHz operation are relative element placement and compensation for gain lost by remnant interactions with the 146-MHz elements.

+
+ +
+

Fig. 1 shows the general outline of the dual quad array with each band active. The graphic identifies each element. On the left, the 146-MHz driver is active, with the feedpoint to the far left and a phase line providing a 90° current phase lead to the next clockwise corner--yielding right polarization. Moving the feedpoint to the lower corner reverses the polarization to left-hand polarization. On the right, the 435.6-MHz driver is active, and the same polarization rules and reversal potentials apply.

+

The 146-MHz Driver and the 435.6-MHz Reflector are in the same plane, requiring a single support structure for both elements. Likewise, the 146-MHz director 1 and 435.6-MHz Director are also in the same plane, and require a single support system. Table 1 provides the specific dimensions for each element within the dual array.

+ 
   Dimensions of the 146/435.6-MHz Dual Quad Satellite Array--Quadrature-Fed
+Frequency   Element     Side Length Hypotenuse  Circumference  Distance from
+  MHz                   in Inches   in Inches   in Inches      146-MHz Reflector
+146 MHz     Reflector   21.91       30.98       87.63          -----
+            Driver      20.78       29.38       83.10          19.40*
+            Dir. 1      19.48       27.54       77.93          44.06**
+            Dir. 2      19.16       27.09       76.64          73.57
+435.6 MHz   Reflector    7.343      10.383      29.372         19.40*
+            Driver       7.020       9.926      28.082         25.91
+            Dir. 1       6.530       9.233      26.120         34.03
+            Dir. 2       6.422       9.081      25.687         44.06**
+            Dir. 3       6.422       9.081      25.687         56.06
+
+Table 1.  Dimensions of the 146/435.6-MHz dual quad array when quadrature fed.
+The 146-MHz elements use AWG #14 copper wire (0.0641" diameter); the 435.6-MHz
+elements use AWG #22 copper wire (0.0253" diameter).  * and ** indicate elements
+that share a single support structure.
+

Quad Positioning: As Fig. 1 and Table 1 clearly indicate, the 435.6-MHz quad begins with its reflector even with the driven element of the 144-MHz array. The positioning does permit two elements on each quad to share support structures, thus simplifying the mechanical design. However, the chief reason for the positioning arises from the design goal of minimizing interactions between the two quads. The quads are positioned relative to each other so that the 435.6-MHz quad activates as little as possible the elements of the 2-meter array surrounding it.

+

When elements of a multi-band array bear a harmonic relationship to each other, activating a higher frequency driver can also activate one or more lower frequency elements. When the elements have a 2:1 frequency relationship, as is often the case for 20-10-meter Yagi arrays, a 20 meter element may dominate. The 20-meter element often pushes the 10-meter passband downward in frequency. When the relationship is 3:1, as it is with a 146-432-MHz array, the dominating lower frequency element often breaks the desired single-lobe pattern into multiple lobes.

+

The cure is to use "control" elements. In linear-element arrays, such as Yagis, the control element for the higher frequency is located behind or toward the driver and closely spaced to the lower frequency elements--sometimes as close as 6-12 inches in HF arrays. With quads, the controlling element may be placed in line with the lower-frequency element, as is the case with the 435.6-MHz second director and the 146-MHz first director. In either case, we need a further director forward of the control element to restore array gain. Hence, the 435.6- MHz quad has one more element than the 146-MHz quad.

+

Quadrature Feed: The two concentric quad beams employ quadrature feed to achieve circular polarization. The simplest form of quadrature feed is a 1/4 wavelength feedline having a characteristic impedance (Zo) that equals the natural resonant impedance of the driver. Both quads are designed for a natural impedance of about 95-100 Ohms. Quadrature-feed results in a net feedpoint impedance that is half the impedance of the individual feedpoints, and the result is a good match for a 50-Ohm main feedline.

+

For 146-MHz, RG-62, with a 93-Ohm Zo, is a satisfactory material for the phasing line. Since the cable has a velocity factor (VF) far less than 1.0, a 1/4 wavelength line will not reach from one corner of the array to the next. As well, a direct line would likely interact with the driver wire length between the two points. Hence, the best line is likely 3/4 wavelengths electrically and routed toward and around the boom at the center of the quads. Separating the two drivers, as in the present design, minimizes interaction between the 146-MHz and the 435.6-MHz phase lines.

+

If we use a length of coax cable for the phasing line, we can achieve a reversible circular polarization simply by installing Tee connectors at the phase-line connection corners. Connecting the main feedline to one corner produces a signal circularly polarized left, while connecting the feedline to the other corner produces a right-hand circular polarization.

+

Common coax cables are 1/4" or more in diameter. Although this diameter is usable at 146 MHz, it creates problematical bulky connections at 435.6 MHz, especially with the use of #22 wire for the element. More applicable to the higher frequency is the use of a glass board as the driver support and as a field for etched phase lines. A well-balanced 100-Ohm line can be etched on the board using both sides. Since the impedance of the line requires that we divide the usual parallel line constant by the dielectric constant of the material between the lines, fabrication of such a line requires knowledge of the board material properties. As well, the board may well create a velocity factor less than 1.0, and we would need to experiment to discover the VF of the material used. The VF might also be affected by the material used to weather protect the phase-line traces on the board.

+

However, a glass board would also permit 2 other conveniences. First, one might construct the driver from etched copper paths on the board perimeter, creating an integrated driver loop and phase line. Second, we might also create a 50-Ohm line down to the boom and connect the main feedline at this structurally sounder position. However, this latter step requires that we know in advance that we would require only one of the two possible circular polarizations. Otherwise, we may use PC-board-mounted feedline connectors at the two relevant corners.

+

We may cut out portions of the board not required for structural or electrical duties to increase the wind-slippage of the board. Finally, we may also adapt these same techniques to the 2-meter driver, although the larger glass board, even with cut-outs--will undoubtedly add significant weight to the array. The added weight need not be a disadvantage, since it may help stabilize an array whose main support lies behind the 2-meter reflector. The parasitic elements require no special treatment to create a directional array when we quadrature-feed the driver.

+

Performance: The array achieves at least 10 dBi forward gain on each of the two bands within the segments used for satellite service. For most satellite operations, this is excess gain relative to minimums required. However, the excess is useful in situations that call for the use of a signal splitter-combiner to allow for a single feedline to the main equipment.

+
+ +
+

Fig. 2 shows the free-space pattern of the 146-MHz array taken at 4 cross-section angles. The modeling technique used here was to create the geometry along the Z-axis, so that all 4 patterns are "elevation" patterns taken at different azimuth angles, giving us a cross-section of the array pattern every 45 degrees. The cross section labeled 0 degrees gives us a pattern running through the main feedpoint to the opposite corner. The cross section labeled 90 degrees runs through the quadrature-fed point through its opposite corner.

+

There are slight asymmetries to the pattern, but they occur in the region of side and rear lobes. The half-power points are not more than 2 degrees off of perfect symmetry.

+
+ +
+

In Fig. 3, we have the corresponding free-space patterns of the array at 435.6 MHz. The side lobes are more evident in the planes running from corner to corner than they are in the planes running through the centers of the sides of the loop structure.

+
+ +
+

Perhaps more significant than the free-space patterns are the patterns over ordinary ground. The array was set 80" above ground at its lowest point. This distance is about 1 wavelength at 146 MHz and about 3 wavelengths at 435.6 MHz. Fig. 4 shows the patterns at 2 meters. The lowest side lobe is inevitable due to ground reflections at the 1 wavelength height.

+
+ +
+

When we examine the 435.6-MHz patterns in Fig. 5, we see the more complex lower lobe structure that goes along with the increase in height. The stronger free-space side lobes at 0 and 90 degrees yield stronger low angle lobes for the array.

+

Nonetheless, the arrays maintain good gain, relatively good forward lobe structure, and a good beamwidth. The gain of an array pointed straight upward is normally the sum of the forward gain and the rearward gain, minus any ground losses. Hence, the 2-meter array shows a gain of about 10.4 dBi, while the 435.6-MHz quad yields nearly 10.8 dBi gain. The -3-dB beamwidth is about 57 degrees at 146 MHz and 54 degrees at 435.6 MHz. In both cases, we achieve a good match between the quads--one of the goals of the exercise.

+

A Dual-Band Single-Feed Satellite Quad Beam

+

Some satellite operators prefer the simplicity of a linear or single feedpoint, preferring to use gain as a substitute for the advantages of circular polarization. Since the array gains exceed minimums needed for satisfactory satellite operation, I redesigned them for single feed to each band driver. One technique of doing this, especially apt if the drivers use glass-board supports, would be to use the array as is and to construct a tapering Zo line from the fed corner to the boom, at which point we might connect the main feedline.

+

The alternative is to redesign the individual quads to achieve a 50-Ohm feed impedance. This redesign requires that we close up the spacing between the driver and the reflector and re-size each loops to restore performance. Table 2 shows the dimensions that resulted from the redesign work.

+ 
    Dimensions of the 146/435.6-MHz Dual Quad Satellite Array--Single-Feed
+Frequency   Element     Side Length Hypotenuse  Circumference  Distance from
+  MHz                   in Inches   in Inches   in Inches      146-MHz Reflector
+146 MHz     Reflector   21.50       30.41       86.00          -----
+            Driver      20.70       29.27       82.80          13.18
+            Dir. 1      19.48       27.54       77.93          37.84
+            Dir. 2      19.16       27.09       76.64          67.35
+435.6 MHz   Reflector    7.240      10.240      28.960         23.98
+            Driver       6.940       9.810      27.760         27.69
+            Dir. 1       6.530       9.233      26.120         35.81
+            Dir. 2       6.422       9.081      25.687         45.84
+            Dir. 3       6.422       9.081      25.687         57.84
+
+Table 2.  Dimensions of the 146/435.6-MHz dual quad array using a single
+feedpoint per band.  The 146-MHz elements use AWG #14 copper wire (0.0641"
+diameter); the 435.6-MHz elements use AWG #22 copper wire (0.0253" diameter).
+

Quad Positioning: The redesign eliminated the possibility of aligning the 435.6-MHz reflector with the 146-MHz driver. (Remember that each quad is now fed at only one corner position.) In fact, the entire 435.6-MHz array required repositioning to restore its operation. See Fig. 6.

+
+ +
+

The higher-frequency quad is moved forward within the 2-meter quad. The first director serves as a control element that lies slightly behind the 2-meter first director. However, both quads retain their 10+ dBi free-space gain values. As well, both quads show a near-resonant feedpoint impedance of 53-55 Ohms.

+

Performance: The relatively small variations in pattern shape that we saw as we took various cross sections of the quadrature-fed version of the array turn into much more significant variations using a single feedpoint for each band. In the following figures, 0 degrees represents a free-space H-plane pattern for the array, and 90 degrees gives us the E-plane pattern.

+
+ +
+

Fig. 7 provides us with the free-space patterns at 146 MHz. The E-plane and H-plane pattern differences are readily apparent. The tiny side lobe in the E-plane becomes a much larger lobe in the H-plane, a phenomenon perfectly normal for both Yagis and quads using linear feed.

+
+ +
+

The patterns at 435.6 MHz, Fig. 8, show much more radical differences between the E-plane and the H-plane patterns. The energy in the H-plane side lobes becomes energy in the E-plane rear lobes. The 45-degree and 135-degree patterns show how this energy is averaged at these intermediate positions.

+
+ +
+

At 146 MHz, the array patterns are well-behaved when the base of the array is 80" above ground, as shown in Fig. 9. The E-plane smaller side lobes result in an absence of low-angle radiation, although the lowest lobe grows as we move to angle closer to the H-plane. The forward gain at 146 MHz is about 10.4 dBi when we set the array about 1 wavelength above ground, pointed straight up.

+
+ +
+

The single-feed version of the array shows much less "good behavior" with its base 80" above ground, as revealed by Fig. 10. The beamwidth varies considerably as we change angles from the H-plane to the E-plane. As well, the forward lobe shows some influence from the 2-meter elements in the development of irregularities in the shape. The lower free-space front-to-back ratio results in a higher forward gain vertically, about 11.3 dBi, up from the 10.7 dBi free-space figure.

+

Ultimately, then, the single-feed version of the two-band array would provide satisfactory performance for those who use linearly polarized feed system--within the limits imposed by not using circular polarization. The individual quads provide a good match to a 50-Ohm feedline, and the single-feed version retains the one-boom structural advantage offered by quads in this service.

+

The Two Arrays at an Angle

+

The use of a vertical orientation for the arrays in assessing their performance provides usable expectations for the two versions of the quad beams for most high angle uses. However, satellites have the disturbing habit of changing their elevation angles continuously as they make their orbital passes. Therefore, a fuller assessment requires that we do something to take this into account.

+

To make the assessment, I used NEC-Win Plus' geometry rotation feature to tilt the models 45 degrees. (This procedure involved saving the EZNEC Pro/4 models as .NEC files, processing then in NEC-Win Plus as .NWP files, and then resaving them as .NEC files for re-importation into EZNEC to produce pattern graphics that coincided with the original vertical models. The process is almost as fast to perform as it is to describe.)

+

The arrays for this exercise have one loop side parallel to the ground. Therefore, the feedpoint(s) are at the corner, corresponding to the 45-degree and 135-degree patterns in earlier figures.

+

Quadrature Feed: At an elevation angle of 45 degrees, the quadrature-fed version of the array shows the patterns given in Fig. 11.

+
+ +
+

At 146 MHz, the gain is about 10.7 dBi, not much different from the value with the antenna vertically oriented. The gain continues to increase as the elevation angle decreases until the ground reflections play a full role in the pattern formation. The horizontal beamwidth grows to about 88 degrees between -3 dB points. The vertical beamwidth is about 60 degrees. However, note that the point of maximum gain is about 2 degrees higher than the aiming point for the array, a function of ground reflections.

+

At 435.6 MHz, the gain is about 10.3 dBi. However, maximum gain occurs in two lobes evident on the elevation plot, one at about 41 degrees, the other at about 52 degrees. At these angles, the forward gain exceeds 11 dBi. The vertical beamwidth is about 52 degrees.

+

Single Feed:

+
+ +
+

Fig. 12 shows the corresponding patterns for the single-feed version of the 2-band quad array. Except for rear lobe performance, the performance is strikingly similar. At 146 MHz, the gain is 10.8 dBi with an 85-degree beamwidth horizontally. The peak gain occurs at about 3 degrees higher than the aiming point, with a 63-degree vertical beamwidth.

+

At 435.6 MHz, the 45-degree-angle gain is about 10.3 dBi, but climbs to about 11.1 dBi at 40 and 51 degrees. The horizontal beamwidth is 78 degrees, and the vertical beamwidth is about 53 degrees.

+

In terms of the shape of the total radiation pattern, then, there seems to be little to choose between the quadrature-fed and the single-feed versions of the array. However, although the pattern figures are useful, they do not tell the complete story. One has to examine the model radiation tables to read out the polarization of the two different array types. To the degree that circular polarization offers a higher potential for reduced signal fading during a satellite pass (and an equal fading of one's transmitted signal), the quadrature-fed array has some distinct advantages. Whether or not they justify the more complex construction related to such feed systems is a decision that only the builder can make.

+

Conclusion

+

We have examined the possibility of reducing the common dual-boom structures used by crossed Yagis into a single boom by the use of concentric quads. Careful design can overcome most of the interaction problems created by the 3:1 frequency ratio between 146 MHz and 435.6 MHz quads. Hence, it is possible to design a potentially successful single boom quad for satellite use that also has greater gain reserves than the 2-3 element quads currently available for this service.

+

The problems inherent in successfully implementing a simple quadrature feed may also be overcome through careful fabrication of glass board etched lines. The final quadrature-fed array is capable of reversed circular polarization. Of course, one may opt for the simple single-feed version.

+

These design notes only scratch the surface of possibilities. However, I hope they have stirred your creative juices so that any implementation will be even more successful than the these ideas presently promise.

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+ +
+

Updated 07-01-2004. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for June, 2004. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Quad, Reversible, Satellite, VHF / UHF


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+

Scaling and Adjusting VHF/UHF Yagis

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+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

A recurring question that I receive on an average of once per week involves one or more aspects of adjusting Yagi designs for the prospective builder's building and operating situation. Therefore, it seems useful to review the entire spectrum of what is involved in adapting a given Yagi design for one's own purposes.

+

There are three fundamental aspects to the adjustment process:

+
    +
  • 1. Design frequency scaling
    • +
  • 2. Adjustments for changes in element diameter
    • +
  • 3. Adjustments for the method of element mounting
    • +
+

Failure to attend to any one or more of these aspects of personalizing a Yagi design can lead to arrays that simply fail to perform to expectations.

+

Frequency Scaling

+

The first aspect of re-design is frequency scaling. The scaling may be from one band to another or within a given band of operation. Let's begin with a 10-element Yagi designed initially for 222 MHz. Fig. 1 shows the general outline of the array.

+
+ +
+

The wide-band design would have a model description close to the following one.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      EZNEC/4 ver. 3.0
+
+10-el OWA Yagi 222 MHz                       6/20/02     6:38:09 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 222 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                -13.449,      0,      0            13.4491,      0,      0     0.125   21
+2                -12.989,5.78212,      0            12.9887,5.78212,      0     0.125   21
+3                -12.167,8.85899,      0             12.167,8.85899,      0     0.125   21
+4                -11.946,16.6905,      0            11.9457,16.6905,      0     0.125   21
+5                -11.969,26.7813,      0            11.9686,26.7813,      0     0.125   21
+6                -11.907,40.3681,      0            11.9075,40.3681,      0     0.125   21
+7                -11.575,56.8802,      0            11.5748,56.8802,      0     0.125   21
+8                -11.279,76.2883,      0            11.2788,76.2883,      0     0.125   21
+9                -11.049,96.4126,      0            11.0486,96.4126,      0     0.125   21
+10               -10.128,114.432,      0            10.1279,114.432,      0     0.125   21
+
+Total Segments: 210
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       2        50.00      50.00    11       1           0         V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

We can illustrate the performance of the Yagi by a pair of graphs. Fig. 2 shows the gain and front-to-back performance. The 180-degree front-back performance is labeled front-to-back ratio, while the worst-case front-to-back performance is labeled front-to-sidelobe ratio. Since there are no forward sidelobes, the front-to-sidelobe ratio effectively represents the worst-case front-to-back ratio. Had there been forward sidelobes, this curve would not have been reliable. To hide matters a bit more, the shape of the rear lobes of the array is such that the 180-degree and the worst-case ratios are the same, and the two curves coincide.

+
+ +
+

Fig. 3 shows the feedpoint performance of the array, with values for resistance, reactance, and 50-Ohm SWR. Note that both the resistance and reactance values are very constant, showing only a slight decrease at the upper end of the passband. These two decreases coincide to the rapid rise of the SWR value to nearly 1.15:1.

+
+ +
+

The importance of these performance graphs is that they will serve as a base-line with which to compare our adjustments as we move the design to a new frequency. Since the OWA design has such a wide-band set of characteristics, we should not consider altering the design for a new frequency in the current band. Instead, let's move it to 2 meters. The wide-band characteristics suggest that we might easily select 146 MHz as the new design frequency.

+

To scale the array to any new frequency, we can apply a simple equation:

+
+ +
+

where Fo is the old frequency, Fn is the new one, and the lambda values are those corresponding to the frequencies. The key to using this equation is to apply it to every dimension (Dim): element length, element spacing, and element diameter. Omitting any one of these dimensions of the array will result in a faulty scaling job.

+

The task is not difficult for a pocket calculator. Some modeling software--such as EZNEC--has an automated scaling feature. Other software, such as NEC-Win Plus--can be set up to provide automated scaling--once dimensions are input in terms of fractions of a wavelength. However we execute the equation, the following type of antenna model description should result.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      EZNEC/4 ver. 3.0
+
+10-el OWA Yagi 146 MHz scale 1               6/20/02     6:38:42 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 146 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                 -20.45,      0,      0              20.45,      0,      0   .190068   21
+2                 -19.75,8.79199,      0              19.75,8.79199,      0   .190068   21
+3                -18.501,13.4705,      0            18.5005,13.4705,      0   .190068   21
+4                -18.164,25.3786,      0            18.1639,25.3786,      0   .190068   21
+5                -18.199,40.7223,      0            18.1988,40.7223,      0   .190068   21
+6                -18.106,61.3816,      0            18.1059,61.3816,      0   .190068   21
+7                  -17.6, 86.489,      0               17.6, 86.489,      0   .190068   21
+8                 -17.15,    116,      0              17.15,    116,      0   .190068   21
+9                  -16.8,  146.6,      0               16.8,  146.6,      0   .190068   21
+10                 -15.4,    174,      0               15.4,    174,      0   .190068   21
+
+Total Segments: 210
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       2        50.00      50.00    11       1           0         V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

To verify our work, let's briefly scan the graphs that results from a frequency scan of the model across 2 meters.

+
+ +
+

Because the 4 MHz of 2-meters is somewhat wider than the 5 MHz span we used earlier in the 222-MHz region, the lower band edge gain of the 2-meter version of the Yagi is a bit lower, as shown in Fig. 4. The peak gain is a bit higher, due to less skin-effect loss at the new lower frequency for the aluminum elements. Nevertheless, the forward gain varies by only 0.2 dB across the band, too small an amount to bother with resetting the frequency of peak gain. Likewise, the front-to-back ratio (180-degree and worst-case) both vary by under 1 dB across the band.

+
+ +
+

As Fig. 5 shows, the low-end 50-Ohm SWR approaches 1.18:1. More important, we once more see the level values of resistance and reactance, with slight dips only at the upper end of the band, where the SWR also begins to rise rapidly.

+

The end result of our work is that the newly scaled design will exactly replicate the performance at its original frequency. However, let's note one minor inconvenience: the required new element diameter is 0.19". Unfortunately, this value is not commonly available. (Since we are setting up an example, we shall blithely ignore the fact that 3/16" (0.1875") aluminum rod is obtainable with relative ease from mail-order sources.)

+

Adjusting for Changes in Element Diameter

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Let's suppose that we wish to build the antenna from 0.25" diameter stock (tubing or rod). Perhaps the most common question that I receive is whether one can simply use the same dimensions with the new diameter or whether each element should be shaved a bit to account for the fatter element. The amount of increase--0.06"--seems almost harmless.

+

Let's see how harmless the increase is by simply changing the element diameter in the recent model description to the 0.25" figure. Otherwise, everything else in the model remains the same. Here is what we get.

+
+ +
+

Fig. 6 shows the gain and front-to-back curves. Note that both curves rapidly fall off at the upper end of the band. The gain variation is now well over 0.5 dB, and the front-to-back variation is about 2.5 dB. These values might satisfy some uses, but they are clearly well off from the original curves.

+
+ +
+

Likewise in Fig. 7, the feedpoint data also shows greater degradation in the upper part of the band. The reactance and resistance both decrease sufficiently to yield a 50-Ohm SWR greater than 1.7:1 at 148 MHz. Clearly, we need to make some adjustments in the element lengths.

+

The typical casual procedure is to shave the element lengths by roughly equal percentages, and then to further shave the driver to center the SWR curve. However, Chapter 7 of the RSGB volume The VHF/UHF DX Book (edited by Ian White, G3SEK, with the antenna chapter written by Guenter Hoch, DL6WU) presents a more precise way of handling the recalculation of element lengths for the new element diameter.

+

We first calculate the element reactance according to an equation derived from the work of Schelkunoff:

+
+ +
+

where X is the element reactance, lambda is the wavelength of the design frequency, D is the original diameter, and L is the original length. We then use this reactance, together with the new element diameter, to arrive at the new element length with this revised ordering of the equation.

+
+ +
+

The terms have the same meaning as in equation 2, but they represent the new values. A version of this equation set is part of the most recent HAMCALC offering from VE3ERP. Hence, the use of a hand calculator--with all of the opportunities for messing up the result with a single missed keystroke--is no longer necessary.

+

If we convert all of the element lengths using these equations, then we come up with the following model description for our 0.25" element diameter version of the 2-meter scaling of our original 222-MHz Yagi.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                      EZNEC/4 ver. 3.0
+
+10-el OWA Yagi 146 MHz .25adj                6/20/02     6:39:53 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 146 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1                -20.464,      0,      0             20.464,      0,      0      0.25   21
+2                -19.723,8.79199,      0            19.7235,8.79199,      0      0.25   21
+3                -18.403,13.4705,      0            18.4025,13.4705,      0      0.25   21
+4                -18.046,25.3786,      0             18.046,25.3786,      0      0.25   21
+5                -18.083,40.7223,      0             18.083,40.7223,      0      0.25   21
+6                -17.985,61.3816,      0             17.985,61.3816,      0      0.25   21
+7                -17.449, 86.489,      0            17.4495, 86.489,      0      0.25   21
+8                -16.974,    116,      0             16.974,    116,      0      0.25   21
+9                -16.604,  146.6,      0            16.6035,  146.6,      0      0.25   21
+10               -15.123,    174,      0             15.123,    174,      0      0.25   21
+
+Total Segments: 210
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       2        50.00      50.00    11       1           0         V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Note that the elements are not altered by anything like a constant amount or percentage. In fact, the prescribed reflector is actually longer than the original for a 0.19" diameter element. Elements longer than a calculated half wavelength will always come out longer for a fatter diameter, while those less than 1/2 wavelength will come out shorter--by increasing amounts as the calculated capacitive reactance gets larger.

+

We have calculated the new element lengths, but can we trust them? The test lies in generating graphs to cover a frequency sweep from 144-148 MHz.

+
+ +
+

Fig. 8 shows the restored centering of the gain curve, with only 0.2 dB variation across the band. The front-to-back curves vary by less than 1 dB across the band, although we can faintly see a slight difference between the 180-degree and worst-case curves in the mid-band region. The conclusion is that the equations are highly usable.

+
+ +
+

The feedpoint curves in Fig. 9 echo the results of the performance curves. The resistance and reactance curves show only gradual downward slopes at the upper band edge so that the SWR curve returns to the shape we saw in the original and initially scaled versions of the antenna. The maximum 50-Ohm SWR is 1.19:1.

+

However, let's enter a limitation of sorts, based upon the faint warning given by elements in the curves. Although perfectly acceptable in terms of operation, the curves show very slight aberrations relative to the 0.19" diameter scaled model. First, the gain peak is not quite up to the original level. Second, the front-to-back curves are not exactly coincident across the entire band. Third, the resistance and reactance drop enough to elevate the upper band-edge SWR very slightly. Operationally, these are insignificant matters, but they are hints of a limitation in the calculation.

+

Let's assume that the array was carefully optimized at its original design frequency. Careful scaling yielded identical proportions at the new frequency, and so performance remained fully optimized. As we change element diameter alone, however, the beam is no longer as fully optimized. A change of diameter alters the mutual coupling between elements and thereby changes the optimal element lengths and spacings for maximum performance.

+

For our small (25%) change of element diameter, the difference is too small to arouse any concern. However, as we change the diameter more significantly--say, by a ratio of 2:1 or of 1:2--departure from optimal performance becomes clearly noticeable. Thinner elements may require closer spacing--and fatter elements require greater spacing. The changes of spacing may require small adjustments in element length. Even our 0.25" diameter version of the Yagi is capable of just a bit more gain across the band with an even smoother SWR curve.

+

However, there is a mis-step that we can make that will foul up the Yagi performance more readily than these small departures from complete optimization.

+

Yagi Element Mounting

+

Home-made VHF and lower UHF Yagis in amateur service tend to use one of the three mounting systems shown in Fig. 10.

+
+ +
+

Although I have omitted details--since they may vary widely--the general principles separating the three mounting systems should be clear. The first version uses a non-conductive plate or other means of insulating and separating the element from the boom. If the separation is sufficient, the boom has virtually no effect upon the element. In such cases, one may use modeled dimensions directly, since the model (whether NEC or MININEC) presumes that the elements are isolated from unmodeled conductors. An alternative to the insulating plate is, of course, to use a non-conductive boom. This technique permits through-boom mounting for the element, but with no change of the effective length of the element.

+

The second mounting system makes a direct metal-to-metal contact between the element and the boom. Although once popular among home-shop antenna makers, this system has fallen into disrepute. The chief reason for the dwindling popularity is that it tends to depend upon unsealed contact between metal objects for electrical continuity. Whatever the fastener, assured long-term solid contact is difficult to maintain, even with the greatest construction care. As a result, weathering tends to introduce unwanted noise products into the antenna, as well as offer the potential for altered characteristics if the contact among the system elements breaks down. Some manufacturers use direct boom mounting by welding elements to the boom, but this technique is usually outside the range of home workshop capabilities.

+

Perhaps the most popular contemporary system for mounting elements to a metal boom is to use insulated shoulder inserts. A tight squeeze is the order of the day for sliding the insert over the element and into the holes in the boom. In some installations, a clamping or compression washer fits over the element and against the insert to hold the element firmly in place.

+

Although less prone to major effects from the boom than metal-to-metal mounts, the through-boom insulated mounting system nevertheless requires element length compensation. As the element passes through the boom, the boom changes the magnetic field near the element center, in effect, acting like a variable diameter expansion of the element. As with all elements whose diameter tapers downward as one moves away from the center, the effective or equivalent uniform diameter decreases, and the element requires lengthening. And like all adjustments solely to the element length, the adjustment will not yield a current distribution precisely identical to that of an isolated linear element. However, remaining errors will be too small to be detected operationally.

+

For a through-boom insulated mounting, the remaining question becomes how much to change the element length to compensate for the boom. A number of reasonable approximations have been used in the past. Only recently has the full complexity of the calculation come to the fore in the work of Lief Asbrink, SM5BSZ, who also works in professional/commercial antenna development. A full account of his investigations appears in a series of technical papers at www.antennspecialisten.com (web.archive.org). (Further information on aspects of VHF/UHF operation, equipment, and antennas appears at his personal home page (web.archive.org).

+

The calculation of the required adjusted element lengths for a given array involves a set of routines that Lief has placed into a stand-alone DOS-based program called BC.EXE. One may download the program from the website containing the technical papers. It includes the code, so that one may investigate the algorithms used in the calculation. The exercise requires the user to set up an input file (to replace the default one with the program), and then the program works out the required element lengths.

+

It may suffice here simply to note the relevant input data list for each element:

+
    +
  • 1. Boom tube outer diameter. (See below.)
    • +
  • 2. Boom tube wall thickness.
    • +
  • 3. Boom hole diameter.
    • +
  • 4. Element diameter.
    • +
  • 5. Initial element length.
    • +
  • 6. Distance to the nearest boom end.
    • +
+

The special note on item 1. of the list refers to the fact that the program accounts for both round and square booms. Hence, if one selects a round boom, one enters the boom diameter. However, if one uses a square boom, then one enters the side dimension.

+

Most estimators of the required element length corrections have hitherto overlooked three factors of significance in Lief's list of input data. First is the thickness of the boom material. Differences in boom wall thickness affect the outcomes of the calculations owing to the magnetic field inside the boom. Second is the gap between the element and the edges of the hole through which it passes. In general, this distance is the thickness of the shoulder insert wall. Third is the distance from the element to the end of the boom. The last factor plays a significant role only if the element is close to the boom end.

+

A reasonable approximation using only the outer diameter of the boom has been developed by joint work between G3SEK and DL6WU. The equation runs

+
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where C is the correction factor as a fraction of the boom diameter, and B is the boom diameter in wavelengths. For example, at 144 MHz, a boom diameter of 1" (25.40 mm) is 0.0122 wavelength. The correction factor is 0.1366 times the boom diameter, or 0.1366" (3.47 mm). Using this equation would result in a lengthening of elements by a little over 1/8" each. The G3SEK/DL6WU correction factor equation has a good track record at 144 and 432 MHz for boom diameters less than 0.055 wavelength. A copy of a program to perform the requisite corrections is available at Ian White's web site, www.ifwtech.co.uk/g3sek/diy-yagi/ele.exe. The entire site, titled "VHF/UHF Long Yagi Workshop," is well worth careful reading. You will find there articles on using 50-Ohm drivers that are not folded dipoles (by F/G8MBI), as well as a program for calculating the elements of a DL6WU long-boom wide-band Yagi. The amount of additional practical information is monumental and is Ian White at his long-standing best.

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You may wish to compare the results of the G3SEK program to the more complete SM5BSZ calculations.

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It is not possible to provide a graph of performance results from applying a through-boom correction factor. Modeling of the through-boom insulated mounting system is generally not feasible (within the boundaries of a reasonable size model) with NEC-2 or NEC-4.

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Although the adjustments are small in many cases, they are significant. The accumulation of errors can throw off the performance of an array or the frequency at which that performance occurs. With narrow-band designs especially, a small error can mean the difference between an excellent and a mediocre Yagi.

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Just how large are the adjustments? We may gain a feel for the amount of difference that the mounting method makes by examining the calculated dimensions of a sample DL6WU Yagi, using the latest version of the DL6WU-2006.EXE program. The program offers adjustment factors, relative to insulated and isolated elements, for through-boom and bonded mounting methods. The calculations require the user to specify the element diameter (with separate entries for the driver and for the parasitic elements) and to enter a boom diameter. The following table lists the calculated element lengths for a 300-MHz 14-element DL6WU design using 0.1875"-diameter elements (3/16") and a 1"-diameter boom. The Element spacing does not change, but the element lengths do change by clearly noticeable amounts.

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+Calculated dimensions of a 14-element DL6WU Yagi for 300 MHz using 0.1875"-diameter elements and a 1" boom.
+All dimensions in inches.  Multiply by 25.4 for dimensions in millimeters.
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+Cumulative   Element                      Element Length
+Spacing                   Isolated         Through-Boom     Bonded
+ -----       Reflector    19.185           19.431           19.677
+  7.869      Driver       18.906           18.906           18.906
+ 10.819      D1           17.275           17.521           17.767
+ 17.901      D2           17.101           17.347           17.593
+ 26.360      D3           16.907           17.153           17.399
+ 36.196      D4           16.720           16.996           17.212
+ 47.212      D5           16.554           16.800           17.046
+ 59.015      D6           16.410           16.656           16.903
+ 71.408      D7           16.285           16.532           16.778
+ 84.391      D8           16.176           16.442           16.668
+ 97.964      D9           16.079           16.325           16.572
+112.128      D10          15.992           16.239           16.485
+126.881      D11          15.914           16.160           16.406
+142.225      D12          15.842           16.088           16.335
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The particular numbers representing the element lengths for the last two columns are specific to the selection of both element diameter and boom diameter. Even with the same element diameter, the values will change if we vary the diameter of the boom for either through-boom or bonded construction. Since NEC and MININEC calculate only axial currents (along the element) and not transverse currents (around the element), the modeling programs cannot provide any assistance in confirming the adjusted designs. At a certain point, field testing must supplant computer-assisted design work.

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At 300 MHz and for the materials selected, the parasitic element lengths change by amounts that are appreciable. In a broadband design, such as the DL6WU, a given operating bandwidth may still fall within the acceptable performance range of the array, even if unadjusted for the style of construction. However, for many narrow-band designs, the length adjustments may be absolutely necessary to achieving the desired performance. Also note that the calcuating program assume that the user will directly feed the 50-Ohm driver and therefore, the element will be insulated and isolated from a conductive boom. As a result, the driver length is the same in all three columns of the table.

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What applies to through-boom insulated mounting systems and to bonded beam construction also applies at every step of the way in the process of scaling and altering a VHF or lower UHF Yagi design. Adapting an existing design to one's personal situation, materials, and operating needs requires careful calculation and even more careful construction.

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Updated 12-01-2002, 07-09-2004, 08-30-2007. © L. B. Cebik, W4RNL. This item appeared in AntenneX, November, 2002. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: VHF / UHF, Yagi


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What is a Slim Jim?

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L. B. Cebik, W4RNL

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The "Slim Jim" antenna has grown so popular among new radio amateurs who need a good antenna to work 2-meter repeaters that is has acquired its own name. Indeed, many newer amateurs think of the slim jim as a unique antenna, and some have claimed extraordinary performance capabilities for it--all without a good sense of what it takes to make such comparisons, of course. The seeming uniqueness of the antenna has even engendered some fairly poor explanations of how the antenna works. Therefore, it might be serviceable to spend a little time looking at the slim jim and seeing what may be its correct electrical origins.

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In one sense, shown in Fig. 1, the slim jim is simply an alternative form of the common J-pole. The J-pole antenna itself is somewhat more complex in principle than it is to construct. It consists of an end-fed 1/2 wavelength radiator. Since the impedance of the radiator section is very high, we find a very old matching system consisting of a 1/4 wavelength section of transmission line. If we short the line at one end, it forms a transformer with a high impedance at the radiator end and a low impedance at the short. We may tap the line at some point above the short and obtain almost any impedance that we need for our transmission line. Today, a 50-Ohm tap is most common, but other impedance values are available. The exact tap point partly depends on the spacing between the matching section conductors and the conductor diameters, since the transformation of impedance along the line rests on the line's characteristic impedance.

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One simple factor prevents us from holding the behavior of the J-pole to this straightforward explanation. The impedance at the top ends of the matching section lines is not equal, since one terminal is unconnected and the other sees a finite impedance at the radiator end. Therefore, the currents within the matching section are not equal in magnitude and opposite in phase. Rather, the currents are complex, having both radiating and transmission-line components. The existence of radiation currents within the matching section means that the entire J-pole structure radiates. The more widely spaced the matching section wires, the greater will be the distortion of the azimuth pattern from a true circle that we expect from vertical radiators, although the distortion does not rise to a level that ever disables the J-pole from effective omni-directional service. For additional information on basic J-pole configurations and operation, see the series at my web site called "Some J-Poles That I Have Known".

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The slim-jim version of the J-pole arose after amateurs discovered that they could construct the antenna from a single length of common TV parallel transmission line or "ribbon" cable. Initially, builders cut one wire at the top of the matching section and stripped away the wire. Cheaper cables simplified the process, since we could get a plier-hold on the unwanted extra conductor length and pull it through the insulation. As a result, we still had the center insulation in which we could drill a hole and hang the antenna from the ceiling or some other convenient support. When not in use, we could wad up the antenna into a small ball for storage. These TV-lead J-poles have served any number of important purposes that have included getting a new amateur started on 2-meters, allowing bed-ridden amateurs to maintain communication with friends, and innumerable emergency services.

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Amateur ingenuity mixed with amateur laziness eventually led to the discovery that we did not have to remove the second wire from the radiator. Instead, we could simply remove a small amount of wire at the top of the matching section and then connect the upper wire at the antenna top to form a continuous folded radiator section. For common TV lead-ins, we needed to reset the tapping point relative to the bottom short, but before long, the entire process became codified so that even the newest amateur could successfully built his or her own slim-jim version of the J-pole.

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Enter the Zeppelin and the Quad

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The J-pole antenna derives from the end-fed Zeppelin antenna that used to stream out behind the airships of the same name. The matching-section principles for feeding the high-impedance end of a wire were the same as used with the J-pole, even though the Zepp used the HF region for most of its communications. Today's end-fed Zepps as ground antenna installations sometimes use the same scheme of matching, although the matching section is at right angles to the antenna wire. This small tribute to historically significant antennas might end here, were it not somewhat mis-used in the case of the slim-jim J-pole design. The mis-use occurs as new users try to figure out why the slim-jim is "so good."

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Fig. 2 shows the antenna that we typically think about as an end-fed Zepp: a 1/2 wavelength wire fitted with the 1/4 wavelength matching section. The end of any antenna shows a high impedance as the current goes to zero and the voltage climbs to very high levels. Hence, we may use the same 1/4 wavelength matching section with a wire that is 1 wavelength. Now, suppose that we fold the 1 wavelength back upon itself so that we still have 1 wavelength of wire but fitted into the space required by a half wavelength wire. Surely, some folks reason, we must obtain an advantage by having the long wire.

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In fact, the fold-back wire provides no significant gain advantage over a single wire and may be the wrong model for understanding what a slim-jim J-pole may be. To understand the operating principles of the slim jim, we should turn to a different sort of antenna, the quad loop. A closed quad loop is a pair of dipoles in phase with each other, but it requires only a single feedpoint by virtue of the connection of the dipoles at the high-voltage, low-current points. The sketch of the closed quad at the upper left of Fig. 3 shows the general principle. The arrows indicate the current polarity at one instant in the life of the antenna. (Of course, the current direction shifts back and forth with radio frequency alternating current. However, by tradition, we use arrows to indicate the relative direction of current, using a time framework consisting of a single instant.)

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The upper right portion of the figures shows a quad loop with a gap at the far right, that is, at one of the high-voltage, low-current points. If we place a small gap at such a point, we disturb the total continuity of the loop, but perfect continuity is not required for the loop to perform its task just as it would if we closed the loop. (Note: we can only create such a gap at the high-voltage, low-current point of the loop. If we create a gap at the point opposite the feedpoint--a high-current, low-voltage point--we shall change the loop's operation, that is, its pattern and its feedpoint impedance.) You may confirm this matter with any modeling software by comparing gapped and closed loops. As you widen the gap, you will need to adjust the element lengths necessary to sustain a resonant feedpoint. However, by moving in small steps, you will be able to convert named closed-loop antennas into named open-ended antennas, for example, changing a right-angle delta SCV into a half-square SCV.

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The lower portion of the figure shows the application of the same principle to the antenna that we call the half wavelength folded dipole. On the left is a closed version, and on the right is a version with an opening at one end. In principle, the two antennas will show the same radiation characteristics. Both versions of the folded dipole provide both radiation and transmission-line currents that yield equal radiation performance and a 4:1 increasev in the feedpoint impedance relative to a linear dipole (assuming that both long elements use equal diameter materials). However, the pattern of transmission-line currents will not be the same for both folded dipoles. If we sort out those currents, the folded dipole's radiating currents prove to be virtually identical to the remaining radiation currents (the only currents) of a half wavelength single wire fed at its center.

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If we feed the folded dipole at one of its closed ends, we may use the 1/4 wavelength matching system that we applied to the Zepp. Because we are feeding the antenna at the high-voltage, low-current position for each of its two wires, the impedance step-up ratio of a mid-element feed system becomes irrelevant to the antenna's operation. Under these conditions, we may have a gap at the far end of the antenna with no harm to the radiation characteristics. Equally, we may use the high-impedance feed system at the gap end of the antenna, connecting it to only one of the wires at the gap. Once more, the radiation characteristic will be unaffected by the feed system. This last condition is the slim-jim antenna.

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Testing the J-poles Many Configurations

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Let's put the account to a test. We may create many J-pole configurations, but we shall need only 5, the ones shown in Fig. 4. The first version is the standard J-pole with a single half wavelength wire as the radiator. (Because we are using a highly interactive radiator and matching system, the radiator of a J-pole is rarely a perfect half wavelength, even accounting for end effect, wire losses, and wire diameter.)

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The second version of the J-pole is a pair of wires joined at the bottom of the radiator and the top of the matching section. We might expect the antenna to act like a single fat wire. The third form of the J-pole uses the typical slim-jim assembly of connecting the wire at the top but not at the bottom. The fourth in the series is almost gratuitous: a J-pole with a double wire, but with the second wire not attached at either the top or the bottom of the radiator section. The last model in the series makes connections at both the top and the bottom of the radiator section, thus creating an end-fed folded dipole.

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All of the models use AWG #20 wire that is 0.032" in diameter. All parallel section of the antennas use a 0.375" spacing center-to-center. These dimensions partially simulate the typical slim-jim construction using typical TV lead-in. However, there are two important reservations, both of which involve the fact that TV lead-in uses vinyl insulation around and between wires. Since the matching section is a form of parallel feedline, its physical length will normally be the electrical length or the free-air length times the line's velocity factor (VF). For flat lines, a typical value for a TV lead VF is about 0.8. In the radiator section, the line is not acting as a transmission line, and so we must apply to it a different value for the VF, one more generally applicable to insulated wire elements. Values in the range between 0.95 to 0.98 are typical, depending on the insulation's conductivity and permittivity (or loss tangent).

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In reaching a 50-Ohm impedance for all of the models, I limited the adjustments that I made to the model. All matching sections have the same total length from the line short to the top of the section: 22.5". I then adjusted the tapping point and the total height of the array. The latter adjustment is equivalent simply to adjusting the length of the radiator. For fine adjustment, I made small adjustments in the gap between the top of the matching section and the beginning of the second wire in parallel-wire radiators. However, the total range of these adjustments amount to 0.1".

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With this much information on the model set-ups, we are ready to examine the data that emerged from the tests. Fig. 5 provides a guide to reading the dimensions listed in Table 1.

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Dimensionally, models SJ-1 (single-wire radiator) and SJ-4 (double wire, no connection) are most alike. The single wire requires a tapping point closest to the matching section termination. It also uses the shortest radiator section that achieves resonance. Adding the second, unconnected wire moves the tapping point upward 0.4" and requires a 1.85" length addition to the radiator section. In fact, SJ-4's second wire acts like a closely and parasitically coupled independent wire. Although very close to the directly fed wire, the second wire creates the greatest front-to-back ratio of the collection of models. (The amount, of course, has only numerical interest and would not be operationally significant.) The operation of model SJ-4 strongly suggests that we need not have connected either end of the extra wire in the twinlead's radiator section when creating our J-pole. With the correct dimensions, the J-pole would have operated correctly.

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The dimensional relationship among models SJ-2, SJ-3, and SJ-5 is striking. The folded-dipole version requires the longest radiator, at 38.3". Both versions that connect only one end use a radiator that is 38.2", regardless of the connected end. For all three models, the gap between the upper end of the matching section and the lower end of the second radiator wire varies by only 0.05". All three models require a tapping point that is considerably higher along the matching section. However, both gapped versions use the same tapping point, with the closed loop folded dipole only 0.1" higher.

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All of the matching section have the same length, spacing, and wire size. Hence, all of them have the same characteristic impedance (Zo) (calculated at about 375 Ohms). The line Zo will be the geometric mean between the impedance at the end of the radiator and the shorted end. Since the shorted end--for all practical purposes--has a constant value that is near zero, the 50-Ohm position on the line will vary with the impedance at the radiator end. Subject to qualifications, the higher the radiator end impedance, the greater the impedance transformation down the line and hence the closer to the shorted end that we shall find the 50-Ohm point. Because radiation from the unbalanced termination will change the line currents relative to their values under perfect conditions, we can only use this basic relationship in broad terms, without precision calculation. However, the low tapping point of the single radiator (SJ-1) suggests that the radiator end shows the highest impedance of the model group. The unconnected second-wire model (SJ-4) moves the position upward a small amount, indicating that the presence of the second wire lowers the impedance at the end of the connected wire (where its end is the top of the matching section). All three of the connected double-wire models (SJ-2, SJ-3, and SJ-5) have a significantly higher tapping point, suggesting that their connections to the matching section exhibit significantly lower impedances. Of more than passing interest is the tight grouping formed by the three tapping points.

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From Dimensions to Performance

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Table 1 also provides modeled data on the performance of all of the J-pole models. The dimensions are simply the ones that yield the feedpoint impedance values (Feed R and Feed X) at a 50-Ohm level within +/-1 Ohm of that value and within +/-j1 Ohm of resonance. All antennas have the same base height of 20' (240") above average soil. The top height of the models varies by only 4.55" from the tallest to the shortest. Therefore, that difference makes no performance difference. All of the double-wire versions of the J-pole have maximum gain values that are within 0.08-dB of each other. The "strongest" of the group shows only a 0.23-dB gain advantage over the single-wire radiator (SJ-1), largely due to the effectively fatter radiators in the double wire versions. All TO angles are either 3.7 or 3.8 degrees. (All patterns taken of these models used an increment of 0.1 degrees in both the elevation and the azimuth patterns.)

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The bottom line is that none of the models shows any operational advantage over any other model in the group. To demonstrate this point, we may overlay the patterns for the slim-jim version (SJ-3) and the folded-dipole version (SJ-5). Fig. 6 shows the result. I know of no way to separate the blue and black lines of the two plots.

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As an incidental, note that the elevation pattern shows a depressed area about 15 degrees above the horizon. The anticipated lobe is not as strong as a smooth curve would yield and the nulls are not as deep as we might expect. This phenomenon is not a function of the antenna or its height above ground. Vertically polarized antennas exhibit this "depression" at the indicated angle over average ground, regardless of the antenna type or the height above ground. Over very good ground, the angle drops to about 12 degrees, and over very poor ground, the angle increases to about 25 degrees. Should the matter interest you, you may set a vertical antenna at perhaps 20 wavelengths above ground and take patterns using the 0.1-degree elevation increment. The high number of lobes and nulls that appear provides a much sharper indicator of the angle for the depression. Then you may systematically vary the ground conductivity and permittivity, treating each variable independently, and obtain some interesting curves. The exercise is electrically interesting but not operationally significant, since we normally are interested in point-to-point communications with vertical antennas at these frequencies.

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The "depression" angle, of course, is the pseudo-Brewster angle (PBA) applied to vertically polarized antennas. Over dry land, where the conductivity is low, the angle is largely a function of the soil's permittivity. Therefore, we may simplify the calculation for general purposes to the following equation.

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The equation omits the intermediate steps of defining a refractive index, which is the square root of the relative permittivity (or relative dielectric constant). At the PBA, we find neither additive nor subtractive effects from direct and reflected rays. Hence, we find neither a lobe or a null, and the gain is approximately the same as the free-space gain of the antenna. For further information on the pseudo-Brewster angle, see Chapter 3 of The ARRL Antenna Book, any recent edition.

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Current Affairs

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The data that we have developed should suffice to establish two ideas. First, since none of the J-pole configurations exhibits an operationally detectable difference relative to any of the others in the sampling range, the slim-jim configuration does not result in a superior J-pole. It simply results in a J-pole, and all properly constructed and matched J-poles are quite good antennas for FM repeater service. They are all free of significant horizontal dimension, since they need no radials to allow performance. Performance quality will largely depend upon the mounting height and the surrounding clutter that may interfere with paths to various targets.

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Second, the tightness in the dimension groups among the models that make any connection to a second wire--as well as the performance similarities--should suffice to establish that the slim jim (SJ-3) and its bottom-connected brother (SJ-2) are forms of folded dipoles with a gap in one or the other end. However, one may wonder to what extent a folded dipole with a gap in one end at a high-voltage, low current point acts like a folded dipole, that is, as an antenna having both radiation and transmission-line currents. To satisfy myself on the matter, I examined the current profiles of the radiator sections of all of the models in the group. A graphic representation of the current magnitude distribution appears in Fig. 7.

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All but one of the models yields a similar curve. Still, there are some pointers about reading the curves that may deserve attention. For example, with SJ-1, we have only a single radiator wire. Its curve is the continuation of the curve on the matching section wire to which it joins. Note that the current magnitude does not go to zero. The other side of the matching section that connects to nothing has a current curve that goes to zero, as indicated in the graphic by the current line touching the element line.

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In SJ-2, we find that same matching section line with no connection going to zero. However, in this bottom-connected model, the connected matching-section line does not connect to either of the curves for the twin radiators. This situation is quite normal, since the current at the tip of the matching section is twice the value at the bottom of either radiator. That is, the radiator current has divided between the two branches, and each branch carries half the current at the junction point as the single line to which the radiators join.

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For the slim-jim model (SJ-3), we show one radiator and one matching-section line with currents that go to zero. These are the unconnected ends. Like the other models, the current magnitude does not go to zero in the continuous wire as it passes the matching-section-to-radiator boundary. In fact, this region is not a boundary except as we need to set construction details. Electrically, it is more of a frontier between the radiating and matching functions.

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SJ-4, of course, shows the current on both radiators going to zero at the top of the radiator section. At the matching-section end, the second wire current goes to zero, while the connected wire shows the "frontier" effect. Like all of the other models up to this point, the radiator current distribution curves are well formed; that is, they show peak current roughly at the center of the radiator length, with minimum values at the extremes.

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The radiator section of SJ-5, the end-fed folded dipole, appears to show a wholly aberrant set of current distribution curves. In the closed folded dipole, we have two sets of currents: the radiation currents and the transmission-line currents. (In fact, in all of the double-wire models, we find both type of currents. However, the transmission-line components are generally too small to disturb the overall pattern of currents shown in the graphs.) Both current magnitudes are sufficiently high to affect the composite current magnitudes on each of the two wires. This result appears at face value to be in conflict with the radiation pattern reports, which show a completely normal set of results compared to the other models.

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The resolution of the difficulty lies in sorting out the two types of current. Radiation currents are in phase with each other and therefore add together to form the radiation pattern. Transmission-line currents have opposite phase angles at any given facing point along the double line. Therefore, relative to radiation, they subtract from each other. The following simplified equations express this situation for each wire (A and B) in the parallel line:

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On wire 1 (IA), we may treat the total current as the sum of the radiation and the transmission-line current, while on wire 2 (IB), we may treat the current as the difference between the transmission line and radiation currents. If we combine these basic relationships, we can calculate the net radiation current (IR) and the net transmission-line current (IT) for the pair of wires forming the folded dipole:

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The information that modeling software (in this case, NEC-4) gives us is the current for each wire at facing points, which translate into segment numbers along the relevant wires. We can use this data to calculate the net radiating and transmission-line current values for each segment. The process, of course, is more involved than the basic equations reveal, since we must account for both the current magnitude and phase angle. (The full NEC output file will provide the current values both in terms of real and imaginary parts and in terms of magnitude and phase angle. We need the real and imaginary parts and can calculate them from the magnitude and phase angle if our software does not give us access to the component parts.) Once we perform the required work on the component parts, we must re-calculate final magnitude and phase values.

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The radiator sections of all models used 14 segments. Table 2 shows the results of sorting the radiation from the transmission-line currents at corresponding points along the radiator of model SJ-5, where segment 1 is at the bottom and segment 14 is at the top.

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The entry columns on the left show the values that produced the curves that we viewed in Fig. 7. What the curves did not show was the phase angle for each segment's current. The next most interesting facet of the table occurs in the phase-angle column of the transmission-line portion of the table. Note that the phase angle is almost the same for every entry. (The one seemingly aberrant entry of 18 degrees is a function of the magnitudes being too low to provide an accurate phase-angle calculation.) The relatively constant phase angle is a hallmark of transmission-line currents in folded dipoles. Had we used a center or current feedpoint for the folded dipole section, the value would have been about 90 degrees different than the source current phase angle. However, we do not use center feeding for a J-pole. For further notes on the current distribution in a folded dipole, see "Unfolding the Story of the Folded Dipole".

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For our purposes, we need only sort the two currents and establish that the radiating current show a relatively normal pattern. Fig. 8 does this job by showing the magnitudes of the two types of current. With respect to the radiation pattern, only the curve for radiating currents is relevant, and its shape is completely normal. We find the maximum current value at about the center point of the radiator section, with values going toward zero at each and. Because the current values in a NEC calculation are taken at the virtual center point of a segment, their values never actually reach zero at element ends.

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In fact, all of the models with double radiator wires, connected or not, show some transmission-line currents in the radiator section. Model SJ-2 had such currents from values of 0.007 to 0.068 at phase angles ranging from 22.1 to 22.8 degrees. Of course all current levels are relative to a source current magnitude of 1.0 at a 0-degree phase angle at the model source. Model SJ-3, the slim-jim version, shows transmission-line currents ranging from 0.003 to 0.10 at phase angles of 50 to 53.8 degrees. Even the unconnected model, SJ-4, shows magnitude values from 0.03 to 0.30 at phase angles of 79.9 to 82.3 degrees. In all three cases, the transmission-line current magnitudes are too small to appear in the distribution curves in Fig. 7 as more than a slight deviation from the curve of a pure radiation current distribution curve, such as the one shown for model SJ-1 with its single-wire radiator section.

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Conclusion

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The so-called slim-jim turns out not to be a special antenna, but only one of many ways to form a J-pole, an end-fed 1/2 wavelength radiator with a 1/4 wavelength matching section. Of course, that simple statement carries the qualification that the unequal impedance at the terminal ends of the matching section results in radiation from the matching section and complex interactions between the matching and radiating sections of the antenna. Whatever the form of the upper or radiating section, it remains a half wavelength fed at its end. So long as the section is a half wavelength, its performance will not vary significantly despite gyrations in the form.

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Nevertheless, however obvious the conclusion may seem, the exercise has been useful in some respects. First, it has allowed the introduction of a more useful way of viewing the slim-jim configuration, that is, as a folded dipole with a gap at one of the high-voltage, low-current points. As well, the exercise has facilitated the analysis of complex currents in the folded dipole model to undergo analysis into their radiating and transmission-line components. Those exercises alone may well justify our original question into what the slim jim might be.

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My junk box has just about enough twinlead to make perhaps 40 of these very useful 2-meter verticals, about 8 of each variety that we have discussed.

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In the course of these notes, we over truncated some of the data presentation in order to progress along the lines of analysis in a reasonably efficient manner. We have a considerable amount of modeled and calculated data that may be of interest to those who may wish to probe more deeply into the J-pole with multiple wires in its radiator section or to examine more thoroughly the current distribution on a current-fed folded dipole. Therefore, I have added an Appendix for the data-hungry.

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Updated 11-01-2006. © L. B. Cebik, W4RNL. This item appeared in AntenneX, October, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Appendix

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Return to Index

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Topics: J-Pole, VHF / UHF, Vertical


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What is a Slim Jim?

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Data Appendix: Radiating and Transmission-Line Currents

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L. B. Cebik, W4RNL

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In our examination of J-poles using parallel wires as the radiator section--with and without connections at either the top of the bottom, we did not present some of the large body of data collected to establish various considerations. Some of the data involves the sorted radiation and transmission-line currents of the J-pole models SJ-1 through SJ-5. Only the last model, with its seeming aberrant current distribution received a full table of information.

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In addition, we also made some basic claims about the performance of current-fed folded dipoles, both closed and open (that is, with an end gap). This set of claims deserves a fuller justification on its own ground, simply to further develop an understanding of the operation of these types of antenna elements. This appendix will provide the missing data collection, with a minimum number of notes along the way to set the data context.

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Models SJ-1 through SJ-5

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Relative to the appearance of composite current magnitude curves, such as those provided by modeling software, we noted that only the closed folded dipole version (SJ-5) of the J-pole showed transmission-line currents in sufficient magnitude to seriously distort the patterns from their appearance if we had shown only radiation currents. See Fig. 7 in the main text to review the composite current magnitude distribution curves. For our purposes, we need only refer to Fig. 1 to review the configurations of each of the five models.

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The models for these versions of the J-pole showed very similar performance values, despite the differences in the radiator sections. As a convenience to data gathering, all of the long radiator-section wires use 14 segments, with segment 1 always at the bottom, that is, closest to the matching section, whether or not directly connected. Therefore, segment 14 is always at the top. The modeling tables will appear in reverse order, starting with model SJ-5. All but the last model (SJ-1) will use 4 columns to present the composite current values provided by NEC-4 software as the starting point in the analysis. Each pair of columns presents the current magnitude and phase angle on each of the two wires. Of course, model SJ-1 is the exception, since it has only 1 wire, and its currents are entirely radiating currents. Hence, Table 5 is complete with only 2 columns of data.

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The last 4 columns for Table 1 through Table 4 present the total radiating current and transmission-line current at each pair of facing segments as we move up the wires. Each current has a magnitude and a phase angle. We shall begin with Table 1 and model SJ-5, the closed folded dipole. The notes at the bottom of the table apply to each of the succeeding tables. As I suggested in the main text, note the relatively constant transmission-line current phase angle throughout the length of the radiator. Also note that the transmission-line current reaches a minimum magnitude at about the mid-point of the radiator.

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When we turn to Table 2 and model SJ-4, we find a relatively constant transmission-line current phase angle, but one that is quite different from the average value for SJ-5. In fact, the phase angles differ by about 60 degrees from each other. Remember that the ends of the second wire in SJ-4 are not connected at either end to the first wire that is continuous with the matching section. Hence, in model SJ-4, the second wire has a parasitic relationship to the first wire, with moderate transmission-line current magnitudes along the entire length.

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Model SJ-3 is the so-called slim-jim configuration, connected at the top between the radiator long wires, but open at the bottom end. Hence, the configuration feeds the end of one of the two long wires. The transmission-line current phase angles in Table 3 do not show as tight a grouping as in the closed folded dipole (SJ-5), but the range is small compared to the range of phase angles shown by the radiating currents. The average phase angle is negative relative to the values shown by models SJ-5 and SJ-4. In addition, the transmission line current magnitude shows a parallel structure to the curve created by model SJ-5, with the minimum value about at the midpoint of the radiator section of the J-pole.

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Model SJ-2 reverses the connection by bringing it to the bottom of the radiator, so that the two radiator wires form parallel-connected branches for the matching section, if we treat it as the simple source of energy. Table 4 shows a relatively constant transmission-line current phase angle of about 22 degrees. Note that, like model SJ-4, the maximum transmission line current magnitude occurs about mid-element, but the value of the peak transmission-line current is considerably lower than we find on SJ-4.

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Model SJ-1 (Table 5), provides the simplest case, since it has only radiating currents.

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The maximum value for the radiating current on model SJ-1 is higher than the values that we calculate for the two-wire radiators, but if we reduce it to about 0.7 of its tabular value, we may create a graphs of radiating current magnitude values for all of the models in the group. Fig. 2 supplies the graph. The values for SJ-1 still rise more rapidly than on the other models because SJ-1 does not undergo either element termination or current division at the junction of the radiator section with the matching section. Otherwise, for the entire collection of double-wire radiators, the radiation current magnitudes show virtually no differences. Model SJ-4, with a wholly unconnected second wire shows a current magnitude graph shape that is more similar to SJ-1 than to the other two-wire models.

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If we perform a similar graphing venture on models SJ2 through SJ-5 (with model SJ-1 automatically disqualified) using the transmission-line current magnitude values, we obtain Fig. 3. The fully closed folded dipole element (SJ-5) and the slim-jim (SJ-3) show similar shapes to the current magnitude curves, although at vastly different magnitude levels. Connecting the feedpoint (from the matching section) to a single wire end best replicates the transmission-line current distribution of the fully closed folded dipole radiator. In contrast, the parasitic model (SJ-4) and the bottom-connected model (SJ-2) have curves that replicate each other in shape, but the parasitic model shows the higher magnitude of transmission-line currents.

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The exercise is both useful and limited. It has revealed the distributions for both radiating and transmission-line current magnitudes and phase angles. Indeed, one may well be able to wrest from the tabular data further insights into multiple-wire radiator performance. In doing so, one should be aware of the limitations of the exercise. The current data used for each segment has undergone calculation through the NEC method-of-moments techniques to yield current magnitude and phase-angle values that appear in rounded form in the tables. The sorting of current types rests on external calculations that also appear in rounded numbers. The methods show slight variations, for example, in the 1 to 3 degree change in the transmission-line current phase angle when the current magnitude values are very small.

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In addition, we have been examining the currents on models that contain more electrical differences than the similarity of their physical structures may suggest. The distance from the tapping point to the top of the matching section and the bottom of the radiator differ among models as a function of the different impedances presented to the matching section by changes we make in the radiator structures. Because the top of the matching section and the bottom of the radiator occur in a region of antenna structure in which impedances change rapidly, very small changes in the radiator may make a considerable difference in the current values reported by the NEC software. Although most of these differences will be unlikely to significantly affect performance, they may make a difference to the calculated values of the current phase angles for both types of currents in the radiator sections of the arrays.

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Nevertheless, the exercises do show some general properties in the currents within various sorts of 1/2 wavelength radiators that we may use with the J-pole.

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Current-Fed Open and Closed Folded Dipoles

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The suggestion that the folded dipole provides the best model for analyzing the performance of the slim-jim configuration (model SJ-3) rested on a comparison of the performance and the current distribution of current-fed folded dipoles with both closed and end-gapped structures. Fig. 4 outlines the general idea presented in the main text. Note that we have indicated current feeding by placing the source or feedpoint at the center of one of the two folded dipole wires.

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In fact, I had modeled folded dipoles for 146 MHz using two 2-mm (0.079") wire separated by 25 mm (about 1"). I created the open-end model simply by removing one of the end wires from the closed model. As suggested in the main text, to restore resonance, I have to increase the length of the long wires by 3.8 mm (0.15") or about 1/2 of 1 percent. Table 6 summarizes the dimensions and the free-space performance of these two versions of a folded dipole.

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As the table suggests, there is no detectable performance difference between the radiation patterns of the two antennas. The feedpoint impedance values differ by only 1/2 of 1 percent, and both values represent the anticipated X4 multiplier over a linear dipole that is resonant at the same frequency. Nevertheless, if we compare the current magnitude distribution curves offered by NEC software, we obtain very different patterns. Fig. 5 gives us a good view of the differences.

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The composite current magnitude plot for the closed folded dipole shows the normal peak value in the mid-element region for both long wires. However, the fact that the currents at the ends of the long elements do not go to zero alerts us to the fact that the currents have both radiating and transmission-line components. In contrast, the currents at the open end of the gapped folded dipole do go to zero, as they must at the element's open end. Although we find a peak in current magnitude in the mid-element region, the current magnitude values at the closed end of the structure are far from approaching zero.

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We may usefully calculate the radiating and the transmission line currents of both types of folded dipole. Table 7 presents the results for the closed dipole, while Table 8 gives comparable results for the end-gapped version. Note that each dipole long wire uses 27 segments and that both increases in segment number from left to right across graphic representations. For the end-gap model, the gap occurs at the left end, that is, at segment 1.

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Despite the seemingly radical difference in structures and composite current distribution, the two models show essentially the same transmission-line phase angle across the entire structure--very close to 90 degrees different from the feedpoint current phase angle. Of equal importance is the fact that the radiation currents for each type of folded dipole also show similar phase-current ranges as we move from one end of the structure to the other. We may portray more easily the radiating current magnitudes in graphical form, as shown in Fig. 6.

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The only difference in the radiating current magnitude level curves occurs at the open end of the end-gap version, where the current on the final segment more closely approaches zero. This difference would be too small to show up in any performance category.

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The transmission-line current magnitude curves in Fig. 7 show the major differences between the operation of each folded dipole type. The closed model shows a smooth and symmetrical curve, centered around the mid-element point, where we located the feedpoint on one wire. In contrast, the gap-end versions shows a magnitude dip at the center, but a steady progression of values toward zero at the open end of the antenna. Note that the transmission-line current magnitude at the closed end of the antenna is about as much higher than the closed dipole at the same point than the open end current is below the level of the closed dipole at that same point.

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Despite the radical change in transmission-line current magnitude along the gap-end version, the radiating currents remain very symmetrical. As a result the radiation patterns for both the closed and open ended folded dipoles overlay each other perfectly with no detectable displacement.

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Shorting the Folded Dipole Center

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For VHF and UHF applications, center-fed folded dipoles of standard design present a challenge for equipment durability and safety. Often mounted in arrays on masts that tower over surrounding objects, ungrounded antenna structures can carry considerable surges to the equipment that they serve. A short-circuit across the center of a folded dipole allows connection of one side of the feedpoint to the feedline ground, changing the DC and lightning potential to the same value as the support structure. Numerous amateurs have wondered whether a center-shorted folded dipole works, and if it does, how it works. We may apply the same analytical tools that we have been using to the center-shorted folded dipole and find a considerable part of the answer.

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Modeling a folded dipole with a center short between the long wires requires a small revision in the wires to create a wire junction on both long wires at the center of the structure. Instead of 27 segments from one end to the other, we shall now have 28 segments, and the source segment will be one segment off center. The required resonant length decreases a small amount, down to 943.0 mm, leaving all other dimensions the same as we used with the sample closed and open-ended versions of the antenna. Fig. 8 shows the outline, along with the composite current distribution curves--with the standard center-fed folded dipole presented for comparison.

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The free-space gain of the version with the center short is 2.13 dBi, the same value that we derived for the earlier folded dipoles. The feedpoint impedance is 281.8 - j0.0 Ohms, a value that indicates a full folded-dipole impedance transformation when both long wires have the same diameter. The composite current distribution curve for the modified folded dipole should have a familiar look, since it is virtually the mirror image of the curve that we showed for the open-ended or gapped folded dipole. In fact, allowing for the opposite-end presentation, there is no significant difference between the radiation and the transmission-line currents. Table 9 provides the data calculated on the basis of the current reports for facing segments along the parallel long wires.

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For both the center-short and the gapped folded dipoles, the radiation currents vary in magnitude from 1.0 at the center down to about 0.1 at the ends (actually, the center of the last segments). The transmission-line current magnitudes vary from a high between 0.7 at one end to less than 0.05 at the other. If we mirror image Fig. 7, it correctly graphs both types of current magnitude on the center-shorted folded dipole. The transmission-line currents are 90 degrees out of phase with the feedpoint or source current.

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The short circuit across the center of the folded dipole does not de-activate the wires on the opposite side of the short relative to the source location. With respect to radiation currents, the entire length of the structure participates equally in the current distribution and the radiation pattern. However, the short circuit does alter the pattern of transmission-line current magnitude, replicating the situation that occurs with the gapped folded dipole. The short does permit the inclusion of a significant safety feature within the antenna structure.

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Conclusion

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The notes in this appendix supplement the main text for those who wish to dig a bit deeper into element operation when the element contains more than one wire and the spacing between the wires is fairly close. Their practical applications may be scant, but they might be useful to modelers trying to understand some of the seemingly strange current values reported along such multi-wire elements by NEC or MININEC software. They may also help to improve our naturalized expectations of performance from folded elements beyond the level normally treated in most texts.

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Then again, they may simply be an expression of where my own curiosity has led me.

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Updated 11-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: J-Pole, VHF / UHF, Vertical


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+

Long-Boom Yagi Sidelobe Suppression
+ or
+ The Silence of the Lambda

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

At one time, not very long ago, gain alone was the name of the game in long-boom Yagi design from 2-meters upward. I still encounter individuals who care nothing about the front-to-back ratio, let alone other unproductive lobes produced by high-gain Yagis. However, as we learn more about the utility of having a truly quiet beam in all but the forward direction within operations calling for weak-signal reception, all of those other lobes have garnered attention once more.

+

The question for the Yagi designer is deceptively simple: how can we suppress or radically attenuate all of the lobes in the antenna pattern for a long-boom Yagi except the one forward lobe? In the following notes, I shall review the general state of the art, beginning with DL6WU designs, and progressively examine some potential improvements that we can make. In the process, we shall gradually change our orientation toward long-boom Yagis from a 2-D E-plane or azimuth perspective to a 3- dimensional view that will also look at the H-plane and at elevation patterns over ground.

+

The reported results of this exercise will not result in beams that are necessarily practical, for this is but a work in progress. The results will try to show what improvements are possible, even if--for the moment--the improved arrays are not especially suited for amateur construction. As well, in the process, we shall be willing to sacrifice gain for unwanted lobe suppression. Arriving at a design with peak gain and maximum unwanted lobe suppression remains a future development. As a further note on the provisionalness of this study, I have placed all NEC-4 models of antennas in the 222-225-MHz U.S. amateur band. The urge to build for the more popular 144-MHz and 432-MHz bands will be slowed just a bit by the need to adjust everything in the antenna designs.

+

The unwanted lobes--which I shall call sidelobes as an encompassing term--include the main rear lobe, rear sidelobes, and forward sidelobes. In weak signal work, every one of them is capable of adding noise to the signal, so my general project will be to see how many we can reduce and by what amount. At this stage of investigation, I shall not presume that any particular level is good enough. Rather, I shall strive to reduce all of them by as much as I can.

+

Getting Oriented

Let's review some radiation pattern basics in order to orient ourselves to the graphical and tabular methods of data presentation to follow. Fig. 1 provides us with a 3-dimensional radiation pattern presentation for a 12-element DL6WU Yagi design at 223.5 MHz. A representation of the antenna also appears in the pattern just to set its position relative to the lobes. +
+ +
+

For a free-space radiation pattern, conventional NEC modeling axes X and Y define the E-plane (parallel to the plane of the elements), while axes X and Z define the H-plane (at right angles to the plane of the elements). Immediately apparent is the fact that the element ends provide some suppression of the minor lobes and the -3 dB beamwidth of the main forward lobe. Hence, the largely neglected H-plane will be of as much concern to us in the suppression of sidelobes as the E-plane.

+
+ +
+

We can capture most of the salient lobe features of a pattern more clearly by examining 2- dimensional polar plots of the e-plane and H-plane patterns, as illustrated in Fig. 2. Immediately apparent is the wider beamwidth and stronger minor lobes of the H-plane pattern.

+ 
            Abbreviations Used in Data Tables and Their Meanings
+Table                   Meaning
+Abbreviation            See Fig. 2
+Gain              The maximum free-space gain in dBi of the main forward lobe.
+180FB             The 180-degree front-to-back ratio in dB of the array.
+HWCFB             The worst-case front-to-back ratio in dB in the horizontal or E-plane.
+VWCFB             The worst-case front-to-back ratio in dB in the vertical or H-plane.
+HSL               The ratio in dB of the main forward lobe to horizontal or E-plane strongest forward
+                  side lobe, where a forward sidelobe is within 90 degrees of the main forward lobe.
+VSL               The ratio in dB of the main forward lobe to vertical or H-plane strongest forward
+                  side lobe, where a forward sidelobe is within 90 degrees of the main forward lobe.
+HBW               The -3 dB beamwidth in degrees in the horizontal or E-plane.
+VBW               The -3 dB beamwidth in degrees in the vertical or H-plane.
+Z                 The feedpoint impedance in Ohms of the array in terms of resistance and
+                  reactance.
+SWR               The 50-Ohm SWR of the array
+
+Table 1.  A list of abbreviations used in subsequent tables of array data.
+

The patterns in Fig. 2 also serve another purpose. In our explorations of various antenna design, we shall present tabular data for each model. Each column heading will use an abbreviated entry. We may track those abbreviations by reference to the patterns in Fig. 2 and Table 1.

+

The list of abbreviations makes an implicit distinction between forward and rear minor lobes. Forward sidelobes include those within 90 degrees of the bearing of the main forward lobe, while rearward sidelobes include those more than 90 degrees away from the bearing of the main forward lobe. There will many instances where the distinction might be blurred. In the lower portion of Fig. 2, we find a lobe on the H-plane pattern that is almost at right angles to the lain forward lobe heading. Such lobes are normally not the strongest in either the forward or the rearward pairs of quadrants. Hence, we may be somewhat arbitrary in our classification of them, using the 90-degree mark as a guide.

+

When we place an array over real ground, the azimuth pattern for a horizontally oriented array varies little from the free-space E-plane pattern, even though there will be a "take-ff" or elevation angle of maximum radiation. However, the elevation pattern of the array over ground shows significant variations from the free-space H-plane pattern due to ground reflection effects. Often, we do not attend closely enough to the relationship between the free-space H-plane pattern and its counterpart over-ground elevation pattern.

+
+ +
+

Fig. 3 overlays half the E-plane pattern over the corresponding elevation pattern when the antenna is modeled at a height of 5 wavelengths (about 22' at 223.5 MHz). The pattern uses a step of 0.1 degrees between registration points to ensure capture of all of the lobes created by ground reflection effects. Overlaid on the real-ground pattern is half the free-space H-plane pattern.

+

The correspondence between the lobes of the two patterns becomes immediately apparent. As we change the antenna height, the thinner real-ground lobes will change position slightly, with a consequent change in their peak values. Nonetheless, they will generally fit within the free-space pattern section. The one exception is the fairly strong (-20 dB) lobe at right angles to the main forward lobe of the E-plane pattern. In the real-ground elevation pattern, this lobe normally shows additional suppression due to ground reflection effects. In the pattern shown, it is more than 30 dB down, that is, suppressed an additional 10 dB relative to the free-space pattern.

+

With this much preparation, we may begin our stroll through a series of arrays that show some progressive improvements in the suppression of all lobes except the main forward lobe.

+

The State of the Art or the Run of the Mill?

+
+ +
+

We should begin with a standard design on which to predicate all further work. I have selected a variation of a classic DL6WU design. Fig. 4 shows the edge and face profiles of the array. The dimensions appear in Table 2.

+ 
                       12-Element DL6WU Yagi Dimensions
+
+Element     Element Length          Cumulative Spacing      Individual Spacing
+            Inches      WL          Inches      WL          Inches      WL
+Reflector   25.398      0.480       -----       -----       -----       -----
+Driver      24.606      0.466       10.350      0.196       10.350      0.196
+Dir 1       22.490      0.426       14.227      0.269        3.877      0.073
+Dir 2       22.310      0.422       23.548      0.446        9.321      0.177
+Dir 3       22.042      0.418       34.673      0.657       11.125      0.211
+Dir 4       21.790      0.412       47.603      0.901       12.430      0.244
+Dir 5       21.564      0.408       62.099      1.176       14.496      0.275
+Dir 6       21.356      0.404       77.616      1.470       15.517      0.294
+Dir 7       21.192      0.402       93.917      1.778       16.301      0.308
+Dir 8       21.042      0.398       111.00      2.102       17.083      0.324
+Dir 9       21.090      0.396       128.85      2.440       17.851      0.338
+Dir 10      20.790      0.394       147.48      2.793       18.627      0.353
+
+Table 2.  Dimensions in inches and wavelengths of a DL6WU 12-element Yagi.  Dimensions in
+wavelengths are for 223.5 MHz.  Elements are 0.25" diameter aluminum.
+

Perhaps the last iteration of DL6WU designs appears in the RSGB book, The VHF/UHF DX Book, edited by Ian White, G3SEK. Chapter 7, by Guenter Hoch, DL6WU, provides guidelines for building beams of his design, beginning with a reflector-driver spacing of 0.200 wavelength and a driver-director1 spacing of 0.075 wavelength. The reason for the variance is two-fold. First, the design frequency for the array is 228.078 MHz. Second, a DL6WU array is inherently a very wide-band affair, and one may choose according to need any operating region within the overall passband. For further details on the wide-band facets of the DL6WU design, see "Appreciating DL6WU Wide-Band Long-Boom Yagi Design: Some Preliminary Notes."

+
+ +
+

Fig. 5 provides both wide-band and narrow-band SWR curves for the array as designed for the 222-225-MHz band. The 50-Ohm SWR is only 1.12:1 and 1.16:1 at the narrow-band edges. The wide- band curve shows a very interesting property: the existence of three SWR dips across the 25-MHz range between 2:1 SWR points. The SWR passband is over 10% of the median operating frequency of 227.5 MHz, close to the array design frequency. The deepest dip in SWR is in the narrow band chosen for this study, because the driver length was selected to minimize the 50-Ohm SWR. Similar adjustment of the driver in other parts of the operating passband would alter the depth of individual dips, although the 3 dips would remain.

+
+ +
+

The modeled gain and 180-degree front-to-back values for the array vary continuously across the operating passband. As shown in Fig. 6, the free-space gain rises continuously to a frequency of 234 MHz and then begins to fall more rapidly than it rose. The 180-degree front-to-back ratio has two major peaks, one between 222 and 223 MHz, the other between 235 and 236 MHz. Because the front-to-back ratio is an indicator of a major sidelobe of concern, the operating region of the array was placed in the frequency region where it is highest, even though the forward gain is a half-dB below its peak value.

+
+ +
+

In every wide-band Yagi, the current magnitude on Director 1, relative to the current magnitude on the driver, exceeds 1.0 for some portion of the operating passband. When this occurs, the first director is operating also as a secondary or slaved driver. In the case of the DL6WU design, the relative current magnitude exceeds 1.0 in two frequency regions, as shown in Fig. 7. Combined with the relative current magnitude curve is the SWR across the operating passband. Careful examination of the graph shows that at those points just after the relative current of director 1 exceeds 1.0, the SWR reaches a maximum (228 and 236 MHz). Likewise, when the relative current falls below 1.0, the array shows an SWR minimum (232 MHz).

+

The properties graphed for the 12-element DL6WU design on a 2.8 wavelength boom apply only to the specified 0.25" aluminum element diameter. Larger diameter elements may achieve higher gain levels overall, but will shift the operating curves as well. Within the 222-225-MHz amateur band, the detailed operating characteristics for the selected version appear in Table 3.

+ 
                  Operating Data for the 12-Element DL6WU Yagi
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    13.88  24.09   20.16  18.34   17.99  13.13  38.0   41.8  47.5-j 4.9 1.12
+223.5  14.12  22.95   21.73  19.54   18.14  13.38  37.2   40.8  52.0-j 0.6 1.04
+225    14.32  20.05   20.05  20.05   18.21  13.54  36.4   39.8  57.8+j 1.7 1.16
+
+Table 3.  Gain, sidelobe, and impedance data for the 12-element DL6WU Yagi from 222 to 225 MHz.
+

In the analysis of sidelobe performance, the key figures are the worst-case front-to-back ratios and the forward sidelobe ratios. DL6WU has noted that his designs are generally capable of 16-18 dB forward E-plane or horizontal sidelobe values, and the tables confirms this estimate. However, note that the H- plane forward sidelobe value is considerably worse, only a little over 13 dB down from the main forward lobe. For the rearward quadrants, the beam shows sidelobe performance to be better than 20 dB down in the E-plane and better than 18 dB down in the H-plane, reflecting the selection of the operating region within the frequency range at which the array displays better rearward performance.

+

You may correlate the tabulated values for 223.5 MHz with the patterns in Fig. 2 with respect to both the E-plane and the H-plane. At a height of 5 wavelengths above ground, the array shows the pattern of Fig. 3 at the mid-band frequency. The forward gain is 19.97 dBi at an elevation angle of 2.8 degrees. The worst-case sidelobe is the forward love at 48.7 degrees elevation, and its is 14.92 dB below the main forward lobe.

+

The DL6WU design is typical of long-boom Yagis with respect to sidelobe performance. although other designers have revised the arrangement of elements to achieve more gain (usually over a much narrower operating bandwidth, the sidelobe performance remains close to the levels in the classic DL6WU design. The question is whether we can do any better, and--if so--by what means.

+

OWA Yagi Sidelobe Performance

The first step in our efforts to suppress sidelobes will be focused on H-plane sidelobes. One Yagi design type has shown that inherent to the design parameters themselves is a significant reduction of E- plane sidelobes. In other words, the sidelobe reduction is not a matter of a series of ad hoc re- adjustments to a design. Instead, the reduction comes with the basic design, even though it was not initially recognized. +

The Optimized Wideband Antenna design emerged in a series of HF Yagis developed by WA3FET and NW3Z. Since these designs did not go beyond 8 elements for 10 meters, sidelobe performance never became a significant concern. Only when we extend the design principles to longer boom VHF and UHF designs does the inherent ability of the design concept to suppress E-plane sidelobes emerge.

+
+ +
+

Fig. 8 shows the profile of a 12-element version of the OWA Yagi for the 222-225-MHz band using 0.125" diameter elements. Table 4 lists the element dimensions for the model used in this study.

+ 
                         12-Element OWA Yagi Dimensions
+
+Element     Element Length           Cumulative Spacing       Individual Spacing
+            Inches       WL          Inches      WL           Inches      WL
+Reflector   26.898       0.509       -----       -----        -----       -----
+Driver      25.977       0.492        5.782      0.109         5.782      0.109
+Dir 1       24.334       0.461        8.859      0.168         3.077      0.059
+Dir 2       23.891       0.452       16.691      0.316         7.832      0.148
+Dir 3       23.937       0.453       26.781      0.507        10.090      0.191
+Dir 4       23.815       0.451       40.368      0.764        13.587      0.257
+Dir 5       23.150       0.438       56.880      1.077        16.512      0.313
+Dir 6       22.558       0.427       76.288      1.445        19.408      0.368
+Dir 7       22.097       0.418       96.413      1.826        20.125      0.381
+Dir 8       21.637       0.410       117.33      2.222        20.917      0.396
+Dir 9       21.177       0.401       138.11      2.615        20.780      0.393
+Dir 10      20.519       0.389       156.52      2.964        18.410      0.349
+
+Table 4.  Dimensions in inches and wavelengths of an OWA 12-element Yagi.  Dimensions in wavelengths
+are for 223.5 MHz.  Elements are 0.125" diameter aluminum.
+

The table will reveal something of the OWA design principles that distinguish it from ordinary wide- band designs. First, the reflector-to-driver and driver-to-director1 spacings are considerably smaller than in standard wide-band designs. The total spacing for these elements is less than 0.17 wavelength, compared to the 0.27 wavelength required by the DL6WU design. Second, directors 2 and 3 are almost the same length in this design. To achieve even wider bandwidth, these elements are often exactly the same length.

+

In the DL6WU design, the first director served as both a secondary driver and as a gain enhancing director. In the OWA, the first director serves more completely as a secondary driver, with the next 2 directors serving the purpose of isolating the first director and setting the passband. In many designs, OWA builders fit an additional director within the same overall boom length to achieve maximum bandwidth and to restore full theoretically possible gain levels without requiring the first director to function significantly in the increase of gain. The present design sacrifices some bandwidth in using 12 elements within a boom length only marginally longer than the DL6WU design.

+
+ +
+

Fig. 9 shows both wide-band and narrow-band SWR curves. The very low values of SWR within the 222-225-MHz band explain why the present design does not need to tap the full bandwidth capabilities of the OWA design concept. The wide sweep for 50-Ohm SWR reveals the degree to which the bandwidth has been contracted. With directors 2 and 3 the same length, even without an added director, the SWR curve around 217 MHz would show a distinct but broad second dip near the 1.1:1 level, with a slower increase in SWR as the frequency decreased. A fuller study of OWA design concepts and potentials is in preparation, but for the moment, we are interested in sidelobe suppression. Table 5 shows the results of turning to the OWA design.

+ 
                   Operating Data for the 12-Element OWA Yagi
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    14.34  24.65   24.53  22.61   27.85  18.12  36.8   40.4  47.5+j 6.1 1.14
+223.5  14.36  24.59   24.12  22.58   26.57  17.40  36.2   39.6  48.9+j 3.3 1.07
+225    14.24  23.08   23.08  21.72   24.97  16.40  35.4   38.8  43.6-j 4.2 1.18
+
+Table 5.  Gain, sidelobe, and impedance data for the 12-element OWA Yagi from 222 to 225 MHz.
+
+ +
+

The improvement in E-plane sidelobe suppression is immediately apparent, with the worst-case value nearly 25 dB below the main lobe. Fig. 10 shows--in the E-plane free-space pattern--the improvement, when we compare this figure to Fig. 2. Improving the E-plane sidelobe levels has a salutatory effect on the H-plane sidelobe levels, although the effect is only a 2-3 dB improvement. The OWA design principally controls the E-plane sidelobes via the lengths and spacings chosen for the elements from the reflector to the 2nd director.

+
+ +
+

When operating a Yagi over real ground, we discover that we should be concerned not only with the strength of H-plane sidelobes, but as well with their direction relative to the main lobe bearing. Fig. 11 overlays the free-space H-plane pattern atop an elevation pattern with the Yagi at a height of 5 wavelengths above average ground. The forward and rearward elevation lobes track well with the outline of the free-space pattern. However, we may note that the sidelobes in the most vertical directions have cancelled, leaving the worst-case sidelobe better than 20 dB down from the main lobe and its secondary forward elevation lobes.

+
+ +
+

For reference, we may note an additional difference between the OWA Yagi design and other wide-band designs, such as those by DL6WU. The OWA design shows a single peak of both the gain and the 180-degree front-to-back curves, as shown in Fig. 12. Indeed, with the DL6WU design, the front-to- back curve multiple peaks are periodic and shift in frequency relative to the gain peak as we change the number of elements. For OWA designs of any length, we may bring the gain and front-to-back peak into much closer coincidence. However, further design work on pure OWA designs must await another occasion. We still have far to go in suppressing both E-plane and H-plane sidelobes.

+

Adding Reflectors

Adding a pair of reflector elements or replacing the single normal Yagi reflector with a plane of reflectors is popular among some designers. However, NEC-4 models of the resulting designs rarely shows any significant performance improvements over the traditional DL6WU and other single reflector designs. Nevertheless, it seemed appropriate to see if one might effect further sidelobe suppression on the OWA design by careful placement of additional reflectors. In the process, one should not unduly disturb other performance characteristics of the design, especially its 50-Ohm SWR curve. +
+ +
+

In fact, adding 2 reflectors--one above and one below the plane of other elements--did improve performance by a noticeable amount. Fig. 13 shows the edge and face profiles of the antenna that emerge--in 14 elements. We may notice that the added reflectors are fairly widely spaced from the original reflector and to the rear of the original reflector. Table 6 provides dimensions to show a. that the original OWA design remains intact and b. that the added reflectors are not necessarily where they appear in standard Yagi designs. Since this design exercise aims at establishing some principles of sidelobe suppression, the structural practicality of the design is still subject to future evaluation.

+ 
             14-Element OWA Yagi (With Added Reflectors) Dimensions
+
+Element     Element Length           Cumulative Spacing       Individual Spacing
+            Inches       WL          Inches      WL           Inches      WL
+Reflector 1 30.708       0.582       -1.181      -0.22        -1.181      -0.22
+Reflector 2 30.708       0.582       -1.181      -0.22        -1.181      -0.22
+Reflector 3 26.898       0.509       -----       -----        -----       -----
+Driver      25.977       0.492        5.782      0.109         5.782      0.109
+Dir 1       24.334       0.461        8.859      0.168         3.077      0.059
+Dir 2       23.891       0.452       16.691      0.316         7.832      0.148
+Dir 3       23.937       0.453       26.781      0.507        10.090      0.191
+Dir 4       23.815       0.451       40.368      0.764        13.587      0.257
+Dir 5       23.150       0.438       56.880      1.077        16.512      0.313
+Dir 6       22.558       0.427       76.288      1.445        19.408      0.368
+Dir 7       22.097       0.418       96.413      1.826        20.125      0.381
+Dir 8       21.637       0.410       117.33      2.222        20.917      0.396
+Dir 9       21.177       0.401       138.11      2.615        20.780      0.393
+Dir 10      20.519       0.389       156.52      2.964        18.410      0.349
+
+Table 6.  Dimensions in inches and wavelengths of an OWA 14-element Yagi (with added out-of-plane
+reflectors).  Dimensions in wavelengths are for 223.5 MHz.  Elements are 0.125" diameter aluminum.  The
+reflectors are 11.811" or 0.224 wavelength above and below the plane of the remaining elements.
+
+ +
+

The placement of the added reflectors resulted from the combined aim of retaining the OWA performance and improving the sidelobe suppression. The resulting positions over 11" out-of-plane for each reflector and nearly 2" behind the original reflector achieved the best compromise between the two goals. As well, the reflectors are nearly 4" longer than the original reflector. Fig. 14 (for comparison with Fig. 9) provides both narrow-band and wide-band 50-Ohm SWR curves to confirm the retention of the OWA operating characteristics.

+

The added reflectors result in two improvements over the basic OWA design. First, the rearward radiation is reduced so that the 180-degree and worst-case front-to-back ratios are both better than 30 dB. Second, the H-plane sidelobes are reduced another 2 dB, averaging 19 dB below the main forward lobe. Table 7 provides the performance data from the models.

+ 
                   Operating Data for the 14-Element OWA Yagi
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    14.44  31.25   31.25  25.93   28.09  20.05  36.8   40.8  49.4+j 6.8 1.15
+223.5  14.46  34.71   34.16  26.19   26.64  19.20  36.2   40.0  51.2+j 3.4 1.07
+225    14.34  34.24   31.41  26.66   24.88  18.03  35.6   39.4  45.5-j 5.3 1.16
+
+Table 7.  Gain, sidelobe, and impedance data for the 14-element OWA Yagi from 222 to 225 MHz.
+
+ +
+

Clearly, the reflectors did not add significantly to the gain, with an average increase of 0.1 dB. However, rearward lobes are more effectively suppressed, with even the worst-case H-plane front-to-back ratio showing an added 3-4 dB improvement. Fig. 15 shows the free-space E-plane and H-plane patterns, with Fig. 16 comparing the free-space H-plane pattern with the elevation pattern of the antenna when we place it 5 wavelengths above average ground. The latter figure is interesting because it shows that all sidelobes outside the free-space main lobe envelope to be more than 30 dB down--except for 2 lobes in the 70-80-degree elevation range that are only about 23 dB down.

+
+ +
+

The addition of 2 reflectors has improved the sidelobe performance of the Yagi design, especially to the rear. However, we have yet to break the 20-25 dB barrier with free-space H-plane forward sidelobes. We need another strategy if we are to make further improvements.

+

The Half-Wavelength Stack

We often think of stacking two or more Yagis solely as a means of obtaining more gain. Therefore, we calculate the array gain and adjust the stacking distance to obtain maximum in-phase power gain. The high the gain of the individual array, the wider the stacking space. Then we go back and adjust the designs to improve the front-to-back ratio, if our stacking efforts has degraded that figure. +

We may also use stacking to control--indeed, to suppress--H-plane sidelobes. Two arrays of any sort--so long as they are each planar--tend to cancel and suppress most radiation in directions at right angles to the plane of the original arrays, if the arrays are very close to 1/2 wavelength apart. Since we are seeking a method to effect further reductions in the H-plane sidelobes, let's consider stacking two reflector-augmented OWA Yagis.

+

For our exploration of sidelobe suppression, I shall consider the two Yagis to form one array, regardless of the structural questions left unanswered. We shall not obtain the maximum added gain by our stacking efforts. In fact, the gain will only be about 1.3 dB better than an individual reflector- augmented OWA Yagi (15.7 vs. 14.4 free-space gain at 223.5 MHz). However, gain is not our goal.

+
+ +
+

Fig. 17 shows the two Yagis set into the stack. Two of the added reflectors almost touch, but their close proximity creates no problems in array performance. The main Yagi planes are about 26.4" apart.

+ 
                   Operating Data for the 14-Element OWA Yagi
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    15.77  34.16   31.59  34.16   24.36  29.16  33.0   31.2  48.2+j 8.2 1.19
+223.5  15.69  46.28   29.85  33.84   23.21  28.19  32.8   31.0  51.5+j 3.3 1.07
+225    15.48  36.65   27.99  32.19   21.75  26.75  33.0   31.0  44.0-j 6.9 1.22
+
+Table 8.  Gain, sidelobe, and impedance data for the 2 14-element OWA Yagi stack from 222 to 225 MHz.
+

We may forego the SWR graphs because the 50-Ohm curves for each Yagi are so similar to those for the independent arrays. I shall assume that the arrays are fed in accord with standard methods to obtain the perfect in-phase feed presumed by the model.

+
+ +
+

Table 8 shows the improvements that we have obtained in the H-plane sidelobe values. Both the worst-case H-plane front-to-back ratio and the strongest H-plane forward sidelobe are down more than 30 dB from the main forward lobe. However, as both the table and Fig. 18 reveal, we have lost ground with respect to the E-plane worst-case front-to-back ratio and the forward sidelobe. Indeed, the horizontal forward sidelobe has suffered most from stacking, compared to its value when a product of a single reflector-augmented OWA Yagi.

+
+ +
+

To gain some appreciation for what we have accomplished with the stack, examine Fig. 19. The graphic overlays the free-space H-plane pattern atop the elevation pattern of the stack, with the bottom level 5 wavelengths above average ground. Every elevation lobe that does not fall within the envelope of the main forward H-plane lobe is more than 30 dB down from maximum forward signal strength. Unfortunately, the azimuth pattern for this array over real ground is identical to the free-space pattern in Fig. 18. Hence, much of what we gain in the vertical sidelobe department is lost in the growth of the horizontal forward sidelobes.

+
+ +
+

To place these remarks in perspective, compare Fig. 20 to Fig. 1. The 3-dimensional free-space pattern somehow seems smaller in the new figure than in the one for the DL6WU Yagi. However, maximum forward signal strength is positioned identically in both cases. The side and rear lobes are very much smaller (meaning lower in strength) for our latest design than for the one which we set forth as a standard. So, we have made progress after all.

+

Unless one had to reduce the sidelobes in one plane more than in the other, there is little to choose (apart from main lobe forward gain) between the single reflector-augmented OWA Yagi and the stack of 2. Given the greater ease of constructing a single such Yagi, it is likely that it represents the best that we have accomplished so far. However, we are still short of our ultimate goal of reducing all sidelobes by 30 dB relative to the main forward lobe. We are not too far way, but the question remains as to whether we can do better.

+

I must confess at this point that I have run out of Yagi strategies. An improved Yagi design may exist or come into being to achieve the sidelobe suppression goal, but I have not yet found it. However, I have found an interesting alternative. Since this is a design exploration only and since gain is not our goal, the alternative array design is worth investigating.

+

The LPDA

Although few weak-signal VHF and UHF operators even consider the log periodic dipole array (LPDA) as a candidate for service, we should not overlook this antenna type in the search for an array that will yield further reductions in sidelobe strength. It is possible to design such arrays, although they will generally require more elements for a given boom length than we are used to using. and their properties are interesting. +

As a frame of reference, the 12-element DL6WU Yagi was 148" long, while the 12-element OWA design was 156" long--with the reflector-augmented version about 2" longer still. These boom lengths will define the general range of LPDAs that we might consider for the 222-225-MHz band. As well, the DL6WU antenna had a free-space gain of about 14.1 dBi, while the OWA gain was about 14.4 dBi. We shall have occasion to return to these numbers as we explore LPDA possibilities.

+

The design of an LPDA for monoband service is subject to a number of considerations, the most basic of which are the selection of Tau and Sigma. Tau defines the rate of change of element length and element spacing, while Sigma defines the initial element length to initial element spacing onto which we apply the rate of change. We work from the rearmost element--about 2% longer than a dipole at the lowest defined frequency and work toward the front end of the array, which we set for a frequency from 1.3 to 1.6 times the highest frequency used. A Tau value of about 0.97 is the highest recommended value for an LPDA, and its associated ideal sigma value is about 0.18.

+

For monoband use, we can also add one or more parasitic elements to improve performance. A parasitic reflector behind the rear-most LPDA element sometimes helps--but not always. More universally, one or two parasitic directors ahead of the forward-most LPDA element usually improves either array gain or pattern characteristics. For more detailed information on LPDA design, see LPDA Notes Vol. 1 and LPDA Notes Vol. 2 on the Books Page.

+

For this exercise, I designed an LPDA that offered promise of gain the approached Yagi levels. LPDAs have beamwidths that are wider in both the E-plane and H-plane than most Yagis of similar boom length. Therefore, we should not expect to achieve a free-space gain over 14 dBi. However, something in the range of 13.2 to 13.4 dBi is feasible. For reasons that will become apparent, I lowered the gain for subsequent design experiments.

+

The First LPDA Series

The first LPDA design set is based on an 18-element basic log periodic with the specified Tau and sigma values. 18-LPDA elements require only about 127" of boom length. Therefore, I supplemented the basic LPDA with a single parasitic director at 150" and later with two directors, the furthest being at a boom length of 163". No reflector appeared to aid array performance using the 18-element basic design. +
+ +
+

Fig. 21 shows the general outline of the LPDA, which remained constant throughout the modeling trials. The single director would hold a position about halfway between the two directors of the later model. Table 9 provides a composite set of dimensions for the three trial array designs.

+ 
                18-Element LPDA (With Added Directors) Dimensions
+
+Element     Element Length           Cumulative Spacing       Individual Spacing
+            Inches       WL          Inches      WL           Inches      WL
+1           26.182       0.496        -----      -----         -----      -----
+2           25.398       0.481        9.425      0.178         9.425      0.178
+3           24.636       0.467       18.569      0.352         9.144      0.174
+4           23.896       0.453       27.438      0.520         8.869      0.168
+5           23.180       0.439       36.041      0.682         8.603      0.162
+6           22.484       0.426       44.385      0.840         8.344      0.158
+7           21.181       0.413       52.480      0.994         8.095      0.154
+8           21.156       0.401       60.331      1.142         7.851      0.148
+9           20.520       0.389       67.947      1.287         7.616      0.145
+10          19.905       0.377       75.334      1.427         7.387      0.140
+11          19.449       0.368       82.500      1.562         7.166      0.135
+12          19.055       0.361       89.481      1.694         6.981      0.132
+13          18.661       0.353       96.193      1.822         6.712      0.128
+14          18.268       0.346       102.73      1.945         6.537      0.123
+15          17.874       0.338       109.08      2.066         6.357      0.121
+16          17.480       0.331       115.23      2.182         6.150      0.115
+17          17.087       0.324       121.20      2.295         5.970      0.113
+18          16.693       0.316       126.99      2.405         5.790      0.110
+Single-Director model
+Dir 1       18.000       0.341       150.00      2.840        23.010      0.435
+Double-Director model
+Dir 1       16.142       0.306       145.67      2.758        18.680      0.353
+Dir 2       14.960       0.283       163.39      3.094        17.720      0.336
+
+Table 9.  Dimensions in inches and wavelengths of the set of 18-element LPDAs (with and without added
+directors).  Dimensions in wavelengths are for 223.5 MHz.  Elements are 0.125" diameter aluminum.  The
+phasing line connecting the LPDA elements has a characteristic impedance of 60 Ohms.
+

The taper of the element lengths is far more severe than we find in Yagi designs. Essentially, the combination of mutual element coupling and phased feed makes the LPDA largely a director-driven array, with significant current levels on all elements forward of the one nearest resonance. Because each forward element has two power sources, the lengths do not correspond to those typical of parasitic Yagi directors.

+ 
      Table 10 summarizes the data for the LPDA alone, that is, for the 18-element array.
+
+                     Operating Data for the 18-Element LPDA
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    13.22  33.46   33.46  32.96   35.73  27.35  42.2   48.0  55.1-j 3.9 1.13
+223.5  13.22  34.86   34.84  32.00   33.90  25.75  42.2   48.0  55.6-j 4.0 1.14
+225    13.19  32.38   32.38  30.80   32.32  24.30  42.4   48.2  56.7-j 5.0 1.17
+
+Table 10.  Gain, sidelobe, and impedance data for the 18-element LPDA from 222 to 225 MHz.
+
+ +
+

We shall examine the data in tabular order. Gain, of course, is down from the Yagis by about 1 dB. The rearward lobes, as shown in both the E-plane and H-plane values, is outstanding. A glance at Fig. 22 will confirm the performance. Indeed, one of the chief motivations for any use of an optimized LPDA is the outstanding rearward performance. The E-plane forward sidelobes are more than 30 dB down from the main forward lobe. However, the H-plane sidelobes--while superior to all of the Yagis when a stack is not used--are still less than 30 dB down from the main forward lobe.

+

The beamwidth of the LPDA in both planes is wider than those of the Yagis--about 6 degrees in the E-plane and 8 degrees in the H-plane. When translated into 3-dimensional terms, the added beamwidth shows clearly why the LPDA cannot match the Yagi for raw forward gain. Nevertheless, we have effected improvements in the sidelobe characteristics of the array, when compared to the Yagis. Therefore, further experimentation seems in order.

+

The first experiment is to add a single parasitic director, with its length and spacing determined by our ability to improve performance overall--even if the improvement is slight. Table 11 summarizes the results.

+ 
    Operating Data for the 18-Element LPDA With a Single Parasitic Director
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    13.38  36.75   30.07  28.71   35.63  28.72  41.6   47.0  52.9-j 4.7 1.11
+223.5  13.39  39.06   30.78  28.87   33.82  26.80  41.6   47.0  53.3-j 2.8 1.09
+225    13.38  30.78   30.46  28.16   32.57  25.46  41.6   47.2  55.9-j 2.0 1.13
+
+Table 11.  Gain, sidelobe, and impedance data for the 18-element LPDA with a single parasitic director
+from 222 to 225 MHz.
+

Although we have improved the gain by nearly 0.2 dB and preserved the 180-degree front-to-back ratio, the added parasitic director has diminished the rearward H-plane lobe suppression by about 4 dB. The increased gain stems largely from the decrease in beamwidth by 1 degree in both planes. Although the H-plane rearward performance decreased, we do see a marginal increase in the suppression of H- plane forward sidelobes.

+
+ +
+

Fig. 23 reveals something of the reason for decreased rearward performance: the lobes have become stronger but narrower in beamwidth. Although the patterns are for 223.5 MHz, the tables should make clear the fact that LPDA results are very closely grouped, and we can expect no changes in performance at the band edges.

+

The use of a single director yielded mixed results in terms of a composite evaluation of all performance categories. Hence, I undertook a second design exercise and replaced the single director with a pair of directors. Note in the dimensions table how different the lengths of these directors are relative to the single director. Table 12 provides the resulting performance data.

+ 
        Operating Data for the 18-Element LPDA With 2 Parasitic Directors
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    13.38  30.50   30.50  30.50   bulge  29.36  41.6   47.2  55.6-j 5.1 1.15
+223.5  13.40  34.72   30.72  34.72   34.37  27.33  41.6   47.0  54.9-j 5.3 1.15
+225    13.38  37.85   36.71  33.43   33.03  25.87  41.8   47.2  55.1-j 5.3 1.15
+
+Table 12.  Gain, sidelobe, and impedance data for the 18-element LPDA with two parasitic directors from
+222 to 225 MHz.
+

The additional director does nothing to increase gain. However, it restores the H-plane rearward sidelobe suppression to above 30 dB. The H-plane forward sidelobe suppression continues to increase, but it still falls a little shy of the 30-dB goal. The entry in the E-plane forward sidelobe column labeled "bulge" indicates a slight departure from a smooth forward lobe curve, but without the distinct fall-rise-fall (or rise-fall-rise) pattern that would enable the identification of a distinct lobe. The bulge nowhere exceeds a -35 dB level.

+
+ +
+

Fig. 24 shows the free-space E-plane and H-plane patterns for the dual-director LPDA. Of special note is the shrinkage of the rearward lobes into a region of very well-controlled behavior. When translated into use above ground, the LPDA shows further improvement in vertical sidelobe suppression. As shown in Fig. 25, only a single vertical lobe outside the main forward envelope crosses the -30 dB line--and just barely. With respect to sidelobe suppression, the dual-director LPDA provides the best performance so far achieved.

+
+ +
+

Nonetheless, as good as the dual director LPDA appears to be with respect to sidelobe suppression, it still falls short of the ultimate goal. A somewhat different design strategy appears to be in order.

+

The Second LPDA Series

Whether we are talking about a Yagi or an LPDA, sidelobes appear and grow as we push the array length--and hence, the forward gain--relative to the number of elements in the array and their interaction. If we are willing to settle for less gain from an array, we may be able to further suppress the sidelobes. A second LPDA design series provides a sample. It is only a sample and does not constitute a reading of the border line as to when sidelobes of any given strength appear or disappear. +
+ +
+

Fig. 26 shows the outline of a 17-element LPDA using the same values of Tau and sigma, but with a slightly lower bottom frequency: 200 vs. 230 MHz for the 18-element array. As a result, the gain in the 222-225-MHz range drops by 0.9 dB without the use of parasitic elements. The figure shows that in this particular design exercise, both a parasitic reflector and a parasitic director proved useful in restoring some of the gain (about 0.4 dB) and in shaping the remaining operating characteristics of the array.

+

Note that the reflector is shorter than the longest LPDA element, while the director is longer than the shortest LPDA element. The seemingly odd lengths emerge since we are tailoring the performance characteristics within a small region of the overall performance capabilities of even this narrow-band LPDA.

+

Later, we shall add a second director to the array. To save space, Table 13 provides dimensions for both versions of the LPDA. As we did with the Yagis, when adding non-standard reflectors, we shall list the reflector dimension as a negative number relative to the cumulative array length. The boom length for the single director version is 145" and for the dual-director version is 164".

+ 
           17-Element LPDA (With Added Parasitic Elements) Dimensions
+
+Element     Element Length           Cumulative Spacing       Individual Spacing
+            Inches       WL          Inches      WL           Inches      WL
+Reflector   27.000       0.511       -7.000
+1           28.056       0.531        -----      -----         -----      -----7
+2           27.212       0.515       10.100      0.191        10.100      0.191
+3           26.394       0.500       19.898      0.377         9.798      0.186
+4           25.606       0.485       29.402      0.557         9.504      0.180
+5           24.834       0.470       38.621      0.731         9.219      0.174
+6           24.086       0.456       47.563      0.901         8.942      0.170
+7           23.370       0.443       56.236      1.065         8.673      0.164
+8           22.670       0.429       64.650      1.224         8.414      0.159
+9           21.984       0.416       72.811      1.379         8.161      0.155
+10          21.322       0.404       80.728      1.529         7.917      0.150
+11          20.686       0.392       88.406      1.674         7.678      0.146
+12          20.062       0.380       95.855      1.815         7.449      0.141
+13          19.465       0.369       103.08      1.952         7.225      0.137
+14          18.882       0.358       110.09      2.085         7.010      0.133
+15          18.315       0.347       116.89      2.213         6.800      0.128
+16          17.764       0.336       123.48      2.338         6.590      0.125
+17          17.228       0.326       129.88      2.459         6.400      0.121
+Director    18.300       0.347       138.00      2.613         8.120      0.154
+Double-Director model
+Dir 2       18.000       0.341       157.00      2.973        19.000      0.360
+
+Table 13.  Dimensions in inches and wavelengths of the set of 17-element LPDAs (with added parasitic
+elements).  Dimensions in wavelengths are for 223.5 MHz.  Elements are 0.125" diameter aluminum.  The
+phasing line connecting the LPDA elements has a characteristic impedance of 60 Ohms.
+

As with all LPDAs, the operating bandwidth--even for a monoband design--tends to be very wide. Hence, we may ignore 50-Ohm SWR curves. The question we may put to the version of the LPDA with a single reflector and a single director is how well the array performance with respect to potential sidelobes. Part of the answer appears in Table 14.

+ 
 Operating Data for the 17-Element LPDA With a Parasitic Reflector and Director
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    12.66  32.93   32.14  31.37   39.64  30.31  44.2   51.4  51.2+j 0.1 1.02
+223.5  12.71  32.13   32.13  32.17   41.54  31.91  44.2   51.2  53.7+j 1.2 1.08
+225    12.75  30.59   30.59  31.66   40.94  30.57  44.0   50.8  57.1+j 1.0 1.14
+
+Table 14.  Gain, sidelobe, and impedance data for the 17-element LPDA with a parasitic reflector and
+director from 222 to 225 MHz.
+
+ +
+

All forward and rear sidelobes are down from the main forward lobe by at least 30 dB, with the forward sidelobes averaging about 40 dB down. Fig. 27 displays these free-space figures as E-plane and H-plane patterns. The cost for obtaining this performance, of course, is the forward gain, which is about 1.7 dB below the best of the single-bay Yagis that we examined. As well, the array has 7 more elements than the 12-element Yagis explored earlier. As well, the beamwidth is significantly wider in both planes than the beamwidth of the higher-gain LPDAs, which was wider still than the beamwidth of the Yagis. Whether the added forward beamwidth holds an advantage or disadvantage for a given type of operation will be a user judgment.

+
+ +
+

We may recover the gain relative to a single bay Yagi by creating a half wavelength stack of 2 of the 17-element LPDAs. At 223.5 MHz, the two arrays will be separated by 26.4046". Fig. 28 provides a side-view profile of the array, which now has 38 elements. When we stacked 2 OWA Yagis, we obtained improvements in the H-plane sidelobe performance, but lost performance in the E-plane sidelobes. However, since the E-plane sidelobes of the LPDA are down by 40 dB, perhaps we may escape an noticeable deterioration with respect to these sidelobes. Table 15 tells the story.

+ 
Operating Data for a Stack of 17-Element LPDAs With a Parasitic Reflector and Director
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    14.28  36.18   30.87  31.96   30.69  36.52  40.2   36.8  53.7+j 3.5 1.10
+223.5  14.32  32.44   31.55  32.44   bulge  bulge  40.2   36.8  58.7+j 2.9 1.18
+225    14.34  30.81   30.81  30.81   bulge  bulge  40.2   36.6  63.2-j 0.9 1.26
+
+Table 15.  Gain, sidelobe, and impedance data for a stack of 17-element LPDAs, each with a parasitic
+reflector and director from 222 to 225 MHz.
+
+ +
+

The gain improvement is clear from the table. The E-plane forward sidelobes have grown by about 9 dB relative to the forward main lobe. However, they appear as mostly "bulges, that is, indistinct aberrations in the normally smooth main forward lobe curve, rather than as distinct lobes. Fig. 29 shows the shape of these bulges at 223.5 MHz. The E-plane bulge is wholly below -30 dB, which the H-plane bulge is below 35 dB. The stack of two LPDAs has maintained the goal of -30 dB for all sidelobes.

+

The E-plane beamwidth has shrunk by 2 degrees, but the H-plane beamwidth has decreased by nearly 15 degrees. Thus, stacking arrays at a half wavelength spacing represents one way of controlling the relative beamwidths for a given antenna design.

+
+ +
+

When we added a second [parasitic director to the 18-element LPDA, we gained a modest amount of gain relative to the same LPDA with a single director. We may wonder if a similar single-bay improvement is possible with the 17-element LPDA, with its reflector and single director. Fig. 30 shows the edge and face profiles of the resulting array. All of the elements in the original augmented LPDA remain intact, and we simply place the new director at an optimal distance ahead of the existing element set. Table 16 provides us with the resulting modeled performance figures.

+ 
Operating Data for the 17-Element LPDA With a Parasitic Reflector and 2 Directors
+
+Freq   Gain   180FB   HWCFB  VWCFB   HSL    VSL    HBW    VBW   Z          SWR
+222    12.84  31.87   31.87  31.87   54.26  33.81  43.6   50.4  51.8-j 2.4 1.06
+223.5  12.91  32.99   32.99  32.99   bulge  35.28  43.4   50.0  52.1-j 1.2 1.05
+225    12.96  31.22   31.22  31.21   bulge  31.22  43.2   49.8  53.9+j 0.5 1.08
+
+Table 16.  Gain, sidelobe, and impedance data for the 17-element LPDA with a parasitic reflector and 2
+directors from 222 to 225 MHz.
+
+ +
+

In fact, we gain very little--perhaps 0.2 dB gain. The sidelobe performance improves marginally, but does create a quandary. As the H-plane free-space pattern in Fig. 31 shows, there are lobes at about -35 dB at nearly a perfect 90-degree angle relative to the main forward lobe. I have chosen to call these forward sidelobes, even though their peaks occur just rearward of the right-angle position. In all such matters, it usually pays to acknowledge such lobes, even if the terms of tabulating data would allow us to ignore them.

+
+ +
+

When we place the antenna 5 wavelengths above average ground, we acquire a bonus: the upward sidelobes diminish even more than they do in free space. Fig. 32 illustrates the bonus. The strongest upward sidelobe not within the overlaid free-space forward and rearward main lobes is about 40 dB down from the maximum signal strength of the array. However, the main forward lobe set shows the effects of the wider beamwidth relative to Yagi performance in the strength of the upper forward lobes within the free-space envelope.

+
+ +
+

The lower gain of the second series of LPDA designs sacrifices gain for pattern purity. Fig. 33 provides a 3-dimensional free-space plot of the final LPDA design at 223.5 MHz. A casual comparison of this pattern with those in Fig. 1 and Fig. 20 will show the degree to which we have been able to suppress the sidelobes that infest array designs that strive for maximum gain with the minimum number of elements for a given boom length. Every sidelobe is down by more than 30 dB relative to the maximum forward gain of the array.

+

Conclusion

The design exercise has explored how far we may suppress both forward and rearward sidelobes. The LPDA offers--when we do not press its gain potential too far--the cleanest pattern of all. Indeed, in the HF region, commercial SW broadcasters have used very large LPDAs covering their entire spectrum of operating frequencies because the design directs so little of the transmitted energy in any direction other than the desired one. Whether such designs are useful for VHF and UHF monoband weak-signal work is moot, since we have not explored any of the critical factors that arise when we transform a paper design into an actual antenna that we must build, tune, and support. +

Perhaps the design with the best sidelobe performance for the weight is the 12-element OWA. It barely misses the H-plane sidelobe goal, while providing excellent E-plane sidelobe performance. Its gain is competitive with the gain of DL6WU and similar wide-band Yagis of similar boom length. Moreover, with due care, we can increase the boom length and the number of elements while preserving most or all of the sidelobe suppression. The OWA sidelobe suppression occurs largely as a function of the basic cell consisting of the reflector, driver, and first three directors. Although we can easily ruin the sidelobe suppression by misplacing the forward-most director, we can as easily retain the level of sidelobe suppression by carefully sizing and placing each new set of directors. However, for each added director, we shall have to adjust the length and position of both the new director and the one immediately behind it. Hence, the task is not quite so simple as adding directors to a DL6WU design.

+

The question that we have not addressed in this exploration of sidelobe suppression is the dividing line between advantageous and superfluous sidelobe reduction. That issue lies beyond the realm of both antenna design and antenna modeling and may vary from one weak-signal activity to another. A further matter that we have still to explore is the effect upon sidelobes of angling arrays away from a plane parallel to the earth's surface. Of course, the fewer and smaller the sidelobes, the less we may need to worry about the effects of pointing an array into space, other than the consequences for the main forward lobe.

+

Indeed, there are numerous other directions to explore. If we are truly serious about achieving single lobe performance, we might try some backyard replications of quadrifilar source antennas and Aricebo-type reflectors. However, such exercises remain as future work. For now, within the realm of planar arrays composed of linear elements, we have surveyed enough territory to show that we may go much further than hitherto appreciated toward the reduction of sidelobes in long-boom amateur antennas.

+
+ +
+

Updated 04-27-2002. © L. B. Cebik, W4RNL. First presented to the South-East VHF Society, April 27, 2002, in Oak Ridge, TN. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

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+

Topics: VHF / UHF, Yagi


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Sidelobe Attenuation and Suppression

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L. B. Cebik, W4RNL

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In 2002, I presented a preliminary study of side-lobe suppression to the Southeastern VHF Society, ( Long-Boom Yagi Sidelobe Suppression ). At the time, I had only developed the OWA series of long-boom Yagis to 12 elements. This note is an extension of that work with a couple of special slants. First, we shall use a 20-element OWA Yagi as our subject antenna. In fact, the design is a bit of an improvement over earlier versions of the array, although it still does not--as a design decision--match the gain of some Yagis of more standard design. Second, we shall look not only at the E-plane sidelobes, but also at the H-plane sidelobes. Finally, we shall examine the difference between sidelobe attenuation and sidelobe suppression as a gauge of work yet to be done.

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Let's first examine the idea of a sidelobe. Fig. 1 shows the sidelobe structure for a pair of very different Yagi designs: a somewhat standard 20-element array and a 20-element OWA Yagi. Despite the differences in the strength of the sidelobes, each Yagi shows (on each side of the boom or centerline) 6 forward and 6 rearward sidelobes. In standard designs, the strength of the sidelobes tends to decrease as the angle between the main lobe and the sidelobe increases. Hence, the strongest forward and rearward lobes tend to be those most closely aligned with the main forward or rearward lobe.

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The rearward lobes can be tricky to count sometimes, because the main rearward lobe can undergo periodic increases and decreases in strength as the array operating frequency changes. (This phemonenon also makes the 180-degree front-to-back ratio an unreliable indicator of rearward array performance. Comparing the 180-degree and worst-case front-to-back ratios provides a more adequate evaluation.) Perhaps the most troublesome case is the "squared-off" rear main lobe, which usually is a combination of the main lobe and the first rearward sidelobes.

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Sidelobes tend to be restricted to end-fire arrays that depend upon the relative current magnitudes and phase angles on the individual elements. Planar and corner reflector arrays--by way of contrast--rarely have any forward sidelobes at any gain level and have few in the rearward direction. Log periodic dipole arrays (LPDAs) tend to have forward lobes that are free of sidelobes if they are well designed with adequate element densities. Sidelobes find their best home in Yagi and related parasitic arrays.

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The number of forward Yagi sidelobes is a function of boom length. Hence, we normally do not encounter forward sidelobes until a Yagi has about 7 elements or so, that is, as the boom length approaches 1 wavelength. The samples in Fig. 1 both use booms that are 6 wavelengths. The question that piques my curiosity is whether the tendency is inevitable for all Yagis or whether it may be possible to eliminate one or more sidelobes.

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Classic long-boom VHF/UHF Yagi designs have tended to overlook sidelobe reduction in favor of achieving the maximum gain of which a given boomlength may be capable. Hence, most of the designs have first forward sidelobes that are only about 16-19 dB below the strength of the main forward lobe. A number of investigators, such as VK3AUU and N4FG, have developed Yagis with a far higher level of sidelobe strength reduction, especially in the E-plane. The attenuation as reached front-to-sidelobe ratios of 20-25 dB.

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The right side of Fig. 1 does allow us to make a distinction between sidelobe attenuation and sidelobe suppression. The general idea of sidelobe attenuation includes the reduction in sidelobe strength. Each sidelobe may not reduce is strength in exact proportion to the other sidelobes, but each sidelobe remains a distinct lobe marked by a clear reduction in strength on either side of the lobe bearing. In contrast, sidelobe suppression involves the elimination or near elimination of a sidelobe so that there is at most a reduction in strength on only one side of the detectable peak of strength. In Fig. 1, forward sidelobe 6 is an example of a sidelobe that is suppressed to a mere slight bulge. In many long-boom Yagi designs, when operated at the upper limit of their passband range, the first forward sidelobe will become a "bulge" rather than a distinct sidelobe. A second feature of sidelobe suppression is that we begin to lose the distinctness of the individual sidelobes. Sidelobes 3 and 4 show signs of merging into a single sidelobe, although the merger is incomplete.

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Because some Yagi designs tend to favor sidelobe attenuation and approach sidelobe suppression, they raise an interesting question: to what degree are Yagi sidelobes capable of suppression rather than just attenuation? Of course, the subject has only restricted interest. First, it is applicable only to those whose operations involve long-boom Yagis. Within that group, some operators prefer to have sidelobes to detect off-axis activity. However, there remains a group for whom insensitivity to off-axis noise is desirable. However, even if there were not such a group, curiosity is enough to attract my attention.

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The 20-Element 2-Meter OWA Yagi

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The OWA (Optimized Wideband Array) Yagis, first presented by NW3Z in short-boom HF versions, showed considerable promise in the pursuit of sidelobe reduction. As I extended the boomlength and number of elements, I eventually arrived at a length that presents a challenging case: 20 elements on a 6 wavelength boom. The latest incarnation of the design appears in the following table of dimensions. For the moment, ignore the elements marked Reflector a and Reflector b. We shall add those elements later. The regular OWA Yagi design includes only the normal reflector, the driver, and the 18 directors.

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+Dimensions of 20-Element OWA Yagi
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+Notes
+1.  Element diameter: 0.1875" (3/16" or 4.76 mm)
+2.  Versions
+       a.  Regular:  Ignore Reflector a and Reflector b; Boomlength 6.08 WL
+       b.  With added Reflectors:  Include Reflectors a and b; Boomlength 6.30 WL
+3.  For dimensions in millimeters, multiply by 25.4
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+Element                Length                  Space from Reflector             Vertical Distance
+                       inches                  inches                           Above/Below Boom
+Reflector a            46.10                    -17.96                          23.05
+Reflector b            46.10                    -17.96                          -23.05
+Reflector              40.90                    -----
+Driver                 39.50                     8.79
+D1                     37.06                    13.47
+D2                     36.48                    25.37
+D3                     36.54                    40.35
+D4                     36.41                    60.56
+D5                     35.61                    85.10
+D6                     34.90                   113.96
+D7                     34.34                   143.87
+D8                     33.80                   174.96
+D9                     33.25                   205.85
+D10                    33.25                   238.11
+D11                    32.15                   270.38
+D12                    31.83                   302.64
+D13                    31.52                   334.90
+D14                    30.88                   367.16
+D15                    30.57                   399.42
+D16                    30.25                   431.68
+D17                    30.25                   464.92
+D18                    29.46                   491.32
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The performance across 2 meters appears partially in Fig. 2, an EZPlot (AC6LA) track of the free-space gain and the 180-degree front-to-back ratio. Note that both the gain and the front-to-back ratio peak just above the 146-MHz design frequency. Hence, the passband edge values are not too far apart, and the total change of values within the passband is reduced to the minimum achievable so far.

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The impedance performance of the array is quite good, using a direct 50-Ohm feed. Fig. 3 shows the resistance, reactance, and 50-Ohm SWR across the passband. The maximum SWR is 1.2:1 across the entire band. The minimum SWR occurs just below the top end of the passband, since the resistance and reactance tend to depart rapidly from the flat range at higher frequencies than the ones shown on the plot. In contrast, the impedance remains relatively stable, with only a slowly rising curve well below 144 MHz, but array performance tends to decrease fairly rapidly.

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As a summary, we can present selected values in the form of a modeled-performance table. "Hor F-S/l" is the E-plane front-to-sidelobe ratio, while "Vert F-S/l" is the corresponding H-plane ratio. "Hor BW" and "Vert BW" are the half-power beamwidths for the E and H planes, respectively.

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+Modeled Performance: Regular (single reflector) 20-element OWA Yagi
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+Freq.  Free-Space      180-Deg. Front-         Hor F-S/l                Vert F-S/l
+MHz    Gain dBi        Back Ratio dB           Ratio dB                 Ratio dB
+144    16.03           24.53                   20.89 (bulge)
+                                               29.27 (lobe)             21.67
+146    16.39           27.93                   26.21                    21.13
+148    16.20           24.85                   23.79                    19.63
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+Freq.  Hor BW          Vert BW         Feedpoint Impedance              50-Ohm
+MHz    degrees         degrees         R +/- jX Ohms                    SWR
+144    31.2            33.2            42.7 + j3.7                      1.19
+146    30.0            31.6            45.6 + j7.5                      1.20
+148    29.2            31.0            47.2 - j7.8                      1.19
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The array gain is a full dB down from the performance of some standard designs with similar boomlengths. However, for some types of operation, the sacrifice of gain may be compensated by some of the other facets of the OWA design. For example, almost all of the sidelobe values are better than 20 dB down from the main forward lobe strength. Add to this feature the relatively small change of values across the passband and the very flat SWR curve, and the design may become more attractive for some applications.

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The OWA is not unique for any single feature, but rather for the combination of design features that it employs. Indeed, we need not design an OWA--as originally conceived by NW3Z--for maximum sidelobe reduction. Rather, that aspect of the design occurs in combination with the other features common to all OWA designs.

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The first OWA design element is the use of a direct 50-Ohm feed system composed of the reflector, the driver, and the first director. The three elements together largely (but not exclusively) establish the feedpoint impedance. The OWA system uses a reflector-driver spacing of about 0.11 wavelength together with a driver-director1 spacing of about 0.058 wavelength to establish the impedance. Since the first director operates as a secondary driver, energized by close coupling to the fed driver, element lengths are also critical to arriving at the desired impedance across the passband. In fact, the secondary driver has a higher current magnitude for about 2/3 of the passband, with the fed driver dominant only for the lower third of the passband.

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Almost any wide-band Yagi uses a similar system of feeding. The DL6WU wide-band Yagis use a reflector-driver spacing of 0.20 wavelength and a driver-director1 spacing of 0.075 wavelength to achieve 50 Ohms. VK3AUU uses the same reflector-driver spacing, but a driver-director1 spacing of 0.035 wavelength. N4FG uses 0.132 wavelength and 0.051 wavelength to achieve the same goal. Within the limits from the widest to the narrowest, it is likely that there are many more spacing combinations that will yield 50 Ohms if we give due attention to the lengths of the elements involved.

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The second aspect--perhaps unique or nearly so with the OWA design--is the use of directors 2 and 3 as control elements. Director 3 is the same length as director 2 or slightly longer. Together, these elements permit the designer to center the peak gain and peak front-to-back ratio at or near the center of the passband. The result tends to be nearly equal front-to-back ratio values at the band edges and the minimum feasible change of gain across the antenna's operating passband.

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The third feature has the greatest affect on the sidelobe emergence in the array. By tapering all elements--with some equal length pair exceptions--to shorter lengths as we move forward along the line of directors (from about director 4 onward), we obtain lower sidelobe levels at the cost of some gain compared to more standard designs. I have created hybrid designs using the OWA core (reflector through director 4 or so) and only obtained the level of sidelobe emergence accruing to the director chain design that I grafted on the OWA core. The conclusion I have so far reached is that the director taper toward the forward-most director is critical to either attenuation or suppression of sidelobes.

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If you refer to the dimension table, you will discover that the forward-most director is shorter than a natural taper would seem to indicate. One of the functions of the forward-most director--for any number of elements from about 8 up in the OWA design--is to act together with the reflector length in setting the SWR passband curve. Once you have achieve a relatively stable combination of reflector and last director lengths, lengthening the reflector will tend to stretch the passband downward in frequency. Likewise, shortening the last director will stretch the passband upward in frequency. These shift, of course, have limits and they are not fully independent of element spacing and interactions with nearby elements. However, final tweaking of a design usually involves iterative adjustments to both elements.

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Fig. 4 shows two outlines for OWA Yagis. We shall work with the lower portion of the figure shortly. The upper outline shows the standard 20-element OWA 2-meter array designed for 146 MHz. You may correlate the elements to the table of dimensions and to the brief summary of OWA design features.

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The sidelobes that emerge with the OWA design are many dB better than with standard Yagi designs using a similar boomlength. The performance table showed that at 144 MHz, there is a nearly suppressed first sidelobe in the E-plane that is only down by about 21 dB, with the first fully formed sidelobe being 29 dB down. Above the low end of the band there are no E-plane or horizontal sidelobes worse than about 24 dB. However, the vertical or H-plane sidelobes average just above 20 dB below the main lobe. For a single-bay Yagi, the element ends and the geometry of the array outline form a means of control for many E-plane array characteristics. In the H-plane, we have no such controls. Hence, as shown in the left portion of Fig. 5, the H-plane sidelobes tend to be larger and more nearly at right angles to the Yagi. Even when they are no stronger than the comparable E-plane sidelobes, they contain more energy due to having a wider compass of included angles.

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Compared to a standard Yagi design, the OWA design appears not only to attenuate sidelobes, but as well to suppress some of them. However, the question remains as to how far we can carry this process in a parasitic array. So we should look at some strategies for achieving, if not suppression, then at least greater attenuation.

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The 20-Element OWA Yagi with 2 Added Reflectors

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One technique for reducing both E-plane and H-plane sidelobes is to add more reflectors to the array. Classic multi-reflector arrays have set them in a flat plane. This arrangement is not the best. As the table of dimensions and the right half of Fig. 4 show, the optimal position with respect to the OWA array is to place the new reflectors about 0.28 wavelength above and below the original reflector and about 0.22 wavelength to the rear. As well, the new reflectors are considerably longer than the original reflector. In the indicated positions, the new reflectors require no changes to the other elements in the array. The following table summarizes the modeled performance of the revised OWA array.

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+Modeled Performance: 20-element OWA Yagi with 2 Added Reflectors
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+Freq.    Free-Space         180-Deg. Front-             Hor F-S/l                   Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      16.10              27.75                       28.60                       21.97
+146      16.46              34.35                       27.43                       21.66
+148      16.23              33.79                       22.79                       19.29
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+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      31.2               33.0               42.7 + j3.5                          1.19
+146      29.8               31.6               45.6 + j7.1                          1.19
+148      29.0               30.8               46.6 - j8.3                          1.20
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Additional reflectors add almost nothing to the array forward gain. Years ago, folks thought that reflectors played a key role in determining parasitic array gain, possibly because corner and planar reflectors play such a role. We have since learned that the directors play the dominant role in setting array gain. However, as shown in Fig. 6, the added reflectors do play a role in increasing the front-to-back ratio.

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The key property change evident from the graph is the increase in front-to-back values, a feature that also shows up on the right side of Fig. 5. If you look closely at Fig. 5, you will see that all of the rearward lobes are diminished relative to the single bay version of the Yagi on the left. As well, the front-to-back peak value has shifted slightly upward in frequency.

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Although the performance characteristics have changed a bit, the feedpoint characteristic remain unchanged. Fig. 7 shows the resistance, reactance, and 50-Ohm SWR across the band. The maximum resistance and reactance changes are under 1 Ohm, relative to the regular OWA Yagi.

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Fig. 5 holds a potential misimpression, since it provides E-plane and H-plane patterns for only the design frequency. We can correct any potential idea that the sidelobe development remains constant across the passband by looking at Fig. 8. This set of details on the development of sidelobes at 3 points along the band shows the evolution of the sidelobes as we increase frequency. These graphs use an outer ring value of 0 dBi. Thus, to arrive at a true value of suppression of the side and rear lobes, add the array gain for each frequency to the amount down that the graph shows. You can extract those numbers from the performance table shown above.

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The E-plane attenuation of sidelobes is clearly superior to the H-plane attenuation, despite the addition of the new reflectors. As well, above the design frequency, there is more energy in the sidelobe directions than at or below the design frequency. Nevertheless, the added reflectors do make a noticeable improvement on the original array, especially with respect to the rearward lobes.

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In many ways, the 20-element OWA Yagi has reached a limit of improved performance and sidelobe attenuation. Part of the reason that it achieves the level of sidelobe reduction shown in the various figures lies in the pattern of current magnitudes along the elements. Fig. 9 shows these current levels as vertical lines of varying length. Note that the added reflector having very low current magnitudes, which is a desirable condition relative to their function. As a result, the regular version of the same antenna would have virtually identical current lines for the 20 main elements.

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First note that secondary driver (main element 3 or director 1) has a higher current magnitude than the fed driver, indicating its role at the 146-MHz design frequency. The next two elements are the control directors and have lower current levels than the next following director. From that point onward, the current magnitude decreases as we move forward along the progression of directors. This feature--more than any other in the design--controls the emergence of sidelobes.

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Although adding supplemental reflectors provides a modicum of performance improvement, the amount of further sidelobe attenuation and/or suppression is too small to be noticed. We are still faced with the fact that H-plane or vertical sidelobes are noticeably stronger than the E-plane sidelobes. Hence, we need another strategy to make improvements in this department.

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A Stack of 2 20+ Element OWA Yagis

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A time-tested method of reducing vertical and near-vertical components to a radiation pattern is to place two identical antennas in a vertical stack with a separation of about 1/2 wavelength. This technique is worth exploring if only to learn what happens when we do so. The vertical stack will have the appearance of Fig. 10, give or take a little separation as we determine the best distance apart for the arrays.

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In fact, for the arrays in question, 0.5 wavelength is not the best separation of the two arrays. First, the closer the two arrays are to each other, the greater the mutual effects on the feedpoint impedance of each array. Second, we are not trying to reduce only the radiation that is perfectly vertical relative to the arrays. Instead, we are hoping to reduce the angular radiation that may be 45 degrees or more off vertical. Hence, a series of trial models produced a separation between 0.6 and 0.625 wavelength as most effective in reducing the H-plane or vertical sidelobes. The following table summarizes the performance for the two limiting separation distances.

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+Modeled Performance: 20-element OWA Yagis with 2 Added Reflectors
+         Stack of 2:  Boom Separation: 0.6 WL (at 146 MHz)
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+Freq.    Free-Space         180-Deg. Front-             Hor F-S/l                   Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      17.97              31.29                       21.63                       25.42
+146      18.06              49.66                       24.84                       30.14
+148      17.66              30.14                       21.33                       25.60
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+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      26.6               24.8               38.9 + j1.8                          1.29
+146      26.0               24.2               43.6 + j8.1                          1.25
+148      26.0               24.2               43.2 - j10.8                         1.32
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+Modeled Performance: 20-element OWA Yagis with 2 Added Reflectors
+         Stack of 2:  Boom Separation: 0.625 WL (at 146 MHz)
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+Freq.    Free-Space         180-Deg. Front-             Hor F-S/l                   Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      17.98              30.83                       21.42                       25.61
+146      18.08              48.20                       24.54                       27.72
+148      17.69              30.26                       21.24                       26.54
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+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      26.6               24.6               38.8 + j2.2                          1.29
+146      26.0               24.0               43.5 + j8.1                          1.25
+148      26.0               24.0               43.4 - j10.1                         1.30
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In most respects, the two performance tables shows no significant difference. However, at the 0.6 wavelength separation distance (at 146 MHz), the performance curves are better centered without need for revising any of the elements within the arrays. Fig. 11 shows the gain and 180-degree front-to-back curves. Peak front-to-back ratio occurs on the design frequency, while the peak gain occurs just below that frequency. Since the high-gain individual antennas are not spaced apart by an amount designed to maximize gain, the total gain increase over a single antenna is only about 1.5 dB.

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For separations under 1 wavelength or so, there will be interactions among the elements such that the feedpoint impedance will change slightly. Relative to a single bay, the resistance on each feedpoint has decreased by about 3 Ohms, while the reactance is about 1.5-Ohm more capacitively reactive. Fig. 12 shows the resistance, reactance, and 50-Ohm SWR values for the 2-stack at 0.6 wavelength separation.

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To show the level of uncorrected detuning, Fig. 13 overlays SWR curves for the single and double arrays. It is likely that some tweaking of the reflector, driver, and forward-most director would re-flatten the 2-stack SWR curve. However, the values shown are for each feedpoint in the array. To feed the 2-stack, you would need to employ standard line-length techniques to transform each impedance to about 100 Ohms so that the parallel result matched the main 50-Ohm line.

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The key question in all of this is to what degree the stacking of two reflector-supplemented 20-element OWA Yagis has managed to reduce sidelobes. With respect to the vertical or H-plane sidelobes, the improvement is a very noticeable 5+ dB improvement. However, the stacking has reduce the E-plane attenuation of sidelobes by almost the same amount. By comparing Fig. 14 with ealier single-bay graphics, you can observe to what degree the preponderance of attentuation has shifted. Although the E-plane lobe peaks are more definite in the 2-stack, you can also see that some of the lobe merging remains in place.

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Although the stack of 2 augmented 20-element Yagis does not reach the E-plane sidelobe reduction level as the single bay, the reduction in vertical sidelobes does have some advantages. They show up best when modeling the array over ground. I place the single bay at 5 wavelengths (33.7') above average ground. Then I placed the lower array in the 2-stack at the same level, resulting in an upper bay at 5.6 wavelengths (37.7') above ground. To show the results, let's combine a modeled performance table with a pair of elevation and azimuth plots. In the table, remember that feedpoint impedances values for the 2-stack apply to each of the 2 feedpoints.

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+Modeled Performance:  Single and 2-Stack 20-element OWA Yagis with 2 Added Reflectors at 146 MHz
+         5 WL Above Average Ground (2nd Yagi in stack 5.6 WL Above Ground)
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+Single Yagi
+Freq.    Gain               TO Angle           180-Deg. Front-             Hor F-S/l          Hor BW            Impedance          50-Ohm
+MHz      dBi                degrees            Back Ratio dB               Ratio dB           degrees           R+/-jX Ohms        SWR
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+146      22.28              2.8                34.26                       27.30              29.6              45.6 + j7.0        1.19
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+Stack of 2 Yagis, 0.6-WL Separation
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+Freq.    Gain               TO Angle           180-Deg. Front-             Hor F-S/l          Hor BW            Impedance          50-Ohm
+MHz      dBi                degrees            Back Ratio dB               Ratio dB           degrees           R+/-jX Ohms        SWR
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+146      23.83              2.6                49.34                       24.74              25.8              43.7 + j8.0        1.25
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The azimuth pattern for the single bay is clearly cleaner than the corresponding pattern for the 2 stack. However, the 2-stack shows far less wasted energy at near-vertical angles. As well, there is less energy in the upper elevation lobes. Whether these small margins justify the construction, support, and maintenance of a second and higher 22-element array is strictly a user judgment.

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Some Mid-Stream Conclusions

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Clearly, the matter of suppressing sidelobes is still short of its ultimate goal: the total suppression of sidelobes in parasitic arrays of any length. These notes only record progress so far with respect to both horizontal and vertical sidelobes in arrays using about 6 wavelength booms. The addition of two relatively passive reflectors displaced to the rear of the Yagi does reduce rearward lobes of all sorts. The element taper and spacing achieves well over 20 dB sidelobe attenuation horizontally, and a stack of 2 such arrays, spaced about 0.6 wavelength apart achieves the same goal with respect to vertical sidelobes.

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However, the two results do not yet combine. Although some lobe merging is apparent with the reduction in lobe strength, full suppression to wholly minimal levels remains as an unfinished task. There are, however, a number of possible directions for future experimentation. The use of more elements per wavelength may reduce design frequency sidelobes further, but a magic formula for maintaining sidelobe-suppression bandwidth (all of 2 meters in this case) is elusive.

+

In the end, many classic Yagi designs are perfectly adequate for contemporary communications needs. The question of the ultimate suppression of parasitic sidelobes is more a matter of curiosity than necessity. Still, some of the most interesting challenges in life emerge from curiosity.

+
+ +
+

Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: Some Further Notes on 12-Element Yagis

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Return to Index

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Topics: VHF / UHF, Yagi


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+

Sidelobe Attenuation and Suppression: Some Further Notes on 12-Element Yagis

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the preceding discussion of sidelobe attenuation, we focused our work on strategies for reducing both E-plane (horizontal) and H-plane (vertical) sidelobes of longer-boom Yagis set up for horizontal polarization. See Sidelobe Attenuation and Suppression.

+

In these notes, I shall aim at identifying--perhaps incompletely--some of the factors that go into reducing the strength of sidelobes. The plan is to use examples of 12-element and 20-element Yagis designed for 146 MHz in order to sample a number of phenomena that appear to be associated with both sidelobe attenuation and sidelobe suppression. We shall eventually look at designs that aim for maximum broadband forward gain with little regard for sidelobes, designs that attempt to the degree possible to suppress sidelobes, designs that trade sidelobe suppression for seemingly improved performance, and designs that aim simply to attenuate sidelobes.

+

Investigators such as David Tanner, VK3AUU, and Fred Griffee, N4GF, have shown that it is possible to attenuate sidelobes to a level that rivals the level so far achieved by suppression techniques. Indeed, it may turn out in the future that the suppression achieved by some OWA designs is simply a consequence of certain design decisions and has no ultimate resolution, or at least no level of improvement that attenuation cannot match. That is one of the possible outcomes of any challenge driven by curiosity. But the investigation is perhaps as informative and useful as the outcome, so the trip is worth taking--at least for me.

+

In the preceding notes, I drew a distinction between sidelobe attenuation and sidelobe suppression. The general idea of sidelobe attenuation includes the reduction in sidelobe strength. Each sidelobe may not reduce is strength in exact proportion to the other sidelobes, but each sidelobe remains a distinct lobe marked by a clear reduction in strength on either side of the main lobe bearing. In contrast, sidelobe suppression involves the elimination or near elimination of a sidelobe in addition to a reduction in sidelobe strength. The left two detail E-plane patterns in Fig. 1 allow us both to identify the sidelobes in a 12-element Yagi of standard design and to see what difference suppression makes, relative to simply reducing the strength of the standard-design sidelobes.

+
+ +
+

The left-most detail identifies the sidelobes, both forward and rearward, that appear with 3 wavelength Yagi designs. The number of forward and the number of rearward sidelobes on each side of the boom-line tends to equal the boom length in wavelengths. The left detail uses a boom just under 3 wavelengths, and one of the rear sidelobes is too small to see clearly, although it shows up definitively on a suitably detailed azimuth pattern of the antenna's model.

+

A Yagi design that seeks to attenuate sidelobes will end up with the same number of distinctly identifiable sidelobes as the left detail, although the strengths may be considerably lower. A standard design tends to show the most strength in the forward-most sidelobe, with decreasing strength in sidelobes that diverge further and further from the bearing of the main forward lobe. Designs that aim only at attenuation may either replicate this pattern at reduced sidelobe levels, or one or more sidelobes will show a reduction in strength that is greater than the attenuation achieved by other lobes. This last condition tends to represent the ill-defined "frontier" between attenuation and suppression.

+

Sidelobe suppression has additional characteristics besides reduced sidelobe levels. Sidelobes may disappear, almost always due to merging by redirection of one or more of them. The center pattern shows the nearly complete merger of the second and third forward sidelobes in addition to the much reduced sidelobe strength.

+

We may also use both the center and right detail patterns to note that rearward sidelobes can sometimes create confusions. The center pattern seems to show a main, somewhat square, rearward lobe with only two sidelobes. However, the right version shows that the main rearward lobe is composed of 3 overlapping lobes, a main lobe and a sidelobe each side of the main lobe. The right detail shows a condition where the main lobe is further reduced in strength--a periodic feature of Yagis. The sidelobes now show their peaks.

+

We shall continue our use of Fig. 1 in the discussion of 12-element Yagi designs as we examine in more detail the design features that produce suppression as well as attenuation.

+

A Selection of 12-Element Yagis

+

The original Yagi design that gave rise to my curiosity about sidelobe suppression is an extension of the Optimized Wideband Array (OWA) designs for HF, originated by NW3Z. Let's note at the outset that the OWA terminology is only a label. OWA Yagis do not have the widest operating passbands possible--that honor appears to go to DL6WU designs that we shall visit along the way. Rather, the OWA concept includes a passband showing a very low 50-Ohm SWR across a designated set of frequencies--usually a specific amateur band. As well, the design concept includes gain and front-to-back peak values that occur within the passband as near to the design frequency as feasible. Alternative to centering the peak values is to place them on a frequency within the passband so that performance at the upper and lower edges of the band is about the same--within very close limits compared to more standard designs. Standard Yagis up to 5 or 6 elements tend to show a rising gain with increases in frequency, even if the front-to-back ratio occurs within the passband. The OWA design allows both peaks to occur within the passband.

+

OWA designs have several features that work together to achieve the desired operating features. The first OWA design element is the use of a direct 50-Ohm feed system composed of the reflector, the driver, and the first director. The three elements together largely (but not exclusively) establish the feedpoint impedance. The OWA system uses a reflector-driver spacing of about 0.11 wavelength together with a driver-director1 spacing of about 0.058 wavelength to establish the impedance. Since the first director operates as a secondary driver, energized by close coupling to the fed driver, element lengths are also critical to arriving at the desired impedance across the passband. In fact, the secondary driver has a higher current magnitude for about 2/3 of the passband, with the fed driver dominant only for the lower third of the passband.

+

The second aspect--perhaps unique or nearly so with the OWA design--is the use of directors 2 and 3 as control elements. Director 3 is the same length as director 2 or slightly longer. Together, these elements permit the designer to center the peak gain and peak front-to-back ratio at or near the center of the passband. The result tends to be nearly equal front-to-back ratio values at the band edges and the minimum feasible change of gain across the antenna's operating passband.

+

The third feature has the greatest affect on the sidelobe emergence in the array. By tapering all elements--with some equal length pair exceptions--to shorter lengths as we move forward along the line of directors (from about director 4 onward), we obtain lower sidelobe levels at the cost of some gain compared to more standard designs. As we shall see, the element taper schedule does not guarantee sidelobe suppression, but acts in concert with the balance of the first two features of the design.

+

We may begin with the original 12-element OWA Yagi design for 146 MHz. The following table provides the dimensions in inches. Multiply by 25.4 to arrive at the dimensions in millimeters. The boomlength is 2.94 wavelengths.

+ 
+Dimensions of "Original" 12-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.90                        -----
+Driver                      39.50                         8.79
+D1                          37.00                        13.47
+D2                          36.33                        25.38
+D3                          36.40                        40.72
+D4                          36.21                        61.38
+D5                          35.20                        86.49
+D6                          34.30                       116.00
+D7                          33.60                       146.60
+D8                          32.90                       178.40
+D9                          32.20                       210.00
+D10                         31.20                       238.00
+
+

To facilitate comparisons, I shall present both graphic and tabular modeled performance data. The tabular data will use 144, 146, and 148 MHz as check points. The data will include free-space gain, 180-degree front-to-back, and the front-to-forward-sidelobe value in the horizontal plane. Vertically, the sidelobe ratio will use simply the strongest H-plane sidelobe, which may be the forward-most lobe or a lobe more tangential to the plane of the array. Unlike the preceding notes, this discussion will only make passing note of vertical or H-plane sidelobes as we focus on the E-plane or horizontal sidelobes.

+ 
+Modeled Performance: "Original" 12-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      14.07              25.19                       25.19                       18.95
+146      14.35              24.65                       27.91                       18.15
+148      14.27              23.09                       25.00                       16.43
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      38.4               42.6               43.1 + j4.9                          1.20
+146      36.8               40.5               47.5 + j6.2                          1.15
+148      35.5               39.0               43.8 - j4.1                          1.17
+
+

Since all of our subject antennas offer broadband performance, graphical data will use a 140-150-MHz passband. In some cases, the graphs will show information for multiple designs in order to conserve space. For example, the 50-Ohm SWR curves in Fig. 2 show the original design and a revised OWA design that we shall discuss shortly.

+
+ +
+

Note that the original OWA design curve has a very slow-rising characteristic below the 2-meter band, but rises rapidly above 148 MHz. This characteristic attaches to many, but not all wide-band Yagis. The SWR within the 2-meter band does not exceed 1.2:1 and reaches a value of 2:1 at 140 MHz. However, it passes the 2:1 mark at 149 MHz on the other end of the band.

+
+ +
+

Using the graph lines marked "original," note that the peak gain occurs at 147 MHz, while the peak front-to-back ratio occurs at 146.5 MHz, a fairly close coincidence. The gain is about 0.5 dB shy of the gain achievable with a standard (DL6WU) design. However, the sidelobes are diminished and suppressed to the level shown both in the center of Fig. 1 and the table of performance values. Across the 2-meter band, the E-plane forward sidelobes are down by at least 25 dB relative to the array's main lobe. Vertical sidelobes remain less attenuated, although as we shall see, they are lower than comparable sidelobes in standard designs.

+

Because some wide-band Yagi designs achieve SWR levels even lower than those shown by the original OWA design, I revised the design to seek a lower maximum SWR value within the 2-meter band. The chief strategy was to change the spacing of driver from the reflector and the first director from the driver. The original reflector-driver spacing was 0.1087 wavelength, and the driver-director1 spacing was 0.0579 wavelength. The new spacing values are 0.1262 wavelength and 0.0529 wavelength, respectively. These changes forced changes to the length of all three elements and a minor revision of the most forward director, including an extension of the boom length to 2.97 wavelengths. The following table shows the revised dimensions.

+ 
+Dimensions of "Revised" "Original" 12-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.97                        -----
+Driver                      39.62                        10.20
+D1                          36.91                        14.48
+D2                          36.33                        26.38
+D3                          36.38                        41.72
+D4                          36.10                        62.38
+D5                          35.22                        87.49
+D6                          34.30                       117.00
+D7                          33.60                       147.60
+D8                          32.90                       179.40
+D9                          32.20                       211.00
+D10                         31.22                       240.00
+
+

In terms of SWR bandwidth, Fig. 2 shows the improvement. The 50-Ohm SWR at 140 MHz drops to 1.5:1, while the upper end of the band shows only a slight improvement. The following checkpoint table of modeled performance values shows the in-band improvements. The highest in-band SWR value is 1.12:1.

+ 
+Modeled Performance: "Revised" "Original" 12-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      14.05              22.44                       24.62                       18.79
+146      14.36              26.24                       28.14                       18.31
+148      14.34              24.75                       25.54                       16.90
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      38.4               42.6               49.4 + j2.6                          1.06
+146      36.8               40.4               51.0 + j5.6                          1.12
+148      35.4               38.8               52.0 - j2.7                          1.07
+
+

Operationally, we find virtually no change in array performance. In part, this result stems from the fact that the revised gain and front-to-back curves in Fig. 3 remain closely aligned. Both the free-space gain and the 180-degree front-to-back ratio occur at 147 MHz. The original and revised designs have gain curves that almost overlay each other. The front-to-back curves have different shapes, but most of the differences in shape occur at ratio values above 20 dB. The right detail in Fig. 1 shows how well matched the revised array is to the original, with only the 180-degree front-to-back heading showing any notable difference.

+

At this point, we cannot show the significance of keeping the gain and front-to-back curves well aligned with each other. We shall later have contrasting examples to show the effects of misalignment. For the moment, we can note that the control elements, that is, directors 2 and 3, play a prominent role in this result, but those elements are not wholly independent of the impedance-setting elements behind them. In a Yagi, if you change something, you usually end up changing everything to match or to compensate. The fact that we effected the improved SWR curve with minimal changes to other aspects of the array is a result of the relative shortness of the array (less than 3 wavelength long) and good luck.

+

One contrast that we can make at this point is between so-called standard Yagi designs and the OWA Yagis that we have just examined. We shall in fact look at both the "official" DL6WU design and a variant by VK6AUU. In addition, we shall examine a highly refined Yagi by N4FG that strives only for maximum sidelobe attenuation. All of these Yagis use 12 elements on 3 wavelength booms.

+

The "official" DL6WU design emerges from the self-executing DOS program DL6WU-GG.EXE, which is available from the web site maintained by Ian White, G3SEK (www.ifwtech.co.uk/g3sek). The algorithms in the program are updated from an earlier version. You may calculate any size DL6WU design up to 40 or so elements, but we shall restrict ourselves at the moment to 12 elements, which require for the element diameter a 2.85 wavelength boom. The design table presents the dimensions in millimeters, using an element diameter of 4.7625 mm, which translates into 0.1875", the same size as the OWA designs. Divide the dimensions by 25.4 to arrive at their equivalents in inches.

+ 
+Dimensions of DL6WU (GG) 12-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in inches, divide by
+25.4
+
+Element                     Length                      Space from Reflector
+                            millimeters                 millimeters
+Reflector                   1004.92                      -----
+Driver                      994.74                       410.7
+D1                          924.21                       564.7
+D2                          916.71                       934.3
+D3                          908.07                      1375.8
+D4                          899.54                      1889.1
+D5                          891.86                      2664.1
+D6                          885.15                      3080.1
+D7                          879.30                      3726.9
+D8                          874.16                      4404.5
+D9                          869.60                      5112.9
+D10                         865.51                      5852.1
+
+

Within the 4 MHz of 2 meters, the beam exhibits modest performance in every category except forward gain. The peak in-band gain occurs at 148 MHz at 14.9 dBi (free-space), while the peak 180-degree front-to-back ratio appears at 149.5 MHz, above the upper band limit. The following table shows the modeled performance characteristics, including the relatively low attenuation of sidelobes, both horizontal and vertical.

+ 
+Modeled Performance: DL6WU (GG) 12-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      14.60              17.52                       18.26                       13.80
+146      14.80              14.98                       17.51                       13.48
+148      14.89              17.31                       16.27                       12.88
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      35.2               38.2               61.7 + j3.4                          1.25
+146      33.4               36.0               57.6 - j9.4                          1.25
+148      31.8               34.0               39.5 + j11.2                         1.41
+
+

Over the enlarged passband, the design shows typical DL6WU design fluctuations in both gain and front-to-back ratio. Fig. 4 shows The double-hump front-to-back curve. As you add elements to the DL6WU design, the humps change in frequency so that some lengths place the maximum front-to-back ratio at the design frequency, while others place a near front-to-back minimum at the design frequency.

+
+ +
+

One special design feature is notable in this context. In contrast to the relatively close spacing of the reflector-driver-director1 assembly in the OWA design, the DL6WU design achieves a direct 50-Ohm feedpoint by using a 0.20 wavelength reflector-to-driver spacing. The distance between the driver and the first director is 0.275 wavelength. As a consequence, the DL6WU official design achieves an exceptionally wide SWR passband, as evidenced in the "GG" SWR curve in Fig. 5. The curve has multiple peaks and nulls in contrast to the simple 2-null curve of the OWA design. The original DL6DU design was aimed at fatter elements than are used in these models, and the SWR curves gets flatter up to at least a 10-mm element diameter.

+
+ +
+

As an alternative to the official DL6WU design. VK3AUU revised the algorithms to achieve best performance at 19 elements. The major revision in his design falls in the region of the reflect-driver-director1 assembly. Like DL6WU, VK3AUU aimed his work at 10-mm elements, so the 4.76-mm elements in my recalculation of his elements does not necessarily represent the best performance of which the array is capable. The dimension table shows the physical results of using the VK3AUU variant on DL6WU design. The boomlength is 2.84 wavelengths.

+ 
+Dimensions of DL6WU (VK3AUU) 12-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in inches, divide by
+25.4
+
+Element                     Length                      Space from Reflector
+                            millimeters                 millimeters
+Reflector                   992                          -----
+Driver                      972                          375
+D1                          904                          543
+D2                          894                          884
+D3                          886                         1326
+D4                          877                         1840
+D5                          870                         2410
+D6                          863                         3026
+D7                          856                         3680
+D8                          850                         4368
+D9                          844                         5085
+D10                         839                         5829
+
+

The revised design moves the gain peak to the design frequency. The front-to-back peak remains above the limit of the 2-meter band, as shown in the second set of curves in Fig. 4. The designer uses a reflector-to-driver spacing of 0.1826 wavelength, with a driver-to-director1 spacing of 0.2644 wavelength. The result is a wide-band SWR curve, as shown in the alternative line in Fig. 5. However, the curve now has only a central region of low SWR, with steep rises at the low and high ends of the expanded passband. The checkpoint table shows the modeled performance within the 2-meter band.

+ 
+Modeled Performance: DL6WU (VK3AUU) 12-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F-S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      14.72              16.27                       18.02                       13.73
+146      14.92              14.43                       16.97                       13.18
+148      14.74              19.70                       14.91 (Bulge)               11.78
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      34.4               37.2               46.5 + j1.2                          1.13
+146      32.6               35.1               51.1 - j7.3                          1.16
+148      31.2               33.4               44.1 + j8.2                          1.24
+
Fig. 6shows the detail of the sidelobe structure of 3 arrays. For the moment, we may focus on the two left patterns for the DL6WU designs. As the modeled performance tables show, both versions of the DL6WU design have strong sidelobes. In fact, the vertical sidelobes are very strong, averaging under 14 dB reduction relative to the main forward lobe. Compare these numbers to the OWA designs that average about 18 dB vertical sidelobe reduction. The improvement in the horizontal sidelobe reduction of the OWA over the DL6WU design is closer to 7 dB. +
+ +
+

The third pattern detail in Fig. 6 belongs to an N4FG design that aims at maximum sidelobe attenuation (in contrast to suppression). Like the DL6WU design, the pattern shows all 3 lobes, both forward and rearward, and their strength has the standard order in which both the most forward and most rearward lobes are the strongest. Compare Fig. 6 to Fig.1, in which the OWA forward sidelobes show a considerable reduction in the forward-most sidelobe and a merging of the second and third forward sidelobes. Nevertheless, as we shall see, the N4FG design does a remarkable job at sidelobe attenuation.

+

Physically, N4FG places 12 elements on a 2.97 wavelength boom. He employs a reflector-to-driver spacing of 0.1339 wavelength and a driver-to-director1 spacing of 0.0521 to achieve excellent broadband performance. The resulting array dimensions appear in the following table.

+ 
+Dimensions of N4FG 12-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.66                        -----
+Driver                      39.67                        10.83
+D1                          37.40                        15.04
+D2                          36.96                        27.14
+D3                          36.58                        39.88
+D4                          35.97                        57.25
+D5                          35.53                        85.20
+D6                          35.50                       110.95
+D7                          33.72                       142.81
+D8                          33.65                       177.01
+D9                          32.66                       211.28
+D10                         32.15                       240.00
+
Within the 2-meter band, the N4FG array--which is not the ultimate design in his continuing design explorations--shows the following performance characteristics. + 
+Modeled Performance: N4FG 12-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      14.33              29.55                       25.47                       18.22
+146      14.55              28.03                       27.15                       16.87
+148      14.37              25.31                       31.55                       16.70
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      37.2               41.0               46.3 + j3.9                          1.12
+146      35.6               39.0               49.0 + j2.2                          1.05
+148      34.6               38.0               53.0 + j5.8                          1.14
+
+
+ +
+

Fig. 7 shows the performance of the array over the expanded passband. The performance is comparable to the OWA designs, with about a 0.2-dB gain advantage to N4FG. However, amount of change for both gain and front-to-back ratio is greater in the N4FG design. In part, this higher amount of overall change in values within the 10-MHz expanded passband results from the fact that the peak values of gain and front-to-back ratio do not closely coincide with respect to frequency. The peaks are 2 MHz apart, compared to 0.5 MHz or less for the two OWA designs.

+

Nevertheless, the N4FG design achieves two important results. First, the horizontal sidelobe attenuation is excellent. Even though all sidelobes have standard form, their level averages very close to the levels achieved in the OWA design. The average vertical sidelobe attenuation is far superior to the DL6WU designs, but not quite at the OWA level. The second achievement of the N4FG design is a very broad 50-Ohm SWR curve. Fig. 8 tells the story on this phenomenon. The curve has much the same shape as the VK3AUU version of the DL6WU design.

+
+ +
+

The N4FG design achieves sidelobe strength comparable to the OWA designs, but does not so much suppress sidelobes as it attenuates them. The interesting question from the perspective of these notes is what design elements may differentiate the N4FG design from the OWA design. In fact, there are three differences of note.

+

First, let's consider the element length taper used in the collection of designs shown so far. All the designs are just under 3 wavelengths long and use 12 elements. Each design uses carefully calculated driver assembly spacing (and elements lengths) to achieve a wide-band 50-Ohm SWR curve. However, if we examine the dimensional tables, we can arrive at some interesting differences in the taper of the elements from the reflector to the most forward director. Let's use as a simple indicator the ratio of the longest element (reflector) to the shortest element (director 10).

+

The DL6WU designs employ a taper ratio of about 1.5:1 or 1.6:1. The N4FG design raises that value to about 1.26:1. As the taper ratio increases, gain decreases--from about 14.8 dBi to about 14.55 dBi. In contrast to these designs, the OWA models use element taper ratios of 1.39:1 and 1.41:1 for the original and revised versions, respectively.

+

The second factor is related to the first, but not in any simple way. As the taper ratio increases, the relative current magnitude on the forward elements decreases. The easiest way to portray this fact is via Fig. 9, which shows the relative current magnitudes as a series of vertical lines. In each case, the driven element current is 1.0.

+
+ +
+

The diagrams also show the relative element spacing, but not the element lengths. Both dimensions play a role in the current distribution. In all three cases, the first director (third element from the left) shows a higher relative current than the fed element or driver. This condition is a mark of almost all wide-band Yagis for the upper 2/3 of the operating passband.

+

Counting from the second director, the DL6WU design shows an interesting almost sinusoidal pattern of current magnitudes. In addition, the relative current on the forward elements remains high. The array shows a regular element taper with respect to length and an increasing director spacing, although this latter factor will become a constant within a few elements. In general, the lower taper ratio tends to indicate a higher gain array, but not exclusively of the relationships between adjacent directors.

+

The N4FG array shows some features of the DL6WU design with respect to the current magnitudes of the first few directors. However, the 5 forward-most directors shows a relatively constant decrease in current magnitude from element to element. The first consequence to note is the decrease in gain relative to the DL6WU array. Together, it would seem, the decrease in current magnitude and the higher element taper ratio show a much higher attenuation of sidelobes.

+

The OWA array shows a similar decreasing current magnitude along the directors past director 3. The array also contains the third notable difference from the other arrays: the use of control directors (2 and 3). The inner control director is slightly shorter than the outer control director, but their positions also contribute to the actual cirrent magnitude levels. Hence, the outer control director has a considerably higher current magnitude than the inner control director. This arrangement appears to redirect some of the sidelobes, allowing a bit of merging and possibly cancellation.

+

We have also viewed a fourth factor which may contribute something to the reduction of sidelobes: the coincidence of the coincidence of the gan and front-to-back peak values and hence of the remainder of the performance curves in these two categories. However, it is too soon in our exploration to reach any conclusions on a number of questions.

+

Which of these 4 differences among arrays counts as a necessary condition of sidelobe attenuation or of sidelobe suppression? The use of control directors is certainly not a necessary condition of sidelobe attenuation, since the N4FG array reduces sidelobe strength significantly, but does not use them. More likely candidates are the element taper ratio and the pattern of relative current magnitudes, although these two factors do not fit into directly comparable categories.

+

What is the role of coinciding frequency peaks of forward gain and front-to-back ratio in the attenuation of sidelobes? The examples that we have viewed here only suggest that the coincidence is desireable, but they do not establish it as in any way necessary.

+

Are the control elements in the OWA design necessary to sidelobe suppression? Of course, the relevantly similar performance figures for the OWA and N4FG arrays suggest that sidelobe suppression is not mandatory. But again, the curiosity factor rules this exploration. Perhaps we may arrive at some further indicators by looking at a new set of examples using a longer boom. To make the contrast as vivid as possible, let's double the boom length to 6 wavelengths. For many designs--but not for all--a 6 wavelength boom holds about 20 elements.

+

Unfortunately, space dictates that we shall need another episode to give each new example its fair share of discussion.

+
+ +
+

Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: Some Further Notes on 20-Element Yagis

+

Return to Index

+

Topics: VHF / UHF, Yagi


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+

Sidelobe Attenuation and Suppression: Some Further Notes on 20-Element Yagis

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In the exploration of 12-element Yagis and their ability to attenuate or suppress sidelobes, we ended with 4 factors that appear to affect the outcome:

+
    +
  • 1. The close frequency-coincidence of the forward gain anf 180-degree front-to-back ratio peak values;
    • +
  • 2. A higher than usual element taper ratio;
    • +
  • 3. A smooth descending curve of relative current magnitude along the directors from the rear-most to the forward-most; and
    • +
  • 4. The presence of control directors.
    • +
+

High sidelobe attenuation tends to be associated with at least 2 of the properties, namely, the element taper ratio and the smooth descending relative current magnitude as we move forward along the train of directors. Of course, the first director tends to act as a secondary driver and will have a varying current level depending upon the operating frequency's relationship to the design frequency. The presence of properly dimensioned control directors seems to mark the difference between sidelobe attenuation and sidelobe suppression, where the latter term shows merged and missing lobes in addition to high sidelobe suppression.

+

For many practical purposes, sidelobe attenuation and suppression may not be needed, while for other purposes, sidelobe attenuation alone may be sufficient. We have noted that sidelobe suppression so far seems to be a relatively unique Yagi property belonging to OWA designs. It comes at a cost of forward gain. Nevertheless, since curiosity rather than practicality drives this investigation, we might move forward. The set of 12-element Yagis provides indicators of the properties of sidelobe suppressing Yagis. Perhaps a different set of arrays may confirm the initial indications. To that end, I have examined a series of 6 wavelength Yagis. Although twice as long as the first set of Yagis, these beams carry 20 elements--with one final exception that carries 25. The designs are similar enough to the 12-element designs to have a potential for showing the same features. At the same time, they have some differences that may allow us to confirm a few suspicions raised by the initial set.

+

A Selection of 20-Element Yagis

+

A typical standard design 20-element Yagi on a 6 wavelength boom shows 6 forward and 6 rearward sidelobes on each side of the boom line. The left detail pattern in Fig. 1 shows the sidelobes. The higher gain of these arrays may make the last of the 6 sidelobes--both fore and aft--somewhat minuscule, but they are all definite.

+
+ +
+

The center detail pattern shows the sidelobes of an OWA-design 20-element Yagi. We can easily count only 4 definite forward and 3 definite rearward sidelobes, where the large rear lobe is composed of an actual main lobe and 2 sidelobes. The gain of the forward sidelobes is very small indeed. (We shall turn to the right pattern in Fig. 1 shortly.)

+

The OWA 20-element design uses a 6.21 wavelength boom and is part of a series of OWA Yagis ranging from 7 to 20 elements. The array has the following dimensions. Note especially the position and lengths of the control directors (D2 and D3), with the forward control director being longer.

+ 
+Dimensions of "Original" 20-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.90                        -----
+Driver                      39.50                         8.79
+D1                          37.00                        13.47
+D2                          36.33                        25.38
+D3                          36.40                        40.73
+D4                          36.21                        61.38
+D5                          35.20                        86.49
+D6                          34.30                       116.00
+D7                          33.60                       146.60
+D8                          32.90                       178.40
+D9                          32.20                       210.00
+D10                         32.20                       243.00
+D11                         30.80                       276.00
+D12                         30.40                       309.00
+D13                         30.00                       342.00
+D14                         29.20                       375.00
+D15                         28.80                       408.00
+D16                         28.40                       441.00
+D17                         28.40                       475.00
+D18                         27.40                       502.00
+
+

Although the 12-element version of the array showed a gain deficit of about a half-dB relative to standard designs, the 20-element version is about 2 dB shy of DL6WU designs using the same boom length and number of elements. The checkpoint data table confirms this deficit.

+ 
+Modeled Performance: "Original" 20-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      15.19              24.51                       29.73 (bulge)
+                                                        31.80 (lobe)                20.95
+146      15.61              26.18                       31.06                       20.61
+148      15.68              25.11                       26.73                       19.66
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      33.8               36.2               42.9 + j4.5                          1.20
+146      32.4               34.6               46.8 + j6.6                          1.16
+148      31.2               33.4               45.1 - j4.0                          1.14
+
+

However, the front-to-back ratio is very good across the 2-meter band, and the sidelobe suppression is very high--approaching 30 dB on average. Like the 12-element arrays, the 20-element arrays are considered wide-band antennas and deserving of a scan from 140-150 MHz. Fig. 2 shows the modeled performance information for the array's free-space forward gain and the 180-degree front-to-back ratio.

+
+ +
+

The gain curve peaks within a MHz of the front-to-back peak, with both peaks well within the primary passband (144-148 MHz). The 20-element OWA Yagi has a 50-Ohm SWR curve almost identical to that of the 12-element version of the design. (As was the case with the 12-element Yagis, all of the 20-element Yagis are designed for a direct 50-Ohm feedline with no required matching network.) The SWR curve of the original design appears in Fig. 3.

+
+ +
+

In answer to a challenge to further reduce the SWR levels across the 2-meter band, I revised the design with this goal in mind. Unlike the 12-element Yagi, which responded well to mutual adjustments between the reflector and the final director, the 20-element version seemed insensitive to final director changes. Therefore, reducing the SWR level across the band required more significant changes to the lengths and spacing of the reflector-driver-director1 assembly. However, the "revised" line in Fig. 3 shows that SWR improvements were possible. The dimension tables shows the physical consequences of the adjustments needed to obtain the new curve. The boomlength is now 6.37 wavelengths.

+ 
+Dimensions of "Revised" "Original" 20-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.95                        -----
+Driver                      39.62                         9.88
+D1                          36.94                        14.18
+D2                          36.32                        25.98
+D3                          36.40                        41.32
+D4                          36.21                        61.98
+D5                          35.20                        87.09
+D6                          34.30                       116.60
+D7                          33.60                       147.20
+D8                          32.90                       179.00
+D9                          32.20                       210.60
+D10                         32.20                       243.60
+D11                         30.80                       276.60
+D12                         30.40                       309.60
+D13                         30.00                       342.60
+D14                         29.20                       375.60
+D15                         28.80                       408.60
+D16                         28.40                       441.60
+D17                         28.40                       476.60
+D18                         27.60                       514.60
+
+

The in-band performance is indicated by the following checkpoint data.

+ 
+
+Modeled Performance: "Revised" "Original" 20-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      15.19              24.77                       27.98 (bulge)
+                                                        32.04 (lobe)                20.70
+146      15.60              22.79                       31.07                       20.46
+148      15.67              25.69                       26.87                       19.69
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      33.6               36.2               49.3 + j4.7                          1.10
+146      32.4               34.6               51.5 + j4.7                          1.10
+148      31.2               33.2               50.8 - j4.8                          1.10
+
+

Overall, the revised design approximates the performance of the original OWA design. However, the sidelobe suppression is not as strong, although attenuation remains high. The right pattern in Fig. 1 shows at least 5 of the rearward sidelobes. The reason for this small degradation in sidelobe suppression has an indicator in the lower front-to-back value for the design frequency in the checkpoint data. The "revised" lines in Fig. 2 show that the gain peak coincides with neither of the two front-to-back peaks that emerged from the revisions. Whether or not sidelobe attenuation requires a coincidence of gain and front-to-back peaks remains an open question at this stage of the exploration. However, the revision gives us good evidence that sidelobe suppression suffers when the two peaks do not coincide closely in frequency.

+

In an effort to increase the gain of the OWA design, I redesigned it. The "improved" design removes about half of the gain deficit shown by the original OWA Yagi relative to standard 20 element designs. The following table shows the physical dimensions of the improved design on its 6.08 wavelength boom.

+ 
+Dimensions of "Improved" 20-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.90                        -----
+Driver                      39.50                         8.79
+D1                          37.06                        13.47
+D2                          36.48                        25.37
+D3                          36.54                        40.35
+D4                          36.41                        60.56
+D5                          35.61                        85.10
+D6                          34.90                       113.96
+D7                          34.34                       143.87
+D8                          33.80                       174.96
+D9                          33.25                       205.85
+D10                         33.25                       238.11
+D11                         32.15                       270.38
+D12                         31.83                       302.64
+D13                         31.52                       334.90
+D14                         30.88                       367.16
+D15                         30.57                       399.42
+D16                         30.25                       431.68
+D17                         30.25                       464.92
+D18                         29.46                       491.32
+
+

Within the 2-meter band, the array shows significant improvement in the gain category. The front-to-back ratio remains high. However, sidelobe suppression has slipped.

+ 
+Modeled Performance: "Improved" 20-Element OWA Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      16.03              24.53                       20.89 (bulge)
+                                                        29.27 (lobe)                21.67
+146      16.39              27.93                       26.21                       21.13
+148      16.20              24.85                       23.79                       19.63
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      31.2               33.2               42.7 + j3.7                          1.19
+146      30.0               31.6               45.6 + j7.5                          1.20
+148      29.2               31.0               47.2 - j7.8                          1.19
+
+
+ +
+

The center detail pattern in Fig. 4 shows that the redesign has moved the Yagi to the fringes of sidelobe suppression, although compared to the standard pattern on the left, attenuation remains quite high. We can count at least 5 forward sidelobes in the pattern. Over the broader passband, The array shows the characteristics of Fig. 5, which indicate a good coincidence between the gain and the front-to-back peaks.

+
+ +
+

Fig. 6 shows the 50-Ohm SWR curves for both the improved array and for its revision that attempts to achieve a lower SWR across the operating passband.

+
+ +
+

The SWR curve of the revised version of the improved array shows a considerable improvement over the original improved array. All of the revised (SWR-improved) versions of the arrays required longer booms than the originals, and the improved array is no exception. As the following dimension table shows, the boomlength is now 6.23 wavelengths.

+ 
+Dimensions of "Revised" "Improved" 20-Element OWA Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   41.50                        -----
+Driver                      39.82                        10.50
+D1                          37.06                        14.80
+D2                          36.48                        26.17
+D3                          36.54                        41.15
+D4                          36.41                        61.36
+D5                          35.61                        85.90
+D6                          34.90                       114.76
+D7                          34.34                       144.67
+D8                          33.80                       175.76
+D9                          33.25                       206.65
+D10                         33.25                       238.91
+D11                         32.15                       271.18
+D12                         31.83                       303.44
+D13                         31.52                       335.70
+D14                         30.88                       367.96
+D15                         30.57                       400.22
+D16                         30.25                       432.48
+D17                         30.25                       465.72
+D18                         29.50                       503.30
+
+

The in-band check data show that improved performance does not accompany improved SWR curves automatically. As the right pattern in Fig. 4 reveals--confirmed by the data table--the revision to the so-called improved Yagi worsens the sidelobe suppression. We can count 5 rearward sidelobes, and the 6th forward sidelobe is just beginning to appear.

+ 
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      15.99              30.77                       20.47 (bulge)
+                                                        29.01 (lobe)                21.04
+146      16.36              23.36                       26.21 (bulge)
+                                                        30.00 (lobe)                21.14
+148      16.21              22.95                       24.31                       20.02
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      31.2               33.0               50.4 + j4.1                          1.09
+146      29.8               31.6               50.9 + j4.9                          1.10
+148      29.0               30.8               51.4 - j4.5                          1.10
+
+

Again, part of the reason for the movement from sidelobe suppression to sidelobe attenuation appears to result from the failure of the gain and front-to-back peaks to coincide with respect to frequency. The "revised" lines in Fig. 5 show just how far apart these peaks are for the present design (over 2 MHz).

+

We have so far examined at least two ways in which high sidelobe suppression degrades into sidelobe attenuation. However, all of the examples so far have begun with a basic 20-element OWA design. For comparison--as we did when examining 12-element designs--we should examine some standard, that is, DL6WU 20-element Yagis. In the following notes, I shall look at designs derived from the DL6WU-GG program and from the VK3AUU modification that aimed for maximum performance from a 19-element Yagi. Like the OWA designs, the element are 3/16" in diameter, but since metrics are in use for these designs, the diameter is 4.7625 mm.

+
+ +
+

The DL6WU-GG version of the array shows the details on the left of Fig. 7. These details emerge from the following dimensions.

+ 
+Dimensions of DL6WU (GG) 20-Element Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in inches, divide by
+25.4
+
+Element                     Length                      Space from Reflector
+                            millimeters                 millimeters
+Reflector                   1004.92                      -----
+Driver                      994.74                       410.7
+D1                          924.21                       564.7
+D2                          916.71                       934.3
+D3                          908.07                      1375.8
+D4                          899.54                      1889.1
+D5                          891.86                      2664.1
+D6                          885.15                      3080.1
+D7                          879.30                      3726.9
+D8                          874.16                      4404.5
+D9                          869.60                      5112.9
+D10                         865.51                      5852.1
+D11                         861.81                      6622.1
+D12                         858.43                      7423.0
+D13                         855.32                      8244.3
+D14                         852.44                      9065.7
+D15                         849.76                      9887.0
+D16                         847.25                      10708.4
+D17                         844.89                      11529.7
+D18                         842.67                      12351.1
+
+

The 12.3-meter boom translates into 6.02 wavelengths at 146 MHz. Within 2 meters, the following table records check-point data.

+ 
+Modeled Performance: DL6WU (GG) 20-Element Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      16.98              17.26                       16.47                       14.38
+146      17.57              25.95                       17.12                       15.22
+148      17.60              19.00                       16.42                       14.87
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      26.8               28.2               51.9 - j5.7                          1.13
+146      25.2               26.2               51.9 + j1.5                          1.26
+148      23.8               24.6               60.5 - j5.2                          1.24
+
+

Unlike the 12-element version of the array, the design frequency coincides with a front-to-back peak frequency. The gain is about a dB better than for even the improved OWA Yagi. However, horizontal sidelobe attenuation is mediocre at best, and vertical sidelobe attenuation is even worse. For a broader view of the antenna's performance, see Fig. 8.

+
+ +
+

One of the hallmarks of standard DL6WU designs is the exceptional SWR bandwidth that all boomlengths achieve. Fig. 9 shows the rippling low 50-Ohm SWR across the expanded passband. The 10-MHz or 7% bandwidth of the scan does not show an SWR value greater than 1.5:1. For this reason, DL6WU designs lend themselves to relatively easy replication in modest home workshops.

+
+ +
+

The VK3AUU revised algorithms do not yield the same bandwidth as the original design equations, as the SWR curve in Fig. 9 clearly shows. Using a different wide-band reflector-driver-director1 assembly, the VK3AUU version of the antenna has the following dimensions on a 6.01 wavelength boom. Most of the variations from the original design are a function of the revised 50-Ohm driving assembly.

+ 
+Dimensions of DL6WU (VK3AUU) 20-Element Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in inches, divide by
+25.4
+
+Element                     Length                      Space from Reflector
+                            millimeters                 millimeters
+Reflector                   992                          -----
+Driver                      972                          375
+D1                          904                          543
+D2                          894                          884
+D3                          886                         1326
+D4                          877                         1840
+D5                          870                         2410
+D6                          863                         3026
+D7                          856                         3680
+D8                          850                         4368
+D9                          844                         5085
+D10                         839                         5829
+D11                         834                         6596
+D12                         830                         7385
+D13                         826                         8194
+D14                         822                         9022
+D15                         818                         9850
+D16                         815                         10677
+D17                         812                         11505
+D18                         802                         12333
+
+

As a measure of in-band performance, the following modeled performance table may be useful.

+ 
+Modeled Performance: DL6WU (VK3AUU) 20-Element Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      17.20              19.82                       17.34                       15.31
+146      17.68              32.86                       17.62                       15.84
+148      17.42              15.83                       15.83                       16.95
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      26.4               27.6               36.5 - j5.5                          1.41
+146      24.8               25.8               50.5 + j14.27                        1.32
+148      23.6               24.4               48.7 - j16.8                         1.40
+
+

The gain across the 2-meter band is more level than with the original DL6WU design, but the front-to-back ratio shows a sharper peak. Horizontal sidelobe attenuation tends to follow the pattern of the front-to-back ratio, although the vertical sidelobe attenuation shows the opposite trend. Fig. 8 shows not only the greater front-to-back ratio peak, but as well the fact that it is offset by about 1 MHz from the forward gain peak. In the end, with respect to sidelobe attenuation, there is little to choose between these versions of the DL6WU 20-element Yagi, as shown by comparing the left and center portions of Fig. 7.

+

A special Note on a 25-Element 6-Wavelength Yagi

+

David Tanner, VK3AUU, has been developing an interesting variation of the 6 wavelength 2-meter Yagi without realizing that fact. His basic work involves a computer-generated design for the 70-cm band. Like the DL6WU designs, one can trim the number of elements without adversely affecting basic performance, except--of course--for the inevitable reduction in gain. When scaled to 146 MHz and trimmed to 6 wavelengths (6.11 wavelengths, to be more precise), the array holds 25 elements, a higher element population density than most other designs. To make the array design match the others in this group, I reduced the element diameter to 3/16". The following table shows the dimensions of this adaptation of the VK3AUU high-density design.

+ 
+Dimensions of VK3AUU 25-Element Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   41.41                        -----
+Driver                      40.60                        16.10
+D1                          37.15                        18.88
+D2                          36.66                        28.63
+D3                          36.23                        41.29
+D4                          35.81                        56.01
+D5                          35.38                        72.34
+D6                          35.03                        89.95
+D7                          34.68                       108.69
+D8                          34.39                       128.38
+D9                          34.04                       148.93
+D10                         33.83                       170.21
+D11                         33.54                       192.16
+D12                         33.33                       214.77
+D13                         33.12                       237.94
+D14                         32.91                       261.63
+D15                         32.97                       285.84
+D16                         32.55                       310.49
+D17                         32.34                       335.58
+D18                         32.20                       361.07
+D19                         32.06                       386.96
+D20                         31.99                       413.21
+D21                         31.85                       439.83
+D22                         31.71                       466.76
+D23                         31.63                       494.03
+
+

The following in-band chart of modeled performance data shows that the array design achieves two significant goals that appear to be in conflict when using only 20-elements on the same 6 wavelength boom. First, his design retains almost all of the DL6WU gain, with a very solid front-to-back ratio. Second, the sidelobe reduction values are excellent, almost at the OWA level. Hence, the design represents a very good compromise that gives us nearly the best of both worlds of design.

+ 
+Modeled Performance: VK3AUU 25-Element Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      16.91              25.01                       20.10                       18.03
+146      17.22              35.59                       22.29                       20.37
+148      17.27              23.61                       24.25                       21.89
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      28.2               29.6               56.5 + j2.8                          1.14
+146      27.0               28.4               59.6 + j3.9                          1.21
+148      26.4               27.6               49.6 + j6.6                          1.14
+
+
+ +
+

As shown in Fig. 10, the broadband performance curves for the array are very respectable, although the gain and front-to-back peaks are separated by 2 MHz. The right-most detail patterns in Fig. 7 shows that the design achieves high attenuation without suppression. We can count all 6 sidelobes, both forward and rearward. The 50-Ohm SWR curve is also excellent, as shown in Fig. 11. The peak value does not reach 1.3:1 anywhere in the expanded passband.

+
+ +
+

It is interesting to compare the relative current magnitude values on the strings of elements making up each of the major strains of Yagi design covered in this exploration. We may also compare the forms created by these values with those of the 12-element Yagis in the preceding episode. Fig. 12 shows the current magnitudes as vertical lines extending from each element upward. The driver element in each case has a relative value of 1.0. In all four samples, the first director or secondary driver shows a higher current level.

+
+ +
+

The DL6WU 20-element design produces a curve that resembles a damped sine wave, an extended version of the curve presented by the 12-element Yagi. In contrast, the original and "improved" OWA design shown a steady downward progression in relative current magnitude. Both versions of the array show the typical pattern of control director currents. However, the rate of decrease in the improved design is smaller, resulting in that array's higher gain.

+

At first sight, the VK3AUU 25-element design appears to follow the OWA pattern of current magnitudes. However, if you create a smooth curve with some sort of linear object, you will discover that the curves actually show traces of the DL6WU sine-wave, that is, the periodic rises and falls of the current level as we move from the first the the last director. Like the performance values--and perhaps as one source of them--the current magnitude curves arrive at a compromise between the DL6WU and OWA curves.

+

I have in the past created hybrids by grafting the VK3AUU set of directors onto the OWA drive section. The results of these test configurations have been disappointing, yielding essentially only the performance of the VK3AUU array without improvement to the sidelobe suppression. However, those test designs made no attempt to significantly alter the dimensions of the control directors to see what these elements might do to improve sidelobe reduction. As a proof-of-principle only design, I approached the hybrid Yagi once more. The goal was to see if adjusting the control directors (D2 and D3) might improve the sidelobe suppression to at least 25 dB and from that point, to also see if there would be a tendency toward sidelobe suppression as well as attenuation.

+

One limitation of the exercise is the element length ratios used by the various designs. The gain-oriented DL6WU designs use for 20 elements a ratio of about 1.19:1 for 20 elements on a 6 wavelength boom. At the opposite end of the scale, the original OWA uses a ratio of about 1.49:1, comparing the longest to the shortest element in the array. The so-called improved version drops the ratio to about 1.39:1, showing that even a small drop in the element ratio can result in a degradation of sidelobe suppression. However, both ratios are well above the 12-element OWA ratio of 1.31:1, a fact that tracks the increased gain deficit in the longer OWA designs relative to the DL6WU standard.

+

The original VK3AUU 25-element array uses a ratio of about 1.26:1, which is not far distant from the ratio employed by the N4FG 12-element array. Hence, the exercise was unlikely to produce the full sidelobe suppression achieved by the original OWA 20-element design. Since the directors from #4 though #23 would remain essentially unchanged, the slight damped sine-wave appearance of the current magnitudes would also likely remain. So the questions boiled down to these three: 1. Could the adjustment of control directors within the hybrid result in sidelobe improvements? 2. If so, at what cost to the array gain and other performance values? 3. What other side effects might result from the exercise? One factor not optimized in the design work was the SWR curve for the array. The effort aimed to see if the combination of ingredients--with special attention to the control elements--might effect changes to the sidelobe suppression level. The original VK3AUU design is perfectly satisfactory for most practical uses requiring very low sidelobes.

+

The dimensions for the VK3AUU/OWA hybrid appear in the following table. The new driver section produced a 6.14 wavelength boom, requiring a 2.5" displacement of the VK3AUU directors. Otherwise, only the dimensions of the first 5 elements differ from the VK3AUU original.

+ 
+Dimensions of VK3AUU/OWA Hybrid 25-Element Yagi
+
+Notes:  Element diameter: 0.1875" (3/16" or 4.76 mm).  For dimensions in millimeters,
+multiply by 25.4
+
+Element                     Length                      Space from Reflector
+                            inches                      inches
+Reflector                   40.70                        -----
+Driver                      39.22                         9.80
+D1                          36.28                        14.00
+D2                          36.62                        26.20
+D3                          36.98                        42.00
+D4                          35.81                        58.51
+D5                          35.38                        74.84
+D6                          35.03                        92.45
+D7                          34.68                       111.19
+D8                          34.39                       130.88
+D9                          34.04                       151.43
+D10                         33.83                       172.71
+D11                         33.54                       194.66
+D12                         33.33                       217.27
+D13                         33.12                       240.44
+D14                         32.91                       264.13
+D15                         32.97                       288.34
+D16                         32.55                       312.99
+D17                         32.34                       338.08
+D18                         32.20                       363.57
+D19                         32.06                       389.46
+D20                         31.99                       415.71
+D21                         31.85                       442.33
+D22                         31.71                       469.26
+D23                         31.63                       496.53
+
+

Element D2 and D3 are the control directors. In the original OWA design, their lengths are 36.48" and 36.54", respectively. To obtain a minimum 25-dB front-to-sidelobe level in the hybrid design, D2 became 36.62" and D3 grew to 36.98". Both elements are much longer than in the original, a fact that is the likely source of not experimenting with them extensively in past hybrid experiments. As well, ratio of lengths in the original is only about 1.002:1. In the new hybrid, the ratio of D3 to D2 is 1.01:1. Further extensions of the control directors is possible for a gradual improvement on sidelobe performance, but the stopping point in this exercise produce a front-to-sidelobe ratio of 25 dB.

+ 
+Modeled Performance: VK3AUU/OWA Hybrid 25-Element Yagi
+
+Freq.    Free-Space         180-Deg. Front-             Hor. F-S/l                  Vert F/S/l
+MHz      Gain dBi           Back Ratio dB               Ratio dB                    Ratio dB
+144      16.41              26.28                       21.86                       19.81
+146      17.02              27.38                       25.00                       20.48
+148      16.91              26.90                       22.68                       19.66
+
+Freq.    Hor BW             Vert BW            Feedpoint Impedance                  50-Ohm
+MHz      degrees            degrees            R +/- jX Ohms                        SWR
+144      27.8               29.2               46.2 + j0.6                          1.08
+146      26.8               28.2               45.1 - j3.1                          1.13
+148      26.9               27.8               30.4 + j12.4                         1.82
+
+

Fig. 13 compares the detailed patterns of the original VK3AUU and the hybrid. Although only on the fringe of true sidelobe attenuation, the pattern shows only 5 rearward lobes. As well, the forward sidelobes show signs of merging into two groups.

+
+ +
+

Fig. 14 shows the current magnitude pattern for the array. Because the SWR curve is not well controlled in this model, the driver current is higher than the current on the first director. The directors past the control directors show the same characteristic curve as the original VK3AUU. That curve is largely responsible for the hybrid model losing only about 0.2 dB gain relative to the original array.

+
+ +
+

The uncontrolled SWR characteristics of the experimental design also result in the gain and front-to-back peak values occurring lower in the passband than with other designs in this series. However, as shown in Fig. 15, the peaks are within 0.5 MHz of each other. In the course of working toward the target sidelobe reduction level, I found that the farther apart the two peak values were, the lower the sidelobe reduction level.

+
+ +
+

Some Tentative Conclusions

+

The one assertion that does not fall among these conclusions is that anyone should in fact build an OWA or hybrid-OWA Yagi design. For practical purposes, sidelobe attenuation will likely satisfy any operational need where the level of sidelobes in a standard design are too strong. However, curiosity rather than practicality drove this exploration, so it is reasonable to carry matters to their conclusion.

+

1. Effective sidelobe suppression is possible on long boom Yagis. However, the element taper ratio required yields a current magnitude pattern that results in a relatively high gain deficit that grows as the boom length grows.

+

2. Effective sidelobe suppression requires an element taper ratio greater than 1.3:1 in shorter boom lengths and greater than 1.45:1 in longer boom lengths.

+

3. Maximum sidelobe suppression tends to occur if the peak gain and peak front-to-back values occur on the same or nearly the same frequency within the operating passband of the array.

+

4. The OWA control directors appear to be an essential ingredient in the move from sidelobe attenuation to sidelobe suppression, wherein sidelobes merge and/or disappear. The apparent mechanism lies in the re-direction of at least some sidelobe angles.

+

5. A high element taper ratio, a smooth descending current magnitude pattern, coincidence of gain and front-to-back peak values, and effective design of the control directors all appear to be necessary conditions of significant sidelobe suppression. However, no one of these factors is itself a sufficient condition of sidelobe suppression. Rather, the combination of the four factors together appears sufficient of suppress sidelobes at a value in the E-plane of about 30 dB or so at and near the design frequency for long boom Yagis. Such values are about 5-7 dB better than virtually all sidelobe attenuation techniques.

+

6. At present, it does not appear to be feasible to suppress all sidelobes in long-boom Yagis. However, even in the most critical situation, sidelobe attenuation greater than 20 dB appears to satisfy virtually any Yagi application need.

+

In the exploration of sidelobe suppression and attenuation, I have looked both forward and backward in time relative to Yagi design considerations for long boom arrays. For EME and similar operational needs calling for a 6 wavelength or longer design, the VK3AUU design is especially attractive for its combination of relatively high gain and relatively tiny sidelobes. The fact that it requires 5 extra directors should be no deterrent to its use, since the boom itself will weigh more than all of the elements combined. However, this expedition has not exhausted the range of long-boom Yagi designs by any means. For a survey of 70-cm band long-boom Yagis, see "Preliminary Studies of Long-Boom Yagis for 420-450 MHz."

+
+ +
+

Updated 10-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/thumb-rules.html b/content/vhf/thumb-rules.html new file mode 100644 index 0000000..831ad90 --- /dev/null +++ b/content/vhf/thumb-rules.html @@ -0,0 +1,18 @@ + + + + + + Long-Boom Yagi Rules of Thumb: A Comparison with Modeling Data + + + +

Long-Boom Yagi Rules of Thumb
+ A Comparison with Modeling Data

+ hr +

Long-Boom Yagi Rules of Thumb: A Comparison with Modeling Data

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: VHF / UHF, Yagi


+ + \ No newline at end of file diff --git a/content/vhf/thumb-rules.pdf b/content/vhf/thumb-rules.pdf new file mode 100644 index 0000000..30a3ec3 Binary files /dev/null and b/content/vhf/thumb-rules.pdf differ diff --git a/content/vhf/tilt.html b/content/vhf/tilt.html new file mode 100644 index 0000000..812362b --- /dev/null +++ b/content/vhf/tilt.html @@ -0,0 +1,17 @@ + + + + + + A Short Note on Tilted Vertical VHF Antennas + + + +

A Short Note on Tilted Vertical VHF Antennas

+ hr +

A Short Note on Tilted Vertical VHF Antennas

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: VHF / UHF, Vertical


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+

What's Wrong With This Turnstile Stack?

+

+
+

L. B. Cebik, W4RNL

+

+
+ +
+

The turnstiled dipole is perhaps the most common horizontally polarized omni-directional antenna used by amateurs from about 10 meters upward into the VHF and UHF area. From about 50 MHz upward, we can stack a pair of turnstiles with a vertical 1/2 wavelength separation. By feeding the two antenna sets in phase, we increase the low-angle gain considerably, while retaining the omni-directional pattern. These techniques go back to the 1950s or earlier. The general outline of the system appears in Fig. 1.

+
+ +
+

Each antenna in the stack consists of two dipoles set at right angle to each other. Since each dipole creates a figure-8 pattern, the sum of the two patterns approximates a circle. However, to achieve this goal, we must feed one dipole with feedpoint current that is equal in magnitude to the other but 90 degrees out of phase. The most common method used by amateurs is the 1/4 wavelength phasing line.

+

The phase lines shown in Fig. 1 do not specify a characteristic impedance (Zo) of physical length. If we start with a resonant dipole, then the feedpoint impedance is about 70 Ohms. The phase line Zo should be equal to that impedance. 70-Ohm line are common and may be standard or foam dielectric coax or that may be parallel line (which is quite difficult to obtain these days). We need to be as precise as possible in this match or the pattern will lose its circularity.

+

The physical length of the line will be a function of the line's velocity factor (VF). The VF of common coax is about 0.66 to 0.67, while foam lines have a VF in the vicinity of 0.78. The physical length of the line will be the VF times the electrical length, which is 1/4 wavelength at the design frequency.

+

The net feedpoint impedance to the feedline or to the matching transformer sections shown in Fig. 1 will be 1/2 the impedance of the individual dipoles. Hence, we can expect a value of 35 Ohms. In order to effect a good match with common 50-Ohm cable used as the main feedline, we need to change this low impedance to something close to 100 Ohms. Then, the two 100-Ohm impedances will be in parallel, yielding a 50-Ohm impedance that closely matches the main feedline Zo.

+

The required matching transformer Zo is the square root of the product of the feedpoint impedance and the main feedline impedance. 35 times 50 is 1750, and the square root is about 42 Ohms. Hence, we may use 50-Ohm line for the transformer sections, although we shall obtain a 71 Ohm impedance at their ends, or a 35.5-Ohm net impedance for the main feedline. However, if the 1.4:1 SWR is not a problem, the system will work. If we use 63-Ohm line for the matching transformer sections, we obtain an end impedance of about 113 Ohms, or about 57 Ohms for the parallel combination. This selection results in an SWR of about 1.13:1 at the main feedline.

+

Since the lines--usually coax--used for the transformer sections also have a VF, and since the antenna sets are 1/2 wavelength apart, we cannot use 1/4 wavelength lines as the transformers. However, we can use 3/4 wavelength lines to achieve the same impedance transformation.

+

Why should we go to all of this trouble to make a stack of 2 turnstiles spaced 1.2 wavelength apart. Fig. 2 tells the story.

+
+ +
+

A single turnstile (where the term "turnstile" will mean here a pair of turnstiled dipoles) yields an elevation pattern like the top pattern in Fig. 2 when we place the antenna 1 wavelength above ground. At 50 MHz, this is just about 20'. Note that the generally useless upper lobe is actually stronger than the lower lobe. We waste power if our goal is omni-directional point-to-point communications.

+

However, the lower pattern shows what happens if we place the lower turnstile at 1 wavelength and the upper at 1.5 wavelength above ground. The 1/2 wavelength spacing reduces the radiation at higher angles to a practical minimum, and enhances the power available at the lowest elevation angle. Due to the presence of the higher turnstile, the elevation angle of the lowest lobe moves from about 14 degrees for a single turnstile to about 11 degrees for the pair.

+
+ +
+

Now, if we have done our work well, we shall obtain the azimuth pattern in Fig. 3. The gain will be close to 8.5 dBi maximum. Because the dipoles cannot yield a perfect circle, there is a maximum variation in the outer circle of about 1.3 dB, but for most purposes, that value is acceptable. (If we wish a more precisely circular pattern, we would have to turn to squares, rectangles, circles, and triangles for the shape of our antenna, but that turn would lead us to an entirely different set of design considerations.)

+

Now let's freeze a design for 50.5 MHz and see what we actually obtain. We shall use 0.44" diameter aluminum as our element. This diameter approximates the effective diameter of a dipole composed of 1/2" inner sections and 3/8" outer tips. We shall perform our design exercise using NEC-4, although NEC-2 would do as well. The total length of a dipole that is resonant at a height of 1 wavelength (20') is 111.5". The impedance is almost exactly 70.0 Ohms.

+

We create a turnstile pair by placing one dipole above the other with a spacing of not more than 1" to ensure that we simulate well the turnstile with dipole at the same level. In the model, we can use a 90-degree long 70-Ohm phase line between the center segments of the dipoles, with a source on only one of the dipoles. Then, we create the second dipole turnstile at 30' or 1.5 wavelength above ground. We use the same the line system. Use care to place the source on dipoles that align with each other, or else the final pattern will not approximate a circle, but show a figure-8 pattern at 45 degrees to the dipole lengths.

+

We need not model the matching transformers, since they will in no way affect the final antenna pattern--unless we create them with serious flaws. We can use separate source for the two dipole sets, so long as we design into the model the require phase lines. The TL facility in NEC makes this part of the design simple, although the lines will not have any loss. However, since the lines are only 1/4 wavelength long, no significant error should emerge from the result.

+

Now, what do we get. See Fig. 4.

+
+ +
+

The pattern in Fig. 4 is no illusion. It has a maximum gain of about 9.1 dBi at 11 degrees elevation angle. The gain variation is more than 3.8 dB around the perimeter. This shape is far from what we intended in our original design. However, the impedance of the turnstile feedpoints will not give us a clue as to what has gone wrong. Each feedpoint reports an impedance of about 37 Ohms, with a 2-Ohm capacitive reactance. Surely this is close to ideal.

+

Unfortunately, designing a turnstile for impedance is one of the most common ways to be misled by the antenna. Turnstiled dipoles exhibit a very broad and flat SWR curve well beyond the frequencies at which the pattern goes to pot. The amateur designer needs to look at the currents at the dipole centers to get a sense of what is happening.

+

The lower dipole pair shows relative currents of 0.62 at 17.6 degrees phase angle and 0.53 at -93.3 degrees. The ratio of currents is not the desired 1:1 but closer to 1.16:1. The phase angle difference is not 90 degrees, but 110.9 degrees. The upper dipoles show values of 0.61 at 17.5 degrees and 0.53 at -93.3 degrees. Once more, the current is 1.15:1, with a phase difference of 110.8 degrees. Little wonder that our resulting turnstile stack shows an azimuth pattern in Fig. 4 that is seriously distorted relative to the ideal pattern in Fig. 3.

+

What Went Wrong and How Do We Fix It?

What went wrong in our stacked turnstile array was a failure on our part to appreciate a fundamental aspect of antenna elements for the same frequency set in close proximity. 1/2 wavelength is not distant for dipoles, and we did align them with each other. Moreover, we set them in a vertical alignment so that radiation downward would reflect upward and enter into the element interactions. +

The mutual coupling of elements is a primary aspect of both phased arrays and parasitic arrays. In many types of amateur antennas, such as the Lazy-H, we tend to ignore mutual coupling, because we intend only to achieve the highest possible gain n a bi-directional pattern and to feed the antenna with parallel line going to an antenna tuner. Since the tuner will take care of any impedance variations owing to construction, we tend to overlook the fine points of Lazy-H design.

+

However, we cannot be so cavalier with a stacked turnstile array. Where our initial design went awry was in our use of a single dipole as the baseline element in the array. To design a more nearly perfect stack of turnstiles, we need to start over again. This time, let's use a 1/2 wavelength spaced stack of single dipoles with the lower one 1 wavelength above ground. This procedure will take into account the mutual coupling between elements as we strive to obtain a resonant length for the 0.44" diameter aluminum elements.

+

If we start by stripping away from our stack model the phase lines and 1 dipole from each set, we can glimpse what went wrong. The resulting stack of dipoles, each 111.5" long, shows a feedpoint impedance of 56 - j 22 Ohms for the lower element and 56 - j 23 Ohms for the upper. These elements are far from resonant in their stacked environment.

+

If we lengthen the elements to 114.7", we come close to resonance. The lower dipole shows an impedance of 61 + j 3 Ohms, while the upper element has a feedpoint impedance of 61 + j 1 Ohms. First, we should note our close approach to perfect resonance. Second, we should note the resistive part of the impedance. We used a 70-Ohm phase line for a single turnstile because the resonant impedance of a single dipole was just about 70 Ohms. The required phase line Zo for the stack is determined by the resonant impedance of the individual dipoles in the stack, or 61 Ohms. A 63-Ohm line seems in order here. Actually, we can make such a line from parallel sections of RG-63, which has a 125-Ohm impedance and is available from The Wireman (of South Carolina).

+

Remember that precision is required in any turnstile design. Going to 70-Ohm line will yield distortions of pattern in each part of our turnstile. So to make a turnstile with close to ideal patterns, we must be sure that the phase line Zo closely matches the resonant impedance of the individual dipoles within the array. Of course, in the process, we should not forget to take into account the VF of the line used in determining the physical length of the phase lines.

+

If we reconstruct our model of the turnstile stack using the new element length and the new phase lines, we obtain exactly the pattern in Fig. 3, since that pattern was taken from this final model. The model presumes turnstile heights of 1.0 and 1.5 wavelength above ground. The ground quality will not make a significant difference in the final design. However, a significant lowering of the array may make some difference. For example, if you plan to place the lower turnstile at only 1/2 wavelength above ground, you should remodel the dipole stack before moving to a full turnstile stack model.

+

The net feedpoint impedances for the turnstiles as re-designed are both 31.5 Ohms with only fractional values for reactance. We need to use 3/4 wavelength impedance transforming sections to arrive at as close to 100 Ohms or a parallel combination of 50 Ohms to match the main feedline. 50-Ohm transformer lines will yield almost an 80 Ohm end impedance or a parallel combination of just under 40 Ohms. Hence, we have a 1.25:1 SWR for the main feedline. A 63-Ohm line (parallel 125-Ohm coax lengths) will yield an impedance of 126 Ohms or a parallel combination of 63 Ohms--again, a 1.25:1 SWR for the 50-Ohm main line. Take your pick, because the SWR value at the main feedline junction will not affect the antenna patterns, but only the level of loss in the main line itself. Most folks have no problems with a 1.25:1 SWR, even at 50 MHz.

+

Most amateurs do not realize how finicky the simple turnstile can be if an omni-directional pattern is the goal. There are techniques for forcing the current division and phase-angle differential that lie outside the somewhat ancient techniques used in this basic construction project. However, with the simple phase line used in this project, the turnstile yields a pattern far from ideal with only small departures from the design values.

+

For turnstile construction--usually viewed as quite simple--there are additional issues. Isolating the lines from each other by eliminating external braid currents is sometimes a difficulty. However, the chief problem that I have seen is the fact that builders seem satisfied that all is well if the feedpoint impedances are close to ideal. As noted earlier, for a common turnstile, the feedpoint impedance is one of the least informative performance figures. As well, design modelers often make the mistake of designing only to the design frequency and failing to explore in a frequency sweep just how well the pattern will hold up at frequencies on either side of the design frequency. For an account of some of the effects of being off target with a turnstile, see "Some Notes on Turnstile-Antenna Properties," QEX (Mar/Apr, 2002), pp. 35-46.

+

The turnstile is also not the most ideal antenna if one desires a truly circular pattern--especially one that holds its shape for at least 0.5 MHz each side of the design frequency. Much simpler are well-designed halos of various shapes. Unfortunately, most halos--interrupted loops in the 0.5-0.8 wavelength total circumference region--are not well designed. However, some recent work on triangular designs appears both promising and relatively simple from a construction perspective. The 1.3-dB variation in gain in our ideal turnstile can be theoretically reduced to under 0.1 dB and practically reduced to under 0.5 dB.

+

Nonetheless, the turnstile remains the most common omni-directional horizontally polarized antenna in use in the VHF/UHF region. If we choose to go that direction and if we wish to stack a pair for higher performance, then we must take into account the mutual coupling between the upper and lower elements to produce a turnstile that comes closer to our goals.

+
+ +
+

Updated 05-15-2002. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
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+

Return to Main Index

+

Topics: Stacking, Turnstile, VHF / UHF


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+

Wide-Band Utility Yagis for 420-450 MHz
+ Part 1: 4- and 6-Element Models

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

High-gain narrow-bandwidth Yagis for the 420-450 MHz band abound in the literature, and there are some very fine designs to be found. Less apparent are small wide-band Yagis for this band that can be used for utility purposes. They may be out there and these notes may be a classic case of reinventing the wheel. However, taking a look at a few such designs might still be useful.

+

The operating goal would be to have useful and relatively even gain across the entire passband. If something must be sacrificed for the operating bandwidth, it may be the front-to-back ratio. However, the SWR curve must be as smooth and low as possible without detracting from the gain. For this reason, I set two goals for the SWR curve.

+

The first goal was to use a 50-Ohm feedpoint impedance and to eliminate the need for matching fixtures. Although matching fixtures associated with Tee networks can be assembled so as to reduce losses to the negligible level, a utility antenna is likely to be assembled quickly and receive many a thump in its travels from one location to another. The fewer fixtures, the better.

+

Second, the target maximum SWR at 50 Ohms was set at 1.3:1 across the passband. Achieving this goal for a 7% passband is a challenge, assuming that one wishes to have some reasonable operating characteristics across the same passband.

+

The choice of 1.3:1 as the SWR limit arose from considering the losses in the cable between the rig and the antenna. The difference in cable loss between a 2:1 and a 1.3:1 SWR for 50' of RG-58 is about 0.375 dB. For RG8X, a commonly used alternative for utility purposes, the difference is about 0.31 dB/50' of line. (Half-inch 50-Ohm hardline would show only a 0.16 dB/50' difference. Exact numbers will vary with the exact cable used, and these numbers are for general guidance only.) Since performance usually decreases toward the band edges--just the place that one tends to find the higher SWR level, even with a wide-band Yagi design--holding the SWR as low as feasible seemed a worthy goal.

+

Let's begin small, say with 4- and 6-element versions of the antenna. Next time, we shall look at an 8-element wide-band Yagi.

+

A 4-Element Wide-Band Yagi

+
+ +
+

Fig. 1 shows the outline of a wide-band 4-element Yagi. In its design are some of the OWA (optimized wide-band antenna) principles that govern the use of the first director to set--in conjunction with the lengths and spacing of the reflector and driver--the feedpoint impedance curve. However, even OWA principles will not cover the wide passband with an acceptable SWR curve without a second step: using "fat" elements.

+

There is a near fetish against the use of fat elements at UHF, mostly bred of experience with very long-boom Yagis. It is claimed that their weight and wind load are simple too high to use. For small utility Yagis, these claims become largely irrelevant. Therefore, the designs shown here use 0.5" (12.7 mm) tubing.

+

Tubing has an advantage over solid rod in UHF design. Even the common 3/16" or 4 mm rods used by most designs show considerable capacitance across the feedpoint at UHF and up due to the faces of the rod ends and the feedpoint gap. Tubing reduces the capacitance. In fact, beveling the tubing from the inside can reduce the capacitance further. Moreover, with some ingenuity, cable or connector connections can be made to the tubing inside, eliminating bumps in the element diameter.

+

The dimensions for the 4-element design are in the following table, with element lengths and spacing from the reflector shown both in inches and in millimeters.

+ 
4-Element Wide-Band Yagi Dimensions
+
+Element           Length                  Spacing From Reflector
+                  Inches      mm          Inches      mm
+Reflector         13.15       334         -----       -----
+Driver            12.17       309          5.81       147.5
+Dir. 1            10.91       277          9.63       244.5
+Dir. 2            10.51       267         15.75       400.0
+

This design was developed on NEC-4 (NEC-4D shows no differences from NEC-4). However, the design effort is not without some issues of its own. One such issue is convergence. Half-inch elements begin to approach the limits of NEC recommendations for length-to-radius ratios as the level of segmentation is increased. The designs were tested at 11, 15, and 19 segments per element. More than 19 segments per element resulted in initial warnings concerning the recommended segment length-to-radius limits. The following table illustrates the differences in results.

+ 
Frequency and                       Segmentation Level
+ Parameter              11 seg/element    15 seg/element    19 seg/element
+420 MHz
+Free-Space Gain dBi     9.13              9.13              9.12
+Front-to-Back dB        11.50             11.49             11.45
+Feed Z (R +/- jX)       45.9 - j 3.0      45.6 - j 3.8      45.0 - j 4.7
+50-Ohm SWR              1.113             1.130             1.154
+435 MHz
+Free-Space Gain dBi     9.30              9.29              9.29
+Front-to-Back dB        12.35             12.34             12.32
+Feed Z (R +/- jX)       60.0 - j 0.0      59.9 - j 0.6      59.6 - j 1.1
+50-Ohm SWR              1.200             1.198             1.193
+450 MHz
+Free-Space Gain dBi     9.58              9.57              9.55
+Front-to-Back dB        14.46             14.35             14.21
+Feed Z (R +/- jX)       47.1 - j 7.9      48.2 - j 8.4      49.4 - j 9.0
+50-Ohm SWR              1.189             1.191             1.198
+

Despite the numeric fluctuation, the values are sufficiently close to consider the model reliable within the context of NEC-4 modeling. In graphs, unless otherwise indicated, the 15 segment/element model is used.

+

However, models for designs such as these can be developed on a variety of modeling platforms. Most common is NEC-2, used in most low end versions of modeling software. An alternative is MININEC 3.13, which is used in such software as ELNEC and NEC4WIN. The latter contains an option for running MININEC as is or with a correction factor that will better match it to NEC-2 results. We can compare these programs in a similar table of end and mid-band values to see what we might expect. For example, there are reports of a deviation at UHF and above between NEC-2 and NEC-4 for narrow-band high-gain Yagis. Finding out whether the difference shows up for small wide-band designs is worth the extra modeling effort. The NEC model uses 15 segments per element, while the MININEC model uses 14 segments per element.

+ 
Frequency and                       Program
+ Parameter              NEC-2             MININEC w/corr    MININEC w/o corr
+420 MHz
+Free-Space Gain dBi     9.17              9.44              8.93
+Front-to-Back dB        11.69             10.79             10.28
+Feed Z (R +/- jX)       47.8 - j 1.1      47.4 - j 5.4      37.5 - j13.2
+50-Ohm SWR              1.053             1.130             1.520
+435 MHz
+Free-Space Gain dBi     9.33              9.59              9.14
+Front-to-Back dB        12.48             12.01             11.86
+Feed Z (R +/- jX)       61.0 - j 0.7      50.6 - j16.2      52.5 - j 1.2
+50-Ohm SWR              1.220             1.380             1.060
+450 MHz
+Free-Space Gain dBi     9.64              9.90              9.32
+Front-to-Back dB        14.99             15.31             12.92
+Feed Z (R +/- jX)       42.7 - j 6.6      24.8 - j 9.2      60.0 - j 4.9
+50-Ohm SWR              1.236             2.110             1.220
+

The NEC-2 numbers are systematically slightly higher than the corresponding NEC-4 values, although the coincidence is sufficient for most design purposes for this antenna. Corrected MININEC is about as much above the NEC values as uncorrected MININEC is below them. The amounts are perhaps more clearly shown in Fig. 2, a graph of the modeled gain levels across the passband.

+
+ +
+

Note in the graph the slightly different curve shapes that indicate not only a difference in calculated values, but as well a frequency displacement of the curves relative to each other.

+

The design of the 4-element wide-band Yagi strove for a relatively smooth gain curve. In the 15-segment/element version, the gain differential across the band is just above 0.4 dB. One consequence is a relatively low front-to-back ratio that varies between 11.6 and 13.3 dB. Fig. 3 provides free-space azimuth patterns at the end and mid-band frequencies to give a sense of the horizontal pattern of the antenna.

+
+ +
+

The key displacement among modeling programs occurs with respect to the SWR curves. Fig. 4 graphs the 50-Ohm SWR curves for all 4 models. Corrected MININEC appears to displace the curve to lower frequencies relative to the desired passband, since the rapid rise in SWR is typical of the NEC-2/-4 curves above the 450 MHz mark. In contrast, uncorrected MININEC appears to shift the passband in the opposite direction, as the rise in SWR at the low end of the band parallels the NEC model curves below 420 MHz.

+
+ +
+

In Fig. 5, I have isolated the NEC-2 and NEC-4 curves for closer examination. Note that there is an approximate 5 MHz displacement of one curve relative to the other. Both curves show the characteristic OWA pattern.

+
+ +
+

For the average home builder, the differences illustrated here would likely wash out in the relative imprecision and trial-until-it-works techniques of construction. However, for precision shops capable of measurements to a millimeter or less and with techniques to control the feedpoint variables, the differences may become very significant. My own shop tools and instruments are not sufficiently precise to judge among the variants on the model.

+

All of the models presume an insulated boom with good RF properties at UHF. Perhaps polycarbonate (trade name Lexan) material would make a good choice for the 16" boom (with whatever extension may be needed for mounting hardware. A metal boom may require adjustment to all of the element lengths.

+

A 6-Element Wide-Band Yagi

+
+ +
+

For a bit more gain, we can try a 6-element wide-band Yagi. The general outline appears in Fig. 6. Adding 2 elements to the utility beam more than doubles its length. The NEC-4 modeled dimensions for the antenna appear in the following table--both in inches and millimeters.

+ 
6-Element Wide-Band Yagi Dimensions
+
+Element           Length                  Spacing From Reflector
+                  Inches      mm          Inches      mm
+Reflector         13.46       342         -----       -----
+Driver            11.89       302          5.95       151.0
+Dir. 1            11.01       282          9.72       247.0
+Dir. 2            10.79       274         16.18       411.0
+Dir. 3            10.20       259         24.94       633.5
+Dir. 4             9.80       249         33.94       862.0
+

The design is obviously different with respect to element lengths and spacing relative to the 4-element design. It is not a case of trying to simply add 2 directors to the earlier design and fudge everything back into a satisfactory SWR pattern. Instead, the design strove to see what might occur if the front-to-back ratio as well as the gain were maximized while sustaining the desired SWR level at 1.3:1 or less.

+

The following table lists the performance reports from both NEC-4 and NEC-2. Somewhat more detail (5-MHz intervals) is listed.

+ 
Frequency and                       Program
+ Parameter              NEC-4             NEC-2
+420 MHz
+Free-Space Gain dBi     10.78             10.91
+Front-to-Back dB        18.27             19.25
+Feed Z (R +/- jX)       44.4 - j 9.6      44.2 - j 8.1
+50-Ohm SWR              1.266             1.237
+425 MHz
+Free-Space Gain dBi     11.00             11.14
+Front-to-Back dB        21.02             22.48
+Feed Z (R +/- jX)       44.7 - j 5.7      44.1 - j 3.9
+50-Ohm SWR              1.179             1.161
+430 MHz
+Free-Space Gain dBi     11.23             11.38
+Front-to-Back dB        24.43             26.15 +
+Feed Z (R +/- jX)       44.7 - j 1.0      44.1 + j 1.2
+50-Ohm SWR              1.121             1.136
+435 MHz
+Free-Space Gain dBi     11.48             11.63
+Front-to-Back dB        25.78 +           25.18
+Feed Z (R +/- jX)       45.1 + j 4.3      44.9 + j 6.8
+50-Ohm SWR              1.147             1.196
+440 MHz
+Free-Space Gain dBi     11.72             11.85
+Front-to-Back dB        22.56             21.11
+Feed Z (R +/- jX)       46.6 + j 9.5      47.2 + j11.5
+50-Ohm SWR              1.231             1.275
+445 MHz
+Free-Space Gain dBi     11.92             12.02
+Front-to-Back dB        19.29             18.22
+Feed Z (R +/- jX)       49.5 + j12.5      50.3 + j12.1
+50-Ohm SWR              1.285             1.273
+450 MHz
+Free-Space Gain dBi     12.07             12.14
+Front-to-Back dB        17.31             16.93
+Feed Z (R +/- jX)       50.7 + j 9.7      46.6 + j 5.6
+50-Ohm SWR              1.213             1.146
+

From the marked (+) front-to-back values, we can once more see an approximate 5 MHz displacement in the curves for identical models run through NEC-2 and NEC-4 in the 430-MHz range. The displacement also appears when we graph the gain values across the band, as in Fig. 7.

+
+ +
+

At first sight, the two curves seem to indicate that one calculated value is simply higher than the other. However, the NEC-2 curves tapers off more rapidly at the high end of the passband. The NEC-4 curve would also reach a similar peak to that of the NEC-2 curve, but at a slightly higher frequency.

+

Compared to the 4-element gain curves, the 6-element gain changes much more radically across the passband--nearly 1.3 dB total change. This is the price to be paid for having a higher front-to-back ratio. Fig. 8 shows the free-space azimuth patterns for the end and mid-band frequencies to give a general idea of the horizontal pattern performance of the antenna across the band.

+
+ +
+

Although the two modeling platforms would be equally apt for the design of this wide-band antenna, the displacement of curves must be kept in mind throughout the process. Fig. 9 shows the displacement of the 50-Ohm SWR curves using the same model with different cores. The NEC-2 model would show a reversal of reactance type and a relatively rapid rise of SWR thereafter at a frequency just above the passband edge. The NEC-4 curve would trail by about 5 MHz.

+

The displacement is a function of the use of fat elements. As a result, the length of each segment is reduced as a function of the element radius. You may avoid most of the displaement effect in NEC-2--relative to NEC-4--by invoking the EK command. Some programs automatically invoke the command (without necessarily notifying the user) whenever the ratio of segment length to wire radius drops to a certain level. The test comparison ran without using the EK command for the NEC-2 data.

+
+ +
+

Applications

+

All construction suggestions applicable to the 4-element utility Yagi also apply to the 6-element design. It hardly needs to be added that the 6-element design, if supported at the rear, needs closer attention to the strength of the 33+" boom.

+

Wide-band Yagis for the 420-450 MHz range are likely to be used most of the time vertically polarized--largely for use with repeaters and mobiles. Besides adding some further constraints to construction, vertical polarization also changes the anticipated patterns somewhat. I modeled the antennas with the booms set to a height of 10 wavelengths--about 23' above good ground.

+
+ +
+

Fig. 10 shows the elevation and azimuth patterns for the 4-element Yagi at 435 MHz. The azimuth pattern is taken at an elevation angle of 1.4 degrees to match the strongest lobe from the elevation pattern. Of special note for those who have not compared Yagis in horizontal and vertical positions is the wider beamwidth for the vertical antenna--about 82 degrees between -3 dB (half-power) points. As well, the rear lobe structure differs considerably from that of the antenna when set up horizontally.

+
+ +
+

Fig. 11 shows a similar situation for the 6-element Yagi at the same frequency. The longer antenna has a beamwidth of about 60 degrees. Although the 180-degree front-to-back ratio is the same as for the antenna set up horizontally (see Fig. 8), the overall front-to-rear performance is reduced. The difference is largely a function of the ability of the element end geometry to limit lobe formation to the sides in the horizontal position. When placed vertically, the side lobe formation is not limited by element ends and is consequently larger in most cases.

+

Nonetheless, small wide-band utility Yagis with reasonable patterns and excellent 50-Ohm SWR performance may have a place in some station operations. Wide-band designs can be obtained if one is willing to use larger diameter elements than is conventional for Yagis in the 420-450 MHz band. Application of OWA principles is not limited to a single set of design goals, as the variations between the two designs shown here illustrate.

+

Next time, we shall look into the design of an 8-element Yagi of equal SWR performance. Since 8-elements approaches the border of numerous present designs for which the number of elements is somewhat optional according to one's desire for gain, we shall also look into a couple of these designs to see whether we really need to apply OWA principles or can use something that already exists.

+
+ +
+

Updated 08-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for July, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: VHF / UHF, Yagi


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+

Wide-Band Utility Yagis for 420-450 MHz
+ Part 2: An 8-Element Model

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

In our last design adventure, we examined a pair of wide-band Yagis for the 420-450 MHz band. The 4- and 6-element designs used 0.5" (12.7 mm) diameter elements and some OWA principles of spacing for the reflector, driver, and first director to obtain some reasonable operating characteristics across the passband. The chief goal of having worthy gain and a 50-Ohm SWR that never exceeds 1.3:1 from 420 to 450 MHz was achieved in both cases, although the design goals of each model varied somewhat. Either of these small Yagis might serve well as a utility antenna for any purpose for which the gain level might be suitable. The 4-element beam was under 16" (400 mm) long (exclusive of end-mounting boom extensions), while the 6-element version was just over 33" (862 mm) long.

+

In this episode, I want to turn attention to the next step along the way: an 8-element Yagi having reasonable gain for its boom length and meeting the 50-Ohm SWR goal of under 1.3:1 across the passband. In this instance, I shall return to the goal of having a relatively smooth gain curve, even if the cost is a less even front-to-back ratio.

+

The 8-element "question" is complicated by the fact that this size Yagi sits on the borderline between a utility antenna and a "serious" antenna, that is, an antenna designed for some specific purpose. Therefore, we find numerous designs for 8-element Yagis. The question is this: do any of them meet the requirements without need for redesign? I would not suggest for a moment that I have seen every design in this category. However, I can note a couple of design directions that are useful for comparison.

+

I shall look at three designs: a typical "Handbook" design, a DL6WU design, and the final half-inch element wide-band design. For reference, their relative sizes appear in Fig. 1.

+
+ +
+

A "Handbook" 8-Element Design

+

There are numerous design sequences that have emerged from various types of calculations and computer programs. One such "Handbook" design that covers 432-MHz designs from a few to very many elements will be our first subject. I choose it because it is typical of many such designs. What typical means will appear presently. For the moment, typical will simply mean that it uses 3/16" (0.1875" or 4.76 mm) element diameters. First, the dimensions.

+

"Handbook" 8-Element Yagi Dimensions

+ 
Element           Length                  Spacing From Reflector
+                  Inches      mm          Inches      mm
+Reflector         13.39       340         -----       -----
+Driver            13.15       334          4.09       104.0
+Dir. 1            12.40       315          5.75       146.0
+Dir. 2            12.05       306          8.82       224.0
+Dir. 3            11.77       299         13.07       332.0
+Dir. 4            11.61       295         18.35       466.0
+Dir. 5            11.46       291         24.49       622.0
+Dir. 6            11.38       289         31.42       798.0
+

If you looked at the first article in this series, you will note that the boom length is shorter than that of the 6-element wide-band beam (33.94" or 862 mm). As well, if you have digested Jim Lawson's classic study of Yagis, you will expect that this 8-element beam may not have exceptionally high gain for the number of elements. The NEC-4 model of this antenna turns up the following performance numbers.

+ 
Frequency and           Calculated
+ Parameter              Value
+420 MHz
+Free-Space Gain dBi     11.59
+Front-to-Back dB        19.53
+Feed Z (R +/- jX)       22.9 - j 7.1
+50-Ohm SWR              2.235
+425 MHz
+Free-Space Gain dBi     11.79
+Front-to-Back dB        26.59
+Feed Z (R +/- jX)       25.2 + j 3.3
+50-Ohm SWR              2.000
+430 MHz
+Free-Space Gain dBi     11.91
+Front-to-Back dB        22.01
+Feed Z (R +/- jX)       33.7 + j11.8
+50-Ohm SWR              1.623
+435 MHz
+Free-Space Gain dBi     11.89
+Front-to-Back dB        16.90
+Feed Z (R +/- jX)       43.7 + j 2.3
+50-Ohm SWR              1.160
+440 MHz
+Free-Space Gain dBi     11.69
+Front-to-Back dB        22.05
+Feed Z (R +/- jX)       22.1 - j 2.9
+50-Ohm SWR              2.277
+445 MHz
+Free-Space Gain dBi     11.30
+Front-to-Back dB        15.82
+Feed Z (R +/- jX)       10.2 + j15.5
+50-Ohm SWR              5.395
+450 MHz
+Free-Space Gain dBi     10.84
+Front-to-Back dB        20.12
+Feed Z (R +/- jX)       15.2 + j34.0
+50-Ohm SWR              4.903
+

Clearly, the antenna is not designed for full coverage of the band. Instead, it is designed for a relatively small portion of the band, if we use a direct feed for the driver. Fig. 2 provides the 50-Ohm SWR curve, which reveals that less than half the band can be covered with under 2:1 SWR. The region available (about 425 MHz to 439 MHz) generally corresponds to the region of peak antenna performance. The element length tapers as one moves forward from the reflector to the front end is one of the give-aways that this is a fairly narrow-band design by nature. Forward of the reflector, all of the elements are longer than any of those on designs that we have so far examined.

+
+ +
+

These notes are not intended in any way to denigrate the design, which I think is quite good for the category of antenna involved. For a short-boom narrow band design, it achieves its goals well, with a good front-to-back ratio in the region of peak gain. Nevertheless, like many other designs of its ilk, it will not satisfy the criteria set up for this exercise.

+

A Modified DL6WU 8-Element Design

+

Guenter Hoch, DL6WU, one of the pioneers in the mathematical design of UHF Yagis, remains the premier designer of wide-band Yagis for the 432-MHz band. His designs have withstood the test of time and amateur experimentation/modification. Granted, one can achieve narrow-band gain with shorter booms than he used, but exceeding his gain vs. bandwidth "product" is a major challenge.

+

We often think of DL6WU designs as very long-boom affairs with more elements than anyone except the builder wishes to count. However, one of the advantages of his log-based designs is the fact that--within reason--one can chop off almost any number of directors and still end up with a Yagi of very respectable wide-band performance. From a 31-element design, I have in past design exercises derived numerous sub-designs down to about 12 elements, each with similar coverage of the band. However, in this case, we shall reduce the total element count to 8. The resulting design, using 4 mm diameter elements, has the following dimensions.

+ 
DL6WU 8-Element Wide-Band Yagi Dimensions
+
+Element           Length                  Spacing From Reflector
+                  Inches      mm          Inches      mm
+Reflector         13.41       340.6       -----       -----
+Driver            12.99       330          5.46       138.8
+Dir. 1            11.97       304          7.51       190.8
+Dir. 2            11.78       299.2       12.43       315.8
+Dir. 3            11.64       295.6       18.31       465.0
+Dir. 4            11.50       292.2       25.13       638.4
+Dir. 5            11.39       289.2       32.79       832.8
+Dir. 6            11.28       286.4       40.98       1040.9
+

Director 5 already exceeds the boom length of the "Handbook" design. The DL6WU element taper is slightly more severe than that of the shorter beam. Let's look at the antenna's modeled performance.

+ 
Frequency and           Calculated
+ Parameter              Value
+420 MHz
+Free-Space Gain dBi     12.18
+Front-to-Back dB        13.87
+Feed Z (R +/- jX)       58.1 - j 9.9
+50-Ohm SWR              1.267
+425 MHz
+Free-Space Gain dBi     12.34
+Front-to-Back dB        13.93
+Feed Z (R +/- jX)       59.1 - j16.0
+50-Ohm SWR              1.401
+430 MHz
+Free-Space Gain dBi     12.48
+Front-to-Back dB        14.57
+Feed Z (R +/- jX)       49.7 - j17.8
+50-Ohm SWR              1.426
+435 MHz
+Free-Space Gain dBi     12.64
+Front-to-Back dB        16.44
+Feed Z (R +/- jX)       38.6 - j 8.6
+50-Ohm SWR              1.381
+440 MHz
+Free-Space Gain dBi     12.79
+Front-to-Back dB        20.06
+Feed Z (R +/- jX)       35.0 + j 9.0
+50-Ohm SWR              1.513
+445 MHz
+Free-Space Gain dBi     12.70
+Front-to-Back dB        19.08
+Feed Z (R +/- jX)       52.9 + j26.9
+50-Ohm SWR              1.681
+450 MHz
+Free-Space Gain dBi     12.05
+Front-to-Back dB        14.18
+Feed Z (R +/- jX)       52.1 - j21.1
+50-Ohm SWR              1.510
+

Considering the boom length and operating bandwidth, the DL6WU would be quite hard to beat. It has a 50-Ohm SWR curve that remains below 1.7:1 all across the band, with a total gain variation of only about 0.7 dB. The front-to-back ratio varies by about 6 dB. The model used here has one variation on the original from which it is derived. Director 1 was increased in length by about 1.2 mm in order to smooth the SWR response. As Fig. 3 reveals, the original SWR curve showed an unnecessary peak in the 445 to 440 MHz region. Lengthening the first director reduced this peak at a very slight cost in the SWR in the lower 2/3 of the band.

+
+ +
+

The trick to maintaining an acceptable SWR across the band is keeping the total change of feedpoint resistance and reactance under control. The DL6WU design manages to hold the change of resistance to about 14 Ohms. However, the reactance changes by about 48 Ohms across the band. Some improvement may be possible if we consider the numbers for the 4- and 6-element designs. The 4-element design, which stressed a smooth gain curve over front-to-back ratio, showed a resistance range of about 15 Ohms with a reactance range of only 9 Ohms. The 6-element design, which strove for a better balance of gain and front-to-back ratio, showed a resistance range of only 6.2 Ohms, but a reactance range of 22 Ohms. It would appear that some improvement over the DL6WU design is possible in terms of feedpoint impedance control.

+

If a slight improvement in feedpoint impedance were the only improvement to be obtained, trying to advance on the DL6WU design might be an exercise in futility. Indeed, the DL6WU design would make an excellent thin-element utility antenna for many, if not most purposes. Enlarging the elements to 0.5" (12.7 mm) is non-standard practice to begin with. As well, increasing element diameters will also involve lengthening the boom further in order to achieve something close to the most effective inter-element coupling. Nevertheless, as a design exercise, it may be worth going through the process.

+

An 8-Element Wide-Band Yagi Design

+

The resulting 8-element wide-band design, using 0.5" diameter elements, has the following dimensions.

+ 
An 8-Element Wide-Band Yagi Dimensions
+
+Element           Length                  Spacing From Reflector
+                  Inches      mm          Inches      mm
+Reflector         13.46       342         -----       -----
+Driver            12.28       312          5.95       151.0
+Dir. 1            11.26       286          9.90       251.0
+Dir. 2            10.91       277         16.14       410.0
+Dir. 3            10.91       277         24.96       634.0
+Dir. 4            10.47       266         34.06       865.0
+Dir. 5            10.16       258         43.74       1111.0
+Dir. 6             9.96       253         53.43       1357.0
+

For the extra foot of boom length, the antenna does achieve a usable gain advantage. Fig. 4 shows the gain curves of the present antenna (at the top), with the DL6WU antenna (just below). The two curves are reasonably congruent. The remaining curves for the "Handbook" narrow-band design and the 6-element design--of similar boom lengths--show the next echelon down of gain values.

+
+ +
+

The gain and front-to-back ratio of the longer design are fairly well controlled, as shown in Fig. 5. Like the DL6WU design, the gain varies by only 0.7 dB across the band. The front-to-back variation is about 6 dB.

+
+ +
+

As with all designs for this frequency range, there are differences between NEC-4 and NEC-2 results: about a 5 MHz displacement in curves due to not using the EK command in NEC-2. Fig. 6 shows the 50-Ohm SWR curves for both NEC-2 and NEC-4 models of the wide-band design. The upturn in SWR for the NEC-4 model occurs above 450 MHz and thus does not appear on the graph. The NEC-4 curve remains below 1.31:1 across the band.

+
+ +
+

The control of the feedpoint resistance and reactance is presented in Fig. 7. The total resistance range is about 16 Ohms, while the reactance range is about 19 Ohms. In general, where the resistance depart most widely from 50 Ohms, the reactance value is quite low, while the extremes of reactance values occur with the resistance quite close to 50 Ohms.

+
+ +
+

For the record, here are the modeled (NEC-4) performance figures in tabular form.

+ 
Frequency and           Calculated
+ Parameter              Value
+420 MHz
+Free-Space Gain dBi     12.80
+Front-to-Back dB        16.71
+Feed Z (R +/- jX)       38.2 + j 0.0
+50-Ohm SWR              1.309
+425 MHz
+Free-Space Gain dBi     13.03
+Front-to-Back dB        15.24
+Feed Z (R +/- jX)       43.6 + j 5.8
+50-Ohm SWR              1.202
+430 MHz
+Free-Space Gain dBi     13.21
+Front-to-Back dB        14.66
+Feed Z (R +/- jX)       49.5 + j 8.3
+50-Ohm SWR              1.183
+435 MHz
+Free-Space Gain dBi     13.38
+Front-to-Back dB        15.13
+Feed Z (R +/- jX)       52.5 + j 7.7
+50-Ohm SWR              1.171
+440 MHz
+Free-Space Gain dBi     13.50
+Front-to-Back dB        17.04
+Feed Z (R +/- jX)       51.5 + j 8.2
+50-Ohm SWR              1.178
+445 MHz
+Free-Space Gain dBi     13.48
+Front-to-Back dB        20.63
+Feed Z (R +/- jX)       53.6 + j10.3
+50-Ohm SWR              1.234
+450 MHz
+Free-Space Gain dBi     13.11
+Front-to-Back dB        20.53
+Feed Z (R +/- jX)       52.3 - j 8.8
+50-Ohm SWR              1.194
+

To give a sense of the pattern shapes, when the antenna is horizontally positioned, Fig. 8 shows the band edge and mid-band free-space azimuth patterns for the wide-band design. The evolution of side lobe development--both forward and rearward--is clearly evident from the patterns.

+
+ +
+

When used vertically positioned, the antenna patterns deviate significantly from those just shown. Therefore, Fig. 9 positions the antenna vertically with the boom 10 wavelengths above ground (about 23'). The azimuth pattern is taken at an elevation angle of 1.4 degrees, corresponding to the take-off or elevation angle of maximum radiation.

+
+ +
+

Conclusions

+

The wide-band design has been allowed to speak for itself in terms of performance. Whether it amounts to an advance on the DL6WU design depends largely on one's perspective. The DL6WU antenna has a bit lower gain in accord with its shorter boom length. The front-to-back values vary in the same amount but in a different pattern from the corresponding variations for the wide-band design. The DL6WU SWR values are not as flat as those of the wide-band design, but they do not exceed 1.7:1. Finally, the DL6WU design uses a common element diameter that is familiar to most beam builders for the 420-450 MHz band.

+

The wide-band Yagi has more gain and a flatter SWR pattern. However, it also requires a longer boom and fatter elements. Whether the benefits of the wide-band design are sufficient to override the requirement to rethink and redesign the mechanical aspects of constructing the beam is a user decision. I suspect that those who build beams as simply a means to operational goals may stick with the tried and true. Those who love to experiment with what may be possible in antenna performance may wish to develop construction techniques that one day might make fat elements as common on 432 MHz as thin elements currently are.

+

Nevertheless, the exercise has been useful in comparing Yagi types for the 420-450 MHz region. If the 8-element design proves insufficiently beneficial to warrant its use as a wide-band utility antenna for the band, perhaps the smaller 4- and 6-element versions may find a niche. In any event, these design endeavors have shown that it is possible to develop Yagis with reasonable performance figures that can cover all of the band with a 1.3:1 or better 50-Ohm SWR.

+
+ +
+

Updated 09-01-2001. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for August, 2001. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: VHF / UHF, Yagi


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+

Appreciating DL6WU Wide-Band Long-Boom Yagi Design
+ Some Preliminary Notes

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

The design of long-boom, high performance Yagis for the VHF region has seem innovations by a number of very notable designers. The designs of Rainer Bertelsmeier, DJ9BV, tend to group directors on 4s, while the designs of Joe Reisert, W1JR, for HyGain found favor in director pairs. For narrow-band, high gain Yagis with the fewest elements for a given boom length, Lief Asbrink, SM5BSZ, has provided some outstanding designs. More traditionally tapered are the designs of Steve Powlishen, K1FO, as found in any recent edition of The ARRL Antenna Book.

+

Underlying all of these Yagi design efforts is the work of Guenter Hoch, DL6WU. His pioneering designs span the 80s and 90s, beginning with a piece on UKW-Berichte in 1982 and culminating in his chapter (7) for the RSGB volume, The VHF/UHF DX Book, edited by Ian White, G3SEK. (The volume is published for RSGB by DIR Publishing, Ltd.) Referring to a 23 cm design series by DL6WU, DJ9BV (DUBUS, 2/1994, p.46) notes that for the home builder, these designs are a premium choice, unequaled in terms of gain, pattern, match and broadband performance. Whatever the band from 144 MHz to 1296 MHz, DL6WU designs form the touchstone to which all other designs tend to compare themselves.

+

To say that DL6WU designs are broad-banded is an understatement. With proper care, a long-boom Yagi from the 432-MHz series can cover all of the band with adequate performance in terms of gain, side- and rear-lobe size, and SWR. One can adapt them for either single element drive at 50 Ohms or folded-dipole drive for 200 Ohms. This is no mean accomplishment for a band whose bandwidth is 7% of its center frequency.

+

However, the notes that I find on the DL6WU designs tend to focus on 432-MHz performance to the exclusion of the total range of performance figures. For example, both the antenna chapter and the 432-MHz chapter of the RSGB book tend to note that certain Yagi lengths (where length can be expressed either in terms of boom length or in terms of the number of elements) have better front-to-back ratios. Although this is true at the 432-MHz design frequency, it is not necessarily true of the entire operating passband for the antenna. Moreover, the individual who wishes to build a DL6WU design has some freedom in tailoring the array characteristics (whatever the boom length) for the desired primary operating sub-range within the band.

+

Therefore, these notes represent a preliminary appreciation of the DL6WU design, seeking to understand a little better the wide-band nature of the designs. However, finding a starting point is not a wholly simple matter. DL6WU design appear in generally 2 formats: tables and graphs found in books and articles and software-generated designs. Since Hoch's designs evolved over the years, the outputs from different sources do not always agree in every detail.

+

For this exercise, I have resorted to the 432-MHz designs found in Chapter 10 of the RSGB book. I have modified them only to the extent of adjusting the driver and first director lengths for the best operating bandwidth, and these adjustments are very small. Element spacing and lengths (with only the two noted exceptions) remain very precisely those specified on page 10-35 of the volume. Selecting these dimensions as a basis for the exploration at least provides a consistent beginning.

+

The exploratory vehicle is NEC-4, which appears to be slightly at variance and presumably more accurate than NEC-2 at 432 MHz. (The actually variance for this set of models is very slight. The variance shows up more fully with larger-diameter elements and a higher segment count. Hence, if available, the use in NEC-2 of the EK extended thin-wire kernel command would be helpful, especially if the segment length to diameter ratio falls under 4:1.) The use of computer modeling software that is adequate to the task holds several advantages over range testing. For example, the test conditions are subject to no variations among models. One can place the arrays in free space and check any and all major parameters for comparative purposes. The condition of the tests is that the elements are presumed to be free, clear, insulated, and isolated from any effects of a conductive boom material. There are numerous resources for discovering what adjustments are required for placing elements near to or through a metallic boom.

+

A second advantage of computer modeling is access to data not usually measured or measurable in range tests. One particular example of special note for this investigation is the relative current magnitude and phase angle along the elements, with special reference to the current at the center of the driver and of the first director. We shall have occasion to examine these currents for several sample arrays.

+

A full study of the DL6WU wide-band Yagi designs would sample each array in the sequence. This study is only preliminary in limiting itself to 3 samples: 12, 19, and 26 elements (10, 17, and 24 directors). Interestingly, there is--relative to the 32-element limit in the RSGB book chart--a boom length progression as well as the addition of 7 elements per step. If we assign the 32-element version a length of 1.0, then the selected arrays fall near the 0.25, 0.50, and 0.75 marks. This phenomenon results from the fact that for directors 13 onward, the director spacing is a standard 0.4 wavelength.

+
+ +
+

Fig. 1 shows the outline of all 32 elements, with the lengths of the samples that we shall scan marked for reference. The following table presents the dimensions in millimeters and in wavelengths. The elements are 4-mm diameter aluminum for all models. One characteristic of DL6WU designs is the use of relatively large-diameter elements. 4 mm at 432 is equivalent to nearly 0.5" at 2 meters.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+32-Element DL6WU Yagi for 432 MHz (with 12, 19, and 26 element versions derived)
+
+Element           Element Length          Cumulative Spacing
+                  mm          wl          mm          wl
+Reflector         340.6       0.491        ---        ---
+Driver            330.0       0.476        138.8      0.200
+1                 301.6       0.435        190.8      0.275
+2                 299.2       0.431        315.8      0.455
+3                 295.6       0.426        465.0      0.670
+4                 292.2       0.421        638.4      0.920
+5                 289.2       0.417        832.8      1.200
+6                 286.4       0.413       1040.9      1.500
+7                 284.2       0.410       1259.5      1.815
+8                 282.2       0.407       1488.6      2.145
+9                 280.4       0.404       1728.0      2.490
+10                278.8       0.402       1977.8      2.850       12-Element
+11                277.4       0.400       2238.0      3.225
+12                276.0       0.398       2508.7      3.615
+13                274.8       0.396       2786.3      4.015
+14                273.8       0.395       3063.9      4.415
+15                272.8       0.393       3341.4      4.815
+16                271.8       0.392       3619.0      5.215
+17                270.8       0.390       3896.6      5.615       19-Element
+18                270.0       0.389       4174.2      6.015
+19                269.2       0.388       4451.8      6.415
+20                268.4       0.387       4729.4      6.815
+21                267.6       0.386       5007.0      7.215
+22                267.0       0.385       5284.5      7.615
+23                266.2       0.384       5562.1      8.015
+24                265.7       0.383       5839.7      8.415       26-Element
+25                265.0       0.382       6117.3      8.815
+26                264.5       0.381       6394.9      9.215
+27                263.9       0.380       6672.5      9.615
+28                263.3       0.379       6950.1      10.015
+29                262.8       0.379       7227.6      10.415
+30                262.3       0.378       7505.2      10.815
+
+Note:  Unnamed numbered elements are directors.  Dimensions follow those listed in
+Chapter 10 of the RSGB volume, The VHF/UHF DX Book, edited by Ian White, G3SEK,
+except for the driver and first director lengths, which have been adjusted slightly
+for maximum bandwidth.  See also Chapter 7 by Guenter Hoch, DL6WU.  Element diameter
+is 4 mm (0.1575") (aluminum).
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Among the design notes for this family of arrays, we find reference to certain lengths having better front-to-back ratios than others, with the 14-15, 19-20, 24-25, and 30-31 element ranges being judged the best. Only one of our sample arrays falls within one of the best front-to-back ranges, the 19-element version. The 26-element array is close, but the 12 element array is well outside any of the favorable groupings. Indeed, the 12-element array is close to the minimum recommended length for any DL6WU array.

+
+ +
+

Fig. 2 presents the modeled free-space azimuth patterns and data for 432 MHz for each sample array. In tabular form, the data looks like this:

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              Modeled Data for 3 Sample DL6WU Yagi designs at 432 MHz
+
+Elements                            12                19                26
+Boomlength--wl                      2.850             5.615             8.415
+Boomlength--mm                      1978              3897              5840
+Boomlength--inches                   77.87            153.41            229.9
+Boomlength--feet                      6.49             12.78             19.16
+Gain:  dBi                          14.73             17.21             18.59
+180-degree F-B: dB                  15.52             30.04             22.13
+Worst-case F-B: dB                  15.52             23.78             22.13
+Main-fwd sidelobe: dB               17.71             17.36             16.41
+Hor. beamwidth: degrees             33.8              26.4              22.6
+Feedpoint Z (R+/-jX Ohms)           60.2-j11.4        57.8+j 6.6        50.2-j0.1
+50-Ohm SWR                          1.319             1.209             1.005
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Besides the expected variations in gain in accord with boom length and the number of elements, the data also provide certain insights into the Yagi design operation, especially when taken in conjunction with the patterns in Fig. 2. The models generally confirm the thesis of the best array sizes for maximum front-to-back performance, at least in terms of the 180-degree front-to-back ratio. However, if we scan the entirety of the rear quadrants, we find that the worst-case front-to-back ratio does not differ by very much between the 19-element and the 26-element arrays.

+

Equally expected are the development of additional forward and rearward sidelobes with increasing boomlength. If we were to judge only from our three samples, then it would appear that the ratio of the main forward lobe to the strongest forward sidelobe decreases with boom length. However, it remains for further study to determine if, within the total range of possible arrays in the series, there are favored boom lengths where the forward-to-sidelobe ratio is maximum. DL6WU himself lists the average ratio as about 17 dB, with instructions for retuning the array should the ratio prove too much lower or too much higher than the average value. The note is perhaps indicative that the array series inventor himself did not fully appreciate the wide-band characteristics of his offspring.

+

General Wide-Band Properties of Sample DL6WU Yagis for the 432-MHz Band.

To sample the wide-band properties of the DL6WU arrays, I subjected the 3 test models to frequency sweeps. I extended the sweeps at the low end to 405 MHz, where 50-Ohm SWR just approaches or passes a 2:1 value. For these tests, all arrays use a single driver to achieve a 50-Ohm SWR. Folded dipole models set for a 200-Ohm reference impedance are certainly possible and, when properly constructed with adjustments to the driver and first director lengths and spacing, may provide an even wider operating bandwidth between 2:1 SWR values. +

At the upper end of the band, the 2:1 SWR value appears between 452 and 456 MHz, depending on the particular array. I extended the sweep range to 460 MHz in order to reveal something of the seemingly erratic value swings for all parameters at this end of the band. For almost all operating parameters, the upper end of the frequency range is far more variable then the well-behaved lower end of the band.

+

As one might expect, the results of these sweeps reveal their data best in a series of graphs.

+
+ +
+

Fig. 3 presents the SWR curves in 1-MHz increments from 405 to 460 MHz for the 3 sample arrays. First impressions may limit themselves to seeing how well behaved the arrays are within the 420-450 MHz range. However, there is more to this graph than this simple impression. Note the number of SWR minima for each array. Within the band, the 12- and 19-element arrays have 3, while the 26-element array has 4. These are unusually large numbers, since most wide-band HF arrays show no more than 2. However, those arrays normally have far fewer than even 12 elements, and the number of possible minima seems to increase with the number of elements.

+

As well, note that the first deep SWR minimum occurs farther along the initial part of the curve as we increase the number of elements in the array. (Note that this appearance is subject to further investigation to determine if it is generally true or if it follows a periodic progression, as does the 432-MHz front-to-back ratio.) The further along the passband that the first deep minimum occurs, the lower the SWR at the upper end of the passband--at least until the value goes wholly out of control.

+
+ +
+

Since SWR is a function of the feedpoint resistance and reactance relative to some standard impedance, it is useful to sweep both the feedpoint resistance and reactance within the passband. Fig. 4 sweeps the resistance at 2.5 MHz intervals. (All except SWR graphs use a 2.5 MHz interval due to the need to hand-transfer data to the spreadsheet graphing program.) If you block out the region above 455 MHz, you will see that the 19- and 26-element arrays undergo far smaller excursions of the feedpoint resistance and begin notable excursions at a higher frequency than the 12-element array.

+
+ +
+

The feedpoint reactance curves in Fig. 5 show the same results: lower and fewer excursions in reactance value across the passband until we pass at least 452 MHz. Above this frequency, excursions for all versions of the array are very wide, swinging back and forth between significant values of inductive and capacitive reactance. We may note in passing that for both the resistance and reactance curves, we find the widest in-band excursions between 440 and 450 MHz, even though the SWR in this region remains quite tame.

+

The exploration of feedpoint values--resistance, reactance, and SWR--does not itself account for the very wide operating bandwidth or for any of the value swings for feedpoint parameters. To more fully account for the curve variations, we must turn to the relationships that exist among the reflector, driver, and first director.

+

The reflector length, in conjunction with its spacing from the driver, tends to set the feedpoint impedance in narrow-band arrays. The wider the spacing, the higher the feedpoint impedance. This relationship tends to hold for arrays in which the first director is more than 0.1 wavelength from the driver.

+

DL6WU recognized that the first director spacing that he used--0.075 wavelength--played a role in setting the driver impedance. In fact, he has referred to this director as a matching element. It is the inter-relationship among the reflector-driver and driver-director#1 spacing, along with the specific lengths of these elements, that sets the operating impedance and the operating bandwidth of the array. (Although some folks tend to call this arrangement a version of OWA or optimized wide-band antenna design, I prefer to reserve that term for the more complex system developed by WA3FET and NW3Z, which also includes the second and third directors as part of the bandwidth-setting cell.)

+

When the first director is closely spaced to the driver--perhaps closer than 0.09 to 0.10 wavelength--several things happen. For a given feedpoint impedance, the reflector may be more closely spaced to the driver than in narrow-band arrays. Second, by proper sizing and spacing of the first director relative to the driver, we may obtain a significant broadening of the operating passband. Under these conditions, the first director serves as something more than a mere matching parasitic element.

+
+ +
+

Fig. 6 traces the relative current magnitude on the first director of our 3 sample DL6WU designs. The current magnitude at all points is relative to a feedpoint magnitude of 1.0 on the driven element. In the lower end of the scanned frequency region, the first director current seems normal enough: a goodly and increasing fraction of the feedpoint current.

+

However, as we approach and pass mid-band, the first director current increases to levels above the current on the driver. The amount by which the first director current surpasses that of the driver increases wit increasing frequency. Whenever the current on the first director is near or above that of the driver, we may view the first director as a secondary or parasitic driver for the array.

+

Equally important to the operation of the DL6WU array are the undulations in the curve of relative current magnitude. There is a tentative correlation to be made between the current transitions through the 1.0 value and the SWR minima and maxima in the upper half of the passband. Downward passages correlate to approaches to SWR minima, while upward transitions correlate to approaches to SWR maxima. Pending further study, at least this much is clear: the current magnitude on the first director strongly influences the feedpoint resistance and reactance and consequently the SWR.

+

These phenomena are not independent of the other elements in the array. The same feedpoint cell (reflector-driver-director#1) with other arrangements of directors do not yield the same types of impedance excursions or the same operating bandwidth. Even within a systematic development of a series of directors, each new director has a determinate influence on the operation of the feedpoint cell. Within the DL6WU scheme of directors, the feedpoint cell provides an exceptionally wide operating bandwidth at all practical boom lengths, despite variations from one length to the next.

+

At the heart of the feedpoint cell design are empirically-determined element lengths and spacings that extend the operating bandwidth further than any other design of which I am currently aware. Other feedpoint cell designs can approximate the DL6WU operating bandwidth, but only by using element diameters several times the 4-mm elements in our sample arrays. However, much investigation remains to be done into this arena of Yagi design.

+

It is one thing to achieve a wide operating bandwidth in terms of feedpoint impedance and quite another to extend the performance parameters of the array over the same bandwidth. The success of the DL6WU array derives as much from its achievements in these categories as it does from its impedance-leveling techniques.

+
+ +
+

Fig. 7 provides gain curves for the three sample arrays across the 405 to 460 MHz spread of our sweeps. The curves are very well-behaved until at least 445 MHz. From this point onward, we find the gain curves to be slightly erratic, with more variable behavior occurring outside the band limits. However, notice that the largest of our sample arrays forestalls the beginning of such behavior until after the 450-MHz mark. The smaller the array, the lower the gain and the further inside the band that the gain curve shows less than smooth behavior. However, this generalization is tentative, pending more complete study of the entire DL6WU series.

+

It is notable that the 432-MHz operating point that is most common for the arrays is not coincident with maximum gain. The amount of extra gain obtainable tends to increase with the overall length of the array. Indeed, the DL6WU design seems intentionally set at a stable gain position such that the home constructor can--using reasonable care--obtain a workable version with good, if not absolutely maximum, gain.

+
+ +
Perhaps the most striking story emerges from the 180-degree front-to-back curves in Fig. 8 for our sample arrays across the scanned frequency spread. The curve for each Yagi shows--with the 420-450-MHz operating range--at least 2 peaks, with the 26-element array showing 3. (Flatted peaks only indicate that the maximum value of 180-degree front-to-back ratio occurs between sampled points.) The 12-element array shows peaks at about 418 and 444 MHz. The corresponding peaks for the 19-element Yagi occur at about 430 and 448 MHz. For the smaller array, 432 MHz is near to a minimum value, while for the mid-size array, 432 MHz is near to a maximum. +

The longest of our arrays peaks at about 422, 436, and 449 MHz. The structure of the curves suggests that with the addition of new directors, the front-to-back peaks drift higher in frequency, with a decrease in the frequency span between peaks. At a certain--and yet to be determined--point in the addition of directors, a new low-end peak emerges and the frequency span between peaks diminishes further. As the frequency span between peak values decreases, the lowest level to which the 180-degree front-to-back ratio may decrease rises, setting a minimum value of front-to-back ratio for the array. The graph makes clear the rising value of minimum 180-degree front-to-back ratio as we increase array length.

+

Subsequent detailed studies of the DL6WU Yagi series at 432 MHz have confirmed the impression reported on the basis of samples. By examining both design-frequency and wide-band behaviors of the array for beam lengths between 10 and 40 elements in 1-element increments, the progression of the front-to-back peaks can be traced and graphed. Each peak does emerge from about 418 MHz and proceeds upward in frequency as we raise the number of elements until it disappears somewhere below about 458 MHz. Over the span from 10 to 40 elements, as many as 10 front-to-back peaks emerge and disappear using a 4-mm element diameter. Recording the number on frequencies of SWR dips toward a 1:1 ratio reveals a very similar set of behaviors.

+

Also notable is the fact that the lowest front-to-back peak curve is also the widest, if we take an arbitrary value as a marker, for example 20 dB. Curves at high frequencies tend to be sharper. Except for those lengths at which 432 MHz corresponds to a front-to-back maximum, if we were to wish to operate the array at a front-to-back maximum, we might sacrifice gain for the sake of selecting a wide SWR upward curve and thus ease the construction precision necessary to obtain it.

+

Throughout, I have referred to the 180-degree front-to-back values for the curve, since these are the most easily obtainable from most modeling programs. However, as we saw in Fig. 2, the 180-degree front-to-back performance does not always coincide with worst-case front-to-back performance for an array. For any specific design effort, both must be checked, along with the accompanying forward sidelobe ratio value. Indeed, for any array, it pays to examine the power in all lobes other than the main forward lobe.

+

Wide-Band Flexibility in the DL6WU Design: Changing Element Diameter

Within a limited range, one may change the element diameter of a DL6WU design and obtain the same performance at the design frequency of 432 MHz. The change in element diameter requires that one use elements of a length having the same reactance. The RSGB volume provides equations for performing the calculation of new element lengths for the new element diameter (p. 7-28), and they have been included in some of the software available for designing Yagis in the series. +

Equivalent reactance elements of different diameters are equivalent at the frequency of calculation and for some frequency spread that is not easily estimated. Therefore, I used the 12-element array from the group of samples to see what the differences in overall performance across the scanned frequency region might be. Conveniently, the same RSGB volume provided me with pre-calculated dimensions for 1/8", 4 mm, and 3/16" diameter elements, giving a series of element diameters from 0.125 to 0.1575 to 0.1875 inches (or 3.175 to 4.0 to 4.7625 mm). The total span covers a 1.5:1 diameter range, which is seemingly modest but wide enough to detect anything significant in the data output.

+

The following tables provide the dimensions of the 1/8" and 3/16" element versions of the 4 mm 12-element Yagi we used in the preceding section of these notes.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12-Element DL6WU Yagi for 432 MHz (using 1/8" diameter elements)
+
+Element           Element Length          Cumulative Spacing
+                  mm          wl          mm          wl
+Reflector         340.9       0.491        ---        ---
+Driver            333.2       0.480        138.8      0.200
+1                 306.0       0.441        190.8      0.275
+2                 302.3       0.436        315.8      0.455
+3                 298.9       0.431        465.0      0.670
+4                 295.6       0.426        638.4      0.920
+5                 292.7       0.422        832.8      1.200
+6                 290.2       0.418       1040.9      1.500
+7                 288.0       0.415       1259.5      1.815
+8                 286.1       0.412       1488.6      2.145
+9                 284.4       0.410       1728.0      2.490
+10                282.9       0.408       1977.8      2.850       12-Element
+
+12-Element DL6WU Yagi for 432 MHz (using 3/16" diameter elements)
+
+Element           Element Length          Cumulative Spacing
+                  mm          wl          mm          wl
+Reflector         340.4       0.491        ---        ---
+Driver            329.4       0.475        138.8      0.200
+1                 299.4       0.431        190.8      0.275
+2                 296.7       0.428        315.8      0.455
+3                 292.9       0.422        465.0      0.670
+4                 289.4       0.417        638.4      0.920
+5                 286.3       0.413        832.8      1.200
+6                 283.6       0.409       1040.9      1.500
+7                 281.3       0.405       1259.5      1.815
+8                 279.2       0.402       1488.6      2.145
+9                 277.4       0.400       1728.0      2.490
+10                275.7       0.397       1977.8      2.850       12-Element
+
+Note:  Unnamed numbered elements are directors.  Dimensions follow those listed in
+Chapter 10 of the RSGB volume, The VHF/UHF DX Book, edited by Ian White, G3SEK,
+except for the driver and first director lengths, which have been adjusted slightly
+for maximum bandwidth.
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The adjustments to the driver and first director were made to obtain performance at 432 MHz as closely coincident as possible for the 3 models. The following table provides the 432-MHz data.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+        Modeled Data for 3 Sample 12-Element DL6WU Yagi designs at 432 MHz
+
+Element Diameter:  inches           0.125             0.1575            0.1875
+Element Diameter:  mm               3.175             4.000             4.7625
+Gain:  dBi                          14.75             14.73             14.73
+180-degree F-B: dB                  15.51             15.52             15.53
+Main-fwd sidelobe: dB               17.71             17.71             17.71
+Feedpoint Z (R+/-jX Ohms)           57.8-j11.0        60.2-j11.4        60.2-j11.1
+50-Ohm SWR                          1.283             1.319             1.315
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

It is possible that the dimensions might be further adjusted to result in even closer alignment of the 432-MHz values.

+
+ +
+

Fig. 9 shows the 50-Ohm SWR curves for the 3 array designs. At the lower end of the frequency range, although the first SWR minimum occurs coincidentally, the largest diameter element version shows a slightly lower SWR at 405 MHz. The difference is not operationally significant, but simply what we would expect from the slight broadband effect of larger elements.

+

At the upper end of the spectrum, the 1/8" element version shows the larger displacement relative to the 4 mm original. The amount of displacement is in part a result of driver and first-director element adjustments needed to set the 432-MHz operating parameters in coincidence. The differences between the 4 mm and 3/16" element version become noticeable beyond the upper band limit. In short, within the 420-450-MHz region, there is nothing significant relative to the SWR curve alone. Hence, it is unnecessary to review the feedpoint resistance and reactance curves.

+
+ +
+

Fig. 10 presents the gain curves for the 3 Yagis. Between 420 and 440 MHz, the curves are indistinguishable, a fact that results from the careful setting of 432-MHz characteristics. The low end of the scanned spectrum reveals a well behaved separation of gain values in accord with element size. A similar separation occurs at the upper end of the spectrum, but with some erratic results as the curves pass out of the scanned range. Such odd variations are not unexpected as the driver cell begins to lose control over array operation.

+
+ +
+

The 180-degree curves for the 3 arrays appear in Fig. 11. If we extrapolate the peaks in front-to-back performance from the sampled frequencies, we can see that the larger the element diameter, the lower (by a very slight amount) the frequency of the first peak. In contrast, using the same extrapolation procedure (or performing frequency sweeps over narrow ranges), we find that the larger the element diameter, the higher the frequency of the peak (again, by a very slight amount). Beyond 450 MHz, we again encounter erratic excursions in the curves, but over a relatively small range.

+

In principle, then, nothing in the performance curves indicates any unwanted effects of using element diameters within a 1.5:1 range for the DL6WU series of Yagis. I used the 12-element version of the array because it appeared to be most sensitive to changes, and yet, changes of significant proportions did not emerge.

+

However, note the procedure used to obtain these results. For the feedpoint cell (reflector, driver, and first director), the pre-calculated results underwent adjustment in order to set the arrays to coincident performance at 432 MHz. For any specific boom length, I would recommend that one check the feedpoint cell element lengths with NEC-4 to arrive at final values that provide the operating curve desired for as much of the spectrum as one plans to use. (Similar advice is apt to the use of a folded dipole driver.)

+

The use of such software to optimize the feedpoint cells to achieve coincident operating properties, of course, simply placed the 12-element array at a low front-to-back ratio region, a bit below the maximum gain possible with the array. While one is using the software--and assuming that one does not need to cover the entire 420-450 MHz band--one might as well change the operating point of the array.

+

Wide-Band Flexibility in the DL6WU Design: Changing the Array Operating Point

To sample the effects of moving the operating point of the array, I performed a 2-step operation. +
+ 1. First, I scaled the array from the frequency of the desired operating condition to 432 MHz. Included in the scaling was returning the element diameter to its original value and rechecking the operating curve in the vicinity of 432 MHz to assure myself that the desired characteristics did not move significantly in frequency. Since the movement was well under a 5% frequency shift, no further readjustment proved necessary. +
+
+ 2. Second, I adjusted the driver length to provide the lowest 50-Ohm SWR at 432 MHz. The desired operating points do not always occur at the lowest SWR points. Therefore, attaining the lowest possible SWR is desirable. The process can include readjustment of any and all elements in the feedpoint cell. However, for this exercise, I limited myself to driver length changes. +
+

To implement this procedure, one must first locate the desired operating points. For the purposes of showing the consequences of these moves, I chose one operating point above 432 MHz and another below the design frequency. The upper operating point was the maximum gain frequency. For the 12-element array, this frequency is about 442 MHz, resulting in a scaling downward by 10 MHz. Frequency scaling downward results in a slightly longer array with slightly longer elements. The following table shows the results of both the scaling and driver adjustment.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12-Element DL6WU Yagi for 432 MHz (scaled for maximum gain)
+
+Element           Element Length          Cumulative Spacing
+                  mm          wl          mm          wl
+Reflector         348.5       0.502        ---        ---
+Driver            330.4       0.476        142.0      0.205
+1                 308.6       0.445        195.2      0.281
+2                 306.1       0.441        323.1      0.466
+3                 302.4       0.436        475.8      0.686
+4                 299.0       0.431        653.2      0.941
+5                 295.9       0.426        852.1      1.228
+6                 293.0       0.422       1065.0      1.535
+7                 290.8       0.419       1288.7      1.857
+8                 288.7       0.416       1523.1      2.195
+9                 286.9       0.413       1768.0      2.548
+10                285.2       0.411       2023.6      2.916       12-Element
+
+Note:  Unnamed numbered elements are directors.  Element diameter is 4 mm (0.1575")
+(aluminum).
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For an upward scaling, I selected the frequency of best front-to-back ratio, where the curve is the broadest. That frequency for the 12-element array was about 418 MHz, for a 24 MHz upward scaling to 432 MHz. The resultant array was shorter than the original, as shown in the following table of dimensions. The dimensions include the return to 4 mm diameter elements and readjustment of the driver length.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+12-Element DL6WU Yagi for 432 MHz (scaled for best front-to-back performance)
+
+Element           Element Length          Cumulative Spacing
+                  mm          wl          mm          wl
+Reflector         340.4       0.475        ---        ---
+Driver            329.4       0.464        134.3      0.194
+1                 299.4       0.421        184.6      0.266
+2                 296.7       0.417        305.6      0.440
+3                 292.9       0.412        449.9      0.648
+4                 289.4       0.407        617.7      0.890
+5                 286.3       0.403        805.8      1.161
+6                 283.6       0.399       1007.2      1.451
+7                 281.3       0.396       1218.7      1.756
+8                 279.2       0.393       1440.4      2.076
+9                 277.4       0.391       1672.0      2.409
+10                275.7       0.389       1913.7      2.758       12-Element
+
+Note:  Unnamed numbered elements are directors.  Element diameter is 4 mm (0.1575")
+(aluminum).
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The question we might now pose is this: what did we achieve for our trouble?

+
+ +
+

Fig. 12 shows the consequential SWR curves, using the original span from 405 to 450 MHz as our limits. Shown on the graph is the SWR curve for the original 12-element array to provide a reference curve. The high-gain curve results in a narrowed overall SWR passband. The low end value is not much below the value for the original design, but the upper end of the band shows considerable shrinkage. Portions of the upper-end curve formerly beyond the scan range now come into view. After one large climb and dip that marks the 460-MHz portion of the original arrangement, the curve climbs into a wholly unusable range.

+

The upward scaling for the front-to-back adjustment is more benign in its effects on the 50-Ohm SWR. Although the curve shows an SWR above 3:1 at 405 MHz, it is below 2:1 at 420 MHz. In fact, the spread between SWR minima within the curve is wider than for the original curve by 2 MHz (18 vs. 16 MHz), indicating that the overall curve may be wider. The ultimate width, however, will depend to some degree on the SWR that we are willing to accept at 432 MHz, since we adjusted the driver for the lowest obtainable SWR at that frequency.

+
+ +
+

Fig. 13 shows the consequences of our redesign work on the array gain between 430 and 435 MHz. The curves are precisely what we might expect before undertaking the re-scaling operations. The "best front-to-back" performance curve is considerably lower than the others and is on the rise. The free-space gain is bout 14.02 dBi at 432 MHz, compared to the 14.73 dBi value we obtained for the original version.

+

The maximum gain point for the array has been moved to 431 MHz rather than 432 MHz for a reason. For the 12-element array, the maximum gain frequency occurs at a 180-degree front-to-back ratio below 20 dB. By sacrificing a mere 0.01 dB of gain, we acquire about 2 dB of added front-to-back ratio.

+
+ +
+

The 180-degree front-to-back figures appear in Fig. 14. The Normal or pre-scaling version of the array reveals how close to the minimum front-to-back ratio the original design had been. The high-gain version shows the fairly rapid change in front-to-back ratio that occurs in the region of high gain for the 12-element array. Much more stable is the curve for the best front-to-back version of the array, despite the sacrifice in gain necessary to achieve that goal.

+

The patterns that we obtain for the arrays also have something to teach us, and they appear in Fig. 15.

+
+ +
+

The original array pattern appears at the top, with associated performance figures that are now quite familiar. Since the front-to-back performance is so poor, the forward sidelobe ratio (to the main forward lobe) does not appear, but remains about 17.71 dB. We shall passingly note the horizontal -3 dB beamwidth of 33.8 degrees.

+

The best front-to-back performance version of the array shows a slightly lower gain, as expected from the graphs, along with a worst-case front-to-back ratio that is just about 20 dB (in contrast to the higher 180-degree front-to-back figure). In some ways, we may consider the performance of the array in this arrangement to be tamer, since the sidelobe structure is simpler or less developed than for the normal array. The forward sidelobe is 18.18 dB down, a slight improvement. As well the horizontal beamwidth is 37.5 degrees. The increased beamwidth is not solely a function of the reduced gain, but as well is a function of the reduced sidelobe structure.

+

The high-gain version of the array illustrates in part the effects of increased sidelobe structure on the -3 dB beamwidth. The primary or first forward lobes are not only stronger than in the other two versions of the array (-16.03 dB), but as well are wide enough to merge with the main lobe. In some designs, the sidelobes are wide enough to create mere "bulges" in the main lobe, sometimes sufficiently to the rear to give the forward lobe a bullet shape. The consequence of strong, wide sidelobes or bulges is generally to narrow the main lobe beamwidth, in this case to 31.6 degrees. The added gain (0.2 dB) is insufficient to account for the degree of added narrowing of the beamwidth from its original level (2.2 degrees).

+

The failure of most simple formulas to accurately calculate the beamwidth of many arrays stems in part from the fact that they do not take into account the effects of forward sidelobes on the beamwidth. The greater the suppression of forward sidelobes, the wider the half-power beamwidth--up to certain limits, of course. In surveying designs with sidelobes ranging from -12 dB through -30 dB, the relationship has held throughout.

+

What About the 32-element Array?

The purpose of these notes has been to gain an appreciation of the wide-band characteristics of the DL6WU family of long-boom Yagis. As well, a secondary purpose has been to show some of the flexibility that the wide-band designs offer in terms of tailoring the design for a frequency and a subset of the array's operating characteristics. +

In setting up examples of how we might change matters to get a particular set of performance characteristics at a desired frequency, we have not stressed gain. Nor have we recommended any of the alterations made to the array. Instead, the goal has been to illustrate and understand how we might use the wide-band performance in various ways. There is not a thing wrong with using a DL6WU array as designed to cover all of the band with very good performance.

+

Nevertheless, a certain curiosity is natural concerning the longest version of the array in the original dimension chart. The full 32-element (30-director) Yagi is just about 11 wavelengths long, or about 24.6'. The rest of the story appears in Fig. 16.

+
+ +
+

The free-space gain is 19.47 dBi, with a combined 180-degree/worst-case front-to-back ratio of 22.35 dB. The longer array shows increased development of sidelobes. Indeed, if the array has a weakness, it lies in the front-to-sidelobe ratio of only 15.91 dB.

+

Despite this performance, let's remember that the longer the array, the greater the differential between the design frequency gain and the maximum gain. For this version of the DL6WU family, the maximum gain is about 19.91 dBi, almost a half dB higher, with an improved front-to-back ratio to boot. I will not speculate on whether these improvements constitute sufficient reason to exercise some of the flexibilities offered by the DL6WU wide-band long-boom Yagi designs.

+
+ +

+
+

Updated 11-02-2001, 07-27-2004, 12-05-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

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+

Topics: VHF / UHF, Yagi


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2 X 3 = 6

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Two Three-Element Yagis for Six Meters

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L. B. Cebik, W4RNL

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Another project required me to model a couple of 3-element Yagis for 6 meters, so I thought I might pass along the designs. They are not especially new, but they might be useful to some one needing to home brew a small Yagi to take advantage of the occasional openings on that band.

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The designs make a useful contrast with each other. Both are a bit over 6' in boom length. However, one presses for higher gain and good front-to- back ratio, while the other sacrifices a bit of gain and front-to-back for a wide operating bandwidth that covers all of 6 meters (50-54 MHz) with under 2:1 SWR with a direct 50-ohm feed.

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Gain

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A 3-element Yagi is capable of around 8 dBi free space gain with a front- to-back ratio of over 20 dB for something over an 3.2% frequency span (+/- 1.6% of the center frequency). In this span the gain will increase with frequency, while the maximum front-to-back ratio will peak in the 25-27 dB range somewhere in the middle of the band spread. +

I have elsewhere shown a 20 meter model using single diameter materials with these properties, adapted from a stepped-diameter model developed by K6STI. The design covers all of 20 meters. When scaled to 6 meters, the design covers about 1.5 MHz with the desired characteristics. Here are the dimensions, using 0.5" aluminum tubing. (single-diameter elements are quite practical from 6-meters on up.)

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Element        Length (ft)    Spacing from Driven Total Boom
+                                Element (ft)       Length (ft)
+Reflector        9.53              3.15
+Driven Element   9.08              ----
+Director         8.536             3.345            6.495
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The performance characteristics are summarized in the following table:

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Frequency      Gain      F-B Ratio      Feed Z         SWR (ref. =
+  MHz           dBi        dB           R+/-jX           25 ohms)
+50.0           7.92      16.55          26.9 - j20.2    2.14
+50.5           8.07      22.59          26.4 - j11.6    1.57
+51.0           8.24      25.86          24.9 - j 2.4    1.10
+51.5           8.43      19.33          22.8 + j 7.8    1.40
+52.0           8.64      14.66          20.3 + j19.2    2.34
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Notice that the 2:1 SWR for this antenna, with a 51 MHz target design frequency, is well over 1 MHz, but assumes the use of a 2:1 feedpoint matching system. This can be a beta match, which will require shortening the driven element until it shows abut 25 ohms capacitive reactance, or a Tee match, which will require a bit of driven element lengthening to show inductive reactance.

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The target center frequency can be adjusted up or down within 6 meters by adjusting all three element lengths by the percent of frequency change without concern for changes in element spacing of diameter. Likewise, for those more concerned with gain than front-to-back ratio, the performance at 52 MHz or a bit above that can be scaled to the target frequency, with the driven element adjusted for either resonance or a desired matching system. Changing the driven element length to create changes in its reactance by as much as 25-30 ohms has very little affect on the other performance figures.

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Operating Bandwidth

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A question often asked is how much gain and front-to-back ratio must be sacrificed to achieve a wide operating bandwidth, especially for a 4 MHz (8 %) bandwidth on 6 meters. The rough answer is about 1 dB of gain and 5 dB of front-to-back ratio. +

From the same 0.5" diameter aluminum tubing, it is possible to build a 3- element Yagi with about 7 dBi free space gain and up to 21 dB front-to-back ratio. Such an antenna will show a 2:1 SWR bandwidth of over 4 MHz on 6 meters and have a direct 50-ohm feed as well. The design below is adapted from an old W6SAI design for 10 meters. The dimensions are these:

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Element        Length (ft)    Spacing from Driven Total Boom
+                                Element (ft)       Length (ft)
+Reflector        9.734             3.391
+Driven Element   9.008             ----
+Director         8.01              2.73             6.121
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The performance characteristics are summarized in the following table:

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Frequency      Gain      F-B Ratio      Feed Z         SWR (ref. =
+  MHz           dBi        dB           R+/-jX           25 ohms)
+50             7.00      14.90          48.4 - j21.2    1.54
+51             6.92      18.08          51.9 - j 9.9    1.22
+52             6.96      20.31          51.9 + j 1.7    1.05
+53             7.13      21.02          48.8 + j15.0    1.35
+54             7.44      18.40          43.0 + j31.1    1.96
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Notice that the gain curve is not the anticipated steady rise across the band, but shows a minor peak just below the band edge, with an insignificant dip and then a return to the normal 3-element rise. The front-to-back ratio does not peak on the target design frequency (52 MHz, for the wide-band model), but above that frequency. The SWR remains below 2:1 for a direct 50-ohm feed from below 49.5 MHz to just above 54 MHz.

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The wide-band model is suited to wide-band interests, perhaps in a mechanical design that permits the user to flip it from horizontal to vertical polarization (where it, like every other Yagi, will show a broader beamwidth and up to 3 dB less gain over real ground). This would permit use with repeaters while allowing the operator to take advantage of SSB and CW openings.

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Comparisons

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Although the beams have comparable boom lengths and driven element lengths, the key differences lie in the parasitical elements. The higher gain model uses a shorter but more closely spaced reflector than the wide-band model. However, the tell-tale difference lies in the director. The higher gain model uses longer director at a considerably greater spacing from the driven element than the shorter, more closely spaced director of the wide- band model. +
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Figure 1 shows in rough scale the difference between the dimensions of the two antennas. Figure 2 contrasts the free space azimuth patterns.

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Either beam is easily constructed from hardware store tubing and other supplies. Both will be very light and easily installed at moderate heights. You can take your pick--or you can use these notes as clues to the design considerations for adapting them to other bands, higher or lower.

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Updated 7-25-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: VHF / UHF, Yagi


+ + diff --git a/content/vhf/yagitrim.html b/content/vhf/yagitrim.html new file mode 100644 index 0000000..54062c0 --- /dev/null +++ b/content/vhf/yagitrim.html @@ -0,0 +1,18 @@ + + + + + + Long-Boom Trimming Yagis: An Accumulation of Data + + + +

Long-Boom Trimming Yagis: An Accumulation of Data

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Long-Boom Trimming Yagis: An Accumulation of Data - Main Text

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Long-Boom Trimming Yagis: An Accumulation of Data - Reference Graphs

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This page exists to include the PDF in the topic index

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Topics: VHF / UHF, Yagi


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Your First 160-Meter Antenna

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L. B. Cebik, W4RNL

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The following notes rest on a small set of assumptions.

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1. You want to get on 160 meters for the first time (or perhaps, for the first time in a long time).

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2. You want to set up the simplest possible effective antenna using all wire construction. In fact, all of the antennas will be made from AWG #14 or AWG #12 wire. 2-mm (0.0787") diameter wire falls right between these sizes, so all of the data will use that value. However, nothing much changes by reducing the diameter to AWG #14 (0.0641") or increasing the diameter to AWG #12 (0.0808").

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3. You do not have unlimited vertical space for your antenna. In these notes, the limit will be about 70'. In fact, I shall use 21 m (68.9') as the standard top height for all antennas.

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I have set these limits so that we can compare the performance of a collection of relatively simple antennas.

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For all comparisons, we shall use average ground with a conductivity of 0.005 S/m and a relative permittivity (dielectric constant) of 13. For vertical antennas especially, you should expect lesser performance from worse ground and better performance from better ground--but not radically worse or better. Horizontal antennas are less affected by ground quality, but the top height is so low (about 1/8 wavelength) that the ground will influence performance much more than for the antennas you place 1 wavelength above ground for the upper HF region.

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160-meter antennas are naturally much larger (longer, taller) than antennas for the other HF amateur bands. Therefore, be prepared to spend a little more money for quality wire and insulators to durably bear the antenna weight. Copperweld is desirable. Supporting structures--whether natural or constructed--need to be stronger and taller than the average sorts of things that populate a backyard. How you handle the support structures I shall leave to you, since every yard is different, as are the locally available materials and the construction skills at hand.

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With those qualifications, let's get started in our work, starting with some vertical antennas.

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160-Meter Wire Verticals

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We shall begin with an antenna that violates the upper height limit of our task: the full-size 1/4 wavelength vertical monopole. A wire version of this antenna needs to be about 39 m (128') tall. The convenience of the vertical monopole is that we can feed it at the base--at or near ground level. The inconvenience is that we must install radials. The radials should be about 1/4 wavelength long and placed as symmetrically as the yard space allows. To see how many radials we might need, I modeled the vertical using 4, 16, and 64 1/4 wavelength radials, each 6" (0.15 m) below the surface. Fig. 1 shows the outlines of the 3 models.

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The following table shows the anticipated results, assuming that the vicinity of the antenna is not filled with RF-eating ground clutter. Conductive objects--even semi-conducting trees and shrubs--can distort antenna patterns and absorb some RF energy, so keeping the antenna area as clean as possible is important to getting the most out of any vertical antenna.

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+1/4-Wavelength Vertical Monopole with Variable Radial Systems
+Average Ground
+No. of            Maximum          TO Angle         Feedpoint Z
+Radials           Gain dBi         degrees          R +/- jX Ohms
+ 4                -0.72            23               57 + j 1
+16                0.48             23               44 - j 8
+64                1.14             23               37 - j12
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Note that we gain about 1.2 dB by increasing the radial field from 4 to 16 wires, with another increase of about 0.7 dB by raising the count to 64. Fig. 2 shows the relative radiation pattern strengths. The radiation plot also shows that a vertical antenna is best for lower-angle long-distance skip signals, but almost unusable for NVIS (Near Vertical Incidence Skywave) very short distance communications. Many vertical users also find a vertical less noisy that a horizontal antenna in terms of QRN from lightning, but more susceptible to local man-made noise sources. As well, as we increase the number of radials, the impedance decreases, indicating a reduction in energy lost to the ground.

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As the impedance decreases due either to the number of radials or ground quality, a number of operators use a simple means of obtaining a good match for coaxial cable. By making the vertical longer, they increase the resistive component of the impedance and the reactance moves from being slightly capacitive to being more definitely inductive. Adding a series capacitor at the feedpoint between the cable center conductor and the feedpoint itself allows them to compensate for the reactance, leaving a nearly perfect match for the 50-Ohm cable. A fixed capacitor may work if you have a specific operating frequency, but a remotely tuned variable is necessary for obtaining a low SWR over a wider operating bandwidth. Since we want the antenna to be at least slightly inductively reactive at all operating frequencies, setting up the antenna for the low edge of the band is the usual practice.

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The full-size vertical monopole is useful as a reference for comparing other vertically polarized antenna candidates. With that data, we can see what we gain or lose from each one. We shall look at 2 candidates, each no more than 70' tall.

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The Tee-Vertical: If we must limit the height to a certain level--70' in our case--but still desire a perfectly circular pattern, we need to create a shorter vertical antenna. Many vertical users opt for inductively loading the vertical either at its base or higher up on the wire. However, inductive loading has two disadvantages. First, the inductor always has a series resistance that reduces the radiated energy. Second, inductive loading reduces the feedpoint impedance faster, the closer the inductor is to the feedpoint.

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One of the simplest and most efficient ways to shorten a vertical monopole is to create a hat at the top. The usual vision of a hat consists of several hat wires radiating from the top of the vertical wire. However, we actually need only 2 wires to effect a hat. (The more wires that we have in a symmetrical arrangement, the shorter that each must be to set the antenna at resonance. However, any wires not in the same line as the supports for the top of the vertical section require additional supports.)

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We shall look at 3 versions of a Tee-vertical: with 4, 16, and 64 radials. Fig. 3 shows the relative complexity of each version. The vertical wire is 21 m (68.9'), and each leg of the Tee is 11.6 m (38') long.

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For the same set of conditions used to model the full-size vertical monopole, the shortened Tee-vertical shows the following performance values.

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+Shortened Tee-Vertical Monopole with Variable Radial Systems
+Average Ground
+No. of            Maximum          TO Angle         Feedpoint Z
+Radials           Gain dBi         degrees          R +/- jX Ohms
+ 4                -1.45            25               42 + j 2
+16                0.20             25               29 - j 6
+64                1.11             25               23 - j11
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The fewer the radials, the more that Tee-vertical performance lags behind the performance of the full-size vertical monopole. With 64 radials, there is almost no difference in performance with respect to gain. The Shorter vertical section of the Tee version does show a 2-degree increase in the TO angle. As well, the impedance at the feedpoint is only about 70% of the value for the full-size vertical. Fig. 4 shows the relative radiation patterns. We do not need azimuth patterns because, like the full size vertical, the Tee-vertical provides virtually a perfect circle of radiation (assuming that there are no nearby objects to distort that pattern).

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The Tee-vertical is amenable to the use of lengthening techniques to raise the feedpoint impedance with a series capacitor to compensate for the inductive reactance. Lengthening the Tee legs (in equal amounts to preserve symmetry) saves you the trouble of increasing the height. However, you will need more horizontal space for the increased Tee-top. If you use a series capacitor at the base of the antenna, I recommend a double waterproofing case system, along with regular preventive maintenance. As well, be sure that you use a beefy capacitor able to handle the high current level at a 50-Ohm impedance.

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The 1/4-Wavelength Inverted-L: A second alternative for our 70' height limitation is the inverted-L. As shown in Fig. 5, the L does not worry about symmetry, but simply uses a horizontal extension of the vertical wire to reach resonance on 160 meters. Because the top is not symmetrical, the horizontal wire radiates. However, the current is lower in the horizontal part of the antenna and the pattern is not seriously distorted on 160 meters. In the model for 1.85 MHz over average ground, the horizontal wire is 19 m (62.3') for the same vertical wire used in the Tee-vertical.

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The performance of the inverted-L is not significantly different from the Tee, as shown by the following performance figures.

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+Shortened Tee-Vertical Monopole with Variable Radial Systems
+Average Ground
+No. of            Maximum          TO Angle         Feedpoint Z
+Radials           Gain dBi         degrees          R +/- jX Ohms
+ 4                -1.53            26               43 + j 3
+16                0.08             26               30 - j 6
+64                0.98             26               24 - j11
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Due to the small horizontal component of the radiation patterns, the elevation angle has increase by another degree. However, the impedance values are almost identical to the corresponding values for the Tee-vertical. Fig. 6 shows the elevation and the azimuth patterns for the inverted-L. Note that the presence of a non-symmetrical horizontal section does not allow the pattern overhead to go to nearly zero, although the level is not strong enough for effective NVIS communications. The azimuth pattern shows a slight push in the direction of the top section of the L. However, the differential is not large enough to be noticed during operation.

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The 160-m 1/4 wavelength inverted-L has another advantage. With a wide-range tuner at the feedpoint (perhaps one of the remote tuners on today's market), the antenna is usable for general communications on virtually all of the amateur bands. Above 160-meters, the radial system acts like a good RF ground between the operating position and the antenna base, since the antenna is 1/2 wavelength or longer on all bands above 160 meters. If you choose to use a remote tuner for such an inverted-L system, add another layer of water-proofing as an additional guard against weather penetration of the tuner and the connection. For further information on multi-band use of the inverted-L, see "Straightening Out the Inverted-L."

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There is one temptation to avoid with the 160-meter 1/4 wavelength inverted-L. Many operators obtain rather poor results because they place the vertical section of the antenna too close to a natural or man-made support. The vertical section needs as much clearance from other objects as the corresponding part of the full-size and the Tee verticals.

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160-Meter Wire Horizontal Antennas

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We have examined the main candidates for vertical wire antennas, although there are manmy variations on the basic designs that we have used as examples. We should also look at some horizontal basic wire antennas. Any horizontal antenna will be severely limited by the 70' height restriction that we placed on the exercise. 70' is only about 1/8 wavelength above ground, a height that is even below optimum for NVIS operation--although it will work quite well in this service. One advantage of the horizontal wire is that it does not require any radials. A second advantage--at least for our work--is that horizontal wires do not change performance characteristics very much as we change ground quality. Therefore, the use of average ground provides a good indication of operation over any soil type. Finally, there are only 2 important horizontal variations that are possible within our height restriction: linear wires and closed horizontal loops.

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The 1/2-Wavelength Dipole: There is no magic about the 1/2 wavelength dipole except that at resonance, it is a reasonably good match for coaxial cable. If we wish to use parallel feedline and a tuner, we can be less critical about the exact length without changing the pattern in any detectable way. Fig. 7 shows the details of our model set-up. The wire is 78 m (256') long.

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Since we have only a single model with which to deal, our performance table is simplified.

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+1/2-Wavelength Horizontal Dipole 70' above Average Ground
+    Maximum          TO Angle         Feedpoint Z
+    Gain dBi         degrees          R +/- jX Ohms
+    6.72             90               49 + j 0
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Note that the horizontal wire provides the strongest radiation (and receiving sensitivity) straight up. Fig. 8 compares the elevation pattern of the dipole with the elevation pattern for the inverted-L with 16 radials. The horizontal wire is superior for NVIS service, but inferior for long-range, low-angle service. The horizontal wire is likely to be more susceptible to lightning noise, but less susceptible to man-made noises. The patterns for the two types of antennas cross at about the 23-degree elevation mark.

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Despite the low height of the dipole when registered as a fraction of a wavelength, the azimuth pattern at almost any elevation angle is still bi-directional and broadside to the wire. Fig. 9 shows the azimuth pattern at a lower angle (25 degrees elevation). Radiation (and reception) off the ends of the wire is about 8-dB or about 1.5 S-units weaker than broadside to the wire.

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Linear wires with open ends can build considerable levels of static charge unless we take measures to bleed it off as it develops. One technique is to place either a high-value resistor or an RF choke across the antenna feedpoint, ensuring that one side is connected to the coax braid--and the coax braid is well grounded. Inserting a transmission-line transformer type of balun at the feedpoint will defeat this measure by physically isolating the feedpoints from the cable braid. However, using a W2DU-type ferrite-bead choke as the balun will allow the bleed-off component to do its work.

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The 2-Wavelength Horizontal Loop: A closed loop antenna is more immune to static charge build-up, but has some special requirements. To understand why the heading specifies a 2 wavelength circumference for the loop horizontal antenna, we should proceed a step at a time. Let's begin with a simple square loop, like the one shown in Fig. 10. Our initial exercise will place the loop in free space and vary the circumference from 1.0 to 2.5 wavelengths.

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The following table lists the free-space performance values for the loop. The column marked "Horizontal Gain" lists the gain in the plane of the loop. The column labeled "Vertical Gain" shows the gain broadside to the face of the loop.

+ 
+Free-Space Performance of Horizontal Loops of Various Sizes
+Circumference     Horizontal     Vertical       Feedpoint Z
+WL                Gain dBi       Gain dBi       R +/- jX Ohms
+1.0               0.09           3.27            124 + j   17
+1.5               1.49           2.97           5300 - j 4700
+2.0               3.07           0.18            300 + j  240
+2.5               2.06           1.09           2600 - j 2700
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The 1 wavelength loop is most useful in parasitic beams called quads, where the individual loops are set up vertically to take advantage of the stronger radiation broadside to the plane of the loop. However, when we place the loop horizontally over ground, the radiation from the edge of the loop--the plane of most interest--is much weaker. As the table shows, the edge, in-plane, or "horizontal" radiation is strongest when the loop is about 2 wavelengths in circumference. For our test model, that length is about 340 m (1115'). Since the loop is not resonant, we shall need parallel transmission line and a tuner. Hence, the exact length is not at all critical. Any total circumference around 1100' will work fine.

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Fig. 11 compares the elevation and azimuth patterns for 1 and 2 wavelength loops 70' above average ground. Note that due to the low height, even the 2 wavelength loop has a relatively high TO angle. However, the 2 wavelength radiation strength (and reception sensitivity) at lower angles is considerably greater than the 1 wavelength loop. The advantage at lower angles appears clearly in the azimuth patterns on the right. The "tilt of the pattern follows the placement of the feedpoint, shown in Fig. 10. Note that the 2 wavelength loop does not produce a circular--or even an oval--pattern. Rather, it has four wide major lobes. The following table completes the equivalent data for all of the loop sizes that we tested in free-space. Note that the impedance reports change relative to the free-space values--as a function of the low height of the antennas above ground. The resistive component is lower, while the reactive component is more inductive.

+ 
+Performance of Horizontal Loops of Various Sizes 70' above Average Ground
+Circumference     Maximum        TO Angle       Feedpoint Z
+WL                Gain dBi       degrees        R +/- jX Ohms
+1.0               7.38           90              100 + j  100
+1.5               6.65           90             2600 - j 5200
+2.0               5.65           50              200 + j  380
+2.5               6.02           53             1400 - j 3300
+
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The pattern shapes and TO angles for a horizontal loop change as we change the shape of the loop. They also change if we move the feedpoint, say, from a corner to the middle of a side. As samples of the sort of changes that we might encounter with relatively symmetrical simple structures, I modeled triangular, square, and hexagonal loops, feeding each structure both at a corner and in the middle of a side. The following table summarizes the results. It adds a column listing the maximum gain at a "standard" 30-degree elevation angle, since the TO angle is considerably higher in most cases and varies from case to case.

+ 
+Performance of 2-Wavelength Horizontal 70' above Average Ground
+Loop and          Maximum        TO Angle       Gain at 30-deg       Feedpoint Z
+Feed positionL    Gain dBi       degrees        dBi                  R +/- jX Ohms
+Triangle-Corner   6.05           54             3.56                 135 + j 315
+Triangle-Side     5.99           58             3.18                 225 + j 300
+Square-Corner     4.92           55             1.24                  75 + j 220
+Square-Side       5.65           50             3.51                 200 + j 380
+Hexagon-Corner    5.65           53             2.75                 140 + j 320
+Hexagob-Side      5.57           54             2.45                 145 + j 320
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The wires of a 2 wavelength loop interact with each other to produce distinctive patterns for each combination of overall shape and feedpoint placement. Fig. 12 shows the azimuth patterns for the two triangles, with plots taken at the TO angle at at a standard 30-degree elevation angle. The insets show the loop outline and the feedpoint placement relative to the pattern for each version of the triangle. In all of the plots of 2 wavelength horizontal loops, the feedpoint will be at the top or 0-degree azimuth direction.

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The two triangle patterns are similar, although there is a small displacement of the pattern toward the long-wire side and away from the triangle point. More significant is the fact that in both cases, the pattern is significantly stronger (by about 3 dB) along a line from the feedpoint through the center than from side to side. Otherwise, there is not much to choose between the two versions of the triangle.

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The patterns in Fig. 13 confirm what the data in the table suggest: the feedpoint position makes a much more important difference to performance with a square loop than with any other form. With a corner feed, we obtain nearly circular patterns, but at lower strength. With a side-feed, we obtain more gain, but the patterns take on the 4-lobe shape. The lower the elevation angle, the more distinct that the lobes become. Whether the pattern shape and gain provide an advantage may depend on the possibilities for laying out the antenna relative to desired communication targets.

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As we make the loop more circular, the exact shape and feedpoint make less difference to performance. The hexagon patterns appear in Fig. 14. Neither the pattern shape nor the gain change very much as we re-orient the loop and the feedpoint. As well, the corner-fed and side-fed versions of the loop exhibit feedpoint impedance values that are much closer together than for either the triangle or the square.

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The most desirable version of a 2 wavelength horizontal loop would be a circle. However, the realities of antenna construction will not only require simpler forms, but as well, they may dictate somewhat irregular shapes. Nonetheless, virtually any horizontal loop will provide very reasonable performance. In addition, unlike a dipole, they will provide a null overhead, much like the nulls of vertical antennas. Therefore, if NVIS operation is the goal, you much either create a 1 wavelength loop or a dipole. For operation in the 20-30-degree elevation range, the 2 wavelength loop will usually provide as much or more gain than a wire vertical. Fig. 15 compares the elevation patterns of the corner-fed hex loop and the inverted-L with 16 radials. The maximum gain limits of the loop are similar to those of the dipole at the same 70' height, but the pattern is nearly circular rather than being bi-directional.

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Both the 160-meter dipole and the 2 wavelength loop are useful as multi-band antennas if we feed them with parallel transmission line and employ an antenna tuner to achieve a match with the transceiver. A number of other items at this site address the kinds of patterns that we can expect from a 250+' doublet and from horizontal loops (HOHPLs) of various shapes across the HF region.

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Conclusion

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We have surveyed some of the simplest antennas used on 160 meters. They are simple in principle, but require a lot of wire, whether used in the element or in radials. Insulation on the wire makes virtually no difference to performance. As noted early on, element wire should be strong, and copperweld is desirable. However, radials may use virtually any wire available. If a sale on wire allows you to add more radials to a vertical system, then it is worth the price. However, exposed elements require good strength or additional supports. As well, use good non-conductive insulators wherever an elevated wire terminates or changes direction. Do not lay a wire directly over a tree limb or wood support. High voltage has been known to gradually sever limbs or to set dry limbs ablaze. Suspend an insulator below the support and run the wire through the insulator. Likewise, use a strain relief fixture for any connection between the element and parallel transmission line.

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We have not examined a number of excellent antenna systems, such as phased or parasitic verticals. 160-meter wire Yagis and LPDAs are also possible. These are advanced projects, and our mission was to set out and compare some basic antennas. However, eventually, you will wish to purchase a copy of ON4UN's book on Low-Band DXing. It is possibly the best collection of 160-meter (and 80- and 40-meter) antenna ideas available.

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Updated 6-7-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Dipole, Horizontal Loop, Inverted L, MF, Vertical


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17-15-12 and Simple

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L. B. Cebik, W4RNL

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A number of casual CW operators have expressed interest in the 17-, 15-, and 12-meter bands as favorites for operating. QRM is less, in general, and the "atmosphere" seems relatively friendly. The smaller population on at least the 2 WARC bands in this collection also makes them easier for the less experienced operator to use.

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A common thread of conversations about antennas for these bands runs something like this: The lobes of the 135' doublet seem to prevent full coverage of all directions. Even though it has somewhat more gain near the ends, the lobes are narrow with deep nulls between.

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As Fig. 1 demonstrates, these problems are correctly diagnosed. Compared to dipole cut for 17 meters, the pattern for the doublet on 17 has many thin fingers. On 15 and 12, there will be more fingers, and thinner.

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However, the typical antenna described as being just for these bands is usually a complex beam of interlaced elements. Construction is usually tricky. A commercial version is expensive. So the conversation next poses this question: Is there something simpler, less expensive, and fuller in beamwidth coverage that might be used?

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The answer is yes. Unfortunately, the idea of using drooping dipole fans turns out not to be the most desirable option. The closeness of frequency of the 3 bands makes the interaction quite strong, even with sizable angles between wires. Hence, feeding one antenna array with a single coax cable may not be the easiest route to success. It can be done with careful pruning, but there may be an easier way.

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We can use a fixed or a rotatable dipole for 17 meters fed with parallel transmission line to an antenna tuner (the one used with the doublet). By cutting the dipole for 17 meters, the antenna will still be only about 2/3 wl long at 12 meters. Hence, the pattern will not change its shape from the dipole figure-8 (in free space) by enough to matter as we raise the frequency through 21 and stop at 24.99 MHz.

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Fig. 2 compares the patterns for a 17-meter dipole in free space in the three desired bands. Operationally, the differences in patterns would not be detectable.

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One important feature will change: the feedpoint impedance. If resonated in the middle of 17 meters, the impedance will be about 72 Ohms. On 15 meters, this same antenna will show a feedpoint impedance of about 130 + j200 Ohms. On 12 meters, the impedance will be in the neighborhood of 270 + j500 Ohms. The exact reactance value will vary with the wire size. 50-Ohm SWR values can get as high as 17:1 to 20:1.

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The upshot is this: if the antenna is to be used on all three bands, it needs to be fed with parallel transmission line and an antenna tuner. This move also frees us from having to use ultra-precision in adjusting the length of the dipole.

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If the antenna is placed at least 1/2 wl up in the air, skip performance will be excellent broadside to the antenna. A half wavelength at 17 meters is only about 27' up, so anything above that level is a bonus in terms of lowering the elevation angle of the main radiation lobes. The beamwidth of the dipole pattern is wide enough to make pointing very non-critical.

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A thirty-foot TV mast might be pressed into duty for this antenna. The metal mast will require some attention to dressing the parallel feedline down to the shack to avoid unbalancing influences, but most handbooks have sage advice in this department. The mast might be set up to turn with a rotator or by hand--what used to be called the Armstrong method. A short piece of strong tubing mounted to the mast with a plate and U-bolts would make room for a removable rod or thinner pipe to ease the turning. The system described here is designed to let you store the turning pipe when not in use for family safety. Other methods both simple and complex can be used.

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The system just described calls for an antenna that can be supported at the center at the mast top. See Fig. 3.

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The sketch shows two ways (among many) to make up the dipole. The tubing sketch makes use of standard aluminum tubing available from places like Texas Towers and others. It comes in 6' lengths and the sizes nest closely in each other. Hence, little work is necessary to lock smaller sections inside larger ones. Handbooks, show hose clamp, bolt, sheet metal screw, and rivet methods of element joining. Pick the one most easily implemented, but do not skimp on the effort to make the junctions secure.

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The tubing lengths in the diagram have a plan. The 33" exposed sections are all 36" long, with a 3" insertion length into the next larger tube section. This feature allows the builder to use a single 6" length of each size--and 6' is the standard shipping length. The 1" sections need 2 6' sections, with a bit left over. (A short section of fiberglass rod or tubing at the center of the 1" sections and running at least the length of the plywood plate can keep the elements aligned and strengthen the mounting.) Hence, even with shipping charges, the materials for this rotatable version of the 3-band dipole are inexpensive.

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The center plate can be a 1' to 1.5' per edge square of exterior grade plywood (exterior on both sides). Orient the plate as a diamond. Several coats of spar varnish weather protect the plate. It pays to use an exterior grade fill on the plywood edges before varnishing. U-bolts hold the element to the plate (4: 2 for each side) and the plate to the mast (1 U-bolt top and bottom). There are sources, like Harbach, for U-bolt assemblies designed specifically for antenna work. Hardware depot supplies should be carefully checked to ensure they are stainless steel.

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Some of the possible construction ideas appear in Fig. 4.

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Use any kind of insulated stand-offs to space the parallel transmission line from the mast. Then get plenty of help to raise things into position, thinking safety all the while. A 26.5' antenna can be somewhat ungainly.

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The fixed wire version can be used, although getting it to rotate is more difficult. However, bamboo may still be available in some areas. Otherwise, one has to live with a fixed wire, so be sure the antenna is broadside to your favorite parts of the world.

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Notice that the thinner wire dipole is actually shorter than the aluminum tapered diameter element. The particular set of element diameters and section lengths used in the tubing model actually is equivalent to a uniform diameter tube about 0.8" in diameter and 310" long. Tapering element diameters downward towards the outer ends calls for longer physical lengths longer than uniform diameter tubes.

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The actual length of the wire version will depend on the wire used. Insulated wire usually requires some physical shortening, since insulation gives antenna wire a velocity factor between .95 and .99 depending on the insulating material and its thickness. However, if we use the parallel feedline, length is less critical since we are no longer striving for a perfect impedance match at any frequency of use.

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Although designed for 17-12 meters, the antenna can be useful up to 10 meters and down to 30 meters. At these frequencies, the tuner might have some difficulty in reaching a match, but changing the parallel line length slightly may present the tuner with values of reactance it can more easily handle.

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A rotatable dipole can be a very effective antenna, since it eliminates QRM off the sides. (A beam reduces QRM on only one more side than the dipole.) Its broad beamwidth makes orientation easy. On many days, it is only necessary to reorient the antenna in late morning and again in late afternoon. (Of course, on other days, skip may come from anywhere, and the run to the antenna for a change of direction can be counted as good exercise.) The simplicity of construction, inexpensive materials, and ease of maintenance go a long way to compensate for lower gain relative to complex, expensive Yagis. Parallel feedline keeps losses low and places the matching problem next to the rig, where it can be handled with ease.

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If you already have your towers and beams, by all means use them. But for the casual CW operator who enjoys a rag chew on the upper bands or the pursuit of QRP with less QRM, a rotatable dipole for 17-15-12 meters may be just the ticket to getting started.

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Updated 5-18-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Dipole, Doublet, HF Upper


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A Tale of 4 Beams: The X, the Hex, the Square, and the Rect

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L. B. Cebik, W4RNL

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From time to time, interest reemerges in some long-standing designs for compact planar (2- dimensional) beams. Unfortunately the interest seems to focus on a single design at a time rather than on the design as a member of a family of designs. Equally unfortunately, the interest usually stems from the publication of some peak performance figures for a particular design rather than from the antenna's performance across an entire band. Consequently, misunderstandings of antenna potentials multiply endlessly.

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One of the family of beams whose members rouse periodic interest is the end-coupled clan. If the ends were connected, these would all make versions of a loop. However, with the ends spaced properly, each member forms a directional beam. Another apt name for the group might refer to the semi-closed geometry of the antennas. With closed loops, these antennas share the feature of tending toward larger dimensions with significant increases of element diameter.

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Under any name, the family has two branches: those whose center structures form Vees that point at each other bottom to bottom and those whose centers parallel each other. Among the features that clan members have in common is a flat structure with an area that is just over 0.6 square wavelengths--in other words, about 1/4 by 1/4 wavelength. Hence, the lure of the family is its compact size.

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It may be useful to explore the main members of the family individually to seek out their potential. I have selected 20 meters as the test band. To keep comparisons fair, I have constructed all models of #12 copper wire. However, some of the family members lend themselves to self-supporting aluminum tubing construction, and I shall note the potential performance changes that may result from building a tubing version of the antenna. The use of tubing for part or all of the structure, of course, will alter the dimensions from the ones used with the #12 wire versions.

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The antennas that we shall examine are these:

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  • 1. The folded X-beam
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  • 2. The hex beam
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  • 3. The VK2ABQ square
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  • 4. The Moxon rectangle
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As yet, I do not have any parallelograms, pentagons, or octagons in my collection.

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The Folded X-Beam

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Fig. A shows the outlines of a folded X-beam. If you are interested in the history and details of the folded X-beam, see "Modeling and Understanding Small Beams: Part 1: The X-Beam," Communications Quarterly, 5 (Winter, 1995), 33-50. Ordinarily, the Vee portions of the folded X-beam are constructed of tubing supported by a center hub. Then wire tails for the driver and director are run from one corner toward the other, often taped to a perimeter cord that also holds the four arms in a fixed arrangement.

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Modeling the usual construction of an X-beam is not feasible with NEC, since the program has an invariant tendency to yield inaccurate results with angular junctions of wires having different diameters. So, I have fashioned a model using #12 copper wire throughout. The performance differences are these: the all-wire version has a slightly lower maximum gain (by about 0.2 dB) and a slightly narrower 2:1 SWR bandwidth (about 50 kHz narrower) than the hybrid tubing/wire version. Incidentally, the hybrid version can be directly modeled with public-domain MININEC if one uses length-tapering toward the sharp angle corners.

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Folded X-beams are normally designed for driver-director arrangements, since it is difficult to obtain significant performance with a driver-reflector arrangement. In the folded configuration of Fig. A, the parasitic element almost "wants" to be a director. In less metaphorical terms, a modestly performing driver-reflector design, with only a slight change of reflector length, will reverse its pattern and hold that reversal, even though the parasitic element is considerably longer than one might expect for a director. It is also possible to tune the director to move the peak front-to-back portion of the operating curve across the band. By lengthening the director and adding a remotely adjusted bit of capacitive reactance at the center, the peak performance region can be moved across an amateur band. However, the model used here employs a fixed construction, as the following table shows.

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X-Beam                                    Frequency = 14.1  MHz.
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+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
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+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -99.000, 17.000,  0.000  W2E1 -99.000, 99.000,  0.000    # 12   15
+2     W1E2 -99.000, 99.000,  0.000  W3E1  -6.000,  3.000,  0.000    # 12   25
+3     W2E2  -6.000,  3.000,  0.000  W4E1   6.000,  3.000,  0.000    # 12    3
+4     W3E2   6.000,  3.000,  0.000  W5E1  99.000, 99.000,  0.000    # 12   25
+5     W4E2  99.000, 99.000,  0.000        99.000, 17.000,  0.000    # 12   15
+6          -99.000,-11.000,  0.000  W7E1 -99.000,-99.000,  0.000    # 12   15
+7     W6E2 -99.000,-99.000,  0.000  W8E1  -6.000, -3.000,  0.000    # 12   25
+8     W7E2  -6.000, -3.000,  0.000  W9E1   6.000, -3.000,  0.000    # 12    3
+9     W8E2   6.000, -3.000,  0.000 W10E1  99.000,-99.000,  0.000    # 12   25
+10    W9E2  99.000,-99.000,  0.000        99.000,-11.000,  0.000    # 12   15
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           2     8 / 50.00   (  8 / 50.00)      1.000       0.000       V
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In Fig. 1, we find both the gain and front-to-back curves of the folded X-beam. Because the direction of the beam reverses between 14.3 and 14.35 MHz, the curves are cut off at 14.3 MHz. (The reversal to a driver-reflector beam yields only poor results, never reaching a 10 dB front-to-back ratio.) One of the inherent difficulties of the folded X-beam is that the maximum gain and the maximum front-to-back ratio are always separated in frequency. The gain at the maximum front-to-back peak is about 0.5 dB below peak. Both the gain and the front-to-back curves are quite steep, indicating a narrow operating passband, whatever the feedpoint impedance characteristics might be. In the past, the chief use of the folded X-beam has been on 10 meters as a home-brew project for those interested in the 28.3 to 28.5 MHz region of the band.

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The SWR curve, in Fig. 2, is referenced to 20 Ohms, which is approximately the impedance at the maximum front-to-back peak. Indeed, this design shows operating characteristics that are directly tied to the feedpoint impedance. A near-50-Ohm impedance is possible at the lowest frequency in the passband, with a low gain and relatively poor front-to-back ratio. Where the front-to-back ratio peaks, the impedance is from 20 to 25 Ohms, depending on the thickness of the element materials. At the maximum gain point, the feedpoint impedance drops to the 10-15-Ohm region. Wire versions of the antenna tend to show impedance values at the low end of the ranges indicated, while tubular and hybrid versions yield impedances values at the higher ends of the ranges.

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The peak gain and 180-degree front-to-back ratio figures can give a misimpression. The peak gain of about 6 dBi (free space) rivals that of a 2-element Yagi whose elements take twice the space side-to-side. Likewise, the peak 180-degree front-to-back ration of over 32 dB sounds impressive. However, the patterns in Fig. 3 tell a somewhat different tale (as do the passband graphs we have viewed. An averaged front-to-rear ratio for the entire rear area of the beam has, within the 200 kHz of prime operation, a value of between 10 and 15 dB--no better than a common 2-element driver-reflector Yagi. The Yagi would also have superior gain over X-beam at every frequency and be able to cover the entire 20-meter band. A 2-element Yagi with about 1/8 wavelength element spacing and loaded elements that are about 3/4ths full size would occupy about the same area as the X-beam with broader performance curves. Hence, the folded X-beam has fallen into relative disuse.

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The Hex Beam

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If we fold the X-beam tails outward, we obtain the basic configuration of the hex(agon) beam, although true hex beams are built as closely to the hexagon geometry as the support structure will permit. Fig. B shows the outline of the model used to generate performance curves. The details of the model used in this study, which is a significantly modified version of a model originally provided by N7CL, follow in the chart.

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hex beam:  20 meters               Frequency = 14.1  MHz.
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+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -108.00, 19.500,  0.000  W2E1 -61.800,113.000,  0.000    # 12   22
+2     W1E2 -61.800,113.000,  0.000  W3E1  -9.950, 25.900,  0.000    # 12   26
+3     W2E2  -9.950, 25.900,  0.000  W4E1   9.900, 25.900,  0.000    # 12    5
+4     W3E2   9.900, 25.900,  0.000  W5E1  61.800,113.000,  0.000    # 12   26
+5     W4E2  61.800,113.000,  0.000       108.000, 19.500,  0.000    # 12   22
+6          -112.00,-12.900,  0.000  W7E1 -61.800,-113.00,  0.000    # 12   23
+7     W6E2 -61.800,-113.00,  0.000  W8E1  -9.950,-25.900,  0.000    # 12   26
+8     W7E2  -9.950,-25.900,  0.000  W9E1   9.950,-25.900,  0.000    # 12    5
+9     W8E2   9.950,-25.900,  0.000 W10E1  61.800,-113.00,  0.000    # 12   26
+10    W9E2  61.800,-113.00,  0.000       112.000,-12.900,  0.000    # 12   23
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           3     3 / 50.00   (  3 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      3/50.0  (  3/50.0)  Short ckt (Short ck)   12.000 in   600.0  1.00
+

One feature of this model is the relatively wide spacing of the centers of the Vee-ed sections. This move tends to lower the feedpoint impedance to the 25-Ohm region, and the model uses a 12" stub of 600-Ohm shorted transmission line as a beta hairpin to effect a 50-Ohm match. It is possible to bring the center points of the driver and reflector closer together to obtain a direct 50-Ohm match. However, two deficits emerge with this move. First, the 50-Ohm match does not extend across the entire 20-meter band because the sharpness of the geometry yields a corresponding tuning sharpness. In contrast, the beta-matched 25-Ohm impedance does cover the entire 20-meter band with a 50-Ohm SWR of under 2:1. Second, with the center Vee points brought closer together, array performance smooths out across the band, but at much lower levels of gain and front-to-back ratio than we obtain from the wider-spaced center region. Therefore, I have chosen to look at the lower impedance version of the antenna with its better performance peaks.

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The hex beam has a design affinity with a number of other members of the end-coupled clan that we shall not examine here. The slope of the outer sections of each end toward the other element is a property shared by several interesting antenna designs, including a 2-element reversible wire beam for 40 meters developed by AA2NN. The antenna uses a double slope, since the elements each form an inverted Vee. As well, each element end approaches the corresponding end of the other element. The result is a beam that requires only two center supports. As well, by using rope on the ends of the elements, the tie down points will also be reduced to 2. Equally related to the outer structure of the hex beam is the 3-element 40-meter reversible Yagi developed by WA3FET. It uses a linear driver and a pair of parasitic elements, each of which is sloped toward the end of the driver. One parasitic element is loaded for reflector duty. One advantage of element tips that slope toward each other rather than point directly at each other, is the greater ease of adjustment. Small changes of spacing of the tips produce less radical effects than when the tip are end-to-end.

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Fig. 4 presents the gain and 180-degree front-to-back ratio figures across 20 meters. The gain variation across the band is nearly 2 dB, a fairly high figure among common 2-element beam designs. The front-to-back ratio shows a very sharp peak, but decreases rapidly to band-edge values in the 8 to 12 dB range. Peak operation of this antenna has a bandwidth of 100 to 150 kHz, with the remainder of the band showing relatively mediocre performance. Nonetheless, like all members of the semi-closed geometry family, the hex beam permits a high front-to-back peak whose decline is steeper below the peak frequency than above it.

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+ +
+

Fig. 5 illustrates one of the illusions of SWR. One could suggest that this model of the hex beam antenna has an operating bandwidth that covers the entire band, since the 50-Ohm SWR is less than 2:1 across 20 meters. However, operating bandwidth involves more parameters than just the SWR. Evaluating the gain and front-to-back ratio is equally as important, if not more so, than the SWR. For this particular design of the hex beam, the only wide-band parameter is SWR. Gain and front-to-back ratio values are relatively narrow band properties.

+
+ +
+

Fig. 6 shows free-space azimuth patterns for the first 200 kHz of 20 meters. The pattern at 14.1 MHz is well controlled, but off peak, the rearward pattern spreads to average values in the 15 dB range. Beyond 14.2 MHz, the rearward pattern spreads larger and the forward gain decreases rapidly.

+

In general, like the X-beam and other beams based upon vee-ing the center parts of the elements, the hex beam shows a quite narrow operating bandwidth relative to gain and front-to-back ratio. The rate and total gain change across the band and the band-edge front-to-back ratio values are very important in evaluating the operating bandwidth of an antenna.

+

For further extensive information on home-brew hexbeams, see G3TXQ's website www.karinya.net/g3txq/hexbeam/ or K4KIO's site www.k4kio.com

+

The VK2ABQ Square

+
+ +
+

The VK2ABQ Square (and the Moxon Rectangle) are more fully described in "Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and The Modified Moxon Rectangle," Communications Quarterly, (Spring, 1995), 55-70. The origins of the square go back to the 1930s, only to disappear and re-emerge in the 1960s. Fig. C shows the outlines of a modified square. The modification consists of loading the reflector with a shorted transmission line stub about 6" long to move the peak performance point without disturbing the square shape.

+

The original VK2ABQ square used very close-spaced element tips--only a literal coat button apart. However, very close tip spacing creates an array with narow-band properties, and small variations in construction can yield large variations in performance. Therefore, the model below uses fairly wide spacing (34") for the element tips.

+ 
VK2ABQ 20 Meters                           Frequency = 14.15  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -118.22, 16.889,  0.000  W2E1 -118.22,106.159,  0.000    # 12    6
+2     W1E2 -118.22,106.159,  0.000  W3E1 118.222,106.159,  0.000    # 12   13
+3     W2E2 118.222,106.159,  0.000       118.222, 16.889,  0.000    # 12    6
+4          -118.22,-16.889,  0.000  W5E1 -118.22,-106.16,  0.000    # 12    6
+5     W4E2 -118.22,-106.16,  0.000  W6E1 118.222,-106.16,  0.000    # 12   13
+6     W5E2 118.222,-106.16,  0.000       118.222,-16.889,  0.000    # 12    6
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           7     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+                -------- TRANSMISSION LINES ---------
+Line  Wire #/% From End 1   Wire #/% From End 1    Length       Z0   Vel Rev/
+      Actual  (Specified)   Actual  (Specified)                Ohms Fact Norm
+1      5/50.0  (  5/50.0)  Short ckt (Short ck)    5.892 in   600.0  1.00
+

As the model shows, this version of the antenna is off square by about 12 inches. In this highly square (if imperfectly square) configuration, the feedpoint impedance is about 100 Ohms, making the antenna a candidate for a 2:1 balun at the feedpoint.

+
+ +
+

As shown by Fig. 7, the VK2ABQ square is a relatively low gain beam, although the gain varies only about 1.1 dB across the band. Hence, the 4.05 dB gain at the high end of the band equals that of the hex beam. The square's 180-degree front-to-back ratio peaks above 34 dB. Although the curves are fairly steep, the band edge values are about 15 dB--not bad for a 2-element parasitic beam that is about 1/4 wavelength on a side.

+
+ +
+

As Fig. 8 shows, the real surprise of the modified VK2ABQ square is the 100-Ohm impedance curve. Across all of 20 meters, the resistive portion of the feedpoint impedance varies by under 6 Ohms, and the reactance varies by a similar amount. Hence, the SWR curve is very flat indeed. A 2:1 balun would permit operation across the entire 20-meter band with an exceptionally low SWR and no conditions to incur losses within the balun.

+
+ +
+

The VK2ABQ was the basis for the later Moxon Rectangle. The key performance feature absorbed from the square was the excellent control of the rear portion of the radiation pattern. Fig. 9 shows the band-edge and mid-band pattern for the square. If the square is constructed of 1" aluminum tubing, the band-edge front-to-back ratio improves to nearly 20 dB, with a small increase in array gain as well.

+

In all, the square is a relatively wide-band array whose characteristic remain reasonably level across the band (gain and impedance) or hold to minimal acceptable levels (front-to- back ratio). However, the chief deficit of the square is gain. In fact, one can preserve the front-to-back performance while improving gain--and as a bonus achieve a direct 50-Ohm match. The cost is going considerably out of square.

+

The Moxon Rectangle

+
+ +
+

Because the 3 family members we have so far examined use relatively wide spacing between facing element tips, many designers have ignored the effects of this dimension. The result has been a number of fairly poor designs. The element tip spacing influences the relative proportions of every other dimension of any of the family members. Nowhere is this more apparent than with the optimized Moxon rectangle, sketched in Fig. D. The combination of close tip coupling as well as more extended parallel element coupling allows the Moxon rectangle to recover the gain lost by the square while maintaining fairly wide-band operating characteristics. It is the longer sections of parallel elements that permit the close tip spacing to be controllable without sudden shifts in the direction of the pattern.

+

The #12 copper wire model for this study reveals that the side-to-side length is about 3/8 wavelength, while the front-to-back size is about 1/8 wavelength. Hence, the total area of the antenna is less than the 1/4 wavelength squares, although the turn radius is greater. The details of the model used here are as follows:

+ 
Moxon rectangle                             Frequency = 14.175  MHz.
+
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -151.74, 64.188,  0.000  W2E1 -151.74,110.377,  0.000 8.08E-02   5
+2     W1E2 -151.74,110.377,  0.000  W3E1 151.740,110.377,  0.000 8.08E-02  35
+3     W2E2 151.740,110.377,  0.000       151.740, 64.188,  0.000 8.08E-02   5
+4          -151.74, 56.433,  0.000  W5E1 -151.74,  0.000,  0.000 8.08E-02   7
+5     W4E2 -151.74,  0.000,  0.000  W6E1 151.740,  0.000,  0.000 8.08E-02  35
+6     W5E2 151.740,  0.000,  0.000       151.740, 56.433,  0.000 8.08E-02   7
+
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          17     2 / 47.14   (  2 / 47.14)      0.707       0.000       V
+

As the model shows, the rectangle is about 50% longer (side-to-side) than the squares. Tip-to-tip spacing is about 8". In the August, 2000, issue of AntenneX, I published a small program that inputs only the design frequency and wire diameter to yield optimized dimensions for Moxon rectangles for the HF and VHF regions. The designs provide a direct 50-Ohm match, whether used for rotatable or reversible beams.

+
+ +
+

The gain curve in Fig. 10 for the Moxon is a full dB better than for the square, although the total change in gain across the band is about the same. Since the Moxon rectangle can easily be fabricated of aluminum tubing, the result will be another 0.2 dB of gain and slightly less change in the gain across the band. As well, the band-edge front-to-back ratio values will improve to nearly 20 dB from the wire values of 15 dB. As with all of the semi-closed geometry designs, the front-to-back ratio is peaked just below the center of the band in order to achieve relatively similar front-to-back values at the band edges.

+

Both the square and the Moxon use the combination of parallel element coupling and end-coupling to achieve a very high front-to-back ratio at a design frequency. Indeed, in both cases, the current magnitude and phasing on the parasitic element center is very close to the precise values needed for a maximum front-to-back ratio if each element were to be independently fed and phased. Only the existence of the "tails," which radiate (if only weakly), prevents the pattern from becoming the deep dimple of a perfectly phased pair of elements.

+
+ +
+

The 50-Ohm SWR curve in Fig. 11 is for a direct match to coaxial cable with no matching required (although a common-mode current suppression choke or 1:1 balun is always in order). Unlike the SWR curve for the VK2ABQ square, the Moxon SWR curve shows a definite slope, although the band edge figures are acceptable under most conditions. The curve flattens further if one uses aluminum tubing of about 1" diameter for the antenna.

+
+ +
+

The Moxon rectangle shares with the VK2ABQ square a nearly cardioidal pattern. The deepest "side" nulls do not occur at 90 degrees off the bearing of maximum gain, but somewhat further toward the rear, as is evident in Fig. 12. The rear lobes are well behaved, that is, they have no large quartering side lobes. The rearward lobes for the band edges shrink as the element diameter becomes larger.

+

Some Tentative Conclusions

+

This survey of semi-closed geometry end-coupled beams should suffice to reveal the family resemblances among the members of the clan. It may be useful to summarize some of the properties that both link and separate the individual members.

+

1. Designs with element center regions that are parallel or only gently sloped outward toward the ends tend to show wider-band characteristics than those whose element centers are Vee-ed toward each other.

+

2. Element tips display two regions of coupling. Wider spacing between tips tends to produce lower gain, although small changes in spacing yield less radical effects. Closely spaced tips tend to be more critical and may be effectively usable only if most of the element length is either parallel or only gently slopes to bring the tips closer together.

+

3. Semi-closed beam designs tend toward loop properties, such as an increase in perimeter dimensions with an increase in element diameter. Sloping element designs are most immune to this effect and may show more typical linear element properties.

+

4. Designs that strive for a minimum turning radius tend either to have narrow-band characteristics or lower gain. The Moxon rectangle represents a compromise geometry that achieves as good or better gain than the other 2-element members of the clan while achieving a high front-to-back ratio and relatively broad-band characteristics. Sometimes the best square is a rectangle.

+

5. Both the front-to-back ratio and SWR curves tend to deteriorate much faster below the design frequency than above it. Therefore, to achieve relatively equal performance at both the lower and upper band edges, the appropriate design frequency is about 1/3 the way up the band. For 2-element driver-reflector designs, whether using a standard Yagi configuration or one of the end-coupled designs, the gain will decrease as frequency increases.

+

I have over the years built and used most of the designs we have discussed here in 10- meter versions, using both wire and aluminum construction. The models employed here are variants of those antennas, as well as of published data. No commercial antennas are modeled for these notes. Their intent is simply to show both the resemblances and differences among members of the end-coupled clan of beams.

+
+ +
+

Updated 9-1-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for August, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
Go to Main Index
+

Topics: HF Upper, Hex Beam, Moxon, X Beam


+ + diff --git a/content/wire/40h.html b/content/wire/40h.html new file mode 100644 index 0000000..9fb5027 --- /dev/null +++ b/content/wire/40h.html @@ -0,0 +1,38 @@ + + + + + + Half-Length Dipoles (for 40 Meters) + + + +
+

Half-Length Dipoles (for 40 Meters)

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Below 20 meters, full-length dipoles (and other antennas based on the dipole) present space problems. For many amateurs, such antennas are simply too long to fit within the modern urban and suburban yards. So the antenna builder begins to think of ways to shorten the dipole. The questions surrounding shortened antennas are complex. Some involve performance levels compared to the full-length dipole. Others concern the relative efficiency of antennas that use different means of shortening. Another group of questions focus on the mechanical issues created by various methods of shortening. Moreover, there are auxiliary matters, such as matching the shortened antenna to one of the standard feedlines in common use.

+

To explore these questions in a somewhat systematic manner, we shall pick a single antenna length on a single amateur band. 40 meters (7.0 to 7.3 MHz in the U.S.) is handy, since the average dipole length is in the vicinity of 67', just on the verge of fitting or not fitting a typical back yard. Let's use a half-length dipole and set its length at a fixed value of 33' for our explorations. Most of our antennas will use AWG #12 (0.0808" diameter) copper wire. With these simple premises, we can examine a myriad of ways of shortening dipoles, including but not limited to, folding back the elements, using inductive loads at the dipole center or along the element length, using end "hat" loads or element extensions, and employing U and other shapes. Each alternative method of shortening the length of a dipole has its own cluster of variations, its own set of issues, and its own set of consequences, for example, when constructing basic parasitic beams with half-length elements

+

This series of PDF documents tries to explore the basic territory in an orderly fashion, beginning with the development of basic properties of full size elements to form a baseline with which we can compare various techniques of shortening. The next step is to look at the performance potential of shortened elements and explore a few ways in which amateurs have simply folded and bent full size elements to fit a half-size space. Actual shortening takes us into the realm of element loading using inductive and other methods to resonate a half-length element. The last step is to look at some consequences of element shortening for the design and performance of directional beams.

+

Since each new step makes use of information developed in the previous step, you may wish to keep earlier episodes open while reading the new one. To return to this master page, use your browser's "previous page" button, since PDF documents have no ready means for returning to this page. The titles for each of the episodes should by self-explanatory.

+

Part 1: The Full-Length Standard

+

Part 2: Shortening and Reshaping the Dipole

+

Part 3: Element Loading to Achieve Dipole Resonance

+

Part 4: Basic Loaded-Element Parasitic Beams

+

Most of the material has appeared in other articles at this site, but under a scattered collection of specific topics and at different test frequencies. Drawing the ideas together may provide you with a more cohesive understanding of the principles involved in radically shortening a dipole and obtaining the best possible performance from it.

+
+ +
+

Updated 12-24-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Dipole, HF Lower, Loading, Yagi


+ + diff --git a/content/wire/40ha.pdf b/content/wire/40ha.pdf new file mode 100644 index 0000000..8d34668 Binary files /dev/null and b/content/wire/40ha.pdf differ diff --git a/content/wire/40hb.pdf b/content/wire/40hb.pdf new file mode 100644 index 0000000..f040351 Binary files /dev/null and b/content/wire/40hb.pdf differ diff --git a/content/wire/40hc.pdf b/content/wire/40hc.pdf new file mode 100644 index 0000000..0abb70a Binary files /dev/null and b/content/wire/40hc.pdf differ diff --git a/content/wire/40hd.pdf b/content/wire/40hd.pdf new file mode 100644 index 0000000..6d32390 Binary files /dev/null and b/content/wire/40hd.pdf differ diff --git a/content/wire/40star-1.gif b/content/wire/40star-1.gif new file mode 100644 index 0000000..34fbaa2 Binary files /dev/null and b/content/wire/40star-1.gif differ diff --git a/content/wire/40star-2.gif b/content/wire/40star-2.gif new file mode 100644 index 0000000..3d17942 Binary files /dev/null and b/content/wire/40star-2.gif differ diff --git a/content/wire/40star-3.gif b/content/wire/40star-3.gif new file mode 100644 index 0000000..5a8ef95 Binary files /dev/null and b/content/wire/40star-3.gif differ diff --git a/content/wire/40star-4.gif b/content/wire/40star-4.gif new file mode 100644 index 0000000..a739f21 Binary files /dev/null and b/content/wire/40star-4.gif differ diff --git a/content/wire/40star-5.gif b/content/wire/40star-5.gif new file mode 100644 index 0000000..bafeb7e Binary files /dev/null and b/content/wire/40star-5.gif differ diff --git a/content/wire/40star.html b/content/wire/40star.html new file mode 100644 index 0000000..92c6634 --- /dev/null +++ b/content/wire/40star.html @@ -0,0 +1,112 @@ + + + + + + A 40-Meter Star + + + +
+

A 40-Meter Star

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The horizontally oriented 1 wavelength square loop is a fairly standard low-HF amateur antenna. It lends itself to use with parallel feedline for multi-band application. However, a 1 wavelength loop tends to radiate broadside to the loop. Therefore, the antenna tends to provide better performance on bands above the lowest.

+

The Standard Square and the 4-Pointed Star Loops

The need for a longer circumference is often at odds with amateurs who have only limited space for wire antennas on the lower HF bands. However, one way to increase the circumference of a loop without increasing its footprint is to draw in the 4 sides of the loop toward the center. The result is a 4-pointed star configuration. Fig. 1 shows the difference between the standard and star loops, as viewed from above (or below, as the case may be). +
+ +
+

Fig. 1 also provides us with a key to the main dimensions of the loop and the star. The length of a side for a square horizontally oriented loop is also the length of one side of its footprint. For the 40-meter (7.15 MHz) test case, each side of the loop is about 36.2' long for a near resonant loop. This provides an antenna and a footprint circumference of 144.8' or about 1.05 wavelengths at 7.15 MHz for a near-resonant loop. On the right side of Fig. 1 is the star. Here, we must distinguish between the wire length and the footprint. For a near resonant loop, we require a footprint side dimension of about 31.9', which results in a footprint circumference of 127.6'. This dimension set is actually smaller than for the square loop. However, as shown in the sketch, each wire is stretched inward toward the center. We cannot make the wire touch at the center, but we can come in rather close. The most radically inset case that I have so far explored positions the apex of each angle formed from the side wires at 1.75' from the antenna center. This yields a distance of about 3.5' between opposing points. The resulting wire length for each side of each point in the star is about 21.35'. The total wire circumference thus becomes about 170.8' or close to 1.25 wavelengths.

+

We can compare the potential performance of the two configurations on 40 meters via the following table of modeled results.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+              Square and Star Loop Performance at 7.15 MHz
+
+Antenna Height 50'.  Antenna Wire AWG #12 copper.  "Insets" refers to the
+distance of the limit of the star side inset point from the exact center
+of the array.
+
+                      Gain       El. Angle        Feed Z
+                      dBi        Degrees          R +/-jX Ohms
+Square                5.54       47               157.5 - j 6.3
+Star: 1.75' insets    5.50       39                65.7 + j 9.0
+Star: 2.0' insets     5.50       39                66.8 + j12.0
+Star: 3.0' insets     5.50       40                71.1 - j 0.6
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Several aspects of the tabular data are significant. First, the 40-meter gain of the two versions of the loop is virtually the same. However, the elevation angle of maximum radiation is considerably lower in the star version. Fig. 2 graphically illustrates these matters by showing the two azimuth patterns, each at is respective TO angle, to exactly overlay each other. However, the elevation pattern of the star along the axis of maximum radiation has a noticeably lower angle of maximum radiation (take-off or TO angle).

+
+ +
+

Second, if operation is contemplated only on 40 meters, then the impedance of the star configuration is suitable for a coaxial cable as the feedline Either 50-Ohm or 75-Ohm cable will do. For similar operation, the square configuration would require either the use of a parallel feedline or the use of a 4:1 balun with a 50-Ohm coaxial cable feedline.

+

Third, the star configuration is not especially sensitive to just how far toward the array center we push the insets. The distances from center shown may be doubled to see how far apart we may place the inner points of the star. There is considerable room for variation before we lose our advantage over the square loop in terms of TO angle. However, note that the 3.0' inset has bumped the TO angle upward one notch. As we further move the inner start points away from center, the antenna slowly returns to the characteristics of a simple square loop.

+

The principle behind the star is an attempt to increase its wire circumference length without increasing its footprint. The 0.2- wavelength increase, while not giving us the almost pure edge-wise radiation of a 2 wavelength loop, does raise the entire wire length in the star loop to 1.25 wavelengths. That much length is sufficient to lower the 40-meter radiation angle by a noticeable amount.

+

The Square Loop as a Multi-Band Wire Antenna

The square loop allows us to feed the antenna on higher bands, relative to the base-line 40-meter band to which we have cut it. We can summarize the performance with the following tabulated samples for the HF bands. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                    40-Meter Square Loop Performance
+
+Antenna Height:  50'.  Antenna Wire AWG #12 copper.
+
+Freq.      Gain       TO angle   Feed Z           Pattern Shape
+MHz        dBi        Degrees    R+/-jX Ohms
+7.15       5.5        47          160 - j    6    Oval
+10.125     4.8        32         3060 + j 3140*   Almost square
+14.1       8.5        19          275 + j  120    4-leaf clover
+18.1       7.2        16         1035 + j 1480*   wobbly oval
+21.1       8.7        13          255 + j   55    4 main lobes, 60
+                                                  degrees off axis
+24.95      8.0        11         1230 - j 1380*   6 near-equal lobes
+28.1       10.8       10          265 + j  115    4 lobes 45 degrees
+                                                  off axis
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

With exceptions, the patterns generally are strongest in a line through the feedpoint and the corresponding center point of the wire opposite. We may call this the main axis of the antenna. On two bands of high interest, however, the patterns depart from the noted tendency.

+
+ +
+

Fig. 3 shows the azimuth patterns of the square loop on 15 and 10 meters, with the axis presumed to run vertically on the page. The 15-meter pattern forms a sort of butterfly, with small lobes along the antenna axis. However, the strongest lobes are angled to the sides by about 60 degrees. The 10-meter pattern has only 4 notable lobes, each about 45 degrees off axis.

+

We may also note in passing the starred entries in the feedpoint impedance (Feed Z) column. Each of the non-harmonic bands presents an impedance where the resistance and the reactive components are both above 1000 Ohms. Without careful attention to the characteristic impedance and length of the parallel feedline used, the impedance at the antenna tuner terminals may fall outside the range of values that it can match.

+

The 4-Pointed Star Loop as a Multi-Band Antenna

We may perform the same modeling experiment with the 4-pointed star loop to evaluate its potential as a multi-band antenna for 40-10 meters. The results appear in the following table. + 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+                     40-Meter Star Loop Performance
+
+Antenna Height:  50'.  Antenna Wire AWG #12 copper.
+
+Freq.      Gain       TO angle   Feed Z           Pattern Shape
+MHz        dBi        Degrees    R+/-jX Ohms
+7.15       5.5        39           65 + j   10    Oval
+10.125     6.7        26         6820 - j 7650*   Diamond
+14.1       9.3        19          540 + j 1850*   4-leaf clover
+18.1       6.9        16          925 + j   75    Broad beam:  F-B 5.2 dB
+21.1       6.2        13          945 - j 1270*   Broad beam:  F-B 1.3 dB
+24.95      6.8        11           55 + j  340    Broad beam:  F-B 2.5 dB
+28.1       6.9        10          715 - j  670    Triple forward lobes
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

For the entries called "Broad beam," the direction of maximum gain is toward the side of the star containing the feedpoints. If we overlay the outline of the antenna on top of the azimuth patterns in Fig. 4, the feedpoint will be above the plot center line across the page.

+
+ +
+

The patterns show one potential advantage of the star as a multi-band antenna. On all bands, there is a main lobe along the antenna axis through the feedpoint. Hence, the user is always aware of the direction of strongest signal. (30 meters is the one exception, but the main lobe to the reverse of the feedpoint side is only 0.7 dB stronger than on the feedpoint side, a difference that will not be detectable in operation.) Although the beam action--that is, having a small front-to-back ratio--is small, the reliability of having the main lobe along the same axis on every band used is a distinct plus.

+

There are three bands on which the reactance rises above 1000 Ohms. However, only on 30 meters are the values for both resistance and reactance so high as to create a very distinct problem for matching the feedline termination to the transceiver 50-Ohm system.

+

Why?

The distinctness of the square loop and the star loop patterns should arouse some curiosity as to the reason for the differences. Fig 5 provides a partial answer. +
+ +
+

The upper diagrams compare the relative current magnitude distribution of the two loops on 40 meters. The current on the star remains higher further outward toward the array corners than on the square loop, and this phenomenon plays a role in lowering the elevation angle of maximum radiation (the take-off or TO angle). Otherwise, the gain and pattern shape of the 2 versions of the loop are the same.

+

The 15-meter case is especially interesting. For the star loop, the current magnitude peaks and valleys appear in close proximity along the outward star-point wires. Hence, the currents (or, more properly, the fields that result) tend to simply add to or subtract from each other-- with due place given to the phase of each current magnitude sampled. However, in the square loop, we have current magnitude peaks more linearly separated from each other, with distinct peaks at the four corners of the array. The result is the 6-lobes pattern, with the largest lobes at a considerable angle from the axis of the antenna.

+

These brief notes suggest that for some users of square loops, modification to a star design may be useful. The array dimensions for 40 meters will easily scale to 80 and 160 meters, although most users will have difficulty in scaling the height as well as the wire length. Since we are only approximating resonance on the lowest band of use and presuming parallel feedline to an antenna tuner, fussiness with dimensions seems out of place. Since the wire of the antenna has a small diameter relative to a wave length, any 50-Ohm resonance on the lowest band of use is likely to be a very narrow-band phenomenon.

+

Nonetheless, for the loop-user who wishes a lower TO angle on the lowest band of use and a pattern that has a maximum along the axis of the antenna on every band used, the 4-point star is viable alternative to the standard square loop. The cost is less than 20% more wire, which is likely to be the cheapest part of the antenna anyway. The star loop is not an answer to every loop problem. However, it does show that it pays to explore different wire geometries to see whether they have any potential for use.

+
+ +

+
+

Updated 04-13-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index Page

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Topics: HF Multi Band, Horizontal Loop


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Screening 40-Meter Vertical Arrays

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L. B. Cebik, W4RNL

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The lower HF amateur bands tend to feature vertical antennas. We find a few horizontal beams, especially on 40 and 30 meters, but they tend to be very large, heavy, and expensive. In contrast, vertical arrays make use of wire and usually use much simpler construction. Hence, their maintenance requirements are also simpler.

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At 40 meters (and by extension and scaling 30 meters as well) the vertical dipole becomes feasible, especially if we find a way to shorten it somewhat without losing significant performance. From the vertical dipole, we may create a large number of array types. In these notes, I want to examine in order of increasing performance capabilities a collection of vertical dipole beams and arrays. So that all comparisons will be fair, every vertical array will use AWG #12 copper wire, perhaps the most common material for amateur wire antennas. As well, all antennas will be over average soil (conductivity 0.005 S/m, relative permittivity 13). The performance of vertical antennas will change with the quality of the soil beneath them and in the far-field reflection zone, but the changes will tend to be consistent within any given soil type. Therefore, if we know the performance of an array over average soil and the relative performance for a simple vertical dipole over both average soil and the specific soil type for a given installation, we may extrapolate the performance values for a more complex antenna system.

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Vertical Dipole Basics

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The root antenna for what follows might seem to be a vertical dipole. Table 1 and Fig. 1 summarize the properties of a vertical dipole that extends from 1' above ground level to a top height of 67.6'. The total wire length is 66.6', but this exact value applies only to a resonant vertical dipole over average soil. Slight adjustments are likely for different soil types, especially since the lower end of the antenna is so close to the ground. As will be the case for all models used in these comparisons, the performance and dimension values do not account for the influence of objects in the immediate area of the antenna installation, that is, the so-called ground clutter. All vertical antennas require as much clearance from ground clutter as the installation site will permit.

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For this and all following antennas, the test frequency will be 7.15 MHz. The clutterless radiation patterns show very normal characteristics--a circular azimuth pattern and a single elevation lobe with a low take-off (TO) angle. Hence, despite the low gain of the antenna, it finds general favor for its coverage and for its insensitivity to high-angle noise and signals. The simple outline sketch shows the current magnitude distribution along the antenna wire. One reason why the antenna patterns show a low TO angle stems from the relatively high position of the feedpoint or the region of highest current magnitude, just about 1/4 wavelength above ground. However, the close proximity to the ground at the lower end of the dipole does elevate its feedpoint impedance--from an expected 70-Ohm value up to the 98-Ohm value reported by NEC-4 for the sample antenna.

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Many amateurs do not have 70' supports for a 40-meter vertical dipole in its simplest form. Individual circumstances vary, but let's suppose that the maximum support height is about 50'. Within this height restriction, we may still install a modified vertical dipole. Rather than accept the losses that center-loading or mid-element loading might create, we shall use end hats. An end hat or cap is a symmetrical structure at right angles to the main plane of the antenna. Radiation from the wires of the end cap largely self-cancels, leaving us with a vertical antenna in terms of the radiation patterns. Since the self-canceling portion of the radiation occurs in the low-current regions of the antenna, we preserve most of the performance that we might obtain from a full-length dipole. Fog. 2 shows the outlines and current distribution on one version of such a T-capped dipole/

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The end hats on a vertical dipole can use any symmetrical arrangement. The more radial arms that we create, the shorter each one must be for a given length of vertical wire in the center. However, many-spoked hats set up very significant support requirements. The T-cap requires only two wires at each end of the dipole, and we may run these wires along the non-conductive ropes that we often use to support wire vertical dipoles between two posts or trees. Reducing the number of hat wires to only two per end does not affect the performance relative to using greater numbers of hat wires. For example, the azimuth pattern of the T-cap dipole in the sketch shows only 0.03-dB of gain variation as we check all 360 degrees of the horizon.

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The T-cap dipole that Fig. 2 shows is only 35.5' long, stretched from 5' to 40.5' above ground. (One might easily raise the antenna by another 4 to 5 feet and still remain below the 50' ceiling that we set. The added height would also increase safety by raising the base wires with their high RF voltages above the level that family, friends, or even pets might touch.) The vertical section, then, is just over 1/4 wavelength. For all following 40-meter vertical antennas, we shall use the vertical section of the T-cap dipole. The two horizontal wires at the top and bottom of the antenna, various called arms or legs, are each exactly 10' long in the sample. Hence, the total width of the antenna is 20'. This width falls well within the clear area that we should have for any type of vertical dipole.

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If we need to make adjustments for obtaining resonance in subsequent arrays that use the T-cap dipole, we shall adjust the length of the legs of the T, thereby leaving the center vertical section intact. The dimensions for the basic T-cap dipole appear in Table 2, along with some basic performance data. Within that data, only the first section is immediately relevant for comparison with the full-length dipole. First, note the 22-degree TO angle. This value is higher than the value for the full-length dipole, but the T-cap vertical's feedpoint is considerably lower (about 0.16 wavelength above ground). Partly as a function of the lower feedpoint height and partly as a function of the vertical-element shortening, the gain of our T-cap dipole is about 0.4-dB lower than the gain of the full-length dipole. Yet the T-cap dipole, as set up in the sample model, is nearly 30' lower in overall height, yielding what is for most amateur operators a much more manageable construction and maintenance situation.

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In the table, we also find some performance values related to improvements that we may make in the local ground immediately beneath the vertical dipole. When we think of local ground improvements together with virtually any vertical antenna, most amateurs immediately think of radials. However, unlike the radials of a monopole, the radials beneath a vertical dipole (either full length or shortened) perform no antenna-completing function. Rather, they simply function to raise the conductivity of the soil immediately beneath the antenna. In cases 2 through 4 in the table, I created radial systems with the hub directly below the antenna. The 1/4 wavelength radials use AWG #12 wire buried 1' deep in the average ground. As the table shows, adding 4 radials amounts to wholly wasted effort, since the gain increase is only 0.04 dB. 16 radials provide a 0.3-dB gain increase, perhaps a marginal amount, considering the work involved. If radial installation is easy, we may increase the field to 64 radials and obtain nearly 0.7 dB gain increase. Fig. 3 provides a view of the 3 radial field along with the T-cap dipole above them. You may estimate the installation work from the sketches.

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Note that none of the radial fields changes the TO angle of the elevation pattern. The TO angle is mostly a function of the far-field reflection zone, with is mostly well outside the radial limits. For the exercises, I did not change the antenna dimensions. Therefore, the major influence of the fields appears in the feedpoint impedance listings. As the size of the radial field increases, the resistive component of the impedance decreases and the reactance becomes more inductive. However, none of the changes in cases 2 through 4 present any operational concerns.

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The last case presents an alternative method of local ground improvement. Instead of using a radial system, I modeled a wire-grid system below ground to simulate laying a screen of some sort below the antenna. The screen is square and 70' on a side. Fig. 4 overlays the 16-radial system on the screen to show the change in ground coverage in the screen corner region. (I used the 16-radials so as not to obscure the grid. However, the most relevant comparison would be between the screen and the 64-radial system.)

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With the screen in place, we obtain almost 1.1 dB gain improvement over untreated soil, and about 0.4-dB improvement over the 64-radial system. The cost of the gain is a 1-degree increase in the TO angle and further drift in the feedpoint impedance. For antennas--like vertical dipoles--that do not require radials to function as the lower half of a dipole, screens may sometimes be the easiest and most effective means on improving soil quality immediately below the antenna. However, they do not provide that same benefits as living over very good soil, since the treatment does not also apply to the far-field reflection zone. For example, local area treatment may reduce ground losses below the antenna, but that results in a higher TO angle, because the improvement increases local reflection almost straight upward. The lower TO angles that we often associate with the same antenna over very good soil results from improved soil conductivity at considerable distances from the antenna.

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In the end, soil improvement is a matter for the antenna user to decide after measuring the anticipated performance improvements against the amount and cost of work involved in local ground treatment. For the remainder of these notes, we shall use untreated soil beneath the antenna, so that the performance values in case 1 in Table 2 become the reference points for all that follows.

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Before we leave the basic T-cap vertical dipole, we should introduce one more set of considerations. We are interested not only in the performance of any antenna at the test frequency, but also across the entire band. 40 meters is a wider (but not the widest) amateur allocation, with a 4.2% bandwidth. Some antennas will handle the entire band; others will not. A basic dipole--either full-length or T-capped--shows only a show change of gain across the band. The case-1 T-cap dipole, for example, changes gain by only 0.07 dB from 7.0 to 7.3 MHz. Note that our performance concerns include not only the SWR properties, shown in Fig. 5, but also such matters of forward gain and front-to-back ratio, both of which will become important as we add directionality to the basic dipole.

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Although the resonant impedance of the basic T-cap dipole is in the vicinity of 75 Ohms, even the 50-Ohm SWR is below 2:1 from one band edge to the other. Hence, we may feed the dipole using either 50-Ohm or 70-Ohm coaxial cable. As usual, one should route the cable at right angles to the vertical dipole for as far as possible, providing supports so that the cable weight does not unduly stress the wire antenna. As well, I recommend the use of 2 common-mode current attenuators, one at the feedpoint to also serve as a balun, and the other at the entry to the operating building to attenuate any currents induced along the cable run.

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A Bi-Directional Pair of T-Cap Dipoles

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Because many of the arrays to follow will use a pair of T-cap dipoles, we should spend a moment two see what happens when we place a pair of these dipoles at a spacing of 1/2 wavelength (about 68.8') and feed them in phase. Because the in-phase fed pair of antennas will interact (or, otherwise put, exhibit mutual coupling), I extended the T arms to 10.31' each. As a result, the total array width, from outer T-tip to outer T-tip is about 89.4'. As shown in Table 3 and the outline portion of Fig. 6, the array height above ground has not changed relative to using a single T-cap dipole.

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Perhaps the most surprising aspect of the array is the 4.1-dB gain improvement over a single T-cap vertical dipole. Of course, the added gain comes at a cost in the available beamwidth, now down to about 62 degrees. Nevertheless, the array is no taller and only a bit wider than a half-square, but provides more gain. The gain that is competitive with a bobtail curtain. In fact, the in-phase-fed pair of vertical dipoles lies at the theoretical core of all SCV (self-contained vertical) antennas, since the basic versions--ranging from deltas to rectangles to half-squares, all place two elements in phase, but at a spacing limited by the single-wire, single-feedpoint configuration. For further information on SCVs, see "Self-Contained Vertically Polarized Wire Antennas: A Family Album"

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The independent feedpoint impedances of the two T-cap dipoles is about 56 Ohms. Therefore, we may equip the phased pair with a common feedpoint by using equal lengths of 70-Ohm feedline to a center point. Since the physical distance between each element's feedpoint and the center point is 1/4 wavelength, and since all 70-Ohm transmission lines have a velocity factor (VF) of well under 1.0, you may need to use 3/4 wavelength section to arrive at the required 100-Ohms at the junction, a value that becomes a good 50-Ohm match in a parallel connection. The lower portion of Fig. 6 provides the modeled 50-Ohm SWR curve. The array covers the entire 40-meter band with an SWR value that is less than 2:1.

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We shall not linger over the in-phase-fed pair of T-cap dipoles and their broadside bi-directional pattern. However, we shall occasion to mention them once more before we close our screening survey. Nevertheless, we should call to attention one more time the gain value produced by the pair of elements. The maximum gain in each direction will exceed the forward gain value that we may achieve from some of the more basic beams that we consider when thinking about a pair of T-cap dipoles and their best use.

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Parasitic Driver-Reflector Beams Using T-Cap Dipoles

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For many operating needs, a front-to-back ratio of at least 10 dB may be more important than additions to the arrays forward gain. In such cases, we may create an endfire array using standard 2-element Yagi principles. In a Yagi with full-length elements, the reflector is normally longer and the driver normally shorter than a freestanding resonant dipole. In creating the driver for a useful Yagi-type beam, we may simply reduce the T-legs to an individual length of 9.6' (for a total element width of 19.2').

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However, we shall not stop to develop a reflector for the T-cap array that uses a larger element. Instead, we shall simply load the reflector and use the same dimensions as for the driver. Reflector loading of a 2-element parasitic array normally does not reduce the forward gain, and it may actually improve the front-to-back performance over a full size reflector. Table 4 supplies the dimensions of the array, which spaces the elements 21' apart. Fig. 7 shows the outline and the radiation patterns that we might expect.

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The azimuth plot overlays two patterns, one in each direction. One of the key advantages of loading the reflector is that--with very little effort--we can reverse the beam's direction. The reflector called for a 55-Ohm load to achieve the desired pattern. Instead of using an inductor as the loading element, we may use a shorted length of feedline, in this case, 50-Ohm cable to match the feedpoint impedance of the driver element. The electrical length would be about 18.24', but the physical length will be the electrical length times the cable's velocity factor. Even a solid dielectric cable will yield a physical length of at least 12', so that cable running from each element can meet in the center of the 21' element spacing. Then, with a suitable remote switch, we can short one cable to make the inductively reactive load for the reflector and connect the other line to the main feedline. With a flip of the switch, we have reversed the beam's direction.

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When we first encounter vertically polarized parasitic arrays, we are sometimes surprised by the facts that their gain is lower and their beamwidth is much greater than the patterns that we find in horizontal arrays using the same number of elements. The beam's gain value is about 3.3 dB higher than for a single T-cap dipole, but less than the bi-directional gain of the phase-fed pair of verticals. The beamwidth is nearly 140 degrees, providing very good coverage in each of the beams two possible directions. Although ground losses have a role to play in setting the gain of all vertical antenna types that are close to the ground, the vertical array's gain would not catch up to the gain of a horizontal counterpart until we reached a height above 20 wavelengths. The key factor in the gain and beamwidth difference that we get from rotating the beam 90 degrees along its real or virtual boom is a function of geometry. The arrangement of element tips restricts the beamwidth in the E-plane, that is, in the plane of the elements. However, the H-plane has no such restrictive influence. Indeed, in free-space, H-plane patterns of a 2-element parasitic array look very much like the pattern of a single vertical dipole but displaced in the direction of the forward gain. A Yagi must have many elements (and be very long) before the H-plane beamwidth narrows significantly.

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Nevertheless, the reversible 2-element vertical array with T-cap elements provides good service across the 40-meter band. As the 50-Ohm SWR curve at the bottom of Fig. 7 shows, the array will cover most of the band with less than 2:1 SWR. However, we early on noted that our bandwidth concerns covered more than just the SWR. We are also interested in how well the antenna performs in terms of gain and front-to-back ratio. Fig. 8 provides a partial answer to our questions.

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The gain curve in the figure shows a 0.4-dB range of forward gain value across the band, a value that we may consider fairly stable for such a wide amateur band using elements composed of relatively thin wire. In contrast, the front-to-back ratio remains above 10 dB only for a small portion of the band. However, it never drops below 5 dB. In fact, with careful adjustment of the reflector load, we may be able to center better the front-to-back curve for relatively similar performance at the band edges. A slightly higher load reactance--meaning a slightly longer length for the shorted stub--would likely do the job. Alternatively, we may favor either the CW-digital end of the band or the phone end of the band, according to our operating needs.

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One limitation of the 2-element driver-reflector array is that we leave some portions of the horizon only weakly covered. It might be useful if we could cover the entire horizon with less than a 2-dB drop in gain around the 360-degree span--and at the same time maintain at least the forward gain that we obtained from the reversible 2-element array. To achieve that goal, we may think in triangles.

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Suppose that we set up a an equilateral triangle of T-cap vertical dipoles. We may designate the corner containing the driven element as the apex. The remaining corner will contain identical T-cap dipoles, but loaded to form reflectors. Table 5 provides the dimensions and test-frequency performance data, while Fig. 9 supplies a sketch and the radiation patterns.

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The T-legs are each 9.5' long for the individual dipoles. Each triangle side is about 30.6' long, yielding a distance between the apex and the center of the triangle base of 26.5'. It does not matter how we orient the T-legs of the dipoles, so long as the legs form a straight line for each dipole. In the triangle shown--and other dimensions are also possible--each reflector dipole requires a j90-Ohm load. We shall again use shorted transmission-line stubs as the source of the required inductive reactance. Since the driver impedance is close to 70 Ohms, we shall use 70-Ohm lines, which require a 19.9' electrical length, with physical shortening that depends on the VF of the line used in the assembly. We shall bring the stubs to a center point within the triangle for switching. At any time, one of the stubs will actually be an extension of the main feedline to the driver, while the switch to form the required reflector loads shorts the other two lines.

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The system gain is about 3.2 dBi, about 0.5-dB higher than for a standard 2-element parasitic array and about 3.7-dB higher than a single T-cap vertical dipole. The 15-dB front-to-back ratio is also several dB higher than we found for the 2-element parasitic beam. With its higher gain, the triangle shows a beamwidth that is about 5 degrees narrower than the beamwidth of the simpler beam. Perhaps the key advantage of the triangle is its ability to cover the entire horizon with only a 2-dB gain deficit at the overlap points between the forward lobes of the beam in each of its positions. Although the switching may be more complex for the triangle than for the reversible beam, the electronics are simple and cheaper than a rotator.

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The lower portion of Fig. 9 shows the 50-Ohm and 70-Ohm SWR curves for the array. A 50-Ohm feedline from the switch junction to the equipment will be satisfactory if SWR values close to 2:1 are satisfactory at the band edges. However, a 70-Ohm line will reduce the maximum SWR value to about 1.5:1 at the band edges. With respect to the gain and front-to-back performance across the 40-meter band, Fig. 10 supplies the appropriate sweep data.

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The performance bandwidth of the triangle is generally similar to the performance bandwidth of the reversible array, but with a smaller range of value change across the band. The gain varies by only about 0.2 dB. The front-to-back ratio remains at 10 dB or more for the entire band. The band-edge values may be equalized by slight adjustments to the load values, that is, the length of the shorted stubs. With the smaller range of performance change over the 300 kHz of amateur allocation (in the U.S.), one may design a triangle for whole-band use and expect only small deficits at each band edge.

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A 2-Element Phased Beam Using T-Cap Dipoles

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Obtaining the maximum possible front-to-back ratio from 2 elements is difficult if not impossible using parasitic techniques and 2 vertical elements that are close to the ground. However, it is easily possible to improve the front-to-back performance and to obtain a nearly cardioidal pattern by phasing 2 T-cap dipoles in an endfire arrangement. In fact, we may do so using commonly available feedline materials, although we may have to do some experimentation to find the optimal cable for the task. Experimenting with modeling software is more rapid and less costly than experimenting with lengths of actual cable.

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Table 6 profiles the phased array that uses two standard T-cap dipoles with 9.6' T-legs and a spacing of 21' (the same spacing used for the reversible parasitic array). Both dipoles use identical construction. The phase line uses two separate lengths that reach a junction where we shall connect the main feedline. The section to elements 1 in Fig. 11 is 084' of RG62, 93-Ohm line with a VF of 0.84. Hence, the electrical length is 1'. The line does NOT undergo a half twist or reversal. However, the line from the junction to the rear element--from the same material--does undergo a reversal. It is 21' physically or 25' electrically.

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The forward gain of the array is comparable to the gain of the reversible parasitic array. However, the front-to-back ratio climbs to over 26 dB at the design frequency. As well, the beamwidth increases to about 145 degrees, providing wide coverage in this essentially mono-directional array. The rearward quadrants of this array promise to be exceptionally quiet.

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The cost of this type of performance lies in the odd feedpoint position before we add matching components. The low impedance has a high inductive reactance. However, the values are nearly optimal for a beta match, so long as we use an open or capacitively reactive stub across the feedpoint terminals. 14.3' of 50-Ohm VF 0.78 cable or its equivalent provides the necessary shunt component for the beta L-network that yields an impedance close to 50 Ohms. With the beta component in place, the SWR curve in Fig. 11 shows well under a 2:1 SWR value at the band edges.

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Fig. 12 provides sweep data for the phased array relative to forward gain and front-to-back ratio. The gain rises steadily across the band over a 0.4-dB range. The front-to-back ratio peaks near the middle of the band and decreases to about 15 dB at the band edges. Compared to parasitic arrays, the whole-band front-to-back performance of the phased array rates very highly. Perhaps the major drawback to phasing is that the array does not succumb easily, if at all, to reversing direction.

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Screen Reflectors and the T-Cap Driver

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Screen or planar reflectors have been used since the 1920s in major arrays. Indeed, in their early years, some called them billboard reflectors. A solid surface properly sized will reflect radio waves in ways that are analogous to the reflection of light from a flat mirror. We find them in wide use in dipole arrays for short-wave broadcasting and in a wide variety of UHF antennas. More recently, I have recommended their use beneath a number of NVIS antennas to increase gain, essentially by elevating the quality of the reflective plane beneath the antenna. In fact, the wire-grid ground improvement technique noted earlier represents a different application of the same technology.

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A wide range of experience shows that planar or screen reflectors are most effective in improving directional gain when they exceed the dimensions of the driver element by between 0.45 and 0.55 wavelength both horizontally and vertically. We can achieve this goal horizontally with our T-cap vertical dipole driver, but any screen reflector will be vertically challenged. The ground, of course, is one limit, preventing the reflector from extending below the driver by the desirable amount. Vertically, we shall be limited as well by some of the height restrictions that we set for this project. If we limit ourselves to a 50' top height, the forward gain will be only a little greater than the gain of the reversible beam. A top height of 100' yields perhaps a half-dB more gain than a 70' height. Therefore, for the comparisons that we shall show, the height of the screens will run from just above ground level to 70'. One might hang such a screen between two widely separated towers that support antennas for higher amateur bands.

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The optimum width turns out to be just about 140', which is 1 wavelength at the test frequency (7.15 MHz) and a half wavelength on each side of the driving dipole. Screen reflectors do not have to be solid surfaces to act like solid surfaces in the HF range. Chicken-wire fencing and open-weave materials will appear solid to 40-meter energy. The model for the screen-reflector array uses a wire-grid, as shown in Fig. 15. The dimensions and performance data appear in Table 7.

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The selected distance from the driver to the reflector is 35' for an array using a single T-cap dipole driver and a 140' by 70' screen reflector. You may ground the screen bottom wires with no effect on performance, but with a considerable affect on safety. The driver uses 9.66' T-leg lengths for an 80-Ohm resonant impedance. With a planar reflector, you may vary two items to set a feedpoint impedance: the dipole dimensions and the spacing from the reflector. In general, closer spacing produces lower feedpoint impedance levels, but narrower operating bandwidths. Each space adjustment will change the coupling between the reflector surface and the driver, requiring adjustments to the T-leg lengths to return to resonance.

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The chief merits of the planar reflector array are forward gain and operating bandwidth, when we compare the results to the reversible parasitic array. The top height of the reflector limits the front-to-back ratio to about 13 dB. A top height of 100' would have added another dB to the ratio, while a more ideal (and unrealistic) height of 140' would add a further dB or two. The array's forward gain is close to 4.7 dBi, about 1.8 dB higher than the 2-element parasitic array. The forward gain comes at the expense of the beamwidth, which is down to 83 degrees, about 50 degrees narrower than the beamwidth of the parasitic beam.

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Despite the 80-Ohm resonant feedpoint impedance at the design frequency, the 50-Ohm SWR curve in Fig. 13 reveals a very low rate of impedance change across the 40-meter band. That curve shows less than 2:1 SWR at the band edges. The lower 80-Ohm curve shows less than 1.5:1 SWR at the band's upper and lower limits. The remaining prime operating parameters are equally slow to change, as shown in the sweep data in Fig. 14.

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The gain across 40 meters changes by only about 0.1 dB, while the front-to-back ratio varies by just over 0.5 dB. It is possible to design driver elements with an inherently wider bandwidth and to use the array to cover both 40 and 30 meters with very little change in performance.

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One common method of constructing a screen is to use a series of wires polarized as the driver element. To sample that option, I reconstructed the screen reflector using 29 AWG #12 wires at 5.0' intervals. The overall horizontal and vertical screen reflector dimensions remained the same. Doubling the wire size (to AWG #6) yielded no performance improvements. The only other change relative to the wire-grid screen was a 3' increase in the spacing of the driver from the reflector, as shown in the dimensions in Table 8.

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As the data and the patterns in Fig. 15 show, the vertical-wire reflector is not quite as effective as the wire-grid version. Gain drops by about a half dB, while the front-to-back ratio decreases by well over 2 dB. Both decreases are indications that the wire version of the screen requires a taller top height or is perhaps "leakier" than the wire-grid. As well, the resonant impedance is 5 Ohms higher and does not produce 50-Ohm SWR values under 2:1 without further matching. However, the lower 75-Ohm SWR curve in the graph does track the wire-grid's 80-Ohm SWR curve very well.

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The sweep information in Fig. 16 shows the same broad curves for both the forward gain and the front-to-back ratio. The gain range is about 0.15 dB across the band, while the front-to-back ratio changes by only 0.8 dB. Even with somewhat lesser performance than the wire-grid reflector, the vertical-wire screen still enjoys a considerable advantage over a parasitic reflector with respect to broadband characteristics.

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To compensate, even if only partially, for ground losses, one may tilt the reflector back, as viewed from bottom to top. Using an 11' tilt (35' at the bottom and 46' at the top for the distance between the driver and the vertical-wire reflector), it is possible to add a few tenths of a dB to the forward gain and a similar amount to the front-to-back ratio. However, the exercise has its own consequences, as revealed in the overlaid patterns of Fig. 17.

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The peak gain lines both forward and rearward are virtually indistinguishable in the patterns. However, note the increased high angle radiation, especially in the rearward lobes. As well, radiation directly overhead to the driver has also increased. In the end, a vertically oriented screen appears to yield the best combination of performance and patterns.

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Earlier in these notes, I promised a second look at the in-phase-fed pair of T-cap dipoles spaced 1/2 wavelength apart. The dipole pair produced a bi-directional pattern with a maximum gain that was over 4 dB stronger than a single T-cap dipole. Since we can readily feed the pair of dipoles from a single feedpoint, using a pair of equal-length lines, we might wonder what would happen if we place the broadside array in front of a screen reflector.

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Ideally, the screen should be over 200' wide. Understanding that we lose performance as we shrink a screen below its ideal proportions, let's continue to use the smaller 70' by 140' wire-grid screen. With the screen 40' behind the driver, the T-legs of each dipole are 10.16' long, longer than for a single dipole driver, but slightly shorter than the T-legs on the bi-directional array. As shown by the dimensions in Table 9 and the outline sketch in Fig. 18, we lose a good bit of the horizontal screen extension that optimizes performance. Nevertheless, the performance is noteworthy.

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The 6.95-dBi forward gain value for the array may require some perspective. First, the value is almost 2.3-dB higher than the gain we obtain from a single driver and the same reflector. A sign that the screen is less than optimal in size comes from the fact that the screenless bi-directional array produces a gain value that was 4 dB greater than a single T-cap dipole. Nevertheless, the phased dipole array and screen produce almost 7.5-dB gain relative to a single T-cap omni-directional dipole. The forward beamwidth is down to 58 degrees, dictating careful aiming of the array.

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The front-to-back ratio is not outstanding, at about 11.4 dB, another sign of using a small screen reflector. Because the unmatched feedpoint impedance of each dipole is in the vicinity of 90 Ohms, we may run equal lengths of RG-62 (VF 0.84) to a center point between the dipoles and obtain a net impedance of 48.9 Ohms. As the 50-Ohm SWR curve shows, the array easily covers 40 meters with a maximum SWR that is less than 1.5:1.

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As the sweep data in Fig. 19 reveal, the dual-dipole-driver array is as stable across 40 meters as the other sample screen-reflector array. Both the gain and the front-to-back ratio show changes of just over 0.2 dB across the band.

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The construction of a screen-reflector is the most difficult portion of the overall project. Therefore, one may well wish to place drivers on either side of the screen for reversible service using separate feedlines all of the way to the equipment location. Whichever driver is in use (whether single or double), the inactive one will remain invisible due to the screen's reflection characteristics. Screen reflector arrays may not be for everyone, but they may serve a few 40-meter operators.

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Conclusion

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The reason for our title is now clear. We have not only surveyed comparatively the performance of vertical antennas and arrays on 40 meters, but we have added screen reflector arrays to the list that we normally see. This last group of arrays presents serious construction challenges, but offers in return increased gain over the values that we may obtain from parasitic arrays.

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All of the driving elements in our comparisons have used AWG #12 copper wire in a T-cap arrangement that extends from 5' to 40.5' above average ground. We changed the length of the T-legs to obtain a resonant feedpoint impedance. The T-cap dipoles provide a uniform element length to help validate the comparisons. Although scarcely longer than 1/4 wavelength, the T-cap dipoles lose very little performance relative to the reference full-length wire dipole with which we began these notes.

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Just because we cannot obtain the gain level of a phase-fed dipole pair with a screen reflector does not relegate the intermediate designs to uselessness. Indeed, many operators use T-cap and similar 40-meter vertical antennas with surprisingly good results. The parasitic arrays offer reversibility and even--with the triangle--full horizonal coverage at the flip of a switch. For maximum front-to-back ratio, the phased array is difficult to surpass, even though it uses no complex networks to achieve a nearly cardioidal pattern.

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By setting the entire range of vertical arrays on common ground at a common frequency with common construction, you may gather a more precise sense of the benefits and costs as you increase the complexity of a vertical array. Virtually all of the designs will scale directly to 30 meters, although bandwidth there is not a major concern beyond the realm of allowing rather casual construction without incurring performance losses. Scaling to 80 meters is also possible, although for most amateurs, the resulting element sizes may prove to be prohibitive. A T-cap dipole of the present design will extend from about 10' to about 81' at the top, depending on the precise frequency to which one scales the design. The T-legs can be trimmed for resonance if you stick with the AWG #12 wire rather than doubling its diameter. If the amount of trimming is not too great, adjusting only the lower T-legs will not disturb the centering of the feedpoint to any significant degree. (The presence of ground below the bottom of the antenna and essentially free space above the top already disturbs the balance that we presume when we physically center the feedpoint on a vertical dipole. Common-mode current attenuation devices are necessary adjuncts to any of these arrays.)

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These notes have focused on performance comparisons and provided very few construction notes. Building any of these arrays, from the simplest to the most complex, will be an exercise in making use of available supports and in using what nature or prior antenna construction provides. In virtually all cases, the result will be far less expensive than a strong tower able to hold the weight of a horizontal beam that shows higher-angle elevation lobes and questionable operating bandwidth.

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First printed in QRP Quarterly, January, 1997. Updated 01-22-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Lower, Vertical


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80-Meter Dipoles and Inverted-Vs
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80-Meter Dipoles and Inverted-Vs A Graphical Scrapbook

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This page exists to include the PDF in the topic index

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Topics: Dipole, HF Lower, Inverted V


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10 Frequency Asked Questions about the All-Band Doublet

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L. B. Cebik, W4RNL

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The all-band doublet horizontal wire antenna has a history almost as long as amateur radio itself. Despite all the words and diagrams in handbooks over the years, newcomers still send me questions about the antenna. I have collected the questions and boiled them down to 10, all of which have many variations. The goal in tackling these frequently asked questions is to help newer hams erect a successful antenna system.

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1. What is an all-band doublet? The all-band doublet is actually an antenna system and not just an antenna alone. Fig. 1 shows the basic elements of the system. The horizontal center-fed wire forms the antenna proper, which accounts for the radiation of transmitted energy and the reception of incoming energy. The parallel transmission line transfers the energy from the antenna to the antenna tuner (or antenna-tuning unit, the ATU) or vice versa. We insert the tuner because the impedance that shows up at its terminals will vary widely from one band to another. So we need a way of matching the impedance at the tuner terminals to the standard 50-Ohm input and output impedance of the transceiver.

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The antenna wire itself can have many lengths, but should be about ½ wavelength at the lowest operating frequency. Table 1 shows common doublet lengths that have appeared in handbooks since the 1930s. It also shows the ham bands covered by the antenna. Note that the 100' wire, while somewhat shorter than ½ wavelength, can be pressed into service on 80 meters, and the 67' wire might be used on 60 meters. However, there are limits that we shall explore as we proceed through the questions.

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2. What's the difference between a doublet and a dipole? This interesting question has 2 answers: none and a lot. Conversationally, the term "dipole" often refers to any antenna that looks like a dipole, that is, a center-fed wire antenna with a feedline going to the shack. In this context, we also tend to call any end-fed antenna a Zepp (although there is a center-fed extended double Zepp) and to refer to any off-center-fed antenna as a Windom (although the original Windom had only a single feed wire).

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In more precise terms, the coax-fed dipole that we sometimes set up for single-band use is a more complex antenna than its appearance suggests. It is actually a center-fed resonant ½ wavelength dipole. The center-feedpoint is obvious from the position of the feedline. It is resonant since the feedpoint impedance is (almost) purely resistive, with little or no reactance. The length is electrically ½ wavelength, which for any real wire or tubular element turns out to be shorter than a physical half wavelength. Finally, it is a dipole because, as Fig. 2 shows, the charge is minimum at the center feedpoint and maximum at the element ends. As a result, the current is maximum at the center and minimum at the wire ends. The dipole undergoes only one transition in charge and in current from the center to the wire end.1

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When we use the antenna on many bands, it becomes electrically longer, because the length of a wave grows shorter with rising frequency. Hence, the charge and current patterns do not satisfy the dipole conditions above the lowest band or two. Fig. 3 shows the current distribution along a 135' wire at 80 meters and at 10 meters. Since the current does not follow the dipole pattern, the charge density is also different from a dipole. In this case, there are many transitions and the current is not maximum at the center feedpoint.

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The term doublet is more generic and less fully descriptive than others. However, it also has a history. In the 1930s, it served as a label for a center fed wire with a special feed system. Later, the antenna was renamed the delta feed and the term doublet became a generic term for center-fed antennas of any length.2 Hence, our antenna is an all-band doublet.

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3. Do I need to measure the wire for precise resonance on the lowest band? In a word, no. When we set up a resonant monoband dipole, we want it to achieve resonance or the lowest possible SWR with our coax cable feedline. However, the all-band doublet antenna system uses (normally) high impedance parallel transmission line. Small variations in antenna wire length will make no difference to doublet performance or to our ability to match the impedance at the shack end of the feedline. We sometimes see radiation patterns for a Yagi antenna change shape as we move from one end of an amateur band to the other. However, the patterns produced by the all band doublet change very slowly with frequency. For example, if we only have room for 125' of wire, then it will do very well and yield the same results as a 135' wire on the lower HF bands. On the upper HF bands, we might see some change in the feedpoint impedances between the two wire lengths, but they normally will not be severe and certainly not large enough for us to abandon the antenna. The recommended lengths in Table 1 are ballpark figures, not precise lengths.

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4. Why do I need parallel transmission line? Why not just coax? Or coax with a 4:1 balun? To get our hands on this question, let's consider only one of the possible doublet lengths: 135'. For this version of the doublet, we can look at the numbers in Table 2. The second column lists the approximate feedpoint impedances for each HF amateur band. These numbers will vary with the exact length of the wire and the height above ground. However, the approximations will serve well for our demonstration.

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Suppose that we connect a typical coaxial cable to the feedpoint and use 100' of the line to reach the shack. RG-8X is popular these days because it is light and easy to handle. How much energy will we lose if we use this cable as a feedline? We can arrive at some answers by using a program like TLW. This highly useful software, written by Dean Straw, N6BV, accompanies The ARRL Antenna Book, which is a worthy long-term investment for any ham. In the table, columns 3 and 4 show the 50-Ohm SWR for each of the impedances and the total cable losses. Notice how many of the loss entries exceed 10 dB. With a 10-dB loss, only 1/10 of the energy at one end of the line is available for use at the other end of the line. The reduction applies whether we are transmitting or receiving.

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The last 2 columns show the SWR for a 450-Ohm parallel transmission line. The type specified uses a vinyl coating with windows along the way. The vinyl coating is simply a good way to keep the wires evenly spaced, but it does introduce losses that are slightly greater than open or true ladder line (bare wire with periodic spacers). Note that even with the highest SWR levels, losses do not exceed 0.5 dB or a little over 10% of the power, even with 100' of the line.

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Parallel lines do have limits however. Remember that we recommended ½ wavelength at the lowest frequency as the shortest antenna wire length. We also suggested that we might press shorter wires into service, but we did not say how much shorter. Let's see what happens below 80 meters as we shorten the wire from a ½ wavelength starting point. Fig. 4 shows the approximate resistance and reactance. Although the curves appear to track each other, remember that the downward path of reactance actually represents increasing capacitive reactance. As we shorten the doublet or lower the frequency, the feedpoint resistance decreases steadily, while the capacitive reactance increases steadily. The result will be a very high 450-Ohm SWR on the parallel line. It will rise to the point where even the seemingly low-loss line shows significant power losses along the way. As a practical matter, try to keep the antenna at least 3/8 wavelength or longer at the lowest frequency used if you cannot manage ½ wavelength. Remember that you can always zigzag the wire legs or let the ends droop downward (but always with their ends out of human reach) in order to lengthen the wire to the full ½ wavelength at the lowest frequency.

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5. What's the most important factor in setting up an all-band doublet? Or, we put up a low-band doublet for Field Day about 10-15' off the ground. We did not make many contacts? What was wrong? The question's second form gives us the answer to the general question. With an all-band doublet, there is no substitute for height. However, hams must work with real conditions and not ideals.

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Let's continue to use the 135' doublet as our antenna and see what happens at various antenna heights that hams actually use. 20' is a typical Field Day height for wire antennas due to the difficulty of erecting and sustaining higher supports. 40' is a nice round number for a backyard doublet supported by mature trees. 60' is out of reach for amateurs unless they have a tower or two supporting rotatable beams. Now look at Table 3. It lists for each sample operating frequency the height above ground as a fraction of a wavelength.

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The height above ground when measured in terms of a wavelength is the most important factor that determines the elevation angle of a horizontal antenna's radiation. (Remember that the radiation angle is also the angle of reception sensitivity.) Fig. 5 provides a catalog of typical elevation patterns for the doublet. Each pattern uses the headings for maximum gain as a basis. The missing bands would show elevation angles of maximum radiation that are part way between the bands in the illustration.

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Note that at 80 meters, all three heights are so low that we detect very little elevation pattern difference. The pattern begins to change significantly as we raise the antenna to 60' when operating on 40 meters. The 20-meter pattern becomes very usable for low-angle skip radiation when we raise the wire to 40', a little bit more than ½ wavelength. 20' is a little over ½ wavelength on 10 meters, and so we obtain reasonable basic performance on that band.

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These notes and graphics cannot change your backyard or field conditions. However, they do provide food for thought. For example, if you really want to operate on 80 and 40 meters, but cannot get the horizontal antenna high enough as a fraction of a wavelength, then you may wish to consider alternative antennas. You might achieve better performance on the lowest HF bands with a different wire antenna, such as the inverted-L.3

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6. I carefully set up my 135' doublet to be broadside to Europe. However, on 15 and 10 meters, signals are much stronger to Africa than to Europe. Is it propagation? Although propagation affects all HF communications, the most likely source of the weak European signals is a misunderstanding of the azimuth patterns produced on the various amateur bands by the 135' doublet.

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As a center-fed wire antenna grows longer in wavelengths, the number of lobes that it produces increases. Table 4 lists the length of our 135' doublet as a function of a wavelength on each operating frequency. It also lists the number of lobes produced in the azimuth pattern, that is, around the horizon. The numbers may seem odd, but there is nothing disorderly about them. As the antenna grows longer (or we increase the operating frequency), lobes emerge, reach a peak value, and then disappear--to be replaced by other emerging lobes. Three main points describe the process. Let n be the length of the antenna rounded to full wavelengths.

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+ 1. If the antenna is n wavelengths long, then the number of lobes will be 2n. On 40 meters, the antenna is about 1 wavelength, so there will be 2 lobes. At 10 meters, the antenna is about 4 wavelengths, so we shall find 8 lobes. +

2. If the antenna is n.5 wavelengths, we shall find the lobes for n wavelengths and the lobes for n+1 wavelengths at close to equal strength. So add the number of lobes for n wavelengths and the number of lobes for n+1 wavelengths to arrive at the total number of lobes. At 17 meters, the antenna is about 2.5 wavelengths. A 2 wavelength wire gives us 4 lobes and a 3 wavelength wire yields 6 lobes. So at the intermediate length, we shall find 4+6=10 lobes.

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3. When the wire is close to n or to n.5 wavelengths, the strongest lobes will be those farthest from broadside to the wire, that is, closest to in line with the wire. Table 5 provides the modeled performance data of the 135' doublet at a height of 40' above ground. Fig. 6 translates those numbers into a gallery of azimuth patterns. The virtual antenna runs up and down on the graph page. Because the take-off (TO) angle (or the elevation angle of maximum radiation) is so high for 80 through 40 meters, the azimuth patterns use an arbitrary elevation angle of 45°. All other patterns use the actual TO angle.

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Except for 30 meters, where the null between the inner lobes is hard to detect, all of the patterns clearly exhibit the number of lobes calculated in Table 4. Since all of the lengths are close to either a full wavelength or the half wavelength mark between full wavelengths, the strongest lobes are those nearest to being in line with the wire. (When the wire is close to n.25 or n.75 wavelengths, other lobes may dominate.)

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Note that when the length is n.5 wavelengths, the large number of lobes in the pattern forces the strongest lobes to be closer to in line with the wire than for the next whole number of wavelengths. Hence, the angle of the lobes away from broadside is greater on 17 meters than on 15 meters--and greater on 12 meters than on 10 meters. Also note that the larger the number of lobes in a pattern, the narrower the beamwidth of each lobe.

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If we had chosen a 67' doublet, the antenna would be ½ wavelengths on 40 meters, 1 wavelength on 20 meters, and 2 wavelengths on 10 meters. Since the azimuth lobes are functions of the wire length in wavelengths, we would obtain different lobe patterns than for the 135' wire. In fact, the 67' wire pattern on 40 would resemble the 135' pattern on 80, and the 67' 10-meter pattern would look very much like the 135' 20-meter pattern.

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How you orient a center-fed doublet depends on understanding both the elevation and the azimuth patterns for the wire. The azimuth patterns show where your signal is likely to go, while the elevation patterns tell you whether the energy is likely to fall within the skip zone. Orient the doublet so that the pattern for the most used band (or bands) covers your most desired target(s) with a strong, low-angle lobe.

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So far, we have concentrated on the wire or antenna-proper portion of the all-band doublet antenna system. We briefly explored the main reason for needing to use parallel transmission lines to connect the antenna to the antenna tuner. Hams who are used to using coax often ask a number of other questions about parallel feedlines.

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7. Can I run the parallel feeders in a PVC tube underground or under my house? This question is actually a confession by the newcomer that he or she knows how to handle coaxial cable, but not parallel feedline. In a coaxial cable, the energy fields exist between the outer surface of the inner or center conductor and the inner surface of the outer conductor, also called the braid. Hence, if the cable has an outer jacket that can handle soil, burying it does not affect its use or operation. As well, we can run the cable near to other wires without significant difficulty.

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Parallel feedline is also called open-wire transmission line, and for good reason. Regardless of whether the wires have insulation, they are open in the sense of having fields that are not confined by the structure. Although the main portion of the field is between the two wires, it also extends around the pair of wires for a considerable distance--up to a few times the spacing between the wires. Nearby conductive and semi-conductive materials can disturb the balance between the lines and cause them to radiate--a job we want the antenna proper to do. As well, we may lose some energy to those objects. So, in a nutshell, the answer to the question is no. Do not run the transmission lines close to or within the ground, even if you give them the double insulation of a conduit.

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Commercially available lines come in 3 general types, each with a different characteristic impedance, construction, velocity factor (VF), and loss value. 300-Ohm transmitting twinlead, sometimes flat and sometimes tubular, has a VF of about 0.80 and a loss of about 0.17 dB per 100' at 3.5 MHz. Remember that line losses increase with frequency. 450-Ohm window line, a form of flat twinlead with cutouts to minimize the vinyl between the wires, has a velocity factor of about 0.91 and a 0.07-dB loss per 100' at 3.5 MHz, half the loss of 300-Ohm line. 600-Ohm open-wire ladder line typically has a velocity factor of about 0.92 or higher and a loss of only about 0.03 dB per 100' at 3.5 MHz. There are also commercially available ladder lines in the 400-500 Ohm range, and their VF and loss values would resemble those of the 600-Ohm line. Of the 3 types, 450-Ohm window line is perhaps the most popular for all-band doublets.

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Parallel feedline has a few simple rules for effective placement to maximize energy transfer from the tuner to the antenna proper. Keep line runs as straight and in the clear as possible. Straight, clear runs are as important indoors as outdoors. Straight is self-evident. Wherever possible, keep direction changes shallow. Never let the line fold back upon itself or roll it in a coil. Clear means as far from other objects as possible, and in no case less than several times the line spacing away from anything.

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Of course, we must bring the line indoors. We can use a short through-wall PVC pipe, perhaps with caps that have slots to keep the line centered. Or we can use a wood or plastic plate with feed-through insulators. The difference in spacing and bolt size on the board relative to the line is not important: it may create a small impedance bump but will minimize losses. Outdoor supports can be of two general types: rings or clamps. We can suspend non-conductive rings (slices of PVC or similar) from limbs and posts to support the line on its way to the antenna. As well, we can create non-conductive guides or clamps that extend outward from tree trunks, posts, or walls to route the transmission line. Be sure to use enough supports.

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At the junction with the antenna, use a strain-relief fixture. A simple insulator may keep the line from being pulled by the antenna wire. However, over a relative short time, the feedline wires will flex back and forth until they break. A fixture that minimizes the flexing at the junction itself will make the connections much more durable.

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8. Will the feedpoint impedance in the tables appear at the antenna tuner terminals? If the feedline is precisely a multiple of an electrical half wavelength, then the feedpoint impedance will reappear at the far end of the line. (The other condition that would allow the feedpoint impedance to reappear is an exact match between the feedpoint impedance and the characteristic impedance of the cable. With 450-Ohm line, Table 2 makes it clear that this condition will not exist.) When the characteristic impedance of the line does not match the feedpoint impedance, the line becomes a continuous impedance transformer and shows a different impedance at each step between the feedpoint and each half wavelength or 180° point along the line.

+
+ +
+

Fig. 7 shows one example of the transformation and applies to 450-Ohm transmission line and a feedpoint impedance of 2000 - j2000 Ohms. This impedance is similar to some values in Table 2. If the reactance had been inductive instead of capacitive, we would see similar curves, but the peaks would appear at 10-15° position along the line (where 0° is the antenna feedpoint and 180° is a half wavelength down the line). Note the very low resistance and the relatively low reactance that appear over much of the line's length. For this reason, placing a 4:1 balun in the line may be a poor choice for converting the balanced line to a single-ended or unbalanced line. The transformer may end up converting a low impedance to a very low impedance, regardless of the balun's ability to handle the reactance at its terminals.

+
+ +
+

Let's change the feedpoint impedance to 20 + j100 Ohms. Some impedances for very short doublets (less than about 3/8 wavelength) show a higher reactance (capacitive), but the peaks become very high and the resistance becomes very low--a very difficult situation to graph. Fig. 8 graphs the resistance and reactance of the selected values along the line. Note that the peaks occur just before the 90° or halfway position. If the reactance had been capacitive, the same peaks would appear just past the halfway point along each half wavelength of transmission line. Once more, note for how much of the line the resistance and reactance are low to very low.

+

The two samples show some of the extremes of impedance transformation along a 450-O transmission line. The closer the feedpoint impedance is to the line's characteristic impedance, the less radical will be the transformation of resistance and reactance. It pays to have a small calculation program to assist in finding and visualizing the data. Earlier, I mentioned the N6BV program, TLW. You can obtain similar graphs on it. In addition, the graphs will show the effects of line losses.

+

The graphs show an electrical half wavelength of line. The physical length of such a line will vary with the operating frequency. Hence, it is very difficult (although not impossible) to design a feedline system so that on each band we end up with just about the same impedance at the shack entry. Most amateurs let the antenna tuner do the work of transforming whatever impedance appears at the terminals to the transceiver's required 50 Ohms.

+

9. What kind of antenna tuner is best for an all-band doublet? The best type of antenna tuner is one with a configuration that naturally has an unbalanced or single-ended input--to accept the transceiver's coaxial cable--and a balanced output. From the earliest days of amateur radio, a common tuner meeting these conditions has been the link-coupled tuner. Fig. 9 provides a simplified schematic diagram of one version of this tuner. It received its name because the input side used a small coil or link that is inductively coupled to the tank or parallel tuned circuit on the output side. The most effective forms of this tuner used additional components on the output side to compensate for the reactance at the terminals. Taps at every turn (or at least at every other turn) of the tank coil allowed the user to find a setting that came closest to providing a good match and maximum power transfer at the same time. The link might also have switched taps with the later addition of the so-called variable coupling series capacitor. In fact, the series capacitor compensates for remnant reactance on the input side, allowing a purely resistive input impedance. Johnson Matchboxes, with simplified tank tapping, a fixed link, and no series input-side capacitor, became famous and still appear at hamfests.

+
+ +
+

From the late 1960s onward, the single-ended network came to rule the commercial manufacture of antenna tuners. Fig. 10 shows 4 popular configurations, with the CLC-T being the most common. It was perhaps the cheapest to produce in a period of rapidly rising component costs. It would also handle a very wide range of impedances at the output terminals. However, the CLC-T was a high-pass filter network and hence provided little harmonic suppression for older rigs. Like all of the single-ended configurations, it required a balun on the output to allow for balanced lines. The standard version of the balun used a 4:1 impedance ratio either though a misunderstanding of the impedances likely to be present at the terminals or because such baluns were cheaper to make than 1:1 baluns. The baluns were transmission-line transformers that are most efficient when the reactance is very low. Most balanced lines, however, did not meet this condition. The average operator did not have multiple tuners to compare and so remained unaware that on some bands with some tuners, efficient power transfer might not occur.

+
+ +
+

In recent years, interest in antennas that require parallel transmission lines has surged, spurring the development of new inherently balanced tuners. Fig. 11 shows three varieties that are either on the market or in handbooks. The single-ended CLC-T network is usable with special precautions not to ground any component except the transceiver side of the 1:1 input balun that is common to all of the tuner designs. One commercial tuner uses a balanced CLC-T network, but the most common balanced network tuner on the market is the reversible-L circuit. Versions exist for high power use. However, as the operating frequency increases, the range of impedances that the reversible-L will match with standard components grows more limited.

+
+ +
+

If you will buy a tuner with an all-band doublet in mind, then one of the balanced network tuners may be the best bet. However, if you already have a tuner--even a single-ended network with a 4:1 balun on the output side--you might as well try it out. Since none of the tuners comes with a relative output indicator, you will have to estimate efficiency on each band indirectly. If you obtain a good match following the maker's suggestions for the best component settings, check the temperature of the balun after (not during) operation. If the balun is warm to the touch, it likely is converting some part of your transmitted energy into heat. In general, the broader the tuning, the lower the tuner losses, although there are exceptions to this rule of thumb. In a tuner designed for all of the HF ham bands, tuning will naturally become sharper with rising frequency.

+

If you cannot obtain a match on a given band, then try inserting a length of transmission line, preferably outdoors. Using knife switches, relays, or a simple manual changeover, add a few feet of line between the line ends of a break that you intentionally make in the feeders. Form the insertion into a single large loop to avoid unwanted self-coupling, and use standard precautions to prevent coupling to other objects. Since the transmission line is a continuous impedance transformer, the new values of resistance and reactance at the tuner terminals may fall within the tuner's range. Since every tuner has a limit to the range of resistance-reactance combinations that it will handle, the potential need for a revision in the total feedline length may apply to all antenna tuner designs.

+

10. My all-band doublet is 50' high and uses open-wire feeders. It works well, but I get a lot of RF interference at home, and my rig sometimes locks up in transmit on CW. How can I overcome these problems? Unwanted coupling into home electronics and into the rig itself has almost as many causes as there are errors that we may make in installing parallel feedlines. The first step is to ensure that all station equipment is well grounded to an earth ground as close to the rig as may be feasible. The second step is to consider rearranging the station so that you position the antenna tuner at the place where the feedline enters the building or shack. Well-grounded coax braid is less likely to couple RF energy to other lines and objects than open-wire transmission line.

+

The third step is to check the routing of the transmission line as it approaches the entry point. Ideally, the line should approach the entry perpendicular to the wall or window. If the line runs vertically down a wall, it may couple energy into various power, telephone, or computer lines. Some of these lines may use shielded cable, but unless that cable is also well grounded, it may carry RF energy to sensitive devices with equally poor grounds.

+

Sensitive devices, including control inputs for the rig, do not require very much energy to show signs of interference. If all else fails, you can try the system shown in Fig. 12. At the building or shack entry, install a 1:1 choke of ferrite beads, following the designs of W2DU. The choke acts as a balun, converting the balanced line to the unbalanced coax. From the coax connector shell, run a very short earth-ground line. Ideally, the choke should go outdoors, but modern building construction may require immediate indoor installation at the entry point. Between the choke and a single-ended network tuner, run less than 20' of the largest, lowest-loss coax that you can obtain.

+
+ +
+

The system shown will generally eliminate most unwanted RF energy transfers if the feeders have not already coupled into house wiring due to improper dress. It bypasses the 4:1 balun in the tuner, avoiding that loss source. However, the system has losses of its own. The 1:1 choke will show losses with high impedances having significant reactive components. The coax will also show some loss. However, if the length is 20', the line losses will usually be fairly small. For example, at 30 MHz, 20' of RG-213 will show a 1.1-dB loss with a 10:1 SWR. A shorter run, lower frequency, or lower SWR will result in lower coax losses. There are also cables with even lower losses. Do not use thin cables like RG-58 for this run, regardless of the operating power level. This system is not ideal, but simply a measure of last resort for very tough cases of RF interference. Before employing this or other radical systems, you should first use the earlier guidelines to optimize the feeder and tuner installation.

+

These notes do not answer every question that we can ask about the all-band doublet. However, I hope the 10 common questions that we have tackled give you a good start for reasoning out answers for yourself.

+

Notes

+

1. Fig. 2 follows Stutzman and Thiele, Antenna Theory and Design, 2nd Ed. (Wiley & Sons, 1998), p.57, although the treatment of the dipole in very short or longer forms is similar in Kraus and in Balanis. (Kraus, especially, (Antennas, 2nd Ed.) is careful not to label longer center-fed wire antennas as dipoles).

+

2. Compare, for example, 2 editions of The Radio Amateur's Handbook: the 13th or 1936 edition, p. 278, and the 24th or 1947 edition, p. 207.

+

3. The inverted-L is a highly usable antenna for general-purpose communication, but requires an entirely different discussion. See "Straightening Out the Inverted-L" in the 2005 Proceedings of FDIM, produced by QRP ARCI.

+
+ +
+

Updated 6-3-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Return to Index

+

Topics: Doublet, HF Multi Band, Matching


+ + diff --git a/content/wire/b-ant-1.gif b/content/wire/b-ant-1.gif new file mode 100644 index 0000000..35b9c7b Binary files /dev/null and b/content/wire/b-ant-1.gif differ diff --git a/content/wire/b-ant-2.gif b/content/wire/b-ant-2.gif new file mode 100644 index 0000000..4c8236e Binary files /dev/null and b/content/wire/b-ant-2.gif differ diff --git a/content/wire/b-ant-3.gif b/content/wire/b-ant-3.gif new file mode 100644 index 0000000..c4cd6f8 Binary files /dev/null and b/content/wire/b-ant-3.gif differ diff --git a/content/wire/b-ant-4.gif b/content/wire/b-ant-4.gif new file mode 100644 index 0000000..2998332 Binary files /dev/null and b/content/wire/b-ant-4.gif differ diff --git a/content/wire/b-ant.html b/content/wire/b-ant.html new file mode 100644 index 0000000..7b44948 --- /dev/null +++ b/content/wire/b-ant.html @@ -0,0 +1,66 @@ + + + + + + The B-Antenna + + + + +
+

The B-Antenna

+

+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+ Having described in a past issue of antenneX the L-antenna, a simple dual- polarized antenna for 10 meters, I received a series of comments, all with the same question. Is there a companion "B" antenna? +

In fact, there is. Moreover, the B-antenna has some interesting features. While I doubt many hams would build one as it is presented here, some aspects of the scheme might be useful in future antenna designs for special circumstances.

+

Imagine yourself limited to either 10' vertically or 10' horizontally as your maximum length for a 10-meter antenna. This is less than 0.3 wavelengths. Most folks would set aside all thoughts of a dipole, either vertical or horizontal. The 1/4 wavelength vertical seems to be the antenna that best fits the space. If a dipole creeps into the picture at all, the assembly would likely involve lossy inductive loads.

+
+ +
+

Enter the "B" as a possible antenna of choice. Figure 1 shows both a straight-line B and a rounded B. (Of course, from the other side, the straight-line B looks like a sigma, but it is too early in the article to destroy an illusion.) The figure also shows both versions in vertical and in horizontal orientations. The dimensions are the same for both.

+

The key to the antenna is the fold-back portion. The fold-back is longer on the straight-line version because the total length of the zig-zag section is less than the length in the double hump of the rounded version. In any event, fold-back lengths are approximate, based on models that used 0.25" diameter aluminum.

+

If you use thinner material, the length could be shorter. "Shorter" cuts against the grain of conventional dipole thinking, where thinner means longer. However, the fold-back creates a more closed geometry in which-- like quads--thinner means shorter. Actually, the antenna is quite stable for a good range of diameters, so the end lengths will mostly be a function of the particular construction method and precision level chosen. Shortening or lengthening the fold-back is the easiest route to resonance.

+

Most straight-line dipoles that employ a fold-back tend to show higher losses than with the B-antenna. The fold-back is so close to the main wire, that considerable cancellation occurs, especially as the end section reaches further into the higher current portions of the dipole wire. With the B-antenna, the fold-back is further from the main wire and the loss of gain is minimal.

+

Performance

The B-antenna models in a straightforward manner on NEC, which gives some important clues to performance. Another sign of the antenna's stability is that the feedpoint impedance does not change much with changes in height. The impedance is about 30 Ohms at resonance. Interestingly, even though this impedance represent an SWR of above 1.6:1, the antenna shows a 50-Ohm SWR curve that just barely hits 2:1 at 28 MHz and again above 29 MHz. In contrast, most loaded dipoles show a much narrower bandwidth than a full- size dipole. The B-antenna is as broad-banded as any shortened antenna I know, and approaches capacity hat loading in this regard. +

In effect, the fold-back is a non-symmetrical capacity hat. All forms of non-symmetrical end loading tend to decrease gain and feedpoint impedance a bit more than symmetrical hats. However, the greater simplicity of fold- backs and other non-symmetrical end extensions may offset those slight deficiencies, depending on the builder's circumstances.

+
+ +
+

Figure 2 shows modeled azimuth (at take-off angle) and elevation patterns for the vertical version of the antenna, with the feedpoint 40' above average soil. The azimuth pattern proves that the B-bulges do not bother the circularity of the azimuth pattern. The gain is quite similar to the gain of a full-size vertical dipole with the feedpoint at the same height.

+
+ +
+

Figure 3 shows modeled azimuth (at take-off angle) and elevation pattern for the horizontal version of the antenna, with the feedpoint 35' over average soil. The maximum gain is only about 0.3 dB less than a full size dipole at the same height, and the elevation angle of maximum radiation is the same. The side rejection equals or surpasses that of a full-size dipole at the same height. As a rotatable dipole, the B would do well at reducing QRM from the sides.

+
+ +
+

Figure 4 is a modeled 50-Ohm SWR curve for the vertical version of the antenna, when set between 35 and 45 feet above ground. This range places the feedpoint at the 40' level. The source reactance from band-edge to band-edge changes from -20 to +19 Ohms, which is quite modest for the band spread involved. The resistive component of the source impedance changes very little at all.

+

Construction

Building possibilities are too numerous to mention exhaustively. However, a couple of ideas come to mind from bits and pieces lying around my shop. +

Consider a vertical version of the rounded B. You can use aluminum rod to form each bulge. An 8' piece is perfect for each bulge. 3/16" or 1/4" diameter material would be ideal. If you have some tubing (3/8" diameter or less), it would also work. Make a half circle from scrap wood. Bend the rod around the form. Setting a bend requires an over-bend so that the material returns to the desired size. Leave the piece with just a little outward flare.

+

Tubing should be filled with sand--or kitty litter, in a pinch. Bend slowly, using nails to pin the bend to the form every few inches.

+

To mount the B-bulges, use a 10' piece of 1" nominal Schedule 40 PVC. Drill holes at each end to pass the rod all the way through the tube. Drill a pair of holes with a small space between them for the rods that almost come together at the center. Since the antenna is a dipole, we shall feed it at this center junction. The outward pressure of the bent pieces will help rigidify the PVC.

+

Use small stainless steel machine screws run through holes in the bent rods or tubes to act as stops, preventing the bent pieces from moving either way through the holes, once they are in place. Alternatively, you can drill smaller holes in the rod or tubing on each side of the PVC and make a c- shaped wire clip to go around the PVC, through the holes, and then in a right-angle bend to keep it in place. Wire that is run down from the outer ends of the bent pieces and along the PVC--taped in place--will work fine for the fold-back lengths.

+

For a horizontal version of the antenna, you can simply rotate the PVC 90 degrees. If this assembly is too heavy, you can always string a pair of UV resistant ropes between two end supports. The ropes should be vertically spaced by 30 inches. Now, zig-zag the wire between ropes, running the fold-back along one of them. Models suggest almost no difference between pointing the peaks up or pointing them down.

+

A 30-Ohm feedpoint impedance is a borderline condition at 10 meters. If it seems too low to you for direct coax connection, you can shorten the antenna to create a modest capacitive reactance. Then, install a hairpin or beta coil across the feedpoint. Any ARRL Antenna Book has details on the beta match. HAMCALC, from VE3ERP, has a handy beta-match hairpin calculator. The feedpoint can also be used with a section of 37.5-Ohm coax as a matching section. (Paralleled 75-Ohm coax will yield this line.) Since the feed impedance is a bit high for a perfect match with 1/4 wavelength of the matching section, you may wish to experiment with shorter sections, in accord with my recent notes in antenneX on when a quarter wavelength is not a quarter wavelength.

+

In the End. . .

I do not want to oversell the B-antenna. It is not a cure for every antenna ill. Instead, it is a "niche" antenna, a design that may be usable for special circumstances that call for a very limited length. It has quite poor potential for parasitical duty, so a "B-beam" is not in the cards, despite the neat sound to the label. +

For those who enjoy experimenting with antennas--either by building or by modeling--The B-antenna is a good test bed to use for looking at the effects of folding back the ends of an antenna element to achieve resonance. The goal is to find compact ways of doing this with the least loss and least reduction in feedpoint impedance. Maintaining a wide operating bandwidth and a stable feedpoint impedance in which the reactance does not change very rapidly are also desirable goals for the project. The B-antenna does quite well on most of these scores, however impractical the geometry might prove to be.

+

What started out as curiosity aroused by a joke turned out to be an instructive exercise. Not every antenna exercise has to result in the world's best radiator in order to be productive and informative. In fact, I have learned as much from examining bad antenna ideas as from analyzing good ones. The B-antenna is not bad; instead, the design has a limited utility and is aimed at that special set of circumstances calling for it.

+

Now if I use an A-frame to support my B-antenna with C-clamps, D-rings, and E-clips, I am well down the road to alphabet insanity.

+
+ +
+

Updated 2-5-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Sep., 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: Dipole, HF Upper


+ + diff --git a/content/wire/bw.html b/content/wire/bw.html new file mode 100644 index 0000000..b3a3eda --- /dev/null +++ b/content/wire/bw.html @@ -0,0 +1,130 @@ + + + + + + Notes on Antenna Bandwidth + + + +
+

Some Notes on Antenna Bandwidth

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

For most of us, the antenna's bandwidth is the number of Hz for which the antenna will exhibit a less than 2:1 SWR. We usually measure bandwidth at the transmitter output, and hence put a large pile of variables on top of the basic idea of SWR bandwidth. So let's begin again and see how the concept actually works.

+

An antenna--for example, a resonant half wavelength dipole operated on its fundamental frequency--has a natural feedpoint impedance. For a lossless wire dipole in free space, that figure is just about 72 ohms. In fact, NEC-2 models of just such an antenna using wire diameters from #30 to over 2.5" show less than 1 ohm variation in the 72-ohm feedpoint impedance.

+

Relative to that impedance, a 2:1 SWR will occur as the feedpoint impedance (off resonance, a complex of resistance and reactance) reaches about 144 ohms at points higher or lower than resonance. The number of Hz (of kHz or MHz) between those frequencies is the 2:1 SWR bandwidth of the antenna. The bandwidth will vary with the diameter of the antenna element in a regular but nonlinear manner.

+

2:1 SWR bandwidth is approximately (but again, nonlinearly) proportional to frequency. For a given wire size, a resonant dipole at 28 MHz will have (about) twice the bandwidth of a resonant dipole at 14 MHz.

+

Below is a typical frequency vs. bandwidth plot for a free space lossless thin-wire dipole, plotted against a 72-ohm resonant feedpoint impedance.

+
+ +
+

To help you gain a reasonable expectation of the 2:1 SWR bandwidth of resonant half wavelength dipoles, I am attaching a small BASIC utility program that will produce bandwidth tables for any HF frequency for wires from #30 (0.01" diameter) to 2.5" diameter. It is roughly calibrated to NEC-2 models for lossless wire resonant dipoles in free space and to 72 ohms. The algorithms are generally accurate to about 5%, with some matrix-center variations reaching about 10%. The figures are roughly applicable also to resonant quarter wavelength vertical antennas.

+

Table 1 summarizes a few data points for thin, medium, and thick antenna elements on 80, 40, 20, and 10 meters. The increase of bandwidth with frequency for a given wire size is evident. Notice also that it takes nearly a 100:1 wire size increase to double the bandwidth of the antenna on any given frequency.

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Table 1: Selected 2:1 SWR Bandwidths in MHz for Wire Antennas
Frequency3.5 MHz7 MHz14 MHz28 MHz
#28 AWG (0.013")0.170.350.731.63
#12 AWG (0.081")0.190.400.861.91
#4 AWG (0.204")0.220.460.982.18
(1")0.300.631.353.06
+
+

The degree of error in the program is of no concern, since real antennas and antenna systems will introduce larger variations that no table can account for in advance. Hence, the program is only for setting some reasonable expectations, not for predicting bandwidth wit precision. The bandwidth you actually measure will vary with the following variables:

+

1. Antenna type: Low impedance antenna types will generally (but not always) have wider bandwidths than high impedance antennas.

+

2. Antenna material: Copper and aluminum have losses that affect antenna bandwidth, especially with small diameter wires (less than #20).

+

3. Antenna environment: Placing an antenna some height above ground less than about 2 wavelengths will alter both the natural feedpoint impedance and the bandwidth at that impedance. Ground clutter in the near field of the antenna will affect both in ways that are for practical purposes unpredictable.

+

4. Feedline mismatch: Feeding a 72-ohm antenna with our common 50-ohm coax starts us out at 1.4:1 SWR, hence decreasing the 2:1 SWR bandwidth. As a rule of thumb, the reduction is approximately the same as the ratio of feedpoint impedance to the feedline impedance--or the inverse of the lowest SWR obtainable. Hence, we should expect about 70% of the program's estimated bandwidth when feeding the dipole with 50-ohm coax. (This fact explains why some claim a slightly wider band width for inverted Vee configurations: being closer to 50 ohm natural feedpoint impedance, Vees introduce less bandwidth narrowing due to the slight mismatch).

+

5. Feedline losses: Even well-matched transmitter-feedline-antenna systems introduce some losses in the feedline. The effect of these losses is to reduce the SWR at the transmitter end of the line, thus giving a wider 2:1 SWR bandwidth. This wider bandwidth is usable, so long as we understand and evaluate the acceptability of the power losses involved.

+

6. Antenna shortening and loading: Although antenna loading for the sake of shortening reduces the feedpoint impedance, it introduces components that raise antenna Q and narrow the bandwidth. As a rule of thumb, bandwidth is reduced by the percentage of shortening of the antenna. For example, a 33' vertical on 80 meters is about half size, and its bandwidth is about 70 kHz for most common loading schemes--just about half the bandwidth of a full size quarter-wave vertical.

+

Understanding these bandwidth-altering factors along with the basic output of the program can give us reasonable expectations for antenna bandwidth for the various bands. If our antenna system is more than about 20% off the mark, then we begin to search for possible problems.

+

Remember that these notes do not apply to antennas fed with parallel feedline and an ATU: those we always tune for 1:1 SWR and maximum power output to the line and antenna.

+

Finally, if you do not like typing BASIC programs or converting them to C, a version of the program appears in VE3ERP's HAMCALC collection.
+

+ 
+10 ' BW.BAS
+20 CLS:SCREEN 0: COLOR 2,,4:CLS
+30 ER$=STRING$(70,32):BW$="###.###":WIRE$="#.###":S$=STRING$(10,32):T$=STRING$(6,
+32)
+40 ' Estimates 2:1 SWR bandwidth of halfwavelength dipoles for a range of
+     common wire and tubing sizes.  Algorithm is based on NEC models of
+     lossless wire dipoles in free space and is based on a feedpoint
+50 ' impedance of 72 ohms.  Program does not account for material losses,
+     feedline losses, mismatches, or the antenna environment.  Accuracy
+     averages 5%.
+60 PRINT "   Estimated 2:1 SWR bandwidth of half wavelength dipoles at any HF
+frequency"
+70 LOCATE 2,25:PRINT "by L. B. Cebik, W4RNL"
+80 LOCATE 3,15:INPUT "Enter any frequency from 3 - 30 MHz:   ",F
+90 IF F>30 OR F<3 THEN LOCATE 3,5:PRINT ER$:GOTO 80
+100 PRINT "Wire size","Wire dia.","Bandwidth";S$;"Wire
+dia.";T$;"Bandwidth"::PRINT "  AWG  ","inches","   MHz  ";S$;"  inches",T$;"
+MHz   "
+110 FOR J=30 TO 2 STEP -2
+120 AWG$=MKS$(J):N=J:AWG=J
+130 K#=(.46/.005)^(1/39):WIRE=.46/K#^(N+3):DIA=WIRE
+140 DIA2=DIA-((.4343*LOG(30/F))*(DIA/(2*(2.56/DIA))))
+150 BWBASE=(.0469+(((F/3)-1)*(.0116/9)))*F
+160 BW=((SQR(DIA2))+.9)*BWBASE
+170 PRINT AWG,:PRINT USING WIRE$;WIRE,:PRINT" ",:PRINT USING BW$;BW
+180 NEXT
+190 FOR J=.375 TO 2.5 STEP .125
+200 DIA=J
+210 DIA2=DIA-((.4343*LOG(30/F))*(DIA/(2*(2.56/DIA))))
+220 BWBASE=(.0469+(((F/3)-1)*(.0116/9)))*F
+230 BW=((SQR(DIA2))+.9)*BWBASE
+240 K=(J*8)+3:LOCATE K,50
+250 PRINT USING WIRE$;J,:PRINT S$;:PRINT USING BW$;BW
+260 NEXT
+270 LOCATE 23,5:PRINT "Another (F)requency or (Q)uit"
+280 A$=INKEY$
+290 IF A$="f" OR A$="F" THEN 10 ELSE IF A$="q" OR A$="Q" THEN 300 ELSE 280
+300 END
+
+

First printed in QRP Quarterly, January, 1997. Updated 01-22-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

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Topics: Dipole, HF Lower, HF Upper


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Understading the Controlled Current Distribution (CCD) Antenna

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L. B. Cebik, W4RNL

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The controlled current distribution (CCD) antenna has been around since the late 1970s. Every so often, it arouses a flurry of questions in my e-mail. So I decided to look into the CCD to see what we might reasonably expect of it.

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Fig. 1 shows the general outline of the center-fed version of the CCD. It consists of a number of straight wire sections of any practical number that we can designate as N. Except for the feedpoint and the wire tips, we must separate each section with a capacitor. Hence, the total number of capacitors will be N-2. The CCD simulates a continuously capacitively loaded 1 wavelength element by using equally spaced discrete components.

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There is also a vertical version of the CCD. One way to create a vertical CCD is to simply use the center-fed antenna in a vertical installation. However, some literature suggests using the antenna against ground as a monopole. Fig. 2 shows the general layout of this configuration.

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Beyond the general claim of "improved performance," I have not encountered a very clear account of what advantages the CCD is supposed to offer. The wire length will be 1 physical wavelength. However, the distributed capacitive loading of the element will electrically shorten the wire. If we select the correct value for all of the capacitors (they are all equal), we can arrive at resonance, that is, a feedpoint impedance with negligible reactance. It appears that the idea behind the CCD is to avoid the very high impedance of a 1 wavelength center-fed wire while preserving its gain and directivity.

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I sometimes hear the terms "aperture" applied to the antenna. Most texts reserve the term for use with highly directive antennas, such as UHF horns and the like. Nevertheless, the calculation of aperture rests--according to one text--on the wavelength, the directivity, the polarization match, and the impedance match. Since a comparison of a CCD with any other antenna will equate the wavelength, polarization, and impedance match, the remaining factor is directivity. Hence, if the CCD is an improvement over a legitimate comparator, then it will show improvements in directivity. We can examine the directivity of the CCD by looking at its gain and beamwidth.

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To simplify the examination, let's look at the CCD on a common frequency. 3.5 MHz is widely used in articles, so that will be our choice. A wavelength at 3.5 MHz is 280.02' long, so we shall make the antenna length 280'. Throughout, we shall use AWG #14 copper wire to reflect typical amateur building practices. Our initial tests will use a free-space environment. In this environment, we must use the center-fed version of the antenna, but we shall not have to be concerned with vertical vs. horizontal orientations.

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I chose to model the antenna in NEC-4, which creates a small difficulty. If I use a single wire for the entire element, I can place load capacitors on individual segments of the wire. However, the feedpoint region will not be quite perfect. Fig. 3 shows the alternative models that I used. The upper model uses a single source segment, but that does not ensure that the wire lengths on each side of the feedpoint are equal to the other segments between capacitors. The lower section uses a split source to simulate a source at the center segment junction. Although this move improves the segment spacing, it can result in somewhat erroneous impedance reports for very high impedances, where the impedance might change significantly with only a small change of feedpoint position or total wire length.

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For all practical purposes, the difference between the models is not great enough to jeopardize the modeling analysis. The required values of capacitance tend to coincide closely with values in the literature. The next task involves the capacitors themselves.

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Literature on the CCD shows that we can build the antenna with almost any number of wire sections and corresponding numbers of capacitors. Since constructing each section involves wiring in a capacitor with appropriate strain relief--a considerable task--I wondered what one might gain by opting for a "large" CCD over a "smaller" CCD, where large and small indicate the number of wire sections and capacitors. Therefore, I created 2 models, one that used 26 wires section and 24 capacitors and another that used 50 wire sections and 48 capacitors.

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The final step involves selecting the capacitor value. Since modeling allows easy variation of the capacitor value, we might explore the performance of the antenna in free space using various capacitor values. Let's start with the larger model. Table 1 shows the results of this modeling exercise.

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Perhaps the first notable feature of the data is that as we raise the value of the capacitors in the string, the gain increases. So too does the resistive component of the feedpoint impedance. The reactive component shows an initial capacitive value that becomes inductive as we increase the capacitor values. This feature is natural enough, since increasing the capacitance value lowers the capacitive reactance along the wire. Since the wire is long compared to a dipole, lowering the compensating capacitive reactance will leave the feedpoint increasingly inductive.

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In fact, more is at stake than just the feedpoint reactance. Note the entries for resonance. At resonance, the feedpoint reactance disappears, marking a balance between the inductive reactance of the wire and the capacitive reactance from the string of inserted components. Let's also examine the data for the "smaller" CCD that uses 26 wire sections and 24 capacitors. Table 2 provides the necessary information, but with fewer steps along the way.

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The antenna gain does not depend for its gain--above some minimum number of capacitors--on the array size in terms of the number of capacitors in each leg. The gain of the smaller array with 500-pF capacitors is the same as the gain of the larger array with 1000-pF capacitors. Likewise for the smaller 1000-pF and the larger 2000-pF entries. The feedpoint impedance reports also track each other in the same manner. This result is also very reasonable, since 24 500-pF capacitors have the same capacitive reactance as 48 1000-pF capacitors if we measure at the same frequency.

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The relative balance between these two factors alters the current distribution along the 1 wavelength wire. Fig. 4 provides some samples of the distribution curves for the smaller array, but curves for corresponding large-array values are virtually identical. The curve for the array with a low capacitance value that yield a capacitively reactive feedpoint impedance is very steep. At the other extreme, where the capacitor value yields an inductively reactive impedance, the curve shows dual current peaks. Only the capacitor values that yield resonance produce a curve that we tend to associate with a dipole.

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The resonant impedance of a center-fed CCD is in the neighborhood of 200 Ohms. Therefore, one may simplify the matching problem by installing a 4:1 balun at the feedpoint and using a standard coaxial cable feedline. Of course, one may also use parallel transmission line to either a tuner or a 4:1 balun at the shack end of the line. Since 200-Ohm feedlines are rare, one likely would need a 300-Ohm feedline cut to the nearest half wavelength (allowing for the line's velocity factor) at the operating frequency to minimize balun losses.

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With the right choice of capacitors in the string, the CCD offers bi-directional performance with a resonant feedpoint impedance. In exchange for the more complex construction of the antenna, we obtain a simplification of matching requirements. However, we have not yet assessed how good that performance is. For that task, we need an appropriate comparator.

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The CCD vs. the Dipole and 1-Wavelength Center-Fed Wire

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In CCD literature, the resonant 1/2 wavelength dipole seems to be the most popular antenna with which to compare the CCD with respect to performance as a horizontal antenna. An alternative comparator is the plain and simple 1 wavelength center-fed wire antenna. The 1 wavelength plain wire is the same length as the CCD. However, the current distribution of the plain wire differs from the current distribution of the resonant CCD. Fig. 5 provides a set of free-space current distribution curves for the resonant dipole and for the 1 wavelength wire for ready comparison to the CCD curves in Fig. 4.

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The dipole curve resembles the resonant CCD curve. Of course, neither are perfectly sinusoidal, since the voltage at the center feedpoint never goes to zero. I have not explored the degree to which each departs from that familiar curve. In contrast, the 1 wavelength wire curve most resembles the CCD when the latter uses a very high value for the capacitors and thus loads the wire least.

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Table 3 compares the free-space performance of the dipole and 1 wavelength wire along with resonant CCDs of the smaller and larger type. Clearly, the CCD has more gain (by about 1.1 dB) than the dipole. However, the CCD falls about 0.7 dB short of the plain 1 wavelength wire. We should have expected this result from the tabular data on the CCDs as we raised the value of the capacitors and lowered the level of loading. (The capacitors in all models are lossless.) As the capacitive reactance decreased, the gain increased. From a certain perspective, we may view the 1 wavelength wire as a CCD with capacitors having an indefinitely high capacitance and hence negligible reactance.

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Fig. 6 overlays the free-space E-plane (azimuth) patterns of the antennas (using only 1 of the resonant CCDs). The CCD pattern most resembles the E-plane pattern of a center-fed plain wire about 0.85 wavelength long, although the CCD beamwidth is close to 10 degrees wider.

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Very few prople operate 3.5-MHz antennas in free space. Therefore, we may usefully transplant all of the antennas in Table 3 to a height of 1 wavelength above ground. With this adjustment, we obtain the data in Table 4.

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The gain differentials that we found in the free-space models hold up when we move the antennas over ground. Of course, the CCD loading technique does not alter the TO angle of the horizontal antenna relative to either comparator. Table 4 records the horizontal beamwidth values for all of the antennas, and we can see that the CCD beamwidth is closer to the value for the dipole than it is to the value for the 1 wavelength plain wire. Fig. 7 records the elevation and azimuth patterns for the antennas in this test group.

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There is no difference among any of the elevation patterns, since those patterns emerge as a function of the height of the horizontal wire above ground. The 2 versions of the CCD show no differences in their azimuth patterns. Hence, the choice among the antennas with respect to performance largely hinges upon the combination of gain and beamwidth.

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One of the seeming advantages of the CCD is the fact that in exchange for more complex construction, one obtains a higher gain with a simple resonant feedpoint. However, the tables have shown near-50-Ohm values for the plain 1 wavelength wire. The technique used to obtain such feedpoint values is very simple and very old. Since the terminal impedance of the 1 wavelength wire is very high, we can attach a 1/4 wavelength section of parallel transmission line. Somewhere very close to the end of the line will be a 50-Ohm matching point. The matching sections for the horizontal 1 wavelength wires use 600-Ohm line. The required length for the impedances shown is 68' (compared to a full 1/4 wavelength of 70.25'). Fig. 8 shows the simple set-up. The antenna environment and construction variables will determine the exact line length required, so the examples use a velocity factor of 1.0. Most 600-Ohm lines may have values between 0.95 and 0.98.

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The matching section may be much simpler to build than the CCD antenna element. However, the 2:1 SWR bandwidth of the plain wire plus matching section is fairly narrow--perhaps 150 kHz at 3.5 MHz. (The resonant CCD has a 200-Ohm SWR bandwidth of about 300 kHz.) Indeed, the wisest feed system for the plain wire may be parallel line all the way to the shack antenna tuner. However, setting the line length to an odd multiple of a quarter wavelength at the most used frequency may ease the tuner's task by a good margin.

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The Vertical CCD and the 1/2-Wavelength Base-Fed Plain Wire

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One application suggested for the CCD is as a vertical antenna. We may hang a full center-fed CCD vertically with its feedpoint at any height above ground that we can manage to support. However, the more interesting case is to use a half CCD as a monopole, with the feedpoint at ground level. A monopole CCD simply uses half the number of wire sections and half the number of capacitors as a center-fed horizontal CCD. Hence, the wire will be 1/2 wavelength long. We shall split the 26-section, 24-capacitor CCD and create a 14-section, 12-capacitor CCD.

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The appropriate comparator for this antenna is a simple 1/2 wavelength monopole. The base feedpoint will use a matching section to arrive at a near-50-Ohm impedance. Because the natural impedance of a base-fed 1/2 wavelength monopole is lower than the impedance of a horizontal center-fed wire, we must use a parallel transmission line with a lower characteristic impedance. 450-Ohm line works well here, and a 68' length allows us to arrive at the desire impedance level. Again, the models use a velocity factor of 1.0, but an actual line would use the actual velocity factor for the selected line. As well, the variables of installation will likely require some experimentation to find the correct length.

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The simplest way to model both antennas is to use a MININEC ground. The presumed advantage of using this ground system is that it allows direct contact between the lower end of the vertical wire and the ground without need for modeling radials. In some contexts, this system can be useful, but not in this case. In fact, the MININEC ground obscures some critical differences between the operation of a CCD and a simple 1/2 wavelength base-fed wire.

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To use a NEC-4 Sommerfeld-Norton ground with the antenna wire touching the ground requires that we install some kind of wire below ground. The simplest below ground wire might be a simulation of an 8' ground rod. Like the MININEC ground, this treatment is applicable to both antennas. Whether such a treatment is advisable is something that the data will tell us.

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Alternatively, we can install a buried radial system using as few or as many radials as the analysis might dictate. The data in Table 5 show 4-, 16-, and 32-radial systems, using 70' AWG #14 copper radials, for the CCD. The 1/2 wavelength wire only uses a 4-radial system for reasons that become apparent in the data.

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Each antenna entry set begins with the MININEC ground. If we were to use this data, we would reach the conclusion that both antennas perform very similarly, with a negligible difference in gain and only a 2-degree difference in the TO angle. However, if we change to the S-N ground with an 8' ground rod, we obtain very different results. With no change in the TO angle, the plain wire outperforms the CCD by about 2.6 dB, a noticeable amount.

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To improve performance of the CCD, we must replace the ground rod with radials. The table shows the results for radial fields of various sizes. For the CCD, adding 4 radials increases the gain by over 1.5 dB. Only when we have 32 radials does the CCD challenge the gain of the plain 1/2 wavelength wire. The data for the plain wire shows that replacing the ground rod with 4 70' radials only increases gain by 0.1 dB. The small gain increment tends to suggest that a radial system is optional with a 1/2 wavelength wire. Fig. 9 overlays the plain wire with ground rod pattern and two CCD patterns: one for the ground-rod model and the other for the model with 16 radials. The patterns reveal not only the gain differences, but also the TO angle differences for the two types of antennas.

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The difference in the radial requirements between the plain wire and the CCD emerges from the different current distributions on the two types of antennas. The sketch on the left in Fig. 10 shows the distribution along the 1/2 wavelength simple wire monopole. The current maximum occurs at the wire center, which is elevated. Hence, the antenna shows a lower TO angle than the CCD. As well, the current reaches a minimum at the base of the antenna. Essentially, the element is complete at that point and requires only a good RF ground. The 4 radials provide a better distributed RF ground than the simple rod, but the performance difference is small.

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In contrast, the CCD design places a current maximum at the base of the monopole installation. Maximum efficiency requires an effective completion of the antenna in the form of a low-loss radial system. The more radials that we have, the more efficient will be the total antenna system, as indicated by the declining resistive component of the feedpoint impedance as we add more radials. Note, however, that as we bring the system to a level of maximum efficiency, the TO angle actually increases. At a high efficiency level, the feedpoint would need a 2:1 impedance transformation device or network for compatibility with the standard 50-Ohm coaxial cable.

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An effective monopole CCD system thus requires two forms of construction complexity relative to the plain 1/2 wavelength wire: the installation of capacitors along the monopole and the burying of a large number of radial wires. In contrast, the plain 1/2 wavelength wire needs no modification of the monopole wire and provides good service at a lower TO angle with only a ground rod or the simplest of radial systems. However, the high impedance of the antenna may require a dedicated network or a carefully tuned matching section to arrive at a 50-Ohm impedance.

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How "Small" Can I Make a CCD?"

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The terms "large" and "small" in connection with the discussion of CCDs in these notes refer to the number of wire sections and the number of capacitors needed to make up a 1 wavelength antenna. In our initial free-space modeling experiments, we saw that there is no significant difference in the performance of a 26-section, 24-capacitor CCD and a 50-section, 48-capacitor version. Since the smaller of the two systems requires less work than the larger, we may naturally pose a question: how small can I make the CCD antenna and still achieve proper performance. Since the goal is a self-resonant 1 wavelength antenna, we have a criterion for success.

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Models of the free-space center-fed CCD seemed unable to achieve resonance with 6 or fewer capacitors. However, an 8-capacitor, 10-section model of the antenna did achieve resonance. The feedpoint impedance was considerably lower than the 200-Ohm target that we have used in order to apply a 4:1 balun at the feedpoint. As well, the gain was down slightly relative to larger models, but not enough to be operationally significant. Table 6 shows the results obtain from several different models leading up to the 26-section, 24-capacitor model.

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Note that between the worst and the best of the model set, we have only a 0.15-dB difference in gain. As well, the beamwidth changes by only 3 degrees, indicating a stable E-plane pattern. However, the feedpoint impedance climbs from about 170 Ohms to well over 200 Ohms. The differences in the gain levels and the feedpoint impedance values result from the fact that the current distribution curve changes as we move from fewer to more wire sections and capacitors. Fig. 11 provides a sense of the evolution of the distribution curve from essentially a triangle to a smooth curve.

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The shapes of the current magnitude distribution curve do not materially affect the shape of the radiation pattern, which remains well-behaved and bi-directional. The absence of any significant change in the beamwidth is a further indication that even the 8-capacitor version of the antenna will perform well.

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The answer to the section's lead question then is that about 8-capacitors and 10 wire section form the smallest practical CCD with full performance and resonance. It is likely that the precision of the match between capacitors and between wire sections will play a stronger role for the small CCD than it does for larger versions.

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Conclusion

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We have taken a short look at the controlled current distribution (CCD) center-fed 1 wavelength antenna with an eye toward understanding its operation and assessing its virtues. The center-fed version of the antenna provides a 200-Ohm resonant feedpoint impedance with the choice of the correct capacitor size, compared to the 70-Ohm impedance of a 1/2 wavelength dipole and the very high impedance of a plain center-fed 1 wavelength wire. The CCD gain and beamwidth values fall between those of the two antennas used as comparators. Models suggest that CCD performance peaks with about 26 wire sections and 24 capacitors. However, CCDs as "small" as 8 capacitors and 10 wire sections may work satisfactorily.

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The vertical monopole version of the antenna is perhaps more problematical, since when ground mounted, it requires an extensive radial system for most efficient operation. Unlike the plain 1/2 wavelength wire monopole that has an elevated point of maximum current, the CCD vertical monopole reaches maximum current at ground level and thus requires radials to complete the radiating structure.

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Essentially, the CCD simulates with discrete components a continuously loaded element with 501 pF/meter. At this loading level, the gain in free space is 3.10 dBi, with a feedpoint impedance of 245 - j0.2 Ohms. The performance reports are virtually identical to those that emerge from the 26-section, 24-capacitor antenna that used 420 pF capacitors.

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The CCD is a viable and potentially useful antenna of its type. Whether the advantages warrant the relatively complex construction compared to simpler wire antennas is a user judgment.

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Updated 02-26-2006 © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, Vertical


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A Comparison of Closed and Interrupted
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L. B. Cebik, W4RNL

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In "The IL-ZX Antenna for 40 Meters", I presented (or resurrected, depending upon one's point of view) a compact interrupted loop antenna for 40 meters. By using folded element wire construction, it provided a coax-compatible feedpoint impedance with no compensating or loading components. Since the overall circumference of the interrupted loop was about 1/2 wavelength, the antenna was very compact, fitting within a 20' wide by 20' High (plus ground clearance) footprint. Fig. 1 on the right shows the essential outline of the ILZX when used vertically. Single wire horizontal versions of the antenna exist. Indeed, in Britain, you may obtain a multi-band version of the antenna.

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On the left in Fig. 1 is an antenna that is similar in size and that also uses a vertical orientation. It is a closed loop with a diameter of about 0.127 wavelength, with a resulting 0.4 wavelength circumference. As we move from the region of very small loops with feedpoint resistive components in the 1-Ohm range up to the medium-loop range (circumferences between about 0.25 and 0.75 wavelength), we find some interesting properties. First, the resistive component of the feedpoint impedance climbs so that we no longer need worry as much about the losses of compensating and matching components or the losses of construction joints. Second, the reactance of the closed loop becomes increasingly inductive. When the loop is electrically about 1/2 wavelength in circumference (which for a closed loop is physically larger than 1/2 wavelength), the reactance reaches a peak inductive value only to suddenly reverse to a peak capacitive reactance value with only a slight further increase in circumference. (This phenomenon is familiar to those who have center-fed linear wire antennas that are abut 1 wavelength long.) At the same time, the performance of the loop improves with increasing size. The result is a compromise. When the loop is about 0.4 wavelength in circumference, The feedpoint resistance approaches 100 Ohms while the inductive reactance has a high but manageable value for which we can compensate with a small (low-pF) series capacitor. By tradition--derived from very small loop construction more than from necessity--most closed loops in this arena use fat elements--often copper pipe.

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Both antennas are interesting, if for not other reason than the similarity of their sizes. One can square the closed-loop circle or circularize the square shape of the ILZX. However the shapes have little bearing on performance. The closed-loop's circle is convenient for the most commonly used materials, while the wire structure of the ILZX lends itself to the used of non-conductive side supports with rope ties to the corners of the square. Therefore, in the discussion to follow, I shall used the modeled construction shown in Fig. 2, which gives the dimensions for both subject antennas.

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In a situation calling for a very compact 40-meter antenna, the structure is likely to be close to the ground. I selected a 5-meter (16.4') bottom height to have a rounded number that accords reasonably well with amateur practice. In both cases, the top height of the antenna is less than 11 meters (or 35') above ground. The radius of the closed loop is 0.0635 wavelength at 7.15 MHz, the selected common test frequency for both antennas. The loop material is 1" copper, a diameter that results in a 98.5% power efficiency according to NEC model reports. (The NEC report does not include losses incurred from the average ground over which I placed both antennas). For an important reason that we shall consider shortly, the dimensional outline of the closed loop does not show the position of the feedpoint or of the required series capacitor.

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The ILZX has several notable features. It uses AWG #12 wire (0.0808" diameter). Although the wire is thin compared to the value used in the closed loop, the power efficiency is over 96%. Instead of viewing the antenna as an interrupted loop, let's think of it as a folded dipole with 3" spacing between wires and with the linear elements bent into a square that is 5.5 meters (18.04') on a side. Like a folded dipole, the equal-diameter elements create a 4:1 impedance transformation (regardless of spacing--within limits). Hence, a single wire version of the antenna might show a feedpoint impedance in the 12- to 16-Ohm range. The folded version shows an impedance in the 50- to 65-Ohm range, depending on orientation and height above ground. With the side feedpoint shown, the impedance is about 64 Ohms.

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The difference between a linear folded dipole and the bent version in the ILZX is the proximity of the element ends, added to the parallel sections of the "top" and "bottom" sections. The element tips exhibit strong coupling. Therefore, the gap between them becomes an important means of setting the reactance at the operating frequency. Note that the tips come to a point on each side of the gap. If we leave the tips blunt--as we might in a regular folded dipole--the gap dimension becomes very finicky. By bringing the tips to a point, we reduce the amount of reactance change with each unit of physical change in the size of the gap. Such antennas actually go back to the 1930s and sometimes used copper pipe construction (on unbelievably heavy wood frames) with gap extensions that consisted of small plates soldered to screw threads for fine tuning.

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The sketches shows the ILZX at a relatively low height, vertically oriented, with a side feedpoint and a side-gap position. This orientation yields the best low angle patterns that we can obtain from the antenna. In contrast, most common implementations of the closed loop have chosen a bottom position for the feedpoint and reactance-compensating capacitor. In fact, the closed loop has properties sufficiently like a very small loop to allow us to position the feedpoint and the required capacitor almost anywhere along the circumference, and not necessarily at the same place. Each selection has consequences that we may accept or reject according to our needs. For example, a very small loop has a current magnitude and phase that remain virtually constant along the length of the loop. In the 0.4 wavelength circumference loop, the current magnitude changes by no more than a 3:1 ratio of maximum to minimum. This change is small compared to the current levels that we find along a linear element. As well, it is small compared to the ratio of maximum to minimum current in a full 1 wavelength loop.

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Let's assume that the terms "top," "bottom," and "side" have conventional meanings relative to the ground. We may place the feedpoint at any one of these positions. Likewise, we may place the series capacitor at any one of these positions. The following table shows what happens to the maximum gain, the elevation angle of maximum radiation, and the feedpoint impedance for various combinations. In all cases, the compensating series capacitor value remains constant and represents a reactance of -j2417 Ohms at 7.15 MHz. As well, the closed loop remain physically constant.

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+ +
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With the feedpoint and capacitor both positioned at either the top or bottom, the pattern for the relatively low and vertically oriented loop is mostly straight up. The dominant polarization is horizontal. Fig. 3 shows the broadside and edgewise elevation patterns for some of the cases. The left pair of elevation plots yield the most NVIS-like upward patterns at a reasonably good gain level. The right side of Fig. 3 shows the elevation patterns for the use of a bottom feedpoint and a top-positioned capacitor. However, the patterns also apply to the case in which the feedpoint is on the side and the capacitor is at the top. The top-mounted series capacitor pattern has a significant lower angle component, but only edgewise to the plane of the loop. These cases appear to illustrate the fact that the position of the series capacitor has a stronger bearing on the pattern shape than the feedpoint position. For example, the table suggests that the feedpoint at the bottom with the capacitor on a side yields patterns very much like those where both the source and the capacitor are positioned on a side.

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+ +
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Only two of the options present a highly workable feedpoint resistance: bottom-bottom and side-side. The side-side position combination does require adjustment to the capacitor value to 9.31 pF to null the remaining loop reactance. The very small amount of required change (0.1 pF) suggests that tuning the loop can be very finicky without either special components or excellent ingenuity.

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Fig. 4 compares the elevation plots of the side-side closed loop and the ILZX. In the configuration shown in Fig. 2, the ILZX shows a maximum edgewise gain of 0.05 dBi at 24 degrees. The maximum edgewise gain is -0.26 dBi at 25 degrees. The average gain of the two antennas is almost identical, while the ILZX exhibits a slightly more circular azimuth pattern. (With the ILZX fed at the bottom and the gap at the top, the resulting patterns are similar to those for the closed loop in the bottom-bottom configuration.)

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+ +
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When oriented at relatively low heights, both the closed loop and the ILZX benefit from side feeding to yield low angle patterns that benefit HF communications. Indeed, their patterns are not sufficiently different to be detectable in ordinary operations. The remaining question is whether there is a more decisive factor to separate the two antennas for amateur operations. There might be, if we assume that most amateurs prefer wider operating bandwidths from their antennas.

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Fig. 5 presents the SWR sweeps for the closed-loop and the ILZX from 7.0 to 7.3 MHz. In each case, the curve is references to the resonant impedance of the individual antenna. For the ILZX, the reference impedance is 64 Ohms. The 98.5-Ohm reference impedance of the closed loop includes the use of a 9.31-pF series capacitor at the side feedpoint. The 2:1 SWR bandwidth of the closed loop is 60-70 kHz. In contrast, the 2:1 SWR bandwidth of the ILZX is about 150 kHz. As well, even without 50-Ohm matching at the feedpoint, the rate of SWR change for the ILZX is low enough that the internal tuners that come with many current transceivers could easily handle the matching task. At 40 meters, the losses of coaxial cables larger than RG-58 would not be troublesome for most operations. Nevertheless, for maximum 40-meter QRN reduction, the narrower bandwidth of the closed loop may serve a useful purpose.

+

When we lay out the physical and the electrical properties of both antenna types, each has advantages and disadvantages. The point of these notes is not to recommend one over the other, but to make the relative properties of each more readily apparent. Perhaps the only general conclusion to these notes is the fact that if we construct either antenna in a vertical plane and at relative low heights, then side feeding is generally highly beneficial for long distance operations, altyhough bottom feeding can create a compact NVIS antenna. Enjoy the interesting conundrum. . .

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Updated 01-15-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Closed and Interrupted Loop, HF Lower


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Blunting the Edge of Cutting Formulas

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L. B. Cebik, W4RNL

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For some reason buried deep in the human psyche, the newer antenna builder craves a set of cutting formulas in order to build an antenna. All cutting formulas have the same general form:

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+ L(feet) = k / f(MHz) or L(meters) = k / f(MHz) +
+

There are also occasional cutting formulas expressed in inches and millimeters. Of course, "k" is the magic number that allows easy calculation of the element length, even without a hand calculator.

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Cutting formulas have a special lure. They look like precise equation, in a class with Ohm's Law.

+
+ I = E / R +
+

They also appear to be universal so that one can calculate the element length for any band whatsoever. They are also independent of the element diameter, a complicating factor. In fact, cutting formulas seem so simple and precise that we have to wonder why all antenna designers do not show the formulas in their work. On the other hand, cutting formulas are so popular that a number of antenna designers have incorporated them into their articles, even when not needed.

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Unfortunately, cutting formulas that appear in many references suffer from a number of faults.

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  1. +

    Cutting formulas are usually imprecise.

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    2. +
  2. +

    Some cutting formulas are simply wrong.

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    3. +
  3. +

    Many cutting formulas are based on crude assumptions.

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    4. +
  4. +

    Cutting formulas fail to take into account the element diameter.

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    5. +
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These faults tend to blunt the seemingly sharp edge of the cutting formula. In fact, I never use them, and I tend to avoid translating antenna designs into cutting formulas. They are too dangerous.

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The Simple Dipole

The most famous and perhaps nearly sacred cutting formula applies to resonant 1/2 wavelength dipoles. The situation appears in Fig. 1, and the following cutting formula fills in the question mark in the sketch. +
+ +
+
+
+ L(feet) = 468 / f(MHz) +
+
+

If you wish the length in meters, then use 143 instead of 468. Now let's trace the origins of this famous equation that most radio amateurs commit to memory.

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1. The magic number derives from shortening the number necessary for a true half wavelength in free space: 492. This half wavelength magic number derives from the number we would use for a full wavelength: 984. However, even the k-number of a full wavelength is imprecise. The frequency at which a wavelength is exactly 1 meter is 299.7925 MHz (with more decimal places possible within the limits of the current figure given in science and engineering sources.) So the magic number for a full wavelength in feet is closer to 983.57 and the corresponding number for a half wavelength is 491.79 (or thereabouts).

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The reply to this news is normally that cutting formulas are designed for backyard wire cutting, not for precise physical laws. Of course, this admission directly contradicts one of the lures of cutting formulas: their appearance of precision. But it is a good admission, a step in the direction of a cure to the cutting-formula affliction.

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2. The move from 492 down to 468 rests on some assumptions about wire dipole operation. There is a shortening effect based on the fact that wire has a physical diameter. Wire also has ends, creating what some simply call the "end effect." As well, wire has a finite conductivity, which also has a shortening effect. The sum of all "real-world" shortening effects for bare wire is about 5%, according to the assumption. 0.95 * 492 = 467.4, which we shall round upward for some unspecified reason to 468. (Note that this applies to bare wire. Insulation also adds to the shortening effect by another 2% to 5%, depending on the relative permittivity and the thickness of the insulation.)

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If we press the assumption of a 5% shortening, it dissolves into a much more complex affair. Shortening effects due to the impossibility of using a wire with an infinitesimal diameter become highly dependent upon the wire diameter. Matters become even more complex at lower frequencies, where we use multiple parallel wires to simulate a single fat wire. At VHF, wire diameters may vary from a thin wire to a large tube or rod.

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So we have to add another element of imprecision into the cutting formula magic number. The cutting formula is looking more and more like a simple phantom of an equation. But we are not done.

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Let's model a simple resonant 1/2 wavelength dipole at various heights about ground. Below a height of about 2 wavelengths, a dipole is more susceptible to influences of the ground than many other sorts of horizontally polarized antennas. We shall look at 2 dipoles for 14 MHz. One is composed of AWG #12 (0.0808" diameter) copper wire. The other is formed from 1" aluminum tubing. We shall place the dipole at heights of 1/4, 1/2, 3/4, and 1 wavelength above average ground, with a free-space entry just for reference. The following table will show the resonant length as a function of a wavelength. That means translating the wire diameters into fractions of a wavelength. AWG #12 wire is very close to 1e-4 wavelength at 14 MHz, while the 1" diameter tube is close to 1e-3 wavelength in diameter. The table will also list the resonant impedance, but only to show that the NEC-4 modeling achieved resonance within +/-0.1 Ohm. Finally, the table will show the calculated "magic" number that should replace 468 for the conditions of the individual test.

+ 
+        Cutting Formula Numbers for a 14-MHz Resonant 1/2-Wavelength Dipole
+Diameter                     1e-4 WL                                  1E-3 WL
+Height         Length       Impedance       K            Length      Impedance       K
+  WL             WL         R+/-jX Ohms                    WL        R+/-jX Ohms
+Free Space     0.4848       72.79 + j0.03   476.8        0.4777      72.06 + j0.05   469.9
+1/4            0.4802       80.42 + j0.09   472.3        0.4714      79.21 + j0.06   463.7
+1/2            0.48795      69.94 - j0.05   479.9        0.4821      69.49 - j0.03   474.2
+3/4            0.4826       74.23 + j0.07   474.7        0.4746      73.25 - j0.02   466.8
+1              0.48655      71.90 - j0.05   478.6        0.4802      71.35 + j0.07   472.3
+
+

Interestingly, none of the values for K falls on the value of 468. Although the cutting formula is based on wire, all of those values are well above 468. At 14 MHz, one has to reach a 1" diameter to come reasonably close to 468. Since scaling the dimensions involves changing not only the wire length, but the diameter as well, at 80 meters, we would need a 4" diameter wire to get similar results. An 80-meter dipole made from AWG #14 or #12 wire or 2-mm wire in metric nations) would need to be be much longer.

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We might speculate that the originators of the sacred dipole cutting formula were--consciously or not--using real-life experience in arriving at their formula, a real life filled with trees, buildings, power lines, and other antenna field impediments. If that speculation has any merit--and it may not--then it neglects the very high variability of antenna fields as we move around the country from tree-filled forests and building-laden urban sites out to wide open spaces in the midwest and west. As well, the origins of the dipole cutting formula go back to the days when amateurs used wavelengths in the 200-meter range.

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In the end, the dipole cutting formula is simply a crude approximation. From the table, we can easily see the wisdom of cutting the wire very much longer than the formula dictates. We shall need some wire to wrap around the insulator to make a mechanically secure connection. We can always make the wrap longer or cut off the excess. Unfortunately, this eminently practical approach to making a wire antenna does not work for any antenna using rods or tubes for elements. If a cutting formula leads us to make an element too long, we can always shave the length. However, if it leads us to make the element too short, we are back to square 1, with a tubular tomato plant stake to show for our initial efforts.

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A variation on the dipole cutting formula is the one used, mainly at VHF/UHF, for 1/4-waveoength monopoles. Fig. 2 outlines the situation.

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+ +
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Let's assume that we cut 4 radials, each 1/4 wavelength long. How long should we make the vertical monopole? The most common answer is to take the magic dipole number and halve it, usually with a conversion to inches for common US ways of measuring.

+
+
+ L(feet) = 234 / f(MHz) or L(inches) = 2808 / f(MHz) +
+
+

Allowing for rounding, of course, we know this is only an approximation. More exactly, but not perfectly exactly, the length of a wave in inches is about 11802.54/f in MHz. That adjustment would change the value of k, the magic number for the cutting formula. More significantly, the diameter of the element will change the value even more. Since VHF monopoles at 146 MHz are normally at least 2 wavelengths or more above ground, we can simply compare free-space monopoles (and radials) made from AWG #12 (0.808" or about 1e-3 wavelength diameter) and from 3/8" (about 5e-3 wavelength) diameter.

+ 
+Cutting Formula Numbers for a 146-MHz Resonant 1/4-Wavelength Monopole with 4 Radials
+Note: all radials exactly 1/4 wavelength long.
+Diameter                     1e-3 WL                                  5E-3 WL
+Height         Length       Impedance       K            Length      Impedance       K
+  WL             WL         R+/-jX Ohms                    WL        R+/-jX Ohms
+Free Space     0.2473       23.59 - j0.04  2918.8        0.2450      28.91 + j0.07  2891.7
+
+

The classic cutting formula magic number is about 5% off the mark and low. In most cases, builders end up either sloping the radials or making them shorter, while increasing the monopole length to come closer to a 50-Ohm feedpoint impedance. As we make these changes, the length of the monopole portion of the antenna changes. We could have easily started with a simple 1/4-wavelegth calculation and been on more solid ground than the cutting formula offers, since it usually ends up with an element that is too short.

+

The dipole and monopole examples are sufficient to illustrate 3 out of the 4 faults that we listed for cutting formulas. Cutting formulas are usually imprecise. They are often based on crude assumptions. Finally, they fail to take into account the element diameter.

+

Delta Loops

Some cutting formulas are simply wrong. However, the sacred dipole cutting formula is not so far off the mark that we can simply call it wrong. We have to turn to another formula for that honor. +

For reasons that we shall examine further on, the classic magic number usually given for a closed 1 wavelength loop of any shape is 1005. That is,

+
+
+ L(feet) = 1005 / f(MHz) +
+
+

To test this value, let's model 4 variations of the vertically oriented delta loop in free space. First, we can construct an equilateral triangle (base down, although that does not really matter in free space). We can feed it typically at the center of the bottom wire for primarily horizontal polarization. Alternatively, we can feed it about 25% of the up (or 1/4 wavelength down) one side for primarily vertical polarization. We can create a similar pair of triangles with a right angle at the apex, using either feed point. In order to be about 1/4 wavelength from the apex, the side-fed right-angle delta has a feedpoint about 16% up from the corner. Fig. 3 outlines the alternatives, along with some critical dimensions for figuring the physical lengths of the sides.

+
+ +
+

If we use an equilateral triangle, the height is about 0.866 times the length of a side, and all 3 sides are the same length. In a right-angle delta, the height is 1/2 the length of the bottom of base wire, and each sloping side is about 1.414 times the height. Where we feed the delta has a major impact on the radiation pattern, as shown in Fig. 4.

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+ +
+

The two left-side azimuth patterns show only small pairs of brown kidneys, which is the remnant vertically polarized radiation. The dominant radiation is horizontally polarized for these two bottom-fed deltas. On the right, we have the equilateral and right-angle deltas using side feeding. The blue clover at the pattern center is about 25-dB down from maximum radiation and represents the remnant horizontally polarized component of the total field. The side-fed delta is a vertically polarized antenna.

+

Against this background, we can now try to find the length of resonant loops and from that information calculate the value of the magic cutting formula number k. We shall use AWG #12 wire at 14 MHz, so the wire is about 1e-4 wavelength in diameter. For these loops, I have relaxed my definition of resonance to a remnant reactance of +/-j1 Ohm. The antennas are in free space.

+ 
+        Cutting Formula Numbers for a 14-MHz Resonant 1-Wavelength Delta Loop
+Note:  All antennas use 1e-4 wavelength diameter wire
+Feedpoint                     Bottom                                   Side
+Dela           Length       Impedance       K            Length      Impedance       K
+ Type            WL         R+/-jX Ohms                    WL        R+/-jX Ohms
+Equilateral    1.0650       117.6 + j0.9   1047.5        1.0656      116.9 + j0.1   1048.1
+Right-Angle    1.0490       196.5 + j0.7   1032.1        1.0720      50.21 + j0.03  1054.3
+
+

We know that the calculated numbers will change if we keep the #12 wire but change frequency, because then the wire will have a different diameter when measured in wavelengths. We also know that the value of k will change if we increase the element diameter. Unlike linear elements whose resonant lengths shrink as the element gets fatter, closed loops (and some nearly closed loops) require a larger perimeter length for resonance with fatter elements.

+

However, there are two much more important factors revealed by this exercise. First, the value of k for a cutting formula is different for all 4 delta loops. Second, none of the values is anywhere near 1005. For delta loops, the cutting-formula value is simply wrong.

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Quads From 1 to 3 Elements

Perhaps the quad antenna is the real home for the magic loop perimeter number of 1005 in cutting formulas. So lets explore quad antennas ranging from 1 to 3 elements, as outlined in Fig. 5. Of course, the loop perimeter is 4 times the length of a side, since we shall look only at square loops, where the feedpoint is always at the center of one side. +
+ +
+

Let's begin our exploration of quad-loop antennas with the single loop. For this antenna, the 1005 magic value of k is routinely cited in cutting formulas. For a change of pace, let's test the value at 28.5 MHz, using AWG #12 copper wire for one version of the free-space square loop and 1" aluminum for the other.

+ 
+        Cutting Formula Numbers for a 28.5-MHz Resonant 1-Wavelength Square Loop
+Diameter                     AWG #12                                  1"
+Environment    Perimeter    Perimeter       K            Perimeter   Perimeter       K
+                 WL           Feet                         WL          Feet
+Free Space     1.0261       36.672         1045.2        1.11398     38.445         1095.7
+
+

The magic cutting formula value for #12 wire at 10 meters is around the values calculated for similar wire in 20-meter delta loops. The 1" version of the antenna shows the effect on k of having a closed loop: the fatter the element, the larger the loop perimeter for resonance at any given frequency. The classic number of 1005 is badly off base, even with thin wire.

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Perhaps the number fares better in the context of a 2-element quad. The most common number in various texts for cutting the elements of a 2-element driver-reflector quad are 1005 for the driver and 1030 for the reflector. Once we enter the realm of multi-element antennas, we must also have a cutting formula number for the element spacing. Classically, no numbers appear, although the some sources list values from about 120 to 125, for a spacing of about 1/8 wavelength. Once more, we can contrast AWG #12 copper wire 2-element quad beams with 1" aluminum versions. The elements are in free space. The quads are optimized for the best combination of gain, front-to-back ratio, and operating bandwidth.

+ 
+Cutting Formula Numbers for a 28.5-MHz Resonant 1-Wavelength Square Loop 2-Element Quad Beam
+Diameter                     AWG #12                                  1"
+Element        Perimeter    Perimeter       K            Perimeter   Perimeter       K
+                 WL           Feet                         WL          Feet
+Driver         1.0131       34.693          996.5        1.0250      35.372         1008.2
+Reflector      1.0737       37.056         1056.1        1.1214      38.701         1103.0
+Spacing        0.1590        5.489          156.4        0.1663       5.740          163.6
+
+

Again, the classic cutting formula numbers prove irrelevant to actual 2-element monoband quad beam design. They are simply too far off to be of use and they fail to account for changes in the diameter of the elements.

+

We cannot leave the arena of quads without considering the 3-element quad beam. The conclusions will not change, but examining 3 element quads allows us to consider two other facets of magic cutting formula use and misuse. The first aspect of quad cutting formula numbers concerns their history. The numbers appearing and reappearing for 3-element quads are 975 for the director, 1005 for the driver, and 1030 for the reflector. These numbers arose in the 1970s as a function of an actual published design. The author calculated cutting formulas for his design, ostensibly as an aid to scaling it to other frequencies, but the source and function of the numbers grew dim with time as they gradually underwent editorial truncation into virtually absolute numbers for all quads, whatever the number of elements or the element diameter. The original set of numbers did not contain values for spacing. In the 1970s, most 20-meter quads used one of two standard spacing schemes. The reflector-driver spacing was either 8' or 10', and the driver-director spacing was usually 8'.

+

Since those days, we have learned a great deal more about quad beam design and performance. For example, we learned that we may design 3-element quads to feature different subsets of the performance values, because we cannot enhance all of the properties simultaneously. This is the second new facet of 3-element quad design: we can design at least 2 different types of 3-element quads. One will have reasonable 3-element gain, but superior front-to-back ratio and operating bandwidth. The other type of design will maximize the gain and front-to-back ratio, but will have a narrower operating bandwidth. Here, the notion of operating bandwidth does not just apply to the feedpoint SWR, but as well to the gain and front-to-back figures. Fig. 5 presents a dual-pattern overlay of the azimuth patterns of the two quad types on their design frequency. Of course, the pattern can only show the gain aspect of the design differences.

+
+ +
+

The two different design goals result in two different sets of dimensions. The following table samples the diversity of the dimensions--and the resulting values for K--for AWG #12 wire versions of each type of design.

+ 
+Cutting Formula Numbers for 28.5-MHz Resonant 1-Wavelength Square Loop 3-Element Quad Beams
+Version                       Wide-Band                                High-Gain
+Element          Perimeter    Perimeter     K              Perimeter   Perimeter     K
+                   WL           Feet                         WL          Feet
+Driver           1.0127       34.950        996.1          1.0218      35.265       1005.0
+Reflector        1.0618       36.644       1044.4          1.0581      36.517       1040.7
+Dr-Ref Spacing   0.1592        5.493        156.6          0.1773       6.117        174.4
+Reflector        0.9398       32.433        924.4          0.9821      33.894        966.0
+Dr-Dir Spacing   0.2986       10.305        293.7          0.2230       7.796        219.3
+
+

In the high-gain design, we can find traces of the original cutting formulas that emerged from earlier days of quad design when builders kept boom lengths short for mechanical integrity. However, the high-gain values also tell us that cutting formulas are dangerous in beam design, since the loop perimeter will vary with the element spacing as well as with the other variables in quad design. Of course, the values for k that emerge also vary with the goals of the design, with considerable differences in dimensions between the wide-band and the high-gain designs. I should not need to note that the values for k developed from actual designs in these notes are themselves next to useless. They appear only for the contrast with the classically received and very wrong cutting formulas that still populate some antenna articles and texts.

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A Yagi Case

Advances in quad design are less well known than enhancements to the design of Yagi arrays over the last quarter century. Hence, I was surprised to find a set of cutting formula values for a 3-element Yagi beam in one text that I explored. The magic numbers are as follows. +
+
    +
  • Reflector: 492
    • +
  • Driver: 478
    • +
  • Director: 461.5
    • +
  • Spacing: 142
    • +
+
+

Fig. 7 shows the application of these numbers in terms of the Yagi structure. Note that the spacing applies equally to the reflector-driver spacing and to the driver-director spacing. As usual, the resulting dimensions are in feet for HF use.

+
+ +
+

At 14 MHz, these formulas result in the following element lengths and element spacing.

+
+
    +
  • Reflector: 34.173'
    • +
  • Driver: 35.143'
    • +
  • Director: 32.964'
    • +
  • Spacing: 10.143'
    • +
  • Boom Length: 20.286'
    • +
+
+

To test these cutting formulas, I construct a NEC-4 model of the Yagi, using 1" diameter aluminum elements. The feedpoint impedance was so low that I gradually reduced the element size until the array showed a resonant feedpoint impedance. The successful element diameter was 3/16" (0.1875"). The performance values for the two versions of the antenna--using the exact element lengths and spacing specified by the cutting formula magic numbers--appear in the following table.

+ 
+Cutting-Formula Yagi for 14 MHz:  NEC-4 Free-Space Performance Reports
+Element         Gain     Front-to-Back      Feedpoint Impedance
+Diameter        dBi      Ratio dB           R +/- jX Ohms
+1"              8.74     12.04               8.77 + j19.3
+0.1875"         7.98     22.32              19.19 + j 0.9
+
+

Fig. 8 shows the azimuth patterns of the 2 versions of the Yagi.

+
+ +
+

The 1" version of the antenna comes closest to the element diameter that a builder might actually use. However, despite its higher gain, it shows a mediocre front-to-back ratio compared to most current designs, and the feedpoint impedance is far lower than current design use to minimize power loss at mechanical junctions and similar lossy parts of construction. The thin-element version is not realistic at 20 meters, but does show better front-to-back and feedpoint impedance values.

+

Now lets add a third factor into the mix. Most HF beam elements use nested tubing in several sizes. The tapered diameter of the resulting elements will call for length adjustments to take this factor into account. The amount of adjustment will vary with the total amount of taper and the relative lengths of each size of tubing used for parts of each element. No simple cutting formula can account for all of the variations possible in developing the element taper for an HF beam.

+

As a result of these considerations, cutting formulas for HF beams using tubular elements are completely useless. The prospective builder must either adhere to a published design in all the details of element structure or the builder must redesign the beam to the materials that he wishes to use. That task has no cutting formulas. However, there are antenna modeling software packages that can eliminate most of the field trials and failures on the road to a successful design.

+

Conclusions

+

We have explored the world of cutting formulas and found them to be more of a hindrance than an advantage. The best of them--for example, the dipole formula--is at most a very crude approximation of required wire length based on equally crude assumptions about the necessary shortening effects of real-world wire antennas. It failed to account for element diameter and for ground effects on the resonant length of a 1/2 wavelength dipole.

+

Some classic cutting formulas have proven to be simply wrong by wide margins, as in the case for the magic value of k normally given for 1 wavelength closed loops. The value of 1005 emerged long ago in a certain context and, by continual repetition and editorial truncation of the context, it came to be viewed as an absolute--an absolutely wrong absolute.

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Cutting formulas for multi-element arrays are also useless. Most value sets originate in outdated designs of yesteryear and fail to account for more recent design developments--especially those developments that now routinely allow us to create multiple versions of a design type, each version optimized to feature a subset of the total performance parameters of the antenna.

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As long as cutting formulas remain a staple of handbooks, texts, articles, and what we teach to new hams, they will continue to create more misunderstanding about antennas than their absence will create troubles getting started with the first amateur band antenna. While it is not possible to eliminate the classic dipole cutting formula from handbooks, since it has sacred status emerging from the mists of the long-ago era of early radio, perhaps we can make some progress by eliminating all other cutting formulas. All of the rest of them are attempts to apply a blunt instrument where a precision tool is both required and available.

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Updated 10-25-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Delta Loop, Design, Dipole, Quad, Quad Loop, Vertical, Yagi


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De-Mystifying the Modern Dipole Curtain Array

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L. B. Cebik, W4RNL

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Long-wire antennas served primarily the needs of point-to-point HF communications in the first half of the 20th century. Although some rhombics remained in service within the short-wave broadcast (SWBC) industry, other antenna designs generally took over. SWBC tends to require a broader beamwidth than a rhombic provides. Although the rhombic had the frequency range necessary for frequency shifts in accord with changing HF skip conditions, other antennas could serve as well--or almost as well. Once aimed, the rhombic had a line of targets; SW broadcasters preferred a large region. Even if the target did not encompass the entire region, slewing the antenna's beam pattern could reduce costs by avoiding the need for second and third large high-gain arrays or complex turning mechanisms.

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Antique and Modern Billboard Antennas

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The solution to the needs of many SW broadcasters arrived with improvements to a very old antenna, once called the billboard. (See Kraus, Antennas, 2nd Ed., p. 547, for a representation of a billboard antenna.) The operational principle is simple. Any bi-directional antenna, such as a dipole, becomes a directional antenna when placed in front of a planar reflector. Planar reflectors find many contemporary uses in the VHF and UHF region today. Hence, we often overlook their continuing service for SW broadcasting. However, their current use depended upon a number of advances, standardizations, and combinatory techniques to give them the relative predominance that they now enjoy.

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Fig. 1 sketches (with many missing details) an antenna about which I have received many inquiries. Vacationers encounter them in unexpected places from coast to coast (and well inland) in the U.S. The sketch is not to scale. The towers are much too fat for the array between them. The figure also lists other missing details that would obscure the main function of the antenna. For example, we would normally find many more guy wires for the towers and many more support and spacing wires and jigs for the key elements that form the antenna's radiation pattern.

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In return for omitting some details, we can clearly see both the dipole elements in a 3-by-3 array and the reflective screen behind them. In many cases, the screen will consist only of horizontal wires, similar to the rod-based planar reflectors in my notes on that subject in past articles. Since the horizontal lines are very long, periodic vertical spacers are necessary to maintain the reflector shape.

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The 3-by-3 array of dipoles also represents an evolution from some of the original billboard antennas that used center-fed full wavelength elements. Note also that the dipoles are closely spaced. The overall reduction in billboard size per driver unit formed one of many reason why the modern dipole array is a primary short-wave broadcast antenna today. Even the original versions effected a major real estate saving over designs such as the rhombic. Of course, many of the original rhombics used timber supports. As steel tower structures became more common and less expensive, they not only replaced existing supports, but also made taller antennas more feasible. Hence, the billboard antenna traded vertical space for longitudinal space, cutting both purchase and maintenance costs. (Never volunteer to mow the lawn beneath a truly long rhombic.)

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The dipole array rarely uses its original "billboard" name, although many folks call it a dipole curtain antenna. "Curtain" refers to the planar reflector behind the driven elements. They could move a bit in the wind. Early designs were not fully appreciated for several reasons. First, the high steel structures and copper wire were subject to corrosion. Breakage required more repair effort than splicing a rhombic leg. However, one of the electrical limitations of the billboard was its narrow operating bandwidth.

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In the first half of the last (20th) century, almost all antenna designers strove to produce as much gain as might be feasible from a given design. This bad habit still infects much of the antenna design for amateur radio. We accept excessive problems in feedpoint matching by designing long-boom Yagis with the minimum number of elements necessary for a certain gain level. Even if we overcome that problem, we continue to accept relatively poor sidelobe suppression because we refuse to add a few more elements to the design. We continue to make excuses for antenna designs that are difficult to replicate due to their narrow operating bandwidth. (There are good reasons in certain circumstances for using a narrow beamwidth, but in general, it is usually a condition with which we are stuck for lack of design imagination.)

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Early billboard antennas suffered from narrow operating bandwidth for several reasons. First, the driving elements used a spacing from the reflector screen that yielded maximum gain. Second, they looked for element-to-reflector spacings that left the feedpoint impedance unchanged relative to the same driver with no reflector. Third, they used driven element lengths and spacings that yielded maximum gain. For example, a collinear pair of 1/2 wavelength elements (or a center-fed full wavelength element) yields a little more gain than a simple 1/2 wavelength dipole. (The high impedance of this type of element, of course, permitted the use of wide-spaced transmission line segment for feeding and phasing, a condition very suitable for high-power SWBC operations.) Although we knew that we might obtain even more gain with a vertical spacing of 5/8 wavelength, 1/2 wavelength became the standard for the ease of feeding a vertical collection of elements in phase. Rarely did we have the room to arrange the elements horizontally at optimal spacing. Initially, we used some very close spacing to reflector screens, sometimes as low as 1/8 wavelength. When we discovered that a wider spacing would yield more gain and weaker rear lobes, we opted to use that spacing despite the fact it still limited the operating bandwidth.

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Modern dipole curtain arrays operate on other principles. Some common ones, found in Chapter 26 of Johnson's Radio Engineering Handbook, 3rd Ed., reappear in Fig. 2. We may note in passing that an engineer for TCI, a leading producer of dipole curtain arrays, wrote the 3rd edition version of the chapter on HF antennas. If the volume is not conveniently available, you may find some of the same data at the TCI website. Look at model 611 for a general description of their dipole curtain arrays.

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The side view of the antenna shows the vertical heights generally used: 1/2 wavelength between dipoles of the array. Studies of planar reflectors strongly suggest that this antenna type achieves maximum gain for a given driver set when the reflector screen exceeds the driver assembly by 1/2 wavelength or so in every direction. Realities, including catenary effects on an all-wire assembly, usually dictate less reflector extension except perhaps at corners.

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The face view shows the equally desirable horizontal reflector extension, although every extra foot of reflector screen adds to costs for perhaps marginal performance improvements. The most notable feature of the face view is the arrangement of the driver dipoles. Since a driven dipole is normally slightly less than a physical half wavelength, we may place the dipoles on 1/2 wavelength centers across the reflector. Because designers still wish to use wide-spaced transmission lines for feeding and phasing, the driven elements are usually some form (in some cases, an exotic form) of a folded dipole.

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The final element to note from the sketch is the recommended spacing of the elements from the reflector screen: 0.3 wavelength. A simple dipole tended to show maximum gain and weakest rearward lobes with considerably closer spacing, but by accepting a lower gain per driver, the designer achieves a wider operating bandwidth. Before we close these notes, we shall look at the combination of ingredients that go into extending the operating bandwidth of a dipole array.

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We (but not necessarily the designers) might express the overall goal in this manner: since wire elements are relatively light, we can obtain more performance by packing more elements within the available space rather than from seeking out the maximum performance from the minimum number of elements. Most of the array weight (but not necessarily stress in adverse weather) lies in the reflector lines or screen. The element spacings in the sketch--and any extension of the sketch--provide the most performance for a given space (side-to-side and vertical) occupied by the array. Performance here includes not only gain, but beamwidth, rear lobes, and feedline SWR for some specified reference impedance.

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How the Dipole Array Achieves Its Performance

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Let's back up a step and see how the modern dipole array achieves its performance. That step requires that we first examine dipoles on their own, that is, with no reflector screen. We shall survey in tabular form the maximum gain of various combinations of dipoles. Of course, the listed gain will be for a bi-directional array. We shall designate each combination by a code of the order mV-nH, indicating the number of dipoles stacked vertically (m) and horizontally (n). Each vertical dipole will be 1/2 wavelength from its neighbor, and horizontal dipole lines will be on 1/2 wavelength centers. The data include both the gain and the horizontal beamwidth. More correctly, the beamwidth is in the E-plane, since all values for this exercise are for free space. All dipoles consist of folded dipole made from AWG #10 copper wire. The test frequency is 10 MHz.

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+Free-Space Performance of Various Dipole Arrays
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+Array Size                1V-1H        1V-2H         1V-3H
+Maximum Gain (dBi)        2.13         3.79          5.30
+Beamwidth (degrees)       78.4         48.2          33.2
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+Array Size                2V-1H        2V-2H         2V-3H
+Maximum Gain (dBi)        5.94         8.01          9.69
+Beamwidth (degrees)       78.5         48.2          32.8
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+Array Size                3V-1H        3V-2H         3V-3H
+Maximum Gain (dBi)        7.80         9.72          11.27
+Beamwidth (degrees)       78.4         48.0          32.8
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The 2V-2H configuration offers the greatest step-gain increase over versions with one less vertical or one less horizontal dipole. The gain steps are not smooth for two reasons. First, gain increases diminish as we add steps in a linear count. As well, the dipoles interact, so that gain is not strictly additive. Slightly different spacing values or even horizontal end-to-end distances may alter some of the numbers. Nevertheless, the overall progression of dipole maximum gain values is a fair representation of the potentials of dipole arrays on 1/2 wavelength centers.

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One interesting fact about the progressions is that the E-plane beamwidth does not significantly change as we add dipoles vertically. Narrower beamwidths result from adding dipoles horizontally. Since the beamwidths of each level of horizontal stacking are constant, regardless of the size of the vertical stack, we can represent the array patterns with samples taken with a vertical stack of 2. Fig. 3 shows the pattern shapes for 1, 2, and 3 horizontal dipole stacks. The patterns for 1 and 2 horizontal dipoles are perfectly normal and familiar. The pattern for 3 dipoles resembles the pattern for a center-fed 1.25 wavelength extended double Zepp doublet.

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Over ground, the E-plane patterns would not change shape significantly. The elevation pattern depends upon the height of the array above ground. Typically, an installation will adjust the dominant elevation angle for a design frequency by adjusting the bottom height for the array selected, which might be still larger than the samples used here. Although literature tends to use the average height of the array as a calculating point, the arrays equivalent height tends to be about 2/3 the distance between the height of the lower dipole and the height of the highest dipole. This figure does not vary much from the array's average height, but it does show up in vertically phased arrays (like the lazy-H) where the lowest height may be a large fraction of a wavelength above ground. Indeed, the lazy-H is a billboard antenna without the billboard, although some amateurs have added screen reflectors for increased directivity.

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Adding a screen to the folded-dipole arrays that we have just surveyed creates a directive beam antenna. As shown in Fig. 2, the recommended spacing between the dipole arrays and the screen reflector is about 0.3 wavelength. The value is not optimal for maximum possible gain. In fact, designing a dipole array for maximum possible gain would require customizing each dipole element and the array spacing for every possible combination. The 0.3 wavelength spacing provides good gain and pattern shaping without regard to customizing the dipoles to account for their interaction. As a test, I created a screen for each folded dipole in the first sequence. Each screen consisted of a wire grid of standard modeling proportions (0.1 wavelength squares with a wire diameter that is the square side divided by PI). Each screen exceeds the dipole array dimensions both vertically and horizontally by 0.5 wavelength. The test frequency remains 10 MHz. To the data in the first table, I have added the 180-degree front-to-back ratio as a measure of rearward performance.

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+Free-Space Performance of Various Dipole Arrays with Screen Reflectors
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+Array Size                1V-1H        1V-2H         1V-3H
+Maximum Gain (dBi)        7.45         8.68          10.11
+Front-to-Back Ratio (dB)  19.24        21.18         21.78
+Beamwidth (degrees)       69.6         48.8          33.0
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+Array Size                2V-1H        2V-2H         2V-3H
+Maximum Gain (dBi)        9.77         11.21         12.85
+Front-to-Back Ratio (dB)  21.44        28.73         28.90
+Beamwidth (degrees)       72.4         48.8          32.8
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+Array Size                3V-1H        3V-2H         3V-3H
+Maximum Gain (dBi)        11.72        13.22         14.87
+Front-to-Back Ratio (dB)  21.58        29.33         29.34
+Beamwidth (degrees)       72.0         48.6          32.8
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Because the rear lobe structure changes, the gallery of E-plane patterns in Fig. 4 includes plots for all of the entries in the table.

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A number of features of the patterns call for note. The beamwidth values do not change very much from the values without the reflector, except that they apply only to the single large forward lobe. The sidelobes of the versions with 3 horizontal dipoles are better than 20 dB lower than the main lobe regardless of the vertical stack size. A single bay consisting of 1 to 3 dipoles arranged either vertically or horizontally has a good front-to-back ratio. However, as soon as we add a second bay in one or the other direction, the ratio approaches 30 dB--even for the 2V-2H version of the array. For values over average ground with a base height of at least 1/2 wavelength, you may add about 5 dB to the gain for a ballpark total gain figure. The gain will slowly climb as we increase the base height of the array, of course, moving the screen upward with the dipoles.

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One advantage that accrues to the dipole array is the ability to shift or slew the main direction of the beam by up to 30 degrees each way, depending on array size. Common installations employ "delay lines" that s hift the phase angle of the current for each vertical bay of dipoles. We may simulate this effect in models simply by using a current source and adjusting the source phase angle while holding the current magnitude constant. Fig. 5 shows the patterns for a 1V-2H array initially with both vertical dipoles in phase. The center pattern uses a phase angle of 30 degrees for the first dipole and 60 degrees for the second. The final pattern uses 60 degrees for the first dipole and 120 degrees for the second. The general rule is to change the phase angle of subsequent vertical dipole bays by a multiplier on the baseline phase angle according to the position of the dipole (or vertical bay of dipoles) relative to the first vertical dipole or bay.

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The first move changed the heading of the main beam by 7 degrees, and the second changed it by 13 degrees. The angles would remain the same regardless of the size of the vertical bays in the array. By the correct selection of delay lines, we can achieve a relatively precise aim at a target of choice within the span of allowable slew angles. As we increase the angle of the main beam by these means, some distortion does appear in the form of forward and rearward sidelobes. At the angles in the sample, the distortions are not severe enough to void the use of slewing. However, they show that slewing has limits. Nevertheless, for a SWBC station that wishes to change its target from one session to the next, the process allows the change without physically altering the antenna or its position. Note that, when used within limits, the beam strength and beamwidth do not change to any noticeable degree.

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The basic capabilities of a fixed position dipole curtain array are quite impressive, even using the ubiquitous amateur monoband Yagi as a standard of comparison. A 2V-2H assembly at a reasonable height above ground would easily match a 5-element Yagi, and delay-line slewing of the beam would permit coverage of all of Europe from the eastern U.S without need for a rotator. If we built equivalent dipole arrays on each side of the reflector, then we might cover Europe on one side and the Pacific on the other, at least from my location in the hills of Tennessee.

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Broadbanding Techniques

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The needs of SWBC stations are quite different from those of the average amateur station. SWBC stations tend to use very high power levels, up to 500 kW in some cases. Since we must provide energy to each dipole, the use of wide-spaced parallel transmission is fairly standard, indicating as well the use of high-impedance antenna feedpoints. A folded dipole of conventional construction--with equal diameter conductors throughout--goes part of the way toward the high-impedance goal. However, if we wish to raise the feedpoint impedance beyond about 280 Ohms, we must resort to more unconventional techniques. For example, if we use a smaller diameter wire for the line with the feedpoint and a much larger diameter wire for the other line, we increase the impedance transformation to almost any desired level within the limits of lines to match it. We may simulate very wide second wires using pairs or cages of wires so that the entire assembly remains lighter than it would be with a single fat wire or tube for the second conductor.

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Obtaining a high impedance feedpoint does not resolve a second goal of dipole array designers: achieving a wide operating bandwidth. The gain of a dipole array changes slowly as we change the operating frequency as a function of the length of the elements relative to the operating frequency. However, being able to match the array over an extended bandwidth requires a combination of techniques. There is no magic to any of them, although amateurs rarely use them in complex combinations.

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The first step is to begin with a wide-band folded dipole. The AWG #10 folded dipole used in our initial dipole array models has a 2:1 SWR bandwidth that runs from 9.6 to 10.5 MHz, a 0.9-MHz spread (given our test frequency of 10 MHz). We need to begin with a folded dipole array that has inherently a broader operating bandwidth. That is step 1 in the process. Most dipole array manufacturers have proprietary designs for their driven elements, designs to which I am not privy. (Even if I had access to one or more of them, I likely could not violate agreements that gave me such access.) So I shall begin with a moderately broadbanded driver of my own design. It will not have the full capability of some commercial driver elements, but it will be sufficient for our small demonstration.

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A fan dipole with a 3:1 length-to-height ratio is capable of increasing the operating bandwidth over a conventional linear dipole. However, the feedpoint impedance is about 50 Ohms. If we create a pair of such fans, we only achieve the standard 4:1 impedance increase that is standard for a conventional folded dipole. However, if we use a single-wire as the fed portion of the folded dipole, the fan represents a much "fatter" second portion, for a significant increase in the feedpoint impedance. We connect the fed wire to the fan at the centers of the vertical sections, since that is the pair of points on the fan with minimum current. The free-space performance data for the arrangement is virtually identical to the standard folded dipole, but the feedpoint impedance at resonance is over 550 Ohms. A 600-Ohm SWR curves shows under 2:1 SWR from 9.4 to 10.8 MHz, a 1.4 MHz spread or about 1.56 times the spread of the standard folded dipole. Like the standard folded dipole, the folded-fan dipole is composed of AWG #10 copper wire in all of the models that we shall consider. Fig. 7 overlays the SWR plots for the standard folded dipole and the folded-fan dipole. Each curve uses its own reference impedance.

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Step 2 in the process of broadening the operating bandwidth is to place the driver assembly ahead of the reflective screen and determine the best distance between the two. Like previous screens, the wire-grid structures used in this sample situation extend about 1/2 wavelength beyond the driver limits in all directions. Fig. 8 shows side and face views of the folded-fan dipole and its screen. In the EZNEC graphic, I have retained the segment and wire junctions dots to lend some color differentiation to the array pieces.

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Fig. 8 shows no spacing value because I examined 2 cases. The first placed the driver 0.245 wavelength ahead of the screen. The free-space gain was 8.34 dBi with a front-to-back ratio of 18.77 dB. The feedpoint impedance with this spacing was close to 800 Ohms. Increasing the distance between a planar reflector generally has 3 easily noted effects. First, it raises the feedpoint impedance of the driver. Second, if the distance is greater than the maximum gain position, performance gradually declines relative to both gain and front-to-back ratio. Finally, increased spacing between the driver and screen tends to widen the operating bandwidth of the array. By increasing the spacing between the driver and screen to 0.3 wavelength, the feedpoint impedance rose toward 1000 Ohms. However, the maximum free-space gain dropped by 0.9 dB to 7.45 dBi, while the front-to-back ratio fell to 16.55 dB. Nevertheless, as shown in Fig. 9, the small increase in spacing widened the 2:1 SWR bandwidth, with each array design using its own reference impedance.

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Although the curves appear similar, note the difference in the frequency limits of each graph. At a more optimal position for array gain, the passband runs from 9.2 to 10.9 MHz or 1.7 MHz. By increasing the spacing, the operating passband now extends from 9.2 to 11.9 MHz or 2.7 MHz. Notice that the SWR in neither case reaches a 1:1 value. That goal is often only an amateur fetish (but is not always a fetish by any stretch of the imagination). By selecting an acceptable reference impedance--generally one that reflects a transmission line that we can use with the system--we can often attain a wider passband within the upper limits of allowable SWR.

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Stretching the operating passband in terms of SWR does not guarantee that the array pattern will be equally usable everywhere within the frequency limits. Fig. 10 presents sample E-plane patterns from the wider passband, using the upper, lower, and mid-band frequencies. Within the span of the antenna, the gain drops from 8.04 dBi down to 5.02 dBi as we raise frequency (and the spacing becomes wider as a function of a wavelength). The 180-degree front-to-back ratio tends to be stable in the 16-18-dB region. However, as we raise the operating frequency, the beamwidth broadens, especially toward the upper passband limit. At 11.9 MHz, the pattern shows twin peaks, although there is no noticeable null between them. However, for some applications, the beamwidth may have become too wide to meet operating criteria.

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Our step-2 exercise has increased the frequency range for allowable operation. In the process, the exercise has also shown us that not every frequency that we can use is one that we can use well.

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The third step on the road to broadening the passband of a dipole array involves what happens when we phase-feed more than 1 driver. For this rudimentary demonstration, I set 3 folded-fan dipoles (without a screen) at vertical intervals of 1/2 wavelength. The center dipole serves as the fed driver relative to the main transmission line. Each outer driver receives energy from a 1/2 wavelength transmission line connected to the center driver. The three drivers are now roughly in parallel. Hence, we can expect a reduction in both the resistance and the reactance at the feedpoint.

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However, the drivers interact with each other. Outer drivers essentially interact with only one other driver, and mutual coupling shifts the feedpoint impedance of each of them by like amounts. However, the center driver mutually couples to both outer drivers and shows a different shift in impedance from the value it would have if used in isolation. By judicious sizing of the drivers we can overcome the impedance difference. However, let's size them in concert, that is, make them all the same size. The left portion of Fig. 11 shows the set-up in outline form.

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Because the impedances on the outer drivers will be increasing for part of the frequency sweep while the center driver impedance decreases--and vice versa--we obtain an additional increment of passband broadening. Fig. 12, at the top shows the new passband, which even without a reflective screen extends from 9.55 to 11.8 MHz or 2.25 MHz. The reference impedance for the curve is 250 Ohms.

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The bi-directional maximum gain of the drivers across the operating passband increases from 7.17 dBi to 8.03 dBi, with well-behaved lobes. Therefore, the driver set seems fit for combining steps 2 and 3, that is, using a phased set of 3 drivers ahead of a screen. The right portion of Fig. 11 shows the ultimate array (at least for our demonstration) in outline form. The lower portion of Fig. 12 reveals the 300-Ohm SWR passband, which now extends from 8.35 up to 11.5 MHz or 3.15 MHz. The following brief table samples the modeled free-space performance values at each ends of the passband and at the mid-band frequency.

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+Modeled Free-Space Performance of a Vertical Stack of 3 folded-Fan Dipoles 0.3 WL Ahead of a Screen Reflector
+Frequency (MHz)                          8.35           9.925          11.5
+Maximum Forward Gain (dBi)               11.99          11.86          10.99
+180-Degree Front-to-Back Ratio (dB)      19.81          20.15          20.00
+E-Plane Beamwidth (degrees)              58.9           68.8           95.8
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Except for not showing relative gain values, the patterns in Fig. 13 put a graphic face on the data in the table.

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The array patterns show the same sort of development that we found in Fig. 10 for a single driver and screen. At the top of the passband, we find dual peak gain levels, but without a noticeable null between them. We also find a rapid rise in the beamwidth above the mid-band frequency--nearly 30 degrees. Although the same cautions apply to the expanded array as also apply to the single driver array, we should note that the operating passband is now about 50% greater.

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Our goal has been only to demonstrate that obtaining a wide operating passband from a dipole curtain array requires a combination of ingredients or steps, as we have called them. The folded-fan dipole is far from being the ideal starting point for effecting the scheme, although its has served well in the demonstration. Some manufacturers of dipole screen arrays claim up to a 2:1 frequency range while also listing tighter SWR limits in their specification sheets. However, all specification sheets are incomplete performance records, so we have no idea of whether the patterns associated with frequencies across a given frequency range are all usable to the same degree as they are at mid-band.

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Regardless of the performance obtained by any given maker, we have seen that through careful design (even at the crude level used in this exploratory account), a dipole array with a screen reflector lends itself to broadband service with gains that one might tailor by selecting the correct array size. A planar reflector, whether solid or composed of lines or screens, offers considerable flexibility in system design. If we give up the amateur habit of always seeking the highest gain from the fewest elements, we can achieve a number of other advantageous performance features in our arrays.

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Back to the Billboard

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Modern screen or curtain arrays employ dipoles. However, in the dim recesses of past times, the original standard driver billboard array was one or more sets of center-fed 1 wavelength elements, also called collinear half wavelength elements. We neglected to test this arrangement to see if it offers any advantage over the use of dipoles. Let's pause before closing to see what happens if we replace dipole drivers with the 1 wavelength drivers.

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To gain some perspective on the question, let's use a 2V-2H dipole driver set as one comparator. The corresponding billboard array would employ a 2V-1H driver set. Both driver arrays would have the same dimensions and require the same size reflector screen. In fact, we may also use the same spacing between the drivers and the screen for both antennas. The top portion of Fig. 14 shows the two outlines.

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Between the two types of driver arrays we find under 0.1-dB difference in gain and only 1 degree difference in beamwidth. The front-to-back ratio of both arrays is near 28 dB. As the sample E-plane patterns show in Fig. 14, Nothing in either pattern gives one or the other array an advantage.

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We have already explored some ins and outs of dipole impedance behavior in a planar-reflector array. The older billboard system shows individual feedpoint impedances that are very high--in excess of 3000 Ohms resistance. For a single frequency, the high impedances are no hindrance to the use of 1 wavelength elements. However, if we wish to change frequencies, we may encounter a need to retune the system. The center of a 1 wavelength element is a region of very large and rapid changes of impedance values as we shift the operating frequency. Unless all wires composing the system are very taut, storm winds may result in some impedance oscillations.

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The much lower impedances of dipoles--even raised to several hundred Ohms--provide the array designer with a much more controllable situation with respect to impedance matching over a wider frequency range. The conversion to dipoles as drivers has made the dipole screen array a mainstay of short-wave broadcasting by providing the necessary gain and beamwidth (including slewing) with the ability to handle high power levels. Increased operating bandwidth supplies the final need of the SWBC industry.

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In these notes, my aim has been to examine some of the features of an antenna type that we often encounter on our travels across the U.S., but seldom have occasion to use personally. The maze of wires--whether active antenna parts or support guys--gives these antennas an air of mystery--or at least considerable puzzlement. (Of course, not all mazes of wires strung between 2 tall support masts are dipole curtain arrays.) Hopefully, this small set of exercises has taken some of the mystery out of the arrays.

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In the course of developing these notes, I have used published information on the antenna type, abetted by some first-order free-space modeling. Hence, my slant on certain features may differ markedly from the perspective brought to bear by an antenna engineer deeply involved in the design and implementation of such arrays. Indeed, I may well have overlooked numerous features that a manufacturer might consider critical and stressed others considered marginal or even trivial. Still, I hope that these notes contain enough analytical information to make the antenna type--the dipole curtain array--more familiar to and understandable by those who see one for the first time.

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Updated 05-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Bowtie / Fan, Broadcast, Dipole, Dipole Curtain Array, HF Lower, HF Upper


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Notes on HF Discone Antennas

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Notes on HF Discone Antennas

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This page exists to include the PDF in the topic index

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Topics: Discone, HF Upper, VHF / UHF, Vertical


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Unfolding the Story of the Folded Dipole

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L. B. Cebik, W4RNL

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The folded dipole is a simple antenna to build. However, it has a acquired something of a complex web of correct and incorrect information surrounding it. The points of these notes is to sort out some of the information, with an emphasis upon what it is correct to say about the folded dipole.

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Fig. 1 shows the essential elements of a folded dipole. It consists of two parallel wires having a constant spacing, S. Each wire has a certain diameter, d1 and d2. The ends of the parallel wires are connected to form a continuous loop. The feedpoint is at the center of the wire having the diameter d1.

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We can construct a folded from common materials ranging from house wire to parallel transmission line. With such materials, we can obtain the pattern shown as a free-space azimuth pattern in Fig. 2--the same pattern as a single-wire dipole. The folded dipole is a reliable antenna, meaning that we can get it to work without lots of finicky adjustments. Something about the ease of building an antenna seems to go hand-in-hand with not getting a firm grasp on why it works.

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In calling the antenna a folded dipole, we should note that the term "dipole" is important to our discussion. "Dipole" is a term that we use as a shorthand for a longer characterization of a single wire antenna. The 1-wire antenna described is a 1/2 wavelength long, resonant, 2-pole antenna. The reference to length is obvious. Being resonant means that the feedpoint impedance will have negligible reactance and hence be purely or close to purely resistive. Having 2 poles means having two transitions from maximum to minimum current--in this case stating at the current maximum located at the center of the antenna.

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Now all that we need to deal with is the folded aspect of the antenna. Folding refers not only to the visual appearance of the antenna, but as well to what folding does. Folding a single wire antenna (and thereby doubling the amount of wire needed) creates a combination of an antenna element and an impedance transformer. The same principle has been used with other antenna types. For example, the side-fed rectangle--a good vertically polarized performer for the lower HF bands--has a low feedpoint impedance. Doubling the loop with a crossover at the far end from the feedpoint raises the impedance of the antenna.

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Using antenna transformer techniques to raise the impedance of an antenna does not reduce any losses inherent in the antenna operation. Loss resistances will also be transformed. These losses are not significant with the standard horizontal folded dipole, but have been a major misunderstanding of its cousin, the folded monopole.

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The Folded Dipole as an Impedance Transformer

Our understanding of the folded dipole has been stunted in part by our use of only a special case within the range of possible transformations. By using the same diameter wire for both d1 and d2, we always end up with a 4:1 impedance transformation relative to a single-wire dipole. However, we usually have no idea why this is so. Let's start with the general transformation properties and work our way back to the special case with which we are familiar. +

Relative to a single-wire dipole, the feedpoint impedance will be transformed upward by the ratio R according to the following equation:

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where the terms S, d1, and d2 have the meanings shown in Fig. 1.

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The log of 2S divided by a wire diameter is a complex quantity that hides some of the consequences of the equation. However, consider that if d1 and d2 are equal diameters, then the division of one log by the other log results in a value of 1. Since 1 plus this value is 2 and the square of 2 is 4, then for wires of equal diameter, the impedance transformation ratio is always 4:1 relative to the impedance of a single wire resonant half wavelength dipole.

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In free space the impedance, the resonant impedance of a single wire resonant half wavelength antenna that is center-fed is between 71 and 72 Ohms for highly conductive materials like copper. Hence, a folded dipole using equal wire diameters for both wires will be about 284 to 288 Ohms.

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Now let's note some other aspects of the equation. There are no rules against using wires of different diameter for d1 and d2. The wire diameter values always occur as divisors (below the division line). Hence, the larger the diameter, the smaller will be the resulting log term. Therefore, we get the following guidelines (remembering that d1 is the diameter of the fed wire):

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  • 1. If d1<d2, then R is always >4.
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  • 2. If d1>d2, then R is always <4.
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However, R must always be >1. That is, 1 is the limit of R as the ratio of the two log values goes to zero, which would imply an immensely large value for d2 or an infinitesimally small value for d1. The result is that a folded dipole cannot be used to reduce the feedpoint impedance relative to a single-wire dipole.

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So far, we have ignored S. Before taking a log for the numerator and for the denominator of the fraction in the equation, we must divide twice the wire spacing by the wire diameter(s). This results in a different value in the numerator and denominator for each different wire spacing we choose. Hence, the impedance transformation ratio will also change with every change of spacing.

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There is one exception to this consequence of spacing. If the two log values result in a value of 1 when we divide one by the other, then the result will always be 4, regardless of the spacing. Hence, for the case where both wires have the same diameter, the feedpoint impedance transformation relative to a single-wire dipole will be 4:1 for any reasonable wire spacing.

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There is a limit to how far apart we can place the wires and still have a folded dipole. That limit, however, is considerably farther apart than the limit for having an effective transmission line with confined fields. It also can be a tiny spacing--just enough to prevent a short circuit between the wires.

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Modeling the Folded Dipole

With exceptions that I shall later note, we can use modern antenna modeling software to calculate the properties of folded dipoles of many sorts. For folded dipoles using wires of equal diameter, both MININEC and NEC will yield very accurate results. Remember that the term "modeling" is used in the mathematical sense of calculating antenna properties using equations derived from Poynting Vectors. Hence, the results are very much more accurate than the small rules of thumb formulae we find in many antenna books. +

The trick to modeling folded dipoles is to use many segments. The end wires connecting the parallel wires are a limiting factor. In NEC, we want the segment lengths in the parallel wires to be less than a 2:1 ratio in length to the segments in the end wires. In MININEC, we want to use many segments so that the end corners are not mathematically "cut off" in the calculation. So for the models in this exercise, I shall use a frequency of 28.5 MHz with 110 segments along the length of each parallel wire in MININEC to allow a perfectly centered feedpoint. 111 segments is required in NEC. These models will fall well within the calculation constraints of each program type. However, in all cases, the results will apply to bare wire.

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As a test case, let's look once more at the question of spacing. We shall use 0.1" diameter copper wires throughout for our initial tests. This diameter is between #12 and #10 AWG wire. I shall present both NEC-2 and MININEC results for comparison. (For reference, the NEC-2 results are from NEC-Win Plus and the MININEC results are from AO 6.5.)

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Let's compare the performance of folded dipoles having 3 different spacing values. A 1" spacing corresponds to the use of ladder line of common commercial sorts. A 4.14" spacing corresponds to one recommendation that we use a spacing of 1/100 wavelength. Finally, a spacing of 13.8" corresponds to another recommendation that we use a spacing of 1/30 wavelength. In the table below, length refers to the resonant length of the folded dipole, while gain is the free-space gain in dBi. The feedpoint impedance is given in standard series R +/- jX Ohms terms.

+ 
+Spacing        Length         Gain           Feedpoint Z
+               inches         dBi            R +/- jX Ohms
+1"
+  Mininec      196.56"        2.10           288.0 + j0.0
+  NEC-2        196.93"        2.12           286.6 - j0.0
+4.14"
+  Mininec      193.70"        2.10           288.0 + j0.0
+  NEC-2        194.20"        2.12           287.0 - j0.1
+13.8"
+  Mininec      186.94"        2.12           287.0 + j0.0
+  NEC-2        187.40"        2.13           285.8 + j0.0
+
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Note that the two calculating systems yield resonant lengths within about a half inch of each other. As well, the predicted gain is never more than 0.02 dB apart--a truly insignificant amount. Even the resonant resistance values diverge by less than 1.5 Ohms. The systems are certainly consistent with each other.

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Nothing in the spacing of the wires of a folded dipoles could produce a difference that would be discernable to the most accurate field measuring equipment available today. There is no aspect of antenna theory that can justify a claim that one spacing value will perform better than another.

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Private experience might result in other claims. However, private experience is fraught with many variables of construction and maintenance, as well as antenna location variables. However, equivalently well-constructed folded dipoles of different spacing values will perform equally well when placed in identical antenna settings.

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Of course, the actual feedpoint impedance encountered by the builder will vary with the height above ground, just as the feedpoint impedance of a single-wire dipole varies with height. The two curves will show a 4:1 ratio in value, but otherwise be congruent.

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Before we leave these folded dipoles, let's note the differences in antenna length. Each antenna was brought to resonance by adjusting its overall length. The wider the spacing, the shorter will be the resonant length. The shortening has two major sources. First, the classic impedance transformation equation does not take into account the end wires. With wide spacing, these wires begin to take up a small part of the antenna length. Second, a 2-wire folded dipole simulates a fat single wire. Just as single-wire dipoles become shorter at resonance with increasing diameter values, so too do folded dipoles with increases in wire spacing.

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The handy "468/f" rule of thumb that we use for dipoles is actually only a crude and often inaccurate guide for wire cutting. The resonant length of single-wire and folded dipoles will vary with wire size, spacing (for folded dipoles), and height above ground. If we turn the matter around and cut the antenna according to the old guide, then we can expect different impedance values--including differences in both the resistive and reactive components--as we change wire diameter, spacing, and/or height above ground.

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Wire Size

Let's sample what happens with different wire sizes. We shall keep d1 and d2 the same, but change both wire diameters together. For this set of tests, let's use a spacing of 3" between wires. Again, we shall look at both NEC-2 and MININEC results. + 
+Wire Size      Length         Gain           Feedpoint Z
+               inches         dBi            R +/- jX Ohms
+0.5"
+  Mininec      192.10"        2.10           287.0 + j0.0
+  NEC-2        193.04"        2.13           285.3 - j0.1
+#10 AWG
+  Mininec      194.54"        2.10           288.0 + j0.0
+  NEC-2        195.09"        2.12           286.9 - j0.0
+#12 AWG
+  Mininec      194.90"        2.10           288.0 - j0.0
+  NEC-2        195.31"        2.12           287.2 - j0.0
+#14 AWG
+  Mininec      195.16"        2.10           289.0 + j0.0
+  NEC-2        195.51"        2.12           287.6 + j0.0
+#18 AWG
+  Mininec      195.63"        2.09           290.0 + j0.0
+  NEC-2        195.88"        2.10           288.5 + j0.0
+
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All values remain within 0.5% of each other for each set of wire sizes between the two calculating systems. More significantly, there is no perceptible difference in performance predicted for the range of wire sizes.

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Although there is a change of resonant length as we change wire size, it is considerably less than the length changes required by differences of wire spacing in the folded dipole. The range of spacing in our tests was 13.8:1, while the range of wire sizes was 12.4:1, comparable ranges. However, the length range was only about 1.5" for the wire size differences, but 4.5" for the spacing differences.

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With respect to length and performance, a folded dipole acts very much like a single fat wire. In fact, a single wire dipole will have a length of about 199.8" using 0.1" diameter copper wire to be resonant and have a free space gain of about 2.10 dBi. All of our folded dipoles are shorter, since all are effectively much larger in diameter. To have a resonant length equal to that of the #18 AWG wire folded dipole above (about 195.8"), a single copper wire would need to be just about 1" in diameter. (Reminder: all tests are at 28.5 MHz for consistency throughout this exercise.)

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Antenna Currents and What They Tell Us

One very unhelpful conception of a folded dipole is to think of it solely as some kind of transmission line. As we shall see, there are currents within a folded dipole that we can call "transmission line" currents, but this notion has a very limited application and has misled any number of antenna builders. We have already seen that folded dipoles will perform normally with wire spacing values considerably larger than is optimal for a transmission line (13.8" at 10 meters). That condition will neither void nor abet the interesting currents that we shall later call transmission line currents. +

At first glance, a folded dipole operates in ways distinctly unlike a transmission line. For example, in a properly functioning transmission line, at any point along the line, the current magnitudes will be equal, but the current phases will be opposite, that is, 180 degrees apart. If a resonant folded dipole acted as a transmission line, we should expect to see the same pattern of current values between the two wires.

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To demonstrate this, we can use the model on the lower half of Fig. 3 to derive the currents along the transmission line. A sample every 20% of the way of a line nearly, but not quite, 1 wavelength long is instructive. We shall present two sets of current phase figures for wire #2: onset derived from the modeling convention of continuously developing the model from left to right, the other from using the dipole junction as the starting point for both wires.

+ 
+    Currents            Wire 1                        Wire 2
+Distance       Magnitude      Phase          Magnitude      Phase
+  0%           1.001          -  0.1         1.001          -  0.0/ 180.0
+ 20%           0.419            18.1         0.419            18.1/-162.0
+ 40%           0.758           173.5         0.758           173.5/-  6.5
+ 60%           0.861          -174.6         0.861          -174.6/   5.4
+ 80%           0.270          - 31.1         0.270          - 31.0/ 148.8
+100%           0.999          -  0.2         0.999          -  0.2/ 179.8
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The modeling convention that runs the transmission line wires in opposite directions shows essentially the same values for each point on the line. The convention that starts and ends them in the same direction shows the 180-degree out-of-phase condition.

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To illustrate what we actually encounter with a folded dipole, let us turn to the upper portion of Fig. 3. The markers represent percentages of distance from the outer end of each wire inward toward the center. If we plot the current magnitudes and phases for a typical folded dipole, we end up with an interesting chart. Let's use our #18 bare copper wire folded dipole with 3" spacing as a test case. Current magnitudes are relative to a maximum value of 1.0, while current phases are relative to a feedpoint value of 0.0 degrees. The first current phase figure for Wire 2 is for continuous modeling so the end 2 of one wire becomes end 1 of the next. The second value presumes a model with both parallel wires starting at the same end of the assembly.

+ 
+    Currents            Wire 1                        Wire 2
+Distance       Magnitude      Phase          Magnitude      Phase
+ 0% (end)      0.256          - 74.5         0.244          -106.4/  73.6
+10%            0.463          - 33.8         0.432          -153.0/  27.0
+20%            0.682          - 20.2         0.659          -166.5/  13.5
+30%            0.855          - 12.4         0.842          -172.6/   7.4
+40%            0.964          -  6.2         0.960          -176.1/   3.9
+50%            1.000             0.0         1.000          -177.9/   2.1
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The chart ends at the antenna center point because the opposite side of the antenna shows virtually identical current values at the prescribed points. Although the current magnitudes are comparable (and would be closer had the wire been without any loss at all), the current phase values show a curious pattern. Corresponding points along the wires show similar absolute current phase values, but they are opposite in sign when both wires are modeled from the same point (e.g., left to right). The pattern is distinctly unlike a transmission line that is acting like a transmission line, even with the far end a short circuit.

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A phase pattern similar to the one shown is necessary if the folded dipole is to radiate. Radiation is simply the ability of the fields that result from the current levels at each point along the antenna to expand without limit. This condition is unlike that in a transmission line, where the fields are confined such that radiation is negligible. For that condition to exist, the current magnitudes would have to be equal, and the phase values must be exactly opposite. So we have a mystery: how can we make sense out of the current magnitudes and phases along a folded dipole?

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The Transmission Line Inside the Folded Dipole

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The pattern of current magnitudes and phase angle hides a small tale, one about the fact that a folded dipole has two sets of currents. It is the combination of these two current sets that results in the readings. One set is the radiation currents (Ir), which should be (if the tale is correct) quite similar to those on a standard dipole. The other set is comprised of what some call "transmission line" currents (It). From the modeled current readings, we can separate the two sets. All we need to do is take half the sum of the currents at corresponding points along the folded dipole and we get the value of Ir. If we take half the difference of the currents on each wire, we arrive at It. Kuecken pointed this out in his book Antennas and Transmission lines.

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The following table provides the modeled values for a bare-wire folded dipole resonant at 28.0 MHz. The values given are for the fed wire (Wire 1), the "other wire" (Wire 2), It (transmission line current), Ir (radiation current), and the corresponding current value for a single wire resonant dipole at the same relative distance from the end. The sampled positions are 10, 30, 50, and 80 percent of the distance from one end of the antenna toward the feedpoint in the center. For each entry, the format is current magnitude/phase angle, where the magnitude is relative to a feedpoint current of 1.0, and the phase angle is in degrees relative to a feedpoint phase angle of 0.0 degrees

+ 
+                     Folded Dipole Currents (with Dipole Currents for Comparison)
+
+                                        Folded Dipole                           Standard Dipole
+Position                Wire 1          Wire 2          It              Ir              I
+ 10             0.3740/-59.38   0.3449/+57.79   0.3069/-89.38   0.1878/-4.59    0.1748/-4.44
+ 30             0.5809/-32.42   0.5437/+27.04   0.2973/-89.38   0.4884/-3.77    0.4771/-3.86
+ 50             0.7769/-19.77   0.7506/+14.68   0.4530/-89.93   0.7295/-2.85    0.7228/-3.06
+ 80             0.9649/- 7.61   0.9584/+ 5.63   0.1109/-89.30   0.9552/-1.01    0.9541/-1.60
+
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There is a very good correlation between the folded-dipole radiation currents as derived by the simple summing method and the single-wire dipole currents at the corresponding points along the antenna length. The correlation cannot be perfect, because the simple summing method does not take into account the currents on the end wires of the folded dipole. They are short, but significant. The current magnitude and phase angle both undergo part of their continuing change in those wires. Nevertheless, the differences between the folded-dipole radiation currents and the corresponding currents on a single-wire dipole are small enough that we should expect to discover any difference in the radiation strength or pattern between the two antennas. And, of course, we do not.

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Ideally, the transmission line currents should all show a phase angle of -90 degrees. The very slight offset is due both to the end wire phase angle changes and to the resistance of the copper wire used in the test model (composed of AWG #18 wire with a diameter of 0.0403" along with a wire spacing of 1"). Also ideally, the magnitudes should be the same at each point, but are not for similar reasons.

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The key element in the transmission line currents is their relative phase angle--almost perfectly -90 degrees out of phase with the source current. Hence, the transmission line currents represent stored energy rather than expended energy, except for the minute offset from a perfect -90 degrees. As a result, the radiation currents consume all of the RF energy supplied to the antenna in the form of its transformation into indefinitely large expanding electromagnetic fields. Despite energy storage, there is none left over at the end of a transmission.

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The existence of transmission line currents within a folded dipole has resulted in a number of erroneous practices based on the use of transmission lines as transmission lines. For example, some folks have proposed that we short the folded dipole at a position equal to a quarter wavelength from the feedpoint outward times the velocity factor of the parallel line used to form the folded dipole. This practice remains to be modeled in NEC-4, which permits the modeler to provide each wire with an insulating sheath with a specified conductivity and dielectric constant.

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The first step in considering antennas made from insulated wire is to consider the normal range of velocity factors that apply to antennas (in contrast to those that apply to transmission lines). I began with a 28-MHz dipole that was 204" long and fed in the center of the bare AWG #14 (0.0641" diameter) wire. Then I modeled an identical antenna, but added an insulated sheath with a dielectric constant of 2.5 (about in the middle of the plastics materials range used for wire) and a conductivity of 1e-10 Ohms/meter (a very good insulator). I made the insulation about .047" thick--a goodly insulation. Then I re-resonated the dipole at a length of 195.66". This yielded a velocity factor for the insulated wire of 0.959, a typical value for heavily insulated wire. Thinner insulation would have yielded higher values--or longer resonant dipoles. This little exercise gives us something against which to compare a folded dipole composed of insulated wire.

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I went through the same exercise with the folded dipole which we examined in its bareness: 2 AWG #18 wires separated by an inch center-to-center. The original folded dipole was 198" long at resonance. Then I covered the wires with insulation that was also 0.47" thick and re-resonated the assembly. The new folded dipole was 191.5" long, for a velocity factor of 0.968, slightly higher than our single wire dipole. In both cases--the single-wire and the folded dipoles, the feedpoint impedance decreased due to the shortening of the wires. The single wire dipole went from 72.8 Ohms bare to 67.7 Ohm thickly covered. The folded dipole dropped from 289.2 Ohms bare to 274.1 Ohms thickly covered.

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I next took down the current readings on both wires so that I could calculate the radiation currents (Ir) and the transmission line currents (It) to see if they corresponded to those in the bare wire folded dipole. The calculations yielded the following table.

+ 
+                     Insulated Folded Dipole Currents (with Dipole Currents for Comparison)
+
+                                        Folded Dipole                           Standard Dipole
+Position                Wire 1          Wire 2          It              Ir              I
+ 10             0.3914/-60.83   0.3531/+57.53   0.3198/-89.89   0.1914/-6.57    0.1748/-4.44
+ 30             0.5946/-34.45   0.5435/+25.88   0.2868/-89.87   0.4922/-5.77    0.4771/-3.86
+ 50             0.7845/-21.40   0.7468/+12.52   0.2241/-89.82   0.7324/-4.87    0.7228/-3.06
+ 80             0.9656/- 8.32   0.9546/+ 2.28   0.0889/-89.49   0.9560/-3.05    0.9541/-1.60
+
+

Nothing in the new table distinguishes the currents in the insulated folded dipole from those of the bare wire version, with the possible exception of a nearly uniform 2-degree displacement of the radiation currents. Allowing for the fact that the technique of calculation is approximate--due to reason noted earlier--nothing in the table suggests that we should treat an insulated folded dipole any differently from a bare-wire folded dipole once each is brought to resonance. In fact, both the bare and insulated versions of the antenna show the same gain.

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Indeed, the current progression in the insulated wires shows only a single set of curves each side of the feedpoint position, just like the progression in the bare wire version. The upshot is that we need not treat a resonant folded dipole made of insulated parallel transmission line like a transmission line. We can ignore the "transmission line" velocity factor and simply adjust the overall antenna length according to the antenna velocity factor created by the line insulation. The practice of shorting out a folded dipole at the point indicated by the transmission line velocity factor has never shown any evidence of doing anything but shorting out the wires at that point. Finding the resonant length of the folded dipole will be challenge enough.

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Other Impedance Values

The folded dipole is ultimately simply a dipole with an impedance transformation mechanism built into its structure. As a dipole, on its fundamental frequency, it provides all of the performance we expect from a dipole--no more and no less. It tends to have a slightly wider SWR operating bandwidth (when transformed to our feedline value) than a single wire dipole because it acts like a fat wire. But it remains in performance simply a dipole. +

The impedance transformation possibilities, however, should not be overlooked. The rules of thumb for transformation ratios that are more than or less than 4:1 can be useful in some contexts. Before looking at potential applications, let's first look briefly at the levels of departure from 4:1 as we systematically vary the element diameters. We shall use the 3" spacing from earlier samples, but this time, we shall run each wire through a range of 0.1 to 0.5 inches in diameter--with one wire increasing as the other decreases.

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To perform the modeling for this task, we shall set aside NEC-2. NEC has a known difficulty in dealing with closely spaced wires of different diameters. Fortunately, MININEC has no such limitation and handles the calculation task with ease. We shall list the impedance ratio calculated by the equation, the resultant feedpoint impedance, and then the modeled values. This should give us a quick view as to whether the calculations and models reliably coincide.

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+--------- Calculated ---------------    --------- Modeled ----------------
+Diameter  Diameter  Z Ratio   Feed Z    Length    Gain      Feed Impedance
+  d1         d2               R=Z Ohms  inches    dBi       R +/- jX Ohms
+0.1       0.5       7.01      498       193.34    2.09      493.0 + j0.0
+0.2       0.4       5.09      361       193.20    2.10      363.0 + j0.0
+0.3       0.3       4.00      284       193.10    2.10      288.0 - j0.0
+0.4       0.2       3.23      229       193.48    2.11      234.0 - j0.0
+0.5       0.1       2.58      183       193.96    2.11      189.0 - j0.0
+
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Given that the calculations do not account for the end wires, the coincidence of models and calculations is excellent. Incidentally, in all models, the end wires were sized to match the smaller of the two diameters involved. Moreover, the absence of any perceptible change of gain in the series of models is notable. However we size the wires in our folded dipole, it gives us dipole performance. To at least some degree, this convention accounts for the very small differences in resonant lengths of the models.

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In many beams using the dipole as a driven element, the feedpoint impedance will be far less than 70-72 Ohms. Values from 10 to 50 Ohms are common, although values above 20-25 Ohms are preferred in order to reduce power losses from the accumulation of small resistances at connections. Using a folded dipole with "designer" values for element diameters and spacing, it is possible to raise the impedance to match almost any value higher than the initial feedpoint impedance. One option is to use a low transformation ratio to arrive directly at 50 Ohms. A second option is to use a higher value to arrive at 200 Ohms and then to use a 4:1 balun at the feedpoint to return to 50 Ohms with an accompanying reduction on possible common mode currents on the coax. Although HF use of folded dipole drivers is rare, at VHF they are still very popular.

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The Folded Dipole as a Doublet

Before departing the land of folded dipoles, we should at least glance at the potential of the folded dipole as a multi-band doublet. As a sample, we can look at the performance potential of an 80-meter folded dipole. I resonated a 132.85' version at 3.5 MHz. Wire spacing is about 2' and the wire are about 0.3" in diameter. I then checked the patterns and performance on other amateur bands. Numbers are rounded, since we are looking only for suggestive results. + 
+Frequency      Max. Gain      Feed Impedance      Pattern
+  MHz            dBi          R +/- jX Ohms       No. of lobes
+ 3.5           2.12           287 - j   1          2
+ 7.0           2.27             5 - j 160          2
+10.1           3.31           540 - j 750          6
+14.0           3.34            25 - j 330          4
+18.1           4.71           480 + j  15         10
+21.0           4.26            85 - j 530          6
+24.9           4.75           550 - j 310         14
+28.0           5.03           225 - j 750          8
+
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The gain figures and the number of pattern lobes coincide with numbers we would obtain from a single-wire dipole pressed into multi-band doublet service. What differs is the impedance value set. The difficulty of using a folded dipole on an even harmonic of the band for which it is initially resonated lies in the very low resistive component of the feedpoint impedance. By the sixth harmonic, we have a value that, while low, is well within the capabilities of most ATUs. In contrast, the second harmonic impedance of 5 Ohms is likely beyond the reach--or at least the efficient range--of most ATUs. The 4th harmonic (20 meters in this sample) might well be matchable, depending upon ATU design.

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Fig. 4 shows the free-space azimuth pattern for 14 MHz, with its typical 2 wavelength 4-lobe pattern. Fig. 5 presents the 6-lobe, 3 wavelength pattern for 21 MHz. The point of these figures shows up in Fig. 6, the pattern for 18.1 MHz. At about 2.5 wavelengths long, the antenna shows both the growing lobes for the 3 wavelength pattern and the diminishing lobes for the 2 wavelength pattern--for a total of 10 lobes.

+

Using a folded dipole as a multi-band doublet--with parallel feedline to an antenna tuner--thus becomes a matter of matching rather than of pattern development. Very low impedances may also be lossy, thus reducing performance even if a match can be obtained from a given ATU and feedline length.

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For multi-band use, a folded dipole offers no advantage over a single-wire doublet of the same approximate length. Indeed, in the final analysis, perhaps the only reason for using a folded dipole is where the impedance transformation is of special interest, that is, where it may resolve an antenna design challenge. A secondary use would be to offer a path to discharge static charge build-up and thus to reduce one (of the many) noise sources. However, there are other means to this same goal.

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Otherwise, the folded dipole performs just like a fat single-wire dipole.

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Two Variations on the Folded Dipole

In its standard form, we normally feed a folded dipole at the center of one of its two long wires. Which wire we select for the feedpoint matters only if the antenna performs a "non-standard" impedance transformation, that is, has two wires with unequal diameters. There are variations on this feedpoint position, if the impedance transformation is unimportant. For example, if we are creating a VHF or UHF J-pole using parallel transmission line as our material, we need not do away with the seemingly unused wire that we separate from the matching section. Instead, we may connect one or both ends to the radiating element that is continuous with the matching section. For further information on J-pole variations of end-fed folded dipoles, see "What is a Slim Jim?". +

There are also two interesting variations of the folded dipole, as suggested in Fig. 7. We may call them the end-gapped version and the center-short version.

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The end-gapped version of the folded dipole simply omits the end wire, but only one end-wire. A folded dipole is actually two linear dipoles in close proximity--close enough that the wires show transmission-line as well as radiation currents. The dipoles meet at high-voltage, low-current points as each end. We may open one of the high-voltage region contacts with very little effect on the basic antenna properties, that is, on the radiation pattern and the feedpoint impedance. We might have to readjust the total length of the antenna if a resonant feedpoint impedance is important to a given antenna installation. But we would not change the performance as a radiating element.

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The version of the folded dipole with the center short from one long wire to the other has a special application. Suppose that we feed the antenna (very slightly off-center, of course) with a transmission line for which one conductor forms a common or ground lead. We might connect the common lead to the short and the other lead to the long wire. In the process, we do not change the essential performance properties of the folded dipole. However, we do obtain a means of connecting the structure to the support mast in the VHF and UHF ranges. That configuration reduces the likelihood that surges from electrical storms will be conveyed to the equipment.

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Although I have run both types of folded-dipole variants through numerous models at VHF, let's set them up using our 10-meter model. The standard version uses two AWG #18 wires spaced 1" apart. With a total length of 198", the model uses 199 segments per long wire. The model of the end-gapped folded dipole simple omits one of the 1-segment end wires, but is otherwise identical to the standard model. The center-short version requires a small set of changes. The long wires each become two wires that meet at the center. Each of these wires has 99 segments. I added a new wire from one center junction to the other. I then placed the feedpoint or source on the first segment of the wire extending from the short to the end. If my descriptions have been correct, we should expect virtually identical performance from the three folded-dipole variations.

+ 
+Modeled performance of 3 folded-dipole variations in a free-space environment
+Version          Gain   Feedpoint Impedance
+                 dBi    R +/- jX Ohms
+Standard         2.10   289.1 + j 2.6
+End-Gapped       2.09   287.8 + j 1.4
+Center-Shorted   2.10   288.0 + j 9.3
+
+

The only way to tell the antennas apart--besides the obvious visible differences--is to perform a current-sorting exercise on the 3 versions. I did this for some VHF folded dipoles. Fig. 8 shows the radiation currents along the standard and the end-gapped version of 2-meter folded dipoles. Because the center-short version has connections at both ends, the currents do not drop as close to zero in the end segments as they do with one end of the end-gap version. (Of course, NEC current reports never go quite to zero in a linear wire end segment because the effective position for the current is at the center of the last segment, not its outer end.) Therefore, the center-short and the standard versions of folded dipole have the same radiation-current curves (within limits that are too small to show up in these kinds of graphs).

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Where the currents for the 3 antennas show significant variation is in the pattern of transmission line currents. Essentially, for all three versions of the folded dipole, the current phase is 90 degrees from the phase of the current at the source or feedpoint. However, the transmission-line current magnitude for the standard folded dipole shows a symmetrical pattern with its minimum at the long-wire center and maximum values at the long-wire ends. Fig. 9 shows this pattern for the standard folded dipole, using a VHF model. Interestingly, both the end-gapped version and the center-short versions show virtually identical patterns that vary from the standard version. From the feedpoint toward the open end of the end-gap version or from the shorting bar away from the feedpoint, the transmission-line currents decrease from their feedpoint region value toward zero. At the same time, the current magnitude distribution on the feedpoint side toward the closed end (to the right on the graph) result in higher current magnitudes--in fact about as much higher than the standard version as the low end is lower than the standard version. However, at the center of the antenna, the transmission-line currents have very comparable values.

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The differences in transmission-line current distribution between standard and variant versions would make a difference only if we end-feed the folded dipole, as in the many variations on the J-pole, and then only in the impedance at the end feedpoint. However, the center-short version of the antenna is normally fed at the center or as close to it as may be feasible. Hence, we would not be able on range tests to tell the difference between the center-short version and a standard version. Equally, the construction difference used for the end-gap version would hide itself in range test, which would show only the radiation patterns and field strengths for any tested version.

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You might note that these notes on the folded dipole do not have a section entitled "conclusion." As well, you may also note the multiple updates to these notes. Each time that I think these notes should end, I learn something new and interesting (at least to me) about folded dipole behavior. I have no good reason to think that my latest additions and revisions should be any different.

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Updated 03-12-2000, 12-04-2001, 09-24-2004, 10-02-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: Dipole, Doublet, HF Lower, HF Upper


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Short Folded Monopoles
+ Some Basic Properties

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L. B. Cebik, W4RNL

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In "What is a Fold Monopole?", we examine some basic properties of resonant folded monopoles using 2, 3, 4, and 5 wire construction. When resonant, modeled folded monopoles show a clear relationship between the reported source impedance and the calculated impedance using the classical equation.

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R is the ratio between the impedance of the new folded antenna and the impedance of a resonant linear antenna that otherwise has the same design. The equation applies equally to folded dipoles and to folded monopoles. Where the diameters of both the fed wire (d1) and the return wire (d2) are the same, the ratio is 4:1. The new impedance follows a very simple equation:

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Since the feedpoint (or source) impedance (Zlinear) of a linear monopole over perfect ground is 36 Ohms, the resonant feedpoint impedance of a folded monopole (Zfolded) is 144 Ohms. If the fed wire is fatter than the return wire, then the impedance ratio is less than 4 but always greater than 1. If the return wire is fatter than the fed wire, then the impedance ratio is always greater than 4.

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The basic principles in our initial foray into folded monopoles neglected a very important aspect of folded monopole use. Many antenna builder use lengths that are shorter than the resonant length. For very short to moderate folded monopole lengths, (where the resonant length might be considered long), the feedpoint impedance will show an inductive reactance. In that property, a short folded monopole bears a resemblance to a transmission-line shorted stub. However, the stub and the antenna have some important differences, crudely marked in Fig. 1.

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The two structures are similar in that the properties are dependent on the diameter of the wires and on the spacing between wires. The letters s, d, d1, and d2 designate these fundamentals that make performance dependent to a significant degree on physical properties of the structure. The folded monopole requires a ground (or a suitable ground plane) in order to operate. The energy source is normally positioned in series with the lower end of one wire (d1) and the ground. In contrast, the shorted stub uses no ground. Rather, the energy source is placed across the two wires of the transmission line opposite the shorted end. As a consequence, the shorted transmission-line stub does not radiate (if properly constructed and isolated from influences that would create imbalance between the lines). It ideally shows only transmission-line currents, which are equal in magnitude and opposite in phase at points along the line that are equidistant from the energy source. The folded monopole radiates and therefore exhibits both transmission-line currents and radiation currents.

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At this point, we have to choose a direction for analyzing the behavior of short folded monopoles. We might legitimately turn to a mathematical treatment of the structures. However, my goal is not to replicate texts on the subject, but rather to familiarize you with the patterns of short folded monopole behavior. Therefore, my chosen route of analysis is modeling some selected folded monopoles to develop some patterns in the behavior. The method will be effective in showing some of the variables that influence the behavior, while also developing some rational expectations of them. We shall choose our modeling software to fit the structure that we are modeling. For our first two case studies, NEC-4 is adequate to the task, although we shall pay close attention to the Average Gain Test (AGT) score (where 1.000 is ideal) in order to adjust numbers as needed.

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Since we shall not be dealing in resonant antenna lengths, we need an increment of folded monopole length to use for our samples. One convention used in the AM BC industry is to list antenna lengths in electrical degrees, where 1 wavelength equals 360 degrees. We may adopt this convention for physical lengths even though we know in advance that 90 degrees physical is longer than the resonant physical length that we would call 90 degrees electrical length. We shall survey folded monopoles every 10 degrees at a standard test frequency of 3.5 MHz for the entire exercise. To reduce the number of variables, we shall use lossless or perfect wire along with a perfect ground. As well, in this initial investigation, we shall work only with 2-wire folded monopoles.

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Case 1: d1 = d2 = 0.1", s = 12"

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We may begin with a folded monopole structure already explored in the earlier item. We shall form a set of folded monopoles where both wires have a diameter of 0.1" and the spacing is 12" between them (center-to-center). The use of 0.1" diameter wire is not accidental. It roughly corresponds to AWG #10 wire, which falls between two practical extremes. Amateurs often used AWG #14 or #12 wire for such structures due to its availability and relatively low cost. Commercial installations may use wire that approximates AWG #6 (0.16").

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At a resonant length of 67.25', the modeled impedance is 143.5 Ohms, compared to the calculated value of 144 Ohms. When we model the antennas in the collection in 10-degree increments, we end up with a set of performance values such as those shown in Table 1.

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Besides showing the length of each model in degrees and feet, the table lists the source resistance and reactance of each model. It also lists the AGT in terms of the score and the gain adjustment in dB (where the adjustment value is subtracted from the reported value). Because all but the 10-degree scores are very close to 1.000, the table makes no adjustments in this case.

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There is much to note in the tabular data. We might begin with the gain values, which we show in terms of the gain broadside to the plane of the 2 wires and in terms of the maximum gain in line or edgewise to the 2 wires. Maximum gain occurs in the direction of the feedpoint. There is always at least a slight difference in the 2 values, but as we make the folded monopole shorter, the differential becomes very noticeable. Fig. 2 compares the elevation patterns for 10-degree and 30-degree versions of the antenna. In each case, the plots overlay the patterns broadside and edgewise to the wires. The shorter antenna shows a large difference that almost completely disappears by the time the antenna is 30 degrees long.

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One way to make sense of the remaining data in the table is to contrast it to corresponding data for an equivalent linear monopole. Therefore, I created a model of a monopole that showed a resonant length of 67.25', the resonant length of the folded monopole. The model required a wire diameter (d) of 2.75" to achieve this goal. Fig. 3 shows a sketch of the 2 antennas.

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I then sampled the antenna in 10-degree intervals to produce a table comparable to the one for the folded monopole. The results of this exercise appear in Table 2. The columns in this table exactly parallel those of Table 1.

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Both tables list the gain of the antenna over perfect ground using 3 different wire compositions: perfect or lossless, copper, and aluminum. Copper has a bulk resistivity of about 1.7E-8 Ohms/meter (corresponding to a conductivity of about 5.8E7 S/m). Aluminum's resistivity is about 4E-8 Ohms/m (conductivity about 2.5E7 S/m). Antenna modeling programs adjust the material losses for frequency and skin affect in actual calculations. Hence, the gain values for perfect or lossless wire would reappear at any frequency, but the gain values will vary a bit as we change frequency if we use copper, aluminum, or any other real wire material.

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Fig. 4 compares the gain values from the tables for all sampled lengths. The values for the 2.75" linear monopole are for aluminum only, since the differences between pefect wire and the worst case used in the sample are so small. However, with wires that are only 0.1" in diameter, the material losses of copper and aluminum are exceptionally significant as we reduce the overall length of a folded monopole. Below a length of about 50 degrees, the thin-wire folded monopole shows a rate of gain decrease that may question the practicality of using such a thin, short structure as an antenna without specific needs that make the highly reduced gain acceptable as a trade-off.

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At resonant length, the folded monopole may rival the linear monopole, but at very short lengths, the very low source radiation resistance becomes only s small fraction of the total source resistance. The wires are too thin to overcome the resistive losses of the material and of skin effect. With real wire, the 10-degree folded monopole shows less than 1% power efficiency. For the shortest thin-wire folded monopoles in the sample, the use of phosphor bronze or stainless steel would increase losses even further.

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The monopoles that we have examined are over perfect ground. Placing them over real (lossy) ground will further reduce the gain available (as well as raising the elevation angle of maximum radiation). Table 4 provides a rough guide to the amount of further gain reduction we are likely to experience over three levels of ground quality. Very good soil has a conductivity of 0.0303 S/m and a relative permittivity of 20. Average soil uses a conductivity of 0.005 S/m and a relative permittivity of 13. Very poor soil uses a conductivity of 0.001 S/m with a relative permittivity of 5. These widely diverse soil types may let you approximate the additional losses of your local soil by rough interpolation. The radial systems use 0.1" wire buried 1' below the ground surface in the NEC-4 models.

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The table is only a first-order estimation device, not a precise gauge. For increased accuracy, you would need to model a proposed short folded monopole using both the actual material ad the actual ground conditions at the proposed site--along with a model of whatever buried radial system the antenna might use.

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Linear monopoles have gained some renown for their low feedpoint resistance values when they are very short. However, if you compare Table 1 with Table 2, you will discover that the feedpoint resistance of the folded monopole does not catch up to the feedpoint resistance of the linear monopole until we reach a total length of about 40 degrees for both antennas. Fig. 5 compares the feedpoint resistance values for both antennas across the span of surveyed heights.

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The linear monopole resistance values show a smooth progression from 10- through 90-degree lengths, reaching a final value of about 41 Ohms. However, the folded monopole shows a very large spike in values between 50 and 60 degrees. The actual peak value is much higher than the largest graphed value, since the peak occurs at a height of about 57 degrees. Then the resistance value decreases rapidly so that between 80 and 90 degrees, it shows an expected slight rise with increasing length in this region. Even at 90 degrees, somewhat beyond resonance, the resistance is 164 Ohms, about 4 times the linear value for the same length.

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The peaking of the resistance value accompanies a peaking of the the reactance value in folded monopoles. Fig. 6 graphs the reactance for both the folded and the linear monopole as we increase the length from 10 to 90 degrees.

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The linear monopole shows a smooth curve that traces the decreasing capacitive reactance as the antenna lengths increases toward resonance. Since the 90-degree length is long relative to resonance, the curve smoothly proceeds into the region of inductive reactance. In contrast, the folded monopole shows very high values of reactance at 50 and 60 degrees. One may interpolate a sudden shift in reactance type at about the length at which the resistance reaches its maximum value. Of course, at this point, we would find a very small region of height at which the reactance would be nearly zero. However, that specific height is unlikely to be achieved in any practical installation. Even if achieved, a slight temperature change would alter the antenna height enough to throw the reactance into a high value region--either inductive or capacitive, depending on the direction of the temperature shift.

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The very high value of resistance and the sudden shift of reactance from inductive to capacitive are typical behaviors of horizontal antennas as they pass the 1 wavelength mark or of ideal vertical monopoles as they pass through the 1/2 wavelength mark. However, the folded monopole is less than 0.16 wavelength long.

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Fig. 6 contains reactance values for one extra case: a shorted transmission-line stub constructed according to the same wire diameters and spacing values that we used for the folded monopole. I arbitrarily cut off the table at +j5000 Ohms since the reactance value of a shorted stub increases without limit at exactly 90 degrees. Table 3 shows the calculated values of the stub's reactance at the line lengths that correspond to the folded monopole's lengths in the survey.

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The table rests on calculating the characteristic impedance (Zo) from the physical dimensions of parallel wires, as indicated in Fig. 1. One common equation for the calculation uses common logs.

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However, there is a more precise equation that uses natural logs.

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For the case in point, the impedance is high enough (657.22 Ohms) that the two equations yield essentially the same results. The more precise equation becomes essential where the wire spacing is very close. Our 12" spacing is not close for 0.1" diameter wires. To calculate the inductive reactance of the stub, we may use another common equation. The l term represents the line length in electrical degrees (or radians).

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The shorted transmission line that uses 0.1" diameter wires and a 12" spacing has a calculated characteristic impedance (Zo) of 657.22 Ohms. For any given length, the inductive reactance is a direct function of the Zo value, and that value always apears as the inductive reactance at a length of 45 degrees for lossless lines.

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I note these equations only to supply the basis for the tabular and graphical results shown. They suffice to show that the source impedance behavior of the short folded monopole--at least for the sample used here--is quite unlike the behavior of a linear monopole and the behavior of a shorted transmission line stub. To test these behaviors and to check for any variability, we need at least one more sample.

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Case 2: d1 = d2 = 0.5", s = 12"

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As a check on our work, let's sample a second folded monopole through the same total height steps. In this case, we shall increase the wire diameter to 0.5", a 5-fold increase over the initial sample folded monopole. The increased wire diameter applies to all parts of the antenna and so will have no effect on the impedance transformation ratio. The resonant impedance of a modeled antenna was 143.1 - j0.1 Ohms at a height above perfect ground of 66.81' (or 99.3% of the height of the resonant version of the first model).

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Although the use of fatter wires with a 1' spacing does not change the folded monopole impedance transformation ratio, it does change the characteristic impedance of the line if used in a shorted stub configuration. The new Zo is 464.17 Ohms (compared to 657.22 Ohms for the version using 0.1" diameter wires). For reference, Table 5 presents the calculated inductive reactance values for the sampled lengths of the stub in 10 degree increments. The 45-degree entry allows a quick reference to the line Zo.

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Except for the lowest 2 heights (10 and 20 degrees), the NEC-4 models of the antenna produce excellent AGT values. Hence, they require no adjustment in the tabular data. Table 6 provides the information gathered from the test runs using the same format and column entries that we used for the thinner model.

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To facilitate comparisons, I also created a linear monopole over perfect ground. I selected an element diameter that would achieve resonance at the same height (66.81') as the folded monopole in question in order to develop a relatively fair comparator. The required diameter was 5". The diameter is 1.8 times the diameter (2.75") of the comparison linear monopole used for the folded monopole with 0.1" elements. Both folded monopoles use the same center-to-center wire spacing. The exercise establishes that finding an equivalent linear monopole diameter to a given folded monopole structure requires attention to the wire diameter as well as to the wire spacing of the original folded structure.

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Table 7 shows the linear monopole data, again using the format established earlier. Of course, the linear monopole requires only one gain figure, since the pattern is uniform in all azimuth directions. Our initial comparisons will be internal to the new sample. We shall make cross-sample comparisons a bit later.

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The relative gain values appear in Fig. 7. Since the gain of the linear monopole varies so inconsequentially over the range of real materials, the aluminum gain curve suffices as a substitute for 3 overlapping lines. The pattern of gain deficiencies with real materials for the folded monopole below a length of about 50 degrees reappears in this graph and in the tabular data. However, the 5-fold increase in folded monopole wire diameters shows up as a significant reduction in the deficiency level.

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In Fig. 8 we find the comparison of linear and folded monopole source resistance values. The linear monopole resistance increases in a regular (but not linear) fashion. In contrast, the folded monopole shows a very sharp peaking of resistance at about 60 degrees. The positions of the adjacent resistance values suggests that the true peak may be at a length very close to 60 degrees.

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Fig. 9 tracks the progression of reactance values. One line shows the inductive reactance of a shorted transmission-line stub. As I did earlier, I cut off the Y-axis arbitraily, since the 90-degree reactance value increases without limit. (The tables show an exceptionally high but not limitless value for 90 degrees due to computer conventions for avoiding errors.) In contrast, the linear monopole shows a continuous, regular decrease in the capacitive reactance as the antenna grows toward its resonant height. Of course, at a physical height of 90 degrees, the antenna is slightly long relative to resonance, and so we find an inductive reactance.

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The reactance curve for the folded monopole shows peak values of reactance at 50 and 60 degrees, with a transition region between them. The actual transition region is very small, as the reactance on either side climbs to values much higher than those recorded at the sampling points. In the length region that is about +/-10 degress either side of resonance, the reactance curve shows a seemingly normal curve that moves from capacitive to inductive as we pass through the resonant folded monopole length.

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A Tentative Comparison of Two Folded Monopoles

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We have looked individually at two folded monopoles that use the same 12" center-to-center wire spacing. The only difference between them is the diameter of the wires: 0.1" vs. 0.5". Hence, the impedance transformation ratio for both monopoles at a resonant height is the same: 4. Since a linear monopole using either wire diameter--or using the equivalent diameters in the comparators--has a resonant impedance of 36 Ohms (+/- 0.03 Ohm), we expect a resonant folded monopole impedance of 144 Ohms. The thin and think folded monopoles show 143.5 and 143.1 Ohms, respectively. We may consider these values to be very much on target, given the fact that our basic impedance transformation equation does not take into account the diameter or the length of the end wires. The models cannot exist without taking these end-wire factors into account.

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When we look at short folded monopoles using the same basic structure, we have to recognize that we cannot expect a precise equivalence. The length increments use the physical length of the structure, not the electrical length relative to the resonant length. The 0.1" antenna was resonant at a length of 67.25', while the 0.5" version resonated at 66.81'. However, the lengths are less than 1% apart, which minimizes any differentials in this area of concern.

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For a sample of the gain differential, Fig. 10 compares the modeled maximum gain edgewise to the wires for both folded monopoles using copper wire. The thinner-wire folded monopole shows a 7-dB gain deficit compared to the fatter-wire model at the shortest length. As we increase the length of the folded monopole, the gain difference decreases in a smooth curve so that by the time we reach a length of 50 or 60 degrees, the differential disappears (depending on our standard of when a differential is too small to be notable). The root source of the differential lies in skin effect. In small loop antennas, builders commonly use the largest practical conductor (sometimes round, sometimes flat) to reduce to the lowest possible level any losses due to the resistivity of real materials. The losses of the linear monopoles suggest that a wire diameter of well over 2" may be needed by folded monopoles shorter than about 50 degrees in order to reduce these losses effectively. Unfortunately, such diameters are not practical for NEC-4 models.

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Fig. 11 superimposes the source resistance and the reactance curves for the two folded monopoles. Due to the paucity of sampling points, the peak values appear to coincide. However, such curves can be somewhat misleading if we seek more than general guidance. Let's look at each folded monopole.

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0.1" Model: A series of models using finer length gradiations set the height at which the reactance passes through zero at about 42.321' or 54.215 degrees. The resistance in the immediate length region rose to 19540 Ohms. The length of the folded monopole was about 62.9% of a resonant version or about 0.157 wavelength electrically.

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0.5" Model: A similar series of models produced a height of 44.270' or 56.711 degrees at which the reactance passed through zero. At this height, the source resistance report was 10480 Ohms. However, the source resistance peaked (10510 Ohms) at about 44.235' or 56.667 degrees. The zero-reactance model was about 66.26% of a resonant version of the antenna or about 0.166 wavelength electrically.

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We may note several interesting items about these numbers after observing an significant caution. The numbers derive from models that show an ideal AGT score, but which remain subject to all of the limitations to which the antenna modeling software (NEC-4) is subject. Hence, the numbers are useful for comparisons, but not necessarily for trying to build a short, resonant, very-high impedance folded monopole.

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The thinner-wire folded monopole shows a much higher peak source resistance than the fatter-wire model. In fact, the ratio of peak source resistance values is 1.86:1. Although the tests did not specifically seek out the peak values of reactance that occur on the limits of the transition region, the thinner folded monopole appeared to reach values at least 1.6 times higher than the thicker model in the sequence of test model height. In both cases, the transition region was about 2 degrees of height, 56-58 degrees for the 0.5" model and 53 to 55 degrees for the 0.1" model. The transition region includes heights at which the initial peak inductive reactance value begins to decrease and--at the opposite end--the height at which the capacitive reactance increases toward but does not reach its peak value.

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The height at which the folded monopoles pass through zero reactance seems initially counter-intuitive, since we might expect the folded monopole using fatter element wires to pass that point at a shorter height in keeping with the slightly shorter height of a 1/4 wavelength resonant version. As well, the 0.5" model's slight difference between the zero-reactance height and the maximum source resistance height may also seem somewhat counter-intuitive to our understanding of high-impedance resonant points. In both cases, the most likely candidate to serve as the source of these interesting results is the end wire. The potential corner coupling of the 0.5" model might account for both phenomena. However, the models are not self-explanatory in this regard. As well, we cannot say from the model alone whether the phenomena is an artifact of modeling or a real phenomena. Models that mix wire diameters at angular junctions quickly become unreliable in NEC (both -2 and -4).

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The differences in behavior between the two folded monopoles using equal legs, but of a different size for each model, are small. More significant is the general behavior trends that show the progression of antenna behavior with increasing length. First, the very low source resistance of shorter lengths (up to and perhaps beyond 30 degrees) results in a very lossy structure when using real materials of even the finest quality. Second, the very high impedance resonance in the 54- to 56-degree region is notable for both its potentials and its limitations relative to using a short folded monopole. The short folded monopole acts neither like a shorted transmission line nor like a short linear monopole.

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Short Folded Monopoles with Dissimilar-Diameter Legs

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Many folded monopoles make use of an existing structure for one leg and add a wire for the second leg. At resonant 1/4 wavelength sizes, we expect the monopoles to closely approximate calculated values of source impedance. We can do some initial modeling to see what happens as we sample shorter lengths, but we cannot do so reliably within NEC. We must turn to a version of MININEC. For the following examples, I used Antenna Model, a highly corrected version of MININEC 3.13. Fortuitously, the program provides AGT scores as a matter of course.

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To limit the stresses upon the limitations of the core, we may restrict our initial investigation of folded monopoles with unequal leg diameters to only 2 leg sizes: 0.1" and 0.5", the sizes that we used in the first two cases. As shown in Fig. 12, the top wires for the new cases will use the thinner wire size. The black dots represent the location of the model source. In NEC, we generally construe the source location to be along or at the center of the lowest segment in the relevant leg. In MININEC, the source is at the junction of the leg with the ground.

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The ratio of leg diameters is 5:1. However, the equation that calculates the impedance transformation does not use that ratio directly, but incorporates the leg diameter within a ratio with twice the space between legs and then takes the common log of both space-diameter ratios. Hence, the resonant linear monopole source resistance becomes (by calculation) about 210 Ohms when we feed the thinner leg and about 105 Ohms when we feed the fatter leg. The proximity of modeled impedances to the calculated ones becomes a second test (in addition to the model's AGT) of the reliability of the reported data on the short folded monopoles.

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Table 8 provides the data for the version of the folded monopole with the source located on the thinner wire, Case 3. The table omits information on gain values for real wire materials, since that information would largely parallel the data for Cases 1 and 2. The perfect-ground gain data generally parallels the corresponding information for folded monopoles with equal-diameter legs. However, the broadside-to-edgewise gain differential is slightly greater. Although the impedance information for the shortest length appears quite reasonable and the AGT is only slightly off ideal, the gain data appears to need further study before we accept it at face value. In the following notes, gain will not be our main focus.

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Table 9 presents the comparable data for Case 4, which feeds the 0.5" leg of the folded monopole. Although the AGT scores are virtually ideal (at least through 3 decimal places), the gain data is subject to further scrutiny. However, the broadside-to-edgewise gain values more closely parallel those we obtained from the first two cases.

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Whatever the reservations we may apply to the gain data, the most significant data resides in the resistance and reactance columns of the tables. Like the equal-diameter cases, both of the new cases shows exceptionally low source resistance values at the shortest lengths. The tables provide an entry for the resonant length information. In both new cases, the modeled resonant impedances are within 1/2 of 1% of the calculated values.

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The curiosity of the folded monopoles with unequal leg diameters appears clearly in Fig. 13. When we feed the thinner wire, the source resistance peaks close to 60 degrees, or higher than either of the length values that we found in the first two models with equal-diameter legs. In contrast, when we feed the fatter leg, the length that shows peak source resistance is closer to 50 degrees. This length is shorter than we found for the first two cases.

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Due to the very high peak resistance values, the lower source resistance values form almost stright lines, forcing us back to the tables for the interesting properties. When we feed the thinner leg of the folded monopole, we discover a very rapid increase in impedance, beginning at a thousandth of an Ohm and climbing in a span of about 0.16 wavelength to an exceptionally high value. Predicting the source resistance of a physical version of the short Case-3 folded monopole would be a daunting task at best. Even temperature changes might yield significant resistance excursions at the feedpoint unless we use a wideband or a lossy matching network. Case-4 monopoles fair no better for lengths from 10 to 50 degrees. However, the region from 60 through 90 degrees shows a much slower rate of resistance change from one step to the next. Unfortunately, this region also shows consistent capacitive reactance.

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Fig. 14 overlays the reactance curves for the two new cases. In general outline, the curves follow the pattern established by te first two cases that use equal-diameter legs. However, the transition regions call for some special attention. Cases 3 and 4 both show that the transition region occurs between lengths of 50 and 60 degrees. Within that 10-degree span, the two new structures differ considerably. By tracking the level of the 50- and the 60-degree peak values, we can obtain a fairly close approximation of the difference. For example, if we feed the thinner wire (Case 3), then the capacitive reactance at 60 degrees is close to -j3000 Ohms, but the inductive peak at 50 degrees is only a little over j1000 Ohms. The zero-crossing point must therefore occur much closer to the 60-degree mark.

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In contrast, in we feed the fatter wire (Case 4), the inductive reactance peaks at about j8000 Ohms at the 50-degree level. By 60 degrees, the capacitive reactance is about -j1000 Ohms. By the same reasoning, we must conclude that the zero-crossing point for this configuration is not much above 50 degrees physical length.

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More generally, we see a widening of the possible range for reactance transitions and resistance peaks with these cases than when we simply change the diameter of equal-diameter versions of the folded monopole. A thin-fed wire to fat-return wire situation tends to push the transition point to a higher length level. In contrast, a fat-fed wire to a thin-return wire pushes the zero-crossing point to a lower total fold monopole height.

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Some Tentative Conclusions

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Modeling demonstrations do not yield proofs of performance. However, from the general trends that we have observed with our four case studies, we may draw some conclusions that we may think of as reasonable expectations of folded monopole performance.

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1. At very short lengths (up to 30 to 40 degrees), 2-wire folded monopoles of any description show very low source resistance values. The values are lower than we obtain with linear monopoles of the same height. In fact, it is in this region that we find the closest coincidence between folded monopole and shorted transmission-line stub behavior with respect to the inductive reactance. When we translate the models to real types of wire, material losses alone are sufficient to create very high gain deficits. Below a total height of about 30 degrees, the losses may be high enough to jeopardize the utility of the structures for communications.

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2. Between heights of 50 and 60 degrees, we find a transition region in which the resistance rises to a very high peak value. In the same region, the reactance peaks both inductively and capacitively, with a very small height region in which it crosses the zero point. The behavior closely resembles the behavior of center-fed linear horizontal antennas as they they approach 1 wavelength or of linear monopoles as they approach 1/2 wavelength. In folded dipoles, the behavior occurs with lengths between 0.14 and 0.17 wavelength.

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3. Although the region of peak values between 50 and 60 degrees dominates graphs of the folded monopole's feedpoint performance, the entire span from 40 to 70 degrees shows rapid changes in both resistance and reactance with only small changes in folded monopole height. These behaviors can make the matching of a folded monopole in this height region a very finicky task. In all cases, one must experimentally determine if the settings used will be stable through the entire set of environmental conditions that the antenna may face.

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4. The most stable region of folded monopole performance occurs at physical lengths between about 70 and somewhere above 90 degrees. In virtually all cases, resonance will occur at physical heights between 80 and 85 degrees. Within the overall region, the resistance changes per unit of height change are relatively small. Reactance changes are likewise small and follow the normal progression from capacitive reactance below resonant length to inductive reactance above resonant length. Therefore, matching networks and wide-band impedance transformers will tend to show the same performance characteristics that they display when used with linear antennas.

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5. For every resonant folded monopole, there is a linear monopole of some diameter that will resonate at the same length. The required diameter for the linear dipole is a mutual function of both the wire diameters and the wire spacing of the folded monopole. Since the equivalent linear monopole will be very large relative to the diameters of the wires within the folded monopole, it will exhibit far lower losses with real materials than the folded monopole using the same real materials, especially at very short lengths. However, the folded monopole may offer a considerable total weight reduction relative to the linear monopole, especially at longer, more stable overall heights.

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In the tables, the numbers recorded are overly precise relative to the general reliability of the models with respect to reality. My reason for recording the reported modeling data in these terms was to ensure accurate graphing. At best, these notes serve as a general guide to reasonable expectations from folded monopoles. By omitting real ground types and real materials from the calculations, the notes do not qualify as guides to building a physical antenna. Nonetheless, the consistency of the general trends may provide some insight into short folded monopole behavior.

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In the cases that we have explored in this set of notes, both legs of the short folded monopoles used the same length, and the top wire shorted the upper end of the structure. However, short folded monopoles often find application where the return wire is longer than the fed wire. We have learned to name such applications, but it is less clear that we have developed any reasonable expectations of behavior. Therefore, we have another trail to explore through the forest of folded monopoles.

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Apprendix: A supplementary Exercise in Current Analysis

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The exercises that we have explored in developing some basic properties of folded monopole antennas focused upon antenna gain and the feedpoint impedance as guides. There is an alternative approach that may provide additional insights into the behavior of short and long folded monopoles. We may analyze the currents in the legs of the folded monopole into two component currents, often called radiation currents and transmission-line currents. At any point along the length of the folded monopole, the sum of the two current magnitudes and phase angles (one on each leg) result in the radiation curreent, while the difference yields the transmission-line current, assuming that we set up the model wires for the legs in parallel fashion, that is, counting from the ground up (or the top down) for both legs. See the Antenna Modeling series of articles, #123, for details of how to set up the calculations. Although NEC output files list the currents in terms of both real and imaginary components and of magnitude and phase angle, EZNEC current tables list only the magnitude and phase angle. Thus, the first step is convert the given values to real and imaginary components, then to perform the additions and subtractions, and finally to reconvert the values back into magnitudes and phase angles. A repetitive spreadsheet is, of course, the most convenient method for automating the required machinations.

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If we perform the operation on a resonant folded monopole at 3.5 MHz, we obtain some interesting results. For the subject antenna using 0.1"-diameter elements and a separation of 1', the resonant length is 67.25 or 86.15 degrees. For comparison, let's also set up a resonant linear monopole of the same length. The linear monopole must have a diameter to 2.75" to be resonant at the prescribed physical length. For simplicity, we shall set both antennas against a perflect ground and use perfect (or zero-loss) conductors. NEC, of course, will provide a direct reading of currents on the linear monopole because it has no currents that we can analyze as transmission-line currents.

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The results of the exercise appear in Table 10. On the left, the first four current magnitude and phase columns provide magnitude and phase-angle values from the EZNEC current table every 5 segments along the antenna's length from the ground upward. The next two columns provide the analyzed radiation current (Irad) magnitude and phase angle for each increment of antenna length. The final two columns list the analyzed transmission-line current (Itl) magnitude and phase angle. To the right are the current values for the linear monopole model.

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Except for the 60th segment, the radiation current magnitude values for both antennas are virtually identical. The slight aberration in the last value is a function of the folded monopole top connecting wire. Minimum current occurs at its center. As well, the pattern, although not the precise values, of radiation current phase is the same for both antennas. With respect to transmission-line currents on the folded monopole, the magnitude values increase from the ground toward the top. However, the phase angle of these currents is the same all along the antenna and 90 degrees out of phase with the feedpoint current. We would see similar results from a folded dipole counting from the feedpoint outward to the antenna end.

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Next, let's examine a short folded monopole, perhaps one that is 20 degrees (15.612') long. We may not only perform a similar analysis (using each of the 12 segments in the model), but as well we may again compare it with the corresponding 2.75"-diameter linear monopole of the same length. The results appear in Table 11.

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The linear monopole on the right displays a normal progesssion of currents from the ground upward, despite the very short length of the antenna. However, the folded monopole shows something entirely different, due to the fact that the overall length falls well below the critical region (between 40- and 60-degree lengths) in which the antenna transitions from transmission-line-like behavior to antenna-like behavior. (See Fig. 6, which shows the reactance of a comparable transmission line, a folded monopole and a linear monopole to see more vividly the critical transition length region.) At the very short length of 20 degrees, the folded monopole shows far higher current magnitude in the transmission-line column than in the radiation column. Because the two wires, treated as a transmission line, are almost perfectly out of phase with each other, the net phase angle is zero and constant along the short length. The minuscule radiation current magnitude is accompanied by a minimal phase-angle shift that only become apparent at the top of the folded monopole.

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Applying the current analysis to the modeled current values for the short folded monopole yields an impression that the short folded monopole is likely to be a relatively poor radiator. In some applications, it might actually be superior to the short linear monopole once we add to the single element the requisite loading coil at a plausible level of Q. Nevertheless, below the critical transition length region, the short folded monopole principally acts like a shorted transmission line rather than like an antenna.

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Updated 01-01-2006, 04-01-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Return to Main Index

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Topics: HF Lower, Vertical


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Short Folded Monopoles
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L. B. Cebik, W4RNL

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In "What is a Fold Monopole?", we briefly explored the use of a folded monopole that was self-resonant but which also used a linear extension. The result, as expected, involved an increase in both the resistance and the inductive reactance at the source or feedpoint. The folded monopole continued its normal antenna function in terms of radiation, with a small increase in gain due to the increased overall length.

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In the first episode of this 2-part examination of short folded monopoles, we explored the properties of complete antennas, that is, folded monopoles that used equal-length legs. We saw a progression of properties from physical lengths of 10 through 90 degrees. The progression may have held some surprises for those not used to folded monopole behavior. At very short lengths (up to 30 degrees or so), the source resistance was very low, lower than for an equivalent linear monopole. In the 50- to 60-degree region, the source resistance became very high, with an accompanying set of peaks for inductive and capacitive reactance--and a narrow zero-crossing length between them. Only as the folded monopole exceeded about 70 degrees did the source impedance curves return to behaviors that we associated with linear monopoles adjusted for the impedance transformation that is inherent to the folded structure.

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In this item, we shall combine the two ideas into a single exploration. We shall look at short folded monopoles from 10 through 90 degrees with linear extensions. One goal will be to see what patterns of antenna performance emerge from the exercises.

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One might well wonder whether the exercise might be simply the satisfaction of idle curiosity. We do not normally hear of extended short folded monopoles among the many classes of antennas used by amateur or commercial interests. Just as a rose by any other name would smell as sweet, so an antenna by any other name would radiate just as well. There are a number of structures composed of extended short folded monopoles that we have managed to re-name--and sometimes, to misunderstand as a result of the different name. In the vagaries of labels lie many roads to misconception.

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Consider the left-hand side of Fig. 1. The sketch shows a grounded tower fed for one of the lower amateur bands by what we call a shunt feed system. We connect a wire parallel to the tower. The top end connects to the tower so that the wire length combined with its distance from the tower allow--so we usually say--coupling to the tower. We strive for a length that will yield a feedpoint impedance we can easily match to coaxial cable using the simplest network for lowest losses. The wire length usually emerges from experience, and AWG #12 is popular for the purpose. One instruction set that I read suggests that if the feedpoint impedance is not within a desirable range, we should change the spacing from the tower until the impedance is acceptable.

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On the right in Fig. 1, we have a short folded monopole that places its top wire at a height which is not the full length of the return wire. The return wire happens to be a tower structure that is very wide. Hence, we obtain a very sizable step-up in impedance relative to a linear wire of the same length. Since the tower goes on above the folded monopole, we anticipate that the feedpoint impedance will show an increase, if we assume that the folded monopole portion is self resonant. If the folded monopole section is shorter than resonant, then our work so far leaves the impedance unknown. So the sketch has added a network at the feedpoint in case we need it to effect a match with the main feedline.

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The perspective that we took in the right portion of the sketch makes clear that the fed wire is as much a part of the radiating structure as the tower. Its function is not simply to couple energy to the tower. Rather, its function is to form with the tower a single radiating element. The 2-wire portion of the structure effects an impedance transformation relative to the tower alone--if base fed--but the radiating currents are a joint function of both wires. Of course, between the left and right sides of Fig. 1, we find no difference in the structure outline. The only differences appear in the labels for the structure's parts.

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The left part of Fig. 2 shows a generalized sketch of a gamma matched element. The most common occurrence of the match these days is for the driven elements of Yagi parasitic arrays in which we wish to connect all elements to the boom. Ordinarily, the impedance of the element without the gamma match is lower than the desired value, usually a value well below the 50-Ohm impedance of standard coaxial cable. We call the portion of the gamma match that parallels part of the element length the gamma rod. We short the end to the element in a position that yields the desired impedance at the new feedpoint. By a judicious selection of rod diameter, rod spacing from the element, and rod length to the connection, we can sometimes produce a purely resistive 50-Ohm impedance. If there is a reactance, we strive to make it inductive so that a simple series capacitor will compensate. Note that we normally consider the gamma rod to be a part of a matching network and not part of the radiating element.

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However, if we redraw the upper half of the sketch and terminate it at ground (instead of at a grounded boom), we obtain the sketch on the right of Fig. 2. In this case, the fed wire or rod becomes one wire of a 2-wire folded monopole, with an extension beyond the folded structure limit. The ground forms--if we wish to think in these terms--an image of the upward or physical portion of the antenna. The gamma match turns out to be a short folded monopole with an extension. As such, both wires in the folded structure make up the radiating element until we reach the extension. From our work with full folded monopoles and their linear equivalents, we know that the equivalent diameter of the folded portion of the antenna is much larger than the diameter of the extension along. Hence, every gamma-matched element contains at least a small imbalance. The related Tee match overcomes the imbalance by using a folded monopole on each side of the boom.

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As a consequence of these instances of short folded monopole applications--whatever the preferred labels--the behavior of short folded monopoles with extensions becomes more than an idle exercise. It holds some possibility of improving our understanding of certain structures that combine impedance transformation and radiation. As well, we might develop some techniques that would be applicable to real antenna planning exercises.

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Oue basic work will follow the pattern on the first episode. We shall place the folded monopoles over perfect ground and use lossless wire in order to eliminate some complex variables. In a real planning situation, we would put into our models the material conductivity of the proposed wire and the best estimate of real ground conditions. As well, our models would include the actual radial system beneath the folded monopole.

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Since we need some usable increment between modeled structures, we shall again use the physical height of the structures in degrees, where 360 degrees is 1 wavelength. We shall explore structures in 10-degree increments at 3.5 MHz. Table 1 provide a convenient correlation between the degree markers and the equivalent height in feet at the test frequency. At 3.5 MHz, a wavelength is about 281.02'.

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We shall create models using an implementation of MININEC 3.13. The program that I am using is Antenna Model, which incorporates a considerable number of correctives to overcome some MININEC shortcomings. Since all of our models will use different diameters for the fed and the return wires, NEC (-2 or -4) will not yield results that pass Average Gain Test (AGT) muster. As we shall eventually see, even MININEC's more ready handling of junctions between wires having dissimilar diameters has limits. However, we shall be able to create some usable models within those limits. If you try to replicate the models using a different implementation of MININEC, expect to find some variance in the output reports. If the implementation does not include an accessible AGT score, you may simply have to guess at the reliability of the model that you create.

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The project itself is simple, although long and occasionally tedious. Fig. 3 shows its general outlines. I shall create a series of short folded monopoles for each test case. Since the most common cases of short folded monopole applications involve return wires that are fatter than the fed wire, the models will all follow this pattern. The folded monopoles will appear in 10 degrees steps, from 10 through 90 degrees. To each folded monopole that is shorter than 90 degrees, I shall attach to the return wire--using the same wire diameter as the return wire--a series of extensions in 10-degree steps. Each series will progress until the total element length is 90 degrees.

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Obviously, one might carry the progressions of folded monopoles beyond 90 degrees or the extensions beyond 90 degrees. However, my goal is not to replicate every possible structure we might use. Rather, it is only to elicit the patterns of behavior of the resulting antennas, with special attention to the feedpoint impedance. We would have to end somewhere, and there is little point in becoming totally lost in a morass of excessive data. Indeed, the data that we shall observe is complex enough for one episode.

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Case 1: D1 = 0.1", D2 = 0.5", Space = 12", 2 Wires

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Our study cases can begin with a structure that we examined in the first episode. It consists of two wires spaced 12" apart. The fed wire will be 0.1", corresponding to AWG #10 wire that is midway between the wires used in amateur and commercial practice. The return wire is 0.5" in diameter to give us a sense of standard 2-wire shunt feeding of an existing mast. I have selected this starting point because the AGT scores are generally very good to excellent within MININEC despite the difference in element diameter. At a resonant length of 67.08', the reported source resistance is about 209 Ohms, compared to a calculated value of 210 Ohms.

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In the present context, we shall look at short monopoles in 10-degree increments. To each of these folded monopoles, we shall add a 0.5" diameter extension in 10-degree increments. The minimum length for each portion of the following data will be the height of the simple folded monopole. However, every folded monopole will end up with a height of 90 degrees. When we later speak of the data, we may use expressions such as "20-50" to designate a line from the table. The first number indicates the height of the folded monopole portion of the antenna, while the second number reports the total height that includes the extension, if any.

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The data includes a report of the AGT, the source resistance and the source reactance. In addition, there are entries for the reported gain broadside to the pair of wire and edgewise to the wires. In the latter case, the maximum gain value appears as a measure of the pattern's circularity or ellipticalness. Table 2 records the data for the present 2-wire case.

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Except for the shortest lengths of both the folded monopole and the extension, the AGT scores are excellent. Therefore, the table makes no adjustments to the reported values. The gain values generally accord with those for folded monopoles that form the complete structure of the entire length. In the last episode, we notes the losses that accompany relatively short structures when we translate our perfect wire into real materials. In practical terms, there is very little difference in the numerical performance and virtually no operational real difference in gain performance among any of the various structures when the total height exceeds perhaps 60 degrees or so.

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The impedance progressions that follow on each folded starting point exhibit interesting patterns. We may use the 10-10 through 10-90 series as a sample. The reactance increases very slowly but steadily. However, as it cross the resonant region (between 80 and 90 degrees total height), we do not find resonance. Instead, we find a reversal of the direction of change of reactance. The resistance for all total length up to 80 degrees is too low to be useful. However, the rate of increase climbs so that with a 90-degree total height, we achieve a matchable pair of resistance and reactance values. If we track the 20-n and the 30-n series of models, we find the same pattern for both the resistance and the reactance, with an adjustment for a new starting value set that emerges from the new length of the folded section.

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Above a folded length of 40 degrees the pattern appears to change. We seem to find more rapidly changing resistance and reactance values. However, we are entering the region in which a a full folded monopole would experience rapidly changing impedance values. The extension portion of each structure has the effect of increasing the folded monopole length by a small amount with each step. Small changes of total length yield large changes in resistance and reactance. Between 40-80 and 40-90, we see a reversal in the inductance, suggesting a narrow resonant region. For the 50-degree folded structure, total height between 70 and 80 degrees records a similar reactance zero crossing. When the folded structure is over 60 degrees high, the antenna begins past the cross-over point and shows predominantly capacitive reactance. However, the 80-90 case yields another matchable impedance combination.

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One of the oddities of matching practices that uses short folded monopole structures is the variability of practice. Gamma matches for Yagi elements tend to use the shortest practical folded section that will effect the desired impedance transformation. In contrast, tower shunt feeding tends to use the longes folded structure that will get the job done. See Chapter 6 of The ARRL Antenna Book, 20th Edition, and Chapter 9 of ON4UN's Low-Band DXing, 2nd Edition, for samples of tower shunt feeding. Gamma and related matching systems appear in Chapter 23 of the ARRL book. In fact, neither Yagi practice nor tower practice seems to take note of the other way of achieving the same goal.

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Although our case study is not itself very realistic relative to either HF Yagis or to MF/HF towers, we may use it as a way to explore a technique for surveying a more complete range of options when using short folded structures to effect impedance matching. We can create graphs of the impedance reports. Fig. 4 handles the reported resistance values for our sample. The X-axis records the total height of the structure, while the individual lines represent different heights for the folded portion of the antenna.

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I have cut off the Y-axis for multiple reasons. I arbitrarily set a 500-Ohm limit to the upper end of the resistance range. The decision in any real case would rest on an estimate of the highest resistance value that might be acceptable. The range should be great enough to show the rate of resistance change from one step to the next. However, it should not be so high as to obscure how close to an ideal value of resistance the modeled value comes. In this case, we might be concerned with 50 Ohms as a target value. Fig. 5 shows a similar treatment for the reported reactance values.

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The reactance values included in the graph range from -j100 Ohms to +j500 Ohms. Most short monopole impedance transformation system seek an inductive reactance (or zero reactance) at the feedpoint to allow matching with only high-Q capacitors. The selected range lets us see both the recorded reactances at the sampling points and the relevant rates of change to the adjacent sampling points.

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The combination of the two graphs allows us to select candidates for implementation. In most cases, we shall find few viable candidates, since we are likely to be working with an existing grounded mast or tower. However, in the exercise, we are free to note any viable combinations. In the present case, the resistance table offers a number of combinations that show (by the graph's definition) usable values with modest rates of change in resistance to the next sampling point. However, the reactance graph reduces the number of candidates. Within the constraints of the exercise, total height values between 80 and 90 degrees combined with folded heights between 10 and 20 degrees offer useable combinations with relatively low rates of change. The longer folded structures that showed promise in terms of their resistance reports in this region tend to disqualify themselves due to the high rate of reactance change between sampling point. Any network that we might use to produce a final resistive impedance of 50 Ohms would likely have at best a very narrow bandwidth.

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Our accumulation and exploration of data shows us how we can use the information as the basis for planning installations. However, the structure that we used is relatively unrealistic. It appears because the models are highly reliable as measured by the AGT values (which are a necessary but not sufficient condition of model adequacy). Perhaps a more realistic scenario might be useful as a second exercise.

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Case 2: D1 = 0.1", D2 = 8.8", Space = 36", 2 Wires

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Real towers that we might use as a shunt-fed vertical antenna vary in face size. We may use a modest tower with a 12" face dimension. For simplicity in the models, we may use the standard AM BC equivalence and multiple the face by 0.74 to obtain an 8.8" diameter wire that approximates the tower. (An actual planning session should model the tower structure as exactly as possible.) This new diameter forms the return wire for the folded structure and the extension above and beyond the folded structure. We may retain the 0.1" diameter fed wire as a realistic value.

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The next step is to determine a workable space between the wires of the folded section. Despite MININEC's superiority in handling junctions of wires having different diameters, it will show limits to its reliability. We not only have a radical difference in wire diameters, but as well, we have two wires that are fairly closely spaced. I sampled variety of spacing values and return-wire diameters using a 30-degree folded structure and an 80-degree total height to see what AGT scores might emerge. The results appear in Table 3.

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For any set spacing, the AGT values degrade as we increase the diameter of the return and extension wires. In some circles, AGT's are considered excellent if they fall between 0.995 and 1.005. They are usable between 0.990 and 1.010. Beyond this latter range, the data becomes questionable. Even within the usable range, we should adjust the data by virtue of the AGT score if we are developing (meaningful and comparative) progressions of values, especially if the AGT value changes from one sample to the next. For the projected diameter of the return and extension wires in the models that we shall run, the minimum spacing for adequate AGT scores is 36" or 3'. This value tends to coincide with commercial practice for folded assemblies, so I shall use it in amassing a data collection.

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AGT scores will tend to improve for longer structures and degrade for shorter total antenna heights. Therefore, we should adjust the reported values to arrive at the best approximation of a final value. Because we are dealing with a folded structure, we must reverse the normal procedure set. Ordinarily, we convert the AGT score into a "dB' value (=10 log AGT) and subtract it from the reported gain. (An AGT less than 1 results in a negative dB value, which increases the reported gain when we do the subtraction.) Experience with the full folded monopoles in previous studies suggests that we must add the AGT-dB to the reported value to obtain gain values that are reasonable in terms of their consistency with values that emerge from models showing an ideal or very-nearly ideal AGT value. We normally adjust impedance values by multiplying the reported number by the AGT itself. However, folded structures appear to require that we divide the report by the AGT in order to obtain values that coincide with calculated impedance transformations.

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With these cautions and conditions, we may proceed to model our erstaz tower and its shunt wire as a series of 2-wire short folded monopoles and extensions. We shall use the same increments that we used for the initial case. Table 4 shows the amassed adjusted data. However, we must add one more reservation. The standard impedance transformation equation for resonant folded dipoles results in an impedance of about 614 Ohms. The resonant version of our new model is 65.286' high and reports an adjust resistance of 574 Ohms. The difference is about 7%. We cannot be truly definitive in assigning a source to the difference. However, the end wire is now 3' long, almost 5% of the total folded monopole height. As well, the impedance ratio is about 17:1, a very large ratio indeed.

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Within the limits of our case study, the gain values are completely normal (with the usual reservations about the very shortest folded and total height values). Broadside gain values at a total height of height of 90 degrees coincide very closely with corresponding values for the smaller and narrower model of Case 1. The edgewise gain values provide a measure of the degree to which the 2-wire structure ovalizes the pattern.

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The significant differences between the values in Table 4 vs. those in Table 2 appear in the resistance and reactance columns. Between the two tables, we note a large difference in both the return/extension wire diameter and the spacing between wires. Therefore, we shall expect to see differences in the impedance values for each increment of folded structure.

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Between folded structures heights of 10 and 30 degrees, perhaps the biggest surprise may be that we see the same general pattern of values that we experienced with Case 1. The resistance values for Case 2 are consistently about 1/3 the level of those for Case 1. However, the reactance values for each increase in the return wire length are comparable between the two cases. The parallel extends even to the decrease in inductive reactance that occurs in the total height interval between 80 and 90 degrees. The amount of decrease for the 8.8" example is somewhat less than for the 0.5" return wire, but it is equally distinct.

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As we increase the height of the folded structure, the parallels remain, but with reservations. For the narrower structure, the reactance zero-crossing first appeared with a folded structure that was 40 degrees high. With our more widely spaced model, the folded structure reaches 60 degrees before we encounter the first zero crossing. If the total height for Case 2 is 90 degrees, we find nearly identical inductive reactance values for folded heights between 50 and 90 degrees. The shorter the folded structure within this range, the lower the resistance value.

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The general trends give us a picture of both consistency with the earlier models and of adjustment for the new values of return/extension wire diameter and spacing. In order to translate those general trends into a more adequate planning venue, we may graph both the resistance and the reactance values. Since we do not have a real tower around which to plan, we may use that same limits applied to the graphs for the earlier case. Fig. 6 shows the relevant resistance values.

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With respect to resistance, the 20- and 30-degree folded structures show perhaps the most promise when used with total heights between 80 and 90 degrees. Especially notable is the relatively slow rate of change in resistance with changes in height over this region. These conditions suggest that variables in the physical structure relative to the model will be manageable in terms of field adjustments toward the final antenna.

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Fig. 7 shows the corresponding reactance graph. It tends to confirm the initial judgment of the promise offered by the 20- and 30-degree folded structures with higher extensions. With the shorter folded structures, the inductive reactance increases with the length of the folded monopole for any given total height. However, it remains manageable. Long folded structures might yield workable values of inductive reactance at a total height of 90 degrees, but the rate of change between 80 and 90 degrees total height is very steep.

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We may note in passing that the resistance curves for all lengths of folded structure show a downward trend between 80 and 90 degrees. Although we are working with a simple straight tower (equivalence) in these models, it is fairly easy for typical amateur towers to exceed 90 degrees in electrical length without passing the 70' mark of our 90-degree tower. Most shunt-fed amateur towers hold one or more Yagi antennas at the top. These structures tend to form rudimentary and imperfect top hats that increase the effective electrical length of the tower considerably. Hence, a 90-degree physical tower may easily become 100 or 110 degrees electrically. The consequences lie outside the limits set on this exercise, but we can expect to find lower resistances and variations in the reactance. If the tower is too tall electrically, we may easily find a shift back into capacitive reactance. Within modest electrical height increases relative to the study limits, we need to study all potential folded structure heights (or shunt lengths). The longest folded structures in conjunction with the longest total heights tend to show very high rates of change in resistance and reactance with small changes in total height. The result is normally a very narrow operating bandwidth for any given set of matching components.

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Case 3: D1 = 0.1", D2 = 8.8", Space = 36", 3 Wires

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One possibility, rarely explored by amateur installations but regularly used commercially, is to provide multiple fed wires. Fig. 8 shows the configurations that we have and shall explore here. Both of our earlier sample cases used 2-wire construction. However, 3-, 4-, and 5-wire construction is feasible, assuming that it might increase the number of options available for shunt feeding a tower or other applications of folded monopole structures.

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In these notes, we shall take up just two of the added options: 3-wire and 5-wire configurations. The 3-wire models will use a pair of 0.1" diameter fed wires on opposite sides of the central 8.8" tower-equivalent return wire and extension. To ensure reasonable AGT values, we shall retain the 36" spacing between the fed wires and the return wire. All of the procedures for adjusting values according to the AGT scores will also apply to this case. The only modeling difference lies in the need for having 2 sources which are, in effect, in parallel relative to the overall structure. If we bring these source together, the composite source impedance will be composed of resistive and reactive components that are each half the value of the values for the individual fed wires.

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The data for the 3-wire assemblies appear in Table 5. Although the simple folded monopoles in the earlier study ("What is a Folded Monopole") all produced circular azimuth patterns at resonant lengths, we find elongated edgewise patterns in these models, likely due to the very large diameter difference between the fed wires and the return wire. However, as we increase the total height of the antenna to 80 degrees for any height of folded structure, the azimuth pattern becomes circular. The more symmetrical structure of the 3-wire models also shows a slight improvement in AGT values relative to the 2 wire models.

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As we have done for the other cases, we shall break the discussion of impedances values into 2 parts for Case 3. The first set of values involves folded structures that are 10 through 30 degrees high. The general trend that we discovered for the earlier cases applies to the 3-wire models. For any folded structure, as we increase the height of the extension, the source resistance slowly rises until we pass the 80-degree total height mark. Then the resistance declines. Interestingly, over this range of folded structures, we do not find very significant differences in the source resistance between 2-wire and 3-wire models. The reactance also slowly increases as we increase the total length of models with 10- through 30-degree folded structures. However, the inductive reactance is considerably lower for the 3-wire models than it was for the 2-wire counterparts.

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When the folded structure exceeds about 40 degrees, the resistance and the reactance change more rapidly in 2-wire models than with shorter folded structures. In corresponding 3-wire models, the resistance tends to change more slowly than in 2-wire models with the same height characteristics. The first reactance zero-crossing occurs in 50-80, with the 60-n series of models showing capacitive reactance at all total heights except 90 degrees. When the folded structure exceeds about 70 degrees, the 2-wire and 3-wire source resistance values become very comparable. However, the reactance values of the 3-wire models appear to be almost uniformly shifted in the direction of inductive reactance.

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The pattern of similarities and differences between 2-wire and 3-wire structures can naturalize us to the performance behaviors, but we require more detailed analysis to see if we have developed any manageable matching potentials. Fig. 9 provides the resistance data for source values up to 500 Ohms. If we can manage source resistance values up to about 250 Ohms, then the graph suggests that we may use some taller folded structures (70 and 80 degrees) in addition to the shorter 20- and 30 degrees structure suggested as possibilities for 2-wire structures--so long as we use a relatively high total structure (>70 degrees).

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Whether any of these potentials has a usable or manageable reactance requires that we examine the graph in Fig. 10. The reactance values at a height of 90 degrees for the tower are well within the range of most networks. However, the rate of change for the reactances associated with the taller folded structures is somewhat steep as the value shift from capacitive to inductive between total heights of 80 and 90 degrees. The more rapid the change in reactance with smaller height changes, the narrower the bandwidth will be for any particular set of matching component values in basic networks. Nevertheless, the slow rate of resistance changes may effect an improvement in operating bandwidth for the taller folded structures.

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Since 3-wire systems are not very much more difficult to install than 2-wire systems, they may prove useful in a number of applications.

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Case 4: D1 = 0.1", D2 = 8.8", Space = 36", 5 Wires

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Developing a data set for 5-wire structures with 4 fed 0.1" wires and an 8.8" diameter return/extension wire requires far more effort to model than to explain. It does not matter what name we give to the structures: caged monopoles, skirted monopoles, or multi-wire folded monopoles. Central to the modeling is providing a symmetrical arrangement of the fed wires and providing each fed wire with a source. The net or parallel source impedance of the antenna will be 1/4 the value that appears on any single leg. MININEC lacks any facility for paralleling sources, so the calculation must be external to the program.

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Table 6 provides the adjusted data gathered for the series of 5-wire models. Increasing the symmetry of the structure provides another slight improvement of AGT values. As well, the 4 wires circularize the azimuth patterns, as indicated by the identical gain values in both the broadside and the edgewise columns. Once we pass very low levels of total height, the gain for the system does not vary significantly regardless of the number of wires.

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Adding two wires to the 3-wire assembly does not greatly change the net source resistance values relative to 3-wire models when both use shorter (10- through 30-degree) folded structures. Indeed, for shorter folded sections, all three series of model (cases 2 through 4) show similar resistance values. The more significant change for shorter folded structures occurs in the level of inductive reactance. The 5-wire models show between 2/3 and 3/4 the level of inductive reactance for each step of total height for any of the shorter folded structures.

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As we increase the folded structure to a height of 40 degrees or more, we find a significant difference in antenna impedance behavior relative to 3-wire models. Model 40-80 shows the first reactance zero crossing, an event that required a 50-80 combination with 3-wire models. With folded structures between 50 and 60 degrees, all of the reactance values are capacitive, including the value for a 90-degree total height. Only with folded structures at least 70 degrees high do we find an inductive reactance with a 90-degree total antenna height. However, almost all of the reactance values are quite low, suggesting the potential for broader bandwidth matching systems.

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In the category of source resistance, Fig. 11 reveals that the 5-wire assembly offers us new candidates for folded structures in terms of manageable values. In addition to the 20- and 30-degree folded structures, we may add 60-90 degrees, with total lengths equal to or longer than the folded structure.

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With a total height of 90 degrees, Fig. 12 informs us that almost any of the resistance candidates will suffice in terms of feedpoint reactance. As we lower the total height to 80 degrees, even the tallest folded structures show less steep curves than for any of the preceding models series. Even a 60-degree folded structure will work well with an 80-degree total height if we can handle a moderate amount of capacitive reactance.

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The 5-wire short folded monopole with extensions expands the number of options available to the application of folded structures to grounded vertical towers. These notes have not explore antenna lengths greater than 90 degrees, so we cannot say off hand whether the advantages of multiple feed wires continue with taller towers.

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Matching and Planning

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In the course of these notes, I have noted that most amateurs who feed existing towers for use on one or more of the lower bands prefer to arrive at an assembly that provides inductive reactance. In many cases, the operator will sacrifice operating bandwidth for the inductive reactance. Indeed, they prefer to arrive at a source resistance that is less than 50 Ohms along with the inductive reactance. We may fairly ask why this custom prevails.

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Fig. 13 provides part of the answer. Under ideal conditions, we can effect the required matching to a coaxial cable with a simple series capacitor, if the antenna feedpoint shows a near-50-Ohm resistive component along with inductive reactance. The upper left sketch shows the condition. If the impedance is less than 50 Ohm resistive and has inductive reactance, then we may use the 2-capacitor matching scheme at the upper right. Since the scheme is a simple L-network, it is not clear why the label "omega" match persists, since nothing in the network resembles the Greek letter in either upper or lower case forms. For many combinations of impedances with under 50 Ohms resistance and an inductive reactance, the system at the lower right will also work. However, it does not always yield the most desirable values (usually meaning the lowest values) of capacitance in either the series or the parallel leg.

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For general matching with resistances above 50 Ohms, we normally require the L-network configuration shown at the lower left in Fig. 13. The sketch shows perhaps the most familiar form of the L-network, often used with horizontal long-wire antennas. However, it functions very well with impedance that are near to 50 Ohms with various levels of inductive or capacitive reactance. Tower shunt feeders have in the past rejected this configuration--and the impedances that require its use--because they have preferred to match entirely with capacitors. One may match a a given impedance over a narrow operating bandwidth with fixed weatherproofed capacitors at the base of the antenna. Vacuum variables can provide fairly weatherproof remote service to vary the match.

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The desire to remotely match an antenna for upper MF and lower HF amateur service makes sense if we consider some of the impedance values that appear in the literature. One set of values involved a resistance of 17 Ohms and a reactance of 580 Ohms. Even if we had a resonant condition, the SWR would begin at 3:1 relative to 50 Ohms and become progressive worse with increasing reactance. With the very high reactive component, the SWR is in the hundreds.

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An alternative offered by multi-wire folded structures is a reduction in the reactance to levels that may not require remote matching. Some of the 5-wire models showed resistance values in the 90s as the total height approached 90 degrees. The inherent SWR relative to a 50-Ohm line is under 2:1 with those conditions. If we raise the reactance to perhaps 100 Ohms (capacitive or inductive, the SWR climbs to about 4.3. If we use 100' of low loss cable (such as LMR600) and reserve matching for inside the operating room, we lose about 1/3 dB. A simple L-network at or near the operating position will effect the required match with little or no concern about the durability of components as the weather passes through its many potentially destructive cycles.

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The possibly attractive alternative, of course, rests on the numbers yielded by the sample models, with all of the qualifications and reservations recorded along the way. Making such a system work in a specific application requires far better modeling, along with considerable preliminary field effort. At a minimum, a proper model should include all of the details shown in Fig. 14. The tower needs full modeling, as do the specific wires to be used as fed wires in the folded portion of the structure. Not only should the model include any extension of the tower, but as well, it should include any mast and beam antenna at the top. In addition, the model should specify the materials for each wire within it, with different values for material conductivity wherever they occur. Only then will the model accurately reflect the above-ground structure and its equivalent electrical length. Of course, the many junctions of wires having different diameters will force the use of MININEC, since a NEC model has a very high probability of being unreliable.

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The below-ground structure has equal importance. A buried radial system deserves below-ground modeling in NEC-4. If we try to substitute the MININEC ground with a set of specifications for conductivity and relative permittivity, we would obtain the impedance for a perfect ground. To resolve the incompleteness of one system without the other, the modeler can first model the antenna structure as a whole in MININEC. Then he or she can develop a simplified substitute model have essentially the same characteristics, but using throughout a single wire diameter. (In many cases, this phase of the effort may require the most ingenuity.) Finally, one may transfer the model to NEC-4 for completion with the buried radial system to be used in practice.

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Of course, Murphy's Law tells us that the individual who bypasses this process and uses initial estimates will spend long days in the field adjusting and readjusting the system because reality and the initial estimates are far apart. Equally, someone who goes through the entire process will conclude that the initial estimates proved to capture reality as well as the most detailed model. Such is the lot of shunt feeders.

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The brief account of detailed planning requirements serves to reinforce my initial notes to the effect that these case studies only establish the interesting patterns of short folded monopole and extension behavior. They do not provide precision guides to building such structures. However, patterns can be useful in familiarizing us with the territory so that what we encounter has fewer surprises. Surprise on the battlefield is an effective offensive weapon. Surprise with antennas is usually simply offensive.

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Updated 1-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Lower, Vertical


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What Is a Folded Monopole? Skirting the Issue

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L. B. Cebik, W4RNL

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Literature about multi-wire monopoles is fraught with odd labels for the structures. We can find terms like folded monopole, folded isopole, caged monopole, and skirted monopole. If we can find legible diagrams for what the labels label, we are in for something of a surprise: they all refer to the same class of antenna. However, some engineers prefer to reserve the title of folded monopole for an antenna with only 2 wires. Others apply the term more generally to all or most multi-wire monopole systems. To the best of my knowledge, the skirted monopole terminology arose when the outer wires served as a means for detuning the monopole--usually a tower--from its sensitivity to interact with nearby (near-field) AM BC transmitting antennas. Hence, detuning skirts are common on urban cell towers. However, we can also feed the skirt on a transmitting tower and obtain a measure of impedance transformation and control that turns out to be useful. We might speculate that the expression caged monopole arose as a somewhat more politically correct than the term skirted monopole. Regardless of the humor we may make out of the terminological morass, we are left with a basic question.

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Is the multi-wire skirted or caged monopole a folded monopole or isn't it?

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Let's start at some sort of beginning by looking at some forms of multi-wire monopoles. Fig. 1 shows a few of the many possible configurations. On the far left is a standard 2-wire folded monopole. It forms a touchstone for all that follows. At this stage, I shall note only one interesting property of the standard folded monopole. Edgewise to the wires, we find a very tiny (and operationally insignificant) asymmetry to the antenna's gain. For ordinary wire spacing, the differential might be up to 0.04 dB in models, favoring the feedpoint side of the antenna. The broadside gain is the average of the edgewise gain values. Next to the 2-wire folded monopole is a 2-wire folded monopole with an extension on the return-wire side. (In practice, it makes no difference whether the extension connects to the fed wire or to the return wire if the connecting wire is short enough as a function of a wavelength.) I drew the antenna in the manner shown because it shows the relationship of a folded monopole with an extension to a gamma or omega matched tower used by some amateurs on 40 meters. If we assume that the antenna would be self-resonant without the extension, then with the extension, we find an increase of both the resistive and the inductive components of the feedpoint impedance. If the fed wire length does not result in a self-resonant antenna without the extension, then we usually call the added fed wire a matching line. The preferred term here is a function of what we are trying to achieve more than it is a difference in the electrical performance of the antenna. Like all folded elements, we shall find both a transmission line function and a radiating function within the folded section.

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The sketches jump to 4- and 5-wire structures. However, a 3-wire monopole system is both possible and interesting. If we place wires on opposite sides of a return wire/tower and if we feed both new wires in parallel, we obtain a rudimentary caged or skirted system. Like the more complex 4- and 5-wire systems in Fig. 1, it produces a symmetrically circular azimuth pattern. In fact, within very narrow limits--largely a function of the fact that the more complex cage systems tend to result in slightly shorter antennas when they are self-resonant--the gain of all types of caged, folded, or skirted monopoles is the same. (Some models of these antennas have shown more deviant values, but they usually correct to the basic value when adjusted for the average gain test (AGT) score of the model.) Over perfect ground using lossless wire, the entire set of self-resonant monopoles show a median gain of 5.15 dBi, with less than about +/-0.04 dB variation.

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The two sketches on the right of Fig. 1 differ in only one small way. The 5-wire monopole uses one or more wires that circle or girdle the outer wires only. In large installations, the connecting wires serve an important mechanical goal to help rigidify the cage of very long out wires. Also note that the sketches show a set of connecting wires at the base with a single feedpoint between the wire and ground. (We shall presume that all return wires in the figure return to ground.) In theory and in practice, the single feedpoint can result in slightly different current magnitudes and phase angles along the outer wires. The connecting wires create short circuits along the structure that tend to equalize currents along the outer wires.

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We may replace the energy source with a network and change the system function from radiation to tower detuning. There are numerous techniques that allow engineers to use essentially the same caging wires to detune a tower from most frequencies within the upper MF range. Some techniques may involve modifications to the cage of wires as well as to the base network. Tower detuning via skirts has become a fairly routine and commonplace engineering service. Its necessity and profitability has increased with the proliferation of cell-phone and other UHF/microwave towers that now pervade urban, suburban, and rural landscapes.

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For our purposes, we may bypass the detuning role of skirts and cages in order to address more directly our initial question: are they forms of folded monopoles? To approach an answer, let's begin by seeing what makes the 2-wire folded monopole so special.

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The Folded Dipole and the Folded Monopole

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Hardly a soul among those interested in antennas does not know about the folded dipole. Unfortunately, what many folks know is only a tiny piece of the story. If we parallel two identical wires at a reaonably close and constant spacing, if we connect the ends and feed one of the wires, and if we bring the antenna to resonance, then the feedpoint impedance on the selected fed wire is 4 times the impedance of a linear resonant dipole. There is much more to the folded dipole story than this, and I have tried to tell some of it in "Unfolding the Story of the Folded Dipole".

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Part of the story involves the fact that a folded dipole and a linear dipole have the same gain and pattern. Another part of the story involves the fact that a folded dipole is two devices in one. It is a dipole and has radiating currents that almost exactly parallel the radiating currents of a linear dipole in both magnitude and phase angle. The folded dipole is also a transmission line (or, counting from the feedpoint, two transmission lines with a common starting point) with a relatively constant current magnitude and phase angle (that is 90 degrees out of phase with the radiating current). John Kuecken showed how to separate the two currents in Antennas and Transmission Lines (pp. 224 ff).

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Perhaps the most significant part of Kuecken's account is that he describes the technique in connection with the hairpin monopole (another name for the folded-monopole list of aliases). The technique applies equally both to folded monopoles and to folded dipoles, since the former is simply half the latter if terminated in a perfect ground or in a ground plane the approximates a perfect ground. If we make the folded structure self-resonant using a perfect ground and lossless wire, a dipole will show about 72 Ohms for a feedpoint or source impedance (resistive, of course), while a linear monopole will show 36 Ohms. Folded versions of the two will shows 288 and 144 Ohms, respectively under suitable conditions. Fig. 2 shows the correlation of the two antennas and their linear roots.

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The "suitable conditions" clause of the folded antenna impedance report presumes that the two wires in the folded structure have the same diameter. As well it presumes that the two wires are close enough to form a transmission line rather than simply an open loop or open half-loop. Unfortunately, too many amateurs are unaware that we may effect other impedance transformations by varying the diameters of the two conductors, or the spacing between them, or both. Fig. 2 hints at that wider range of potentials by designating the wire spacing as s, the diameter of the fed wire as d1, and the diameter of the return wire as d2. How these dimensions (all in the same unit of measure) go together to effect an impedance transformation appears in the following equation.

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If d1 and d2 are equal, then the right side of the expression in () is 1, and to that number we add 1, to get 2, which squares to 4 as the value of R, the ratio. Hence, the most common case of a folded dipole multiplies the linear dipole impedance by 4. A folded monopole meeting the same conditions does likewise. Next, let's make the return wire diameter go to an infinitesimal value. We cannot let it go to zero or we cannot have a return wire, but an infinitesimal diameter will suffice to leave us with a wire, but one that reduces the d2-diameter and right side of the expression in () to a value insignificantly different from zero. Within the () we now have a value of simply 1, which squares to 1. This condition sets the minimum transformation in a folded dipole or monopole. In other words, a folded mono-/di-pole cannot transform an impedance downward from the linear value--only upward. On the other hand, making the return wire very small drives the denominator on the right side of the expression in () toward zero, increasing the value of the fraction to an indefinitely high value. For most antenna work, resulting ratios (R) greater than 10:1 are seldom encountered. However, we often find conversion ratios above 4:1, especially in gamma-match structures, where the gamma rod is considerably thinner than the main element to which it attaches.

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Fig. 2 also labels the end wires that must be part of any real folded antenna. I note these wires because they do have an effect on the physical version of what we calculate from the equation. The wires must be short enough that their effect is relatively insignificant. However, their effect is real and shows up in computer models of folded dipoles and monopoles. One easy way to see the effect is to create a resonant model of a folded dipole using wires having different diameters. Now alternately use the fat wire or the thin wire diameter for the end wires and recheck the required length for resonance. You may also wish to look at the current tables available in NEC and MININEC for additional confirmation of the effect of end wires. To make the effect more vivid, use a lower frequency with a fairly wide physical spacing (such as 3' at 3.5 MHz) and use enough total segments so that the end wires have multiple segments.

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If we create a multi-wire cage around the center wire, we can achieve two different orders of phenomena. Of we place the source on the center wire, then the set of cage wires (any number from 2 upward for a total folded antenna count of 3 upward) increases the impedance transformation ratio. We rarely encounter this situation. However, users of cages around a central mast or tower in the upper MF and lower HF regions often feed the cage wires in parallel, allowing the fat center wire to serve as the return wire. This practice serves a number of ends. First, it allows the central tower a direct connection to ground. Not only does this move simplify the tower's mechanical structure, it also is an important safety measure. Second, using the central mast or tower as the return wire results in an impedance transformation ratio that is lower than 4:1. By choosing the correct number of wires for the cage or skirt and feeding them in parallel, we can obtain an impedance that is higher than a monopole's 36-Ohm value over perfect ground but much lower than the 4:1 value of 144 Ohms. Indeed, a 4-wire cage provides a value that is very close to 50 Ohms, virtually ideal for coaxial cable.

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The Root of the Issue

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The problem that we encounter with both physical antennas and their NEC models is that the resultant impedance does not coincide with the basic folded dipole/monopole equation. The resultant impedances that we encounter when connecting parallel sources together for a caged or skirted monopole do not answer to any simple relationship to the 2-wire folded monopole (or dipole). As a consequence, some engineers hesitate to identify the caged or skirted monopole with the 2-wire monopole.

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We might initially treat caged monopoles in a variety of ways. For example, we might consider the structure to be a version of a coaxial monopole in which the return wire forms a center conductor, with the outer wires forming the outer conductor corresponding to the braid on an ordinary coaxial cable. However attractive this picture may be, we also must recognize that the outer wires leave mostly empty space. In addition, if we apply the 2-wire equation to this situation, then the value of d1, the fed wire, becomes identical to the value of 2s, that is, twice the spacing between conductors. The common log of 1 is zero, resulting in an impedance transformation of 1. Hence, a resonant monopole under this treatment would show a 36-Ohm impedance. However, cage monopoles show a higher impedance, with the actual value being partially a function of the number of wires.

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Alternatively, we may model various samples of cage monopoles and, with due attention to AGT scores, arrive at reasonable estimates of the resulting impedance. We quickly discover a factor that the coaxial treatment cannot take into account directly. For any given return wire (d2) diameter, as we change the diameter of the outer wires, the resultant antenna impedance will change. The coaxial treatment can use only one value for d1, taken just now to mean the overall outside diameter of the cage system. It is possible to obtain from the basic equation an impedance that is equal to the modeled (or field tested) value by using a selected value of diameter for d1. However, this treatment is initially ad hoc. It involves varying the diameter of d1 until the impedance value matches the modeled or field value. If we survey enough values, then we might use some form of regression analysis to arrive at correlations that would be usable for almost any (practical) combination of center diameters, spacing values, and cage-wire thicknesses. Nevertheless, regression analysis is an excellent tool for establishing a mathematical correlation to a set of curves derived from observation, but it does not provide an explanation of the correlation. The equations would not necessarily fit any set of known electrical foundation equations to provide a seamless continuum between 2-wire and multi-wire folded dipoles.

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The absence of a means of direct derivability that might ensure that cage monopoles are a variety of folded monopole--or that might provide sufficient reason to withhold the connection--does not mean that we must give up on the problem. There may be other alternatives yet to be explored. Any such alternative must recognize that the presence of multiple fed wires that do not surround the center conductor or return wire will present disturbances to a strict correlation. Indeed, perhaps part of the past thinking that wishes to claim that a cage monopole is not a folded monopole has looked too strictly at what a cage does not do and too little at what it does do. Granted, a cage lacks the solidity to form a true coaxial surface. However, let us suppose that each fed wire forms with the central return wire a 2-wire folded dipole. Under this supposition, we can expect the fed wires to interact or mutually couple. The degree of interaction would vary with the diameter of the center return wire, the spacing, the diameter of each out fed wire, and, of course, the relative diameters of the fed and return wires. Despite the variables, we should still be able to detect a pattern of values that we can trace to the results of a 2-wire folded monopole.

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A Test and Its Limitations

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Within certain limits, we may set up a fairly simple modeling test. For the test we shall use a series of monopoles, as shown in Fig. 3. Each monopole will be resonant at a given test frequency. Since we shall use lossless wire and perfect ground to minimize the number of extraneous variables, virtually any frequency will do. My test frequency will be 3.5 MHz. When modeling each test structure, the monopole will be resonated to within +/-j0.1 Ohm.

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The outer wires will have a constant diameter, 0.1". I shall vary the diameter of the center or return wire in steps. Since a zero diameter is not possible, I shall use 0.1-Ohm as the minimum return wire diameter. The remaining steps will be linear: 0.25", 0.5", 0.75", and 1". I shall end the progression at this point for modeling reasons. As the diameter of the center conductor increases, the AGT score departs ever further away from the ideal value. Using NEC-4, the value becomes unreliable more quickly than with MININEC (using a suitably corrected implementation of the public domain version 3.13), but both programs eventually fail to yield very usable results. However, we shall be able to track the requisite results over the range of selected values and arrive at some preliminary conclusions. The procedure is no less and perhaps no more approximate than the industry-standard practice of using single wire substitutes for complex geometries that more adequately reflect open tower structures. The AM BC industry regularly uses a wire radius of 0.37 times the face dimension of a triangular tower and 0.56 times the face of a square tower.

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Besides varying the diameter of the return wire, the test models will also vary the center-to-center spacing between the return wire and the fed wire(s). I shall use spacing values of 12", 24", and 36". The top wires will use a diameter of 0.1", the same used for the fed wire. Each top wire will use a segment length of 1' (12"). The vertical wires will use 60 segments each, a value that produces segment lengths between about 0.9 and 0.95 of a foot. The very small disparity between the top-wire segment lengths and the vertical wire segment lengths does not jeopardize current calculations in NEC 4.1, since the feedpoint is in the lowest segment of each outer vertical wire. Tests using segment lengths that are as a close to 12" as possible result in variations of the feedpoint impedance by no more than 0.02 Ohm relative to either the resistive or reactive component.

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One aspect may be unique to these test models, although it is a common modeling practice. The uniqueness is the attention that we shall give to it. Most NEC modelers attempt to supply the model with a single feedpoint to end up with an overall impedance for the structure. There are a number of ways in which we can perform the feat. We might elevate the ends of the fed wires and provide shorting wires between legs ends. Then we may run a single wire to ground and place a source on this wire. Alternatively, we may run transmission lines to a remote wire and place a source on it. If we select a near-zero length for the transmission line lengths (which are independent of the actual distance to the remote wire), we effectively connect the four base segments in parallel.

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In MININEC we must--and in NEC, we may--simply place sources at the ground end of each fed wire. Of course, the number of sources will be one less than the number of vertical wires in the model. A 5-wire cage monopole will have 4 sources. Since the impedance values for all of the sources will be identical, the net impedance will be the resistance and the reactance at each source divided by the number of sources. This derived value will be the same as the one we would produce by using the transmission-line technique of paralleling the sources. What differs is that we shall have--and pay close attention to--the source impedances of the individual fed wires.

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The test will include 2-wire folded monopoles, even though we may calculate the impedance transformation ratio from the standard equation. We shall be as interested in how close the fit may be between the model and the equation result as for any other form of folded monopole. A series of monopole models of lossless wire over perfect ground yields a resonant impedance of 36 Ohms. Hence, the reference impedance for each new combination of return wire diameter (d2) and spacing (s) will be 36 Ohms times the equation-based ratio. We shall be comparing the modeled impedance values for each fed wire with the reference impedance value.

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The test will initially yield reported values of source impedance. As well, each test will have an AGT score. Over perfect ground, the ideal AGT is 2.000, although the value is 1.000 in free space. The free-space equivalent of the ideal perfect-ground AGT is simple 1/2 the perfect-ground value. I shall use this free-space equivalent value in test reports, since it plays an important role in arriving at a usable impedance value. One reason for resonating the folded monopoles to such close tolerances is to allow us to use the AGT score to arrive at reasonably reliable values of resistive impedance.

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However, with folded structures, we must alter NEC manual procedures somewhat. For a linear element--whether a dipole or a monopole--we normally multiply the AGT times the reported impedance to arrive at a corrected source impedance. The correction is most reliable when the impedance is virtually resistive. With folded dipoles and monopoles, we must reverse the correction procedure. To arrive at the usable impedance value, we must divide the reported impedance by the AGT score. As a matter of course, we shall also report the net impedance of the structure. More significant for our interests will be the ratio of the adjusted or corrected impedance value for each leg to the calculated 2-wire impedance for a folded monopole having the wires and spacing applicable to a single fed wire and the center return wire.

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Some Test Results

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Table 1 provides the results for the series of modeling tests that I just described. The table lists 5 test sequences, each of which uses a different diameter for the inner, center, or return wire. The first column lists the 3 steps of spacing. The second column tells us the total number of vertical wires in the assembly. The number of fed wires is 1 less than the total. The third column lists the height in feet of the resonated skirt-fed monopole. The "Raw R" column lists the NEC 4.1 source resistance value before correction. The "Raw X" column provides a record of how close the model came to perfect resonance. The final column of raw data lists the AGT score using hemispherical increments of 5 degrees.

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The remaining columns list the operations performed on the raw NEC data. The adjusted source resistance per leg results from dividing the raw resistance by the AGT score. The net source resistance appears in 2 columns, the first dividing the raw leg resistance by the number of source, the second dividing the adjusted leg resistance by the number of sources. The final column lists the ratio of the adjusted leg resistance to the calculated 2-wire impedance.

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The resonant antenna height has only suggestive utility beyond showing the trends that confirm the propriety of model construction. As we increase the number of wires or the diameter of the center return wires, or the spacing between any fed wire and the return wire, the resonant height decreases over perfect ground. Although the trends are true, the exact resonant height of an actual folded monopole will vary somewhat with the ground quality and the number of radials forming the ground system. The AM BC standard of 120 quarter wavelength radials with shorter intervening radials remains applicable to all monopoles, whether linear or folded. With respect to the source impedance of an assembly, such a system best replicates perfect ground. (Of course, the overall ground quality plays a significant role in determining the far field patterns for the antenna.

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The AGT values provide an indication of the reason for halting the systematic modeling venture with a 10:1 ratio between the return wire and each of the fed wires. As we increase the diameter of the return wire, the AGT score decreases. By a 10:1 ratio, the score reaches 0.915. Beyond this value, I would not fully trust the reliability of the reported data, even when applying the corrective to the per-leg source resistance value. The impedance transformation ratio for a 2-wire system is largely a function of the physical properties of the folded monopole. Hence, the use of a large diameter tower (or its equivalent 3- or 4-face open tower) with standard wire sizes for the fed cage structure becomes problematical from a modeling perspective. 0.1" diameter wire approximates AWG #10, a value that falls about halfway between AWG #12 and #14, popularly used by radio amateurs, and AWG #6, sometimes used by commercial installations.

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The net adjusted source resistance columns indicate one reason why cage-fed or skirt-fed monopoles are finding proponents. As we add fed wires (symmetrically, of course) to a center return wire, the net source impedance of the parallel-fed outer wires brings down the overall source impedance. With equal-diameter wires for the fed and return legs, we have the familiar 4:1 up conversion of the impedance for each leg. As we increase the return wire diameter, the source impedance in each leg increases in step with standard expectations from the 2-wire equation, although we cannot obtain a precise number for more than a 2-wire system. Nevertheless, when we parallel the leg sources, the net impedance decreases as we increase the number of fed outer wires. For any given combination of fed and return wire sizes, increasing the spacing decreases the net impedance. However, for any number of fed sources, increasing the return wire diameter increases the impedance. A 5-wire (4-source) cage indicates impedances that are close to optimal for direct coax feeding with either no matching or minimal matching requirements. Construction variables relative to both the cage and the return mast or tower, along with ground and radial system conditions will modify the values shown. Nevertheless, the trends are useful in system planning, even if NEC-4 models may fail to be reliable at the return structure diameter that might be used. For example, a triangular tower with a 12" face might show an equivalent diameter of 8.88", which--even with 36" spacing--would yield models of very dubious reliability.

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For any given spacing and return-wire diameter, the per-leg source resistance shows a relatively tight grouping of values as we move from a 2-wire to a 5-wire folded monopole. About 50 Ohms separates the lowest from the highest value in each group. The variations within each group tend to suggest the level of mutual coupling among the fed wires and other interactions. Data patterns alone do not provide the details of the complex interactions. However, the close proximity of the values within each group relative to the calculated impedance value for a 2-wire folded monopole strongly indicates that each fed wire and the return wire form a 2-wire folded monopole, modified in impedance performance by the interactions. If each pair of wires in a complex multi-wire monopole forms a folded monopole, then we may legitimately call the entire structure, regardless of the number of cage or skirt wires, a folded monopole.

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We may regroup the final columns of values that show the ratio of calculated to modeled values of per-leg source resistance and graph them by reference to the spacing between the fed wire and the return wire. Fig. 4 shows the results for a spacing of 12". Each line represents one of the folded-monopole systems. The X-axis shows the increase in the return wire diameter. Note that the lowest value (0.1") is not a true linear increment relative to the other increments on the graph.

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The 2-wire graphed line establishes that using corrected per-leg impedance values yields models that are always well within 1% of the calculated value of impedance. The per-leg values for 3-wire systems are always below those for 4-wire and 5-wire monopoles. For a spacing of 12", the lowest per-leg value is about 0.83 of the calculated 2-wire value. In contrast, the highest value is about 1.4 times the calculated value. Although these limits are fairly wide, each curve shows a much narrower range of departure from the calculated value, which the 2-wire curve indicates.

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As we increase the spacing to 24", as shown in Fig. 5, the ratio of calculated to modeled adjusted per-leg impedance increases, except for the 2-wire model. It continues to show its tight correlation to the calculated impedance value. Perhaps only the effects of requiring a top wire prevent the ratio from reaching 1 to 1. The ratio values for the larger folded monopoles show slight increases for all of the more complex assemblies. Interestingly, about half of the data points fall above the 1:1 ratio lines, and half below it.

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The graph for a spacing of 36" between the return wire and each fed wire appears in Fig. 6. The overall grouping has all of the properties that we saw in the preceding graphs. However, the majority of data points now fall above the 1:1 ratio line. The differences among the 3 graphs are not great, but they are noticeable as a function of the increased spacing.

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Perhaps more interesting than the differences are the similarities among the graphs. For each size of folded-monopole assembly, regardless of spacing, the curve shapes are regular and similar. (Even the 2-wire curve shows a very slight drop in value as we increase the diameter of the return wire.) As well, the values within each graph show a relatively tight clustering around the calculated impedance value. 5-wire systems show the highest level of departure from the calculated value, a fact that appears to coincide with the closer proximity of the fed wires to each other. Determining the effects of mutual coupling would require a different sort of study from the present effort. In each case, I have resonated the total folded monopole system in order to arrive at as pure a resistive impedance as feasible. Interactive analysis of the wires might require a study using a set of fixed-length wires.

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Neverthless, the data shows that caged and skirted monopoles have their roots in 2-wire folded monopoles and are an extension of the basic structure. The variations are insufficient to deny the use of the term folded monopole as a generic label for all such structures.

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In many ways, however, settling the terminological preferences of engineers has only been a pretext for the true point of these notes. Too many amateurs are unfamiliar with the general properties of folded monopoles, both simple and complex. These notes represent one small attempt to fill the void and to acquaint the amateur with the range of labels that he or she might encounter in basic reading about these antennas. A secondary goal has been to show the nature and the limits of modeling these antennas using NEC-4. AGT values for NEC-2 versions of the models would be even worse. We might extend the range of the sampling of return-wire diameters by using a well-corrected version of MININEC 3.13, but even that program will eventually show less reliable results before we reach the tower dimensions that we might encounter in reality.

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Nevertheless, the trends shown in these notes may be useful in establishing realistic expectations from multi-wire folded monopole assemblies. The data shown here cannot eliminate the need for extensive field adjustment, but they may go some distance toward reducing the time involved.

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Updated 12-06-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Lower, Vertical


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The G5RV Antenna System Re-Visited
+ Part 1: The G5RV on 20 meters

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L. B. Cebik, W4RNL

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Louis Varney's "G5RV" was and is not an antenna, that is, an array of elements. It is an antenna system including a radiating element and a length of transmission line designed to present a "correct" impedance at a design frequency.

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The 1984 RADCOM Version of the Antenna System

The most familiar part of the system is the wire: a center-fed doublet 102' long. Actually, Varney calculated the length to be 3/2 wavelengths long at 14.15 MHz using a long standing equation: +
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The letter 'n' is the number of half wavelengths in the antenna. The result is 102.57' or 31.27 m. It is interesting that Varney notes in his 1984 article in RADCOM that he can shorten the wire to 102' or 31.1 m, since the entire system will be handled by an antenna tuning unit (or ASTU--antenna system tuning unit--as Varney preferred).

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(The entire 1984 article has been reprinted in Erwin David, G4LQI, HF Antenna Collection, published by RSGB in 1991. In the G5RV article, the author makes reference to his initial 1966 presentation of the basic idea. An adapted version appears in The ARRL Antenna Compendium, Vol. 1, 1985.)

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However, we conventionally sketch the G5RV antenna system as in Fig. 1. The center-fed doublet has a section of parallel transmission line extending from the radiating wire feedpoint to a junction with the "main" feedline.

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Curiously, Varney specifies the length of the matching section as 34.0' or 10.36 m. Using the same constant for a half wavelength (492), the section is a half wavelength at 14.47 MHz. The prescribed length assumed a velocity factor (VF) in the line section of 0.98--hence the final length.

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Many folks presume that the original impedance of the matching section line used in the G5RV is 450 Ohms. However, Varney specifies home-made open wire feeder composed of AWG #16 copper wire spaced 2" (5 cm) apart. The characteristic impedance of such line by standard calculations is closer to 525 Ohms. At 14.15 MHz, the line is 1/2 wavelength long, thus replicating the feedpoint impedance. Hence, the line Zo is--at 20 meters--of little consequence.

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A 3/2 wavelength wire--if properly cut--should present a feedpoint impedance slightly higher than a 1/2 wavelength resonant dipole: about 90 Ohms. Hence, the impedance at 14.15 MHz at the base of the matching section should also be about 90 Ohms. Thus did Varney design the G5RV antenna system for a 75-Ohm "twinlead" or coaxial feeder.

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There seemed to be an instant misunderstanding of the 1/2 wavelength line used by Varney in his antenna system, since recommendations immediately began to appear for the use of twinleads other than the home-made open- wire feeder used in the original. At 14.15 MHz, 300-Ohm solid ribbon twinlead with a VF of 0.82 (using numbers from the RADCOM article) requires 28.5' or 8.69 m of line for the matching section. However, the recommended length is 28' or 8.5 m. This latter value is closer to but not identical with applying the ribbon VF value to Varney's 34' length--which already has a VF of 0.98 built into its length. Likewise 300-Ohm ribbon with windows has a VF (in the article) of 0.90. Calculating its length using the 492 constant yields 31.29' or 9.54 m. However, the recommended length of such line is 30.6' or 9.3 m, the values one would arrive at by applying the 0.90 VF value to Varney's 34' length.

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With so much confusion built into the basic accounts of the G5RV, there can be little wonder that the antenna has become the subject of endless variations, some being serious attempts to arrive at an ideal antenna of its type, others being generated simply to sell commercial versions of the antenna.

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We have not yet tried to place the antenna on bands other than 20 meters. It is in pursuit of this goal that the G5RV has been taken well past its original intent. Remember that, even though Varney thought the G5RV would provide a good match on 20 meters for a 75-Ohm main feedline, he believed in using an ATU at the rig end of the line.

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Some Small Facts About Wire Antennas

Before we take the plunge into other bands, we should pause to review the methods by which the G5RV antenna system emerged and how well they play in the 21st century. The review will not be simple, because many of the notes are partially accounted for by the developer of the system. However, those same notes may be at odds with common but erroneous interpretations of the antenna. This feature will hold true without ever leaving 20 meters or straying very far from the design frequency, 14.15 MHz. +

The equation for calculating the length of an antenna consisting of multiple half wavelengths has a long and honored history when well used. In fact, it is very well used when calculating non-resonant antennas or antennas for which resonance is not at all crucial. Where we require some degree of precision in determining the length of a resonant antenna, the equation turns out to be quite off the mark.

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Since Louis Varney stated that he intended to use the antenna system with an antenna tuner, he effectively implied that the equation used to determine the 102' length was sufficiently accurate for that method of operation. As well, his estimate of the feedpoint impedance, repeated at the end of the 34' matching section of parallel transmission line, was also within the limits of accuracy necessary for using the system with an ATU. However, 102' is not a resonant length of wire at 14.15 MHz, and its resistive impedance component is not 90 Ohms.

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These latter facts, which we shall embellish shortly, would be not problem if the general conception of the G5RV antenna system included the use of an antenna tuner. However, the antenna has acquired a reputation for being able to provide under 2:1 SWR on more than one band--without qualifications needed to confine the claim to a reasonably clear arena of truth. So the following notes are more applicable to understanding why the general conception--rather than Varney's--is off base.

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We should note two facts about wire antennas. First, in the HF region, we have tended to blithely ignore the fact that changes of wire diameter have an effect upon the resonant length of a wire antenna and upon the feedpoint impedance. We tend to use "cutting" formulas as if they were wholly unrestricted in scope and always accurate, regardless of the wire we select. For HF wire antennas in the U.S., we tend to use wires as small as AWG #18 (0.0403" diameter)--such as copperweld--and as large as AWG #12 (0.0808" diameter) hard drawn copper, not to mention the common sizes in between. The wire diameter is small compared to a wavelength (about 834.5" at 14.15 MHz); nevertheless, a 2:1 change of wire diameter will have a recordable affect on the wire's resonant length and feedpoint impedance.

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Second, as we move a horizontal wire antenna to varying heights below about 1 wavelength, we shall find a second source of variation in the resonant length and feedpoint impedance of a wire antenna. Unlike variations due to wire diameter, which are quite regular, the variations due to height tend to follow cyclical patterns that repeat every half wavelength.

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We can sample some of these variations from the tables that follow. In each case, I modeled 102' copper wires from AWG #18 through AWG #12, using NEC-4, which is more than adequate to provide accurate data. The models used 101 segments with a source centered on the wire. The test models were initially modeled in free space and then at two different heights above average ground (conductivity: 0.005 s/m; permittivity: 13). The upper height was 65.62' or 20 m, close to 1 wavelength above ground. The lower height was 32.81' or 10 m above ground. Let's see what the models report.

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+              Source Impedance of a 102' Wire at 14.15 MHz
+
+Free Space
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             102 - j 48                  1.869
+      #14             103 - j 51                  1.914
+      #16             104 - j 53                  1.958
+      #18             105 - j 55                  1.999
+65.62'/20m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             104 - j 49                  1.883
+      #14             104 - j 51                  1.928
+      #16             105 - j 54                  1.972
+      #18             106 - j 56                  2.012
+32.81'/10m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             111 - j 56                  2.048
+      #14             112 - j 59                  2.093
+      #16             112 - j 61                  2.136
+      #18             113 - j 63                  2.177
+
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The SWR numbers are overly precise relative to the rounded impedance values. The intent is to show clearly the general trends. The thinner the copper wire, the higher the resistive component of the impedance, despite the fact that the wire is ever shorter of resonance. As well, although the impedance values at a 1 wavelength antenna height are very close to the free-space values, the impedance figures at a 1/2 wavelength height show some departure from the free-space values.

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Finally, the wire is well short of resonance at the design frequency. Otherwise put, for precision of resonant length, the traditional equation simply will not do.

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I replicated the exercise when I added in a 34' or 10.36-m length of 525-Ohm feedline with a velocity factor of 0.98. This provides an electrical half wavelength of line, that is, the equivalent of 34.77' or 10.60 m at 14.15 MHz. Remember that the intent of this line section on the design frequency is to replicate the wire feedpoint impedance at the end of the so-called matching section.

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For this exercise, it is unnecessary to model the parallel transmission line with physical wires. One may use the TL facility within NEC-4 software to provide a non-radiating mathematical model of a perfect (lossless) transmission line. Since Varney's writings anticipate that the antenna builder will respect the requirement of parallel transmission line to sustain its balance, the non-radiating aspect of the NEC TL facility is within the bounds of the exercise. Because the line is relatively short, the difference between a lossless line and a real line constructed according to Varney's specifications will almost too small to notice. On the other hand, because we are using a physical length that is only close to but not exactly a half wavelength at the design frequency, we should expect to see small variations in the resulting impedance and SWR values. The following table records the results of this exercise.

+ 
 
+        Source Impedance of a 102' Wire and 34' Line at 14.15 MHz
+
+Free Space
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             102 - j 52                  1.933
+      #14             103 - j 54                  1.979
+      #16             104 - j 57                  2.024
+      #18             105 - j 59                  2.066
+65.62'/20m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             104 - j 52                  1.946
+      #14             104 - j 55                  1.993
+      #16             105 - j 57                  2.037
+      #18             106 - j 59                  2.079
+32.81'/10m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             111 - j 60                  2.111
+      #14             111 - j 62                  2.158
+      #16             112 - j 64                  2.203
+      #18             113 - j 66                  2.245
+
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There are only slight differences between the two tables, and the bulk of those differences result from the fact of choosing a physical approximation of a 1/2 wavelength line rather than using an exact 1/2 wavelength line. However, it is likely that the modeled line is closer to 1/2 wavelength than will be most lines cut for a physical implementation of the G5RV antenna system.

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At the design frequency, we need not explore the consequences of using something other than the line specified for the antenna. The use of 300-, 400-, and 450-Ohm lines--if each is an electrical half wavelength--will result in virtually identical tables for 14.15 MHz.

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A more important question concerns the antenna length. As initially specified, the wire is too short to be resonant at 14.15 MHz. But what length might seem more resonant? The spread of impedance figures suggests that we might use a compromise between the resonance at a 20-m height and resonance at a 10-m height. In fact, I used this compromise to arrive at a length of 103.35' or 31.5 m.

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The compromise does not represent an ideal situation, only a convenient one. The change of impedance and resonant length does not follow a simple progression with decreases in height. Instead, the values change cyclically in half wavelength increments (ignoring height below about 0.2 wavelengths above ground). The sample heights used here do not necessarily represent the extremes that might appear at other heights.

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With these qualifications, we can examine the data reported by NEC-4 for the revise wire length with the 34' line attached. Since the free-space values and the 20-m height values are so similar, I have omitted the free-space portion of the exercise.

+ 
 
+      Source Impedance of a 103.35' Wire and 34' Line at 14.15 MHz
+
+65.62'/20m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             111 + j  7                  1.494
+      #14             112 + j  7                  1.497
+      #16             112 + j  6                  1.504
+      #18             113 + j  6                  1.515
+32.81'/10m
+      Wire Dia.       Feedpoint Impedance         75-Ohm
+      AWG             R +/- j X Ohms              SWR
+      #12             119 - j  1                  1.586
+      #14             119 - j  2                  1.592
+      #16             120 - j  2                  1.601
+      #18             120 - j  3                  1.613
+
+

Increasing the length of the wire toward resonance, of course, increases the resistive component of the source impedance. Hence, there is a limit as to how low the 75-Ohm SWR can go by this strategy. As well, as the wire thins, the resistive component goes up.

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We seem to have gained a usable 75-Ohm SWR at the design frequency, but obviously the 50-Ohm SWR would be well above 2:1. In the days before fixed-tuned output circuits in transmitters, the old pi-network amplifier output circuits--with variable "tune" and "load" controls--would have easily provided a match to these impedance values in 20 meters. As well, they fall well within the range of almost any ATU, even the limited range versions incorporated into some modern transceivers.

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However, an SWR value at a spot frequency does not tell the entire story about antenna performance. We are as interested in the SWR bandwidth as we are in the particular value at some given frequency. So I ran frequency sweeps of the two versions of the G5RV antenna, both with the 34' line attached.

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Fig. 2 shows the curves for the short and the long antennas. Clearly, the longer length favors the lower end of 20 meters, while the 102' length favors the upper end of the band. The impedance level of a G5RV is high enough that we cannot obtain full band coverage from the wire and line combinations. In addition, the 1/2 wavelength line section is 1/2 wavelength only at the design frequency. Hence, it contributes to a narrowing of the SWR bandwidth.

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We may note in passing that a common resonant 1/2 wavelength dipole of any of the wire sizes sampled in this exercise would easily cover the 20-meter band with under 2:1 SWR. Moreover, an ATU would free us from concern about the 2:1 SWR that marks the limit of full output from most modern transceiver designs. Nonetheless, it is interesting to note that the 3/2 wavelength wire tends to show a narrower SWR bandwidth than the shorter half wavelength dipole. The narrower operating bandwidth will, of course, be a matter of concern for anyone who tries to use a G5RV antenna system without an intervening ATU. Unfortunately, this latter mode of operation seems to be the rule rather than the exception--at least until one experiences first hand the limitations of the system.

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A Side-Note on Height vs. Feedpoint Impedance

I have noted that for any single-wire doublet, the source impedance varies with the height above ground. The variation is most significant in the region below a 1 wavelength height. The differences in the G5RV feedpoint impedance reflected this variation, but perhaps not as convincingly as it ought to do. +

Let's begin with a common center-fed dipole at 14.15 MHz. We shall make it from AWG #12 copper wire. Our model will be resonant in free-space. A length of 33.727' or 10.28 m satisfies this requirement within +/-j 1 Ohm reactance. The wire's impedance in free space is 72.9 + j 0.7 Ohms.

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I then set the antenna over real average ground, beginning at 0.2 wavelength and continuing in 0.05 wavelength increments to 1.2 wavelengths. The effects of the height changes on the feedpoint resistance and reactance appear in Fig. 3.

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As noted earlier, the resistance and reactance cycles peak at 0.5 wavelength intervals of height. However, the resistance and reactance curves are not synchronized. The reactance peaks occur about 0.15 wavelength higher than their closest resistance peaks.

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The reactance swings allow us to re-interpret the data in this way: The resonant length of a 1/2 wavelength dipole changes with height, especially within the range of heights shown in Fig. 3. But, even if we resonate the dipole at each height, the feedpoint impedance will still show cyclical changes as we increase the height throughout the range that we have sampled.

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A 3/2 wavelength doublet exhibits the same sort of impedance swing. Let's construct a 14.15-MHz resonant 3/2 wavelength doublet from the same AWG #12 copper wire. If we resonate it in free space, it will be 103.117' or 31.43-m long. Its free-space feedpoint impedance will be 108.1 + j 0.2 Ohms. Now we are ready to perform the same set of exercises that we performed on the dipole.

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Fig. 4 shows the results of our test runs. Once more, the resistance and reactance vary considerably as we change heights. The reactance reaches its peaks about 0.15 wavelength higher than height at which the resistance values peak. Perhaps the most notable differences between the dipole and doublet graphs are two: First, the doublet peaks and dipole peaks do not occur at the same heights above ground, although the impedance components for both antennas show 1/2 wavelength cycles. Second, the feedpoint impedance of the longer doublet smoothes out rapidly above 1 wavelength, while the 1/2 wavelength dipole impedance components continue to show noticeable cycles.

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Not only does the impedance show differences with height, but so too do the elevation and azimuth patterns. Here, we may illustrate by taking the elevation and azimuth patterns of the 3/2 wavelength doublet at 20-m and at 10-m heights above ground.

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The elevation pattern in Fig. 5 shows the typical double lobe structure of any horizontal antenna just below 1 wavelength above ground. The azimuth pattern presumes that the antenna wire is stretched horizontally across the graphic and is taken at the antenna's take-off (TO) angle (the elevation angle of maximum radiation), namely, 14 degrees. It shows 6 lobes, just as we would expect of any wire antenna half-way between 1- and 2 wavelengths long. Note the distinctness of the angular lobes; that is, note the depth of the null off the ends of the antenna.

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Fig. 6 shows the equivalent patterns when the antenna is half the height of the first model. At just below a half wavelength in height, we have only a single elevation lobe, just as would any horizontal single-wire antenna at the same height. The azimuth pattern uses a TO angle of 28 degrees and is clearly kin to the one taken at 20 m above ground. However, note the shallower null off the ends of the antenna wire. Radiation off the ends of the wire is down only about 4 dB compared to radiation at the maximum gain angles, compared to a 12-dB differential for the higher version of the antenna.

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Like any other wire antenna, the 3/2 wavelength doublet--the heart of the G5RV antenna system at 20 meters--requires reasonable careful orientation if the user has in mind any particular target areas for communications. Likewise, height will always benefit a single-wire antenna, at least to the point where the vertical beamwidth matches as best possible the typical variations in the skip angles on 20 meters.

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Conclusion to Part 1

We have reviewed some of the design elements that went into the G5RV antenna system at its design frequency of 14.15 MHz, including some apparent confusions surrounding alternative "matching section" lengths when using different parallel transmission lines. As well, we have shown some of the limitations within the simplified design procedure used to develop the basic G5RV length. +

Perhaps of equal or greater significance has been our foray into understanding some of the factors that influence the operation of wire doublets that are usually absent from simplified cutting formulas. Every change that we make from a design that we use as a starting point has consequences for how well the antenna performs compared to the original. The importance of these changes can range from negligible to monumental, depending upon our operating circumstances and our expectations.

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Louis Varney expected to use his G5RV antenna system with an ATU on many bands without much regard for where on each band his strongest lobes were pointed. Consequently, the antenna worked very well for him. However, much of the indirect reputation of the G5RV has to do with operating on at least some bands without an ATU. As well, expectations of lobe direction have largely been silent, leaving each user to bring his or her own expectations to the table. As a result, many users have been overjoyed, while many other have been disappointed.

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Since we have extracted about as much useful data as we can for the basic design frequency--the 20-meter band--we may next turn to trying to use the G5RV on other bands.

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Updated 05-21-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: The G5RV on all HF Bands

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Go to Part 3: The Almost-No-ATU ZS6BKW

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Go to Main Index

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Topics: G5RV / ZS6BKW, HF Multi Band


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The G5RV Antenna System Re-Visited
+ Part 2: The G5RV on all HF Bands

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+

L. B. Cebik, W4RNL

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The original G5RV antenna system consists of a center-fed horizontal 102' wire plus a 34' length of open-wire 525-Ohm feeder. Louis Varney, the antenna system's developer, intended two other features. First, the main feeder that we connect to the base of the open-wire section should be 75-Ohm twinlead or coaxial cable. Second, the main feeder should go to an antenna tuning unit (ATU) and not directly to a transceiver.

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In Part 1, we examined some of the basic properties of the G5RV antenna system at its basic design frequency, 14.15 MHz. We explored some of the variations created by varying the height of the antenna above ground and by using different wire diameters. While none of these variations has much of an effect if we use an ATU between the main feeder and the transceiver, they become important if we attempt to use the antenna system without a tuner. With the physical dimension selected by Varney, the system provides only a partial coverage of 20 meters with a 75-Ohm SWR under 2:1, although a tuner would easily permit full band coverage.

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Somewhere along the line of time, the G5RV antenna system has acquired a false aura: namely, that it can cover many amateur bands in the HF region without the use of an antenna tuner. Since almost any rudimentary analysis of the antenna system can show this reputation to be false--and not consistent with what Varney wrote about his antenna system--we shall not dwell on that matter. We shall, of course, present some modeling data that confirms the inaccuracy of the reputation. However, there is a much more interesting question to investigate.

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If the antenna system will not provide the desired coverage without an antenna tuner, why use the matching section at all? Why not simply run a feedline of one impedance all the way from the antenna wire to an antenna tuner? Varney recognized that this mode of operation is quite feasible. Nevertheless, he believed that his matching section offered some advantages on most amateur bands. Let's see if we can uncover them.

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The 102' Wire Doublet

In Varney's 1984 RADCOM article, he noted that whatever feed system the user might provide, the patterns on each of the HF amateur bands depended solely on the radiation from the antenna wire itself. Over the years, I have discovered that many multi-band wire-antenna users remain unaware of the patterns produced by their antennas on different bands. Therefore, it may be useful to review the pattern situation for the 102' wire that is the radiating portion of the G5RV. +

A single center-fed linear element (regardless of the element diameter) will have a pattern that is broadside to the element from a length of about 1/3 wavelength (about the shortest practical doublet length) to a length that is a bit over 1 wavelength. The electrical length of a fixed length physical doublet will increase as we increase the operating frequency. A 3/2 wavelength doublet at 14.15 MHz is 1/2 wavelength at one third that frequency, or about 4.7 MHz. Obviously, the 102' wire is well under 1/2 wavelength in the 80-meter band. At 3.75 MHz, the wire is about 0.39 wavelength.

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As we increase the operating frequency, the wire become electrically longer. When it is about 1.25 wavelengths, we obtain the typical extended double Zepp pattern with the strongest broadside main lobes that we can achieve from a single element, but with "ears." The ears are emerging new lobes that are part of the natural process of pattern evolution. As we increase frequency--that is, as we make the wire electrically longer--the lobes will evolve in a regular fashion.

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At 1 wavelength, we have 2 lobes--one on each broadside to the wire. At 2 wavelengths, we have 4 lobes, each at quartering angles relative to the wire orientation. At 3 wavelengths, we obtain 6 lobes. In fact, the total number of lobes for any wire that is an integral number of wavelengths will simply be twice the length as measured in wavelengths.

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However, lobes do no simply pop into and out of existence. As we pass any integral wavelength marker in making our wire electrically longer, the old lobes will gradually diminish and the new lobes associated with the next integral wavelength marker will emerge and increase in size. At the 1.25 wavelength point of the extended double Zepp, the 1 wavelength broadside lobe have reached their peak and are ready to diminish, while the new lobes--associated with a 2 wavelength wire--have made their appearance. As we move the wire closer to 1.5 wavelengths, the lobes reach a point of roughly equal strength. Since we have both the 1 wavelength and the 2 wavelength lobes, our lobe total is 6. We can apply similar counting methods to any wire that is x.5 wavelengths, where x is any integer.

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So for any wire of any electrical length, we can predict the lobe structure. With that fact in mind, let's survey the patterns that we can obtain from a 102' wire. For the sake of brevity, I shall select only one of the 102' wires and one of the heights that we examined in Part 1. Let's use AWG #12 copper wire and place it 20 m or 65.62' above average ground.

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The fixed physical height above ground, of course, will have a bearing upon the pattern by changing the take-off (TO) angle, or the elevation angle of maximum radiation as we change frequency. As we increase frequency and shorten the length of a wave, the antenna will be electrically higher. Hence, the TO angle will be lower. As a rule of thumb--although calculation equations exist in the handbooks--the TO angle of an antenna at 1/2 wavelength height is about 25-26 degrees. At 1 wavelength, the TO angle is 14 degrees. At 2 wavelengths, the angle drops to the 7-8-degree mark. One of the benefits of using a single multi-band wire antennas is that the TO angle tends to correlate with skip properties. As we increase frequency, the dominant skip angles decrease, matching our wire antenna TO angles, if we have it high enough in the first place.

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Fig. 1 shows the anticipated azimuth patterns of the 102' wire at a height of 20 m above ground--about 1 wavelength high at 20 meters. Unlike the patterns for a long-boom Yagi, which might change across the span of a single amateur band, the patterns of a single wire antenna are stable and change slowly. Hence, there will be no significant difference in the 15-meter patterns from one end to the other of this 450-kHz wide band.

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+ +
+

Each pattern in Fig. 1 shows the frequency at which it was taken, along with the TO angle. 102' represent a little over 1 wavelength at 10.125 MHz, and so we see two broadside lobes. The antenna is about 2 wavelengths long at 17 meters, revealing a 4-lobe pattern. At 10 meters, the antenna is close to 3 wavelengths long and shows 6 distinct lobes.

+

At 20 meters, where the wire is 3/2 wavelengths, we also find 6 lobes, but these are the product of the 1 wavelength and the 2 wavelength lobes, one set enlarging and the other set diminishing. The other bands shows lobes in various states of emergence or disappearance because the 102' wire in somewhere between the convenient marker lengths that we have designated.

+

With any multi-band single-wire antenna, the user has some decisions to make. If he has some latitude in orienting the antenna, he can choose a favorite band and orient the wire so that a major lobe points in the direction or directions of favored target communications areas. Or he can spend nights of pencil and paper planning trying to figure out the best orientation that will yield the best possible results on all favored bands.

+

Before we try to feed this wire, let's examine one other feature of the lobe structure of the 102' wire. The following table provides the maximum gain and TO angle of the 102' wire as we installed it at 20 m above ground. Maximum gain is the strength of the most major lobe (of which there may be more than one).

+ 
 
+1.  102' AWG #12 Copper Wire Gain and TO Angles
+
+Band       Freq.            Max Gain        TO Angle
+Meters     MHz              dBi             degrees
+80         3.75              6.00           60
+40         7.1               7.94           29
+30         10.125            9.68           20
+20         14.15             8.37           14
+17         18.118            9.37           11
+15         21.1             10.05           10
+12         24.94            10.57            8
+10         28.1             10.12            7
+
+Note: Antenna height = 20 m.  Maximum gain = gain of the strongest lobe.
+TO angle = elevation angle of maximum radiation.
+
+

There is a general trend toward higher gains in the major lobes as we increase the electrical length of the wire by increasing frequency. This property applies to any horizontal wire antenna, regardless of any special name we might give it. However, increase major lobe gain is accompanied by a disadvantage: the width of the major lobes decreases as we electrically lengthen the antenna wire and place more lobes into the pattern. Hence, the higher the frequency of our 102' wire, the more finicky becomes the aim at a target area.

+

You may also note another trend in the number, most clearly revealed by examining the numbers of 30, 20, and 17 meters. Note that the maximum gain on 20 meters is less than the values for 30 and 17 meters. One of the phenomena of lobe emergence is that, in general, when we are at the x.5 wavelength region, the emerging and diminishing lobes will have a bit less strength, because we are combining two lobe structures.

+

The final feature that we want to notice is the feedpoint impedance of the 102' wire as taken at the center point of the wire itself. These values will give us some clue as to the rationale behind the G5RV antenna system.

+ 
 
+2.  102' AWG #12 Copper Wire Feedpoint Impedances
+
+Band       Freq.            Feedpoint Impedance   Notes
+Meters     MHz              R +/- j X Ohms
+80         3.75               46 - j  339         High relative X
+40         7.1               397 + j 1037         High relative X
+30         10.125           1220 - j 2522         High Z and relative X
+20         14.15             104 - j   49         Low X
+17         18.118           2281 + j 1624         High Z
+15         21.1              337 - j 1038         High relative X
+12         24.94             203 + j  328         Moderate relative X
+10         28.1             2669 + j  678         High Z
+
+Note: Antenna height = 20 m
+
+

Notice the large range of the resistive components of the impedances on the HF bands--all the way from 46 to 2600 Ohms. (The resistive component at 3.5 MHz would be even lower than 46 Ohms.) As well, note how many of the bands present relatively high values of reactance--some inductive, others capacitive.

+

To feed this antenna with a single transmission line, we would normally select a characteristic impedance somewhere in the vicinity of the geometric mean between the extremes. Something in the 400-600-Ohm vicinity should prove usable. However, the impedance at the antenna tuner terminals depends upon three general factors--ignoring line losses for the moment: the feedpoint impedance, the characteristic impedance of the feedline, and the electrical length of the feedline. Unless there is a perfect match between the antenna feedpoint impedance and the characteristic impedance of the transmission line, the line itself will continuously transform the impedance components along each half wavelength of line at the frequency of operation. It is not at all unusual to encounter values of resistance and/or reactance at the tuner terminals that fall outside the matching range of the tuner. The most ready cure is often to insert an additional length of line to see if we cannot arrive at resistance and reactance values within the tuner's range. If we are lucky, the insertion may allow matching at all used frequencies. If we are not so lucky, then we may need to developing a switching system to insert the added line length on the bands for which we need it.

+

Now we are ready to understand part of the rationale behind the G5RV antenna system, with its 34' of 525-Ohm transmission line.

+

The G5RV Antenna System and Some Variants on All HF Bands

Varney performed a rudimentary standing wave analysis for his antenna system in his 1984 article. Let's begin by reviewing his results in tabular form. Remember that he is analyzing the likely impedance that will appear at the lower terminals of the matching section. + 
 
+3.  G5RV's analysis of the system at all HF frequencies
+Note:  Load Impedance is the impedance at the end of the "matching
+section."
+
+Band       Analysis                               Load Impedance
+80 meters  Wire + Section = shortened Dipole      Reactive (R+/-jX)
+40         Wire + Section = partially folded
+           2-half-waves in phase                  Reactive (R+/-jX)
+30         Wire + Section = partially folded
+           2-half-waves in phase                  Reactive (R+/-jX)
+20         3-half-waves                           Resistive (ca. 90 Ohms)
+17         2-full-waves in phase                  High Z, slight X
+15         5-half-waves                           High Z, resistive
+12         5-half-waves                           Resistive (90-100 Ohms)
+10         2 x 3-half-waves in phase              High Z, slight X
+
+

This sort of information style makes it difficult for us to directly compare the results with the matching section with the modeled results that we obtained without the matching section. Therefore, let's do some NEC-4 modeling, using the same TL facility matching section construct that we used in Part 1. As we did initially, we shall confine ourselves to a 20-m height for the 102' AWG #12 copper wire.

+

While we are at the task, we can also examine some slight variations in the G5RV antenna system. All of the variations represent slight modifications in the matching section transmission line.

+
+ Version 1: the original G5RV with 34' of 525-Ohm 0.98 VF open wire line. +

Version 2: the common U.S. implementation of the G5RV using 34' of 450-Ohm 0.91 VF vinyl-covered window line.

+

Version 3: a second common implementation using 28' of 300-Ohm 0.82 VF TV-type ribbon or solid vinyl covered line, noted in the 1984 article.

+

Version 4: 300-Ohm 0.9 VF windowed vinyl-covered TV-type ribbon line (in the U.S., available from The Wireman in SC, but check his specification for the VF).

+
+

Allowing for the possible confusion of the VF attached to the original open-wire line by those who suggest alternative line for the matching section, the sections are all cut to be about 1/2 wavelength at 14.15 MHz. Hence, we should see about the same impedance values in all version as we obtained for the wire alone.

+

The following table shows the modeled impedance values at the base of the matching section for each version on each of the test frequencies spread across the HF region. As well, for reference, the tables also provide the 75-Ohm SWR values in keeping with Varney's intent that the remaining transmission line to the ATU be 75-Ohm twinlead or coaxial cable.

+ 
 
+4.  Impedances at the base of the "Matching Section" for 4 Variations on
+the G5RV Antenna System
+
+All Versions use a 102' AWG #12 copper wire at 20 m above average ground.
+differences appear in the "Matching Section."
+Version 1:  34' (10.36 m) 525-Ohm, VF 0.98 open wire system (G5RV
+recommendation)
+Version 2:  34' (10,36 m) 450-Ohm, VF 0.91 windowed parallel line (common
+implementation)
+Version 3:  28.0' (8.53 m) 300-Ohm, VF 0.82 solid TV-type parallel line
+Version 4:  30.6' (9.33 m) 300-Ohm, Vf 0.90 windowed TV-type parallel
+line
+
+                      Version 1                   Version 2
+Band       Freq       Impedance        75-Ohm     Impedance       75-Ohm
+meters     MHz        R+/-jX           SWR        R+/-jX          SWR
+80         3.75         35 + j  136     9.6         31 + j  112    8.0
+40         7.1          88 - j  230     9.9         60 - j  110    4.5
+30         10.125       95 + j  584    50.0        103 + j  682   62.0
+20         14.15       104 - j   52     1.9        104 + j   51    1.9
+17         18.118      157 - j  517    25.2         73 - j  230   11.6
+15         21.1         77 + j  219    10.2         86 + j  376   23.9
+12         24.94       144 - j   73     2.5        145 + j  156    4.5
+10         28.1       2398 + j 1002    37.6        409 - j  917   33.0
+
+                      Version 3                   Version 4
+Band       Freq       Impedance        75-Ohm     Impedance       75-Ohm
+meters     MHz        R+/-jX           SWR        R+/-jX          SWR
+80         3.75         20 - j   10     3.8         20 - j   11    3.8
+40         7.1          29 - j   83     5.9         29 - j   85    6.1
+30         10.125       25 + j  270    41.9         25 + j  266   41.1
+20         14.15       106 - j   64     2.2        106 - j   68    2.3
+17         18.118       55 - j  315    26.2         57 - j  326   26.9
+15         21.1         24 + j   44     4.2         24 + j   38    4.0
+12         24.94        83 + j   24     1.4         83 + j   18    1.3
+10         28.1        825 + j 1261    36.8        666 + j 1171   36.4
+
+

Let's initially look at a couple of bands in the whole range. Although all of the matching sections show similar impedances at 14.15 MHz, we cannot be assured that the 20 meter SWR curves will be identical for all 4 versions. Therefore, Fig. 2 shows the 75-Ohm curves for the 4 versions.

+
+ +
+

Versions 1, 3, and 4 show similar curves, since they were cut close to a half wavelength for the line used. However, the common US implementation of the G5RV simply replaces one line with another without allowing for the difference in velocity factor. Hence, the impedance transformation undergoes more than 1/2 wavelength, and the resulting impedance away from the design frequency differs from the other versions. The lesson is that if one wishes to replicate the G5RV system at 20 meters with a different matching section line, one must use some care in accounting for differences in the velocity factor.

+

Of all the bands, 12 meters shows the greatest promise for avoiding the need for an ATU. Fig. 3 presents the SWR curves for this narrow ham band.

+
+ +
+

As may be evident, the two 300-Ohm systems provide a good 75-Ohm SWR, while the two higher-impedance matching sections do not. The unsuspecting novice builder of a G5RV may wonder why.

+

The matching section is 1/2 wavelength long at 14.15 MHz. However, it has a different electrical length at every other frequency across the amateur bands. Lines having different characteristic impedances will yield different impedance transformations.

+

We are likely familiar with the fact by now that a transmission line of any characteristic impedance will replicate the wire feedpoint impedance if the line is electrically 1/2 wavelength. We may also be familiar with the fact that if a line is electrically an odd number of quarter wavelengths, then the impedance at the base or "sending" end will be the square of the line's characteristic impedance divided by the load impedance--in this case the wire feedpoint impedance.

+

However, these simplified relationships derive from a much more complex equation describing the transformation of the load impedance for any length of line whatsoever. The following equation shows the transformation, but still simplified by omitting the calculation of line losses. As noted in Part 1, the modeling software uses a lossless-line model for its calculations, and the losses in the short parallel line composing the matching section are almost small enough to be negligible.

+
+ +
+

The terms l and lambda are in the same units, where l is the electrical length of the transmission line, while lambda is a wave length. Zo is the characteristic impedance of the line; ZL is the load impedance, and Zs equals the impedance at the sending end of the line. This particular version of the impedance transformation equation comes from page 186 of Terman's Radio Engineers' Handbook. Of course, ZL may be complex (R +/- jX), and so, too, may be Zs. There are a number of utility computer programs that will calculate the impedance transformation--with or without losses--including the resistive and reactive components.

+

The message of the equation for this context is that the complex transformation of impedance along a transmission line, when the load impedance and the line's characteristic impedance are not a perfect match, depends on the line length and the line's characteristic impedance. The transformation on all bands for which the line is not a nearly exact multiple of a half wavelength will differ as we change the characteristic impedance of the line. Therefore, as we develop alternative types of transmission line for the matching section of a G5RV, we should not expect to replicate the impedance values of Varney's original version on bands other than 20 meters.

+

We can see the effect of moving from the 450-to-525-Ohm region down to 300 Ohms by looking at the impedance values for the bands below 20 meters. The higher impedance lines yield resistive components between 35 and 95 Ohms, while the 300-Ohm lines produce values in the 20-30-Ohm range. These values are also a good reason not to run the feedline to the 4:1 balun that inhabits so many network tuners in common use today. We do not need an already low resistive component further reduced.

+

However, the 300-Ohm line has a small advantage. It yields impedance values on more bands with 75-Ohm SWR values under 10:1. Although there is no guarantee, given the very wide variety of components used in today's tuners, the lower the overall SWR value, the more likely it is that the feedline from the matching section to the tuner will provide values within the tuning range of the ATU.

+

Indeed, it is now time to perform one more comparison: between the overall impedance values in the table for the 4 versions of the G5RV and the impedance values for the feedpoint of the 102' wire alone. In general, the matching section yields lower values of both resistance and reactance. Therefore, with a 75-Ohm line from the matching section to the ATU, we are likely to be able to effect a match. We would only be able to achieve this goal with parallel transmission line all the way from the wire to the ATU--and might have to insert some line on some bands.

+

The final question in this series in inquiries is simple: why do the job in the G5RV manner?

+

Setting Up a G5RV Antenna System

For a G5RV antenna system--at least as indicated by both Varney himself and by the modeling results--we shall need several components: +
+

102' of strong copper or copperweld wire--along with sundry end rope, insulators, and a center-junction piece.

+

A length of parallel transmission line cut to 1/2 wavelength at about 14.15 MHz, accounting for the line's velocity factor.

+

A length of feedline from the matching section to the ATU. For network tuners, we might as well use 75-Ohm or even 50-Ohm cable. However, since the line will be subject to considerable SWR and hence voltage and current excursions along its length, we should use the shortest possible length to minimize losses. As well, we should use the fattest, lowest loss line that we can obtain (RG-213 or better). Because 75-Ohm transmitting twinlead is no longer made in the U.S., we can only implement the G5RV using coaxial cable, unless we are willing to build our own low-impedance parallel line.

+

A choke to place at the junction of the matching section and the coaxial cable, as noted in the 1984 RADCOM article.

+

A wide-range network tuner.

+
+

Fig. 4 sketches the essential ingredients of the antenna from the wire down to the network tuner.

+
+ +
+

When used with a wide-range tuner, there is little to choose among the versions of the matching section illustrated in these notes--or among a large lot of other potential sections. Each should be 1/2 wavelength at about 14.15 MHz. Perhaps the only general rule involved is that the higher the characteristic impedance of the matching section transmission line, the higher the impedance that is likely on the bands below 20 meters. However, 300-Ohm line (the transmitting variety, for lowest losses) offers fewer bands with very high SWR values relative to either 50- or 75-Ohm cable.

+

Perhaps the only other component of the system calling for comment is the choke. Very often we hear such devices being called choke-baluns or simply 1:1 baluns. Such devices have two functions that are inter-related. They provide a transition between balanced line on the one side and unbalanced line on the other. They also tend to attenuate common-mode currents on the braid of the coax. In fact, these two functions are one and the same, for the only reason for needing a transition device where we effect no impedance transformation is to suppress common-mode currents.

+

Newcomers to antenna work are sometimes confused by calling these current common-mode currents and also saying that they appear on the coax braid. Normal transmission line currents are ideally equal in magnitude but opposite in phase anywhere along a transmission line. Common-mode currents have the same phase on both conductors. On parallel line, such currents are of equal magnitude on each line. However, on coaxial cable, due to the skin effect which tends to cancel currents at the center of a conductor and place all current at the surface, the current is most measurable on the braid.

+

Louis Varney warned against the use of transformer-wound 1:1 baluns because many designs show considerable losses when the load reactance is significant. Indeed, Jerry Sevick, W2FMI, who has published the most material on transmission-line transformers, recommends that all reactance compensation occur on the load side of the balun.

+

In place of such baluns to suppress common-mode currents, Varney recommends a 6" diameter coil of about 8 to 10 turns of the feedline coaxial cable at the junction of the matching section and the main feedline. I have found that W2DU-type ferrite bead chokes also perform well in this function.

+

One recommendation that I have seen from vendors of commercially prepared G5RV kits is to use as long a run of coaxial cable as possible. Coaxial cable is inherently lossier than parallel transmission line. Any SWR factor acts as a multiplier on the basic matched-line loss of a cable at a given frequency. Hence, the only reason that I can think of for using a very long run of coaxial cable--other than one of necessity for extending from the shack to the antenna--is to use the line losses to mask the SWR at the shack end of the line. If the measured SWR at the shack end of the line is very significantly lower than the sorts of figures produced by these models--or models customized to the system proposed by a user--then they result from line losses. And the only purpose for accepting such losses would be to operate the system without a tuner.

+

With a wide-range tuner, one achieves the lowest feasible loss level with the shortest possible coaxial cable run.

+

For a good analysis of the losses associated with various ways of employing combinations of parallel line, coaxial cables, and tuners with the basic G5RV wire, see the extensive notes of Owen Duffy, VK1OD, at owenduffy.net/antenna/G5RV/.

+

Conclusion to Part 2

From Louis Varney's own writings, we can derive and confirm with NEC-4 models the fact that the G5RV antenna system is suitable for multi-band operation, just as any wire from about 88 to 140 feet might be. The matching system comes into play, not to do away with the need for an ATU, but to permit the use of a coaxial cable as the main feedline with SWR values that are considerably lower than they would be without the matching section on most HF bands. Nevertheless, the ATU remains an essential part of the G5RV antenna system. +

The use of coaxial cable for the main feedline has some advantages in the modern home. Contemporary homes have walls, ceilings, and floors that are rampant with wiring and other metallic conductors associated with heating and air conditioning systems. Hence, indoors, the chances of a parallel line encountering environments that would disrupt the line balance have multiplied with time. A coaxial cable main feedline properly immunized from common-mode currents with a suitable choke offers some isolation from the conductive contents of the modern home with only small losses as the cost.

+

50-Ohm cable has come to rule the field of amateur feedlines. As well, the ATU remains among many folks a suspect device, since it adds to the number of boxes on the operating desk. As a result, after the appearance of the G5RV antenna system, a search ensued for a combination of antenna wire length and matching section that would yield the highest number of amateur bands offering ATU-less operation on a 50-Ohm cable. We shall devote a final part to this series to explore a G5RV variant, perhaps the most successful effort to reach the 50-Ohm cable goal.

+
+ +
+

Updated 05-21-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: The Almost-No-ATU ZS6BKW

+

Go to Part 1: The G5RV on 20 meters

+

Go to Main Index

+

Topics: G5RV / ZS6BKW, HF Multi Band


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+

The G5RV Antenna System Re-Visited
+ Part 3: The Almost-No-ATU ZS6BKW

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

In the mid-1980s, Brian Austin (then ZS6BKW, now G0GSF) addressed the quest left as a nearly mythical heritage of the G5RV antenna system: to develop an antenna system that, for the maximum number of HF bands possible, would permit no-ATU operation of the system with a 50-Ohm coaxial cable as the main feedline. There had been other cousins of the G5RV, such as the W5ANB transmission-line translation featured in QST for November, 1981 (pp. 26-27). Serious researchers traced the overall design concept to the 300-Ohm based Collins version of the 1930s. However, virtually all of these cousins satisfied themselves--as did Varney--with moderate impedances that would fall easily in the range of the average antenna tuner. They did not seek to free the user completely from the ATU in multi-band operation.

+

The ZS6BKW/G0GSF Antenna System

+

Austin's amateur developments appear in RADCOM for August, 1985, and in Radio ZS for June 1985, with professional efforts reported in Elecktron for June/July, 1986, and the Journal of IERE (UK) for July/August, 1987. G3BDQ's Practical Wire Antennas volume reports on the amateur version of Austin's antenna on p. 22. Essentially, his task was to find a length and characteristic impedance for a matching section that will transform the impedance at the center of a wire of a given length to something close to 50 Ohms. So we have several variables (using Austin's notation) in combination:

+
+ L1: the length of the horizontal wire; +

L2: the length of the matching section;

+

Z2: the characteristic impedance (Zo) of the matching section; and

+

Z4: the characteristic impedance of the main feedline, which is 50 Ohms for most amateur applications.

+
+

By computer calculation, Austin arrived at a workable set of relationships that permitted the largest number of bands to arrive at a direct 50-Ohm feed with an acceptable SWR value. Let L1 approximately equal 204/Flow meters or 669.3/Flow feet, where Flow is the lowest frequency to be used. For a Zo of 400 Ohms, let L2 approximately equal 92/Flow meters or 301.8/Flow feet. Of course, L2 must be adjusted according to the velocity factor of the actual parallel transmission line used. (A 400-Ohm Window line is available from The Wireman of SC).

+

It is interesting that the sum of the two lengths is about 1% under 1 wavelength. More significant than this accidental result is the fact that the combination of L1 and L2 provides a good 50-Ohm match in the following progression of ratios: 1 : 2.02 : 2.57 : 3.54 : 4.14, etc. If we let the lowest used frequency be about 7 MHz, then we may have acceptable matches on 20, 17, 12, and 10 meters. 5 bands with one doublet and no ATU is no mean feat.

+
+ +
+

Fig. 1 shows the outline for a ZS6BKW/G0GSF antenna system for 40 through 10 meters. The wire length is 28.4 m or 93.18'. The matching section uses 400-Ohm parallel line and a length of 13.6 m or 44.62'. We shall examine various wire sizes for L1 later, but for the moment we may note the following small table of values for constructing 400-Ohm open wire transmission line using common copper wire sizes.

+ 
 
+                   400-Ohm Open-Wire Transmission Line
+
+Wire Size        Center-to-Center      Wire Size       Center-to-Center
+AWG              Spacing (inches)      AWG             Spacing (inches)
+ 12                   1.137             16                  0.715
+ 14                   0.901             18                  0.567
+
+

There are some commercially available vinyl-covered windowed lines that are closer to 400 Ohms than our expected 450-Ohm value. Therefore, if you do not wish to make up the 45' of 400-Ohm line, you may wish to check with vendors. Obtain the velocity factor to determine how much to physically shorten the line to achieve the required electrical length in Fig. 1. However, do not rely on the report. Whether you build or buy the match-section line, measure its velocity factor.

+

The Hayes volume reports the Austin results in the following manner with respect to SWR at the junction of L2 and the main 50-Ohm feedline.

+ 
 
+  50-Ohm SWR Values for the ZS6BKW Antenna System
+
+Freq.            50-Ohm            Notes
+MHz               SWR
+ 3.65             11.8:1           poor
+ 7                 1.8:1           good
+ 10                 88:1           very poor
+ 14                1.3:1           good
+ 18                1.6:1           good
+ 21.2               67:1           very poor
+ 24                1.9:1           fairly good
+ 29                1.8:1           good
+
+

Austin used a free-space calculation of the impedance of L1 as the basis for his matching section calculations. It is not clear that the equations factor in either the effects of height or wire size on the quality of 50-Ohm match. As well, the spot checks of the match do not provide us with a good portrait of the operating bandwidth potential for each band.

+

Consequently, it may be useful to subject the ZS6BKW/G0GSF antenna system to the same sorts of NEC-4 modeling that we used for the G5RV. We shall begin with a basic model using AWG #12 copper wire, placing it in free space and then at heights of 20 m and 10 m (65.62' and 32.81') above average ground. The models produce the following results.

+ 
 
+           Modeled Results for the ZS6BKW/G0GSF Antenna System
+
+Free Space
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+80         3.75               13 + j   79              13.23
+40         7.15               55 + j    6               1.15
+30         10.125            502 + j 1506              >100
+20         14.175             42 + j   16               1.47
+17         18.118             68 + j   37               1.99
+15         21.2             1333 + j 1783              74.36
+12         24.94              65 + j   28               1.74
+10         28.8               77 + j    7               1.56
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+20 m/65.62' Above Average Ground
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+80         3.75               16 + j   82              11.68
+40         7.15               56 - j    4               1.14
+30         10.125            490 + j 1576              >100
+20         14.175             43 + j   13               1.37
+17         18.118             67 + j   35               1.94
+15         21.2             1381 + j 1783              73.69
+12         24.94              64 + j   26               1.68
+10         28.8               78 + j    6               1.57
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+10 m/32.81' Above Average Ground
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+80         3.75               11 + j   84              18.03
+40         7.15               57 + j   19               1.47
+30         10.125            598 + j 1460              83.33
+20         14.175             43 + j   11               1.31
+17         18.118             67 + j   30               1.81
+15         21.2             1305 + j 1920              82.61
+12         24.94              67 + j   31               1.83
+10         28.8               75 + j    7               1.53
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The modeled values for the spot frequencies coincide quite closely with Austin's initially charted SWR reports. 80, 30, and 15 meters are essentially non-usable. 17 and 12 meters show 50-Ohm SWR values near the limits of where modern transceivers begin to reduce power. However, with most coax runs, the SWR values shown at the transceiver will be reduced as a function of line losses on these bands. The SWR values for 40, 20, and 10 meters are highly promising.

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Side note: Examine the SWR values for the free-space and the 20-m models. In both cases, the reactance is identical and high. However, the free-space resistive component is lower than the 20-m value, but the SWR is higher. Newcomers often believe that higher impedance values automatically produce higher SWR values and fail to appreciate the role played in the complex SWR calculation equations of the ratio of reactance to resistance in yielding the final result.

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Let's look a bit further into the usable bands by taking 50-Ohm sweeps at each height across the bands. This exercise will give us a bit of insight into the operating bandwidth for the antenna system.

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Fig. 2 provides us with a triple sweep of 40 meters. Only the curve for the 20-m height covers the entire band with an acceptable (less than 2:1) 50-Ohm SWR. On 40 meters, that height is about 1/2 wavelength up, while the lower 10-m height is only a quarter wavelength.

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The 20-meter curves, shown in Fig. 3, coincide more closely, since the heights are 1/2 and 1 wavelength. The SWR bandwidth favors the low end of the band and is narrower than would be the SWR curve for an AWG #12 copper dipole resonated somewhere in the middle of the band.

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The 17-meter band is marginal with respect to a 2:1 SWR bandwidth, as shown in Fig. 4. With a length of 50-Ohm coax between the matching section and the rig, the measured SWR near the transmitter would be a bit less, allowing the use of this band without triggering most power-reduction features associated with solid-state final amplifiers.

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12 meters (Fig. 5) shows a similar phenomenon where the 50-Ohm SWR passes the 2:1 mark within the band. However, for most heights, the SWR is a bit lower than on 17, and the same length of coax would show a bit more loss and hence a bit lower SWR at the transmitter end of the line. Hence, the 12-meter band might prove a bit less problematical relative to triggering power reduction circuitry.

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Because the "good-match" frequency ratios are not harmonically related, the ZS6BKW/G0GSF antenna system favors the upper end of the first MHz of 10 meters, as shown in Fig. 6. The window is small, but quite usable. If the transceiver has a built-in narrow range tuner, of course, the entire band would be usable, and the marginal and narrow band conditions on other bands would no longer be a problem.

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The ZS6BKW/G0GSF antenna system is also somewhat sensitive to the wire diameter. To show this fact, I modeled the antenna using AWG #8, #12, and #18 wire. The #8 selection is fatter than almost all amateurs would use, but--in conjunction with the other wires--it provides a reasonably graphic illustration of the effects of wire diameter on the performance of the antenna system. The following tables provide the spot frequency data for the runs. For this set of models, the height is 20 m above average ground. The unusable bands have been omitted.

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+         ZS6BKW Performance Data with AWG #8, #12, and #18 Wire
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+AWG #82
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+40         7.15               61 - j   11               1.31
+20         14.175             46 + j   26               1.73
+17         18.118             73 + j   30               1.86
+12         24.94              67 + j   41               2.11
+10         28.8               86 + j    2               1.72
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+AWG #12
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+40         7.15               56 - j    4               1.14
+20         14.175             43 + j   13               1.37
+17         18.118             67 + j   35               1.94
+12         24.94              64 + j   26               1.68
+10         28.8               78 + j    6               1.57
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+AWG #18
+Band       Freq.            Feedpoint Impedance        50-Ohm
+Meters     MHz              R +/- j X Ohms             SWR
+40         7.15               50 + j    7               1.14
+20         14.175             40 - j    5               1.29
+17         18.118             59 + j   42               2.18
+12         24.94              60 + j    7               1.25
+10         28.8               68 + j   13               1.46
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Like all other small adjustments to the ZS6BKW/G0GSF antenna system, including changes of wire length, match section length, and match section Zo, the 17-meter match and the 12-meter match tend to show opposite effects. An improvement to one is accompanied by a degradation of the other.

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For the wider usable bands, we might again look at comparative 50-Ohm SWR sweeps using the three wire sizes for an antenna wire at 20 m above average ground.

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Fig. 7 shows the effects of changing wire diameter across the 40-meter band. #18 through #12 wire seem to show the best promise of full band coverage, although a wire as large as #8 is usable with an in-rig tuner.

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See Fig. 8: on 20 meters, as the operating bandwidth narrows, the thinner end of the wire scale offer fuller band coverage, with the #18 wire favoring the upper end of the band. Those who use only the low end of the band for CW or digital work might prefer a larger diameter wire for the antenna.

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On 10 meters, thinner is definitely better in terms of total operating bandwidth, as demonstrated by Fig. 9. However, all three curves miss the popular 28.3 to 28.5 MHz window of major 10-meter activity, along with the "CW" end of the band. In these regions, there is little to choose among the wire sizes, and an in-rig tuner would likely provide the necessary match.

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Of the unusable bands--80, 30, and 15 meters--a wide range external ATU would likely provide a usable match on 80 and 75 meters. Since the losses of coaxial cable are low in this band and the SWR loss multiplier for the 10:1 to 13:1 range is moderate, the band might prove to be feasible. The higher losses at 30 and 15 meters, accompanied by very high SWR values, do not bode well for effective use of these bands with the ZS6BKW/G0GSF antenna system. Cable losses may show a lower measured SWR at the transceiver end of the line, and a tuner may effect a match of some sort, but the losses in the cable will remain. As well, the tuner network may operate in a high-loaded-Q condition, further adding to overall losses.

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I have not shown azimuth patterns for Austin's antenna system, since those patterns are a function of the radiating wire length. Patterns for a 93' wire and a 102' wire are too similar to need repetition. So you may refer to the patterns in Part 2 for a good idea of where the lobes will go on each usable band with the ZS6BKW/G0GSF system.

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Conclusion to Part 3

Of all the G5RV antenna system cousins, the ZS6BKW/G0GSF antenna system has come closest to achieving the goal that is part of the G5RV mythology: a multi-band HF antenna consisting of a single wire and simple matching system to cover as many of the amateur HF bands as possible. From 80 to 10 meters, Austin's system provides an acceptable match on 5 out of the 8 bands under most conditions without an antenna tuner. This is the best result that has been achieved of any of the systems that has come to my attention. +
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There are at least three other classic horizontal wire antenna designs that are proven performers in terms of using a coaxial cable as the feedline and in requiring no ATU. They are illustrated in Fig. 10. One is the trap doublet. One can make a dipole for as many bands as one wishes by using traps to terminate the wire at the desired length for a given band. Of course, the traps between the feedpoint and the termination for the band in use provided loads, so the antenna would be shorter than full size on the lowest band in use. How short it would be depends on the number of bands for which the builder installs traps.

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Since the trap dipole or doublet is a semi-true dipole for each band used, it provides a resonant feedpoint impedance close to optimal for 50- or 75-Ohm cable. The exact feedpoint impedance depends in part on a. the terminating trap design and b. the amount of element loading provided by the interior traps relative to the band in use. The patterns will be broadside oval, peanut, or figure-8 shapes--depending upon antenna height in wavelengths above ground. However, when the ratio of the highest to lowest frequencies is greater than 3:1, there may be significant radiation from the outer portion of the antenna at the higher frequencies, resulting in odd lobes relative to dipole expectations.

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The advantages that accrue to the trap dipole or doublet are a 50-75-Ohm feedpoint impedance and mostly true dipole patterns. However, the loading of interior traps creates user worries about losses. As well, the L-C traps are weighty and complex compared to the simple light structure of a single-wire doublet. As well, the bandwidth tends to be narrower than for a simple dipole using the same diameter wire.

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The second classic design for direct coax feed on multiple bands is the fan of dipoles. One can support in the normal way a dipole for the lowest band to be used. Then, from the same feedpoint, one can run other dipoles suspended beneath the longest one. The more one allows the higher-band dipoles to droop beneath the longest one, the less the interaction of elements and the greater the ease of trimming each dipole to resonance.

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As one adds bands to a single fan structure, the heavier it becomes, with more area to intercept the wind. Hence, durability becomes a significant issue relative to a simple doublet. As well, the initial trimming of the dipole lengths tends to become more finicky, and the operating bandwidth narrows relative to a single dipole for the same band.

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A third system, pioneered by C. L. Buchanan, W3DZZ, uses a single trap each side of the feedpoint to provide multi-band coverage. Al Buxton, W8NX, extended the technique. The required traps demand careful construction and placement, and band coverage is not complete. Moreover, the patterns on all bands are not completely predictable by reference to the wire length, since interactions may exist between the inner and outer sections of the wire. Nevertheless, such antennas are capable of covering several bands with acceptable SWR levels on a single coaxial cable feedline.

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These classic one-coax-feedline antennas provide part of the rationale for pursuing the G5RV myth of a single doublet for many bands with a single coax feedline and no ATU. A single doublet is mechanically simple for good durability. Operation without an ATU removes one box from the operating desk or field table. The belief that the G5RV antenna system itself could attain these goals--which it could not--literally invented the demand for an antenna that could. And that created the pursuit of techniques that would find a combination of wire length and matching section characteristic impedance and length to come closet to the goal.

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These notes are not designed to recommend a particular multi-band wire antenna system to the potential user. There are too many situational variables for me to do much more than mislead someone. Instead, these notes are designed to clarify to some degree the capabilities of the G5RV and the ZS6BKW/G0GSF antenna systems so that you can have reasonable expectations of them. Understanding an antenna system is one way of overcoming the mythology that spreads itself in truncated conversational claims and in advertising.

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The G5RV antenna system comes in many commercial packages, simply because it is cheap and easy to produce in a kit. A length of wire, a length of parallel feedline, a few insulators, and a couple of junctions form a low vendor cost high profit item. If all vendors were both honest and knowledgeable, they would label such kits with a warning to use with an ATU. If they wish to sell kits for use without an ATU, they might well consider packaging the ZS6BKW/G0GSF system instead. But even then, they should clearly identify the non-usable bands. (A commercial version of the ZS6BKW/G0GSF antenna system is available from The Wireman of SC.)

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Antenna systems using a wire and matching system are but one route to HF all-band antenna service. A simple doublet, parallel transmission line, and an ATU is still an effective system, although truly balanced ATUs are difficult to find. For coaxial feedlines, we have briefly noted three alternative systems that move the complexity of a tuner to the antenna end of the line in the form of traps or multiple dipoles. Selecting the all-band wire antenna system, in the end, depends on the user's careful definition of his needs, limitations, and desires. Some understanding of the requirements of each competing system also goes a long way to assisting the decision-making process. These notes hope to have added a bit to understanding the single-wire-and-matching-section system of achieving multi-band HF operation.

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Updated 05-21-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 1: The G5RV on 20 meters

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Go to Part 2: The G5RV on all HF Bands

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Go to Main Index

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Topics: G5RV / ZS6BKW, HF Multi Band


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How High is My Antenna?

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L. B. Cebik, W4RNL

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The question of antenna height in the HF region mysteriously remains somewhat a mystery to many amateurs. We know some basic facts about the antenna, like its height in feet or meters. But many of us fail to realize what the physical height implies about performance. So let's spend some time looking at a couple of standard cases--where the antenna is all at one height--to find out what height means to performance. Then, let's look at a few antennas that have multiple heights of interest. For example, the inverted-V has a peak height at the center and an end height. The quad beam has an upper and lower height. Finally, a stack of two or three Yagis has a top beam and a bottom beam.

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Notice that our discussion will involve only antennas that are essentially horizontal. The height of vertical antennas is another discussion entirely, and we shall reserve it for another occasion.

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The 1-Height Antenna

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The basic height of an antenna is only indirectly connected with the physical height. The more important question is how high the antenna is as measured in wavelengths at the operating frequency. We can perform an easy approximation. Take the height in feet and convert it to meters by multiplying the height by 0.3048. Now check the operating band. If your height works out to 10 meters and you are using the antenna on 20 meters, then the height is roughly 1/2 wavelength. I call the value "rough" because the band designators for amateur allocations are only approximate. But the exercise will get you started in the right direction.

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The next stage is to figure out what the antenna height in wavelengths tells us that might be important. Basically, the antenna height tells us what the angle will be for our elevation pattern. Since the elevation pattern determines the skip angle for our antenna, we shall soon discover whether the antenna is good for DX or only for local and/or regional communications. (Remember that propagation can do funny things, and even an antenna that is mostly useful for shorter range contacts can sometimes let us contact the rare DX station.)

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There is an equation for determining the elevation angle of each lobe in the pattern of a horizontal antenna:

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ALN is the elevation of the lobe or null above the horizon. We count for this equation by assigning lobes odd numbers (N). So the first lobe is 1, while the second lobe (if it exists) is 3. (Nulls get even numbers, and ground level--0--is the first null.) The antenna height (h) is in wavelengths or fractions of a wavelength. Table 1 lists the values for the ideal first-lobe elevation angle based on the equation.

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We shall discover that these values are a bit too high. The equation presumes perfect ground and a simple dipole. Real ground and the antenna structure will slightly modify these values. However, as a rule of thumb, these values are good ones to memorize as an easy reference. Note, of course, that as we raise the height of the antenna, the first elevation lobe has its peak gain at a lower angle. Since propagation angles for long-distance communication tend to favor lower angles, we can see the wisdom of the old advice that with a horizontal antenna, height comes before almost any other concern.

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Let's start our survey of real antennas with a 1/2 wavelength dipole made from wire, and let's place it over average ground. Our main modeling tests will be at 20 meters (14.175 MHz), which is about in the middle of the amateur HF region. Let's see what happens when we run a dipole with heights or 0.5, 1.0, and 2.0 wavelengths. Fig. 1 shows the antenna and the elevation patterns, while Table 2 provides the numerical data.

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First, we notice that the elevation angle of the first lobe is lower than predicted by the equation for each of our sample heights. Second, there is no magic in the exact number for that angle. Terrain will make a difference to its real value. As well, I have recorded the vertical beamwidth value for the lobe to illustrate that there is a span of angles (and not simply a single angle) that marks the range of angles of strong radiation (and equally strong sensitivity for reception). Third, take note of the fact that as we raise the antenna, we obtain slightly more gain.

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To establish that these phenomena are quite general, let's substitute a 10-meter dipole for our original 20-meter antenna. The 10-meter dipole will have half the physical height of the longer antenna in order to establish our test heights from 0.5 wavelength to 2 wavelengths. Fig. 2 and Table 3 provide the patterns and the data.

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The values for the elevation angle of the first lobe and the lobe's vertical beamwidth are virtually identical to those for the 20-meter dipole. Almost incidentally, we can note the slight differences in the maximum gain values. The lower the antenna, the lower the 10-meter gain relative to the 20-meter gain. The amount is far too low to make an operational difference, but the fact that the lower gain shows up is a function of the fact that ground losses increase with frequency. As we raise the antenna farther from ground, it has less effect on a horizontal antenna. By a height of 2 wavelengths, the effect is nearly completely gone.

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Many amateurs (erroneously) believe that making a horizontal antenna longer may improve the radiation angle. To test this belief, let's create a 20-meter 1 wavelength center-fed wire. It is twice as long as the original 20-meter dipole. If length does make a difference to the elevation angle, the effect should show up. Now let's examine Fig. 3 and the data in Table 4. The representation of the antenna carries the current distribution curves to establish that it is not just another 1/2 wavelength dipole.

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We can easily see the added gain that the 1 wavelength wire gives is. As with all horizontal antennas, the gain increases slowly with increasing antenna height. However, we do not find any difference in the elevation angle or the vertical beamwidth. (The decimal place in the values for the angles is not operationally significant. It will only play a role a bit later on in this discussion, when we look at antennas having more than one height of interest to us.)

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While we are looking at antennas that have only one height, let's see what we obtain for values from antennas having gain in a favored direction. We can begin with a 3-element Yagi of fairly standard design. Fig. 4 and Table 5 tell the essential story.

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The gain increase with increasing height once more shows up. In fact, the phenomenon is so universal to horizontal antennas that we shall only mention it one more time from this point forward. More significant is the elevation angle behavior. If we look at the table from the bottom up, which means from the highest level down, we see that the numbers gradually depart from the dipole values. The lower that we place the Yagi, the lower its elevation angle becomes relative to the standard values for the dipole. Again, we have the ground to thank for the variation. A Yagi radiates from its entire structure, not just from the driver. Each element has a set of "rays" that intercept the ground at very slightly different angles due to the physical displacement of the elements from each other. The closer to the ground that we bring the antenna, the more that these differences show up in the antenna's radiation pattern. The complex interactions show up as a lower elevation angle at the lowest sample height. As we move the antenna upward, the effect grows less noticeable. By a height of 2 wavelengths, the effect is virtually gone.

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At the same time, note that the vertical beamwidth of the lowest lobe generally tracks with the elevation angle. At lower mounting heights, the beamwidth is slightly greater than the elevation angle of the lobe. The difference decreases as we raise the antenna and lower the elevation angle of the lowest lobe. For VHF antennas that we normally mount quite a few wavelengths above ground, we can equate the two numbers without fearing any error.

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Let's increase the antenna size and forward gain a bit more. A 5-element Yagi at 20 meters often serves as a big antenna for the DXer. Fig. 5 and Table 6 show us what happens.

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The long-boom Yagi shows a further lowering of the elevation angle when we mount it at the unlikely height of 1/2 wavelength above ground. Ground effects still show up--although not to an operationally significant degree--when the antenna is 1 wavelength above ground. However, by the time we move the antenna to 2 wavelengths above ground, those effects have completely disappeared.

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Our last mention of the antenna gain-vs.-height situation requires that we look at the tables for all of the 20-meter antennas. For the single wire antennas, the total gain difference between heights of 0.5 wavelength and 2.0 wavelengths is only about 0.5 dB. That difference grows to about 1.5 dB for the 3-element Yagi and to 2.1 dB for the 5-element Yagi. The difference is becoming not only noticeable, but also significant. For this reason, many DXers like to mount their long-boom Yagis as high as they can safely maintain.

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Our small survey gives us a fairly good foundation in knowing what to expect from a horizontal antenna at any height above ground, when we measure the height in wavelengths. More significant to the rest of our work in these notes is the fact that the demonstrations show what significance we place on the height of horizontal antennas in terms of our anticipations of performance for long-distance communications. Height correlates to the elevation angle of the lowest lobe, and that factor relates to the propagation angles that most usually come into and go out of our antenna. (Note that in many circumstances, incoming and outgoing angles of propagating signals may differ with respect to the ionospheric conditions between my antenna and yours.)

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The net result is this: we may equate the height of two antennas if they have the same elevation angles for the lowest lobe in the pattern. The equation cannot be exact, since--as we have seen--the antenna may have some structural factors that affect the elevation angle at lower mounting heights. However, we can come close.

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Six Sample Multi-Level Antennas

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The equation for estimating the elevation angle of the first lobe of a horizontal antenna applies only when the elements are linear relative to the ground and when we have only one X-Y plane for the elements. The equation does not guide us when we have sloping elements, such as the ones we find in an inverted-V. As well, the equation fails us when we have an antenna with multiple X-Y planes, that is, when we have a vertical stack of antennas.

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There is a rule of thumb: the effective height of an antenna with multiple height considerations is about 2/3 of the distance between the lowest height and the highest height for the antenna. Like the human thumb, which varies in size and shape from one person to the next, this rule of thumb varies in its accuracy depending on the type of antenna and the actual lowest and highest heights. If we look at several types of antennas and place them at various heights above ground, we might be able to refine the rule. Of course, once we run the exercise, we likely shall no longer need the rule, since we shall have some data that will allow more precise interpolations.

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Case 1: the Inverted-V

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Inverted-V antennas are less common on 20 meters than they are on 160, 80, and 40 meters. However, to be consistent in our comparisons, we shall use a 20-meter wire inverted-V as the subject antenna. We shall seek out the effective height of an inverted-V to see if it corresponds with the lowest point, the highest point, or some other point between the two. Fig. 6 shows the outline of our project.

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One useful way to find an effective height is to compare the inverted-V to a linear dipole. The V is simply a sloping version of the dipole, although the slope does modify the antenna's performance characteristics. Suppose that we take the TO angles for the dipole and move the V up and down until it yields about the same TO angle (within a few tenths of a degree). Then the lowest and highest points of the V will tell us something about how the 2 antennas are related. However, inverted-Vs come in many angles of slope, where the angle of slope is the angle of each half element relative to flat ground. We cannot cover every possible angle, but we can sample inverted-Vs with slope angles of 30 degrees and 45 degrees.

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The 30-Degree V: The data for the 30-degree V appear in Table 7, while the pattern are in Fig. 8.

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In the table, note that the left-most column shows the effective height, that is, the physical height that most closely approximates a linear dipole at 0.5, 1.0, or 2.0 wavelengths above ground. The next 2 columns list the lowest and upper heights of the 30-degree V. The remaining data provides a basis for making comparisons with Table 2, the data for the linear dipole. We may instantly notice that the 30-degree V has slightly less gain than a linear dipole at the same effective height, but not enough less to be operationally noticeable. As well, if we compare the pattern in Fig. 7 with those in Fig. 1, we can see some small differences, but again, not sufficient to worry us in the least.

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Perhaps the most interesting fact to emerge from the data is that the 30-degree V has an apex that is above the dipole height only for the lowest version. As we increase the V's height, the apex height and the effective height come together. (The very slight differences between the top height and the effective height are well within the boundaries for calling them equal, since the TO angles do not change fast enough to allow for greater precision.) Therefore, the rule of thumb, if it applies at all, works only for inverted-Vs with top heights below 1/2 wavelength. Of course, most 30-degree inverted-Vs for 160 through 40 meters tend to be well below 1/2 wavelength at the top, and their ends are much closer to the ground as a fraction of a wavelength. Hence, the 2/3-rule is more likely to be accurate for Vs on the lower HF bands. Higher Vs tend to act almost exactly like linear dipoles with respect to their TO angle.

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The 45-Degree V: For smaller spaces, amateurs often give the inverted-V a slope angle of up to 45 degrees. What happens with this version of the inverted-V appears in Fig. 8 and in Table 8.

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Since the 45-degree inverted-V patterns are for their effective heights relative to the TO angle of a comparable dipole, they show virtually no difference from the 30-degree V patterns. The clues to the effects of the higher slope angle appear in the numerical data, especially in the gain column. Relative to a dipole, the 45-degree V loses the better part of a dB of gain at every height. The lost gain would reappear in radiation along the axis of the wire. Otherwise, the 45-degree V replicates what we discovered for the 30-degree V. If the height is low, then the apex of the V is above the effective height. The lower the height as a function of a wavelength, the higher the apex will be with respect to the effective height. However, if we raise the 45-degree V to a wavelength, then the apex and the effective height are just about equal. Once more, the 2/3-rule of thumb is applicable only to those low inverted Vs for 160 through 40 meters that we see in backyards.

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Note that we are separating the TO angle from the overall pattern shape for the inverted Vs. The maximum gain value is an indicator that an inverted-V's azimuth pattern is likely to be more oval than the azimuth pattern for a linear dipole when both patterns have the same TO angle, that is, are at the same effective height. In a different exercise, we might easily confirm this fact. However, the direction of radiation at the TO angle does not itself effect (and is not affected by) the TO angle to any significant degree. With very low inverted-Vs, the ground can get into the overall sum of influences, but for higher Vs, the TO angle is relatively independent of the gain.

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In this exercise, we are working with inverted-V antennas used on their fundamental frequency, that is, when they are about 1/2 wavelength long and close to being resonant. Under these conditions, we see only small differences in performance between the 30-degree and the 45-degree V. Multi-band use of the inverted-V is another matter. In this application, the slope angle may make a big difference in performance on bands well above the fundamental operating frequency. For notes on this subject, see "The Multi-Band Inverted-V from Many Angles".

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Case 2: the Quad Beam

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A quad loop consists of two dipoles that are in phase. Because they are only 1/4 wavelength apart, the ends can fold down and touch, forming a continuous loop with a single feedpoint. A single quad loop has a gain advantage over a linear dipole of about 1.15 dB. When we add one or more parasitic loops, we end up with a beam whose principles are the same as for a Yagi with the same number of elements. In this case study, we shall look at 2-element quad beams.

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The procedures will be the same as those used with the inverted-V. We need to make two adjustments. The first is to add one more measurement to the list of heights with which we are concerned. Besides the lowest and highest points of the quad loops, we shall also note the height of the boom or the hub. This point is halfway between the upper and lower elements. See Fig. 9 for an outline of this situation.

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The square quad beam: Commonly we find two forms of the quad: the square shape and the diamond. (The delta is also a form of quad with 3 sides instead of 4. As well, we can make many-side quad loops, including perfect--or imperfect--circles.) In general, we shall follow the inverted-V procedure, but we also need a new comparator. A quad beam has front-to-back structure. Therefore, we shall use the TO values for the 3-element Yagi as the most similar single-plane antenna. We shall move the quad beam up and down until the TO angle is about the same as we obtained from the Yagi. Fig. 10 and Table 9 show the results of our juggling.

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The patterns for the 2-element square quad resemble those for the 3-element Yagi, but not perfectly. Most of the differences are in the rear quadrants and at the highest angles. The maximum gain of the quad is a little more than 1 dB under the Yagi's capabilities. The physical height midpoint--the hub--is always below the effective height by a few per cent. Otherwise expressed, the effective height is a little more than halfway up the distance between the lower and the upper wires. Had we used the dipole as the comparator for marking effective heights, the difference would have been greater--perhaps enough to approach the 2/3-rule of thumb.

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The diamond quad beam: The most common alternative structure for a quad is the diamond, which gives us somewhat different upper and lower points for measurement. Still, as shown in Fig. 11, the hub remains at the center of the structure and provides a good point to compare with the effective height.

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In general, the performance of the square and the diamond quads are equivalent. The patterns in Fig. 12 and the data in Table 10 bear out this situation. The gain values for the two types of quads do not vary enough at any of the sampled heights to be detected in operation. The patterns at each height are virtually identical to those in Fig. 10.

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The relationship between the effective heights and the hub heights for the diamond quad also follow the pattern set by the square quad. Had we used a 2-element Yagi as the comparator, its TO angle at the lowest height would have been about midway between the TO angles for the dipole and for the 3-element Yagi. Finding the physical quad height for that slightly higher TO angle would have brought the hub height below 0.5 wavelength. Overall, the hub of the diamond quad is at or below the effective height of the antenna. The average distance from the lowest to the highest points for the effective height is about 56-57% of the total distance. The rule of thumb may use too large a value, but it serves as an indicator that the effective height of a quad is somewhat higher than the hub.

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Stacked Yagis

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In the past, stacked Yagis gave a misimpression. Two identical Yagis in a vertical array with both antennas fed in phase certainly yielded more gain than a single Yagi. Some folks also believed that the stack had a TO angle that was lower than the TO angle of either antenna alone. In fact, the TO angle is always lower than the bottom Yagi's solitary TO angle, but is it always higher than the TO of the top Yagi when used alone. Where in the middle the TO angle lies is what we wish to know. To sample the field, let's stack Yagis at 1/2 wavelength vertical intervals and feed them in phase. The 1/2 wavelength spacing does not yield the highest possible gain. However, it is a convenient height for our work. Once we know the TO angle of the stack, we can set up a single Yagi of the same general type and find the height at which it has the same TO angle as the stack.

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A stack of 2 3-element Yagis: The 2-stack is perhaps the simplest place to begin. A 2-stack of 3-element Yagis will add a bit more than 2-dB to the array gain over a single Yagi. Fig. 13 outlines the stack as a reference.

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The tables for our Yagi stacks will differ from preceding ones by listing the heights of the Yagis in the stack. In this case, we shall set the Yagis at 0.5 and 1.0, 1.0 and 1.5, and finally 1.5 and 2.0 wavelengths above ground. The height at which a single Yagi yields the same TO angle registers the effective height of the array. Fig. 14 and Table 11 record the results of our work.

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The use of 1/2 wavelength spacing between Yagis changes the appearance of the elevation patterns relative to those for a single Yagi in Fig. 4. Half wavelength spacing tends to suppress very high-angle radiation. Therefore, the highest lobes of the patterns in Fig. 14 are "under-developed" relative to those in Fig. 4.

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The most notable aspect of the tabular data is the height of the single Yagi that produces the same TO angle as the stack and its distance from the lowest to the highest beam in the stack. The closer that the stack is to the ground, the higher the effective height as measured by the TO angle. With stack heights of 1 and 1.5 wavelengths, the distance just about matches the rule of thumb.

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A stack of 3 3-element Yagis: A 3-stack is a major structural undertaking for any amateur, but 3-stacks are quite common among avid DXers and contesters. Fig. 15 outlines the 3-stack situation.

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I shall follow the same procedure for the 3-stack that I used for the 2-stack. The only difference in the tabular data is that the basic height column will list 3 values. The bottom heights will be 0.5, 1.0, and 1.5 wavelengths, with corresponding middle and top heights at 0.5 wavelength intervals. Once we know the stack TO angle, we can set a single 3-element Yagi at a height that produces the same TO angle and call that the effective height of the stack. Fig. 16 and Table 12 provide the patterns and the numerical data.

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The 3-stack patterns show relatively greater suppression of higher-angle lobes than for a single Yagi or for a 2-stack. The most significant data in the table (with respect to this exercise) is the range of effective stack heights. The range runs from 69% of the distance from the lowest to the highest antenna in the stack for the lowest array down to 55% for the highest set of 3 Yagis. The distances are slightly lower than for the 2-stack when measured as a percentage of the distance from stack bottom to top, but still close enough to the rule of thumb to make it a useful quick estimate.

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Conclusion

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We have looked at the basics of antenna height and its relationship to the elevation angle of the lowest lobe--the one that we tend to presume is doing most of the work in long-distance amateur communications in the HF range. Because antennas having horizontal polarization but a vertical physical dimension present complex situations, we examined a number of typical antennas in this very general class. The lower that we place an inverted-V, the closer it comes to meeting the rule of thumb, but as we raise the V, the more its TO angle corresponds to the angle for a linear dipole. Quads and Yagi stacks respond in a different manner. The effective height of these types of arrays is always above the mid-point between the lowest and the highest points in the array. While the rule of thumb is inadequate to precisely characterize the effective height of these types of antennas, it is rarely much off the mark to say that the effective height is about 2/3 the way from array bottom to array top. If you have a special interest in any one of the antenna types in our little survey, the tabular data will provide a more accurate means of estimating the effective height for the antennas that you encounter.

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Updated 02-15-2006 © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Dipole, Doublet, HF Upper, Inverted V, Quad, Stacking, Yagi


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Notes on All-Band Use of Horizontal-Plane Loops

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L. B. Cebik, W4RNL

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The general summary is this: on 80, either loop is a cloud burner, but with pretty good gain at 45 degrees elevation. In general, except for 40 meters, the corner-fed loop shows more bi-directional patterns (with minor side lobes), mostly through the corners where the feedpoint is the backside. On bands from 20 meters, there is up a slight (3-4 dB) front-to-back ratio.

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Fed on one side (rather than at a corner), there is a tendency for the antenna to exhibit more lobes per band, with those to the far side from the feedpoint being slightly stronger--again by no more than 2-4 dB.

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Both the corner-fed and the side-fed antennas, as the charts will show, represent easy work on an antenna tuner, with very reasonable values of R and X. Indeed, a 300- ohm line will likely show the smallest excursions of R and X along the line length, although 450-ohm line is perfectly good as well. From the values in the chart, line length should not be critical.

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In the charts below, all maximum gain figures use the TO angle (elevation angle of maximum radiation) except for 80 meters, whether the gain is at a 45-degree TO angle.

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1 wl loop (70'/side), corner-fed: #12 copper 35' up over medium earth:
+Freq.     TO angle  Max Gain  Feed Z         Pattern notes
+ MHz       degrees    dBi     R+/-jX
+ 3.58     90        5.16@45    67 +j  4      oval thru corners
+ 7.1      48        5.69       84 -j150      oval across corners
+10.1      41        9.32      370 -j575      narrow oval thru corners
+14.1      27        10.51     305 -j105      clover leaves thru corners
+18.1      20        13.75     350 +j240      EDZ-like thru corners
+21.1      17        13.63     245 -j105      clover
+24.95     14        14.09     320 +j110      thru crnrs w/side lobes
+28.1      12        12.92     225 -j145      12 lobes
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+1 wl loop (70'/side, side-fed:) #12 copper 35' up over medium earth:
+Freq.     TO angle  Max Gain  Feed Z         Pattern notes
+ MHz       degrees    dBi     R+/-jX
+ 3.58     90        5.09@45    65 +j  4      oval thru sides
+ 7.1      44        6.73      275 +j130      oval thru sides
+10.1      35        6.86      285 -j535      lobes at corners
+14.1      27        9.69      265 -j165      4 lobes at corners
+18.1      21        11.65     400 +j180      6 lobes, strong=far side
+21.1      18        10.61     400 -j120      many lobes, strng=far side
+24.95     15        11.08     370 +j 45      many lobes, strng=far side
+28.1      11        11.83     250 -j180      many lobes, strng=far side
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The side-fed shows slightly less max gain on the upper bands, but has more stronger lobes other than the corner-fed version. If the pattern notes can be deciphered, you can choose whichever suits your operating desires most.

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To assiset in interpreting the brief pattern notes, the following azimuth patterns of corner-fed and side-fed HP loops at 10.1, 21.1, and 28.1 MHz may be useful. For each pattern, the antenna is a square aligned with the graphic borders. The corner-fed model is fed at the lower left corner of the graphic. The side-fed model is fed at the middle of the left side.

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The 10.1 MHz patterns show the most unique differences, with the corner-fed model having a beam-like pattern, while the side-fed model pattern is somewhat non-descript but more omni-directional.

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At 21.1 MHz, the side-fed model shows much broader lobes, while the energy from the corner-fed model is concentrated in 4 fairly narrow lobes.

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By the 10 meter band, there is little to choose from between the two antennas.

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As a general rule, the horizontal loop offers more directions, especially in the side-fed version, than the single wire, which concentrates its energy more toward the ends as the frequency goes up. A compendium of patterns for 135' doublets and for 102' doublets appears in notes taken from the series done for Low Down. The loop has fewer bands with problematical impedances than any of the doublets.

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For all-band use, the HP loop seems to offer more than the VP loop. The HP loop elevation angles are close to those of a single wire doublet, which places them lower and stronger than those for a VP loop. In general, with either mode of feeding, expect strongest results in the quadrants across the way from the feedpoint.
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Updated 10-28-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Topics: HF Multi Band, Horizontal Loop


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Horizontal Wire Loops
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L. B. Cebik, W4RNL

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A number of years ago, I provided some extensive notes on horizontally oriented, horizontally polarized wire loop antennas (HOHPLs). See Horizontally Oriented, Horizontally Polarized Large Wire Loop Antennas. I have received enough e-mail as a result of those notes to convince me that perhaps there is such a things as cramming in too much information so that the result is a collection of difficulties in sorting it all out. As well, when I wrote those notes, the most common practice with horizontal loops was using a 1 wavelength circumference at the lowest operating frequency. Since then, I have changed the recommendation that I usually make, depending on the space available to the loop builder.

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So let's begin again and work with a different plan. My plan of attack is based on the 3 most asked questions:

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  • How Big?
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  • How High?
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  • What Shape?
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Since we shall defer the question of shape until last, we shall need a paradigm model with which to begin. Let's use a nearly perfectly circular loop as our starting point, as outlined in Fig. 1. The loop uses 40 wires to form the circle, so the approximation is quite good. For our first 2 questions, the feedpoint will be on the right, in the +X direction. (We shall alter that for our last question for reasons that will become apparent when we arrive at questions of shape.) Note the orientation of the X, Y, and Z axes in the outline drawing. These axes lines will be important to orienting ourselves to some of the patterns in upcoming figures.

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A circular loop as a starting point has some advantages over beginning with other shapes. With both regular and irregular polygons, we tend to find performance differences depending on whether we feed the antenna at a corner or somewhere within a side. Since a circle has no sides (or infinitesimal ones, at best), we can avoid those differences until we reach our last question.

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How Big?

The question of how big to make a horizontal loop antenna is a function of frequency, specifically, the lowest frequency of intended use. Virtually any size will work to some degree, but some sizes are better than others. Remember that here, we are speaking of relatively large loops, not mini- or micro-loops used as table-top antennas. Since I cannot know the lowest frequency of intended use, let's express dimensions as a function of a wavelength at the lowest operating frequency. Since a horizontal loop is usually used as a multi-band antenna, we shall likely feed it with parallel transmission line and an antenna tuner. Hence, ultra precision of dimension is not necessary (as it might be for an antenna that must have some particular feedpoint impedance). So if I suggest a length, such as 3 wavelengths, for a loop size, anything relatively close to that size will do fine. "Relatively close" means about +/-15% of the suggested size. +

The basic dimension of loop size is normally its circumference, that is, the total length of wire making up the loop. Of course, being a loop implies that there is relative parity of cross dimensions, although distended rectangles, rhombics, etc. will work. However, we have to confine our work to what we can handle, so we shall stay with regular polygons throughout these notes.

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For our work, if you wish to translate a length in wavelengths into an English measure, you may use a very simple equation: L(feet) = (984 / F(MHz)) * n, where n is the number of wavelengths specified. If you wish to go metric, then use this equation: L(meters) = (300 / F(MHz)) * n. These equations are not precise, but they are within the limits that we need to convert a horizontal loop into a length of wire.

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To see how big to make our loop at the lowest operating frequency, let's put the loop into free-space and examine some 3-dimensional radiation patterns. These patterns will tell us something about why I have changed my recommended length for a horizontal loop. The following table provides the key dimensions of the loops whose patterns appear in Fig. 2. The basic loop size is the circumference, but the diameter gives you an idea of the backyard space needed to hold the loop.

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+Some Possible Circular Loop Sizes
+(All dimensions in Wavelengths)
+Circumference     Diameter
+0.5 WL            0.159 WL
+1.0               0.318
+1.5               0.476
+2.0               0.636
+3.0               0.955
+4.0               1.273
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The 3-D patterns may seem a bit confusing, but let's align ourselves with Fig. 1 and its axes lines. The X-axis and the Y-axis indicate horizontal directions relative to the orientation of the loop, presumed to be horizontal, even if we are working in free space with no real "ups" and "downs." The Z-axis is the vertical direction at right angles to the plane formed by the loop.

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Since each 3-D pattern has about the same total volume, relative to the axis lines, we can see a few trends. First, the 1/2 wavelength loop forms an oval with slightly stronger radiation in the X direction than in the Z-direction. The next two loops (1.0 wavelength and 1.5 wavelength) have stronger radiation along the Z-axis than along either the X- or Y-axes. Not until we reach a circumference of 2 wavelengths does radiation strength occur predominantly in the X-Y plane. Another way of expressing this is to say that when a loop reaches a circumference of 2 wavelengths, it radiates more strongly off the loop edge than it does broadside to the loop.

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This conclusion tallies well with our practice of using 1 wavelength loops in quad beams that rely on radiation broadside to the plane of the loop. If we want a 2 wavelength loop to radiate more strongly in the broadside direction, we must break the connection across from the feedpoint. However, our job is not to make a quad beam, but to see what a wire horizontal loop can do for our signals. So we may omit any consideration of broken loops.

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The longer loops also show stronger radiation in the X-Y plane than in the +/-Z direction. However, their patterns are so convoluted that it is almost impossible to see exactly where the radiation is going. To get a better handhold on the radiation of all of the loop sizes, let's return almost to earth. We shall place each loop 1 wavelength above average soil. (With horizontal antennas, the actual soil quality makes little difference to the signal, so using average soil will not distort the conclusions that we reach.) Fig. 3 presents the modeled elevation and azimuth patterns for the loops sizes surveyed in Fig. 2. Each pattern indicates the strongest lobe, and the small inset of the loop shows how that lobe is oriented relative to the loop's feedpoint.

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The primary feature to note is that for loops with a 1.0- or 1.5 wavelength circumference, the upper elevation lobes are stronger that the lower lobe. Given the high elevation angle (about 35 degrees) of the upper lobe, the lower lobe is obviously that one that we rely upon for most communication (NVIS excepted, of course). When we reach a circumference of about 2 wavelengths, the lower lobe begins to dominate once more. Hence, for skip communications, the smallest advisable circumference for a horizontal loop is about 2 wavelengths at the lowest operating frequency. Smaller loops will work, but at reduced signal strengths.

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The second notable feature is the fact that horizontal loops above a helf wavelength over ground answer to the standard lobe development angles that apply to virtually all horizontal antennas and arrays. All of the lower lobes, regardless of loop length, have a 14-degree elevation angle. The length of a loop does not change the elevation angle.

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For a given power from the transmitter, all of the loops radiate the same power over the hemisphere above ground. Hence, they differ only in the maximum gain created by the formation of lobes and nulls in the pattern (both horizontal and vertical). The following table summarizes the gain of the strongest lower lobe and gives an indication of the impedance at the feedpoint. That impedance may vary considerably with variations in the actual wire length used to make a loop.

+ 
+General Performance Values for Circular Loops
+Height: 1 wavelength above Average Ground
+Elevation Angle: 14 degrees
+Circumference     Gain     Impedance
+wavelengths       dBi      R+/-jX Ohms
+0.5               7.03     >100k - j85k
+1.0               6.09     125 - j110
+1.5               5.56     9200 + j6500
+2.0               7.23     180 - j125
+3.0               8.16     215 - j130
+4.0               9.26     235 - j135
+
+

Loops that are integral multiples of 1 wavelength tend to have lower impedances, while those in the n.5 wavelength caregory tend to have very high impedances. Although the gain value for the 1/2 wavelength loop looks quite usable--when compared to the other values--the feedpoint impedance is not especially promising. As well, a 1/2 wavelength loop becomes a 1 wavelength loop on the next band upward in frequency, and we lose a lot of gain in the lower lobe on that band.

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You may relate the improving signal strength maximum values that accompany longer loops with the width of the lobes for those larger loops in Fig. 3. Hence, as we make a loop longer, the beamwidth of the individual lobes grows narrower. As we increase the number of lobes, we also increase the number of nulls, where signal strength decreases to a level that may prevent communications.

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Finally, for a circular loop (but not necessarily for other shapes), the number of lobes follows a regular pattern. The number of lobes is twice the loop circumference in wavelengths. Hence, a 4 wavelength loop shows 8 distinct lobes. When we disturb the circular shape of the loop, the flat sides that we produce will alter this pattern of lobes and nulls, and we shall sample those alterations before we finish.

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To obtain an estimate on how good a loop may be in our own backyard, let's pause to make a comparison. We shall place a 1/2 wavelength dipole at 1 wavelength above average ground. For that antenna, we obtain the following performance report.

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+General Performance Values for 1/2-Wavelength Dipole
+Height: 1 wavelength above Average Ground
+Elevation Angle: 14 degrees
+Dipole Length     Gain     Impedance
+wavelengths       dBi      R+/-jX Ohms
+0.5               7.98     72 + j2
+
+

Fig. 4 shows the dipole, its 3-D free-space pattern, and its elevation and azimuth patterns at the specified height. The dipole has as many lobes as a 1 wavelength circular loop, but they are stronger at the prime 14-degree elevation angle.

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The loop does not catch up to the dipole until we reach a circumference of 2 wavelengths, where we also have the loop's 4 lobes.

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How High?

Those who do not seem to have much luck with loops--even when at least 2 wavelengths long--very often have neglected the role of height in the performance of any horizontally polarized antenna. Most of these antennas are aimed at improving performance on the lower HF bands. However, the average height (from my e-mail reports) seems to be between 35' and 50' above ground. This height range covers about 0.06 to 0.11 wavelength on 160 and 0.12 to 0.18 wavelength on 80 meters (low end figures). +

So far, we have looked at the circular loop when it is 1 wavelength above average ground. We do not know what the patterns might look like at other heights. Therefore, let's take a 2 wavelength circumference loop and place it at a number of different heights, from a high and improbable 2 wavelengths up to a low value of 0.15 wavelength above ground. The shape of the azimuth pattern will not change significantly from the view at 1 wavelength. However, the elevation patterns will change considerably.

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For contrast, let's also look at the numbers for a dipole at the same height. As always, we shall list the maximum gain of the strongest lobe or lobes. More important than gain will be the TO angle, that is, the elevation angle of maximum radiation. The following table summarizes the loop and dipole results. Since the data should be applicable to any lowest frequency of use, the heights are functions of a wavelength.

+ 
+Comparative Performance of a Circular 2 wavelength Loop and a Dipole at Various Heights
+                      Circular Loop                   Dipole
+Height          Max. Gain     TO Angle        Max. Gain     TO Angle
+wavelengths     dBi           degrees         dBi           degrees
+2.0             7.36           7              8.05           7
+1.0             7.27          14              7.98          14
+0.75            7.75          19              7.57          19
+0.5             7.43          29              7.91          28
+0.25            5.94          47              6.33          60
+0.15            4.76          52              6.59          90
+
+

Both types of antenna show the same or nearly the same TO angles down to 1/2 wavelength above ground. As well, they both show the same pattern of maximum gain levels. The slight depression of the maximum gain value that the dipole shows at a height of 0.75 wavelength appears in the loop at a height of 1 wavelength.

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However, the loop shows a faster reduction in gain as it gets close to the ground, but it sustains a lower TO angle with height reductions. If you re-examine the patterns in Fig. 4, you can clearly understand why the dipole TO angle climbs rapidly as we reduce the height below 1/2 wavelength. The dipole in free space shows as much radiation vertically as it shows horizontally. Close to ground, the radiation directed upward dominates. At heights from about 0.15 to 0.25 wavelength, the dipole makes a quite good simple NVIS antenna.

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In contrast, if you return to Fig. 2, you will see that the 2 wavelength circular loop has stronger radiation off its edges than it has perpendicular to the plane of the loop. As a result, the loop (at a closed circumference of 2 wavelengths) does not make a particularly good NVIS antenna. If you examine Fig. 5, you will see that the loop lacks radiation straight up. Hence, its TO angle is lower than that of the dipole when close to the ground.

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The comparison between the dipole and the circular 2 wavelength loop does not mean that the loop is a stellar performer when close to the ground. For general propagation conditions, angles of 47 and 52 degrees are still to high for strong communications. However, if you look also at the half-power angles in the diagrams (the red line on either side of the main-lobe center line), you will see that the lower of these angles does tend to fall within the set of angles that provide relatively reliable communications in the lower HF region. (See a recent edition of The ARRL Antenna Book for further information on typical propagation angles on the various amateur bands.)

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So the reputation of the loop for improved communications relative to a dipole at the same height has some truth to it for antenna heights below 1/2 wavelength. However, examine the gain values for these heights and then subtract another 2-3 dB for working near the half-power angles. Raising the antenna higher not only yields a higher maximum gain value, but also places the TO angle nearer to--if not within--the range of angles providing stronger communications.

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For any horizontal wire antenna, there is no substitution for height. This rule of thumb applies up to at least 1.25 wavelengths above ground, if not higher. On the lowest amateur bands (160 and 80 meters), there is always room for height improvement before reaching the limits of the rule of thumb. What we lack normally are the means to support the antenna at the most desirable height.

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What Shape?

We have so far confined our examination of loops to a circular shape--mostly to ensure that all comparative figures are fair. However, few of us have the means to set up a truly circular horizontal loop on the lowest amateur bands. In most cases, we are lucky to approximate a regular polygon. Hence, it is not possible to cover here all of the possible loop shapes that your circumstances might dictate. In fact, we shall confine ourselves to the circle, the triangle, and the square. +

There are two reasons for the confinement. First, polygons with limited numbers of sides have two general feedpoint positions. One is at a corner, where the wire changes direction. The other is the midpoint of a side. Of course, we can feed a loop anywhere along a side, but, again, that would give us too many variables to cover. So we shall look at 1 circle, but 2 triangles and 2 squares.

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Second, most horizontal loops are intended for multi-band use. So for each option, we need to look at several options. If a 2 wavelength loop is cut for 160 meters, then 80, 40, and 20 meters constitute a progression of frequencies (F) that include 2F, 4F, and 8F. If we cut the original antenna to be 2 wavelengths at 80 meters, then the corresponding harmonically related bands are 40, 20, and 10 meters for the same F, 2F, 4F, and 8F progression. Space does not permit us to include non-harmonically related bands in the progressions.

+

As we increase the operating frequency, the height of the antenna also changes when related to a wavelength. Hence, if we start 1 wavelength above ground, the upper bands will see the antenna at 2, 4, and 8 wavelengths above ground. The 14-degree TO angle at a 1-wavelenght height becomes progressively 7, 4, and 2 degrees (with the angle confined to integer values).

+

Under these conditions, the 2 wavelength circular loop shows the azimuth patterns in Fig. 6. I have moved the feedpoint to the "left" on the antenna so that its position corresponds to the feedpoint position of the remain shapes that we shall explore. Although the lobes increase in number as earlier noted, we might think of them as having equal strength. However, the 8F pattern makes clear the fact that the lobes have slight variations in strength despite the fact that all of the models use lossless wire. The interaction among the sections of the circle are sufficient to create the small differences. These differences will not be small with other shapes.

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We might be tempted to mentally draw a line connecting the outermost tips of the lobes and think that the antenna has the resulting near circle as its pattern. However, every pair of lobes has an intervening null. The practical effect of having a large number of narrow lobes and nulls tends to be a rapid fluctuation in signal strength, especially on windy days, that can slightly alter the exact orientation of the wire antenna. At lower frequencies, where the lobes are broad, the antenna is nearly immune to this effect.

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One popular arrangement for a 2 wavelength loop is a triangle, since that shape needs the fewest support posts or trees. We shall first look at a triangle fed at a corner, specifically, the left-most corner relative to the orientation of the patterns. Of course, we shall retain the 2 wavelength circumference and the 1 wavelength antenna height.

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Fig. 7 shows the patterns that result for each frequency when using a corner-fed triangle. The nearly equal strength of the lobes disappears, even at the lowest frequency. The antenna has a slight beaming effect along a line that runs from the feedpoint to the middle of the side opposite the feedpoint. In all cases, the strongest radiation is in the direction of that far side of the triangle. Therefore, if you use an equilateral triangle for a loop, it pays to orient the atenna toward a primary communications target region.

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If we feed a triangle in the middle of a side, as shown in Fig. 8, we obtain patterns that in general terms are not very different from the ones for a corner feedpoint. However, note that the patterns for 2F and 4F are strongest across the antenna and away from the feedpoint side, while the patterns for F and 8F are strongest to the side containing the feedpoint.

+

When we move to square shapes, a side-fed loop looks square, while a corner-fed square looks like a diamond in terms of the orientation to the patterns. We shall look at the side-fed square first. The patterns are in Fig. 9.

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The square has a pattern at F that is very similar to the one for the circle. However, from that frequency upward, everything changes. Each pattern has fewer lobes than the corresponding pattern for a triangle. As well, the strongest lobes are not aligned with the feedpoint and the opposite side of the square. Instead, the strongest lobes occur at oblique angles to the square for 2F through 4F. Since that angle changes with the operating frequency, finding a good orientation for all intended frequencies may be difficulty.

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+ +
+

When we feed the square at a corner, we once more align the patterns along a line from the feedpoint corner to the opposite corner of the diamond, at least through 4F. Fig. 10 provides the patterns. At 8F, the strongest lobes are at an angle to the array. The following table provides a summary of the modeled maximum gain values. However, above about 2F (a circumference of 4 wavelengths), the lobes become so narrow that a maximum gain value can be quite misleading as a guide to the general communications capabilities of each antenna.

+ 
+Maximum Gain Values for Each Antenna at Each Sampled Frequency
+All loops are 2 wavelengths at F.
+            Frequency              F       2F       4F       8F
+            TO angle (degrees)     14       7        4        2
+Antenna
+Circle                             7.27     9.22    10.71    11.57
+Triangle, corner-fed               8.34     9.95    14.38     8.41
+Triangle, Side-fed                 8.34    10.45    13.24     8.94
+Square, side-fed                   8.42    11.29    13.59    14.29
+Square, corner-fed                 6.95    11.51    14.28    14.92
+Reference Dipole/Doublet           7.99     9.66     9.64    11.16
+
+

The gain data is only useful in comparing the outer rings of each pattern. Note the reduction in gain for the two triangles when operated at 8 times the lowest frequency. I have included the data for a 1/2 wavelength dipole at F to allow comparisons on the various harmonics when using that antenna as a multi-band doublet. The patterns for the doublet appear in Fig. 11. Only up to 2F (or 1 wavelength) does the doublet show its strongest lobes broadside to the wire. Above that frequency, the strongest lobes depart at oblique angles that change with frequency.

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These small demonstrations show that a loop's shape can make a great deal of difference to the azimuth patterns of radiation from it. I shall select no version as better than the others, since I cannot know the lay of the land for each installation. However, it does appear that operating a 2 wavelength loop much above twice the design frequency does yield narrow lobes that may or may not be useful to communications. The remaining body of radiation in the pattern is considerably weaker than the main lobes. For patterns associated with other loop shapes, see the article mentioned at the beginning of this one.

+

Conclusions

+

Based on what we have explored in the realm of wire horizontal loops, we can draw a few conclusions. These recommendations are based on the idea of using the loop for more than one band.

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1. How Big? The loop should be at least 2 wavelengths in circumference, regardless of the final shape. For most purposes, the antenna should be considered for use over a 2:1 frequency range, even though it will load on other bands well above the design frequency. The exception to this recommendation is the case in which the antenna is for NVIS use on the lower band and for normal skip communications above that band. In that case, a 1 wavelength loop at the lower frequency will provide the best compromise.

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1. How High? Because the antenna is used mostly on the lower HF bands, it is safe to suggest that the antenna should be as high as feasible. A height of 1 wavelength above ground is certainly not too high, although in most circumstances the antenna will be restricted to lower heights. The exception is the case in which the antenna serves for NVIS communications on the lower band. In that case, the 1 wavelength loop should be between 0.15 and 0.25 wavelength above ground for the strongest upward pattern. On the second harmonic, the antenna will be 2 wavelengths long and between 0.3 and 0.5 wavelength above ground for better, if not ideal, longer-range communications.

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3. What Shape? Of the sampled shapes, the circular version produces the most even set of lobes on all frequencies. Hence, a polygon that approaches circularity is more likely to have fewer interactions among the sections of the antenna to produce a pattern with only a few spiky lobes. However, even a circular design will produce 4 main lobes when it is 2 wavelengths in circumference.

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None of these recommendations is absolute, since the loop will work at many lengths, heights, and shapes. It is not possible to cover all eventualities in a single set of notes or even many sets of notes. Hence, the prospective loop builder should strongly consider obtaining at least a rudimentary antenna modeling softare package to test any possible design. In that way, you can predict more accuractely the performance of a loop designed to fit a given yard.

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Updated 10-21-2004. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index Page

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Topics: HF Multi Band, Horizontal Loop


+ + diff --git a/content/wire/hsyg.html b/content/wire/hsyg.html new file mode 100644 index 0000000..fe95695 --- /dev/null +++ b/content/wire/hsyg.html @@ -0,0 +1,119 @@ + + + + + + Lower HF Wire Beams + + + +
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Some Notes on Lower HF Wire Beams

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L. B. Cebik, W4RNL

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Fixed position wire beams still have a place in amateur communications from 40 through 160 meters. However, I am not certain we always make the right and patient choices in selecting and building wire beams. We tend to treat them as Field Day temporary antennas rather than really building them to do a job.

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+

The Wire Yagi

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Consider the 2-element wire 40 meter beam. It is an improvement over the dipole in several ways. 1. It provides forward gain; 2. It provides rear attenuation; and 3. It lowers the elevation angle of maximum radiation by a few degrees. Most of these advantages are captured in the elevation plot below: Gain = 9.5 dBi; Front-to-back ratio = 14 dB; TO angle = 35 degrees; Feedpoint Z = about 50 ohms, all at a height of 50' over average ground, centered at 7.15 MHz.

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For reasons that appear below, let me give the performance figures for an elevation angle of 18 degrees, near the lower -3 dB point. Gain = 7.5 dB; F-B = 12.7 dB.

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Here are the dimensions that will yield this performance. Driven element = 66'; reflector = 70'; spacing = 20' with #12 or #14 copper wire. However, the 2:1 SWR bandwidth of the antenna covers only about 2/3rds of the 40 meter band. Moreover, especially on the low end of the band, the pattern goes to pot.

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Let's redesign the antenna by making one simple change: increase the wire size to 2" in diameter. The dimensions for this fat wire Yagi are these: Driven element = 64'; reflector = 70'; spacing = 20'. Now the 2:1 SWR bandwidth of the beam exceeds the limits of 40 meters, as the following table demonstrates:

+ 
Frequency      Gain      Front-to-Back       Feedpoint Impedance  SWR
+  MHz           dBi           dB                  R +/- jX ohms
+7.0            7.9            11.1           36.4 - 13.4         1.6:1
+7.1            7.6            12.5           45.3 +  3.3         1.1:1
+7.2            7.4            12.6           54.0 + 18.3         1.4:1
+7.3            7.3            11.9           62.2 + 32.0         1.8:1
+
+

Of course, 2" wire is impractical, and 2" diameter tubing is too heavy for any installation. So the antenna is impractical--unless we remember that we can simulate fat wire with an array of thin wires spaced apart. The simplest scheme to achieve most of the benefits is to use two wires making a flat wire about twice the diameter of the wire used in the model. This 2:1 rule of thumb is not precise, but adequate for most simple design cases. Take two wires and a bunch of spacers (1/2" thin wall CPVC is an adequate substitute for varnished or parafinned wooden dowels) and make lengths of flat 4" wide wire. Not only connect the ends, but as well solder shorts across the wire periodically. Now we have the material for a wide-band 40-meter beam.

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Reversible Wire Beams

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Carrol Allen, AA2NN, has allowed me to share a pair of designs that take the wire beam process one step further. He developed 40-meter models of reversible wire Yagis and Moxon rectangles using a sound technique of employing identical elements and loading the reflector with a length of transmission line. He modeled his beams at 55' over medium earth to fit his location, but his designs are widely applicable. +

Below are outlines of the two beams. Taking the Yagi first, he uses 2 65' long #12 wires, spaced 21' apart. From each, he hangs a length of 50-ohm transmission line (9914 with a velocity factor of 0.78). The lines go to a switch, whose common terminal goes to the coax coming from the shack. Carrol switches in one direction, making the hanging line in that direction an extension of the shack coax and hence, the line to the driven element. The remaining line is not connected and becomes the load for the reflector.

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For this Yagi design, to maximize the performance pattern, the reflector needed an inductively reactive load of about 75 ohms. Transmission lines between 0 and 90 degrees long, when shorted, provide inductive reactance. Between 90 and 180 degrees, transmission lines provide inductive reactance when open circuited. Carrol chose open-circuit 146-degree lines (43' 4") to suit his situation. However, you can also use shorted lines of 56.5 degrees (16' 8.7") to do the job. If you need to bring the line near the ground for switching, you can add 180 degrees (53' 2.3") for a total shorted line length of 70'. If you use shorted lines, just be sure that the "unused" switch or relay positions go to ground; if you use open circuit lengths, leave the contacts open.

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The next figure provides azimuth and elevation patterns of the beam at its projected 55' height.

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Note the gain--a little over 10 dBi--and the front-to-back ratio--a little over 14 dB. Although not astounding when compared to highly elevated many-element 20 meter beams, the antenna will enhance 40 meter operations very nicely--and in two directions.

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Searching for a little better front-to-back ratio, AA2NN adapted the Moxon rectangle for reversible operation. The sketch provides the dimensions of Carrol's #12 copper wire model. Because the equalized Moxon rectangle optimized for front-to-back ratio has a slightly higher feedpoint impedance, Carrol used 70-75 ohm cable as his projected feedline. The "hanging" feed-load lines are 75-ohm, 0.83 velocity factor coax. Carrol used 42' 7" lengths of open circuit line for this antenna, although corresponding shorted lines might also have been used. AA2NN does remind us that coax loading lines are not lossless and may be lower in Q than we may initially think, especially when we use them in longer lengths for convenience. The resistive losses will decrease gain by a small amount.

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The projected performance of the Moxon version of the reversible beam shows clearly the enhanced front-to-back ratio and the reduced gain relative to the reversible Yagi. Which of these two very usable antennas one might select will depend both on the needs of one's operating situation and on how much high horizontal space one can give to the antenna. The Moxon is almost 20' shorter than the Yagi.

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My thanks to AA2NN for letting me add these antennas to this note.

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The Parasitical Half-Square

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The wire Yagi is the ultimate in simplicity for a directional antenna, but it may not be the best for all types of operating goals. We often forget that we can add parasitical elements to almost any wire antenna. Parasitical extended double Zepps were known back in 1938. More practically, a half square will fit the half wavelength horizontal space of our Yagi, with vertical wires dangling from the 50' high point to about 12 to 14 feet or so above ground. Can we add a reflector about 20' or so behind a half square and change the bi-directional pattern to a mono-directional one? Yes, as the plot below demonstrates. The operating performance of a #12 wire parasitical half square is given by these numbers: Gain = 6.6 dBi; F-B = 23 dB; TO-angle = 18 degrees; Feedpoint impedance = 56.9 + 3.4 ohms. The reason for giving the 18-degree performance figures of the Yagi is now apparent.

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The dimensions of this wire parasitical half-square are these: Horizontal length of both elements = 68'; driven element vertical length = 34.8'; reflector vertical length = 35.9'; spacing = 20.4'.

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The advantage of the half-square is that at elevation angles below 18 degrees, its gain drops off much more slowly than does the Yagi gain. In addition, it lacks significant gain above 35 degrees, reducing incoming high angle QRM and QRN. These are, of course, advantages to the DX operator; the Field Day and Sweepstakes operator may prefer the Yagi precisely because of its higher angle radiation pattern.

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One distinct disadvantage of the wire parasitical half-square is narrow bandwidth--about 100 kHz on 40 meters. To increase the bandwidth both in terms of 2:1 SWR and pattern retention, we must increase the wire size to about 6" in diameter. Then we obtain these dimensions: horizontal length of both elements = 68'; driven element vertical length = 35.2'; reflector vertical length = 37.6'; spacing = 20.4'. Some may find it odd that we increase the element lengths as we fatten the wire of the half-square. However, remember that the half square belongs to the family of 1 wl loop antennas, and like a quad, lengths grows with wire diameter.

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With these dimensions, we can achieve the elevation plot below.

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Here is a chart of performance checkpoints through the 40-meter band:

+ 
Frequency      Gain      Front-to-Back       Feedpoint Impedance  SWR
+  MHz           dBi           dB                  R +/- jX ohms
+7.0            6.9            10.1           37.5 - 21.8         1.8:1
+7.1            6.9            21.2           60.5 +  4.6         1.2:1
+7.2            6.5            18.6           79.3 + 15.1         1.7:1
+7.3            6.1            10.0           85.9 + 23.1         1.9:1
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The design center of the fat-wire half square was 7.07 MHz. Selecting this lower frequency was necessary to preserve a directional pattern across the band with a reasonable SWR figure at both band edges.

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Like the fat-wire Yagi, the fat-wire parasitical half-square requires construction of the antenna wires using the same principles, but this time with a spacing of about 12".

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The figure below compares the shapes of the two antennas and summarizes both #12 and fat-wire dimensions.

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The Parasitical Right-Angle Delta

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As with the half-square, it is also possible with delta loops to derive well above 3 dB forward gain (relative to a single loop) and a front-to-back ratio of 10-15 dB by placing two vertical loops about 0.15 wl apart. The result is a parasitical 2-element beam with the same low TO angle. The beamwidth will be fairly wide: 80-90 degrees, without the side nulls we are used to with upper HF high altitude Yagis. Feedpoint impedance will be to the 60-65 ohms range at resonance. +

Expect both the driven loop and the reflector to be a bit shorter than a resonated single loop, with the driven element shorter than the reflector.

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If you care to scale some numbers from 7.15 MHz, here is a right angle delta loop and its 2-element counterpart. Given are the baseline and height (one is twice the other), and the sides are about 1.414 the height. This model had a maximum height of 60.4' which was held constant for the 2-element version to achieve comparable TO angles (17 degrees for the model)

+ 
Antenna               Baseline          Height           Spacing
+single ra delta        60.8'            30.4'             ---
+2-el ra delta
+  driv. el.            59.3'            29.65'
+  reflector            60.6'            30.3'             20.5'
+
+

When made into a parasitical beam, the deltas also show reduced 2:1 SWR bandwidth (relative to their resonant impedance). At 40 meters, both SWR and pattern begin disintegrating somewhere around +/- 50 kHz from the design point with #12 wire. Widening that bandwidth depends upon using truly fat wires with equivalent diameters of about 6" at 40 meters for full band coverage with reasonable gain and F-B (arbitrarily defined here as 3 dB gain over a single loop, greater than 10 dB F-B, and less than 2:1 SWR).

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K1KP uses a simplified version of the ON4UN feed for his 80 meter delta loops, which have their apices up at 70 feet and base legs about 8 feet off the ground. The apices are spaced 20 feet apart, with the bases spread to a distance of about 50 feet. He reports that the feedpoint impedance is close to 100 ohms. Each feedpoint runs to a central switch, roughly as sketched in the drawing. (Not shown in the drawing are baluns at each loop feedpoint to isolate each antenna. Also not shown is the tilt of each loop toward the other.)

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Coax sections A and B to the switches are lengths of RG-11/U foam (with a higher velocity factor than non-foam coax) coax, 36 feet long. The switch is a relay that selects one feed as the driven element. 16 more feet of RG-11/U foam coax adds to the 36 feet on the driven element to form a quarter wave matching section, yielding a 50-ohm impedance for the coax to the shack.

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The relay also shorts out the end of the other line forming the reflector. The shorted 36 foot coax line functions as a loading inductance to lengthen the electrical size of the loop in use as a reflector.

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K1KP reports reasonable flat SWR and detectable gain over the single loop with this system, which is fairly close-spaced (average distance = about 1/8 wl) as parasitical systems go. It represents an ingenious way to switch beam directions and simplify feedline requirements without sacrificing performance from the wire array.

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Incidentally, models of the half square and the single loop DMS (otherwise known as a side-fed rectangle) show about a dB gain advantage over the delta loops, and this gain also transfers to parasitical arrays of them. Of the antennas investigated, the half-square has the highest gain and front-to-back potential at more than 6.5 dBi and more than 23 dB respectively. The side-fed rectangle shows nearly comparable figures, but is among the most narrow-banded of the SCV configurations in parasitical application. The side-fed rectangle should be used in a single-loop configuration for parasitical use, since the feedpoint impedance reaches about 40 ohms at a spacing of 25' on 40 meters, while the double loop variety has a feedpoint impedance of over 120 ohms at the same spacing.

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Moreover, it is feasible to electrically tune the reflector of any of the SCV parasitical arrays with no significant change of beam performance. This fact makes it possible to design two identical loops/half squares for resonance in the beam configuration and lengthen the reflector with a coaxial stub. The stub can become part of the feed cable when the loop serves as a driven element and can function as an inductive reactance when the loop is a reflector. Using a switching system similar to the one used by K1KP, but designed for direct 50-ohm feed and reflector stub, a reversible beam results with excellent front-to-back ratio and about 3.2 dB greater forward gain than a single loop/half square. Remember that if the required reactance is low, calling for a short stub that will not reach the switch in the center of the two loops, you can use at least two means of getting a longer stub. First, you can add a half wavelength of coax (remembering velocity factor) to the stub. Second, an open ended stub, which is capacitive at less than 1/4 wl become inductive over 1/4 wl. This latter technique will likely be the most useful for these applications.

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As the figure shows, a 2-element wire Yagi may give the same or slightly more gain at 17 degrees elevation when mounted at the apex height of the delta. However, its elevation angle of maximum radiation is about double that of the SCV group, and the SCVs have higher gain below the 17 degree mark, with 1/2 power points ranging from 7-10 degrees elevation, depending on the actual antenna height. Hence, the choice of antenna types depends on the user's operating goals.

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The 70' by 21' rectangular area necessary for these antennas is about the same. If the concept of a fixed position wire beam is useful, then the decision as to which antenna to build may rest on which performance characteristics one prefers relative to one's operating goals. However, whichever you build, it is wise to take the added pains of fattening the wires to give good performance across the band.

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Updated 9-7-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Delta Loop, HF Lower, Half Square, Moxon, Reversible, Yagi


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The IL-ZX Antenna for 40 Meters

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L. B. Cebik, W4RNL

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Every antenna design has a niche in the overall world of amateur radio antennas. The one described here has a quite small niche: it is for the individual who requires operation on 40 meters at low elevation angles, but who does not have the real estate to erect one of the SCV (self-contained vertically polarized 1 wavelength loop) antennas. The IL-ZX provides low-elevation angle radiation within a narrow operating bandwidth at low gain with a bi-directional pattern and reduced radiation at higher angles. It can be fed directly with 50-ohm coaxial cable, although a network antenna tuner will likely be useful for increasing the usable bandwidth.

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IL-ZX is shorthand for Intermediate Loop-Impedance Transformation antenna. The design has some of the properties of a small loop, for example radiation off the edges of the loop rather than off the face. However, it does not require the level of mechanical care associated with small loops and replaces the capacitor with a simple capacitive gap, the spacing of which resonates the loop. The native feedpoint impedance of such a loop, about 1/2 wavelength in circumference, is around 10 ohms. By using a double-loop form of construction, the impedance is raised to about 40 ohms.

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Small Loops

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The small loop is defined by some experimenters, such as W5QJR, as a loop whose circumference is between 0.1 and 0.3 wavelengths. Figure 1 shows the elevation pattern of one such loop resonated at 7.2 MHz. The maximum gain for copper loops and lossless capacitors is relatively constant across the range of defined size at 0.4 to 0.45 dBi at low elevation angles. Feedpoint impedances range from 0.5 ohms for the smaller sizes to about 1.5 ohms for the larger sizes. Below 0.1 wavelength circumference, the loop gain drops rapidly, as does the feedpoint impedance. +
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Small loops require extreme care in construction, since every fraction of an ohm connection loss results in large increases in power lost to heat. Hence, 3/4" diameter copper water pipe, soldered at every joint, is a common material. The required resonating capacitor demands special care of construction and attachment. If one has the skills to build one, a small loop can be a very effective antenna. With a stepper motor operating the capacitor, a 2:1 frequency range of operation is easily possible with good results.

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Large Loops

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In contrast, a large loop is thought of as a full wavelength in circumference, such as the quad loop. This loop has a natural resonant feedpoint impedance of 125 to 130 ohms. Many users reduce this impedance with a 1/4 wavelength section of 75-ohm coax so that it presents a reasonable match to 50-ohm coax for the remainder of the run. The antenna offers a fairly wide operating bandwidth without further adjustment. +

The full wavelength loop is capable of higher gain than a dipole placed at the center height of the loop. However, a large loop is about 1/4 wavelength on a side, about 35' horizontally and vertical on 40 meters. If fed at the bottom or top, the radiation pattern is largely horizontally polarized and subject to the same high-angle of maximum radiation as a dipole. Hence, low mounting heights reduce the effectiveness of this antenna.

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Fed in the middle of one side, the antenna offers low angle radiation, largely vertically polarized. However, for maximum effectiveness, the antenna requires about 10' spacing above ground, raising its top height to about 45' or so. Figure 2 shows the pattern of a vertically polarized 40-meter large loop.

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The full-size quad loop is but one of several SCV designs for achieving low angle vertically polarized radiation without need for a ground plane and without high angle radiation or reception of QRM and QRN from those upper angles. They have come into increased use by those who have directly or indirectly read into materials researched by ON4UN and others. Another entry in this series of notes attempts to put into perspective the entire spectrum of SCV antennas.

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SCVs require significant real estate, either or both horizontally and vertically. The modern city lot or rental property does not always offer sufficient space even for a 40-meter SCV.

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The Intermediate Loop

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The Intermediate Loop (IL) is a small loop enlarged to approach 1/2 wavelength in circumference. Because the antenna approaches a natural resonant point, its operating bandwidth enlarges, reducing its gain at any single frequency. However, the antenna offers lower construction losses because the resonance can be established simply by adjusting the width of the gap at the top of the antenna. Capacitance from one wire end to the other is sufficient for the task, but the low-C high L nature of this circuit also contributes to broader response and lower gain. Figure 3A shows the outline of the basic IL, which has a natural resonant feedpoint impedance of about 10 ohms. Relative to a small loop with an adjustable capacitor, the IL-ZX is a one-band antenna. +
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The feedpoint impedance can be raised to about 40 ohms by doubling the loop and feeding only one of the wires, as shown in Figure 3B. (Hence, ZX = Impedance Transformation.) This method is essentially the same impedance transforming technique used in the folded dipole. With wires of the same diameter at any spacing, the transformation is 4:1. This transformation applies to both radiation and heat components of the impedance, so no magical reduction in losses occurs--and likewise, no magical increase in gain occurs. However, the feedpoint impedance is now more manageable for use with 50-ohm coax.

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A second benefit of the double loop is that it offers the builder standard techniques of wire antenna construction. The loops may be spaced from 6" to 3' apart with corner CPVC spacers. Wire joints should be carefully constructed and soldered. The antenna benefits from the use of large wire sizes, with 1" wire showing an additional 0.5 dB gain over #12 wire. Therefore, one may wish to build the antenna from such materials as 450-ohm parallel line for each loop to simulate fatter wire. If such a method is selected, it is usually wise to solder a short across the parallel line periodically to ensure equal currents on each wire. (Do not short the two loops except at the top gap.)

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Figure 4 shows two arrangements for the top gap. In one case, the loops are brought together as a point; in the other they approach each other as a bar across the loop ends. Since the gap is actually the dielectric space for a capacitor formed by the loop ends, the difference in construction can make a big difference in antenna size and adjustment. Models of the point- gap required about 18' per side for the antenna, with a gap between 0.2 and 1.0' wide, depending on spacing of the loops. The flat-gap antenna, for loops spaced at 2' and a gap of 0.8' required sides of only 17' each. The flat-gap construction will make side length a much more sensitive function of the loop spacing, since the capacitance between ends will change more radically with loop spacing and the consequential lengthening or shortening of the wires facing each other. In all cases, the builder should be prepared to do considerable experimentation to achieve resonance.

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Performance

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The IL-ZX offers the would-be 40 meter operator a relatively small antenna, no more than 18' per side. Its best low angle performance occurs with the center about 15' high and its bottom wire therefore about 6' off the ground. The high point becomes about 24' up. +

The 2:1 VSWR operating bandwidth is about 100 kHz at 40 meters. However, a network ATU in the line should expand this without introducing significant losses on this lower HF band where a full wavelength of coax feedline is over 90' long (accounting for velocity factor).

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The primary signal direction of the IL is like that of the small loop: off the edges of the loop, as shown in Figure 5. With a center height of 15' or so, the elevation angle of maximum gain is 21 to 22 degrees, similar to SCV angles. Front-to-side ratio is generally around 10 dB.

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In the process of further experimenting with the IL-ZX design, I discovered that you can easily create a virtually circular low angle pattern--still of relatively low gain--by turning the IL-ZX "on its side." In this orientation, we need to raise the antenna to a base height of about 15' (for a top height of about 33') in order to eliminate excessive influence of the ground on one side of the antenna wire run more than on the other. At the 15' height, the impedance is about 64 + j15 Ohms, still an easy match for coax.

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Figure 6 shows the circularized pattern at about the same take-off angle as the "upright" IL-ZX. Gain is not significantly different from one version to the other. Hence, which orientation you choose to use is largely a matter of the pattern that you desire and the ease of feeding the antenna at the side vs. at the bottom.

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The principle disadvantage to the IL-ZX antenna is low gain. The antenna gain at maximum is about 3 dB less than that of a full size quad loop and about 4.5 dB less than that of a half square, when each of these is at optimum height. The reduction is less than a full S-unit in signal strength.

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However, the antenna offers two advantages that offset the reduction in gain. First, although not as narrow in reception bandwidth as a small loop, the sensitivity of the antenna to reception noise is considerably less than that of a resonant dipole or large loop. Second, the attenuation of signals at higher angles (in the 45-degree elevation angle range) reduces the reception strength of QRN and QRM. Hence, the signal-to-noise ratio of the antenna should be quite good for signals in the desired main lobes of the antenna. Since most receivers have excess gain at 40 meters, reception of desired distant signals should be a matter of increasing either pre-filtration or post-filtration gain.

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Even if we become very conservative and estimate performance at 6 dB down (1 S-unit) from an optimized half square, the transmitting success ratio should only go down in contest and pile-up conditions. For QRP operation, raising power from an initial 1 watt to a final 4 watts would restore signal strength at the reception end.

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The IL-ZX is not by any means a perfect antenna, designed to outperform anything else on the market. However, neither is any other antenna. Every set of performance figures carries with it a set of operating specifications within which performance is measured. We too often ignore this fact when evaluating antennas.

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If vertical and horizontal space are at a premium and skills needed to build an effective small loop are somewhere in the future, the IL-ZX may serve as an effective low radiation angle antenna in the interim until a perfect antenna site can be purchased. If you decide that you do not like the antenna, you can likely put the materials to use on other projects.

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The ILZX Horizontally

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Considerable interest has grown up in the last few years relative to the intermediate or interrupted loop used in a horizontal position. One or more such antennas--strung together for multi-band use--have appeared on the market within the British Commonwealth; one is called trhe "Cobbweb." However, a single-wire intermediate loop shows a very low impedance and requires a matching system for the ubiquitous coaxial cable feedlines preferred by many amateurs.

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The ILZX form of the interrupted loop is quite usable in a horizontal position. In fact, with almost no adjustments, the vertical ILZX for 40 meters can be used horizontally. In the following notes, we shall build the model ILZX in the same way for horizontal use that we used for vertical applications. The #12 elements will be separated by 6" and form a square that is 18' on a side. The tips that approach each other will form a "spear tip" pair for ease of adjusting the gap to refine the source impedance. The tips will be 1' apart.

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If we place the antenna at 50' above ground, we find a pattern resembling the one in Fig. 7. Note that the pattern is stronger along the axis formed by the feedpoint and the gap. The feedpoint impedance under these conditions is about 53 Ohms, with about the same bandwidth as the vertical version: 100-150 kHz or about 1/2 of the 40-meter band. Since the antenna is set for mid-band, a user would have to adjust the dimensions to favor either the CW or the SSB portion of the band.

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One myth surrounding interrupted loops is that they have a circular pattern. They do not. Due to the current distribution along the wire, radiation from the region on each side of the feedpoint yields a stronger pattern on the feedpoint-gap axis. In order to develop a circular pattern, one must readjust the shape of the ILZX into a long rectangle with shorter feed-region and gap-region dimensions. An example of such an antenna appears in the "Experimental Omni-Directional Antennas for 6-Meters". The general proportions would be a partial guide to developing a truly omni-directional interrupted loop for any other band. However, expect to make considerable adjustments for differences in the wire spacing, the wire size as a function of a wavelength, and the shape of the wire ends at the gap.

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The maximum gain of the horizontal ILZX is about 5.1 dBi at a 37-degree TO angle. The minimum or side gain is 3 dB less. Nevertheless, the pattern shows considerable side-pattern development, as displayed in Fig. 8. The graphic shows both the vertical and horizontal components of the total pattern. The vertical components are largely a function of ground reflections, but they still contribute to the overall useful radiation. Since 3 dB difference between the main and cross axes amounts to about half an S-unit, the radiation might be considered to be adequate for omni-directional operation.

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Compared to a dipole, the horizontal ILZX holds its own quite well, as demonstrated in Fig. 9. I modeled a resonant dipole at 50' above average ground for comparison. The dipole's maximum gain is about 1.1-dB higher than the maximum for the ILXZ. However, the dipole shows about 7-dB difference between its maximum and minimum gain, where the minimum is off the ends of the antenna. Note that for dipoles well under 1 wavelength above ground, we do not obtain a true figure-8, but only a peanut. Brought closer to ground, the pattern becomes a broad oval.

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Since the ILZX has a naturally oval pattern, it better approaches the omni-directional pattern favored by many hams who have only a single, fixed-position antenna. Erecting an ILZX requires only an 18' by 18' space, but does require 4 corner support posts for the 40-meter version. A version for 20 meters would require only a 9' by 9' space and might be supported on a single mast with fiberglass spreaders. The higher the frequency, the easier the ILZX will be to support. Because the antenna has a pattern that approaches the omnidirectional, it requires no rotator. However, it does call for orienting the strongest axis in the direction(s) of the most favored communications targets.

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Although the antenna looks something like a beam, it is not. Hence, it will not provide the QRM attenuation to the sides and/or rear of a beam. Indeed, the gain is less than that of a dipole (and hence considerably less than the gain of any well-designed beam). That is the price one pays for omnidirectional coverage. About the only way to obtain more gain from the ILZX is to extract it from the high-angle radiation. One (impractical) scheme for doing so is to stack and feed in-phase two ILZXs spaced 1/2 wavelength vertically. The result is about 3-dB more gain in every direction.

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The horizontal ILZX is suited to an exceptionally wide variety of construction techniques, depending on the frequency of operation and the exact layout of the loop and gap structures. Nested multi-band version may use a fairly low impedance line to connect feedpoints. The system of closed sleeve coupling sometimes works best when the main feedpoint is the highest frequency loop. Wire interactions will require loop adjustments, especially for the inner loops. As well, expect significant current on the inactive band loops and consequential modifications of the overall pattern on some bands. Finally, if one or more bands seem hard to bring into line, try moving the composite feedpoint to a different element relative to the one initially used. Be certain to check the SWR bandwidth for each trial arrangement before finalizing the selection.

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For a multi-band antenna, you may have better luck separating the bands. 20-15-10 provides less element-to-element interaction than a 5-band version of the antenna, although the harmonic relationship of 20 and 10 meters may show some pattern deviations. Of course, a second smaller array for 17 and 12 meters makes a good antenna to stack on top of the tri-band model.

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The ILZX principle of raising the feedpoint impedance simplifies the matching problem that faces single-wire interrupted loops. However, it requires greater care in supporting the double-wire loops. The wire problem might be resolved by using TV twinlead or 450-Ohm window line. Such insulated transmission lines will likely require adjustment of the dimensions downward by 2 to 5 percent to account for the antenna velocity factor of the vinyl coatings.

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Every variation of the horizontal ILZX will demand ingenuity and considerable experimentation. As well, remember that the horizontal ILZX resembles every horizontal antenna in the relationship of its elevation angle of maximum radiation to the height above ground. The original vertically polarized ILZX provided low-angle radiation, but suffered gain losses due to its proximity to ground. The horizontal ILZX provides more gain, but at higher elevation angles until the antenna is at least 1/2 wavelength above ground. The higher the operating frequency, the easier it is to meet the height requirement for long-distance communications.

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Happy experimenting!

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Updated 6-30-1997, 12-27-2001, 9-27-2003. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: Closed and Interrupted Loop, HF Lower


+ + diff --git a/content/wire/intloop.html b/content/wire/intloop.html new file mode 100644 index 0000000..1cf389e --- /dev/null +++ b/content/wire/intloop.html @@ -0,0 +1,17 @@ + + + + + + Half-Wavelength Interrupted Loops: Their Evolution and Uses + + + +

Half-Wavelength Interrupted Loops: Their Evolution and Uses

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Half-Wavelength Interrupted Loops: Their Evolution and Uses

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This page exists to include the PDF in the topic index

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Topics: Closed and Interrupted Loop, HF Lower, HF Upper


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The Isolated Off-Center-Fed Antenna (2 Parts)

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The Isolated Off-Center-Fed Antenna: Some Less-Explored Facets

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160- vs. 80-Meter Isolated Off-Center-Fed Antennas

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This page exists to include the PDF in the topic index

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Topics: HF Multi Band, Off Center Fed Dipole


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The "Lazy-8JK"
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L. B. Cebik, W4RNL

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For many years, The ARRL Antenna Book has shown a combination collinear, broadside, endfire array, for example on pages 8-51 to 8-54 of the 19th Edition. The array looks something like the outline in Fig. 1.

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The dimensions are locked up in 3 key factors.

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1. L = Element Length: Length may vary from 1/2 wavelength up to well over 1 wavelength.

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2. SP = Horizontal Element Spacing: Horizontal spacing may range from 1/4 wavelength to 3/8 wavelength.

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3. H = Vertical Element Spacing: Vertical spacing may range from 3/8 wavelength to 3/4 wavelength.

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The write-up shows a typical pattern with good bi-directional gain. However, a myriad of questions remains for anyone contemplating building such an array. However, we can boil the questions down to just two.

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What do we get? What do we pay?

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If we look carefully at the sketch, we can see that the array in Fig. 1 only becomes a collection of collinear elements when the element lengths approach and pass beyond the 1 wavelength mark, at which time, we can consider them to be collinear half wavelength elements. The vertical dimensions surround those that we associate with the Lazy-H antenna. If we look carefully at the sketch, we can see that the two left-side elements are in phase with each other, since the lines to each left-side element have half-twists. Likewise, the right-side elements are also in phase with each other. The 2 top elements are out of phase with each other, the sign of a W8JK array. Likewise for the bottom 2 elements. Of course, all of this assumes that all 4 lines from the central junction are equal in both length and characteristic impedance.

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Therefore, I have dubbed the array the "Lazy-8JK." This name is very much shorter than calling the assembly a collinear, broadside, endfire array. The latter expression is descriptive, because the top and bottom elements form pairs that are endfire arrangements, while the left and right pairs are broadside arrangements.

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Identifying the array as related to both the Lazy-H and the W8JK gives us a means of answering the latter question, at least in part. What we pay is something over twice the complexity of either the 8JK or the Lazy-H. Before we are finished, we shall examine some other costs for the array, but this much is a beginning.

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The tougher question is knowing what we get for our effort. However, identifying the array as a combination of Lazy-H and 8JK arrays gives us a foundation from which we can work. Let's transform the question into this one: What are the advantages in performance of the Lazy-8JK over either the Lazy-H alone or the W8JK alone? Now we have something with which to work.

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A Review of the Lazy-H Broadside Array

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In its basic form, the Lazy-H is a very old but well-proven antenna design with distinct advantages among wire arrays. Originally, it consisted of two 1 wavelength elements vertically spaced 1/2 wavelength apart. However, users later discovered that the antenna would operate effectively over a wide frequency range using a parallel transmission line and a wide-range antenna tuner.

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In Fig. 2, we see the essential electrical components of the Lazy-H. The horizontal wires marked L are the elements. PL, the phase-line, is broken into two equal parts, PL1 and PL2. As the diagram indicates, the two elements are fed in-phase with no twists on either phase line section. The main feedline, attached at the junction of PL1 and PL2, provides equal power to each element. Essentially, then, the Lazy-H consists of two doublets, vertically spaced and fed in-phase, in order to obtain considerable gain over a single doublet of the same length mounted at the approximate array center.

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The array produces bi-directional patterns on all bands within the operating range. The elements must be no more than about 1.25 wavelengths to achieve a bi-directional pattern. The antenna will operate at higher frequencies, but the pattern breaks down into multiple lobes as the electrical length of the elements increases at higher frequencies. As well, maximum gain occurs when the elements are about 5/8 wavelength apart. At the highest frequency of bi-directional operation, the antenna has been called the extended or expanded Lazy-H.

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Fig. 3 shows one common form of the Lazy-H that is useful for operation on amateur bands from 10 meters down to 40 meters. On 10 meters, the 44' wires are about 1.25 wavelengths, dropping to 1 wavelength on 15 meters, and becoming progressively electrically shorter as we reduce frequency. The 22' spacing is 5/8 wavelength on 10, 1/2 wavelength on 15, and electrically closer on lower frequencies. We shall use this model as a foundation for this evaluation of the Lazy-8JK in order to provide a consistent set of dimension throughout. In addition, we shall place the bottom wire of the Lazy-H at 44', with the top wire at 66'. With these dimensions and heights, we obtain the performance in the following table.

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+                  Extended Lazy-H Performance Potential
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+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.1       15.3        9         31                40 + j 305
+24.95      14.6       10         41                20 + j 100
+21.1       12.5       11         52                25 - j  35
+18.118     10.9       13         61                50 - j 145
+14.1        9.0       17         73               495 - j 145
+10.125      8.1       24         85                50 + j 105
+7.1         6.3       33         99                10 - j 100
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Because the elements grow shorter and the spacing becomes closer with decreasing frequency, the gain drops with frequency. That fact becomes clear from the overlaid azimuth patterns in Fig. 4. The 10-meter azimuth pattern shows its extended-double-Zepp family resemblance, while the 15-meter pattern has the classic shape for 1 wavelength elements. Although the full usable operating band-spread for the antenna appears in the table and pattern graphic, we shall focus only on operation in the 5 highest HF bands from 20 meters onward.

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A Review of the W8JK Endfire Array

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In its basic form, the 8JK is a very old but well-proven antenna design with distinct advantages among wire arrays. The array name derives from its inventor, John D. Kraus, W8JK, who wrote on various forms and facets of the antenna from 1937 to the present. Originally, the 8JK consisted of two 1/2 wavelength elements horizontally spaced from 1/8 to 1/2 wavelength. However, users later discovered that the antenna would operate effectively over a wide frequency range using a parallel transmission line and a wide-range antenna tuner.

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In Fig. 5, we see the essential electrical components of the 8JK. The horizontal wires marked L are the elements. PL, the phase-line, is broken into two equal parts, PL1 and PL2. As the diagram indicates, the two elements are fed out-of-phase with a half-twist on one of the phase line sections. The main feedline, attached at the junction of PL1 and PL2, provides equal power to each element. Essentially, then, the 8JK consists of two doublets, horizontally spaced and fed out-of-phase, in order to obtain considerable gain over a single doublet of the same length mounted at the approximate array center.

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The array produces bi-directional patterns on all bands within the operating range. The elements must be no more than about 1.25 wavelengths to achieve a bi-directional pattern. The antenna will operate at higher frequencies, but the pattern breaks down into multiple lobes as the electrical length of the elements increases at higher frequencies. The element spacing is subject to significant variation among builders. The version that we shall explore uses a spacing of 5/8 wavelength at the highest operating frequency. This spacing becomes electrically smaller as we reduce frequency, but still is not the spacing for the highest possible gain. In fact, the array tends to increase gain with closer spacing, although the impedance at the feedpoint becomes impractically low. The advantage of the 5/8 wavelength spacing used in this model is that it yields almost constant gain over the entire operating range of the antenna.

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The version that we shall explore uses the same wire lengths and spacing as the Lazy-H in Fig. 3. The only differences are the fact that the antenna is placed in a horizontal position and there is a half-twist in one (and only one) of the phase lines from the common junction to the elements. Since the Lazy-H has elements at both 44' and 66' above ground, we shall sample performance on 20 through 10 meters at each of these heights.

+ 
+                  Extended Lazy-H Performance Potential
+
+44' Above Ground
+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.1       11.8       11         33               160 + j 505
+24.95      11.8       13         41                35 + j 170
+21.1       11.1       15         50                25 + j  25
+18.118     11.0       17         55                25 - j  75
+14.1       10.5       21         61               110 - j 420
+
+66' Above Ground
+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.1       11.7        8         33               165 + j 505
+24.95      11.9        9         40                35 + j 170
+21.1       11.4       10         40                20 + j  25
+18.118     11.3       11         54                25 - j  75
+14.1       10.8       14         60               110 - j 410
+
+

In these tables--indeed, in all of the tables--the impedance figures are representative values modeled with 450-Ohm transmission line for the phase lines. The actual feedpoint values will tend to vary with changes in either the characteristic impedance or the velocity factor of the line selected. for that reason, I recommend that any prospective builder of any one of these arrays model the installation including the characteristic impedance and velocity factor of the phase lines to be used. From these values, you may calculate the anticipated impedance at the antenna tuner using any one of a number of available transmission line programs, such as TLW or TLD.

+

At either height, the gain variation is less than 1 dB from 20 through 10 meters. Although the gain is generally lower, on 20 meters the 8JK outperforms the Lazy-H. Fig. 6 provides the overlaid azimuth patterns for the W8JK in extended operation to even lower frequencies. Once more, the extended-double-Zepp origins of the 10-meter pattern are apparent.

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The gain differences between the 8JK and the Lazy-H are largely due to differences in the amount of energy radiated at high elevation angles. Fig. 7 shows selected elevation patterns for the two arrays, with the 8JK patterns taken for a 66' height above ground.

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At 21 MHz, where the Lazy-H spacing is almost a perfect half wavelength, the Lazy-H effectively suppresses high-angle radiation, in contrast to the multiple strong upper-angle lobes of the 8JK. On 10 meters, the Lazy-H does not suppress overhead radiation perfectly due to the wider spacing, but overall suppression of high-angle radiation is excellent. Still, the 8JK shows even more high-angle lobes. The 8JK begins to exceed the Lazy-H in gain in the lowest lobe on 20 meters. The Lazy-H spacing is down to about 5/16 wavelength, a value that is too close for effective suppression of high angle radiation.

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The "Lazy-8JK" Array

+

Against this background, we may now combine a Lazy-H with an 8JK to arrive at the collinear broadside endfire array, that is, at the Lazy-8JK. The elements of Fig. 1 describe the most common version of the antenna. For our comparisons, we shall use 44' element lengths, which is about 1.25 wavelengths at 10 meters. The vertical spacing will use the Lazy-H value of 22'.

+

However, we cannot use the 22' element spacing of the 8JK that we have reviewed. At that spacing, the Lazy-8JK actually shows less gain than a single Lazy-H for 15 through 10 meters. We must compress the horizontal spacing to about 8-11 feet to obtain any usable additional gain from the 4-doublet array. The modeled data are based upon the 11' spacing, although the differences between 8' and 11' are not operationally significant.

+

In addition, there is an alternative feed system to the one shown in Fig. 1, where each of 4 equal-length phase lines combine at a central feedpoint. As shown in Fig. 8, we may also construct individual Lazy-H arrays with center feedpoints. We then run equal lines to a center position, giving one and only one of those lines the necessary half twist to place the left-side doublets out of phase with the right-side doublets.

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For the 44' elements at 44' and 66' above ground, 11' left-to-right spacing requires two 5.5' phase lines. For the data in the tables, I again used 450-Ohm line for all phase lines.

+ 
+                  Lazy-8JK Performance Potential
+
+Standard Feed System (Fig. 1)
+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.1       16.5        9         33                50 + j 300
+24.95      15.4       10         37                 9 + j  90
+21.1       13.8       11         45                 6 + j  10
+18.118     12.8       13         51                 7 - j  40
+14.1       11.6       16         58                42 - j 260
+
+Alternative Feed System (Fig. 8)
+Freq.      Gain       TO angle   Beamwidth        Feed Z
+MHz        dBi        degrees    degrees          R+/-jX Ohms
+28.1       16.5        9         33              1590 + j1870
+24.95      15.4       10         37                35 + j 465
+21.1       13.8       11         45                10 + j 190
+18.118     12.8       13         51                 9 - j  85
+14.1       11.6       16         58                30 - j 135
+
+

1. Gain Factors: There is no difference in the gain performance between the two feed systems for the Lazy-8JK. The Lazy-8JK provides a variable gain value according to frequency according to the Lazy-H part of its origins. However, the W8JK portion of its origins shows up in the increments of gain above each of the corresponding simpler arrays. The following table tracks the gain advantage of the Lazy-8JK over the Lazy-H and the W8JK, where the latter uses values for a 66' height above ground.

+ 
+           Gain Advantage of the Lazy-8JK
+All gain values are in dBi at the elevation angle of maximum radiation.
+
+Freq.       Lazy-     Lazy-     Added     W8JK     Added
+MHz         8JK       H         Gain               Gain
+28.1        16.5      15.3      1.2       11.7     4.8
+24.95       15.4      14.6      0.8       11.9     3.5
+21.1        13.8      12.5      1.3       11.4     2.4
+18.12       12.8      10.9      1.9       11.3     1.5
+14.1        11.6       9.0      2.6       10.8     0.8
+
+

The Lazy-8JK adds only about 1 dB gain to a single Lazy-H in the upper-most bands. However, the 8JK portion of its origins increases the gain on 20 meters by about 2.6 dB. In contrast, the Lazy-8JK shows its highest gain additions over a single 8JK on the top bands, with reduced gain additions with descending frequency. Additionally, the beamwidths for the Lazy-8JK are slightly narrower than for the standard 8JK as a function of the additional gain.

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+

Fig. 9 shows selected elevation patterns corresponding to those shown for the Lazy-H and the W8JK. The added gain is largely due to a continuing progression of upper lobe suppression. A comparison of 20-meter patterns among all three arrays is especially notable.

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+ +
+

To complete the comparisons, Fig. 10 shows overlaid azimuth patterns for each band, with each pattern taken at the elevation angle of maximum radiation.

+

From the perspective of gain, then, there are two considerations facing the builder who may weigh the increase in construction complexity against the performance advantage. First, the more complex array shows a better balance of gain than a single Lazy-H, with improvements especially in the 20-meter performance. Second, the Lazy-8JK increases gain on the upper bands over the sampled standard 8JK array. Whether the total improvement is sufficient to warrant the increased construction problems is ultimately a user judgment.

+

2. Impedance Considerations: The differences in the two ways of feeding the Lazy-8JK lie wholly in the area of the feedpoint impedances. The standard X-form of the phase lines (Fig. 1) yields more bands on which the feedpoint impedance is under 10 Ohms resistive. Under these conditions, every fraction of an Ohm of loss resistance in the connections transforms a proportionately higher percentage of the power into heat. Hence, great care must be used in the assembly of the system, and equal periodic maintenance care is required.

+

The alternative configuration for feeding the Lazy-8JK has fewer instances of very low resistive components to the feedpoint impedance. However, 10 meters present a high impedance, with both the resistive and reactive components above 1500 Ohms. As a result of the high variability in feedpoint impedances, the builder very likely will have to pay close attention to the line length between the antenna feedpoint and the tuner terminals to present impedances within the tuner's matching capabilities. This aspect of the Lazy-8JK is the second half of the answer to the original question of what do we pay.

+

Conclusion

+

The Lazy-8JK (or collinear broadside endfire) array offers different advantages over the standard Lazy-H and the standard 8JK. Since these advantages change with each upper HF band, there is no single answer to the question of whether the larger array is worth the effort of construction.

+

Nevertheless, by setting up reasonable comparators, these notes will hopefully provide a better sense of both the advantages and disadvantages of going to the more complex arrangement. There are additional dimensions of the final decision. For example, the Lazy-8JK does not lend itself to the relatively simple triangular arrangements of Lazy-H arrays that permit switched directional changes. Nor does the Lazy-8JK allow one to construct an easily rotated version of the array, as is possible with a single 8JK. Yet, the lure of added gain is likely to appeal to at least some aficionados of wire antenna construction. With dimensions of 44' by 22' by 11', it is still a fairly compact upper HF bi-directional array with outstanding performance potential.

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Updated 11-1-2005. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Oct., 2005. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Return to Amateur Radio Page

+

Topics: HF Upper, Phased Array, W8JK


+ + diff --git a/content/wire/lant.html b/content/wire/lant.html new file mode 100644 index 0000000..446c877 --- /dev/null +++ b/content/wire/lant.html @@ -0,0 +1,91 @@ + + + + + + The L-Antenna + + + + +
+

The L-Antenna

+

+
+

L. B. Cebik, W4RNL

+

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+ +

+
+ Diversity-polarization reception is often handy, especially on 10 meters. We use the same antenna for both horizontally polarized SSB locals and vertically polarized FM repeaters and whip-equipped mobiles. And when the band is really open, we can work distant stations about as well as we might with a vertical or horizontal dipole. All we need is the right antenna. +

Actually, the antenna itself is simplicity personified. Let's design it from two different angles.

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+ +
+

First, consider the common inverted Vee, shown in Figure A. When the legs make a 45-degree angle with the landscape or with a vertical line drawn between them, the impedance drops from the usual dipole value of 70 Ohms to about 50 Ohms. Let's imagine such a Vee with the apex about 30' in the air. Place a pin in the center feedpoint and start rotating the antenna until one leg is horizontal and the other points straight up. What happens to the convenient feedpoint impedance? Nothing. It remains in the 50-Ohm ball park.

+
+ +
+

Let's try that again, but this time, begin with a 1/4 wavelength ground plane vertical with the base at the 30' mark, as shown in Figure B. This vertical antenna is actually a special type of dipole, one where one of the legs consists of 4 wires arranged symmetrically and at right angles to the vertical part. The radiation from the four horizontal legs cancels out, so the antenna has a vertically polarized pattern. We could have used any number of ground plane legs greater than 1, so long as they form a symmetrical arrangement to insure cancellation of horizontally polarized radiation.

+

But what happens if we have only one ground plane leg. There is no opposite member to cancel out the radiation. So, we have not only the vertically polarized radiation from the vertical leg, but also the horizontally polarized radiation from the horizontal leg.

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+

What has happened is that the rotated Vee and the 1-legged vertical have turned into the same antenna, which is simply the L-Antenna. Figure 1 shows a sketch of how to build one from 3/8" diameter aluminum tubing. I claim no originality for the antenna, since a version of it has appeared in Moxon's Antennas for All Locations. Apparently, the first commercial version appeared in the 1950s.

+

Actually, you can build such an antenna out of any good antenna materials you have handy. Tubing from 3/8" to 1" diameter will work for the vertical element. Tubing or wire will do fine for the horizontal element. Spar- varnished wood, PVC, or other materials will make a good center mount.

+

With the version of the antenna shown, the design center or resonant frequency was set at 28.85 MHz. The feedpoint impedance is about 45.5 Ohms at that frequency. If you use larger diameter tubing, expect to shorten the elements a bit and find a slightly lower feedpoint impedance. If you use wire for some or all of the antenna, then expect to use longer dimensions and have a slightly higher feedpoint impedance.

+

Notice in the sketch that the vertical portion happens to be a little shorter than the horizontal portion. All that this means is that the antenna is fed very slightly off center and has a very slightly higher feedpoint impedance than if fed at the exact center.

+

Now consider that the usual hardware store tubing comes in 8' lengths. If you use a larger diameter vertical tube that is 8' long, then the horizontal section will have to be increased in length to resonate the antenna. The further distance off-center for the feedpoint will slightly raise the feedpoint impedance to offset the use of fatter tubing, at least in the vertical portion of the antenna.

+

The horizontal section can be tubing, especially if it runs off into thin air. If you mount this antenna on your roof, then you can run the horizontal wire or tubing along the ridge-top and support the opposite end.

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Before deciding just how you want to run the antenna, consider the azimuth pattern for the antenna. The one shown in Figure 2 is modeled at a height of 30' above average ground where the elevation angle of maximum radiation is about 15 degrees.

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+

Notice that the vertically polarized circle of radiation is slightly offset from being truly symmetrical around the antenna. That shift is due to the presence of the horizontal leg. The horizontally polarized radiation shows the typical dipole figure-8 pattern, but not as strong as it would be if both halves of the antenna were horizontal.

+

The total pattern is a mild kidney beam, with unequal side rejection amounts (-5 dB for the side with the leg and - 8 dB for the side without the leg). This total pattern is important only for skip communications. For local point-to-point communications, think about each of the sub- patterns. In planning an installation, try to orient the antenna so that the horizontal radiation covers the local areas of greatest communications interest. The vertical pattern will largely take care of itself.

+

The reason for taking such care in laying out the antenna is that cross- polarization of local radiation results in a large drop in signal strength. Skipping radiation through the ionosphere largely (but sometimes not completely) skews the polarization. So local coverage is the chief concern for laying out the L-antenna.

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+ +
+

Figure 3 shows the elevation pattern of the antenna, again at 30 feet up. The pattern is taken through the axis of maximum gain, which is--for the total field--about 5 degrees off a true perpendicular line drawn to the horizontal element.

+

One of the advantages of the antenna for local work--or as a back-up for a more complex 10-meter antenna--is it broad operating bandwidth. By setting the resonant frequency up somewhat in the 10-meter band, the 2:1 SWR operating bandwidth of the antenna is the entire 10-meter band from 28.0 to 29.7 MHz. It may appear to be even wider, if readings are taken at the end of a length of coax.

+

For the record, here are the modeled impedance readings for the antenna across the band:

+
+ 
  Frequency           Feedpoint Impedance
+  (MHz)               (R +/- jX Ohms)
+
+ 28.00                41.1 - j 31.0
+ 28.25                42.4 - j 21.7
+ 28.50                43.6 - j 12.5
+ 28.75                45.0 - j  3.2
+ 29.00                46.3 + j  6.1
+ 29.25                47.7 + j 15.4
+ 29.50                49.1 + j 24.7
+ 29.75                50.5 + j 34.1
+
+

Figure 4 shows the same information graphically. You should be able to obtain similar results across the band by judicious choice of materials and the feed point. Changing the lengths of the elements a little bit in either direction produces no significant change in performance.

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+ +
+

Since materials and mounting positions will vary so much from one installation to another, I shall leave the construction details to you. I do recommend a height of over 25' for the base of the antenna, with a least a foot or two between the horizontal portion and any non-conductive rook top it might rest over. The greater the separation of the horizontal portion from other objects, the better the performance.

+

This antenna is not designed to compete in gain or directionality with any other type of antenna. Rather, it is designed to be simple, to provide both horizontal and vertically polarized radiation, and to have a feedpoint impedance that is compatible with common coaxial cable. As such, it can fill a useful niche in the array of ham antennas available for various purposes. The L-antenna is likely easy to scale to 12 meters as a utility antenna, but beyond that, may require some special effort to make it mechanically sound.

+

If you need a simple means to test the waters on 10 or to keep track of all the local operation, the L-antenna just might do the job for you--cheap and easy.

+

For a look at the construction details of one installation, see the well-illustrated article on a 10-meter L (web.archive.org) by John and Kathy Croft (K3NJ and KC3T). Other possibilities appear in a late 1999 QST article.

+

6-Meter Versions

+

Feedback has resulted in a number of implementations for 6-meters, where local SSB nets, band openings, and some FM work are a common mix of activities. For either 3/8" or 1/2" tubing, each leg can be about 4.75' (57"), with slight trimmings for the best SWR curve. I cut the antenna for 51 MHz, which is slightly above most SSB work. However, with either of the 2 tubing sizes, the antenna shows a 50-Ohm SWR curve that is under 1.5:1 from 50-52 MHz.

+

As with a common dipole, bandwidth will be a function of the element diameter. Hence, the sizes listed--or a combination of the two--are recommended. Of course, if you have a pair of collapsible whips that each extend to 60 inches, you can use those for a field version of the antenna.

+

For 6-meter work, rooftop or higher mounting is useful to maximize the coverage.

+

You may make variants for almost any band by simply scaling all of the antenna dimensions, including the element diameter. To adjust the antenna to resonance, increase the leg lengths if you new diameter is smaller than the original and decrease the leg lengths if the new tubing is larger than the original (with the word "original" meaning the diameter after scaling).

+

The hub and feedpoint will always be the section of the antenna calling for the most ingenuity and adaptation of local materials. As you move the antenna upward in frequency, the legs grow lighter. Hence, you can more easily adapt hardware center plastics to the job. Be sure to seal the coax connector-to-leg junctions with something like Plasti-Dip to keep weather out of your coax.

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+ +
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Updated 2-5-99, 10-5-2000, 11-25-2002. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Jul., 1998. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+

Return to Amateur Radio Page

+

Topics: HF Upper, VHF / UHF


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+

Some Notes on Linear Resonators
+ Part 1: 20 and 15 Meters

+
+
+

L. B. Cebik, W4RNL

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+
+ +
+

Amateurs are always searching for ways to obtain multi-band service from a single element. Of course, we can always feed a wire with parallel feedline and an antenna tuner. However, amateurs tend to have a fetish for 50-Ohm coaxial cables. Of all the myths upon which the coax preference rests, perhaps the only valid one is that we may route a coaxial cable with less care for what surrounds the cable than we can when using parallel transmission line.

+

One popular multi-band technique has come to dominate all others: the trap. A high-Q trap tuned at or just below a higher operating frequency tends to terminate the antenna element length at the trap. At lower frequencies--within limits--the trap appears as a mid-element loading inductive reactance, allowing operation on a lower frequency. Trap verticals tend to outnumber trap dipoles, perhaps because they require half the number of weather-protected parallel combinations of inductance and capacitance.

+

In his justly well-known work, HF Antennas for All Locations, Les Moxon, G6XN, reported on and analyzed an alternative scheme for obtaining 2-band performance from a single element. The technique required only a single capacitor and enough wire or rod to span the center of a lower frequency element. With the right combination of ingredients, we can obtain a dipole-type near-resonant impedance at a desired higher frequency. Although Moxon makes use of the linear resonator in several projects within his book, the relevant analysis of the technique appears on page 117-120 of the 1982 edition and on pages 140-143 of the 1993 2nd edition. In a recent issue ofQEX (Mar/Apr, 2006, pp. 46-50), Vidi la Grange, ZS1EL, reports on a use to which he put the linear resonator. However, the lack of solid technical analysis of the resonator left me curious about the technique--and why amateurs have generally failed to make use of it more widely.

+

Moxon's Analysis and the Amateur's Questions

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A linear resonator consists of a length of wire stretching equally on each side of the center of a lower-frequency element. The ends of the new wire connect to the lower-frequency element. At the center of the new bridging wire, we place a properly sized capacitor. At the lower frequency, the added structure and component have little effect on the performance of the element. Some writers suggest that it has no effect, but that will prove wrong. However, the effect is small. At some higher frequency, the bridge wire and capacitor will form essentially a series tuned circuit that will create a low-impedance path, resulting in a second resonant point for the wire. Theoretically, we can calculate the higher frequency by knowing a few properties of the additions to the initial element. Note that I do not here specify that the element is a fed dipole. In principle, the additions would apply to parasitic elements as well as driven elements. In fact, Moxon's own analysis is independent of the element having a feedpoint or not. Fig. 0 shows the key elements of Moxon's rendition of the key elements in the linear resonator.

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The equations are nearly but not quite self-explanatory. L and C, of course, are the values of inductance (of the wire length within the confines of the linear resonator) and of capacitance. The term r is the "turns-ratio" of the main or lower frequency element and the added linear resonator elements when treated as lumped components. Note that the diagram uses the term M to represent the mutual coupling between the main element and the linear resonator element. In contrast, the equations make use of a mathematically related concept, k, the coefficient of coupling. If we know the effective turns-ratio between the two wires, we can solve for r. Where we use the same diameter conductors for the element and the linear resonator, we end up with a 1:1 ratio for r, but that condition is rare in practice.

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The key blockage to our ability to calculate the requisite values for a linear resonator lies in the mutual coupling, that is, the value of k. Although there are standard techniques for measuring either M or k when using lumped components, few amateurs have any inkling of how to determine the value for an antenna structure. Since we cannot effectively calculate the values that we need for a linear resonator, those who wish to try the technique do so by experimentation. They change the physical variables until they either give up in frustration or succeed in obtaining usable proportions.

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Although I have no magic method of determining the coefficient of coupling within a linear resonator circuit, it may be possible to evaluate which of the physical variables that go into such an antenna are most sensitive and which are least sensitive to changes. Modeling the simplest case, a 2-band dipole--may give us some useful clues should we wish to experiment with the idea. As a start, I picked an arbitrary frequency and dipole: 20 meters or, more specifically, 14.175 MHz. The dipole of choice is 0.875" in diameter. Because we shall later explore the effect of changing the main element diameter in a dual-band dipole, I also modeled dipoles using 1.0" and 0.75" diameter wire. Table 1 provides the data. I have purposely over-modeled the dipole to bring the resonant impedances as close together as feasible, noting the required change in dipole length to achieve this goal. Although the impedances match up to unrealistically small fractions, the length change between 0.75" and 1.0" material is over 1" or about 0.3% of the total length.

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Modeling a dual-band dipole with a linear resonator, however, is not quite so simple as modeling a mono-band dipole.

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Some Modeling Issues

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For the dual-band dipole, I selected 20 and 15 meters, specifically, 14.175 and 21.225 MHz. (As we shall see, I also selected structural values that showed <2:1 50-Ohm SWR across both bands.) A total of about 50-51 segments on the main element, divided into 3 wires, allows us to manipulate most of the structural variables and still maintain reasonable good equality among the segment lengths. As shown in Fig. 1, the linear resonator adds 3 wires to the basic dipole, along with a capacitor at the center of the linear resonator structure.

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The sketch indicates some of the structural variables in a linear resonator dipole. Table 2 provides a more complete list.

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My initial model required a main element that is 384" in total length, compared to about 398" for the monoband 20-meter dipole. Subsequent models maintained that length, suggesting that the idea that the linear resonator makes little or no difference to lower-frequency operation may be overstated. At 20 meters, an element length change of 14" is quite significant (about 3.5%). Both elements use 0.875" diameter wire in the model with the same total segmentation.

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HF tubular dipoles are unlikely to use the same diameter material for the linear resonator additions as for the main element. In most cases, the linear resonator will be considerable thinner. I selected--again arbitrarily--0.25" as an appropriate diameter for rods that the main element would support. (We shall later vary that diameter to see what happens.) My initial successful models used a rod length of 96", extending 48" on either side of center. I used three wires in the main element of the antenna so that the resonator rod and the center main element tube would have the same number of segments. Single-segment wires (0.25" diameter) connect the resonator rod ends to the junctions of wires making up the main element. The spacing (center-to-center) between the rod and the main element is initially 6" (although we shall also vary that value later).

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Here we encounter a modeling challenge. NEC has accuracy difficulties with junctions of wires that have different diameters. NEC-2 is worse than NEC-4. In fact, my initial NEC-4 models showed average gain test (AGT) scores of 0.971 on 20 meters and 0.963 on 15 meters. (NEC-2 models showed AGT values of 0.944 and 0.932 for the two bands, and I excluded the use of this core.)

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In contrast, my best implementation of MININEC 3.13 (Antenna Model) showed values in excess of 0.998 on both bands, simply because MININEC does not respond inaccurately to junctions of wires having different diameters. However, the only critical difference between the MININEC and NEC-4 models was in the value of capacitance necessary to arrive at a successful 15-meter resonance while using identical sizes for the physical parts of the dual-band dipole. MININEC required a capacitance of 16.9 pF, while NEC-4 reported a value of 15.7 pF. Absolute values of gain and impedance are not here in question. Rather, we are more interested in trends and rates of change. Therefore, the NEC-4 models are quite usable with the understanding that the impedances and the capacitance values shown may be a bit low. My preference for NEC-4 is not a bias--the MININEC models are more accurate in this situation--but a matter of practicality. It is more convenient for me to transfer data from my NEC-4 programs to other programs, such as spreadsheets, than it is for me to do so with my extant MININEC programs. Since graphic curves will play a significant role in what follows, I opted for the easier data transport.

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Some Basic Dual-Band Dipole Properties When Using a Linear Resonator

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The initial model that I have just described is satisfactory for exploring some of the basic properties of a dual-band dipole for 20 and 15 meters when using a linear resonator. Perhaps foremost among the easily detectable properties is the impedance behavior. On 20 meters, the impedance will no longer be 72 Ohms, but about half that value. At 21.225 MHz, the feedpoint impedance may cover a wider range, depending on the specific values assigned to the physical variables. For the initial model, the impedance was about 60 Ohms.

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Fig. 2 shows the current magnitude distribution on the antenna at the two selected frequencies. On 20 meters, the center-section current is much higher (by a factor of about 5) than the current on the linear resonator. On 15 meters, we have a reversal, with the linear resonator wire having a higher current magnitude than the main element (even allowing for the curve displacement, which is relative to the wire to which it applies, not to a common baseline). The reason that both magnitudes on the 15-meter representation are higher than the currents at the inner ends of the outer wires is that the currents are almost out of phase with each other. If we assign an arbitrary phase angle of 0 degrees to the actual feedpoint, on 15 meters the center of the linear resonator shows a phase angle in the range of -160 to -165 degrees. (NEC counts from 0 to +180 degrees and to -180 degrees when it comes to phase angles.) Essentially, Moxon's representation of current directions in Fig. 0 is correct--within 15 to 20 degrees.)

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One popular statement about linear resonator dipoles is that we obtain essentially dipole patterns at both frequencies. The truth of this statement depends on the degree of precision upon which we might insist. In very loose terms, the statement is correct. However, as we lengthen a center-fed wire beyond 1/2 wavelength, the gain increases steadily, and the dual-band dipole with a linear resonator shows this increase. Fig. 3 overlays free-space patterns for the model at the two frequencies. We can clearly see the slightly higher gain and narrower beamwidth at the higher frequency.

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The gain difference is about a half-dB, while the beamwidth difference is about a dozen degrees. These differences may have little effect on the performance of our antenna as a simple dipole. However, they may have more significant effects if we attempt to apply them to multi-element parasitic or phased arrays.

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Although most design work focuses narrowly on the two frequencies of interest, we may take a larger look at the feedpoint behavior of the dipole and its linear resonator. Fig. 4 shows the resistance and reactance from 13 to 22 MHz. The two components of the feedpoint impedance do not peak at the same frequency. In fact, the reactance peaks about 1.5 MHz lower and has a relatively steep curve of value change as the resistance crosses the 50-Ohm mark. Hence, the 15-meter resistance value is not ideal relative to 50-Ohm cable, although it is certainly usable. At the lower end of the swept frequencies, the resistance is well below 50 Ohms as the reactance cross the zero-point and becomes significantly inductively reactive. As we change some of the physical structure, we shall see that the most profound effects occur at the upper end of the swept band, while the lower end remains relatively stable.

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The 50-Ohm SWR curve for the dual-band dipole also focuses on the entire span from below 20 meters to above 15 meters, as shown in Fig. 5. Although this curve is typical for all variations in physical structures, we shall find some small but significant variations along the way. In general, the curve shows two narrow but adequate SWR windows for use of the antenna. Like a trap dipole, the antenna is useful only on the frequencies for which the structural elements are designed.

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These notes have so far shown what we may call the typical performance of a dual-band dipole with a linear resonator. Immediately, the experimenter wonders if changing any of the variables in Table 2 might give us some advantage--perhaps a better feedpoint impedance at one or both test frequencies, perhaps a wider SWR curve. . .. The only way to find out--without having to build and rebuild many dual dipoles--is to do some systematic modeling.

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Varying the Dual-Band Dipole Physical Structure

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If we cannot easily determine the mutual coupling between the inductances represented by the center length of the main element and the resonator rod, we can at least explore how the operating conditions change as we systematically vary some of the structure features of the dual-band dipole equipped with a linear resonator. From the outset, we should be aware of the restrictions of this exploration. First, we are working with two frequencies that have close to a 1.5:1 ratio. Experience by past experimenters has suggested to others that frequency ratios below about 1.4:1 are unlikely to allow successful linear-resonator treatment. How far upward in frequency spread we might successfully go seems to be unexplored territory.

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As well, we are working with relatively fat elements, that is, elements that are not thin wires. Hence, any dimensional scaling is likely to be limited in success, although scaling the dimensions used here might serve as a starting point for a series of more specific models. As well, the main element is fixed at a uniform diameter. Stepped diameter elements will likely be longer for the same frequencies used, although the length difference between a mono-band dipole and a dual-band dipole will be similar.

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Third, we are using NEC-4 for the study. Hence, the impedance values might be a bit low relative to reality. The required capacitance values may also be a bit low. However, the progressions of values and the rates of change will be close to correct.

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The bottom line, then, is that the following notes are indicators of what to expect from a 20-15-meter linear-resonator dipole, but not a set of building plans.

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Varying the Length of the Resonator Rod

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Perhaps the most reasonable physical dimension to vary initially is the length of the linear resonator rod. In this exercise, we shall retain the initial dimensions for all other structures. The main element will use a 0.875" diameter wire and be 384" long overall. The linear resonator rod will be 0.25" in diameter and spaced 6" from the main element.

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For the exercise, I varied the length of the linear resonator rod in 4" increments from 78" to 102". (Our initial model used a 96" rod.) Table 3 shows the feedpoint impedance values at 14.175 MHz and at 21.225 MHz. In addition, the table shows the capacitance value necessary to produce the most acceptable 50-Ohm SWR values within each of the two bands. The final column shows the relative current phase at the center of the linear resonator rod at 21.225 MHz, where the feedpoint current has a presumed current phase of 0 degrees.

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The table provides some relevant performance numbers at two specific interesting frequencies. However, it does not show the overall performance characteristics, which are also interesting. For example, if we sweep frequencies between 13 and 22 MHz, we obtain the gain curves shown in Fig. 6.

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The curves use only 3 widely spread resonator rod lengths because using all of them would have yielded a single wide blurry line. The result is clear: varying the rod length has no significant effect on the gain of the dual-band dipole. The curve shows a normal rise in gain with increasing length when measured as a function of a wavelength. In fact, we shall not bother with gain curves for the remaining variations in physical structure, since they would all show the same result. Since the gain curve does not vary with the physical variations, so too the beamwidth does not change relative to our initial model.

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Perhaps the most significant changes occur with respect to the dipole feedpoint impedance. As shown in the table, the required linear resonator capacitance for acceptable SWR curves within 20 and 15 meters changes by about 0.35 pF per 2" change in resonator length. The rate of change is nearly linear. Fig. 7 shows the swept 50-Ohm SWR curve for 3 widely separate samples from the table.

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There is not much difference in the curves, although the shorter resonator rods show the lowest peak SWR value between the bands. However, far more significant to the builder are the SWR values within the bands of interest and the reasons for those values. The table shows that the 20-meter feedpoint impedance changes very little despite the 40% variation in rod length (once we readjust the capacitance). However, the 15-meter impedance changes considerably. Fig. 8 graphs the resistance variation for the same cases shown in the SWR graph.

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Between 13 and 16 MHz, the resonator rod length makes very little difference to the feedpoint resistance. It does have a slightly more noticeable effect on the feedpoint reactance, as shown by the transition from capacitive to inductive reactance as we increase the resonator rod length. In contrast, the resonator rod length makes a much larger difference on the 15-meter feedpoint resistance. As we increase the rod length, the feedpoint resistance reaches its peak value at ever-higher frequencies so that the value is higher at 21 MHz.

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Despite the relatively wide range of 15-meter impedance values that occur as we change the resonator rod length, the current phase angle changes very slowly. A linear resonator tends not to give the builder any sudden performance changes to indicate when a varied structure has gone too far in one or another direction.

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Interestingly, the most optimal version of the dual-band dipole occurs with a rod length of 92", only a bit shorter than our initial model. Although this model does not change the relatively low 20-meter feedpoint impedance, it does provide a 15-meter value that most closely approximates the best match to a 50-Ohm coaxial cable. Therefore, we shall use this model as the starting point for exploring other variations that we may impose on the dual-band dipole.

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Varying the Spacing between the Resonator Rod and the Main Element

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If we freeze the rod length at 92", we may vary one of the other dimensions of the physical structure. The initial model used a 6" space between the rod and the main element. Let's vary this spacing in 2" increments between 2" and 10" to see what emerges. The basic results of this exercise appear in Table 4. Remember that in this exercise, we are holding constant the main element length and diameter and the resonator rod length and diameter.

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The change in resonator rod spacing once more has only a small effect on the 20-meter impedance. The reactance tends to become more inductive as we increae the spacing. The key differences appear on 15 meters. As we increase the spacing, the 15-meter impedance increases in both resistance and inductive reactance. Fig. 9 shows what happens to the wide-band SWR curves.

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Although all of the 3 curves shown are usable, close spacing reduces the feedpoint resistance to a low value, while wide spacing increases it. Both extremes raise the 50-Ohm SWR on 15 meters.

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The 2" spacing value did not yield a value of capacitance that would produce an SWR of less than 2:1 on 15 meters. However, this result is uncertain. The wires that form the connections between the main element and the resonator rod have become seriously shorter than the segment lengths on the two parallel elements. Hence, it is not wholly clear whether the result emerges from the spacing or from modeling limitations.

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In many cases, the linear resonator rod would not by fully self-supporting. Instead, it would likely have a center non-conductive support extending between the main element and the rod. Some builders might use the support as a means of flexing the resonator rod at the center to either increase of decrease its distance from the main element. I have not modeled this situation, although the technique may serve as a method for fine tuning the assembly.

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We may note in passing that spacing occasions a small variation in the resonator current phase. As well, the capacitor value required to achieve the acceptable SWR curves does not change in a linear manner. The closer the spacing, the larger the capacitor must be. It is likely that the capacitor value changes according to changes in the mutual inductance between the rod and the main element center, and that value is also not linear with distance between the coupled lengths.

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Varying the Diameter of the Linear Resonator Rod

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Changes in resonator rod length and spacing from the main element produce clear and significant differences in the impedance performance of the dual-band dipole. If we confine ourselves to practical building dimensions, other structural dimensions that we might vary produce less dramatic effects. Most builders who begin with a tubular structure for a 20-meter dipole would likely choose a smaller diameter for the linear resonator rod in order to hold the total element weight to the minimal practical level. That reasoning underlies the initial choice of a 0.25" diameter resonator rod. However, we might have as easily selected rods or tubes ranging from 1/8" to 1/2". Let's survey the sizes readily available in the U.S.. All the while we shall hold constant the main element length and diameter, and employ the 92" resonator rod spaced 6" from the main element. For our efforts, we obtain the results shown in Table 5.

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Altough the 0.125" rod is a bit difficult to tame, we may obtain essentially the same 15-meter performance with any diameter of resonator rod. In fact, the 15-meter performance--with only small changes in the required capacitance--shows almost identical feedpoint impedances and current phase angles at 21.225 MHz from 0.25" through 0.5", a 2:1 diameter ratio. In addition, the ratio of main element to resonator rod diameter changes considerably over the range of rod diameters. Fig. 10 shows the resulting wide-band SWR curves.

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At the 20-meter end of the scale, we may note some warning signals. Although all of the rod diameters produce acceptable values, increasing the rod diameter does show a downward trend in an already low feedpoint resistance value. With a 6" spacing, raising the diameter of the rod to parity with the main element might press our ability to obtain an acceptable 20-meter SWR curve.

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Varying the Main Element Diameter

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The final dimensional variation that we shall explore is changing the main element diameter. We shall use the 92" long, 0.25" diameter resonator rod that is 6" from the main element. I began this exercise prepared to change the main element length as I changed diameter, but within the narrow limits of practical size changes, the 384" main element length proved to be a constant. Because we are working with tubular elements at 20 meters, the range of practical tubing sizes is limited. I examined only 0.75" and 1.0" diameter tubes for comparison with the original 0.875" size. The results appear in Table 6.

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The table suggests that the wide-band SWR curves will show little difference among them. Fig. 11 confirms our suspicions.

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The changes in main element diameter yield only minuscule changes in the required capacitance and the resultant 15-meter resonator rod current phase. As we increase the element diameter, we find a rising 20-meter feedpoint resistance and a decreasing 15-meter feedpoint resistance. However, both changes are small. In general, a 1.3:1 change in main element diameter produces no performance change that rises above the level of construction and field testing variations that we are likely to encounter if we translate a model into a physical antenna.

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Concluding Thoughts

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These notes have not aimed at producing a buildable design for a dual-band 20-15-mter dipole with a linear resonator. Instead, they have had as their goal an examination of some of the basic properties of such an antenna, along with an exploration of the effects of varying parts of the structure. The numbers are less important than the trends, which an experimenter may use with almost any frequency combination and with any materials. Indeed, the ultimate goal is to make linear-resonator techniques sufficiently familiar to encourage further experimentation and exploration.

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Much remains yet to be done in detail. Linear resonators on wire antennas offer an open region for both modeling and actual building of experimental antennas. Although there are reports of directional antennas using drivers with linear resonators, they are so few and scattered that the backyard builder has few resources for guidance.

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In most instances, linear resonators are the province of the experimenter. Hence, it is wise to do the initial work with scrap or dispensable materials--to account for initial unsuccessful tries. As well, you might consider giving yourself maximum flexibility. For example, compare the standard (modeled) resonator structures at the top left in Fig. 12. The lower sketch shows a more flexible design that allows for fine adjustment by the size of the spacer at the center of the assembly.

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The right side of Fig. 12 shows two practical capacitors. The upper view shows concentric tubes (or a tube and a center rod) with a non-conductive sheathing on the center rod. The system offers maximum capacitance per inch due to the maximizing of facing surfaces. However, the system requires a mounting system for connection to the rod presumed to be at the right. The lower sketch shows paralleled rod lengths, with a non-conductive sheath on one rod. The system offers less capacitance per inch, but may be useful in fine-tuning. As well, the parallel capacitor does not require a physical connection between the capacitor leads and plates, since they are the same. Both systems require a means of securely fixing the final settings and perhaps heat-shrink tubing to protect against weathering effects.

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These are but starter thoughts toward further experimentation that is possible with linear resonators. As well, there is considerable design work yet to be done. For example, one might consider other frequency spreads to see what linear resonators might require for success. Wire antennas require design work relative to both dimensions and fabrication. Future parts of these notes will explore some--but by no means all--of these directions.

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How useful linear resonators may become and how easily we may work around some of their limitations depends upon how much ingenuity we are willing to devote to their development.

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Updated 03-05-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Return to Index

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Topics: Dipole, HF Upper, Loading


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Some Notes on Linear Resonators
+ Part 2: 20-10 and 15-10 Meters

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L. B. Cebik, W4RNL

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In Part 1, we examined the fundamentals of linear resonators and then explored their use for 20 and 15 meters with tubular elements for both the main element and the resonator rod. We varied many of the structural variables for the dipole. A 20-meter independent resonant dipole is about 398" long with common tubing sizes and has a feedpoint impedance of about 72 Ohms. The 20-15 dual-band linear-resonator dipole turned out to have a 384" main element to achieve resonance on 20 meters. The 0.25" linear resonator rod spaced 6" from the main element used a length of about 92" with a 16.4 pF capacitor to achieve resonance on 15 meters. We systematically varied most of the individual structural dimensions, but certainly did not cover all possible combinations.

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The 20-15-meter dipole shows a 20 meter feedpoint resistance of about 35 Ohms, about half the value for the independent dipole. The resonant impedance on 15 meters varied with the selection of rod length and spacing, as well as the capacitance at the rod center. These values are quite general and not immediately suitable for the construction of a linear-resonator dual-band dipole because the study used NEC-4, which shows a small but significant offset in reported values due to the junction of wires having different diameters. However, we were largely interested in the trends that might prove useful to the experimenter. Changing the main element and the resonator rod had only small effects. The main variables turned out to be the rod length and its spacing from the main element. As we increased the rod length, the required capacitance for 15-meter resonance decreased (and the capacitor's reactance increased). As we widened the spacing between the main element and the resonator rod, the required capacitance decreased (and its reactance increased). Although we encountered at least one case in which we could not find a workable combination of resonator rod length and spacing that would provide a usable passband on 15 meters, most of the variations were usable, with only a preference for a 50-Ohm impedance on 15 meters to determine the "best" dimensions. In virtually all cases, the 20-meter impedance remained relatively stable throughout the range of variations.

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We also discovered that the radiation patterns at the two frequencies are not identical. While the lower band provides a typical dipole figure-8 pattern, the upper band shows higher gain with a narrower beamwidth. The change in pattern shape results from the fact that on the upper band, the element is longer than 1/2 wavelength. The use of a linear radiator does not void the pattern changes that occur as center-fed elements exceed 1/2 wavelength.

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As our starting point, we used the combination of 20 and 15 meters, perhaps the most common application of linear-resonator techniques. The 1.5:1 frequency ratio is above the commonly believed 1.4:1 lower limit of linear resonator use. Whether the 1.4:1 limit (based on Moxon's citation of the square root of 2 in one of his notes on the subject) is absolute or not forms one of the questions that remain for us to explore. At the other end of the scale, we should also see what happens to linear resonators when we use a wider frequency ratio--perhaps 2:1.

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In this part of our exploration of linear resonators, we shall look at the wider frequency ratio using the combination of 20 and 10 meters. We shall also press the lower limit by seeing if we can develop a dual-band linear-resonator dipole for 15 and 10 meters. To be consistent with the work in the first part, we shall continue to use tubular elements.

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A 20-10-Meter Dual-Band Linear-Resonator Dipole

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Fig. 1 shows the general model used for the examination of a wider frequency spread. Compared to the earlier models, the new one uses fewer segments in the center section, because it is shorter. The goal is to maintain as closely as possible the same segment length between the end sections and the center section of the main element. We shall continue to use NEC-4 models. In fact, the 20-10-meter antenna showed an average gain test (AGT) score of 0.986 on the lower band and 1.007 on the upper band. Both values are closer to the ideal (1.000) than we found when using the 20-15-meter model.

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The 20-meter or main element uses 0.875" diameter tubing. The resonator rod and its 6" connections to the main element are 0.25" in diameter. The first change to note is that the 20-10-meter combination requires a 1" increase in the length of the main element (from 384" to 385") to achieve resonance on 20 meters. The change is small but not insignificant. Wider frequency separations require longer main elements for a constant lower band.

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The second change involves the radiation patterns. Fig. 2 overlays the free-space E-plane patterns for 20 and 15 meters for one of the models in the total set. In fact, the new dipole parallels the ones used in earlier notes in that the gain on both bands does not change by even 0.1-dB as we vary the important physical dimensions. However, the two patterns depart from one another due to the increased length of the element at 10 meters as a function of what we expect from a 1/2 wavelength dipole. The antenna length at 10 meters is nearly a full wavelength, and the pattern shows further increases in gain and beamwidth narrowing that we expect from antennas nearing that length.

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If you look careful at the overlaid patterns in Fig. 3 of Part 1, you will see that the side null depth on 15 meters is not as great as on 20 meters. The 10-meter pattern continues this trend and shows even shallower side nulls that are only about 20-dB below the maximum gain level. (On the 20-15-meter models, the side null depth at 21.225 MHz was about 25 dB.)

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The resonator rod assembly, including its 6" connecting rods, is an appreciable structure. As such, it adds a small H-plane component to the radiation pattern that accounts for the shallower side nulls at the upper frequency. In the models, all resonator-rod assemblies are "above" the main element relative to the plane of the radiation patterns shown. Had we taken the pattern on a plane through the main element and the resonator rod, we would discover a small directional affect. The pattern would show on the upper band a slight offset with higher gain in the direction of the resonator rod. The 20-15-meter combination shows a 0.5-dB front-to-back ratio on 15 meters. The 20-10-meter combination has a 0.6-dB front-to-back ratio on 10 meters. Remember from our basic discussion of dual-band linear-resonator dipoles that the current on the resonator rod at the upper frequency is very high--higher even than the current on the main element in the same region. Hence, on the upper band, the resonator rod contributes to the radiation pattern shape and strength. In contrast, on the lower band, the resonator-rod current is quite low. In fact, it distorts the expected dipole pattern by well under 0.1 dB and yields side nulls that are greater than 40 dB.

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The third major change between the 20-15-meter and the 20-10-meter dual-band dipoles is the wide-band SWR curve. We shall continue to use a 50-Ohm standard. As shown in Fig. 3, the wider frequency span between the two design frequencies allows the 50-Ohm SWR to climb to very high values before it decreases as we approach the new upper band.

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The graphs both begin at 13 MHz, but they terminate separately. The 20-15-meter curve just about reaches 6:1 as a maximum value between the dips that mark the usable frequencies. In contrast, the 20-10-meter combination exceeds an SWR value of 11:1 between the dips. As we shall see, the peak SWR value does not have a significant affect on the upper band SWR bandwidth.

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However, if we compare the SWR values of both curves near the lower end of the swept passband, we discover the fourth change between the 20-15 and the 20-10 combinations. Fig. 4 expands the graph by sweeping a narrower frequency range with a smaller increment.

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The 20-10 combination shows a lower minimum SWR value that stems from the higher value of the resistive component of the feedpoint impedance on the 20-meter band. The 20-15-meter combination exhibited a resistive impedance value of about 35 Ohms. The 20-10-meter combination has a resistive impedance of about 49 Ohms (consistently for all models in the group). Although this value is over 20 Ohms lower than an independent resonant 20-meter dipole, it does suggest a trend: the wider the frequency spread between the lower and upper frequencies of a linear-resonator dipole, the higher will be the lower-band resistive impedance. We shall have a chance to confirm this trend before we complete this part of our work.

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One consequence of the higher low-band impedance is that we may focus our examination on the upper band (10-meters) as we begin to vary the physical dimensions of the new 20-10-meter combination. We learned from our work with the 20-15-meter combination that the rod diameter and the main element diameter have little effect on the required capacitance for a resonant upper band. Therefore, we shall concentrate on the effects of the rod length and the spacing of the rod from the main element as we examine the 20-10-meter combination.

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Resonator Rod Length

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The 20-10-meter dipole uses a 385" long 0.875" diameter main element. The initial placement of the 0.25" diameter resonator rod is 6" from the main element (measured center-to-center). Within these fixed dimensions, we may use rod length from about 100" to 112" and obtain usable results on 10 meters. Since 10 meters is a very wide HF band, I have let the first MHz of the band (28.0 to 29.0 MHz) serve as the spread for which we shall want to have less than 2:1 50-Ohm SWR. Table 1 shows the modeling results for changes on resonator rod length in 4" increments.

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As expected, the 20-meter (14.175-MHz) impedance values vary only slightly as we change the rod length. Note that the impedance is very close to 50 Ohms due to the wide separation of the two operating ranges. The 10-meter (28.5-MHz) impedance varies more widely across the sampled range of rod lengths. In addition, the range of required resonating capacitance is very small: 4.9 to 6.0 pF. Since the capacitance is very low, a parallel or side-by-side rod arrangement (see Part 1) is likely to allow fine tuning more easily than a concentric capacitor made from a center rod and a surrounding tube.

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The 10-meter resonator rod current phase is about 10 degrees closer to being directly out of phase with the feedpoint current (at 0 degrees phase angle) than we found for the 20-15-meter combination. As well, it varies over a small range, as does the reactance at 10 meters. As a result, we can fairly easily (assuming mastery of capacitor adjustment) arrive at an SWR curve that covers nearly the entire first MHz of 10 meters. Fig. 5 shows the SWR curves between 27.5 and 29.5 MHz to confirm this fact.

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The 104" rod produces perhaps the broadest SWR curve, but only by a narrow margin. Obtaining satisfactory 10-meter operation should be fairly straightforward, since the linear resonator may have a variety of lengths and still function effectively. Only the very low value of required tuning capacitance might hinder implementation of the scheme.

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Resonator-Rod-to-Element Spacing

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Let's select the 104" resonator rod as a prime candidate. As well, we shall retain the 385" long, 0.875" diameter main element, along with the 0.25" diameter resonator rod. With these constant, we may vary the spacing between the rod and the main element in appropriate increments to see what happens to the performance and to the required capacitance for our desired SWR bandwidth. Since 10-meter is a higher frequency than 15 meters, we shall vary the spacing in 1" increments. Table 2 shows the results of these modeling experiments.

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Once more, the 20-meter impedance varies over a very small range as we change the rod spacing. At 10 meters, we obtain a wider impedance range and a wider range of required capacitance values. Likewise, the 10-meter resonator current phase also varies over a wider range.

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Fig. 6 shows the SWR curves for the center (6") spacing and for the extremes within the set (4" and 8"). Very close spacing limits the SWR bandwidth due to the lower resistive impedance (about 35 Ohms). However, as spacing increases, the rate of 10-meter impedance change slows considerably. Although the 6" spacing shows a marginal improvement over 8", both values are very close to the best that we may obtain.

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Once we set up a linear resonator within the proper "ball park," final adjustments--except for the finicky capacitor--are likely to be very easy. The chief initial problem is likely to be estimating what rod length and spacing to use. Although these modeling results are subject to the slightly non-ideal AGT values produced by the NEC-4 models, they may serve to reduce the initial fumbling and frustration in developing a dual-band 20-10-meter linear-resonator dipole--at least of the tubular variety.

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A 15-10-Meter Dual-Band Linear-Resonator Dipole

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One apparently popular belief about linear resonator dipoles is that we may obtain satisfactory operation only if the frequency ratio between the higher and the lower band is greater than 1.4:1. We may put this idea to a simple test by trying to create a linear-resonator dipole for 15 and 10 meters. Here the frequency ratio is only about 1.3:1. Since the lower frequency is a bit higher than in previous combinations, I have reduced the main element diameter to 0.75". At 21.225, a self-resonant dipole with a 0.75" diameter is about 265". For our trials, we shall have to use a slightly short main element: 262". This main-element length reduction is far less than we needed when working with the 20-15-meter combination. The earlier main element shrank by about 3.5%, while the present reduction is just over 1.1%.

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Resonator Rod Length

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Since I have fixed the main element, you may assume that the experimental models were successful in obtaining resonance on both 15 and 10 meters (21.225 and 28.5 MHz). The initial resonator rod for tuning to 10 meters used the same 0.25" diameter material and the same 6" spacing that we have used throughout these trials. The next question then is what length must we use for the resonator--and what value of tuning capacitor? Table 3 shows a range of rod lengths between 42" and 50" and associated capacitor values.

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On 15 meters, the resistive impedance is down to 33-34 Ohms. However, as we lengthen the resonator rod, the resistance goes down and the inductive reactance goes up. Hence, we may expect somewhat less satisfactory 15-meter SWR curves with longer rods. In contrast, lengthening the resonator rod tends to raise the resistive impedance toward 50 Ohms on 10 meters, while reducing the capacitive reactance. As a result, longer rods produce somewhat better 10-meter SWR curves. Fig. 7 shows the contrasting trends in a wide bandwidth SWR curve set.

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Perhaps the 46" rod yields the best compromise between the SWR curves at 15 and 10 meters. Note that the smaller frequency difference between the lower and upper bands also limits the peak SWR between bands to about 3:1. Since the precise SWR limit tends to be less problematical in receivers than with transmitters, the 15-10-meter combination dipole would likely be quite usable for short wave listening between the two amateur bands, as well as somewhat below the 15-meter band.

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Resonator-Rod-to-Element Spacing

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Let's use the 46" long resonator rod and vary its spacing from the main element from 4" to 8" (the same spacing range used for the 20-10-meter combination). We shall discover that the 15-meter impedance varies only slightly across this range, as shown in Table 4.

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The table also shows that rate of impedance change on 10 meters decreases as we increase the spacing of the rod from the main element. This is one of the results that appears to be consistent for all of our models. It suggests that in experimenting with linear resonators, we should not be too anxious to form a very compact element and resonator structure. A little extra spacing may result in easier final adjustments. Fig. 8 shows the SWR curves for the extremes and the middle of the spacing range.

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Once more, we see the conflict that emerged with our rod-length experiments. In this case, close (4") spacing yields a broader 15-meter SWR curve but a less satisfactory 10-meter curve. At the other extreme (8"), we have the best 10-meter curve, but a shallow 15-meter curve. Once more, the best compromise for the other fixed values in the model is the 6" spacing. However, other factors that may enter into the design process may dictate one of the other spacing values.

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The 10-meter current phasing values have fallen back into the -160-Ohm range, roughly comparable to the values that we encountered with the 20-15-meter combination. As well, the require capacitance is between 16 and 19 pF, values that also are closer to those we encountered with the 20-15-meter combination. The higher capacitance should ease the process of adjusting the 15-10-meter linear resonator.

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The smaller frequency ratio between the two operating frequencies also affects the radiation patterns. Fig. 9 overlays the 15- and 10-meter free-space E-plane patterns broadside to the resonator structure. Since at 10-meters the antenna is only a bit long as measured in wavelengths and compared to a standard 1/2 wavelength dipole, its gain and beamwidth do not vary much from the 15-meter pattern. As well, because the resonator structure is smaller, the side nulls are about 25 dB lower in gain than the main lobes. In the plane of the resonator structure and te main element, we find a 0.5-dB front-to-back ratio.

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Our exercise has been successful in developing models of a dual-band linear resonator dipole for a frequency ratio of about 1.3:1. Whether we can tighten the ratio even further is dubious, since the lower-band impedance appears to decrease with a shrinking frequency ratio. Nonetheless, a 15-10-meter tubular combination is certain feasible.

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A Few Comparisons Among All the Modeled Combination Dipoles

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We have explored three different dual-band combination dipoles using linear resonators: a 20-15-meter version, a 20-10-meter combination, and finally a 15-10-meter antenna. All three antennas provide 2-band dipole service with adequate 50-Ohm SWR bandwidths for the selected operating frequencies. The main elements are all tubular, using 0.875" diameter material for basic 20-meter operation and 0.75" diameter material for basic 15-meter service. However, in many respects the three antennas have significant differences. Table 5 shows some of those differences, using mid-range models from each group.

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We might begin with the frequency ratios of each antenna. As the ratio between the upper and lower frequency decreases, so too does the lower-band impedance. Each lower-band dipole would be self-resonant as an independent structure at about 72 Ohms. The impedance drops to less than 34 Ohms with a frequency ratio of 4:3 (1.33:1). Although there is only a small difference between the 20-15 and the 15-10 combinations on each antenna's lower band, it appears that the lower-band impedance will eventually become too low to produce a satisfactory 2:1 or less 50-Ohm SWR across the band.

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As the frequency ratio becomes smaller, we find that the upper band resonator phase angle departs further from 180 degrees. As well, the required tuning capacitance becomes greater. If we treat the linear resonator as a series-tuned circuit, then we might be tempted to determine the reactance of the capacitor as being equal to the reactance of the combined reactances yielded by the two element lengths and the mutual inductance between them. The results would look like the simple calculations in Table 6.

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Although the calculations hold well enough to establish the approximate series-tuned-circuit resonant frequency at the higher frequency, the role of this circuit in the antenna is far from simple. One clue is the departure of the legs from being out of phase with each other. A more important clue lies in the main element ends after we subtract the linear resonator section. Table 7 lists the remaining leg length after removing the linear resonator section of each antenna. On the left for reference are the lengths of resonant independent dipoles.

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One popular notion about linear resonators is that they simply short out the center section of the dipole. If that assumption were true, then the leg ends should show more than a distant correlation to the length of a dipole at the upper frequency. In the 20-15-meter combination, the leg ends are 27" or 10% longer than a 15-meter dipole. Similarly, for the 15-10-meter combination, the leg ends are 19" or just under 10% longer than a 10-meter dipole. The most drastic difference occurs with the 20-10-meter combination where the leg ends are 84" longer than a 10-meter dipole, a 43% difference.

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This exercise in Table 6 only establishes that there is no simplistic relationship between the linear resonator components and the operation of the antenna on the either band. The modeling is insufficient to establish what the more complex relationship is, but it does reflect the free-space E-plane patterns that we viewed along the way. As the frequency ratio increases, the upper-band radiation pattern showed a higher gain and a narrower beamwidth, consistent with a longer effective element length. The pattern results are consistent with the longer element ends that we see for each upper band in the chart.

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At this juncture, perhaps the only safe statement to make is that the linear-resonator structure--including the capacitor--modifies the current distribution along an element to yield a bi-directional pattern and a usable 50-Ohm feedpoint impedance on the upper band of operation. The structure is largely but not wholly inert at the lower frequency, as demonstrated by the required main element shortening relative to an independent lower-band dipole. Even with a 2:1 frequency ratio, the lower band resistance drops to 2/3 the value of an independent self-resonant dipole. With closer frequency ratios, the feedpoint resistance on the lower band drops to less than half the value of an independent dipole. The degree of main element shortening is too small relative to the impedance decrease to treat the center section as an inductive reactance similar to a center-loading coil.

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The role of the tuned circuit then is not merely to establish resonance at the upper frequency, but as well to establish a current distribution on both bands that yields the best approximation of acceptable feedpoint impedances. In Part 1, we showed the relative current magnitudes on each sections of a 20-15-meter linear-resonator dipole. The curves re-appear in Fig. 10.

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The separation of the center main-element currents from the resonator-rod currents without accounting for the phase angle of each on both bands creates a difficulty in visualizing the overall current distribution. Fig. 11 corrects the visualization by providing a single curve for the antenna for each of the two mid-band frequencies.

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We can obtain a set of approximate values for each segment by taking the vector sum of the currents and their phase angles at each corresponding segment within the center section of the antenna. The calculated net values will only be approximate because they do not account for the connecting wire between the main element and the resonator rod. However, they will be close enough to provide smoothed curves, such as those shown in Fig. 11. Table 8 provides a sample of the calculations for the two frequencies. The sample points refer to the numbered segments in Fig. 11. Points 5 and 6 are the first two segments on the common end wire. Point 7 is the end segment to establish the approximate total phase change along the wire. The values for sample 7 in both cases yield total phase changes that closely correlate with a single wire of the same length as the linear-resonator dipole when used at each frequency.

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The calculations and the graphed curves show the typical dipole current distribution on 20 meters. On 15 meters, we have a double peak for the current, with the peaks just beyond sample point 6. The double peak is typical of a center-fed wire antenna that is a little less than 0.7 wavelength long. The current distribution, of course, is fully consistent with the different radiation patterns that we obtain for the two bands.

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Because a dual-band linear resonator dipole is not amenable to simple treatment, it will remain for now in the experimenter's domain. These notes may give some general guidance, but they are far from definitive. One limitation noted along the way is the offset created by NEC-4's variable accuracy with junctions of wires that have different diameters. A second limitation is the fact that materials used by antenna builders may vary across a very wide range of diameters--for both the main element and the resonator rod.

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Indeed, we have so far restricted ourselves to working with relative fat elements. One may only wonder what the results might be had we begun the exercises with thin wire, perhaps the ubiquitous AWG #12 (0.0808" or 2.05-mm diameter). That exploration demands an entirely new modeling effort.

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Updated 03-07-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 3

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Return to Index

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Topics: Dipole, HF Upper, Loading


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Some Notes on Linear Resonators
+ Part 3: Wire Linear-Resonator Dipoles

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L. B. Cebik, W4RNL

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In Part 1 and Part 2, we looked at dual-band linear-resonator dipoles for the upper HF region that used elements having a substantial diameter. 20-meter main elements used 7/8" tubing, while 15-meter main elements used 3/4" tubing. One major consequence of the material selection was our ability to use a fairly wide separation between the main element and the 1/4"-diameter linear-resonator rod. We centered our focus on 6", but explored some narrower and wider spacing values between 4" and 8".

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In this final excursion into the land of linear resonators, we shall reduce the main element diameter to wire size. One consequence of the reduction is that we shall be able to use the same diameter material for both the main element and the linear resonator. Since all wires in the NEC-4 models will have the same diameter, the modeling accuracy, as indicated by the average gain test (AGT) scores, should improve. However, there will be a second consequence for the models (and for any physical implementation of a wire-based linear-resonator dipole). The ability to find acceptable dimensions to achieve a set of resonant points on 2 band with a 50-Ohm SWR of less than 2:1 depends in large measure on the mutual coupling between the parallel wires within the linear-resonator section of the antenna. Since we are wholly dependent on the wires as linear inductors for the mutual coupling, the degree of coupling depends upon the wire diameters and the spacing between them. As we reduce the diameter of the wires, we must bring them closer together to achieve the same level of coupling.

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Suppose that we reduce the wire size by a factor of 7:1. That is, suppose that we reduce the diameter from 7/8" to about 1/8". The required spacing between the wires is roughly proportional to the element diameter. Hence, the spacing between the main element and the linear-resonator rod will decrease from about 6" to the vicinity of 1". As we shall see, the narrow spacing will be quite critical in dual-band dipoles with small ratios between the upper and lower frequencies, but will be less critical with higher frequency ratios.

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To sample both possibilities, let's explore two different wire-based linear-resonator dipoles. The first will cover 20 and 15 meters. The 3:2 frequency ratio falls at the lower end of the scale. As well, the combination allows us to compare the results with the model used in Part 1 of this series. Later, we shall examine a 20-10-meter combination. The larger 2:1 frequency ratio will show us both the advantages and the disadvantages of the alternate design.

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A 20-15-Meter Wire Linear-Resonator Dipole

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The 20-15-meter combination dipole that we explored in Part 1 proved that the linear-resonator technique can be successful if we observe its limitations. The large-diameter (0.875" diameter) model allowed us a wide SWR bandwidth on 15 meters. However, the 20-meter impedance dropped to the vicinity of about 35 Ohms. Obtaining coverage of 20 meters required careful attention to the overall length of the antenna. The 1/4"-diameter linear-resonator rod--spaced 6" from the main element--was a little under 100" long and required a capacitor value of about 16 pF for 15-meter resonance.

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Translating that "fat-element" model to wire size requires that we reduce both the element diameter and the rod-to-element spacing. For reasons that will become evident a little later, I did not start with the usual amateur AWG #12 wire 0.0808" or 2.05 mm diameter). Instead, I used the less common AWG #8 wire (0.1285" or 3.26 mm diameter). As well, I reduce the rod-to-element spacing down to 1". Since the end wires of the resonator section are so short, I had to increase the overall segmentation density of the model to preserve some semblance of segment-length equality. Fig. 1 shows both an overall outline of the model and an expanded view of the linear-resonator section.

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Quite likely, any implementation of a wire-based linear-resonator dipole will require the use of parallel sections of rod to effect the resonating capacitance. The development of a homemade concentric capacitor that is thin enough to avoid touching the main element is difficult at best. For our initial model, all wires are AWG #8. The proximity of the wires does not yield perfect AGT scores. However, the values (0.985-0.988) are significantly improved relative to earlier models that had junctions of wires with different diameters.

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The close spacing between the wires does not affect the general radiation pattern of the dipole. As shown in Fig. 2, the 15-meter performance includes slightly high gain and a slightly narrower beamwidth than we obtain on 20 meters. The free-space patterns show a 0.5-dB difference in gain. In the plane formed by the main element and the resonator rod, the close spacing does make a difference. In this plane, the front-to-back ratio is down to 0.1 dB, a reduction from the 0.5-dB value we obtained from the fatter model. As a consequence, the 15-meter pattern shows deeper side nulls than we obtained using fatter elements: about 25 dB below the level of maximum gain.

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Smaller diameter elements do produce other effects that are noteworthy. For a linear element, a smaller diameter element generally produces an antenna with a narrower SWR bandwidth. We can observe this effect in a general way by looking at a typical wide-band SWR sweep. Fig. 3 shows a 50-Ohm sweep from 13 to 22 MHz to include the bands of interest.

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The peak 50-Ohm SWR value between bands was between 5:1 and 6:1 for the fatter models of Part 1. For our wire versions, the peak value will climb to the 8:1 or higher region. The actual value is not important in operation, but it does provide a caution to experimenters. Finding the precise values for all dimensions, including the capacitor setting, will likely be somewhat more finicky for a wire-base dipole than for a tube-based dipole.

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By the terms of our project, we are looking for dimensions that will produce 50-Ohm coverage on both 20 and 15 meters with less than a 2:1 SWR. (Indeed, if we forget this project specification, we might as well use a simple wire with a parallel feedline and an antenna tuner.) As we did for the fat-element models, we shall freeze some dimensions and vary others to obtain a sense of the trends at work.

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Varying the Resonator Rod Length

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The first set of tests will use AWG #8 wire throughout. A simple dipole for 14.175 MHz would normally require a length of about 403". One feature that we shall look for is the amount of reduction that the use of a linear resonator forces on the overall element length. With the tubular models, we found a usable constant main-element length that was about 14" or 3.5% shorter than a self-resonant 20-meter dipole. Shifting to wire does not change the level of reduction, but it does introduce a new factor into the building equation. Changing the length of the resonator also requires a change in the length of the main element. For every 4" decrease in resonator rod length, we find a 2" increase in the main element length.

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As shown by the data in Table 1, the survey covers rod lengths from 92" to 108". At the same time, the main element changes from 390" to 382". The range of resonating capacitance for the entire spread is about 3 pF--from 18 to 21 pF. The average value is itself about 3-pF higher than the average value needed for the tubular models of Part 1.

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We have already viewed a wide-band SWR sweep for a typical dipole from the group. In fact, that sweep used the version with a 100" rod and a 386" main element. We may therefore confine our examination of 50-Ohm SWR values to the specific operating bands. The impedance values at 14.175 MHz give us an additional reason for taking a close look at the in-band SWR values. As we reduced the element sizes in Part 1, we saw a decrease in the 20-meter resistive impedance. We also wondered at what rate the impedance would continue to decrease as we reduced the element size further. At some diameter, the impedance might slip below 25 Ohms, removing all hope of obtaining 20-meter performance with less than a 2:1 50-Ohm SWR. As the mid-band impedance values show, we are getting close.

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Using AWG #8 wire allows us to obtain a barely usable SWR curve across 20 meters. The shorter the resonator rod (and the longer the main element), the better SWR curve that we obtain. Unlike the tubular elements, the wire elements required that we adjust both the main element and the rod lengths to arrive at this result.

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The corresponding SWR curves for 15 meters appear in Fig. 5. On this band we face a different challenge created by the increasingly narrow-banded performance of thinner elements. Between rod-length increment changes, the mid-band impedance on 15 meters changes more rapidly, and this factor limits our ability to obtain a satisfactory SWR curve.

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The 92" resonator rod that gave us the best 20-meter SWR curve produces the least satisfactory SWR curve on 15 meters--although the performance is usable. As the rod length increases, the SWR curve tends to improve, at least through the 100" length. Further increases in rod length degrade the SWR curve. Nevertheless, all of the 15-meter curves within the set are usable. In general, 15-meter performance is less problematical than 20-meter performance with a wire-based dual-band dipole.

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Varying the Rod-to-Element Spacing

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For further tests, I selected the model that used a 100" rod and a 386" main-element length as perhaps (but not absolutely) the best compromise in performance on both bands. The next test involves seeing what happens as we increase the spacing in small increments from the 1" initial value. (I judged that a smaller spacing is probably not feasible in most practical applications.) In these tests, the wire diameter remains constant (AWG #8). However, all other dimensions of the antenna are allowed to change. Table 2 shows the results of these modeling tests.

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As we increase spacing between the main element and the resonator rod, the required lengths of the main element and of the resonator rod decrease. So too does the required capacitance for the resonator capacitor. (Otherwise expressed, the capacitive reactance increases.) These numbers show the physical demands of increasing the spacing.

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The spacing increase also has consequences for the impedances on each band and the resulting SWR performance. Fig. 6 provides SWR curves for 20 meters.

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The mid-band impedance values for 20 meters suggest that the 50-Ohm SWR curve may grow less satisfactory as we increase the spacing between wires. Fig. 6 confirms the suspicion. Indeed, although the curve for 2" spacing appears barely to meet the standard, it might not be so easy a matter to place that curve precisely when pruning an actual antenna. In general, 20-meter performance depends upon using the narrowest feasible spacing between the resonator and the main element wires.

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The 15-meter 50-Ohm SWR curves in Fig. 7 tell much the same story. As the spacing increases, the SWR curves grow less satisfactory. On 15 meters, the problem is not a decreasing feedpoint impedance. Rather, the problem arises from an increasing resonant impedance. The bottom line for the spacing tests is that a wire-based linear-resonator dipole does not offer the flexibility of fatter elements. Narrow spacing is a requisite on both bands when the frequency ratio is fairly low.

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Varying the Wire Size

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Admittedly, AWG #8 wire is somewhat impractical for end-supported antennas. In copper, its weight is excessive, and in aluminum, the wire junctions become difficult. I selected #8 because it permitted me to find all of the dimensions required in the model for a successful design using a 1" spacing between wires in the assembly. Whether AWG #8 represents a limit for a practical antenna depends on what we find if we vary the wire size. For this test, I held the spacing constant at 1". As well, I held the rod length to a constant 100" length. I used standard AWG wire gauges from #6 through #12, letting the remaining physical dimensions settle at the most optimal values. Table 3 shows the results of this test set.

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The table has a special section noting the most optimal settings for the AWG #6 sample. By increasing the length of the resonator rod 8", we obtain a marginally higher 20-meter impedance. We also obtain a superior 15-meter impedance and a capacitor value that approximates the value used with AWG #8 wire at its optimal resonator rod length. I did not include in the table models for AWG #10 and #12 wire with similar adjustments to the resonator lengths. Each of those models would have required significant resonator-rod shortening to obtain the desired 15-meter results. However, those rod lengths would have produced lower impedances on 20 meters, disallowing the use of the antenna on that band within the project terms of a maximum 2:1 SWR value.

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With the values shown in the table, the 20-meter SWR curves become increasingly marginal as we reduce the wire size, as revealed by Fig. 8. The major problem of trying to optimize the resonator rod lengths with thinner wire is not so much the mid-band impedance. We likely can find a satisfactory impedance with less than a 2:1 50-Ohm SWR. The major difficulty lies at the band edges, where every reduction in resistance provides the reactance with a proportionately higher influence on the SWR level.

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The difficulty does not extend to 15 meters. The SWR curves in Fig. 9 all fall within the highly acceptable range. The curve for AWG #6 wire is for the model using a 100" resonator rod. With a 108" rod, the curve largely overlaps the curve for AWG #8 wire.

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Some Summary Thought for the 20-15-Meter Wire Dipole

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Increasing the diameter of the wires in a linear-resonator dipole with a frequency ratio of 1.5:1 between bands is always advisable. The increased diameter of the elements raises the flexibility of the antenna to accept wider spacing. Although I have not modeled such an antenna, one might consider using wire pairs for the main element and the resonator rod to simulate fatter conductors in a wire structure.

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The essential difficulty faced by anyone experimenting with a wire version of the 20-15-meter dipole is the impedance on 20 meters. As the wire grows thinner, we require narrower spacing between rod and element wires to prevent the 20-meter impedance from dropping below the critical 25-Ohm value. Thinner wires also reduce the capacitance-per-inch of the rod wires that form a capacitor at the center. Finally, the narrow-band nature of thin wires increases the finickiness of adjustments--and their ability to hold during extremes of weather.

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Nevertheless, the intrepid experimenter may wish to see what is possible with wire in a 20-15-meter linear-resonator dipole. To this end, the modeling experiments may serve as a guide. As with all of the modeling experiments, these are not design plans. Rather, they illustrate some of the trends in operation for a linear-resonator dipole with a small frequency ratio.

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A 20-10-Meter Wire Linear-Resonator Dipole

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In Part 2, we examined a fat-element linear-resonator dipole for 20 and 10 meters. Using a 0.875"-diameter 20-meter dipole and a 0.25"-diameter resonator rod, with a spacing of 6", we obtain some results that reversed the difficulties for the antenna. On 20 meters, the antenna showed a near-50-Ohm impedance that easily yielded excellent SWR curves. However, 10-meters proved more problematical, since we barely obtained full-band coverage, even reducing the band to the first MHz.

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When we reduce the elements to wire size, two major questions confront us. First, will the 20-meter operation continue to show near-50-Ohm impedance values? Second, will the narrow-band properties of thinner wires result in reduced 10-meter coverage?

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Interestingly, some of the difficulties that we experienced with the 20-15 combination do not reappear with the 20-10-meter version. For example, as subsequent tables will show, an AWG #8 wire settles in at 392" long for all cases. The presence of the linear resonator section does result in a shorter 20-meter antenna than we find with a simple 20-meter dipole (392" vs. 403"). However, variations in the resonator rod length and the spacing have very little affect on the overall element length, since the second frequency is so far removed from the first. As well, the 20-10 version is an average of about 3" longer than the 20-15 combination.

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Like the 20-15 antenna, the 20-10 dipole requires increased segmentation to handle the 1" spacing between the element and the resonator rod. Fig. 10 shows both the overall structure and an expanded view of the linear resonator area of the model used. The segmentation detail differs slightly from the earlier model, since the 10-meter linear resonator sections are longer than those used to cover 15 meters. Nevertheless, the AGT scores of the antennas for both bands are very similar.

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Just because we have reduced the element diameter and the spacing between wires, we do not lose the radical difference between the patterns for 20 and 10 meters. Fig. 11 shows overlaid free-space E-plane patterns for 14.175 MHz and 28.5 MHz using a typical AWG #8 wire antenna. The 10-meter pattern has a 1.6-dB gain advantage over the 20-meter pattern, with a corresponding reduction in beamwidth.

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Like the 20-15-meter antenna, the reduced spacing between wires yields a much smaller differential in gain in the plane of the resonator on the higher band. The difference is only 0.1 dB. As well, the 10-meter front-to-side ratio is nearly 34 dB, a considerable improvement over the models using fatter elements.

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In concert with the 20-15-meter wire antenna, the 20-10 wire model shows a much higher 50-Ohm SWR peak value between operating frequencies than did the fat-element antenna for the same coverage. Fig. 12 provides a wide-frequency sweep (13-30 MHz) to show the overall performance tendency.

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The peak 50-Ohm SWR value approaches 25:1 in the middle region of the plot, nearly twice as high as the peak value for the antenna with a 7/8"-diameter element. The increased peak 50-Ohm SWR value suggests that the operating bandwidth as defined by a 2:1 SWR maximum value may be reduced relative to either the wire 20-15 model or the fat-element 20-10 model.

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Even though some dimensions of the wire 20-10-meter dipole may remain stable, the data to follow will have the same form as used with the 20-15 antenna. Except for the spacing test, the models will use a 1" uniform spacing between the main element and the resonator rod. I shall allow all other dimensions to settle to their near-optimum values.

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Varying the Resonator Rod Length

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The initial test involves finding the resonator rod length and the corresponding capacitor value that most closely approaches perfection on both bands, as determined by the SWR curves. In fact, I found no significant reason to vary the main element from 392" in the entire set of test runs. The 10-meter resonator rods average about 20" longer than the rods required by the 20-15 wire model. Table 4 shows the results for varying the rod length from 112" up to 124".

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The table shows mid-band impedances for 20 meters that are very close to those found in fat-element models. For the larger frequency ratio in this antenna, we may obtain a nearly ideal impedance at the middle of 20 meters. As the band-specific SWR curve in Fig. 13 reveals, 20-meter SWR is not a significant concern, despite the use of thin elements. The lowest SWR shifts position as we change the length of the resonator rod, but never enough to elevate the SWR to 1.5:1 at the band edges.

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As we change the length of the resonator rod, the required capacitance varies over a narrow range from 5.6 to 6.7 pF. This range is very comparable to the range for the fatter model in Part 2 (4.9-6.0 pF). However, the resonator rod ranges differ: 100"-112" for the earlier model and 112" to 124" for the current wire model. Some of that difference results from the longer main element length of the wire model (392") over the 7/8"-diameter model (385").

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As we suspected, the use of thinner wire elements results in narrower coverage on 10 meters. Fig. 14 shows the 50-Ohm SWR curves for several of the rod lengths sampled.

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All of the curves show just above a 2:1 SWR at 28 MHz. However, only the shorter rod lengths provide coverage as high as 28.7 MHz with a 2:1 SWR. The mid-band impedance values in Table 4 do not themselves reveal the more rapid change of impedance for each small frequency increment, relative to the fat-element models that allowed coverage of a full MHz of the band. One of the limitations of the 20-10 thin-wire model, then, is reduced upper-band coverage.

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Varying the Rod-to-Element Spacing

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In concert with the 20-15-meter wire model, I varied the spacing between the main element and the resonator rod in half-inch increments between 1" and 2". The baseline model used a 120" resonator rod with 1" spacing. I allowed the dimensions to settle at the most desirable values for each spacing increment. Table 5 shows the results of this small experiment.

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In all cases, the main element held its length. The 20-meter mid-band impedance does show a small decline as we increase the spacing. However, the decrease is in no way fatal to the SWR curves, which appear in Fig. 15. In fact, I have not identified the curves individually, since they form too tight a group to distinguish individual lines.

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The data show that as we increase the spacing, we must reduce the length of the resonator rod in order end up with a near-50-Ohm impedance at 28.5 MHz. The required capacitance also goes down with increased spacing (indicating an increase in capacitive reactance). The effects of these changes on the SWR curves for 10 meters appear in Fig. 16.

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The curves do not show any significant difference of bandwidth, although increased spacing does appear to have a small advantage over narrow spacing. However, increased spacing does require a lower capacitance value and may prove harder to adjust to perfection. The displacement of the curve for a 2" space results from my restriction of capacitance increments to 0.1 pF. Linear adjustment of parallel or side-by-side rods used to implement the resonator capacitor might make finer adjustment feasible, but difficult to hold as the weather changes from summer to winter and back gain.

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Due to the ever-lower value of required capacitance, I limited the test range to a maximum spacing of 2". In terms of raw impedance values, we might in theory continue the progression, since the 20-meter impedance changes very slowly and increased spacing may yield wider 10-meter operating bandwidths. At a rate of about 0.4-pF-per-inch of spacing, it is doubtful that the spacing could reasonably approach the 6" value used for the fat-element models.

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Varying the Wire Size

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Despite the narrower coverage of 10 meters, the use of thinner wire may be feasible for frequency ratios in the 2:1 range. The chief obstacle to using thinner wire for the wire 20-15 combination was the reduced 20-meter impedance as the wire grew thinner. The models that we have surveyed so far for 20 and 10 meters suggest that this problem will not occur. Therefore, I surveyed wires sizes from AWG #6 to AWG #12 using the 1" spacing and letting all other values settle to their optimal levels. The results appear in Table 6. We may initially note that by letting each resonator rod settle at its most perfect length, we obtain tuning capacitance values that vary over a very small range.

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All models in the set required no alteration in overall length. With the 392" main element length and resonator rods suited to the 10-meter requirements, the mid-band 20-meter impedance decreases quite slowly as we thin the wire to AWG #12. Fig. 17 shows the resulting 20-meter 50-Ohm SWR curves for AWG #6 and AWG #12 wire. Although these curves are distinguishable, adding the other two wire sizes would have created a fat blurry line. As the curves make clear, the 50-Ohm SWR is always less than 1.5"1 across the 20-meter band with any of the wire sizes.

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The situation differs a bit on 10 meters. Due to the use of a 0.1-pF increment in the tuning capacitance, the SWR curves for 10-meters do not overlay each other as neatly as they do in 20 meters. Hence, the curves in Fig. 18 require a bit of interpretation. Essentially, at the 2:1 SWR crossing points, the AWG #12 curve is only about 93% of the width of the curve for AWG #6 wire, despite the 2:1 ratio of wire diameters. The difference amounts to about 50 kHz (750 kHz vs. 800 kHz--approximately).

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Although the use of AWG #12 wire is not fatal to the construction of a 20-10 combination with 1" element-to-rod spacing, the narrower operating bandwidth will make antenna adjustment more difficult. As well, as we increase the diameter of the element, we also gain some flexibility in selecting the rod-to-element spacing. Nevertheless, for any size element, the most difficult adjustment to master and to make endure through all kinds of weather will be the capacitance.

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Conclusion

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In this final section of our work, we have established that wire-based dual-band linear-resonator dipoles are feasible if we are willing to observe some restrictions. Foremost among the limitations is the need for close spacing of the resonator rod and the main element. Especially for antennas with a lower frequency ratio, such as 1.5:1, the close spacing is necessary to achieve even a usable impedance on the lower band--using 50 Ohms as the standard. Close spacing is not quite as necessary where the frequency ratio is higher, such as 2:1, but wider spacing does reduce the required capacitance to a level at which stability may become a problem.

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The second restriction requires that we use the largest diameter wire feasible. For lower frequency ratios, thin wire may reduce the low-band impedance below the acceptable level. Again, high frequency ratios are less of a problem on the lower band, but thinner wire tends to reduce the upper band operating bandwidth.

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Wire versions of linear-resonator dual-band antennas also suffer from some finickiness of tuning, since virtually no dimension is fixed. Hence, adjustments to the resonator-rod length may affect the overall main element length. This potential difficulty is especially apparent with lower frequency ratios.

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Perhaps the most difficult challenge for linear-resonator antennas using a higher frequency ratio involves the high capacitive reactance and low capacitor value required for precise tuning. Concentric and parallel capacitors formed by the resonator rods and associated materials are subject to linear expansion and contraction as the temperature changes. Replacing a test set-up with a wide-temperature-range fixed capacitor may prove useful in some cases. However, the experimenter must gauge this move against the knowledge that the linear resonator rod itself will change length with frequency.

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As we close our look at linear-resonator dipoles, I should again remind you that all of the numbers fall far short of design plans. Rather, they reliably indicate only the trends in values. In an assembly as tricky as a linear-resonator dipole, field experimentation and adjustment must take precedence over NEC modeling results.

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Nevertheless, linear resonators are a feasible means of producing a double 50-Ohm resonance from essentially a single element. It may be the case that frequency ratios of 1.7:1 or 1.8:1 produce the most desirable results. The low-band impedance would be less marginal and the high-band operating bandwidth would be more adequate and less finicky to establish. As well, the required tuning capacitance would likely fall around 9-10 pF, a value that might be usable in practice. Combinations for 30 and 17 meters or for 20 and 12 meters fall in this range. In both cases, the upper band is quite narrow, so tuning in one season would not yield an unusable SWR 6 months later.

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Whether the linear resonator has applications in multi-element arrays remains in the category of work to be done. The wider we make the frequency ratio, the more that the radiation pattern changes from the lower to the higher frequency. How that change might affect the required dimensions for a multiband array remains to be discovered. For the moment, we may be doing all that we can by digesting the basic properties, potentials, and limitations of linear-resonator dial-band dipoles.

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Updated 03-09-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: Dipole, HF Upper, Loading


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The All-Band Center-Fed Inverted-L

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L. B. Cebik, W4RNL

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+ When I wrote on "The L-Antenna" for 10-meters a few months back, I noted that the antenna was not likely new. I have since learned that the basic idea seems to have originated with VK3AM in the early 1950s and is described in L. A. Moxon's (G6XN) classic HF Antennas for All Locations (pp. 154-156 of the first edition). This antenna is a standing L, although Moxon has no problems with viewing it inverted. Ralph Holland, VK1BRH, includes the L in his computer study of several antennas, including an interesting variant of the L: the 1/2 wl inverted-L. (VK1BRH's interesting modeling studies, published in Amateur Radio, the journal of the Australian Wireless Association, can be found at his web site: http://www2.dynamite.com.au/vk1brh/Antsim.htm) Perhaps the earliest article on the inverted-L as an all-band antenna may have been "The 'Inverted L' Ham Antenna," by Bob See, W5LTD, which appeared in Radio and TV News, January, 1959, pp. 64-65. Bob used base feeding to operate the antenna as a standard inverted-L monopole with a ground plane on 80 and as an end- or voltage-fed longer wire above 80, as his measured impedance figures attest. The 1/2 wl inverted-L can also be center-fed using parallel feedline and an ATU. We shall focus on the center-fed version: it is an antenna with excellent potential as an all-band substitute for the 135' center-fed doublet. +

The 1/2 wl inverted-L which we shall examine differs from standard 1/4 wl inverted-Ls in 2 ways: First, it is longer, of course. Second, it is normally current fed at the center (although end- or voltage-feeding is always possible, even if not always convenient). Hence, it can be viewed as an inverted Vee tilted over by 45 degrees. Alternatively, it can be viewed as a 1-leg-ground-plane 1/4 wl vertical upside down.

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If the upside-down vertical had a second leg going in exactly the opposite direction, the result would be--to a large degree--cancellation of the horizontally polarized radiation. Let's call this antenna the T.

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Both the L and the T differ from the standard 1/4 wl ground plane vertical by being complete antennas--dipoles as it were. Hence, neither requires a ground plane beneath them. For some situations, this fact can simplify construction. The figure below shows the structural differences among the three antennas for models set at 3.7 MHz. The L and T models were set at a top height of 70', with the vertical arm terminated 4.5' off the ground.

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Each antenna was modeled using #14 copper wire and average ground throughout. Note that the inverted-L and the T present challenges to the builder in terms of routing the parallel feedline to the top feedpoint. We shall do some comparisons, but first, let's become a bit more familiar with the inverted-L basic pattern.

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The elevation pattern above shows the vertical, horizontal, and total field components of the inverted-L radiation pattern taken broadside to the horizontal arm of the antenna, where radiation is strongest. In the plane off the ends of the horizontal arm, horizontally polarized radiation is somewhat weaker, but the vertically polarized radiation remains at full strength, with some pattern bending away from the horizontal arm.

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A fair comparison might be made among elevation patterns for the L, T, and vertical. Since the total pattern of the L is a broad oval, let's take the strongest direction also of the T, which happens to be off the ends of the horizontal arms. The vertical is truly omni-directional, so let's set at least 20 radials beneath it.

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The comparative pattern above shows the rough equality of the T and the ground-plane-vertical patterns under the specified conditions. Surprisingly, the inverted-L comes close to both antennas in low angle radiation. It also has stronger high angle radiation--without becoming a cloud burner--which is useful for shorter skip contacts. In other words, the inverted-L has potential as an all-purpose low-band antenna.

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The azimuth patterns of the three antennas--taken at elevation angles between 24 and 28 degrees--show the slight oval of the T and the slightly more radical oval of the inverted-L. The L's azimuth pattern also shows the slight displacement in the direction away from the horizontal arm. However, these effects are small enough not to stand in the way of using the antenna for general operating purposes.

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The Ground-Plane Question

In principle, as a complete 1/2 wl antenna, the inverted-L requires no ground plane. Likewise, the T should require none. In contrast, the 1/4 wl vertical requires a ground plane to complete the antenna. To test the relative need and utility of a ground plane, I modeled all three antennas with ground planes, first using 4 wires and then using 20 wires. I set each ground plane first at 1' below ground, then at the surface, and finally at 1' above ground. The vertical's source segment touches the ground, which gives erroneous results in NEC-4. Therefore, the surface ground plane for the vertical was set 0.1' above ground. The radial wires were the same length as the vertical radiators, which means slightly shorter radials for the vertical than for the L or T. +

The following table summarizes results for the three antennas with 4 and 20 wire ground planes.

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Antenna/GP level    Gain      TO angle       Source Impedance
+                    dBi       degrees        R +/- jX Ohms
+4-radial tests
+Inverted-L
+No GP               1.93      44             66.1 + j 3.8
+GP -1'              1.97      45             66.1 + j 4.5
+GP  0'              1.96      44             66.0 + j 4.0
+GP +1'              2.03      46             65.6 + j 4.5
+T
+No GP               0.56      28             42.7 - j 5.2
+GP -1'              0.61      28             42.7 - j 4.6
+GP  0'              0.60      28             42.7 - j 5.0
+GP +1'              0.58      28             42.3 - j 5.2
+Vertical
+No GP               -0.78     24             48.2 + j 0.2
+GP -1'              -2.38     25             68.5 + j 8.1
+GP  0'              -0.79     25             45.5 + j32.5
+GP +1'              -0.21     24             39.6 - j 9.3
+20-radial tests
+Inverted-L
+No GP               1.93      44             66.1 + j 3.8
+GP -1'              2.11      45             65.4 + j 6.5
+GP  0'              1.99      44             66.3 + j 4.4
+GP +1'              2.10      46             64.5 + j 4.7
+T
+No GP               0.56      28             42.7 - j 5.2
+GP -1'              0.81      28             41.9 - j 3.0
+GP  0'              0.65      29             42.9 - j 4.7
+GP +1'              0.62      28             41.3 - j 5.2
+Vertical
+No GP               -0.78     24             48.2 + j 0.2
+GP -1'              -0.47     25             45.3 - j 0.9
+GP  0'               0.02     24             37.1 - j 3.9
+GP +1'               0.06     24             36.8 - j14.6
+

Although the tables give the most data, comparisons are more difficult than with a graph.

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The antenna gains are compared in the graph above. The line connections between points are not real connections, but only let the eye tell which data points go together. As is evident, NEC-4 modeling strongly suggests that the addition of a ground plane adds virtually nothing to antenna performance for the inverted-L and the T, both of which we have described as complete antennas. In contrast, the vertical is dependent upon the most extensive (up to 60-100 radials) that a builder can install. (The vertical antenna data point for "No Ground Plane" should be used for reference and does not represent accurate data relative to a real antenna.) I further modeled the vertical with 64 radials. At a depth of 1', the antenna gain increased to 0.19 dBi, while setting them 1' above ground yielded a gain of 0.02 dBi. Modeling has consistently suggested that for perfectly symmetrical ground planes above ground, more than 6-8 radials may be superfluous. This conclusion does not necessarily apply to ground planes that are not perfectly symmetrical.

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An alternative to high-altitude center feeding of the inverted-L is to base feed it at the low end of the vertical. Models of this mode of feeding the antenna show patterns quite consistent with those for center feeding, with a source impedance in the neighborhood of 5000 Ohms. Once more, the addition of a ground plane does not aid antenna performance in any way, as the following elevation plot shows.

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However, the absence of need for a ground plane should not be mistaken for an absence of a need for a good RF ground. In turn, we should not presume that the ground rod near the shack, which provides AC and DC power grounding for safety, also provides an adequate RF ground. Army tests established a couple of decades ago that a good RF ground needs periodic short (<2') rods connected by a perimeter wire or strap that essentially surrounds the entire station location.

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Installation Variations

Knowing that not everyone tempted to use the inverted-L will have all of the space needed, I checked some variants that represent typical construction compromises or changes. Since the antenna will be fed with parallel transmission line, matching is not a major problem. However, changes of gain and elevation angle may indicate that some variations are better than others. +

1. Height: elevating the inverted-L is a route to slightly more gain and a lower take-off angle broadside to the horizontal arm. Here is a table of values modeled with top heights at every 5' from 70 to 100 feet up.

+ 
Top Ht.   Bottom Ht.     Gain      TO Angle       Feed Impedance
+feet      feet           dBi       degrees        R +/- jX Ohms
+70         4.5           1.93      44             66.1 + j 3.8
+85         9.5           2.20      42             62.8 - j 4.2
+80        14.5           2.43      41             60.1 - j 9.3
+85        19.5           2.63      38             57.6 - j12.8
+90        24.5           2.83      37             55.3 - j15.4
+95        29.5           3.02      34             53.0 - j17.2
+100       34.5           3.22      33             50.9 - j18.5
+

Nothing drastic happens between any two levels, but the trends are clear. Gain increases and take-off angle decreases. The antenna plays shorter, the higher we go. However, unless one plans to use a monoband coax feed system, the precise dimensions are not at all critical.

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The elevation patterns in the figure compare the antenna at 70' and at 100' and add visual confirmation of the conclusion drawn from the table.

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2. Sloping and Bending: The more normal problem for home installation is too little vertical or horizontal space. As the figure below shows, there are a number of installation "tricks" we might use. The question at hand is how much each will hurt performance.

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Bending the vertical at the bottom: The first way to save vertical space or to protect family members from the high voltage at the antenna element end is to bend the lower end of the vertical to the side. The upper horizontal arm remains 65.5' long. The overall length of the vertical is also 65.5', but part is now vertical and part horizontal. I tested three scenarios, listed in the table below:

+ 
Max. Ht   Vert. Wire     Low Hor.       Gain      TO Angle  Feed Impedance
+feet      feet           feet           dBi       degrees   R +/- jX Ohms
+ 70       60              5.5           2.04      45        64.2 - j 4.4
+ 70       55             10.5           2.22      47        61.8 - j11.3
+ 65       55             10.5           1.92      49        64.8 - j 2.7
+

The chief effect of the bend is to raise the high angle radiation strength a small bit and to raise the elevation angle of maximum radiation. The latter figure indicates a slight loss in the lowest angle radiation, which one would anticipate from shortening the vertical length. None of these small changes in dimension affect the usableness of the antenna.

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Sloping the horizontal arm down: One might wish to use the antenna where there is only one truly tall support and the support for the far end of the horizontal arm is lower. The result is a sloping horizontal arm. Using a peak height of 70' and keeping the dimensions of each wire at 65.5', I tested 2 scenarios, representing two degrees of slope, against the standard installation.

+ 
Max. Vert Ht   Hor. End Ht         Gain      TO Angle  Feed Impedance
+feet           feet                dBi       degrees   R +/- jX Ohms
+ 70            70 (no slope)       1.93      44        66.1 + j 3.8
+ 70            60                  2.26      51        58.6 + j 8.4
+ 70            50                  2.66      58        52.4 + j32.0
+

Gain increases are at high angles of radiation, with some loss of low angle radiation strength. Although a true horizontal is perhaps the best compromise for maximum low and high angle performance, the patterns with a modest slope to the horizontal arm do not make the antenna unusable by any means.

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Bending the horizontal arm far end down: If horizontal space is limited, a common practice is to bend (or dangle) the outer ends of a dipole downward. since the region is the high voltage and low current portion of the antenna, the radiation pattern is least affected by modifying the geometry. Again, I compared 2 scenarios to the full-length horizontal arm configuration.

+ 
Max. Ht   Hor. Arm Lth   Bent Length    Gain      TO Angle  Feed Impedance
+feet      feet           feet           dBi       degrees   R +/- jX Ohms
+ 70       65.5            0.0           1.93      44        66.1 + j 3.8
+ 70       55.5           10.0           1.82      45        62.7 - j 5.9
+ 70       45.5           20.0           1.62      43        54.6 - j12.2
+

Low angle radiation remains essentially constant, since the vertical arm has not been altered. Further shortening of the horizontal arm would show a gradual further reduction in maximum gain and in the take-off angle. Higher-angle radiation is decreased, although the antenna remains eminently usable.

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Like many wire antennas, the inverted-L will tolerate moderate alterations of geometry to fit the space available and still yield good, if not peak, performance.

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Multi-Band Use of the Inverted-L

One disadvantage of the 135' horizontal doublet when used on the upper HF bands is that the pattern breaks into a collection of fairly narrow lobes with deep nulls between them. Since the nulls change position from band- to-band, the user is often surprised to discover that signals from certain directions are weaker than expected. +

The inverted-L, when fed with parallel transmission line and an antenna tuner, is not wholly exempt from this phenomenon. However, since one arm is fully vertical, the nulls tend to be much shallower. At the same time, gain peaks are less pronounced.

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The following table provides a rough guide on what to expect from each of the amateur HF bands:

+ 
Frequency      Gain      To angle  Feed Impedance      Pattern Shape
+ MHz           dBi       degrees   R +/- jX Ohms       (approximate)
+ 3.7           1.93      44          66 + j   4        Broadside oval
+ 7.1           4.09      26        6500 + j 300        Broadside oval
+10.1           4.04      20         150 - j 500        Square
+14.1           5.38      14        2000 + j2300        4 lobes
+18.1           6.99      33         165 - j 255        Square
+21.2           6.74       9         750 + j1400        6 lobes
+24.9           6.63       8         210 - j 520        6 lobes
+28.5           7.55       7         575 + j1000        8 lobes
+

Even harmonics of the antenna's fundamental frequency show high impedances, in some cases with a high reactive component. The WARC bands show more moderate impedances at the antenna feedpoint. Use of 450-Ohm or 600-Ohm parallel feedline is recommended in order to provide reasonable values of impedance at the antenna tuner terminals. As with all such antennas, if a tuner seems unable to effect a match on a given band, adding a short section of feedline between the existing line and the tuner output terminals will often correct the situation.

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The annotation "square" to describe the azimuth pattern is illustrated by the 18.1 MHz pattern. On this band, the strongest signal occurs at the second elevation lobe. There is a usable but less strong lobe at about 16 degrees elevation. Note the absence of sharp nulls and lobes.

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+ +
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Even where lobes and nulls do occur, both are much less pronounced than they are with a standard doublet. The figure shows the differences for the 20-meter band. Doublet nulls exceed -25 dB relative to the lobes, whereas inverted-L nulls are under -10 dB relative to the lobes, which are also broader than those of the doublet. Of course, peak gain of the lobes is about 4 dB less than for the doublet lobes. For some types of operation, but certainly not for all, the absence of strong nulls can be more advantageous than a few extra dB of gain in very specific directions.

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The 100' Center-Fed Inverted-L

Many hams who cannot erect a full 135' long inverted-L can often manage a 100' version of the antenna. This length would require 50' of horizontal run and about 55' of height to place the vertical section at least 5' off the ground. As we have seen, higher installations will yield better results, but the present values will provide a kind of worst-case scenario for modeling that antenna. Since the sketches for this shortened version of the inverted-L, which is about 70% full size at 80 meters, would be the same as those for longer versions, we can jump directly to a table of values for multi-band use of the antenna. Note the cases in which the ratio of reactance to resistance is very high: these conditions tend to increase line losses and to challenge tuners in finding satisfactory and high-efficiency matching settings. + 
Frequency      Gain      To angle  Feed Impedance      Pattern Shape
+ MHz           dBi       degrees   R +/- jX Ohms       (approximate)
+ 3.7           1.32      51          30 + j 425        Broadside oval
+ 7.1           3.13      31         305 + j1010        Broadside oval
+10.1           4.95      24        2150 - j3100        Broadside oval
+14.1           4.64      19         120 - j 185        Square
+18.1           5.51      34         965 + j1785        4-Leaf clover
+21.2           5.00      12         475 - j1300        4-Leaf clover
+24.9           6.07      10         160 + j  95        6 lobes
+28.5           7.03       9        1775 + j1990        6 lobes
As one might expect, the shorter antenna breaks into multiple lobes more slowly with increases in frequency. Moreover, the pattern of high and low feedpoint impedances differs greatly from the pattern for the 135' version. Given the lower top height, the elevation angles of maximum radiation are somewhat higher, especially on the lowest bands of operation. (Note that the band on which an unexpected high angle of maximum radiation occurs for both versions also shows a lobe of nearly the same strength at a lower angle--just about 20 degrees lower. Hence, useful radiation occurs on that band--in this case 17 meters.) Shorter antennas--down to about 90' overall wire length can be built and used on 80 meters. Below about 90' overall wire length, the antenna becomes essentially a 40-meter-and-up inverted-L. +

Conclusion

The center-fed inverted-L has the potential to be a quite satisfactory all-band wire antenna suited to certain environments. The length can be almost anything about 3/8 wl or longer for the lowest frequency of intended operation. Although the overall gain will be lower for each band than the gain of a horizontal doublet using the same overall wire length, the elevation angle of maximum radiation for the L will be lower than for a doublet with the same top height. +

There is little evidence, despite the vertical position of one arm of the antenna, that the inverted-L would benefit from a ground plane beneath the antenna. The actual low-angle gain of the inverted-L will, however, vary with the quality of the soil in the region of reflection at a distance from the vertical arm. All patterns were taken over average soil, and soils that are either poor or better than average will tend to show a higher gain and lower take-off angle, at least on the fundamental frequency.

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The electrical lineage of the center-fed inverted-L is from the dipole by way of the inverted-Vee. For the amateur yard that is short on horizontal space but long on tall supports, the inverted-L may be the antenna of choice as an all-band wire--whether used as the primary station antenna or as the back- up for more complex arrangements.

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Updated 3-6-99, 3-14-99, 6-14-99. © L. B. Cebik, W4RNL. This item first appeared in AntenneX, Feb., 1999, and has been revised to include later data. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Amateur Radio Page

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Topics: HF Multi Band, Inverted L


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Long-Wire Antennas
+ Part 1: Center-Fed and End-Fed Unterminated Long-Wire Antennas

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+

L. B. Cebik, W4RNL

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Among the oldest directional antennas are the ones labeled "long-wire" antennas. Dating to the late 1920s and early 1930s, we still find some of these antennas in active use--not only in amateur circles, but as well in government and military service. Classic names, such as Beverage and Bruce attach to early developments of long-wire antennas. In the group, we include bi-directional antennas such as the long center-fed doublet and end-fed wire, along with more directional arrays such as the terminated long-wire, the terminated V-beam, and the rhombic.

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The theory of long-wire antennas appears early on in most college antenna texts. Once noted, along with the obligatory collection of basic equations that describe some long-wire properties, most authors pass on, never to touch the long-wire group again. Amateurs come upon one or more representatives of the group and wonder what they do and how they do it. Few have access to the seminal articles out of which long-wire technology arose or even to classic books in the field, such as Harper's Rhombic Antenna Design or Walter's Traveling Wave Antennas. Today, some of the terminology surrounding long-wire antennas seems strange. For example, how long is a long-wire antenna? Some folks see a 135' doublet (or even a 135' end-fed wire) and think of it as a long-wire antenna. On 80 meters, where the wire is about 1/2 wavelength, it is not a long-wire. However, on 10 meters, the wire is 4 wavelengths and is entering into the realm of long-wire aerials. There is no definite boundary that marks the entry point to long-wire antennas. However, when we examine the properties of long wires to see what performance properties that we want to derive from them, then we shall quickly learn that "long-wire" means for practical purposes "many wavelengths long."

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The ready availability of a vast literature on long-wire antennas seemingly makes these note superfluous. The end of each episode in this series has a short list of basic references. However, I receive numerous questions about the properties of long-wire, enough to suggest that a review of long-wire technology might be in order. We shall have occasion in these notes to touch upon a few of the equations defining long-wire antennas, but we shall mostly try to develop a more visually intuitive understanding of their basic properties. Antenna modeling software has the ability to provide polar plots of antenna patterns and other important data that will assist us in this process. As well, by the judicious use of the software, we shall discover that some of the more complex equations that define some of the equally complex forms of long-wire antennas will become unnecessary: we can design optimized long-wire arrays wholly within the software.

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Along the way, we, we shall encounter some traditional terms, such as rhombic "tilt angle" and "traveling-wave" antenna. Many college texts are gradually replacing the term "traveling-wave" with "non-resonant" or "terminated." As we shall discover, a terminated antenna is one that ends with a resistance. Since the resistance will dominate the feedpoint impedance, the antenna becomes non-resonant over a fairly wide operating bandwidth. How these two ideas relate to the term "traveling-wave" we shall learn at the proper place along our path.

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Everything begins with the wire antenna, plain and simple. So our journey will start with the center-fed doublet that is familiar in its shorter forms. We shall also look at longer forms of the doublet, as well as at long end-fed wires. Virtually everything in long-wire technology depends on how lobes develop as we increase the length of a wire. Most important will be the direction in which the strongest or main lobes point relative both to the broadside direction (that is, the direction for the lobes of a half wavelength dipole) and to the axis of the wire itself.

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Understanding lobe development is a major part, but only one part of our foundation in understanding long-wire antennas. In Part 2, we shall introduce a second critical element to the creation of long-wire beams, a resistor to terminate the end-fed wire and create a directional long-wire antenna. Along the way, we shall look at a number of interesting questions involving antenna height, wire losses, and ground quality as they bear upon long-wire antennas. These factors introduce both physical antenna issues and modeling issues. Therefore, we shall have to reserve the final steps of our meanderings for the later episodes. There, we shall encounter the V-beam and the rhombic. Both classic arrays have terminated and unterminated forms, as well as a few complexities. The V antennas will occupy the whole of Part 3, while the rhombic will occupy us for Parts 4 and 5.

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Before we can fully appreciate the early work that developed the V-beam and the rhombic, we must begin our trek in more familiar territory. Since--as noted--everything begins with the doublet, that is the place to take the first step.

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The Center-Fed Doublet

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We shall want to examine what happens to a center-fed wire doublet as we change its length in 1 wavelength increments from 1 to 11 wavelengths. We might extend the exercise further, but the rate of change decreases as the antenna becomes longer, and the limit set here is long enough for us to get hold of all of the fundamental ideas. One key to understanding long-wire antennas is to shift our thinking about antenna size. Instead of thinking in physical lengths, such as X meters or Y feet, we shall think wholly in terms of wavelengths. Hence, as we increase the frequency, the physical length of a wave becomes shorter. So a 10 wavelength antenna at 80 meters is physically 8 times longer than a 10 wavelength antenna at 10 meters.

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The Model: If we are to make fair comparisons among antennas--even in modeled form--we must set up some parameters that will remain unchanged from model to model. Obviously, the antenna length from end to end will always be variable in every exercise. For simplicity, I shall use the physical length (measured in wavelengths) rather than the actual electrical length as the increment. The electrical length of a wire antenna is always slightly more than the physical length due to end effects. The actual physical shortening required to obtain an exact electrical length varies somewhat, but many books cite a general value of about 0.95 as the ratio for a simple 1/2 wavelength dipole. If we cut a dipole to be physically 1/2 wavelength, then it will be about 5% long electrically and show inductive reactance at the feedpoint. However, the so-called end-effect occurs for only 1 half wavelength of a long-wire antenna, since it has only 2 ends, no matter what its overall length may be. Therefore, the longer the antenna, the less that the end effect creates a difference between the physical and electrical lengths. At 1 wavelength overall, the 5% dipole difference is only 2.5%. At 10 wavelengths, the differential is only 0.25%. All antenna models will use 20 segments per wavelength.

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All real wire materials have some loss that varies with frequency, but not in a linear manner. Not only does the material loss decrease the maximum gain obtainable, it also has a small affect on the feedpoint impedance. Moreover, it has a further small shortening effect--like the end effect itself, but somewhat smaller in scale. However, material loss shortening of the physical wire acts all along the antenna and not just at the ends. To eliminate this factor, our models will use lossless or perfect wire.

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We need a test environment. I shall place all long-wire models 1 wavelength above average ground (conductivity 0.005 S/m, permittivity 13). In theory, the main elevation lobe of a horizontal antenna is tightly connected to the height of the antenna above ground. Texts on long-wire antennas usually give an equation for selecting the height of a proposed antenna in terms of the desired elevation angle required for a communications link.

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Hwl = 1 / (4 sin a)

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where H is the height in wavelengths and a (usually given as alpha) is the elevation angle. Since a good bit of science now prefers to count angles from the zenith (overhead) downward as a theta angle, a or alpha is simply 90 - theta, and vise versa. We may estimate the elevation angle of our antennas initially by reversing the equation:

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a = arcsin 1 / ( 4 Hwl)

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You may see arcsin written also as sin-1. Theoretically, our 1 wavelength height should produce elevation angles that are consistently 14.48 degrees. We shall set the software to increment patterns in 1-degree intervals. Since the calculated angle is almost directly between increments, we shall be satisfied if the angles appear as either 14 or 15 degrees.

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The effects of ground are not constant for all frequencies. Even for a horizontal wire 1 wavelength above ground, the ground losses change, increasing as we raise the frequency. To sample the degree of change, let's set the wire diameter for all models at the test frequency of 3.5 MHz. We shall use 0.16" diameter wire, approximately AWG #6. If we perfectly scale our antenna for other frequencies, then the wire size changes as well. At 7 MHz, it is 0.08" (AWG #12). At 14 MHz, it is 0.04" (AWG #18). At 28 MHz, the size drops to 0.02" (AWG #24). Next, let's use a 1 wavelength wire at 1 wavelength height and scale it over the set of frequencies to sample the maximum gain values.

+ 
+Maximum Gain Values:  1 WL Wire at 1 WL Above Average Ground
+Frequency     Wire Dia.     Maximum Gain
+MHz           inches        dBi
+3.5           0.16          9.83
+7.0           0.08          9.67
+14.0          0.04          9.54
+28.0          0.02          9.47
+Gain differential 3.5 vs. 28 MHz:  0.36 dBi
+
+

Although the differential is small, it is numerically evident. Hence, we should conduct all modeling tests using as consistent a set of values for all possible aspects of the antenna and modeling environment. Our choice of the ground quality also has an effect upon gain values. Indeed, the effect of changing the ground quality is more pronounced than the effect of changing the test frequency. Let's take our 1 wavelength antenna at its 1 wavelength height and check it using 3 different levels of soil quality.

+ 
+Maximum Gain Values:  1 WL Wire at 1 WL above Various Grounds
+Ground     Conductivity  Relative      Maximum Gain     Maximum Gain
+Label      S/m           Permittivity  dBi @ 3.5 MHz    dBi @ 28.0 MHz
+Very Poor  0.001          5             9.41            9.01
+Average    0.005         13             9.83            9.47
+Very Good  0.0303        20            10.02            9.75
+Gain differential: VP to VG Soil        0.61            0.74
+
+

Although the differentials between very good (VG) soil and very poor (VP) soil are similar, it is clear that ground effects on antenna losses are not completely linear. Nevertheless, the effects do not change enough to invalidate the general trends in center-fed doublet patterns if we select any other HF frequency to replace the 3.5-MHz test frequency for our investigation.

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One way to eliminate the effects of all loss sources is to model all antennas in free space using perfect or lossless wire. These condition allow us to scale an antenna with no change in performance values. Scaling, of course, means proportionately adjusting for frequency or wavelength the length of elements, the spacing between elements in a multi-element array, and the diameter of the elements. However, to make the comparisons among long-wire antennas reasonably realistic, we shall employ a given height (1 wavelength) and a specific ground quality (called "average") and omit only the smallest loss sources, such as wire material and frequency.

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The Center-Fed Doublet and Its Patterns: We are now ready to show the results of setting up long-wire center-fed doublets ranging from 1 wavelength to 11 wavelengths in 1 wavelength increments. For each increment, we shall be very interested in 3 key data items. First is the maximum gain of the strongest lobe or lobes in the doublet radiation pattern. We shall call this value simply the maximum gain. Second, we shall note the elevation angle of maximum gain for the main lobe or lobes, also called the TO or take-off angle. The number should--by theory--always be 14 degrees. Finally, we shall note the azimuth angle of one of the main lobes relative to the antenna wire. If the main lobe is perfectly broadside to the wire, the angle will be 0 degrees. We shall count in a consistent direction away from broadside toward one end of the antenna wire if the main lobe departs from the broadside direction. The larger the number for the azimuth angle, the closer the main lobe comes to aligning with the wire end. A value of 90 degrees will indicate that the main lobe is directly off of and aligned with the antenna wire from end to end. Since our investigation is confined to pattern properties, we shall not list the feedpoint impedance or other data that models might give us. The following table gives us the results of our examination.

+ 
+Center-Fed Doublet Data
+Total Length    Maximum      Elevation     Azimuth Angle of
+WL              Gain dBi     Angle deg     Main Lobe deg
+ 1               9.83          14             0
+ 2               9.36          14            33
+ 3              10.16          14            45
+ 4              10.93          14            52
+ 5              11.47          14            57
+ 6              11.85          14            61
+ 7              12.14          14            63
+ 8              12.43          13            65
+ 9              12.65          13            67
+10              12.82          13            68
+11              13.01          13            70
+
+

The chart shows the growing gain of the main lobes of the center-fed doublet, once the number of lobes reaches 4 (at the 2 wavelength mark). The increased strength of the main lobe is accompanied by a decreasing beamwidth. As well, the angle moves steadily toward the ends of the wire, but never reaches that point. In fact, at 11 wavelengths, the main lobes are still 20 degrees shy of a true end-orientation. Also note that the elevation angle of the strongest lobe drops slightly as the antenna length passes the 7 wavelength point. The angle would show a smoother curve if the increment between sampling points had been smaller than 1 degree. However, the drop is real and may be more dramatic with other types of long-wire antennas.

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What the chart cannot show is the growth in the number of lobes and their relative strengths as we increase the length of the antenna. Fig. 1 provides a gallery of sample elevation and azimuth plots to illustrate the growth of lobes in both directions. You may gauge the shrinking beamwidth from the red line marking the half-power points on the main lobes. The elevation patterns are taken along a line using the azimuth angle in the table. The azimuth patterns are taken at the listed elevation angles.

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+ +
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The pattern selections are closer together for shorter versions of the doublet, since the azimuth angle of the main lobes changes more rapidly. As the antenna grows longer, the rate of azimuth-angle change decreases. However, of considerable note is the total number of lobes in each pattern. For antennas that are very close to integral numbers of wavelengths long, we can express the total number of lobes in a simple equation.

+
+ Ndblt = 2 Lwl +
+

where Ndblt is the number of identifiable lobes and L is the doublet length in wavelengths. Lobes do not suddenly appear, but rather emerge, grow, peak, diminish, and finally disappear. The cycle occurs for every progression from one integral wavelength to the next. At the midpoint between integral lengths, L.5 wavelengths, the number of doublet lobes becomes considerable larger. The antenna pattern shows the growing lobes of the next integral length plus the diminishing lobes of the preceding integral length. So the equation becomes somewhat messier.

+
+ Ndblt = 2 (Lwl + L+1wl) +
+

where L is the preceding integral wavelength value and L+1 is the next integral wavelength value. Since a 2 wavelength doublet has 4 lobes and a 3 wavelength doublet has 6 lobes, a 2.5 wavelength doublet has 10 total lobes. The main lobes are still those furthest from the broadside angle to the wire. The existence of 10 lobes forces the azimuth angle of the main or outer lobes to be further from broadside than for either of the two integral lengths (2 and 3 wavelengths) used in the sample calculation.

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The End-Fed Long-Wire Antenna

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Understanding the pattern evolution of the center-fed doublet gives us a baseline against which to measure succeeding steps in the development of long-wire antennas, and eventually directional long-wire antennas. The doublet patterns were all very symmetrical as a consequence of feeding the antenna at the center. However, most practical long-wire antennas feed the antenna at one end. In terms of models, we may simply move the feedpoint to the last segment. The segmentation remains the same: 20 segments per wavelength. The test frequency remains 3.5 MHz, and the lossless wire is still 0.16" in diameter. The antennas are 1 wavelength above average ground.

+

Therefore, we may proceed directly to the table of results that tells us the maximum gain, the elevation angle, and the azimuth angle of the main lobe(s) of the end-fed wires. Note that we here avoid any use of terms like "end-fed Zepp" and similar informal names for the antenna. They are all end-fed wires. As well, we by-pass any discussion of antenna installation practicalities, such as the imbalance of current magnitudes and phases on the parallel feedline normally used with such antennas.

+

However, we shall expand the table of gathered data by reducing the increment of length between antennas in the list. Instead of proceeding in 1 wavelength increments, we shall step along in 0.5 wavelength intervals.

+ 
+End-Fed Wire Antenna Data
+Total Length    Maximum      Elevation     Azimuth Angle of
+WL              Gain dBi     Angle deg     Main Lobe deg
+ 1               8.44          14            37
+ 1.5             9.45          14            49
+ 2              10.27          13            56
+ 2.5            10.86          13            60
+ 3              11.32          13            63
+ 3.5            11.68          13            65
+ 4              11.99          13            67
+ 4.5            12.26          13            69
+ 5              12.48          13            70
+ 5.5            12.71          12            71
+ 6              12.90          12            72
+ 6.5            13.08          12            73
+ 7              13.24          12            74
+ 7.5            13.38          12            75
+ 8              13.50          12            76
+ 8.5            13.64          11            76
+ 9              13.72          11            77
+ 9.5            13.87          11            77
+10              13.96          11            77
+10.5            14.07          11            78
+11              14.15          11            78
+
+

The end-fed wire antenna begins at 1 wavelength by showing a small gain deficit relative to the center-fed doublet. However, the end-fed wire quickly catches up and shows more gain in the main lobe than the corresponding doublet. In fact, by the 11 wavelength version, the end-fed wire has over a 1.1-dB gain advantage. The added maximum gain accompanies a larger decrease in the elevation angle of maximum radiation as the antenna grows longer. The third column adds further information to digest: the azimuth angles are much larger for any given total end-fed antenna length than for doublets of the same length. In fact, the 1 wavelength version shows an azimuth angle that is greater than zero, suggesting that it has more than 2 lobes. Fig. 2 can go a long way toward clearing up the differences between doublet and end-fed wire patterns when both have the same length.

+
+ +
+

The increased maximum-gain value of the end-fed antenna over the doublet arises from the fact that even with lossless wire, the end-fed azimuth pattern shows a displacement away from the fed end and toward the open end of the antenna. The difference in strength between the strongest lobes away from the feedpoint and those toward the feedpoint is just about twice the value of the improved maximum gain figure. Expressed in other terms, if the 10 wavelength antenna has a 1.1-dB advantage over the doublet in maximum gain, then it also shows about a 2.2-dB front-to-back ratio. The lobes toward the feedpoint will be about 1.1-dB weaker than the corresponding lobes for a doublet. The end-fed wire is already directional, but not to a very significant degree.

+

The more obvious feature of the radiation pattern gallery is the increase in the total number of lobes for each antenna length. In fact, the end-fed wire answers to a quite different equation for calculating the number of lobes:

+
+ Nef = 4 Lwl +
+

where Nef is the total number of identifiable end-fed wire lobes and L is the end-fed wire length in wavelengths. So the 10 wavelength end-fed wire has a total of 40 lobes. To squeeze that many lobes into the same 360-degree pattern requires that each lobe have a smaller beamwidth (that is, be narrower). As well, the main lobes have an angle farther from broadside and closer to the wire end than for a doublet of the same length. In fact, the two main lobes at each end of the antenna wire begin to fuse into a single large lobe with a deep inset. Compare these lobes with the very separate lobes of the doublet.

+

The data that we gather from the end-fed single long-wire unterminated antenna will play an important role in the design of more complex arrays. The data is in many ways height-specific (with additional cautions regarding the soil quality as a possible further modifier of the data). The azimuth angle of the main lobe varies with the antenna height and length. Using an increment of 1 wavelength between antenna lengths, the following table compares data for lossless long-wires 0.5-, 1-, and 2 wavelengths over average ground.

+ 
+Comparative Data:  Unterminated Long-Wire Antennas at 0.5- 1-, and 2-Wavelengths Above Average Ground.
+                Height = 0.5 Wavelength                   Height = 1.0 Wavelength                   Height = 2.0 Wavelength
+Length    Maximum      Elevation     Azimuth        Maximum      Elevation     Azimuth        Maximum      Elevation     Azimuth
+WL        Gain dBi     Angle deg     Angle deg      Gain dBi     Angle deg     Angle deg      Gain dBi     Angle deg     Angle deg
+ 1         7.99        27            40              8.44        14            37              8.75         7            37
+ 2         9.11        25            61             10.27        13            56             10.75         7            54
+ 3         9.85        24            70             11.32        13            63             11.72         7            61
+ 4        10.33        22            74             11.99        13            67             12.62         7            66
+ 5        10.68        21            78             12.48        13            70             13.23         7            68
+ 6        10.95        20            81             12.90        12            72             13.75         7            70
+ 7        11.19        19            83             13.24        12            74             14.22         7            72
+ 8        11.40        18            84             13.50        12            76             14.62         7            73
+ 9        11.60        17            85             13.72        12            77             14.97         7            74
+10        11.79        16            85             13.96        11            77             15.28         6            75
+11        11.97        15            85             14.15        11            78             15.57         6            76
+
+

Fig. 3 compares the maximum gain of the end-fed wire antenna at each height and length. These curves are completely unexceptional, but may be useful as a reference.

+
+ +
+

Although we may be tempted to focus upon the gain data, those numbers may not be the most important for the long-term use of the information. The elevation angle columns tells us that the lower we place a single unterminated long-wire antenna, the faster the elevation angle of maximum radiation decreases as we increase the long-wire antenna length. Fig. 4 converts the numbers in curves. The stair-stepping results from the fact that elevation angles use a 1-degree increment.

+
+ +
+

Still more significant for designing more complex long-wire arrays is the azimuth angle of the strongest lobe relative to the broadside direction (in these models). For any given antenna length, the azimuth angle of the strongest lobes changes with antenna height. Fig. 5 shows the amount of change with height for each sampled antenna length. Once more, the 1-degree radiation pattern increment limits the smoothness of the curves. However, we may clearly see that the lower the antenna height for any given antenna length, the closer that the main lobes approach the axis of the wire and the closer they grow to each other on each side of the wire.

+
+ +
+

The azimuth angle has been a very convenient measure for our initial examination of both center-fed and end-fed long wire antennas. It has shown us by how much the main or strongest lobes of the antenna pattern move from the broadside or zero-degree position as we make the wire longer, as counted in wavelengths. In other applications, for example, the discussion of V and rhombic arrays to come in future parts of this series, we shall view the same angle from a different perspective. We shall be interested in the amount by which the main lobe is displaced from the axis of the wire, defined as a line drawn along and beyond the antenna wire. In literature about long-wire arrays, the off-axis angle is usually designated as "alpha," although we shall use the letter "A" as a designation in these notes. Fig. 6 shows the relationship of the 2 angles.

+
+ +
+

We shall eventually convert the azimuth-angle values to angle-A values with respect to the wire. The relationship is simply this: Angle A = 90 - (Az Ang) degrees. We need not do the aritmetic now. However, these angles and their derivatives will come in handy in later parts of this series.

+

Since most of our experience is with shorter antennas--say about 1/2 wavelength long--we may not fully appreciate the difference between center and end feeding for wires that are the same length. For example, a 1 wavelength doublet has only 2 lobes, while a 1 wavelength end-fed wire has 4 lobes. Both antennas show 2 complete excursions of current magnitude, showing 2 maximum current points at approximately 1/4 and 3/4 wavelength along the wire. The only other significant variable is the phase of the currents in each excursion. Fig. 7 shows us the difference in this parameter.

+
+ +
+

The center-fed doublet graph shows that the currents have the same phase in each half of the overall antenna length. Hence, the radiation pattern has only two lobes with contributions from each half of the total wire length. Not until the antenna reaches a significantly greater length (2 wavelengths is the next step in our pattern development sequence) will each half of the doublet show a current phase reversal. Therefore, we do not find 4 lobes until we reach the 2 wavelength mark. (Of course, a 1.5 wavelength antenna will show 6 lobes as the initial 2 diminish and the next 4 emerge and grow.) With the end-fed wire, the currents in each half of the initial 1 wavelength wire are 180 degrees out of phase relative to each other. Hence, we see 4 lobes at this shorter length.

+

Unlike the center-fed doublet, the end-fed wire shows only a single progression of the number of lobes in the azimuth pattern. Therefore, the single equation for calculating the number of lobes applies not only to wire lengths that are at or near integral wavelengths; as well, it applies to wire lengths at are at or near N.5 wavelengths.

+

Indeed, the way in which lobes appear and grow differs markedly between center-fed and end-fed antennas that are the same length. Fig. 8 provides a glimpse of the process by tracking the lobe structure of the two types of antennas from 2 wavelengths to 3 wavelengths, in 0.25 wavelength increments. I chose this set of lengths so that the lobes are clear and countable--even when they are very small. However, similar graphs are possible between any 2 length markers.

+
+ +
+

At 2.5 wavelengths, the two patterns are almost identical, differing only in the end-fed wire's small front-to-back ratio that results from a slight forward tilt to the pattern. The center-fed antenna shows its new lobes at angles outside the existing set of 4 lobes, and in between any pair of existing lobes. The presence of the new outer-most lobes forces the existing lobes toward a more broadside direction. At 2.25 wavelengths, the old lobes are still the strongest, but show a more broadside angle than when they were alone at 2 wavelengths. Beyond 2.5 wavelengths, the new lobes dominate and the old ones shrink. At 2.75 wavelengths, the old lobes are barely visible. By 3 wavelengths, we find only 6 lobes at their familiar positions. The following table tracks the progression.

+ 
+Lobe Development in Center-Fed and End-Fed Wires Between 2 and 3 wavelengths
+   Antenna              Center-Fed                        End-Fed
+Length          Max. Gain       Main Lobe        Max. Gain       Main Lobe
+WL              dBi             Az. Angle        dBi             Az. Angle
+2.0              9.36           33 deg           10.27           56 deg
+2.25            10.22           28               11.37           59
+2.5             10.33           59               10.86           60
+2.75            10.33           51               10.91           62
+3.0             10.16           45               11.32           63
+
+

In contrast to the center-fed lobe development progression, the end-fed antenna has new lobes that emerge just to the rear of the broadside direction, where we define "rear" with respect to the general direction toward the end-fed wire's feedpoint. The 2.25 wavelength and 2.75 wavelength end-fed antennas are comparable, as each one introduces a new lobe pair. The lobe progression acquires symmetry on each side of the wire (except for the slight differential in the main lobes) only as the antenna approaches a multiple of a half wavelength.

+

We should not neglect the elevation patterns in the gallery shown in Fig. 2. If we compare the number of elevation lobes for the doublet and for the end-fed wire, we find more lobes in each corresponding end-fed wire pattern. This feature of end-fed wire antennas will eventually play a role in our evaluation of terminated end-fed long-wire directional antennas. Just how complex the overall pattern of an end-fed wire may become shows up in the 3-dimensional pattern from a 10 wavelength end-fed wire in Fig. 9. The pattern is limited to a 5-degree increment between pattern readings, so some details are missing. However, reducing the increment to show more detail would convert the line-based sketch into a solid black blob.

+
+ +
+

Two features of the 3-dimensional pattern are especially prominent. First, the upper angles in every direction show a plethora of lobes. A free-space representation of the far-field radiation would show a tunnel with relatively smooth ridge rings for each new lobe, counting back from the tunnel entrance formed by the strongest lobes. However, our radiation pattern takes place over real (or "lossy") ground, disturbing the ring structure as we increase the elevation angle of interest. Many of the upper-angle lobes have significant strength. Second, the forward-most lobes (along the axis labeled Y) have an interesting feature. The lowest and strongest lobe (at 10 degrees in the graphic) shows the deep null along the Y-axis between lobe peaks on either side. However, at 15 degrees elevation, the forward lobe structure displays a far-more-even front, with only a small gain depression along the Y-axis. This feature of end-fed wire patterns will become very prominent when we tackle the terminated end-fed antenna in Part 2.

+

Before we leave the open-ended long-wire antenna, we should briefly note that the ground plays an ever-more profound role in end-fed wire antenna performance as the wire grows longer. Let's compare the 10 wavelength end-fed wire over very good, average, and very poor grounds. In contrast to our original notes, which used a 1 wavelength doublet, we shall now be looking at a very long antenna (856.55 m or 2810' at 3.5 MHz).

+ 
+Maximum Gain Values:  1 WL Wire at 1 WL above Various Grounds
+Ground     Conductivity  Relative      Maximum Gain     Elevation     Azimuth Angle of
+Label      S/m           Permittivity  dBi @ 3.5 MHz    Angle deg     Main Lobe deg
+Very Poor  0.001          5            13.55             10            77
+Average    0.005         13            13.96             11            77
+Very Good  0.0303        20            14.65             12            79
+Gain differential: VP to VG Soil        1.10
+
+

The ground quality not only changes the maximum gain attainable from the antenna, but as well changes the elevation angle of maximum radiation. The better the soil, the higher the TO angle. But even over very good soil, the elevation angle of maximum radiation is significantly lower than the calculated value of 14.5 degrees.

+

Conclusion to Part 1

+

In some respects, we have not gone very far in our exploration of long-wire antennas. We have merely contrasted the behavior of center-fed doublets and end-fed wires from 1 to 11 wavelengths. Along the way, we have examined many of the variables that might alter the performance progressions in the tables. Our goal has been to become familiar with the performance parameters of long unterminated wires. The pattern galleries and tables can serve to remind us of these properties as we proceed further.

+

The end-fed wire, in particular, holds great importance for our future exploration. It is the foundation of all other long-wire arrays. That collection, of course, includes both complex rhombics and the simplest of the directional terminated antennas. Hopefully, from the perspective of developing reasonable expectations from end-fed wires, the foundation in these notes is sufficiently solid to make succeeding steps smoother on the trail of terminated long-wire antennas.

+

A Few Basic References

+

Entire books exist on the subject of terminated directional long-wire antennas, with special attention to the V-beam and the rhombic. However, for a basic introduction to the subject, the following college texts, handbooks, and seminal articles might be useful.

+

Balanis, C. A., Antenna Theory: Design and Analysis, 2nd Ed., pp. 488-505: a college text.

+

Boswell, A. G. P., "Wideband Rhombic Antennas for HF," Proceedings of the 5th International Conference on Antennas and Propagation (ICAP87), April, 1987: a source of wide-band rhombic design information.

+

Bruce E., "Developments in Short-Wave Directive Antennas," Proceedings of the IRE, August, 1931, Volume 19, Number 8: the introduction of the terminated inverted V and diamond (rhombic) antennas.

+

Bruce E., Beck A.C., and Lowry L.R., "Horizontal Rhombic Antennas," Proceedings of the IRE, January, 1935, Volume 23, Number 1: the classic treatment of rhombic design, repeated in many text books.

+

Carter P. S., Hansell C. W., and Lindenblad N. E., "Development of Directive Transmitting Antennas by R.C.A Communications, Inc.," Proceedings of the IRE, October, 1931, Volume 19, Number 10: a fundamental treatment of long-wire V antennas, along with the next entry.

+

Carter P. S., "Circuit Relations in Radiating Systems and Applications to Antenna Problems," Proceedings of the IRE, June, 1932, Volume 20, Number 6: the second of the fundamental analyses behind long-wire V antennas.

+

Foster, Donald, "Radiation from Rhombic Antennas," Proceedings of the IRE, October, 1937, Volume 25, Number 10: a more general treatment of rhombic design, with the introduction of stereographic design aids.

+

Graham, R. C, "Long-Wire Directive Antennas," QST, May, 1937: an excellent summary of long-wire technology to the date of publication.

+

Harper, A. E., Rhombic Antenna Design (1941): a fundamental text on rhombics, based on engineering experience, with tables and nomographs as design aids..

+

Johnson, R. C. (Ed.), Antenna Engineering Handbook, 3rd. Ed., Chapter 11, "Long-Wire Antennas" by Laport: similar but not identical material to the relevant pages of Laport's own volume.

+

Kraus, J. D., Antennas, 2nd Ed., pp. 228-234; 502-509: a college text.

+

Laport, E. A., Radio Antenna Engineering, pp. 55-58, 301-339: a summary of long-wire technology up to the date of publication (1950).

+

Laport, E. A., "Design Data for Horizontal Rhombic Antennas," RCA Review, March, 1952, Volume XIII, Number 1: rhombic design data based on the use of stereographic aids developed by Foster.

+

Laport E. A., and Veldhuis, A. C., "Improved Antennas of the Rhombic Class," RCA Review, March, 1960, Volume XXI, Number 1: the introduction of the off-set dual rhombic.

+

Straw, D. (Ed.), The ARRL Antenna Book, 20th Ed., Chapter 13, "Long-Wire and Traveling-Wave Antennas." See also older versions of the volume, for example, Chapter 5 of the 1949 edition, which gives long-wire technology a more thorough treatment on its own ground, rather than in comparison to modern Yagi technology.

+

Stutzman, W. L., and Thiele, G. A., Antenna Theory and Design, 2nd Ed., pp. 225-231: a college text.

+

Walter, C. H., Traveling Wave Antennas (1965): a classic and very thorough text on traveling-wave fundamentals for all relevant types of antennas.

+
+ +
+

Updated 06-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Return to Index

+

Topics: HF Multi Band, Longwire


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+

Long-Wire Antennas
+ Part 2: Terminated End-Fed Long-Wire Directional Antennas

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In Part 1 of this series, we examined some fundamental properties of both center-fed and end-fed unterminated long-wire antennas. Without the kind of data that our basic investigation showed, the terminated version of the end-fed long-wire antenna might seem more odd than natural. As we move from the symmetry of an unterminated antenna, sometimes called a "standing-wave" antenna, to the asymmetry of the patterns of a terminated wire that is the same length, the assimilation of the nature and growth of both elevation and azimuth lobes will hopefully carry over to naturalize the new patterns and performance values. The mark of success in the process might be that we are able to predict in very general terms "what happens next."

+

The Terminated End-Fed Long-Wire Directional Antenna

+

In both of our unterminated antennas, we find an interesting picture of the current and voltage along the wire. They each form standing waves (following the accounts of Balanis and of Kraus) with peaks every half wavelength and nulls every half wavelength such that the peaks and nulls are 1/4 wavelength apart. The voltage peaks where the current has a null and vice versa. This portrait of voltage and current behavior forms the basis for a large part of basic antenna analysis. It derives in part from treating the antenna as an open transmission line. At the end of any transmission line, an open condition results in the complete reflection of energy toward the source. Traditionally, such antennas have received the label "standing-wave" antennas, and the group includes most of the antennas that we commonly use.

+

In a long-wire antenna, we may add to the end of the wire away from the feedpoint an impedance or termination. If we select the right impedance, then the reverse or reflected energy flow is decreased ideally to zero, as suggested by the top portion of the sketch in Fig. 1. Under these ideal conditions, the fields or waves emerging as a consequence of the uni-directional energy flow result in radiation wholly directed toward the terminated end of the antenna wire. As well, the current at any position along the antenna wire will be the same. These conditions define the idea of a "traveling-wave" antenna.

+
+ +
+

Any implementation of the terminated long-wire antenna consists not only of the wire that is parallel to the ground, but as well to 2 vertical sections. At one end of the antenna, we have a feedpoint, usually taken between the vertical leg and ground. At the other end, we find a vertical line as long as necessary to connect to the terminating impedance. The terminating impedance normally has one end directly connected to ground with the other end connected to the vertical wire. When the height of the antenna is very small relative to a wavelength, the antennas receive the label "Beverage antennas," after the individual who generated them originally. Today, such antennas--which are very long and low to the ground--find use as MF and lower HF receiving antennas. When the antenna is an appreciable distance above ground--as in the case of our wires that are 1 wavelength high--we may simply call it a terminated end-fed long-wire directional antenna.

+

The idealization of our terminated long-wire antenna normally does not account for the vertical wires needed to make both feedpoint and termination connections. (See Balanis and Kraus for different approaches to the analysis of such antennas. We shall by-pass their mathematical accounts, since our goal is to make such antennas more intuitively sensible.) Ideally, we can find a loading impedance that will provide the proper conditions for achieving full traveling-wave status. The calculation is based once more on treating the wire as a transmission line, and the load impedance must equal the characteristic impedance of the line. Balanis provides the following equation to approximate the proper value of the termination.

+
+ RL = 138 log10 (4h/d) +
+

where RL is the value of the impedance load in Ohms, h is the height of the wire, and d is the wire diameter, when both are in the same units. Note that the impedance of the line and hence the approximate load value is independent of frequency and dependent only upon a set of physical measurements that use the same units of measurement. Our wires will be 85.655 meters above ground. The wire diameter is 0.16" or 0.004064 meters. Plugging these numbers into the Balanis equations gives us an approximate load impedance of 680 Ohms. As we shall see, values between 600 and 1000 Ohms are quite usable, although we shall eventually settle on 800 Ohms as a useful value for our initial models.

+

As Kraus notes, a lumped impedance may greatly reduce reflections from the termination, but it cannot provide a non-reflecting termination. In fact, the most common form of termination is a non-inductive resistor (or series/parallel combination of resistors). Under these conditions, some standing waves remain, as shown in the lower portion of the sketch in Fig. 1. The lower rendition of a 10 wavelength terminated long-wire antenna derives from an EZNEC model and uses its facility to generate the pattern of current magnitude along the wires. One consequence of incomplete reflection elimination is to wind up with a feedpoint impedance that is not identical to the load resistance. The feedpoint impedance for the models in this part of the investigation were 600 Ohms or below. However, this impedance value is convenient, since open ladder line commonly comes in a 600-Ohm value, and the match is good (SWR 1.25:1 or less). Hence, the user of such antennas has a wide choice of means at the operating end of the line for effecting a match to the usual 50-Ohm input/output of a transceiver.

+

One common misconception about terminated long-wire antennas is that the reduction or elimination of reflected energy results in half the power being dissipated by the terminating impedance (resistor). In fact, the far end load on the antennas in this exercise dissipates about 25% of the power, as calculated by NEC.

+

Modeling Issues: Modeling the terminated long-wire antenna presents a number of options and challenges, since NEC has some limitations that bear upon the models. Fig. 2 outlines the options available.

+
+ +
+

Option A brings the vertical elements of the antenna down to ground. The source or feedpoint is the first segment above ground of the left wire, while the terminating load appears on the last segment above ground at the far end of the antenna. In the EZNEC Pro/4 implementation of NEC, we have at least 4 ways to model the structure: over perfect ground, with a Sommerfeld-Norton (SN) average ground using NEC-4, with an SN average ground using NEC-2, and with a MININEC ground. Use of a perfect ground provides a reference baseline for checking the sensibleness of other models. However, neither NEC-2 nor NEC-4 recommends bringing a source wire to ground, since at a minimum, the source impedance is likely to be off the mark. The MININEC ground does not provide accurate impedance reports for the ground quality selected, since it is restricted to using the impedance report for perfect ground.

+

Despite the limitations, we can tabulate the results. As a test case, I shall use a 10 wavelength terminated antenna alternately using termination resistors of 600, 800, and 1000 Ohms. For each option, I shall list the maximum gain, the reported 180-degree front-to-back ratio, the elevation angle of maximum radiation, the beamwidth, the source impedance, and the 600-Ohm SWR at the test frequency.

+ 
+Test Performance Values for Modeling Option A
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Perfect Ground
+600             13.98        29.04             26.4          15            439 + j 24      1.37
+800             13.91        26.38             26.2          15            476 + j 43      1.28
+1000            13.87        19.57             26.2          15            504 + j 59      1.23
+2.  Average SN Ground, NEC-4
+600             11.54        11.57             35.2          11            460 + j593      3.01
+800             11.49        12.63             35.2          11            495 + j588      2.85
+1000            11.45        12.87             35.2          11            524 + j587      2.75
+3.  Average SN Ground, NEC-2
+600             10.79        24.23             35.6          11            479 + j 14      1.26
+800             10.74        21.78             35.6          11            509 + j 35      1.19
+1000            10.72        18.11             35.6          11            532 + j 52      1.16
+3.  Average MININEC Ground, NEC-4
+600             11.09        23.58             35.4          11            439 + j 24      1.37
+800             11.01        22.71             35.4          11            476 + j 43      1.28
+1000            10.98        18.55             35.4          11            504 + j 59      1.23
+
+

Using the sequence over perfect ground as a background reference, the NEC-2 results for the SN average ground and the MININEC average ground data appear to coincide fairly well. However, the NEC-4 runs for the SN average ground appear to yield somewhat high gain values with more than anticipated inductive reactance in the source impedance.

+

Option B represents an adaptation of a NEC-2 techniques for modeling vertical antennas with ground-plane radials. The return line between the load resistor and the source is 0.0001 wavelength above ground, about 3 times the diameter of the wire. Hence, the model violates no constraints, but as the following results for both NEC-2 and NEC-4 show, it yields a poor model of the terminated long-wire antenna.

+ 
+Test Performance Values for Modeling Option B
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Average SN Ground, NEC-4
+600              7.68        16.93             35.4          11            1170 - j 97      1.97
+800              7.73        14.44             35.4          11            1182 - j 80      1.98
+1000             7.77        13.36             35.4          11            1192 - j 67      2.00
+2.  Average SN Ground, NEC-2
+600              7.68        16.10             35.4          11            1167 - j 99      1.96
+800              7.72        14.59             35.4          11            1179 - j 82      1.98
+1000             7.76        13.50             35.4          11            1188 - j 69      1.99
+
+

Although NEC-2 and NEC-4 show a very close coincidence of data, the low gain, low front-to-back ratio, and high feedpoint impedance reports combine to suggest that this model is highly inadequate. However, the beamwidth and elevation-angle reports are consistent with the other models. NEC-4 does allow the use of a subterranean return wire, shown in option C in Fig. 2. To test this option, I placed a return wire 0.01 wavelength below ground level, connecting it to the above-ground vertical wires with short segments. Both the source and the load for the antenna remain above ground. Since this option is available only in NEC-4, the test-result table is quite short.

+ 
+Test Performance Values for Modeling Option C
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Average SN Ground, NEC-4
+600             10.38        22.53             35.6          11             526 + j 87      1.23
+800             10.37        19.94             35.6          11             556 + j104      1.22
+1000            10.36        17.10             35.6          11             579 + j118      1.23
+
+

The results are modest, but coincide roughly with the NEC-2 results in Option A. The front-to-back reports are consistent with those for perfect ground. The difficulties with the model include the model size, since the return wire requires as many segments as its above-ground counterpart, and the return wire may actually yield slightly low gain reports by carrying more current than the ground itself. A real installation would not likely use a buried ground wire.

+

Therefore, I tried option D, which replaces the below-ground structure of option C with 2 simple ground rods. Each rod is a 1-segment wire about 0.05 wavelength, which is the length of the segments in the vertical wires above ground. Therefore, the source has equal length segments on each side of the feedpoint segment. 0.05 wavelength is about 4.3 meters or 14'. This length may be longer than the average ground rod, but substituting shorter segments did not change the reports by any significant amount. The results of the test appear in the following table.

+ 
+Test Performance Values for Modeling Option D
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Average SN Ground, NEC-4
+600             10.49        22.94             35.6          11             513 + j 69      1.22
+800             10.47        20.30             35.6          11             544 + j 87      1.20
+1000            10.46        17.29             35.6          11             567 + j102      1.20
+
+

Except for the predicted very slight increase in maximum gain, all of the values correspond very well with those of the buried-return-wire model (C), but with a 45% reduction in model size. For users of NEC-4, it is likely that this style of model is about as adequate as we may get for a terminated long-wire directional antenna. In fact, for users of NEC-2, the basic model (option A) coincides well enough for general guidance. In physical reality, there will be structural variables that will inevitably limit the precision attainable by any model. For example, the models presume a flat wire horizontal to the ground, which is not likely to appear with copper wire and real supports. Even if all supports provide the same height, catenary effects will vary the actual wire height above ground along the antenna pathway.

+

During the model-testing procedures, I explored 2 other directions. One direction led to the variety of soil types over which one might place a terminated long-wire antenna. So I modeled the test series of 10 wavelength antennas over very good and very poor soil to see the effect upon the performance parameters.

+ 
+Test Performance Values for Modeling Option D over Various Soil Qualities
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Very Good SN Ground, NEC-4
+600             11.86        25.20             33.6          12             474 + j 57      1.30
+800             11.81        23.43             33.5          12             508 + j 75      1.24
+1000            11.79        19.00             33.4          12             534 + j 89      1.22
+2.  Average SN Ground, NEC-4
+600             10.49        22.94             35.6          11             513 + j 69      1.22
+800             10.47        20.30             35.6          11             544 + j 87      1.20
+1000            10.46        17.29             35.6          11             567 + j102      1.20
+3.  Very Poor SN Ground, NEC-4
+600              9.21        21.93             33-S          10             630 - j 53      1.10
+800              9.23        17.54             33-S          10             653 - j 30      1.10
+1000             9.25        14.66             33-S          10             671 - j 11      1.12
+
+

As we move from better soils to worse soils, the gain decreases by about 1.3-dB per step. However, note that over very poor soil, the gain trend reverses relative to the value of the terminating resistor. The front-to-back ratio reports also decrease with worsening soil. Each soil quality yields its own consistent beamwidth and elevation angle. The annotations for very poor soil indicate that the null between maximum gain peaks is sufficient to record separate lobes with at least a 3-dB null between. Hence, the beamwidth is an estimate. The resistive portion of the feedpoint impedance shows a non-linear rise with worsening soil quality. Nevertheless, all of the 600-Ohm SWR values fall well within the usable range.

+

The second direction of additional modeling shows the effects of using copper wire instead of perfect wire in the 10 wavelength antenna. Both tests use average SN ground.

+ 
+Test Performance Values for Modeling Option D with Lossless and Copper Wire
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     600-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+1.  Average SN Ground, NEC-4, Lossless Wire
+600             10.49        22.94             35.6          11             513 + j 69      1.22
+800             10.47        20.30             35.6          11             544 + j 87      1.20
+1000            10.46        17.29             35.6          11             567 + j102      1.20
+2.  Average SN Ground, NEC-4, Copper Wire
+600             10.28        23.06             35.5          11             518 + j 70      1.21
+800             10.27        19.70             35.5          11             548 + j 85      1.19
+1000            10.26        17.37             35.5          11             571 + j 97      1.19
+
+

Despite the very long length of the wire, copper losses at the test frequency only lower the gain by about 0.2 dB. All other performance values remain quite constant.

+

The reason that we are taking the trouble to model as adequately as feasible the terminated long-wire directional antenna is the difference that we find between its pattern and the pattern of an unterminated end-fed long-wire antenna. The differences appear in Fig. 3 for 10 wavelength versions of both antennas. Although the terminated directional antenna is laden with sidelobes, the entire pattern provides a good front-to-rear ratio that can enhance communications by reducing rearward interference levels. Indeed, it is possible to use a remotely controlled switch to remove the load and return the antenna to an unterminated state for communications to the rear.

+
+ +
+

When looking over the tabulated results for various ground qualities during the modeling testing procedure, we met with split lobes over very poor soil. In order to see better the progression of the forward-most lobes of the terminated antenna, we can examine Fig. 4. It provides the azimuth patterns over the 3 soil qualities and over perfect ground.

+
+ +
+

The pattern over perfect ground has a single forward lobe, but all of the patterns over real ground show two peaks. As the soil quality decreases, the peaks grow farther apart, with an ever deeper depression in gain between them. Over very poor soil, the depression becomes an identifiable null, exceeding 3-dB relative to the maximum lobe strengths. Hence, the pattern identifies the peaks as separate lobes. The patterns strongly suggest that anyone who proposes to construct a terminated long-wire directional antenna should account in advance for the ground quality beneath and in the vicinity of the antenna. Depending upon the specifications of a given communications operation, the 3-dB null at the center of the 2 peaks over very poor soil might make a difference to antenna planning.

+

The terminated long-wire antenna has a very wide operating range in terms of the feedpoint SWR. The terminating resistor combined with the antenna height largely control the feedpoint impedance. As a specimen test, Fig. 5 provides the 600-Ohm SWR curve for the test antenna using an 800-Ohm terminating impedance. The curve involves no change in the antenna, although the height--in wavelengths--varies from about 0.66 to 1.34 wavelengths above ground. It is clear that the 2:1 frequency range of the test run does not exhaust the usable SWR span for the antenna. However, it does cover one of the more usual amateur applications of a terminated wire, that is, operation from 20 through 10 meters.

+
+ +
+

The End-Fed Terminated Long-Wire Directional Antenna and Its Patterns: To produce a table of results for terminated long-wire antennas of various lengths and an associated gallery of patterns, I settled on an 800-Ohm termination for the models, using option D as the NEC-4 modeling foundation. The horizontal lossless wire is 1 wavelength above average ground. The total length value is the length of the horizontal span of the antenna and does not include the vertical legs. As in the test data, if the main lobe is split into 2 lobes with a distinct null (>3 dB) between them, the beamwidth is an estimate with the letter "S" added to denote the split. TR Loss provides NEC's calculation of the percentage of applied power dissipated in the terminating resistor.

+ 
+End-Fed Terminated Long-Wire Directional Antenna Data
+Total Length    Maximum    Front-Back  Elevation     Beamwidth    Feedpoint Z   600-Ohm    TR Loss
+WL              Gain dBi   Ratio dB *  Angle deg     degrees      R+/-jX Ohms   SWR        %
+ 3               7.11      15.32         14            69-S       537 + j92     1.22       26
+ 4               7.99      16.48         13            59-S       539 + j90     1.21       25
+ 5               8.65      17.91         13            51-S       541 + j89     1.21       24
+ 6               9.15      18.30         12            46-S       543 + j89     1.20       24
+ 7               9.57      19.30         12            43.8       543 + j88     1.20       24
+ 8               9.92      19.51         12            40.2       544 + j88     1.20       23
+ 9              10.20      20.12         12            37.0       544 + j88     1.20       23
+10              10.47      20.30         11            35.6       544 + j87     1.20       23
+11              10.70      20.58         11            33.4       544 + j87     1.20       23
+
+

The most constant data are the values for feedpoint impedance, 600-Ohm SWR, and power dissipated in the terminating resistor. The front-to-back ratio increases with antenna length. However, this value has a flag, since the value is related to the heading of peak gain, which is not the center of the pattern, that is, is not aligned directly with the wire itself. The maximum gain, the beamwidth and the elevation angle of maximum gain decrease with increasing total length.

+

The patterns associated with selected entries in the table appear in Fig. 6. Because the rate of change slows as we reach the upper length values, there are more patterns for the shorter lengths than for the longer. The azimuth patterns reflect both the tabular value entries plus the anticipated growth in the number of total sidelobes. However, because there are 2 1 wavelength vertical legs, the total number of lobes and peaks will be greater than for a corresponding unterminated end-fed long-wire antenna. Do not neglect the elevation patterns. They show a very complex structure that will call for further comment before we conclude.

+
+ +
+

The terminated end-fed long-wire directional antenna is inexpensive and simple, assuming that one has access to the required non-inductive terminating resistor. It has 2 chief properties of merit, neither of which is raw gain. It is quite directional, although fraught with sidelobes. It is also extremely broad-banded in terms of SWR. The termination largely controls the feedpoint impedance. Large frequency excursions, of course, change not only the length of the antenna, but also the height above ground, when we measure both in terms of wavelength. However, a single antenna can cover most of the HF spectrum, if high and long enough at the lowest frequency. With increasing frequency, we obtain a narrower beamwidth and higher gain. Offsetting these variable qualities is the absence of any need for further impedance matching once we transform the average feedpoint impedance of the antenna to the value required by the transmitting and receiving equipment. Hence, the antenna is useful for directional low-angle communications that may require extreme frequency-changing agility.

+

The following table compares the maximum gain for terminated and unterminated end-fed long-wire antennas for lengths from 3 to 11 wavelengths. Note that the unterminated version is essentially bi-directional, although gain is slightly greater away from the feedpoint. As the antennas grow longer, the gain deficit for the directional long-wire antenna grows smaller. However, it is unlikely to become as low as 3 dB until the terminated long-wire antenna reaches wholly impractical lengths.

+ 
+Gain and Elevation Angle Comparison
+                Terminated Long-Wire          Unterminated Long-Wire         Gain
+Total Length    Maximum      Elevation        Maximum        Elevation       Difference
+WL              Gain dBi     Angle deg        Gain dBi       Angle deg       dB
+ 3               7.11        14               11.32          13              4.21
+ 4               7.99        13               11.99          13              4.00
+ 5               8.65        13               12.48          13              3.83
+ 6               9.15        12               12.90          12              3.75
+ 7               9.57        12               13.24          12              3.67
+ 8               9.92        12               13.50          12              3.58
+ 9              10.20        12               13.72          12              3.52
+10              10.47        11               13.96          11              3.49
+11              10.70        11               14.15          11              3.45
+
+

One final property set needs illustration before we close the book on terminated long-wire directional antennas. We have noted the complexity of the lobe structure in both azimuth and elevation patterns. These 2-dimensional slices of the overall radiation pattern of the long-wire antenna do not do full justice to the overall radiation pattern of the antenna. To rectify this gap, at least partially, Fig. 7 provides a 3-dimensional pattern for the 10 wavelength terminated antenna. The pattern is limited to 5-degree increments, lest finer detail turn the entire graphic into a simple opaque black-ink ball. The junction of the X, Y, and Z axes represents the antenna position relative to the pattern. Since the graphic shows a far-field pattern, the antenna itself is infinitesimally small. However, the wire extends along the Y-axis, with the terminating resistor on the +Y end (toward the field's projection of higher gain).

+
+ +
+

The graphic shows us two very significant features that might be lost if we confine ourselves solely to 2-dimensional patterns. First, the overall field is littered with a morass of sidelobes in virtually every direction except downward. This facet of very long-wire antennas concerned early developers of long-wire technology. The sidelobes waste power that deserves re-direction into the main forward lobe(s). As well, the sidelobes create and receive interference. Moreover, they do nothing to secure a point-to-point link, but instead allow reception of possibly sensitive communications to the sides of the antenna.

+

Second, the forward lobe structure contains an interesting oddity. Careful inspection is necessary to perceive the anomaly. At the second-lowest elevation angle (10 degrees in the graphic), we find the split lobe that marks the highest gain that the antenna can attain. At the next level (15 degrees in the graphic), the field has very nearly the same gain across the lower-level split region, but at a slightly lower gain value. Under some propagation conditions, the higher-angle smoother pattern might obscure the presence of the lower-angle split-lobe pattern. The complexity of even the forward-most lobe structure should be an important planning investigation, especially if one contemplates installing a terminated long-wire directional antenna over poor to very poor soil.

+

Bending the Terminated Long-Wire Antenna: There is a technique by which we can remove the split radiation lobe of the terminated long-wire antenna, at least when the wire is many wavelengths long. We may bend it horizontally in the middle. In effect, we create a 2-element long-wire antenna, where each element is half the total horizontal wire length. (In this sample, we shall leave the 1 wavelength vertical wire and the "ground rods" from model D just as they are.) Fig. 8 shows the general layout.

+
+ +
+

One of the forward main lobes from the feedpoint-end section tends to align itself with one of the main forward lobes of the termination-end section, and the two lobes are aligned with the wire termination points. Fig. 8 provides data for the 8 wavelength (or dual-4 wavelength) bent terminated longwire antenna. The required angle relative to the pattern centerline is 24 degrees for maximum gain. This value is a function of the antenna's 1 wavelength height, the average soil quality, and the wire length. Since the total horizontal wire length is 8 wavelengths, the angle creates a maximum antenna width of 1.63 wavelengths, but shortens the overall length to 7.31 wavelengths.

+

The following brief table compares the performance of the straight and bent 8 wavelength antennas. Bending the wire adds about 2.5-dB of overall gain, due to the additive affect of aligned lobes. However, the front-to-back ratio suffers by a like amount. The impedance hardly changes between the 2 antennas. The most notable change of all is the reduction in beamwidth from 40 to 20 degrees.

+ 
+End-Fed Terminated Long-Wire Directional Antenna Data:  Straight and Bent 8-Wavelength Models
+Version            Maximum    Front-Back  Elevation     Beamwidth    Feedpoint Z   600-Ohm
+(800-Ohm TR)       Gain dBi   Ratio dB    Angle deg     degrees      R+/-jX Ohms   SWR
+Straight 8 WL       9.92      19.51         12            40.2       544 + j88     1.20
+Bent 24 deg.       12.39      15.36         13            20.3       531 + j71     1.19
+
+

The difference in beamwidth becomes readily apparent when we examine azimuth patterns for the 2 antennas in the table. Fig. 9 provides the patterns. The bent version has eliminated the null between peaks by creating a single forward main lobe. As well, the bent antenna's patterns shows irregular sidelobe structures that result from off-axis additions and cancellations, relative to the clean lobe structure of the straight antenna. However, most of the bent antenna sidelobes tend to be weaker than those of the straight antenna.

+
+ +
+

The bent terminated long-wire antenna is rarely used today. The straight terminated long-wire beam has lower gain, but it also enjoys 2 advantages: wider beamwidth and the ability to operate over a very wide frequency range at a constant impedance. The bent antenna might match the straight antenna's SWR curve, but the radiation pattern would become unusable beyond perhaps a 2:1 frequency range. The physical wire angle remains constant, but the electrical length of the wire--measured in wavelengths--changes for every change in operating frequency. The angle simply becomes incorrect to produce maximum gain in a single lobe as the operating frequency goes too high or too low. If we wish to obtain the added gain of the bent antenna's aligned main lobes, there are other designs that achieve the goal with more regular sidelobes and, in some cases, weaker sidelobes. In future episodes, we shall encounter some of those designs.

+

Conclusion to Part 2

+

So far, we have explored some of the performance properties of the simplest long-wire antennas, a single very long piece of wire placed horizontally over the ground. The notes have tried to impart a good sense of what happens as we lengthen the wire under 3 different feeding conditions: center feeding, end-feeding, and terminated end-feeding. By the use of extensive tabulated data and patterns from models of the antennas, I hope to have left reasonable expectations for the relative performance of the 3 basic types of long-wire antennas. Along the way, I have explored some of the modeling issues to reveal both my rationale for use the models involved and so that anyone else can recreate or improve them. Bending the wire at the end of the present episode in fact gives us a preview of the techniques that inform more complex long-wire arrays.

+

Still, we have only begun to explore long-wire technology. We have seen some of the shortcomings of the simple straight terminated long-wire directional antenna. The lobes are split. There are many side lobes. The forward gain is low. In an effort to overcome these problems, early designers ingeniously developed the V-beam and the rhombic. I have heard that Bruce would have preferred that his name be attached to the rhombic, for which he was a pioneer, rather than to the planar array that bears his name in many handbooks. In Parts 3 through 5, we shall not try to change the names of antennas, but we shall try to understand better both the long-wire V-beam and the rhombic antenna using some of the same techniques employed in the notes for Parts 1 and 2.

+
+ +
+

Updated 07-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Jun, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

Return to Index

+

Topics: HF Multi Band, Longwire


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+

Long-Wire Antennas
+ Part 3: V Arrays and Beams

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In Parts 1 and 2, we examined the simplest unterminated and terminated long-wire arrays using a single end-fed wire in both cases. Unterminated wires yield essentially bi-directional patterns in line with the wire--more in line as the wire grows longer as measured in wavelengths. There is a small residual front-to-back ratio associated with long-wire end-fed wires, with the stronger lobes toward the open or un-fed end of the wire. Adding a terminating resistor converts the bi-directional wire into a directional beam, although the gain is about 4 dB lower than the strongest lobes of the unterminated wire of the same length. At the end of Part 2, we summarized the shortcomings of the single-wire terminated end-fed wire beam: "The lobes are split. There are many side lobes. The forward gain is low." To overcome some of these problems, early antenna experimenters invented the unterminated V array and the terminated V beam. We shall look at each of these antennas in order, since we have some questions that parallel those connected with the single wire terminated and unterminated antennas. For example, will the terminated V beam show the same gain deficit relative to the unterminated V array as the terminated single-wire did relative to its unterminated version? The V antennas are so intimately related to the single long-wire antennas that before we move onward to rhombics, we shall do a more detailed comparison.

+

V-Array Basics

+

The V array derives directly from the single long-wire antenna. In fact, a V array is nothing more than two single long-wires connected at a feedpoint junction and fed in series. The V array makes use of one of the problems for a single wire: the two main lobes do not come completely together to form a single lobe. The V array turns the problem into an advantage. If we angle each leg of the V in just the right way, we can get two of the lobes--one from each leg--to point in the same direction and let their gain levels add. Fig. 1 shows the outline of how we obtain a true bi-directional unterminated array from 2 long-wire antennas.

+
+ +
+

On the left is a representation of a single long-wire antenna (bold solid line) and the headings of its main or strongest lobes (dotted line). Note that we use the wire center as a conventional origin of the lobe indicators. Since the dotted lines represent a far field pattern, the antenna (in relation to the pattern) would have an infinitesimal size. When thinking about the pattern, mentally shrink the antenna until it almost disappears.

+

In Parts 1 and 2, we represented the angle taken by the individual lobes as an angle relative to the tangent to the wire, that is, relative to a broadside direction. In this episode, we are interested in angle A (usally shown as an alpha in texts). The old angular value and A add up to 90 degrees, so conversion is easy.

+

If we now use 2 wires to form a V, we can set each one at angle A relative to the centerline of the V. So the total angle between wires is 2A. By aligning the wires in this way, a main lobe from each wire at each end will fall into alignment and add up to a new higher gain level. As well, there will be only 1 main lobe in each direction in line with the wire. The remnant lobes become sidelobes of the array. Note that this strategy is in principle similar to the strategy of bending a long single wire in the middle to obtain lobes that add rather than going in different directions. Indeed, the required angle for each type of design is almost the same: angle A. Indeed, for the same quantity of horizontal wire, a directional V beam and a terminated bent single wire have about the same gain. The difference is largely one of halving the total overall length (and the acreage required beneath the antenna) for a doubling of the smaller required width.

+

We are fortunate, since we can refer to Part 1 and find the heading of the main azimuth lobes for each test length of long wire antenna. The following table lists those headings as well as the resultant value of angle A. The table also shows several other values. The next column lists a calculated value for angle A that we shall explain following the table. The final columns show the angles associated with corresponding long-wire terminated beams. These values will not play a role in our work. They only illustrate the fact that forming a terminated beam from the long-wire antenna does compress the angle between the maximum gain points on the beam forward pattern, in part due to the presence of the vertical wires necessary to complete a practical installation.

+ 
+Long-Wire Azimuth angles of Maximum Radiation and Corresponding A-Angles
+                   Unterminated Long-Wire                    Terminated Long-Wire
+Antenna     Azimuth Angle  Angle A   Calculated Angle      Azimuth Angle   Angle A
+Length WL   degrees        degrees   A degrees             degrees         degrees
+ 2          56             34        35.4                  -----           -----
+ 3          63             27        27.6                  66              24
+ 4          67             23        23.0                  70              20
+ 5          70             20        19.8                  72              18
+ 6          72             18        17.6                  74              16
+ 7          74             16        15.8                  75              15
+ 8          76             14        14.4                  77              13
+ 9          77             13        13.2                  78              12
+10          77             13        12.2                  78              12
+11          78             12        11.3                  79              11
+
+

If we did not have access to NEC-calculated values for the azimuth angles for the strongest long-wire lobes, we could have resorted to an approximation equation for calculating the value of angle A.

+
+ Angle A = arccos [(N-0.5) / N] - 6 +
+

Angle A is in degrees, while N is the length of the long-wire legs in wavelengths. I adapted and adjusted this equation from one found in Balanis' account of long-wire antennas. Within the confines of the lengths used for our test NEC-model cases, the equation is quite adequate for forming models of V arrays. More complex angle calculation devices exist, but they turn out to be almost spuriously precise. The gain of a V array changes very little using angle-A values that are plus or minus a full degree from the listed values. The tolerances become considerably tighter, however, if we increase the leg length well beyond the limits of the table. Hence, NEC models may be the best way to indirectly obtain the requisite values for angle A. (For much longer antennas, it may be useful to increase the resolution of the azimuth patterns from which we indirectly derive angle A. NEC is fully capable of handling 0.1-degree increments between pattern samples. In such cases, the headings for the strongest lobe will also resolve to a tenth of a degree.)

+

Note: The models in this part of our work make use of angle A as derived from our modeling of single long-wire antennas. They do not necessarily optimize that angle for maximum gain. There is a slight difference.

+

For basic model testing, I chose the 10 wavelength V array using 13 degrees as the value of angle A. Relative to the array centerline, shown in Fig. 1, the array is 9.75 wavelengths long and 4.5 wavelengths wide at the open end. Like the antennas in Parts 1 and 2, this one also uses perfect or lossless wire at 20 segments per wavelength. The main tests will place the antenna 1 wavelength above average ground (conductivity 0.005 S/m, permittivity 13). However, for initial tests on the 10 wavelength model, I placed it over very good, average, and very poor soil in order to see what differences ground quality might make to performance. The following table emerged from those tests.

+ 
+10-Wavelength Unterminated V Array 1-Wavelength Above the Indicated Soil Type
+Angle A = 13 degrees; Elevation angle = 10 degrees
+Soil Type    Gain    Front-Back     Beamwidth
+             dBi     Ratio dB       degrees
+Very Good    17.21    2.55           11.0
+Average      17.24    2.47           10.2
+Very Poor    17.17    2.37            9.8
+
+

Unlike other antennas that we have surveyed in this collection of notes, the V array showed almost no change in its pattern, despite the wide range of soil qualities. The conductivity of the soils ran from 0.0303 S/m for very good ground down to 0.001 S/m for very poor ground. The relative permittivity range from very good to very poor was 20 down to 5. Fig. 2 overlays the azimuth patterns for the 3 models. Except for a few distinguishable differences in nulls, the patterns almost perfectly coincide with each other. In the realm of bi-directional unterminated long-wire antennas, the V array may prove to be a good selection for use over relatively poor soils.

+
+ +
+

In the initial tests, I also tried the 10 wavelength V array using copper wire over average ground to obtain a sense of what wire losses might be. As in past models, the wire diameter is 0.16" (AWG #6) to allow scaling of the 3.5 MHz test models to other frequencies in the amateur HF range.

+ 
+10-Wavelength Unterminated V Array 1-Wavelength Above Average Soil
+Angle A = 13 degrees; Elevation angle = 10 degrees
+Wire Type    Gain    Front-Back     Beamwidth
+             dBi     Ratio dB       degrees
+Lossless     17.24    2.47           10.2
+Copper       16.73    2.68           10.2
+
+

As the simple comparison shows, we lose about 0.5-dB relative to maximum gain by using copper wire. I would view such losses as insignificant, especially since we have no way to recover them without a 20 wavelength supply of super-conducting wire.

+

In order to compare the performance of a single unterminated wire to that of a V array, I constructed models of the V array using legs that ran from 2 to 11 wavelengths. The following table lists the value of angle A, the elevation angle for maximum gain, the maximum gain value, the remnant front-to-back ratio, and the beamwidth of the strongest main lobe. In addition, for easy reference, the table also lists the maximum gain of the corresponding single unterminated long-wire antenna and the gain differential between it and the V array.

+ 
+Performance of V Arrays 1-Wavelength Above Average Ground                 Single Long-Wire
+Leg Length   Angle A   Elevation  Max. Gain   Front-Back   Beamwidth      Max. Gain       Difference
+WL           degrees   Angle deg  dBi         Ratio dB     degrees        dBi             dB
+ 2           34        13         13.60       1.37         20.2           10.27           3.33
+ 3           26        13         14.65       1.84         17.2           11.32           3.33
+ 4           23        12         15.48       1.88         14.4           11.99           3.49
+ 5           20        12         15.97       2.05         13.2           12.48           3.49
+ 6           18        12         16.25       2.27         12.2           12.90           3.35
+ 7           16        11         16.56       2.36         11.8           13.24           3.32
+ 8           14        11         16.75       2.44         11.8           13.50           3.25
+ 9           13        11         16.99       2.44         11.4           13.72           3.27
+10           13        10         17.24       2.47         10.2           13.96           3.28
+11           12        10         17.35       2.56         10.2           14.15           3.20
+
+

The tabulated data shows the usual progression of increasing gain and decreasing beamwidth as we lengthen the legs of the antenna. As well, length-for-length, the V array shows a maximum gain that is somewhat over 3-dB greater than the gain of a single long-wire antenna having the same length. (One might well dispute the length equivalence, arguing that the centerline of the V array is always shorter than the centerline of the corresponding single long-wire antenna. However, with 10 wavelength legs, the centerline difference is only about 1/4 wavelength due to the gradual narrowing of the angle (2A) between the wires.)

+

Perhaps the most intriguing set of numbers falls in the beamwidth column. For leg lengths beyond about 3 wavelengths, the antenna requires careful alignment for the main lobe (or lobes) to hit a communications target. In fact, V arrays (and beams) found their main use as antennas having communications targets falling within a small radius. One technique used to steer the antenna's main lobe was to set multiple Vs in a physically serial arrangement that did not necessarily form a straight line Thus, one antenna could bend the beam of the first. We should also remember that high quality copper wire in the late 1920s and through the 1930s was not as cheap as it is today, when measured against other prices. Many amateurs used less expensive phosphor-bronze wire for antennas, and government and commercial wire antenna installations were major investments. Although we today may doubt the precision that one might achieve by attaching wire to wooden telephone and telegraph poles, the engineering calculations were as precise a available techniques permitted. (Laport's Radio Antenna Engineering from 1952 has an interesting gallery of photos of mainly RCA antenna installation going back as far as the 1930s. Wooden poles--some spliced to increase their height--outnumber metal masts and towers. We may also find it interesting that many installers working with hand tools wore neckties and fedora hats on the job.)

+

The V array is not an antenna for broad coverage of the horizon. Its wire foundation makes it immovable, and the gain comes at the expense of beamwidth. Hence, its best use is as a point-to-point antenna, where the reliability of a single communications link is more important than communications with many diverse places on the horizon. The gallery of sample elevation and azimuth patterns in Fig. 3 will reinforce this judgment.

+
+ +
+

Compared to the single long-wire antenna, the V array shows significantly smaller elevation lobes above the main lobes. The azimuth sidelobes, while still pronounced in the off-heading forward areas, are generally smaller than those of a single unterminated wire antenna. Many of the sidelobes from each leg tend to counter corresponding sidelobes from other legs, in part due to having different headings and in part due to the spacing between the legs. The azimuth pattern for the 4 wavelength model shows perhaps the tightest wasp-waisted pattern. In contrast, the elevation upper lobes tend to decrease in strength in more direct proportion to the length of the legs. However, due to the interaction of the lobes from each leg and the changing included angle from one model to the next, we cannot characterize the patterns by reference to the number of lobes, as we did with the single long-wire end-fed antenna.

+
+ +
+

The 3-dimensional radiation pattern shown in Fig. 4 has a peculiarly crystalline appearance, given the 5-degree increment between sampling points. Nevertheless, the main lobe extremities show well. Still, one might best refer to the 2-dimensional plots before attempting to characterize the upper-angle lobes. Although there are still many lobes--as there will be for virtually any long-wire antenna--their strength relative to the main lobes is considerably weaker than is the case for a single wire.

+

There is no rule that we must always optimize a V array for maximum gain. At certain values for angle A, the beamwidth will widen. Of course, the new value for A varies with the length of the legs. As well, a widening of a few degrees will actually narrow the beamwidth. However, by judicious modeling or experimentation, one can find a usable beamwidth before the pattern degenerates into peaks with a very deep null between them. For example, with 5 wavelength legs, the peak-gain angle is 20 degrees (or 40 degrees between wires). The beamwidth is 13.2 degrees. By widening angle A to 29 degrees (58 degrees between wires), the effective beamwidth becomes about 35 degrees. With a pre-planned selection of centerline headings, it is possible to cover much of the horizon in a switched set of V arrays in which each interior leg serves 2 arrays. Fig. 5 shows the general scheme and a sample azimuth pattern. For some installations, similar schemes can be tailored to the operating site and communication needs. The 13.4-dBi gain of each V-pair still out-performs individual 5 wavelength wires.

+
+ +
+

The potentials for V arrays are larger than suggested by this introduction to them. However, it is time to terminate this initial discussion and the V array itself.

+

V-Beam Basics

+

The terminated V array forms a V-beam, that is, a directional terminated V array. The technique seems simple enough. We simply place a non-inductive terminating resistor at the end of each leg. However, the resistor cannot simply float at the terminating end of the wire. One option is to bring the terminated end of the leg wire to ground. Alternatively, we may run a wire between the two terminated wires end and place the non-inductive resistor at the center.

+
+ +
+

Fig. 6 shows 4 classic implementations of the terminated V-beam. Model A places the feedpoint close to ground and slopes the legs upward to their normal (1 wavelength) height. (The opposite slope for the array is also possible. See model A1.) The terminated ends run vertically to the ground, with the terminating resistors at ground level. The model will use the same ground-rod technique used in constructing models of single terminated long-wire directional antennas. However, none of the models will use a vertical wire at the feedpoint end. The single long-wire beams could use the vertical feedpoint end with the actual feedpoint close to ground. If we apply that same technique to the V-beam, we end up with the 2 legs in parallel, which does not yield much gain or directivity. The source-ends of the legs must have the feedline across them in a series connection to yield the correct addition of peak lobes from each leg.

+

Selecting the correct values of the 2 terminating resistors is not so simple as it was with the single long-wire beam. As the following trial table shows, the value is not exceptionally critical, although we may have reasons for choosing one value over another. For design purposes, the reasons may involve the best compromise among gain, front-to-back ratio, and impedance. In practical installations, the reasons generally focus on what non-inductive resistors may be available. The test table (and others to follow) uses NEC-4 models with 5 wavelength legs 1-wavelegnth above an average SN ground.

+ 
+Test Performance Values for Modeling Option A
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     1000-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+
+600 x2           8.89        23.15             12.2          15             988 + j184      1.20
+700 x2           8.91        22.40             12.4          15            1043 + j145      1.16
+800 x2           8.93        20.58             12.4          15            1091 + j109      1.14
+
+

The sloping version of the terminated V-beam shows a serious gain deficit relative to level models (options B, C, and D in Fig. 6). Gain is 4- to 5-dB lower than for the other versions. Therefore, we should test further V-beam designs. NEC calculates that each terminating resistor dissipates about 21% of the applied power, using the 700-Ohm resistor in each leg.

+

If we slope the V-beam in the other direction, with the feedpoint high and the terminations low, we do not see much change in the performance, except for a reduction in the front-to-back ratio and a reduction in the terminating resistor. Let's call the reverse slope model A1.

+ 
+Test Performance Values for Modeling Option A1
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     1000-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+
+400 x2           8.60        18.90             21.0          14            1032 + j107      1.12
+500 x2           8.60        18.06             21.2          14            1096 - j  6      1.10
+600 x2           8.63        15.99             21.2          14            1141 - j109      1.18
+
+

The theory behind the reverse slope is an attempt to lower the elevation angle of maximum radiation. However, the result is an antenna that is on average much lower than a model that is level at 1 wavelength. Hence, the net elevation angle, while 1 degree lower than for version A is still higher by 2 degrees than the other models (B, C, and D) in this sequence. The model A gain deficit still remains, with a gain level that is barely 1 dB higher than a 1/2 wavelength dipole at 1 wavelength above average ground.

+

Model B uses the same layout as Model A, but raises the feedpoint to the same height as the remainder of the antenna. Like Model A, B uses a pair of terminating resistors. The gain and elevation angle of maximum gain return to normal values, as shown in the following test table.

+ 
+Test Performance Values for Modeling Option B
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     800-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+
+600 x2          13.00        20.62             13.8          12             830 + j133      1.18
+800 x2          13.02        18.41             13.8          12             926 + j190      1.30
+1000 x2         13.07        16.00             13.8          12            1002 + j242      1.42
+
+

The gain level of this model changes very slowly with changes in the values of the terminating resistors. Hence, the table proceeds in 200-Ohm increments. Selecting the most optimal combination requires some decision-making based on criteria. In the absence of practical operating goals, I chose the 600-Ohm resistors, since they yielded the highest front-to-back ratio in the group, along with having the lowest order of feedpoint reactance. The 600-Ohm resistors dissipate about 22% of the applied power--each.

+

Model C uses the same feedpoint treatment as model B. However, instead of bringing 2 vertical wires to ground, with 2 attached resistors, model C uses a straight connecting wire between the far ends of each leg. For the 5 wavelength legs of the test model, the crossing wire is about 3.4 wavelengths. At the center of the wire, we place a single non-inductive resistor. As the following table will show, the connecting wire is not inert, but an active part of the overall antenna.

+ 
+Test Performance Values for Modeling Option C
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     900-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+
+800             14.38        12.73             12.6          12             981 + j192      1.25
+900             14.35        13.76             12.6          12             949 + j147      1.18
+1000            14.34        14.73             12.6          12             919 + j110      1.13
+
+

The crossing horizontal wire between the V-leg ends contributes to the array gain in both directions. Hence, the peak forward gain is slightly higher than for model B, but the front-to-back ratio is much lower. If we select the 900-Ohm terminating resistor, NEC calculates that it will dissipate about 46% of the applied power.

+

Model D also uses a crossing wire with a single terminating resistor at its center. However, it brings the crossing wire much closer to ground level. In the model, the wire is 0.001 wavelength above ground, just enough for the wire to clear the ground by several wire diameters. Each end of the V assembly runs a vertical wire down to the junction with the low crossing wire. As the table shows, this arrangement produces one of the most stable configurations relative to changes of gain with changes of the terminating resistor value.

+ 
+Test Performance Values for Modeling Option D
+
+Terminating     Maximum      Front-to-Back     Beamwidth     Elevation     Feedpoint Z     750-Ohm
+Load Ohms       Gain dBi     Ratio dB          degrees       Angle deg     R+/-jX Ohms     SWR
+
+600             13.02        21.26             13.4          12             761 - j 49      1.07
+800             13.03        20.64             13.4          12             754 - j 55      1.08
+1000            13.03        20.19             13.4          12             749 - j 59      1.08
+1200            13.03        19.85             13.4          12             744 - j 63      1.09
+
+

Not only is the gain stable across a 2:1 range of resistor values, but as well both the front-to-back ratio and the feedpoint impedance are equally stable. NEC calculates that in its altered position, the 1000-Ohm terminating resistor dissipates only 2.8% of the applied power, although this result stems from the proximity of the crossing wire to ground in the model. The actual dissipation may be much larger for only small increases in resistor and wire height. Nevertheless, using a very low crossing wire removes it from having a significant affect on the radiation pattern. In fact, the data for models B and D are quite similar, although model D appears to be the more stable. Further test of the V-beam using various leg lengths will employ this model and its 1000-Ohm resistor.

+
+ +
+

Fig. 7 provides azimuth patterns for each of the 5 wavelength V-beam models. They show a family resemblance, especially in the forward structure of the lobes. The sidelobes of model A appear stronger because the forward gain is 4-dB or more weaker than for the other models. The data had suggested a close correlation between model B and model D, and the azimuth patterns tend to confirm the suggestion.

+

Although the 4 models of a V-beam use different arrangements and terminating resistor values to arrive at their patterns, all of them have the wide-band characteristic that we saw in the case of single long-wire beams. Fig. 8 provides the SWR curves over a 2:1 frequency range using the optimal feedpoint impedance relative to the indicated values of terminating resistor or resistors. In each case, for the range tested and beyond, a single impedance-transformation device would suffice to match the antenna to most equipment. What all the SWR patterns share in common is the existence of ripples of non-harmful but noticeable proportions. These ripples are indications that the selected terminating resistor value(s) did not result in the closest equality between the terminating resistor and the feedpoint impedance. Instead, the final component selection rested on other criteria, such as the resulting pattern, etc.

+
+ +
+

The broad SWR bandwidth of the single long-wire directional antenna is completely reliable, since the general pattern of the antenna is predictable in terms of gain and beamwidth. However, the V-beam has a more limited usable bandwidth due to restrictions created by the angle between the wires (2A). At some frequency above and at another below the design frequency, the value of angle A will no longer be suitable to support a single forward lobe. As shown in Fig. 9, a 2:1 operational range is feasible for the 5 wavelength V-beam that is 1 wavelength above ground at the center frequency.

+
+ +
+ 
+Performance of a 5-Wavelength 3.5-MHz V-beam 1 Wavelength Above Average Ground
+Model D: Terminating Resistor: 1000 Ohms
+Frequency       Maximum      Front-to-Back     Beamwidth     Elevation
+Mhz             Gain dBi     Ratio dB          degrees       Angle deg
+
+2.3              9.84        33.30             21.8          17
+3.5             13.03        20.19             13.4          12
+4.7             14.42        23.77              9.8           9
+
+

When evaluating both the patterns and the tabular data, remember that at the low end of the sweep, the antenna is only 0.66 wavelength above ground, accounting for the higher elevation angle. Similarly, at the top of the sweep, the antenna is 1.34 wavelengths above ground. The changing height is an additional variable relative to the departure from an optimal value for angle A, and both contribute to the listed performance values.

+

Parallel to our investigation of the unterminated V array, I ran model D with a 1000-Ohm terminating resistor over several ground types. As shown in the table below, the gain changes by under 0.5 dB across the range of soils. The other values are equally stable, presenting no difficulties to using the V-beam over virtually any ground environment.

+ 
+5-Wavelength Terminated V Array 1-Wavelength Above the Indicated Soil Type
+Angle A = 20 degrees; Elevation Angle = 12 degrees
+Soil Type    Gain    Front-Back     Beamwidth    Feedpoint Z     750-Ohm
+             dBi     Ratio dB       degrees      R +/- jX Ohms   SWR
+Very Good    13.18   18.89           14.4        753 - j 97      1.14
+Average      13.03   20.19           13.4        749 - j 59      1.08
+Very Poor    12.72   24.15           13.0        782 - j 27      1.06
+
+

Likewise, the use of a real material, such as copper wire, in place of the modeled perfect wires, offers no hindrance to the V-beam. As the following table shows, the loss due to the use of copper wire for the 5 wavelength V-beam is about 0.1-dB over average ground. All of the other performance values are completely stable.

+ 
+5-Wavelength Unterminated V Array 1-Wavelength Above Average soil
+Angle A = 20 degrees; Elevation Angle = 12 degrees
+Wire Type    Gain    Front-Back     Beamwidth    Feedpoint Z     750-Ohm
+             dBi     Ratio dB       degrees      R +/- jX Ohms   SWR
+Lossless     13.03   20.19           13.4        749 - j 59      1.08
+Copper       12.93   20.43           13.4        752 - j 52      1.07
+
+

The full table of performance values below rests on model D, the version with a single terminating resistor centered on a wire between the V-leg end, but very close to ground level. The table does not include power dissipation values, since they likely depend on the very close proximity of the modeled resistance to the ground, as well as energy lost to ground due to the proximity. Hence, the exact dissipation values will vary with the actual height of the cross connecting wire. The table does include values for angle A, the elevation angle of maximum gain, the modeled maximum gain, the 180-degree front-to-back value, the beamwidth, the feedpoint impedance, and the 750-Ohm SWR. In addition, the table shows the maximum gain of the corresponding unterminated V array and the gain difference relative to the V-beam.

+

Note: Once again, the value of angle A is derived from our long-wire antennas and is not adjusted to achieve maximum gain.

+ 
+Performance of V Beams 1-Wavelength Above Average Ground                                           Unterminated V Array
+Leg Length   Angle A   Elevation  Max. Gain   Front-Back   Beamwidth   Feedpoint Z    750-Ohm      Max. Gain   Difference
+WL           degrees   Angle deg  dBi         Ratio dB     degrees     R +/- jX Ohms  SWR          dBi         dB
+ 2           34        13          9.88       36.86        21.0        772 + j16      1.04         13.60       3.72
+ 3           26        13         11.41       21.70        17.4        750 - j66      1.09         14.65       3.24
+ 4           23        12         12.35       22.90        14.8        772 - j38      1.06         15.48       3.13
+ 5           20        12         13.03       20.19        13.4        749 - j59      1.08         15.97       2.94
+ 6           18        11         13.50       19.97        12.4        741 - j39      1.06         16.25       2.75
+ 7           16        11         13.86       20.17        12.0        742 - j40      1.06         16.56       2.70
+ 8           14        11         14.07       19.89        12.0        731 - j42      1.06         16.75       2.68
+ 9           13        11         14.29       19.54        11.4        724 - j51      1.08         16.99       2.70
+10           13        10         14.59       19.32        10.4        721 - j42      1.07         17.24       2.65
+11           12        10         14.74       19.40        10.2        716 - j43      1.08         17.35       2.61
+
+

The table shows a very normal increase in gain with leg length at the optimal angle A. Both the elevation angle and the beamwidth for the V-beam tightly correspond to comparable values for the unterminated V array, with no decrease in beamwidth as we experienced with the transition from unterminated long-wire to terminated long-wire antennas. The 180-degree front-to-back ratio holds around the 20-dB mark, and the impedance is exceptionally stable throughout the span of leg lengths. (The stability of the impedance values is an especially good marker of the adequacy of using values for angle A derived from the unterminated single long-wire models.) As a side note, compare the V-beam entry for 4 wavelength legs to the data for the bent terminated long-wire in Part 2. The gain values a virtually identical, although the V-beam improves the front-to-back ratio and reduces many of the sidelobes. Both antenna require 8 wavelengths of horizontal wire.

+

The V-beam, like the terminated long-wire antenna, shows a decrease in maximum forward gain relative to the unterminated version of the antenna. However, the V-beam decrease is about a dB less than for the single long-wire beam. Nevertheless, the reason for using a V-beam instead of an unterminated V array is the directivity of the pattern, with the loss of gain accepted as a fair penalty for the reduced sensitivity to the rear. If rearward pattern reduction is not a priority for a given installation, then the unterminated V array may be the better choice of antennas. Fig. 10 provides a gallery of selected elevation and azimuth plots that show the evolution of radiation patterns with increasing leg length in the V-beam. You may wish to compare these plots directly to corresponding plots in Fig. 3 for the unterminated V array.

+
+ +
+

The azimuth patterns have two major characteristics that we should note. First is the narrowing of the beamwidth as we make the antenna longer, a feature that also attaches to the V array. Second is the development of the secondary lobes in the 2 forward quadrants. These lobes are a function of the narrowing angle between wires and the lobes on each wire that do not add to form the strongest center lobe.

+

The most notable elevation-plot feature is the relative absence of strong secondary elevation lobes. Only the lobes closest to the main elevation lobe exceed the -20-dB level in strength relative to the main lobe. We may better gauge the upper-level lobe structure from a 3-dimensional radiation pattern, such as the one in Fig. 11. The 10 wavelength V-beam used to generate the plot clearly shows the lowest level. The apparent second level is actually a part of the main lobe. The stepped appearance is due to the 5-degree increments in pattern sampling. The next strongest level to the main lobe occurs near the 40-45-degree region and is 15-20-dB weaker than the main lobe. Although there are still many upper-level lobes in the pattern, their strength is operationally insignificant.

+
+ +
+

Perhaps an appropriate way to conclude our exploration of the V-beam is by comparing it, length for length, with the corresponding single long-wire terminated beam. Fig. 12 provides a pattern comparison, using 10 wavelength versions of both antennas. The elevation patterns shows the V-beam's reduction in relatively useless upper level lobes. The azimuth pattern shows the V-beam's tighter control of sidelobes, especially in the forward quadrants. However, for some communications tasks, the terminated long-wire may have the more useful beamwidth, despite the null between forward peaks.

+
+ +
+

The following table summarizes the gain and beamwidth differentials between the 2 terminated long-wire directional antennas.

+ 
+Long-Wire and V-beam Gain and Beamwidth Values for 3- to 11-Wavelength Arrays
+              Terminated Long-Wire        Terminated V-Beam
+Length        Gain      Beamwidth         Gain      Beamwidth        Gain Difference
+WL            dBi       degrees           dBi       degrees          dB
+ 3             7.11     69                11.41     17               4.30
+ 4             7.99     59                12.35     15               4.36
+ 5             8.65     51                13.03     13               4.38
+ 6             9.15     46                13.50     12               4.35
+ 7             9.57     44                13.86     12               4.29
+ 8             9.92     40                14.07     12               4.15
+ 9            10.20     37                14.29     11               4.09
+10            10.47     36                14.59     10               4.12
+11            10.70     33                14.74     10               4.04
+
+

The V-beam shows a consistent 4-dB+ gain advantage over the terminated long-wire antenna, but its beamwidth is consistently 1/3 to 1/5 the values for the long-wire. The terminated long-wire directional antenna, of course, shows a null between peaks, and for lengths from 3 to 6 wavelengths, the null is deep enough (>3dB) for modeling software to recognize two distinct forward lobes. The table does not itself make a judgment, but simply facilitates a comparison of the results in Part 2 of this series and the results obtained for this part.

+

Conclusion to Part 3

+

On this leg of our journey through the classical long-wire antennas, we have focused on the V antenna in both unterminated and terminated forms. By properly angling the legs of the V, the antenna combines a major lobe from each wire to form a single lobe in the forward direction. Of course, the unterminated V array has a similar lobe to the rear and it is is only slightly weaker than the lobe pointing away from the feedpoint. Terminating the legs of the Vee creates a directional antenna with superior properties to the single long-wire in terms of gain and the suppression of both elevation and azimuth sidelobes. However, the improved directional characteristics come at the expense of some of the unterminated V's gain. As well the V antennas have a very narrow beamwidth that limits the potential applications for either the terminated or unterminated versions.

+

Although there may be many variants on long-wire design, classical literature shows only one more major pathway to traverse: the rhombic. A Bruce development from the 1930s, the rhombic sometimes bears the title of the king of wire antennas. The antenna has had a lure that will take us 2 episodes to cover, and then only in an introductory way. One humorist has wished for his ideal antenna, and it was a very long rhombic installed on a rotatable island. Our task will be to see if there is any good sense hiding behind the humor.

+
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Updated 08-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Jul, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 4

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Return to Index

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Topics: HF Multi Band, Longwire


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Long-Wire Antennas
+ Part 4: Rhombic Arrays and Beams

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L. B. Cebik, W4RNL

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Every step along our path through traveling-wave antennas has led us to new heights of gain per unit of wire length (as measured in wavelengths)--and to narrower beamwidths. The final steps take us to the pinnacle of long-wire development: the rhombic antenna. (We should note that there are some "fishbone" designs that may be able to achieve more gain per acre of ground than the designs with which we are working. However, these antennas use a quite different design and require at least 2 to 4 wavelengths of wire per wavelength of forward antenna dimension. We shall not cover them here. However, the ARRL Antenna Book chapter and the Laport volume, both cited in the short list of references, cover the basics of these designs.)

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The rhombic antenna derives its name from its shape: the rhombus. In geometry, a rhombus is an equilateral parallelogram, that is, a closed 4-sided figure with all sides the same length, but with all corner angles normally using other than right angles. Fig. 1, at the top, shows a basic rhombus, with indications of the key dimensions.

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An alternative way to look at the rhombus is to see it as 2 V antennas end-to-end. This orientation makes clear that the centerline is correctly identified, and it gives the elongated shape some sense, assuming that Part 3 of this series has had its impact. The length L, in wavelengths, defines the length of each leg, suggesting that each rhombic antenna that we examine will likely be twice as long overall as a corresponding V antenna with the same leg length.

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Also apparent in the sketch is angle A (usually represented by a Greek alpha). When we examined V antennas, we used the angle of the strongest lobe of a single long-wire of length L to determine the value of angle A. We then found that angling each V wire from the centerline by the value of A produced additive lobes along the centerline. Since the far end of any rhombic antenna is a mirror image of the feedpoint end, the lobes for the far-end wires will also be aligned with the center line. Hence, we can expect more gain from a rhombic antenna than from a corresponding V antenna.

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The earliest literature, starting with the classic article by Bruce, Beck, and Lowry ("Horizontal Rhombic Antennas," Proc. IRE, 1935), began the practice of referring to angle B in Fig. 1 as the tilt angle. The normal character for this angle is a Greek phi, although I have seen other characters as well. Angle B is simply 90 degrees minus angle A.

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Basic rhombic calculations emerge from a situation that is usually not very realistic for the average amateur installation. The premise is that angle A represents 2 different angles in the antenna installation. First, it represents the elevation angle of maximum radiation. Hence,

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+ HWL = [1 / (4 sin A)] +
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where HWL is the required antenna height in wavelengths. As well, angle A represents the required V'ing angle, the same angle that we used in the V-antennas. To align the major lobe with the elevation angle, we calculate the leg-length as follows:

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+ LWL = [0.371 / (sin2 A)] +
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where LWL is the leg-length in wavelengths. For maximum gain at the chosen elevation angle,

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+ LWL = [0.5 / (sin2 A)] +
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The difficulty faced by amateur installations is that the height is rarely a matter of open choice. As a matter of fact, neither is the length open to selection based solely on calculations. Instead, the maximum height for an installations is usually prescribed by any number of limiting circumstances. All of the examples used in this series have set the antennas at 1 wavelength above ground on the premise that most long-wire antennas will ultimately fall in the upper HF range. 1 wavelength at 14 MHz is about 70'. Property lines usually define the absolute limits of overall array length, abetted by complexities such as the availability and feasibility of supporting very long runs of wire.

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Initial and later studies in rhombic antennas provide more complex equations to calculate compromises where the elevation and the V'ing angle do not match. Some of the equations appear in nomographic form. For example, one such nomograph appears in the ARRL chapter on long-wire and traveling-wave antennas, as well as in articles and text devoted specifically to the design of rhombic antennas. (See the Harper volume in the reference list.) Such nomographs are capable of guiding the rhombic designer to excellent results, as we shall see before we close this last segment of our long-wire trek.

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However, via NEC modeling, we have an easier route to designing rhombics. The process started in Part 1, with the modeling of end-fed unterminated wires, from which we obtained the values of angle A within the limits of the modeling exercise. We standardized the wire height at 1 wavelength. We might as easily develop a compendium of models using the same (or different) increments of wire length at a number of different heights. For a practical design project, we likely would select a single height dictated by whatever constraints will govern the installation. Then, we can collect data on angle A for any set of wire lengths desired.

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We may use the selected height and the associated values of angle A to design any number of rhombic antennas. In fact, we can use a simple long-wire as the starting point. NEC allows us, via the GM command, to rotate the wire by the required number of degrees dictated by the value of angle A for a given wire length. (Programs like EZNEC use a different but equally effective method of rotating wires.) Hence, we can easily create a V and find its coordinates. From those coordinates, we can complete the rhombic by doubling the overall length and bringing 2 new wires back together--or almost together. See the lower part of Fig. 1 for 2 possible versions of an unterminated rhombic configuration.

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The use of angle A assures us of lobe direction coincidence and gain addition along the centerline of the antenna. We may then let NEC calculate the gain and actual elevation angle for the selected antenna height over any selected soil. Before we close this series, we shall find that NEC's handling of rhombic design and at least one nomographically based design turn out to be virtually identical. Traditional methods are quite accurate, but in the present age of computerized antenna design, the modeling process is often simpler. As we have seen from our experience with single long-wire and V antennas, the modeling method also provides ready supplementary information, for example about sidelobes, feedpoint impedances, and power dissipation in the load resistance of terminated antennas.

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In our exploration of rhombic antennas, we shall simply extend our modeling methods. First, we shall leave the antenna at 1 wavelength above average ground (conductivity 0.005 S/m, permittivity 13). The test frequency will be 3.5 MHz, and the lossless wire will be 0.16" in diameter. Part 1 of the series sampled some of the variations on these choices, so you may readily extrapolate additional losses or gain from selecting different background parameters. Better yet, you may easily model most of the antennas yourself, using your own selection of parameters. Some beginning programs are limited to 500 segments. A few of the longer rhombics may require up to 900 segments if we adhere to our 20-segment per wavelength standard. However, a full 6 wavelength-per-leg rhombic comes in at under the 500 segment mark.

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Unterminated Rhombic Antennas

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The lower portion of Fig. 1 shows two ways of modeling an unterminated rhombic antenna. We may separate the far end point by a small space. This configuration is perhaps the most common understanding of an unterminated (sometimes called a resonant) rhombic. However, we may equally bring the ends together to short-circuit the gap. The options expose something of a misimpression of the rhombic antenna. If we were given to extreme (and unfortunately, contentious) modes of expression, we might suggest that there is no such thing as an unterminated rhombic antenna.

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The single long-wire unterminated antenna and the V array both make good sense of the idea of a wire without a resistive termination. Any form of termination requires extra wires and ultimately a ground connection--although there is a version of the V-beam that does not use ground at the far end of the array. The rhombic returns the 2 wires of the antenna to close proximity. In the models that we shall explore, the gap will be 0.002 wavelength. At 3.5 MHz, that distance is 170 mm, where a wavelength is over 85.6 m long. If we leave the gap open, we can treat the terminating resistance as simply indefinitely large. One modeling technique for rhombics is to use a short wire to bridge the gap. To create a terminated rhombic--as the term is generally used--we place a load resistor of a desired value on the bridge wire. To create an open circuit, we might specify the load resistance as 1e10 Ohms or higher. To short out the gap, we can either remove the load resistor or give it a value of 0 Ohms. Alternatively, we can remove the bridge wire and simply bring the 2 legs to the same point on the coordinate scheme.

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Despite the existence of a reasonably plausible claim that all rhombics are terminated to one or another degree, we shall adhere to the common referential terms. Without a mid-range non-inductive resistor at the far end of the antenna, the rhombic will be unterminated in either the open or closed configuration. The chief difference between the open and closed versions of the unterminated rhombic antennas lies in the sidelobes, not in the small differences in gain and inherent front-to-back ratio that is a part of all end-fed long-wire antennas. Fig. 2 contrasts the structure of the sidelobes for open and closed unterminated rhombics. Note that the closed version shows larger sidelobes than the open version, suggesting less complete cancellation of lobes from the parallel legs.

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For comparison and contrast, Fig. 2 also presents two azimuth patterns from corresponding unterminated V arrays. The pattern on the lower left uses 3 wavelength legs, the same length as the legs in the rhombics. On the lower right is the pattern for a V array using 6 wavelength legs. These legs give the V array the same overall length as the rhombic with a small margin of difference due to the difference in the value of angle A. (Both rhombics are 5.39 wavelengths, while the long V is 5.71 wavelengths overall.) On the whole, the long V antenna pattern resembles in general sidelobe strength the closed rhombic pattern. However, the V patterns show the combination of many sidelobes that combine to form fewer distinct lobes and nulls. In contrast, the double-V configuration of the rhombic reduces these indefinite lobe formations down to distinct lobes and nulls. In fact, both rhombic azimuth patterns show a total of 20 lobes. The lower strength levels of the lobes at near-right-angles to the 2 main lobes for the open version of the antenna make lobe counting impossible at the scale of Fig. 2, but expanded renderings of the plot reveal them all. In contrast, even large renderings of the V-antennas do not permit an accurate count of the lobes and the bulges that form incipient lobes.

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Clear lobe definition and numeric limitation together comprise one of the advantages of the rhombic over corresponding V antennas. The other major rhombic advantage is gain. The following table provides modeled data for both open and closed unterminated rhombics with varying leg lengths from 2 through 11 wavelengths. Remember that the overall length of the rhombic is just under twice the leg length. Like all long-wire antennas, the rhombic suffers the blight of diminishing returns as we strive to make it longer. Doubling the leg length from 2 to 4 wavelengths provides nearly 2.5-dB more gain. However, the next doubling to 8 wavelength legs adds slightly under 2 dB of gain.

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Note: The values of angle A derive from our earlier work with single long-wire antennas. I have not optimized those values to achieve maximum gain. There is a slight difference.

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+Performance of Unterminated Rhombic Antennas 1-Wavelength Above Average Ground
+Type     Leg Length   Angle A   Elevation  Max. Gain   Front-Back   Beamwidth
+         WL           degrees   Angle deg  dBi         Ratio dB     degrees
+Open      2           34        14         16.41       2.41         20.4
+Closed    2           34        14         15.84       2.90         20.6
+Open      3           26        14         17.81       2.40         17.2
+Closed    3           26        14         17.50       2.66         17.2
+Open      4           23        13         18.89       2.58         14.1
+Closed    4           23        13         18.61       2.83         14.4
+Open      5           20        13         19.57       2.57         12.8
+Closed    5           20        13         19.35       2.77         12.8
+Open      6           18        12         20.12       2.55         11.6
+Closed    6           18        13         19.95       2.71         11.8
+Open      7           16        12         20.53       2.48         11.2
+Closed    7           16        12         20.39       2.60         11.2
+Open      8           14        12         20.82       2.32         11.0
+Closed    8           14        12         20.69       2.42         11.0
+Open      9           13        12         21.17       2.27         10.4
+Closed    9           13        12         21.03       2.38         10.4
+Open     10           13        11         21.52       2.37          9.4
+Closed   10           13        11         21.39       2.47          9.4
+Open     11           12        11         21.73       2.29          9.0
+Closed   11           12        11         21.61       2.38          9.0
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At the top of the table, the gain differential between open and closed rhombics appears to be significant: nearly 0.6 dB. However, the differential shrinks continuously as we lengthen the legs. By the time the legs are 11 wavelengths, the gain differential is only a bit over 0.1 dB. Elevation angles, front-to-back ratios, and beamwidths all remain very comparable for both types of unterminated rhombic antennas.

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All of the closed unterminated rhombics show a modest feedpoint impedance at the integral leg lengths that appear in the table. The resistive component varies between 235 and 290 Ohms, while the reactance ranges from -j160 to -j190 Ohms. In contrast, all of the open rhombics show very high impedance levels, with resistive components running from 2900 to 3300 Ohms. The reactance seems to have a wide range--from +j130 to +j460 Ohms. However, as a fraction of the total impedance, the range is small. The differential between open and closed rhombic impedances is real, but in practical terms of designing a system, it is also illusory. The curves for changes of feedpoint resistance and reactance for the two types of unterminated rhombics are virtually identical, but displaced from each other by about 1/4 wavelength of leg length.

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Fig. 3 presents the unterminated rhombic gallery of sample elevation and azimuth plots for leg lengths of 2, 4, 6, 8, and 10 wavelengths. By comparing the plots with Fig. 2, you can verify that the gallery uses the open version of each rhombic.

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The open unterminated rhombic shows excellent sidelobe control compared to the other long-wire antennas that we have surveyed. In general, azimuth sidelobes are 10 dB of more down, with a very good front-to-side ratio for headings near or at the 90-degree mark off the main lobes. Secondary elevation lobes are 10 to 15 dB down, depending upon rhombic length. Fig. 4 provides a 3-dimensonal radiation pattern in 5-degree increments of the rhombic with 10 wavelength legs. Although the upper elevation angles still bristle with lobes, they are generally all of low strength and therefore untroublesome to antenna performance.

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As a way to summarize our meandering through various unterminated bi-directional wire antennas, the following table presents the modeled maximum gain values for each type that we have surveyed. All values are for perfect-wire antennas 1 wavelength above average ground. Remember that the center-fed and end-fed long-wire antennas show maximum gain off-axis to the wire, while the V and rhombic antennas show maximum gain in line with the antenna centerline. In addition, the rhombics overall are twice as long as the single-wire and V antennas listed for the same leg length.

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+Maximum Gain of Various Types of Unterminated Long-Wire Antennas
+Leg                            Maximum Gain dBi
+Length    Center-Fed   End-Fed      V            Closed       Open
+WL        Doublet      Wire         Array        Rhombic      Rhombic
+ 2         9.36        10.27        13.60        15.84        16.41
+ 3        10.16        11.32        14.65        17.50        17.81
+ 4        10.93        11.99        15.48        18.61        18.89
+ 5        11.47        12.48        15.97        19.35        19.57
+ 6        11.85        12.90        16.25        19.95        20.12
+ 7        12.14        13.24        16.56        20.39        20.53
+ 8        12.43        13.50        16.75        20.69        20.82
+ 9        12.65        13.72        16.99        21.03        21.17
+10        12.82        13.96        17.24        21.39        21.52
+11        13.01        14.15        17.35        21.61        21.73
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Although some of the gain increase that we see with longer and more complex long-wire antennas comes from sidelobe control, most of it emerges at the expense of beamwidth. We have noted this fact in past episodes, but it needs a reminder here. Short V and rhombic antennas (2 wavelength legs) have beamwidths just over 20 degrees. With 10 wavelength legs, the beamwidth is less than half that value. Although the high gain of long Vs and rhombics seems attractive to many, the utility of a fixed position narrow-beamwidth antenna is for point-to-point communications, not for general communications across the horizon. For comparison, a half wavelength dipole has a beamwidth of about 80 degrees, while the beamwidth of a 1.25 wavelength extended double Zepp is about 30-35 degrees. In many cases, the key design question for fixed long-wire antennas is less "With whom do I wish to communicate?" and more "With whom am I willing not to communicate?"

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Terminated Rhombic Antennas

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The terminated version of the rhombic antenna is identical to the unterminated versions with the exception that the far junction of the wires has an intervening non-inductive resistor (or combination of resistors in series and/or parallel connection) with the desired value. Fig. 5 shows the outline of the general arrangement. Ordinarily, the terminating resistor is somewhat arbitrarily selected in the 600-800-Ohm range. Angles A (alpha) and B (phi) play the same role in the terminated rhombic that they play in the unterminated versions. L remains the leg length measured in wavelengths, and the leg length plus the angles form unique combinations to achieve maximum gain at some prescribed antenna height.

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The models for the unterminated rhombics have used only 4 wires, one for each leg. The model source consists of a split source, that is, two sources in series. The sources go on the segments adjacent to the junction of the wires at the feedpoint end of the antenna. As the right side of Fig. 5 reveals, I used a similar technique to place the terminating resistor. Non-reactive resistive loads go on the last segment of each far-end wire, with each resistance equaling half the total terminating resistance. These techniques of placing sources and loads preclude the need to create a short wire at each end of the rhombic structure. To preserve an equality of segment lengths, the bridge wire would have to be long enough that it would not preserve the value of angle A. Alternatively, to maintain the value of angle A, the source/load wire would be significantly shorter than adjacent leg segments, a condition on the source wire that NEC does not recommend for the most accurate calculations. Split sources and split loads preserve both the geometry of the model and the best conditions for calculation.

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Like all other models in this series, the lossless 0.16"-diameters wires use 20 segments per wavelength. All terminated rhombics are 1 wavelength above average soil with a test frequency of 3.5 MHz.

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Before we present a table of modeled performance values, we must select a value for the terminating resistor. Many rhombic builders rely on the tradition that the terminating resistor controls the feedpoint impedance. Since 600-Ohm ladder line is readily available or easily built, 600 Ohms has been a popular resistance for the rhombic termination. For spot frequencies in otherwise well-designed rhombics, a 600-Ohm termination produces a low 600-Ohm SWR. However, many rhombics find use over at least a 2:1 frequency range. Therefore, I swept the version of the rhombic with 3 wavelength legs from the design frequency to twice the frequency to observe the likely undulations of resistance, reactance, and 600-Ohm SWR. Fig. 6 shows the results.

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In many ways, the resistance and reactance swings appear to be modest. Indeed, the SWR curve shows low values for 3.5, 5.25, and 7 MHz (which would correspond to 14, 21, and 28 MHz on a properly scaled version of the model). However, the SWR for 4.53 MHz (scale value: 18.118 MHz) is greater than 2:1, and the value for 6.24 MHz (scale value: 24.94 MHz) is approaching 2:1. These values would not be troublesome for a wide-range antenna tuner between the shack end of the feedline and the transceiver. However, they may be high enough to defeat the low-loss use of a wide-range impedance transformation device, such as a transmission-line transformer balun.

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Higher values of terminating resistance yield smaller resistance and reactance excursions. The result is a set of smaller SWR swings, all within an acceptable range. Fig. 7 shows the same frequency sweep using an 850-Ohm terminating resistor, referenced at the feedpoint to 850 Ohms.

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Comparing the resistance and reactance lines between Fig. 6 and Fig. 7 reveals the smaller swings in these impedance components. The SWR (blue) line swings may appear similar in the 2 graphs. However, note the smaller limit to the Y-axis in Fig. 7: its highest value is 1.45:1. Although creating a wide-range impedance transformation device may be more difficult with the higher reference impedance (850 Ohms), the technique will be applicable with low losses across the 2:1 frequency range of the rhombic.

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Within the usual range of terminating resistor values, the lower the terminating resistance value, the higher the the array gain--but only slightly so. Fig. 8 overlays the gain values of the rhombic beam for both the 600- and the 850-Ohm resistors. Throughout the 2:1 frequency range, the 600-Ohm version provides the higher gain, but by no more than 0.01 to 0.02 dB.

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In the range of terminating resistance between 600 and 900 Ohms, certain performance parameters remain extremely stable. The elevation angle of maximum radiation and the beamwidth are two values that remain the same throughout the range of terminating resistors, at least for the sample rhombics using leg lengths that change in 1 wavelength increments between models. The impedance is also relatively stable at the test frequency for each model through the 600- to 900-Ohm resistor range. The maximum spread of resistance goes from a low of about 730 at 600 Ohms to a high of 870 at 900 Ohms, although the range is a bit smaller for any one leg-length model. The reactance swing is equally small, ranging from a -j40-Ohm value at 600 Ohms to a +j40-Ohm value at 900 Ohms.

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My reason for selecting the 850-Ohm terminating resistor has as much to do with drama than with good electronics. Normal construction variables and the selection of leg lengths that are not perfect integral increments of a wavelength would likely alter the results. However, as the following performance table reveals, 850 Ohms as the termination value yields very high values of 180-degree front-to-back ratio, resulting in radiation patterns in which the main forward lobe and the sidelobes take center stage. The shortest of the rhombics has the lowest front-to-back value because the 40+-dB ratio occurs with an 800-Ohm terminating resistance. In practice, values from 750 to 900 Ohms will likely yield indistinguishable results, although the higher end of the scale will usually result in the smoothest SWR curve. However, we tend to obtain the flattest wide-range SWR curves when the terminating resistance and the feedpoint impedance are as close together as possible.

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The tabular data shows the value of angle A (alpha), the elevation angle of maximum radiation, the maximum forward gain, the 180-degree front-to-back ratio, the half-power beamwidth, the modeled feedpoint impedance, and the 850-Ohm SWR. For reference, the far-right columns provide the maximum gain values for the corresponding unterminated open rhombics, along with the gain differential between the terminated and unterminated versions of the antenna.

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Note: The values of angle A are not optimized for maximum rhombic gain, but derive from earlier work with single long-wire antennas.

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+Performance of Terminated Rhombic Beams (R = 850 Ohms) 1-Wavelength Above Average Ground           Unterminated Rhombics
+Leg Length   Angle A   Elevation  Max. Gain   Front-Back   Beamwidth   Feedpoint Z    850-Ohm      Max. Gain   Difference
+WL           degrees   Angle deg  dBi         Ratio dB     degrees     R +/- jX Ohms  SWR          dBi         dB
+ 2           34        14         14.60       30.40        20.6        862 + j23      1.03         16.41       1.81
+ 3           26        14         16.04       41.16        17.2        864 + j23      1.03         17.81       1.77
+ 4           23        13         17.27       43.97        14.4        869 + j27      1.04         18.89       1.62
+ 5           20        13         17.97       44.71        12.8        867 + j23      1.03         19.57       1.60
+ 6           18        13         18.51       44.78        11.6        863 + j24      1.03         20.12       1.61
+ 7           16        12         18.85       42.78        11.2        861 + j24      1.03         20.53       1.68
+ 8           14        12         18.98       43.63        11.0        856 + j24      1.03         20.82       1.84
+ 9           13        12         19.27       43.90        10.4        854 + j24      1.03         21.17       1.90
+10           13        11         19.73       44.52         9.4        855 + j23      1.03         21.52       1.79
+11           12        11         19.86       43.84         9.0        852 + j24      1.03         21.73       1.87
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As we move from a single long-wire antenna to a V-beam and finally to a rhombic, the gain differential between the unterminated and the terminated versions has decreased. The differential was 3.5 to 4.5 dB for the single long-wire terminated antenna. The V-beam showed a range of 2.7 to 3.7 dB differential. In both cases, the differential decreased as the length of the legs increased. For the rhombic, the differentials range from 1.6 to 1.9 dB, a tight range for which there is no apparent correlation between gain differential and leg length.

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The gallery of sample elevation and azimuth patterns of the terminated rhombic beam appear in Fig. 9. The gallery includes patterns for leg lengths of 2, 4, 6, 8, and 10 wavelengths. Because the arrays are twice as long overall as corresponding V-beams and single terminated long-wire antennas, the transitions in pattern shape are smaller from one increment to the next in the series. Hence, we may use fewer plots to show the evolution of rhombic radiation patterns.

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Careful inspection of the sidelobe structures will show that the strength of the forward-most sidelobes--and also the strongest sidelobes--is somewhere between the corresponding sidelobes for the open and the closed versions of the unterminated rhombics. See Fig. 2 to estimate the limits and where between them the terminated rhombic sidelobes fall. The phenomenon suggests that there is a continuity in sidelobe strength across a range of termination values ranging from an open circuit through a mid-range resistance and ending at a short circuit.

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Fig. 10 provides a 3-dimensional pattern for the rhombic with 10 wavelength legs. It reveals that the terminated rhombic exerts the most control over the morass of small lobes that populate the overall radiation pattern. You may directly compare this pattern with the one in Fig. 4 for the unterminated rhombic to correlate various lobes and their relative strengths. As well, you may compare it with corresponding patterns for other terminated long-wire arrays in earlier parts of this series.

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One quick comparison that we may tabulate is the maximum gain of each of the 3 types of terminated beams that we have encountered along the long-wire pathway. Remember that the maximum gain value for the single terminated long-wire is an off-axis value, that is, not in alignment with the wire itself.

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+Maximum Gain of Various Types of Terminated Long-Wire Antennas
+Leg              Maximum Gain dBi
+Length    Single       V            Rhombic
+WL        Long-Wire    Beam
+ 2         ----         9.88        14.60
+ 3         7.11        11.41        16.04
+ 4         7.99        12.35        17.27
+ 5         8.65        13.03        17.97
+ 6         9.15        13.50        18.51
+ 7         9.57        13.86        18.85
+ 8         9.92        14.07        18.98
+ 9        10.20        14.29        19.27
+10        10.47        14.59        19.73
+11        10.70        14.74        19.86
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The gain of the single terminated long-wire would not justify its narrow-band use, since we can obtain similar gain levels from antenna ranging from dipoles to extended double Zepps at a great savings in both wire and supporting structures. The single terminated long-wire acquires its usefulness from the relative constant feedpoint impedance, allowing great frequency agility. The terminated V adds about 4-dB of gain, while maintaining a broad SWR operating bandwidth. However, any angle used as the basis for the array has frequency limits for a good pattern: outside those limits, the forward pattern breaks into multiple lobes. As we change frequency, the antenna legs change length as measured in terms of a wavelength at the new operating frequency. Hence, the wire angles are no longer optimal to add in a forward direction.

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The rhombic shares the frequency limits of the V-beam. To sense its truer gain advantage, you may wish to compare the rhombic with a given leg length to a V beam with twice the leg length. For example, a rhombic with 5 wavelength legs and neqrly 18 dBi gain is roughly equivalent in overall length to a V-beam with 10 wavelength legs and a 14.6-dBi gain level. Like the V beam, the rhombic is capable of good performance over a 2:1 frequency range with good gain and a relatively constant feedpoint impedance. In fact, before we end out trek through long-wire antennas, we should take one more look at the ARRL rhombic from Chapter 13 of the 20th Edition of The Antenna Book. But not today.

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Conclusion to Part 4

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In this episode, we have moved beyond the V array and beam to examine what some call the highest development in long-wire antennas: the rhombic. We learned how to close the V with another V, using the same technique of aligning lobes from each wire to form a rhombus. Modeling allowed us to develop effective rhombic antennas without reference to classical equations by setting the intended height and the leg-lengths that we might use. We explored both open and closed forms of unterminated rhombic arrays, and then we turned to the most common rhombic form, the terminated beam.

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By splitting both the source and load, we found a very economical way to model the terminated rhombic beam. We also uncovered some relationships between the value of the terminating resistor and the feedpoint impedance that bear on the smoothness of SWR curves that cover a 2:1 frequency range. Indeed, there is more to be said on this subject. . .

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Indeed, I had planned to close the series at this point. However, we have a significant amount of unfinished business with the rhombic.

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1. The Multi-Band Rhombic: We have not yet evaluated the ARRL Antenna Book rhombic for 14-28 MHz. This design has is roots in nomographic design data from Harper's well-known book. (See the list of references at the end of each Part.) The antenna gives us a chance to compare modeling design techniques with classical methods.

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2. The Multi-Wire Rhombic: One common method of trying to improve rhombic beam performance is to use more than 1 wire for each leg. The usual arrangement consists of 3 wires that come together at the rhombic points and spread in the middle by relatively arbitrary distances. The arrangement presents both theoretical and modeling challenges, and careless modeling of a 3-wire rhombic can lead to erroneous results.

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3. The Multi-Element Rhombic: In the 1950s, Laport developed the multi-element rhombic beam to improve both gain and sidelobe suppression. Since the antenna has seen use on the UHF amateur bands, the design bears at least an initial exploration to look at both design and modeling issues.

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With so many outstanding rhombic ideas, I would be remiss if I did not extend the series one more episode. Even then, we shall not have examined every variation on the long-wire, V, and rhombic arrays. However, perhaps we shall have encountered enough designs along our pathway so that you may continue the trek on your own.

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Updated 09-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Aug, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 5

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Return to Index

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Topics: HF Multi Band, Longwire, Rhombic


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Long-Wire Antennas
+ Part 5: Multi-Band, Multi-Wire, and Multi-Element Rhombics

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L. B. Cebik, W4RNL

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Because the rhombic antenna, especially when terminated, offers very high gain, it has received more design attention than any of the other long-wire antennas. The straightforward basic design data sampled in Part 4 does not exhaust the significant variations on the basic configuration. One potential particularly suited to amateur service in the upper HF range is the possibility of operating a rhombic over a 2:1 frequency range, thus allowing coverage of 20 through 10 meters. We shall examine one tried and true design and try to find out the basic design premise that allows it to be successful.

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When an antenna is good at what it does, we can count on efforts to make the good even better. For narrow-beamwidth point-to-point communications, the rhombic is very good. One very old technique to improve performance somewhat is the use of multiple wires in each side of the rhombic. They come together at the feedpoint and at the terminating resistor end, but spread vertically where the facing Vs are widest. Some claims about the technique will prove correct, such as the addition of a small increment of gain. However, other claims may turn out to have other foundations than the use of multiple wires.

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Finally, we shall address an interesting technique for further suppressing the remnant sidelobes in the rhombic radiation pattern. Laport developed a scheme for using closely spaced rhomboid structures in parallel. The centerlines for each of the independent rhomboids fed in parallel are offset from each other. The technique will offer a small gain advantage over the single-wire rhombic, but will reduce sidelobes by a very significant amount.

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Although these developments are worth our notice here, they will not exhaust the variations on the rhombic. There is, for example, the so-called half-rhombic, consisting of one side of a rhombic played against ground. Unfortunately, lossy soil does not permit the antenna to play like a true rhombic, due to ground reflections and losses. Despite its name, the antenna operates more like a terminated, end-fed, inverted V, and highest performance occurs with only a slight elevation of the centerpoint above ground. The antenna appears in Bruce's 1931 article and he calls it simply an inverted-V. The name "half-rhombic" came later from other builders. Other variations on the rhombic have emerged in answer to specific commercial and governmental communication needs. The result has been highly complex arrangements of wire structures well beyond the scope of these introductory notes. Nevertheless, the variations that we have selected should provide a sufficient foundation to let you examine the classical literature on advanced rhombic designs with understanding.

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Multi-Band Rhombics

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Although we have briefly mentioned multi-band use of long-wire antennas, we have not paused long to investigate their performance in broadband service. We shall rectify this situation, if only briefly, by looking the ARRL rhombic intended for upper HF service from 14 through 28 MHz. The antenna first appeared in The ARRL Antenna Book somewhere between 1965 and 1974, and has been a prime example in the book's treatment of traveling-wave antennas. Fig. 1 shows the general outlines of the antenna.

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One notable feature of the antenna is that its design emerged long before modeling software became available. Hence, its outline rests directly on the original rhombic design equations, as filtered into design nomographs. The design begins with 3 wavelength legs at 14 MHz along with a height of about 70' or 1 wavelength at the lowest frequency of use. It uses a prescribed tilt angle of 64 degrees and hence an angle A value of 26 degrees. These values coincide perfectly with the values developed via computer modeling. For this model, I followed the typical amateur conventions and used a 600-Ohm termination and an SWR reference impedance of 600 Ohms. The following table lists the modeled performance of the antenna over the 5 amateur bands between 14 and 28 MHz.

+ 
+Modeled Performance of the ARRL Upper HF Rhombic with a 600-Ohm Termination
+Frequency MHz      14.0        18.118      21.0       24.94      28.0
+Parameter
+Gain dBi           16.04       17.89       18.38      18.31      17.33
+El. Angle deg      14          10          9          7          6
+Front-Back dB      19.93       15.28       24.68      15.27      32.12
+Beamwidth deg      17.0        13.0        10.8       8.6        7.0
+600-Ohm SWR        1.25        1.79        1.22       1.65       1.22
+
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The gain values parallel almost exactly the curves in Fig. 8 in Part 4, which is also for a rhombic with 3 wavelength legs and an angle A of 26 degrees. The three differences between the earlier model and the present one are the design frequency (3.5 vs. 14 MHz), the wire (perfect 0.16" vs. copper AWG #12 or 0.0808"), and the terminating resistor value (850 vs. 600 Ohms). Fig. 2 shows a gallery of elevation and azimuth patterns at each of the test frequencies. Note that this gallery differs from the galleries in the earlier parts of this series because angle A is optimized in combination with the leg length only at the lowest operating frequency.

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The sidelobe structure (including the rear-most lobe) of the patterns for frequencies above 14 MHz does not parallel any of the patterns in the earlier galleries (Fig. 9 in Part 4, for example) because angle A (and the tilt angle B) remain constant while the leg length changes as a function of the ever higher operating frequency. As a result, we find lobes that do not appear in the main gallery of optimized designs for each leg length. They result from incomplete cancellations that occur with a non-optimal combination of leg length and angle A. As well, the use of the relatively low terminating resistor value (600 Ohms) results in a set of SWR values that approximates those shown for the frequency sweep in Fig. 6 of Part 4.

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The ARRL rhombic design nevertheless shows itself to be a very competent performer over its 2:1 frequency range. It captures perhaps the key element in multi-band rhombics: optimize the design for the lowest anticipated frequency, accounting for both antenna height and anticipated leg length. As the frequency increases, the gain will rise, as indicated by 2 of the leg-length equations early in Part 4. According to those equations, peak gain would occur somewhere close to 15 meters. With a satisfactory terminating resistor, the antenna will perform quite well over a 2:1 frequency range. With a higher value than 600 Ohms, the SWR curve would smooth out more completely, if we use a reference impedance to match the termination (and hence a feedline with a higher characteristic impedance than 600 Ohms).

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The general procedure has exceptions. For example, the idea of optimizing the rhombic at the lowest frequency in the 2:1 requires careful selection of the value of angle A. If we increase the angle in order to raise the gain at the lowest frequency, we shall find that we have limited the operating frequency range upward. The gallery of azimuth patterns shows that, at 28 MHz, the innermost sidelobes are almost as strong as the main lobe. If we select a maximum gain value of angle A for 14 MHz, the 10-meter pattern will show 3 lobes, and the lobe that is on-axis with the array will no longer be the strongest. Such a condition defeats the main goal of creating a rhombic in the first place: the desire to achieve point-to-point communications on a heading in line with the two acute angles of the rhombus. If we reduce the value of angle A at 14 MHz, then the main lobe broadens with a loss of gain. For the selected height, the ARRL rhombic antenna selects a value of angle A at 14 MHz that yields roughly equal gain on both 20 and 10 meters, which is generally a good selection for amateur service. It also illustrates why much of the classical rhombic literature recommends no more than a 2:1 frequency range for the antenna, even though the range of acceptable matching is much wider.

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Multi-Wire Rhombics

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Perhaps the most common variation on the single-wire rhombic beam involves the use of multiple wires running from the feedpoint to the terminating resistor on each side of the centerline. The added wires join the level wire at both the feedpoint and the terminating resistor. However, they spread above and below the level wire at the widest points in the array. In general, the wires are the same length as the level wire, theoretically resulting in the wires being further offset from any support post toward the centerline. However, the amount of differential is a very small fraction of the total wire length along each leg, and allowing the spread wires to be slightly longer in order to align the supports will create no performance problems.

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In order to model the multi-wire rhombic, using 3 wires as a sample version, we must alter the means by which we create the antenna geometry. The left side of Fig. 3 shows the method used in Part 4. It consists of only 4 wires per rhombic, with a split source and a split load. At the source end, we simply place a source on each of the segments adjacent to the wire junction. Since they are in series, the feedpoint impedance is the sum of the source impedance values reported for each source. The split load simply creates a balance at the far end of the array by placing a load resistor on each of the wire segments adjacent to the junction. The overall terminating resistor value is simply the sum of the 2 load resistance values. To use a real example from the last episode, the 4 wavelength-leg version of the terminated rhombic used legs that are 4.00 wavelengths long. The distance from centerline to a side peak is 1.563 wavelengths, while the distance from the midline to either end junction is 3.682 wavelengths. The resulting angle A is 23.0 degrees, and the overall rhombic length is 7.364 wavelengths.

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The "pointy" ends of the model do not permit ready feeding for a multi-wire version of the antenna. Therefore, we must revise the modeling system to allow the wires to terminate together for a common feedpoint and for a common load resistor. The right side of Fig. 3 shows the general technique. We create a flat or blunt end at each rhombic point. To ensure that the source segment has adjacent segments of equal length on each side, we make the blunt end-wires 3 segments long. So that the wires will have segments as close as possible in length to the segments in the long side wires, the blunt end wires are 0.14 wavelength, based on the use of 20 segments per wavelength in the side wires. Now let's set the total length of the rhombic to 7.36 wavelengths, with a 3.68 wavelength distance from either end to the midline. The distance from the centerline to the peaks will be 1.56 wavelength. The angle (A) from the centerline to a peak will be 22.97 degrees. However, the overall wire length will not be exactly 4.0 wavelengths. Instead, the sloping portion of the side wire will be 3.97 wavelengths, added to half of the blunt end-wire (0.07 wavelength) for a total length of 4.04 wavelength. All figures are for rhombics 1 wavelength above average ground with lossless 0.16" wire at 3.5 MHz.

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I have recorded seemingly insignificant variations in models because these variations do create differences in the reported performance of the antennas. The following table explores the performance of the 4-wire "pointy" version of the antenna using various terminating resistor (RL) values.

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+Performance of a Pointy Single Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 600                 17.30           18.07               737 - j 40
+ 700                 17.28           23.13               793 - j 13
+ 800                 17.27           33.22               844 + j 14
+ 850 *               17.27           43.97               869 + j 27
+ 900                 17.28           32.75               892 + j 41
+1000                 17.29           24.29               936 + j 67
+1100                 17.30           20.40               977 + j 94
+1200                 17.32           17.94              1015 + j120
+
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We should note 2 special items in this table. First, the starred item represents the version of the antenna selected for inclusion in the larger table in Part 4. There are 2 reason for selecting this terminating resistor value. It does result in the highest front-to-back ratio, although this reason is secondary to another. Without becoming too finicky, the load resistor and the resistive component of the feedpoint impedance are most closely matched. With smaller values of terminating resistance, the resistive component of the feedpoint impedance is always higher than the load resistance. For all terminating resistors larger than the selected value, the feedpoint resistance is always lower than the terminating resistance. Since a terminated long-wire antenna operates in a similar manner to a transmission line, matching the load resistance to the feedpoint resistance results in the widest SWR bandwidth when referenced to the load resistance value. The required value does not change with changes in the leg length so long as the angle A is selected to align the lobes for maximum gain. However, it will change with even small departures from the ideal geometry. It will also change with the height of the antenna above ground and with the quality of the ground itself, since both of these factors will change the effective impedance of the antenna when viewed as a length of transmission line.

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Second, note the remnant inductive reactance in the feedpoint impedance. The reactance is inductive. One traditional reason for using multiple wires in the rhombic legs is that it introduces a compensating capacitive reactance due to interactions among the wires. A capacitive reactance represents--with respect to feedpoint impedance--a slight electrical shortening of the antenna circumference. Wire interaction is unnecessary to explain the electrical shortening of the overall rhombic loop. All closed loops of a preset total circumference become electrically shorter if we increase the wire diameter--exactly the opposite effect of fattening elements in open-ended elements. Since the 3-wire rhombics will have effectively a fatter element, even though variable in equivalent diameter along the leg lengths, the loop will become electrically shorter and thus show a more capacitive reactance at the feedpoint.

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The blunt-end version of the 4 wavelength-leg rhombic makes only one change among the factors that tend to affect the optimal value of load resistance: the geometry. The shape changes are very small overall, but they do have consequences, as shown in the following table that parallels the one for the pointy version of the same rhombic.

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+Performance of a Blunt Single Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 600                 17.40           15.26               806 + j121
+ 700                 17.37           18.48               857 + j 81
+ 800                 17.35           22.87               903 + j 41
+ 900                 17.35           30.23               945 + j  2
+ 975 *               17.35           38.04               973 - j 27
+1000                 17.35           35.88               982 - j 37
+1100                 17.36           26.68              1016 - j 74
+1200                 17.38           22.27              1046 - j110
+
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The closest match between the terminating resistor and the feedpoint resistance occurs with a value of about 975 Ohms. The difference between the 2 models of 125 Ohms may seem significant, but it is likely that construction variables would wash out the difference in terms of trying to determine which model better captures a physical rhombic with 4 wavelength legs at a height of 1 wavelength above average ground. As well, small changes in the segmentation per wavelength will also change the reported values somewhat. Note also that the progression of inductive to capacitive reactance is the reverse of the pointy geometry. Nevertheless, the pattern of the feedpoint resistance remains: below the optimal load resistance, the feedpoint resistance is higher than the load resistor and above the optimal load, the feedpoint resistance is less than the load resistance.

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The blunt-end version of the modeled 4 wavelength-leg rhombic will become the standard against which we measure 3-wire rhombics using the same leg length. However, modeling the 3-wire rhombic presents another modeling challenge of its own. Theoretically, the wires must join on each side of both the feedpoint wire and the load resistance wire. The relevant modeling sketch of this situation appears on the left in Fig. 4. There is a difficulty built into this scheme. Because the wires are not widely spaced relative to their length, the segments at the junction interpenetrate for a considerable distance along the segment length. Even though the level of inter-penetration may not reach a level that raises flags within NEC, it may still be sufficient to alter the performance reports of the array, since the inter-penetration does affect NEC's current calculations.

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To test the model, let's explore what happens as we pass the model through a number of loading resistor values. The side wire expansion is very modest, reaching only 0.0125 wavelength at the midline. That distance amounts at 3.5 MHz to about 1.06 m or 3.49', with an antenna that is over 630 m (2068') long. Like all of the models, the 0.16"-diameter wire is lossless and the wires are 1 wavelength above average ground.

+ 
+Performance of an Angled 3-Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 600                 18.92           16.76               795 + j335
+ 700                 18.92           18.57               834 + j319
+ 800                 18.92           19.64               870 + j305
+ 900 *               18.93           19.68               902 + j291
+1000                 18.94           18.96               933 + j278
+1100                 18.95           17.93               961 + j266
+1200                 18.96           16.87               987 + j255
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Although we are not yet positioned to evaluate the gain improvements, the impedance column should give us pause. The very large rise in inductive reactance relative to the blunt single-wire model exceeds what we might otherwise reasonably expect from adding 2 wires with fairly narrow spacing relative to the frequency. In addition, the indicated "ideal" termination resistor value (900 Ohms), does not coincide with long-standing empirical experience, which suggests a value closer to 600 Ohms.

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We may reformulate the model using some techniques that have proven useful with quad loops and similar structures. The right side of Fig. 4 outlines the techniques at each and of the antenna. At the feedpoint end, we prevent the wires from meeting, but bring them to a 0.001 wavelength spacing (about 86 mm or 3.4"). Next, we create a bridge wire for each loop. The source excitation goes to the center (level) wire on the middle segment of the bridge wire. From the corresponding segments on the upper and lower section, run 600-Ohm transmission lines to the source segment. The impedance is not critical, because the lines will be only 0.000001 wavelength long, a number that the modeler specifies in the transmission line entry. Hence, the three wires have a common source in parallel, while preventing the inter-penetration of any wires.

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The termination end of the beam uses the same modeling technique of bringing the wires close (0.001 wavelength) but not allowing them to touch. We cannot create a single parallel connection using the transmission line technique, because any load resistor would be in series with the line and hence outside it. Instead, we provide each bridge wire with a load resistance that is 3 times the desired terminating resistor value. If we run the same tests on the reformulated model, we obtain the results in the following table. Note that the actual terminating resistance values are 3 times the value in the table, but occur on 3 bridge wires.

+ 
+Performance of a Separated 3-Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Narrow (0.0125-Wavelength) Maximum Wire Separation
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 400                 18.60           17.14               586 + j 22
+ 500                 18.60           22.29               619 - j  4
+ 600                 18.60           31.34               648 - j 32
+ 650 *               18.61           36.44               662 - j 37
+ 700                 18.61           31.37               675 - j 42
+ 800                 18.63           24.01               695 - j 73
+ 900                 18.64           20.33               714 - j 95
+1000                 18.66           18.02               733 - j105
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The gain improvements over the single-wire model are more modest: about 1.3 dB. The rounded ideal load value comes very close to matching the feedpoint resistance and also corresponds to the highest 180-degree front-to-back ratio value. As expected, the capacitive reactance is slightly higher than for the blunt single-wire model, but only slightly so, since the average wire-diameter increase for the closed loop is not great as a function of a wavelength. Finally, the selected terminating load and feedpoint impedance tend to match reasonably with reported experience with these types of rhombic beams.

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Most amateur rhombics cover the upper HF spectrum, and the spacing used at these frequencies is 3' to 4'. Therefore it seems prudent to test our 3.5 MHz model with a wider spacing than the 0.0125 wavelength used in the initial model. Using the same loop separation techniques, I increased the spacing at the midline to 0.025 wavelength (about 2.1 m or 7'). All other modeling parameters remain constant. The results appear in the following table.

+ 
+Performance of a Separated 3-Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Medium (0.025-Wavelength) Maximum Wire Separation
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 400                 18.74           17.46               597 + j 26
+ 500                 18.74           22.45               629 + j 10
+ 600                 18.74           30.19               656 + j  7
+ 650 *               18.75           33.08               669 - j 11
+ 700                 18.75           30.20               682 - j 15
+ 800                 18.76           24.04               701 - j 55
+ 900                 18.78           20.56               721 - j 63
+1000                 18.79           18.30               739 - j 71
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As one might expect, by enlarging the average wire diameter by a significant amount, the gain reports increase by a very small but numerically noticeable amount. More telling is the array of front-to-back values. The peak value does not reach the level attained by the narrower 3-wire array, and that value, in turn, did not reach the peak value of the single wire blunt-end rhombic beam. However, the wider 3-wire array shows a smaller fall-off in front-to-back value as we vary the terminating load across the same range as used with the narrower 3-wire version. Compare values for this antenna with 600-Ohm and with 1000-Ohm loads with the corresponding values for te narrow 3-wire rhombic.

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The near-ideal load resistance remains unchanged at 650 Ohms or thereabouts. However, the capacitive reactance at that load value is not as great as with the narrow 3-wire rhombic. The important data on the reactance is not its value at the ideal load resistance so much as it is the total range of reactance across the total set of load resistors. The narrow 3-wire rhombic shows a range of 162 Ohms, while the medium spacing (twice the narrow spacing) reduces the range to 134 Ohms--for the same set of load values.

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Let's increase the maximum wire spacing at array midline one more time. We shall again double the spacing to 0.05 wavelength (about 4.3 m or 14.1'). All other parameters remain the same. Each outer leg is now about 0.0003 wavelength longer than the level center wire--about 1". With all other model parameters unchanged, we obtain the following table of modeled values.

+ 
+Performance of a Separated 3-Wire Rhombic with 4-Wavelength Legs and Various Terminating Resistors
+Wide (0.05-Wavelength) Maximum Wire Separation
+Terminating          Maximum         Front-Back         Feedpoint Z
+Resistor (Ohms)      Gain dBi        Ratio              R+/-jX Ohms
+ 400                 18.88           17.79               607 + j 59
+ 500                 18.88           22.46               638 + j 37
+ 600                 18.89           28.31               664 + j 23
+ 650 *               18.89           29.64               676 - j 10
+ 700                 18.90           28.16               686 - j 14
+ 800                 18.91           23.71               707 - j  9
+ 900                 18.92           20.62               724 - j 38
+1000                 18.93           18.50               738 - j 56
+
+

Once more, we find the small improvement in gain, which is now about 1.5-dB higher than the blunt single-wire array. The peak front-to-back ratio continues to diminish, but the values with a 400-Ohm and with a 1000-Ohm load are higher. The curve--as we might expect for increasing wire diameter--has less of a sharp peak and covers a broader range with higher values. Although I might have increased the ideal terminating resistor to 700 Ohms, continuing to use the 650-Ohm value allows us to see the other curve changes more easily. The reactance range has shrunk to 96 Ohms total. The anomalous value for the 800-Ohm terminating resistor is accurate to what NEC reports. It may be a function of secondary effects that the other tables do not show given the 100-Ohm increment in terminating resistor values.

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The use of 3-wires, whatever the spacing, does not change the essential elements of the rhombic pattern. Fig. 5 compares the patterns for the blunt single-wire model and for the widest 3-wire model in both separate patterns and with an overlay. The overlaid patterns show the comparative raw gain of each lobe. The separate pattern establishes that there is no essential change in the relative strength of the lobes. The only exception, of course, is the 180-degree lobe.

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Amateur lore on rhombic antennas suggests that the 3-wire design may be capable of a smoother SWR curve across a broad passband than a single wire model. That lore tends to neglect the need to match the terminating resistor to the feedpoint impedance--and that impedance to the characteristic impedance of the feedline. To test this way of looking at the impedance question, I ran each of the 4 main blunt models through an SWR sweep from the design frequency to twice that frequency (3.5 to 7.0 MHz). The single-wire blunt model used a 975-Ohm SWR reference impedance, while the 3 3-wire models used a 650-Ohm reference impedance. The result appear in Fig. 6.

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In practical terms, we have no way to make a selection among the antenna models. All 4 curves remain below 1.2:1 relative to their reference impedances across the entire range. Any device capable of broadband impedance transformation at the desired ratio would operate under very low-loss conditions. The exercise, however, does show one interesting fact: none of the 3-wire models improves upon the blunt single-wire model SWR curve. The only advantage shared by the 3-wire models is that they may better use a commercial 600-Ohm parallel transmission line than the single-wire model. However, a 975-Ohm line requires more patience than skill to fabricate in one's own shop.

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The 3-wire rhombic, then, has 3 advantages over a single-wire rhombic. First, the gain improvement is real, but might not be sufficient to be noticeable in practice. Second, from a practical perspective, the ideal conditions for a 3-wire rhombic--at least one that is 1 wavelength above average soil--yield a terminating resistor and feedpoint impedance that more nearly coincides with off-the-shelf components. (Note: this result applies only to the subject antenna and requires verification for any variation in height and soil condition.) Third, the "fat-wire" effect of using wider spacing gradually widens the operating curves of some operating parameters.

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Besides mechanical complexity, the 3-wire rhombics have only one almost insignificant down side. The front-to-sidelobe ratio shows a very small but steady decline as we increase the effective wire diameter. Between the blunt single-wire model and the widest 3-wire model, the decline is only about 0.2 dB. However, it appears to be a real phenomenon and runs counter to the design goals of many rhombic designers. The design goal of reducing rhombic sidelobes leads us to the third of our bits of unfinished business.

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Multi-Element Rhombics

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Rhombic development persisted long after its primary period of HF service in the 1930s and 1940s. With the advent of commercial broadcast VHF television in the 1950s, followed by UHF television in the 1960s, engineers searched for wide-band antennas with high gain to satisfy consumer needs in fringe reception areas. In this period, Laport published his work on the adaptation of the rhombic for this and other services. The sidelobes for a single rhombic with an overall length of about 5 wavelengths were down less than 10 dB, a situation that made the antenna susceptible to multi-path ghosting and other forms of interference. Laport's solution to the problem was to develop a dual rhombic antenna with offset axes.

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Laport's dial offset rhombic is a variant of the basic idea of using two rhombics of different sizes, each with its own terminating resistor. Only certain combinations of rhombics are eligible for such use. The main criteria is that the sidelobes of one size align closely with the side nulls of the other. The result is a significant decrease in the net sidelobe strength. The combination of a rhombic with 3.5 wavelength legs and one with 6 wavelength legs provides a prime candidate for dual rhombic service. We can shorten the overall length of the combination by combining one leg from each rhombic on each side of a pair of rhomboids. The dual offset rhombic offered higher gain and greater sidelobe suppression. Fig. 7 shows both the general outline and the critical dimensions.

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The lower half of the sketch shows the dimensions needed. If we set L1 at 3.5 wavelengths and L2 at 6.0 wavelengths, then angle A becomes 26.1 degrees and angle B is 18.85 degrees. Simple trig relations yield the physical dimensions, including the amount of offset of the far junction from the array centerline (c). To compare the dual rhombic with a single rhombic I scaled my early VHF model down to our test frequency (3.5 MHz) and set it 1 wavelength above average ground. Since the 0.16" wire diameter is much thinner at 3.5 MHz than AWG #12 is at 100 MHz, I set the spacing between wires at 0.08 wavelength and used 900-Ohm terminating resistors in each rhombic in the pair. Even so, the front-to-back ratio is only good, but not optimal. However, the combination of spacing and the terminating resistor values are adjustable in the design to improve these figures without affecting the forward gain or the sidelobe suppression.

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The best single rhombic for comparison with the dual version is the model using 5 wavelength legs. It is only slightly longer overall (9.4 wavelengths vs. 8.95 wavelengths for the dual rhombic). The following table presents some of the basic performance data.

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+A Preliminary Comparison of Equal Length Single and Dual Rhombics
+Antenna     Leg Length   Elevation  Max. Gain   Front-Back   Beamwidth   Feedpoint Z
+            WL           Angle deg  dBi         Ratio dB     degrees     R +/- jX Ohms
+Single      5            13         17.97       44.71        12.8        867 + j23
+Dual        3.5/6.0      12         19.82       25.03        12.2        447 + j 9
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The feedpoint impedance is the parallel combination of the impedances of the individual offset rhombics in the pair. At VHF and UHF, where the wire is proportionately thicker as a function of a wavelength, dual rhombics would normally use lower values for the terminating resistors and have feedpoint impedances closer to 300 Ohms. The table shows that the dual rhombic has a 2-dB gain advantage over the single rhombic. However, the benefit of the dual design is less the added gain than the sidelobe suppression. Fig. 8 provides elevation and azimuth patterns for the 2 antennas. It also overlays the two azimuth patterns for a more direct comparison of relative sidelobe strength.

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The dual rhombic's strongest sidelobe is about 5-dB weaker than the strongest sidelobe of the single rhombic. We can add 2-dB to that figure when considering the sidelobe strength relative to the strength of the main forward lobe. The sidelobe strength has diminished to a level that equals the sidelobe strength of many (but not all) long-boom Yagi designs with approximately the same forward gain and front-to-back ratio values. For a further discussion of dual rhombics in VHF and UHF service, see Modeling the Dual Rhomboid: Parts 1-3 at my web site.

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Conclusion to the Series

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The study of long-wire antennas--both terminated and unterminated--is far from complete in these note. There are numerous theoretical directions one can take to intensify one's understanding of the relationship of these antennas to fundamental mathematical concepts governing all antennas. Likewise, both historical practical applications and future possibilities leave much room for exploration, in terms of both available literature and physical experimentation. (I am, for example, unaware of any experiments using dual rhombics in the GHz range, with both rhomboids using copper strips bound to separate sides of a substrate.)

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Neverthess, this series of notes has reached its end. Beginning with all-too-often overlooked fundamentals, we explored the basics of lobe formation on both center-fed and end-fed wires ranging from 1 to 11 wavelengths. The galleries of elevation and azimuth patterns should provide a handy reference. At the same time, we looked at the modeling issues and variables involved in portraying long-wire antennas, including changes of ground quality, changes of wire and material, and changes of height. We also saw that as we lengthen a long-wire, the elevation angle of maximum radiation gradually decreased below the traditionally calculated value. We next explored antennas that add a terminating resistor between the far end of the long-wire and ground. These end-fed terminated or traveling-wave antennas formed the simplest fixed beams, although the use of such a resistor reduced the available forward gain relative to unterminated wires of the same length. The terminating resistor largely--but not completely--controls the feedpoint impedance of the antenna, allowing the use of a terminated long-wire beam over 2 or more octaves of frequency change.

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The unterminated single long-wire antennas provided us with a critical piece of information in the development of more complex long-wire arrays. The maximum gain for any long-wire antenna does not coincide with the wire end itself, but occurs at an angle that varies with the wire length. V and rhombic arrays depend on this angle to align a major lobe from each individual wire so that the lobes add to increase array gain. Long-wire V antennas are usable in both unterminated and terminated forms. In both cases, the gain is considerably higher than for a single long-wire antenna, and the strongest lobe is in line with the wire. However, the higher gain comes at the expense of beamwidth, as the main lobe becomes very narrow at longer wire lengths. Once more, the terminated V-beam has somewhat less gain than the more bi-directional unterminated V array, but the termination provides considerable bandwidth. The limiting factor for bandwidth is that the leg length changes when measured in wavelengths as the operating frequency changes. As a result, the wire angle no longer is correct for aligning the lobes from the individual wires and the pattern breaks down.

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The rhombic is perhaps the largest and most refined of the long-wire antennas, consisting of two Vs, open-end to open-end. The result is 4 wires contributing aligned lobes for higher gain and narrower beamwidth. Although the rhombic suppresses unwanted sidelobes better than the V antenna, significant sidelobes remain. The effort to further suppress the sidelobes has resulted in the development of more complex rhombic designs using multiple rhombic elements offset from each other. Although the unterminated rhombic is usable and has more gain than the terminated version, the gain differential is less than for other types of long-wire antennas. If we optimally design a terminated rhombic--by reference to the correct wire angle relative to the antenna height and leg length--we may obtain at least a 2:1 frequency ratio of high performance at a nearly constant feedpoint impedance.

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Although the facts about long-wire antennas are readily available from a variety of sources, these notes have used antenna modeling software as an alternative technique in determining the correct wire angle for maximum antenna performance for any given height and leg length. Starting with the unterminated end-fed long-wire, we can determine the lobe angle and use this information in designing both V and rhombic antennas that use the same wire length for their legs. Although the models used to provide basic comparisons within each antenna type and among types employed a set height (1 wavelength) and lossless wire of a suitable size for the test frequency, modeling software, such as NEC, allows one to vary these elements and rapidly optimize a complete design. Allied to these basic design techniques are methods of placing sources (the feedpoint) and loads (the terminating resistor) to produce accurate calculations without disturbing the basic geometry of the antenna. As the antennas grew more complex, the modeling issues became more significant, although they grew in a stepped fashion with the step-wise increase in the complexity of long-wire antenna geometry.

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Long-wire technology dates back to the earliest attempts to control antenna radiation patterns and to obtain gain beyond the levels of single wires. However, the techniques may still have application today and tomorrow. At the same time, modeling design methods can shorten at least some of the calculation time needed to produce a workable long-wire antenna, whatever the type. Our trek through long-wire technology ends here, but the antennas themselves may still have far to go.

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Updated 10-01-2006. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for Sep, 2006. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: HF Multi Band, Longwire, Rhombic


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The M3KXZ 2-Element Vertical Phased Array

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L. B. Cebik, W4RNL

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In July, 2006, Pete Millis, M3KXZ, published to the internet an array of 2 vertical antennas that he calls "'No-counterpoise' antenna: 2-element phased array." You can find his article at www.outsideshack.com/no_counterpoise_phased_array.pdf (web.archive.org). The latest incarnation follows a 1-element version of the antenna.

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The antenna is interesting in several respects. First, it uses a very simple structure and common materials that you can obtain from Radio Shack and hardware sources. Pete uses speaker wire and PVC supports for the vertical elements. Perhaps the only specialized antenna items are the baluns that he winds on ferrite cores and the encased 4:1 balun he uses at the center of the 2-element version of his array. However, we shall have occasion to evaluate the need for these items as we look into the antenna.

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The second significant aspect of the antenna is its performance. A single element length covers a spread of bands, for example, 20 meters to 6 meters using a total length of 25'. The normal limit for either a 1/4 wavelength monopole or a 1/2 wavelength dipole is about 2.5:1, which would suggest a cut-off of about 35-36 MHz, if the original antenna is cut for 14 MHz. Once a monopole exceeds about 5/8 wavelength or a dipole exceeds 1-1/4 wavelengths, the main radiation is no longer broadside to the wire. For a vertical antenna, the long lengths result in very high angle radiation, rather than the low angle radiation that we normally need. However, the M3KXZ antenna and array yield very usable patterns from 20 through 6 meters. In addition, the gain of the antenna is close to the gain available from either vertical dipole/doublets or from elevated monopoles with radials on all bands.

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For these reasons, it seems that the antenna in both its 1-element and 2-element versions deserves a closer look, if only to understand its operation better. As well, if one wanted to replicate his antenna using different materials, we shall need to look at some of the pieces in his arrangement.

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A Frame of Reference

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As a basic for evaluating the behavior and performance of the M3KXZ antenna and array, let's first catalog comparable data for a more familiar antenna, the straight vertical wire element. Since we shall look at the 20-6-meter version of the M3KXZ antenna, we may cut the wire for 20 meters. We shall use AWG #12 copper wire and place the lower end 1' above the ground, the height that we shall use for the other elements. However, a straight wire that is vertical requires a top height of 34.6'. For our basic work, we shall use average ground as the soil throughout.

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We have 3 choices for feeding our vertical wire. We might select the center, which would be natural for a 1/2 wavelength dipole. Of course, the wire becomes a doublet as the length grows longer than 1/2 wavelength and the current peak and voltage minimum no longer occur at the center of its length. Alternatively, we might select a feedpoint based on the M3KXZ design, that is, a position 2/3 of the distance down from the antenna top, considering the 12.5' fold back in the M3KXZ design as the lower 1/3 of the antenna. Finally, we might place the feedpoint at the lower end of the antenna.

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Table 1 summaries some of the key performance data for each of the three versions of the vertical wire at the center of all amateur bands from 20 through 6 meters.

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As we would expect, the feedpoint impedance values (Feed R and Feed X) differ widely among the antenna versions. More significant for eventual comparative purposes is the performance of each version. None of the three can sustain a low elevation angle for the main radiation lobe across the range of bands covered by the survey. Moreover, we find differences within each band depending on the feedpoint position, and the differences involve more than small changes in the maximum gain. For an example, we may use 24.94 MHz. The center-fed version produces a main lobe at 13 degrees elevation. The off-center-fed version's main lobe is at 40 degrees, while the end or bottom-fed version main lobe is at 39 degrees elevation.

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The radiation pattern differences result from differences in the current magnitude distribution along the wire on this band--and on any other band where the wire is longer than 1/2 wavelength. Fig. 1 shows the differences that occur on 12 meters. Most evident is that the current minimum occurs ever lower on the structure as we move from center feeding to bottom-end feeding. As well, but to a lesser degree, the differences in the current curve between the off-center-fed and the end-fed version play a role in the ultimate shape and strength of the pattern lobes for the vertical wire.

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Only the center-fed version of the straight wire doublet manages to cover 20 through 10 meters with the man lobe at a low elevation angle. The other versions give way to having their main lobes at higher and generally undesired elevation angles well under 10 meters. Despite our interest in the radiation patterns, we shall also discover that the impedance columns of Table 1 will hold importance as we attempt to see what lies behind the behavior of the M3KXZ antenna.

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Some M3KXZ Antenna Basics

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The full 2-element array appears in Fig. 2 in outline form. I have selected the 20-6-meter version for a detailed look. A single-element version of the antenna would simply omit the second element and the two phase-lines marked TL1 and TL2.

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In modeling the antenna, I departed from the original, which uses speaker wire. To yield adequate models, I spaced the AWG #12 copper wires 1" apart in the lower half. Parallel wires at this separation have a transmission-line impedance of about 400-450 Ohms. Although I have seen no tests of insulated speaker wires, the characteristic impedance of a pair is likely to fall into the 75-100-Ohm range, due to both the spacing and the relative permittivity (dielectric constant) of the insulation between them. In addition, Pete twines the wire along a length of PVC for support, but without introducing any significant inductance. Although we can view his elements as essentially straight, we should understand at the outset that all models will be only approximations of his antenna.

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We should also enter a modeling caution to those who may wish to replicate the models used in this study. The separation between the long and the short sections of the element is 1". Although one would normally use 1" segment lengths for the remainder of the model, there is a different overriding consideration. Very closely spaced wires in NEC are subject to errors, even when we precisely align the segment junctions. In order to obtain a fair set of comparisons between the M3KXZ element and the straight wire element, it is necessary to adjust the segmentation to obtain an average gain test (AGT) score that is as close to 1.00 as may be feasible. For the models used here, 120 segments in the long section and 60 segments in the short section produced an AGT score of 1.004, indicating that gain and impedance values will be very much on a par with those drawn from the straight wire element with its essentially perfect AGT score. AGT values below near-perfect will yield low gain and high impedance reports, while AGT scores above near perfect will yield values that are too high for the gain and too low for the impedance. For very closely spaced wires, the segmentation density alone is enough to yield gain values up to 1.5 dB off the mark. Hence, close attention of the model's AGT score is essential, especially when comparing the performance of models have different geometries.

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Before we turn to the full phased array, let's see what we might obtain from a single M3KXZ element. Table 2 lists the NEC-4 reports from the model, which places the 25' element at a height of 1' above ground. I placed the antenna over a range of soils from very good to very poor in order to determine if the soil quality had a significant bearing on performance, given the close proximity of ground to the lower end of the element.

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If we examine the gain and TO angle columns of Table 2 under average soil, we discover that on all bands through 10 meters, the M3KXZ element yields competitive gain values and TO angles that are only slightly worse than those we gather from the center-fed straight wire. The M3KXZ element TO values are slightly higher largely because the top height is about 30% lower than the top height of the center-fed doublet. Nonetheless, all of the TO angles shown in the table are suitably low, although they do vary with the ground quality.

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There is an incidental but interesting pattern to note. We normally think of ground losses as increasing as soil quality decreases so that as we move toward bad soils, the gain of a vertical element decreases. However, this thinking has a frequency limit. The old thinking applies in small amounts from 20 through 15 meters. However, on 12 meters, maximum gain occurs over average soil. Above 12 meters, maximum gain occurs over very poor soil. The trend reversal is accompanied by a shrinkage in the differential in gain as we change soil, but the reversal is quite real.

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Soil quality changes do not make a large difference in the feedpoint impedance at the antenna base, where the short and the long wires meet. However, the range of feedpoint impedances is considerable. Hence, the use of a coaxial cable between the antenna base and the antenna tuner may prove a considerable loss source unless the length is very short. With the possible exception of 10 meters, all of the impedances fall within the easily matched range of a remote antenna tuner place at the element feedpoint. Otherwise, the use of parallel feedline--suitably elevated from the ground to prevent unwanted coupling--may be necessary. However, the very low impedance on 20 meters may incur some losses even with parallel feedlines.

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Fig. 3 provides a gallery of elevation and azimuth patterns for the bands covered by the array. Although the azimuth patterns all appear to be quite circular, note the shifting angle of the line that indicates the bearing of maximum gain. Any antenna with a fold-back--including the well-known J-pole--will exhibit at least a slight pattern distortion due to radiation from the two wires in the fold-back region. The closer that we space the wires, the less will be the distortion, and with the 1" spacing, the differential is never more than about 0.03 dB. However, as the shifting line bearings show, the distortion will change a bit from one band to the next. The fact is not operationally significant, but will prompt some further investigation.

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The elevation patterns reveal one of the most essential aspects of the antenna's performance, the well-behaved radiation at low angles with very little higher-angle radiation until we reach 52 MHz. At the upper limit of the operating spectrum, the second elevation lobe nearly equals the gain of the lower lobe over average ground, and over very good soil, the second lobe at an angle of 50 degrees is actually stronger. However, the low-angle gain remains serviceable. For comparison, a straight vertical dipole fed 1/3rd of the way up its length shows a considerable upper-angle lobe on 15 meters, and at 12 and 10 meters, the higher second lobe dominates the pattern.

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The well-behaved patterns are one of the effects of the 12.5' fold-back. That fold-back is not just a convenient way of feeding the antenna at a point 1/3 of its total length (25' plus 12.5'). For example, if we feed a 20-meter vertical dipole at the 1/3rd point, we obtain resistance values ranging from 100 to 3100 Ohms, and reactance values from -600 to +700 Ohms. The values shown in Table 2 are far tamer than they are for an off-center-fed straight dipole--or for any of the other versions of the straight-wire element in Table 1.

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In fact, the fold-back forms a transmission line section that is 12.5' long. Whatever impedance appears at the junction of the single-wire top section and the beginning of the double-wire section undergoes a transformation according to the electrical length of the double section and its characteristic impedance. Note once more that modeling requirements have dictated a 1" spacing, and that the characteristic impedance is not the same as it would be for the speaker wire. Hence, the impedance numbers in Table 2 are only representative. As well, they do not account for the transmission-line velocity factor of the insulated speaker wires used in the original.

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Fig. 4 presents a collection of current magnitude distribution graphs taken from the EZNEC models. At the far right, I have expanded the 20-meter graph in order to show that the current magnitude undergoes a small but noticeable shift at the point where the top single wire meets the double-wire section. The jog indicates that below the junction, the graph is showing a combination of both radiation and transmission-line currents.

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The remainder of the current magnitude graphs show that we should not try to apply a simplistic J-pole or end-fed Zepp model to the situation. As the patterns show, the junction between the top and bottom sections does not occur at a maximum voltage, minimum current point on any band. As well, the double-line length is not 1/4 wavelength on any band, although it comes close on 10 meters. Therefore, the impedance transformation differs for each band in terms of both the impedance at the section junction and the amount of transformation that occurs in the lower section. One might use a number of means to roughly calculate the start and end values for the transformation, but given the higher characteristic impedance in the model relative to the speaker wire used in the original, such an exercise might prove to be operationally useless. For any given installation, the most practical effort is to measure the impedance at the feedpoint for every planned frequency of operation.

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One consequence of the lower double-wire or transmission-line section is that the dominant radiation currents do not follow the patterns that they would in a straight dipole/doublet, whatever the feedpoint. Hence, M3KXZ has found essentially an antenna designer's grail or silver bullet: an arrangement of wires that extends the range of desirable pattern formation beyond its normal limits while sustaining good gain for an antenna of its type and leaving quite workable feedpoint impedance values.

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The 2-Element M3KXZ Phased Array

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The 2-element version of the M3KXZ antenna, shown in Fig. 2, consists of 2 elements connected by equal lengths of a transmission line, with a common junction for connection to the main feedline. For the 25' version of the antenna, intended to cover 20 through 6 meters, the spacing between elements is 10'. The spacing is not accidental, since at 52 MHz, it represent about 0.53 wavelength, the maximum that we would wish to space phase-fed elements.

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Since we shall ultimately feed the antenna at a center point between the two elements, we have two choices of phasing. We may connect the two lines so that each long-section wire goes to the same side of the junction for in-phase feeding. Alternatively, we may give one (and only one) of the two lines a half twist so that connections to long-section wires go to opposite junction points and thus end up with out-of-phase feeding. The original design used plugs and jacks at the center junction box to allow a quick reversal of the junction connections. A remote switch might achieve the same goal with control transferred to the equipment location. Fig. 5 shows the differences in the current distribution curves that result from the alternative feedpoint connections.

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In-phase feeding of the two elements results in a broadside azimuth pattern relative to the plane of the two elements, comparable to the patterns that we obtain from converting a lazy-H into a standing-H. The gain yielded by the pattern over the gain of a single element is a function of the narrowing beamwidth in the plane of the array. The elevation pattern is not materially affected by the dual feed. How much gain increase and beamwidth reduction we obtain is a function of the spacing between the elements measured in wavelengths at the frequency of operation. Gain increases slowly from virtually single-element performance at very close spacing to maximum with a spacing that is just over 0.5 wavelength. With an exact 0.5 wavelength spacing, the azimuth pattern is a perfect figure-8. Gain continues to increase with slightly wider spacing, but small sidelobes develop in the plane of the elements. Above about 0.55 wavelength spacing, the sidelobes grow so fast that the gain broadside to the antenna decreases.

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Fig. 6 provides a gallery of elevation and azimuth patterns for the model of the 25' M3KXZ array with the 10' spacing between elements. Note that the elevation patterns, taken broadside to the plane of the two elements, do not differ significantly from the single-element elevation patterns. The azimuth patterns do not show relative gain values. Instead, each pattern uses the outer ring as the pattern limit to reveal more clearly the pattern shapes. If we look at the azimuth pattern for 52 MHz, we can see the beginnings of the sidelobes that develop as a result of the 0.53 wavelength spacing between elements. However, at lower frequencies, the spacing between elements is considerably less than the 0.5 wavelength ideal. As a results, as we move down in frequency, the patterns become more circular, indicating both broader beamwidth values and lower gain values. At 20 meters, where the spacing is only about 0.14 wavelength, we should expect--and we obtain--very little gain increase over a single element.

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Table 3 provides 2 sets of performance values, both sets taken over average ground. The left-most columns give the modeled gain and TO angle for the patterns in Fig. 6. You may compare these values to the values obtain for a single M3KXZ elements over average ground in Table 2. At 20 meters, the gain advantage only about 0.6 dB due to the close spacing of the in-phase-fed elements. At 10 meters, the gain advantage of the 2-element array increases to about 1.9 dB as the spacing increases to nearly 0.3 wavelength. At the more nearly ideal spacing on 6 meters, the gain advantage jumps to about 4.4 dB, with a commensurate decrease in the beamwidth of the two broadside lobes.

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The table's center columns provide modeled values for the performance of the array when fed out-of-phase by giving one of the two equal-length lines a single half-twist. The method of feeding is a simple evolution from the W8JK array that we usually see in horizontal form. The same principles apply. The antenna becomes a bi-directional endfire array with the main radiation in the plane of the elements. Fig. 7 provides a gallery of elevation and azimuth patterns as they apply to out-of-phase feeding of the two elements with their 10' spacing. The elevation patterns are taken in the plane of the elements.

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Except for the 52-MHz plot, the azimuth patterns all show comparable beamwidths. If we compare the out-of-phase gain values to the in-phase values, we find a sudden jump and a leveling off, so that we show only a slow rise in gain as we increase the operating frequency. The behavior of an end-fire out-of-phase fed array differs considerably from the in-phase-fed version. Two general rules apply. First, the closer the element spacing, the higher the gain will be over a single element. This trend gives precedence to 20 and 17 meters, where element spacing is closest. Second, the gain advantage increases as we increase the element length relative to an initial length. This trend gives precedence to the higher frequencies, where the M3KXZ elements are electrically longer. The broadening of the beamwidth at 52 MHz suggests that at higher frequencies (and therefore longer element electrical lengths), the pattern will break into 4 lobes, ruining the bi-directional characteristic of the antenna with out-of-phase feeding. The net result of combining the two trends is a much tighter grouping of gain figures for the out-of-phase version relative to the broadside in-phase version of the array.

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The purpose of switching the phase of feeding is to obtain maximum possible gain from two fixed vertical elements in the direction of the signal. An in-phase/out-of-phase switch at the junction of the two lines marked TL1 and TL2 in Fig. 2 provides a means of switching the axes of the bi-directional beaming. The beamwidths of the lobes in each version are complementary so that little or none of the horizon is excluded from performance equal to or better than the omni-directional patterns of a single element. Of course, in the 2-element phased version of the M3KXZ array, the elevation patterns retain their low TO angles.

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Thus far, the M3KXZ array displays considerable ingenuity in providing low-angle vertically polarized radiation over a wide passband. However, the array faces one final challenge: feeding the system and matching the junction impedance for either phase condition to the equipment. Here, we can use the modeled elements only with great caution. M3KXZ constructed his entire system with speaker wire, an inexpensive but dubious choice for outdoor durability. Speaker wires generally carry no rating for performance under the summer-to-winter weather extremes, and so the quality of such wires will vary from one maker to another, depending upon the quality of the insulation. In addition, such wires carry no rating for their characteristic impedance at RF frequencies. However, similar wires with standard "poly-plastic" insulations usually show an impedance in the 75- to 100-Ohm range. Due to modeling limitations, we have had to use a lower or double-wire section composed of bare wires 1" apart, for a characteristic impedance in the 400- to 450-Ohm range. Therefore, the impedance transformation that occurs in this section from the junction with the single-wire upper section and the end feedpoint will differ from the transformation obtained in the original version.

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Adding phase lines to a central junction is another matter. We may sample a variety of lines, that is, a range of characteristic impedance values, by using the TL facility within NEC. The line impedance will not change the antenna radiation pattern, but it will change the impedance that we obtain at the junction of the two lines under each of the phasing conditions. In creating a survey of values, I have simply used a velocity factor of 1.0 for two reasons. First, the element feedpoint impedance values are already off their marks if we use a double-wire section with a difference characteristic impedance. Second, common feedlines tend to come in several versions, each with a specific velocity factor.

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Nevertheless, we can obtain a view of the type and size of the feedpoint impedance challenge using two 5' lengths of transmission line to a central junction. For the survey, I selected characteristic impedance values of 50, 75, 125, and 300 Ohms. The 50-Ohm value is for the most common variety of coaxial cable. 125-Ohms is the value for RG-63, a very useful but often overlooked cable. 75-Ohm covers both some common coaxial cables and so-called twisted pairs of insulated wires. 300 Ohms, of course, applies to common TV-type parallel feedline. Table 4 provides the results of the survey, where R and X are the impedance components at the junction of the two cables (TL1 and TL2) under each phasing condition.

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The number of cases in which we obtain very low impedances, regardless of the characteristic impedance values for the phasing lines, raises a strong question about using a 4:1 balun at the junction of the two lines. Converting an impedance that is already well below 50 Ohms down to an even lower values seems to make little sense, especially if one uses the 50-Ohm main feedline shown in the originator's sketches. 4:1 baluns come in numerous designs, some of which may prove to suffer losses when used with high reactive components or when used outside the range of their winding's characteristic impedance. The result may be artificially favorable impedance values at the terminals that may disguise what is actually occurring within the device. There are few values in Table 4 that would benefit from even an accurate 4:1 downward impedance transformation.

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In addition, the author uses 1:1 baluns supposedly to force equal currents on to the short and long sections. Actually, the current imbalance on each side of the feedpoint is part of what allows the array to achieve its broadband characteristics. A balun or choke might be more applicable at each element feedpoint if TL1 and TL2 are both coaxial cables, where transmission-line currents are inside the cable between the center conductor and the inner side of the braid, and common-mode currents are on the outside of the braid. Indeed, parallel transmission lines may not be the most ideal phase lines for the array.

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The author also correctly notes that he obtains good impedance matches between whatever impedance the array presents at the junction--after transformation down the 50-Ohm main feedline--via his antenna tuner. We shall bypass any losses incurred by the impedance mis-match between the cable's impedance and the load impedance at the phase-line junction. The low-impedance loads, if transferred to a tuner, present challenges of their own.

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Depending upon the type of network used, low-impedance loads sometimes result in acceptable but imperfect impedance matches, where the best obtainable SWR value at the tuner is perhaps 1.3:1 to 1.6:1. These conditions generally indicate a limit to the range of the components within the tuner relative to the impedance at the terminals. In the table, note that many modeled values show much higher reactive components than resistive components. Although the match is acceptable, the efficiency of power transfer may not be as high as we too often presume. If the network has a low loaded or operating Q (Terman's "delta" term from the 1940s), we may find a difference in the settings required for resonance (that is, for zero reactance), for maximum power transfer, and for impedance matching. As the circuit's delta increases to about 10, these settings resolve to a single point. However, so long as tuners continue to lack any form of relative output indicator, we cannot easily tell if the impedance match that we obtain is also the point of maximum efficiency.

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The junction of the two phasing lines is a balanced feedpoint. Ideally, the array might be fed at that feedpoint by a remote, balanced, weatherproof ATU with a very wide range of impedance matching capabilities. Such tuners are not generally available, although we can press existing components into service. In general, placing the tuner at the balanced feedpoint that joins the two phase-lines allows the use of a 50-Ohm cable to the equipment with minimum loss. At the input to the tuner we likely should install a common-mode current attenuator, such as an unun or a ferrite bead choke. System ground should occur at the equipment side of the unun or the choke, not either at the tuner output or at the tuner input. (The tuner input is likely to have a common ground system with the output, and we would want the tuner to "float." Grounding the braid of the coax at the equipment side of a ferrite bead choke would provide for static discharge.)

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Conclusion

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The M3KXZ antenna and array constitute an ingenious arrangement of element parts that achieves low-angle vertically polarized radiation over an extended operating bandwidth that common configurations cannot match. The 2-element version of the array offers some gain and pattern shaping for bi-directional operating. Even with improved materials designed for both RF service and durability through seasonal weather cycles, the antennas are inexpensive. Moreover, they a relatively short for a given frequency range, adding to their neighborhood acceptability.

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The challenges presented by the antenna and the array revolve around the matching and the feed system. Increased attention to these details may result in a very serviceable, wide-band vertical array.

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Updated 06-16-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: HF Upper, Phased Array, Vertical


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Some Notes on NVIS Antennas

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L. B. Cebik, W4RNL

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About a decade ago, I placed some casual notes on NVIS antennas under the present title, using the term "cloud burner" as it was once used to describe these antennas. The intervening years have produced two important developments. One has been the emerging realization that near-vertical incidence skywave (NVIS) propagation has a very significant role to play in emergency communications, especially for major natural disasters that eliminate most of the up-to-date communications modes. Amateur operations following a pair of major hurricanes in the U.S. gulf coast region demonstrated the importance of this communications mode, a fact that the U.S. and other military organizations had begun to realize as early as in World War II.

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The second development is personal. Over the decade since the early notes, I have accumulated a considerable body of modeling data born of my interest in seeing how much of NVIS antenna talk was correct and how much was in need of correction. The original notes that filled this space did not so much require amendment as they needed very serious supplementation. The additional material consists partly of more thorough investigations into the radiation properties of NVIS antennas for 75 and 40 meters, the two most popular amateur bands for NVIS operation. Mythologies and sound bites concerning the ideal height for a NVIS antenna required not a single replacement value, but an exploration of ideal heights for various types of antennas over various ground qualities. Indeed, the role of ground quality has received scarce attention up until recently.

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At the bottom line relative to this site, the result has been the development of a series of notes on the fundamentals of NVIS antennas, with emphasis upon the most basic NVIS antenna types: the dipole, the inverted-V, and the 1 wavelength loop. Each collection of notes uses the PDF format. At present, the collection includes the following items.

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As the entries suggest, the list of possible topics is far from closed. However, I hope that the notes provide some useful data on NVIS antenna properties for anyone planning a fixed-station installation. These antennas have become a significant part of amateur contributions to emergency communications.

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Updated 03-15-1998, 01-12-1999, 03-15-1999, 11-05-2002, 02-20-2008, 02-23-2008. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Dipole, Doublet, HF Lower, Horizontal Loop, Inverted V, Moxon, NVIS, Traps, Yagi


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NVIS and ALE: Some Preliminary Studies

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L. B. Cebik, W4RNL

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In 2005, I conducted some preliminary analyses of antennas that are used and some antennas that might be used for combined NVIS-ALE work. Although the studies are far short of definitive--suggestive or indicative might be better terms for them--the papers might be useful to those traveling the same exploratory routes. Therefore, the entries below lead to three items in PDF format (for ease of transfer to the site).

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NVIS, of course, stands for Near Vertical Incidence Skywave. Often casually called cloud-burning, the idea is simple: to direct a radio signal upward and have it refracted/reflected downward for relative short-range communications in the upper MF and the lower HF region, where the ionosphere supports such operation. Although amateurs tend to focus on 80 and 40 meters for NVIS efforts, other communications services may use frequencies between 2 and about 10 MHz. The range depends as much on antenna design as it does on propagation. Hence, the antenna beamwidth upward is a major concern. As shown in other notes on NVIS-related subjects, the more gain provided by an array, the narrower the beamwidth becomes. Hence, the ideal NVIS antenna for a given need strikes a balance between appropriate gain and a beamwidth that allows coverage of the target area. For narrow-band antennas, such as those used by amateurs on 80 and 40 meters, any number of practical antennas exist, despite the tendency of many NVIS aficionados to use inadequate government surplus antennas. The antenna design problem becomes truly interesting when we add operating bandwidth to the equation. How can we cover 2 through 10 MHz with adequate NVIS patterns throughout the operating range?

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Now let's add in a second operating desire: ALE. ALE stands for Automatic Link Establishment and is the method developed over the last 10 years or so to improve HF communications and make it more usable by untrained operators. It has two main benefits: 1) it automatically selects the best frequency out of many, and 2) it takes advantage of short-term ionospheric conditions that can improve connectivity by as much as 20 dB with respect to conventional HF predictions.

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The ALE system begins with "sounding list" or "scan list" for a communications net. A receiver then operates in the scan mode, sequentially listening for a call on a list of perhaps 10 or 20 frequencies. The CPUs are can detect calls made to their particular address, or a general call can be sent to many receivers. If one or more signals are received at a desired station, the computer there performs a link quality analysis (LQA) by computing the relative "score" on each channel, usually bit error rate. The receiving station then answers on the channel with the highest LQA score. The initial station then acknowledges the link-up and begins to send the message. All this is done with push-to-talk techniques as usual, although some protocols are now available for automatic data transmissions. But most of the applications are for SSB Voice.

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ALE (originally called "adaptive HF") evolved to a second generation, which is now fielded throughout the military. A most interesting set of developments includes the expansion of ALE techniques to amateur radio operations and to various Homeland Security participants, such as the Civil Air Patrol. The FAA is also interested, especially in locations like Alaska, where downed aircraft needing location and rescue are common.

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Third-generation radios have very accurate frequency standards and may thus be synchronized, so the receiving station that may be in a covert situation need not engage in the LQA handshaking. In that case, the receiver simply answers on the best frequency, having performed it's own LQA, and the distant transmitter, having reverted to it's own scanning mode, receives the message, which is usually a short burst. Most of these radios work in the data mode, and send e-mail-like traffic.

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ALE places high demands on the radio equipment itself. However, successful ALE operations are equally dependent upon antennas that can support this mode. ALE places a high emphasis on NVIS techniques, since much of the communication is within a radius of 500 miles. Hence, there are needs for special antennas having a broad operating bandwidth and a very high radiation angle. Among the most popular field antennas are terminated folded dipoles and related antennas. Terminated antennas achieve the requisite broad SWR passband via the terminating resistance, but, of course, suffer considerable loss relative to a similar antenna with no termination. Among the unterminated antenna types available commercially are fan dipoles, vertically oriented LPDAs and vertically oriented LP loops. In general, the unterminated antenna types are far more complicated--and expensive--than the simpler terminated antennas.

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The combination of NVIS and ALE is presently defined by essentially military needs and resultant communications standards. It is not clear at the moment of writing whether these standards will or should apply to non-military work, such as emergency services. In some links, they make more sense; in others they make less. For example, transfer of a heavy emergency traffic load from a devastated hurricane site to a relatively near unaffected station might make good use of burst transmission technology with high frequency agility. However, if we are trying to communicate with a downed aircraft in the wilderness, a slower-paced form of ALE seems in order. As we reduce the pace of frequency sampling and selection, we gain the ability to perform many mechanical operations between hand-shaking trials, such as switching antennas or components in a matching circuit. The ability to work at a slower pace also opens many possibilities for antennas that may be more effective that the low-gain very-broadband terminated systems in present use.

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The following preliminary studies follow both lines of thought: single broadband antennas and collections of tuned antennas requiring switching of one sort or another. The field is wide open beyond these two more obvious paths, so these notes are simply a start along some lines of thought.

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Updated 03-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Multi Band, NVIS


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Horizontal Heights and Sound Bites
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L. B. Cebik, W4RNL

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All too often, we absorb information about antennas in the form of sound bites. The information is not necessarily false, but it is context-limited. However, the sound bite does not carry a trace of the context. Context, of course, tells us when we may accurately apply the information. Perhaps even more important, context tells us when not to apply the information. Misapplied information can lead us well astray of good antenna design and application.

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Let's focus on just one of those pesky sound bites. "For a horizontal antenna, ground losses for any soil quality are (insignificant) (immaterial) (irrelevant) [pick any one or more of the 3 options]." Curiously, I find such statements not only in amateur literature, but as well in commercial brochures of antennas designed for commercial or government services.

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My question is not whether the quasi-quoted statement is true. Rather, I want to ask when it is true, that is, under what conditions it is true--and to what degree.

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A Context for Making the Sample Statement True

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Perhaps the main arena in which the statement concerning ground losses and horizontal antennas may be true involves a dipole or similar antenna placed well above (say, 1 wavelength) ground. We can easily test the situation with almost any modeling software. Let's make a dipole from AWG #12 copper wire and place it exactly 1 wavelength above ground. The physical length will be about 0.48 wavelength to be resonant at the test frequency: 3.5 MHz.

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Next, let's systematically alter the ground quality, starting with a perfectly reflective ground. Then we can go to very good ground (conductivity 0.0303 S/m, permittivity 20) and proceed downward through average ground (conductivity 0.005 S/m, permittivity 13) and wind up at very poor ground (conductivity 0.001 S/m, permittivity 5).

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Table 1 shows us the results of our little survey in tabular form. From perfect ground to very poor ground, the total gain differential is only 0.65 dB. That difference does not make much of a difference. The table also lists the depth of the null above the lowest and strongest elevation lobe of the antenna pattern. As the gain decreases, so too does the depth of the null. Perhaps in numeric form that fact seems to make no great difference, so let's examine the elevation patterns for our surveyed ground types. In all cases, the antenna remains unchanged.

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Besides outlining the test case, the graphic shows why it is dangerous to present antenna patterns over perfect ground if the ground of actual use is not perfect. First, note the relative strength equality of the first and second lobes. Second, note the depth of the null between the first and second lobes. Third, note the absence of any radiation straight upward. Then, compare the pattern for perfect ground with the other three patterns for increasingly lossier ground.

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As the ground becomes lossier, the second lobe becomes weaker relative to the lower and stronger lobe. As well, the null between these two lobes becomes shallower. Finally, note that over real ground, there is almost always a component of radiation straight upward, a lobe or dome that grows stronger as the ground becomes lossier.

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Nevertheless, in most amateur installations, we are only interested in the lowest lobe, the one most likely to coincide in angle with the prevailing skip conditions. This first lobe carries the small gain differential that we noted from the tabulated data. As well, the TO angle or angle of maximum radiation does not change with changes in the ground quality. Now let's add in one final fact. Since the ground reflections that form the lobes of the antenna pattern occur numerous wavelengths away from the antenna, there is virtually nothing that most amateurs can do about the ground quality in the critical zone.

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We have noted a few minor differences created by ground quality for the performance of our horizontal antenna, but they are too small to make large arguments out of them. 0.65-dB is too small a gain differential for us to detect during operation of the horizontal dipole. Moreover, short of moving to a different part of the country, we can do virtually nothing about the ground conditions. So an a real sense, the quality of the ground beneath our horizontal dipole when it is 1 wavelength above ground is indeed a non-critical facet of antenna design, installation, and operation.

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A Case in Which Ground Quality Can Make a Difference to a Horizontal Antenna

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Suppose that we wish to operate in the Near Vertical Incidence Skywave (NVIS) mode for short-range communications. We can use our near-resonant dipole simply by lowering it to the height above ground that yields maximum gain straight up. Of course, the pattern will have a certain beamwidth both broadside to the wire and off the ends of the wire. So we shall not be restricted to talking to our next-door neighbor. Although most NVIS activity on our 80/75-meter band occurs in the SSB portion, we shall leave the test frequency at 3.5 MHz for consistency with the data on the antenna when it was 1 wavelength above ground.

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As we lower the antenna, 2 important questions come to mind. 1. At what height shall we place the antenna? 2. What performance can we expect from the antenna? The answer to both questions is the same: it all depends on the quality of the ground. As a test, I placed the antenna at a height of 0.185 wavelength (just about 52') above ground. I checked the maximum gain upward for perfect ground and for several lesser quality grounds. Next, I searched for the height (in 0.005 wavelength increments) at which the antenna yielded maximum gain. The results of the small investigation appear in Table 2.

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Each part of the table tells us something useful. With the antenna at a constant height, the quality of the ground alone created a nearly 3-dB differential in gain from the best to the worst tested. When signals may be very close to the threshold of being detected at all, 3 dB can make a significant performance difference. Second, the better the soil quality, the lower the antenna for maximum gain. Fig. 2 graphs the 2 gain curves--one for the constant height and one for optimized height. Only over salt water and perfect ground does the difference become at least visually significant. So for most situations, a height between 0.175 and 0.185 wavelength makes a good compromise. In practical measures at 3.5 MHz, that is 49' to 52' up.

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Fig. 3 overlays the elevation patterns for very good, average, and very poor soil. The gain differential is evident. Also clear is the fact the a dipole has a significantly greater beamwidth broadside to the wire than along the axis of the wire. This feature of a dipole in NVIS service is useful if I need bi-directional coverage, but it may hinder communications if I need uniform or omni-directional coverage.

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Although optimizing the antenna height for ground quality over most soils is not especially significant once we have a good range with which to work, we can still go some distance in eliminating the gain differential between very poor and very good ground. We need a reflector. Simple one wire and multi-wire ground screens are simply not good enough to make a major difference. We need a screen to create a planar reflector. For most applications, the screen needs to extend at least 1/2 wavelength beyond the limits of the antenna array above it in order to perform effectively as a flat reflector based on principles derived from optics. In our dipole case, that requirement means a reflector 1.5 wavelengths long by 1 wavelength wide. The reflector can go directly on the ground, but not below it. You do not need a tight screen or solid surface. Chicken wire will do, although its lifetime may be limited. Fig. 4 outlines the screen used with our test dipole.

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Table 3 compares with modeling results with and without the screen. The table omits perfect ground, since the screen is nearly touching ground. Note the very small difference in maximum gain from one end of the soil spectrum to the other. As well, note that the optimal height above ground virtually constant.

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Table 3 also contains a result that may seem contrary to expectations. The gain tends to improve as the soil gets worse. Is something wrong with the model? Yes and no. Actually, NEC-4 is doing exactly what it says it will do. It is calculating gain based on the antenna array's geometry and placement above a homogenous earth below it. The reflection of waves occurs not only within the boundaries of the screen, but well beyond it. Hence, to some degree--limited in this instance--the pattern is the result of reflection off the copper screen and off the ground. Some of the reflections result in far-field cancellations. The better the soil, the stronger those reflections are. As the soil grows "worse," it actually is less conductive and begins to approach the status of an insulator, which is transparent to RF. However, the wire-grid beneath the antenna is not 100% adequate, due to the conflicting needs of having a workable file size, a screen very close to the ground, and a wire diameter that coincides with the wire-grid cell size to simulate a nearly solid surface. Hence, part of the deviation may be due to this shortcoming of the model.

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Do not expect a real-world antenna to provide even the small bit of extra gain shown in the model. Real ground is highly stratified. Below the ground that someone has measured and entered into a chart lie other layers of ground that may have properties quite different from the near surface values. The most likely effect is that most soils will yield gain values close to the lowest values in the table. Since the total range is small, you will not be able to detect the differences.

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Ground effects are not constant from one frequency to another, although general trends persist throughout the HF spectrum. As a sample, I scaled the dipole (without a screen) to both 1.8 MHz and 7.0 MHz. The results appear in Table 4.

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Except for highly conductive salt water and for a perfect ground, the performance trends are clear. For very good down to very poor soil, increasing the frequency increases the optimum antenna height for maximum gain, when we measure height as a function of a wavelength. The differential is very small and makes little difference in practice, but it is numerically noticeable. More significantly, the higher the frequency, the lower the maximum gain for all soils up through very good. Hence, a screen of sufficient size is advisable wherever it is feasible.

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Conclusion

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The old sound bite about ground quality not being significant to horizontal antenna operation turns out to be true only under certain circumstances. If a horizontal antenna is high enough above ground, then the gain and pattern variations created by different soil qualities are relatively small and are largely beyond control.

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However, for horizontal antennas very close to the ground--such as is necessarily the case with NVIS antennas--the quality of the ground can make a significant difference in antenna performance. The difference is great enough to suggest system improvements that will largely equalize performance, regardless of the soil quality.

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In the end, sound bites are a poor way to store antenna information. Most antenna data requires a context to give the information sensible, reliable, and usable truth.

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Updated 06-20-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: Dipole, NVIS


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The Slippery Sloper Argument

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L. B. Cebik, W4RNL

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A perennial e-mail question that I receive is why there are no notes at the site on the sloper. This antenna has become very popular for amateurs with limited space under certain conditions. Hence, it seems to deserve some kind of treatment. For reasons that will become clear as we proceed, these notes are about the best I can do in terms of the antenna's basic operating characteristics.

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One of the most common sloper installations uses an existing tower that supports a beam at the top as the upper-end support for a sloper. Other amateurs string them from trees or other existing structures. While we can begin by looking at the sloper as if it stood free and clear of everything, reality intrudes its multi-faceted set of interactions that will prevent us from drawing too neat a set of conclusions about sloper performance.

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In these notes, we shall work with a sloper made from AWG #12 copper wire. The test frequency will be 7.1 MHz, since the 40-meter band is the lowest band for the common use of a sloping dipole, otherwise known as a full sloper. (A sloper fed at the upper end, nearest the support, has been dubbed a half-sloper.) We shall pose a number of fundamental questions first, such as when a sloper becomes a sloper and not just a vertical with a slight tilt, and what may be the best (rough) angle for a sloper.

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Our second set of questions will involve the sloper and its support. We shall begin by contrasting true vertical dipoles and nearby vertical objects with a roughly preferred slope and the vertical object that supports the upper end. Those questions will very quickly become too complex in terms of installation variables for us to give anything like a systematic set of answers. Ultimately, it will become the responsibility of the installer and the user to evaluate whether the sloper is the right antenna for a particular job.

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Vertical and Sloper Basics

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Let's begin in the abstract world in which we can construct an antenna that is free and clear of all supports. The world is antenna-modeling software, of course, where we may support an antenna wire simply by specifying its coordinates. This world is limited, but it does offer us the opportunity to contrast true vertical dipoles with slopers having various tilt angles. I all cases, we shall specify a sloper's tilt by its departure from a true vertical orientation. Fig. 1 shows the range of sloper models that we shall consider.

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As the sketch suggests, one of the variables that we can work with within modeling software is the base height of the sloper above ground. Base height simply means the height of the antenna element's lower end above the surface of the ground. A second variable that we can use in the evaluation of basic performance is the ground quality. We shall use 3 types of ground. At one extreme is very poor ground with a conductivity of 0.001 s/m and a permittivity or dielectric constant of 5. More the norm is the so-called average ground with a conductivity of 0.005 s/m and a permittivity of 13. A few fortunate amateurs live above very good soil with a conductivity of 0.0303 s/m and a permittivity of 20. As we shall see, for any degree of slope from 0 through 45 degrees, both the base height above ground and the ground quality will make a difference in the anticipated performance.

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1. The True Vertical: A 40-meter vertical dipole is a very useful antenna for amateurs who desire a very low elevation angle and very little radiation at (or reception from) very high angles. Table 1 catalogs the modeled performance of 7.1-MHz vertical dipoles with base heights from 1' to 20' over each of the three soil types. We can draw a few immediate inferences from the data. First, the greater the base height (up to only the limit of the table), the lower will be the TO angle (take off angle or elevation angle of maximum gain). Second, the better the soil, the higher will be the antenna's gain for any given base height. However, note that over very good soil, the gain peaks with a base height of 10', but over worse soils, the gain continues to increase to the sampled limits. We might also note in passing that the gain variation from the lowest to the highest base level decreases as we improve the soil quality.

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The feedpoint impedance entries simply give us an idea of how the impedance changes of over each soil type as we change the base height. The model was resonated (approximately) over average soil with a base height of 10'. The data change as a body as we change the soil type. Within each soil type, we find a range of impedance variation that is interesting. The values are always within the range of our ability to prune the dipole length.

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The table also lists a vertical beamwidth, the angular distance between the half-power points. To gain a sense of what those values mean to operation, we should examine the gallery of sample patterns in Fig. 2. At very low base heights, the pattern shape does not vary much as we change soil types. However, as we increase the base height, we find the emergence of secondary lobes at high elevation angles. At a height of 10', the secondary lobes are not significant, although we should note that as the soil quality improves, the lobes are much more distinct. At a height of 20' at the lower end of the vertical dipole, the secondary high-angle lobes are becoming stronger. This factor may play a role in planning a vertical dipole installation in terms of a compromise between obtaining the lowest TO angle possible and the strength of high-angle noise that we are willing to handle during operation.

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We have reviewed the basic properties of vertical dipoles because these are the antennas against which we measure the potential advantages and disadvantages of a sloper.

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2. The 15-Degree Sloper: Fortunately, vertical dipole properties do not change rapidly as we tilt the antenna from its initial position. In fact, a 15-degree sloping vertical dipole (using the same base height and ground quality variations) shows very little change in its performance values relative to the vertical dipole. As shown in the data in Table 2, the maximum gain and TO-angle values are only marginally higher than those we encountered with the true vertical antenna. The feedpoint impedance values are almost identical.

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The most noticeable increases occur in the vertical beamwidth entries. To understand how these values grow, we may examine Fig. 3. In all cases, the antenna is set so the its lower end is right of its upper end relative to the elevation patterns. The 15-degree tilt is sufficient to increase the vertical beamwidth of the lobe away from the angle and to shrink the beamwidth of the lobe included by the antenna. In the direction of maximum gain, the lobe is strong enough to admit considerably more higher angle radiation and noise than we obtain with the true vertical dipole, and we lose a little bit with respect to our desire for a very low TO angle.

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The elevation patterns alone might be misleading, since they appear similar to the elevation patterns of 2-element beams with a poor front-to-back ratio. Therefore, I have included a set of representative azimuth patterns--all at the listed TO angles in the table--for 15-degree slopers with a 10' base height. Although the rearward (or left) portion of the pattern has a smaller beamwidth, the overall azimuth pattern is simply a distorted circle. Whether the small changes in pattern shape justify a 15-degree sloper is a question that we shall hold open until we complete our survey.

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3. The 30-Degree Sloper: 30 degrees is a handy angle for a sloping dipole, since it parallels the angle of typical guy wires or ropes stabilizing typical amateur tower-and-beam installations. As we examine the data on 30-degree slopers in Table 3, we can see that the trends started with the 15-degree version continue. The maximum gain and TO angle values continue to rise, at least over very poor and average soil. Over very good soil, the gain values decline. Moreover, the gain values over very poor soil are now systematically higher than the values over average soil. For a home installation, soil quality does make a difference in the final decision on whether to install a true or nearly true vertical or whether to move to a 30-degree tilt angle.

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The vertical beamwidth angles in the table alert us to the fact that we should expect some very different patterns in the gallery in Fig. 4. The additional tilt of the antenna produces strong radiation (and reception sensitivity) at quite high angles. As we improve the soil quality, we begin to see that the very large vertical beamwidth is a function of 2 elevation lobes that essentially merge at an angle where we might expect to find a null.

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With the increased tilt angle, we begin to see a more distinct potential for a usable front-to-back ratio. The sample azimuth patterns for a base height of 10' show that the potential is highest over very poor soil, with an 8-9-dB difference between the forward and rearward directions. The ratio decreases to about 2-dB by the time we use very good soil. Indeed, over very good soil, we find in the elevation patterns very little difference between the forward and the rearward direction, with a consequent decrease in the maximum gain that we can obtain from the antenna.

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The 45-Degree Sloper: I have included the 45-degree sloping dipole to show that there is a limit to how much we can tilt a dipole from the vertical and still gain some advantage. As shown by the data in Table 4, there is very little difference among the maximum gain values for equal base heights over the different soil types. Moreover, the TO angles have increased to values that we normally do not associate with long-distance communications. Indeed, these values resemble more the TO angles we might expect from a horizontal dipole at a relatively low highest (as a fraction of a wavelength).

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A further alert that we may be exceeding the boundaries of good sloper tilt angles appears in the vertical beamwidth column. All of the versions of the 45-degree sloper show strong radiation straight upward, a trait that we normally associate with antenna expressly designed for NVIS operation. The pattern gallery in Fig. 5 confirms this suspicion. Over very poor soil, we still obtain a good front-to-back ratio, despite the vary high TO angle, but as we improve the soil, the TO angle continues to climb, while the difference in radiation forward and aft disappears.

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The 45-degree sloper is, in general, a good NVIS antenna. In fact, many amateurs who do not have ready-made support points for a level dipole make use of this form of sloper, even though they set out to install a horizontal dipole. However, most amateurs who consciously wish to install a sloper are seeking long-distance communications. The 45-degree version of the slope offers perhaps the worst of all options, with the combination of a high TO angle and very strong sensitivity to high-angle radiation and noise.

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In the abstract, then, the 30-degree sloper is the best in show. The 15-degree version acts much like a true vertical, while the 45-degree version acts like a horizontal dipole (over most soils). The 30-degree sloper provides some directivity, a little front-to-back ratio, and finally the primary ingredient in sloper installations: convenience. It needs only one high support point and a ground anchor of some sort. Remember that our survey has used 15-degree increments, so all angles are approximations. Plus or minus 5 degrees from a target angle will make little or no difference to performance. In fact, other installation considerations will create much greater performance variations and mess up our seemingly systematic progressions.

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The Support Question

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The realities of 40-meter true verticals and full slopers is that they often depend upon a nearby structure to support the upper end. We usually acknowledge that a nearby vertically oriented object may have "some" effect on performance without fully appreciating the extent of the effect. Therefore, I ran a series of modeling tests to gauge the general parameters of the effect. Precision is not possible in this realm. Support objects may range from masts to towers to trees. Masts and towers vary in diameter from a little over an inch to towers with faces up to 24", but more normally, 12" or 18", with some crank-up towers using a graduated face width. Moreover, these supports may be ungrounded, poorly grounded, or well grounded.

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Tree supports are even more variable, since they may differ in both diameter and in the resistivity of the material. A single tree may vary its resistivity according to the current weather, the season, and numerous other environmental variables. Trees are not insulators, but at best semi-conductors. Experiments have shown that we can even use trees as antennas, although very lossy ones.

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As a consequence, we cannot be as systematic in looking at verticals and slopers plus their supports as we managed to be with slopers in the abstract. However, we can perform a few tests to obtain a general idea of the interaction between verticals and slopers on the one hand and their supports on the other. Let's begin by using a 40-meter antennas with its base 10' above ground. The support will be a vertical object that is 90' tall and 12" in diameter. The 12" diameter is a compromise between the circular equivalent of towers with a face width of 12" and a face width of 18". The AM BC industry uses (and has confirmed by both models and measurements) a simple set of equivalence equations. The diameter of a circular element is 0.74 times the face width of a triangular tower (relevant here) and 1.12 times the face width of a square tower. A 12" 3-sided tower face calls for an 8.88" diameter, while a 12" tower face requires a 13.44" element diameter.

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To preserve a reasonable segment length to diameter ratio, the 90' support object uses 31 segments. In raw NEC, I might have used the LD2 or LD3 command to continuously load the tower at various levels to simulate the range (but in no case the specific value) of a lossy support object. Since only spot loads are available within the software used (EZNEC), I simply placed a load on each segment of the support tower or object. The values in the next two tables will show the load value per segment, and the total resistance across the length of the object is that value times 31. There is no magic in the selection of resistance values except for one. I stopped the progression when the performance of the antenna came close to suggesting that the support object was RF transparent.

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We shall create two sets of tests using a true vertical antenna, one with the support tower ungrounded (that is, separated from the ground by 0.1'), and the other with the tower grounded by a tower extension of 9' below the ground surface. We shall repeat these tests for the 30-degree sloper.

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1. The True Vertical: Since we have set up a true vertical dipole as a baseline against which to compare and contrast various sloper angles, we might as well use it in our first test series. Indeed, I often receive the question of how far from an existing structure, such as a tower or a tree, to place a vertical antenna. Assuming that "the next county" is not a usable answer, let's see what the spacing should be between a vertical dipole and a support object that has various levels of resistance. Remember that we are working with only one object height and one configuration (truly vertical with no taper and no branches), so the data can only be suggestive at a first-order level. We shall begin with the ungrounded tower.

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Table 5 shows the results of the initial tests for spacing values of 1, 2, 5, 10, and 17 feet. (The last entry is roughly 1/8 wavelength at 40 meters.) Just above the notes are the modeled performance values of the same vertical dipole when free and clear of all surrounding objects. As the feedpoint impedance entries indicate, the closer the vertical dipole is to a support object, the more profound is the effect on performance. Likewise, as we increase the resistance of the support object, the interaction weakens. With 1000-Ohms per segment, the interaction is minimal with a spacing of at least 5' between the antenna and the object. However, lesser values of resistance show significant interaction across the entire range of spacing values used in the sampling.

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With very low resistance values, the interaction can be significant at least up to 1/8 wavelength and possibly farther. A resistance value of zero in these tests does not indicate a perfect conductor. The load value is in addition to the material loss assigned to the antenna element and its support object. Increasing the resistance in the object, especially at relatively close spacing values (for example, 2' or 5' at 40 meters) results in power absorption and dissipation by the support object. The table shows a consistent reduction in the elevation lobe strengths as we move from zero Ohms to about 10 Ohms or more. These are values that we might expect from trees or uncoated wooden structures used to support a vertical dipole. The numbers in the table do not hide the emergence of strong lobes at 90 degrees to the elevation pattern, which is in a line from the tower to the dipole. Fig. 6 overlays elevation and azimuth patterns for a spacing of 1' using zero and 10 Ohms added resistance per segment. As the patterns show, when we use the 10-Ohm value, some energy is simply missing from the far-field radiation patterns, relative to zero Ohms. Also note that as we exceed 100 Ohms per segment and move toward 1000 Ohms per segment, the support object becomes virtually RF transparent.

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For spacing values less than 10' and depending upon the lossiness of the support, the vertical dipole gain can be significantly lower than when the antenna is free and clear. Moreover, some combinations of tower height and spacing between the tower and the dipole can result in parasitic element effects from the tower. Fig. 7 overlays elevation patterns for a tower and a dipole at various spacing values, ranging from 2' to 17'. Note that the 17' spacing--about 1/8 wavelength at 40 meters--results in a directional pattern with about 2-dB forward gain and 5-dB front-to-back ratio relative to a freestanding vertical dipole. Not all combinations of support tower and dipole spacing will yield this result.

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To use this effect, the individual installer must establish that the right relationship exists between the support tower and the dipole element, a task that might be difficult if the tower also supports a beam for the upper HF region. To preserve omni-directional coverage, one suggested vertical dipole support system seems to have merit, assuming that the antenna builder wishes to preserve the omni-directional pattern. That system uses two supports at a considerable distance from each other, with a non-conductive support rope between them. The wire dipole extends downward from a point midway between the distant support objects. The alternative to this method of support is to create a wire dipole that is freestanding.

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The numbers, of course, apply only to a 90' support object with a 1' diameter. Other support lengths will yield different results using the same tests. As well, the tests used only a single base height and did not account for any other possible objects near to either modeled object. Therefore, the results are in no way exhaustive or definitive. However, they do show the potential for interaction between a vertical dipole and one kind of support object.

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Before we leave the true vertical and its nearby support tower, let's consider an additional factor: how well the tower is grounded. I repeated the same series of tests that we found in Table 5, but extended the tower 9' below ground. We may compare the modeled performance values by examining Table 6. For the particular tower that we are using for the tests, improved grounding results in lower gain values, less directionality, and higher TO angles, as a general rule. However, with high values of resistance per segment, the support object becomes just about as RF transparent as the ungrounded tower. Generally, the region of about 10-Ohms per segment shows the greatest absorption and dissipation of energy.

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How well a supporting tower (or simply a nearby tower) is grounded suffices to significantly alter the vertical's pattern. Thus it adds one more variable to our growing collection. We shall see this variable at work again as we turn to the 30-degree sloper.

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The 30-Degree Sloper: The most usual form of full-sloper installation supports the upper end of the antenna near a tower or other tall vertical object. The wire then extends away from the support object toward its base. With a 10' base height (to be roughly comparable to the vertical dipole tests), the remaining distance to the ground is normally a non-conductive line to a ground anchor of some sort. Because the sloper has a 30-degree tilt angle, the lower end is about 35' from the support object, and the dipole feedpoint is about 17' from the support. Since the dipole is slightly less than 70' long, the upper end will be about 0.75' (or about 9") away from the surface of the 12" diameter support object.

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One consequence of the necessary conditons of installing a 30-degree 40-meter sloper is that we need only one test sequence to test the effects of varying the support object resistance. However, we shall run two tests, one with a support object that is 70' tall, and the other with a 90' tall object. These heights correspond to two heights of towers in wide amateur use. Our goal is to see whether support-object height makes a difference to the sloper's performance. We shall again use ungrounded and grounded support objects for each tower height. Table 7 provides some interesting tabular data for the 70' support object.

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The 70' support object shows significant directionality in the sloper pattern with both ungrounded and grounded supports up to loss levels of 10 Ohms per segment. The ungrounded tower acts more like a parasitic reflector than the grounded version, but the data show that both versions increase the front-to-back ratio over the natural values of an independent full sloper with the same 10' base height. The relatively high front-to-back ratios for the ungrounded tower also accompany more radical changes in the sloper feedpoint impedance and lower values of vertical beamwidth until the tower loss approaches RF transparency.

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If we replace the 70' tower with a 90' tower, the numbers change, as shown in Table 8. There is little difference in the gain values between the two grounding states for the 90' support, although the ungrounded tower yields higher front-to-back ratios. We do find a differential effect on the feedpoint impedance values, with the ungrounded support (at low-loss assignments) yielding impedances that are lower than a free-standing sloper and the grounded version providing impedance values that are higher.

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Fig. 8 reveals part of the reason for the numerical differences by showing the current magnitude distribution along each of the tower situations (with zero additional loss). Grounded and ungrounded towers show different points along the height at which the current is maximum. As well the peak current on all four tower models shows different values. (The curves for the sloper itself have been equalized to the degree possible within the graphical system used by EZNEC. These same limits also do not allow the 4 model outlines to be in exact scale with each other.)

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Some of the far-field radiation pattern differences among the 4 variations of a support tower do not become evident from the tabular data alone. Fig. 9 shows the elevation patterns that accompany the current magnitude distribution curves in Fig. 8. The shape of the main forward lobe is one significant area of interest, since it largely determines the vertical beamwidth. Both ungrounded towers yield smaller vertical beamwidth values with less sensitivity to very high-angle radiation and noise. Unfortunately, failing to ground a tower tends to raise serious safety issues.

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Although our survey so far has introduced us to a number of variables that have consequences for full sloper performance, we need to add a final variable that generally affects only highly conductive towers.

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The Tower Support with a Beam on Top: Many slopers use an existing tower as the support for the top of a 30-degree full sloper. Normally, the tower has an appurtenance at the top, namely, an upper-HF beam. The beam may be simple or complex. At the small end, we might find a 10-meter 2-element Yagi. At the large end of the scale might be a 16-element tri-band array on a 30' boom--or something even larger.

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The beam at the tower top usually has an electrical connection to the tower, although that connection may or may not include the driven element. It we treat the tower as a vertical element, the beam becomes a form of "top" or end loading, that is, an irregularly shaped extension of the element with its structure at right angles to the tower. Normally, such structures on active elements lower the resonant frequency of the element without altering the current distribution along the element. Essentially, the beam-hat plays little or no role in the radiation from the tower itself. However, the sloper antenna to which we supply energy has both a vertical and a horizontal component to its radiation, and the horizontal component is more than incidental. Therefore, the top section of the beam-hatted tower may interact directly with the sloper antenna.

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In this space, we cannot sample every possible combination of beam and tower. We can look at two simple cases: a 3-element 20-meter Yagi with a 24' boom and a 6-element 20-meter Yagi on a 48' boom. We can place each antenna on either a 70' or a 90' tower to which we have attached our 7.1-MHz AWG #12 copper-wire 30-degree sloper. Of course, given our recent modeling, we can have each tower in an ungrounded condition or a well-grounded condition. As well, we can align the Yagi boom with the tower-sloper line or set the beam cross-wise to that line (or at any intermediate angle). Since our variations are already numerous, we shall set the sloper with a base height of 10' above average soil as fixed values, even though we might easily vary both the base height and the soil quality. Even within these restrictions, we end up with the 2-column data set on Table 9. For reference, the table includes values for each tower with no beam on top.

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The tabulated data show no clear trends in the numbers. Changing the beam orientation does affect the values, as does changing the beam size. It is likely the even changing the beam design with the same general boom length and the same number of elements might occasion changes in the modeled values. For the 3-element beam, at least, we do find a greater difference in pattern shapes between ungrounded and grounded 70' towers than for the same grounding states for 90' towers. Fig. 10 shows the overlaid azimuth patterns for the two tower heights.

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Nevertheless, the 4 variations on the 3-element aligned Yagi do have significant consequences that appear in the elevation patterns shown in Fig. 11. Grounding either tower reduces the vertical beamwidth dramatically, but perhaps more radically with a 70' tower than with a 90' version. Both models of the 70' tower show the appearance of a secondary lobe (which most NEC software implementations would identify by a definite reversal in the progression of gain values in the trace progression, regardless of the size of that variation). At least three of the sloper installations modeled would be useful for NVIS communications.

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Our graphic sampling so far has used the 3-element Yagi aligned with the tower-sloper line. Fig. 12 provides a sample using the 6-element beam crosswise to the tower-sloper line. If we contrast grounded and ungrounded 90' support towers, we find very different current distribution curves. Not only do the current magnitude values on the tower differ in placement and value, but as well we find differences in the current magnitudes on the beam elements. The result is a set of quite different elevation patterns for the two situations, with the ungrounded tower and beam yielding the greatest change from the pattern we would expect of a free-standing full 30-degree sloper.

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We cannot extrapolate from these cases any general conclusions. Even monoband beams for 20 meters come in different element configurations, and--of course--the beam on top of the tower might be of any design that has appeared commercially or been developed as strictly a personal project. All that our simple demonstration can show is that a top beam can and often does make a difference to the performance of the sloper attached at its upper end to the tower supporting the beam.

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Conclusion

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As soon as we pass from the abstractions of independent element performance to the realm of actual installations, both the true vertical antenna and the 30-degree sloper fall into a realm of almost innumerable variables for which no set of calculations or models can provide much usable guidance. The utility of the exercise has been to show that any one or more of these variables can alter the actual performance of the sloper. Moreover, we saw that even true vertical antennas are subject to interaction with both highly conductive and lossy nearby objects, whether or not they play an active role in support the antenna. In the case of the sloper, such objects are unavoidable in a real installation.

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The performance of a sloper results from the totality of the property variables, including the sloper position, the diameters of the materials, the lengths of the elements (sloper and tower), the base height of the sloper above ground, the ground quality, the quality of support tower grounding, and the loading effects of an indefinitely large variety of beams that might be on top of the tower. This list does not include other nearby objects that may also affect especially the vertical component of the sloper's radiation and potential interactions.

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For most antennas, we can work with the basic antenna design in isolation and then make adjustments for the installation environment. The sloper differs in having a necessary upper support point in proximity to an existing structure. Under these conditions, the data about the antenna in isolation holds far less guidance than it does for most other types of antennas. In the end, no sloper is a textbook case. Rather, each one is an experiment that combines differing values for each of the many variables. The sloper builder can only make his best estimate and then proceed by operating tests and measurements to find, within the real limitations of the installation site and available materials, the adjustments that yield as close as possible to optimal operation.

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These notes perhaps do only one thing well: they explain why I tend not to provide notes at this site on the sloper antenna.

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Updated 11-24-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index +

Topics: HF Lower, Vertical


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Modeling the T2FD

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L. B. Cebik, W4RNL

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The "terminated, tilted folded dipole" (T2FD) antenna has been subject to much recent conversation, some of which has come my way in the form of questions about modeling the antenna. So I decided to take a systematic look at models of the T2FD. The original T2FD was intended for use as a vertical or a sloping antenna, often as an appendage to the tall tower. Leter (WWII), the antenna found use as a horizontal "all-band" wire antenna used in either flat or inverted-V configurations. These notes will deal largely with the vertical and sloping versions. For further and deeper looks into the horizontal versions, see "Notes on the Terminated Wide-Band Folded Dipole".

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The two models I investigated are sketched in Fig. 1 (shown horizontally to save space). Both are similar in that they are indeed folded and dipoles, although not folded dipoles in the normal sense of that term. The resistor placed opposite the feedpoint limits the impedance excursions at the feedpoint relative to an unterminated folded dipole. At the same time, the resistor also introduces losses into the antenna in the form of converting some of the RF energy into heat.

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Both antenna are designed for use from 2 MHz through 30 MHz as an initial design criteria. We shall explore limitations in that frequency spread along the way. The "Wide-Long" version coincides with standard construction formulations, since the antenna is about 300/F(MHz) long and 10/F(MHz) wide. (Excessively fussy cutting formulas for this antenna are largely superfluous, since strict resonance is not in question.) The "Narrow-Short" version generally approximates or approaches the dimensions of commercial versions of the T2FD, even if that name is not used for the antenna. Both antennas use #12 copper wire.

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Modeling the T2FD involves nothing that in any way presses the limitations of NEC (either -2 or -4), so long as the segment length in the long wires is not out of balance with the segment length in the short wires and as long as sufficient segments are used per wavelength for all frequencies to be investigated. In short, nothing in the antenna design suggests that NEC should not give accurate predictions of performance.

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We shall look at several questions that seem to perpetually arise in connection with the T2FD. The first involves the antenna's feedpoint impedance across the frequency range of intended use, relative to the selected value of terminating resistor. The second will involve antenna patterns when the antenna is oriented vertically. Related to this second question is the matter of tilting the antenna, as our third inquiry. Finally, we shall look at the question of losses relative to uses to which one might put the T2FD.

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Since these are notes on two models of the T2FD, they do not yield more than suggestive results. Hence, nothing in these notes should be construed as fixed, final, or necessarily in rebuttal of existing claims, many of which may be based on different version of the antenna type.

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Impedance, SWR, and the Terminating Resistor

All modeling runs for the T2FD (both versions) were made with the antenna lower end 20' above average ground and with the antenna vertical. Check runs with the antenna tilted 45 degrees produced no significant differences in the impedance results. +

One common recommendation for the T2FD is to use a 390-Ohm resistor for the termination and to employ 300-Ohm feedline. (The general recommendation is to use a terminating resistor that is about 5% to 10% higher in value than the feedline characteristic impedance.) I performed frequency sweeps with this configuration using both models. The technique is to obtain an SWR curve from 2 to 30 MHz using as a standard the characteristic impedance of the desire line, with a resistive load in the model matching the desired terminating resistor.

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Fig. 2 shows the results of the 390-300 Ohm combination for the standard T2FD configuration cut for 2 MHz. (The model used is the 165' long wide version from Fig. 1. Although called a 2-MHz antenna, The antenna is about 1.2 wavelength long at 3 MHz.) The SWR excursions are very wide, ranging from about 1.2:1 to nearly 9:1.

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I could provide a mass of similar graphics representing my search for a combination of terminating resistor and feedpoint impedance standard that would yield the shallowest SWR excursions. Instead, I shall drop to the bottom line. For the standard "wide" T2FD configuration cut for a lowest frequency of use of 2 MHz, a loading resistor of 850 Ohms combined with a feedpoint impedance standard of 900 Ohms yields the following "best" SWR curve.

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In Fig. 3, the highest value of SWR relative to 900 Ohms is about 2.1:1, with peaks in this vicinity occurring every 6 MHz from 4 to 28 MHz. This value does not coincide with any one particular feedpoint impedance, as the following table shows.

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+Freq.       R +/- jX
+ 4        1435 - j 615
+10        1085 - j 700
+16         855 - j 665
+22         690 - j 575
+28         590 - j 466
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Although the reactive component is consistently negative at these frequencies, the resistive component ranges from well above to well below the 900-Ohm standard. The resistive component of the source impedance ranged from 450 to over 1400 Ohms, while the reactive component ranged from +j250 to -j700 Ohms across the frequency span. These ranges must be considered tentative, since the check points are 1 MHz apart.

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Interestingly, the narrow version of the T2FD with its shorter length (100') also required an SWR standard of 900 Ohms, with a terminating resistor only 50 Ohms less (that is, 800 Ohms) than that used for the optimized wide T2FD version.

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With these conditions, as shown in Fig. 4, one can obtain an SWR curve between 2 and 30 MHz of under 2:1 relative to 900 Ohms. The peak values occur at 10 MHz intervals: 7, 17, and 27 MHz. The wire is about 1.2 wavelength long at 5.5 MHz. However, the extreme resistive and reactive component values are not very different from those of the standard configuration.

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In principle, it would seem that some scheme to transform the standard impedance value for both versions of the antenna (900 Ohms) down to a desired feedline value (perhaps a 50-Ohm coaxial cable) might be necessary. For a 50-Ohm result, an 18:1 transformation would be in order, perhaps done in two steps: 9:1 followed by 2:1. However, due to the high values of reactance present at the feedpoint at numerous frequencies within the overall antenna design range, one would need to use great care in selecting the means of impedance transformation. Some methods and materials may combine to yield losses which might then show artificially low values of SWR on the final feedline. These losses would be in addition to those incurred via the terminating resistor. Whether these additional losses would be acceptable might well depend upon the application proposed for the antenna.

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Patterns and Frequency Limitations of the T2FD

Although a properly designed T2FD-type antenna is capable of providing (with suitable matching devices or networks) a low SWR over a very wide frequency range, the utility of the antenna displays other limitations, as some simple elevation patterns can illustrate. +
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Fig. 5 shows the elevation pattern of the standard vertical configuration T2FD (as cut for a 2 MHz lower limit or a length of 165') at 5 MHz. The low angle of radiation is one of the features of the T2FD that make it appealing in certain applications. The antenna remains 20' above average earth at the lower end. Note that the pattern is not symmetrical when taken across the plane of the wires (with a 5' separation), with slightly less gain in the direction of the loaded wire. In general, the closer the wire spacing, the less the gain differential. Broadside to the plane of the wires, the elevation pattern would be symmetrical with a gain intermediate to the high and low values shown in this edgewise view.

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In Fig. 6, we find the elevation pattern for the same vertical antenna at 10 MHz. (Note that the wider standard configuration tends to show some pattern displacement to one side or the other, due to the spacing of the wires. The more dominant side depends on the frequency of operation. The narrow version shows an almost perfectly circular pattern.)

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The most noteworthy aspect of Fig. 6 is the absence of low angle radiation, with the first main lobe peaking at greater than 30 degrees above the horizon. The high-angle of the main radiation lobes results from the fact that at 10 MHz, the antenna is well over 1.5 wavelengths long. A linear vertical doublet would show a low radiation angle to a length of about 1.25 wavelengths. As the antenna becomes longer, the main lobes are no longer broadside to the wire, but at angles to the wire. This shows up in the vertical configuration as high-angle radiation rather than low-angle radiation that would correspond to a broadside pattern in free space (or when used horizontally)

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To establish that Fig. 6 is no fluke, Fig. 7 is the elevation pattern for the antenna at 15 MHz.

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The explanation for these less than optimal patterns is the nature of the antenna. Although terminated, the antenna is still a folded doublet and shows in free space all of the pattern tendencies of any dipole. So long as the antenna is 1.25 wl long or less, then there is in free space a single main lobe broadside to the antenna wire. (In the range of 1.1 to 1.35 wl long, the antenna shows the side lobes typical of the extended double Zepp.) The main lobe, when the antenna is vertically oriented over ground, results in a low-angle lobe of radiation or reception sensitivity.

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As the antenna length approaches 1.5 wl, the broadside lobes give way to dominant angular lobes relative to the plane of the wire. When the antenna is vertically oriented, these lobes combine to form high angle radiation maxima, with low angle radiation either much reduced or wholly absent.

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The standard T2FD at 165' long reaches the 1.25 wl limit at about 7.5 MHz, while the shorter 100' version reaches the same limit at about 12.3 MHz. Beyond 8 MHz for one and 13 MHz for the other, high angle patterns become standard. When any version of a T2FD reaches a length relative to the operating frequency of more than 1.25 MHz, its utility for low angle radiation may become less than desired.

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The solution to this problem is fairly simple: the construction of a second T2FD. A T2FD (this time in the narrow configuration) of 40' overall length and 0.25' width, using the same loading resistor and feedpoint standard impedance was modeled. The SWR graph is a single curve that does not reach 2:1 from 7 through 30 MHz when the antenna bottom is 20' above average earth. In fact, the peak value of SWR relative to a 900-Ohm standard is 1.72, which occurs between 19 and 20 MHz. This new antenna is already over 0.5 wl long at 14 MHz and does not reach a length of 1.25 wl until nearly 31 MHz.

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Fig. 8 shows the elevation pattern of the second T2FD at 15 MHz, for comparison with the pattern for the long T2FD in Fig. 7. Although the peak gain value is lower with the shorter antenna, the radiation is at an angle of greater utility in most applications.

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To Tilt or Not to Tilt: That is the Question

All of the patterns shown so far use a vertical T2FD. Tilting the T2FD alters its pattern considerably. Modeling does not confirm reports of omni-directional performance from a tilted T2FD. We may illustrate this fact with a simple comparison at 5 MHz using the standard version of the T2FD. In one pattern, the antenna is vertical; in the other, it is tilted 45 degrees. +
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Fig. 9 shows the two patterns. The vertically oriented T2FD shows minimal pattern displacement from one direction to the other. However, the tilted version shows a heavy pattern displacement, but in neither direction is the radiation field as strong as at the peak of the lowest lobe of the vertical version.

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Fig. 10 shows the orientation of the pattern displacement to the tilt of the antenna. The patterns off the sides of the antenna are equal and approach those of the vertically oriented antenna. Nothing in the models shows any advantage to tilting the antenna with respect to skip communications or reception. Perhaps the only advantage may be mechanical, for those lacking a suitable high support from which to hang the antenna vertically.

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Terminator Resistor Losses

Although transmitting uses have been made of the T2FD, its chief use appears to be as a short wave reception antenna. In this application, the excess available receiver gain can largely make up for losses incurred in the terminating resistor. +

The losses in the terminating resistor are considerable, ranging from nearly half power to amounts in excess of 90% of the available RF power. The pattern of losses is not a simple smooth curve, but varies throughout the operating range of the antenna. The following graph plots the losses in terms of dB. For reference, a 3 dB power loss represents half the power being dissipated in the resistor. Higher values indicate more of the power being dissipated rather than being radiated (or transferred to the receiver).

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Fig. 11 is notable because it tracks the SWR curves for the two versions of the T2FD in quite interesting ways. The lowest losses in the wide or standard version of the T2FD (165' long) occur at the same frequencies as the peaks in SWR. For the shorter (100') version, the lowest loss points show a slight displacement (1 MHz) but occur at the same intervals. The actual loss within the resistor is a function of the current on that segment of the antenna. Other lengths and load resistors will show different levels and patterns of loss from the terminating resistor.

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It should not be surprising that the shorter T2FD shows much higher losses at the lowest frequencies of operation, since the antenna is about 0.2 wl long at 2 MHz. Basic antenna efficiency increases rapidly as the antenna length passes the 0.3 wl mark, which is well above 3 MHz for the shorter antenna. Indeed, we may call the frequency at which the antenna is about 1/2 wavelength long the "knee" frequency. Below the knee, gain frops rapidly and losses (as well as dissipation in the terminating resistor) increase with equal rapidity.

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The losses incurred in the terminating resistor occur in the form of heat. For reception-only applications, simple low-wattage non-inductive resistors may be used. For transmitting purposes, heat dissipation for the terminating resistor assembly becomes a major factor in antenna design.

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Conclusion

The purpose of these notes is not to recommend or disrecommend the vertical or sloping T2FD. Instead, the purpose has been to explore what modeling might tell us about the basic performance characteristics of the T2FD. Actual use decisions must measure the antenna performance characteristics (refined for the actual proposed design) against the application. +

There are a number of questions that modeling cannot answer, even if precise design and installation data are supplied. For example, the standard version of the T2FD is said to be quieter than random wires and doublets in receiving applications. The closed loop construction with wider spacing between wires may well account for this report, but modeling cannot itself show the phenomenon.

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Nonetheless, the models used here were constructed with sufficient care to warrant reasonable trust in the analytical results. These notes may provide a basis for prospective users to check out their proposed designs prior to installation to ensure that the resulting antenna has a good chance of meeting expectations.

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Updated 06-07-1999. 02-17-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: Dipole, HF Multi Band


+ + diff --git a/content/wire/tlocf.html b/content/wire/tlocf.html new file mode 100644 index 0000000..1f2e31a --- /dev/null +++ b/content/wire/tlocf.html @@ -0,0 +1,17 @@ + + + + + + How Much Coaxial Cable? A Case Study + + + +

How Much Coaxial Cable? A Case Study

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How Much Coaxial Cable? A Case Study

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This page exists to include the PDF in the topic index

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Topics: HF Multi Band, Off Center Fed Dipole


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To Trap or Not to Trap

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L. B. Cebik, W4RNL

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The trap antenna, whether a doublet or a one-sided vertical, was invented mostly to permit the operator to use coaxial cable as a feedline. It was not invented for maximum efficiency. A with all antennas, trap antenna adherents claim they get good results--and indeed they do. Whether they get better results than they would with other types of antennas of comparable size is a question few are positioned to answer. The answer would require that the trap antenna and the alternative be placed in nearly the same position at the same height, and few of us can afford the space, time, or money for such side-by-side comparisons.

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There are two types of trap antennas, with examples illustrated in Figure 1. The most common are those with traps, or parallel tuned circuits, that are resonant at or just below the edge of the higher frequency band to be covered, with extensions to make up the length of the lower band. These antennas will be shorter than a full-size dipole at the lower frequency, since the trap acts like an inductor at the lower frequency, much like a mid-element loading coil. However, the inductive reactance is not a product of the coil alone, but of the tuned circuit making up the trap.

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The second type of trap antenna is one with a parallel tuned circuit with the components and position selected to permit the antenna to show a low SWR one several of the ham bands. W8NX, who has done a great deal of work on these types of antennas, published an 80/40/17/10 meter antenna with only one trap each side of center, and it was tuned to 5.16 MHz (QST, July, 1996).

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Let's look at the more conventional trap antenna first and simplify it to just 2 bands, like 80/40 or 20/10. A full size #14 copper wire resonant dipole will have a gain of about 2.1 dBi in free space, but it has this gain only in one ham band. We may use the gain figure as a standard against which to measure trap antennas for two bands. The first thing we note is that performance of a two band trap antenna of conventional design is dependent very heavily on the Q of the trap. There are many trap designs, but here is a table of one pretty good design with coils of various Qs. The gain is for free space. Comparisons between dipoles and doublets at the same height above real ground will show the same differentials.

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      Q            High-Band Gain (dBi)      Low-Band Gain (dBi)
+       50                 0.7                       1.7
+      100                 1.4                       1.8
+      200                 1.8                       1.9
+      400                 2.1                       2.0
+      800                 2.2                       2.0
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Avoid low-Q trap coil designs. It is fairly easy to homebrew airwound coils with a Q of 200, and common coil stock usually meets this figure. Even the best series-wound coaxial trap coils will not have Qs higher than about 400, and most coils with Qs claimed to be higher than 400 will not retain that Q under the influence of the our chemistry-lab atmosphere. Nonetheless, a dipole with a gain of 1.8 or so will not yield results noticeably worse than a full size dipole, since a half dB of lost gain translates into less than a tenth of an S-unit. (Where these small losses mount up is in multiband beams with traps in every element, since the losses of each trap tend to be cumulative. They also add up in antennas with many traps for many bands.)

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The sample conventional 80/40-meter trap dipole in Figure 1 uses traps tuned to 6.75 MHz. With a Q of 200, the traps equalize performance on the two bands at just above 1.85 dBi in free space. This is only about 0.35 dB down from a full size dipole for each band.

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Well, that's not too bad. What about the other type of antenna, like the W8NX improved trap antenna? Since the trap is not resonant at any ham band, the antenna is functional over its entire length at all advertised frequencies. On the three upper bands, the trap mostly adjusts the reactance that appears at the feedpoint so that coax can handle the feed task. On 80 meters, as Al Buxton notes, the trap does exhibit significant losses--about 0.6 dB relative to the gain of the wire of the same length (83.6') without the trap. (The 80 meter performance is down by a bit over 1 dB from a full-size dipole for 80 meters.) Since most of the impedances are close to 100 ohms, replacing the recommended 1:1 balun with a 4:1 balun will likely create no problems.

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Since the W8NX antenna is operative along its entire length, its patterns are not true dipole patterns on all but 80 and 40. On the upper bands, they are multi-lobe patterns typical of a wire of the same length fed with a parallel transmission line and an antenna tuner--and at the same lobe strengths. So unlike the conventional trap antenna, the special trap design acts like a simple doublet.

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Now we have an additional selection criterion for our decision-making machine. If we just have to have coax, then a trap design is desirable, especially if we do not have space for a yard full of standard dipoles. If we have to have standard dipole figure-8 or (at low heights) oval patterns, then the conventional trap design is indicated. If we have to have the coax, but are willing to accept patterns that are a function of the antenna length, then the special trap design may be useful.

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But--what if we do not really have to have coax. What if we could use parallel feedline and an antenna tuner. And--what if the dipole pattern were not too important to us. Should we still opt for a trap antenna? Probably not.

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First, traps are always a maintenance problem. More than their losses, their inability to withstand weather without periodical disassembly and cleaning is a disadvantage to most users. Open traps are an invitation to big bug nests and closed traps invite little insects that get into weep holes and eventually clog them.

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Second, a doublet with an ATU allows one to put a signal on all the ham bands. The W8NX antenna, without the traps, is about the right length for an EDZ on 20 meters, but the high reactance requires parallel feedline to avoid losses. With the traps and a coaxial feedline, the band is not accessible without significant power losses in the line.

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Third, in the short run, a trap antenna may be cheaper than an ATU, but since ATUs are not out in the weather, they tend to last a lifetime. Hence, you can prorate their costs over many years more than a trap antenna.

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So if you need the exact things a trap antenna offers, then opt for either the conventional or the special design types. On the other hand, if you prefer general operating on all bands, then simply put up a doublet and feed it with parallel feedline and an ATU. The 121' of the conventional trap antenna would translate into a good doublet at 80 meters and up. Even the 83' length of the W8NX antenna--which is short by G5RV standards--when used as a doublet without traps, will still give performance every bit as good as any trap antenna and on more bands. The length of a doublet is not critical, but a. try to make it at least close to 3/8 wavelengths long on the lowest frequency needed and b. be ready to change parallel feedline lengths in case you run into the occasional impedance condition your tuner cannot handle well.

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Remember that there is no magic to any kind of trap or doublet antenna. For the band in use, the elevation angle of maximum radiation will be the same as a dipole at the same height above ground. Therefore, more height is always a key to improved performance of any trap or doublet antenna.

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My object is not to downgrade traps: use them where your system's specifications demand them. But do not neglect the multiband doublet, which can be just as good and occasionally better for many installations. Hopefully, setting the two side-by-side here will let you make a more reasoned decision for your installation.

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For more detailed information on the nature and operation of traps, as well as on how to model them, return to the "Radio" page index and look under the section of material devoted to modeling antennas.

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Updated 12-20-97. © L. B. Cebik, W4RNL. A version of this item appeared in QRP Quarterly, October, 1997. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author

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Go to Amateur Radio Page

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Topics: Dipole, HF Multi Band, Traps


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The Turnstile
+ An Omni-Directional Horizontally Polarized Antenna

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L. B. Cebik, W4RNL

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I have received a number of inquiries over the last year or so concerning the best way to get omni-directional radiation from a horizontally polarized antenna on the HF bands. We have often tried to use the inverted Vee, but that antenna only turns the dipoles peanut-shaped pattern into an oval. The radiation off the ends of the wire is usually down by 8 to 12 dB--depending on the slope of the Vee legs--relative to the maximum gain broadside to the wire.

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If you are truly serious about having an omni-directional horizontally polarized pattern, try the turnstile antenna. The turnstile was often used on VHF, especially in the days before repeaters, that is, when horizontal polarization was still standard. The antenna has dropped out of sight, but may have a new home on the HF bands for those who must use a fixed antenna but who also wish to have roughly equal radiation in all directions. The basic outlines are shown in Fig. 1.

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The turnstile consists of two resonant dipoles at right angles to each other and crossing in the center. The two antennas do not touch. The main feedline (the usual 50-Ohm coax, with a 1:1 balun) goes to one dipole's feedpoint connections. A 90-degree phasing line of 72-Ohm coax goes from the main feedline connections to the other dipole feedpoint connections. The 90-degree phasing of the two dipoles is crucial in obtaining an omni-directional pattern.

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The phasing line length will depend on the velocity factor of the line you use. 72-Ohm coax comes with either solid or foam insulation. The solid insulation usually gives the line a 0.66 velocity factor, while foam lines have a velocity factor of about 0.78.

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Use the velocity factor as a multiplier on the basic 1/4 wavelength calculated from the frequency and wavelength of use in order to determine the physical length of the line. Let's use 10-meters as an example. 1/4 wavelength is about 8.63' at 28.5 MHz. A 0.66 VF line will be about 5.69' long, while a 0.78 VF line will be about 6.73' long. As with any antenna, be sure to weatherproof all connections to prevent rain from entering the coax line. Technically, coax is not necessary, but 72-Ohm parallel line is almost impossible to obtain in the U.S. Although the example is for 10 meters, the turnstile concept is relevant to any frequency whatsoever, from LF to UHF.

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To build a turnstile, first build a single dipole and trim it to resonance. Then construct the second dipole to exactly the same dimensions. The construction details will depend on the band and materials. Add the phasing line, calculated for the band in use. Finally add the main feedline.

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Let the phasing line hang down from the dipole junction. You can tape the "down" and "up" halves of the line together to control erratic swaying in the wind. However, it is best to space the line a bit from any metal mast you might use to support the antenna center.

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Now the big question: what do we get for our efforts? The turnstile azimuth pattern for nearly any antenna height appears in Fig. 2.

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The patterns is nearly circular. The maximum flattening along the sides is 2 dB or under for most common heights. The following table will give you some idea of the gain of the lowest lobe and the degree of "flattening" of the circle for various heights above ground in terms of wavelengths.

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Height    Max. Gain      TO Angle       Flattening     Feedpoint Z
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+0.25      3.9            45 (arbitrary)   0             35.7
+0.50      5.2            28               2.5           37.0
+0.75      4.5*           18               1.5           36.0
+1.00      4.7*           14               2.0           36.0
+1.25      5.6*           11               1.5           36.1
+1.50      5.2*            9               1.5           36.0
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For lower HF use, a wire turnstile will rarely reach above a 1/2 wavelength in height. Since there is only a single elevation lobe at this height, the antenna might be viewed as operating under the most optimal conditions. See Fig. 3.

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Despite having a single elevation lobe, the maximum gain will still be about 2 dB lower than the maximum gain of a single dipole. However, the single dipole has only 2 lobes, whereas the turnstile has 4 overlapping lobes that form its omni-directional pattern. To fill the dipole "gaps," power has to come from somewhere, and it is from the maximum lobes of each dipole. Hence, slightly less gain for the turnstile, but gain in every direction around the compass.

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The starred (*) gain entries list the gain at the lowest elevation lobe. However, these lobes are not the strongest in the antenna pattern. It has long been known that between 3/4 and 7/8 wavelength of height, a dipole actually exhibits a reduction in gain from its lowest lobe. This phenomenon is due to the formation of a new second lobe at very high radiation angles.

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The turnstile shows the same phenomenon, but somewhat more extremely. The situation is shown in Fig. 4, the elevation pattern for a turnstile at a height of 3/4 wavelengths.

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The strongest lobe is straight up. However, the lower lobes are still usable, being only 1.25 dB weaker than the upper lobe.

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As the antenna is raised further to about 1 wavelength in height, the upper lobes decrease their angle and equalize with the lower lobes. See. Fig. 5. The 1 wavelength height might be considered a dual-purpose antenna, with lower lobes for DX and higher lobes for short skip.

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As you raise the antenna further--to the 1.25 to 1.5 wavelength region--a new third lobe makes its appearance. Again, the new lobe is initially straight up. A simple dipole at this height would show its major strength in its lowest lobe. However, the dual dipole arrangement of the turnstile places maximum gain in the new lobe, although the difference in strength among lobes is much less than at the 3/4 wavelength height.

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The lobe formation characteristics of the turnstile are simply one of its limitations. For lower HF use, most wire dipole arrays will be 1/2 wavelength or lower, a fact that eliminates the limitation. Heights up to about 5/8 wavelength tend to be ideal. For upper HF use, a height of just about 1 wavelength may be best: that height will equalize the lobes and provide dual skip performance.

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The turnstile has other limitations as well. It is essentially a monoband antenna, since the phasing line is specific to a narrow frequency range. Operating the antenna on other bands is possible with a parallel feedline and an antenna tuner. However, with the phasing line in place, the patterns will be erratic.

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One possible solution to this problem is to install a relay switching system at the feedpoint for bands other than the fundamental frequency to which the dipoles are cut. One can remove the phasing line and use either dipole to provide fairly standard patterns on frequencies higher than the fundamental. One more switch position for the relay system might permit switching from one wire to the other to obtain the strongest signal.

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In fact, this system might also be useful at the fundamental frequency. Having omni-directional reception would allow you to hear signals that would disappear in the end-nulls of a single dipole. Then, switching whichever dipole provides the strongest signal might improve contact ease by up to about 2 dB (or nearly half an S-unit as meters are usually calibrated).

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Construction of the turnstile will be largely a matter of the materials used. Wire construction will require special attention to the weight of two coax lines at the junction. For this kind of application, copperweld strength is recommended. For upper HF use, aluminum tubing becomes a possibility, and this type of construction usually involves a central mast. To mount the antenna elements, you can use a plywood or Lexan plate--or even crossed 2x2s (weather sealed, of course). Dipoles can be mounted on opposite sides of the plate or cross--or they can go on one side if the feedpoint ends are separated to prevent contact.

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Adding a relay box requires attention both to securing it well and to weatherproofing the box. Of course, a set of control lines to activate the relays will be needed as an added cable weight to the pair of coax lines already noted.

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Tuning up the turnstile system requires some care. Begin by adjusting a single dipole for resonance and then add a second dipole of identical construction. There is an important reason for this procedure, based on the properties of the two dipoles when phased by 90 degrees.

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The feedpoint impedance of properly adjusted turnstile dipole pairs is just about 36 Ohms. This value yields an SWR between 1.3:1 and 1.4:1 at the feedpoint. Normally, we try to reduce the SWR to the lowest possible value. Do NOT use this procedure with the turnstile.

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The turnstile exhibits a very broad stable feedpoint impedance. When properly adjusted, the antenna will easily cover any of the ham bands, including all of 10 meters. So SWR is only an indicator that you have made all of your connections properly.

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What becomes unstable as the antenna is operated at frequencies up to 3% or 4% away from the design frequency is the omni-directional pattern. It is possible to lower the operating frequency until you obtain the lowest 50-Ohm SWR. Equivalent to this move is shortening the dipole elements until you get the same result. Unfortunately, in the process, you will have lost the omni-directional pattern--as well as the ability to operate each dipole independently at a low SWR.

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Fig. 6 shows the azimuth pattern of a turnstile adjusted for the lowest possible 50-Ohm SWR. The side nulls are now deeper than 6 dB, partially cancelling the advantage for which we wanted to use a turnstile. (If one reverses the connections at one end of the phasing line, then the pattern will tilt in the other direction.) Unfortunately, this condition yields no significant added gain to the main lobes, so it is not a substitute for the suggested switching system for using the dipoles independently after locating a desired signal.

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The best procedure for constructing the turnstile is the one recommended, starting with a single dipole. When both are in place, carefully cut the phasing line, and then add the main feedline--plus any desired switching system. This procedure will prevent inadvertent loss of the antenna's omni-directional properties.

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There are other temptations to avoid. One prominent one is to bend the outer ends of the dipoles to form an incomplete square along the perimeter--in an effort to save space. Moves like this will also ruin the omni-directional pattern, since the radiation from the bent wire ends will partially cancel the necessary radiation balance. Once more, the pattern will degrade into something like the one in Fig. 6. If a bi-directional pattern is what you need, a single simple dipole will do the job better.

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Likewise, avoid making the turnstile into an inverted Vee. At downward angles between 30 and 45 degrees, you would need to use a 50-Ohm phasing line, and the feedpoint impedance will drop into the 20-25-Ohm range. As well, the gain from the antenna will decrease. If some shortening of the elements is necessary to fit a given space, the best procedure appears to be to equally fold down the ends of each dipole.

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The turnstile is not a magic answer to every horizontally polarized antenna need. Instead, it is one answer to a special need for omni-directional patterns for either transmitting or receiving in a specific frequency band. Among all of the schemes designed to achieve omni-directional radiation with maximum efficiency, the turnstile has one of the very best patterns, along with the simplest construction. Perhaps we have consigned it to the annals of VHF history too long and have forgotten that it is a design that is equally adept at fulfilling HF needs as well.

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Improving the Match

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Since the appearance of the turnstile note, I have received suggestions for improving the match of the antenna from the present 36-Ohm value encountered by the 50-Ohm coax line. One system came from Leland Scott, KC8LDO, in the form of a useful MathCAD worksheet. See Fig. 7 for the outlines of the basic scheme.

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The "short cable" will be 1/8 wl long for a pair of resonant dipoles. The "long cable" will be 3/8 wl long. (If the antenna feedpoints presents some reactance, the requisite lengths will be offset from the 1/8 and 3/8 wl figures used for resonant individual dipoles.) Both are RG-62, a 93-Ohm cable with a velocity factor of 0.86. The differential in cable length maintains the 1/4 wl phasing between dipoles. In addition, it provides a pair of impedances at the junction between the two cables and the main line of about 100 Ohms. The 1/4 wl differential in length yields conjugate reactances which cancel when connected in parallel. The resulting impedance presented by the parallel cables is exceptionally close to 50 Ohms resistive. The short cable is 3.71' and the long cable is 11.13' for a 28.5 MHz design frequency. Models of the antenna using this system show a maximum SWR of about 1.16:1 over the span from 28 to 29 MHz. Relative to the version using a single 72-Ohm phasing line, the only drawback to the system that the models suggest is a slightly higher non-circularity to the patterns. The maximum to minimum gain span averages about 3.34 dB, compared to 2.12 dB for the 72-Ohm phase-line model. It is unlikely that the degree of increased non-symmetry would be operationally noticeable.

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It is also possible to improve the match of the original model without disturbing the phasing or the pattern by using a 1/4 wl section composed of paralleled pieces of RG-62, as shown in Fig. 8. The 7.42' section of parallel RG-62 has an impedance of about 46.5 Ohms. The impedances presented to the main 50-Ohm feedline range between 56.5 and 60 Ohms, with virtually no reactance, for a maximum SWR of 1.2:1 in the 28 to 29 MHz range.

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Further possibilities exist for improving the match of a turnstile to a 50-Ohm cable without upsetting the near-circularity of the pattern, for example, the series matching techniques described by Regier and outlined in another note in this collection. Whatever scheme is used, it is first crucial to establish correct phasing for the most circular pattern possible and then to become concerned with matching the unit to a given main feedline characteristic impedance. For non-symmetrical patterns, there are likely better antenna choices available.

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Updated 03-06-2000. © L. B. Cebik, W4RNL. This item appeared in antenneX, January, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author

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Go to Main Index

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Topics: HF Upper, Turnstile


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The Multi-Band Inverted-V from Many Angles

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L. B. Cebik, W4RNL

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The smaller the backyard, the less room that we have to construct a full-size 135' level center-fed doublet as an all-band HF antenna. As a work-around, many amateurs try the inverted-V configuration. It requires only one very tall center support, with lower supports for the wire ends. Handbooks reassure us that the inverted-V will perform quite well, with only a small reduction in gain and a slight expansion of the radiation pattern off the ends of the wire. So we dutifully build the inverted-V and then wonder why neighboring hams are doing so much better at hearing stations. We rationalize that perhaps our antenna is broadside in the wrong direction. We may think that we have to grow taller trees to raise the feedpoint of the antenna even higher. Possibly, we need to buy a new rig. We never stop to think that the basic antenna may be at fault, especially on the upper bands. After all, the handbooks have reassured us that the all-band inverted-V is a good general purpose antenna.

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Let's back up a step and make a plan to study the situation. The first step is to review what we can expect from a level doublet with the same feedpoint height as our inverted-V. We cannot possibly survey every feedpoint height in this exercise. So I shall set the feedpoint at 60' above average ground. That level is somewhat high for the average backyard, but I have reasons for picking it, and they will appear in a moment.

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The second step is to replace the level doublet with an inverted-V, keeping the same feedpoint height. The immediate problem that we face is selecting an angle at which to slope the wires relative to the doublet. Again, we cannot possibly survey every sloping angle. However, we likely only need to look at two angles. One is a slope of 30 degrees down from the doublet. The other angle is 45 degrees down from the doublet. The difference is only 15 degrees, but--as we shall see--what a big difference those 15 degrees will make. Fig. 1 sketches the 3 antennas that we shall include in our survey.

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If we start on the right in the figure, we can see why I chose the 60' feedpoint height. The wire ends are between 11' and 12' above ground. Letting inverted-V ends go any lower is an invitation for someone to receive an RF burn, since the wire ends will carry a high voltage when we transmit. Hence, safety dictates that we keep the inverted-V ends at least 10' above ground, and higher, if feasible.

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The inverted-V sketches show the length of the legs, with the total wire length in parentheses. All three antennas are resonant at 3.5 MHz (using AWG #12 or 0.0808" diameter wire). As we slope the wires into the inverted-V configuration, we need slightly more wire to achieve resonance at the baseline frequency.

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We can also see the important reason for using an inverted-V instead of a doublet. Every addition degree of slope reduces the required end-to-end span for the antenna. The 45-degree slope allows the antenna to fit a yard with a maximum dimension of 100'. For this exercise, then, I shall assume that the backyard has one mighty oak--or Douglas fir--or ancient magnolia--that is precisely positioned to let us construct an inverted-V to use on all of the HF bands.

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The next question is simple: what can we expect from our antenna. To create a basic answer and set up some reasonable expectations, we should survey all of the HF amateur bands. Therefore, I shall sample each amateur band, jotting down some basic information and creating both elevation and azimuth patterns for the antennas. For each band, I shall use the lowest frequency in the band, since the patterns will not change much within a given band. The one exception is 75 meters, where I used 4.0 MHz to allow us to see how much the very wide 80/75-meter ham band changes antenna performance.

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My procedures will be fairly simple, but there will be a twist or two along the way. I shall collect information on the gain level of the strongest lobe(s) in the pattern. In the azimuth patterns, I shall record the first maximum-gain lobe away from the broadside direction to the wire, unless the strongest lobe is exactly broadside to the wire. I shall also record the take-off (TO) angle, that is, the elevation angle of strongest radiation. Wherever the strongest lobe is not broadside to the wire, I shall make my elevation pattern using the direction of the strongest lobe. If the elevation angle of maximum radiation is above 45 degrees, I shall create the corresponding azimuth pattern at 45 degrees. Under these conditions, you must assume that the azimuth pattern has a maximum strength that is lower than the maximum possible gain, since that gain value is for another elevation angle.

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For reference, I shall also record the modeled feedpoint impedance as a series resistance and reactance--rounding just a bit. This impedance will be at the antenna feedpoint. However, you will undoubtedly use a parallel transmission line--probably with an impedance between 300 and 600 Ohms--to connect your antenna to an antenna tuner in the shack. Since the transmission line impedance will rarely--if ever--match the antenna feedpoint impedance, the line will become an impedance transformer. The impedance that appears at the antenna tuner terminals will be a function of the antenna impedance, the line impedance, and the length of the line. Since I cannot cover every possible type of line and every possible line length, the antenna feedpoint impedances will have to do for our information collection.

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For each antenna, we shall create two graphical documents. The first is a table of information gathered from the antenna model. The second is a page of elevation and azimuth patterns. My reason for creating both the tables and the patterns as graphics is simple. You may be keeping a notebook of what you learn about antennas. You can copy and save the graphics from these HTML notes as separate files. Then, you can import them into a word processing program, such as Word. The program's importation feature should size the galleries of patterns to fit the margins of your paper. Printing the gallery and its associated tables of data will let you store the information nearly in your notebook. That way, you can omit the commentary that I weave around the tables and the patterns.

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The 135' Center-Fed Doublet

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Although our main topic is the inverted-V, we need a point of reference in order to make sense of the data that we gather. The doublet is the root antenna, of which the inverted-V is one variation. Therefore, reviewing what happens to the patterns of a center-fed doublet is critical to our overall understanding. The doublet that we shall use is 135' long, just long enough to be a resonant dipole at 3.5 MHz, at least when we place the antenna 60' above ground and build it from AWG #12 copper wire. 60' is not very high if we measure the distance as a fraction of a wavelength. In fact, the height is less than 1/4 wavelength at the root frequency. If we lower the height of the antenna, then the 80-meter TO angle will be higher, whereas if we raise the antenna, the TO angle will be lower. To really obtain good DX results from a horizontal dipole or doublet, we should increase its height to 3/8 wavelength--and much more if possible. But 3/8 wavelength on 80 meters is close to 100', and so we may have to settle for mostly regional contacts on that band. Of course, as we raise the operating frequency, the antenna height increase as measured in wavelengths. By 40 meters, the antenna is getting close to 1/2 wavelength above ground. For all higher bands, 60' is not a significant problem for a general purpose antenna, even though the old saying that higher is better still applies to this or any other horizontal antenna (but not necessarily to HF vertical antennas).

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Let's see what we derive from our 135' doublet on the amateur HF bands. Table 1 provides the tabular data, while Fig. 2 presents the gallery of patterns.

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We can begin with the table and immediately jump to the feedpoint-impedance column. The values seem to be all over the place, with some very high values and some fairly low values of resistance. The reactance also shows very wide swings. To make sense out of the column, we have to think about the antenna length. At 3.5 MHz, the antenna is 1/2 wavelength, and so we expect and receive a lower impedance with almost no reactance. At 7, 14, 21, and 28 MHz, the antenna is close to 1, 2, 3, and 4 wavelengths, respectively. At these lengths, we expect very high impedances--and get them. At 10.1, 18.068, and 24.89 MHz, the antenna is 3, 5, and 7 half wavelengths, respectively--or thereabouts. Since these bands dov not have a direct harmonic relationship to 3.5 MHz, we cannot expect precision. But can can expect and obtain fairly low impedance values with relatively modest reactance values. So the impedance values in the table do make sense after all.

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Note in both the table and the gallery that on 80 and 75 meters, the TO angle is higher than 45 degrees, and that requires azimuth patterns at 45 degrees. There is nothing magical in my selection of 45 degrees. It is too high for good DX work and too low for most NVIS work. Its one claim to fame is that it gives us a reasonably good picture of the azimuth pattern shape at that angle and below. Hence, we can clearly see the gradual narrowing of the beamwidth up through 40 meters, although the azimuth pattern remains broadside to the wire.

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From 30 meters through 10 meters, we find that the pattern is breaking into many lobes. For a center-fed doublet, let's measure the antenna length in wavelengths. For lengths that are near an integral multiple of a wavelength (that is, 1 wavelength, 2 wavelengths, etc.), the number of lobes will be twice the antenna length in wavelengths. Hence, at 20 meters, the antenna is 2 wavelengths and we find 4 lobes. The situation changes for lengths that are odd multiples of 1/2 wavelength (that is, 3/2 wavelengths, 5/2 wavelengths, etc.). Now the number of lobes will be twice the number of half wavelengths. So at 24.89 MHz, we have close to 7 half wavelengths, and we find 14 lobes. Since lobes do not simply pop into and out of existence, we find on odd frequencies a mixture of lobes emerging or decaying. Note that when the antenna length is closer to an odd multiple of 1/2 wavelength, we not only see more lobes, but the strongest lobe is further away from a direction that is broadside to the wire and closer to the axis of the wire. Hence, the tabular data shows an up-and-down swing to the azimuth angle of the strongest lobe as we check out the bands from 20 through 10 meters.

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The elevation angle of maximum radiation or TO angle of a doublet is almost wholly a function of the height of the antenna above ground. An antenna that is about 1/2 wavelength up will show a TO angle of about 25-26 degrees. When 1 wavelength up, the angle drops to about 14 degrees. If we physically raise or lower the entire antenna, we can change the elevation angle, but the lobe structure of the azimuth patterns will remain intact.

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You can use the table and the gallery when planning an all-band doublet installation, assuming that you have some room to maneuver. Pick your favorite bands and see where the lobes go. Then align the antenna wire so that the lobes are in the direction of your choice communications targets. It is likely that you will have to compromise--not only in terms of lobe direction, but also in terms of the limitations of your yard. However, be careful of making to strict of a compromise, or your lobes may miss all of your targets.

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If you shorten the antenna--perhaps making it resonant at 4 MHz instead of 3.5 MHz--then you will have to create your own gallery of patterns. You will not find much trouble on most bands, but the highest 2 or 3 bands may be a good bit away from the antenna lengths that produced these patterns. Hence, the exact directions of the lobes may differ enough to make a difference. I recommend that you obtain a rudimentary antenna modeling package and master it enough to plan an effective all-band doublet.

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A 30-Degree 135.6' Inverted-V

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The level doublet provides a touchstone for the results that we receive from any inverted-V antenna. We shall first look at a modest inverted-V, one with legs that slope downward 30 degrees from the horizontal. With a 60' feedpoint, the ends are about 26' above ground. 30-degree slopes on each side of the feedpoint mean that the angle between wires is 120 degrees (instead of the 180-degree value that applies to the level doublet). This version of the inverted-V is perhaps typical of amateur installations, although the exact top height may change from one location to another.

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Without further ado, let's see what kind of performance we can expect from the 30-degree inverted-V. Table 2 provides the tabular data, and Fig. 3 gives us a gallery of patterns.

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We shall not find very significant changes in the impedance column. Since the antenna is resonant at 3.5 MHz, its electrical length is similar to the length of the doublet on every band. The sloping wires do interact a bit, and the wire ends are closer to the ground. But the changes to the feedpoint impedance are moderate to modest.

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If we look at the column of TO angles, we find that they are typically higher than the TO angles for the doublet. In fact, the azimuth patterns for 80 through 30 meters require a default 45-degree elevation angle for the azimuth patterns due to the higher TO angles. (The doublet required this treatment only on 80 and 75 meters.) Even though the inverted-V has the same feedpoint height, it is lower at every other point along the wire. In general, the effective height of an inverted-V is about 2/3 of the way upward between the lowest point and the highest point along the wire. Hence, our inverted-V is effectively lower than the doublet at every operating frequency.

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We can easily compare the two tables and see that the inverted-V yields a lower value for maximum gain than the doublet. The lower effective height is partially responsible. In addition, there is some radiation off the ends of the wires, since they now slope and have a vertical as well as a horizontal component. That energy has to come from somewhere, and a good part of it comes from a reduction of the gain of the main lobe or lobes. Nevertheless, the amount of reduction is not enough to disqualify the 30-degree inverted-V as a good general-purpose all-band HF antenna.

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We should also compare with some care the gallery of patterns for both the doublet and the 30-degree inverted-V. From 80 through 40 meters, we notice seemingly small changes. For example, the inverted-V 40-meter pattern is an oval that has lost the "peanut" waist of the doublet. However, from 30 meters upward, the pattern changes are much more pronounced. For example, the doublet on 30 meters had 6 lobes, but we can only identify 4 in the inverted-V pattern for the same band. As we continue to increase the operating frequency, the sharply defined doublet azimuth lobes give way to less defined undulations, especially on 17 and 12 meters, two bands in which the patterns have many lobes.

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Do not forget to review the two galleries with respect to the elevation patterns. On the highest bands, note the growth of the high-angle lobes relative to the much more modest development of the same lobes with the level doublet. Energy that goes almost straight upward is not available at the lower angles more favorable to making contacts. As a result, the maximum gain values of the inverted-V shows a greater high-band deficit relative to the doublet than the gain values for the lower bands. What is more important, perhaps, is that these high-angle lobes foreshadow what is to come with our next inverted-V.

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A 45-Degree 136.6' Inverted-V

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If we add only 15 degrees to the slope of each inverted-V leg, can anything harmful happen? The legs now slope downward by 45 degrees relative to the horizontal. The angle between the legs is 90 degrees. Since the antenna will fit inside my 100' lot, it is a tempting construction project.

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To find the answer to our question, we need only examine the information. The changes in patterns and performance that we saw between the doublet and the 30-degree inverted-V suggest that we might see some further evolution in key properties. However, I wonder if we are prepared for some surprises. Table 3 supplies the tabular data, while Fig. 4 gives us the associated pattern gallery.

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Once more, the impedance column in the table gives us no clues to revolutionary changes, since the values show only a small evolution in the progressions of values that began with the doublet. As well, the gain column seems a bit odd, with lower values for the lower bands and higher values for the higher bands. The most meaningful changes occur in the two columns that list the azimuth angle of the strongest lobe and the TO angle. All TO angles are very high, indicating that on all bands, the predominant energy focus is straight upward or nearly so. The gain values shown are all for frying clouds and little else.

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As a result of the very high TO angles, all azimuth patterns are at 45 degrees elevation. The azimuth patterns show some lobe development at this angle. However, the maximum number of lobes is 6. Up to 14 MHz, we find only 2 lobes. At 28 MHz, the old lobes that are broadside to the wire have finally disappeared, leaving only the 4 lobes that emerged around 18 MHz. In effect, the 45-degree inverted-V shows only half the number of lobes that we find in a doublet of the same overall wire length. Moreover, these lower-angle lobes are considerably weaker than the very-high-angle main lobe. As the elevation patterns suggest, the 45-degree inverted-V provides relatively weak radiation at angles suitable for long-distance communications.

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Although the 45-degree inverted-V might be useful for NVIS or regional communications through about 30 meters, it is not a desirable antenna for use above that band. In effect, the added 15 degrees of slope to each leg transformed the performance of the inverted-V. Given the normal desire for lower-angle radiation, the transformation has indeed been harmful. There is a limit to the slope of an inverted-V if we intend to use it for an all-band HF antenna. That limit is not much beyond a 30-degree slope.

+

Conclusion

+

By reviewing the properties of a 135' level doublet on all HF bands, we have been able to watch the evolution of inverted-V patterns as we increased the wire slope from 30 degrees to 45 degrees. While the 30-degree inverted-V gave useful general purpose performance, the 45-degree version of the antenna became generally useless on most bands for normal HF skip communications.

+

Had we begun with a set of antennas with a resonant 40-meter length, the results would not have ultimately changed. However, the complete degradation of patterns would not have occurred until about 20 MHz with a 45-degree inverted-V. If we had started with an antenna whose length was suitable for 160 meters, the patterns would have gone to pot at around 5 MHz. Indeed, the 45-degree inverted-V yields such poor performance that one might well do better by eliminating one leg and feeding the remaining leg at its center as a sloping doublet. Alternatively, an inverted-L--either base or center fed--might also yield better performance. The lesson is simple: if you must use an inverted-V as an all-band HF antenna, do not make the V too sharp.

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+ +
+

Updated 01-24-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ +
+

Return to Amateur Radio Page

+

Topics: Doublet, HF Multi Band, Inverted V


+ + diff --git a/content/wire/vrd.html b/content/wire/vrd.html new file mode 100644 index 0000000..163f110 --- /dev/null +++ b/content/wire/vrd.html @@ -0,0 +1,116 @@ + + + + + + Vertically Radiating Horizontal Antennas + + + +
+


+ VERTICALLY RADIATING HORIZONTAL ANTENNAS:
+ SOME METHODOLOGICAL PROBLEMS

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

Horizontal antennas include such old friends as the center-fed resonant half wavelength dipole, the inverted Vee variant, and a host of similar antennas. Recently, it was discovered that we could use versions of MININEC and NEC-2 to model what might happen if, in addition to the horizontal wire, a portion of the feedline also radiated. The general modeling procedure was to drop a quarter wavelength vertical wire down from the normal feedpoint (braid side) to simulate radiation from the outer surface of the braid. The physical analog to this model has been the installation of a line isolator 1/4 wl down the coax.

+

Unfortunately, the model wire antennas emerging from these exercises appear to have gathered more acronyms and call-sign labels than careful analysis. Full modeling details have rarely been given, and results are hardly replicable. However, even if the models can be replicated, there remain strong questions about whether the models are adequate representations of the realities of antenna construction and installation. In short, it is dubious whether anything near the modeled performance can be achieved with real wire antennas. It may be instructive to examine some of the modeling techniques involved in promoting vertical radiation concepts.

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+

Bad Models Make Bad Antenna Theory

+
Let's begin with dipoles and inverted Vees. Figure 1 illustrates the supposed difference between standard and vertically radiating dipoles and Vees. The standard horizontal antenna consists of a half wavelength of horizontally or sloped wire fed by a coaxial transmission line. An isolating balun installed at the feedpoint is optional, although many experts recommend one as a means of preventing the outer surface of the coaxial cable from carrying antenna currents and consequently radiating in unpredictable ways. Many users of these antennas have found no balun to be necessary. +
+ +
+

Vertically radiating horizontal antennas presume that the current originating on the inner surface of the coaxial cable braid will divide between the antenna wire attached to the braid and the outer surface of the braid. Also presumed is the idea that this outer surface is somehow floating, being too distant from an earth or system ground to be considered grounded, but having no other currents on it other than those developed as a result of the antenna-feedline junction. This permits the outer surface of the braid to act as another antenna wire. A line isolator--usually a device similar in principle to a W2DU ferrite-cores-over-a-length-of-coax--is installed 1/4 wl down the coax braid and terminates the radiating section of braid. The result is a current of full strength along the antenna wire connected to the coaxial cable center conductor and a divided current from the inner surface of the braid, part traveling along the antenna wire and part along the outer surface of the braid.

+

Since the outer surface of the braid is vertically oriented, the dominant polarization of its radiated field is vertical, with a consequential lowering of the overall radiation angle of the antenna's total pattern and a reduction in the front-to-side ratio of the antenna. If a wire dipole or inverted Vee exhibits something like a figure-8 or a peanut-shaped pattern, the vertically radiating versions of the same antennas are reported to exhibit oval or nearly round azimuth patterns.

+

If we accept all the premises of this scenario for the moment, it is possible to model both standard and vertically radiating dipoles and Vees using common materials and conditions, and to make a comparison between the resultant antennas patterns taken under identical modeling conditions. Let us choose copper wire, perhaps #14 as a commonly used size. Let us also select average earth as the soil under the antenna with a conductivity of 0.005 Siemens/meter and a dielectric constant of 13. These initial choices reflect how such antennas will actually be used, since few, in any, hams have access to lossless wire and perfect ground beneath the antenna.

+

In constructing our models, we may choose either MININEC or NEC-2 (since NEC-4 is just now becoming available, but at a price beyond the means of most amateurs). NEC-2 has some limitations in this exercise, since it requires a separate wire to which one applies the source, which is centered in the added segment. This short segment must meet adjacent segment length requirements of the program, which enlarges the number of segments in the total model if the feed wire is to be kept short. However, to reduce the number of segments, one may taper the segment lengths shorter toward the feed wire to maintain recommended ratios of adjacent wires. Additionally, the vertical wire must be about the same diameter as the antenna wire, since NEC-2 outputs become unreliable when wires of different diameter are joined in many modeling situations. However, NEC-2 includes a higher quality ground analysis system.

+

MININEC can handle wires of different diameter, but it is not without its own restrictions. First, for reasonable accuracy, segment lengths should be tapered when wires join at tight angles, and a right angle qualifies. Second, one must be careful with the placement of the source. MININEC sources are applied at one or the other end of a segment, which end must attach to another segment or wire. The end of the first wire is not a permitted source point if multiple junctions are present. Likewise, the junction end of the down wire is not a permitted source point, since it does not reflect the series connection of the coaxial cable to the horizontal wire, but instead treats the down wire as one side of the antenna and both sides of the horizontal portion as the other side of the antenna. One solution is to add a 2-segment wire as a feed point, placing the feed at the end of one segment within the wire. Additionally, one may also taper segment lengths within the wires as they approach the feed wire to ensure that adjacent wires meet program rules. Since MININEC has only a limited accuracy ground system, dropping the vertical wire below 0.2 wl above ground without creating a true ground-mounted vertical antenna may strain MININEC limits.

+

Figure 2 illustrates some of the salient points of NEC-2 and MININEC models of a vertically radiating dipole.

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+ +
+

The next question concerns the frequency of operation, which has implications for wire length and the height of the assembly above ground. With a quarter wavelength of vertically oriented coaxial cable setting a minimum height, I decided against 80 meters. The antenna would have to be a minimum of 68-70' above ground. More typical amateur heights range from 35 to 50' above ground. Therefore, the test frequency selected was 7.15 MHz. Antenna heights for models could then range from 35' to 50' for the horizontal section, with the bottom of the vertical section ranging from about 1' to 15' above ground.

+

Elevation patterns provide a general indicator of an antenna's gain when directed in the azimuth bearing of maximum radiation. Since low angle radiation has been one of the claimed hallmarks of the vertically radiating horizontal antenna, an elevation angle of 20 degrees has been chosen for the azimuth patterns. Figure 3 shows comparative patterns between a standard dipole and a vertically radiating version at a 35' height. These patterns happen to be taken with NEC-2, but are not significantly dissimilar to patterns taken with MININEC.

+
+ +
Table 1 below compares three models at heights of 35', 40', 45', and 50': one is a NEC-2 model with #14 copper wire as the vertical element; the second is a MININEC model using the same constraint; and the third is a MININEC model using a 0.5" copper vertical element in combination with the #14 horizontal wire. Although gain, elevation angle of maximum radiation, and feedpoint impedance vary, there is no significant change in the overall antenna pattern among any of the models or heights.
+
+ 
        A Comparison of Three Modeled Vertically Radiating Dipoles
+
+MININEC model: all #14 copper wire over average MININEC ground; with
+tapered segments to a short 2-segment feed wire.  Horizontal length: 67';
+vertical length: 33.5'
+
+Height    Gain at 20°    Azimuth angle  Maximum   Take-off  Feedpoint
+(feet)    in dBi         of maximum     gain-dBi  angle     Impedance
+                         radiation                          (R +/- jX)
+50'       3.05           79°            4.98      38°       63 - j14
+45'       2.35           78°            4.75      42°       66 - j8
+40'       1.73           76°            4.66      48°       67 + j1
+35'       1.17           75°            4.57      55°       61 + j13
+
+MININEC model: #14 horizontal copper wire with 0.5" vertical copper wire
+over average MININEC ground; with tapered segments to a short 2-segment
+feed wire.  Horizontal length: 67'; vertical length: 33'
+
+Height    Gain at 20°    Azimuth angle  Maximum   Take-off  Feedpoint
+(feet)    in dBi         of maximum     gain-dBi  angle     Impedance
+                         radiation                          (R +/- jX)
+50'       3.11           79°            5.07      38°       64 - j15
+45'       2.41           78°            4.85      42°       67 - j9
+40'       1.79           76°            4.76      48°       68 - j1
+35'       1.24           75°            4.70      55°       62 + j11
+
+NEC-2 model: all #14 copper wire over average Sommerfeld ground; with
+tapered segments to a short feed wire.  Horizontal length: 67'; vertical
+length: 33.5'
+
+Height    Gain at 20°    Azimuth angle  Maximum   Take-off  Feedpoint
+(feet)    in dBi         of maximum     gain-dBi  angle     Impedance
+                         radiation                          (R +/- jX)
+50'       3.51           79°            5.42      38°       57 - j11
+45'       2.76           78°            5.15      42°       60 - j7
+40'       2.02           77°            4.94      48°       61 - j1
+35'       1.19           77°            4.66      56°       59 + j9
+
+Note: NEC-2 and MININEC models using short segments rather than tapered
+segment lengths do not differ significantly from the figures presented for
+these models.  All models at all heights exhibit the same kidney-shaped
+azimuth pattern.
+
+Table 1.  A comparison of three modeled vertically radiating dipoles.
+

+

Obvious in Figure 3 is the displacement of the narrowed portion of the azimuth pattern toward the horizontal arm connected to the braid, relative to the overlaid pattern for a dipole. Overall gain in the most favored direction of the antennas is similar to that of a dipole, as is the overall gain to the sides (off the antenna ends). The latter is simply displaced. Nowhere does there appear the grand ovals and circles of omnidirectionality advertised for the vertically radiating antennas. Indeed, there seems to be a misconception about low standard dipoles, to the effect that they are exclusively horizontally polarized antennas. To dispel this misconception, Figure 4 compares the field components of a standard and a vertically radiating dipole azimuth pattern. Although the vertically radiating version shows naturally significantly greater vertically polarized radiation, the standard dipole has a significant amount that contributes to the broadening of the free space Figure 8 into the mere shell of a peanut.

+
+ +
+

Within these modeling strictures, which attempt to use modeling program features to replicate reality to the degree to which the programs are capable, there appears little to choose between the standard and the vertically radiating versions of the dipole. The displacement differential off the ends of the antenna would be difficult to detect in actual operation, even using antenna range A-B testing techniques. However, that differential might prove marginally useful to someone with certain QRM problems.

+

Why do these patterns differ so radically from some which claim oval or nearly circular radiation patterns for vertically radiating antennas? The answer lies in certain dubious modeling practices. One of these is the assumption of perfect ground under the antennas. (Some claims for 80-meter VRDs use the almost as rare very good or excellent ground.) This assumption permits the vertical portion of the antenna to seemingly radiate with much greater efficiency in models than a user is ever likely to achieve, even with a radial system under the antenna. Another is the use of lossless wire. A third is the selection of some precise distance of the vertical wire above ground, thereby optimizing conditions as no real user is likely to be able to replicate. These factors do not include obvious violations of the modeling constraints of the available programs, as noted earlier. Figure 5 shows what illusions may be wrought from unrealistic modeling.

+
+ +
+

When modeled as close to reality as MININEC and NEC-2 will permit and within program constraints, vertically radiating dipoles and Vees do not constitute radical departures from standard versions of these antennas. Rather, they represent predictable pattern distortions that may be of some use to some operators under some conditions. However, questions about modeling adequacy are only one aspect of the inquiry. There are some significant questions to be raised about the physical means be which a vertically radiating dipole or Vee is to be implemented.

+

I fear that many an investigator pursuing vertically radiating horizontal antennas has been fooled by antenna modeling possibilities into accepting uncritically the reality, regularity, and reliability of what adding an extra wire to a dipole seems to show under tenuous modeling assumptions. Until there emerges a more adequate analysis of the reported and modeled phenomenon, the vertically radiating horizontal antenna likely deserves to be set aside as an interesting example of unsatisfactory antenna modeling.
+

+
+ +

+
+

Updated 3-15-97. © L. B. Cebik, W4RNL Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Return to Amateur Radio Page

+

Topics: Dipole, HF Lower, Inverted V


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+

Notes on the Terminated Wide-Band "Folded Dipole"

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

As space for antennas continues to shrink in the present era of smaller urban and suburban yard, hams have begun to turn to 1-antenna solutions to their operating needs. Among the choices for a horizontal antenna that operates on all of the HF amateur bands, the wide-band "folded dipole" (WBFD) has been gaining popularity. I thought that it might be useful to do some comparative studies using this antenna as a base-line.

+

The basic WBFD looks something like Fig. 1.

+
+ +
+

The antenna design appears to be a folded dipole. However, a folded dipole is a resonant antenna, while the WBFD is designed to operate with a low feedpoint impedance across a wide range of frequencies. Moreover, the WBFD contains a non-inductive terminating resistor usually located at the point in the loop directly opposite the feedpoint. Normally, the resistor is in the 800-900 Ohm range. This impedance is roughly replicated at the feedpoint. Therefore, builders install a 16:1 RF transformer (either of transmission-line transformer or normal transformer design) at the feedpoint. The result is a low SWR value for 50-Ohm coaxial cable across the entire frequency range.

+

For receiving use, such as in SWL service, the terminating resistor can be a low wattage carbon type. For transmitting service, the resistor must have a power value capable of dissipating a fair share of the applied power. The exact amount will vary with frequency, but commercial versions of the antenna are often rated for reduced power at the low end of the operating range, where power dissipation is highest.

+

Commonly, WBFD antennas are offered in a 90 to 100 foot length (27-28 meters) for service between 2 and 30 MHz. However, one can build WBFD antennas in almost any length. Only the effective operating range of frequencies will change.

+

Since we may also construct doublets of the same length and feed them with parallel transmission line to an antenna tuner, it seemed fair to compare the gain of such a doublet with that of a WBFD of the same length across the 2-30 MHz range. The model I chose for the WBFD is 27.2 m (89.24') long, with the wires separated 0.2 m (7.8"). The terminating resistor is 820 Ohms, a standard value used in some commercial models. (Other commercial units use 900 Ohms, often composed of 3 2700-Ohm resistors in parallel.) The wire is #14 AWG. The doublet is a simple length of #14 copper wire exactly as long as the WBFD.

+
+ +
+

Fig. 2 compares the free-space gain of the two antennas at 1 MHz intervals from 2 to 30 MHz. Since the elevation angle of maximum radiation will be the same for both antennas for any height above ground and for any ground conditions, any differences that show up in the free-space model will also show up in actual antennas at any height above ground.

+

Several instructive notes emerge from the comparison of gain in Fig. 2. First, the overall average difference in gain between the two antennas is nearly 6.3 dB, with the advantage going to the doublet. If we neglect frequencies below 7 MHz, the average difference diminishes to 5.0 dB. For most of the range of use of the WBFD, then, there is about a 1 S-unit deficit in gain relative to a standard doublet of the same length in the same position.

+

Second, the WBFD gain curve displays a significant knee--a frequency below which its gain deteriorates rapidly. In the case of the current model, that frequency is about 6 MHz. At or below the knee-frequency, the terminating resistor dissipates more and more of the power. The result is not only a large decrease in gain and higher temperature stresses on the resistor, but as well, very low SWR values at the feedpoint. The knee-effect as the WBFD becomes significantly short relative to the length of a resonant dipole easily accounts for the need to de-rate the antenna relative to transmitting power below a certain frequency.

+

The deficit in gain is not necessarily a disadvantage for receiving purposes. Modern receivers tend to be equipped with receiving pre-amplifiers that the user can switch in as desired. The gain may range from 10 to 20 dB, depending upon design, and in some receivers may be stepped or variable. Therefore the gain deficit can be largely made up in the lower HF range. Moreover, the basic receiver, apart from pre-amplification, already has excess gain that is rarely used in the lower HF region.

+

In addition, one of the major problems in reception in the lower HF range, especially with respect to SW broadcast stations, is front-end overload from excessive signal strength. The overload also tends to produce spurious products within the receiver. Hence, reduced gain of the antenna can be in some circumstances an advantage rather than a disadvantage. Combined with the RF attenuator built into many receivers--which may be a single reduction value or stepped--the WBFD offers a potential for excellent lower HF reception, free of some of the problems that occur with higher gain antennas.

+

Because the WBFD is also a closed loop with a terminating resistor, many users claim quieter reception relative to doublets for a given receiver input signal strength. The degree to which this is both true and separable from the freedom from front-end overload is difficult to determine. Nonetheless, SWLs have found the WBFD a very useful tool for their efforts.

+

In order to establish that the WBFD has the same pattern as a doublet of the same length for any given frequency and height above ground, let's look at a couple of sample free-space patterns. For example, see Fig. 3.

+
+ +
+

The 27.2 meter WBFD and its comparison doublet exhibit a bi-directional pattern at 10 MHz. The shape of the pattern is identical, with only the 6 dB gain differential separating the two antennas. The -3 dB beamwidth points are also virtually identical. Since the take-off angle (elevation angle of maximum radiation), the reflection from a given set of ground conditions, and other such factors are not dependent upon signal strength, the two antennas would also show elevation patterns for any equal antenna height that are likewise congruent.

+
+ +
+

Fig. 4 shows comparative free-space azimuth patterns for the two antennas at 25 MHz. The WBFD pattern is simply a "mini" version of the doublet pattern, with about a 6 dB difference in strength.

+

There is an additional point in displaying these patterns. The exact pattern of lobes and nulls in the azimuth readings for a WBFD is identical to that of a doublet. As the length of the antenna exceeds 1.25 wavelength and approaches 1.5 wavelength, the bi-directional pattern at lower frequencies will break up into a collection of lobes and a collection of nulls. Therefore, the antenna is variably selective in its favored directions of good signal strength as one changes frequency. Those who contemplate installing either a doublet or a WBFD antenna need to consider well the patterns at key frequencies of interest in order to orient the antenna for maximum effectiveness.

+

The antenna type has also been used vertically to provide omni-directional coverage. However, in this orientation, when the antenna exceeds 1.25 wavelength in over length, the pattern begins to show primarily high angle radiation--exactly the opposite of what one normally desires from the upper HF band. As a result, some installations may use a pair of vertical WBFDs for full low-angle HF coverage.

+

A Note on Knees and Length

+

The knee of our 27.2-meter wide-band folded dipole occurs at about the frequency at which a center-fed doublet of the same length would be self-resonant, that is about 1/2 wavelength. We know that a doublet that is shorter than 1/2 wavelength exhibits a feedpoint resistance that declines with length and a capacitive reactance that increases with length.

+

The knee we observed in the gain of the 27.2 meter WBFD is interesting, since it suggests that we may vary the low frequency gain by changing the length of the antenna. Altering the length, of course, will also change the frequency at which the antenna transitions from a bi-directional pattern into a multi-lobed pattern.

+

To examine this question, I recreated the 27.2-m antenna model to perform frequency sweeps on both longer and shorter versions. As a sample, I ran a 50-m version and a 15-m version. All of the models used 820-Ohm terminating resistors, #14 AWG copper wire, and a spacing of 0.2 meters.

+
+ +
+

Fig. 5 compares the gain of the three antennas from 2 through 30 MHz in 1 MHz steps. As suspected, the 50-m antenna reduces the knee frequency to about 3 MHz. In contrast, the 15-m version increases the knee frequency to about 10 MHz. In general, a home builder may interpolate values for the knee frequency for other lengths in the overall range.

+

The longest of the antenna models shows a mere -10 dBi gain at 2 MHz, a value easily made up by the receiver and only about 1.5 to 2 S-units below the average gain of the antenna. Hence, it is likely to be more satisfactory as a transmitting antenna in the lower HF region. In contrast, the 2 MHz performance of the 15-m version is more than 30 dB lower than the average antenna performance, making it more suitable for higher HF transmitting.

+

The variations in gain among the curves in the relatively flat region of performance are a function of lobe formation. Maximum gain tends to attach to the major lobes of patterns taken at just higher than integral multiple of a wavelength, relative to antenna length. Minimum gain levels tend to be associated with antenna lengths near the "x+.5" wavelength (where x is an integer) points. When an antenna is 1.5, 2.5, 3.5, etc. wavelengths long, its pattern consists of a combination of emerging and disappearing lobes, all of relatively equal strength. For example, a 1 wavelength wire has 2 strong lobes that are 180 degrees apart and a 2 wavelength wire has 4 strong lobes that are roughly 90 degrees apart. A 1.5 wavelength wire has 6 lobes, as the 1 wavelength lobes diminish and the 2 wavelength lobes grow. Hence, coverage is wide, but at a reduction in maximum strength.

+

The number of peaks and valleys in the three gain curves is a function of length. The 50-m antenna passes through many more transitions from x wavelength to x.5 wavelength (where x is an integer) across the frequency span than do either of the shorter antennas. Hence, we should expect more highs and lows in the gain pattern.

+
+ +
+

One question posed by various recommended wire spacings in past literature is whether wire spacing makes a difference to performance. Fig. 5a provides something of an answer as it compares the gain values for models of a 15-meter long version in 0.2-m and 0.45-m spacing. The gain values are insignificantly different, ranging from 0.2 to 0.4 dB.

+
+ +
+

We find that the curve of SWR relative to the value of the terminating resistor will also show similar transitions according to WBFD antenna length. Fig. 6 shows the SWR pattern for the three antenna models. If we look at the most dramatic fluctuations--in the case of the 50-m antenna, we discover SWR peaks at x+2/3 wavelength points (where x is an integer). In contrast, we find SWR minimum values at the x+1/6 wavelength points (where x is an integer). The frequency span between points relative to the antenna length is 1/2 wavelength. The shorter antennas show the same pattern. However, the pattern is less evident because there are fewer maximum and minimum values to sample.

+

We may also note that the longer the WBFD, the higher the SWR excursions for a given value of terminating resistor. However, if we examine the lowest values of minimum SWR and exclude the region below the gain knee of the curve, the corresponding low points in the curve show the longest antenna also to exhibit the lowest minimum value of SWR. In other words, for a given wire size, spacing, and terminating resistor, longer WBFDs will exhibit a larger range within any given SWR cycle. As we approach the upper HF range, the values may exceed the desired 2:1 SWR limit.

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The amount by which a long WBFD exceeds a 2:1 SWR is not great, but it is noticeable. For receiving applications, mild excursions beyond the 2:1 limit have virtually no affect on the received signal strength for any length of 50-Ohm coax. Some transmitters use automatic power reduction circuitry as the SWR approaches 2:1 (using an internal reverse voltage sensor), and some linear amplifiers begin reducing power at lower levels of SWR in order to protect expensive transmitting tubes.

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There are two means of overcoming the potential problems of "high" SWR. Some manufacturers recommend the use of very long coaxial cables. Since the losses in the line increase with frequency, the SWR observed at the station end of the line will be lower at higher HF frequencies than at lower HF frequencies for any given value of SWR at the antenna end of the cable. The result of using longer coaxial cable runs will then be an SWR curve at the transmitter output that never exceeds 2:1. Compared to the reduced gain already inherent in WBFD design, the added losses of a long cable run are not considered excessive when totaling the overall system gain.

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Alternatively, modern amateur transceivers (and those in other services) are routinely (but not universally) equipped with automatic antenna tuner circuitry. Although limited in range compared to a wide-range external antenna tuner, these tuners are certainly adequate to handle the modest SWR values presented by even the longest WBFDs. Hence, the transmitter output circuitry prior to the tuner will show a very low SWR.

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Construction

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The decision to use a WBFD involves an evaluation of one's goals in operating or listening. Only with a set of specifications of this order can one decide whether the WBFD will meet the needs. The description of the antenna's advantages and limitations must be set against the operating specifications and along side other potential antennas that are candidates. Then selection becomes a matter of choosing the antenna that does most of the jobs well enough.

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If you do decide to use a WBFD, you can purchase one of the commercially made types. B&W (USA), Giovannini (Italy), and others produce these antennas in a variety of lengths. Alternatively, you can build your own.

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The antenna proper uses standard techniques of wide-spaced folded dipole construction. You will need twice the length of wire as you determine the antenna length to be. There is nothing critical about the exact length, although the general length will be a function of where you decide to place the frequency that forms the knee separating relative even performance at higher frequencies from diminishing gain at lower frequencies.

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Fig. 7 shows just 2 of many ways to space the wires along their length. In the 1930s, we might have used wood dowels boiled in paraffin. Today, we have access to a variety of better materials. Part A of the sketches shows fiberglass rods, with holes drilled to pass the size wire we decide to use. #12 to #14 AWG copper wire (0.06-0.08" or 1.5-2.0 mm) is likely to be the most common choice. The end post can be longer to hold tie-off ropes for the assembly. Fiberglass rods can be purchased from mail order sources. However, local home improvement centers often carry adaptable materials. For example, I recently spotted some 1/2" diameter fiberglass rod under the guise of chimney flue brush extension handles.

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Alternatively, I have also had good luck using 1/2" diameter CPVC, a thin-wall form of PVC tubing that replicates copper tubing sizes, shown in Part B of Fig. 7. A hacksaw cut in each end leads to a hole drilled to pass the chosen wire size. The wire press fits down the slot and into the hole. If the holes are not deburred, the wires stay put, although the spacers can be repositioned with fair ease.

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These are simply two of many ways to make the required spacers. Narrow strips of polycarbonate, acrylic, or Plexiglas would also work. Polycarbonate likely has the best UV resistance of this group. When adapting materials to a new use and environment, it is wise to check the structure every so often to ensure that it is wearing well under the influence of sunlight, precipitation, and temperature excursions. Of course, cut any spacers that you use to the desired length--about 8" (0.2 m) between wire holes for the models examined here. However, this spacing is not very critical.

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Locating a non-inductive resistor of sufficient power dissipation is likely to be the chief problem for WBFD builders who intend to transmit with the antenna. Unless you can find a suitable resistor at one of the surplus outlets, purchasing an antenna may prove economical in the long run, if we add both cost and parts-searching time together. Any value in the 800-900 Ohm range--or even "thereabouts," if a bargain appears--will serve.

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Manufacturers use different methods of packaging the resistor into the antenna assembly. Some prefer a total enclosure to weatherproof and bug-proof the resistor. However, one might have to de-rate the resistor's power handling capability under these circumstances. To maximize power dissipation, the resistor can be placed within a tube that is about twice the diameter and about 1.5 times the resistor's length. Air passing through the tube provides cooling, while the tube itself protects against immediate weather impacts. Since the antenna wire and resistor terminals will attach to strips of metal bonded to the tube, the resistor itself is relieved of strain. The down side of this technique is the need to clean out bugs and others debris on a regular basis. However, semi-annual inspection and antenna maintenance is always a good policy.

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For receiving-only applications, the resistor problem is much simplified. A series-parallel combination of carbon resistors with a net value of about 820 Ohms is easy to arrange. 1 to 5 watt non-inductive resistors provide the sturdiest construction. The assembly should be mounted in a UV-resistant plastic housing with strong terminals for connecting the antenna wires.

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The other challenging component is the 16:1 RF transformer. The builder has two general types of transformers to use: a transmission-line transformer or a standard wide-bandwidth transformer using a toroidal core. Transmission-line transformers are slightly more efficient for transmitting purposes, although they prefer purely resistive loads. Jerry Sevick, W2FMI, has written extensively on these units, with instructions on how to build them for many impedance transformation ratios. In a pinch, one might place two 4:1 baluns in series.

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There are proponents of standard RF transformers using toroidal cores. Doug DeMaw, W1FB, has written on their use, including calculating the power-handling capability of various cores. For receiving-only applications, small cores can be used, and the basic requirements and calculations are described in recent editions of the ARRL Handbook, Chapter 6.

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Whatever form of RF transformer you use, package it to withstand weather. A sealed UV-resistant plastic box with a correctly placed "weep" hole for moisture drainage is a good choice. Obviously, you will need connections for the antenna wires as well as a coax connector.

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A 3-Wire Version of the WBFD

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The WBFD has many variations, and from time to time--as I encounter and model them--I shall add a few notes on them. The first addition to the list is a 3-wire WHFD, outlined in Fig. 8, with the 2-wire version shown for contrast.

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For comparative purposes, I have made each antenna 27.2-m long, with a 0.2-m separation between wires. The 3-wire version places the terminating resistor in the "center" wire and parallel feeds the two "outer" wires. Although the arrangements is shown as a flat configuration, one can, as a variation, create a triangle of wires.

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With two parallel-fed wires, the terminating resistor needs to be about 1.5 times the anticipated center feedpoint impedance. Hence, the model uses a 900-Ohm resistor, with 600-Ohms as the expected feedpoint impedance. Of course, the feedpoint impedance is a nominal value, since the actual resistive component of the impedance will fluctuate continuously above and below that value as we move across the operating span.

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In general, the 3-wire version of the WBFD is capable of about 1-3 dB (depending upon frequency) gain advantage over the 2-wire version. The following brief table provides a glimpse at the fluctuations for the 27.2-m antennas. All gain values are for free-space.

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+Frequency       2-Wire          3-Wire          3-Wire
+MHz             Gain dBi        Gain dBi        Advantage dB
+ 5              -4.39           -1.62           2.77
+10              -2.51           -1.11           1.40
+15              -2.42           -0.39           2.02
+20              -0.56           +0.74           1.30
+25              -1.20           +0.53           1.73
+30              +1.28           +2.58           1.30
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Despite these fluctuations, the gain curves for the two versions of the WBFD are remarkable congruent, as shown in Fig. 9. The dual or parallel feed system of the 3-wire WBFD increases gain by feeding 2 wires, but it does not change the main characteristics of the antenna. Besides the congruence of gain curves, the patterns yielded by the 3-wire antenna differ from those of the 2-wire version only in peak gain, but not in strength. Since the gain increase is marginal, both antennas have patterns that replicate those of a simple doublet (with its widely varying impedance with changes in frequency), but remain smaller, that is, have much lower peak gain values. +
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The cost for the small increase in gain is a wider fluctuation in the impedance about a central impedance value. The reactance tends to be somewhat higher than for the 2-wire WBFD. Fig. 10 shows the comparative SWR curves for the two antennas, with each one using its own reference value: 820 Ohms for the 2-wire version and 600 Ohms for the 3-wire version.

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In addition to having higher peak values in the 2-30-MHz span, the 3-wire version curve slopes differ from the corresponding 2-wire slopes. The shallower parts of the curves are on opposite sides of the peaks.

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The construction of a 3-wire WBFD can generally follow the same set of techniques used for the 2-wire antenna, with the separators enlarged to handle the broader plane. The additional wire will increase the weight of the antenna proper by nearly 50%, and center support of the terminating resistor and the feedpoint area is advisable. Short sections of 600-Ohm (or thereabouts) open-wire feedline can create the feedpoint junction. Like the 2-wire WBFD, the 3-wire version requires a balun system or a wide-band transformer to match a 50-Ohm coax feedline.

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WBFDs can be used in inverted-Vee configurations. However, expect a decrease in the broadside gain and some vertically polarized radiation off the ends of the array--just as you would find in a simple doublet. The steeper the angle of the two side of the antenna, the greater will be the radiation off its ends. As the antenna length exceeds 1 wavelength, the patterns may increasingly differ from those of the antenna used horizontally.

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A Common Mistaken View of the Wide-Band Folded Dipole

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We may look at the wide-band folded dipole from another perspective, one encouraged by a 1983 B&W patent (#4,423,423). The patent sketch shows shorting wires close to the center of the array. The wires connect the feedpoint to the terminating resistor. In addition, they also connect the inner or feedpoint ends of each wire pair.

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The result of this variation is an antenna that is NOT a WBFD. Instead, as revealed by the sketch portion of Fig. 11, the new configuration places the resistor in a simple parallel connection with the feedpoint. The wires extending from the junctions of this parallel connection form virtual "fat" single wires to complete what amounts to a center-fed doublet.

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The sketch shows a 900-Ohm resistor in parallel with the feedpoint of the 27.2-m antenna. The SWR curve that accompanies the sketch reveals a property that is unlike the true WBFD antenna: a resonant feedpoint at about 5.2 MHz. The actual reported resonant impedance is about 63 Ohms. The parallel combination of 900 Ohms (the resistor) and 70 Ohms (the typical resonant dipole resistance) is about 65 Ohms.

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Fig. 12 provides a set of SWR curves across the 2-30-MHz span that we have used in the examination of the true WBFD. Since the increment between readings is 1 MHz, the 50-Ohm curves do not necessarily show the best SWR values possible. However, the 3 SWR minimum points show that the antenna acts completely normally when treated as a center-fed doublet. The 3 low 50-Ohm SWR values occur at the fundamental, the 3rd harmonic, and the 5th harmonic frequencies for the wire.

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The 900-Ohm SWR curve, of course, shows the opposite trend relative to the 50-Ohm curve. Minimum SWR values occur at the 2nd and 4th harmonic frequencies of the wire (between 10 and 11 MHz and again between 20 and 21 MHz). At these frequencies, the antenna feedpoint impedance would show very high values of resistance and reactance (except for a tiny frequency region where the reactance passes through zero as it changes type). Under these conditions, the 900 Ohm resistor dominates the parallel combination.

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We may compare the gain performance of this "faux" WBFD with a true WBFD of the same length. Construction would be identical except for the use or non-use of the shorting wires. At the fundamental and the odd harmonic frequencies, as shown in Fig. 13, the new antenna shows higher gain. However, at the 2nd and 4th harmonics, the gain values are virtually the same for both antennas.

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The dominant problem with the faux WBFD is the changing feedpoint requirement as we alter the frequency of operation. A direct coaxial feed is applicable in only 3 narrow frequency regions of the spectrum. Likewise, the 16:1 balun treatment shows equally limited application. Given the feeding limitations, one might well use a simple center-fed doublet with a parallel feedline and a wide-range antenna tuner. Fig. 14 overlays free-space E-plane (azimuth) patterns for 5.2, 10.4, 15.6, and 20.8 MHz to provide a better performance comparison among the doublet, the WBFD, and the faux WBFD.

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In all cases, the center-fed doublet exhibits the highest maximum gain. On the fundamental and the odd harmonics, the faux WBFD is nearly as strong, and the true WBFD is considerably weaker. On even harmonics, the doublet's gain is very significantly higher than both versions of the folded antenna with a resistor. The consistent aspect of the patterns is their shape. They are perfectly congruent throughout, differing only in the gain value.

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The faux WBFD turns out to be a simple center-fed doublet with a resistor that parallels the feedpoint terminals. Unless one needs an antenna that operates only on even harmonics of the antenna's fundamental length, it offers no useful advantages over the single-wire doublet without the resistor. At many frequencies, its gain deficit can be a distinct disadvantage.

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What Kind of Antenna is the True WBFD?

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We have been exploring the behavior of the WBFD so intently, that we have overlook an interesting and significant question: What kind of antenna is the WBFD? We have already shown some reasons why it is not a true folded dipole. But, we have not placed the WBFD into an appropriate category of antennas.

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The answer to our question is both easy and difficult: the terminated folded is a variety of traveling-wave antenna. Entire books have been devoted to traveling wave antennas. See, for example, C. H. Walter, Traveling Wave Antennas (1965): a classic and very thorough text on traveling-wave fundamentals for all relevant types of antennas. More commonly recognized traveling wave antennas are terminated long-wires, V-beams, and rhombics. However, many types of traveling wave antennas require no resistive or other termination.

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For our very limited purposes, we may contrast standing-wave and traveling-wave antennas in an over-simplified manner. Consider a transmission line that is lossless or perfect. If we leave the load end of the line without a load in an open condition, the entirety of the energy from the source returns to the source. In a transmission line, we usually view this condition as a system fault, since we obtain no useful work from the source energy. However, if we separate the transmission-line wires to create a doublet, something else happens. We have the energy reaching the line ends and returning. The result is a set of standing waves along the wire. Since the separate-wire situation creates a transducer, we obtain useful work in the conversion of the energy into into a field that expands without limit. An ideal antenna would show standing waves that reach the same peak value (however measured) at every peak. As well, all wave minimums would go to zero.

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There is no such thing as a perfect standing-wave antenna. Consider a 5 wavelength center-fed doublet composed of lossless wire. It will show a feedpoint current minimum value that is limited by the impedance at the feedpoint. As well, other current minimum points will not reach zero except at the very ends of the antenna. Likewise, the peak values will not be identical along with wire, with the highest peaks occurring closest to and farthest from the feedpoint. The top portion of Fig. 15 shows a typical (imperfect) standing wave current pattern.

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The lower portion of Fig. 15 shows the current distribution along a terminated end-fed long-wire, one of the simplest traveling-wave antennas. Since we have a terminating impedance, the ideal situation would show a constant current magnitude all along the wire. The termination impedance prevents the return of energy necessary to create stading waves. For a variety of reasons, terminated wires fail to achieve a perfect traveling-wave status. The termination is normally and for highly practical reasons a non-inductive resistor. However, the required impedance turns out to be both complex and finicky. So we only approximate a traveling wave, a basic current level with superimposed standing waves that are small but detectable. (The example shown uses a technique for setting up a traveling-wave long wire described by E. A. Laport in Radio Antenna Engineering, pp. 55-58, 301-339 (1950).)

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The relevance of these notes to the WBFD and related antennas is straightforward: we may use the current distribution along an antenna to determine in a general way whether an antenna is a standing-wave or a traveling-wave antenna. Fig. 16 shows the current distribution at 10.4 MHz of several antennas, all 27.2 m long. 10.4 MHz is the second harmonic of the 5.2-MHz fundamental frequency. The arbitrary feedpoint current for all of the antennas is 1.0 (A) with a 0.0-degree phase angle. All current values are relative to this convenient value.

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The center-fed single-wire doublet, a prime example of a standing-wave antenna, shows peak current values about half-way between the feedpoint and the wire ends. The peak currents are over 5 times the feedpoint value, a typical situation for a 1 wavelength doublet. The second antenna is a folded dipole operated at its second harmonic. It gain is low due to the very low value of the feedpoint resistance (about 7 Ohms). Hence, even the copper wire construction removes almost 3 dB of the antenna's theoretical gain if made from lossless wire. Nevertheless, within these restrictions, the antenna shows the folded-dipole version of a standing wave. Relative to the single-wire doublet, the standing wave is displaced by a quarter wavelength along the wire due to the fact that folded dipoles show a combination of radiation and transmission-line currents. (For more on this subject, see "Unfolding the Story of the Folded Dipole".) Note that the current minimums are very close to zero (actually about 0.02 to 0.03 relative magnitude).

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The next two antennas shown in Fig. 16 are alternative narrow-spaced and wide-space versions of the true WBFD. The narrow version spaces the wires by 0.2 m; the wide version uses a spacing of 1.0 m. In the wide version, each current curve is relative in height to the distance from its associated wire. In both cases, the antennas exhibit a standing-wave property, but overlaid on a traveling-wave current value of about .75 relative magnitude. The standing-wave component is about +/-0.30 relative magnitude. Hence, the minimum current level is a bit over 0.45 relative to the feedpoint value. (Values for the 2 versions of the antenna may vary by about 0.03 in relative magnitude from the listed values or about 5%.) The fact that we see the overlaid standing-wave component in current graphs may obscure the basic traveling-wave component of the current distribution until we realize that the current magnitude never approaches zero and remains well above zero throughout the antenna structure.

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All traveling-wave antennas that use terminations dissipate energy in the resistive portion of the termination. Although "sound-bite" wisdom about terminations uses a dissipation value of 50%, we should generally ignore that figure. The actual dissipation in the termination depends on the antenna configuration and frequency of operation. The actual value may be over or under that value by a considerable amount. However, any energy dissipated is unavaiable for the radiated field, and hence, we obtain the WBFD gain levels that fall considerably short of comparable fields from the center-fed doublet.

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The bottom current distribution pattern in Fig. 16 completes the survey by including the curves for the faux WBFD. The curves have the general shape of those for the center-fed single-wire doublet and the minimum values approach zero. The parallel resistor does not change the antenna's classification as essentially a standing-wave antenna.

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Although the last antenna is indeed a faux WBFD, since is has no relationship except physical appearance to a folded dipole of any sort, I have avoided calling the WBFD a faux folded dipole. The WBFD is not a true folded dipole because it is a traveling-wave antenna. Nevertheless, it retains more than vestigial traces of its folded-dipole origins in the overlaid standing wave pattern on the baseline traveling-wave current level.

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Conclusion

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A WBFD antenna is not for everyone. However, gaining some understanding of its operation, its nature, its advantages, and its limitations may be useful in the process of choosing an antenna--or even simply learning more about what various antenna types can do. The WBFD has its niche among amateur, governmental/military, and SWL antennas, but that niche is certainly not universal. The government and the military find the antenna useful for ALE (very rapid frequency excursions), and some amateurs are experimenting with these techniques. Within more normal time periods allowed for frequency changes, antenna tuner automation is generally fast enough for most contest environments, and manual tuning suffices for other communications--using a single-wire doublet.

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Receiving versions of the antenna can be home built for not much more than the cost of the wire, since the materials necessary for low-power terminating resistors and wide-band RF transformers are low. However, building a transmitting version of the antenna at home may be much more problematical, since parts may be hard to find or hard to fabricate. The alternative, of course, is one of the commercial versions, in an exchange of bucks for bother.

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Updated 6-1-2000, 7-19-2000, 2-13-2004, 10-22-2005. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Dipole, HF Multi Band


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Notes on Wide-Band Multi-Wire "Folded Dipoles"
+ Part 1: Some Idealized Illusions

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L. B. Cebik, W4RNL

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In "Notes on the Terminated Wide-Band 'Folded Dipole'", I briefly touched on the 3-wire version of the antenna. In this note, I want to expand a bit on that antenna as part of a larger look at multi-wire "folded dipole" antennas using a terminating resistor to extend the SWR bandwidth. In fact, we shall review and expand coverage of 4 antennas: the standard single-wire doublet, the most familiar 2-wire terminated version, the sometimes mis-drawn 3-wire version, and a 5-wire version of the antenna. The goal is to enlarge our understanding of how these antennas work and what features count as advantages and disadvantages of them.

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In the process, we shall examine some interesting properties of models of wide-band multi-wire terminated antennas based on idealized models. There are some techniques of model formation that are very useful under certain circumstances. However, if inappropriately relied upon, they can mislead us. As well, we may sometimes collect only partial data from an antenna model and be equally led astray. In this first part of the exercise, let's allow ourselves to be led and see where the path may wind.

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The basic antenna will be 27.2 m (89.14') long. Fig. 1 outlines the single-wire doublet and the common 2-wire version of the terminated antenna having the same length. The sketch does not specify any particular spacing between wires of the terminated antenna. Any reasonable spacing will work, from very close to some larger spacing that is still only a small percentage of the total length. The models for this antenna us a spacing of 0.2 m (6.5"), which is well under 1% of the antenna's length. However, before we close, we shall explore the effects of using the relatively narrow spacing of our initial models and using wider element spacing.

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The TR (terminating resistor) element in the 2-wire wide-band antenna is 820 Ohms in this model. However, values between 800-900 Ohms are most common, and versions exist with resistors ranging from 400 Ohms to 1200 Ohms. The resistor must be non-inductive, ruling out wire-wound power resistors. The resistor inductance would count as a loading coil, adding very significant reactance. In fact, the reactance would climb with frequency and eventually form an effective RF choke. To overcome the problem of finding a desired resistance power value that will not over-weight the center of the antenna, many builders use higher value resistors in parallel. For receiving only, the resistors can be of any power value. However, for transmitting, the terminating resistor must be capable of dissipating about one half of the anticipated power applied to the antenna. Paralleled resistors must allow for air flow to carry away heat, while at the same time providing protection from the weather in which the antenna operates. Weight, heat, and weather are the three primary enemies of a terminated "folded dipole."

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The terminated "folded dipole" only looks like a folded dipole. The wire configuration does not perform an impedance transformation like an ordinary folded dipole without the terminating resistor. As well, the standard folded dipole is a narrow-band antenna, like the simple dipole. In a terminated 2-wire wide-band antenna, the impedance at the feedpoint is a function of the terminating resistor. In fact, the actual impedance at any frequency is a joint function of the termination and the antenna length in wavelengths.

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The chief reason for using a 2-wire wide-band terminated antenna is to obtain a satisfactory feedline SWR level across a wide range of frequencies. For the 27.2-m antenna, I shall sample 2 through 30 MHz as a preliminary operating range. Fig. 2 outlines on the same graph the SWR of a single-wire doublet and of a 2-wire terminated antenna. The most common feedline used with a single wire doublet is parallel 450-Ohm transmission line. Therefore, the doublet SWR curve uses that reference impedance. For all frequencies, the SWR ranges from moderately high to very high. The doublet works by having low line losses, even with fairly high SWR levels, and an antenna tuner in the shack provides the impedance transformation to the 50-Ohm input/output of the transceiver or other equipment. The impedance at the antenna tuner terminals is unlikely to be the same as at the antenna feedpoint terminals. When the feedpoint impedance and the characteristic impedance of the line are different, the transmission line acts as an impedance transformer for each electrical half wavelength. Hence, the tuner terminals show an impedance that is a joint function of the original feedpoint impedance, the line characteristic impedance, and the electrical length of the transmission line.

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+

The wide-band 2-wire terminated antenna SWR curve uses 820 Ohms as its reference impedance. The precise value is non-critical so long as it is close to the value of the terminating resistor. The curve in Fig. 2 shows only minor peaks above the 2:1 level, and those peaks tend to grow with increasing frequency. However, most versions of the antenna employ 50-Ohm coaxial cable as the feedline. The reference impedance and the cable impedance show a 16:1 ratio. Although a 16:1 balun is possible, many builders employ 2 4:1 baluns (although one of them can be an unun). Many balun designs become lossy with rising reactance. Although those losses may be low compared to the power dissipated in the terminating resistor, some antenna makers use a standard transformer to effect the wide-band match. The key factor in any such transformer is to avoid core saturation. See the end of Chapter 6 of the ARRL Handbook for a brief characterization of the 2 types of impedance transformers and the basic needs of each kind. A final alternative involving impedance transformation concerns the terminating resistor itself. I have heard of using a 50-Ohm resistor and placing a 16:1 transformer between it and the wire to create the effect of an 800-Ohm terminating resistor.

+

To take care of any remnant SWR peaks that exceed 2:1 at the junction with the coaxial cable and the antenna and its impedance transforming devices, some wide-band antenna makers recommend very long lengths of coaxial cable. The rationale is simple. Coaxial cable losses are real, but will be relatively small--even at 30 MHz--compared to the losses due to the dissipation of applied energy in the terminating resistor. Hence, the use of a long cable is operationally insignificant relative to antenna performance. Moreover, the long cable will usually prevent the triggering of fold-back circuitry that protects the final amplifier in the presence of excessive SWR values.

+

The 3-wire terminated wide-band antenna is an extension of the 2-wire version. The general claim associated with the 3-wire version is higher gain with equal or better SWR curves. We shall eventually examine the gain claim in some detail. For the moment, we may simply see the schematic outlines of the 3-wire wide-band antenna in Fig. 3. For the sample model, the terminating resistor is 900 Ohms.

+
+ +
+

The right side of the sketch shows the parallel connection of the antenna feedpoint terminals on the 2 non-terminated lines. This configuration yields proper connections for wide-band service. In some sketches (that do not pretend to be electrical schematic diagrams of the antenna), I have seen simplified connections that can mislead the home builder. The sketches seem to show the center point of each non-terminated wire as comprising each side of a proper series feedpoint. For normal installations with no special components, this system will not work. Fig. 4 shows why.

+
+ +
+

The left side of the sketch shows the circuit path of the antenna if we join the center points and connect the source between them. The path leads at any instant away from one connection and toward the other through 2 parallel paths. At the ends of the antenna (obviously not drawn to scale in Fig. 4), the junctions with the line carrying the terminating resistor at its center have equal voltage. The net voltage drop across the resistor is therefore zero, and that component has no function in the antenna, when set up in this way. In fact, models created using this system show no difference of pattern, impedance, or termination-line current for any value of resistor, from zero to very high.

+

The system on the right provides the correct path for the terminating resistor to do its work. When I modeled the antenna, I used the terminating resistor line as a center point. Then I set up the fed lines 0.2 m away from the center line. The need to connect the feedpoints in parallel presents an interesting geometry challenge if we model the antenna using only wire entries. However, there is a simple technique of connecting feedpoints in parallel that may be useful to newer antenna modelers. The following model description from EZNEC may illustrate the general technique.

+ 
+                      EZNEC/4 ver. 4.0
+
+3-Wire Wide-Band FD                          6/24/05     9:28:16 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+
+Frequency = 12 MHz
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+No.            End 1     Coord. (m)              End 2     Coord. (m)       Dia (mm)  Segs
+          Conn.      X       Y       Z       Conn.      X       Y       Z
+1          W4E2    -13.6,      0,     15      W2E1     13.6,      0,     15       #12   69
+2          W5E1     13.6,      0,     15      W3E1     13.6,      0,   15.2       #12   1
+3          W2E2     13.6,      0,   15.2      W4E1    -13.6,      0,   15.2       #12   69
+4          W3E2    -13.6,      0,   15.2      W7E2    -13.6,      0,     15       #12   1
+5          W1E2     13.6,      0,     15      W6E1     13.6,      0,   14.8       #12   1
+6          W5E2     13.6,      0,   14.8      W7E1    -13.6,      0,   14.8       #12   69
+7          W6E2    -13.6,      0,   14.8      W1E1    -13.6,      0,     15       #12   1
+8                   -0.1,      1,     15                0.1,      1,     15       #20   1
+
+Total Segments: 212
+
+              -------------- SOURCES --------------
+
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       8        50.00      50.00    1        1           0         V
+
+          -------------- LOADS (R + jX Type) --------------
+
+Load     Specified Pos.     Actual Pos.         R          X
+       Wire #  % From E1  % From E1  Seg      (ohms)     (ohms)
+1       1        50.00      50.00    35       900        0
+
+                -------- TRANSMISSION LINES ---------
+
+No.    End 1 Specified Pos End 1 Act  End 2 Specified Pos End 2 Act  Length      Z0       VF  Rev/Norm
+       Wire #    % From E1 % From E1  Wire #    % From E1 % From E1  (m)        (ohms)
+1      3           50.00     50.00    8           50.00     50.00    0.01         500     1      N
+2      6           50.00     50.00    8           50.00     50.00    0.01         500     1      N
+
+Ground type is Free Space
+
+
+

Wire 1 is the terminated line, as indicated by the Load entry. Wires 3 and 6 are the lines with the feedpoints shown in the original antenna sketch. Wires 2, 4, 5, and 7 are the end-connecting wires. Wire 8 is the feedpoint wire segments, as indicated by the Source entry in the description. The wire is only a meter away from the main wires, but it is so short and thin (0.2 m by AWG #20) that it does not materially affect the performance figures of the main wires.

+

Now note the 2 transmission-line entries. Each runs from the center of one of the fed wires to the new distant source wire. A transmission line is not a physical or radiating wire within a model. It is only a mathematical construct factored into the model after completion of basic matrix calculations. In fact, the physical or geometrical distance between the source wire and the wire segment at the other end of the transmission line does not define the line length. Instead, we specify the line's electrical length (as well as the characteristic impedance) when we enter the transmission line data, and calculations use this length. Note that the length for each of the 2 lines is 10 cm (about 4"). We could have made it even shorter (down to something like 1e-10). But 4" effects virtually no impedance transformation down the line. In fact, the specified characteristic impedance (500 Ohms) is also non-critical, and changing it by a few hundred Ohms creates virtually no impact on the reported final feedpoint impedance.

+

The technique of using near-zero lengths of transmission line to connect wires in parallel is very useful to many types of models that connect feedpoints in parallel. NEC-2 and -4 have some limitations with very shallow angles that are often involved in these kinds of connections. The wire surface can penetrate the center third of the other wire segment at the junction, creating errors in the current calculations. The transmission-line technique avoids those problems. As well--and especially apt to this case--the technique avoids involving us in extra wires, odd changes of wire direction, and the inevitable expansion of the model size as measured by the number of segments. Nevertheless, we must recognize that our models are idealizations. Any implementation of a 3-wire wide-band terminated antenna will necessarily have leads to the common feedpoint at which we find the impedance transformation device. Whether the ease of modeling with the TL-based parallel connections serves us well or ill we shall not determine until we explore Part 2 of the exercise.

+

I used a similar system to parallel-connect the feedpoints of 4 wires surrounding a terminating resistor wire. The 5-wire wide-band terminated antenna appears in schematic form in Fig. 5. The schematic does not attempt to replicate the modeled physical structure, but is handy to represent the 4 paralleled feedpoints. The sketch on the right gives an end-on view of the antenna. The two new wires are at right angles to the existing wires, forming a cage of sorts around the center wire. The square represents the terminating resistor at the center of the center wire.

+
+ +
+

As an alternative version, I modeled the 5-wire wide-band terminated antenna as a planar construct. The far right sketch shows the general idea, but not at all to scale. The fed wires lie in a single plane with the termination wire, 2 above and 2 below the terminating resistor. The model uses the same spacing--0.2 m--between each wire. As well, the model uses the same short transmission-line technique to connect the feedpoints in parallel. In both versions of the 5-wire antenna, the terminating resistor is 800 Ohms. The planar version seems to show slightly better performance than the square version, so I shall use it for the initial data-gathering exercise.

+

We can now examine the SWR bandwidths of the 2 expanded versions of the wide-band terminated antenna. Fig. 6 shows the 500-Ohm SWR curve for the 3-wire version and the 300-Ohm curve for the 5-wire version. The 3-wire antenna shows a very well-behaved SWR curve, with an excursion above 2:1 only between 3 and 4 MHz, below the frequency that I shall eventually recommend as the minimum usable frequency for all of these 27.2-m antennas. However, note a change relative to the 2-wire antenna. For the smaller antenna, the center of the feedpoint impedance excursions occurs at about the same impedance as the terminating resistor. However, the SWR reference for the 3-wire antenna is only about 55% of the value of the terminating resistor (500 vs. 900 Ohms).

+
+ +
+

The curve for the planar 5-wire version of the wide-band array is less well behaved, with 3 humps above the 2:1 SWR level. Although the terminating resistor is 800 Ohms, the reference level for the SWR is down to 300 Ohms, or under 40%. As we drop the necessary reference impedance, due to having more wire feedpoints in parallel, the reactance at any given frequency plays a larger role in determining the SWR. Hence, the lower the feedpoint reference level, the more likely we are to find higher SWR levels.

+

The 3- and 5-wire antennas shows interesting parallels between the curves, with peaks near 3-4, 7-8, 14-15, 20, and 25-26 MHz. In this respect, the curves are only vaguely similar to the 2-wire version of the antenna, despite the similarities in the terminating resistor values (800-900 Ohms). For SWR bandwidth, either the 2-wire or the 3-wire versions of the antenna show the more promise. While the 2-wire antenna requires a 16:1 impedance transformation for use with 50-Ohm coaxial cable, the 3-wire antenna requires a 10:1 transformation. The 5-wire version sets up a conflict: the reference impedance requires a 6:1 transformation, a value within construction limits for a single balun. However, the SWR excursions suggest a considerable reactive component that may induce higher losses in at least some balun designs.

+

If SWR bandwidth were the only consideration, then the simplicity of the 2-wire antenna would dictate its use. The addition of more wires complicates the antennas structure and adds weight, especially in the separators needed to keep the antenna from corkscrewing in the wind. So our final question is whether we obtain any advantage in turning to a more complex wide-band terminated "folded dipole."

+

The brief answer is a qualified "yes:" we obtain more gain from adding fed wires to the system. The following table illustrates the gain advantage of adding wires.

+ 
+Comparison of Maximum Free-Space Gain Values of 27.2-m Antennas at Selected Frequencies
+Frequency              6 MHz         12 MHz          18 MHz          24 MHz
+Antenna                               Free-Space Gain dBi
+1-Wire Doublet         2.18          4.37            3.73            4.59
+5-Wire Wide-Band       1.32          0.19            2.78            1.56
+3-Wire Wide-Band       -0.36         -0.80           1.64            0.50
+2-Wire Wide-Band       -2.59         -2.36           0.04            -1.07
+
+

For each of the selected frequencies in 6-MHz increments, the larger the number of wires in the wide-band antenna, the higher the gain. In some cases, the 5-wire antenna comes within 0.9 dB of matching the non-terminated doublet, while in other instances, the differential is almost 4.2 dB. However, by the time we get down to 2 wires in the terminated antenna, the gain differential can be as much as 6.7 dB. Fig. 7 provides maximum free-space gain curves for all 4 antennas from 2 through 30 MHz in 1 MHz intervals.

+
+ +
+

The curves show several items of interest. First, the more wires in the array, the greater the variability of maximum gain across the entire scanned range. Despite the higher variability of gain in the 5-wire curve, the gain curves for the 3 terminated antennas show a tight parallelism. On a few of the sampled frequencies (1-MHz increments), the 5-wire antenna comes close to equaling the gain of the doublet used as a standard. However, a 3-dB differential is more common. The 2-wire antenna averages about 5-6 dB differential from the doublet values. Note that all of the models set up their wires parallel to the Z-axis, so the gain reports are taken in the X-Y plane or broadside to the plane of the wires.

+

More significant is the fact that all 3 terminated antennas show a knee in their curves, Below the knee frequency, the gain drops very rapidly. The knee frequency occurs when the antenna passes below an electrical 1/2 wavelength at the operating frequency. Broadly speaking, the knee for the 27.2-m antennas occurs around 5.5 MHz. The larger the antenna, the lower the knee frequency, as the multitude of wires act like a fatter single wire. However, below the knee frequency, the 5-wire antenna loses gain faster than the simpler wide-band versions. Although the doublet exhibits quite reasonable gain below the knee frequency, at a certain point, the gain may be unobtainable in practical terms. As an antenna falls to 3/8 wavelength or shorter, the reactance climbs rapidly while the resistance sinks to a very low value. The combination will show considerable line loss, even using low-loss parallel transmission line, and the antenna tuner may have difficulties in effecting a match to the values that appear at its terminals.

+

To obtain a better view of comparative gain with the recommended operating range, we may omit the region at and below the knee from our graph. Fig. 8 provides the same data as Fig. 7, but the frequency range restriction expands the Y-axis. With a knee at about 5.5 MHz, the recommended operating range for the 27.2-m antennas is about 6-30 MHz. For operation down to 2 MHz, I would suggest an antenna (of any of the 4 types) that is about 71-72 m (about 235'). Since we are not seeking precise resonance, the exact length is not important so long as the antenna is at least 1/2 wavelength at the lowest operating frequency.

+
+ +
+

The expanded curves in Fig. 8 show more clearly the parallel structure of the 2-wire, 3-wire, and 5-wire gain values across the recommended spectrum. As well, Y-axis expansion shows the high variability of the 5-wire gain curve. It sometimes almost reaches the level of the doublet, but on other frequencies, it falls closer to the level attained by the 3-wire antenna. Of course, the exact structure of these curves is subject to variation with small changes in construction--either overall length or spacing--or in the exact value of the terminating resistor. Nevertheless, the most notable trends remain intact.

+

Gain variations are NOT the result of any changes in antenna pattern as we move from one 27.2-m antenna to another. In fact, the antenna patterns are functions of the overall wire length, and the presence of multiple wires and the terminating resistor does not affect any other property than lobe strength. (This statement requires a bit of modification: the wire length is the electrical length of the antenna rather than its simple physical length. Multiple wires tend to act like a single fat wire, making the antenna longer by a wider margin than a single wire. Hence, if all the subject antennas from 1 to 5 wires are the same physical length, the larger the number of wires, the electrically longer the antenna. The planar 5-wire may further complicate the calculation of electrical length due to the end connecting wires. Fig. 9 overlays the patterns of all 4 antennas at 12 MHz. Perhaps the only difference detectable is at the junction of the main lobe with each of the minor lobes. The more wires, the softer the curve at the junction. It is likely that the need for end wires to connect the horizontal wires is the main reason for the softened junction.

+
+ +
+

The pattern test is repeatable on any frequency. Fig. 10 provides a second sample of overlaid patterns at 24 MHz. Where lobes join (at pattern nulls), we once more find that if we have more wires and end wires in the antenna structure, the null points soften into curves. Other than that single phenomenon, the patterns are wholly congruent and vary only in lobe strength.

+
+ +
+

Before we close this exploration, it may be wise to examine the effect of spacing between the wires in a terminated array. In a standard folded dipole, there is no significant difference in performance between narrow and wide spacing values, at least up to the point where the distance exceeds a value that will support 2-wire transmission-line operation. However, as we have noted, the terminated arrays only look like folded dipoles.

+

All of the terminated antennas used so far are 27.2 m long with a spacing between wires of 0.2 m (about 7.9"). I revised the spacing for a series of test models to a value of 1.5 m (59"). Because initial tests using diamond and fan configurations proved unpromising, I maintained the parallel runs of AWG #12 wires.

+
+ +
Fig. 11 compares the maximum free-space gain values for the 2 versions of the 2-wire terminated array. The wider array shows an average gain increase of about 1 dB, although that increase does not appear at every frequency in the test range (using 6 MHz as a starting frequency). The original narrow version of the antenna used an 820-Ohm terminating resistor and a similar value for the SWR reference impedance. Widening the antenna required an increase in both values to 900 Ohms. Fig. 12 compares the SWR curves for both 2-wire antennas on the assumption that each will use an optimized impedance transformation device for any adjustment to match a coaxial cable. The SWR curves show no features that would dictate the use of one antenna version over the other. +
+ +
+

The 3-wire version of the terminated array used the same 1.5-m spacing in the wide version. The result is an array that is 3-m wide overall, with the terminated line between the fed wires. Fig. 13 shows the comparative gain curves for the two antennas. The wide-version curve shows similar characteristics to the corresponding curve for the 2-wire antenna. However, the gain differential between wide and narrow antennas averages close to 1.5 dB.

+
+ +
+

The terminating resistor for both the narrow and wide antennas is 900 Ohms. However, the best reference impedance for the wide version is about 450 Ohms, about 50 Ohms less than for the narrow version. Fig. 14 traces both SWR curves. The curve for the wider version of the antenna shows larger excursions, but remains below 2:1 across the entire test range.

+
+ +
+

Although the 5-wire array remains the same length, its area grows by a factor of 7.5. The inner fed wires are 1.5 m from the terminated center wire, while the outer fed wires are 3.0 m from center. Fig. 15 provides one measure of whether the increased width is worth while in terms of the overall gain advantage of the wider antenna. The wide array provides almost 2-dB average gain over the narrower (0.8-m) version. Unlike the 2-wire and 2-wire arrays, where the gain lines cross at certain frequencies, the wide 5-wire antenna shows a gain advantage throughout the operating spectrum.

+

(Remember that the gain measurements are for free space and are taken broadside to the plane of the wires. Part 2 in this exercise will give us good reasn to remember these limiting factors of this initial study.)

+
+ +
+

Both versions of the 5-wire antenna use 800-Ohm terminating resistors. As well, the reference impedance for both SWR curves is 300 Ohms. The average 300-Ohm SWR is lower for the wide antenna, although the specific value may vary at some selected frequencies. Unlike the narrow array, from 6 MHz upward, the wide array SWR makes only one excursion above the 2:1 level and remains below 2.2:1 at 13 and 14 MHz.

+
+ +
+

The following short table samples some of these results in tabular form. For a few frequencies between 6 and 12 MHz, the table lists the maximum free-space gain of each of the 6 terminated arrays. For comparison, the table adds a 7th gain column, listing the maximum gain of a single wire 27.2-m doublet.

+ 
+Maximum Gain Comparison Among 27.2-m Antennas at Selected Frequencies.
+                                               Maximum Free-Space Gain dBi
+Frequency     Doublet     2-Wire       2-Wire       3-Wire       3-Wire        5-Wire      5-Wire
+                          Narrow       Wide         Narrow       Wide          Narrow      Wide
+6             2.18        -2.59        -2.47        -0.36        -0.05         1.32        1.62
+8             2.66        -2.22        -1.27        -0.70         0.58         0.50        1.99
+10            3.38        -2.51        -1.15        -1.11         0.55        -0.25        1.91
+12            4.37        -2.36        -1.20        -0.80         0.63         0.19        2.35
+
+

The table makes clear that the narrow 3-wire array is superior in gain to the wide 2-wire antenna and that the narrow 5-wire array is superior in gain to the wide 3-wire antenna. However, each wide version is superior in gain to its corresponding narrow version. However, even the highest-gain terminated array (the wide 5-wire planar version) is deficient in gain by 0.5 to 2.0 dB relative to the single-wire unterminated doublet of the same length.

+

These results emerge from exploring only the plane that is broadside to the axis of the multi-wire antennas. We have not looked at the plane that would be edgewise to the wires. Nor have compared patterns taken broadside and edgewise to the plane of the wires. Moreover, we have not explored the relative gain of the various antennas at some common height above a specified ground quality.

+

Some Tentative Conclusions

+

This initial attempt to take a fresh look at multi-wire terminated wide-band antennas seems to justify a few general conclusions. These conclusions rest on 2 features of the investigation. One is the use of idealized models for 3- and 5-wire arrays that use virtual zero-spacing between the wires forming the parallel connections at the feedpoint. The second feature is the use of only partial data from the collection available to us from the models. Nevertheless, the project appears to show high promise for potentially improving the multi-wire wide-band terminated antennas that we might build.

+
+

1. All terminated wide-band "folded dipoles" have knee frequencies, below which the gain drops very rapidly. The recommended operating range for any of the antennas is from an electrical length of about 1/2 wavelength upward in frequency.

+

2. As we add more fed wires to a terminated antenna, we increase its average gain over the operating spectrum. The gain increase never quite reaches the level of a single-wire doublet.

+

3. As we add more wires to a terminated wide-band antenna, the center or reference SWR impedance decreases both intrinsically and with respect to the value of the terminating resistor.

+

4. 2- and 3-wire terminated wide-band arrays show stable SWR curves through their operating ranges. However, adding further wires tends to produces curves with greater SWR excursions relative to the reference impedance.

+

5. Terminated wide-band antennas show increased gain by widening the distance between wires. Spacing adjustments may require revision of the optimal terminating resistor value and the reference SWR impedance.

+
+

Some of these conclusions are in fact generally true. Others may be only partially true or simply illusions based on the limiting factors of model formation and use in gathering data. In Part 2, we shall explore the available data in greater detail and develop some all-wire models of the various arrays. That effort will allow us to sort out which of the conclusions are useful as they stand and which require modification, revision, or deletion.

+

For the moment, we may simply allow ourselves to be enthusiastic about the potential improvements that we have seemingly uncovered.

+
+ +
+

Updated 05-01-2007. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for April, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2

+

Go to Main Index

+

Topics: Dipole, HF Multi Band


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+

Notes on Wide-Band Multi-Wire "Folded Dipoles"
+ Part 2: Some More Real Potentials

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

In Part 1 of this exercise, I developed idealized models of multi-wire terminated wide-band antennas as a pathway to understanding better their performance. I replicated 2-, 3-, and 5-wire terminated arrays using idealized techniques of feeding the antennas and examining the free-space patterns taken broadside to the plane of the wires. The patterns were all tidy, and the data seemed to show improved performance as a. we increased the number of wires and b. we increased the spacing between the wires.

+

In this follow-up episode, we shall try to rectify some of the shortcomings of the initial models. For the 3- and 5-wire antennas, we shall reform the models into all-wire versions for comparison with the idealized models. We shall also explore both the broadside and edge-wise patterns to see if we can find any differences of note. One of our goals is to improve upon the partial and sometimes faulty understanding offered by Part 1. Another goal is to stress the need for a full exploration of alternative ways of forming models and of the complete data set offered by modeling programs before declaring the work complete.

+

One major departure from the models in Part 1 rests upon some of the data that we acquired. Although terminated wide-band antennas offer a good match when we use them at frequencies below the knee frequency, rapidly increasing losses to the terminating resistor render such operations marginal to useless. Therefore, I increased the antenna length to 250', the length needed to ensure that the antenna was electrically at least 1/2 wavelength at the lowest test frequency: 2 MHz. A simple doublet of this length shows considerable inductive reactance at a center feedpoint. Hence, we can be assured that the new models operate completely above the knee frequency. I also increased the wire size to AWG #10 on the premise that this size is a relatively wise selection for a 250' span of wire.

+

2-Wire Terminated Wide-Band Antennas

+

The traditional 2-wire terminated wide-band antenna is a good starting point for our work. It does not require special treatment for the feedpoint, since we may place the modeling source at the center of the unterminated wire. Hence, we shall have only 2 major concerns, both of which apply to the models in Part 1. First, we shall look at the effects of taking patterns edgewise to the wire plane instead of taking them broadside to the 2 wires. See Fig. 1 for an outline sketch of the two orientations.

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Second, we shall review the effects of spacing the wires. We must increase the basic spacing in proportion to the scaling of the antenna that moved the knee from about 5.5 MHz down below 2 MHz. I shall employ a simple set of spacing values that will apply to all models in this part.

+ 
+    Spacing Standards for This Exercise Set
+Category       Spacing Between Parallel Wires (Feet)
+Narrow                     1
+Medium                     5
+Wide                      15
+
+

Most wide-band terminated antennas use a spacing between wires that is 1' or less. I chose 1' because it allows a reasonable narrow space for versions of the models scaled for higher frequencies and shorter lengths. At the other end of the line, 15' is a little under 5 meters, the scaled value that emerges from the wide versions of the antennas in Part 1. (Compare 250:15 and 27.2:1.5) Of course, I rounded the new numbers for bookkeeping simplicity.

+

For the new antennas, I also selected a single value for the terminating resistors in all versions: 900 Ohms. This value is especially useful, since one might create it from a parallel combination of 3 2700-Ohm non-inductive resistors. As noted in Part 1, there are other techniques for creating the terminating resistor.

+

Regardless of spacing, the 250' 2-wire antenna shows a very usable 900-Ohm SWR curves from 2 to 30 MHz. Fig. 2 overlays the curves for the 3 spacing values. The SWR spikes occur at intervals a little under 4 MHz, since the antenna passes integral full wavelengths (electrically) at those points. The narrow version shows a few peaks just above 2:1 in the upper part of the overall passband. However, both wider versions manage to remain below the standard limit. In fact, the widest version shows a declining curve with increasing frequency.

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Note that the SWR reference impedance is the same as the value of the terminating resistor. This fact will become more interesting as we later look at the 3-wire and 5-wire antennas using the same 900-Ohm terminating resistor. For the moment, we may classify the SWR behavior of the 2-wire antenna--in any width--as quite well behaved.

+

The remaining question is whether the patterns are as well behaved as the SWR curve. In Part 1, we could not fairly evaluate this facet of performance because we took the patterns broadside to the plane of the two wires. In practice, at least the narrow versions of the antenna twist and turn in the wind and weather and hence may wash out any difference that we might find between edgewise and broadside behavior. However, the wider versions of the antenna would likely have a fixed non-twisting installation set-up. Most likely, that set-up would place all of the wires parallel to the ground. Hence, it will be useful to look at the edgewise performance.

+

The following brief table samples both the edgewise and broadside free-space gain values of the narrow, medium, and wide versions of the 250' 2-wire terminated antenna.

+ 
+Free-Space Maximum Gain Values for 3 Versions of the 250' 2-Wire Wide-Band Antenna
+Frequency                 2            3            4            5           15
+Maximum Gain (dBi)   E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S
+Antenna
+Narrow (1')         -3.37  -3.45  -2.67  -2.74  -2.87  -2.88  -2.20  -2.32   1.61   1.47
+  F/B Ratio dB       0.16          0.13          0.01          0.23          0.29
+Medium (5')         -3.00  -3.30  -1.71  -1.94  -2.02  -2.08  -1.47  -1.96   2.12   1.98
+  F/B Ratio dB       0.61          0.49          0.16          1.08          0.48
+Wide (15')          -2.38  -3.03  -1.07  -1.47  -1.17  -1.53  -0.56  -1.97   3.28   2.20
+  F/B Ratio dB       1.45          1.01          1.07          3.65          4.50
+Reference Doublet           2.08          2.77          3.93          4.99          5.39
+Note:  E/W = Edgewise; B/S = Broadside; F/B = Front-to-Back
+
+

Despite its brevity and incompleteness, the chart generally confirms the trend noted in Part 1: as we increase the spacing between the conductors of a 2-wire terminated antenna, the gain generally rises. The rise does not occur for all frequencies at every widening, as shown by the move from 5' to 15' at 5 MHz, if we look at the broadside gain value. Nevertheless, the general gain trend is upward with wider element spacing.

+

At the same time, sampling the edgewise gain values introduces a new dimension to 2-wire performance: a gain differential between the heading of maximum gain and a heading 180 degrees opposite. The chart calls this difference a front-to-back ratio. For narrow spacing, the differential is minuscule and operationally insignificant. Even at medium spacing (5' for a 250' antenna or 2%), only one of the listed values is potentially problematical. However, when the spacing reaches 15' (6%), the differential grows to troublesome proportions. At 15 MHz, the maximum gain in the favored direction is 3.28 dBi, but in the opposite direction the gain drops to -1.22 dBi. For modest front-to-back values, the front-to-back ratio is roughly twice the differential between the edgewise and the broadside gain. However, as we increase frequency and encounter higher differentials, the front-to-back ratio climbs at a faster rate. This phenomenon suggests that the pattern may undergo some serious distortion relative to the nearly perfect bi-directional patterns we expect from the narrow version of the antenna.

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+

Fig. 3 provides a small demonstration by providing edgewise patterns for all three spacing values at 2, 5, and 15 MHz. In all cases, view the antenna as running up and down the page or graph. The right side of the pattern is the direction toward the feedpoint and away from the terminating resistor. The left side of the pattern is the direction toward the resistor and away from the source. The 2-MHz patterns show a classical figure-8 pattern with a growing lobe toward the feedpoint side as we increase spacing. In contrast, the 5-MHz patterns show their growth toward the terminating-resistor side of the antenna. In addition, note that the widest spacing yields a difference in pattern shape. What we would call the main lobe on the higher-gain side becomes weaker on the opposite side, and the side lobes grow in strength to equal it.

+

The 15-MHz plots show major distortions of the pattern established by the narrow version of the antenna. If you closely examine the medium-version pattern, you can see a very slight displacement of the lobes toward the higher-gain side of the antenna. When we reach the limits of our spacing exercise, the pattern is very seriously distorted relative to the narrow-spacing version. Moreover, we find extra lobes. Of course, the overall loop circumference at the widest spacing is about 5.5% longer than at the narrowest spacing. As well, the 15' end wires are 0.2 wavelength. At that spacing, the mutual coupling between wires does not form a single element, but acts somewhat like a distended loop antenna that is about 530' in total circumference--about 8 wavelengths overall.

+

The 2-wire terminated wide-band antenna is notorious for its low gain relative to a simple doublet. The table lists maximum gain values for the listed frequencies. The doublet's patterns as virtually identical in shape to those of the narrow version of the antenna, but the gain differentials for just the listed values range from about 4 dB to over 7 dB. Hence, the temptation to widen the spacing to obtain higher gain is strong. As shown in Fig. 2, the wider versions of the antenna sustain the SWR curves. However, before embarking upon the widening process, one must closely examine all patterns to determine if they will satisfy the needs of the application for the revised antenna. For general skip communications, the medium (5') version might fulfill the need, although the gain increment is marginal relative to the increased complexity of construction.

+

3-Wire Terminated Wide-Band Antennas

+

The 3-wire terminated wide-band antenna is especially interesting by virtue of its symmetry. Two outer wires, equally spaced from the center wire that contains the terminating resistor, are fed in parallel. The balanced layout results in a symmetrical edgewise pattern. From this perspective, the 3-wire array eliminates the front-to-back problem that appears in wider versions of the 2-wire antenna. However, effectively modeling the 3-wire version of the wide-band antenna presents challenges. Fig. 4 outlines 2 ways to proceed with the modeling.

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The modeling scheme on the left uses the NEC transmission-line (TL) facility to create near-zero-length lossless leads to a remote source wire. I used this method of modeling in Part 1 as an initial assessment of the potentials for the antenna. For this exercise, I replicated the system with the 250' long 3-wire antenna, creating 3 variations. The narrow version uses a spacing of 1' between wires for an overall antenna width of 2'. The medium version uses 5' spacing for a total width of 10'. The wide version uses 15' spacing and results in a 30' maximum antenna width. Nevertheless, the leads from the wires to the combined parallel source remain very short electrically. Fig. 5 overlays the SWR curves for the 3 versions of the 3-wire antenna.

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+

The idealized model provides very well-behaved SWR curves for all 3 versions of the antenna. Note that the reference impedance is 450 Ohms, half the value used for the 2-wire antenna and half the value of the 900-Ohm terminating resistor. We obtained similar SWR curves in Part 1 with the shorter 27.2-m (89') 3-wire antenna.

+

Although useful as a preliminary modeling venture, the idealized model does not represent structural reality for any of the 3 versions of the 3-wire antenna. For parallel feeding of the antenna, we must use wires that reach from the outer element center to a common feedpoint. Therefore, I remodeled the antenna according to the right-hand sketch. The limitation of this modeling method is the need for the center or source wire to equal in length a segment on the outer wire and for the segments on the connecting wires to be as equal in length as feasible to the other segment lengths. These requirements are not always well met, but the resulting models are adequate enough to detect general departures from the idealized model.

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Fig. 6 shows the overlaid 450-Ohm SWR curves for the revised model. The all-wire model suggests that the narrow version of the array is usable above 28 MHz before the SWR seriously exceeds 2:1. (We shall not consider impedance transformation losses and cable losses that might show a lower SWR at the operating position.) The medium version begins to show serious SWR excursions from about 22 MHz upward. The widest version starts to exceed the 2:1 SWR standard at about 15 MHz. These curves are based on a feedpoint 1' below the terminating resistor and may vary in detail with different positions. As well, the exact structure of the feed segment and the connecting wires may further alter the curves. Nevertheless, we can see that the idealized model gives us too optimistic a portrait of the SWR behavior of the 3-wire wide-band array.

+

The picture is not necessarily bleak, however. Many applications for a antenna of this sort do not require full spectrum coverage. As well, numerous receiving applications may use relaxed SWR standards, perhaps up to 3:1 relative to the reference impedance. So the 3-wire antenna remains a viable alternative to the 2-wire wide-band antenna, while offering freedom from the front-to-back differential that besets wider versions of the 2-wire array. The questions is whether the promise of higher gain will justify the more complex 3-wire array. As a sampling, I have set up a table similar to the one used for the 2-wire array.

+ 
+Free-Space Maximum Gain Values for 3 Versions of the 250' 3-Wire Wide-Band Antenna
+Frequency                 2            3            4            5           15            30
+Maximum Gain (dBi)   E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S
+Antenna
+Narrow (1')         -0.26  -0.26  -0.96  -0.96  -1.35  -1.34   0.00   0.01   2.85   2.92   6.46   6.53
+Medium (5')         -0.92  -0.91  -0.65  -0.65  -0.81  -0.76  -0.07   0.03   2.66   2.98   4.93   5.50
+Wide (15')          -0.80  -0.67  -0.24   0.02  -0.23   0.24  -0.68   0.15   1.49   4.14   2.69   6.76
+Reference Doublet           2.08          2.77          3.93          4.99          5.39          8.11
+Note:  E/W = Edgewise; B/S = Broadside
+
+

In virtually every sampled case, the 3-wire gain exceeds the 2-wire gain, and often by a significant margin. The rough average of the gain differential between the 3-wire narrow antenna and the doublet is about 3 dB, just over half the deficit shown by the 2-wire array. From a raw gain perspective, the 3-wire array is attractive for applications committed to a wide-band terminated antenna.

+

However, the 3-wire array is not immune to pattern distortion. One form is evident from the tabulated data. As we widen the spacing between wires and increase frequency, the broadside gain shows ever-larger values relative to the edgewise gain. The differential likely makes no great difference up through medium spacing. However, the wide-space version shows well over a 1-dB differential from the frequency mid-range upward. Note that the differential shows itself most vividly in the frequency region in which the wide-space version shows the largest SWR excursions. As well, the tabulated data does not show a clear gain advantage over medium and narrow spacing.

+

A second form of pattern distortion appears in the wide version of the array within the upper frequency edgewise patterns themselves. Fig. 7 shows the 15-MHz patterns for both the broadside and edgewise planes of the wide version of the antenna. For the edgewise pattern, visualize the antenna as extending vertically within the plot. For the broadside pattern, orient the antenna horizontally with respect to the graph. On the right side of the figure are the patterns for the narrow version of the antenna. These plots follow the form of a single-wire doublet, but at lesser strength. The broadside pattern for the wide version of the antenna almost replicates the pattern for the narrow 3-wire antenna. However, the edgewise pattern for the wide version is significantly different. As well, the tabulated data shows this pattern to be not only weaker than the broadside pattern, but also weaker than the edgewise pattern for the medium and narrow versions of the array.

+
+ +
+

To establish that the 15-MHz pattern is not an isolated instance of more severe pattern distortion, Fig. 8 shows the patterns for 30 MHz, using the same format. Once more, the patterns for the narrow antenna show little, if any, difference between broadside and edgewise views. However, the wide antenna shows changes to both patterns. The broadside patterns shows a widening and shrinking of the peak values of the minor lobes. The edgewise pattern shows the opposite development, although some careful observation is necessary to see it. In the narrow edgewise pattern, careful scrutiny will show some very tiny minor lobes between the larger minor lobes--almost invisible without either a table of radiation pattern values or a gross enlargement of the pattern. In the edgewise pattern for the wide antenna, those lobes have grown to equal size with the other minor lobes to form a large and complex set of lobes.

+
+ +
+

Unlike the 2-wire wide-band terminated antenna, which showed a significant improvement of gain as we widened the space between wires, the 3-wire array does not show the same gain development when we model it using an all-wire configuration. Rather, we find the relative gain values of the 3 widths simply to vary across the spectrum. In some cases, the narrow version yields the highest gain; in others, it does not. When we add to this gain variability the fact that only the narrow version promises a stable SWR curve across the entire operating spectrum, we begin to approach a conclusion. Add in the absence of significant pattern distortion and a relative simplicity of construction and the conclusion becomes more solid. In a 3-wire wide-band array, the narrow version has perhaps the most potential of the 3 widths for actual use.

+

The narrow 3-wire array holds the promise of higher gain by a significant margin over the 2-wire array, although the actual gain margin will change from one frequency to the next. However, even the 3-wire array falls significantly short of the gain offered by a single wire doublet that uses no termination. In amateur radio service, where the use of parallel transmission line and a wide-range antenna tuner in the shack may serve very well to handle frequency changes, the single-wire doublet is still the antenna of choice. For short-wave reception--especially in Europe, where overloading signals are common--the 2-wire terminated system may be the antenna of choice, since the overall signal reduction may prevent or at least ease receiver overload and resultant spurious products. Only where a system needs both to transmit as well as receive and to be able to change frequencies without any equipment retuning does the 3-wire system come into its own--so long as there is excess receiving gain to compensate for the loss of sensitivity and there is excess power available to make up for the losses within the terminating resistor.

+

5-Wire Terminated Wide-Band Antennas

+

The 5-wire terminated wide-band antenna showed great promise of better approaching the level of gain performance achieved by the simple single-wire doublet while providing a possibly usable SWR curve. Of course, like all of the antennas in our survey, the initial models checked only the broadside free-space patterns and used the idealized model for initial checks. The leftmost part of Fig. 9 shows the end view of that modeling scheme.

+
+ +
+

Converted to the scale used in this exercise, the antenna is now 250' long and has a total width of 4' for the narrow version, 20' for the medium type, and 60' for the widest version, using parallel wire spacing of 1', 5', and 15', respectively. In addition, we shall orient the antenna so that the edgewise view is parallel to the ground, although we shall take interest in the differential between the edgewise and broadside patterns in free space.

+

The antenna uses a 900-Ohm terminating resistor, the same value as used in all of the other wide-band antennas in this exercise. The required SWR reference impedance turns out to be 300 Ohms for all variations on the 5-wire antenna. We may note in passing that the decrease in the required SWR reference impedance undergoes a regular progression in its descent as we add wires to the array.

+
+ +
+

Fig. 10 reviews the 2-30-MHz SWR curves for the narrow, medium, and wide versions of the 5-wire array. Even under the idealized feed conditions with near-zero-length leads for the parallel-connected wires, the SWR curve is somewhat limited. The narrow antenna provides the best curve, although the SWR is somewhat high at the low end of the operating spectrum. As we increase spacing, the curve improves at the lowest frequencies, but the wide version appears to be usable only up to the middle of the spectrum (about 16 MHz).

+

We may proceed in two general ways to create all-wire models with more realistic feed systems. The center sketch in Fig. 9 shows a 2-lead version (A). Wires extend from the inner fed element to the central feedpoint 1' below the terminating resistor. The outer elements simply connect to the inner elements to complete the overall feed system. In effect, the outer elements acquire extra length compared to the inner wires, with another increment of length added at the far end of the wires. Fig. 11 shows the resulting SWR curves for the 3 antenna widths.

+
+ +
+

Note that the SWR curves begin to gyrate widely, and somewhat wildly for the widest version. In common, the curves show increasingly high peak SWR values as we raise the operating frequency. The narrow version of the array is the only one usable for most of the operating spectrum, but only if we relax the 2:1 SWR limit standard.

+

As an alternative, I modeled the arrays with separate leads from each fed wire to the common feedpoint. The right-most sketch in Fig. 9 shows the general outline of the 4-lead model (B). The question was whether this feed system would alter the SWR curves relative to the 2-lead model. Fig. 12 shows the results of the trials.

+
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+

Clearly, we do not gain anything by using the alternative feed method. Although the details differ in terms of the exact frequencies and values for SWR peaks, only the narrow version of the 5-wire antenna shows potential for extended frequency use. The medium-width version of the antenna is again usable up to about the middle of the spectrum, and the wide version shows a rapid decay of good SWR performance above about 7 MHz. Varying the reference impedance does not alter the performance significantly. The key problem in all versions of the 5-wire array is the presence of very significant reactance levels at most frequencies.

+

Despite the initial optimism offered by the idealized model in terms of developing a 5-wire wide-band antenna, remodeling the array more realistically with wire leads to the center feedpoint presents serious obstacles to further development. Only the narrow version of the antenna has a bandwidth potential resembling the curves that we obtained for the 2-wire and 3-wire antennas--and then only if we relax the SWR standard. However, one feature that gave the basic idea of a 5-wire array its allure was the potential for significantly higher gain than either of the smaller antennas. Despite the SWR problems, we should explore this facet of the antenna. The following table of sample values parallels the one for the 3-wire antenna to provide for direct comparisons. As we did when checking maximum gain for the 3-wire antenna, we shall provide gain values for both the edgewise and broadside planes relative to the antenna. In addition, we shall examine values for both the 2-lead and the 4-lead versions of the array.

+ 
+Free-Space Maximum Gain Values for 3 Versions of the 250' 5-Wire Wide-Band Antenna
+Frequency                 2            3            4            5           15            30
+Maximum Gain (dBi)   E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S    E/W    B/S
+2-Lead Antenna
+Narrow (1')          1.59   1.59   0.28   0.28  -0.16  -0.14   1.72   1.74   3.74   3.83   7.14   7.29
+Medium (5')          0.93   0.97   0.73   0.82   0.73   0.90   1.56   1.85   3.33   4.19   5.46   6.56
+Wide (15')           0.84   1.19   0.92   1.71   1.07   2.60  -0.42   2.50   0.79   6.92   4.93  -0.22
+4-Lead Antenna
+Narrow (1')          1.44   1.44   0.36   0.37   0.03   0.04   1.74   1.76   3.81   3.91   7.02   7.16
+Medium (5')          0.81   0.85   0.53   0.62   0.56   0.73   1.46   1.75   2.54   3.36   4.17   0.78
+Wide (15')           0.76   1.11   0.71   1.50   0.94   2.47  -0.42   2.55   1.54   8.82   5.11  -0.71
+Reference Doublet           2.08          2.77          3.93          4.99          5.39          8.11
+Note:  E/W = Edgewise; B/S = Broadside
+
+

As expected, the wider the array and the higher the operating frequency, the greater differential that we find between edgewise and broadside maximum free-space gain values. In general, there is no significant difference between the gain behavior of the 2-lead and 4-lead versions of the 5-wire antenna. Both narrow versions show a good coincidence between the edgewise and broadside gain values. However, as we widen the antenna, the upper spectrum values actually show a decline relative to the narrow version of the antenna. As well, the differentials grow to considerable proportions, with one value set showing a 7-dB differential. Initially, then, the first order conclusion might be that only the narrow version of the array holds potential for wide frequency use. Interestingly, this conclusion from free-space gain data coincides with the conclusion suggested by the SWR data.

+

The sampled gain values reveal another interesting pattern to antenna performance. Let's overlay a few patterns for the single-wire reference doublet and the 5-wire narrow antenna, using the 2-lead version. However, let's examine both the free-space values and the values 75' above average ground (conductivity 0.005 S/M, permittivity 13). Additionally, we shall restrict the frequency range to extend from 2 to 6 MHz. This last measure operates on the premise that not all applications of wide-band antennas require coverage of the entire HF spectrum. Instead, some operational needs require no-tune operation of some part of the spectrum. Fig. 13 provides the SWR curves for the 5-wire array using the 300-Ohm standard and for the single-wire doublet using a 75-Ohm standard.

+
+ +
+

The antenna height (75') is only a small fraction of a wavelength at the lower end of the spectrum. Hence, we find deterioration of the SWR curve for both antennas relative to the free-space model. The doublet curves clearly show that the antenna is longer than 1/2 wavelength at the lowest operating frequency. As well, the doublet curves show the need for extesive impedance matching efforts as we change frequency. Although the 5-wire SWR curves are not perfect, they present far less of a matching challenge to 300 Ohms (and from that value down to a coaxial cable value via a wide-band impedance transformer).

+

Now let's compare the maximum gain values, letting ground-reflection phenomena settle any remnant differential between edgewise and broadside gain values that we encountered in free space. The following table tracks doublet and 5-wire narrow values every half-MHz for our reduced operating spectrum.

+ 
+Maximum Gain values for a Single-Wire Doublet and a 5-Wire 2-Lead Narrow Array 75' above Average Ground
+Single Wire Doublet
+Frequency            2      2.5    3      3.5    4      4.5    5      5.5    6
+Maximum Gain (dBi)   6.84   7.07   7.09   7.30   7.87   8.73   9.42   8.09   7.64
+Elevation Angle      90     90     71     55     48     41     36     33     28
+5-Wire 2-Lead Wide-Band Antenna
+Frequency            2      2.5    3      3.5    4      4.5    5      5.5    6
+Maximum Gain (dBi)   6.22   5.77   4.53   3.95   4.19   5.20   6.51   6.11   7.53
+Elevation Angle      90     90     72     56     47     41     36     33     29
+
+

The table shows that at the low and high ends of the restricted operating range, the gain values for the 5-wire array virtually match those of the single-wire doublet. At the center of the range, from 3.5 to 4.5 MHz, we find the greatest difference in values, with a 3.5-dB deficit. Fig. 14 provides a few sample patterns for both antennas, overlaid to show the degree of coincidence or difference.

+
+ +
+

Once the antenna passes the 1.25 wavelength mark in electrical length, it of course results in a pattern where the main lobes are no longer broadside to the wire, as shown by the 6-MHz pattern. However, we may also view a more fundamental correlation by jointly examining Fig. 13 and Fig. 14 (or the table). The doublet 75-Ohm SWR values--and hence, the general level of the feedpoint impedance--are lowest at or near those frequencies for which the 5-wire array shows a gain level that most closely matches the doublet's gain. When the parallel combination of fed wires in the wide-band antenna would present a very low impedance, the terminating resistor absorbs (and dissipates) the least energy, resulting in the highest gain. When the resistor value is low relative to the feedpoint impedance without it, the resistor handles a proportionately higher percentage of the power, leaving less for radiation. This theory of operation applies to all multi-wire wide-band antennas using a terminating resistor. The 5-wire version of the antenna simply makes the process more graphically apparent.

+

With a restricted operating range, the antenna models make apparent the danger of simply taking an average value of gain deficit of a wide-band antenna relative to a doublet. The more pressing question facing a design engineer is whether the worst-case deficit falls above or below the level of acceptability relative to the intended application.

+

Since we have explored the difference between the SWR curves for the 5-wire, 2-lead antenna over a limited range, we might also explore whether the differences apply to other parts of the overall operating spectrum. Fig. 15 shows the comparative plots for the narrow 2-wire wide-band antenna. The antenna is 75' above average ground for all comparisons. As the plots show, the SWR curves diverge until about 9 MHz. At that frequency, the antenna is about 0.7 wavelength above ground. Below that frequency, we find small differences in the curves that likely would not create any operational problems.

+
+ +
+

In Fig. 16, the graph compares SWR curves for free-space and over-ground versions of the narrow 3-wire wide-band antenna. The curves overlay each other very well down to just below 10 MHz. Again, the 0.7 wavelength (or perhaps the 0.75 wavelength) height marks the beginning of SWR curve divergence. Note that in this case, the modeled over-ground value for the all-wire antenna just exceeds 2:1 at 2 MHz. The actual test measurement for the antenna under these conditions would depend upon impedance transformation and line losses, as well as construction variables relative to the model.

+
+ +
+

Fig. 17 expands the narrow 5-wire, 2-lead SWR curves shown in Fig. 13 to encompass the entire potential operating spectrum. Once more, the free-space and over-ground curves track each other very well from about 9.5- to 10-MHz and upward. Below the transition frequency area, the curves diverge, with the over-ground curve showing a higher SWR value at the lowest frequency in the spectrum covered. Lengthening the antenna might well move the SWR from 2 to 6 MHz below 2:1, but at the same time, it would reduce the frequency span over which we can obtain bi-directional patterns. The relative importance of each factor is an application-specific determination.

+
+ +
+

Construction Variables

+

The sensitivity of the multi-wire terminated antenna arrays to changes in width relative to various performance characteristics suggests that these notes inevitably fall far short of covering all possible design variations. However, length and width are not the only variables available for alteration. One significant variable may escape attention. The all-wire models place the common feedpoint 1' below the terminating resistor and its element wire. We may vary that placement and see what might happen. To test the matter, I created a very narrow version of the 3-wire (all-wire) antenna using a spacing of 0.5' between wires. Then I set the feedpoint 1, 2, and 3 feet below the antenna, using a free-space model. The key question in this exercise focused on the effects of the 3 placements on the SWR curve. Fig. 18 shows the results.

+
+ +
+

The very narrow version of the 3-wire array shows the most acceptable SWR curve with the common feedpoint 3' below the terminating resistor wire, the limit of this particular exercise. The 450-Ohm SWR does not exceed 2:1 until the operating frequency reaches 29 MHz, and then not by much. To see whether the phenomenon is unique to the very narrow spacing or more general, I repeated the test using the standard narrow 3-wire spacing (1'). The results appear in Fig. 19.

+
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The results for the standard narrow spaced 3-wire array are less dramatic. The closest feedpoint spacing shows the widest excursions of SWR--both high and low--for most of the operating range. The widest feedpoint spacing appears to improve SWR performance in the upper range, but not to the degree possible with very narrow spacing.

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Wide-band terminating-resistor arrays are subject to many construction variables, and these simple exercises provide only a sample. However, they do show that we cannot assume that any particular variable is either significant or insignificant until we examine it in detail.

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Conclusion

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At the end of Part 1, based on a limited exploration of terminated antenna properties, I reached a set of conclusions. We may now assess how well each holds up and what qualifiers we may have to place on some of them.

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1. All terminated wide-band "folded dipoles" have knee frequencies, below which the gain drops very rapidly. The recommended operating range for any of the antennas is from an electrical length of about 1/2 wavelength upward in frequency.

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The first conclusion remains correct, although we by-passed testing it in this exercise by using an antenna that was longer than the critical minimum length at the lowest test frequency.

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2. As we add more fed wires to a terminated antenna, we increase its average gain over the operating spectrum. The gain increase never quite reaches the level of a single-wire doublet.

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We must heavily qualify this statement. Although the average gain of the 3-wire array exceeds the average gain of the 2-wire version, and the 5-wire average gain is higher still, average gain may not be the key factor in making design decisions. The gain will be highest wherever the equivalent doublet length shows the lowest impedance. However, we must keep a sharp eye out for the lowest gain levels within a proposed operating span to determine if the gain at critical frequencies is high enough for the proposed communications application. We may examine that gain as an intrinsic value or as a deficit relative to the single-wire doublet, depending on the frame of reference.

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3. As we add more wires to a terminated wide-band antenna, the center or reference SWR impedance decreases both intrinsically and with respect to the value of the terminating resistor.

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Our extended exercises actually provided a bit more precision to this statement by standardizing the terminating resistor at 900 Ohms and watching the required SWR reference impedance. The criteria for setting the SWR reference impedance are not precise, since the setting requires a judgment call as to what counts as the smoothest obtainable SWR curve over a given operating region. Nevertheless, the 2-wire array showed its best curves when the SWR reference impedance matched the value of the terminating resistor. The 3-wire array gave the best results when the SWR reference impedance was 1/2 the value of the terminating resistor. With the 5-wire arrays, the best reference impedance was 1/3 the value of the terminating resistor.

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4. 2- and 3-wire terminated wide-band arrays show stable SWR curves through their operating ranges. However, adding further wires tends to produces curves with greater SWR excursions relative to the reference impedance.

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Once we modified the 3-wire and 5-wire antennas to provide all-wire model construction, the stability of even the 3-wire curves began to slip badly as we widened the array. The SWR performance for the 3-wire array showed wide SWR swings in the wide version. The 5-wire all-wire model strongly suggested that it was useful only over restricted frequency ranges, and then only in the narrow version.

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5. Terminated wide-band antennas show increased gain by widening the distance between wires. Spacing adjustments may require revision of the optimal terminating resistor value and the reference SWR impedance.

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The final conclusion in the series requires the greatest modification. The initial models registered gain as a function of free-space patterns broadside to the plane of the wires. Hence, they could not show the growing differential of edgewise and broadside gain as we increased the spacing between wires. Our exploration of the 5-wire models in this extended exercise shows that the net gain of a wide model may not always exceed that of a narrow model. Moreover, the existence of any differential at all makes a strong recommendation for modeling a proposed design over ground at the anticipated height of actual use. At the low end of the operating range, we may fairly gauge the effects of the mounting height and soil type on the SWR performance. As we move up the spectrum, the gain differentials increase, and modeling over ground allows us to arrive at a single gain value, whether we handle it independently or in comparison to the single-wire doublet that the wide-band antenna ostensibly replaces.

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To the list of conclusion derived from Part 1 and modified here, we may add a new one.

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6. Due to the many construction variations possible with a multi-wire wide-band terminated antenna, range testing at the anticipated use height and over the anticipated ground quality is an essential ingredient in the development of a successful antenna.

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Updated 06-01-2007. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for May, 2007. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index
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Topics: Dipole, HF Multi Band


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Notes of Mr. Windom's "Ethereal Adornments"

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Notes of Mr. Windom's "Ethereal Adornments"

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This page exists to include the PDF in the topic index

+ hr
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Topics: HF Multi Band, Off Center Fed Dipole


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A Note on Substituting Wire Elements in Lower HF Arrays

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L. B. Cebik, W4RNL

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Wire beams are commonplace in the lower HF region. They have some uses at HF as well, for example, in LPDAs. In both cases, we sometimes fall into the belief that the wire array has all of the gain and performance of a comparatively similar array made from fat tubular elements.

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Of course, that belief is simply false. A reduction in the diameter of elements of the proportions of a move from a fat tube to a skinny wire reduces not only the operating bandwidth (sometimes), but as well reduces the inter-element coupling that is critical to deriving full performance from a beam. For example, standard LPDA calculations make use of the element length-to-diameter ratio in determining element lengths, but little has been noted about the lowering of gain in moving from fat to skinny elements. Even a beam like the LPDA, that is utterly dependent upon phasing connections, remains equally dependent upon inter-element (mutual) coupling, and that coupling decreases with decreases in element diameter for a given Tau and Sigma.

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In many cases, tubular elements cannot be used due to their length and/or weight. Hence, the builder is forced to use wire. However, he need not be confined necessarily to reduced performance. I have shown in a couple of places a method for using wire elements that retain the performance of fatter tubular elements.

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The technique is quite straight forward, as indicated by Fig. 1. For each element of a design originally created for single fat elements, create a double wire of the same length. Then, most likely through modeling (although field testing will also work), adjust the wire spacing so that the element is self-resonant on the same frequency as the original tubing element. The required spacing will vary with the wire size used. If a modeling approach is used to estimate the spacing, there are a few constraints that we shall look at further on.

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It turns out that this arrangement works well for smaller diameter tubing equivalencies--say, up to 1 inch or 25 mm. For larger tubing, we encounter some limitations. The average tubing size--even in elements that start out at the element center as quite sizable--ends up quite modest even in lower HF beams. You can check out the equivalent uniform diameter for almost any tapered-diameter element on NEC-2 programs having Leeson corrections by looking at the substitute elements used in the actual NEC calculations. Access to these substitute elements is available in EZNEC, NEC-Win Plus, and similar programs.

+

However, we sometimes scale up array sizes from proven upper HF designs. Proper scaling requires that we increase all dimensions, including the element diameter, if we are to have what amounts to a true scaling. And only by a true scaling can we assure that the array will perform at the lower frequency to the level it promises at the higher frequency.

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I had occasion to go through this exercise with a 3-element 20-meter beam adapted from a K6STI design. The exercise was initially theoretical, so I was not the least troubled by the resultant 4" diameter elements that emerged in the 80-meter model. Fig. 2 shows the basic outline of the Yagi, which will become the center of attention in what follows. Here is a table of dimensions.

+ 
3-Element Yagi:  3.6 MHz:  4" diameter elements
+Element        Element Length (ft)      Spacing from Reflector (ft)
+Reflector      136.08                   ----
+Driver         129.94                   41.167
+Director       122.26                   88.767
+

Wondering what the antenna might do if made from wire, I recreated it from 0.1" diameter wire. This diameter is between #12 and #10 AWG. The conversion required some proportional lengthening of elements to achieve a coincidence of maximum front-to-back ratio and driver resonance. The element spacing was retained, and only the element lengths were changed. The resulting wire beam had these modeling specifications.

+ 
3-Element Yagi:  3.6 MHz:  0.1" diameter elements
+Element        Element Length (ft)      Spacing from Reflector (ft)
+Reflector      138.40                   ----
+Driver         132.40                   41.167
+Director       124.60                   88.767
+

Both antennas were modeled as copper elements in free space for comparisons. For the design frequency of 3.6 MHz, the results were interesting, to say the least.

+ 
NEC-4 Modeled Performance:  3-Element Yagis:  3.6 MHz
+Model          Gain      F-B Ratio      Feedpoint Z    Efficiency
+               dBi       dB             R +/- jX Ohms    %
+4"             8.14      27.3           25.5 - j 0.9   99.81
+0.1"           7.06      19.9           43.3 - j 2.9   95.87
+

Using wire reduced gain by over 1 dB and the front-to-back ratio by about 7 dB. The feedpoint impedance increases nearly 70%, much more than the increased wire losses would indicate. The 4% differential in efficiency is not large enough to account for the source impedance increase. (NEC recognizes only wire material losses and spot load and other network losses in calculating efficiency. The latter will not be relevant to this exercise. Efficiency figures can be useful reference points, so long as we do not try to use them to account for every gain or loss in performance when comparing designs.)

+

If we use a current source of 1.0 at a phase angle of 0.0 degrees, we can gain further insight into the comparative performance of these arrays. We simply need to look at the element center current magnitudes and phase angles for the reflector and director elements for both beams.

+ 
NEC-4 Modeled Element Currents:  3-Element Yagis:  3.6 MHz
+Model          Reflector I                   Director I
+               Magnitude      Phase          Magnitude      Phase
+4"             0.405          143.5          0.601          -134.0
+0.1"           0.414          126.1          0.456          -119.2
+

Since the elements are both parasitic, the differential in current magnitudes and phase angles is reflective of the difference in mutual coupling between the elements and the driver. If the current values for the 4" model are to be considered as more ideal, then the values that appear on the elements of the 0.1" model are considerably off target.

+

In fact, the wire version of the array might require considerable redesign to peak its performance, including adjustments to element spacing and length. This fact is revealed in frequency sweeps of both antennas from 3.55 through 3.65 MHz.

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Fig. 3 shows the modeled free-space gain curves for both antennas. The 4" model shows the gain curve across the modeled passband that we have come to expect from high performance 3 element Yagis: a modest but continuous increase of gain with frequency. In contrast, the wire model shows the lowest gain at the design frequency. This dip is indicative antenna operation at a different portion of the potential gain curve--somewhat lower in frequency than the corresponding curve positions for each of the 4" model gain numbers.

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However, as shown in Fig. 4, the front-to-back peak has been sustained at or just below the design frequency. In this aspect of design, the 4" model curve encompasses the wire model curve.

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The wire model actually has a wider operating VSWR bandwidth than the 4" model, as shown in Fig. 5. The wider VSWR bandwidth results in part from the higher resonant source resistance, so that equal amounts of reactance have a lesser effect on the SWR in terms of increasing its value. In fact, the wire model reactance from one passband limit to the other is only about 37% greater than that for the 4" model (40.3 vs. 29.5 Ohms), while the source resistance has climbed by 70 percent (43.3 vs. 25.5 Ohms). Hence, relative to the individual resonant source resistances, the wire beam will permit operation over more of 80 meters.

+

Despite the wider operating bandwidth, my aim was to see if I might obtain 4" performance from a wire version of the antenna. So I applied the two-wire technique described at the beginning of the exercise, only to be disappointed by the results. 2-wire elements, each the same length as those of the 4" model, but spaced to resonate at the same self-resonant frequencies, only brought me half way to the gain goal.

+

The 2-wire element substitutes required a spacing of 13" between 0.1" wires. Here we must note that my models will not use full precision in the interests of keeping numbers as rounded and simple as possible. So 13" spacing became convenient and close to the mark. However, the rounding of the spacing value was not sufficient to account for the gain value of 7.77 dBi, nearly 0.4 dB short of the mark.

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The answer lies in the insufficient coupling provided by the 2-wire model elements. So I added a third wire exactly between the 2, as shown in Fig. 6. The half-elements shown are matched by equivalent mirror images to the unseen right of the figure. The third wire does not substantially change the resonant frequency of the resulting element, so I left the outer spacing of 13" and hence ended up with a spacing of 6.5" between wires.

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Before we look at the results of the wire-beam models in detail, we can pause a moment to examine the element models, partially shown in Fig. 7. The rules for NEC note that closely spaced wires should have all segment junctions parallel to each other. As well, angular junctions should have segment lengths of approximately equal lengths. Finally, the source segment should be protected from multiple wire junctions, which results in a 3-segment center section for each element. (Although the parasitical elements might have been made continuous, I preserved the center sections in each that resulted from initial resonating tests.) Finally, results will be most accurate for multi-wire elements where the wires are closely spaced and parallel if the source wire is centered so that it meets equal wire lengths in both components of the element. The wires are joined at the outer ends.

+

Since the segments length of the wire from the center or source wire to the outer wires is 6.5" long, I made this value the segment length for the entire array. The center wire is 19.5" long in 3 segments. The elements beyond the limits of the figure have over 100 segments per wire on each side of center. Hence, the 2-wire model has over 1400 segment, while the 3-wire model tops 2100 segments. Although for some, this would be overkill, it meets all NEC guidelines. Only a little patience is needed while NEC grinds out the results during frequency sweeps.

+

Part of my interest in the wire models was to determine if each of these models had a single-wire model of roughly corresponding performance. That model would consist of a single fat wire per element, with the diameter chosen to approximate the performance of the corresponding wire model. Of course, the element lengths had to be adjusted relative to those for the 4" model in order to place peak performance at the design frequency.

+

1. The 2-Wire Model and a 1" Single Wire Model: A 1" diameter element model yielded a set of performance curves roughly similar to those of the 2-wire model. We know the physical dimensions of the 2-wire model from the discussion above. The following table presents the physical aspects of the 1" model.

+ 
3-Element Yagi:  3.6 MHz:  1" diameter elements
+Element        Element Length (ft)      Spacing from Reflector (ft)
+Reflector      137.50                   ----
+Driver         131.50                   41.167
+Director       123.76                   88.767
+

The design-frequency (3.6 MHz) performance for the two models is in this table.

+ 
NEC-4 Modeled Performance:  3-Element Yagis:  3.6 MHz
+Model          Gain      F-B Ratio      Feedpoint Z    Efficiency
+               dBi       dB             R +/- jX Ohms    %
+1"             7.77      25.7           32.7 - j 0.3   99.42
+2x0.1"         7.77      23.7           30.4 + j 2.6   96.73
+

The comparable performance at the design frequency is readily apparent. Note, however, that the efficiency of the single wire 1" model is significantly higher than that of the 2-wire model, owing to the higher material losses and smaller surface area available from the pair of thinner wires. Indeed, the surface area ratio is about 5:1 in favor of the 1" model. Nevertheless, the increased mutual coupling made possible by the 2 spaced wires is sufficient to overcome the increased material losses and nets the same gain at the design frequency as the more efficient fat-wire model.

+

The comparison can be extended to the current magnitude and phase found on the parasitic elements with a source current of 1.0 at 0.0 degrees.

+ 
NEC-4 Modeled Element Currents:  3-Element Yagis:  3.6 MHz
+Model          Reflector I                   Director I
+               Magnitude      Phase          Magnitude      Phase
+1"             0.407          134.9          0.556          -127.8
+2x0.1"         0.391          136.7          0.583          -132.1
+

Note that the parasitic element current values of these two models are closer to each other than either is to the standard 4" model. The models might have more closely corresponded had the elements in the 2-wire model been spaced more precisely than the 13" used in the model. In fact, the 2-Ohm reactance value indicates not only a slight driver over-length for the spacing, but as well a similar situation for the other elements as well. Hence, the best SWR value and front-to-back peak occurs below the design frequency. In addition, for an equal-gain situation, the required mutual coupling among elements to overcome the higher material losses in the 2-wire model would also dictate slightly different parasitic element current values relative to the single wire model.

+
+ +
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The similarities and differences between the two models become more apparent when we perform frequency sweeps. In this case, due to the remnant inductive reactance of the 2-wire element replacements, I have dropped the lower limit of the sweep to 3.525 MHz. In the case of the gain sweep, shown in Fig. 8, the differences show up in different rates of increase in gain across the passband--not widely different, but different nevertheless.

+
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Fig. 9 shows the front-to-back ratio sweep for the two models. The 1" model reaches peak front-to-back ratio just below the design frequency, while the 2-wire model shows its peak about 25 kHz below the design frequency. The curve confirms the note above that some fine tuning of the 2-wire spacing (a slight narrowing) is necessary to create a true overlap of curves. However, the ultimate front-to-back peaks of both antenna are quite close, pushing above 27 dB. Moreover, extending the sweep scale shows that the curves are quite congruent, since the lower end differential is about the same as the upper end differential.

+
+ +
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The SWR curve in Fig. 10, tells a similar tale. The passband end differentials are reasonably close so that the offset between the curves does not lead to any misleading conclusions about the 2:1 operating bandwidths of the 2 models. They are essentially the same.

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The end result--despite the small offsets in the curves and number--is the conclusion that for practical purposes, the 2 0.1" diameter wire elements with 13" spacing in the Yagi model provide the same performance potential as a single 1" tubular element set in the same model. The higher mutual coupling of the wire model offsets the higher material losses, resulting in a beam with the same performance over the range of vital performance parameters as that of a single fat element model.

+

1. The 3-Wire Model and a 2.85" Single Wire Model: I would like to be able to say that the 3-wire model overcame all remaining differentials with the 4" model of the 3-element Yagi. However, some differential remained, although it might be considered minor. A 2.85" diameter element model yielded a set of performance curves roughly similar to those of the 3-wire model. Once, more, we know the physical dimensions of the 3-wire model from the discussion above. The following table presents the physical aspects of the 2.85" model.

+ 
3-Element Yagi:  3.6 MHz:  2.85" diameter elements
+Element        Element Length (ft)      Spacing from Reflector (ft)
+Reflector      136.48                   ----
+Driver         130.30                   41.167
+Director       122.66                   88.767
+

The design-frequency (3.6 MHz) performance for the two models is in this table.

+ 
NEC-4 Modeled Performance:  3-Element Yagis:  3.6 MHz
+Model          Gain      F-B Ratio      Feedpoint Z    Efficiency
+               dBi       dB             R +/- jX Ohms    %
+2.85"          8.04      27.6           27.4 - j 1.7   99.75
+3x0.1"         8.04      21.7           26.0 + j 6.1   97.32
+

The comparable performance at the design frequency is readily apparent. Note, however, that the efficiency of the single wire 2.85" model is still significantly higher than that of the 3-wire model, owing to the higher material losses and smaller surface area available from the trio of thinner wires. Indeed, the surface area ratio is about 9.5:1 in favor of the 2.85" model. Nevertheless, just as with the 2-wire model, the increased mutual coupling made possible by the 3 spaced wires is sufficient to overcome the increased material losses and net the same gain at the design frequency as the more efficient fat-wire model.

+

The comparison can be extended to the current magnitude and phase found on the parasitic elements with a source current of 1.0 at 0.0 degrees.

+ 
NEC-4 Modeled Element Currents:  3-Element Yagis:  3.6 MHz
+Model          Reflector I                   Director I
+               Magnitude      Phase          Magnitude      Phase
+2.85"          0.410          141.1          0.588          -132.0
+3x0.1"         0.387          141.3          0.623          -137.2
+

Once more, there are differences between the two models with respect to current magnitudes and phases on the parasitic element centers--but not great ones. The remnant 6-Ohm reactance on the 3-wore driver element is a result of having performed no adjustments in the spacing to compensate for the addition of the center wire. In fact, the reactance value on the driver also indicates not only a slight driver over-length for the spacing, but as well a similar situation for the other elements as well. Hence, the best SWR value and front-to-back peak occurs below the design frequency. As with the 2- wire model, for an equal-gain situation, the required mutual coupling among elements to overcome the higher material losses in the 3-wire model would also dictate slightly different parasitic element current values relative to the single wire model.

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However, when we make allowances for the offset in self-resonant frequencies of the individual elements, the curves for the single 2.85" element model and for the 3-wire model remain remarkable congruent. Fig. 11 shows the gain curves, which show even smaller differences than those we saw in Fig. 9 across the same passband for the frequency sweep.

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Likewise, the two front-to-back ratio curves in Fig. 12, display excellent congruence with a displacement that is almost exactly 25 kHz. Compare not only the offsets at the front-to-back peaks, but as well the lower frequency 19+ dB point and the higher frequency 17+ dB points.

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Fig. 13 portrays a similar offset with respect to the SWR curve for both models. The shapes of the curves are virtually identical, despite the 25 kHz offset between them. In effect, bringing the entire set of curves for the two models into alignment would likely be a matter simply of adjusting the spacing of the wires in the 3-wire elements.

+

Alternatively, one might also slightly shorten the elements of the 3-wire model slightly. In actual construction practice, this procedure would become the most practical, since it is likely that the wire elements, including spacers, would be fixed in construction phases that precede raising the antenna to operating height.

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The 3-wire model ends up slightly short of the goal of achieving the full gain of the initial 4" diameter element model. However, the deficit is only about 0.1 dB. Front-to-back performance can be as good as the initial model, and the feedpoint impedance will be comparable.

+

In effect, the exercise has established that it is possible to create thin wire models with multiple wires per element that simulate effectively the performance of fat tubular elements in beams and arrays--at least for this 3-element Yagi model. The requisite spacing and possibly the number of wires required will vary with the wire size chosen and the diameter of the element being simulated.

+

It is not sufficient simply to create elements from multiple wires. The spacing of the wires is of great significant in increasing the mutual coupling between wires that yields the desired level of performance, understanding that some excess coupling may be needed to overcome higher material losses in the wire substitutes. If nothing else, this exercise has suggested some interesting relationships between the roles of material losses and mutual element coupling in beam performance.

+

Besides the flat plane, other wire configurations are possible, including triangles, squares, and the traditional cage hexagon of wires. However, the extra weight of 6 wires, relative to the 3-wire plane used in the models presented here, may not be needed to effectively simulate fat wires. In the final analysis, two pieces of design work are needed. One is, for any proposed array, a set of models to establish the relative structures of equivalent multi-wire substitutes for a given fat single element. The other, of course, is a mechanical analysis to determine the best compromise among the physical properties of the resultant element. The properties might include ease of construction, durability in the proposed environment, and ease of raising the structure to its operating height.

+

Of course, the home antenna builder might well decide that using single wire elements is the simplest construction method and that the performance deficits relative to the ideal still fall within an acceptable level. While it is one thing to tangle at a computer with complex models of substitute multi-wire element substitutes, it is quite another to have to wrestle with the real thing, namely, the tangle-prone wire elements that require raising into operating position.

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Updated 03-10-2000. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: HF Lower, Yagi


+ + diff --git a/content/wire/wiresize.html b/content/wire/wiresize.html new file mode 100644 index 0000000..f8739cc --- /dev/null +++ b/content/wire/wiresize.html @@ -0,0 +1,76 @@ + + + + + + Wire Size and Material + + + +
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A Note on Wire Size and Material

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+

L. B. Cebik, W4RNL

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+
+ Recent discussions about the use of various materials in antennas posed some interesting questions about the advisability of using such materials as stainless steel and phosphor bronze in different types of antennas. +

Initial models that I used to explore the question all used wire diameters that were relatively large for the wavelength involved. For example, I used 0.1" (3 mm) elements for a VHF (225 MHz) antenna. For a 3-element beam showed only about 0.17 dB less gain for a stainless steel model relative to an aluminum model.

+ 
Material                      Gain dBi  F-B dB    Source Z
+                                                  R ± jX Ohms
+6061-T6 Aluminum              8.25      24.80     24.4 - j 0.8
+Stainless Steel Type 302      8.08      23.65     25.0 + j 0.1
+

If we use only such large wire diameters relative to wavelength, the large surface area can mislead us into thinking that perhaps phosphor bronze and stainless steel are satisfactory for all antenna applications.

+

Of course, the question here is the electrical properties of the material, not the physical and chemical properties. Weight, corrosion, and other such factors must be considered in addition to these notes on the electrical properties of certain kinds of wire in antenna applications.

+

Proper tests of antenna wire types should press them toward levels of thinness relative to a wavelength that begin to show their limitations. Hence, the low HF wire dipole become a better test vehicle. It can show to some degree at what point one is better off leaving some materials alone, even if they offer some good physical and chemical properties. Materials that offer good performance when fat often reach their limits of application when thinned down.

+

All runs were made with NEC-Win Pro a version of NEC-2. Exact numbers may vary in the last decimal place with other programs--or if you simply choose a different level of segmentation. 21 segments per dipole was the segmentation density used for these simple tests.

+

Test 1: #14 wire dipole for 7.0 MHz

In this test, I took a resonant dipole model using lossless wire and then changed materials (from the usual list of materials) to see what the effect might be. Here is data on free space gain, source impedance, and efficiency for a number of materials. 6063-T843 and 6061-T6 are common aluminum allows used mostly in tubing that we find in HF and VHF beam antennas. The "Ey" notation is common computereze for "x 10 to the y power." Note where the list changes from E7 to E6. + 
Conductivity   Material            Gain      Source Z       Efficiency
+  S/m                              dBi       R ± jX Ohms        %
+Perfect        (lossless)          2.13      72.2 + j 0.1   100.00
+6.2893E7       Silver              2.04      73.7 + j 1.4    98.09
+5.8001E7       Copper              2.04      73.7 + j 1.5    98.01
+3.7665E7       Pure Al.            2.02      74.1 + j 1.8    97.54
+3.0769E7       6063-T832           2.01      74.3 + j 1.9    97.28
+2.4938E7       6061-T6             2.00      74.6 + j 2.2    96.98
+1.5625E7       Brass               1.96      75.2 + j 2.7    96.19
+9.0909E6       Phosphor Bronze     1.91      76.2 + j 3.6    95.02
+1.3889E6       Stnlss Stl 302      1.55      83.0 + j 8.8    87.53
+
+

Note that even silver (untarnished) shows a 2% efficiency loss and a 0.1 dB gain loss relative to perfection. Even if silver were cheap, I would not waste it on a wire antenna of this kind, given the performance of copper. Also note the larger step drops as you move below pure aluminum on the list.

+

Test 2. 4 MHz Wire dipole

The second modeling test took a different approach. With a 4 MHz wire dipole, what is the minimum AWG wire size necessary to achieve 1.75 dBi free space gain? Each change of material brought about a re-resonating of the antenna. I chose 1.75 dBi as the threshold of acceptability because this value resulted in wire sizes on the available list of automated selections in the program used. + 
Material       Source Z       Effici-   Gain dBi  Length    AWG Wire
+               R ± jX Ohms    ency %              Meters    Size
+
+Stls. Steel    78.3 + j 0.1   91.64     1.75      36.36     # 8
+Ph. Bronze     78.3 - j 0.4   91.75     1.75      36.46     #16
+Brass          78.1 + j 0.1   92.06     1.77      36.50     #18
+6061-T6        78.1 - j 0.0   92.08     1.77      36.52     #20
+6063-T832      77.5 - j 0.6   92.85     1.81      36.52     #20
+Pure Alum.     78.3 - j 0.5   91.88     1.76      36.53     #22
+Copper         78.4 - j 0.5   91.76     1.75      36.55     #24
+Silver         78.2 + j 0.4   92.08     1.77      36.57     #24
+

First, the gain numbers are not exactly 1.75 dBi, but the value closest to it on the high side yielded by the smallest wire size that would yield at least 1.75 dBi.

+

Second, within those limits, notice that there is an equality of source impedance and efficiency for a specific gain level. What differs among the antennas is the length necessary for resonance and the wire size.

+

Third, notice the wide range of antenna sizes in the list. As the wire grows thin for a given wavelength, the material losses play an increasing role in performance. If we use a conservative minimum gain of 1.75 dBi free space as the limit of acceptability, stainless steel--the strongest of the wires--would require a #8 AWG size to meet the standard. The electrical performance is at odds with its physical advantages.

+

Phosphor bronze is marginal under this test, requiring a minimum size of #16 AWG. If we set the gain standard higher, perhaps at 2.0 dBi free space, then phosphor bronze might fail to meet the electrical standard at an acceptable diameter.

+

Whether phosphor bronze will meet a given standard or whether the gain level obtainable with an available diameter of phosphor bronze wire is acceptable to a user is not a decision that can be made here. Instead, this note and the tests reported in it yield the advice not to misapply test results, not even these.

+

The selection of wire material requires that you set standards of performance for a given application. Then, model (or build) your antenna using the range of possible materials to see if each material meets the standard. When the diameter of the wire becomes thin enough relative to a wavelength, you may encounter a threshold situation in which some materials simply fail the electrical test.
+

+
+ +

+
+

Updated 8-8-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: Dipole, HF Lower, Hardware


+ + diff --git a/content/wire/zzdd-1.gif b/content/wire/zzdd-1.gif new file mode 100644 index 0000000..7f98dfa Binary files /dev/null and b/content/wire/zzdd-1.gif differ diff --git a/content/wire/zzdd-2.gif b/content/wire/zzdd-2.gif new file mode 100644 index 0000000..fbafcaa Binary files /dev/null and b/content/wire/zzdd-2.gif differ diff --git a/content/wire/zzdd-3.gif b/content/wire/zzdd-3.gif new file mode 100644 index 0000000..5a9fa6c Binary files /dev/null and b/content/wire/zzdd-3.gif differ diff --git a/content/wire/zzdd-4.gif b/content/wire/zzdd-4.gif new file mode 100644 index 0000000..1dfdbbc Binary files /dev/null and b/content/wire/zzdd-4.gif differ diff --git a/content/wire/zzdd-5.gif b/content/wire/zzdd-5.gif new file mode 100644 index 0000000..3abc34a Binary files /dev/null and b/content/wire/zzdd-5.gif differ diff --git a/content/wire/zzdd-6.gif b/content/wire/zzdd-6.gif new file mode 100644 index 0000000..624586e Binary files /dev/null and b/content/wire/zzdd-6.gif differ diff --git a/content/wire/zzdd-7.gif b/content/wire/zzdd-7.gif new file mode 100644 index 0000000..9a7b5a9 Binary files /dev/null and b/content/wire/zzdd-7.gif differ diff --git a/content/wire/zzdd.html b/content/wire/zzdd.html new file mode 100644 index 0000000..847cc95 --- /dev/null +++ b/content/wire/zzdd.html @@ -0,0 +1,88 @@ + + + + + + The Zig-Zag Dipole-Doublet + + + +
+

The Zig-Zag Dipole-Doublet

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+
+

L. B. Cebik, W4RNL

+
+
+ +
+

One over-age myth about wire antennas is that they must be straight. Ideally, we would like them to be truly linear. However, even a kinky wire can perform quite well.

+
+ +
+

Consider the scenario sketched in Fig. 1. A standard 1/2 wl dipole for 80 meters--about 135' long when about 50' up--would look like the upper sketch if we had the room for a 67.5' long wire runs on each side of the feedpoint. However, suppose that we do not have the room for the full length of the wires. We can settle for a shorter wire antenna, but we do have another option if supports are available: the zig-zag special. What we did with dimension A in the top drawing, we shall now do with A + B in the lower drawing.

+

The antenna could have been made into a U, but the loss of gain would have been slightly higher than with the zig-zag--due to the partial cancellation of the radiation from the facing end sections. However, the amount is small enough that, if a U is all that you can manage on a site, "U"se it.

+

To see what happens when we zig-zag our traditional dipole I ran a series of models, each of #12 copper wire over average soil. Modeling is limited in that it assumes clear, level terrain, and so it cannot take into account the hills, valleys, and ground clutter of the typical ham installation. Nonetheless, the trends are quite useful for comparative purposes.

+

If the antenna is set 50' up, the typical dipole pattern at an elevation angle of about 20 degrees is an oval at right angles to the wire. Let's see what happens as we turn more and more of the antenna into opposing end pieces. For the example, I used 5% increments of the half length, thus shortening each side of center by 3 3/8' with each move. Theoretically, the end piece should grow by that amount to keep the antenna resonant. Actually, we shall have to lengthen the ends slightly with each change in order to compensate for coupling between the wires near the corners.

+

The following table lists the wire lengths each side of center (A) with both the calculated and actual end pieces (B) need to restore resonance at 3.5 MHz. The feedpoint resistive impedance at resonance is also shown, along with the maximum gain. The final figure is the number of degrees off broadside that the pattern tilts as a result of the zig-zag ends.

+ 
End (B)   Calc.     Act.     Length A   Gain      Pat. Tilt      Feed R
+  %       Feet      feet      feet       dBi      degrees         Ohms
+  0         0         0       67.5       0.06       0             70.0
+  5        3.4       3.7      64.2       0.06       0             67.6
+ 10        6.8       7.3      60.8       0.04       1             66.4
+ 15       10.1      11.0      57.4       0.02       1             64.9
+ 20       13.5      14.5      54.0      -0.01       2             62.3
+ 25       16.9      18.2      50.6      -0.05       2             59.7
+ 30       20.3      21.7      47.3      -0.09       5             56.2
+

The total loss in gain within the situation set up is 0.15 dB for the entire spread from a linear wire to an antenna with 30% of each side turned at right angles to the main wire. If the zig-zag happens to be more open than the right angle used in the example as an extreme case, the loss will be less. However, it is already so low as to be undetectable in operation.

+

Had we bent the ends to form a U, the gain in the most extreme case would have been very slightly lower than for the zig-zag dipole, and so too would have been the source resistance at resonance. Another comparison of note is between the 20% zig-zag model and a wire 108' long and linear--something close to the traditional G5RV length. The G5RV would have shown about 0.1 dB less gain than the zig-zag, which would have been far less operationally significant than the high capacitive reactance at the feedpoint. However, if we feed the antenna with parallel feedline and an antenna tuner, all of these differences fall among the trivial.

+

The greater the amount of antenna devoted to the zig-zag ends, the longer the wire must be to restore resonance. Again, a more open zig-zag will show smaller amounts of required lengthening. Likewise, the feedpoint resistance goes down more rapidly as the zig-zag becomes more extreme.

+

The amount of pattern tilt is very mild, even at the 30% zig-zag mark. Fig. 2 below sows an overlay of the straight wire and the zig-zag azimuth patterns for the 20-degree elevation angle. Again, in real operation, the difference will be unnoticeable. Notice that the pattern tilt is away from the bent ends.

+
+ +
+

As the zig-zag involves more than 30% of the wire on each side of center, the pattern tilt becomes more extreme, exceeding 10 degrees as the lengths A and B approach each other. We can view this amount of tilt as a disadvantage, or we can put it to use. Suppose the main supports we have will place the broadside pattern some 10 degrees off target for our desired operation. Making the antenna into a zig-zag dipole can put us back on target.

+

The Dipole Becomes a Doublet

+

If we choose to use the zig-zag on other HF bands, what happens?

+

The first thing that happens is that the antenna is no longer a dipole. A dipole is an antenna with a single current maximum at its center and voltage maxima at its ends. It is a center-fed dipole in the version with which we are working. However, since its length will no longer be apt to produce the current and voltage conditions along its length once we increase the frequency of operation, it will no longer be a dipole. Typically, a multi-band single (simple) wire is best termed a "doublet," a term that implies nothing in itself about the current and voltage distribution along the length.

+

The second thing that happens is this: the exact length is no longer of great consequence. Our first tests intentionally strove for resonance at 3.5 MHz in order to see what happened to the length of the end pieces. In multi-band use with parallel feeders and an antenna tuner, the length is no longer critical. The patterns will not significantly change with up to 5% differences in overall length, and antenna resonance is no longer a serious consideration.

+

A third phenomena is the variation of the patterns of lobes and nulls from those that we are used to associating with a straight-wire doublet. To see what happens, let's use 40, 20, 15, and 10 meters as test bands to compare the patterns of a straight-wire doublet and our 30% zig-zag doublet--both of #12 copper wire 50' up. Of course, if we use a smaller amount of zig- zagging, then any deviations of patterns from the normal doublet pattern will be that much less.

+

In each of the patterns shown below, the antenna extends from one side of the pattern to the other. The zig-zag legs bend downward (relative to the page) on the left and upward on the right. Hence, most of the pattern tilting will be to the upper left corner of the page, at least at lower frequencies.

+
+ +
+

At 7.0 MHz, the zig-zag pattern shows a 5-degree tilt relative to the broadside lobes of the normal doublet. The elevation angle of maximum radiation is still very high, so a 20-degree elevation angle has been selected for the comparison to reflect something approximating normal skip angles. The gain of the zig-zag is slightly less (by about 0.5 dB) than that of the straight wire and is accompanied by a broadening of the beamwidth in both directions. Since the antenna is about 1 wl long, the feedpoint impedance is very high. The zig-zag side nulls are shallower than those of the normal doublet. However, none of these differences are likely to result in any gained or lost contacts.

+
+ +
+

Lest we simply presume that the remaining HF bands will show essentially similar parallels between the straight and the zig-zag doublets, operation of the antennas at 14.0 MHz serves as a reminder that difference might emerge at any frequency. The elevation angle of maximum radiation on 20 meters is 20 degrees with the antenna at the 50' mark. Hence, the patterns show the maximum gain of the antenna. The straight-wire doublet shows the familiar 4-leaf clover pattern typical of a wire 2 wl long.

+

In contrast, the zig-zag antenna shows much greater tilt, with the peaks being about 20 degrees distant from those of the normal doublet. The nulls are just barely perceptible, but with that improved coverage comes a price: the lobes are weaker than those of the normal doublet by about 1.3 dB.

+
+ +
+

At 21 MHz, the normal and the zig-zag patterns almost oppose each other, with zig-zag lobes filling normal nulls and vice versa. Once more, the normal doublet shows a higher maximum gain (by about 1 dB), but the zig-zag doublet tends to have shallower nulls.

+

Part of the reason for the especially strong zig-zag lobes off the ends of the antenna is that each bent section of the zig-zag is approximately 1/2 wl long at 15 meters. Had the zig-zag "B" length been shortened, the end radiation would have decreased rapidly. When operating the antenna at multiples of its initial frequency, the current magnitude shows a number of peaks, and the geometric configuration plays an increasingly significant role on the ultimate azimuth pattern generated.

+
+ +
+

On 10 meters, at 28 MHz, there are so many lobes that the differences in the two patterns becomes less significant operationally. In fact, there is no significant difference in the strength of the largest lobes of the two antennas. However, we may note the two small lobes off the end of the zig- zag antenna. Because the end of "B" lengths are no longer close to 1/2 wl long, they develop lesser lobes. Some of the versions of the zig-zag with shorter "B" dimensions might well show stronger radiation off the antenna ends.

+

The feedpoint impedance of both antennas at the even harmonics of the original 1/2 wl frequency of the antenna will be high. The exact figures will be functions of the antenna's exact length. At harmonics, effects of the zig-zag will vary slightly from band to band, and hence the feedpoint impedances will not be identical to those of the straight wire. Values of resistance in the 1,000 to 4,000 Ohm range and values of reactance from 500 to 1200 Ohms are likely to be common for both the straight-wire and the zig-zag doublets. What values appear at the antenna tuner terminals will depend not only on these load values, but as well on the characteristics and length of the feedline used. If a tuner cannot handle the values presented on a certain band, insertion of a short length of additional feedline will usually correct the situation.

+

Other Variations

+

We have already noted that when the ends of the antenna are bent in the same horizontal direction, the resulting U-shaped antenna is only a tiny bit lower in gain than the 30% zig-zag. A more common scenario is to droop both ends downward. At the fundamental frequency, this configuration tends to lower gain still further, since the ends are closer to the ground. However, the result is far from disastrous. At higher frequencies of operation, the ends may show significant vertically polarized radiation, but the net effect will not be sufficient to alter the basic horizontally polarized patterns for each band.

+
+ +
+

Perhaps the ultimate utility of the zig-zag doublet is to fit a full 80- meter length into a fairly restricted yard size, as suggested in Fig. 7. running the antenna diagonally across the yard for the available space and then tilting the wires back along the yard lines (assuming supports are available) can make a multi-band doublet available to almost anyone.

+

The principle can also be applied to hidden roof-top or attic antennas. The ends can be run along the rafters and roof trusses, if appropriate care is taken to give clearance to conductive materials.

+

The urban dweller can still operate effectively even if circumstance seems to dictate undersized antennas. The key is to think in designer shapes, of which the zig-zag is a perennial winner. The losses, compared to traditional straight-line designs, may be far smaller than initially imagined.

+
+ +
+

Updated 01-01-2000. © L. B. Cebik, W4RNL. This item appeared in AntenneX, December, 1999. And QRP Quarterly April, 2000, pp. 19-21. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Main Index

+

Topics: Dipole, Doublet, HF Multi Band


+ + diff --git a/content/yagi/30m-3l.html b/content/yagi/30m-3l.html new file mode 100644 index 0000000..8ad98aa --- /dev/null +++ b/content/yagi/30m-3l.html @@ -0,0 +1,17 @@ + + + + + + A 3-Element Wire Yagi Design for 10.1373 MHz + + + +

A 3-Element Wire Yagi Design for 10.1373 MHz

+ hr +

A 3-Element Wire Yagi Design for 10.1373 MHz

+

This page exists to include the PDF in the topic index

+ hr
+

Topics: HF Lower, Yagi


+ + \ No newline at end of file diff --git a/content/yagi/30m-3l.pdf b/content/yagi/30m-3l.pdf new file mode 100644 index 0000000..975fad9 Binary files /dev/null and b/content/yagi/30m-3l.pdf differ diff --git a/content/yagi/3l-1.gif b/content/yagi/3l-1.gif new file mode 100644 index 0000000..95b1495 Binary files /dev/null and b/content/yagi/3l-1.gif differ diff --git a/content/yagi/3l.html b/content/yagi/3l.html new file mode 100644 index 0000000..c485f17 --- /dev/null +++ b/content/yagi/3l.html @@ -0,0 +1,185 @@ + + + + + + Three-Element Yagi Models: Standards of Comparison + + + +
+

Three-Element Yagi Models:
+ Standards of Comparison
+ L. B. Cebik, W4RNL

+
+
+ +

+
+

I have had numerous requests for models of the 3-element Yagis that I use regularly as a standard of comparison for other models. To make the models more readily available for use or improvement, I have placed them at the end of this note. They are in the form of EZNEC antenna descriptions and contain all the information needed to create AO, NEC-Wires, NEC-Win, NEC4WIN, ELNEC, and EZNEC models. In fact, the antenna geometries are quite simple, consisting of 3 wires of 21 segments each. (Reduce the segments to 20 per element for versions of MININEC.) The original source of the models is a 20- meter Yagi included in an earlier version of AO and modified to simplify construction as a model.

+

The antennas have not been modeled to build. A real Yagi would likely use elements of tapered diameter sections. The models use a constant diameter for each band: 0.5" for 10 meters; 0.75" for 15 meters; and 1.0" for 20 meters. In fact, all three antennas are essentially the same antenna, frequency scaled and then tweaked a bit to use standard size element diameters.

+

Each model has a center design frequency, but the performance center (in this case, maximum front-to-back ratio) has been moved to provide close to band- edge to band-edge 2:1 SWR bandwidth relative to a feedpoint impedance of 25 ohms. The premise is that a well-designed beta match would only require shortening of the driven element to supply the needed capacitive reactance, while a gamma match would require driven element lengthening. In both cases, beam performance would be altered hardly at all.

+

The beams have been modeled in free space. Performance and matching hold up well at heights from 1 wavelength upward. Adjustments would be necessary for some lower heights.

+

The following tables show the modeled performance of the beams on each band in free space. Note that performance is very good for the boom lengths involved. However, one might well tweak slightly better performance from the beams with further optimization--better, but not too much better, unless one is aiming for either gain or front-to-back ratio without regard for other parameters. These models strove for a balance of gain, front-to-back ratio, and operating bandwidth as examples of what a decent 3-element Yagi might achieve. Figures are seriously exact from NEC-4 models.

+ 
Antenna:  3-element 20 meter Yagi:  1.0" diameter al. elements; boom =
+22.544'
+
+Frequency      Gain (dBi)     F-B (dB)       Feed (R+/-jX)  SWR (25 ohms)
+14.0           7.94           20.81          27.04 - 13.25       1.665
+14.1           8.03           27.30          26.50 -  6.35       1.288
+14.2           8.14           25.68          25.38 +  0.93       1.041
+14.3           8.27           19.82          23.81 +  8.78       1.439
+14.35          8.35           17.69          22.90 + 12.96       1.723
+
+Antenna:  3-element 15 meter Yagi:  0.75" diameter al. elements; boom =
+15.074'
+
+Frequency      Gain (dBi)     F-B (dB)       Feed (R+/-jX)  SWR (25 ohms)
+21.0           8.01           24.58          26.17 -  9.15       1.432
+21.1           8.08           28.57          25.60 -  4.49       1.196
+21.2           8.16           26.72          24.80 +  0.37       1.017
+21.3           8.25           21.84          23.80 +  5.48       1.258
+21.4           8.34           18.57          22.65 + 10.88       1.590
+21.45          8.39           17.24          22.04 + 13.70       1.802
+
+Antenna:  3-element 10 meter Yagi:  0.50" diameter al. elements; boom =
+11.212'
+
+Frequency      Gain (dBi)     F-B (dB)       Feed (R+/-jX)  SWR (25 ohms)
+28.0           7.87           17.35          27.04 - 18.07       1.985
+28.1           7.91           19.64          27.09 - 14.74       1.758
+28.2           7.95           22.42          26.98 - 11.37       1.554
+28.3           8.00           25.76          26.70 -  7.94       1.368
+28.4           8.05           28.44          26.27 -  4.43       1.197
+28.5           8.11           27.15          25.70 -  0.80       1.043
+28.6           8.17           23.87          25.02 +  2.95       1.125
+28.7           8.23           20.99          24.23 +  6.86       1.323
+28.8           8.30           18.65          23.36 + 10.94       1.574
+28.9           8.37           16.71          22.43 + 15.19       1.896
+29.0           8.44           15.06          21.45 + 19.63       2.309
+
+ +
+

The figure shows the free space azimuth pattern for the 20 meter model, which differs by little from the models for the other bands. Note that for each model, the highest front-to-back ratio is in the lower half of the operating band, while the gain climbs beyond the upper limit of the operating band defined by the 2:1 SWR ratio. The antennas can each be retuned for resonance at a higher gain, but at the expense of a lower front-to-back ratio and a lower feedpoint impedance. Further performance improvements might also be garnered through the use of a longer boom.

+

Remember, however, that these are not antennas to be built. Significant adjustments to element lengths and even some slight revisions of spacing might be required with typical Yagi building materials. Those tapered- diameter element sections would complicate these models, which are only standards for comparison.

+
+

Using the Standards

+
Modeling standards have a number of proper uses, so long as we remember that they do not define the limits of performance in any category. +

1. Experimental Platforms: the models are useful as models for a number of initial experiments in modeling. For example, we can get a fair idea of stacking performance for antennas of similar gain from a set of these models. Likewise, we can obtain initial ideas about antenna interaction as we place pairs of these antennas at various horizontal spacings and directional orientations. How the gain, front-to-back and feedpoint impedance vary from the baseline values can give direction to the most productive modeling we can do with more complex and slower running of models of actual antennas in their class.

+

2. Comparison with Experimental Designs: Antennas come in more sizes and shapes than pills in a pharmacy, and new shapes are emerging with great regularity (although most are spin-offs of rather ancient basic designs). Evaluating whether a new shape is worth building is a matter of judging whether the improvements to be made are likely to be worth the effort involved. Since a 3-element Yagi is a fairly standard amateur antenna, comparing the modeled performance of the new antenna against the modeled performance of the standard can aid one in the evaluation. The models need to be transferred to the proposed height over the proper type ground for the new antenna to make the comparison tighter, and both azimuth and elevation patterns require study. Additionally, if terrain modeling software is available, it should also be brought into play.

+

3. Comparison with Models of Real Antennas: Antennas we see in magazines may or may not have performance figures associated with them. Even where performance figures are given, their source and reliability may sometimes be open to question. Modeling these real antennas and comparing them to the standards can clarify source claims and provide a common setting for various other comparisons. However, these comparisons are meaningful only if due account is taken of the real antenna type. 2-element Yagis should not be expected to have the performance of 3-element Yagis. Likewise, 3-element trap beams should not be expect to be the equal of 3-element optimized monobanders. Within the limits of each type, appropriate accurate models of real antennas within a common modeling framework can take much of the guesswork out of comparisons.

+

There are other uses for standards, but these are enough to provide the start toward their proper use. And if you get the urge to modify, improve, and actually build one of these antennas, so much the better. But be sure you do some investigation into good Yagi construction techniques (in other words, read Leeson's fine book, Physical Design of Yagi Antennas) before investing in a batch of aluminum tubing.

+ 
+                      EZNEC/4  ver. A2.11
+
+3 el Yagi 1" elements                        06-22-1997     08:49:34
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+Segs
+
+1          -17.280,  0.000, 70.000        17.280,  0.000, 70.000 1.00E+00  21
+2          -16.500, 10.455, 70.000        16.500, 10.455, 70.000 1.00E+00  21
+3          -15.525, 22.544, 70.000        15.525, 22.544, 70.000 1.00E+00  21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+-----------------------------------------------------------------------------
+                      EZNEC/4  ver. A2.11
+
+3 el Yagi 3/4" el                            06-22-1997     08:49:51
+
+
+Frequency = 21.2  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+Segs
+
+1          -11.554,  0.000,  0.000        11.554,  0.000,  0.000 7.50E-01  21
+2          -11.032,  6.991,  0.000        11.032,  6.991,  0.000 7.50E-01  21
+3          -10.381, 15.074,  0.000        10.381, 15.074,  0.000 7.50E-01  21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+-----------------------------------------------------------------------------
+                      EZNEC/4  ver. A2.11
+
+3 el Yagi 1/2" al elements                   06-22-1997     08:53:38
+
+
+Frequency = 28.5  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in)
+Segs
+
+1           -8.595,  0.000,  0.000         8.595,  0.000,  0.000 5.00E-01  21
+2           -8.207,  5.200,  0.000         8.207,  5.200,  0.000 5.00E-01  21
+3           -7.722, 11.212,  0.000         7.722, 11.212,  0.000 5.00E-01  21
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+----------------------------------------------------------------------------
+

+
+
+ +

+
+

Updated 6-21-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+

Return to Amateur Radio Page

+

Topics: HF Upper, Yagi


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+

I Want to Build a 3-Element Yagi

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

There are many sources of information on how to construct a 3-element Yagi. Some articles are even geared to the builder's first major construction effort with aluminum tubing and associated clamps and hardware. Most of these otherwise fine articles tend to offer a stock design for the 3-element Yagi. They end up giving the new Yagi-user very little information about the electrical design decisions involved in selecting the right 3-element Yagi for one's home station.

+

This series of articles, which first appeared in antenneX, is not so much about construction as it is about electrical design. They focus on monoband Yagis so that the data can be clear and relatively precise. Multiband Yagis are advanced design exercises and best left, at the beginning, to the professional designers.

+

There are a number of questions the prospective Yagi builder needs to ask himself or herself. Each of the articles attempts to answer one of them--not exhaustively, but at least thoroughly enough to permit you to make intelligent decisions.

+

Here are the questions we shall tackle.

+ +
+ +
+

Updated 07-31-99. © L. B. Cebik, W4RNL. These items appeared in AntenneX between April and July, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/3lyg1.html b/content/yagi/3lyg1.html new file mode 100644 index 0000000..2d9d0e1 --- /dev/null +++ b/content/yagi/3lyg1.html @@ -0,0 +1,129 @@ + + + + + + Build a 3-Element Yagi Part 1: How Big Shall I Make It? + + + +
+

I Want to Build a 3-Element Yagi
+ Part 1: How Big Shall I Make It?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Those of us with more time than money get the urge to upgrade our antennas from dipoles to beams in the home workshop. The logical first step might be a 2-element Yagi. Often, we skip this step because we have heard or seen evidence that 2-element Yagis do not quite have the specifications we want. If we make use the common reflector-driver design, the gain is low and the front-to-back ratio is poor. If we opt for a driver-director design, we get more gain and better front-to-back ratio, but a very narrow beam width and a potentially very low feedpoint impedance. So we immediately jump to 3-element designs.

+

Our next step is usually a semi-fatal one. We search the magazines and handbooks on our shelves for a design that looks like one we can build. We know what the author claims the beam will do, but we are not ever sure of how it does what it is supposed to do or whether our version is doing the same thing.

+

So let's back up a bit and look at some 3-element Yagi basics. I shall focus on monoband beams, because they are much easier than multi-band beams to model and to build so that their performance matches the model. Even if you have your heart set on buying a tribander, perhaps these basics will help you better to understand both the antenna maker's claims and the performance you actually get.

+

The basics I have in mind have little to do with the theory of parasitic element operation. The ARRL Antenna Book and some references I shall mention along the way do a good job at that level of explanation. Instead, I shall begin in the middle of things with some distinctions among Yagi designs. There are so many Yagi designs floating around today that they can be at first sight a bit bewildering.

+

High Performance Designs

+

The first decision we have to make is whether we wish to have a wide-band Yagi or a high-performance Yagi. Let's begin with the high-performance designs, since these have very great initial appeal. We shall return later to some wide-band designs.

+

Once we have opted for a high-performance design, we have to figure out what we mean by that term. First, there is the matter of size. The element lengths will not vary by a large amount from one design to another (but they will vary significantly in terms of the performance). So, size turns out to be a question of boom length.

+

James Lawson, W2PV, developed most fully the notion that the gain of a Yagi is highly dependent upon the boom length. His book, Yagi Antenna Design, has become one of the classic references for those interested in basic Yagi theory. Based on his work, many designers have optimized 3-element Yagis of various lengths for maximum performance.

+

Maximum performance is a balanced mix of high gain, good front-to-back performance, and a satisfactory feedpoint impedance. Let's work backwards through the list.

+

For almost any length boom, one can get a little more gain from a Yagi by so spacing and sizing the elements that the feedpoint impedance drops to about 10 Ohms or less. Most high performance designs you will encounter tend to opt for feedpoint impedances closer to 25 Ohms. The reasons are many, but one good reason is a matter of losses. Suppose that the total resistance of all the connections at the feedpoint, including those of a matching system for 50-Ohm coaxial cable, amount to 1 Ohm. (That is a quite high value and can be reduced by good construction practices.) With a 10-Ohm feedpoint impedance, about 9-10% of the power is going to heat. If the feedpoint impedance is 25 Ohms, then the loss is closer to 4%.

+

To this consideration, we can add the fact that it is generally easier to design low-loss matching systems for a 25-to-50 Ohm conversion than for a 10-to-50 Ohm conversion. So 25 Ohms becomes a kind of de facto (but not absolute) limit to a Yagi's feedpoint impedance.

+

For the higher feedpoint impedance, it is also somewhat easier to design a 3-element Yagi whose gain and front-to-back performance figures hold up across such HF bands as 20 and 15 meters--as well as the first MHz of 10 meters. As well, the designs can be replicated in the home shop with moderate building skills and are not so finicky as to require industrial laser measuring equipment in setting the dimensions.

+

Within these constraints, then, lets look at three good designs for 3- element Yagis.

+
+ +
+

As revealed in Fig. 1, the designs I have in mind use three different boom lengths. The long-boom design, shown for 28-29 MHz, is adapted from an optimized design by K6STI. It uses an 11.31' boom, which is nearly 1/3 wl long. The K9EUV design uses a 9.88' boom, and has the additional feature of using equal spacing between elements. (A fourth director element at the same spacing and the same length as the present director provides good 4- element Yagi performance.) The third design is a short boom Yagi, also by K6STI, that requires a 7.5' boom. For construction, you should round these boom-length numbers upward to the next whole foot to provide room for mounting plates and hardware. So we have 12, 10, and 8 foot boom 3-element Yagis.

+

Caution: Do NOT build these designs as given here. They all use uniform diameter elements. Converting them to the actual lengths needed by physical designs that employ tubing that decreases in diameter will net us different dimensions. But that is a subject for a future episode.

+

The 10-meter designs all use 0.5" aluminum tubing. We can scale them for any band in the following way. Take the ratio of the new design frequency (for example 14.175 or 21.22 MHz) to the present design frequency (28.5 MHz) and invert it (since lower frequencies will require longer, fatter elements). Now multiply the element lengths, the element spacings, and the element diameters by this figure.

+

As a sample, here is a collection of dimensions for the three basic designs for 10, 15, and 20 meter versions of the antenna.

+ 
Long-Boom
+Frequency (MHz)          28.5                21.22               14.175
+Element Lengths (feet)
+     Reflector           17.90               23.11               34.56
+     Driver              16.41               22.06               33.00
+     Director            15.44               20.76               31.05
+Spacing (feet)
+     Ref-Driver           5.2                 6.99               10.46
+     Driver-Dir           6.01                8.08               12.09
+Element dia. (inches)    0.5                 0.75                1.0
+
+Medium-Boom
+Frequency (MHz)          28.5                21.22               14.175
+Element Lengths (feet)
+     Reflector           17.27               23.20               34.72
+     Driver              16.63               22.34               33.43
+     Director            15.62               20.99               31.41
+Spacing (feet)
+     Ref-Driver           4.94                6.63                9.92
+     Driver-Dir           4.94                6.63                9.92
+Element dia. (inches)    0.5                 0.75                1.0
+
+Short-Boom
+Frequency (MHz)          28.5                21.22               14.175
+Element Lengths (feet)
+     Reflector           17.65               23.73               35.50
+     Driver              16.15               21.71               32.47
+     Director            15.41               20.71               30.98
+Spacing (feet)
+     Ref-Driver           3.00                4.03                6.03
+     Driver-Dir           4.50                6.05                9.05
+Element dia. (inches)    0.5                 0.75                1.0
+

Clearly, I have violated my own scaling scheme by using the closest standard value of aluminum tubing as the element diameter. Hence, some very small adjustments are required in the element lengths and spacings, but generally, these are too small to make an operational difference. Nonetheless, some of the difference shows up numerically in the design frequency performance figures for the three designs. Here the table divides the designs by bands.

+ 
20-Meters:  14.175 MHz
+Antenna Design           Free Space          Front-to-      Feed Impedance
+                         Gain dBi             Back dB       R +/- jX Ohms
+Long-Boom                8.11                27.31          25.71 - j 0.93
+Medium-Boom              7.78                35.50          27.02 + j 0.50
+Short-Boom               7.13                41.35          27.46 + j 0.01
+
+15-Meters:  21.22 MHz
+Antenna Design           Free Space          Front-to-      Feed Impedance
+                         Gain dBi             Back dB       R +/- jX Ohms
+Long-Boom                8.16                26.12          24.80 + j 0.37
+Medium-Boom              7.81                34.88          26.06 + j 0.94
+Short-Boom               7.17                61.67          26.56 - j 0.00
+
+10-Meters:  28.5 MHz
+Antenna Design           Free Space          Front-to-      Feed Impedance
+                         Gain dBi             Back dB       R +/- jX Ohms
+Long-Boom                8.11                27.15          25.70 - j 0.80
+Medium-Boom              7.80                34.77          26.51 + j 1.69
+Short-Boom               7.12                41.66          27.45 - j 0.01
+

These tables of predicted performance from NEC models show a number of things, including how to be misled. First, the numbers--even though slightly different in the decimal columns--illustrate that for each design, the performance is identical on all three bands. The excess decimals are given because NEC reports them and because they show how little different the performance varies as we correctly scale a beam from one band to another.

+

However, the front-to-back figures can mislead us into thinking that the short-boom model has an almost miraculously better front-to-back performance than the other beams, as good as they are. The figure given is for the 180-degree front-to-back ratio, which is usually a very convenient figure to obtain. That figure may not be indicative of the performance of the antenna in all its rearward directions.

+
+ +
+

Fig. 2 provides an overlay of the 28.5 MHz free space azimuth patterns of all three antenna designs. We may note the forward gain peaks, which just about correlate to the differentials in boom length. The rear lobes give us much more valuable information. Here we see that the long-boom design has three small lobes of roughly equal size so that the front-to-back ratio in the table gives a fair appraisal of the overall front-to-rear performance. In contrast, the other two models have deeper 180-degree "dimples," combined with much stronger angling lobes. When averaged out, none of the antennas has much of an advantage over the other. Indeed, anything above 20-dB front-to-back ratio overall might be considered outstanding.

+

To this point, it may seem that the decision we need to make is one of gain advantage vs. mechanical disadvantage to a longer boom. However, let us not be so swift to judgment. For I have once more misled you by giving you the peak or nearly peak performance of the antenna at one frequency. The next question is how each of these designs performs across an entire ham band.

+

Since the first MHz of 10 meters is the greatest stretch for these designs (because 20 and 15 are proportionately narrower), let's sweep the antennas across the 28 to 29 MHz range and see how the performance of each holds up.

+
+ +
+

In Fig. 3, we have the gain of the three designs across the pass band. Note that the gain figures in the tables are intermediate values. The gain across the band can vary by as much as 0.4 dB in at least one of the designs. In selecting a design, we must also ask whether the lowest gain--which occurs at the low end of the band for 3-element Yagi designs--is an acceptable figure (when weighed against all of the other factors involved in our decision to build).

+
+ +
+

Fig. 4 records the 180-degree front-to-back ratios across the pass band. Here we can either be impressed by the peak values, or we can take a closer look at the values at the band edges. The short-boom design actually excels in this department, with no value falling below 20 dB. The other two designs are remarkably close in their band edge values, which are about 17 dB at the low end and 15-16 dB at the high end. Before settling on a design for the two lower bands, we should remember that these bands are only 68% to 70% as wide as the 10-meter passband. Hence, we can achieve better band-edge results by centering the peaks in our final design.

+
+ +
+

A rough measure of whether we shall be able to effect a wide-band match to a 50-Ohm cable can be derived from the SWR curve of the antenna related to the resonant impedance before matching. Since the feedpoint impedance of all three models is so close to 25 Ohms, we can use that number as representative of the resonant feedpoint impedance. Then we can evaluate the SWR curves in Fig. 5.

+

For all three designs, the SWR climb more quickly above the resonant design frequency than below it. On 10 meters, this means exceeding a 2:1 SWR value at the upper end of the pass band for two of the three designs. However, all three designs will likely show under 2:1 SWR across the narrower reaches of 20 and 15 meters. The short boom design shows the flattest curve.

+

Although the designs were set up for a resonant feedpoint impedance (little or no reactance), one can extend or shrink the driver length as necessary to use any of the common matching system: beta, gamma, Tee. Of course, a 1/4 wl section of 35-37 Ohm coax will provide a matching section to a 50-Ohm main line if we leave the feedpoints resonant. We shall look in more detail at typical matching systems before we are done.

+

So it looks like we are almost ready to make a decision. Seemingly, all we need to do is to look at how the elements might change if we use several diameters of tubing for each one.

+

Not so fast. We have not yet looked at truly wide-band designs to see if they hold any advantages and what those advantages might be. So while we are still in this preliminary stage of design evaluation, let's look next month at a pair of wide-band Yagi designs.

+
+ +
+

Updated 07-31-99. © L. B. Cebik, W4RNL. This item appeared in antenneX, April, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 2: How Wide-Band Shall I Make It?

+

Return to Index

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/3lyg2.html b/content/yagi/3lyg2.html new file mode 100644 index 0000000..8eebbbe --- /dev/null +++ b/content/yagi/3lyg2.html @@ -0,0 +1,115 @@ + + + + + + Build a 3-Element Yagi Part 2: How Wide-Band Shall I Make It? + + + +
+

I Want to Build a 3-Element Yagi
+ Part 2: How Wide-Band Shall I Make It?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Last time, we looked at the basic design of high-performance 3-element Yagis. All had similar front-to-back and feedpoint impedance characteristics. They differed in gain in accord with the length of their booms. For 10-meter models, here are the design center figures as a reference for this month's investigation:

+ 
10-Meters:  28.5 MHz
+Antenna Design           Free Space          Front-to-      Feed Impedance
+                         Gain dBi             Back dB       R +/- jX Ohms
+Long-Boom      12'       8.11                27.15          25.70 - j 0.80
+Medium-Boom    10'       7.80                34.77          26.51 + j 1.69
+Short-Boom      8'       7.12                41.66          27.45 - j 0.01
+

Each of these designs is capable of performance close to that at the design frequency across the first MHz of 10 meters. When scaled to 20 and 15 meters, the designs will cover the entire bands--and, of course, cover the WARC bands when scaled to those frequencies.

+

However, there is an alternative design philosophy. This philosophy sacrifices some gain in favor of wide-band characteristics. For example, the high-performance models might vary in gain by almost 0.5 dB across the span from 28 to 29 MHz. A wide-band design might vary in gain across the same span by only 0.15 dB. Likewise, a high-performance design with a feedpoint impedance in the mid-20s might just barely allow a 2:1 SWR at the band edges. A wide-band design might show those figures over the entire 10-meter band, with a corresponding shallow SWR curve within the first MHz of 10 meters.

+

Consequently, before we freeze our design decisions, let's look at the basic wide-band 3-element Yagi design a little more closely.

+

Wide-Band 3-Element Yagi Design

+

To create a wide-band 3-element Yagi requires more boom length for a given gain than used in the high-performance designs we surveyed last time. A 12' boom on 10 meters will yield about 1 dB less gain. What, then, is the rationale for such a design?

+

The fundamental reasons for going to a wide-band design are two:

+

1. The wide-band design provides reasonably smooth and quite adequate performance figures for the entire 10-meter band, which is 1.7 MHz wide. Hence, a single beam will cover the CW/SSB and the FM/satellite portions of the band. When scaled to 20 or 15 meters, the beam will show less change in gain, front-to-back ratio, and feedpoint impedance across those bands.

+

2. The wide-band design can be set for a feedpoint impedance very close to 50 Ohms, thus eliminating the need for any sort of matching network at the feedpoint. (However, a choke or 1:1 choke balun remains recommended to attenuate common mode currents.)

+

When these two reasons are combined, the result is a very close match to a standard 50-Ohm coaxial cable feedline with very small changes in SWR across the band of choice. This eases not only matching problems, but as well the sensitivity of some transmitting equipment to even low SWR levels that often result in automated power output reductions. Accompanying this feature is consistent gain and front-to-back ratio performance across the band.

+

There is an additional feature occasionally anecdotally noted by some operators. They claim superior performance results from Yagis with higher input impedances. Since these claims do not show themselves in NEC models, the vehicle we are using to evaluate performance potential, no comment can be made upon those experiences in this context.

+

Since the performance of wide-band models shows up most clearly on 10-meter models, we shall focus solely upon them. You can extrapolate the most relevant portions of performance curves for the other HF bands.

+

Two notable designs for wide-band 3-element Yagis have appeared in US antenna literature in the last decade. In the May, 1990, issue of Ham Radio, Bill Orr, W6SAI presented a wide-band design in one of his columns. In the Winter, 1998, issue of Communications Quarterly, Joe Reisert, W1JR, present a similar design, along with scalable design equations.

+
+ +
+

Fig. 6 shows schematically both the Orr and the Reisert designs, set for 10 meters. As we noted in connection with the high-performance designs, do NOT commit to using these dimensions to construct either design. Both are predicated on uniform diameter elements: 0.5" for the Reisert design, 1.0" for the Orr design. In common practice, Yagi elements consist of two or more sections of tubing each side of center, each section having a smaller diameter than the preceding one. This tapered-diameter schedule results in a need to lengthen elements relative to uniform-diameter models. We shall explore this topic next time.

+

For the moment, we want to look at the wide-band designs as concepts rather than as finished products. Both the designs require 12' booms (with allowance at each end for element-mounting hardware). The dimensions of the two antennas are sufficiently close to each other that we suspect similar performance will emerge from the antennas. And we get it.

+
+ +
+

The free-space azimuth patterns in Fig. 7 overlay the Orr and Reisert designs at their resonant frequencies. The differences are too small to require comment. Gain is within 0.02 dB; front-to-back difference is less than 1 dB; and the feed point impedances are within 1 Ohm of each other at resonance. For reference, here is a handy table of values:

+ 
Antenna        Resonant       Free Space     Front-to-      Feed Impedance
+               Freq. MHz       Gain dBi       Back dB       R +/- jX Ohms
+Orr, 1990      28.80          7.11           21.60          47.08 + j 0.98
+Reisert, 1998  28.85          7.13           20.92          46.01 + j 0.20
+

The slight differential in resonant frequency owes to the slight design differences, which in turn yield slightly different performance curves on 10 meters. Moving the resonant point allows one to obtain a satisfactory SWR curve across the band. We can easily sample the performance by running frequency sweeps. In the following graphs, I have used 29.5 MHz as an arbitrary upper limit in order to limit the number of data points.

+
+ +
+

The free-space gain figures for the two designs appear in Fig. 8. The Reisert model shows the smoother gain curve, although the differences are marginal. Note that in wide-band designs, there is often a dip in the gain at the low end of the band. The dip reaches minimum for the Orr design below the lower end of 10 meters.

+

If we translate the first MHz of the band into roughly equivalent performance across 20 or 15 meters, the Reisert design, especially, shows a very small change in gain. The consistency of performance across the band is one of the advantages of a wide-band design.

+
+ +
+

What the Orr design gives up in gain, it reacquires in front-to-back performance, as shown in Fig. 9. If we use a 20-dB front-to-back ratio as a plateau figure of merit, then the Orr design would show this across all of 20 and 15 meters. However, the Reisert design averages only about 1 dB less performance in this category, an amount unlikely to be either noticed or measurable.

+

With either design, the 180-degree front-to-back ratio used in the graph is a reasonable approximation of overall front-to-rear performance. The smooth rear quadrant lobe shown earlier in the azimuth patterns ensures a reasonable correlation between the 180-degree front-to-back ratio and the other two common measure of rearward performance: an averaged front-to- rear ratio and a worst-case front-to-back performance figure.

+
+ +
+

Where the wide-band designs shine is in the flatness of the SWR curves. As shown in Fig. 10, the 50-Ohm SWR curves for both designs permit a ready match directly to 50-Ohm feedline across 10 meters. If the curve centers are translated into equivalent 20 and 15 meter versions, achieving a maximum band-edge SWR of 1.35:1 is no real challenge.

+

For those willing to accept a slightly lower gain on the HF band of choice, the wide-band design offers consistent performance across the band with an ease of matching to 50-Ohm feedlines systems that the high-performance models cannot duplicate. The wide-band models, however, offer only the gain that the high-performance models achieve with a boom 2/3 as long.

+

Before we close out this preliminary survey of designs, let's take a moment to review what we are seeking to do when we decide that we want to build a 3-element Yagi.

+

A Pair of 2-Element Yagi Designs

+

Although we can design a 2-element driver-director Yagi of excellent performance and very compact size for the WARC bands, covering the wider HF bands requires that we look to 2-element driver-reflector designs. In order to see just why we might want a 3-element version, let's look at two versions of the 2-element Yagi. One uses narrow spacing, the other wide spacing.

+
+ +
+

Fig. 11 shows the dimensions of both models, which use 1" uniform diameter elements. In these very standard designs, the element lengths are quite similar, with only small changes needed to accommodate the difference in boom length. At the design frequency of 28.5 MHz, the short boom is just under 1/8 wavelength long, while the long boom is somewhat over 1/6 wavelength long. At the design frequency, the modeled performance characteristics are these:

+ 
Antenna        Design         Free Space     Front-to-      Feed Impedance
+               Freq. MHz       Gain dBi       Back dB       R +/- jX Ohms
+Narrow Space   28.50          6.27           11.24          32.65 - j 0.32
+Wide Space     28.50          6.13           10.65          51.71 + j 9.23
+

As the table makes clear, the design frequency gain is about 1 dB less than that of the wide-band 3-element Yagi and 2 dB less than the 12' boom high- performance version.

+
+ +
+

The gain curve in Fig. 12 shows that, contrary to the curves for Yagis with a director, the gain for a driver-reflector Yagi descends as the frequency increases. Were we inclined to mislead you, we might do one of two things. First, we might suggest--based on the gain value for ONLY the low end of 10 meters--that there is little difference in performance between 2- and 3-element Yagis, using either the short boom high-performance or the wide-band 3-element Yagi as a comparator. Second, using ONLY the gain value for the high end of the pass band graphed in the figure, we might try to convince you that a 3-element Yagi has an inordinately high gain advantage over the 2-element version. Both claims would be equally inaccurate. Only a graph of values over a relevant frequency range tells a full story.

+

With respect to the 2 2-element designs, the narrow-spaced version has the higher gain across the pass band. For this exercise, only the first MHz of 10 meters is shown, although the wide-spaced version will be usable across the entire 10-meter band.

+
+ +
+

The overall front-to-back ratio of a 2-element driver-reflector Yagi is fairly weak, failing to reach 12 dB as shown in Fig. 13. (Note: this weaker front-to-back ratio can be an advantage in certain kinds of net and contest operations where total exclusion of signals from the rear quadrants can be a hindrance to efficient operation.) The narrow-spaced version has the stronger values, but the curve is clearly sharper than the gentler slope of the values for the wide-spaced version. The wide-spaced model front-to-back ratio is about 10 dB at the upper limit of the 10-meter band.

+
+ +
+

The SWR curves in Fig. 14 for the two models tell different stories. The sharp curve for the narrow-spaced model has a resonant point of about 32.5 Ohms. Hence, the antenna will require a matching network for a 50-Ohm main feedline. In contrast, the curve for the wide-spaced model is based on 50 Ohms. The curve has been intentionally shifted downward in frequency to show the shallow rise in value above the lowest value. By moving the center point of the curve upward in frequency simply by shortening the driver element slightly, the SWR can be held below 2:1 across the entire 10-meter band. This permits direct matching to a coax line with no matching network needed (but with the recommended choke or choke balun in place, as always).

+

With the 2-element Yagi curves in mind, we can make more precise our reasons for wanting to move to a 3-element Yagi.

+

1. Most prominently, for operations that need it, the front-to-back values for all versions of the 3-element Yagi are considerably superior to those of the 2-element driver-reflector Yagi.

+

2. The gain of a high-performance, long-boom 3-element Yagi show about a 2 dB advantage over the 2-element Yagis. This amount of gain is significant. The short-boom and the wide-band 3-element Yagis show about half that value of extra gain, and the significance of the difference is reduced accordingly.

+

3. Both 2- and 3-element Yagis can be designed for 50-Ohm feedpoint impedances that hold up even across the wide reaches of 10-meters. However, in both 2- and 3-element designs, narrower spacing allows more gain per unit-length of boom.

+
+ +
+

Fig. 15 shows comparative free-space azimuth patterns for the narrow-spaced 2-element Yagi, the wide-band 3-element Yagi, and the 12' boom high-performance Yagi. The steps of performance improvement are clear in the graphic. What the patterns cannot show is that, where narrower band operation and a 25-Ohm feedpoint impedance are acceptable, the short-boom 3-element Yagi will provide roughly the same gain and front-to-back ratio as the wide-band model with 2/3 the boom length.

+

In the end, the final decision as to which design meets our needs will use some mixture of the performance figures, plus a measure of the physical properties of the structure we propose to build. Hence, every such decision will be very individualized. The various models we have presented are intended only to provide some comparative measures as a background against which to make the final decision.

+

Still, we have not addressed some of the structural considerations that go into the decision. Boom length so far is a matter of a number, not a real physical property. As well, we need to look at what real tapered-diameter elements may imply for the antenna design. Both of these questions mean that we shall have to add a "Part 3" to this series--next time.

+
+ +
+

Updated 07-31-99. © L. B. Cebik, W4RNL. This item appeared in antenneX, May, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3: What Real Dimensions Shall I Use?

+

Return to Index

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/3lyg3.html b/content/yagi/3lyg3.html new file mode 100644 index 0000000..931dfa0 --- /dev/null +++ b/content/yagi/3lyg3.html @@ -0,0 +1,168 @@ + + + + + + Build a 3-Element Yagi Part 3: What Real Dimensions Shall I Use? + + + +
+

I Want to Build a 3-Element Yagi
+ Part 3: What Real Dimensions Shall I Use?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Had the 3-element Yagis we explored in the first two parts of this investigation been designed for VHF, we might have been able to use the dimensions as given. At VHF and above, we often use elements with uniform diameters. However, at HF, the most common practice is to use elements composed of tubing whose diameter decreases as we move outward from the element center. That makes a big difference--perhaps the difference between a beam that works and one that only seems to work.

+

Tapered-Diameter Elements

+

The relationship between uniform-diameter and tapered-diameter elements has long been guessed at, but only in the last decade or two has it been fully appreciated. Perhaps the most complete treatment of that relationship appears in David Leeson, W6QHS, Physical Design of Yagi Antennas. Leeson's conversion equations are built into some antenna modeling software (EZNEC and NEC-Win Plus).

+

When an element in the vicinity of 1/2 wavelength long is composed of materials which taper downward in diameter away from the center point, the required length for resonance increases relative to an element of equivalent uniform diameter. Moreover, the equivalent uniform diameter is not simply the average diameter of the materials used.

+
+ +
+

Fig. 16 gives us some examples to explore. Each shows 1/2 of a resonant aluminum element for 28.5 MHz. At the top, the element is roughly equally divided. The second element uses the same sequence of tubing, but in unequal lengths. The bottom element uses the same inner section lengths as the first example, but with a steeper taper.

+

In this example, and in all element-diameter taper schedules, only the exposed part of each tubing size is shown. Where one tube fits inside another, an additional overlap length of about 3" is generally recommended. Anything more tends to add weight without adding strength, and much less than the 3" overlap may jeopardize junction strength.

+

The examples show that the required length for resonance changes if we change the relative lengths for a given taper schedule or if we change the taper schedule itself. The following table can make the changes even clearer.

+ 
Example   Required       Average   Equivalent     Length of      Feed Z
+(Fig. 16) Length in      Dia. in.  Dia. inches    Equiv. El.     R +/- jX
+Top       100.8          0.623     0.631          98.58          71.8-j0.1
+Middle    100.6          0.634     0.598          98.67          71.8-j0.1
+Bottom    102.4          0.742     0.739          98.39          71.8-j0.2
+

The more radical the taper, the longer the required length for resonance. Variable length sections alter the length and the equivalent uniform diameter. Sometimes the equivalent diameter is close to the average--and sometimes not.

+

Many home Yagi builders tend to freely substitute materials in a design, unconcerned about the changes in element length that may be required to get the same performance as the original. These same builders often lack any means of checking performance other than an SWR meter. Hence, they assumed that if the antenna has the same feedpoint characteristics as the original, it must yield the same performance. The assumption is very often a bad one.

+

Without sophisticated antenna test range equipment, the best method available to check a Yagi without any element loading for performance is antenna modeling software. Both MININEC and NEC (the latter with tapered- diameter corrections built in) have been calibrated and tested extensively, and Yagi designs that pass the modeling test generally perform as modeled. There are almost always slight variations between the model and the physical version of the antenna, but in most cases, they are far smaller and less detrimental to performance than the guess work that marked the first 30 years of home Yagi design after World War II.

+

Let's look at some dimensions for 3-element monoband Yagis using various diameter taper schedules for 10, 15, and 20 meters. The differences from our uniform-diameter study models may be instructive. The following notes will use common US aluminum tubing sizes, which tend to come in 1/8" increments. A common wall size of 0.58" permits succeeding tube sizes to mate closely and still have enough play to slide one within another with ease. Since builders in other parts of the world must work with available sizes, usually specified in millimeters, here is a small table of equivalencies.

+ 
US Size        Size in mm          US Size        Size in mm
+in inches                          in inches
+0.375           9.5                1.0            25.4
+0.5            12.7                1.125          28.6
+0.625          15.9                1.25           31.8
+0.75           19.1                1.5            38.1
+0.875          22.2                2.0            50.8
+

Because non-US antenna elements will likely have a different set of element diameter transitions, it is especially important to remodel a Yagi design when changing the element dimensions from English to metric.

+

Some 10-Meter Designs

+

We shall look at only two of the many possible element taper schedules one might use for 10-meter beams. See Fig. 17.

+
+ +
+

Following the work of K6STI, we shall call the upper schedule the high- loading schedule, because it was thought to be better able to withstand higher winds. The lower version is called the medium wind load schedule. Other schedules are not only possible, but are in use by both home builders and commercial manufacturers. Some beam-makers prefer heavier, more rigid element designs, while others prefer more "aggressive" tapers that flex without breaking. End diameters of 7/16" and 3/8" are used in some commercial designs. A builder who wishes to depart from one of the "ordinary" element designs may wish to consult a computer program called YagiStress to check the survivability potential of a proposed element diameter schedule.

+

As a consequence of the many possible element designs, we can only sample a couple, with the goal of ultimately comparing tapered element lengths to the uniform lengths used in our initial look at different Yagi design philosophies. Our point will be, in part, to verify that the performance promised by the uniform-diameter designs can be obtained with tapered elements.

+

10 meters is a good starting point, because the diameter changes in a given element are the fewest. Let's begin by comparing the dimensions of our short boom study design with version built from the taper schedules shown in Fig. 17. Dimensions will be in inches. The "end" section length will simply be the difference of half the total length and the distance from element center up to the start of the last tubing section.

+ 
Antenna        Uniform-Dia (0.5")       High Load      Medium Load
+Dimension
+Refl. Length        211.8               216.0          215.0
+Refl.-DE Space       36.0                36.0           36.0
+DE Length           193.8               203.6          202.0
+DE-Dir. Space        54.0                54.0           54.0
+Dir. Length         184.9               189.0          187.2
+

All of these antennas use the same element spacing. The parasitical element dimension extension of the tapered-element designs runs from 3 to 5 inches, but the driven element required for resonance is 8 to 10 inches longer than the uniform element.

+

One evidence that the antennas are comparable is the feedpoint impedance (R +/- jX Ohms) at 28, 28.5, and 29 MHz.

+ 
Antenna        Uniform-Dia (0.5")  High Load           Medium Load
+Frequency
+28.0           27.0 - j 11.5       28.8 - j 11.0       30.0 - j 10.6
+28.5           27.5 - j  0.0       28.9 - j  0.3       30.1 + j  0.2
+29.0           22.6 + j 14.0       23.5 + j 13.6       24.7 + j 13.9
+

We can make a similar comparison between the uniform-diameter wide-band Yagi and a tapered version. Let's use the Reisert design, along with a "high-load" tapered version of the same antenna.

+ 
Antenna        Uniform-Dia (0.5")       High Load
+Dimension
+Refl. Length        211.8               214.8
+Refl.-DE Space       69.2                70.0
+DE Length           193.8               199.2
+DE-Dir. Space        63.8                63.0
+Dir. Length         177.8               184.8
+

In this case, we have made some slight but important changes in the element spacing to achieve performance across the entire 10-meter band, mainly in centering the front-to-back curve so that performance at the band edges is comparable. Both the original and the tapered version of the antenna provide under 2:1 50-Ohm SWR across the band. However, the dimensions of the tapered version differ significantly from the uniform-diameter version. Thus, even if a designer provides neat equations for calculating uniform- diameter elements, those equations disappear from utility once one moves to tapered-diameter elements.

+

To establish that the modified beams perform like the originals, let's look at a pair of graphs.

+
+ +
+

Fig. 18 provides gain curves from 28 to 29 MHz for all 5 Yagis in the tables above. The gain values for the high-performance, short boom models are within a few hundredths of a dB of each other. The difference between the tapered and untapered wide-band Yagis averages under 0.1 dB.

+
+ +
+

The front-to-back curves in Fig. 19 tell a very similar story. All three of the high-performance, short boom Yagis show the same high mid-band peak in 180-degree front-to-back ratio, with similar pass band edge performance. The wide-band models show insignificant differences and also end up at very similar values at the wider band edges of the design. In short, with some care in adjusting element lengths--and occasionally the element spacing-- one can achieve the same basic performance from a tapered-diameter Yagi as from a uniform-diameter version of the same design.

+

Some 15-Meter Designs

+

In Fig. 20, we can examine the differences between high-load and medium- load element tapers for 15 meters.

+
+ +
+

Obviously, each level requires an additional, larger tubing segment to accommodate the longer element. Corresponding design dimensions for the original uniform-tape design and tapered-diameter designs appear in the following table.

+ 
Antenna        Uniform-Dia (0.75")      High Load      Medium Load
+Dimension
+Refl. Length        284.4               289.0          286.0
+Refl.-DE Space       48.4                48.0           48.0
+DE Length           260.5               274.0          271.0
+DE-Dir. Space        72.6                92.0           92.0
+Dir. Length         248.5               254.0          251.0
+

The difference in overall boom length is immediately noticeable--a matter of 19" or over 10% of the total length. In some respects, the tapered- element beams are not the same design as the study model, although the longer elements required by element-diameter tapering are apparent. The 15-meter study model was scaled directly from the 10-meter model, while the taper-diameter models came from work by K6STI.

+

One consequence of the longer boom with about the same reflector-driven element spacing is a lower feedpoint impedance. The following table shows the difference:

+ 
Antenna        Uniform-Dia (0.75") High Load           Medium Load
+Frequency
+21.0           27.4 - j  6.2       20.5 - j  9.2       21.4 - j  9.9
+21.225         26.6 - j  0.0       20.4 + j  1.0       22.1 + j  0.3
+21.45          23.5 + j  9.0       20.7 + j 10.0       22.5 + j  9.4
+

The shorter, uniform-diameter model would permit more versatility in matching and would likely be amenable even to a 35-Ohm 1/4 wl matching section. The lower impedances of the longer tapered-diameter models would likely require a beta match or similar, with suitable adjustments to the length of the driven element.

+

However, there may be compensation for the lower source impedance.

+
+ +
+

The gain curves in Fig. 21 show the nearly half dB gain advantage accrued from using a longer boom. Not only is the gain higher, but it changes less across the 15-meter band.

+
+ +
+

In Fig. 22, we discover that all three models have excellent front-to-back ratios, never worse than 20 dB. Since the peak value reflects a deep dimple in the rearward lobes, differences have less importance: roughly equally high marks go to all three designs.

+

In the end, the decision comes down to whether the lower feedpoint impedance and the 19" of additional boom are worth the added gain. The shorter length boom with tapered elements can be developed into a beam having characteristics very close to the study model--as we saw in the case of 10-meter beams.

+

Some 20-Meter Designs

+

Tapered element design can become quite complex as we move to the 20-meter band. See Fig. 23.

+
+ +
+

The medium load element adds one more section to the corresponding 15-meter element. However, the high-load model adds two sections. In addition, the 1/4" jump in diameter as we enter the center section of the element generally suggests that two tubing sections of the same length are used: a 1.125" diameter section inside the 1.25" section.

+

Once more, if we turn to our short-boom model, we obtain dimensions of the following values.

+ 
Antenna        Uniform-Dia (1.0")       High Load      Medium Load
+Dimension
+Refl. Length        425.9               447.3          438.0
+Refl.-DE Space       72.4                80.0           90.0
+DE Length           389.6               421.6          414.0
+DE-Dir. Space       108.6               106.0          106.0
+Dir. Length         371.7               393.3          386.0
+

Despite the use of larger diameter sections in each element, the high-load element has the more radical taper and results in a greater required element length at each position than the thinner but less radically tapered medium-load element. The element position adjustments, necessary to sustain performance across the 20-meter band, elevate the source impedance from about 25 Ohms to about 30 Ohms.

+

A similar significant lengthening occurs with the long-boom (24') high performance Yagi design.

+ 
Antenna        Uniform-Dia (1.0")       High Load
+Dimension
+Refl. Length        414.7               433.8
+Refl.-DE Space      125.5               125.5
+DE Length           396.0               415.0
+DE-Dir. Space       145.1               145.1
+Dir. Length         372.6               391.0
+

Note that the boom length is here preserved. The average element length increase is about 19" for the radically tapered high-load element or nearly 5% of the total element length.

+
+ +
+

The gain curves in Fig. 24 show that for each type of beam, we obtain similar gain curves relative to untapered and tapered models.

+
+ +
+

In Fig. 25, we can see the front-to-back performance. The two high- performance models have values that closely overlap. The short-boom models place their front-to-back peaks at different frequencies. If the high-load model peak were moved upward in frequency by just a bit, its band-edge performance would closely parallel the other two models.

+

Some Miscellany

+

The point of our exercises has been to familiarize you with the effects of element-diameter tapering on overall Yagi dimensions. Moving from a uniform-diameter design to one that includes multiple tubing sizes requires careful redesign to take into account the actual element-diameter taper used. This is no casual design process, but rather a task of optimizing dimensions throughout the design. Programs such as YO and YagiMax can mechanize the process to a great degree.

+

The particular models used in this exercise do not mean that any particular design is recommended. However, the range of models does suggest a set of standards, relative to performance expectations and boom length.

+

Several items have not be covered. For example, the models surveyed so far all assume insulated mounting relative to the boom. We have not looked at the so-called "plumber's delight" element mounting system. One technique for dealing with the effects of direct electrical mounting to the boom is to create a short, large-diameter wire at the very center of the element.

+

Also missing is a consideration of the requirements and the hazards of long booms. When viewed from the mast-to-boom mounting assembly, the boom is a pair of lever arms. The longer the arm, the greater force exerted by an element of some preset size. Seemingly small increases in boom length can require close attention to boom strength. The increase in boom length can also create larger wind forces as viewed from mast. Nonetheless, very durable assemblies have been created for Yagis far larger then our 3-element models.

+

Although the high number of variables involved in the physical structure of 3-element Yagis would make a short discussion less than useful, there is a subject to which we might devote one more part in this series: feeding and matching the antenna to a standard 50-Ohm coaxial cable feedline.

+
+ +
+

Updated 07-31-99. © L. B. Cebik, W4RNL. This item appeared in AntenneX, June, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 4: How Shall I Feed the Antenna?

+

Return to Index

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/3lyg4.html b/content/yagi/3lyg4.html new file mode 100644 index 0000000..aa4a242 --- /dev/null +++ b/content/yagi/3lyg4.html @@ -0,0 +1,111 @@ + + + + + + Build a 3-Element Yagi Part 4: How Shall I Feed the Antenna? + + + +
+

I Want to Build a 3-Element Yagi
+ Part 4: How Shall I Feed the Antenna?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

Because our purpose has been to look at the basic electronic design aspects of the 3-element Yagi, we have omitted structural details. We shall also bypass matters of supporting and rotating the antenna, even though they involve some interesting facets of horizontal antenna performance at various heights above ground. Most of these items are relevant to almost any horizontal antenna, and we wish to remain focused on the 3-element monoband Yagi.

+

One detail that we dare not overlook is the method of feeding the Yagi. Actually, the term "feeding" is a bit of a misnomer, since it involves the establishment of an impedance match between the antenna and the main feedline. We shall assume that the main feedline is a standard 50-Ohm coaxial cable. (You may, of course, feed the Yagi with any parallel feedline, using an antenna tuner at the shack end of the line. This would permit use of the antenna on many bands, although directional characteristics would be optimal on only one band. However, some remnant directivity may exist on bands adjacent to the one for which the Yagi is designed.)

+

Feeding the wide-band designs is simplicity itself. To attenuate common mode currents, a choke or 1:1 choke balun is recommended at the antenna feedpoint. Designs ranging from 1:1 toroidal baluns to ferrite-bead baluns to a coil of coax sized for the band in use appear in the standard references, such as the ARRL Antenna Book.

+

Feeding the high-performance beams we have surveyed is another matter entirely. For these designs, the antenna feedpoint impedance ranged from 20 to 30 Ohms. All of the driven elements were set to resonance, but we can make any adjustments necessitated by the type of matching system we use. Changing the length of a driver by 2 to 3% makes no operational difference in the antenna performance, although it may change the resistive component of feedpoint impedance by a few Ohms. However, it will be the change in the reactive component of the feedpoint impedance that will be most critical to adjusting the matching system.

+

One common criticism of using matching networks with Yagis is that they introduce losses. However, calculations show that with reasonable care in design, these losses no where exceed 2% of the applied power, a loss of only about 0.08 dB. By contrast, most 3-element Yagi designs that do not need a matching network have gains that are near to or exceed 1 dB lower than those of the high-performance designs. Hence, the use of a matching system should not be considered a negative aspect of a design, so long as the feedpoint impedance does not go too low. Good construction and maintenance practice is, of course, assumed in this note.

+

Tees and Gammas

+

Two related forms of feeding a Yagi and at the same time elevating the feedpoint impedance to 50 Ohms are the Tee and the Gamma. (The "Tee" is actually named the "T" for its shape, but adding the "ee" ensures that the single letter is not missed by the reader.) Both methods of feed permit the direct physical and electrical connection of the driven element to the boom.

+
+ +
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As Fig. 26 shows, we make our feedline connection to a rod or double rod that parallels the element for a distance, at which point we connect a shorting strap to the rod and the element. The gamma match permits a direct conversion of the antenna feedpoint impedance to 50 Ohms. In the gamma match, the coax braid is connected directly to the electrical center of the element.

+

The Tee double rod system is most effective in raising the impedance to a much higher value than 50 Ohms. 200 Ohms is a convenient value, since a 4:1 balun then provides a fine 50-Ohm match, while performing the task of attenuating common mode currents at the same time.

+

In VHF beams, many builders have noted and measured some pattern distortion with the gamma match. Hence, the Tee has almost become a standard for beams having other than a 50-Ohm feedpoint impedance. HF beam makers have more confidence in the gamma match, whose parts are a relatively smaller proportion of the driver structure than they are at VHF and UHF. However, the Tee is inherently balanced.

+

The dimensions of both matching systems depend upon the relative sizes of and the spacing between the element and the rod material. Calculations are best done with software specifically designed for the task. YO (Yagi Optimizer), by K6STI, for example, has such auxiliary software, and independent utility calculation programs are available as freeware from many sources.

+

Note that the sketches in Fig. 26 did not include a series capacitor at the feedpoint and rod junction, a standard feature in many basic system sketches. In most instances, variable capacitors do not withstand well the rigors of weather. Moreover, the reactance of the system can be set (or nulled, depending upon one's perspective) by adjusting the length of the driven element.

+

The Beta Match

+

If you are willing to use a driven element that is insulated from the boom, matching networks become very much simplified. Let's begin with the beta match. Many hams distrust the beta match because the small "hairpin" they see across the feedpoint looks like a short circuit. They just do not understand how the beta match works.

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+ +
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In Fig. 27, we see a common L-network to match a source impedance that is high to a load impedance that is lower. One way to accomplish this is the place a shunt (or parallel) inductor across the source and add a series capacitor to the load. The network arrangement assumes that both the source and the load impedance are purely resistive.

+

The equations for calculating the proper values for an L-network are very simple. First, let's calculate delta, a figure of "merit" (sometimes called network Q) for the proposed network. For this purpose, we can use the equation

+
+ +
+

where Rs is the source resistive impedance and Ra is the load resistive impedance. As noted., Rs is higher than Ra. From delta and the values for Rs and Ra, we can calculate the reactances of the shunt and series components of the network:

+
+ +
+

Xa, the series reactance, can be converted into a value of capacitance for the design frequency, although we shall not have to do this in our application. The value designated as Xl gives the reactance the shunt component. In principle, we can use a series inductor and a parallel capacitor as easily as we might use as series capacitor and a shunt inductor. In most, but not all, antenna applications, the series capacitive reactance and shunt inductive reactance is more usual--and is most apt to our 3-element high-performance Yagi designs.

+

As the lower part of Fig. 27 indicates, we can obtain the series capacitive reactance without using a separate capacitor. We simply shorten the driven element which changes the resonant resistive feedpoint impedance to a complex value having a capacitive reactance component. How much do we shorten the element?

+

The answer to this question has two parts. First, we need to know what amount of series capacitive reactance we need. If we assume that Rs is 50 Ohms, the characteristic impedance of our main feedline and the transmitter connected to it, then we can calculate the required value of both the series and the shunt reactances. Since all of our beams had feedpoint impedances between 20 and 30 Ohms, we can reduce the problem to a little chart.

+ 
Load Res.                     Source Resistance, Rs = 50 Ohms
+  Ra (Ohms)                   30             25             20
+delta                         0.817          1.0            1.225
+Series Xa (Ohms)              24.5           25             24.5
+Shunt Xl (Ohms)               61.2           50.0           40.8
+

The chart tells us several things, including the answer to the second part of our question about the series capacitive reactance. We need to shorten the driven element by an amount that will yield a series capacitive reactance that is near to 25 Ohms. For a 20-meter driven element using aluminum tubing, the overall shortening of the element will be about 10" or so. On 10 meters, half the shortening will yield about the same capacitive reactance at the feedpoint. Shortening the element by this much may lower the resistive component of the feedpoint impedance by an Ohm or perhaps two, but, as you can see from the chart, the required series capacitive reactance will not change by a significant amount.

+

The value that changes most with changes in the resistive component of the feedpoint impedance is the shunt inductive reactance necessary to effect the match to the 50-Ohm source.

+
+ +
+

We can provide a shunt inductive reactance in two normal ways. We can convert the inductive reactance for the design frequency into a value of inductance using standard handbook equations. Then we can design a simple coil (a single layer solenoid, as it is called) of #14 to #10 wire having the right inductance. For the small values involved, it is fairly easy to design an inductor with a Q between 200 and 300. Since the network losses are roughly (but not exactly) equal to the value of delta divided by the coil Q, we can see that in ordinary circumstances, losses will be under 1%. Moreover, we can adjust the precise inductance of the small coil by spreading or squeezing the turns until the 50-Ohm SWR at the network terminals is 1:1.

+

An alternative to the inductor is the shorted transmission line stub. For the most compact assembly and widest bandwidth, a wide-spaced "hairpin" made of wire or rod creates a shorted parallel transmission line section with a high characteristic impedance. The required length is a function of the wire diameter, the spacing, the frequency, and the required reactance. Handbook equations can be used for this calculation, although independent utility software exists to combine all of the calculations into one exercise. One such program was created by WA1SPI and is included in the HAMCALC collection available from VE3ERP.

+

Although some builders prefer to have an adjustable shorting bar as the rear part of the hairpin, my own preference is for a single hairpin with longer legs. We adjust the hairpin length by clamping down at the antenna feedpoint on the legs at the right points. This system reduces the number of mechanical connections by 2, which in turn reduces the number of potential resistive loss points.

+

The hairpin tends not to answer directly to standard Q formulations, since it changes the value of reactance in a manner different from the way in which coils change reactance values as we move off the design frequency. However, a hairpin with a characteristic impedance above 600 Ohms tends to have a similar bandwidth characteristic to a beta coil with a Q of 300 or more.

+
+ +
+

Fig. 29 shows the 50-Ohm SWR values across 20 meters for one of our 3-element models set up with a beta match consisting of a 600-Ohm shorted transmission line a little over 11" long. Modeling software does not show transmission line losses, but parallel lines that are about 1/70 of a wavelength do not have much loss when composed of wires or rods sufficiently thick to handle the currents involved.

+

One caution is necessary with beta matches. It is possible to find a setting for a coil or a hairpin that effects a match when the series capacitive reactance is not optimal. Often, these settings result in additional and unnecessary losses from the network. Hence, it is important that the builder set the driven element as close as possible to the correct length for the required value of capacitive reactance at the feedpoint.

+

The Quarter-Wavelength Matching Section

+

For designs that have a resonant feedpoint impedance close to 25 Ohms, we can use the driven element as given and effect a match to a 50-Ohm line in another way: the 1/4 wavelength matching section.

+
+ +
+

In Fig. 30, we can see the simplicity of the system. Although 35-Ohm transmission line runs about $3 a foot, it provides a set-and-forget matching system (except, of course, at our semi-annual inspection and maintenance sessions).

+

The use of 35-Ohm cable for the matching section is based on the standard impedance transformation effects of 1/4 wavelength transmission line sections, which answer to the equations

+
+ +
+

where Zo is the characteristic impedance of the matching system, Zin is one of the two resistive impedance values being matched, and Zout is the other value being matched. The 1/4 wave line length, of course, is the electrical length, and the physical length must be adjusted for the velocity factor of the line--which yields for all coaxial lines a physical length that is shorter than the electrical length. In many cases, the 1/4 wavelength section can be coiled to act as a common mode current choke while still performing its matching duties.

+

The losses of a 1/4 wavelength matching section will be as low as those of any other matching system. Programs such as N6BV's TLA or TLW can be used to check line losses both at the resonant frequency and at the band edges, using projected feedpoint impedance values supplied by an antenna modeling program.

+
+ +
+

As shown in Fig. 31, a quarter wavelength matching section is capable of performance very similar to a beta match when it comes to 50-Ohm SWR values across 20 meters. The values in Fig. 31 are insignificantly different from those recorded in Fig. 29.

+

However, the two methods of impedance transformation are sufficiently different to yield actual impedance values that are also different, despite the fact that the values result in quite similar SWR values. The following table shows the modeled feedpoint impedance values for the same Yagi model with a beta match in one instance and with a quarter wavelength matching section in the other.

+ 
Matching                      Source Impedance (R +/- jX Ohms)
+System              14.0                14.175              14.35
+Beta                79.6 + j 11.3       50.9 - j  2.7       27.9 - j  0.5
+     50-Ohm SWR          1.65                1.06                1.79
+1/4 WL Section      35.8 + j 17.8       47.6 + j  1.7       39.5 - j 22.9
+     50-Ohm SWR          1.70                1.06                1.75
+

Conclusions (Of a Sort)

+

In the end, the selection of a Matching system for a high-performance 3- element Yagi with a feedpoint impedance in the 20-30-Ohm range will depend on a number of factors outside the limits of electrical design. First, the selection of construction design will limit the matching network options. Direct connection of the driven element to the boom will eliminate both the beta and the quarter wavelength matching systems. The Tee can be used with insulated or uninsulated drivers (relative to the boom). In general, most but not all commercial designs have gravitated toward the used of drivers that are insulated from the boom. In fact, a number of available designs insulate all elements from the boom.

+

If cost is a factor, the beta match using either a home-made hairpin or coil is likely the cheapest matching system available--but it is no less effective for its low cost. (Although the hairpin is about as cheap as you can get, it is no license to skimp on the quality of hardware used anywhere in the beam. Low quality hardware tends to result in both mechanical and electrical problems with any beam antenna.)

+

The beta is also fairly easy to adjust, since it is located very close to the hub of the antenna boom-to-mast region. Hence, readjustment at the tower top is easier than with Tees or Gammas. Often, settings chosen in near-ground preliminary assembly phases hold good at the final antenna height.

+

This entire series has been devoted to some of the electrical design options available to the builder of his or her first 3-element Yagi. A Yagi of this size and performance makes an excellent project for the home builder, since most of the materials can be obtained with reasonable ease. Multi-band Yagis, on the other hand, are best left for later exercises, once one has become thoroughly familiar with all of the parameters of Yagi design--or they are best left to the professional designers who can spend 8 hours or more each day on this difficult task.

+

If you have never used an antenna as good as a 3-element monoband Yagi, you are in for some real surprises and adventures in operating--once you complete the project. Where your dream designs take you after that will be your own responsibility.

+
+ +
+

Updated 07-31-99. © L. B. Cebik, W4RNL. This item appeared in antenneX, July, 1999. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Index

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Topics: HF Upper, Yagi


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+

Wide-Band 40-Meter Yagis
+ Part 1: Standard and Non-Standard Designs

+
+
+

L. B. Cebik, W4RNL

+

+
+ +
+

In my Notes on Wide-Band Yagis, I discussed several 40-meter designs for full-band coverage (Volume 2, Chapter 7). Since the appearance of those notes, QEX has published an interesting new design by J. V. Evans, N3HBX. It promises (and delivers) the performance of a full-size wide-band 3-element Yagi in about 2/3 the boom length (31' vs. 45'). The key feature is the absence of a reflector element. Some years back, I noted in converting a 2-element pair of phased elements into a beam that a reflector was unnecessary, since the directors control both the gain and the front-to-back ratio. N3HBX provides further confirmation of this fact with his beam.

+

In addition, the beam also calls to our attention a facet of designing antennas by computer modeling techniques, one usually overlooked in the modeling process. One facet of converting a computer design into a physical reality is the sensitivity of the design to the inevitable small construction variations from the computer design. The more able a design is to absorb these variables without changing essential characteristics, the more buildable is the design. As we review some standard wide-band designs and the N3HBX design, we shall have an opportunity to examine this matter more closely and to show how we can use the design software to arrive at a probable answer to the question: "How buildable is the antenna?"

+

Some Essential Background on 40-Meter Yagis

+

The U.S. 40-meter allocation runs from 7.0 to 7.3 MHz. If we measure the band in kHz, it is narrower than 20, 15, and 10 meters. However, in terms of bandwidth, as the term applies to antennas (and other components and circuits), we cannot use a simple kHz-count. Instead, we should measure the bandwidth as a percentage of the center frequency. If we divide the 300 kHz bandwidth by 7.15 MHz (and multiply by 100, of course), we arrive at a bandwidth of 4.2%. Compare this value to the 2.5% bandwidth of 20, the 2.1% bandwidth of 15, and the 3.5% bandwidth of the first MHz of 10 meters. Obviously, covering the full width of the U.S. 40-meter band with a single effective Yagi is a challenge.

+

However, the challenge only begins with bandwidth. To an important degree, the element diameter influences the available bandwidth of a Yagi design. Suppose that we begin with a wide-band 10-meter design capable of covering the first MHz of that band. One way to obtain the coverage with relatively smooth performance figures is to use larger tubing. On 10, we might use an element taper schedule the begins with 3/4" tubing and goes down to 3/8" tubing. Such elements often have equivalent uniform diameters close to 0.5". If we scale the design to 40 meters, we must have an equivalent uniform diameter of about 2.0".

+

Unfortunately, we cannot simply scale the 10-meter elements. Rather, we must build tubular elements from many tubing sizes so that the element can support itself in a reasonable wind. The beefiest 40-meter element structure that I have so far encountered in U.S.-made beams begins with 2.5" tubing at the center and gradually reduces to 0.375" tubing. Fig. 1 shows the steps in this element. You may assume that where the steps are greater than 1/8", tubing has been doubled or tripled for greater strength in the sections that bear the highest loads. I shall not perform a full stress analysis on this element structure. However, I shall use it in all of the models that we shall review here. In that way, each model is subject to the same set of potentials and limitations related to potential physical structure.

+
+ +
+

The taper schedule of our standardized element yields an equivalent uniform diameter between 1.3" and 1.6", depending on the exact length of the element. This value falls far short of the requisite 2" to obtain equivalent operating bandwidth to a wide-band design that might appear at 10 meters. Therefore, we shall have to substitute design ingenuity for the convenience of electrically fat elements.

+

The extreme taper of the element presents a small challenge for modeling it. MININEC has no significant difficulties with stepped-diameter element construction, but NEC-2 is notorious for the errors that such element construction produces. NEC-4 revised the current calculation algorithms to overcome the problem, but it does so only if the steps are small and if the region of highest current has the fewest and smallest steps. If we look at the half-element diagram, we find that the inner half of the half-element decreases by a full inch in diameter, in steps that reach as high as 3/8". NEC-4 alone cannot handle this structure without error. Hence, whether using NEC-2 or NEC-4, one must invoke Leeson corrections and calculate on the basis of equivalent uniform-diameter elements.

+

We complete our list of design challenges with one more peculiar fact about wide-band Yagis on 40 meters. The operators who are most likely to invest high dollars in a large 40-meter Yagi, along with the massive support structure to hold it at an advantageous height and to rotate it around the horizon, tend to be avid contesters. Their equipment usually includes power amplifiers capable of the full legal amateur limit using any mode of operation. Many of these amplifiers contain protection circuits to ensure long life from the expensive components within them. One of those protection mechanisms is a circuit that cuts off the amplifier when the return voltage sample indicates an SWR value above a certain level. In amateur circles, we are most used to using a 2:1 SWR level as a convenient marker for operating bandwidth that will satisfy the modern generation of amateur transceivers. However, in many amplifiers, the cut-off limit is 1.5:1. Therefore, we must design with that limit in mind.

+

The Designs That We Shall Review

+

In the course of these notes, we shall examine the characteristics of 4 Yagi designs ranging from 2 to 4 elements. Fig. 2 shows the 4 designs in outline. The outlines are close to being in scale with each other. Hence, you can see the growth in the overall boomlength of each design as we move from 2 to 4 elements. The shortness of the N3HBX design becomes clearly evident.

+
+ +
+

Since every element uses essentially the same structure, we can supply the necessary additions to let you replicate the models. The following table lists the progressive element spacing, using the reflector as the baseline. It then lists the element half-length. Multiply by 2 for the total element length. The final column lists the tip length. A zero or a negative entry means that the element has no 3/8" tip section, and the value in the column represents an adjustment to the 0.5" element section shown in Fig. 1. You may also use that graphic to fill in the requisite wires for any models that you create from the following table.

+ 
+Dimensions of the Yagis Discussed in These Notes
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+2-Element    Reflector           0           451             65
+             Driver              282         412             26
+3-Element    Reflector           0           463             77
+             Driver              305         428             42
+             Director            540         386             0
+4-Element    Reflector           0           449             63
+             Driver              245         436             50
+             Director 1          329         407             21
+             Director 2          622         379            -7
+4-El N3HBX   Slaved Driver 1     0           456.5           70.5
+             Fed Driver          62          440             54
+             Slaved Driver 2     107         420             34
+             Director 1          367         383.5          -2.5
+
+

For any given design, the required element lengths will change if you a. change the equivalent uniform diameter or b. change the taper schedule for the tubing. If the effective diameter does not change by much, you likely will not need to adjust the element spacing, since spacing is relatively less sensitive than is element length. Just how sensitive the element lengths are in a given design will be one of our later subjects.

+

2-, 3-, and 4-Element "Standard" Yagi Designs

+

In the 1980s, Bill Orr, W6SAI, presented a pair of designs for 10 meters. I have generally ascribed the designs to him, since he did not specify if he obtained them or generated them himself. The basic principle underlying both his 2-element and his 3-element design is straightforward. The reflector-driver spacing in a standard Yagi largely determines the feedpoint impedance level of the array. In the 1980s, most Yagis used fairly narrow spacing and ended up with feedpoint impedances ranging from about 18 to 25 Ohms.

+

In a 2-element Yagi that uses a reflector and a driver, widening the spacing actually has 3 effects. First, it lowers the gain and the front-to-back ratio by a small amount, but not enough to be operationally significant if 2-element performance is useful. Second, it raises the feedpoint impedance. A spacing of about 1/8 wavelength yields about the best performance compromise in a normal 2-element Yagi, but the feedpoint impedance is between 30 and 35 Ohms. Raising that spacing to a range of 0.14 to 0.17 wavelength increases the impedance to a good match for 50-Ohm coaxial cable. Third, the wider spacing also increases the SWR bandwidth. So the sample 2-element 40-meter Yagi uses a spacing of 0.17 wavelength. As a result, we obtain the following table of results, sampled at the band edges and at mid-band.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.50              9.89             40.7 - j 19.4             1.60
+7.15            5.96             10.70             53.1 + j  3.5             1.09
+7.3             5.52              9.71             63.5 + j 24.2             1.63
+
+

To convert the raw numbers into a more graphical form, Fig. 3 presents curves that track the free-space gain, front-to-back ratio, resistance, reactance, and 50-Ohm SWR across the 40-meter band.

+
+ +
+

2-element driver-reflector Yagi gain naturally decreases with increasing frequency. The design creates a front-to-back peak ratio about mid-band. The feedpoint resistance rises only 23 Ohms across the band, while the reactance shows a 44-Ohm spread. As a result, we obtain acceptable 2-element Yagi performance with an SWR well below 2:1. However, we have missed the more desirable 1.5:1 ratio at the band edges. One standard commercial spacing used for 40-meter 2-element Yagis is 20'. Our wide-band Yagi uses a 23.5' boom.

+

The 3-element Yagi also uses an Orr-derived 10-meter design as its foundation. Once more, wider reflector-to-driver spacing increases the feedpoint impedance. By properly sizing and positioning the director, we can obtain good patterns and reasonable forward gain. However, the gain level is more appropriate to a shorter boomlength when designed for a lower impedance. For example, a boom length of about 0.22 wavelength in a conventional Yagi will yield about 7 dBi free-space gain, while a boomlength of about 0.33 wavelength will yield about 8 dBi gain, both with feedpoint impedances in the 25-Ohm range. Our 50-Ohm direct feed Yagi design yields about 7 dBi gain on the longer boom. However, we need that 45' boom to give us the wide-band performance values shown in the following table.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.92             19.16             51.6 - j 17.6             1.41
+7.15            7.03             21.54             48.9 - j  1.3             1.04
+7.3             7.37             19.00             41.6 + j 18.8             1.57
+
+

We just miss having a 20-dB front-to-back ratio from one end of the band to the other. The 3-element Yagi almost reaches the goal of a 1.5:1 50-Ohm SWR all across the band. Fig. 4 provides the graphs and patterns to establish the utility of the design, even if the Yagi is twice as long as the 2-element version.

+
+ +
+

The gain curve is apropos to any Yagi having a single driver and at least one director: it rises as we increase frequency. The front-to-back ratio peaks about mid-band. The resistance and reactance excursions are between half and two-thirds of the amounts shown by the 2-element Yagi. Nevertheless, we have only come close to the most desired SWR limit.

+

The third design uses 4 elements on a 52' (0.38 wavelength) boom. The added element and increased boom length yields about a full dB of additional gain while preserving the front-to-back ratio levels. The design is an adaptation of a 10-meter design that I developed several years ago. The element called Director 1 in Fig. 2 also functions as a slaved driver to broaden the operating passband of the antenna. With the dual driver or master-slave system, the reflector tends to exert some control on the pattern properties at the low end of the band, while the remaining forward director has greater control of the high end of the band. The following table samples the modeled values.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             7.90             18.08             46.8 - j  9.0             1.22
+7.15            8.00             23.99             50.2 - j  0.2             1.01
+7.3             8.21             18.64             44.9 + j  7.0             1.20
+
+

The most notable feature of the design is the SWR curve in association with the values of feedpoint resistance and reactance. Fig. 5 shows the data in graphical form. The 50-Ohm SWR never reaches 1.25:1 anywhere within the band. To obtain this level of performance, we must use a very long boom with very heavy elements on its ends. Hence, the support system for this beam would likely require heavy-duty trusses for both the individual elements and for the boom itself.

+
+ +
+

The 4-element wide-band Yagi has appeared in many guises, ranging from the lower HF range up to UHF. With suitably fat elements on 70 cm, the antenna is capable of covering the entire band with usable--if less than optimum--performance. The drawback of all of the designs is that they pay little heed to boomlength. On 40-meters, the shorter the boom, the more easily that we may convert a design into a physical antenna.

+

The 4-element N3HBX Yagi

+

N4HBX experimented with modeling 40-meter Yagi designs using a pair of slaved drivers that surround the fed driver. The triple combination, he reasoned, would offer even greater operating bandwidth. In the process of his design work, he discovered that he could eliminate the reflector. He lost some gain in the process, but the amount by which the boom became shorter more than offset the loss. His final boomlength is only about 0.22 wavelength or 31'.

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Surrounding the fed driver with slaved drivers that use relatively tight spacing tends to give the slaved drivers control over the array's properties. Hence, the gain shows a mid-band dip (insignificantly small) as well as dips in the SWR curve. The front-to-back curve shows a small mid-band peak, but remains at 20 dB or better across 40 meters.

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The cost is an impedance curve that varies around the 25-Ohm level. In the data table and impedance graphs, I have attached a quarter wavelength section of 35-Ohm transmission line to match the impedance to a main 50-Ohm cable. You can construct the matching section from 35-Ohm coax or from paralleled lengths of 70-Ohm cable. The following table lists both the pre-match and post-match impedance and SWR values.

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+Frequency       Free-Space       Front-Back        Pre-Match Z        25-Ohm        Post-match Z       50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms      SWR           R +/- jX Ohms      SWR
+7.0             7.21             20.91             16.3 - j  2.8      1.57          67.7 + j 20.5      1.59
+7.15            7.18             25.20             31.7 + j  0.4      1.27          38.7 - j  0.1      1.29
+7.3             7.46             20.69             15.7 + j  4.8      1.69          72.6 - j 20.4      1.65
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The SWR values for the sampling points do not show the SWR minimum values that occur about 50 kHz from each band edge. These appear clearly in the graph in Fig. 6. The figure also includes the gain and front-to-back curves, as well as sampled patterns that correspond to those shown for the other beams in the collection. The gain reaches its minimum value at about the same frequency on which we find the maximum value of front-to-back ratio.

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The N3HBX design achieves well under 2:1 matched SWR at the band edges. However, it does not achieve the ideal 1.5:1 level. The reason is that slaved drivers generally have a narrower operating bandwidth than a fed driver. Hence, the two slaved drivers lose control of the feedpoint impedance before we arrive at the band edges. Optimizing the driver lengths for a lower SWR value at the band edges results in a much higher mid-band SWR value, since the pair of slaved drivers effectively prevents the fed driver from controlling that portion of the band with respect to antenna properties. Therefore, we see only 2 SWR minimums and 2 gain maximums rather than 3. Nevertheless, the beam has generally very even performance from one end of 40 meters to the other--all on a relatively short boom.

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Perhaps the key design element in the N3HBX design is the removal of the reflector. Many radio amateurs are wedded to the notions of "reflector" and "director" that suggest to the imagination that some real reflection and direction is occurring. In fact, all elements are directors in the sense of being positioned and sized so that the signal is highly directional. The reflector does not reflect in the sense that a flashlight reflector reflects. Rather, the length and position of the reflector sets up a current magnitude and phase angle that contributes to the overall directionality of the antenna's radiation field. Where we have only a driver and a reflector, the parasitic rear element plays a key role in the pattern shape. But as we saw in the 2-element Yagi design, the reflector only helps the gain and the front-to-back ratio a little bit. Directors are the key elements in controlling both the gain and the front-to-back ratio of a standard design Yagi. Once we add directors, the reflector's role is reduced largely to establishing the general level of the feedpoint impedance on the driver. Without a reflector, the N3HBX design could not achieve a direct 50-Ohm feedpoint connection, although the 25-Ohm level proves to be perfectly matchable to coaxial cable.

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While exploring the properties of phased elements about 5 years ago (August, 1998), I experimented with adding a director to a pair of phased elements. I set the phased pair of elements to be nearly the same length and used a phasing line that set them up for very close to the maximum gain possible from 2 elements--a little over 7 dBi in free space. As Fig. 7 shows, that configuration yields a very poor front-to-back ratio compared to the very high ratio we can obtain from the same pair of elements at the same spacing just by altering the relative current magnitude and phase angles. (However, when set for maximum front-to-back ratio, the gain drops to just about 6 dBi.) The next step was to add a single director without altering the phased element pair. The 17.2' director (at 12 meters) is 9' from the phased element pair. The figure shows the resulting free-space E-plane pattern with 8.6 dBi gain and over 30-dB front-to-back ratio.

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The experimental beam has quite narrow-band properties and requires a reverse beta match for a 50-Ohm cable (that is, a capacitor across the feedpoint to complete the L-network). The narrow-band properties of the phagi (or phased-Yagi combination) follow from the fact that the setting of a phased element pair for maximum gain is itself a narrow-band property. (For further information on the experimental beam, see Horizontal Phased Arrays with Parasitic Directors.) If this analysis is correct, then the driver set of the N3HBX array--without the director--should show some pattern properties that are as wide-band as the total Yagi itself. See Fig. 8 for confirmation of this condition. The patterns display values that would be quite usable in a 2-element Yagi. Unfortunately, in the absence of the director, the feedpoint impedances are not practical.

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It does not matter whether we call the two un-fed elements slaved drivers or parasitic elements functioning as a very close-spaced set of reflector and director elements. In both cases, the elements have positions and lengths to effect current magnitudes and phase angles that result in a directional pattern. The director plays the key role in altering the patterns to their final desired shapes within the limits of what any parasitic element might do.

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I am not advocating the general removal of reflectors. An operational Yagi is a blend and balance of many properties. Where one or more directors are present, the reflector remains a primary method of setting the general level of the feedpoint impedance to a convenient level for use with common feedlines. In most designs, that function is significant. In the case of the N3HBX array, shortening the overall boomlength proved to have a higher priority, and the resulting un-matched feedpoint proved to be quite usable without the reflector. For many other designs, doing away with the reflector would be highly impractical.

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Moving from Model to Reality

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One question normally overlooked by individuals who are new to designing antennas via computer software is the "buildability" of the resulting design. Even if we follow the computer-generated plan as closely as possible, the physical elements will rarely match the design dimensions exactly. Hardware will create "lumps and bumps" on elements. Even mounting hardware that we insulate from the elements may detune them by a very slight amount. Unless we have a very extensive or commercial-grade shop, our element-section lengths may vary a fractional amount from the model. Finally, even if we insulate the boom from the elements, we may encounter a small amount of coupling that the model cannot show due to its inability to handle transverse as well as axial current along elements.

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Despite these potentials for a divergence between the model and reality, innumerable successful antennas have emerged from computer design processes. In most cases, the differences turn out to be negligible when measured in terms of predicted and actual antenna performance. However, that fact is not true of all designs. Therefore, the designer needs to develop a system for evaluating the likelihood that a given antenna will be sensitive to construction variables.

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The need for such a system emerges from the modeling process itself. As we approach the dimensions of the "final" design, we tend to sneak up on the element lengths and positions. In other words, we vary each dimension in very small amounts until we optimize performance or at least achieve acceptable performance. Rarely do we keep track of the increments we use in varying element lengths. More important, we rarely take note of the significance of those design-variation increments. If we do not normally take this step during design, then we should systematically evaluate the design once we have frozen it.

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No single system of pre-testing a design will satisfy every antenna on every band built in every situation. Commercial makers can usually cut tubing within a few thousandths of an inch, while the home-shop builder may be restricted to the accuracy of his eyes and the markings on the tape measure he uses. A half-inch variation limit in element length on 10 meters is equivalent to about 2" as a limit on 40 meters. Both figures represent about a quarter of 1% for the bands involved. Therefore, whatever tests we perform on the design models are likely to vary from one antenna design to another and from one part of the frequency spectrum to the next.

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To obtain a first-order measure of how sensitive the 40-meter wide-band antennas are to construction variables, I set up a very simple test. Since the Yagis in this collection are set on 40 meters, I varied the individual element lengths by +2" and then by -2" from their design values. For each variation, I recorded the most telling data at the design frequency limits (7.0 and 7.3 MHz). We already have the values for the design dimensions in the tables associated with each Yagi. Of course, after looking at each element, I returned it to its design length before varying the length of the next element. After looking at the variations due to element length, I also varied the spacing between element by the same +2" and -2". Since element spacing is less sensitive to change than element length, I did not expect to find significant performance variations in that department. However, since some of the designs use parasitic or slaved drivers, the checks were necessary.

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The "standard" designs all turn out to be quite buildable within the limits of the test. That is, changes of the order used in the test did not materially affect the radiation or the impedance performance by more than very small amounts. In no case did they jeopardize the utility of the antenna for its intended purpose. However, the N3HBX design raises a few question marks.

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To abbreviate the test report, we may compare the N3HBX design with the longer 3-element Yagi that has similar performance. Fig. 9 shows the general parameters of the test runs.

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The charts of values for the two antennas cover several sheets of paper. However, we can summarize the results by taking the maximum variation in each performance category. Very often a single element of spacing will account for the variation in a given category, and we may annotate the table accordingly. The following table provides the results for the standard 3-element design.

+ 
+Results of Varying Dimension by +/-2" for the 3-Element Wide-Band 40-Meter Yagi
+
+Category                 Variation          Variation         Notes
+                         Range 7.0 MHz      Range 7.3 MHz
+Gain (dBi)               0.05               0.11              Equal range from reflector and director length variations
+Front-Back Ratio (dB)    0.62               0.60              Sources variable
+FP Resistance (Ohms)     1.11               2.68              Director length
+FP Reactance (Ohms)      4.16               4.29              Driver length
+50-Ohm SWR               0.115              0.117             Driver length
+
+

As expected, changes in the element spacing did not yield value changes that approached the high and low values that define the range of variation in each category. More significantly, the range of change in each category is very small. For that reason, I have characterized the 3-element wide-band design as quite buildable in the average home shop--assuming that the shop can handle the basic materials required. A commercial-grade shop or factory is not necessary to build this antenna successfully, if we again assume the same quality of components and basic construction techniques.

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When we turn to the N3HBX design, we obtain a different set of values in each sampled category. The following table provides the data from the modeled variations. The model used contained the quarter wavelength matching section. Hence, typical band-edge feedpoint resistance values are all above 50 Ohms.

+ 
+Results of Varying Dimension by +/-2" for the 4-Element N3HBX Wide-Band 40-Meter Yagi
+
+Category                 Variation          Variation         Notes
+                         Range 7.0 MHz      Range 7.3 MHz
+Gain (dBi)               0.08               0.06              Rear-driver length at 7.0; director length at 7.3
+Front-Back Ratio (dB)    3.78               0.98              Rear-driver length at 7.0; director length at 7.3
+FP Resistance (Ohms)     9.11               18.99             Rear-driver and fed driver length at 7.0;
+                                                                front-driver length at 7.3
+FP Reactance (Ohms)      13.84              20.32             Fed-driver length at 7.0; front-driver length at 7.3
+50-Ohm SWR               0.290              0.643             Rear-driver length at 7.0; front-driver length at 7.3
+
+

If we compare the 4-element Yagi table to the table for the 3-element design, we find greater variations among band-edge values in every category except forward gain. Gain, however, is rarely critical in a wide-band design. The N3HBX design shows modest changes in the front-to-back ratio at the upper band edge, since the director largely controls that value. At the low end of the band, the reflector normally performs the same function. However, the design lacks a true reflector, and the front-to-back value changes by almost 4 dB due to changes in the length of the rear slaved driver.

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The feedpoint resistance changes by a factor of 9 at both ends of the band, relative to the changes we saw in the 3-element design. The rear slaved driver and the fed driver contribute equally to the resistance changes at 7.0 MHz, while the forward slaved driver accounts for the larger range of change we see at 7.3 MHz. The fed driver is the source of the widest reactance range at 7.0 MHz. At 7.3 MHz, the forward slaved driver again yields an even wider range of reactance values as we alter its length by the +/-2" amount defined for the test. Note that the forward slaved driver' length contributes most to the wider range of both resistance and reactance values. These values move in the same direction, resulting the very large change in SWR value. In fact, if we decrease the forward slaved driver length by 2", the band-edge 50-Ohm SWR drops to 1.39:1, while a 2" length increase yields an SWR increase to 2.03:1.

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The overall picture for the N3HBX design is especially interesting, since a 2" length change to any one of the elements becomes the source of at least one tabulated value reaching a surveyed limit. The element with the most influence on the performance curves for the antenna is the forward slaved driver. The tests suggest that construction variables may well move the performance at 7.3 MHz outside the useful range of values.

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The test establishes that the N3HBX 4-element design is more sensitive to slight variations in construction than we find for the 3-element design. We might have intuited this situation from the compressed spacing within the driver cell. Very closely spaced elements change their mutual coupling with only small changes in length and in spacing. Experience with master-slaved driver arrangements would also have taught us that the forward slaved driver tends to be the most sensitive element in any array using virtually any variation on that system. (Many wide-band VHF beams use first directors that in fact function as slaved drivers over half or more of the Yagi's passband, even though the spacing may not suggest this function. However, the function usually becomes clear if we track the relative current magnitudes on the fed driver and the first director across a given passband.)

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These notes on sensitivity to change certainly do not condemn the N3HBX design. Indeed, it is potentially a highly competent beam that is competitive with 3-element designs that require much long booms. Instead, the notes simply offer a few cautions. A commercial shop could easily fabricate successful replicas of a field-adjusted prototype. In the home shop, where 1 and only 1 beam will emerge, the lesson is that we cannot simply build and mount the antenna with expectations that it will necessarily perform to specification. We have to be ready for field adjustments to bring the performance to specification. Since this procedure is wise for any Yagi, no matter how forgiving the computer design, we might alter the forewarning to this: for the N3HBX design, we should be prepared for extensive field adjustments.

+

The prospective size of the field adjustment task is one of the factors that does or should go into the building plans of anyone who constructs his own beams. How much weight we give this task varies from one builder to the next. The more sensitive a beam design is to small changes in its dimensions is a measure of the likely size of the adjustment task. These notes do not intend to establish the weight we give the task. Instead, they only provide one method of evaluating the size of the prospective task while the antenna design is still within the computer.

+

Conclusion

+

Adding the N3HBX 4-element reflector-less wide-band 40-meter Yagi to the collection of extant wide-band designs promises 3-element performance from a boom that is not much longer than we find on 2-element full-size 40-meter Yagis. The design is a good example of using a self-contained driver system--in this case, a master-slaved driver system--to achieve wide-band performance. Unexplored alternatives to the N3HBX drive system are direct driver coupling via very short lengths of transmission line and possibly a phased pair or triplet of drivers. Both systems--if successful--would add a few feet to the boomlength but still result in a beam that is quite a bit shorter than the comparably performing 3-element design.

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The 4-element reflector-less design with a closely spaced driver cell has also provided me with a pretext for reminding home-designers of Yagi antennas to check the sensitivity of the antenna design to small changes in its dimensions. The results--especially when compared to results for a beam known to be forgiving of small dimension shifts--allows us to estimate the ease or difficulty of replicating the design using real aluminum tubes and stainless steel hardware. That information leads to better planning and decision-making within the overall task of constructing our own Yagis.

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Updated 02-01-2006. © L. B. Cebik, W4RNL. This item originally appeared in antenneX, (Jan., 2006). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: HF Lower, Yagi


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Wide-Band 40-Meter Yagis
+ Part 2: Alternative 4-Element Designs

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+

L. B. Cebik, W4RNL

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In Part 1 of our expanded notes on wide-band 40-meter Yagis, we looked at some standard and non-standard Yagi design ideas. The 2- and 3-element Orr-derived Yagis employed wide element spacing to accomplish 2 goals: to raise the general feedpoint impedance to the 50-Ohm level and to increase the operating passband to cover all of 40 meters with under 2:1 SWR. However, only the relatively long-boom 4-element Yagi that used a master-slaved dual driver system achieved the most desirable end of having well under 1.5:1 SWR across the band while raising the gain level to about 8 dBi in free space. We also examined the recent N4HBX reflector-less design that employed a fed driver and bracketing slaved drivers to obtain about 7 dBi gain with under 2:1 SWR across the band.

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In the interest of making fair comparisons among the designs, we employed the same element-diameter schedule in all elements of all beam designs. Fig. 1 replicates the taper schedule. As we proceed through the new notes, the structure tables will list only the element spacing (using the reflector as the baseline), along with the total element half-length and the tip length. You only need to add the 3/8"-diameter tip length to the schedule in Fig. 1 in order to replicate any model within the series.

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As we closed the first part of these notes, we noted that we had not exhausted all of the design options that we might apply to Yagis in order to achieve full band coverage. In the following notes, we shall take up the design challenge in 2 directions. One path uses direct-coupled dual drivers as a substitute for the open-sleeve coupling system used in two of the Part-1 designs. The other roadway leads to phased pairs of elements used as drivers. In both directions, we shall restrict ourselves to 4-element designs that produce between 7 and 7.4 dBi gain with a good front-to-back ratio across the band. We shall aim at both shorter and longer versions of each design both to display the performance differences and to once again stay below 1.5:1 50-Ohm SWR from 7.0 to 7.3 MHz--if possible. A shorter Yagi version will be one that is between 31 and 36 feet long, while a longer version will be between 36 and 42 feet. All arrays will be shorter than the 45' boom required by the standard 3-element wide-band Yagi that also yields forward gain in the same low-7-dBi free-space range.

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Before we move into precise design details, however, we should look more closely at all of the varied Yagi driving schemes for widening the operating bandwidth of a beam. Each type of driving system achieves its goal by different means.

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How Drivers Drive a Yagi

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A standard Yagi has a single driving or fed element, along with a one or more parasitic elements. By convention, any element behind the driver--relative to the direction of the antenna's main lobe--is a reflector, and any parasitic element ahead of the driven element is a director. In an open-sleeve coupled driving system, we directly feed only one element. Hence, various sources may call the slaved driving element either part of the driver or a director. Either title is technically correct, since a slaved driver obtains its energy parasitically. It becomes a driver by dominating the current magnitude from which other elements derive energy parasitically. In the notes that immediately follow, I shall identify the driving elements, whether directly connected to the source or not.

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In most standard designs, the reflector and director elements are sufficiently distant from the driven element to qualify strictly as parasitic but not driving elements. Again, the distinction is more conventional than strictly technical, since every parasitic element contributes to forming the antenna's radiation pattern. Let's consider the 3-element standard wide-band Yagi from Part 1. If we provide the driver with a relative current magnitude of 1.0, and then, if we move the antenna across the band, we find that the current magnitude levels on the parasitic elements changes along the way. The following table shows the relative current magnitudes on all of the element centers at 7.0, 7.15, and 7.3 MHz.

+ 
+Relative Current Magnitude on the Elements of a 3-Element Wide-Band 40-Meter Yagi
+Element              7.0 MHz          7.15 MHz           7.3 MHz
+Reflector            0.385            0.289              0.219
+Driver               1.0              1.0                1.0
+Director             0.525            0.625              0.734
+
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The table does not show the phase angle of the currents. The driver, by model set-up, is always at 0 degrees. The reflector normally shows a positive phase angle that falls anywhere between 100 and 150 degrees relative to the driver. The director phase angle is normally negative relative to the driver and may be anywhere between 80 and 150 degrees. The exact phase angle for each parasitic element derives largely from the position and size of each element relative to the driver. If you see only a current table for a set of elements without designations such as "reflector" and "director," you can still tell the direction of the main beam by looking at the phase-angle entries.

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Fig. 2 replicates the data in the table using a more graphical presentation. The pink vertical lines represent the relative current magnitude on each element at each sampled frequency. The figures may make the progression of current values more readily apparent.

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Very noticeable in the table for the standard 3-element Yagi is the fact that as the frequency increases, the relative reflector current magnitude decreases. In Part 1, I noted in connection with certain designs that the reflector size has a greater effect on lower frequency performance than on higher frequency performance. Equally, the director size has a larger effect on the higher-frequency performance. As the table shows, the director current magnitude increases as we raise the beam's operating frequency.

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The pattern of current magnitudes for the 4-element open-sleeve coupled design in Part 1 shows a similar progression of current values for the reflector and the most forward element, which I shall simply call the director. The exact values differ from those of the 3-element Yagi because the element lengths and position differ between the two designs. The center 2 elements form the master and slaved driving elements, and we should pay close attention to them. Since we feed only one element, its current magnitude is always 1.0. In the following table, note the relative current magnitude on the slaved driving element as we increase frequency. Also follow the current magnitudes in the graphical representation in Fig 3, which appears just below the table.

+ 
+Relative Current Magnitude on the Elements of a 4-Element Wide-Band 40-Meter Yagi
+Element              7.0 MHz          7.15 MHz           7.3 MHz
+Reflector            0.569            0.413              0.276
+Master (Fed) Driver  1.0              1.0                1.0
+Slaved Driver        0.683            0.909              1.120
+Director             0.435            0.544              0.646
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As we increase the frequency, the current magnitude on the slaved driver reaches and then exceeds the current on the fed driver element, the one to which we have connected the feedline. (Remember that the current levels are relative to an assumed value of 1.0 at the feedpoint.) If we were to remove the slaved driver, then, at 7.3 MHz, the current level on the director would fall considerably--or its phase angle would change radically--with the net result that the beam's performance would decline in one, and usually several, categories. In designs like this one, we tend to cut the directly fed driver long to obtain good low-end performance and then to cut the slaved driver high to extend the performance at the high end of the band. If we carefully select the reflector spacing, we obtain a very wide SWR curves with a low value across the band. Essentially, the slaved driver's control of the beam's pattern at the higher end of the band--where the relative current equals or exceeds the driver current magnitude--extends back to the feedpoint so that the impedance at the junction with the transmission line remains stable. You may recall that the 4-element design in Part 1 showed a 50-Ohm SWR that did not grow to 1.25:1 anywhere within the 40-meter band.

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Many classic Yagi designs have used the open-sleeve dual driver system without realizing that fact. Early literature on the famous DL6WU VHF/UHF Yagi series used a reflector-to-driver space of 0.2 wavelength and a driver-to-director-1 spacing of about 0.05 wavelength. The result was a wide-band Yagi that covered all of the 70-cm band with an acceptably low SWR. Current analyses of the driver and first director elements show that the two form a master-slaved driver pair. Other well-known designs have followed this lead, using other spacing combinations. In the HF range, the OWA (optimized wideband antenna) Yagis used the same type of driving system, with different relative element spacings. However, the OWA series of beams also used special treatments of the second and third directors that stabilized a number of other performance properties. Hence, a Yagi may be a wide-band Yagi by using open-sleeve coupling between a fed driver and the next forward element without being an OWA Yagi. Since we shall not have enough directors to provide the special OWA treatment, all of our examples will simply be wide-band Yagis.

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The N3HBX reflector-less Yagi uses a 3-element driving cell, with slaved driving elements behind and ahead of the fed driver. Since the driving cell is an example of open-sleeve coupling among the elements, we should expect a pattern of changing current on each element, with the rear driver showing reduced current and the forward driver showing elevated current as we increased frequency. The following table and Fig. 4 confirm our suspicions.

+ 
+Relative Current Magnitude on the Elements of a 4-Element N3HBX Wide-Band 40-Meter Yagi
+Element              7.0 MHz     7.05 MHz     7.15 MHz     7.25 MHz      7.3 MHz
+Rear Slaved Driver   0.985       1.014        0.686        0.422         0.221
+Master (Fed) Driver  1.0         1.0          1.0          1.0           1.0
+ForwardSlaved Driver 0.520       0.930        1.092        1.541         1.282
+Director             0.286       0.458        0.481        0.625         0.433
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+ +
+

The relative driver current magnitude levels do not disappoint our expectations. I have added 2 extra columns to the table because we noted that the impedance and SWR curves for the Yagi design showed peak performance values just inside each band-edge. The current values reflect the performance data. At 7.05 MHz, the rear slaved driver has close to its highest value. Likewise, the forward driver shows nearly peak magnitude at about 7.25 MHz.

+

Many antenna designers use open-sleeve coupling for multi-band antennas, tuning each slaved driver to a band that is usually higher in frequency than the band to which they tune the fed driver. The technique has seen successfully use in both vertical monopole systems and in multi-band Yagis. One of the earliest conscious in-band uses of open-sleeve coupling involved the design of a dipole to cover all of the 80-75-meter band, or at least selected portions of the band.

+

An alternative to open-sleeve coupling for multi-band antennas is direct coupling, sometimes called closed-sleeve coupling. Optimbeam Yagis use such a system, and the Bencher Skyhawk changed its feed system from open- to closed-sleeve coupling a few years back. One advantage of direct coupling over open-sleeve coupling is a broader bandwidth on frequencies higher than the lowest covered by the antenna system. The principle of direct coupling is simple-sounding, but electrically somewhat complex. Let's take a pair of driver elements. Let one be connected to the main feedline. Between that element and the other, we shall make a direct connection with a fairly low-impedance transmission line. The line will be short and not reversed. The close proximity of the two drivers produces parasitic or high mutual coupling similar to that found in open sleeve coupling system. However, we have also fed power directly to both elements. One result is that directly coupled drivers usually use element spacing that is greater than for driver pairs that use only parasitic coupling. A second result is the need to carefully balance the connecting transmission line impedance with the element size and spacing.

+

Most direct-coupled driver system emerge from computer experimentation, which is far more rapid than physically varying the components with a prototype antenna. When successful, the multi-band driver set--amid the other elements forming a Yagi--shows a good match to the main feedline on each band. However, where we connect the feedline may vary, with some feedlines connecting to the higher-frequency element and some to the lower-frequency element.

+

When we translate a directly coupled driver pair from multi-band to in-band service, we may encounter some surprises in the sense of needing a configuration unlike those that we saw in open-sleeve coupled driver systems. The following table and Fig. 5 track element currents for a shorter 4-element 40-meter wide-band Yagi that uses a pair of directly coupled drivers, with a short, direct 50-Ohm transmission line between the driving elements. Note from the graphic that the feedpoint is on the rear driver of the pair. This driver is also the shorter of the two interconnected elements.

+ 
+Relative Current Magnitude on the Elements of a 4-Element Wide-Band 40-Meter Yagi
+  with a Directly Coupled Driver Pair
+Element              7.0 MHz          7.15 MHz           7.3 MHz
+Reflector            0.505            0.395              0.300
+Rear Driver          0.194            0.144              0.300
+Forward Driver       0.780            0.935              1.357
+Director             0.398            0.548              0.783
+
+
+ +
+

The rear driver appears to carry a very low current magnitude, but the directly coupled pair yields a large operating bandwidth--as large at least as the bandwidth of the long-boom 3-element Yagi, but on a boom that is 10' shorter. How the directly coupled pair operate in this particular design is quite interesting. The phase angle of the rear driver is positive and almost as large as the positive phase angle of the reflector. The parasitic reflector element shows a decrease in relative current magnitude as we increase the frequency, but the rear driver shows an increase in current over that same span. The net effect is fairly smooth performance over the entire 40-meter band. Since we have a division of current at the main feedpoint, neither element shows a relative current magnitude of 1.0. As well, we also have changes in the phase angle from the feedpoint or source value of 0 degrees. Since even a short low-impedance transmission line will show impedance-transforming properties, the driver magnitudes do not add arithmetically. The directly coupled driver pair used in this design exercise is not the only one that we might employ, but it is satisfactory to our goal of producing a wide-band 40-meter beam.

+

Our final example involves the use of a driver pair arranged to form a system traditionally called phased feeding. The two driver elements are more widely spaced and use a reversed (or half-twist) transmission line section to achieve proper phasing. Phasing does not directly concern the feedpoint impedance at each element in the pair. Rather, we arrange the element lengths and their spacing, as well as the line impedance between them, to achieve a desired relative current magnitude and phase on each element. Since the phased pair of elements forms a 2-element LPDA arrangement, the resultant beam that we produce when we add a reflector and a director often bears the name "log-cell Yagi." However, for small log cells (fewer than 4 elements), the driver pair usually emerges from experimentation rather than the application of LPDA equations. The systems used in our wide-band 40-meter designs employ a 250-Ohm phase line, and the feedpoint is on the forward element of the pair. The following table and Fig. 6 provide data on the shorter of the two versions of the wide-band log-cell Yagi that we shall later examine in more detail.

+ 
+Relative Current Magnitude on the Elements of a 4-Element Wide-Band 40-Meter Yagi
+  with a Pair of Phased Driver Elements
+Element              7.0 MHz          7.15 MHz           7.3 MHz
+Reflector            0.223            0.155              0.102
+Rear Driver          0.654            0.655              0.453
+Forward Driver       0.674            0.824              1.030
+Director             0.610            0.905              1.163
+
+
+ +
+

The reflector shows decreasing relative current, while the director shows increasing relative current as we increase the operating frequency. The rear driver trend is downward, while the forward driver trend is upward. However, perhaps the most notable aspect of the system is the relative unimportance of the reflector and the very high importance of the director in terms of their relative current levels all across the band. We can remove the reflector and sustain the feedpoint impedance at nearly the 50-Ohm level and the overall operating bandwidth. The director plays the most important role in setting the radiation pattern behavior. You may relate this discussion of relative current levels to the Part-1 discussion of reflector-less Yagis using a phased pair of driver elements.

+

Although our excursion into Yagi element currents has delayed our introduction of additional wide-band Yagi designs, it has shown us a few things, and has potential for showing us others. The diversity of parasitic arrangements by which we can achieve a set of operating goals within an overall beam structure continues to grow as designers bring their ingenuity to bear on their challenges. An understanding of the current patterns that emerge as we track a design through its operating range contribute to our better understanding of the design, even in the absence of explicit design equations. In fact, we might even use the information that we have just surveyed to understand some of the behavioral quirks in the designs to come.

+

The Design Challenge

+

In Part 1, we examined a 3-element standard Yagi on a 45' boom. It provided the performance listed in the following table from that discussion.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.92             19.16             51.6 - j 17.6             1.41
+7.15            7.03             21.54             48.9 - j  1.3             1.04
+7.3             7.37             19.00             41.6 + j 18.8             1.57
+
+

The Yagi averages about 7.1-dBi forward gain and close to 20-dB front-to-back ratio. It shows a rising gain curve as we increase frequency. The 50-Ohm SWR curve is very shallow and just misses the 40-meter grail of being under 1.5:1 at the upper end of the band. (We shall not here debate the merits of calculating the SWR at the end of some arbitrary length of lossy coaxial cable.) Boomlength remains the key drawback to the design and is not eliminable. A shorter boom would narrow the operating bandwidth and lower the resistive component of the feedpoint impedance, thus increasing the SWR over a large part of the band.

+

In contrast, the 4-element N3HBX design requires only 31' of boom. The triple-driver section with a single director produces the performance shown in the following table, repeated from Part 1.

+ 
+Frequency       Free-Space       Front-Back        Pre-Match Z        25-Ohm        Post-match Z       50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms      SWR           R +/- jX Ohms      SWR
+7.0             7.21             20.91             16.3 - j  2.8      1.57          67.7 + j 20.5      1.59
+7.15            7.18             25.20             31.7 + j  0.4      1.27          38.7 - j  0.1      1.29
+7.3             7.46             20.69             15.7 + j  4.8      1.69          72.6 - j 20.4      1.65
+
+

Forward gain averages about 7.25 dBi, with a 22-dB front-to-back ratio. The average feedpoint impedance is in the vicinity of 25 Ohms. So the array requires a matching network. The quarter wavelength section of 35-Ohm transmission line yields the final columns of impedance and SWR values. Although the antenna does not produce as low a set of SWR values as the 3-element array, it remains well under 2:1, with a savings of 14' of boom but a cost of the weight of one more element.

+

Obviously, the challenge facing any competing design is to improve upon one or more sets of figures while maintaining the shortest possible boomlength. We shall look at 2 different ways of approaching the challenge.

+

4-Elements and Directly Coupled Drivers

+

The first design direction involves the use of a driver pair with directly coupled elements. A length of 50-Ohm transmission line connects the 2 drivers. The rear driver is the shorter one and also serves as the feedpoint for a direct connection to 50-Ohm cable. To this pair of drivers we shall add a reflector and a director. The following table provides dimensions for the shorter version of the 4-element wide-band Yagi with directly coupled drivers.

+ 
+Dimensions of the 4-Element Wide-Band Yagis with Directly Coupled Drivers
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+Short        Reflector           0           461             75
+             Rear Driver         112         397             11
+             Forward Driver      177         425             39
+             Director 2          418         386             0
+Long         Reflector           0           461             75
+             Rear Driver         192         398             12
+             Forward Driver      257         425             39
+             Director 2          498         386             0
+
+

The short version of the array has a boomlength just under 35'. Within those limits, it produces the performance figures that appear in the following table.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             7.05             22.35             28.4 - j  7.1             1.81
+7.15            7.07             24.54             36.1 + j  2.6             1.39
+7.3             7.31             22.06             45.2 + j 22.0             1.60
+
+

The curves in Fig. 7 translate the sample values into a full-band picture of performance. Below the graphs are free-space E-plane patterns at the sampled frequencies.

+
+ +
+

The gain and front-to-back figures are very comparable to those for the N3HBX beam without some of the dimensional finickiness that goes along with the triple-driver that uses a master and 2 slaved driving elements. The directly coupled system provide well under 2:1 50-Ohm SWR on a boom only 4' long than the N3HBX boom, but it does not result in the desired 1.5:1 50-Ohm SWR maximum.

+

Since the resistive component of the impedance values is uniformly low, we can increase it by increasing the distance between the reflector and the rear driver. As we increase this distance, the feedpoint resistance does not rise as fast as it might with a single driver. As noted earlier, the rear driver exerts reflector-like influence on the radiation pattern due to the positive phase angle of the element-center current, an angle that almost equals the phase angle of the reflector current. Therefore, we must increase the distance by nearly 7' to achieve the desired SWR curve. So the final boomlength of the long version of the 4-eleent directly coupled driver Yagi is about 41.5'--still short of the boomlength for the simple 3-element wide-band Yagi. The following table samples the performance.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             7.13             21.01             36.9 - j 10.9             1.48
+7.15            7.19             24.23             42.1 - j  1.5             1.19
+7.3             7.42             21.59             49.6 + j 18.8             1.45
+
Fig. 8 converts the sampled data into full-band curves and provides the e-plane patterns. +
+ +
+

The only changes in the long version, relative to the shorter one, involve moving the reflector and changing the length of the rear driver by 2" (1" per half-element length). Since the director position and size do not change, the radiation pattern performance does not change, although the gain does increase by a paltry 0.1 dB. However, the array does not exceed a 50-Ohm SWR value of 1.5:1 across the whole band. Although shorter than the 3-element Yagi, the array is considerably longer than the N3HBX beam (by 10.5'). However, the long directly coupled Yagi is about 10' shorter than the original 4-element Yagi with its added dB of gain and its impressive SWR curve.

+
+ +
+

The use of a directly coupled driver pair puts the potential builder in a quandary. Fig. 9 compares the outlines of the 2 beams and reveals the key difference: the driver-to-reflector spacing needed to achieve the better SWR performance. At the short length, and if a 2:1 SWR curve is satisfactory, the design would be competitive with the N3HBX and show less sensitivity to construction variables.

+

4-Elements and Phased Drivers

+

We may also use a log-cell driver system consisting of 2 fed element connected by a reversed transmission line. Although related to LPDA structures, small log cells of 2 to 3 elements usually emerge from trial-and-error experimentation when used in conjunction with parasitic elements to form log-cell Yagis. Such cells are normally used for monoband Yagis, but may also appear in some multi-band Yagi designs. A log cell--even if only 2 elements long--generally lengthens the overall length of a Yagi without adding to its overall gain or front-to-back potential. However, the cell is capable of widening the effective bandwidth of virtually all of the Yagi's properties.

+

For our experimental 40-meter designs using the prescribed element-diameter schedule, I created a 2-element cell with a reflector and a director to form a 4-element beam. The log cell has a normal form, with a longer rear element and a shorter forward element connected by a 250-Ohm phase line using a single half twist. The forward element center serves as the connection point for the main (50-Ohm) feedline. The following table provides the critical dimensions.

+ 
+Dimensions of the 4-Element Wide-Band Yagis with Phased Drivers
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+Short        Reflector           0           462             76
+             Rear Driver         194         439             53
+             Forward Driver      290         412             26
+             Director 2          427         399             13
+Long         Reflector           0           463             77
+             Rear Driver         192         432             46
+             Forward Driver      290         401             15
+             Director 2          467         388             2
+
+

Between the two versions, numerous dimensions change by greater or lesser amounts. However, the reflector-to-driver spacing remains almost unchanged, with the major boomlength change between the forward driver and the director. The shorter version is just over 35.5', while the longer version is just under 39'.

+

As the following table reveals, the shorter version of the antenna achieves virtually all of the array goals except one: it falls just under the desired 20-dB front-to-back ratio at the band edges. Fig. 10 shows the curves and patterns that permit a fuller evaluation of the antenna's potential performance/

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             7.01             18.41             36.5 + j  7.0             1.42
+7.15            7.07             21.78             47.1 + j  5.8             1.14
+7.3             7.26             19.83             40.9 - j 14.5             1.46
+
+
+ +
+

Like the other models that we have surveyed, the performance across the band is very smooth, with only operationally undetectable changes in the radiation pattern from 7.0 to 7.3 MHz. The chief merit in the phased driver system is the achievement of the more rigorous 50-Ohm SWR standard in a beam under 36' long.

+

The longer version of the phased-driver Yagi extends the boom by 40", making a few changes in the element lengths in order to re-center the performance curves. Since the SWR curve of the shorter design was satisfactory, the reflector-to-rear-driver spacing remained almost unchanged. The additional boomlength or driver-to-director spacing gave the array an unnoticeable increment of additional gain. More importantly, it raised the overall level of the front-to-back ratio by an average of over 5 dB. In the process, the SWR curve improved, mostly due to a narrowing of the total range of reactance change across the band. The following table samples the values, followed by Fig. 11, which presents the data in graphical form.

+ 
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             7.10             22.34             40.4 - j  1.7             1.24
+7.15            7.15             31.49             44.4 - j  1.6             1.13
+7.3             7.35             25.35             43.8 - j  9.9             1.28
+
+
+ +
+

The longer phased-driver Yagi's SWR curve does not exceed 1.3:1 across the band and hence rivals the SWR performance of the long-boom (51') 4-element Yagi described in Part 1 (but without the 8+ dBi forward gain). It also provides a detectable improvement in the front-to-back ratio. Even though the cited figure is for the 180-degree ratio, the rearward performance generally holds good for the whole of the rear quadrants.

+
+ +
+

Fig. 12 compares the outlines of the short and long Yagis with phased drivers. The increased spacing from the driver to the director is clear in the long version sketch.

+

Optibeam of Germany makes available a 4-element Yagi with a phased driver pair. The boomlength is similar to the one used in this design. I do not know the element taper schedule or precise dimensions used by the commercial offering. It does use some inductive loading to shorten the elements. This fact should not alter the SWR curve or the front-to-back ratio in any noticeable way. However, it may reduce forward gain slightly, depending upon the actual degree of element shortening and the inductor Q. These notes are neither for or against the Optibeam design. Rather I note them in passing to confirm that the phased driver system is a viable technique for obtain relatively high performance across the entirety of the (U.S) 40-meter band.

+

3-Elements and Phased Drivers

+

Let's review a couple of facts about 40-meter beams as presently used on the band. First, the most common varieties use boomlengths of about 20-22 feet, most of the time with only 2 elements. The wide-band design in Part 1 calls for 2 elements on a 23.5' boom. For reference, let's repeat the dimensions and the performance table.

+ 
+Dimensions of the 2-Element Wide-Band Yagi
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+2-Element    Reflector           0           451             65
+             Driver              282         412             26
+
+Performance
+
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.50              9.89             40.7 - j 19.4             1.60
+7.15            5.96             10.70             53.1 + j  3.5             1.09
+7.3             5.52              9.71             63.5 + j 24.2             1.63
+
+

The gain and front-to-back values are typical for a 2-element driver-reflector Yagi. We obtained full-band coverage by widening the element spacing from the usual 40-meter 20' value.

+

The second fact from Part 1 is the ability of Yagis to operate satisfactorily without a reflector, if the driver cell can handle the chore of setting the basic feedpoint impedance level. In the phased driver cell used in the preceding pair of designs, we have such a cell. If we remove the reflector, the impedance does not change beyond our ability to adjust by lengthening the director by a few inches on each end. We may leave all other elements just as they occur in the 4-element design and also retain the spacing values. The result is a 3-element Yagi with a phased pair of drivers and a single director on a 22.9' boom. Fig. 13 shows the outline.

+
+ +
+

The following table and Fig. 14 surveys the potential performance of the shorter array across 40 meters.

+ 
+Dimensions of the 3-Element Wide-Band Yagi with Phased Drivers
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+3-Element    Rear Driver         0           432             46
+             Forward Driver      98          401             15
+             Director            275         393             7
+Performance
+
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.13             13.56             38.2 + j  5.5             1.35
+7.15            6.57             15.30             48.4 + j  1.8             1.05
+7.3             7.05             13.49             45.2 - j 15.2             1.40
+
+
+ +
+

The data suggest a Yagi with performance intermediate between a standard 2-element driver-reflector design and the full 4-element phased-driver design with a reflector. Indeed, the performance is similar to that of an optimized driver-director 2-element Yagi, but without the usual restriction that comes with such designs--an exceptionally narrow operating bandwidth. Both the gain and front-to-back ratio exceed what is possible in the 2-element Yagi, but do not quite reach the level achieved by the 4-element design. However, the patterns are very well-behaved, and the 50-Ohm SWR curve never rises to 1.5:1.

+

Adding the weight of a third element to a 2-element Yagi is not a small adjustment. The overall beam will weigh about 30% more and call for support strengthening. However, the shorter boomlength reduces overall structural stressing in the wind relative to one of the longer boom 4-element designs. With a 23' boom, the 3-element phased-driver arrangement may be the most promising way to achieve the desired contester SWR curve with quite reasonable performance everywhere in the band. Indeed, the short boom allows room for further tweaking of the phased drivers to allow even further improvements in the SWR curve, as well as further adjustments to the length and position of the director for small performance improvements. The design improves on the sample 12-meter antenna (with a loss in gain and front-to-back ratio) by beginning with a wide-band phased pair of elements rather than the maximum gain pair used in the earlier experiment. In addition, the design also shows what the reflector in the 4-element long design adds to performance--assuming that its 39' boomlength is not a hindrance to implementation.

+

Conclusion

+

These designs complete our small survey of wide-band 40-meter Yagis. They do suggest that there are a number of alternative designs capable of covering the band with adequately high performance with boomlengths under 40', with not much lost as we shorten the array down to 35' or so. The new additions appear to have the additional merit of not being as sensitive to changes in some critical elements as the N3HBX design. Indeed, the final 3-element Yagi with phased drivers seems to be the most practical among all of the designs

+

Along the way, we have had occasion to probe various Yagi properties often overlooked by both Yagi users and home Yagi builders. Since few radio amateurs have the wherewithal to build or sustain a full size 3- or 4-element 40-meter Yagi, these additional discussions may prove in the long run to have more utility than the design suggestions. Indeed, the designs would require considerable revision and refinement to meet whatever one chose as a usable element taper schedule for implementation. Hence, they are only first-order design examples useful for comparisons among the collection of Yagi ideas.

+

The U.S. 40-meter amateur band is a special case within the HF spectrum. It is just narrow enough to lead us to believe that we can cover the entire band with a single antenna. However, the mechanical requirements for tubular elements restrict the achievable bandwidth with standard designs. Full band coverage calls for design ingenuity and some specialized techniques for extending coverage while maintaining a manageable boomlength (assuming that element length presents no insurmountable problems). As a consequence, it is a good band for learning one or two new things about wide-band Yagi performance and design.

+
+ +
+

Updated 03-01-2006. © L. B. Cebik, W4RNL. This item originally appeared in antenneX, (Feb., 2006). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 3

+

Go to Main Index

+

Topics: HF Lower, Yagi


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+

Wide-Band 40-Meter Yagis
+ Part 3: A 3-Element Wire Design

+
+
+

L. B. Cebik, W4RNL

+

+
+ +
+

At the end of Part 2 in this series, we introduced a 3-element Yagi beam that used phased drivers and a single director to provide reasonably good performance on 40 meters. Fig. 1 shows the general outline.

+
+ +
+

The phased-driver and director system offers a number of advantages over other designs.

+
    +
  • 1. The boom length is shorter than a driver-reflector Yagi with a similar operating bandwidth.
    • +
  • 2. The 3-element arrangement offers higher gain (overall) and a better front-to-back ratio than a two-element design.
    • +
  • 3. The performance is only a bit shy of the performance of a wide-band 3-element Yagi expressly designed for broadband operation, but uses a much shorter boom.
    • +
  • 4. The phased-driver system allows full-band coverage with a 50-Ohm SWR that is below 1.5:1 across the entire band.
    • +
+

Fig. 2 graphically summarizes the beam's performance, with selected numerical data in Table 1.

+ 
+Table 1.  Dimensions of the 3-Element Wide-Band Yagi with Phased Drivers
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Tip Length
+3-Element    Rear Driver         0           432             46
+             Forward Driver      98          401             15
+             Director            275         393             7
+Performance
+
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             6.13             13.56             38.2 + j  5.5             1.35
+7.15            6.57             15.30             48.4 + j  1.8             1.05
+7.3             7.05             13.49             45.2 - j 15.2             1.40
+
+
+ +
+

Like all Yagis with directors, the beam shows a rising gain curve with increased operating frequency. The front-to-back ratio peaks near the band center with roughly equal values at the band edges. The phased drivers require no matching system for compatibility with a standard 50-Ohm coaxial cable feedline (although a common-mode attenuation device is always in order).

+

The dimensions for the beam presume a very husky aluminum tubing taper schedule. The two driver elements require insulation and isolation from the boom for the feedline and phase line connections. Hence, the gap insulation structure and the mechanical boom connections demand special attention to ensure strength. Even within the genre of tubing-based 40-meter full size beams, the addition of a third element represents major increases in beam weight and wind loading. Still, the boom stress and the wind loading are not as high as would be the case for a wide-band standard 3-element design with its much longer boom.

+

Full-size heavy Yagis with all of the required supporting mechanisms and structures lie beyond the capabilities of a very large number of amateurs. Many members of the excluded group would be happy with a fixed position beam composed of wire. However, obtaining very wide-band performance requires considerable real estate, especially since single-wire element designs cannot match the performance of fat-element tubular designs. Hence, wire-beam designers often add elements or use very wide element spacing to obtain good results across the entire 40-meter band (as defined for the U.S., that is, from 7.0 to 7.3 MHz).

+

So we have an unanswered question: can the 3-element phased-driver design undergo adaptation to the needs of the fixed-position wire-beam user? The answer is affirmative, if we are willing to make only a small set of concessions.

+

The 3-Element Phased-Driver-Director Yagi in Wire Form

+

Adapting a Yagi design intended for use with aluminum tubing in a complex taper schedule to a uniform wire size requires multiple steps. There is no absolute order to them, but a good first effort is to find the uniform-diameter length and diameter for the elements in the original design. One may use either the facility within a modeling program or an external calculator (program or spreadsheet) to arrive at the values. For the 3-element beam described above, we find the following equivalent uniform-diameter elements:

+
    +
  • Rear Driver: Length: 801.3", Diameter: 1.38"
    • +
  • Forward Driver: Length: 750.3", Diameter: 1.50"
    • +
  • Director: Length: 737.4", Diameter: 1.54"
    • +
+

When we use an invariant set of diameter sets for all elements and vary only the length of the outer tip, the diameter value progression is not unusual. The longer rear element tip results in a smaller equivalent uniform diameter than we find for the director with its shorter tip section. Nevertheless, the variation in diameters is less significant in this case than the fact that all three diameters are nearly 1.5".

+

The most commonly used antenna wire size is AWG #12. With a diameter of 0.0808", this wire is only about 0.05 of the tubular element diameter. Such a small-diameter wire has two consequences of special import in this context. One is the fact that the mutual coupling between adjacent elements is much less than for the tubular elements. The phased drivers are just as dependent upon mutual coupling (in conjunctions with the phase line between them) as are the director and the drivers in a conventional parasitic arrangement. Therefore, a single-wire element set would require very significant compression of the element spacing, as well as adjustments to the element lengths to arrive at a working beam of the current design.

+

The second consequence is that the small diameter wire will result in a shrinking operating bandwidth that includes gain and front-to-back ratio as well as SWR. One of the goals of the adaptation is to see how much of the large-element performance we can preserve using wire elements. The single-wire route is not promising.

+

We can simulate larger diameter wires by using multiple wires in each element. We need not resort to cages, since we can approximate the full tubular element diameter with a 2-wire pair using a spacing of about 3" or so. While 3" spacing is feasible, we might also try closer spacing and see how a commonly available material might work. For example, we can purchase open-wire transmission line (ladder line) composed of AWG #12 conductors and about a 1" spacing. The rough equivalent single-wire diameter would be about 1/2". Fig. 3 provides an outline of how we would use the line for the elements in the beam.

+
+ +
+

The two drivers require a center insulator to provide a gap between element halves. The 50-Ohm cable connects to the forward driver. The 250-Ohm phase line with a single half twist runs between the forward and the rear drivers. For a wire beam, one should use home-built line. Table 2 provides dimensions for 250-Ohm lines using various wire diameters.

+ 
+Table 2. 250-Ohm open-wire transmission line dimensions
+AWG Wire Size  Wire Diameter  Center-to-Center Spacing
+#14            0.0641"        0.262"
+#12            0.0808"        0.330"
+#10            0.1019"        0.416"
+#8             0.1285"        0.525"
+
+

You will need spacers about every 3" to maintain the wire spacing accurately. The best way to make spacers is to drill the wire holes in a long strip of polycarbonate, Plexiglas, or similar plastic. Cut the spacers to size after you complete the drilling. Do not make the holes too large; you want a tight fit. A drop of one of the superglues at each hole will lock the spacers in place. The velocity factor of this phase-line will be very close to 1.0. You will need just under 8' of the phase line.

+

You can construct the ladder-line elements in a similar manner, or you can purchase commercial ladder line if the conductors are hard-drawn copper. Using this type of material, the required dimensions with both length and spacing adjustments appear in Table 3. Both drivers are slightly longer than the uniform-diameter equivalent lengths, as fits the smaller equivalent diameter of the ladder-line elements. To compensate for the reduced mutual coupling, the spacing between the drivers shrinks by 5". The director is considerably longer than the uniform-diameter equivalent and about 10" closer to the driver set. The resulting "boom" length is a total of 260", about 15" shorter than the boom length of the tubular version of the beam.

+

The selected data in Table 3 and the graphs in Fig. 4 show that some compromises are at work in preserving as much performance as possible. The resistance, reactance, and SWR data show that the minimum SWR is not quite as ideal as in the tubular version, although the maximum SWR remains below 1.5:1 across the band. It is possible to tweak the dimensions further. For example, reducing the director spacing from the drivers will increase the gain and front-to-back slightly, but at the cost of the broad SWR curve.

+ 
+Table 3.  Dimensions of the 3-Element Wide-Band Wire Yagi with Phased Drivers
+
+Note:  All dimensions are in inches.  Multiply by 2.54 for centimeters,
+       0.0254 for meters.
+
+Antenna      Element             Spacing     Half-Length     Full Length
+3-Element    Rear Driver         0           403             806
+             Forward Driver      93          379             758
+             Director            260         377             754
+Performance
+
+Frequency       Free-Space       Front-Back        Feedpoint Z               50-Ohm
+ MHz            Gain dBi         Ratio dB          R +/- jX Ohms             SWR
+7.0             5.92             12.89             35.8 + j  4.0             1.42
+7.15            6.42             15.48             50.9 + j  5.2             1.11
+7.3             6.97             13.22             54.5 - j 20.0             1.48
+
+
+ +
+

The average gain across 40 meters for the wire version of the antenna is about 0.15 dB less than for the very heavy tubular array. The band-edge front-to-back ratio declines by about a half-dB. One could not detect these amounts in operations for beams at the same height. A comparison of the E-plane pattern shapes at the bottom of Fig. 2 and of Fig. 4 shows that the ladder-line version of the antenna preserves the beam width of the forward lobe and the rear lobe shape across the band.

+

On this basis, one may judge the ladder-line elements to be a successful adaptation of the original design. Of course, there are no rules against constructing one's own wider 2-wire elements. Every increase in wire spacing will improve the operating bandwidth of the array. However, the task is somewhat daunting, since the elements require a total of about 2400" (200') of 2-wire element line. As well, widening the spacing between wires in the elements will require adjustments to the element lengths and spacing values. In most cases, the adjusted values will fall between the values for the tubular beam and those for the ladder-line version.

+

Installation and Expectations

+

Installing a wire Yagi or other flattop array of any sort involves establishing 4 corner vertical supports and then developing a perimeter rope assembly to hold the elements both at the desired height and also in relationship to each other. Fig. 5 sketches the barest outline of such a system. Actual systems will be as varied as the installation sites.

+
+ +
+

The vertical posts can be anything that is tall and sturdy. In some areas, trees are plentiful. The distance from the tree to the array corner may vary at each corner so long as the installer adjusts overall tension to hold the wires in the correct position. One may also use existing towers for upper-HF beams. Other arrangements are possible. Stresses in the direction of the beam are generally less critical within the limits of strength of the non-conductive ropes used. However, the stress along each element should be sufficient to prevent undue catenary sag without pressing the limits of the wire strength.

+

The feedpoint at the forward driver deserves extra thought for support. The coaxial cable feedline and any common-mode attenuator tend to be heavy compared to other portions of the beam. Adding a vertical post beneath the feedpoint to minimize the unsupported cable run is one way to minimize the stress.

+

Most 40-meter beams will serve at lower heights--as measured in fractions of a wavelength--than upper HF beams. This fact will be true regardless of the beam construction. The rule of height ("the higher, the better") remains in effect at 40 meters. Fig. 6 overlays the elevation patterns for the 40-meter 3-element Yagi at 35', 70', 105', and 140'. The last height is about 1/2 wavelength. The patterns show the lowering of the lowest lobe as the height increases, thus improving low-angle long-distance skip transmission and reception.

+
+ +
+

The use of phased drivers does not wholly eliminate the effects of ground on the feedpoint impedance. However, it does minimize them to a generally acceptable degree. Fig. 7 provides the 50-Ohm SWR sweeps for all four heights. The SWR remains well below 2:1 at all heights. With some element adjustment, one may be able to hold the value at less than 1.5:1 at the band edges at any of the heights with the 2-wire construction.

+
+ +
+

Generally, when adjusting the phased driver lengths, the following rules of thumb will apply. To lower the frequency of minimum SWR either lengthen the rear driver or shorten the forward driver--or both. To raise the frequency of minimum SWR, do the opposite. Be prepared also to adjust the length of the director to center the SWR curve within the passband for roughly equal band-edge SWR values. In most cases, these adjustments will be so minor as not to affect the general beam performance across the band. These rules are not absolute, since they do not take into account possible interactions with other objects at the installation site.

+

Conclusion

+

These notes do not add anything new to the general ideas on wide-band 40-meter beams covered in Parts 1 and 2. They do show that it is possible to adapt such designs to wire construction. In general, single wire elements tend not to provide the desired wire operating bandwidth when we include gain and front-to-back ratio to the usual SWR conception of operating bandwidth. However, even the relatively narrow spacing of ladder line is sufficient to preserve the performance of fat tubular element designs to a degree that makes a wire beam in a fixed position worthwhile.

+
+ +
+

Updated 12-31-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
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+

Go to Main Index

+

Topics: HF Lower, Yagi


+ + diff --git a/content/yagi/5l20-6.gif b/content/yagi/5l20-6.gif new file mode 100644 index 0000000..928df9c Binary files /dev/null and b/content/yagi/5l20-6.gif differ diff --git a/content/yagi/5l20.html b/content/yagi/5l20.html new file mode 100644 index 0000000..022e61f --- /dev/null +++ b/content/yagi/5l20.html @@ -0,0 +1,630 @@ + + + + + + Modeling 6 Long-Boom Yagis + + + +
+

Modeling 6 Long-Boom Yagis

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+
+

L. B. Cebik, W4RNL

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+
+ +

+
+ Over the last year or so, I accumulated designs for 5 different 20- meter Yagis with boom between 45 and 55 feet long and having either 5 or 6 elements. After the appearance of a preliminary version of these notes, a 6th was donated. All display an average free space gain from 14.0 to 14.35 MHz of over 10 dBi, with good front-to-back ratios averaging well over 20 dB across the band. It seemed to be an interesting project to model all 6 on the same versions of NEC (in this case, NEC-2 with Leeson corrections and NEC-4, using EZNEC Pro) and do some comparative assessment. +

What actually emerged is a lesson in some of the difficulties in making such assessments. Some of those difficulties arise from limitations of the programs (and every version of NEC/MININEC has limitations). Others emerge from differences among models and specification sheets that cannot be resolved without additional data not at hand. Hasty modeling and simplistic conclusions can yield fog where clarity is desired.

+

The Six Beams

The six beams are the following: +
    +
  • 1. A 5-element, 45' boom design by W6NGZ, published in CQ for October, 1996, p. 22.
    • +
  • 2. A 5-element, 48' boom design by K6STI, published among the beams in YA, which accompanies the ARRL Antenna Book--this is a medium strength model.
    • +
  • 3. A 5-element, 48' boom design by W3LPL, published on the World Wide Web.
    • +
  • 4. A 5-element, 55' boom design by K4SB, originally developed in monotaper for 10 meters, modified for this study by me for a somewhat arbitrary element taper (used by permission).
    • +
  • 5. A 6-element, 48' boom design by NW3Z, published on the World Wide Web.
    • +
  • 4. A 5-element, 48' sent to me by WB0DGF and once published on the Hy-Gain web site as HG205XLB.
    • +
+

The beams are interesting for their differing design features, not the least of which is the choice in element spacing, as shown in the figure below.

+
+ +
+

The K6STI has the lowest design feedpoint impedance, which is indicated in the reflector-driver spacing. The W6NGZ design aims for a higher feedpoint impedance and uses a correspondingly wider reflector-driver spacing. The W3LPL design has a comparable feedpoint impedance and hence a similar reflector-driver spacing to the W6NGZ design, despite the differences in boom length. These three designs are similar beyond the driver in that the directors are proportionally spaced, relative to each other. However, do not ignore the ability of D2 to affect feedpoint impedance. The WB0DGF design demonstrates how a different taper schedule may influence the required spacing for a design, since its reflector-drive spacing is greater than the K6STI antenna, but the DGF version has only a moderately higher feedpoint impedance.

+

The longest model (K4SB) tries for a direct 50-Ohm feed and uses the widest reflector-driver spacing. D1 is not especially different in spacing from the driver relative to the first three models. The truly different design is the NW3Z 6-element Yagi, which uses a moderately wide spacing between the reflector and driver combined with the closely spaced D1 to set the basic parameters of the antenna. However, D2 also plays a crucial role in setting the feedpoint impedance: at correct spacing, the feedpoint impedance is a good coax match; with D2 40" closer to D1, the feedpoint impedance drops to the 25-Ohm neighborhood without seriously affecting the gain and front-to-back characteristics of the antenna.

+

These notes are not designed to recommend one design over another, either overtly or tacitly. That would require a detailed construction analysis plus the resolution to some modeling questions which I intend to leave open.

+

Some Modeling Preliminaries

Unfortunately, modeling Yagis within the amateur community has become somewhat of a casual process, without the care and attention to detail used by serious designers, such as the author's of the designs shown here. Whatever the source of the design--YO, Yagi-Max, or simply manual design on AO or EZNEC--evaluation of a design requires good modeling practice. +

NEC-2 without a correction factor cannot accurately model a linear element using a tapered-diameter schedule. For that reason, some implementations of NEC-2 include Leeson or similar corrections, which substitute a carefully calculated mono-tapered element for each tapered-diameter element in an array. However, it is possible to disturb the substitute element by paying too little attention to segment length equality. Especially at current nodes (the center of near-1/2 wl elements), segment length needs to be equalized along a linear element whether it is a single dipole or a part of a larger array). Since the Leeson corrections modify the length and diameter of a wire but not its segmentation, segment lengths should be equalized in advance. This factor plays an especially important role where the designer may place a very-large diameter short segment at the element center to simulate boom-to-element mounting plates and hardware. Often--as with the K6STI and WB0DGF models--the length of this segment sets the approximate length of segments in the adjoining sections of the element.

+

Therefore, for the models at hand, segmentation was increased to yield segment lengths between 8" and 12", depending upon the model. The K6STI and WB0DGF models use the shorter lengths due to their center "lumps." (Note that the WB0DGF model omits the center "lump" on the driven element, while the K6STI model preserves it.) The W6NGZ model uses 12" segments, because they came out most even with the element sections in the design.

+

Other beams used 8" (W3LPL) or 10" (K4SB, NW3Z) per segment for similar reasons: the chosen segment length turned out to be the best way to achieve roughly equal length segments on the most elements. Despite best efforts, some variations inevitably result. Designers will always have, for any segment length chosen, a section that comes out to be n.5 segments long. Some will choose center sections that for any reasonable segment length seem to require an even number of segments. Adding extra segment is necessary for the driver--and hence, for the other elements in order to keep segment junctions as well aligned as possible.

+

NEC-4, by its initial reports, overcomes the NEC-2 weakness with tapered-diameter elements. Unfortunately, the initial reports have proven overly optimistic. Although NEC-4 is a vast improvement over uncorrected NEC-2, it falls short of the standard set by NEC-2-corrected, which also correlates with MININEC results. (MININEC does not have a tapered-diameter element problem, although it has other limitations.)

+

The NEC-4 limitation is somewhat minor for general purpose modeling, unless the element shows too large a diameter change between wires in the element, especially close to the current node, with the driven element the most crucial. This condition exists with the K6STI model.

+

In order to show the modeling differences between NEC-2-corrected and NEC-4, I have modeled all 6 beams in both programs via EZNEC Pro. (I could have applied the Leeson equations to the NEC-4 runs, but that would have produced the same results as the NEC-2 runs.) I graphed data comparatively for NEC-2-corrected and for NEC-4, to include free space gain in dBi, 180-degree front-to-back ratio, feedpoint resistance, and feedpoint reactance. SWR data is also shown wherever the source impedance is close enough to 50-Ohms to make such data relevant. All graphs run from 13.8 to 14.4 MHz in order to show downward slides of NEC-4 curves.

+

Let's look at the designs individually.

+

The W6NGZ 5-element, 45' boom model

+
+ +
The W6NGZ model is the shortest of the five, but it sustains a free space gain of over 10 dBi across the band, with better than 20 dB front-to-back ratio everywhere on 20. The element taper is from the CQ article, and it contains no compensation for element mounting plates at the element center. Within these constraints, NEC-4 and NEC-2-corrected tell very similar graphical stories about the beam. Differentials are marginal at best, although a wee bit of excess gain estimation and a slide of the curves downward in frequency are both evident. +
+ +
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+

As the graphics make plain, the antenna close being a very good match for 50-ohm cable.

+

The K6STI 5-element, 48' boom model

+
+ +
The K6STI design, with its center "bulge" in place, models quite well in NEC-2-corrected. It also displays very well the weakness of NEC-4 in dealing with the large change of diameter so close to the source or highest current point on the elements, despite extensive efforts to equalize segment lengths. NEC-4 gain data is almost a full dB higher than the more reasonable NEC-2 data, with a curve displacement lower in frequency, which also shows up on the front-to-back graph. The source resistance and reactance graphs show a similar slide, with the resistance values low in the NEC-4 run. Since current, impedance, and far field strength are related, the coincidence of these value differences from those in the NEC-2 run are not unexpected. +
+ +
+
+ +
+
+ +
+
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+

No SWR curve is shown, since the antenna is designed for a matching system such as a beta/hairpin match.

+

The W3LPL 5-element, 48' boom model

+
+ +
The W3LPL beam was designed for use with a Tee match, which neither NEC-2 nor NEC-4 can physically model accurately. Interestingly, W3LPL designed the antenna with non-conductive boom-to-element mounting plates in mind. Nonetheless, the curves--plus a look at the antenna characteristics just below 14 MHz--suggests that there is an approximate 50 kHz offset in frequency, with the elements in the model again playing short in the NEC-4 run, relative to the NEC-2-corrected run. Gain is still a little high in NEC-4. Given the W6NGZ model runs, this much difference is somewhat unexpected. The chief difference in the modeled data is that the W3LPL antenna shows considerable and constant inductive reactance, due to its intended use with a Tee-matching system. +
+ +
+
+ +
+
+ +
+
+ +
+
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+

I have included the 50-Ohm SWR curve for the W3LPL antenna because it makes a good contrast with that of the W6GNZ antenna, even though the antenna designer specifically introduced the inductive reactance in the driver to set up conditions for a no-capacitor Tee match system for a 200-Ohm feed impedance. Shortening the driver to resonance in an attempt to reduce the SWR will result in a decrease in the resistive component so that no great improvement actually occurs. However, those wishing a direct 50-Ohm feed without a Tee match may wish to consider a beta match using a shunt capacitor, instead of the usual shunt inductor, which is applied when the driver element is capacitively reactive. A capacitor value of about 90 Ohms reactance (about 125 pF) with sufficient voltage and current handling capabilities would come close to serving the need.

+

The K4SB 5-element, 55' boom model

+
+ +
I received this model from K4SB (with whose permission it is used here) in simplified form, using monotapered elements on 10-meters. I frequency-scaled it to 20-meters and then assigned it an element taper schedule, readjusting the element lengths until it closely approximated the monotaper performance. The antenna shows the greatest gain and front-to-back differential across the band of all the models, and this exhibits the effects of using wide reflector spacing alone to raise the feedpoint impedance of the beam. +

This beam is for me simply a modeling exercise and does not take into account any variations in building technique. It does not compensate for the effects of boom-to-element hardware. Considerable model tweaking would likely be required before construction.

+
+ +
+
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+
+ +
+
+ +
+
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+

The SWR curve is quite good. There is a significant variation in reactance across the band, to go along with the variations in gain and front-to-back ratio, although the beam demonstrates close to the optimum of what may be achieved using reflector spacing alone to determine a 50-Ohm feedpoint match.

+

The NW3Z 6-element, 48' boom model

+
+ +
The NW3Z design adds a director close to the driven element. Along with the spacing of director D2 for impedance control and the spacing of the remaining directors for performance characteristics, this design provides a very tight near-50-Ohm feedpoint impedance with very little variation in other antenna performance characteristics across 20 meters. Indeed, everything remains stable for a little ways below the lower end of 20 meters. +

As with all other designs, NEC-4 tends to overestimate gain and move the performance characteristics lower in frequency relative to NEC-2 curves. Since this model uses a 96" constant diameter center section in each element, the effect is not too extreme, but still greater than for the W6NGZ design.

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+
+ +
+
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+
+ +
+

Beware of misreading the steep SWR curves: first read the axis values. Only then can you compare the numbers with those appearing in the other beam graphs.

+

The WB0DGF 5-element, 48' boom model

+
+ +
The WB0DGF design, provides an interesting contrast to both the K6STI and the NW3Z designs with respect to modeled properties. It contains center "bulge" sections that limit segment length to 8". However, these occur on only the parasitical elements. Moreover, the design uses a wider reflector spacing than some of the other designs. The result is a far less extreme overestimation of gain, but a significant shift in the NEC-4 curves lower in frequency than the NEC-2 curves. These phenomena are clear on all four of the graphs. +

Since this antenna design was set up for potential use with a beta match system, no SWR curve is shown.

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+

Conclusions

Because of the open questions left along the way, no evaluative assessment is warranted by this exercise alone. However, two reminders are in order. +

1. The beams do reveal something of the broader aspects of large Yagi behavior in the means we use to design specific feedpoint impedances while retaining the highest levels of gain and front-to-back performance. Study of the spacing sketch alone (made more precise by the EZNEC Pro file descriptions appended to this note) may give some insight into future Yagi design directions. Yagi design innovations are far from exhausted.

+

2. Modeling comparisons are not to be undertaken lightly or hastily. Analyzing the foundations of received models as well as those inherent in one's own creations is a necessary step if models are to be compared against some set of design or analysis goals. It would have been very easy to see two of the designs above as simply inadequate to cover the entirety of 20 meters by looking solely at NEC-4 curves, when what is more likely at work is a frequency offset. Add to this the limitations of each core used to model the structures unambiguously, and the simple conjunction of models would become a disservice to understanding the antennas involved.

+

Within these handicaps, the comparison of some of the best of extant long- boom 20-meter Yagi design provides an interesting and potentially productive exercise. It can assist us in understanding both antenna design and antenna modeling just a little bit better.

+

EZNEC Wire Tables for the 5 Yagis

+ 
                      EZNEC/4  ver. 2.0
+
+5L45' W6NGZ CQ 10-96 p 22                      07-19-1998     07:44:08
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -215.60,  0.000,  0.000  W2E1 -156.00,  0.000,  0.000 6.25E-01   5
+2     W1E2 -156.00,  0.000,  0.000  W3E1 -120.00,  0.000,  0.000 7.50E-01   3
+3     W2E2 -120.00,  0.000,  0.000  W4E1 -72.000,  0.000,  0.000 8.75E-01   4
+4     W3E2 -72.000,  0.000,  0.000  W5E1  72.000,  0.000,  0.000 1.00E+00  13
+5     W4E2  72.000,  0.000,  0.000  W6E1 120.000,  0.000,  0.000 8.75E-01   4
+6     W5E2 120.000,  0.000,  0.000  W7E1 156.000,  0.000,  0.000 7.50E-01   3
+7     W6E2 156.000,  0.000,  0.000       215.605,  0.000,  0.000 6.25E-01   5
+8          -205.95, 79.800,  0.000  W9E1 -156.00, 79.800,  0.000 6.25E-01   4
+9     W8E2 -156.00, 79.800,  0.000 W10E1 -120.00, 79.800,  0.000 7.50E-01   3
+10    W9E2 -120.00, 79.800,  0.000 W11E1 -72.000, 79.800,  0.000 8.75E-01   4
+11   W10E2 -72.000, 79.800,  0.000 W12E1  72.000, 79.800,  0.000 1.00E+00  13
+12   W11E2  72.000, 79.800,  0.000 W13E1 120.000, 79.800,  0.000 8.75E-01   4
+13   W12E2 120.000, 79.800,  0.000 W14E1 156.000, 79.800,  0.000 7.50E-01   3
+14   W13E2 156.000, 79.800,  0.000       205.950, 79.800,  0.000 6.25E-01   4
+15         -198.21,155.160,  0.000 W16E1 -156.00,155.160,  0.000 6.25E-01   4
+16   W15E2 -156.00,155.160,  0.000 W17E1 -120.00,155.160,  0.000 7.50E-01   3
+17   W16E2 -120.00,155.160,  0.000 W18E1 -72.000,155.160,  0.000 8.75E-01   4
+18   W17E2 -72.000,155.160,  0.000 W19E1  72.000,155.160,  0.000 1.00E+00  13
+19   W18E2  72.000,155.160,  0.000 W20E1 120.000,155.160,  0.000 8.75E-01   4
+20   W19E2 120.000,155.160,  0.000 W21E1 156.000,155.160,  0.000 7.50E-01   3
+21   W20E2 156.000,155.160,  0.000       198.209,155.160,  0.000 6.25E-01   4
+22         -196.55,337.920,  0.000 W23E1 -156.00,337.920,  0.000 6.25E-01   3
+23   W22E2 -156.00,337.920,  0.000 W24E1 -120.00,337.920,  0.000 7.50E-01   3
+24   W23E2 -120.00,337.920,  0.000 W25E1 -72.000,337.920,  0.000 8.75E-01   4
+25   W24E2 -72.000,337.920,  0.000 W26E1  72.000,337.920,  0.000 1.00E+00  13
+26   W25E2  72.000,337.920,  0.000 W27E1 120.000,337.920,  0.000 8.75E-01   4
+27   W26E2 120.000,337.920,  0.000 W28E1 156.000,337.920,  0.000 7.50E-01   3
+28   W27E2 156.000,337.920,  0.000       196.548,337.920,  0.000 6.25E-01   3
+29         -189.90,530.400,  0.000 W30E1 -156.00,530.400,  0.000 6.25E-01   3
+30   W29E2 -156.00,530.400,  0.000 W31E1 -120.00,530.400,  0.000 7.50E-01   3
+31   W30E2 -120.00,530.400,  0.000 W32E1 -72.000,530.400,  0.000 8.75E-01   4
+32   W31E2 -72.000,530.400,  0.000 W33E1  72.000,530.400,  0.000 1.00E+00  13
+33   W32E2  72.000,530.400,  0.000 W34E1 120.000,530.400,  0.000 8.75E-01   3
+34   W33E2 120.000,530.400,  0.000 W35E1 156.000,530.400,  0.000 7.50E-01   3
+35   W34E2 156.000,530.400,  0.000       189.900,530.400,  0.000 6.25E-01   4
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           7    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+
+ 
                      EZNEC/4  ver. 2.0
+
+5L48' K6STI YA                               07-19-1998     07:44:45
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -216.50,  0.000,  0.000  W2E1 -138.00,  0.000,  0.000 5.00E-01  10
+2     W1E2 -138.00,  0.000,  0.000  W3E1 -96.000,  0.000,  0.000 6.25E-01   6
+3     W2E2 -96.000,  0.000,  0.000  W4E1 -48.000,  0.000,  0.000 7.50E-01   6
+4     W3E2 -48.000,  0.000,  0.000  W5E1  -4.000,  0.000,  0.000 8.75E-01   5
+5     W4E2  -4.000,  0.000,  0.000  W6E1   4.000,  0.000,  0.000 3.42E+00   1
+6     W5E2   4.000,  0.000,  0.000  W7E1  48.000,  0.000,  0.000 8.75E-01   5
+7     W6E2  48.000,  0.000,  0.000  W8E1  96.000,  0.000,  0.000 7.50E-01   6
+8     W7E2  96.000,  0.000,  0.000  W9E1 138.000,  0.000,  0.000 6.25E-01   6
+9     W8E2 138.000,  0.000,  0.000       216.500,  0.000,  0.000 5.00E-01  10
+10         -203.50, 72.000,  0.000 W11E1 -138.00, 72.000,  0.000 5.00E-01   8
+11   W10E2 -138.00, 72.000,  0.000 W12E1 -96.000, 72.000,  0.000 6.25E-01   6
+12   W11E2 -96.000, 72.000,  0.000 W13E1 -48.000, 72.000,  0.000 7.50E-01   6
+13   W12E2 -48.000, 72.000,  0.000 W14E1  -4.000, 72.000,  0.000 8.75E-01   5
+14   W13E2  -4.000, 72.000,  0.000 W15E1   4.000, 72.000,  0.000 3.42E+00   1
+15   W14E2   4.000, 72.000,  0.000 W16E1  48.000, 72.000,  0.000 8.75E-01   5
+16   W15E2  48.000, 72.000,  0.000 W17E1  96.000, 72.000,  0.000 7.50E-01   6
+17   W16E2  96.000, 72.000,  0.000 W18E1 138.000, 72.000,  0.000 6.25E-01   6
+18   W17E2 138.000, 72.000,  0.000       203.500, 72.000,  0.000 5.00E-01   8
+19         -201.75,160.000,  0.000 W20E1 -138.00,160.000,  0.000 5.00E-01   8
+20   W19E2 -138.00,160.000,  0.000 W21E1 -96.000,160.000,  0.000 6.25E-01   6
+21   W20E2 -96.000,160.000,  0.000 W22E1 -48.000,160.000,  0.000 7.50E-01   6
+22   W21E2 -48.000,160.000,  0.000 W23E1  -4.000,160.000,  0.000 8.75E-01   5
+23   W22E2  -4.000,160.000,  0.000 W24E1   4.000,160.000,  0.000 3.42E+00   1
+24   W23E2   4.000,160.000,  0.000 W25E1  48.000,160.000,  0.000 8.75E-01   5
+25   W24E2  48.000,160.000,  0.000 W26E1  96.000,160.000,  0.000 7.50E-01   6
+26   W25E2  96.000,160.000,  0.000 W27E1 138.000,160.000,  0.000 6.25E-01   6
+27   W26E2 138.000,160.000,  0.000       201.750,160.000,  0.000 5.00E-01   8
+28         -198.88,359.000,  0.000 W29E1 -138.00,359.000,  0.000 5.00E-01   8
+29   W28E2 -138.00,359.000,  0.000 W30E1 -96.000,359.000,  0.000 6.25E-01   5
+30   W29E2 -96.000,359.000,  0.000 W31E1 -48.000,359.000,  0.000 7.50E-01   6
+31   W30E2 -48.000,359.000,  0.000 W32E1  -4.000,359.000,  0.000 8.75E-01   6
+32   W31E2  -4.000,359.000,  0.000 W33E1   4.000,359.000,  0.000 3.42E+00   1
+33   W32E2   4.000,359.000,  0.000 W34E1  48.000,359.000,  0.000 8.75E-01   6
+34   W33E2  48.000,359.000,  0.000 W35E1  96.000,359.000,  0.000 7.50E-01   6
+35   W34E2  96.000,359.000,  0.000 W36E1 138.000,359.000,  0.000 6.25E-01   5
+36   W35E2 138.000,359.000,  0.000       198.875,359.000,  0.000 5.00E-01   8
+37         -191.62,570.000,  0.000 W38E1 -138.00,570.000,  0.000 5.00E-01   7
+38   W37E2 -138.00,570.000,  0.000 W39E1 -96.000,570.000,  0.000 6.25E-01   5
+39   W38E2 -96.000,570.000,  0.000 W40E1 -48.000,570.000,  0.000 7.50E-01   6
+40   W39E2 -48.000,570.000,  0.000 W41E1  -4.000,570.000,  0.000 8.75E-01   6
+41   W40E2  -4.000,570.000,  0.000 W42E1   4.000,570.000,  0.000 3.42E+00   1
+42   W41E2   4.000,570.000,  0.000 W43E1  48.000,570.000,  0.000 8.75E-01   6
+43   W42E2  48.000,570.000,  0.000 W44E1  96.000,570.000,  0.000 7.50E-01   6
+44   W43E2  96.000,570.000,  0.000 W45E1 138.000,570.000,  0.000 6.25E-01   5
+45   W44E2 138.000,570.000,  0.000       191.625,570.000,  0.000 5.00E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           1    14 / 50.00   ( 14 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+ 
                      EZNEC/4  ver. 2.0
+
+5L48' W3LPL WWW                              07-19-1998     07:45:37
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -217.00,  0.000,  0.000  W2E1 -150.00,  0.000,  0.000 7.50E-01   8
+2     W1E2 -150.00,  0.000,  0.000  W3E1 -117.00,  0.000,  0.000 8.75E-01   4
+3     W2E2 -117.00,  0.000,  0.000  W4E1 -84.000,  0.000,  0.000 1.00E+00   4
+4     W3E2 -84.000,  0.000,  0.000  W5E1 -33.750,  0.000,  0.000 1.12E+00   6
+5     W4E2 -33.750,  0.000,  0.000  W6E1  33.750,  0.000,  0.000 1.25E+00   9
+6     W5E2  33.750,  0.000,  0.000  W7E1  84.000,  0.000,  0.000 1.12E+00   6
+7     W6E2  84.000,  0.000,  0.000  W8E1 117.000,  0.000,  0.000 1.00E+00   4
+8     W7E2 117.000,  0.000,  0.000  W9E1 150.000,  0.000,  0.000 8.75E-01   4
+9     W8E2 150.000,  0.000,  0.000       217.000,  0.000,  0.000 7.50E-01   8
+10         -212.00, 86.000,  0.000 W11E1 -150.00, 86.000,  0.000 7.50E-01   8
+11   W10E2 -150.00, 86.000,  0.000 W12E1 -117.00, 86.000,  0.000 8.75E-01   4
+12   W11E2 -117.00, 86.000,  0.000 W13E1 -84.000, 86.000,  0.000 1.00E+00   4
+13   W12E2 -84.000, 86.000,  0.000 W14E1 -33.750, 86.000,  0.000 1.12E+00   6
+14   W13E2 -33.750, 86.000,  0.000 W15E1  33.750, 86.000,  0.000 1.25E+00   9
+15   W14E2  33.750, 86.000,  0.000 W16E1  84.000, 86.000,  0.000 1.12E+00   6
+16   W15E2  84.000, 86.000,  0.000 W17E1 117.000, 86.000,  0.000 1.00E+00   4
+17   W16E2 117.000, 86.000,  0.000 W18E1 150.000, 86.000,  0.000 8.75E-01   4
+18   W17E2 150.000, 86.000,  0.000       212.000, 86.000,  0.000 7.50E-01   8
+19         -199.38,171.000,  0.000 W20E1 -135.88,171.000,  0.000 7.50E-01   8
+20   W19E2 -135.88,171.000,  0.000 W21E1 -102.88,171.000,  0.000 8.75E-01   4
+21   W20E2 -102.88,171.000,  0.000 W22E1 -69.875,171.000,  0.000 1.00E+00   4
+22   W21E2 -69.875,171.000,  0.000 W23E1 -22.000,171.000,  0.000 1.12E+00   6
+23   W22E2 -22.000,171.000,  0.000 W24E1  22.000,171.000,  0.000 1.25E+00   5
+24   W23E2  22.000,171.000,  0.000 W25E1  69.875,171.000,  0.000 1.12E+00   6
+25   W24E2  69.875,171.000,  0.000 W26E1 102.875,171.000,  0.000 1.00E+00   4
+26   W25E2 102.875,171.000,  0.000 W27E1 135.875,171.000,  0.000 8.75E-01   4
+27   W26E2 135.875,171.000,  0.000       199.380,171.000,  0.000 7.50E-01   8
+28         -196.25,349.000,  0.000 W29E1 -119.25,349.000,  0.000 7.50E-01  10
+29   W28E2 -119.25,349.000,  0.000 W30E1 -86.250,349.000,  0.000 8.75E-01   4
+30   W29E2 -86.250,349.000,  0.000 W31E1 -53.250,349.000,  0.000 1.00E+00   4
+31   W30E2 -53.250,349.000,  0.000 W32E1 -22.000,349.000,  0.000 1.12E+00   4
+32   W31E2 -22.000,349.000,  0.000 W33E1  22.000,349.000,  0.000 1.25E+00   5
+33   W32E2  22.000,349.000,  0.000 W34E1  53.250,349.000,  0.000 1.12E+00   4
+34   W33E2  53.250,349.000,  0.000 W35E1  86.250,349.000,  0.000 1.00E+00   4
+35   W34E2  86.250,349.000,  0.000 W36E1 119.250,349.000,  0.000 8.75E-01   4
+36   W35E2 119.250,349.000,  0.000       196.250,349.000,  0.000 7.50E-01  10
+37         -183.75,570.000,  0.000 W38E1 -131.75,570.000,  0.000 7.50E-01   7
+38   W37E2 -131.75,570.000,  0.000 W39E1 -98.750,570.000,  0.000 8.75E-01   4
+39   W38E2 -98.750,570.000,  0.000 W40E1 -65.750,570.000,  0.000 1.00E+00   4
+40   W39E2 -65.750,570.000,  0.000 W41E1 -22.000,570.000,  0.000 1.12E+00   5
+41   W40E2 -22.000,570.000,  0.000 W42E1  22.000,570.000,  0.000 1.25E+00   5
+42   W41E2  22.000,570.000,  0.000 W43E1  65.750,570.000,  0.000 1.12E+00   5
+43   W42E2  65.750,570.000,  0.000 W44E1  98.750,570.000,  0.000 1.00E+00   4
+44   W43E2  98.750,570.000,  0.000 W45E1 131.750,570.000,  0.000 8.75E-01   4
+45   W44E2 131.750,570.000,  0.000       183.750,570.000,  0.000 7.50E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    14 / 50.00   ( 14 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+ 
                      EZNEC/4  ver. 2.0
+
+K4SB 5-element, 55' boom                        07-19-1998     07:46:17
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -217.00,  0.000,  0.000  W2E1 -152.00,  0.000,  0.000 5.00E-01   7
+2     W1E2 -152.00,  0.000,  0.000  W3E1 -116.00,  0.000,  0.000 6.25E-01   4
+3     W2E2 -116.00,  0.000,  0.000  W4E1 -72.000,  0.000,  0.000 7.50E-01   4
+4     W3E2 -72.000,  0.000,  0.000  W5E1 -48.000,  0.000,  0.000 8.75E-01   2
+5     W4E2 -48.000,  0.000,  0.000  W6E1  48.000,  0.000,  0.000 1.00E+00   9
+6     W5E2  48.000,  0.000,  0.000  W7E1  72.000,  0.000,  0.000 8.75E-01   2
+7     W6E2  72.000,  0.000,  0.000  W8E1 116.000,  0.000,  0.000 7.50E-01   4
+8     W7E2 116.000,  0.000,  0.000  W9E1 152.000,  0.000,  0.000 6.25E-01   4
+9     W8E2 152.000,  0.000,  0.000       217.000,  0.000,  0.000 5.00E-01   7
+10         -207.50,182.504,  0.000 W11E1 -152.00,182.504,  0.000 5.00E-01   6
+11   W10E2 -152.00,182.504,  0.000 W12E1 -116.00,182.504,  0.000 6.25E-01   4
+12   W11E2 -116.00,182.504,  0.000 W13E1 -72.000,182.504,  0.000 7.50E-01   4
+13   W12E2 -72.000,182.504,  0.000 W14E1 -48.000,182.504,  0.000 8.75E-01   2
+14   W13E2 -48.000,182.504,  0.000 W15E1  48.000,182.504,  0.000 1.00E+00   9
+15   W14E2  48.000,182.504,  0.000 W16E1  72.000,182.504,  0.000 8.75E-01   2
+16   W15E2  72.000,182.504,  0.000 W17E1 116.000,182.504,  0.000 7.50E-01   4
+17   W16E2 116.000,182.504,  0.000 W18E1 152.000,182.504,  0.000 6.25E-01   4
+18   W17E2 152.000,182.504,  0.000       207.500,182.504,  0.000 5.00E-01   6
+19         -195.53,269.544,  0.000 W20E1 -152.00,269.544,  0.000 5.00E-01   4
+20   W19E2 -152.00,269.544,  0.000 W21E1 -116.00,269.544,  0.000 6.25E-01   4
+21   W20E2 -116.00,269.544,  0.000 W22E1 -72.000,269.544,  0.000 7.50E-01   4
+22   W21E2 -72.000,269.544,  0.000 W23E1 -48.000,269.544,  0.000 8.75E-01   2
+23   W22E2 -48.000,269.544,  0.000 W24E1  48.000,269.544,  0.000 1.00E+00   9
+24   W23E2  48.000,269.544,  0.000 W25E1  72.000,269.544,  0.000 8.75E-01   2
+25   W24E2  72.000,269.544,  0.000 W26E1 116.000,269.544,  0.000 7.50E-01   4
+26   W25E2 116.000,269.544,  0.000 W27E1 152.000,269.544,  0.000 6.25E-01   4
+27   W26E2 152.000,269.544,  0.000       195.530,269.544,  0.000 5.00E-01   4
+28         -192.48,448.494,  0.000 W29E1 -152.00,448.494,  0.000 5.00E-01   4
+29   W28E2 -152.00,448.494,  0.000 W30E1 -116.00,448.494,  0.000 6.25E-01   4
+30   W29E2 -116.00,448.494,  0.000 W31E1 -72.000,448.494,  0.000 7.50E-01   4
+31   W30E2 -72.000,448.494,  0.000 W32E1 -48.000,448.494,  0.000 8.75E-01   2
+32   W31E2 -48.000,448.494,  0.000 W33E1  48.000,448.494,  0.000 1.00E+00   9
+33   W32E2  48.000,448.494,  0.000 W34E1  72.000,448.494,  0.000 8.75E-01   2
+34   W33E2  72.000,448.494,  0.000 W35E1 116.000,448.494,  0.000 7.50E-01   4
+35   W34E2 116.000,448.494,  0.000 W36E1 152.000,448.494,  0.000 6.25E-01   4
+36   W35E2 152.000,448.494,  0.000       192.480,448.494,  0.000 5.00E-01   4
+37         -189.42,656.474,  0.000 W38E1 -152.00,656.474,  0.000 5.00E-01   4
+38   W37E2 -152.00,656.474,  0.000 W39E1 -116.00,656.474,  0.000 6.25E-01   4
+39   W38E2 -116.00,656.474,  0.000 W40E1 -72.000,656.474,  0.000 7.50E-01   4
+40   W39E2 -72.000,656.474,  0.000 W41E1 -48.000,656.474,  0.000 8.75E-01   2
+41   W40E2 -48.000,656.474,  0.000 W42E1  48.000,656.474,  0.000 1.00E+00   9
+42   W41E2  48.000,656.474,  0.000 W43E1  72.000,656.474,  0.000 8.75E-01   2
+43   W42E2  72.000,656.474,  0.000 W44E1 116.000,656.474,  0.000 7.50E-01   4
+44   W43E2 116.000,656.474,  0.000 W45E1 152.000,656.474,  0.000 6.25E-01   4
+45   W44E2 152.000,656.474,  0.000       189.420,656.474,  0.000 5.00E-01   4
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    14 / 50.00   ( 14 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+ 
                      EZNEC/4  ver. 2.0
+
+NW3Z 6 el, 48' boom WWW                      07-19-1998     07:47:18
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -217.73,  0.000,  0.000  W2E1 -152.00,  0.000,  0.000 5.00E-01   7
+2     W1E2 -152.00,  0.000,  0.000  W3E1 -116.00,  0.000,  0.000 6.25E-01   4
+3     W2E2 -116.00,  0.000,  0.000  W4E1 -72.000,  0.000,  0.000 7.50E-01   4
+4     W3E2 -72.000,  0.000,  0.000  W5E1 -48.000,  0.000,  0.000 8.75E-01   2
+5     W4E2 -48.000,  0.000,  0.000  W6E1  48.000,  0.000,  0.000 1.00E+00   9
+6     W5E2  48.000,  0.000,  0.000  W7E1  72.000,  0.000,  0.000 8.75E-01   2
+7     W6E2  72.000,  0.000,  0.000  W8E1 116.000,  0.000,  0.000 7.50E-01   4
+8     W7E2 116.000,  0.000,  0.000  W9E1 152.000,  0.000,  0.000 6.25E-01   4
+9     W8E2 152.000,  0.000,  0.000       217.730,  0.000,  0.000 5.00E-01   7
+10         -210.70, 90.000,  0.000 W11E1 -152.00, 90.000,  0.000 5.00E-01   6
+11   W10E2 -152.00, 90.000,  0.000 W12E1 -116.00, 90.000,  0.000 6.25E-01   4
+12   W11E2 -116.00, 90.000,  0.000 W13E1 -72.000, 90.000,  0.000 7.50E-01   4
+13   W12E2 -72.000, 90.000,  0.000 W14E1 -48.000, 90.000,  0.000 8.75E-01   2
+14   W13E2 -48.000, 90.000,  0.000 W15E1  48.000, 90.000,  0.000 1.00E+00   9
+15   W14E2  48.000, 90.000,  0.000 W16E1  72.000, 90.000,  0.000 8.75E-01   2
+16   W15E2  72.000, 90.000,  0.000 W17E1 116.000, 90.000,  0.000 7.50E-01   4
+17   W16E2 116.000, 90.000,  0.000 W18E1 152.000, 90.000,  0.000 6.25E-01   4
+18   W17E2 152.000, 90.000,  0.000       210.700, 90.000,  0.000 5.00E-01   6
+19         -200.80,139.520,  0.000 W20E1 -152.00,139.520,  0.000 5.00E-01   5
+20   W19E2 -152.00,139.520,  0.000 W21E1 -116.00,139.520,  0.000 6.25E-01   4
+21   W20E2 -116.00,139.520,  0.000 W22E1 -72.000,139.520,  0.000 7.50E-01   4
+22   W21E2 -72.000,139.520,  0.000 W23E1 -48.000,139.520,  0.000 8.75E-01   2
+23   W22E2 -48.000,139.520,  0.000 W24E1  48.000,139.520,  0.000 1.00E+00   9
+24   W23E2  48.000,139.520,  0.000 W25E1  72.000,139.520,  0.000 8.75E-01   2
+25   W24E2  72.000,139.520,  0.000 W26E1 116.000,139.520,  0.000 7.50E-01   4
+26   W25E2 116.000,139.520,  0.000 W27E1 152.000,139.520,  0.000 6.25E-01   4
+27   W26E2 152.000,139.520,  0.000       200.800,139.520,  0.000 5.00E-01   5
+28         -194.62,266.700,  0.000 W29E1 -152.00,266.700,  0.000 5.00E-01   4
+29   W28E2 -152.00,266.700,  0.000 W30E1 -116.00,266.700,  0.000 6.25E-01   4
+30   W29E2 -116.00,266.700,  0.000 W31E1 -72.000,266.700,  0.000 7.50E-01   4
+31   W30E2 -72.000,266.700,  0.000 W32E1 -48.000,266.700,  0.000 8.75E-01   2
+32   W31E2 -48.000,266.700,  0.000 W33E1  48.000,266.700,  0.000 1.00E+00   9
+33   W32E2  48.000,266.700,  0.000 W34E1  72.000,266.700,  0.000 8.75E-01   2
+34   W33E2  72.000,266.700,  0.000 W35E1 116.000,266.700,  0.000 7.50E-01   4
+35   W34E2 116.000,266.700,  0.000 W36E1 152.000,266.700,  0.000 6.25E-01   4
+36   W35E2 152.000,266.700,  0.000       194.620,266.700,  0.000 5.00E-01   4
+37         -194.63,388.440,  0.000 W38E1 -152.00,388.440,  0.000 5.00E-01   4
+38   W37E2 -152.00,388.440,  0.000 W39E1 -116.00,388.440,  0.000 6.25E-01   4
+39   W38E2 -116.00,388.440,  0.000 W40E1 -72.000,388.440,  0.000 7.50E-01   4
+40   W39E2 -72.000,388.440,  0.000 W41E1 -48.000,388.440,  0.000 8.75E-01   2
+41   W40E2 -48.000,388.440,  0.000 W42E1  48.000,388.440,  0.000 1.00E+00   9
+42   W41E2  48.000,388.440,  0.000 W43E1  72.000,388.440,  0.000 8.75E-01   2
+43   W42E2  72.000,388.440,  0.000 W44E1 116.000,388.440,  0.000 7.50E-01   4
+44   W43E2 116.000,388.440,  0.000 W45E1 152.000,388.440,  0.000 6.25E-01   4
+45   W44E2 152.000,388.440,  0.000       194.630,388.440,  0.000 5.00E-01   4
+46         -187.39,570.000,  0.000 W47E1 -152.00,570.000,  0.000 5.00E-01   4
+47   W46E2 -152.00,570.000,  0.000 W48E1 -116.00,570.000,  0.000 6.25E-01   4
+48   W47E2 -116.00,570.000,  0.000 W49E1 -72.000,570.000,  0.000 7.50E-01   4
+49   W48E2 -72.000,570.000,  0.000 W50E1 -48.000,570.000,  0.000 8.75E-01   2
+50   W49E2 -48.000,570.000,  0.000 W51E1  48.000,570.000,  0.000 1.00E+00   9
+51   W50E2  48.000,570.000,  0.000 W52E1  72.000,570.000,  0.000 8.75E-01   2
+52   W51E2  72.000,570.000,  0.000 W53E1 116.000,570.000,  0.000 7.50E-01   4
+53   W52E2 116.000,570.000,  0.000 W54E1 152.000,570.000,  0.000 6.25E-01   4
+54   W53E2 152.000,570.000,  0.000       187.390,570.000,  0.000 5.00E-01   4
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           5    14 / 50.00   ( 14 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+ 
                      EZNEC/4  ver. 2.0
+
+Hy-Gain 205-XLB, 48' Boom (WB0DGF)                07-19-1998     07:55:56
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+
+1          -286.00,-223.75,  0.000  W2E1 -286.00,-166.00,  0.000 4.38E-01   7
+2     W1E2 -286.00,-166.00,  0.000  W3E1 -286.00,-142.00,  0.000 6.25E-01   3
+3     W2E2 -286.00,-142.00,  0.000  W4E1 -286.00,-91.500,  0.000 8.75E-01   6
+4     W3E2 -286.00,-91.500,  0.000  W5E1 -286.00,-45.500,  0.000 1.12E+00   6
+5     W4E2 -286.00,-45.500,  0.000  W6E1 -286.00, -3.625,  0.000 1.25E+00   5
+6     W5E2 -286.00, -3.625,  0.000  W7E1 -286.00,  3.625,  0.000 4.00E+00   1
+7     W6E2 -286.00,  3.625,  0.000  W8E1 -286.00, 45.500,  0.000 1.25E+00   5
+8     W7E2 -286.00, 45.500,  0.000  W9E1 -286.00, 91.500,  0.000 1.12E+00   6
+9     W8E2 -286.00, 91.500,  0.000 W10E1 -286.00,142.000,  0.000 8.75E-01   6
+10    W9E2 -286.00,142.000,  0.000 W11E1 -286.00,166.000,  0.000 6.25E-01   3
+11   W10E2 -286.00,166.000,  0.000       -286.00,223.750,  0.000 4.38E-01   7
+12         -170.00,-209.50,  0.000 W13E1 -170.00,-156.50,  0.000 4.38E-01   7
+13   W12E2 -170.00,-156.50,  0.000 W14E1 -170.00,-132.50,  0.000 6.25E-01   3
+14   W13E2 -170.00,-132.50,  0.000 W15E1 -170.00,-82.000,  0.000 8.75E-01   6
+15   W14E2 -170.00,-82.000,  0.000 W16E1 -170.00,-36.000,  0.000 1.12E+00   6
+16   W15E2 -170.00,-36.000,  0.000 W17E1 -170.00,-10.000,  0.000 1.25E+00   3
+17   W16E2 -170.00,-10.000,  0.000 W18E1 -170.00, 10.000,  0.000 1.25E+00   3
+18   W17E2 -170.00, 10.000,  0.000 W19E1 -170.00, 36.000,  0.000 1.25E+00   3
+19   W18E2 -170.00, 36.000,  0.000 W20E1 -170.00, 82.000,  0.000 1.12E+00   6
+20   W19E2 -170.00, 82.000,  0.000 W21E1 -170.00,132.500,  0.000 8.75E-01   6
+21   W20E2 -170.00,132.500,  0.000 W22E1 -170.00,156.500,  0.000 6.25E-01   3
+22   W21E2 -170.00,156.500,  0.000       -170.00,209.500,  0.000 4.38E-01   7
+23         -80.000,-206.25,  0.000 W24E1 -80.000,-156.50,  0.000 4.38E-01   6
+24   W23E2 -80.000,-156.50,  0.000 W25E1 -80.000,-132.50,  0.000 6.25E-01   3
+25   W24E2 -80.000,-132.50,  0.000 W26E1 -80.000,-82.000,  0.000 8.75E-01   6
+26   W25E2 -80.000,-82.000,  0.000 W27E1 -80.000,-36.000,  0.000 1.12E+00   6
+27   W26E2 -80.000,-36.000,  0.000 W28E1 -80.000, -3.625,  0.000 1.25E+00   4
+28   W27E2 -80.000, -3.625,  0.000 W29E1 -80.000,  3.625,  0.000 4.00E+00   1
+29   W28E2 -80.000,  3.625,  0.000 W30E1 -80.000, 36.000,  0.000 1.25E+00   4
+30   W29E2 -80.000, 36.000,  0.000 W31E1 -80.000, 82.000,  0.000 1.12E+00   6
+31   W30E2 -80.000, 82.000,  0.000 W32E1 -80.000,132.500,  0.000 8.75E-01   6
+32   W31E2 -80.000,132.500,  0.000 W33E1 -80.000,156.500,  0.000 6.25E-01   3
+33   W32E2 -80.000,156.500,  0.000       -80.000,206.250,  0.000 4.38E-01   6
+34          86.000,-203.25,  0.000 W35E1  86.000,-156.50,  0.000 4.38E-01   6
+35   W34E2  86.000,-156.50,  0.000 W36E1  86.000,-132.50,  0.000 6.25E-01   3
+36   W35E2  86.000,-132.50,  0.000 W37E1  86.000,-82.000,  0.000 8.75E-01   6
+37   W36E2  86.000,-82.000,  0.000 W38E1  86.000,-36.000,  0.000 1.12E+00   6
+38   W37E2  86.000,-36.000,  0.000 W39E1  86.000, -3.625,  0.000 1.25E+00   4
+39   W38E2  86.000, -3.625,  0.000 W40E1  86.000,  3.625,  0.000 4.00E+00   1
+40   W39E2  86.000,  3.625,  0.000 W41E1  86.000, 36.000,  0.000 1.25E+00   4
+41   W40E2  86.000, 36.000,  0.000 W42E1  86.000, 82.000,  0.000 1.12E+00   6
+42   W41E2  86.000, 82.000,  0.000 W43E1  86.000,132.500,  0.000 8.75E-01   6
+43   W42E2  86.000,132.500,  0.000 W44E1  86.000,156.500,  0.000 6.25E-01   3
+44   W43E2  86.000,156.500,  0.000        86.000,203.250,  0.000 4.38E-01   6
+45         286.000,-193.12,  0.000 W46E1 286.000,-138.25,  0.000 4.38E-01   7
+46   W45E2 286.000,-138.25,  0.000 W47E1 286.000,-114.25,  0.000 6.25E-01   3
+47   W46E2 286.000,-114.25,  0.000 W48E1 286.000,-63.750,  0.000 8.75E-01   6
+48   W47E2 286.000,-63.750,  0.000 W49E1 286.000,-17.750,  0.000 1.12E+00   6
+49   W48E2 286.000,-17.750,  0.000 W50E1 286.000, -3.625,  0.000 1.25E+00   2
+50   W49E2 286.000, -3.625,  0.000 W51E1 286.000,  3.625,  0.000 4.00E+00   1
+51   W50E2 286.000,  3.625,  0.000 W52E1 286.000, 17.750,  0.000 1.25E+00   2
+52   W51E2 286.000, 17.750,  0.000 W53E1 286.000, 63.750,  0.000 1.12E+00   6
+53   W52E2 286.000, 63.750,  0.000 W54E1 286.000,114.250,  0.000 8.75E-01   6
+54   W53E2 286.000,114.250,  0.000 W55E1 286.000,138.250,  0.000 6.25E-01   3
+55   W54E2 286.000,138.250,  0.000       286.000,193.125,  0.000 4.38E-01   7
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1           2    17 / 50.00   ( 17 / 50.00)      0.707       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+

Any transcription errors in the above models are strictly my own fault, and I shall gladly correct any found.
+

+
+ +

+
+

Updated 7-20-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Amateur Radio Page

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/8075.html b/content/yagi/8075.html new file mode 100644 index 0000000..40f2d27 --- /dev/null +++ b/content/yagi/8075.html @@ -0,0 +1,96 @@ + + + + + + Wire Beam for 80 and 75 Meters + + + + +
+

Notes on a Wire Beam for 80 and 75 Meters

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+ Wire beams for the lower HF bands still have a vital place for those who cannot field the hardware necessary for rotatable arrays at those frequencies. However, the CW and SSB ends of the 3.5-4.0 MHz amateur band are so far apart that a single beam will not have the necessary bandwidth to perform respectably at both ends. Add the bandwidth narrowing thinness of wire, in contrast to large aluminum tubing, and the situation seems to call for complex measures. +

Hanging a wire beam for 80 or 75 meters is difficult enough without having also to support complex matching networks. Separate beams appear to call for separate antennas and feedlines--again, a double weight. Enter open sleeve coupling. It is possible to construct beams for 80 and 75 and to position them so that feeding only the 80 meter driven element will provide adequate performance at both ends of the band.

+

The general outlines of such a 2-element wire beam appear in Figure 1. The higher frequency driven element--the one not connected to the feedline--is ahead of the driven 80-meter element, with the corresponding reflectors appropriately aligned.

+
+ +
+

To see what such a beam might look like in practice, I modeled a couple of versions using slightly different driven element spacings and slightly different basic driven-element-to-reflector spacings. In common, both version use #12 copper wire and both beams are 136' above ground, approximately 1/2 wavelength. At that height, the angle of maximum radiation is approximately 27 degrees, assuming as NEC does, level terrain.

+

As a suggestive beginning for refinement by builders, here are the dimensions of each version and the NEC-derived anticipated performance from one end of the band to the other.

+ 
Version 1:  Driven element spacing 3'; overall front-to-back distance 42'9"
+
+Dimensions:
+
+75 DE (no connex)  122'5" long  space =   0
+80 DE (coax conx)  134'0"               - 3'
+75 REF             128'4"               -36'8"
+80 REF             139'0"               -42'9"
+
+Predicted performance:
+FQ       Gain dBi    F-B dB     Feed Z ohms    SWR @ 75 ohm line
+3.5      11.4        11.5        47 - j 18      1.7
+3.55     11.0        13.0        76 - j  5      1.1
+3.6      10.3         8.0        88 - j  9      1.2
+3.65      9.2         3.7        79 - j 11      1.2
+3.7       8.7         2.5        52 + j  7      1.5  Reverse direction
+3.75      9.5         1.1        45 + j 81      4.0  Reverse direction
+3.8      11.6        11.7       158 + j 73      2.7
+3.85     11.2        11.6       107 + j  3      1.4
+3.9      10.8         9.8        51 + j 24      1.7
+3.95     10.1         9.1        21 - j 64      6.3
+4.0       8.2         9.7         8 + j106     28.0
+
+
+ 
Version 2:  Driven element spacing 3'6"; overall front-to-back distance 39'6"
+
+Dimensions:
+
+75 DE (no connex)  121'8" long  space =   0
+80 DE (coax conx)  133'0"               - 3'6"
+75 REF             127'5"               -33'2"
+80 REF             138'0"               -39'6"
+
+Predicted performance:
+FQ       Gain dBi    F-B dB     Feed Z ohms    SWR @ 75 ohm line
+3.5      11.2         6.8        28 - j 37      3.4
+3.55     11.3        14.0        55 - j  7      1.4
+3.6      11.7        10.3        82 - j  2      1.1
+3.65      9.9         5.9        86 - j 10      1.2
+3.7       8.4         1.6        68 - j  8      1.2
+3.75      9.9         7.3        37 + j 25      2.3  Reverse direction
+3.8      10.9         4.9        70 + j114      4.2
+3.85     11.4        12.4       147 + j 34      2.1
+3.9      10.9        10.6        72 + j 11      1.2
+3.95     10.3         9.5        29 + j 49      3.9
+4.0       9.0         9.7        11 + j 93     17.6
+
+

The two versions are peaked at slightly different points on the band, but there is little to choose between them. Indeed, with appropriate tweaking of reflector lengths and spacings, performance improvements can be garnered. However, improvements are more likely to be those suited to an individual's desired "main" frequency rather than to overall performance across the band.

+

The phrase "Reverse direction" refers to the forward lobe of the beam being in the reverse direction or toward the reflectors for the frequencies indicated. The 80-75 meter ham band is sufficiently wide, relative to the frequencies involved, that with a wire antenna, 3 beams would be required for full band coverage without reversal or excessive SWR somewhere along the way.

+

One limitation of these antennas relative to reality is that they were modeled flat, without the usual droop of wire. However, the absence of major differences between the two versions, despite the changes in driven element spacing and the D.E-to-reflector spacing suggest that droop alone will not seriously change performance.

+

75-ohm coax, with a choke or bead balun, seems the most versatile feed system for these antennas. At 80-75 meters, moderately high SWRs do not incur nearly the level of line losses as they do in the upper HF region; consequently, an ATU should allow matching to rigs with SWRs of 5:1 and under.

+

These notes are not intended to be definitive, but only suggestive of one more way to obtain gain and directivity in the 80-75 meter band. construction details will be dictated by available support structures, and final design will fit the refinements occasioned by specific operating goals. The models do suggest very strongly that open-sleeve coupling is not confined to upper HF beams and lower HF dipoles. A single-feed wire beam for both the CW and SSB portions of the 80-75 meter amateur band is both possible and practical.
+

+
+ +

+
+

Updated 4-9-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+

Go to Amateur Radio Page

+

Topics: HF Lower, Yagi


+ + diff --git a/content/yagi/80751.gif b/content/yagi/80751.gif new file mode 100644 index 0000000..a29a16b Binary files /dev/null and b/content/yagi/80751.gif differ diff --git a/content/yagi/bb.html b/content/yagi/bb.html new file mode 100644 index 0000000..2de931f --- /dev/null +++ b/content/yagi/bb.html @@ -0,0 +1,275 @@ + + + + + + Director/Driven Element 2-Element Yagis for 12 and 17 Meters + + + +
+

Director/Driven Element 2-Element Yagis
+ Some Ideas for 12 and 17 Meters

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+ I have in other notes made mention of the Director/Driven Element configuration of the 2-element Yagi. When pressed to maximum gain, these antennas are capable of over 7 dBi free space gain, about a dB higher than the conventional Reflector/Driven Element configuration tuned for maximum front-to-back ratio. However, these antennas have a low feedpoint impedance and fairly narrow band widths. +

Jerry Haigwood, W5JH, reminded me that with a beta match, the low impedance can be overcome, and on the WARC bands, narrow bandwidth is not a real concern. Jerry is exactly correct, and his comments and other good ideas raised some interesting design possibilities.

+

Jerry prefers spacing his director about 0.08 wl from the driven element. The range from 0.07 to 0.09 wl is a good choice. Even though one might get a bit more gain from the antenna, the 1/12th wl spacing holds the feedpoint impedance of a D/DE Yagi set for a good front-to-back ratio at about 20 ohms, which is quite workable.

+
+ +
+

Figure 1 shows the construction of a reasonable D/DE Yagi. The 1" elements of this 10-meter model are feasible hardware store material, but the model is designed less to build than to set the properties of the genre of beam. With wider spacing, the antenna gain drops off, although the feedpoint impedance goes up. Closer spacing raises gain for a while, but continuously drops the feedpoint impedance. The model antenna, set for 28.5 MHz, has a feedpoint impedance of 20.5 - j23.5 ohms, just about right for a hairpin or inductor beta match of very conventional design.

+

Incidentally, HAMCALC has a very nice program for calculating beta matches, including the hairpin. The equivalent inductance is also given, which permits you to use another program on HAMCALC to create a coil instead. See the basic "Radio" page for the address of VE3ERP, the master of this suite of GW BASIC utility programs.

+

With only slight readjustments, the basic 2-element D/DE Yagi can be swept through a variety of radiation patterns. Three of them are illustrated in Figure 2. The Maximum Front-to-Back settings will yield a modest gain (about 6.5 dBi free space) and a very good (greater than 20 dB) front-to-back ratio with a feedpoint impedance of about 20 ohms. At the other extreme, maximum gain provides over 7 dBi gain but under 10 dB front-to-back and a feedpoint impedance of about 10 ohms. There is a midpoint setting shown in the patterns, where the gain is intermediate, the front-to-back is respectable, and the feedpoint Z is about 15 ohms.

+
+ +
+

These setting are not so very far apart, and a frequency difference of about 1.5% will sweep you through them. A little further, and you will experience pattern reversal. On 10 meters, this is under 400 kHz. So unless your needs are very frequency specific, the D/DE Yagi may not be a good design choice.

+

However, on the WARC bands, no such problems occur. On 12 and 17 meters, the available bandwidth is about 1/2 of 1% of the frequency, and the D/DE design can easily cover this spread with stable characteristics.

+

Back-to-Back 12-17-Meter Yagis

+

One of the chief attractions of the D/DE design is the short boom length required for the antenna. For example, 0.07 wl is only 3.8' at 17 meters (with elements between 26 and 28') and 2.75' at 12 meters (with elements between 18 and 20'). Modeling suggests that individual antennas for these two bands show very little interaction when placed back-to-back and separated by about a foot or more. Hence, an 8' boom would hold back-to- back individual antennas.

+

Individual antennas, however, require separate feedlines or a switching system. We can make life even simpler and cut the feedline needs down to 1 feedline. By placing the driven elements close together, we can use open-sleeve coupling. This involves connecting the feedline permanently to the 17 meter driven element and letting it excite the 12-meter element when fed with 12 meter energy. The required spacing is just about 4" which requires that we retune the 12 meter elements for this configuration. Once done, however, the two beams do their jobs with few signs of other interactions. Moreover, the two antennas require only a 7' boom.

+

To test this idea, I created models of a double D/DE Yagi using open sleeve coupling and placed back-to-back. I used an aggressive stepped diameter tubing schedule to keep the antenna array as light as possible. Figure 3 shows a sketch of the overall dimensions of the antenna.

+
+ +
+

Since the tubing schedule would not show well in the sketch, here is the antenna description file with a detailed list of lengths and diameters of aluminum tubing.

+ 
              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : ft)  Conn. -- End 2 (x,y,z : ft)  Dia(in)
+
+12-meter director
+1           -9.570,  3.080,  0.000  W2E1  -6.500,  3.080,  0.000 3.75E-01
+2     W1E2  -6.500,  3.080,  0.000  W3E1  -2.500,  3.080,  0.000 5.00E-01
+3     W2E2  -2.500,  3.080,  0.000  W4E1  -1.000,  3.080,  0.000 6.25E-01
+4     W3E2  -1.000,  3.080,  0.000  W5E1   1.000,  3.080,  0.000 7.50E-01
+5     W4E2   1.000,  3.080,  0.000  W6E1   2.500,  3.080,  0.000 6.25E-01
+6     W5E2   2.500,  3.080,  0.000  W7E1   6.500,  3.080,  0.000 5.00E-01
+7     W6E2   6.500,  3.080,  0.000         9.570,  3.080,  0.000 3.75E-01
+12-meter driven element
+8          -10.120,  0.330,  0.000  W9E1  -6.500,  0.330,  0.000 3.75E-01
+9     W8E2  -6.500,  0.330,  0.000 W10E1  -2.500,  0.330,  0.000 5.00E-01
+10    W9E2  -2.500,  0.330,  0.000 W11E1  -1.000,  0.330,  0.000 6.25E-01
+11   W10E2  -1.000,  0.330,  0.000 W12E1   1.000,  0.330,  0.000 7.50E-01
+12   W11E2   1.000,  0.330,  0.000 W13E1   2.500,  0.330,  0.000 6.25E-01
+13   W12E2   2.500,  0.330,  0.000 W14E1   6.500,  0.330,  0.000 5.00E-01
+14   W13E2   6.500,  0.330,  0.000        10.120,  0.330,  0.000 3.75E-01
+17-meter director
+15         -13.000, -3.785,  0.000 W16E1  -9.000, -3.785,  0.000 5.00E-01
+16   W15E2  -9.000, -3.785,  0.000 W17E1  -3.500, -3.785,  0.000 6.25E-01
+17   W16E2  -3.500, -3.785,  0.000 W18E1  -1.500, -3.785,  0.000 7.50E-01
+18   W17E2  -1.500, -3.785,  0.000 W19E1   1.500, -3.785,  0.000 8.75E-01
+19   W18E2   1.500, -3.785,  0.000 W20E1   3.500, -3.785,  0.000 7.50E-01
+20   W19E2   3.500, -3.785,  0.000 W21E1   9.000, -3.785,  0.000 6.25E-01
+21   W20E2   9.000, -3.785,  0.000        13.000, -3.785,  0.000 5.00E-01
+17-meter driven element
+22         -13.850,  0.000,  0.000 W23E1  -9.000,  0.000,  0.000 5.00E-01
+23   W22E2  -9.000,  0.000,  0.000 W24E1  -3.500,  0.000,  0.000 6.25E-01
+24   W23E2  -3.500,  0.000,  0.000 W25E1  -1.500,  0.000,  0.000 7.50E-01
+25   W24E2  -1.500,  0.000,  0.000 W26E1   1.500,  0.000,  0.000 8.75E-01
+26   W25E2   1.500,  0.000,  0.000 W27E1   3.500,  0.000,  0.000 7.50E-01
+27   W26E2   3.500,  0.000,  0.000 W28E1   9.000,  0.000,  0.000 6.25E-01
+28   W27E2   9.000,  0.000,  0.000        13.850,  0.000,  0.000 5.00E-01
+

The feedpoint is on wire #25, the center of the 17-meter driven element. Do not expect the model to be exact on the spacing for the open sleeve coupling distance. Rather, experiment and measure the impedance on both bands as you work.

+

The center of gravity should be just on the 17-meter side of the 17-meter driven element, minimizing the need for coax to run along the boom. Almost any boom in the 1.25" range should do, even a length of the lighter TV mast (which is too light for mast use), as long as it is weather protected so that it does not rust out in a year. Even hardware store aluminum with a wall thickness of 0.055" should handle the job, although inserts at the element clamping points should be used to prevent tube crush. Alternatively, you can use short sections of the next tubing size up as strengtheners at the element clamping points. The model is designed for elements insulated from the boom, so if you use direct clamping to the boom, expect to adjust element lengths a bit.

+

The feedpoint impedance is just about 21 ohms resonant for both frequency ranges. This permits the use of a broad-band balun to feed the antenna and effect an impedance transformation to the 50-ohm coax line. Alternatively, the antenna lengths can be reset to show capacitive reactance. A Beta match usually is effective not only at the frequency for which it is designed, but as well at higher frequencies, and with a little juggling of dimensions, a 2-band match should be obtained.

+
+ +
+

Figure 4 shows the patterns of the two antennas in one back-to-back pattern at free space. At 70' up, the gain is in the neighborhood of 12 dBi, a little under 5 dB better than a dipole, and with a strong front-to-back ratio.

+

The back-to-back open-sleeve D/DE Yagis are not world beaters, but they are a. inexpensive to build, and b. lots better than some of the antennas being pressed into service for these bands. The entire antenna, boom and all, should weight in at less than 20 pounds, making it a good candidate for stacking on top of an existing antenna.

+

If you separate the two antennas, you will have to adjust the dimensions--especially of the 12-meter model--for independent use. Likewise, if you use different materials or a different schedule of diameter steps, you will also have to adjust the dimensions to restore the pattern and the feedpoint impedance. But that comes with the territory of antenna experimenting and home-brewing.

+

12-17-Meter 2-Element Yagis Facing the Same Way

+

Is it feasible to place the two antennas in the same plane using the open-sleeve coupling system for a single feed line? The answer is yes and no. Yes, it is possible to develop a set of dimensions that will produce good performance at a desirable feed impedance for one frequency within the upper band. (The lower band is not affected.) However, both elements for the upper band are inside the elements for the lower band, producing a "cage" effect. The chief problem created is an extreme narrow bandwidth for desirable characteristics. In terms of this design, when the beams face in opposite directions, they show an operating bandwidth for under 2:1 SWR in excess of the 100 kHz width of the bands. When caged (or facing in the same direction), the operating bandwidth of the upper band beam is far less than the width of the band. For building and tuning, this also means that hitting the precisely needed dimensions is very tricky--and the settings are very susceptible to the need for change with changes of antenna height below about 1.5 wl. Hence, my recommendation is for opposing directions or for combinations of beam types, where the upper band antenna is "uncaged." (Yes, I know, I watch too many wildlife documentaries and it is affecting my choice of terminology.)

+

There is an alternative that achieves the uncaging. It has the disadvantages, relative to the Janus-faced design above, of requiring a longer boom (10') and sacrificing a good bit of 17-meter front-to-back ratio. On the other hand, the beams face the same direction and require a single directly-matched 50-Ohm feed to cover both bands.

+

The design is a DE-Reflector for 17 and a DE-Director for 12. By keeping the elements for each band together, they remain uncaged. In addition, there is a slight forward stagger effect so that the beams have marginally higher values than when they are independent. With the spacing used, the feedpoint impedance on both bands is close to 50 Ohms. The outline dimensions are shown in Figure 5.

+
+ +
+

The same caution about spacing of the open-sleeve coupled driven elements applies to both designs: the builder will have to adjust both length and spacing of the 12-meter slaved driver, since the modeling program is close to its limits for handling closely spaced elements of different lengths. However, the model should be quite close.

+

In addition, the antenna was designed with a tapering schedule in place. Here is the detailed wire table.

+ 
              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+12-meter Director
+1           -9.500,  3.130,  0.000  W2E1  -6.500,  3.130,  0.000 3.75E-01   5
+2     W1E2  -6.500,  3.130,  0.000  W3E1  -2.500,  3.130,  0.000 5.00E-01   5
+3     W2E2  -2.500,  3.130,  0.000  W4E1  -1.000,  3.130,  0.000 6.25E-01   2
+4     W3E2  -1.000,  3.130,  0.000  W5E1   1.000,  3.130,  0.000 7.50E-01   3
+5     W4E2   1.000,  3.130,  0.000  W6E1   2.500,  3.130,  0.000 6.25E-01   2
+6     W5E2   2.500,  3.130,  0.000  W7E1   6.500,  3.130,  0.000 5.00E-01   5
+7     W6E2   6.500,  3.130,  0.000         9.500,  3.130,  0.000 3.75E-01   5
+12-meter Driver
+8          -10.070,  0.380,  0.000  W9E1  -6.500,  0.380,  0.000 3.75E-01   5
+9     W8E2  -6.500,  0.380,  0.000 W10E1  -2.500,  0.380,  0.000 5.00E-01   5
+10    W9E2  -2.500,  0.380,  0.000 W11E1  -1.000,  0.380,  0.000 6.25E-01   2
+11   W10E2  -1.000,  0.380,  0.000 W12E1   1.000,  0.380,  0.000 7.50E-01   3
+12   W11E2   1.000,  0.380,  0.000 W13E1   2.500,  0.380,  0.000 6.25E-01   2
+13   W12E2   2.500,  0.380,  0.000 W14E1   6.500,  0.380,  0.000 5.00E-01   5
+14   W13E2   6.500,  0.380,  0.000        10.070,  0.380,  0.000 3.75E-01   5
+17-meter Driver
+15         -13.100,  0.000,  0.000 W16E1  -9.500,  0.000,  0.000 3.75E-01   4
+16   W15E2  -9.500,  0.000,  0.000 W17E1  -6.750,  0.000,  0.000 5.00E-01   4
+17   W16E2  -6.750,  0.000,  0.000 W18E1  -4.000,  0.000,  0.000 6.25E-01   4
+18   W17E2  -4.000,  0.000,  0.000 W19E1   4.000,  0.000,  0.000 7.50E-01  11
+19   W18E2   4.000,  0.000,  0.000 W20E1   6.750,  0.000,  0.000 6.25E-01   4
+20   W19E2   6.750,  0.000,  0.000 W21E1   9.500,  0.000,  0.000 5.00E-01   4
+21   W20E2   9.500,  0.000,  0.000        13.100,  0.000,  0.000 3.75E-01   4
+17-meter Reflector
+22         -14.100, -6.800,  0.000 W23E1  -9.500, -6.800,  0.000 3.75E-01   4
+23   W22E2  -9.500, -6.800,  0.000 W24E1  -6.750, -6.800,  0.000 5.00E-01   4
+24   W23E2  -6.750, -6.800,  0.000 W25E1  -4.000, -6.800,  0.000 6.25E-01   4
+25   W24E2  -4.000, -6.800,  0.000 W26E1   4.000, -6.800,  0.000 7.50E-01  11
+26   W25E2   4.000, -6.800,  0.000 W27E1   6.750, -6.800,  0.000 6.25E-01   4
+27   W26E2   6.750, -6.800,  0.000 W28E1   9.500, -6.800,  0.000 5.00E-01   4
+28   W27E2   9.500, -6.800,  0.000        14.100, -6.800,  0.000 3.75E-01   4
+

As always, since the taper schedule affects performance, you will have to adjust dimensions to suit the materials you have on hand. Four light-weight elements on a 10' boom should not stress an extended mast used to stack this simple beam above a heavy-weight tri-bander.

+

As Figure 6 shows, the gain of the two beams is about the same--between 6.3 and 6.4 dBi in free space. However, the 17-meter front-to-back ratio is reduced considerably. However, until the WARC bands become seriously over-crowded, this may not be a major problem.

+
+ +
+

Back-to-Back with a 30-Meter Dipole Between

A couple of requests came in for an odd combo: a 30-m dipole wit the back to back 17-12 Yagi combo. This combo would fit on an 8' boom, with the big dipole (48.6') centered at the mast--but perhaps due to the greater weight of the 17-meter Yagi and the longer boom to that side, offset so that the dipole did not sit right on the mast. Such an antenna is possible, and the sketch shows its outline (Figure 7) +
+ +
+

The dipole is now the fed element, with both Yagi drivers open-sleeve coupled. The frequency ratio for the 17-meter driver (10.125:18.118) is low enough to make it easy to preserve the full performance of the 2-element DE-Dir beam (6.5 dBi/28 dB F-B) with a 53-Ohm feedpoint impedance. The frequency ratio for the 12-meter driver (10.125:24.95) is large enough to adversely affect performance to a small degree (6.3 dBi/20 dB F-B) with a 47-Ohm feedpoint impedance. The dipole pattern is slightly flattened as the Yagis stretch it in the planar directions--the amount is about 0.2 dB. The dipole impedance in free space showed about 78 Ohms. In all cases, the impedance figures are good enough for standard coax feed systems.

+

Here is the modeled wire table for the 3-band antenna. Unfortunately, I lack ftp capabilities and cannot provide a downloadable .NEC or .EZ file.

+ 
              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+12-m director
+1           -9.600,  3.340,  0.000  W2E1  -6.500,  3.340,  0.000 3.75E-01   5
+2     W1E2  -6.500,  3.340,  0.000  W3E1  -2.500,  3.340,  0.000 5.00E-01   5
+3     W2E2  -2.500,  3.340,  0.000  W4E1  -1.000,  3.340,  0.000 6.25E-01   2
+4     W3E2  -1.000,  3.340,  0.000  W5E1   1.000,  3.340,  0.000 7.50E-01   3
+5     W4E2   1.000,  3.340,  0.000  W6E1   2.500,  3.340,  0.000 6.25E-01   2
+6     W5E2   2.500,  3.340,  0.000  W7E1   6.500,  3.340,  0.000 5.00E-01   5
+7     W6E2   6.500,  3.340,  0.000         9.600,  3.340,  0.000 3.75E-01   5
+12-m driver
+8          -10.050,  0.600,  0.000  W9E1  -6.500,  0.600,  0.000 3.75E-01   5
+9     W8E2  -6.500,  0.600,  0.000 W10E1  -2.500,  0.600,  0.000 5.00E-01   5
+10    W9E2  -2.500,  0.600,  0.000 W11E1  -1.000,  0.600,  0.000 6.25E-01   2
+11   W10E2  -1.000,  0.600,  0.000 W12E1   1.000,  0.600,  0.000 7.50E-01   3
+12   W11E2   1.000,  0.600,  0.000 W13E1   2.500,  0.600,  0.000 6.25E-01   2
+13   W12E2   2.500,  0.600,  0.000 W14E1   6.500,  0.600,  0.000 5.00E-01   5
+14   W13E2   6.500,  0.600,  0.000        10.050,  0.600,  0.000 3.75E-01   5
+17-m driver
+15         -13.780, -0.620,  0.000 W16E1  -9.000, -0.620,  0.000 5.00E-01   6
+16   W15E2  -9.000, -0.620,  0.000 W17E1  -3.500, -0.620,  0.000 6.25E-01   6
+17   W16E2  -3.500, -0.620,  0.000 W18E1  -1.500, -0.620,  0.000 7.50E-01   3
+18   W17E2  -1.500, -0.620,  0.000 W19E1   1.500, -0.620,  0.000 8.75E-01   5
+19   W18E2   1.500, -0.620,  0.000 W20E1   3.500, -0.620,  0.000 7.50E-01   3
+20   W19E2   3.500, -0.620,  0.000 W21E1   9.000, -0.620,  0.000 6.25E-01   6
+21   W20E2   9.000, -0.620,  0.000        13.780, -0.620,  0.000 5.00E-01   6
+17-m director
+22         -13.050, -4.480,  0.000 W23E1  -9.000, -4.480,  0.000 5.00E-01   6
+23   W22E2  -9.000, -4.480,  0.000 W24E1  -3.500, -4.480,  0.000 6.25E-01   6
+24   W23E2  -3.500, -4.480,  0.000 W25E1  -1.500, -4.480,  0.000 7.50E-01   3
+25   W24E2  -1.500, -4.480,  0.000 W26E1   1.500, -4.480,  0.000 8.75E-01   5
+26   W25E2   1.500, -4.480,  0.000 W27E1   3.500, -4.480,  0.000 7.50E-01   3
+27   W26E2   3.500, -4.480,  0.000 W28E1   9.000, -4.480,  0.000 6.25E-01   6
+28   W27E2   9.000, -4.480,  0.000        13.050, -4.480,  0.000 5.00E-01   6
+30-m dipole
+29         -24.300,  0.000,  0.000 W30E1 -17.500,  0.000,  0.000 5.00E-01   5
+30   W29E2 -17.500,  0.000,  0.000 W31E1 -12.650,  0.000,  0.000 6.25E-01   5
+31   W30E2 -12.650,  0.000,  0.000 W32E1  -7.150,  0.000,  0.000 7.50E-01   5
+32   W31E2  -7.150,  0.000,  0.000 W33E1  -5.150,  0.000,  0.000 8.75E-01   2
+33   W32E2  -5.150,  0.000,  0.000 W34E1  -2.000,  0.000,  0.000 1.00E+00   3
+34   W33E2  -2.000,  0.000,  0.000 W35E1   2.000,  0.000,  0.000 1.12E+00   3
+35   W34E2   2.000,  0.000,  0.000 W36E1   5.150,  0.000,  0.000 1.00E+00   3
+36   W35E2   5.150,  0.000,  0.000 W37E1   7.150,  0.000,  0.000 8.75E-01   2
+37   W36E2   7.150,  0.000,  0.000 W38E1  12.650,  0.000,  0.000 7.50E-01   5
+38   W37E2  12.650,  0.000,  0.000 W39E1  17.500,  0.000,  0.000 6.25E-01   5
+39   W38E2  17.500,  0.000,  0.000        24.300,  0.000,  0.000 5.00E-01   5
+

As with the other designs, you will have to experiment for other taper schedules to the elements. Likewise, the exact lengths and spacing of the drivers from the dipole will also be am tter of experimentation.

+

If you shorten the dipole by any other means than a capacity hat on each end, the performance of the Yagis will be thrown off due to the altered current levels along parts of the dipole providing the drive for the coupled Yagi drivers. Even mid-element loads throw everything off. Capacity hats do preserve the current levels along the shortened dipole at the same magnitude as with a full size dipole; however, the hats will necessarily by large enough to possible couple to the Yagi driver ends.

+

No doubt further modeling time could yield improved performance from the 12-m Yagi, with many iterations of element length, spacing, and spacing from the dipole changes. But the figures shown here should suffice as a starting point for individual experimentation.

+

A Forward-Facing 17-12 Combo with Higher Gain on 12

It is possible to obtain greater gain on 12 meters with a forward-facing combination of a Driver-Reflector Yagi for 17 and a driver-director Yagi for 12, using the same forward-stagger and open-sleeve principles of the earlier 4-element (2 per band) we looked at earlier. The way to more gain is to add another director for 12 meters. The general outline looks like Figure 8. +
+ +
+

If we compare this 5-element Yagi to the forward-facing 4-element version earlier, we shall see several differences. First, the reflector spacing has been increased. The chief result of this move is to increase the resistive component of the feedpoint impedance. The essential performance on 17 is not changed. You can feel free to use any spacing from the close spacing of the 4-element version to the wide spacing of this version.

+

Second, adding a second director changes the director dimensions and lengthens the boom considerable--a total of 17' for the entire array. However, besides obtaining better gain on 12, the array is less sensitive to minor changes of length of the 2 directors. What you might change slightly by a small alteration of one element's length can be restored by slightly altering the length of the other director.

+

The NEC-4 modeled performance of this array is given in the following table:

+ 
Freq           Gain FS        F-B       R +/- jX       SWR
+18.068         6.30           11.89     62.1 - j 4.7   1.26
+18.118         6.25           11.92     64.2 - j 3.1   1.29
+18.168         6.20           11.91     66.3 - j 1.6   1.32
+
+24.89          7.16           13.75     57.1 + j 6.9   1.20
+24.94          7.21           13.82     54.9 + j 8.9   1.22
+24.95          7.26           13.87     52.8 + j11.1   1.25
+

It is possible to optimize this design further. The 17-meter section can be set closer to 50 Ohms, although significant increases in gain and front-to-back ratio are not possible with only 2 elements. The gain and front-to-back ratio on 12 can also be altered, but improving one results in decreases to the other. This version has opted for gain and only a modest front-to-back ratio. Comparative patterns for the 2 bands appear in Figure 9.

+
+ +
+

As always, models of open sleeve coupling are approximate only. Therefore, expect to play a bit with the length of the 12-meter slaved driver and its spacing from the 17-meter fed driver to achieve the desired 12-meter feedpoint impedance. Such adjustments have little or no effect on the 17-meter feedpoint impedance or other operating parameters on that band. Also, if you select a different tapering schedule for your elements, do two things. 1. Check out the potential durability of the element, using a program like YagiStress or use a model of element taper that has a proven record. 2. Adjust the element lengths to suit the Leeson corrected substitute uniform diameter elements that are equivalent to the ones shown here. This latter task can be handled with one of the antenna modeling programs. The details of the model on which this note is based appear in the following EZNEC antenna description.

+ 
              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : ft)  Conn. --- End 2 (x,y,z : ft)   Dia(in) Segs
+17-Meter Reflector
+1          -14.100,  0.000,  0.000  W2E1 -12.250,  0.000,  0.000 5.00E-01   2
+2     W1E2 -12.250,  0.000,  0.000  W3E1  -9.500,  0.000,  0.000 6.25E-01   3
+3     W2E2  -9.500,  0.000,  0.000  W4E1  -6.750,  0.000,  0.000 7.50E-01   3
+4     W3E2  -6.750,  0.000,  0.000  W5E1  -4.000,  0.000,  0.000 8.75E-01   3
+5     W4E2  -4.000,  0.000,  0.000  W6E1   4.000,  0.000,  0.000 1.00E+00   9
+6     W5E2   4.000,  0.000,  0.000  W7E1   6.750,  0.000,  0.000 8.75E-01   3
+7     W6E2   6.750,  0.000,  0.000  W8E1   9.500,  0.000,  0.000 7.50E-01   3
+8     W7E2   9.500,  0.000,  0.000  W9E1  12.250,  0.000,  0.000 6.25E-01   3
+9     W8E2  12.250,  0.000,  0.000        14.100,  0.000,  0.000 5.00E-01   2
+17-Meter Fed Driver
+10         -13.167,  9.158,  0.000 W11E1 -11.250,  9.158,  0.000 5.00E-01   2
+11   W10E2 -11.250,  9.158,  0.000 W12E1  -8.500,  9.158,  0.000 6.25E-01   3
+12   W11E2  -8.500,  9.158,  0.000 W13E1  -5.750,  9.158,  0.000 7.50E-01   3
+13   W12E2  -5.750,  9.158,  0.000 W14E1  -4.000,  9.158,  0.000 8.75E-01   3
+14   W13E2  -4.000,  9.158,  0.000 W15E1   4.000,  9.158,  0.000 1.00E+00   9
+15   W14E2   4.000,  9.158,  0.000 W16E1   5.750,  9.158,  0.000 8.75E-01   3
+16   W15E2   5.750,  9.158,  0.000 W17E1   8.500,  9.158,  0.000 7.50E-01   3
+17   W16E2   8.500,  9.158,  0.000 W18E1  11.250,  9.158,  0.000 6.25E-01   3
+18   W17E2  11.250,  9.158,  0.000        13.167,  9.158,  0.000 5.00E-01   2
+12-meter "Slave" Driver
+19          -9.833,  9.575,  0.000 W20E1  -6.250,  9.575,  0.000 3.75E-01   4
+20   W19E2  -6.250,  9.575,  0.000 W21E1  -2.500,  9.575,  0.000 5.00E-01   4
+21   W20E2  -2.500,  9.575,  0.000 W22E1  -0.500,  9.575,  0.000 6.25E-01   3
+22   W21E2  -0.500,  9.575,  0.000 W23E1   0.500,  9.575,  0.000 7.50E-01   1
+23   W22E2   0.500,  9.575,  0.000 W24E1   2.500,  9.575,  0.000 6.25E-01   3
+24   W23E2   2.500,  9.575,  0.000 W25E1   6.250,  9.575,  0.000 5.00E-01   4
+25   W24E2   6.250,  9.575,  0.000         9.833,  9.575,  0.000 3.75E-01   4
+12-Meter Director 1
+26          -9.500, 10.683,  0.000 W27E1  -6.250, 10.683,  0.000 3.75E-01   4
+27   W26E2  -6.250, 10.683,  0.000 W28E1  -2.500, 10.683,  0.000 5.00E-01   4
+28   W27E2  -2.500, 10.683,  0.000 W29E1  -0.500, 10.683,  0.000 6.25E-01   3
+29   W28E2  -0.500, 10.683,  0.000 W30E1   0.500, 10.683,  0.000 7.50E-01   1
+30   W29E2   0.500, 10.683,  0.000 W31E1   2.500, 10.683,  0.000 6.25E-01   3
+31   W30E2   2.500, 10.683,  0.000 W32E1   6.250, 10.683,  0.000 5.00E-01   4
+32   W31E2   6.250, 10.683,  0.000         9.500, 10.683,  0.000 3.75E-01   4
+12-Meter Director 2
+33          -8.833, 16.967,  0.000 W34E1  -6.250, 16.967,  0.000 3.75E-01   4
+34   W33E2  -6.250, 16.967,  0.000 W35E1  -2.500, 16.967,  0.000 5.00E-01   4
+35   W34E2  -2.500, 16.967,  0.000 W36E1  -0.500, 16.967,  0.000 6.25E-01   3
+36   W35E2  -0.500, 16.967,  0.000 W37E1   0.500, 16.967,  0.000 7.50E-01   1
+37   W36E2   0.500, 16.967,  0.000 W38E1   2.500, 16.967,  0.000 6.25E-01   3
+38   W37E2   2.500, 16.967,  0.000 W39E1   6.250, 16.967,  0.000 5.00E-01   4
+39   W38E2   6.250, 16.967,  0.000         8.833, 16.967,  0.000 3.75E-01   4
+

The element taper used here is an adaptation of a commercial design for other bands. 6061-T6 tubing or its equivalent is available from numerous sources. This beam is far from optimized to its maximum possible performance. However, it may provide a further alternative for experimentation. Since numerous commercial beams use booms in the vicinity of 18', a design such as this makes a possible conversion project once you spring for the very long boom tri-bander to use on 20-15-10 meters

+

The End Result is This . . .

+

As W5JH reminded me, the D/DE 2-element Yagi has a natural home on the WARC bands, especially 12 and 17. Matching is straight forward, and performance will be stable across these narrow bands. 0.07 to 0.09 wl makes a good element spacing for a 20-ohm feedpoint impedance, an easy beta match. Combining DE-Dir and DE-Ref designs is certainly feasible and can effect simplicities of matching and use. Combining back-to-back Yagis with a 30-meter dipole is also possible.

+

Whether you go 2-faced or long-boomed, these designs and innumerable possible variations on them should serve many needs on 12 and 17. Moreover, as this little exercise has shown, the possibilities for experimentation are endless.

+
+ +

+
+

Updated 7-25-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Amateur Radio Page

+

Topics: HF Upper, Yagi


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+

What Can We Expect from a 2-Element Beam?

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

I have heard lots of 2-element Yagi performance numbers bandied about over the years. Some are reasonable and well explained. Some are reasonable, but not well-explained. Some are unreasonable and demand explanation. The numbers are disparate enough to keep 2-element Yagi performance a mystery to the relative newcomer.

+

Having modeled and built a very large number of 2-element Yagis over the years, I thought a refresher might be in order, if only to clarify what count as reasonable expectations. The information is available in almost any solid reference, but perhaps a different type of presentation might be useful. If this is your first entry to these notes, I recommend that you read the parts in order.

+

The refresher is long and broken into a number of sections. The original version of this small series had no illustrations, but only tabular data. Since 9 years have passed since the original 1997 version of the notes, I have decided to rewrite and expand some of the coverage. In the process, I have re-modeled everything, since software has advanced considerably over the near-decade since I last examined this work in detail. Mostly, I have added some graphics to make the notes easier to digest. For example, Fig. 1.

+
+ +
+

The sketch shows the elements (but not the boom or the mast) of 3 types of 2-element beams, only 2 of which are Yagis. 2-element Yagi beams come in two varieties: reflector-driver arrays and driver-director arrays. Do not think of a beam like a flashlight. Consider the beam's forward direction, that is the direction in which signals are strongest (both transmitting and receiving). The reflector is simply any element to the rear of the driver, while a director is simply any element forward of the driver. For most purposes, but certainly not for all, the reflector-driver version is the more popular--and for some very good reasons that we shall note along the way. The driver-director version has some interesting properties that suit it to special purposes.

+

The third 2-element beam is not a Yagi. Rather, it uses a current phasing line between the elements. Only one of several possible versions appears here--the ZL-Special variety. However, one might redesign the array to have the feedpoint at the center, at the rear, or somewhere else along the phasing line. Since I have dealth extensively with phased arrays in another series of notes, we shall stick to 2-element Yagis in this series. (For information on horizontal phased arrays, see "Some Notes on Two-Element Horizontal Phased Arrays" In fact, most of the notes will apply to the reflector-driver type of 2-element Yagi because it is so versatile.

+
+

Contents

+
+
+ Part 1: Method, Units of Measure, and the Dipole Standard of Reference +

Part 2: The Full-Size 2-Element Yagi

+

Part 3: Shortened Dipoles and Capacity Hat Yagis

+

Part 4: Loaded Yagis

+

Part 5: Strategies for Improving Forward and Rearward Performance

+
+
+ +
+

Updated 05-09-1997, 04-25-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Yagi


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+

What Can We Expect from a 2-Element Beam?

+
+
+

Part 1: Method, Units of Measure, and the Dipole Standard of Reference

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+
+

Method

+
A 2-element Yagi can be configured either as a director and driven element or as a driven element and reflector. We shall concentrate on the latter, because it is the most common and perhaps the most versatile configuration used. +

Developing a basic understanding of 2-element Yagis requires a consistent method. My method will be computer antenna modeling, using a variety of software: MININEC, NEC-2, and NEC-4. The advantage of the latter two engines is the availability of the Sommerfeld-Norton ground equations for more accurate modeling of antennas over real ground. However, some results will be crosschecked with MININEC in order to understand any differences that may arise. Models are convergence tested and use more than the minimum recommended number of segments per half wavelength. Ground parameters will be average earth throughout.

+

Frequency: All models will be for 10-meters, with a design center of 29 MHz. Although this frequency is well up the band from the region of greatest activity, it allows an examination of performance curves that cover maximum gain, maximum front-to-back ratio, and feedpoint impedance while trying to stay within the ham band. However, what applies to 10 meters also applies to all other ham bands with suitable adjustments.

+

Element Diameter: The 10-meter models will employ single diameter aluminum elements. (Real elements may use stepped-diamet4er elements or a "tapered-diameter schedule." Such elements are a special topic all unto itself. In general, if we taper the diameter as we move away from the element center, then the element will be longer than an element using a uniform diameter, even if the average tapered element diameter is somewhat larger than the uniform-diameter element. In fact, changing the taper schedule may call for a change in some element lengths to return a design to its original performance specifications.) I have chosen 0.375" (3/8") elements because they scale well to other bands. The equivalencies from band to band for element diameter appear in Table 1:

+
+ +
+

In fact, all antennas for 10 meters noted below have been scaled for each of the ham bands mentioned, and--as expected--give identical performance figures. When scaling an antenna, the diameter changes slowly within any ham band, so picking the closest real value to a calculated size usually does no harm to a design. However, picking a random value can create problems. In the table, each diameter is about the same fraction of a wavelength for each band.

+

Scaling. The idea of scaling an antenna from one band to another often creates a bit of confusion for newcomers. If we wish to scale the dimensions of an antenna for 10 meters to 20 meters, let's first take the ratio of the old frequency to the new frequency--and use some precision in the process. For example, if the 10-meter design is for 29.0 MHz and the new or scaled design is for 14.2 MHz, then the ratio of old to new is 29.5/14.2 or 2.077.

+

Next, lets multiply all dimensions by the scaling ratio. The dimensions include the length of each element, the spacing between elements, and the diameter of the element. Most casual builders forget this last factor. Indeed, it is common for newcomers to see a magazines article and think that they can build the antenna from whatever materials may be convenient. If we are dealing with very thin wire (for example, AWG #12 wire is very thin as a function of a wavelength on 40 meters), then no great harm occurs. However, for fatter elements, such as the tubing used in beams, changing the element diameter will throw the design off frequency and out of its original design specifications.

+

The bottom line is simple: if you cannot scale all of the dimensions to a new frequency, then you will have to adjust the complete dimension set for the new frequency. That task is not a casual one.

+

Antenna Height above Ground: When we work with antennas and take the ground into consideration, we add another factor into the analysis. Antenna heights will be given in fractions of a wavelength as well as feet. This procedure will permit more ready scaling of results to antennas designed for other bands. As a reference, the Table 2 lists the heights of an antenna at 29 MHz in terms of both feet and fractions of a wavelength. Heights in feet are rounded to the nearest tenth of a foot.

+
+ +
+

Scaling for lower ham bands by up to a factor of 8 should introduce no significant errors in results. Note that although heights of antennas for 10 meters would rarely be placed at a 4' level, antenna heights for the lowest amateur bands are often forced to correspondingly low heights. An 80-meter dipole at 35' is very close to 1/8 wavelength above ground.

+

MININEC models of antennas at a height of 1/8 wavelength are not reliable, since the program only begins to approach reliability at antenna heights of 0.2 wavelength or greater. (One highly corrected MININEC program, Antenna Model, has grafted the NEC ground system to its MININEC core with very good results.) NEC with Sommerfeld-Norton (S-N) ground implemented is reliable at the lower heights.

+

None of the models will press any of the other internal modeling limitations. All elements will be of a single diameter and linear, thus assuring easy convergence of results. Indeed, NEC-2 and NEC-4 should provide identical results, +/-1 digit in the last decimal place of the output.

+

Models do have other limitations. Modeling programs assume level uniform terrain. Local variations can change some performance figures, such as the elevation angle of maximum radiation and feedpoint impedance. However, they do not change the basic expectation limits for any given design when related to other designs, since each design will be equally affected by the local terrain variations.

+
+

Units of Measure

+
One of the most confusing aspects of antenna performance figures lies in the units of measure. Therefore, let me explain the units used here, working from the least confusing to the most confusing. +

SWR (standing wave ratio). SWR, wherever apt to produce a curve, will be given relative to the resonate impedance of the test model at the design frequency. Hence, all antennas modeled will show close to 1:1 SWR at or close to the design center frequency. Curves will assume that appropriate matching is employed, wherever applicable, to the user's desired feedline impedance, with no examination of matching circuit losses. For certain models, a 50-ohm reference may also be used, since some common designs can be developed specifically for 50-ohm cable use.

+
+ +
+

Fig. 1 compares sample SWR curves from 2 kinds of 2-element Yagis. Each curve is relative to the resonant feedpoint resistive impedance. The driver-reflector Yagi uses a 40-Ohm reference, while the driver-director array uses a 17-Ohm standard. The fact that the driver-reflector Yagi has a much wider frequency span between the points at which it crosses the 2:1 SWR line is one reason why this general design is more widely used than the driver-director version of the antenna.

+

Feedpoint Impedance (Z). Feed point impedance will always be given as a complex number involving resistance and reactance (R +/- jX) in Ohms. Resonance will be defined as a reactance less than +/-1 Ohm.

+

Both the resistance and the reactance of any antenna vary across any stretch of frequencies we might use for operation. Fig. 2 shows a sample graph of the changes in both resistance and reactance on 10 meters for the driver-reflector Yagi used for the SWR curve in Fig. 1.

+
+ +
+

Note that the reactance crosses the 0-line (right Y-axis) at about the point where the SWR curve shows its lowest value. Although the resistance is also change with frequency, the reactance is changing faster, and so reactance is often (but not always) the limiting factor in SWR curves.

+

Front-to-Back Ratio (F-B). Front-to-back ratio will be given in dB below the maximum gain of the forward lobe. Front-to-back ratio is taken at a 180-degree angle from the forward lobe. One may also employ a notion of front-to-rear ratio, using the simple or complex mean of values in the quadrant extending for 180 degrees (or some other number of degrees) to the rear of the forward lobe. For the present enterprise, this procedure is unnecessary, since the rear lobe of a 2-element beam is usually geometrically simple. Hence, front-to-back ratio is a sufficient performance indicator for these tests.

+
+ +
+

Special Note on Front-to-Back Ratios. Fig. 3 uses the azimuth pattern of a driver-director Yagi to illustrate the variety of front-to-back ratio concepts that you may find in both articles and manufacturer specification sheets. The 180-degree ratio uses a straight line to the rear opposite the heading of maximum forward gain and compares the two gain readings. The worst-case ratio (sometimes called the front-to-rear ratio) compares the maximum forward gain to the gain of the strongest rearward lobe. The front-to-rear ratio (sometimes called the average front-to-back ratio) averages the gain across the entire rearward quadrants and compares that value to the maximum forward gain. When reading about beams, always try to determine which front-to-back ratio calculation that the author is using.

+

Forward gain: The most complex question for the selection of units of measure is a proper characterization of gain. In Fig. 3, we can easily determine the direction of maximum forward gain, but the pattern does not tell us how to quantify that gain.

+

The most universal standard is gain in dBi, or dB over an isotropic source. An isotropic source is a hypothetical concept that one can approximate with various types of real antennas (but only in free space). It radiates equally well in any direction: up, down, left, right, etc. Hence, it is a universal comparator. Whenever two antennas require comparison, one simply subtracts one dBi-gain figure from the other to find the relative gain advantage or disadvantage.

+

A second common gain figure is dBd, dB relative to a dipole. The dipole standard arose in connection with horizontal antennas, since horizontal dipoles were in common use from the earliest days of radio. However, when gain is registered in dBd, at least 2 different measures may be indicated:

+

dBd(i): Gain in dBd(i) is gain relative to a free space dipole composed of lossless wire of infinitely thin diameter. This idea of a dipole is as hypothetical as a true isotropic source, and real dipoles only approximate the ideal. We may easily relate this notion of dBd to the notion of dBi by the following equation: Gain dBi = Gain dBd(i) + 2.15. This notion of dBd has limited utility, but appear in some tables.

+

dBd(r): Gain in dBd(r) is gain relative to a real dipole in the same defined situation as the test antenna. For modeling purposes, the dipole should be made from the same materials as the test antenna or from some predefined (and stated) set of materials. For these tests, the dipole will use the same material and element diameter as the test Yagi.

+

The notion of dBd(r) may also be used where gain figures result from range measurements. Whenever the notion is so employed, the complete set of test conditions for both the test antenna and the reference dipole should be explained. Otherwise, the figures cannot be meaningful, since replication of the test would not be possible. Range measurements will not be included in these notes. Therefore, dBd(r) will always refer to the gain of a full-length dipole of similar materials as the test antenna, and situated within the same parameters of height and ground specification.

+

However, a further complication arises in the use of dBd(r). Even 2-element Yagi antennas exhibit for the same antenna height, a (usually slightly) lower elevation angle of maximum radiation than a dipole, especially for antenna height less than 1 wavelength. Therefore, simple gain figures must be accompanied by the elevation angle for those figures if a reasonable comparison is to be made.

+

Beamwidth: We think of a vertical antenna as omni-directional, radiating equally well in all azimuth or compass directions. By comparison, even a dipole is directional, although it shows lobes that are identical in two directions. Hence, it falls in the group of antennas that we think of as bi-directional. When we use the term "directional" without a qualifier, we usually mean an antenna--like our sample Yagis--that shows very strong radiation in only one direction, with considerably weaker radiation in all other directions.

+

However, bi-directional and directional antennas do not radiate on a single compass heading. Rather, the gain slowly grows weaker as we move away from the heading of maximum forward gain. At a certain angular distance in either direction from the heading of maximum forward gain, we would find that the transmitted energy has half the power that it has in the direction of maximum power. These half-power points will show 3-dB less gain than in the maximum forward gain direction. We use these points as a convenient measure of an antenna's beamwidth, as measured in degrees between the two points. The pattern in Fig. 3 shows a beamwidth of about 67 degrees from one limit to the other.

+

These notes on basic beam specification concepts all presume that the antenna we are using is oriented horizontally relative to the ground. When we place beams above ground and orient them vertically, the azimuth pattern shape changes, and so too does the maximum forward gain at the heights we use in the HF range. However, the meanings of terms like forward gain, front-to-back ratio, and beamwidth will not change. Since we will normally use a 2-element beam horizontally on 80 through 10 meters, we shall bypass the vertical orientation in these notes. However, if you decide to build a VHF beam for repeater serve, remember that the horizontal patterns and numbers will not be applicable.

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Where Does Beam Gain Come From?

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A beam derives its gain from 3 main sources: ground reflection, directionality, and beamwidth. The total radiated energy from a beam can never be greater than from a dipole or an isotropic source (ignoring element resistances). Any directional antenna acquires gain by re-directing energy in a desired (or usable) direction. +

Free space is equivalent to outer space with no population of particles or waves other than those produced by an antenna under study. In free space, there is no up or down to define azimuth and elevation. So we generally (but not always) consider radiation in the plane of a wire to be the E-plane or electrical plane. At right angles to the plane of the linear elements in the antenna, we have the H-plane or the magnetic plane. If we place the same array of linear element over ground with the elements parallel to the ground, this plane becomes the elevation pattern. (For convenience, modeling software will call any pattern taken in the +/-Z-plane an elevation pattern. Any plot taken in the X-Y-plane becomes an azimuth pattern.)

+

Antennas in free space show a maximum gain that less than the value we find when we place the antenna over a ground surface. In free space, the radiation can equally go "up" and "down." However, the moment that we introduce the ground, we ultimately have only the "up" direction. What initially starts downward reflects (with some loss) back upward. Compare the free-space and over-ground patterns for a simple dipole, looking along the length of the element.

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The energy the goes "downward" in free space becomes reflected upward by the ground. However, the angle of the downward energy, once reflected, determines whether the waves will mutually add, mutually subtract, or something in between the two. Hence, the elevation pattern of an antenna over ground may show both lobes and nulls. The test antenna is 1 wavelength above ground. In general and subject to some modification for long-boom antennas, we can estimate the angle of any lobe (or null) from a horizontal (but not a vertical) antenna by using a simple equation.

+
+

ALN = arcsin(N / 4h)

+
+

ALN is the angle of the lobe or null above the horizon. The term h is the height of the antenna above ground measured in wavelengths or fractions thereof. N is the lobe or null number. We give lobes odd numbers, so that the first lobe is 1, the second lobe is 3, etc. Nulls receive even numbers. Most often, we are concerned with the first lobe. In this case, for N=1, and h=1, we want the arcsin (or sin-1) of 0.25. On any calculator, we take the inverse sin function of .25 and get a little over 14 degrees for the value of ALN.

+

The peak gain at 14 degrees elevation for the sample dipole is about 7.6 dBi, compared to a gain value of 2.1 dBi in free space. If the ground did not have any losses, we would see a 6-dB difference. However, over real ground, we find a 5.5-dB gain differential.

+

The second way in which a beam acquires gain is in developing a pattern that favors a single direction. The dipole is already directional, but in two directions. We can further increase gain in a single favored direction by arranging the elements so that we have one large main (forward) lobe with only one or more minor lobes in other directions. Compare the overlaid azimuth patterns for a dipole and a 2-element driver-reflector Yagi in Fig. 5.

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Note that, relative to the dipole, the 2-element Yagi shifts energy to the right in the pattern and removes energy toward the left. In free space, this particular sample beam has a maximum forward gain of about 6.0 dBi. Over ground, the maximum gain at 14 degrees elevation is about 11.4 dBi. The ground provides 5.4 dB of gain relative to free space. The gain of this beam is about 3.8 to 3.9 dB higher than the gain of a dipole--in the favored direction only.

+

The beamwidth of the beam is about 69 degrees. Although we shall not examine them closely, we may want to ask here how longer Yagis with more elements obtain higher gain levels in the favored direction. The answer is both simple and complex at once. The simple part is the general statement that the longer Yagis reduce their beamwidth in order to produce a higher gain in the favored direction. Fig. 6 shows both independent and overlaid patterns for our sample 2-element Yagi and for a sample 6-element Yagi.

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+ +
+

The 6-element Yagi has somewhat less rearward radiation, and so it acquires a bit of gain from that source. But only a little. The main source of the increased forward energy and gain comes from the narrowing of the beamwidth--from 69 down to 53 degrees in this example.

+

The picture given by these plots is incomplete, which is why the answer is more complex than it may initially seem. Not only does the longer Yagi decrease the horizontal beamwidth, it also decreases the vertical beamwidth. This 3-dimensional beamwidth reduction shows up well when we start with free-space patterns, but for now we can simply use the azimuth patterns as an indicator of how beamwidth reduction becomes a source of additional gain in long Yagis and certain other kinds of horizontal beam antennas. However, Fig. 7 shows the relationship between E-plane and H-plane patterns in free space and between elevation and azimuth patterns over ground for our sample 2-element driver-reflector Yagi.

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+

Before we grow too attached to the 2-element Yagi, we need to understand a bit more about the behavior of a simple dipole over ground.

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The Dipole Standard of Reference

+
All Yagis ultimately rest on the linear dipole. The elements relate to a resonant 1/2 wavelength dipole, with reflectors being slightly longer and directors slightly shorter. Therefore, understanding the behavior of a dipole over ground is a crucial factor in appreciating the behavior of 2-element beams. +

Table 3 present some interesting data for a full-size 3/8" aluminum dipole for various heights from 1/8 to 1-1/4 wavelength using 1/16 wavelength increments. Gain values use both dBi and dBd to familiarize you with the differences in the gain recording systems. El. Angle refers to the elevation angle of maximum radiation at which the gain figure is taken. Feed R and Feed X refer to the resistance and reactance at the feedpoint.

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+ +
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Fig. 8 shows the gain values and the elevation angle of maximum radiation (also called the take-off or TO angle) for the sequence of models. The gain values are significant in several respects. First, note the very low gain at very low antenna heights. MININEC users may see very different results below about 0.2 wavelength heights, because the ground system used by that program is very unreliable at low antenna heights. Next, note that the gain of a dipole does not rise and level off smoothly. Although the differences are not operationally significant, they do undulate as we raise the antenna, change its length to arrive at resonance, and then check the gain. We find small gain peaks at heights of 3/16, 5/8, and 1-1/8 wavelength. We also find dips at 1/4, and 13/16 wavelengths, with the curve headed toward another dip at the end of the model sequence. (In a future episode, we shall show you a handy marketing trick that you can play if you should ever desire.) Perhaps the only consistent curve is the one for the elevation angle of maximum radiation. It decreases as we increase height, and the progression is very orderly.

+

It should be clear from the table that, except in the most unusual circumstance, the concept of dBd adds nothing to the analysis not already contained in the notion of dBi. For purposes of determining gain relative to a dipole with respect to test antennas, we shall simply subtract the appropriate value of gain in dBi for the dipole from the value of gain in dBi for the test antenna at the same height. However, it is wise to keep the 2 notions of dBd (that is, dBd(i) and dBd(r)) in the back of your mind because some antenna manufacturers use one or the other to portray the performance of their offerings. dBd remains popular among European antenna builders.

+
+ +
+

As shown in the table and in Fig. 9, the required length of the dipole to achieve resonance varied from 15.9' to 16.4' but not in a linear progression. Short lengths appear at heights of 3/16, 3/4, and 1-1/4 wavelength, a progression that does not quite correspond to the peaks or dips in gain. Likewise, long lengths appear at heights of 7/16 and 1 wavelength, again without coincidence with the gain curve.

+
+ +
+

The feedpoint impedance also varies with height, but not in a pattern that corresponds to the variance in length. However, the feedpoint resistance values tend to coincide with the changes in gain. Low feedpoint resistance values appear at 1/8, 5/8, and 1-1/8 wavelength heights, roughly corresponding to the gain peaks. High feedpoint values occur at heights of 5/16 and 7/8 wavelength, roughly corresponding to the gain dips.

+

One factor, but not the only factor, that plays a role in the undulations of gain is the changing spread of elevation lobes as we raise the antenna higher. Fig. 10 provides only a few elevation patterns to illustrate how lobes emerge and change with changing antenna height.

+
+ +
+

As we increase the height of an antenna, new lobes do not simply appear. Rather, they make their first appearance as vertical or near-vertical lobes. (The pattern for a height of 1/4 wavelength makes it clear why those who pursue Near-Vertical Incidence Skywave (NVIS) operations favor a relatively low horizontal antenna.) As we raise the antenna, the nearly vertical lobe splits and gradually lowers its angle of maximum radiation. At certain heights, we find almost no radiation straight up, and the lower lobes contain all of the radiated energy. Further increases in height show the emergence of a new upward lobe, which then undergoes the same transformation as we continue the upward trend in antenna height. In general, we acquire a new lobe with each 1/2 wavelength addition to the antenna height. For most purposes, we are only concerned with the lowest and strongest elevation lobe, since it usually comes closest to matching the favored radiation angles for long-distance HF communications.

+

A Final Question about Gain

+

Before we leave the subject of antenna gain, let's look at an all-too-typical claim. Suppose someone says that a certain antenna at a height of 7/8 wavelengths has a gain of 5 dBd. How are we to understand this claim without further and full specification of what the idea of dBd means in this context? If we interpret the claim to mean dBd(i), then the assertion is that the antenna has only the gain of a dipole, since a dipole at 7/8 wavelength has a gain of 5.00 dBi (assuming similar materials). If the antenna is an array, that would be a disappointing result.

+

If the claim is that the antenna has a gain of 5 dBd(r) (as applicable to modeling), then we would expect the antenna to have a gain of 12.15 dBi, since the gain of a dipole in dBi at 7/8 wavelength (assuming similar materials) is 7.15 dBi. Our next question is whether this claim is reasonable. To make such a judgment, we need to have some clear expectations of 2-element Yagi performance capabilities and limitations. That is the next stop on this road towqard understanding 2-element beams.

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+ +

+
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Updated 05-09-1997, 04-25-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2: The Full-Size 2-Element Yagi
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+ Return to Index

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Topics: HF Upper, Yagi


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What Can We Expect from a 2-Element Beam?

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Part 2: The Full-Size 2-Element Yagi

+
+
+

L. B. Cebik, W4RNL

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+

In this episode, we shall develop some basic ideas about driver-reflector 2-element Yagis. The relatively broadband characteristics of the driver-reflector Yagi open it to relatively easy reproduction by the newcomer. As well, as we shall discover in the following 2 episodes, it is amenable to certain kinds of compacting. Therefore, we shall set aside the director in favor of the configuration shown in Fig. 1.

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+ +
+

By working with a full-size 2-element Yagi, we simplify construction. Besides a mast and boom, all that we need are linear elements, usually made from aluminum tubing. As in the first episode, we shall use 3/8"-diameter elements. In practice, a builder would usually use elements with a tapered-diameter schedule. Typical element tubing ranges are 3/4-5/8-1/2-inch for very high wind loads or 5/8-1/2-3/8-inch for moderate wind loads.

+
+

The Full-Size 2-Element Yagi

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+

Two-element Yagis have several variables around which the design revolves.

+
+

1. Spacing between elements;

+

2. Length of reflector; and

+

3. Length of driven element.

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+

We can also handle these variables in a number of ways. for example, we can

+
+

1. Optimize gain at the design frequency;

+

2. Optimize front-to-back ratio at the design frequency;

+

3. Strive for resonance;

+

4. Strive for maximum operating bandwidth (perhaps as defined by a 2:1 SWR); and/or

+

5. Strive for a 50-ohm match.

+
+

The mix and match of design goals leads to an almost indefinitely large number of antenna designs, according to what compromises the designer reaches. A maximum gain design may yield a combination of elements leaving considerable reactance at the feedpoint. Altering the driven element toward resonance may yield an element combination, even when the reflector is re-maximized for gain, which is slightly off peak. Similar compromises apply to any other combination of ingredients in the design goals.

+
+

Designing for Maximum Font-to-Back Ratio

+
We shall look at several models in free space using different spacing values. We shall optimize the design for maximum front-to-back ratio and resonance for each spacing value. The degree of element lengthening needed for a gamma or Tee match, or the degree of shortening needed for a beta match, is too small to make a significant difference in performance. To see why designers lean toward the maximum front-to-back ratio frequency as the design center (or near-center), we shall later examine some beams designed for maximum gain at the design center frequency. We shall also look at some models over real ground using one or two spacing values and optimized for front-to-back ratio at antenna resonance to determine the operating bandwidth characteristics of the array. +

In general, 2-element Yagis optimized for maximum front-to-back ratio have resonant feedpoint impedances in the mid-30-Ohm range with spacing values of about 1/8 wavelength and in the 50-ohm range with spacing values in the vicinity of 0.16 wavelength. These values represent a range of 4.1 to 5.4 feet at 29 MHz, which you can scale to any other frequency with an appropriate multiplier.

+

Let's take a more comprehensive look at this collection of antennas by specifying a sequence of spacing at 0.04 wavelength intervals from 0.08 wavelength through 0.24 wavelength (2.7' through 8.1'). The models will be in free space. The dimensions used for these models appear in Table 1.

+ 
+Table 1.  Dimensions of models used in evaluating performance vs. element spacing.  All elements 3/8" aluminum.
+Spacing          Driver Length       Reflector Length
+WL     Feet      WL      Feet        WL      Feet
+0.08   2.71      0.472   16.01       0.502   17.02
+0.12   4.07      0.466   15.82       0.503   17.06
+0.16   5.43      0.464   15.74       0.503   17.05
+0.20   6.78      0.464   15.75       0.503   17.05
+0.24   8.14      0.466   15.82       0.502   17.03
+
+

Although there may not be very much difference between element lengths for each step, obtaining adequate performance over a desired bandwidth requires very careful building.

+

Table 2 provides data on the modeled performance of these beams using NEC (either -2 or -4). The gain values are for free space. To obtain an estimate of the gain at 1 wavelength above ground, add about 5.4 dB to the gain values in the tables. The driven element is resonant within j+/-1 Ohms in each case. Gain figures will be for 29 MHz, although that is the frequency of maximum front-to-back ratio. Maximum gain occurs somewhat lower in frequency.

+ 
+Table 3.  Modeled NEC (-2 or -4) performance of the 2-element Yagis in Table 1.
+(Reference dipole gain in free space = 2.13 dBi)
+Spacing   Gain (dBi)     Gain (dBdr)    F-B (dB)       Feed Z (R +/- jX)
+0.08 wl   6.32           4.19           11.37          17.27 + j0.06
+0.12      6.25           4.12           11.20          32.04 - j0.00
+0.16      6.12           3.99           10.84          46.87 + j0.03
+0.20      5.88           3.75           10.35          61.07 - j0.13
+0.24      5.56           3.43            9.71          73.01 - j0.34
+
+

Let's make the same run with MININEC (Table 3). Typically, MININEC yields dimensions that are about 0.04' (1/2") shorter than NEC at 29 MHz, although some versions of MININEC have a correction factor to bring them into alignment as frequency increases. (The MININEC program Antenna Model has been so thoroughly corrected that its results correlate almost perfectly with NEC.)

+ 
+Table 3.  Modeled MININEC performance of the 2-element Yagis in Table 1.
+(Reference dipole gain in free space = 2.12 dBi)
+Spacing   Gain (dBi)     Gain (dBdr)    F-B (dB)       Feed Z (R +/- jX)
+0.08 wl   6.31           4.19           11.40          17.09 - j0.59
+0.12      6.25           4.13           11.19          32.33 + j0.17
+0.16      6.09           3.97           10.86          46.84 - j0.56
+0.20      5.87           3.75           10.34          61.12 + j0.07
+0.24      5.56           3.44            9.72          72.42 - j0.59
+
+

The differences between the two modeling systems are not great enough to make a difference under any practical circumstance. If you create your own models using the dimensions in Table 1, you may find very small differences in the results that you obtain. Different implementations of both NEC and MININEC exhibit very small (and operationally insignificant) differences due to methods of compilation. As well, different CPUs may also show slight differences in results, even though using the same program. These differences would only matter if they reach the level of being operationally significant.

+

To understand why designers tend to select spacing values of 0.12 wavelength to 0.16 wavelength, we need one additional data table in hand: the SWR of the antennas across the band from 28 to 30 MHz (given here at 0.5 wavelength, using the SWR sweep facility of EZNEC). Each sweep in Table 4 is centered on the resistive component of the feedpoint impedance at the design center frequency. Values greater than 1.0 occur at that frequency because of the remnant reactance.

+ 
+Table 4.  SWR values relative to the resonant impedance for the test models.
+Spacing   SWR at    28        28.5      29        29.5      30   MHz
+0.08 wl             30.3      5.64      1.02      3.01      5.66
+0.12                7.34      2.37      1.00      1.82      2.78
+0.16                3.52      1.70      1.00      1.47      2.00
+0.20                2.31      1.42      1.00      1.31      1.66
+0.24                1.82      1.29      1.01      1.23      1.48
+
+

Fig. 2 provides a graphic view of the same data so that you may better see the rates of change of SWR both above and below the design frequency.

+
+ +
+

Obviously, the widest spacing offers the greatest operating bandwidth, but at the cost of reduced gain and front-to-back ratio. Consequently, a design tends to compromise among the highest gain, the highest front-to-back ratio, adequate operating bandwidth, and feedpoint impedance. 0.16 wavelength spacing offers the opportunity for a direct match to 50-ohm coax feedlines with a fairly useful bandwidth for most of the HF ham bands. (Remember to reduce the bandwidth by dividing the 10-meter figure by the ratio of 29 MHz to the frequency of interest for lower HF bands.) Spacing values closer to 0.12 wavelength yield higher gains and front-to-back ratios, but over a narrower bandwidth.

+

There are two other design problems one must consider. First, the frequency of maximum gain is well below the frequency of maximum front-to-back ratio. The gain tapers gradually as the frequency increases within the operating bandwidth. Second, SWR increases rapidly below the design frequency and more slowly above it. When this factor is combined with the gain situation, one can design an illusion: an antenna with decent SWR but very little gain or front-to-back ratio in the upper half of its operating range.

+

To illustrate this situation, let's look at the models in more detail, examining their gain and front-to-back patterns across 10 meters. Table 5 presents sampled data in 0.5-MHz increments.

+ 
+Table 5. Performance of the 2-element Yagis from 28 to 30 MHz.
+Frequency      28        28.5      29        29.5      30  MHz
+0.08 wl spacing
+Gain (dBi)     6.37      6.92      6.32      5.77      5.37
+Gain (dBdr)    4.24      4.79      4.19      3.64      3.24
+F-B (dB)       1.82      8.65      11.38     10.12     8.57
+0.12 wl spacing
+Gain (dBi)     6.98      6.74      6.25      5.82      5.48
+Gain (dBdr)    4.85      4.61      4.12      3.69      3.35
+F-B (dB)       5.46      9.79      11.19     10.37     9.18
+0.16 wl spacing
+Gain (dBi)     6.88      6.55      6.12      5.74      5.43
+Gain (dBdr)    4.75      4.42      3.99      3.61      3.30
+F-B (dB)       6.66      9.84      10.86     10.29     9.32
+0.20 wl spacing
+Gain (dBi)     6.64      6.28      5.87      5.50      5.20
+Gain (dBdr)    4.51      4.15      3.74      3.37      3.07
+F-B (dB)       7.31      9.66      10.35     9.87      9.03
+0.24 wl spacing
+Gain (dBi)     6.37      5.98      5.56      5.18      4.86
+Gain (dBdr)    4.24      3.85      3.43      3.05      2.73
+F-B (dB)       7.36      9.22      9.73      9.29      8.51
+
+

Fig. 3 provides a graph of the gain curves for the three values of spacing (0.08, 0.16, and 0.24 wavelength). Had I used only the 3 middle values from the table, the gain curve lines would not be clear. The increment used in the sweeps is 0.1 MHz.

+
+ +
+

The gain curves are generally parallel to each other. However, the display of the curve for the closest spacing shows what happens at some frequency below the design frequency. The gain rises slowly, but at a certain frequency, it begins to drop rapidly. The same phenomenon occurs with the curves for the wider spacing of elements, but the frequency at which the gain drops off falls below the limit of the sweep. The gain curve for the driver-reflector type of Yagi is unique. Any Yagi with at least one director will produce a curve with the opposite characteristic, that is, the gain will rise as frequency increases.

+
+ +
+

Fig. 4 shows the 180-degree front-to-back ratios for the same three Yagi designs. At the design frequency, closer spacing yields a higher front-to-back ratio. However, closer spacing yields a smaller range over which the front-to-back ratio remains near its peak value. In contrast, wider spacing yields a lower value of peak front-to-back ratio, but the ratio remains near the peak value over a wider range of frequencies. Note that, like the SWR, the front-to-back ratio tends to decrease more rapidly below the design frequency than above it.

+
+ +
+

Fig. 5 shows three free-space patterns for the Yagi with 0.16 wavelength element spacing. It illustrates typical patterns at 28, 29, and 30 MHz. Note that the rear lobe changes its size or strength, but it remains "well behaved." That is, it does not develop large multiple lobes, but remains a single rearward lobe. The patterns also illustrate why we may use the 180-degree front-to-back ratio as a marker of performance with this series of beams. The 180-degree ratio and the worst-case ratio are identical. As we saw in the first episode, this feature does not hold true for every possible 2-element Yagi design.

+

From tables and graphs we can draw several conclusions applicable to 2-element Yagis on any band.

+
+

1. Reading across the tables, it is clear that the maximum gain frequency is within the sweep for the closest spaced beam, but at or beyond the lower frequency limit for the other models. The closer the spacing, the closer together are the frequencies of maximum gain and maximum front-to-back ratio.

+

2. The wider the spacing, the lower the overall values of gain for the entire sweep.

+

3. Gain falls off somewhat rapidly above the design center frequency. It rises even more rapidly below the design center frequency, although that curve is invisible in these tables.

+

4. If we compare SWR and gain data, it is clear that maximum gain occurs in a region of high SWR when the beam is designed for maximum front-to-back ratio.

+

5. Front-to-back ratio holds up best at spacing values between 0.12 and 0.20 wavelengths, inclusive.

+
+

It is therefore possible to design a beam with a wide operating (2:1 SWR) bandwidth using spacing values of 0.20 or 0.24 wavelength, but accrue little more than 3 dB gain over a dipole and a front-to-back ratio under 10 dB for most of that bandwidth. Equally, achieving more than 4 dB gain over a dipole and a front-to-back ratio greater than 10 dB for a large portion of the operating bandwidth is not feasible with a full size 2-element driver-reflector Yagi.

+

As a result of these limiting conditions, when a 2-element Yagi is designed for maximum front-to-back ratio, design compromises are necessary. When the bandwidth requirements are narrow, as on 17 and 12 meters, a spacing in the vicinity of 0.12 wavelength is often chosen for the best combination of gain and front-to-back ratio, along with a sufficiently high feedpoint impedance to assure efficiency. For wider bands, a spacing around 0.16 wavelength is favored, trading some gain and front-to-back ratio for operating bandwidth and an easy match to 50-Ohm coax.

+
+

Designing for Maximum Gain

+
The alternative design strategy we might use is to design our beam so that the array resonates at or close to the frequency of maximum gain. Table 6 provides the dimensions for the new series of 2-element driver-reflector Yagis. + 
+Table 6.  Dimensions of  maximum-gain models used in evaluating performance vs. element spacing.  All elements 3/8" aluminum.
+Spacing          Driver Length       Reflector Length
+WL     Feet      WL      Feet        WL      Feet
+0.08   2.71      0.477   16.18       0.490   16.63
+0.12   4.07      0.470   15.95       0.488   16.54
+0.16   5.43      0.467   15.83       0.484   16.42
+0.20   6.78      0.465   15.76       0.481   16.33
+0.24   8.14      0.464   15.74       0.479   16.25
+
+

Compared to the Yagis designed for maximum front-to-back ratio at the design frequency, the maximum-gain versions have longer drivers and shorter reflectors, with the reflector length-differences being more radical. These difference yield a significant difference in performance at the design frequency (29.0 MHz), as shown in Table 7.

+ 
+Table 7.  Modeled free-space performance of 2-element driver-reflector Yagis designed for maximum gain at resonance.
+NEC (-2 or -4)  (Reference dipole gain in free space = 2.13 dBi)
+Spacing   Gain (dBi)     Gain (dBdr)    F-B (dB)       Feed Z (R +/- jX)
+0.08 wl   7.02           4.89           6.16            9.54 + j0.20
+0.12      6.99           4.86           6.38           19.59 - j0.23
+0.16      6.88           4.75           5.95           30.83 + j0.29
+0.20      6.69           4.56           5.85           43.47 + j0.11
+0.24      6.43           4.30           5.65           55.92 - j0.24
+
+

The gain figure for the 0.08 wavelength spaced Yagi optimized for gain approaches the absolute maximum gain obtainable from a 2-element parasitical array. However, this gain is obtained at a cost: a severe reduction in the front-to-back ratio and a very low feedpoint impedance. As spacing is increased, the maximum obtainable gain also decreases, along with the front-to-back ratio at that gain figure. Despite the severe reduction in the front-to-back ratio, which makes the beam almost a narrow-beamwidth dipole, the patterns remain well behaved with one exception. Fig. 6 provides a sample pattern set at 28, 29, and 30 MHz to reveal the exception. The element spacing for the sample is 0.16 wavelength.

+
+ +
+

At 30 MHz, the pattern almost replicates the maximum front-to-back ratio version pattern at its design frequency. However, at the other end of the swept range, we find that the pattern has reversed itself, with the major lobe in the formerly rearward direction. The illustration has some importance in thinking about Yagis. Just because a parasitic element happens to be longer than the driver, it does not automatically become a reflector. Its function as a reflector or as a director depends upon the relative current magnitude and phase on the two elements, and those values change with each change in frequency for a fixed set of dimensions.

+

Maximum-gain 2-element Yagi designs have very limited SWR bandwidths, as demonstrated in Table 8 and in Fig. 7.

+
+ +
+ 
+Table 8.  SWR from 28 to 30 MHz relative to the resonant impedance of the Yagi.
+Spacing   SWR at    28        28.5      29        29.5      30   MHz
+0.08 wl             39.8      16.1      1.02      7.03      14.43
+0.12                15.1      5.22      1.01      3.00      5.37
+0.16                7.09      2.84      1.01      2.07      3.21
+0.20                4.24      2.03      1.00      1.65      2.28
+0.24                2.97      1.67      1.01      1.43      1.83
+
+

Only at a spacing of 0.24 wavelength do we obtain any significant operating bandwidth, and by that spacing, gain and front-to-back ratio have fallen severely. In fact, gain has decreased to the levels of more closely spaced maximum front-to-back designs.

+

As if these factors were insufficient reasons for designers to move the operating point of the array toward the maximum front-to-back region, an additional problem emerges if one examines the beam's properties across a frequency span. Table 9 provides a rough indication of the difficulty.

+ 
+Table 9.  Operating characteristics from 28 to 30 MHz of Yagis designed for maximum gain.
+Frequency      28        28.5      29        29.5      30  MHz
+0.08 wl spacing
+Gain (dBi)     7.14 R    6.08 R    7.02      6.60      6.04
+Gain (dBdr)    5.01 R    3.95 R    4.89      4.47      3.91
+F-B (dB)       10.44     0.86      6.16      10.54     10.57
+0.12 wl spacing
+Gain (dBi)     6.92 R    6.23      6.99      6.67      6.21
+Gain (dBdr)    4.79 R    4.10      4.86      4.54      4.08
+F-B (dB)       4.49      1.31      6.38      9.97      10.87
+0.16 wl spacing
+Gain (dBi)     6.30 R    6.37      6.88      6.63      6.23
+Gain (dBdr)    4.17 R    4.24      4.75      4.50      4.10
+F-B (dB)       2.21      1.96      5.95      9.09      10.51
+0.20 wl spacing
+Gain (dBi)     5.52 R    6.37      6.69      6.45      6.06
+Gain (dBdr)    3.39 R    4.24      4.56      4.32      3.93
+F-B (dB)       0.50      2.65      5.85      8.50      9.91
+0.24 wl spacing
+Gain (dBi)     5.41      6.26      6.43      6.17      5.78
+Gain (dBdr)    3.29      4.13      4.30      4.04      3.65
+F-B (dB)       0.63      3.07      5.65      7.87      9.17
+
+

The entries labeled "R" indicate gain in the reverse direction from that of the remainder of the entries. The maximum gain point in the geometry of a 2-element Yagi occurs just above the frequency at which the parasitical element begins to function as a reflector. Below a certain critical frequency that varies with spacing, the parasitical element becomes a director, even though it is physically longer than the driven element. (It would be shorter if the driven element were lengthened to resonance.) Fig. 8 shows the transition in graphical form using 3 of the sampled spacing values (0.08, 0.16, and 0.24 wavelength).

+
+ +
+

The curve for a spacing of 0.24 wavelength does not undergo the reversal. However, the curves for the closer spacing values show a distinct minimum value, and below the frequency at which this occurs, the gain rises again, but in the reverse direction. Even though the graph uses 0.1-MHz increments, the minimum gain values do not approach zero. The actual transition occurs between sampled points and occurs over a very narrow frequency span. The frequency of transition, as a spread from the design frequency, is about 600 kHz for 0.16 wavelength spacing and only 400 kHz for 0.08 wavelength spacing. As spacing is increased, the frequency at which the beam flips directions grows more distant from the frequency of maximum gain. However, performance of the beam in the range between reversal and maximum gain is marginal at best.

+

The front-to-back curves, shown in Fig. 9 for the same three samples, provide the same information relative to the frequencies at which the pattern reverses itself. The indicator is the minimum value of front-to-back ratio for each of the curves. From the rapidly declining value of front-to-back ratio, the 0.24 wavelength sample beam might reverse itself within 100-200 kHz below the limit of the sweep.

+
+ +
+

We may note in passing, with an eye on the 0.08 wavelength spaced beam, that the driven-element-director configuration is capable of slightly higher gain than the driven-element-reflector arrangement.

+

The purpose of these latter tables and graphs is twofold. First, they demonstrate the maximum gain of which a full size 2-element driven-element-reflector Yagi is capable, and the conditions surrounding that achievement. Second, they also illustrate why designers tend to give up maximum gain in favor of maximum front-to-back ratio as the design focus: adequate gain, wider operating bandwidth, higher feedpoint impedances, and higher front-to-back ratios. We may reiterate that above the frequency of maximum front-to-back ratio, the feedpoint SWR (referenced to the impedance at the design center frequency) decreases more slowly than below the maximum F-B frequency, but both gain and F-B ratio decrease together. Hence, specifying the peak values of gain, front-to-back ratio, and operating bandwidth does not always give a fair indication of beam performance. That is why we need to view tables or graphs of performance over the entire operating passband. We may also note that in no case of normal directional operation does the driven-element-reflector reach 5 dBd(r).

+
+

Height above Ground

+
The characteristics of a given 2-element Yagi design are not constant with height above ground until the beam is well above 1 wavelength high. Table 10 provides data on gain, elevation angle, front-to-back ratio and feedpoint impedance for one of the 2-element Yagis that we have explored in free space. To maximize gain while having a workable feedpoint impedance, I have selected the version with a spacing of 0.12 wavelength between the driver and reflector. However, with suitable changes in the exact numbers, any of the beams in the free-space collection would show similar trends as we vary the height above ground. +
+ +
+

To gather an appreciation of this data, you may wish to simultaneously view the data in episode 1 on the dipole at the same heights above average ground. Both the dipole and the Yagi use the same element material: 3/8" diameter aluminum. Therefore, we may make some fair comparisons between the two antennas.

+
+ +
+

Fig. 10 shows elevation patterns for the Yagi at increments of 1/4 wavelength in height. These patterns correspond to the dipole elevation patterns in episode-1's Fig. 10. For every dipole elevation lobe and null, there is a corresponding lobe and null in the Yagi patterns. However, we find two major differences between the patterns. The first difference is obvious: the lobes to the rear of the Yagis forward direction are much weaker than the corresponding dipole lobes. We might easily overlook the second difference. Compare the emerging dipole and Yagi lobes at the highest elevation angles, especially at heights of 0.75 and 1.25 wavelength. The Yagi higher-angle lobes are always smaller than corresponding dipole lobes. In episode 1, we noted that beams obtain forward gain from several sources, one of which was a reduction in both the vertical and the horizontal beamwidth. The reduction in the strength of the Yagi upper-angle lobes is part of the reduction in the vertical beamwidth.

+
+ +
+

As we observed in the behavior of the dipole, the gain of the 2-element Yagi does not increase smoothly as we increase its height above ground. However, the Yagi gain curve (in dBi), shown in Fig. 11, is much smoother than the dipole curve in episode 1. In fact, the only section of Table 10 that shows a very tiny decline in gain is between heights of 1.125 wavelengths and 1.25 wavelengths. That decline is only 0.02 dB.

+

The curve designated dBd shows a different curvature than the one marked dBi. The dBd gain is based on the difference in gain in dBi between the Yagi and the dipole in episode 1. Since the gain of the dipole varies over a greater range than does the Yagi gain, the Yagi gain in dBd shows higher peaks and deeper nulls. Now suppose that you were selling a 2-element that is for all practical purposes identical to the Yagi sold by a competitor. If you check the gain of your antenna at a height of 7.8 wavelength, you may claim a gain of 4.22 dBd. If you check your competitor's beam at 5/8 wavelength, then its gain is only 4.48 dBd. By "judiciously" omitting the details of how you obtained the figures, you might even claim in your sales literature that your Yagi has more than a half-dB higher gain than your competitors. This small demonstration perhaps enlightens you as to why we shall focus upon dBi as the more useful unit of gain measurement.

+
+ +
+

The undulations in the front-to-back ratio with changing antenna height are much more pronounced than the small changes in forward gain. Fig. 12 graphs the 180-degree front-to-back ratio of our sample Yagi. Using the right Y-axis, the graph also tracks the changes in the feedpoint resistance. The Yagi uses a single set of physical measurements, shown in Table 1. Hence, as Table 10 makes clear, the reactance drifts slightly off resonance relative to the free-space value of the original design. However, the reactance drift is small and varies from being slightly capacitive to being slightly inductive, depending upon the exact height.

+

More significant than the reactance drift--especially for our understanding of 2-element Yagi behavior--is the fact that above a height of about 3/16 wavelength, the feedpoint resistance and the front-to-back ratio curves track each other very closely. In contrast, the gain curves--to the degree that one can detect peaks and nulls--are offset from these two curves. In a 2-element driver-reflector Yagi, the feedpoint impedance and the front-to-back ratio are very closely related. This and related height phenomena were reported upon extensively in "The Effects of Antenna Height on Other Antenna Properties: A Computer Study," Communications Quarterly, 2 (Fall, 1992), 57-79. See Magazines Page.

+

Needless to say, when fine shades of performance comparison are at stake, mere numbers for gain, front-to-back ratio, and operating bandwidth are normally meaningless without a complete specification of their derivation. Even summaries of typical cases of derivation can make comparison elusive, since they often leave ambiguous which derivation was used for a particular antenna. Until buyers of amateur radio antennas are provided with the same detailed information that can be demanded by military, government, and private corporations for contract fulfillment, caveat emptor must still rule the marketplace.

+

With this caution, we may complete our sampling of 2-element driver-reflector behavior--at least so far as full-size Yagis are concerned. However, modern-day urban and suburban amateurs are cramped for antenna space. They wonder if they can effectively shrink an antenna and still derive adequate performance from it. Since the 2-element Yagi seems the simplest beam to shrink, we should explore the possibilities.

+
+ +

+
+

Updated 05-09-1997, 04-25-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +

+
+ Go to Part 3: Shortened Dipoles and Capacity Hat Yagis
+
+ Return to Index
+

Topics: HF Upper, Yagi


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+

What Can We Expect from a 2-Element Beam?

+
+
+

Part 3: Shortened Dipoles and Capacity Hat Yagis

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

There are two very general ways in which we may shorten a linear element and maintain resonance or some other desired property. One method is to add in one form or another inductive reactance to the capacitively reactive shortened element. The two most popular positions for placing inductive reactances are at the element center and somewhere outward from the center position. We normally use a single inductive reactance when we center-load an element. However, mid-element-loading requires 2 equal reactances placed equally distant from the element center.

+

The second form of achieving shorter but still resonant elements is to add hats at the element ends. Although we shall examine only symmetrical hats, it is also possible to use non-symmetrical structures, including lengths of wire compressed into a solenoid configuration. Since there are more forms of center- and mid-element-loading than of hats, let's begin with the hat.

+
+

Shortened Yagis with Capacity Hats

+
No 2-element driven-element-reflector Yagi with shortened elements can achieve the gain of a full-size Yagi of the same configuration over an extended bandwidth. However, a shortened Yagi often achieves a significantly higher front-to-back ratio than its full-size counterpart. +

There is one seeming exception to these principles: the shortened Yagi "loaded" at the element outer ends with so-called capacity hats. The exception is an illusion, because the hatted dipole is not loaded in the conventional sense. Rather, the main linear element section is shortened and the remaining length is composed of a symmetrical array of wires that is at right angles to the linear section and whose net radiation is at or near zero. Fig. 1 illustrates the hat-loaded dipole, and shows several configurations of hats.

+
+ +
+

Hats that use spokes alone require a larger radius than when the same number of spokes are terminated by a perimeter wire. Essentially, the perimeter wire continues each spoke in two directions, so that the zero-current point is midway between two spoke tips. With or without a perimeter wire, we require shorter spokes as we increase their number. Once we reach about 60 spokes, the length decrease ends, since the structure effectively simulates a solid disc.

+
+ +
+

Fig. 2 compares the current distribution along a standard full-size dipole and a hatted dipole that is about 70% full-size. Both antennas use 3/8" diameter aluminum elements throughout. Current along the linear section of the hatted dipole at the point where the hat begins is the same as it would be on a full-size linear element at the same distance from the feedpoint. The current divides among the wires of the hat array, and the hat array must be large enough to permit the element to reach resonance at the same frequency as the full-size element. The two assemblies in Fig. 2 are 16.24' and 11.33' long, respectively for the full-size and the shortened antennas. The 4 spokes on the two ends of the hatted dipole are each 12" long.

+

Under these conditions, the performance of a full-size dipole and a shortened, hatted version will be very similar, at least with shortening no greater than about 70% of full size. Since the distribution of current along the dipole element is roughly (but not perfectly) sinusoidal, most of the current contributing to the antenna radiation pattern occurs along the linear section of the elements and very little in the hat arrays.

+

Modeling an element-end hat is not so problematical in NEC as modeling closely spaced wires of complex geometries. Because the net radiation from a hat is zero, interactions with the main element that might make results unreliable when adjacent segments differ in diameter are minimized. NEC hat models correspond very closely with those created with MININEC. The potential slight differences are minimized in this exercise by making the hat wires of the same diameter as the main element: 0.375 inch.

+ 
+Table 1.  A comparison between a full-size and a 70%-hatted dipole
+Antenna   Frequency      F-S Gain            Feedpoint Z         SWR
+          MHz            dBi                 Ohms
+Full      28             2.09                64.82 - j35.98      1.700
+Hat                      2.00                52.77 - j33.78      1.833
+Full      28.5           2.11                68.34 - j17.87      1.296
+Hat                      2.01                55.61 - j16.39      1.338
+Full      29             2.12                72.04 + j 0.18      1.003
+Hat                      2.02                58.60 + j 0.95      1.018
+Full      29.5           2.14                75.94 + j18.20      1.286
+Hat                      2.03                61.75 + j18.27      1.356
+Full      30             2.16                80.05 + j36.19      1.622
+Hat                      2.04                65.06 + j35.58      1.776
+
+

Although the hatted dipole at 70% of full size has a lower feedpoint impedance and a 0.1 dB lower gain, in practice, no difference in performance could be detected by any station using the two antennas side-by-side. If we plot the SWR performance of each type of dipole, as in Fig. 3, we discover that the hatted dipole has an SWR curve with nearly the same operating bandwidth as the curve for the full-size dipole. In fact, for any level of element shortening, hatting provides a wider operating bandwidth than any method of inductive loading. Nonetheless, all forms of element shortening result in lower feedpoint resistive impedance values. With a length of 70% of full size, the shortened dipole has an impedance about 14 Ohms less than the full-size antenna. For a fixed element length, all forms of inductive loading result in much lower impedance values.

+
+ +
+

A similar situation accrues to 2-element Yagis when we shorten each element to 70% full size and add hats. Let's compare the full-size Yagi from the last episode to a version that uses the 4-spoke hats of the dipole that we just created. Fig. 4 shows the comparative sizes of each beam, using 0.12 wavelength (4.1') spacing.

+
+ +
+

Note an important aspect of Yagi design. Just because we may use various means to shorten the element lengths of a Yagi, we cannot significantly shorten the element spacing and hope for comparable performance. Table 2 shows the dimensions of each array.

+ 
+Table 2.  Dimensions of full-size and 70% hatted Yagis.  All elements 3/8" aluminum.
+Spacing          Driver Length       Reflector Length     Hat-Spoke Length
+WL     Feet      WL      Feet        WL      Feet         WL      Feet
+Full Size Yagi
+0.12   4.07      0.466   15.82       0.503   17.06        ---     ---
+70% Hatted Yagi
+0.12   4078      0.322   10.92       0.348   11.80        .0293   0.99
+
+

There are numerous ways in which to apply hats to elements. The technique used here, which has proven itself in prototypes, is to set a fixed size for the hats, regardless of whether they go on the driven element or on the reflector. As a result, the linear portions of the two elements have different lengths. This technique appears to yield somewhat better performance that using the same length for both linear element sections, with differences in the length of the spokes of the hat.

+

Table 3 provides a comparison between the performance of full-size and hatted Yagis.

+ 
+Table 3.  A comparison of the modeled performance of full-size and 70% hatted Yagis
+Antenna   Frequency      Gain      F-B       Feedpoint Z         SWR
+            MHz          dBi       dB        Ohms
+Full      28             6.98      5.43      15.49 - j48.55      7.34
+Hat                      6.53      2.47      10.39 - j48.51      11.29
+Full      28.5           6.74      9.79      23.05 - j22.49      2.37
+Hat                      6.94      9.28      16.99 - j21.54      2.88
+Full      29             6.25      11.20     32.14 - j 0.00      1.00
+Hat                      6.35      13.85     26.74 + j 0.77      1.03
+Full      29.5           5.82      10.37     40.83 + j20.05      1.82
+Hat                      5.78      12.41     36.03 + j19.22      1.95
+Full      30             5.48      9.17      48.75 + j38.76      2.78
+Hat                      5.34      10.15     43.81 + j35.77      2.99
+
+

The designer may select almost any proportion to use in dividing the element lengths between the linear section and the hat spokes. The combination used here actually gives the hatted Yagi a slight performance improvement at the design frequency. As is clearly visible in Fig. 5, the chief advantage occurs with respect to the hatted Yagi's front-to-back ratio.

+
+ +
+

If we only view the data and patterns for the design frequency, we might go away with a misimpression about the seeming superiority of the hatted Yagi. However, a careful check of the tabular data across the 28-30-MHz sweep suggests that the hatted Yagi has a somewhat narrower operating bandwidth in every category. For example, as shown in Fig. 6, the hatted Yagi's gain curve is somewhat steeper than the curve for the full-size version, especially at the low end of the sweep. The hatted Yagi is on its way toward the point of pattern reversal, just where the full-size Yagi is reaching maximum gain.

+
+ +
+

The same general phenomenon appears in the curves for the front-to-back ratio, shown in Fig. 7. The hatted curve is steeper, and the increased rate of fall-off is especially apparent at the low end of the sweep. In both cases, one might juggle the reflector length slightly so that the curves have equal front-to-back ratios at both ends of the sweep span, although the change might move the frequency at which the ratio reaches its peak value.

+
+ +
+

Because we have shortened the elements in the hatted Yagi, the design-frequency resonant impedance will be lower than for the full-size Yagi. In addition, as shown in Fig. 8, the SWR curves relative to the resonant impedance is steeper, resulting in a reduced operating bandwidth using perhaps the 2:1 SWR value as the bandwidth marker. Nevertheless, as we examine other forms of loaded Yagis in the next episode, it will be useful to keep these curves and the data in Table 3 at hand for comparisons. In general, hatting elements of a set length yields the widest operating bandwidth of any form of element shortening.

+

As will be evident later, hatted Yagis perform like what they are: almost full size beams. The slight performance differences are due to two variables: the shorter elements and the revised geometric relationships offered by those shorter elements.

+
+

Loaded Dipoles

+
A truly shortened element is one that terminates at its linear end. Such elements are not inherently resonant, but show significant capacitive reactance. To achieve resonance requires the insertion of a largely non-radiating inductive reactance. The form of the inductive reactance can be either a solenoid inductor or a shorted transmission line length: the latter are usually called linear loads. Linear loads are placed at the feedpoint (even when they may appear to have been placed elsewhere). Solenoid inductors are placed either at the feedpoint (center-loading) or somewhere farther out along the element as a pair of solenoids, one on each side of the feedpoint (mid-element loading). +

Wherever an inductive load is placed, there is a current gradient representing the missing linear length for which the loading element substitutes. Compare the current distribution curves in Fig. 9 for a full-size and a loaded dipole. Note the sharper step in current at the loading coil positions. Because such loads are only effective where antenna current is relatively high, the missing lengths of linear element represent radiation that for all practical purposes does not occur. Moreover, inductive loads, whatever their form, have losses associated with their resistance. Even high Q inductors introduce losses into the antenna element.

+
+ +
+

Both of these phenomena may be demonstrated by reference to shortened dipoles relative to full-size counterparts. Some loads are more difficult to model than others, but simple solenoid inductors may be modeled well within the limits of variables affecting any model's transfer to fabricated reality. NEC models treat solenoid inductances as wholly non-radiating elements, which is largely but not absolutely true in reality. Physical coils do radiate a bit as a function of the fact that the current magnitude at each end of the coil is not equal, a necessary condition for a solenoid being a "pure" inductance. However, the model also assigns the coil an effective zero space by distributing its loss along the element segment to which it assigned. That segment functions like a linear element, which in a real antenna is missing and replaced by the coil. The results remain as accurate to real antennas as any other aspect of antenna modeling. The more significant keys to accurate modeling lie in the realm of using adequate load values, placing them precisely, and using the proper technique of load assignment for the modeling task at hand.

+

To see effects of shortening antenna lengths alone, however, requires no load, but only an examination of short dipoles. For any model, the capacitive reactance at the feedpoint can be canceled by a lossless center inductance without any change of antenna radiating characteristics. Notice in Table 4 the reduction of gain of the following antennas gradually shortened from full size to 40% of full size. All antennas are at 29 MHz in free space, with the same 0.375" diameter aluminum element.

+ 
+Table 4.  The effects of simply shortening the length of a dipole.
+% of Full      Gain      Feed R         Feed Xc
+100            2.13      72.04          0.79
+ 90            2.05      52.41          102.3
+ 80            1.98      37.76          205.0
+ 70            1.92      26.71          312.5
+ 60            1.87      18.33          430.8
+ 50            1.83      12.01          568.6
+ 40            1.79       7.31          741.6
+
+

These gain reductions are equivalent to using lossless center inductors as loading elements, each sized exactly to compensate for the capacitive reactance remaining at the feedpoint. Although the loss of gain is modest per step, it adds up quickly as we shorten the antenna. Missing gain in the individual dipoles of a 2-element Yagi cannot be restored for any given design. Notice also the reduction of resonant feedpoint impedance down to values where basic efficiency may become a concern.

+

If we use real inductors having a finite Q, the losses grow even faster with element shortening. Table 5 gives free space gain figures for coil Qs ranging from 300 to 50. Although higher values of Q are possible using coils with a high radius-to-length ratio, a Q of 300 may be about the best obtainable in a practical coil before weathering effects reduce that value. A Q of 50 represents a worst-case scenario where maintenance is lax and acid rain is heavy.

+ 
+Table 5.  Some dipole gain values for center-loaded dipoles of various lengths with inductors having various values of Q.
+% of full      Gain with Q =  300       200       100        50
+ 90                           2.02      2.00      1.96      1.88
+ 80                           1.90      1.86      1.75      1.53
+ 70                           1.75      1.67      1.44      1.01
+ 60                           1.54      1.39      0.95      0.20
+ 50                           1.19      0.90      0.14      -1.07
+ 40                           0.52      -0.01     -1.25     -3.03
+
+

A dipole 50% of full size with a loading coil Q of 300 has lost nearly a full dB of gain, while the loss at 70% of full length is less 0.4 dB. Obviously, the gain loss increases faster than the rate of shortening. The rate of loss for lower Qs increases proportionately.

+

A center-loaded dipole can present the user with an illusion of well-being. The feedpoint impedance at resonance will be roughly the sum of the feedpoint impedance with no losses plus the resistive component of the coil's Q. With time, weathering, and lowering Q, a short, loaded dipole may seem to show an improvement in SWR relative to a 50-ohm feedline. In actuality, it is more likely that coil losses are increasing, and the additional resistance is simply converting power to heat.

+

An alternative to center loading is mid-element loading, that is, the placement of loading inductors somewhere along each element away from the feedpoint. Fig. 10 shows the physical difference between the two methods of applying inductive element loading. Claims for significantly increased efficiency unfortunately do not materialize from this arrangement, although the arrangement does show a slightly lower rate of gain decline.

+
+ +
+

As the loading coil is split and moved outward from the antenna center, the required value of inductive reactance necessary to achieve resonance increases. By the time the coils are midway between the element center and the element ends, each coil must have an inductive reactance of about 93% of what a single center-loading inductor would require. For equivalent coil Q, the nearly doubled series resistance of mid-element loading coils tends to wash out most of the gain increase occasioned by letting full current exist at and near the feedpoint.

+

As Table 6 shows, gain improvements are marginal. The chief benefit of mid-element loading is that the feedpoint impedance remains higher than with center loading. As with the previous table, dipoles are 3/8" diameter aluminum in free space.

+ 
+Table 6.  Dipole Performance with mid-element loading coils of various values of Q.
+Coils are located at the mid-point of each element half.
+% full    Load coil Feed R    Gain  (dBi) for Q =
+          reactance Ohms      inf.      300       200       100        50
+          per coil
+ 90        93.0     63.16     2.06      2.03      2.02      1.98      1.90
+ 80       188.0     53.66     2.00      1.93      1.89      1.78      1.57
+ 70       288.0     43.86     1.94      1.80      1.71      1.50      1.09
+ 60       399.0     34.20     1.89      1.59      1.45      1.05      0.35
+ 50       528.0     25.02     1.84      1.27      1.01      0.32      -0.8
+ 40       690.0     16.78     1.80      0.68      0.21      -0.9      -2.6
+
+

Mid-element feedpoint impedance figures average about 10 ohms higher than center-loaded dipole feedpoint impedances for equivalent shortening. However, even with this improvement, illusions of well being are possible. If one ends up with loading coils with a Q of 50 in a dipole only 40% of full size, the antenna will seem to match a coax cable very well--because the RF resistance in the coils will roughly add to the natural resonant impedance of the antenna. In that extreme case, the loss resistance would double the antenna resistance and occupy corresponding amounts of power.

+

In the end, there is little to choose between center and mid-element loading except feedpoint impedance and such mechanical considerations as may apply to the antenna structure. Center loads are more easily supported, but in some cases are a problem to feed. Mid-element loading coils often require one or two upward steps in element diameter to support the coil. Gains for the two systems, with coils of equivalent Q, would be indistinguishable in practice.

+
+

Linear-Loaded Dipoles

+
An alternative to either system of loading is the use of a linear load. Once veiled in mystery, linear loads turn out to be simplicity itself. In purest form, they are nothing more nor less than shorted series transmission line stubs used to provide the necessary inductive reactance for center loading. Each side of the feedline attaches to a section of line run parallel to the main element. The line continues back to the original center junction area and attaches to the main element. Fig. 11 shows two popular ways to configure linear loads. +
+ +
+

If both lines are equidistant from the main element, then straightforward shorted transmission line stub calculations are sufficient to calculate the required length of each stub. Each stub will provide 1/2 of the reactance required for center loading. If the stub lines are not equidistant from the main element, unequal currents will be induced by the field from the main element, resulting in longer linear load lines for the same degree of loading. (For more on this subject, see "Modeling and Understanding Small Beams: Part 4: Linear-Loaded Yagis." Communications Quarterly, Summer, 1996, pp. 85-106.)

+

In some commercial beams, the linear load is made to appear to be placed farther out along the element. The main (large-diameter) element is fed and, on each side, breaks at some distance from center. Smaller lines are run back toward the feedpoint, make a turn and return to the break, to be connected beyond the break point. Despite appearances, these antennas have center-loading linear loads composed of one fat wire and one thin wire. The main antenna element is actually the return thin wire back to the break point where it attaches to the tubing used to finish the element. Although the system has much in the way of mechanical soundness to recommend it, and although the difficulty of calculating the precise length of needed linear load makes empirical experimentation more efficient in antenna development, the system is electrically quite normal.

+

To gain a sense of the advantages of linear loading, let's look at a dipole 70% of full length (11.4') and try to model linear loads of varying proportions upon it. For consistency and comparability of results, all models were done in NEC-4. Due to constraints within NEC, this procedure restricted the construction of linear loads using the same diameter material as the main element: 3/8" diameter aluminum.

+

Two types of linear loads were modeled: those placing both load lines equidistant from the main element and those lining up the lines vertically beneath the element. For these rough samples, variations were limited to changing the spacing from the main element and from line to line. The spacing values were equalized; that is, if the space between lines was 3", then the space from the main element was also 3" for both types of loads. Where E = equidistant load lines and V = vertically suspended load lines, the sample models appear in Table 7:

+ 
+Table 7.  Sample linear load models used for comparisons
+Antenna        Specification
+E3             Equidistant lines 3" apart and 3" from the main element
+E6             Equidistant lines 6" apart and 6" from the main element
+V1             Vertically suspended lines with 1.5" spacing
+V3             Vertically suspended lines with 3" spacing
+V6             Vertically suspended lines with 6" spacing
+
+

In Table 8, the meaning of all values is obvious, except perhaps equivalent Q. Replacing the linear load with an inductor of sufficient size to resonate the antenna and then adding resistive losses until the element gain equals the gain of the linear-loaded element derives the value of equivalent Q. Although these values are useful markers with respect to gain, they will be less useful with respect to operating bandwidth. "Length" indicates the total length of the linear load from outer tip to outer tip.

+ 
+Table 8.  Modeled performance of the sample linear-loaded dipoles
+Antenna        Length    Gain dBi       Feed Z              Equiv. Q
+                                        (R +/- jX Ohms)
+E3             4.46'     1.88           24.1 + j0.12        1150
+E6             3.14'     1.89           21.3 + j0.32        1400
+V1             7.50'     1.71           25.7 - j0.37         230
+V3             5.36'     1.83           22.9 + j0.16         500
+V6             3.64'     1.90           20.2 + j0.31        2000
+
+

For each type of linear load (equidistant and vertically spaced), wider spacing results in a shorter load length. The inductive ractance of a shorted transmission line is the characteristic impedance of the line times the tangent of the lines electrical length. Since we need the same reactance in each case, as the characteristic impedance of the lines goes up the length comes down. As we increase the spacing between the lines, the characteristic impedance goes up. Even though vertically spaced linear loads do not adhere strictly to the general equations due to varable coupling on the two lines of the load, they do follw the trands very well. From these few samples, some other trends (verified by a large number of file samples) are also evident:

+

1. The wider the spacing among elements, the higher the element gain and equivalent Q at the design frequency.

+

2. Vertically suspended linear loads vary more widely in length, gain, and equivalent Q than equidistant linear loads.

+

3. The wider the spacing (between lines and from the antenna to the lines), the lower the feedpoint impedance of the resonant element.

+

Most notable is the lack of significant variation in the gain of the two equidistant linear load models. The spacing is doubled between the two, but the gain varies by almost nothing. These models correspond most closely to a pair of series connected shorted transmission line stubs. Independent calculation of required stub lengths produces values for each side of center that are longer than the modeled stubs by about the length of the vertical connectors. The connecting lines are not the entire story here, since stub line calculations presume that the shorting connection at the stub end is insignificant. However, 3" and 6" connecting rods are likely of some significance at 29 MHz.

+

Vertically suspended linear loads vary more widely, in part due to the unequal induced currents from the nearby main element. For these loads, the designer is faced with a trade-off: load spacing and element gain on the one hand and feedpoint impedance on the other. Equidistant load lines may be placed close to the main element to increase the feedpoint impedance without significant loss of element gain.

+

For a final comparison, we may look at the operating bandwidths of all the loaded elements, including those with a center-loading inductor, mid-element-loading inductors, and linear loads. As before, the table will show calculated SWR values for 28 through 30 MHz at 0.5 MHz intervals. Linear loaded antennas will be designated as given in this section. Center-loaded and mid-element-loaded antennas will be called CL and ML, respectively, and followed by a number representing a value of Q used in earlier comparisons. The inductor-loaded antennas will be restricted to those 70% of full size to correspond to the linear loaded models. A full-size dipole and a 70% hatted dipole for 29 MHz are included for comparison. See Table 9.

+

Figures for inductor-loaded models were developed by introducing the model load(s) as inductors (values of inductance in uH) with the requisite reactance for resonance at the design center frequency. Since reactance varies with frequency, using a constant reactance in the load model would have produced too optimistic a set of SWR figures. All models retain the 3/8" diameter aluminum construction, and figures are for free space.

+ 
+Table 9.  SWR performance of all of the types of dipoles in this episode
+Note: all shortened dipoles are 70% of full size.
+
+Antenna   SWR at    28        28.5      29        29.5      30   MHz
+
+Full size dipole    1.71      1.30      1.00      1.28      1.62
+
+70% hatted dipole   1.83      1.34      1.02      1.36      1.78
+
+CL-300              4.06      2.06      1.00      1.99      3.57
+CL-200              3.96      2.03      1.00      1.96      3.50
+CL-100              3.72      1.96      1.00      1.90      3.31
+CL-50               3.32      1.84      1.00      1.79      3.00
+
+ML-300              3.77      2.00      1.02      1.89      3.32
+ML-200              3.70      1.98      1.02      1.86      3.28
+ML-100              3.51      1.92      1.02      1.81      3.11
+ML-50               3.20      1.83      1.02      1.71      2.82
+
+E3                  4.35      2.14      1.01      2.08      3.87
+E6                  4.34      2.12      1.02      2.10      3.88
+
+V1                  4.53      2.22      1.01      2.10      4.03
+V3                  4.30      2.12      1.01      2.08      3.85
+V6                  4.35      2.12      1.02      2.10      3.88
+
+

Carrying out SWR to 2 decimal figures is largely spurious in terms of practical operation. However, adding the final decimal place makes the trends clearer and also clarifies the lowest SWR on which the other figures are based.

+

All forms of element loading narrow the operating bandwidth and are roughly related to the Q of the loading element(s). For inductor loading, the 2:1 SWR bandwidth increases as Q decreases, but the differences are small. The differences between comparable Q-values for center and mid-element loading are smaller yet.

+

The operating bandwidth for a linear loaded element shows the inherently higher Q of the system, but the actual figures are not directly related to an assignable value of Q. Among the vertically suspended linear loads, V1 had the lowest assignable Q in terms of gain equivalence, but also displays the narrowest bandwidth of the entire group. Once a certain lower limit of element spacing is exceeded, operating bandwidth tends to be the same for all practical purposes.

+

In the end, the use of linear loading trades higher gain for a narrower operating bandwidth than inductor loading. Mid-element loading provides a higher feedpoint impedance than either form of center-loading. (However, the hat-method of shortening elements yields the broadest bandwidth of all of these 70%-length elements.)

+

The next question is how the characteristics of inductively loaded elements will show up in 2-element Yagis.

+
+ +

+
+

Updated 05-06-1997, 04-25-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
p Go to Part 4: Loaded Yagis +

Return to Index

+

Topics: HF Upper, Loading, Yagi


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+

What Can We Expect from a 2-Element Beam?

+
+
+

Part 4: Loaded Yagis

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

One poorly appreciated fact about shortened Yagis is to what degree the antenna geometry plays a role in optimizing performance. When looking at shortened Yagis with hatted elements, we found a set of dimensions for the driven element and the reflector which provided close to the best obtainable performance for a 2-element beam designed to maximize front-to-back ratio and to resonate the beam. Interestingly, if we retain a driven element that is about 70% full size, we may use virtually the same main element dimensions with all forms of loading and achieve close to the best performance obtainable.

+
+

Inductively Loaded Yagis

+
In essence, all methods of loading (center inductor, mid-element inductors, or linear loading) are doing the same job in the same manner: replacing a linear section of antenna element with inductive reactance. A beam with elements about 70% of full size will have the same optimal geometry, whichever loading method is used. +

Because maximum gain at the design center frequency results in poor, if not unusable, performance below the center frequency, the models we shall examine will by optimized for maximum front-to-back ratio and resonance. For some models, the maximum gain frequency will lie very close to (and below) the front-to-back peak frequency, and the beam reversal point for a few samples will fall inside the 2 MHz 10-meter span we have chosen as our test bed. In fact, for loaded Yagis, the performance below the center frequency drops off much more rapidly than performance above the center frequency, especially when compared to the rates of degradation for a full size beam.

+

We may begin with 3 models: 1 each of the center inductor, mid-element inductors, and linear loaded variety. Each antenna will be spaced 0.12 wavelength (4.1' at 29 MHz). The elements will be close to 70% of full size. The driven element will be 11.48' long, with a reflector 11.95' long. Elements, as in all the models in this refresher, will be 3/8" diameter aluminum.

+

The center-inductor loaded model called for an inductive reactance for each element of 288 Ohms. This translates into a solenoid with an inductance of 1.5806 uH to achieve resonance and very close to peak front-to-back ratio.

+

The mid-element loading coils that we needed to yield the same result had 281 Ohms reactance or an inductance for each of the 4 coils of 1.5422 uH. Fig. 1 shows the outlines of the two types of inductively loaded Yagis.

+
+ +
+ 
+Table 1.  Modeled performance of inductively loaded 2-element Yagis
+
+Antenna   Resistance     Gain (dBi)     F-B (dB)  Feed Z (R +/- jX)
+
+Full-size       --       6.25           11.20     32.14 - j0.00
+
+Center-load
+Infinite Q       0       6.20           20.04     17.07 - j0.00
+Q=300          0.96      5.79           18.31     18.14 - j0.68
+Q=200          1.44      5.59           17.57     18.67 - j1.00
+Q=100          2.88      5.03           15.71     20.28 - j1.92
+
+Mid-element-load
+Infinite Q       0       6.29           16.84     24.14 + j0.41
+Q=300          0.93      5.87           15.66     25.76 - j0.53
+Q=200          1.40      5.67           15.14     26.58 - j0.98
+Q=100          2.80      5.09           13.75     29.03 - j2.30
+
+

Table 1 lists the gain, front-to-back ratio, and feedpoint impedance of these two initial antennas. The table also shows a series load resistance that is necessary to produce coil Qs of 300, 200, and 100, in order to investigate the effects of Q on performance. Models are in free space for this initial design test. The table includes a full-size Yagi of the same (0.12 wavelength) spacing for comparison.

+

Let's first look at the patterns, shown in Fig. 2. Each patterns set includes the full size Yagi for comparisom. The other plots shows (for effective contrast) the patterns for an infinite Q and a low Q of 100. In both cases, the patterns show that loaded elements often do better at improving the front-to-back ratio at the design frequency than they do with respect to gain. Only with infinite Q does the loaded Yagi gain equal the full size Yagi gain. But, of course, all loading inductors have a finite Q.

+
+ +
+

Gain: Once we introduce a finite Q, the gain drops rapidly, as is evident if Fig. 3, which tracks the gain over the levels of Q in Table 1. Note that the X-axis is not a linear scale. With an optimistic Q of 300, the gain of either load model approaches a half dB less than a full size Yagi with the same design goals. Another 3/4 dB disappears in the transition from a Q of 300 to a Q of 100. Most coils cited in commercial designs have had values below 300 and above 100, so the actual gain of such antennas will be between 5 and 5.75 dBi (or around 3 to 3.5 dB better than a dipole in free space). Gain expectations for a beam 70% full size and spaced 0.12 wavelength that are higher than this value are unwarranted.

+
+ +
+

Front-to-back ratio: Shortened Yagis are capable of much higher front-to-back ratios than full size 2-element Yagis, as is clear in Fig. 2. As shown in Fig. 4, the front-to-back ratio does decrease as the Q decreases. The center-loaded model has a theoretic 3 dB advantage over the mid-element model, although that advantage begins to evaporate with finite Qs. Nonetheless, one true advantage of a loaded Yagi over a full-size model is the superior front-to-back ratio.

+
+ +
+

Feedpoint impedance: Fig. 5 tracks the feedpoint resistance for both forms of loading as we change the load Q. The resistance increases in step with the series resistance of the loading inductors. The center-loaded model exhibits the lowest feedpoint impedance of any of the loaded 2-element Yagis. Although it can be used with coax and a beta match, the low impedance raises questions of basic efficiency in terms of power consumed by resistive losses throughout any practical assembly. Note that as Q decreases, the feedpoint impedance increases proportionally to the total series resistance in the driven element.

+
+ +
+

It is also significant to examine the operating bandwidth of loaded 2-element Yagis. We would expect something narrower than a full-size Yagi, and figures do not disappoint us. Models for obtaining operating bandwidth and other figures across a span of frequencies must enter the resistance and inductance of the loading coils (rather than resistance and reactance) and allow NEC to calculate the reactances for each frequency selected. Again, the full-size Yagi is presented in Fig. 6 and in Table 2 for comparison with only the Q=200 models of loaded Yagis. (The use of a Q of 200 corresponds closely to the Qs of coils used in trapped and loaded commercial beams.)

+
+ +
+ 
+Table 2.  A comparison of SWR values relative to driver resonance
+Note:  All antennas spaced 0.12 wavelength
+
+Antenna   SWR at    28        28.5      29        29.5      30   MHz
+Full-size            7.34     2.37      1.00      1.82      2.78
+Center-ld, Q=200    22.85     8.96      1.11      2.45      4.12
+Mid-el-ld, Q=200    21.90     8.77      1.12      2.71      4.75
+
+

The operating bandwidth of the loaded Yagis is so narrow that the 2 MHz spread is too wide to be informative. It is clear that the SWR climbs very much more slowly above the design center frequency than below it. Whether the antenna has worthwhile characteristics in that region requires that we look at most of the antenna's properties over a narrower spread of frequencies--perhaps a half MHz either side of center. Therefore, Table 3 provides data for 28.5 to 29.5 MHz in 0.25-MHz increments.

+ 
+Table 3.  Detailed performance from 28.5 to 29.5 MHz
+
+Frequency      28.5      28.75     29        29.25     29.5 MHz
+
+Full size Yagi
+Gain (dBi)     6.74      6.49      6.25      6.02      5.82
+F-B (dB)       9.79      10.91     11.20     10.41     10.37
+SWR            2.37      1.48      1.00      1.39      1.82
+
+Center-loaded Yagi, Q=200
+Gain (dBi)     4.87      5.92      5.61      5.08      4.64
+F-B (dB)       2.24      9.90     17.63     13.16      9.69
+SWR            8.96      2.70      1.11      1.75      2.45
+
+Mid-element-loaded Yagi, Q=200
+Gain (dBi)     4.86      5.93      5.67      5.17      4.74
+F-B (dB)       1.98      9.01     15.14     12.74      9.75
+SWR            8.77      2.70      1.12      1.85      2.71
+
+

If the design center frequency is shifted downward by about 150 kHz, the full size Yagi would provide a 2:1 SWR operating bandwidth over the full 1 MHz spread. Gain and front-to-back ratio would be respectable throughout the range (for an antenna of this type).

+

The operating bandwidth for the loaded Yagis is less than 700 kHz. The maximum gain frequency occurs within this spread and marks the limit of the lower frequency excursion for a 2:1 SWR. Above the design center frequency, the SWR climbs at half the rate as below it. Gain and front-to-back ratio fall off much more rapidly than with a full size model. Fig. 7 shows the gain from 28 to 30 MHz for the 3 antennas using an increment of 0.1-MHz to reveal the finer detail. Note the gain dip at or very near to 28.4 MHz, indicating the frequency at which the forward pattern reverses direction. The reversal point for the full-size Yagi occurs below the limit of the sweep.

+
+ +
+

Indeed, the higher front-to-back ratio obtainable with shortened and loaded elements now shows itself for what it is: a fairly narrow peak with extended values closer to those of the full size antenna. At the upper frequency limit, gain is less than 3 dB better than a dipole. Fig 8 gives us a wider view that once more shows the pattern-reversal frequency to be near to 28.4 MHz.

+
+ +
+

The performance of the two inductively loaded Yagis parallels to a very high degree the performance of the full-size Yagi as we vary the height of the antenna above average ground. Table 4 provides data from 0.0625 wavelength to 1.0 wavelength above ground for the loaded Yagis with indortor Q values of 200--with the full-size Yagi for comparison. The table lists only one column for the elevation angle of maximum radiation, since that value is the same within +/-1 degrees at the very low heights and is exactly the same above a height of 3/8 wavelength.

+
+ +
+

Fig. 9 provides some insight into the variations of gain and front-to-back ratio for the antennas by overlaying elevation and azimuth patterns at heights of 7/16, 11/16, and 1 wavelength. The elevation patterns show the deacreasing elevation angle of the main lobe as the hight increases, along with the development of higher angle lobes. As well, note the varying strength of the rearward lobe in the elevation patterns.

+
+ +
+

The azimuth paterns show the growth of forward gain with increasing antenna height. However, a more significant feature is the evolution of the rearward lobe or lobes as the height varies. Although these patterns derive from the center-loaded model, they also apply with only very small modification to the mid-element-loadedc and the full-size Yagis.

+
+ +
+

In general, the overlapping gain lines for the two inductively loaded Yagis track very well with the gain of the full-sixe Yagi, as is evident in Fig. 10. However, both loaded Yagis show greater sensitivity than the full size Yagi in the height region around 7/8 wavelength. Note the visible decrease in gain (that is nonetheless operationally insignificant) in that height region.

+

The front-to-back curves are more distinct for the three antennas, as shoen in Fig. 11. At the design frequency, 29 MHz, the full-size Yagi shows the lowest front-to-back ratio. However, the full-size antenna curve is also the shallowest in terms of its peaks and valleys. In contrast, the difference between a peak value and the adjacent low value is considerably greater for the loaded Yagis.

+
+ +
+

In the preceding episode, we determined the recording gain values in dBd could be both misleading and a source of mischief. Simply subtracting 2.15 from the gain in dBi is a fairly useless exercise. Comparing the antenna gain over ground with a dipole at thje same height yields curve of dubious utility. Therefore, these exercises have omitted that data. However, the dipole information is available in past episodes for anyone who wishes to perform the simple calculations.

+

Between the two types of inductively loaded Yagis, the center-loaded model yields higher peak front-to-back ratios, while the mid-element-loaded model has higher feedpoint impedances for lower losses for loss sources other than the loading coils. The final decision on which type of loaded Yagi to build is an individual option that may depend upon construction and matching variables as well as basic performance. Both loaded Yagis use elements that are 70% of full size, which is about the recommend limit to shortening. If the element lengths decrease any further, the gain would fall rapidly as a function of both the short elements and the higher losses in practical loading inductors. As well, the operating bandwidth would also decrease, limiting the utility of the antenna on all but the smallest amateur bands (such as 30m 17, and 12 meters).

+
+

Linearly Loaded Yagis

+
+

I have purposely excluded the linear-loaded 2-element Yagi of 70% full size from the comparison so far because it has some interesting properties. Linear-loading, especially when executed using loading elements the same size as the main element, is inherently high Q, with all the advantages and disadvantages. Let's scan one of the linear-loaded models, choosing the one with load lines equidistant form the main element by 3" and 3" apart. With the 3/8" diameter aluminum elements 11.48' and 11.95' for the driven element and reflector, respectively, the load lines were 2.37' either side of center (4.75' overall) for resonance and maximum front-to-back ratio. Because the linear-loading elements are directly modeled as physical entities, there are no mathematical loads in the model. Fig. 12 provides the general outline of the beam.

+
+ +
+

If we use the restristed passband (28.5 to 29.5 MHz) that we used for the inductively loaded beams, we can sample the performance of the antenna at 0.25-MHz intervals. See Table 5.

+ 
+Table 5.  Performance of a 70% linear-loaded Yagi from 28.5 to 29.5 MHz
+
+Frequency        28.5           28.75          29             29.25          29.5 MHz
+Gain (dB         4.78           6.26           5.95           5.15           4.50
+F-B (dB)         0.86           6.05           16.31          16.81          11.19
+R +/- jX         6.36-j34.83    8.08-j16.56    14.54+j0.03    22.35+j12.14   28.35+j21.34
+SWR              15.82          4.47           1.00           2.14           3.27
+
+

The SWR-based operating bandwidth for this high-Q model is under 400 kHz at 29 MHz (and proportionately less for lower band models). Peak values are comparable to those obtainable from inductor-loading, but very short-lived as one changes frequency. In fact, within even this restricted passband, the pattern revesal occurs, as indicated by the dips in both the forward gain and the front-to-back values, shown in Fig. 13.

+
+ +
+

The graph uses a sweept increment of 0.1-MHz, and the lowest values occur at 28.5 MHz. However, the reversal occurs slightly above this frequency, but below 28.6 MHz. To illustrate how sudden and complete the pattern reversal is below the frequency of maximum gain, Fig. 14 shows free-space patterns for the linear loaded Yagi at half-MHz intervals.

+
+ +
+

Although the front-to-back ratio at 28.5 MHz is negligible, the forward lobe has definitely change direction. with its ingerently high-Q linear loading system, the sample Yagi is useful only over a very narrow bandwidth. Indeed, for most purposes, the lower Q of the sample inductively-loaded versions may be more useful. Nevertheless, they do not have very wide bandwidths, just slightly larger spreads than the linear-loaded version.

+
+

Strategies for Increasing the Bandwidth of Loaded Yagis

+
Can anything be done to increase the operating bandwidth of this antenna? One strategy that is open to all three forms of loading is to increase the spacing between elements. If we select 0.16 wavelength (5.4' at 29 MHz), we can expect not only a wider operating bandwidth, but somewhat higher feedpoint impedances, along with reductions in gain and front-to-back ratio. +

Table 6 presents the results of this design experiment. A full-size version of the antenna appears as a comparator for the 3 loaded Yagis.

+ 
+Table 6.  Performance of full-size and loaded Yagis with 0.16 wavelength spacing
+
+Frequency      28.5         28.75        29           29.25        29.5 MHz
+Full size Yagi
+Gain (dBi)     6.56         6.34         6.12         5.92         5.74
+F-B (dB)       9.79         10.60        10.84        10.68        10.29
+R +/- jX       36.9-j19.8   41.9-j9.5    46.9-j0.0    51.5+j9.1    55.8+j17.9
+SWR            1.70         1.27         1.00         1.22         1.47
+
+Center-loaded Yagi, Q=200
+Gain (dBi)     6.29         6.15         5.75         5.34         4.98
+F-B (dB)       6.78         11.35        13.98        12.86        10.87
+R +/- jX       13.5-19      17.9-9       22.4-1       26.0+5       28.7+11
+SWR            3.12         1.66         1.06         1.28         1.62
+
+Mid-element-loaded Yagi, Q=200
+Gain (dBi)     6.17         6.11         5.72         5.32         4.97
+F-B (dB)       6.97         13.05        15.84        13.12        10.62
+R +/- jX       14.3-30      20.5-14      27.7-.4      34.1+10      39.4+20
+SWR            4.51         1.89         1.02         1.50         2.02
+
+Linear-loaded Yagi
+Gain (dBi)     6.62         6.59         5.91         5.28         4.79
+F-B (dB)       4.30         10.84        14.87        11.95        9.26
+R +/- jX       9.3-22       14.3-9       20.1+.4      24.3+8       26.9+15
+SWR            4.96         1.85         1.02         1.49         2.08
+
+

At a spacing of 0.16 wavelength, a full-size 2-element Yagi is a good match (with a 1:1 balun or choke) for 50-ohm coaxial cable. The other beams require a beta match (or similar). However, note the table carefully: the center-loaded models--both inductor and linear--improved their operating bandwidths and increased their feedpoint impedances by a greater amount than the mid-element-loaded model. At the closer (0.12 wavelength) spacing, the center and mid-element inductor loaded models were very similar in operating bandwidth, with the linear-loaded version much narrower. With the wider (0.16 wavelength) spacing, the mid-element and linear loaded models are on a par with each other (with the linear-loaded model showing a slightly narrower bandwidth), while the center-loaded model shows at least 100 kHz wider operating bandwidth.

+

At the same time, the wider mid-element-loaded model has lost less of its gain and front-to-back ratio relative to the closer-spaced model than either of the other two antennas. The advantage of one method of loading over another is marginal and may be secondary to structural and other design concerns. The general effect of wider spacing to increase the operating passband of a 2-element Yagi is most effective on the center-loaded models and least effective on the mid-element-loaded model.

+
+

Pint-Sized Loaded Yagis

+
Before drawing this refresher to a close, let's briefly look at a pair of beams with elements that have been shortened even further: to 50% of full size point. At 29 MHz, the driven element would be about 4' long, with the reflector 4.095' long with a spacing of 0.12 wavelength. We shall compare a center inductor with mid-element inductors as loads with a Q of 300. By now, we know not to expect wide differences between the two types of loading. More interesting are expectations of operating bandwidth, gain, and front-to-back ratio. As always, the elements are 3/8" diameter aluminum, and these models are once more in free space. +

Table 7 provides the modeled data for free-space. A linear-loaded model does not appear due to the very large size of the loading transmission-line stubs. In the gain column, R means that the pattern shows gain in the reverse direction. To maximize the potential of these beams, I have raised the inductor Q to 300.

+ 
+Table 7.  Performance of half-length Yagis using inductive loading with 0.12 wavelength element spacing
+
+Frequency      28.5         28.75        29           29.25        29.5 MHz
+Center-loaded Yagi, Q=300
+Gain (dBi)     2.06 R       3.73         4.46         3.97         3.46
+F-B (dB)       1.09         6.07         27.15        11.07        7.11
+R +/- jX       5.5-j27      6.6-j14      12.8-j3      19.2+j2      20.7+j5
+SWR            12.7         4.56         1.23         1.52         1.76
+
+Mid-element-loaded Yagi, Q=300
+Gain (dBi)     6.32 R       4.16         4.59         4.07         3.57
+F-B (dB)       0.98         7.18         31.15        11.04        7.27
+R +/- jX       10.6-47      13.4-j24     25.0-j.4     35.3+j6      38.9+j15
+SWR            11.1         3.79         1.16         1.50         1.90
+

At the design frequency, gain has dropped to about 2.5-dB higher than a dipole, and the rate of change is higher than for the 70% models with which we have experimented. However, as elements are radically shortened, it is possible to achieve for very narrow frequency limits indeed exceptional front-to-back ratios with a 2-element Yagi. Of course, the front-to-back ratio quickly diminishes off the design frequency to ordinary levels associated with an antenna with a very narrow operating bandwidth.

+

Newer operators, especially those whose prior antenna experience has been limited to verticals or simple wire dipoles, often make an error when they use their first beam. Received stations in the forward direction seem to be clearer and stand out above the background noise, whether atmospheric or from other stations. The new beam user tends to assume that the increased signal-to-noise ratio is a function of gain. As a result, many a mediocre beam has enjoyed an unwarranted reputation for its forward gain.

+

The attribution of clarity to gain is very often an illusion. For very small beams--like the 2-element Yagis with which we have experimented--the improvement in received signals may be largely do the the antenna's front-to-back ratio. More correctly, it is due to the general reduction of gain to the rear quadrants. Even a 10-dB front-to-back ratio tend to indicate an average gain level to the rear that is 15 or more dB lower than in the forward direction. (Remember that for almost all of our designs, the 180-degree front-to-back ratio is also the worst-case front-to-back ratio.) For reception, the front-to-back ratio is as important--and often more important--than forward gain in allowing us to hear well in the favored direction.

+

The actual forward gain plays its most important role with the transmitted signal. Whether the station on the otheer end can hear us is a joint function of our forward gain and the conditions between us. (In many instances, the outgoing and the incoming conditions may not be the same, and so what we receive may not indicate correctly what is happening in the ionosphere to the signal that we transmit.) Since we lack means to separate and measure the two factors, we tend to over-estimate the gain of our 2-element antenna. The illusion may create a happy feeling, but it is often just an illusion.

+

There is one more design illusion we can create with this half-size beam. Note that the SWR increases above the design frequency at a slow rate. The antenna is capable, in strictly SWR terms, of an operating bandwidth of over 0.5 MHz. However, in the upper half of the range, gain exceeds a dipole only by about 1.5 dB or so, and the front-to-back ratio is on a constantly descending curve. Citing the design frequency performance figures and then, without further explanation, providing a figure for operating bandwidth, might easily mislead a potential builder with respect to performance anticipation.

+

It would be interesting to see to what degree the problems associated with half-size 2-element Yagis might be overcome by increasing the spacing. Therefore, let's look at these same antennas re-optimized for front-to-back ratio and resonance with a spacing of 0.16 wavelength (5.4' at 29 MHz). Table 8 supplies the modeling data.

+ 
+Table 8.  Performance of half-length Yagis using inductive loading with 0.16 wavelength element spacing
+
+Frequency      28.5         28.75        29           29.25        29.5 MHz
+Center-loaded Yagi, Q=300
+Gain (dBi)     2.75         4.83         4.61         3.92         3.40
+F-B (dB)       0.34         8.56         17.16        9.99         7.90
+R +/- jX       6.7-j22      9.1-j11      14.2-j3      16.6+j2      17.2+j8
+SWR            7.78         2.72         1.22         1.25         1.71
+
+Mid-element-loaded Yagi, Q=300
+Gain (dBi)     2.89         4.95         4.78         4.13         3.61
+F-B (dB)       0.15         7.78         15.94        10.55        7.40
+R +/- jX       13.3-j41     17.7-j19     27.2-j2      33.1+j8      35.3+j20
+SWR            7.00         2.50         1.10         1.40         1.96
+
+

Interestingly, the wider spaced versions of the half-size Yagi achieve marginally more gain than the closer spaced versions, although the front-to-back ratio peak is much smaller for these Q=300 models. As a reminder, the fact that the SWR does not go to 1.0 is due to the modeling process used: the antennas were resonated with lossless coils and then losses were added to achieve the desired Q.

+

Clearly, the SWR curve is also flatter for these antennas than for the closer models, and operation over a 600 kHz span of 10 meters should be possible (with proportionately smaller bandwidths on lower bands to which the antennas might be scaled). Although the resistive component of the feedpoint impedance of the center-loaded model is low enough to cause concern, the impedance of the mid-element model is high enough for an efficient beta match to coaxial cable.

+

As a parting shot, let's place the mid-element-loaded version of the half-size 2-element Yagi, with its 3/8" diameter aluminum elements, over real ground and see what we get. Table 8 tells the story.

+ 
+Table 8.  Mid-element-loaded Yagi, Q=300, at various heights above average ground
+Height    TO Angle    Gain dBi     F-B dB      Feed Z Ohms
+FS        --           4.78        15.94       27.23 - j2.46
+1/8 wl    58           3.92         5.82       22.13 - j4.73
+1/4       45           7.17        11.40       23.94 + j0.08
+3/8       34           8.46        17.41       28.24 + j0.36
+1/2       26           9.47        19.13       29.74 - j3.01
+5/8       21           9.89        14.38       26.65 - j4.49
+3/4       18           9.81        13.85       25.69 - j2.09
+7/8       16           9.91        16.20       27.41 - j1.13
+1         14          10.19        18.14       28.49 - j2.58
+
+

Compared to a dipole, the half-size Yagi suffers at low heights (below 3/8 wavelength) due to its high elevation (or take-off) angle of maximum radiation angle. Above that height, it provides a consistent gain over a dipole in the 2.5 dB ballpark. Front-to-back ratio and feedpoint impedance are stable with height increases, making the antenna quite predictable. The one limiting factor in these figures is that they are peak figures. Performance in one or another way will be less as we move off the design frequency.

+

This and the other models should make usable antennas, especially when scaled for lower frequencies--so long as we do not expect of them or claim for them more than they can do.

+
+

Conclusion to Notes on Driver-Reflector Yagis

+
We have just about exhausted the potential for the 2-element driver-reflector Yagi, at least in broad outline. Or goal has been to develop an understanding of the pefrformance patterns and limitations of these antennas, not only at their design frequency, but also across a reasnable operating passband. Some of the designs are subject to refinement, and some we should likely not waste our time on in trying to achieve better performance from them. +

A word about the models: although every effort has been made to optimize them in accord with the expressed design goals of maximum front-to-back ratio at antenna resonance, there is no guarantee that another few hundredths or even a tenth of a dB might not be garnered by even more painstaking modeling. However, do not expect NEC or MININEC to yield much more than these models. If a model seems to deliver a lot more than the ones in this refresher, it is likely that the model has a problem or in some way presses one or more of the limits of the modeling program.

+

Two-element driver-reflector Yagis, in either full-size or shortened versions, have an important place in amateur radio. Understanding what they can and cannot do is critical to station and operation planning. I hope this refresher on 2-element performance contributes something to that cause. However, we have wholly neglected the driver-director 2-element Yagi. Therefore, let's spend one more episode on this type of Yagi and other methods of increasing 2-element Yagi gain.

+
+ +

+
+

Updated 05-07-1997; 04-29-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Part 5: Strategies for Improving Forward and Rearward Performance

+

Return to Index

+

Topics: HF Upper, Loading, Yagi


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+

What Can We Expect from a 2-Element Beam?

+
+
+

Part 5: Strategies for Improving Forward and Rearward Performance

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+ There are strategies to improve the gain and/or the front-to-back ratio of a 2-element array. The gain and front-to-back performance given in earlier sections are the best obtainable within the design goals (maximum front-to-back ratio and resonance) for a 29 MHz Yagi model using 3/8" aluminum elements in a reflector-driven element arrangement. As noted, these elements scale to reasonable values for lower HF bands, but are not the final word on desirable element sizes. Limitations of both the antenna type and the method of study have been noted throughout. +

Let's look at some of the strategies for improvement and divide the work into 2 parts: strategies that can improve front-to-back ratio and strategies that may improve both the gain and the front-to-back ratio. Additionally, we shall look at only some samples of strategies, because the total number of ways to go about the process is limited only by the antenna designer's imagination. However, we shall be able to note some very interesting general trends.

+
+

Improving Rearward Performance

+
There are two chief ways to improve front-to-back performance of a 2-element array: phasing the two elements and altering standard 2-element geometry. +

The 2-Element Phased Array: I have done an extensive study of the ZL Special, in "Understanding and Modeling Small Beams: Part 5: The ZL Special," Communications Quarterly, (Winter, 1997), 72-90. The ZL Special became popular in the 50s after a series of articles by ZL3MH/ZL2QQ, George Prichard, with some quick test work by G2BCX. Claims of 7 dBd gain and 40 dB front-to-back ratios were common, mostly because the antenna outperformed many of the ill-designed 3-element Yagis of the period. It remained almost a constant claim that the antenna was a phased array 1/8 wavelength separated and using a twisted 45-degree phase line to give 135-degree phasing. It was Roy Lewallen who pointed out in the 1980s that is was not the impedance at the rear element that was critical, but the current, and this changed the analysis ball game, although it appears few have taken up the challenge.

+
+ +
+

The ZL-Special is only one of several types of the 2-element horizontal phased arrays, and Fig. 1 does not show all of the possibilities. While the ZL-Special, with a single phase-line, is popular in the U.S and in the British Commonwealth, the HB9CV, with 2 phase lines fed at the center point between elements is popular in the rest of Europe. Due to the impedances of the lines and the elements, it usually requires a gamma match at each element. A much simpler double phase-line arrangement appears under the title "modified." The two lines have unequal lengths, with the feedpoint at the junction of the two lines. It achieves the same goal as the other two designs, but allows the use of common transmission lines, such as coaxial cable, as the phase line. The variety of phasing techniques led me to do a multi-part study for The National Contest Journal a few years ago, and the episodes are at this website. See "Some Notes on Two-Element Horizontal Phased Arrays." Note that in Fig. 1, we do not refer to the elements as a driver and reflector, since we are driving both elements. In fact, both elements receive energy via direct feed and by coupled energy from the other element. Generally, we call the element in the direction of the forward lobe element 1 and the rearward wire element 2.

+

Since current goes through a 360-degree cycle, not a 180-degree cycle like impedance along a transmission line, the proper analysis of a one-line ZL-Special must treat it as a -45-degree phased array. The minus sign is the product of the phase line twist. Once we make this shift in perspective, we can analyze the relationships of the current magnitudes and phases along the line such that they yield correct values for the spacing used and wind up with identical voltage magnitudes and phases at the junction with the feedline. For a given situation, line length, characteristic impedance, and velocity factor combine so that few values will satisfy the requirements, and fewer still if we stick to available commercial lines.

+

The spacing need not be precisely 1/8 wavelength, since every spacing between a very small one and something just under 1/4 wavelength has a current magnitude and phase requirement for the rear element that will yield maximum front-to-back ratio. In fact, for 1/8 wavelength spacing, the current phasing must be about -43-44 degrees, at 0.1 wavelength spacing, the current phasing must be about -34 degrees, and at 0.15 wavelength spacing, the current phase must be about -53 degrees. A similar analysis applies to other types of phased arrays. Indeed, the goal of the phase lines, if we have more than one of them, is to establish the relative current magnitude and phase relationship required for a desired pattern based on the length of the two elements and on the spacing between them. The element diameter will have a small but noticeable effect on the process, since it also affects the mutual coupling between elements.

+

In general, a pair of phased horizontal elements is not capable of a maximum forward gain in excess of about 7.1 dBi in free space. That gain level is approximately the peak gain of the 2-element parasitic Yagi when set for maximum gain. Like the maximum-gain Yagi, the phased array--when set for maximum gain--has a very poor front-to-back ratio, usually well below 10 dB. The phased element pair, however, can achieve a much higher front-to-back ratio than the parasitic driver-reflector Yagi. Because we can control the current magnitude and phase-angle relationship between the two elements, we can reach front-to-back levels as high as 50 dB at a design frequency. The high front-to-back ratio has several limitations. First, it occurs at a specific frequency and decreases immediately as we move above or below that frequency. Second, the gain the accompanies the maximum front-to-back ratio is slightly less than we can get from driver-reflector Yagis with element spacing values between 0.12 and 0.16 wavelength.

+

For these reasons, most serious phased-array designer aim for a middle ground between maximum gain and maximum front-to-back ratio. There is a middle ground that shows a small gain improvement but a considerable (8 to 10 dB) front-to-back ratio improvement over the driver-reflector Yagi. The benefit of designing in this region is that one can usually spread the benefits over a sizable operating bandwidth.

+

As a sample phased array, let's look at a design that I published several years ago using different element structures than the 3/8" aluminum elements used throughout this series of notes. One interesting feature of this design is that we can use the beam as a reflector-driver Yagi or as a phased array with a variety of phase-line arrangements. Fig. 2 shows the basic outline of the array.

+
+ +
+

Element 1 or the driver is 16.13' long, while the reflector or element 2 is 17.41' long. The spacing between elements is 4.8' or 0.139 wavelength. This spacing is at the edge of the Yagi broadband spacing range and allows a direct 50-Ohm feedpoint when we use the antenna in this mode.

+

When we wish to convert the antenna into a phased array, we have at least 2 choices, We can use a single 35-Ohm cable (RG-83) in ZL-Special style. The line length will be 4.83' for a cable with 0.66-velocity factor (VF). The resulting feedpoint impedance at the junction of the phase line with the forward element is close to 25 Ohms. So we need a roughly quarter wavelength matching section (5.69') of 35-37-Ohm, 0.66-VF line. We can make up such a line with parallel sections of RG-59 cable. If we cannot obtain 35-Ohm cable for the phase line, we can use 50-Ohm RG-8X with a velocity factor of 0.78. However, we need two sections. A 6" section goes from the feedpoint junction to the forward element, while a 64" (5.33') section goes from the junction to the rear element. The impedance at the junction will not be identical to what we obtain from the 35-Ohm phase line, but a 34" (3') matching section of paralleled RG-59 will yield a 50-Ohm match.

+
+ +
+

The performance difference between the Yagi and phased modes of operation shows up in the overlaid patterns in Fig. 3 at the design frequency of 28.5 MHz for this antenna. The phased version has about 1/3-dB higher gain, but the main benefit occurs in the rearward direction. The phased version has double the front-to-back ratio of the Yagi version. For a broader view of the antenna's performance, Table 1 presents modeled free-space values at 28 and 29 MHz as well as at the design frequency.

+ 
+Table 1.  Performance of a two element array as a Yagi and as a phased-array
+
+Antenna                          Frequency (MHz)
+               28                  28.5                29
+Yagi
+Gain (dBi)     6.61                6.14                5.74
+F-B (dB)       10.06               11.01               10.21
+Feed Z         30.6 - j17.1        40.5 + j4.4         49.4 + j23.7
+50-Ohm SWR     1.91                1.26                1.61
+
+Phased Array
+Gain (dBi)     6.00                6.50                6.99
+F-B (dB)       21.02               22.91               12.51
+Feed Z         75.9 - j12.5        51.4 - j9.3         32.7 + j5.5
+50-Ohm SWR     1.59                1.20                1.56
+
+

Both versions of the antenna offer very good SWR curves for a 50-Ohm cable across the entire first MHz of 10 meters. Fig. 4 provides the modeled SWR values in 0.1-MHz increments. Note that the Yagi version requires no matching section, but the phased array version requires both a phase line and a matching section. The fact that the phased array version shows a descending feedpoint resistance as the frequency increases results from the impedance transformation within the matching section.

+
+ +
+

The gain curves for the two antenna show opposite trends, as is evident in Fig. 5. The Yagi shows the typical driver-reflector trend of decreasing gain with increasing frequency. In contrast, the phased array shows increasing gain with frequency, a trend that is more typical of parasitic Yagis with one or more directors.

+
+ +
+

Fig. 6 shows the two front-to-back curves for the Yagi and the phased array. The Yagi curve is very flat across the entire passband for the antenna. In contrast, the phased array shows a definite peak. Because the phased array is an adapted use of a Yagi design, the peak does not occur at the design frequency, but about 200 kHz lower. Still, the front-to-back ratio remains higher than the value for the Yagi throughout the operating passband. However, we note in passing that as the gain approaches the 7-dBi mark, the front-to-back ratio is in serious decline.

+
+ +
+

The sample phased array has provided us with a good sample of typical performance and a good comparison with a comparable driver-reflector Yagi. Since there are so many ways to handle the phasing and matching requirements of phased arrays, other sampled arrays will yield other results. However, all will fall within the limits of what is possible for phasing with 2 elements.

+

The Moxon Rectangle: What the phased array does with phasing lines, the Moxon rectangle does with geometry, that is, establish the correct rear element current magnitude and phasing for maximum front-to-back ratio. Derived from the VK2ABQ square, which is actually a rather poor performer, but with a germinal insight, the G6XN modification arose from practical considerations rather than a through understanding of what was going on. In fact, Moxon himself used the antenna with remotely tuned elements in order to flip the direction, and did not provide any solid basic information on its design. That led me to a considerable study of the antenna. See "Modeling and Understanding Small Beams: Part 2: VK2ABQ Squares and Moxon Rectangles," Communications Quarterly, (Spring, 1995), 55-70. Since that time, the Moxon rectangle has evolved steadily as a 50-Ohm 2-element beam. There are numerous articles at the web site on various aspects of Moxon rectangle design, assembly, and application. See the general listing called "Moxon Rectangles and Online Calculator" for a list of available articles.

+

The Moxon rectangle bends the forward and rear elements of a Yagi toward each other, with a small but critical space between the ends. The precise dimensions are a matter of design goal choice. Broader bandwidth of the front-to-back ratio occurs with squarer versions, but at a higher feedpoint impedance (80 ohms or so). One can also build versions that are narrow from front to back, and hence a bit wider from side to side, and achieve a 50-Ohm feedpoint impedance, although the front-to-back ratio goes down toward the edges of a frequency sweep. Models can be built with anything from wire to aluminum tubing. I have also developed a set of algorithms for designing Moxon rectangles from uniform-diameter elements from wire-size to fat tubing that covers the HF, VHF, and UHF ranges.

+
+ +
+

Fig. 7 shows the outline of a Moxon rectangle for a direct 50-Ohm coaxial-cable connection. Because we have bent the elements, the side-to-side dimension is only about 70% of the length of comparable Yagi elements. For an element diameter of 3/8", the dimension for 28.5 MHz model is 150.3" or 12.54'. The spacing between the driver and the reflector is 55.5" or 4.63'. The driver tails are 21.0". Hence, the total driver length is 192.3" or 16.03'. The reflector tails are 28.6" long, for a total reflector length of 207.5" or 17.29'. Note that the overall element lengths are not far distant from lengths that we meet with driver-reflector Yagis with linear elements. However, the operation of the Moxon depends on the element bends and the second form of coupling formed by the gap between the tails. The gap distance depends on the element diameter. Our 3/8" elements require a 5.9" gap at 28.5 MHz.

+

In one sense, the Moxon has slightly less forward gain than a 2-element Yagi or a phased, about 0.3-0.5-dB down on average. However, that gain applies over a much wider beamwidth. A typical 2-element Yagi has a beamwidth between half-power (-3dB) points of about 70 degrees. Moxon half-power points are typically 80 degrees or more apart, and the pattern circle extends beyond the 90-degree side direction. Hence, the proper application of a Moxon is where one wishes a broad forward hearing area and silence from the rear. It is ideal in the US for stations on the coast wanting to work the US without QRM from DX--or to work the DX across the water with silence from the US. Fig. 8 shows the patterns from the sample Moxon rectangle across the first MHz of 10 meters.

+
+ +
+

The figure presents 4 patterns rather than the usual 3 for an interesting reason. Both the front-to-back ratio and the SWR grow worse than ideal at a slower rate above the actual design frequency than below it. Hence, to obtain roughly equal front-to-back and SWR values at both the upper and lower operating frequency limits, the best design frequency is between 0.35 and 0.4 of the passband width above the lower end. For the sample model, I chose 28.35 MHz, the frequency that yields the best SWR and the best front-to-back ratio. As Table 2 shows, I came close to but did not hit the precise frequency that would yield equal performance values at both 28 and 29 MHz.

+ 
+Table 2.  Modeled free-space performance of a Moxon rectangle
+
+Frequency      28                  28.5                29
+
+Gain (dBi)     6.43                5.87                5.39
+F-B (dB)       16.96               26.21               14.88
+Feed Z         38.2 - j16.3        56.3 + j1.1         69.8 + j12.6
+50-Ohm SWR     1.58                1.13                1.48
+
+
+ +
+

Fig. 9 translates the data into graphical form for the forward gain and the front-to-back ratio. The gain curve shows the typical trend of a parasitic driver-reflector array. The front-to-back curve does not show the peak value because that value occurs between sampling points. However, the curve amply illustrates the more rapid decline in the front-to-back ratio below the design frequency than above it.

+
+ +
+

The 50-Ohm SWR curve in Fig. 10 mirrors the front-to-back curve. The Moxon rectangle has a broad SWR curve that makes the beam fairly easy to replicate successfully in a home workshop. Of course, the SWR passband will vary with the element diameter used, with wire showing a steeper curve and fatter elements (such a 1") showing a flatter curve across the first MHz of 10 meters.

+

The dual coupling between element ends and between the parallel portions of the elements does with antenna geometry much of what a phasing line does in a phased array. That is, it sets (on the design frequency) nearly ideal current magnitude and phase angle relationships that yield a very high front-to-back ratio. Because the geometry that yields the correct current magnitude and phase on the rear element to maximize front-to-back and front-to-rear ratio is frequency specific, the ratio falls off more rapidly than with the phased array sampled earlier--which was purposely not design for absolutely maximum front-to-back ratio. However, the Moxon rectangle remains superior to a standard 2-element Yagi driver-reflector array across the entire frequency sweep. It does all this from an antenna about 3/4ths the size of a standard Yagi.

+

Other designs have also been used to increase the front-to-back performance of the 2-element Yagi, but these two designs reveal what is at stake in making them work.

+
+

Improving Forward Performance: The Driver-Director Yagi

+
To improve the forward performance of 2-element parasitical beams, one can always use longer, higher gain elements. Or one may add an element. However, for the standard reflector-driven element Yagi using half wavelength dipoles, there are only a few routes to slightly increasing forward gain. Up to a certain point, one can improve the performance of a 2-element Yagi by increasing the size of the elements. Table 3 illustrates both the gains and the limits on this tactic. + 
+Table 3.  The effect of element diameter on 2-element driver-reflector Yagi performance
+
+Element        Gain      F-B ratio      Feed Z
+inches         dBi       dB             R +/- jX Ohms
+
+Full size; 0.16 wl spacing
+0.375          6.12      10.86          46.67 - j0.35
+0.75           6.15      10.89          46.01 - j0.31
+1.50           6.15      10.92          45.34 - j0.64
+3.00           6.15      10.95          44.62 - j0.39
+
+Fill size; 0.12 wl
+0.375          6.25      11.19          32.47 + j0.23
+0.75           6.31      11.23          31.33 - j0.98
+1.50           6.31      11.27          31.08 - j0.52
+3.00           6.30      11.31          30.74 - j0.99
+
+

Clearly, elements with diameters larger than 3/4" add virtually nothing more to the gain of the antenna. In each case, the beams in question used re-sized element lengths to achieve the best combination of gain and front-to-back ratio. As the element diameter grows, the required length decreases. As we learned early on with respect to dipole, shortening the dipole reduces its gain. At a certain point, the gain increase resulting from increasing element diameter crosses the gain decrease resulting from reduced length. Hence, the tactic becomes self-defeating beyond a certain point.

+

An alternative is to give up operating bandwidth and front-to-back ratio in favor of higher gain over a narrower passband. In our exploration of full-size reflector-driven element Yagis, we saw that the closer the elements, the higher the gain of the antenna. We need only review the antennas when the elements are spaced 0.08 (2.8') and 0.12 (4.1') wavelengths: see Table 4.

+ 
+Table 4.  Relative performance of driver-reflector Yagis with closely spaced
+and moderately spaced elements
+
+Frequency      28        28.5      29        29.5      30  MHz
+
+Maximum front-to-back-ratio designs
+
+0.08 wl spacing
+Gain (dBi)     6.37      6.92      6.32      5.77      5.37
+F-B (dB)       1.82      8.65      11.38     10.12     8.57
+SWR            31.2      5.88      1.04      2.91      5.52
+
+0.12 wl spacing
+Gain (dBi)     6.98      6.74      6.25      5.82      5.48
+F-B (dB)       5.46      9.79      11.19     10.37     9.18
+SWR            7.12      2.33      1.01      1.81      2.76
+
+Maximum gain designs
+
+Frequency      28        28.5      29        29.5      30  MHz
+0.08 wl spacing
+Gain (dBi)     7.15 R    6.01 R    7.02      6.59      6.02
+F-B (dB)       10.29     0.72      6.29      10.61     10.54
+SWR            40.6      16.4      1.01      6.87      14.2
+
+0.12 wl spacing
+Gain (dBi)     6.94 R    6.13      6.99      6.70      6.24
+F-B (dB)       4.74      1.05      6.12      9.80      10.87
+SWR            14.7      5.20      1.01      3.03      5.43
+
+

If a higher gain is desired and the conditions of obtaining it are acceptable, then a 2-element driver-director Yagi may serve the purposes at hand. Due to its narrow operating passband, the driver-director 2-element Yagi has restricted use. It is most apt for covering one of the narrow amateur bands, such as 30, 17, or 12 meters. In addition, amateurs who wish specialized antennas to cover only the CW-digital part or the SSB part of a wider amateur band may sometimes find the 2-element driver-director Yagi suitable.

+

The Driver-Director 2-Element Yagi A director plus driven element is capable of higher gain at close spacing values than a reflector plus driven element. The general outline of this Yagi type appears in Fig. 11.

+
+ +
+

If we use 3/8" aluminum elements (to be consistent with all of the other beam designs in these notes), we can optimize a series of 2-element driver-director Yagis at 29 MHz using different values of element spacing from 0.06 wavelength (2.03') up to 0.14 wavelength (4.75') on 0.02 wavelength intervals. The results of our first step appear in Table 5. Each version of this type of Yagi has been optimized for maximum front-to-back ratio at the design frequency.

+ 
+Table 5.  Dimensions and 29-MHz performance of 2-element driver-director Yagis in free space
+
+El. Spacing (WL/feet)          0.06 / 2.03     0.08 / 2.71     0.10 / 3.39     0.12 / 4.07     0.14 / 4.75
+Driver Length (WL/feet)        0.474 / 16.07   0.467 / 15.85   0.462 / 15.66   0.457 / 15.50   0.452 / 15.34
+Director Length (WL/feet)      0.499 / 16.92   0.497 / 16.85   0.494 / 16.74   0.490 / 16.62   0.487 / 16.52
+Gain dBi                       6.51            6.50            6.42            6.32            6.12
+Front-to-Back Ratio dB         45.18           20.95           14.83           11.33           8.91
+Feed Z (R +/- jX)              14.82 - j0.11   22.98 + j0.06   29.69 + j0.16   34.53 - j0.05   38.94 + j0.20
+
+

As we increase the spacing between the elements, the lengths of both the driver and the director decrease. In addition, the gain also decreases as we increase the spacing between elements. The gain values at 0.12 wavelength and at 0.14 wavelength closely resemble the values that we might obtain from a driver-reflector Yagi.

+

Perhaps the most notable feature of the driver-director Yagi is the front-to-back ratio. If we use a close spacing value that is less than 0.10 wavelength, we can exceed the front-to-back ratio that we can obtain from the most common designs of the driver-reflector version of the Yagi. However, we pay a price: the resonant feedpoint impedance decreases to levels that we may find more difficult to match without also incurring losses.

+
+ +
+

Fig. 12 overlays sample patterns from the 0.06-, 0.10-, and 0.14 wavelength versions of the antenna. The overlay shows the development of the rearward radiation pattern, and you may easily interpolate the patterns for the missing plots (that would have made the overall graphic difficult to read). Note especially the rearward pattern for the smallest element spacing. Although the 180-degree front-to-back ratio is about 45 dB, the worst-case value at the center of each rearward lobe would be closer to 20 dB. The radiation in these directions does not change in strength as we increase the spacing. As a consequence, the best compromise design spacing might be in the vicinity of 0.08 wavelength, a value that yields a 21-dB 180-degree front-to-back ratio. This value would also approximate the worst-case value and the average values of front-to-back ratio over the entirety of the rearward quadrants. At the same time, the feedpoint impedance is about 23 Ohms, a value that is well within the ability of either a gamma or a beta match to provide a relatively low-loss matching system for a 50-Ohm feedline. Finally, the 0.08 wavelength spacing also provides a bit of added forward gain relative to common driver-reflector Yagi designs.

+

So far, we have examined the driver-director Yagi at its design frequency. We should reserve final evaluations of any of the design versions until we examine the patterns of performance behavior over an operating passband. For the sample values in Table 6, we have returned to the wide passband that runs from 28 to 30 MHz. Using this passband will facilitate comparisons with full-size driver-reflector Yagis. The SWR values in the following table are relative to the resonant feedpoint impedance at 29 MHz.

+ 
+Table 6.  Performance of driver-director Yagis from 28 to 30 MHz
+
+Frequency        28              28.5           29            29.5           30  MHz
+
+0.06 wl spacing
+Gain (dBi)       4.69            5.46           6.51          7.21           6.46R
+F-B (dB)         7.36            10.51          45.18         6.90           2.12
+Feed Z           39.5 - j 42.0   27.4 - j24.8   14.8 - j0.1   6.89 + j31.1   5.9 + j64.3
+SWR              5.82            3.59           1.01          11.90          49.57
+
+0.08 wl spacing
+Gain (dBi)       4.86            5.58           6.50          7.26           6.02
+F-B (dB)         7.98            12.13          20.95         8.79           0.57
+Feed Z           44.4 - j 37.9   34.9 - j21.9   23.0 + j0.1   13.1 + j29.5   9.6 + j63.8
+SWR              3.57            2.35           1.00          5.05           21.15
+
+0.10 wl spacing
+Gain (dBi)       4.95            5.61           6.42          7.14           6.61
+F-B (dB)         8.06            11.29          14.83         9.05           2.15
+Feed Z           46.5 - j 36.2   39.5 - j20.1   26.7 + j0.2   19.8 + j27.2   14.8 + j60.6
+SWR              2.78            1.89           1.01          3.10           10.72
+
+0.12 wl spacing
+Gain (dBi)       4.99            5.60           6.32          6.94           6.71
+F-B (dB)         7.69            9.90           11.33         8.12           2.83
+Feed Z           47.1 - j 36.6   42.1 - j19.8   34.5 + j0.1   26.1 + j25.2   20.7 + j56.9
+SWR              2.50            1.72           1.01          2.36           6.59
+
+0.14 wl spacing
+Gain (dBi)       4.59            5.50           6.12          6.67           6.64
+F-B (dB)         6.91            8.28           8.91          7.06           3.24
+Feed Z           47.8 - j 36.9   44.4 - j19.4   38.9 + j0.2   32.3 + j24.0   27.3 + j53.6
+SWR              2.34            1.62           1.01          1.99           4.60
+
+

The feedpoint impedance and the SWR figures make clear that the driver-director 2-element Yagi is not inherently a wide-band antenna. Only with the widest spacing do we achieve an operating passband that is 1-MHz wide at 10 meters, but by the time we reach 0.14-wavlength spacing, the front-to-back ratio has fallen below the levels that we might expect from a driver-reflector Yagi with similar element spacing. Fig. 13 overlays 3 of the SWR curves to provide a more visual idea of the shrinkage of the operating passband as we tighten the spacing and improve the performance at the design frequency.

+
+ +
+

Nevertheless, the sample Yagis have something to teach us about their basic behavior. In a driver-reflector array, we expect the feedpoint resistance to increase as we raise the operating frequency. The driver-director Yagi has the opposite tendency. The feedpoint resistance decreases with rising frequency. The feedpoint resistance trend parallels the trend in forward gain as we increase the frequency. As shown in Fig. 14, the forward gain of the driver-director Yagi increases as the operating frequency rises. This characteristic holds true of larger Yagis of standard design, a fact that gives us some idea of the relatively greater control exerted by directors relative to reflectors in general Yagi theory.

+
+ +
+

The reversal in the gain trend for the driver-director array holds true of some other characteristics of this Yagi form. Note that the gain decreases more slowly from its peak as we lower the operating frequency than when we raise it. In fact, the forward lobe direction reversal that occurs within the sweep range for the narrowest element spacing occurs at the upper end of the sweep range. For driver-reflector Yagis, the reversal occurred at the lower end (or outside the lower limit) of the sweep. We also find the same trend when we examine the impedance and the SWR values. For a driver-director Yagi, the SWR increases more rapidly above the design frequency than below it.

+
+ +
+

The selected front-to-back curves in Fig. 15 confirm that the trends also apply to the front-to-back ratio. The high peak front-to-back value for the array with the closest element spacing may obscure some of the fine detail. However, the front-to-back ratios at the high limit of the sweep are universally lower than the values for the low end of the sweep range.

+

The sweep data tends to confirm our initial evaluation. The driver-director 2-element Yagi is a relatively narrow-band array for performance values that exceed what we may obtain from a driver-reflector Yagi. The best compromise among all of the values for a practical version of the antenna might use element spacing in the vicinity of 0.08 wavelength. At this spacing and over a confined operating bandwidth, we can achieve a bit more gain and a lot more front-to-back ratio relative to driver-reflector Yagis. These notes do not include an examination of driver-director arrays with shortened elements. As we saw in connection with shrunken driver reflector arrays, element loading reduces the operating passband. For high performance driver-director designs, the passband is already very small, and further reductions would almost defy replicating the beam in a home workshop.

+
+

Conclusion

+
In the end, the pursuit of gain with a 2-element Yagi is always at the expense of something else: either or both operating bandwidth and front-to-back ratio. More gain with respectable operating bandwidths and front-to-back ratios requires more elements, longer elements, or other antenna configurations, such as a stacked parasitical collinear extended double Zepp array or a long-boom Yagi with many elements. +

This survey of strategies for improved forward and rearward 2-element performance is necessarily incomplete. But hopefully, it will alert you to both the opportunities and the pitfalls of the search.

+
+ +

+
+

Updated 05-08-1997, 05-01-2006. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Return to Index

+

Topics: HF Upper, Yagi


+ + diff --git a/content/yagi/byag.html b/content/yagi/byag.html new file mode 100644 index 0000000..3a89877 --- /dev/null +++ b/content/yagi/byag.html @@ -0,0 +1,56 @@ + + + + + + The G4ZU Bird Yagi + + + +
+

The G4ZU Bird Yagi

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

The 20th Century Original

+

In the ARRL Antenna Compendium, Volume 2 (ARRL, 1989, pp. 58-60), Dick Bird, G4ZU, presented an interesting variant on the 3-element Yagi. He claimed pretty good numbers for gain and front-to-back ratio, although the frame of reference remained somewhat a mystery. Having modeled this antenna over the years with everything from MININEC to NEC-4 in answer to individual questions, I thought a note on the antenna might be worthwhile.

+

The antenna uses an interesting structure: lightweight fiberglass (or similar) tubes supporting a wire structure of elements. As shown in Figure 1, the director and reflector are bent toward the ends of the driven element, giving the antenna a hint of Moxon rectangle phenomena: parasitically induced currents plus element end coupling. Dimensions are shown for 10 meters. The only difference in my free space model and G4ZU's recommendations is a slight reduction in driven element length.

+
+ +
+

The antenna is easy enough to build. In fact, it recommends itself for Field Day type activities, since we can build it, tear it down, and reassemble the antenna at the site with minimal difficulty.

+

The dotted lines represent rope strung around the perimeter of the side-to- side and front-to-back supports. Wire can then simply be taped to the rope. Note that this antenna is over 16' side-to-side and 12' front-to- back.

+

How does the antenna play? To even the playing field, I modeled the Bird Yagi and 3 others: a simple 2-element Yagi, a wide-band Yagi, and a narrow-band Yagi. The Bird, the 2-el., and the 3-el. WB models all have feedpoint impedances close to 50 ohms and can be fed across at least the first MHz of 10 meters directly with coax (choke "balun" recommended). The narrow-band 3-element Yagi has a resonant feedpoint impedance close to 20 ohms and would require a beta match or similar. All the antennas use aluminum tubing except the Bird, which uses #12 copper wire.

+

All the antennas were modeled in free space. The differences in performance will reappear at virtually any antenna height from about 20' on up at 10 meters (5/8 wl or higher). For low heights, of course, driven element adjustment will be needed for all models. Figure 2 overlays the free space azimuth patterns.

+
+ +
+

First, find the Bird Yagi in Figure 2's maze of lines. Note that the pattern differs significantly from both the standard Yagi patterns and the Moxon pattern. The Yagi shows excellent side rejection, while the Bird is down only about 11 dB off the sides. (This could be either an advantage or a disadvantage for a Field Day operation, depending on the ease of beam turning, etc.) The Moxon pattern, not shown here, is a large cardioid pattern that takes in the entire forward region, but shuts down completely in the rear. The Bird Yagi front-to-rear ratio ranges from 11 dB to a peak of over 14 dB across the band. (Again, for some kinds of operations, such as area nets, this can be an advantage, since the existence of a station to the rear will be evident, if reduced. However, for other operations, more front-to-back is desirable.)

+

The gain of the Bird Yagi is not high as 3-element Yagis go: about 6.5 dBi in free space. This is less than 0.5 dB greater than the 2-element Yagi, although the wide-band, direct coax feed 2-element antenna has a fairly low front-to-back ratio.

+

The wide-band 3-element Yagi, which substitutes direct coax feed and a wide SWR bandwidth for gain, still manages an extra half dB gain over the Bird. In addition, the wide-band Yagi exceeds 19-dB front-to-back ratio across the first MHz of 10 meters. (Details on this antenna will appear in a forthcoming installment of "An-Ten-Ten-nas.")

+

The narrow-band 3-element Yagi is optimized for gain and front-to-back ratio, although the model shown does not retain these numbers across a wide bandwidth (about 0.5 MHz at 10 meters). However, it is a good portrait of what can be achieved with a 3-element beam: over 8.1 dBi free space gain and a front-to-back ratio of 30 dB (with a front-to-rear ratio no worse than 23 dB). These numbers are more than 1.5 dB gain better than the Bird, and about double the front-to-back ratio, with excellent side rejection thrown in for good measure.

+

These comparisons do NOT mean that the Bird Yagi is a deficient antenna for its intended use: it is a light weight, easily constructed, cheap directive antenna designed for home building and casual use. Within that category, the Bird holds its own.

+

The ultimate decision on whether to play with a Bird Yagi should be made after deciding that this is the category of antenna one wants. Then, it can be compared structurally with other antennas in the same class. Many decisions may ultimately depend on available materials and skills as much as on a half dB of gain differential.

+

Although the Bird seems easy enough to support on 10-meters, the ends will likely need support by descending ropes from a central spike extending above the antenna. For bands lower than 10 meters, the array of ropes could be a problem for some installations.

+

Consider also that, front-to-back, the antenna is 12' long. In fact, this is no longer than the boom of the wide-band 10-meter 3-element Yagi, with its superior performance figures (or the boom of the narrow-band 3-element Yagi, for that matter). Whether one is more comfortable with wire and rope or with tubing may make the difference in the building decision. For even more compactness, the 2-element Yagi--whose performance figures are only a bit down from the Bird--requires only a 6' boom at 10 meters, and that boom can be anything from aluminum tubing to PVC. (I described this antenna in some detail in a past installment of "An-Ten-Ten-nas.")

+

The Bird has its niche in the array of amateur antennas. However, whether it is right for you will depend on many factors, some of which have little to do with antenna modeling. Hopefully, these notes will give you a larger perspective within which to make your antenna building decisions.

+

The 21st Century Spiderbeam

+

Since the Bird Yagi made its appearance, its appeal as a field antenna using light-weight construction has not flagged. Cornelius Paul (Con, DF4SA) has developed a multiband Yagi using some of the G4ZU principles, but perfected via computer modeling and updated for modern (non-corroding and UV-resistant) materials. The result is, first, a tri-band (20-15-10) version and, second, a 5-band (20-17-15-12-10) version. The latter uses 2 elements on 17 and 12, but 3 elements on 20 and 15, and 4 on 10. Since the parasitic elements form Vees, just as in the G4ZU original "Bird Yagi," the support arms form a diamond that is 1000 cm (about 32.8') from tip-to-tip in both directions. The total weight is only about 6 kg (about 12 lb), so hand turning in the field or a TV rotator should serve well.

+

The Spiderbeam website contains a wealth of information on the design, along with detailed model patterns, including information across the entire operating passband (a rarity in the world of commercial antennas). The antenna uses a single feedline with direct line coupling to all drivers for single-feedline use. I am not promoting this antenna. Rather, since you can obtain the complete construction manual in PDF format from the site, you can acquire enough information to build your own or create any number of variations on the idea.

+
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Updated 04-02-1997, 03-01-2005. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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+ Go to Amateur Radio Page
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Topics: HF Upper, Yagi


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Dream Beams

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L. B. Cebik, W4RNL

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A number of years ago, I did a small presentation called "dream beams." Since that time, I have had occasion to refine some of the designs, and so I thought that making the notes available to a wider audience might be enjoyable for some-if for no other purpose than to dream on a cold winter's night. The premise of the exercise is simple. Suppose that we have room for only one tower in a suburban back yard. Our options for very large upper HF multi-band beams are somewhat restricted by current practice. Essentially, we have three types of beams from which to choose: LPDAs, quads, and Yagis. These idealistic notes will look at all three possibilities in as large a size as will fit into our simple backyard where space is limited, but dream dollars are not.

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For each design that we consider, I shall present a considerable amount of design data in tabular and graphical form. In the context of a mere dream antenna, the data may be a bit of an overload. However, it does represent the complete data picture that is part of another dream that I have. Perhaps someday, all beam-makers will provide equivalent information to their potential customers.

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The notes come in 2 parts, as the titles below reveal. The format is PDF. Therefore, after downloading a document, you will have to hit the "Back" button on the browser in order to return here to access the second document. Then you return here once more to go back to the main index of articles at the site.

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Dream Beams: Part 1: LPDAs and Quads

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Dream Beams: Part 2: Forward-Stagger and Interlaced Yagis

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Happy Dreaming!

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Updated 07-01-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Upper, LPDA, Quad, Yagi


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Modeling Yagis by Equation
+ Part 1. Background and One Example

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L. B. Cebik, W4RNL

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Introduction: Some Yagi Myths and Realities

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In the past, I have created some NEC-Win Plus equation-based models of the Moxon Rectangle and quad beams of various sizes. All the user needs to do is select the desired unit of measure, enter the element diameter in that unit of measure, and specify a design frequency. The model calculates the correct element dimensions and spacing at that frequency and element diameter for a beam that operates in accord with the parameters set for each model. For example, the Moxon rectangles produce maximum 180-degree front-to-back ratio and close to the selected feedpoint impedance (50 Ohms or 95 Ohms), with the maximum gain possible under those conditions. The quads have similar properties, although there are two versions of the 3-element quad: one for the widest feasible operating bandwidth (since the SWR bandwidth exceeds the front-to-back bandwidth), and the other for the highest feasible gain, but with a narrower bandwidth.

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See the articles at my web site on Moxon rectangles and on monoband quads for available downloads of the NEC-Win Plus models. The algorithms are also available for some of the designs in GW Basic, in a Windows program, and in on-line scripts either at my site or via a link from my site.

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From time to time, I receive requests for similar equation-based models or algorithms for Yagis. A recent request wanted a fool-proof algorithm set for a very long-boom Yagi, but not one of the DL6WU designs, which are available in a couple of GW Basic programs. Up to this point, I have resisted the urge to develop such equation-based models. However, I recently undertook the task for 3-element Yagis. My goal was not so much to produce automated models of and dimensions for such Yagis as it was to develop a means for explaining why the task may be--in the long run--somewhat open-ended and possibly futile.

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In this episode, we shall look at some facts and fictions regarding 3-element Yagis and develop 1 equation based model. It will handle uniform-diameter element 3-element Yagis designed within a certain range of element diameters with the design goal of yielding a maximum front-to-back ratio at the design frequency. In the next episode, we shall look at higher-gain and very-wide-band versions of the 3-element Yagi, as well as deal with what the potential Yagi builder must do after using one of the equation-based models.

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Like almost all antennas, the history of Yagis is littered with so-called cutting formulas. Whatever the element diameter, the formulas specify element lengths and spacing in wavelengths for the reflector, driver, and director of the Yagi. Such cutting formulas rarely work in practice, because--whatever the design goals--the element lengths and the spacing between elements are functions--among other things--of the element diameter. If you find a set of dimensions and some performance numbers that you like, the quickest way not to get the designer's performance is to change the element diameter relative to the original design to which the other dimensions apply.

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A second myth about Yagis is that there is a single Yagi design for each number of elements. In fact, there are innumerable designs. We may distinguish designs by boom length (on which gain depends, as Lawson showed), feedpoint impedance (roughly but not wholly a function of the reflector-driver relationship), operating bandwidth (considering not just SWR, but gain and front-to-back ratio as well), and numerous other factors. Indeed, the first step in deciding on a Yagi design is finding out what goals you have in mind for the antenna. As you change design goals, you change the dimensions of a Yagi that will fulfill those goals.

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Fig. 1 shows 3 3-element Yagis, all for the same frequency, and the 3 outlines are to scale. The labels are perfectly general, but not precise. The "high-gain" version has a higher gain than the other 2 versions, but not the highest gain obtainable. The design criteria also include a 20-dB front-to-back ratio and a feedpoint impedance above 20 Ohms. The "maximum front-to-back ratio" design also sacrifiecs some gain for a feedpoint impedance above 20 Ohms. The "wide-band" version uses a 50-Ohm direct-feed impedance as the basis for its broad SWR curve, relinquishing gain in the process. Every Yagi design is therefore a compromise of performance figures based on a chosen set of priorities. Those priorities rest, in turn, on the intended use for the antenna, as well as any circumstantial limitations.

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A third myth surrounding Yagi performance leans on the idea of opting for the maximum gain possible from a given boom length and a set number of elements. The old NBS series of Yagis from many decades before computer design techniques wrested up to 9 dBi free-space gain out of 3 elements. However, these outmoded designs had 2 drawbacks. First, the front-to-back ratio was paltry, at best. Second, the feedpoint impedances were very low, sometimes in the range of 10 Ohms. Regardless of the effectiveness of matching techniques, the lower the impedance at the antenna driver terminals, the higher the losses. Every fractional-Ohm of resistance in the connections takes up a greater percentage of the power supplied as you lower the impedance. As the antenna assembly weathers, those losses tend to climb. Hence, modern design tends to focus on a minimal feedpoint impedance of about 20 Ohms or so, with higher values preferred if we can obtain them without significantly jeopardizing other operating parameters.

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Every design, then, requires a carefully selected set of design goals, and the result will be a compromise among them based on the priorities that we set among those goals. We cannot get everything from a single design, as illustrated in the 3 free-space azimuth patterns in Fig. 2. The high-gain version of the 3-element Yagi has more forward gain (a bit over 8 dBi free-space) than the other versions, but it also has a lower feedpoint impedance and a narrower operating bandwidth than the other two versions. The maximum front-to-back version has a very high 180-degree front-to-back value at the design frequency. However peak values of front-to-back performance are vary narrow band phenomena, suitable mostly for antennas used in direction finding. The overall operating bandwidth is wider than for the high-gain version, but the gain is lower (in the 7.7 dBi free-space range). The very-wide-band version of the antenna has the lowest gain (just over 7 dBi free-space), but maintains a very low SWR value and at least 20 dB of front-to-back ratio over a considerable set of frequencies. For example, it is possible to design the antenna to cover all of 6 meters (a 7.7% bandwidth) with relatively equal performance.

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To better understand some of the limiting factors, let's look at 2-meter versions of the 3 types of designs, remembering that the categories are somewhat arbitrary and the these are not the only categories possible. Each antenna uses 0.25" diameter elements for consistency. The models use NEC-4 and presume well insulated and isolated elements relative to a conductive boom (or the use of a non-conductive boom). Fig. 3 shows the combined gain and front-to-back curves for the high-gain version of the antenna across the 2-meter band.

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The "front-to-side-lobe ratio" curve represents in these designs the worst-case front-to-back ratio. For the high-gain version of the antenna, the worst-case and 180-degree front-to-back ratios are the same, resulting in overlaid curves. The peak front-to-back ratio by design occurs at the mid-band design frequency. However, indicative of the narrower operating bandwidth for the antenna, the value drops to 17-18 dB at the band edges. The usual amateur standard of a 20-dB front-to-back ratio occurs only over a portion of the band.

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More significant than operating bandwidth is the fact that the gain shows a rising curve across the entire 2-meter band. This characteristic is endemic to 3-element Yagis. Longer-boom Yagis with more elements can so arrange those elements to yield gain and front-to-back peaks that are close to coincident. The OWA series of Yagis about which I have written in the past is an example of such control. However, a 3-element Yagi has limited control over its operating parameters, so the rising gain curve is typical of the entire set of designs. (Side note: 2-element reflector-driver Yagis show a descending gain curve with rising frequency. However, 2-element driver-director Yagis show the rising gain curve in common with all Yagis having directors--except of course, for designs with many elements in which some function to control the curves.)

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Fig. 4 shows the same gain and front-to-back curves for the maximum front-to-back version of the 3-element Yagi. The rising gain curve once more appears. However, the dimensions of the antenna allow the 180-degree front-to-back ratio to peak above 50 dB for a narrow region around the design frequency. The front-to-back ratio--in both 180-degree and worst-case terms--remains above 20 dB across the entire band. In fact, when we apply a proper matching network to the antenna, the SWR bandwidth also covers the entire band with a value under 2:1.

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The final version of the antenna, as shown in Fig. 5, shows a rising curve for both the gain and the front-to-back ratio. Neither peaks within the 2-meter band. These phenomena are the price for having a 50-Ohm impedance for a direct feed with a coaxial cable not only across the 2-meter band, but for a considerable span outside the band.

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Sometimes I do not know which is worse: a full myth or a half myth. For example, it is true to a great extent--but not completely--that the reflector-driver relationship controls the feedpoint impedance, while the driver-director relation ship controls both the gain and the front-to-back values. However, return to Fig. 1 and examine the spacing between the reflector and driver for the high-gain and maximum front-to-back version of the 3-element Yagi. As a general rule, the wider the spacing between the reflector and driver, the higher the resonant feedpoint impedance of the array. In this case, the maximum front-to-back version has a closer reflector-driver spacing, but a higher feedpoint impedance. Obviously, the radically different placements of the directors in the 2 designs has more than a little influence on the feedpoint impedance. Likewise, the reflector can influence the front-to-back ratio, very often by helping to set the frequency of its maximum value.

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The end result of these preliminary notes is the conclusion that there is no single fixed set of element length or spacing values for good performance, as defined by a set of design goals. In fact, even within a tightly confined set of goals, multiple sets of element lengths and spacing may produce equally acceptable results. This variability forms a background against which we design 3-element Yagis. At best, we can only automate the design process by first setting design goals and second by finding paradigm examples from which to form algorithms for design. Even the tightest constraints will have limitations.

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The Maximum Front-to-Back Ratio Design The first type of 3-element Yagi design that I committed to automation was the maximum front-to-back ratio version. The primary design goal for the exercise was to develop a 180-degree front-to-back ratio that exceeded 50 dB. A secondary goal was to have all beams in the collection exhibit the same resonant feedpoint impedance within a fraction of an Ohm. The free-space gain would have to take care of itself.

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From the perspective of an automated equation-based model, there are 3 goals. First, the user selects the desired unit of measure. Second, the user selects the diameter of the elements. This step presumes that all elements of the array have a uniform diameter throughout the model. Any adjustments for stepped-diameter elements--common at HF--require the use of external calculations. As a consequence, the results of the design work are directly applicable mostly to VHF and UHF antennas. Third, the user selects a design frequency.

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The two sets of goals interact in ways that may differ according to the type of Yagi under consideration. For example, a maximum front-to-back ratio Yagi would ordinarily find its use in direction finding. In that case, the design frequency would be the frequency on which the user conducts DF activities. However, in other instances, the user may select the design because it is capable of reasonably good operation across a 3% bandwidth, sufficient to cover many amateur bands. In that case--as we shall see shortly--the design frequency becomes a function of the performance at the band edges. The desired frequency may or may not be the center of the band for which it is designed, depending on how wide the band may be. (Bandwidth as a percentage is simply the ratio of the width of the band to the band's center frequency when both are in the same units--usually MHz--with the result multiplied by 100 to arrive at a percentage.)

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The technique for arriving at an automated design model involves regression analysis of a suitable sample of hand-optimized models that use a selected set of element diameters. Regression analysis is a collection of techniques for creating polynomial equations that essentially connect the "dots" or data points created by the samples. The higher the order of the polynomial, the more exacting will be the curve with respect to the sampled values. Fourth-order polynomials tend to provide very exact overlays of the curve with the end points of the range of samples. This function is useful for extending the use of the algorithms somewhat beyond the range for which they are calibrated.

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Range of Calibration: The range of element diameters for which I took hand-optimized samples as data points runs from 3.16226E-4 wavelength to 1E-2 wavelength. These end values translate into common diameters according to Table 1.

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+Table 1.  Diameter in Wavelengths vs. Inches
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+Frequency         3.16226E-4              1E-2
+MHz               WL                      WL
+3.5               1.0664" (27 mm)         33.7224"
+7.1               0.5256" (13.4 mm)       16.6237"
+14.1              0.2647" (6.7 mm)         8.3708"
+21.1              0.1769" (4.5 mm)         5.5938"
+28.1              0.1328" (3.4 mm)         4.2003"
+50.1              0.0745" (2mm)            2.3559" (59.8 mm)
+146               0.0256"                  0.8084" (20.5 mm)
+223               0.0167"                  0.5293" (13.4 mm)
+432               0.0086"                  0.2732" (7 mm)
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The table makes clear that the result will not be calibrated for thin wire beams on the lowest HF bands. As well the smallest diameter element for which the automation is calibrated at 432 MHz is about 1/4". The use of the automated model beyond the limits is uncertified, but is likely to yield reasonably good results for diameters down to 1/2 the smallest value shown and up to twice the highest value shown for each band.

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The critical dimensions: For each sample, there must be a separate algorithm for each of the following critical Yagi dimensions: reflector length, driver length, director length, reflector-to-driver spacing, and reflector-to-director spacing. As an alternative, one might use the driver-to-director spacing as a substitute for the reflector-to-director spacing. For modeling purposes, the lengths may in fact be half-lengths, since the norm for setting up an element is to assign values of +/-Y for the end coordinates to assure a centered boom line along the X-axis.

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The more nearly linear the progression of sampled points (or, in this case, element diameters), the more likely the regression algorithms are to yield relatively precise values for the design dimensions. The curves for element lengths and spacing become less steep if we use a progression of element diameters that result in a linear set of the log (base 10) of the element diameters. Hence, the actual diameters sampled for hand-optimizing are the antilogs of that linear progression, which runs from -3.5 to -2 in this exercise. Table 2 shows the half-element lengths and spacing values for the set of 7 data points used to set up the regression polynomials.

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+Table 2.  Hand-Optimized Models for Regression Analysis
+Element Length = Half-Lengths
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+Element     Log of      Reflector   Driver      Director    Ref.-Dr.    Ref-Dir.
+Diameter    Diameter    Length      Length      Length      Spacing     Spacing
+WL                      WL          WL          WL          WL          WL
+3.16228E-4  -3.5        0.2517      0.242       0.2285      0.1255      0.2785
+5.6234E-4   -3.25       0.2513      0.24115     0.2269      0.133       0.285
+1E-3        -3          0.2509      0.24022     0.2251      0.143       0.2924
+1.7783E-3   -2.75       0.2496      0.2387      0.2226      0.153       0.302
+3.16228E-3  -2.5        0.24927     0.23667     0.21875     0.1545      0.303
+5.6234E-3   -2.25       0.247       0.2347      0.2152      0.1735      0.3162
+1E-2        -2          0.2429      0.23445     0.2123      0.219       0.3455
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Even with high care in setting up the hand-optimized data points, the data points will not form a perfectly smooth curve on their own. For the exercise, all front-to-back ratios exceeded 50 dB, and all resonant driver impedances had the same value within only a small range measured in fractions of an Ohm of both resistance and reactance. However, the interactions noted in the first part of this exercise dictate that there will be no single set of Yagi dimensions that will yield these results. A fractional change to the reflector length may change the director length and spacing for values of front-to-back ratio and impedance that meet the tight restrictions. Hence, low-order polynomials will not capture the required curves to yield correct results across the span of element diameters.

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Fig. 6 shows the worst-case variation from the 4th-order polynomial used for the automated algorithms. The deviation applies to the reflector length, which is fortunate, since this dimension is less sensitive to slight variations than some others in the array. The need for a high-order polynomial to come this close to the curve for the sample data points illustrates the difficulties inherent to optimizing Yagis for a smooth curve. Although it might seem like a simple matter to create a smooth curve with a lower-order equation, we must remember that we have 5 dimensions. Any change to one of them forces changes to all of them.

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Modeled Performance: The hand-optimized models used as data points have a number of interesting characteristics as a set. Fig. 7 shows the gain values for 4 of the element diameters (skipping the n.25 and n.75 log values). Above a certain point on the graph, the gain values show a parallelism that reflects the element diameter. However, the lower (or left) part of the graph shows a near coincidence of values and at the left most edge a large decrease in gain for the smallest diameter element.

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The anomalies in the curve structure are not solely a function of the variability of hand-optimized data-point models. More significant is the fact that the models are optimized to a combination of 2 parameters: peak 180-degree front-to-back ratio and a common feedpoint impedance. The latter requirement changes the element relationships so that at the thinnest diameter, the design begins to pass beynd the limits of smooth performance across the prescribed passband. Incidentally, the driver is near-resonant. However, shortening the driver to accommodate a beta or gamma match will lower the reistive portion of the impedance to about 26 or 26 Ohms.

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The frequency scale of the graph reveals that I optimized the models at 30 MHz. Since the models use perfect or lossless wires, the actual optimizing frequency makes no difference. However, it does provide a caution--if not a warning--that using the results with a common antenna material--such as copper or aluminum--will show a growing deviation from the automated results as the frequency increases. Since skin effect is not a direct function of frequency, it is excluded from being contained in the automated model.

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Fig. 8 reveals how narrow the peak front-to-back ratio is as a percentage of passband used in the graph. In fact, closer sampling of the frequencies would change the central straight lines to the peak into curves that would yield an even narrower passband for the peak values. Of equal interest is the fact that below 29.5 MHz and above 30.5 MHz, the front-to-back ratio drops to relatively mediocre values. In fact, at the edges of the 1-MHz span (creating a 3% bandwidth), only the fattest elements exceed 20 dB.

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As in many parasitic array designs, the limiting factors tend to be the gain and front-to-back ratio rather than the 2:1 SWR curve. If we set the passband edges at 28.75 MHz and 30.75 MHz for a design frequency of 30 MHz, we obtain the SWR curves in Fig. 9 for the same set of element diameters. Only the fattest element approaches a 2:1 curve that runs nearly from end to end, with the SWR bandwidth shrinking quickly with thinner elements. Typical of 3-element Yagis, the rate of SWR degradation (and other performance degradation as well) tends to be lower below the design frequency than above the design frequency. Since this phenomenon holds true of both the SWR and the front-to-back curves, the design frequency is near the upper end of the total defined passband.

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Table 3 combines the design frequency NEC-4 results for all 7 data-point models. Of note is that fact that all peak front-to-back values exceed 54 dB. The total variation in the feedpoint resistance is 0.43 Ohm, while the variation in reactance is only 0.127 Ohm. Table 2 above shows the dimensions of the models producing these results. + 
+Table 3.  NEC-4 Performance: Hand-Optimized Models, Pre-Regression Analysis
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+Element           Free-Space        180-Degree        Feedpoint
+Diameter          Gain dBi          Front-Back        Impedance
+WL                                  Ratio dB          R +/- jX Ohms
+3.16228E-4        7.66              54.10             29.18 - j0.089
+5.6234E-4         7.72              54.85             29.26 - j0.105
+1E-3              7.76              59.35             29.54 + j0.018
+1.7783E-3         7.84              54.61             29.11 - j0.057
+3.16228E-3        7.83              54.20             29.25 - j0.056
+5.6234E-3         7.89              54.14             29.24 - j0.027
+1E-2              7.89              54.39             29.29 - j0.109
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The actual process of deriving 4th-order polynomials for the model algorithms is simple compared to the task of hand-optimizing the data-point models. Programs such as Data-Fit automate the production of equations based on entering the X and Y data. In this case, X-values are the logs of the element diameters and Y-values are the dimensions critical to 3-element Yagi design.

+

The Actual NEC-Win Plus Equation-Based Model for the Maximum Front-to-Back Yagi

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The process of setting up the result of the regression analysis to create an autmated Yagi design model in NEC-Win Plus requires attention to both the "Equations" page and the "Wires" page of the model. Let's begin with the equations page, which has 2 faces, according to the highlighting of the Fn button. Fig. 10 shows both versions of the page.

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On the right are the set of regression results for each critical dimension in columns E through I. The final equations employing each of these constants appear in line 8 at the end of each column. I have highlighted one of the equations so that it shows its full form on the working line. All of the polynomials have the same form, but with column cell references specific to each Yagi dimension. Note that the X^n term is referenced to cell D8, which is the log of the wire diameter after conversion from the entry unit to a fraction of a wavelength.

+

Two user-relevant entries occur in the column of Variables. Variable A is the design frequency. For the example shown, that frequency is widely divergent from the listed starting and stopping frequency entries. By making the design frequency an independent entry, we can alter the frequency sweep later and even alter its parameters without having any effect on the design of the Yagi. Cell D4 converts the design frequency entered in A into a wavelength for use in the remaining calculations.

+

Variable B is the diameter of the elements entered in the unit of measure current at the time of design. Hence, as a preliminary step, you must change to the desired unit of measure as indicated in the lower right corner of the "Geometry" box at the top of the screen. Clicking on the current unit opens the comments and unit of measure screen for the program. Cell D6 converts the diameter entered as variable B into a fraction of a wavelength, and D8 takes the log of the value in D6. As noted, D8 forms the X^n value for the calculating equations.

+

The output of the equations in line 8 provide the required dimensions in wavelengths. Variables C through H on the left convert these values into the current unit of measure by multiplying each times the design frequency wavelength. (In the example, the design wavelength is 1.0, so the equation results are the same as the final values of the variables.)

+

The list of entered and calculated variables will have no effect on the model unless we set up the Wires page to use them. See Fig. 11 as a reference for the following notes.

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The wires page entries involve all of the variables from B through H. You may identify the location of each one and check its dimensional role by comparing Fig. 10 and Fig. 11. All the the resulting values, of course, are in the unit of measure with which we started.

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The ultimate question is how well the algorithms actually calculate the required dimensions for a maximum front-to-back ratio 3-element Yagi between the limits of the element diameters. Table 4 shows the performance data for models created with the calculations, but using the NEC-4 core. Since NEC-Win Plus is also the user-assistance insert for NEC-Win Pro and for GNEC, one can simply open the equation-based model within those programs to create a Yagi for any frequency or element diameter desired. It may also be possible to transfer the essential equations to Multi-NEC (by AC6LA) for use with any core to which you have access.

+ 
+
+Table 4.  NEC-4 Performance: Calculated Models, Post-Regression Analysis
+
+Element           Free-Space        180-Degree        Feedpoint
+Diameter          Gain dBi          Front-Back        Impedance
+WL                                  Ratio dB          R +/- jX Ohms
+3.16228E-4        7.66              53.53             29.17 - j0.041
+5.6234E-4         7.71              61.41             29.32 - j0.285
+1E-3              7.78              57.30             29.41 + j0.212
+1.7783E-3         7.82              63.89             29.29 + j0.003
+3.16228E-3        7.85              54.73             29.12 - j0.316
+5.6234E-3         7.89              53.78             29.32 + j0.153
+1E-2              7.89              54.35             29.26 - j0.149
+
+

The gain and front-to-back ratio values are very acceptable at all element diameters. The variation of the feedpoint resistance has dropped to 0.29 Ohm, but the reactance now varies by 0.403 Ohms. All in all, the automated equation-based model does what it is supposed to do.

+

There are two major limitations to the automated model. First, it will not calculate stepped-diameter elements for HF and 6-meter beams. In the next episode, we shall discuss a work-around for this limitation.

+

Second, for those using a NEC-2 core, the NEC program will give erroneous results as the element diameter approaches 0.005 wavelength. The ratio of segment length to diameter is between 4:1 and 3:1, the region in which the NEC-2 manual recommends using the EK command to implement the extended thin-wire kernel. With the EK command active, there is no significant difference between NEC-2 and NEC-4 results. However, Fig. 12 shows the difference between those two cases and the use of NEC-2 without the EK command for an element diameter of 0.01 wavelength.

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With EK, NEC-2 produces results too close those in the table to need repetition. However, without the EK command, the NEC-2 core shows a gain of 7.95 dBi with a front-to-back ratio of only 34.39 dB. The reported feedpoint impedance is 27.8 + j2.3 Ohms. Unfortunately, many entry-level programs do not make the EK command available to the modeler, although it appears automatically in such programs as NEC2GO. Hence, the only workaround is to use caution with NEC-2 patterns and data when the element diameter is near the upper end of the calibrated range.

+

We have a considerable body of unfinished business. Most significantly, we have not yet discovered whether we can develop similar algorithms for the high-gain and the wide-band versions of the 3-element Yagi. Second, we need to explore further the limitations of any such automated design program for Yagis with respect to the work that is left to the modeler-builder. When done, I shall place all 3 NEC-Win Plus equation-based Yagi models in the download section of my web site--with a link to obtaining them.

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Updated 12-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Nov., 2005). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Part 2

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Go to Main Index

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Topics: HF Upper, Yagi


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+

Modeling Yagis by Equation
+ Part 2. High-Gain and Wide-Band Yagis

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+

L. B. Cebik, W4RNL

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In the first episode of this short series, we examined some of the properties of Yagi arrays that make the task of automated design somewhat tentative. At the bottom line, for any given performance parameter--and often for sets of parameters--there is no single set of dimensions that will achieve the goal. Despite this limitation and others pertaining to the use of algorithms as a basis for antenna construction, we did put together enough data points for a 4th-order regression polynomial set that is reliable with respect to the maximum front-to-back version of the 3-element Yagi. The emergent calculated models have 180-degree front-to-back ratios in excess of 50 dB and resonant feedpoint impedances very close to 29 Ohms throughout the range of calibration (that is, element diameters between 3E-4 and 1E-2 wavelength).

+

This episode will complete the work--so far as it has gone--by examining high gain and wide-band versions of the 3-element Yagi. As well, before closing the book on the project, we shall look again at the limitations of the effort and what they mean for the builder.

+

High-Gain 3-Element Yagis

+

The term "high gain" could be misleading if we do not quialify it from the start. Every 3-element Yagi exhibits a rising gain curve as frequency increases across the passband, assuming that the design also calls for some value of front-to-back ratio and some value of near-resonant feedpoint impedance. Hence, the term "high gain" means only the highest obtainable gain consistent with the other parameters in the set of design goals.

+

At the design frequency, I chose the highest gain possible with a front-to-back ratio of at least 24 dB. I selected the front-to-back figure as a means of ensuring that the design would meet the usual amateur standard of 20 dB front-to-back ratio across a span of frequencies. The second parameter is a feedpoint impedance of 25 Ohms. 3-element Yagis may obtain higher gain at lower impedances, but the target value of 25 Ohms tends to minimize losses and allows for very straightforward impedance matching techniques for a 50-Ohm coaxial cable. The high-gain design does not change its resistance as fast as the maximum front-to-back design with equivalent element lengthening or shortening. Hence, setting the driver for a gamma or a beta match will generally yield a resistive component no smaller than 22 Ohms. Of course, the builder can also use a 1/4 wavelength section of 35-Ohm cable (or parallel sections of 70-Ohm cable) to obtain a 50-Ohm match without changing the driver length relative to its listed resonant length.

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Fig. 1 shows the relevant dimensions for the Yagi designs that we shall examine. The diagram will be equally applicable to wide-band design that we shall consider later. In accord with the conventions adopted in part 1 of this series, we shall use the reflector-to-director spacing rather than the driver-to-director spacing as one of our critical dimensions. As well, we shall calculate on the basis of element half-lengths, since those values are convenient to most antenna modeling. As in the first episode, we are aiming at equation-based designs making use of the spreadsheet facility built into NEC-Win Plus. The process begins with a set of data-point hand-optimized designs forming the basis for regression analysis. The polynomials from that analysis become the equations for the model.

+ 
+Table 1.  Hand-Optimized Models for Regression Analysis
+Element Length = Half-Lengths
+
+Element     Log of      Reflector   Driver      Director    Ref.-Dr.    Ref-Dir.
+Diameter    Diameter    Length      Length      Length      Spacing     Spacing
+WL                      WL          WL          WL          WL          WL
+3.16228E-4  -3.5        0.2496      0.24093     0.230       0.1579      0.3291
+5.6234E-4   -3.25       0.2488      0.23995     0.2285      0.167       0.3359
+1E-3        -3          0.2480      0.23853     0.22621     0.171       0.35084
+1.7783E-3   -2.75       0.2465      0.23668     0.22285     0.175       0.3465
+3.16228E-3  -2.5        0.2449      0.2342      0.2187      0.173       0.346
+5.6234E-3   -2.25       0.2435      0.23105     0.2134      0.171       0.34495
+1E-2        -2          0.24243     0.2273      0.2067      0.1675      0.3431
+
+

Table 1 lists the data-point models for the high-gain set. They use the same element diameters we employed for the maximum front-to-back data-point models. However, the dimensions are quite different. Factors such as a longer overall boom length and shorter reflectors and drivers are functions of the high-gain goal. Fig. 2 illustrates the gain curves for selected models.

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Within the set of curves, we can notice an interesting pattern. The fatter the element, the shallower the slope of the curve with the rising frequency. Hence, some of the mid-size elements have a higher gain at the upper limit of the defined passband.

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However, the properties do not all stem from a simple increase in element diameter. The highest gain at the design frequency--here set as 30 MHz--does not accrue to the largest-diameter element. That honor goes to the mid-range element diameter. The following table of NEC-4 performance values provides further evidence of that fact. See Table 2.

+ 
+Table 2.  NEC-4 Performance: Hand-Optimized Models, Pre-Regression Analysis
+
+Element           Free-Space        180-Degree        Feedpoint
+Diameter          Gain dBi          Front-Back        Impedance
+WL                                  Ratio dB          R +/- jX Ohms
+3.16228E-4        8.22              25.52             25.17 - j0.017
+5.6234E-4         8.27              25.43             25.18 - j0.112
+1E-3              8.31              24.90             25.04 - j0.096
+1.7783E-3         8.33              24.80             25.06 - j0.129
+3.16228E-3        8.32              24.79             25.16 - j0.152
+5.6234E-3         8.30              24.79             25.13 - j0.138
+1E-2              8.28              24.82             25.21 - j0.006
+
+

The combination of setting a resonant feedpoint impedance and a minimum front-to-back ratio together create conditions that alter the general progression of gain curves. At the target impedance and front-to-back values, the fattest elements cannot achieve the gain level of some thinner elements. However, as elements grow even thinner, their gain levels drop from their peak value. At the same time, for the set feedpoint impedance, their front-to-back ratio potential increases. It peaks just below the design frequency, as shown in the graph of front-to-back ratios in Fig. 3.

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Despite the shift in the frequency of peak front-to-back ratio, the passband-edge values generally follow expectations: the fatter the element, the higher the front-to-back ratio at 29.1 and 30.7 MHz. I chose the indicated passband for exploration because it is the widest 2:1 SWR passband for the thickest element. Fig. 4 gives us representative SWR curves for the range of element diameters for which the ultimate equation-based model holds good. Between the calibration limits, the 2:1 SWR passband ranges from 5% of the design frequency for the largest element down to 2.5% for the smallest. These values are considerably smaller than those associated with the maximum front-to-back ratio version of the Yagi and represent the price of obtaining higher gain from 3-elements.

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The decay of design-frequency operating parameters also shows up in the free-space E-plane patterns for the data-point models. Fig. 5 compares patterns at the passband edges and at the design frequency for the thinnest and the thickest elements in the range. Even if we could match the thin-element version of the array to 50 Ohms while at a band edge, we would lack the front-to-back ratio that is important to many (but not to all) amateur operations.

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The maximum front-to-back Yagis used a pair of design criteria: maximum front-to-back ratio and a set feedpoint impedance. The high-gain versions balance 3 criteria: maximum gain, a minimum value of front-to-back ratio, and a set feedpoint impedance. As a result, we do not obtain a simple set of curves, all headed in the same direction. As shown in Fig. 6, the reflector-to-driver spacing reverses the direction from increasing with element diameter to decreasing with element diameter. The curve in the figure smoothes the ragged data points that result also from mixing so many variables in the hand-optimizing process.

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Some curves are even more complex, as evidenced by the reflector-director spacing, as shown in Fig. 7. Nevertheless, the element length curves are all "normal," that is, they all show decreasing lengths with increasing element diameters.

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Despite the oddities that results from combining operating parameters, regression curves fit neatly into NEC-Win Plus equations. Fig. 8 shows the equations page in 2 forms, one displaying the equations themselves and the other showing the calculated values. If you wish to transfer the algorithms to another venue, such as a Windows utility program, the list of regression constants and the form of the equations appear in this figure. Writing the equations in Java script or C is straightforward. As with the previous equation-based models, the user decides on a unit of measure and enters the element diameter in that unit along with a design frequency.

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To go along with the equation page entries, we must have the wires page set up in variables, as shown in Fig. 9. The conversion of the maximum front-to-back equation-based model into a high-gain model actually required only that I change the entries for the constants on the equations page. All of the other entries and calculations (such as converting the diameter to a fraction of a wavelength and then taking its base-10 log) are exactly the same for both cases.

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Although the high-gain data-point models employ some different curves relative to the maximum front-to-back models, the end result is a set of quite accurate results. Table 3 shows the NEC-4 reports on the operating potential for calculated models. You may compare these results to those for the initial data-point models to discover that they compare as well as the corresponding sets for the maximum front-to-back models.

+ 
+Table 3.  NEC-4 Performance: Calculated Models, Post-Regression Analysis
+
+Element           Free-Space        180-Degree        Feedpoint
+Diameter          Gain dBi          Front-Back        Impedance
+WL                                  Ratio dB          R +/- jX Ohms
+3.16228E-4        8.22              25.58             25.19 + j0.004
+5.6234E-4         8.27              25.25             25.09 - j0.187
+1E-3              8.31              25.04             25.22 + j0.003
+1.7783E-3         8.32              24.91             25.32 - j0.025
+3.16228E-3        8.32              24.76             25.24 - j0.180
+5.6234E-3         8.30              24.79             25.11 - j0.108
+1E-2              8.28              24.82             25.21 - j0.014
+
+

The data-point model impedances varied over a very small range, with the resistance changing only by 0.17 Ohm and the reactance by 0.15 Ohm. The calculated versions do almost as well, with the resistance varying by 0.23 Ohm and the reactance by 0.19 Ohm. Note that I have again used NEC-4 results. At the largest diameters, the segment-length-to-diameter ratio enters a region in NEC-2 that yields errors unless the EK command is available. For example, using uncorrected NEC-2,the largest model reports a gain of 8.33 dBi with a front-to-back ratio of 24.31 dB and feedpoint impedance of 24.53 + j2.25 Ohms. Because the performance figures for the high-gain models are not quite so individually critical as was the maximum front-to-back frequency of the earlier model, we might find the NEC-2 results usable for all practical purposes. However, being aware of the NEC-2 limitation is useful and often significant.

+

The Wide-Band 3-Element Yagi

+

When we develop a wide-band 3-element Yagi, we must change our perspective. We shall select a feedpoint impedance of 50 Ohms, although that value alone is not the ultimate impedance parameter. Instead, we shall seek the flattest 50-Ohm SWR curve feasible for each element diameter, even if it means that the value at the design frequency is not exactly 50 Ohms resistive. In addition, we shall seek a reasonable gain and front-to-back ratio. The goal will be a smooth set of gain and front-to-back curves so that performance is roughly the same everywhere in the passband.

+

Unfortunately, I have so far only been able to approximate these goals for the range of wire diameters used in the exercise (3E-4 to 1E-2 wavelength). Obtaining a 50-Ohm impedance is one of the main constraints, since it generally requires an increase in the reflector-to-driver spacing as the element diameter increases. Maintaining control on the array gain and front-to-back ratio results in array dimensions that are quire different from those we encounter in the maximum front-to-back ratio and high-gain designs. For example, the reflector length exceeds 1/2 wavelength and thus increases in length with increases in element diameter to maintain its reactance. The reflector length changes by about 4% over the range of element diameters, but the director changes by over 8%--in the normal direction, that is, by decreasing in length with increases in element diameter. The decrease in director length is accompanied by a decrease in the driver-to-director spacing.

+

The result of these dimensional changes--all of which have different rates of change--is a very noticeable change in the general proportions of the wide-band 3-element Yagi over the range of element diameters. Fig. 10 shows the extremes of the range. The small-diameter version has the proportions of a general purpose Yagi, except that the gain is not yet approaching peak value. In contrast, the version with the largest element diameter is unique among the versions of the Yagi that we have encountered.

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+ +
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The design used in these models derives from a Bill Orr (W6SAI) design from about 1990. (Joe Reisert, W1JR, later developed a similar design.) His initial work aimed at 10-meter use, with element diameters appropriate to upper HF antennas. The diameter was between about 0.0018 and 0.0025 wavelength. The design continuum used in developing the automated design model shows its best potential (but not its widest operating or SWR bandwidth) in this range of diameters.

+

Table 4 shows the dimensions of the hand-optimized data-point models developed in this exercise.

+ 
+Table 4.  Hand-Optimized Models for Regression Analysis
+Element Length = Half-Lengths
+
+Element     Log of      Reflector   Driver      Director    Ref.-Dr.    Ref-Dir.
+Diameter    Diameter    Length      Length      Length      Spacing     Spacing
+WL                      WL          WL          WL          WL          WL
+3.16228E-4  -3.5        0.2523      0.2409      0.2234      0.1510      0.2815
+5.6234E-4   -3.25       0.2526      0.2394      0.2198      0.1565      0.2935
+1E-3        -3          0.2530      0.2380      0.2160      0.1620      0.3050
+1.7783E-3   -2.75       0.2534      0.2367      0.2135      0.1765      0.3199
+3.16228E-3  -2.5        0.2545      0.2355      0.2104      0.1970      0.3378
+5.6234E-3   -2.25       0.2589      0.2345      0.2076      0.2220      0.3600
+1E-2        -2          0.2630      0.2380      0.2060      0.2670      0.3820
+
+

The criteria that I used in the development of hand-optimized data-point models included the following items.

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+
    +
  • 1. Maximum 50-Ohm SWR and operating bandwidth.
    • +
  • 2. Peak 180-degree front-to-back ratio at 30.50 MHz for a design frequency of 30.0 MHz.
    • +
  • 3. Minimum 50-Ohm SWR at 30.25 MHz for a design frequency of 30.0 MHz.
    • +
  • 4. Upper 2:1 SWR frequency: 31.25 MHz.
    • +
+
+

Three of the four criteria involve the 50-Ohm SWR characteristics of the array. Fig. 11 shows the curves for 4 of the 7 data-point models. Because the SWR value rises much more rapidly above the design frequency than below it, a relatively constant upper-end 2:1 frequency seemed warranted. For 3 of the 4 displayed curves, the models achieve the goal, but the thinnest wires proved incapable of setting the 2:1 value at the designated frequency and achieving the minimum SWR at 30.25 MHz. In order to extend the higher-frequency side of the curve, the impedance at the design frequency shows capacitive reactance (4.5 to 6 Ohms). Despite these design maneuvers, the curve remains broader below the design frequency for all element diameters.

+
+ +
+

SWR bandwidth is not the sole consideration in a wide-band Yagi. The array must also have usable performance parameters that include both gain and front-to-back ratio. There is only a minor variation between the 180-degree ratio and the worst-case ratio, so these notes will use the 180-degree value as a reference point. To the degree possible, the front-to-back ratio peaks at 30.50 MHz in order to extend the operating bandwidth as far as possible on both sides of the design frequency (30 MHz in the initial design work). Fig. 12 shows the curves for the same element diameters shown in the SWR curves.

+
+ +
+

By setting the peak front-to-back ratio at 30.50 MHz, all of the curves--except for the thinnest element--pass through a value of about 18 dB at about 31.25 MHz and all have a 20-dB front-to-back ratio at 31 MHz. The curves all show a shallower rate of decrease in the front-to-back value below the peak frequency. The rate of decrease is inversely proportional to the element diameter. The thinnest wire reaches its lowest value before the lower limit of the frequency span sampled by the frequency sweep.

+

Ultimately, I defined the operating bandwidth in terms of the frequency span between the points at which the front-to-back ratio passed through the 18 dB mark. Although this value is a bit below the usual amateur standard of 20 dB, it seemed reasonable in light of the modest peak values reached by all of the data-point models. As well, wide-band Yagis normally have utility (multi-faceted or general purpose) functions in which the peak value is less important than a relatively even front-to-back performance.

+

The gain values for the Yagis are generally quite smooth from the lower limit of the operating passband for each version up through the design frequency. Above the design frequency, the gain shows a rising curve. The curve is similar for all 4 sample models. Fig. 13 shows the curves for our 4 sample data-point models.

+
+ +
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Below the design frequency, the two versions using thinner elements show an interesting "knee" in the gain curve. At a certain frequency below the design frequency, the gain drops at a more precipitous rate. The two versions using larger diameter elements also have knees, but those frequencies are below the limits of the frequency sweep. Equally interesting is the fact that the versions of the wide-band Yagi using elements with the largest diameters do not exhibit design-frequency gain levels equal to those of the mid-range elements. As the element diameter increases, the dimensions required to obtain the required 50-Ohm bandwidth and the front-to-back bandwidth are in conflict with dimensions needed for higher gain from the array. The needs of the continuum dictated that I accept the lower gain of the largest diameter version. One may, however, create an independent design that further optimizes gain with only a small cost to the front-to-back ratio within the operating passband. However, the independently developed version is likely to require a greater total boom length (reflector-to-director spacing).

+

Table 5 presents the design-frequency NEC-4 performance calculations for the entire set of data-point models. Compared to past tables of similar data, the present table includes 2 new columns. The SWR and the operating bandwidths are expressed as percentages by taking frequency range between the upper and lower limits and dividing it by the design frequency--with the obligatory multiplication by 100 to arrive at a percentage. The SWR limits use the usual 2:1 50-Ohm reference. Front-to-back values of about 18 dB define the operating bandwidth limits.

+ 
+Table 5.  NEC-4 Performance: Hand-Optimized Models, Pre-Regression Analysis
+SWR Bandwidth = 2:1 50-Ohm SWR range/design frequency.
+Operating Bandwidth = 18-dB front-to-back range/design frequency.
+
+Element           Free-Space  180-Degree  Feedpoint         SWR         Operating
+Diameter          Gain dBi    Front-Back  Impedance         Bandwidth   Bandwidth
+WL                            Ratio dB    R +/- jX Ohms     %           %
+3.16228E-4        7.06        20.09       48.27 - j6.023    6.2         4.5
+5.6234E-4         7.05        20.09       48.45 - j5.847    7.0         4.7
+1E-3              7.06        20.16       48.56 - j4.513    7.5         5.3
+1.7783E-3         7.10        20.94       49.12 - j5.193    8.3         5.5
+3.16228E-3        7.09        21.46       50.24 - j5.564    9.2         5.8
+5.6234E-3         7.09        22.09       48.84 - j5.484    10.3        6.7
+1E-2              6.88        23.37       47.40 - j4.660    11.1        7.5
+
+

The operating bandwidth is about 65-70% of the SWR bandwidth, allowing for the fact that the numbers derive from graphical interpolations of frequency sweep figures. As comparative samples, the 20-meter amateur band has a 2.5% bandwidth, while all of 10 meters has a 5.9% bandwidth. The US 6-meter band has a 7.7% bandwidth, while the seemingly larger 70-cm band has only a 6.9% bandwidth. The wide-band 3-element Yagis in this set hold promise of providing coverage within the limits that define operating bandwidth for all of the bands listed for at least one or more of the listed element diameters. (Covering all of 6 meters may require either a reduction of operating standards to a 17-dB front-to-back ratio or individual tweaking of the design. However, for coverage of the upper 3 MHz of the band for a vertically polarized antenna used for FM and other communications with mobile stations, the required bandwidth is only 5.7%, which can be achieved with 3/4"-diameter elements, that is, 0.003 wavelength elements.)

+

Except for slight differences in gain and front-to-back ratio, all of the data-point models produce similar patterns, as shown in Fig. 14. The patterns are for the E-plane. H-plane patterns would show considerably more beamwidth. Unless the array--when vertically positioned--is at least 5 wavelengths or more above ground, the H-plane patterns above ground will have less gain than E-plane patterns for horizontally positioned antennas at the same center height.

+
+ +
+

Regression analysis of the data-point models produced a very usable collection of 4th-order polynomials. Hence, creation of the automated design model in NEC-Win Plus required only two steps. 1. I replaced the set of regression constants in one of the existing models. 2. I changed the model file name before saving the file. Fig. 15 shows the two versions of the equations page of the wide-band design model.

+
+ +
+

There is no need also to display the wires page in either the "variables" or the "values" version. Fig. 9 provides a view of the relevant forms used, since the wires page remains constant in its variable assignments for all 3 of the automated design models. Since Fig. 15 shows all constants and the form of the regression equations, it has all of the information necessary for re-creating the design program in an alternative programming format.

+

To confirm the correctness of the design model, I recreated the data-point models using the design model as the source and running the resulting models in NEC-4. Table 6 provides the NEC-4 performance calculations. You may compare the results with those in Table 5. As in all of the models, beware of using NEC-2 to develop performance figures for the largest diameter elements unless the EK command is available.

+ 
+Table 6.  NEC-4 Performance: Calculated Models, Post-Regression Analysis
+
+Element           Free-Space        180-Degree        Feedpoint
+Diameter          Gain dBi          Front-Back        Impedance
+WL                                  Ratio dB          R +/- jX Ohms
+3.16228E-4        7.06              20.02             48.34 - j5.933
+5.6234E-4         7.05              20.21             48.16 - j6.120
+1E-3              7.07              20.16             48.82 - j4.468
+1.7783E-3         7.09              20.71             49.96 - j4.715
+3.16228E-3        7.09              21.57             49.62 - j5.909
+5.6234E-3         7.07              22.21             49.10 - j5.531
+1E-2              6.89              23.38             47.39 - j4.580
+
+

Of the three automated design models, the wide-band 3-element Yagi is perhaps the least perfect. The maximum front-to-back version of the array had a very definite marker of when the data-point model reached its goal: a 180-degree front-to-back ratio in excess of 50 dB, combined with the 29-Ohm resonant feedpoint impedance. The high-gain model required a judgment call on the point of optimizing completion, since the gain shows a rising curve with frequency. However, peaking the front-to-back ratio with a feedpoint impedance of 25 Ohms provided a reliable marker for all but the largest diameter element. The criteria for the wide-band version of the 3-element Yagi form a more complex set. Therefore, there is less assurance that the design has in all cases achieved the maximum bandwidth at reasonable performance parameters. Like the high-gain model, it shows a decreasing gain at the highest element diameter, suggesting that in both cases, one might wish to begin but not end the optimizing process with the automated design model.

+

What the Automated Models Cannot Do

+

As already noted, the automated models do not cover all possible 3-element Yagi design possibilities. If the front-to-back ratio is not a significant figure, it is possible to design higher gain Yagis on longer booms. If the feedpoint impedance has no minimum acceptable level, then free-space gain levels over 9 dB are obtainable.

+

As a practical matter, the range of diameters for which the automated models are calibrated do not cover thin-wire Yagis for the HF range. Only at VHF and UHF is the minimum diameter small enough to cover most wire elements. A 0.0003 wavelength element diameter is about 0.024" at 2 meters--about AWG #22 wire. However, for values in the middle ranges of element diameters within the model coverage, many practical designs are available.

+

Perhaps the most limiting HF restriction for the automated models is the fact that they produce dimensions for uniform-diameter elements. Above 55 MHz, uniform-diameter elements are the rule, but for up through 6 meters, uniform-diameter elements are the exception. More common is the practice of using tapered diameter elements. There are some utility programs available for converting uniform-diameter element dimensions into various combinations of stepped-diameter equivalents. However, there may be a simpler procedure that requires only entry-level software (EZNEC or NEC-Win Plus) that has the usual Leeson substitute element feature.

+

First, develop a set of dimensions from the automated program using your best guess at the average element diameter in the proposed stepped-diameter version. This is only a starting point from which to develop a more detail set of element tubes.

+

Second, using the element lengths derived from the first step as initial guides, develop a progression of element diameters and inner section lengths for the elements. You may use some published Yagis as guides, such as those appearing in the ARRL Antenna Book (ant recent edition). These guides, or software such as YagiStress by Kurt Andress, K7NV, will let you set up element diameter progressions with known values of wind survival. The key point here is to be certain that the end section of the thinnest tubing has room to expand its length relative to the length suggested by the automated model.

+

Third, make a model of the stepped diameter element and employ the stepped-diameter correction feature in your modeling software. Note the substitute uniform-element diameter.

+

Fourth, use the subsitute uniform-element diameter in the automated model to arrive at a new set of antenna dimensions.

+

Fifth, create a full model of the proposed antenna, using the stepped diameter inner sections. and the spacing provided by the automated model. Adjust the end lengths or outer element section lengths until the Leeson substitute element lengths match those of the automated design version.

+

If the Leeson substitute element diameter has not changed significantly, the resulting model should show performance values almost identical to those of the automated model. There may be slight differences due to remnant diameter differences and to the differences in the segmentation. In all cases, when using stepped-diameter elements, try to keep the segment lengths along each element the same, whether the element sections are long or short.

+

Because automated 3-element Yagi design has restricted utility, I likely shall not try to extend it to Yagis with more elements. With each additional element, the number of variables climbs and the results become less certain. For longer boom Yagis with more elements, I recommend the use of one of the Yagi optimizing programs. They require more exacting element structure information at the input end, but can produce a custom-optimized design according to the weight that you assign to the performance variables available for user entry.

+

Nevertheless, for utility 3-element Yagis of a few diverse designs, the automated models may be handy. As well, by studying the variations in design dimensions with changes in the element diameter, you may improve the accuracy of your rational expectations of Yagi performance in all of their operating categories.

+

If you wish to download one or more of the NEC-Win Plus automated design models, use the following links.

+
+

Maximum Front-to-Back Model

+

High Gain Model

+

Wide Band Model

+
+

Also see the Antenna Modeling Programs page for more information.

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+ +
+

Updated 01-01-2005. © L. B. Cebik, W4RNL. This item originally appeared in antenneX (Dec., 2005). Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: HF Upper, Yagi


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2-Element Yagis: How Short Can We Go?

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2-Element Yagis: How Short Can We Go?

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This page exists to include the PDF in the topic index

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Topics: HF Upper, Loading, Yagi


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+ Lobe Formation With Height Increases in Horizontal Antennas

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+

L. B. Cebik, W4RNL

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+

A considerable while ago, I did a modeling investigation into "The Effects of Antenna Height on Other Antenna Properties: A Computer Study," Communications Quarterly, 2 (Fall, 1992), 57-79. See Magazines Page. However, I still find that folks are not wholly familiar with the change of elevation lobes as one changes the height of a horizontal antenna. So I thought a note might be in order.

+

By now, most folks are familiar with how to derive the angle at which lobes and nulls exist for any given height. The angle for any lobe of a horizontally-oriented antenna can be estimated from the simple equation

+
+ +
+

where ALN is the angle of the lobe or null above the horizon and h is the antenna height in wavelengths or fractions thereof. Odd values of N represent lobes (points of maximum radiation) while even values of N represent nulls (points of minimum radiation). Hence, if N=3, the lobe in question is the second above the horizon.

+

The existence of lobes and the angle at which each shows maximum gain is, of course, valuable information. With this data, we can choose (if we have a choice) the most optimal height for an antenna for a desired angle of radiation relative to a favored propagation path at the frequency of interest.

+

What is less well known is the fact that changing the height of the antenna has other consequences as a result of the changing pattern of lobes that develop between some given minimum height and some given maximum height. Between a height of 0.5 wl and a height of 1.5 wl, the maximum gain of a dipole may shift by over 0.5 dB. For a beam antenna, the front-to-back ratio can swing by as much as 10 dB. For antennas more complex than dipoles, design will have much to do with the change in properties with changes in height, but even within a single design class--for example, Yagis with the same number of elements--there are variables.

+

Since the point of this note is to illustrate the phenomenon, I can give the best advice up front: for any given antenna, it is best to model it at a series of heights to understand the potential variations of performance. In some cases, the results may make a difference in the selected installation height; in other cases, the results may give the installer a free hand.

+

The Dipole

Virtually everything horizontal begins with the resonant 1/2 wl center-fed dipole. So that is where we shall begin. Let's take a simple dipole and resonate it in free space. The material will be copper and the diameter will be about 0.2" at 14 MHz or 0.1" (#10 AWG) at 28 MHz. In terms of wavelengths, the antenna will be 0.241 wl long and 2.4e-4 wl in diameter. The model will use 21 segments. Here are the gain and source impedance numbers for three frequencies: + 
     7.0 MHz                  14.0 MHz                 28.0 MHz
+Gain  Source Impedance   Gain  Source Impedance   Gain  Source Impedance
+dBi   R +/- jX Ohms      dBi   R +/- jX Ohms      dBi   R +/- jX Ohms
+2.12  72.1 - j 0.5       2.12  72.2 - j 0.4       2.11  72.3 - j 0.3
+

When we place this antenna over average ground (Cond. 0.005 S/m; D.C. 13), and change its height in 1/8 wl increments from 0.5 wl to 1.5 wl, we get the following table of values.

+ 
             7.0 MHz                14.0 MHz               28.0 MHz
+Height    Gain Source Imp.       Gain Source Imp.       Gain  Source Imp.
+WL        dBi  R +/- jX Ohms     dBi  R +/- jX Ohms     dBi   R +/- jX Ohms
+0.5       7.57 66.8 - j10.5      7.33 68.0 - j 9.8      7.21  68.8 - j 9.6
+0.625     8.00 63.7 + j 3.5      7.82 64.3 + j 2.8      7.74  64.6 + j 2.3
+0.75      7.39 75.3 + j 6.7      7.31 74.7 + j 6.3      7.28  74.4 + j 6.3
+0.875     7.26 78.3 - j 3.1      7.18 78.1 - j 2.5      7.13  78.1 - j 2.0
+1.0       7.80 69.9 - j 6.0      7.68 70.5 - j 5.6      7.61  71.0 - j 5.4
+1.125     8.05 67.1 + j 1.4      7.94 67.5 + j 1.1      7.89  67.8 + j 0.8
+1.25      7.70 73.8 + j 4.0      7.64 73.5 + j 3.8      7.62  73.4 + j 3.8
+1.375     7.56 76.2 - j 2.0      7.50 76.0 - j 1.6      7.47  76.1 - j 1.2
+1.5       7.88 70.8 - j 4.3      7.80 71.2 - j 3.9      7.75  71.5 - j 3.8
+

For easier reading, the following graph tracks the gain curves for the three frequencies. (See Fig. 1.) The curves are "spiky" because of the interval between readouts. Smaller increments would have produced smoother curves, but no essential difference in the data.

+
+ +
+

Although incidental to the present exercise, the reduction in gain with frequency increase for exactly scaled dipoles is a useful reminder that material and ground losses do not frequency-scale as perfectly as antenna dimensions for resonance. The increased losses with frequency show up not only in the gain curves, but as well when one compares the maximum and minimum reactance excursions at the three frequencies: A lesser excursion indicates a higher loss. Although the differences are not operationally significant in this case, the general trend is worth remembering.

+

More significant to our exercise is the gain differential of the dipole at 0.875 wl and at 1.125 wl: nearly 0.8 dB at 7 MHz. The curve shows gain peaks at 0.625 and 1.125 wl antenna height, with minima at 0.875 and 1.275 wl. The differential between maxima and minima decreases with antenna height increases, although the curve is distinct well beyond a height of 2 wl.

+

Where the power goes when the gain of the lowest lobe decreases is illustrated in Fig. 2.

+
+ +
+

The elevation pattern for the dipole at a height of 0.5 wl shows a single "fat" lobe in each direction. At a height of 0.75 wl, the second lobe has emerged. However, it is a large lobe of energy pointed almost straight up, more suitable for NVIS use than for DX skip. The vertical dimension of the lower lobes has decreased. If we assume that the area under each curve is the same (which is not precise, but reasonably close), and that total power is represented by this area, then the amount of energy sent straight up with the emergence of the new lobe can be seen to be considerable.

+

When the antenna reaches a height of 1 wl, the second lobe has moved downward, while the lowest lobe has moved slightly outward, while still showing a reduction in its vertical dimension. Maximum gain is the highest of the three situations. However, note the slight center (90-degree elevation) bulge in the pattern. A new lobe will emerge in the nearly vertical plane to reach a peak, with a reduction in gain in the lowest lobe, at about 1.375 wl. The cycle of lobe emergence continues indefinitely with further increases in antenna height, but each succeeding new elevation lobe has a decreasing effect on the gain of the lowest lobe.

+

With a simple dipole, there is a rough reverse correlation between gain maxima and minima and the source impedance maxima and minima. That is, the source impedance is highest when the gain is lowest--and vice versa--as we move up the scale of increasing antenna heights. Like the gain highs and lows, the impedance highs and lows grow less extreme with increases in height.

+

2-Element Yagis

When we examine the behavior of multi-element parasitic arrays--otherwise known as the Yagi--some aspects of the height vs. gain graph change. Moreover, we add a new parameter of interest--the front-to-back ratio. We can only sample a few models, but they will prove interesting and instructive. +

Let's begin with a standard 2-element driver-reflector Yagi. The one we shall examine uses a 0.230 wl driver and a 0.254 wl reflector, spaced 0.125 wl apart, with 1.81E-3 wl element diameters. The material is aluminum. We shall test the antenna over average ground only at 14 MHz, after resonating the antenna in a free space model. In tabular form, our results look like this:

+ 
Height         Gain      F-B Ratio      Source Impedance
+WL             dBi       dB             R +/- jX Ohms
+Free Space      6.06     11.05          36.2 - j 0.9
+0.5            10.74     12.39          40.3 - j 3.3
+0.625          11.14      9.62          34.2 - j 4.0
+0.75           11.15      9.98          33.7 + j 0.5
+0.875          11.24     11.88          38.1 + j 1.4
+1.0            11.47     12.11          38.3 - j 1.7
+1.125          11.59     10.38          35.3 - j 2.7
+1.25           11.55     10.30          34.6 - j 0.2
+1.375          11.57     11.53          36.7 + j 0.6
+1.5            11.68     11.79          37.6 - j 1.3
+

Graphically, the pattern of gain and of the front-to-back ratio appear as shown in Fig. 3.

+
+ +
+

The gain maxima continue to occur at the 0.625 and 1.125 wl marks, but the gain minima for this antenna are less distinct and somewhat offset from the dipole model. Minima occur almost 1/8 wl below those for the simple dipole--a function of the Yagi's second element. Since different designs for even 2-element Yagis will place the two elements at different spacings, we cannot assume that Fig. 3 represents all possible designs. If the height vs. antenna parameter relationship is of interest, it should be checked for each specific design.

+

The front-to-back pattern of maxima and minima are especially variable among designs. If you examine the table, you will discover a rough correlation between the maxima and minima for both the front-to-back ratio and the source impedance.

+
+ +
+

The developmental pattern for new lobes follows that of the dipole, with adjustments for the directional nature of the 2-element Yagi. As shown in Fig. 4, the new lobe in the 0.75 wl height pattern provides power largely in a vertical direction. At a height of 1 wl, the new lobe bends forward, with a consequential flattening of the lower lobe.

+

3-Element Yagis

We can test whether the curves of these models are typical of a genre or specific to individual antenna design by checking out two different 3- element Yagis. The first is a modified K6STI design optimized for the best combination of gain and front-to-back ratio, with a source impedance in the mid-20s. The director is 0.224 wl long, the driver is 0.238 wl long, and the reflector is 0.249 wl long, with 0.325 wl director-driver spacing and 0.151 driver-reflector spacing. The elements are 1.20e-3 wl diameter and are aluminum. The operating parameters of this antenna at 14 MHz over average ground are as follows: + 
Height         Gain      F-B Ratio      Source Impedance
+WL             dBi       dB             R +/- jX Ohms
+Free Space      8.11     27.31          25.7 - j 0.9
+0.5            12.29     25.35          24.6 - j 0.7
+0.625          12.85     24.58          25.8 + j 0.2
+0.75           13.08     36.69          26.6 - j 1.0
+0.875          13.23     30.15          25.6 - j 1.6
+1.0            13.39     25.19          25.1 - j 0.9
+1.125          13.50     25.63          25.6 - j 0.3
+1.25           13.56     32.37          26.2 - j 0.9
+1.375          13.62     29.32          25.7 - j 1.3
+1.5            13.67     25.46          25.3 - j 1.0
+

We can show the gain and front-to-back curves graphically in Fig. 5.

+
+ +
+

For this well-designed 3-element Yagi, the gain curve shows no gain dips. However, by carefully tracing the curve, one can see very slight reductions in the rate of gain increase in the 0.75-0.875 wl region and again in the 1.25-1.375 wl region. These values are of no operating significant whatsoever for this design, but are only remnants that establish the origins of the Yagi in the basic dipole.

+

The front-to-back curve is another matter. It tends to peak where the gain minima would have been--at the 0.75 wl and the 1.25 wl region. For this design, the front-to-back peaks tend to correspond to source impedance peaks. However, the overall excursions of both the resistive and reactive components of the source impedance are very small.

+

Let us contrast this design with another 3-element Yagi design that has been pressed for gain. Consequently, the front-to-back ratio is lower than our first design, and the source impedance is very low. The director is 0.236 wl long, the driver is 0.241 wl long, and the reflector is 0.251 wl long, with 0.253 wl director-driver spacing and 0.152 driver-reflector spacing. The elements are 2.41e-3 wl diameter and are aluminum. The operating parameters of this antenna at 14 MHz over average ground are as follows:

+ 
Height         Gain      F-B Ratio      Source Impedance
+WL             dBi       dB             R +/- jX Ohms
+Free Space      8.30     11.26           5.6 + j 6.2
+0.5            12.28     13.70           5.9 + j 6.4
+0.625          12.88     12.66           5.8 + j 6.0
+0.75           13.12     10.82           5.5 + j 6.1
+0.875          13.31     11.05           5.5 + j 6.4
+1.0            13.51     12.15           5.8 + j 6.3
+1.125          13.64     12.06           5.7 + j 6.1
+1.25           13.69     10.97           5.5 + j 6.2
+1.375          13.75     10.99           5.6 + j 6.3
+1.5            13.83     11.72           5.7 + j 6.3
+

We can show the gain and front-to-back curves graphically in Fig. 6.

+
+ +
+

Like the first 3-element Yagi design, this alternative shows a steady rise in gain with antenna height, with only a slightly greater flattening of the curve in the regions of lower gain in a dipole. However, the pattern of front-to-back ratio is almost precisely the reverse that of the first 3- element Yagi: the new model shows maxima and minima just where the first model shows the opposite. If there is a lesson here, it is that each design must be checked for its own characteristics. However, there is a rough correlation between front-to-back maxima and minima and corresponding highs and lows in the source impedance values.

+

The second Yagi design cautions us to presume nothing about the performance of an antenna design. This lesson is especially important in the development of interlaced Yagis for multi-band operation. The complex interaction of the elements--and the assembly with the ground--can yield some surprises--not to mention the emergence of advantageous heights and heights to avoid.

+

The 2-Element Quad

An interesting intermediate design between 2- and 3-element Yagis is the 2- element quad beam. It shares with the 20-element Yagi the use of only a driver and a reflector. However, the fact that the antenna can be roughly analyzed as a pair of 2-element Yagis vertically arrayed alters the expectations of performance. +

Let's look at a 2-element quad with a driver having director sides 0.126 wl long and reflector sides 0.133 wl long, spaced 0.125 wl. The elements are copper and are 1.93E-4 wl diameter. As with the other antennas, we shall run the model over average ground at 14 MHz.

+ 
Height         Gain      F-B Ratio      Source Impedance
+WL             dBi       dB             R +/- jX Ohms
+Free Space      7.32     21.58          94.4 + j 0.4
+0.5            11.36     18.75          99.4 + j 4.1
+0.625          11.99     21.12          97.4 - j 4.0
+0.75           12.15     27.06          91.0 - j 1.8
+0.875          12.29     21.70          92.3 + j 3.2
+1.0            12.53     19.99          96.8 + j 2.5
+1.125          12.71     22.15          96.2 - j 1.8
+1.25           12.71     24.30          92.5 - j 1.1
+1.375          12.74     21.46          93.0 + j 2.2
+1.5            12.85     20.40          96.0 + j 1.9
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We can show the gain and front-to-back curves graphically in Fig. 7.

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More like the 2-element Yagi, the quad shows deviations from a smooth curve in the regions where the dipole shows reductions in gain. However, the front-to-back curve resembles that of the optimized 3-element Yagi in the placement of maxima and minima. What both these models share in common is having been optimized for a best combination of gain and front-to-back ratio.

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Nonetheless, the quad has a feature unlike the other models: the front-to- back ratio maxima correspond to source impedance minima and vice versa. (The other models examined had a direct correlation between source impedance and front-to-back ratio.) Hence, we once more encounter patterns that dictate the checking of each new antenna design, if the performance at various heights is of interest.

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In our little foray into the variables of antenna performance with changing antenna height, we have looked only at the formation of the second lobe in the 0.75 to 0.875 wl region. For reference, it may be useful to look at both the quad and the optimized 3-element Yagi at 1.25 wl, where the third lobe begins to emerge. See Fig. 8.

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The higher gain and directivity of the 3-element Yagi has some consequences of note relative to the quad. At a height of 1.25 wl, the Yagi top lobe is already bent forward, while the quad top lobe shows more area in the vertical direction. Otherwise--with allowance for the gain and front-to- back differential, the lobes show an exact correspondence. Once more, let us uses the area within the overall pattern as a rough and inexact gauge of total power. If the Yagi has more gain, it comes from expending less in the upward direction than from the differences in the rear lobes. (Note that relative beam widths for the two models has not been taken into account in this comparison.)

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Some horizontal antenna designs are immune (or almost immune) to the effects of lobe development in the vertical plane. Most of these designs involve phased elements. The in-phase fed elements of the 8JK flat-top tend to yield a cancellation of vertical radiation. Hence, the gain curve is smooth as antenna height is increased. Even the Lazy-H and the extended Lazy-H, vertically arranged in-phase fed 2-element arrays show a great reduction in vertical radiation compared to dipoles and parasitic arrays. Notable but lesser reductions in vertical radiation occur with some arrays phased at other angles.

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Conclusion

We have come to appreciate the elevation angles of the lobes and nulls that are a function of the height of a horizontal antenna above ground. The consequences of antenna height and lobe emergence for other performance parameters can be equally significant. +

Although almost any horizontal antenna can be related to dipole performance with respect to lobe emergence, specific antenna designs will add enough variables to the mix to require separate height analysis for each one. In most cases, the region from 0.75 wl to 0.875 wl should be avoided, if possible. But even this generalization is subject to modification based on the analysis of a specific design.

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A Footnote on dBd Gain

Let's suppose for a moment that I sell a 3-element 20-meter Yagi of the well-designed type shown above. With a free-space gain of about 8.1 dBi and a 180-degree front-to-back ratio of over 25 dB, I'd have a decent product to sell (assuming good mechanical construction and a suitable matching system for coaxial cable). The Yagi has just about 6.0 dB gain over a dipole in free space. However, let's see how this antenna stacks up agains a 14-MHz dipole over real (average) ground. +
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Fig. 9 compares the gain at heights of 0.5 to 1.5 wl above average ground. We notice the smoothness the of the Yagi curve and the slight wave in the dipole curve. The question is this: can we make use of this data? Of course we can. A graph of the gain differentials shows us how in Fig. 10.

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By carefully selecting the 1.375 wl height, we can claim that the antenna has a gain of over 6.1 dBd. Note that only at that height and at 0.875 wl does the Yagi achieve its free space gain advantage of 6 dB or more. (All gain figures are taken at the elevation angle of maximum radiation or "take-off" angle.)

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With equal care, a competitor might choose to claim that other antenna designs, including this one, have a gain of only a little over 5 dBd, using (at the extreme) the 0.626 wl height as the evidence. A more conservative competitor might claim that "other" 3-element Yagis of the same boom length have only a little over 5.5 dBd gain, using the 1.125 wl height data. Now, this competitor might also claim 6.1 dBd gain for his product, using the 1.375 wl height data. Of course, heights of data backing the claim would not appear in advertising literature.

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Which would you buy: a 3-element Yagi with just over 5.5 dBd or one with 6.1 dBd? Of course, the competitor's design is identical to the original.

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This exercise is not designed to comment on the practices of any manufacturer. Instead, it is designed to graphically illustrate that the use of gain values in dBd must be handled with exceptional care and with complete data for the conditions of establishing the numbers. Only then can the reader be in a position to evaluate competing claims. This point is not just applicable to advertised antennas. It applies with equal force to reports of antenna designs that appear in journals of all levels, from magazines for beginners to peer-reviewed engineering journals. The point is equally applicable to antenna comparisons made at different times: the results may not be directly comparable unless all of the testing conditions--including antenna height--are the same for each testing session.

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Gain in dBd must always have a warning label: HWC. Handle with care.

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Updated 4-30-99, 5-7-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Return to Main Index

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Topics: HF Lower, HF Upper, Yagi


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Short Beams and Operating Bandwidth

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The Evolution of a Modeling Design

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L. B. Cebik, W4RNL

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+ Some discussions about short (half-size) 40-meter beams revealed that at least a few folks are not certain why one beam might have a wide operating bandwidth than another, when both seem to have about the same length elements and the same length boom. Because we are wedded to 50-ohm coaxial cable and limited-range transmitter output networks, we have come to define operating bandwidth as the frequency span between 2:1 SWR points on the feedpoint SWR curve. +

Actually, the SWR measurements are made in many places: at the antenna feedpoint, at the coax-to-antenna network input terminals, and even at some prescribed length of some prescribed type of coaxial cable connected to the matching network and the antenna. However, for our purposes, the 2:1 SWR figure may be references to the antenna's resonant impedance on the premise that a matching network will transform that impedance to 50 ohms resistive.

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So our question is this: how do we get decent operating bandwidth from a half size Yagi? Understanding a few of the principles involved may also assist the average ham to understand a little the problems of antenna design that require careful engineering by manufacturers.

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Dipoles: Loaded and Unloaded

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Our first stop on the way toward the Yagi is, as always, the dipole. The more we understand dipoles, the easier it is to understand Yagis. +

Consider full size dipoles. Let's compare three dipoles at a height of 70' above average ground. In fact, all of the antenna models we explore here will be set 70' above average ground so that the results will be directly comparable. Besides, 70' is just about a half wavelength at 7.15 MHz, our design target frequency.

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Let's use #12 copper wire for one of them, a most common choice. The antenna will be 67.3' long, at least in the model. Let's also use 0.5" and 1.0" aluminum tubing. for antennas that are 66.9' and 66.6' long, respectively. As we all know, the fatter the antenna wire, the shorter the antenna at resonance.

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However, within limits, fattening the wire also raises the antenna gain a bit. Not by enough to make an operational difference, but at least in a mathematically significant way. The chart of dipole gains for the three antennas from 7.0 to 7.3 MHz clearly shows the differences.

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Newcomers are sometimes surprised to see the gain increase as the frequency increases. As frequency increases, the antenna become longer relative to a resonant half wavelength, and a longer antenna means higher far field gain. In fact, the gain increase steadily (at the cost of beamwidth) until the length of the antenna exceeds 1.25 wavelengths. Somewhere between this point and about 1.5 wavelengths, the main lobes begin to split, and each lobe shrinks a bit for a while.

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However, our interest in dipoles is for the sake of their use in Yagis, so lengths near to a half wavelength will be our focus. Not only does the gain go up as the wire gets fatter, but as well, the operating bandwidth gets wider. As the next graph shows, all three antennas will show under 2:1 SWR across 40 meters, but the fatter models show a much slower increase in SWR as we move away from the design center frequency.

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What happens to this operating bandwidth if we shorten and load the dipole. Since the most common form of loading used in 40-meter antenna design is mid-element loading, we shall follow that lead. Second, because the most common element length used in common 40-meter beams is about half size, we shall set 36' (432") as our general target.

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Since we are not actually designing a real beam, but only trying to see some of the principles involved, we shall arbitrarily freeze one variable: element diameter. We shall use 1" aluminum tubing throughout. We should understand that the actual lengths used by manufacturers may depart from 36' by virtue of choosing not just a different element diameter, but as well a tapering schedule. A tapering schedule is simply a fancy name for the progression of smaller tube section diameters, working from the boom outward.

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Working with a 36' section of 1" diameter aluminum tubing, we next set inductive loads about halfway between the boom and the element ends. The required inductive reactance needed to resonate the 36' piece of aluminum at 7.15 MHz is 511 ohms per load. This value works out to be 11.375 microH at the design frequency. (If we are to run reasonably accurate frequency sweeps across 40 meters, we must ultimately enter the load into the modeling program as an inductance--with a series resistance for Qs less than infinity.)

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Before we look at Q, let's first see what we might use to make the inductive load. First is a coil with the required inductance. We all know that coils have values of Q (unloaded, to be precise) determined by dividing the coil's reactance by its AC resistance at the frequency in question. Some bad or highly encrusted or corroded coils may have a Q as low as 50, but for the most part, well maintained coils found in commercially-made antennas have Qs ranging from over 100 to something over 300.

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Second, we might choose for out inductive load a shorted section of transmission line. In antenna work, these lines are often called linear loads. If laid out symmetrically with respect to the antenna element, standard shorted stub calculations will accurately set the length of the line. Some lines change spacing along the loading element, but that is simply a line of varying characteristic impedance--a bit harder to calculate with respect to required length, but very straightforward. If the wires are not equi-spaced from the antenna element, the unequal currents induced in the lines will require lengths that differ from transmission line stubs and are ordinarily longer than stubs.

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Nonetheless, linear loading transmission line stubs provide the required reactance for the loads, whether they hang straight down from the element or are brought into a position parallel to the element. As such, they are equivalent to standard inductors, but usually with a higher Q. The less symmetrical with respect to the element, the lower the Q. Worst case Qs range somewhere above 300, while well designed linear loading transmission line stubs can have Qs from 800 to 1500.

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Although high, these values of Q indicate that linear loads are not, as some would suggest, lossless. Only loads made from superconductors providing an infinitely high Q would truly be lossless. And the connections to the antenna element itself would introduce a modicum of resistance to the load network.

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We may model loads as inductance in series with resistance. To explore the effects of Q on our shortened, loaded dipole, we may assign some resistance values to establish a reasonable series of Q levels. In all of the following examples, using a load reactance of 511 ohms, we can use resistance values of 0, 0.511, 1.022, 2.044, 4.088, and 8.176 ohms to set Q values of infinity, 1000, 500, 250, 125, and 62.5. One limit to this technique is that linear load transmission line stubs do not change values of inductive reactance at the same rate as coils with respect to changes in frequency. However, the results will still show us the trends.

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The chosen values of Q will let us explore from the best to the worst cases we are ever likely to encounter. We may even discover that we might select a Q value for a design in order to set one or more antenna properties where we want it.

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Reducing Q reduces dipole gain, as a simple function of the increasing resistive losses in the antenna. The results are graphed below. Note, however, that even for the case of zero resistance, antenna gain is less than that for a full-size dipole. This is the effect of using a shorter element.

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By the time Q is reduced to 250, we have lost over 0.5 dB relative to a lossless load. If our loads decay to a Q of 62.5, we will have lost nearly 2 dB relative to a lossless load.

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On the other side of the coin, a half-size dipole element with mid-element loading has a quite narrow operating bandwidth. With a lossless or very high Q load set, the operating bandwidth of our 1" diameter antenna is only about 100 kHz. At the lowest Q on the graph, the bandwidth exceeds 150 kHz on 40 meters.

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Now suppose that you are designing a 36' 40-meter dipole for hams to use. You have some design decisions to make. You can provide more gain with less operating bandwidth or more operating band width with less gain. Part of your decision will be based on expert judgment of at what point the gain decrease becomes operationally significant. The other part of your decision may be based on what you perceive to be demands of potential buyers in terms of operating bandwidth.

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Remember that you may combine this exercise with the earlier one concerning antenna diameter and operating bandwidth. By using fatter elements, you may increase operating bandwidth for any given Q in the graphs, getting a modicum more gain in the process. However, both the weight and the cost of the resulting antenna will increase.

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We can note in passing that fatter elements combined with inductors with naturally lower Qs will have a wider operating bandwidth than higher Q linear transmission line stub loads and smaller diameter elements. However, it is unlikely (from our full-size dipole graphs) that the increased gain of the fatter elements will completely offset the losses of lower Q loads. It is more likely that for equally carefully designed loads, one linear and the other an inductor, the narrow-banded linear- loaded dipole will have about a half dB advantage in gain on average, assuming the same antenna element length.

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Which is the more important--operating bandwidth or gain--is a judgment call by the user based upon operating needs.

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The half size-dipoles show a range of feedpoint impedances from about 26 ohms for a lossless load set to over 40 ohms for the lossiest set. If we assume the use of a matching network for the transition to 50-ohm coaxial cable, we have both network and other small losses that will slightly increase the operating bandwidth as measured at the network input terminals. If we measure the operating bandwidth at some distance down the coaxial line, we shall see a further increase in operating bandwidth based upon line losses. Hence, the contrast between 100 and 150 kHz in our example may in practice turn out to be a difference between 150 and 200+ kHz at the operating position. The exact amount of bandwidth increase depends on variables beyond the scope of this exercise to calculate. However, N6BV's transmission line and tuner loss program may be of use in analyzing each operator's situation.

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From Dipole to Yagi

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Once you have become adept at designing loaded dipoles, you may turn to the 2-element Yagi. Let us arbitrarily set a distance of 20' to separate a driven element from a reflector. This distance is between 0.14 and 0.15 wavelength, a good distance for a compromise between gain and front-to-back ratio with a 2-element, shortened-element Yagi. +
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We shall leave the loads in the elements just where we placed them in the dipole. In modeling terms, this appears as a percentage of distance from each end. As we adjust element lengths a bit for various reasons, the loads will move about a small amount, but not enough to disturb the general trends we want to observe. (If we were designing a real antenna, we might want to freeze the positions of the loads.) We shall continue to use the 11.375 microH inductances (511-ohm reactances) and adjust the element ends as needed to obtain various characteristics.

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One of the easiest ways to design a Yagi is to set the elements at the desired spacing and then adjust the length of the driven element for resonance at the target frequency, in this case 7.15 MHz. Then, we might increase the length of the reflector for either maximum gain or maximum front-to-back ratio. The result would be a 2-element Yagi of excellent performance at the design frequency: at 70' up, over 11 dBi gain and over 30 dB front-to-back ratio with lossless loads. The resulting dimensions for the antenna are a driven element 17.67' long and a reflector 18.05' long. As the Q of the loads is decreased, the driven element must become longer to reset resonance within the +/- j1 Ohm reactance limit for the definition of resonance in this exercise. At the lowest Q of 62.5, the driven element is 17.80' long.

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The antenna has some interesting properties, some of which may be graphed. However, let me present the frequency scan for the antenna using lossless loads to note one or two peculiar properties that are not evident in the graphs.

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Frequency      Gain      Front-to-Back  SWR relative to
+in MHz         in dBi    in dB          resonant impedance
+7.00            9.75*     4.13*         23.904
+7.05           10.26*     3.31*         17.229
+7.10           10.95      3.55           6.242
+7.15           11.20     30.43           1.001
+7.20           10.14      9.95           1.704
+7.25            9.47      6.17           2.227
+7.30            9.08      4.50           3.309
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Most notable are the starred entries: at 7 to above 7.05 MHz, the antenna shows a reversed pattern, with gain to the rear. Hence, even apart from operating bandwidth SWR considerations, the antenna is useful only from about 7.1 MHz on upward. Only at the lowest Q in the following graphs does the region of reversed pattern drop below 7.05 MHz.

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The remaining characteristics are reasonably well represented by the graphing of antenna performance with the same Q levels as we imposed upon the shortened dipoles. Antenna gain, as shown below drops significantly, especially when the load Qs drop below 250. Peak gain and peak front-to- back ratio are quite close to each other in frequency.

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The front-to-back ratio shows a very sharp peak at the design frequency. Although gain drops steadily with decreasing load Qs, the front-to-back ratio actually increases for the first two steps of load Q decrease from the lossless load. This is natural. There appears to be for any 2-element design an optimum load Q for maximum front-to-back ratio at the design frequency. However, above the design frequency, front-to-back ratios closely coincide, with lowest Q front-to-back values actually exceeding those of higher Qs by an insignificant amount.

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As a single-frequency 2-element beam design, this antenna is excellent. However, in operating bandwidth, the antenna is seriously deficient. It achieves a 150 kHz operating bandwidth only with the lowest Q loads, where the gain and the front-to-back ratio are mediocre at their peak. With a load Q of 250 or more, the operating bandwidth is barely 100 kHz. (As with the shortened dipole, these values are subject to increase depending where along the antenna-matching network-transmission line system that the measurements are made. The antenna shows a feedpoint impedance ranging from about 23 ohms for a lossless load set to nearly 39 ohms for loads with the lowest Q. Hence, a matching network may be presumed as part of the design.)

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Although intriguing, the simple Yagi design is not satisfactory for most amateur 40-meter applications. How can we achieve greater operating bandwidth and preserve for each level of load Q all or most of the operating performance figures?

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The answer lies largely in moving the performance peaks away from the resonant frequency of the antenna. Moving the performance peaks downward in frequency while holding the antenna resonance at the target design frequency of 7.15 MHz has the effect of changing the length ratio between the driven element and the reflector. From a design evolution standpoint, this means lengthening the reflector and then re-resonating the driven element. The reflector length will change more than the driven element length, thus altering the ratio of the two.

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The process can go on until the designer is satisfied with the results. For this exercise, I chose to stop at a point perhaps short of where a practical designer might have gone. However, the resulting antenna is instructive with respect to several antenna properties. The basic properties of the antenna are illustrated in the following table of values corresponding to those of the earlier design, both list with lossless loads.

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Frequency      Gain      Front-to-Back  SWR relative to
+in MHz         in dBi    in dB          resonant impedance
+7.00           10.09*     1.94*         16.424
+7.05           11.50      7.84           5.283
+7.10           10.80     18.27           1.411
+7.15            9.86      8.39           1.006
+7.20            9.30      5.58           1.384
+7.25            8.96      4.20           2.086
+7.30            8.74      3.38           3.214
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For this design, peak gain is very close to 7.05 MHz, where the pattern is now in the correct direction. Only at 7.00 MHz is the pattern reversed, and this would easily be resolved by scaling the antenna elements equally longer. The seemingly lower peak front-to-back ratio is actually well above 20 dB, but at a frequency between 7.07 and 7.08 MHz. Although the front-to-back ratio tapers rapidly. the gain holds up well across the band. Even at this very high load Q, operating bandwidth exceeds 170 kHz, a 70% increase from the previous model.

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Incidentally, the driven element was 17.81' long, while the reflector was 18.35' long. This ratio of 1.03 R/DE is larger than that of the original model (1.02), and may be made larger still. As the operating bandwidth increases, however, performance begins to fall off for any given load Q level.

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The following graph shows the gain of the antenna across 40 meters for each load Q level. Values are not significantly different from those of the preceding model, although the peak occurs at a lower frequency.

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The graph of front-to-back ratios shows an increasing value down to about a load Q of 500. This is partly real and partly a function of the peak value gradually moving upward toward the 7.10 MHz frequency mark. As with the previous model, the front-to-back ratios for frequencies above the peak value are actually higher with lower load Q values.

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With respect to operating bandwidth, the general graph below, when compared to that for the earlier model, shows a distinct widening of operating bandwidth for all load Q levels.

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Let's remove the high value for 7.00 MHz and redraw the graph. Now the difference among the Q levels are more apparent. At the lowest Q level, an operating bandwidth of 200 kHz is quite possible. Indeed, when measured at the operating position, the antenna might appear to cover almost the entire band. Alternatively viewed, the 200 kHz operating bandwidth, when measured at the operating position, might be obtainable with higher-Q loads.

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Note that one may use all of the operating bandwidth widening techniques, even with this second design. Larger elements, measurements farther down the line, a line-to-antenna matching network, lower load Qs, and further separation of the resonant frequency from the peak performance frequency would all contribute to a wider operating bandwidth. The antenna showed a range of feedpoint impedances at resonance of about 36 for lossless loads to about 46 for a Q of 62.5. Further separation of the resonant frequency from the peak performance frequencies would likely result in an antenna that provided a direct match to 50-ohm coaxial cable.

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There is a second way to increase the feedpoint impedance of the mid-loaded antenna: to move the loads outward. so far, we have used a stand mid- element spacing about 25% inward from the element ends. Let's change that spacing to about 20% inward from the element ends.

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This takes us briefly back to the dipole. The first thing we discover with our 36' dipole is that the new loads must be larger to achieve resonance: 625 ohms each or 13.9 microH. The second discovery is that the feedpoint impedance (a value for resistance at resonance) climbs by about 10%. The following table compares the "25%" and the "20%" dipoles at 7.15 MHz with respect to gain and feedpoint impedance for values of Q from infinity down to 62.5:

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Antenna:            "25%"                    "20%"
+Q         Gain in dBi    Feed Z (R)     Gain in dBi    Feed Z (R)
+lossless  7.40           26.32          7.41           28.87
+1000      7.24           27.26          7.24           29.96
+ 500      7.10           28.20          7.09           31.06
+ 250      6.82           30.08          6.79           33.25
+ 125      6.30           22.90          6.25           37.63
+  62.5    5.43           41.43          5.34           46.38
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As Q decreases, the very slightly greater resistive losses result in a noticeable but operationally insignificant decrease in gain for the "20%" antenna relative to the "25%" model. The increase in feedpoint impedance, however, is high enough at reasonably achievable Qs (125-250) to permit the use of 50-ohm at the feedpoint. However, the SWR curves for each level of load Q are virtually indistinguishable from those for the "25%" model when SWR is related to resonant feedpoint impedance at the target design frequency (7.15 MHz).

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The prospect of direct 50-ohm feeding of the "20%" antenna model improves as we translate the dipole design directly into a version of the wider-band Yagi shown above. The following table shows the gain, front-to-back ratio and SWR across 40 meters for the new model at a Q of 250. However, in this table, the SWR relative to a 50-ohm standard is shown.

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Frequency      Gain      Front-to-Back  SWR relative
+in MHz         in dBi    in dB          to 50 ohms
+7.00            7.48*     1.31*         >10
+7.05            9.27      7.71          >4
+7.10            9.78     17.54           1.697
+7.15            9.22      8.32           1.213
+7.20            8.74      5.50           1.402
+7.25            8.42      4.12           1.997
+7.30            8.20      3.30           2.905
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The 7.15 MHz resonance of the antenna is about 41 ohms, about 7% higher than that of the earlier "25%" model. Further juggling of the reflector- to-driver ratio and load placement might easily result in a direct 50-ohm feed antenna with a slightly wider operating bandwidth. Add to this a bit of reasonable element fattening, possibly a slightly lower Q, and measurement at the end of a prescribed feedline, and well over 2/3 of 40 meters can be within the perceived operating bandwidth of the antenna system.

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Conclusion

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Nothing in this little exercise is unknown to experienced antenna designers. I have tried to go through the design exercise in such a way as to make clear some of the techniques that may be used to widen operating bandwidth of a shortened 2-element Yagi. Some of those means maintain and even slightly improve antenna performance as measured in terms of gain and front-to-back ratio. Others involve a compromise where operating bandwidth comes at the expense of gain and/or front-to-back ratio. Other things being equal, high-Q loads present narrower operating bandwidths, while low Q loads widen the operating bandwidth. However, design techniques like separating the antenna resonant frequency from the peak performance frequency can go a significant distance in overcoming the need for lowering the load Q too far to achieve an acceptable operating bandwidth. +

Hopefully, understanding some of these (incompletely listed) aspects of shortened antenna design will help you understand also some of the design differences among shortened antennas on the market both today and in days to come. Plug your own operating needs and desires into the equation, and the result will likely be the most optimal antenna selection possible.
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Updated 10-5-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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Go to Amateur Radio Page

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Topics: HF Lower, Yagi


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+

Three Forward-Stagger 5-Band Yagis from ON4ANT

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

Part 1: 50' Boom Models, August, 1998

Johan Van de Velde, ON4ANT, shared with me some fascinating designs for a 5-band Yagi. He wished to make the designs more widely available as food for thought by others and asked me if I would place them at my site. Although I normally only place my own work at my site, since there are perhaps better outlets for the original work of others, these designs are worth examining on at least two counts. First, the idea that a 5-band Yagi within a finite boom is not possible is laid to rest. Second, the work is a fine example of the forward stagger principle, noted in some other places at the site. +

Here is the brief account Johan shared about how he came to these designs:

+

"Having a 15 meter boom with a 4" diameter available made me think about the possibility of putting some elements to arrive at a beam that covered the 5 highest HF bands, 10 to 20 meters. The design goal was to achieve a gain for each band comparable to the gain of a 3-element monoband Yagi.

+

"As I started, I took several designs for monoband beams for 10, 15, and 20 meters and placed them on the boom. Then I added WARC band mono-banders, and the result was very productive.

+

"The average gain for 3-element mono-banders was 7.0 to 7.3 dBi (free space gain). After placing everything on the boom, the gain increased to over 8 dBi, an average increase of 1 dB per band. The designs looked to perform more like 4-element mono-banders on all bands.

+

"The designs consist of 3 elements on 20, 3 elements on 17, 2 elements on 15, 2 elements on 12, and 4 elements on 10 meters. The result is an average gain of over 8.0 dBi free space, with excellent front-to-back ratio and good operating bandwidth for 14.0-14.28, 21.0-21.35, 28.0-28.6, and full WARC band coverage."

+
+ +
+

Figure 1 shows the outlines for the two designs. The first is focused on band coverage, while the second focuses on peak gain. At the end of this note are the modeling descriptions of the antennas, given both as AO models and as EZNEC model descriptions. The results of Johan's work have been cross checked on NEC-4, and, as one might expect for these untapered initial designs, the results are in close agreement.

+

Here are tables of performance figures from NEC-4 for each model, taking the band edges and the band center as markers. For the non-WARC bands, the limits are wider than John set as design goals, but the designs hold up well on almost all bands to the very limits of the wider bands.

+ 
14-28 X1
+
+Frequency      Gain dBi       F-B dB         Z (R+/-jX)
+14.0           8.07           28.38          32.7 - j 2.5
+14.175         8.16           30.48          28.9 + j 5.4
+  AO           (8.14)         (29.27)        (29.2 + j 5.1)
+14.35          8.30           24.17          22.8 + j16.1
+
+18.068         8.08           21.70          19.8 + j 3.5
+18.118         8.09           22.08          21.1 + j 5.7
+  AO           (8.11)         (23.75)        (23.7 - j 0.5)
+18.168         8.11           22.52          22.8 + j 8.2
+
+21.0           8.22           22.04          20.0 - j 0.8
+21.225         8.29           21.78          32.0 + j 7.9
+  AO           (8.21)         (20.96)        (34.8 + j 5.7)
+21.45          8.39           21.60          34.5 + j16.2
+
+24.89          8.59           25.08          12.9 + j 6.8
+24.94          8.62           24.50          13.2 + j 8.7
+  AO           (8.64)         (25.82)        (10.8 + j 4.0)
+24.99          8.65           23.96          13.4 + j10.6
+
+28.0           7.90           34.52          22.3 + j 0.6
+28.5           8.15           24.59          23.0 + j16.2
+  AO           (8.22)         (22.56)        (26.9 + j13.8)
+29.0           8.42           19.98          23.4 + j33.2
+

Reference AO values for center band are included to show the agreement. Only the lowest end of 10 meters shows a gain lower than 8.0 dBi, and only the upper end of 10 meters shows a 180-degree front-to-back ratio under 20 dB (just barely). The lower source impedance of the 12-meter run is inevitable, given the nearness in length of the 10- and 12-meter elements, making almost all of the 10-meter elements added directors that increase 12-meter gain. On 10, the 12-meter elements function as added reflectors and have little influence on the 10-meter performance.

+ 
14-28 X3
+
+Frequency      Gain dBi       F-B dB         Z (R+/-jX)
+14.0           8.11           24.43          31.4 - j 5.3
+14.175         8.18           23.45          31.5 + j 2.8
+14.35          8.30           22.09          29.1 + j11.6
+
+18.068         8.16           22.21          24.6 - j 1.3
+18.118         8.18           22.80          25.3 - j 0.7
+18.168         8.20           23.55          25.7 + j 0.1
+
+21.0           8.39           19.78          26.2 - j 4.4
+21.225         8.50           19.41          27.9 + j 5.2
+21.45          8.61           19.10          29.5 + j14.8
+
+24.89          8.65           25.90          13.2 + j 2.5
+24.94          8.67           25.16          13.2 + j 4.3
+24.99          8.70           24.50          13.1 + j 6.2
+
+28.0           8.42           23.08          31.1 - j 1.0
+28.5           8.57           21.57          20.0 + j 2.3
+29.0           7.90           26.62           3.9 + j25.9
+

The X3 design achieves some added low band-end gain on some of the bands, especially 15-10 meters. However, there is some small sacrifice of front-to-back ratio on 15 and a narrower operating bandwidth on 10 meters. For some operating situations, these gain and sacrifices may be in order; for other operating situations, the broader X1 design may be favored.

+
+ +
+

Figure 2 shows a typical pattern, with its very small rearward "ball" of gain. This pattern holds for almost all bands on both designs and is more typical of 4-element designs than of 3-element Yagis. Those who wish to model either or both of these antennas will benefit from examining the current tables to discover which elements are active to a significant degree as each band is fed.

+

The designs call for separate feeds, with the feed elements indicated in the AO models. All dimensions are in meters. US readers who model the antenna in EZNEC can convert the dimensions to feet or inches within the program. Incidentally, the 15-meter boom translates to about 49.2' long. The boom is similar to the boom length of a long 20-meter mono-bander, whose free space gain would be about 10.0 to 10.2 dBi for a well-designed 5-element version. See the note on the comparative performance of six 5/6-element 20 meter mono-banders in another note in this series for further details. However, in the same space, Johan has packed 5 bands of 3+ element performance.

+

These designs are worth study and further experimentation.

+ 
+====================================================================
+AO model
+
+14-28X1.ANT
+
+114-18-21-24-28 yagi
+;Over real ground
+Free space
+;14.150 MHz
+;18.118 MHz
+;21.200 MHz
+;24.940 MHz
+;28.300 MHz
+14.175 MHz
+13 wires, meters
+r = 5.45       ;reflector20
+s = 5.2             ;driver20
+t = 4.9             ;dir 20
+a = 4.15       ;reflector 17 + director2 20
+b = 4.02       ;driver 17
+d = 3.8             ;dir 17 + refl 15
+e = 3.395      ;driver 15
+f = 3.02       ;dir 15 + refl 12
+g = 2.91       ;driver 12
+h = 2.78       ;dir 12 + refl 12
+i = 2.55       ;driver 10
+j = 2.355      ;dir1 10
+k = 2.265      ;dir2 10
+;
+pr = 0              ;refl 20
+ps = 2              ;driver 20
+pt = 3.6       ;dir 20
+pa = 5.25      ;refl 17 -dir 20
+pb = 6.2       ;driver 17
+pd = 7.2       ;dir 17 - refl 15
+pe = 8.4       ;driver 15
+pf = 9.5       ;dir 15 - refl 12
+pg = 10.3      ;driver 12
+ph = 11.6      ;dir 12 - refl 10
+pi = 12.45          ;driver 10
+pj = 13.4      ;dir 10
+pk = 15             ;dir2 10
+dia = .02      ;tubing diameter --> must be tapered
+shift z 24
+;
+1     pr -r 0    pr r 0   dia   ;14 refl
+1     ps -s 0    ps s 0   dia   ;14 driven
+1     pt -t 0    pt t 0   dia   ;14 dir1
+1     pa -a 0    pa a 0   dia   ;18 refl - 14 dir2
+1     pb -b 0    pb b 0   dia   ;18 driven
+1     pd -d 0    pd d 0   dia   ;18 dir2 - 21 refl
+1     pe -e 0    pe e 0   dia   ;21 driven
+1     pf -f 0    pf f 0   dia   ;21 dir1 - 24 refl
+1     pg -g 0    pg g 0   dia   ;24 driven
+1     ph -h 0    ph h 0   dia   ;24 dir1 - 28 refl
+1     pi -i 0    pi i 0   dia   ;28 driven
+1     pj -j 0    pj j 0   dia   ;28 dir1
+1     pk -k 0    pk k 0   dia   ;28 dir2
+1 source
+Wire 2, center    ; driver 20
+;Wire 5, center    ; driver 18
+;Wire 7, center    ; driver 15
+;Wire 9, center    ; driver 12
+;Wire 11, center    ; driver 10
+
+========================================================
+EZNEC model description
+
+                      EZNEC/4  ver. 2.5
+
+ON4ANT 5-b Yagi:  14-28xl                    08-28-1998     20:11:19
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 2.00E+01 37
+2           -5.200,  2.000,  0.000         5.200,  2.000,  0.000 2.00E+01 35
+3           -4.900,  3.600,  0.000         4.900,  3.600,  0.000 2.00E+01 34
+4           -4.150,  5.250,  0.000         4.150,  5.250,  0.000 2.00E+01 28
+5           -4.000,  6.200,  0.000         4.000,  6.200,  0.000 2.00E+01 27
+6           -3.640,  7.200,  0.000         3.640,  7.200,  0.000 2.00E+01 25
+7           -3.395,  8.400,  0.000         3.395,  8.400,  0.000 2.00E+01 23
+8           -3.020,  9.500,  0.000         3.020,  9.500,  0.000 2.00E+01 21
+9           -2.910, 10.300,  0.000         2.910, 10.300,  0.000 2.00E+01 21
+10          -2.720, 11.600,  0.000         2.720, 11.600,  0.000 2.00E+01 19
+11          -2.560, 12.450,  0.000         2.560, 12.450,  0.000 2.00E+01 19
+12          -2.355, 13.400,  0.000         2.355, 13.400,  0.000 2.00E+01 17
+13          -2.265, 14.800,  0.000         2.265, 14.800,  0.000 2.00E+01 16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+========================================================
+AO Model
+
+14-28X3.ANT
+
+14-18-21-24-28 yagi
+;Over real ground
+Free space
+;14.150 MHz
+;18.118 MHz
+;21.200 MHz
+;24.940 MHz
+28.300 MHz
+13 wires, meters
+;r = 5.450          ;reflector20
+;s = 5.152          ;driver20
+;t = 4.892          ;dir 20
+;a = 4.148               ;reflector 17 + director2 20
+;b = 4.021          ;driver 17
+;d = 3.802          ;dir 17 + refl 15
+e = 3.375      ;driver 15
+f = 3.019      ;dir 15 + refl 12
+g = 2.905      ;driver 12
+h = 2.781      ;dir 12 + refl 10
+i = 2.6        ;driver 10
+j = 2.498      ;dir1 10
+k = 2.35       ;dir2 10
+;
+;pr = 0             ;refl 20
+ps = 1.874          ;driver 20
+pt = 3.6       ;dir 20
+pa = 5.25      ;refl 17 -dir 20
+pb = 6.194          ;driver 17
+pd = 7.2       ;dir 17 - refl 15
+pe = 8.21      ;driver 15
+pf = 9.5       ;dir 15 - refl 12
+pg = 10.487         ;driver 12
+ph = 11.6      ;dir 12 - refl 10
+pi = 12.34          ;driver 10
+pj = 13.02          ;dir 10
+pk = 15        ;dir2 10
+dia = .02      ;tubing diameter --> must be tapered
+;
+1     0 -5.450 0     0  5.450 0   dia   ;14 refl
+1     ps -5.142 0    ps 5.142 0   dia   ;14 driven
+1     pt -4.820 0    pt 4.820 0   dia   ;14 dir1
+1     pa -4.148 0    pa 4.148 0   dia   ;18 refl - 14 dir2
+1     pb -4.021 0    pb 4.021 0   dia   ;18 driven
+1     pd -3.802 0    pd 3.802 0   dia   ;18 dir2 - 21 refl
+1     pe -e 0    pe e 0   dia   ;21 driven
+1     pf -f 0    pf f 0   dia   ;21 dir1 - 24 refl
+1     pg -g 0    pg g 0   dia   ;24 driven
+1     ph -h 0    ph h 0   dia   ;24 dir1 - 28 refl
+1     pi -i 0    pi i 0   dia   ;28 driven
+1     pj -j 0    pj j 0   dia   ;28 dir1
+1     pk -k 0    pk k 0   dia   ;28 dir2
+1 source
+;Wire 2, center    ; driver 20
+;Wire 5, center    ; driver 18
+;Wire 7, center    ; driver 15
+;Wire 9, center    ; driver 12
+Wire 11, center    ; driver 10
+
+=====================================================================
+                      EZNEC/4  ver. 2.5
+
+ON4ANT 5-b Yagi:  14-28x3                    08-28-1998     20:11:52
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 2.00E+01 37
+2           -5.142,  1.874,  0.000         5.142,  1.874,  0.000 2.00E+01 35
+3           -4.820,  3.600,  0.000         4.820,  3.600,  0.000 2.00E+01 34
+4           -4.148,  5.250,  0.000         4.148,  5.250,  0.000 2.00E+01 28
+5           -4.021,  6.194,  0.000         4.021,  6.194,  0.000 2.00E+01 27
+6           -3.802,  7.200,  0.000         3.802,  7.200,  0.000 2.00E+01 25
+7           -3.375,  8.210,  0.000         3.375,  8.210,  0.000 2.00E+01 23
+8           -3.019,  9.500,  0.000         3.019,  9.500,  0.000 2.00E+01 21
+9           -2.905, 10.487,  0.000         2.905, 10.487,  0.000 2.00E+01 21
+10          -2.781, 11.600,  0.000         2.781, 11.600,  0.000 2.00E+01 19
+11          -2.600, 12.340,  0.000         2.600, 12.340,  0.000 2.00E+01 19
+12          -2.498, 13.020,  0.000         2.498, 13.020,  0.000 2.00E+01 17
+13          -2.350, 15.000,  0.000         2.350, 15.000,  0.000 2.00E+01 16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       V
+
+No loads specified
+
+No transmission lines specified
+
+Ground type is Free Space
+
+ +
+

Part 2: 60' Boom Model, April, 1999

Johan has sent me his latest design--a 14-element forward stagger 5-band Yagi design. By giving himself an extra 10' of boom (now up to 60' long), he has improved performance throughout, but especially on the upper bands. Johan intends to use a gamma match for each driven element. +

The following table gives the NEC-4 readouts of potential performance for the design frequency in each band, with data in () for the band edges. The numbers confirm the modeling results Johan derived from AO.

+ 
Freq.     Gain      F-B       Feed Impedance
+MHz       dBi       dB        R +/- jX Ohms
+20
+(14.0     8.16      30.80     32.4 - j 2.4)
+14.15     8.26      30.20     28.7 + j 5.7
+(14.35    8.40      23.03     22.8 + j16.4)
+17
+18.118    8.26      21.29     30.5 + j 6.9
+15
+(21.0     8.70      23.13     29.5 + j 2.5)
+21.2      8.79      23.33     32.4 + j10.5
+(21.45    8.92      23.45     35.4 + j20.1)
+12
+24.89     9.57      36.73     24.4 + j 9.3
+10
+(27.6     9.58      21.86     20.4 - j17.1)
+(28.0     9.79      26.48     22.0 - j 7.1)
+28.35     9.88      38.14     23.3 + j 3.2
+(28.8     9.50      31.15     24.8 + j 1.0)
+(28.9     9.29      31.34     15.8 + j 1.1)
+(29.0     8.90      31.07      7.8 + j 7.4)
+

Band edge data for 10 meters includes extra checks, which show that the operating cut-off is about 28.85 MHz, although some "surplus" performance and matchable feedpoint impedance exist below the lower end of 10-meters.

+

The AO and EZNEC descriptions are appended for those wishing to model this extraordinary design. The two models correspond wire for wire, so that the driven element locations for each band listed in the AO model also apply to the EZNEC model.

+ 
==================================================
+AO Model
+14->28 yagi
+;gain & F/B is 8.2/30 8.2/21 8.7/23 9.4/31 9.85/27
+Free space
+14.150 MHz
+;18.118 MHz
+;21.200 MHz
+;24.940 MHz
+;28.350 MHz
+14 wires, meters
+r = 5.45  ;refl  20
+s = 5.2  ;driver20
+t = 4.9  ;dir   20
+a = 4.15          ;refl  17
+b = 4   ;driver17
+d = 3.64  ;refl  15
+e = 3.4  ;driver15
+f = 3.02  ;refl  12
+g = 2.9  ;driver12
+h = 2.68  ;refl  10
+i = 2.55  ;driver10
+j = 2.47  ;dir1  10
+k = 2.44  ;dir2  10
+l = 2.31  ;dir3  10
+;
+pr = 0            ;refl  20
+ps = 2            ;driver20
+pt = 3.6         ;dir   20
+pa = 5.25      ;refl  17 - dir 20
+pb = 6.4        ;driver17
+pd = 7.2        ;dir   17 - refl 15
+pe = 8.4        ;driver15
+pf = 9.5         ;dir   15 - refl 12
+pg = 10.8      ;driver12
+ph = 12         ;dir   12 - refl 10
+pi = 12.914   ;driver10
+pj = 13.829   ;dir   10
+pk = 15.556  ;dir2  10
+pl = 17.944    ;dir3  10
+dia = .02
+1     pr -r  0     pr  r  0   dia   ;14 refl
+1     ps -s 0     ps  s  0   dia   ;14 driven
+1     pt -t  0     pt   t  0   dia   ;14 dir
+1     pa -a 0     pa  a 0   dia   ;18 refl
+1     pb -b 0    pb  b 0   dia   ;18 driven
+1     pd -d 0    pd d  0   dia   ;18 dir2 - 21 refl
+1     pe -e 0     pe e  0   dia   ;21 driven
+1     pf  -f  0     pf  f  0   dia   ;21 dir1 - 24 refl
+1     pg -g 0     pg g  0   dia   ;24 driven
+1     ph -h 0     ph h  0   dia   ;24 dir1 - 28 refl
+1     pi -i   0     pi  i   0   dia   ;28 driven
+1     pj -j   0    pj  j   0   dia   ;28 dir
+1     pk -k 0    pk k  0   dia   ;28 dir 2
+1     pl  -l  0    pl   l   0   dia   ;28 dir 3
+1 source
+Wire 2, center     ; driver 20
+;Wire 5, center    ; driver 17
+;Wire 7, center    ; driver 15
+;Wire 9, center    ; driver 12
+;Wire 11,center    ; driver 10
+==================================================
+                      EZNEC/4  ver. 2.5
+
+ON4ANT 5-b Yagi:  14-28X2                    04-18-1999     17:55:29
+
+
+Frequency = 14.175  MHz.
+
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 2.00E+01  37
+2           -5.200,  2.000,  0.000         5.200,  2.000,  0.000 2.00E+01  35
+3           -4.900,  3.600,  0.000         4.900,  3.600,  0.000 2.00E+01  34
+4           -4.150,  5.250,  0.000         4.150,  5.250,  0.000 2.00E+01  28
+5           -4.000,  6.400,  0.000         4.000,  6.400,  0.000 2.00E+01  27
+6           -3.640,  7.200,  0.000         3.640,  7.200,  0.000 2.00E+01  25
+7           -3.400,  8.400,  0.000         3.400,  8.400,  0.000 2.00E+01  23
+8           -3.020,  9.500,  0.000         3.020,  9.500,  0.000 2.00E+01  21
+9           -2.900, 10.800,  0.000         2.900, 10.800,  0.000 2.00E+01  21
+10          -2.680, 12.000,  0.000         2.680, 12.000,  0.000 2.00E+01  19
+11          -2.550, 12.914,  0.000         2.550, 12.914,  0.000 2.00E+01  19
+12          -2.470, 13.829,  0.000         2.470, 13.829,  0.000 2.00E+01  17
+13          -2.440, 15.556,  0.000         2.440, 15.556,  0.000 2.00E+01  16
+14          -2.310, 17.994,  0.000         2.310, 17.994,  0.000 2.00E+01  16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+
+ +
+

Part 3: 18.25 m Boom Model, July, 1999

+
+ +
+

Johan has sent me the "final" or constructed version of his 5-band forward stagger Yagi. He has made a few changes in structure to improve 10-meter performance, especially at the lower end of the band. The result was a 0.25-m lengthening of the boom, plus some spacing changes and some minor element length changes. The model he sent me now uses non-tapered elements, but of different diameters that increase as the frequency decreases. This technique allowed him to better approximate the behavior of the beam when the tapered-diameter element schedule was added before construction. The photograph attests to both the size and the construction quality of the antenna.

+
+ +
+

The sketch, taken from an EZNEC antenna view, better shows the final proportions and the location of the feedpoints. The following table shows the modeled performance of the antenna as forecast by NEC-4.

+ 
Freq.     Gain      F-B       Feed Impedance
+MHz       dBi       dB        R +/- jX Ohms
+20
+14.0      8.30      36.74     28.8 - j 0.4
+14.175    8.41      27.35     24.7 + j 7.9
+14.35     8.55      20.57     19.0 + j18.8
+17
+18.118    8.35      23.06     31.7 - j 4.9
+15
+21.0      8.73      23.12     34.1 + j 2.0
+21.225    8.86      23.15     35.9 + j10.3
+21.45     8.99      23.04     37.4 + j18.6
+12
+24.94     9.70      37.50     23.4 + j14.6
+10
+28.0      9.92      26.58     30.0 - j 8.8
+28.35     9.99      39.15     33.5 - j 4.7
+28.7      9.69      34.30     20.3 - j12.2
Gain figures are up a bit, with the F-B ratio maintained and good coverage across all of four bands and the portion of the 10-meter band of interest to Johan. He reports that gamma matches for each band were easily set up for most bands, with only a couple that he would like to tweak up a bit. His initial tests against a neighbor's large commercial multi-band Yagi at the same height and over similar terrain give the forward-stagger design a considerable advantage--something over an S-unit on his rig. For reference, I am adding Johan's AO file and the EZNEC model description I used to obtain the projected free space operating parameters. Johan's design work will appear in an issue of the Belgian national amateur radio society journal. It will include extensive construction details. + 
==============================================================
+AO File:
+14->28 yagi
+; gain calculated is 8.3/34 8.3/21 8.7/23 9.6/38.4 10.0/29.0 in free space
+Free space
+14.150 MHz
+;18.118 MHz
+;21.200 MHz
+;24.940 MHz
+;28.350 MHz
+14 wires, meters
+r = 5.45                ;refl  20
+s = 5.2         ;driver20
+t = 4.9         ;dir   20
+a = 4.15                ;refl  17
+b = 4.02                ;driver17
+d = 3.8         ;refl  15
+e = 3.395               ;driver15
+f = 3.02                ;refl  12
+g = 2.91                ;driver12
+h = 2.68                ;refl  10
+i = 2.55                ;driver10
+j = 2.47                ;dir1  10
+k = 2.44                ;dir2  10
+l = 2.31                ;dir3  10
+;
+pr = 0          ;refl  20               32mm
+ps = 2.0                ;driver20               32mm
+pt = 3.6                ;dir   20               32mm
+pa = 5.25               ;refl  17 -dir 20       32mm
+pb = 6.4                ;driver17               25mm
+pd = 7.2                ;dir   17 - refl 15     25mm
+pe = 8.4                ;driver15               25mm
+pf = 9.5                ;dir   15 - refl 12     25mm
+pg = 10.8               ;driver12               25mm
+ph = 12.0               ;dir   12 - refl 10     23mm
+pi = 13.014             ;driver10               23mm
+pj = 13.816             ;dir   10               23mm
+pk = 15.775             ;dir2  10               23mm
+pl = 18.25              ;dir3  10               23mm
+dia = .023
+diam = .032
+dian = .025
+;I use different element diameters for the different bands
+;it makes things easier afterwards, when you want to taper
+shift Z 24
+1     pr -r 0    pr r 0   diam   ;14 refl
+1     ps -s 0    ps s 0   diam   ;14 driven
+1     pt -t 0    pt t 0   diam   ;14 dir1
+1     pa -a 0    pa a 0   dian   ;14 dir2 - 18 refl
+1     pb -b 0    pb b 0   dian   ;18 driven
+1     pd -d 0    pd d 0   dian   ;18 dir2 - 21 refl
+1     pe -e 0    pe e 0   dian   ;21 driven
+1     pf -f 0    pf f 0   dian   ;21 dir1 - 24 refl
+1     pg -g 0    pg g 0   dian   ;24 driven
+1     ph -h 0    ph h 0   dia    ;24 dir1 - 28 refl
+1     pi -i 0    pi i 0   dia    ;28 driven
+1     pj -j 0    pj j 0   dia    ;28 dir1
+1     pk -k 0    pk k 0   dia    ;28 dir2
+1     pl -l 0    pl l 0   dia    ;28 dir3
+1 source
+Wire 2, center    ; driver 20
+;Wire 5, center    ; driver 18
+;Wire 7, center    ; driver 15
+;Wire 9, center    ; driver 12
+;Wire 11,center    ; driver 10
+;
+;Important note: Those wishing to increase gain on 20m can easily do this without
+;too much sacrifice, making the 18Mhz reflector longer will increase the gain with 0.5 db
+;Given the fact I use a gamma match and wanted to avoid nasty surprises like freq shift
+;when putting the antenna on top of a 80ft tower, I preferred the wide bandwidth.
+=============================================================
+                      EZNEC/4  ver. 2.5
+
+ON4ANT 5-b Yagi:  14-28 Final                07-16-1999     08:02:03
+
+Frequency = 14.175  MHz.
+Wire Loss: Aluminum -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+
+Wire Conn. --- End 1 (x,y,z : m )  Conn. --- End 2 (x,y,z : m )   Dia(mm) Segs
+
+1           -5.450,  0.000,  0.000         5.450,  0.000,  0.000 3.20E+01  37
+2           -5.200,  2.000,  0.000         5.200,  2.000,  0.000 3.20E+01  35
+3           -4.900,  3.600,  0.000         4.900,  3.600,  0.000 3.20E+01  34
+4           -4.150,  5.250,  0.000         4.150,  5.250,  0.000 2.50E+01  28
+5           -4.020,  6.400,  0.000         4.020,  6.400,  0.000 2.50E+01  27
+6           -3.800,  7.200,  0.000         3.800,  7.200,  0.000 2.50E+01  25
+7           -3.395,  8.400,  0.000         3.395,  8.400,  0.000 2.50E+01  23
+8           -3.020,  9.500,  0.000         3.020,  9.500,  0.000 2.50E+01  21
+9           -2.910, 10.800,  0.000         2.910, 10.800,  0.000 2.50E+01  21
+10          -2.680, 12.000,  0.000         2.680, 12.000,  0.000 2.30E+01  19
+11          -2.550, 13.014,  0.000         2.550, 13.014,  0.000 2.30E+01  19
+12          -2.470, 13.816,  0.000         2.470, 13.816,  0.000 2.30E+01  17
+13          -2.440, 15.775,  0.000         2.440, 15.775,  0.000 2.30E+01  16
+14          -2.310, 18.250,  0.000         2.310, 18.250,  0.000 2.30E+01  16
+
+              -------------- SOURCES --------------
+
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          18     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+No loads specified
+No transmission lines specified
+Ground type is Free Space
+
+ +
+

Updated 08-28-98; 4-18-99, 7-16-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Yagi


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+

Notes on Reversible Yagi Arrays

+
+
+

L. B. Cebik, W4RNL

+

+
+ +

+
+

Many hams in the U.S. are fortunately located so that good amateur radio target area lie in a 180-degree (or close to it) line. In Tennessee, Europe is northeast and Australia and New Zealand are southwest. If I were content to work these regions as my predominant interest, then I would not need a tower, rotator, and the other paraphernalia that goes with a high gain beam. I might set up a bi-directional array, such as an extended Lazy-H. However, if I wish some protection from QRM coming from the wrong direction. I might opt instead for a system of wire Yagis.

+

The reversible wire Yagi array has been around for a long time. There are many ways to construct such arrays, including fancy switching systems in the wire elements, reflector and director loading stubs, and even reflector and director loading using lumped components. These techniques all use the minimum number of wires and electrically or electro- mechanically alter their electrical lengths within the array. We can either change directions using these methods or we can change the properties to peak performance within a given band.

+

In these notes, we shall explore some alternatives that trade the complexity of such system for the use of some additional wire.

+

Wire Yagis are noted by their good performance potential combined with a relatively narrow bandwidth. In exchange for the light weight of AWG #12 or #14 wire, we suffer with a smile the narrower bandwidth characteristics that thin elements provide. As well, thicker elements provide some gain increase due to the larger surface area of the elements. A larger surface area has lower skin-effect losses and allows somewhat higher mutual coupling over a broader frequency range between elements. Parasitic arrays, of course, depend upon the mutual coupling between elements. It is not unfair to think of thin wire arrays as being "half-band" beams on 40 through 20 meters. On 160 and 80, their coverage can be even narrower.

+

In most cases, stringing one or two extra wires within the space allocated to a wire beam may be easier than arranging for complex switching mechanisms that require weather protection. From this premise arose a different sort of reversible beam based on the fact that wires behind the reflector of a Yagi have little influence on the performance of wires ahead of the reflector. Instead of switching within the wires of a Yagi, let's just build two Yagis back-to-back, using a common reflector.

+
+ +
+

Fig. 1 shows two common and one less common configuration of reversible Yagis. On the left is a 3-wire, 2-element Yagi, consisting of a reflector and a driver for each direction. We can increase performance by using a 5-wire, 3-element reversible Yagi, as shown on the upper right. Under special conditions--that we shall explore later--we might even cut the number of wires to 4 and still have a reversible 3-element Yagi. The lower right portion of the diagram shows the layout and the space that we save by using only 4 wires, since all three outline are approximately the same scale.

+
+ +
+

It is not difficult to satisfy oneself that a reversible Yagi of this sort actually works. Fig. 2 shows the relative current magnitudes on each of the elements of a 5-wire array when the right driver is active and radiation is to the right, relative to the sketch. The reflector is normally active, but the inactive driver and inactive director have very low current levels, indicating their relative inertness. If we switch the active driver to the on the left, with radiation also to the left, then the right driver and director would become nearly inert.

+

The beauty of the system is that to make such a reversible Yagi, we do not need to design from scratch. If we already have a good design for a 2- or 3-element Yagi, we can make a reversible Yagi simply by adding the driver and other elements--if present--on the opposite side of the reflector. We do not need to alter the original Yagi design to achieve the same performance in two directions. (Remember, however, that we do not get the two directions at once, but only serially as we change the active driver.)

+

A 2-Element, 3-Wire Yagi Array

+

Among the simplest arrays from which to create a reversible Yagi is the simple reflector-driver version of the Yagi. Although modest in performance, a 2-element Yagi provides very noticeable gain over a wire dipole, along with enough front-to-back ratio to satisfy many operating needs.

+
+ +
+

Fig. 3 shows the two patterns of a reversible 2-element Yagi using 3 wires. Although these patterns are representative of performance on any of the HF bands, the examples that we shall use are all designed for 7.15 MHz. The design frequency free-space gain is a bit over 6.2 dBi, with nearly 10 dB of front-to-back ratio.

+

The dimensions that I used to obtain these values will appear in terms of fractions of a wavelength. This notation will make it simple for anyone to change the design frequency to either the upper or lower end of 40 meters. As well, the values should hold without significant adjustments if we scale them up to 30 or 20 meters or down to 80 meters, all the while using the AWG #12 copper wire of the original design. The only exception to this generalization is that gain will decrease on lower frequency band and increase on higher frequency bands, largely due to the change in wire diameter as a fraction of a wavelength.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Dimensions of a 3-Wire, 2-Element Yagi Reversible Array
+
+Element          Length (wl)     "Boom" Length (wl)    Inter-Element
+                                                       Spacing (wl)
+Driver 1         0.476           0                     --------
+Reflector        0.502           0.146                 0.146
+Driver 2         0.476           0.292                 0.146
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The total "boom" length (where the idea of a boom means a virtual boom) is less than 0.3 WL, which is considerably less than the 0.5 WL width of the array. Hence, in many situations, if one can accommodate the width of a 2-element wire beam, the total "boom" length is usually not a great space problem.

+

Performance, of course, is not constant across the entire 40-meter band. Fig. 4 presents the gain and front-to-back curves for the array. A review of Fig. 3 will make it clear that the 180-degree and worst-case front-to-back ratios are identical for this array.

+
+ +
+

Both the gain and front-to-back ratio fall off more rapidly below the design frequency than above it. Hence, any such 2-element wire Yagi (reversible or not, requires a choice on the part of the builder relative to a favor operating region of the band. Redesigning the array for about 7.05 MHz would cover the CW portion of the band with peak performance, while designing for about 7.2 to 7.25 MHz would yield the same results for the SSB portion of the band. Overall, the peak free-space gain is 6.26 dBi, with a minimum value of 5.99 dBi. The gain spread might be acceptable, but the front-to-back ratio is unlikely to satisfy most operators below the design frequency. The peak front-to-back ratio approaches 10 dB, but falls to a mere 3 dB 150 kHz below the design frequency. Above the design frequency, it remain relatively constant.

+
+ +
+

One of the benefits of the 2-element Yagi is that its feedpoint resistance and reactance vary in such a way as to make the SWR curve generally follow the gain and front-to-back curves. As Fig. 5 shows, the 50-Ohm SWR is acceptable for nearly 2/3 of the ham band, and the favorable segment of the band is at and above the design frequency. Hence, redesigning the array for either the upper or lower portion of the band becomes a simple matter of adjusting the dimensions.

+

I have given free-space patterns and values in order to make fair comparisons among the total number of arrays that we shall cover. Any give array will vary in performance according to its height, with heights below 1/2 WL subject to the greatest variation. Hence, if you anticipate building an array such as this one or the others that we shall touch upon, it may be wise to model it first at the intended height of operation.

+

A 3-Element, 5-Wire Yagi Array

+

If we expand our basic Yagi to 3 elements, we can obtain additional gain and improved front-to-back ratio. As well, we improve the isolation of the inactive or rearward elements. In a reflector-driver design Yagi, the two elements interact so as to mutual control the forward gain, the front-to-back ratio, and the driver feedpoint impedance. If we add a director to the system, it tends to take control of the forward gain and front-to-back ratio, leaving the reflector-driver relationship to control the feedpoint impedance of the array. Since the pattern-shape controlling elements are at an increased distance from each other, the isolation between the two halves of our reversible array increases.

+
+ +
+

Fig. 6 compares the free-space E-plane patterns for a 3-element wire Yagi that is identical to one half of the reversible array to the 5-wire array itself. As the pattern shows, there is little or nothing to choose between the two patterns. The average gain and front-to-back ratio peak of the two arrays differ by less than 0.1 dB in each parameter.

+
+ +
+

Fig. 7 compares the gain and front-to-back curves across the entire 40-meter band. The gain of the independent Yagi is slightly flatter, although the difference is more numeric than significant. Combining two Yagis into a reversible array does move the peak front-to-back ratio by about 50 kHz, although the reversible array has a slower fall-off rate above the design frequency.

+

The free-space gain of the array at the design frequency is about 7.6-7.6 dBi, with a front-to-back ratio that exceeds 24 dB. Both of these values are worthy increases relative to the 2-element, 3-wire reversible Yagi we explored earlier.

+

The following table lists the dimensions of the array, once more using fractions of a wavelength as the unit of measure.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Dimensions of a 5-Wire, 3-Element Yagi Reversible Array
+
+Element          Length (wl)     "Boom" Length (wl)    Inter-Element
+                                                       Spacing (wl)
+Director 1       0.464           0                     --------
+Driver 1         0.486           0.174                 0.174
+Reflector        0.502           0.325                 0.151
+Driver 2         0.486           0.476                 0.151
+Director 2       0.464           0.650                 0.174
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

Perhaps the major item of interest in the dimension chart is the fact that the reversible 3-element Yagi is more than twice as long ("boom" length) as its 2-element Yagi counterpart, but without an increase in the side-to-side dimension. The virtual boom is now significantly longer than the length of the longest element. It therefore requires considerably more real estate, not to mention adding dimensions to the meas of supporting the wire elements.

+
+ +
+

The 5-wire reversible array is designed for a feedpoint resistance of about 30 Ohms. At the design frequency, the array is resonant. As Fig. 8 reveals, we obtain a 50-Ohm SWR under 2:1 from about 7.05 MHz to about 7.21 MHz, just over half the 40 meter band. Since the resistance makes a very small excursion, one might adjust the minimum SWR position to virtually anywhere in the band simply by adjusting the lengths of the two driver elements. The change of reactance across the band is virtually linear, making adjustment predictions fairly reliable.

+

However, the 50-Ohm SWR never falls below about 1.5:1. For many applications that employ sensitive SWR detection systems, the entire SWR curve may be unsatisfactory. Hence, the use of an antenna tuner is recommended. At 40 meters and below, coax losses tend to be very low. Hence, a simple network tuner will generally suffice. The one danger in this tuning procedure is that one may lose sight of the fact that the front-to-back ratio falls off as one moves away from the design frequency, especially at the lower end of the band. Like the 2-element Yagi array, this reversible 3-element Yagi is a half-band antenna on 40 meters. If we forget this fact due to the ease of obtaining a match with an antenna tuner, we shall have to rely upon QRM to remind us.

+

A 3-Element, 4-Wire Yagi Array

+

Bill Desjardins, W1ZY, called my attention to his modification of the 5-wire reversible Yagi design, one that he has used. I have not seen other references to the modification, but they may exist. Instead of using 5 wires for a 2-way 3-element beam, let's use only 4.

+

By referring to Fig. 1 and some of the general properties of 3-element Yagis, you can follow the reasoning behind Bill's design. We need a reflector, driver, and director in each direction. Yagis of 3 elements or more become insensitive to the driver length (within reason) relative to other performance parameters, such as gain and the front-to-back ratio. Since we are likely to need an antenna tuner even with the 5-wire design, why not plan for one from the beginning. There is no reason why the driver cannot be the same length as the reflector, if we can accept the increase in inductive reactance that the increased driver length entails. Since we must switch drivers anyway in order to change beam directions, we can let the inner wires of the array do double duty as both reflectors and drivers. Hence, we cut down the overall "boom" length by one notch and the number of wires goes to 4.

+ 
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+Dimensions of a 4-Wire, 3-Element Yagi Reversible Array
+
+Element          Length (wl)     "Boom" Length (wl)    Inter-Element
+                                                       Spacing (wl)
+Director 1        0.464          0                     --------
+Driver/Reflector  0.502          0.174                 0.174
+Reflector/Driver  0.502          0.325                 0.151
+Director 2        0.464          0.499                 0.174
+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
+

The dimensions shown are optimized somewhat from Bill's initial design. Indeed, except for the driver length, they replicate the values for each Yagi in the 5-wire design. Where the designs differ most is in the overall "boom" length, which has shrunk from 0.65 wl down to 0.5 wl. In fact, the array now makes an almost perfect square.

+
+ +
+

The immediate question is whether the 4-wire array performs as well as the 5-wire version. Fig. 9 tells the story. There is no significant difference in either the forward gain or the front-to-back ratio between the two variations on the 3-element reversible Yagi concept. The gain at the design frequency is about 7.7 dBi, with a front-to-back ratio of 23 dB. Fig. 10 plots the free-space gain and the front-to-back ratio across 40 meters. The curves closely resemble those we saw in Fig. 7, in the comparison between a single 3-element wire Yagi and the 5-wire reversible model.

+
+ +
+

Because the driven element of the 4-wire design is intentionally long, an SWR curve would provide little or no information. However, the feedpoint resistance and reactance curves in Fig. 11 may be helpful in understanding operation of the antenna. As with the 5-wire array, the reactance increases virtually linearly with frequency. However, it is purely inductive and reaches zero only well below the lower band edge. The resistance changes slowly, but does decrease above the design frequency. Hence, the 35-Ohm value that occurs at 7.15 MHz, drops to about 25 Ohms at the upper band edge.

+
+ +
+

The values listed are those that occur at the driver terminals. The value obtained at the terminals of an antenna tuner will vary with both the characteristic impedance and the length of the transmission line used. Since basic impedance at the design frequency is fairly low (35 + j 50 Ohms), some users may prefer a low impedance coaxial cable, accepting the coax matched and additional SWR losses. Other users may prefer to use parallel transmission line in order to hold the losses as low as possible. However, with a line impedance of 400-600 Ohms, the excursions in impedance will be much greater, thereby increasing the chances that the tuner may see values that fall outside its tuning range--or its efficient tuning range. Of course, one cure for terminal impedance values outside of a tuner's range is to change the length of line from the antenna to the tuner. If you pre-calculate the likely terminal impedance, be certain to include the line velocity factor in the calculations.

+

Switching Directions

+

Switching directions with any of the arrays involves two facets. One is to switch the active driver element. The other is to ensure that the inactive element has a low or zero impedance across the feedpoint terminals. The second facet of switching is less important with the 3-and 5-wire designs, but it is critical to the 4-wire array. Since the inactive driver functions as the reflector, there must be effective continuity across the terminals.

+
+ +
+

Fig. 12 shows one way to accomplish the double task. A simple switch--DPDT--switches the pair of leads from the antenna to the transmitter or antenna tuner. If the lines from the switch to the antenna are an odd multiple of 1/4 wl (taking into account the velocity factor of the line), then an open circuit at the switch end of the line will appear as a short circuit (or close to it) at the antenna end of the line.

+

So long as the length condition is met, the lines may be any length and even reach to the shack for indoor switching. Such a system eliminates any problems of weatherproofing the switch. However, the lines from the switch to their respective drivers should be well separated if one uses open wire transmission line. The object is to avoid interactions between the lines, in addition to the usual precaution of avoiding interactions between the lines and other objects along the run from shack to antenna.

+

Whichever type of reversible array that you choose, assuming that your circumstances make one of them attractive, concentrate on achieving the highest mounting level feasible. Like any horizontally polarized array, the reversible beams perform best when above 1/2 wl.

+

Of the 3 arrays, perhaps the 4-wire design of W1ZY is most attractive for its ability to pack 3-element Yagi performance in two directions in only about 0.2 wl more boom length than required for 2-element performance. However, the 3-wire, 2-element design will show up very well if one has only had a single wire dipole to use in the past. The reversible beam concept in the forms indicated eliminates the need for sophisticated remote switching in weatherproof containers, which may make Yagi performance more accessible to the average builder.

+

The arrays are also part of a larger collection of bi-directional and reversible arrays. Lazy-Hs and extended-Lazy-Hs offer good gain with relatively narrow beamwidths. They take only the ground space of a single wire, but their demands extend vertically instead. For the individual with less ground space than even a 2-element reversible array requires, there is the reversible Moxon rectangle, described in a number of sources and forms. It is even possible to design a reversible array for 160 meters, one that is frequency nimble within the band as well a reversible in direction. But that is an exercise at least 2 to 3 orders of magnitude beyond the simple designs we have explored here. Despite its complexity, that array will only perform to the level of the simpler designs in 4 and 5 wires that we have examined. So if you can live with a half-band on 40 or 20 (or all of 30 meters), then one of these designs may increase your DX effectiveness--at least in two directions.

+
+ +
+

Updated 09-01-2003. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for August, 2003. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Main Index

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Topics: HF Lower, Reversible, Yagi


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+

Some Notes on Stacked Beams

+
+
+

L. B. Cebik, W4RNL

+

+
+
+ +

+
+

A. The Effects of Opposed Beams in a Stack

Some beam stackers have experienced a rise in SWR if the beams are pointed in opposite directions. Others have not. The degree of SWR rise was not specified. +

To shed some light on this question, I ran a pair of identical beams through NEC-4. The individual beams, cut to be resonant at 14.175 MHz had the following free space properties:

+ 
TO angle      Gain (dBi)     F-B ratio (dB)     Beamwidth      Feed Z
+ (degrees)                                       (degrees)      (R+/jX)
+  ---           8.1           26.6                62            25.5 - 0.1
+
+

Here are the numbers for the beam alone at heights of 1 wl (70') and at 1.5 wl (105')

+ 
70'
+  13           13.4           24.3                62            25.0 - 0.0
+105'
+   9           13.7           24.7                62            25.2 - 0.0
+
+

(In all elevation plots, the outer ring is 18 dBi, to permit comparison of patterns for all the antennas plotted in these notes.)

+
+ +
+
+ +
+

The differential in elevation angles suggests that a switching system to permit use of Upper-Only, Lower-Only, and Both may be useful in sorting out signals by incoming/outgoing elevation paths.

+

Let's stack the beams and feed each separately to see if interaction changes anything. Remember, the beams are stacked just about 1/2 wl apart.

+ 
Feed lower only:
+  14           13.3           21.5                62            25.7 - 1.0
+Feed upper only:
+   9           13.6           21.7                60            26.0 - 1.1
+Feed both:
+  10           15.8           20.8                62      Lower: 24.6 + 1.3
+                                                          Upper: 24.7 + 1.2
+
+
+ +
+

Notice that at 1/2 wl spacing, where the lower beam is 1 wl up, the only possibly significant change is a decrease in F-B ratio in the 3-4 dB range.

+

Now let's point the beams in opposite directions and see what a dual feed produces:

+ 
+  9            11.3           1.2                 60      Lower: 23.7 - 5.2
+                                                          Upper: 23.8 - 5.4
+
+

Depending upon the sensitivity of the feed system to changes under 10% in Z and depending upon the basic match between antenna feed, antenna match and lines, and in which direction any small mismatch might go, one may well see a small rise in SWR. although 5+ ohms of reactance may not be considered much, at an R of 25 ohms, it is 20% of the R value. Although this does not change R significantly, it changes SWR more significantly. (See some older ARRL books for calculating SWR directly from Zo and R +/- jX.)

+

Some prefer to stack beams at a 5/8 wl spacing to maximize gain. So I raised the upper beam 9' to 114' to check the results. Easier on NEC than on a tower.

+ 
Feed lower only:
+  12           14.2           18.8                64            24.4 + 0.1
+Feed upper only:
+   9           14.6           19.5                64            24.9 + 0.4
+Feed both:
+  10           16.2           17.4                62      Lower: 24.0 + 1.3
+                                                          Upper: 24.5 + 1.7
+
+
+ +
+

Notice the slight parasitical improvement in individual beam gain, as well as the higher stacked gain, relative to 1/2 wl spacing. However, notice also the continued degradation in F-B performance. You pays your money and you takes your choice.

+

Now let's point the beams in opposite directions and see what a dual feed produces:

+ 
+  9            11.9           0.9                 62      Lower: 21.2 - 1.7
+                                                          Upper: 22.0 - 1.5
+
+

Although the reactance has not climbed very much, the feedpoint resistance is down about 12% or so. Again, depending upon the sensitivity of the matching system to changes of this order and in which direction any inaccuracies in match are directed, a rise in SWR can be expected in many cases. If a perfect 1:1 is initially established, a 1.2-1.3:1 may result-- noticeable, but not in any sense fatal.

+

However, I have idealized the case with a very nice 25-ohm natural feedpoint Z so that accurately cut feedlines can do all the matching. commercial beams have their own systems to place 50 ohms at the coax connection, and we construct phase lines from there. Sensitivity to 10-15% mismatches is thus not predictable by NEC alone. However, if one does not see that slight rise, one has to wonder if it is function of losses somewhere in the system.

+

All models done in NEC-4 over S-N .005/13 ground, with Al elements.
+

+
+ +

+
+

B. Mis-phasing of Stacked Beams

About mis-phasing of stacked beams, there are two questions one can ask. 1. Is something wrong when stacked beams are mis-phased? 2. Can I do anything useful by reversing the phase of one of a stack of beams. +

To see what might happen, I modeled the same 3-element Al 20 meter beam as in the last example over S-N ground .005/13 on EZNEC/4. I added transmission lines--1/4 wl section joined to form a feedpoint. Since NEC feedlines are mathematical, not physical, I simply used the sections to transform the 25 ohm resonant Z of the individual beams to 100 ohms each, in parallel for a pair of beams making 50 ohms. This provided a baseline for watching variations.

+

The 3-3 stack used 1/2 wl separation, again at 70' and 105' (which may be translated for any upper HF band in terms of wavelengths of height and separation) Here are the results:

+ 
+TO angle      Gain (dBi)     F-B ratio (dB)     Beamwidth      Feed Z
+ (degrees)                                       (degrees)      (R+/jX)
+In-phase:
+  10           15.83           20.8               60           50.6 - 2.8
+
+
+ +
+

As predicted in model construction, the transmission line transformers yield a very matchable condition.

+ 
Out-of-phase:
+  50           12.34           18.9               82 (oval)    45.9 + 6.4
+  25           11.47           28.8               66
+
+ +
+

Reverse phasing produces two major lobes in the elevation pattern at the indicated angles, each down at least 3.5 dB from the main lobe of the in- phase model. Both lobes are quite high relative to desired dx angles. However, such a configuration, if switchable, might be useful for a domestic contest. The upper lobes on the in-phase model are down by 9 dB or more.

+

I next tried a 3-3-3 stack at .5-1.0-1.5 wl (70'-105'-140'). I again used 1/4 wl transmission line transformers joined at a distant feedpoint, resulting in an anticipated baseline feedpoint impedance of 33.3 ohms R. since throughout the exercise I used 41 segments per 1/2 wl to ensure convergence without having to recheck each model, the 370-segment model was the limit of my efforts. Here are the results.

+ 
+TO angle      Gain (dBi)     F-B ratio (dB)     Beamwidth      Feed Z
+ (degrees)                                       (degrees)      (R+/jX)
+In-phase:
+    8          17.3            21.7               60           32.7 - 1.7
+
+
+ +
+

This result tallies well with expectations. Notable in the 3-beam stack is a return of some of the F-B ratio lost in the 2-beam stack. The stack has lesser lobes at 26 degrees (down 8.5 dB) and at 41 degrees (down 15 dB): these figures are given for comparison with lobes, both main and secondary, of the same stack with one of the beams out of phase with the other two.

+ 
Highest out-of-phase:
+   17          13.5            21.3               62           33.8 + 1.2
+   36          13.2            29.2               68
+
+ +
+

Although the gain of each lobe is no more than that of a single beam, the elevation angles may also be useful for domestic work. The feedpoint impedance is quite usable.

+ 
Middle out-of-phase:
+  55          13.3            14.5               88            27.7 + 8.0
+
+
+ +
+

This configuration may be least useful due to the very high angle of the main lobe. There are lesser lobes at 8 degrees (down 6 dB) and at 33 degrees (down 4.5 dB). The feedpoint impedance is down 18% on the resistance side, with a significant reactance, which may show an undesirable rise in SWR in a switched system, even after the anticipated 33 ohms is matched back to a 50-ohm cable.

+ 
Lowest out-of-phase:
+   22          14.3            21.6              62             34.1 + 1.0
+
+ +
+

This configuration shows lesser lobes at 7 degrees (down 4 dB) and at 28 degrees (down 3.5 dB). The feedpoint impedance is acceptable. The configuration may be useful as an alternative dx configuration, despite the loss of gain from in-phase maximum, since--under some circumstances-- capturing the proper elevation of signal angle may be more important than raw gain.

+

The exercise strongly suggests that a switchable phasing system may prove useful, depending upon one's operating goals and activities. Although some options may yield less than useful patterns, most of the patterns-- especially in terms of altered elevation angles of maximum radiation--have a certain utility.

+

I suspect that the upshot to consider is this: If you are going that high with that much rotatable metal, you might as well throw in a phase-reversal switching system, just in case . . .. Combined with a single-beam vs. stack switching system, great versatility in elevation angle may be achieved--even to the point of overkill for any one individual's operating needs.

+

And that is using only 3-element Yagis as the foundation. There is no reason to believe that results for larger individual beams cannot be extrapolated with reasonable reliability--or that 5/8 wl spacing will not show similar small gains above 1/2 wl spacing. In the latter case, however, phase reversal patterns might differ, since beam interaction differs a bit.

+

C. Stacked Beams: The Rest of the Story

Member of towertalk@contesting.com supplied information on their stacks, and I am indebted to this group of helpful hams for sharing the data. Although not absolutely complete, I have tried to model almost all the stacks "in principle." Here are the restrictions: the heights are in terms of a fraction of a wavelength, so you have to translate that into feet. That will allow you to equate a 10 or 15 meter installation with the modeled 20 meter antennas. Next, the model beams are 3 element "ideals" and you will have to estimate the amount of gain over the 3-element beam your 4, 5, 6, or 7, element beam has. The gain numbers will give you a basis for making relative judgments such as, "Will I gain anything by raising the top beam in my stack by another fraction of a wavelength?" +

In order to handle stacks with up to four beams, I reduced the number of segments per half wavelength in my NEC-4 models. (The program would have handled it, but available time was limited by other projects.) Hence, the tables below start from scratch with some baseline data. That will validate the comparisons.

+

Everything will be by way of tables, without commentary. Some unworthy options will be evident. Others may depend on two factors: a. your own readout of experience or IONCAP results for paths from your QTH to your targets, and b. what your operating activities and interests are and hence what your targets are. These are variables that method of moments cannot model.

+

1. Baseline 3-element Yagi Characteristics: 1 antenna by height in wl:

+ 
+Height         TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ in wl         degrees   dBi       dB   degrees        R +/- jX ohms
+1/2            25        12.3      25.2      64        24.7 - 0.7
+5/8            21        12.9      24.9      64        25.9 + 0.1
+3/4            17        13.1      40.1      62        26.5 - 1.2
+7/8            15        13.3      29.0      62        25.5 - 1.6
+1              14        13.4      25.1      62        25.1 - 0.9
+1.5            9         13.7      25.3      62        25.3 - 0.9
+2              7         13.8      25.6      62        25.4 - 0.9
+2.5            6         13.8      25.9      62        25.5 - 0.9
+
+

Note: This model chosen for its generally good performance as a 3-element Yagi plus the convenience of using simple transmission line modeling techniques for stacking beams with a resultant 50-ohm overall feed.

+

2. Two beams stack, single feed at various spacings. Abbreviations: Both in = both in phase; both out = both, but out of phase; Top only = only top beam fed, but lower present in stack; Bot only = only bottom beam fed, although upper present in stack. A second line for an entry indicates a secondary elevation lobe worth noting.

+

2a. 2 beams at 1 wl and 1.5 wl up.

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        11        15.8      21.3      60        50.6 - 0.9
+Both out       50        12.3      18.5      82        45.0 + 7.5
+               25        11.5      28.8      66
+Top only        9        13.6      22.3      60        26.1 - 1.9
+Bot only       14        13.3      22.1      62        26.0 - 1.9
+
+

2b. 2 beams at 1 wl and 1.63 wl up.

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        10        16.2      17.6      62        51.4 - 1.7
+Both out       47        12.7      23.1      76        49.0 + 6.5
+               23        12.5      31.4      64
+Top only        9        13.9      18.6      62        22.1 - 1.1
+Bot only       13        13.6      17.9      62        24.5 - 1.5
+
+

2c. 2 beams at 1 wl and 2 wl up.

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in         8        15.7      39.3      62        46.7 + 2.3
+Both out       20        14.7      22.2      62        51.9 + 1.4
+               39        12.9      26.6      70
+Top only        7        13.7      35.5      62        25.6 - 1.1
+Bot only       14        13.4      26.7      62        25.3 - 1.1
+
+

2d. 2 beams at 0.7 and 1.4 wl up. (This corresponds roughly to 50-55' lower and 100-110' upper on 20 meters.)

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        11        15.7      15.0      64        50.7 - 5.7
+Both out       28        13.8      25.8      64        49.7 + 7.1
+               58         9.1      18.6      86
+Top only       10        13.9      16.4      64        24.4 - 0.8
+Bot only       18        13.2      18.9      64        25.5 - 0.2
+
+

Whether the characteristics of 3-element Yagis in a stack can be reliably extrapolated to longer Yagis is an important question, since antennas with 4 to 7 elements are common choices among DXers and contesters. Therefore, I repeated the exercise with a 5-element Yagi model.

+

1. Baseline 5-element Yagi Characteristics: 1 antenna by height in wavelengths:

+ 
Height         TO angle  Gain      F-B  Beamwidth   Feedpoint Impedance
+ in wl         degrees   dBi       dB   degrees        R +/- jX ohms
+
+1              13        15.4      23.3      52        36.7 + 0.2
+1.5            9         15.8      23.4      52        36.7 + 0.2
+2              7         15.9      23.4      52        36.7 + 0.3
+2.5            6         16.0      23.4      52        36.7 + 0.3
+

2-2. Two beams stack, single feed at various spacings:

+

2a. 2 beams at 1 wl and 1.5 wl up:

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        10        17.2      18.0      50        48.4 + 2.3
+Both out       24        14.0      26.0      56        54.6 + 3.1
+               49        12.5      16.4      62
+Top only        9        14.7      19.4      50        36.0 - 2.0
+Bot only       15        14.4      21.0      50        36.0 - 2.0
+
+

2b. 2 beams at 1 wl and 1.63 wl up:

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        10        17.4      15.6      50        51.0 + 0.1
+Both out       23        14.7      33.8      54        54.5 - 0.5
+               45        12.7      21.6      58
+Top only        8        15.1      16.4      50        35.1 + 0.1
+Bot only       14        14.8      18.0      52        35.5 - 0.1
+
+

2c. 2 beams at 1 wl and 2 wl up:

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in         8        17.9      25.1      52        50.3 + 0.5
+Both out       20        16.4      21.2      52        50.6 - 1.1
+               38        12.9      19.6      54
+Top only        7        16.0      25.4      52        36.9 + 0.1
+Bot only       13        15.4      24.4      52        36.9 + 0.1
+
+

2d. 2 beams at 0.7 and 1.4 wl up:

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+Both in        11        17.0      14.3      52        51.3 - 1.4
+Both out       27        15.6      44.5      54        53.3 - 2.1
+               55         7.0      15.6      62
+Top only        9        15.3      16.7      52        35.7 + 0.9
+Bot only       19        14.5      18.0      52        35.4 + 1.2
+
+

Although the in-phase-fed 5-element stack has more gain than the 3- element stack, it is by no more than the advantage of one 5-element beam over one 3-element beam--about 2 dB or less. The 5-element Yagis appear to interact more strongly at spacings less than 1 wl, as evidenced by not only the larger reduction in front-to-back ratio for stacked beams fed in phase, but as well by the reduced performance figures of both the top and bottom beams when fed alone compared to single beams at the same height. Note also that the maximum in-phase-fed stack gain occurs at 1 wl separation, not at the 0.63 wl separation of the 3-element stack. On the other hand, the 5-element beams, when fed out of phase, yielded dominant lobes at lower elevation angles than the 3-element counterparts.

+

Two models do not make an assured conclusion. However, it is at least safe to say that long Yagis do not necessarily perform in stacks in a way identical to shorter Yagis.

+

3. 3 beams stacked at 1, 1.5, and 2 wl. Added abbreviations: Top out = top out of phase with other two; Mid out = middle out of phase with other two; Bot out = bottom out of phase with other two; Mid only = middle beam only fed, but with other two present.

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+All in phase    9        17.25     22.3      60        50.3 - 0.9
+Top out        17        13.4      22.1      62        51.4 + 3.6
+               36        13.2      30.8      68
+Mid out        55        13.3      14.3      88        41.3 + 12.9
+               32         8.9      18.5      68
+Bot out        22        14.3      22.1      64        51.9 + 3.3
+                7        10.3      19.7      60
+Top only        7        13.6      24.5      60        26.2 - 2.1
+Mid only        9        13.6      19.0      60        26.7 - 3.2
+Bot only       14        13.3      23.1      62        25.8 - 2.0
+
+

4. 4 beams stacked at 1, 1.5, 2, 2.5 wl up. Beams are designated top, 2nd, 3rd, bot from top to bottom.

+ 
+Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+All in phase    7        18.3      21.3      60        49.8 - 2.6
+Top out        12        15.1      21.8      60        49.5 + 2.8
+               28        12.2      24.5      64
+2nd out        40        13.5      28.2      71        48.9 + 8.6
+                9        11.3      22.2      60
+3rd out         6        12.3      20.6      60        48.6 + 7.8
+               30        12.0      22.2      66
+Bot out        20        14.9      22.3      62        49.4 + 2.9
+                6        14.1      20.4      60
+Top 2 out      17        16.0      20.6      62        52.1 - 0.6
+               32        13.3      21.8      66
+Mid 2 out      26        14.4      24.8      64        52.2 + 2.3
+               43        13.7      29.8      74
+Top/3rd out    57        14.0      12.8      91        38.5 + 16.7
+Top only        6        13.7      21.3      60        25.5 - 0.3
+2nd only        7        13.5      20.2      60        26.5 - 3.4
+3rd only        9        13.4      21.4      60        26.5 - 3.2
+Bot only       14        13.2      23.8      62        25.8 - 2.0
+
+

Note: "Top 2 out" above is equivalent to "Bot 2 out" and "Top/3rd" out is equivalent to "2nd/Bot out."

+

5. 2 beams at 1 wl height, horizontally spaced, where spacing is given in wl fractions from tip to tip of the elements (add 1/2 wl for boom-to-boom spacing). Side ears represent side lobes similar to those from an EDZ-- only gain is given. Out of phase condition produces two lobes with a deep center null. "Split" = degrees each side of centerline of the lobes.

+
+ +
+
+ +
+ 
Stack          TO angle  Gain      F-B  Beamwidth      Feedpoint
+Impedance
+ set-up        degrees   dBi       dB   degrees        R +/- jX ohms
+
+a. 1/4 wl sp
+In phase       13        16.1      22.8      32        50.3 - 0.6
+  side ears              -2.9
+Out of phase   13        13.4      39.8                48.2 + 4.2
+  split                                      28
+
+b. 1/2 wl sp
+In phase       14        16.5      22.3      26        49.6 + 0.1
+  side ears               5.8
+Out of phase   13        14.2      30.8                50.1 + 3.0
+  split                                      24
+
+c. 5/8 wl sp
+In phase       13        16.5      24.3      24        49.0 + 0.6
+  side ears               8.2
+Out of phase   13        14.6      27.9                50.4 + 2.4
+  split                                      22
+
+d. 1 wl sp
+In phase       13        16.4      26.5      18        49.3 + 1.9
+  side ears              11.7
+Out of phase   13        15.4      25.1                50.1 + 1.3
+  split                                      18
+
+

Note that as the spacing grows wider, the out-of-phase split grows narrower, but the ears grow larger.

+

I hope this data is useful to you as a point of departure in your stack building and revision planning (used in conjunction with other data).

+

Updated 3-2-97. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
+

Topics: HF Upper, Stacking, Yagi


+ + diff --git a/content/yagi/stack0.html b/content/yagi/stack0.html new file mode 100644 index 0000000..7690123 --- /dev/null +++ b/content/yagi/stack0.html @@ -0,0 +1,42 @@ + + + + + + Stacking Yagis (3 Articles) + + + +
+

Stacking Yagis

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+

L. B. Cebik, W4RNL

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To save space on the the main page, I have gathered together the three items on Yagi stacking. Some of this information appears in "Stacking Yagis: What Can I Expect?" National Contest Journal (July-August, 1997), pp. 7-10. Other items will be added from time to time. Related to vertical stacking is horizontal stacking, which is, in turn, related to phase-fed Yagis and their EDZ parasitic beam counterparts. There are some notes in the "VHF" section of the index on this topic.

+ +
+ +
+

Updated 09-17-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Stacking, Yagi


+ + diff --git a/content/yagi/stacksup.html b/content/yagi/stacksup.html new file mode 100644 index 0000000..2595ac1 --- /dev/null +++ b/content/yagi/stacksup.html @@ -0,0 +1,177 @@ + + + + + + Supplementary Notes on Stacking + + + +
+

Supplementary Notes on Stacking

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+

L. B. Cebik, W4RNL

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+

Background

In March of 1997, Roger Cox, WB0DGF, of Telex/Hy-Gain sent me a table of recommended stacking heights (spacing between beams in a 2-beam vertical stack) based on extensive modeling he had done. Roger's work showed that for maximum gain from the stack (which often does not coincide with maximum front-to-back ratio), the separation required depends almost wholly on the initial gain of the single antennas in the stack. His table provided a range of maximum array gain separation heights for his subdivisions in the original antenna gains he studied. +

This discovery, apparently first made a number of years ago, has an origin unknown to me. Someone suggested that it appeared in older editions of the ARRL antenna book, but a search of the seven editions on my shelf turned up nothing. The data remain relatively unknown and unappreciated by hams, but deserve preservation, and hence, I am adding this note to my collection to make the information more readily available.

+

Almost any antenna modeler can confirm for himself or herself the general trends noted by Roger. In fact, Tom Schiller, N6BT, of Force 12 sent me a very similar table. Naturally, those involved in amateur antenna design would use antenna modeling software to confirm the original findings, using their own antenna designs as test subjects. The table Tom sent me reads as follows:

+ 
Free space      # of          Boom Length         Vertical Spacing
+Gain in dBi    Elements         wl / ft           for Max Gain (wl)
+ 6.6           2              0.15 / 10.5         0.4 - 0.6
+ 7.6           3              0.25 / 17.5         0.5 - 0.7
+ 8.8           4              0.43 / 30.1         0.7 - 0.9
+ 9.9           5              0.60 / 42.0         0.9 - 1.1
+10.5           6              0.75 / 52.5         1.0 - 1.1
+11.6           8              1.10 / 77.0         1.3 - 1.4
+

Why this phenomenon occurs is not hard to understand. The easiest way to get a handle on what is happening is to look at overlays of far field patterns in free space for both low gain and high gain antennas. You will notice that the H-plane pattern (the elevation pattern in conventional modeling graphics) of the high gain antenna is pushed considerably forward relative to the low gain antenna. Now this use of far-field patterns is not strictly correct (which is why I do not introduce a graphic here), since the immediate field surrounding the antenna elements in the stack is more complex. However, it would be a routine, although drudgery-filled task to calculate the height differences necessary for these displaced fields to join in phase for maximum additive field strength. The more forward the individual patterns, the greater the height necessary for maximum additive field strength (with a few minor variables tossed in to keep the calculator modest).

+

Phase 1

Tom, like Roger, noted that these figures apply only to the search for maximum forward gain. They also note that anyone can verify this table with a little modeling. This is, in fact, what I did. I modeled a collection of 11 Yagis, each with a different gain ranging from a free space gain of 6.38 dBi to 13.47 dBi. (I actually modeled a number of others, but included only 11 in this collection so as 6not to lose sight of the progressions in a morass of excess data.) Besides models already in my own collection of models, I used the untapered (all too often called by the illogical name "monotapered") element dimensions of numerous Yagis provided in the Brian Beezley, K6STI, collection within YA, the Yagi evaluation program supplied with the ARRL Antenna Book in recent editions. The test frequency was 14.175, in the middle of 20 meters. Although the untapered element models are impractical to build, K6STI also provides in YA the recommended set of tapered element lengths. +

Some of the higher gain antennas are also impractical from another standpoint: they are downward-frequency-upward-mechanical scalings from antennas for 15 and 10 meters. I doubt that most builders would attempt Yagis on 60' to 120' booms. However, the antennas show excellent characteristics.

+

The following table characterizes the basic data about each antenna's performance, both in free space, and at 70' and 140' (1 and 2 wl) above medium level homogenous earth. Feedpoint impedance is omitted, as it appears to play no role in stacking heights. All of the usual reservations about antenna models apply.

+ 
No. of    Boom FS Gain   FS F-B    70' Gain  70' F-B   140' Gain
+140' F-B
+Elements  Ft   dBi       dB        dBi       dB        dBi       dB
+2          10   6.38     11.15     11.80     12.71     12.12     11.84
+3          24   7.02     21.07     12.40     20.15     12.75     20.72*
+3          16   7.22     35.55     12.56     34.97     12.94     59.01**
+3          24   8.11     27.28     13.39     25.05     13.81     25.61***
+4          26   8.58     22.32     13.80     21.47     14.26     21.47
+5          34   9.28     26.69     14.44     26.37     14.94     26.58
+5          40   9.81     22.99     14.93     23.04     15.47     23.24
+5          48  10.55     25.56     15.60     24.91     16.19     25.22
+6          60  11.05     29.81     16.06     28.91     16.69     30.06
+7          90  12.35     25.07     17.12     25.46     17.90     25.95
+7         120  13.47     22.42     17.88     23.97     18.94     22.73
+

The 3-element Yagis marked with stars were used to see if boom length had any significant influence on stacking separation. Hence, a wide-band 24' boom model was contrasted to a shorter boom model with similar gain and a 24' boom model with higher gain. Boom length appears to exhibit an insignificant effect upon stacking separation.

+

Results of the modeling exercise form a reasonably ordered progression of the included gain values at nice intervals for comparison. However, the gain values do not form a linear set, so that the results are best presented as bar graphs without an artificial connecting line.

+

The progression is not absolutely orderly. However, the stacking spacing in terms of fractions of a wavelength required for maximum gain performance shows a close relationship to the gain over real ground of the lower antenna alone. The multiplier to derive the spacing in wavelengths ranges from about 0.05 times gain in dBi for the lowest gain beams to about 0.8 times gain in dBi for the highest gain Yagis. Moreover, as the gain of the individual antennas is increased and stacking space increases, so too does the range of space within which the maximum stack gain varies by only 0.01 to 0.02 dB, a difference from maximum that is too small to make the slightest difference to any operation. For example, at either the lower or higher altitudes, the stacks of the highest gain beams held their peak value for at least 5' or more. In contrast, maximum gain for the lower gain antennas peaked more sharply. In general, peaks with higher stacks were broader than peaks with lower stacks.

+

Separate "peaking runs" were made with the lower antenna at 1 wl (70') and with the lower antenna at 2 wl (140'). (The actual wavelength at 14.175 MHz is 69.38774' long, a little less than 1% shorter than the rounded height used.) Figure 1 shows the required separation for maximum gain with the antennas ordered in accord with their individual gain at 70'.

+
+ +
+

The following table shows the relationship of individual gain to maximum gain attained in models and the range of separation for peak stack gain. also shown is the front-to-back ratio for the stack.

+ 
No. of    Boom 70' Gain  70' F-B   Stack     Stack     Separation
+Elements  Ft   dBi       dB        gain dBi  F-B dB    in WL
+2          10  11.80     12.71     15.02     13.58     .59-.62
+3          24  12.40     20.15     15.36     12.15     .62-.63
+3          16  12.56     34.97     15.59     15.69     .65
+3          24  13.39     25.05     16.21     17.56     .65-.68
+4          26  13.80     21.47     16.58     23.23     .76
+5          34  14.44     26.37     17.17     24.19     .81-.82
+5          40  14.93     23.04     17.53     17.56     .94-.95
+5          48  15.60     24.91     18.11     37.34     .95-1.01
+6          60  16.06     28.91     18.46     28.78     1.07-1.11
+7          90  17.12     25.46     19.49     24.00     1.25-1.31
+7         120  17.88     23.97     20.36     24.33     1.40-1.46
+

Single separation values do necessarily indicate especially sharper peaks than those covering a span of 2-3% of a wavelength, since often the next lower value of gain holds longer for the single value peaks. However, the general trend of having wider latitude of separation selection while still achieving maximum gain for Yagis with higher gain holds good.

+

A second set of runs were made with the lower antenna set at 140' (2 wl). The run is significant in that it shows some small departures from the lower level runs. Most significant are some small but definite variations in the progression of spacing required. Equally significant is the fact that for beams of nearly the same gain, the required separation for maximum gain was greater if the beams were higher than if lower. Compare, for example, the 7-element beams. The 90' boom model has, at 140', virtually the same gain as the 120' boom model at 70' up. However, the higher array demands about 1.42 wl spacing, while the lower one requires about 1.32 wl spacing. Similar results can be found elsewhere in the following figure and table.

+
+ +
+ 
No. of    Boom 140' Gain 140' F-B  Stack     Stack     Separation
+Elements  Ft   dBi       dB        gain dBi  F-B dB    in WL
+2          10  12.12     11.84     15.60     12.66     .60-.63
+3          24  12.75     20.72     15.95     11.88     .63-.63
+3          16  12.94     59.01     16.21     15.75     .68-.69
+3          24  13.81     25.61     16.87     17.69     .71-.72
+4          26  14.26     21.69     17.27     22.86     .75-.78
+5          34  14.94     26.58     17.89     24.72     .84
+5          40  15.47     23.24     18.30     19.04     .97-.99
+5          48  16.19     25.22     18.96     32.07     1.05
+6          60  16.69     30.06     19.41     29.68     1.17-1.25
+7          90  17.90     25.95     20.55     24.66     1.28-1.38
+7         120  18.94     22.73     21.51     23.94     1.43-1.51
+

An interesting side note on the data stream is that the wider the separation of beams required for maximum stack gain, the more likely the stack is to hold most or all of the front-to-back ratio of the individual antennas.

+

Yagis are as full of variables as they are full of regularities. Anomalies in the progressions appear at various points, especially between the curves for the 1-wl base and the 2-wl base. The following graph, using the 1 wl gain as the key to the models, parallels the separation requirements suggested by models for each antenna. Some, but by no means all, of the minor anomalous behavior of the progressions can be attributed to the fact that I took the simple mean between extremes for the range of separation giving peak gain as the graphed value. However, as the graph shows, other variations remain. None of the variations is sufficient to result in any detectable difference in performance using the stack separations suggested by the models or from using figures developed to create smoother curves.

+
+ +
+

Phase 2

The peak gains of the antennas and their required stacking heights approximate those of the table early in these notes. However, there are minor variations that led me back to the models for a second look. Suppose we look at the gain figures in another way. Instead of seeking only the peak gain, let's also set a limit for a range of heights such that the antenna pair gain is down no more than 0.1 dB from the peak. This gives us a chance to choose a near maximum gain and to select a height with hopefully a better front-to-back ratio, if that is possible. Only the data for antenna pairs with the lower antenna at 70' up at 14.175 MHz were examined in detail. The following two tables and graphs summarize the findings. + 
No. of    Boom Min Ht.   Min Ht.   Peak Ht.  Peak Ht.  Max Ht.   Max Ht.
+Elements  Ft   feet      wl        feet      wl        feet      wl
+2          10   38       .54       42        .60       46        .66
+3          24   38       .54       43.5      .62       49        .70
+3          16   40       .57       45        .64       50        .72
+3          24   41       .59       46        .66       53        .76
+4          26   46       .66       53        .76       60        .86
+5          34   50       .72       56.5      .81       64        .92
+5          40   54       .77       60.5      .87       68        .97
+5          48   60       .86       68        .97       77       1.10
+6          60   68       .97       75.5     1.08       85       1.22
+7          90   78      1.12       89       1.27      102       1.46
+7         120   88      1.26       99       1.42      109       1.56
+

Here is the range for each figure in graphical form.

+
+ +
+

The second table lists the gain and front-to-back ratios of the stacked pairs at the minimum and maximum heights for 0.1 dB down from peak gain, along with the heights for maximum front-to-back ratio and the gain and ratio achieved at that height. Peak gain figures for both gain and front- to-back ratio are available in an earlier table.

+ 
No.   Boom Min Ht.  Min Ht    Max Ht    Max Ht    Max F-B  Max F-B  Max F-B
+El.   Ft   gain dBi F-B dB    gain dBi  F-B dB    Ht. f/wl gain dBi F-B dB
+2     10   14.93    18.66     14.94     10.90     34 / .49  14.65   27.15
+3     24   15.25    13.75     15.25     12.27     15 / .21  13.64   30.35
+3     16   15.48    15.34     15.50     16.80      7 / .10  12.94   20.54
+3     24   16.12    18.16     16.11     20.01     26 / .37  15.19   26.52
+4     26   16.47    18.81     16.48     27.48     60 / .86  16.48   27.48
+5     34   17.06    23.01     17.07     23.73     57 / .82  17.17   24.19
+5     40   17.43    16.15     17.43     19.45     13 / .19  14.96   25.50
+5     48   18.00    30.02     18.02     28.39     66 / .94  18.11   39.57
+6     60   18.37    29.94     18.36     29.59     60 / .86  18.04   31.49
+7     90   19.39    23.84     19.39     26.23    110 /1.57  19.23   27.58
+7    120   20.26    24.55     20.26     23.69     83 /1.19  20.13   24.62
+

The following graph may make the data clearer by setting the maximum front- to-back separations next to the peak gain separations.

+
+ +
+

From the data, several things are clear. First, there is not an exact agreement with the initial tables supplied me and the findings from these models, although the ranges are quite close indeed. The differences may stem from several sources. 1. The model antennas used are different in each case, so no exact correlation can be drawn between any two antennas, chosen one each from the supplied and the developed results. 2. Modeling programs will differ in their gain figures, both as a result of differences in the modeling machine and as a consequence of the ground calculations used by the program. MININEC, for example, uses a simplified ground approximation, while NEC-2 and -4 use the more accurate Sommerfeld-Norton calculation. Hence, the differences in the recommended ranges are not significant.

+

Second, the ideal maximum front-to-back ratio separation height between two identical antennas may be above, below, or within the range of maximum gain. In some cases, the front-to-back ratio of a stack is acceptable at one of the maximum gain heights, even if not fully maximized. In some other cases, the front-to-back ratio may be low enough at a maximum gain height to adversely affect operations. There is no easy correlation between the maximum front-to-back height and any single or pair of antenna properties, including number of elements, boom length, feedpoint impedance, or the front-to-back ratio of a single antenna.

+

Phase 3

It pays to look carefully at the elevation patterns of stacks. The nulls are just as important as the lobes. Moreover, the elevation angle of maximum radiation of a stack is always lower than the take-off angle of the top beam alone, since the stack is a single array with a composite pattern equivalent to a single planar antenna at some intermediate height. Moreover, although the effect may be small in a well-designed stack, the use of one of the two antennas while the other is passive will alter at least slightly the figures for the individual antennas. +

To illustrate these points, I set up a stack of identical 4 element Yagis from my collection of models for mid-band on 15 meters. For this beam design (about 8.6 dBi forward gain in free space), a separation of 35' yielded nearly maximum forward gain for the pair while preserving a better than 20 dB front-to-back ratio. The feed Z was about 25 - 28 Ohms.

+

I placed the beams at 100' and 135' up. Here are the figures for these beams when each is the only beam on the tower:

+ 
Height    Gain      To angle  Vert B/W  2nd lobe  F-B
+feet      dBi       degrees   degrees   degrees   dB
+100'      14.27     6.4       6.5       20.0      23.08
+135'      14.36     4.8       4.8       14.7      21.92
+

Now let's stack the beams.

+ 
Height    Gain      To angle  Vert B/W  2nd lobe  F-B
+feet      dBi       degrees   degrees   degrees   dB
+Both      17.33     5.4       5.5       16.5      20.77
+135'      14.28     4.8       4.7       14.7      20.81
+

As you can see, the figures for the 135' only and the 135' w/100' passive are very slightly different, but operationally insignificantly different in this arrangement. The feed Zs also differ in resistance by about 1 Ohm (4%).

+

Moreover, the TO angle of the main lobe is lower for the stack than for the top beam, either only or w/100' passive. You can repeat this exercise with innumerable beams in well arranged stacks.

+

Now compare the "Both" entry with the following:

+ 
Height    Gain      To angle  Vert B/W  2nd lobe  F-B
+feet      dBi       degrees   degrees   degrees   dB
+120'      14.33     5.4       5.4       16.7      20.80
+

The stack fed in phase is angularly (but not gain) equivalent to a single beam at 120', about 57% of the distance of separation.

+

For all of these exercises, I have let the software calculate patterns to 0.1 degrees so that differences are not washed out, even if they do not make a big or even a little difference operationally. Since the two beams in this modeled stack are about 2.15 wl and 2.9 wl up respectively, differences become small, and comparative modeling should go to smaller angular resolution in order to see differences that are at least mathematically significant.

+

But now let's explore those 2nd lobes I added to the scheme. These lobes are in fact not down by much relative to the main lobe. However, between the lowest lobe and the next one up is a null (the one to which I originally referred) that may be 20 dB or more deep at its pinpoint extreme. The null is at about 9.8 degrees for the 135'-only operation, 11.0 degrees for the stack, and 13.2 degrees for the 100' only operation. On some occasions, the incoming signal angle may be well into one of these nulls, but never all three simultaneously--because the nulls are exceptionally sharp.

+
+ +
+

It is easy to see the importance of having the ability to switch among arrangements in order to change the null position--or more operationally, to change the lobe position to catch the signal. A couple of degrees difference in the lobe angle (either the lowest or the 2nd) might indeed make a 15-20 dB signal strength difference. Moreover, to fill the null completely, a stack of 3 might be even more useful, since it would offer the use of beams 1-3, 1-2, 2-3, and the individual beams.

+

Of course, when beams are lower in height relative to a wavelength at the operating frequency, the lobes are vertically wider. This variation in lobe size as well as all of the variables of individual beam placement in the stack for the many possible installations makes this an exercise each stacker should carry out for his or her own installation.

+

The upshot is that a stack is as likely to miss some action as the top beam alone or the bottom beam alone, since at a given moment, the particular path of interest may fall into the null between the first and second lobes. If you plan a stack, especially one with a top height well over 2 wl (and here approaching 3 wl), switching capability may be the key to using the stack effectively.

+

Now the usual disclaimer: modeling via NEC is over flat ground with no bumps or clutter. For other types of terrain, the angles may change, but the progressions will not. Use either the N6BV or the K6STI terrain software to translate these figures into those which better fit your situation.

+

Conclusion

The achievement of maximum gain from a stack of two identical monoband Yagis is straightforwardly determined. The traditional range charts are very close for almost any antenna selected having a similar free space gain. +

However, selection of antennas for a stack requires close attention to design for maximum results with respect to gain, take-off angle, and front-to-back ratio. Given the diverse results for both 3-element beams and 5-element beams--and remembering that a different arrangement of elements on a similar boom length might give different front-to-back results in a stack-- the only safe course for a stacker is to model or have modeled a range of potential antenna pairs. And, if one goes to this trouble in order to maximize the cost-benefit ratio, one might as well also subject the proposed stack to either N6BV's or K6STI's terrain analysis programs.

+

Considering the size of the investment needed for a stack and all of the supplementary mechanical and material supplies to make the stack work, selecting antennas that promise both high gain and excellent front-to-back properties may not significantly raise the cost. Such careful selection, however, may improve the operating capabilities of the stacked array.
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Updated 10-2-97. 05-01-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
+

+
+ +

+
+ Go to Amateur Radio Page
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Topics: HF Upper, Stacking, Yagi


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Stacking: What Difference Does Difference Make?

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L. B. Cebik, W4RNL

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Dave Leeson recently sent me a quandary concerning the effect that a beta match inductive reactance might have on a stack of 2 (or more) antennas. The beta match, of course, is an L-network, and network outputs have their voltage and current shifted in phase relative their input phases. If two identical beta-matched antennas are stacked and are fed exactly in phase, then the network phase shifts would be equal, and the two antenna element arrays would also be in phase with each other.

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However, discussions in various quarters have suggested that many hams are stacking different antennas, each ostensibly for the same band. I have a feeling in retrospect that this may have been what Dave had in mind when he raised the question. The question in fact is not a simple one and may have at least two dimensions. On the one hand, some hams are stacking antennas having different forward gain values. On the other, they may be stacking antennas having different matching systems to yield a terminal 50-Ohm impedance.

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Together, the two questions present an almost endless array of combinations for any possible installation. Therefore, no definitive set of answers can be generated for a particular installation without extensive measurement at the site itself. Nevertheless, modeling can indicate some suggestive directions for the individual stacker to investigate if he is concerned about such a situation.

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Let's divide the questions into two parts and look first at the differential gain situation.

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Differential Gain Antennas in a Stack

If we place two antennas of different gain values in a stack, how will they perform? What will be the maximum gain achievable from the stack? What will be the take-off angle (elevation angle of maximum radiation)? +

To get an initial purchase on this question, I took two 20-meter 3-element beams out of my files. One is a short boom (16') model with a little over 7 dBi free space gain at 14.175 MHz. The other is a longer-boom (24') model with a little over 8 dBi free space gain at the same frequency. I placed each over average ground at a height of 70' (a rounded 1 wl). The basic single antenna performance at that height for each was as follows:

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Antenna                  Gain 70'  TO 70'    F-B 70'
+                         dBi       deg       dB
+#1:  3-el/16' boom       12.56     14        34.97
+#2:  3-el/24' boom       13.39     14        25.05
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I next created stacks of two identical antennas of each kind. I sought out the separation above the 70' height of the lower antenna that would yield maximum gain, without regard for front-to-back ratio. In some cases, only a single height for the second antenna produces maximum gain--in other cases, the maximum gain may be spread over several feet of differential separation. For the two antennas, here are the results:

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2 x Antenna #1:  lower antenna at 70'
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+Height upper   space in ft    space in wl    Gain      TO        F-B
+115'           45'            .65            15.59     10        15.69
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+2 x Antenna #2:  lower antenna at 70'
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+Height upper   space in ft    space in wl    Gain      TO        F-B
+115'           45'            .65            16.21     10        17.52
+116'           46'            .66            16.21     10        17.56
+117'           47'            .68            16.21     10        17.69
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For the lower gain antenna, the net stacking gain is 2.03 dB, while for the higher gain antenna, the net stacking gain is 1.82 dB. The upper antenna alone exhibits a marginally lower TO angle, but a more significant reduction in gain. For example, Antenna #2, the higher gain model, when placed at 116', shows a gain of 13.71 dBi with a TO angle of 8 degrees. Of course, it maintains a high front-to-back ratio, in this case 27.4 dB.

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Now suppose we combine one antenna of each type. We have a choice to make as to which of the two goes on top. This choice may be governed by other than performance figures. Weight distribution on a mast and similar installation considerations may in fact outweigh the performance numbers. However, it is interesting to discover what those numbers might be, at least in modeled form.

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The two situations were similarly modeled, placing first one and then the other on top. Throughout, I assumed that the two could be truly fed in phase in order to keep that other question separated from this one. As with the stack of two identical beams, I sought out the heights/separations that yielded maximum gain without reference to the consequences on the front-to-back ratio. Here are the results:

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Antenna #1 low--Antenna #2 high:  lower antenna at 70'
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+Height upper   space in ft    space in wl    Gain      TO        F-B
+118'           48'            .69            15.79      9        17.70
+119'           49'            .71            15.79      9        17.95
+120'           50'            .72            15.79      9        18.25
+121'           51'            .74            15.79      9        18.60
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+Antenna #2 low--Antenna #1 high:  lower antenna at 70'
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+Height upper   space in ft    space in wl    Gain      TO        F-B
+116'           46'            .66            15.61     10        16.34
+117'           47'            .68            15.61     10        16.39
+118'           48'            .69            15.61     10        16.50
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Placing the higher gain antenna on top of the stack above the lower gain antenna requires greater separation than simply stacking two of the higher gain antennas. The result is a TO angle that is a degree lower than stacks of two identical antennas. However, the gain is intermediate between the two stacks of identical antennas.

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Placing the lower gain antenna on top requires at least as much separation as a stack of two identical higher gain antennas. Yet, the peak gain is not significantly different than a stack of two of the lower gain antennas.

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The upshot is a suggestive conclusion--not by any means a firm, let along a decisive one: Stacking beams of dissimilar gain is a useful practice, although the ultimate gain of the system will be closer to the value for two of the lower gain antennas rather than to the value for two of the higher gain antennas. Wherever possible, the higher gain antenna deserves to be on top to maximize performance from the pair, whether or not in practical terms it can in fact be on top. Expect maximum gain to occur with slightly greater spacing than might be used for identical beams.

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Confirmation of these conclusions would require very extensive modeling just to reach the stage of a firm conclusion. In the absence of such a large scale systematic study, every potential stacker should equip himself to analyze his own situation in detail, including that very elusive task of arriving at a reliable figure for each of the commercial antennas involved in the proposed stack.

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The Feed-Phase Question

The initial foray into stacking dissimilar gain antennas assumed in phase feeding without further question. What happens when the antennas see differential phasing on their drive elements? This question is an extremely complex one, because both the magnitude and the phase of the source current may differ between two antennas. Since the combinations one might try are nearly endless, we shall have to settle once more for a suggestive answer dealing only in the simplest case. +

Let us assume that the current magnitude at the antenna sources are equal in all cases. The lower antenna of a stack of two identical antennas (the higher gain model #2 above) will have an arbitrary current magnitude of 1.0 at a phase angle of 0.0 degrees. The spacing of the antennas is set by the upper antenna also having the same source current magnitude and phase. In this case, the spacing is 46'. Now we can address the question of what happens if the phase angle of the source current varies from that of the fixed lower antenna values.

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It is not possible in advance to say what a likely region of a possible 359 degree variation in current phase angles might be. For example, two beta matches might be set slightly different to each other, perhaps the result of using slightly different lengths for the driver. The consequence might be a few degrees difference in feed current phase angle. At the other extreme, one might combine two different antennas (of equal gain) having radically different matching systems and thus creating a large difference in the source current phase at the antenna elements.

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The only practical solution for a first order look at the possible problem is simply to vary the current phase at the source of the upper antenna in regular increments and see what happens. Therefore, I modeled the system of identical antennas simply by changing the source current phase in 10- degree increments. The following long table is what I obtained by way of modeling output.

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Table of Feed Phase Differences
+Imag = 1.0/1.0      Iphase = 0.0/X degrees
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+A. Reference:
+1 Antenna Gain      TO   2nd lobe  TO        F-B       Zlower    Zupper
+          dBi       deg  dBi       deg       dB        R/jX      R/jX
+ 70'      13.39     14   ---       --        25.1      25.1-0.9  ---
+ 116'     13.71      8   ---       --        27.4      25.9-0.6  ---
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+B.  Systematic Variation of the Top Antenna Source (2) Current Phase
+Source 2  Gain      TO   2nd lobe  TO        F-B       Zlower    Zupper
+Phase     dBi       deg  dBi       deg       dB        R/jX      R/jX
+  0       16.21     10   ---       ---       17.6      24.1+0.9  24.8+1.2
+ 10       16.17     10   ---       ---       17.5      23.7+0.8  25.2+1.2
+ 20       16.06     10   ---       ---       16.1      23.4+0.7  25.6+1.2
+ 30       15.88     10   ---       ---       17.3      23.1+0.5  25.9+1.0
+ 40       15.63     10   ---       ---       17.3      22.8+0.3  26.2+0.8
+ 50       15.30     10   ---       ---       17.2      22.6-0.0  26.5+0.6
+ 60       14.89      9   ---       ---       17.2      22.4-0.3  26.7+0.3
+ 70       14.41      9   ---       ---       17.1      22.2-0.7  26.9+0.0
+ 80       13.82      9   ---       ---       17.0      22.2-1.0  27.0-0.3
+ 90       13.13      9   ---       ---       16.9      22.2-1.4  27.1-0.7
+100       12.30      9   ---       ---       16.8      22.2-1.8  27.1-1.1
+110       11.32      9   ---       ---       16.7      22.3-2.1  27.0-1.4
+120**     11.41     47   11.19     24        ---       22.5-2.4  26.9-1.8
+130       11.81     46   11.58     24        ---       22.8-2.7  26.7-2.1
+140       12.13     46   11.92     23        ---       23.0-2.9  26.5-2.4
+150       12.39     46   12.21     23        ---       23.4-3.1  26.2-2.6
+160       12.57     46   12.43     23        ---       23.7-3.3  25.9-2.8
+170       12.68     46   12.58     23        ---       24.1-3.3  25.5-2.9
+180       12.73     46   12.66     23        ---       24.4-3.3  25.2-3.0
+190       12.71     46   12.69     23        ---       24.8-3.3  24.8-3.0
+200**     12.65     23   12.63     46        ---       25.1-3.2  24.4-2.9
+210       12.54     23   12.48     46        ---       25.5-3.0  24.1-2.8
+220       12.38     23   12.26     46        ---       25.7-2.7  23.8-2.6
+230       12.14     23   11.96     46        ---       26.0-2.5  23.5-2.3
+240       11.83     23   11.59     46        ---       26.2-2.1  23.3-2.1
+250**     11.53     10   ---       ---       18.9      26.3-1.8  23.1-1.7
+260       12.49     10   ---       ---       18.7      26.4-1.4  23.0-1.4
+270       13.30     10   ---       ---       18.5      26.4-1.1  22.9-1.0
+280       13.98     10   ---       ---       18.3      26.3-0.7  22.9-0.7
+290       14.58     10   ---       ---       18.2      26.2-0.4  23.0-0.3
+300       15.02     10   ---       ---       18.1      26.0-0.0  23.1+0.0
+310*      15.41     10   ---       ---       18.0      25.8+0.2  23.3+0.4
+320*      15.71     10   ---       ---       17.9      25.5+0.5  23.5+0.6
+330*      15.94     10   ---       ---       17.8      25.2+0.7  23.8+0.9
+340*      16.10     10   ---       ---       17.7      24.8+0.8  24.1+1.0
+350       16.19     10   ---       ---       17.7      24.5+0.9  24.5+1.2
+360       16.21     10   ---       ---       17.6      24.1+0.9  24.8+1.2
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The ** indicator shows where the lobe of maximum gain undergoes a large shift. When the angle of maximum radiation is high, I have ignored front- to-back figures and given instead the strength of the accompanying secondary lobe, which is ordinarily notably strong relative to the primary lobe. Where the main lobe is at a low angle, front-to-back is given. In cases of a low-angle main lobe, I ignored the secondary lobe except to note some instances where it was very weak, as indicated by the single *.

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Most notable in the current phase circle is that for over a third of the possible values, the main and secondary lobes are angled too high for effective DX use. For over three-fourths of the values, the forward gain is less than that of a single antenna at the lower height of the stacked pair. The window of maximum gain, arbitrarily defined here as within 0.25 dB of the highest value of which the system is capable is +/-20 degrees of a perfect in-phase condition. Doubling the margin of acceptability to 0.5 dB down from peak capability increases the range of acceptable phase differentials to +/- 40 degrees.

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Although there is a certain comparability as we move equal amounts plus and minus of a perfect in-phase condition, there is no symmetry. The following three elevation overlays--taken at +/-30, +/-60, and +/-90 degrees provides ample evidence of the differences.

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This single demonstration is but one of innumerable others that might run the same ring with the top antenna having more or less than equal current magnitude relative to the bottom antenna (which is fixed at a current magnitude of 1.0 and a phase of 0.0 degrees for the exercise). To reveal the most optimal set(s) of conditions between the two antennas in the stack would require a catalog of runs. For values of top-beam source current magnitude from 0.9 through 1.10 relative to that of the bottom beam, a perfect in-phase condition between the two currents does yield maximum system gain under the prescribed set-up of the stack used in this sample exercise.

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Current Magnitude and Phase

Dean Straw, N6BV, recently (May, '99) reminded me that the current magnitude cannot be ignored in these calculations, and, of course, he is correct. A source connected on the input side of a beta (or other) match does not yield a current equal to the source current on the antenna side of the match. Hence, not only will the phase of the current shift, but so too will its magnitude. If we place antennas with different matching parameters into a stack, the antennas may produce something other than peak performance. At the time I worked up the original note, I did not have models of sufficiently similar operating characteristics to demonstrate this point. I have since acquired some. +

To make a practical test of this within the models at hand, I took two different antennas of approximately the same capability. The models are fully described in another note, Modeling 6 Long-Boom Yagis. The Yagis selected include the one designated as K6STI, a design developed by N6BV on YO for the YA program. It has a free space gain at 14.175 MHz of 10.52 dBi (NEC-4 uncorrected) with a front-to-back ratio of 23.64 dB. The native source impedance is 23.6 - j27.6 Ohms.

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The other Yagi selected is the W3LPL design, but without the Tee match used by the designer. Its free space gain at 14.175 MHz is 10.30 dBi, with a front-to-back ratio of 22.80 dB (NEC-4 uncorrected). The feedpoint impedance of the design as given is 39.1 + j17.9 Ohms. In performance, at the selected frequency, the beams would be indistinguishable except for the feedpoint impedance.

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My first step was to reduce the length of the W3LPL driver until the source impedance showed a considerable capacitive reactance. The resultant source impedance was 31.5 - j23.6 Ohms with no change of performance. I then applied beta match shorted stubs to the source segments of each antenna: 48 Ohms (101" shorted stub of 50-Ohm, VF=1 perfect transmission line) for the N6BV/K6STI beam and 65 Ohms (122" shorted stub of 50-Ohm, VF=1 perfect transmission line) for the W3LPL Yagi. These matches brought each antenna to under 1.2:1 50-Ohm VSWR.

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Next, I created a stack with the N6BV/K6STI beam at 70' and the W3LPL antenna at 140' above average ground. Each antenna source was connected to a common (remote modeling) wire through 1/4 wl sections of 75-Ohm transmission line to effect an impedance transformation to about 100 Ohms. The parallel combination should yield a net impedance very close to 50 Ohms for connection to a main feedline.

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The stack produced a reported gain of 17.90 dBi at TO angle of 8 degrees, with a front-to-back ratio of 30.32 dB. The feedpoint impedance of the combination was 52.6 + j 1.1 Ohms. The currents for the antenna driver feed segments are (relative to a source current of magnitude 1 and phase angle 0) as follows: Lower: 1.11 at -39.3 degrees; Upper: 0.89 at -52.3 degrees. The net difference in magnitude is 0.22 and the difference in phase is 13.0 degrees. These are fairly small differences which do not detract significantly from peak performance of the array. (Two in-phase-fed W3LPL beams stacked at 70' and 140' show a maximum gain of 17.91 dBi, while two of the N6BV/K6STI beams in the same position show a maximum gain of 18.05 dBi.)

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Next I created for the W3LPL beam in its original configuration (an inductively reactive driver) a -103-Ohm (capacitive) reactance open stub from 60" of open 50-Ohm perfect line. (Although rarely used, a beta match may employ a series inductive reactance and a shunt capacitive reactance.) With this open stub shunt, the performance characteristics remained as before, but the feedpoint impedance was altered to 47.3 - j0.2 Ohms. I then replaced the upper beam in the 70-140 stack with the new version of the W3LPL antenna and reconnected the feed system used in the first test.

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The new stack, which is identical to the old in every way except the driver matching scheme of the upper antenna, produced a reported gain over average ground of 17.05 dBi, again at an 8-degree TO angle, with a front-to-back ratio of 33.20 dB. The combined net source impedance was 54.9 - j0.8 Ohms for a 50-Ohm VSWR figure of under 1.1:1.

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The relative source segment currents were as follows: Lower: 1.13 at -39.5 degrees; Upper: 0.79 at -113.6 degrees. The differential amount to 0.34 in magnitude and 74.1 degrees in phase. The consequence is a loss of nearly a dB in gain from the array relative to the more closely matched first test configuration. Moreover, there are noticeable differences in the elevation patterns of the two configurations, as shown in Fig. 4.

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S2 represents the stack with the two beta matches that use shorted stubs. S4 represents the combination of shorted lower and open upper stub beta matches. Note not only the gain of the lowest lobe, but as well the rear quadrant. Although the lower gain combination has the smaller rear lobe at the first level, its upper rear lobes are significantly larger than those of S2. Note also the second forward lobe of S4, which blends into the lower lobe.

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As Dean noted to me, there are still antennas around with native source impedances between 12 and 20 Ohms, and these will show even wider variations in current magnitude. Unfortunately, I do not have in my collection any models that match up well in performance characteristics to those with higher source impedances. Hence, a modeling exercise would not be able to separate the consequences of current magnitude and phase differences from the consequences of performance differences. Nevertheless, the small demonstration given here should suffice to indicate in a broad way that current magnitude and phase together can have an impact on stack performance, even if the antennas stacked are very closely matched in performance characteristics. The wider the difference of source segment current magnitude and phase, the more likely the stack is to perform at less than its full potential.

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A Short Note on Networks

The phase shift created by networks between the feeding phase lines and the post-network antenna terminals depends on the nature of the network and the conditions under which it is operating. The latter conditions include both the complex impedance transformation involved and the "delta" of the network. L-networks--with two reactance arms--are limited to phase shifts of +/- 90 degrees, while the 3-armed PI and Tee networks may have any desired phase shift value. Very often, one designs for the impedance transformation and accepts whatever phase shift results. This result is not a problem for a single network feeding a single antenna as its load. Since this is the standard case, introductions in ham literature often stress the conditions of impedance transformation and efficiency, while bypassing significant notice of the conditions of phase shift. Phase shift information tends to appear in antenna manuals, especially in chapters devoted to the "phasing" of vertical antenna elements in an array. +

The current literature and techniques of network analysis often begin at a level somewhat daunting to the average ham who is simply trying to design an antenna installation using commercially-made components. However, the fundamental relationships for the most common network can be found in Terman, Radio Engineers' Handbook, Section 3, "Paragraph" 25 (pp. 210-215 of the 1943 edition). Equations 113 and 114 are useful for getting a "feel" for how the basic elements of the network interrelate in Tee and PI networks. The preceding paragraph is drawn from this section. Those already beyond this introductory level can amend and supplement the treatment in many ways, especially in showing the PI, Tee, and L networks to be special cases of more general principles.

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Phase shifts in networks can be calculated via a number of available utility programs. TLA, by N6BV, will handle networks as well as transmission lines when used rightly. There are also utilities in the HAMCALC collection to perform similar functions. And these are just two of a number of sources.

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Impedance transformation, efficiency, and phase shift are interrelated determinable conditions for all common types of networks, but not necessarily easily determined conditions for any particular installation. Perhaps in the end, the most common advice is the soundest: in the absence of detailed measurements and calculations of the post-network antenna terminal current phase conditions, strive for identity between the antennas in the stack.

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These notes are intended only to suggest the dimensions of an aspect of antenna stacking. In no way do they pretend either to solve a problem or to create one where one does not presently exist for a given installation. Hopefully, they may contribute at an introductory level in a better understanding of what stacking may involve when the antennas stacked are not identical either in gain or in the current magnitude and phase shift created by an impedance transformation network incorporated into the antenna feedpoint system.

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Updated 11-21-98, 05-19-99. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Topics: HF Upper, Stacking, Yagi


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1-2-3: 1 Boom, 2 Bands, 3 Elements Each

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The Evolution of a Modeling Design

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L. B. Cebik, W4RNL

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1. The Project and Its Specifications

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I have long been curious about the design of multiband Yagis. Although sometimes maligned by monoband purists, these beams serve a vital function in amateur radio and elsewhere. The problems of getting a single array of elements to perform adequately on 2 or more bands is a design challenge of the first order. That the products on the market are very serviceable is a tribute to a number of fine designers around the world. +

The most usual method of designing a multiband Yagi is to begin with 20 meters and then graft on elements to serve other bands. The 20-meter design remains relatively unaffected by laying in elements for 15 or 10 or other higher frequency bands, and only minor tweaking is needed to restore its original performance.

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The other bands are another matter. Laying in a 15 meter Yagi within the confines of a 20 meter beam will normally cage the performance of the 15 meter antenna to less than the same antenna would do were it free and clear. Some designers add elements to restore the performance, thus getting essentially 3-element monoband performance out of 4 elements. Obviously, the weight goes up with the element count.

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To counteract this trend, designers use a number of means to press elements into double duty, including traps. Traps are handy at the 20- meter driven element, since they permit the use of a single element as the driver and a single feedline for the array. However, log periodic assemblies and open sleeve coupling are alternatives that permit single feedlines, but all of the single-feed methods are implemented at the expense of design complexity, subtlety, and a certain order of finickiness.

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If we can live with multiple feedlines (or a switching system at the mast), perhaps some of the complexity of multiband design might be overcome. Separate feedlines would permit placement of the driven element wherever it was needed. We might even overcome the mind set of placing driven elements for different bands in close proximity to each other.

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The caging effect that requires extra elements or other design complexities might also be overcome--perhaps by sliding the upper band beams forward on the boom. If the lowest band uses only a reflector and driven element, then sliding higher frequency elements forward is simple. However, once we hit 3 elements, staggered beams become cumbersome in terms of boom length.

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So I set myself a little modeling exercise: to develop a buildable design for a 2-band beam (20 and 15 meters) of 3-elements for each band on one medium length boom. The beams would be separately fed and, to the highest degree possible within reason, would retain their independent monoband performance.

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2. The First Step: Trial Models

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Beam Selection: Among my collection of models is a 3-element design for 20 meters originally supplied by Brian Beezley, K6STI, with AO-5. The model uses 1" untapered elements and provides about 8.1 dBi free space mid-band gain and better than 20 dB front-to-back ratio over the first 2/3 of the band. The intended boom length is 24 feet. +

Because a seriously tapered set of elements that are mechanically sound will be equivalent to much thinner untapered elements, the beam would have to be re-tuned for that purpose. Additionally, it would require scaling to 15 meters. Finally, the beams would require conversion to tapered elements and readjusted accordingly.

+

Boom Length: The project goal was to use a "medium-length boom," which is a fuzzy concept unless given some definition. Using the lowest band to set parameters, we might call a medium length boom one that is generally about twice the length of the antenna turning radius, as defined by the longest elements. This measure is not precise, since the turning radius is a function of the 20-meter reflector length and the distance of the element from the boom-mast junction. However, 35' at 20 meters seems not unreasonable as a good number and is commonly used (plus or minus a foot or so) for multiband beams. Anything more than 10% longer gets into long boom Yagis (40' or so at 20 meters) and anything less than 2/3 this length (less than 24') is usually classed as a short boom at 20.

+
+ +
+

The goal was also to keep the boom length as short as feasible while retaining essentially monoband performance for the individual beams. This goal meant that I could not simply set one beam in front of the other to get a composite of 24' plus 16' plus a little extra for a 45' long antenna. Something closer to 30' seemed a decent limit, but it meant that at least some of the elements would have to interlace.

+

First-Things-First: The Individual Beams: Having set the project goals, the first step was to ascertain the monoband performance of the rescaled beams. I modeled the 20 meter beam using 5/8" diameter elements with the following results across 20 meters

+ 
+Fq             14.0                14.15               14.35
+Gain dBi       8.03                8.18                8.45
+F-B dB         21.41               26.33               16.20
+Feed Z ohms    67.6 - j29.6        50.7 - j10.7        32.4 + j11.8
+SWR 50         1.79                1.24                1.69
+
+

I also scaled the antenna for 15 meters, using 1/2" diameter elements. After re-tweaking, I obtained these results across the band.

+ 
+Fq             21.0                21.2                21.45
+Gain dBi       8.13                8.28                8.51
+F-B dB         23.29               25.22               16.75
+Feed Z ohms    60.4 - j27.8        48.8 - j9.7         35.3 + j11.6
+SWR 50         1.71                1.22                1.56
+
+

The slightly stronger performance (which shows only in decimal places that are meaningless to actual operation) on 15 is a result of the fact that the beam elements are essentially fatter on that band, relative to a wavelength.

+

As anticipated, front-to-back ratio fell off in the upper portion of the band, which gain continued to increase.

+

For reference, the wire lengths and spacings of the 2 beams are included here.

+ 
+Frequency = 14.15  MHz.
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z :in) Conn.--- End 2 (x,y,z :in) Dia(in) Segs
+
+1    -208.00,  0.000,  0.000       208.000,  0.000,  0.000 6.25E-01  21
+2    -197.00,127.000,  0.000       197.000,127.000,  0.000 6.25E-01  21
+3    -188.00,275.000,  0.000       188.000,275.000,  0.000 6.25E-01  21
+              -------------- SOURCES --------------
+Source  Wire    Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+        Seg.     Actual      (Specified)
+1         1     2 / 50.00   (  2 / 50.00)    1.000       0.000       I
+-----------------------------------------------------------------------
+
+Frequency = 21.2  MHz.
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z :in) Conn.--- End 2 (x,y,z :in) Dia(in) Segs
+
+1    -138.80,  0.000,  0.000       138.800,  0.000,  0.000 5.00E-01  15
+2    -131.50, 85.000,  0.000       131.500, 85.000,  0.000 5.00E-01  15
+3    -125.50,184.000,  0.000       125.500,184.000,  0.000 5.00E-01  15
+              -------------- SOURCES --------------
+Source  Wire    Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+        Seg.     Actual      (Specified)
+1         8     2 / 50.00   (  2 / 50.00)    1.000       0.000       I
+
+

Feedpoint Impedance: a Pseudo-Beta Match: The raw feedpoint impedances for the models actually show the standard values one might anticipate-- about 25 ohms resistive with more than 10 ohms capacitive reactance at the target center frequencies. 50-ohm performance figures were created by modeling a pseudo-beta match. The procedure is straightforward. The driven elements were subdivided into 3 wires according to the following scheme. A left end used 1/2 the total segments, as did a right half of the element. Each half element was terminated 1/2 the length of a segment within it from the center point. A single-segment wire was placed between the halves. The following sketch may be helpful here.

+
+ +
+

Then three 1-segment wires were constructed, each of the same length as the other segments and of the same diameter as the element. This latter step is necessary to overcome some inaccuracy introduced when NEC encounters angular junctions of dissimilar diameter wires. Two of the new wires are oriented vertically from the junctions with the 1-segment center wire. The third wire connects the open upper ends of the first two.

+

The third wire is loaded with a value of inductive reactance. This value may not be the same as the value one might calculate for a beta match, because the vertical wires present physical structures that amount to parallel transmission line lengths and which exhibit capacitance between them. The required reactance values for the independent antennas were about double what might be expected, and in all cases required lengthening the driven element to eliminate remnant inductive reactance. Nonetheless, the matching system simulates with reasonable accuracy a beta match and provides what is needed for a 50-ohm target frequency match.

+

Accuracy can be improved by using the maximum number of segments possible without violating the NEC limits for segment length-to-diameter ratio. This procedure will minimize the physically modeled structure and its affects on the required loading. However, in multiband beams with stepped segment diameters, a model may easily become unmanageable.

+

Although the resulting impedance figures may be adequately accurate to estimate operating bandwidth, the physical structure also increases gain slightly (often up to 0.1 dB). This is a false increase created by the physical structure of the pseudo-beta match.

+

For purposes of making operating bandwidth estimates, the inductive reactance is converted into a value of inductance placed in a parallel loading circuit. Of course, the value of capacitance for this mode of loading is left zero. I normally leave the resistance zero (recorded by NEC as missing), which produces the highest Q and narrowest operating bandwidth, so that estimates are conservative. As the sample beams show, a simple beta match has no difficulty providing full band operation with under 2:1 50-ohm SWR.

+

Combining the Untapered Beams: All modeling of the individual beams was done with segments about 10" long: 21 segments for the 20-meter elements and 15 segments for the 15-meter elements. These lengths were retained for the composite attempt to model the antenna on one boom. Remember that the goal was to retain, insofar as possible, monoband performance on a medium length (less than 35') boom.

+

The figure shows the layout. The 15-meter driver and reflector were placed forward of the 20-meter driver and reflector, so that the 15-meter director is well forward of the 20-meter reflector.

+

The following element chart shows the final element lengths and spacings. All 20-meter elements are 5/8" diameter, while all 15-meter elements are 1/2" diameter. The elements are grouped by bands, so that the 20 meter director is physically out of place in the chart, but electrically grouped with its cohorts.

+ 
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z :in) Conn.--- End 2 (x,y,z :in) Dia(in) Segs
+1    -208.00,  0.000,  0.000       208.000,  0.000,  0.000 6.25E-01  21
+2    -197.00,127.000,  0.000       197.000,127.000,  0.000 6.25E-01  21
+3    -188.00,275.000,  0.000       188.000,275.000,  0.000 6.25E-01  21
+4    -138.00,137.000,  0.000       138.000,137.000,  0.000 5.00E-01  15
+5    -130.50,235.000,  0.000       130.500,235.000,  0.000 5.00E-01  15
+6    -125.50,334.000,  0.000       125.500,334.000,  0.000 5.00E-01  15
+              -------------- SOURCES --------------
+Source  Wire   Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+        Seg.     Actual      (Specified)
+For 15 meters
+1        8     5 / 50.00   (  5 / 50.00)      1.000       0.000       I
+For 20 meters
+1        8     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+
+ +
+

By simple calculations, you will see that minor adjustments in 15-meter element spacing and lengths were required to tweak the design in its semi- caged setting. Little or no change was necessary for the 20-meter beam. The entire assembly is under 28' long, a good fit for a 30' boom.

+

Although the pseudo-beta match model wires are not shown in order to maintain clarity, they were present in the runs that produced the following results for the two bands.

+ 
+Fq             14.0                14.15               14.35
+Gain dBi       8.23                8.37                8.60
+F-B dB         22.87               23.30               15.11
+Feed Z ohms    87.1 - j23.7        57.8 - j 4.9        33.0 + j18.2
+SWR 50         1.93                1.19                1.83
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.39                8.45                8.67
+F-B dB         19.57               20.09               14.70
+Feed Z ohms    79.1 - j41.6        56.6 - j15.6        30.3 + j18.7
+SWR 50         2.19                1.37                1.98
+
+

Several things stand out in these results. The 15-meter operating bandwidth is just sufficient so that with any length of coax at all, it will show less than 2:1 SWR at the operating position. A beta inductance with any finite Q will also likely widen the operating band width. What the use of the pseudo-beta match in the model obscures is the actual feedpoint impedances without the match in place. The 20-meter portion of the antenna shows a normal feedpoint impedance in the mid-20s. The 15- meter feedpoint impedance is closer to 15 ohms--a low but usable figure.

+

Beyond the feedpoint impedance, the performance of the antennas is enhanced (although not in a major way) with respect to gain on both bands. The presence of the elements for the other band adds a modicum of gain when most of the longer elements are to the rear and most of the shorter ones are to the front. However, 15-meter front-to-back ratio is down somewhat, again not too significantly except for the very upper end of the band.

+

The Results So Far: The exercise using simple models proved the principle that two 3-element beams for separate bands can be placed on a single moderate length boom in such a way as to preserve for all practical purposes the performance of each beam when used as a monobander. Although the assembly requires separate feedlines for each antenna, it is otherwise a model of simplicity, using no extra elements or components. Thus it is, in principle, amenable to straightforward construction techniques by the home builder. Incidentally, a 4-element monobander for 20 meters of about the same boom length will have a center-band gain of about 8.5-8.6 dBi, but will hold a front-to-back ratio of about 23 dB across the band. The present design places two antennas in the same space with reasonably competitive performance.

+
+

3. From Principle to Practicality

+
A Buildable Model: The initial simplified (untapered-element) model was developed to prove a principle (luckily, it was provable). However, the untapered elements are generally unsuitable for construction. Hence, the next step was to adopt a set of element tapers and redo the project. Although some readjustment of element length and spacing was anticipated, the untapered-element models provided initial guidelines on which to rapidly develop something approaching a buildable model. +

The Element Taper: For purposes of the exercise, a fairly standard set of element tapers was selected from other Yagis. The following table shows the taper chosen and represents the lengths each side of the boom the all the elements of each band:

+ 
+Band      1"        .875"     .75"      .625"     .5"  (tip section)
+20        72"       20"       42"       20"       35-62"
+15        --        30"       36"       18"       40-60"
+
+

Although other taper schedules can certainly be used, the one above will suffice for the exercise. The 20-meter schedule can be strengthened if the inner 4' of tubing is increased to 1.125" stock. As given, simple models of the individual antennas required 27 wires on 20 and 21 wires on 15, while the eventual composite model involves 48 wires. In all cases, to the degree permitted by the segmentation, individual segment lengths were equalized as much as possible, with 10" being the average segment length.

+

The Individual Antennas: Relative to the untapered models, both the 20- meter and 15-meter Yagis required adjustment both to elements lengths and to spacing. Since tapering yields an element which has a quite small effective diameter, element lengths grew. Moreover, as the performance charts below show, the front-to-back ratio available in the untapered versions could not be sustained, although the decrease is not large. Here are the wire tables and performance figures from the tapered models of individual antennas.

+ 
+Frequency = 14.15  MHz.
+
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in) Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+1      -215.00,  0.000,  0.000  W2E1 -154.00,  0.000,  0.000 5.00E-01   5
+2 W1E2 -154.00,  0.000,  0.000  W3E1 -134.00,  0.000,  0.000 6.25E-01   2
+3 W2E2 -134.00,  0.000,  0.000  W4E1 -92.000,  0.000,  0.000 7.50E-01   4
+4 W3E2 -92.000,  0.000,  0.000  W5E1 -72.000,  0.000,  0.000 8.75E-01   2
+5 W4E2 -72.000,  0.000,  0.000  W6E1  72.000,  0.000,  0.000 1.00E+00  11
+6 W5E2  72.000,  0.000,  0.000  W7E1  92.000,  0.000,  0.000 8.75E-01   2
+7 W6E2  92.000,  0.000,  0.000  W8E1 134.000,  0.000,  0.000 7.50E-01   4
+8 W7E2 134.000,  0.000,  0.000  W9E1 154.000,  0.000,  0.000 6.25E-01   2
+9 W8E2 154.000,  0.000,  0.000       215.000,  0.000,  0.000 5.00E-01   5
+10     -201.00,129.000,  0.000 W11E1 -154.00,129.000,  0.000 5.00E-01   5
+11W10E2 -154.00,129.000,  0.000 W12E1 -134.00,129.000,  0.000 6.25E-01   2
+12W11E2 -134.00,129.000,  0.000 W13E1 -92.000,129.000,  0.000 7.50E-01   4
+13W12E2 -92.000,129.000,  0.000 W14E1 -72.000,129.000,  0.000 8.75E-01   2
+14W13E2 -72.000,129.000,  0.000 W15E1  72.000,129.000,  0.000 1.00E+00  11
+15W14E2  72.000,129.000,  0.000 W16E1  92.000,129.000,  0.000 8.75E-01   2
+16W15E2  92.000,129.000,  0.000 W17E1 134.000,129.000,  0.000 7.50E-01   4
+17W16E2 134.000,129.000,  0.000 W18E1 154.000,129.000,  0.000 6.25E-01   2
+18W17E2 154.000,129.000,  0.000       201.000,129.000,  0.000 5.00E-01   5
+19      -188.00,300.000,  0.000 W20E1 -154.00,300.000,  0.000 5.00E-01   5
+20W19E2 -154.00,300.000,  0.000 W21E1 -134.00,300.000,  0.000 6.25E-01   2
+21W20E2 -134.00,300.000,  0.000 W22E1 -92.000,300.000,  0.000 7.50E-01   4
+22W21E2 -92.000,300.000,  0.000 W23E1 -72.000,300.000,  0.000 8.75E-01   2
+23W22E2 -72.000,300.000,  0.000 W24E1  72.000,300.000,  0.000 1.00E+00  11
+24W23E2  72.000,300.000,  0.000 W25E1  92.000,300.000,  0.000 8.75E-01   2
+25W24E2  92.000,300.000,  0.000 W26E1 134.000,300.000,  0.000 7.50E-01   4
+26W25E2 134.000,300.000,  0.000 W27E1 154.000,300.000,  0.000 6.25E-01   2
+27W26E2 154.000,300.000,  0.000       188.000,300.000,  0.000 5.00E-01   5
+              -------------- SOURCES --------------
+Source    Wire    Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1         6    14 / 50.00   ( 14 / 50.00)      1.000       0.000       I
+
+Fq             14.0                14.15               14.35
+Gain dBi       8.00                8.08                8.23
+F-B dB         18.36               20.75               16.44
+Feed Z ohms    27.2 - j24.0        28.0 - j12.7        27.7 + j 3.1
+
+--------------------------------------------------------------------------
+
+Frequency = 21.2  MHz.
+              --------------- WIRES ---------------
+
+Wire Conn.--- End 1 (x,y,z : in) Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+
+1       -142.50,  0.000,  0.000  W2E1 -84.000,  0.000,  0.000 5.00E-01   6
+2  W1E2 -84.000,  0.000,  0.000  W3E1 -66.000,  0.000,  0.000 6.25E-01   2
+3  W2E2 -66.000,  0.000,  0.000  W4E1 -30.000,  0.000,  0.000 7.50E-01   3
+4  W3E2 -30.000,  0.000,  0.000  W5E1  30.000,  0.000,  0.000 8.75E-01   7
+5  W4E2  30.000,  0.000,  0.000  W6E1  66.000,  0.000,  0.000 7.50E-01   3
+6  W5E2  66.000,  0.000,  0.000  W7E1  84.000,  0.000,  0.000 6.25E-01   2
+7  W6E2  84.000,  0.000,  0.000       142.500,  0.000,  0.000 5.00E-01   6
+8       -134.00, 86.000,  0.000  W9E1 -84.000, 86.000,  0.000 5.00E-01   6
+9  W8E2 -84.000, 86.000,  0.000 W10E1 -66.000, 86.000,  0.000 6.25E-01   2
+10 W9E2 -66.000, 86.000,  0.000 W11E1 -30.000, 86.000,  0.000 7.50E-01   3
+11W10E2 -30.000, 86.000,  0.000 W12E1  30.000, 86.000,  0.000 8.75E-01   7
+12W11E2  30.000, 86.000,  0.000 W13E1  66.000, 86.000,  0.000 7.50E-01   3
+13W12E2  66.000, 86.000,  0.000 W14E1  84.000, 86.000,  0.000 6.25E-01   2
+14W13E2  84.000, 86.000,  0.000       134.000, 86.000,  0.000 5.00E-01   6
+15      -125.50,200.000,  0.000 W16E1 -84.000,200.000,  0.000 5.00E-01   6
+16W15E2 -84.000,200.000,  0.000 W17E1 -66.000,200.000,  0.000 6.25E-01   2
+17W16E2 -66.000,200.000,  0.000 W18E1 -30.000,200.000,  0.000 7.50E-01   3
+18W17E2 -30.000,200.000,  0.000 W19E1  30.000,200.000,  0.000 8.75E-01   7
+19W18E2  30.000,200.000,  0.000 W20E1  66.000,200.000,  0.000 7.50E-01   3
+20W19E2  66.000,200.000,  0.000 W21E1  84.000,200.000,  0.000 6.25E-01   2
+21W20E2  84.000,200.000,  0.000       125.500,200.000,  0.000 5.00E-01   6
+              -------------- SOURCES --------------
+Source    Wire    Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1         4    11 / 50.00   ( 11 / 50.00)      1.000       0.000       I
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.05                8.14                8.27
+F-B dB         18.96               20.78               17.29
+Feed Z ohms    26.8 - j19.1        27.4 - j9.3         27.1 + j 3.5
+
+

To decrease model complexity and because the beta matches are too similar to those of the untapered models to need rerunning with this pair of models, the raw feedpoint impedances are shown in the tables. They are typical, well-behaved mid-20s values.

+

Again, the 15-meter model surpasses by amounts detectable only in models the 20-meter model because the effective diameter of the elements is slightly greater.

+

More significant are the required changes in element spacing necessary to optimize performance. The 15-meter boom grew by 16" while the 20-meter boom is over 2' longer than the untapered model boom. Moreover, the element placement for the 15-meter antenna will have to be changed from that used for the untapered model in order to set its rear 2 elements between the forward 2 20-meter elements.

+

These changes show up clearly when the antenna is modeled using the proposed element taper schedule for actual construction. Had a tapered model been built from the composite untapered model, performance would likely have been disappointing unless one were willing to spend endless hours physically juggling elements.

+

The Composite Tapered-Element 2-Band Beam: With a little tweaking here and there, the final composite model emerged. The chief mechanical difference is that the boom is now 29.5' long, barely under the 30' goal. Differences in element lengths and spacing will be clear with a little comparison with the individual tapered-element models. Similarly to the untapered-element composite model, elements are grouped by band and therefore are not in physical order. Here is the wire table for the antenna:

+ 
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+1       -214.00,  0.000,  0.000  W2E1 -154.00,  0.000,  0.000 5.00E-01   5
+2  W1E2 -154.00,  0.000,  0.000  W3E1 -134.00,  0.000,  0.000 6.25E-01   2
+3  W2E2 -134.00,  0.000,  0.000  W4E1 -92.000,  0.000,  0.000 7.50E-01   4
+4  W3E2 -92.000,  0.000,  0.000  W5E1 -72.000,  0.000,  0.000 8.75E-01   2
+5  W4E2 -72.000,  0.000,  0.000  W6E1  72.000,  0.000,  0.000 1.00E+00  11
+6  W5E2  72.000,  0.000,  0.000  W7E1  92.000,  0.000,  0.000 8.75E-01   2
+7  W6E2  92.000,  0.000,  0.000  W8E1 134.000,  0.000,  0.000 7.50E-01   4
+8  W7E2 134.000,  0.000,  0.000  W9E1 154.000,  0.000,  0.000 6.25E-01   2
+9  W8E2 154.000,  0.000,  0.000       214.000,  0.000,  0.000 5.00E-01   5
+10      -201.50,128.000,  0.000 W11E1 -154.00,128.000,  0.000 5.00E-01   5
+11W10E2 -154.00,128.000,  0.000 W12E1 -134.00,128.000,  0.000 6.25E-01   2
+12W11E2 -134.00,128.000,  0.000 W13E1 -92.000,128.000,  0.000 7.50E-01   4
+13W12E2 -92.000,128.000,  0.000 W14E1 -72.000,128.000,  0.000 8.75E-01   2
+14W13E2 -72.000,128.000,  0.000 W15E1  72.000,128.000,  0.000 1.00E+00  11
+15W14E2  72.000,128.000,  0.000 W16E1  92.000,128.000,  0.000 8.75E-01   2
+16W15E2  92.000,128.000,  0.000 W17E1 134.000,128.000,  0.000 7.50E-01   4
+17W16E2 134.000,128.000,  0.000 W18E1 154.000,128.000,  0.000 6.25E-01   2
+18W17E2 154.000,128.000,  0.000       201.500,128.000,  0.000 5.00E-01   5
+19      -188.50,298.000,  0.000 W20E1 -154.00,298.000,  0.000 5.00E-01   5
+20W19E2 -154.00,298.000,  0.000 W21E1 -134.00,298.000,  0.000 6.25E-01   2
+21W20E2 -134.00,298.000,  0.000 W22E1 -92.000,298.000,  0.000 7.50E-01   4
+22W21E2 -92.000,298.000,  0.000 W23E1 -72.000,298.000,  0.000 8.75E-01   2
+23W22E2 -72.000,298.000,  0.000 W24E1  72.000,298.000,  0.000 1.00E+00  11
+24W23E2  72.000,298.000,  0.000 W25E1  92.000,298.000,  0.000 8.75E-01   2
+25W24E2  92.000,298.000,  0.000 W26E1 134.000,298.000,  0.000 7.50E-01   4
+26W25E2 134.000,298.000,  0.000 W27E1 154.000,298.000,  0.000 6.25E-01   2
+27W26E2 154.000,298.000,  0.000       188.500,298.000,  0.000 5.00E-01   5
+28      -141.00,164.000,  0.000 W29E1 -84.000,164.000,  0.000 5.00E-01   6
+29W28E2 -84.000,164.000,  0.000 W30E1 -66.000,164.000,  0.000 6.25E-01   2
+30W29E2 -66.000,164.000,  0.000 W31E1 -30.000,164.000,  0.000 7.50E-01   3
+31W30E2 -30.000,164.000,  0.000 W32E1  30.000,164.000,  0.000 8.75E-01   7
+32W31E2  30.000,164.000,  0.000 W33E1  66.000,164.000,  0.000 7.50E-01   3
+33W32E2  66.000,164.000,  0.000 W34E1  84.000,164.000,  0.000 6.25E-01   2
+34W33E2  84.000,164.000,  0.000       141.000,164.000,  0.000 5.00E-01   6
+35      -134.50,255.000,  0.000 W36E1 -84.000,255.000,  0.000 5.00E-01   6
+36W35E2 -84.000,255.000,  0.000 W37E1 -66.000,255.000,  0.000 6.25E-01   2
+37W36E2 -66.000,255.000,  0.000 W38E1 -30.000,255.000,  0.000 7.50E-01   3
+38W37E2 -30.000,255.000,  0.000 W39E1  30.000,255.000,  0.000 8.75E-01   7
+39W38E2  30.000,255.000,  0.000 W40E1  66.000,255.000,  0.000 7.50E-01   3
+40W39E2  66.000,255.000,  0.000 W41E1  84.000,255.000,  0.000 6.25E-01   2
+41W40E2  84.000,255.000,  0.000       134.500,255.000,  0.000 5.00E-01   6
+42      -129.00,354.000,  0.000 W43E1 -84.000,354.000,  0.000 5.00E-01   6
+43W42E2 -84.000,354.000,  0.000 W44E1 -66.000,354.000,  0.000 6.25E-01   2
+44W43E2 -66.000,354.000,  0.000 W45E1 -30.000,354.000,  0.000 7.50E-01   3
+45W44E2 -30.000,354.000,  0.000 W46E1  30.000,354.000,  0.000 8.75E-01   7
+46W45E2  30.000,354.000,  0.000 W47E1  66.000,354.000,  0.000 7.50E-01   3
+47W46E2  66.000,354.000,  0.000 W48E1  84.000,354.000,  0.000 6.25E-01   2
+48W47E2  84.000,354.000,  0.000       129.000,354.000,  0.000 5.00E-01   6
+             -------------- SOURCES --------------
+Source    Wire    Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+For 15 meters
+1         4    38 / 50.00   ( 38 / 50.00)      1.000       0.000       I
+For 20 meters
+1         4    14 / 50.00   ( 14 / 50.00)      1.000       0.000       I
+
+
+ +
+

As with the individual models, the pseudo-beta matches have been omitted from both the wire table and the impedance figures below. The following table will illustrate the range of impedances to be matched, by whatever means a given builder prefers.

+ 
Fq             14.0                14.15               14.35
+Gain dBi       8.19                8.29                8.42
+F-B dB         17.64               20.47               16.50
+Feed Z ohms    24.5 - j26.5        25.8 - j14.5        26.4 + j 2.0
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.25                8.37                8.60
+F-B dB         17.59               19.39               15.44
+Feed Z ohms    14.0 - j17.6        14.8 - j 7.6        14.1 + j 5.1
+

Just as before, the array slightly enhances gain and detracts by a comparable amount from the front-to-back ratio compared to the individual beams. 15-meter feedpoint impedance is low but manageable.

+

This model--or some variant of it--appears to be a very buildable dual 3- element Yagi, for someone so inclined.

+

The Result: The staggered array is not a new idea; rather, it is an idea that needed a little refreshing. In the search for means of using a single feedline and then complicating the sequence of elements on the way to a multiband beam that approximates 3-element Yagi performance, we often forget that there may be more direct routes to a goal, especially if one does not have access to an engineering department for all the hours of design work needed. The 2-band composite beam shown here may be one practical solution within the reach of a home builder.

+

Although the beam itself is highly interesting and instructive with respect to the question of uncaging Yagi performance in a multiband array, this note has primarily recorded an exercise in the progression of modeling from developing a potential project through proving the principle to finalizing a buildable antenna. By letting the surprises and major adjustments be functions of the model, construction time and "What-do-I- do-next?" time for such an antenna as this is minimized.

+

However, do not expect models to be precision plans for an actual antenna. Unless you take steps to eliminate all factors that can interfere with the translation of the model into physical reality, further adjustments will be needed during the building and tuning process. Indeed, eliminating the bumps and couplings natural to the use of real materials is rarely possible without weakening the antenna structure. Nonetheless, a modeling exercise like this one--applied to your own pet project--can maximize productive time and minimize the frustration of not knowing what to do next to peak the antenna performance.

+

The result of the exercise is also a quite feasible antenna for the home builder. Both bands ought to compete well with any 3-element Yagi monobander and with most tri-banders (on two of the bands). The 6 simple elements ought to hold up for years--although annual maintenance is always to be recommended.

+
+

Addendum 1: A 2007 Update from K7JA

+
+

In April, 2007, Chip Margelli, K7JA, sent me information on an interesting variation of the original 2-band, 3-element/band staggered Yagi design. Chip had a few local goals. First, he wanted to re-use some materials from a commercial beam with which he was dissatisfied. Second, he wanted to overcome the somewhat finicky matching requirements on 15 meters in the original design. One way to do this was to achieve a 50-Ohm feedpoint on each of the two bands. Since he had the materials, he added to each beam a secondary driver (or, if you wish, a new first director) closely spaced to the original driver to control both the operating bandwidth and the impedance. It is a technique that appears in other designs in these pages and derives ultimately from the OWA work of KW3Z. Chip's redesign makes use of the original design's elements and simply adds 2 new secondary drivers, as indicated in the outline below.

+
+ +
+

The model for Chip's new beam appears in the EZNEC description that follows. The element diameters and individual element section lengths are a function of re-using existing materials.

+ 
+                      EZNEC/4 ver. 4.0
+Dipole in free space                         4/16/2007     9:20:44 AM
+
+         --------------- ANTENNA DESCRIPTION ---------------
+Frequency = 14.175 MHz
+Wire Loss: Aluminum (6061-T6) -- Resistivity = 4E-08 ohm-m, Rel. Perm. = 1
+
+              --------------- WIRES ---------------
+No.            End 1     Coord. (in)              End 2     Coord. (in)       Dia (in)  Segs       Insulation
+          Conn.      X       Y       Z       Conn.      X       Y       Z                   Diel C  Thk(in) Loss Tan
+1                   -215,      0,    840      W2E1     -154,      0,    840       0.5   5       1        0        0
+2          W1E2     -154,      0,    840      W3E1     -134,      0,    840     0.625   2       1        0        0
+3          W2E2     -134,      0,    840      W4E1      -92,      0,    840      0.75   4       1        0        0
+4          W3E2      -92,      0,    840      W5E1      -72,      0,    840     0.875   2       1        0        0
+5          W4E2      -72,      0,    840      W6E1       72,      0,    840         1   11       1        0        0
+6          W5E2       72,      0,    840      W7E1       92,      0,    840     0.875   2       1        0        0
+7          W6E2       92,      0,    840      W8E1      134,      0,    840      0.75   4       1        0        0
+8          W7E2      134,      0,    840      W9E1      154,      0,    840     0.625   2       1        0        0
+9          W8E2      154,      0,    840                215,      0,    840       0.5   5       1        0        0
+10                  -210,    128,    840     W11E1     -154,    128,    840       0.5   5       1        0        0
+11        W10E2     -154,    128,    840     W12E1     -134,    128,    840     0.625   2       1        0        0
+12        W11E2     -134,    128,    840     W13E1      -92,    128,    840      0.75   4       1        0        0
+13        W12E2      -92,    128,    840     W14E1      -72,    128,    840     0.875   2       1        0        0
+14        W13E2      -72,    128,    840     W15E1       72,    128,    840         1   11       1        0        0
+15        W14E2       72,    128,    840     W16E1       92,    128,    840     0.875   2       1        0        0
+16        W15E2       92,    128,    840     W17E1      134,    128,    840      0.75   4       1        0        0
+17        W16E2      134,    128,    840     W18E1      154,    128,    840     0.625   2       1        0        0
+18        W17E2      154,    128,    840                210,    128,    840       0.5   5       1        0        0
+19                -188.5,    298,    840     W20E1     -154,    298,    840       0.5   5       1        0        0
+20        W19E2     -154,    298,    840     W21E1     -134,    298,    840     0.625   2       1        0        0
+21        W20E2     -134,    298,    840     W22E1      -92,    298,    840      0.75   4       1        0        0
+22        W21E2      -92,    298,    840     W23E1      -72,    298,    840     0.875   2       1        0        0
+23        W22E2      -72,    298,    840     W24E1       72,    298,    840         1   11       1        0        0
+24        W23E2       72,    298,    840     W25E1       92,    298,    840     0.875   2       1        0        0
+25        W24E2       92,    298,    840     W26E1      134,    298,    840      0.75   4       1        0        0
+26        W25E2      134,    298,    840     W27E1      154,    298,    840     0.625   2       1        0        0
+27        W26E2      154,    298,    840              188.5,    298,    840       0.5   5       1        0        0
+28                  -142,    164,    840     W29E1      -84,    164,    840       0.5   6       1        0        0
+29        W28E2      -84,    164,    840     W30E1      -66,    164,    840     0.625   2       1        0        0
+30        W29E2      -66,    164,    840     W31E1      -30,    164,    840      0.75   3       1        0        0
+31        W30E2      -30,    164,    840     W32E1       30,    164,    840     0.875   7       1        0        0
+32        W31E2       30,    164,    840     W33E1       66,    164,    840      0.75   3       1        0        0
+33        W32E2       66,    164,    840     W34E1       84,    164,    840     0.625   2       1        0        0
+34        W33E2       84,    164,    840                142,    164,    840       0.5   6       1        0        0
+35                  -139,    255,    840     W36E1      -84,    255,    840       0.5   6       1        0        0
+36        W35E2      -84,    255,    840     W37E1      -66,    255,    840     0.625   2       1        0        0
+37        W36E2      -66,    255,    840     W38E1      -30,    255,    840      0.75   3       1        0        0
+38        W37E2      -30,    255,    840     W39E1       30,    255,    840     0.875   7       1        0        0
+39        W38E2       30,    255,    840     W40E1       66,    255,    840      0.75   3       1        0        0
+40        W39E2       66,    255,    840     W41E1       84,    255,    840     0.625   2       1        0        0
+41        W40E2       84,    255,    840                139,    255,    840       0.5   6       1        0        0
+42                  -129,    354,    840     W43E1      -84,    354,    840       0.5   6       1        0        0
+43        W42E2      -84,    354,    840     W44E1      -66,    354,    840     0.625   2       1        0        0
+44        W43E2      -66,    354,    840     W45E1      -30,    354,    840      0.75   3       1        0        0
+45        W44E2      -30,    354,    840     W46E1       30,    354,    840     0.875   7       1        0        0
+46        W45E2       30,    354,    840     W47E1       66,    354,    840      0.75   3       1        0        0
+47        W46E2       66,    354,    840     W48E1       84,    354,    840     0.625   2       1        0        0
+48        W47E2       84,    354,    840                129,    354,    840       0.5   6       1        0        0
+49                  -136,    280,    840     W50E1      -84,    280,    840       0.5   6       1        0        0
+50        W49E2      -84,    280,    840     W51E1      -66,    280,    840     0.625   2       1        0        0
+51        W50E2      -66,    280,    840     W52E1      -30,    280,    840      0.75   3       1        0        0
+52        W51E2      -30,    280,    840     W53E1       30,    280,    840     0.875   7       1        0        0
+53        W52E2       30,    280,    840     W54E1       66,    280,    840      0.75   3       1        0        0
+54        W53E2       66,    280,    840     W55E1       84,    280,    840     0.625   2       1        0        0
+55        W54E2       84,    280,    840                136,    280,    840       0.5   6       1        0        0
+56                  -198,    154,    840     W57E1     -154,    154,    840       0.5   5       1        0        0
+57        W56E2     -154,    154,    840     W58E1     -134,    154,    840     0.625   2       1        0        0
+58        W57E2     -134,    154,    840     W59E1      -92,    154,    840      0.75   4       1        0        0
+59        W58E2      -92,    154,    840     W60E1      -72,    154,    840     0.875   2       1        0        0
+60        W59E2      -72,    154,    840     W61E1       72,    154,    840         1   11       1        0        0
+61        W60E2       72,    154,    840     W62E1       92,    154,    840     0.875   2       1        0        0
+62        W61E2       92,    154,    840     W63E1      134,    154,    840      0.75   4       1        0        0
+63        W62E2      134,    154,    840     W64E1      154,    154,    840     0.625   2       1        0        0
+64        W63E2      154,    154,    840                198,    154,    840       0.5   5       1        0        0
+
+Total Segments: 264
+
+              -------------- SOURCES --------------
+No.      Specified Pos.     Actual Pos.      Amplitude    Phase    Type
+       Wire #  % From E1  % From E1  Seg       (V/A)     (deg.)
+1       14       50.00      50.00    6        1           0         I  20-meter feedpoint
+(1      38       50.00      50.00    6        1           0         I  15-meter feedpoint)
+
+

The modeled performance is equal to the performance of the original with two exceptions. First, the re-design improves the front-to-back ratio across both bands. Second, we can add 50-Ohm SWR values to the performance table to show the smooth curves that promise relatively easy initial tune-up of the beam. The values suggest that high-power amplifiers with sensitive fold-back circuits will not encounter power-reducing SWR values.

+ 
+Modeled free-space performance of the K8JA revised staggered 2-band beam
+
+Fq             14.0                14.15               14.35
+Gain dBi       8.21                8.30                8.44
+F-B dB         22.30               22.98               17.99
+Feed Z ohms    53.8 - j 5.7        61.4 - j 1.6        75.2 - j 4.1
+50-Ohm SWR     1.14                1.23                1.46
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.11                8.20                8.33
+F-B dB         21.53               24.73               18.33
+Feed Z ohms    45.5 + j 4.8        55.5 - j 0.7        51.7 - j17.7
+50-Ohm SWR     1.15                1.11                1.42
+
+

Chip's re-designed staggered Yagi for 20 and 15 meters also makes a handsome addition to his tower of beams, as shown in the photo. The guardian bird apparently is optional--with the whim of the bird.

+
+ +
+

K7JA's revised stagger design not only proves the principles behind the original design, but makes significant improvements. Amateurs are reticent to use more aluminum than the absolute minimum. However, Chip's addition of secondary drivers confirms that we may often profitably add an element to improve performance. The improvement may not show up in terms of gain--largely a function of the boom length--but may allow us to achieve a broader operating bandwidth in all categories of performance.

+
+

Addendum 2: Can It Be done With 4 Elements Each?

+
The Basic Beams: Yes, it is possible to create a similar combination beam using 4-element Yagis as the basis. Once more I began with a K6STI design for a 26' boom, not much longer than the 24' boom used for the basic 3- element 20-meter beam. I set up the Yagis using 0.75" tubing for 20 and 0.5" tubing for 15. (What this means is that I scaled the 20-meter antenna to 15 meters and accepted the resulting dimensions without further ado.) Here are the wire tables and performance numbers. + 
+20 Meters
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+1       -208.50,  0.000,  0.000       208.500,  0.000,  0.000 7.50E-01  21
+2       -197.00, 72.000,  0.000       197.000, 72.000,  0.000 7.50E-01  21
+3       -195.40,132.000,  0.000       195.400,132.000,  0.000 7.50E-01  21
+4       -183.10,306.000,  0.000       183.100,306.000,  0.000 7.50E-01  21
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+Fq             14.0                14.15               14.35
+Gain dBi       8.41                8.49                8.62
+F-B dB         21.31               23.48               21.73
+Feed Z ohms    25.2 - j32.7        28.0 - j30.3        19.8 - j25.2
+
+----------------------------------------------------------------------
+
+15 Meters
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+1       -139.00,  0.000,  0.000       139.000,  0.000,  0.000 5.00E-01  15
+2       -131.33, 48.000,  0.000       131.333, 48.000,  0.000 5.00E-01  15
+3       -130.27, 88.000,  0.000       130.267, 88.000,  0.000 5.00E-01  15
+4       -122.07,204.000,  0.000       122.067,204.000,  0.000 5.00E-01  15
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+
+1          11     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.41                8.48                8.58
+F-B dB         21.32               23.67               21.71
+Feed Z ohms    25.2 - j32.7        28.0 - j29.9        23.0 - j27.2
+
+

The chief advantage of these antennas over the 3-element models is a smoother performance across the bands of interest, both in terms of gain and front-to-back ratio. Notice also from the wire charts that these beams concentrate the three rear-most elements together, with the most forward director well-spaced from the other elements.

+

The Combination: I only checked these antennas at the level of principle, so the following scheme might require significant variation before achieving a workable beam with stepped-diameter elements. Nonetheless, the combination works well in principle, preserving most of the front-to-back ratio and enhancing the forward gain slightly.

+
+ +
+

The largest drawback to this configuration is the very low feedpoint impedance imposed on the 15-meter beam.

+

The required configuration places 2 of the directors forward of the forward-most 20-meter director, creating a beam needing a 38' boom. Whether the gains over the dual 3-element array outweigh the disadvantages of the longer boom and lower 15-meter feedpoint impedance is a builder decision.

+

Here is the wire table:

+ 
+              --------------- WIRES ---------------
+Wire Conn.--- End 1 (x,y,z : in)  Conn.--- End 2 (x,y,z : in) Dia(in) Segs
+1       -139.00,250.000,  0.000       139.000,250.000,  0.000 5.00E-01  15
+2       -133.50,298.000,  0.000       133.500,298.000,  0.000 5.00E-01  15
+3       -130.27,338.000,  0.000       130.267,338.000,  0.000 5.00E-01  15
+4       -122.07,454.000,  0.000       122.067,454.000,  0.000 5.00E-01  15
+5       -210.00,  0.000,  0.000       210.000,  0.000,  0.000 7.50E-01  21
+6       -199.00, 72.000,  0.000       199.000, 72.000,  0.000 7.50E-01  21
+7       -195.40,132.000,  0.000       195.400,132.000,  0.000 7.50E-01  21
+8       -182.00,306.000,  0.000       182.000,306.000,  0.000 7.50E-01  21
+             -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           8     2 / 50.00   (  2 / 50.00)      1.000       0.000       I
+(15-meter source shown--20-meter source is 2/50.)
+
+

In this table, the 15 meter elements appear first.

+

The performance of the model is as follows:

+ 
+Fq             14.0                14.15               14.35
+Gain dBi       8.61                8.66                8.77
+F-B dB         20.92               20.30               21.29
+Feed Z ohms    30.0 - j22.1        32.4 - j21.6        20.95- j17.8
+
+Fq             21.0                21.2                21.45
+Gain dBi       8.42                8.51                8.66
+F-B dB         22.69               21.66               20.33
+Feed Z ohms    9.83 - j22.5        8.18 - j14.6        10.0 - j 7.4
+
+

Remember that all performance numbers are subject to variations, with gains varying as much as 0.1 dB and front-to-back ratios changing by as much as 1 dB, depending upon the particular modeling software used (assuming that the models are comparable to begin with).

+

This model suggests that a dual 4-element Yagi system is feasible, but may be approaching the limits of the technique. The boom has grown significantly, and the 15-meter feedpoint impedance has decreased to a level where physical connection losses begin to counteract gain improvements. Increasing the 15-meter feedpoint impedance requires element placement or dimensions that either reduce 15 meter gain or narrow the performance bandwidth on that band.

+

Further optimizing is possible and would certainly be necessary for a set of stepped-diameter elements.

+

A Tapered-Element Test: For some time after working with the 4-element Yagis with uniform element diameters, I hesitated to devote the time to exploring what might happen with Yagis using tapered-diameter elements. However, Gene, UA4RZ, asked me to look into some beam designs he was working on, so the time was right to try the staggered system on some designs one might really build. The beams employ, in good and traditional ham fashion, element materials that are accessible to the builder.

+

First, the models: It was necessary to make two minor modifications to Gene's models. I eliminated a 0.1" section of 0.85" diameter tubing from the 20 meter reflector and director, absorbing the 0.1" length in the adjacent section. This allowed me to use segments just about 10" long, which is close to the length of the center section. I also reduced the center section diameter to 2" diameter, because NEC-4 still has some limitations when the diameter of an element changes too much too abruptly.

+

20 meter antenna:

+ 
+Frequency = 14.175  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -217.63,  0.000,  0.000  W2E1 -164.10,  0.000,  0.000 7.00E-01   5
+2     W1E2 -164.10,  0.000,  0.000  W3E1 -89.000,  0.000,  0.000 1.20E+00   7
+3     W2E2 -89.000,  0.000,  0.000  W4E1  -4.000,  0.000,  0.000 1.50E+00   8
+4     W3E2  -4.000,  0.000,  0.000  W5E1   4.000,  0.000,  0.000 2.00E+00   1
+5     W4E2   4.000,  0.000,  0.000  W6E1  89.000,  0.000,  0.000 1.50E+00   8
+6     W5E2  89.000,  0.000,  0.000  W7E1 164.100,  0.000,  0.000 1.20E+00   7
+7     W6E2 164.100,  0.000,  0.000       217.634,  0.000,  0.000 7.00E-01   5
+8          -201.30, 71.995,  0.000  W9E1 -189.00, 71.995,  0.000 8.50E-01   1
+9     W8E2 -189.00, 71.995,  0.000 W10E1 -89.000, 71.995,  0.000 1.20E+00  10
+10    W9E2 -89.000, 71.995,  0.000 W11E1  -4.000, 71.995,  0.000 1.50E+00   8
+11   W10E2  -4.000, 71.995,  0.000 W12E1   4.000, 71.995,  0.000 2.00E+00   1
+12   W11E2   4.000, 71.995,  0.000 W13E1  89.000, 71.995,  0.000 1.50E+00   8
+13   W12E2  89.000, 71.995,  0.000 W14E1 189.000, 71.995,  0.000 1.20E+00  10
+14   W13E2 189.000, 71.995,  0.000       201.302, 71.995,  0.000 8.50E-01   1
+15         -197.00,131.990,  0.000 W16E1 -189.00,131.990,  0.000 8.50E-01   1
+16   W15E2 -189.00,131.990,  0.000 W17E1 -89.000,131.990,  0.000 1.20E+00  10
+17   W16E2 -89.000,131.990,  0.000 W18E1  -4.000,131.990,  0.000 1.50E+00   8
+18   W17E2  -4.000,131.990,  0.000 W19E1   4.000,131.990,  0.000 2.00E+00   1
+19   W18E2   4.000,131.990,  0.000 W20E1  89.000,131.990,  0.000 1.50E+00   8
+20   W19E2  89.000,131.990,  0.000 W21E1 189.000,131.990,  0.000 1.20E+00  10
+21   W20E2 189.000,131.990,  0.000       197.003,131.990,  0.000 8.50E-01   1
+22         -183.53,305.977,  0.000 W23E1 -164.10,305.977,  0.000 7.00E-01   2
+23   W22E2 -164.10,305.977,  0.000 W24E1 -89.000,305.977,  0.000 1.20E+00   7
+24   W23E2 -89.000,305.977,  0.000 W25E1  -4.000,305.977,  0.000 1.50E+00   8
+25   W24E2  -4.000,305.977,  0.000 W26E1   4.000,305.977,  0.000 2.00E+00   1
+26   W25E2   4.000,305.977,  0.000 W27E1  89.000,305.977,  0.000 1.50E+00   8
+27   W26E2  89.000,305.977,  0.000 W28E1 164.100,305.977,  0.000 1.20E+00   7
+28   W27E2 164.100,305.977,  0.000       183.529,305.977,  0.000 7.00E-01   2
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1    11 / 50.00   ( 11 / 50.00)      1.000       0.000       V
+
+

Gain: 8.77 dBi free space
+ F-B: 23.26 dB
+ Source impedance: 25.96 - j21.76 ohms (about right for a beta match)

+

15 meter antenna:

+ 
+Frequency = 21.224  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -142.01,  0.000,  0.000  W2E1 -114.00,  0.000,  0.000 7.00E-01   3
+2     W1E2 -114.00,  0.000,  0.000  W3E1  -4.000,  0.000,  0.000 1.00E+00  11
+3     W2E2  -4.000,  0.000,  0.000  W4E1   4.000,  0.000,  0.000 2.00E+00   1
+4     W3E2   4.000,  0.000,  0.000  W5E1 114.000,  0.000,  0.000 1.00E+00  11
+5     W4E2 114.000,  0.000,  0.000       142.013,  0.000,  0.000 7.00E-01   3
+6          -133.99, 48.000,  0.000  W7E1 -114.00, 48.000,  0.000 7.00E-01   2
+7     W6E2 -114.00, 48.000,  0.000  W8E1  -4.000, 48.000,  0.000 1.00E+00  11
+8     W7E2  -4.000, 48.000,  0.000  W9E1   4.000, 48.000,  0.000 2.00E+00   1
+9     W8E2   4.000, 48.000,  0.000 W10E1 114.000, 48.000,  0.000 1.00E+00  11
+10    W9E2 114.000, 48.000,  0.000       133.995, 48.000,  0.000 7.00E-01   2
+11         -129.89, 82.000,  0.000 W12E1 -114.00, 82.000,  0.000 7.00E-01   2
+12   W11E2 -114.00, 82.000,  0.000 W13E1  -4.000, 82.000,  0.000 1.00E+00  11
+13   W12E2  -4.000, 82.000,  0.000 W14E1   4.000, 82.000,  0.000 2.00E+00   1
+14   W13E2   4.000, 82.000,  0.000 W15E1 114.000, 82.000,  0.000 1.00E+00  11
+15   W14E2 114.000, 82.000,  0.000       129.888, 82.000,  0.000 7.00E-01   2
+16         -119.54,198.000,  0.000 W17E1 -114.00,198.000,  0.000 7.00E-01   1
+17   W16E2 -114.00,198.000,  0.000 W18E1  -4.000,198.000,  0.000 1.00E+00  11
+18   W17E2  -4.000,198.000,  0.000 W19E1   4.000,198.000,  0.000 2.00E+00   1
+19   W18E2   4.000,198.000,  0.000 W20E1 114.000,198.000,  0.000 1.00E+00  11
+20   W19E2 114.000,198.000,  0.000       119.539,198.000,  0.000 7.00E-01   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1     8 / 50.00   (  8 / 50.00)      1.000       0.000       V
+
+

Gain: 8.76 dBi free space
+ F-B: 22.97 dB
+ Source impedance: 31.7 - j16.41 ohms

+

Combination: I staggered the 15 meter antenna interlaced with the 20. Initially, I placed the reflector at 177" from the 0-point of the 20 meter reflector. This placed all but the forward director between the two 20- meter directors. I then moved the 15 meter assembly forward in 10" increments (reference to the reflector) until the inner director on 15 and the outer director on 20 were nearly touching. Here is what I got:

+ 
+15 Ref         20 meters                     15 meters
+from 0    Gain      F-B       Feed Z         Gain      F-B       Feed Z
+177       8.96      20.64     26.5-19.5      8.26      15.73     58.5-2.0
+187       8.98      20.46     26.9-19.5      8.38      15.74     46.5+11.7
+197       8.99      20.33     27.3-19.5      8.47      15.63     30.1+15.6
+207       9.00      20.28     27.6-19.6      8.51      15.30     16.7+11.6
+217       9.01      20.40     27.7-19.9      8.50      14.55      8.0+4.4
+

Here, I ran out of room, but the 15 meter F-B is still low, while the 15 meter feed Z goes very low. 20-meters is hardly affected at all. So I moved the 15 meter antenna 20" forward, which places the two directors in front of the 20 meter forward director.

+ 
+237       9.05      20.02     28.7-20.4      8.67      17.46      6.8-5.8
+247       9.07      19.98     29.1-20.9      8.75      19.86      5.8-13.9
+250       9.08      19.92     29.1-21.1      8.78      20.49      4.7-17.0
+
+

Here I again ran out of room. The 15 meter gain is up, and the F-B is climbing, but the feed Z is very very low. So I moved all but the reflector ahead of the 20-meter forward director.

+ 
+270       9.13      19.53     30.0-22.1      8.62      24.42     14.9-17.1
+275       9.15      19.42     30.2-22.4      8.62      24.38     19.8-16.2
+280       9.16      19.36     30.3-22.8      8.62      24.24     23.6-16.1
+
+

This last position or two (15 meter reflector at 275 or 280 inches forward of the 20-meter reflector) appear to be the best compromise for both antennas. However, the total assembly is longer than the monotapered version in the original study. Nonetheless, if a 40' boom is feasible, the pair of antennas would just about fit and give a very good account of themselves. Of course, one can always select one of the intermediate settings, going all the way back to the 177" mark, if slightly lower gain and F-B is acceptable on 15.

+

For reference, here is the description of the model in the final position:

+ 
+Frequency = 14.175  MHz.
+Wire Loss: Copper -- Resistivity = 1.74E-08 ohm-m, Rel. Perm. = 1
+              --------------- WIRES ---------------
+Wire Conn. --- End 1 (x,y,z : in)  Conn. --- End 2 (x,y,z : in)   Dia(in) Segs
+1          -217.63,  0.000,  0.000  W2E1 -164.10,  0.000,  0.000 7.00E-01   5
+2     W1E2 -164.10,  0.000,  0.000  W3E1 -89.000,  0.000,  0.000 1.20E+00   7
+3     W2E2 -89.000,  0.000,  0.000  W4E1  -4.000,  0.000,  0.000 1.50E+00   8
+4     W3E2  -4.000,  0.000,  0.000  W5E1   4.000,  0.000,  0.000 2.00E+00   1
+5     W4E2   4.000,  0.000,  0.000  W6E1  89.000,  0.000,  0.000 1.50E+00   8
+6     W5E2  89.000,  0.000,  0.000  W7E1 164.100,  0.000,  0.000 1.20E+00   7
+7     W6E2 164.100,  0.000,  0.000       217.634,  0.000,  0.000 7.00E-01   5
+8          -201.30, 71.995,  0.000  W9E1 -189.00, 71.995,  0.000 8.50E-01   1
+9     W8E2 -189.00, 71.995,  0.000 W10E1 -89.000, 71.995,  0.000 1.20E+00  10
+10    W9E2 -89.000, 71.995,  0.000 W11E1  -4.000, 71.995,  0.000 1.50E+00   8
+11   W10E2  -4.000, 71.995,  0.000 W12E1   4.000, 71.995,  0.000 2.00E+00   1
+12   W11E2   4.000, 71.995,  0.000 W13E1  89.000, 71.995,  0.000 1.50E+00   8
+13   W12E2  89.000, 71.995,  0.000 W14E1 189.000, 71.995,  0.000 1.20E+00  10
+14   W13E2 189.000, 71.995,  0.000       201.302, 71.995,  0.000 8.50E-01   1
+15         -197.00,131.990,  0.000 W16E1 -189.00,131.990,  0.000 8.50E-01   1
+16   W15E2 -189.00,131.990,  0.000 W17E1 -89.000,131.990,  0.000 1.20E+00  10
+17   W16E2 -89.000,131.990,  0.000 W18E1  -4.000,131.990,  0.000 1.50E+00   8
+18   W17E2  -4.000,131.990,  0.000 W19E1   4.000,131.990,  0.000 2.00E+00   1
+19   W18E2   4.000,131.990,  0.000 W20E1  89.000,131.990,  0.000 1.50E+00   8
+20   W19E2  89.000,131.990,  0.000 W21E1 189.000,131.990,  0.000 1.20E+00  10
+21   W20E2 189.000,131.990,  0.000       197.003,131.990,  0.000 8.50E-01   1
+22         -183.53,305.977,  0.000 W23E1 -164.10,305.977,  0.000 7.00E-01   2
+23   W22E2 -164.10,305.977,  0.000 W24E1 -89.000,305.977,  0.000 1.20E+00   7
+24   W23E2 -89.000,305.977,  0.000 W25E1  -4.000,305.977,  0.000 1.50E+00   8
+25   W24E2  -4.000,305.977,  0.000 W26E1   4.000,305.977,  0.000 2.00E+00   1
+26   W25E2   4.000,305.977,  0.000 W27E1  89.000,305.977,  0.000 1.50E+00   8
+27   W26E2  89.000,305.977,  0.000 W28E1 164.100,305.977,  0.000 1.20E+00   7
+28   W27E2 164.100,305.977,  0.000       183.529,305.977,  0.000 7.00E-01   2
+29         -142.01,280.000,  0.000 W30E1 -114.00,280.000,  0.000 7.00E-01   3
+30   W29E2 -114.00,280.000,  0.000 W31E1  -4.000,280.000,  0.000 1.00E+00  11
+31   W30E2  -4.000,280.000,  0.000 W32E1   4.000,280.000,  0.000 2.00E+00   1
+32   W31E2   4.000,280.000,  0.000 W33E1 114.000,280.000,  0.000 1.00E+00  11
+33   W32E2 114.000,280.000,  0.000       142.013,280.000,  0.000 7.00E-01   3
+34         -133.99,328.000,  0.000 W35E1 -114.00,328.000,  0.000 7.00E-01   2
+35   W34E2 -114.00,328.000,  0.000 W36E1  -4.000,328.000,  0.000 1.00E+00  11
+36   W35E2  -4.000,328.000,  0.000 W37E1   4.000,328.000,  0.000 2.00E+00   1
+37   W36E2   4.000,328.000,  0.000 W38E1 114.000,328.000,  0.000 1.00E+00  11
+38   W37E2 114.000,328.000,  0.000       133.995,328.000,  0.000 7.00E-01   2
+39         -129.89,362.000,  0.000 W40E1 -114.00,362.000,  0.000 7.00E-01   2
+40   W39E2 -114.00,362.000,  0.000 W41E1  -4.000,362.000,  0.000 1.00E+00  11
+41   W40E2  -4.000,362.000,  0.000 W42E1   4.000,362.000,  0.000 2.00E+00   1
+42   W41E2   4.000,362.000,  0.000 W43E1 114.000,362.000,  0.000 1.00E+00  11
+43   W42E2 114.000,362.000,  0.000       129.888,362.000,  0.000 7.00E-01   2
+44         -119.54,478.000,  0.000 W45E1 -114.00,478.000,  0.000 7.00E-01   1
+45   W44E2 -114.00,478.000,  0.000 W46E1  -4.000,478.000,  0.000 1.00E+00  11
+46   W45E2  -4.000,478.000,  0.000 W47E1   4.000,478.000,  0.000 2.00E+00   1
+47   W46E2   4.000,478.000,  0.000 W48E1 114.000,478.000,  0.000 1.00E+00  11
+48   W47E2 114.000,478.000,  0.000       119.539,478.000,  0.000 7.00E-01   1
+              -------------- SOURCES --------------
+Source    Wire      Wire #/Pct From End 1    Ampl.(V, A)  Phase(Deg.)  Type
+          Seg.     Actual      (Specified)
+1           1    11 / 50.00   ( 11 / 50.00)      1.000       0.000       V
+20-meter Source location shown.  15-meter (21.224 MHz) source is Wire 36.
+
+

The size of this file suggests why I hesitated to place something this size on line. (On the other hand, compared to some models, this one is rather small.) However, the opportunity to work with a model of a beam someone might actually build seemed worth the effort. As the following figure of the final version of the model shows, the untapered 4-4 model was optimistic in its length, since it did not show quite so severe a reduction in feedpoint impedance with two of the 15-meter elements inside the forward 20-meter director. With tapered elements of the types proposed, a workable feedpoint impedance only occurs if three of the 15-meter elements are forward of the forward-most 20-meter director.

+
+ +
+

Is this the only way to get full performance from a dual-band beam? Not necessarily. What this study has shown is simply one way to get virtually the full performance of individual beams of a given boom length and number of elements when combined in-line and at least somewhat interlaced. There are other approaches, such as changing the relative element spacings and element lengths, and possibly ending up with tighter interlacing with full performance for the boom length assigned to each band. These days, such beams are produced largely with reiterative optimizing techniques rather than the simplified technique used here of simply moving the elements as a group. The optimizing techniques, however, do not always guarantee success in achieving full boomlength-number of elements performance for the Yagis interlaced.

+
+ +
+

Updated 03-07-1998, 04-20-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

+
+ +
+

Go to Amateur Radio Page

+

Topics: HF Upper, Yagi


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+

Yagi Element Diameter
+ Differences Do Make a Difference

+
+
+

L. B. Cebik, W4RNL

+
+
+ +

+
+

I often hear a complaint: "I built my Yagi to the exact dimensions in the book (or magazine or web page). It works OK, but not nearly as good as the author claims."

+

About 10 years ago, this complaint often revealed that the author had over-estimated the performance of his antenna. However, in this era of precision Yagi modeling via both NEC and specialized Yagi programs, the complaint usually means something else entirely. Virtually all of the Yagi designs appearing in current radio journals list the modeled performance figures, whether they are drawn from YO, YagiMax, MININEC, or NEC. These numbers are within cumulative rounding errors of each other and, hence, any slight differences should be too small to be perceived in operation.

+

When the complaints are addressed to me, I usually follow up with a double-barrel question: Exactly what materials did the author specify and what materials did you use? The answers usually show differences in the element diameters and taper schedules for the elements. Hams use what they have on hand, often from antennas that are no longer operational. Broken beams can be inexpensive hamfest purchases and provide a ready source of material for a new beam. Since hams are talented adapters of old materials to new jobs, the freshly constructed beam may have significant material differences from the original published design.

+

So let's jump to the bottom line and then go back to fill in the space:

+

1. In Yagi design, changes in element diameters and taper schedules can make a significant difference in performance.

+

2. When contemplating "copying" a good published design with materials that differ from the original, re-model the design to determine the element lengths required by the copy.

+

Re-modeling is virtually the only reliable technique open to hams to optimize a beam. Few antenna builders have access to a reliable test range and test equipment that will enable them to optimize forward gain with a front-to-back peak located at a desired frequency. What hams do is generally to prune the driven element until there is a good match to the coax and accept whatever gain and front-to-back ratio emerge--often believing that the design has been optimized. This is a route to long-term disappointment for most builders, with only an occasional shot of pure luck to keep this bad practice alive.

+

Modeling Yagis has proven to be a much more reliable means of obtaining excellent performance from the finished product, with model-to-product deviations of 1% or less (with the most careful modeling). Whatever Yagi modeling program you prefer, it must accurately handle changes in element diameter and element diameter taper schedules. Many programs can handle these needs with ease.

+

Now, let's fill in the blanks and give some substance to these recommendations.

+

Uniform-Diameter Yagi Elements

+

First, let's set up a base-line of data on designs with uniform-diameter elements. To keep the task within the boundaries of easy comprehension, we shall look at only one Yagi design: a 3-element long-boom design that originated with K6STI. The outline of the Yagi appears in Fig. 1.

+
+ +
+

The design will be for 20 meters. All dimensions (lengths, spacings, and diameters) will be given in inches. I originally optimized the design for a frequency of 14.175 MHz, the middle of the 20-meter band, using 1" diameter aluminum elements. Here are the modeled dimensions in all of their excess decimal places.

+ 
1" diameter 3-element Yagi
+Element                 Length            Spacing to Reflector
+Reflector               414.72"           -----
+Driver                  396.00"           125.46"
+Director                372.60"           270.53"
+

I resonated the driven element within +/- 1 Ohm reactance. Using this model, I then decreased the element diameters to 0.5" and then increased them to 1.5". I held the element spacing constant to the 1" model, but changed the element lengths as a batch to arrive at resonance at the design frequency of 14.175 MHz. Here are the element lengths that resulted.

+ 
Element                 0.5" Lengths      1.5" lengths
+Reflector               417.80"           413.12"
+Driver                  398.94"           394.46"
+Director                375.36"           371.16"
+

My reason for keeping the original spacing between elements was to make the result accord with typical amateur building practice. As we shall see, there are indications from the resulting models that this practice does not yield absolutely optimal designs. But that is jumping ahead of the story by a small bit.

+

The first difference of note is the gain of the three beams. See Fig. 2.

+
+ +
+

Between the 0.5" and 1.5" element diameters, there is a difference of about 0.3 dB gain. However, the rate of gain increase slows down as we increase the diameter. In contrast, we see no significant differences in front-to-back ratio with increases in diameter, as evidenced by the curves in Fig. 3.

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Peak front-to-back ratio occurs between 14.1 and 14.15 MHz for this design. The seeming oddity of the front-to-back peaks in the graph stems from something a bit more subtle in the array behavior. The peak front-to-back for the 0.5" diameter element model occurs almost exactly at 14.125 MHz. The peak for the 1" diameter model occurs closer to 14.15 MHz, while the corresponding peak for the 1.5" models occurs closer to 14.1 MHz. The slight differences result from the fact that the variant models (relative to the 1" base-line version) were not optimized fully in terms of element spacing as well as element length. Changing element diameter does have an impact--even if only a small one--on all operating parameters, including the frequency at which certain values peak.

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A similar set of slight variances occurs with respect to the VSWR curves in Fig. 4, all of which are referenced to the resonant impedance of each model. Interestingly, the 0.5" diameter model has the broadest curve. However, this curve is partly a function of the fact that the feedpoint impedance at resonance is highest for the smallest diameter elements. In fact, the following table of band-edge and band-center performance figures is also instructive.

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  Element Diameter
+Frequency         Free-Space        Front-to-Back     Feedpoint Z       VSWR
+MHz               Gain dBi          Ratio dB          R +/-jX Ohms      (resonance)
+  Element Diameter:  0.5"
+14.0              7.70              21.3              30.6 - j 13.2     1.55
+14.175            7.91              26.1              29.6 - j  0.1     1.00
+14.35             8.12              17.4              26.6 + j 14.6     1.69
+  Element Diameter:  1.0"
+14.0              7.94              20.8              27.0 - j 13.3     1.65
+14.175            8.11              27.3              25.7 - j  0.9     1.03
+14.35             8.35              17.7              22.9 + j 13.0     1.72
+  Element Diameter:  1.5"
+14.0              8.05              21.9              24.8 - j 11.7     1.63
+14.175            8.25              26.0              23.1 + j  0.3     1.01
+14.35             8.50              16.9              20.3 + j 14.0     1.91
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As we increase the element diameter, the differential in gain between the low and high ends of the band increases--from a low of 0.34 dB to a high of 0.45 dB. The decrease in the resistive component of the feedpoint impedance with increases in element diameter is also apparent. Moreover, as the element diameter increases, the differential between the low and high ends of the band also increases--from 3.95 to 4.5 Ohms. In contrast, the spread of reactance from one end of the band to the other decreases with an increase in element diameter--from 27.88 down to 25.65 Ohms.

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Although these changes are very small and would not affect general operation of any version of the array, the directions and rates of change are indicative of beam performance as we change element sizes. Noting these changes can aid in analyzing what may be occurring when the time comes to field adjust an array based upon some initial measurements. It always makes good sense to note trends--however small--in the performance of modeled antennas as one does spot or swept frequency checks.

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Stepped-Diameter Elements

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At 20 meters, common construction practice calls for stepped diameter elements, that is, elements that are composed of descending diameters of tubing as one works from the beam center-line outward. Since the element diameter decreases toward the outer ends, the element always acts shorter than its physical length. Otherwise put, a stepped-diameter (also called a tapered-diameter) element must be physically longer than a corresponding uniform-diameter element serving the same function.

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The tapering schedules used for elements in amateur arrays cover a wide territory. The normal 20-meter element may use from 4 to 6 sections, with diameters ranging from 1.25" to 0.375". We shall examine just 4 samples of tapering schedules, as shown in Fig. 5.

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The figure shows the 4 examples as functions of regular decreases in diameter. Only half-elements are shown, since normal practice would make the missing side simply the mirror image of what is shown. In many, but not all beams, the inner sections will all have the same section lengths, with only the tip making up the differences among the reflector, driver, and director. However, in a number of commercial and personal designs, the tapering schedule may vary from one element to the next, as dictated by element stress analysis.

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Fig. 5 lists the lengths of the individual sections for each of the 4 examples we shall explore. Although this procedure makes a compact chart, it does not give a good sense of the section proportions among the examples. To give some idea of how section proportions may vary from one design to another, Fig. 6 shows two of the examples sketched with proportional divisions.

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It is readily apparent that the sections within an element may be short or long, close to equal or very unequal, fat or thin. Every variation in the element construction changes the equivalent uniform diameter of the element and the equivalent electrical length.

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Yagi modeling programs that effectively handle stepped-diameter elements generally perform calculations on a uniform-diameter element of equivalent electrical length to the stepped-diameter version. Most commonly, the Leeson corrections are used to give very accurate predictions of array performance, based on his work in The Physical Design of Yagi Antennas.

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This facility to create electrically equivalent uniform-diameter elements makes it relatively straight forward to formulate element dimensions for 3-element Yagis have the same spacing as used in our earlier models, but using each of the taper schedules shown in Fig. 5. The procedure is simply a matter of making each element tip long enough so that the corrected uniform-diameter element ends up the same length as in the original design. We shall use as our design standard the 1" diameter model with which we began. However, along the way, we shall note that the uniform-diameter element generated by applying the correction factor will vary from element to element and model to model--and this factor will have a bearing on the array performance projections. Let's proceed through the examples in the order given, which corresponds to a progression from the slimmest to the fattest equivalent uniform diameter elements. We shall also speak in terms of half-element lengths (or half-lengths, for short).

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Example 1: The example uses the smallest diameter elements in a regular progression. Let's remember that the half-lengths for the 1" uniform-diameter model were 207.36", 198.00", and 186.30", working from the reflector to the director. To achieve electrical lengths equal to these, the stepped-diameter elements must be considerably longer, as shown in the following table. Refer to Fig. 5 for the lengths of inner sections of the elements.

+ 
Example 1
+Element           Half-Element Length     Tip Length        Equiv. dia.
+Reflector         213.00"                 75.00"            0.670"
+Driver            204.20"                 66.20"            0.680"
+Director          191.35"                 53.35"            0.694"
+

These elements are between 5" and 6" longer than the uniform-diameter elements of the original model. Note also that the equivalent diameter for each element differs as a function of the differing tip lengths and their proportion of the whole element. Hence, the director, with the shortest tip, is effectively the electrically fattest element of the group.

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To certify performance, the following table shows the band-edge and band-center performance predicted for this array.

+ 
Frequency         Free-Space        Front-to-Back     Feedpoint Z       VSWR
+MHz               Gain dBi          Ratio dB          R +/-jX Ohms      (resonance)
+14.0              7.84              18.3              29.0 - j 13.1     1.57
+14.175            7.98              27.9              28.5 - j  0.6     1.02
+14.35             8.18              19.6              26.0 + j 13.4     1.64
+

With one exception, the performance predictions fall between those for the 0.5" and 1" diameter models earlier explored. The front-to-back curve suggests that further work is possible with respect to bringing the curve more into alignment with the earlier models, although it seems very reasonably symmetrical across the band.

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Example 2: The second example uses a very aggressive 6-section element ranging from 1" at the center to 3/8" at the outer end. The relatively short tips will give this element an electrically fatter equivalent diameter than the element we just surveyed. The data is as follows.

+ 
Example 2
+Element           Half-Element Length     Tip Length        Equiv. dia.
+Reflector         216.25"                 36.25"            0.707"
+Driver            206.70"                 26.70"            0.726"
+Director          193.30"                 13.30"            0.753"
+

Despite the larger equivalent diameter, relative to the first example, the aggressive element taper requires elements that are 2 to 3 inches longer to achieve the same equivalent length. In short, how the taper is implemented has a strong bearing on the required physical length for a given electrical performance. Had the elements been set to the uniform-diameter lengths, the resulting beam would not have performed anywhere near to expectations. The performance data of the revised model appears in the following table.

+ 
Frequency         Free-Space        Front-to-Back     Feedpoint Z       VSWR
+MHz               Gain dBi          Ratio dB          R +/-jX Ohms      (resonance)
+14.0              7.87              18.9              28.3 - j 13.6     1.62
+14.175            8.02              28.2              27.6 - j  0.9     1.04
+14.35             8.23              18.9              25.0 + j 13.1     1.65
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As expected, the larger equivalent diameter of the elements (relative to Example 1) provides slight numeric (but insignificant operational) increases in gain and slightly lower values for the feedpoint resistance.

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Example 3: The third example begins at the element center with the same diameter tubing as in the preceding example. However, by using longer lengths of each tubing size, the element needs only 4 sections, with a minimum diameter of 5/8". For this example, we should expect shorter required element lengths and a fatter equivalent diameter.

+ 
Example 3
+Element           Half-Element Length     Tip Length        Equiv. dia.
+Reflector         212.25"                 56.25"            0.851"
+Driver            202.80"                 46.80"            0.862"
+Director          190.36"                 34.36"            0.878"
+

With equivalent element diameters in the vicinity of 7/8", the calculated performance of this array should approach that of the full 1" array.

+ 
Frequency         Free-Space        Front-to-Back     Feedpoint Z       VSWR
+MHz               Gain dBi          Ratio dB          R +/-jX Ohms      (resonance)
+14.0              7.91              20.3              27.7 - j 13.2     1.62
+14.175            8.08              27.7              26.5 - j  0.7     1.03
+14.35             8.30              18.0              23.8 + j 13.3     1.71
+

The performance table does not disappoint us, as this element arrangement replicates closely in almost every detail the corresponding table for our initial design. (Note that this correspondence is only of electrical interest and does not represent a recommendation for the tapering schedule in the example.)

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Example 4: The last example presents a very beefy element indeed. It centers at 1.25" in diameter and uses 5 sections, with a long 3/4" diameter tip. Although the equivalent uniform diameter is larger than that of the preceding example, this fact alone does not dictate element length overall. In fact, the required element lengths of this last example are actually a tiny bit larger than those of Example 3.

+ 
Example 4
+Element           Half-Element Length     Tip Length        Equiv. dia.
+Reflector         212.50"                 62.50"            0.988"
+Driver            203.00"                 53.00"            1.000"
+Director          190.85"                 40.85"            1.020"
+

The reason for the "longer" elements lies in the tapering schedule. The corrected elements calculate for each section diameter and length. The 5-section taper shows a larger gradient of decrease than for Example 3, and hence requires longer elements than had the element simply followed the schedule of Example 3 with larger diameter elements.

+ 
Frequency         Free-Space        Front-to-Back     Feedpoint Z       VSWR
+MHz               Gain dBi          Ratio dB          R +/-jX Ohms      (resonance)
+14.0              7.97              21.7              26.7 - j 11.9     1.59
+14.175            8.15              26.3              25.2 + j  0.6     1.02
+14.35             8.35              17.0              22.3 + j 14.8     1.87
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As expected, the fatter equivalent elements yield the highest gain of all our examples, along with the lowest feedpoint resistance values.

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We should remember that none of these examples has been further optimized with respect to spacing and additional tweaking of element lengths to achieve the absolute best performance curves. Instead, they were simply equalized to the length dimensions of the original design sample.

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Moreover, whatever the performance differences among the models, none of the element tapering schedules is endorsed or recommended. That task would require a more detailed stress analysis using software like YagiStress by Kurt Andress. Moreover, the final selection of an element taper may involve trade-offs with respect to size and weight, not to mention the use of available materials.

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Rather, the exercises have been designed to demonstrate the importance--indeed, the necessity--of re-modeling a Yagi design whenever we propose to alter the element tapering schedule of the initial design. We encountered a number of phenomenon related to the electrical equivalents of stepped-diameter elements, and the end results were not always intuitively obvious.

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The electrical performance of a stepped-diameter element depends not only on the sizes of tubing used along the way, but as well on the aggressiveness of the taper and lengths of each section within the whole element. The only safe way to ensure that a substitute element is correctly sized for the task at hand is to model it. An hour's work with one of the Yagi modeling packages can save a lot of hard and uncertain work up on the tower and a lot of disappointment down the road.

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Updated 7-1-2000. © L. B. Cebik, W4RNL. The original item appeared in AntenneX for June, 2000. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Upper, Stepped Diameter, Yagi


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The Inverted-U as a Field Yagi

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L. B. Cebik, W4RNL

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In May, 2005, QST published an article describing a simple field dipole using nested aluminum tubing, hitch-pin clips, and a simple center feedpoint assembly. ("The Inverted-U," pp. 28-32) Besides the use of techniques that allowed easy field assembly and disassembly, as well as compact storage and transport, the dipole featured the use of a 100" element length and aluminum fence wire (AWG #17) as vertical end tips to extended the total element length from its native 10-meter resonance to lower bands. Separate tips wires allowed coverage of 10 through 20 meters. Fig. 1 shows the basic structure of the main horizontal element (actually, half of the element). Refer to the original article for additional construction details, including the use of hitch-pin clips and the method of holding the tip wires in place.

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Since the article appeared. I have received e-mails from individuals interested in developing the basic inverted-U into a 2-element Yagi. Within limits (that we shall explore as we move along) it is possible to develop an inverted-U Yagi. However, the first reminder at this point is the fact that the antenna physical design is aimed at short-term field use, not permanent home installation. Any long-term installation will need to check the tubing lengths against a program, such as YagiStress, to ensure that it will handle local wind loads. As well, the junctions of tubing sections will require more permanent fasteners for durable electrical contact and physical security.

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The second reminder concerns the difference between designing a simple dipole and a 2-element Yagi. The dipole is easy. Starting with a 10-meter resonant element, we simple add tip wires for a desired band and trim the ends for a satisfactory SWR value at the operating frequency. Dipole patterns do not change much with SWR excursions, so we generally assume that the bi-directional pattern is satisfactory once we achieve the desired SWR reading. The original article shows some sample patterns that take into account the increasing vertical tip lengths as we lower the frequency. Other patterns account for the fact that maximum gain goes down and the elevation goes up if we place the antenna at a fixed height and lower the frequency of operation with longer tip wires.

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A 2-element Yagi increases the complexity of the design considerably. The pattern shape changes rapidly with changes that may seem small when applied to a dipole. The best compromise among gain, front-to-back ratio, and feedpoint impedance rests on the interaction of the different lengths of the 2 elements (a driver and a reflector in this exercise) and the spacing of the elements. Since the elements are not linear, we have additional design decisions to make before we develop any dimensions.

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As suggested in Fig. 1, I used the basic element structure of the inverted-U dipole as the foundation for designing 2-element Yagis. On 10 meters, the driver will be shorter and the reflector will be longer than the original 10-meter dipole. This arrangement allows the antenna to function as a 2-element Yagi of standard performance without the use of any tip wires. The decision also restricted the designs to field use. Changes of tubing sizes for stronger home versions of the antenna will require redesign, since element diameter affects the pattern shape as well as the feedpoint impedance. Once we enter the world of parasitic Yagis, pruning for resonance is a secondary field adjustment rather than the primary and sometimes the only adjustment needed with a dipole.

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Since the antenna design is for field use, the feedpoint impedance should require no matching device that might require either assembly or adjustment in the field. Therefore, I used a 10-meter element spacing of 0.17 wavelength so that the feedpoint impedance would come as close as possible to 50 Ohms. The difference in the patterns between a more closely spaced driver-reflector Yagi and a 50-Ohm Yagi are numerically determinable but operationally insignificant. At a spacing of about 1/8 (0.125) wavelength, an optimized 2-element driver-reflector Yagi will show about a half dB more front-to-back ratio, about 0.1 dB more gain, and a feedpoint impedance in the low 30-Ohm range. Since 2-element driver-reflector Yagis (without reflector loading) have maximum front-to-back ratios in the 11-12-dB region, the convenience of a 50-Ohm feedpoint seemed warranted.

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As a result of the decision to use a 50-Ohm Yagi design, the driver requires the same sort of construction that I used in the original inverted-U dipole. Fig. 2 shows the general layout of the 2-element field Yagi. You can use the same plates designed for the dipole, although they will now attach to and hang under a boom. You can use a fairly lightweight boom, since each element will weigh only about 2 pounds (including the plate assembly and boom-to-element U-bolts). The original dipole used a length of non-conductive rod or tube inside the 0.75" short center tubes to effect the feedpoint gap. For the reflector, you can use a single center tube, since the reflector is a continuous element. In fact, if you wish to keep the smallest end tubing section shorter than the listed value, you can increase the length of the largest tube attached to the reflector plate. In this way, you can reduce the length of the nested tubes during storage and transport.

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Note in Fig. 2 that the spacing will be variable. The optimal spacing grows physically wider to maintain the 0.17 wavelength element spacing. However, we encounter another design limitation. Because the elements have longer tip wires as we lower the operating frequency, the impedance increases more slowly with element spacing at lower frequencies. Therefore, we need to increase the spacing--up to about 0.19 wavelength at 20 meters. That fact, plus some others, may limit the utility of the design beyond 2 or 3 bands below 10 meters.

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I also made a further design decision based on the intended application of the 2-element field Yagi. I set the tip-wire length for each band so that all 4 tip wires are interchangeable, that is, have the same length. This decision simplifies band changes in the field, since we do not need to locate a specific wire. As well, the core 10-meter elements remain constant and require no changes when we change frequency. However, this decision also restricts our ability to obtain the most optimal patterns from a 2-element Yagi with inverted-U elements.

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Application decisions can have a far reaching effect on the design and its performance or shape. Although an inverted-U Yagi may have only limited use for field operators, the decision to retain the field-use features of the original inverted-U dipole determined a number of dimensions that a builder with other applications can change. For example, one might make both elements the same length and use driver and reflector tips with different lengths. Making both elements 196" long (98" per half-element) would require short tip wires on the reflector on 10 meters. For monoband applications in which the inverted-U element shape is simply a way to save horizontal space, one can use closer element spacing. The feedpoint impedance will drop, but there are a number of matching schemes available to raise it to 50 Ohms for the standard amateur coaxial cable--including beta and gamma networks as well as 1/4 wavelength sections. Before we close, we shall briefly examine some other alternatives based on some limitations that we encounter with the field-application design.

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A Band-by-Band Look at Inverted-U Yagi performance

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The inverted-U dipole showed bi-directional gain that gradually dropped (even in free space environments) due to the constant horizontal length and the increasing vertical tip-wire length as we moved from 10 to 20 meters. However, the 20-meter performance remained quite usable and the feedpoint impedance remained high enough to be directly compatible with coaxial cable feedlines. In contrast, the inverted-U Yagi, we must balance 2 element lengths and the spacing between them to yield acceptable 2-element Yagi performance. As well, driver-reflector Yagis show impedance levels that--for any reasonable spacing--remain lower than the impedance of the dipole. Hence, we shall encounter difficulties covering all 5 bands for which the dipole was applicable. To see how the limitations evolve, let's examine the performance of the inverted-U Yagi starting with 10 meters. The performance evolution may provide some insights into the operation of both 2-element Yagis and elements with the inverted-U shape.

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For each band, we shall look at 3 essential sets of data. First will be a performance table that provides modeled data for the band edges and the design frequency--the passband center. The table will also include the critical figures for the wire tip lengths and the elements spacing required to arrive at the performance data. The listed tip-length values are from free-space models. Be prepared to make field adjustments to these lengths because the ground will interact with the elements at normal field heights. However, strive to keep all tips the same length. Next, we shall examine the free-space E-plane pattern for the modeled antenna. The free-space E-plane pattern is virtually identical to an azimuth pattern taken at any reasonable height above ground, although the latter requires a maximum gain adjustment of 5 to 6 dB, depending upon the actual antenna height. Finally, we shall look at the 50-Ohm SWR curve for the antenna and correlate its shape to the spot performance values in the table. The following table shows the tip lengths and other essential dimensions for the beam on each band.

+ 
+Basic Dimensions of the Inverted-U Field Yagis
+Basic Antenna:  10-Meter Yagi
+Driver Length:      98"  See Fig. 1 for element structure.  All length adjustments
+Reflector Length:  107"  made to outer 3/8" diameter section.
+AWG #17 aluminum fence-wire vertical end wires
+(4 required for each band, all of equal length)
+Band       Wire Length (")
+10         None
+12          22.5"
+15          50"
+17          77"
+20         127"
+
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10 Meters: The 10-meter passband is restricted to 28.0 to 29.0 MHz. We can redesign the beam to cover the entire 10-meter band (which extends to 29.7 MHz). However, the lower first MHz contains most of the non-AM activity that uses horizontal polarization. As noted from the start, the basic beam design requires no vertical tip wires, making the antenna indistinguishable from other 2-element Yagis in its class. The element spacing is 72" (6'), which yields a 50-Ohm feedpoint impedance.

+ 
+Inverted-U Yagi 10-Meter Performance
+No vertical end wires required
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 72"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+28.0          6.51           10.01          42.8 - j15.4            1.44
+28.5          6.13           10.64          52.6 + j 1.8            1.06
+29.0          5.79           10.14          61.4 + j17.7            1.46
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10 meters is the widest of the bands explored here. Like all 2-element driver-reflector Yagis, the gain decreases as the frequency increases across the passband. The design tries to reach peak front-to-back ratio about mid-band, and the value remains at or above 10 dB across the band. As shown by the patterns in Fig. 3, the 180-degree and worst-case front-to-back ratios are the same due to the shape of the rearward lobe.

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Fig. 4 provides the 50-Ohm SWR curve for the basic antenna. Note that the SWR values are virtually identical at both ends of the operating passband. Since both values are under 1.5:1, the array is suitable for use with equipment with sensitive fold-back or shut-down limits. From the curve shape, it is clear that we could have moved the design frequency to about 28.85 MHz and covered the entire band. However, the front-to-back ratio at each band edge would have been lower than the 10-dB figure shown.

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12 Meters: The proximity of 12 meters to 10 meters and the narrowness of the passband (100 kHz) gives us some options that we shall not find on the lower bands. The optimal spacing for the array, with its 22.5" end wires, is about 82". However, with only a slight reduction in the feedpoint resistance (and a commensurate rise in the 50-Ohm SWR), we may use the same spacing that we set for 10 meters: 72". This option may simplify some field operations without jeopardizing performance. In fact, as shown by the table of modeled free-space values, the closer spacing may actually improve the performance numbers--although by an amount that we could not measure in the field.

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+Inverted-U Yagi 12-Meter Performance
+Vertical end wires: 22.5"
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 82"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+24.89         6.28           10.59          47.7 - j 0.5            1.05
+24.94         6.24           10.65          48.9 + j 1.5            1.04
+24.99         6.19           10.69          50.0 + j 3.5            1.07
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 72"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+24.89         6.40           10.81          39.9 - j 1.7            1.26
+24.94         6.35           10.88          41.06+ j 0.5            1.22
+24.99         6.30           10.92          42.17+ j 2.6            1.20
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Because the band is so narrow, we may use a single E-plane pattern for the entire band. However, Fig. 5 presents 2, one for each spacing option. The difference is almost undetectable. However, compare both plots with those for 10 meters. Note that the 12-meter side nulls (90 degrees away from the main forward heading) are not as deep as 10-meter nulls. Even with a short length of vertical tip wire on each element end, we see one of the main results of using inverted-U elements. Of course, at 12 meters. the reduction in the side nulls is not yet operationally significant.

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The SWR values for the two spacing options yield essentially straight-line SWR curves over the narrow 12-meter passband. See Fig. 6. In both cases, we have only a 2-3-Ohm change of resistance and about 4-Ohms change of reactance. The SWR values for the closer spacing are numerically higher than those for optimal spacing, but well within the range of excellent SWR performance. Indeed, even with the closer spacing, the SWR passband is broad enough to make initial and field adjustments quite easy.

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15-Meters: 15 meters is a relatively wide amateur band and requires 50" tip wires to bring the antenna to optimal performance for the configuration. As well, the required spacing is 100" (8.3'), which is somewhat higher than the spacing needed for equivalent impedance performance on 10 meters. The spacing is about 0.19 wavelength, a fact that gives us a clue to one of the inverted-U Yagi's limitations. Lengthening the vertical wires as we decrease the operating frequency from band to band results in lower feedpoint resistance values for the same spacing when expressed as a fraction of a wavelength. We need a wider spacing to restore near-50-Ohm feedpoint resistance values, a requirement that gradually takes its toll on the basic performance values. However, because the increased proportion of vertical tip wire to horizontal element is also increasing, we cannot say precisely how much performance reduction results from each factor. As shown by the tabulated data, the reduction in maximum gain is noticeable, but not operationally serious.

+ 
+Inverted-U Yagi 15-Meter Performance
+Vertical end wires: 50"
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 100"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+21.0          6.29           10.22          41.8 - j 4.0            1.22
+21.225        5.99           10.65          47.8 + j 7.1            1.16
+21.45         5.71           10.37          53.3 + j17.6            1.41
+
+

The E-plane patterns, shown in Fig. 7, show the evolution of the side nulls, that is, a further decrease in depth. The null depth is now only 20-25 dB, compared to a value of over 40 dB or more for the basic 10-meter design. Beyond that fact, the patterns remain typical of 2-element driver-reflector Yagi designs.

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The SWR curve for 15 meters is quite good, with band-edge values of 1.20 and 1.45 to 1. Fig. 8 provides the pattern, with the tabular data showing the spot data. First, note that the range of resistance change has climbed to nearly 12 Ohms and the range of reactance is about 20 Ohms. Compare those values to the 10-meter values, even though 10 meters is a wider band. (Bandwidth is normally recorded as a percentage, using the total passband width divided by the band's center frequency and multiplied by 100 to arrive at a percentage.) Second, note that the resonant point of the driver has drifted downward in frequency. This situation suggests that there may be limits to balancing pattern shape and impedance performance using equal-length wire tips. Still, the 15-meter SWR value never rises to 1.5:1, giving us perfectly acceptable performance.

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17 Meters: On 17 meters, the element spacing (or boom length) increases to 120" (10') to arrive at an input impedance of about 40 Ohms. As the tabulated data show, we begin to encounter significant changes in performance across even the 100-kHz passband, although the narrow band allows acceptable performance. The key question is whether we can increase the boom from 8.3' to 10' or whether we need to use narrower spacing and a matching network. The latter option might be applicable to a monoband version of the antenna used for a WARC-band only and having a small horizontal footprint.

+ 
+Inverted-U Yagi 17-Meter Performance
+Vertical end wires: 77"
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 120"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.04           10.07          38.0 - j 2.5            1.32
+18.118        5.95           10.26          39.6 + j 0.5            1.26
+18.168        5.85           10.35          41.1 + j 3.5            1.23
+
+

Fig. 9 shows the continuing evolution of the E-plane pattern. The side nulls are now only about 17 dB below the maximum gain level, which is, in turn, only about 7 dB more rejection than the front-to-back ratio. The pattern has changed from a pair of lobes--one forward, one rearward--into a pear-shaped affair.

+
+ +
+

Despite the longer boom and the reduced side rejection, the 17-meter version of the inverted-U Yagi does obtain a perfectly usable SWR curve, largely as a function of the narrowness of the 17-meter band. Fig. 10 shows the curve--a virtual straight line--for the 50-Ohm SWR values.

+
+ +
+

20 Meters: Whether or not the inverted-U Yagi, when built within the design constraints described at the beginning of this exercise, is suitable for 20-meter use depends on how much performance reduction we are willing to accept and how much boom length that we can accommodate. The tip wires are now 127" apiece. The boom required for adequate impedance performance rises to 160" (13.3'). As the tabulated data show, these factors add up to a highly noticeable decline in both gain and front-to-back ratio across the wider 20-meter band, with only adequate 50-Ohm SWR performance.

+ 
+Inverted-U Yagi 20-Meter Performance
+Vertical end wires: 127"
+Driver Length: 196"   Reflector Length: 214"  Element Spacing: 160"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+14.0          5.62            9.26          28.3 - j 5.1            1.80
+14.175        5.02            9.24          34.1 + j 9.6            1.56
+14.35         4.52            8.07          38.4 + j23.6            1.81
+
+

As shown in Fig. 11, the pattern shape has lost almost all side rejection, with only a tapering gain value as we move from the front to the rear of the pattern. The absence of side rejection and the reduction in rear rejection is commensurate with the reduction in forward gain compared especially to the basic 10-meter version of the antenna that uses no element-end tip wires. However, we can also see that the pattern has taken a serious jump to lower performance from the 17-meter version of the antenna.

+
+ +
+

Although we can use the 160" boom to produce a 50-Ohm SWR curve (shown in Fig. 12) that remains below 2:1, we cannot get the lowest value down to 1.5:1. Indeed, the antenna in this configuration would require a 35-Ohm cable (or 2 70-Ohm cables set up in parallel).

+
+ +
+

Although the 20-meter version of the inverted-U dipole using exactly the same tubing structure was highly usable, we cannot say the same for the 20-meter version of the inverted-U Yagi. For the performance level attained and the mediocre SWR curve, the long boom seems almost unjustified.

+

Conclusion

+

The inverted-U driver-reflector Yagi, when built for field service, seems most apt as a 3-band and at most a 4-band antenna. Performance in all respects is quite good in terms of 2-element Yagi standards from 10 through 15 meters, with 17 meters a possibility if we wish to use a longer boom. However, 20-meter performance seems almost not worth the effort for most types of field operations.

+

Those who need a 17-meter or a 20-meter Yagi with a limited footprint do have some options. Suppose that we were to develop a 15-meter beam as the baseline. The element would be about 22' long compared to the 16-17' 10-meter elements. With a 15-meter baseline. the required wire tips for 17 and 20 meters would be considerably shorter, and performance would improve to about the levels of the 12- and 15-meter beams based on the 10-meter baseline.

+

Such a beam could serve either field or home applications, depending on the element diameter taper chosen for the array. Indeed, for any home or long-term installation, there are many handbook designs that will show element diameter taper schedules designed for the higher anticipated wind loads. The design exercise will then be to plug those 15-meter elements into a modeling program and to determine the most likely tip wire lengths required for either 17-meter or 20-meter performance. Such a beam would still use elements about 35% shorter than a full size 2-element 20-meter Yagi with relatively undetectable differences in performance. Since the exact dimensions will vary from one element diameter taper schedule to another--as well as with the selection of the desired element spacing and feedpoint impedance--we shall not attempt such a design in this exercise. Such a beam might well use stiffer wire for the tip sections, such as AWG #14 or AWG #12.

+

For the present exercise, it is sufficient, I think, to have shown the requirements for designing 2-element inverted-U Yagis using the 10-meter baseline. The exercise has alowed us to show the evolutionary factors in the design that offer potentially good performance, but over a more restricted range of frequency bands than the inverted-U dipole might serve. The exercise has also allowed us the chance to remind potential builders that long-term applications require stricter attention to strong and durable electrical and physical requirements in the construction process.

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+

Updated 06-12-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Upper, Inverted U, Portable, Yagi


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+

The Inverted-U Yagi on 20 Meters
+ And an Alternative

+
+
+

L. B. Cebik, W4RNL

+
+
+ +
+

In the last episode, we examined the conversion of a 10-meter-based dipole inverted-U antenna into a 2-element Yagi. Although the dipole proved highly useful from 10 through 20 meters, the Yagi showed some limitations. Below 15 meters, the boom length became excessively long to call the antenna compact. The 20-meter tips grew to 127" (10.6') each. As well, 20-meter performance lost a full dB of gain and of front-to-back ratio, not to mention almost all of the front-to-side nulls. Nevertheless, the 15-meter performance remained high enough and the size small enough to make a viable 2-element Yagi.

+

The search for a compact 20-meter beam might not include the 10-meter-based inverted-U. However, a 15-meter 2-element Yagi might form the basis for an inverted-U 20-meter antenna. In theory, at least, the 15-meter performance of the 10-meter-based inverted-U should transfer to 20 meters if we use a 15-meter Yagi as the baseline. In this exercise, we shall explore this possibility. Our goal will not only be to see what potentials and limitations accompany the design. We shall additionally call attention to a certain tunnel vision that sets in when we pursue an idea to its limits. We tend to concentrate so hard on making the original idea work that we overlook other possibilities that might offer more satisfactory routes to the same goal. In this case, our goal is a compact 20-meter 2-element beam with adequate performance. As we shall see, there are alternatives to the inverted-U Yagi.

+

In the process of evaluating the use of a 15-meter 2-element Yagi as the foundation for a 20-meter inverted-U Yagi, we shall also alter our construction. The 10-meter versions of the antenna used very light materials suited only for short-term field conditions. The element taper schedule was not suitable to handle high wind loads, and the hitch-pin fasteners require replacement with more durable electrical and mechanical connectors. Since we shall move to a larger base-line beam, we shall employ element-diameter taper schedules more suited to long-term installations.

+

The ARRL Antenna Book has long had a very good section on Yagis and Yagi construction. The catalog of models that accompanies the book is contained in the program YW (the Windows version of the older DOS YA). The sample beams use taper schedules designed for medium duty (about 80 mph) wind loads and heavy duty (about 100 mph) wind loads. For the design exercises, I have adapted these element-diameter taper schedules for the 15-meter beams to the present effort. I shall assume that any implementation of the design will use adequate element overlap and secure fasteners in the final assembly.

+
+ +
+

Fig. 1 shows the two taper schedules in terms of each element half. Both versions of the element structure include two tip lengths: one for the driver and one for the reflector. Remember to add about 3" for element section overlap. At the center, you may extended the second section all the way to the center to increase strength near the boom. In addition to the increased element strength, the new beams also use AWG #12 wire for the vertical tips. To avoid bi-metallic electrolysis, use aluminum wire for the tips (and stainless steel hardware throughout the beam).

+

As we did with the 10-meter-based inverted-U Yagis, let's move band-by-band from 15 to 20 meters. The exercise will let us review the performance evolution and the requirements to reach the performance goals. As in the initial exercise, we shall design 2-element Yagis with drivers and reflectors. As well, the Yagis will display a 50-Ohm feedpoint impedance so that we can directly connect the coax cable (through a common-mode current suppressing choke) to the antenna.

+

15 Meters: The baseline 15-meter 2-element Yagi uses standard design techniques to arrive at a driver-reflector array with usable performance and a 50-Ohm feedpoint impedance. As the following table reveals, the element taper does affect the require element lengths for essentially the same performance levels. Note that the thinner elements of the medium-duty version result in slightly shorter elements, which is contrary to our intuitions that derive from examining uniform-diameter elements. However, the heavy-duty version has an extra diameter step, resulting in a more severe total element taper. This factor--along with the exact positions of the section steps--controls the resulting equivalent uniform-diameter element and the required element length. Although the element lengths differ slightly between the 2 element-diameter taper schedules, the element spacing is the same for both antennas. All designs in this exercise emerged from NEC-4 models.

+ 
+Inverted-U Yagi 15-Meter Performance
+No vertical end wires required
+Heavy-duty version: Driver Length: 264"   Reflector Length: 288"  Element Spacing: 92"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+21.0          6.36           10.50          44.2 - j 9.5            1.27
+21.225        6.13           10.71          50.0 + j 1.3            1.03
+21.45         5.91           10.47          55.4 + j11.5            1.27
+Medium-duty version: Driver Length: 262"   Reflector Length: 284"  Element Spacing: 92"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+21.0          6.35           10.55          44.4 - j 9.9            1.27
+21.225        6.10           10.72          50.3 + j 1.2            1.03
+21.45         5.88           10.44          55.7 + j11.7            1.28
+
+

The free-space E-plane (azimuth) patterns for the 15-meter beam appear in Fig. 2. I show only the heavy-duty version patterns because there is insufficient difference in the patterns of the two versions to warrant 2 sets of plots. Nevertheless, we can note that the 15-meter beam that uses no vertical tip sections displays the same clean patterns with very deep side nulls that we saw in the patterns for the 10-meter baseline beam in the preceding episode. In short, the antenna is a perfectly normal 2-element Yagi.

+
+ +
+

The 50-Ohm Yagi designs gives up very small amounts of gain and front-to-back ratio to arrive not only at a 50-Ohm feedpoint impedance, but also a large bandwidth. The 50-Ohm SWR curve, shown in Fig. 3, never rises to 1.3:1 across the 15-meter amateur band for either version of the array.

+
+ +
+

17 Meters: On 17 meters, we have the same choices that we had with the 10-meter Yagi when U'ed to 12 meters. We can use the initial (15-meter) spacing (92" or 0.14 wavelength on 17) or a more optimal 112" (0.17 wavelength). When we combine this choice with the heavy- and medium-duty element-diameter taper schedules, we end up with a 4-part table for a very small band. As expected, the more closely spaced version of either construction style shows more gain and a higher front-to-back ratio, although the difference is operationally marginal. Note that, for both levels of construction, the closely spaced and the optimally spaced versions of the array require slightly different tip-wire lengths.

+ 
+Inverted-U Yagi 17-Meter Performance
+Heavy-duty version: Driver Length: 264"   Reflector Length: 288"  Element Spacing: 92"
+Close spaced version: AWG #12 Vertical End Wires: 35"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.38           10.95          36.1 - j 2.8            1.39
+18.118        6.30           11.03          37.6 + j 0.4            1.33
+18.168        6.23           11.06          39.1 + j 3.5            1.29
+Heavy-duty version: Driver Length: 264"   Reflector Length: 288"  Element Spacing: 112"
+Optimally spaced version: AWG #12 Vertical End Wires: 34.5"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.28           10.54          46.3 - j 2.8            1.10
+18.118        6.21           10.64          47.9 + j 0.1            1.04
+18.168        6.15           10.71          49.5 + j 2.9            1.06
+Medium-duty version: Driver Length: 262"   Reflector Length: 284"  Element Spacing: 92"
+Close spaced version: AWG #12 Vertical End Wires: 35"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.31           11.08          37.1 - j 0.4            1.35
+18.118        6.23           11.12          38.7 + j 2.8            1.30
+18.168        6.16           11.10          40.2 + j 6.0            1.29
+Medium-duty version: Driver Length: 262"   Reflector Length: 284"  Element Spacing: 112"
+Optimally spaced version: AWG #12 Vertical End Wires: 34.5"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+18.068        6.22           10.65          47.2 - j 0.7            1.06
+18.118        6.15           10.73          48.8 + j 2.2            1.05
+18.168        6.08           10.75          50.3 + j 5.1            1.11
+
+

Fig. 4 shows free-space band-center E-plane (azimuth) patterns for the heavy-duty version of both the closely spaced and the optimally spaced models of the inverted U Yagi. As we noted in the case of the 12-meter inverted-U Yagi based on a 10-meter baseline, the side nulls diminish in depth as we add the 3' vertical wires to the original element ends.

+
+ +
+

The 50-Ohm SWR graph overlays the plots for the heavy-duty closely spaced and optimally spaced arrays. We define optimal spacing as the driver-to-reflector distance that yields a very good match to 50-Ohm cable. Hence, it appears in the lower line. The upper line for the close spaced model still represents a highly usable direct feed system.

+
+ +
+

20 Meters: Our ultimate goal is a reasonably compact 20-meter 2-element Yagi. By extending the tip sections to about 90", we obtain the 20-meter inverted-U Yagi using the 15-meter baseline array. The tip lengths again vary with the level of construction but are about 3' shorter than the required tip sections for the 10-meter baseline beam. As the table shows, we gain about a half-dB of gain and about a full dB of front-to-back ratio by using the 15-meter beam as the basis for the inverted-U elements. However, the element spacing must be about 160" (0.19 wavelength) to achieve a 50-Ohm feedpoint impedance.

+ 
+Inverted-U Yagi 20-Meter Performance
+Heavy-duty version: Driver Length: 264"   Reflector Length: 288"  Element Spacing: 160"
+Optimally spaced version: AWG #12 Vertical End Wires: 90"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+14.0          6.27            9.21          38.0 - j12.6            1.49
+14.175        5.87           10.32          45.2 + j 1.1            1.11
+14.35         5.50           10.13          51.4 + j13.7            1.31
+Medium-duty version: Driver Length: 262"   Reflector Length: 284"  Element Spacing: 160"
+Close spaced version: AWG #12 Vertical End Wires: 89.5"
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+14.0          6.25            9.31          38.0 - j11.4            1.46
+14.175        5.84           10.38          45.4 + j 2.5            1.12
+14.35         5.45           10.09          51.5 + j15.3            1.35
+
+

As shown by the patterns in Fig. 6, the pattern shape has degraded from distinct forward and rearward lobes into a pear-shaped affair with a very significant reduction in the side nulls. As well, the front-to-back ratio does not maintain a minimum value of 10 dB all the way across the 20-meter band. (Although the 20-meter band is only 350 kHz, compared to the 450 kHz on the 15-meter band, the 20-meter band is wider when expressed as a percentage of the band center frequency: 2.5% vs. 2.1%. Beam characteristics tend to vary as a function of the bandwidth expressed as a percentage. Hence, the 15-meter inverted-U Yagi with the 10-meter baseline obtained the requisite minimum front-to-back ratio, but the 20-meter beam based on a 15-meter array did not. The small difference in the bandwidth percentages gives us a measure of how fast the inverted-U properties tail off outside the band limits.)

+
+ +
+

By using a 160" spacing between the driver and reflector on 20 meters, we obtain a very good 50-Ohm SWR curve on 20 meters, as shown in Fig. 7. The same spacing applied to the 20-meter inverted-U version of the 10-meter baseline beam produced a curve that did not reach a minimum value of 1.5:1. Hence, the 160" spacing of the present version of the beam makes better use of the spacing.

+
+ +
+

In general, the 20-meter inverted-U Yagi based on a 15-meter beam provides adequate performance as a 2-element array. For a permanent installation, a designer can use closer element spacing (perhaps down to 0.125 wavelength or about 105") and accept the need for a matching network to change the lower feedpoint impedance to 50 Ohms. Nevertheless, the resulting beam will still have 3 dimensions: the listed side-to-side value for a 15-meter beam, the selected front-to-back dimension, and the vertical length of the end-wire tips. The tip wires present challenges with respect to both siting and safety. Their ends carry high voltages and must be well above a level that someone might accidentally touch. As well, they must clear any object (such as a house, barn, or garage) on which one might mount the array in a rotating configuration. Finally, for the long-term construction envisioned in this design exercise, the tips may require a periodic return to their vertical positions after long periods of bending forces by normal winds.

+

Thinking about Alternatives

+

In our efforts to arrive at a workable 20-meter inverted-U 2-element Yagi, we have allowed ourselves the luxury of tunnel vision, focusing solely on the goal of achieving the 20-meter design within the prescribed boundaries of the exercise. However, in the real world, we should never settle for a narrow view of available antenna technology until we have surveyed all of the options, including those that may appear only to well-trained peripheral vision. We have many options for a 2-element 20-meter beam, even assuming that we wish wide-band operation. For example, we might consider a full size 2-element Yagi with 35-36' elements.

+

If we wish to have a more compact footprint--something in the 25' range for a maximum side-to-side dimension--we have fewer choices. One alternative is the Moxon rectangle. Fig. 8 shows a scaled comparison of the 20-meter inverted-U Yagi next to a Moxon rectangle designed for the same frequency coverage. The Moxon is only about a foot longer from side-to-side than the inverted-U Yagi, but it is about 4.5' shorter front-to-back (108" vs. 160").

+
+ +
+

I have in the past developed some algorithms for calculating the dimensions of Moxon rectangles for any frequency and for any uniform-diameter element size. Because the elements used in this model employ a stepped-diameter tubing schedule, the actual dimension vary considerably from those of a uniform-diameter model. As in the case of the Yagi, the side-to-side dimension becomes longer due to the stepped element diameter. The top portion of Fig. 9 shows the conventional way of charting dimensions for a uniform-diameter Moxon rectangle. For comparison, I have mapped the dimensions of the present design against a uniform-diameter Moxon rectangle with 0.626" diameter elements--about the average of the tubing sizes used in the tapered design. Dimension E is to total front-to-back size, the sum of dimensions B, C, and D.

+ 
+A Comparison of the Dimensions of a Tapered Element Diameter Moxon and a Uniform-Diameter Moxon
+
+Dimension     Tapered Model     Uniform Model
+A             317"              301.45"
+B              42.5"             42.52"
+C               7.5"             11.39"
+D              58"               57.27"
+E             108"              111.18"
+
+
+ +
+

The lower portion of Fig. 9 shows the modeled element-diameter taper schedule used in the design. The half-element schedule shown applies to both sides of the element centerline. Tube diameters range from 1" at the center to 3/8" for the tips. Past the center-most section, the numbers come in two parts. The first shows the exposed length, while the second shows the insertion length. Note that the 7/8" tube extends inside the 1" tube all the way to the center. Since the element length is tip to tip, subtract a small amount from the center-most sections for the feedpoint gap. The tip sections, which fold back and point at each other, use 3/8" tubing. Before we close the investigation, we shall briefly discuss some of the construction issues that are common to both the inverted-U Yagi and the Moxon, as well as some that are unique to each type of array.

+

In fact, AerialActs of Silver Spring, MD (web.archive.org) (Craig Roberts, W3CRR) markets a commercially made Moxon rectangle (called the MaxiMoxon) that employs similar but not identical structures as the present model. The MaxiMoxon employs a different taper schedule than the model shown here.

+

The side-to-side dimension for the elements is 317", about 30" more than required by the longest 15-meter Yagi element in the inverted-U beam design. The total front-to-back dimension--including both the driver and the reflector tails and the gap between them--is 106". The 3/8" driver tail is 42.5", while the reflector tail is 58". The gap--perhaps the most critical dimension in the collection--is 7.5". In all model-based designs, the dimensions run from one element centerline to the opposing element centerline. With the given dimension, we obtain the modeled performance shown in the following table. Note that the proper design frequency for a Moxon rectangle is about 1/3 the way from the bottom of the operating passband to achieve good values of front-to-back ratio and 50-Ohm SWR at the band edges. The Moxon design shown is for a direct 50-Ohm connection (via the usual common-mode current suppressing choke or 1:1 balun).

+ 
+Moxon Rectangle 20-Meter Performance
+See text for dimensions.
+Frequency     Free-Space     Front-Back     Feedpoint Impedance     50-Ohm
+MHz           Gain dBi       Ratio dB       R +/- jX Ohms           SWR
+14.0          6.46           18.11          38.1 - j11.7            1.46
+14.15         6.13           28.42          48.5 - j 0.2            1.03
+14.35         5.73           18.09          60.6 + j11.6            1.33
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+

In general, the Moxon and the inverted-U Yagi achieve the same gain levels and have similar SWR curves. Where the Moxon shows the greatest performance edge is in the front-to-back ratio, averaging a 10-dB improvement across the 20-meter band. Fig. 10 graphs the gain and the front-to-back curves, including both 180-degree and worst-case values. (The worst-case front-to-back ratio is called the front-to-sidelobe ration on the graph.) Note that the two curves are nearly the same. As in all 2-element parasitic beams using a driver and a reflector, the gain decreases nearly linearly across the operating passband. Fatter elements would yield a flatter gain curve with a slower rate of change, while thinner elements will show a steeper curve.

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Fig. 11 shows the progression of feedpoint resistance and reactance across the passband. Both curves change values at about the same rate, allowing for easy coverage of the 20-meter band. The 50-Ohm SWR never exceed 1.46:1, and the curve can under go further refinement during field adjustments. Like the gain curve, the SWR curve is flatter with fatter elements, although--of course, changing the element diameter schedule would require re-design of the array.

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The evolution of the free-space E-plane (azimuth) patterns appears in Fig. 12. The progression is normal for a Moxon rectangle. The side nulls do not appear at 90 degrees from the main forward heading, but between 100 and 120 degrees away from that heading. A uniform diameter Moxon array is capable of a maximum front-to-back ratio of 40 dB or more at the design frequency. The stepped-diameter version approaches 30 dB. However, the band-edge values (>18 dB) are similar to those of a comparable uniform diameter model. I did not try to refine the design frequency front-to-back ratio further, but instead held dimension changes in the design process to 0.5" for easier construction.

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Because the Moxon rectangle is flat and has a smaller horizontal footprint overall than the inverted-U Yagi, it may be in principle a better route to obtaining 2-element directional performance on 20 meters. As well, the increased front-to-back ratio may aid operation, especially reception. As a result, it is a useful alternative as we expand our thinking and escape the narrow focus the comes with trying to perfect a single design.

+

A Few Construction Notes

+

The Moxon rectangle is not the only alternative to the inverted-U Yagi for obtaining a directional beam with 2-element Yagi performance, but with a considerable saving in overall array size. However, it suffices to show the advantages of stepping outside a commitment to a single design and to considering alternatives for the achievement of a complex set of design and operating goals. In this instance, our goals included shrinking the overall size of a normal 20-meter Yagi, but retaining as much of the performance as possible. In addition, we set up an element taper schedule that better suited a long-term installation.

+

Both the inverted-U and the Moxon rectangle use a direct 50-Ohm feedpoint, which calls for a split driver to make connections at the element center. At HF, the size of the gap is generally not critical, although the actual gap is in principle simply the distance between the two conductors of the feedline cable. The leads from the cable or from the cable connector are part of the driven element. The element dimensions from end-to-end do not change, so we subtract half the gap size from each half-element in the driver.

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Modeled designs also presume that all elements are well insulated and isolated from any conductive boom that might provide physical support. A 10' section of 1.25" outside diameter aluminum tubing is probably the most common boom material. Although the assembly is fairly light, a 1/8" wall tube or nested sections of 1.25" and 1.125" tubing is wise to support the wind-induced twisting loads on the entire assembly. Fig. 13 shows one method (out of several) for constructing the feedpoint. A polycarbonate or similar plate provides the element isolation and supports the boom U-bolts. If we insert a non-conductive tube into the ends of each element half, we assure element alignment with only 2 U-bolts and also establish an anchor point for the gap and the feedpoint connections. If we also run the inner tube to the gap, then it also provides support that will keep the aluminum elements from crushing as we tighten the U-bolts. The outside diameter of the gap-setting tube should just fit inside the center tube section of the element. For the doubled Moxon 1" element section and for the 7/8" inverted-U element section, the required size would by 3/4". All hardware is stainless steel to prevent corrosion and to avoid bimetallic electrolysis.

+

As shown in Fig. 14, we may treat the reflector of either beam design in a similar manner. In this case, we bring the ends of the tubes together to form a continuous element or we use a single piece of tube to form the center element section. The advantage of using a split section at the reflector center is that we may use an interior piece of aluminum tubing to form the physical and electrical junction of the 2 element halves. Alternatively, we may use a single outer tube at the reflector center and then run the next smaller size tube from each side to the center of the outer tube. Extending the inner tube to the center of the outer tube provides the same insurance against U-bolt crushing that we obtained from the non-conductive tube in the driver elements.

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The inverted-U element tips may use a simple eye-ring and bolt assembly for attachment. However, the Moxon tips require more thought, since we must meet several criteria. First, we must turn a corner. Second, we must maintain the gap size, even in the face of winds. Third, we must keep the tail ends aligned. For 3/8" diameter tubing, turning a corner is not difficult. Starting with a tube section that is longer than needed, we can bend one end in the same tubing bender used for small copper tubing. We can insert the short end into the 0.5" diameter section. The small curve at the corner will not alter the overall element length enough to cause any noticeable change of performance if we keep the total element length equal to the sum of all of the exposed portions of the sections. Fig. 15 shows the general scheme.

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The figure also shows a simple way to maintain the gap and to keep the ends aligned. We simply insert a 1/4" non-conductive tube or rod into the tail ends and fasten it with stainless steel sheet metal screws. The result is a physically closed rectangle. Because the Moxon rectangle in this configuration is subject to racking forces, we likely should reduce the wind load capacity of the elements by a small amount. The structure shown in Fig. 9 should handle winds up to about 80 mph.

+

There are as many variations on physical construction as there are potential element-diameter taper schedules. Therefore, consider these notes as simply a starting point for your own ingenuity.

+

Conclusion

+

We have explored the use of an inverted-U Yagi as a means of obtaining a usable 2-element beam on 20 meters that is smaller than the normal 20-meter Yagi. To obtain nearly full performance, we had to begin with a 15-meter Yagi and add vertical tail sections. The longest element in the array was 24', with 90" vertical tails. To obtain a 50-Ohm feedpoint impedance, we required 160" between the 2 elements. We might use about 110" spacing if we are willing to add a matching network to the driver to raise the low impedance that results from closer spacing.

+

Since the size reduction that we achieve with the inverted-U Yagi on 20 meters results in adding a vertical dimension to the beam, we also looked at one alternative (among several that are possible) as a way of obtaining the same performance, having a 50-Ohm feedpoint, and further shrinking the antenna footprint. The Moxon rectangle is a good candidate, since it is a 2-dimensional array. With the element taper schedule used for the sample model, we ended up with a package that is 26.4' by 9.0', with no vertical dimension beyond the thickness of the elements and the mounting assembly. As well, we improved the front-to-back performance of the array.

+

The contrast of the two arrays shows us two significant facets of design work. First, a tight focus is required to bring an array to the point of maximizing its performance within the design criteria. Second, once we reach maximum performance, we need to widen our view to consider alternative approaches to reach the same goal and possibly to reach higher standards. The inverted-U dipole proved to be a useful field antenna. Within limits, it can also serve as a 2-element Yagi. However, when we take the design out of the field and plan for its use in a more permanent installation, it begins to show some of its limitations. We might easily have overlooked those limitations had we not examined a potential alternative design. The contrast strongly suggests that the inverted-U serves best as a simple dipole with changeable ends. Even as a Yagi, its best place may be in the field. For durable installations, there are better designs available.

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Updated 06-12-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

+

Topics: HF Upper, Inverted U, Yagi


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Horizontal and Vertical Yagi Orientation

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L. B. Cebik, W4RNL

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+ A number of folks have posed some basic questions about Yagi performance when the beam is laid out horizontally and when it is laid out vertically. Since pictures may be useful, I decided to do this short note to help them get oriented. +

First, let's imagine a dipole. It is a typical antenna composed of a linear (straight) element. Now lets draw a circle so that the circumference touches each end of the dipole. We shall call this the E-plane. Next, let's draw a second circle and position it so that the end (either one) of the dipole makes a dot at the circle's center. We shall call this the H-plane.

+

Every antenna composed of linear elements has a distinct E-plane and H-plane. By convention, if the antenna has several elements, like a typical Yagi, we draw the E-plane circle so that it cuts all the elements. We center the H-plane circle on the driven element (and usually let the line of elements be horizontal across the circle).

+

These conventions are more than just arbitrary, because antennas composed of linear elements perform differently in each plane.

+

Consider an old friend, the isotropic source. The isotropic source is a hypothetical point without dimension that radiates equally well in every direction in free space--that is, space with no other objects or reflecting surfaces in it. If we were to trace a line of constant signal strength at some distance from the source, we would get equal size circles in both the E-plane and the H-plane. (In fact, we would not know just what to call the E-plane and the H-plane, except that they would have to be 90 degrees different in direction.)

+

The minute we change the type of antenna, equality disappears. Let's immediately jump to the Yagi beam, since that is where we ultimately want to go. The figure below shows a hypothetical 3-element Yagi and identifies the E-plane and the H-plane. (Save the bottom of the picture for the moment.)

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If we plot the performance of a typical 3-element Yagi in free space, we would want to examine both the E-plane and the H-plane. On most modeling programs, we tend to orient the antenna so that the E-plane corresponds to the azimuth and the H-plane corresponds to the elevation. Therefore, our plots will look like the figure below.

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Notice that the E-plane pattern is highly confined, with a major lobe forward, some minor lobes to the rear, and strong nulls to the sides. The current magnitude and phase along the elements act together to produce this confinement of radiation.

+

Now examine the H-plane pattern. Since there are no linear element ends (and resultant current magnitude and phase level pattern along the element) to confine the radiation, the pattern is nearly a circle, simply displaced forward of the driven element. The variation of the pattern from a true circle is a product of the interaction of the radiation from the three elements.

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These patterns will be replicated with some variation for every antenna composed of linear elements in a plane. A very long UHF Yagi or a complex phased array of Extended-Double-Zepp elements might narrow the beam width in the E-plane from the 3-element Yagi's 50-60 degrees down to less than 20 degrees. Large arrays with many elements often show somewhat ragged edges to the equal-signal strength lines. But allowing for these variations, the E-plane and H-plane free space patterns of the antennas will show their kinship.

+

Now return to the original picture and examine the bottom. Here we have introduced the earth and have placed our Yagi over it in two different orientations. On the left, the plane of the antenna (the E-plane) is parallel to the earth and we call the orientation horizontal. On the right, the plane of the antenna is at right angles to the earth and we call the orientation vertical.

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What is crucial about the difference is that when the antenna is horizontal, it is the H-plane which the earth cuts off in the form of reflecting signals that would have been directed downward. The E-plane radiation pattern is largely unaffected. When the antenna is vertical, the E-plane is cut off in the form of signal reflection, and the H-plane pattern is unaffected.

+

We can show the consequences of each with a small sample. Let us place the Yagi 1 wavelength above the earth, as measured by the position of the boom that holds the elements in alignment. If the antenna is horizontal with respect to the earth, then the antenna pattern looks like that in the following figure (assuming, as we do in all modeling, a flat, uncluttered earth surface).

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The patterns above are the azimuth and elevation patterns of the Yagi oriented horizontally with respect to the earth's surface. First of all, note that the azimuth pattern shape is almost the same as the E-plane pattern in free space. The beam width of 50-60 degrees coincides closely to the free space value.

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The only significant difference is the gain, which is now something over 5 dB higher than in free space. Arrayed over good, but not perfect ground, the gain is typical for 3-element Yagis 1 wl up. The quality of ground makes a small and operationally insignificant difference in the antenna's gain. Larger variations show up as the antenna height is changed between, say, 0.5 wl and 2 wl. Gain maxima occur roughly at 5/8, 1 1/8, and 1 5/8 wl heights, while minima occur at 7/8 and 1 3/8 wl heights. These maxima and minima become indistinct the higher we raise the antenna.

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Where the added signal strength comes from is revealed by the elevation pattern. The signal which in free space would have radiated downward is reflected by the earth (with only a very small loss for horizontally oriented antennas). It combines with the direct signal radiated upward. At some points, the two signals combine in phase and add to create a lobe. At other points, the signals combine out of phase to create a null.

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The lobes and nulls form a regular pattern. The general formula for lobes and nulls is

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where Ae is the elevation angle of the lobe or null, N is an integer indicating the number of the lobe or null from lowest upward, and h is the antenna height in wavelengths or a fraction thereof. Odd integers indicate lobes and even integers indicate nulls.

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For convenience, the following table provides the elevation angles of the first lobe, usually the strongest, and second lobe for horizontal antennas at heights of 0.5 wl up to 2 wl.

+ 
Antenna height      Angle of first      Angle of second
+ in wl                   lobe                lobe
+     0.5                 30 deg              none
+     0.75                19                  90 deg
+     1.0                 14                  49
+     1.25                12                  37
+     1.5                 10                  30
+     1.75                 8                  25
+     2.0                  7                  22
+

The table gives elevation angles in whole numbers for two reasons. First, a fraction of a degree makes no operational difference in a lobe that has considerable vertical dimension, as shown in the elevation pattern above. Second, the real properties of the antenna and of the ground will alter the exact angle of maximum radiation, especially at lower heights. For example, NEC-4 models of 3-element Yagis over average earth tend to show maximum elevation angles of radiation between 24 and 26 degrees, rather than the calculated 30 degrees. These difference tend to wash out as the antenna is raised higher. However, this chart will serve as a general guide to expectations. (Note: Hasan Shiers, N0AN, has posted similar information on one of the antenna-related lists.)

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Now let us consider what happens if we build the Yagi in a vertical orientation with the boom 1 wl up. The resultant patterns are these:

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As the azimuth pattern demonstrates, the side-to-side pattern resembles very closely the H-plane pattern of the free space model. The beam is about 100 degrees wide between -3 dB power points, about twice as wide as the beamwidth of the Yagi when horizontally oriented. However, compare the maximum gains of the horizontal and vertical Yagis: the vertical Yagi has for this particular case almost 5 dB less gain.

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Because the element ends are within 3/4 wl of the ground, the gain deficit relative to the horizontal Yagi of identical design is fairly high. As the height of the antenna increases, the gain deficit diminishes for antennas many wavelengths up as would be the case with most VHF/UHF Yagis. A 2-meter 3-element Yagi 5 wavelengths up shows a gain differential of about 1.5 dB between vertical and horizontal orientations. Moreover, because vertically oriented linear antennas are more dependent on ground quality than horizontal antennas, the degree of gain deficit will vary with the ground quality. Again, the degree of differential will diminish as the antenna height is increased.

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The elevation pattern of the vertically oriented Yagi also differs considerably from that of the horizontal Yagi. For low Yagis with boom heights under 2 wl, the first two lobes tend to blend into a front. The angle of maximum radiation is 10 degrees for the case of the Yagi with a boom 1 wl up, but that point is part of a broad, flatted field face of considerable vertical dimension. The vertical beamwidth of the elevation pattern is about 30 degrees.

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These properties do not make the vertically oriented HF Yagi useless by any means. Granted, for rotatable beams atop high towers, horizontal orientation has become an accepted standard for good reason. However, not every amateur installation can raise such Yagis. Wire antennas in fixed positions are often necessary for a variety of reasons. An array of 4 vertically oriented Yagis would provide world-wide coverage. With some ingenuity, one might use a single driven element with only 4 other vertical wires. By using inductive and/or capacitive reactance, the other 4 wires can be converted into directors or reflectors--or de-tuned to not be part of the array. Hence, world-wide coverage might be achieved with a 4-way switch, a few relays, some transmission-line stubs, and one or more weather proof boxes to house the junctions. Even with tubular elements, the cost will be considerably less than a tower and rotator, and the maintenance ease is likely to be considerably greater.

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Such systems have been built in the past and will be built again. Their exact design goes far beyond the point of this note, which has been to provide some basic acquaintance with the consequences on far field patterns of orienting a Yagi horizontally and vertically. If the patterns displayed here add a bit to your rational expectations of antennas, they will have done their work.
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Supplementary Note:
+ The Evolution of the E-Plane and the H-Plane

+
The conventions of speaking about the E-plane and the H-plane with respect to antenna patterns has remained a bit elusive, if questions I have received are any indicators. So perhaps a bit of a non-mathematical derivation of the names might be useful as an addendum to this note. +

The names for the plane derive from basic antenna fields, electrical and magnetic. For a succinct mathematical treatment of these fields, see "Fundamentals of Antennas," by Henry Jasik in Johnson (ed.), Antenna Engineering Handbook, 3rd Ed, pp. 2-1 to 2-7. For a more thorough non-mathematical treatment, see The ARRL Antenna Book, pp. 2-7 to 2-9.

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Linear antenna elements produce two types of fields: the E or electrical field, in which lines of force roughly parallel a linear element, and the M or magnetic field, in which lines of force are tangential to the linear element. The figure above is suggestive of the fields, but--like all the other 2-D approximations I have encountered--is not wholly accurate. Note that the lines in the figure are rounded and I just said they are parallel. Neither is strictly true.

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This next figure gives a different slant on the fields from the perspective of a vertical monopole and adapted from the ARRL figure 23-1. I have modified the figure to give a sense of lines of force. Electrical lines, running top to bottom are nearly straight, while magnetic lines circle the antenna element.

+

Now place a dipole is free space and think about the electrical and magnetic fields. The lines of force of one project roughly in line with the antenna element and this is the E-field. The lines of force of the other project in circles about the element at right angles to it, and this is the M-field.

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The circles in the figure above show one way of looking at the fields. One major line of force of the magnetic field will intersect a tangent line drawn through the center of the dipole. I have added big dots to associate the circle with the correct line.

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The lines of force for the electric field are in the plane of the antenna, which means that for illustrative purposes, they touch the ends of the antenna. This defines part of the E-field.

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The E-field defines and creates the E-plane. The M-field defines and creates the M-plane.

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Now for the crooked shift: when we consider very distant field strength--the far field--we consider virtually only the E-field. However, we preserve the E-plane and the M-plane that the different fields have created and lent their names to.

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The above far field pattern is taken in an E-plane of a dipole in free space. It records on a line of equal field strength a pattern of interest to use. This particular pattern is an E-plane pattern labeled in dB.

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Since we are in free space, we can also take a 360-degree H-plane pattern, that is, a pattern at right angles or tangential to the linear dipole. However, this field records the electrical field (not the magnetic field), just as did the E-plane field.

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The circularity of the H-plane pattern tells us that we could have taken any slice through the element and create another E-plane at some angle to the one we chose to use.

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The figure above indicates that there are an indefinitely large number of possible E-planes and E-plane patterns with a single dipole element, which the figure shows end-on. In free space, one is as good as another.

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However, the instant we go to 2 elements, the elements reduce the E-plane to one field in the plane of both elements. As shown in the figure, the E-plane cuts both elements equally. From this point, you can move back to the representation in the very first figure in the note on polarization. The arrow heads on the plane representations are simple indicators that the antenna in question has directional gain and a rear null. The actual E-plane and H-plane extend indefinitely far in their 2-dimensional extensions.

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All of this is bound to raise some questions. For example, suppose three elements are not in line, but make some kind of triangle when viewed end-on. Suppose an antenna element has wires that go every which-a-way.

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Since we are dealing with conventions, we might as well add another. Complex antenna geometries are usually initially referenced to their intended application over the ground. Then a line parallel to the ground can be drawn through the array of elements viewed end-on. This is the E-plane. If such a line cannot be drawn because of the orientation of the elements, then a parallel to high current node of the antenna can be drawn and this becomes the E-plane. A second plane at right angles to the first can be drawn to cut at least some of the elements and this becomes the conventionalized H-plane.

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Some antennas, like the delta loop fed as a vertically polarized 1-wl array, defy even this treatment. However, by the time we get to this advanced state of affairs, we have added the ground to our system and can reference the antennas to it. In such cases, we speak of the less confusing vertical and horizontal polarization of radiation from the antenna. Talk of E-plane and H-plane is best suited to simple antennas in free space. They are reminders of certain fundamental concepts in antenna operation. However, for many complex arrays of elements, it is far less confusing to view them over a ground and then, if necessary, export the vertical and horizontal notions back into free space, referencing them to the X, Y, and Z coordinates of a familiar Cartesian system.
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Updated 4-22-98, 10-13-98. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.
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+ Go to Amateur Radio Page
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Topics: Yagi


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V-Yagi is it a 3-Element Moxon?

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L. B. Cebik, W4RNL

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In the exploration of the V-Yagi, we ended with an unanswered question based on the performance and pattern characteristics of the antenna. The pattern and some of the performance curves resemble those associated with the 2-element Moxon rectangle that uses dual coupling--from the parallel elements and from element tip to element tip. However, the Moxon rectangle uses close tip spacing between the driver and reflector. The V-Yagi uses wider spacing between parasitic element tips, with an intervening driver. Hence, the question mark.

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We can formulate the question in several ways. Is the V-Yagi a 3-element Moxon rectangle? This question is actually a disguised form of another: Does the V-Yagi derive its patterns and performance curves from dual forms of element coupling? Or, are the V-shaped elements in the V-Yagi sufficient to account for the analogous behaviors between it and the Moxon? An affirmative answer to the latter question would suggest that there may be a critical angle for parasitic elements that produces, at the design frequency, a nearly cardioidal pattern. This result would be consistent with studies of the VK2ABQ square. In that design, which uses the same kind of fold-back elements as the Moxon, we find 2 versions: a narrow-spaced version that forms a squared Moxon and a wide-spaced (or large-gap) version that appears less dependent upon the gap for its characteristics.

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The questions posed here have very few practical implications. They do not change the recommended dimensions for the V-Yagi or alter its performance. Instead, the matter simply piques my curiosity. My analytic tools focus on careful modeling of the antenna. However, the calculations performed by the NEC core do not automatically signal the number and types of coupling modes that may be at work with relatively close spaced elements in an array. Rather, the program calculates interactions among all segments as a single large matrix, taking into account the geometric structure of segments, some of which are connected to others and some of which form unconnected wire ends.

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However, NEC offers indirect evidence for single or dual element coupling. (Actually, all elements within the inductive or close-in near field range are dual coupled. However, the more parallel the elements and the farther apart, the weaker that end coupling will be until we may almost dismiss it. However, NEC does calculate the end effect of wires and takes this factor into account in the overall calculation of the interactive matrix.) We need to devise a strategy that will allow us to distinguish between patterns that result from Vee'd parasitic elements and those that emerge from dual coupling.

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We can obtain the necessary clues if we pay close attention to the patterns and performance curves of a series of antennas. Fig. 1 shows the sequence that we shall use. All antennas in the series are scaled to each other, relative to the models that we shall examine. In fact, all of the models will use the 10-meter amateur band (28.0 to 29.0 MHz) as the test arena. Except for the V-Yagi, all models will use 0.5" diameter elements. The V-Yagi model will use a 1" driver with AWG #14 parasitic elements. (The diameter of AWG #14 wire is 0.0641".) The first antenna is a short-boom standard-design Yagi. Its patterns and performance curves will form a reference against which we can compare the results from other models.

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The second antenna is the V-Yagi. We shall be interested in examining the details of how the pattern and performance curves differ from those of a standard Yagi. Then we may compare the data for both antennas against a model of a Moxon rectangle to see if we may find points of similarity and of difference. However, this comparison alone will not provide us with sufficient information to be decisive about our initial question.

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If there is dual coupling between the parasitic elements of a V-Yagi, we ought to be able to enhance that phenomenon by creating a rectangular version of the antenna, shown at the bottom of Fig. 1. The sketch of the rectangle is incomplete, since it shows a shortened driver. We may bring the driver to resonance by adding symmetrical extensions at right angles to the driver. We shall look at 2 variations on this process to see if they have any significant affect the antenna performance.

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The sum of these maneuvers should provide us with sufficient information to determine whether or not the V-Yagi obtains its Moxon-esque patterns and performance curves solely from the parasitic Vee element shapes or also from coupling between element tips. Table 1 provides the dimensions for most of our test models. I shall explain any special designations in the course of working with each antenna.

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The Standard Yagi

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Standard 3-element Yagis come in a variety of boom lengths and element layouts. The 10-meter version used here is a short-boom model with a 90" spacing between the reflector and the director (with the standard 0.5" diameter elements). For added gain, we can increase the boom length by up to 50% with only a small reduction in the 2:1 SWR passband. However, the short-boom model perhaps most closely corresponds to the V-Yagi and other models. The native driver impedance is close to 25 Ohms, so I have equipped the model with a beta match to yield 50-Ohm SWR curves, which appear for all other models in the series. In general, the operating passband of an antenna does not change significantly when we add a well designed impedance-matching network. As well, such networks have no effect upon the pattern shape, the forward gain, or the rear lobes of the array.

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Fig. 2 shows the free-space azimuth or E-plane patterns of the antenna at the band edges (28.0 and 29.0 MHz) and at the design frequency (28.5 MHz). The design selects element length and spacing values to yield at least a 20-dB 180-degree front-to-back ratio at each band edge. Perhaps the most important pattern feature to notice is the side nulls at 90 degrees off the main forward heading of the pattern. Because the elements are parallel to each other and because each element has negligible end radiation, the radiation far field goes to virtually zero at right angles to the boom in a free-space context. (Over ground, the nulls become shallower as we bring the antenna closer to ground.)

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Since the patterns do not show the relative gain values, the following small table of spot values will fill the blanks. The table shows excessive decimal places in values, but you may truncate the values wherever you please.

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+Spot Free-Space Performance of the Short-Boom Standard Yagi
+Frequency                              28.0             28.5             29.0
+Gain dBi                               7.08             7.12             7.36
+180-Deg. Front-to-Back Ratio dB        20.74            41.84            20.59
+Beamwidth degrees                      66.8             66.6             65.6
+Feedpoint Resistance Ohms              79.78            53.98            30.54
+Feedpoint Reactance Ohms               6.89             0.12             -1.41
+50-Ohn SWR                             1.615            1.080            1.639
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We can enhance the spot values by performing a frequency sweep at 0.1-MHz intervals. The result will be a better sense of how values progress from one end of the band to the other. Fig. 3 shows the curves for forward gain and front-to-back ratios. The line labeled front/back ratio gives the 180-degree values, while the line labeled front/side ratio provides the worst-case front-to-back ratio (since the short-boom array has no forward sidelobes). Note that the worst-case front-to-back ratio does not change very much over the entire 3.5% bandwidth

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What the spot chart does not show us is the fact that, at the low end of this wide passband, the gain actually dips as frequency increases befor entering the steady rise in value that we ordinarily associate with Yagis having 1 or more directors. The dip is operationally insignificant but will be interesting as a reference when we compare other array performance curves with this one. The position of the 180-degree front-to-back ratio values tells us that the peak value occurs just above the design frequency.

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The chart of feedpoint resistance, reactance, and 50-Ohm SWR in Fig.4 shows the reverse characteristic created by the use of a matching network at the feedpoint. Without the network, the 25-Ohm lines would have shown a rising feedpoint resistance across the band, with a reactance that began as capacitive at 28.0 MHz and ended as inductive at 29.0 MHz. Like the curves that result from the presence of a matching network, the progressions of resistance and reactance would have been nearly linear. Since in either case, I would have set the array dimensions for roughly comparable SWR values at each end of the band, the SWR curve would also have shown a reverse characteristic, rising more rapidly below the design frequency than above it.

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The data on the standard-design 3-element Yagi give us a fair catalog of array characteristics to use as we proceed through the comparisons. As well, they serve as a useful review of what to expect from a well-designed 3-element short-boom Yagi.

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The V-Yagi

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As shown in Table 1, I have selected a simplified model of the V-Yagi for this exercise. Rather than using a tapered-diameter driver, I have set the diameter at 1" with AWG #14 wire parasitic elements. The total boom length from one parasitic center to the other is 122". The total side-to-side dimension of the array is slightly smaller than for the standard-design Yagi, since we load the reflector with an inductive reactance of 110 Ohms (a 12.04" shorted stub of 600-Ohm line). Nevertheless, despite the fatter diameter of the driver relative to the same element in the standard-design Yagi, it is slightly longer.

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Perhaps the most intriguing aspect of V-Yagi performance are the free-space azimuth (or E-plane) patterns. They appear in Fig. 5, showing the band edge shapes and the shape for the design frequency. In order to yield comparable front-to-back values at the band edges, the design frequency is 28.3 MHz. At the design frequency, the front-to-back ratio is very high, since the 180-degree and worst-case values are identical. As the rear pattern degrades away from the design frequency, the rear lobes grow in a manner quite unlike those of the standard-design Yagi.

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In addition to the differences in the rear lobe growth in the V-Yagi, the array shows its side nulls at an angle (with respect to the main forward lobe) that is not 90 degrees. In fact, the side nulls occur at about 120 degrees off the main heading. One consequence of this feature is a wider beamwidth than we find in a standard design. In the following table of spot values, compare the beamwidth values to those for the standard Yagi presented earlier. The V-Yagi beamwidth is 6 to 7 degrees wider.

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+Spot Free-Space Performance of the V-Yagi
+Frequency                              28.0             28.3             29.0
+Gain dBi                               7.05             6.91             6.92
+180-Deg. Front-to-Back Ratio dB        16.35            34.00            14.42
+Beamwidth degrees                      72.8             73.2             72.2
+Feedpoint Resistance Ohms              37.95            42.43            31.69
+Feedpoint Reactance Ohms               3.29             4.29             16.98
+50-Ohn SWR                             1.331            1.208            1.855
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When we examine the arrays over the full passband, the V-Yagi performance does not fully match the performance of the standard short-boom 3-element Yagi with respect either to gain or to front-to-back ratio. However, for the present investigation, we are less concerned with this fact than with a comparison of the performance curves. Fig. 6 presents the gain and front-to-back ratio curves for the V-Yagi for comparison with Fig. 3.

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Partly because V-Yagi construction calls for wire parasitic elements, the front-to-back curves do not hold up at the band edges to the level achieved by the short-boom standard Yagi. However, the 180-degree and the worst-case front-to-back ratios are the same throughout the passband. The gain curve is especially interesting. It shows a decreasing value as we move upward from the low end of the passband, followed by an upward swing at the top of the passband. The reduction in forward gain with increasing frequency resembles in a more dramatic--if not drastic--way the curve for the short-boom standard Yagi. The gain curve is not directly dependent upon the front-to-back ratio, since the front-to-back peak and the gain null occur at significantly different frequencies within the passband. More directly related to the gain curve are the values for the beamwidth: the higher the gain, the narrower the beamwidth. The amounts are small, but the phenomenon exists.

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Fig. 7 shows the resistance, reactance, and direct 50-Ohm SWR of the V-Yagi from 28.0 to 29.0 MHz. Compare the curves to Fig. 4. The standard Yagi shows nearly linear resistance and reactance curves. Without the matching network, these curves would show the opposite slope, but retain their near linearity. In contrast, the V-Yagi resistance curve shows its highest value at the design frequency, with lower values away from that frequency (28.3 MHz). As well, the reactance curve is not close to linear. The SWR shows a relatively high value (although still below 2:1) at the top end of the band, because I resonated the array at the design frequency. However, in the V-Yagi, the resonant driver frequency requires only a slight adjustment of the driver length and is almost independent of the dimensions for the parasitic elements. Therefore, we might easily adjust the driver for equal SWR values at both band edges. We may also perform this adjustment on the standard Yagi. Its modeled length is not inherently resonant, but set for the application of a beta match. Resonating the driver of that array would make it fit for a 1/4 wavelength matching section instead of the beta match stub.

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The Moxon Rectangle

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The question that we posed in the beginning--whether a V-Yagi exhibits dual coupling--requires that we add a Moxon rectangle to our list of examinees. The Moxon rectangle clearly exhibits both parallel and tip coupling, and so its characteristics become an important for comparison. However, the Moxon is a 2-element driver-reflector array, and we shall have to adjust some of our expectations accordingly.

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Fig. 8 supplies the dimension designations that correlate to the actual 10-meter dimensions shown in Table 1. Note that the overall driver and reflector lengths are approximately normal for a 2-element driver-reflector parasitic array. The key to the Moxon's performance lies in the gap between the tips. As we decrease the element diameter, the required tip gap needed to restore performance grows smaller. As well, the gap is more sensitive to construction variation than any of the length measurements.

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Like the V-Yagi, the Moxon requires a design frequency about 1/3 of the way up the operating passband to achieve comparable front-to-back ratios. In this exercise, I lowered the design frequency to match the frequency used for the V-Yagi. For equal front-to-back values at the band edges, a design frequency of about 28.35 MHz or so would have been superior. (Since the array has only 2 elements, the same technique is also necessary to achieve comparable 50-Ohm SWR values at the band edges.) Fig. 9 shows the patterns for the Moxon model across the passband. As the table of spot performance values shows, the band-edge front-to-back values are comparable to those of the V-Yagi. Because the array has only 2 elements, gain values are lower.

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+Spot Free-Space Performance of the Moxon Rectangle
+Frequency                              28.0             28.3             29.0
+Gain dBi                               6.35             6.03             5.38
+180-Deg. Front-to-Back Ratio dB        19.13            43.99            14.75
+Beamwidth degrees                      77.4             78.0             78.6
+Feedpoint Resistance Ohms              40.62            51.22            70.07
+Feedpoint Reactance Ohms               -13.73           -3.58            12.39
+50-Ohn SWR                             1.443            1.078            1.486
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The spot performance checks suggest that the Moxon has both similarities to and differences from the V-Yagi with respect to performance curves. Like the V-Yagi, the Moxon shows a wider beamwidth than standard Yagi designs. At the design frequency, the Moxon beamwidth is actually wider than for the V-Yagi and nearly 12 degrees wider than for a standard 3-element Yagi. Fig. 10 provides the curves for forward gain and front-to-back ratio for the Moxon. Like any 2-element driver-reflector parasitic array, the Moxon shows a steady decline in gain as we increase the operating frequency. If the curve differs from a standard 2-element Yagi, it is in the nearly linear gain curve across the passband.

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The front-to-back curves show differences between the 180-degree and the worst-case values in the center region of the passband. The remnant lobes at the design frequency--apparent in Fig. 9--show why the worst-case value is lower than the 180-degree value. However, as we move toward the passband edges, the rear lobe becomes a single bulbous affair. Under this condition, the worst-case and the 180-degree front-to-back ratios become identical.

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One of the most useful features of the Moxon rectangle is the slow rise in both resistance and reactance across the 10-meter band, as shown in Fig. 11. The result is a wide SWR passband. In this case, the 50-Ohm SWR does not rise to 1.5:1 between 28.0 and 29.0 MHz. Neither the V-Yagi nor the standard 3-element short-boom Yagi can match this performance, although both of these antennas have band-edge SWR values below 2:1.

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One feature of the Moxon that is not amenable to graphing concerns the phase angle of the current on the tip segment of each element. By increasing the number of model segments per element, we can obtain rough values that are useful for first-order comparisons. Ideally, we would like to know the current phase angle as close to the tip as feasible, but initially, we may use 40-50 segments per element to arrive at a general indication of what is happening. The exercise requires that we take the difference in current phase angle between the center segment of each element and the phase angle of the tip segment. Since the tip region is an area of high rates of change in both current and voltage, we cannot expect exactitude from the model. However, we may find something that is suggestive.

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In a standard 2-element Yagi using a driver and a reflector, with 51 segments per element, the sum of the phase angle changes for the two elements (relative to values at the element centers) is about 5 degrees. In a similarly segmented Moxon rectangle, the sum of the phase-angle changes is over 15 degrees. The equivalent sum (for 3 elements) in a V-Yagi with similar segmentation is under 6 degrees. The numbers, while far from definitive, strongly suggest that the V-Yagi does not have significant levels of tip-to-tip coupling. The corollary to this tentative conclusion is that the V-Yagi patterns are functions almost exclusively of the Vee geometry and not of element end coupling.

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The question that remains is whether we can devise a more definitive test.

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The 3-Element Rectangle

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One potential route to confirming our initial very tentative conclusion is to re-form the V-Yagi into a rectangle. In rectangular form, the end coupling--if any--will be enhanced by the fact that the parasitic elements will face each other, tip to tip. As well, the parts of the parasitic elements not within the facing tails will be truly parallel to each other. Several experimental models suggest that the minimum side-to-side dimension for the rectangle is about 160", 10" wider than the Moxon rectangle. The 160" size allows for a direct 50-Ohm feedpoint.

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Since the driver length is almost wholly independent of the mutual performance of the parasitic elements, we may allow it a full length or we may use various means of shortening it. Inductive loading tends to lower the feedpoint impedance. However, end hats sustain the feedpoint impedance better than any other means of reducing the side-to-side dimension of the driver. We shall need to reduce the driver by a total of nearly 40" or about 20" per end. If we add to the driver ends a pair of extensions at right angles to the driver, and if we make them about 12.8" long (each), the driver will approach resonance at the design frequency.

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The next step in the design process is to decide on the direction of the Tee's driver ends. Essentially, we have a choice between placing them vertically or placing them in line with the parasitic element tails. In fact, a fairer test of the possibility of end coupling between parasitic elements is to use both orientations in successive tests. Fig. 12 shows outline sketches of the two driver orientations. If there are significant performance differences between the two versions of the driver, then there will be some disruption of tip-to-tip coupling in at least one of the cases. Our initial clue to the results of this experiment appears in Table 2. Note that the only difference in the dimensions of the two antenna models is in the 5-Ohm difference in the required loading reactance of the 600-Ohm shorted stub on the reflector.

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Relative to the V-Yagi, the 3-element rectangle is 20% shorter side-to-side, a function of shortening the driver. As well, the boom length from the center of the reflector to the center of the director is 82", 40" shorter than the required boom for the V-Yagi. Not all of the reduction comes from converting the Vee parasitic elements into rectangular form. The tip of each parasitic element is 4" closer to the driver in the rectangle than in the V-Yagi. This adjustment is necessary to produce a near-50-Ohm feedpoint impedance. Since none of the elements has an unusual geometry and these are only test models--not intended for actual construction--all elements are 0.5" in diameter.

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The Vertical-T Driver 3-Element Rectangle: The rectangularized version of the V-Yagi performs in a manner that is comparable to the V-Yagi. The fatter parasitic elements of the rectangle give it better front-to-back and SWR performance across the passband than the AWG #14 parasitic elements of the V-Yagi. Fig. 13 provides a view of the band-edge and design-frequency free-space azimuth or E-plane patterns for the version of the antenna using vertically oriented driver Tees.

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The most notable aspect of the azimuth patterns is the position of the side nulls. They occur at 90-degree angle relative to the main forward heading of the beam. In general--as shown in the spot performance data in the table--the beamwidth averages about 3 degrees wider than for the standard 3-element short-boom Yagi.

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+Spot Free-Space Performance of the 3-Element Yagi Rectangle with Vertical Driver Tees
+Frequency                              28.0             28.5             29.0
+Gain dBi                               6.95             6.77             6.89
+180-Deg. Front-to-Back Ratio dB        21.41            35.00            23.94
+Beamwidth degrees                      69.6             69.8             69.2
+Feedpoint Resistance Ohms              40.41            41.65            32.96
+Feedpoint Reactance Ohms               -4.98            -2.57            6.69
+50-Ohn SWR                             1.271            1.211            1.564
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As shown in Fig. 14, the worst-case front-to-back ratio is nearly constant across the passband, despite the peak in the 180-degree figure. The band-edge values are 5 to 9 dB better than the corresponding V-Yagi values. So far, we have seen that the 3-element rectangle with vertical Tees has a normal Yagi pattern with better front-to-back values than the V-Yagi. What the V-Yagi and the first of our 3-element rectangles share is the progression of gain values across the first MHz of 10 meters. Both beams show a deep curve with the lowest gain value near the center of the passband. (See Fig. 6 to compare gain curves.)

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Because the driver length is relatively independent of other array performance characteristics (within limits, of course), the selection of an operating point is within designer control. Fig. 15 shows the characteristics for the current model. The peak resistance occurs close to 28.3 MHz, with the actual resonant point at about 28.7 MHz. In contrast, the listed design frequency is 28.5 MHz since the 180-degree front-to-back peak occurs between 28.4 and 28.5 MHz. Overall, the 3-element rectangle has a wider SWR bandwidth than the V-Yagi and the standard-design 3-element short-boom Yagi.

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With vertically oriented driver Tee extensions, the 3-element rectangle produces patterns very similar to those of the full-size short-boom Yagi with which we started this exploration. Although the bent parasitic elements produce a gain curve like the one associated with the V-Yagi, in all other respects the array operates like a standard-design Yagi, with gain reductions that are commensurate with the slightly shorter boom length (82" vs. 90" for the short-boom design). With the driver Tees vertical, the array shows no signs of tip-to-tip coupling.

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The In-Line-Tee Driver 3-Element Rectangle: The alternative arragement for the driver Tees is to place them in line with the tails of the parasitic elements. As Table 2 showed, the revision produces no changes in the physical dimensions of the 3-element rectangle. In fact, the only difference is a 5-Ohm reduction in the reflector loading to center the performance within the passband. Fig. 16 shows the free-space azimuth or E-plane patterns of the resulting array.

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There is little, if anything, to distinguish the patterns in Fig. 16 from those in Fig. 13. Even with the driver tails in line with the parasitic tails, the array shows azimuth patterns that are the norm for standard-design Yagis. However, compare the pattern for 28 MHz with the one in Fig. 2 for the standard design Yagi. With the rectangle, the rear lobes resemble those that we ordinarily find above the design frequency rather than below it. The rectangle appears to find the peak of its front-to-back performance in the center of the design region in which the 3-element Yagi shows a 3-lobe rearward pattern. In many designs, the peak rearward performance occurs to one or the other side of the 3-lobe rearward design region.

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+Spot Free-Space Performance of the 3-Element Yagi Rectangle with In-Line Driver Tees
+Frequency                              28.0             28.5             29.0
+Gain dBi                               7.03             6.85             6.98
+180-Deg. Front-to-Back Ratio dB        20.89            34.32            21.19
+Beamwidth degrees                      69.6             69.8             69.2
+Feedpoint Resistance Ohms              39.21            40.43            31.51
+Feedpoint Reactance Ohms               -2.23            -0.03            9.75
+50-Ohn SWR                             1.282            1.237            1.693
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As the table of spot performance characteristics shows, the array does not deviate in any significant way from its performance with the driver Tee vertically oriented. Gain is up marginally and the feedpoint resistance is down marginally. However, as shown in Fig. 17, the gain and front-to-back curves show the same progressions of values as in the first rectangle.

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The resistance, reactance, and 50-Ohm SWR curves in Fig. 18 tell the same story. The feedpoint resistance peaks at 28.3 MHz, while resonance occurs at 28.6 MHz. The SWR curve is steeper above the center of the band because the in-line driver Tees reduce the average feedpoint resistance by about 1.2 Ohms.

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If there had been significant tip-to-tip coupling between the parasitic elements, moving the driver Tees from a vertical position to an in-line position should have shown significant changes in the performance characteristics of the array. The absence of such changes is fairly conclusive evidence--when combined with the Yagi-normal azimuth patterns--that the level of tip-to-tip coupling is insignificant. If such coupling does not occur with the rectangle, then it also does not occur with the V-Yagi, which places the element ends a total of 8" farther apart.

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We may gain a further bit of evidence by comparing the sum of all element phase shifts from element center to element tips for the 3-element Yagis that we have explored. That sum was just under 5.5 Ohms for the V-Yagi. In fact, the standard 3-element short-boom design shows a sum of just under 10.0 Ohms. The corresponding figures for the two rectanglular 3-element Yagis are 10.0 Ohms and 11.4 Ohms for the vertical Tees and the in-line Tees, respectively. In short, the rectangles perform very much like ordinary Yagis.

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Conclusion

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We began with a question born of curiosity: does the V-Yagi produce its large beamwidth patterns solely from the Vee shape of its elements or from a combination of element coupling means found in the Moxon rectangle. By comparing a large number of performance facets of a considerable collection of relevant parasitic arrays, we have arrived at a reasonably conclusive answer: the V-Yagi pattern shapes result from the Vee-shape of the parasitic elements. If we create a rectangular 3-element parasitic array, we retain some performance characteristics, such as the gain curve, but others revert to properties we find in standard-design Yagis with similar boom lengths. Curiosity is satisfied, and the survey of different array types has been instructive, especially for performance details that we normally overlook.

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So far, I have been unable to create a 3-element parasitic rectangle with closely spaced element tips. Unlike the Moxon rectangle, the 3 elements of a director-based array do not appear amenable to the same treatment as the driver-reflector arrangement of the Moxon rectangle. Indeed, I have not succeeded in finding a driver-director version of the 2-element Moxon rectangle. If a driver-director version of the Moxon does not exist--that is, one in which we may use dual coupling to enhance the overall azimuth pattern--then it is unlikely that any parasitic array with 3 or more elements would succeed. End or element-tip coupling does not have the same effect with a director as with a reflector. In fact, we may achieve a reasonably high front-to-back ratio with a standard (linear-element) driver-director array, if we can handle the low feedpoint impedance and narrow bandwidth. Values up to about a 20-dB front-to-back ratio are possible. Remember that the reason for using the driver-reflector Moxon rectangle is--in part--to achieve higher front-to-back ratios (by 10 dB or more) than are possible with driver-reflector parasitic arrays using linear elements. The Moxon also has a wider passband than 2-element arrays with the same boomlength.

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As a consequence, it is unlikely that we shall uncover or even need multi-element versions of the Moxon rectangle. The V-Yagi has its niche among amateur parasitic arrays for two reasons. First, its yields lighter-weight lower-HF beams with good passband coverage. Second, its provides beamwidths similar to those of a Moxon rectangle with about a dB of extra gain. The V-Yagi does not need dual coupling to achieve these results.

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Updated 06-12-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Upper, Yagi


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Notes on the V-Yagi

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L. B. Cebik, W4RNL

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In the May, 1998, issue of QST, Nathan Miller, NW3Z, and Jim Breakall, WA3FET, presented an article on "The V-Yagi: A Lightweight Rotatable Antenna for 40 Meters." (See pp. 38-40.) The antenna appears to have attracted some attention at the time of publication, but interest in the antennas seems to have waned over the last 7 years or so. Perhaps one reason for the dwindling interest is the idea that it is simply an evolutionary development based on the earlier G4ZU "Bird" Yagi. This antenna appeared in The ARRL Antenna Compendium, Vol. 2, 1n 1989. See G. A. Bird, G4ZU, "New Techniques for Rotary Beam Construction," on pages 58-60 of that volume.

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In overall general outline, the 2 antennas appear to be similar, as shown in Fig. 1. Both use a linear driver element with Vee'd parasitic elements. However, the differences are also worth noting.

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The Bird Yagi (designed for 10 meters) uses crossing tapered fiberglass supports. The linear driver is wire of the same size as the wire used for the Vee'd parasitic elements. Dick Bird only intended to obtain the best performance possible from a standard 3-element Yagi. Note the fact that the director and the reflector elements do not align their tips, but simply go as far as the element length requires. Under these conditions, the main inter-element coupling is the same as for a Yagi with 3 parallel linear elements. Since the parasitic elements have a slight Vee shape, there is radiation off the beam sides so that the side nulls that we expect with a set of parallel elements become weaker. Fig. 2 shows 3 free-space 10-meter patterns for the Bird Yagi.

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Nevertheless, the Bird Yagi provides a competent level of performance in a very lightweight structures and with a 50-Ohm feedpoint impedance. The design is also eminently adaptable. For example, the German multi-band Spiderbeam is an ingenious outgrowth of the Bird design, with some interesting additional techniques to cover the entire upper HF range. The Spiderbeam web site contains a wealth of information on the design, along with detailed model patterns, including information across the entire operating passband (a rarity in the world of commercial antennas). The antenna uses a single feedline with direct line coupling to all drivers for single-feedline use.

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The V-Yagi on the right takes a somewhat different direction to obtain its particular characteristics. Note that the parasitic element ends are aligned and carefully spaced. The authors intended each element to function as a director, and they switched in a stub to one or the other to make it function as a reflector. Depending on wire size and other variables, the stubs require a reactance of 110 to 130 Ohms to increase the electrical length of the element enough to perform optimally as a reflector. As well, the driver element is a rather hefty tapered-diameter tubular element designed to support the weight of the lower-HF beam with the aid of top trusses. The fatter driver adds to the array gain, although the parasitic elements are wire.

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The original authors of the 40-meter version of the antenna used an optimizer program to arrive at the final dimensions. Unfortunately, optimizers arrive at good performance numbers, but do not tell the full story of how a given beam operates. The patterns, shown in a 10-meter version in Fig. 3, reveal more than the optimizer.

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The similarity between these patterns and those produced by a 2-element Moxon rectangle should not escape our attention. Not only do we find at the design frequency a very high front-to-back ratio, but we also discover other parallel properties to the Moxon. One such property is the expanded beamwidth relative to a standard Yagi pattern. The Veeing yields the equivalent of the Moxon tails. A second factor is the need to design the antenna for a frequency about 1/3rd of the way up the passband so that the front-to-back ratios at both ends of the passband are similar. A normal Yagi may use a mid-band design frequency. Third, we do not find standard rising gain curve across the passband. The key difference between a Moxon rectangle and the V-Yagi--besides the obvious 3rd element in the latter--is the wider spacing between the tips of the parasitic elements in the V-Yagi, a result of having the intervening driver element.

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The V-Yagi is capable of superior performance relative to the Bird Yagi. Table 1 presents performance number for 10-meter versions of both beams. The Bird can be tweaked for slightly higher performance, but it remains a competent lightweight performer just as originally designed. Its Veeing achieves part of what the V-Yagi achieves--namely, a wider beamwidth than we would normally obtain from a 3-element Yagi with linear elements. The V-Yagi performance highlights focus on the improved front-to-back ratio across the passband and a somewhat wider 50-Ohm SWR curve.

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The V-Yagi shows an average of about 0.5-dB more gain than the Bird Yagi. However, the front-to-back ratio advantage of the V-Yagi is perhaps more significant. In a 2-element parasitic beam, the front-to-back ratio is largely a function of the relative current magnitude and phase angle at the center of the reflector compared to the same measurements at the center of the driver. With a 3-element Yagi, the director has the most influence in setting the front-to-back ratio. Let's set the driver at a constant current magnitude value of 1.0 with a zero-degree phase angle. If we independently drive each element of various 3-element designs in which the elements are linear, the requisite current magnitudes and phase angles for the reflectors will tend to vary with the boom length. However, the directors for a maximum 180-degree front-to-back ratio value will show considerable consistency, with relative current magnitudes of about 0.62 and -116-degree phase angles (relative to the constant driver values of 1.0 and 0.) When parasitic designs are down from a 50-dB front-to-back ratio by any significant amount, the actual front-to-back ratio will depend on the relationship of the director values to the reflector values. In general, front-to-back ratios are higher when both director and reflector relative current phase angles increase together.

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The Bird Yagi at its design frequency shows a relative current magnitude of about 0.74 at -124 degrees. The higher than ideal relative current magnitude combines with a lower than ideal reflector phase angle. As well, the reflector relative current magnitude is about twice as high as ideal for 3-element designs. Hence, the front-to-back ratio is relatively low compared to what is possible with a 12' boom length. Remember that, in this context, ideal does not mean maximum gain or even the best combination of gain and front-to-back ratio. Instead, it means maximum front-to-back ratio.

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In contrast, the V-Yagi shows a set of director relative current values of about 0.6 and 118 degrees. These values are only slightly off the ideal for maximum front-to-back ratio. As well, the reflector values are high in magnitude (about 0.65 compared to a more ideal 0.4) and low in phase angle (about 112 degrees, compared to a more ideal 123 degrees). The wider variance of the reflector from some idealized all-driven samples with parallel elements suggest the stronger influence of the director on the front-to-back ratio. The improvement in the current conditions for improved front-to-back performance of the V-Yagi over the Bird Yagi stem largely from the end coupling between the parasitic element tips, which the V-Yagi aligns and gaps for optimal performance.

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V-Yagi Structure and Dimensions

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To set the end gap of the V-Yagi, we cannot simply bring the line of the parasitic elements to a simple termination where the driver ends. The actual required angle is shallower than that line. Therefore, we either must extend the driver with non-conductive material to accommodate the shallower angle or we must add a cross piece near the end of the driver, just past where the parasitic element ends. Fig. 4 shows the outline of the latter system of construction.

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The cross pieces near the driver ends are ideally non-conductive material. On the lower HF bands, the lengths of these supports may require a combination of conductive and non-conductive materials to maintain a light weight and insignificant sag. In the upper-HF region, light fiberglass tubes (UV protected, of course) will work as well. The sketch also shows insulators terminating the parasitic elements. Remember that parasitic elements have high voltages at their ends, even though not directly driven. If we use support ropes or cords that can handle the voltages, the insulators can be of any type that provide strain relief for both the support cords and the parasitic wire ends. We shall also need a spacing insulator at the peak of the reflector Vee for the installation of the stub.

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To support the peaks of the parasitic wire elements, we shall need a lightweight but rigid boom. The boom can be metallic so long as we insulate and isolate the parasitic elements from it--just as we would for a standard Yagi. However, since the boom only supports light-weight wire parasitic elements, the boom does not require the heavy structure of a standard Yagi boom. Instead, it can take on the structure that we might normally use for an active element of the length required. That length will vary from 40' on 40 meters to 10' on 10 meters.

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In contrast, the driven element will need to be stronger (and hence fatter) than most elements that we might find in standard Yagis. We are loading the ends with the weight of the cross supports and the wire terminations. The fatter driven element does provide a small increment of additional gain for the array by increasing the mutual coupling between the driver and both thin parasitic elements.

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Fig. 5 redraws the outline of the V-Yagi without the support lines in order to provide guidance to the table of rough dimensions (Table 2). The driver length (Dl) is the driver half-length from the boom centerline outward and is a function of the taper schedule used. The more severe the taper schedule, the longer will be the driver length compared to an equivalent uniform-diameter element set in its place. However, uniform-diameter elements are highly impractical as drivers for the V-Yagi, since they would lack the wind-stress strength needed for the array.

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Pl gives the wire length for each half of the parasitic elements, counting from the boom centerline outward. Since the wire is angled, Pa gives the distance from the centerline outward parallel to the driver, while Pb gives the distance from the Vee peak back toward the driver along the boom. B is the half-length of the boom, counting from the driver either forward to the director or backward to the reflector. The gap or G is the distance from the driver element to the tip of either parasitic element. Remember that the reflector requires a gap for the installation of the shorted transmission line stub. The Wire column lists the AWG wire size for each of the models. The parasitic wires decrease in diameter as we increase the model's frequency.

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The value of Sl is the length of a 600-Ohm transmission line stub providing the correct reactance to lengthen the reflector element electrically so that the array shows close to maximum front-to-back ratio at the design frequency--about 30 dB or so. The adjoining column lists the corresponding reactance. The modeled stubs use lossless transmission lines, so the actual front-to-back ratios may be slightly higher than the values reported later for modeled array performance.

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Every array has a myriad of construction variables that require field adjustment to bring the array to its desired performance level. The length of the director and the gap between the reflector and director tips will have the greatest affect on the frequency of the front-to-back peak. The stub length will have some role to play in the front-to-back peak frequency, but will more greatly affect the feedpoint impedance at resonance. The driver requires adjustment to place resonance either on the design frequency or on a frequency that yields the most desired SWR passband. Its adjustment in terms of diameter or length has little affect on either the gain or the front-to-back peak.

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For reference, Table 3 shows the taper schedule used in the models. These taper schedules served only to establish plausible driver elements of larger than normal diameter. They have not been tested for wind stress in programs such as YagiStress. This step is essential before building any Yagi for the HF region. Remember that the ends of the driver are weight-loaded by the cross supports and the wire ends. Where the step between sections is 0.25", the tubing of the larger section may require doubling with the intermediate size of standard thickness (nominally 1/16" but actually 0.058" in 6063-T832 or 6061-T6 tubing). Use sufficient overlap for each section, and if strength requires, extend the smaller section all the way back to the inner end of the preceding section.

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For further hints at structuring the driver or the wire-support boom, see the original QST article.

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V-Yagi Performance

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The V-Yagi provides consistent performance as a monoband 3-element parasitic array as we move through the HF spectrum from 40 meters to 10 meters. Table 4 shows the modeled free-space performance values for each version of the antenna. For bands having a bandwidth of at least 1%, the performance values include the band edges as well as the design frequency. Bandwidth is simply the width of the band divided by the center frequency, with the result converted to a percentage. The final column of the table shows the rounded bandwidth for each of the amateur bands covered. Because 10-meter operators have an interest in 28.8 MHz as well as the defined band limit of 29.0 MHz, I have included that set of figures within the table.

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In general, the design process for a dual-coupled parasitic array, such as the Moxon rectangle, calls for a design frequency about 1/3 of the way upward from the lower frequency limit to the upper frequency limit. In the 2-element array, the reflector is a principle component in setting both the driver resonant drequency and the front-to-back ratio peak frequency. As a result, the two curves tend to track each other. Setting the front-to-back ratio peak frequency at a point about 1/3 up from the lower frequency limit results in band-edge values for both the front-to-back ratio and the 50-Ohm SWR that closely correspond with each other.

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The V-Yagi differs in design due to having 3 elements, with the parasitic elementxs sloping back toward the driver. The director has the greatest affect on the peak front-to-back frequency, while the driver tends to set the resonant frequency. The reflector and the gap have a strong influence on the resistive impedance at resonance. Since the beam is symmetrical with respect to the driver, the front-to-back ratio peak frequency and the feedpoint resistance represent compromise values. As a result, the potential builder is free to redesign the array in a slightly asymmetrical manner to change the feedpoint resistance if the beam is not intended for reversing by the use of switched stubs that convert either director into a reflector. However, tip alignment appears to be essential to the design.

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Since the driver length does not significantly affect other performance values, the length can be adjusted to place resonance anywhere within the operating passband. For these explorations, I have left its resonant frequency roughly coincident with the front-to-back peak frequency. As a result, the 50-Ohm SWR is higher at the high end of the band than at the low end.

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Fig. 6 provides a frequency sweep of the gain and 180-degree front-to-back values for the 10-meter version of the V-Yagi. 10 meters and 40 meters are the widest of the bands for which the design is applicable. Hence, they both show the tendency of the gain value to decrease over part of the band and then increase toward the upper band edge. Narrower bands, such as 20 and 15 meters show only the decreasing gain in the tabulated values. The total gain range for the array across even the widest of the HF bands in the table is less 0.25 dB, an amount that an operator could not notice in practice. The V-Yagi shows a fairly sharp peak in the front-to-back ratio with reasonable band-edge values. Judicious re-design of the array can center the highest front-to-back value anywhere within the passband.

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The patterns in Fig. 3 explain why the graph does not include values for the worst-case front-to-back ratio. Essentially, the 180-degree and the worst-case front-to-back values are the same across the band. Unlike Yagis with parallel elements, the V-Yagi does not develop a deep 180-degree null while leaving very significant quartering sidelobes that require a separate performance accounting.

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Fig. 7 supplies the sweep graphs for the feedpoint resistance, reactance, and 50-Ohm SWR of the 10-meter version of the array. As noted earlier, you may move the minimum SWR point by judiciously changing the driver length to change the resonant frequency. The resistive component of the feedpoint impedance changes slowly, reaching a high value at or near resonance. However, as is the case with the Moxon rectangle, both the front-to-back ratio and the 50-Ohm SWR change more rapidly below the design frequency than above it. Hence, you would not need to move the resonant frequency upward very much to achieve roughly equal SWR values at the band edges.

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When we began this exploration into the operation and scaling of the V-Yagi, we compared its performance to the performance of a Bird Yagi. We made that comparison to show the differences in design between the 2 arrays that both use Vee'd parasitic elements. However, anyone who contemplates building a V-Yagi for any band will be interested in assessing the V-Yagi performance numbers against 3-element Yagis of standard design. Therefore, I have taken from my files 2 different standardized Yagi designs that I call short-boom and long-boom models. Their models use 0.5" diameter elements on 10 meters. Fatter elements can increase gain by 0.1 to 0.2 dB, depending on element design. However, the basic elements of performance do not change. For comparative purposes, both designs have resonant drivers at their design frequency (28.5 MHz). However, the resistive impedance is in the 25-28-Ohm range, calling for a matching network or a quarter wavelength line between the antenna feedpoint and the usual 50-Ohm cable used to feed amateur antennas.

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One feature of considerable interest to the potential antenna builder is the azimuth pattern shape for each beam at the design frequency. Fig. 8 overlays the free-space patterns for the 3 beams. The long-boom design, taken from a modified model originally developed by K6STI for 20 meters, obviously has slightly more gain (about 1 dB) than the other 2 versions. The short-boom model, adapted from an N6BV design in the program YW, has insignificantly greater gain than the V-Yagi. As we move away from the heading of peak forward gain, we may notice a more significant difference. The standard Yagis show deep nulls 90 degrees away from the maximum gain heading. However, the Vee'd parasitic elements of the V-Yagi move the side nulls to a position roughly 120 degrees behind the maximum forward gain heading. The V-Yagi pattern is nearly cardioidal and has a wider beamwidth than a standard Yagi.

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The rear lobes illustrate 2 of the conditions that are typical for standard Yagis. The long-boom version of the antenna is not capable of a deep 180-degree null that produces an extremely high front-to-back ratio. In fact, if we force the model to have on each element the relative current magnitude and phase angle that yields such a null, the forward gain drops by nearly 1 dB. Hence, the long-boom standard Yagi shows a typical 3-lobe rearward pattern. I have modified the original short-boom design to place the maximum front-to-back ratio at the design frequency. As a result, the 180-degree ratio is actually better by nearly 10 dB than the 180-degree value for the V-Yagi. However, the standard short boom Yagi has very significant rearward sidelobes with as much or more energy than the rearward lobes of the long-boom design. In contrast, the V-Yagi has a small, simple, single rearward lobe.

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For a broader view of the comparative performance of these 3 beam designs, Table 5 presents the design and band-edge frequency performance data for all 3 arrays. Both of the standard Yagis show the typical gain pattern that rises in value with increasing frequency across the band. Longer-boom Yagis (for a set number of elements) tend to show a more rapid change of gain as a function of the narrower bandwidth that accompanies longer booms. The short-boom Yagi shows a range of variation more like the modest figure of the V-Yagi--about 0.25 dB.

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The narrower bandwidth of the long-boom Yagi also appears in both the front-to-back and the SWR columns. The 180-degree front-to-back ratio is well below 20 dB at the defined band edges (28.0 and 29.0 MHz). As well, SWR at the upper band edge is well above the 2:1 ratio usually taken as the amateur limit. In contest, the short-boom version of the antenna trades gain for a broader bandwidth. It shows a 20-dB front-to-back value at the band edges and has an SWR below 2:1 at those operating extremes.

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The V-Yagi does not achieve the gain of the long-boom Yagi or the high 180-degree front-to-back ratio of the short-boom Yagi across 10 meters. However, it does match the short-boom Yagi in the low rate of gain change across the band and shows an improved SWR curve. Incidentally, the boomlength of the V-Yagi is about halfway between that values for the 2 standard Yagis (10' vs. just under 8' and just under 12'). In the end, the selection of design will depend in part in what you want to get out of the design.

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Conclusion

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I have explored the properties of the V-Yagi more out of curiosity than from a motive of recommending the design. It seemed at least marginally important to see how the design differs from the older Bird Yagi and to see why the design exhibited properties that partially resemble those of a Moxon rectangle. The critical factor turned out to be the alignment of the parasitic element ends and the shallower angle of the parasitic elements, relative to the Bird Yagi. These features appear in the original design that set up 2 directors in order to be able to reverse the beam direction by switching in the stub to create a reflector--all without needing a rotator.

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As a matter of course, I scaled the design to each of the amateur bands from 40 to 10 meters. My interest lay in tracing the performance characteristics on bands of varying width. The narrow WARC bands, of course, show virtually no change of performance from one band edge to the other. The more modest wider bands (20 and 15 meters) show very good performance over a wider span of frequencies. We might rate the performance on 10 and 40 meters--the widest bands--as highly usable at the band edges and very good to excellent near the design frequency (depending upon the stress we place on any particular performance parameter).

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The V-Yagi trades lighter weight for some unusual construction, especially with respect to the crossing end supports for the wire parasitic elements. Weight reduction, of course, is far more important in the lower HF region than at higher HF frequencies. Whether or not the V-Yagi becomes a true candidate for construction, the design deserves more than a single print appearance.

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The V-Yagi performance has numerous correlations to the performance of the 2-element Moxon rectangle. Fig. 9 overlays the free-space azimuth patterns for both antennas using a common design frequency. The V-Yagi has nearly a dB gain advantage over the smaller Moxon with a similar near-cardioidal pattern and a similar broad bandwidth.

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However, the outlines of the 2 antennas reveal more than casual differences in the scaled sketches. The Moxon tails come to a small gap that varies with the diameter of the element. In contrast, the aligned tips of the V-Yagi parasitic elements form a very wide gap, casting doubt on the amount--if any--of end coupling between them. If there is no end coupling, then the V-Yagi achieves its performance characteristics solely by virtue of the angle of the parasitic element slope. From a practical perspective, the question may be moot: if an operation needs the kind of performance characteristics provided by the V-Yagi, then just how the antenna yields those characteristics becomes secondary to having them. Still, the question exists to tweak our curiosity and to give an added dimension of interest to the V-Yagi design.

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Updated 06-12-2007. © L. B. Cebik, W4RNL. Data may be used for personal purposes, but may not be reproduced for publication in print or any other medium without permission of the author.

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Go to Amateur Radio Page

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Topics: HF Upper, Yagi


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L. B. Cebik W4RNL (SK) Website and Document Collection

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    + + + +
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    • +
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  • + A copy of the site is hosted in GitHub at github.com/antenna2, the repo can be cloned, forked, or downloaded in ZIP archive under the green Code button. +
    • +
+
+

About L. B. Cebik W4RNL

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Cebik was well known in the ham radio community and maintained a website with a vast collection of articles on antenna design and modeling. He wrote numerous articles about antennas and antenna modeling in most U.S. amateur radio magazines, regular columns, and over a dozen books.

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Cebik passed away in April 2008, the notices published by ARRL and QCWA contain more information.


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Why Maintain This?

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Cebik's website was a treasure trove of information one could spend hours exploring, reading, and learning from.

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The original Cebik website disappeared at some point, along with the antenneX site around 2017 which offered for purchase various books and modeling file sets that were referenced throughout the website.

+

Marcel De Canck ON5AU (SK) made available a copy of Cebik's website, some books, and magazine articles at www.on5au.be. Marcel also wrote several books including Advanced Antenna Modeling, and was close friends with John Devoldere ON4UN (SK) who wrote ON4UN's Low Band DXing Book. For anyone interested in these subjects they are both well worth getting.

+

Regrettably Marcel also became silent key in October 2023. Not knowing what might happen with Marcel's website I made a snapshot of it, and started looking at the Cebik Pages..


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Updates / Edits

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The version of Cebik's site hosted here is derived from what Marcel had hosted.

+

There were two versions - one appears to be from an antenneX CDROM mostly as-is, and another with different index pages. This one is the antenneX version as it was the most original, with additional and missing content merged into it to create the most up-to-date version possible.

+

The Cebik website style and layout is very dated by today's standards, it appears most of the pages were created with HTMLed Pro which dates back to the 90s, some from Word documents, and others possibly written by hand in a text editor.

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Updates include:

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  • Pages updated to syntax correct HTML with CSS setting the styling. +
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    • However they still contain obsolete HTML3 elements.
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    +
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  • Some missing/orphaned modeling, VHF, and wire antenna content found and added.
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  • For better readability, background image replaced with similar solid background color, preformatted text no longer bold and has a different background color set with borders.
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  • De-duplicated symposiums and magazine articles, linked original HTML pages the PDFs were created from.
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  • Broken internal links have been fixed, and where possible external broken links have been updated with copies stored by the Internet Archive. +
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  • The online Moxon Rectangle calculator has been updated and moved to the top of the page.
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  • Topic index, page title updates (used for the link names in the topic index).
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  • Page header text and formatting (some pages), and switching from h2 to h1 tag (SEO).
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  • A combination of custom Python scripts (written with help from ChatGPT) and HTML Tidy were used to tidy and update the HTML with styling set by one CSS file. As a result the pages load and render faster. A copy of the scripts can be found on Github here. +
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  • Otherwise the overall look and feel of the Cebik site is maintained.
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To do:

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  • Magazines page: Find better/smaller file size PDF copies of "NEC and MININEC Guide to Further Information" (4.4 mb), and "NEC-4.1: Limitations of Importance to Hams" (22mb) - these are images.
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  • Edit PDF files to remove references to defunt cebik and antennex domains.
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  • Finish updating page titles and set meta keywords on the magazine column pages (around 250 pages), and add them into the Topic Index.
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  • Improve viewing on mobile devices.
    • +

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Contact Info

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Feedback or suggestions are welcome, please contact Lonney K1LH at lonney@gmail.com.

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Visitor Statistics Last 30 Days (GoAccess script).

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© 2024 Disclaimer.

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Magazine Articles and Columns

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Cebik wrote many magazine articles and regular columns, some were from existing website articles, others were made available after publishing. Where possible these have been identified and linked, others are in PDF format.


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73 Magazine

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antenneX

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Communications Quarterly

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CQ Magazine

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Ham Radio

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Low Down

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The journal of the Colorado QRP Club.

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National Contest Journal

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Ten-Ten News

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QEX

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QEX Antenna Options Column

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QRP Quarterly

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+

QST

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Some QST articles appear to be based on older website articles that were updated for publication in QST.

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+

⇦ Back to main page

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Symposiums

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⇦ Back to main page

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+ +